diff --git a/0CdxkgAjsDA.txt b/0CdxkgAjsDA.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7cf44a5ab2180fa3c1a32233d420eaef57fe783 --- /dev/null +++ b/0CdxkgAjsDA.txt @@ -0,0 +1,6355 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right morning everyone I + + align:start position:0% +ocw.mit.edu all right morning everyone I + + + align:start position:0% +ocw.mit.edu all right morning everyone I +hope you all had a great spring + + align:start position:0% +hope you all had a great spring + + + align:start position:0% +hope you all had a great spring +break and during which I hope you can + + align:start position:0% +break and during which I hope you can + + + align:start position:0% +break and during which I hope you can +have more of six over + + align:start position:0% +have more of six over + + + align:start position:0% +have more of six over +six today we're going to look at Network + + align:start position:0% +six today we're going to look at Network + + + align:start position:0% +six today we're going to look at Network +flow and two things in network + + align:start position:0% + + + + align:start position:0% + +flow the first one is Atmos carp + + align:start position:0% +flow the first one is Atmos carp + + + align:start position:0% +flow the first one is Atmos carp +algorithm and uh after that we're going + + align:start position:0% +algorithm and uh after that we're going + + + align:start position:0% +algorithm and uh after that we're going +to look at some two + + align:start position:0% +to look at some two + + + align:start position:0% +to look at some two +applications and in particular they are + + align:start position:0% +applications and in particular they are + + + align:start position:0% +applications and in particular they are +called + + align:start position:0% +called + + + align:start position:0% +called +bipartite + + align:start position:0% + + + + align:start position:0% + +matching and + + align:start position:0% + + + + align:start position:0% + +cover okay so uh we'll start + + align:start position:0% +cover okay so uh we'll start + + + align:start position:0% +cover okay so uh we'll start +with uh simpler algorithm which is for + + align:start position:0% +with uh simpler algorithm which is for + + + align:start position:0% +with uh simpler algorithm which is for +[Applause] + + align:start position:0% + + + + align:start position:0% + +Focus uh can someone remind us what F + + align:start position:0% +Focus uh can someone remind us what F + + + align:start position:0% +Focus uh can someone remind us what F +fusen + + align:start position:0% +fusen + + + align:start position:0% +fusen +does + + align:start position:0% + + + + align:start position:0% + +go ahead every time you + + align:start position:0% +go ahead every time you + + + align:start position:0% +go ahead every time you +have get it it gets rid of it + + align:start position:0% +have get it it gets rid of it + + + align:start position:0% +have get it it gets rid of it +yep uh what's your name by Mish uh okay + + align:start position:0% +yep uh what's your name by Mish uh okay + + + align:start position:0% +yep uh what's your name by Mish uh okay +so well Misha gave a very brief + + align:start position:0% +so well Misha gave a very brief + + + align:start position:0% +so well Misha gave a very brief +description but let's be a little more + + align:start position:0% +description but let's be a little more + + + align:start position:0% +description but let's be a little more +bit more detailed so we have a graph gra + + align:start position:0% +bit more detailed so we have a graph gra + + + align:start position:0% +bit more detailed so we have a graph gra +Network flow uh G and the first thing it + + align:start position:0% +Network flow uh G and the first thing it + + + align:start position:0% +Network flow uh G and the first thing it +go going to do is that given the flow it + + align:start position:0% +go going to do is that given the flow it + + + align:start position:0% +go going to do is that given the flow it +will transform G from a resue graph + + align:start position:0% +will transform G from a resue graph + + + align:start position:0% +will transform G from a resue graph +everyone remembers that then uh FF + + align:start position:0% +everyone remembers that then uh FF + + + align:start position:0% +everyone remembers that then uh FF +algorithm will find the + + align:start position:0% + + + + align:start position:0% + +path of going from source + + align:start position:0% +path of going from source + + + align:start position:0% +path of going from source +to + + align:start position:0% + + + + align:start position:0% + +sync in this resue graph + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% + + + + align:start position:0% + +augment this + + align:start position:0% + + + + align:start position:0% + +path uh augment just means augmenting + + align:start position:0% +path uh augment just means augmenting + + + align:start position:0% +path uh augment just means augmenting +just means uh increasing the flow on + + align:start position:0% +just means uh increasing the flow on + + + align:start position:0% +just means uh increasing the flow on +that path by how + + align:start position:0% + + + + align:start position:0% + +much yeah the minimum Edge on the path + + align:start position:0% +much yeah the minimum Edge on the path + + + align:start position:0% +much yeah the minimum Edge on the path +uh let me just Define that to be the + + align:start position:0% +uh let me just Define that to be the + + + align:start position:0% +uh let me just Define that to be the +capacity of the path which which is the + + align:start position:0% +capacity of the path which which is the + + + align:start position:0% +capacity of the path which which is the +capacity of the weakest + + align:start position:0% +capacity of the weakest + + + align:start position:0% +capacity of the weakest +link okay then uh what's the last step + + align:start position:0% +link okay then uh what's the last step + + + align:start position:0% +link okay then uh what's the last step +we're missing + + align:start position:0% + + + + align:start position:0% + +here so after argumenting our flow + + align:start position:0% +here so after argumenting our flow + + + align:start position:0% +here so after argumenting our flow +changed from F + + align:start position:0% +changed from F + + + align:start position:0% +changed from F +to F + + align:start position:0% +to F + + + align:start position:0% +to F +Prime and then we're going to loop back + + align:start position:0% +Prime and then we're going to loop back + + + align:start position:0% +Prime and then we're going to loop back +we have a f Prime then GF F Prime find + + align:start position:0% +we have a f Prime then GF F Prime find + + + align:start position:0% +we have a f Prime then GF F Prime find +find the path in GF Prime and uh + + align:start position:0% +find the path in GF Prime and uh + + + align:start position:0% +find the path in GF Prime and uh +continue from + + align:start position:0% + + + + align:start position:0% + +there so this algorithm in some sense is + + align:start position:0% +there so this algorithm in some sense is + + + align:start position:0% +there so this algorithm in some sense is +not even a very detailed algorithm + + align:start position:0% +not even a very detailed algorithm + + + align:start position:0% +not even a very detailed algorithm +because it doesn't say how to find a + + align:start position:0% +because it doesn't say how to find a + + + align:start position:0% +because it doesn't say how to find a +path in the second + + align:start position:0% + + + + align:start position:0% + +step and that's indeed a problem because + + align:start position:0% +step and that's indeed a problem because + + + align:start position:0% +step and that's indeed a problem because +we have seen + + align:start position:0% +we have seen + + + align:start position:0% +we have seen +uh pathologically Bad + + align:start position:0% + + + + align:start position:0% + +Case + + align:start position:0% +Case + + + align:start position:0% +Case +where + + align:start position:0% + + + + align:start position:0% + +um each capacity is a + + align:start position:0% +um each capacity is a + + + align:start position:0% +um each capacity is a +billion and the correct way to do it is + + align:start position:0% +billion and the correct way to do it is + + + align:start position:0% +billion and the correct way to do it is +simply like augmenting this path and + + align:start position:0% +simply like augmenting this path and + + + align:start position:0% +simply like augmenting this path and +then that path oh sorry there's a edge + + align:start position:0% +then that path oh sorry there's a edge + + + align:start position:0% +then that path oh sorry there's a edge +one right then we'll be done but uh the + + align:start position:0% +one right then we'll be done but uh the + + + align:start position:0% +one right then we'll be done but uh the +pathologically bad case is we keep going + + align:start position:0% +pathologically bad case is we keep going + + + align:start position:0% +pathologically bad case is we keep going +through this middle + + align:start position:0% +through this middle + + + align:start position:0% +through this middle +Edge okay so admon + + align:start position:0% +Edge okay so admon + + + align:start position:0% +Edge okay so admon +C is a Improvement to this algor + + align:start position:0% + + + + align:start position:0% + +let me just write it + + align:start position:0% + + + + align:start position:0% + +here it's + + align:start position:0% +here it's + + + align:start position:0% +here it's +uh it's first step third and fourth + + align:start position:0% +uh it's first step third and fourth + + + align:start position:0% +uh it's first step third and fourth +steps are actually exactly the same no + + align:start position:0% +steps are actually exactly the same no + + + align:start position:0% +steps are actually exactly the same no +change from for focuson the only thing + + align:start position:0% +change from for focuson the only thing + + + align:start position:0% +change from for focuson the only thing +it does is that it finds a special + + align:start position:0% +it does is that it finds a special + + + align:start position:0% +it does is that it finds a special +path um did really cover this in the + + align:start position:0% +path um did really cover this in the + + + align:start position:0% +path um did really cover this in the +lecture that what path uh ATM car + + align:start position:0% +lecture that what path uh ATM car + + + align:start position:0% +lecture that what path uh ATM car +finds I see some people noding okay go + + align:start position:0% +finds I see some people noding okay go + + + align:start position:0% +finds I see some people noding okay go +ahead run search + + align:start position:0% +ahead run search + + + align:start position:0% +ahead run search +from the source to the sink GF take the + + align:start position:0% +from the source to the sink GF take the + + + align:start position:0% +from the source to the sink GF take the +shortest okay does everyone agree with + + align:start position:0% +shortest okay does everyone agree with + + + align:start position:0% +shortest okay does everyone agree with +that so admon carp finds the shortest + + align:start position:0% + + + + align:start position:0% + +path + + align:start position:0% + + + + align:start position:0% + +from I guess can you see that + + align:start position:0% +from I guess can you see that + + + align:start position:0% +from I guess can you see that +part nope oh sorry about + + align:start position:0% + + + + align:start position:0% + +that find the shortest path uh here + + align:start position:0% +that find the shortest path uh here + + + align:start position:0% +that find the shortest path uh here +shortest just means least number of hops + + align:start position:0% +shortest just means least number of hops + + + align:start position:0% +shortest just means least number of hops +here uh in this pathologically bad + + align:start position:0% +here uh in this pathologically bad + + + align:start position:0% +here uh in this pathologically bad +example at cup will do much better + + align:start position:0% +example at cup will do much better + + + align:start position:0% +example at cup will do much better +because it would find this path instead + + align:start position:0% +because it would find this path instead + + + align:start position:0% +because it would find this path instead +of this weird path right because that + + align:start position:0% +of this weird path right because that + + + align:start position:0% +of this weird path right because that +path is distance is two and the one + + align:start position:0% +path is distance is two and the one + + + align:start position:0% +path is distance is two and the one +going across the middle is + + align:start position:0% + + + + align:start position:0% + +three okay now we are going to prove + + align:start position:0% +three okay now we are going to prove + + + align:start position:0% +three okay now we are going to prove +that this algorithm runs in order + + align:start position:0% + + + + align:start position:0% + +v² so okay uh so one step back do we + + align:start position:0% +v² so okay uh so one step back do we + + + align:start position:0% +v² so okay uh so one step back do we +have to prove that it's + + align:start position:0% +have to prove that it's + + + align:start position:0% +have to prove that it's +correct + + align:start position:0% +correct + + + align:start position:0% +correct +that it indeed finds the uh maximum + + align:start position:0% + + + + align:start position:0% + +flow MH yeah I don't I claim I don't + + align:start position:0% +flow MH yeah I don't I claim I don't + + + align:start position:0% +flow MH yeah I don't I claim I don't +have to do that because it's the same + + align:start position:0% +have to do that because it's the same + + + align:start position:0% +have to do that because it's the same +thing as uh for focusing you can find + + align:start position:0% +thing as uh for focusing you can find + + + align:start position:0% +thing as uh for focusing you can find +any + + align:start position:0% +any + + + align:start position:0% +any +path + + align:start position:0% +path + + + align:start position:0% +path +now we want to show we want to bound + + align:start position:0% +now we want to show we want to bound + + + align:start position:0% +now we want to show we want to bound +this runtime uh so any idea high level + + align:start position:0% +this runtime uh so any idea high level + + + align:start position:0% +this runtime uh so any idea high level +idea how we are going to do that in + + align:start position:0% +idea how we are going to do that in + + + align:start position:0% +idea how we are going to do that in +which several + + align:start position:0% + + + + align:start position:0% + +steps + + align:start position:0% + + + + align:start position:0% + +okay so uh okay a simpler question + + align:start position:0% +okay so uh okay a simpler question + + + align:start position:0% +okay so uh okay a simpler question +what's the what's the complexity of this + + align:start position:0% +what's the what's the complexity of this + + + align:start position:0% +what's the what's the complexity of this +second step find the shortest path from + + align:start position:0% +second step find the shortest path from + + + align:start position:0% +second step find the shortest path from +source to + + align:start position:0% + + + + align:start position:0% + +sync go ahead uh o plus e o plus e and + + align:start position:0% +sync go ahead uh o plus e o plus e and + + + align:start position:0% +sync go ahead uh o plus e o plus e and +uh in this case + + align:start position:0% +uh in this case + + + align:start position:0% +uh in this case +actually V is always less than e right + + align:start position:0% +actually V is always less than e right + + + align:start position:0% +actually V is always less than e right +so I can simply say + + align:start position:0% +so I can simply say + + + align:start position:0% +so I can simply say +o + + align:start position:0% +o + + + align:start position:0% +o +now how long does it take to augment + + align:start position:0% +now how long does it take to augment + + + align:start position:0% +now how long does it take to augment +that path if we have found + + align:start position:0% + + + + align:start position:0% + +it o that's + + align:start position:0% + + + + align:start position:0% + +correct but I claim I we can say we can + + align:start position:0% +correct but I claim I we can say we can + + + align:start position:0% +correct but I claim I we can say we can +also say it's all + + align:start position:0% +also say it's all + + + align:start position:0% +also say it's all +V right because the shortest + + align:start position:0% +V right because the shortest + + + align:start position:0% +V right because the shortest +path uh at least have at most has v + + align:start position:0% +path uh at least have at most has v + + + align:start position:0% +path uh at least have at most has v +Hops and then from F to F + + align:start position:0% +Hops and then from F to F + + + align:start position:0% +Hops and then from F to F +Prime okay so I think in some sense + + align:start position:0% +Prime okay so I think in some sense + + + align:start position:0% +Prime okay so I think in some sense +these two are the same steps and also of + + align:start position:0% +these two are the same steps and also of + + + align:start position:0% +these two are the same steps and also of +v and then updating the rescue graph is + + align:start position:0% +v and then updating the rescue graph is + + + align:start position:0% +v and then updating the rescue graph is +also of V so one of this + + align:start position:0% +also of V so one of this + + + align:start position:0% +also of V so one of this +iteration each iteration + + align:start position:0% +iteration each iteration + + + align:start position:0% +iteration each iteration +takes how + + align:start position:0% + + + + align:start position:0% + +long or V right this is + + align:start position:0% +long or V right this is + + + align:start position:0% +long or V right this is +the uh most expensive step in one + + align:start position:0% +the uh most expensive step in one + + + align:start position:0% +the uh most expensive step in one +iteration okay so what else do we have + + align:start position:0% +iteration okay so what else do we have + + + align:start position:0% +iteration okay so what else do we have +to do to prove this bound + + align:start position:0% +to do to prove this bound + + + align:start position:0% +to do to prove this bound +number we need to show that the number + + align:start position:0% +number we need to show that the number + + + align:start position:0% +number we need to show that the number +of + + align:start position:0% +of + + + align:start position:0% +of +iterations + + align:start position:0% + + + + align:start position:0% + +is O of V * e if we can show + + align:start position:0% + + + + align:start position:0% + +that then we are pretty much + + align:start position:0% +that then we are pretty much + + + align:start position:0% +that then we are pretty much +done + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +okay now to prove that bound uh we first + + align:start position:0% +okay now to prove that bound uh we first + + + align:start position:0% +okay now to prove that bound uh we first +need a + + align:start position:0% +need a + + + align:start position:0% +need a +LMA which uh we + + align:start position:0% +LMA which uh we + + + align:start position:0% +LMA which uh we +call + + align:start position:0% + + + + align:start position:0% + +monotonic so let me + + align:start position:0% + + + + align:start position:0% + +Define delta + + align:start position:0% + + + + align:start position:0% + +FV this is + + align:start position:0% +FV this is + + + align:start position:0% +FV this is +the length of the shortest path from s + + align:start position:0% +the length of the shortest path from s + + + align:start position:0% +the length of the shortest path from s +from the source to V which is a Noe in + + align:start position:0% +from the source to V which is a Noe in + + + align:start position:0% +from the source to V which is a Noe in +the + + align:start position:0% +the + + + align:start position:0% +the +graph the length of that + + align:start position:0% +graph the length of that + + + align:start position:0% +graph the length of that +in residue graph of + + align:start position:0% + + + + align:start position:0% + +f okay is that definition + + align:start position:0% + + + + align:start position:0% + +clear and this + + align:start position:0% +clear and this + + + align:start position:0% +clear and this +says Delta + + align:start position:0% +says Delta + + + align:start position:0% +says Delta +FV for any vertex + + align:start position:0% +FV for any vertex + + + align:start position:0% +FV for any vertex +V does not + + align:start position:0% + + + + align:start position:0% + +decrease okay so it can only uh + + align:start position:0% +decrease okay so it can only uh + + + align:start position:0% +decrease okay so it can only uh +monotonically in uh + + align:start position:0% + + + + align:start position:0% + +increases okay we're going to prove + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +so we'll prove by contradiction assume + + align:start position:0% +so we'll prove by contradiction assume + + + align:start position:0% +so we'll prove by contradiction assume +this is not the + + align:start position:0% + + + + align:start position:0% + +case that means + + align:start position:0% +case that means + + + align:start position:0% +case that means +um there is some V that in F Prime which + + align:start position:0% +um there is some V that in F Prime which + + + align:start position:0% +um there is some V that in F Prime which +is the uh new Rescue + + align:start position:0% + + + + align:start position:0% + +graph is shortest path the uh from The + + align:start position:0% +graph is shortest path the uh from The + + + align:start position:0% +graph is shortest path the uh from The +Source in the new residue graph is less + + align:start position:0% +Source in the new residue graph is less + + + align:start position:0% +Source in the new residue graph is less +than the old + + align:start position:0% +than the old + + + align:start position:0% +than the old +one right that's + + align:start position:0% + + + + align:start position:0% + +uh we are going to derive a + + align:start position:0% +uh we are going to derive a + + + align:start position:0% +uh we are going to derive a +contradiction to + + align:start position:0% + + + + align:start position:0% + +that but uh so there may be many such + + align:start position:0% +that but uh so there may be many such + + + align:start position:0% +that but uh so there may be many such +vertices that drop but I'm uh but if + + align:start position:0% +vertices that drop but I'm uh but if + + + align:start position:0% +vertices that drop but I'm uh but if +there if there's any I'm going to Define + + align:start position:0% +there if there's any I'm going to Define + + + align:start position:0% +there if there's any I'm going to Define +V + + align:start position:0% +V + + + align:start position:0% +V +to be the + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +smallest + + align:start position:0% +smallest + + + align:start position:0% +smallest +Delta in F + + align:start position:0% + + + + align:start position:0% + +Prime okay any questions about this + + align:start position:0% + + + + align:start position:0% + +step + + align:start position:0% +step + + + align:start position:0% +step +so there could be like V1 V2 V3 that or + + align:start position:0% +so there could be like V1 V2 V3 that or + + + align:start position:0% +so there could be like V1 V2 V3 that or +I make this happen I'm going to choose + + align:start position:0% +I make this happen I'm going to choose + + + align:start position:0% +I make this happen I'm going to choose +the one among those that has the + + align:start position:0% +the one among those that has the + + + align:start position:0% +the one among those that has the +smallest distance from The + + align:start position:0% + + + + align:start position:0% + +Source + + align:start position:0% + + + + align:start position:0% + +okay now here is my + + align:start position:0% +okay now here is my + + + align:start position:0% +okay now here is my +source uh we have a + + align:start position:0% +source uh we have a + + + align:start position:0% +source uh we have a +path to V + + align:start position:0% +path to V + + + align:start position:0% +path to V +in in graph uh GF + + align:start position:0% + + + + align:start position:0% + +Prime okay so this is a path then I can + + align:start position:0% +Prime okay so this is a path then I can + + + align:start position:0% +Prime okay so this is a path then I can +always find the + + align:start position:0% +always find the + + + align:start position:0% +always find the +predecessor which will call which I'll + + align:start position:0% +predecessor which will call which I'll + + + align:start position:0% +predecessor which will call which I'll +call you + + align:start position:0% + + + + align:start position:0% + +here right if this is the shortest path + + align:start position:0% +here right if this is the shortest path + + + align:start position:0% +here right if this is the shortest path +to V uh what can I say + + align:start position:0% + + + + align:start position:0% + +about + + align:start position:0% +about + + + align:start position:0% +about +datta of v + + align:start position:0% +datta of v + + + align:start position:0% +datta of v +and datta of + + align:start position:0% + + + + align:start position:0% + +U what can I say about these two + + align:start position:0% + + + + align:start position:0% + +quantities can decreas mhm can can we + + align:start position:0% +quantities can decreas mhm can can we + + + align:start position:0% +quantities can decreas mhm can can we +decrease one of them this one is greater + + align:start position:0% +decrease one of them this one is greater + + + align:start position:0% +decrease one of them this one is greater +than + + align:start position:0% + + + + align:start position:0% + +that one of them is greater than the + + align:start position:0% +that one of them is greater than the + + + align:start position:0% +that one of them is greater than the +other that's always true right for any + + align:start position:0% + + + + align:start position:0% + +two U + + align:start position:0% +two U + + + align:start position:0% +two U +one okay Misha said V is u+ one does + + align:start position:0% +one okay Misha said V is u+ one does + + + align:start position:0% +one okay Misha said V is u+ one does +that make sense to + + align:start position:0% + + + + align:start position:0% + +everyone cuz that's the shortest path + + align:start position:0% +everyone cuz that's the shortest path + + + align:start position:0% +everyone cuz that's the shortest path +Tov it goes through + + align:start position:0% + + + + align:start position:0% + +U + + align:start position:0% +U + + + align:start position:0% +U +okay that's + + align:start position:0% + + + + align:start position:0% + +correct so because I okay maybe I wasn't + + align:start position:0% +correct so because I okay maybe I wasn't + + + align:start position:0% +correct so because I okay maybe I wasn't +clear about that I defined U to be V's + + align:start position:0% +clear about that I defined U to be V's + + + align:start position:0% +clear about that I defined U to be V's +predecessor on the shortest + + align:start position:0% +predecessor on the shortest + + + align:start position:0% +predecessor on the shortest +path okay then + + align:start position:0% +path okay then + + + align:start position:0% +path okay then +definitely uh Delta fime of V is Delta + + align:start position:0% +definitely uh Delta fime of V is Delta + + + align:start position:0% +definitely uh Delta fime of V is Delta +fime Delta F Prime U + one okay now I'll + + align:start position:0% +fime Delta F Prime U + one okay now I'll + + + align:start position:0% +fime Delta F Prime U + one okay now I'll +use U to be my steps St back to the + + align:start position:0% +use U to be my steps St back to the + + + align:start position:0% +use U to be my steps St back to the +original graph + + align:start position:0% +original graph + + + align:start position:0% +original graph +F I want to say something about this + + align:start position:0% +F I want to say something about this + + + align:start position:0% +F I want to say something about this +quantity + + align:start position:0% +quantity + + + align:start position:0% +quantity +and Delta u in graph F what can I say + + align:start position:0% +and Delta u in graph F what can I say + + + align:start position:0% +and Delta u in graph F what can I say +about + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +this is a tricky + + align:start position:0% + + + + align:start position:0% + +part this one is greater than that or + + align:start position:0% +part this one is greater than that or + + + align:start position:0% +part this one is greater than that or +the entire thing is greater than + + align:start position:0% + + + + align:start position:0% + +that okay I'm going to claim this one + + align:start position:0% +that okay I'm going to claim this one + + + align:start position:0% +that okay I'm going to claim this one +is greater than Delta F + one uh by + + align:start position:0% +is greater than Delta F + one uh by + + + align:start position:0% +is greater than Delta F + one uh by +which I'm I'm claiming this quantity is + + align:start position:0% +which I'm I'm claiming this quantity is + + + align:start position:0% +which I'm I'm claiming this quantity is +larger than + + align:start position:0% +larger than + + + align:start position:0% +larger than +that can anyone give a reason why I can + + align:start position:0% +that can anyone give a reason why I can + + + align:start position:0% +that can anyone give a reason why I can +claim + + align:start position:0% + + + + align:start position:0% + +that so recall how I defined + + align:start position:0% + + + + align:start position:0% + +V can + + align:start position:0% +V can + + + align:start position:0% +V can +you good question so V uh so there there + + align:start position:0% +you good question so V uh so there there + + + align:start position:0% +you good question so V uh so there there +are several probably several V's that + + align:start position:0% +are several probably several V's that + + + align:start position:0% +are several probably several V's that +have uh Delta F Prime less than Delta F + + align:start position:0% +have uh Delta F Prime less than Delta F + + + align:start position:0% +have uh Delta F Prime less than Delta F +right I'm going to Define V + + align:start position:0% +right I'm going to Define V + + + align:start position:0% +right I'm going to Define V +to be the be the one with smallest Delta + + align:start position:0% +to be the be the one with smallest Delta + + + align:start position:0% +to be the be the one with smallest Delta +F okay among all those nodes that have a + + align:start position:0% +F okay among all those nodes that have a + + + align:start position:0% +F okay among all those nodes that have a +job in Delta F in + + align:start position:0% + + + + align:start position:0% + +Delta right this is probably a tricky + + align:start position:0% +Delta right this is probably a tricky + + + align:start position:0% +Delta right this is probably a tricky +part then by + + align:start position:0% +part then by + + + align:start position:0% +part then by +definition since Delta fu is less than + + align:start position:0% +definition since Delta fu is less than + + + align:start position:0% +definition since Delta fu is less than +Delta of V + + align:start position:0% +Delta of V + + + align:start position:0% +Delta of V +right and I defined V to be the to be + + align:start position:0% +right and I defined V to be the to be + + + align:start position:0% +right and I defined V to be the to be +the one with the smallest Delta that + + align:start position:0% +the one with the smallest Delta that + + + align:start position:0% +the one with the smallest Delta that +satisfy that so all the 's so U is a + + align:start position:0% +satisfy that so all the 's so U is a + + + align:start position:0% +satisfy that so all the 's so U is a +pressor of V so U shouldn't be one of + + align:start position:0% +pressor of V so U shouldn't be one of + + + align:start position:0% +pressor of V so U shouldn't be one of +those SES who that have a job in delta + + align:start position:0% +those SES who that have a job in delta + + + align:start position:0% +those SES who that have a job in delta +in + + align:start position:0% +in + + + align:start position:0% +in +Delta right so I I know this is probably + + align:start position:0% +Delta right so I I know this is probably + + + align:start position:0% +Delta right so I I know this is probably +a tricky part and uh yeah I'll stop for + + align:start position:0% +a tricky part and uh yeah I'll stop for + + + align:start position:0% +a tricky part and uh yeah I'll stop for +questions and yeah make sure we resolve + + align:start position:0% +questions and yeah make sure we resolve + + + align:start position:0% +questions and yeah make sure we resolve +this part before we move + + align:start position:0% + + + + align:start position:0% + +on how many people get + + align:start position:0% +on how many people get + + + align:start position:0% +on how many people get +it okay only two that's not good okay + + align:start position:0% +it okay only two that's not good okay + + + align:start position:0% +it okay only two that's not good okay +I'm confused about how B can be the one + + align:start position:0% +I'm confused about how B can be the one + + + align:start position:0% +I'm confused about how B can be the one +with the small Delta F if we have a + + align:start position:0% +with the small Delta F if we have a + + + align:start position:0% +with the small Delta F if we have a +predecessor with a smaller Delta + + align:start position:0% + + + + align:start position:0% + +F okay + + align:start position:0% +F okay + + + align:start position:0% +F okay +so uh okay may v to be the smallest the + + align:start position:0% +so uh okay may v to be the smallest the + + + align:start position:0% +so uh okay may v to be the smallest the +one with smallest F such + + align:start position:0% +one with smallest F such + + + align:start position:0% +one with smallest F such +that Delta F Prime is less than Delta + + align:start position:0% +that Delta F Prime is less than Delta + + + align:start position:0% +that Delta F Prime is less than Delta +F okay okay maybe yeah that's that's why + + align:start position:0% +F okay okay maybe yeah that's that's why + + + align:start position:0% +F okay okay maybe yeah that's that's why +uh yeah I confused you guys sorry about + + align:start position:0% +uh yeah I confused you guys sorry about + + + align:start position:0% +uh yeah I confused you guys sorry about +that so we have a bunch of nodes who + + align:start position:0% +that so we have a bunch of nodes who + + + align:start position:0% +that so we have a bunch of nodes who +have a job in Delta and I Define V to be + + align:start position:0% +have a job in Delta and I Define V to be + + + align:start position:0% +have a job in Delta and I Define V to be +the one among them that has the smallest + + align:start position:0% +the one among them that has the smallest + + + align:start position:0% +the one among them that has the smallest +Delta F + + align:start position:0% +Delta F + + + align:start position:0% +Delta F +Prime question sorry I'm l what Delta f + + align:start position:0% +Prime question sorry I'm l what Delta f + + + align:start position:0% +Prime question sorry I'm l what Delta f +is versus + + align:start position:0% +is versus + + + align:start position:0% +is versus +delta okay Delta F + + align:start position:0% +delta okay Delta F + + + align:start position:0% +delta okay Delta F +uh of a node is the shortest path from + + align:start position:0% +uh of a node is the shortest path from + + + align:start position:0% +uh of a node is the shortest path from +source to that Noe in G of f which is + + align:start position:0% +source to that Noe in G of f which is + + + align:start position:0% +source to that Noe in G of f which is +the rescue graph given a flow right so f + + align:start position:0% +the rescue graph given a flow right so f + + + align:start position:0% +the rescue graph given a flow right so f +is uh well some flow and F Prime is the + + align:start position:0% +is uh well some flow and F Prime is the + + + align:start position:0% +is uh well some flow and F Prime is the +flow after we augmenting a certain path + + align:start position:0% +flow after we augmenting a certain path + + + align:start position:0% +flow after we augmenting a certain path +so F Prime is one step after + + align:start position:0% +so F Prime is one step after + + + align:start position:0% +so F Prime is one step after +F okay how many people get that + + align:start position:0% +F okay how many people get that + + + align:start position:0% +F okay how many people get that +now right still not + + align:start position:0% + + + + align:start position:0% + +everyone okay any questions about + + align:start position:0% + + + + align:start position:0% + +that how how many people like still + + align:start position:0% +that how how many people like still + + + align:start position:0% +that how how many people like still +haven't got + + align:start position:0% +haven't got + + + align:start position:0% +haven't got +that H okay so some people it's like + + align:start position:0% +that H okay so some people it's like + + + align:start position:0% +that H okay so some people it's like +shers cut it's in the middle + + align:start position:0% + + + + align:start position:0% + +state + + align:start position:0% + + + + align:start position:0% + +well then I'll have to move on and I'll + + align:start position:0% +well then I'll have to move on and I'll + + + align:start position:0% +well then I'll have to move on and I'll +assume you all get this I'll get that + + align:start position:0% + + + + align:start position:0% + +one now as the last step so of course + + align:start position:0% +one now as the last step so of course + + + align:start position:0% +one now as the last step so of course +we'll + + align:start position:0% +we'll + + + align:start position:0% +we'll +ask what's the relation between this guy + + align:start position:0% +ask what's the relation between this guy + + + align:start position:0% +ask what's the relation between this guy +and Delta F of + + align:start position:0% +and Delta F of + + + align:start position:0% +and Delta F of +V right cuz final because in the end we + + align:start position:0% +V right cuz final because in the end we + + + align:start position:0% +V right cuz final because in the end we +want to show we want to show + + align:start position:0% +want to show we want to show + + + align:start position:0% +want to show we want to show +contradiction that Delta FV is probably + + align:start position:0% +contradiction that Delta FV is probably + + + align:start position:0% +contradiction that Delta FV is probably +greater or equal to Delta F of + + align:start position:0% + + + + align:start position:0% + +V this is another tricky + + align:start position:0% +V this is another tricky + + + align:start position:0% +V this is another tricky +part + + align:start position:0% + + + + align:start position:0% + +uh so let me ask uh maybe simpler + + align:start position:0% +uh so let me ask uh maybe simpler + + + align:start position:0% +uh so let me ask uh maybe simpler +question now so that is our G of f Prime + + align:start position:0% +question now so that is our G of f Prime + + + align:start position:0% +question now so that is our G of f Prime +so we also have G of f right it has the + + align:start position:0% +so we also have G of f right it has the + + + align:start position:0% +so we also have G of f right it has the +source some U here V + + align:start position:0% +source some U here V + + + align:start position:0% +source some U here V +there sync there + + align:start position:0% + + + + align:start position:0% + +uh does this Edge + + align:start position:0% +uh does this Edge + + + align:start position:0% +uh does this Edge +exist in this + + align:start position:0% +exist in this + + + align:start position:0% +exist in this +graph so I know it that edge exists + + align:start position:0% +graph so I know it that edge exists + + + align:start position:0% +graph so I know it that edge exists +because I defined U to be the + + align:start position:0% +because I defined U to be the + + + align:start position:0% +because I defined U to be the +predecessor of V right but UV is in that + + align:start position:0% +predecessor of V right but UV is in that + + + align:start position:0% +predecessor of V right but UV is in that +graph doesn't necessarily mean UV is in + + align:start position:0% +graph doesn't necessarily mean UV is in + + + align:start position:0% +graph doesn't necessarily mean UV is in +the old + + align:start position:0% + + + + align:start position:0% + +graph so it could certainly exist but is + + align:start position:0% +graph so it could certainly exist but is + + + align:start position:0% +graph so it could certainly exist but is +it possible that this + + align:start position:0% +it possible that this + + + align:start position:0% +it possible that this +Edge + + align:start position:0% +Edge + + + align:start position:0% +Edge +didn't + + align:start position:0% +didn't + + + align:start position:0% +didn't +exist how many people would say uh that + + align:start position:0% +exist how many people would say uh that + + + align:start position:0% +exist how many people would say uh that +edge definitely + + align:start position:0% + + + + align:start position:0% + +exists how many people would say maybe + + align:start position:0% +exists how many people would say maybe + + + align:start position:0% +exists how many people would say maybe +it doesn't + + align:start position:0% + + + + align:start position:0% + +exist okay it doesn't matter because we + + align:start position:0% +exist okay it doesn't matter because we + + + align:start position:0% +exist okay it doesn't matter because we +can prove both cases so let's say case + + align:start position:0% + + + + align:start position:0% + +one uh + + align:start position:0% +one uh + + + align:start position:0% +one uh +UV is indeed in the original graph + + align:start position:0% +UV is indeed in the original graph + + + align:start position:0% +UV is indeed in the original graph +GFF okay in that case can I say + + align:start position:0% +GFF okay in that case can I say + + + align:start position:0% +GFF okay in that case can I say +something about that last + + align:start position:0% + + + + align:start position:0% + +step + + align:start position:0% + + + + align:start position:0% + +greater or equal + + align:start position:0% +greater or equal + + + align:start position:0% +greater or equal +to Del + + align:start position:0% +to Del + + + align:start position:0% +to Del +V okay why is that um + + align:start position:0% +V okay why is that um + + + align:start position:0% +V okay why is that um +because V was on the shortest + + align:start position:0% + + + + align:start position:0% + +path yeah so the shortest path + + align:start position:0% + + + + align:start position:0% + +either yeah the the shortest path from V + + align:start position:0% +either yeah the the shortest path from V + + + align:start position:0% +either yeah the the shortest path from V +either pass + + align:start position:0% +either pass + + + align:start position:0% +either pass +correct does everyone get that so the + + align:start position:0% +correct does everyone get that so the + + + align:start position:0% +correct does everyone get that so the +shortest path in this graph to V is not + + align:start position:0% +shortest path in this graph to V is not + + + align:start position:0% +shortest path in this graph to V is not +necessarily this one + + align:start position:0% +necessarily this one + + + align:start position:0% +necessarily this one +right but if it's some other one okay so + + align:start position:0% +right but if it's some other one okay so + + + align:start position:0% +right but if it's some other one okay so +in case one I'm assuming this Edge + + align:start position:0% +in case one I'm assuming this Edge + + + align:start position:0% +in case one I'm assuming this Edge +exists + + align:start position:0% +exists + + + align:start position:0% +exists +right then no matter what the shortest + + align:start position:0% +right then no matter what the shortest + + + align:start position:0% +right then no matter what the shortest +path is it's definitely shorter than I + + align:start position:0% +path is it's definitely shorter than I + + + align:start position:0% +path is it's definitely shorter than I +first go to from s to U and then U to + + align:start position:0% +first go to from s to U and then U to + + + align:start position:0% +first go to from s to U and then U to +V right the shortest path between s to V + + align:start position:0% +V right the shortest path between s to V + + + align:start position:0% +V right the shortest path between s to V +is definitely short shorter then I first + + align:start position:0% +is definitely short shorter then I first + + + align:start position:0% +is definitely short shorter then I first +go from s to U and then U to + + align:start position:0% +go from s to U and then U to + + + align:start position:0% +go from s to U and then U to +V make + + align:start position:0% +V make + + + align:start position:0% +V make +sense okay + + align:start position:0% +sense okay + + + align:start position:0% +sense okay +so case one are done it's a + + align:start position:0% +so case one are done it's a + + + align:start position:0% +so case one are done it's a +contradiction because we showed that + + align:start position:0% +contradiction because we showed that + + + align:start position:0% +contradiction because we showed that +Delta F Prime of V is greater or equal + + align:start position:0% +Delta F Prime of V is greater or equal + + + align:start position:0% +Delta F Prime of V is greater or equal +to Delta F of + + align:start position:0% +to Delta F of + + + align:start position:0% +to Delta F of +V any questions about + + align:start position:0% + + + + align:start position:0% + +that okay okaye + + align:start position:0% + + + + align:start position:0% + +to UV is not in G + + align:start position:0% +to UV is not in G + + + align:start position:0% +to UV is not in G +GF okay so how can that even + + align:start position:0% +GF okay so how can that even + + + align:start position:0% +GF okay so how can that even +happen is it + + align:start position:0% + + + + align:start position:0% + +possible and that this + + align:start position:0% +possible and that this + + + align:start position:0% +possible and that this +Edge didn't + + align:start position:0% + + + + align:start position:0% + +exist backwards faing Edge that you + + align:start position:0% + + + + align:start position:0% + +add okay great Point that's exactly + + align:start position:0% +add okay great Point that's exactly + + + align:start position:0% +add okay great Point that's exactly +right so it it is possible that this + + align:start position:0% +right so it it is possible that this + + + align:start position:0% +right so it it is possible that this +Edge didn't exist but only appeared + + align:start position:0% +Edge didn't exist but only appeared + + + align:start position:0% +Edge didn't exist but only appeared +after we go from F to F Prime how can + + align:start position:0% +after we go from F to F Prime how can + + + align:start position:0% +after we go from F to F Prime how can +that happen that must mean we are + + align:start position:0% +that happen that must mean we are + + + align:start position:0% +that happen that must mean we are +augmenting a path that goes right + + align:start position:0% +augmenting a path that goes right + + + align:start position:0% +augmenting a path that goes right +through it right but this Edge doesn't + + align:start position:0% +through it right but this Edge doesn't + + + align:start position:0% +through it right but this Edge doesn't +exist so we cannot be augmenting a path + + align:start position:0% +exist so we cannot be augmenting a path + + + align:start position:0% +exist so we cannot be augmenting a path +that cross this way we must be + + align:start position:0% +that cross this way we must be + + + align:start position:0% +that cross this way we must be +augmenting a + + align:start position:0% + + + + align:start position:0% + +path that goes like + + align:start position:0% +path that goes like + + + align:start position:0% +path that goes like +that right first from s to V and then V + + align:start position:0% +that right first from s to V and then V + + + align:start position:0% +that right first from s to V and then V +to U and then U to + + align:start position:0% +to U and then U to + + + align:start position:0% +to U and then U to +T if we are augmenting such a path then + + align:start position:0% +T if we are augmenting such a path then + + + align:start position:0% +T if we are augmenting such a path then +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +remove this Edge from V to U but we will + + align:start position:0% +remove this Edge from V to U but we will + + + align:start position:0% +remove this Edge from V to U but we will +add uh + + align:start position:0% +add uh + + + align:start position:0% +add uh +u2v to the next graph + + align:start position:0% + + + + align:start position:0% + +okay did everyone get + + align:start position:0% + + + + align:start position:0% + +that so now uh here more formally I'm + + align:start position:0% +that so now uh here more formally I'm + + + align:start position:0% +that so now uh here more formally I'm +going to claims if we assume you u v is + + align:start position:0% +going to claims if we assume you u v is + + + align:start position:0% +going to claims if we assume you u v is +not in GF F and we also know + + align:start position:0% +not in GF F and we also know + + + align:start position:0% +not in GF F and we also know +UV is in GF + + align:start position:0% +UV is in GF + + + align:start position:0% +UV is in GF +Prime what does that mean these + + align:start position:0% +Prime what does that mean these + + + align:start position:0% +Prime what does that mean these +two can only be caused by the fact that + + align:start position:0% +two can only be caused by the fact that + + + align:start position:0% +two can only be caused by the fact that +UV is in GFF G uh G of f not only in + + align:start position:0% +UV is in GFF G uh G of f not only in + + + align:start position:0% +UV is in GFF G uh G of f not only in +that graph it must be on the uh it must + + align:start position:0% +that graph it must be on the uh it must + + + align:start position:0% +that graph it must be on the uh it must +be on the path we are augmenting + + align:start position:0% + + + + align:start position:0% + +makes + + align:start position:0% + + + + align:start position:0% + +sense okay so given that can we say + + align:start position:0% +sense okay so given that can we say + + + align:start position:0% +sense okay so given that can we say +something + + align:start position:0% +something + + + align:start position:0% +something +about Delta F of U and do of + + align:start position:0% + + + + align:start position:0% + +ofv + + align:start position:0% + + + + align:start position:0% + +so here is our + + align:start position:0% +so here is our + + + align:start position:0% +so here is our +P right + + align:start position:0% +P right + + + align:start position:0% +P right +this this entire thing + + align:start position:0% + + + + align:start position:0% + +here and P is the augmenting + + align:start position:0% + + + + align:start position:0% + +path correct right so so if that is the + + align:start position:0% +path correct right so so if that is the + + + align:start position:0% +path correct right so so if that is the +augmenting path in admon car we are + + align:start position:0% +augmenting path in admon car we are + + + align:start position:0% +augmenting path in admon car we are +looking for the shortest path right so V + + align:start position:0% +looking for the shortest path right so V + + + align:start position:0% +looking for the shortest path right so V +is the predecessor of U then Delta of U + + align:start position:0% +is the predecessor of U then Delta of U + + + align:start position:0% +is the predecessor of U then Delta of U +is Delta of V + one that means that + + align:start position:0% +is Delta of V + one that means that + + + align:start position:0% +is Delta of V + one that means that +quantity + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +is Delta F of + + align:start position:0% +is Delta F of + + + align:start position:0% +is Delta F of +V + 2 + + align:start position:0% + + + + align:start position:0% + +okay so it's also a + + align:start position:0% +okay so it's also a + + + align:start position:0% +okay so it's also a +contradiction to what we + + align:start position:0% + + + + align:start position:0% + +assumed + + align:start position:0% + + + + align:start position:0% + +okay so that proves the our LMA of uh + + align:start position:0% +okay so that proves the our LMA of uh + + + align:start position:0% +okay so that proves the our LMA of uh +every node Delta monotonically + + align:start position:0% +every node Delta monotonically + + + align:start position:0% +every node Delta monotonically +increases now here I'm going to show + + align:start position:0% +increases now here I'm going to show + + + align:start position:0% +increases now here I'm going to show +that uh our final + + align:start position:0% +that uh our final + + + align:start position:0% +that uh our final +theorem that we have at most V number of + + align:start position:0% + + + + align:start position:0% + +iterations so the way we're going to + + align:start position:0% +iterations so the way we're going to + + + align:start position:0% +iterations so the way we're going to +show that is + + align:start position:0% + + + + align:start position:0% + +uh we're going to show we're going to + + align:start position:0% +uh we're going to show we're going to + + + align:start position:0% +uh we're going to show we're going to +Define uh a capacity of the + + align:start position:0% +Define uh a capacity of the + + + align:start position:0% +Define uh a capacity of the +path it must be the capacity of its + + align:start position:0% +path it must be the capacity of its + + + align:start position:0% +path it must be the capacity of its +weakest link we're going to Define is + + align:start position:0% +weakest link we're going to Define is + + + align:start position:0% +weakest link we're going to Define is +weakest link is + + align:start position:0% +weakest link is + + + align:start position:0% +weakest link is +UV okay and we are going to show that UV + + align:start position:0% +UV okay and we are going to show that UV + + + align:start position:0% +UV okay and we are going to show that UV +uh we'll call + + align:start position:0% +uh we'll call + + + align:start position:0% +uh we'll call +that critical + + align:start position:0% +that critical + + + align:start position:0% +that critical +Edge we we're going to show UV can be + + align:start position:0% + + + + align:start position:0% + +critical only of V + + align:start position:0% +critical only of V + + + align:start position:0% +critical only of V +times if that if that holds for every + + align:start position:0% +times if that if that holds for every + + + align:start position:0% +times if that if that holds for every +Edge then I claim uh all the edges + + align:start position:0% +Edge then I claim uh all the edges + + + align:start position:0% +Edge then I claim uh all the edges +combined can only be augmented of V + + align:start position:0% + + + + align:start position:0% + +times + + align:start position:0% +times + + + align:start position:0% +times +now uh how do we show + + align:start position:0% +now uh how do we show + + + align:start position:0% +now uh how do we show +that so + + align:start position:0% +that so + + + align:start position:0% +that so +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +again let's assume we are augmenting a + + align:start position:0% +again let's assume we are augmenting a + + + align:start position:0% +again let's assume we are augmenting a +path from that goes through U + + align:start position:0% + + + + align:start position:0% + +Tov if we do + + align:start position:0% +Tov if we do + + + align:start position:0% +Tov if we do +that by our algorithm we will get rid of + + align:start position:0% +that by our algorithm we will get rid of + + + align:start position:0% +that by our algorithm we will get rid of +this path right and have a + + align:start position:0% +this path right and have a + + + align:start position:0% +this path right and have a +edge + + align:start position:0% +edge + + + align:start position:0% +edge +backwards when we go from F to some + + align:start position:0% +backwards when we go from F to some + + + align:start position:0% +backwards when we go from F to some +other F + + align:start position:0% +other F + + + align:start position:0% +other F +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +now when can I augment UV + + align:start position:0% + + + + align:start position:0% + +again it can only happen if at some + + align:start position:0% +again it can only happen if at some + + + align:start position:0% +again it can only happen if at some +point I come back to augment the path + + align:start position:0% +point I come back to augment the path + + + align:start position:0% +point I come back to augment the path +going from V to U right and because that + + align:start position:0% + + + + align:start position:0% + +will eliminates this back uh back Edge + + align:start position:0% +will eliminates this back uh back Edge + + + align:start position:0% +will eliminates this back uh back Edge +and + + align:start position:0% +and + + + align:start position:0% +and +and adds back our Ed + + align:start position:0% + + + + align:start position:0% + +UV okay let's see what happens there + + align:start position:0% + + + + align:start position:0% + +uh now let I'll call this graph F this + + align:start position:0% +uh now let I'll call this graph F this + + + align:start position:0% +uh now let I'll call this graph F this +graph F + + align:start position:0% + + + + align:start position:0% + +Prime so in F Prime we know we are + + align:start position:0% +Prime so in F Prime we know we are + + + align:start position:0% +Prime so in F Prime we know we are +argumenting the path from V to U by the + + align:start position:0% +argumenting the path from V to U by the + + + align:start position:0% +argumenting the path from V to U by the +same argument Delta U is Delta V + 1 in + + align:start position:0% +same argument Delta U is Delta V + 1 in + + + align:start position:0% +same argument Delta U is Delta V + 1 in +Fr Prime + + align:start position:0% +Fr Prime + + + align:start position:0% +Fr Prime +correct and we know this one doesn't + + align:start position:0% +correct and we know this one doesn't + + + align:start position:0% +correct and we know this one doesn't +drop right so it's greater or equal than + + align:start position:0% +drop right so it's greater or equal than + + + align:start position:0% +drop right so it's greater or equal than +Delta F of V + + + align:start position:0% +Delta F of V + + + + align:start position:0% +Delta F of V + +one + + align:start position:0% +one + + + align:start position:0% +one +okay and we also know in f v is the + + align:start position:0% +okay and we also know in f v is the + + + align:start position:0% +okay and we also know in f v is the +predecessor of + + align:start position:0% +predecessor of + + + align:start position:0% +predecessor of +U so this one is equal to Delta F of + + align:start position:0% +U so this one is equal to Delta F of + + + align:start position:0% +U so this one is equal to Delta F of +u+ + + align:start position:0% +u+ + + + align:start position:0% +u+ +2 what does that mean it + + align:start position:0% +2 what does that mean it + + + align:start position:0% +2 what does that mean it +means in between uh two times UV is + + align:start position:0% +means in between uh two times UV is + + + align:start position:0% +means in between uh two times UV is +Argent is + + align:start position:0% +Argent is + + + align:start position:0% +Argent is +augmented Delta of U must increase by at + + align:start position:0% +augmented Delta of U must increase by at + + + align:start position:0% +augmented Delta of U must increase by at +least + + align:start position:0% + + + + align:start position:0% + +two then how large can datta of a + + align:start position:0% +two then how large can datta of a + + + align:start position:0% +two then how large can datta of a +certain node possibly be + + align:start position:0% +certain node possibly be + + + align:start position:0% +certain node possibly be +is definitely bounded by of V right + + align:start position:0% +is definitely bounded by of V right + + + align:start position:0% +is definitely bounded by of V right +bounded by V so then I claim this + + align:start position:0% +bounded by V so then I claim this + + + align:start position:0% +bounded by V so then I claim this +particular Edge UV can only be involved + + align:start position:0% +particular Edge UV can only be involved + + + align:start position:0% +particular Edge UV can only be involved +can only be critical P edge of V times + + align:start position:0% +can only be critical P edge of V times + + + align:start position:0% +can only be critical P edge of V times +actually half of V times + + align:start position:0% +actually half of V times + + + align:start position:0% +actually half of V times +strictly so then every Edge combined + + align:start position:0% +strictly so then every Edge combined + + + align:start position:0% +strictly so then every Edge combined +there can only + + align:start position:0% +there can only + + + align:start position:0% +there can only +be half of V * + + align:start position:0% +be half of V * + + + align:start position:0% +be half of V * +e number of + + align:start position:0% + + + + align:start position:0% + +augmentation + + align:start position:0% + + + + align:start position:0% + +okay any questions about that part about + + align:start position:0% +okay any questions about that part about + + + align:start position:0% +okay any questions about that part about +the entire + + align:start position:0% + + + + align:start position:0% + +proof + + align:start position:0% + + + + align:start position:0% + +if not we'll move + + align:start position:0% + + + + align:start position:0% + +on okay this is not part of the uh + + align:start position:0% +on okay this is not part of the uh + + + align:start position:0% +on okay this is not part of the uh +required in the recitation but I'll + + align:start position:0% +required in the recitation but I'll + + + align:start position:0% +required in the recitation but I'll +quickly say a few words about uh even + + align:start position:0% +quickly say a few words about uh even + + + align:start position:0% +quickly say a few words about uh even +better algorithm + + align:start position:0% +better algorithm + + + align:start position:0% +better algorithm +DC which runs + + align:start position:0% +DC which runs + + + align:start position:0% +DC which runs +in of V squ * e so this is a Improvement + + align:start position:0% +in of V squ * e so this is a Improvement + + + align:start position:0% +in of V squ * e so this is a Improvement +to admon carp and its idea is that I'm + + align:start position:0% +to admon carp and its idea is that I'm + + + align:start position:0% +to admon carp and its idea is that I'm +going to + + align:start position:0% + + + + align:start position:0% + +find all the shortest + + align:start position:0% +find all the shortest + + + align:start position:0% +find all the shortest +path in one goal from s to + + align:start position:0% +path in one goal from s to + + + align:start position:0% +path in one goal from s to +T okay I'm going to augment all of + + align:start position:0% +T okay I'm going to augment all of + + + align:start position:0% +T okay I'm going to augment all of +them at the same time + + align:start position:0% + + + + align:start position:0% + +time then because they are all shortest + + align:start position:0% +time then because they are all shortest + + + align:start position:0% +time then because they are all shortest +path when I augment that each path will + + align:start position:0% +path when I augment that each path will + + + align:start position:0% +path when I augment that each path will +be broken right maybe I'll get rid this + + align:start position:0% +be broken right maybe I'll get rid this + + + align:start position:0% +be broken right maybe I'll get rid this +Edge this Edge and that edge and the + + align:start position:0% +Edge this Edge and that edge and the + + + align:start position:0% +Edge this Edge and that edge and the +thesis is that the shortest path uh will + + align:start position:0% +thesis is that the shortest path uh will + + + align:start position:0% +thesis is that the shortest path uh will +increase right here the shortest path is + + align:start position:0% +increase right here the shortest path is + + + align:start position:0% +increase right here the shortest path is +three but I have destroyed all the + + align:start position:0% +three but I have destroyed all the + + + align:start position:0% +three but I have destroyed all the +shortest path of length three so I'm + + align:start position:0% +shortest path of length three so I'm + + + align:start position:0% +shortest path of length three so I'm +going to show this part of + + align:start position:0% +going to show this part of + + + align:start position:0% +going to show this part of +four if they do that you can bound the + + align:start position:0% +four if they do that you can bound the + + + align:start position:0% +four if they do that you can bound the +number of iterations to all V because + + align:start position:0% +number of iterations to all V because + + + align:start position:0% +number of iterations to all V because +your shortest path can no long can be at + + align:start position:0% +your shortest path can no long can be at + + + align:start position:0% +your shortest path can no long can be at +most V but uh each iteration is slightly + + align:start position:0% +most V but uh each iteration is slightly + + + align:start position:0% +most V but uh each iteration is slightly +more complicated because you need to + + align:start position:0% +more complicated because you need to + + + align:start position:0% +more complicated because you need to +find all the TR path and it happens that + + align:start position:0% +find all the TR path and it happens that + + + align:start position:0% +find all the TR path and it happens that +they can show you can find it in V * e + + align:start position:0% +they can show you can find it in V * e + + + align:start position:0% +they can show you can find it in V * e +that gives the V Square V okay that's + + align:start position:0% +that gives the V Square V okay that's + + + align:start position:0% +that gives the V Square V okay that's +not the important part and the more + + align:start position:0% +not the important part and the more + + + align:start position:0% +not the important part and the more +interesting part is that actually the + + align:start position:0% +interesting part is that actually the + + + align:start position:0% +interesting part is that actually the +author of this + + align:start position:0% +author of this + + + align:start position:0% +author of this +algorithm is his name is + + align:start position:0% +algorithm is his name is + + + align:start position:0% +algorithm is his name is +Denis but his algorithm is very hard to + + align:start position:0% +Denis but his algorithm is very hard to + + + align:start position:0% +Denis but his algorithm is very hard to +understand that what well nobody yeah + + align:start position:0% +understand that what well nobody yeah + + + align:start position:0% +understand that what well nobody yeah +nobody got that and there is some other + + align:start position:0% +nobody got that and there is some other + + + align:start position:0% +nobody got that and there is some other +guy who whose name is I think is Ian uh + + align:start position:0% +guy who whose name is I think is Ian uh + + + align:start position:0% +guy who whose name is I think is Ian uh +he he understood the problem and started + + align:start position:0% +he he understood the problem and started + + + align:start position:0% +he he understood the problem and started +advertising to people and giving + + align:start position:0% +advertising to people and giving + + + align:start position:0% +advertising to people and giving +lectures uh on Denis algorithm so he + + align:start position:0% +lectures uh on Denis algorithm so he + + + align:start position:0% +lectures uh on Denis algorithm so he +popular popularized the algorithm but + + align:start position:0% +popular popularized the algorithm but + + + align:start position:0% +popular popularized the algorithm but +unfortunately he got the name of the + + align:start position:0% +unfortunately he got the name of the + + + align:start position:0% +unfortunately he got the name of the +author wrong and so that's why this + + align:start position:0% +author wrong and so that's why this + + + align:start position:0% +author wrong and so that's why this +algorithm is henceforth called denx + + align:start position:0% +algorithm is henceforth called denx + + + align:start position:0% +algorithm is henceforth called denx +algorithm this is useful to know why + + align:start position:0% +algorithm this is useful to know why + + + align:start position:0% +algorithm this is useful to know why +because you can tell this story to other + + align:start position:0% +because you can tell this story to other + + + align:start position:0% +because you can tell this story to other +people so they will assume that you know + + align:start position:0% +people so they will assume that you know + + + align:start position:0% +people so they will assume that you know +a lot about DX algorithm well in fact + + align:start position:0% +a lot about DX algorithm well in fact + + + align:start position:0% +a lot about DX algorithm well in fact +you probably don't and that's exactly + + align:start position:0% +you probably don't and that's exactly + + + align:start position:0% +you probably don't and that's exactly +what I'm doing + + align:start position:0% + + + + align:start position:0% + +here uh + + align:start position:0% + + + + align:start position:0% + +okay now let's look at one + + align:start position:0% + + + + align:start position:0% + +application uh by + + align:start position:0% +application uh by + + + align:start position:0% +application uh by +partite + + align:start position:0% + + + + align:start position:0% + +matching + + align:start position:0% +matching + + + align:start position:0% +matching +uh okay so the problem is that we have + + align:start position:0% +uh okay so the problem is that we have + + + align:start position:0% +uh okay so the problem is that we have +like several + + align:start position:0% +like several + + + align:start position:0% +like several +person and several + + align:start position:0% +person and several + + + align:start position:0% +person and several +tasks uh let me get rid of one person + + align:start position:0% +tasks uh let me get rid of one person + + + align:start position:0% +tasks uh let me get rid of one person +because I don't want to do that many + + align:start position:0% +because I don't want to do that many + + + align:start position:0% +because I don't want to do that many +stuff so we have a graph like + + align:start position:0% +stuff so we have a graph like + + + align:start position:0% +stuff so we have a graph like +that and each + + align:start position:0% +that and each + + + align:start position:0% +that and each +Edge if there's an edge that means this + + align:start position:0% +Edge if there's an edge that means this + + + align:start position:0% +Edge if there's an edge that means this +person is capable of Performing that + + align:start position:0% + + + + align:start position:0% + +task and the problem is is that uh find + + align:start position:0% +task and the problem is is that uh find + + + align:start position:0% +task and the problem is is that uh find +the matching which means the assignment + + align:start position:0% +the matching which means the assignment + + + align:start position:0% +the matching which means the assignment +from people to tasks such that we get as + + align:start position:0% +from people to tasks such that we get as + + + align:start position:0% +from people to tasks such that we get as +many tasks done as + + align:start position:0% +many tasks done as + + + align:start position:0% +many tasks done as +possible okay so one person can only do + + align:start position:0% +possible okay so one person can only do + + + align:start position:0% +possible okay so one person can only do +one task and one task only needs one + + align:start position:0% +one task and one task only needs one + + + align:start position:0% +one task and one task only needs one +person so here you can see a bad uh + + align:start position:0% +person so here you can see a bad uh + + + align:start position:0% +person so here you can see a bad uh +matching which is I assign this first + + align:start position:0% +matching which is I assign this first + + + align:start position:0% +matching which is I assign this first +guy to task one then no one can do task + + align:start position:0% +guy to task one then no one can do task + + + align:start position:0% +guy to task one then no one can do task +two + + align:start position:0% +two + + + align:start position:0% +two +right so if I'm smarter I'll assign one + + align:start position:0% +right so if I'm smarter I'll assign one + + + align:start position:0% +right so if I'm smarter I'll assign one +of these guys to that task and have this + + align:start position:0% +of these guys to that task and have this + + + align:start position:0% +of these guys to that task and have this +uh person handle the other task is the + + align:start position:0% +uh person handle the other task is the + + + align:start position:0% +uh person handle the other task is the +problem + + align:start position:0% + + + + align:start position:0% + +clear so uh this is called bip partal + + align:start position:0% +clear so uh this is called bip partal + + + align:start position:0% +clear so uh this is called bip partal +graph because uh well which means you + + align:start position:0% +graph because uh well which means you + + + align:start position:0% +graph because uh well which means you +can partition the graph into two parts + + align:start position:0% +can partition the graph into two parts + + + align:start position:0% +can partition the graph into two parts +and within each part there is no Edge + + align:start position:0% +and within each part there is no Edge + + + align:start position:0% +and within each part there is no Edge +connecting any pair of + + align:start position:0% +connecting any pair of + + + align:start position:0% +connecting any pair of +vertices and you can also Define this + + align:start position:0% +vertices and you can also Define this + + + align:start position:0% +vertices and you can also Define this +problem for General + + align:start position:0% + + + + align:start position:0% + +graph + + align:start position:0% +graph + + + align:start position:0% +graph +the goal is the same that find a subset + + align:start position:0% +the goal is the same that find a subset + + + align:start position:0% +the goal is the same that find a subset +of + + align:start position:0% + + + + align:start position:0% + +edges uh such that no two edges are + + align:start position:0% +edges uh such that no two edges are + + + align:start position:0% +edges uh such that no two edges are +connected to the + + align:start position:0% +connected to the + + + align:start position:0% +connected to the +same + + align:start position:0% +same + + + align:start position:0% +same +vertex okay but we are going to look at + + align:start position:0% +vertex okay but we are going to look at + + + align:start position:0% +vertex okay but we are going to look at +uh bipartite uh graph and we claim in + + align:start position:0% +uh bipartite uh graph and we claim in + + + align:start position:0% +uh bipartite uh graph and we claim in +bipot graph this can be solved using Max + + align:start position:0% +bipot graph this can be solved using Max + + + align:start position:0% +bipot graph this can be solved using Max +flow + + align:start position:0% +flow + + + align:start position:0% +flow +okay I'll give you one minute to think + + align:start position:0% +okay I'll give you one minute to think + + + align:start position:0% +okay I'll give you one minute to think +about that how to transform that problem + + align:start position:0% +about that how to transform that problem + + + align:start position:0% +about that how to transform that problem +to a Max flow + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% + + + + align:start position:0% + +for + + align:start position:0% + + + + align:start position:0% + +any + + align:start position:0% + + + + align:start position:0% + +ideas + + align:start position:0% + + + + align:start position:0% + +okay a hint uh I will add a source here + + align:start position:0% +okay a hint uh I will add a source here + + + align:start position:0% +okay a hint uh I will add a source here +and the sync there + + align:start position:0% + + + + align:start position:0% + +and I'll have create these + + align:start position:0% + + + + align:start position:0% + +edges okay how do I restrict the + + align:start position:0% +edges okay how do I restrict the + + + align:start position:0% +edges okay how do I restrict the +capacity of all the edges such that I + + align:start position:0% +capacity of all the edges such that I + + + align:start position:0% +capacity of all the edges such that I +can + + align:start position:0% +can + + + align:start position:0% +can +guarantee uh + + align:start position:0% +guarantee uh + + + align:start position:0% +guarantee uh +no like each person is no person is + + align:start position:0% +no like each person is no person is + + + align:start position:0% +no like each person is no person is +taking two tasks and no task is assigned + + align:start position:0% +taking two tasks and no task is assigned + + + align:start position:0% +taking two tasks and no task is assigned +to two + + align:start position:0% + + + + align:start position:0% + +people + + align:start position:0% +people + + + align:start position:0% +people +make all of them weight one okay make + + align:start position:0% +make all of them weight one okay make + + + align:start position:0% +make all of them weight one okay make +all of them weight + + align:start position:0% +all of them weight + + + align:start position:0% +all of them weight +one okay if I we do that one one one one + + align:start position:0% +one okay if I we do that one one one one + + + align:start position:0% +one okay if I we do that one one one one +one and everything here is weight one + + align:start position:0% +one and everything here is weight one + + + align:start position:0% +one and everything here is weight one +then that's definitely correct what's + + align:start position:0% +then that's definitely correct what's + + + align:start position:0% +then that's definitely correct what's +your + + align:start position:0% +your + + + align:start position:0% +your +name c okay + + align:start position:0% +name c okay + + + align:start position:0% +name c okay +uh if we do that then well because each + + align:start position:0% +uh if we do that then well because each + + + align:start position:0% +uh if we do that then well because each +person only has one incoming + + align:start position:0% +person only has one incoming + + + align:start position:0% +person only has one incoming +Edge oh sorry maybe I I should have + + align:start position:0% +Edge oh sorry maybe I I should have + + + align:start position:0% +Edge oh sorry maybe I I should have +drawn the arrows here + + align:start position:0% + + + + align:start position:0% + +each person only has one incoming Edge + + align:start position:0% +each person only has one incoming Edge + + + align:start position:0% +each person only has one incoming Edge +so it cannot take care of two tasks at + + align:start position:0% +so it cannot take care of two tasks at + + + align:start position:0% +so it cannot take care of two tasks at +the same time right same thing for each + + align:start position:0% +the same time right same thing for each + + + align:start position:0% +the same time right same thing for each +task it's only it only has one outgoing + + align:start position:0% +task it's only it only has one outgoing + + + align:start position:0% +task it's only it only has one outgoing +Edge so it cannot be taken care of by + + align:start position:0% +Edge so it cannot be taken care of by + + + align:start position:0% +Edge so it cannot be taken care of by +multiple + + align:start position:0% + + + + align:start position:0% + +people okay so if we find if the max + + align:start position:0% +people okay so if we find if the max + + + align:start position:0% +people okay so if we find if the max +flow is + + align:start position:0% +flow is + + + align:start position:0% +flow is +K that means we can find + + align:start position:0% + + + + align:start position:0% + +that the max matching is also okay and + + align:start position:0% +that the max matching is also okay and + + + align:start position:0% +that the max matching is also okay and +we can get K tasks done it's very easy + + align:start position:0% +we can get K tasks done it's very easy + + + align:start position:0% +we can get K tasks done it's very easy +to see because we can have a cut + + align:start position:0% +to see because we can have a cut + + + align:start position:0% +to see because we can have a cut +here and if the max flow is K that + + align:start position:0% +here and if the max flow is K that + + + align:start position:0% +here and if the max flow is K that +clearly K taxs are taken care + + align:start position:0% + + + + align:start position:0% + +of okay any question about that + + align:start position:0% + + + + align:start position:0% + +so the question is can we do all these + + align:start position:0% +so the question is can we do all these + + + align:start position:0% +so the question is can we do all these +things uh find a assignment from uh + + align:start position:0% +things uh find a assignment from uh + + + align:start position:0% +things uh find a assignment from uh +people to task to get as many tasks done + + align:start position:0% +people to task to get as many tasks done + + + align:start position:0% +people to task to get as many tasks done +as possible so how many tasks can we uh + + align:start position:0% + + + + align:start position:0% + +handle okay so I'm doing a a different + + align:start position:0% +handle okay so I'm doing a a different + + + align:start position:0% +handle okay so I'm doing a a different +topic from the recitation note in the + + align:start position:0% +topic from the recitation note in the + + + align:start position:0% +topic from the recitation note in the +recitation note uh we are consider ing + + align:start position:0% +recitation note uh we are consider ing + + + align:start position:0% +recitation note uh we are consider ing +another problem called bipot cover which + + align:start position:0% +another problem called bipot cover which + + + align:start position:0% +another problem called bipot cover which +is exactly the same thing as + + align:start position:0% + + + + align:start position:0% + +that so cover also by partal graph is + + align:start position:0% +that so cover also by partal graph is + + + align:start position:0% +that so cover also by partal graph is +defin to as + + align:start position:0% +defin to as + + + align:start position:0% +defin to as +uh let's find several vertices in this + + align:start position:0% +uh let's find several vertices in this + + + align:start position:0% +uh let's find several vertices in this +graph such that each + + align:start position:0% +graph such that each + + + align:start position:0% +graph such that each +node at least okay let uh let me me + + align:start position:0% +node at least okay let uh let me me + + + align:start position:0% +node at least okay let uh let me me +color several nodes in this graph such + + align:start position:0% +color several nodes in this graph such + + + align:start position:0% +color several nodes in this graph such +that each Edge uh is connected to at + + align:start position:0% +that each Edge uh is connected to at + + + align:start position:0% +that each Edge uh is connected to at +least one dark + + align:start position:0% + + + + align:start position:0% + +node okay and this the nodes I colored + + align:start position:0% +node okay and this the nodes I colored + + + align:start position:0% +node okay and this the nodes I colored +is called a cover I want to find a + + align:start position:0% +is called a cover I want to find a + + + align:start position:0% +is called a cover I want to find a +minimum cover you can of course you can + + align:start position:0% +minimum cover you can of course you can + + + align:start position:0% +minimum cover you can of course you can +of course cover all the nodes that's + + align:start position:0% +of course cover all the nodes that's + + + align:start position:0% +of course cover all the nodes that's +trip hold but we are looking for the + + align:start position:0% +trip hold but we are looking for the + + + align:start position:0% +trip hold but we are looking for the +minimum cover and the claim is + + align:start position:0% +minimum cover and the claim is + + + align:start position:0% +minimum cover and the claim is +that mean cover + + align:start position:0% +that mean cover + + + align:start position:0% +that mean cover +is K if and only if Max + + align:start position:0% +is K if and only if Max + + + align:start position:0% +is K if and only if Max +flow sorry uh Max + + align:start position:0% + + + + align:start position:0% + +matching is + + align:start position:0% +matching is + + + align:start position:0% +matching is +K why is that because in that matching + + align:start position:0% +K why is that because in that matching + + + align:start position:0% +K why is that because in that matching +uh if we have a matching then we have a + + align:start position:0% +uh if we have a matching then we have a + + + align:start position:0% +uh if we have a matching then we have a +set + + align:start position:0% +set + + + align:start position:0% +set +of disjoint edges right no two edges are + + align:start position:0% +of disjoint edges right no two edges are + + + align:start position:0% +of disjoint edges right no two edges are +connected to the same node so if we want + + align:start position:0% +connected to the same node so if we want + + + align:start position:0% +connected to the same node so if we want +to cover these edges we at least have to + + align:start position:0% +to cover these edges we at least have to + + + align:start position:0% +to cover these edges we at least have to +add one of these guy right one of color + + align:start position:0% +add one of these guy right one of color + + + align:start position:0% +add one of these guy right one of color +one of these two and one of these two + + align:start position:0% +one of these two and one of these two + + + align:start position:0% +one of these two and one of these two +right so if we have K matching + + align:start position:0% +right so if we have K matching + + + align:start position:0% +right so if we have K matching +edges then we at least need K nodes to + + align:start position:0% +edges then we at least need K nodes to + + + align:start position:0% +edges then we at least need K nodes to +cover + + align:start position:0% + + + + align:start position:0% + +them for example I can col cover them + + align:start position:0% +them for example I can col cover them + + + align:start position:0% +them for example I can col cover them +like + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +uh but this is not a fullprof because I + + align:start position:0% +uh but this is not a fullprof because I + + + align:start position:0% +uh but this is not a fullprof because I +also need to show I can indeed find the + + align:start position:0% +also need to show I can indeed find the + + + align:start position:0% +also need to show I can indeed find the +cover that that is + + align:start position:0% + + + + align:start position:0% + +K okay let me think about whether I + + align:start position:0% +K okay let me think about whether I + + + align:start position:0% +K okay let me think about whether I +should prove + + align:start position:0% + + + + align:start position:0% + +that okay I'm going to give it a try um + + align:start position:0% +that okay I'm going to give it a try um + + + align:start position:0% +that okay I'm going to give it a try um +uh if you don't get that that's fine + + align:start position:0% + + + + align:start position:0% + +um what cover is okay + + align:start position:0% +um what cover is okay + + + align:start position:0% +um what cover is okay +cover cover is a set of nodes such that + + align:start position:0% +cover cover is a set of nodes such that + + + align:start position:0% +cover cover is a set of nodes such that +every Edge in the graph is connected to + + align:start position:0% +every Edge in the graph is connected to + + + align:start position:0% +every Edge in the graph is connected to +at least one of the node in a + + align:start position:0% +at least one of the node in a + + + align:start position:0% +at least one of the node in a +cover okay so this is not a cover + + align:start position:0% +cover okay so this is not a cover + + + align:start position:0% +cover okay so this is not a cover +because this Edge is not + + align:start position:0% + + + + align:start position:0% + +covered now so in this case I probably + + align:start position:0% +covered now so in this case I probably + + + align:start position:0% +covered now so in this case I probably +have to add that as + + align:start position:0% +have to add that as + + + align:start position:0% +have to add that as +well but clearly there's a better cover + + align:start position:0% +well but clearly there's a better cover + + + align:start position:0% +well but clearly there's a better cover +even a smaller cover which is those + + align:start position:0% +even a smaller cover which is those + + + align:start position:0% +even a smaller cover which is those +two right + + align:start position:0% + + + + align:start position:0% + +yeah so how are we going to transform + + align:start position:0% +yeah so how are we going to transform + + + align:start position:0% +yeah so how are we going to transform +that matching to cover so uh let me go + + align:start position:0% +that matching to cover so uh let me go + + + align:start position:0% +that matching to cover so uh let me go +first give a matching here One Max + + align:start position:0% +first give a matching here One Max + + + align:start position:0% +first give a matching here One Max +matching should be something like this I + + align:start position:0% +matching should be something like this I + + + align:start position:0% +matching should be something like this I +have this Edge and one of those two + + align:start position:0% + + + + align:start position:0% + +that is a matching right that is a Max + + align:start position:0% + + + + align:start position:0% + +matching no question about + + align:start position:0% +matching no question about + + + align:start position:0% +matching no question about +that + + align:start position:0% +that + + + align:start position:0% +that +so let me get rid of all + + align:start position:0% +so let me get rid of all + + + align:start position:0% +so let me get rid of all +these one way to transform this into a + + align:start position:0% +these one way to transform this into a + + + align:start position:0% +these one way to transform this into a +cover is that uh I will first color + + align:start position:0% +cover is that uh I will first color + + + align:start position:0% +cover is that uh I will first color +these two + + align:start position:0% +these two + + + align:start position:0% +these two +guys uh I'll color the nodes on the left + + align:start position:0% +guys uh I'll color the nodes on the left + + + align:start position:0% +guys uh I'll color the nodes on the left +where they are connected to a matching + + align:start position:0% +where they are connected to a matching + + + align:start position:0% +where they are connected to a matching +Edge right after that I'm going to start + + align:start position:0% +Edge right after that I'm going to start + + + align:start position:0% +Edge right after that I'm going to start +from this one + + align:start position:0% +from this one + + + align:start position:0% +from this one +and uh jump between noes taking + + align:start position:0% +and uh jump between noes taking + + + align:start position:0% +and uh jump between noes taking +alternating path meaning I'll take a + + align:start position:0% +alternating path meaning I'll take a + + + align:start position:0% +alternating path meaning I'll take a +unmatched Edge and then take a matched + + align:start position:0% +unmatched Edge and then take a matched + + + align:start position:0% +unmatched Edge and then take a matched +Edge and then take a unmatched Edge + + align:start position:0% +Edge and then take a unmatched Edge + + + align:start position:0% +Edge and then take a unmatched Edge +again but there's no such + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% + + + + align:start position:0% + +okay and if I take this jump I will swap + + align:start position:0% +okay and if I take this jump I will swap + + + align:start position:0% +okay and if I take this jump I will swap +them make that + + align:start position:0% + + + + align:start position:0% + +dark okay this graph is a little + + align:start position:0% + + + + align:start position:0% + +strange + + align:start position:0% +strange + + + align:start position:0% +strange +ah okay now I claim this is a + + align:start position:0% +ah okay now I claim this is a + + + align:start position:0% +ah okay now I claim this is a +cover is that yeah that is one + + align:start position:0% + + + + align:start position:0% + +right and uh if there is another like + + align:start position:0% +right and uh if there is another like + + + align:start position:0% +right and uh if there is another like +unmatched Edge going out then I'll keep + + align:start position:0% +unmatched Edge going out then I'll keep + + + align:start position:0% +unmatched Edge going out then I'll keep +taking that alternate alternating path + + align:start position:0% +taking that alternate alternating path + + + align:start position:0% +taking that alternate alternating path +but I have to stop because there's no + + align:start position:0% +but I have to stop because there's no + + + align:start position:0% +but I have to stop because there's no +such Edge + + align:start position:0% +such Edge + + + align:start position:0% +such Edge +anymore how can I say why can I prove + + align:start position:0% +anymore how can I say why can I prove + + + align:start position:0% +anymore how can I say why can I prove +why can I claim this is a + + align:start position:0% +why can I claim this is a + + + align:start position:0% +why can I claim this is a +cover so clearly this is if this is a + + align:start position:0% +cover so clearly this is if this is a + + + align:start position:0% +cover so clearly this is if this is a +cover then it's a cover of size K right + + align:start position:0% +cover then it's a cover of size K right + + + align:start position:0% +cover then it's a cover of size K right +so it's we have proved the entire thing + + align:start position:0% +so it's we have proved the entire thing + + + align:start position:0% +so it's we have proved the entire thing +uh then we're going to consider several + + align:start position:0% +uh then we're going to consider several + + + align:start position:0% +uh then we're going to consider several +things + + align:start position:0% + + + + align:start position:0% + +separately so I I'm going to first claim + + align:start position:0% +separately so I I'm going to first claim + + + align:start position:0% +separately so I I'm going to first claim +if I have a match the edge then it's + + align:start position:0% +if I have a match the edge then it's + + + align:start position:0% +if I have a match the edge then it's +definitely + + align:start position:0% +definitely + + + align:start position:0% +definitely +covered because uh one of its end points + + align:start position:0% +covered because uh one of its end points + + + align:start position:0% +covered because uh one of its end points +is dark right we only do a switching + + align:start position:0% +is dark right we only do a switching + + + align:start position:0% +is dark right we only do a switching +between dark and white if it is inde if + + align:start position:0% +between dark and white if it is inde if + + + align:start position:0% +between dark and white if it is inde if +it's uh matched Edge itself right so I + + align:start position:0% +it's uh matched Edge itself right so I + + + align:start position:0% +it's uh matched Edge itself right so I +only need to show that there this thing + + align:start position:0% +only need to show that there this thing + + + align:start position:0% +only need to show that there this thing +doesn't happen there's a edge that's + + align:start position:0% +doesn't happen there's a edge that's + + + align:start position:0% +doesn't happen there's a edge that's +unmatched and two of its end points are + + align:start position:0% +unmatched and two of its end points are + + + align:start position:0% +unmatched and two of its end points are +both + + align:start position:0% +both + + + align:start position:0% +both +white okay I'm going to first + + align:start position:0% +white okay I'm going to first + + + align:start position:0% +white okay I'm going to first +claim uh this node cannot have a match + + align:start position:0% +claim uh this node cannot have a match + + + align:start position:0% +claim uh this node cannot have a match +Edge because if it does then this is + + align:start position:0% +Edge because if it does then this is + + + align:start position:0% +Edge because if it does then this is +alternating path and I'm going to switch + + align:start position:0% +alternating path and I'm going to switch + + + align:start position:0% +alternating path and I'm going to switch +that to switch this + + align:start position:0% +that to switch this + + + align:start position:0% +that to switch this +two okay make sense + + align:start position:0% + + + + align:start position:0% + +okay so this doesn't + + align:start position:0% +okay so this doesn't + + + align:start position:0% +okay so this doesn't +exist so it can only have unmatched Edge + + align:start position:0% +exist so it can only have unmatched Edge + + + align:start position:0% +exist so it can only have unmatched Edge +now what can I say about this note I + + align:start position:0% +now what can I say about this note I + + + align:start position:0% +now what can I say about this note I +claim this note needs at least one + + align:start position:0% +claim this note needs at least one + + + align:start position:0% +claim this note needs at least one +matched + + align:start position:0% +matched + + + align:start position:0% +matched +Edge because if it doesn't right then I + + align:start position:0% +Edge because if it doesn't right then I + + + align:start position:0% +Edge because if it doesn't right then I +should add this guy into my + + align:start position:0% +should add this guy into my + + + align:start position:0% +should add this guy into my +matching right it doesn't violate any + + align:start position:0% +matching right it doesn't violate any + + + align:start position:0% +matching right it doesn't violate any +constraint right I didn't add that + + align:start position:0% +constraint right I didn't add that + + + align:start position:0% +constraint right I didn't add that +because there is probably a matched Edge + + align:start position:0% +because there is probably a matched Edge + + + align:start position:0% +because there is probably a matched Edge +connecting to this guy + + align:start position:0% +connecting to this guy + + + align:start position:0% +connecting to this guy +then I'm going to so then this guy has + + align:start position:0% +then I'm going to so then this guy has + + + align:start position:0% +then I'm going to so then this guy has +to be dark because this one is + + align:start position:0% +to be dark because this one is + + + align:start position:0% +to be dark because this one is +not then how did this one become dark it + + align:start position:0% +not then how did this one become dark it + + + align:start position:0% +not then how did this one become dark it +must come from some other guy on the + + align:start position:0% +must come from some other guy on the + + + align:start position:0% +must come from some other guy on the +left right so there is alternating path + + align:start position:0% +left right so there is alternating path + + + align:start position:0% +left right so there is alternating path +going back and + + align:start position:0% + + + + align:start position:0% + +forth something like this there is an + + align:start position:0% +forth something like this there is an + + + align:start position:0% +forth something like this there is an +alternating path starting from left but + + align:start position:0% +alternating path starting from left but + + + align:start position:0% +alternating path starting from left but +ends here + + align:start position:0% +ends here + + + align:start position:0% +ends here +right because we showed that this guy is + + align:start position:0% +right because we showed that this guy is + + + align:start position:0% +right because we showed that this guy is +not connecting to any matched edges in + + align:start position:0% +not connecting to any matched edges in + + + align:start position:0% +not connecting to any matched edges in +that case what I'm going to do is match + + align:start position:0% +that case what I'm going to do is match + + + align:start position:0% +that case what I'm going to do is match +this Edge match this Edge match this + + align:start position:0% +this Edge match this Edge match this + + + align:start position:0% +this Edge match this Edge match this +Edge and unmatch these two edges and + + align:start position:0% +Edge and unmatch these two edges and + + + align:start position:0% +Edge and unmatch these two edges and +that's a larger + + align:start position:0% +that's a larger + + + align:start position:0% +that's a larger +matching I removed the two I added + + align:start position:0% + + + + align:start position:0% + +three + + align:start position:0% +three + + + align:start position:0% +three +that means uh + + align:start position:0% +that means uh + + + align:start position:0% +that means uh +uh Max matching of K leads to a minimum + + align:start position:0% +uh Max matching of K leads to a minimum + + + align:start position:0% +uh Max matching of K leads to a minimum +cover of K as well which also means U + + align:start position:0% +cover of K as well which also means U + + + align:start position:0% +cover of K as well which also means U +Max flow of K in our Network + + align:start position:0% +Max flow of K in our Network + + + align:start position:0% +Max flow of K in our Network +flow okay so this part this equivalence + + align:start position:0% +flow okay so this part this equivalence + + + align:start position:0% +flow okay so this part this equivalence +is not + + align:start position:0% + + + + align:start position:0% + +required and you you should know uh this + + align:start position:0% +required and you you should know uh this + + + align:start position:0% +required and you you should know uh this +proof the proof of admon carp and know + + align:start position:0% +proof the proof of admon carp and know + + + align:start position:0% +proof the proof of admon carp and know +that matching and cover can be solved by + + align:start position:0% +that matching and cover can be solved by + + + align:start position:0% +that matching and cover can be solved by +Network flow and that din name is + + align:start position:0% +Network flow and that din name is + + + align:start position:0% +Network flow and that din name is +spelled not as + + align:start position:0% + + + + align:start position:0% + +din okay and that's everything for + + align:start position:0% +din okay and that's everything for + + + align:start position:0% +din okay and that's everything for +today \ No newline at end of file diff --git a/1S_QU0PmYrU.txt b/1S_QU0PmYrU.txt new file mode 100644 index 0000000000000000000000000000000000000000..086935161689da2da3c05f37983b5791023c5d9d --- /dev/null +++ b/1S_QU0PmYrU.txt @@ -0,0 +1,1171 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +one egg + + align:start position:0% +one egg + + + align:start position:0% +one egg +every every 100 + + align:start position:0% +every every 100 + + + align:start position:0% +every every 100 +GR now let's add all the eggs and then + + align:start position:0% +GR now let's add all the eggs and then + + + align:start position:0% +GR now let's add all the eggs and then +mix and this should shouldn't need extra + + align:start position:0% +mix and this should shouldn't need extra + + + align:start position:0% +mix and this should shouldn't need extra +water we will see it's going to be + + align:start position:0% +water we will see it's going to be + + + align:start position:0% +water we will see it's going to be +really hard okay you + + align:start position:0% + + + + align:start position:0% + +to Fen you start wide and then you get + + align:start position:0% +to Fen you start wide and then you get + + + align:start position:0% +to Fen you start wide and then you get +thinner so you you first do then it + + align:start position:0% +thinner so you you first do then it + + + align:start position:0% +thinner so you you first do then it +actually needs the dough when you do + + align:start position:0% +actually needs the dough when you do + + + align:start position:0% +actually needs the dough when you do +it to ground see as wide as + + align:start position:0% +it to ground see as wide as + + + align:start position:0% +it to ground see as wide as +possible are start as yes so really just + + align:start position:0% +possible are start as yes so really just + + + align:start position:0% +possible are start as yes so really just +be + + align:start position:0% +be + + + align:start position:0% +be +forceful try to put it + + align:start position:0% +forceful try to put it + + + align:start position:0% +forceful try to put it +[Music] + + align:start position:0% + + + + align:start position:0% + +together so 20 people at a + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% + + + + align:start position:0% + +big dishes like this that were like + + align:start position:0% +big dishes like this that were like + + + align:start position:0% +big dishes like this that were like +T you know what her cigaro was my mother + + align:start position:0% +T you know what her cigaro was my mother + + + align:start position:0% +T you know what her cigaro was my mother +she used SP a little white wine in her T + + align:start position:0% +she used SP a little white wine in her T + + + align:start position:0% +she used SP a little white wine in her T +it makes + + align:start position:0% +it makes + + + align:start position:0% +it makes +them right no I'm just saying do you do + + align:start position:0% +them right no I'm just saying do you do + + + align:start position:0% +them right no I'm just saying do you do +that yeah it makes it a little more + + align:start position:0% +that yeah it makes it a little more + + + align:start position:0% +that yeah it makes it a little more +tender just a tiny bit of white so by + + align:start position:0% +tender just a tiny bit of white so by + + + align:start position:0% +tender just a tiny bit of white so by +the way here we have extra + + align:start position:0% +the way here we have extra + + + align:start position:0% +the way here we have extra +Farina we will need to sprinkle the + + align:start position:0% +Farina we will need to sprinkle the + + + align:start position:0% +Farina we will need to sprinkle the +machine because um otherwise it tends to + + align:start position:0% +machine because um otherwise it tends to + + + align:start position:0% +machine because um otherwise it tends to +stick yeah and this is afterwards we + + align:start position:0% +stick yeah and this is afterwards we + + + align:start position:0% +stick yeah and this is afterwards we +will to make + + align:start position:0% + + + + align:start position:0% + +the oh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +mozarella you don't have the pasta + + align:start position:0% +mozarella you don't have the pasta + + + align:start position:0% +mozarella you don't have the pasta +machine what you can do you can + + align:start position:0% +machine what you can do you can + + + align:start position:0% +machine what you can do you can +use the P it's hard you can do it will + + align:start position:0% +use the P it's hard you can do it will + + + align:start position:0% +use the P it's hard you can do it will +that be too thick no that's fine go + + align:start position:0% +that be too thick no that's fine go + + + align:start position:0% +that be too thick no that's fine go +ahead it it'll it'll pull it through one + + align:start position:0% +ahead it it'll it'll pull it through one + + + align:start position:0% +ahead it it'll it'll pull it through one +person you know + + align:start position:0% + + + + align:start position:0% + +what turn it this + + align:start position:0% + + + + align:start position:0% + +way don't be afraid to go fast go go + + align:start position:0% +way don't be afraid to go fast go go + + + align:start position:0% +way don't be afraid to go fast go go +there you + + align:start position:0% +there you + + + align:start position:0% +there you +go it turn it into put them together yep + + align:start position:0% +go it turn it into put them together yep + + + align:start position:0% +go it turn it into put them together yep +just like that yep and this do it + + align:start position:0% + + + + align:start position:0% + +again see how it's already getting + + align:start position:0% +again see how it's already getting + + + align:start position:0% +again see how it's already getting +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +worked + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +that's what we're trying to do + + align:start position:0% +that's what we're trying to do + + + align:start position:0% +that's what we're trying to do +okay the other kind of fasta that we're + + align:start position:0% +okay the other kind of fasta that we're + + + align:start position:0% +okay the other kind of fasta that we're +[Music] + + align:start position:0% + + + + align:start position:0% + +making so you have to roll it in the + + align:start position:0% +making so you have to roll it in the + + + align:start position:0% +making so you have to roll it in the +same + + align:start position:0% +same + + + align:start position:0% +same +way roll roll like + + align:start position:0% +way roll roll like + + + align:start position:0% +way roll roll like +with okay + + align:start position:0% +with okay + + + align:start position:0% +with okay +so we skipped a step here which would be + + align:start position:0% +so we skipped a step here which would be + + + align:start position:0% +so we skipped a step here which would be +to let the pasta rest okay yeah okay + + align:start position:0% +to let the pasta rest okay yeah okay + + + align:start position:0% +to let the pasta rest okay yeah okay +it's easier if you let the pasta + + align:start position:0% +it's easier if you let the pasta + + + align:start position:0% +it's easier if you let the pasta +rest we just have to keep + + align:start position:0% +rest we just have to keep + + + align:start position:0% +rest we just have to keep +rolling you see this we have + + align:start position:0% + + + + align:start position:0% + +around okay so what you do you first + + align:start position:0% +around okay so what you do you first + + + align:start position:0% +around okay so what you do you first +like + + align:start position:0% +like + + + align:start position:0% +like +this okay and + + align:start position:0% +this okay and + + + align:start position:0% +this okay and +then you just try to squeeze it a little + + align:start position:0% +then you just try to squeeze it a little + + + align:start position:0% +then you just try to squeeze it a little +bit more and you you give the or the + + align:start position:0% +bit more and you you give the or the + + + align:start position:0% +bit more and you you give the or the +shape so you you don't want to flatten + + align:start position:0% +shape so you you don't want to flatten + + + align:start position:0% +shape so you you don't want to flatten +it you want to keep + + align:start position:0% +it you want to keep + + + align:start position:0% +it you want to keep +it right yeah but you see + + align:start position:0% +it right yeah but you see + + + align:start position:0% +it right yeah but you see +Okay okay something like + + align:start position:0% +Okay okay something like + + + align:start position:0% +Okay okay something like +this and then you put them to dry upside + + align:start position:0% +this and then you put them to dry upside + + + align:start position:0% +this and then you put them to dry upside +down uhhuh yes like that this is the + + align:start position:0% +down uhhuh yes like that this is the + + + align:start position:0% +down uhhuh yes like that this is the +trick is like + + align:start position:0% +trick is like + + + align:start position:0% +trick is like +this so you first do this movement well + + align:start position:0% +this so you first do this movement well + + + align:start position:0% +this so you first do this movement well +we going to let the pasta rest so it + + align:start position:0% +we going to let the pasta rest so it + + + align:start position:0% +we going to let the pasta rest so it +right here and then yes and then you + + align:start position:0% +right here and then yes and then you + + + align:start position:0% +right here and then yes and then you +just give it the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +shake there's + + align:start position:0% + + + + align:start position:0% + +idea okay did you put water on um oil I + + align:start position:0% +idea okay did you put water on um oil I + + + align:start position:0% +idea okay did you put water on um oil I +know I + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% +know + + + align:start position:0% +know +[Music] + + align:start position:0% + + + + align:start position:0% + +they about 5 mm wide if you were using + + align:start position:0% +they about 5 mm wide if you were using + + + align:start position:0% +they about 5 mm wide if you were using +something that's wider then you will + + align:start position:0% +something that's wider then you will + + + align:start position:0% +something that's wider then you will +make the same thing just + + align:start position:0% +make the same thing just + + + align:start position:0% +make the same thing just +wider so this pasta is a little too dry + + align:start position:0% +wider so this pasta is a little too dry + + + align:start position:0% +wider so this pasta is a little too dry +start rolling so ideally we want to use + + align:start position:0% +start rolling so ideally we want to use + + + align:start position:0% +start rolling so ideally we want to use +in this St a little try but + + align:start position:0% +in this St a little try but + + + align:start position:0% +in this St a little try but +not + + align:start position:0% +not + + + align:start position:0% +not +and you want to be sure that the stick + + align:start position:0% +and you want to be sure that the stick + + + align:start position:0% +and you want to be sure that the stick +together so you always sprink with a + + align:start position:0% +together so you always sprink with a + + + align:start position:0% +together so you always sprink with a +little bit Sprinkles with a little + + align:start position:0% + + + + align:start position:0% + +flow that's not + + align:start position:0% +flow that's not + + + align:start position:0% +flow that's not +Italian Italy is becoming an + + align:start position:0% +Italian Italy is becoming an + + + align:start position:0% +Italian Italy is becoming an +Italian yeah that + + align:start position:0% + + + + align:start position:0% + +waser I really like the pizza after the + + align:start position:0% +waser I really like the pizza after the + + + align:start position:0% +waser I really like the pizza after the +soito we cooked the mushrooms with then + + align:start position:0% +soito we cooked the mushrooms with then + + + align:start position:0% +soito we cooked the mushrooms with then +we added heavy cream + + align:start position:0% +we added heavy cream + + + align:start position:0% +we added heavy cream +Cina and finally at the very end Prolo + + align:start position:0% +Cina and finally at the very end Prolo + + + align:start position:0% +Cina and finally at the very end Prolo +we didn't want the Prolo to cook so we + + align:start position:0% +we didn't want the Prolo to cook so we + + + align:start position:0% +we didn't want the Prolo to cook so we +add it once we remove the pot from the + + align:start position:0% +add it once we remove the pot from the + + + align:start position:0% +add it once we remove the pot from the +stove this is + + align:start position:0% +stove this is + + + align:start position:0% +stove this is +ready while + + align:start position:0% + + + + align:start position:0% + +here we have a mix + + align:start position:0% +here we have a mix + + + align:start position:0% +here we have a mix +of + + align:start position:0% + + + + align:start position:0% + +moella Basil here we cut it we can also + + align:start position:0% +moella Basil here we cut it we can also + + + align:start position:0% +moella Basil here we cut it we can also +leave basil the leaves as a whole that's + + align:start position:0% +leave basil the leaves as a whole that's + + + align:start position:0% +leave basil the leaves as a whole that's +absolutely fine and and then we also + + align:start position:0% +absolutely fine and and then we also + + + align:start position:0% +absolutely fine and and then we also +grated a little bit of peino ROM then we + + align:start position:0% +grated a little bit of peino ROM then we + + + align:start position:0% +grated a little bit of peino ROM then we +added salt extra virgin olive oil and we + + align:start position:0% +added salt extra virgin olive oil and we + + + align:start position:0% +added salt extra virgin olive oil and we +just let it rest and soak when the pasta + + align:start position:0% +just let it rest and soak when the pasta + + + align:start position:0% +just let it rest and soak when the pasta +ready we we will just mix + + align:start position:0% + + + + align:start position:0% + +and with like the scrap pieces we do + + align:start position:0% +and with like the scrap pieces we do + + + align:start position:0% +and with like the scrap pieces we do +what we call Mal Mal Mal + + align:start position:0% +what we call Mal Mal Mal + + + align:start position:0% +what we call Mal Mal Mal +malti so what does mal talati badly cut + + align:start position:0% +malti so what does mal talati badly cut + + + align:start position:0% +malti so what does mal talati badly cut +badly cut yeah badly cut but it's the + + align:start position:0% +badly cut yeah badly cut but it's the + + + align:start position:0% +badly cut yeah badly cut but it's the +kind of pasta you can even buy the + + align:start position:0% + + + + align:start position:0% + +supermarket yeah they're just cut so + + align:start position:0% +supermarket yeah they're just cut so + + + align:start position:0% +supermarket yeah they're just cut so +especially when you use the rolling + + align:start position:0% +especially when you use the rolling + + + align:start position:0% +especially when you use the rolling +thing you might have a lot of pieces + + align:start position:0% +thing you might have a lot of pieces + + + align:start position:0% +thing you might have a lot of pieces +that not really fit in in your shape and + + align:start position:0% +that not really fit in in your shape and + + + align:start position:0% +that not really fit in in your shape and +then that's perfect you just make my + + align:start position:0% +then that's perfect you just make my + + + align:start position:0% +then that's perfect you just make my +malasi and if you make too much pasta + + align:start position:0% +malasi and if you make too much pasta + + + align:start position:0% +malasi and if you make too much pasta +you can even free + + align:start position:0% +you can even free + + + align:start position:0% +you can even free +I'm going to cook for about 10 minutes + + align:start position:0% +I'm going to cook for about 10 minutes + + + align:start position:0% +I'm going to cook for about 10 minutes +then we drain them not super well we + + align:start position:0% +then we drain them not super well we + + + align:start position:0% +then we drain them not super well we +want to keep a little bit of the water + + align:start position:0% +want to keep a little bit of the water + + + align:start position:0% +want to keep a little bit of the water +and then once we drain them we put them + + align:start position:0% +and then once we drain them we put them + + + align:start position:0% +and then once we drain them we put them +in our + + align:start position:0% +in our + + + align:start position:0% +in our +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +C do we have any other o + + align:start position:0% +C do we have any other o + + + align:start position:0% +C do we have any other o +we have this one just this one is + + align:start position:0% + + + + align:start position:0% + +okay okay these Lally just need a few + + align:start position:0% + + + + align:start position:0% + +minut extra olive oil salt and also some + + align:start position:0% +minut extra olive oil salt and also some + + + align:start position:0% +minut extra olive oil salt and also some +extrao we + + align:start position:0% +extrao we + + + align:start position:0% +extrao we +[Music] + + align:start position:0% + + + + align:start position:0% + +already + + align:start position:0% +already + + + align:start position:0% +already +the other + + align:start position:0% + + + + align:start position:0% + +one I + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +made \ No newline at end of file diff --git a/2y4tCiWbVRI.txt b/2y4tCiWbVRI.txt new file mode 100644 index 0000000000000000000000000000000000000000..b24c0eaf8661aba9d0ccdf0a24672ac64cb7f1ba --- /dev/null +++ b/2y4tCiWbVRI.txt @@ -0,0 +1,299 @@ +align:start position:0% + +hi my name is Joel Lewis at the time of + + align:start position:0% +hi my name is Joel Lewis at the time of + + + align:start position:0% +hi my name is Joel Lewis at the time of +this filming in 2010 I'm a graduate + + align:start position:0% +this filming in 2010 I'm a graduate + + + align:start position:0% +this filming in 2010 I'm a graduate +student in the math department at MIT + + align:start position:0% +student in the math department at MIT + + + align:start position:0% +student in the math department at MIT +and I'm also a TA for ocw scholar 1801 + + align:start position:0% +and I'm also a TA for ocw scholar 1801 + + + align:start position:0% +and I'm also a TA for ocw scholar 1801 +and 1802 hi I'm Christine Brer I'm a + + align:start position:0% +and 1802 hi I'm Christine Brer I'm a + + + align:start position:0% +and 1802 hi I'm Christine Brer I'm a +more instructor here at MIT and for ocw + + align:start position:0% +more instructor here at MIT and for ocw + + + align:start position:0% +more instructor here at MIT and for ocw +scholar I'll be a teaching assistant for + + align:start position:0% +scholar I'll be a teaching assistant for + + + align:start position:0% +scholar I'll be a teaching assistant for +1801 and for + + align:start position:0% +1801 and for + + + align:start position:0% +1801 and for +1802 my name is David Jordan and uh I'm + + align:start position:0% +1802 my name is David Jordan and uh I'm + + + align:start position:0% +1802 my name is David Jordan and uh I'm +a graduate student here at MIT and I'm a + + align:start position:0% +a graduate student here at MIT and I'm a + + + align:start position:0% +a graduate student here at MIT and I'm a +TA for open courseware scholar + + align:start position:0% +TA for open courseware scholar + + + align:start position:0% +TA for open courseware scholar +1802 so I thought I would say a little + + align:start position:0% +1802 so I thought I would say a little + + + align:start position:0% +1802 so I thought I would say a little +bit about uh about what we do with + + align:start position:0% +bit about uh about what we do with + + + align:start position:0% +bit about uh about what we do with +recitations here at MIT so the purpose + + align:start position:0% +recitations here at MIT so the purpose + + + align:start position:0% +recitations here at MIT so the purpose +of the recitations is uh for you to + + align:start position:0% +of the recitations is uh for you to + + + align:start position:0% +of the recitations is uh for you to +apply what you've learned in lecture + + align:start position:0% +apply what you've learned in lecture + + + align:start position:0% +apply what you've learned in lecture +towards solving uh specific concrete + + align:start position:0% +towards solving uh specific concrete + + + align:start position:0% +towards solving uh specific concrete +problems and then uh for you to compare + + align:start position:0% +problems and then uh for you to compare + + + align:start position:0% +problems and then uh for you to compare +your solutions to those problems with + + align:start position:0% +your solutions to those problems with + + + align:start position:0% +your solutions to those problems with +those of your ta the purpose of the + + align:start position:0% +those of your ta the purpose of the + + + align:start position:0% +those of your ta the purpose of the +recitations on ocw scholar is really the + + align:start position:0% +recitations on ocw scholar is really the + + + align:start position:0% +recitations on ocw scholar is really the +same purpose that David described for + + align:start position:0% +same purpose that David described for + + + align:start position:0% +same purpose that David described for +recitations here at MIT what we want you + + align:start position:0% +recitations here at MIT what we want you + + + align:start position:0% +recitations here at MIT what we want you +to do is have an opportunity to work + + align:start position:0% +to do is have an opportunity to work + + + align:start position:0% +to do is have an opportunity to work +varying levels of problems and then see + + align:start position:0% +varying levels of problems and then see + + + align:start position:0% +varying levels of problems and then see +us give detailed solutions to those + + align:start position:0% +us give detailed solutions to those + + + align:start position:0% +us give detailed solutions to those +problems so that you can see how we + + align:start position:0% +problems so that you can see how we + + + align:start position:0% +problems so that you can see how we +think about mathematics almost all of + + align:start position:0% +think about mathematics almost all of + + + align:start position:0% +think about mathematics almost all of +our videos have a natural moment where + + align:start position:0% +our videos have a natural moment where + + + align:start position:0% +our videos have a natural moment where +you can pause after the problem's been + + align:start position:0% +you can pause after the problem's been + + + align:start position:0% +you can pause after the problem's been +stated and we really strongly suggest + + align:start position:0% +stated and we really strongly suggest + + + align:start position:0% +stated and we really strongly suggest +you work out the problem on a piece of + + align:start position:0% +you work out the problem on a piece of + + + align:start position:0% +you work out the problem on a piece of +paper before going back to the video and + + align:start position:0% +paper before going back to the video and + + + align:start position:0% +paper before going back to the video and +and seeing our Solutions this will help + + align:start position:0% +and seeing our Solutions this will help + + + align:start position:0% +and seeing our Solutions this will help +you do mathematics rather than be able + + align:start position:0% +you do mathematics rather than be able + + + align:start position:0% +you do mathematics rather than be able +just to see mathematics hope you enjoy + + align:start position:0% +just to see mathematics hope you enjoy + + + align:start position:0% +just to see mathematics hope you enjoy +the + + align:start position:0% + + + + align:start position:0% + +course \ No newline at end of file diff --git a/3Cij8HYKXOk.txt b/3Cij8HYKXOk.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ee778d5e9582650863552096a7dff9542148f80 --- /dev/null +++ b/3Cij8HYKXOk.txt @@ -0,0 +1,1523 @@ +align:start position:0% + +I want to just elucidate a little more + + align:start position:0% +I want to just elucidate a little more + + + align:start position:0% +I want to just elucidate a little more +what are the eigenstates here so with in + + align:start position:0% +what are the eigenstates here so with in + + + align:start position:0% +what are the eigenstates here so with in +with angular momentum we measure L + + align:start position:0% +with angular momentum we measure L + + + align:start position:0% +with angular momentum we measure L +squared and we measure LZ so with spin + + align:start position:0% +squared and we measure LZ so with spin + + + align:start position:0% +squared and we measure LZ so with spin +will measure spin squared and s Z and SZ + + align:start position:0% +will measure spin squared and s Z and SZ + + + align:start position:0% +will measure spin squared and s Z and SZ +is interesting would be spin or angular + + align:start position:0% +is interesting would be spin or angular + + + align:start position:0% +is interesting would be spin or angular +momentum in the Z direction so let's + + align:start position:0% +momentum in the Z direction so let's + + + align:start position:0% +momentum in the Z direction so let's +look at that as Z this is the operator + + align:start position:0% +look at that as Z this is the operator + + + align:start position:0% +look at that as Z this is the operator +the measurable it's this time nothing + + align:start position:0% +the measurable it's this time nothing + + + align:start position:0% +the measurable it's this time nothing +else than a simple matrix is not a + + align:start position:0% +else than a simple matrix is not a + + + align:start position:0% +else than a simple matrix is not a +momentum operator is not an angular + + align:start position:0% +momentum operator is not an angular + + + align:start position:0% +momentum operator is not an angular +momentum operator with derivative it's + + align:start position:0% +momentum operator with derivative it's + + + align:start position:0% +momentum operator with derivative it's +an angular momentum operator but it sort + + align:start position:0% +an angular momentum operator but it sort + + + align:start position:0% +an angular momentum operator but it sort +of seems to have come out of thin air + + align:start position:0% +of seems to have come out of thin air + + + align:start position:0% +of seems to have come out of thin air +but it hasn't so here it is oh and it's + + align:start position:0% +but it hasn't so here it is oh and it's + + + align:start position:0% +but it hasn't so here it is oh and it's +diagonal already so the eigenstates are + + align:start position:0% +diagonal already so the eigenstates are + + + align:start position:0% +diagonal already so the eigenstates are +easily found I have one state and I want + + align:start position:0% +easily found I have one state and I want + + + align:start position:0% +easily found I have one state and I want +to call it I'll call it 1 0 it's one + + align:start position:0% +to call it I'll call it 1 0 it's one + + + align:start position:0% +to call it I'll call it 1 0 it's one +state and that an eigenstate of it we'll + + align:start position:0% +state and that an eigenstate of it we'll + + + align:start position:0% +state and that an eigenstate of it we'll +call it for simplicity up we'll see why + + align:start position:0% +call it for simplicity up we'll see why + + + align:start position:0% +call it for simplicity up we'll see why +s Z acting on up is equal to H bar over + + align:start position:0% +s Z acting on up is equal to H bar over + + + align:start position:0% +s Z acting on up is equal to H bar over +2 1 0 0 minus 1 acting on 1 0 that's H + + align:start position:0% +2 1 0 0 minus 1 acting on 1 0 that's H + + + align:start position:0% +2 1 0 0 minus 1 acting on 1 0 that's H +bar over 2 and the matrix if you 1 0 so + + align:start position:0% +bar over 2 and the matrix if you 1 0 so + + + align:start position:0% +bar over 2 and the matrix if you 1 0 so +it is an eigenstate because its h-bar + + align:start position:0% +it is an eigenstate because its h-bar + + + align:start position:0% +it is an eigenstate because its h-bar +over 2 up the 1 0 state again so this + + align:start position:0% +over 2 up the 1 0 state again so this + + + align:start position:0% +over 2 up the 1 0 state again so this +thing we call it up because has up + + align:start position:0% +thing we call it up because has up + + + align:start position:0% +thing we call it up because has up +component of the Z angular momentum so + + align:start position:0% +component of the Z angular momentum so + + + align:start position:0% +component of the Z angular momentum so +it's a spin up state + + align:start position:0% +it's a spin up state + + + align:start position:0% +it's a spin up state +what is the spin down state would be + + align:start position:0% +what is the spin down state would be + + + align:start position:0% +what is the spin down state would be +zero one is the spin down and SZ on the + + align:start position:0% +zero one is the spin down and SZ on the + + + align:start position:0% +zero one is the spin down and SZ on the +spin down it's also an eigenstate this + + align:start position:0% +spin down it's also an eigenstate this + + + align:start position:0% +spin down it's also an eigenstate this +time with minus h-bar over two spin down + + align:start position:0% +time with minus h-bar over two spin down + + + align:start position:0% +time with minus h-bar over two spin down +and we call it spin 1/2 because of this + + align:start position:0% +and we call it spin 1/2 because of this + + + align:start position:0% +and we call it spin 1/2 because of this +1/2 and you'd say no you you just put + + align:start position:0% +1/2 and you'd say no you you just put + + + align:start position:0% +1/2 and you'd say no you you just put +that concept because you want it they're + + align:start position:0% +that concept because you want it they're + + + align:start position:0% +that concept because you want it they're +not true if I would have put a different + + align:start position:0% +not true if I would have put a different + + + align:start position:0% +not true if I would have put a different +constant here in defining this I would + + align:start position:0% +constant here in defining this I would + + + align:start position:0% +constant here in defining this I would +not have gotten this without any + + align:start position:0% +not have gotten this without any + + + align:start position:0% +not have gotten this without any +constant that it's how angular momentum + + align:start position:0% +constant that it's how angular momentum + + + align:start position:0% +constant that it's how angular momentum +works so if I use 2 by 2 matrices I'm + + align:start position:0% +works so if I use 2 by 2 matrices I'm + + + align:start position:0% +works so if I use 2 by 2 matrices I'm +forced to get spin 1/2 you cannot get + + align:start position:0% +forced to get spin 1/2 you cannot get + + + align:start position:0% +forced to get spin 1/2 you cannot get +anything else the one half of the spin + + align:start position:0% +anything else the one half of the spin + + + align:start position:0% +anything else the one half of the spin +is already there the component of + + align:start position:0% +is already there the component of + + + align:start position:0% +is already there the component of +angular momentum is h-bar over 2 if you + + align:start position:0% +angular momentum is h-bar over 2 if you + + + align:start position:0% +angular momentum is h-bar over 2 if you +have a photon it has spin 1 the + + align:start position:0% +have a photon it has spin 1 the + + + align:start position:0% +have a photon it has spin 1 the +components of Angermann this plus h or + + align:start position:0% +components of Angermann this plus h or + + + align:start position:0% +components of Angermann this plus h or +minus h if you have the two circularly + + align:start position:0% +minus h if you have the two circularly + + + align:start position:0% +minus h if you have the two circularly +polarized waves so this is actually + + align:start position:0% +polarized waves so this is actually + + + align:start position:0% +polarized waves so this is actually +interesting but it it bakes for another + + align:start position:0% +interesting but it it bakes for another + + + align:start position:0% +interesting but it it bakes for another +question because we have a good + + align:start position:0% +question because we have a good + + + align:start position:0% +question because we have a good +intuition and this is spin up along the + + align:start position:0% +intuition and this is spin up along the + + + align:start position:0% +intuition and this is spin up along the +Z direction because it has a Z component + + align:start position:0% +Z direction because it has a Z component + + + align:start position:0% +Z direction because it has a Z component +I can value H over 2 so the last + + align:start position:0% +I can value H over 2 so the last + + + align:start position:0% +I can value H over 2 so the last +question I want to ask is how do I get a + + align:start position:0% +question I want to ask is how do I get a + + + align:start position:0% +question I want to ask is how do I get a +spin state to point in the X direction + + align:start position:0% +spin state to point in the X direction + + + align:start position:0% +spin state to point in the X direction +or in the Y direction you see the + + align:start position:0% +or in the Y direction you see the + + + align:start position:0% +or in the Y direction you see the +interpretation of this spin state is + + align:start position:0% +interpretation of this spin state is + + + align:start position:0% +interpretation of this spin state is +that it at R it it's a spin State + + align:start position:0% +that it at R it it's a spin State + + + align:start position:0% +that it at R it it's a spin State +that has the spin up in the Z direction + + align:start position:0% +that has the spin up in the Z direction + + + align:start position:0% +that has the spin up in the Z direction +because that's what you can measure or + + align:start position:0% +because that's what you can measure or + + + align:start position:0% +because that's what you can measure or +spin down in the down direction of SZ + + align:start position:0% +spin down in the down direction of SZ + + + align:start position:0% +spin down in the down direction of SZ +can I get spin states that point along + + align:start position:0% +can I get spin states that point along + + + align:start position:0% +can I get spin states that point along +the X direction or Y direction and and + + align:start position:0% +the X direction or Y direction and and + + + align:start position:0% +the X direction or Y direction and and +here is where the problem seems to hit + + align:start position:0% +here is where the problem seems to hit + + + align:start position:0% +here is where the problem seems to hit +you and you see I'm in trouble I have + + align:start position:0% +you and you see I'm in trouble I have + + + align:start position:0% +you and you see I'm in trouble I have +this state spin up it's been down along + + align:start position:0% +this state spin up it's been down along + + + align:start position:0% +this state spin up it's been down along +Z and it's a two dimension vector space + + align:start position:0% +Z and it's a two dimension vector space + + + align:start position:0% +Z and it's a two dimension vector space +because two by two matrices and SX sy is + + align:start position:0% +because two by two matrices and SX sy is + + + align:start position:0% +because two by two matrices and SX sy is +these three dimensions how am I going to + + align:start position:0% +these three dimensions how am I going to + + + align:start position:0% +these three dimensions how am I going to +get three dimensions out of two + + align:start position:0% +get three dimensions out of two + + + align:start position:0% +get three dimensions out of two +dimensions how you just have spin States + + align:start position:0% +dimensions how you just have spin States + + + align:start position:0% +dimensions how you just have spin States +along the up and down now + + align:start position:0% +along the up and down now + + + align:start position:0% +along the up and down now +they spin up and spin down moreover are + + align:start position:0% +they spin up and spin down moreover are + + + align:start position:0% +they spin up and spin down moreover are +orthogonal states this two are + + align:start position:0% +orthogonal states this two are + + + align:start position:0% +orthogonal states this two are +orthogonal stage you see to do the inner + + align:start position:0% +orthogonal stage you see to do the inner + + + align:start position:0% +orthogonal stage you see to do the inner +product transpose this you get this and + + align:start position:0% +product transpose this you get this and + + + align:start position:0% +product transpose this you get this and +times that so they are orthogonal and as + + align:start position:0% +times that so they are orthogonal and as + + + align:start position:0% +times that so they are orthogonal and as +you imagine this vector plus this vector + + align:start position:0% +you imagine this vector plus this vector + + + align:start position:0% +you imagine this vector plus this vector +is a full basis for the vector space + + align:start position:0% +is a full basis for the vector space + + + align:start position:0% +is a full basis for the vector space +because the vector space is a B and now + + align:start position:0% +because the vector space is a B and now + + + align:start position:0% +because the vector space is a B and now +you see that this is a comes up plus B + + align:start position:0% +you see that this is a comes up plus B + + + align:start position:0% +you see that this is a comes up plus B +comes down so anything is a + + align:start position:0% +comes down so anything is a + + + align:start position:0% +comes down so anything is a +superposition of up and down so how do I + + align:start position:0% +superposition of up and down so how do I + + + align:start position:0% +superposition of up and down so how do I +ever get something that points along X + + align:start position:0% +ever get something that points along X + + + align:start position:0% +ever get something that points along X +or something that points along Y well + + align:start position:0% +or something that points along Y well + + + align:start position:0% +or something that points along Y well +let's let's try to see that well + + align:start position:0% +let's let's try to see that well + + + align:start position:0% +let's let's try to see that well +consider SX you have an SX operator + + align:start position:0% +consider SX you have an SX operator + + + align:start position:0% +consider SX you have an SX operator +which is h-bar over 2 0 1 1 0 and you + + align:start position:0% +which is h-bar over 2 0 1 1 0 and you + + + align:start position:0% +which is h-bar over 2 0 1 1 0 and you +know lacking you can try to diagonalize + + align:start position:0% +know lacking you can try to diagonalize + + + align:start position:0% +know lacking you can try to diagonalize +this but it's kind of more entertaining + + align:start position:0% +this but it's kind of more entertaining + + + align:start position:0% +this but it's kind of more entertaining +to imagine other things + + align:start position:0% +to imagine other things + + + align:start position:0% +to imagine other things +to say look I've I've gotten this vector + + align:start position:0% +to say look I've I've gotten this vector + + + align:start position:0% +to say look I've I've gotten this vector +1 0 which is up and 0 1 which is down + + align:start position:0% +1 0 which is up and 0 1 which is down + + + align:start position:0% +1 0 which is up and 0 1 which is down +I can try maybe a vector that has the up + + align:start position:0% +I can try maybe a vector that has the up + + + align:start position:0% +I can try maybe a vector that has the up +and the down maybe they happen the down + + align:start position:0% +and the down maybe they happen the down + + + align:start position:0% +and the down maybe they happen the down +is a vector that points nowhere who + + align:start position:0% +is a vector that points nowhere who + + + align:start position:0% +is a vector that points nowhere who +knows whatever if I want to normalize it + + align:start position:0% +knows whatever if I want to normalize it + + + align:start position:0% +knows whatever if I want to normalize it +I have to put a 1 over square root of 2 + + align:start position:0% +I have to put a 1 over square root of 2 + + + align:start position:0% +I have to put a 1 over square root of 2 +and now I know it's 1 over square root + + align:start position:0% +and now I know it's 1 over square root + + + align:start position:0% +and now I know it's 1 over square root +of 2 up plus down that's what this + + align:start position:0% +of 2 up plus down that's what this + + + align:start position:0% +of 2 up plus down that's what this +vector is but let's see what SX does on + + align:start position:0% +vector is but let's see what SX does on + + + align:start position:0% +vector is but let's see what SX does on +it SX is h-bar over so on 1 over square + + align:start position:0% +it SX is h-bar over so on 1 over square + + + align:start position:0% +it SX is h-bar over so on 1 over square +root of 2 1 1 is h-bar over 2 1 over + + align:start position:0% +root of 2 1 1 is h-bar over 2 1 over + + + align:start position:0% +root of 2 1 1 is h-bar over 2 1 over +square root of 2 0 1 1 0 on 1 1 h-bar + + align:start position:0% +square root of 2 0 1 1 0 on 1 1 h-bar + + + align:start position:0% +square root of 2 0 1 1 0 on 1 1 h-bar +over 2 1 over square root of 2 and let's + + align:start position:0% +over 2 1 over square root of 2 and let's + + + align:start position:0% +over 2 1 over square root of 2 and let's +see that gives me 1 it gives me another + + align:start position:0% +see that gives me 1 it gives me another + + + align:start position:0% +see that gives me 1 it gives me another +one up I got the same vector I started + + align:start position:0% +one up I got the same vector I started + + + align:start position:0% +one up I got the same vector I started +with it is an eigenstate so this thing + + align:start position:0% +with it is an eigenstate so this thing + + + align:start position:0% +with it is an eigenstate so this thing +this + and down superimpose is an + + align:start position:0% +this + and down superimpose is an + + + align:start position:0% +this + and down superimpose is an +eigenstate of SX so this is actually a + + align:start position:0% +eigenstate of SX so this is actually a + + + align:start position:0% +eigenstate of SX so this is actually a +spin that points up but in the X + + align:start position:0% +spin that points up but in the X + + + align:start position:0% +spin that points up but in the X +direction whenever we don't put anything + + align:start position:0% +direction whenever we don't put anything + + + align:start position:0% +direction whenever we don't put anything +we're talking about Z but this is the + + align:start position:0% +we're talking about Z but this is the + + + align:start position:0% +we're talking about Z but this is the +spin up in the X direction and it + + align:start position:0% +spin up in the X direction and it + + + align:start position:0% +spin up in the X direction and it +appeared as a sum of a spin up and spin + + align:start position:0% +appeared as a sum of a spin up and spin + + + align:start position:0% +appeared as a sum of a spin up and spin +down in the 1 in the Z direction it may + + align:start position:0% +down in the 1 in the Z direction it may + + + align:start position:0% +down in the 1 in the Z direction it may +not be too surprising for you to imagine + + align:start position:0% +not be too surprising for you to imagine + + + align:start position:0% +not be too surprising for you to imagine +that if you put 1 over square root of 2 + + align:start position:0% +that if you put 1 over square root of 2 + + + align:start position:0% +that if you put 1 over square root of 2 +1 minus 1 that vector is orthogonal to + + align:start position:0% +1 minus 1 that vector is orthogonal to + + + align:start position:0% +1 minus 1 that vector is orthogonal to +this one yes you do the transpose and + + align:start position:0% +this one yes you do the transpose and + + + align:start position:0% +this one yes you do the transpose and +this one is orthogonal so this is 1 over + + align:start position:0% +this one is orthogonal so this is 1 over + + + align:start position:0% +this one is orthogonal so this is 1 over +square root of 2 up + + align:start position:0% +square root of 2 up + + + align:start position:0% +square root of 2 up +- down that is the down spin along X so + + align:start position:0% +- down that is the down spin along X so + + + align:start position:0% +- down that is the down spin along X so +the up and down spins along X come out + + align:start position:0% +the up and down spins along X come out + + + align:start position:0% +the up and down spins along X come out +like that we form the linear + + align:start position:0% +like that we form the linear + + + align:start position:0% +like that we form the linear +combinations so finally you would say + + align:start position:0% +combinations so finally you would say + + + align:start position:0% +combinations so finally you would say +well I'm going to push my luck and try + + align:start position:0% +well I'm going to push my luck and try + + + align:start position:0% +well I'm going to push my luck and try +to get spins along the Y direction but I + + align:start position:0% +to get spins along the Y direction but I + + + align:start position:0% +to get spins along the Y direction but I +now form those linear combinations what + + align:start position:0% +now form those linear combinations what + + + align:start position:0% +now form those linear combinations what +else could I do these linear + + align:start position:0% +else could I do these linear + + + align:start position:0% +else could I do these linear +combinations are there and I'm kind of + + align:start position:0% +combinations are there and I'm kind of + + + align:start position:0% +combinations are there and I'm kind of +I've got already two things and you say + + align:start position:0% +I've got already two things and you say + + + align:start position:0% +I've got already two things and you say +well that's fair you're a + + align:start position:0% +well that's fair you're a + + + align:start position:0% +well that's fair you're a +two-dimensional vector space so you're + + align:start position:0% +two-dimensional vector space so you're + + + align:start position:0% +two-dimensional vector space so you're +getting two things spin States along X + + align:start position:0% +getting two things spin States along X + + + align:start position:0% +getting two things spin States along X +and spin States along of Z but actually + + align:start position:0% +and spin States along of Z but actually + + + align:start position:0% +and spin States along of Z but actually +we didn't run out of things to try we + + align:start position:0% +we didn't run out of things to try we + + + align:start position:0% +we didn't run out of things to try we +could try a state of the form 1 over + + align:start position:0% +could try a state of the form 1 over + + + align:start position:0% +could try a state of the form 1 over +square root of 2 something like this we + + align:start position:0% +square root of 2 something like this we + + + align:start position:0% +square root of 2 something like this we +could try the state up and then you know + + align:start position:0% +could try the state up and then you know + + + align:start position:0% +could try the state up and then you know +we've put a plus but now we could put a + + align:start position:0% +we've put a plus but now we could put a + + + align:start position:0% +we've put a plus but now we could put a +plus I staked down so this would be a + + align:start position:0% +plus I staked down so this would be a + + + align:start position:0% +plus I staked down so this would be a +state of a farm 1 I and what does it do + + align:start position:0% +state of a farm 1 I and what does it do + + + align:start position:0% +state of a farm 1 I and what does it do +well let's see for what it does with sy + + align:start position:0% + + + + align:start position:0% + +1 I and the sy matrix is h-bar over 2 + + align:start position:0% +1 I and the sy matrix is h-bar over 2 + + + align:start position:0% +1 I and the sy matrix is h-bar over 2 +minus I I 0 0 1 I + + align:start position:0% + + + + align:start position:0% + +and there's one over square root of two + + align:start position:0% +and there's one over square root of two + + + align:start position:0% +and there's one over square root of two +so it's one over square root of 2 or H + + align:start position:0% +so it's one over square root of 2 or H + + + align:start position:0% +so it's one over square root of 2 or H +bar over 2 1 over square root of 2 and + + align:start position:0% +bar over 2 1 over square root of 2 and + + + align:start position:0% +bar over 2 1 over square root of 2 and +let's see what we get minus I times I is + + align:start position:0% +let's see what we get minus I times I is + + + align:start position:0% +let's see what we get minus I times I is +1 and the second one is I we get the + + align:start position:0% +1 and the second one is I we get the + + + align:start position:0% +1 and the second one is I we get the +same state yes it is an eigenstate so + + align:start position:0% +same state yes it is an eigenstate so + + + align:start position:0% +same state yes it is an eigenstate so +with a plus I here this is the spin up + + align:start position:0% +with a plus I here this is the spin up + + + align:start position:0% +with a plus I here this is the spin up +along the Y direction and of the spin + + align:start position:0% +along the Y direction and of the spin + + + align:start position:0% +along the Y direction and of the spin +down along the Y direction would be up - + + align:start position:0% +down along the Y direction would be up - + + + align:start position:0% +down along the Y direction would be up - +I down this is orthogonal to that vector + + align:start position:0% +I down this is orthogonal to that vector + + + align:start position:0% +I down this is orthogonal to that vector +it's 1 minus I and it's the spin down in + + align:start position:0% +it's 1 minus I and it's the spin down in + + + align:start position:0% +it's 1 minus I and it's the spin down in +the Y direction you can calculate the + + align:start position:0% +the Y direction you can calculate the + + + align:start position:0% +the Y direction you can calculate the +eigenvalue it's minus h-bar over 2 and + + align:start position:0% +eigenvalue it's minus h-bar over 2 and + + + align:start position:0% +eigenvalue it's minus h-bar over 2 and +it's pointing down so your complex + + align:start position:0% +it's pointing down so your complex + + + align:start position:0% +it's pointing down so your complex +numbers play the crucial role if you + + align:start position:0% +numbers play the crucial role if you + + + align:start position:0% +numbers play the crucial role if you +didn't have complex numbers there was no + + align:start position:0% +didn't have complex numbers there was no + + + align:start position:0% +didn't have complex numbers there was no +way you could ever get a state that this + + align:start position:0% +way you could ever get a state that this + + + align:start position:0% +way you could ever get a state that this +pointing in all possible directions and + + align:start position:0% +pointing in all possible directions and + + + align:start position:0% +pointing in all possible directions and +you also see finally that this thing has + + align:start position:0% +you also see finally that this thing has + + + align:start position:0% +you also see finally that this thing has +nothing to do with your usual wave + + align:start position:0% +nothing to do with your usual wave + + + align:start position:0% +nothing to do with your usual wave +functions functions of X theta fine no + + align:start position:0% +functions functions of X theta fine no + + + align:start position:0% +functions functions of X theta fine no +spin is an additional world with two + + align:start position:0% +spin is an additional world with two + + + align:start position:0% +spin is an additional world with two +degrees of freedom an extra thing it + + align:start position:0% +degrees of freedom an extra thing it + + + align:start position:0% +degrees of freedom an extra thing it +doesn't have a simple way for so the + + align:start position:0% +doesn't have a simple way for so the + + + align:start position:0% +doesn't have a simple way for so the +spin wave functions are these two column + + align:start position:0% +spin wave functions are these two column + + + align:start position:0% +spin wave functions are these two column +vectors but there is angular momentum in + + align:start position:0% +vectors but there is angular momentum in + + + align:start position:0% +vectors but there is angular momentum in +there as you discovered here there is a + + align:start position:0% +there as you discovered here there is a + + + align:start position:0% +there as you discovered here there is a +commutation relations of angular + + align:start position:0% +commutation relations of angular + + + align:start position:0% +commutation relations of angular +momentum the units of angular momentum + + align:start position:0% +momentum the units of angular momentum + + + align:start position:0% +momentum the units of angular momentum +the eigenvalues of angular momentum and + + align:start position:0% +the eigenvalues of angular momentum and + + + align:start position:0% +the eigenvalues of angular momentum and +this great thing is that the such a nice + + align:start position:0% +this great thing is that the such a nice + + + align:start position:0% +this great thing is that the such a nice +simple piece of + + align:start position:0% +simple piece of + + + align:start position:0% +simple piece of +mathematics has an enormous utility it + + align:start position:0% +mathematics has an enormous utility it + + + align:start position:0% +mathematics has an enormous utility it +describes the spins of particles so this + + align:start position:0% +describes the spins of particles so this + + + align:start position:0% +describes the spins of particles so this +it's an introduction in some sense to + + align:start position:0% +it's an introduction in some sense to + + + align:start position:0% +it's an introduction in some sense to +what 805 is all about spin systems are + + align:start position:0% +what 805 is all about spin systems are + + + align:start position:0% +what 805 is all about spin systems are +extremely important practical + + align:start position:0% +extremely important practical + + + align:start position:0% +extremely important practical +applications these things because they + + align:start position:0% +applications these things because they + + + align:start position:0% +applications these things because they +have basically two states are + + align:start position:0% +have basically two states are + + + align:start position:0% +have basically two states are +essentially qubit for a quantum computer + + align:start position:0% +essentially qubit for a quantum computer + + + align:start position:0% +essentially qubit for a quantum computer +within these systems we understand in + + align:start position:0% +within these systems we understand in + + + align:start position:0% +within these systems we understand in +the simplest way entanglement Bell + + align:start position:0% +the simplest way entanglement Bell + + + align:start position:0% +the simplest way entanglement Bell +inequalities superposition all kinds of + + align:start position:0% +inequalities superposition all kinds of + + + align:start position:0% +inequalities superposition all kinds of +very very interesting phenomena so it's + + align:start position:0% +very very interesting phenomena so it's + + + align:start position:0% +very very interesting phenomena so it's +a good place to stop \ No newline at end of file diff --git a/3GHk5vlb26o.txt b/3GHk5vlb26o.txt new file mode 100644 index 0000000000000000000000000000000000000000..bdd6b935fd734e1a9ad05a65b4fe30bd3f7b8e04 --- /dev/null +++ b/3GHk5vlb26o.txt @@ -0,0 +1,1611 @@ +align:start position:0% + +hello + + align:start position:0% +hello + + + align:start position:0% +hello +so in the last video we looked at ranges + + align:start position:0% +so in the last video we looked at ranges + + + align:start position:0% +so in the last video we looked at ranges +of forces + + align:start position:0% +of forces + + + align:start position:0% +of forces +so we already saw one aspect in order to + + align:start position:0% +so we already saw one aspect in order to + + + align:start position:0% +so we already saw one aspect in order to +learn about + + align:start position:0% +learn about + + + align:start position:0% +learn about +what kind of interaction happens when + + align:start position:0% +what kind of interaction happens when + + + align:start position:0% +what kind of interaction happens when +you when you study + + align:start position:0% +you when you study + + + align:start position:0% +you when you study +um specific force you learn about the + + align:start position:0% +um specific force you learn about the + + + align:start position:0% +um specific force you learn about the +force carrier from + + align:start position:0% +force carrier from + + + align:start position:0% +force carrier from +noting the range in which forces + + align:start position:0% +noting the range in which forces + + + align:start position:0% +noting the range in which forces +interact + + align:start position:0% +interact + + + align:start position:0% +interact +in this class we talk about decays but + + align:start position:0% +in this class we talk about decays but + + + align:start position:0% +in this class we talk about decays but +in more general terms when we + + align:start position:0% +in more general terms when we + + + align:start position:0% +in more general terms when we +want to measure properties of forces we + + align:start position:0% +want to measure properties of forces we + + + align:start position:0% +want to measure properties of forces we +have basically three concepts at hand + + align:start position:0% +have basically three concepts at hand + + + align:start position:0% +have basically three concepts at hand +which can be experimentally determined + + align:start position:0% +which can be experimentally determined + + + align:start position:0% +which can be experimentally determined +the first one is masses of bound stakes + + align:start position:0% +the first one is masses of bound stakes + + + align:start position:0% +the first one is masses of bound stakes +so you might remember from atomic + + align:start position:0% +so you might remember from atomic + + + align:start position:0% +so you might remember from atomic +physics that you learn a lot about the + + align:start position:0% +physics that you learn a lot about the + + + align:start position:0% +physics that you learn a lot about the +electromagnetic interaction by studying + + align:start position:0% +electromagnetic interaction by studying + + + align:start position:0% +electromagnetic interaction by studying +for example the hydrogen atom where you + + align:start position:0% +for example the hydrogen atom where you + + + align:start position:0% +for example the hydrogen atom where you +have an electron + + align:start position:0% +have an electron + + + align:start position:0% +have an electron +circling around the proton and you can + + align:start position:0% +circling around the proton and you can + + + align:start position:0% +circling around the proton and you can +study in detail + + align:start position:0% +study in detail + + + align:start position:0% +study in detail +in an aspect of the electromagnetic + + align:start position:0% +in an aspect of the electromagnetic + + + align:start position:0% +in an aspect of the electromagnetic +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +um the second aspect is decay rates of + + align:start position:0% +um the second aspect is decay rates of + + + align:start position:0% +um the second aspect is decay rates of +unstable particles or the width of an + + align:start position:0% +unstable particles or the width of an + + + align:start position:0% +unstable particles or the width of an +unstable particle + + align:start position:0% +unstable particle + + + align:start position:0% +unstable particle +so in quantum mechanics the lifetime of + + align:start position:0% +so in quantum mechanics the lifetime of + + + align:start position:0% +so in quantum mechanics the lifetime of +the particle is related to the width + + align:start position:0% +the particle is related to the width + + + align:start position:0% +the particle is related to the width +and so that's what we're going to + + align:start position:0% +and so that's what we're going to + + + align:start position:0% +and so that's what we're going to +discuss in this video and then lastly we + + align:start position:0% +discuss in this video and then lastly we + + + align:start position:0% +discuss in this video and then lastly we +can look at the + + align:start position:0% +can look at the + + + align:start position:0% +can look at the +reaction rates expressed as cross + + align:start position:0% +reaction rates expressed as cross + + + align:start position:0% +reaction rates expressed as cross +sections and that's topic of the next + + align:start position:0% +sections and that's topic of the next + + + align:start position:0% +sections and that's topic of the next +video after this + + align:start position:0% + + + + align:start position:0% + +so let's talk about decays um so we can + + align:start position:0% +so let's talk about decays um so we can + + + align:start position:0% +so let's talk about decays um so we can +define + + align:start position:0% +define + + + align:start position:0% +define +this new symbol the decay rate lambda + + align:start position:0% +this new symbol the decay rate lambda + + + align:start position:0% +this new symbol the decay rate lambda +and s as a function of time the + + align:start position:0% +and s as a function of time the + + + align:start position:0% +and s as a function of time the +probability that a particle will survive + + align:start position:0% +probability that a particle will survive + + + align:start position:0% +probability that a particle will survive +at least until some time t um + + align:start position:0% +at least until some time t um + + + align:start position:0% +at least until some time t um +we can now discuss this and say okay you + + align:start position:0% +we can now discuss this and say okay you + + + align:start position:0% +we can now discuss this and say okay you +know the probability at some time + + align:start position:0% +know the probability at some time + + + align:start position:0% +know the probability at some time +t relates to the probability at some + + align:start position:0% +t relates to the probability at some + + + align:start position:0% +t relates to the probability at some +time t + + align:start position:0% +time t + + + align:start position:0% +time t +plus delta t by the likelihood + + align:start position:0% +plus delta t by the likelihood + + + align:start position:0% +plus delta t by the likelihood +one minus the decay rate times the time + + align:start position:0% +one minus the decay rate times the time + + + align:start position:0% +one minus the decay rate times the time +interval + + align:start position:0% +interval + + + align:start position:0% +interval +delta t and some from this we find + + align:start position:0% +delta t and some from this we find + + + align:start position:0% +delta t and some from this we find +that the change of the probability for + + align:start position:0% +that the change of the probability for + + + align:start position:0% +that the change of the probability for +the particle to survive + + align:start position:0% +the particle to survive + + + align:start position:0% +the particle to survive +is proportional to that probability and + + align:start position:0% +is proportional to that probability and + + + align:start position:0% +is proportional to that probability and +decay rate + + align:start position:0% +decay rate + + + align:start position:0% +decay rate +so now if we integrate this we find that + + align:start position:0% +so now if we integrate this we find that + + + align:start position:0% +so now if we integrate this we find that +the log + + align:start position:0% +the log + + + align:start position:0% +the log +of this probability is equal to some + + align:start position:0% +of this probability is equal to some + + + align:start position:0% +of this probability is equal to some +constant + + align:start position:0% +constant + + + align:start position:0% +constant +times lambda decay rate times time + + align:start position:0% +times lambda decay rate times time + + + align:start position:0% +times lambda decay rate times time +so now if you simply assume that the + + align:start position:0% +so now if you simply assume that the + + + align:start position:0% +so now if you simply assume that the +particle existed + + align:start position:0% +particle existed + + + align:start position:0% +particle existed +at the initial time t we said we said we + + align:start position:0% +at the initial time t we said we said we + + + align:start position:0% +at the initial time t we said we said we +set + + align:start position:0% +set + + + align:start position:0% +set +k equal to zero we find this very famous + + align:start position:0% +k equal to zero we find this very famous + + + align:start position:0% +k equal to zero we find this very famous +exponential decay law e to the power of + + align:start position:0% +exponential decay law e to the power of + + + align:start position:0% +exponential decay law e to the power of +minus + + align:start position:0% +minus + + + align:start position:0% +minus +lambda t and this shown here in this + + align:start position:0% +lambda t and this shown here in this + + + align:start position:0% +lambda t and this shown here in this +picture as you see this is exponential + + align:start position:0% +picture as you see this is exponential + + + align:start position:0% +picture as you see this is exponential +so far so good um we can now + + align:start position:0% +so far so good um we can now + + + align:start position:0% +so far so good um we can now +you know define and look at this + + align:start position:0% +you know define and look at this + + + align:start position:0% +you know define and look at this +distribution a little bit more + + align:start position:0% +distribution a little bit more + + + align:start position:0% +distribution a little bit more +um we can for example look at the + + align:start position:0% +um we can for example look at the + + + align:start position:0% +um we can for example look at the +average time for particle + + align:start position:0% +average time for particle + + + align:start position:0% +average time for particle +that a particle lifts um for this + + align:start position:0% +that a particle lifts um for this + + + align:start position:0% +that a particle lifts um for this +average time tau + + align:start position:0% +average time tau + + + align:start position:0% +average time tau +is simply given by the integral from + + align:start position:0% +is simply given by the integral from + + + align:start position:0% +is simply given by the integral from +zero to infinite + + align:start position:0% +zero to infinite + + + align:start position:0% +zero to infinite +so you basically integrate over this + + align:start position:0% +so you basically integrate over this + + + align:start position:0% +so you basically integrate over this +distribution to get the average time for + + align:start position:0% +distribution to get the average time for + + + align:start position:0% +distribution to get the average time for +the particle + + align:start position:0% +the particle + + + align:start position:0% +the particle +and that's equal to one over the decay + + align:start position:0% +and that's equal to one over the decay + + + align:start position:0% +and that's equal to one over the decay +rate one over lambda + + align:start position:0% +rate one over lambda + + + align:start position:0% +rate one over lambda +so you can do the algebra yourself and + + align:start position:0% +so you can do the algebra yourself and + + + align:start position:0% +so you can do the algebra yourself and +try to follow this + + align:start position:0% +try to follow this + + + align:start position:0% +try to follow this +um so if you now express + + align:start position:0% +um so if you now express + + + align:start position:0% +um so if you now express +this probability for the particle to + + align:start position:0% +this probability for the particle to + + + align:start position:0% +this probability for the particle to +survive until temp time t + + align:start position:0% +survive until temp time t + + + align:start position:0% +survive until temp time t +uh through the lifetime we find this is + + align:start position:0% +uh through the lifetime we find this is + + + align:start position:0% +uh through the lifetime we find this is +equal to e + + align:start position:0% +equal to e + + + align:start position:0% +equal to e +to the to minus t over the the + + align:start position:0% +to the to minus t over the the + + + align:start position:0% +to the to minus t over the the +the lifetime of the particle so you + + align:start position:0% +the lifetime of the particle so you + + + align:start position:0% +the lifetime of the particle so you +might + + align:start position:0% +might + + + align:start position:0% +might +not want to look at one particle by the + + align:start position:0% +not want to look at one particle by the + + + align:start position:0% +not want to look at one particle by the +ensemble of particles sum of particles + + align:start position:0% +ensemble of particles sum of particles + + + align:start position:0% +ensemble of particles sum of particles +and look at the time dependence of the + + align:start position:0% +and look at the time dependence of the + + + align:start position:0% +and look at the time dependence of the +number of particles which survived + + align:start position:0% +number of particles which survived + + + align:start position:0% +number of particles which survived +so this is equal to the + + align:start position:0% +so this is equal to the + + + align:start position:0% +so this is equal to the +number of particles as a function of + + align:start position:0% +number of particles as a function of + + + align:start position:0% +number of particles as a function of +times equal to the initial number of + + align:start position:0% +times equal to the initial number of + + + align:start position:0% +times equal to the initial number of +particles times the probability that any + + align:start position:0% +particles times the probability that any + + + align:start position:0% +particles times the probability that any +given particle survives + + align:start position:0% +given particle survives + + + align:start position:0% +given particle survives +and that's again given by this + + align:start position:0% +and that's again given by this + + + align:start position:0% +and that's again given by this +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +all right in nuclear physics + + align:start position:0% +all right in nuclear physics + + + align:start position:0% +all right in nuclear physics +one often talks about the half line half + + align:start position:0% +one often talks about the half line half + + + align:start position:0% +one often talks about the half line half +life time of the particle or + + align:start position:0% +life time of the particle or + + + align:start position:0% +life time of the particle or +specifically nuclei + + align:start position:0% +specifically nuclei + + + align:start position:0% +specifically nuclei +and that's given as you would assume by + + align:start position:0% +and that's given as you would assume by + + + align:start position:0% +and that's given as you would assume by +the time it takes + + align:start position:0% +the time it takes + + + align:start position:0% +the time it takes +four half of the particles to decay so n + + align:start position:0% +four half of the particles to decay so n + + + align:start position:0% +four half of the particles to decay so n +of tau one half is equal to the number + + align:start position:0% +of tau one half is equal to the number + + + align:start position:0% +of tau one half is equal to the number +of initial particles and not over two + + align:start position:0% +of initial particles and not over two + + + align:start position:0% +of initial particles and not over two +and you find then that this half lines + + align:start position:0% +and you find then that this half lines + + + align:start position:0% +and you find then that this half lines +with + + align:start position:0% +with + + + align:start position:0% +with +half half life is related to the + + align:start position:0% +half half life is related to the + + + align:start position:0% +half half life is related to the +lifetime of the particle + + align:start position:0% +lifetime of the particle + + + align:start position:0% +lifetime of the particle +within factor of about two thirds + + align:start position:0% + + + + align:start position:0% + +yes this is uh leads to some confusion + + align:start position:0% +yes this is uh leads to some confusion + + + align:start position:0% +yes this is uh leads to some confusion +in numerical values sometimes when + + align:start position:0% +in numerical values sometimes when + + + align:start position:0% +in numerical values sometimes when +when you ask for specific answers for + + align:start position:0% +when you ask for specific answers for + + + align:start position:0% +when you ask for specific answers for +nuclear so + + align:start position:0% +nuclear so + + + align:start position:0% +nuclear so +any experiments + + align:start position:0% +any experiments + + + align:start position:0% +any experiments +all right so there's another aspect of + + align:start position:0% +all right so there's another aspect of + + + align:start position:0% +all right so there's another aspect of +the case which arises + + align:start position:0% +the case which arises + + + align:start position:0% +the case which arises +which comes from a fundamental property + + align:start position:0% +which comes from a fundamental property + + + align:start position:0% +which comes from a fundamental property +of quantum mechanics + + align:start position:0% +of quantum mechanics + + + align:start position:0% +of quantum mechanics +so if you have an unstable state or any + + align:start position:0% +so if you have an unstable state or any + + + align:start position:0% +so if you have an unstable state or any +unstable state does not have exact + + align:start position:0% +unstable state does not have exact + + + align:start position:0% +unstable state does not have exact +energy state and this follows + + align:start position:0% +energy state and this follows + + + align:start position:0% +energy state and this follows +if you want from the uncertainty + + align:start position:0% +if you want from the uncertainty + + + align:start position:0% +if you want from the uncertainty +principle + + align:start position:0% +principle + + + align:start position:0% +principle +so the width of a particle + + align:start position:0% + + + + align:start position:0% + +is quantized and it's quantized with + + align:start position:0% +is quantized and it's quantized with + + + align:start position:0% +is quantized and it's quantized with +this thing with lambda here and as you + + align:start position:0% +this thing with lambda here and as you + + + align:start position:0% +this thing with lambda here and as you +can see lambda relates again to the + + align:start position:0% +can see lambda relates again to the + + + align:start position:0% +can see lambda relates again to the +decay rate + + align:start position:0% +decay rate + + + align:start position:0% +decay rate +over the lifetime of of the particle + + align:start position:0% +over the lifetime of of the particle + + + align:start position:0% +over the lifetime of of the particle +another complication can occur when + + align:start position:0% +another complication can occur when + + + align:start position:0% +another complication can occur when +there's multiple ways for the particle + + align:start position:0% +there's multiple ways for the particle + + + align:start position:0% +there's multiple ways for the particle +to decay + + align:start position:0% +to decay + + + align:start position:0% +to decay +for example you know you have a higgs + + align:start position:0% +for example you know you have a higgs + + + align:start position:0% +for example you know you have a higgs +boson as you will see on the next slide + + align:start position:0% +boson as you will see on the next slide + + + align:start position:0% +boson as you will see on the next slide +which might decay into multiple + + align:start position:0% +which might decay into multiple + + + align:start position:0% +which might decay into multiple +has a way to decay into multiple + + align:start position:0% +has a way to decay into multiple + + + align:start position:0% +has a way to decay into multiple +particles + + align:start position:0% +particles + + + align:start position:0% +particles +here we define a partial width where + + align:start position:0% +here we define a partial width where + + + align:start position:0% +here we define a partial width where +the partial width is defined as the half + + align:start position:0% +the partial width is defined as the half + + + align:start position:0% +the partial width is defined as the half +the width of the particle to decay into + + align:start position:0% +the width of the particle to decay into + + + align:start position:0% +the width of the particle to decay into +specific mode + + align:start position:0% +specific mode + + + align:start position:0% +specific mode +and then the total width of the particle + + align:start position:0% +and then the total width of the particle + + + align:start position:0% +and then the total width of the particle +is given by the sum of the partial + + align:start position:0% +is given by the sum of the partial + + + align:start position:0% +is given by the sum of the partial +widths of all + + align:start position:0% +widths of all + + + align:start position:0% +widths of all +possible ways for the particle to decay + + align:start position:0% +possible ways for the particle to decay + + + align:start position:0% +possible ways for the particle to decay +using this you can also decay + + align:start position:0% +using this you can also decay + + + align:start position:0% +using this you can also decay +to calculate the likelihood of a + + align:start position:0% +to calculate the likelihood of a + + + align:start position:0% +to calculate the likelihood of a +particle to decay in a specific way + + align:start position:0% +particle to decay in a specific way + + + align:start position:0% +particle to decay in a specific way +that's called the branching fraction and + + align:start position:0% +that's called the branching fraction and + + + align:start position:0% +that's called the branching fraction and +that's given by + + align:start position:0% +that's given by + + + align:start position:0% +that's given by +the partial width divided by the total + + align:start position:0% +the partial width divided by the total + + + align:start position:0% +the partial width divided by the total +width + + align:start position:0% +width + + + align:start position:0% +width +or the partial decay rate divided by the + + align:start position:0% +or the partial decay rate divided by the + + + align:start position:0% +or the partial decay rate divided by the +total liquid + + align:start position:0% +total liquid + + + align:start position:0% +total liquid +again the total has to be one the + + align:start position:0% +again the total has to be one the + + + align:start position:0% +again the total has to be one the +probability for the particle decay in + + align:start position:0% +probability for the particle decay in + + + align:start position:0% +probability for the particle decay in +any mode is one + + align:start position:0% +any mode is one + + + align:start position:0% +any mode is one +therefore the sum of the function ratios + + align:start position:0% +therefore the sum of the function ratios + + + align:start position:0% +therefore the sum of the function ratios +is one as well + + align:start position:0% +is one as well + + + align:start position:0% +is one as well +all right so looking at a specific + + align:start position:0% +all right so looking at a specific + + + align:start position:0% +all right so looking at a specific +example + + align:start position:0% +example + + + align:start position:0% +example +um the higgs boson is probably my famous + + align:start position:0% +um the higgs boson is probably my famous + + + align:start position:0% +um the higgs boson is probably my famous +favorite + + align:start position:0% +favorite + + + align:start position:0% +favorite +example in this entire class um you'll + + align:start position:0% +example in this entire class um you'll + + + align:start position:0% +example in this entire class um you'll +find here + + align:start position:0% +find here + + + align:start position:0% +find here +given branch infractions or ratios for + + align:start position:0% +given branch infractions or ratios for + + + align:start position:0% +given branch infractions or ratios for +specific decay modes this is not all + + align:start position:0% +specific decay modes this is not all + + + align:start position:0% +specific decay modes this is not all +ways in which the exposure and decay was + + align:start position:0% +ways in which the exposure and decay was + + + align:start position:0% +ways in which the exposure and decay was +the most dominant one + + align:start position:0% +the most dominant one + + + align:start position:0% +the most dominant one +the most prominent one is the one where + + align:start position:0% +the most prominent one is the one where + + + align:start position:0% +the most prominent one is the one where +the higgs boson decays into a pair of + + align:start position:0% +the higgs boson decays into a pair of + + + align:start position:0% +the higgs boson decays into a pair of +beak works + + align:start position:0% +beak works + + + align:start position:0% +beak works +um you will later see maybe even as an + + align:start position:0% +um you will later see maybe even as an + + + align:start position:0% +um you will later see maybe even as an +exercise + + align:start position:0% +exercise + + + align:start position:0% +exercise +why the distribution of branching ratios + + align:start position:0% +why the distribution of branching ratios + + + align:start position:0% +why the distribution of branching ratios +is the way it's being shown here + + align:start position:0% +is the way it's being shown here + + + align:start position:0% +is the way it's being shown here +so the higgs boson has been measured + + align:start position:0% +so the higgs boson has been measured + + + align:start position:0% +so the higgs boson has been measured +with a mass of 125 gb in a little bit + + align:start position:0% +with a mass of 125 gb in a little bit + + + align:start position:0% +with a mass of 125 gb in a little bit +and you see at this mass here the + + align:start position:0% +and you see at this mass here the + + + align:start position:0% +and you see at this mass here the +vomiting decay mod is into pv bar but + + align:start position:0% +vomiting decay mod is into pv bar but + + + align:start position:0% +vomiting decay mod is into pv bar but +it's also possible for the higgs boson + + align:start position:0% +it's also possible for the higgs boson + + + align:start position:0% +it's also possible for the higgs boson +to decay into pair of w bosons + + align:start position:0% +to decay into pair of w bosons + + + align:start position:0% +to decay into pair of w bosons +uh we are an interesting loop diagram + + align:start position:0% +uh we are an interesting loop diagram + + + align:start position:0% +uh we are an interesting loop diagram +into gluons even so gluons are massless + + align:start position:0% +into gluons even so gluons are massless + + + align:start position:0% +into gluons even so gluons are massless +or taus + + align:start position:0% +or taus + + + align:start position:0% +or taus +charm zebras and so on and we just + + align:start position:0% +charm zebras and so on and we just + + + align:start position:0% +charm zebras and so on and we just +showed here showed you in a paper which + + align:start position:0% +showed here showed you in a paper which + + + align:start position:0% +showed here showed you in a paper which +was submitted today + + align:start position:0% +was submitted today + + + align:start position:0% +was submitted today +to the archive that exporter also can + + align:start position:0% +to the archive that exporter also can + + + align:start position:0% +to the archive that exporter also can +decay + + align:start position:0% +decay + + + align:start position:0% +decay +into a pair of neurons with a branching + + align:start position:0% +into a pair of neurons with a branching + + + align:start position:0% +into a pair of neurons with a branching +ratio of 2 times 10 to the minus 4. so + + align:start position:0% +ratio of 2 times 10 to the minus 4. so + + + align:start position:0% +ratio of 2 times 10 to the minus 4. so +it's rather rare but it's possible \ No newline at end of file diff --git a/3Kn1LzkT5sA.txt b/3Kn1LzkT5sA.txt new file mode 100644 index 0000000000000000000000000000000000000000..ae78b85773de9b25a544507d7a2e0de5e5cd4154 --- /dev/null +++ b/3Kn1LzkT5sA.txt @@ -0,0 +1,19 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you + + align:start position:0% +you + + + align:start position:0% +you +[Music] \ No newline at end of file diff --git a/3kxnPEDecIA.txt b/3kxnPEDecIA.txt new file mode 100644 index 0000000000000000000000000000000000000000..120f5e3d137963b565e5033a2618c8d1fd4255a3 --- /dev/null +++ b/3kxnPEDecIA.txt @@ -0,0 +1,1147 @@ +align:start position:0% + +we now revisit the exponential random + + align:start position:0% +we now revisit the exponential random + + + align:start position:0% +we now revisit the exponential random +variable that we introduced earlier and + + align:start position:0% +variable that we introduced earlier and + + + align:start position:0% +variable that we introduced earlier and +develop some intuition about what it + + align:start position:0% +develop some intuition about what it + + + align:start position:0% +develop some intuition about what it +represents we do this by establishing a + + align:start position:0% +represents we do this by establishing a + + + align:start position:0% +represents we do this by establishing a +memorylessness property similar to the + + align:start position:0% +memorylessness property similar to the + + + align:start position:0% +memorylessness property similar to the +one that we established earlier in the + + align:start position:0% +one that we established earlier in the + + + align:start position:0% +one that we established earlier in the +discrete case for the geometric PMF + + align:start position:0% +discrete case for the geometric PMF + + + align:start position:0% +discrete case for the geometric PMF +suppose that it is known that light + + align:start position:0% +suppose that it is known that light + + + align:start position:0% +suppose that it is known that light +bulbs have a lifetime until they burn + + align:start position:0% +bulbs have a lifetime until they burn + + + align:start position:0% +bulbs have a lifetime until they burn +out which is an exponential random + + align:start position:0% +out which is an exponential random + + + align:start position:0% +out which is an exponential random +variable you go to a store and you are + + align:start position:0% +variable you go to a store and you are + + + align:start position:0% +variable you go to a store and you are +given two choices to buy a new light + + align:start position:0% +given two choices to buy a new light + + + align:start position:0% +given two choices to buy a new light +bulb or to buy a used light bulb that + + align:start position:0% +bulb or to buy a used light bulb that + + + align:start position:0% +bulb or to buy a used light bulb that +has been working for some time and has + + align:start position:0% +has been working for some time and has + + + align:start position:0% +has been working for some time and has +not yet + + align:start position:0% +not yet + + + align:start position:0% +not yet +burned out which one should you take we + + align:start position:0% +burned out which one should you take we + + + align:start position:0% +burned out which one should you take we +want to approach this question + + align:start position:0% +want to approach this question + + + align:start position:0% +want to approach this question +mathematically so let us denote by + + align:start position:0% +mathematically so let us denote by + + + align:start position:0% +mathematically so let us denote by +capital T the lifetime of the bulb so + + align:start position:0% +capital T the lifetime of the bulb so + + + align:start position:0% +capital T the lifetime of the bulb so +time starts at time zero and then at + + align:start position:0% +time starts at time zero and then at + + + align:start position:0% +time starts at time zero and then at +some random time that we denote by + + align:start position:0% +some random time that we denote by + + + align:start position:0% +some random time that we denote by +capital T the light bulb will burn out + + align:start position:0% +capital T the light bulb will burn out + + + align:start position:0% +capital T the light bulb will burn out +and we assume that this random variable + + align:start position:0% +and we assume that this random variable + + + align:start position:0% +and we assume that this random variable +is exponential with some given parameter + + align:start position:0% +is exponential with some given parameter + + + align:start position:0% +is exponential with some given parameter +lambda in one of our earlier + + align:start position:0% +lambda in one of our earlier + + + align:start position:0% +lambda in one of our earlier +calculations we have shown that the + + align:start position:0% +calculations we have shown that the + + + align:start position:0% +calculations we have shown that the +probability that capital T is larger + + align:start position:0% +probability that capital T is larger + + + align:start position:0% +probability that capital T is larger +than some value little X Falls + + align:start position:0% +than some value little X Falls + + + align:start position:0% +than some value little X Falls +exponentially with that value X we are + + align:start position:0% +exponentially with that value X we are + + + align:start position:0% +exponentially with that value X we are +now told that a certain light bulb has + + align:start position:0% +now told that a certain light bulb has + + + align:start position:0% +now told that a certain light bulb has +already been operating for T time units + + align:start position:0% +already been operating for T time units + + + align:start position:0% +already been operating for T time units +without failing so we know that the + + align:start position:0% +without failing so we know that the + + + align:start position:0% +without failing so we know that the +value of the random variable capital T + + align:start position:0% +value of the random variable capital T + + + align:start position:0% +value of the random variable capital T +is larger than little T we're interested + + align:start position:0% +is larger than little T we're interested + + + align:start position:0% +is larger than little T we're interested +in how much longer the light bulb will + + align:start position:0% +in how much longer the light bulb will + + + align:start position:0% +in how much longer the light bulb will +be operating and so we look at capital X + + align:start position:0% +be operating and so we look at capital X + + + align:start position:0% +be operating and so we look at capital X +which is the remaining life time from + + align:start position:0% +which is the remaining life time from + + + align:start position:0% +which is the remaining life time from +the current time until the light bulb + + align:start position:0% +the current time until the light bulb + + + align:start position:0% +the current time until the light bulb +burns out so capital X is this + + align:start position:0% +burns out so capital X is this + + + align:start position:0% +burns out so capital X is this +particular random variable here and it + + align:start position:0% +particular random variable here and it + + + align:start position:0% +particular random variable here and it +is equal to capital t minus little T let + + align:start position:0% +is equal to capital t minus little T let + + + align:start position:0% +is equal to capital t minus little T let +us now calculate the probability that + + align:start position:0% +us now calculate the probability that + + + align:start position:0% +us now calculate the probability that +the light bulb lasts for another little + + align:start position:0% +the light bulb lasts for another little + + + align:start position:0% +the light bulb lasts for another little +x time unit + + align:start position:0% +x time unit + + + align:start position:0% +x time unit +that is that this random variable + + align:start position:0% +that is that this random variable + + + align:start position:0% +that is that this random variable +capital X is at least as large as some + + align:start position:0% +capital X is at least as large as some + + + align:start position:0% +capital X is at least as large as some +little X that is that the light bulb + + align:start position:0% +little X that is that the light bulb + + + align:start position:0% +little X that is that the light bulb +remains alive until time T plus X we use + + align:start position:0% +remains alive until time T plus X we use + + + align:start position:0% +remains alive until time T plus X we use +the definition of conditional + + align:start position:0% +the definition of conditional + + + align:start position:0% +the definition of conditional +probabilities to write this expression + + align:start position:0% +probabilities to write this expression + + + align:start position:0% +probabilities to write this expression +as the probability that capital X is + + align:start position:0% +as the probability that capital X is + + + align:start position:0% +as the probability that capital X is +bigger than little X on the other hand + + align:start position:0% +bigger than little X on the other hand + + + align:start position:0% +bigger than little X on the other hand +capital X is t minus T so we write it + + align:start position:0% +capital X is t minus T so we write it + + + align:start position:0% +capital X is t minus T so we write it +this way t minus T is bigger than little + + align:start position:0% +this way t minus T is bigger than little + + + align:start position:0% +this way t minus T is bigger than little +X and also that T is bigger than little + + align:start position:0% +X and also that T is bigger than little + + + align:start position:0% +X and also that T is bigger than little +T divided by the probability of the + + align:start position:0% +T divided by the probability of the + + + align:start position:0% +T divided by the probability of the +conditioning event just write this event + + align:start position:0% +conditioning event just write this event + + + align:start position:0% +conditioning event just write this event +in a cleaner form capital T being larger + + align:start position:0% +in a cleaner form capital T being larger + + + align:start position:0% +in a cleaner form capital T being larger +than little t plus X and being larger + + align:start position:0% +than little t plus X and being larger + + + align:start position:0% +than little t plus X and being larger +than little T again divided by the + + align:start position:0% +than little T again divided by the + + + align:start position:0% +than little T again divided by the +probability of the conditioning event + + align:start position:0% +probability of the conditioning event + + + align:start position:0% +probability of the conditioning event +and now notice that capital T will be + + align:start position:0% +and now notice that capital T will be + + + align:start position:0% +and now notice that capital T will be +greater than little T and also greater + + align:start position:0% +greater than little T and also greater + + + align:start position:0% +greater than little T and also greater +than little t plus X that is capital T + + align:start position:0% +than little t plus X that is capital T + + + align:start position:0% +than little t plus X that is capital T +is larger than this number and this + + align:start position:0% +is larger than this number and this + + + align:start position:0% +is larger than this number and this +number if and only if it is larger than + + align:start position:0% +number if and only if it is larger than + + + align:start position:0% +number if and only if it is larger than +this second number here so in other + + align:start position:0% +this second number here so in other + + + align:start position:0% +this second number here so in other +words the intersection of these two + + align:start position:0% +words the intersection of these two + + + align:start position:0% +words the intersection of these two +events is just this event here that + + align:start position:0% +events is just this event here that + + + align:start position:0% +events is just this event here that +capital T is larger than little T plus X + + align:start position:0% + + + + align:start position:0% + +now we can use the formula for the + + align:start position:0% +now we can use the formula for the + + + align:start position:0% +now we can use the formula for the +probability that capital T is larger + + align:start position:0% +probability that capital T is larger + + + align:start position:0% +probability that capital T is larger +than something we apply this formula + + align:start position:0% +than something we apply this formula + + + align:start position:0% +than something we apply this formula +except that instead of little X we have + + align:start position:0% +except that instead of little X we have + + + align:start position:0% +except that instead of little X we have +T plus X and so here we have e to the + + align:start position:0% +T plus X and so here we have e to the + + + align:start position:0% +T plus X and so here we have e to the +minus lambda T plus X divided by the + + align:start position:0% +minus lambda T plus X divided by the + + + align:start position:0% +minus lambda T plus X divided by the +probability that capital T is bigger + + align:start position:0% +probability that capital T is bigger + + + align:start position:0% +probability that capital T is bigger +than T so we use this formula but with + + align:start position:0% +than T so we use this formula but with + + + align:start position:0% +than T so we use this formula but with +little T in the place of little X and we + + align:start position:0% +little T in the place of little X and we + + + align:start position:0% +little T in the place of little X and we +obtain e to the minus lambda t we have a + + align:start position:0% +obtain e to the minus lambda t we have a + + + align:start position:0% +obtain e to the minus lambda t we have a +cancellation and we're left with e to + + align:start position:0% +cancellation and we're left with e to + + + align:start position:0% +cancellation and we're left with e to +the minus lambda X which is the final + + align:start position:0% +the minus lambda X which is the final + + + align:start position:0% +the minus lambda X which is the final +answer in this calculation what we + + align:start position:0% +answer in this calculation what we + + + align:start position:0% +answer in this calculation what we +observe here the probability that the + + align:start position:0% +observe here the probability that the + + + align:start position:0% +observe here the probability that the +used light bulb will live for another X + + align:start position:0% +used light bulb will live for another X + + + align:start position:0% +used light bulb will live for another X +time units is exactly the same as the + + align:start position:0% +time units is exactly the same as the + + + align:start position:0% +time units is exactly the same as the +corresponding probability that a new + + align:start position:0% +corresponding probability that a new + + + align:start position:0% +corresponding probability that a new +light bulb will be alive for another X + + align:start position:0% +light bulb will be alive for another X + + + align:start position:0% +light bulb will be alive for another X +time units so new and used light bulbs + + align:start position:0% +time units so new and used light bulbs + + + align:start position:0% +time units so new and used light bulbs +are described by the same probabilities + + align:start position:0% +are described by the same probabilities + + + align:start position:0% +are described by the same probabilities +and they are probabilistically identical + + align:start position:0% +and they are probabilistically identical + + + align:start position:0% +and they are probabilistically identical +the same differently said the used light + + align:start position:0% +the same differently said the used light + + + align:start position:0% +the same differently said the used light +bulb does not remember and it is not + + align:start position:0% +bulb does not remember and it is not + + + align:start position:0% +bulb does not remember and it is not +affected by how long it has been running + + align:start position:0% +affected by how long it has been running + + + align:start position:0% +affected by how long it has been running +and this is the memorylessness property + + align:start position:0% +and this is the memorylessness property + + + align:start position:0% +and this is the memorylessness property +of exponential random variables let us + + align:start position:0% +of exponential random variables let us + + + align:start position:0% +of exponential random variables let us +now build some additional insight on + + align:start position:0% +now build some additional insight on + + + align:start position:0% +now build some additional insight on +exponential random variables we have a + + align:start position:0% +exponential random variables we have a + + + align:start position:0% +exponential random variables we have a +formula for the density the PDF and from + + align:start position:0% +formula for the density the PDF and from + + + align:start position:0% +formula for the density the PDF and from +this we can calculate the probability + + align:start position:0% +this we can calculate the probability + + + align:start position:0% +this we can calculate the probability +that T lies in a small interval for + + align:start position:0% +that T lies in a small interval for + + + align:start position:0% +that T lies in a small interval for +example for a small Delta this + + align:start position:0% +example for a small Delta this + + + align:start position:0% +example for a small Delta this +probability here is going to be + + align:start position:0% +probability here is going to be + + + align:start position:0% +probability here is going to be +approximately equal to the density of T + + align:start position:0% +approximately equal to the density of T + + + align:start position:0% +approximately equal to the density of T +evaluated at 0 times Delta which is + + align:start position:0% +evaluated at 0 times Delta which is + + + align:start position:0% +evaluated at 0 times Delta which is +lambda times e to the 0 which is 1 times + + align:start position:0% +lambda times e to the 0 which is 1 times + + + align:start position:0% +lambda times e to the 0 which is 1 times +Delta what if we're told that the line + + align:start position:0% +Delta what if we're told that the line + + + align:start position:0% +Delta what if we're told that the line +bob has been alive for tea-time units + + align:start position:0% +bob has been alive for tea-time units + + + align:start position:0% +bob has been alive for tea-time units +what is the probability that it burns + + align:start position:0% +what is the probability that it burns + + + align:start position:0% +what is the probability that it burns +out during the next Delta time units + + align:start position:0% +out during the next Delta time units + + + align:start position:0% +out during the next Delta time units +since I used but still alive light bulb + + align:start position:0% +since I used but still alive light bulb + + + align:start position:0% +since I used but still alive light bulb +is probabilistically identical to a new + + align:start position:0% +is probabilistically identical to a new + + + align:start position:0% +is probabilistically identical to a new +one this conditional probability is the + + align:start position:0% +one this conditional probability is the + + + align:start position:0% +one this conditional probability is the +same as this probability here that a new + + align:start position:0% +same as this probability here that a new + + + align:start position:0% +same as this probability here that a new +light bulb burns out in the next Delta + + align:start position:0% +light bulb burns out in the next Delta + + + align:start position:0% +light bulb burns out in the next Delta +time units and so this is also + + align:start position:0% +time units and so this is also + + + align:start position:0% +time units and so this is also +approximately equal to lambda Delta so + + align:start position:0% +approximately equal to lambda Delta so + + + align:start position:0% +approximately equal to lambda Delta so +we see that independently of how long a + + align:start position:0% +we see that independently of how long a + + + align:start position:0% +we see that independently of how long a +light bulb has been alive during the + + align:start position:0% +light bulb has been alive during the + + + align:start position:0% +light bulb has been alive during the +next Delta time units it will have a + + align:start position:0% +next Delta time units it will have a + + + align:start position:0% +next Delta time units it will have a +lambda Delta probability of failing one + + align:start position:0% +lambda Delta probability of failing one + + + align:start position:0% +lambda Delta probability of failing one +way of thinking about this situation is + + align:start position:0% +way of thinking about this situation is + + + align:start position:0% +way of thinking about this situation is +that the time interval is split into + + align:start position:0% +that the time interval is split into + + + align:start position:0% +that the time interval is split into +little intervals of length Delta and as + + align:start position:0% +little intervals of length Delta and as + + + align:start position:0% +little intervals of length Delta and as +long as the light bulb is alive if it is + + align:start position:0% +long as the light bulb is alive if it is + + + align:start position:0% +long as the light bulb is alive if it is +alive at this point it will have + + align:start position:0% +alive at this point it will have + + + align:start position:0% +alive at this point it will have +probability lambda Delta of burning out + + align:start position:0% +probability lambda Delta of burning out + + + align:start position:0% +probability lambda Delta of burning out +during the next interval of length Delta + + align:start position:0% +during the next interval of length Delta + + + align:start position:0% +during the next interval of length Delta +this is like flipping a coin once every + + align:start position:0% +this is like flipping a coin once every + + + align:start position:0% +this is like flipping a coin once every +Delta time steps there is a probability + + align:start position:0% +Delta time steps there is a probability + + + align:start position:0% +Delta time steps there is a probability +lambda Delta that there is success in + + align:start position:0% +lambda Delta that there is success in + + + align:start position:0% +lambda Delta that there is success in +that coin flip where success corresponds + + align:start position:0% +that coin flip where success corresponds + + + align:start position:0% +that coin flip where success corresponds +to having the light bulb actually burned + + align:start position:0% +to having the light bulb actually burned + + + align:start position:0% +to having the light bulb actually burned +down and the exponential random variable + + align:start position:0% +down and the exponential random variable + + + align:start position:0% +down and the exponential random variable +corresponds to the total time elapsed + + align:start position:0% +corresponds to the total time elapsed + + + align:start position:0% +corresponds to the total time elapsed +until the first success in this sense + + align:start position:0% +until the first success in this sense + + + align:start position:0% +until the first success in this sense +the exponential random variable is a + + align:start position:0% +the exponential random variable is a + + + align:start position:0% +the exponential random variable is a +close analog of the geometric random + + align:start position:0% +close analog of the geometric random + + + align:start position:0% +close analog of the geometric random +variable which was the time until the + + align:start position:0% +variable which was the time until the + + + align:start position:0% +variable which was the time until the +first success in a discrete time setting + + align:start position:0% +first success in a discrete time setting + + + align:start position:0% +first success in a discrete time setting +this analogy turns out to be the + + align:start position:0% +this analogy turns out to be the + + + align:start position:0% +this analogy turns out to be the +foundation behind the Poisson process + + align:start position:0% +foundation behind the Poisson process + + + align:start position:0% +foundation behind the Poisson process +that we will be studying later in this + + align:start position:0% +that we will be studying later in this + + + align:start position:0% +that we will be studying later in this +course \ No newline at end of file diff --git a/44lqcpQcNzQ.txt b/44lqcpQcNzQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..46ec5e61088cb0facd501fccb468dea277a90515 --- /dev/null +++ b/44lqcpQcNzQ.txt @@ -0,0 +1,3787 @@ +align:start position:0% + +I would like to uh have a slightly + + align:start position:0% +I would like to uh have a slightly + + + align:start position:0% +I would like to uh have a slightly +different kind of a pinup today than + + align:start position:0% +different kind of a pinup today than + + + align:start position:0% +different kind of a pinup today than +usual and I'll + + align:start position:0% +usual and I'll + + + align:start position:0% +usual and I'll +explain + + align:start position:0% +explain + + + align:start position:0% +explain +um you become very very connected to + + align:start position:0% +um you become very very connected to + + + align:start position:0% +um you become very very connected to +your + + align:start position:0% +your + + + align:start position:0% +your +work sometimes you can't see anything + + align:start position:0% +work sometimes you can't see anything + + + align:start position:0% +work sometimes you can't see anything +except your own + + align:start position:0% +except your own + + + align:start position:0% +except your own +work and you get into it so far that you + + align:start position:0% +work and you get into it so far that you + + + align:start position:0% +work and you get into it so far that you +get lost or get um let us say you get + + align:start position:0% +get lost or get um let us say you get + + + align:start position:0% +get lost or get um let us say you get +hopelessly lost inide your own + + align:start position:0% +hopelessly lost inide your own + + + align:start position:0% +hopelessly lost inide your own +project perhaps not hopelessly but you + + align:start position:0% +project perhaps not hopelessly but you + + + align:start position:0% +project perhaps not hopelessly but you +certainly um only see that and I'd like + + align:start position:0% +certainly um only see that and I'd like + + + align:start position:0% +certainly um only see that and I'd like +to have you step back from that today + + align:start position:0% +to have you step back from that today + + + align:start position:0% +to have you step back from that today +and see your project in a little + + align:start position:0% +and see your project in a little + + + align:start position:0% +and see your project in a little +different way that is not so connected + + align:start position:0% +different way that is not so connected + + + align:start position:0% +different way that is not so connected +personally to you so that maybe you can + + align:start position:0% +personally to you so that maybe you can + + + align:start position:0% +personally to you so that maybe you can +be a little bit more objective about it + + align:start position:0% +be a little bit more objective about it + + + align:start position:0% +be a little bit more objective about it +so the format for the review is very + + align:start position:0% +so the format for the review is very + + + align:start position:0% +so the format for the review is very +simple but it gets at that + + align:start position:0% +simple but it gets at that + + + align:start position:0% +simple but it gets at that +notion and that is that you're going to + + align:start position:0% +notion and that is that you're going to + + + align:start position:0% +notion and that is that you're going to +have a partner and I've teamed you up + + align:start position:0% +have a partner and I've teamed you up + + + align:start position:0% +have a partner and I've teamed you up +for various reasons because + + align:start position:0% +for various reasons because + + + align:start position:0% +for various reasons because +same uh sit together or similar project + + align:start position:0% +same uh sit together or similar project + + + align:start position:0% +same uh sit together or similar project +or for whatever + + align:start position:0% +or for whatever + + + align:start position:0% +or for whatever +um and we're going to have about a + + align:start position:0% +um and we're going to have about a + + + align:start position:0% +um and we're going to have about a +10-minute + + align:start position:0% +10-minute + + + align:start position:0% +10-minute +time so you're going to have a a + + align:start position:0% +time so you're going to have a a + + + align:start position:0% +time so you're going to have a a +teammate first of all and I'll tell you + + align:start position:0% +teammate first of all and I'll tell you + + + align:start position:0% +teammate first of all and I'll tell you +who they are and you're going to have + + align:start position:0% +who they are and you're going to have + + + align:start position:0% +who they are and you're going to have +about 10 minutes to uh both of you + + align:start position:0% +about 10 minutes to uh both of you + + + align:start position:0% +about 10 minutes to uh both of you +explain to each + + align:start position:0% +explain to each + + + align:start position:0% +explain to each +other what your project is and what was + + align:start position:0% +other what your project is and what was + + + align:start position:0% +other what your project is and what was +important so these are two that are + + align:start position:0% +important so these are two that are + + + align:start position:0% +important so these are two that are +teamed up she explains what she's + + align:start position:0% +teamed up she explains what she's + + + align:start position:0% +teamed up she explains what she's +doing uh to her project to hon and hen + + align:start position:0% +doing uh to her project to hon and hen + + + align:start position:0% +doing uh to her project to hon and hen +explains what he's doing to + + align:start position:0% +explains what he's doing to + + + align:start position:0% +explains what he's doing to +her + + align:start position:0% +her + + + align:start position:0% +her +then after that I'm going to ask in this + + align:start position:0% +then after that I'm going to ask in this + + + align:start position:0% +then after that I'm going to ask in this +case hen to present her + + align:start position:0% +case hen to present her + + + align:start position:0% +case hen to present her +project and she has to sit there + + align:start position:0% +project and she has to sit there + + + align:start position:0% +project and she has to sit there +quietly and then she presents his PL + + align:start position:0% +quietly and then she presents his PL + + + align:start position:0% +quietly and then she presents his PL +project and further I'm going to ask + + align:start position:0% +project and further I'm going to ask + + + align:start position:0% +project and further I'm going to ask +them to make one comment as to how they + + align:start position:0% +them to make one comment as to how they + + + align:start position:0% +them to make one comment as to how they +could make it + + align:start position:0% +could make it + + + align:start position:0% +could make it +better so you're getting outside + + align:start position:0% +better so you're getting outside + + + align:start position:0% +better so you're getting outside +yourself got it say how she could make + + align:start position:0% +yourself got it say how she could make + + + align:start position:0% +yourself got it say how she could make +she is presenting hasson's what he's + + align:start position:0% +she is presenting hasson's what he's + + + align:start position:0% +she is presenting hasson's what he's +trying to do and at the end she says I + + align:start position:0% +trying to do and at the end she says I + + + align:start position:0% +trying to do and at the end she says I +think that hen could um improve it by + + align:start position:0% +think that hen could um improve it by + + + align:start position:0% +think that hen could um improve it by +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this so and and um he's sitting there + + align:start position:0% +this so and and um he's sitting there + + + align:start position:0% +this so and and um he's sitting there +quietly can't say hey that's not the way + + align:start position:0% +quietly can't say hey that's not the way + + + align:start position:0% +quietly can't say hey that's not the way +I wanted it it was something else he had + + align:start position:0% +I wanted it it was something else he had + + + align:start position:0% +I wanted it it was something else he had +um he has to remain quiet got it so you + + align:start position:0% +um he has to remain quiet got it so you + + + align:start position:0% +um he has to remain quiet got it so you +can't jump in and say hey just and then + + align:start position:0% +can't jump in and say hey just and then + + + align:start position:0% +can't jump in and say hey just and then +of course we'll have a discussion after + + align:start position:0% +of course we'll have a discussion after + + + align:start position:0% +of course we'll have a discussion after +and the point of that is to get you + + align:start position:0% +and the point of that is to get you + + + align:start position:0% +and the point of that is to get you +outside your own + + align:start position:0% +outside your own + + + align:start position:0% +outside your own +project so that you might be able to see + + align:start position:0% +project so that you might be able to see + + + align:start position:0% +project so that you might be able to see +it in a different eyes all right + + align:start position:0% +it in a different eyes all right + + + align:start position:0% +it in a different eyes all right +probably remember the skating is and the + + align:start position:0% +probably remember the skating is and the + + + align:start position:0% +probably remember the skating is and the +rock climbing is the central ideas so + + align:start position:0% +rock climbing is the central ideas so + + + align:start position:0% +rock climbing is the central ideas so +she wanted to put that in the central + + align:start position:0% +she wanted to put that in the central + + + align:start position:0% +she wanted to put that in the central +part of the building and make the + + align:start position:0% +part of the building and make the + + + align:start position:0% +part of the building and make the +activities connect the building um + + align:start position:0% +activities connect the building um + + + align:start position:0% +activities connect the building um +vertically and so that from everywhere + + align:start position:0% +vertically and so that from everywhere + + + align:start position:0% +vertically and so that from everywhere +in the building you can see down into + + align:start position:0% +in the building you can see down into + + + align:start position:0% +in the building you can see down into +the skating and to the rock climbing um + + align:start position:0% +the skating and to the rock climbing um + + + align:start position:0% +the skating and to the rock climbing um +um so I'll just take you through it the + + align:start position:0% +um so I'll just take you through it the + + + align:start position:0% +um so I'll just take you through it the +entrance is here this is the street + + align:start position:0% +entrance is here this is the street + + + align:start position:0% +entrance is here this is the street +coming like this you enter into here + + align:start position:0% +coming like this you enter into here + + + align:start position:0% +coming like this you enter into here +this is the food area which is um clear + + align:start position:0% +this is the food area which is um clear + + + align:start position:0% +this is the food area which is um clear +and so it's visible from the outside and + + align:start position:0% +and so it's visible from the outside and + + + align:start position:0% +and so it's visible from the outside and +um you can come eat and here and you + + align:start position:0% +um you can come eat and here and you + + + align:start position:0% +um you can come eat and here and you +these are uh circulation they're either + + align:start position:0% +these are uh circulation they're either + + + align:start position:0% +these are uh circulation they're either +going to be ramps or stairs you + + align:start position:0% +going to be ramps or stairs you + + + align:start position:0% +going to be ramps or stairs you +can escalator or escalator sorry + + align:start position:0% +can escalator or escalator sorry + + + align:start position:0% +can escalator or escalator sorry +so so the first floor is mainly the food + + align:start position:0% +so so the first floor is mainly the food + + + align:start position:0% +so so the first floor is mainly the food +or you can go over here the rock + + align:start position:0% +or you can go over here the rock + + + align:start position:0% +or you can go over here the rock +climbing this is all connected obviously + + align:start position:0% +climbing this is all connected obviously + + + align:start position:0% +climbing this is all connected obviously +and the second floor has um an area for + + align:start position:0% +and the second floor has um an area for + + + align:start position:0% +and the second floor has um an area for +concerts the area sort of the rental + + align:start position:0% +concerts the area sort of the rental + + + align:start position:0% +concerts the area sort of the rental +area for um climbing and for skating I + + align:start position:0% +area for um climbing and for skating I + + + align:start position:0% +area for um climbing and for skating I +guess you can rent and then the third + + align:start position:0% +guess you can rent and then the third + + + align:start position:0% +guess you can rent and then the third +floor has more of a learning for the + + align:start position:0% +floor has more of a learning for the + + + align:start position:0% +floor has more of a learning for the +climbing area and the general Hangout + + align:start position:0% +climbing area and the general Hangout + + + align:start position:0% +climbing area and the general Hangout +spot + + align:start position:0% +spot + + + align:start position:0% +spot +um let's see in terms of well in terms + + align:start position:0% +um let's see in terms of well in terms + + + align:start position:0% +um let's see in terms of well in terms +of materials the floor mainly is + + align:start position:0% +of materials the floor mainly is + + + align:start position:0% +of materials the floor mainly is +concrete this is actually transparent so + + align:start position:0% +concrete this is actually transparent so + + + align:start position:0% +concrete this is actually transparent so +you can look down and see people skating + + align:start position:0% +you can look down and see people skating + + + align:start position:0% +you can look down and see people skating +by and um it's like right on top of the + + align:start position:0% +by and um it's like right on top of the + + + align:start position:0% +by and um it's like right on top of the +skate paths I guess and this part here + + align:start position:0% +skate paths I guess and this part here + + + align:start position:0% +skate paths I guess and this part here +is more open because it's um well it + + align:start position:0% +is more open because it's um well it + + + align:start position:0% +is more open because it's um well it +wants to focus on the big area the + + align:start position:0% +wants to focus on the big area the + + + align:start position:0% +wants to focus on the big area the +second floor is more + + align:start position:0% +second floor is more + + + align:start position:0% +second floor is more +closed and um because it has more of the + + align:start position:0% +closed and um because it has more of the + + + align:start position:0% +closed and um because it has more of the +rental + + align:start position:0% +rental + + + align:start position:0% +rental +area Okay the hangout spot has a slanted + + align:start position:0% +area Okay the hangout spot has a slanted + + + align:start position:0% +area Okay the hangout spot has a slanted +window um because she wanted you to be + + align:start position:0% +window um because she wanted you to be + + + align:start position:0% +window um because she wanted you to be +able to look down onto everything but + + align:start position:0% +able to look down onto everything but + + + align:start position:0% +able to look down onto everything but +sort of not be seen so that you're + + align:start position:0% +sort of not be seen so that you're + + + align:start position:0% +sort of not be seen so that you're +watching but you can just sort of you + + align:start position:0% +watching but you can just sort of you + + + align:start position:0% +watching but you can just sort of you +know be doing your own thing at the same + + align:start position:0% +know be doing your own thing at the same + + + align:start position:0% +know be doing your own thing at the same +time the oh right the roofs the roofs + + align:start position:0% +time the oh right the roofs the roofs + + + align:start position:0% +time the oh right the roofs the roofs +also direct the light into the main area + + align:start position:0% +also direct the light into the main area + + + align:start position:0% +also direct the light into the main area +that you wanted to emphasize so light + + align:start position:0% +that you wanted to emphasize so light + + + align:start position:0% +that you wanted to emphasize so light +comes in through here down here down + + align:start position:0% +comes in through here down here down + + + align:start position:0% +comes in through here down here down +here + + align:start position:0% +here + + + align:start position:0% +here +down and if you turn this + + align:start position:0% + + + + align:start position:0% + +around you can see that there's actually + + align:start position:0% +around you can see that there's actually + + + align:start position:0% +around you can see that there's actually +another entrance in here to go into the + + align:start position:0% +another entrance in here to go into the + + + align:start position:0% +another entrance in here to go into the +food place and this is this floor + + align:start position:0% +food place and this is this floor + + + align:start position:0% +food place and this is this floor +extends out and so this is an area that + + align:start position:0% +extends out and so this is an area that + + + align:start position:0% +extends out and so this is an area that +you can sort of hang out in and you can + + align:start position:0% +you can sort of hang out in and you can + + + align:start position:0% +you can sort of hang out in and you can +also enter + + align:start position:0% +also enter + + + align:start position:0% +also enter +here and um so you can go rock climbing + + align:start position:0% +here and um so you can go rock climbing + + + align:start position:0% +here and um so you can go rock climbing +out here or + + align:start position:0% +out here or + + + align:start position:0% +out here or +indoors + + align:start position:0% +indoors + + + align:start position:0% +indoors +and let me + + align:start position:0% +and let me + + + align:start position:0% +and let me +see oh one thing she changed from last + + align:start position:0% +see oh one thing she changed from last + + + align:start position:0% +see oh one thing she changed from last +time was + + align:start position:0% +time was + + + align:start position:0% +time was +that + + align:start position:0% + + + + align:start position:0% + +the the walkway that she had coming + + align:start position:0% +the the walkway that she had coming + + + align:start position:0% +the the walkway that she had coming +wrapping around you can now walk all the + + align:start position:0% +wrapping around you can now walk all the + + + align:start position:0% +wrapping around you can now walk all the +way around the platforms whereas before + + align:start position:0% +way around the platforms whereas before + + + align:start position:0% +way around the platforms whereas before +she had platform and here and another + + align:start position:0% +she had platform and here and another + + + align:start position:0% +she had platform and here and another +one starts there so now you can walk + + align:start position:0% +one starts there so now you can walk + + + align:start position:0% +one starts there so now you can walk +around the whole building so it's sort + + align:start position:0% +around the whole building so it's sort + + + align:start position:0% +around the whole building so it's sort +of a horizontal + + align:start position:0% +of a horizontal + + + align:start position:0% +of a horizontal +connection um that puts everything + + align:start position:0% +connection um that puts everything + + + align:start position:0% +connection um that puts everything +together + + align:start position:0% +together + + + align:start position:0% +together +and as far as + + align:start position:0% +and as far as + + + align:start position:0% +and as far as +suggestions um one suggestion was maybe + + align:start position:0% +suggestions um one suggestion was maybe + + + align:start position:0% +suggestions um one suggestion was maybe +a more direct path for the food to this + + align:start position:0% +a more direct path for the food to this + + + align:start position:0% +a more direct path for the food to this +sort of balcony hang out area because + + align:start position:0% +sort of balcony hang out area because + + + align:start position:0% +sort of balcony hang out area because +right now you have to like go all the + + align:start position:0% +right now you have to like go all the + + + align:start position:0% +right now you have to like go all the +way + + align:start position:0% + + + + align:start position:0% + +around + + align:start position:0% + + + + align:start position:0% + +hey um so that's a suggestion sort of a + + align:start position:0% +hey um so that's a suggestion sort of a + + + align:start position:0% +hey um so that's a suggestion sort of a +practical one + + align:start position:0% +practical one + + + align:start position:0% +practical one +um + + align:start position:0% + + + + align:start position:0% + +and I don't well I don't don't quite + + align:start position:0% +and I don't well I don't don't quite + + + align:start position:0% +and I don't well I don't don't quite +know the structure of the roof and how + + align:start position:0% +know the structure of the roof and how + + + align:start position:0% +know the structure of the roof and how +that's working I'm sure that'll be + + align:start position:0% +that's working I'm sure that'll be + + + align:start position:0% +that's working I'm sure that'll be +figured out at some point um and I don't + + align:start position:0% +figured out at some point um and I don't + + + align:start position:0% +figured out at some point um and I don't +know the safety of this but it might be + + align:start position:0% +know the safety of this but it might be + + + align:start position:0% +know the safety of this but it might be +interesting if you could keep going + + align:start position:0% +interesting if you could keep going + + + align:start position:0% +interesting if you could keep going +because you keep climbing and you hit + + align:start position:0% +because you keep climbing and you hit + + + align:start position:0% +because you keep climbing and you hit +the roof and you keep climbing you hit a + + align:start position:0% +the roof and you keep climbing you hit a + + + align:start position:0% +the roof and you keep climbing you hit a +roof I it's cool just to keep + + align:start position:0% +roof I it's cool just to keep + + + align:start position:0% +roof I it's cool just to keep +climbing main idea was she had + + align:start position:0% +climbing main idea was she had + + + align:start position:0% +climbing main idea was she had +researched that a lot of events go on a + + align:start position:0% +researched that a lot of events go on a + + + align:start position:0% +researched that a lot of events go on a +lot of parades take place around this + + align:start position:0% +lot of parades take place around this + + + align:start position:0% +lot of parades take place around this +area and she wanted to make a place + + align:start position:0% +area and she wanted to make a place + + + align:start position:0% +area and she wanted to make a place +where uh people can come together from + + align:start position:0% +where uh people can come together from + + + align:start position:0% +where uh people can come together from +Boston and + + align:start position:0% +Boston and + + + align:start position:0% +Boston and +make the floats in this area but also + + align:start position:0% +make the floats in this area but also + + + align:start position:0% +make the floats in this area but also +have tourists and people not necessarily + + align:start position:0% +have tourists and people not necessarily + + + align:start position:0% +have tourists and people not necessarily +making them observe uh the process of + + align:start position:0% +making them observe uh the process of + + + align:start position:0% +making them observe uh the process of +making these floats so our buildings + + align:start position:0% +making these floats so our buildings + + + align:start position:0% +making these floats so our buildings +kind of organized so that the public + + align:start position:0% +kind of organized so that the public + + + align:start position:0% +kind of organized so that the public +enters from the stairs from the right + + align:start position:0% +enters from the stairs from the right + + + align:start position:0% +enters from the stairs from the right +here and goes the bottom floor is a + + align:start position:0% +here and goes the bottom floor is a + + + align:start position:0% +here and goes the bottom floor is a +general art store so it's a very public + + align:start position:0% +general art store so it's a very public + + + align:start position:0% +general art store so it's a very public +area and then next most public is the + + align:start position:0% +area and then next most public is the + + + align:start position:0% +area and then next most public is the +stairs from the right for the general + + align:start position:0% +stairs from the right for the general + + + align:start position:0% +stairs from the right for the general +public they enter through the building + + align:start position:0% +public they enter through the building + + + align:start position:0% +public they enter through the building +in here and um there's a museum and + + align:start position:0% +in here and um there's a museum and + + + align:start position:0% +in here and um there's a museum and +exhibition place and information + + align:start position:0% +exhibition place and information + + + align:start position:0% +exhibition place and information +information center where they can uh + + align:start position:0% +information center where they can uh + + + align:start position:0% +information center where they can uh +learn about like the history of Boston + + align:start position:0% +learn about like the history of Boston + + + align:start position:0% +learn about like the history of Boston +and stuff like that and + + align:start position:0% +and stuff like that and + + + align:start position:0% +and stuff like that and +uh see there's a good + + align:start position:0% +uh see there's a good + + + align:start position:0% +uh see there's a good +view + + align:start position:0% +view + + + align:start position:0% +view +from + + align:start position:0% +from + + + align:start position:0% +from +behind of uh how they enter in through + + align:start position:0% +behind of uh how they enter in through + + + align:start position:0% +behind of uh how they enter in through +this Museum area across a ramp that + + align:start position:0% +this Museum area across a ramp that + + + align:start position:0% +this Museum area across a ramp that +looks down over the space place where + + align:start position:0% +looks down over the space place where + + + align:start position:0% +looks down over the space place where +all the floats are being built which is + + align:start position:0% +all the floats are being built which is + + + align:start position:0% +all the floats are being built which is +the main a large area um and you can + + align:start position:0% +the main a large area um and you can + + + align:start position:0% +the main a large area um and you can +continue down that bridge into this + + align:start position:0% +continue down that bridge into this + + + align:start position:0% +continue down that bridge into this +other area which is more Museum and + + align:start position:0% + + + + align:start position:0% + +information uh exhibition Gallery + + align:start position:0% +information uh exhibition Gallery + + + align:start position:0% +information uh exhibition Gallery +space on this second floor in here with + + align:start position:0% +space on this second floor in here with + + + align:start position:0% +space on this second floor in here with +the clear windows and that also looks + + align:start position:0% +the clear windows and that also looks + + + align:start position:0% +the clear windows and that also looks +down into this uh construction + + align:start position:0% +down into this uh construction + + + align:start position:0% +down into this uh construction +area Sor very delicate it's + + align:start position:0% +area Sor very delicate it's + + + align:start position:0% +area Sor very delicate it's +and uh okay so that's where it focuses + + align:start position:0% +and uh okay so that's where it focuses + + + align:start position:0% +and uh okay so that's where it focuses +mainly on the public and then for the + + align:start position:0% +mainly on the public and then for the + + + align:start position:0% +mainly on the public and then for the +participants for building the floats + + align:start position:0% +participants for building the floats + + + align:start position:0% +participants for building the floats +they enter through this left side this + + align:start position:0% +they enter through this left side this + + + align:start position:0% +they enter through this left side this +glass box like area is all the + + align:start position:0% +glass box like area is all the + + + align:start position:0% +glass box like area is all the +circulation where all the stairs are to + + align:start position:0% +circulation where all the stairs are to + + + align:start position:0% +circulation where all the stairs are to +go between the different levels um so + + align:start position:0% +go between the different levels um so + + + align:start position:0% +go between the different levels um so +they enter from the left and the first + + align:start position:0% +they enter from the left and the first + + + align:start position:0% +they enter from the left and the first +floor there's this long hallway where + + align:start position:0% +floor there's this long hallway where + + + align:start position:0% +floor there's this long hallway where +there's wood shops metal shops that are + + align:start position:0% +there's wood shops metal shops that are + + + align:start position:0% +there's wood shops metal shops that are +all open to this construction area the + + align:start position:0% +all open to this construction area the + + + align:start position:0% +all open to this construction area the +main construction area in the middle and + + align:start position:0% +main construction area in the middle and + + + align:start position:0% +main construction area in the middle and +then on the second floor you know was + + align:start position:0% +then on the second floor you know was + + + align:start position:0% +then on the second floor you know was +the gallery space but then if the um + + align:start position:0% +the gallery space but then if the um + + + align:start position:0% +the gallery space but then if the um +Builders of the floats go up to the + + align:start position:0% +Builders of the floats go up to the + + + align:start position:0% +Builders of the floats go up to the +third floor there's smaller rooms where + + align:start position:0% +third floor there's smaller rooms where + + + align:start position:0% +third floor there's smaller rooms where +they can focus on building smaller + + align:start position:0% +they can focus on building smaller + + + align:start position:0% +they can focus on building smaller +components of the larger float um places + + align:start position:0% +components of the larger float um places + + + align:start position:0% +components of the larger float um places +for people to paint things stuff like + + align:start position:0% +for people to paint things stuff like + + + align:start position:0% +for people to paint things stuff like +that and then there's a roof deck that + + align:start position:0% +that and then there's a roof deck that + + + align:start position:0% +that and then there's a roof deck that +goes in the direction of the street that + + align:start position:0% +goes in the direction of the street that + + + align:start position:0% +goes in the direction of the street that +the parades go or the floats move down + + align:start position:0% +the parades go or the floats move down + + + align:start position:0% +the parades go or the floats move down +um and there's also a parallel deck over + + align:start position:0% +um and there's also a parallel deck over + + + align:start position:0% +um and there's also a parallel deck over +here that's for the + + align:start position:0% +here that's for the + + + align:start position:0% +here that's for the +public uh her + + align:start position:0% +public uh her + + + align:start position:0% +public uh her +roofs are designed to contrast the more + + align:start position:0% +roofs are designed to contrast the more + + + align:start position:0% +roofs are designed to contrast the more +rectangular plan of the building um + + align:start position:0% +rectangular plan of the building um + + + align:start position:0% +rectangular plan of the building um +they're kind of give the illusion of + + align:start position:0% +they're kind of give the illusion of + + + align:start position:0% +they're kind of give the illusion of +floating over a lot of activity + + align:start position:0% +floating over a lot of activity + + + align:start position:0% +floating over a lot of activity +signifying all the different + + align:start position:0% +signifying all the different + + + align:start position:0% +signifying all the different +construction and energy that's going on + + align:start position:0% +construction and energy that's going on + + + align:start position:0% +construction and energy that's going on +underneath it underneath it and a lot of + + align:start position:0% +underneath it underneath it and a lot of + + + align:start position:0% +underneath it underneath it and a lot of +lights entering through here um there's + + align:start position:0% +lights entering through here um there's + + + align:start position:0% +lights entering through here um there's +copper and translucent material glass on + + align:start position:0% +copper and translucent material glass on + + + align:start position:0% +copper and translucent material glass on +the vertical uh + + align:start position:0% +the vertical uh + + + align:start position:0% +the vertical uh +openings + + align:start position:0% +openings + + + align:start position:0% +openings +um so there's + + align:start position:0% +um so there's + + + align:start position:0% +um so there's +also uh a couple + + align:start position:0% +also uh a couple + + + align:start position:0% +also uh a couple +things uh we talked about where she + + align:start position:0% +things uh we talked about where she + + + align:start position:0% +things uh we talked about where she +maybe wants to develop a better uh + + align:start position:0% +maybe wants to develop a better uh + + + align:start position:0% +maybe wants to develop a better uh +design for the roof deck are area uh a + + align:start position:0% +design for the roof deck are area uh a + + + align:start position:0% +design for the roof deck are area uh a +different way to maybe improve the + + align:start position:0% +different way to maybe improve the + + + align:start position:0% +different way to maybe improve the +circulation instead of the area instead + + align:start position:0% +circulation instead of the area instead + + + align:start position:0% +circulation instead of the area instead +of having uh the glass box but + + align:start position:0% +of having uh the glass box but + + + align:start position:0% +of having uh the glass box but +um mainly I think like the roof and the + + align:start position:0% +um mainly I think like the roof and the + + + align:start position:0% +um mainly I think like the roof and the +rest of the structure is delicate and + + align:start position:0% +rest of the structure is delicate and + + + align:start position:0% +rest of the structure is delicate and +like interest interesting and pretty + + align:start position:0% +like interest interesting and pretty + + + align:start position:0% +like interest interesting and pretty +intricate but then you just kind of have + + align:start position:0% +intricate but then you just kind of have + + + align:start position:0% +intricate but then you just kind of have +this thing that's very literally + + align:start position:0% +this thing that's very literally + + + align:start position:0% +this thing that's very literally +pointing out to the street in this + + align:start position:0% +pointing out to the street in this + + + align:start position:0% +pointing out to the street in this +rectangular shape so that can maybe um + + align:start position:0% +rectangular shape so that can maybe um + + + align:start position:0% +rectangular shape so that can maybe um +match the depth of design for the rest + + align:start position:0% +match the depth of design for the rest + + + align:start position:0% +match the depth of design for the rest +of the the project but that's lias + + align:start position:0% +of the the project but that's lias + + + align:start position:0% +of the the project but that's lias +okay very good guys you two guys happy + + align:start position:0% +okay very good guys you two guys happy + + + align:start position:0% +okay very good guys you two guys happy +mhm maybe you should hire each other to + + align:start position:0% + + + + align:start position:0% + +Pro um it has the quality of of lace or + + align:start position:0% +Pro um it has the quality of of lace or + + + align:start position:0% +Pro um it has the quality of of lace or +it has the quality of filters it has a + + align:start position:0% +it has the quality of filters it has a + + + align:start position:0% +it has the quality of filters it has a +lightness to it it's uh has a quality of + + align:start position:0% +lightness to it it's uh has a quality of + + + align:start position:0% +lightness to it it's uh has a quality of +being an incredible Dynamic building + + align:start position:0% +being an incredible Dynamic building + + + align:start position:0% +being an incredible Dynamic building +this building is on the move and you + + align:start position:0% +this building is on the move and you + + + align:start position:0% +this building is on the move and you +have that VI and it has the quality of + + align:start position:0% +have that VI and it has the quality of + + + align:start position:0% +have that VI and it has the quality of +wanting to go in and see what's going on + + align:start position:0% +wanting to go in and see what's going on + + + align:start position:0% +wanting to go in and see what's going on +in there it's it's very mysterious in + + align:start position:0% +in there it's it's very mysterious in + + + align:start position:0% +in there it's it's very mysterious in +not in an opaque way but it has that + + align:start position:0% +not in an opaque way but it has that + + + align:start position:0% +not in an opaque way but it has that +feeling of something exciting is + + align:start position:0% +feeling of something exciting is + + + align:start position:0% +feeling of something exciting is +happening inside of that um and I think + + align:start position:0% +happening inside of that um and I think + + + align:start position:0% +happening inside of that um and I think +it's very very powerful um these the way + + align:start position:0% +it's very very powerful um these the way + + + align:start position:0% +it's very very powerful um these the way +the roofs are the way that you've gone + + align:start position:0% +the roofs are the way that you've gone + + + align:start position:0% +the roofs are the way that you've gone +from the copper to the transparent to + + align:start position:0% +from the copper to the transparent to + + + align:start position:0% +from the copper to the transparent to +the clear when you turned it around you + + align:start position:0% +the clear when you turned it around you + + + align:start position:0% +the clear when you turned it around you +got this incredible lace like f of these + + align:start position:0% +got this incredible lace like f of these + + + align:start position:0% +got this incredible lace like f of these +small but many numers which are making + + align:start position:0% +small but many numers which are making + + + align:start position:0% +small but many numers which are making +in this up which I think is is it's + + align:start position:0% +in this up which I think is is it's + + + align:start position:0% +in this up which I think is is it's +terrific um so it's a good start and + + align:start position:0% +terrific um so it's a good start and + + + align:start position:0% +terrific um so it's a good start and +it's so much on the a scale this is like + + align:start position:0% +it's so much on the a scale this is like + + + align:start position:0% +it's so much on the a scale this is like +it's a real place you can imagine being + + align:start position:0% +it's a real place you can imagine being + + + align:start position:0% +it's a real place you can imagine being +in here and I'm sorry you didn't make a + + align:start position:0% +in here and I'm sorry you didn't make a + + + align:start position:0% +in here and I'm sorry you didn't make a +flp because of a nice see a float inside + + align:start position:0% +flp because of a nice see a float inside + + + align:start position:0% +flp because of a nice see a float inside +of this and get the scale of that + + align:start position:0% +of this and get the scale of that + + + align:start position:0% +of this and get the scale of that +because it the reason I say that is the + + align:start position:0% +because it the reason I say that is the + + + align:start position:0% +because it the reason I say that is the +float also has this quality of a kind of + + align:start position:0% +float also has this quality of a kind of + + + align:start position:0% +float also has this quality of a kind of +a stage set and so does the whole + + align:start position:0% +a stage set and so does the whole + + + align:start position:0% +a stage set and so does the whole +building so it nice to see the two + + align:start position:0% +building so it nice to see the two + + + align:start position:0% +building so it nice to see the two +together um I would just want to say + + align:start position:0% +together um I would just want to say + + + align:start position:0% +together um I would just want to say +that Stephanie I think you're right on + + align:start position:0% +that Stephanie I think you're right on + + + align:start position:0% +that Stephanie I think you're right on +there is + + align:start position:0% +there is + + + align:start position:0% +there is +a uh what I call Collision architecture + + align:start position:0% +a uh what I call Collision architecture + + + align:start position:0% +a uh what I call Collision architecture +that we're now seeing for the first time + + align:start position:0% +that we're now seeing for the first time + + + align:start position:0% +that we're now seeing for the first time +between the wonderful lace likee quality + + align:start position:0% +between the wonderful lace likee quality + + + align:start position:0% +between the wonderful lace likee quality +of the main building and the other + + align:start position:0% +of the main building and the other + + + align:start position:0% +of the main building and the other +building and the connection or I will + + align:start position:0% +building and the connection or I will + + + align:start position:0% +building and the connection or I will +call it a dance between the two is not + + align:start position:0% +call it a dance between the two is not + + + align:start position:0% +call it a dance between the two is not +yet + + align:start position:0% +yet + + + align:start position:0% +yet +resolved the dance between this look at + + align:start position:0% +resolved the dance between this look at + + + align:start position:0% +resolved the dance between this look at +that is that one the dance between this + + align:start position:0% +that is that one the dance between this + + + align:start position:0% +that is that one the dance between this +and this is very delicate right in there + + align:start position:0% +and this is very delicate right in there + + + align:start position:0% +and this is very delicate right in there +and right there is where it falls apart + + align:start position:0% +and right there is where it falls apart + + + align:start position:0% +and right there is where it falls apart +mm it's like somebody they hired a very + + align:start position:0% +mm it's like somebody they hired a very + + + align:start position:0% +mm it's like somebody they hired a very +well-known architect to do this and then + + align:start position:0% +well-known architect to do this and then + + + align:start position:0% +well-known architect to do this and then +they ran out of money because she was so + + align:start position:0% +they ran out of money because she was so + + + align:start position:0% +they ran out of money because she was so +difficult so much for a commission I had + + align:start position:0% +difficult so much for a commission I had + + + align:start position:0% +difficult so much for a commission I had +a kind of a hack architect to do this + + align:start position:0% +a kind of a hack architect to do this + + + align:start position:0% +a kind of a hack architect to do this +trunk you could care less what she did + + align:start position:0% +trunk you could care less what she did + + + align:start position:0% +trunk you could care less what she did +and that's where it shows up right there + + align:start position:0% +and that's where it shows up right there + + + align:start position:0% +and that's where it shows up right there +yeah it actually is supposed to be + + align:start position:0% +yeah it actually is supposed to be + + + align:start position:0% +yeah it actually is supposed to be +higher but it fell it doesn't Ro yeah it + + align:start position:0% +higher but it fell it doesn't Ro yeah it + + + align:start position:0% +higher but it fell it doesn't Ro yeah it +doesn't hold okay well that's a + + align:start position:0% +doesn't hold okay well that's a + + + align:start position:0% +doesn't hold okay well that's a +technical model problem but in terms of + + align:start position:0% +technical model problem but in terms of + + + align:start position:0% +technical model problem but in terms of +design there is something that isn't + + align:start position:0% +design there is something that isn't + + + align:start position:0% +design there is something that isn't +quite resolved in yeah now watch out + + align:start position:0% +quite resolved in yeah now watch out + + + align:start position:0% +quite resolved in yeah now watch out +because she asked me the other day + + align:start position:0% +because she asked me the other day + + + align:start position:0% +because she asked me the other day +should um the out out lines of this + + align:start position:0% +should um the out out lines of this + + + align:start position:0% +should um the out out lines of this +follow the outlines of the roof no it's + + align:start position:0% +follow the outlines of the roof no it's + + + align:start position:0% +follow the outlines of the roof no it's +two different systems so it it is not + + align:start position:0% +two different systems so it it is not + + + align:start position:0% +two different systems so it it is not +that that geometry should in fact govern + + align:start position:0% +that that geometry should in fact govern + + + align:start position:0% +that that geometry should in fact govern +everything that goes on it can be + + align:start position:0% +everything that goes on it can be + + + align:start position:0% +everything that goes on it can be +entirely different it is that there's a + + align:start position:0% +entirely different it is that there's a + + + align:start position:0% +entirely different it is that there's a +dance between the two and this is what I + + align:start position:0% +dance between the two and this is what I + + + align:start position:0% +dance between the two and this is what I +call the 10% solution it is not a major + + align:start position:0% +call the 10% solution it is not a major + + + align:start position:0% +call the 10% solution it is not a major +major change it's actually a 5% it's + + align:start position:0% +major change it's actually a 5% it's + + + align:start position:0% +major change it's actually a 5% it's +just a slight subtle change maybe this + + align:start position:0% +just a slight subtle change maybe this + + + align:start position:0% +just a slight subtle change maybe this +being lower or being some of that + + align:start position:0% +being lower or being some of that + + + align:start position:0% +being lower or being some of that +geometry but very little into it and + + align:start position:0% +geometry but very little into it and + + + align:start position:0% +geometry but very little into it and +then you know you're sort of home so fre + + align:start position:0% +then you know you're sort of home so fre + + + align:start position:0% +then you know you're sort of home so fre +we haven't seen the other side it would + + align:start position:0% +we haven't seen the other side it would + + + align:start position:0% +we haven't seen the other side it would +be nice now because you built almost all + + align:start position:0% +be nice now because you built almost all + + + align:start position:0% +be nice now because you built almost all +that that you would do this actually all + + align:start position:0% +that that you would do this actually all + + + align:start position:0% +that that you would do this actually all +you have to do is this + + align:start position:0% +you have to do is this + + + align:start position:0% +you have to do is this +right the other thing that concerns me + + align:start position:0% +right the other thing that concerns me + + + align:start position:0% +right the other thing that concerns me +is the incredible and it has always + + align:start position:0% +is the incredible and it has always + + + align:start position:0% +is the incredible and it has always +concerned me the incredible height for + + align:start position:0% +concerned me the incredible height for + + + align:start position:0% +concerned me the incredible height for +that tissue that entrance with it's huge + + align:start position:0% +that tissue that entrance with it's huge + + + align:start position:0% +that tissue that entrance with it's huge +and there's is that it is that somebody + + align:start position:0% +and there's is that it is that somebody + + + align:start position:0% +and there's is that it is that somebody +that's yeah uh yeah that's good that's a + + align:start position:0% +that's yeah uh yeah that's good that's a + + + align:start position:0% +that's yeah uh yeah that's good that's a +huge + + align:start position:0% +huge + + + align:start position:0% +huge +distance in in terms of what you + + align:start position:0% +distance in in terms of what you + + + align:start position:0% +distance in in terms of what you +perceive it's quite large it could be + + align:start position:0% +perceive it's quite large it could be + + + align:start position:0% +perceive it's quite large it could be +not that we can reduce the the height of + + align:start position:0% +not that we can reduce the the height of + + + align:start position:0% +not that we can reduce the the height of +that because we've been through this + + align:start position:0% +that because we've been through this + + + align:start position:0% +that because we've been through this +before because she's starting down here + + align:start position:0% +before because she's starting down here + + + align:start position:0% +before because she's starting down here +with something that's okay and she's + + align:start position:0% +with something that's okay and she's + + + align:start position:0% +with something that's okay and she's +working her way up but it is possible + + align:start position:0% +working her way up but it is possible + + + align:start position:0% +working her way up but it is possible +that we can break this facade which I + + align:start position:0% +that we can break this facade which I + + + align:start position:0% +that we can break this facade which I +think is going to be the sub theme of + + align:start position:0% +think is going to be the sub theme of + + + align:start position:0% +think is going to be the sub theme of +this afternoon we could break this + + align:start position:0% +this afternoon we could break this + + + align:start position:0% +this afternoon we could break this +facade uh into maybe more + + align:start position:0% +facade uh into maybe more + + + align:start position:0% +facade uh into maybe more +translution panels or even Peg panels up + + align:start position:0% +translution panels or even Peg panels up + + + align:start position:0% +translution panels or even Peg panels up +in here so we bring the scale down to + + align:start position:0% +in here so we bring the scale down to + + + align:start position:0% +in here so we bring the scale down to +something that's more human okay I know + + align:start position:0% +something that's more human okay I know + + + align:start position:0% +something that's more human okay I know +this has to solve the function of + + align:start position:0% +this has to solve the function of + + + align:start position:0% +this has to solve the function of +getting huge floats out and people in + + align:start position:0% +getting huge floats out and people in + + + align:start position:0% +getting huge floats out and people in +yeah but you can have both you can have + + align:start position:0% +yeah but you can have both you can have + + + align:start position:0% +yeah but you can have both you can have +your cake and eat it too you can have + + align:start position:0% +your cake and eat it too you can have + + + align:start position:0% +your cake and eat it too you can have +the human scale and the float scale so + + align:start position:0% +the human scale and the float scale so + + + align:start position:0% +the human scale and the float scale so +to speak so that's a couple things now + + align:start position:0% +to speak so that's a couple things now + + + align:start position:0% +to speak so that's a couple things now +if I could over here which is also uh a + + align:start position:0% +if I could over here which is also uh a + + + align:start position:0% +if I could over here which is also uh a +remarkable piece of work um in terms of + + align:start position:0% +remarkable piece of work um in terms of + + + align:start position:0% +remarkable piece of work um in terms of +its uh flowing you two got together + + align:start position:0% +its uh flowing you two got together + + + align:start position:0% +its uh flowing you two got together +because of the root thing um you both + + align:start position:0% +because of the root thing um you both + + + align:start position:0% +because of the root thing um you both +have kind floating roofs but this has an + + align:start position:0% +have kind floating roofs but this has an + + + align:start position:0% +have kind floating roofs but this has an +incredible sense of flowing to it uh you + + align:start position:0% +incredible sense of flowing to it uh you + + + align:start position:0% +incredible sense of flowing to it uh you +know the skateboard is boozing in and + + align:start position:0% +know the skateboard is boozing in and + + + align:start position:0% +know the skateboard is boozing in and +out like a pinball machine you get + + align:start position:0% +out like a pinball machine you get + + + align:start position:0% +out like a pinball machine you get +everything happen just it's incredible + + align:start position:0% +everything happen just it's incredible + + + align:start position:0% +everything happen just it's incredible +it's one more place that you want to go + + align:start position:0% +it's one more place that you want to go + + + align:start position:0% +it's one more place that you want to go +to just to hang out to have your lunch + + align:start position:0% +to just to hang out to have your lunch + + + align:start position:0% +to just to hang out to have your lunch +even if you don't like skateboarding + + align:start position:0% +even if you don't like skateboarding + + + align:start position:0% +even if you don't like skateboarding +just as I like to hang out here on a + + align:start position:0% +just as I like to hang out here on a + + + align:start position:0% +just as I like to hang out here on a +winter day um so there's an incredible + + align:start position:0% +winter day um so there's an incredible + + + align:start position:0% +winter day um so there's an incredible +kind of flow in + + align:start position:0% +kind of flow in + + + align:start position:0% +kind of flow in +this which I think is very is very very + + align:start position:0% +this which I think is very is very very + + + align:start position:0% +this which I think is very is very very +positive the thing that is so amazing is + + align:start position:0% +positive the thing that is so amazing is + + + align:start position:0% +positive the thing that is so amazing is +that the same person who did this + + align:start position:0% +that the same person who did this + + + align:start position:0% +that the same person who did this +delicate flowing did this ugly staircase + + align:start position:0% +delicate flowing did this ugly staircase + + + align:start position:0% +delicate flowing did this ugly staircase +that is just I it's + + align:start position:0% +that is just I it's + + + align:start position:0% +that is just I it's +outrageous slope + + align:start position:0% +outrageous slope + + + align:start position:0% +outrageous slope +the I mean nobody in the right mind is + + align:start position:0% +the I mean nobody in the right mind is + + + align:start position:0% +the I mean nobody in the right mind is +going to go up that staircase and if + + align:start position:0% +going to go up that staircase and if + + + align:start position:0% +going to go up that staircase and if +it's a ramp they're just going to roll + + align:start position:0% +it's a ramp they're just going to roll + + + align:start position:0% +it's a ramp they're just going to roll +down so it's not very gentle whereas + + align:start position:0% +down so it's not very gentle whereas + + + align:start position:0% +down so it's not very gentle whereas +everything else has an incredible kind + + align:start position:0% +everything else has an incredible kind + + + align:start position:0% +everything else has an incredible kind +of feeling to it of uh gracefulness even + + align:start position:0% +of feeling to it of uh gracefulness even + + + align:start position:0% +of feeling to it of uh gracefulness even +the skateboard + + align:start position:0% +the skateboard + + + align:start position:0% +the skateboard +that doesn't and that's what was it was + + align:start position:0% +that doesn't and that's what was it was + + + align:start position:0% +that doesn't and that's what was it was +subtly hinted to I think by your + + align:start position:0% +subtly hinted to I think by your + + + align:start position:0% +subtly hinted to I think by your +spokesperson so this + + align:start position:0% +spokesperson so this + + + align:start position:0% +spokesperson so this +staircase or whatever it is you said you + + align:start position:0% +staircase or whatever it is you said you + + + align:start position:0% +staircase or whatever it is you said you +turned it into an escalator I think by + + align:start position:0% +turned it into an escalator I think by + + + align:start position:0% +turned it into an escalator I think by +default but uh this thing could wind its + + align:start position:0% +default but uh this thing could wind its + + + align:start position:0% +default but uh this thing could wind its +way through that space as well different + + align:start position:0% +way through that space as well different + + + align:start position:0% +way through that space as well different +but there's a one that goes it was went + + align:start position:0% +but there's a one that goes it was went + + + align:start position:0% +but there's a one that goes it was went +through that um and therefore you could + + align:start position:0% +through that um and therefore you could + + + align:start position:0% +through that um and therefore you could +sense that space more this is more like + + align:start position:0% +sense that space more this is more like + + + align:start position:0% +sense that space more this is more like +going to get to your airplane you know + + align:start position:0% +going to get to your airplane you know + + + align:start position:0% +going to get to your airplane you know +with your baggage on it you're going up + + align:start position:0% +with your baggage on it you're going up + + + align:start position:0% +with your baggage on it you're going up +something to it doesn't have that + + align:start position:0% +something to it doesn't have that + + + align:start position:0% +something to it doesn't have that +feeling so that's like a + + align:start position:0% +feeling so that's like a + + + align:start position:0% +feeling so that's like a +complete um Miss to + + align:start position:0% +complete um Miss to + + + align:start position:0% +complete um Miss to +me the next thing is that I think was + + align:start position:0% +me the next thing is that I think was + + + align:start position:0% +me the next thing is that I think was +ingenious of your spokes person to + + align:start position:0% +ingenious of your spokes person to + + + align:start position:0% +ingenious of your spokes person to +suggest if it's + + align:start position:0% +suggest if it's + + + align:start position:0% +suggest if it's +possible because it's kind of the idea + + align:start position:0% +possible because it's kind of the idea + + + align:start position:0% +possible because it's kind of the idea +of your building Stephanie that the the + + align:start position:0% +of your building Stephanie that the the + + + align:start position:0% +of your building Stephanie that the the +skateboard people are moving through it + + align:start position:0% +skateboard people are moving through it + + + align:start position:0% +skateboard people are moving through it +and under it and out into the copper + + align:start position:0% +and under it and out into the copper + + + align:start position:0% +and under it and out into the copper +tube that was on the other Mel I think + + align:start position:0% +tube that was on the other Mel I think + + + align:start position:0% +tube that was on the other Mel I think +was brilliant suggestion that if there + + align:start position:0% +was brilliant suggestion that if there + + + align:start position:0% +was brilliant suggestion that if there +was a way that this thing could move out + + align:start position:0% +was a way that this thing could move out + + + align:start position:0% +was a way that this thing could move out +of the building maybe a little + + align:start position:0% +of the building maybe a little + + + align:start position:0% +of the building maybe a little +dangerous and how you make the enclosure + + align:start position:0% +dangerous and how you make the enclosure + + + align:start position:0% +dangerous and how you make the enclosure +there is not clear but it would be + + align:start position:0% +there is not clear but it would be + + + align:start position:0% +there is not clear but it would be +really neat as a rope as a climber um to + + align:start position:0% +really neat as a rope as a climber um to + + + align:start position:0% +really neat as a rope as a climber um to +climb out out of the building if I could + + align:start position:0% +climb out out of the building if I could + + + align:start position:0% +climb out out of the building if I could +do so and I don't know exactly how you + + align:start position:0% +do so and I don't know exactly how you + + + align:start position:0% +do so and I don't know exactly how you +do that mechanically you have to figure + + align:start position:0% +do that mechanically you have to figure + + + align:start position:0% +do that mechanically you have to figure +that out but as opposed to stopping it + + align:start position:0% +that out but as opposed to stopping it + + + align:start position:0% +that out but as opposed to stopping it +just here and therefore the vertical is + + align:start position:0% +just here and therefore the vertical is + + + align:start position:0% +just here and therefore the vertical is +equivalent to the horizontal because + + align:start position:0% +equivalent to the horizontal because + + + align:start position:0% +equivalent to the horizontal because +that's what's happening in the vertical + + align:start position:0% +that's what's happening in the vertical + + + align:start position:0% +that's what's happening in the vertical +now there having said that there's some + + align:start position:0% +now there having said that there's some + + + align:start position:0% +now there having said that there's some +uh technical problems somehow you got to + + align:start position:0% +uh technical problems somehow you got to + + + align:start position:0% +uh technical problems somehow you got to +open things up and close + + align:start position:0% +open things up and close + + + align:start position:0% +open things up and close +them finally + + align:start position:0% +them finally + + + align:start position:0% +them finally +um you get the award for U the least + + align:start position:0% +um you get the award for U the least + + + align:start position:0% +um you get the award for U the least +amount of roof held up by um something + + align:start position:0% +amount of roof held up by um something + + + align:start position:0% +amount of roof held up by um something +that we don't know I mean the roof is is + + align:start position:0% +that we don't know I mean the roof is is + + + align:start position:0% +that we don't know I mean the roof is is +uh is is going to fly away it's very + + align:start position:0% +uh is is going to fly away it's very + + + align:start position:0% +uh is is going to fly away it's very +thin it's very flimsy and there is this + + align:start position:0% +thin it's very flimsy and there is this + + + align:start position:0% +thin it's very flimsy and there is this +we get feeling anchored back this one is + + align:start position:0% +we get feeling anchored back this one is + + + align:start position:0% +we get feeling anchored back this one is +not + + align:start position:0% +not + + + align:start position:0% +not +connected uh and it's so small actually + + align:start position:0% +connected uh and it's so small actually + + + align:start position:0% +connected uh and it's so small actually +all the horizontal planes are probably + + align:start position:0% +all the horizontal planes are probably + + + align:start position:0% +all the horizontal planes are probably +under scale in this but + + align:start position:0% +under scale in this but + + + align:start position:0% +under scale in this but +particularly uh the connection between + + align:start position:0% +particularly uh the connection between + + + align:start position:0% +particularly uh the connection between +the RO the gracefulness of that + + align:start position:0% +the RO the gracefulness of that + + + align:start position:0% +the RO the gracefulness of that +roof which has got some size to it it's + + align:start position:0% +roof which has got some size to it it's + + + align:start position:0% +roof which has got some size to it it's +not just it's got to be a little bit + + align:start position:0% +not just it's got to be a little bit + + + align:start position:0% +not just it's got to be a little bit +more than that yeah uh just for like + + align:start position:0% +more than that yeah uh just for like + + + align:start position:0% +more than that yeah uh just for like +model making purposes I couldn't get + + align:start position:0% +model making purposes I couldn't get + + + align:start position:0% +model making purposes I couldn't get +them to glue to the glass but really + + align:start position:0% +them to glue to the glass but really + + + align:start position:0% +them to glue to the glass but really +it's like it'll have plastic and then + + align:start position:0% +it's like it'll have plastic and then + + + align:start position:0% +it's like it'll have plastic and then +this is a structure and then plastic on + + align:start position:0% +this is a structure and then plastic on + + + align:start position:0% +this is a structure and then plastic on +the other side sandwiched and they + + align:start position:0% +the other side sandwiched and they + + + align:start position:0% +the other side sandwiched and they +wouldn't be flat either so I just didn't + + align:start position:0% +wouldn't be flat either so I just didn't + + + align:start position:0% +wouldn't be flat either so I just didn't +give them so they I didn't have to have + + align:start position:0% +give them so they I didn't have to have + + + align:start position:0% +give them so they I didn't have to have +them on there and be unslightly just + + align:start position:0% +them on there and be unslightly just + + + align:start position:0% +them on there and be unslightly just +like cure glass roof and this would + + align:start position:0% +like cure glass roof and this would + + + align:start position:0% +like cure glass roof and this would +almost be like the yeah yeah right well + + align:start position:0% +almost be like the yeah yeah right well + + + align:start position:0% +almost be like the yeah yeah right well +then if that's the case I still think + + align:start position:0% +then if that's the case I still think + + + align:start position:0% +then if that's the case I still think +that as a detail where the column is + + align:start position:0% +that as a detail where the column is + + + align:start position:0% +that as a detail where the column is +hitting this this gets filled in and + + align:start position:0% +hitting this this gets filled in and + + + align:start position:0% +hitting this this gets filled in and +it's taking the weight mm and not it's + + align:start position:0% +it's taking the weight mm and not it's + + + align:start position:0% +it's taking the weight mm and not it's +not always stream light I can't do it + + align:start position:0% + + + + align:start position:0% + +back I don't + + align:start position:0% +back I don't + + + align:start position:0% +back I don't +know I think you had a pointy + + align:start position:0% +know I think you had a pointy + + + align:start position:0% +know I think you had a pointy +thing + + align:start position:0% +thing + + + align:start position:0% +thing +yeah but now the other thing I just want + + align:start position:0% +yeah but now the other thing I just want + + + align:start position:0% +yeah but now the other thing I just want +to mention that once again and again I + + align:start position:0% +to mention that once again and again I + + + align:start position:0% +to mention that once again and again I +think this may be your topic this + + align:start position:0% +think this may be your topic this + + + align:start position:0% +think this may be your topic this +afternoon is there's so much more that + + align:start position:0% +afternoon is there's so much more that + + + align:start position:0% +afternoon is there's so much more that +could be done with the facade on this + + align:start position:0% +could be done with the facade on this + + + align:start position:0% +could be done with the facade on this +one also where there are just complete + + align:start position:0% +one also where there are just complete + + + align:start position:0% +one also where there are just complete +planes of glass which you probably want + + align:start position:0% +planes of glass which you probably want + + + align:start position:0% +planes of glass which you probably want +in + + align:start position:0% +in + + + align:start position:0% +in +cases um you may have overdone it there + + align:start position:0% +cases um you may have overdone it there + + + align:start position:0% +cases um you may have overdone it there +could be places where you could break + + align:start position:0% +could be places where you could break + + + align:start position:0% +could be places where you could break +this down even more um that is it could + + align:start position:0% +this down even more um that is it could + + + align:start position:0% +this down even more um that is it could +be a upper level for light to come in + + align:start position:0% +be a upper level for light to come in + + + align:start position:0% +be a upper level for light to come in +even the notion of light shelves are + + align:start position:0% +even the notion of light shelves are + + + align:start position:0% +even the notion of light shelves are +bouncing light in and then a lower level + + align:start position:0% +bouncing light in and then a lower level + + + align:start position:0% +bouncing light in and then a lower level +mhm so these are relatively simplistic + + align:start position:0% +mhm so these are relatively simplistic + + + align:start position:0% +mhm so these are relatively simplistic +kinds + + align:start position:0% +kinds + + + align:start position:0% +kinds +of uh facade + + align:start position:0% +of uh facade + + + align:start position:0% +of uh facade +definitions but it's beautiful it's a + + align:start position:0% +definitions but it's beautiful it's a + + + align:start position:0% +definitions but it's beautiful it's a +great start the uh challenge for both of + + align:start position:0% +great start the uh challenge for both of + + + align:start position:0% +great start the uh challenge for both of +these is how to keep this + + align:start position:0% +these is how to keep this + + + align:start position:0% +these is how to keep this +building this wonderful uh transparency + + align:start position:0% +building this wonderful uh transparency + + + align:start position:0% +building this wonderful uh transparency +that you have that's + + align:start position:0% +that you have that's + + + align:start position:0% +that you have that's +inviting but at the same time + + align:start position:0% +inviting but at the same time + + + align:start position:0% +inviting but at the same time +control controlling light and access a + + align:start position:0% +control controlling light and access a + + + align:start position:0% +control controlling light and access a +little bit more again that is not like a + + align:start position:0% +little bit more again that is not like a + + + align:start position:0% +little bit more again that is not like a +major change that you're in the all of + + align:start position:0% +major change that you're in the all of + + + align:start position:0% +major change that you're in the all of +you are in the area of minor changes as + + align:start position:0% +you are in the area of minor changes as + + + align:start position:0% +you are in the area of minor changes as +opposed to + + align:start position:0% + + + + align:start position:0% + +Major \ No newline at end of file diff --git a/44mSNs6kl8c.txt b/44mSNs6kl8c.txt new file mode 100644 index 0000000000000000000000000000000000000000..ccd92857773d9f74c64e6eb0b9dcd07ff9e89b40 --- /dev/null +++ b/44mSNs6kl8c.txt @@ -0,0 +1,8274 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open coreware in general + + align:start position:0% +license and MIT open coreware in general + + + align:start position:0% +license and MIT open coreware in general +is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so um we're going to finish + + align:start position:0% +ocw.mit.edu so um we're going to finish + + + align:start position:0% +ocw.mit.edu so um we're going to finish +up uh acidbase + + align:start position:0% +up uh acidbase + + + align:start position:0% +up uh acidbase +titration stuff today and I think it's + + align:start position:0% +titration stuff today and I think it's + + + align:start position:0% +titration stuff today and I think it's +actually most of you have probably + + align:start position:0% +actually most of you have probably + + + align:start position:0% +actually most of you have probably +ventured into the problem set which is + + align:start position:0% +ventured into the problem set which is + + + align:start position:0% +ventured into the problem set which is +great um I think the best way to learn + + align:start position:0% +great um I think the best way to learn + + + align:start position:0% +great um I think the best way to learn +acid-based titrations is usually you + + align:start position:0% +acid-based titrations is usually you + + + align:start position:0% +acid-based titrations is usually you +hear a little bit about acid-based + + align:start position:0% +hear a little bit about acid-based + + + align:start position:0% +hear a little bit about acid-based +titrations then sit down and try to do + + align:start position:0% +titrations then sit down and try to do + + + align:start position:0% +titrations then sit down and try to do +problems go back and revisit uh how to + + align:start position:0% +problems go back and revisit uh how to + + + align:start position:0% +problems go back and revisit uh how to +do the problems and then try it again + + align:start position:0% +do the problems and then try it again + + + align:start position:0% +do the problems and then try it again +this is one of the units where you + + align:start position:0% +this is one of the units where you + + + align:start position:0% +this is one of the units where you +really can't learn how to do it by just + + align:start position:0% +really can't learn how to do it by just + + + align:start position:0% +really can't learn how to do it by just +sort of listening to a lecture you have + + align:start position:0% +sort of listening to a lecture you have + + + align:start position:0% +sort of listening to a lecture you have +to sit down and work numerous problems + + align:start position:0% +to sit down and work numerous problems + + + align:start position:0% +to sit down and work numerous problems +so um that may be true in other units + + align:start position:0% +so um that may be true in other units + + + align:start position:0% +so um that may be true in other units +but I think it's particularly true in + + align:start position:0% +but I think it's particularly true in + + + align:start position:0% +but I think it's particularly true in +this one that it's all about practicing + + align:start position:0% +this one that it's all about practicing + + + align:start position:0% +this one that it's all about practicing +doing the problems so it's really + + align:start position:0% +doing the problems so it's really + + + align:start position:0% +doing the problems so it's really +important to work through a number of + + align:start position:0% +important to work through a number of + + + align:start position:0% +important to work through a number of +them and you'll have uh other + + align:start position:0% +them and you'll have uh other + + + align:start position:0% +them and you'll have uh other +opportunities of course this will be + + align:start position:0% +opportunities of course this will be + + + align:start position:0% +opportunities of course this will be +material on exam three but um also + + align:start position:0% +material on exam three but um also + + + align:start position:0% +material on exam three but um also +acidbase titrations always makes an + + align:start position:0% +acidbase titrations always makes an + + + align:start position:0% +acidbase titrations always makes an +appearance on the final so um it will be + + align:start position:0% +appearance on the final so um it will be + + + align:start position:0% +appearance on the final so um it will be +well worth your time to work these + + align:start position:0% +well worth your time to work these + + + align:start position:0% +well worth your time to work these +problems they'll be worth a number of + + align:start position:0% +problems they'll be worth a number of + + + align:start position:0% +problems they'll be worth a number of +points for the rest of the semester and + + align:start position:0% +points for the rest of the semester and + + + align:start position:0% +points for the rest of the semester and +as I said you'll see all this + + align:start position:0% +as I said you'll see all this + + + align:start position:0% +as I said you'll see all this +information again um in organic + + align:start position:0% +information again um in organic + + + align:start position:0% +information again um in organic +chemistry and biochemistry and a lot of + + align:start position:0% +chemistry and biochemistry and a lot of + + + align:start position:0% +chemistry and biochemistry and a lot of +other courses that you take you talk + + align:start position:0% +other courses that you take you talk + + + align:start position:0% +other courses that you take you talk +about PKA and buffers and biology you'll + + align:start position:0% +about PKA and buffers and biology you'll + + + align:start position:0% +about PKA and buffers and biology you'll +see all this + + align:start position:0% +see all this + + + align:start position:0% +see all this +again all right so we were talking about + + align:start position:0% +again all right so we were talking about + + + align:start position:0% +again all right so we were talking about +the titration of a weak acid with a + + align:start position:0% +the titration of a weak acid with a + + + align:start position:0% +the titration of a weak acid with a +strong base and we went through uh this + + align:start position:0% +strong base and we went through uh this + + + align:start position:0% +strong base and we went through uh this +figure on on Monday and uh the + + align:start position:0% +figure on on Monday and uh the + + + align:start position:0% +figure on on Monday and uh the +particular problem that that we were + + align:start position:0% +particular problem that that we were + + + align:start position:0% +particular problem that that we were +working so we're going to go through and + + align:start position:0% +working so we're going to go through and + + + align:start position:0% +working so we're going to go through and +look at different time points along the + + align:start position:0% +look at different time points along the + + + align:start position:0% +look at different time points along the +titration and calculate what the pH is + + align:start position:0% +titration and calculate what the pH is + + + align:start position:0% +titration and calculate what the pH is +and the problem we were we were working + + align:start position:0% +and the problem we were we were working + + + align:start position:0% +and the problem we were we were working +was 25 Ms of A.1 molar solution of a + + align:start position:0% +was 25 Ms of A.1 molar solution of a + + + align:start position:0% +was 25 Ms of A.1 molar solution of a +weak acid titrated with a strong base in + + align:start position:0% +weak acid titrated with a strong base in + + + align:start position:0% +weak acid titrated with a strong base in +this case NaOH and that was 0.15 molar + + align:start position:0% +this case NaOH and that was 0.15 molar + + + align:start position:0% +this case NaOH and that was 0.15 molar +and you were given the KA for the weak + + align:start position:0% +and you were given the KA for the weak + + + align:start position:0% +and you were given the KA for the weak +acid in this + + align:start position:0% +acid in this + + + align:start position:0% +acid in this +problem so um we had done one time + + align:start position:0% +problem so um we had done one time + + + align:start position:0% +problem so um we had done one time +point and that was at the initial time + + align:start position:0% +point and that was at the initial time + + + align:start position:0% +point and that was at the initial time +point when no strong base had been added + + align:start position:0% +point when no strong base had been added + + + align:start position:0% +point when no strong base had been added +yet so let me just put that down so + + align:start position:0% +yet so let me just put that down so + + + align:start position:0% +yet so let me just put that down so +we're plotting the volume of the strong + + align:start position:0% +we're plotting the volume of the strong + + + align:start position:0% +we're plotting the volume of the strong +base that's added versus + + align:start position:0% +base that's added versus + + + align:start position:0% +base that's added versus +pH and we had one time point and that + + align:start position:0% +pH and we had one time point and that + + + align:start position:0% +pH and we had one time point and that +was a pH of 2. + + align:start position:0% +was a pH of 2. + + + align:start position:0% +was a pH of 2. +38 and that was at when there were zero + + align:start position:0% +38 and that was at when there were zero + + + align:start position:0% +38 and that was at when there were zero +Ms of the strong base added so just the + + align:start position:0% +Ms of the strong base added so just the + + + align:start position:0% +Ms of the strong base added so just the +pH of the weak acid in water was 2.38 + + align:start position:0% +pH of the weak acid in water was 2.38 + + + align:start position:0% +pH of the weak acid in water was 2.38 +for pH and then we had started + + align:start position:0% +for pH and then we had started + + + align:start position:0% +for pH and then we had started +calculating what happens at five Ms when + + align:start position:0% +calculating what happens at five Ms when + + + align:start position:0% +calculating what happens at five Ms when +five Ms of the strong base is added and + + align:start position:0% +five Ms of the strong base is added and + + + align:start position:0% +five Ms of the strong base is added and +that's this time Point here so here + + align:start position:0% +that's this time Point here so here + + + align:start position:0% +that's this time Point here so here +we're in between zero and the volume at + + align:start position:0% +we're in between zero and the volume at + + + align:start position:0% +we're in between zero and the volume at +the equivalence point and we have the + + align:start position:0% +the equivalence point and we have the + + + align:start position:0% +the equivalence point and we have the +five + + align:start position:0% +five + + + align:start position:0% +five +Ms so let me just review we talked about + + align:start position:0% +Ms so let me just review we talked about + + + align:start position:0% +Ms so let me just review we talked about +this right at the end of class so the + + align:start position:0% +this right at the end of class so the + + + align:start position:0% +this right at the end of class so the +first uh step in doing this type of + + align:start position:0% +first uh step in doing this type of + + + align:start position:0% +first uh step in doing this type of +problem is to figure out many moles of + + align:start position:0% +problem is to figure out many moles of + + + align:start position:0% +problem is to figure out many moles of +both the weak acid that you have in the + + align:start position:0% +both the weak acid that you have in the + + + align:start position:0% +both the weak acid that you have in the +problem and the number of moles of + + align:start position:0% +problem and the number of moles of + + + align:start position:0% +problem and the number of moles of +strong base that have been added so far + + align:start position:0% +strong base that have been added so far + + + align:start position:0% +strong base that have been added so far +so for the acid there was 25 Ms + + align:start position:0% +so for the acid there was 25 Ms + + + align:start position:0% +so for the acid there was 25 Ms +originally of 0.1 molar solution so 2.5 + + align:start position:0% +originally of 0.1 molar solution so 2.5 + + + align:start position:0% +originally of 0.1 molar solution so 2.5 +* 10 to Theus 3 moles of the weak acid + + align:start position:0% +* 10 to Theus 3 moles of the weak acid + + + align:start position:0% +* 10 to Theus 3 moles of the weak acid +and for the strong base now we've added + + align:start position:0% +and for the strong base now we've added + + + align:start position:0% +and for the strong base now we've added +five Ms and the of a .15 molar + + align:start position:0% +five Ms and the of a .15 molar + + + align:start position:0% +five Ms and the of a .15 molar +concentration so so far we've added 75 * + + align:start position:0% +concentration so so far we've added 75 * + + + align:start position:0% +concentration so so far we've added 75 * +10 to the minus 3 moles so this strong + + align:start position:0% +10 to the minus 3 moles so this strong + + + align:start position:0% +10 to the minus 3 moles so this strong +base will react with the acid it'll pull + + align:start position:0% +base will react with the acid it'll pull + + + align:start position:0% +base will react with the acid it'll pull +off a hydrogen ion or a proton from the + + align:start position:0% +off a hydrogen ion or a proton from the + + + align:start position:0% +off a hydrogen ion or a proton from the +weak acid and convert it to its + + align:start position:0% +weak acid and convert it to its + + + align:start position:0% +weak acid and convert it to its +conjugate base so now we need to figure + + align:start position:0% +conjugate base so now we need to figure + + + align:start position:0% +conjugate base so now we need to figure +out how much we have left after this + + align:start position:0% +out how much we have left after this + + + align:start position:0% +out how much we have left after this +reaction so we had 2.5 * 10us 3 moles of + + align:start position:0% +reaction so we had 2.5 * 10us 3 moles of + + + align:start position:0% +reaction so we had 2.5 * 10us 3 moles of +the weak acid we've now used converted + + align:start position:0% +the weak acid we've now used converted + + + align:start position:0% +the weak acid we've now used converted +over 75 * 10us 3 moles so we have 1.75 * + + align:start position:0% +over 75 * 10us 3 moles so we have 1.75 * + + + align:start position:0% +over 75 * 10us 3 moles so we have 1.75 * +10us 3 moles of the acid left and now we + + align:start position:0% +10us 3 moles of the acid left and now we + + + align:start position:0% +10us 3 moles of the acid left and now we +formed 75 * 10us 3 moles of the + + align:start position:0% +formed 75 * 10us 3 moles of the + + + align:start position:0% +formed 75 * 10us 3 moles of the +conjugate so 75 minus um time 10us 3 + + align:start position:0% +conjugate so 75 minus um time 10us 3 + + + align:start position:0% +conjugate so 75 minus um time 10us 3 +moles have been converted from acid to + + align:start position:0% +moles have been converted from acid to + + + align:start position:0% +moles have been converted from acid to +the conjugate base now we need to know + + align:start position:0% +the conjugate base now we need to know + + + align:start position:0% +the conjugate base now we need to know +the Mari of those amounts so we take the + + align:start position:0% +the Mari of those amounts so we take the + + + align:start position:0% +the Mari of those amounts so we take the +weak acid uh the number of moles divided + + align:start position:0% +weak acid uh the number of moles divided + + + align:start position:0% +weak acid uh the number of moles divided +by the total volume now which is 25 plus + + align:start position:0% +by the total volume now which is 25 plus + + + align:start position:0% +by the total volume now which is 25 plus +the five we just added or 30 milliliters + + align:start position:0% +the five we just added or 30 milliliters + + + align:start position:0% +the five we just added or 30 milliliters +and we have a concentration and then we + + align:start position:0% +and we have a concentration and then we + + + align:start position:0% +and we have a concentration and then we +do the same with the weak base number of + + align:start position:0% +do the same with the weak base number of + + + align:start position:0% +do the same with the weak base number of +moles that we have uh divided by the new + + align:start position:0% +moles that we have uh divided by the new + + + align:start position:0% +moles that we have uh divided by the new +volume gives you the + + align:start position:0% +volume gives you the + + + align:start position:0% +volume gives you the +marity so right at the end of class we + + align:start position:0% +marity so right at the end of class we + + + align:start position:0% +marity so right at the end of class we +said that okay the next thing you can do + + align:start position:0% +said that okay the next thing you can do + + + align:start position:0% +said that okay the next thing you can do +there are two different options one + + align:start position:0% +there are two different options one + + + align:start position:0% +there are two different options one +option which we talked about was set up + + align:start position:0% +option which we talked about was set up + + + align:start position:0% +option which we talked about was set up +this little equilibrium table and the + + align:start position:0% +this little equilibrium table and the + + + align:start position:0% +this little equilibrium table and the +important point to remember and when you + + align:start position:0% +important point to remember and when you + + + align:start position:0% +important point to remember and when you +set this up is that you have the weak + + align:start position:0% +set this up is that you have the weak + + + align:start position:0% +set this up is that you have the weak +acid and its conjugate over here and the + + align:start position:0% +acid and its conjugate over here and the + + + align:start position:0% +acid and its conjugate over here and the +other problem when you just have a weak + + align:start position:0% +other problem when you just have a weak + + + align:start position:0% +other problem when you just have a weak +acid in water problem you just have the + + align:start position:0% +acid in water problem you just have the + + + align:start position:0% +acid in water problem you just have the +weak acid or if you have a weak base in + + align:start position:0% +weak acid or if you have a weak base in + + + align:start position:0% +weak acid or if you have a weak base in +water problem you just start with a weak + + align:start position:0% +water problem you just start with a weak + + + align:start position:0% +water problem you just start with a weak +base but here this is really like a + + align:start position:0% +base but here this is really like a + + + align:start position:0% +base but here this is really like a +buffer problem you have both the acid + + align:start position:0% +buffer problem you have both the acid + + + align:start position:0% +buffer problem you have both the acid +and its conjugate to some amount so you + + align:start position:0% +and its conjugate to some amount so you + + + align:start position:0% +and its conjugate to some amount so you +need to put things on both sides so we'd + + align:start position:0% +need to put things on both sides so we'd + + + align:start position:0% +need to put things on both sides so we'd +come up with a pH of + + align:start position:0% +come up with a pH of + + + align:start position:0% +come up with a pH of +3.38 and you have to you know set up + + align:start position:0% +3.38 and you have to you know set up + + + align:start position:0% +3.38 and you have to you know set up +using Ka uh check your assumptions + + align:start position:0% +using Ka uh check your assumptions + + + align:start position:0% +using Ka uh check your assumptions +calculate pH so there's another way that + + align:start position:0% +calculate pH so there's another way that + + + align:start position:0% +calculate pH so there's another way that +you can do this particular problem and + + align:start position:0% +you can do this particular problem and + + + align:start position:0% +you can do this particular problem and +that's option two the first part is the + + align:start position:0% +that's option two the first part is the + + + align:start position:0% +that's option two the first part is the +same you have to do all the calculations + + align:start position:0% +same you have to do all the calculations + + + align:start position:0% +same you have to do all the calculations +of the number of moles and calculate + + align:start position:0% +of the number of moles and calculate + + + align:start position:0% +of the number of moles and calculate +marity uh the second part is different + + align:start position:0% +marity uh the second part is different + + + align:start position:0% +marity uh the second part is different +instead of setting up that equilibrium + + align:start position:0% +instead of setting up that equilibrium + + + align:start position:0% +instead of setting up that equilibrium +table you can use the Henderson hosbach + + align:start position:0% +table you can use the Henderson hosbach + + + align:start position:0% +table you can use the Henderson hosbach +equation so in this case you need to + + align:start position:0% +equation so in this case you need to + + + align:start position:0% +equation so in this case you need to +know PKA and you know Ka so you take the + + align:start position:0% +know PKA and you know Ka so you take the + + + align:start position:0% +know PKA and you know Ka so you take the +minus log of Ka to get PKA and then you + + align:start position:0% +minus log of Ka to get PKA and then you + + + align:start position:0% +minus log of Ka to get PKA and then you +can fill in your concentration your + + align:start position:0% +can fill in your concentration your + + + align:start position:0% +can fill in your concentration your +concentration of the weak acid and the + + align:start position:0% +concentration of the weak acid and the + + + align:start position:0% +concentration of the weak acid and the +concentration of the conjugate base + + align:start position:0% +concentration of the conjugate base + + + align:start position:0% +concentration of the conjugate base +that's formed after the addition of 5 Ms + + align:start position:0% +that's formed after the addition of 5 Ms + + + align:start position:0% +that's formed after the addition of 5 Ms +uh and then you can calculate and you + + align:start position:0% +uh and then you can calculate and you + + + align:start position:0% +uh and then you can calculate and you +should definitely get the same pH out of + + align:start position:0% +should definitely get the same pH out of + + + align:start position:0% +should definitely get the same pH out of +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +3.38 now this equation the Henderson + + align:start position:0% +3.38 now this equation the Henderson + + + align:start position:0% +3.38 now this equation the Henderson +hosbach equation only works with the + + align:start position:0% +hosbach equation only works with the + + + align:start position:0% +hosbach equation only works with the +assumption that X is small so that 5% + + align:start position:0% +assumption that X is small so that 5% + + + align:start position:0% +assumption that X is small so that 5% +rule that we talked about and that's + + align:start position:0% +rule that we talked about and that's + + + align:start position:0% +rule that we talked about and that's +because in the Henderson hosbach + + align:start position:0% +because in the Henderson hosbach + + + align:start position:0% +because in the Henderson hosbach +equation if you remember back we're + + align:start position:0% +equation if you remember back we're + + + align:start position:0% +equation if you remember back we're +making an assumption so we're assuming + + align:start position:0% +making an assumption so we're assuming + + + align:start position:0% +making an assumption so we're assuming +that the initial concentrations that we + + align:start position:0% +that the initial concentrations that we + + + align:start position:0% +that the initial concentrations that we +have are the same as the concentrations + + align:start position:0% +have are the same as the concentrations + + + align:start position:0% +have are the same as the concentrations +we have at equilibrium which is + + align:start position:0% +we have at equilibrium which is + + + align:start position:0% +we have at equilibrium which is +basically saying X is small so you can + + align:start position:0% +basically saying X is small so you can + + + align:start position:0% +basically saying X is small so you can +only use it if x is in fact small and so + + align:start position:0% +only use it if x is in fact small and so + + + align:start position:0% +only use it if x is in fact small and so +the way that you would check in this + + align:start position:0% +the way that you would check in this + + + align:start position:0% +the way that you would check in this +case is you have to back calculate so + + align:start position:0% +case is you have to back calculate so + + + align:start position:0% +case is you have to back calculate so +you know your answer your pH answer and + + align:start position:0% +you know your answer your pH answer and + + + align:start position:0% +you know your answer your pH answer and +then you have to calculate then what the + + align:start position:0% +then you have to calculate then what the + + + align:start position:0% +then you have to calculate then what the +Hy hydronium ion concentration was which + + align:start position:0% +Hy hydronium ion concentration was which + + + align:start position:0% +Hy hydronium ion concentration was which +is easy because pH just equals minus log + + align:start position:0% +is easy because pH just equals minus log + + + align:start position:0% +is easy because pH just equals minus log +of hydronium ion concentration and so + + align:start position:0% +of hydronium ion concentration and so + + + align:start position:0% +of hydronium ion concentration and so +you can get this answer out and then you + + align:start position:0% +you can get this answer out and then you + + + align:start position:0% +you can get this answer out and then you +take this and then you divide by uh + + align:start position:0% +take this and then you divide by uh + + + align:start position:0% +take this and then you divide by uh +these either of these two I mean you + + align:start position:0% +these either of these two I mean you + + + align:start position:0% +these either of these two I mean you +want to use really the smaller one or + + align:start position:0% +want to use really the smaller one or + + + align:start position:0% +want to use really the smaller one or +both of them and see is X small um and + + align:start position:0% +both of them and see is X small um and + + + align:start position:0% +both of them and see is X small um and +in this case both of those are less than + + align:start position:0% +in this case both of those are less than + + + align:start position:0% +in this case both of those are less than +5% so 4.2 * 10us 4 is less than 5% of + + align:start position:0% +5% so 4.2 * 10us 4 is less than 5% of + + + align:start position:0% +5% so 4.2 * 10us 4 is less than 5% of +this number and of this number so that + + align:start position:0% +this number and of this number so that + + + align:start position:0% +this number and of this number so that +assumption is okay if it wasn't okay you + + align:start position:0% +assumption is okay if it wasn't okay you + + + align:start position:0% +assumption is okay if it wasn't okay you +would have to have used option one and + + align:start position:0% +would have to have used option one and + + + align:start position:0% +would have to have used option one and +used the quadratic equation equation so + + align:start position:0% +used the quadratic equation equation so + + + align:start position:0% +used the quadratic equation equation so +if X is not small the only way you can + + align:start position:0% +if X is not small the only way you can + + + align:start position:0% +if X is not small the only way you can +do it is option one with quadratic but + + align:start position:0% +do it is option one with quadratic but + + + align:start position:0% +do it is option one with quadratic but +most of the time x is small because + + align:start position:0% +most of the time x is small because + + + align:start position:0% +most of the time x is small because +we're talking about weak acids and bases + + align:start position:0% +we're talking about weak acids and bases + + + align:start position:0% +we're talking about weak acids and bases +and a lot of people find the Henderson + + align:start position:0% +and a lot of people find the Henderson + + + align:start position:0% +and a lot of people find the Henderson +hosbach a faster way to get the answer + + align:start position:0% +hosbach a faster way to get the answer + + + align:start position:0% +hosbach a faster way to get the answer +and as you know you're doing these + + align:start position:0% +and as you know you're doing these + + + align:start position:0% +and as you know you're doing these +problem set you realize these problems + + align:start position:0% +problem set you realize these problems + + + align:start position:0% +problem set you realize these problems +take take a while to do and on a + + align:start position:0% +take take a while to do and on a + + + align:start position:0% +take take a while to do and on a +50-minute exam uh part of the uh the + + align:start position:0% +50-minute exam uh part of the uh the + + + align:start position:0% +50-minute exam uh part of the uh the +process and thinking about how to do + + align:start position:0% +process and thinking about how to do + + + align:start position:0% +process and thinking about how to do +these problems would be how can I do the + + align:start position:0% +these problems would be how can I do the + + + align:start position:0% +these problems would be how can I do the +problem the fastest uh to get to get it + + align:start position:0% +problem the fastest uh to get to get it + + + align:start position:0% +problem the fastest uh to get to get it +done and a lot of people find this to be + + align:start position:0% +done and a lot of people find this to be + + + align:start position:0% +done and a lot of people find this to be +a little bit of a faster way to do it um + + align:start position:0% +a little bit of a faster way to do it um + + + align:start position:0% +a little bit of a faster way to do it um +Henderson hasselbach only works for + + align:start position:0% +Henderson hasselbach only works for + + + align:start position:0% +Henderson hasselbach only works for +buffers so it only works under + + align:start position:0% +buffers so it only works under + + + align:start position:0% +buffers so it only works under +conditions where you have you're + + align:start position:0% +conditions where you have you're + + + align:start position:0% +conditions where you have you're +starting with an acid in its conjugate + + align:start position:0% +starting with an acid in its conjugate + + + align:start position:0% +starting with an acid in its conjugate +base or base in its conjugate AET so + + align:start position:0% +base or base in its conjugate AET so + + + align:start position:0% +base or base in its conjugate AET so +only in the buffer region will Henderson + + align:start position:0% +only in the buffer region will Henderson + + + align:start position:0% +only in the buffer region will Henderson +hosel boach apply but when it does apply + + align:start position:0% +hosel boach apply but when it does apply + + + align:start position:0% +hosel boach apply but when it does apply +you should think about using + + align:start position:0% +you should think about using + + + align:start position:0% +you should think about using +it all right so let's put our our other + + align:start position:0% +it all right so let's put our our other + + + align:start position:0% +it all right so let's put our our other +uh ph up here so after we've + + align:start position:0% +uh ph up here so after we've + + + align:start position:0% +uh ph up here so after we've +added five + + align:start position:0% +added five + + + align:start position:0% +added five +Ms then we have a pH of + + align:start position:0% +Ms then we have a pH of + + + align:start position:0% +Ms then we have a pH of + + align:start position:0% + + + + align:start position:0% + +38 okay now we reach to a special Point + + align:start position:0% +38 okay now we reach to a special Point + + + align:start position:0% +38 okay now we reach to a special Point +called the half equivalence point so + + align:start position:0% +called the half equivalence point so + + + align:start position:0% +called the half equivalence point so +this is right in the middle of this + + align:start position:0% +this is right in the middle of this + + + align:start position:0% +this is right in the middle of this +buffering region + + align:start position:0% +buffering region + + + align:start position:0% +buffering region +and again the buffering region is the + + align:start position:0% +and again the buffering region is the + + + align:start position:0% +and again the buffering region is the +part of the curve that's flat where + + align:start position:0% +part of the curve that's flat where + + + align:start position:0% +part of the curve that's flat where +you're adding your strong base but it's + + align:start position:0% +you're adding your strong base but it's + + + align:start position:0% +you're adding your strong base but it's +not changing the pH very much because + + align:start position:0% +not changing the pH very much because + + + align:start position:0% +not changing the pH very much because +the solution is being buffered so the pH + + align:start position:0% +the solution is being buffered so the pH + + + align:start position:0% +the solution is being buffered so the pH +is staying the same so it's the flat + + align:start position:0% +is staying the same so it's the flat + + + align:start position:0% +is staying the same so it's the flat +part of the curve and right in the + + align:start position:0% +part of the curve and right in the + + + align:start position:0% +part of the curve and right in the +middle of the flat part um you find the + + align:start position:0% +middle of the flat part um you find the + + + align:start position:0% +middle of the flat part um you find the +half equivalence point so that's when + + align:start position:0% +half equivalence point so that's when + + + align:start position:0% +half equivalence point so that's when +you've added in this case half the + + align:start position:0% +you've added in this case half the + + + align:start position:0% +you've added in this case half the +amount of the strong base that you need + + align:start position:0% +amount of the strong base that you need + + + align:start position:0% +amount of the strong base that you need +to reach the equivalence point so at the + + align:start position:0% +to reach the equivalence point so at the + + + align:start position:0% +to reach the equivalence point so at the +equivalence point the number of moles of + + align:start position:0% +equivalence point the number of moles of + + + align:start position:0% +equivalence point the number of moles of +strong base are equal to the number of + + align:start position:0% +strong base are equal to the number of + + + align:start position:0% +strong base are equal to the number of +moles of weak acid you had to begin with + + align:start position:0% +moles of weak acid you had to begin with + + + align:start position:0% +moles of weak acid you had to begin with +at the half equivalence point you've + + align:start position:0% +at the half equivalence point you've + + + align:start position:0% +at the half equivalence point you've +converted half over to the conjugate + + align:start position:0% +converted half over to the conjugate + + + align:start position:0% +converted half over to the conjugate +base so you have the half of the acid + + align:start position:0% +base so you have the half of the acid + + + align:start position:0% +base so you have the half of the acid +you started with and half of it's being + + align:start position:0% +you started with and half of it's being + + + align:start position:0% +you started with and half of it's being +converted so this is in the buffering + + align:start position:0% +converted so this is in the buffering + + + align:start position:0% +converted so this is in the buffering +region and so you can use the Henderson + + align:start position:0% +region and so you can use the Henderson + + + align:start position:0% +region and so you can use the Henderson +hasselbach equation and you see if you + + align:start position:0% +hasselbach equation and you see if you + + + align:start position:0% +hasselbach equation and you see if you +plugged in um values into here and you + + align:start position:0% +plugged in um values into here and you + + + align:start position:0% +plugged in um values into here and you +would have equal amounts of these two + + align:start position:0% +would have equal amounts of these two + + + align:start position:0% +would have equal amounts of these two +you've converted half the amount so you + + align:start position:0% +you've converted half the amount so you + + + align:start position:0% +you've converted half the amount so you +have half the this and half that and uh + + align:start position:0% +have half the this and half that and uh + + + align:start position:0% +have half the this and half that and uh +you solve the log you find this term + + align:start position:0% +you solve the log you find this term + + + align:start position:0% +you solve the log you find this term +drops out and so pH just equals + + align:start position:0% +drops out and so pH just equals + + + align:start position:0% +drops out and so pH just equals +PK so if you know the pka and usually + + align:start position:0% +PK so if you know the pka and usually + + + align:start position:0% +PK so if you know the pka and usually +the KA is given so you can easily + + align:start position:0% +the KA is given so you can easily + + + align:start position:0% +the KA is given so you can easily +calculate the pka then that's the pH so + + align:start position:0% +calculate the pka then that's the pH so + + + align:start position:0% +calculate the pka then that's the pH so +the pka um is + + align:start position:0% +the pka um is + + + align:start position:0% +the pka um is +3.75 so that's then also the pH at the + + align:start position:0% +3.75 so that's then also the pH at the + + + align:start position:0% +3.75 so that's then also the pH at the +half equivalence + + align:start position:0% + + + + align:start position:0% + +point + + align:start position:0% + + + + align:start position:0% + +so here would be + + align:start position:0% +so here would be + + + align:start position:0% +so here would be +3.75 at the half equivalence point + + align:start position:0% +3.75 at the half equivalence point + + + align:start position:0% +3.75 at the half equivalence point +now when you when I was mentioning that + + align:start position:0% +now when you when I was mentioning that + + + align:start position:0% +now when you when I was mentioning that +you know on an exam you're going to look + + align:start position:0% +you know on an exam you're going to look + + + align:start position:0% +you know on an exam you're going to look +for fast ways to solve the problem if + + align:start position:0% +for fast ways to solve the problem if + + + align:start position:0% +for fast ways to solve the problem if +you're ask about the pH at a half + + align:start position:0% +you're ask about the pH at a half + + + align:start position:0% +you're ask about the pH at a half +equivalence point you can write phal PKA + + align:start position:0% +equivalence point you can write phal PKA + + + align:start position:0% +equivalence point you can write phal PKA +equal 3.75 that's it it might be a + + align:start position:0% +equal 3.75 that's it it might be a + + + align:start position:0% +equal 3.75 that's it it might be a +number of points question but that's all + + align:start position:0% +number of points question but that's all + + + align:start position:0% +number of points question but that's all +you're looking for and you give the + + align:start position:0% +you're looking for and you give the + + + align:start position:0% +you're looking for and you give the +answer so this is a fast problem + + align:start position:0% +answer so this is a fast problem + + + align:start position:0% +answer so this is a fast problem +so um make sure that you remember this + + align:start position:0% +so um make sure that you remember this + + + align:start position:0% +so um make sure that you remember this +trick you can work it out the long way + + align:start position:0% +trick you can work it out the long way + + + align:start position:0% +trick you can work it out the long way +and figure out the same answer but this + + align:start position:0% +and figure out the same answer but this + + + align:start position:0% +and figure out the same answer but this +is a perfectly acceptable answer to say + + align:start position:0% +is a perfectly acceptable answer to say + + + align:start position:0% +is a perfectly acceptable answer to say +that pH equals PKA equals + + align:start position:0% +that pH equals PKA equals + + + align:start position:0% +that pH equals PKA equals +3.75 so that's a shortcut for doing + + align:start position:0% +3.75 so that's a shortcut for doing + + + align:start position:0% +3.75 so that's a shortcut for doing +these + + align:start position:0% + + + + align:start position:0% + +problems okay then we get to the + + align:start position:0% +problems okay then we get to the + + + align:start position:0% +problems okay then we get to the +equivalence point I mean sometimes you + + align:start position:0% +equivalence point I mean sometimes you + + + align:start position:0% +equivalence point I mean sometimes you +might have here this has Point D also in + + align:start position:0% +might have here this has Point D also in + + + align:start position:0% +might have here this has Point D also in +the curve uh but we'll skip that you + + align:start position:0% +the curve uh but we'll skip that you + + + align:start position:0% +the curve uh but we'll skip that you +would do that problem the same way you + + align:start position:0% +would do that problem the same way you + + + align:start position:0% +would do that problem the same way you +did the problem on the other side of the + + align:start position:0% +did the problem on the other side of the + + + align:start position:0% +did the problem on the other side of the +half equivalence point so we can uh skip + + align:start position:0% +half equivalence point so we can uh skip + + + align:start position:0% +half equivalence point so we can uh skip +over that and move right to the + + align:start position:0% +over that and move right to the + + + align:start position:0% +over that and move right to the +equivalence point so again the + + align:start position:0% +equivalence point so again the + + + align:start position:0% +equivalence point so again the +equivalence point also called the + + align:start position:0% +equivalence point also called the + + + align:start position:0% +equivalence point also called the +stochiometric point is when you have + + align:start position:0% +stochiometric point is when you have + + + align:start position:0% +stochiometric point is when you have +added the amount of strong base the + + align:start position:0% +added the amount of strong base the + + + align:start position:0% +added the amount of strong base the +moles of strong base that are equal to + + align:start position:0% +moles of strong base that are equal to + + + align:start position:0% +moles of strong base that are equal to +the moles of the weak acid you had to + + align:start position:0% +the moles of the weak acid you had to + + + align:start position:0% +the moles of the weak acid you had to +begin with so you've converted all of + + align:start position:0% +begin with so you've converted all of + + + align:start position:0% +begin with so you've converted all of +your weak acid to its + + align:start position:0% +your weak acid to its + + + align:start position:0% +your weak acid to its +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +so about in terms of the + + align:start position:0% +so about in terms of the + + + align:start position:0% +so about in terms of the +pH the pH is going to depend on the salt + + align:start position:0% +pH the pH is going to depend on the salt + + + align:start position:0% +pH the pH is going to depend on the salt +that's formed as a result of uh of this + + align:start position:0% +that's formed as a result of uh of this + + + align:start position:0% +that's formed as a result of uh of this +addition in the case when you're + + align:start position:0% +addition in the case when you're + + + align:start position:0% +addition in the case when you're +titrating a weak acid with a strong base + + align:start position:0% +titrating a weak acid with a strong base + + + align:start position:0% +titrating a weak acid with a strong base +you're going to get a pH greater than + + align:start position:0% +you're going to get a pH greater than + + + align:start position:0% +you're going to get a pH greater than +seven because all of your weak acid will + + align:start position:0% +seven because all of your weak acid will + + + align:start position:0% +seven because all of your weak acid will +be converted to the conjugate base so + + align:start position:0% +be converted to the conjugate base so + + + align:start position:0% +be converted to the conjugate base so +all you're going to have around is + + align:start position:0% +all you're going to have around is + + + align:start position:0% +all you're going to have around is +conjugate base and base is is basic so + + align:start position:0% +conjugate base and base is is basic so + + + align:start position:0% +conjugate base and base is is basic so +you're going to be greater than + + align:start position:0% +you're going to be greater than + + + align:start position:0% +you're going to be greater than +seven so in this case you'll get uh the + + align:start position:0% +seven so in this case you'll get uh the + + + align:start position:0% +seven so in this case you'll get uh the +conjugate base in the form of a salt and + + align:start position:0% +conjugate base in the form of a salt and + + + align:start position:0% +conjugate base in the form of a salt and +water so the uh Na plus doesn't do + + align:start position:0% +water so the uh Na plus doesn't do + + + align:start position:0% +water so the uh Na plus doesn't do +anything for you it has no effect on ph + + align:start position:0% +anything for you it has no effect on ph + + + align:start position:0% +anything for you it has no effect on ph +all group one and group two uh have no + + align:start position:0% +all group one and group two uh have no + + + align:start position:0% +all group one and group two uh have no +effect on ph but we have a conjugate + + align:start position:0% +effect on ph but we have a conjugate + + + align:start position:0% +effect on ph but we have a conjugate +base so we're going to have a pH greater + + align:start position:0% +base so we're going to have a pH greater + + + align:start position:0% +base so we're going to have a pH greater +than seven at the equivalence point and + + align:start position:0% +than seven at the equivalence point and + + + align:start position:0% +than seven at the equivalence point and +this is a good way to quickly check your + + align:start position:0% +this is a good way to quickly check your + + + align:start position:0% +this is a good way to quickly check your +math if you know what kind of problem it + + align:start position:0% +math if you know what kind of problem it + + + align:start position:0% +math if you know what kind of problem it +is and you don't get a pH that's greater + + align:start position:0% +is and you don't get a pH that's greater + + + align:start position:0% +is and you don't get a pH that's greater +than seven for this type of problem you + + align:start position:0% +than seven for this type of problem you + + + align:start position:0% +than seven for this type of problem you +know you made some kind of math mistake + + align:start position:0% +know you made some kind of math mistake + + + align:start position:0% +know you made some kind of math mistake +somewhere along and you can go back and + + align:start position:0% +somewhere along and you can go back and + + + align:start position:0% +somewhere along and you can go back and +try to find + + align:start position:0% + + + + align:start position:0% + +that all right so how do you do the + + align:start position:0% +that all right so how do you do the + + + align:start position:0% +that all right so how do you do the +problems you want to find the pH then at + + align:start position:0% +problems you want to find the pH then at + + + align:start position:0% +problems you want to find the pH then at +the equivalence point the exact pH you + + align:start position:0% +the equivalence point the exact pH you + + + align:start position:0% +the equivalence point the exact pH you +know it's greater than seven but what is + + align:start position:0% +know it's greater than seven but what is + + + align:start position:0% +know it's greater than seven but what is +it exactly so the first thing you need + + align:start position:0% +it exactly so the first thing you need + + + align:start position:0% +it exactly so the first thing you need +to do is find the volume the total + + align:start position:0% +to do is find the volume the total + + + align:start position:0% +to do is find the volume the total +volume and you need to know the volume + + align:start position:0% +volume and you need to know the volume + + + align:start position:0% +volume and you need to know the volume +of NaOH that you added to the solution + + align:start position:0% +of NaOH that you added to the solution + + + align:start position:0% +of NaOH that you added to the solution +to get to the equivalence point so you + + align:start position:0% +to get to the equivalence point so you + + + align:start position:0% +to get to the equivalence point so you +know how many moles of acid you had to + + align:start position:0% +know how many moles of acid you had to + + + align:start position:0% +know how many moles of acid you had to +begin with 2.5 * 10us 3 so that's how + + align:start position:0% +begin with 2.5 * 10us 3 so that's how + + + align:start position:0% +begin with 2.5 * 10us 3 so that's how +many moles then of conjugate base you + + align:start position:0% +many moles then of conjugate base you + + + align:start position:0% +many moles then of conjugate base you +formed and that must be how many moles + + align:start position:0% +formed and that must be how many moles + + + align:start position:0% +formed and that must be how many moles +of O you needed to add to get to the + + align:start position:0% +of O you needed to add to get to the + + + align:start position:0% +of O you needed to add to get to the +equivalence point so you needed this + + align:start position:0% +equivalence point so you needed this + + + align:start position:0% +equivalence point so you needed this +number of moles this was your + + align:start position:0% +number of moles this was your + + + align:start position:0% +number of moles this was your +concentration and so that's how many uh + + align:start position:0% +concentration and so that's how many uh + + + align:start position:0% +concentration and so that's how many uh +liters needed to be added to get to the + + align:start position:0% +liters needed to be added to get to the + + + align:start position:0% +liters needed to be added to get to the +equivalence point and in terms of your + + align:start position:0% +equivalence point and in terms of your + + + align:start position:0% +equivalence point and in terms of your +total volume then you had 25 milliliters + + align:start position:0% +total volume then you had 25 milliliters + + + align:start position:0% +total volume then you had 25 milliliters +to begin with you're adding 16.7 of the + + align:start position:0% +to begin with you're adding 16.7 of the + + + align:start position:0% +to begin with you're adding 16.7 of the +base so now you're at + + align:start position:0% +base so now you're at + + + align:start position:0% +base so now you're at +41.7 milliliters um of + + align:start position:0% + + + + align:start position:0% + +volume all right so just to just to show + + align:start position:0% +volume all right so just to just to show + + + align:start position:0% +volume all right so just to just to show +this again in cartoon form the point to + + align:start position:0% +this again in cartoon form the point to + + + align:start position:0% +this again in cartoon form the point to +remember at this equivalence point is + + align:start position:0% +remember at this equivalence point is + + + align:start position:0% +remember at this equivalence point is +that this is all you have you just have + + align:start position:0% +that this is all you have you just have + + + align:start position:0% +that this is all you have you just have +that conjugate base so if you had four + + align:start position:0% +that conjugate base so if you had four + + + align:start position:0% +that conjugate base so if you had four +molecules of weak acid to begin with you + + align:start position:0% +molecules of weak acid to begin with you + + + align:start position:0% +molecules of weak acid to begin with you +added four molecules of NaOH then the + + align:start position:0% +added four molecules of NaOH then the + + + align:start position:0% +added four molecules of NaOH then the +each molecule of um NaOH or of O will + + align:start position:0% +each molecule of um NaOH or of O will + + + align:start position:0% +each molecule of um NaOH or of O will +pluck one of these hydrogen ions off and + + align:start position:0% +pluck one of these hydrogen ions off and + + + align:start position:0% +pluck one of these hydrogen ions off and +uh will leave you then just with the + + align:start position:0% +uh will leave you then just with the + + + align:start position:0% +uh will leave you then just with the +conjugate base so you're going to have + + align:start position:0% +conjugate base so you're going to have + + + align:start position:0% +conjugate base so you're going to have +equal moles here to what you had + + align:start position:0% + + + + align:start position:0% + +here so you have these equal + + align:start position:0% +here so you have these equal + + + align:start position:0% +here so you have these equal +moles so in terms then of the marity of + + align:start position:0% +moles so in terms then of the marity of + + + align:start position:0% +moles so in terms then of the marity of +this you have to have the same number of + + align:start position:0% +this you have to have the same number of + + + align:start position:0% +this you have to have the same number of +moles now of the weak base is what you + + align:start position:0% +moles now of the weak base is what you + + + align:start position:0% +moles now of the weak base is what you +had of the weak acid to start with + + align:start position:0% +had of the weak acid to start with + + + align:start position:0% +had of the weak acid to start with +you've converted all of it to the weak + + align:start position:0% +you've converted all of it to the weak + + + align:start position:0% +you've converted all of it to the weak +base so you have that many moles and you + + align:start position:0% +base so you have that many moles and you + + + align:start position:0% +base so you have that many moles and you +calculated the total volume so you know + + align:start position:0% +calculated the total volume so you know + + + align:start position:0% +calculated the total volume so you know +your new + + align:start position:0% + + + + align:start position:0% + +marity so this is just a weak base and + + align:start position:0% +marity so this is just a weak base and + + + align:start position:0% +marity so this is just a weak base and +water problem and we talked already + + align:start position:0% +water problem and we talked already + + + align:start position:0% +water problem and we talked already +about how to do this so we can set up + + align:start position:0% +about how to do this so we can set up + + + align:start position:0% +about how to do this so we can set up +this uh this table here and now all we + + align:start position:0% +this uh this table here and now all we + + + align:start position:0% +this uh this table here and now all we +have is the weak base we don't have any + + align:start position:0% +have is the weak base we don't have any + + + align:start position:0% +have is the weak base we don't have any +of this left it's all been converted so + + align:start position:0% +of this left it's all been converted so + + + align:start position:0% +of this left it's all been converted so +all we have is this so we have + + align:start position:0% +all we have is this so we have + + + align:start position:0% +all we have is this so we have +006 uh 00 molar - x x and x now again + + align:start position:0% +006 uh 00 molar - x x and x now again + + + align:start position:0% +006 uh 00 molar - x x and x now again +you can't use the Henderson hosle Bo + + align:start position:0% +you can't use the Henderson hosle Bo + + + align:start position:0% +you can't use the Henderson hosle Bo +here it's not a buffer problem uh so we + + align:start position:0% +here it's not a buffer problem uh so we + + + align:start position:0% +here it's not a buffer problem uh so we +have to solve it using KB uh because + + align:start position:0% +have to solve it using KB uh because + + + align:start position:0% +have to solve it using KB uh because +it's a Bas in water we can't use Ka we + + align:start position:0% +it's a Bas in water we can't use Ka we + + + align:start position:0% +it's a Bas in water we can't use Ka we +have to use uh KB for a base and water + + align:start position:0% +have to use uh KB for a base and water + + + align:start position:0% +have to use uh KB for a base and water +so KB is the base ionization constant so + + align:start position:0% +so KB is the base ionization constant so + + + align:start position:0% +so KB is the base ionization constant so +if I was given a Ka how would I find the + + align:start position:0% +if I was given a Ka how would I find the + + + align:start position:0% +if I was given a Ka how would I find the +KB for the conjugate what would I + + align:start position:0% +KB for the conjugate what would I + + + align:start position:0% +KB for the conjugate what would I +use KW right so that's an easy + + align:start position:0% +use KW right so that's an easy + + + align:start position:0% +use KW right so that's an easy +conversion uh using kW to calculate KB + + align:start position:0% +conversion uh using kW to calculate KB + + + align:start position:0% +conversion uh using kW to calculate KB +and then that would be equal to x^2 over + + align:start position:0% +and then that would be equal to x^2 over + + + align:start position:0% +and then that would be equal to x^2 over +06 - x we can uh simplify that if x is + + align:start position:0% +06 - x we can uh simplify that if x is + + + align:start position:0% +06 - x we can uh simplify that if x is +small double check that that's okay and + + align:start position:0% +small double check that that's okay and + + + align:start position:0% +small double check that that's okay and +if we do that we find that the O + + align:start position:0% +if we do that we find that the O + + + align:start position:0% +if we do that we find that the O +concentration uh is 1.83 * 10us 6 molar + + align:start position:0% +concentration uh is 1.83 * 10us 6 molar + + + align:start position:0% +concentration uh is 1.83 * 10us 6 molar +then we can calculate a p and from that + + align:start position:0% +then we can calculate a p and from that + + + align:start position:0% +then we can calculate a p and from that +we can calculate the pH so be 14 minus + + align:start position:0% +we can calculate the pH so be 14 minus + + + align:start position:0% +we can calculate the pH so be 14 minus +this and the pH is 8.2 26 and that's + + align:start position:0% +this and the pH is 8.2 26 and that's + + + align:start position:0% +this and the pH is 8.2 26 and that's +greater than seven so that makes + + align:start position:0% +greater than seven so that makes + + + align:start position:0% +greater than seven so that makes +sense so we can draw that up + + align:start position:0% + + + + align:start position:0% + +here so we have + + align:start position:0% +here so we have + + + align:start position:0% +here so we have +8.26 at the equivalence + + align:start position:0% + + + + align:start position:0% + +point and that is greater than + + align:start position:0% +point and that is greater than + + + align:start position:0% +point and that is greater than +seven which is what we expect it should + + align:start position:0% +seven which is what we expect it should + + + align:start position:0% +seven which is what we expect it should +be + + align:start position:0% +be + + + align:start position:0% +be +basic + + align:start position:0% +basic + + + align:start position:0% +basic +now a lot of people forget because + + align:start position:0% +now a lot of people forget because + + + align:start position:0% +now a lot of people forget because +they're going quickly to convert from po + + align:start position:0% +they're going quickly to convert from po + + + align:start position:0% +they're going quickly to convert from po +to pH and that should be a way to double + + align:start position:0% +to pH and that should be a way to double + + + align:start position:0% +to pH and that should be a way to double +check if you find out that you're at the + + align:start position:0% +check if you find out that you're at the + + + align:start position:0% +check if you find out that you're at the +equivalence point and the pH is less + + align:start position:0% +equivalence point and the pH is less + + + align:start position:0% +equivalence point and the pH is less +than seven you realize that some + + align:start position:0% +than seven you realize that some + + + align:start position:0% +than seven you realize that some +something is is wrong and hopefully + + align:start position:0% +something is is wrong and hopefully + + + align:start position:0% +something is is wrong and hopefully +you'll remember to convert then to + + align:start position:0% +you'll remember to convert then to + + + align:start position:0% +you'll remember to convert then to +pH so greater than seven all right so + + align:start position:0% +pH so greater than seven all right so + + + align:start position:0% +pH so greater than seven all right so +beyond the equivalence point so the last + + align:start position:0% +beyond the equivalence point so the last + + + align:start position:0% +beyond the equivalence point so the last +kind of point that you may have in a + + align:start position:0% +kind of point that you may have in a + + + align:start position:0% +kind of point that you may have in a +curve up here um beyond the equivalence + + align:start position:0% +curve up here um beyond the equivalence + + + align:start position:0% +curve up here um beyond the equivalence +point you still have your conjugate base + + align:start position:0% +point you still have your conjugate base + + + align:start position:0% +point you still have your conjugate base +hanging out you still have all that all + + align:start position:0% +hanging out you still have all that all + + + align:start position:0% +hanging out you still have all that all +that you had here but that wasn't making + + align:start position:0% +that you had here but that wasn't making + + + align:start position:0% +that you had here but that wasn't making +the solution really very basic there + + align:start position:0% +the solution really very basic there + + + align:start position:0% +the solution really very basic there +wasn't much it was like 10 Theus 6 molar + + align:start position:0% +wasn't much it was like 10 Theus 6 molar + + + align:start position:0% +wasn't much it was like 10 Theus 6 molar +there wasn't much of it and so the pH is + + align:start position:0% +there wasn't much of it and so the pH is + + + align:start position:0% +there wasn't much of it and so the pH is +really going to be determined only by + + align:start position:0% +really going to be determined only by + + + align:start position:0% +really going to be determined only by +the amount of excess o That's added to + + align:start position:0% +the amount of excess o That's added to + + + align:start position:0% +the amount of excess o That's added to +the solution so now you can forget all + + align:start position:0% +the solution so now you can forget all + + + align:start position:0% +the solution so now you can forget all +about your your weak acids and weak + + align:start position:0% +about your your weak acids and weak + + + align:start position:0% +about your your weak acids and weak +bases at this point and just look at + + align:start position:0% +bases at this point and just look at + + + align:start position:0% +bases at this point and just look at +this problem as a strong base problem + + align:start position:0% +this problem as a strong base problem + + + align:start position:0% +this problem as a strong base problem +you're swamping the system with your + + align:start position:0% +you're swamping the system with your + + + align:start position:0% +you're swamping the system with your +excess strong + + align:start position:0% +excess strong + + + align:start position:0% +excess strong +base so this is this kind of problem at + + align:start position:0% +base so this is this kind of problem at + + + align:start position:0% +base so this is this kind of problem at +the end past the equivalence point is + + align:start position:0% +the end past the equivalence point is + + + align:start position:0% +the end past the equivalence point is +going to be a strong acid strong base + + align:start position:0% +going to be a strong acid strong base + + + align:start position:0% +going to be a strong acid strong base +type problem in this case a strong base + + align:start position:0% +type problem in this case a strong base + + + align:start position:0% +type problem in this case a strong base +problem so we know how to do this + + align:start position:0% +problem so we know how to do this + + + align:start position:0% +problem so we know how to do this +already we talked about this before um + + align:start position:0% +already we talked about this before um + + + align:start position:0% +already we talked about this before um +if you're 5 Ms Beyond and you say five + + align:start position:0% +if you're 5 Ms Beyond and you say five + + + align:start position:0% +if you're 5 Ms Beyond and you say five +Ms times the concentration so you have + + align:start position:0% +Ms times the concentration so you have + + + align:start position:0% +Ms times the concentration so you have +7.5 * 10-4 moles of excess base and the + + align:start position:0% +7.5 * 10-4 moles of excess base and the + + + align:start position:0% +7.5 * 10-4 moles of excess base and the +only trick to this problem is + + align:start position:0% +only trick to this problem is + + + align:start position:0% +only trick to this problem is +remembering the entire volume that you + + align:start position:0% +remembering the entire volume that you + + + align:start position:0% +remembering the entire volume that you +have in there so you know how many moles + + align:start position:0% +have in there so you know how many moles + + + align:start position:0% +have in there so you know how many moles +you have um and it's 5 Ms pass you had + + align:start position:0% +you have um and it's 5 Ms pass you had + + + align:start position:0% +you have um and it's 5 Ms pass you had +25 MLS to begin with you added 16.7 to + + align:start position:0% +25 MLS to begin with you added 16.7 to + + + align:start position:0% +25 MLS to begin with you added 16.7 to +get to the equivalence point add those + + align:start position:0% +get to the equivalence point add those + + + align:start position:0% +get to the equivalence point add those +together and you can get the + + align:start position:0% +together and you can get the + + + align:start position:0% +together and you can get the +concentration now remember the + + align:start position:0% +concentration now remember the + + + align:start position:0% +concentration now remember the +concentration we had at the equivalence + + align:start position:0% +concentration we had at the equivalence + + + align:start position:0% +concentration we had at the equivalence +point of O was like 10 the minus 6 so + + align:start position:0% +point of O was like 10 the minus 6 so + + + align:start position:0% +point of O was like 10 the minus 6 so +that's still around but if you add + + align:start position:0% +that's still around but if you add + + + align:start position:0% +that's still around but if you add +something of 10 Theus 6 to this number + + align:start position:0% +something of 10 Theus 6 to this number + + + align:start position:0% +something of 10 Theus 6 to this number +it's not significantly going to change + + align:start position:0% +it's not significantly going to change + + + align:start position:0% +it's not significantly going to change +it at all so you can ignore that and + + align:start position:0% +it at all so you can ignore that and + + + align:start position:0% +it at all so you can ignore that and +only consider the concentration of the O + + align:start position:0% +only consider the concentration of the O + + + align:start position:0% +only consider the concentration of the O +that's due to that excess strong base + + align:start position:0% +that's due to that excess strong base + + + align:start position:0% +that's due to that excess strong base +added and calculate the PO and then from + + align:start position:0% +added and calculate the PO and then from + + + align:start position:0% +added and calculate the PO and then from +that the + + align:start position:0% +that the + + + align:start position:0% +that the +pH so our final point on the curve + + align:start position:0% + + + + align:start position:0% + +then somewhere up + + align:start position:0% +then somewhere up + + + align:start position:0% +then somewhere up +here + + align:start position:0% + + + + align:start position:0% + +12.21 and this is 5 Ms beyond the + + align:start position:0% +12.21 and this is 5 Ms beyond the + + + align:start position:0% +12.21 and this is 5 Ms beyond the +equivalence + + align:start position:0% +equivalence + + + align:start position:0% +equivalence +point so there we have a titration curve + + align:start position:0% +point so there we have a titration curve + + + align:start position:0% +point so there we have a titration curve +where we've calculated various points + + align:start position:0% +where we've calculated various points + + + align:start position:0% +where we've calculated various points +along the + + align:start position:0% +along the + + + align:start position:0% +along the +way so the point to remember in doing + + align:start position:0% +way so the point to remember in doing + + + align:start position:0% +way so the point to remember in doing +these problems is that you just need to + + align:start position:0% +these problems is that you just need to + + + align:start position:0% +these problems is that you just need to +break down each part of the curve and + + align:start position:0% +break down each part of the curve and + + + align:start position:0% +break down each part of the curve and +Define it as a different type of problem + + align:start position:0% +Define it as a different type of problem + + + align:start position:0% +Define it as a different type of problem +so here we started out and we did a weak + + align:start position:0% +so here we started out and we did a weak + + + align:start position:0% +so here we started out and we did a weak +acid problem + + align:start position:0% +acid problem + + + align:start position:0% +acid problem +then we were in the buffering region and + + align:start position:0% +then we were in the buffering region and + + + align:start position:0% +then we were in the buffering region and +we did a buffer problem we had the + + align:start position:0% +we did a buffer problem we had the + + + align:start position:0% +we did a buffer problem we had the +special category of buffer when we're at + + align:start position:0% +special category of buffer when we're at + + + align:start position:0% +special category of buffer when we're at +the half equivalence point and then uh + + align:start position:0% +the half equivalence point and then uh + + + align:start position:0% +the half equivalence point and then uh +we moved up here all the weak acid was + + align:start position:0% +we moved up here all the weak acid was + + + align:start position:0% +we moved up here all the weak acid was +converted to weak base at this point so + + align:start position:0% +converted to weak base at this point so + + + align:start position:0% +converted to weak base at this point so +it's just a weak base problem and then + + align:start position:0% +it's just a weak base problem and then + + + align:start position:0% +it's just a weak base problem and then +beyond the equivalence point it's a + + align:start position:0% +beyond the equivalence point it's a + + + align:start position:0% +beyond the equivalence point it's a +strong base + + align:start position:0% +strong base + + + align:start position:0% +strong base +problem so the titration curves this why + + align:start position:0% +problem so the titration curves this why + + + align:start position:0% +problem so the titration curves this why +it takes a long time to do these because + + align:start position:0% +it takes a long time to do these because + + + align:start position:0% +it takes a long time to do these because +it's really many problems all wrapped up + + align:start position:0% +it's really many problems all wrapped up + + + align:start position:0% +it's really many problems all wrapped up +into one problem and the other thing to + + align:start position:0% +into one problem and the other thing to + + + align:start position:0% +into one problem and the other thing to +remember especially if you're given + + align:start position:0% +remember especially if you're given + + + align:start position:0% +remember especially if you're given +different subsections you're not always + + align:start position:0% +different subsections you're not always + + + align:start position:0% +different subsections you're not always +going to be working through it + + align:start position:0% +going to be working through it + + + align:start position:0% +going to be working through it +systematically you may be asked to start + + align:start position:0% +systematically you may be asked to start + + + align:start position:0% +systematically you may be asked to start +here or start down here and so you + + align:start position:0% +here or start down here and so you + + + align:start position:0% +here or start down here and so you +always have to ask yourself what kind of + + align:start position:0% +always have to ask yourself what kind of + + + align:start position:0% +always have to ask yourself what kind of +problem is this and uh I tell people who + + align:start position:0% +problem is this and uh I tell people who + + + align:start position:0% +problem is this and uh I tell people who +are grading the exam that if you write + + align:start position:0% +are grading the exam that if you write + + + align:start position:0% +are grading the exam that if you write +on the top of the problem this is really + + align:start position:0% +on the top of the problem this is really + + + align:start position:0% +on the top of the problem this is really +a buffer problem or this is a weak Bas + + align:start position:0% +a buffer problem or this is a weak Bas + + + align:start position:0% +a buffer problem or this is a weak Bas +problem at the equivalence point if you + + align:start position:0% +problem at the equivalence point if you + + + align:start position:0% +problem at the equivalence point if you +write something down that tells me that + + align:start position:0% +write something down that tells me that + + + align:start position:0% +write something down that tells me that +you know what type of problem is that's + + align:start position:0% +you know what type of problem is that's + + + align:start position:0% +you know what type of problem is that's +worth some points right there even if + + align:start position:0% +worth some points right there even if + + + align:start position:0% +worth some points right there even if +you get lost in the math so if you think + + align:start position:0% +you get lost in the math so if you think + + + align:start position:0% +you get lost in the math so if you think +about these a way it help you do them + + align:start position:0% +about these a way it help you do them + + + align:start position:0% +about these a way it help you do them +and you also might give you some a + + align:start position:0% +and you also might give you some a + + + align:start position:0% +and you also might give you some a +little uh partial credit on on the + + align:start position:0% +little uh partial credit on on the + + + align:start position:0% +little uh partial credit on on the +test all right so again they're just + + align:start position:0% +test all right so again they're just + + + align:start position:0% +test all right so again they're just +these kind of types of problems and it's + + align:start position:0% +these kind of types of problems and it's + + + align:start position:0% +these kind of types of problems and it's +a matter of picking and choosing and + + align:start position:0% +a matter of picking and choosing and + + + align:start position:0% +a matter of picking and choosing and +putting them all together so there's not + + align:start position:0% +putting them all together so there's not + + + align:start position:0% +putting them all together so there's not +a huge number of types of problems but + + align:start position:0% +a huge number of types of problems but + + + align:start position:0% +a huge number of types of problems but +it's hard sometimes for people to figure + + align:start position:0% +it's hard sometimes for people to figure + + + align:start position:0% +it's hard sometimes for people to figure +out where they are and which which one + + align:start position:0% +out where they are and which which one + + + align:start position:0% +out where they are and which which one +of these things to + + align:start position:0% +of these things to + + + align:start position:0% +of these things to +apply all right so that moves into + + align:start position:0% +apply all right so that moves into + + + align:start position:0% +apply all right so that moves into +today's handout and I'm going to finish + + align:start position:0% +today's handout and I'm going to finish + + + align:start position:0% +today's handout and I'm going to finish +I'm going to start today's handout + + align:start position:0% +I'm going to start today's handout + + + align:start position:0% +I'm going to start today's handout +finishing acid base and I did this for + + align:start position:0% +finishing acid base and I did this for + + + align:start position:0% +finishing acid base and I did this for +the first time last year this kind of + + align:start position:0% +the first time last year this kind of + + + align:start position:0% +the first time last year this kind of +little cheat sheet on on how to solve + + align:start position:0% +little cheat sheet on on how to solve + + + align:start position:0% +little cheat sheet on on how to solve +these problems and I'll write this stuff + + align:start position:0% +these problems and I'll write this stuff + + + align:start position:0% +these problems and I'll write this stuff +on the board and as maybe some of you + + align:start position:0% +on the board and as maybe some of you + + + align:start position:0% +on the board and as maybe some of you +remember I mentioned that last year we + + align:start position:0% +remember I mentioned that last year we + + + align:start position:0% +remember I mentioned that last year we +had the best performance on acid base + + align:start position:0% +had the best performance on acid base + + + align:start position:0% +had the best performance on acid base +that I think we've seen in 5111 for a + + align:start position:0% +that I think we've seen in 5111 for a + + + align:start position:0% +that I think we've seen in 5111 for a +really long time uh you know they people + + align:start position:0% +really long time uh you know they people + + + align:start position:0% +really long time uh you know they people +did really really well on this and so + + align:start position:0% +did really really well on this and so + + + align:start position:0% +did really really well on this and so +I'd like to continue that trend of + + align:start position:0% +I'd like to continue that trend of + + + align:start position:0% +I'd like to continue that trend of +having fantastic + + align:start position:0% +having fantastic + + + align:start position:0% +having fantastic +uh acid-based titration answers where + + align:start position:0% +uh acid-based titration answers where + + + align:start position:0% +uh acid-based titration answers where +you know there's little smiley faces + + align:start position:0% +you know there's little smiley faces + + + align:start position:0% +you know there's little smiley faces +drawn on the exams where everything is + + align:start position:0% +drawn on the exams where everything is + + + align:start position:0% +drawn on the exams where everything is +really perfect so let's see if we can uh + + align:start position:0% +really perfect so let's see if we can uh + + + align:start position:0% +really perfect so let's see if we can uh +keep this keep this + + align:start position:0% + + + + align:start position:0% + +going all right so let's work on our + + align:start position:0% +going all right so let's work on our + + + align:start position:0% +going all right so let's work on our +cheat sheet and how you go about solving + + align:start position:0% +cheat sheet and how you go about solving + + + align:start position:0% +cheat sheet and how you go about solving +all the different kinds of problems all + + align:start position:0% +all the different kinds of problems all + + + align:start position:0% +all the different kinds of problems all +right so first uh we'll just quickly + + align:start position:0% +right so first uh we'll just quickly + + + align:start position:0% +right so first uh we'll just quickly +review uh this type the uh weak acid + + align:start position:0% +review uh this type the uh weak acid + + + align:start position:0% +review uh this type the uh weak acid +being titrated with the strong + + align:start position:0% + + + + align:start position:0% + +base okay so let's consider now when + + align:start position:0% +base okay so let's consider now when + + + align:start position:0% +base okay so let's consider now when +we're going to we'll work backwards + + align:start position:0% +we're going to we'll work backwards + + + align:start position:0% +we're going to we'll work backwards +through this when we're beyond the + + align:start position:0% +through this when we're beyond the + + + align:start position:0% +through this when we're beyond the +equivalence point and I guess I should + + align:start position:0% +equivalence point and I guess I should + + + align:start position:0% +equivalence point and I guess I should +say so this is weak + + align:start position:0% +say so this is weak + + + align:start position:0% +say so this is weak +acid strong + + align:start position:0% + + + + align:start position:0% + +base okay so beyond the equivalence + + align:start position:0% +base okay so beyond the equivalence + + + align:start position:0% +base okay so beyond the equivalence +point then is a strong base problem as + + align:start position:0% +point then is a strong base problem as + + + align:start position:0% +point then is a strong base problem as +we just did so it's really due to the + + align:start position:0% +we just did so it's really due to the + + + align:start position:0% +we just did so it's really due to the +excess strong base that we had so we + + align:start position:0% +excess strong base that we had so we + + + align:start position:0% +excess strong base that we had so we +would solve this problem saying okay the + + align:start position:0% +would solve this problem saying okay the + + + align:start position:0% +would solve this problem saying okay the +extra + + align:start position:0% +extra + + + align:start position:0% +extra +strong + + align:start position:0% +strong + + + align:start position:0% +strong +base and that's the number of + + align:start position:0% +base and that's the number of + + + align:start position:0% +base and that's the number of +moles over the total + + align:start position:0% +moles over the total + + + align:start position:0% +moles over the total +volume and that's going to give you the + + align:start position:0% +volume and that's going to give you the + + + align:start position:0% +volume and that's going to give you the +concentration of hydroxide ion and then + + align:start position:0% +concentration of hydroxide ion and then + + + align:start position:0% +concentration of hydroxide ion and then +You' can find p + + align:start position:0% +You' can find p + + + align:start position:0% +You' can find p +and then pH so that's how you would do + + align:start position:0% +and then pH so that's how you would do + + + align:start position:0% +and then pH so that's how you would do +uh that category of problem + + align:start position:0% + + + + align:start position:0% + +here so let's move then to volume equals + + align:start position:0% +here so let's move then to volume equals + + + align:start position:0% +here so let's move then to volume equals +the volume at the equivalence point and + + align:start position:0% +the volume at the equivalence point and + + + align:start position:0% +the volume at the equivalence point and +this is a salt problem that gets broken + + align:start position:0% +this is a salt problem that gets broken + + + align:start position:0% +this is a salt problem that gets broken +down into a weak base + + align:start position:0% + + + + align:start position:0% + +problem because now we've converted all + + align:start position:0% +problem because now we've converted all + + + align:start position:0% +problem because now we've converted all +our weak acid into its comp conjugate + + align:start position:0% +our weak acid into its comp conjugate + + + align:start position:0% +our weak acid into its comp conjugate +base so this is an A minus plus + + align:start position:0% +base so this is an A minus plus + + + align:start position:0% +base so this is an A minus plus +water going to ha plus O type problem + + align:start position:0% +water going to ha plus O type problem + + + align:start position:0% +water going to ha plus O type problem +and we would use KB because we're + + align:start position:0% +and we would use KB because we're + + + align:start position:0% +and we would use KB because we're +talking about a base in water we'd use + + align:start position:0% +talking about a base in water we'd use + + + align:start position:0% +talking about a base in water we'd use +KB uh to + + align:start position:0% +KB uh to + + + align:start position:0% +KB uh to +find the concentration of hydroxide ions + + align:start position:0% +find the concentration of hydroxide ions + + + align:start position:0% +find the concentration of hydroxide ions +then you would calculate + + align:start position:0% +then you would calculate + + + align:start position:0% +then you would calculate +p and then + + align:start position:0% + + + + align:start position:0% + +pH and you should know how to write an + + align:start position:0% +pH and you should know how to write an + + + align:start position:0% +pH and you should know how to write an +equation out for all the types of + + align:start position:0% +equation out for all the types of + + + align:start position:0% +equation out for all the types of +problems you're doing it'll help you uh + + align:start position:0% +problems you're doing it'll help you uh + + + align:start position:0% +problems you're doing it'll help you uh +figure out what you're doing in the + + align:start position:0% +figure out what you're doing in the + + + align:start position:0% +figure out what you're doing in the +problem so when your volume equals the + + align:start position:0% +problem so when your volume equals the + + + align:start position:0% +problem so when your volume equals the +volume at the half equivalence + + align:start position:0% +volume at the half equivalence + + + align:start position:0% +volume at the half equivalence +point pH equals + + align:start position:0% +point pH equals + + + align:start position:0% +point pH equals +PKA and and that's really + + align:start position:0% + + + + align:start position:0% + +it you might have to find PKA from Ka + + align:start position:0% +it you might have to find PKA from Ka + + + align:start position:0% +it you might have to find PKA from Ka +but that's uh pretty + + align:start position:0% + + + + align:start position:0% + +straightforward okay so now when you're + + align:start position:0% +straightforward okay so now when you're + + + align:start position:0% +straightforward okay so now when you're +in the buffering region again the + + align:start position:0% +in the buffering region again the + + + align:start position:0% +in the buffering region again the +buffering region is where the pH uh + + align:start position:0% +buffering region is where the pH uh + + + align:start position:0% +buffering region is where the pH uh +titration curve is in the flat region so + + align:start position:0% +titration curve is in the flat region so + + + align:start position:0% +titration curve is in the flat region so +this is a buffer + + align:start position:0% + + + + align:start position:0% + +problem and here mostly you want to try + + align:start position:0% +problem and here mostly you want to try + + + align:start position:0% +problem and here mostly you want to try +to use the Henderson hosle block + + align:start position:0% +to use the Henderson hosle block + + + align:start position:0% +to use the Henderson hosle block +equation pH equals PKA minus the log of + + align:start position:0% +equation pH equals PKA minus the log of + + + align:start position:0% +equation pH equals PKA minus the log of +ha divided by a minus of your at weak + + align:start position:0% +ha divided by a minus of your at weak + + + align:start position:0% +ha divided by a minus of your at weak +acid and the conjugate base and you can + + align:start position:0% +acid and the conjugate base and you can + + + align:start position:0% +acid and the conjugate base and you can +use this if the + + align:start position:0% +use this if the + + + align:start position:0% +use this if the +5% rule + + align:start position:0% +5% rule + + + align:start position:0% +5% rule +applies but that usually does so that's + + align:start position:0% +applies but that usually does so that's + + + align:start position:0% +applies but that usually does so that's +probably going to be your your first + + align:start position:0% +probably going to be your your first + + + align:start position:0% +probably going to be your your first +route uh to to do these + + align:start position:0% +route uh to to do these + + + align:start position:0% +route uh to to do these +calculations and again to find the you + + align:start position:0% +calculations and again to find the you + + + align:start position:0% +calculations and again to find the you +have to find the concentrations of these + + align:start position:0% +have to find the concentrations of these + + + align:start position:0% +have to find the concentrations of these +so you have to remember that the amount + + align:start position:0% +so you have to remember that the amount + + + align:start position:0% +so you have to remember that the amount +of strong base you're adding is + + align:start position:0% +of strong base you're adding is + + + align:start position:0% +of strong base you're adding is +converting some of the weak acid to the + + align:start position:0% +converting some of the weak acid to the + + + align:start position:0% +converting some of the weak acid to the +conjugate so you need to Fig out how + + align:start position:0% +conjugate so you need to Fig out how + + + align:start position:0% +conjugate so you need to Fig out how +much gets converted find these + + align:start position:0% +much gets converted find these + + + align:start position:0% +much gets converted find these +concentrations and then plug it into + + align:start position:0% +concentrations and then plug it into + + + align:start position:0% +concentrations and then plug it into +this equation so this is this equation + + align:start position:0% +this equation so this is this equation + + + align:start position:0% +this equation so this is this equation +only works for a buffer problem and I + + align:start position:0% +only works for a buffer problem and I + + + align:start position:0% +only works for a buffer problem and I +also just want to say that every once in + + align:start position:0% +also just want to say that every once in + + + align:start position:0% +also just want to say that every once in +a while people decide instead of PKA + + align:start position:0% +a while people decide instead of PKA + + + align:start position:0% +a while people decide instead of PKA +let's rewrite this equation for pkb + + align:start position:0% +let's rewrite this equation for pkb + + + align:start position:0% +let's rewrite this equation for pkb +instead don't do that uh that's my + + align:start position:0% +instead don't do that uh that's my + + + align:start position:0% +instead don't do that uh that's my +little tip uh it's been tried and it's + + align:start position:0% +little tip uh it's been tried and it's + + + align:start position:0% +little tip uh it's been tried and it's +never actually succeeded in yielding the + + align:start position:0% +never actually succeeded in yielding the + + + align:start position:0% +never actually succeeded in yielding the +correct answer if someone wants to say + + align:start position:0% +correct answer if someone wants to say + + + align:start position:0% +correct answer if someone wants to say +on this test I'll come up with this new + + align:start position:0% +on this test I'll come up with this new + + + align:start position:0% +on this test I'll come up with this new +equation using pkb and I'll prove that + + align:start position:0% +equation using pkb and I'll prove that + + + align:start position:0% +equation using pkb and I'll prove that +we can get you can do that if you want + + align:start position:0% +we can get you can do that if you want + + + align:start position:0% +we can get you can do that if you want +but I think it's best to stick with this + + align:start position:0% +but I think it's best to stick with this + + + align:start position:0% +but I think it's best to stick with this +equation just from a previous + + align:start position:0% + + + + align:start position:0% + +experience okay so um then + + align:start position:0% +experience okay so um then + + + align:start position:0% +experience okay so um then +lastly volume equals zero so this is a + + align:start position:0% +lastly volume equals zero so this is a + + + align:start position:0% +lastly volume equals zero so this is a +weak acid + + align:start position:0% + + + + align:start position:0% + +problem and uh a weak acid problem you + + align:start position:0% +problem and uh a weak acid problem you + + + align:start position:0% +problem and uh a weak acid problem you +have your acid in + + align:start position:0% +have your acid in + + + align:start position:0% +have your acid in +water going to hydronium ion + + align:start position:0% +water going to hydronium ion + + + align:start position:0% +water going to hydronium ion +concentrations and your conjugate base + + align:start position:0% +concentrations and your conjugate base + + + align:start position:0% +concentrations and your conjugate base +so you're going to use + + align:start position:0% +so you're going to use + + + align:start position:0% +so you're going to use +Ka the acid uh equilibrium constant to + + align:start position:0% + + + + align:start position:0% + +find hydronium ion + + align:start position:0% +find hydronium ion + + + align:start position:0% +find hydronium ion +concentration and then from that you can + + align:start position:0% +concentration and then from that you can + + + align:start position:0% +concentration and then from that you can +calculate + + align:start position:0% + + + + align:start position:0% + +pH so those are the different ways that + + align:start position:0% +pH so those are the different ways that + + + align:start position:0% +pH so those are the different ways that +that um breaks down so now let's do the + + align:start position:0% +that um breaks down so now let's do the + + + align:start position:0% +that um breaks down so now let's do the +same thing for a weak base strong + + align:start position:0% + + + + align:start position:0% + +acid + + align:start position:0% + + + + align:start position:0% + +and I'll move my uh that on to the next + + align:start position:0% +and I'll move my uh that on to the next + + + align:start position:0% +and I'll move my uh that on to the next +so to start with start at the uh top of + + align:start position:0% +so to start with start at the uh top of + + + align:start position:0% +so to start with start at the uh top of +the uh chart so here in the beginning + + align:start position:0% +the uh chart so here in the beginning + + + align:start position:0% +the uh chart so here in the beginning +when volume equals zero all you have is + + align:start position:0% +when volume equals zero all you have is + + + align:start position:0% +when volume equals zero all you have is +your weak base and then as your ad acid + + align:start position:0% +your weak base and then as your ad acid + + + align:start position:0% +your weak base and then as your ad acid +the pH is going to + + align:start position:0% +the pH is going to + + + align:start position:0% +the pH is going to +drop so in the beginning when volume + + align:start position:0% +drop so in the beginning when volume + + + align:start position:0% +drop so in the beginning when volume +equals + + align:start position:0% + + + + align:start position:0% + +zero this is a weak B base + + align:start position:0% + + + + align:start position:0% + +problem and so you can draw that as your + + align:start position:0% +problem and so you can draw that as your + + + align:start position:0% +problem and so you can draw that as your +base in + + align:start position:0% +base in + + + align:start position:0% +base in +water going to the conjugate + + align:start position:0% +water going to the conjugate + + + align:start position:0% +water going to the conjugate +acid and hydroxide ion + + align:start position:0% +acid and hydroxide ion + + + align:start position:0% +acid and hydroxide ion +concentration so now you're going to + + align:start position:0% +concentration so now you're going to + + + align:start position:0% +concentration so now you're going to +use KB the base ionization equilibrium + + align:start position:0% +use KB the base ionization equilibrium + + + align:start position:0% +use KB the base ionization equilibrium +constant to + + align:start position:0% +constant to + + + align:start position:0% +constant to +find the + + align:start position:0% +find the + + + align:start position:0% +find the +concentration of O minus + + align:start position:0% + + + + align:start position:0% + +then you can + + align:start position:0% +then you can + + + align:start position:0% +then you can +calculate p and from that calculate + + align:start position:0% + + + + align:start position:0% + +pH so next we'll consider the buffering + + align:start position:0% +pH so next we'll consider the buffering + + + align:start position:0% +pH so next we'll consider the buffering +region when the volume is in between + + align:start position:0% +region when the volume is in between + + + align:start position:0% +region when the volume is in between +zero and the volume at the equivalence + + align:start position:0% +zero and the volume at the equivalence + + + align:start position:0% +zero and the volume at the equivalence +point and so this is a buffer + + align:start position:0% +point and so this is a buffer + + + align:start position:0% +point and so this is a buffer +problem and again I recommend using + + align:start position:0% +problem and again I recommend using + + + align:start position:0% +problem and again I recommend using +Henderson hosle block as written with + + align:start position:0% +Henderson hosle block as written with + + + align:start position:0% +Henderson hosle block as written with +PKA and so here you need to know the + + align:start position:0% +PKA and so here you need to know the + + + align:start position:0% +PKA and so here you need to know the +concentration of the conjugate acid over + + align:start position:0% +concentration of the conjugate acid over + + + align:start position:0% +concentration of the conjugate acid over +the + + align:start position:0% +the + + + align:start position:0% +the +concentration of the weak base that you + + align:start position:0% +concentration of the weak base that you + + + align:start position:0% +concentration of the weak base that you +had and so you can use this if the 5% + + align:start position:0% +had and so you can use this if the 5% + + + align:start position:0% +had and so you can use this if the 5% +rule + + align:start position:0% + + + + align:start position:0% + +applies and you can check that by calcul + + align:start position:0% +applies and you can check that by calcul + + + align:start position:0% +applies and you can check that by calcul +back calculating so this will also work + + align:start position:0% +back calculating so this will also work + + + align:start position:0% +back calculating so this will also work +now remember you're starting then with + + align:start position:0% +now remember you're starting then with + + + align:start position:0% +now remember you're starting then with +your with your weak base you've + + align:start position:0% +your with your weak base you've + + + align:start position:0% +your with your weak base you've +converted some of it to the conjugate + + align:start position:0% +converted some of it to the conjugate + + + align:start position:0% +converted some of it to the conjugate +acid depending on how much strong acid + + align:start position:0% +acid depending on how much strong acid + + + align:start position:0% +acid depending on how much strong acid +you've added so before you can plug in + + align:start position:0% +you've added so before you can plug in + + + align:start position:0% +you've added so before you can plug in +numbers here you have to subtract how + + align:start position:0% +numbers here you have to subtract how + + + align:start position:0% +numbers here you have to subtract how +many moles of the strong acid were added + + align:start position:0% +many moles of the strong acid were added + + + align:start position:0% +many moles of the strong acid were added +so that means how many moles of the weak + + align:start position:0% +so that means how many moles of the weak + + + align:start position:0% +so that means how many moles of the weak +base do you have left how many moles of + + align:start position:0% +base do you have left how many moles of + + + align:start position:0% +base do you have left how many moles of +the conjugate acid have been formed so + + align:start position:0% +the conjugate acid have been formed so + + + align:start position:0% +the conjugate acid have been formed so +again we're in this region so if you had + + align:start position:0% +again we're in this region so if you had + + + align:start position:0% +again we're in this region so if you had +say four molecules to begin with and you + + align:start position:0% +say four molecules to begin with and you + + + align:start position:0% +say four molecules to begin with and you +added one molecule of the strong acid + + align:start position:0% +added one molecule of the strong acid + + + align:start position:0% +added one molecule of the strong acid +then you'd be left with three and you'd + + align:start position:0% +then you'd be left with three and you'd + + + align:start position:0% +then you'd be left with three and you'd +have one converted so these problems all + + align:start position:0% +have one converted so these problems all + + + align:start position:0% +have one converted so these problems all +involve uh subtraction before you can + + align:start position:0% +involve uh subtraction before you can + + + align:start position:0% +involve uh subtraction before you can +plug in your numbers to the Henderson + + align:start position:0% +plug in your numbers to the Henderson + + + align:start position:0% +plug in your numbers to the Henderson +hasselbach + + align:start position:0% + + + + align:start position:0% + +equation okay so then we have the + + align:start position:0% +equation okay so then we have the + + + align:start position:0% +equation okay so then we have the +special category of buffer where your + + align:start position:0% +special category of buffer where your + + + align:start position:0% +special category of buffer where your +volume equals the volume at the half + + align:start position:0% +volume equals the volume at the half + + + align:start position:0% +volume equals the volume at the half +equivalence point and again you can just + + align:start position:0% +equivalence point and again you can just + + + align:start position:0% +equivalence point and again you can just +solve this pH equals PKA if you're given + + align:start position:0% +solve this pH equals PKA if you're given + + + align:start position:0% +solve this pH equals PKA if you're given +a KB you'll have to convert to a Ka to + + align:start position:0% +a KB you'll have to convert to a Ka to + + + align:start position:0% +a KB you'll have to convert to a Ka to +find your PKA but this will still this + + align:start position:0% +find your PKA but this will still this + + + align:start position:0% +find your PKA but this will still this +will still + + align:start position:0% + + + + align:start position:0% + +work okay + + align:start position:0% +work okay + + + align:start position:0% +work okay +um yeah maybe I'll write in this next + + align:start position:0% +um yeah maybe I'll write in this next + + + align:start position:0% +um yeah maybe I'll write in this next +board okay so then your volume at the + + align:start position:0% +board okay so then your volume at the + + + align:start position:0% +board okay so then your volume at the +equivalence point + + align:start position:0% +equivalence point + + + align:start position:0% +equivalence point +and this is again a salt problem and uh + + align:start position:0% +and this is again a salt problem and uh + + + align:start position:0% +and this is again a salt problem and uh +but the salt problem breaks down to a + + align:start position:0% +but the salt problem breaks down to a + + + align:start position:0% +but the salt problem breaks down to a +weak acid problem because when you have + + align:start position:0% +weak acid problem because when you have + + + align:start position:0% +weak acid problem because when you have +a strong acid its conjugate is neutral + + align:start position:0% +a strong acid its conjugate is neutral + + + align:start position:0% +a strong acid its conjugate is neutral +and if you have a weak base its + + align:start position:0% +and if you have a weak base its + + + align:start position:0% +and if you have a weak base its +conjugate is also a weak acid so the + + align:start position:0% +conjugate is also a weak acid so the + + + align:start position:0% +conjugate is also a weak acid so the +salt that's formed in this problem is + + align:start position:0% +salt that's formed in this problem is + + + align:start position:0% +salt that's formed in this problem is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +acidic so we can write that + + align:start position:0% + + + + align:start position:0% + +down + + align:start position:0% + + + + align:start position:0% + +so we have our conjugate acid that's + + align:start position:0% +so we have our conjugate acid that's + + + align:start position:0% +so we have our conjugate acid that's +formed as a result of the titration in + + align:start position:0% +formed as a result of the titration in + + + align:start position:0% +formed as a result of the titration in +water forming the conjugate base and + + align:start position:0% +water forming the conjugate base and + + + align:start position:0% +water forming the conjugate base and +hydronium ion + + align:start position:0% +hydronium ion + + + align:start position:0% +hydronium ion +concentrations so now we can use + + align:start position:0% +concentrations so now we can use + + + align:start position:0% +concentrations so now we can use +Ka to + + align:start position:0% +Ka to + + + align:start position:0% +Ka to +find hydronium ion + + align:start position:0% +find hydronium ion + + + align:start position:0% +find hydronium ion +concentration and then we can calculate + + align:start position:0% +concentration and then we can calculate + + + align:start position:0% +concentration and then we can calculate +pH so again at the equivalence point you + + align:start position:0% +pH so again at the equivalence point you + + + align:start position:0% +pH so again at the equivalence point you +converted all of the weak base you had + + align:start position:0% +converted all of the weak base you had + + + align:start position:0% +converted all of the weak base you had +down to uh two weak acid you've added + + align:start position:0% +down to uh two weak acid you've added + + + align:start position:0% +down to uh two weak acid you've added +enough acid that it's protonated all of + + align:start position:0% +enough acid that it's protonated all of + + + align:start position:0% +enough acid that it's protonated all of +the weak base you have and now all you + + align:start position:0% +the weak base you have and now all you + + + align:start position:0% +the weak base you have and now all you +have left is acid so it's really just an + + align:start position:0% +have left is acid so it's really just an + + + align:start position:0% +have left is acid so it's really just an +acid and water + + align:start position:0% + + + + align:start position:0% + +problem and then finally if you're + + align:start position:0% +problem and then finally if you're + + + align:start position:0% +problem and then finally if you're +beyond the equivalence point now you're + + align:start position:0% +beyond the equivalence point now you're + + + align:start position:0% +beyond the equivalence point now you're +just pouring excess acid in and so this + + align:start position:0% +just pouring excess acid in and so this + + + align:start position:0% +just pouring excess acid in and so this +is a strong acid problem + + align:start position:0% +is a strong acid problem + + + align:start position:0% +is a strong acid problem +so you still will have a little acid + + align:start position:0% +so you still will have a little acid + + + align:start position:0% +so you still will have a little acid +solution left from uh the titration but + + align:start position:0% +solution left from uh the titration but + + + align:start position:0% +solution left from uh the titration but +that's going to be overwhelmed by the + + align:start position:0% +that's going to be overwhelmed by the + + + align:start position:0% +that's going to be overwhelmed by the +amount of strong acid so you can solve + + align:start position:0% +amount of strong acid so you can solve + + + align:start position:0% +amount of strong acid so you can solve +that by just saying uh how many extra + + align:start position:0% +that by just saying uh how many extra + + + align:start position:0% +that by just saying uh how many extra +moles of strong + + align:start position:0% +moles of strong + + + align:start position:0% +moles of strong +acid over the total + + align:start position:0% + + + + align:start position:0% + +volume and that's going to give you + + align:start position:0% +volume and that's going to give you + + + align:start position:0% +volume and that's going to give you +hydronium ion concentration and then you + + align:start position:0% +hydronium ion concentration and then you + + + align:start position:0% +hydronium ion concentration and then you +can calculate pH so at this point it's + + align:start position:0% +can calculate pH so at this point it's + + + align:start position:0% +can calculate pH so at this point it's +just a very simple calculation the only + + align:start position:0% +just a very simple calculation the only + + + align:start position:0% +just a very simple calculation the only +tricky part is to figure out the total + + align:start position:0% +tricky part is to figure out the total + + + align:start position:0% +tricky part is to figure out the total +volume to get that number + + align:start position:0% + + + + align:start position:0% + +right so that's the cheat sheet which + + align:start position:0% +right so that's the cheat sheet which + + + align:start position:0% +right so that's the cheat sheet which +should help you lead you through um the + + align:start position:0% +should help you lead you through um the + + + align:start position:0% +should help you lead you through um the +rest of the problem set and also + + align:start position:0% +rest of the problem set and also + + + align:start position:0% +rest of the problem set and also +problems for the + + align:start position:0% +problems for the + + + align:start position:0% +problems for the +exam + + align:start position:0% +exam + + + align:start position:0% +exam +okay so let's uh do a little bit we have + + align:start position:0% +okay so let's uh do a little bit we have + + + align:start position:0% +okay so let's uh do a little bit we have +just a little bit that I want to do + + align:start position:0% +just a little bit that I want to do + + + align:start position:0% +just a little bit that I want to do +today on oxidation reduction reactions + + align:start position:0% +today on oxidation reduction reactions + + + align:start position:0% +today on oxidation reduction reactions +and so this is the next unit that we're + + align:start position:0% +and so this is the next unit that we're + + + align:start position:0% +and so this is the next unit that we're +moving into and uh today we're just + + align:start position:0% +moving into and uh today we're just + + + align:start position:0% +moving into and uh today we're just +going to talk in the in the last uh 15 + + align:start position:0% +going to talk in the in the last uh 15 + + + align:start position:0% +going to talk in the in the last uh 15 +minutes about some simple rules uh for + + align:start position:0% +minutes about some simple rules uh for + + + align:start position:0% +minutes about some simple rules uh for +doing oxidation reduction so we're also + + align:start position:0% +doing oxidation reduction so we're also + + + align:start position:0% +doing oxidation reduction so we're also +we're moving away from the acid base but + + align:start position:0% +we're moving away from the acid base but + + + align:start position:0% +we're moving away from the acid base but +you'll find there's a lot of parallels + + align:start position:0% +you'll find there's a lot of parallels + + + align:start position:0% +you'll find there's a lot of parallels +between these units we're still going to + + align:start position:0% +between these units we're still going to + + + align:start position:0% +between these units we're still going to +be talking about equilibrium constants + + align:start position:0% +be talking about equilibrium constants + + + align:start position:0% +be talking about equilibrium constants +we're still going to be talking about + + align:start position:0% +we're still going to be talking about + + + align:start position:0% +we're still going to be talking about +Delta G as we go along so this is + + align:start position:0% +Delta G as we go along so this is + + + align:start position:0% +Delta G as we go along so this is +another application of uh of + + align:start position:0% +another application of uh of + + + align:start position:0% +another application of uh of +thermodynamics and chemical + + align:start position:0% +thermodynamics and chemical + + + align:start position:0% +thermodynamics and chemical +equilibrium so there's some + + align:start position:0% +equilibrium so there's some + + + align:start position:0% +equilibrium so there's some +rules to start with most of them are + + align:start position:0% +rules to start with most of them are + + + align:start position:0% +rules to start with most of them are +actually pretty simple and you need to + + align:start position:0% +actually pretty simple and you need to + + + align:start position:0% +actually pretty simple and you need to +know what these rules are for assigning + + align:start position:0% +know what these rules are for assigning + + + align:start position:0% +know what these rules are for assigning +uh oxidation numbers so uh here are the + + align:start position:0% +uh oxidation numbers so uh here are the + + + align:start position:0% +uh oxidation numbers so uh here are the +rules if you have a free + + align:start position:0% +rules if you have a free + + + align:start position:0% +rules if you have a free +element the oxidation number is going to + + align:start position:0% +element the oxidation number is going to + + + align:start position:0% +element the oxidation number is going to +be + + align:start position:0% + + + + align:start position:0% + +zero if you have + + align:start position:0% +zero if you have + + + align:start position:0% +zero if you have +ions then um + + align:start position:0% +ions then um + + + align:start position:0% +ions then um +then your oxidation number is lithium + + + align:start position:0% +then your oxidation number is lithium + + + + align:start position:0% +then your oxidation number is lithium + +one you have an oxidation number of + + + align:start position:0% +one you have an oxidation number of + + + + align:start position:0% +one you have an oxidation number of + +one so it's equal to the oxidation + + align:start position:0% +one so it's equal to the oxidation + + + align:start position:0% +one so it's equal to the oxidation +number is equal to the charge on the + + align:start position:0% +number is equal to the charge on the + + + align:start position:0% +number is equal to the charge on the +atom and uh we find that group one are + + align:start position:0% +atom and uh we find that group one are + + + align:start position:0% +atom and uh we find that group one are +always going to have plus one group two + + align:start position:0% +always going to have plus one group two + + + align:start position:0% +always going to have plus one group two +metals in the periodic table are always + + align:start position:0% +metals in the periodic table are always + + + align:start position:0% +metals in the periodic table are always +going to be plus two and aluminum is + + align:start position:0% +going to be plus two and aluminum is + + + align:start position:0% +going to be plus two and aluminum is +always going to be+ three and so those + + align:start position:0% +always going to be+ three and so those + + + align:start position:0% +always going to be+ three and so those +are the ones that that will help guide + + align:start position:0% +are the ones that that will help guide + + + align:start position:0% +are the ones that that will help guide +you you through doing these these + + align:start position:0% +you you through doing these these + + + align:start position:0% +you you through doing these these +problems oxygen is a little bit more + + align:start position:0% +problems oxygen is a little bit more + + + align:start position:0% +problems oxygen is a little bit more +tricky but it's almost always minus two + + align:start position:0% +tricky but it's almost always minus two + + + align:start position:0% +tricky but it's almost always minus two +The Only Exception uh is in peroxides + + align:start position:0% +The Only Exception uh is in peroxides + + + align:start position:0% +The Only Exception uh is in peroxides +where you have a + + align:start position:0% +where you have a + + + align:start position:0% +where you have a +minus1 state and so this will also help + + align:start position:0% +minus1 state and so this will also help + + + align:start position:0% +minus1 state and so this will also help +you in solving a lot of these problems + + align:start position:0% +you in solving a lot of these problems + + + align:start position:0% +you in solving a lot of these problems +but you're actually going to have a + + align:start position:0% +but you're actually going to have a + + + align:start position:0% +but you're actually going to have a +couple examples where um where oxygen is + + align:start position:0% +couple examples where um where oxygen is + + + align:start position:0% +couple examples where um where oxygen is +a bit different okay hydrogen also is + + align:start position:0% +a bit different okay hydrogen also is + + + align:start position:0% +a bit different okay hydrogen also is +usually plus one but there are + + align:start position:0% +usually plus one but there are + + + align:start position:0% +usually plus one but there are +exceptions and you'll actually see a + + align:start position:0% +exceptions and you'll actually see a + + + align:start position:0% +exceptions and you'll actually see a +number of exceptions in this unit so uh + + align:start position:0% +number of exceptions in this unit so uh + + + align:start position:0% +number of exceptions in this unit so uh +you should know that in these particular + + align:start position:0% +you should know that in these particular + + + align:start position:0% +you should know that in these particular +cases um you're going to be it's will be + + align:start position:0% +cases um you're going to be it's will be + + + align:start position:0% +cases um you're going to be it's will be +minus one so here we have group one and + + align:start position:0% +minus one so here we have group one and + + + align:start position:0% +minus one so here we have group one and +group two metals which will always be + + align:start position:0% +group two metals which will always be + + + align:start position:0% +group two metals which will always be +plus and so in this case hydrogen is + + align:start position:0% +plus and so in this case hydrogen is + + + align:start position:0% +plus and so in this case hydrogen is +minus + + align:start position:0% + + + + align:start position:0% + +one okay Florine is always minus one um + + align:start position:0% +one okay Florine is always minus one um + + + align:start position:0% +one okay Florine is always minus one um +other halogens are usually usually minus + + align:start position:0% +other halogens are usually usually minus + + + align:start position:0% +other halogens are usually usually minus +one but there are some exceptions uh so + + align:start position:0% +one but there are some exceptions uh so + + + align:start position:0% +one but there are some exceptions uh so +when you combine it with oxygen you have + + align:start position:0% +when you combine it with oxygen you have + + + align:start position:0% +when you combine it with oxygen you have +an exception to that and so then then + + align:start position:0% +an exception to that and so then then + + + align:start position:0% +an exception to that and so then then +you would have a you could have a + + align:start position:0% +you would have a you could have a + + + align:start position:0% +you would have a you could have a +different oxidation state when it's + + align:start position:0% +different oxidation state when it's + + + align:start position:0% +different oxidation state when it's +combined in these Oxo acids and so then + + align:start position:0% +combined in these Oxo acids and so then + + + align:start position:0% +combined in these Oxo acids and so then +you would have a positive oxidation + + align:start position:0% +you would have a positive oxidation + + + align:start position:0% +you would have a positive oxidation +state or oxidation + + align:start position:0% +state or oxidation + + + align:start position:0% +state or oxidation +number all right things need to add up + + align:start position:0% +number all right things need to add up + + + align:start position:0% +number all right things need to add up +so in neutral molecules the sum of all + + align:start position:0% +so in neutral molecules the sum of all + + + align:start position:0% +so in neutral molecules the sum of all +the oxidation numbers needs to be equal + + align:start position:0% +the oxidation numbers needs to be equal + + + align:start position:0% +the oxidation numbers needs to be equal +to zero if you have a polyatomic anion + + align:start position:0% +to zero if you have a polyatomic anion + + + align:start position:0% +to zero if you have a polyatomic anion +the sum of the oxidation numbers needs + + align:start position:0% +the sum of the oxidation numbers needs + + + align:start position:0% +the sum of the oxidation numbers needs +to add up to the uh the net charge on + + align:start position:0% +to add up to the uh the net charge on + + + align:start position:0% +to add up to the uh the net charge on +that particular ion so things need to + + align:start position:0% +that particular ion so things need to + + + align:start position:0% +that particular ion so things need to +you need to be able to sum to get the + + align:start position:0% +you need to be able to sum to get the + + + align:start position:0% +you need to be able to sum to get the +overall charge of the + + align:start position:0% + + + + align:start position:0% + +molecule all right so uh let's look at + + align:start position:0% +molecule all right so uh let's look at + + + align:start position:0% +molecule all right so uh let's look at +an + + align:start position:0% +an + + + align:start position:0% +an +example + + align:start position:0% +example + + + align:start position:0% +example +nh4+ what would the oxidation number of + + align:start position:0% +nh4+ what would the oxidation number of + + + align:start position:0% +nh4+ what would the oxidation number of +hydrogen be in this + + align:start position:0% + + + + align:start position:0% + +case so it'll be+ one + + align:start position:0% +case so it'll be+ one + + + align:start position:0% +case so it'll be+ one +here what about + + align:start position:0% + + + + align:start position:0% + +nitrogen and so the sum needs to add up + + align:start position:0% +nitrogen and so the sum needs to add up + + + align:start position:0% +nitrogen and so the sum needs to add up +and so if you have four + 1's minus + + align:start position:0% +and so if you have four + 1's minus + + + align:start position:0% +and so if you have four + 1's minus +three gives you + + + align:start position:0% +three gives you + + + + align:start position:0% +three gives you + +one so there's one uh example + + align:start position:0% +one so there's one uh example + + + align:start position:0% +one so there's one uh example +all right another + + align:start position:0% +all right another + + + align:start position:0% +all right another +rule is that uh they don't always have + + align:start position:0% +rule is that uh they don't always have + + + align:start position:0% +rule is that uh they don't always have +to be integers most of the time they are + + align:start position:0% +to be integers most of the time they are + + + align:start position:0% +to be integers most of the time they are +but uh the oxidation number of oxygen in + + align:start position:0% +but uh the oxidation number of oxygen in + + + align:start position:0% +but uh the oxidation number of oxygen in +uh in O2 minus1 would be + + align:start position:0% +uh in O2 minus1 would be + + + align:start position:0% +uh in O2 minus1 would be +[Music] + + align:start position:0% + + + + align:start position:0% + +what be minus a half for each individual + + align:start position:0% +what be minus a half for each individual + + + align:start position:0% +what be minus a half for each individual +oxygen uh atom in there so that's kind + + align:start position:0% +oxygen uh atom in there so that's kind + + + align:start position:0% +oxygen uh atom in there so that's kind +of one of the only exceptions to this + + align:start position:0% +of one of the only exceptions to this + + + align:start position:0% +of one of the only exceptions to this +you won't see this very very often all + + align:start position:0% +you won't see this very very often all + + + align:start position:0% +you won't see this very very often all +right so let's look at a couple more + + align:start position:0% +right so let's look at a couple more + + + align:start position:0% +right so let's look at a couple more +examples to get you used to doing these + + align:start position:0% +examples to get you used to doing these + + + align:start position:0% +examples to get you used to doing these +problems and + + align:start position:0% +problems and + + + align:start position:0% +problems and +um H yeah I'll just erase this part + + align:start position:0% +um H yeah I'll just erase this part + + + align:start position:0% +um H yeah I'll just erase this part +right + + align:start position:0% + + + + align:start position:0% + +here okay so let's look at lithium to + + align:start position:0% +here okay so let's look at lithium to + + + align:start position:0% +here okay so let's look at lithium to +oxide so what's oxygen going to be in + + align:start position:0% +oxide so what's oxygen going to be in + + + align:start position:0% +oxide so what's oxygen going to be in +this + + align:start position:0% +this + + + align:start position:0% +this +compound + + align:start position:0% +compound + + + align:start position:0% +compound +will be min-2 and lithium will + + align:start position:0% +will be min-2 and lithium will + + + align:start position:0% +will be min-2 and lithium will +be+ one lithium is always going to be + + + align:start position:0% +be+ one lithium is always going to be + + + + align:start position:0% +be+ one lithium is always going to be + +one and so if we have plus 2 minus 2 + + align:start position:0% +one and so if we have plus 2 minus 2 + + + align:start position:0% +one and so if we have plus 2 minus 2 +that gives us zero which is the overall + + align:start position:0% +that gives us zero which is the overall + + + align:start position:0% +that gives us zero which is the overall +charge there was no charge that was a + + align:start position:0% +charge there was no charge that was a + + + align:start position:0% +charge there was no charge that was a +neutral molecule so that works + + align:start position:0% +neutral molecule so that works + + + align:start position:0% +neutral molecule so that works +out so let's look at + + align:start position:0% + + + + align:start position:0% + +pcl5 what's chloride going to be in this + + align:start position:0% +pcl5 what's chloride going to be in this + + + align:start position:0% +pcl5 what's chloride going to be in this +case minus1 so we have 5 * -1 + + align:start position:0% +case minus1 so we have 5 * -1 + + + align:start position:0% +case minus1 so we have 5 * -1 +so what does that give us for + + align:start position:0% +so what does that give us for + + + align:start position:0% +so what does that give us for +phosphorus plus + + align:start position:0% +phosphorus plus + + + align:start position:0% +phosphorus plus +five you'll actually find in this unit + + align:start position:0% +five you'll actually find in this unit + + + align:start position:0% +five you'll actually find in this unit +on oxidation reduction we're going to go + + align:start position:0% +on oxidation reduction we're going to go + + + align:start position:0% +on oxidation reduction we're going to go +into balancing oxidation reduction + + align:start position:0% +into balancing oxidation reduction + + + align:start position:0% +into balancing oxidation reduction +equations too and oxidation numbers it's + + align:start position:0% +equations too and oxidation numbers it's + + + align:start position:0% +equations too and oxidation numbers it's +counting this unit lots of counting so + + align:start position:0% +counting this unit lots of counting so + + + align:start position:0% +counting this unit lots of counting so +uh it's maybe a little break I think + + align:start position:0% +uh it's maybe a little break I think + + + align:start position:0% +uh it's maybe a little break I think +people find the acid based titrations a + + align:start position:0% +people find the acid based titrations a + + + align:start position:0% +people find the acid based titrations a +little bit more they have to think more + + align:start position:0% +little bit more they have to think more + + + align:start position:0% +little bit more they have to think more +here you count so that might be a little + + align:start position:0% +here you count so that might be a little + + + align:start position:0% +here you count so that might be a little +nice relief uh coming up okay + + align:start position:0% +nice relief uh coming up okay + + + align:start position:0% +nice relief uh coming up okay +so + + align:start position:0% + + + + align:start position:0% + +hno3 what's what would be + + align:start position:0% + + + + align:start position:0% + +oxygen minus two and we have three of + + align:start position:0% +oxygen minus two and we have three of + + + align:start position:0% +oxygen minus two and we have three of +those uh what's hydrogen going to be + + align:start position:0% +those uh what's hydrogen going to be + + + align:start position:0% +those uh what's hydrogen going to be +here plus one and so what does that + + align:start position:0% +here plus one and so what does that + + + align:start position:0% +here plus one and so what does that +leave us for + + align:start position:0% +leave us for + + + align:start position:0% +leave us for +nitrogen plus five right to get our + + align:start position:0% +nitrogen plus five right to get our + + + align:start position:0% +nitrogen plus five right to get our +overall sum uh equal to zero + + align:start position:0% +overall sum uh equal to zero + + + align:start position:0% +overall sum uh equal to zero +and one last one + + align:start position:0% +and one last one + + + align:start position:0% +and one last one +n2o what's oxygen here min-2 so what + + align:start position:0% +n2o what's oxygen here min-2 so what + + + align:start position:0% +n2o what's oxygen here min-2 so what +does that mean nitrogen has to be plus + + align:start position:0% +does that mean nitrogen has to be plus + + + align:start position:0% +does that mean nitrogen has to be plus +one 2 plus plus one to give us zero you + + align:start position:0% +one 2 plus plus one to give us zero you + + + align:start position:0% +one 2 plus plus one to give us zero you +see nitrogen can have lots of different + + align:start position:0% +see nitrogen can have lots of different + + + align:start position:0% +see nitrogen can have lots of different +numbers and a number of atoms can so + + align:start position:0% +numbers and a number of atoms can so + + + align:start position:0% +numbers and a number of atoms can so +that's why knowing some things and the + + align:start position:0% +that's why knowing some things and the + + + align:start position:0% +that's why knowing some things and the +rules about oxygen chloride and other + + align:start position:0% +rules about oxygen chloride and other + + + align:start position:0% +rules about oxygen chloride and other +things will help you figure out then + + align:start position:0% +things will help you figure out then + + + align:start position:0% +things will help you figure out then +what that other molecule has to be + + align:start position:0% + + + + align:start position:0% + +okay right here are the whole set of + + align:start position:0% +okay right here are the whole set of + + + align:start position:0% +okay right here are the whole set of +rules okay oops going in the wrong + + align:start position:0% +rules okay oops going in the wrong + + + align:start position:0% +rules okay oops going in the wrong +direction all right so let's look at a + + align:start position:0% +direction all right so let's look at a + + + align:start position:0% +direction all right so let's look at a +few + + align:start position:0% +few + + + align:start position:0% +few +definitions um oxidation most of these + + align:start position:0% +definitions um oxidation most of these + + + align:start position:0% +definitions um oxidation most of these +should be familiar to people oxidation + + align:start position:0% +should be familiar to people oxidation + + + align:start position:0% +should be familiar to people oxidation +means that you are losing an + + align:start position:0% +means that you are losing an + + + align:start position:0% +means that you are losing an +electron reduction means that you are + + align:start position:0% +electron reduction means that you are + + + align:start position:0% +electron reduction means that you are +gaining an + + align:start position:0% +gaining an + + + align:start position:0% +gaining an +electron and then we have an oxidizing + + align:start position:0% +electron and then we have an oxidizing + + + align:start position:0% +electron and then we have an oxidizing +agent and an oxidizing agent agent is + + align:start position:0% +agent and an oxidizing agent agent is + + + align:start position:0% +agent and an oxidizing agent agent is +something that accepts electrons and + + align:start position:0% +something that accepts electrons and + + + align:start position:0% +something that accepts electrons and +gets reduced itself and a reducing agent + + align:start position:0% +gets reduced itself and a reducing agent + + + align:start position:0% +gets reduced itself and a reducing agent +is something that is going to donate the + + align:start position:0% +is something that is going to donate the + + + align:start position:0% +is something that is going to donate the +electrons give electrons away so it + + align:start position:0% +electrons give electrons away so it + + + align:start position:0% +electrons give electrons away so it +itself becomes oxidized and these two uh + + align:start position:0% +itself becomes oxidized and these two uh + + + align:start position:0% +itself becomes oxidized and these two uh +terms often confuse people because an + + align:start position:0% +terms often confuse people because an + + + align:start position:0% +terms often confuse people because an +oxidizing agent goes and oxidizes other + + align:start position:0% +oxidizing agent goes and oxidizes other + + + align:start position:0% +oxidizing agent goes and oxidizes other +things but it itself is reduced so it's + + align:start position:0% +things but it itself is reduced so it's + + + align:start position:0% +things but it itself is reduced so it's +an agent of oxidation it's running + + align:start position:0% +an agent of oxidation it's running + + + align:start position:0% +an agent of oxidation it's running +around trying to oxidize other things so + + align:start position:0% +around trying to oxidize other things so + + + align:start position:0% +around trying to oxidize other things so +that's the part to remember um it's it's + + align:start position:0% +that's the part to remember um it's it's + + + align:start position:0% +that's the part to remember um it's it's +uh sometimes people get these these + + align:start position:0% +uh sometimes people get these these + + + align:start position:0% +uh sometimes people get these these +parts backwards so those are really only + + align:start position:0% +parts backwards so those are really only + + + align:start position:0% +parts backwards so those are really only +these are really a lot of the + + align:start position:0% +these are really a lot of the + + + align:start position:0% +these are really a lot of the +definitions you need to know there are + + align:start position:0% +definitions you need to know there are + + + align:start position:0% +definitions you need to know there are +not so many definitions in this + + align:start position:0% +not so many definitions in this + + + align:start position:0% +not so many definitions in this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +unit one other term that you need to be + + align:start position:0% +unit one other term that you need to be + + + align:start position:0% +unit one other term that you need to be +familiar with in here is these + + align:start position:0% +familiar with in here is these + + + align:start position:0% +familiar with in here is these +disproportionation + + align:start position:0% +disproportionation + + + align:start position:0% +disproportionation +reactions and so like we saw with with + + align:start position:0% +reactions and so like we saw with with + + + align:start position:0% +reactions and so like we saw with with +acid base where we could have something + + align:start position:0% +acid base where we could have something + + + align:start position:0% +acid base where we could have something +that could serve as an acid in a base as + + align:start position:0% +that could serve as an acid in a base as + + + align:start position:0% +that could serve as an acid in a base as +aeric we also find that you can have an + + align:start position:0% +aeric we also find that you can have an + + + align:start position:0% +aeric we also find that you can have an +element that can be both oxidized and + + align:start position:0% +element that can be both oxidized and + + + align:start position:0% +element that can be both oxidized and +reduced in a particular uh reaction so + + align:start position:0% +reduced in a particular uh reaction so + + + align:start position:0% +reduced in a particular uh reaction so +we saw that with acid base we had water + + align:start position:0% +we saw that with acid base we had water + + + align:start position:0% +we saw that with acid base we had water +plus water going to hydronium ion and + + align:start position:0% +plus water going to hydronium ion and + + + align:start position:0% +plus water going to hydronium ion and +hydroxide ion where one molecule water + + align:start position:0% +hydroxide ion where one molecule water + + + align:start position:0% +hydroxide ion where one molecule water +was acting as an acid another was acting + + align:start position:0% +was acting as an acid another was acting + + + align:start position:0% +was acting as an acid another was acting +as a base uh similar kind of idea here + + align:start position:0% +as a base uh similar kind of idea here + + + align:start position:0% +as a base uh similar kind of idea here +but in this case we're we're having one + + align:start position:0% +but in this case we're we're having one + + + align:start position:0% +but in this case we're we're having one +thing be oxidized and and reduced so + + align:start position:0% +thing be oxidized and and reduced so + + + align:start position:0% +thing be oxidized and and reduced so +let's uh take a quick look at that + + align:start position:0% +let's uh take a quick look at that + + + align:start position:0% +let's uh take a quick look at that +um so we can break this down to two + + align:start position:0% +um so we can break this down to two + + + align:start position:0% +um so we can break this down to two +different + + align:start position:0% +different + + + align:start position:0% +different +equations and sodium is a spectator ion + + align:start position:0% +equations and sodium is a spectator ion + + + align:start position:0% +equations and sodium is a spectator ion +per sodium really doesn't get to do much + + align:start position:0% +per sodium really doesn't get to do much + + + align:start position:0% +per sodium really doesn't get to do much +of anything in in both this unit and the + + align:start position:0% +of anything in in both this unit and the + + + align:start position:0% +of anything in in both this unit and the +last unit um and we're only focusing on + + align:start position:0% +last unit um and we're only focusing on + + + align:start position:0% +last unit um and we're only focusing on +uh on these species + + align:start position:0% +uh on these species + + + align:start position:0% +uh on these species +here so you're going to have uh one cl + + align:start position:0% +here so you're going to have uh one cl + + + align:start position:0% +here so you're going to have uh one cl +minus going to cl3 minus and another one + + align:start position:0% +minus going to cl3 minus and another one + + + align:start position:0% +minus going to cl3 minus and another one +going to Chloride minus + + align:start position:0% +going to Chloride minus + + + align:start position:0% +going to Chloride minus +so what's happening here so let's take a + + align:start position:0% +so what's happening here so let's take a + + + align:start position:0% +so what's happening here so let's take a +look at what's happening let's look at + + align:start position:0% +look at what's happening let's look at + + + align:start position:0% +look at what's happening let's look at +the oxidation numbers so oxygen here + + align:start position:0% +the oxidation numbers so oxygen here + + + align:start position:0% +the oxidation numbers so oxygen here +will be minus 2 so what does that leave + + align:start position:0% +will be minus 2 so what does that leave + + + align:start position:0% +will be minus 2 so what does that leave +for this uh + + align:start position:0% + + + + align:start position:0% + +chloride so if we write that out all has + + align:start position:0% +chloride so if we write that out all has + + + align:start position:0% +chloride so if we write that out all has +to be equal to one so that would be + + + align:start position:0% +to be equal to one so that would be + + + + align:start position:0% +to be equal to one so that would be + +one and let's consider what's going on + + align:start position:0% +one and let's consider what's going on + + + align:start position:0% +one and let's consider what's going on +over here so again this minus 2 three of + + align:start position:0% +over here so again this minus 2 three of + + + align:start position:0% +over here so again this minus 2 three of +them here and so uh it all needs to be + + align:start position:0% +them here and so uh it all needs to be + + + align:start position:0% +them here and so uh it all needs to be +equal to minus1 over here so what does + + align:start position:0% +equal to minus1 over here so what does + + + align:start position:0% +equal to minus1 over here so what does +that leave for + + align:start position:0% +that leave for + + + align:start position:0% +that leave for +this yeah so we have plus 5 so we're + + align:start position:0% +this yeah so we have plus 5 so we're + + + align:start position:0% +this yeah so we have plus 5 so we're +going from + one here to + + + align:start position:0% +going from + one here to + + + + align:start position:0% +going from + one here to + +five and so um this particular guy is + + align:start position:0% +five and so um this particular guy is + + + align:start position:0% +five and so um this particular guy is +being oxidized so it's losing it's + + align:start position:0% +being oxidized so it's losing it's + + + align:start position:0% +being oxidized so it's losing it's +losing electrons here so now let's look + + align:start position:0% +losing electrons here so now let's look + + + align:start position:0% +losing electrons here so now let's look +down here we already did this one it's + + align:start position:0% +down here we already did this one it's + + + align:start position:0% +down here we already did this one it's +the same so we're at + one and here + + align:start position:0% +the same so we're at + one and here + + + align:start position:0% +the same so we're at + one and here +we're going to minus one so so we have + + align:start position:0% +we're going to minus one so so we have + + + align:start position:0% +we're going to minus one so so we have +this particular guys going from + one to + + align:start position:0% +this particular guys going from + one to + + + align:start position:0% +this particular guys going from + one to +minus one so it's being reduced so you + + align:start position:0% +minus one so it's being reduced so you + + + align:start position:0% +minus one so it's being reduced so you +have the same chloride in both cases but + + align:start position:0% +have the same chloride in both cases but + + + align:start position:0% +have the same chloride in both cases but +in one reaction it's being oxidized and + + align:start position:0% +in one reaction it's being oxidized and + + + align:start position:0% +in one reaction it's being oxidized and +in the other it's being reduced so + + align:start position:0% +in the other it's being reduced so + + + align:start position:0% +in the other it's being reduced so +that's an example of a + + align:start position:0% +that's an example of a + + + align:start position:0% +that's an example of a +disproportionation reaction and also + + align:start position:0% +disproportionation reaction and also + + + align:start position:0% +disproportionation reaction and also +another uh another example of how you + + align:start position:0% +another uh another example of how you + + + align:start position:0% +another uh another example of how you +look at what the oxidation numbers + + align:start position:0% +look at what the oxidation numbers + + + align:start position:0% +look at what the oxidation numbers +are all right + + align:start position:0% +are all right + + + align:start position:0% +are all right +so let's see if we can actually get + + align:start position:0% +so let's see if we can actually get + + + align:start position:0% +so let's see if we can actually get +through some of this this is balancing + + align:start position:0% +through some of this this is balancing + + + align:start position:0% +through some of this this is balancing +reactions how many people have seen + + align:start position:0% +reactions how many people have seen + + + align:start position:0% +reactions how many people have seen +balancing oxidation reduction reactions + + align:start position:0% +balancing oxidation reduction reactions + + + align:start position:0% +balancing oxidation reduction reactions +before a lot of people again it's + + align:start position:0% +before a lot of people again it's + + + align:start position:0% +before a lot of people again it's +counting so I think we can go through + + align:start position:0% +counting so I think we can go through + + + align:start position:0% +counting so I think we can go through +this pretty fast so you have to consider + + align:start position:0% +this pretty fast so you have to consider + + + align:start position:0% +this pretty fast so you have to consider +whether an acid solution or basic + + align:start position:0% +whether an acid solution or basic + + + align:start position:0% +whether an acid solution or basic +solution at least some of the time and + + align:start position:0% +solution at least some of the time and + + + align:start position:0% +solution at least some of the time and +let's do acid solution first + + align:start position:0% +let's do acid solution first + + + align:start position:0% +let's do acid solution first +so um you can take this and uh write + + align:start position:0% +so um you can take this and uh write + + + align:start position:0% +so um you can take this and uh write +your unbalanced uh equations out for + + align:start position:0% +your unbalanced uh equations out for + + + align:start position:0% +your unbalanced uh equations out for +this breaking down into into two halves + + align:start position:0% +this breaking down into into two halves + + + align:start position:0% +this breaking down into into two halves +and figure out what's happening so again + + align:start position:0% +and figure out what's happening so again + + + align:start position:0% +and figure out what's happening so again +uh here we have -2 * 7 and it all has to + + align:start position:0% +uh here we have -2 * 7 and it all has to + + + align:start position:0% +uh here we have -2 * 7 and it all has to +be min-2 so uh this oxidation number + + align:start position:0% +be min-2 so uh this oxidation number + + + align:start position:0% +be min-2 so uh this oxidation number +would be + + align:start position:0% + + + + align:start position:0% + +what six uh time 2 so we're plus 6 to + + + align:start position:0% +what six uh time 2 so we're plus 6 to + + + + align:start position:0% +what six uh time 2 so we're plus 6 to + +three over here so plus 6 to + three and + + align:start position:0% +three over here so plus 6 to + three and + + + align:start position:0% +three over here so plus 6 to + three and +so we have a reduction so we're going + + align:start position:0% +so we have a reduction so we're going + + + align:start position:0% +so we have a reduction so we're going +down in in number here and so this one + + align:start position:0% +down in in number here and so this one + + + align:start position:0% +down in in number here and so this one +is the reduction and that's good because + + align:start position:0% +is the reduction and that's good because + + + align:start position:0% +is the reduction and that's good because +over here we have plus two to+ three so + + align:start position:0% +over here we have plus two to+ three so + + + align:start position:0% +over here we have plus two to+ three so +we have our oxidation in the other part + + align:start position:0% +we have our oxidation in the other part + + + align:start position:0% +we have our oxidation in the other part +so you're always going to have oxidation + + align:start position:0% +so you're always going to have oxidation + + + align:start position:0% +so you're always going to have oxidation +reduction you'll always have something + + align:start position:0% +reduction you'll always have something + + + align:start position:0% +reduction you'll always have something +being oxidized and something else being + + align:start position:0% +being oxidized and something else being + + + align:start position:0% +being oxidized and something else being +reduced so now we have to balance this + + align:start position:0% +reduced so now we have to balance this + + + align:start position:0% +reduced so now we have to balance this +and so the first thing you're going to + + align:start position:0% +and so the first thing you're going to + + + align:start position:0% +and so the first thing you're going to +do uh you're going to look and insert + + align:start position:0% +do uh you're going to look and insert + + + align:start position:0% +do uh you're going to look and insert +coefficients to balance the elements uh + + align:start position:0% +coefficients to balance the elements uh + + + align:start position:0% +coefficients to balance the elements uh +except for oxygen and hydrogen on both + + align:start position:0% +except for oxygen and hydrogen on both + + + align:start position:0% +except for oxygen and hydrogen on both +sides so um do we need to do something + + align:start position:0% +sides so um do we need to do something + + + align:start position:0% +sides so um do we need to do something +up here if so + + align:start position:0% +up here if so + + + align:start position:0% +up here if so +what multiply by two what about down + + align:start position:0% +what multiply by two what about down + + + align:start position:0% +what multiply by two what about down +here nothing so now we're going to add + + align:start position:0% +here nothing so now we're going to add + + + align:start position:0% +here nothing so now we're going to add +water to balance + + align:start position:0% +water to balance + + + align:start position:0% +water to balance +oxygen and again we only need to worry + + align:start position:0% +oxygen and again we only need to worry + + + align:start position:0% +oxygen and again we only need to worry +about one side there's seven oxygen here + + align:start position:0% +about one side there's seven oxygen here + + + align:start position:0% +about one side there's seven oxygen here +so we have to add seven waters on the + + align:start position:0% +so we have to add seven waters on the + + + align:start position:0% +so we have to add seven waters on the +other side + + align:start position:0% +other side + + + align:start position:0% +other side +so we have our seven Waters here so now + + align:start position:0% +so we have our seven Waters here so now + + + align:start position:0% +so we have our seven Waters here so now +we want to balance hydrogens and you can + + align:start position:0% +we want to balance hydrogens and you can + + + align:start position:0% +we want to balance hydrogens and you can +add H+ the book uses hydronium ion which + + align:start position:0% +add H+ the book uses hydronium ion which + + + align:start position:0% +add H+ the book uses hydronium ion which +makes it much harder so I suggest you + + align:start position:0% +makes it much harder so I suggest you + + + align:start position:0% +makes it much harder so I suggest you +don't do that and just add H+ so if you + + align:start position:0% +don't do that and just add H+ so if you + + + align:start position:0% +don't do that and just add H+ so if you +just add h plus how much do you need to + + align:start position:0% +just add h plus how much do you need to + + + align:start position:0% +just add h plus how much do you need to +add you need to add 14 to the other side + + align:start position:0% +add you need to add 14 to the other side + + + align:start position:0% +add you need to add 14 to the other side +again nothing down + + align:start position:0% +again nothing down + + + align:start position:0% +again nothing down +here and so now you need to balance + + align:start position:0% +here and so now you need to balance + + + align:start position:0% +here and so now you need to balance +charge by adding electron + + align:start position:0% +charge by adding electron + + + align:start position:0% +charge by adding electron +bonds so in this case it's going to be + + + align:start position:0% +bonds so in this case it's going to be + + + + align:start position:0% +bonds so in this case it's going to be + +6 we have 14 - 2 uh on this side and uh + + align:start position:0% +6 we have 14 - 2 uh on this side and uh + + + align:start position:0% +6 we have 14 - 2 uh on this side and uh +we have this uh this six on the other + + align:start position:0% +we have this uh this six on the other + + + align:start position:0% +we have this uh this six on the other +side and then over here what do we have + + align:start position:0% +side and then over here what do we have + + + align:start position:0% +side and then over here what do we have +to + + align:start position:0% +to + + + align:start position:0% +to +add just have to add + + align:start position:0% +add just have to add + + + align:start position:0% +add just have to add +one so now we take this and now we need + + align:start position:0% +one so now we take this and now we need + + + align:start position:0% +one so now we take this and now we need +to multiply the reaction so the number + + align:start position:0% +to multiply the reaction so the number + + + align:start position:0% +to multiply the reaction so the number +of electrons are equal so we'd multiply + + align:start position:0% +of electrons are equal so we'd multiply + + + align:start position:0% +of electrons are equal so we'd multiply +by six + + align:start position:0% +by six + + + align:start position:0% +by six +here and now our electrons are equal the + + align:start position:0% +here and now our electrons are equal the + + + align:start position:0% +here and now our electrons are equal the +electrons have to cancel out if they + + align:start position:0% +electrons have to cancel out if they + + + align:start position:0% +electrons have to cancel out if they +don't you've done something + + align:start position:0% +don't you've done something + + + align:start position:0% +don't you've done something +wrong so now we add and make the + + align:start position:0% +wrong so now we add and make the + + + align:start position:0% +wrong so now we add and make the +appropriate uh + + align:start position:0% +appropriate uh + + + align:start position:0% +appropriate uh +cancellations so uh here's the whole + + align:start position:0% +cancellations so uh here's the whole + + + align:start position:0% +cancellations so uh here's the whole +equation and we should be able to cancel + + align:start position:0% +equation and we should be able to cancel + + + align:start position:0% +equation and we should be able to cancel +out electrons if we don't we did + + align:start position:0% +out electrons if we don't we did + + + align:start position:0% +out electrons if we don't we did +something + + align:start position:0% +something + + + align:start position:0% +something +wrong and uh can we cancel anything else + + align:start position:0% + + + + align:start position:0% + +out not really so you want to double + + align:start position:0% +out not really so you want to double + + + align:start position:0% +out not really so you want to double +check that it's balanced 14 H's here two + + align:start position:0% +check that it's balanced 14 H's here two + + + align:start position:0% +check that it's balanced 14 H's here two +chromium uh you have the seven oxygens + + align:start position:0% +chromium uh you have the seven oxygens + + + align:start position:0% +chromium uh you have the seven oxygens +and the six irons that's the same on the + + align:start position:0% +and the six irons that's the same on the + + + align:start position:0% +and the six irons that's the same on the +other side same charge on both sides and + + align:start position:0% +other side same charge on both sides and + + + align:start position:0% +other side same charge on both sides and +then finally if it's in basic solution + + align:start position:0% +then finally if it's in basic solution + + + align:start position:0% +then finally if it's in basic solution +all we're going to do same steps and + + align:start position:0% +all we're going to do same steps and + + + align:start position:0% +all we're going to do same steps and +adjust the pH by adding o so if we had + + align:start position:0% +adjust the pH by adding o so if we had + + + align:start position:0% +adjust the pH by adding o so if we had +14 plus we'd add 14 O's and then come + + align:start position:0% +14 plus we'd add 14 O's and then come + + + align:start position:0% +14 plus we'd add 14 O's and then come +along and uh you'd add those up and then + + align:start position:0% +along and uh you'd add those up and then + + + align:start position:0% +along and uh you'd add those up and then +you can cancel again and so now instead + + align:start position:0% +you can cancel again and so now instead + + + align:start position:0% +you can cancel again and so now instead +of having H+ we have o and so in acidic + + align:start position:0% +of having H+ we have o and so in acidic + + + align:start position:0% +of having H+ we have o and so in acidic +solution you'd have uh H+ and in basic + + align:start position:0% +solution you'd have uh H+ and in basic + + + align:start position:0% +solution you'd have uh H+ and in basic +solution you have o so that's balancing + + align:start position:0% +solution you have o so that's balancing + + + align:start position:0% +solution you have o so that's balancing +it's pretty simple you just have to make + + align:start position:0% +it's pretty simple you just have to make + + + align:start position:0% +it's pretty simple you just have to make +sure that everything adds + + align:start position:0% + + + + align:start position:0% + +up \ No newline at end of file diff --git a/4HEi-ZDXYho.txt b/4HEi-ZDXYho.txt new file mode 100644 index 0000000000000000000000000000000000000000..55fb5ea2a206870c0f153dd64b59a6a40c1e7469 --- /dev/null +++ b/4HEi-ZDXYho.txt @@ -0,0 +1,298 @@ +OK. +3.53 is an elective. + +It is a technical elective in +the graduate program here in the + +Department of Material Science +and Engineering. + +That it is to say it is not a +core requirement. + +So that poses some different +challenges for the instructor. + +In a core class you have a +captive audience. + +The students have to take the +class because it satisfies some + +degree of requirement and so +they are there whether they like + +it or not. +In 3.53, the students who are + +taking 3.53 are taking it +because they want to learn the + +material because presumably it +is of relevance to their + +research. +So you have the luxury of + +teaching a group that is +self-selected. + +They want to learn the +material, they are interested in + +the material, +and they are fairly far + +advanced in their education. +The view of the class is to + +give students a mastery of the +elements of electrochemical + +processes, whether they are +passive, as in the case of + +corrosion, or active as in the +case of electrodeposition. + +And so I spend about the first +20% of the class giving sort of + +my view of electrochemical +processes at the atomistic level + +so that students understand what +the origins are of the various + +kinetic parameters. +And then after that the class + +pretty much follows a very good +textbook in the field written by + +Allen Bard and Larry Faulkner on +Electrochemical Methods. + +And these are methods in which +electrochemical techniques are + +used to characterize +electrochemical processes. + +And we go through pretty much +chapter and verse studying the + +various techniques. +And, on the platform that I + +have erected, +understanding how these + +techniques differ from one +another and how some of them are + +superior to others in particular +settings. + +There is no best technique. +It's sort of like asking what + +is the best wine. +It depends on what are you + +trying to measure, +to what degree of accuracy, + +et cetera. +And I build in a lot of time + +for question and answer. +And so it allows, + +at some level, +for me to be running what I + +consider to be a clinic where +students come in with their, + +you know, I am having trouble +in my experiment these days. + +And, well, let's lay it out in +front of the class and let + +everybody participate. +And we will learn from the + +experience. +OK. + +This is a class that has been +around for a long time. + +I started teaching it in the +late `80s. + +Sometime after I got tenure, +my department head said to me, + +you know, X and Y have been +alternating the teaching of + +electrochemistry. +It is time you took this over. + +And I said, great, +well, I will be sure to go talk + +to them and, you know, +get their take on it. + +He said no, no, +no, no, I don't want you + +talking to them. +He said I want you to start + +with a clean sheet of paper, +and I want you to write on that + +clean sheet of paper what your +vision is for a modern + +electrochemistry subject in a +material science department in + +the last days of the 20th +century. + +OK. +So that is what I did. + +And mapped out what I thought +are the key elements that need + +to go into that class. +And mercifully found a really + +good book that would help me +with the middle third of the + +class as it was laid out at the +time. + +When I launched the class, +I found that I was teaching far + +too much of old style aqueous +solution chemistry, + +there is this Debye-Huckel +model of dilute electrolytes and + +a whole bunch of other things +that, you know, + +ultimately people don't use +that much. + +But the central part, +the techniques, + +I found that the students +really wanted to learn more + +about the techniques because it +cemented their understanding of + +kinetics and it also made use of +the special ability these MIT + +graduate students have with the +mathematics. + +So I enlarged the second part. +And then the last part involves + +industrial electrochemistry. +And I have kept that to varying + +degrees, depending on the makeup +of the class. + +I don't want to give the +students the impression that + +there is a right answer because +sometimes there is plurality of + +right answers. +And I don't want to give the + +students the impression that +there is the right way to solve + +the problem. +There is a plurality of ways, + +a plurality of approach, +so I am putting forward one way + +to solve the problem leading to +one answer. + +In many of the cases, +especially in the formative + +stages, it is a simple numerical +problem which is basically + +making sure that they know how +to use the formula. + +In some cases, +it is not so much how do you + +get the right answer. +It is that you have to make a + +decision between several +alternatives. + +And so, within adequate data +and other shortcomings, + +you have to make engineering +judgments. + +And, in some cases, +the solution consists of + +eliminating that which you can +verify cannot be the answer. + +And all of these +problem-solving techniques are + +valuable for engineers so they +need to be cultivated. + +And I guess calling the +solutions model solutions or + +sometimes I use the term +solution outlines just starts to + +nurture that idea that it is not +crisp. + +There is uncertainty. +It is a noisy system. + +And you need to master the +various techniques as opposed to + +say this is the answer key. +47.2, that's it. + +No. \ No newline at end of file diff --git a/4X0SGGrXDiI.txt b/4X0SGGrXDiI.txt new file mode 100644 index 0000000000000000000000000000000000000000..5efe948e3a8ac505ddfc7a530d082e9d9965880f --- /dev/null +++ b/4X0SGGrXDiI.txt @@ -0,0 +1,3186 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Well, +OK, Professor Frey + +invited me to give the +two lectures this week + +on first order equations, like +that one, first order dy dt. + +And the lectures next week will +be on second order equation. + +So we're looking for, you could +say, formulas for the solution. + +We'll get as far as we +can with formulas, then + +numerical methods. + +Graphical methods take over +in more complicated problems. + +This is a model problem. + +It's linear. + +I chose it to have +constant coefficient a, + +and let me check the units. + +Always good to see the +units in a problem. + +So let me think of this +y, as the money in a bank, + +or bank balance, so y as in +dollars, and t, time, in years. + +So we're looking at the ups +and downs of bank balance y. + +The rate of change, so the +units then are dollars per year. + +So every term in the equation +has to have the right units. + +So y is in dollars, +so the interest rate a + +is percent per +year, say 6% a year. + +So a could be 6%-- that's +dimensionless-- per year, + +or half a percent per +month if we change. + +So if we change +units, the constant a + +would change from 6 to a half. + +But let's stay with 6. + +And then q of t represents +deposits and withdrawals, + +so that's in dollars +per year again. + +Has to be. + +So that's continuous. + +We think of the deposits +and the interest + +as being computed continuously +as time goes forward. + +So if that's a constant-- and +I'll take that case first, + +q equal 1-- that would +mean that we're putting in, + +depositing $1 per year, +continuously through the year. + +So that's the model that comes +from a differential equation. + +A difference equation would +give us finite time steps. + +So I'm looking for the solution. + +And with constant +coefficients, linear, we're + +going to get a formula +for the solution. + +I could actually deal +with variable interest + +rate for this one +first order equation, + +but the formula becomes messy. + +But you can still do it. + +After that point, for a +second order equations + +like oscillation, +or for a system + +of several equations +coupled together, + +constant coefficients is +where you can get formulas. + +So let's go with that case. + +So how to solve that equation? + +Let me take first of all, a +constant, constant source. + +So I think of q as +the source term. + +To get one nice formula, let me +take this example, ay plus 1, + +let's say. + +How do you find y +of t to solve that? + +And you start with some +initial condition y of 0. + +That's the opening deposit +that you make at time 0. + +How to solve that equation? + +Well, we're looking +for a solution. + +And solutions to linear +equations have two parts. + +So the same will happen +in linear algebra. + +One part is a solution +to that equation, + +so we're just looking +for one, any one, + +and we'll call it a +particular solution. + +And the associated null +equation, dy dt equal ay. + +So this is an equation +with q equals 0. + +That's why it's called null. + +And it's also +called homogeneous. + +So more textbooks use that +long word homogeneous, + +but I use the word null +because it's shorter + +and because it's the same +word in linear algebra. + +So let me call yn +the null solution, + +the general null solution. + +And y, I'm looking here for +a particular solution yp, + +and I'm going to-- here's +the key for linear equations. + +Let me take that off and +focus on those two equations. + +How does solving the null +equation, which is easy to do, + +help me? + +Why can I, as I plan +to do, add in yn to yp? + +I just add the two equations. + +Can I just add +those two equations? + +I get the derivative of yp +plus yn on the left side. + +And I have a times yp plus yn. + +And that is a critical moment +there when we use linearity. + +I had a yp a yn, and I +could put them together. + +If it was y squared, yp +squared and yn squared + +would not be the same +as yp plus yn squared. + +It's the linearity that +comes, and then I add the 1. + +So what do I see from this? + +I see that yp plus yn +also solves my equation. + +So the whole family of +solutions is 1 yp plus any yn. + +And why do I say any yn? + +Because when I find +one, I find more. + +The solutions to +this equation are + +yn could be e to the at, +because the derivative of e + +to the at does bring +down a factor a. + +But you see, I've left space +for any multiple of e to the at. + +This is where that long +word homogeneous comes from. + +It's homogeneous means I can +multiply by any constant, + +and I still solve the equation. + +And of course, the +key again is linear. + +So now I have-- well, you could +say I've done half the job. + +I've found yn, the general yn. + +And now I just have +to find one yp, + +one solution to the equation. + +And with this source +term, a constant, + +there's a nice way to +find that solution. + +Look for a constant solution. + +So certain right +hand sides, and those + +are the like the +special functions + +for the special source terms +for differential equation, + +certain right hand +sides-- and I'm just + +going to go down a +list of them today. + +The next one on the +list-- can I tell you + +what the next one +on the list will be? + +y prime equal ay. + +I use prime for-- +well, I'll write dy dt, + +but often I'll write y prime. + +dy dt equal ay plus +an exponential. + +That'll be number two. + +So I'm just preparing +the way for number two. + +Well, actually number +one, this example + +is the same as that exponential +example with exponent + +s equal 0, right? + +If s is 0, then I +have a constant. + +So this is a special +case of that one. + +This is the most +important source term + +in the whole subject. + +But here we go +with a constant 1. + +So we've got yn. + +And what's yp? + +I just looked to see. + +Can I think of one? + +And with these +special functions, + +you can often find a +solution of the same form + +as the source term. + +And in this case, +that means a constant. + +So if yp is a constant, +this will be 0. + +So I just want to +pick the constant that + +makes this thing 0. + +And of course, their right hand +side is 0 when yp is minus 1 + +over a. + +So I've got it. + +We've solved that +equation, except we + +didn't match the +initial condition yet. + +Let me if you take +that final step. + +So the general y is any +multiple, any null solution, + +plus any one particular +solution, that one. + +And we want to match it +to y of 0 at t equals 0. + +So I want to take that solution. + +I want to find that +constant, here. + +That's the only remaining +step is find that constant. + +You've done it in the homework. + +So at t equals 0, +y of 0 is-- at t + +equals 0, this is C. This +is the minus 1 over a. + +So I learn what the C has to be. + +And that's the final step. + +C is bring the 1 over +a onto that side, + +so C will be y of 0 e to the +at minus 1 over a e to at. + +And here we had +a minus 1 over a. + +Well, it'll be plus +1 over a e to the at. + +So now I've just put in the C, +y of 0 plus 1 over a. y of 0 + +plus 1 over a has gone +in for C. And now I + +have to subtract this 1 over a. + +Here, I see a 1 over a, +so I can do it neatly. + +Got a solution. + +We can check it, of course. + +At t equals 0, this +disappears, and this is y of 0. + +And it has the form. + +It's a multiple of e to the +at and a particular solution. + +So that's a good one. + +Notice that to get the +initial condition right, + +I couldn't take C to be y of +0 to get the initial condition + +right. + +To get the initial +condition right, + +I had to get that, this +minus 1 over a in there. + +Good for that one? + +Let me move to the +next one, exponentials. + +So again, we know that the +null equation with no source + +has this solution e to the at. + +And I'm going to suppose +that the a in e to the + +at in the null solution +is different from the s + +in the source function, +which will come up + +in the particular solution. + +So you're going to +see either the st + +in the particular +solution and an e to the + +at in the null solution. + +And in the case when s equals +a, that's called resonance, + +the two exponents are the +same, and the formula changes + +a little. + +Let's leave that case for later. + +How do I solve this? + +I'm looking for a +particular solution + +because I know the +null solutions. + +How am I going to get +a particular solution + +of this equation? + +Fundamental observation, +the key point + +is it's going to be a +multiple of e to the st. + +If an exponential goes in, then +that will be an exponential. + +Its derivative will +be an exponential. + +I'll have e to the +st's everywhere. + +And I can get the number right. + +So I'm looking for y try. + +So I'll put try, knowing it's +going to work, as some number + +times e to the st. +So this would be + +like the exponential response. + +Response, do you know +that word response? + +So response is the solution. + +The input is q, and +the response is Y. + +And here, the input +is e to the st, + +and the response is a multiple +of e to the st. So plug it in. + +The timed derivative +will be Y. Taking + +the derivative will bring down +a 1. e to the st equals aY. + +A aY e to the st plus 1 e to +the st. Just what we hoped. + +The beauty of +exponentials is that when + +you take their derivatives, +you just have more exponential. + +That's the key thing. + +That's why exponential is +the most important function + +in this course, absolutely +the most important function. + +So it happened here. + +I can cancel e to the +st, because every term + +has one of them. + +So I'm seeing that-- +what am I getting for Y? + +Getting a very important +number for Y. So + +I bring aY onto +this side with sY. + +On this side I just have a 1. + +Maybe it's worth putting +on its own board. + +Y is, so Ys aY comes with a +minus, and the 1, 1 over-- + +so Y was multiplied +by s minus a. + +That's the right quantity to +get a particular solution. + +And that 1 over s +minus a, you see + +why I wanted s to +be different from a. + +I If s equaled a in that +case, in that possibility + +of resonance when the two +exponents are the same, + +we would have 1 over 0, and we'd +have to look somewhere else. + +The name for that-- this has to +have a name because it shows up + +all the time. + +The exponential +response function, + +you could call it that. + +Most people would call +it the transfer function. + +So any constant coefficient +linear equation's + +going to have a transfer +function, easy to find. + +Everything easy, that's +what I'm emphasizing, here. + +Everything's straightforward. + +That transfer function +tells you what + +multiplies the exponential. + +So the source was here. + +And the response is here, the +response factor, you could say, + +the transfer function. + +Multiply by 1 over s minus a. + +So if s is close to a, +if the input is almost + +at the same exponent as the +natural, as the null solution, + +then we're going to +get a big response. + +So that's good. + +For a constant coefficient +problem second order, + +other problems we can find +that response function. + +It's the key function. + +It's the function +if we have, or if we + +were to look at Laplace +transforms, that + +would be the key. + +When you take +Laplace transforms, + +the transfer function shows up. + +Then when you take inverse +Laplace transforms, + +you have to find what function +has that Laplace transform. + +So did we get the-- we +got the final answer then. + +Let me put it here. y is e +to the st times this factor. + +So I divide by s minus a. + +A nice solution. + +Let me also anticipate +something more. + +An important case for e to +the st is e to the i omega t. + +e to the st, we think about +as exponential growth, + +exponential decay. + +But that's for positive +s and negative s. + +And all important in +applications is oscillation. + +So coming, let me say, +coming is either late today + +or early Wednesday will +be s equal i omega, + +so where the source term +is e to the i omega t. + +And alternating, so this +is electrical engineers + +would meet it constantly from +alternating voltage source, + +alternating current source, +AC, with frequency omega, + +60 cycles per +second, for example. + +Why don't I just +deal with this now? + +Because it involves +complex numbers. + +And we've got to take a little +step back and prepare for that. + +But when we do it, +we'll get not only e + +to the i omega t, +which I brought out, + +but also, it's real part. + +You remember the great +formula with complex numbers, + +Euler's formula, +that e to the i omega + +t is a combination of cosine +omega t, the real part, + +and then the imaginary +part is sine omega t. + +So this is looking +like a complex problem. + +But it actually solves two +real problems, cosine and sine. + +Cosine and sine will be on our +short list of great functions + +that we can deal with. + +But to deal with them neatly, +we need a little thought + +about complex numbers. + +So OK if I leave +e to the i omega + +t for the end of the list, here? + +So I'm ready for another +one, another source term. + +And I'm going to pick +the step function. + +So the next example is going to +be dy dt equals ay plus a step. + +Well, suppose I +put H of t there. + +Suppose I put H of t. + +And I ask you for the +solution to that guy. + +So that step function, +its graph is here. + +It's 0 for negative time, +and it's 1 for positive time. + +So we've already solved +that problem, right? + +Where did I solve this equation? + +This equation is +already on that board. + +Because why? + +Because H of t is +for t positive. + +That's the only +place we're looking. + +This whole problem, we're +not looking at negative t. + +We're only looking +at t from 0 forward. + +And what is H of +t from 0 forward? + +It's 1. + +It's a constant. + +So that problem, as it stands, +is identical to that problem. + +Same thing, we have a 1. + +No need to solve that again. + +The real example is when +this function jumps up + +at some later time T. Now I have +the function is H of t minus T. + +Do you see that, why the step +function that jumps at time T + +has that formula? + +Because for little +t before that time, + +in here, this is-- +what's the deal? + +If little t is +smaller than big T, + +then t minus T is +negative, right? + +If t is in here, then +t minus capital T + +is going to be a +negative number. + +And H of a negative number is 0. + +But for t greater than capital +T, this is a positive number. + +And H of a positive number is 1. + +Do you see how if you +want to shift a graph, + +if you want the graph +to shift, if you want + +to move the starting time, +then algebraically, the way + +you do it is to change t to +t minus the starting time. + +And that's what I want to do. + +So physically, what's +happening with this equation? + +So it starts with +y of 0 as before. + +Let's think of a bank balance +and then other things, too. + +If it's a bank balance, we put +in a certain amount, y of 0. + +We hope. + +And that grew. + +And then starting +at time, capital T, + +this switch turns on. + +Actually, physically, +step function + +is really often describing a +switch that's turned on, now. + +This source term act +begins to act at that time. + +And it acts at 1. + +So at time capital T we start +putting money into our account. + +Or taking it out, of course. + +If this with a minus sign, +I'd be putting money in. + +Sorry, I would start with +some money in, y of 0. + +I would start with money in. + +Yeah, actually, tell +me what's the solution + +to this equation that +starts from y of 0? + +What's the solution up until +the switch is turned on? + +What's the solution before +this switch happens, + +this solution while +this is still 0? + +So let's put that part +of the answer down. + +This is for t smaller +than T. What's the answer? + +This is all common sense. + +It's coming fast, so I'm +asking these questions. + +And when I asked that question, +it's a sort of indication + +that you can really +see the answer. + +You don't need to go back +to the textbook for that. + +What have we got here? + +Yeah? + +AUDIENCE: Is it the null +solution [INAUDIBLE]? + +PROFESSOR: It'll be this guy. + +Yeah, the particular +solution will be 0. + +Right, the particular solution +is 0 before this is on. + +I'm sorry, the +null solution is 0, + +and the particular solution, +well, the particular solution + +is a guy that starts right. + +I don't know. + +Those names were not important. + +And then the question +is-- so it's just + +our initial deposit growing. + +Now, all I ask, what +about after time T? + +What about after time T? + +For t after time T, and +hopefully, equal time T, + +what do you think +y of t will be? + +Again, we want to +separate in our minds + +the stuff that's starting +from the initial condition + +from the stuff that's piling +up because of the source. + +So one part will be that guy. + +I haven't given the +complete answer. + +But this is continuing to grow. + +And because it's linear, we're +always using this neat fact + +that our equation is linear. + +We can watch things +separately, and then + +just add them together. + +So I plan to add +this part, which + +comes from initial +condition to a part + +that-- maybe we can guess it-- +that's coming from the source. + +And how do we have any +chance to guess it? + +Only because that particular +source, once it's turned on, + +jumps to a constant +1, and we've solved + +the equation for a constant 1. + +Let me go back here. + +I think our answer +to this question-- + +so this is like just first +practice with a step function, + +to get the hang of +a step function. + +So I'm seeing this same y of +0 e to the at in every case, + +because that's what happens +to the initial deposit. + +I'll say grow, assuming +the bank's paying + +a positive interest rate. + +And now, where did +this term comes from? + +What did that term represent? + +AUDIENCE: The money +that [INAUDIBLE]. + +PROFESSOR: The money that, yeah? + +AUDIENCE: They had +each of [INAUDIBLE]. + +PROFESSOR: The money +that came in and grew. + +It came in, and then +it grew by itself, + +grew separately from +that these guys. + +So the initial condition +is growing along. + +And the money we put +in starts growing. + +Now, the point is what? + +That over here, it's going +to look just like that. + +So I'm going to have a 1 over a. + +And I'm going to have +something like that. + +But can you just guess +what's going to go in there? + +When I write it down, +it'll make sense. + +So this term is representing +what we have at time little t, + +later on, from the +deposits we made, + +not the initial one, but +the source, the continuing + +deposits. + +And let me write it. + +It's going to be a 1 over a +e to the a something minus 1. + +It's going to look +just like that guy. + +When I say that guy, let +me point to it again-- + +e to the at minus 1. + +But it's not quite +e to the at minus 1. + +What is it? + +AUDIENCE: t minus [INAUDIBLE]. + +PROFESSOR: t minus +capital T, because it + +didn't start until that time. + +So I'm going to leave that as, +like, reasonable, sensible. + +Think about a step function +that's turned on a capital time + +T. Then it grows from that time. + +Of course, mentally, I +never write down a formula + +like that without +checking at t equal to T, + +because that's the one important +point, at t equal capital + +T. What is this at +t equal capital T? + +It's 0. + +At t equal capital T, this is +e to the 0, which is 1 minus 1 + +altogether 0. + +And is that the right answer? + +At t equal capital T is 0, +should I have nothing here? + +Yes? + +No? + +Give me a head shake. + +Should I have nothing +at t equal capital T? + +I've got nothing. + +e to the 0 minus +1, that's nothing? + +Yes, yes that's the right thing. + +Because at capital T, the +source has just turned on, + +hasn't had time to +build up anything, + +just that was the +instant it turned on. + +So that's a step function. + +A step function is a +little bit of a stretch + +from an ordinary +function, but not as much + +of a stretch as its derivative. + +In a way, this is like the +highlight for today, coming up, + +to deal with not only a step +function, but a delta function. + +I guess every author +and every teacher + +has to think am I going +to let this delta function + +into my course or into the book? + +And my answer is yes. + +You have to do it. + +You should do it. + +Delta functions are-- +they're not true functions. + +As we'll see, no +true function can + +do what a delta function does. + +But it's such an +intuitive, fantastic model + +of things happening over +a very, very short time. + +We just make that +short time into 0. + +So we're saying with +the delta function, + +we're going to say that +something can happen in 0 time. + +Something can happen in 0 time. + +It's a model of, you know, +when a bat hits a ball. + +There's a very short time. + +Or a golf club hits a golf ball. + +There's a very +short time interval + +when they're in contact. + +We're modeling that by 0 +time, but still, the ball + +gets an impulse. + +Normally, for 0 time, if you're +doing things continuously, + +what you do over 0 +time is no importance. + +But we're not doing things +continuously, at all. + +So here we go. + +You've seen this guy, I think. + +But if you haven't, +here's the time to see it. + +So the delta function +is the derivative + +of-- so I've written three +important functions up here. + +Let me start with +a continuous one. + +That function, the ramp +is 0, and then the ramp + +suddenly ramps up to t. + +Take its derivative. + +So the derivative, the +slope of the ramp function + +is certainly 0 there. + +And here, the slope is 1. + +So the slope jumped from 0 to 1. + +The slope of the ramp +function is the step function. + +Derivative of ramp equals step. + +Why don't I write +those words down? + +Derivative of ramp equals step. + +So there is already +the step function. + +In pure calculus, +the step function + +has already got a +little question mark. + +Because at that point, the +derivative in a calculus course + +doesn't exist, +strictly doesn't exist, + +because we get a +different answer + +0 on the left side from the +answer, 1 on the right side. + +We just go with that. + +I'm not going to +worry about what + +is its value at that point. + +It's 0 up for t negative, +and it's 1 for t positive. + +And often, I'll take it +1 for t equals 0, also. + +Usually, I will. + +That's the small problem. + +Now, the bigger problem is the +derivative of the-- so this + +is now the derivative +of the step function. + +So what's the derivative +of this step function? + +Well, the derivative along +there is certainly 0. + +The derivative along +here is certainly 0. + +But the derivative, +when that jumped, + +the derivative, the +slope was infinite. + +That line is vertical. + +Its slope is infinite. + +So at that one point, you have +an affinity, here, delta of 0. + +You could say delta +of 0 is infinite. + +But you haven't +said much, there. + +Infinite is too vague. + +Actually, I wouldn't +know if you gave + +me infinite or 2 times infinite. + +I couldn't tell the difference. + +So I'll put it in quotes, +because it sort of gives us + +comfort. + +But it doesn't mean much. + +What does mean much? + +Somehow that's important. + +Can I tell you how to +work with delta functions, + +how to think about +delta functions? + +It's the right way to +think about delta function. + +So here's some comment +on delta function. + +Giving the values of the +function, 0, and infinity, + +and 0, is not the best. + +What you can do with +a delta function + +is you can integrate it. + +You can define the +function by integrals. + +Integrals of things are nice. + +Do you think in your mind +when you take derivatives, + +as we did going left to right, +we were taking derivatives. + +The function was getting crazy. + +When we go right to left, take +integrals, those are smoothing. + +Integrals make +functions smoother. + +They cancel noise. + +They smooth the function out. + +So what we can do is to take the +integral of the delta function. + +We could take it from +any negative number + +to any positive number. + +And what answer would we get? + +What would be the right, +well, the one thing people + +know about the +delta function is-- + +and actually, it's the +key thing-- the integral + +of the delta function. + +Again, I'm integrating +the delta function + +from some negative number +up to some positive number. + +And it doesn't matter where n +is, because the function is 0 + +there and there. + +But what's the answer here? + +Put me out of my misery. + +Just tell me the number +I'm looking for, here, + +the integral of +the delta function. + +Or maybe you haven't met it. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's? + +It's the one good +number you could guess. + +It's 1. + +Now, why is it 1? + +Because if the delta function +is the derivative of the step + +function, this should be the +step function evaluated between + +N and P. This should be +the step function, , here, + +minus the step function, there + +And what is the step function? + +You have to keep it straight. + +Am I talking about +the delta function? + +No, right now, I've +integrated it to get H of t. + +So this is H of P at +the positive side, + +minus H of N. That's +what integration's about. + +And what do I get? + +1, because H of P, the +step function here, H is 1. + +And here, it's 0, so I get 1. + +Good, that's the +thing that everybody + +remembers about +the delta function. + +And now I can make sense out of +2 delta function, 2 delta of t. + +That could be my source. + +So if 2 delta of +t was my source, + +what's the graph +of 2 delta of t? + +Again, it's 0 infinite 0. + +You really can't tell from +the infinity what's up, + +but what would be the +integral of 2 delta of t, + +the integral of 2 delta +of t or some other? + +Well, let me put in the 2, here? + +What's the integral of 2 +delta of t, would be 2H of t. + +Keep going. + +What do I get here? + +AUDIENCE: 2. + +PROFESSOR: It would +be 2 of these guys, 2 + +of these, 2 of these, 2. + +All right? + +So we made sense out of the +strength of the impulse, + +how hard the bat hit the ball. + +But of course, we +need units in there. + +We have to have units. + +And here, the value +for that unit was 2. + +Now, I'm going to-- because +this is really worth + +doing with delta functions. + +I didn't ask at the start +have you seen them before. + +But they are worth seeing. + +And they just take +a little practice. + +But then in the +end, delta functions + +are way easier to work with than +some complicated function that + +attempts to model this. + +We could model that by some +Gaussian curve or something. + +All the integrations would +become impossible right away. + +We could model it by +a step function up + +and a step function down. + +Then the integrations +would be possible. + +But still, we have +this finite width. + +I could let that +width go to 0 and let + +the height go to infinity. + +And what would happen? + +I'd get the delta function. + +So that's one way to create a +delta function, if you like. + +If you're OK with +step functions, + +then one way to create delta +is to take a big step up, step + +down, and then let the +size of the step grow + +and the width of +the steps shrink. + +Keep the area 1, because +area is integral. + +So I keep this, +that little width, + +times this big +height equal to 1. + +And in the end, I get delta. + +Now again, my point is +that delta functions, + +that you really understand them. + +What you can legitimately do +with them is integrate them. + +But now in later problems, +we might have not a 1 or a 2, + +but a function in here, like +cosine t, or e to the t, + +or q of t. + +Can I practice with those? + +Can I put in a function f of t? + +I didn't leave enough +space to write f of t, + +so I'm going to put it in +here. f of t delta of t dt. + +And I'm going to go +for the answer, there. + +My question is what +does that equal? + +You see what the question is? + +I got my delta function, +which I only just met. + +And I'm multiplying it by +some ordinary function. + +f of t gives us no problems. + +Think of cosine t. + +Think of e to the t. + +What do you think is the +right answer for that? + +What do you think +is the right answer? + +And this tells you +what the delta function + +is when you see this. + +What do I need to know about +f of t to get an answer, here? + +Do I need to know what f +is at t equals minus 1? + +You could see from +the way my voice asked + +that question that +the answer is no. + +Why do I not care +what f is at minus 1? + +Yeah? + +AUDIENCE: Because you're +multiplying by [INAUDIBLE]. + +PROFESSOR: Because +I'm multiplying + +by somebody that's 0. + +And similarly, at f equal minus +1/2, or at f equal plus 1/3, + +all those f's make +no difference, + +because they're +all multiplying 0. + +What does make a difference? + +What's the key information +about f that does + +come into the answer? + +f at? + +At just at that one point, f at? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: 0, f at +0 is the action. + +The impulse is happening. + +The bat's hitting the ball. + +So we're modeling +rocket launching, here. + +We're launching in 0 seconds +instead of a finite time. + +So in other words, +well, I don't know + +how to put this answer down +other than just to write it. + +I guess I'm hoping +you're with me + +in seeing that +what it should be. + +Can I just write it? + +All that matters +is what f is at t + +equals 0, because that's +where all the action is. + +And that f of 0, +if f of 0 was the 2 + +that I had there a little while +ago, then the answer will be 2. + +If f of 0 is a 1, if the +answer is f of 0 times + +1-- and I won't write times 1. + +That's ridiculous. + +Now we can integrate +delta functions, not just + +a single integral of +delta, but integral + +of a function, a nice +function times delta. + +And we get f of 0. + +So can I just, while we're on +the subject of delta functions, + +ask you a few examples? + +What is the integral of +e to the t delta of t dt? + +AUDIENCE: It's 1. + +PROFESSOR: Yeah, say it again? + +AUDIENCE: It's 1. + +PROFESSOR: It's 1. + +It's 1, right. + +Because e to the t, at the only +point we care about, t equal 0 + +is 1. + +And what if I change +that to sine t? + +Suppose I integrate +sine t times delta of t? + +What do I get now? + +I get? + +AUDIENCE: 0. + +PROFESSOR: 0, right. + +And actually, that's +totally reasonable. + +This is a function, which is +yeah, it's an odd function. + +Anyway, sine, if I switch t to +negative t, it goes negative. + +0 is the right answer. + +Let me ask you this one. + +What about delta of t squared? + +Because if we're up for a delta +function, we might square it. + +Now we've got a +high-powered function, + +because squaring this +crazy function delta of t + +gives us something truly crazy. + +And what answer would +you expect for that? + +AUDIENCE: 1. + +PROFESSOR: Would you expect 1? + +So this is like? + +I'm just getting +intuition working, here, + +for delta functions. + +What do you think? + +I'm looking at the energy +when I square something. + +OK, so we had a guess of 1. + +Is there another guess? + +Yeah? + +AUDIENCE: A third? + +PROFESSOR: Sorry? + +AUDIENCE: 1/3. + +PROFESSOR: 1/3, that's +our second guess. + +I'm open for other +guesses before I-- OK, we + +have a rule here for f of t. + +And now what is the f of t that +I'm asking about in this case? + +It's delta of t, right? + +If f of t is delta of t, +then that would match this. + +And therefore, the +answer should match. + +Do you see what I'm +shooting for, yeah? + +AUDIENCE: It'd be infinity? + +PROFESSOR: It'd be infinity. + +It would be infinity. + +That's delta of t squared +is that's an infinite energy + +function. + +You never meet it, actually. + +I apologize, so so +write it down there. + +I could erase it right +away because you basically + +never see it. + +It's infinite energy. + +Well, I think you'd see it. + +I mean, we're really going back +to the days of Norbert Wiener. + +When I came to the +math department, + +Norbert Wiener was still +here, still alive, still + +walking the hallway by touching +the wall and counting offices. + +And hard to talk to, because +he always had a lot to say. + +And you got kind of +allowed to listen. + +So anyway, Wiener +was among the first + +to really use delta +functions, successfully + +use delta functions. + +Anyway, this is the big one. + +This is the big one. + +Now, so what's all that about? + +I guess I was trying +to prepare by talking + +about this function +prepare for the equation + +when that's the source. + +So dy equal ay plus +a delta function. + +Let me bring that delta +function in at time T. + +So how do you interpret +that equation? + +So like part of this +morning's lecture + +is to get a first +handle on an impulse. + +So let me write that +word impulse, here. + +Where am I going to write it? + +So delta is an impulse. + +That's our ordinary +English word for something + +that happens fast. + +And y of t is the +impulse response. + +And this is the most important. + +Well, I said e to the st +was the most important. + +How can I have two most +important examples? + +Well, they're a tie, let's say. + +e to the st is the most +important ordinary function. + +It's the key to +the whole course. + +Delta of t, the impulse, +is the important one + +because if I can solve +it for a delta function, + +I can solve it for anything. + +Let's see if we can solve +it for a delta function, + +a delta function, an impulse +that starts at time T. Again, + +I'm just going to start +writing down the solution + +and ask for your help +what to write next. + +So what do you expect as a +first term in the solution? + +So I'm starting +again from y of 0. + +Let's see if we can +solve it by common sense. + +So how do I start +the solution to this? + +Everybody sees what +this equation is saying. + +I have an initial deposit of +y of 0 that starts growing. + +And then at time capital +T I make a deposit. + +At that moment, at that +instant, I make a deposit of 1. + +That's an instant deposit of 1. + +Which is, of course, +what I do in reality. + +I take $1 to the bank. + +They've got it now. + +At time T, I give them that $1, +and it starts earning interest. + +So what about y of t? + +What do you think? + +What's the first term +coming from y of 0? + +So the term coming +from y of 0 will + +be y of 0 to start +with, e to at. + +That takes care of the y of 0. + +Now, I need something. + +It's like this, plus +I need something + +that accounts for what +this deposit brings. + +So up until time +T, what do I put? + +So this is for t smaller +than T and t bigger than T. + +So what goes there? + +For t smaller than +T, what's the benefit + +from the delta function? + +0, didn't happen yet. + +For t bigger than T, +what's the benefit + +from the delta function? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: For t bigger +than T, well, that's right. + +OK, but now I've +made that deposit + +at time capital T. +Whatever's going + +there is whatever I'm +getting from that deposit. + +At time capital +T, I gave them $1, + +and they start paying +interest on it. + +What's going to go there? + +So if I gave them $1 at that +initial time, so that $1 + +would have been part of y of 0. + +What did I get at a later time? + +e to the at. + +Now I'm waiting. + +I'm giving them the +dollar at time capital T, + +and it starts growing. + +So what do I have +at a later time, + +for t later than capital T? + +What has that $1 grown into? + +e to the a times the-- +right, it's critical. + +It's the elapsed time. + +It's the time since the deposit. + +Is that right? + +So what do I put here? + +AUDIENCE: t minus capital T? + +PROFESSOR: t minus +capital T, good. + +Apologies to bug you about +this, but the only way + +to learn this stuff from a +lecture is to be part of it. + +So I constantly ask you, instead +of just writing down a formula. + +I think that looks good. + +So suddenly, what does this +amount to at t equal capital T? + +Maybe I should allow +t equal capital T. + +At t equal capital T, +what do I have here? + +AUDIENCE: 1. + +PROFESSOR: 1. + +That's my $1. + +At t equal capital +T, we've got $1. + +And later it's grown. + +So we have now solved. + +We have found the +impulse response. + +We have found the +impulse response + +when the impulse happened at +capital T. That was good going. + +Now, I've given you +my list of examples + +with the pause on +the sine and cosine. + +I pause on the sine and +cosine because one way + +to think about sine and cosine +is to get into complex numbers. + +And that's really for next time. + +But apart from that, we've +done all the examples, + +so are we ready? + +Oh yeah, I'm going to try for +the big thing, the big formula. + +So this is the key +result of section 1.4, + +the solution to this equation. + +So I'm going back to +the original equation. + +And just see if we can write +down a formula for the answer. + +So let me write +the equation again. + +dy dt is ay plus some source. + +I think we can write down +a formula that looks right. + +And we could then actually +plug it in and see, yeah, + +it is right. + +So what's going to +go into this formula? + +We got enough examples, so now +let's go for the whole thing. + +So y of t, first of +all, comes whatever + +depends on the +initial condition. + +So how much do we have +at a later time when + +our initial deposit was y of 0? + +So that's the one we've +seen in every example. + +Every one of these things +has this term growing out + +of y of 0. + +So let me put that in again. + +So the part that grows out of +y of 0 is y of 0 e to the at. + +That's OK. + +So that's what the initial. + +So our money is coming from two +sources, this initial deposit, + +which was easy, and this +continuous, over time deposit, + +q of t. + +And I have to ask +you about that. + +That's going to be like +the particular solution, + +the particular solution that +comes from the source term. + +This is the solution it comes +from the initial condition. + +So what do you think +this thing looks like? + +I just think once we see +it, we can say, yeah, + +that makes sense. + +So now I'm saying what? + +If we've deposited q of +t in varying amounts, + +maybe a constant for a while, +maybe a ramp for awhile, + +maybe whatever, a step, how am +I going to think about this? + +So at every time t +equal to s, so I'm + +using little t for +the time I've reached. + +Right? + +Here's t starting at 0. + +Now, let me use s for +a time part way along. + +So part way along, I input. + +I deposit q of s. + +I deposit it at time s. + +And then what does it do? + +That money is in the +bank with everybody else. + +It grows along with +everything else. + +So what's the growth factor? + +What's the growth factor? + +This is the amount I +deposited at time s. + +And how much has +it grown at time t? + +This is the key question, +and you can answer it. + +It went in a time s. + +I'm looking at time t. + +What's the factor? + +AUDIENCE: Is it e +to the a t minus s. + +PROFESSOR: e to the a t minus s. + +So that's the contribution +to our balance at time t + +from our input at time s. + +But now, I've been +inputting all the way along. + +s is running all the +way from here to here. + +So finish my formula. + +Put me out of my misery. + +Or it's not misery, actually. + +Its success at this moment. + +What do I do now? + +I? + +AUDIENCE: Integrate. + +PROFESSOR: I integrate, exactly. + +I integrate. + +I integrate. + +So all these deposits went in. + +They grew that amount +in the remaining time. + +And I integrate from 0 +up to the current time t. + +So you see that formula? + +Have a look at it. + +This is a general formula, and +every one of those examples + +could be found +from that formula. + +If q of s was 1, that was +our very first example. + +We could do that integration. + +If q of s was e to the-- +anyway, we could do every one. + +I just want you to see that +that formula makes sense. + +Again, this is what grew out +of the initial condition. + +This is what grew out of +the deposit at time s. + +And the whole point of +calculus, the whole point + +of learning [? 1801 ?], +the integral equation + +part, the integrals part, +is integrals just add up. + +This term just adds up +all the later deposits, + +times the growth factor +in the remaining time. + +And as I say, if I took q of s +equal 1-- the examples I gave + +are really the examples where +you can do the integral. + +If q of s is e to the i omega +s, I can do that integral. + +Actually, it's not hard to do +because e to the at doesn't + +depend on s. + +I can bring an e to the +at out in this case. + +That formula is just +worth thinking about. + +It's worth understanding. + +I didn't, like, derive it. + +And the book does, of course. + +There's something called +an integrating factor. + +You can get at this +formula systematically. + +I'd rather get at it +and understand it. + +I'm more interested +in understanding + +what the meaning of that +formula is than the algebra. + +Algebra is just a +goal to understand, + +and that's what I +shot for directly. + +And as I say, that +the book also, + +early section of the book, +uses practice in calculus. + +Substitute that in +to the equation. + +Figure out what is dy dt. + +And check that it works. + +It's worth actually +looking at that end of what + +you need to know from +calculus It's is. + +You should be able +to plug that in for y + +and see that solves +the equation. + +Right, now I have enough +time to do cosine omega t. + +But I don't have enough time +to do it the complex way. + +So let me do as a final +example, the equation. + +Let me just think. + +I don't know if I have +enough space here. + +I'm now going to do dy dt-- +can I call that y prime to save + +a little space-- equal +ay plus cosine of t. + +I'll take omega to be 1. + +Now, how could we +solve that one? + +I'm going to solve it +without complex numbers, + +just to see how easy +or hard that is. + +And you'll see, +actually, it's easy. + +But complex numbers +will tell us more. + +So it's easy, but +not totally easy. + +So what did I do in +the earlier example + +if the right hand side +was a 1, a constant? + +I look for the solution +to be a constant. + +If the right hand side +was an exponential, + +I look for the solution +to be an exponential. + +Now, my right hand side, my +source term, is a cosine. + +So what form of the solution +am I going to look for? + +I naturally think, +OK, look for a cosine. + +We could try y equals +some number M cosine t. + +Now, you have to see what +goes wrong and how to fix it. + +So if I plug that in, +looking for M the same way + +I look for capital Y +earlier, I plug this in, + +and I get aM cosine t cosine t. + +But what do I get for y prime? + +Sine t. + +And I can't match. + +I can make it work. + +I can't make a sine there +magic a cosine here. + +So what's the solution? + +How do I fix it? + +I better allow my +solution to include + +some sine plus N sine t. + +So that's the problem with +doing it, keeping things real. + +I'll push this +through, no problem. + +But cosine by itself won't work. + +I need to have sines there, +because derivatives bring out + +sines. + +So I have a combination +of cosine and sine. + +I have a combination +of cosine and sine. + +So the complex method +will work in one shot + +because e to the i omega t is a +combination of cosine and sine. + +Or another way to say it +is when I see cosine here, + +that's got two exponentials. + +That's got e to the it +and e to the-- anyway. + +Let's go for the real one. + +So I'm going to plug +that into there. + +So I'll get sines +and cosines, right? + +When I plug this +into there, I'll + +have some sines +and some cosines, + +and I'll just match +the two separately. + +So I'm going to +get two equations. + +First of all, let me say +what's the cosine equation? + +And then what's +the sine equation? + +So when I match cosine +terms, what do I have? + +What cosine terms do I +get out of y prime, here? + +The derivative. + +Well, the derivative +of cosine is a sine. + +That that's not a cosine term. + +The derivative of +sine is cosine. + +I think I get, if I +just match cosines, + +I think I get an N cosine. + +N cosine t equal ay. + +How many cosines do I +have from that term? + +ay has an M cosine t. + +I think I have an aM, +and here I've got 1. + +That was a natural +step, but new to us. + +I'm matching the cosines. + +I have on the left side, with +this form of the solution, + +the derivative will +have an N cosine t. + +So I had N cosines, aM +cosines, and 1 cosine. + +Now, what if I match signs? + +What happens there? + +We're pushing more +than an hour, so + +hang on for another five +minutes, and we're there. + +Now, what happens if +I match sines, sine t? + +How do I get sine t in y prime? + +So take the derivative of +that, and what do you have? + +AUDIENCE: Minus [INAUDIBLE]. + +PROFESSOR: Minus M sine t. + +That tells me how many +sine t's are in there. + +And on the right +hand side, a times y, + +how many sine t's +do I have from that? + +AUDIENCE: You have N t's. + +PROFESSOR: N, good thinking. + +And what about from this term? + +None, no sine there. + +So I have two equations by +matching the cosines and sines. + +Once you see it, you +could do it again. + +And we can solve +those equations, + +two ordinary, very simple +equations for M and N. + +Let's see if I make space. + +Why don't I do it here, +so you can see it. + +So how do I solve +those two equations? + +Well, this equation gives me-- +easy-- gives me M as minus aN. + +So I'll just put that in for N. + +So I have N equals aM. + +But M is minus aN. + +I think I've got minus +a squared N plus that 1. + +All I did was solve the +equation, just by common sense. + +You could say by linear +algebra, but linear algebra's + +got a little more +to it than this. + +So now I know M, and now I know +N. So now I know the answer. + +y is M, so M is minus aN. + +Oh, well, I have to figure +out what N is, here. + +What is N? + +This is giving me N, but +I better figure it out. + +What is N from that +first equation? + +And then I'll plug in. + +And then I'm quit. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: 1 over, yeah. + +AUDIENCE: 1 plus a squared. + +PROFESSOR: 1 plus +a squared, good. + +Because that term goes +over there, and we have 1 + +plus a squared. + +So now y is M cosine t. + +So M is minus aN. + +So minus aN is 1 over 1 +plus a squared cosine t. + +Is that right? + +That was the cosines. + +And we had N sine t. + +But N is just 1-- I think +I just add the sine t. + +Have I got it? + +I think so. + +Here is the N sine t, +and here is the M cos t. + +It was just algebra. + +Typical of these +problems, there's + +a little thinking and +then some algebra. + +The thinking led us to this. + +The thinking led us to the fact +we needed cosines in there, + +as well as cosines. + +But then once we did +it, then the thinking + +said, OK, separately match the +cosine terms and the sine term. + +And then do the algebra. + +Now, I just want to +do this with complex. + +So y prime equals +ay plus e to the it. + +To get an idea, you see the two. + +And then I have +to talk about it. + +You see, I'm only going +to go part way with this + +and then save it for Wednesday. + +But if I see this, what +solution do I assume? + +This is like an e to the st. I +assume y is some Y e to the it. + +See, I don't have cosines +and sines anymore. + +I have e to the it. + +And if I take the +derivative of e to the it, + +I'm still in the +e to the it world. + +So I do this. + +I plug it in. + +Uh-huh, let me leave +that for Wednesday. + +We have to have some +excitement for Wednesday. + +So we'll get a complex +answer, and then we'll + +take the real part to +solve that problem. + +So we've got two steps, +one way or the other way. + +Here, we had two steps because +we had to let sines sneak in. + +Here, we have two steps +because I could solve it, + +and you could solve +that right away. + +But then you have to +take the real part. + +I'll leave that. + +Is there questions? + +Do you want me to recap +quickly what we've done. + +AUDIENCE: Yes. + +PROFESSOR: I try to +leave on the board + +enough to make a recap possible. + +Everything was +about that equation. + +We have only +solved-- I shouldn't + +say only-- we have solved the +constant coefficient, model + +constant coefficient, +first order equation. + +Wednesday comes +nonlinear equation. + +This one today was +strictly linear. + +So what did we do? + +We solved this equation, +first of all, for q equal 1; + +secondly, for q equal +e to the st; thirdly, + +for q equal a step; fourthly +for q equal-- where is it? + +Where is that delta of t? + +Maybe it's here. + +Ah, it got erased. + +So the fourth guy was y prime +equal ay plus delta of t, + +or delta of t minus +capital T. So those + +were our four examples. + +And then what did we finally do? + +So if we're recapping, +compressing, + +we're compressing +everything into two minutes. + +We solved those four +examples, and then we + +solved the general problem. + +And when we solved +the general problem, + +that gave us this integral, +which my whole goal was + +that you should understand that +this should seem right to you. + +This is adding up +the value at time t + +from all the inputs +at different times s. + +So to add them up, we +integrate from 0 to t. + +And finally, we +returned to the question + +of cos t, all +important question. + +But awkward question, +because we needed to let sine + +t in there too. \ No newline at end of file diff --git a/55ncRlBZstA.txt b/55ncRlBZstA.txt new file mode 100644 index 0000000000000000000000000000000000000000..7741e189d9c73df40b37494dbc18d090c03e255c --- /dev/null +++ b/55ncRlBZstA.txt @@ -0,0 +1,1259 @@ +align:start position:0% + +welcome back to + + align:start position:0% +welcome back to + + + align:start position:0% +welcome back to +recitation uh in this segment we're + + align:start position:0% +recitation uh in this segment we're + + + align:start position:0% +recitation uh in this segment we're +going to talk about the product rule for + + align:start position:0% +going to talk about the product rule for + + + align:start position:0% +going to talk about the product rule for +three functions and then we're going to + + align:start position:0% +three functions and then we're going to + + + align:start position:0% +three functions and then we're going to +do an example and what I want to do + + align:start position:0% +do an example and what I want to do + + + align:start position:0% +do an example and what I want to do +first is remind you the product rule for + + align:start position:0% +first is remind you the product rule for + + + align:start position:0% +first is remind you the product rule for +two functions because we're going to use + + align:start position:0% +two functions because we're going to use + + + align:start position:0% +two functions because we're going to use +that to figure out the product rule for + + align:start position:0% +that to figure out the product rule for + + + align:start position:0% +that to figure out the product rule for +three functions so throughout this this + + align:start position:0% +three functions so throughout this this + + + align:start position:0% +three functions so throughout this this +segment we are going to assume that u + + align:start position:0% +segment we are going to assume that u + + + align:start position:0% +segment we are going to assume that u +and v and W are all functions of X so + + align:start position:0% +and v and W are all functions of X so + + + align:start position:0% +and v and W are all functions of X so +I'm going to drop the of X just so it's + + align:start position:0% +I'm going to drop the of X just so it's + + + align:start position:0% +I'm going to drop the of X just so it's +a little easier to write this notation + + align:start position:0% +a little easier to write this notation + + + align:start position:0% +a little easier to write this notation +should be familiar with things you saw + + align:start position:0% +should be familiar with things you saw + + + align:start position:0% +should be familiar with things you saw +in the lecture so for two functions let + + align:start position:0% +in the lecture so for two functions let + + + align:start position:0% +in the lecture so for two functions let +me remind + + align:start position:0% +me remind + + + align:start position:0% +me remind +you if you have UV the product and you + + align:start position:0% +you if you have UV the product and you + + + align:start position:0% +you if you have UV the product and you +take its derivative so Prime will denote + + align:start position:0% +take its derivative so Prime will denote + + + align:start position:0% +take its derivative so Prime will denote +GDX then we can take the derivative of + + align:start position:0% +GDX then we can take the derivative of + + + align:start position:0% +GDX then we can take the derivative of +the first times the second function left + + align:start position:0% +the first times the second function left + + + align:start position:0% +the first times the second function left +alone plus the derivative of the second + + align:start position:0% +alone plus the derivative of the second + + + align:start position:0% +alone plus the derivative of the second +function times the first left alone so + + align:start position:0% +function times the first left alone so + + + align:start position:0% +function times the first left alone so +this should again be familiar from class + + align:start position:0% +this should again be familiar from class + + + align:start position:0% +this should again be familiar from class +um and now what we want to do is expand + + align:start position:0% +um and now what we want to do is expand + + + align:start position:0% +um and now what we want to do is expand +that to to the product of three + + align:start position:0% +that to to the product of three + + + align:start position:0% +that to to the product of three +functions U * V * W and we're going to + + align:start position:0% +functions U * V * W and we're going to + + + align:start position:0% +functions U * V * W and we're going to +explicitly use this rule + + align:start position:0% +explicitly use this rule + + + align:start position:0% +explicitly use this rule +so + + align:start position:0% +so + + + align:start position:0% +so +uvw Prime is what we want to look at so + + align:start position:0% +uvw Prime is what we want to look at so + + + align:start position:0% +uvw Prime is what we want to look at so +we're just G to we're just going to take + + align:start position:0% +we're just G to we're just going to take + + + align:start position:0% +we're just G to we're just going to take +advantage of what we know to figure out + + align:start position:0% +advantage of what we know to figure out + + + align:start position:0% +advantage of what we know to figure out +what this expression will be what this + + align:start position:0% +what this expression will be what this + + + align:start position:0% +what this expression will be what this +product of three functions when I take + + align:start position:0% +product of three functions when I take + + + align:start position:0% +product of three functions when I take +its derivative will be so in order to do + + align:start position:0% +its derivative will be so in order to do + + + align:start position:0% +its derivative will be so in order to do +this easily what we're going to do is + + align:start position:0% +this easily what we're going to do is + + + align:start position:0% +this easily what we're going to do is +treat V * W as a single function okay so + + align:start position:0% +treat V * W as a single function okay so + + + align:start position:0% +treat V * W as a single function okay so +V * W will be our second function that + + align:start position:0% +V * W will be our second function that + + + align:start position:0% +V * W will be our second function that +that essentially takes the place of the + + align:start position:0% +that essentially takes the place of the + + + align:start position:0% +that essentially takes the place of the +V up here okay so using the product rule + + align:start position:0% +V up here okay so using the product rule + + + align:start position:0% +V up here okay so using the product rule +for two functions what I get when I take + + align:start position:0% +for two functions what I get when I take + + + align:start position:0% +for two functions what I get when I take +this this derivative is I get U Prime + + align:start position:0% +this this derivative is I get U Prime + + + align:start position:0% +this this derivative is I get U Prime +Time + + align:start position:0% +Time + + + align:start position:0% +Time +VW plus I take the derivative of this + + align:start position:0% +VW plus I take the derivative of this + + + align:start position:0% +VW plus I take the derivative of this +second thing which is + + align:start position:0% +second thing which is + + + align:start position:0% +second thing which is +VW Prime and then I leave the U alone + + align:start position:0% +VW Prime and then I leave the U alone + + + align:start position:0% +VW Prime and then I leave the U alone +okay we're not quite done but you can + + align:start position:0% +okay we're not quite done but you can + + + align:start position:0% +okay we're not quite done but you can +see now again we if we compare to what's + + align:start position:0% +see now again we if we compare to what's + + + align:start position:0% +see now again we if we compare to what's +above you take the derivative of the + + align:start position:0% +above you take the derivative of the + + + align:start position:0% +above you take the derivative of the +first function you leave the second + + align:start position:0% +first function you leave the second + + + align:start position:0% +first function you leave the second +function alone you take the derivative + + align:start position:0% +function alone you take the derivative + + + align:start position:0% +function alone you take the derivative +of the second function you leave the + + align:start position:0% +of the second function you leave the + + + align:start position:0% +of the second function you leave the +first function alone but now again what + + align:start position:0% +first function alone but now again what + + + align:start position:0% +first function alone but now again what +do we do here well we have a product + + align:start position:0% +do we do here well we have a product + + + align:start position:0% +do we do here well we have a product +rule for two functions so let's use it + + align:start position:0% +rule for two functions so let's use it + + + align:start position:0% +rule for two functions so let's use it +so I'll leave the first thing alone U + + align:start position:0% +so I'll leave the first thing alone U + + + align:start position:0% +so I'll leave the first thing alone U +Prime oops that does not look like a v v + + align:start position:0% +Prime oops that does not look like a v v + + + align:start position:0% +Prime oops that does not look like a v v +w plus now let's let's expand this take + + align:start position:0% +w plus now let's let's expand this take + + + align:start position:0% +w plus now let's let's expand this take +the derivative of the first function + + align:start position:0% +the derivative of the first function + + + align:start position:0% +the derivative of the first function +there that's V Prime I leave the W alone + + align:start position:0% +there that's V Prime I leave the W alone + + + align:start position:0% +there that's V Prime I leave the W alone +plus the derivative of the second + + align:start position:0% +plus the derivative of the second + + + align:start position:0% +plus the derivative of the second +function that's W Prime I leave the V + + align:start position:0% +function that's W Prime I leave the V + + + align:start position:0% +function that's W Prime I leave the V +alone and I keep the U there okay I'm + + align:start position:0% +alone and I keep the U there okay I'm + + + align:start position:0% +alone and I keep the U there okay I'm +going to just expand and write it in a + + align:start position:0% +going to just expand and write it in a + + + align:start position:0% +going to just expand and write it in a +nice order so we can see sort of exactly + + align:start position:0% +nice order so we can see sort of exactly + + + align:start position:0% +nice order so we can see sort of exactly +what happens + + align:start position:0% +what happens + + + align:start position:0% +what happens +so U Prime V W plus v Prime U W plus W + + align:start position:0% +so U Prime V W plus v Prime U W plus W + + + align:start position:0% +so U Prime V W plus v Prime U W plus W +Prime U u v so what you can see here is + + align:start position:0% +Prime U u v so what you can see here is + + + align:start position:0% +Prime U u v so what you can see here is +what happens you take the derivative of + + align:start position:0% +what happens you take the derivative of + + + align:start position:0% +what happens you take the derivative of +the first function you leave the second + + align:start position:0% +the first function you leave the second + + + align:start position:0% +the first function you leave the second +and third alone then you take the + + align:start position:0% +and third alone then you take the + + + align:start position:0% +and third alone then you take the +derivative of the second function you + + align:start position:0% +derivative of the second function you + + + align:start position:0% +derivative of the second function you +leave the first and third alone and you + + align:start position:0% +leave the first and third alone and you + + + align:start position:0% +leave the first and third alone and you +take the derivative of the third + + align:start position:0% +take the derivative of the third + + + align:start position:0% +take the derivative of the third +function you leave the first and second + + align:start position:0% +function you leave the first and second + + + align:start position:0% +function you leave the first and second +alone and you you add up those three + + align:start position:0% +alone and you you add up those three + + + align:start position:0% +alone and you you add up those three +terms I would imagine that uh at this + + align:start position:0% +terms I would imagine that uh at this + + + align:start position:0% +terms I would imagine that uh at this +point you anticipate a pattern so if I + + align:start position:0% +point you anticipate a pattern so if I + + + align:start position:0% +point you anticipate a pattern so if I +had a fourth function if I did U * V * W + + align:start position:0% +had a fourth function if I did U * V * W + + + align:start position:0% +had a fourth function if I did U * V * W +* Z let's say and I took that derivative + + align:start position:0% +* Z let's say and I took that derivative + + + align:start position:0% +* Z let's say and I took that derivative +with respect to X um you could probably + + align:start position:0% +with respect to X um you could probably + + + align:start position:0% +with respect to X um you could probably +anticipate you would have four terms + + align:start position:0% +anticipate you would have four terms + + + align:start position:0% +anticipate you would have four terms +when you added them up and that fourth + + align:start position:0% +when you added them up and that fourth + + + align:start position:0% +when you added them up and that fourth +term would have to include a derivative + + align:start position:0% +term would have to include a derivative + + + align:start position:0% +term would have to include a derivative +of the fourth function so from here + + align:start position:0% +of the fourth function so from here + + + align:start position:0% +of the fourth function so from here +actually you can probably uh tell me + + align:start position:0% +actually you can probably uh tell me + + + align:start position:0% +actually you can probably uh tell me +what the derivative of the product of n + + align:start position:0% +what the derivative of the product of n + + + align:start position:0% +what the derivative of the product of n +functions is um and you could check it + + align:start position:0% +functions is um and you could check it + + + align:start position:0% +functions is um and you could check it +using the same kind of rule but what + + align:start position:0% +using the same kind of rule but what + + + align:start position:0% +using the same kind of rule but what +we're going to do at this point is we're + + align:start position:0% +we're going to do at this point is we're + + + align:start position:0% +we're going to do at this point is we're +going to just make sure we understand + + align:start position:0% +going to just make sure we understand + + + align:start position:0% +going to just make sure we understand +this we're going to compute an example + + align:start position:0% +this we're going to compute an example + + + align:start position:0% +this we're going to compute an example +so since we know uh products or we know + + align:start position:0% +so since we know uh products or we know + + + align:start position:0% +so since we know uh products or we know +derivatives of powers of X and we know + + align:start position:0% +derivatives of powers of X and we know + + + align:start position:0% +derivatives of powers of X and we know +derivatives of the of the basic trig + + align:start position:0% +derivatives of the of the basic trig + + + align:start position:0% +derivatives of the of the basic trig +functions we'll do a product rule using + + align:start position:0% +functions we'll do a product rule using + + + align:start position:0% +functions we'll do a product rule using +those functions so let me let me take an + + align:start position:0% + + + + align:start position:0% + +example so we'll say F + + align:start position:0% +example so we'll say F + + + align:start position:0% +example so we'll say F +ofx = + + align:start position:0% +ofx = + + + align:start position:0% +ofx = +x^2 sin + + align:start position:0% +x^2 sin + + + align:start position:0% +x^2 sin +x cosine + + align:start position:0% +x cosine + + + align:start position:0% +x cosine +X okay and I want you to + + align:start position:0% +X okay and I want you to + + + align:start position:0% +X okay and I want you to +find + + align:start position:0% +find + + + align:start position:0% +find +fime of + + align:start position:0% + + + + align:start position:0% + +X okay I'm going to give you a moment to + + align:start position:0% +X okay I'm going to give you a moment to + + + align:start position:0% +X okay I'm going to give you a moment to +do it uh you should probably pause the + + align:start position:0% +do it uh you should probably pause the + + + align:start position:0% +do it uh you should probably pause the +video here make sure you can do it and + + align:start position:0% +video here make sure you can do it and + + + align:start position:0% +video here make sure you can do it and +then you can you can restart the video + + align:start position:0% +then you can you can restart the video + + + align:start position:0% +then you can you can restart the video +when you want to check your + + align:start position:0% + + + + align:start position:0% + +answer coming up in five + + align:start position:0% +answer coming up in five + + + align:start position:0% +answer coming up in five +four okay so we have a product rule for + + align:start position:0% +four okay so we have a product rule for + + + align:start position:0% +four okay so we have a product rule for +three functions we have an example that + + align:start position:0% +three functions we have an example that + + + align:start position:0% +three functions we have an example that +that I asked you to determine and um and + + align:start position:0% +that I asked you to determine and um and + + + align:start position:0% +that I asked you to determine and um and +gave you to do it so now I will actually + + align:start position:0% +gave you to do it so now I will actually + + + align:start position:0% +gave you to do it so now I will actually +work out the example over here to the + + align:start position:0% +work out the example over here to the + + + align:start position:0% +work out the example over here to the +right so I will determine frime of X now + + align:start position:0% +right so I will determine frime of X now + + + align:start position:0% +right so I will determine frime of X now +what are our three functions well we + + align:start position:0% +what are our three functions well we + + + align:start position:0% +what are our three functions well we +have x s is the first sin x is the + + align:start position:0% +have x s is the first sin x is the + + + align:start position:0% +have x s is the first sin x is the +second cosine X is the third so we'll + + align:start position:0% +second cosine X is the third so we'll + + + align:start position:0% +second cosine X is the third so we'll +have three terms the first term has to + + align:start position:0% +have three terms the first term has to + + + align:start position:0% +have three terms the first term has to +have the derivative of the X squ that's + + align:start position:0% +have the derivative of the X squ that's + + + align:start position:0% +have the derivative of the X squ that's +going to give me a 2X and I leave the + + align:start position:0% +going to give me a 2X and I leave the + + + align:start position:0% +going to give me a 2X and I leave the +other two terms alone so I have 2X sin x + + align:start position:0% +other two terms alone so I have 2X sin x + + + align:start position:0% +other two terms alone so I have 2X sin x +cosine + + align:start position:0% +cosine + + + align:start position:0% +cosine +X Plus I may want to just write these + + align:start position:0% +X Plus I may want to just write these + + + align:start position:0% +X Plus I may want to just write these +below okay now in the next term I should + + align:start position:0% +below okay now in the next term I should + + + align:start position:0% +below okay now in the next term I should +take the derivative of the sin x and + + align:start position:0% +take the derivative of the sin x and + + + align:start position:0% +take the derivative of the sin x and +leave the x^ squ and the cosine X alone + + align:start position:0% +leave the x^ squ and the cosine X alone + + + align:start position:0% +leave the x^ squ and the cosine X alone +derivative of sin x is cosine X so I'm + + align:start position:0% +derivative of sin x is cosine X so I'm + + + align:start position:0% +derivative of sin x is cosine X so I'm +actually going to write this underneath + + align:start position:0% +actually going to write this underneath + + + align:start position:0% +actually going to write this underneath +so we'll have going to put the plus + + align:start position:0% +so we'll have going to put the plus + + + align:start position:0% +so we'll have going to put the plus +underneath also so we remember it's a + + align:start position:0% +underneath also so we remember it's a + + + align:start position:0% +underneath also so we remember it's a +sum plus so the derivative of sin x is + + align:start position:0% +sum plus so the derivative of sin x is + + + align:start position:0% +sum plus so the derivative of sin x is +cosine X and then we have a time x s + + align:start position:0% +cosine X and then we have a time x s + + + align:start position:0% +cosine X and then we have a time x s +times oops another cosine X of what the + + align:start position:0% +times oops another cosine X of what the + + + align:start position:0% +times oops another cosine X of what the +third + + align:start position:0% +third + + + align:start position:0% +third +function okay and then the third term I + + align:start position:0% +function okay and then the third term I + + + align:start position:0% +function okay and then the third term I +take the derivative of the third + + align:start position:0% +take the derivative of the third + + + align:start position:0% +take the derivative of the third +function and I leave the first and + + align:start position:0% +function and I leave the first and + + + align:start position:0% +function and I leave the first and +second alone the derivative of cosine X + + align:start position:0% +second alone the derivative of cosine X + + + align:start position:0% +second alone the derivative of cosine X +is negative sinx so I actually have a + + align:start position:0% +is negative sinx so I actually have a + + + align:start position:0% +is negative sinx so I actually have a +sinx * x^2 * the sinx + + align:start position:0% + + + + align:start position:0% + +here I can do some simplifying if I want + + align:start position:0% +here I can do some simplifying if I want + + + align:start position:0% +here I can do some simplifying if I want +um but maybe uh if I were trying to + + align:start position:0% +um but maybe uh if I were trying to + + + align:start position:0% +um but maybe uh if I were trying to +write this nicely for someone who was + + align:start position:0% +write this nicely for someone who was + + + align:start position:0% +write this nicely for someone who was +reading mathematics I would put all of + + align:start position:0% +reading mathematics I would put all of + + + align:start position:0% +reading mathematics I would put all of +the the pols in front and all of the + + align:start position:0% +the the pols in front and all of the + + + align:start position:0% +the the pols in front and all of the +coefficients in front so to be very kind + + align:start position:0% +coefficients in front so to be very kind + + + align:start position:0% +coefficients in front so to be very kind +to someone I might write it like + + align:start position:0% + + + + align:start position:0% + +this and notice cosine x cosine X is + + align:start position:0% +this and notice cosine x cosine X is + + + align:start position:0% +this and notice cosine x cosine X is +cosine 2 x and then minus + + align:start position:0% +cosine 2 x and then minus + + + align:start position:0% +cosine 2 x and then minus +x^2 sin^2 x and there are other ways I + + align:start position:0% +x^2 sin^2 x and there are other ways I + + + align:start position:0% +x^2 sin^2 x and there are other ways I +could I could rewrite this and and using + + align:start position:0% +could I could rewrite this and and using + + + align:start position:0% +could I could rewrite this and and using +trig identities but this is a sufficient + + align:start position:0% +trig identities but this is a sufficient + + + align:start position:0% +trig identities but this is a sufficient +answer at this point so this is actually + + align:start position:0% +answer at this point so this is actually + + + align:start position:0% +answer at this point so this is actually +um a good way to write the derivative of + + align:start position:0% +um a good way to write the derivative of + + + align:start position:0% +um a good way to write the derivative of +that function f ofx and this is where + + align:start position:0% +that function f ofx and this is where + + + align:start position:0% +that function f ofx and this is where +we'll + + align:start position:0% +we'll + + + align:start position:0% +we'll +stop \ No newline at end of file diff --git a/5IGTFgPqlkw.txt b/5IGTFgPqlkw.txt new file mode 100644 index 0000000000000000000000000000000000000000..68f3b71fcad5832a337b5b73983a414f7e1297fa --- /dev/null +++ b/5IGTFgPqlkw.txt @@ -0,0 +1,995 @@ +align:start position:0% + +hi and welcome today we're gonna do a + + align:start position:0% +hi and welcome today we're gonna do a + + + align:start position:0% +hi and welcome today we're gonna do a +problem about powers of a matrix our + + align:start position:0% +problem about powers of a matrix our + + + align:start position:0% +problem about powers of a matrix our +problem is just to find is first to find + + align:start position:0% +problem is just to find is first to find + + + align:start position:0% +problem is just to find is first to find +a formula for the K power of this matrix + + align:start position:0% +a formula for the K power of this matrix + + + align:start position:0% +a formula for the K power of this matrix +see this is a 2 by 2 matrix that depends + + align:start position:0% +see this is a 2 by 2 matrix that depends + + + align:start position:0% +see this is a 2 by 2 matrix that depends +on variables a and B and the second part + + align:start position:0% +on variables a and B and the second part + + + align:start position:0% +on variables a and B and the second part +of our problem is to calculate C to the + + align:start position:0% +of our problem is to calculate C to the + + + align:start position:0% +of our problem is to calculate C to the +to the 100th in the special case where a + + align:start position:0% +to the 100th in the special case where a + + + align:start position:0% +to the 100th in the special case where a +and B are negative 1 okay you can hit + + align:start position:0% +and B are negative 1 okay you can hit + + + align:start position:0% +and B are negative 1 okay you can hit +pause now and I'll give you a minute to + + align:start position:0% +pause now and I'll give you a minute to + + + align:start position:0% +pause now and I'll give you a minute to +do the problem yourself and then I'll + + align:start position:0% +do the problem yourself and then I'll + + + align:start position:0% +do the problem yourself and then I'll +come back and we can do it together + + align:start position:0% + + + + align:start position:0% + +okay we're back now what's the first + + align:start position:0% +okay we're back now what's the first + + + align:start position:0% +okay we're back now what's the first +step in finding powers of a matrix well + + align:start position:0% +step in finding powers of a matrix well + + + align:start position:0% +step in finding powers of a matrix well +we need to find the eigenvalues and the + + align:start position:0% +we need to find the eigenvalues and the + + + align:start position:0% +we need to find the eigenvalues and the +eigenvectors of this matrix so how do we + + align:start position:0% +eigenvectors of this matrix so how do we + + + align:start position:0% +eigenvectors of this matrix so how do we +do that we compute the determinant of C + + align:start position:0% +do that we compute the determinant of C + + + align:start position:0% +do that we compute the determinant of C +minus lambda I which is just the + + align:start position:0% +minus lambda I which is just the + + + align:start position:0% +minus lambda I which is just the +determinant of this matrix to be minus a + + align:start position:0% +determinant of this matrix to be minus a + + + align:start position:0% +determinant of this matrix to be minus a +minus lambda to be minus 2a a minus B + + align:start position:0% +minus lambda to be minus 2a a minus B + + + align:start position:0% +minus lambda to be minus 2a a minus B +and 2a minus B minus lambda okay if you + + align:start position:0% +and 2a minus B minus lambda okay if you + + + align:start position:0% +and 2a minus B minus lambda okay if you +compute this well we have a lambda + + align:start position:0% +compute this well we have a lambda + + + align:start position:0% +compute this well we have a lambda +squared term okay + + align:start position:0% +squared term okay + + + align:start position:0% +squared term okay +our lambda term if you look at it you'll + + align:start position:0% +our lambda term if you look at it you'll + + + align:start position:0% +our lambda term if you look at it you'll +see we get 2b minus a plus to a minus B + + align:start position:0% +see we get 2b minus a plus to a minus B + + + align:start position:0% +see we get 2b minus a plus to a minus B +which is just a plus B and we have a + + align:start position:0% +which is just a plus B and we have a + + + align:start position:0% +which is just a plus B and we have a +negative sign that's negative a plus B + + align:start position:0% +negative sign that's negative a plus B + + + align:start position:0% +negative sign that's negative a plus B +times lambda and our last term is a + + align:start position:0% +times lambda and our last term is a + + + align:start position:0% +times lambda and our last term is a +little tougher to compute so I'll let + + align:start position:0% +little tougher to compute so I'll let + + + align:start position:0% +little tougher to compute so I'll let +you do it yourself but you're just gonna + + align:start position:0% +you do it yourself but you're just gonna + + + align:start position:0% +you do it yourself but you're just gonna +get plus a B and this will factor as + + align:start position:0% +get plus a B and this will factor as + + + align:start position:0% +get plus a B and this will factor as +lambda minus a times lambda minus B good + + align:start position:0% +lambda minus a times lambda minus B good + + + align:start position:0% +lambda minus a times lambda minus B good +so our eigenvalues are just a and B okay + + align:start position:0% +so our eigenvalues are just a and B okay + + + align:start position:0% +so our eigenvalues are just a and B okay +now we need to find our eigen vectors so + + align:start position:0% +now we need to find our eigen vectors so + + + align:start position:0% +now we need to find our eigen vectors so +how do we do that + + align:start position:0% +how do we do that + + + align:start position:0% +how do we do that +well what we need to do is we need to + + align:start position:0% +well what we need to do is we need to + + + align:start position:0% +well what we need to do is we need to +look at C minus a times the identity and + + align:start position:0% +look at C minus a times the identity and + + + align:start position:0% +look at C minus a times the identity and +we need to find the null space of this + + align:start position:0% +we need to find the null space of this + + + align:start position:0% +we need to find the null space of this +matrix so what do we get here we get 2b + + align:start position:0% +matrix so what do we get here we get 2b + + + align:start position:0% +matrix so what do we get here we get 2b +minus 2a + + align:start position:0% + + + + align:start position:0% + +and then our next entry here when you + + align:start position:0% +and then our next entry here when you + + + align:start position:0% +and then our next entry here when you +get to a minus B minus a so this is a + + align:start position:0% +get to a minus B minus a so this is a + + + align:start position:0% +get to a minus B minus a so this is a +minus B good so you can see that this + + align:start position:0% +minus B good so you can see that this + + + align:start position:0% +minus B good so you can see that this +matrix has the same the same columns and + + align:start position:0% +matrix has the same the same columns and + + + align:start position:0% +matrix has the same the same columns and +this the same rows and so you you can + + align:start position:0% +this the same rows and so you you can + + + align:start position:0% +this the same rows and so you you can +see that um a vector in the null space + + align:start position:0% +see that um a vector in the null space + + + align:start position:0% +see that um a vector in the null space +since this column is negative two times + + align:start position:0% +since this column is negative two times + + + align:start position:0% +since this column is negative two times +this column we can see that our first + + align:start position:0% +this column we can see that our first + + + align:start position:0% +this column we can see that our first +eigenvector is just or one two I should + + align:start position:0% +eigenvector is just or one two I should + + + align:start position:0% +eigenvector is just or one two I should +say it's just one two good now um well I + + align:start position:0% +say it's just one two good now um well I + + + align:start position:0% +say it's just one two good now um well I +guess we have space to do the second one + + align:start position:0% +guess we have space to do the second one + + + align:start position:0% +guess we have space to do the second one +- why not let's so so let's write out + + align:start position:0% +- why not let's so so let's write out + + + align:start position:0% +- why not let's so so let's write out +the second one also on here we're + + align:start position:0% +the second one also on here we're + + + align:start position:0% +the second one also on here we're +subtracting B instead of a get B minus a + + align:start position:0% +subtracting B instead of a get B minus a + + + align:start position:0% +subtracting B instead of a get B minus a +get to be minus 2 a we get minus B and + + align:start position:0% +get to be minus 2 a we get minus B and + + + align:start position:0% +get to be minus 2 a we get minus B and +what do we have here we have 2a minus 2b + + align:start position:0% + + + + align:start position:0% + +okay so now what's what's in the null + + align:start position:0% +okay so now what's what's in the null + + + align:start position:0% +okay so now what's what's in the null +space of this matrix well what you can + + align:start position:0% +space of this matrix well what you can + + + align:start position:0% +space of this matrix well what you can +see is that this is that this this this + + align:start position:0% +see is that this is that this this this + + + align:start position:0% +see is that this is that this this this +column is negative one times that column + + align:start position:0% +column is negative one times that column + + + align:start position:0% +column is negative one times that column +so our second eigenvector is just going + + align:start position:0% +so our second eigenvector is just going + + + align:start position:0% +so our second eigenvector is just going +to be one one okay and I should remind + + align:start position:0% +to be one one okay and I should remind + + + align:start position:0% +to be one one okay and I should remind +you that if you have a harder example + + align:start position:0% +you that if you have a harder example + + + align:start position:0% +you that if you have a harder example +you can just find these null spaces by + + align:start position:0% +you can just find these null spaces by + + + align:start position:0% +you can just find these null spaces by +elimination like we always do great now + + align:start position:0% +elimination like we always do great now + + + align:start position:0% +elimination like we always do great now +we have our eigen values and our eigen + + align:start position:0% +we have our eigen values and our eigen + + + align:start position:0% +we have our eigen values and our eigen +vectors so now we can write C in a nice + + align:start position:0% +vectors so now we can write C in a nice + + + align:start position:0% +vectors so now we can write C in a nice +easy way that allows us to take powers + + align:start position:0% +easy way that allows us to take powers + + + align:start position:0% +easy way that allows us to take powers +of it so what's that way + + align:start position:0% +of it so what's that way + + + align:start position:0% +of it so what's that way +so that's C equals + + align:start position:0% +so that's C equals + + + align:start position:0% +so that's C equals +s lambda s inverse right so this is just + + align:start position:0% +s lambda s inverse right so this is just + + + align:start position:0% +s lambda s inverse right so this is just +what is s remember s is our matrix of + + align:start position:0% +what is s remember s is our matrix of + + + align:start position:0% +what is s remember s is our matrix of +eigenvectors so s is the matrix 1 2 1 1 + + align:start position:0% +eigenvectors so s is the matrix 1 2 1 1 + + + align:start position:0% +eigenvectors so s is the matrix 1 2 1 1 +good now what is lambda lambda is the + + align:start position:0% +good now what is lambda lambda is the + + + align:start position:0% +good now what is lambda lambda is the +matrix of eigenvalues right so it's just + + align:start position:0% +matrix of eigenvalues right so it's just + + + align:start position:0% +matrix of eigenvalues right so it's just +a and B those are my the diagonal + + align:start position:0% +a and B those are my the diagonal + + + align:start position:0% +a and B those are my the diagonal +entries of my lambda matrix and then we + + align:start position:0% +entries of my lambda matrix and then we + + + align:start position:0% +entries of my lambda matrix and then we +just find s inverse so we just take + + align:start position:0% +just find s inverse so we just take + + + align:start position:0% +just find s inverse so we just take +negative signs here and recall that we + + align:start position:0% +negative signs here and recall that we + + + align:start position:0% +negative signs here and recall that we +have to divide by 1 over or we have to + + align:start position:0% +have to divide by 1 over or we have to + + + align:start position:0% +have to divide by 1 over or we have to +divide by the determinant and the + + align:start position:0% +divide by the determinant and the + + + align:start position:0% +divide by the determinant and the +determinant of this matrix is just + + align:start position:0% +determinant of this matrix is just + + + align:start position:0% +determinant of this matrix is just +negative 1 so we just changed the s + + align:start position:0% +negative 1 so we just changed the s + + + align:start position:0% +negative 1 so we just changed the s +signs there good so this is this is our + + align:start position:0% +signs there good so this is this is our + + + align:start position:0% +signs there good so this is this is our +nice decomposition of C now how do we + + align:start position:0% +nice decomposition of C now how do we + + + align:start position:0% +nice decomposition of C now how do we +take powers of C well C to the K is just + + align:start position:0% +take powers of C well C to the K is just + + + align:start position:0% +take powers of C well C to the K is just +s lambda to the K s inverse all right + + align:start position:0% +s lambda to the K s inverse all right + + + align:start position:0% +s lambda to the K s inverse all right +one one-to-one a to the K B to the K + + align:start position:0% +one one-to-one a to the K B to the K + + + align:start position:0% +one one-to-one a to the K B to the K +negative 1 1 to negative 1 good and + + align:start position:0% +negative 1 1 to negative 1 good and + + + align:start position:0% +negative 1 1 to negative 1 good and +multiplying these matrices 2 together + + align:start position:0% +multiplying these matrices 2 together + + + align:start position:0% +multiplying these matrices 2 together +just do a little arithmetic here get a + + align:start position:0% +just do a little arithmetic here get a + + + align:start position:0% +just do a little arithmetic here get a +bunch of powers of a and B because we + + align:start position:0% +bunch of powers of a and B because we + + + align:start position:0% +bunch of powers of a and B because we +take powers of the eigen values we have + + align:start position:0% +take powers of the eigen values we have + + + align:start position:0% +take powers of the eigen values we have +here we have 2 B to the K minus a to the + + align:start position:0% +here we have 2 B to the K minus a to the + + + align:start position:0% +here we have 2 B to the K minus a to the +K have a to the K minus B to the K have + + align:start position:0% +K have a to the K minus B to the K have + + + align:start position:0% +K have a to the K minus B to the K have +2 B to the K minus 2 a to the K and + + align:start position:0% +2 B to the K minus 2 a to the K and + + + align:start position:0% +2 B to the K minus 2 a to the K and +finally we get to a to the K minus B to + + align:start position:0% +finally we get to a to the K minus B to + + + align:start position:0% +finally we get to a to the K minus B to +the K + + align:start position:0% +the K + + + align:start position:0% +the K +and this is our case power matrix good + + align:start position:0% +and this is our case power matrix good + + + align:start position:0% +and this is our case power matrix good +a quick check it's always good to a + + align:start position:0% +a quick check it's always good to a + + + align:start position:0% +a quick check it's always good to a +check here I'll work here + + align:start position:0% +check here I'll work here + + + align:start position:0% +check here I'll work here +let's plug in K equals 1 and what do we + + align:start position:0% +let's plug in K equals 1 and what do we + + + align:start position:0% +let's plug in K equals 1 and what do we +get we get to B minus a a minus B to B + + align:start position:0% +get we get to B minus a a minus B to B + + + align:start position:0% +get we get to B minus a a minus B to B +minus 2 a and 2 a minus B and if we can + + align:start position:0% +minus 2 a and 2 a minus B and if we can + + + align:start position:0% +minus 2 a and 2 a minus B and if we can +go all the way back to our matrix at the + + align:start position:0% +go all the way back to our matrix at the + + + align:start position:0% +go all the way back to our matrix at the +very beginning all the way back here + + align:start position:0% +very beginning all the way back here + + + align:start position:0% +very beginning all the way back here +that agrees perfectly with what we + + align:start position:0% +that agrees perfectly with what we + + + align:start position:0% +that agrees perfectly with what we +started with so that's good that means + + align:start position:0% +started with so that's good that means + + + align:start position:0% +started with so that's good that means +that we did this decomposition right + + align:start position:0% +that we did this decomposition right + + + align:start position:0% +that we did this decomposition right +good so now we've computed the K power + + align:start position:0% +good so now we've computed the K power + + + align:start position:0% +good so now we've computed the K power +of this matrix let's do a particular + + align:start position:0% +of this matrix let's do a particular + + + align:start position:0% +of this matrix let's do a particular +example so let's plug in a and B R minus + + align:start position:0% +example so let's plug in a and B R minus + + + align:start position:0% +example so let's plug in a and B R minus +1 so a equals B equals minus 1 and K + + align:start position:0% +1 so a equals B equals minus 1 and K + + + align:start position:0% +1 so a equals B equals minus 1 and K +equals 100 then what do we get well + + align:start position:0% +equals 100 then what do we get well + + + align:start position:0% +equals 100 then what do we get well +minus 1 to the 100th is just 1 so we're + + align:start position:0% +minus 1 to the 100th is just 1 so we're + + + align:start position:0% +minus 1 to the 100th is just 1 so we're +just plugging in 1 for B to the K and a + + align:start position:0% +just plugging in 1 for B to the K and a + + + align:start position:0% +just plugging in 1 for B to the K and a +to the K everywhere and we just get in + + align:start position:0% +to the K everywhere and we just get in + + + align:start position:0% +to the K everywhere and we just get in +this case C the 100th is just well 1 0 0 + + align:start position:0% +this case C the 100th is just well 1 0 0 + + + align:start position:0% +this case C the 100th is just well 1 0 0 +1 it's just the identity matrix great + + align:start position:0% +1 it's just the identity matrix great + + + align:start position:0% +1 it's just the identity matrix great +great + + align:start position:0% +great + + + align:start position:0% +great +ok now to to summarize how do we take + + align:start position:0% +ok now to to summarize how do we take + + + align:start position:0% +ok now to to summarize how do we take +powers of a matrix + + align:start position:0% +powers of a matrix + + + align:start position:0% +powers of a matrix +well first we diagonalize we write our + + align:start position:0% +well first we diagonalize we write our + + + align:start position:0% +well first we diagonalize we write our +matrix as s lambda s inverse and then we + + align:start position:0% +matrix as s lambda s inverse and then we + + + align:start position:0% +matrix as s lambda s inverse and then we +just take powers of the diagonal matrix \ No newline at end of file diff --git a/5JxShDZ_ylo.txt b/5JxShDZ_ylo.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a5c6c48a69af94f97c18d1cebd524a74973e3d3 --- /dev/null +++ b/5JxShDZ_ylo.txt @@ -0,0 +1,2840 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: I want to +talk about two things, + +maybe, depending on +the level of interest. + +We can talk a little bit +about PSET five and the things + +that I think are weird in +the coding part of PSET five. + +By the way, how many +people started PSET five? + +[LAUGHTER] + +AUDIENCE: I downloaded it. + +PROFESSOR: Hmm, maybe we are not +going to talk about P set five. + +You guys need to start early! + +AUDIENCE: I did. + +PROFESSOR: You did. + +Yeah. + +I guess I can't punish +you for everyone else. + +So P set five, and I +can talk about graphs. + +I can talk about whatever +didn't make sense in class + +and I can talk about +background stuff for graphs. + +So how do people feel? + +Who wants talk about the +PSET that we haven't read? + +[LAUGHTER] + +Who wants to talk about graphs? + +AUDIENCE: It's really easy. + +We took 604 two. + +PROFESSOR: Yeah, if you took +604 two, nothing here is new. + +I mean nothing in the +recitation is new. + +We're going to take it to new +heights of graph knowledge, + +and you'll be able to +do many more cool things + +that you're able to do before. + +OK, so PSET. + +For people who +started early, what + +was the gist of the +coding assignments? + +AUDIENCE: So we have +to speed up something. + +When I ran the tests-- do I +say what I got as results? + +PROFESSOR: The time isn't on +the PSET so you can say what you + +got as -- + +AUDIENCE: Pardon? + +PROFESSOR: The time +isn't on the PSET + +so you can say what +you got as a time. + +AUDIENCE: OK, the slowest +was like add for me. + +PROFESSOR: You should look +to see add is a valid answer. + +Look at the questions and +see if add is a valid answer. + +AUDIENCE: OK. + +PROFESSOR: It's not like what +was lowest function, right? + +There's more text there. + +You should read the +rest of the text + +and see if add makes +sense as a valid answer. + +AUDIENCE: Sure. + +OK. + +PROFESSOR: What you're +doing-- big picture-- + +is you have some processor, +that's not a real processor, + +and it can do arithmetic +with bytes and 16-bit words. + +And we give you the +basic operations + +and then they give you a library +for large number arithmetic + +because, guess what? + +16 bytes addition, subtraction? + +Not going to cut it for +science applications + +are for cryptography, +what we want to play with. + +What are the basic operations +that that processor can do? + +Front of the PSET, +so even if you + +didn't get to the +coding assignment + +you can still tell me. + +AUDIENCE: Divide, +and zeros, I think. + +Zeros. + +PROFESSOR: Plus, minus, +multiply, divide, and mod. + +Let's start to these. + +So you have two primitives +in that processor. + +You have have bytes, which +are basically 8-bit digits. + +There's 200. + +The range is 0 to 256. + +And the word is 16-bit, +from 0 to the 16 minus 1. + +If you care to know +this is 6, 5, 5, 3, 5. + +So, if you take two bytes +and add them together what do + +you get? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Not right. + +It's a trick question. + +You get word. + +The processor cannot do +simple math on bytes. + +It converts them up to words and +all the math happens on words. + +Now if you guess two words, +and add them up together + +what do you get? + +AUDIENCE: Two words? + +PROFESSOR: You do if +we're not that nice. + +AUDIENCE: A world in carry bit? + +PROFESSOR: Sorry, +you just get word. + +At least nobody said a byte. + +I was like, please don't say +byte, please don't say byte. + +You said carry bit. + +Why do we care +about the carry bit? + +What is the problem if +you do addition this way? + +AUDIENCE: If you're +going too high. + +If the highest bit is +one on both of them. + +Then it's like +overflow, kind of. + +PROFESSOR: Yep. + +Suppose we're trying to add +2 to the 16 minus 1 plus 2 + +to the 16 minus 1. + +By the way, does anyone +remember hex notation? + +Hexadecimal? + +OK, people who started +the PSET remember. + +That's good. + +It will be easy to write +things hex for the PSET. + +If you try to add these numbers +you're going to get 1, F, F, F, + +E. You can use the +math here to see + +that this is more +than the words. + +So you would like to know that +this thing overflows, right? + +You like to know that there is. + +Well we don't give you that. + +All you get to this. + +So addition happens, +modulo 2 to the 16. + +If you want to be able to detect +overflow what they have to do? + +AUDIENCE: Just tests those bits. + +PROFESSOR: That one +way of doing it. + +It would take quite a +few instructions, though. + +If you want to do +overflow detection, + +the easiest way I think of +doing it this to use this form. + +So suppose you have two bytes. + +This is the maximum +value in a byte, right? + +255, 2 to the 8 minus 1. + +If you have 2 bytes and +you add them all together + +you're going to +get 1, F, E. Right? + +It's just like the case here, +except you have a fewer F's. + +Where is the carry here? + +AUDIENCE: Could be the 1, right? + +PROFESSOR: Yep. + +This guy here is the carry +and this guy's the low result. + +Does anyone know how +these are called? + +If you have a word and +you have two bytes, what + +is the first byte, what +is the second bytes? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Most +significant byte, + +M, S, B, and least +significant byte, + +L, S, B. If you want to +figure out your carries, + +then you should do +your math this way. + +You're going to have +byte 1 plus byte 2. + +Add them together. + +And then you call L, S, +B to get the byte result. + +And then you call M, +S, B to get the carry. + +This is addition. + +Everyone with me so far? + +By the way, are these +numbers signed or unsigned? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: No negative +numbers, right? + +So no support for +negative numbers. + +Everything is going +to be positive. + +And we're going to +build everything + +we need off of positive +numbers because they're + +easier to deal with. + +What if I have two words +and I subtract them? + +What do I get? + +AUDIENCE: Word. + +PROFESSOR: OK. + +What if I have 0 minus 1? + +What do I get? + +AUDIENCE: 0. + +PROFESSOR: Not quite. + +AUDIENCE: If you're +not using signs? + +Do you get O, 1? + +PROFESSOR: O, 1's, OK. + +AUDIENCE: Ya. + +Wait-- + +PROFESSOR: So, O 1's +would be this, F, F, F, F. + +AUDIENCE: That's assuming +if you signed then. + +It will overflow. + +That's a really big number then. + +PROFESSOR: So fancy +CS, 2's complement. + +For people who think in +math mode, what is this? + +AUDIENCE: I think. + +PROFESSOR: It's minus +1 mod 2 to the 16. + +Remember, when we were doing +modular arithmetic before, + +to figure out a number's +multiplicative inverse? + +And when we were +doing rolling hashes? + +We didn't want negative numbers. + +We made them positive. + +So minus 1 lot to the +16 is 2 to the 16. + +Minus 1, and comes +out to this value. + +So you get minus 1, +it's just that you + +have to know your basis. + +So we got the addition +and subtraction. + +Let's talk about multiplication. + +What do you do for +multiplication? + +What can you multiply? + +Two bytes, very good. + +Just two bytes. + +What do you get? + +A word. + +Thank you. + +You multiply two +bytes, you get a word. + +What if there's overflow? + +It's a trick question. + +AUDIENCE: There's no overflow. + +PROFESSOR: There is no overflow. + +So two bytes, 2 to the +eighth minus 1 times 2 + +to the eighth minus 1, +is 2 to the 16 minus 2 + +to the 8th minus 2 +to the eighth plus 1. + +You can say this safely without +doing the arithmetic, right? + +This is how much you can +hold, in other words. + +This is how much you +can holding in a byte. + +AUDIENCE: Why do you minus 1? + +PROFESSOR: Ya, minus 1. + +There's a minus 1 here, +and there's a minus 1 here, + +but I can't find it +here, so roughly this. + +But there is an overflow. + +AUDIENCE: But where did +you get the minus 1 from? + +PROFESSOR: Where do +you get the-- so, + +this is how much you +can hold in a byte. + +Byte has 8 bits, right? + +From 0 0 to F F. This is +2 to the eighth minus 1. + +AUDIENCE: OK. + +PROFESSOR: OK, so +multiplication? + +There is an overflow. + +I don't have to deal with that. + +You guys have to figure +out how to deal with it. + +How about division? + +What can you divide? + +AUDIENCE: Some words? + +PROFESSOR: Almost. + +AUDIENCE: Words like-- + +PROFESSOR: A word +divided by a byte. + +What do you get out of it? + +AUDIENCE: Words? + +PROFESSOR: That would be nice. + +Nope. + +Sorry, you get a byte. + +And if you do module, +you also get a byte. + +What if there's overflow +in the division? + +What happens? + +What would you expect to happen? + +AUDIENCE: We don't have any +best flowing point numbers, + +so, we shouldn't +get overflow, right? + +PROFESSOR: How about 2 to +the 16 minus 1 divided by 1? + +So what do get? + +AUDIENCE: Same thing? + +PROFESSOR: Will this +fit in the byte? + +AUDIENCE: Yes? + +No. + +[LAUGHTER] + +No. + +Well, that time I +don't get a word. + +PROFESSOR: You don't get a word. + +I promise you get a byte. + +What will that byte be? + +AUDIENCE: It's going +to be modulo something. + +Most significant-- + +PROFESSOR: That's +reasonable, right? + +Modulo to 56 because +that's what it can carry. + +What about modulo? + +What happens there +if you get overflow? + +AUDIENCE: The same thing. + +It's just going to loop, right? + +0? + +PROFESSOR: So if +you do a modulo, + +this is going to be, +at most, 255 right? + +If you do modulo +255, the remainder + +is going to be +between 0 and 254. + +Will that ever overflow byte? + +No overflow. + +No need to worry about it. + +Word addition can overflow. + +Subtraction can overflow. + +Multiplication doesn't overflow. + +Division overflows, +modulo doesn't. + +AUDIENCE: What do you mean, like +will it see the space confined? + +PROFESSOR: Yes. + +It sees the space of the result. + +Because here, if you're +adding two words, + +the result exceeds +the space of a word. + +Which is what you get. + +AUDIENCE: Is it just in all +cases it's just [INAUDIBLE]. + +PROFESSOR: Exactly. + +So the reason you have to +deal with this weird system + +is this is, pretty much, how +Intel does their arithmetic. + +If you look at old school, +16-bit Intel processors, + +you have registers and you +have exactly these operations. + +For newer processors, there are +32 bits, but then it's just, + +you write more F's on the board +and you get the same thing. + +AUDIENCE: Is it most significant +bit, or most significant byte? + +PROFESSOR: Most +significant byte. + +On a real processor, +you have registers + +that are the size +of a word and then + +you can pull out the +bytes in constant time. + +What constant do we have? + +These are the operations. + +What constants do we have? + +Only two constants, 0 and 1. + +What if you want to +get something bigger? + +What if you want to get 2? + +How do you get 2? + +AUDIENCE: Two 1's? + +1 plus 1? + +PROFESSOR: Yep. + +What if you want +to get this number? + +AUDIENCE: Do that several times? + +[LAUGHTER] + +PROFESSOR: It's kind +of painful to type, + +even if you copy paste. + +There's a method on +Word called from-bytes. + +And it takes an M, +S, B and an L, S, B + +and it gives you a word. + +So what would I give it? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Let's give it +a 1 and let's give it a 0. + +So this will get 1, +0, 0 and then minus 1. + +Yes? + +OK. + +Intel is pretty nice +about constants, + +but some other +processors aren't. + +So I figured, why not +let's get you acquainted + +to these kind of tricks, to too. + +Let's make the PSETS +more interesting. + +All right, so any questions +on this fake processor + +that you have to code for? + +AUDIENCE: Can you explain +the last one again? + +PROFESSOR: Here? + +AUDIENCE: Yeah, Word from-bytes. + +PROFESSOR: So in Word +from-bytes a word is 2 bytes. + +One next to the other. + +It gives you the first byte, +and gives you the second byte. + +In this case, the +first byte is 1. + +The second byte is 0. + +Right? + +So 2 bytes. + +A 1 and a 0. + +How do you write this in hex? + +1, 0, 0. + +One byte, second byte. + +And then I subtract +1 and I get this. + +While I erase the +board, I want you guys + +to think of graph +questions because this + +is the other topic +we're looking at today. + +What was unclear +about the lecture? + +What is unclear about +graphs in general? + +Do guys remember the +handshaking lemma? + +What does it mean? + +How do you prove it? + +Things of that sort. + +What do you guys +want to cover today? + +AUDIENCE: Handshaking, +that's the thing where + +you have a bunch nodes +and they're all connected, + +like they're all in a closed +graph, that the number of edges + +is equal to twice the +number of vertices? + +PROFESSOR: OK. + +AUDIENCE: That's +all it is, right? + +PROFESSOR: The +number of vertices? + +No. + +AUDIENCE: The +number of handshakes + +that occurred are twice +the number of edges. + +You said the number +of vertices, wait-- + +PROFESSOR: No, vertices and +edges are not related in here. + +AUDIENCE: Yeah, think +of a triangle, right? + +That's three edges, +three vertices. + +Which is like not two times, +which is what you said. + +It's the number of degrees +is twice the number of edges. + +That's what I was +thinking of then. + +PROFESSOR: All right, so +let's start with simple stuff. + +What's a graph? + +AUDIENCE: Nodes and edges? + +PROFESSOR: All right. + +Fancy word for nodes? + +AUDIENCE: Vertex. + +PROFESSOR: Vertex. + +Vertices and edges. + +How do I draw vertices? + +How do I draw edges? + +AUDIENCE: Circles and lines. + +PROFESSOR: Circles and lines. + +AUDIENCE: 0's and 1's. + +Possibly arrows. + +PROFESSOR: Possibly arrows. + +I like that. + +You want to get fancy. + +[LAUGHTER} + +PROFESSOR: When do I +draw an edge as a line? + +When do I draw it as an arrow? + +AUDIENCE: Directed under. + +PROFESSOR: Which one's which? + +AUDIENCE: Directed as an arrow. + +Character number. + +PROFESSOR: Cool. + +Let's draw this graph here. + +Yeah, looks like a +pretty boring graph. + +Is this graph connected or not? + +AUDIENCE: Yes. + +PROFESSOR: What's +a connected graph? + +AUDIENCE: I think +that we can get + +to any other node +following some path. + +PROFESSOR: There's a path +from any to any other node. + +How do I make this +unconnected using + +the least amount of effort? + +It's a bit of a trick question. + +Any guess is fine. + +AUDIENCE: What was +the question again? + +PROFESSOR: How do I +make this unconnected + +using the least amount +of effort on my behalf? + +AUDIENCE: Just add a node? + +PROFESSOR: I heard +you move pages. + +I don't like you racing +because I don't like the-- So + +I like that answer out +of the two I heard. + +Now it's not a connected graph. + +How many connected +component does it have? + +Two and five. + +AUDIENCE: Or one +connected component, + +but there are two components? + +PROFESSOR: OK, what's +a connected component? + +AUDIENCE: It's like in that part +of the graph the neck follows + +the prognito beacon and puts +them in two parts [INAUDIBLE] + +two connected components-- + +PROFESSOR: So, a +connected component + +is a bunch of vertices such +that you can get from one vertex + +to all the other vertices. + +If the graph is +undirected, that's + +true for any vertex in the set. + +We also want the +sets to be maximal + +because, if we say this +is a connected component, + +it's not very useful. + +Noticing that this whole +thing is a connected component + +is useful. + +So this is one component. + +This is the other component. + +Make sense? + +So, we have the world. + +We have cities. + +You can bike from a city to +another city and that's it. + +No other a route +of transportation. + +How many connected components? + +AUDIENCE: Seven? + +PROFESSOR: OK. + +Roughly seven. + +Why? + +OK, so it only seven? + +AUDIENCE: Seven continents? + +PROFESSOR: OK. + +Let's say roughly seven. + +So this is what I wanted. + +I wanted some thinking. + +If you try to get from a +continent to another continent, + +presumably you'd go +through some patch of sea. + +Otherwise, why are they +calling them continents? + +Does anyone want to +give out another answer? + +I asked this in the +previous section + +and some people there give +me some very precise answers + +that are not continents. + +This is what I had +in mind, by the way. + +As far as I'm concerned, +this is a good answer. + +Come on guys, world. + +Two things, islands and +Europe and Asia are connected, + +so you can go from +one to the other. + +They're weird. + +Why are they +separate continents? + +I have no idea. + +The geography people might-- + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sorry? + +AUDIENCE: You roll mountains? + +PROFESSOR: OK, so it would +be a pain bike through them, + +but presumably you can. + +If you have a robot that +doesn't get tired or something + +you can bike. + +AUDIENCE: It doesn't +mind falling off cliffs. + +PROFESSOR: The answer, +depending on my geography, + +we know is somewhere +between 7 and 10,000, + +or whatever the +number of islands is. + +There are a lot of tiny +island somewhere, right? + +Anyways, between seven +and a big number. + +These are connected +components in the world. + +What's the degree of A? + +2. + +What's the degree of the D? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Very good. + +Let's make this. + +The degrees of F, +G, H are 2, 2, 2. + +The degree of C is 2. + +The degree of B is? + +AUDIENCE: --2. + +PROFESSOR: Thank you. + +And the degree of E is? + +AUDIENCE: 2. + +PROFESSOR: If you add up all +these numbers together what + +you get? + +18. + +I can't do math, so +I couldn't possibly + +have added all these +numbers together, right? + +I used something else. + +How many edges do I +have in the graph? + +1, 2, 3, 4, 5, 6, 7, 8, 9. + +Do you see your connection here? + +AUDIENCE: Yeah. + +PROFESSOR: This is +the handshaking lemma. + +That's all there is to it. + +So if you look at +the degrees of a node + +each edge adds one +to two degrees. + +For instance, this edge +adds one to C's degree + +and adds one to D's degree. + +If you're a math person +and you write this up, + +you have to write sums. + +You have big sums using +intimidating notation, + +so it's not as obvious. + +But this is really +all there is to it. + +Each edge contributes +one to two nodes degrees. + +If you add up all +the degrees, you're + +going to get to times +the number of edges. + +So far so good? + +What if we have directed graphs? + +What if I had this? + +A, B, C, D, E, F. What +is the degree of A? + +AUDIENCE: 2? + +PROFESSOR: Not quite. + +Sorry, that was trick question. + +A doesn't have a degree. + +If you have directed graphs, +you don't have degrees. + +You have in degrees +and out degrees. + +Now that I've said that +you have no idea, right? + +What's the out degree of A? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Sometimes this is +known as the degree of edges. + +This is 2. + +What's the in degree of A? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So A has two edges +going out, 0 edges going in. + +How about D? + +What's the out degree of D? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Come on guys. + +Don't scare me. (LAUGHS) +What's the in degree of D? + +AUDIENCE: 2? + +PROFESSOR: 2, very good. + +PROFESSOR: So what's +the equivalent + +of the handshaking lemma +on oriented graphs? + +AUDIENCE: The sum of the +in degrees and out degrees? + +PROFESSOR: OK, what about them? + +AUDIENCE: They're equal to +twice the number of vertices? + +PROFESSOR: Not quite. + +They're equal to? + +You had 80 percent +of the answer. + +AUDIENCE: Oh. (LAUGHS) + +PROFESSOR: So the sum of the in +degrees and the sum of the out + +degrees. + +AUDIENCE: So add them up? + +PROFESSOR: If you +add them up, you + +will get two times +the number of edges. + +That is correct. + +But, I want something more-- + +AUDIENCE: They equal each other? + +PROFESSOR: Yep. + +This is cooler, right? + +So why is that? + +Does anyone see why +that's the case? + +Each edge-- Come on, guys. + +So what does each edge do? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So if I +look at this edge here, + +this edge is going to +contribute 1 to B's out degree, + +and 1 to D's in degree. + +Each edge contributes +1 to an out degree + +and 1 to an in degree. + +That means that total +sum of out degrees + +equals the total +sum of in degrees. + +Both of them are E and +they combined to E. Sorry, + +eyed I don't know why that +didn't click to me right away. + +AUDIENCE: OK. + +PROFESSOR: The +intuition behind this + +is, that for every node, +if you take an edge + +you're going to +get somewhere else. + +If the sum of the out +degrees was bigger, + +then you have a +black hole somewhere. + +If you go on an edge +you don't come back. + +Same four in degrees. + +OK, how do we represent graphs? + +AUDIENCE: I think we just did. + +PROFESSOR: Sure, if +you're drawing them + +on the board that's what +you do, but if you're + +in Python what do you do? + +AUDIENCE: You can +have a link list. + +PROFESSOR: Of? + +AUDIENCE: Of each node having +its neighbors linked with. + +PROFESSOR: OK, so I +have one big link list? + +Or how does this work? + +AUDIENCE: You'd have a +starting point of some sort. + +A starting node. + +Then from that node you can have +its neighbors connected to it. + +So it was a link list , I guess. + +PROFESSOR: I wasn't precise. + +That is not trivial to build. + +By the time we build that we're +done with this recitation. + +What do you get is the +vertices and the edges. + +We want an easier representation +that just looks at the vertices + +and build something, +then looks at the edges + +and builds something. + +AUDIENCE: You could +have a table of values. + +Like, A has these +neighbors-- a dictionary. + +PROFESSOR: Let's go for that. + +So we have a dictionary. + +For each vertex +you have the list + +of vertices that +are connected to it. + +What's the list for A? + +AUDIENCE: B and C? + +PROFESSOR: OK, what's +the list for B? + +AUDIENCE: A, D, and E. + +PROFESSOR: All right. + +For Python this would +be a dictionary, right? + +So how much total +space does this take? + +AUDIENCE: The number of nodes? + +PROFESSOR: The number of-- + +AUDIENCE: --nodes. + +Well, then there's also the +space you made for the list, + +though. + +PROFESSOR: If these were +actual slots in an array-- + +so this would be an array-- I +would have the number of nodes. + +You're giving away the +answer to my next question. + +So I have these slots here. + +This would be an array. + +It's order V just to store this. + +The thing in Python is that +have these dictionaries that + +are fancy hashes where +they grow as you need them. + +For example, you +have 10,000 vertices + +but you don't have any edge. + +Your dictionary size is going +to be order 1 because it only + +grows as you add edges to it. + +So this is assuming that +I don't store empty lists. + +If I have a stray +node here, if I + +have a node I-- say this is +I-- if I don't store anything, + +I don't have to pay for it. + +If I store an empty list here, +then I have to pay for it. + +There is an order V +component that you mentioned. + +AUDIENCE: Let's say, if +there's a graph there, + +everything is not connected +so there are a bunch of words + +instead. + +Then in that case it +would be order V, right? + +PROFESSOR: It's order V +if we store empty lists + +for the nodes that +don't have edges. + +AUDIENCE: Right. + +And if none of the +nodes have edges, + +they're all unconnected-- + +PROFESSOR: On the other hand, +if I don't store anything + +for the nodes that don't +have edges, it's order 1. + +AUDIENCE: If you get no +edges do we do an empty list + +or do we not store it? + +PROFESSOR: Depends +on what you want. + +So if we store +empty lists you're + +going to have an +order V cost here. + +But your code is going to +be simpler, presumably, + +because you don't have +to check if something + +is or isn't in the dictionary. + +How about this stuff? + +What's the total size +of this stuff here? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: OK. + +Order E. How many elements +do I have in here in total? + +In this thing here. + +So what's the sum of +the length of the lists? + +AUDIENCE: Average value of E +times the number of vertices? + +PROFESSOR: Let's go +over something else. + +AUDIENCE: The degree-- + +PROFESSOR: All right. + +That's what I wanted to hear. + +A lists its neighbors, right? + +The number of neighbors that +A has is the degree of A. B + +lists its neighbors, so +this is the degree of B. + +If you sum up over all of them, +what is the sum of all the + +agrees in the graph? + +AUDIENCE: 2, E. + +PROFESSOR: 2, E. We +learned about this, right? + +The handshaking +lemma, 2, E. So what + +is the total cost for +storing this data structure? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: So V plus E, +assuming empty lists. + +Let's look at another +data structure + +for storing things in a graph. + +So instead of using +lists, let's use a matrix. + +A, B, C, D, E on top, and +A, B, C, D, E on the left. + +Let's pretend our graph is +just that component over there. + +Otherwise, it just gets big +and there's no extraneous site. + +Does anyone know +how this is called? + +If I put numbers +here, does anyone + +know what this is called? + +AUDIENCE: Is that a matrix? + +PROFESSOR: There's +a fancy name for it. + +It ends with matrix. + +OK. + +I don't think we taught +it to you, so don't worry. + +The fancy name is maybe it's +misspelled, but something + +that looks and sounds like +this., adjacency matrix. + +Misspelled? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I hope +someone will help me. + +OK so if this is an +adjacency matrix, + +what should this element +between B and A tell me? + +If it's an adjacency +matrix, it better + +tell me if they're adjacent. + +They're adjacent if they +have an edge between them. + +For A and B, what +does it happen to be? + +AUDIENCE: One? + +PROFESSOR: OK. + +A and A? + +What do we do? + +AUDIENCE: What with 1? + +It's adjacent to itself. + +PROFESSOR: What's +easier for the algorithm + +that you're trying to implement? + +AUDIENCE: 1? + +PROFESSOR: So it +doesn't really matter. + +We use 1's most of the +time, but sometimes it's + +easier to use a 0. + +AUDIENCE: Then you can +get to A from A, right? + +PROFESSOR: Yeah. + +So that's why you'd use a 1. + +Sometimes, though, you +don't want to in code. + +So someone dictate this to me. + +Or, everyone dictate this to +me so I know it makes sense. + +A and C, is there an +edge between them? + +AUDIENCE: Yes. + +PROFESSOR: What do I write? + +AUDIENCE: 1. + +PROFESSOR: A and D? + +A and E? + +AUDIENCE: 0. + +PROFESSOR: B, A? + +AUDIENCE: 1. + +PROFESSOR: B, C? + +AUDIENCE: 0. + +PROFESSOR: B, D? + +AUDIENCE: 1. + +PROFESSOR: The E? + +AUDIENCE: 1. + +PROFESSOR: OK. + +C, A? + +AUDIENCE: 1. + +PROFESSOR: C, B? + +AUDIENCE: 2. + +PROFESSOR: C, D? + +AUDIENCE: 1. + +PROFESSOR: C, E? + +AUDIENCE: 0. + +PROFESSOR: All right. + +Now I'm going to +use the bits you + +gave me to come to get this. + +Let's see if I can +do it correctly. + +And D? + +I'm not looking at the graph, +by the way, I'm trusting you. + +So you better give +me the right answer. + +D? + +AUDIENCE: 1. + +PROFESSOR: How many +1's do I have in this? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: To see if +you guys are thinking. + +AUDIENCE: 2, E? [INAUDIBLE]. + +PROFESSOR: Each edge +contributes to two 1's, right? + +And that accounts +for most of the 1's. + +AUDIENCE: O plus V. + +PROFESSOR: So this is +how many 1's I have. + +How many 0's do I have? + +AUDIENCE: V squared +minus 2, E plus V? + +PROFESSOR: This is +a non-boring way + +of asking how many elements +I have in this matrix. + +This is what I was looking for. + +So V columns, right? + +Zeros V squared's +total elements. + +How much memory do I +need to store this? + +AUDIENCE: V squared. + +PROFESSOR: V squared. what? + +If I want to store it as +compactly as possible? + +I want to pack these +as tight as I can. + +AUDIENCE: You mean you need +the entire array arranged? + +PROFESSOR: Yes, so +what do I store? + +V squared what? + +AUDIENCE: Oh, you mean units. + +PROFESSOR: Yeah. + +What's the unit? + +AUDIENCE: 1 bit? + +PROFESSOR: All right! + +So V squared bits Whereas, +this is V plus E words + +because you have to store +pointers everywhere here. + +So sometimes if your +graph is really dense + +you might prefer +this representation. + +Let me see, how much do I have? + +Oh, plenty of time. + +Who remembers +breadth-first search? + +Yes? + +AUDIENCE: Basically you +just start at some node + +and you check all its neighbors, +and check all those neighbors. + +PROFESSOR: All right. + +In breadth-first +search we have a graph. + +What did I draw there? + +A. B, E. So suppose +this is our graph. + +And I do a breadth-first +search starting at A. + +How does that work? + +I started with the list of the +nodes that I'm going to visit. + +I initialization it with A +because this is the only node + +that I know about. + +What happens next? + +AUDIENCE: It goes with B and C. + +PROFESSOR: All right. + +So I take out of the list +the first thing that I can. + +This is my current node. + +You said I visit B and C +because they're the neighbors. + +Right. + +I took A out of the list. + +A was definitely visited. + +And I'm visiting B and C. What +do I do when I visit them? + +AUDIENCE: Put them in the list. + +PROFESSOR: Put them in the list. + +This means I discovered them and +I'm going to visit the later. + +So I discovered them and +I know of their existence. + +What happens next? + +AUDIENCE: Check if +B is what you want. + +PROFESSOR: So B gets out of +the list, and what do I do? + +AUDIENCE: Discover +it's neighbors. + +PROFESSOR: All right, +so its neighborhoods + +are A, B, and E. What Now? + +AUDIENCE: If they +haven't already + +been on that list then +add a [INAUDIBLE]. + +PROFESSOR: A was +already visited. + +D and E weren't. + +D and E, then what happens? + +AUDIENCE: Then you +check C's neighbors. + +PROFESSOR: Any neighbor's +that I haven't seen? + +Nope. + +Then? + +AUDIENCE: D? + +AUDIENCE: D and? + +AUDIENCE: E. + +PROFESSOR:OK. + +And then? + +PROFESSOR: I guess +you could go to F, + +but it's not +connected to anything. + +But how did you +get A then, right? + +PROFESSOR: So A +is the first node. + +I started with A +because I said I'm + +doing a breadth-first +search starting from A. + +So BFS starts from somewhere. + +A BFS has a source. + +We'll see why that +matters in a bit. + +So you ever get to see F? + +AUDIENCE: No. + +PROFESSOR: Nope. + +So if I start at A what +are the nodes that I visit + +and what are the nodes +that I don't visit? + +AUDIENCE: Well you visit all +the ones in the connected graph. + +PROFESSOR: All right, in +the connected component. + +So the whole graph can be +connected or not connected. + +The nodes that I +visit are the nodes + +in A's connected component +because, by definition, those + +are the nodes that +I can reach from A. + +If I have many kind +of the components + +and I use BFS starting +from one node, + +I might not visit +the entire graph. + +How do I keep track of what +node that I've discovered + +and haven't discovered? + +What data structure do I +use for these smiley faces? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR:So for +the smiley faces. + +For this thing I +probably want a queue. + +We'd teach you +something simpler, + +but most of the time when +you write the code you + +actually use queue. + +What do I want for +the smiley faces? + +When I pull a node out, +say I pulled out B, + +and I see A, D, E, I want +to know that I visited A + +and I didn't visit the D +and E. You guys remember + +that we didn't visit D and E, +right, by the time we got to 2? + +OK. + +So I want to be able to check +whether I visited a node + +or not really fast. + +What data structure should +I use for the smileys? + +AUDIENCE: A hash table. + +PROFESSOR: A has table. + +Cool. + +What's a hash table in Python? + +AUDIENCE: A dictionary. + +PROFESSOR: A dictionary. + +All right, so this is +going to be a seen, which + +is a dictionary, and it +maps vertices to maybe true. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR:Yep. + +Python has a set, right? + +So you can use that. + +The smileys needs to be +some sort of a dictionary. + +So given that, and +assuming that this + +is a queue that we +can extract and you + +can start from in +constant time, what + +is the running time of BFS? + +Let's make life easy. + +Let's assume the graph is +connected and let's assume just + +doesn't exist. + +BFS was the running time. + +AUDIENCE: [INAUDIBLE] visiting. + +PROFESSOR: So you +visit every node once, + +so it's at least +V. That's a start. + +Now what do you do when +you visit the node? + +AUDIENCE: Check out all the-- + +PROFESSOR: All the +neighbors, right? + +Given the node, you have +to go to the data structure + +that you have that's +either this or this, + +and you have to get +a list of neighbors. + +If I have this data +structure, how fast + +do I get a list of +neighbors for a node? + +AUDIENCE: Order of the degree? + +PROFESSOR: Yep. + +Order of the degree of the node. + +That's good. + +How about this data structure? + +AUDIENCE: Same-- oh, +no that's order of V. + +PROFESSOR: Yep. + +So in this data structure, +for example, C only + +has two edges coming out of it. + +But I have to go through the +entire lining of the matrix + +to see where I have my 0's +and where I have my 1's. + +In order to list the neighbors, +here is straight up order V, + +whereas this is order of +the degree of the node + +that I'm looking for. + +So for this, where it's +nice and simple, order of V, + +what is the total running time? + +AUDIENCE: Wait, because +it's B plus B. Oh no, it's + +the same one. + +PROFESSOR: So for +each node I have to? + +AUDIENCE: V squared. + +PROFESSOR: OK. + +So we're up to V +squared already. + +What else do we need to do? + +Anything that they need to +do on a node is order of V, + +so V squared is going to +be the total running time. + +That's it. + +So if we use an +adjacency matrix we + +get order of V squared as +the total running time. + +What about if we lists, +what the running time? + +I'll give you a hint. + +You have to use +amortized analysis. + +Shivers anyone? + +[LAUGHTER] + +We know it's order +V because we're + +going to visit every node. + +And you guys didn't see what +I was going to write here. + +[LAUGHTER] + +OK. + +So for every node I go +through the neighbors + +and I do something to them. + +Right? + +I check if they're in +seen, if not then I + +add them to the list. + +So for every node the work is? + +AUDIENCE: it's degrees. + +PROFESSOR: Yep. + +So if I look at all the nodes? + +AUDIENCE: That's E. + +PROFESSOR: Yep. + +For every node I have +to look at its neighbors + +and I have to see which +neighbors are in seen. + +For the neighbors +that are not in seen + +I have to add to my queue. + +Checking if a neighbor is +in seen or not is order 1. + +Adding it to the +queue is order 1. + +So the total work +for a node is order + +of neighbors because of the +adjacency list, not matrix. + +If I look at the +entire graph, here I + +can't do a local analysis +like I did before. + +If I look at the entire graph +and I look at all the nodes + +slash vertices, +then the total work + +is the sum of their degrees. + +For each node is degree. + +For total work, +sum of the degrees. + +And I have that nice +handshaking lemma + +that says that the sum +of the degrees is 2, + +E. So order E. So +total running time? + +V plus E. + +OK, can I say that the +running time is order E? + +With no V's? + +AUDIENCE: No, because you +have to look at every-- + +PROFESSOR: Is it? + +AUDIENCE: V greater +than [INAUDIBLE] + +in case of not +connected components? + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: It's +possible that you could + +have more vertices than edges-- + +PROFESSOR: OK. + +So it's possible that I have +more vertices than edges. + +I agree with that, but I +do anything to the vertices + +that I haven't seen? + +So this is subtle. + +The difference +between this and this + +is a matter of how you +implement everything. + +In CLRS they assume that +the seen is an array. + +So all of their nodes +have numbers from 1 to V. + +So then they initialize an +array, everything is false, + +and then they set +the true elements. + +In Python we can +use a dictionary + +and not initialize +it with anything. + +So if you do it that way in +Python and code carefully, + +you can get to order E. +The parts of the graph + +that you don't discover, you +don't have to pay for them. + +If you look at CLRS +code, it is definitely + +V plus E. The difference +between this and this + +depends on the code. + +What's the point +of BFS, by the way? + +Why do we care? + +What does it give us? + +AUDIENCE: The +shortest word path. + +PROFESSOR:The shortest +path from point? + +AUDIENCE: From your start +to where you're going. + +PROFESSOR:So it gives you the +shortest path from the node + +that I'm starting the BFS from. + +So only from this node? + +If I start BFS at A +it's going to give me + +the length of the shortest +path from A to which node? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: All the nodes? + +AUDIENCE: Yeah. + +PROFESSOR: All +the nodes that are + +visited by BFS are reachable +and we have a path from them. + +How do you compute +this distance? + +Let's see, so what's the +distance from A to A? + +AUDIENCE: 0? + +PROFESSOR: 0. + +When I start from A and I see +that its neighbors are B and C, + +what's the distance from +A to B and from A to C? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: OK. + +Now I look at B. What's the +distance between A and A? + +A is B's neighbor. + +AUDIENCE: With A and A? + +PROFESSOR: Yeah. + +So I have three neighbors. + +B has three neighbors, +A, D, and E. + +So I care about the distances +between A and A, D, E. Distance + +A, A, distance A, D, and +distance A, E. This one is 0. + +How about the distances +between A and D and A and E? + +They're 2. + +So the way I would +compute these distances + +is that I start with A being 0. + +The distance from A to A is 0. + +And then when I look at a node, +when I discover the neighbors, + +all the neighbors that don't +have smiley faces on them + +get the node's distance plus 1. + +You can get to them by +getting in the current node + +and then traversing an edge. + +When you do that it's +important that you don't update + +the distances of the nodes +that have smiley faces. + +If you do, you're going to say +that the distance from A to A + +is 2 and all hell +breaks lose from there. + +AUDIENCE: Wait, why would +you say it would be 2? + +PROFESSOR: If I forget the +fact that it has a smiley face. + +So if I go through +all these neighbors + +and I say the +distance from A to B + +is one then the distance from +A to all of B's neighbors + +has to be 2. + +That would be wrong. + +AUDIENCE: Wait, +from A to all of-- + +PROFESSOR: B's neighbors. + +AUDIENCE: From A to all of-- +Oh, because A is one Of-- + +PROFESSOR: B's neighbors. + +AUDIENCE: Yeah OK. + +PROFESSOR: The +smileys tell me which + +vertices I've already +seen and I've already, + +presumably computed +distances for them. + +We don't want to update those. + +OK this is BFS in essence. + +One question. + +Between Facebook and +Twitter, which one's directed + +and which one's undirected? + +AUDIENCE: Facebook +is undirected. + +PROFESSOR: OK. + +Facebook is undirected. + +Why is it undirected? + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: When you follow +someone they don't necessarily + +follow you. + +PROFESSOR: OK. + +So this is Twitter, right? + +Twitter, directed +because of follows. + +Has anyone used +Facebook recently? + +Did you guys see +there's a new option? + +AUDIENCE: The little +scroll bar on the side? + +PROFESSOR: Subscribers. + +AUDIENCE: Oh, ya. + +PROFESSOR: OK, so how +do subscribers work? + +AUDIENCE: You subscribe. + +It's like google plus. + +[LAUGHTER] + +PROFESSOR: OK. + +Directed are undirected? + +If I subscribe to you do +you have to subscribe to me? + +AUDIENCE: Directed. + +PROFESSOR: So which one is it? + +AUDIENCE: I guess Facebook +is kind of directed now + +because you can +unsubscribe from people. + +PROFESSOR: Is it? + +So Facebook has +two graphs in it. + +They happen to have +the same vertices. + +The people are the +vertices in both graphs. + +But the friends relationship +defines an undirected graph. + +The subscribers relationship +defines a directed graph. + +The graphs are +completely different. + +And there are two graphs. + +That's the right way +to reason about them. + +that's why it was +slightly tricky. + +Can someone think of a cool +way to use BFS on Facebook? + +AUDIENCE: That's +networks, right? + +Figuring out how many people +are in the first degree + +or second degree. + +MySpace was really into that. + +PROFESSOR: Lincoln +also does that, right? + +How many people +are your friends? + +How many people are +your friend's friends? + +So and so forth. + +Now suppose you want to +get to someone in Facebook + +and you don't know +them directly. + +They're not your friends. + +Presumably, you +want to get to them + +through the minimum +amount of effort. + +So you want to see do you +have a friend that knows them? + +If not, do you +have a friend that + +knows a friend that knows them? + +Do you have a friend +that knows a friend that + +knows a friend that knows them? + +So and so forth. + +So BFS will give you +that minimum path. + +OK. + +do the graphs make sense? + +So by the way, the +BFS on Facebook + +is just the beginning +of a ton of cool things + +you can with graph algorithms. \ No newline at end of file diff --git a/5cF5Bgv59Sc.txt b/5cF5Bgv59Sc.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4ace7fde9baaa1f3d82a598ee8ba52c3c901032 --- /dev/null +++ b/5cF5Bgv59Sc.txt @@ -0,0 +1,10635 @@ +align:start position:0% + +hi everyone welcome to the + + align:start position:0% +hi everyone welcome to the + + + align:start position:0% +hi everyone welcome to the +uh 11th lecture of 6006 + + align:start position:0% +uh 11th lecture of 6006 + + + align:start position:0% +uh 11th lecture of 6006 +our first lecture on weighted shortest + + align:start position:0% +our first lecture on weighted shortest + + + align:start position:0% +our first lecture on weighted shortest +paths + + align:start position:0% +paths + + + align:start position:0% +paths +until uh now we've only been talking + + align:start position:0% +until uh now we've only been talking + + + align:start position:0% +until uh now we've only been talking +about graphs that + + align:start position:0% +about graphs that + + + align:start position:0% +about graphs that +uh where we measure distance in terms of + + align:start position:0% +uh where we measure distance in terms of + + + align:start position:0% +uh where we measure distance in terms of +the number of edges + + align:start position:0% +the number of edges + + + align:start position:0% +the number of edges +in a path right today we're going to + + align:start position:0% +in a path right today we're going to + + + align:start position:0% +in a path right today we're going to +generalize that notion but i just want + + align:start position:0% +generalize that notion but i just want + + + align:start position:0% +generalize that notion but i just want +to + + align:start position:0% +to + + + align:start position:0% +to +go over what we've talked about in the + + align:start position:0% +go over what we've talked about in the + + + align:start position:0% +go over what we've talked about in the +last two lectures uh + + align:start position:0% +last two lectures uh + + + align:start position:0% +last two lectures uh +in the last two lectures we've talked + + align:start position:0% +in the last two lectures we've talked + + + align:start position:0% +in the last two lectures we've talked +about two algorithms breadth first + + align:start position:0% +about two algorithms breadth first + + + align:start position:0% +about two algorithms breadth first +search and depth first search + + align:start position:0% +search and depth first search + + + align:start position:0% +search and depth first search +to solve a range of problems here's some + + align:start position:0% +to solve a range of problems here's some + + + align:start position:0% +to solve a range of problems here's some +of the problems that we've + + align:start position:0% +of the problems that we've + + + align:start position:0% +of the problems that we've +been solving single source shortest + + align:start position:0% +been solving single source shortest + + + align:start position:0% +been solving single source shortest +paths + + align:start position:0% +paths + + + align:start position:0% +paths +where distances are measured in number + + align:start position:0% +where distances are measured in number + + + align:start position:0% +where distances are measured in number +of edges in a path + + align:start position:0% +of edges in a path + + + align:start position:0% +of edges in a path +and we use bfs to solve this problem + + align:start position:0% +and we use bfs to solve this problem + + + align:start position:0% +and we use bfs to solve this problem +starting from a single source usually a + + align:start position:0% +starting from a single source usually a + + + align:start position:0% +starting from a single source usually a +vertex s + + align:start position:0% +vertex s + + + align:start position:0% +vertex s +that we we call uh and and we solved + + align:start position:0% +that we we call uh and and we solved + + + align:start position:0% +that we we call uh and and we solved +that in linear time + + align:start position:0% +that in linear time + + + align:start position:0% +that in linear time +right and we solved that in + + align:start position:0% +right and we solved that in + + + align:start position:0% +right and we solved that in +order v plus + + align:start position:0% +order v plus + + + align:start position:0% +order v plus +e that's what we called linear time for + + align:start position:0% +e that's what we called linear time for + + + align:start position:0% +e that's what we called linear time for +a graph + + align:start position:0% +a graph + + + align:start position:0% +a graph +for the special case of single source + + align:start position:0% +for the special case of single source + + + align:start position:0% +for the special case of single source +reachability + + align:start position:0% +reachability + + + align:start position:0% +reachability +here we had to return a shortest path + + align:start position:0% +here we had to return a shortest path + + + align:start position:0% +here we had to return a shortest path +distance for every vertex + + align:start position:0% +distance for every vertex + + + align:start position:0% +distance for every vertex +and there was at most e things reachable + + align:start position:0% +and there was at most e things reachable + + + align:start position:0% +and there was at most e things reachable +from a vertex + + align:start position:0% +from a vertex + + + align:start position:0% +from a vertex +so this is uh + + align:start position:0% +so this is uh + + + align:start position:0% +so this is uh +the bound we got but in the special case + + align:start position:0% +the bound we got but in the special case + + + align:start position:0% +the bound we got but in the special case +for single source reachability + + align:start position:0% +for single source reachability + + + align:start position:0% +for single source reachability +when our output only has to list the + + align:start position:0% +when our output only has to list the + + + align:start position:0% +when our output only has to list the +vertices that are reachable from me + + align:start position:0% +vertices that are reachable from me + + + align:start position:0% +vertices that are reachable from me +the the number of things reachable in a + + align:start position:0% +the the number of things reachable in a + + + align:start position:0% +the the number of things reachable in a +uh basically a spanning tree of the + + align:start position:0% +uh basically a spanning tree of the + + + align:start position:0% +uh basically a spanning tree of the +connected component of my source + + align:start position:0% +connected component of my source + + + align:start position:0% +connected component of my source +can almost be of order e and so + + align:start position:0% +can almost be of order e and so + + + align:start position:0% +can almost be of order e and so +for all the little singleton vertices in + + align:start position:0% +for all the little singleton vertices in + + + align:start position:0% +for all the little singleton vertices in +my graph + + align:start position:0% +my graph + + + align:start position:0% +my graph +i don't really care right so i can get + + align:start position:0% +i don't really care right so i can get + + + align:start position:0% +i don't really care right so i can get +this in order e but that's kind of a + + align:start position:0% +this in order e but that's kind of a + + + align:start position:0% +this in order e but that's kind of a +little optimization the next + + align:start position:0% +little optimization the next + + + align:start position:0% +little optimization the next +thing we did was we talked about + + align:start position:0% +thing we did was we talked about + + + align:start position:0% +thing we did was we talked about +connected components + + align:start position:0% +connected components + + + align:start position:0% +connected components +and we didn't just reduce to using a + + align:start position:0% +and we didn't just reduce to using a + + + align:start position:0% +and we didn't just reduce to using a +search algorithm + + align:start position:0% +search algorithm + + + align:start position:0% +search algorithm +like a single source reachability + + align:start position:0% +like a single source reachability + + + align:start position:0% +like a single source reachability +algorithm like bfs or dfs + + align:start position:0% +algorithm like bfs or dfs + + + align:start position:0% +algorithm like bfs or dfs +we put a for loop around that to explore + + align:start position:0% +we put a for loop around that to explore + + + align:start position:0% +we put a for loop around that to explore +the entire graph by basically saying if + + align:start position:0% +the entire graph by basically saying if + + + align:start position:0% +the entire graph by basically saying if +i've + + align:start position:0% +i've + + + align:start position:0% +i've +explored one connected component + + align:start position:0% +explored one connected component + + + align:start position:0% +explored one connected component +then i can look at any other vertex i + + align:start position:0% +then i can look at any other vertex i + + + align:start position:0% +then i can look at any other vertex i +haven't seen + + align:start position:0% +haven't seen + + + align:start position:0% +haven't seen +and explore the next one right and so + + align:start position:0% +and explore the next one right and so + + + align:start position:0% +and explore the next one right and so +that actually with some + + align:start position:0% +that actually with some + + + align:start position:0% +that actually with some +a little analysis also got linear time + + align:start position:0% +a little analysis also got linear time + + + align:start position:0% +a little analysis also got linear time +because i'm at most + + align:start position:0% +because i'm at most + + + align:start position:0% +because i'm at most +traversing any component of my graph + + align:start position:0% +traversing any component of my graph + + + align:start position:0% +traversing any component of my graph +once + + align:start position:0% +once + + + align:start position:0% +once +that's kind of the the idea and then and + + align:start position:0% +that's kind of the the idea and then and + + + align:start position:0% +that's kind of the the idea and then and +we can use that using + + align:start position:0% +we can use that using + + + align:start position:0% +we can use that using +bfs or dfs really because we're just + + align:start position:0% +bfs or dfs really because we're just + + + align:start position:0% +bfs or dfs really because we're just +trying to get + + align:start position:0% +trying to get + + + align:start position:0% +trying to get +a thing that searches an entire + + align:start position:0% +a thing that searches an entire + + + align:start position:0% +a thing that searches an entire +connected component + + align:start position:0% +connected component + + + align:start position:0% +connected component +and then this topological sort we did at + + align:start position:0% +and then this topological sort we did at + + + align:start position:0% +and then this topological sort we did at +the end of the last lecture + + align:start position:0% +the end of the last lecture + + + align:start position:0% +the end of the last lecture +we used full dfs to give an ordering of + + align:start position:0% +we used full dfs to give an ordering of + + + align:start position:0% +we used full dfs to give an ordering of +the vertices + + align:start position:0% +the vertices + + + align:start position:0% +the vertices +in a dag i maybe i'll specify + + align:start position:0% +in a dag i maybe i'll specify + + + align:start position:0% +in a dag i maybe i'll specify +clearly that this is only for a dag + + align:start position:0% +clearly that this is only for a dag + + + align:start position:0% +clearly that this is only for a dag +right + + align:start position:0% +right + + + align:start position:0% +right +where we uh have an ordering of the + + align:start position:0% +where we uh have an ordering of the + + + align:start position:0% +where we uh have an ordering of the +vertices so all the edges go + + align:start position:0% +vertices so all the edges go + + + align:start position:0% +vertices so all the edges go +forward in that order for example okay + + align:start position:0% +forward in that order for example okay + + + align:start position:0% +forward in that order for example okay +and that we also did in linear time + + align:start position:0% + + + + align:start position:0% + +all right in this lecture and in + + align:start position:0% +all right in this lecture and in + + + align:start position:0% +all right in this lecture and in +actually the next four lectures + + align:start position:0% +actually the next four lectures + + + align:start position:0% +actually the next four lectures +what we're going to do is + + align:start position:0% +what we're going to do is + + + align:start position:0% +what we're going to do is +instead of measuring distance in terms + + align:start position:0% +instead of measuring distance in terms + + + align:start position:0% +instead of measuring distance in terms +of the number of edges in a path + + align:start position:0% +of the number of edges in a path + + + align:start position:0% +of the number of edges in a path +so previously distance + + align:start position:0% + + + + align:start position:0% + +equaled number of edges + + align:start position:0% +equaled number of edges + + + align:start position:0% +equaled number of edges +we're going to generalize that notion so + + align:start position:0% +we're going to generalize that notion so + + + align:start position:0% +we're going to generalize that notion so +instead of counting + + align:start position:0% +instead of counting + + + align:start position:0% +instead of counting +an edge we're going to count + + align:start position:0% +an edge we're going to count + + + align:start position:0% +an edge we're going to count +an integer associated with that edge + + align:start position:0% +an integer associated with that edge + + + align:start position:0% +an integer associated with that edge +it's going to be called a weight + + align:start position:0% +it's going to be called a weight + + + align:start position:0% +it's going to be called a weight +all right so here's an example of a + + align:start position:0% +all right so here's an example of a + + + align:start position:0% +all right so here's an example of a +weighted graph g and i've labeled in red + + align:start position:0% +weighted graph g and i've labeled in red + + + align:start position:0% +weighted graph g and i've labeled in red +weights for each of these edges there's + + align:start position:0% +weights for each of these edges there's + + + align:start position:0% +weights for each of these edges there's +a directed graph on eight vertices + + align:start position:0% +a directed graph on eight vertices + + + align:start position:0% +a directed graph on eight vertices +and i've got a integer associated with + + align:start position:0% +and i've got a integer associated with + + + align:start position:0% +and i've got a integer associated with +each edge you'll notice some of them + + align:start position:0% +each edge you'll notice some of them + + + align:start position:0% +each edge you'll notice some of them +are positive some of them are negative + + align:start position:0% +are positive some of them are negative + + + align:start position:0% +are positive some of them are negative +it's okay to be zero as well + + align:start position:0% +it's okay to be zero as well + + + align:start position:0% +it's okay to be zero as well +it's just any integer edge weight here + + align:start position:0% +it's just any integer edge weight here + + + align:start position:0% +it's just any integer edge weight here +so generally we're going to be along + + align:start position:0% +so generally we're going to be along + + + align:start position:0% +so generally we're going to be along +with our graph g + + align:start position:0% +with our graph g + + + align:start position:0% +with our graph g +we're going to be given a weight + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% +function + + + align:start position:0% +function +that maps uh the edges of g + + align:start position:0% +that maps uh the edges of g + + + align:start position:0% +that maps uh the edges of g +to we're gonna say integers + + align:start position:0% +to we're gonna say integers + + + align:start position:0% +to we're gonna say integers +okay in this class anyway + + align:start position:0% +okay in this class anyway + + + align:start position:0% +okay in this class anyway +uh in other contexts in mathematics you + + align:start position:0% +uh in other contexts in mathematics you + + + align:start position:0% +uh in other contexts in mathematics you +might have this be real numbers but in + + align:start position:0% +might have this be real numbers but in + + + align:start position:0% +might have this be real numbers but in +this class we're going to deal with + + align:start position:0% +this class we're going to deal with + + + align:start position:0% +this class we're going to deal with +integers + + align:start position:0% +integers + + + align:start position:0% +integers +so each edge if you have an edge + + align:start position:0% +so each edge if you have an edge + + + align:start position:0% +so each edge if you have an edge +we're going to say this is the + + align:start position:0% +we're going to say this is the + + + align:start position:0% +we're going to say this is the +edge weight the weight of this edge e + + align:start position:0% +edge weight the weight of this edge e + + + align:start position:0% +edge weight the weight of this edge e +from e we we might sometimes if if this + + align:start position:0% +from e we we might sometimes if if this + + + align:start position:0% +from e we we might sometimes if if this +edge e is u + + align:start position:0% +edge e is u + + + align:start position:0% +edge e is u +v right we might sometimes say + + align:start position:0% +v right we might sometimes say + + + align:start position:0% +v right we might sometimes say +the weight from u to v + + align:start position:0% +the weight from u to v + + + align:start position:0% +the weight from u to v +since we have a simple graph that's + + align:start position:0% +since we have a simple graph that's + + + align:start position:0% +since we have a simple graph that's +unambiguous + + align:start position:0% +unambiguous + + + align:start position:0% +unambiguous +right all right so but this is just + + align:start position:0% +right all right so but this is just + + + align:start position:0% +right all right so but this is just +talking about our notation so + + align:start position:0% +talking about our notation so + + + align:start position:0% +talking about our notation so +in general for example the weight from + + align:start position:0% +in general for example the weight from + + + align:start position:0% +in general for example the weight from +vertex + + align:start position:0% +vertex + + + align:start position:0% +vertex +b to f in this graph is what can someone + + align:start position:0% +b to f in this graph is what can someone + + + align:start position:0% +b to f in this graph is what can someone +tell me + + align:start position:0% +tell me + + + align:start position:0% +tell me +minus 4 right it's right here and i'll + + align:start position:0% +minus 4 right it's right here and i'll + + + align:start position:0% +minus 4 right it's right here and i'll +be consistent with my coloring + + align:start position:0% +be consistent with my coloring + + + align:start position:0% +be consistent with my coloring +because i've got colored chalk today + + align:start position:0% +because i've got colored chalk today + + + align:start position:0% +because i've got colored chalk today +-4 happiness all right so + + align:start position:0% +-4 happiness all right so + + + align:start position:0% +-4 happiness all right so +why do we care about adding weights to + + align:start position:0% +why do we care about adding weights to + + + align:start position:0% +why do we care about adding weights to +our graph + + align:start position:0% +our graph + + + align:start position:0% +our graph +well this comes up a lot in many + + align:start position:0% +well this comes up a lot in many + + + align:start position:0% +well this comes up a lot in many +applications for example + + align:start position:0% +applications for example + + + align:start position:0% +applications for example +you know distances in a road network + + align:start position:0% +you know distances in a road network + + + align:start position:0% +you know distances in a road network +right if i have a road from + + align:start position:0% +right if i have a road from + + + align:start position:0% +right if i have a road from +here uh so so from mass ave + + align:start position:0% +here uh so so from mass ave + + + align:start position:0% +here uh so so from mass ave +uh front of mit to central square + + align:start position:0% +uh front of mit to central square + + + align:start position:0% +uh front of mit to central square +we might think of that as one road maybe + + align:start position:0% +we might think of that as one road maybe + + + align:start position:0% +we might think of that as one road maybe +maybe you've got + + align:start position:0% +maybe you've got + + + align:start position:0% +maybe you've got +uh each road is a connection between two + + align:start position:0% +uh each road is a connection between two + + + align:start position:0% +uh each road is a connection between two +intersections + + align:start position:0% +intersections + + + align:start position:0% +intersections +in my road network but an edge + + align:start position:0% +in my road network but an edge + + + align:start position:0% +in my road network but an edge +it takes longer to go from say vassar + + align:start position:0% +it takes longer to go from say vassar + + + align:start position:0% +it takes longer to go from say vassar +street + + align:start position:0% +street + + + align:start position:0% +street +to amherst that takes a shorter amount + + align:start position:0% +to amherst that takes a shorter amount + + + align:start position:0% +to amherst that takes a shorter amount +of time than it does to go from + + align:start position:0% +of time than it does to go from + + + align:start position:0% +of time than it does to go from +memorial drive across the river to + + align:start position:0% +memorial drive across the river to + + + align:start position:0% +memorial drive across the river to +beacon street + + align:start position:0% +beacon street + + + align:start position:0% +beacon street +right so we might want to associate a + + align:start position:0% +right so we might want to associate a + + + align:start position:0% +right so we might want to associate a +larger distance or a weight + + align:start position:0% +larger distance or a weight + + + align:start position:0% +larger distance or a weight +associated with that edge right + + align:start position:0% +associated with that edge right + + + align:start position:0% +associated with that edge right +latency in a in a in a network for + + align:start position:0% +latency in a in a in a network for + + + align:start position:0% +latency in a in a in a network for +example + + align:start position:0% +example + + + align:start position:0% +example +maybe strength of relationships in a + + align:start position:0% +maybe strength of relationships in a + + + align:start position:0% +maybe strength of relationships in a +social network and you could imagine + + align:start position:0% +social network and you could imagine + + + align:start position:0% +social network and you could imagine +that it's possible maybe you're + + align:start position:0% +that it's possible maybe you're + + + align:start position:0% +that it's possible maybe you're +frenemies with someone + + align:start position:0% +frenemies with someone + + + align:start position:0% +frenemies with someone +right like you you don't like them and + + align:start position:0% +right like you you don't like them and + + + align:start position:0% +right like you you don't like them and +so maybe you have a negative weight + + align:start position:0% +so maybe you have a negative weight + + + align:start position:0% +so maybe you have a negative weight +associated + + align:start position:0% +associated + + + align:start position:0% +associated +with an edge in a social network i'm not + + align:start position:0% +with an edge in a social network i'm not + + + align:start position:0% +with an edge in a social network i'm not +sure + + align:start position:0% +sure + + + align:start position:0% +sure +maybe not but there are lots of + + align:start position:0% +maybe not but there are lots of + + + align:start position:0% +maybe not but there are lots of +applications where you might want + + align:start position:0% +applications where you might want + + + align:start position:0% +applications where you might want +weights on your edges + + align:start position:0% +weights on your edges + + + align:start position:0% +weights on your edges +so that that comes to the next question + + align:start position:0% +so that that comes to the next question + + + align:start position:0% +so that that comes to the next question +of how do i represent how do i give + + align:start position:0% +of how do i represent how do i give + + + align:start position:0% +of how do i represent how do i give +the user or the algorithm these weights + + align:start position:0% +the user or the algorithm these weights + + + align:start position:0% +the user or the algorithm these weights +in my graph right we had a represent + + align:start position:0% +in my graph right we had a represent + + + align:start position:0% +in my graph right we had a represent +representation for a graph + + align:start position:0% +representation for a graph + + + align:start position:0% +representation for a graph +right our common way to represent a + + align:start position:0% +right our common way to represent a + + + align:start position:0% +right our common way to represent a +graph was + + align:start position:0% +graph was + + + align:start position:0% +graph was +store a set data structure on the + + align:start position:0% +store a set data structure on the + + + align:start position:0% +store a set data structure on the +vertices + + align:start position:0% +vertices + + + align:start position:0% +vertices +mapping to the adjacencies + + align:start position:0% +mapping to the adjacencies + + + align:start position:0% +mapping to the adjacencies +of each vertex which we stored in what + + align:start position:0% +of each vertex which we stored in what + + + align:start position:0% +of each vertex which we stored in what +we called an adjacency list which really + + align:start position:0% +we called an adjacency list which really + + + align:start position:0% +we called an adjacency list which really +could be any data structure + + align:start position:0% +could be any data structure + + + align:start position:0% +could be any data structure +right uh commonly it's just a + + align:start position:0% +right uh commonly it's just a + + + align:start position:0% +right uh commonly it's just a +an array of the adjacencies but you + + align:start position:0% +an array of the adjacencies but you + + + align:start position:0% +an array of the adjacencies but you +could also have that be + + align:start position:0% +could also have that be + + + align:start position:0% +could also have that be +a set data structure where you can + + align:start position:0% +a set data structure where you can + + + align:start position:0% +a set data structure where you can +query in constant time uh what + + align:start position:0% +query in constant time uh what + + + align:start position:0% +query in constant time uh what +if a particular adjacency exists in that + + align:start position:0% +if a particular adjacency exists in that + + + align:start position:0% +if a particular adjacency exists in that +graph + + align:start position:0% +graph + + + align:start position:0% +graph +so a common way there are two kind of + + align:start position:0% +so a common way there are two kind of + + + align:start position:0% +so a common way there are two kind of +common ways + + align:start position:0% +common ways + + + align:start position:0% +common ways +to store these weights one + + align:start position:0% +to store these weights one + + + align:start position:0% +to store these weights one +is just with every adjacency i'm going + + align:start position:0% +is just with every adjacency i'm going + + + align:start position:0% +is just with every adjacency i'm going +to store its weight + + align:start position:0% +to store its weight + + + align:start position:0% +to store its weight +maybe just in a tuple some you know + + align:start position:0% +maybe just in a tuple some you know + + + align:start position:0% +maybe just in a tuple some you know +with each + + align:start position:0% +with each + + + align:start position:0% +with each +adjacency + + align:start position:0% + + + + align:start position:0% + +also store + + align:start position:0% +also store + + + align:start position:0% +also store +weight of the edge that it corresponds + + align:start position:0% +weight of the edge that it corresponds + + + align:start position:0% +weight of the edge that it corresponds +to + + align:start position:0% +to + + + align:start position:0% +to +right just in any way right uh a second + + align:start position:0% +right just in any way right uh a second + + + align:start position:0% +right just in any way right uh a second +way + + align:start position:0% +way + + + align:start position:0% +way +instead of trying to modify our graph + + align:start position:0% +instead of trying to modify our graph + + + align:start position:0% +instead of trying to modify our graph +structure that we gave you before + + align:start position:0% +structure that we gave you before + + + align:start position:0% +structure that we gave you before +let's just have a dictionary of all the + + align:start position:0% +let's just have a dictionary of all the + + + align:start position:0% +let's just have a dictionary of all the +edges mapping to their weights + + align:start position:0% +edges mapping to their weights + + + align:start position:0% +edges mapping to their weights +right and we already know how to do that + + align:start position:0% +right and we already know how to do that + + + align:start position:0% +right and we already know how to do that +just so any set data structure + + align:start position:0% +just so any set data structure + + + align:start position:0% +just so any set data structure +any separate + + align:start position:0% +any separate + + + align:start position:0% +any separate +set data structure mapping + + align:start position:0% + + + + align:start position:0% + +edges to their i guess + + align:start position:0% +edges to their i guess + + + align:start position:0% +edges to their i guess +weights bad notation but you get the + + align:start position:0% +weights bad notation but you get the + + + align:start position:0% +weights bad notation but you get the +idea + + align:start position:0% +idea + + + align:start position:0% +idea +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +it doesn't really matter how we're doing + + align:start position:0% +it doesn't really matter how we're doing + + + align:start position:0% +it doesn't really matter how we're doing +this the the assumption that we're going + + align:start position:0% +this the the assumption that we're going + + + align:start position:0% +this the the assumption that we're going +to rely on here + + align:start position:0% +to rely on here + + + align:start position:0% +to rely on here +is that we given an edge + + align:start position:0% +is that we given an edge + + + align:start position:0% +is that we given an edge +right given this vertex pair i can query + + align:start position:0% +right given this vertex pair i can query + + + align:start position:0% +right given this vertex pair i can query +what + + align:start position:0% +what + + + align:start position:0% +what +the weight of that edge is in constant + + align:start position:0% +the weight of that edge is in constant + + + align:start position:0% +the weight of that edge is in constant +time right + + align:start position:0% +time right + + + align:start position:0% +time right +and so if i'm going to do that i can + + align:start position:0% +and so if i'm going to do that i can + + + align:start position:0% +and so if i'm going to do that i can +either store it with a + + align:start position:0% +either store it with a + + + align:start position:0% +either store it with a +maybe a hash table of hash tables right + + align:start position:0% +maybe a hash table of hash tables right + + + align:start position:0% +maybe a hash table of hash tables right +a hash table + + align:start position:0% +a hash table + + + align:start position:0% +a hash table +mapping the set of vertices to their + + align:start position:0% +mapping the set of vertices to their + + + align:start position:0% +mapping the set of vertices to their +adjacencies and then each + + align:start position:0% +adjacencies and then each + + + align:start position:0% +adjacencies and then each +adjacency list stores its adjacencies in + + align:start position:0% +adjacency list stores its adjacencies in + + + align:start position:0% +adjacency list stores its adjacencies in +a hash table and that way + + align:start position:0% +a hash table and that way + + + align:start position:0% +a hash table and that way +in constant time i can check what the + + align:start position:0% +in constant time i can check what the + + + align:start position:0% +in constant time i can check what the +weight is there or here i'm just + + align:start position:0% +weight is there or here i'm just + + + align:start position:0% +weight is there or here i'm just +i could even have just a single hash + + align:start position:0% +i could even have just a single hash + + + align:start position:0% +i could even have just a single hash +table mapping the pair + + align:start position:0% +table mapping the pair + + + align:start position:0% +table mapping the pair +the the edge the tuple + + align:start position:0% +the the edge the tuple + + + align:start position:0% +the the edge the tuple +constant size uh to its weight + + align:start position:0% +constant size uh to its weight + + + align:start position:0% +constant size uh to its weight +right so either way is fine uh we're + + align:start position:0% +right so either way is fine uh we're + + + align:start position:0% +right so either way is fine uh we're +just going to assume that we can + + align:start position:0% +just going to assume that we can + + + align:start position:0% +just going to assume that we can +query an edge in constant time the + + align:start position:0% +query an edge in constant time the + + + align:start position:0% +query an edge in constant time the +weight of an edge in constant time + + align:start position:0% +weight of an edge in constant time + + + align:start position:0% +weight of an edge in constant time +okay so this is a that graph + + align:start position:0% +okay so this is a that graph + + + align:start position:0% +okay so this is a that graph +example it's a little busy here i'm + + align:start position:0% +example it's a little busy here i'm + + + align:start position:0% +example it's a little busy here i'm +probably going to erase that in just a + + align:start position:0% +probably going to erase that in just a + + + align:start position:0% +probably going to erase that in just a +second + + align:start position:0% +second + + + align:start position:0% +second +but we're going to move on to what + + align:start position:0% +but we're going to move on to what + + + align:start position:0% +but we're going to move on to what +giving these edges + + align:start position:0% +giving these edges + + + align:start position:0% +giving these edges +weights implies for uh kind of these + + align:start position:0% +weights implies for uh kind of these + + + align:start position:0% +weights implies for uh kind of these +problems that we've defined in terms of + + align:start position:0% +problems that we've defined in terms of + + + align:start position:0% +problems that we've defined in terms of +unweighted graphs right + + align:start position:0% +unweighted graphs right + + + align:start position:0% +unweighted graphs right +in particular we're going to be + + align:start position:0% +in particular we're going to be + + + align:start position:0% +in particular we're going to be +concentrating on + + align:start position:0% +concentrating on + + + align:start position:0% +concentrating on +single source shortest paths again at + + align:start position:0% +single source shortest paths again at + + + align:start position:0% +single source shortest paths again at +least for the next three lectures we'll + + align:start position:0% +least for the next three lectures we'll + + + align:start position:0% +least for the next three lectures we'll +generalize that even still uh in the + + align:start position:0% +generalize that even still uh in the + + + align:start position:0% +generalize that even still uh in the +in the next lecture i mean in the fourth + + align:start position:0% +in the next lecture i mean in the fourth + + + align:start position:0% +in the next lecture i mean in the fourth +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in three lectures from now + + align:start position:0% +in three lectures from now + + + align:start position:0% +in three lectures from now +but what we had here was that the + + align:start position:0% +but what we had here was that the + + + align:start position:0% +but what we had here was that the +distance before + + align:start position:0% +distance before + + + align:start position:0% +distance before +in an unweighted graph was the number of + + align:start position:0% +in an unweighted graph was the number of + + + align:start position:0% +in an unweighted graph was the number of +edges in the path + + align:start position:0% +edges in the path + + + align:start position:0% +edges in the path +here we're going to generalize that + + align:start position:0% +here we're going to generalize that + + + align:start position:0% +here we're going to generalize that +notion kind of + + align:start position:0% +notion kind of + + + align:start position:0% +notion kind of +obviously two weighted paths + + align:start position:0% +obviously two weighted paths + + + align:start position:0% +obviously two weighted paths +right and the weight + + align:start position:0% + + + + align:start position:0% + +of a path i'm going to call it pi so + + align:start position:0% +of a path i'm going to call it pi so + + + align:start position:0% +of a path i'm going to call it pi so +some weight of + + align:start position:0% +some weight of + + + align:start position:0% +some weight of +path pi + + align:start position:0% +path pi + + + align:start position:0% +path pi +right is just going to be the sum of the + + align:start position:0% +right is just going to be the sum of the + + + align:start position:0% +right is just going to be the sum of the +weights in the edges in the path right + + align:start position:0% +weights in the edges in the path right + + + align:start position:0% +weights in the edges in the path right +so + + align:start position:0% +so + + + align:start position:0% +so +edge in the path i'm going to sum + + align:start position:0% + + + + align:start position:0% + +their weights right so that's all this + + align:start position:0% +their weights right so that's all this + + + align:start position:0% +their weights right so that's all this +the weight of a path means it's just i'm + + align:start position:0% +the weight of a path means it's just i'm + + + align:start position:0% +the weight of a path means it's just i'm +going to sum + + align:start position:0% +going to sum + + + align:start position:0% +going to sum +all the weights in a path so if i took a + + align:start position:0% +all the weights in a path so if i took a + + + align:start position:0% +all the weights in a path so if i took a +look at the maybe there's a particular + + align:start position:0% +look at the maybe there's a particular + + + align:start position:0% +look at the maybe there's a particular +path here the path from a to b + + align:start position:0% +path here the path from a to b + + + align:start position:0% +path here the path from a to b +to f to g right is going to be + + align:start position:0% +to f to g right is going to be + + + align:start position:0% +to f to g right is going to be +minus 5 minus 4 2 + + align:start position:0% +minus 5 minus 4 2 + + + align:start position:0% +minus 5 minus 4 2 +that's going to be minus 9 plus 2 is -7 + + align:start position:0% +that's going to be minus 9 plus 2 is -7 + + + align:start position:0% +that's going to be minus 9 plus 2 is -7 +right okay so just as an example + + align:start position:0% +right okay so just as an example + + + align:start position:0% +right okay so just as an example +so uh then + + align:start position:0% +so uh then + + + align:start position:0% +so uh then +then what is the shortest path then well + + align:start position:0% +then what is the shortest path then well + + + align:start position:0% +then what is the shortest path then well +kind of obviously among + + align:start position:0% +kind of obviously among + + + align:start position:0% +kind of obviously among +all paths between two vertices it's + + align:start position:0% +all paths between two vertices it's + + + align:start position:0% +all paths between two vertices it's +going to be one with the + + align:start position:0% +going to be one with the + + + align:start position:0% +going to be one with the +minimum weight right yeah question can i + + align:start position:0% +minimum weight right yeah question can i + + + align:start position:0% +minimum weight right yeah question can i +use the same edge more than once + + align:start position:0% +use the same edge more than once + + + align:start position:0% +use the same edge more than once +can i use the same edge more than once + + align:start position:0% +can i use the same edge more than once + + + align:start position:0% +can i use the same edge more than once +right now you're asking about the + + align:start position:0% +right now you're asking about the + + + align:start position:0% +right now you're asking about the +distinction + + align:start position:0% +distinction + + + align:start position:0% +distinction +uh in an art class which we have between + + align:start position:0% +uh in an art class which we have between + + + align:start position:0% +uh in an art class which we have between +paths and simple paths + + align:start position:0% +paths and simple paths + + + align:start position:0% +paths and simple paths +right so here a weighted path doesn't + + align:start position:0% +right so here a weighted path doesn't + + + align:start position:0% +right so here a weighted path doesn't +really care if we visit an edge more + + align:start position:0% +really care if we visit an edge more + + + align:start position:0% +really care if we visit an edge more +than once + + align:start position:0% +than once + + + align:start position:0% +than once +right so if an edge appears more than + + align:start position:0% +right so if an edge appears more than + + + align:start position:0% +right so if an edge appears more than +once in + + align:start position:0% +once in + + + align:start position:0% +once in +pi we have to count that more than once + + align:start position:0% +pi we have to count that more than once + + + align:start position:0% +pi we have to count that more than once +in the edge + + align:start position:0% +in the edge + + + align:start position:0% +in the edge +weight in the weight of the path okay + + align:start position:0% +weight in the weight of the path okay + + + align:start position:0% +weight in the weight of the path okay +great question + + align:start position:0% +great question + + + align:start position:0% +great question +um but what we're going to see later on + + align:start position:0% +um but what we're going to see later on + + + align:start position:0% +um but what we're going to see later on +is shortest paths + + align:start position:0% +is shortest paths + + + align:start position:0% +is shortest paths +cannot repeat an edge more than once + + align:start position:0% +cannot repeat an edge more than once + + + align:start position:0% +cannot repeat an edge more than once +uh in in certain contexts + + align:start position:0% +uh in in certain contexts + + + align:start position:0% +uh in in certain contexts +right so so we're going to get to the + + align:start position:0% +right so so we're going to get to the + + + align:start position:0% +right so so we're going to get to the +the + + align:start position:0% +the + + + align:start position:0% +the +problem there a little later in this + + align:start position:0% +problem there a little later in this + + + align:start position:0% +problem there a little later in this +lecture and we're going to solve that + + align:start position:0% +lecture and we're going to solve that + + + align:start position:0% +lecture and we're going to solve that +in tomorrow's lecture but if you have + + align:start position:0% +in tomorrow's lecture but if you have + + + align:start position:0% +in tomorrow's lecture but if you have +we're getting a little ahead of + + align:start position:0% +we're getting a little ahead of + + + align:start position:0% +we're getting a little ahead of +ourselves but when we have negative + + align:start position:0% +ourselves but when we have negative + + + align:start position:0% +ourselves but when we have negative +weights in a graph + + align:start position:0% +weights in a graph + + + align:start position:0% +weights in a graph +it's possible that things go wrong we're + + align:start position:0% +it's possible that things go wrong we're + + + align:start position:0% +it's possible that things go wrong we're +going to get there in about five lines + + align:start position:0% +going to get there in about five lines + + + align:start position:0% +going to get there in about five lines +okay great so uh + + align:start position:0% +okay great so uh + + + align:start position:0% +okay great so uh +the the shortest path + + align:start position:0% + + + + align:start position:0% + +and in this case i'm going to clarify + + align:start position:0% +and in this case i'm going to clarify + + + align:start position:0% +and in this case i'm going to clarify +that this is the weighted shortest path + + align:start position:0% +that this is the weighted shortest path + + + align:start position:0% +that this is the weighted shortest path +right + + align:start position:0% + + + + align:start position:0% + +is a minimum + + align:start position:0% + + + + align:start position:0% + +mom sure uh + + align:start position:0% +mom sure uh + + + align:start position:0% +mom sure uh +is a minimum weight + + align:start position:0% + + + + align:start position:0% + +path you know + + align:start position:0% +path you know + + + align:start position:0% +path you know +from s to t + + align:start position:0% +from s to t + + + align:start position:0% +from s to t +right nothing too interesting here + + align:start position:0% +right nothing too interesting here + + + align:start position:0% +right nothing too interesting here +but there's actually some subtleties we + + align:start position:0% +but there's actually some subtleties we + + + align:start position:0% +but there's actually some subtleties we +have to deal with here + + align:start position:0% +have to deal with here + + + align:start position:0% +have to deal with here +right uh we're going to call + + align:start position:0% +right uh we're going to call + + + align:start position:0% +right uh we're going to call +just like we did with uh uh breadth + + align:start position:0% +just like we did with uh uh breadth + + + align:start position:0% +just like we did with uh uh breadth +first search when we talked about + + align:start position:0% +first search when we talked about + + + align:start position:0% +first search when we talked about +shortest paths we're going to define + + align:start position:0% +shortest paths we're going to define + + + align:start position:0% +shortest paths we're going to define +the uh uh an expression for what the + + align:start position:0% +the uh uh an expression for what the + + + align:start position:0% +the uh uh an expression for what the +distance or the shortest path weight + + align:start position:0% +distance or the shortest path weight + + + align:start position:0% +distance or the shortest path weight +is between two vertices and that's going + + align:start position:0% +is between two vertices and that's going + + + align:start position:0% +is between two vertices and that's going +to i'm going to represent that by a + + align:start position:0% +to i'm going to represent that by a + + + align:start position:0% +to i'm going to represent that by a +delta + + align:start position:0% +delta + + + align:start position:0% +delta +right a delta from a vertex + + align:start position:0% +right a delta from a vertex + + + align:start position:0% +right a delta from a vertex +s to t is going to be + + align:start position:0% +s to t is going to be + + + align:start position:0% +s to t is going to be +let's i'm going to do the wrong thing + + align:start position:0% +let's i'm going to do the wrong thing + + + align:start position:0% +let's i'm going to do the wrong thing +first + + align:start position:0% +first + + + align:start position:0% +first +the minimum over the weight of all paths + + align:start position:0% + + + + align:start position:0% + +for all paths pi + + align:start position:0% +for all paths pi + + + align:start position:0% +for all paths pi +from s to + + align:start position:0% +from s to + + + align:start position:0% +from s to +t okay + + align:start position:0% +t okay + + + align:start position:0% +t okay +so there's a couple things that go wrong + + align:start position:0% +so there's a couple things that go wrong + + + align:start position:0% +so there's a couple things that go wrong +here + + align:start position:0% +here + + + align:start position:0% +here +first thing that goes wrong is the same + + align:start position:0% +first thing that goes wrong is the same + + + align:start position:0% +first thing that goes wrong is the same +thing that went wrong + + align:start position:0% +thing that went wrong + + + align:start position:0% +thing that went wrong +with breadth first search right anyone + + align:start position:0% +with breadth first search right anyone + + + align:start position:0% +with breadth first search right anyone +remember what could go wrong with + + align:start position:0% +remember what could go wrong with + + + align:start position:0% +remember what could go wrong with +breadth first search + + align:start position:0% +breadth first search + + + align:start position:0% +breadth first search +for this delta definition maybe there's + + align:start position:0% +for this delta definition maybe there's + + + align:start position:0% +for this delta definition maybe there's +no path + + align:start position:0% +no path + + + align:start position:0% +no path +right right so if the in except + + align:start position:0% +right right so if the in except + + + align:start position:0% +right right so if the in except +if no path + + align:start position:0% + + + + align:start position:0% + +just by convention we're setting uh + + align:start position:0% +just by convention we're setting uh + + + align:start position:0% +just by convention we're setting uh +delta s t to equal + + align:start position:0% +delta s t to equal + + + align:start position:0% +delta s t to equal +infinity but there's one additional + + align:start position:0% +infinity but there's one additional + + + align:start position:0% +infinity but there's one additional +problem with weighted shortest paths + + align:start position:0% +problem with weighted shortest paths + + + align:start position:0% +problem with weighted shortest paths +and it's a little subtle it's possible + + align:start position:0% +and it's a little subtle it's possible + + + align:start position:0% +and it's a little subtle it's possible +that a finite shortest uh finite length + + align:start position:0% +that a finite shortest uh finite length + + + align:start position:0% +that a finite shortest uh finite length +shortest path doesn't exist + + align:start position:0% +shortest path doesn't exist + + + align:start position:0% +shortest path doesn't exist +and what do i mean by that it means uh + + align:start position:0% +and what do i mean by that it means uh + + + align:start position:0% +and what do i mean by that it means uh +i could keep going through edges in my + + align:start position:0% +i could keep going through edges in my + + + align:start position:0% +i could keep going through edges in my +graph + + align:start position:0% +graph + + + align:start position:0% +graph +and continually getting a shorter + + align:start position:0% +and continually getting a shorter + + + align:start position:0% +and continually getting a shorter +path right so if i can if the the + + align:start position:0% +path right so if i can if the the + + + align:start position:0% +path right so if i can if the the +shortest + + align:start position:0% +shortest + + + align:start position:0% +shortest +the minimum weight of a path from s to t + + align:start position:0% +the minimum weight of a path from s to t + + + align:start position:0% +the minimum weight of a path from s to t +actually goes through an infinite number + + align:start position:0% +actually goes through an infinite number + + + align:start position:0% +actually goes through an infinite number +of edges + + align:start position:0% +of edges + + + align:start position:0% +of edges +then this isn't really well defined + + align:start position:0% +then this isn't really well defined + + + align:start position:0% +then this isn't really well defined +right so + + align:start position:0% +right so + + + align:start position:0% +right so +i'm going to change this minimum here to + + align:start position:0% +i'm going to change this minimum here to + + + align:start position:0% +i'm going to change this minimum here to +in in mathematics we + + align:start position:0% +in in mathematics we + + + align:start position:0% +in in mathematics we +just to be specific we call it an + + align:start position:0% +just to be specific we call it an + + + align:start position:0% +just to be specific we call it an +infiema + + align:start position:0% +infiema + + + align:start position:0% +infiema +right so if in the case where there + + align:start position:0% +right so if in the case where there + + + align:start position:0% +right so if in the case where there +where + + align:start position:0% +where + + + align:start position:0% +where +the uh the weight of a shortest path can + + align:start position:0% +the uh the weight of a shortest path can + + + align:start position:0% +the uh the weight of a shortest path can +approach + + align:start position:0% +approach + + + align:start position:0% +approach +arbitrarily small right then we'll call + + align:start position:0% +arbitrarily small right then we'll call + + + align:start position:0% +arbitrarily small right then we'll call +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +minus infinity okay so + + align:start position:0% +minus infinity okay so + + + align:start position:0% +minus infinity okay so +when does that occur + + align:start position:0% + + + + align:start position:0% + +when does that occur when could we + + align:start position:0% +when does that occur when could we + + + align:start position:0% +when does that occur when could we +have our shortest path go through lots + + align:start position:0% +have our shortest path go through lots + + + align:start position:0% +have our shortest path go through lots +and lots of vertices well + + align:start position:0% +and lots of vertices well + + + align:start position:0% +and lots of vertices well +let's actually take a look at this + + align:start position:0% +let's actually take a look at this + + + align:start position:0% +let's actually take a look at this +example here can someone tell me what + + align:start position:0% +example here can someone tell me what + + + align:start position:0% +example here can someone tell me what +the shortest path + + align:start position:0% +the shortest path + + + align:start position:0% +the shortest path +is from a + + align:start position:0% + + + + align:start position:0% + +to actually any vertex in this graph + + align:start position:0% + + + + align:start position:0% + +ah okay so well we could + + align:start position:0% +ah okay so well we could + + + align:start position:0% +ah okay so well we could +look at this this path i have to be + + align:start position:0% +look at this this path i have to be + + + align:start position:0% +look at this this path i have to be +let's just take a look at b + + align:start position:0% +let's just take a look at b + + + align:start position:0% +let's just take a look at b +right i have a path going from a to b + + align:start position:0% +right i have a path going from a to b + + + align:start position:0% +right i have a path going from a to b +that is minus five okay that's pretty + + align:start position:0% +that is minus five okay that's pretty + + + align:start position:0% +that is minus five okay that's pretty +good that's pretty small + + align:start position:0% +good that's pretty small + + + align:start position:0% +good that's pretty small +right and it seems that if i go + + align:start position:0% +right and it seems that if i go + + + align:start position:0% +right and it seems that if i go +around this graph through another way it + + align:start position:0% +around this graph through another way it + + + align:start position:0% +around this graph through another way it +might be bigger right so i go + + align:start position:0% +might be bigger right so i go + + + align:start position:0% +might be bigger right so i go +seven plus three plus + + align:start position:0% +seven plus three plus + + + align:start position:0% +seven plus three plus +eight that's 15 minus one that's 14 + + align:start position:0% +eight that's 15 minus one that's 14 + + + align:start position:0% +eight that's 15 minus one that's 14 +that's that's much bigger than my minus + + align:start position:0% +that's that's much bigger than my minus + + + align:start position:0% +that's that's much bigger than my minus +five so + + align:start position:0% +five so + + + align:start position:0% +five so +it seems like minus five should be good + + align:start position:0% +it seems like minus five should be good + + + align:start position:0% +it seems like minus five should be good +right anyone have a problem with this + + align:start position:0% +right anyone have a problem with this + + + align:start position:0% +right anyone have a problem with this +path + + align:start position:0% +path + + + align:start position:0% +path +or the problem with this being the + + align:start position:0% +or the problem with this being the + + + align:start position:0% +or the problem with this being the +shortest path + + align:start position:0% +shortest path + + + align:start position:0% +shortest path +and what your colleague just informed me + + align:start position:0% +and what your colleague just informed me + + + align:start position:0% +and what your colleague just informed me +was that there's something interesting + + align:start position:0% +was that there's something interesting + + + align:start position:0% +was that there's something interesting +happening + + align:start position:0% +happening + + + align:start position:0% +happening +here in this graph in particular + + align:start position:0% +here in this graph in particular + + + align:start position:0% +here in this graph in particular +we have a cycle from b + + align:start position:0% +we have a cycle from b + + + align:start position:0% +we have a cycle from b +to f to g to c + + align:start position:0% +to f to g to c + + + align:start position:0% +to f to g to c +that has negative total weight right + + align:start position:0% +that has negative total weight right + + + align:start position:0% +that has negative total weight right +back back to b + + align:start position:0% +back back to b + + + align:start position:0% +back back to b +right this has minus four plus two + + align:start position:0% +right this has minus four plus two + + + align:start position:0% +right this has minus four plus two +plus one minus one right so that total + + align:start position:0% +plus one minus one right so that total + + + align:start position:0% +plus one minus one right so that total +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +has a cycle weight + + align:start position:0% +has a cycle weight + + + align:start position:0% +has a cycle weight +of minus two right this is negative + + align:start position:0% +of minus two right this is negative + + + align:start position:0% +of minus two right this is negative +weight cycle + + align:start position:0% +weight cycle + + + align:start position:0% +weight cycle +so uh if i wanted to get to b + + align:start position:0% +so uh if i wanted to get to b + + + align:start position:0% +so uh if i wanted to get to b +i could go there via this minus five + + align:start position:0% +i could go there via this minus five + + + align:start position:0% +i could go there via this minus five +weight edge + + align:start position:0% +weight edge + + + align:start position:0% +weight edge +but every time i circled around this + + align:start position:0% +but every time i circled around this + + + align:start position:0% +but every time i circled around this +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +i incur -2 to my pathway + + align:start position:0% +i incur -2 to my pathway + + + align:start position:0% +i incur -2 to my pathway +right so i just keep going around this + + align:start position:0% +right so i just keep going around this + + + align:start position:0% +right so i just keep going around this +cycle + + align:start position:0% +cycle + + + align:start position:0% +cycle +over and over and over and over and over + + align:start position:0% +over and over and over and over and over + + + align:start position:0% +over and over and over and over and over +and over again + + align:start position:0% +and over again + + + align:start position:0% +and over again +and i don't have any finite length + + align:start position:0% +and i don't have any finite length + + + align:start position:0% +and i don't have any finite length +minimum weight path + + align:start position:0% +minimum weight path + + + align:start position:0% +minimum weight path +right in in such cases we just say that + + align:start position:0% +right in in such cases we just say that + + + align:start position:0% +right in in such cases we just say that +delta + + align:start position:0% +delta + + + align:start position:0% +delta +is minus infinity right so uh the the + + align:start position:0% +is minus infinity right so uh the the + + + align:start position:0% +is minus infinity right so uh the the +problem here + + align:start position:0% +problem here + + + align:start position:0% +problem here +is that uh we could have negative weight + + align:start position:0% +is that uh we could have negative weight + + + align:start position:0% +is that uh we could have negative weight +cycles + + align:start position:0% + + + + align:start position:0% + +deserves a capital letter negative + + align:start position:0% +deserves a capital letter negative + + + align:start position:0% +deserves a capital letter negative +weight + + align:start position:0% + + + + align:start position:0% + +cycles + + align:start position:0% + + + + align:start position:0% + +it's a problem + + align:start position:0% +it's a problem + + + align:start position:0% +it's a problem +in particular if + + align:start position:0% + + + + align:start position:0% + +there exists a + + align:start position:0% +there exists a + + + align:start position:0% +there exists a +path from + + align:start position:0% +path from + + + align:start position:0% +path from +s to some vertex v + + align:start position:0% + + + + align:start position:0% + +that goes + + align:start position:0% + + + + align:start position:0% + +through + + align:start position:0% +through + + + align:start position:0% +through +a vertex + + align:start position:0% + + + + align:start position:0% + +on a negative + + align:start position:0% +on a negative + + + align:start position:0% +on a negative +weight cycle + + align:start position:0% + + + + align:start position:0% + +then i can take that path to that vertex + + align:start position:0% +then i can take that path to that vertex + + + align:start position:0% +then i can take that path to that vertex +circle around the negative weight cycle + + align:start position:0% +circle around the negative weight cycle + + + align:start position:0% +circle around the negative weight cycle +and then proceed to v + + align:start position:0% +and then proceed to v + + + align:start position:0% +and then proceed to v +and i can take that cycle as many times + + align:start position:0% +and i can take that cycle as many times + + + align:start position:0% +and i can take that cycle as many times +as i want then + + align:start position:0% +as i want then + + + align:start position:0% +as i want then +this delta sv we're going to set to + + align:start position:0% +this delta sv we're going to set to + + + align:start position:0% +this delta sv we're going to set to +minus infinity okay and in such cases + + align:start position:0% +minus infinity okay and in such cases + + + align:start position:0% +minus infinity okay and in such cases +in our shortest paths algorithm we don't + + align:start position:0% +in our shortest paths algorithm we don't + + + align:start position:0% +in our shortest paths algorithm we don't +really care + + align:start position:0% +really care + + + align:start position:0% +really care +about what the shortest path is right + + align:start position:0% +about what the shortest path is right + + + align:start position:0% +about what the shortest path is right +we're not even going to deal with + + align:start position:0% +we're not even going to deal with + + + align:start position:0% +we're not even going to deal with +parent pointers here right because there + + align:start position:0% +parent pointers here right because there + + + align:start position:0% +parent pointers here right because there +is no + + align:start position:0% +is no + + + align:start position:0% +is no +finite length shortest path so i'm + + align:start position:0% +finite length shortest path so i'm + + + align:start position:0% +finite length shortest path so i'm +just going to kind of throw my hands in + + align:start position:0% +just going to kind of throw my hands in + + + align:start position:0% +just going to kind of throw my hands in +the air and say you know what i can't + + align:start position:0% +the air and say you know what i can't + + + align:start position:0% +the air and say you know what i can't +return you a shortest path + + align:start position:0% +return you a shortest path + + + align:start position:0% +return you a shortest path +but i might want to return to you + + align:start position:0% +but i might want to return to you + + + align:start position:0% +but i might want to return to you +a negative weight cycle right if you + + align:start position:0% +a negative weight cycle right if you + + + align:start position:0% +a negative weight cycle right if you +told me that this thing has bad + + align:start position:0% +told me that this thing has bad + + + align:start position:0% +told me that this thing has bad +weight right maybe i want you to tell me + + align:start position:0% +weight right maybe i want you to tell me + + + align:start position:0% +weight right maybe i want you to tell me +what a path is that goes through a + + align:start position:0% +what a path is that goes through a + + + align:start position:0% +what a path is that goes through a +negative weight cycle + + align:start position:0% +negative weight cycle + + + align:start position:0% +negative weight cycle +to get back to s right so that's what + + align:start position:0% +to get back to s right so that's what + + + align:start position:0% +to get back to s right so that's what +we're going to talk about next lecture + + align:start position:0% +we're going to talk about next lecture + + + align:start position:0% +we're going to talk about next lecture +this lecture + + align:start position:0% +this lecture + + + align:start position:0% +this lecture +we are not going to talk about that we + + align:start position:0% +we are not going to talk about that we + + + align:start position:0% +we are not going to talk about that we +are going to talk about weighted + + align:start position:0% +are going to talk about weighted + + + align:start position:0% +are going to talk about weighted +shortest paths though + + align:start position:0% +shortest paths though + + + align:start position:0% +shortest paths though +that's what uh the remainder + + align:start position:0% +that's what uh the remainder + + + align:start position:0% +that's what uh the remainder +of this uh this unit on graphs is really + + align:start position:0% +of this uh this unit on graphs is really + + + align:start position:0% +of this uh this unit on graphs is really +about is weighted shortest paths + + align:start position:0% +about is weighted shortest paths + + + align:start position:0% +about is weighted shortest paths +okay so in weighted shortest paths we + + align:start position:0% +okay so in weighted shortest paths we + + + align:start position:0% +okay so in weighted shortest paths we +actually know + + align:start position:0% +actually know + + + align:start position:0% +actually know +an algorithm already to solve a subset + + align:start position:0% +an algorithm already to solve a subset + + + align:start position:0% +an algorithm already to solve a subset +of weighted shortest paths namely + + align:start position:0% +of weighted shortest paths namely + + + align:start position:0% +of weighted shortest paths namely +bfs right now + + align:start position:0% +bfs right now + + + align:start position:0% +bfs right now +you're like wait jason bfs doesn't solve + + align:start position:0% +you're like wait jason bfs doesn't solve + + + align:start position:0% +you're like wait jason bfs doesn't solve +weighted shortest paths we didn't even + + align:start position:0% +weighted shortest paths we didn't even + + + align:start position:0% +weighted shortest paths we didn't even +know about weighted + + align:start position:0% +know about weighted + + + align:start position:0% +know about weighted +graphs then right how does that solve + + align:start position:0% +graphs then right how does that solve + + + align:start position:0% +graphs then right how does that solve +weighted shortest paths well + + align:start position:0% +weighted shortest paths well + + + align:start position:0% +weighted shortest paths well +there's a couple cases where we might be + + align:start position:0% +there's a couple cases where we might be + + + align:start position:0% +there's a couple cases where we might be +able to reduce + + align:start position:0% +able to reduce + + + align:start position:0% +able to reduce +to solving shortest paths using bfs + + align:start position:0% +to solving shortest paths using bfs + + + align:start position:0% +to solving shortest paths using bfs +can anyone think of such a scenario + + align:start position:0% + + + + align:start position:0% + +uh so let's say + + align:start position:0% +uh so let's say + + + align:start position:0% +uh so let's say +i mean kind of what we did before was we + + align:start position:0% +i mean kind of what we did before was we + + + align:start position:0% +i mean kind of what we did before was we +counted the number of edges + + align:start position:0% +counted the number of edges + + + align:start position:0% +counted the number of edges +right so if we gave a weight of one + + align:start position:0% +right so if we gave a weight of one + + + align:start position:0% +right so if we gave a weight of one +to every edge in my graph then + + align:start position:0% +to every edge in my graph then + + + align:start position:0% +to every edge in my graph then +just that graph that weighted graph + + align:start position:0% +just that graph that weighted graph + + + align:start position:0% +just that graph that weighted graph +corresponds to + + align:start position:0% +corresponds to + + + align:start position:0% +corresponds to +an unweighted graph using the other + + align:start position:0% +an unweighted graph using the other + + + align:start position:0% +an unweighted graph using the other +distance metric + + align:start position:0% +distance metric + + + align:start position:0% +distance metric +right so in that case bfs just solves + + align:start position:0% +right so in that case bfs just solves + + + align:start position:0% +right so in that case bfs just solves +our problem + + align:start position:0% +our problem + + + align:start position:0% +our problem +and in fact we can generalize further + + align:start position:0% +and in fact we can generalize further + + + align:start position:0% +and in fact we can generalize further +what if all of our weights were positive + + align:start position:0% +what if all of our weights were positive + + + align:start position:0% +what if all of our weights were positive +but the same value + + align:start position:0% +but the same value + + + align:start position:0% +but the same value +right if it was all positive and the + + align:start position:0% +right if it was all positive and the + + + align:start position:0% +right if it was all positive and the +same value + + align:start position:0% +same value + + + align:start position:0% +same value +then we could just to you know divide by + + align:start position:0% +then we could just to you know divide by + + + align:start position:0% +then we could just to you know divide by +that value + + align:start position:0% +that value + + + align:start position:0% +that value +right now we have a weighted an + + align:start position:0% +right now we have a weighted an + + + align:start position:0% +right now we have a weighted an +unweighted + + align:start position:0% +unweighted + + + align:start position:0% +unweighted +uh graph which we can run bfs and then + + align:start position:0% +uh graph which we can run bfs and then + + + align:start position:0% +uh graph which we can run bfs and then +multiply shortest path distances by that + + align:start position:0% +multiply shortest path distances by that + + + align:start position:0% +multiply shortest path distances by that +value + + align:start position:0% +value + + + align:start position:0% +value +later on and in fact there's one further + + align:start position:0% +later on and in fact there's one further + + + align:start position:0% +later on and in fact there's one further +generalization we could make + + align:start position:0% +generalization we could make + + + align:start position:0% +generalization we could make +which is a little bit of a tricky graph + + align:start position:0% +which is a little bit of a tricky graph + + + align:start position:0% +which is a little bit of a tricky graph +transformation problem + + align:start position:0% +transformation problem + + + align:start position:0% +transformation problem +but we can also get this linear time + + align:start position:0% +but we can also get this linear time + + + align:start position:0% +but we can also get this linear time +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +for weighted single source shortest + + align:start position:0% +for weighted single source shortest + + + align:start position:0% +for weighted single source shortest +paths + + align:start position:0% +paths + + + align:start position:0% +paths +in contexts where + + align:start position:0% +in contexts where + + + align:start position:0% +in contexts where +the weights aren't that large okay so + + align:start position:0% +the weights aren't that large okay so + + + align:start position:0% +the weights aren't that large okay so +if i have positive edge weights + + align:start position:0% +if i have positive edge weights + + + align:start position:0% +if i have positive edge weights +right if i have a positive edge weight + + align:start position:0% +right if i have a positive edge weight + + + align:start position:0% +right if i have a positive edge weight +let's say + + align:start position:0% + + + + align:start position:0% + +using using my weight color here + + align:start position:0% +using using my weight color here + + + align:start position:0% +using using my weight color here +that's like weight of four right + + align:start position:0% +that's like weight of four right + + + align:start position:0% +that's like weight of four right +that's that's kind of problematic + + align:start position:0% +that's that's kind of problematic + + + align:start position:0% +that's that's kind of problematic +because i don't know how to simulate + + align:start position:0% +because i don't know how to simulate + + + align:start position:0% +because i don't know how to simulate +that using an unweighted graph + + align:start position:0% +that using an unweighted graph + + + align:start position:0% +that using an unweighted graph +or do i anyone have an idea of how i + + align:start position:0% +or do i anyone have an idea of how i + + + align:start position:0% +or do i anyone have an idea of how i +could + + align:start position:0% +could + + + align:start position:0% +could +simulate an edge of weight + + align:start position:0% +simulate an edge of weight + + + align:start position:0% +simulate an edge of weight +four with an unweighted graph yeah + + align:start position:0% +four with an unweighted graph yeah + + + align:start position:0% +four with an unweighted graph yeah +i have four edges of weight one yeah i + + align:start position:0% +i have four edges of weight one yeah i + + + align:start position:0% +i have four edges of weight one yeah i +can just put four edges of weight one + + align:start position:0% +can just put four edges of weight one + + + align:start position:0% +can just put four edges of weight one +in parallel here sorry in series + + align:start position:0% +in parallel here sorry in series + + + align:start position:0% +in parallel here sorry in series +the opposite of parallel okay i can just + + align:start position:0% +the opposite of parallel okay i can just + + + align:start position:0% +the opposite of parallel okay i can just +convert this + + align:start position:0% +convert this + + + align:start position:0% +convert this +here into one two + + align:start position:0% +here into one two + + + align:start position:0% +here into one two +three four edges + + align:start position:0% +three four edges + + + align:start position:0% +three four edges +and if i do that for every edge in my + + align:start position:0% +and if i do that for every edge in my + + + align:start position:0% +and if i do that for every edge in my +graph and we have positive edge weights + + align:start position:0% +graph and we have positive edge weights + + + align:start position:0% +graph and we have positive edge weights +then that that transformation can hold + + align:start position:0% +then that that transformation can hold + + + align:start position:0% +then that that transformation can hold +now that's not necessarily a good + + align:start position:0% +now that's not necessarily a good + + + align:start position:0% +now that's not necessarily a good +transformation to make + + align:start position:0% +transformation to make + + + align:start position:0% +transformation to make +y + + align:start position:0% + + + + align:start position:0% + +yeah the weights might be very big + + align:start position:0% +yeah the weights might be very big + + + align:start position:0% +yeah the weights might be very big +compared to the number of vertices and + + align:start position:0% +compared to the number of vertices and + + + align:start position:0% +compared to the number of vertices and +edges in my graph + + align:start position:0% +edges in my graph + + + align:start position:0% +edges in my graph +however if the sum of all weights in my + + align:start position:0% +however if the sum of all weights in my + + + align:start position:0% +however if the sum of all weights in my +graph + + align:start position:0% +graph + + + align:start position:0% +graph +is asymptotically less than + + align:start position:0% +is asymptotically less than + + + align:start position:0% +is asymptotically less than +v plus e right we can get a linear time + + align:start position:0% +v plus e right we can get a linear time + + + align:start position:0% +v plus e right we can get a linear time +algorithm again + + align:start position:0% +algorithm again + + + align:start position:0% +algorithm again +by reducing to bfs okay so that's great + + align:start position:0% +by reducing to bfs okay so that's great + + + align:start position:0% +by reducing to bfs okay so that's great +today uh but but in general that that + + align:start position:0% +today uh but but in general that that + + + align:start position:0% +today uh but but in general that that +gives us a linear time algorithm in this + + align:start position:0% +gives us a linear time algorithm in this + + + align:start position:0% +gives us a linear time algorithm in this +in these very special cases + + align:start position:0% +in these very special cases + + + align:start position:0% +in these very special cases +and in general it's an open problem we + + align:start position:0% +and in general it's an open problem we + + + align:start position:0% +and in general it's an open problem we +don't know + + align:start position:0% +don't know + + + align:start position:0% +don't know +uh whether we can solve the single + + align:start position:0% +uh whether we can solve the single + + + align:start position:0% +uh whether we can solve the single +source + + align:start position:0% +source + + + align:start position:0% +source +single source shortest paths uh problem + + align:start position:0% +single source shortest paths uh problem + + + align:start position:0% +single source shortest paths uh problem +in the weighted context + + align:start position:0% +in the weighted context + + + align:start position:0% +in the weighted context +for general graphs in linear time we + + align:start position:0% +for general graphs in linear time we + + + align:start position:0% +for general graphs in linear time we +don't know how to do it + + align:start position:0% +don't know how to do it + + + align:start position:0% +don't know how to do it +right but what we do know are some + + align:start position:0% +right but what we do know are some + + + align:start position:0% +right but what we do know are some +algorithms that do + + align:start position:0% +algorithms that do + + + align:start position:0% +algorithms that do +pretty well and that's what we use all + + align:start position:0% +pretty well and that's what we use all + + + align:start position:0% +pretty well and that's what we use all +the time + + align:start position:0% +the time + + + align:start position:0% +the time +but in the sp one more special case + + align:start position:0% +but in the sp one more special case + + + align:start position:0% +but in the sp one more special case +we're going to go over today + + align:start position:0% +we're going to go over today + + + align:start position:0% +we're going to go over today +is when we have this really nice + + align:start position:0% +is when we have this really nice + + + align:start position:0% +is when we have this really nice +structure + + align:start position:0% +structure + + + align:start position:0% +structure +where we have a dag a directed acyclic + + align:start position:0% +where we have a dag a directed acyclic + + + align:start position:0% +where we have a dag a directed acyclic +graph like we were talking about + + align:start position:0% +graph like we were talking about + + + align:start position:0% +graph like we were talking about +in the last lecture we can actually for + + align:start position:0% +in the last lecture we can actually for + + + align:start position:0% +in the last lecture we can actually for +any set of edge weights right remember + + align:start position:0% +any set of edge weights right remember + + + align:start position:0% +any set of edge weights right remember +with bfs we kind of + + align:start position:0% +with bfs we kind of + + + align:start position:0% +with bfs we kind of +we needed to restrict our edge weights + + align:start position:0% +we needed to restrict our edge weights + + + align:start position:0% +we needed to restrict our edge weights +to be positive + + align:start position:0% +to be positive + + + align:start position:0% +to be positive +and maybe bounded to get this good + + align:start position:0% +and maybe bounded to get this good + + + align:start position:0% +and maybe bounded to get this good +running time uh + + align:start position:0% +running time uh + + + align:start position:0% +running time uh +for any set of edge weights if our graph + + align:start position:0% +for any set of edge weights if our graph + + + align:start position:0% +for any set of edge weights if our graph +structure is a dag + + align:start position:0% +structure is a dag + + + align:start position:0% +structure is a dag +really has nothing to do with the + + align:start position:0% +really has nothing to do with the + + + align:start position:0% +really has nothing to do with the +weights if the graph structure is a dag + + align:start position:0% +weights if the graph structure is a dag + + + align:start position:0% +weights if the graph structure is a dag +then we can actually solve this single + + align:start position:0% +then we can actually solve this single + + + align:start position:0% +then we can actually solve this single +short shortest paths problem in linear + + align:start position:0% +short shortest paths problem in linear + + + align:start position:0% +short shortest paths problem in linear +time + + align:start position:0% +time + + + align:start position:0% +time +which is pretty awesome right + + align:start position:0% +which is pretty awesome right + + + align:start position:0% +which is pretty awesome right +now for general graphs + + align:start position:0% +now for general graphs + + + align:start position:0% +now for general graphs +we're going to show you in the next + + align:start position:0% +we're going to show you in the next + + + align:start position:0% +we're going to show you in the next +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +how to for any graph even with cycles + + align:start position:0% +how to for any graph even with cycles + + + align:start position:0% +how to for any graph even with cycles +even with negative weight cycles + + align:start position:0% +even with negative weight cycles + + + align:start position:0% +even with negative weight cycles +we're going to show you how to solve + + align:start position:0% +we're going to show you how to solve + + + align:start position:0% +we're going to show you how to solve +this single source shortest paths + + align:start position:0% +this single source shortest paths + + + align:start position:0% +this single source shortest paths +problem + + align:start position:0% +problem + + + align:start position:0% +problem +in something like a quadratic running + + align:start position:0% +in something like a quadratic running + + + align:start position:0% +in something like a quadratic running +time bound now this isn't the best known + + align:start position:0% +time bound now this isn't the best known + + + align:start position:0% +time bound now this isn't the best known +but it's a really practical algorithm + + align:start position:0% +but it's a really practical algorithm + + + align:start position:0% +but it's a really practical algorithm +and people use it all the time + + align:start position:0% +and people use it all the time + + + align:start position:0% +and people use it all the time +okay and and it we're going to + + align:start position:0% +okay and and it we're going to + + + align:start position:0% +okay and and it we're going to +uh show bellman ford in the context of + + align:start position:0% +uh show bellman ford in the context of + + + align:start position:0% +uh show bellman ford in the context of +the dag algorithm we're going to + + align:start position:0% +the dag algorithm we're going to + + + align:start position:0% +the dag algorithm we're going to +solve today okay so that's the very + + align:start position:0% +solve today okay so that's the very + + + align:start position:0% +solve today okay so that's the very +general case in terms of restrictions on + + align:start position:0% +general case in terms of restrictions on + + + align:start position:0% +general case in terms of restrictions on +our graph + + align:start position:0% +our graph + + + align:start position:0% +our graph +but in reality most problems that + + align:start position:0% +but in reality most problems that + + + align:start position:0% +but in reality most problems that +that come up in applications occur with + + align:start position:0% +that come up in applications occur with + + + align:start position:0% +that come up in applications occur with +graphs + + align:start position:0% +graphs + + + align:start position:0% +graphs +that have positive edge weights okay you + + align:start position:0% +that have positive edge weights okay you + + + align:start position:0% +that have positive edge weights okay you +can think of a road network + + align:start position:0% +can think of a road network + + + align:start position:0% +can think of a road network +you've got or non-negative ones anyway + + align:start position:0% +you've got or non-negative ones anyway + + + align:start position:0% +you've got or non-negative ones anyway +right that you you're you're traveling + + align:start position:0% +right that you you're you're traveling + + + align:start position:0% +right that you you're you're traveling +along + + align:start position:0% +along + + + align:start position:0% +along +right uh and it's not ever useful to + + align:start position:0% +right uh and it's not ever useful to + + + align:start position:0% +right uh and it's not ever useful to +kind of go back to where you came from + + align:start position:0% +kind of go back to where you came from + + + align:start position:0% +kind of go back to where you came from +because you want to make progress to + + align:start position:0% +because you want to make progress to + + + align:start position:0% +because you want to make progress to +where you're going + + align:start position:0% +where you're going + + + align:start position:0% +where you're going +okay so in the context where you + + align:start position:0% +okay so in the context where you + + + align:start position:0% +okay so in the context where you +don't have negative weights you don't + + align:start position:0% +don't have negative weights you don't + + + align:start position:0% +don't have negative weights you don't +have this problem where you have + + align:start position:0% +have this problem where you have + + + align:start position:0% +have this problem where you have +negative weight cycles + + align:start position:0% +negative weight cycles + + + align:start position:0% +negative weight cycles +we can actually do a lot better by + + align:start position:0% +we can actually do a lot better by + + + align:start position:0% +we can actually do a lot better by +exploiting that property + + align:start position:0% +exploiting that property + + + align:start position:0% +exploiting that property +uh and we get a bound that's a little + + align:start position:0% +uh and we get a bound that's a little + + + align:start position:0% +uh and we get a bound that's a little +bit that looks a little bit more like + + align:start position:0% +bit that looks a little bit more like + + + align:start position:0% +bit that looks a little bit more like +n log n right like it's it's pretty + + align:start position:0% +n log n right like it's it's pretty + + + align:start position:0% +n log n right like it's it's pretty +close to linear + + align:start position:0% +close to linear + + + align:start position:0% +close to linear +you're losing a log factor on the number + + align:start position:0% +you're losing a log factor on the number + + + align:start position:0% +you're losing a log factor on the number +of vertices + + align:start position:0% +of vertices + + + align:start position:0% +of vertices +okay but it's pretty good this is called + + align:start position:0% +okay but it's pretty good this is called + + + align:start position:0% +okay but it's pretty good this is called +dijkstra and we'll get to that in two + + align:start position:0% +dijkstra and we'll get to that in two + + + align:start position:0% +dijkstra and we'll get to that in two +lectures + + align:start position:0% +lectures + + + align:start position:0% +lectures +okay so that's kind of the roadmap of + + align:start position:0% +okay so that's kind of the roadmap of + + + align:start position:0% +okay so that's kind of the roadmap of +what we're going to do for at least the + + align:start position:0% +what we're going to do for at least the + + + align:start position:0% +what we're going to do for at least the +next three lectures + + align:start position:0% +next three lectures + + + align:start position:0% +next three lectures +uh but before we go on to showing you + + align:start position:0% +uh but before we go on to showing you + + + align:start position:0% +uh but before we go on to showing you +how to solve + + align:start position:0% +how to solve + + + align:start position:0% +how to solve +single source shortest paths in a dag + + align:start position:0% +single source shortest paths in a dag + + + align:start position:0% +single source shortest paths in a dag +using this algorithm called + + align:start position:0% +using this algorithm called + + + align:start position:0% +using this algorithm called +that i'm calling dag relaxation here + + align:start position:0% +that i'm calling dag relaxation here + + + align:start position:0% +that i'm calling dag relaxation here +uh i'm going to go back to a thing that + + align:start position:0% +uh i'm going to go back to a thing that + + + align:start position:0% +uh i'm going to go back to a thing that +we talked about in + + align:start position:0% +we talked about in + + + align:start position:0% +we talked about in +breadth first search where in breadth + + align:start position:0% +breadth first search where in breadth + + + align:start position:0% +breadth first search where in breadth +first search when we solve single source + + align:start position:0% +first search when we solve single source + + + align:start position:0% +first search when we solve single source +shortest paths + + align:start position:0% +shortest paths + + + align:start position:0% +shortest paths +we output two things right we output + + align:start position:0% +we output two things right we output + + + align:start position:0% +we output two things right we output +single source shortest paths these + + align:start position:0% +single source shortest paths these + + + align:start position:0% +single source shortest paths these +deltas right for + + align:start position:0% +deltas right for + + + align:start position:0% +deltas right for +the other definition of distance + + align:start position:0% +the other definition of distance + + + align:start position:0% +the other definition of distance +you know the weights i mean not the + + align:start position:0% +you know the weights i mean not the + + + align:start position:0% +you know the weights i mean not the +weights the uh the distances the + + align:start position:0% +weights the uh the distances the + + + align:start position:0% +weights the uh the distances the +shortest distances + + align:start position:0% +shortest distances + + + align:start position:0% +shortest distances +uh but we also return parent pointers + + align:start position:0% +uh but we also return parent pointers + + + align:start position:0% +uh but we also return parent pointers +right we return parent pointers back + + align:start position:0% +right we return parent pointers back + + + align:start position:0% +right we return parent pointers back +along paths to the source + + align:start position:0% +along paths to the source + + + align:start position:0% +along paths to the source +along shortest paths right we called + + align:start position:0% +along shortest paths right we called + + + align:start position:0% +along shortest paths right we called +this the shortest path tree so + + align:start position:0% +this the shortest path tree so + + + align:start position:0% +this the shortest path tree so +i'm going to revisit this topic of + + align:start position:0% +i'm going to revisit this topic of + + + align:start position:0% +i'm going to revisit this topic of +shortest paths tree + + align:start position:0% +shortest paths tree + + + align:start position:0% +shortest paths tree +shortest path trees + + align:start position:0% +shortest path trees + + + align:start position:0% +shortest path trees +shortest + + align:start position:0% + + + + align:start position:0% + +path trees + + align:start position:0% +path trees + + + align:start position:0% +path trees +okay and in particular it's kind of + + align:start position:0% +okay and in particular it's kind of + + + align:start position:0% +okay and in particular it's kind of +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +annoying to talk about both of these + + align:start position:0% +annoying to talk about both of these + + + align:start position:0% +annoying to talk about both of these +quantities + + align:start position:0% +quantities + + + align:start position:0% +quantities +right distances and parent pointers + + align:start position:0% +right distances and parent pointers + + + align:start position:0% +right distances and parent pointers +as we go through all three of these + + align:start position:0% +as we go through all three of these + + + align:start position:0% +as we go through all three of these +algorithms right it's basically going to + + align:start position:0% +algorithms right it's basically going to + + + align:start position:0% +algorithms right it's basically going to +be bookkeeping + + align:start position:0% +be bookkeeping + + + align:start position:0% +be bookkeeping +to distances are actually sufficient for + + align:start position:0% +to distances are actually sufficient for + + + align:start position:0% +to distances are actually sufficient for +us + + align:start position:0% +us + + + align:start position:0% +us +to reconstruct parent pointers if we + + align:start position:0% +to reconstruct parent pointers if we + + + align:start position:0% +to reconstruct parent pointers if we +need them later okay + + align:start position:0% +need them later okay + + + align:start position:0% +need them later okay +so what i'm going to show for you prove + + align:start position:0% +so what i'm going to show for you prove + + + align:start position:0% +so what i'm going to show for you prove +to you now is that if i give you + + align:start position:0% +to you now is that if i give you + + + align:start position:0% +to you now is that if i give you +the shortest path distances + + align:start position:0% +the shortest path distances + + + align:start position:0% +the shortest path distances +for the subset of the the graph + + align:start position:0% +for the subset of the the graph + + + align:start position:0% +for the subset of the the graph +reachable from + + align:start position:0% +reachable from + + + align:start position:0% +reachable from +s that doesn't go through negative + + align:start position:0% +s that doesn't go through negative + + + align:start position:0% +s that doesn't go through negative +weight cycles + + align:start position:0% +weight cycles + + + align:start position:0% +weight cycles +right if i'm giving you those distances + + align:start position:0% +right if i'm giving you those distances + + + align:start position:0% +right if i'm giving you those distances +i can reconstruct + + align:start position:0% +i can reconstruct + + + align:start position:0% +i can reconstruct +parent pointers along shortest paths in + + align:start position:0% +parent pointers along shortest paths in + + + align:start position:0% +parent pointers along shortest paths in +linear time + + align:start position:0% + + + + align:start position:0% + +for any graph i might give you if i give + + align:start position:0% +for any graph i might give you if i give + + + align:start position:0% +for any graph i might give you if i give +you those shortest path distances + + align:start position:0% +you those shortest path distances + + + align:start position:0% +you those shortest path distances +okay so that's what i'm going to try to + + align:start position:0% +okay so that's what i'm going to try to + + + align:start position:0% +okay so that's what i'm going to try to +show to you now + + align:start position:0% +show to you now + + + align:start position:0% +show to you now +uh so here's the + + align:start position:0% +uh so here's the + + + align:start position:0% +uh so here's the +uh algorithm + + align:start position:0% + + + + align:start position:0% + +for weighted uh there's the caveat here + + align:start position:0% +for weighted uh there's the caveat here + + + align:start position:0% +for weighted uh there's the caveat here +i'm going to write down + + align:start position:0% +i'm going to write down + + + align:start position:0% +i'm going to write down +for weighted shortest paths + + align:start position:0% + + + + align:start position:0% + +only need + + align:start position:0% +only need + + + align:start position:0% +only need +parent pointers for + + align:start position:0% + + + + align:start position:0% + +v with + + align:start position:0% +v with + + + align:start position:0% +v with +a finite + + align:start position:0% + + + + align:start position:0% + +shortest path distance okay + + align:start position:0% +shortest path distance okay + + + align:start position:0% +shortest path distance okay +only finite shortest path distance right + + align:start position:0% +only finite shortest path distance right + + + align:start position:0% +only finite shortest path distance right +we don't care about the + + align:start position:0% +we don't care about the + + + align:start position:0% +we don't care about the +infinite ones or the minus infinite ones + + align:start position:0% +infinite ones or the minus infinite ones + + + align:start position:0% +infinite ones or the minus infinite ones +just the finite ones okay + + align:start position:0% +just the finite ones okay + + + align:start position:0% +just the finite ones okay +so here's the algorithm i'm going to + + align:start position:0% +so here's the algorithm i'm going to + + + align:start position:0% +so here's the algorithm i'm going to +initialize + + align:start position:0% + + + + align:start position:0% + +all pv + + align:start position:0% +all pv + + + align:start position:0% +all pv +to equal uh sorry + + align:start position:0% +to equal uh sorry + + + align:start position:0% +to equal uh sorry +oh + + align:start position:0% + + + + align:start position:0% + +getting out of myself i'm writing down + + align:start position:0% +getting out of myself i'm writing down + + + align:start position:0% +getting out of myself i'm writing down +dag all right + + align:start position:0% +dag all right + + + align:start position:0% +dag all right +uh init all + + align:start position:0% + + + + align:start position:0% + +and knit my parent pointer data + + align:start position:0% +and knit my parent pointer data + + + align:start position:0% +and knit my parent pointer data +structure right + + align:start position:0% +structure right + + + align:start position:0% +structure right +to be empty + + align:start position:0% + + + + align:start position:0% + +okay right first i'm not going to store + + align:start position:0% +okay right first i'm not going to store + + + align:start position:0% +okay right first i'm not going to store +any parent pointers + + align:start position:0% +any parent pointers + + + align:start position:0% +any parent pointers +but at the beginning i'm going to set + + align:start position:0% +but at the beginning i'm going to set + + + align:start position:0% +but at the beginning i'm going to set +the parent pointer + + align:start position:0% +the parent pointer + + + align:start position:0% +the parent pointer +of the source to be none + + align:start position:0% +of the source to be none + + + align:start position:0% +of the source to be none +right so that's what we kind of did in + + align:start position:0% +right so that's what we kind of did in + + + align:start position:0% +right so that's what we kind of did in +breadth first search as well + + align:start position:0% +breadth first search as well + + + align:start position:0% +breadth first search as well +right now + + align:start position:0% +right now + + + align:start position:0% +right now +what i've given you is i'm trying to + + align:start position:0% +what i've given you is i'm trying to + + + align:start position:0% +what i've given you is i'm trying to +show that given all the shortest path + + align:start position:0% +show that given all the shortest path + + + align:start position:0% +show that given all the shortest path +distances i can + + align:start position:0% +distances i can + + + align:start position:0% +distances i can +construct these parent pointers + + align:start position:0% +construct these parent pointers + + + align:start position:0% +construct these parent pointers +correctly so what i'm going to do is + + align:start position:0% +correctly so what i'm going to do is + + + align:start position:0% +correctly so what i'm going to do is +for each + + align:start position:0% + + + + align:start position:0% + +vertex u + + align:start position:0% +vertex u + + + align:start position:0% +vertex u +in my graph where + + align:start position:0% + + + + align:start position:0% + +my delta s of u + + align:start position:0% +my delta s of u + + + align:start position:0% +my delta s of u +is finite + + align:start position:0% +is finite + + + align:start position:0% +is finite +what am i going to do i'm going to say + + align:start position:0% +what am i going to do i'm going to say + + + align:start position:0% +what am i going to do i'm going to say +well + + align:start position:0% +well + + + align:start position:0% +well +let's take a look at all my outgoing + + align:start position:0% +let's take a look at all my outgoing + + + align:start position:0% +let's take a look at all my outgoing +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +okay this is kind of what we do in every + + align:start position:0% +okay this is kind of what we do in every + + + align:start position:0% +okay this is kind of what we do in every +graph algorithm + + align:start position:0% +graph algorithm + + + align:start position:0% +graph algorithm +for each + + align:start position:0% +for each + + + align:start position:0% +for each +v in the adjacency the outgoing + + align:start position:0% +v in the adjacency the outgoing + + + align:start position:0% +v in the adjacency the outgoing +adjacencies of + + align:start position:0% +adjacencies of + + + align:start position:0% +adjacencies of +u + + align:start position:0% + + + + align:start position:0% + +if there's no parent pointer assigned to + + align:start position:0% +if there's no parent pointer assigned to + + + align:start position:0% +if there's no parent pointer assigned to +this v + + align:start position:0% +this v + + + align:start position:0% +this v +right there's the potential that i + + align:start position:0% +right there's the potential that i + + + align:start position:0% +right there's the potential that i +you i you this this u this vertex u + + align:start position:0% +you i you this this u this vertex u + + + align:start position:0% +you i you this this u this vertex u +is the parent of v it's possible right + + align:start position:0% +is the parent of v it's possible right + + + align:start position:0% +is the parent of v it's possible right +it's an in it's some incoming edge + + align:start position:0% +it's an in it's some incoming edge + + + align:start position:0% +it's an in it's some incoming edge +to v okay when will it be an + + align:start position:0% +to v okay when will it be an + + + align:start position:0% +to v okay when will it be an +incoming edge to v if i haven't said + + align:start position:0% +incoming edge to v if i haven't said + + + align:start position:0% +incoming edge to v if i haven't said +if uh v + + align:start position:0% +if uh v + + + align:start position:0% +if uh v +not in p right i haven't assigned it a + + align:start position:0% +not in p right i haven't assigned it a + + + align:start position:0% +not in p right i haven't assigned it a +parent pointer + + align:start position:0% +parent pointer + + + align:start position:0% +parent pointer +and so this means + + align:start position:0% +and so this means + + + align:start position:0% +and so this means +it could be my parent + + align:start position:0% +it could be my parent + + + align:start position:0% +it could be my parent +when is it my parent along the shortest + + align:start position:0% +when is it my parent along the shortest + + + align:start position:0% +when is it my parent along the shortest +path + + align:start position:0% +path + + + align:start position:0% +path +sure sum the distance along the edge + + align:start position:0% +sure sum the distance along the edge + + + align:start position:0% +sure sum the distance along the edge +yeah so we have some edge from u to v + + align:start position:0% +yeah so we have some edge from u to v + + + align:start position:0% +yeah so we have some edge from u to v +it has some weight right if i + + align:start position:0% +it has some weight right if i + + + align:start position:0% +it has some weight right if i +already know the shortest path distance + + align:start position:0% +already know the shortest path distance + + + align:start position:0% +already know the shortest path distance +to u and i know the shortest path + + align:start position:0% +to u and i know the shortest path + + + align:start position:0% +to u and i know the shortest path +distance to v + + align:start position:0% +distance to v + + + align:start position:0% +distance to v +right if + + align:start position:0% +right if + + + align:start position:0% +right if +the shortest path distance from s to u + + align:start position:0% +the shortest path distance from s to u + + + align:start position:0% +the shortest path distance from s to u +let's let's draw a picture here we've + + align:start position:0% +let's let's draw a picture here we've + + + align:start position:0% +let's let's draw a picture here we've +got s we've got some path here + + align:start position:0% +got s we've got some path here + + + align:start position:0% +got s we've got some path here +to u and we've got an edge + + align:start position:0% +to u and we've got an edge + + + align:start position:0% +to u and we've got an edge +from u to v okay + + align:start position:0% + + + + align:start position:0% + +if this shortest path distance + + align:start position:0% +if this shortest path distance + + + align:start position:0% +if this shortest path distance +plus this edge weight is equal to the + + align:start position:0% +plus this edge weight is equal to the + + + align:start position:0% +plus this edge weight is equal to the +shortest path distance + + align:start position:0% +shortest path distance + + + align:start position:0% +shortest path distance +from s to v + + align:start position:0% + + + + align:start position:0% + +then it better i mean there may be more + + align:start position:0% +then it better i mean there may be more + + + align:start position:0% +then it better i mean there may be more +than one shortest path but this is + + align:start position:0% +than one shortest path but this is + + + align:start position:0% +than one shortest path but this is +certainly a shortest path + + align:start position:0% +certainly a shortest path + + + align:start position:0% +certainly a shortest path +so we can assign a parent pointer back + + align:start position:0% +so we can assign a parent pointer back + + + align:start position:0% +so we can assign a parent pointer back +to you okay right so let's write that + + align:start position:0% +to you okay right so let's write that + + + align:start position:0% +to you okay right so let's write that +condition down + + align:start position:0% +condition down + + + align:start position:0% +condition down +if the shortest path distance from s to + + align:start position:0% +if the shortest path distance from s to + + + align:start position:0% +if the shortest path distance from s to +v + + align:start position:0% +v + + + align:start position:0% +v +equals the shortest path distance from s + + align:start position:0% +equals the shortest path distance from s + + + align:start position:0% +equals the shortest path distance from s +to u + + align:start position:0% +to u + + + align:start position:0% +to u +and then traversing the edge from u to v + + align:start position:0% + + + + align:start position:0% + +then then exists + + align:start position:0% +then then exists + + + align:start position:0% +then then exists +shortest path + + align:start position:0% + + + + align:start position:0% + +that uses + + align:start position:0% + + + + align:start position:0% + +edge uv right in particularly + + align:start position:0% +edge uv right in particularly + + + align:start position:0% +edge uv right in particularly +in particular this one right + + align:start position:0% +in particular this one right + + + align:start position:0% +in particular this one right +so set the parent + + align:start position:0% +so set the parent + + + align:start position:0% +so set the parent +of you a v + + align:start position:0% +of you a v + + + align:start position:0% +of you a v +to you okay so this is the algorithm + + align:start position:0% +to you okay so this is the algorithm + + + align:start position:0% +to you okay so this is the algorithm +i'm not going to prove to you that this + + align:start position:0% +i'm not going to prove to you that this + + + align:start position:0% +i'm not going to prove to you that this +is correct + + align:start position:0% +is correct + + + align:start position:0% +is correct +but it kind of intuitively makes sense + + align:start position:0% +but it kind of intuitively makes sense + + + align:start position:0% +but it kind of intuitively makes sense +right if i have these + + align:start position:0% +right if i have these + + + align:start position:0% +right if i have these +shortest path distances right you can + + align:start position:0% +shortest path distances right you can + + + align:start position:0% +shortest path distances right you can +prove by induction that not only does + + align:start position:0% +prove by induction that not only does + + + align:start position:0% +prove by induction that not only does +this + + align:start position:0% +this + + + align:start position:0% +this +parent pointer point to the right place + + align:start position:0% +parent pointer point to the right place + + + align:start position:0% +parent pointer point to the right place +along some shortest path here + + align:start position:0% +along some shortest path here + + + align:start position:0% +along some shortest path here +right but it also does so in linear time + + align:start position:0% +right but it also does so in linear time + + + align:start position:0% +right but it also does so in linear time +because i'm looping over all the + + align:start position:0% +because i'm looping over all the + + + align:start position:0% +because i'm looping over all the +vertices + + align:start position:0% +vertices + + + align:start position:0% +vertices +and looping over its outgoing + + align:start position:0% +and looping over its outgoing + + + align:start position:0% +and looping over its outgoing +adjacencies once same analysis as we had + + align:start position:0% +adjacencies once same analysis as we had + + + align:start position:0% +adjacencies once same analysis as we had +for + + align:start position:0% +for + + + align:start position:0% +for +both bfs and dfs essentially + + align:start position:0% +both bfs and dfs essentially + + + align:start position:0% +both bfs and dfs essentially +right and then since we can do this + + align:start position:0% +right and then since we can do this + + + align:start position:0% +right and then since we can do this +since we can con + + align:start position:0% +since we can con + + + align:start position:0% +since we can con +compute parent pointers from these + + align:start position:0% +compute parent pointers from these + + + align:start position:0% +compute parent pointers from these +distances + + align:start position:0% +distances + + + align:start position:0% +distances +we're going to kind of ignore computing + + align:start position:0% +we're going to kind of ignore computing + + + align:start position:0% +we're going to kind of ignore computing +these parent pointers from now on + + align:start position:0% +these parent pointers from now on + + + align:start position:0% +these parent pointers from now on +right we're just going to concentrate on + + align:start position:0% +right we're just going to concentrate on + + + align:start position:0% +right we're just going to concentrate on +computing the distances because + + align:start position:0% +computing the distances because + + + align:start position:0% +computing the distances because +you know we're gonna have to take linear + + align:start position:0% +you know we're gonna have to take linear + + + align:start position:0% +you know we're gonna have to take linear +time anyway right + + align:start position:0% +time anyway right + + + align:start position:0% +time anyway right +at least and all these other things take + + align:start position:0% +at least and all these other things take + + + align:start position:0% +at least and all these other things take +more time + + align:start position:0% +more time + + + align:start position:0% +more time +so we can compute the distances in more + + align:start position:0% +so we can compute the distances in more + + + align:start position:0% +so we can compute the distances in more +time and then + + align:start position:0% +time and then + + + align:start position:0% +time and then +compute the parents after okay + + align:start position:0% +compute the parents after okay + + + align:start position:0% +compute the parents after okay +so that's what we're going to do + + align:start position:0% + + + + align:start position:0% + +okay so now with all that build up + + align:start position:0% +okay so now with all that build up + + + align:start position:0% +okay so now with all that build up +let's show an algorithm right how do we + + align:start position:0% +let's show an algorithm right how do we + + + align:start position:0% +let's show an algorithm right how do we +compute shortest single source shortest + + align:start position:0% +compute shortest single source shortest + + + align:start position:0% +compute shortest single source shortest +paths in a dag + + align:start position:0% +paths in a dag + + + align:start position:0% +paths in a dag +in linear time okay + + align:start position:0% +in linear time okay + + + align:start position:0% +in linear time okay +well a debt i mean this is actually a + + align:start position:0% +well a debt i mean this is actually a + + + align:start position:0% +well a debt i mean this is actually a +super useful convenient thing + + align:start position:0% +super useful convenient thing + + + align:start position:0% +super useful convenient thing +in algorithms in general dags are just + + align:start position:0% +in algorithms in general dags are just + + + align:start position:0% +in algorithms in general dags are just +nice things right they're kind of + + align:start position:0% +nice things right they're kind of + + + align:start position:0% +nice things right they're kind of +ordered in a way right there's this + + align:start position:0% +ordered in a way right there's this + + + align:start position:0% +ordered in a way right there's this +topological sore order + + align:start position:0% +topological sore order + + + align:start position:0% +topological sore order +that we were talking about before this + + align:start position:0% +that we were talking about before this + + + align:start position:0% +that we were talking about before this +is going to play a key role + + align:start position:0% +is going to play a key role + + + align:start position:0% +is going to play a key role +right there's a really nice structure to + + align:start position:0% +right there's a really nice structure to + + + align:start position:0% +right there's a really nice structure to +dags not having cycles + + align:start position:0% +dags not having cycles + + + align:start position:0% +dags not having cycles +not having to deal with this negative + + align:start position:0% +not having to deal with this negative + + + align:start position:0% +not having to deal with this negative +weight cycle problem + + align:start position:0% +weight cycle problem + + + align:start position:0% +weight cycle problem +right you can only kind of go in one + + align:start position:0% +right you can only kind of go in one + + + align:start position:0% +right you can only kind of go in one +direction + + align:start position:0% +direction + + + align:start position:0% +direction +along this graph right + + align:start position:0% +along this graph right + + + align:start position:0% +along this graph right +it's very nice structure to exploit and + + align:start position:0% +it's very nice structure to exploit and + + + align:start position:0% +it's very nice structure to exploit and +so we're going to exploit it + + align:start position:0% +so we're going to exploit it + + + align:start position:0% +so we're going to exploit it +and here's the idea dag relaxation + + align:start position:0% + + + + align:start position:0% + +what it's going to do is it's going to + + align:start position:0% +what it's going to do is it's going to + + + align:start position:0% +what it's going to do is it's going to +start out with some + + align:start position:0% +start out with some + + + align:start position:0% +start out with some +estimates of what these distances should + + align:start position:0% +estimates of what these distances should + + + align:start position:0% +estimates of what these distances should +be right + + align:start position:0% +be right + + + align:start position:0% +be right +okay so maintain + + align:start position:0% + + + + align:start position:0% + +maintain distance + + align:start position:0% +maintain distance + + + align:start position:0% +maintain distance +estimates + + align:start position:0% + + + + align:start position:0% + +and now i'm going to try to be careful + + align:start position:0% +and now i'm going to try to be careful + + + align:start position:0% +and now i'm going to try to be careful +here about how i draw my + + align:start position:0% +here about how i draw my + + + align:start position:0% +here about how i draw my +d's + + align:start position:0% + + + + align:start position:0% + +okay this is a d + + align:start position:0% + + + + align:start position:0% + +this is a delta okay this is + + align:start position:0% +this is a delta okay this is + + + align:start position:0% +this is a delta okay this is +shortest paths this is a distance + + align:start position:0% +shortest paths this is a distance + + + align:start position:0% +shortest paths this is a distance +estimate + + align:start position:0% +estimate + + + align:start position:0% +estimate +okay so that's what i'm going to be + + align:start position:0% +okay so that's what i'm going to be + + + align:start position:0% +okay so that's what i'm going to be +using for the the rest of this time + + align:start position:0% +using for the the rest of this time + + + align:start position:0% +using for the the rest of this time +so we're going to initialize maintain + + align:start position:0% +so we're going to initialize maintain + + + align:start position:0% +so we're going to initialize maintain +these + + align:start position:0% +these + + + align:start position:0% +these +uh estimates of distance d which are + + align:start position:0% +uh estimates of distance d which are + + + align:start position:0% +uh estimates of distance d which are +gonna start at + + align:start position:0% +gonna start at + + + align:start position:0% +gonna start at +uh initially + + align:start position:0% +uh initially + + + align:start position:0% +uh initially +infinite right okay i don't know what + + align:start position:0% +infinite right okay i don't know what + + + align:start position:0% +infinite right okay i don't know what +they are + + align:start position:0% +they are + + + align:start position:0% +they are +right i don't know what the shortest + + align:start position:0% +right i don't know what the shortest + + + align:start position:0% +right i don't know what the shortest +paths are but they better be less than + + align:start position:0% +paths are but they better be less than + + + align:start position:0% +paths are but they better be less than +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +or else i don't care right so i'm going + + align:start position:0% +or else i don't care right so i'm going + + + align:start position:0% +or else i don't care right so i'm going +to that's the kind of worst case + + align:start position:0% +to that's the kind of worst case + + + align:start position:0% +to that's the kind of worst case +scenario + + align:start position:0% +scenario + + + align:start position:0% +scenario +right it can't be worse than this for + + align:start position:0% +right it can't be worse than this for + + + align:start position:0% +right it can't be worse than this for +every vertex + + align:start position:0% +every vertex + + + align:start position:0% +every vertex +and we're going to maintain the property + + align:start position:0% +and we're going to maintain the property + + + align:start position:0% +and we're going to maintain the property +that + + align:start position:0% + + + + align:start position:0% + +estimates + + align:start position:0% + + + + align:start position:0% + +upper bound + + align:start position:0% + + + + align:start position:0% + +that should probably be two words upper + + align:start position:0% +that should probably be two words upper + + + align:start position:0% +that should probably be two words upper +bound + + align:start position:0% +bound + + + align:start position:0% +bound +uh delta sv + + align:start position:0% + + + + align:start position:0% + +uh we're going to maintain that the + + align:start position:0% +uh we're going to maintain that the + + + align:start position:0% +uh we're going to maintain that the +upward bound this thing + + align:start position:0% +upward bound this thing + + + align:start position:0% +upward bound this thing +and gradually lower + + align:start position:0% + + + + align:start position:0% + +until they are equal + + align:start position:0% + + + + align:start position:0% + +okay so this is the idea we start from + + align:start position:0% +okay so this is the idea we start from + + + align:start position:0% +okay so this is the idea we start from +an overestimate an upper bound on the + + align:start position:0% +an overestimate an upper bound on the + + + align:start position:0% +an overestimate an upper bound on the +distance estimate and then + + align:start position:0% +distance estimate and then + + + align:start position:0% +distance estimate and then +we're repeatedly going to lower that + + align:start position:0% +we're repeatedly going to lower that + + + align:start position:0% +we're repeatedly going to lower that +value + + align:start position:0% +value + + + align:start position:0% +value +as we gain more information about the + + align:start position:0% +as we gain more information about the + + + align:start position:0% +as we gain more information about the +graph + + align:start position:0% +graph + + + align:start position:0% +graph +maintaining that we're always upper + + align:start position:0% +maintaining that we're always upper + + + align:start position:0% +maintaining that we're always upper +bounding the distance + + align:start position:0% +bounding the distance + + + align:start position:0% +bounding the distance +and we're going to keep doing it keep + + align:start position:0% +and we're going to keep doing it keep + + + align:start position:0% +and we're going to keep doing it keep +doing it keep doing it until + + align:start position:0% +doing it keep doing it until + + + align:start position:0% +doing it keep doing it until +as we will try to prove to you these + + align:start position:0% +as we will try to prove to you these + + + align:start position:0% +as we will try to prove to you these +estimates + + align:start position:0% +estimates + + + align:start position:0% +estimates +reach actually reach down all the way to + + align:start position:0% +reach actually reach down all the way to + + + align:start position:0% +reach actually reach down all the way to +our shortest path distances + + align:start position:0% +our shortest path distances + + + align:start position:0% +our shortest path distances +okay so when do we lower these things + + align:start position:0% + + + + align:start position:0% + +when do we lower these things we're + + align:start position:0% +when do we lower these things we're + + + align:start position:0% +when do we lower these things we're +going to lower + + align:start position:0% +going to lower + + + align:start position:0% +going to lower +these distance estimates whenever the + + align:start position:0% +these distance estimates whenever the + + + align:start position:0% +these distance estimates whenever the +distance at estimates violate what we're + + align:start position:0% +distance at estimates violate what we're + + + align:start position:0% +distance at estimates violate what we're +going to call + + align:start position:0% +going to call + + + align:start position:0% +going to call +the triangle inequality okay what is the + + align:start position:0% +the triangle inequality okay what is the + + + align:start position:0% +the triangle inequality okay what is the +triangle inequality + + align:start position:0% + + + + align:start position:0% + +triangle inequality is actually a pretty + + align:start position:0% +triangle inequality is actually a pretty + + + align:start position:0% +triangle inequality is actually a pretty +intuitive notion + + align:start position:0% +intuitive notion + + + align:start position:0% +intuitive notion +okay it's basically saying if i have + + align:start position:0% +okay it's basically saying if i have + + + align:start position:0% +okay it's basically saying if i have +three points + + align:start position:0% +three points + + + align:start position:0% +three points +that's thus triangle right uh + + align:start position:0% +that's thus triangle right uh + + + align:start position:0% +that's thus triangle right uh +maybe bigger so i can write a letter in + + align:start position:0% +maybe bigger so i can write a letter in + + + align:start position:0% +maybe bigger so i can write a letter in +them + + align:start position:0% + + + + align:start position:0% + +okay it's basically saying that if i + + align:start position:0% +okay it's basically saying that if i + + + align:start position:0% +okay it's basically saying that if i +have a vertex u + + align:start position:0% +have a vertex u + + + align:start position:0% +have a vertex u +a vertex v vertex x for example + + align:start position:0% +a vertex v vertex x for example + + + align:start position:0% +a vertex v vertex x for example +right the shortest path distance + + align:start position:0% + + + + align:start position:0% + +right the shortest path distance delta + + align:start position:0% +right the shortest path distance delta + + + align:start position:0% +right the shortest path distance delta +of uv + + align:start position:0% +of uv + + + align:start position:0% +of uv +that's the shortest path distance from u + + align:start position:0% +that's the shortest path distance from u + + + align:start position:0% +that's the shortest path distance from u +to v + + align:start position:0% +to v + + + align:start position:0% +to v +it can't be bigger than a shortest path + + align:start position:0% +it can't be bigger than a shortest path + + + align:start position:0% +it can't be bigger than a shortest path +from u to v that also goes through x + + align:start position:0% +from u to v that also goes through x + + + align:start position:0% +from u to v that also goes through x +right right i'm i'm of of my paths i'm + + align:start position:0% +right right i'm i'm of of my paths i'm + + + align:start position:0% +right right i'm i'm of of my paths i'm +now restricting the + + align:start position:0% +now restricting the + + + align:start position:0% +now restricting the +paths that i have to the ones that go + + align:start position:0% +paths that i have to the ones that go + + + align:start position:0% +paths that i have to the ones that go +through x + + align:start position:0% + + + + align:start position:0% + +right the shortest path distance from u + + align:start position:0% +right the shortest path distance from u + + + align:start position:0% +right the shortest path distance from u +to v can't be bigger than + + align:start position:0% +to v can't be bigger than + + + align:start position:0% +to v can't be bigger than +restricting paths that go through x and + + align:start position:0% +restricting paths that go through x and + + + align:start position:0% +restricting paths that go through x and +taking that shortest distance + + align:start position:0% +taking that shortest distance + + + align:start position:0% +taking that shortest distance +right getting the shortest path distance + + align:start position:0% +right getting the shortest path distance + + + align:start position:0% +right getting the shortest path distance +from here and adding it to the shortest + + align:start position:0% +from here and adding it to the shortest + + + align:start position:0% +from here and adding it to the shortest +path distance here + + align:start position:0% +path distance here + + + align:start position:0% +path distance here +right delta u x + + align:start position:0% +right delta u x + + + align:start position:0% +right delta u x +delta x v + + align:start position:0% +delta x v + + + align:start position:0% +delta x v +right + + align:start position:0% + + + + align:start position:0% + +i mean that that's just a statement of i + + align:start position:0% +i mean that that's just a statement of i + + + align:start position:0% +i mean that that's just a statement of i +i'm restricting to a subset of the paths + + align:start position:0% +i'm restricting to a subset of the paths + + + align:start position:0% +i'm restricting to a subset of the paths +i can't + + align:start position:0% +i can't + + + align:start position:0% +i can't +increase my i can't decrease my minimum + + align:start position:0% +increase my i can't decrease my minimum + + + align:start position:0% +increase my i can't decrease my minimum +distance right + + align:start position:0% +distance right + + + align:start position:0% +distance right +so this is the statement of the triangle + + align:start position:0% +so this is the statement of the triangle + + + align:start position:0% +so this is the statement of the triangle +inequality right that the + + align:start position:0% +inequality right that the + + + align:start position:0% +inequality right that the +shortest path distance from u to v + + align:start position:0% +shortest path distance from u to v + + + align:start position:0% +shortest path distance from u to v +is can't be uh bigger + + align:start position:0% +is can't be uh bigger + + + align:start position:0% +is can't be uh bigger +than the shortest path distance from u + + align:start position:0% +than the shortest path distance from u + + + align:start position:0% +than the shortest path distance from u +to x + + align:start position:0% +to x + + + align:start position:0% +to x +plus the shortest path distance from x + + align:start position:0% +plus the shortest path distance from x + + + align:start position:0% +plus the shortest path distance from x +to v + + align:start position:0% +to v + + + align:start position:0% +to v +for any x in my graph that's not u and v + + align:start position:0% +for any x in my graph that's not u and v + + + align:start position:0% +for any x in my graph that's not u and v +okay so that's the triangle inequality + + align:start position:0% +okay so that's the triangle inequality + + + align:start position:0% +okay so that's the triangle inequality +pretty intuitive notion right okay why + + align:start position:0% +pretty intuitive notion right okay why + + + align:start position:0% +pretty intuitive notion right okay why +is this useful + + align:start position:0% +is this useful + + + align:start position:0% +is this useful +okay well if i find + + align:start position:0% + + + + align:start position:0% + +if i find an edge in my graph + + align:start position:0% +if i find an edge in my graph + + + align:start position:0% +if i find an edge in my graph +if there's an edge u v + + align:start position:0% +if there's an edge u v + + + align:start position:0% +if there's an edge u v +in my graph + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% + + + + align:start position:0% + +this condition is violated for the + + align:start position:0% +this condition is violated for the + + + align:start position:0% +this condition is violated for the +estimates that i have + + align:start position:0% +estimates that i have + + + align:start position:0% +estimates that i have +right it obviously can't be violated on + + align:start position:0% +right it obviously can't be violated on + + + align:start position:0% +right it obviously can't be violated on +my shortest path distances but if it + + align:start position:0% +my shortest path distances but if it + + + align:start position:0% +my shortest path distances but if it +violates it on the estimates + + align:start position:0% +violates it on the estimates + + + align:start position:0% +violates it on the estimates +u v is bigger + + align:start position:0% +u v is bigger + + + align:start position:0% +u v is bigger +than u x uh sorry u + + align:start position:0% +than u x uh sorry u + + + align:start position:0% +than u x uh sorry u +how am i going to do this i want this to + + align:start position:0% +how am i going to do this i want this to + + + align:start position:0% +how am i going to do this i want this to +be s + + align:start position:0% +be s + + + align:start position:0% +be s +i'm calculating shortest path distances + + align:start position:0% +i'm calculating shortest path distances + + + align:start position:0% +i'm calculating shortest path distances +from + + align:start position:0% +from + + + align:start position:0% +from +s and shortest test distances from + + align:start position:0% +s and shortest test distances from + + + align:start position:0% +s and shortest test distances from +s to some incoming vertex u + + align:start position:0% +s to some incoming vertex u + + + align:start position:0% +s to some incoming vertex u +plus the edge weight from u + + align:start position:0% +plus the edge weight from u + + + align:start position:0% +plus the edge weight from u +to v okay all right so + + align:start position:0% +to v okay all right so + + + align:start position:0% +to v okay all right so +what is this doing i have some edge + + align:start position:0% +what is this doing i have some edge + + + align:start position:0% +what is this doing i have some edge +u v in my graph okay basically what i've + + align:start position:0% +u v in my graph okay basically what i've + + + align:start position:0% +u v in my graph okay basically what i've +said is that + + align:start position:0% +said is that + + + align:start position:0% +said is that +i have some distance estimate to you + + align:start position:0% +i have some distance estimate to you + + + align:start position:0% +i have some distance estimate to you +but going through making a path to v + + align:start position:0% +but going through making a path to v + + + align:start position:0% +but going through making a path to v +by going through u and then the edge + + align:start position:0% +by going through u and then the edge + + + align:start position:0% +by going through u and then the edge +from u to v + + align:start position:0% +from u to v + + + align:start position:0% +from u to v +is better than my current estimate + + align:start position:0% +is better than my current estimate + + + align:start position:0% +is better than my current estimate +my shortest path estimate to v + + align:start position:0% + + + + align:start position:0% + +that's bad right that's violating the + + align:start position:0% +that's bad right that's violating the + + + align:start position:0% +that's bad right that's violating the +triangle inequality these cannot be the + + align:start position:0% +triangle inequality these cannot be the + + + align:start position:0% +triangle inequality these cannot be the +right weights right these cannot be the + + align:start position:0% +right weights right these cannot be the + + + align:start position:0% +right weights right these cannot be the +right + + align:start position:0% +right + + + align:start position:0% +right +distances so how we're going to do that + + align:start position:0% +distances so how we're going to do that + + + align:start position:0% +distances so how we're going to do that +is + + align:start position:0% +is + + + align:start position:0% +is +lower this is what we said repeatedly + + align:start position:0% +lower this is what we said repeatedly + + + align:start position:0% +lower this is what we said repeatedly +lower + + align:start position:0% +lower + + + align:start position:0% +lower +these distance estimates i'm going to + + align:start position:0% +these distance estimates i'm going to + + + align:start position:0% +these distance estimates i'm going to +lower this guy down to equal this thing + + align:start position:0% +lower this guy down to equal this thing + + + align:start position:0% +lower this guy down to equal this thing +in a sense this constraint was violated + + align:start position:0% +in a sense this constraint was violated + + + align:start position:0% +in a sense this constraint was violated +but now we're relaxing that constraint + + align:start position:0% +but now we're relaxing that constraint + + + align:start position:0% +but now we're relaxing that constraint +so that this is no longer violated + + align:start position:0% +so that this is no longer violated + + + align:start position:0% +so that this is no longer violated +right so that's i'm + + align:start position:0% +right so that's i'm + + + align:start position:0% +right so that's i'm +relaxes a little weird word here we're + + align:start position:0% +relaxes a little weird word here we're + + + align:start position:0% +relaxes a little weird word here we're +using it for historical reasons + + align:start position:0% +using it for historical reasons + + + align:start position:0% +using it for historical reasons +but that's what we mean by when we say + + align:start position:0% +but that's what we mean by when we say + + + align:start position:0% +but that's what we mean by when we say +relax this thing + + align:start position:0% +relax this thing + + + align:start position:0% +relax this thing +is a violated constraint it's got some + + align:start position:0% +is a violated constraint it's got some + + + align:start position:0% +is a violated constraint it's got some +pressure to be + + align:start position:0% +pressure to be + + + align:start position:0% +pressure to be +resolved right and so what we're doing + + align:start position:0% +resolved right and so what we're doing + + + align:start position:0% +resolved right and so what we're doing +is to resolve it we're just setting + + align:start position:0% +is to resolve it we're just setting + + + align:start position:0% +is to resolve it we're just setting +this guy equal to this so it at least + + align:start position:0% +this guy equal to this so it at least + + + align:start position:0% +this guy equal to this so it at least +resolves locally that constraint now it + + align:start position:0% +resolves locally that constraint now it + + + align:start position:0% +resolves locally that constraint now it +may + + align:start position:0% +may + + + align:start position:0% +may +violate the triangle inequality + + align:start position:0% +violate the triangle inequality + + + align:start position:0% +violate the triangle inequality +otherwise other places + + align:start position:0% +otherwise other places + + + align:start position:0% +otherwise other places +now that we've done this change but at + + align:start position:0% +now that we've done this change but at + + + align:start position:0% +now that we've done this change but at +least this constraint + + align:start position:0% +least this constraint + + + align:start position:0% +least this constraint +is now relaxed and satisfied okay so uh + + align:start position:0% +is now relaxed and satisfied okay so uh + + + align:start position:0% +is now relaxed and satisfied okay so uh +relax + + align:start position:0% + + + + align:start position:0% + +edge by + + align:start position:0% +edge by + + + align:start position:0% +edge by +lowering + + align:start position:0% + + + + align:start position:0% + +d of sv + + align:start position:0% +d of sv + + + align:start position:0% +d of sv +to this thing okay that's what we're + + align:start position:0% +to this thing okay that's what we're + + + align:start position:0% +to this thing okay that's what we're +going to mean by relaxing an edge + + align:start position:0% +going to mean by relaxing an edge + + + align:start position:0% +going to mean by relaxing an edge +okay and relaxing an edge + + align:start position:0% + + + + align:start position:0% + +is what i'll call safe it's safe to do + + align:start position:0% +is what i'll call safe it's safe to do + + + align:start position:0% +is what i'll call safe it's safe to do +okay what do i mean by relaxation is + + align:start position:0% +okay what do i mean by relaxation is + + + align:start position:0% +okay what do i mean by relaxation is +safe it means that + + align:start position:0% +safe it means that + + + align:start position:0% +safe it means that +as i am computing these shortest path + + align:start position:0% +as i am computing these shortest path + + + align:start position:0% +as i am computing these shortest path +distances + + align:start position:0% +distances + + + align:start position:0% +distances +right i'm going to maintain this + + align:start position:0% +right i'm going to maintain this + + + align:start position:0% +right i'm going to maintain this +property that + + align:start position:0% +property that + + + align:start position:0% +property that +each one of these estimates sorry + + align:start position:0% +each one of these estimates sorry + + + align:start position:0% +each one of these estimates sorry +these estimates here has the property + + align:start position:0% +these estimates here has the property + + + align:start position:0% +these estimates here has the property +that it's either + + align:start position:0% +that it's either + + + align:start position:0% +that it's either +infinite or it is the weight + + align:start position:0% +infinite or it is the weight + + + align:start position:0% +infinite or it is the weight +of some path to v okay + + align:start position:0% +of some path to v okay + + + align:start position:0% +of some path to v okay +so that's that's the thing that + + align:start position:0% +so that's that's the thing that + + + align:start position:0% +so that's that's the thing that +relaxation is safe + + align:start position:0% +relaxation is safe + + + align:start position:0% +relaxation is safe +so each + + align:start position:0% + + + + align:start position:0% + +uh distance estimate sv + + align:start position:0% +uh distance estimate sv + + + align:start position:0% +uh distance estimate sv +is weight + + align:start position:0% +is weight + + + align:start position:0% +is weight +of some path + + align:start position:0% + + + + align:start position:0% + +from s to v + + align:start position:0% +from s to v + + + align:start position:0% +from s to v +or infinite okay + + align:start position:0% +or infinite okay + + + align:start position:0% +or infinite okay +and this is a pretty easy thing to prove + + align:start position:0% +and this is a pretty easy thing to prove + + + align:start position:0% +and this is a pretty easy thing to prove +right if i had the invariant that + + align:start position:0% +right if i had the invariant that + + + align:start position:0% +right if i had the invariant that +these were all weights of shortest paths + + align:start position:0% +these were all weights of shortest paths + + + align:start position:0% +these were all weights of shortest paths +let's try to relax an edge + + align:start position:0% +let's try to relax an edge + + + align:start position:0% +let's try to relax an edge +right and we need to show that this + + align:start position:0% +right and we need to show that this + + + align:start position:0% +right and we need to show that this +property is maintained + + align:start position:0% +property is maintained + + + align:start position:0% +property is maintained +relax edge uv okay + + align:start position:0% +relax edge uv okay + + + align:start position:0% +relax edge uv okay +now if i relax edge uv what do i do + + align:start position:0% + + + + align:start position:0% + +i set this thing + + align:start position:0% + + + + align:start position:0% + +or uh sorry i set this thing my shortest + + align:start position:0% +or uh sorry i set this thing my shortest + + + align:start position:0% +or uh sorry i set this thing my shortest +path + + align:start position:0% +path + + + align:start position:0% +path +distance to v to be this thing plus this + + align:start position:0% +distance to v to be this thing plus this + + + align:start position:0% +distance to v to be this thing plus this +thing + + align:start position:0% +thing + + + align:start position:0% +thing +right this is an a weight of an edge + + align:start position:0% +right this is an a weight of an edge + + + align:start position:0% +right this is an a weight of an edge +from u to v + + align:start position:0% +from u to v + + + align:start position:0% +from u to v +now by my assumption that we're + + align:start position:0% +now by my assumption that we're + + + align:start position:0% +now by my assumption that we're +maintaining + + align:start position:0% +maintaining + + + align:start position:0% +maintaining +that this is a the weight of some path + + align:start position:0% +that this is a the weight of some path + + + align:start position:0% +that this is a the weight of some path +in my graph + + align:start position:0% +in my graph + + + align:start position:0% +in my graph +right if this thing is bigger + + align:start position:0% +right if this thing is bigger + + + align:start position:0% +right if this thing is bigger +i'm setting it to the weight of some + + align:start position:0% +i'm setting it to the weight of some + + + align:start position:0% +i'm setting it to the weight of some +path in my graph to u + + align:start position:0% +path in my graph to u + + + align:start position:0% +path in my graph to u +plus an edge from u to v and so this + + align:start position:0% +plus an edge from u to v and so this + + + align:start position:0% +plus an edge from u to v and so this +checks out + + align:start position:0% +checks out + + + align:start position:0% +checks out +so + + align:start position:0% + + + + align:start position:0% + +assign + + align:start position:0% + + + + align:start position:0% + +d of s to v + + align:start position:0% +d of s to v + + + align:start position:0% +d of s to v +to weight + + align:start position:0% + + + + align:start position:0% + +of some path + + align:start position:0% + + + + align:start position:0% + +okay i i'm not going to write down all + + align:start position:0% +okay i i'm not going to write down all + + + align:start position:0% +okay i i'm not going to write down all +the argument that i just said here + + align:start position:0% +the argument that i just said here + + + align:start position:0% +the argument that i just said here +but basically since this distance + + align:start position:0% +but basically since this distance + + + align:start position:0% +but basically since this distance +estimate + + align:start position:0% +estimate + + + align:start position:0% +estimate +was by supposition before the weight of + + align:start position:0% +was by supposition before the weight of + + + align:start position:0% +was by supposition before the weight of +some path to v + + align:start position:0% +some path to v + + + align:start position:0% +some path to v +to to u right then this is again + + align:start position:0% +to to u right then this is again + + + align:start position:0% +to to u right then this is again +the weight of some path to v okay great + + align:start position:0% +the weight of some path to v okay great + + + align:start position:0% +the weight of some path to v okay great +so now we're ready to + + align:start position:0% +so now we're ready to + + + align:start position:0% +so now we're ready to +actually go through this algorithm + + align:start position:0% + + + + align:start position:0% + +so dag relaxation + + align:start position:0% +so dag relaxation + + + align:start position:0% +so dag relaxation +from over there + + align:start position:0% + + + + align:start position:0% + +initializes + + align:start position:0% +initializes + + + align:start position:0% +initializes +all of our distance estimates to equal + + align:start position:0% +all of our distance estimates to equal + + + align:start position:0% +all of our distance estimates to equal +infinity + + align:start position:0% +infinity + + + align:start position:0% +infinity +just like we did in bfs + + align:start position:0% + + + + align:start position:0% + +then set + + align:start position:0% + + + + align:start position:0% + +my distance estimate to myself to be + + align:start position:0% +my distance estimate to myself to be + + + align:start position:0% +my distance estimate to myself to be +zero + + align:start position:0% +zero + + + align:start position:0% +zero +right now it's possible that this might + + align:start position:0% +right now it's possible that this might + + + align:start position:0% +right now it's possible that this might +be + + align:start position:0% +be + + + align:start position:0% +be +minus infinity or negative at some point + + align:start position:0% +minus infinity or negative at some point + + + align:start position:0% +minus infinity or negative at some point +but right now i'm just setting it to + + align:start position:0% +but right now i'm just setting it to + + + align:start position:0% +but right now i'm just setting it to +zero okay + + align:start position:0% +zero okay + + + align:start position:0% +zero okay +and either way zero is going to upper + + align:start position:0% +and either way zero is going to upper + + + align:start position:0% +and either way zero is going to upper +bound the distance to s + + align:start position:0% +bound the distance to s + + + align:start position:0% +bound the distance to s +right so in particular + + align:start position:0% +right so in particular + + + align:start position:0% +right so in particular +at initialization + + align:start position:0% + + + + align:start position:0% + +anything not reachable from s + + align:start position:0% +anything not reachable from s + + + align:start position:0% +anything not reachable from s +is set correctly and s + + align:start position:0% +is set correctly and s + + + align:start position:0% +is set correctly and s +itself is set as an upper bound to the + + align:start position:0% +itself is set as an upper bound to the + + + align:start position:0% +itself is set as an upper bound to the +shortest path distance okay + + align:start position:0% +shortest path distance okay + + + align:start position:0% +shortest path distance okay +now we're going to process + + align:start position:0% +now we're going to process + + + align:start position:0% +now we're going to process +each vertex + + align:start position:0% +each vertex + + + align:start position:0% +each vertex +you in a + + align:start position:0% +you in a + + + align:start position:0% +you in a +topological + + align:start position:0% + + + + align:start position:0% + +sort order + + align:start position:0% +sort order + + + align:start position:0% +sort order +so remember our input to dag relaxation + + align:start position:0% +so remember our input to dag relaxation + + + align:start position:0% +so remember our input to dag relaxation +is a deck + + align:start position:0% +is a deck + + + align:start position:0% +is a deck +so this thing has a topological sort + + align:start position:0% +so this thing has a topological sort + + + align:start position:0% +so this thing has a topological sort +order we're going to process these + + align:start position:0% +order we're going to process these + + + align:start position:0% +order we're going to process these +vertices in that order + + align:start position:0% +vertices in that order + + + align:start position:0% +vertices in that order +okay you can imagine we're starting at + + align:start position:0% +okay you can imagine we're starting at + + + align:start position:0% +okay you can imagine we're starting at +the top + + align:start position:0% +the top + + + align:start position:0% +the top +and all my vertices are all my edges are + + align:start position:0% +and all my vertices are all my edges are + + + align:start position:0% +and all my vertices are all my edges are +pointed away from me + + align:start position:0% +pointed away from me + + + align:start position:0% +pointed away from me +and i'm just processing each vertex down + + align:start position:0% +and i'm just processing each vertex down + + + align:start position:0% +and i'm just processing each vertex down +this topological + + align:start position:0% +this topological + + + align:start position:0% +this topological +sort line okay and then for each of + + align:start position:0% +sort line okay and then for each of + + + align:start position:0% +sort line okay and then for each of +these vertices + + align:start position:0% +these vertices + + + align:start position:0% +these vertices +what am i going to do i'm going to look + + align:start position:0% +what am i going to do i'm going to look + + + align:start position:0% +what am i going to do i'm going to look +at all the outgoing + + align:start position:0% +at all the outgoing + + + align:start position:0% +at all the outgoing +neighbors and if the triangle inequality + + align:start position:0% +neighbors and if the triangle inequality + + + align:start position:0% +neighbors and if the triangle inequality +is violated + + align:start position:0% +is violated + + + align:start position:0% +is violated +i'm going to relax that edge it's the + + align:start position:0% +i'm going to relax that edge it's the + + + align:start position:0% +i'm going to relax that edge it's the +algorithm is as simple as that + + align:start position:0% +algorithm is as simple as that + + + align:start position:0% +algorithm is as simple as that +for each + + align:start position:0% + + + + align:start position:0% + +outgoing neighbor + + align:start position:0% + + + + align:start position:0% + +of v sorry of u + + align:start position:0% + + + + align:start position:0% + +i always get u and v mixed up here okay + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +my shortest path estimate to v + + align:start position:0% +my shortest path estimate to v + + + align:start position:0% +my shortest path estimate to v +violates the triangle inequality + + align:start position:0% +violates the triangle inequality + + + align:start position:0% +violates the triangle inequality +for an edge + + align:start position:0% +for an edge + + + align:start position:0% +for an edge +for an incoming edge then i'm going to + + align:start position:0% +for an incoming edge then i'm going to + + + align:start position:0% +for an incoming edge then i'm going to +set + + align:start position:0% +set + + + align:start position:0% +set +relax + + align:start position:0% + + + + align:start position:0% + +uv ie + + align:start position:0% +uv ie + + + align:start position:0% +uv ie +set d + + align:start position:0% +set d + + + align:start position:0% +set d +s b equal to d + + align:start position:0% +s b equal to d + + + align:start position:0% +s b equal to d +s u plus w + + align:start position:0% +s u plus w + + + align:start position:0% +s u plus w +u v okay so that's the algorithm + + align:start position:0% +u v okay so that's the algorithm + + + align:start position:0% +u v okay so that's the algorithm +so if i were to take a look at this uh + + align:start position:0% +so if i were to take a look at this uh + + + align:start position:0% +so if i were to take a look at this uh +example graph over here maybe + + align:start position:0% +example graph over here maybe + + + align:start position:0% +example graph over here maybe +a is my start vertex i initialize it to + + align:start position:0% +a is my start vertex i initialize it to + + + align:start position:0% +a is my start vertex i initialize it to +uh this is not a dag thank you + + align:start position:0% +uh this is not a dag thank you + + + align:start position:0% +uh this is not a dag thank you +let's make it a dag + + align:start position:0% + + + + align:start position:0% + +i claim to now this is a deck + + align:start position:0% +i claim to now this is a deck + + + align:start position:0% +i claim to now this is a deck +okay in particular a topological sort + + align:start position:0% +okay in particular a topological sort + + + align:start position:0% +okay in particular a topological sort +order is + + align:start position:0% +order is + + + align:start position:0% +order is +when there's a path through all the + + align:start position:0% +when there's a path through all the + + + align:start position:0% +when there's a path through all the +vertices then there's a unique + + align:start position:0% +vertices then there's a unique + + + align:start position:0% +vertices then there's a unique +topological sort order + + align:start position:0% +topological sort order + + + align:start position:0% +topological sort order +a b e f g h + + align:start position:0% +a b e f g h + + + align:start position:0% +a b e f g h +d c this is a topological order you can + + align:start position:0% +d c this is a topological order you can + + + align:start position:0% +d c this is a topological order you can +check all the vertices the edges + + align:start position:0% +check all the vertices the edges + + + align:start position:0% +check all the vertices the edges +so i'm going to start with a uh + + align:start position:0% + + + + align:start position:0% + +by setting + + align:start position:0% + + + + align:start position:0% + +the uh well actually let's use e + + align:start position:0% +the uh well actually let's use e + + + align:start position:0% +the uh well actually let's use e +let's do shortest paths from e why not + + align:start position:0% +let's do shortest paths from e why not + + + align:start position:0% +let's do shortest paths from e why not +okay + + align:start position:0% +okay + + + align:start position:0% +okay +shortest paths for me + + align:start position:0% + + + + align:start position:0% + +vertex a actually comes before e in the + + align:start position:0% +vertex a actually comes before e in the + + + align:start position:0% +vertex a actually comes before e in the +topological order + + align:start position:0% +topological order + + + align:start position:0% +topological order +right so it has no i mean it's shortest + + align:start position:0% +right so it has no i mean it's shortest + + + align:start position:0% +right so it has no i mean it's shortest +path distance when i initialize + + align:start position:0% +path distance when i initialize + + + align:start position:0% +path distance when i initialize +i'm going to initialize this to zero and + + align:start position:0% +i'm going to initialize this to zero and + + + align:start position:0% +i'm going to initialize this to zero and +initialize this to infinite + + align:start position:0% +initialize this to infinite + + + align:start position:0% +initialize this to infinite +infinite infinite infinite + + align:start position:0% +infinite infinite infinite + + + align:start position:0% +infinite infinite infinite +all these things to infinite these are + + align:start position:0% +all these things to infinite these are + + + align:start position:0% +all these things to infinite these are +my estimates these are not quite the + + align:start position:0% +my estimates these are not quite the + + + align:start position:0% +my estimates these are not quite the +shortest paths yet + + align:start position:0% +shortest paths yet + + + align:start position:0% +shortest paths yet +distances but when i get here + + align:start position:0% +distances but when i get here + + + align:start position:0% +distances but when i get here +clearly i can't be + + align:start position:0% + + + + align:start position:0% + +distance to me being infinite can never + + align:start position:0% +distance to me being infinite can never + + + align:start position:0% +distance to me being infinite can never +violate the triangle inequality with + + align:start position:0% +violate the triangle inequality with + + + align:start position:0% +violate the triangle inequality with +something infinite or + + align:start position:0% +something infinite or + + + align:start position:0% +something infinite or +finite doesn't matter right so + + align:start position:0% +finite doesn't matter right so + + + align:start position:0% +finite doesn't matter right so +i don't do anything to a anything before + + align:start position:0% +i don't do anything to a anything before + + + align:start position:0% +i don't do anything to a anything before +my source vertex in the topological + + align:start position:0% +my source vertex in the topological + + + align:start position:0% +my source vertex in the topological +order + + align:start position:0% +order + + + align:start position:0% +order +can't be visited right because it's b4 + + align:start position:0% +can't be visited right because it's b4 + + + align:start position:0% +can't be visited right because it's b4 +in the topological order that's that's + + align:start position:0% +in the topological order that's that's + + + align:start position:0% +in the topological order that's that's +the kind of the point there's no path + + align:start position:0% +the kind of the point there's no path + + + align:start position:0% +the kind of the point there's no path +from my source vertex to anything before + + align:start position:0% +from my source vertex to anything before + + + align:start position:0% +from my source vertex to anything before +it in the topological order + + align:start position:0% +it in the topological order + + + align:start position:0% +it in the topological order +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +same with b b is before it in the + + align:start position:0% +same with b b is before it in the + + + align:start position:0% +same with b b is before it in the +topological order + + align:start position:0% +topological order + + + align:start position:0% +topological order +okay now i'm at e + + align:start position:0% +okay now i'm at e + + + align:start position:0% +okay now i'm at e +and it's possible we are violating + + align:start position:0% +and it's possible we are violating + + + align:start position:0% +and it's possible we are violating +triangle inequality + + align:start position:0% +triangle inequality + + + align:start position:0% +triangle inequality +in particular here right i think + + align:start position:0% +in particular here right i think + + + align:start position:0% +in particular here right i think +the shortest path distance to f is + + align:start position:0% +the shortest path distance to f is + + + align:start position:0% +the shortest path distance to f is +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +but actually if i go to e + + align:start position:0% +but actually if i go to e + + + align:start position:0% +but actually if i go to e +through this edge with + + align:start position:0% +through this edge with + + + align:start position:0% +through this edge with +a weight 3 i know that this is violating + + align:start position:0% +a weight 3 i know that this is violating + + + align:start position:0% +a weight 3 i know that this is violating +triangle inequality + + align:start position:0% +triangle inequality + + + align:start position:0% +triangle inequality +so actually this thing is wrong + + align:start position:0% + + + + align:start position:0% + +and i can set it equal to 3. + + align:start position:0% +and i can set it equal to 3. + + + align:start position:0% +and i can set it equal to 3. +okay now that might not be the shortest + + align:start position:0% +okay now that might not be the shortest + + + align:start position:0% +okay now that might not be the shortest +path distance + + align:start position:0% + + + + align:start position:0% + +but right now it's a better estimate + + align:start position:0% +but right now it's a better estimate + + + align:start position:0% +but right now it's a better estimate +right so we've said it + + align:start position:0% +right so we've said it + + + align:start position:0% +right so we've said it +okay now i'm moving on i'm done with + + align:start position:0% +okay now i'm moving on i'm done with + + + align:start position:0% +okay now i'm moving on i'm done with +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +i move to the next vertex in my + + align:start position:0% +i move to the next vertex in my + + + align:start position:0% +i move to the next vertex in my +topological order and again i relax + + align:start position:0% +topological order and again i relax + + + align:start position:0% +topological order and again i relax +edges out of f okay so here + + align:start position:0% +edges out of f okay so here + + + align:start position:0% +edges out of f okay so here +looking at eight three plus eight is + + align:start position:0% +looking at eight three plus eight is + + + align:start position:0% +looking at eight three plus eight is +better than infinite + + align:start position:0% +better than infinite + + + align:start position:0% +better than infinite +so we'll say that that's eleven + + align:start position:0% + + + + align:start position:0% + +and three plus two is better than + + align:start position:0% +and three plus two is better than + + + align:start position:0% +and three plus two is better than +infinite so that's + + align:start position:0% +infinite so that's + + + align:start position:0% +infinite so that's +five okay now i keep going in the + + align:start position:0% +five okay now i keep going in the + + + align:start position:0% +five okay now i keep going in the +topological order g is the next + + align:start position:0% +topological order g is the next + + + align:start position:0% +topological order g is the next +five plus one is 6. okay so we found a + + align:start position:0% +five plus one is 6. okay so we found a + + + align:start position:0% +five plus one is 6. okay so we found a +better estimate here + + align:start position:0% +better estimate here + + + align:start position:0% +better estimate here +right so this 11 is not as good + + align:start position:0% +right so this 11 is not as good + + + align:start position:0% +right so this 11 is not as good +6 is better so we replace it + + align:start position:0% +6 is better so we replace it + + + align:start position:0% +6 is better so we replace it +here we haven't visited before it's + + align:start position:0% +here we haven't visited before it's + + + align:start position:0% +here we haven't visited before it's +still infinite so + + align:start position:0% +still infinite so + + + align:start position:0% +still infinite so +5 plus minus two is three + + align:start position:0% +5 plus minus two is three + + + align:start position:0% +5 plus minus two is three +okay this is the next in the topological + + align:start position:0% +okay this is the next in the topological + + + align:start position:0% +okay this is the next in the topological +order three + + align:start position:0% +order three + + + align:start position:0% +order three +plus nine is bigger than six so that's + + align:start position:0% +plus nine is bigger than six so that's + + + align:start position:0% +plus nine is bigger than six so that's +not a shorter path + + align:start position:0% +not a shorter path + + + align:start position:0% +not a shorter path +three plus four is certainly smaller + + align:start position:0% +three plus four is certainly smaller + + + align:start position:0% +three plus four is certainly smaller +than infinite so + + align:start position:0% +than infinite so + + + align:start position:0% +than infinite so +set that equal to seven then seven plus + + align:start position:0% +set that equal to seven then seven plus + + + align:start position:0% +set that equal to seven then seven plus +five + + align:start position:0% +five + + + align:start position:0% +five +is also bigger than six and actually if + + align:start position:0% +is also bigger than six and actually if + + + align:start position:0% +is also bigger than six and actually if +you can + + align:start position:0% +you can + + + align:start position:0% +you can +you can confirm that these are all the + + align:start position:0% +you can confirm that these are all the + + + align:start position:0% +you can confirm that these are all the +shortest path distances + + align:start position:0% +shortest path distances + + + align:start position:0% +shortest path distances +from e okay so this + + align:start position:0% +from e okay so this + + + align:start position:0% +from e okay so this +algorithm seems to work does it actually + + align:start position:0% +algorithm seems to work does it actually + + + align:start position:0% +algorithm seems to work does it actually +work + + align:start position:0% + + + + align:start position:0% + +let's take a look the claim to you + + align:start position:0% +let's take a look the claim to you + + + align:start position:0% +let's take a look the claim to you +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +is that at the end of relaxation this + + align:start position:0% +is that at the end of relaxation this + + + align:start position:0% +is that at the end of relaxation this +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +we've set + + align:start position:0% + + + + align:start position:0% + +claim + + align:start position:0% + + + + align:start position:0% + +at end + + align:start position:0% +at end + + + align:start position:0% +at end +all the estimates + + align:start position:0% + + + + align:start position:0% + +equal shortest path distances + + align:start position:0% +equal shortest path distances + + + align:start position:0% +equal shortest path distances +okay the basic idea here is that + + align:start position:0% +okay the basic idea here is that + + + align:start position:0% +okay the basic idea here is that +if i take uh a + + align:start position:0% +if i take uh a + + + align:start position:0% +if i take uh a +the cave vertex in the topological order + + align:start position:0% +the cave vertex in the topological order + + + align:start position:0% +the cave vertex in the topological order +assuming that these distances are all + + align:start position:0% +assuming that these distances are all + + + align:start position:0% +assuming that these distances are all +equal + + align:start position:0% +equal + + + align:start position:0% +equal +for the ones before me in the + + align:start position:0% +for the ones before me in the + + + align:start position:0% +for the ones before me in the +topological order i can prove by + + align:start position:0% +topological order i can prove by + + + align:start position:0% +topological order i can prove by +induction + + align:start position:0% +induction + + + align:start position:0% +induction +right we can consider a shortest path + + align:start position:0% +right we can consider a shortest path + + + align:start position:0% +right we can consider a shortest path +from s to v + + align:start position:0% +from s to v + + + align:start position:0% +from s to v +right the kth vertex and look at the + + align:start position:0% +right the kth vertex and look at the + + + align:start position:0% +right the kth vertex and look at the +vertex preceding me along the shortest + + align:start position:0% +vertex preceding me along the shortest + + + align:start position:0% +vertex preceding me along the shortest +path right that that + + align:start position:0% +path right that that + + + align:start position:0% +path right that that +vertex better be uh + + align:start position:0% +vertex better be uh + + + align:start position:0% +vertex better be uh +before me in the topological order or + + align:start position:0% +before me in the topological order or + + + align:start position:0% +before me in the topological order or +we're not a dag + + align:start position:0% +we're not a dag + + + align:start position:0% +we're not a dag +right and we've already set it short as + + align:start position:0% +right and we've already set it short as + + + align:start position:0% +right and we've already set it short as +path distance to be equal + + align:start position:0% +path distance to be equal + + + align:start position:0% +path distance to be equal +to the correct thing by induction + + align:start position:0% +to the correct thing by induction + + + align:start position:0% +to the correct thing by induction +so then when we processed u right + + align:start position:0% + + + + align:start position:0% + +s to u to v + + align:start position:0% +s to u to v + + + align:start position:0% +s to u to v +when we processed u in dag + + align:start position:0% +when we processed u in dag + + + align:start position:0% +when we processed u in dag +relaxation here processed the vertex and + + align:start position:0% +relaxation here processed the vertex and + + + align:start position:0% +relaxation here processed the vertex and +looked at all its outgoing adjacencies + + align:start position:0% +looked at all its outgoing adjacencies + + + align:start position:0% +looked at all its outgoing adjacencies +we would have relaxed this edge + + align:start position:0% +we would have relaxed this edge + + + align:start position:0% +we would have relaxed this edge +to be no greater than that shortest path + + align:start position:0% +to be no greater than that shortest path + + + align:start position:0% +to be no greater than that shortest path +distance + + align:start position:0% + + + + align:start position:0% + +so this is correct you can also think of + + align:start position:0% +so this is correct you can also think of + + + align:start position:0% +so this is correct you can also think of +it as + + align:start position:0% +it as + + + align:start position:0% +it as +the dag relaxation algorithm for + + align:start position:0% +the dag relaxation algorithm for + + + align:start position:0% +the dag relaxation algorithm for +each vertex looks all at its incoming + + align:start position:0% +each vertex looks all at its incoming + + + align:start position:0% +each vertex looks all at its incoming +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +assuming that their shortest path + + align:start position:0% +assuming that their shortest path + + + align:start position:0% +assuming that their shortest path +distances are computed correctly already + + align:start position:0% +distances are computed correctly already + + + align:start position:0% +distances are computed correctly already +right any shortest path distance to me + + align:start position:0% +right any shortest path distance to me + + + align:start position:0% +right any shortest path distance to me +needs to be composed of a shortest path + + align:start position:0% +needs to be composed of a shortest path + + + align:start position:0% +needs to be composed of a shortest path +distance to one of my incoming neighbors + + align:start position:0% +distance to one of my incoming neighbors + + + align:start position:0% +distance to one of my incoming neighbors +through an edge to me + + align:start position:0% +through an edge to me + + + align:start position:0% +through an edge to me +so i can just check all of them that's + + align:start position:0% +so i can just check all of them that's + + + align:start position:0% +so i can just check all of them that's +what dag relaxation kind of does + + align:start position:0% +what dag relaxation kind of does + + + align:start position:0% +what dag relaxation kind of does +and again we're looping over every + + align:start position:0% +and again we're looping over every + + + align:start position:0% +and again we're looping over every +vertex and looking at its adjacencies + + align:start position:0% +vertex and looking at its adjacencies + + + align:start position:0% +vertex and looking at its adjacencies +doing constant work + + align:start position:0% +doing constant work + + + align:start position:0% +doing constant work +this again takes linear time okay so + + align:start position:0% +this again takes linear time okay so + + + align:start position:0% +this again takes linear time okay so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +shortest paths in a dag + + align:start position:0% +shortest paths in a dag + + + align:start position:0% +shortest paths in a dag +next time we'll look at for general + + align:start position:0% +next time we'll look at for general + + + align:start position:0% +next time we'll look at for general +graphs + + align:start position:0% +graphs + + + align:start position:0% +graphs +how we can use kind of the same + + align:start position:0% +how we can use kind of the same + + + align:start position:0% +how we can use kind of the same +technique + + align:start position:0% +technique + + + align:start position:0% +technique +in an algorithm we call bellman ford + + align:start position:0% +in an algorithm we call bellman ford + + + align:start position:0% +in an algorithm we call bellman ford +okay that's it for today \ No newline at end of file diff --git a/6RbIUZ-ZvZs.txt b/6RbIUZ-ZvZs.txt new file mode 100644 index 0000000000000000000000000000000000000000..b775aa727a8f938ef4db3197fb888e75e60cd865 --- /dev/null +++ b/6RbIUZ-ZvZs.txt @@ -0,0 +1,2145 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So I want to +do two things today. + +One is wrap up what I +was doing last time. + +And the rest of the time, or a +part of the rest of the time, + +I want to spend kind of going +back to the questions of what + +have we learned, or what do +we think we have learned? + +So this is mostly +continuation. + +So let me just remind you +what I'm continuing. + +The basic point I was trying +to make last time is that + +there are always many things +you can do to make even bad + +systems allow for relatively +wide range of possible + +interventions. + +And in reverse, even in good +systems, if you have bad + +interventions, they're bad. + +The fact that the system is good +has no guarantee that the + +interventions that get +chosen are bad. + +If you like, in that sequence of +arguments, this is the last + +one, which is can you actually +turn bad politics-- + +is it really prior to policy? + +So does it exist outside +politics? + +And we sort of made the case +that that's not entirely true + +already because we've been +saying things like if people + +have some idea of who they +should vote for then they vote + +more discriminatively. + +Part of the reason why they +don't necessarily use a lot of + +discrimination is because +they're not necessarily that + +interested in the election. + +And that's partly because they +don't have much information. + +Here's a nice experiment which +sort of emphasizes that point + +on how policies can +mold politics. + +This has to do with attitudes +toward women leaders in India. + +In India there's a rule which +says that panchayats are the + +lowest level of government in +India, these are village + +governments essentially. + +And India has a rule which says +that 1/3 of all seats of + +leader of panchayat, the role of +the boss of the panchayat, + +have to be filled by women. + +And it turns out that partly +for political reasons they + +decided that which of them will +be reserved for women + +will be decided by a lottery. + +So there was a lottery to decide +out of the 3,000 or how + +many thousand villages in this +particular state, how many of + +them will have a woman +lead at this time. + +And then in principle the +idea is that next time + +there will a rotation. + +And so the places that are +reserved this time will not be + +reserved the next time +and vice versa. + +And that didn't actually +happen entirely. + +And I'll tell you something +about that in a minute. + +But right now think of +it as a lottery and + +then we see what happens. + +So the advantage of it being a +lottery is that the government + +in a sense performed an +experiment for us because they + +chose these places +by a lottery. + +So we kind of know that they're + +identical to start with. + +So there was a bunch of +places which had to + +have a woman leader. + +These places were not a +priori any different + +from any other places. + +They ended up with +a woman leader. + +Now, in terms of outcomes, +there's data that therefore + +allows you to compare the +villages that had a woman + +leader with places +that didn't. + +And there's an outcome that +seems clear that woman leaders + +are not obviously worse +than men leaders. + +They seem to spend about the +same amount of money. + +And when you ask villagers their +view of corruption in + +government, they're less likely +to say the government + +is corrupt. + +So overall if you look at just +the numbers, women seem to be + +just as effective as men. + +Now, this is not obvious. + +Indeed, it's quite surprising +because the women are actually + +less experienced. + +Often this is the first time +they've had a political job. + +Many of them, this is not just +the first time they've had a + +political job. + +This is the first time they've +ever had a job. + +They're less educated than the +men, and they're less likely + +to have had run a business +than the men. + +That's not surprising. + +But given all that, that's often +all of those things that + +often are seen as +being attributes + +of successful leaders. + +It's not surprising maybe that +people still sort of feel that + +they should not be able to lead +because people only have + +a theory, which is often kind +of a common theory, which is + +that if you have been a business +leader or you've had + +a business you might be better +at running government. + +And so this is a theory you +encounter in the press here + +all the time. + +So maybe people might very +well believe that. + +So the question that's being +asked in this experiment-- + +so the first round of kind of +this lottery, people observed + +what happened. + +And, as I said, the answer was +that the women did no worse + +than the men. + +However, there were still some +hitches in the system. + +So on the next round what was +supposed to have happened was + +that now there would +be no lottery. + +People would just reverse. + +And so let's say you had a woman +leader before, now you + +wouldn't have one +and vice versa. + +That was what supposed +to happen. + +In fact, that didn't happen. + +What happened was that there +was some political + +negotiation. + +And they had a second lottery. + +So there were places that were +randomly chosen again. + +And because there was a second +lottery, some places had women + +leaders twice just because they +happened to kind of win + +the lottery twice. + +Some of them had a lose, +depending on + +your point of view. + +Some of them had women +leaders once. + +And some of them +had zero times. + +So this data is after +10 years. + +So the data we're going to look +at is at least after more + +than five years. + +So these are places which +have had a women + +leader for several years. + +So they've had her first for +five years and then possibly + +for another couple of years. + +Or they've had men leaders. + +So this is sort of data after a +fairly long period of time. + +And, as I said, there are three +different groups here. + +There are people who've had +women leaders for two terms or + +at least one and one plus term, +people who have had + +women leaders for one term, and +people who have had women + +leaders for zero terms. + +So that's the comparison we're +going to be interested in. + +So the way the comparison will +be done is interesting. + +So they took a real speech that +was given by a leader, a + +man leader in this case. + +And then they had a woman sort +of speak out the same speech. + +So they had two recordings of +the same speech, identical + +speech, one in a woman's voice +and one in a man's voice. + +And then what they did was they +took these two speeches + +to the villagers and asked them +to, you know, and took, + +like, a random sample of +villagers and asked them to + +say which of the speeches they +thought reflected leader's + +competence. + +They were hearing a man +speak, a woman speak. + +They were hearing exactly +the same speech. + +And you're asking them which +one sounds more competent. + +So some people were asked about +men, others were asked + +about women. + +And the idea was precisely to +see if it is the case that the + +same speech gets graded +differently, so if people are + +bringing something to +the speech which + +is not in the speech. + +The speech is just a voice +saying the same words. + +Are you bringing something +different to it? + +You're bringing some +prejudice to it? + +You think that women are better, +women are worse, + +whatever it is. + +This is an attempt to +measure prejudice. + +Yeah. + +AUDIENCE: I have a +quick question. + +If a woman's a leader do people +in the community think + +she does whatever her husband +tells her to do? + +PROFESSOR: Yeah. + +For example, that's an +interesting question. + +So when this was implemented, +people basically said this is + +not going to change anything. + +Women leaders are going to +be just like men leaders. + +Why? + +Because men will lead +in any case. + +The women just will +be decorative. + +They'll be on the ballot but +not actually leading. + +And indeed in many villages +there is somebody who people + +talk about quite casually as +the husband of the leader. + +They have a word for it in +Hindi, which is the husband of + +the leader. + +And that's kind of like First +Lad or something. + +So people thought this +will have no effect. + +In fact, when you look at the +data, it's clear that places + +that were randomly assigned a +woman leader are much more + +likely to have investments in +things women care about. + +So women mostly care +about water. + +And places where women +are leader have more + +investment in water. + +Water's a big woman issue +because women have to find + +drinking water. + +Let's say drinking water +is a huge woman issue. + +And so when you look at the +village meetings, women ask + +questions about water, +drinking water. + +And then you look at what +happens if a woman is the head + +of the village, you see exactly +that, which is you see + +women leaders generate more. + +So going back to this +experiment, they were + +basically asked to +grade the speech. + +And the speech was, as +I said, identical. + +So if you thought the man was +more competent, the woman was + +more competent, you're bringing +some data to it that + +was not in the speech itself. + +The speech was word for +word identical. + +So this is the comparison +mostly of never reserved + +versus twice reserved. + +OK, that's the simplest +comparison, one that had a + +woman leader twice with +one where it's + +never had a woman leader. + +The first set of columns, set of +bars, I guess, are for men. + +The second set of bars +are for women. + +So when it says reserved, male, +that means a man in the + +village that has been +reserved twice. + +What does the man say? + +And the difference is woman's +speech versus + +man speech, the rating. + +And the result is +quite dramatic. + +Men, in general, if you're +never reserved, think the + +woman's speech is much worse. + +That's the blue bar. + +It's negative. + +Nonetheless, if you see what +happens after it's reserved + +twice, the men change +their mind. + +Now the woman's speech +is better. + +For women, the original +prejudice was smaller and the + +swing is smaller. + +That's not maybe surprising +because women start with less + +prejudice and then they don't +react as much as well. + +On the other hand, they also +ask a different question. + +This was kind of a measure +of competence, right? + +This was actually asking +them does the + +person sound competent? + +If you'd actually asked them the +question should a woman be + +a leader, they still say no. + +So it's not that they +changed their mind. + +It's that objective judgment +has changed. + +They feel less negative +about women. + +The test is still +against women. + +But somehow once you've been +exposed to women leaders, you + +realize that they're just +as good as men. + +You might feel that they're +really not a good idea. + +Women should not +be in this job. + +But when you look at who does +the job, you figure that + +they're just as good +as others. + +There's a similar experiment +that was done in-- + +so this is sort of continuing +that same data. + +This is actually election +outcome. + +So this is comparing how what +fraction of women get elected. + +Now, in unreserved seats-- + +so these were seats in 2008 that +had been reserved once, + +twice, or zero times. + +That's what you're comparing. + +You're taking seats in 2008 +that are not reserved. + +Now, some of these seats in '98 +and 2003 were reserved. + +Some were reserved once. + +Some were reserved twice. + +This is the third election. + +So do you understand? + +So instead of asking what is +your preferences, this is + +asking what did you observe? + +How did you vote actually? + +Did you support women? + +And, here, again you see +the same pattern. + +These are two different jobs. + +So the greens are +different jobs. + +So the Pradhan is +the top leader. + +The ward councillor is the +next level leader. + +And if you look at both, +you just see that they + +just keep going up. + +So if you reserve more, you +vote more for women. + +These are unreserved seats. + +So right now you're not required +to vote for women. + +And if you start with the +ones which are never + +reserved, you get 9%. + +The ones who you reserved twice, +you get twice as much. + +So basically people's political +judgments are + +substantially shifted by +being reserved twice. + +Yeah. + +AUDIENCE: Is there any data on +the quality of leadership + +between women who run in the non +reserved village versus in + +a reserved village? + +PROFESSOR: There's certainly +data on-- + +I don't know the answer +to that question. + +My guess is that if women who +won the unreserved villages + +are better. + +And that's what you'd expect. + +And I remember somebody saying +that they're more educated + +definitely. + +So if you have the confidence to +run without any reservation + +then you are probably better +situated in any case. + +And that seems to be true. + +I don't remember. + +The same data that is used to +say that women leaders are + +less corrupt than men leaders +must also say something about + +reserved versus unreserved +women. + +I just don't know the answer. + +Yeah. + +AUDIENCE: Could this just be +because more women are running + +in areas [INAUDIBLE]? + +PROFESSOR: Oh, absolutely. + +But that's an outcome, right? + +Women are running. + +And so part of it is that +they're more incumbent. + +But the fact is that, for +whatever reason, once you + +expose people to the possibility +that they can vote + +for women, they vote +for women. + +So in other words, policies +change politics. + +That's the point I wanted to +make, which was sort of + +something I've been pushing +for a while, but just to + +understand this we +talked about. + +And so basically to summarize +it's not that political + +constraints are not important. + +And lots of political events +have huge consequences. + +But that shouldn't stop us. + +The main point we're making here +is that that shouldn't + +stop us in the fight for looking +for better policies + +because, A, better policies are +implementable even when + +the politics is often bad. + +You often still get some +good policies. + +And second, if you have got a +chance to have a good policy, + +you better have one ready. + +So imagine the politics shifted +and somebody asked + +you, this is what +I want to do. + +What would you do? + +You would do something very, +very, very, different if you + +knew or if you thought +about it. + +And, moreover, if you do +undertake better policies, + +voters react. + +So there's no fixed prejudice +that makes voters completely + +unresponsive to performance. + +If you show performance, +voters seem to react. + +And especially if there's +strong evidence that the + +policy is working, people +react even more. + +So the one story that I think is +on this slide and is worth + +mentioning is the story of a +program called Progresa, which + +is a Mexican program which has +now been imitated in many, + +many countries, including, +briefly, by Mayor Bloomberg in + +New York City. + +This is a program called a +conditional cash transfer, + +basically a program which told +parents that if their children + +were immunized and sent to +school, they'll get a little + +bit of money or quite a bit +of money, actually. + +So they were paying parents to +make sure that the parents + +send their children to school. + +So when this program was +launched, the person who + +launched it realized that in +Mexico every six years the + +president changes and all +the policies change. + +And so the policy would die in +six years even if it was a + +great policy. + +So what he did is he actually +got a bunch of people from + +University of Pennsylvania, +University of California + +involved in evaluating +the program. + +And it was introduced in a +random way so you could + +compare the places where the +policies was implemented to + +the places that were not. + +And there was a bunch of well +known scholars from all over + +the world who were +evaluating it. + +Their results came out +very positive. + +So as the guy who had +implemented it expected, the + +party that was in power then +lost the elections. + +So a new president came in +from a different party. + +And he immediately said we have +to shut down Progresa + +because Progresa is a previous +government's program. + +We don't like it. + +So it was shut down. + +But immediately he replaced it +with a slightly different + +program which was essentially +identical to it called + +Oportunidades. + +So basically the fact that there +was all this evidence + +out there made it very difficult +for them to actually + +shut it down. + +And so the program actually +survived and now has spread to + +many countries. + +So the general point to be made +here is that I think it's + +too easy to assume that, +well, the political + +system is very powerful. + +We just cannot change +anything. + +And, therefore, we shouldn't +intervene. + +But, in fact, when you actually +are strategic about + +playing that game, you do +get lots of leverage. + +This Progresa example is an +excellent example of how you + +need to be strategic about +the user information. + +But if you are strategic then +you might be capable of + +generating lots of change. + +So that's sort of one general +point I wanted to make. + +But I have a set of slides +which are an attempt to + +summarize all the general points +we wanted to make. + +So let me just go +through them. + +So what I want to do is +this is the heading. + +The end of our book is called +"in place of a sweeping + +conclusion." And you can imagine +why we don't want a + +sweeping conclusion since our +whole point is that there is + +not one conclusion. + +There's not one solution +that will solve all the + +problems in the world. + +There's no sense in claiming +that there is one answer. + +However it's sort of useful +to illustrate some general + +principles. + +And so what I'm going to do is +I'm going to go through a few + +of, I think, the five key +principles that we think are + +useful to keep in mind whenever +you're thinking about + +these issues. + +So this is the first one. + +So do you remember any +examples of this? + +Yeah. + +AUDIENCE: I think it was they +believe, for health and + +disease stuff, they believe +that the suggestions the + +religious leaders were giving +were better than + +the medicines that-- + +PROFESSOR: For example. + +Others? + +There were many. + +Sorry? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: What about examples +of situations where the poor + +seem to act as if they don't +have key pieces of information + +or they have beliefs which are +sort of maybe misplaced? + +We went over many during +the-- yeah. + +AUDIENCE: Education has an +S-shaved curve to it. + +PROFESSOR: Right. + +That education has very high +returns at the top and almost + +no returns at the bottom. + +Yeah. + +AUDIENCE: Probably make more +sense to invest in education + +for women [INAUDIBLE]. + +PROFESSOR: Yeah. + +We talked about, for example, +the belief that you should get + +a shot rather than a tablet +whenever you get sick. + +Typically a tablet is much safer +than a shot and does + +exactly the same thing. + +What's another example? + +The other examples that we +discussed a lot are examples + +not so much of the wrong belief +as much as the lack of + +belief, that people often don't +seem to believe that + +different technologies are +as effective as we think. + +So one of the reasons why people +don't want bed nets is + +they don't seem to believe +that bed nets will work. + +And when you give people bed +nets and they use them, a year + +later they're willing to +buy it at full price. + +A lot more of them are willing +to buy it at full price + +because they see that they're +useful and usable. + +The fact that you go and tell +them this is great for you is + +not enough. + +They don't believe you. + +So when they use it, they +start believing you. + +Or another example of rather +weak beliefs is immunization. + +People sort of think that +immunization, maybe it works, + +maybe it doesn't. + +It's not that they don't go to +get immunized, but they don't + +really make sure that their +children get all the + +immunizations. + +Yeah. + +AUDIENCE: Well, fertilizer is +kind of a counter example in + +that they know it works, but +then they try [INAUDIBLE]. + +PROFESSOR: Absolutely. + +So the converse was +not being claimed. + +It's not that the poor +only believe + +things which are false. + +AUDIENCE: That was just a lack +of information [INAUDIBLE]. + +PROFESSOR: Yeah. + +You're right. + +It's a good example. + +But it is something where that's +certainly not what we + +were claiming. + +The second one is we say that +the poor bear responsibility + +for far too much +of their lives. + +And what do we mean here? + +What are examples? + +AUDIENCE: There are examples +in health. + +For instance, they have to +decide every time about + +purification of water. + +And [INAUDIBLE] + +many examples. + +AUDIENCE: I was going to +mention those, too. + +But also maybe education. + +You have a system +of [INAUDIBLE] + +school systems working well in +poor villages [INAUDIBLE] + +no idea that there's children +not learning anything actually + +at school [INAUDIBLE]. + +PROFESSOR: Exactly. + +That's a nice example. + +Water's a very good example. + +Typically I think lots of people +have said why don't + +poor people use, like, +water purification? + +And it's true that they +should use it. + +But think of what it means. + +It means every time you use +water, you have to make sure + +it's purified. + +Whereas for us, we just don't +even worry about it. + +We run the tap. + +So in some sense we +have it so easy. + +So think about pensions. + +If you work at MIT, somebody +deducts pension money from + +your salary, puts it into an +account, and somebody else + +invests it for you. + +And you have no choice +over it. + +But on the other hand, you know +that something's being + +done about it. + +If you're poor, you have to +invest the money all by + +yourself and make sure that, +you know, it's getting the + +right returns or finding +a place that's safe. + +We don't solve any of +those problems. + +Education's a great +one actually. + +I think we can take +as given that the + +school systems are rated. + +We have the ability to +evaluate what our + +children are learning. + +If you're poor then you +really don't know. + +If you want to actually make +sure your child is learning, + +you have to go and find somebody +else who does know + +how to read and write and get +him to intervene and make sure + +that the child is learning. + +Do you want-- + +yeah? + +AUDIENCE: I don't know if this +falls under what [INAUDIBLE]. + +It probably does. + +But insurance because I think +bearing responsibility for + +major things that are external +to their future [INAUDIBLE], + +whereas if you bring +[INAUDIBLE]. + +PROFESSOR: Right. + +So that's absolutely right. + +In the US, if there's a big +storm then FEMA steps in. + +And sometimes it doesn't work +so well like in New Orleans. + +But it's on average that there's +a huge number of + +federal agencies that are there +to guarantee you some + +minimum living and to help you +rebuild your houses and all + +that disaster relief. + +If the same storm happens in +some less well run country + +then in some sense +you know that is + +going to be your problem. + +So you spend all your time +worrying about what will you + +have to do about it. + +In the US, you basically know +that if it's something that's + +really out of control then it +will be taken care of mostly. + +And that's even more true +in other countries. + +Among rich countries, the US is +particularly laissez faire. + +AUDIENCE: [INAUDIBLE] you're +saying [INAUDIBLE] + +poor people than +poor countries. + +Because I think that a lot of +this stuff, this also does + +apply [INAUDIBLE]. + +PROFESSOR: Absolutely. + +So I think poor people in rich +countries have many of the + +same issues. + +For example, if you don't have +a regular job, you don't get + +health insurance. + +You don't get pensions. + +So you have to then decide to +do your savings on your own. + +You have to find a way to fund +your health problems on your + +own, et cetera. + +You bear much more response-- +for an MIT professor, so many + +things are taken care of, which +if you were poor, they + +wouldn't be. + +So that's absolutely right. + +This is also true, as Melissa +said, of poor people all over + +the world, including the US. + +Markets will work less +well for poor people. + +And the corollary of that is +therefore you should not + +always pin your fate on +markets delivering. + +So what's an example of markets +working less well for + +people and why would they +work less well? + +Yeah. + +AUDIENCE: The insurance market, +performing [INAUDIBLE] + +just because the information +[INAUDIBLE] + +to form institutions in some of, +I guess, the [INAUDIBLE]. + +So that's why they form more +informal insurance markets + +where family members and +community members try to + +insure against a bad shock. + +PROFESSOR: Right. + +That's a great example. + +You don't really have access +to formal insurance because + +maybe you are just not valuable +enough and you're too + +far away from the insurance +company. + +Yeah. + +AUDIENCE: I guess the mosquito +net market because they don't + +see the importance +or the value of + +buying a mosquito net. + +So you have to give it away +first to convince them of its + +importance. + +But you also have to make sure +to give it away [INAUDIBLE]. + +PROFESSOR: They don't mostly. + +I think we talked about the +evidence [INAUDIBLE]. + +Yep. + +AUDIENCE: There's talk about the +fertilizer market and how + +people might have had money +at the right time when + +[INAUDIBLE]. + +PROFESSOR: If you have +no place to sort of-- + +one thing that makes life very +difficult for people in + +agriculture it that they +get their entire + +salary all at once. + +And then they have to figure out +a way to spend it smoothly + +over a period of time because +they're going to get no money + +for a long time. + +We get paid every week +or every month. + +So even if you spent the last +month's income, we have this + +month's income coming in. + +If you have an income every six +months, you have to have + +that much more self restraint. + +And so poor people are often +farmers, and they have to deal + +with these very large ups and +downs in incomes which we + +don't have a deal with at all. + +Yeah. + +AUDIENCE: Maybe of giving +things away. + +You have to give away +a bag of rice to get + +people to get vaccines. + +So it's more about +the [INAUDIBLE]. + +PROFESSOR: Yeah. + +Exactly. + +Once the market doesn't +work then you have to + +think of what to do. + +We talked about the credit +market where in the credit + +market the reason why the poor +end up paying much higher + +interest rates is because +there's this vicious circle of + +if you are poor then nobody's +going to lend + +you a lot of money. + +So since you're going to be lent +a very small amount of + +money then the interest rate +will have to cover the cost of + +enforcing the loan. + +And that's kind of +a fixed cost. + +So if that's, let's say, $10 +and you are borrowing $10 + +million, then that's nothing. + +If you were borrowing $10, then +that's, you know, 100%. + +So you get a much bigger +kick from having + +high interest rates. + +And then it turns into this kind +of further vicious cycle + +because if the interest rate is +high then the incentive to + +default is higher and then you +have to spend even more money + +making sure that people +don't default. + +But that then raises the +interest rate even more. + +So you get this vicious cycle of +you start by being poor and + +you end up with a very +high interest rate. + +That's one of the reasons why +the poor find it very + +difficult to borrow. + +So this one we talked +about already. + +This is the one we were +talking about a lot. + +So I'll skip it and go to the +last one, which is that a lot + +of what keeps people in +poverty is just the + +expectations of hopelessness +and + +expectations of negative outcomes. + +Do you want to give +examples of that? + +Yeah. + +AUDIENCE: [INAUDIBLE] + +give them a test and then told +them to stay for the test or + +not, like, making them +aware [INAUDIBLE]. + +PROFESSOR: Louder. + +AUDIENCE: Basically, in +education, students + +[INAUDIBLE]. + +PROFESSOR: Right. + +So students are often told that +because they didn't do + +well in their first grade test +that they're stupid. + +And if they believe they're +stupid, they stop trying. + +What's another example? + +AUDIENCE: That, like, we saw +that if the poor believe that + +they are not going to earn +much from a particular + +profession then they will not +pursue that [INAUDIBLE] + +business. + +PROFESSOR: Right. + +So if you think that the rewards +that you're going to + +get from some investment are +pretty small so your life + +won't really change in any +substantial way then you might + +just give up and not try very +much to do anything + +innovative. + +Yeah. + +AUDIENCE: There's also the +savings example of always + +expecting [INAUDIBLE] + +about that can be suspended as +who's qualified [INAUDIBLE]. + +Knowing that some things can +come up that's going to + +require money gives an incentive +to try to save. + +PROFESSOR: Right. + +So you might expect that +somebody will tax it away + +somehow and then you'll +never want to save. + +Any other examples? + +So I just wanted to then wrap +up in a couple of minutes. + +Let me say a couple of things. + +I'm going to wrap up in +a couple of minutes. + +One thing is that you should +really give us the evaluation + +for this class. + +It's the first time we taught it +in this format, and I have + +no idea what the specific +problems are and + +what we could do better. + +So it will be helpful for us. + +And it's only fair to the two +TAs who work very hard on this + +to get feedback on what they've +done because that + +actually matters for, for +example, when they go in the + +job market. + +This is something +that matters. + +I know it's something +easy to forget. + +But you should remember +to do it. + +Other than that, I guess, just +to wrap up, this was an + +attempt to kind of expose +you to how people-- + +I think mostly people from +sort of the community of + +people associated with the +Poverty Action Lab but also, I + +think, development, economics +more generally think about + +issues around poverty. + +And I think the thing that I +think you should take away + +from this is not that we have +solved the problem of poverty. + +I think that would be an +overstatement by some margin. + +But at least that at this point +that there's a huge gap + +between the way, kind of, the +journalistic accounts of + +poverty operate, the level at +which they operate and the + +level at which all of us now +after this conversation should + +approach it. + +In some ways there is a very +large and relatively stable + +body of knowledge about what +the big issues are and what + +the sticking points are. + +There's a sense in +which we are-- + +I don't know that we have +all the answers or + +even all the problems. + +But at least some problems have +been clearly identified. + +They keep coming back, +the same problems. + +And we kind of know how to think +about them, what can we + +do about it. + +In that sense there is a sense +in which I think there's + +reason to be optimistic. + +If you think about something I +keep saying, is that if you + +think about sort of social +policy and policy against + +poverty, the first thing to +remember is that this is an + +extraordinarily modern +invention, that basically + +other than supporting the +extremely destitute at some + +very low level there was no +government policy to help the + +poor at all really ever. + +If you were extremely poor, +somebody would feed you. + +But mostly there was +nothing else. + +I mean the education systems +really didn't exist except for + +the elites. + +Health systems didn't exist +except in the private market. + +And other forms of insurance +didn't exist. + +If you look at the world in +1900, the most striking fact + +about it is how small +governments are. + +No government is spending +more than 10% of GDP. + +Tax collections are maximum +10% of GDP. + +Now, if you take, like, Sweden, +tax collections are + +55% of GDP-- + +so just to think of the range. + +So what has happened over the +last 100 years, and actually + +not even 100 years, really after +the First World War, was + +a massive expansion of things +that governments do. + +And more generally a massive +expansion of systematic + +interventions to help people +live their lives better. + +Education systems massively +expanded. + +Health care massively +expanded. + +Social support programs +massively expanded. + +In general the world of sort +of interventions is a very + +modern world. + +This whole idea that there +should be social policy to + +help the poor and all of us +should worry about it is a + +very, very recent idea. + +So the fact that we haven't +got it right + +already is no surprise. + +In some sense, what happened was +even between 1920 or 1910 + +and 1950, there's a massive +expansion of governments in + +rich countries. + +Then a bunch of poor countries +became independent and they + +imitated the rich countries by +also substantially expanding + +their government. + +And then they often didn't have +the experience, the state + +capacity, the bureaucratic +capacity to + +implement those programs. + +So you've got a lot of things +happening which shouldn't have + +happened, lots of disasters. + +But in my view that +says very little. + +If you see that in the sweep of +history, in the last 10,000 + +years of history, this is +a period of 30 years in + +developing countries between +1960 and 1990. + +Governments expanded a lot. + +They tried a bunch +of new programs. + +Many of them failed. + +There was lots of corruption. + +But I think if you see the sweep +of history, we are just + +at the beginning of a process +of trying to create a more + +humane social policy. + +We're nowhere near the point +where we would like to be. + +And this is no accident. + +We just started. + +And in that sense, if you want +to take that perspective that + +this is really the beginning +in terms of any historical + +perspective, we are kind of at +a very early point, then I + +think the main lesson that we +suggest here should seem more + +plausible, which is that we +really don't know very much. + +We've been shooting +in the dark. + +We expanded too fast. + +We didn't know what +we were doing. + +And we're still very early +in the process. + +And what we need to do is step +back and figure out what works + +and how to make it work. + +And if you had to take +one lesson away from + +this class, it's that. + +But there is a way to learn much +better about what works + +and what doesn't. + +We haven't used it. + +And that's no accident +because we are just + +getting started really. + +I think once you remember that +lesson of history, I think + +things look less depressing and +more promising than they + +would look otherwise. + +I'm going to stop there. + +Thank you and good luck for the +final exam and for all the + +things you're going to +be doing after this. + +[APPLAUSE] \ No newline at end of file diff --git a/7io-8_I6ZXA.txt b/7io-8_I6ZXA.txt new file mode 100644 index 0000000000000000000000000000000000000000..079dec047195ca1229abf7afa8e85a2b72fe7c71 --- /dev/null +++ b/7io-8_I6ZXA.txt @@ -0,0 +1,3299 @@ +align:start position:0% + +so let's look at a little more detail at + + align:start position:0% +so let's look at a little more detail at + + + align:start position:0% +so let's look at a little more detail at +the + + align:start position:0% +the + + + align:start position:0% +the +equilibrium size of respiratory droplets + + align:start position:0% +equilibrium size of respiratory droplets + + + align:start position:0% +equilibrium size of respiratory droplets +that are emitted + + align:start position:0% +that are emitted + + + align:start position:0% +that are emitted +during breathing or coughing or speaking + + align:start position:0% +during breathing or coughing or speaking + + + align:start position:0% +during breathing or coughing or speaking +and the key idea is that these droplets + + align:start position:0% +and the key idea is that these droplets + + + align:start position:0% +and the key idea is that these droplets +are not pure liquid + + align:start position:0% +are not pure liquid + + + align:start position:0% +are not pure liquid +as explained in the wells curve pure + + align:start position:0% +as explained in the wells curve pure + + + align:start position:0% +as explained in the wells curve pure +droplets + + align:start position:0% +droplets + + + align:start position:0% +droplets +that are small enough will shrink + + align:start position:0% +that are small enough will shrink + + + align:start position:0% +that are small enough will shrink +completely and evaporate + + align:start position:0% +completely and evaporate + + + align:start position:0% +completely and evaporate +however these droplets contain a + + align:start position:0% +however these droplets contain a + + + align:start position:0% +however these droplets contain a +significant amount of + + align:start position:0% +significant amount of + + + align:start position:0% +significant amount of +uh of solutes and those solutes + + align:start position:0% +uh of solutes and those solutes + + + align:start position:0% +uh of solutes and those solutes +in the case of mucus coming from your + + align:start position:0% +in the case of mucus coming from your + + + align:start position:0% +in the case of mucus coming from your +lungs or from your vocal + + align:start position:0% +lungs or from your vocal + + + align:start position:0% +lungs or from your vocal +cords your nasopharynx are full of + + align:start position:0% +cords your nasopharynx are full of + + + align:start position:0% +cords your nasopharynx are full of +proteins and other macromolecules + + align:start position:0% +proteins and other macromolecules + + + align:start position:0% +proteins and other macromolecules +carbohydrates + + align:start position:0% +carbohydrates + + + align:start position:0% +carbohydrates +and also there are always in bodily + + align:start position:0% +and also there are always in bodily + + + align:start position:0% +and also there are always in bodily +fluids + + align:start position:0% +fluids + + + align:start position:0% +fluids +plenty of dissolved salts such as sodium + + align:start position:0% +plenty of dissolved salts such as sodium + + + align:start position:0% +plenty of dissolved salts such as sodium +and chloride + + align:start position:0% +and chloride + + + align:start position:0% +and chloride +or calcium or potassium ions + + align:start position:0% +or calcium or potassium ions + + + align:start position:0% +or calcium or potassium ions +also in saliva many of these species are + + align:start position:0% +also in saliva many of these species are + + + align:start position:0% +also in saliva many of these species are +present although it's not + + align:start position:0% +present although it's not + + + align:start position:0% +present although it's not +quite as thick of a liquid + + align:start position:0% +quite as thick of a liquid + + + align:start position:0% +quite as thick of a liquid +and of course virions as well we'll find + + align:start position:0% +and of course virions as well we'll find + + + align:start position:0% +and of course virions as well we'll find +themselves + + align:start position:0% +themselves + + + align:start position:0% +themselves +here and are also constitute solutes so + + align:start position:0% +here and are also constitute solutes so + + + align:start position:0% +here and are also constitute solutes so +the idea is that we don't just have a + + align:start position:0% +the idea is that we don't just have a + + + align:start position:0% +the idea is that we don't just have a +pure liquid so there is + + align:start position:0% +pure liquid so there is + + + align:start position:0% +pure liquid so there is +some initial volume fraction + + align:start position:0% +some initial volume fraction + + + align:start position:0% +some initial volume fraction +of solute in the liquid + + align:start position:0% + + + + align:start position:0% + +and in addition to that most of these + + align:start position:0% +and in addition to that most of these + + + align:start position:0% +and in addition to that most of these +liquids + + align:start position:0% +liquids + + + align:start position:0% +liquids +uh these these these sorry the solutes i + + align:start position:0% +uh these these these sorry the solutes i + + + align:start position:0% +uh these these these sorry the solutes i +should say + + align:start position:0% +should say + + + align:start position:0% +should say +are charged + + align:start position:0% + + + + align:start position:0% + +and thus hygroscopic + + align:start position:0% + + + + align:start position:0% + +what that means is that of course the + + align:start position:0% +what that means is that of course the + + + align:start position:0% +what that means is that of course the +salt + + align:start position:0% +salt + + + align:start position:0% +salt +those ions are literally charged species + + align:start position:0% +those ions are literally charged species + + + align:start position:0% +those ions are literally charged species +but also the proteins and other + + align:start position:0% +but also the proteins and other + + + align:start position:0% +but also the proteins and other +macromolecules have many charged + + align:start position:0% +macromolecules have many charged + + + align:start position:0% +macromolecules have many charged +residues and sites on the on their on + + align:start position:0% +residues and sites on the on their on + + + align:start position:0% +residues and sites on the on their on +their uh + + align:start position:0% +their uh + + + align:start position:0% +their uh +along the along the molecule which + + align:start position:0% +along the along the molecule which + + + align:start position:0% +along the along the molecule which +attract water and + + align:start position:0% +attract water and + + + align:start position:0% +attract water and +essentially there is a layer of bound + + align:start position:0% +essentially there is a layer of bound + + + align:start position:0% +essentially there is a layer of bound +water + + align:start position:0% +water + + + align:start position:0% +water +solvating all of these species i just + + align:start position:0% +solvating all of these species i just + + + align:start position:0% +solvating all of these species i just +mentioned including the virus + + align:start position:0% +mentioned including the virus + + + align:start position:0% +mentioned including the virus +so i'll just kind of sketch that there's + + align:start position:0% +so i'll just kind of sketch that there's + + + align:start position:0% +so i'll just kind of sketch that there's +you know kind of you know lots of bound + + align:start position:0% +you know kind of you know lots of bound + + + align:start position:0% +you know kind of you know lots of bound +water + + align:start position:0% +water + + + align:start position:0% +water +which is kind of surrounding each each + + align:start position:0% +which is kind of surrounding each each + + + align:start position:0% +which is kind of surrounding each each +species including the virus + + align:start position:0% +species including the virus + + + align:start position:0% +species including the virus +there's essentially a layer of water + + align:start position:0% +there's essentially a layer of water + + + align:start position:0% +there's essentially a layer of water +mostly around + + align:start position:0% +mostly around + + + align:start position:0% +mostly around +these uh molecules here and other + + align:start position:0% +these uh molecules here and other + + + align:start position:0% +these uh molecules here and other +species + + align:start position:0% +species + + + align:start position:0% +species +so it's solutes plus the bound water + + align:start position:0% +so it's solutes plus the bound water + + + align:start position:0% +so it's solutes plus the bound water +that's coming from solvation + + align:start position:0% +that's coming from solvation + + + align:start position:0% +that's coming from solvation +of these molecules and liquid so that + + align:start position:0% +of these molecules and liquid so that + + + align:start position:0% +of these molecules and liquid so that +water is pretty firmly attached and + + align:start position:0% +water is pretty firmly attached and + + + align:start position:0% +water is pretty firmly attached and +even if you dry the the material a lot + + align:start position:0% +even if you dry the the material a lot + + + align:start position:0% +even if you dry the the material a lot +of that water will still be left over it + + align:start position:0% +of that water will still be left over it + + + align:start position:0% +of that water will still be left over it +takes a significant amount of energy + + align:start position:0% +takes a significant amount of energy + + + align:start position:0% +takes a significant amount of energy +to remove it and so + + align:start position:0% +to remove it and so + + + align:start position:0% +to remove it and so +if we think that the if we describe + + align:start position:0% +if we think that the if we describe + + + align:start position:0% +if we think that the if we describe +there's initial volume of the droplet v0 + + align:start position:0% +there's initial volume of the droplet v0 + + + align:start position:0% +there's initial volume of the droplet v0 +and a radius uh + + align:start position:0% +and a radius uh + + + align:start position:0% +and a radius uh +r zero so let's say it's initially a + + align:start position:0% +r zero so let's say it's initially a + + + align:start position:0% +r zero so let's say it's initially a +circular droplet + + align:start position:0% +circular droplet + + + align:start position:0% +circular droplet +there is an initial amount of solid v s + + align:start position:0% +there is an initial amount of solid v s + + + align:start position:0% +there is an initial amount of solid v s +which is phi s zero times v zero so a + + align:start position:0% +which is phi s zero times v zero so a + + + align:start position:0% +which is phi s zero times v zero so a +certain amount of solutes in + + align:start position:0% +certain amount of solutes in + + + align:start position:0% +certain amount of solutes in +there which cannot be removed so the + + align:start position:0% +there which cannot be removed so the + + + align:start position:0% +there which cannot be removed so the +water can evaporate but the solutes + + align:start position:0% +water can evaporate but the solutes + + + align:start position:0% +water can evaporate but the solutes +will not so let's think a little bit + + align:start position:0% +will not so let's think a little bit + + + align:start position:0% +will not so let's think a little bit +about what the consequences of that are + + align:start position:0% +about what the consequences of that are + + + align:start position:0% +about what the consequences of that are +so let me do a brief derivation here uh + + align:start position:0% +so let me do a brief derivation here uh + + + align:start position:0% +so let me do a brief derivation here uh +from the looking at the thermodynamics + + align:start position:0% +from the looking at the thermodynamics + + + align:start position:0% +from the looking at the thermodynamics +of this system + + align:start position:0% +of this system + + + align:start position:0% +of this system +and the key idea is just to get to the + + align:start position:0% +and the key idea is just to get to the + + + align:start position:0% +and the key idea is just to get to the +final result i don't want to dwell on + + align:start position:0% +final result i don't want to dwell on + + + align:start position:0% +final result i don't want to dwell on +the details of thermodynamics + + align:start position:0% +the details of thermodynamics + + + align:start position:0% +the details of thermodynamics +but an important concept here is the + + align:start position:0% +but an important concept here is the + + + align:start position:0% +but an important concept here is the +relative + + align:start position:0% +relative + + + align:start position:0% +relative +humidity of the air + + align:start position:0% +humidity of the air + + + align:start position:0% +humidity of the air +so there's moisture in the air there's + + align:start position:0% +so there's moisture in the air there's + + + align:start position:0% +so there's moisture in the air there's +water vapor and + + align:start position:0% +water vapor and + + + align:start position:0% +water vapor and +it's at a certain level so + + align:start position:0% +it's at a certain level so + + + align:start position:0% +it's at a certain level so +we often write that rh for relative + + align:start position:0% +we often write that rh for relative + + + align:start position:0% +we often write that rh for relative +humidity + + align:start position:0% +humidity + + + align:start position:0% +humidity +and that can be defined as the + + align:start position:0% +and that can be defined as the + + + align:start position:0% +and that can be defined as the +concentration of vapor + + align:start position:0% +concentration of vapor + + + align:start position:0% +concentration of vapor +water vapor in the air relative + + align:start position:0% +water vapor in the air relative + + + align:start position:0% +water vapor in the air relative +to the vapor concentration that would be + + align:start position:0% +to the vapor concentration that would be + + + align:start position:0% +to the vapor concentration that would be +in + + align:start position:0% +in + + + align:start position:0% +in +equilibrium with pure liquid so when + + align:start position:0% +equilibrium with pure liquid so when + + + align:start position:0% +equilibrium with pure liquid so when +the concentration of water vapor gets + + align:start position:0% +the concentration of water vapor gets + + + align:start position:0% +the concentration of water vapor gets +high enough + + align:start position:0% +high enough + + + align:start position:0% +high enough +eventually you start to nucleate water + + align:start position:0% +eventually you start to nucleate water + + + align:start position:0% +eventually you start to nucleate water +droplets + + align:start position:0% +droplets + + + align:start position:0% +droplets +and you start to have condensation water + + align:start position:0% +and you start to have condensation water + + + align:start position:0% +and you start to have condensation water +that's essentially how rain + + align:start position:0% +that's essentially how rain + + + align:start position:0% +that's essentially how rain +forms from the clouds so + + align:start position:0% +forms from the clouds so + + + align:start position:0% +forms from the clouds so +that's that ratio so relative humidity + + align:start position:0% +that's that ratio so relative humidity + + + align:start position:0% +that's that ratio so relative humidity +is telling you how close you are to + + align:start position:0% +is telling you how close you are to + + + align:start position:0% +is telling you how close you are to +basically having water liquid water come + + align:start position:0% +basically having water liquid water come + + + align:start position:0% +basically having water liquid water come +out of the air okay now + + align:start position:0% +out of the air okay now + + + align:start position:0% +out of the air okay now +the relative humidity also tells us + + align:start position:0% +the relative humidity also tells us + + + align:start position:0% +the relative humidity also tells us +something about the + + align:start position:0% +something about the + + + align:start position:0% +something about the +uh sort of how far you are from that + + align:start position:0% +uh sort of how far you are from that + + + align:start position:0% +uh sort of how far you are from that +phase transition point + + align:start position:0% +phase transition point + + + align:start position:0% +phase transition point +and as a very simple approximation i'll + + align:start position:0% +and as a very simple approximation i'll + + + align:start position:0% +and as a very simple approximation i'll +put approximate here + + align:start position:0% +put approximate here + + + align:start position:0% +put approximate here +we can also write that this is + + align:start position:0% +we can also write that this is + + + align:start position:0% +we can also write that this is +scales width and is can be in fact close + + align:start position:0% +scales width and is can be in fact close + + + align:start position:0% +scales width and is can be in fact close +to + + align:start position:0% +to + + + align:start position:0% +to +the liquid volume fraction in + + align:start position:0% +the liquid volume fraction in + + + align:start position:0% +the liquid volume fraction in +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +inside the drop so that'll be the water + + align:start position:0% +inside the drop so that'll be the water + + + align:start position:0% +inside the drop so that'll be the water +volume fraction of water liquid + + align:start position:0% +volume fraction of water liquid + + + align:start position:0% +volume fraction of water liquid +inside the droplet at least you can see + + align:start position:0% +inside the droplet at least you can see + + + align:start position:0% +inside the droplet at least you can see +here in this relationship + + align:start position:0% +here in this relationship + + + align:start position:0% +here in this relationship +when this volume fraction is one in + + align:start position:0% +when this volume fraction is one in + + + align:start position:0% +when this volume fraction is one in +other words we have pure water + + align:start position:0% +other words we have pure water + + + align:start position:0% +other words we have pure water +then the rate of humidity is 100 okay + + align:start position:0% +then the rate of humidity is 100 okay + + + align:start position:0% +then the rate of humidity is 100 okay +and on the other hand when you have + + align:start position:0% +and on the other hand when you have + + + align:start position:0% +and on the other hand when you have +let's say only you know 50 + + align:start position:0% +let's say only you know 50 + + + align:start position:0% +let's say only you know 50 +water over here that's like having + + align:start position:0% +water over here that's like having + + + align:start position:0% +water over here that's like having +relative humidity 50 + + align:start position:0% +relative humidity 50 + + + align:start position:0% +relative humidity 50 +where this can be derived by more + + align:start position:0% +where this can be derived by more + + + align:start position:0% +where this can be derived by more +careful consideration of the ideal + + align:start position:0% +careful consideration of the ideal + + + align:start position:0% +careful consideration of the ideal +entropy of mixing + + align:start position:0% +entropy of mixing + + + align:start position:0% +entropy of mixing +where essentially this term here is + + align:start position:0% +where essentially this term here is + + + align:start position:0% +where essentially this term here is +taking into account the excluded volume + + align:start position:0% +taking into account the excluded volume + + + align:start position:0% +taking into account the excluded volume +and the fact that sort of all the sites + + align:start position:0% +and the fact that sort of all the sites + + + align:start position:0% +and the fact that sort of all the sites +uh you know in this + + align:start position:0% +uh you know in this + + + align:start position:0% +uh you know in this +uh in this in this droplet are not + + align:start position:0% +uh in this in this droplet are not + + + align:start position:0% +uh in this in this droplet are not +available for the water + + align:start position:0% +available for the water + + + align:start position:0% +available for the water +so they're being excluded by all the + + align:start position:0% +so they're being excluded by all the + + + align:start position:0% +so they're being excluded by all the +solutes and the bound water that are + + align:start position:0% +solutes and the bound water that are + + + align:start position:0% +solutes and the bound water that are +present + + align:start position:0% +present + + + align:start position:0% +present +and similarly we have a buildup of uh + + align:start position:0% +and similarly we have a buildup of uh + + + align:start position:0% +and similarly we have a buildup of uh +sort of free energy in the in the in the + + align:start position:0% +sort of free energy in the in the in the + + + align:start position:0% +sort of free energy in the in the in the +bulk as well + + align:start position:0% +bulk as well + + + align:start position:0% +bulk as well +so basically this comes from some + + align:start position:0% +so basically this comes from some + + + align:start position:0% +so basically this comes from some +thermodynamic considerations of + + align:start position:0% +thermodynamic considerations of + + + align:start position:0% +thermodynamic considerations of +equilibrium between water vapor + + align:start position:0% +equilibrium between water vapor + + + align:start position:0% +equilibrium between water vapor +and water liquid we can write this + + align:start position:0% +and water liquid we can write this + + + align:start position:0% +and water liquid we can write this +as 1 minus the volume fraction + + align:start position:0% +as 1 minus the volume fraction + + + align:start position:0% +as 1 minus the volume fraction +in equilibrium of the solid + + align:start position:0% +in equilibrium of the solid + + + align:start position:0% +in equilibrium of the solid +okay now the thing is that we can now uh + + align:start position:0% +okay now the thing is that we can now uh + + + align:start position:0% +okay now the thing is that we can now uh +write this so if we multiply um through + + align:start position:0% +write this so if we multiply um through + + + align:start position:0% +write this so if we multiply um through +we can write this as one + + align:start position:0% +we can write this as one + + + align:start position:0% +we can write this as one +minus the uh + + align:start position:0% +minus the uh + + + align:start position:0% +minus the uh +so so what is the volume so when we get + + align:start position:0% +so so what is the volume so when we get + + + align:start position:0% +so so what is the volume so when we get +to equilibrium this droplet is going to + + align:start position:0% +to equilibrium this droplet is going to + + + align:start position:0% +to equilibrium this droplet is going to +change its shape it's going to reach a + + align:start position:0% +change its shape it's going to reach a + + + align:start position:0% +change its shape it's going to reach a +new shape which we're going to calculate + + align:start position:0% +new shape which we're going to calculate + + + align:start position:0% +new shape which we're going to calculate +our new volume + + align:start position:0% +our new volume + + + align:start position:0% +our new volume +v equilibrium and so what this would be + + align:start position:0% +v equilibrium and so what this would be + + + align:start position:0% +v equilibrium and so what this would be +would be v + + align:start position:0% +would be v + + + align:start position:0% +would be v +solid which is phi s + + align:start position:0% +solid which is phi s + + + align:start position:0% +solid which is phi s +0 v 0 divided by v equilibrium + + align:start position:0% +0 v 0 divided by v equilibrium + + + align:start position:0% +0 v 0 divided by v equilibrium +so it's a new volume v equilibrium which + + align:start position:0% +so it's a new volume v equilibrium which + + + align:start position:0% +so it's a new volume v equilibrium which +will be + + align:start position:0% +will be + + + align:start position:0% +will be +you know achieved then and then we'll + + align:start position:0% +you know achieved then and then we'll + + + align:start position:0% +you know achieved then and then we'll +end up with the equilibrium volume + + align:start position:0% +end up with the equilibrium volume + + + align:start position:0% +end up with the equilibrium volume +fraction + + align:start position:0% +fraction + + + align:start position:0% +fraction +so if i take these equations here and i + + align:start position:0% +so if i take these equations here and i + + + align:start position:0% +so if i take these equations here and i +solve + + align:start position:0% +solve + + + align:start position:0% +solve +i get a fundamental result which is that + + align:start position:0% +i get a fundamental result which is that + + + align:start position:0% +i get a fundamental result which is that +uh the equilibrium volume of the droplet + + align:start position:0% +uh the equilibrium volume of the droplet + + + align:start position:0% +uh the equilibrium volume of the droplet +relative to the initial volume + + align:start position:0% +relative to the initial volume + + + align:start position:0% +relative to the initial volume +is equal to well we have + + align:start position:0% +is equal to well we have + + + align:start position:0% +is equal to well we have +uh put this on the other side then we + + align:start position:0% +uh put this on the other side then we + + + align:start position:0% +uh put this on the other side then we +have 1 minus rh + + align:start position:0% +have 1 minus rh + + + align:start position:0% +have 1 minus rh +and we divide that out and we find that + + align:start position:0% +and we divide that out and we find that + + + align:start position:0% +and we divide that out and we find that +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +initial volume fraction of solutes + + align:start position:0% +initial volume fraction of solutes + + + align:start position:0% +initial volume fraction of solutes +divided by 1 minus + + align:start position:0% +divided by 1 minus + + + align:start position:0% +divided by 1 minus +rh that is our key result + + align:start position:0% +rh that is our key result + + + align:start position:0% +rh that is our key result +and let's plot what this looks like so + + align:start position:0% +and let's plot what this looks like so + + + align:start position:0% +and let's plot what this looks like so +uh + + align:start position:0% + + + + align:start position:0% + +so if we plot the relative humidity on + + align:start position:0% +so if we plot the relative humidity on + + + align:start position:0% +so if we plot the relative humidity on +the horizontal axis + + align:start position:0% +the horizontal axis + + + align:start position:0% +the horizontal axis +from zero to a hundred percent so at a + + align:start position:0% +from zero to a hundred percent so at a + + + align:start position:0% +from zero to a hundred percent so at a +hundred percent + + align:start position:0% +hundred percent + + + align:start position:0% +hundred percent +the water vapor is saturating the air + + align:start position:0% +the water vapor is saturating the air + + + align:start position:0% +the water vapor is saturating the air +and you would start to + + align:start position:0% +and you would start to + + + align:start position:0% +and you would start to +nucleating condensed water liquid from + + align:start position:0% +nucleating condensed water liquid from + + + align:start position:0% +nucleating condensed water liquid from +that at zero the air is completely dry + + align:start position:0% +that at zero the air is completely dry + + + align:start position:0% +that at zero the air is completely dry +and there's essentially + + align:start position:0% +and there's essentially + + + align:start position:0% +and there's essentially +no water vapor present so that's the + + align:start position:0% +no water vapor present so that's the + + + align:start position:0% +no water vapor present so that's the +range and typical comfortable rooms have + + align:start position:0% +range and typical comfortable rooms have + + + align:start position:0% +range and typical comfortable rooms have +a relative humidity around 50 + + align:start position:0% +a relative humidity around 50 + + + align:start position:0% +a relative humidity around 50 +is a typical number and let's plot on + + align:start position:0% +is a typical number and let's plot on + + + align:start position:0% +is a typical number and let's plot on +this axis + + align:start position:0% +this axis + + + align:start position:0% +this axis +the vol the equilibrium volume + + align:start position:0% +the vol the equilibrium volume + + + align:start position:0% +the vol the equilibrium volume +it could also be the equilibrium radius + + align:start position:0% +it could also be the equilibrium radius + + + align:start position:0% +it could also be the equilibrium radius +because i should say + + align:start position:0% +because i should say + + + align:start position:0% +because i should say +that if there are spheres that this is + + align:start position:0% +that if there are spheres that this is + + + align:start position:0% +that if there are spheres that this is +also equal to our equilibrium + + align:start position:0% +also equal to our equilibrium + + + align:start position:0% +also equal to our equilibrium +divided by r0 q + + align:start position:0% +divided by r0 q + + + align:start position:0% +divided by r0 q +so i can also take a cube root of this + + align:start position:0% +so i can also take a cube root of this + + + align:start position:0% +so i can also take a cube root of this +and i would have the ratio of radii so + + align:start position:0% +and i would have the ratio of radii so + + + align:start position:0% +and i would have the ratio of radii so +we would know if we started at a certain + + align:start position:0% +we would know if we started at a certain + + + align:start position:0% +we would know if we started at a certain +radius what's the final radius + + align:start position:0% +radius what's the final radius + + + align:start position:0% +radius what's the final radius +okay so we can talk about volume we can + + align:start position:0% +okay so we can talk about volume we can + + + align:start position:0% +okay so we can talk about volume we can +talk about radius + + align:start position:0% +talk about radius + + + align:start position:0% +talk about radius +so here is the initial size of the drop + + align:start position:0% +so here is the initial size of the drop + + + align:start position:0% +so here is the initial size of the drop +and somewhere down here + + align:start position:0% +and somewhere down here + + + align:start position:0% +and somewhere down here +is v s which is the solute + + align:start position:0% +is v s which is the solute + + + align:start position:0% +is v s which is the solute +volume which is phi s + + align:start position:0% +volume which is phi s + + + align:start position:0% +volume which is phi s +0 times v 0. now what is this value + + align:start position:0% +0 times v 0. now what is this value + + + align:start position:0% +0 times v 0. now what is this value +it depends on the kind of liquid so + + align:start position:0% +it depends on the kind of liquid so + + + align:start position:0% +it depends on the kind of liquid so +saliva + + align:start position:0% +saliva + + + align:start position:0% +saliva +is mostly water with some salt and a few + + align:start position:0% +is mostly water with some salt and a few + + + align:start position:0% +is mostly water with some salt and a few +other molecules + + align:start position:0% +other molecules + + + align:start position:0% +other molecules +but in saliva the volume fraction + + align:start position:0% + + + + align:start position:0% + +phi s0 is 0.5 + + align:start position:0% +phi s0 is 0.5 + + + align:start position:0% +phi s0 is 0.5 +uh in saliva okay so that's just gives + + align:start position:0% +uh in saliva okay so that's just gives + + + align:start position:0% +uh in saliva okay so that's just gives +you a sense so this is + + align:start position:0% +you a sense so this is + + + align:start position:0% +you a sense so this is +quite far down right but then + + align:start position:0% +quite far down right but then + + + align:start position:0% +quite far down right but then +if you look in mucus it depends which + + align:start position:0% +if you look in mucus it depends which + + + align:start position:0% +if you look in mucus it depends which +mucus you're talking about but the mucus + + align:start position:0% +mucus you're talking about but the mucus + + + align:start position:0% +mucus you're talking about but the mucus +that comes from the lungs or from + + align:start position:0% +that comes from the lungs or from + + + align:start position:0% +that comes from the lungs or from +from the pharynx it can vary but + + align:start position:0% +from the pharynx it can vary but + + + align:start position:0% +from the pharynx it can vary but +what has also been measured in droplets + + align:start position:0% +what has also been measured in droplets + + + align:start position:0% +what has also been measured in droplets +that are emitted by breathing + + align:start position:0% +that are emitted by breathing + + + align:start position:0% +that are emitted by breathing +is that this can range anywhere from + + align:start position:0% +is that this can range anywhere from + + + align:start position:0% +is that this can range anywhere from +five to ten percent + + align:start position:0% +five to ten percent + + + align:start position:0% +five to ten percent +so a fairly significant amount of the + + align:start position:0% +so a fairly significant amount of the + + + align:start position:0% +so a fairly significant amount of the +volume of the droplet + + align:start position:0% +volume of the droplet + + + align:start position:0% +volume of the droplet +is containing all these molecules and + + align:start position:0% +is containing all these molecules and + + + align:start position:0% +is containing all these molecules and +the bound water around that now we know + + align:start position:0% +the bound water around that now we know + + + align:start position:0% +the bound water around that now we know +that because mucus is very sticky it's a + + align:start position:0% +that because mucus is very sticky it's a + + + align:start position:0% +that because mucus is very sticky it's a +non-newtonian fluid + + align:start position:0% +non-newtonian fluid + + + align:start position:0% +non-newtonian fluid +it doesn't maintain a nice round shape + + align:start position:0% +it doesn't maintain a nice round shape + + + align:start position:0% +it doesn't maintain a nice round shape +even it can kind of + + align:start position:0% +even it can kind of + + + align:start position:0% +even it can kind of +have an irregular shape it flows slowly + + align:start position:0% +have an irregular shape it flows slowly + + + align:start position:0% +have an irregular shape it flows slowly +it has a high viscosity + + align:start position:0% +it has a high viscosity + + + align:start position:0% +it has a high viscosity +and that's because it has a large amount + + align:start position:0% +and that's because it has a large amount + + + align:start position:0% +and that's because it has a large amount +of these + + align:start position:0% +of these + + + align:start position:0% +of these +hygroscopic solutes so mucous might be a + + align:start position:0% +hygroscopic solutes so mucous might be a + + + align:start position:0% +hygroscopic solutes so mucous might be a +little bit higher up + + align:start position:0% +little bit higher up + + + align:start position:0% +little bit higher up +but in any case what you then find is uh + + align:start position:0% + + + + align:start position:0% + +we can sketch different regions of this + + align:start position:0% +we can sketch different regions of this + + + align:start position:0% +we can sketch different regions of this +plot now + + align:start position:0% +plot now + + + align:start position:0% +plot now +so this curve this this formula i + + align:start position:0% +so this curve this this formula i + + + align:start position:0% +so this curve this this formula i +derived here + + align:start position:0% +derived here + + + align:start position:0% +derived here +when the relative minute is zero we + + align:start position:0% +when the relative minute is zero we + + + align:start position:0% +when the relative minute is zero we +start here + + align:start position:0% +start here + + + align:start position:0% +start here +so that's saying when there's no water + + align:start position:0% +so that's saying when there's no water + + + align:start position:0% +so that's saying when there's no water +in the air you completely dry the + + align:start position:0% +in the air you completely dry the + + + align:start position:0% +in the air you completely dry the +droplet and you're left + + align:start position:0% +droplet and you're left + + + align:start position:0% +droplet and you're left +just with the molecules the solute + + align:start position:0% +just with the molecules the solute + + + align:start position:0% +just with the molecules the solute +molecules and + + align:start position:0% +molecules and + + + align:start position:0% +molecules and +possibly the bound water around it + + align:start position:0% +possibly the bound water around it + + + align:start position:0% +possibly the bound water around it +depending on how dry the air actually is + + align:start position:0% +depending on how dry the air actually is + + + align:start position:0% +depending on how dry the air actually is +and then it rises up like it and blows + + align:start position:0% +and then it rises up like it and blows + + + align:start position:0% +and then it rises up like it and blows +up at 100 percent so + + align:start position:0% +up at 100 percent so + + + align:start position:0% +up at 100 percent so +when you get 100 then droplets are + + align:start position:0% +when you get 100 then droplets are + + + align:start position:0% +when you get 100 then droplets are +getting + + align:start position:0% +getting + + + align:start position:0% +getting +really large okay and if you actually + + align:start position:0% +really large okay and if you actually + + + align:start position:0% +really large okay and if you actually +hit hundred percent then you can't + + align:start position:0% +hit hundred percent then you can't + + + align:start position:0% +hit hundred percent then you can't +really speak of an equilibrium size + + align:start position:0% +really speak of an equilibrium size + + + align:start position:0% +really speak of an equilibrium size +because you'll just start to get lots + + align:start position:0% +because you'll just start to get lots + + + align:start position:0% +because you'll just start to get lots +and lots of water + + align:start position:0% +and lots of water + + + align:start position:0% +and lots of water +um so that's that's that limit and so + + align:start position:0% +um so that's that's that limit and so + + + align:start position:0% +um so that's that's that limit and so +now we can look at sort of three + + align:start position:0% +now we can look at sort of three + + + align:start position:0% +now we can look at sort of three +different regimes + + align:start position:0% +different regimes + + + align:start position:0% +different regimes +uh of the kinds of droplets that we'd + + align:start position:0% +uh of the kinds of droplets that we'd + + + align:start position:0% +uh of the kinds of droplets that we'd +expect to see + + align:start position:0% +expect to see + + + align:start position:0% +expect to see +so down here at zero percent or close to + + align:start position:0% +so down here at zero percent or close to + + + align:start position:0% +so down here at zero percent or close to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +we have a sort of dried + + align:start position:0% +we have a sort of dried + + + align:start position:0% +we have a sort of dried +droplet nuclei as they're called in the + + align:start position:0% +droplet nuclei as they're called in the + + + align:start position:0% +droplet nuclei as they're called in the +public health field + + align:start position:0% +public health field + + + align:start position:0% +public health field +uh these respiratory aerosols if they + + align:start position:0% +uh these respiratory aerosols if they + + + align:start position:0% +uh these respiratory aerosols if they +completely dry out + + align:start position:0% +completely dry out + + + align:start position:0% +completely dry out +and you're left with just these solutes + + align:start position:0% +and you're left with just these solutes + + + align:start position:0% +and you're left with just these solutes +then that's called a droplet nucleus so + + align:start position:0% +then that's called a droplet nucleus so + + + align:start position:0% +then that's called a droplet nucleus so +it doesn't necessarily mean it's a + + align:start position:0% +it doesn't necessarily mean it's a + + + align:start position:0% +it doesn't necessarily mean it's a +nucleus for a phase transformation as we + + align:start position:0% +nucleus for a phase transformation as we + + + align:start position:0% +nucleus for a phase transformation as we +use that term + + align:start position:0% +use that term + + + align:start position:0% +use that term +in say engineering or in physics but + + align:start position:0% +in say engineering or in physics but + + + align:start position:0% +in say engineering or in physics but +it's really just sort of + + align:start position:0% +it's really just sort of + + + align:start position:0% +it's really just sort of +refers to the core of just the sort of + + align:start position:0% +refers to the core of just the sort of + + + align:start position:0% +refers to the core of just the sort of +hydrated solutes + + align:start position:0% +hydrated solutes + + + align:start position:0% +hydrated solutes +so if i could sketch what that looks + + align:start position:0% +so if i could sketch what that looks + + + align:start position:0% +so if i could sketch what that looks +like that would be + + align:start position:0% +like that would be + + + align:start position:0% +like that would be +for example all those molecules i just + + align:start position:0% +for example all those molecules i just + + + align:start position:0% +for example all those molecules i just +sketched there you know might be kind of + + align:start position:0% +sketched there you know might be kind of + + + align:start position:0% +sketched there you know might be kind of +condensed into some little blob + + align:start position:0% +condensed into some little blob + + + align:start position:0% +condensed into some little blob +which by the way could include a virion + + align:start position:0% +which by the way could include a virion + + + align:start position:0% +which by the way could include a virion +in fact it could even be just one virion + + align:start position:0% +in fact it could even be just one virion + + + align:start position:0% +in fact it could even be just one virion +if that were all that were in the in + + align:start position:0% +if that were all that were in the in + + + align:start position:0% +if that were all that were in the in +this in there + + align:start position:0% +this in there + + + align:start position:0% +this in there +and you would have a little bit of bound + + align:start position:0% +and you would have a little bit of bound + + + align:start position:0% +and you would have a little bit of bound +water + + align:start position:0% +water + + + align:start position:0% +water +around it but you essentially have a + + align:start position:0% +around it but you essentially have a + + + align:start position:0% +around it but you essentially have a +dried up + + align:start position:0% +dried up + + + align:start position:0% +dried up +kind of blob of just the solutes okay + + align:start position:0% +kind of blob of just the solutes okay + + + align:start position:0% +kind of blob of just the solutes okay +and so that and then of course the + + align:start position:0% +and so that and then of course the + + + align:start position:0% +and so that and then of course the +smallest volume you can get + + align:start position:0% +smallest volume you can get + + + align:start position:0% +smallest volume you can get +is just the salt the initial solute + + align:start position:0% +is just the salt the initial solute + + + align:start position:0% +is just the salt the initial solute +volume that you started with + + align:start position:0% +volume that you started with + + + align:start position:0% +volume that you started with +plus the bound water on the other end + + align:start position:0% +plus the bound water on the other end + + + align:start position:0% +plus the bound water on the other end +if we are near 100 relative humidity + + align:start position:0% +if we are near 100 relative humidity + + + align:start position:0% +if we are near 100 relative humidity +then the fact that these are hydroscopic + + align:start position:0% +then the fact that these are hydroscopic + + + align:start position:0% +then the fact that these are hydroscopic +solutes which like to have water near + + align:start position:0% +solutes which like to have water near + + + align:start position:0% +solutes which like to have water near +them will form as a nucleation site to + + align:start position:0% +them will form as a nucleation site to + + + align:start position:0% +them will form as a nucleation site to +actually cause + + align:start position:0% +actually cause + + + align:start position:0% +actually cause +more and more water to grow and be + + align:start position:0% +more and more water to grow and be + + + align:start position:0% +more and more water to grow and be +absorbed into this droplet + + align:start position:0% +absorbed into this droplet + + + align:start position:0% +absorbed into this droplet +and not only do the droplets not shrink + + align:start position:0% +and not only do the droplets not shrink + + + align:start position:0% +and not only do the droplets not shrink +as predicted by the wells curve + + align:start position:0% +as predicted by the wells curve + + + align:start position:0% +as predicted by the wells curve +for a pure liquid but they can actually + + align:start position:0% +for a pure liquid but they can actually + + + align:start position:0% +for a pure liquid but they can actually +grow so if the size here is small enough + + align:start position:0% +grow so if the size here is small enough + + + align:start position:0% +grow so if the size here is small enough +to begin with let's say we're + + align:start position:0% +to begin with let's say we're + + + align:start position:0% +to begin with let's say we're +you know several micron droplet to begin + + align:start position:0% +you know several micron droplet to begin + + + align:start position:0% +you know several micron droplet to begin +with but it contains a lot of solutes + + align:start position:0% +with but it contains a lot of solutes + + + align:start position:0% +with but it contains a lot of solutes +and we're at very high humidity + + align:start position:0% +and we're at very high humidity + + + align:start position:0% +and we're at very high humidity +actually the particle can grow so over + + align:start position:0% +actually the particle can grow so over + + + align:start position:0% +actually the particle can grow so over +here + + align:start position:0% +here + + + align:start position:0% +here +we could end up with a + + align:start position:0% +we could end up with a + + + align:start position:0% +we could end up with a +even larger droplet than we started with + + align:start position:0% +even larger droplet than we started with + + + align:start position:0% +even larger droplet than we started with +where now + + align:start position:0% +where now + + + align:start position:0% +where now +because the humidity is so high we have + + align:start position:0% +because the humidity is so high we have + + + align:start position:0% +because the humidity is so high we have +the same number of molecules in there + + align:start position:0% +the same number of molecules in there + + + align:start position:0% +the same number of molecules in there +that i sketched before + + align:start position:0% + + + + align:start position:0% + +but it's more dilute now and there's + + align:start position:0% +but it's more dilute now and there's + + + align:start position:0% +but it's more dilute now and there's +maybe a virus + + align:start position:0% +maybe a virus + + + align:start position:0% +maybe a virus +or virion here and there and of course + + align:start position:0% +or virion here and there and of course + + + align:start position:0% +or virion here and there and of course +there's also + + align:start position:0% +there's also + + + align:start position:0% +there's also +some salt but basically the droplet is + + align:start position:0% +some salt but basically the droplet is + + + align:start position:0% +some salt but basically the droplet is +growing + + align:start position:0% +growing + + + align:start position:0% +growing +so here we have a + + align:start position:0% + + + + align:start position:0% + +hydroscopic growth + + align:start position:0% + + + + align:start position:0% + +and also we have what's called delhi + + align:start position:0% +and also we have what's called delhi + + + align:start position:0% +and also we have what's called delhi +quiescence + + align:start position:0% + + + + align:start position:0% + +which refers to water that's absorbing + + align:start position:0% +which refers to water that's absorbing + + + align:start position:0% +which refers to water that's absorbing +around these salt molecules and even + + align:start position:0% +around these salt molecules and even + + + align:start position:0% +around these salt molecules and even +causing some other molecules or charges + + align:start position:0% +causing some other molecules or charges + + + align:start position:0% +causing some other molecules or charges +on these macromolecules to dissolve into + + align:start position:0% +on these macromolecules to dissolve into + + + align:start position:0% +on these macromolecules to dissolve into +solution because there's more water + + align:start position:0% +solution because there's more water + + + align:start position:0% +solution because there's more water +present and it can solvate more species + + align:start position:0% +present and it can solvate more species + + + align:start position:0% +present and it can solvate more species +and so whereas hydroscopic growth refers + + align:start position:0% +and so whereas hydroscopic growth refers + + + align:start position:0% +and so whereas hydroscopic growth refers +to water being absorbed sort of into a + + align:start position:0% +to water being absorbed sort of into a + + + align:start position:0% +to water being absorbed sort of into a +more solid-like framework you can also + + align:start position:0% +more solid-like framework you can also + + + align:start position:0% +more solid-like framework you can also +be generating more aqueous solution + + align:start position:0% +be generating more aqueous solution + + + align:start position:0% +be generating more aqueous solution +which is deli questions + + align:start position:0% +which is deli questions + + + align:start position:0% +which is deli questions +so basically the droplet can actually + + align:start position:0% +so basically the droplet can actually + + + align:start position:0% +so basically the droplet can actually +grow and that would be sort of like when + + align:start position:0% +grow and that would be sort of like when + + + align:start position:0% +grow and that would be sort of like when +you're here let's just say + + align:start position:0% +you're here let's just say + + + align:start position:0% +you're here let's just say +and this might be when you're you know + + align:start position:0% +and this might be when you're you know + + + align:start position:0% +and this might be when you're you know +here + + align:start position:0% +here + + + align:start position:0% +here +and then of course when you're at 50 + + align:start position:0% +and then of course when you're at 50 + + + align:start position:0% +and then of course when you're at 50 +relative to midi you can see the droplet + + align:start position:0% +relative to midi you can see the droplet + + + align:start position:0% +relative to midi you can see the droplet +has shrunken + + align:start position:0% +has shrunken + + + align:start position:0% +has shrunken +but not all the way down to the initial + + align:start position:0% +but not all the way down to the initial + + + align:start position:0% +but not all the way down to the initial +solute volume fraction but something + + align:start position:0% +solute volume fraction but something + + + align:start position:0% +solute volume fraction but something +larger + + align:start position:0% +larger + + + align:start position:0% +larger +and in fact if the relative mini is 50 + + align:start position:0% +and in fact if the relative mini is 50 + + + align:start position:0% +and in fact if the relative mini is 50 +you end up at exactly twice the solid + + align:start position:0% +you end up at exactly twice the solid + + + align:start position:0% +you end up at exactly twice the solid +volume fraction + + align:start position:0% +volume fraction + + + align:start position:0% +volume fraction +so uh so if the solid volume fraction of + + align:start position:0% +so uh so if the solid volume fraction of + + + align:start position:0% +so uh so if the solid volume fraction of +mucus is 10 + + align:start position:0% +mucus is 10 + + + align:start position:0% +mucus is 10 +you may end up with a droplet uh that is + + align:start position:0% +you may end up with a droplet uh that is + + + align:start position:0% +you may end up with a droplet uh that is +maybe 20 percent of the volume so maybe + + align:start position:0% +maybe 20 percent of the volume so maybe + + + align:start position:0% +maybe 20 percent of the volume so maybe +looks you know something like this + + align:start position:0% +looks you know something like this + + + align:start position:0% +looks you know something like this +okay and so we have a little bit of + + align:start position:0% +okay and so we have a little bit of + + + align:start position:0% +okay and so we have a little bit of +shrinking going on + + align:start position:0% + + + + align:start position:0% + +and maybe there's even a virus in there + + align:start position:0% +and maybe there's even a virus in there + + + align:start position:0% +and maybe there's even a virus in there +as well + + align:start position:0% +as well + + + align:start position:0% +as well +but there is still plenty of water and + + align:start position:0% +but there is still plenty of water and + + + align:start position:0% +but there is still plenty of water and +so you can see also now the value of + + align:start position:0% +so you can see also now the value of + + + align:start position:0% +so you can see also now the value of +having + + align:start position:0% +having + + + align:start position:0% +having +solutes in mucus in terms of + + align:start position:0% +solutes in mucus in terms of + + + align:start position:0% +solutes in mucus in terms of +making the virions more viable and more + + align:start position:0% +making the virions more viable and more + + + align:start position:0% +making the virions more viable and more +easily transmittable because they hold + + align:start position:0% +easily transmittable because they hold + + + align:start position:0% +easily transmittable because they hold +onto the water + + align:start position:0% +onto the water + + + align:start position:0% +onto the water +so that the virion is in a sort of + + align:start position:0% +so that the virion is in a sort of + + + align:start position:0% +so that the virion is in a sort of +stable environment so that when it ends + + align:start position:0% +stable environment so that when it ends + + + align:start position:0% +stable environment so that when it ends +up + + align:start position:0% +up + + + align:start position:0% +up +being inhaled into someone else's lungs + + align:start position:0% +being inhaled into someone else's lungs + + + align:start position:0% +being inhaled into someone else's lungs +that it can then more easily + + align:start position:0% +that it can then more easily + + + align:start position:0% +that it can then more easily +sort of diffuse out of that that region + + align:start position:0% +sort of diffuse out of that that region + + + align:start position:0% +sort of diffuse out of that that region +and infect the host cells + + align:start position:0% +and infect the host cells + + + align:start position:0% +and infect the host cells +in contrast if you have a nearly pure + + align:start position:0% +in contrast if you have a nearly pure + + + align:start position:0% +in contrast if you have a nearly pure +liquid that the virion is in + + align:start position:0% +liquid that the virion is in + + + align:start position:0% +liquid that the virion is in +let's say pure water or even saliva + + align:start position:0% +let's say pure water or even saliva + + + align:start position:0% +let's say pure water or even saliva +which is actually mostly water + + align:start position:0% +which is actually mostly water + + + align:start position:0% +which is actually mostly water +then the droplet will shrink by a factor + + align:start position:0% +then the droplet will shrink by a factor + + + align:start position:0% +then the droplet will shrink by a factor +of 100 + + align:start position:0% +of 100 + + + align:start position:0% +of 100 +and it might be just literally a virion + + align:start position:0% +and it might be just literally a virion + + + align:start position:0% +and it might be just literally a virion +with a couple salt molecules + + align:start position:0% +with a couple salt molecules + + + align:start position:0% +with a couple salt molecules +a couple ions kind of just enveloped + + align:start position:0% +a couple ions kind of just enveloped + + + align:start position:0% +a couple ions kind of just enveloped +with a tiny bit of water and maybe and + + align:start position:0% +with a tiny bit of water and maybe and + + + align:start position:0% +with a tiny bit of water and maybe and +that + + align:start position:0% +that + + + align:start position:0% +that +i in some cases would be not as viable + + align:start position:0% +i in some cases would be not as viable + + + align:start position:0% +i in some cases would be not as viable +uh of a situation for the virion so + + align:start position:0% +uh of a situation for the virion so + + + align:start position:0% +uh of a situation for the virion so +basically the mucous fragments + + align:start position:0% +basically the mucous fragments + + + align:start position:0% +basically the mucous fragments +are likely to be the more common source + + align:start position:0% +are likely to be the more common source + + + align:start position:0% +are likely to be the more common source +of the aerosols + + align:start position:0% +of the aerosols + + + align:start position:0% +of the aerosols +that will stay in the air and remain + + align:start position:0% + + + + align:start position:0% + +infectious \ No newline at end of file diff --git a/81ZWzdj-I9w.txt b/81ZWzdj-I9w.txt new file mode 100644 index 0000000000000000000000000000000000000000..22728f9e70a869aaee34851c509787b8e9365330 --- /dev/null +++ b/81ZWzdj-I9w.txt @@ -0,0 +1,906 @@ +Welcome back guys. + +Today we're going to work on +a problem that tests your + +knowledge of joint PMFs. + +And we're also going to get +some practice computing + +conditional expectations and +conditional variances. + +So in this problem, we +are given a set of + +points in the xy plane. + +And we're told that these points +are equally likely. + +So there's eight of them. + +And each point has a + +probability of 1/8 of occurring. + +And we're also given this +list of questions. + +And we're going to work +through them together. + +So in part a, we are asked to +find the values of x that + +maximize the conditional +expectation of y given x. + +So jumping right in, this +is the quantity + +we're interested in. + +And so this quantity +is a function of x. + +You plug-in various +values of x. + +And then this will spit +out a scalar value. + +And that value will correspond +to the conditional expectation + +of y conditioned on the value +of x that you put in. + +So let's see, when x is equal +to 0, for instance, let's + +figure out what this value is. + +Well, when x is equal to 0 +we're living in a world, + +essentially, on this line. + +So that means that +only these two + +points could have occurred. + +And in particular, y can only +take on the values of 1 and 3. + +Now, since all these points in +the unconditional universe + +were equally likely, in the +conditional universe they will + +still be equally likely. + +So this happens with +probability 1/2. + +And this happens with +probability 1/2. + +And therefore, the expectation +would just be 3/2 plus 1/2 + +which is 4/2, or 2. + +But a much faster way of seeing +this-- and it's the + +strategy that I'm going to use +for the rest of the problem-- + +is to remember that +expectation acts + +like center of mass. + +So the center of mass, when +these two points are equally + +likely, is just the midpoint, +which of course is 2. + +So we're going to use that +intuition on the other ones. + +So I'm skipping to x is +equal to 2 because 1 + +and 3 are not possible. + +So when x is equal to 2, +y can only take on the + +values of 1 or 2. + +Again, they're equally likely. + +So the center of mass is in the +middle which happens at + +1.5 or 3/2. + + + +Similarly, x is equal to 4. + +We're living in this conditional +universe, where y + +can take on of these +four points with + +probability 1/4 each. + +And so again, we expect +the center of mass to + +be at 1.5 or 3/2. + +And this quantity is undefined +otherwise. + + + +OK, so we're almost done. + +Now we just need to find which +value of x maximizes this. + +Well, let's see, 2 is the +biggest quantity out of all of + +these numbers. + +So the maximum is 2. + +And it occurs when +x is equal to 0. + +So we come over here. + +And we found our answer. + +x is equal to 0 is the value, +which maximizes the + +conditional expectation +of y given x. + +So part b is very similar +to part a. + +But there is slightly more +computation involved. + +Because now we're dealing with +the variance and not an + +expectation. + +And variance is usually a little +bit tougher to compute. + +So we're going to start +in the same manner. + +But I want you guys to see if +you can figure out intuitively + +what the right value is. + +I'm going to do the entire +computation now. + +And then you can compare whether +your intuition matches + +with the real results. + +So variance of x conditioned +on a particular value of y, + +this is now a function of y. + +For each value of y you plug in +you're going to get out a + +scalar number. + +And that number represents the +conditional variance of x when + +you condition on the value +of y that you plugged in. + +So let's see, when y is equal +to 0 we have a nice case. + +If y is equal to 0 we have no +freedom about what x is. + +This is the only point that +could have occurred. + +Therefore, x definitely +takes on a value of 4. + +And there's no uncertainty +left. + +So in other words, the +variance is 0. + +Now, if y is equal to 1, x can +take on a value of 0, a value + +of 2 or a value of 4. + +And these all have the same +probability of occurring, of + +1/3, + +And again, the reasoning behind +that is that all eight + +points were equally likely in +the unconditional universe. + +If you condition on y being +equal to 1 these outcomes + +still have the same relative +frequency. + +Namely, they're still +equally likely. + +And since there are three +of them they now have a + +probability of 1/3 each. + +So we're going to go ahead and +use a formula that hopefully, + +you guys remember. + +So in particular, variance is +the expectation of x squared + +minus the expectation +of x all squared, + +the whole thing squared. + +So let's start by computing +this number first. + +So conditioned on y +is equal to 1-- + +so we're in this line-- + +the expectation of x +is just 2, right? + +The same center-of-mass +to argument. + +So this, we have a minus +2 squared over here. + +Now, x squared is only slightly +more difficult. + +With probability 1/3, +x squared will take + +on a value of 0. + +With probability 1/3, +x squared will take + +on a value of 4. + +I'm just doing 2 squared. + +And with probability 1/3, x +squared takes on a value of 4 + +squared or 16. + +So writing down when I just +said, we have 0 times 1/3 + +which is 0. + +We have 2 squared, which +is 4 times 1/3. + +And then we have 4 squared, +which is 16 times 1/3. + +And then we have our minus +4 from before. + +So doing this math out, we get, +let's see, 20/3 minus + +12/3, which is equal +to 8/3, or 8/3. + +So we'll come back up +here and put 8/3. + +So I realize I'm going through +this pretty quickly. + +Hopefully this step didn't +confuse you. + +Essentially, when I was doing +is, if you think of x squared + +as a new random variable, x +squared, the possible values + +that it can take on are 0, +4, and 16 when you're + +conditioning on y +is equal to 1. + +And so I was simply saying +that that random variable + +takes on those values with +equal probability. + +So let's move on to +the next one. + +So if we condition on y is equal +to 2 we're going to do a + +very similar computation. + +Oops, I shouldn't have +erased that. + +OK, so we're going to use the +same formula that we just + +used, which is the expectation +of x given y is equal to 2. + +Sorry, x squared minus the +expectation of x conditioned + +on y is equal to +2, all squared. + +So conditioned on y +is equal to 2, the + +expectation of x is 3. + +Same center of mass argument. + +So 3 squared is 9. + +And then x squared can +take on a value of 4. + +Or it can take on +a value of 16. + +And it does so with +equal probability. + +So we get 4/2, 4 +plus 16 over 2. + +So this is 2 plus 8, which +is 10, minus 9. + +That'll give us 1. + +So we get a 1 when +y is equal to 2. + +And last computation and +then we're done. + +I'm still recycling +the same formula. + +But now we're conditioning +on y is equal to 3. + +And then we'll be done with +this problem, I promise. + +OK, so when y is equal to 3 x +can take on the value of 0. + +Or it can take on +the value of 4. + +Those two points happen with +probability 1/2, 1/2. + +So the expectation is right +in the middle which is 2. + +So we get a minus 4. + +And similarly, x squared can +take on the value of 0. + +When x takes on the value of +0-- and that happens with + +probability 1/2-- + +similarly, x squared can take +on the value of 16 when x + +takes on the value of 4. + +And that happens with +probability 1/2. + +So we just have 0/2 +plus 16/2 minus 4. + +And this gives us 8 minus +4, which is simply 4. + +So finally, after all that +computation, we are done. + +We have the conditional +variance of x given y. + +Again, we're interested in when +this value is largest. + +And we see that 4 is the biggest +value in this column. + +And this value occurs when +y takes on a value of 3. + +So our answer, over here, +is y is equal to 3. + +All right, so now we're going to +switch gears in part c and + +d a little bit. + +And we're going to +be more concerned + +with PMFs, et cetera. + +So in part c, we're given a +random variable called r which + +is defined as the minimum +of x and y. + +So for instance, this +is the 0.01. + +The minimum of 0 and 1 is 0. + +So r would have a +value of 0 here. + +Now, we can be a little bit +smarter about this. + +If we plot the line, +y is equal to x. + +So that looks something +like this. + + + +We see that all of the points +below this line satisfy y + +being less or equal to x. + +And all the points above this +line have y greater than or + +equal to x. + +So if y is less than or equal to +x, you hopefully agree that + +here the min, or r, +is equal to y. + +But over here, the min, r, is +actually equal to x, since x + +is always smaller. + +So now we can go +ahead quickly. + +And I'm going to write the value +of r next each point + +using this rule. + +So here, r is the value +of y, which is 1. + +Here, r is equal to 0. + +Here r is 1. + +Here r is 2. + +Here r is 3. + +Over here, r is the +value of x. + +So r is equal to 0. + +And r is equal to 0 here. + +And so the only point we didn't +handle is the one that + +lies on the line. + +But in that case it's easy. + +Because x is equal to 2. + +And y is equal to 2. + +So the min is simply 2. + +So with this information +I claim we're now done. + +We can just write down +what the PMF of r is. + +So in particular, r takes +on a value of 0. + + + +When this point happens, +this point happens, + +or this point happens. + +And those collectively have a + +probability of 3/8 of occurring. + +r can take on a value of 1 +when either of these two + +points happen. + +So that happens with +probability 2/8. + + + +r is equal to 2. + +This can happen in two ways. + +So we get 2/8. + +And r equal to 3 can happen +in only one way. + +So we get 1/8. + +Quick sanity check, 3 plus +2 is 5, plus 2 is + +7, plus 1 is 8. + +So our PMF sums to 1. + +And to be complete, we +should sketch it. + +Because the problem asks +us to sketch it. + +So we're plotting PR +of r, 0, 1, 2, 3. + +So here we get, let's +see, 1, 2, 3. + +For 0 we have 3/8. + +For 1 we have 2/8. + +For 2 we have 2/8. + +And for 3 we have 1/8. + +So this is our fully labeled +sketch of Pr of r. + +And forgive me for erasing so +quickly, but you guys can + +pause the video, presumably, +if you need more time. + +Let's move on to part d. + +So in part d we're given an +event named a, which is the + +event that x squared is greater +than or equal to y. + +And then we're asked to find the +expectation of xy in the + +unconditional universe. + +And then the expectation of x +times y conditioned on a. + +So let's not worry about the +conditioning for now. + +Let's just focus on +the unconditional + +expectation of x times y. + +So I'm just going to +erase all these r's + +so I don't get confused. + +But we're going to follow a very +similar strategy, which + +is at each point I'm going to +label what the value of w is. + +And we'll find the expectation +of w that way. + +So let's see, here, +we have 4 times 0. + +So w is equal to 0. + +Here we have 4 times 1. + +w is equal to 4. + +4 times 2, w is equal to 8. + +4 times 3, w is equal to 12. + +w is equal to 2. + +w is equal to 4. + +w is equal to 0. + +w is equal to 0. + +OK, so that was just algebra. + +And now, I claim again, we can +just write down what the + +expectation of x times y is. + +And I'm sorry, I didn't +announce my notation. + +I should mention that now. + +I was defining w to be the +random variable x times y. + +And that's why I labeled +the product of x + +times y as w over here. + +My apologies about not defining +that random variable. + +So the expectation of w, well, +w takes on a value of 0. + +When this happens, this happens +or that happens. + +And we know that those +three points occur + +with probability 3/8. + +So we have 0 times 3/8. + +I'm just using the normal +formula for expectation. + +w takes on a value of 2 +with probability 1/8. + +Because this is the lead +point in which it + +happens, 2 times 1/8. + +Plus it can take on the value +of 4 with probability + +2/8, 4 times 2/8. + +And 8, with 1/8 probability. + +And similarly, 12 with +1/8 probability. + +So this is just algebra. + +The numerator sums up to 30. + +Yes, that's correct. + +So we have 30/8, which +is equal to 15/4. + +So this is our first +answer for part d. + +And now we have to do this +slightly trickier one, which + +is the conditional expectation +of x times y, or w + +conditioned on a. + +So similar to what I did in part +c, I'm going to draw the + +line y equals x squared. + +So y equals x squared +is 0 here, 1 here. + +And at 2, it should take +on a value of 4. + +So the curve should look +something like this. + +This is the line y is +equal to x squared. + +So we know all the points below +this line satisfy y less + +than or equal to x squared. + +And all the points above this +line have y greater than or + +equal to x squared. + +And a is y less than or +equal to x squared. + +So we are in the conditional +universe where only points + +below this line can happen. + +So that one, that one, that +one, that one, that + +one and that one. + +So there are six of them. + +And again, in the unconditional +world, all of + +the points were equally +likely. + +So in the conditional world +these six points are still + +equally likely. + +So they each happen with +probability 1/6. + +So in this case, the expectation +of w is simply 2 + +times 1/6 plus 0 times 1/6. + +But that's 0. + +So I'm not going to write it. + +4 times 2/6 plus 4 times 2/6 +plus 8 times 1/6, plus 12 + +times 1 over 6. + +And again, the numerator +summed to 30. + +But this time our denominator +is 6. + +So this is simply 5. + +So we have, actually, finished +the problem. + +Because we've computed this +value and this value. + +And so the important takeaways +of this problem are, + +essentially, honestly, just to +get you comfortable with + +computing things involving +joint PMFs. + +We talked a lot about finding +expectations quickly by + +thinking about center +of mass and the + +geometry of the problem. + +We've got practice computing +conditional variances. + +And we did some derived +distributions. + +And we'll do a lot more +of those later. \ No newline at end of file diff --git a/868odGqmB1E.txt b/868odGqmB1E.txt new file mode 100644 index 0000000000000000000000000000000000000000..f8bc4c631f16b1d3476fff9a076d76747e4681ea --- /dev/null +++ b/868odGqmB1E.txt @@ -0,0 +1,1955 @@ +align:start position:0% + +great so I will begin with phase shifts + + align:start position:0% +great so I will begin with phase shifts + + + align:start position:0% +great so I will begin with phase shifts +and do the introduction of how to make + + align:start position:0% +and do the introduction of how to make + + + align:start position:0% +and do the introduction of how to make +sure we can really so this is the + + align:start position:0% +sure we can really so this is the + + + align:start position:0% +sure we can really so this is the +important part of this just like when we + + align:start position:0% +important part of this just like when we + + + align:start position:0% +important part of this just like when we +added the reflected and transmitted way + + align:start position:0% +added the reflected and transmitted way + + + align:start position:0% +added the reflected and transmitted way +if we could find a solution I'm going to + + align:start position:0% +if we could find a solution I'm going to + + + align:start position:0% +if we could find a solution I'm going to +try to explain why with these things we + + align:start position:0% +try to explain why with these things we + + + align:start position:0% +try to explain why with these things we +can find solutions in general so this is + + align:start position:0% +can find solutions in general so this is + + + align:start position:0% +can find solutions in general so this is +subject of partial waves and it's a nice + + align:start position:0% +subject of partial waves and it's a nice + + + align:start position:0% +subject of partial waves and it's a nice +subject a little technical there might + + align:start position:0% +subject a little technical there might + + + align:start position:0% +subject a little technical there might +seem to be a lot of formulas here but + + align:start position:0% +seem to be a lot of formulas here but + + + align:start position:0% +seem to be a lot of formulas here but +the ideas are relatively simple once one + + align:start position:0% +the ideas are relatively simple once one + + + align:start position:0% +the ideas are relatively simple once one +keeps in mind one-dimensional analogies + + align:start position:0% +keeps in mind one-dimensional analogies + + + align:start position:0% +keeps in mind one-dimensional analogies +the one-dimensional analogies are very + + align:start position:0% +the one-dimensional analogies are very + + + align:start position:0% +the one-dimensional analogies are very +valuable here and we will emphasize them + + align:start position:0% +valuable here and we will emphasize them + + + align:start position:0% +valuable here and we will emphasize them +a lot so of we will discuss partial + + align:start position:0% +a lot so of we will discuss partial + + + align:start position:0% +a lot so of we will discuss partial +waves and phase shifts + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so it's time to simplify this matters a + + align:start position:0% +so it's time to simplify this matters a + + + align:start position:0% +so it's time to simplify this matters a +little bit and to do that I will assume + + align:start position:0% +little bit and to do that I will assume + + + align:start position:0% +little bit and to do that I will assume +from now on that the potential is + + align:start position:0% +from now on that the potential is + + + align:start position:0% +from now on that the potential is +central so V of R is equal to V of R + + align:start position:0% +central so V of R is equal to V of R + + + align:start position:0% +central so V of R is equal to V of R +that will simplify the azimuthal + + align:start position:0% +that will simplify the azimuthal + + + align:start position:0% +that will simplify the azimuthal +dependence there will be no azimuthal + + align:start position:0% +dependence there will be no azimuthal + + + align:start position:0% +dependence there will be no azimuthal +dependences you know you see the famous + + align:start position:0% +dependences you know you see the famous + + + align:start position:0% +dependences you know you see the famous +fira cailli symmetric but still you're + + align:start position:0% +fira cailli symmetric but still you're + + + align:start position:0% +fira cailli symmetric but still you're +coming from a particular direction the Z + + align:start position:0% +coming from a particular direction the Z + + + align:start position:0% +coming from a particular direction the Z +so you can expect now that the scatter + + align:start position:0% +so you can expect now that the scatter + + + align:start position:0% +so you can expect now that the scatter +wave depends on the angle of the + + align:start position:0% +wave depends on the angle of the + + + align:start position:0% +wave depends on the angle of the +particle with respect to Z because it's + + align:start position:0% +particle with respect to Z because it's + + + align:start position:0% +particle with respect to Z because it's +very totally similar but it shouldn't + + align:start position:0% +very totally similar but it shouldn't + + + align:start position:0% +very totally similar but it shouldn't +depend on Phi the angle Phi should just + + align:start position:0% +depend on Phi the angle Phi should just + + + align:start position:0% +depend on Phi the angle Phi should just +depend on theta so expect F of theta now + + align:start position:0% + + + + align:start position:0% + +a free particle is something we all know + + align:start position:0% +a free particle is something we all know + + + align:start position:0% +a free particle is something we all know +how to solve eetu the ikx why do we + + align:start position:0% +how to solve eetu the ikx why do we + + + align:start position:0% +how to solve eetu the ikx why do we +bother with the free particle in so many + + align:start position:0% +bother with the free particle in so many + + + align:start position:0% +bother with the free particle in so many +ways because the free particle is very + + align:start position:0% +ways because the free particle is very + + + align:start position:0% +ways because the free particle is very +important part of the solution is free + + align:start position:0% +important part of the solution is free + + + align:start position:0% +important part of the solution is free +particles to some degree far away it is + + align:start position:0% +particles to some degree far away it is + + + align:start position:0% +particles to some degree far away it is +free particles as well and we need to + + align:start position:0% +free particles as well and we need to + + + align:start position:0% +free particles as well and we need to +understand free particles in spherical + + align:start position:0% +understand free particles in spherical + + + align:start position:0% +understand free particles in spherical +coordinates so it's something with done + + align:start position:0% +coordinates so it's something with done + + + align:start position:0% +coordinates so it's something with done +in 805 and sometimes you need o4 and we + + align:start position:0% +in 805 and sometimes you need o4 and we + + + align:start position:0% +in 805 and sometimes you need o4 and we +look at the radial equation which is + + align:start position:0% +look at the radial equation which is + + + align:start position:0% +look at the radial equation which is +associated the spherical coordinates for + + align:start position:0% +associated the spherical coordinates for + + + align:start position:0% +associated the spherical coordinates for +a free particle so we'll consider free + + align:start position:0% +a free particle so we'll consider free + + + align:start position:0% +a free particle so we'll consider free +particle and we'd say well that's very + + align:start position:0% +particle and we'd say well that's very + + + align:start position:0% +particle and we'd say well that's very +simple but it's not all that simple in + + align:start position:0% +simple but it's not all that simple in + + + align:start position:0% +simple but it's not all that simple in +spherical coordinates and you would say + + align:start position:0% +spherical coordinates and you would say + + + align:start position:0% +spherical coordinates and you would say +okay if it's not simple in spherical + + align:start position:0% +okay if it's not simple in spherical + + + align:start position:0% +okay if it's not simple in spherical +chorus why do we bother we bother + + align:start position:0% +chorus why do we bother we bother + + + align:start position:0% +chorus why do we bother we bother +because + + align:start position:0% +because + + + align:start position:0% +because +Karin is happening in spherical + + align:start position:0% +Karin is happening in spherical + + + align:start position:0% +Karin is happening in spherical +coordinates so we can't escape having to + + align:start position:0% +coordinates so we can't escape having to + + + align:start position:0% +coordinates so we can't escape having to +do the free particle in spherical + + align:start position:0% +do the free particle in spherical + + + align:start position:0% +do the free particle in spherical +coordinates is something you have to do + + align:start position:0% +coordinates is something you have to do + + + align:start position:0% +coordinates is something you have to do +so what are solutions in spherical + + align:start position:0% +so what are solutions in spherical + + + align:start position:0% +so what are solutions in spherical +coordinates we have solution side of our + + align:start position:0% +coordinates we have solution side of our + + + align:start position:0% +coordinates we have solution side of our +remember the language is fira + + align:start position:0% +remember the language is fira + + + align:start position:0% +remember the language is fira +concordance was a u of r divided by r + + align:start position:0% +concordance was a u of r divided by r + + + align:start position:0% +concordance was a u of r divided by r +and of yl m of omega that was a typical + + align:start position:0% +and of yl m of omega that was a typical + + + align:start position:0% +and of yl m of omega that was a typical +solution a single solution of the + + align:start position:0% +solution a single solution of the + + + align:start position:0% +solution a single solution of the +Schrodinger equation will you only + + align:start position:0% +Schrodinger equation will you only + + + align:start position:0% +Schrodinger equation will you only +depends on L the M disappears so this is + + align:start position:0% +depends on L the M disappears so this is + + + align:start position:0% +depends on L the M disappears so this is +our this ours are ours without the + + align:start position:0% +our this ours are ours without the + + + align:start position:0% +our this ours are ours without the +vector because you're already talking + + align:start position:0% +vector because you're already talking + + + align:start position:0% +vector because you're already talking +about the radial equation so and depend + + align:start position:0% +about the radial equation so and depend + + + align:start position:0% +about the radial equation so and depend +on the energy and depend on the value of + + align:start position:0% +on the energy and depend on the value of + + + align:start position:0% +on the energy and depend on the value of +the L want number so what is the + + align:start position:0% +the L want number so what is the + + + align:start position:0% +the L want number so what is the +Schrodinger equation the radial equation + + align:start position:0% +Schrodinger equation the radial equation + + + align:start position:0% +Schrodinger equation the radial equation +is minus H squared over 2m the secondly + + align:start position:0% +is minus H squared over 2m the secondly + + + align:start position:0% +is minus H squared over 2m the secondly +R squared plus h squared over 2m l times + + align:start position:0% +R squared plus h squared over 2m l times + + + align:start position:0% +R squared plus h squared over 2m l times +l plus 1 over r square remember the + + align:start position:0% +l plus 1 over r square remember the + + + align:start position:0% +l plus 1 over r square remember the +potential centrifugal barrier + + align:start position:0% +potential centrifugal barrier + + + align:start position:0% +potential centrifugal barrier +ineffective potential then you would + + align:start position:0% +ineffective potential then you would + + + align:start position:0% +ineffective potential then you would +have V of R here but it's free particle + + align:start position:0% +have V of R here but it's free particle + + + align:start position:0% +have V of R here but it's free particle +so V of R is equal to 0 so nothing else + + align:start position:0% +so V of R is equal to 0 so nothing else + + + align:start position:0% +so V of R is equal to 0 so nothing else +U of L of little R is equal to the + + align:start position:0% +U of L of little R is equal to the + + + align:start position:0% +U of L of little R is equal to the +energy which is H squared K squared over + + align:start position:0% +energy which is H squared K squared over + + + align:start position:0% +energy which is H squared K squared over +2m u al and that's a parameterization of + + align:start position:0% +2m u al and that's a parameterization of + + + align:start position:0% +2m u al and that's a parameterization of +the energy in terms of a K squared like + + align:start position:0% +the energy in terms of a K squared like + + + align:start position:0% +the energy in terms of a K squared like +that + + align:start position:0% + + + + align:start position:0% + +well with lots of H squared K squared + + align:start position:0% +well with lots of H squared K squared + + + align:start position:0% +well with lots of H squared K squared +and two M's so we can get rid of them + + align:start position:0% +and two M's so we can get rid of them + + + align:start position:0% +and two M's so we can get rid of them +cancel the H squared over 2m you get + + align:start position:0% +cancel the H squared over 2m you get + + + align:start position:0% +cancel the H squared over 2m you get +minus this second the R squared plus L + + align:start position:0% +minus this second the R squared plus L + + + align:start position:0% +minus this second the R squared plus L +times L plus 1 over R u e L is equal to + + align:start position:0% +times L plus 1 over R u e L is equal to + + + align:start position:0% +times L plus 1 over R u e L is equal to +K squared UEL it's a nice equation is + + align:start position:0% +K squared UEL it's a nice equation is + + + align:start position:0% +K squared UEL it's a nice equation is +the equation of the free particle in + + align:start position:0% +the equation of the free particle in + + + align:start position:0% +the equation of the free particle in +spherical coordinates now this is like a + + align:start position:0% +spherical coordinates now this is like a + + + align:start position:0% +spherical coordinates now this is like a +Schrodinger equation and I think of when + + align:start position:0% +Schrodinger equation and I think of when + + + align:start position:0% +Schrodinger equation and I think of when +you look at that you could get puzzled + + align:start position:0% +you look at that you could get puzzled + + + align:start position:0% +you look at that you could get puzzled +whether or not the value of K squared or + + align:start position:0% +whether or not the value of K squared or + + + align:start position:0% +whether or not the value of K squared or +the energy might end up being quantized + + align:start position:0% +the energy might end up being quantized + + + align:start position:0% +the energy might end up being quantized +what was shown in the equation many + + align:start position:0% +what was shown in the equation many + + + align:start position:0% +what was shown in the equation many +times quantizes the energy but here it + + align:start position:0% +times quantizes the energy but here it + + + align:start position:0% +times quantizes the energy but here it +shouldn't happen this is a free particle + + align:start position:0% +shouldn't happen this is a free particle + + + align:start position:0% +shouldn't happen this is a free particle +all values of K should be allowed so + + align:start position:0% +all values of K should be allowed so + + + align:start position:0% +all values of K should be allowed so +there should be no quantization this is + + align:start position:0% +there should be no quantization this is + + + align:start position:0% +there should be no quantization this is +an R squared here and the reason you can + + align:start position:0% +an R squared here and the reason you can + + + align:start position:0% +an R squared here and the reason you can +see one reason at least analytically + + align:start position:0% +see one reason at least analytically + + + align:start position:0% +see one reason at least analytically +that there's no quantization is that you + + align:start position:0% +that there's no quantization is that you + + + align:start position:0% +that there's no quantization is that you +can define a new variable Rho equal kr + + align:start position:0% +can define a new variable Rho equal kr + + + align:start position:0% +can define a new variable Rho equal kr +and then this whole differential + + align:start position:0% +and then this whole differential + + + align:start position:0% +and then this whole differential +equation becomes minus the second the + + align:start position:0% +equation becomes minus the second the + + + align:start position:0% +equation becomes minus the second the +Rho squared plus L times L plus one over + + align:start position:0% +Rho squared plus L times L plus one over + + + align:start position:0% +Rho squared plus L times L plus one over +Rho squared well I can put the other + + align:start position:0% +Rho squared well I can put the other + + + align:start position:0% +Rho squared well I can put the other +number in there as well or should I not + + align:start position:0% +number in there as well or should I not + + + align:start position:0% +number in there as well or should I not +no it's not done here ue l is equal to + + align:start position:0% +no it's not done here ue l is equal to + + + align:start position:0% +no it's not done here ue l is equal to +UE elf + + align:start position:0% +UE elf + + + align:start position:0% +UE elf +and the K squared disappeared completely + + align:start position:0% + + + + align:start position:0% + +that tells me that the K square cannot + + align:start position:0% +that tells me that the K square cannot + + + align:start position:0% +that tells me that the K square cannot +get quantized if there is a solution of + + align:start position:0% +get quantized if there is a solution of + + + align:start position:0% +get quantized if there is a solution of +this differential equation it halts for + + align:start position:0% +this differential equation it halts for + + + align:start position:0% +this differential equation it halts for +all values of K and these are going to + + align:start position:0% +all values of K and these are going to + + + align:start position:0% +all values of K and these are going to +be like plane waves and maybe that's + + align:start position:0% +be like plane waves and maybe that's + + + align:start position:0% +be like plane waves and maybe that's +another reason you can think that K + + align:start position:0% +another reason you can think that K + + + align:start position:0% +another reason you can think that K +doesn't get quantized because these + + align:start position:0% +doesn't get quantized because these + + + align:start position:0% +doesn't get quantized because these +solutions are not normalizable anyway so + + align:start position:0% +solutions are not normalizable anyway so + + + align:start position:0% +solutions are not normalizable anyway so +it shouldn't get quantized so with this + + align:start position:0% +it shouldn't get quantized so with this + + + align:start position:0% +it shouldn't get quantized so with this +equation in here we get the two main + + align:start position:0% +equation in here we get the two main + + + align:start position:0% +equation in here we get the two main +solutions the solutions of this + + align:start position:0% +solutions the solutions of this + + + align:start position:0% +solutions the solutions of this +differential equation are Bessel + + align:start position:0% +differential equation are Bessel + + + align:start position:0% +differential equation are Bessel +function spherical Bessel functions UEL + + align:start position:0% +function spherical Bessel functions UEL + + + align:start position:0% +function spherical Bessel functions UEL +is equal to a constant + + align:start position:0% +is equal to a constant + + + align:start position:0% +is equal to a constant +al times Rho times the Bessel function + + align:start position:0% +al times Rho times the Bessel function + + + align:start position:0% +al times Rho times the Bessel function +lowercase J of Rho there's a Rho times + + align:start position:0% +lowercase J of Rho there's a Rho times + + + align:start position:0% +lowercase J of Rho there's a Rho times +that function that's the way it shows up + + align:start position:0% +that function that's the way it shows up + + + align:start position:0% +that function that's the way it shows up +it's kind of interesting it's because in + + align:start position:0% +it's kind of interesting it's because in + + + align:start position:0% +it's kind of interesting it's because in +fact you have to divide you by R so that + + align:start position:0% +fact you have to divide you by R so that + + + align:start position:0% +fact you have to divide you by R so that +would mean dividing you by a row and + + align:start position:0% +would mean dividing you by a row and + + + align:start position:0% +would mean dividing you by a row and +means that the radial function is just + + align:start position:0% +means that the radial function is just + + + align:start position:0% +means that the radial function is just +the Bessel function without anything + + align:start position:0% +the Bessel function without anything + + + align:start position:0% +the Bessel function without anything +else and then there's the other Bessel + + align:start position:0% +else and then there's the other Bessel + + + align:start position:0% +else and then there's the other Bessel +function the n sub L a row time said M + + align:start position:0% +function the n sub L a row time said M + + + align:start position:0% +function the n sub L a row time said M +sub L of Rho so those are spherical + + align:start position:0% +sub L of Rho so those are spherical + + + align:start position:0% +sub L of Rho so those are spherical +Bessel functions as you're familiar from + + align:start position:0% +Bessel functions as you're familiar from + + + align:start position:0% +Bessel functions as you're familiar from +the notation that J is the one that is + + align:start position:0% +the notation that J is the one that is + + + align:start position:0% +the notation that J is the one that is +healthy at Rho equals zero doesn't + + align:start position:0% +healthy at Rho equals zero doesn't + + + align:start position:0% +healthy at Rho equals zero doesn't +diverge the N is a solution that + + align:start position:0% +diverge the N is a solution that + + + align:start position:0% +diverge the N is a solution that +diverges at the origin and both of them + + align:start position:0% +diverges at the origin and both of them + + + align:start position:0% +diverges at the origin and both of them +behave nicely far away so JL of X goes + + align:start position:0% +behave nicely far away so JL of X goes + + + align:start position:0% +behave nicely far away so JL of X goes +like 1 over X sine of + + align:start position:0% +like 1 over X sine of + + + align:start position:0% +like 1 over X sine of +X minus L PI over 2 and ADA L of X + + align:start position:0% +X minus L PI over 2 and ADA L of X + + + align:start position:0% +X minus L PI over 2 and ADA L of X +behaves like minus 1 over X cosine of X + + align:start position:0% +behaves like minus 1 over X cosine of X + + + align:start position:0% +behaves like minus 1 over X cosine of X +minus L PI over 2 + + align:start position:0% +minus L PI over 2 + + + align:start position:0% +minus L PI over 2 +this is 4x big X much greater than 1 you + + align:start position:0% +this is 4x big X much greater than 1 you + + + align:start position:0% +this is 4x big X much greater than 1 you +have this behavior so these are our + + align:start position:0% +have this behavior so these are our + + + align:start position:0% +have this behavior so these are our +solutions and here is the thing that we + + align:start position:0% +solutions and here is the thing that we + + + align:start position:0% +solutions and here is the thing that we +have to do we have to rewrite our + + align:start position:0% + + + + align:start position:0% + +solutions in terms of spherical waves + + align:start position:0% +solutions in terms of spherical waves + + + align:start position:0% +solutions in terms of spherical waves +because this was a spherical wave so we + + align:start position:0% +because this was a spherical wave so we + + + align:start position:0% +because this was a spherical wave so we +should even write this part the + + align:start position:0% +should even write this part the + + + align:start position:0% +should even write this part the +spherical wave and this is a very + + align:start position:0% +spherical wave and this is a very + + + align:start position:0% +spherical wave and this is a very +interesting and in some ways strange + + align:start position:0% +interesting and in some ways strange + + + align:start position:0% +interesting and in some ways strange +representation of e to the i kz you have + + align:start position:0% +representation of e to the i kz you have + + + align:start position:0% +representation of e to the i kz you have +e to the ikj then you have an intuition + + align:start position:0% +e to the ikj then you have an intuition + + + align:start position:0% +e to the ikj then you have an intuition +for it as a plane wave in the Z + + align:start position:0% +for it as a plane wave in the Z + + + align:start position:0% +for it as a plane wave in the Z +direction represented as an infinite sum + + align:start position:0% +direction represented as an infinite sum + + + align:start position:0% +direction represented as an infinite sum +of incoming and outgoing spherical waves + + align:start position:0% +of incoming and outgoing spherical waves + + + align:start position:0% +of incoming and outgoing spherical waves +that's what's gonna happen + + align:start position:0% +that's what's gonna happen + + + align:start position:0% +that's what's gonna happen +so if we have so this is last thing I'm + + align:start position:0% +so if we have so this is last thing I'm + + + align:start position:0% +so if we have so this is last thing I'm +gonna do here + + align:start position:0% + + + + align:start position:0% + +we have that e to the I KZ is a plane + + align:start position:0% +we have that e to the I KZ is a plane + + + align:start position:0% +we have that e to the I KZ is a plane +wave solution so it's a solution of a + + align:start position:0% +wave solution so it's a solution of a + + + align:start position:0% +wave solution so it's a solution of a +free particle so I should be able to + + align:start position:0% +free particle so I should be able to + + + align:start position:0% +free particle so I should be able to +ride the superpositions of this + + align:start position:0% +ride the superpositions of this + + + align:start position:0% +ride the superpositions of this +solutions that we have found so it + + align:start position:0% +solutions that we have found so it + + + align:start position:0% +solutions that we have found so it +should be a superposition of solutions + + align:start position:0% +should be a superposition of solutions + + + align:start position:0% +should be a superposition of solutions +of this type so it could be a sum of + + align:start position:0% +of this type so it could be a sum of + + + align:start position:0% +of this type so it could be a sum of +coefficients al times + + align:start position:0% + + + + align:start position:0% + +well alm you think some ace times + + align:start position:0% +well alm you think some ace times + + + align:start position:0% +well alm you think some ace times +solutions + + align:start position:0% +solutions + + + align:start position:0% +solutions +remember we're writing a full solution + + align:start position:0% +remember we're writing a full solution + + + align:start position:0% +remember we're writing a full solution +so a full solution u divided by r so u + + align:start position:0% +so a full solution u divided by r so u + + + align:start position:0% +so a full solution u divided by r so u +divided by this quantity so you could + + align:start position:0% +divided by this quantity so you could + + + align:start position:0% +divided by this quantity so you could +have an a LM j L of Rho plus B L m8l of + + align:start position:0% +have an a LM j L of Rho plus B L m8l of + + + align:start position:0% +have an a LM j L of Rho plus B L m8l of +Rho times ylm so this should be a + + align:start position:0% +Rho times ylm so this should be a + + + align:start position:0% +Rho times ylm so this should be a +general solution and that would be a sum + + align:start position:0% +general solution and that would be a sum + + + align:start position:0% +general solution and that would be a sum +over else and a mess of all of those + + align:start position:0% +over else and a mess of all of those + + + align:start position:0% +over else and a mess of all of those +quantities but that's a lot more than + + align:start position:0% +quantities but that's a lot more than + + + align:start position:0% +quantities but that's a lot more than +what you need first this does not + + align:start position:0% +what you need first this does not + + + align:start position:0% +what you need first this does not +diverge near a more equal zero it has no + + align:start position:0% +diverge near a more equal zero it has no + + + align:start position:0% +diverge near a more equal zero it has no +divergence anywhere and the eita or the + + align:start position:0% +divergence anywhere and the eita or the + + + align:start position:0% +divergence anywhere and the eita or the +ends i think their ends actually not a + + align:start position:0% +ends i think their ends actually not a + + + align:start position:0% +ends i think their ends actually not a +thus the ends diverge for Rho equal to + + align:start position:0% +thus the ends diverge for Rho equal to + + + align:start position:0% +thus the ends diverge for Rho equal to +zero so none of this are necessary so I + + align:start position:0% +zero so none of this are necessary so I + + + align:start position:0% +zero so none of this are necessary so I +I can erase those + + align:start position:0% + + + + align:start position:0% + +our name but there is more + + align:start position:0% +our name but there is more + + + align:start position:0% +our name but there is more +this function is invariant and there are + + align:start position:0% +this function is invariant and there are + + + align:start position:0% +this function is invariant and there are +see beautiful rotations if you have your + + align:start position:0% +see beautiful rotations if you have your + + + align:start position:0% +see beautiful rotations if you have your +axis here here is the Z and you have a + + align:start position:0% +axis here here is the Z and you have a + + + align:start position:0% +axis here here is the Z and you have a +point here and you rotate that the value + + align:start position:0% +point here and you rotate that the value + + + align:start position:0% +point here and you rotate that the value +of Z doesn't change it's independent of + + align:start position:0% +of Z doesn't change it's independent of + + + align:start position:0% +of Z doesn't change it's independent of +Phi for a given theta Z just depends on + + align:start position:0% +Phi for a given theta Z just depends on + + + align:start position:0% +Phi for a given theta Z just depends on +R of cosine theta so there's no Phi + + align:start position:0% +R of cosine theta so there's no Phi + + + align:start position:0% +R of cosine theta so there's no Phi +dependence but all the ylm's with M + + align:start position:0% +dependence but all the ylm's with M + + + align:start position:0% +dependence but all the ylm's with M +different from 0 have Phi dependence so + + align:start position:0% +different from 0 have Phi dependence so + + + align:start position:0% +different from 0 have Phi dependence so +M cannot be here either M must be 0 so + + align:start position:0% +M cannot be here either M must be 0 so + + + align:start position:0% +M cannot be here either M must be 0 so +you must be down to sum over L a L some + + align:start position:0% +you must be down to sum over L a L some + + + align:start position:0% +you must be down to sum over L a L some +coefficient J L of Rho why L 0 and all + + align:start position:0% +coefficient J L of Rho why L 0 and all + + + align:start position:0% +coefficient J L of Rho why L 0 and all +of those would be perfectly good plane + + align:start position:0% +of those would be perfectly good plane + + + align:start position:0% +of those would be perfectly good plane +wave solutions whatever numbers you + + align:start position:0% +wave solutions whatever numbers you + + + align:start position:0% +wave solutions whatever numbers you +choose for the little a else + + align:start position:0% +choose for the little a else + + + align:start position:0% +choose for the little a else +those are good solutions because we've + + align:start position:0% +those are good solutions because we've + + + align:start position:0% +those are good solutions because we've +build them by taking linear combinations + + align:start position:0% +build them by taking linear combinations + + + align:start position:0% +build them by taking linear combinations +of exact solutions of this equation but + + align:start position:0% +of exact solutions of this equation but + + + align:start position:0% +of exact solutions of this equation but +to represent this quantity the a else + + align:start position:0% +to represent this quantity the a else + + + align:start position:0% +to represent this quantity the a else +must take particular values so what is + + align:start position:0% +must take particular values so what is + + + align:start position:0% +must take particular values so what is +that formula that formula is quite + + align:start position:0% +that formula that formula is quite + + + align:start position:0% +that formula that formula is quite +famous and perhaps even you could + + align:start position:0% +famous and perhaps even you could + + + align:start position:0% +famous and perhaps even you could +discuss this in recitation e to the i kz + + align:start position:0% +discuss this in recitation e to the i kz + + + align:start position:0% +discuss this in recitation e to the i kz +which is e to the i k r cosine theta is + + align:start position:0% +which is e to the i k r cosine theta is + + + align:start position:0% +which is e to the i k r cosine theta is +the sum for pi now you have to get all + + align:start position:0% +the sum for pi now you have to get all + + + align:start position:0% +the sum for pi now you have to get all +the concerts right square root of 4 pi + + align:start position:0% +the concerts right square root of 4 pi + + + align:start position:0% +the concerts right square root of 4 pi +sum from l equals 0 to infinity square + + align:start position:0% +sum from l equals 0 to infinity square + + + align:start position:0% +sum from l equals 0 to infinity square +root of 2l plus 1 coefficients are + + align:start position:0% +root of 2l plus 1 coefficients are + + + align:start position:0% +root of 2l plus 1 coefficients are +pretty funny they get worse very fast + + align:start position:0% +pretty funny they get worse very fast + + + align:start position:0% +pretty funny they get worse very fast +now you have a + + align:start position:0% +now you have a + + + align:start position:0% +now you have a +I to the L I to the L y l0f ADA doesn't + + align:start position:0% +I to the L I to the L y l0f ADA doesn't + + + align:start position:0% +I to the L I to the L y l0f ADA doesn't +depend on Phi J L of K R this is the + + align:start position:0% +depend on Phi J L of K R this is the + + + align:start position:0% +depend on Phi J L of K R this is the +expansion that we need there's no way we + + align:start position:0% +expansion that we need there's no way we + + + align:start position:0% +expansion that we need there's no way we +can make progress with this problem + + align:start position:0% +can make progress with this problem + + + align:start position:0% +can make progress with this problem +unless we have this expansion but now if + + align:start position:0% +unless we have this expansion but now if + + + align:start position:0% +unless we have this expansion but now if +y the intuition that I was telling you + + align:start position:0% +y the intuition that I was telling you + + + align:start position:0% +y the intuition that I was telling you +of these waves coming in and out well + + align:start position:0% +of these waves coming in and out well + + + align:start position:0% +of these waves coming in and out well +you have e to the IQ z you some an + + align:start position:0% +you have e to the IQ z you some an + + + align:start position:0% +you have e to the IQ z you some an +infinite sum over partial waves a + + align:start position:0% +infinite sum over partial waves a + + + align:start position:0% +infinite sum over partial waves a +partial wave is a different value of L + + align:start position:0% +partial wave is a different value of L + + + align:start position:0% +partial wave is a different value of L +these are partial waves as I was saying + + align:start position:0% +these are partial waves as I was saying + + + align:start position:0% +these are partial waves as I was saying +any solution is the sum of partial waves + + align:start position:0% +any solution is the sum of partial waves + + + align:start position:0% +any solution is the sum of partial waves +it's a sum over L and where are the + + align:start position:0% +it's a sum over L and where are the + + + align:start position:0% +it's a sum over L and where are the +waves well the JL of K R is a far away + + align:start position:0% +waves well the JL of K R is a far away + + + align:start position:0% +waves well the JL of K R is a far away +it's a sign and a sign of X is an + + align:start position:0% +it's a sign and a sign of X is an + + + align:start position:0% +it's a sign and a sign of X is an +exponential I X minus e to the minus I X + + align:start position:0% +exponential I X minus e to the minus I X + + + align:start position:0% +exponential I X minus e to the minus I X +over 2 so here you have exponential zuv + + align:start position:0% +over 2 so here you have exponential zuv + + + align:start position:0% +over 2 so here you have exponential zuv +e to the IKr and Exponential's of e to + + align:start position:0% +e to the IKr and Exponential's of e to + + + align:start position:0% +e to the IKr and Exponential's of e to +the minus IKr + + align:start position:0% +the minus IKr + + + align:start position:0% +the minus IKr +which are waves that are here like + + align:start position:0% +which are waves that are here like + + + align:start position:0% +which are waves that are here like +outgoing waves an incoming wave so the e + + align:start position:0% +outgoing waves an incoming wave so the e + + + align:start position:0% +outgoing waves an incoming wave so the e +to the I case is a sum of annoying and + + align:start position:0% +to the I case is a sum of annoying and + + + align:start position:0% +to the I case is a sum of annoying and +outgoing spherical waves and that's an + + align:start position:0% +outgoing spherical waves and that's an + + + align:start position:0% +outgoing spherical waves and that's an +intuition that we will exploit very + + align:start position:0% +intuition that we will exploit very + + + align:start position:0% +intuition that we will exploit very +clearly to solve this problem so we will + + align:start position:0% +clearly to solve this problem so we will + + + align:start position:0% +clearly to solve this problem so we will +do that next \ No newline at end of file diff --git a/870y6GUKbwc.txt b/870y6GUKbwc.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bd34c0eb0b4ce07d494ba12ef49c98dfe211dd3 --- /dev/null +++ b/870y6GUKbwc.txt @@ -0,0 +1,366 @@ +You have probably heard entropy defined or +described as "disorder." The usual example + +is that of a college dorm room, which, without +regular tidying, becomes "messier" or "less + +ordered" over time. Supposedly the entropy +of the messy room is higher than that of the + +tidy room. This analogy is easy to picture, +but it's misleading. In this video, you'll + +learn a more accurate description of entropy +and understand how it relates to the concept + +of spontaneity. + +This video is part of the Governing Rules +video series. A small number of rules describe + +the physical and chemical interactions that +are possible in our universe. + +Hi. My name is John Lienhard and I am a professor +in the Department of Mechanical Engineering + +at MIT. + +Today, I'm going to talk to you about entropy, +a fascinating, but often confusing topic. + +In order to understand the topic of this video, +you should be familiar with the idea that + +energy is quantized and the thermodynamic +definition of a system and its surroundings. + +After watching this video, you should be able +to describe, at a basic level, the concept + +of a microstate. You should also be able to +discuss what entropy measures in a conceptual + +way. + +First, what do we mean by a spontaneous process? +In thermodynamics, a spontaneous process is + +one that will occur without any outside intervention +given enough time. + +In the world around us, many everyday events +proceed in a particular manner. We would call + +them spontaneous. You have observed spontaneous +processes yourself, but because they seem + +so natural, you may not have taken particular +note of them. + +For example, think of an inflated balloon +that hasn't been tied and is simply pinched + +between someone's fingers. Once the person +releases the balloon, what is going to happen? + +Experience tells us that the gas inside the +balloon will rapidly escape from the opening, + +moving from high pressure to low pressure. +This will propel the balloon through the air, + +until finally, we are left with a deflated +balloon. The gas that was once in the balloon + +is now dispersed throughout the surroundings. + +You have probably also seen food coloring +or hydrophilic dye dropped into water. What + +happens? From experience, you may know that +the dye disperses. + +You may also have had some experience removing +hot pans from the stovetop. While they come + +off of the stovetop hot, we know they will +eventually cool. Here, we see a liquid crystal + +in the pan change color, first as the pan +is heated, and then again, as the pan cools. + +Experience tells us in which direction these +everyday events will proceed. But what about + +processes with which we don't have experience? + +For example, it would be nice if we had a +way of knowing whether or not a given chemical + +reaction will happen at given conditions. + +The 2nd law of thermodynamics can help us +with this. + +The 2nd law of thermodynamics states that +during any spontaneous process, the total + +entropy change of a system and its surroundings +is positive. In other words, the entropy of + +the "universe," that is, the system plus surroundings, +can only increase. + +But what is entropy? Is entropy a magical +force that overturns your furniture and creates + +havoc in your office or home? No. + +Entropy is a measure of the number of possible +ways energy can be distributed in a system + +of molecules. Molecules in a system at equilibrium +have the same average energy. However, at + +a given instant in time, it is highly unlikely +that all of the molecules have the same exact + +energy. + +Molecules in a system are constantly interacting +and transferring energy amongst each other. + +As a result, one molecule may have a certain +amount of energy at one instant and at the + +next; it could have more or less. Depending +on the energy the molecule has, it will be + +able to access different energy levels. + +The total energy of the system, determines +what energy levels will be accessible to the + +molecules. Higher energy levels will not be +accessible because the energy required to + +reach them is not available. + +So when we say that entropy is a measure of +the number of possible ways energy can be + +distributed in a system of molecules, we have +to account for all of the possible combinations. + +And the way we do that is by considering the +microstates available to the molecules in + +the system. +Let's use an analogy to understand the term + +"microstate". + +Let's say that you have two dice. What are +all of the possible sums for a pair of dice? + +Pause the video here and take a moment to +jot them down. + +Okay, you should have a list that looks something +like this. We would call these sums possible + +macrostates of our system -- the macrostate +doesn't tell us what each individual die reads + +when we roll them, just the total, or "macroscopic +view" if you will. + +What are all of the possible dice combinations +that will produce each of those sums? For + +example, we can produce the sum of three by +rolling a one on the first die and a two on + +the 2nd die. Or, we can roll a 2 on the first +die and a one on the 2nd die. So there are + +two combinations that will produce the sum +of 3. + +The dice combinations that produce the remaining +sums are shown here. + +We would call each of these combinations "microstates" +that correspond to each macrostate. The microstate + +gives us information about the individual +conditions of each die. + +We see that the most likely macrostate, a +sum of 7, has the greatest number of possible + +microstates. + +Do you think that the entropy change for the +system (the cold bar) was positive, negative, + +or equal to zero? + +Please pause the video here and discuss your +reasoning with a classmate. + +Let's start with the system first. The transfer +of energy to the cold bar will allow the molecules + +in the cold bar to access new energy levels +that they could not reach before, increasing + +the number of possible microstates for that +system. So we would suspect that the entropy + +change for the system is positive. + +But what about the surroundings? + +The total entropy of a system and its surroundings +has to increase if the process is spontaneous. + +Let's use a very simplified diagram to think +about the heat diffusion demo. We have two + +bars made of the same material. One bar is +hot and one is cold. We'll look at 4 atoms + +making up each bar. The hot bar has more energy +than the cold bar -- its atoms are moving + +more than the atoms in the cold bar, which +seem barely to move. + +Now, before we put the cold bar in contact +with the hot bar, let's think about each bar + +separately. In our simplified drawing of the +cold bar, let's say that three of the atoms + +have no energy and one atom has one quantum +of energy and is at a slightly higher energy + +level, symbolized by the set of curved lines +representing its motion. How many different + +microstates can this system exhibit? +If we think about the different ways we can + +distribute the quantum of energy amongst the +4 atoms, we see that there are 4 possible + +microstates. +If we do the same for our hot bar, where we + +have 5 quanta of energy that can be distributed +in a variety of ways amongst the 4 atoms, + +we use some math to see that there are 56 +possible microstates. + +When we brought the two bars in contact in +our demonstration, we saw that they reached + +thermal equilibrium. +Here, in our simplified example, we will bring + +the cold bar (defined as our system) and the +hot bar (defined as our surroundings) together + +and divide the 6 quanta of energy equally +between the two. The first law of thermodynamics + +tells us that the total of 6 quanta will be +conserved. + +Now, how many microstates are now possible +in each bar? + +As you might have expected, the number of +possible microstates in what was originally + +our hot bar decreased, and the number of possible +microstates in what was originally our cold + +bar increased. +Let's see what this means for our total entropy + +change. We will use a relationship for entropy +that was derived by Ludwig Boltzmann. It states + +that entropy is equal to a constant, called +the Boltzmann constant, times the natural + +log of the number of microstates. + +When calculating entropy change, whether it +be for the system or surroundings, delta S + +would be equal to Boltzmann's constant times +the natural log of the ratio of the final + +number of microstates to the initial number +of microstates. + +The entropy change in our cold bar was positive +while the entropy change in our hot bar was + +negative. But remember, it's the total entropy +change that matters. We see that our total + +entropy change for this process is positive. +The spontaneous transfer of heat from our + +hot bar to our cold bar is consistent with +the 2nd law of thermodynamics. + +If you did a similar calculation for the reverse +process, that of heat transferring from the + +cold bar to the hot bar, the total entropy +change would be negative indicating that it + +is not spontaneous. +As we hinted earlier and as you may have guessed + +by our very simplified scenario, calculating +the number of microstates in a real system + +can be very challenging. Generally speaking, +you will be calculating entropy in terms of + +measurable macroscopic quantities such as +heat capacity or enthalpy of phase change. + +However, having a qualitative understanding +of the physical meaning of entropy will help + +you properly interpret the entropy changes +caused by various processes. + +To Review, for a process to proceed spontaneously, +the total entropy change for a system and + +its surroundings must be positive. Entropy +measures the number of possible ways energy + +can be distributed in a system of molecules. +A microstate is an instantaneous catalog that + +describes the energy of each molecule in a +system. Because molecules are constantly interacting + +and exchanging energy, this description constantly +needs to be revised. A given system has a + +large number of possible microstates. As we +saw with the Boltzmann equation, entropy is + +proportional to the number of microstates. \ No newline at end of file diff --git a/87_aoFA748s.txt b/87_aoFA748s.txt new file mode 100644 index 0000000000000000000000000000000000000000..77023318490f033edaa26f649e2869ab6f6b7ab0 --- /dev/null +++ b/87_aoFA748s.txt @@ -0,0 +1,891 @@ +align:start position:0% + +welcome back + + align:start position:0% +welcome back + + + align:start position:0% +welcome back +to getting up to speed in biology i hope + + align:start position:0% +to getting up to speed in biology i hope + + + align:start position:0% +to getting up to speed in biology i hope +your first class was helpful + + align:start position:0% +your first class was helpful + + + align:start position:0% +your first class was helpful +and that you have started to know the + + align:start position:0% +and that you have started to know the + + + align:start position:0% +and that you have started to know the +names of + + align:start position:0% +names of + + + align:start position:0% +names of +certain biological terms and understand + + align:start position:0% +certain biological terms and understand + + + align:start position:0% +certain biological terms and understand +certain biological + + align:start position:0% +certain biological + + + align:start position:0% +certain biological +concepts that were unfamiliar before + + align:start position:0% +concepts that were unfamiliar before + + + align:start position:0% +concepts that were unfamiliar before +today we're going to move on to the + + align:start position:0% +today we're going to move on to the + + + align:start position:0% +today we're going to move on to the +next topic i'd like to cover with you in + + align:start position:0% +next topic i'd like to cover with you in + + + align:start position:0% +next topic i'd like to cover with you in +lecture two the cell and how it works + + align:start position:0% +lecture two the cell and how it works + + + align:start position:0% +lecture two the cell and how it works +and again they're going to be a lot of + + align:start position:0% +and again they're going to be a lot of + + + align:start position:0% +and again they're going to be a lot of +class exercises or a lot of + + align:start position:0% +class exercises or a lot of + + + align:start position:0% +class exercises or a lot of +exercises that you can do to make sure + + align:start position:0% +exercises that you can do to make sure + + + align:start position:0% +exercises that you can do to make sure +that you have the concepts and are able + + align:start position:0% +that you have the concepts and are able + + + align:start position:0% +that you have the concepts and are able +to use them + + align:start position:0% +to use them + + + align:start position:0% +to use them +as we've talked about them what i'd like + + align:start position:0% +as we've talked about them what i'd like + + + align:start position:0% +as we've talked about them what i'd like +to do today + + align:start position:0% +to do today + + + align:start position:0% +to do today +is three things i first + + align:start position:0% +is three things i first + + + align:start position:0% +is three things i first +going to talk about cellular chemistry + + align:start position:0% +going to talk about cellular chemistry + + + align:start position:0% +going to talk about cellular chemistry +and some key concepts there then we'll + + align:start position:0% +and some key concepts there then we'll + + + align:start position:0% +and some key concepts there then we'll +talk about organization + + align:start position:0% +talk about organization + + + align:start position:0% +talk about organization +of the cell and then we'll talk about + + align:start position:0% +of the cell and then we'll talk about + + + align:start position:0% +of the cell and then we'll talk about +cell division + + align:start position:0% + + + + align:start position:0% + +so let's move right in to the question + + align:start position:0% +so let's move right in to the question + + + align:start position:0% +so let's move right in to the question +of cellular chemistry here are three + + align:start position:0% +of cellular chemistry here are three + + + align:start position:0% +of cellular chemistry here are three +topics for the day + + align:start position:0% +topics for the day + + + align:start position:0% +topics for the day +and let's talk about to begin + + align:start position:0% + + + + align:start position:0% + +this notion of cellular chemistry + + align:start position:0% +this notion of cellular chemistry + + + align:start position:0% +this notion of cellular chemistry +the cell as i mentioned yesterday + + align:start position:0% +the cell as i mentioned yesterday + + + align:start position:0% +the cell as i mentioned yesterday +in the previous meeting + + align:start position:0% +in the previous meeting + + + align:start position:0% +in the previous meeting +is full of chemical reactions + + align:start position:0% +is full of chemical reactions + + + align:start position:0% +is full of chemical reactions +it is a bag of chemical reactions + + align:start position:0% +it is a bag of chemical reactions + + + align:start position:0% +it is a bag of chemical reactions +and the sum of all chemical reactions in + + align:start position:0% +and the sum of all chemical reactions in + + + align:start position:0% +and the sum of all chemical reactions in +the cell + + align:start position:0% +the cell + + + align:start position:0% +the cell +is called metabolism + + align:start position:0% + + + + align:start position:0% + +so metabolism is all the chemical + + align:start position:0% +so metabolism is all the chemical + + + align:start position:0% +so metabolism is all the chemical +reactions + + align:start position:0% +reactions + + + align:start position:0% +reactions +in a cell there are two major types of + + align:start position:0% +in a cell there are two major types of + + + align:start position:0% +in a cell there are two major types of +chemical reactions that you should know + + align:start position:0% +chemical reactions that you should know + + + align:start position:0% +chemical reactions that you should know +there are catabolic reactions + + align:start position:0% +there are catabolic reactions + + + align:start position:0% +there are catabolic reactions +which break down molecules + + align:start position:0% +which break down molecules + + + align:start position:0% +which break down molecules +for example if you have + + align:start position:0% +for example if you have + + + align:start position:0% +for example if you have +some kind of polymer here's a monomer + + align:start position:0% +some kind of polymer here's a monomer + + + align:start position:0% +some kind of polymer here's a monomer +joined to another monomer if you add + + align:start position:0% +joined to another monomer if you add + + + align:start position:0% +joined to another monomer if you add +water to that polymer + + align:start position:0% +water to that polymer + + + align:start position:0% +water to that polymer +you will get out two separate monomers + + align:start position:0% +you will get out two separate monomers + + + align:start position:0% +you will get out two separate monomers +each with their own hydroxyl group + + align:start position:0% +each with their own hydroxyl group + + + align:start position:0% +each with their own hydroxyl group +this is a catabolic reaction and it is + + align:start position:0% +this is a catabolic reaction and it is + + + align:start position:0% +this is a catabolic reaction and it is +also because you're adding water called + + align:start position:0% +also because you're adding water called + + + align:start position:0% +also because you're adding water called +a hydrolysis reaction the flip of this + + align:start position:0% +a hydrolysis reaction the flip of this + + + align:start position:0% +a hydrolysis reaction the flip of this +is an anabolic reaction + + align:start position:0% +is an anabolic reaction + + + align:start position:0% +is an anabolic reaction +where you build up molecules + + align:start position:0% +where you build up molecules + + + align:start position:0% +where you build up molecules +and these release water in general + + align:start position:0% +and these release water in general + + + align:start position:0% +and these release water in general +as they are being performed and they are + + align:start position:0% +as they are being performed and they are + + + align:start position:0% +as they are being performed and they are +called condensation + + align:start position:0% +called condensation + + + align:start position:0% +called condensation +reactions for example + + align:start position:0% +reactions for example + + + align:start position:0% +reactions for example +two monomers each with a hydroxyl group + + align:start position:0% +two monomers each with a hydroxyl group + + + align:start position:0% +two monomers each with a hydroxyl group +will then give rise to a polymer + + align:start position:0% +will then give rise to a polymer + + + align:start position:0% +will then give rise to a polymer +mom with the release of water + + align:start position:0% + + + + align:start position:0% + +these two types of chemical reactions + + align:start position:0% +these two types of chemical reactions + + + align:start position:0% +these two types of chemical reactions +are really pivotal + + align:start position:0% +are really pivotal + + + align:start position:0% +are really pivotal +to how the cell functions let's take a + + align:start position:0% +to how the cell functions let's take a + + + align:start position:0% +to how the cell functions let's take a +look at a couple of slides + + align:start position:0% + + + + align:start position:0% + +this first one introduces me + + align:start position:0% +this first one introduces me + + + align:start position:0% +this first one introduces me +to and introduces you + + align:start position:0% +to and introduces you + + + align:start position:0% +to and introduces you +to the notion of the cell as a factory + + align:start position:0% +to the notion of the cell as a factory + + + align:start position:0% +to the notion of the cell as a factory +this beautiful painting + + align:start position:0% + + + + align:start position:0% + +lays for us a kind of framework of + + align:start position:0% +lays for us a kind of framework of + + + align:start position:0% +lays for us a kind of framework of +thinking about the cell + + align:start position:0% +thinking about the cell + + + align:start position:0% +thinking about the cell +as a production process a production + + align:start position:0% +as a production process a production + + + align:start position:0% +as a production process a production +plant + + align:start position:0% +plant + + + align:start position:0% +plant +where things are made they're broken + + align:start position:0% +where things are made they're broken + + + align:start position:0% +where things are made they're broken +down they're made again + + align:start position:0% +down they're made again + + + align:start position:0% +down they're made again +and so i want you to bear that in mind + + align:start position:0% +and so i want you to bear that in mind + + + align:start position:0% +and so i want you to bear that in mind +as we talk more about the cell and its + + align:start position:0% +as we talk more about the cell and its + + + align:start position:0% +as we talk more about the cell and its +chemistry + + align:start position:0% +chemistry + + + align:start position:0% +chemistry +here are a couple of diagrams of real + + align:start position:0% +here are a couple of diagrams of real + + + align:start position:0% +here are a couple of diagrams of real +condensation and hydrolysis reactions + + align:start position:0% +condensation and hydrolysis reactions + + + align:start position:0% +condensation and hydrolysis reactions +as the slide points out both of these + + align:start position:0% +as the slide points out both of these + + + align:start position:0% +as the slide points out both of these +involve formation and breakdown of + + align:start position:0% +involve formation and breakdown of + + + align:start position:0% +involve formation and breakdown of +covalent bonds some of those very strong + + align:start position:0% +covalent bonds some of those very strong + + + align:start position:0% +covalent bonds some of those very strong +bonds we spoke about previously + + align:start position:0% +bonds we spoke about previously + + + align:start position:0% +bonds we spoke about previously +and you can see that this single + + align:start position:0% +and you can see that this single + + + align:start position:0% +and you can see that this single +reaction + + align:start position:0% +reaction + + + align:start position:0% +reaction +what which is either the production of + + align:start position:0% +what which is either the production of + + + align:start position:0% +what which is either the production of +the disaccharide lactose + + align:start position:0% +the disaccharide lactose + + + align:start position:0% +the disaccharide lactose +or its breakdown into its component + + align:start position:0% +or its breakdown into its component + + + align:start position:0% +or its breakdown into its component +monosaccharides + + align:start position:0% +monosaccharides + + + align:start position:0% +monosaccharides +can go in both directions in one + + align:start position:0% +can go in both directions in one + + + align:start position:0% +can go in both directions in one +direction it's a condensation reaction + + align:start position:0% +direction it's a condensation reaction + + + align:start position:0% +direction it's a condensation reaction +as lactose is being made and in the + + align:start position:0% +as lactose is being made and in the + + + align:start position:0% +as lactose is being made and in the +other it's a hydrolysis reaction + + align:start position:0% +other it's a hydrolysis reaction + + + align:start position:0% +other it's a hydrolysis reaction +as the disaccharide is being broken down + + align:start position:0% +as the disaccharide is being broken down + + + align:start position:0% +as the disaccharide is being broken down +into its component + + align:start position:0% +into its component + + + align:start position:0% +into its component +parts so this really exemplifies + + align:start position:0% +parts so this really exemplifies + + + align:start position:0% +parts so this really exemplifies +what you need to know about condensation + + align:start position:0% +what you need to know about condensation + + + align:start position:0% +what you need to know about condensation +and hydrolysis reactions + + align:start position:0% +and hydrolysis reactions + + + align:start position:0% +and hydrolysis reactions +the idea is that when you build + + align:start position:0% +the idea is that when you build + + + align:start position:0% +the idea is that when you build +up molecules you generally need + + align:start position:0% +up molecules you generally need + + + align:start position:0% +up molecules you generally need +energy to do so and when you break down + + align:start position:0% +energy to do so and when you break down + + + align:start position:0% +energy to do so and when you break down +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +energy is generally released we're going + + align:start position:0% +energy is generally released we're going + + + align:start position:0% +energy is generally released we're going +to see that that's not entirely true in + + align:start position:0% +to see that that's not entirely true in + + + align:start position:0% +to see that that's not entirely true in +a moment + + align:start position:0% +a moment + + + align:start position:0% +a moment +but it's a reasonable first + + align:start position:0% +but it's a reasonable first + + + align:start position:0% +but it's a reasonable first +approximation + + align:start position:0% +approximation + + + align:start position:0% +approximation +so i'd like you now to take a look at + + align:start position:0% +so i'd like you now to take a look at + + + align:start position:0% +so i'd like you now to take a look at +this first exercise + + align:start position:0% +this first exercise + + + align:start position:0% +this first exercise +and practice figuring out if it's a + + align:start position:0% +and practice figuring out if it's a + + + align:start position:0% +and practice figuring out if it's a +condensation + + align:start position:0% +condensation + + + align:start position:0% +condensation +or a hydrolysis reaction \ No newline at end of file diff --git a/8PcPpVQK7N8.txt b/8PcPpVQK7N8.txt new file mode 100644 index 0000000000000000000000000000000000000000..9e5c1521b97f10d4b1158cbc3a30058a7751a365 --- /dev/null +++ b/8PcPpVQK7N8.txt @@ -0,0 +1,14851 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +so my talk is going to be mostly about + + align:start position:0% +so my talk is going to be mostly about + + + align:start position:0% +so my talk is going to be mostly about +faces in many ways I'm going to connect + + align:start position:0% +faces in many ways I'm going to connect + + + align:start position:0% +faces in many ways I'm going to connect +to what Jim DeCarlo was talking about + + align:start position:0% +to what Jim DeCarlo was talking about + + + align:start position:0% +to what Jim DeCarlo was talking about +today and what Nancy talked about today + + align:start position:0% +today and what Nancy talked about today + + + align:start position:0% +today and what Nancy talked about today +I just start preparing for this that I + + align:start position:0% +I just start preparing for this that I + + + align:start position:0% +I just start preparing for this that I +should say a few things about primates + + align:start position:0% +should say a few things about primates + + + align:start position:0% +should say a few things about primates +and intelligence and like how face or + + align:start position:0% +and intelligence and like how face or + + + align:start position:0% +and intelligence and like how face or +condition might be connected both to the + + align:start position:0% +condition might be connected both to the + + + align:start position:0% +condition might be connected both to the +species we're studying and to the + + align:start position:0% +species we're studying and to the + + + align:start position:0% +species we're studying and to the +overall question of intelligence and I + + align:start position:0% +overall question of intelligence and I + + + align:start position:0% +overall question of intelligence and I +thought the most important thing to do + + align:start position:0% +thought the most important thing to do + + + align:start position:0% +thought the most important thing to do +this at MBL would be to start with this + + align:start position:0% +this at MBL would be to start with this + + + align:start position:0% +this at MBL would be to start with this +kind of creature so you might have seen + + align:start position:0% +kind of creature so you might have seen + + + align:start position:0% +kind of creature so you might have seen +that the paper nature that came out last + + align:start position:0% +that the paper nature that came out last + + + align:start position:0% +that the paper nature that came out last +week that the genome of the octopus was + + align:start position:0% +week that the genome of the octopus was + + + align:start position:0% +week that the genome of the octopus was +sequenced there was really heralded in + + align:start position:0% +sequenced there was really heralded in + + + align:start position:0% +sequenced there was really heralded in +the public press finally proving their + + align:start position:0% +the public press finally proving their + + + align:start position:0% +the public press finally proving their +intelligence the argument is that there + + align:start position:0% +intelligence the argument is that there + + + align:start position:0% +intelligence the argument is that there +are 33,000 genes 10,000 more than humans + + align:start position:0% +are 33,000 genes 10,000 more than humans + + + align:start position:0% +are 33,000 genes 10,000 more than humans +that's of course not a very strong + + align:start position:0% +that's of course not a very strong + + + align:start position:0% +that's of course not a very strong +argument there are plans to 45,000 genes + + align:start position:0% +argument there are plans to 45,000 genes + + + align:start position:0% +argument there are plans to 45,000 genes +so that really doesn't tell you very + + align:start position:0% +so that really doesn't tell you very + + + align:start position:0% +so that really doesn't tell you very +much about intelligence but amongst + + align:start position:0% +much about intelligence but amongst + + + align:start position:0% +much about intelligence but amongst +those genes that were found where lots + + align:start position:0% +those genes that were found where lots + + + align:start position:0% +those genes that were found where lots +of genes that are important for + + align:start position:0% +of genes that are important for + + + align:start position:0% +of genes that are important for +development of the brain and there's + + align:start position:0% +development of the brain and there's + + + align:start position:0% +development of the brain and there's +very high heterogeneity in certain gene + + align:start position:0% +very high heterogeneity in certain gene + + + align:start position:0% +very high heterogeneity in certain gene +families that are controlling + + align:start position:0% +families that are controlling + + + align:start position:0% +families that are controlling +development in nervous system so it's + + align:start position:0% +development in nervous system so it's + + + align:start position:0% +development in nervous system so it's +one example of how a better and better + + align:start position:0% +one example of how a better and better + + + align:start position:0% +one example of how a better and better +understanding the intelligence of other + + align:start position:0% +understanding the intelligence of other + + + align:start position:0% +understanding the intelligence of other +creatures in your terms even in + + align:start position:0% +creatures in your terms even in + + + align:start position:0% +creatures in your terms even in +creatures like the octopus which is very + + align:start position:0% +creatures like the octopus which is very + + + align:start position:0% +creatures like the octopus which is very +difficult to study the point I would + + align:start position:0% +difficult to study the point I would + + + align:start position:0% +difficult to study the point I would +like to stress about the octopus is + + align:start position:0% +like to stress about the octopus is + + + align:start position:0% +like to stress about the octopus is +there's really nothing social about + + align:start position:0% +there's really nothing social about + + + align:start position:0% +there's really nothing social about +these species actually almost + + align:start position:0% +these species actually almost + + + align:start position:0% +these species actually almost +simultaneously with this paper there was + + align:start position:0% +simultaneously with this paper there was + + + align:start position:0% +simultaneously with this paper there was +one report about sexual reproduction in + + align:start position:0% +one report about sexual reproduction in + + + align:start position:0% +one report about sexual reproduction in +one particular species of octopus where + + align:start position:0% +one particular species of octopus where + + + align:start position:0% +one particular species of octopus where +it's not clear if it's violence or more + + align:start position:0% +it's not clear if it's violence or more + + + align:start position:0% +it's not clear if it's violence or more +affectionate but this is really the one + + align:start position:0% +affectionate but this is really the one + + + align:start position:0% +affectionate but this is really the one +exception to otherwise the life that's + + align:start position:0% +exception to otherwise the life that's + + + align:start position:0% +exception to otherwise the life that's +pretty much non social at all so in the + + align:start position:0% +pretty much non social at all so in the + + + align:start position:0% +pretty much non social at all so in the +octopus you have like the ex the agent + + align:start position:0% +octopus you have like the ex the agent + + + align:start position:0% +octopus you have like the ex the agent +in this larva which I had seen very + + align:start position:0% +in this larva which I had seen very + + + align:start position:0% +in this larva which I had seen very +early on there's no like interaction + + align:start position:0% +early on there's no like interaction + + + align:start position:0% +early on there's no like interaction +with mom or anything like this they go + + align:start position:0% +with mom or anything like this they go + + + align:start position:0% +with mom or anything like this they go +to the surface of the ocean and they + + align:start position:0% +to the surface of the ocean and they + + + align:start position:0% +to the surface of the ocean and they +start feeding and try to grow as fast as + + align:start position:0% +start feeding and try to grow as fast as + + + align:start position:0% +start feeding and try to grow as fast as +they can because only a few of them are + + align:start position:0% +they can because only a few of them are + + + align:start position:0% +they can because only a few of them are +gonna + + align:start position:0% +gonna + + + align:start position:0% +gonna +then we production is a very scary + + align:start position:0% +then we production is a very scary + + + align:start position:0% +then we production is a very scary +enterprise many many octopus the male + + align:start position:0% +enterprise many many octopus the male + + + align:start position:0% +enterprise many many octopus the male +has to be careful not to be eaten by the + + align:start position:0% +has to be careful not to be eaten by the + + + align:start position:0% +has to be careful not to be eaten by the +female and the process when it's + + align:start position:0% +female and the process when it's + + + align:start position:0% +female and the process when it's +successful then actually the male stops + + align:start position:0% +successful then actually the male stops + + + align:start position:0% +successful then actually the male stops +eating is going to die even before most + + align:start position:0% +eating is going to die even before most + + + align:start position:0% +eating is going to die even before most +of the youngsters are gonna hatch and + + align:start position:0% +of the youngsters are gonna hatch and + + + align:start position:0% +of the youngsters are gonna hatch and +all that mom is gonna do is basically to + + align:start position:0% +all that mom is gonna do is basically to + + + align:start position:0% +all that mom is gonna do is basically to +make sure the freshwater is going to be + + align:start position:0% +make sure the freshwater is going to be + + + align:start position:0% +make sure the freshwater is going to be +delivered to the eggs and that's it and + + align:start position:0% +delivered to the eggs and that's it and + + + align:start position:0% +delivered to the eggs and that's it and +in terms of like social life so you can + + align:start position:0% +in terms of like social life so you can + + + align:start position:0% +in terms of like social life so you can +be very intelligent like an octopus and + + align:start position:0% +be very intelligent like an octopus and + + + align:start position:0% +be very intelligent like an octopus and +who knows I just gave it as mentioned + + align:start position:0% +who knows I just gave it as mentioned + + + align:start position:0% +who knows I just gave it as mentioned +extraterrestrial life maybe other + + align:start position:0% +extraterrestrial life maybe other + + + align:start position:0% +extraterrestrial life maybe other +species out there might also be that + + align:start position:0% +species out there might also be that + + + align:start position:0% +species out there might also be that +social and so that doesn't necessarily + + align:start position:0% +social and so that doesn't necessarily + + + align:start position:0% +social and so that doesn't necessarily +have to be a connection between + + align:start position:0% +have to be a connection between + + + align:start position:0% +have to be a connection between +sociality intelligence second thing is + + align:start position:0% +sociality intelligence second thing is + + + align:start position:0% +sociality intelligence second thing is +you can be like very social and get like + + align:start position:0% +you can be like very social and get like + + + align:start position:0% +you can be like very social and get like +a warm fuzzy feeling of being with + + align:start position:0% +a warm fuzzy feeling of being with + + + align:start position:0% +a warm fuzzy feeling of being with +others and you get lots of protection + + align:start position:0% +others and you get lots of protection + + + align:start position:0% +others and you get lots of protection +being in the group but following your + + align:start position:0% +being in the group but following your + + + align:start position:0% +being in the group but following your +instincts in this way doesn't + + align:start position:0% +instincts in this way doesn't + + + align:start position:0% +instincts in this way doesn't +necessarily make you very smart so I + + align:start position:0% +necessarily make you very smart so I + + + align:start position:0% +necessarily make you very smart so I +don't want to argue against the + + align:start position:0% +don't want to argue against the + + + align:start position:0% +don't want to argue against the +connection between sociality + + align:start position:0% +connection between sociality + + + align:start position:0% +connection between sociality +intelligence in the form of social + + align:start position:0% +intelligence in the form of social + + + align:start position:0% +intelligence in the form of social +intelligence but we have to be careful + + align:start position:0% +intelligence but we have to be careful + + + align:start position:0% +intelligence but we have to be careful +there's no necessary connection between + + align:start position:0% +there's no necessary connection between + + + align:start position:0% +there's no necessary connection between +those however for primates there is this + + align:start position:0% +those however for primates there is this + + + align:start position:0% +those however for primates there is this +idea the social intelligence and parthis + + align:start position:0% +idea the social intelligence and parthis + + + align:start position:0% +idea the social intelligence and parthis +is that really what made primate so + + align:start position:0% +is that really what made primate so + + + align:start position:0% +is that really what made primate so +intelligent is their sociality and so + + align:start position:0% +intelligent is their sociality and so + + + align:start position:0% +intelligent is their sociality and so +let's consider little bit what the + + align:start position:0% +let's consider little bit what the + + + align:start position:0% +let's consider little bit what the +arguments are it was most strongly put + + align:start position:0% +arguments are it was most strongly put + + + align:start position:0% +arguments are it was most strongly put +forward by any countryman and in 76 but + + align:start position:0% +forward by any countryman and in 76 but + + + align:start position:0% +forward by any countryman and in 76 but +there are several precursors to this + + align:start position:0% +there are several precursors to this + + + align:start position:0% +there are several precursors to this +idea so who are these primates the + + align:start position:0% +idea so who are these primates the + + + align:start position:0% +idea so who are these primates the +primates are a small group of mammals + + align:start position:0% +primates are a small group of mammals + + + align:start position:0% +primates are a small group of mammals +with about 400 plus species they're very + + align:start position:0% +with about 400 plus species they're very + + + align:start position:0% +with about 400 plus species they're very +diverse it can have very small primates + + align:start position:0% +diverse it can have very small primates + + + align:start position:0% +diverse it can have very small primates +just like 30 grams all the way to two + + align:start position:0% +just like 30 grams all the way to two + + + align:start position:0% +just like 30 grams all the way to two +and a kilogram animals they evolved + + align:start position:0% +and a kilogram animals they evolved + + + align:start position:0% +and a kilogram animals they evolved +starting like 65 85 million years ago + + align:start position:0% +starting like 65 85 million years ago + + + align:start position:0% +starting like 65 85 million years ago +there was this mass extinction and so + + align:start position:0% +there was this mass extinction and so + + + align:start position:0% +there was this mass extinction and so +you have this high diversity within the + + align:start position:0% +you have this high diversity within the + + + align:start position:0% +you have this high diversity within the +mammals starting from this point on so + + align:start position:0% +mammals starting from this point on so + + + align:start position:0% +mammals starting from this point on so +they have certain things in common + + align:start position:0% +they have certain things in common + + + align:start position:0% +they have certain things in common +obviously with other mammals but they're + + align:start position:0% +obviously with other mammals but they're + + + align:start position:0% +obviously with other mammals but they're +also very special in many ways all of + + align:start position:0% +also very special in many ways all of + + + align:start position:0% +also very special in many ways all of +the primate species are social and + + align:start position:0% +the primate species are social and + + + align:start position:0% +the primate species are social and +anatomist use social but they're all + + align:start position:0% +anatomist use social but they're all + + + align:start position:0% +anatomist use social but they're all +social they developed very slowly so + + align:start position:0% +social they developed very slowly so + + + align:start position:0% +social they developed very slowly so +it's really very different from the + + align:start position:0% +it's really very different from the + + + align:start position:0% +it's really very different from the +octopus a lot of investment is made into + + align:start position:0% +octopus a lot of investment is made into + + + align:start position:0% +octopus a lot of investment is made into +the offspring they're not very many + + align:start position:0% +the offspring they're not very many + + + align:start position:0% +the offspring they're not very many +offspring and the lifespan of these + + align:start position:0% +offspring and the lifespan of these + + + align:start position:0% +offspring and the lifespan of these +animals is pretty long the octopus + + align:start position:0% +animals is pretty long the octopus + + + align:start position:0% +animals is pretty long the octopus +Lifeson is like 3 to 5 years + + align:start position:0% +Lifeson is like 3 to 5 years + + + align:start position:0% +Lifeson is like 3 to 5 years +they're very visual rather than other + + align:start position:0% +they're very visual rather than other + + + align:start position:0% +they're very visual rather than other +mammals which are very off + + align:start position:0% +mammals which are very off + + + align:start position:0% +mammals which are very off +oriented binocular vision menu have + + align:start position:0% +oriented binocular vision menu have + + + align:start position:0% +oriented binocular vision menu have +color vision so vision is very important + + align:start position:0% +color vision so vision is very important + + + align:start position:0% +color vision so vision is very important +for primates and they have on average + + align:start position:0% +for primates and they have on average + + + align:start position:0% +for primates and they have on average +larger brains than other mammals have so + + align:start position:0% +larger brains than other mammals have so + + + align:start position:0% +larger brains than other mammals have so +our understanding of the anatomy of + + align:start position:0% +our understanding of the anatomy of + + + align:start position:0% +our understanding of the anatomy of +primates and what makes this special is + + align:start position:0% +primates and what makes this special is + + + align:start position:0% +primates and what makes this special is +actually very rudimentary but there a + + align:start position:0% +actually very rudimentary but there a + + + align:start position:0% +actually very rudimentary but there a +few points that should be of interest so + + align:start position:0% +few points that should be of interest so + + + align:start position:0% +few points that should be of interest so +if you look at the million brains + + align:start position:0% +if you look at the million brains + + + align:start position:0% +if you look at the million brains +obviously they're very very complex + + align:start position:0% +obviously they're very very complex + + + align:start position:0% +obviously they're very very complex +mammalian brains that are not primate + + align:start position:0% +mammalian brains that are not primate + + + align:start position:0% +mammalian brains that are not primate +wire ones and the main factor wiliest + + align:start position:0% +wire ones and the main factor wiliest + + + align:start position:0% +wire ones and the main factor wiliest +body mass so the bigger an animal is + + align:start position:0% +body mass so the bigger an animal is + + + align:start position:0% +body mass so the bigger an animal is +this is allometric plot of body weight + + align:start position:0% +this is allometric plot of body weight + + + align:start position:0% +this is allometric plot of body weight +so a body weight person's brain weight + + align:start position:0% +so a body weight person's brain weight + + + align:start position:0% +so a body weight person's brain weight +and you can see there's a lock lock + + align:start position:0% +and you can see there's a lock lock + + + align:start position:0% +and you can see there's a lock lock +relationship between the two that's + + align:start position:0% +relationship between the two that's + + + align:start position:0% +relationship between the two that's +something that you find all over the + + align:start position:0% +something that you find all over the + + + align:start position:0% +something that you find all over the +animal kingdom but if you compare + + align:start position:0% +animal kingdom but if you compare + + + align:start position:0% +animal kingdom but if you compare +primates to other non-primate mammals + + align:start position:0% +primates to other non-primate mammals + + + align:start position:0% +primates to other non-primate mammals +you can see that there is a larger + + align:start position:0% +you can see that there is a larger + + + align:start position:0% +you can see that there is a larger +increase with body massive brain mass + + align:start position:0% +increase with body massive brain mass + + + align:start position:0% +increase with body massive brain mass +and also if you count the number of + + align:start position:0% +and also if you count the number of + + + align:start position:0% +and also if you count the number of +neurons the number of brain yours is + + align:start position:0% +neurons the number of brain yours is + + + align:start position:0% +neurons the number of brain yours is +increasing more steeply with body mass + + align:start position:0% +increasing more steeply with body mass + + + align:start position:0% +increasing more steeply with body mass +than it is in other mammals this is + + align:start position:0% +than it is in other mammals this is + + + align:start position:0% +than it is in other mammals this is +obviously very good measurement there + + align:start position:0% +obviously very good measurement there + + + align:start position:0% +obviously very good measurement there +are others if you look for brains + + align:start position:0% +are others if you look for brains + + + align:start position:0% +are others if you look for brains +roughly the same weight you can again + + align:start position:0% +roughly the same weight you can again + + + align:start position:0% +roughly the same weight you can again +see like in in primates you have many + + align:start position:0% +see like in in primates you have many + + + align:start position:0% +see like in in primates you have many +more neurons there are non primates just + + align:start position:0% +more neurons there are non primates just + + + align:start position:0% +more neurons there are non primates just +by these two examples here so there + + align:start position:0% +by these two examples here so there + + + align:start position:0% +by these two examples here so there +seems to be something different the + + align:start position:0% +seems to be something different the + + + align:start position:0% +seems to be something different the +organization the other measures you can + + align:start position:0% +organization the other measures you can + + + align:start position:0% +organization the other measures you can +look at so for example the neuron size + + align:start position:0% +look at so for example the neuron size + + + align:start position:0% +look at so for example the neuron size +is increasing with brain size and + + align:start position:0% +is increasing with brain size and + + + align:start position:0% +is increasing with brain size and +rodents so like a larger brain and + + align:start position:0% +rodents so like a larger brain and + + + align:start position:0% +rodents so like a larger brain and +rodents is not necessarily one that has + + align:start position:0% +rodents is not necessarily one that has + + + align:start position:0% +rodents is not necessarily one that has +many more neurons but these numerous are + + align:start position:0% +many more neurons but these numerous are + + + align:start position:0% +many more neurons but these numerous are +just getting bigger and primates this is + + align:start position:0% +just getting bigger and primates this is + + + align:start position:0% +just getting bigger and primates this is +really not so much the case so the size + + align:start position:0% +really not so much the case so the size + + + align:start position:0% +really not so much the case so the size +of the neuron pretty much stays constant + + align:start position:0% +of the neuron pretty much stays constant + + + align:start position:0% +of the neuron pretty much stays constant +even decrease the size of the brain or + + align:start position:0% +even decrease the size of the brain or + + + align:start position:0% +even decrease the size of the brain or +how much white meta do you actually need + + align:start position:0% +how much white meta do you actually need + + + align:start position:0% +how much white meta do you actually need +per neuron to connect other brain + + align:start position:0% +per neuron to connect other brain + + + align:start position:0% +per neuron to connect other brain +regions and rodents + + align:start position:0% +regions and rodents + + + align:start position:0% +regions and rodents +apparently the fiber caliber is + + align:start position:0% +apparently the fiber caliber is + + + align:start position:0% +apparently the fiber caliber is +increasing with brain size so again your + + align:start position:0% +increasing with brain size so again your + + + align:start position:0% +increasing with brain size so again your +brain might grow just because the + + align:start position:0% +brain might grow just because the + + + align:start position:0% +brain might grow just because the +anatomy of the basic element requires + + align:start position:0% +anatomy of the basic element requires + + + align:start position:0% +anatomy of the basic element requires +the ability to more space but in + + align:start position:0% +the ability to more space but in + + + align:start position:0% +the ability to more space but in +primates that's not the case if you get + + align:start position:0% +primates that's not the case if you get + + + align:start position:0% +primates that's not the case if you get +more white brain matter that's like it + + align:start position:0% +more white brain matter that's like it + + + align:start position:0% +more white brain matter that's like it +because the connectivity is more complex + + align:start position:0% +because the connectivity is more complex + + + align:start position:0% +because the connectivity is more complex +Brian might bring a primate brains also + + align:start position:0% +Brian might bring a primate brains also + + + align:start position:0% +Brian might bring a primate brains also +fold faster with increasing size and + + align:start position:0% +fold faster with increasing size and + + + align:start position:0% +fold faster with increasing size and +volunteers so these are all just like + + align:start position:0% +volunteers so these are all just like + + + align:start position:0% +volunteers so these are all just like +very coarse + + align:start position:0% +very coarse + + + align:start position:0% +very coarse +indications that maybe there's something + + align:start position:0% +indications that maybe there's something + + + align:start position:0% +indications that maybe there's something +special about the primate brain compared + + align:start position:0% +special about the primate brain compared + + + align:start position:0% +special about the primate brain compared +to other mammal Romanian brains so + + align:start position:0% +to other mammal Romanian brains so + + + align:start position:0% +to other mammal Romanian brains so +further along the anatomy so I mentioned + + align:start position:0% +further along the anatomy so I mentioned + + + align:start position:0% +further along the anatomy so I mentioned +that primates have + + align:start position:0% +that primates have + + + align:start position:0% +that primates have +forward-facing eyes they can do + + align:start position:0% +forward-facing eyes they can do + + + align:start position:0% +forward-facing eyes they can do +binocular vision the color vision they + + align:start position:0% +binocular vision the color vision they + + + align:start position:0% +binocular vision the color vision they +have skulls with a large cranium that's + + align:start position:0% +have skulls with a large cranium that's + + + align:start position:0% +have skulls with a large cranium that's +something that makes them special from + + align:start position:0% +something that makes them special from + + + align:start position:0% +something that makes them special from +other mammals they're also special in + + align:start position:0% +other mammals they're also special in + + + align:start position:0% +other mammals they're also special in +other ways that are + + align:start position:0% +other ways that are + + + align:start position:0% +other ways that are +horton if you think about embodied + + align:start position:0% +horton if you think about embodied + + + align:start position:0% +horton if you think about embodied +cognition you don't have to buy into all + + align:start position:0% +cognition you don't have to buy into all + + + align:start position:0% +cognition you don't have to buy into all +these points but obviously if you have a + + align:start position:0% +these points but obviously if you have a + + + align:start position:0% +these points but obviously if you have a +hand as complex as ours which we share + + align:start position:0% +hand as complex as ours which we share + + + align:start position:0% +hand as complex as ours which we share +with many primate species there lots of + + align:start position:0% +with many primate species there lots of + + + align:start position:0% +with many primate species there lots of +things you can do and that requires you + + align:start position:0% +things you can do and that requires you + + + align:start position:0% +things you can do and that requires you +to be able to control it and this gives + + align:start position:0% +to be able to control it and this gives + + + align:start position:0% +to be able to control it and this gives +you power to interact with your + + align:start position:0% +you power to interact with your + + + align:start position:0% +you power to interact with your +environment that other animals might not + + align:start position:0% +environment that other animals might not + + + align:start position:0% +environment that other animals might not +have so the shoulders is more mobile + + align:start position:0% +have so the shoulders is more mobile + + + align:start position:0% +have so the shoulders is more mobile +there's an opposable thumb and many + + align:start position:0% +there's an opposable thumb and many + + + align:start position:0% +there's an opposable thumb and many +species and then in the face they are + + align:start position:0% +species and then in the face they are + + + align:start position:0% +species and then in the face they are +changes that you might already have seen + + align:start position:0% +changes that you might already have seen + + + align:start position:0% +changes that you might already have seen +here so if you go or go sort of up in + + align:start position:0% +here so if you go or go sort of up in + + + align:start position:0% +here so if you go or go sort of up in +the more complex animals this knot + + align:start position:0% +the more complex animals this knot + + + align:start position:0% +the more complex animals this knot +region is becoming increasingly reduced + + align:start position:0% +region is becoming increasingly reduced + + + align:start position:0% +region is becoming increasingly reduced +and I will tell you later likewise why + + align:start position:0% +and I will tell you later likewise why + + + align:start position:0% +and I will tell you later likewise why +this might be important so these + + align:start position:0% +this might be important so these + + + align:start position:0% +this might be important so these +anatomical specialization primates + + align:start position:0% +anatomical specialization primates + + + align:start position:0% +anatomical specialization primates +sociality is very important as well and + + align:start position:0% +sociality is very important as well and + + + align:start position:0% +sociality is very important as well and +so there are four main organizational + + align:start position:0% +so there are four main organizational + + + align:start position:0% +so there are four main organizational +principles of sociality in primates the + + align:start position:0% +principles of sociality in primates the + + + align:start position:0% +principles of sociality in primates the +dominating one is the second one here + + align:start position:0% +dominating one is the second one here + + + align:start position:0% +dominating one is the second one here +it's called a mail transfer system so + + align:start position:0% +it's called a mail transfer system so + + + align:start position:0% +it's called a mail transfer system so +it's a polygamous multi mail + + align:start position:0% +it's a polygamous multi mail + + + align:start position:0% +it's a polygamous multi mail +organization and what it and this is + + align:start position:0% +organization and what it and this is + + + align:start position:0% +organization and what it and this is +very important for the social life of + + align:start position:0% +very important for the social life of + + + align:start position:0% +very important for the social life of +primates because what it means is that + + align:start position:0% +primates because what it means is that + + + align:start position:0% +primates because what it means is that +the social behavior has to be complex so + + align:start position:0% +the social behavior has to be complex so + + + align:start position:0% +the social behavior has to be complex so +there can be cooperation like grooming + + align:start position:0% +there can be cooperation like grooming + + + align:start position:0% +there can be cooperation like grooming +defense and hunting which all the + + align:start position:0% +defense and hunting which all the + + + align:start position:0% +defense and hunting which all the +animals of a troop might engage in but + + align:start position:0% +animals of a troop might engage in but + + + align:start position:0% +animals of a troop might engage in but +at the same time there's competition for + + align:start position:0% +at the same time there's competition for + + + align:start position:0% +at the same time there's competition for +food mates dominance hierarchies and + + align:start position:0% +food mates dominance hierarchies and + + + align:start position:0% +food mates dominance hierarchies and +it's a function of the complexity of the + + align:start position:0% +it's a function of the complexity of the + + + align:start position:0% +it's a function of the complexity of the +social environment so primate social + + align:start position:0% +social environment so primate social + + + align:start position:0% +social environment so primate social +life was beautifully described by + + align:start position:0% +life was beautifully described by + + + align:start position:0% +life was beautifully described by +Dorothy Cheney and then Robert ciphered + + align:start position:0% +Dorothy Cheney and then Robert ciphered + + + align:start position:0% +Dorothy Cheney and then Robert ciphered +in this wonderful book of metaphysics + + align:start position:0% +in this wonderful book of metaphysics + + + align:start position:0% +in this wonderful book of metaphysics +and just gonna quote from that so they + + align:start position:0% +and just gonna quote from that so they + + + align:start position:0% +and just gonna quote from that so they +studied the boon monkeys in the wild and + + align:start position:0% +studied the boon monkeys in the wild and + + + align:start position:0% +studied the boon monkeys in the wild and +here's what they have to say about this + + align:start position:0% +here's what they have to say about this + + + align:start position:0% +here's what they have to say about this +so the domain of expertise for baboons + + align:start position:0% +so the domain of expertise for baboons + + + align:start position:0% +so the domain of expertise for baboons +and indeed for all monkeys and apes is + + align:start position:0% +and indeed for all monkeys and apes is + + + align:start position:0% +and indeed for all monkeys and apes is +social life most problems live in + + align:start position:0% +social life most problems live in + + + align:start position:0% +social life most problems live in +multi-male multi-female groups that + + align:start position:0% +multi-male multi-female groups that + + + align:start position:0% +multi-male multi-female groups that +typically include eight or nine + + align:start position:0% +typically include eight or nine + + + align:start position:0% +typically include eight or nine +Metrolina families which means that the + + align:start position:0% +Metrolina families which means that the + + + align:start position:0% +Metrolina families which means that the +the females they stay in the group and + + align:start position:0% +the females they stay in the group and + + + align:start position:0% +the females they stay in the group and +they found families and they're going to + + align:start position:0% +they found families and they're going to + + + align:start position:0% +they found families and they're going to +stay constant over a long period of time + + align:start position:0% +stay constant over a long period of time + + + align:start position:0% +stay constant over a long period of time +they have a linear dominance hierarchy + + align:start position:0% +they have a linear dominance hierarchy + + + align:start position:0% +they have a linear dominance hierarchy +of males that changes often and the + + align:start position:0% +of males that changes often and the + + + align:start position:0% +of males that changes often and the +linear hierarchy of females in the + + align:start position:0% +linear hierarchy of females in the + + + align:start position:0% +linear hierarchy of females in the +offsprings that can be stable for + + align:start position:0% +offsprings that can be stable for + + + align:start position:0% +offsprings that can be stable for +generations + + align:start position:0% +generations + + + align:start position:0% +generations +daily life in a baboon group includes + + align:start position:0% +daily life in a baboon group includes + + + align:start position:0% +daily life in a baboon group includes +small scale alliances that may involve + + align:start position:0% +small scale alliances that may involve + + + align:start position:0% +small scale alliances that may involve +only three individuals and occasional + + align:start position:0% +only three individuals and occasional + + + align:start position:0% +only three individuals and occasional +large scale 4,000,000 battles that + + align:start position:0% +large scale 4,000,000 battles that + + + align:start position:0% +large scale 4,000,000 battles that +involve all of the members of three or + + align:start position:0% +involve all of the members of three or + + + align:start position:0% +involve all of the members of three or +four metro lines + + align:start position:0% +four metro lines + + + align:start position:0% +four metro lines +males and females can form shortened + + align:start position:0% +males and females can form shortened + + + align:start position:0% +males and females can form shortened +bonds that lead to reproduction or + + align:start position:0% +bonds that lead to reproduction or + + + align:start position:0% +bonds that lead to reproduction or +longer-term friendships the d2 + + align:start position:0% +longer-term friendships the d2 + + + align:start position:0% +longer-term friendships the d2 +cooperative child-rearing + + align:start position:0% +cooperative child-rearing + + + align:start position:0% +cooperative child-rearing +the result of all the social intrigue is + + align:start position:0% +the result of all the social intrigue is + + + align:start position:0% +the result of all the social intrigue is +the kind of Jane Austen melodrama in + + align:start position:0% +the kind of Jane Austen melodrama in + + + align:start position:0% +the kind of Jane Austen melodrama in +which each individual must predict the + + align:start position:0% +which each individual must predict the + + + align:start position:0% +which each individual must predict the +behavior of others and form those + + align:start position:0% +behavior of others and form those + + + align:start position:0% +behavior of others and form those +relationships that we turn the greatest + + align:start position:0% +relationships that we turn the greatest + + + align:start position:0% +relationships that we turn the greatest +benefits these are the problems that the + + align:start position:0% +benefits these are the problems that the + + + align:start position:0% +benefits these are the problems that the +blue mind must solve and this is the + + align:start position:0% +blue mind must solve and this is the + + + align:start position:0% +blue mind must solve and this is the +environment in which it has involved + + align:start position:0% +environment in which it has involved + + + align:start position:0% +environment in which it has involved +most of the problems facing the boons + + align:start position:0% +most of the problems facing the boons + + + align:start position:0% +most of the problems facing the boons +can be expressed in two words other + + align:start position:0% +can be expressed in two words other + + + align:start position:0% +can be expressed in two words other +balloons and so this is really important + + align:start position:0% +balloons and so this is really important + + + align:start position:0% +balloons and so this is really important +so again like you if you're social you + + align:start position:0% +so again like you if you're social you + + + align:start position:0% +so again like you if you're social you +don't necessarily have to be very smart + + align:start position:0% +don't necessarily have to be very smart + + + align:start position:0% +don't necessarily have to be very smart +you can be very smart about to be social + + align:start position:0% +you can be very smart about to be social + + + align:start position:0% +you can be very smart about to be social +but there's something special apparently + + align:start position:0% +but there's something special apparently + + + align:start position:0% +but there's something special apparently +about primates that links our + + align:start position:0% +about primates that links our + + + align:start position:0% +about primates that links our +intelligence to our sociology so again + + align:start position:0% +intelligence to our sociology so again + + + align:start position:0% +intelligence to our sociology so again +so the social intelligence of parthis is + + align:start position:0% +so the social intelligence of parthis is + + + align:start position:0% +so the social intelligence of parthis is +what works in its favor is that the + + align:start position:0% +what works in its favor is that the + + + align:start position:0% +what works in its favor is that the +primates have large brains and primates + + align:start position:0% +primates have large brains and primates + + + align:start position:0% +primates have large brains and primates +apparently group size is correlated with + + align:start position:0% +apparently group size is correlated with + + + align:start position:0% +apparently group size is correlated with +brain size across different species and + + align:start position:0% +brain size across different species and + + + align:start position:0% +brain size across different species and +not the home range size this is an + + align:start position:0% +not the home range size this is an + + + align:start position:0% +not the home range size this is an +alternative hypothesis is that maybe you + + align:start position:0% +alternative hypothesis is that maybe you + + + align:start position:0% +alternative hypothesis is that maybe you +have to forage more complex and forest + + align:start position:0% +have to forage more complex and forest + + + align:start position:0% +have to forage more complex and forest +environments and so like a similar proxy + + align:start position:0% +environments and so like a similar proxy + + + align:start position:0% +environments and so like a similar proxy +for the complexity of your social life + + align:start position:0% +for the complexity of your social life + + + align:start position:0% +for the complexity of your social life +and your physical life predicts there's + + align:start position:0% +and your physical life predicts there's + + + align:start position:0% +and your physical life predicts there's +a better correlation of brain size with + + align:start position:0% +a better correlation of brain size with + + + align:start position:0% +a better correlation of brain size with +the social life than physical life the + + align:start position:0% +the social life than physical life the + + + align:start position:0% +the social life than physical life the +complexity of and individual social + + align:start position:0% +complexity of and individual social + + + align:start position:0% +complexity of and individual social +relationships increases exponentially + + align:start position:0% +relationships increases exponentially + + + align:start position:0% +relationships increases exponentially +with group size and the groups are not + + align:start position:0% +with group size and the groups are not + + + align:start position:0% +with group size and the groups are not +small and when I get back to this point + + align:start position:0% +small and when I get back to this point + + + align:start position:0% +small and when I get back to this point +a little bit the Boone's now the + + align:start position:0% +a little bit the Boone's now the + + + align:start position:0% +a little bit the Boone's now the +primates know their peers dominance rank + + align:start position:0% +primates know their peers dominance rank + + + align:start position:0% +primates know their peers dominance rank +and social relations everything the + + align:start position:0% +and social relations everything the + + + align:start position:0% +and social relations everything the +dimension the previous slide is good + + align:start position:0% +dimension the previous slide is good + + + align:start position:0% +dimension the previous slide is good +evidence for behavioral work that + + align:start position:0% +evidence for behavioral work that + + + align:start position:0% +evidence for behavioral work that +actually primates know something about + + align:start position:0% +actually primates know something about + + + align:start position:0% +actually primates know something about +it this social knowledge contrasts with + + align:start position:0% +it this social knowledge contrasts with + + + align:start position:0% +it this social knowledge contrasts with +surprising cases of ignorance + + align:start position:0% +surprising cases of ignorance + + + align:start position:0% +surprising cases of ignorance +outside of the social domain even when + + align:start position:0% +outside of the social domain even when + + + align:start position:0% +outside of the social domain even when +it's something as important as a as a + + align:start position:0% +it's something as important as a as a + + + align:start position:0% +it's something as important as a as a +predator so chaining ciphered they also + + align:start position:0% +predator so chaining ciphered they also + + + align:start position:0% +predator so chaining ciphered they also +studied vervet monkeys and what they + + align:start position:0% +studied vervet monkeys and what they + + + align:start position:0% +studied vervet monkeys and what they +observed is that rabbit monkeys one of + + align:start position:0% +observed is that rabbit monkeys one of + + + align:start position:0% +observed is that rabbit monkeys one of +the main predators to them is the python + + align:start position:0% +the main predators to them is the python + + + align:start position:0% +the main predators to them is the python +and the Python of it walked it across in + + align:start position:0% +and the Python of it walked it across in + + + align:start position:0% +and the Python of it walked it across in +the sand at least behind a trail and + + align:start position:0% +the sand at least behind a trail and + + + align:start position:0% +the sand at least behind a trail and +there's absolutely no indication of the + + align:start position:0% +there's absolutely no indication of the + + + align:start position:0% +there's absolutely no indication of the +world monkeys make the connection + + align:start position:0% +world monkeys make the connection + + + align:start position:0% +world monkeys make the connection +between these trails and the presence of + + align:start position:0% +between these trails and the presence of + + + align:start position:0% +between these trails and the presence of +a Python which is really striking you + + align:start position:0% +a Python which is really striking you + + + align:start position:0% +a Python which is really striking you +would imagine this is like the first + + align:start position:0% +would imagine this is like the first + + + align:start position:0% +would imagine this is like the first +thing that they would have to learn so + + align:start position:0% +thing that they would have to learn so + + + align:start position:0% +thing that they would have to learn so +there are cases where they she fall in + + align:start position:0% +there are cases where they she fall in + + + align:start position:0% +there are cases where they she fall in +the trailer to the ocean and they're + + align:start position:0% +the trailer to the ocean and they're + + + align:start position:0% +the trailer to the ocean and they're +very surprised to find find a pipe in + + align:start position:0% +very surprised to find find a pipe in + + + align:start position:0% +very surprised to find find a pipe in +there another example is our leopard so + + align:start position:0% +there another example is our leopard so + + + align:start position:0% +there another example is our leopard so +on the environment leopards of course + + align:start position:0% +on the environment leopards of course + + + align:start position:0% +on the environment leopards of course +predators will also feed on the velvet + + align:start position:0% +predators will also feed on the velvet + + + align:start position:0% +predators will also feed on the velvet +monkeys leopards have a way of putting + + align:start position:0% +monkeys leopards have a way of putting + + + align:start position:0% +monkeys leopards have a way of putting +the carcasses of animals they hunted + + align:start position:0% +the carcasses of animals they hunted + + + align:start position:0% +the carcasses of animals they hunted +down into the trees to protect them from + + align:start position:0% +down into the trees to protect them from + + + align:start position:0% +down into the trees to protect them from +larger predators like lions so the + + align:start position:0% +larger predators like lions so the + + + align:start position:0% +larger predators like lions so the +presence of a carcass would actually + + align:start position:0% +presence of a carcass would actually + + + align:start position:0% +presence of a carcass would actually +indicate you that likely there is a + + align:start position:0% +indicate you that likely there is a + + + align:start position:0% +indicate you that likely there is a +leopard around and again the robot + + align:start position:0% +leopard around and again the robot + + + align:start position:0% +leopard around and again the robot +monkeys they don't make that connection + + align:start position:0% +monkeys they don't make that connection + + + align:start position:0% +monkeys they don't make that connection +so if there's the carcass + + align:start position:0% +so if there's the carcass + + + align:start position:0% +so if there's the carcass +they're they're not particularly scared + + align:start position:0% +they're they're not particularly scared + + + align:start position:0% +they're they're not particularly scared +about it it doesn't mean that they're + + align:start position:0% +about it it doesn't mean that they're + + + align:start position:0% +about it it doesn't mean that they're +ignorant so they even following alarm + + align:start position:0% +ignorant so they even following alarm + + + align:start position:0% +ignorant so they even following alarm +calls from other species as to whether + + align:start position:0% +calls from other species as to whether + + + align:start position:0% +calls from other species as to whether +an eagle is approaching or if cattle is + + align:start position:0% +an eagle is approaching or if cattle is + + + align:start position:0% +an eagle is approaching or if cattle is +approaching so it's not that they are + + align:start position:0% +approaching so it's not that they are + + + align:start position:0% +approaching so it's not that they are +generally dumb in this way but there's + + align:start position:0% +generally dumb in this way but there's + + + align:start position:0% +generally dumb in this way but there's +really this this very big contrast about + + align:start position:0% +really this this very big contrast about + + + align:start position:0% +really this this very big contrast about +like all the details doesn't know about + + align:start position:0% +like all the details doesn't know about + + + align:start position:0% +like all the details doesn't know about +the social world and the Oblivion's that + + align:start position:0% +the social world and the Oblivion's that + + + align:start position:0% +the social world and the Oblivion's that +they can express for for non social + + align:start position:0% +they can express for for non social + + + align:start position:0% +they can express for for non social +factors then we have specializations + + align:start position:0% +factors then we have specializations + + + align:start position:0% +factors then we have specializations +we're going to talk about this in the + + align:start position:0% +we're going to talk about this in the + + + align:start position:0% +we're going to talk about this in the +brain for processing social stimuli and + + align:start position:0% +brain for processing social stimuli and + + + align:start position:0% +brain for processing social stimuli and +then there's actually evidence that + + align:start position:0% +then there's actually evidence that + + + align:start position:0% +then there's actually evidence that +females who have better social abilities + + align:start position:0% +females who have better social abilities + + + align:start position:0% +females who have better social abilities +that they are less stressed and they + + align:start position:0% +that they are less stressed and they + + + align:start position:0% +that they are less stressed and they +have better reproductive success and so + + align:start position:0% +have better reproductive success and so + + + align:start position:0% +have better reproductive success and so +so this all works to say that if you are + + align:start position:0% +so this all works to say that if you are + + + align:start position:0% +so this all works to say that if you are +socially smart in a baboon environment + + align:start position:0% +socially smart in a baboon environment + + + align:start position:0% +socially smart in a baboon environment +or an environment of many primate + + align:start position:0% +or an environment of many primate + + + align:start position:0% +or an environment of many primate +species they actually have better + + align:start position:0% +species they actually have better + + + align:start position:0% +species they actually have better +success reproducing therefore there's a + + align:start position:0% +success reproducing therefore there's a + + + align:start position:0% +success reproducing therefore there's a +good argument to be made that your + + align:start position:0% +good argument to be made that your + + + align:start position:0% +good argument to be made that your +social intelligence will they have to go + + align:start position:0% +social intelligence will they have to go + + + align:start position:0% +social intelligence will they have to go +to the next generation this is like how + + align:start position:0% +to the next generation this is like how + + + align:start position:0% +to the next generation this is like how +social intelligence might improve I + + align:start position:0% +social intelligence might improve I + + + align:start position:0% +social intelligence might improve I +think there's one important point that's + + align:start position:0% +think there's one important point that's + + + align:start position:0% +think there's one important point that's +oftentimes not made and that's if you + + align:start position:0% +oftentimes not made and that's if you + + + align:start position:0% +oftentimes not made and that's if you +become smart and smarter and there can + + align:start position:0% +become smart and smarter and there can + + + align:start position:0% +become smart and smarter and there can +be the physical environment your + + align:start position:0% +be the physical environment your + + + align:start position:0% +be the physical environment your +physical environment does not change + + align:start position:0% +physical environment does not change + + + align:start position:0% +physical environment does not change +very much but if you were interacting + + align:start position:0% +very much but if you were interacting + + + align:start position:0% +very much but if you were interacting +with the social environment getting + + align:start position:0% +with the social environment getting + + + align:start position:0% +with the social environment getting +smart and smarter + + align:start position:0% +smart and smarter + + + align:start position:0% +smart and smarter +interacting with the social environment + + align:start position:0% +interacting with the social environment + + + align:start position:0% +interacting with the social environment +the elements in your social environment + + align:start position:0% +the elements in your social environment + + + align:start position:0% +the elements in your social environment +interacting with they're also getting + + align:start position:0% +interacting with they're also getting + + + align:start position:0% +interacting with they're also getting +smarter and smarter + + align:start position:0% +smarter and smarter + + + align:start position:0% +smarter and smarter +so actually setting forth an arms race + + align:start position:0% +so actually setting forth an arms race + + + align:start position:0% +so actually setting forth an arms race +where you're not only improving your + + align:start position:0% +where you're not only improving your + + + align:start position:0% +where you're not only improving your +situation by getting smarter but we have + + align:start position:0% +situation by getting smarter but we have + + + align:start position:0% +situation by getting smarter but we have +to get smart in order keep pace with the + + align:start position:0% +to get smart in order keep pace with the + + + align:start position:0% +to get smart in order keep pace with the +others who are outsmarting you and so + + align:start position:0% +others who are outsmarting you and so + + + align:start position:0% +others who are outsmarting you and so +you can see like how they could be a + + align:start position:0% +you can see like how they could be a + + + align:start position:0% +you can see like how they could be a +connection between sociology and + + align:start position:0% +connection between sociology and + + + align:start position:0% +connection between sociology and +intelligence that that really this arms + + align:start position:0% +intelligence that that really this arms + + + align:start position:0% +intelligence that that really this arms +race does not occur for physical + + align:start position:0% +race does not occur for physical + + + align:start position:0% +race does not occur for physical +interactions but for social interactions + + align:start position:0% +interactions but for social interactions + + + align:start position:0% +interactions but for social interactions +so that they actually have to be able to + + align:start position:0% +so that they actually have to be able to + + + align:start position:0% +so that they actually have to be able to +better predict the next move of someone + + align:start position:0% +better predict the next move of someone + + + align:start position:0% +better predict the next move of someone +else in your in your group and you have + + align:start position:0% +else in your in your group and you have + + + align:start position:0% +else in your in your group and you have +to know something about that individual + + align:start position:0% +to know something about that individual + + + align:start position:0% +to know something about that individual +for you to be successful so their + + align:start position:0% +for you to be successful so their + + + align:start position:0% +for you to be successful so their +arguments against the social + + align:start position:0% +arguments against the social + + + align:start position:0% +arguments against the social +intelligence hypothesis and so in + + align:start position:0% +intelligence hypothesis and so in + + + align:start position:0% +intelligence hypothesis and so in +particularly ignorant about many other + + align:start position:0% +particularly ignorant about many other + + + align:start position:0% +particularly ignorant about many other +species so there are other social + + align:start position:0% +species so there are other social + + + align:start position:0% +species so there are other social +species hyenas for example have complex + + align:start position:0% +species hyenas for example have complex + + + align:start position:0% +species hyenas for example have complex +societies but Hina's have not been + + align:start position:0% +societies but Hina's have not been + + + align:start position:0% +societies but Hina's have not been +studied as much as as monkeys have we + + align:start position:0% +studied as much as as monkeys have we + + + align:start position:0% +studied as much as as monkeys have we +also don't know about the complexity + + align:start position:0% +also don't know about the complexity + + + align:start position:0% +also don't know about the complexity +mostly for this reason where they're + + align:start position:0% +mostly for this reason where they're + + + align:start position:0% +mostly for this reason where they're +really compare compared to waves and + + align:start position:0% +really compare compared to waves and + + + align:start position:0% +really compare compared to waves and +whales for example primate societies are + + align:start position:0% +whales for example primate societies are + + + align:start position:0% +whales for example primate societies are +more complex and this of course would be + + align:start position:0% +more complex and this of course would be + + + align:start position:0% +more complex and this of course would be +like a crucial conjecture of this social + + align:start position:0% +like a crucial conjecture of this social + + + align:start position:0% +like a crucial conjecture of this social +intelligence hypothesis + + align:start position:0% +intelligence hypothesis + + + align:start position:0% +intelligence hypothesis +then within the primate orders they + + align:start position:0% +then within the primate orders they + + + align:start position:0% +then within the primate orders they +actually some other correlations that + + align:start position:0% +actually some other correlations that + + + align:start position:0% +actually some other correlations that +the do predict brain sites very well and + + align:start position:0% +the do predict brain sites very well and + + + align:start position:0% +the do predict brain sites very well and +so then the primate order social + + align:start position:0% +so then the primate order social + + + align:start position:0% +so then the primate order social +learning innovation and tool use are + + align:start position:0% +learning innovation and tool use are + + + align:start position:0% +learning innovation and tool use are +strongly correlated with brain size and + + align:start position:0% +strongly correlated with brain size and + + + align:start position:0% +strongly correlated with brain size and +not with group size so you could imagine + + align:start position:0% +not with group size so you could imagine + + + align:start position:0% +not with group size so you could imagine +a scenario actually the evolution of + + align:start position:0% +a scenario actually the evolution of + + + align:start position:0% +a scenario actually the evolution of +basic social intelligence is something + + align:start position:0% +basic social intelligence is something + + + align:start position:0% +basic social intelligence is something +that's very basic to primates but then + + align:start position:0% +that's very basic to primates but then + + + align:start position:0% +that's very basic to primates but then +if you go to different species within + + align:start position:0% +if you go to different species within + + + align:start position:0% +if you go to different species within +the primate order and ask like why did + + align:start position:0% +the primate order and ask like why did + + + align:start position:0% +the primate order and ask like why did +they become so smart like arrange a + + align:start position:0% +they become so smart like arrange a + + + align:start position:0% +they become so smart like arrange a +tensor or chimp so you can use tools + + align:start position:0% +tensor or chimp so you can use tools + + + align:start position:0% +tensor or chimp so you can use tools +then it really might be the tool uses + + align:start position:0% +then it really might be the tool uses + + + align:start position:0% +then it really might be the tool uses +maybe you have more importance than the + + align:start position:0% +maybe you have more importance than the + + + align:start position:0% +maybe you have more importance than the +Sociology okay so the movie here that + + align:start position:0% +Sociology okay so the movie here that + + + align:start position:0% +Sociology okay so the movie here that +actually lists rates these two different + + align:start position:0% +actually lists rates these two different + + + align:start position:0% +actually lists rates these two different +hypotheses so you see social + + align:start position:0% +hypotheses so you see social + + + align:start position:0% +hypotheses so you see social +interactions here and a rope of tonkin + + align:start position:0% +interactions here and a rope of tonkin + + + align:start position:0% +interactions here and a rope of tonkin +macaque monkeys you can see the facial + + align:start position:0% +macaque monkeys you can see the facial + + + align:start position:0% +macaque monkeys you can see the facial +displays you can see that they are + + align:start position:0% +displays you can see that they are + + + align:start position:0% +displays you can see that they are +tending to each other and well you might + + align:start position:0% +tending to each other and well you might + + + align:start position:0% +tending to each other and well you might +think that they are trying to figure out + + align:start position:0% +think that they are trying to figure out + + + align:start position:0% +think that they are trying to figure out +what's actually going on here and here's + + align:start position:0% +what's actually going on here and here's + + + align:start position:0% +what's actually going on here and here's +the alternative hypothesis so this is + + align:start position:0% +the alternative hypothesis so this is + + + align:start position:0% +the alternative hypothesis so this is +tool use so you can see this guy really + + align:start position:0% +tool use so you can see this guy really + + + align:start position:0% +tool use so you can see this guy really +just invented a cool to dos pick and so + + align:start position:0% +just invented a cool to dos pick and so + + + align:start position:0% +just invented a cool to dos pick and so +it's anyone's guess what's more + + align:start position:0% +it's anyone's guess what's more + + + align:start position:0% +it's anyone's guess what's more +important to your intelligence your + + align:start position:0% +important to your intelligence your + + + align:start position:0% +important to your intelligence your +being able to read the social signals + + align:start position:0% +being able to read the social signals + + + align:start position:0% +being able to read the social signals +from other individuals in your troop or + + align:start position:0% +from other individuals in your troop or + + + align:start position:0% +from other individuals in your troop or +your ability to emit a nice nose pick so + + align:start position:0% +your ability to emit a nice nose pick so + + + align:start position:0% +your ability to emit a nice nose pick so +and the last point I wanted to make is + + align:start position:0% +and the last point I wanted to make is + + + align:start position:0% +and the last point I wanted to make is +it's a question so there are the + + align:start position:0% +it's a question so there are the + + + align:start position:0% +it's a question so there are the +primates abilities in social knowledge + + align:start position:0% +primates abilities in social knowledge + + + align:start position:0% +primates abilities in social knowledge +really intelligent or inter just more + + align:start position:0% +really intelligent or inter just more + + + align:start position:0% +really intelligent or inter just more +like idiot savant likability so like a + + align:start position:0% +like idiot savant likability so like a + + + align:start position:0% +like idiot savant likability so like a +like a unique specialization where they + + align:start position:0% +like a unique specialization where they + + + align:start position:0% +like a unique specialization where they +good at the argument that chaining + + align:start position:0% +good at the argument that chaining + + + align:start position:0% +good at the argument that chaining +ciphers made is the following so the + + align:start position:0% +ciphers made is the following so the + + + align:start position:0% +ciphers made is the following so the +knowledge that they have should actually + + align:start position:0% +knowledge that they have should actually + + + align:start position:0% +knowledge that they have should actually +be true knowledge and just not like + + align:start position:0% +be true knowledge and just not like + + + align:start position:0% +be true knowledge and just not like +Laurent associations and the reason has + + align:start position:0% +Laurent associations and the reason has + + + align:start position:0% +Laurent associations and the reason has +to do with the complexity of the social + + align:start position:0% +to do with the complexity of the social + + + align:start position:0% +to do with the complexity of the social +environment if you have a division + + align:start position:0% +environment if you have a division + + + align:start position:0% +environment if you have a division +individuals which is the typical case + + align:start position:0% +individuals which is the typical case + + + align:start position:0% +individuals which is the typical case +for these boon monkeys you have 3160 + + align:start position:0% +for these boon monkeys you have 3160 + + + align:start position:0% +for these boon monkeys you have 3160 +pairs of animals in eighty 2160 triads + + align:start position:0% +pairs of animals in eighty 2160 triads + + + align:start position:0% +pairs of animals in eighty 2160 triads +it's going to be virtually impossible + + align:start position:0% +it's going to be virtually impossible + + + align:start position:0% +it's going to be virtually impossible +for you to learn all these different + + align:start position:0% +for you to learn all these different + + + align:start position:0% +for you to learn all these different +pairwise relationships and then behave + + align:start position:0% +pairwise relationships and then behave + + + align:start position:0% +pairwise relationships and then behave +intelligently based upon it + + align:start position:0% +intelligently based upon it + + + align:start position:0% +intelligently based upon it +secondly these relationships can change + + align:start position:0% +secondly these relationships can change + + + align:start position:0% +secondly these relationships can change +very fast so it would not be very smart + + align:start position:0% +very fast so it would not be very smart + + + align:start position:0% +very fast so it would not be very smart +to try to have like a list of all these + + align:start position:0% +to try to have like a list of all these + + + align:start position:0% +to try to have like a list of all these +pairwise interactions and then act upon + + align:start position:0% +pairwise interactions and then act upon + + + align:start position:0% +pairwise interactions and then act upon +that no single behavioral metrics seems + + align:start position:0% +that no single behavioral metrics seems + + + align:start position:0% +that no single behavioral metrics seems +to be necessary or sufficient to + + align:start position:0% +to be necessary or sufficient to + + + align:start position:0% +to be necessary or sufficient to +recognize associations like Metrolina + + align:start position:0% +recognize associations like Metrolina + + + align:start position:0% +recognize associations like Metrolina +kin so human observers apparently are + + align:start position:0% +kin so human observers apparently are + + + align:start position:0% +kin so human observers apparently are +not very good to predict this if they + + align:start position:0% +not very good to predict this if they + + + align:start position:0% +not very good to predict this if they +don't know the animals very well + + align:start position:0% +don't know the animals very well + + + align:start position:0% +don't know the animals very well +personally then you might think well + + align:start position:0% +personally then you might think well + + + align:start position:0% +personally then you might think well +maybe it's not exist exactly like a list + + align:start position:0% +maybe it's not exist exactly like a list + + + align:start position:0% +maybe it's not exist exactly like a list +but you don't really learn this much and + + align:start position:0% +but you don't really learn this much and + + + align:start position:0% +but you don't really learn this much and +you apply like a simple rule to it and + + align:start position:0% +you apply like a simple rule to it and + + + align:start position:0% +you apply like a simple rule to it and +that also doesn't seem to + + align:start position:0% +that also doesn't seem to + + + align:start position:0% +that also doesn't seem to +very well because social relationships + + align:start position:0% +very well because social relationships + + + align:start position:0% +very well because social relationships +like friendships they're intransitive so + + align:start position:0% +like friendships they're intransitive so + + + align:start position:0% +like friendships they're intransitive so +if a and B are friends B&C are friends + + align:start position:0% +if a and B are friends B&C are friends + + + align:start position:0% +if a and B are friends B&C are friends +that doesn't mean that a necessarily + + align:start position:0% +that doesn't mean that a necessarily + + + align:start position:0% +that doesn't mean that a necessarily +have to be friends + + align:start position:0% +have to be friends + + + align:start position:0% +have to be friends +others like family relationships are + + align:start position:0% +others like family relationships are + + + align:start position:0% +others like family relationships are +complex the non-associative of Ace the + + align:start position:0% +complex the non-associative of Ace the + + + align:start position:0% +complex the non-associative of Ace the +mother of B actually means that B is not + + align:start position:0% +mother of B actually means that B is not + + + align:start position:0% +mother of B actually means that B is not +the mother of a so there's a more + + align:start position:0% +the mother of a so there's a more + + + align:start position:0% +the mother of a so there's a more +complex interaction there as well and + + align:start position:0% +complex interaction there as well and + + + align:start position:0% +complex interaction there as well and +then fine oops finally there can be some + + align:start position:0% +then fine oops finally there can be some + + + align:start position:0% +then fine oops finally there can be some +attains membership in multiple classes + + align:start position:0% +attains membership in multiple classes + + + align:start position:0% +attains membership in multiple classes +and again for you to be able to keep + + align:start position:0% +and again for you to be able to keep + + + align:start position:0% +and again for you to be able to keep +track of this you better have a + + align:start position:0% +track of this you better have a + + + align:start position:0% +track of this you better have a +cognitive model of what's going on + + align:start position:0% +cognitive model of what's going on + + + align:start position:0% +cognitive model of what's going on +rather than just like a list of + + align:start position:0% +rather than just like a list of + + + align:start position:0% +rather than just like a list of +associations that you learned it's very + + align:start position:0% +associations that you learned it's very + + + align:start position:0% +associations that you learned it's very +difficult in experiments actually to + + align:start position:0% +difficult in experiments actually to + + + align:start position:0% +difficult in experiments actually to +prove that's not Association but I think + + align:start position:0% +prove that's not Association but I think + + + align:start position:0% +prove that's not Association but I think +these are very good arguments to + + align:start position:0% +these are very good arguments to + + + align:start position:0% +these are very good arguments to +consider that actually these primates + + align:start position:0% +consider that actually these primates + + + align:start position:0% +consider that actually these primates +have active knowledge of the social + + align:start position:0% +have active knowledge of the social + + + align:start position:0% +have active knowledge of the social +environment so there's one example for + + align:start position:0% +environment so there's one example for + + + align:start position:0% +environment so there's one example for +this where you can issue make the point + + align:start position:0% +this where you can issue make the point + + + align:start position:0% +this where you can issue make the point +very nice and this is the story of Allah + + align:start position:0% +very nice and this is the story of Allah + + + align:start position:0% +very nice and this is the story of Allah +so Allah is a baboon monkey and she was + + align:start position:0% +so Allah is a baboon monkey and she was + + + align:start position:0% +so Allah is a baboon monkey and she was +actually living with farmers in + + align:start position:0% +actually living with farmers in + + + align:start position:0% +actually living with farmers in +Southwest Africa so there was a habit at + + align:start position:0% +Southwest Africa so there was a habit at + + + align:start position:0% +Southwest Africa so there was a habit at +the time to actually pretty place dogs + + align:start position:0% +the time to actually pretty place dogs + + + align:start position:0% +the time to actually pretty place dogs +who were herding goats with baboons and + + align:start position:0% +who were herding goats with baboons and + + + align:start position:0% +who were herding goats with baboons and +so you can see Allah sitting here you + + align:start position:0% +so you can see Allah sitting here you + + + align:start position:0% +so you can see Allah sitting here you +can see here here adopting some of the + + align:start position:0% +can see here here adopting some of the + + + align:start position:0% +can see here here adopting some of the +havior of the goats + + align:start position:0% +havior of the goats + + + align:start position:0% +havior of the goats +so she's licking salt here which is + + align:start position:0% +so she's licking salt here which is + + + align:start position:0% +so she's licking salt here which is +something that baboons would naturally + + align:start position:0% +something that baboons would naturally + + + align:start position:0% +something that baboons would naturally +not do she would continue to engage in + + align:start position:0% +not do she would continue to engage in + + + align:start position:0% +not do she would continue to engage in +social behaviors the typical baboons so + + align:start position:0% +social behaviors the typical baboons so + + + align:start position:0% +social behaviors the typical baboons so +she would groom the goats for example + + align:start position:0% +she would groom the goats for example + + + align:start position:0% +she would groom the goats for example +but the most amazing thing about her + + align:start position:0% +but the most amazing thing about her + + + align:start position:0% +but the most amazing thing about her +which is a little hard to see as you see + + align:start position:0% +which is a little hard to see as you see + + + align:start position:0% +which is a little hard to see as you see +oh here she is carrying one of the + + align:start position:0% +oh here she is carrying one of the + + + align:start position:0% +oh here she is carrying one of the +little Yin links here and brings it to + + align:start position:0% +little Yin links here and brings it to + + + align:start position:0% +little Yin links here and brings it to +its mother and the description of what + + align:start position:0% +its mother and the description of what + + + align:start position:0% +its mother and the description of what +what this animal was doing was when when + + align:start position:0% +what this animal was doing was when when + + + align:start position:0% +what this animal was doing was when when +the goats are brought home and then + + align:start position:0% +the goats are brought home and then + + + align:start position:0% +the goats are brought home and then +sometimes they were separated separating + + align:start position:0% +sometimes they were separated separating + + + align:start position:0% +sometimes they were separated separating +the mother goats from the offspring she + + align:start position:0% +the mother goats from the offspring she + + + align:start position:0% +the mother goats from the offspring she +would actually go manic and try to pair + + align:start position:0% +would actually go manic and try to pair + + + align:start position:0% +would actually go manic and try to pair +them up and and would not stop until she + + align:start position:0% +them up and and would not stop until she + + + align:start position:0% +them up and and would not stop until she +was finished and this would even happen + + align:start position:0% +was finished and this would even happen + + + align:start position:0% +was finished and this would even happen +it's like multiple goats were calling + + align:start position:0% +it's like multiple goats were calling + + + align:start position:0% +it's like multiple goats were calling +for the healings and advice' vice versa + + align:start position:0% +for the healings and advice' vice versa + + + align:start position:0% +for the healings and advice' vice versa +and so she would have to put order into + + align:start position:0% +and so she would have to put order into + + + align:start position:0% +and so she would have to put order into +the social world that she was living in + + align:start position:0% +the social world that she was living in + + + align:start position:0% +the social world that she was living in +and she wouldn't stop until this order + + align:start position:0% +and she wouldn't stop until this order + + + align:start position:0% +and she wouldn't stop until this order +was restored and the farmer said that + + align:start position:0% +was restored and the farmer said that + + + align:start position:0% +was restored and the farmer said that +they were not able to tell any of the + + align:start position:0% +they were not able to tell any of the + + + align:start position:0% +they were not able to tell any of the +adult goals or the healings or know any + + align:start position:0% +adult goals or the healings or know any + + + align:start position:0% +adult goals or the healings or know any +of the pairs but this was like her world + + align:start position:0% +of the pairs but this was like her world + + + align:start position:0% +of the pairs but this was like her world +this was like a social environment that + + align:start position:0% +this was like a social environment that + + + align:start position:0% +this was like a social environment that +she was in and she would structured + + align:start position:0% +she was in and she would structured + + + align:start position:0% +she was in and she would structured +according to her cognitive demands so + + align:start position:0% +according to her cognitive demands so + + + align:start position:0% +according to her cognitive demands so +the point is that primates have + + align:start position:0% +the point is that primates have + + + align:start position:0% +the point is that primates have +intricate social knowledge so they know + + align:start position:0% +intricate social knowledge so they know + + + align:start position:0% +intricate social knowledge so they know +about the status of individuals like the + + align:start position:0% +about the status of individuals like the + + + align:start position:0% +about the status of individuals like the +age of + + align:start position:0% +age of + + + align:start position:0% +age of +gender they know about the interactions + + align:start position:0% +gender they know about the interactions + + + align:start position:0% +gender they know about the interactions +of individuals are they recognized in + + align:start position:0% +of individuals are they recognized in + + + align:start position:0% +of individuals are they recognized in +very simply like rooming and mothering + + align:start position:0% +very simply like rooming and mothering + + + align:start position:0% +very simply like rooming and mothering +and then based on these observations of + + align:start position:0% +and then based on these observations of + + + align:start position:0% +and then based on these observations of +the different individuals in the social + + align:start position:0% +the different individuals in the social + + + align:start position:0% +the different individuals in the social +world they built these cognitive + + align:start position:0% +world they built these cognitive + + + align:start position:0% +world they built these cognitive +structures like friendship kinship and + + align:start position:0% +structures like friendship kinship and + + + align:start position:0% +structures like friendship kinship and +hierarchy are there an interesting + + align:start position:0% +hierarchy are there an interesting + + + align:start position:0% +hierarchy are there an interesting +complicated structure to them all of + + align:start position:0% +complicated structure to them all of + + + align:start position:0% +complicated structure to them all of +this is rooted in the concept of the + + align:start position:0% +this is rooted in the concept of the + + + align:start position:0% +this is rooted in the concept of the +person and this is very important and as + + align:start position:0% +person and this is very important and as + + + align:start position:0% +person and this is very important and as +I'm going to be talking about face or + + align:start position:0% +I'm going to be talking about face or + + + align:start position:0% +I'm going to be talking about face or +condition have to emphasize these are + + align:start position:0% +condition have to emphasize these are + + + align:start position:0% +condition have to emphasize these are +two different things you can recognize a + + align:start position:0% +two different things you can recognize a + + + align:start position:0% +two different things you can recognize a +person from the face but if you can + + align:start position:0% +person from the face but if you can + + + align:start position:0% +person from the face but if you can +recognize the face it doesn't mean that + + align:start position:0% +recognize the face it doesn't mean that + + + align:start position:0% +recognize the face it doesn't mean that +you know who it is who's behind the face + + align:start position:0% +you know who it is who's behind the face + + + align:start position:0% +you know who it is who's behind the face +so the person content will include like + + align:start position:0% +so the person content will include like + + + align:start position:0% +so the person content will include like +something like this is a juvenile female + + align:start position:0% +something like this is a juvenile female + + + align:start position:0% +something like this is a juvenile female +monkey it's the daughter of X and so on + + align:start position:0% +monkey it's the daughter of X and so on + + + align:start position:0% +monkey it's the daughter of X and so on +and so forth so this is knowledge that + + align:start position:0% +and so forth so this is knowledge that + + + align:start position:0% +and so forth so this is knowledge that +you have and that you've been shown in + + align:start position:0% +you have and that you've been shown in + + + align:start position:0% +you have and that you've been shown in +rhesus monkeys the monkeys that we work + + align:start position:0% +rhesus monkeys the monkeys that we work + + + align:start position:0% +rhesus monkeys the monkeys that we work +with today she have this person of lunch + + align:start position:0% +with today she have this person of lunch + + + align:start position:0% +with today she have this person of lunch +so why do we study faces so far faces + + align:start position:0% +so why do we study faces so far faces + + + align:start position:0% +so why do we study faces so far faces +really are the ideal intersection + + align:start position:0% +really are the ideal intersection + + + align:start position:0% +really are the ideal intersection +between object recognition the study of + + align:start position:0% +between object recognition the study of + + + align:start position:0% +between object recognition the study of +which attorney kollet-- talked about in + + align:start position:0% +which attorney kollet-- talked about in + + + align:start position:0% +which attorney kollet-- talked about in +social cognition so as Jim was alluding + + align:start position:0% +social cognition so as Jim was alluding + + + align:start position:0% +social cognition so as Jim was alluding +to yesterday vision is really important + + align:start position:0% +to yesterday vision is really important + + + align:start position:0% +to yesterday vision is really important +in primates about a third of the primate + + align:start position:0% +in primates about a third of the primate + + + align:start position:0% +in primates about a third of the primate +brain is thought to be involved in + + align:start position:0% +brain is thought to be involved in + + + align:start position:0% +brain is thought to be involved in +visual function so this is a lot and + + align:start position:0% +visual function so this is a lot and + + + align:start position:0% +visual function so this is a lot and +this is testimony the fact that there's + + align:start position:0% +this is testimony the fact that there's + + + align:start position:0% +this is testimony the fact that there's +a lot of information to be gathered from + + align:start position:0% +a lot of information to be gathered from + + + align:start position:0% +a lot of information to be gathered from +the outside visual world but also that + + align:start position:0% +the outside visual world but also that + + + align:start position:0% +the outside visual world but also that +it's difficult computationally to gather + + align:start position:0% +it's difficult computationally to gather + + + align:start position:0% +it's difficult computationally to gather +this + + align:start position:0% +this + + + align:start position:0% +this +and so Jim was explaining some of the + + align:start position:0% +and so Jim was explaining some of the + + + align:start position:0% +and so Jim was explaining some of the +computational challenges that Octavian + + align:start position:0% +computational challenges that Octavian + + + align:start position:0% +computational challenges that Octavian +has to solve yesterday and I will come + + align:start position:0% +has to solve yesterday and I will come + + + align:start position:0% +has to solve yesterday and I will come +back to some of these points of the + + align:start position:0% +back to some of these points of the + + + align:start position:0% +back to some of these points of the +later so what is an object so Jim was + + align:start position:0% +later so what is an object so Jim was + + + align:start position:0% +later so what is an object so Jim was +saying that it's the base unit of + + align:start position:0% +saying that it's the base unit of + + + align:start position:0% +saying that it's the base unit of +cognition and just very quickly what it + + align:start position:0% +cognition and just very quickly what it + + + align:start position:0% +cognition and just very quickly what it +actually is it's more than a collection + + align:start position:0% +actually is it's more than a collection + + + align:start position:0% +actually is it's more than a collection +of features so the Gustad roots of + + align:start position:0% +of features so the Gustad roots of + + + align:start position:0% +of features so the Gustad roots of +perception actually emphasize this if + + align:start position:0% +perception actually emphasize this if + + + align:start position:0% +perception actually emphasize this if +you have proximity of elements you group + + align:start position:0% +you have proximity of elements you group + + + align:start position:0% +you have proximity of elements you group +them together if these elements share + + align:start position:0% +them together if these elements share + + + align:start position:0% +them together if these elements share +similarity you group them together into + + align:start position:0% +similarity you group them together into + + + align:start position:0% +similarity you group them together into +larger entities if there's good + + align:start position:0% +larger entities if there's good + + + align:start position:0% +larger entities if there's good +continuation you group these local + + align:start position:0% +continuation you group these local + + + align:start position:0% +continuation you group these local +elements together into lines if there's + + align:start position:0% +elements together into lines if there's + + + align:start position:0% +elements together into lines if there's +common faith you group them again + + align:start position:0% +common faith you group them again + + + align:start position:0% +common faith you group them again +together to larger entities and + + align:start position:0% +together to larger entities and + + + align:start position:0% +together to larger entities and +something similar is true for faces if + + align:start position:0% +something similar is true for faces if + + + align:start position:0% +something similar is true for faces if +you have different face parts then the + + align:start position:0% +you have different face parts then the + + + align:start position:0% +you have different face parts then the +wrong organization but now you put them + + align:start position:0% +wrong organization but now you put them + + + align:start position:0% +wrong organization but now you put them +together correctly you can suddenly + + align:start position:0% +together correctly you can suddenly + + + align:start position:0% +together correctly you can suddenly +recognize the face so there's a larger + + align:start position:0% +recognize the face so there's a larger + + + align:start position:0% +recognize the face so there's a larger +scale organization to not really it goes + + align:start position:0% +scale organization to not really it goes + + + align:start position:0% +scale organization to not really it goes +beyond just being a collection of + + align:start position:0% +beyond just being a collection of + + + align:start position:0% +beyond just being a collection of +features and maybe something similar is + + align:start position:0% +features and maybe something similar is + + + align:start position:0% +features and maybe something similar is +going on for higher order condition that + + align:start position:0% +going on for higher order condition that + + + align:start position:0% +going on for higher order condition that +I'm sure other people going to talk + + align:start position:0% +I'm sure other people going to talk + + + align:start position:0% +I'm sure other people going to talk +about and it's in the physical + + align:start position:0% +about and it's in the physical + + + align:start position:0% +about and it's in the physical +interactions we infer causality from + + align:start position:0% +interactions we infer causality from + + + align:start position:0% +interactions we infer causality from +just the sequence of events or social + + align:start position:0% +just the sequence of events or social + + + align:start position:0% +just the sequence of events or social +interactions like anhydrous I move + + align:start position:0% +interactions like anhydrous I move + + + align:start position:0% +interactions like anhydrous I move +where you are telling yourself like a + + align:start position:0% +where you are telling yourself like a + + + align:start position:0% +where you are telling yourself like a +complex social story unfold even when + + align:start position:0% +complex social story unfold even when + + + align:start position:0% +complex social story unfold even when +there's just like simple geometric + + align:start position:0% +there's just like simple geometric + + + align:start position:0% +there's just like simple geometric +shapes moving around so this creation of + + align:start position:0% +shapes moving around so this creation of + + + align:start position:0% +shapes moving around so this creation of +like higher order representations I + + align:start position:0% +like higher order representations I + + + align:start position:0% +like higher order representations I +think this is essential for our table + + align:start position:0% +think this is essential for our table + + + align:start position:0% +think this is essential for our table +cognition + + align:start position:0% +cognition + + + align:start position:0% +cognition +it's a constructive process that the + + align:start position:0% +it's a constructive process that the + + + align:start position:0% +it's a constructive process that the +brain imposes on the piece of + + align:start position:0% +brain imposes on the piece of + + + align:start position:0% +brain imposes on the piece of +information it gets from the eyes it's + + align:start position:0% +information it gets from the eyes it's + + + align:start position:0% +information it gets from the eyes it's +just in the collection of features it's + + align:start position:0% +just in the collection of features it's + + + align:start position:0% +just in the collection of features it's +kind of the basis of symbolic + + align:start position:0% +kind of the basis of symbolic + + + align:start position:0% +kind of the basis of symbolic +representations it can create meaning + + align:start position:0% +representations it can create meaning + + + align:start position:0% +representations it can create meaning +especially if you think about the face + + align:start position:0% +especially if you think about the face + + + align:start position:0% +especially if you think about the face +if it's the face of someone you know + + align:start position:0% +if it's the face of someone you know + + + align:start position:0% +if it's the face of someone you know +that's very meaningful and it makes + + align:start position:0% +that's very meaningful and it makes + + + align:start position:0% +that's very meaningful and it makes +information actionable and these are + + align:start position:0% +information actionable and these are + + + align:start position:0% +information actionable and these are +really I think the the important links + + align:start position:0% +really I think the the important links + + + align:start position:0% +really I think the the important links +between Africa condition and social + + align:start position:0% +between Africa condition and social + + + align:start position:0% +between Africa condition and social +cognition and faces are smack in the + + align:start position:0% +cognition and faces are smack in the + + + align:start position:0% +cognition and faces are smack in the +middle of this okay so I already showed + + align:start position:0% +middle of this okay so I already showed + + + align:start position:0% +middle of this okay so I already showed +this movie to use again I emphasize the + + align:start position:0% +this movie to use again I emphasize the + + + align:start position:0% +this movie to use again I emphasize the +social communication that's taking place + + align:start position:0% +social communication that's taking place + + + align:start position:0% +social communication that's taking place +here you can see the facial displace + + align:start position:0% +here you can see the facial displace + + + align:start position:0% +here you can see the facial displace +here so the older male who's chasing the + + align:start position:0% +here so the older male who's chasing the + + + align:start position:0% +here so the older male who's chasing the +younger animals is making the state of + + align:start position:0% +younger animals is making the state of + + + align:start position:0% +younger animals is making the state of +this place by the way you've most of you + + align:start position:0% +this place by the way you've most of you + + + align:start position:0% +this place by the way you've most of you +will never seen a chunky macaque and + + align:start position:0% +will never seen a chunky macaque and + + + align:start position:0% +will never seen a chunky macaque and +still you kind of understand what's + + align:start position:0% +still you kind of understand what's + + + align:start position:0% +still you kind of understand what's +going on there right and this is + + align:start position:0% +going on there right and this is + + + align:start position:0% +going on there right and this is +something very special again that you + + align:start position:0% +something very special again that you + + + align:start position:0% +something very special again that you +don't have in all animals this facial + + align:start position:0% +don't have in all animals this facial + + + align:start position:0% +don't have in all animals this facial +displace and Charles Darwin was actually + + align:start position:0% +displace and Charles Darwin was actually + + + align:start position:0% +displace and Charles Darwin was actually +again one of the first people to notice + + align:start position:0% +again one of the first people to notice + + + align:start position:0% +again one of the first people to notice +it in 1872 is that you use your face to + + align:start position:0% +it in 1872 is that you use your face to + + + align:start position:0% +it in 1872 is that you use your face to +express your emotional state otherwise + + align:start position:0% +express your emotional state otherwise + + + align:start position:0% +express your emotional state otherwise +the emotions are private to you but you + + align:start position:0% +the emotions are private to you but you + + + align:start position:0% +the emotions are private to you but you +use body language and then face facial + + align:start position:0% +use body language and then face facial + + + align:start position:0% +use body language and then face facial +language to actually suppress your + + align:start position:0% +language to actually suppress your + + + align:start position:0% +language to actually suppress your +emotions and oftentimes you do it even + + align:start position:0% +emotions and oftentimes you do it even + + + align:start position:0% +emotions and oftentimes you do it even +if you don't want to it just happens + + align:start position:0% +if you don't want to it just happens + + + align:start position:0% +if you don't want to it just happens +automatically and that's not possible in + + align:start position:0% +automatically and that's not possible in + + + align:start position:0% +automatically and that's not possible in +all animals so if you are a fish or a + + align:start position:0% +all animals so if you are a fish or a + + + align:start position:0% +all animals so if you are a fish or a +frog there are lots of really cool + + align:start position:0% +frog there are lots of really cool + + + align:start position:0% +frog there are lots of really cool +things you can do you know you can sit + + align:start position:0% +things you can do you know you can sit + + + align:start position:0% +things you can do you know you can sit +on the front porch and enjoy the day so + + align:start position:0% +on the front porch and enjoy the day so + + + align:start position:0% +on the front porch and enjoy the day so +lots of things that you can have in + + align:start position:0% +lots of things that you can have in + + + align:start position:0% +lots of things that you can have in +common with with primates but safely + + align:start position:0% +common with with primates but safely + + + align:start position:0% +common with with primates but safely +communication really requires something + + align:start position:0% +communication really requires something + + + align:start position:0% +communication really requires something +more that's very mammalian specific and + + align:start position:0% +more that's very mammalian specific and + + + align:start position:0% +more that's very mammalian specific and +mammals you actually have in the face + + align:start position:0% +mammals you actually have in the face + + + align:start position:0% +mammals you actually have in the face +musculature that is not attached see + + align:start position:0% +musculature that is not attached see + + + align:start position:0% +musculature that is not attached see +from bone to bone but it's now attaching + + align:start position:0% +from bone to bone but it's now attaching + + + align:start position:0% +from bone to bone but it's now attaching +to the skin and so if you look at these + + align:start position:0% +to the skin and so if you look at these + + + align:start position:0% +to the skin and so if you look at these +two rats here where the whiskers may I + + align:start position:0% +two rats here where the whiskers may I + + + align:start position:0% +two rats here where the whiskers may I +hope you can see it here in the end are + + align:start position:0% +hope you can see it here in the end are + + + align:start position:0% +hope you can see it here in the end are +labeled you can see they're actively + + align:start position:0% +labeled you can see they're actively + + + align:start position:0% +labeled you can see they're actively +exploring each other's faces in a sort + + align:start position:0% +exploring each other's faces in a sort + + + align:start position:0% +exploring each other's faces in a sort +of sensory fashion that's possibly + + align:start position:0% +of sensory fashion that's possibly + + + align:start position:0% +of sensory fashion that's possibly +because they can move their whiskers + + align:start position:0% +because they can move their whiskers + + + align:start position:0% +because they can move their whiskers +because of this musculature and that's a + + align:start position:0% +because of this musculature and that's a + + + align:start position:0% +because of this musculature and that's a +specialization that's becoming more and + + align:start position:0% +specialization that's becoming more and + + + align:start position:0% +specialization that's becoming more and +more refined in primates on rhesus + + align:start position:0% +more refined in primates on rhesus + + + align:start position:0% +more refined in primates on rhesus +monkeys and chimps and humans you have + + align:start position:0% +monkeys and chimps and humans you have + + + align:start position:0% +monkeys and chimps and humans you have +23 different facial muscles they're + + align:start position:0% +23 different facial muscles they're + + + align:start position:0% +23 different facial muscles they're +becoming more and more flexible I + + align:start position:0% +becoming more and more flexible I + + + align:start position:0% +becoming more and more flexible I +mentioned before that the snout region + + align:start position:0% +mentioned before that the snout region + + + align:start position:0% +mentioned before that the snout region +is increasingly reduced and primacy of + + align:start position:0% +is increasingly reduced and primacy of + + + align:start position:0% +is increasingly reduced and primacy of +some simpler primates where they're + + align:start position:0% +some simpler primates where they're + + + align:start position:0% +some simpler primates where they're +still as strong snout which is limiting + + align:start position:0% +still as strong snout which is limiting + + + align:start position:0% +still as strong snout which is limiting +the ability of the face to move but the + + align:start position:0% +the ability of the face to move but the + + + align:start position:0% +the ability of the face to move but the +more complex the parameters getting the + + align:start position:0% +more complex the parameters getting the + + + align:start position:0% +more complex the parameters getting the +more more flexible these muscles become + + align:start position:0% +more more flexible these muscles become + + + align:start position:0% +more more flexible these muscles become +and the more expressive the faces become + + align:start position:0% +and the more expressive the faces become + + + align:start position:0% +and the more expressive the faces become +so the + + align:start position:0% +so the + + + align:start position:0% +so the +this is not now becomes richer and + + align:start position:0% +this is not now becomes richer and + + + align:start position:0% +this is not now becomes richer and +richer with social signals that you can + + align:start position:0% +richer with social signals that you can + + + align:start position:0% +richer with social signals that you can +read out and in rhesus monkeys which are + + align:start position:0% +read out and in rhesus monkeys which are + + + align:start position:0% +read out and in rhesus monkeys which are +shown here we have a fixed set of facial + + align:start position:0% +shown here we have a fixed set of facial + + + align:start position:0% +shown here we have a fixed set of facial +expressions that again for a system that + + align:start position:0% +expressions that again for a system that + + + align:start position:0% +expressions that again for a system that +can analyze these it's very important + + align:start position:0% +can analyze these it's very important + + + align:start position:0% +can analyze these it's very important +information about the emotional state of + + align:start position:0% +information about the emotional state of + + + align:start position:0% +information about the emotional state of +another animal primates also very + + align:start position:0% +another animal primates also very + + + align:start position:0% +another animal primates also very +interested in faces I very much like to + + align:start position:0% +interested in faces I very much like to + + + align:start position:0% +interested in faces I very much like to +show this movie which is showing a + + align:start position:0% +show this movie which is showing a + + + align:start position:0% +show this movie which is showing a +three-day-old attack monkey and I'll + + align:start position:0% +three-day-old attack monkey and I'll + + + align:start position:0% +three-day-old attack monkey and I'll +tell you what the point of this study is + + align:start position:0% +tell you what the point of this study is + + + align:start position:0% +tell you what the point of this study is +so you can see that he's attending by + + align:start position:0% +so you can see that he's attending by + + + align:start position:0% +so you can see that he's attending by +closer to the faces he experimenter of + + align:start position:0% +closer to the faces he experimenter of + + + align:start position:0% +closer to the faces he experimenter of +course there were bananas you might + + align:start position:0% +course there were bananas you might + + + align:start position:0% +course there were bananas you might +think would also be oriented in sazon + + align:start position:0% +think would also be oriented in sazon + + + align:start position:0% +think would also be oriented in sazon +proof that there's this specialization + + align:start position:0% +proof that there's this specialization + + + align:start position:0% +proof that there's this specialization +for faces that nancy was alluding to + + align:start position:0% +for faces that nancy was alluding to + + + align:start position:0% +for faces that nancy was alluding to +before but it's at least intuitive the + + align:start position:0% +before but it's at least intuitive the + + + align:start position:0% +before but it's at least intuitive the +second thing why I like to show this + + align:start position:0% +second thing why I like to show this + + + align:start position:0% +second thing why I like to show this +movies exactly what happened right now + + align:start position:0% +movies exactly what happened right now + + + align:start position:0% +movies exactly what happened right now +it's like you are all getting really + + align:start position:0% +it's like you are all getting really + + + align:start position:0% +it's like you are all getting really +excited about this absolutely adorable + + align:start position:0% +excited about this absolutely adorable + + + align:start position:0% +excited about this absolutely adorable +little critter right and I've seen this + + align:start position:0% +little critter right and I've seen this + + + align:start position:0% +little critter right and I've seen this +movie now like an hundreds of times and + + align:start position:0% +movie now like an hundreds of times and + + + align:start position:0% +movie now like an hundreds of times and +it's still like this it's still like my + + align:start position:0% +it's still like this it's still like my + + + align:start position:0% +it's still like this it's still like my +emotional charging so here's the third + + align:start position:0% +emotional charging so here's the third + + + align:start position:0% +emotional charging so here's the third +reason the equipment is making some + + align:start position:0% +reason the equipment is making some + + + align:start position:0% +reason the equipment is making some +facial movements here you can see is + + align:start position:0% +facial movements here you can see is + + + align:start position:0% +facial movements here you can see is +getting really excited about this game + + align:start position:0% +getting really excited about this game + + + align:start position:0% +getting really excited about this game +very active and now he's reproducing + + align:start position:0% +very active and now he's reproducing + + + align:start position:0% +very active and now he's reproducing +these facial movements as best as he can + + align:start position:0% +these facial movements as best as he can + + + align:start position:0% +these facial movements as best as he can +there's a specific facial interaction + + align:start position:0% +there's a specific facial interaction + + + align:start position:0% +there's a specific facial interaction +that's happening in human babies I think + + align:start position:0% +that's happening in human babies I think + + + align:start position:0% +that's happening in human babies I think +for three months seven in these rhesus + + align:start position:0% +for three months seven in these rhesus + + + align:start position:0% +for three months seven in these rhesus +monkeys for two weeks and you can see + + align:start position:0% +monkeys for two weeks and you can see + + + align:start position:0% +monkeys for two weeks and you can see +that there is an intricate connection + + align:start position:0% +that there is an intricate connection + + + align:start position:0% +that there is an intricate connection +between what they're perceiving and then + + align:start position:0% +between what they're perceiving and then + + + align:start position:0% +between what they're perceiving and then +what they're acting on in an automatic + + align:start position:0% +what they're acting on in an automatic + + + align:start position:0% +what they're acting on in an automatic +fashion but this emotional part I think + + align:start position:0% +fashion but this emotional part I think + + + align:start position:0% +fashion but this emotional part I think +is really important you know there's + + align:start position:0% +is really important you know there's + + + align:start position:0% +is really important you know there's +nothing it's just emphasizing point that + + align:start position:0% +nothing it's just emphasizing point that + + + align:start position:0% +nothing it's just emphasizing point that +you can control these things faces + + align:start position:0% +you can control these things faces + + + align:start position:0% +you can control these things faces +really get very deep into your emotional + + align:start position:0% +really get very deep into your emotional + + + align:start position:0% +really get very deep into your emotional +and social brain automatically and so + + align:start position:0% +and social brain automatically and so + + + align:start position:0% +and social brain automatically and so +one of the lines of research in my lab + + align:start position:0% +one of the lines of research in my lab + + + align:start position:0% +one of the lines of research in my lab +is that you to try and figure out the + + align:start position:0% +is that you to try and figure out the + + + align:start position:0% +is that you to try and figure out the +circuits that make that possible and + + align:start position:0% +circuits that make that possible and + + + align:start position:0% +circuits that make that possible and +then you use this to get an enroll into + + align:start position:0% +then you use this to get an enroll into + + + align:start position:0% +then you use this to get an enroll into +the social brain function beyond face + + align:start position:0% +the social brain function beyond face + + + align:start position:0% +the social brain function beyond face +perception okay + + align:start position:0% +perception okay + + + align:start position:0% +perception okay +so amongst the cigarettes the faces are + + align:start position:0% +so amongst the cigarettes the faces are + + + align:start position:0% +so amongst the cigarettes the faces are +sending so you can dice Charles Darwin + + align:start position:0% +sending so you can dice Charles Darwin + + + align:start position:0% +sending so you can dice Charles Darwin +sirs identity they're getting their + + align:start position:0% +sirs identity they're getting their + + + align:start position:0% +sirs identity they're getting their +social communication there's emotional + + align:start position:0% +social communication there's emotional + + + align:start position:0% +social communication there's emotional +responses and it's also gaze following + + align:start position:0% +responses and it's also gaze following + + + align:start position:0% +responses and it's also gaze following +so direction that the eyes are looking + + align:start position:0% +so direction that the eyes are looking + + + align:start position:0% +so direction that the eyes are looking +to we are falling automatically we can + + align:start position:0% +to we are falling automatically we can + + + align:start position:0% +to we are falling automatically we can +control this later but there's initial + + align:start position:0% +control this later but there's initial + + + align:start position:0% +control this later but there's initial +automatic response + + align:start position:0% +automatic response + + + align:start position:0% +automatic response +here's one very nice illustration from + + align:start position:0% +here's one very nice illustration from + + + align:start position:0% +here's one very nice illustration from +the British TV show you have people + + align:start position:0% +the British TV show you have people + + + align:start position:0% +the British TV show you have people +wearing these glasses and actually a + + align:start position:0% +wearing these glasses and actually a + + + align:start position:0% +wearing these glasses and actually a +large background - when people wearing + + align:start position:0% +large background - when people wearing + + + align:start position:0% +large background - when people wearing +these glasses where their eyes drawn on + + align:start position:0% +these glasses where their eyes drawn on + + + align:start position:0% +these glasses where their eyes drawn on +these glasses that are going to one + + align:start position:0% +these glasses that are going to one + + + align:start position:0% +these glasses that are going to one +direction and so you know that these are + + align:start position:0% +direction and so you know that these are + + + align:start position:0% +direction and so you know that these are +not real eyes but what's happening is + + align:start position:0% +not real eyes but what's happening is + + + align:start position:0% +not real eyes but what's happening is +your attention is drawn constantly to + + align:start position:0% +your attention is drawn constantly to + + + align:start position:0% +your attention is drawn constantly to +this upper right region and it's getting + + align:start position:0% +this upper right region and it's getting + + + align:start position:0% +this upper right region and it's getting +annoying over time because they know + + align:start position:0% +annoying over time because they know + + + align:start position:0% +annoying over time because they know +that there's nothing there + + align:start position:0% +that there's nothing there + + + align:start position:0% +that there's nothing there +you know that they're not really paying + + align:start position:0% +you know that they're not really paying + + + align:start position:0% +you know that they're not really paying +attention there but automatically + + align:start position:0% +attention there but automatically + + + align:start position:0% +attention there but automatically +attention is drawn there and you come + + align:start position:0% +attention is drawn there and you come + + + align:start position:0% +attention is drawn there and you come +back again your attentions going out + + align:start position:0% +back again your attentions going out + + + align:start position:0% +back again your attentions going out +there again and so this is another thing + + align:start position:0% +there again and so this is another thing + + + align:start position:0% +there again and so this is another thing +that comes from the face that gets deep + + align:start position:0% +that comes from the face that gets deep + + + align:start position:0% +that comes from the face that gets deep +into your attentional control system + + align:start position:0% +into your attentional control system + + + align:start position:0% +into your attentional control system +okay so social perception what can start + + align:start position:0% +okay so social perception what can start + + + align:start position:0% +okay so social perception what can start +with faces but faces are the most + + align:start position:0% +with faces but faces are the most + + + align:start position:0% +with faces but faces are the most +important visual sources of information + + align:start position:0% +important visual sources of information + + + align:start position:0% +important visual sources of information +we can gender an aged person identity + + align:start position:0% +we can gender an aged person identity + + + align:start position:0% +we can gender an aged person identity +even things like perceived + + align:start position:0% +even things like perceived + + + align:start position:0% +even things like perceived +trustworthiness or attractiveness from + + align:start position:0% +trustworthiness or attractiveness from + + + align:start position:0% +trustworthiness or attractiveness from +just a very brief look at the face and + + align:start position:0% +just a very brief look at the face and + + + align:start position:0% +just a very brief look at the face and +then then these dynamical signals like + + align:start position:0% +then then these dynamical signals like + + + align:start position:0% +then then these dynamical signals like +Newton over direction of attention that + + align:start position:0% +Newton over direction of attention that + + + align:start position:0% +Newton over direction of attention that +we also get from the face so how does + + align:start position:0% +we also get from the face so how does + + + align:start position:0% +we also get from the face so how does +this all work so Jim was already + + align:start position:0% +this all work so Jim was already + + + align:start position:0% +this all work so Jim was already +explaining some of the challenges face + + align:start position:0% +explaining some of the challenges face + + + align:start position:0% +explaining some of the challenges face +of optical condition to you and so here + + align:start position:0% +of optical condition to you and so here + + + align:start position:0% +of optical condition to you and so here +are some of the challenges so first of + + align:start position:0% +are some of the challenges so first of + + + align:start position:0% +are some of the challenges so first of +all is a social scene like this one here + + align:start position:0% +all is a social scene like this one here + + + align:start position:0% +all is a social scene like this one here +lighting conditions can sometimes be non + + align:start position:0% +lighting conditions can sometimes be non + + + align:start position:0% +lighting conditions can sometimes be non +optimal and so the first thing for you + + align:start position:0% +optimal and so the first thing for you + + + align:start position:0% +optimal and so the first thing for you +to analyze to say the the social signals + + align:start position:0% +to analyze to say the the social signals + + + align:start position:0% +to analyze to say the the social signals +which are in this scene is to localize + + align:start position:0% +which are in this scene is to localize + + + align:start position:0% +which are in this scene is to localize +where the faces are I'm going to take a + + align:start position:0% +where the faces are I'm going to take a + + + align:start position:0% +where the faces are I'm going to take a +little bit about what we understand + + align:start position:0% +little bit about what we understand + + + align:start position:0% +little bit about what we understand +about the newer mechanisms of that then + + align:start position:0% +about the newer mechanisms of that then + + + align:start position:0% +about the newer mechanisms of that then +once you know where the faces are you + + align:start position:0% +once you know where the faces are you + + + align:start position:0% +once you know where the faces are you +actually want to analyze them further + + align:start position:0% +actually want to analyze them further + + + align:start position:0% +actually want to analyze them further +you might want to know like who these + + align:start position:0% +you might want to know like who these + + + align:start position:0% +you might want to know like who these +individuals are and I just realized that + + align:start position:0% +individuals are and I just realized that + + + align:start position:0% +individuals are and I just realized that +the images that I had from this which + + align:start position:0% +the images that I had from this which + + + align:start position:0% +the images that I had from this which +are of course also taking from the + + align:start position:0% +are of course also taking from the + + + align:start position:0% +are of course also taking from the +Godfather might not be the best but who + + align:start position:0% +Godfather might not be the best but who + + + align:start position:0% +Godfather might not be the best but who +where's the other picture of this + + align:start position:0% +where's the other picture of this + + + align:start position:0% +where's the other picture of this +individual here and in this display of + + align:start position:0% +individual here and in this display of + + + align:start position:0% +individual here and in this display of +these five faces up all right and then + + align:start position:0% +these five faces up all right and then + + + align:start position:0% +these five faces up all right and then +there's another individual this is Don + + align:start position:0% +there's another individual this is Don + + + align:start position:0% +there's another individual this is Don +Corleone and it's another person down + + align:start position:0% +Corleone and it's another person down + + + align:start position:0% +Corleone and it's another person down +here with two different directions and + + align:start position:0% +here with two different directions and + + + align:start position:0% +here with two different directions and +then if the light let's go down a little + + align:start position:0% +then if the light let's go down a little + + + align:start position:0% +then if the light let's go down a little +bit more you could see this better the + + align:start position:0% +bit more you could see this better the + + + align:start position:0% +bit more you could see this better the +cool thing is that we have a way of + + align:start position:0% +cool thing is that we have a way of + + + align:start position:0% +cool thing is that we have a way of +relating these two pictures to each + + align:start position:0% +relating these two pictures to each + + + align:start position:0% +relating these two pictures to each +other knowing that they're from the same + + align:start position:0% +other knowing that they're from the same + + + align:start position:0% +other knowing that they're from the same +person even though physically on a + + align:start position:0% +person even though physically on a + + + align:start position:0% +person even though physically on a +pixel-by-pixel basis these two actually + + align:start position:0% +pixel-by-pixel basis these two actually + + + align:start position:0% +pixel-by-pixel basis these two actually +much more similar to each other and so + + align:start position:0% +much more similar to each other and so + + + align:start position:0% +much more similar to each other and so +we'd like to figure out like how the + + align:start position:0% +we'd like to figure out like how the + + + align:start position:0% +we'd like to figure out like how the +brain is doing that achieving actually + + align:start position:0% +brain is doing that achieving actually + + + align:start position:0% +brain is doing that achieving actually +recognition in this case face + + align:start position:0% +recognition in this case face + + + align:start position:0% +recognition in this case face +recognition in a manner that's invariant + + align:start position:0% +recognition in a manner that's invariant + + + align:start position:0% +recognition in a manner that's invariant +to transformations that are not + + align:start position:0% +to transformations that are not + + + align:start position:0% +to transformations that are not +intrinsic to to the object this is just + + align:start position:0% +intrinsic to to the object this is just + + + align:start position:0% +intrinsic to to the object this is just +a reminder that facial condition + + align:start position:0% +a reminder that facial condition + + + align:start position:0% +a reminder that facial condition +actually is very difficult so this is of + + align:start position:0% +actually is very difficult so this is of + + + align:start position:0% +actually is very difficult so this is of +course I just made up from coca + + align:start position:0% +course I just made up from coca + + + align:start position:0% +course I just made up from coca +enthusiasm but there is a condition that + + align:start position:0% +enthusiasm but there is a condition that + + + align:start position:0% +enthusiasm but there is a condition that +many of you will have heard about + + align:start position:0% +many of you will have heard about + + + align:start position:0% +many of you will have heard about +prosopagnosia and to prosopagnosia + + align:start position:0% +prosopagnosia and to prosopagnosia + + + align:start position:0% +prosopagnosia and to prosopagnosia +person whose face blind the social world + + align:start position:0% +person whose face blind the social world + + + align:start position:0% +person whose face blind the social world +might look like this so a person with no + + align:start position:0% +might look like this so a person with no + + + align:start position:0% +might look like this so a person with no +success great difficulty telling one + + align:start position:0% +success great difficulty telling one + + + align:start position:0% +success great difficulty telling one +individual from another this is at least + + align:start position:0% +individual from another this is at least + + + align:start position:0% +individual from another this is at least +the most typical condition and you can + + align:start position:0% +the most typical condition and you can + + + align:start position:0% +the most typical condition and you can +imagine that your social life would be + + align:start position:0% +imagine that your social life would be + + + align:start position:0% +imagine that your social life would be +really difficult and your enthusiasm + + align:start position:0% +really difficult and your enthusiasm + + + align:start position:0% +really difficult and your enthusiasm +about socially interacting would really + + align:start position:0% +about socially interacting would really + + + align:start position:0% +about socially interacting would really +be curbed + + align:start position:0% +be curbed + + + align:start position:0% +be curbed +if like all the individuals looked like + + align:start position:0% +if like all the individuals looked like + + + align:start position:0% +if like all the individuals looked like +this and look all the same so there must + + align:start position:0% +this and look all the same so there must + + + align:start position:0% +this and look all the same so there must +be something about this the newer + + align:start position:0% +be something about this the newer + + + align:start position:0% +be something about this the newer +mechanisms that it's very very precise + + align:start position:0% +mechanisms that it's very very precise + + + align:start position:0% +mechanisms that it's very very precise +so what's the new basis of Facebook + + align:start position:0% +so what's the new basis of Facebook + + + align:start position:0% +so what's the new basis of Facebook +ignition so this story really starts + + align:start position:0% +ignition so this story really starts + + + align:start position:0% +ignition so this story really starts +with Charles gross many years back in + + align:start position:0% +with Charles gross many years back in + + + align:start position:0% +with Charles gross many years back in +the late 60s early 70s he was recording + + align:start position:0% +the late 60s early 70s he was recording + + + align:start position:0% +the late 60s early 70s he was recording +from a few temporal cortex I was showing + + align:start position:0% +from a few temporal cortex I was showing + + + align:start position:0% +from a few temporal cortex I was showing +pictures of monkey faces other social + + align:start position:0% +pictures of monkey faces other social + + + align:start position:0% +pictures of monkey faces other social +stimuli like the monkey hand he would + + align:start position:0% +stimuli like the monkey hand he would + + + align:start position:0% +stimuli like the monkey hand he would +scramble the face and then look at the + + align:start position:0% +scramble the face and then look at the + + + align:start position:0% +scramble the face and then look at the +responses of sales and he was the first + + align:start position:0% +responses of sales and he was the first + + + align:start position:0% +responses of sales and he was the first +to find a face elected neuron here's one + + align:start position:0% +to find a face elected neuron here's one + + + align:start position:0% +to find a face elected neuron here's one +so these vertical lines are the action + + align:start position:0% +so these vertical lines are the action + + + align:start position:0% +so these vertical lines are the action +potentials the cell is firing this is + + align:start position:0% +potentials the cell is firing this is + + + align:start position:0% +potentials the cell is firing this is +the period of time this face was shown + + align:start position:0% +the period of time this face was shown + + + align:start position:0% +the period of time this face was shown +and this is the period of time the + + align:start position:0% +and this is the period of time the + + + align:start position:0% +and this is the period of time the +control object the hand was shown and + + align:start position:0% +control object the hand was shown and + + + align:start position:0% +control object the hand was shown and +you can see this the cells responding + + align:start position:0% +you can see this the cells responding + + + align:start position:0% +you can see this the cells responding +selectively to the face and not to the + + align:start position:0% +selectively to the face and not to the + + + align:start position:0% +selectively to the face and not to the +head so this was very nice finding if + + align:start position:0% +head so this was very nice finding if + + + align:start position:0% +head so this was very nice finding if +you took him some time to convince + + align:start position:0% +you took him some time to convince + + + align:start position:0% +you took him some time to convince +himself that he could publish it because + + align:start position:0% +himself that he could publish it because + + + align:start position:0% +himself that he could publish it because +he thought people would not believe it + + align:start position:0% +he thought people would not believe it + + + align:start position:0% +he thought people would not believe it +it's a recording in anesthetized animal + + align:start position:0% +it's a recording in anesthetized animal + + + align:start position:0% +it's a recording in anesthetized animal +but luckily he did publish it many many + + align:start position:0% +but luckily he did publish it many many + + + align:start position:0% +but luckily he did publish it many many +years later and so this is the first + + align:start position:0% +years later and so this is the first + + + align:start position:0% +years later and so this is the first +evidence that there is a specialization + + align:start position:0% +evidence that there is a specialization + + + align:start position:0% +evidence that there is a specialization +in the brain for faces if on many other + + align:start position:0% +in the brain for faces if on many other + + + align:start position:0% +in the brain for faces if on many other +cells that like other things than than + + align:start position:0% +cells that like other things than than + + + align:start position:0% +cells that like other things than than +faces and I think people thought that + + align:start position:0% +faces and I think people thought that + + + align:start position:0% +faces and I think people thought that +they were intermingled with other + + align:start position:0% +they were intermingled with other + + + align:start position:0% +they were intermingled with other +objects so this was the view this is + + align:start position:0% +objects so this was the view this is + + + align:start position:0% +objects so this was the view this is +Hydra from the Carrick brain this is the + + align:start position:0% +Hydra from the Carrick brain this is the + + + align:start position:0% +Hydra from the Carrick brain this is the +superior temporal circus the one big + + align:start position:0% +superior temporal circus the one big + + + align:start position:0% +superior temporal circus the one big +sockets in the monkey brain and all + + align:start position:0% +sockets in the monkey brain and all + + + align:start position:0% +sockets in the monkey brain and all +these symbols here indicating positions + + align:start position:0% +these symbols here indicating positions + + + align:start position:0% +these symbols here indicating positions +where people found face light of neurons + + align:start position:0% +where people found face light of neurons + + + align:start position:0% +where people found face light of neurons +the thought was the intermingled with + + align:start position:0% +the thought was the intermingled with + + + align:start position:0% +the thought was the intermingled with +object recognition hardware it's + + align:start position:0% +object recognition hardware it's + + + align:start position:0% +object recognition hardware it's +basically the view that there is the big + + align:start position:0% +basically the view that there is the big + + + align:start position:0% +basically the view that there is the big +IT cortex where everything a fever + + align:start position:0% +IT cortex where everything a fever + + + align:start position:0% +IT cortex where everything a fever +condition can happen and yes of course + + align:start position:0% +condition can happen and yes of course + + + align:start position:0% +condition can happen and yes of course +you would have some cells that a face + + align:start position:0% +you would have some cells that a face + + + align:start position:0% +you would have some cells that a face +elect if you would have other sales that + + align:start position:0% +elect if you would have other sales that + + + align:start position:0% +elect if you would have other sales that +a non face selective and the mixture and + + align:start position:0% +a non face selective and the mixture and + + + align:start position:0% +a non face selective and the mixture and +the complex pattern of activity really + + align:start position:0% +the complex pattern of activity really + + + align:start position:0% +the complex pattern of activity really +is what gives you the identity of the + + align:start position:0% +is what gives you the identity of the + + + align:start position:0% +is what gives you the identity of the +object then Nancy used fMRI to discover + + align:start position:0% +object then Nancy used fMRI to discover + + + align:start position:0% +object then Nancy used fMRI to discover +face selective areas + + align:start position:0% +face selective areas + + + align:start position:0% +face selective areas +so first the future from face areas we + + align:start position:0% +so first the future from face areas we + + + align:start position:0% +so first the future from face areas we +now know if multiple face errors that + + align:start position:0% +now know if multiple face errors that + + + align:start position:0% +now know if multiple face errors that +she was talking about before so here + + align:start position:0% +she was talking about before so here + + + align:start position:0% +she was talking about before so here +different slices to this and the thought + + align:start position:0% +different slices to this and the thought + + + align:start position:0% +different slices to this and the thought +from these images really was that know + + align:start position:0% +from these images really was that know + + + align:start position:0% +from these images really was that know +that they may be within this large + + align:start position:0% +that they may be within this large + + + align:start position:0% +that they may be within this large +experience of object recognition heart + + align:start position:0% +experience of object recognition heart + + + align:start position:0% +experience of object recognition heart +where there might be very specialized + + align:start position:0% +where there might be very specialized + + + align:start position:0% +where there might be very specialized +regions that are really there + + align:start position:0% +regions that are really there + + + align:start position:0% +regions that are really there +selectively to process faces and so + + align:start position:0% +selectively to process faces and so + + + align:start position:0% +selectively to process faces and so +here's the FFA and so the question you + + align:start position:0% +here's the FFA and so the question you + + + align:start position:0% +here's the FFA and so the question you +would ask us you know is this really a + + align:start position:0% +would ask us you know is this really a + + + align:start position:0% +would ask us you know is this really a +region that's devoted to face processing + + align:start position:0% +region that's devoted to face processing + + + align:start position:0% +region that's devoted to face processing +in face processing only so are these + + align:start position:0% +in face processing only so are these + + + align:start position:0% +in face processing only so are these +regions really face processing modules + + align:start position:0% +regions really face processing modules + + + align:start position:0% +regions really face processing modules +of the devoted to face processing or is + + align:start position:0% +of the devoted to face processing or is + + + align:start position:0% +of the devoted to face processing or is +it just the tip of the iceberg based on + + align:start position:0% +it just the tip of the iceberg based on + + + align:start position:0% +it just the tip of the iceberg based on +your sadistic analysis that this region + + align:start position:0% +your sadistic analysis that this region + + + align:start position:0% +your sadistic analysis that this region +just looks a little bit more face like + + align:start position:0% +just looks a little bit more face like + + + align:start position:0% +just looks a little bit more face like +in the neighboring regions and second do + + align:start position:0% +in the neighboring regions and second do + + + align:start position:0% +in the neighboring regions and second do +monkeys also this localized states like + + align:start position:0% +monkeys also this localized states like + + + align:start position:0% +monkeys also this localized states like +humans and you got the ends already yes + + align:start position:0% +humans and you got the ends already yes + + + align:start position:0% +humans and you got the ends already yes +they do + + align:start position:0% +they do + + + align:start position:0% +they do +and then what is the distribution of + + align:start position:0% +and then what is the distribution of + + + align:start position:0% +and then what is the distribution of +face cells within this regions or this + + align:start position:0% +face cells within this regions or this + + + align:start position:0% +face cells within this regions or this +outside so this is really the research + + align:start position:0% +outside so this is really the research + + + align:start position:0% +outside so this is really the research +agenda the doors sound I engaged on many + + align:start position:0% +agenda the doors sound I engaged on many + + + align:start position:0% +agenda the doors sound I engaged on many +years ago used fMRI macaque monkeys same + + align:start position:0% +years ago used fMRI macaque monkeys same + + + align:start position:0% +years ago used fMRI macaque monkeys same +technology as in humans slightly + + align:start position:0% +technology as in humans slightly + + + align:start position:0% +technology as in humans slightly +different coils and this is the picture + + align:start position:0% +different coils and this is the picture + + + align:start position:0% +different coils and this is the picture +that we got very consistently across + + align:start position:0% +that we got very consistently across + + + align:start position:0% +that we got very consistently across +different animals here in the temporal + + align:start position:0% +different animals here in the temporal + + + align:start position:0% +different animals here in the temporal +lobe you of six face-selective regions + + align:start position:0% +lobe you of six face-selective regions + + + align:start position:0% +lobe you of six face-selective regions +that you find that anatomically specific + + align:start position:0% +that you find that anatomically specific + + + align:start position:0% +that you find that anatomically specific +regions there's some variation from one + + align:start position:0% +regions there's some variation from one + + + align:start position:0% +regions there's some variation from one +individual to the other but with the + + align:start position:0% +individual to the other but with the + + + align:start position:0% +individual to the other but with the +exception of the most posterior area you + + align:start position:0% +exception of the most posterior area you + + + align:start position:0% +exception of the most posterior area you +actually find all these areas in all + + align:start position:0% +actually find all these areas in all + + + align:start position:0% +actually find all these areas in all +individuals on both hemispheres there + + align:start position:0% +individuals on both hemispheres there + + + align:start position:0% +individuals on both hemispheres there +are also three areas in prefrontal + + align:start position:0% +are also three areas in prefrontal + + + align:start position:0% +are also three areas in prefrontal +cortex which are little harder to find + + align:start position:0% +cortex which are little harder to find + + + align:start position:0% +cortex which are little harder to find +but the one in all the furniture court + + align:start position:0% +but the one in all the furniture court + + + align:start position:0% +but the one in all the furniture court +is a she's as reducible as the one in + + align:start position:0% +is a she's as reducible as the one in + + + align:start position:0% +is a she's as reducible as the one in +the temporal lobe so yes there are + + align:start position:0% +the temporal lobe so yes there are + + + align:start position:0% +the temporal lobe so yes there are +monkeys have localized face areas like + + align:start position:0% +monkeys have localized face areas like + + + align:start position:0% +monkeys have localized face areas like +humans and as Nancy was alluding to we + + align:start position:0% +humans and as Nancy was alluding to we + + + align:start position:0% +humans and as Nancy was alluding to we +actually have quite a bit of evidence by + + align:start position:0% +actually have quite a bit of evidence by + + + align:start position:0% +actually have quite a bit of evidence by +now that these systems might be + + align:start position:0% +now that these systems might be + + + align:start position:0% +now that these systems might be +homologous very very difficult to prove + + align:start position:0% +homologous very very difficult to prove + + + align:start position:0% +homologous very very difficult to prove +that there are Monica's but all the + + align:start position:0% +that there are Monica's but all the + + + align:start position:0% +that there are Monica's but all the +evidence we have so far is really + + align:start position:0% +evidence we have so far is really + + + align:start position:0% +evidence we have so far is really +pointing in this direction okay so how + + align:start position:0% +pointing in this direction okay so how + + + align:start position:0% +pointing in this direction okay so how +face like of are these face patches and + + align:start position:0% +face like of are these face patches and + + + align:start position:0% +face like of are these face patches and +what Doris and I did was to lower + + align:start position:0% +what Doris and I did was to lower + + + align:start position:0% +what Doris and I did was to lower +recording electrodes into these face + + align:start position:0% +recording electrodes into these face + + + align:start position:0% +recording electrodes into these face +areas and record from cells inside this + + align:start position:0% +areas and record from cells inside this + + + align:start position:0% +areas and record from cells inside this +F identified areas and I'm going to show + + align:start position:0% +F identified areas and I'm going to show + + + align:start position:0% +F identified areas and I'm going to show +to you a movie of one of the first sales + + align:start position:0% +to you a movie of one of the first sales + + + align:start position:0% +to you a movie of one of the first sales +be recorded from one of these regions so + + align:start position:0% +be recorded from one of these regions so + + + align:start position:0% +be recorded from one of these regions so +it's actually video we took from a + + align:start position:0% +it's actually video we took from a + + + align:start position:0% +it's actually video we took from a +control monitor so it shows the same + + align:start position:0% +control monitor so it shows the same + + + align:start position:0% +control monitor so it shows the same +thing the monkey shows the quality is + + align:start position:0% +thing the monkey shows the quality is + + + align:start position:0% +thing the monkey shows the quality is +not great because it's an actual video + + align:start position:0% +not great because it's an actual video + + + align:start position:0% +not great because it's an actual video +camera we took to take this image in + + align:start position:0% +camera we took to take this image in + + + align:start position:0% +camera we took to take this image in +addition to what the animals saw you + + align:start position:0% +addition to what the animals saw you + + + align:start position:0% +addition to what the animals saw you +will also see this black square which is + + align:start position:0% +will also see this black square which is + + + align:start position:0% +will also see this black square which is +indicating where the MN looked on the + + align:start position:0% +indicating where the MN looked on the + + + align:start position:0% +indicating where the MN looked on the +screen but the animal did not see this + + align:start position:0% +screen but the animal did not see this + + + align:start position:0% +screen but the animal did not see this +and you're going to hear clicks if + + align:start position:0% +and you're going to hear clicks if + + + align:start position:0% +and you're going to hear clicks if +everything works fine when the action + + align:start position:0% +everything works fine when the action + + + align:start position:0% +everything works fine when the action +potential is fired anyway here's the + + align:start position:0% +potential is fired anyway here's the + + + align:start position:0% +potential is fired anyway here's the +quantification so with 96 different + + align:start position:0% +quantification so with 96 different + + + align:start position:0% +quantification so with 96 different +stimuli on in this image set 16 faces + + align:start position:0% +stimuli on in this image set 16 faces + + + align:start position:0% +stimuli on in this image set 16 faces +and 18 on face stimuli this is the + + align:start position:0% +and 18 on face stimuli this is the + + + align:start position:0% +and 18 on face stimuli this is the +average response which is normalized + + align:start position:0% +average response which is normalized + + + align:start position:0% +average response which is normalized +between minus 1 and 1 and you can see + + align:start position:0% +between minus 1 and 1 and you can see + + + align:start position:0% +between minus 1 and 1 and you can see +that the biggest response of this + + align:start position:0% +that the biggest response of this + + + align:start position:0% +that the biggest response of this +particular cell actually occurs to the + + align:start position:0% +particular cell actually occurs to the + + + align:start position:0% +particular cell actually occurs to the +16 faces and not to any of the control + + align:start position:0% +16 faces and not to any of the control + + + align:start position:0% +16 faces and not to any of the control +objects you can see that there's some + + align:start position:0% +objects you can see that there's some + + + align:start position:0% +objects you can see that there's some +stimuli here and the gadget category for + + align:start position:0% +stimuli here and the gadget category for + + + align:start position:0% +stimuli here and the gadget category for +example that are eliciting responses + + align:start position:0% +example that are eliciting responses + + + align:start position:0% +example that are eliciting responses +that are quite respectable relative to + + align:start position:0% +that are quite respectable relative to + + + align:start position:0% +that are quite respectable relative to +the faces but really the biggest + + align:start position:0% +the faces but really the biggest + + + align:start position:0% +the faces but really the biggest +responses occur to the faces so then we + + align:start position:0% +responses occur to the faces so then we + + + align:start position:0% +responses occur to the faces so then we +went online we color coded this we have + + align:start position:0% +went online we color coded this we have + + + align:start position:0% +went online we color coded this we have +a response vector off the sale where red + + align:start position:0% +a response vector off the sale where red + + + align:start position:0% +a response vector off the sale where red +is now symbolizing response enhancement + + align:start position:0% +is now symbolizing response enhancement + + + align:start position:0% +is now symbolizing response enhancement +and blue + + align:start position:0% +and blue + + + align:start position:0% +and blue +symbolizing response impression below + + align:start position:0% +symbolizing response impression below + + + align:start position:0% +symbolizing response impression below +baseline and the Avengers using the + + align:start position:0% +baseline and the Avengers using the + + + align:start position:0% +baseline and the Avengers using the +summit is that you can now stack all the + + align:start position:0% +summit is that you can now stack all the + + + align:start position:0% +summit is that you can now stack all the +response vectors you get from all the + + align:start position:0% +response vectors you get from all the + + + align:start position:0% +response vectors you get from all the +sales recording day of the day of today + + align:start position:0% +sales recording day of the day of today + + + align:start position:0% +sales recording day of the day of today +from this one face area and you get a + + align:start position:0% +from this one face area and you get a + + + align:start position:0% +from this one face area and you get a +population response matrix and the way + + align:start position:0% +population response matrix and the way + + + align:start position:0% +population response matrix and the way +that this works is like cell number is + + align:start position:0% +that this works is like cell number is + + + align:start position:0% +that this works is like cell number is +organized from top to bottom pitch + + align:start position:0% +organized from top to bottom pitch + + + align:start position:0% +organized from top to bottom pitch +number from left to right and you can + + align:start position:0% +number from left to right and you can + + + align:start position:0% +number from left to right and you can +see very quickly that most of the cells + + align:start position:0% +see very quickly that most of the cells + + + align:start position:0% +see very quickly that most of the cells +here are either selectively enhanced or + + align:start position:0% +here are either selectively enhanced or + + + align:start position:0% +here are either selectively enhanced or +selectively suppressed by faces there's + + align:start position:0% +selectively suppressed by faces there's + + + align:start position:0% +selectively suppressed by faces there's +a small group here in between something + + align:start position:0% +a small group here in between something + + + align:start position:0% +a small group here in between something +like 10 percent of the cells or it's not + + align:start position:0% +like 10 percent of the cells or it's not + + + align:start position:0% +like 10 percent of the cells or it's not +so clear what they are doing but if you + + align:start position:0% +so clear what they are doing but if you + + + align:start position:0% +so clear what they are doing but if you +do the population average you can see + + align:start position:0% +do the population average you can see + + + align:start position:0% +do the population average you can see +much bigger responses to other faces + + align:start position:0% +much bigger responses to other faces + + + align:start position:0% +much bigger responses to other faces +then to the non-face objects if you look + + align:start position:0% +then to the non-face objects if you look + + + align:start position:0% +then to the non-face objects if you look +more closely what these pictures are + + align:start position:0% +more closely what these pictures are + + + align:start position:0% +more closely what these pictures are +they're eliciting these intermediate + + align:start position:0% +they're eliciting these intermediate + + + align:start position:0% +they're eliciting these intermediate +responses these are like clock faces + + align:start position:0% +responses these are like clock faces + + + align:start position:0% +responses these are like clock faces +apples pears there are things that have + + align:start position:0% +apples pears there are things that have + + + align:start position:0% +apples pears there are things that have +physical properties in common with faces + + align:start position:0% +physical properties in common with faces + + + align:start position:0% +physical properties in common with faces +so you can kind of fool the system to + + align:start position:0% +so you can kind of fool the system to + + + align:start position:0% +so you can kind of fool the system to +give like a partial response and this is + + align:start position:0% +give like a partial response and this is + + + align:start position:0% +give like a partial response and this is +one clue to what this area might be + + align:start position:0% +one clue to what this area might be + + + align:start position:0% +one clue to what this area might be +doing it should be doing like a visual + + align:start position:0% +doing it should be doing like a visual + + + align:start position:0% +doing it should be doing like a visual +analysis of the incoming stimuli to try + + align:start position:0% +analysis of the incoming stimuli to try + + + align:start position:0% +analysis of the incoming stimuli to try +and figure out these faces or not so + + align:start position:0% +and figure out these faces or not so + + + align:start position:0% +and figure out these faces or not so +these are cells in the middle face + + align:start position:0% +these are cells in the middle face + + + align:start position:0% +these are cells in the middle face +patches I was actually going over this + + align:start position:0% +patches I was actually going over this + + + align:start position:0% +patches I was actually going over this +pretty fast but I'm going to use this + + align:start position:0% +pretty fast but I'm going to use this + + + align:start position:0% +pretty fast but I'm going to use this +nomenclature quite a bit so let's wind + + align:start position:0% +nomenclature quite a bit so let's wind + + + align:start position:0% +nomenclature quite a bit so let's wind +back we have one posterior area here to + + align:start position:0% +back we have one posterior area here to + + + align:start position:0% +back we have one posterior area here to +middle face areas in the middle face + + align:start position:0% +middle face areas in the middle face + + + align:start position:0% +middle face areas in the middle face +patches and then 3 and here ones I'm + + align:start position:0% +patches and then 3 and here ones I'm + + + align:start position:0% +patches and then 3 and here ones I'm +mostly going to talk about this one here + + align:start position:0% +mostly going to talk about this one here + + + align:start position:0% +mostly going to talk about this one here +al and this one am in addition to the + + align:start position:0% +al and this one am in addition to the + + + align:start position:0% +al and this one am in addition to the +middle face patches + + align:start position:0% + + + + align:start position:0% + +so so we think that I should this is + + align:start position:0% +so so we think that I should this is + + + align:start position:0% +so so we think that I should this is +another automatic phase of conditioned + + align:start position:0% +another automatic phase of conditioned + + + align:start position:0% +another automatic phase of conditioned +feet where you can stop you know feeling + + align:start position:0% +feet where you can stop you know feeling + + + align:start position:0% +feet where you can stop you know feeling +sorry for these peppers you know they've + + align:start position:0% +sorry for these peppers you know they've + + + align:start position:0% +sorry for these peppers you know they've +been just cut in half and so they seem + + align:start position:0% +been just cut in half and so they seem + + + align:start position:0% +been just cut in half and so they seem +to be screaming and then you know they + + align:start position:0% +to be screaming and then you know they + + + align:start position:0% +to be screaming and then you know they +okay but still you feel like something + + align:start position:0% +okay but still you feel like something + + + align:start position:0% +okay but still you feel like something +really bad just happened and so we can't + + align:start position:0% +really bad just happened and so we can't + + + align:start position:0% +really bad just happened and so we can't +stop having these these inferences about + + align:start position:0% +stop having these these inferences about + + + align:start position:0% +stop having these these inferences about +peppers or they look like faces and one + + align:start position:0% +peppers or they look like faces and one + + + align:start position:0% +peppers or they look like faces and one +reason could be that we have this you + + align:start position:0% +reason could be that we have this you + + + align:start position:0% +reason could be that we have this you +know specialized circuitry that's got + + align:start position:0% +know specialized circuitry that's got + + + align:start position:0% +know specialized circuitry that's got +just getting acted if you can write + + align:start position:0% +just getting acted if you can write + + + align:start position:0% +just getting acted if you can write +features even you know you know these + + align:start position:0% +features even you know you know these + + + align:start position:0% +features even you know you know these +are not faces okay so when the faces + + align:start position:0% +are not faces okay so when the faces + + + align:start position:0% +are not faces okay so when the faces +were discovered by Charles gross this + + align:start position:0% +were discovered by Charles gross this + + + align:start position:0% +were discovered by Charles gross this +really fell in very fertile grounds and + + align:start position:0% +really fell in very fertile grounds and + + + align:start position:0% +really fell in very fertile grounds and +I should just discuss some of the + + align:start position:0% +I should just discuss some of the + + + align:start position:0% +I should just discuss some of the +implications so David Hume entrusted me + + align:start position:0% +implications so David Hume entrusted me + + + align:start position:0% +implications so David Hume entrusted me +just discovered a few we a few years + + align:start position:0% +just discovered a few we a few years + + + align:start position:0% +just discovered a few we a few years +before orientation selectivity so it's + + align:start position:0% +before orientation selectivity so it's + + + align:start position:0% +before orientation selectivity so it's +like a big jump from like the early + + align:start position:0% +like a big jump from like the early + + + align:start position:0% +like a big jump from like the early +processing where I could see how + + align:start position:0% +processing where I could see how + + + align:start position:0% +processing where I could see how +selectivity of sales was getting more + + align:start position:0% +selectivity of sales was getting more + + + align:start position:0% +selectivity of sales was getting more +complex some like more concentric + + align:start position:0% +complex some like more concentric + + + align:start position:0% +complex some like more concentric +representations to elongated ones from + + align:start position:0% +representations to elongated ones from + + + align:start position:0% +representations to elongated ones from +simple sales to complex sales for + + align:start position:0% +simple sales to complex sales for + + + align:start position:0% +simple sales to complex sales for +complex sales our air selective and + + align:start position:0% +complex sales our air selective and + + + align:start position:0% +complex sales our air selective and +simple sales but don't really care for + + align:start position:0% +simple sales but don't really care for + + + align:start position:0% +simple sales but don't really care for +spatial location all the way up to look + + align:start position:0% +spatial location all the way up to look + + + align:start position:0% +spatial location all the way up to look +at the opposite end of the visual system + + align:start position:0% +at the opposite end of the visual system + + + align:start position:0% +at the opposite end of the visual system +where now you find a calf a selected + + align:start position:0% +where now you find a calf a selected + + + align:start position:0% +where now you find a calf a selected +neuron Jerome Levin just had coined the + + align:start position:0% +neuron Jerome Levin just had coined the + + + align:start position:0% +neuron Jerome Levin just had coined the +term grandmother neuron which some of + + align:start position:0% +term grandmother neuron which some of + + + align:start position:0% +term grandmother neuron which some of +you brought up yesterday the idea is + + align:start position:0% +you brought up yesterday the idea is + + + align:start position:0% +you brought up yesterday the idea is +that there should be one neuron in your + + align:start position:0% +that there should be one neuron in your + + + align:start position:0% +that there should be one neuron in your +brain or this is a hypothetical scenario + + align:start position:0% +brain or this is a hypothetical scenario + + + align:start position:0% +brain or this is a hypothetical scenario +you came up with one in your brain + + align:start position:0% +you came up with one in your brain + + + align:start position:0% +you came up with one in your brain +that's firing if and only if you see a + + align:start position:0% +that's firing if and only if you see a + + + align:start position:0% +that's firing if and only if you see a +grandmother no matter what she's wearing + + align:start position:0% +grandmother no matter what she's wearing + + + align:start position:0% +grandmother no matter what she's wearing +which direction you see her from that's + + align:start position:0% +which direction you see her from that's + + + align:start position:0% +which direction you see her from that's +the neural correlate of you perceiving + + align:start position:0% +the neural correlate of you perceiving + + + align:start position:0% +the neural correlate of you perceiving +your grandmother is activity of this one + + align:start position:0% +your grandmother is activity of this one + + + align:start position:0% +your grandmother is activity of this one +neuron and there were other concepts + + align:start position:0% +neuron and there were other concepts + + + align:start position:0% +neuron and there were other concepts +like Jersey canastas lost the unit had + + align:start position:0% +like Jersey canastas lost the unit had + + + align:start position:0% +like Jersey canastas lost the unit had +made the same point then horse bariloche + + align:start position:0% +made the same point then horse bariloche + + + align:start position:0% +made the same point then horse bariloche +came up with this idea maybe it's not + + align:start position:0% +came up with this idea maybe it's not + + + align:start position:0% +came up with this idea maybe it's not +like one sale but like multiple sales + + align:start position:0% +like one sale but like multiple sales + + + align:start position:0% +like one sale but like multiple sales +but give a sparse presentation of sort + + align:start position:0% +but give a sparse presentation of sort + + + align:start position:0% +but give a sparse presentation of sort +of Pontifical sales a few of them at the + + align:start position:0% +of Pontifical sales a few of them at the + + + align:start position:0% +of Pontifical sales a few of them at the +top of a processing hierarchy and that's + + align:start position:0% +top of a processing hierarchy and that's + + + align:start position:0% +top of a processing hierarchy and that's +actually how we present faces and then + + align:start position:0% +actually how we present faces and then + + + align:start position:0% +actually how we present faces and then +of course this the opposite view of + + align:start position:0% +of course this the opposite view of + + + align:start position:0% +of course this the opposite view of +Donald Hebb talked about cell assemblies + + align:start position:0% +Donald Hebb talked about cell assemblies + + + align:start position:0% +Donald Hebb talked about cell assemblies +and says no you know things are there + + align:start position:0% +and says no you know things are there + + + align:start position:0% +and says no you know things are there +like large ensembles or sales or + + align:start position:0% +like large ensembles or sales or + + + align:start position:0% +like large ensembles or sales or +collection at what mass action and + + align:start position:0% +collection at what mass action and + + + align:start position:0% +collection at what mass action and +actually were completely against + + align:start position:0% +actually were completely against + + + align:start position:0% +actually were completely against +functional specialization if you look at + + align:start position:0% +functional specialization if you look at + + + align:start position:0% +functional specialization if you look at +a plot like this I think one of the + + align:start position:0% +a plot like this I think one of the + + + align:start position:0% +a plot like this I think one of the +things you want to emphasize is that + + align:start position:0% +things you want to emphasize is that + + + align:start position:0% +things you want to emphasize is that +these cells really don't fall into any + + align:start position:0% +these cells really don't fall into any + + + align:start position:0% +these cells really don't fall into any +of these categories so you can have + + align:start position:0% +of these categories so you can have + + + align:start position:0% +of these categories so you can have +cells did a very very face selected but + + align:start position:0% +cells did a very very face selected but + + + align:start position:0% +cells did a very very face selected but +adult have to be very sparse they will + + align:start position:0% +adult have to be very sparse they will + + + align:start position:0% +adult have to be very sparse they will +appear sparse if you probe them over and + + align:start position:0% +appear sparse if you probe them over and + + + align:start position:0% +appear sparse if you probe them over and +over and over with non face stimuli + + align:start position:0% +over and over with non face stimuli + + + align:start position:0% +over and over with non face stimuli +because they're gonna respond to those + + align:start position:0% +because they're gonna respond to those + + + align:start position:0% +because they're gonna respond to those +but within the domain of faces they're + + align:start position:0% +but within the domain of faces they're + + + align:start position:0% +but within the domain of faces they're +going to respond you know to pretty much + + align:start position:0% +going to respond you know to pretty much + + + align:start position:0% +going to respond you know to pretty much +all faces there are differences between + + align:start position:0% +all faces there are differences between + + + align:start position:0% +all faces there are differences between +this different + + align:start position:0% +this different + + + align:start position:0% +this different +sailes I'm going to come back to that as + + align:start position:0% +sailes I'm going to come back to that as + + + align:start position:0% +sailes I'm going to come back to that as +well but it's one example where we can + + align:start position:0% +well but it's one example where we can + + + align:start position:0% +well but it's one example where we can +actually ask them what these deep + + align:start position:0% +actually ask them what these deep + + + align:start position:0% +actually ask them what these deep +questions about what is the newer code + + align:start position:0% +questions about what is the newer code + + + align:start position:0% +questions about what is the newer code +the quantitative matter by focusing on + + align:start position:0% +the quantitative matter by focusing on + + + align:start position:0% +the quantitative matter by focusing on +the right stimulus in the right place to + + align:start position:0% +the right stimulus in the right place to + + + align:start position:0% +the right stimulus in the right place to +look at okay so we have some evidence + + align:start position:0% +look at okay so we have some evidence + + + align:start position:0% +look at okay so we have some evidence +that monkeys like humans have faced like + + align:start position:0% +that monkeys like humans have faced like + + + align:start position:0% +that monkeys like humans have faced like +regions and the monkey face patches + + align:start position:0% +regions and the monkey face patches + + + align:start position:0% +regions and the monkey face patches +appear to be dedicated domain-specific + + align:start position:0% +appear to be dedicated domain-specific + + + align:start position:0% +appear to be dedicated domain-specific +modules the practical implications of + + align:start position:0% +modules the practical implications of + + + align:start position:0% +modules the practical implications of +this is that now we have unprecedented + + align:start position:0% +this is that now we have unprecedented + + + align:start position:0% +this is that now we have unprecedented +access to functionally Majin as + + align:start position:0% +access to functionally Majin as + + + align:start position:0% +access to functionally Majin as +populations of cells that coding for one + + align:start position:0% +populations of cells that coding for one + + + align:start position:0% +populations of cells that coding for one +high-level object category and we know + + align:start position:0% +high-level object category and we know + + + align:start position:0% +high-level object category and we know +this category we can make stimuli and we + + align:start position:0% +this category we can make stimuli and we + + + align:start position:0% +this category we can make stimuli and we +can modify the stimuli sometimes in + + align:start position:0% +can modify the stimuli sometimes in + + + align:start position:0% +can modify the stimuli sometimes in +parametric sessions and so we can get + + align:start position:0% +parametric sessions and so we can get + + + align:start position:0% +parametric sessions and so we can get +very deep insights into how these cells + + align:start position:0% +very deep insights into how these cells + + + align:start position:0% +very deep insights into how these cells +actually are processing faces how they + + align:start position:0% +actually are processing faces how they + + + align:start position:0% +actually are processing faces how they +are extracting properties from these + + align:start position:0% +are extracting properties from these + + + align:start position:0% +are extracting properties from these +faces and we can do causal tests and + + align:start position:0% +faces and we can do causal tests and + + + align:start position:0% +faces and we can do causal tests and +actually show whether these cells are + + align:start position:0% +actually show whether these cells are + + + align:start position:0% +actually show whether these cells are +involved in face or condition behavior + + align:start position:0% +involved in face or condition behavior + + + align:start position:0% +involved in face or condition behavior +and just going to go with this way + + align:start position:0% +and just going to go with this way + + + align:start position:0% +and just going to go with this way +quickly this is work that see Watson's + + align:start position:0% +quickly this is work that see Watson's + + + align:start position:0% +quickly this is work that see Watson's +undergo pan as done he actually gave me + + align:start position:0% +undergo pan as done he actually gave me + + + align:start position:0% +undergo pan as done he actually gave me +this picture of himself this combines + + align:start position:0% +this picture of himself this combines + + + align:start position:0% +this picture of himself this combines +the front view and in a profile view the + + align:start position:0% +the front view and in a profile view the + + + align:start position:0% +the front view and in a profile view the +logic is very simple it's going to + + align:start position:0% +logic is very simple it's going to + + + align:start position:0% +logic is very simple it's going to +inactivate one particular region ml I'm + + align:start position:0% +inactivate one particular region ml I'm + + + align:start position:0% +inactivate one particular region ml I'm +going to tell you in a second why ml why + + align:start position:0% +going to tell you in a second why ml why + + + align:start position:0% +going to tell you in a second why ml why +the monkey will be engaged in tests like + + align:start position:0% +the monkey will be engaged in tests like + + + align:start position:0% +the monkey will be engaged in tests like +this ways to find a face in the + + align:start position:0% +this ways to find a face in the + + + align:start position:0% +this ways to find a face in the +individual scene the visual scene that + + align:start position:0% +individual scene the visual scene that + + + align:start position:0% +individual scene the visual scene that +we constructed looks a bit like this is + + align:start position:0% +we constructed looks a bit like this is + + + align:start position:0% +we constructed looks a bit like this is +displayed on a touchscreen monitor so + + align:start position:0% +displayed on a touchscreen monitor so + + + align:start position:0% +displayed on a touchscreen monitor so +the animals free to move around it has + + align:start position:0% +the animals free to move around it has + + + align:start position:0% +the animals free to move around it has +to find the face in the scene and the + + align:start position:0% +to find the face in the scene and the + + + align:start position:0% +to find the face in the scene and the +scene is composed of a pink noise + + align:start position:0% +scene is composed of a pink noise + + + align:start position:0% +scene is composed of a pink noise +background embedded in which there 24 + + align:start position:0% +background embedded in which there 24 + + + align:start position:0% +background embedded in which there 24 +different objects and the target object + + align:start position:0% +different objects and the target object + + + align:start position:0% +different objects and the target object +in this case the face is going to be + + align:start position:0% +in this case the face is going to be + + + align:start position:0% +in this case the face is going to be +varying in visibility across like ten + + align:start position:0% +varying in visibility across like ten + + + align:start position:0% +varying in visibility across like ten +different levels we would have other + + align:start position:0% +different levels we would have other + + + align:start position:0% +different levels we would have other +tasks where the monkey body was included + + align:start position:0% +tasks where the monkey body was included + + + align:start position:0% +tasks where the monkey body was included +which you will not be able to see her + + align:start position:0% +which you will not be able to see her + + + align:start position:0% +which you will not be able to see her +but there's a monkey body here or the + + align:start position:0% +but there's a monkey body here or the + + + align:start position:0% +but there's a monkey body here or the +monkey was looking for a shoe then we + + align:start position:0% +monkey was looking for a shoe then we + + + align:start position:0% +monkey was looking for a shoe then we +would infuse Muslim oil which is a + + align:start position:0% +would infuse Muslim oil which is a + + + align:start position:0% +would infuse Muslim oil which is a +pharmacological agent that is in + + align:start position:0% +pharmacological agent that is in + + + align:start position:0% +pharmacological agent that is in +activating sails along with the contrast + + align:start position:0% +activating sails along with the contrast + + + align:start position:0% +activating sails along with the contrast +agent gadolinium which we can measure an + + align:start position:0% +agent gadolinium which we can measure an + + + align:start position:0% +agent gadolinium which we can measure an +MRI and then this yellow region is the + + align:start position:0% +MRI and then this yellow region is the + + + align:start position:0% +MRI and then this yellow region is the +face area ml and this white region is + + align:start position:0% +face area ml and this white region is + + + align:start position:0% +face area ml and this white region is +the actual injection site that we used + + align:start position:0% +the actual injection site that we used + + + align:start position:0% +the actual injection site that we used +and so this gives like like a way for + + align:start position:0% +and so this gives like like a way for + + + align:start position:0% +and so this gives like like a way for +every experiment to control our we + + align:start position:0% +every experiment to control our we + + + align:start position:0% +every experiment to control our we +insert the face area are we outside and + + align:start position:0% +insert the face area are we outside and + + + align:start position:0% +insert the face area are we outside and +we can use the outside injections as + + align:start position:0% +we can use the outside injections as + + + align:start position:0% +we can use the outside injections as +controls what Batson found is shown here + + align:start position:0% +controls what Batson found is shown here + + + align:start position:0% +controls what Batson found is shown here +so we have a psychometric curve so a + + align:start position:0% +so we have a psychometric curve so a + + + align:start position:0% +so we have a psychometric curve so a +normal behavior you getting better and + + align:start position:0% +normal behavior you getting better and + + + align:start position:0% +normal behavior you getting better and +better + + align:start position:0% +better + + + align:start position:0% +better +finding the face and the scene as you're + + align:start position:0% +finding the face and the scene as you're + + + align:start position:0% +finding the face and the scene as you're +increasing its Willits visibility if + + align:start position:0% +increasing its Willits visibility if + + + align:start position:0% +increasing its Willits visibility if +you're in activating you get a reduced + + align:start position:0% +you're in activating you get a reduced + + + align:start position:0% +you're in activating you get a reduced +face detection behavior I should + + align:start position:0% +face detection behavior I should + + + align:start position:0% +face detection behavior I should +emphasize that we are only in activating + + align:start position:0% +emphasize that we are only in activating + + + align:start position:0% +emphasize that we are only in activating +face area out of 12 in the temporal lobe + + align:start position:0% +face area out of 12 in the temporal lobe + + + align:start position:0% +face area out of 12 in the temporal lobe +beyond activating one hemisphere and + + align:start position:0% +beyond activating one hemisphere and + + + align:start position:0% +beyond activating one hemisphere and +what Gimli Kalos emphasizing yesterday's + + align:start position:0% +what Gimli Kalos emphasizing yesterday's + + + align:start position:0% +what Gimli Kalos emphasizing yesterday's +there is Rhetta not happy at this level + + align:start position:0% +there is Rhetta not happy at this level + + + align:start position:0% +there is Rhetta not happy at this level +of processing so the animal can actually + + align:start position:0% +of processing so the animal can actually + + + align:start position:0% +of processing so the animal can actually +use a scanning strategy to go one + + align:start position:0% +use a scanning strategy to go one + + + align:start position:0% +use a scanning strategy to go one +direction and overcome this this deficit + + align:start position:0% +direction and overcome this this deficit + + + align:start position:0% +direction and overcome this this deficit +and so likely this effect would be much + + align:start position:0% +and so likely this effect would be much + + + align:start position:0% +and so likely this effect would be much +stronger if we didn't activate it on + + align:start position:0% +stronger if we didn't activate it on + + + align:start position:0% +stronger if we didn't activate it on +both hemispheres or whatever control + + align:start position:0% +both hemispheres or whatever control + + + align:start position:0% +both hemispheres or whatever control +precisely for the eye movement but we + + align:start position:0% +precisely for the eye movement but we + + + align:start position:0% +precisely for the eye movement but we +often give a natural behavior and the + + align:start position:0% +often give a natural behavior and the + + + align:start position:0% +often give a natural behavior and the +control so bodies and shoes are there's + + align:start position:0% +control so bodies and shoes are there's + + + align:start position:0% +control so bodies and shoes are there's +no effect there we print lots of + + align:start position:0% +no effect there we print lots of + + + align:start position:0% +no effect there we print lots of +controls in Oh ventricles in the next + + align:start position:0% +controls in Oh ventricles in the next + + + align:start position:0% +controls in Oh ventricles in the next +data to the behavior with interdictions + + align:start position:0% +data to the behavior with interdictions + + + align:start position:0% +data to the behavior with interdictions +outside as I mentioned it's very + + align:start position:0% +outside as I mentioned it's very + + + align:start position:0% +outside as I mentioned it's very +specific for inactivation inside the + + align:start position:0% +specific for inactivation inside the + + + align:start position:0% +specific for inactivation inside the +face area that the the most basic of + + align:start position:0% +face area that the the most basic of + + + align:start position:0% +face area that the the most basic of +face recognition abilities face + + align:start position:0% +face recognition abilities face + + + align:start position:0% +face recognition abilities face +detection is impaired and so there's + + align:start position:0% +detection is impaired and so there's + + + align:start position:0% +detection is impaired and so there's +this way you might visualize it so one + + align:start position:0% +this way you might visualize it so one + + + align:start position:0% +this way you might visualize it so one +way to explain this behavior would be + + align:start position:0% +way to explain this behavior would be + + + align:start position:0% +way to explain this behavior would be +that the visibility of a face like this + + align:start position:0% +that the visibility of a face like this + + + align:start position:0% +that the visibility of a face like this +would actually with inactivation looks + + align:start position:0% +would actually with inactivation looks + + + align:start position:0% +would actually with inactivation looks +something like this where it's going to + + align:start position:0% +something like this where it's going to + + + align:start position:0% +something like this where it's going to +be harder to to detect the second way we + + align:start position:0% +be harder to to detect the second way we + + + align:start position:0% +be harder to to detect the second way we +can take advantage of this is that we + + align:start position:0% +can take advantage of this is that we + + + align:start position:0% +can take advantage of this is that we +have no access to the natural sounds we + + align:start position:0% +have no access to the natural sounds we + + + align:start position:0% +have no access to the natural sounds we +actually has more precise questions + + align:start position:0% +actually has more precise questions + + + align:start position:0% +actually has more precise questions +about how they're processing faces and + + align:start position:0% +about how they're processing faces and + + + align:start position:0% +about how they're processing faces and +actually this an activation study was + + align:start position:0% +actually this an activation study was + + + align:start position:0% +actually this an activation study was +motivated by earlier work we've done on + + align:start position:0% +motivated by earlier work we've done on + + + align:start position:0% +motivated by earlier work we've done on +selectivity of these cells for features + + align:start position:0% +selectivity of these cells for features + + + align:start position:0% +selectivity of these cells for features +that should be relevant for face + + align:start position:0% +that should be relevant for face + + + align:start position:0% +that should be relevant for face +detection this is what the child hyoeun + + align:start position:0% +detection this is what the child hyoeun + + + align:start position:0% +detection this is what the child hyoeun +did when he was a grad student with + + align:start position:0% +did when he was a grad student with + + + align:start position:0% +did when he was a grad student with +Doris is actually now a postdoc with Jim + + align:start position:0% +Doris is actually now a postdoc with Jim + + + align:start position:0% +Doris is actually now a postdoc with Jim +and again the question is how can you + + align:start position:0% +and again the question is how can you + + + align:start position:0% +and again the question is how can you +detect faces even when the lighting + + align:start position:0% +detect faces even when the lighting + + + align:start position:0% +detect faces even when the lighting +conditions are very difficult there's + + align:start position:0% +conditions are very difficult there's + + + align:start position:0% +conditions are very difficult there's +beautiful work from Pavan Sinha that's + + align:start position:0% +beautiful work from Pavan Sinha that's + + + align:start position:0% +beautiful work from Pavan Sinha that's +emphasizing that course contrast + + align:start position:0% +emphasizing that course contrast + + + align:start position:0% +emphasizing that course contrast +relationships in the face of very good + + align:start position:0% +relationships in the face of very good + + + align:start position:0% +relationships in the face of very good +heuristics to do that the reason is that + + align:start position:0% +heuristics to do that the reason is that + + + align:start position:0% +heuristics to do that the reason is that +the 3d structure of our face stays the + + align:start position:0% +the 3d structure of our face stays the + + + align:start position:0% +the 3d structure of our face stays the +same even when the lighting conditions + + align:start position:0% +same even when the lighting conditions + + + align:start position:0% +same even when the lighting conditions +are changing and so no matter whether + + align:start position:0% +are changing and so no matter whether + + + align:start position:0% +are changing and so no matter whether +light is shining from typically the eye + + align:start position:0% +light is shining from typically the eye + + + align:start position:0% +light is shining from typically the eye +regions because they were seated + + align:start position:0% +regions because they were seated + + + align:start position:0% +regions because they were seated +relative to nose and forehead or darker + + align:start position:0% +relative to nose and forehead or darker + + + align:start position:0% +relative to nose and forehead or darker +the nose and forehead and so he found + + align:start position:0% +the nose and forehead and so he found + + + align:start position:0% +the nose and forehead and so he found +that in human psychophysics you have + + align:start position:0% +that in human psychophysics you have + + + align:start position:0% +that in human psychophysics you have +like 12 heuristics like this the + + align:start position:0% +like 12 heuristics like this the + + + align:start position:0% +like 12 heuristics like this the +forehead brighter than left eye for + + align:start position:0% +forehead brighter than left eye for + + + align:start position:0% +forehead brighter than left eye for +better than right eye nose whiter than + + align:start position:0% +better than right eye nose whiter than + + + align:start position:0% +better than right eye nose whiter than +mouth and so on and so forth 12 of these + + align:start position:0% +mouth and so on and so forth 12 of these + + + align:start position:0% +mouth and so on and so forth 12 of these +characteristics that actually together + + align:start position:0% +characteristics that actually together + + + align:start position:0% +characteristics that actually together +can allow you to detect the face and + + align:start position:0% +can allow you to detect the face and + + + align:start position:0% +can allow you to detect the face and +affect your face detector and your cell + + align:start position:0% +affect your face detector and your cell + + + align:start position:0% +affect your face detector and your cell +phone is using a very similar surgery as + + align:start position:0% +phone is using a very similar surgery as + + + align:start position:0% +phone is using a very similar surgery as +well trying to find the course quantized + + align:start position:0% +well trying to find the course quantized + + + align:start position:0% +well trying to find the course quantized +relationships in the scene so what I did + + align:start position:0% +relationships in the scene so what I did + + + align:start position:0% +relationships in the scene so what I did +was he said where the real face he would + + align:start position:0% +was he said where the real face he would + + + align:start position:0% +was he said where the real face he would +parse it into 11 parts and then randomly + + align:start position:0% +parse it into 11 parts and then randomly + + + align:start position:0% +parse it into 11 parts and then randomly +assign 11 different luminance values to + + align:start position:0% +assign 11 different luminance values to + + + align:start position:0% +assign 11 different luminance values to +these 11 different parts and changed us + + align:start position:0% +these 11 different parts and changed us + + + align:start position:0% +these 11 different parts and changed us +rapidly and then the analysis would look + + align:start position:0% +rapidly and then the analysis would look + + + align:start position:0% +rapidly and then the analysis would look +like this so no matter what the overall + + align:start position:0% +like this so no matter what the overall + + + align:start position:0% +like this so no matter what the overall +pattern looks like he's going to look + + align:start position:0% +pattern looks like he's going to look + + + align:start position:0% +pattern looks like he's going to look +for a particular + + align:start position:0% +for a particular + + + align:start position:0% +for a particular +a conscious relationship for the + + align:start position:0% +a conscious relationship for the + + + align:start position:0% +a conscious relationship for the +forehead versus the left eye and he's + + align:start position:0% +forehead versus the left eye and he's + + + align:start position:0% +forehead versus the left eye and he's +going to ask it's new in responding + + align:start position:0% +going to ask it's new in responding + + + align:start position:0% +going to ask it's new in responding +differently in these conditions where + + align:start position:0% +differently in these conditions where + + + align:start position:0% +differently in these conditions where +the forehead is brighter than the left + + align:start position:0% +the forehead is brighter than the left + + + align:start position:0% +the forehead is brighter than the left +eye versus in these conditions where the + + align:start position:0% +eye versus in these conditions where the + + + align:start position:0% +eye versus in these conditions where the +left eye is brighter than the Deaf + + align:start position:0% +left eye is brighter than the Deaf + + + align:start position:0% +left eye is brighter than the Deaf +forehead and you can do this for all + + align:start position:0% +forehead and you can do this for all + + + align:start position:0% +forehead and you can do this for all +pairs of combinations of eleven + + align:start position:0% +pairs of combinations of eleven + + + align:start position:0% +pairs of combinations of eleven +different parts and we can in these + + align:start position:0% +different parts and we can in these + + + align:start position:0% +different parts and we can in these +fifty five different combinations we can + + align:start position:0% +fifty five different combinations we can + + + align:start position:0% +fifty five different combinations we can +mark by arrows the prediction from human + + align:start position:0% +mark by arrows the prediction from human + + + align:start position:0% +mark by arrows the prediction from human +psychophysics so humans psychophysics + + align:start position:0% +psychophysics so humans psychophysics + + + align:start position:0% +psychophysics so humans psychophysics +told us 12 of these contrast pairs are + + align:start position:0% +told us 12 of these contrast pairs are + + + align:start position:0% +told us 12 of these contrast pairs are +going to be important it also told us + + align:start position:0% +going to be important it also told us + + + align:start position:0% +going to be important it also told us +what the polarity was this was going to + + align:start position:0% +what the polarity was this was going to + + + align:start position:0% +what the polarity was this was going to +be important for detecting your face + + align:start position:0% +be important for detecting your face + + + align:start position:0% +be important for detecting your face +again for it brighter than I or I + + align:start position:0% +again for it brighter than I or I + + + align:start position:0% +again for it brighter than I or I +brighter than forehead okay and this is + + align:start position:0% +brighter than forehead okay and this is + + + align:start position:0% +brighter than forehead okay and this is +what what we actually found so but this + + align:start position:0% +what what we actually found so but this + + + align:start position:0% +what what we actually found so but this +shows is a population diagram of all the + + align:start position:0% +shows is a population diagram of all the + + + align:start position:0% +shows is a population diagram of all the +cells that I found and it was half of + + align:start position:0% +cells that I found and it was half of + + + align:start position:0% +cells that I found and it was half of +the sales that he recorded from that + + align:start position:0% +the sales that he recorded from that + + + align:start position:0% +the sales that he recorded from that +showed some selectivity to some of these + + align:start position:0% +showed some selectivity to some of these + + + align:start position:0% +showed some selectivity to some of these +contrast features into some of these + + align:start position:0% +contrast features into some of these + + + align:start position:0% +contrast features into some of these +contrast polarities what's plotted here + + align:start position:0% +contrast polarities what's plotted here + + + align:start position:0% +contrast polarities what's plotted here +upwards is for one contrast polarity in + + align:start position:0% +upwards is for one contrast polarity in + + + align:start position:0% +upwards is for one contrast polarity in +one particular contrast pair the number + + align:start position:0% +one particular contrast pair the number + + + align:start position:0% +one particular contrast pair the number +of sales he found that were selective + + align:start position:0% +of sales he found that were selective + + + align:start position:0% +of sales he found that were selective +and as you go through the entire diagram + + align:start position:0% +and as you go through the entire diagram + + + align:start position:0% +and as you go through the entire diagram +you see that there are only very few + + align:start position:0% +you see that there are only very few + + + align:start position:0% +you see that there are only very few +examples of contrast pairs who actually + + align:start position:0% +examples of contrast pairs who actually + + + align:start position:0% +examples of contrast pairs who actually +different sales like different + + align:start position:0% +different sales like different + + + align:start position:0% +different sales like different +polarities like here for example you + + align:start position:0% +polarities like here for example you + + + align:start position:0% +polarities like here for example you +have more than sixty seventy sales that + + align:start position:0% +have more than sixty seventy sales that + + + align:start position:0% +have more than sixty seventy sales that +all like one polarity another single one + + align:start position:0% +all like one polarity another single one + + + align:start position:0% +all like one polarity another single one +that likes the opposite polarity and + + align:start position:0% +that likes the opposite polarity and + + + align:start position:0% +that likes the opposite polarity and +this is true for all these polarities so + + align:start position:0% +this is true for all these polarities so + + + align:start position:0% +this is true for all these polarities so +it's very consistent pattern second we + + align:start position:0% +it's very consistent pattern second we + + + align:start position:0% +it's very consistent pattern second we +can explain all the human psychophysics + + align:start position:0% +can explain all the human psychophysics + + + align:start position:0% +can explain all the human psychophysics +preferences here not only that these are + + align:start position:0% +preferences here not only that these are + + + align:start position:0% +preferences here not only that these are +important dimensions for these sales but + + align:start position:0% +important dimensions for these sales but + + + align:start position:0% +important dimensions for these sales but +in all these cases the sales care for + + align:start position:0% +in all these cases the sales care for + + + align:start position:0% +in all these cases the sales care for +the exact same polarity that they would + + align:start position:0% +the exact same polarity that they would + + + align:start position:0% +the exact same polarity that they would +have predicted from human psychophysics + + align:start position:0% +have predicted from human psychophysics + + + align:start position:0% +have predicted from human psychophysics +in addition there are other contrast + + align:start position:0% +in addition there are other contrast + + + align:start position:0% +in addition there are other contrast +pairs that apparently don't believe this + + align:start position:0% +pairs that apparently don't believe this + + + align:start position:0% +pairs that apparently don't believe this +much in human psychophysics but the + + align:start position:0% +much in human psychophysics but the + + + align:start position:0% +much in human psychophysics but the +sales also care about so they seem to be + + align:start position:0% +sales also care about so they seem to be + + + align:start position:0% +sales also care about so they seem to be +using this discourse contrast features + + align:start position:0% +using this discourse contrast features + + + align:start position:0% +using this discourse contrast features +and they again they were useful for face + + align:start position:0% +and they again they were useful for face + + + align:start position:0% +and they again they were useful for face +detection now we got the behavior that + + align:start position:0% +detection now we got the behavior that + + + align:start position:0% +detection now we got the behavior that +we know that the areas involved in the + + align:start position:0% +we know that the areas involved in the + + + align:start position:0% +we know that the areas involved in the +face detection with stimuli where it's + + align:start position:0% +face detection with stimuli where it's + + + align:start position:0% +face detection with stimuli where it's +actually hard to make out the detail + + align:start position:0% +actually hard to make out the detail + + + align:start position:0% +actually hard to make out the detail +then try to the control I thought this + + align:start position:0% +then try to the control I thought this + + + align:start position:0% +then try to the control I thought this +was really the coolest thing ever + + align:start position:0% +was really the coolest thing ever + + + align:start position:0% +was really the coolest thing ever +he's a computer scientist and so of + + align:start position:0% +he's a computer scientist and so of + + + align:start position:0% +he's a computer scientist and so of +course knew about databases and how to + + align:start position:0% +course knew about databases and how to + + + align:start position:0% +course knew about databases and how to +use them and he would say okay can we + + align:start position:0% +use them and he would say okay can we + + + align:start position:0% +use them and he would say okay can we +actually fool these cells into + + align:start position:0% +actually fool these cells into + + + align:start position:0% +actually fool these cells into +responding to non face stimuli that + + align:start position:0% +responding to non face stimuli that + + + align:start position:0% +responding to non face stimuli that +comply by the rules of this course + + align:start position:0% +comply by the rules of this course + + + align:start position:0% +comply by the rules of this course +contrast of faces so here are some + + align:start position:0% +contrast of faces so here are some + + + align:start position:0% +contrast of faces so here are some +examples you know this is just like a + + align:start position:0% +examples you know this is just like a + + + align:start position:0% +examples you know this is just like a +bit patter and where there are some dark + + align:start position:0% +bit patter and where there are some dark + + + align:start position:0% +bit patter and where there are some dark +regions when the human face eyes might + + align:start position:0% +regions when the human face eyes might + + + align:start position:0% +regions when the human face eyes might +be and so and so forth this is like a + + align:start position:0% +be and so and so forth this is like a + + + align:start position:0% +be and so and so forth this is like a +pattern that only has like one of these + + align:start position:0% +pattern that only has like one of these + + + align:start position:0% +pattern that only has like one of these +12 contrast + + align:start position:0% +12 contrast + + + align:start position:0% +12 contrast +correct but also human faces you can + + align:start position:0% +correct but also human faces you can + + + align:start position:0% +correct but also human faces you can +find some you know when a person smiling + + align:start position:0% +find some you know when a person smiling + + + align:start position:0% +find some you know when a person smiling +wearing reflective glasses lots of these + + align:start position:0% +wearing reflective glasses lots of these + + + align:start position:0% +wearing reflective glasses lots of these +contrasts I should not interface that + + align:start position:0% +contrasts I should not interface that + + + align:start position:0% +contrasts I should not interface that +should be there so they are so very + + align:start position:0% +should be there so they are so very + + + align:start position:0% +should be there so they are so very +contrast correct faces and there are + + align:start position:0% +contrast correct faces and there are + + + align:start position:0% +contrast correct faces and there are +some faces that a not very contrast + + align:start position:0% +some faces that a not very contrast + + + align:start position:0% +some faces that a not very contrast +correct and now you can ask like how + + align:start position:0% +correct and now you can ask like how + + + align:start position:0% +correct and now you can ask like how +does the response of the cells in the + + align:start position:0% +does the response of the cells in the + + + align:start position:0% +does the response of the cells in the +middle face patch change as your + + align:start position:0% +middle face patch change as your + + + align:start position:0% +middle face patch change as your +increase in the mouth quiet contrasts + + align:start position:0% +increase in the mouth quiet contrasts + + + align:start position:0% +increase in the mouth quiet contrasts +either on the face or non face stimuli + + align:start position:0% +either on the face or non face stimuli + + + align:start position:0% +either on the face or non face stimuli +and the answer is this if you're + + align:start position:0% +and the answer is this if you're + + + align:start position:0% +and the answer is this if you're +increasing them of contrast in the face + + align:start position:0% +increasing them of contrast in the face + + + align:start position:0% +increasing them of contrast in the face +the cells respond more and more if you + + align:start position:0% +the cells respond more and more if you + + + align:start position:0% +the cells respond more and more if you +change the contrast non-face objects the + + align:start position:0% +change the contrast non-face objects the + + + align:start position:0% +change the contrast non-face objects the +cells don't care so there's something + + align:start position:0% +cells don't care so there's something + + + align:start position:0% +cells don't care so there's something +else they cost contest as DeSales care + + align:start position:0% +else they cost contest as DeSales care + + + align:start position:0% +else they cost contest as DeSales care +abouts they're not easily fooled to + + align:start position:0% +abouts they're not easily fooled to + + + align:start position:0% +abouts they're not easily fooled to +respond to things that clearly aren't + + align:start position:0% +respond to things that clearly aren't + + + align:start position:0% +respond to things that clearly aren't +heard faces when the course contrasts + + align:start position:0% +heard faces when the course contrasts + + + align:start position:0% +heard faces when the course contrasts +are correct and we could actually have + + align:start position:0% +are correct and we could actually have + + + align:start position:0% +are correct and we could actually have +predict that something like this should + + align:start position:0% +predict that something like this should + + + align:start position:0% +predict that something like this should +happen from an earlier study so the + + align:start position:0% +happen from an earlier study so the + + + align:start position:0% +happen from an earlier study so the +first study we did when we took + + align:start position:0% +first study we did when we took + + + align:start position:0% +first study we did when we took +advantage of the fact that in the face + + align:start position:0% +advantage of the fact that in the face + + + align:start position:0% +advantage of the fact that in the face +selective area we can record from faces + + align:start position:0% +selective area we can record from faces + + + align:start position:0% +selective area we can record from faces +over and over again and that they have + + align:start position:0% +over and over again and that they have + + + align:start position:0% +over and over again and that they have +similar properties what a study we + + align:start position:0% +similar properties what a study we + + + align:start position:0% +similar properties what a study we +looked at the effect of part and whole + + align:start position:0% +looked at the effect of part and whole + + + align:start position:0% +looked at the effect of part and whole +this is one of the central features and + + align:start position:0% +this is one of the central features and + + + align:start position:0% +this is one of the central features and +psychophysics of human faces is that you + + align:start position:0% +psychophysics of human faces is that you + + + align:start position:0% +psychophysics of human faces is that you +can get information from the face + + align:start position:0% +can get information from the face + + + align:start position:0% +can get information from the face +without any detail just from the gist of + + align:start position:0% +without any detail just from the gist of + + + align:start position:0% +without any detail just from the gist of +the face an example is again from Pavan + + align:start position:0% +the face an example is again from Pavan + + + align:start position:0% +the face an example is again from Pavan +Sinha if you have a blurred face of a + + align:start position:0% +Sinha if you have a blurred face of a + + + align:start position:0% +Sinha if you have a blurred face of a +famiy individual like some of you might + + align:start position:0% +famiy individual like some of you might + + + align:start position:0% +famiy individual like some of you might +recognize Woody Allen in here of course + + align:start position:0% +recognize Woody Allen in here of course + + + align:start position:0% +recognize Woody Allen in here of course +with the glasses it's a little bit + + align:start position:0% +with the glasses it's a little bit + + + align:start position:0% +with the glasses it's a little bit +cheating but you can recognize them and + + align:start position:0% +cheating but you can recognize them and + + + align:start position:0% +cheating but you can recognize them and +the other examples in the study where + + align:start position:0% +the other examples in the study where + + + align:start position:0% +the other examples in the study where +people don't wear glasses so you can + + align:start position:0% +people don't wear glasses so you can + + + align:start position:0% +people don't wear glasses so you can +recognize the famous face just from this + + align:start position:0% +recognize the famous face just from this + + + align:start position:0% +recognize the famous face just from this +justified you don't need the details on + + align:start position:0% +justified you don't need the details on + + + align:start position:0% +justified you don't need the details on +the other end we can process details we + + align:start position:0% +the other end we can process details we + + + align:start position:0% +the other end we can process details we +can't focus on details and so do these + + align:start position:0% +can't focus on details and so do these + + + align:start position:0% +can't focus on details and so do these +how do these two things relate to each + + align:start position:0% +how do these two things relate to each + + + align:start position:0% +how do these two things relate to each +other what we did was we constructed a + + align:start position:0% +other what we did was we constructed a + + + align:start position:0% +other what we did was we constructed a +face space a cartoon face space based on + + align:start position:0% +face space a cartoon face space based on + + + align:start position:0% +face space a cartoon face space based on +very very simple geometric shapes so + + align:start position:0% +very very simple geometric shapes so + + + align:start position:0% +very very simple geometric shapes so +these faces are just made out of ovals + + align:start position:0% +these faces are just made out of ovals + + + align:start position:0% +these faces are just made out of ovals +and triangles and lines so very simple + + align:start position:0% +and triangles and lines so very simple + + + align:start position:0% +and triangles and lines so very simple +geometric shapes but if they put + + align:start position:0% +geometric shapes but if they put + + + align:start position:0% +geometric shapes but if they put +together they actually look like faces + + align:start position:0% +together they actually look like faces + + + align:start position:0% +together they actually look like faces +now we can parameterize this face space + + align:start position:0% +now we can parameterize this face space + + + align:start position:0% +now we can parameterize this face space +we can vary certain parameters so we had + + align:start position:0% +we can vary certain parameters so we had + + + align:start position:0% +we can vary certain parameters so we had +faces the change in aspect ratio they go + + align:start position:0% +faces the change in aspect ratio they go + + + align:start position:0% +faces the change in aspect ratio they go +from sesame character Ernie here to Bert + + align:start position:0% +from sesame character Ernie here to Bert + + + align:start position:0% +from sesame character Ernie here to Bert +we have pupil size like no pupils here + + align:start position:0% +we have pupil size like no pupils here + + + align:start position:0% +we have pupil size like no pupils here +very big pupils we have entire distance + + align:start position:0% +very big pupils we have entire distance + + + align:start position:0% +very big pupils we have entire distance +here so these eyes are close together + + align:start position:0% +here so these eyes are close together + + + align:start position:0% +here so these eyes are close together +like almost little cyclopean fashion or + + align:start position:0% +like almost little cyclopean fashion or + + + align:start position:0% +like almost little cyclopean fashion or +they can be very far apart from each + + align:start position:0% +they can be very far apart from each + + + align:start position:0% +they can be very far apart from each +other + + align:start position:0% +other + + + align:start position:0% +other +straddling the outside of the face and + + align:start position:0% +straddling the outside of the face and + + + align:start position:0% +straddling the outside of the face and +so on and so forth + + align:start position:0% +so on and so forth + + + align:start position:0% +so on and so forth +and we would now randomly change these + + align:start position:0% +and we would now randomly change these + + + align:start position:0% +and we would now randomly change these +features in all these 19 different + + align:start position:0% +features in all these 19 different + + + align:start position:0% +features in all these 19 different +feature dimensions randomly choosing a + + align:start position:0% +feature dimensions randomly choosing a + + + align:start position:0% +feature dimensions randomly choosing a +new value every time we show this face + + align:start position:0% +new value every time we show this face + + + align:start position:0% +new value every time we show this face +it looks a bit like a cartoon character + + align:start position:0% +it looks a bit like a cartoon character + + + align:start position:0% +it looks a bit like a cartoon character +who's trying to talk to you but the way + + align:start position:0% +who's trying to talk to you but the way + + + align:start position:0% +who's trying to talk to you but the way +we analyze this is very simple so we + + align:start position:0% +we analyze this is very simple so we + + + align:start position:0% +we analyze this is very simple so we +just asked no matter what these other + + align:start position:0% +just asked no matter what these other + + + align:start position:0% +just asked no matter what these other +features are for the first feature + + align:start position:0% +features are for the first feature + + + align:start position:0% +features are for the first feature +dimension that's the file of the sale + + align:start position:0% +dimension that's the file of the sale + + + align:start position:0% +dimension that's the file of the sale +change as we're changing this feature + + align:start position:0% +change as we're changing this feature + + + align:start position:0% +change as we're changing this feature +dimension then the assets for the second + + align:start position:0% +dimension then the assets for the second + + + align:start position:0% +dimension then the assets for the second +dimension of the third dimension and so + + align:start position:0% +dimension of the third dimension and so + + + align:start position:0% +dimension of the third dimension and so +on and so forth for all these 90 + + align:start position:0% +on and so forth for all these 90 + + + align:start position:0% +on and so forth for all these 90 +different dimensions what we found as + + align:start position:0% +different dimensions what we found as + + + align:start position:0% +different dimensions what we found as +shown here for one example sale so we + + align:start position:0% +shown here for one example sale so we + + + align:start position:0% +shown here for one example sale so we +get 19 different tuning curves and of + + align:start position:0% +get 19 different tuning curves and of + + + align:start position:0% +get 19 different tuning curves and of +these 19 different tuning curves for are + + align:start position:0% +these 19 different tuning curves for are + + + align:start position:0% +these 19 different tuning curves for are +significantly cured for this particular + + align:start position:0% +significantly cured for this particular + + + align:start position:0% +significantly cured for this particular +Sailor was phase despot ratio so didn't + + align:start position:0% +Sailor was phase despot ratio so didn't + + + align:start position:0% +Sailor was phase despot ratio so didn't +like earn it like Bert it like the ice + + align:start position:0% +like earn it like Bert it like the ice + + + align:start position:0% +like earn it like Bert it like the ice +may close together not far apart it like + + align:start position:0% +may close together not far apart it like + + + align:start position:0% +may close together not far apart it like +the ice a little bit narrow not white + + align:start position:0% +the ice a little bit narrow not white + + + align:start position:0% +the ice a little bit narrow not white +and like big RS is not small ones what's + + align:start position:0% +and like big RS is not small ones what's + + + align:start position:0% +and like big RS is not small ones what's +very typical for how these cells are + + align:start position:0% +very typical for how these cells are + + + align:start position:0% +very typical for how these cells are +processing these features are these ramp + + align:start position:0% +processing these features are these ramp + + + align:start position:0% +processing these features are these ramp +shape tuning curves so more than + + align:start position:0% +shape tuning curves so more than + + + align:start position:0% +shape tuning curves so more than +two-thirds of the students have this + + align:start position:0% +two-thirds of the students have this + + + align:start position:0% +two-thirds of the students have this +ramp shape which means that these cells + + align:start position:0% +ramp shape which means that these cells + + + align:start position:0% +ramp shape which means that these cells +are relaying the information that they + + align:start position:0% +are relaying the information that they + + + align:start position:0% +are relaying the information that they +are measuring and almost like one to one + + align:start position:0% +are measuring and almost like one to one + + + align:start position:0% +are measuring and almost like one to one +session so let's take a look at tune + + align:start position:0% +session so let's take a look at tune + + + align:start position:0% +session so let's take a look at tune +this is not what the sales actually + + align:start position:0% +this is not what the sales actually + + + align:start position:0% +this is not what the sales actually +doing it's just a metaphor but it's + + align:start position:0% +doing it's just a metaphor but it's + + + align:start position:0% +doing it's just a metaphor but it's +almost like the taking a ruler measuring + + align:start position:0% +almost like the taking a ruler measuring + + + align:start position:0% +almost like the taking a ruler measuring +into a distance and they'll relay in + + align:start position:0% +into a distance and they'll relay in + + + align:start position:0% +into a distance and they'll relay in +this feature and almost one-to-one + + align:start position:0% +this feature and almost one-to-one + + + align:start position:0% +this feature and almost one-to-one +session and they are out input another + + align:start position:0% +session and they are out input another + + + align:start position:0% +session and they are out input another +implication is that most of your coding + + align:start position:0% +implication is that most of your coding + + + align:start position:0% +implication is that most of your coding +capacity is actually at the extremes + + align:start position:0% +capacity is actually at the extremes + + + align:start position:0% +capacity is actually at the extremes +because many sales were big responses + + align:start position:0% +because many sales were big responses + + + align:start position:0% +because many sales were big responses +there are many customers more responses + + align:start position:0% +there are many customers more responses + + + align:start position:0% +there are many customers more responses +so most of the capacities there that's + + align:start position:0% +so most of the capacities there that's + + + align:start position:0% +so most of the capacities there that's +the range where caricatures to live and + + align:start position:0% +the range where caricatures to live and + + + align:start position:0% +the range where caricatures to live and +oftentimes we have better able to + + align:start position:0% +oftentimes we have better able to + + + align:start position:0% +oftentimes we have better able to +recognize individuals based on + + align:start position:0% +recognize individuals based on + + + align:start position:0% +recognize individuals based on +characters and didn't rejoice themselves + + align:start position:0% +characters and didn't rejoice themselves + + + align:start position:0% +characters and didn't rejoice themselves +ok so in the middle of face patches + + align:start position:0% +ok so in the middle of face patches + + + align:start position:0% +ok so in the middle of face patches +they're causally in selectively relevant + + align:start position:0% +they're causally in selectively relevant + + + align:start position:0% +they're causally in selectively relevant +for face detection the cells are + + align:start position:0% +for face detection the cells are + + + align:start position:0% +for face detection the cells are +virtually all face selective based on + + align:start position:0% +virtually all face selective based on + + + align:start position:0% +virtually all face selective based on +these two findings we actually suggest + + align:start position:0% +these two findings we actually suggest + + + align:start position:0% +these two findings we actually suggest +one's a little bit like like Nancy said + + align:start position:0% +one's a little bit like like Nancy said + + + align:start position:0% +one's a little bit like like Nancy said +as a as a strong symbol putting out that + + align:start position:0% +as a as a strong symbol putting out that + + + align:start position:0% +as a as a strong symbol putting out that +you get to get backlash if there is so + + align:start position:0% +you get to get backlash if there is so + + + align:start position:0% +you get to get backlash if there is so +we do think that they are modules that + + align:start position:0% +we do think that they are modules that + + + align:start position:0% +we do think that they are modules that +are they are for face processing of face + + align:start position:0% +are they are for face processing of face + + + align:start position:0% +are they are for face processing of face +processing only ok the gain of tuning + + align:start position:0% +processing only ok the gain of tuning + + + align:start position:0% +processing only ok the gain of tuning +curves is modulated by the presence of + + align:start position:0% +curves is modulated by the presence of + + + align:start position:0% +curves is modulated by the presence of +the entire face there's this ramp shape + + align:start position:0% +the entire face there's this ramp shape + + + align:start position:0% +the entire face there's this ramp shape +tuning which is by useful the cells are + + align:start position:0% +tuning which is by useful the cells are + + + align:start position:0% +tuning which is by useful the cells are +sensitive to contrast ratios which is + + align:start position:0% +sensitive to contrast ratios which is + + + align:start position:0% +sensitive to contrast ratios which is +very useful for face detection so we can + + align:start position:0% +very useful for face detection so we can + + + align:start position:0% +very useful for face detection so we can +really get mechanistic about + + align:start position:0% +really get mechanistic about + + + align:start position:0% +really get mechanistic about +understanding face recognition it's not + + align:start position:0% +understanding face recognition it's not + + + align:start position:0% +understanding face recognition it's not +just we can say okay these cells are + + align:start position:0% +just we can say okay these cells are + + + align:start position:0% +just we can say okay these cells are +responding more to faces but we can say + + align:start position:0% +responding more to faces but we can say + + + align:start position:0% +responding more to faces but we can say +like why they're responding more to some + + align:start position:0% +like why they're responding more to some + + + align:start position:0% +like why they're responding more to some +places and to others in fact you can + + align:start position:0% +places and to others in fact you can + + + align:start position:0% +places and to others in fact you can +predict from the cartoon results how the + + align:start position:0% +predict from the cartoon results how the + + + align:start position:0% +predict from the cartoon results how the +cells are responding to pictures of + + align:start position:0% +cells are responding to pictures of + + + align:start position:0% +cells are responding to pictures of +actual + + align:start position:0% +actual + + + align:start position:0% +actual +people with a very fine details + + align:start position:0% +people with a very fine details + + + align:start position:0% +people with a very fine details +physically and so it delivered the + + align:start position:0% +physically and so it delivered the + + + align:start position:0% +physically and so it delivered the +mid-face patches we already have some of + + align:start position:0% +mid-face patches we already have some of + + + align:start position:0% +mid-face patches we already have some of +the requirements for a face of induction + + align:start position:0% +the requirements for a face of induction + + + align:start position:0% +the requirements for a face of induction +system so we have mechanisms for face + + align:start position:0% +system so we have mechanisms for face + + + align:start position:0% +system so we have mechanisms for face +detection we have some encoding of + + align:start position:0% +detection we have some encoding of + + + align:start position:0% +detection we have some encoding of +facial features and with encoding of + + align:start position:0% +facial features and with encoding of + + + align:start position:0% +facial features and with encoding of +configurations + + align:start position:0% +configurations + + + align:start position:0% +configurations +okay so Nancy said I should talk about + + align:start position:0% +okay so Nancy said I should talk about + + + align:start position:0% +okay so Nancy said I should talk about +this I'm going to talk about this so the + + align:start position:0% +this I'm going to talk about this so the + + + align:start position:0% +this I'm going to talk about this so the +best umbrella was a wonderful grad + + align:start position:0% +best umbrella was a wonderful grad + + + align:start position:0% +best umbrella was a wonderful grad +student with Orson me and he did the + + align:start position:0% +student with Orson me and he did the + + + align:start position:0% +student with Orson me and he did the +following the ask the following question + + align:start position:0% +following the ask the following question + + + align:start position:0% +following the ask the following question +so whether the face patches are + + align:start position:0% +so whether the face patches are + + + align:start position:0% +so whether the face patches are +connected to each other or not if you + + align:start position:0% +connected to each other or not if you + + + align:start position:0% +connected to each other or not if you +look at the overall organization these + + align:start position:0% +look at the overall organization these + + + align:start position:0% +look at the overall organization these +face errors are very far apart from each + + align:start position:0% +face errors are very far apart from each + + + align:start position:0% +face errors are very far apart from each +others the most posted to the most + + align:start position:0% +others the most posted to the most + + + align:start position:0% +others the most posted to the most +anteriors one inch apart it's the third + + align:start position:0% +anteriors one inch apart it's the third + + + align:start position:0% +anteriors one inch apart it's the third +of the entire extent of the primate + + align:start position:0% +of the entire extent of the primate + + + align:start position:0% +of the entire extent of the primate +brain they live in different sites were + + align:start position:0% +brain they live in different sites were + + + align:start position:0% +brain they live in different sites were +architectonic environments you could + + align:start position:0% +architectonic environments you could + + + align:start position:0% +architectonic environments you could +also imagine that maybe the connectivity + + align:start position:0% +also imagine that maybe the connectivity + + + align:start position:0% +also imagine that maybe the connectivity +is most local on the other hand they are + + align:start position:0% +is most local on the other hand they are + + + align:start position:0% +is most local on the other hand they are +all interested in faces and so you would + + align:start position:0% +all interested in faces and so you would + + + align:start position:0% +all interested in faces and so you would +imagine that maybe they are specialized + + align:start position:0% +imagine that maybe they are specialized + + + align:start position:0% +imagine that maybe they are specialized +connections between them the way we + + align:start position:0% +connections between them the way we + + + align:start position:0% +connections between them the way we +address this was with micro stimulation + + align:start position:0% +address this was with micro stimulation + + + align:start position:0% +address this was with micro stimulation +inside the scanner so we would first + + align:start position:0% +inside the scanner so we would first + + + align:start position:0% +inside the scanner so we would first +image the face areas within lower an + + align:start position:0% +image the face areas within lower an + + + align:start position:0% +image the face areas within lower an +electrode to one of the face areas here + + align:start position:0% +electrode to one of the face areas here + + + align:start position:0% +electrode to one of the face areas here +would record from sales to make sure + + align:start position:0% +would record from sales to make sure + + + align:start position:0% +would record from sales to make sure +it's a selective but then we would use + + align:start position:0% +it's a selective but then we would use + + + align:start position:0% +it's a selective but then we would use +this electrode to pass a car and through + + align:start position:0% +this electrode to pass a car and through + + + align:start position:0% +this electrode to pass a car and through +inside the scanner passing a current + + align:start position:0% +inside the scanner passing a current + + + align:start position:0% +inside the scanner passing a current +through the lecture is going to activate + + align:start position:0% +through the lecture is going to activate + + + align:start position:0% +through the lecture is going to activate +cells that in turn is going to change + + align:start position:0% +cells that in turn is going to change + + + align:start position:0% +cells that in turn is going to change +blood flow and oxygenation so soon as we + + align:start position:0% +blood flow and oxygenation so soon as we + + + align:start position:0% +blood flow and oxygenation so soon as we +can pick up in the scanner and so yes if + + align:start position:0% +can pick up in the scanner and so yes if + + + align:start position:0% +can pick up in the scanner and so yes if +this worked you should get a swath of + + align:start position:0% +this worked you should get a swath of + + + align:start position:0% +this worked you should get a swath of +activity around your stimulation side + + align:start position:0% +activity around your stimulation side + + + align:start position:0% +activity around your stimulation side +but if these sales at your stimulation + + align:start position:0% +but if these sales at your stimulation + + + align:start position:0% +but if these sales at your stimulation +side have projections that are strong + + align:start position:0% +side have projections that are strong + + + align:start position:0% +side have projections that are strong +and focal enough to drive downstream + + align:start position:0% +and focal enough to drive downstream + + + align:start position:0% +and focal enough to drive downstream +neurons you might also find activation + + align:start position:0% +neurons you might also find activation + + + align:start position:0% +neurons you might also find activation +that spatially remote locations and you + + align:start position:0% +that spatially remote locations and you + + + align:start position:0% +that spatially remote locations and you +can then then see where these locations + + align:start position:0% +can then then see where these locations + + + align:start position:0% +can then then see where these locations +are relative to the face areas so here + + align:start position:0% +are relative to the face areas so here + + + align:start position:0% +are relative to the face areas so here +is a computer flattened map of the of + + align:start position:0% +is a computer flattened map of the of + + + align:start position:0% +is a computer flattened map of the of +the brain of one macaque monkeys the + + align:start position:0% +the brain of one macaque monkeys the + + + align:start position:0% +the brain of one macaque monkeys the +green areas indicate by outline the + + align:start position:0% +green areas indicate by outline the + + + align:start position:0% +green areas indicate by outline the +extent of the face areas we placed our + + align:start position:0% +extent of the face areas we placed our + + + align:start position:0% +extent of the face areas we placed our +estimation electrode in one of the face + + align:start position:0% +estimation electrode in one of the face + + + align:start position:0% +estimation electrode in one of the face +areas and this is the map you got for + + align:start position:0% +areas and this is the map you got for + + + align:start position:0% +areas and this is the map you got for +micro stimulation was a snow micro + + align:start position:0% +micro stimulation was a snow micro + + + align:start position:0% +micro stimulation was a snow micro +stimulation so there's no visual + + align:start position:0% +stimulation so there's no visual + + + align:start position:0% +stimulation so there's no visual +stimulus they are actually that work + + align:start position:0% +stimulus they are actually that work + + + align:start position:0% +stimulus they are actually that work +students sleep to in complete darkness + + align:start position:0% +students sleep to in complete darkness + + + align:start position:0% +students sleep to in complete darkness +so the yes we get is what have a tivity + + align:start position:0% +so the yes we get is what have a tivity + + + align:start position:0% +so the yes we get is what have a tivity +around the stimulation side and we get + + align:start position:0% +around the stimulation side and we get + + + align:start position:0% +around the stimulation side and we get +multiple spatially disjunct regions that + + align:start position:0% +multiple spatially disjunct regions that + + + align:start position:0% +multiple spatially disjunct regions that +are activated so they're strongly driven + + align:start position:0% +are activated so they're strongly driven + + + align:start position:0% +are activated so they're strongly driven +by the cells in this region and these + + align:start position:0% +by the cells in this region and these + + + align:start position:0% +by the cells in this region and these +overlap with the face areas and this was + + align:start position:0% +overlap with the face areas and this was + + + align:start position:0% +overlap with the face areas and this was +thought to be found very consistent + + align:start position:0% +thought to be found very consistent + + + align:start position:0% +thought to be found very consistent +across different face areas of you + + align:start position:0% +across different face areas of you + + + align:start position:0% +across different face areas of you +stimulate outside you also get this + + align:start position:0% +stimulate outside you also get this + + + align:start position:0% +stimulate outside you also get this +patchy pattern of connectivity but now + + align:start position:0% +patchy pattern of connectivity but now + + + align:start position:0% +patchy pattern of connectivity but now +it's outside of the safe system and so + + align:start position:0% +it's outside of the safe system and so + + + align:start position:0% +it's outside of the safe system and so +this is the picture that we got is that + + align:start position:0% +this is the picture that we got is that + + + align:start position:0% +this is the picture that we got is that +the sd's face areas are actually part of + + align:start position:0% +the sd's face areas are actually part of + + + align:start position:0% +the sd's face areas are actually part of +a network of face areas that are + + align:start position:0% +a network of face areas that are + + + align:start position:0% +a network of face areas that are +strongly integrated + + align:start position:0% +strongly integrated + + + align:start position:0% +strongly integrated +with each other there's no data from + + align:start position:0% +with each other there's no data from + + + align:start position:0% +with each other there's no data from +which we trace of studies where you find + + align:start position:0% +which we trace of studies where you find + + + align:start position:0% +which we trace of studies where you find +that 90 percent of the cell bodies that + + align:start position:0% +that 90 percent of the cell bodies that + + + align:start position:0% +that 90 percent of the cell bodies that +are labeled after an injection inside + + align:start position:0% +are labeled after an injection inside + + + align:start position:0% +are labeled after an injection inside +the face area are inside other face + + align:start position:0% +the face area are inside other face + + + align:start position:0% +the face area are inside other face +areas or in the same face areas so it's + + align:start position:0% +areas or in the same face areas so it's + + + align:start position:0% +areas or in the same face areas so it's +a surprisingly specialized anatomically + + align:start position:0% +a surprisingly specialized anatomically + + + align:start position:0% +a surprisingly specialized anatomically +specialized and close network + + align:start position:0% +specialized and close network + + + align:start position:0% +specialized and close network +okay so what's happening in these areas + + align:start position:0% +okay so what's happening in these areas + + + align:start position:0% +okay so what's happening in these areas +and again my movies are not going to + + align:start position:0% +and again my movies are not going to + + + align:start position:0% +and again my movies are not going to +work so in this area al with more + + align:start position:0% +work so in this area al with more + + + align:start position:0% +work so in this area al with more +anterior also virtually all the sales + + align:start position:0% +anterior also virtually all the sales + + + align:start position:0% +anterior also virtually all the sales +are face selective but you have a + + align:start position:0% +are face selective but you have a + + + align:start position:0% +are face selective but you have a +property emerge here which you didn't + + align:start position:0% +property emerge here which you didn't + + + align:start position:0% +property emerge here which you didn't +have before and that is mirror symmetric + + align:start position:0% +have before and that is mirror symmetric + + + align:start position:0% +have before and that is mirror symmetric +confusion and it's something that we did + + align:start position:0% +confusion and it's something that we did + + + align:start position:0% +confusion and it's something that we did +not expect we're still puzzled by we + + align:start position:0% +not expect we're still puzzled by we + + + align:start position:0% +not expect we're still puzzled by we +have now maybe one explanation why it's + + align:start position:0% +have now maybe one explanation why it's + + + align:start position:0% +have now maybe one explanation why it's +happening but in this area you have + + align:start position:0% +happening but in this area you have + + + align:start position:0% +happening but in this area you have +cells that like a profile even if they + + align:start position:0% +cells that like a profile even if they + + + align:start position:0% +cells that like a profile even if they +like one profile view they also like the + + align:start position:0% +like one profile view they also like the + + + align:start position:0% +like one profile view they also like the +opposite profile you in this region here + + align:start position:0% +opposite profile you in this region here + + + align:start position:0% +opposite profile you in this region here +may if I mentioned initially that some + + align:start position:0% +may if I mentioned initially that some + + + align:start position:0% +may if I mentioned initially that some +of the sales did not really seem to be + + align:start position:0% +of the sales did not really seem to be + + + align:start position:0% +of the sales did not really seem to be +face-selective it's a small percentage + + align:start position:0% +face-selective it's a small percentage + + + align:start position:0% +face-selective it's a small percentage +but actually these cells are selected + + align:start position:0% +but actually these cells are selected + + + align:start position:0% +but actually these cells are selected +for a facial profile and but if they + + align:start position:0% +for a facial profile and but if they + + + align:start position:0% +for a facial profile and but if they +like one profile right they don't like + + align:start position:0% +like one profile right they don't like + + + align:start position:0% +like one profile right they don't like +left if they like left it under like + + align:start position:0% +left if they like left it under like + + + align:start position:0% +left if they like left it under like +right in Al this has been confused and + + align:start position:0% +right in Al this has been confused and + + + align:start position:0% +right in Al this has been confused and +then if you go to am you have cells that + + align:start position:0% +then if you go to am you have cells that + + + align:start position:0% +then if you go to am you have cells that +some such a respond to all faces doesn't + + align:start position:0% +some such a respond to all faces doesn't + + + align:start position:0% +some such a respond to all faces doesn't +matter where they are doesn't matter who + + align:start position:0% +matter where they are doesn't matter who + + + align:start position:0% +matter where they are doesn't matter who +they are it doesn't matter how big they + + align:start position:0% +they are it doesn't matter how big they + + + align:start position:0% +they are it doesn't matter how big they +are and the other cells that also don't + + align:start position:0% +are and the other cells that also don't + + + align:start position:0% +are and the other cells that also don't +care like where they are and who they + + align:start position:0% +care like where they are and who they + + + align:start position:0% +care like where they are and who they +where they are and how big they are but + + align:start position:0% +where they are and how big they are but + + + align:start position:0% +where they are and how big they are but +they care exquisitely about identity so + + align:start position:0% +they care exquisitely about identity so + + + align:start position:0% +they care exquisitely about identity so +they can be very very finely tuned + + align:start position:0% +they can be very very finely tuned + + + align:start position:0% +they can be very very finely tuned +identity in particular to people that + + align:start position:0% +identity in particular to people that + + + align:start position:0% +identity in particular to people that +the animals never seen in real life so + + align:start position:0% +the animals never seen in real life so + + + align:start position:0% +the animals never seen in real life so +there seems to be competition going on + + align:start position:0% +there seems to be competition going on + + + align:start position:0% +there seems to be competition going on +from here to here where in Germany Kalos + + align:start position:0% +from here to here where in Germany Kalos + + + align:start position:0% +from here to here where in Germany Kalos +a conceptual framework you could imagine + + align:start position:0% +a conceptual framework you could imagine + + + align:start position:0% +a conceptual framework you could imagine +that there's a manifold that's now + + align:start position:0% +that there's a manifold that's now + + + align:start position:0% +that there's a manifold that's now +becoming sort of letter and more getting + + align:start position:0% +becoming sort of letter and more getting + + + align:start position:0% +becoming sort of letter and more getting +like a more expensive representation and + + align:start position:0% +like a more expensive representation and + + + align:start position:0% +like a more expensive representation and +for some reason creating this has to go + + align:start position:0% +for some reason creating this has to go + + + align:start position:0% +for some reason creating this has to go +through this mirror symmetry confusion I + + align:start position:0% +through this mirror symmetry confusion I + + + align:start position:0% +through this mirror symmetry confusion I +just want to highlight so we need to + + align:start position:0% +just want to highlight so we need to + + + align:start position:0% +just want to highlight so we need to +touch upon to the question whether face + + align:start position:0% +touch upon to the question whether face + + + align:start position:0% +touch upon to the question whether face +areas should do different computations + + align:start position:0% +areas should do different computations + + + align:start position:0% +areas should do different computations +from one face areas and actually some my + + align:start position:0% +from one face areas and actually some my + + + align:start position:0% +from one face areas and actually some my +intuition about this was I was actually + + align:start position:0% +intuition about this was I was actually + + + align:start position:0% +intuition about this was I was actually +white the opposite so I thought they + + align:start position:0% +white the opposite so I thought they + + + align:start position:0% +white the opposite so I thought they +would likely do the same computation or + + align:start position:0% +would likely do the same computation or + + + align:start position:0% +would likely do the same computation or +hopefully the same computations outside + + align:start position:0% +hopefully the same computations outside + + + align:start position:0% +hopefully the same computations outside +areas just on different material and so + + align:start position:0% +areas just on different material and so + + + align:start position:0% +areas just on different material and so +why didn't other face areas why don't + + align:start position:0% +why didn't other face areas why don't + + + align:start position:0% +why didn't other face areas why don't +you want to mix these sales because one + + align:start position:0% +you want to mix these sales because one + + + align:start position:0% +you want to mix these sales because one +study that's a little too complicated to + + align:start position:0% +study that's a little too complicated to + + + align:start position:0% +study that's a little too complicated to +explain here that gives some clues but + + align:start position:0% +explain here that gives some clues but + + + align:start position:0% +explain here that gives some clues but +some computation work from Joel libel + + align:start position:0% +some computation work from Joel libel + + + align:start position:0% +some computation work from Joel libel +was a grad student with Tommy actually + + align:start position:0% +was a grad student with Tommy actually + + + align:start position:0% +was a grad student with Tommy actually +gives some clues to that so Joel and + + align:start position:0% +gives some clues to that so Joel and + + + align:start position:0% +gives some clues to that so Joel and +then Tommy were thinking about + + align:start position:0% +then Tommy were thinking about + + + align:start position:0% +then Tommy were thinking about +invariance and Tommy Tommy is going to + + align:start position:0% +invariance and Tommy Tommy is going to + + + align:start position:0% +invariance and Tommy Tommy is going to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +this at some later point in the course + + align:start position:0% +this at some later point in the course + + + align:start position:0% +this at some later point in the course +the different kinds of transformations + + align:start position:0% +the different kinds of transformations + + + align:start position:0% +the different kinds of transformations +easy ones and difficult ones the easy + + align:start position:0% +easy ones and difficult ones the easy + + + align:start position:0% +easy ones and difficult ones the easy +ones are affine transformations we're + + align:start position:0% +ones are affine transformations we're + + + align:start position:0% +ones are affine transformations we're +just shifting something in space or in + + align:start position:0% +just shifting something in space or in + + + align:start position:0% +just shifting something in space or in +size I ordered it in plane and so if you + + align:start position:0% +size I ordered it in plane and so if you + + + align:start position:0% +size I ordered it in plane and so if you +learn how to correct for this + + align:start position:0% +learn how to correct for this + + + align:start position:0% +learn how to correct for this +transformation for just like three dots + + align:start position:0% +transformation for just like three dots + + + align:start position:0% +transformation for just like three dots +off light you can do it for any image + + align:start position:0% +off light you can do it for any image + + + align:start position:0% +off light you can do it for any image +that you can ever see so this is + + align:start position:0% +that you can ever see so this is + + + align:start position:0% +that you can ever see so this is +relatively easy but then they're they're + + align:start position:0% +relatively easy but then they're they're + + + align:start position:0% +relatively easy but then they're they're +not and fine transformations are they're + + align:start position:0% +not and fine transformations are they're + + + align:start position:0% +not and fine transformations are they're +actually changing the picture and they + + align:start position:0% +actually changing the picture and they + + + align:start position:0% +actually changing the picture and they +are very difficult so if you change your + + align:start position:0% +are very difficult so if you change your + + + align:start position:0% +are very difficult so if you change your +facial expression for example or if + + align:start position:0% +facial expression for example or if + + + align:start position:0% +facial expression for example or if +lighting conditions are changing or if + + align:start position:0% +lighting conditions are changing or if + + + align:start position:0% +lighting conditions are changing or if +you're turning your head in depth this + + align:start position:0% +you're turning your head in depth this + + + align:start position:0% +you're turning your head in depth this +is a non affine transformation so it's + + align:start position:0% +is a non affine transformation so it's + + + align:start position:0% +is a non affine transformation so it's +not predictable from just like three + + align:start position:0% +not predictable from just like three + + + align:start position:0% +not predictable from just like three +dots and you can learn something there + + align:start position:0% +dots and you can learn something there + + + align:start position:0% +dots and you can learn something there +that could tell you how this picture + + align:start position:0% +that could tell you how this picture + + + align:start position:0% +that could tell you how this picture +would look like under this one a fine + + align:start position:0% +would look like under this one a fine + + + align:start position:0% +would look like under this one a fine +transformation and one of the insights + + align:start position:0% +transformation and one of the insights + + + align:start position:0% +transformation and one of the insights +from Joel was that if you learn this + + align:start position:0% +from Joel was that if you learn this + + + align:start position:0% +from Joel was that if you learn this +non-affine transformation on a + + align:start position:0% +non-affine transformation on a + + + align:start position:0% +non-affine transformation on a +particular object category let's say + + align:start position:0% +particular object category let's say + + + align:start position:0% +particular object category let's say +faces you actually have learned nothing + + align:start position:0% +faces you actually have learned nothing + + + align:start position:0% +faces you actually have learned nothing +about another object category like ours + + align:start position:0% +about another object category like ours + + + align:start position:0% +about another object category like ours +that's actually quite surprising to me + + align:start position:0% +that's actually quite surprising to me + + + align:start position:0% +that's actually quite surprising to me +but there could be like a reason why you + + align:start position:0% +but there could be like a reason why you + + + align:start position:0% +but there could be like a reason why you +might want to have like all the sales + + align:start position:0% +might want to have like all the sales + + + align:start position:0% +might want to have like all the sales +that have to learn representations + + align:start position:0% +that have to learn representations + + + align:start position:0% +that have to learn representations +across one transformation put them all + + align:start position:0% +across one transformation put them all + + + align:start position:0% +across one transformation put them all +in like one location the second insight + + align:start position:0% +in like one location the second insight + + + align:start position:0% +in like one location the second insight +they had and I think it's it's something + + align:start position:0% +they had and I think it's it's something + + + align:start position:0% +they had and I think it's it's something +that is still very surprising to me that + + align:start position:0% +that is still very surprising to me that + + + align:start position:0% +that is still very surprising to me that +if you work so easily + + align:start position:0% +if you work so easily + + + align:start position:0% +if you work so easily +is to give a computation account for the + + align:start position:0% +is to give a computation account for the + + + align:start position:0% +is to give a computation account for the +system that I just described to you in a + + align:start position:0% +system that I just described to you in a + + + align:start position:0% +system that I just described to you in a +qualitative terms so we have here three + + align:start position:0% +qualitative terms so we have here three + + + align:start position:0% +qualitative terms so we have here three +levels of processing so we have here + + align:start position:0% +levels of processing so we have here + + + align:start position:0% +levels of processing so we have here +like a front end where cells are useful + + align:start position:0% +like a front end where cells are useful + + + align:start position:0% +like a front end where cells are useful +for face detection they all very face + + align:start position:0% +for face detection they all very face + + + align:start position:0% +for face detection they all very face +selective so you could think of this + + align:start position:0% +selective so you could think of this + + + align:start position:0% +selective so you could think of this +it's like a three level processing + + align:start position:0% +it's like a three level processing + + + align:start position:0% +it's like a three level processing +hierarchy where the level one is like a + + align:start position:0% +hierarchy where the level one is like a + + + align:start position:0% +hierarchy where the level one is like a +face filter that's just going to tell + + align:start position:0% +face filter that's just going to tell + + + align:start position:0% +face filter that's just going to tell +you it's their face or not the top level + + align:start position:0% +you it's their face or not the top level + + + align:start position:0% +you it's their face or not the top level +you want to go identification and didn't + + align:start position:0% +you want to go identification and didn't + + + align:start position:0% +you want to go identification and didn't +show the examples again I hope with + + align:start position:0% +show the examples again I hope with + + + align:start position:0% +show the examples again I hope with +other connection to the monitor I can + + align:start position:0% +other connection to the monitor I can + + + align:start position:0% +other connection to the monitor I can +show you the actual movies you have some + + align:start position:0% +show you the actual movies you have some + + + align:start position:0% +show you the actual movies you have some +sense they're very very finely selective + + align:start position:0% +sense they're very very finely selective + + + align:start position:0% +sense they're very very finely selective +for facial identity and you know what + + align:start position:0% +for facial identity and you know what + + + align:start position:0% +for facial identity and you know what +pattern we do techniques you can read + + align:start position:0% +pattern we do techniques you can read + + + align:start position:0% +pattern we do techniques you can read +out identity extremely reliably + + align:start position:0% +out identity extremely reliably + + + align:start position:0% +out identity extremely reliably +if you know play like have been learning + + align:start position:0% +if you know play like have been learning + + + align:start position:0% +if you know play like have been learning +whether maybe Tommy is gonna explain + + align:start position:0% +whether maybe Tommy is gonna explain + + + align:start position:0% +whether maybe Tommy is gonna explain +this to you more you actually get + + align:start position:0% +this to you more you actually get + + + align:start position:0% +this to you more you actually get +something pretty magic so you do get + + align:start position:0% +something pretty magic so you do get + + + align:start position:0% +something pretty magic so you do get +invariance at level number three which + + align:start position:0% +invariance at level number three which + + + align:start position:0% +invariance at level number three which +is kind of what you wanted it might not + + align:start position:0% +is kind of what you wanted it might not + + + align:start position:0% +is kind of what you wanted it might not +be surprised by but it's a byproduct you + + align:start position:0% +be surprised by but it's a byproduct you + + + align:start position:0% +be surprised by but it's a byproduct you +are getting mirror symmetry at level two + + align:start position:0% +are getting mirror symmetry at level two + + + align:start position:0% +are getting mirror symmetry at level two +and that's something you didn't stick + + align:start position:0% +and that's something you didn't stick + + + align:start position:0% +and that's something you didn't stick +into the system and just happens not + + align:start position:0% +into the system and just happens not + + + align:start position:0% +into the system and just happens not +like magic but there's an explanation + + align:start position:0% +like magic but there's an explanation + + + align:start position:0% +like magic but there's an explanation +for Hawaii this happens a lot of very + + align:start position:0% +for Hawaii this happens a lot of very + + + align:start position:0% +for Hawaii this happens a lot of very +general assumptions about the system so + + align:start position:0% +general assumptions about the system so + + + align:start position:0% +general assumptions about the system so +the point I want to make you you know + + align:start position:0% +the point I want to make you you know + + + align:start position:0% +the point I want to make you you know +this particular model could be + + align:start position:0% +this particular model could be + + + align:start position:0% +this particular model could be +but it's something about like how + + align:start position:0% +but it's something about like how + + + align:start position:0% +but it's something about like how +knowing something about the overall + + align:start position:0% +knowing something about the overall + + + align:start position:0% +knowing something about the overall +inhalation of the system might actually + + align:start position:0% +inhalation of the system might actually + + + align:start position:0% +inhalation of the system might actually +reveal underlying relationships that you + + align:start position:0% +reveal underlying relationships that you + + + align:start position:0% +reveal underlying relationships that you +might not think about so the fact that + + align:start position:0% +might not think about so the fact that + + + align:start position:0% +might not think about so the fact that +there are three layers of processing and + + align:start position:0% +there are three layers of processing and + + + align:start position:0% +there are three layers of processing and +at four or five or six might actually + + align:start position:0% +at four or five or six might actually + + + align:start position:0% +at four or five or six might actually +impact whether you find mirror symmetry + + align:start position:0% +impact whether you find mirror symmetry + + + align:start position:0% +impact whether you find mirror symmetry +or not or whether you find mirror + + align:start position:0% +or not or whether you find mirror + + + align:start position:0% +or not or whether you find mirror +symmetry one level or another level and + + align:start position:0% +symmetry one level or another level and + + + align:start position:0% +symmetry one level or another level and +you don't necessarily get this + + align:start position:0% +you don't necessarily get this + + + align:start position:0% +you don't necessarily get this +automatically just put like any + + align:start position:0% +automatically just put like any + + + align:start position:0% +automatically just put like any +processing system together because that + + align:start position:0% +processing system together because that + + + align:start position:0% +processing system together because that +was mentioning of facial motion I would + + align:start position:0% +was mentioning of facial motion I would + + + align:start position:0% +was mentioning of facial motion I would +like to give like a brief and yet of + + align:start position:0% +like to give like a brief and yet of + + + align:start position:0% +like to give like a brief and yet of +that and that's actually I was + + align:start position:0% +that and that's actually I was + + + align:start position:0% +that and that's actually I was +emphasizing here oops + + align:start position:0% +emphasizing here oops + + + align:start position:0% +emphasizing here oops +emphasizing here transformations along + + align:start position:0% +emphasizing here transformations along + + + align:start position:0% +emphasizing here transformations along +this direction but you can see that at + + align:start position:0% +this direction but you can see that at + + + align:start position:0% +this direction but you can see that at +least at the two levels of processing + + align:start position:0% +least at the two levels of processing + + + align:start position:0% +least at the two levels of processing +there are actually two phase errors here + + align:start position:0% +there are actually two phase errors here + + + align:start position:0% +there are actually two phase errors here +one lateral to the STS and the other one + + align:start position:0% +one lateral to the STS and the other one + + + align:start position:0% +one lateral to the STS and the other one +deep inside and so one of the questions + + align:start position:0% +deep inside and so one of the questions + + + align:start position:0% +deep inside and so one of the questions +we had was going on here like how they + + align:start position:0% +we had was going on here like how they + + + align:start position:0% +we had was going on here like how they +are different and so one way you might + + align:start position:0% +are different and so one way you might + + + align:start position:0% +are different and so one way you might +think about this is again like + + align:start position:0% +think about this is again like + + + align:start position:0% +think about this is again like +connecting faces to to social perception + + align:start position:0% +connecting faces to to social perception + + + align:start position:0% +connecting faces to to social perception +so there are some faces out there that + + align:start position:0% +so there are some faces out there that + + + align:start position:0% +so there are some faces out there that +are not really faces and so the faces of + + align:start position:0% +are not really faces and so the faces of + + + align:start position:0% +are not really faces and so the faces of +doors are just like one example so + + align:start position:0% +doors are just like one example so + + + align:start position:0% +doors are just like one example so +physically they are faces but you can + + align:start position:0% +physically they are faces but you can + + + align:start position:0% +physically they are faces but you can +actually tell that they are not really + + align:start position:0% +actually tell that they are not really + + + align:start position:0% +actually tell that they are not really +real they let agents and people like + + align:start position:0% +real they let agents and people like + + + align:start position:0% +real they let agents and people like +Talia weekly are wondering about + + align:start position:0% +Talia weekly are wondering about + + + align:start position:0% +Talia weekly are wondering about +questions also creepy so there is you + + align:start position:0% +questions also creepy so there is you + + + align:start position:0% +questions also creepy so there is you +know an expectation that the face should + + align:start position:0% +know an expectation that the face should + + + align:start position:0% +know an expectation that the face should +belong to a real agent and their + + align:start position:0% +belong to a real agent and their + + + align:start position:0% +belong to a real agent and their +different clues that can give it away so + + align:start position:0% +different clues that can give it away so + + + align:start position:0% +different clues that can give it away so +if it faces on top of a body more likely + + align:start position:0% +if it faces on top of a body more likely + + + align:start position:0% +if it faces on top of a body more likely +it's an agent than just like an + + align:start position:0% +it's an agent than just like an + + + align:start position:0% +it's an agent than just like an +artificial stimulus if the face is + + align:start position:0% +artificial stimulus if the face is + + + align:start position:0% +artificial stimulus if the face is +moving that's like another cludes an + + align:start position:0% +moving that's like another cludes an + + + align:start position:0% +moving that's like another cludes an +agent and this will change fundamentally + + align:start position:0% +agent and this will change fundamentally + + + align:start position:0% +agent and this will change fundamentally +how you're interacting with it right + + align:start position:0% +how you're interacting with it right + + + align:start position:0% +how you're interacting with it right +your interaction with a doll is likely + + align:start position:0% +your interaction with a doll is likely + + + align:start position:0% +your interaction with a doll is likely +going to be very different than with a + + align:start position:0% +going to be very different than with a + + + align:start position:0% +going to be very different than with a +baby and so again like updates in the + + align:start position:0% +baby and so again like updates in the + + + align:start position:0% +baby and so again like updates in the +meaning I'm making the next one in + + align:start position:0% +meaning I'm making the next one in + + + align:start position:0% +meaning I'm making the next one in +different ways and we have to understand + + align:start position:0% +different ways and we have to understand + + + align:start position:0% +different ways and we have to understand +what the circuits are I should make this + + align:start position:0% +what the circuits are I should make this + + + align:start position:0% +what the circuits are I should make this +possible so one way to look at this + + align:start position:0% +possible so one way to look at this + + + align:start position:0% +possible so one way to look at this +again is to think about this facial + + align:start position:0% +again is to think about this facial + + + align:start position:0% +again is to think about this facial +displace I showed the donkey in macaques + + align:start position:0% +displace I showed the donkey in macaques + + + align:start position:0% +displace I showed the donkey in macaques +and Clark Fisher was an MD PhD student + + align:start position:0% +and Clark Fisher was an MD PhD student + + + align:start position:0% +and Clark Fisher was an MD PhD student +in the lab wasn't she addressing this + + align:start position:0% +in the lab wasn't she addressing this + + + align:start position:0% +in the lab wasn't she addressing this +question + + align:start position:0% +question + + + align:start position:0% +question +and so he made movies like this one here + + align:start position:0% +and so he made movies like this one here + + + align:start position:0% +and so he made movies like this one here +luckily there's no sound so we can + + align:start position:0% +luckily there's no sound so we can + + + align:start position:0% +luckily there's no sound so we can +actually play them these are like movies + + align:start position:0% +actually play them these are like movies + + + align:start position:0% +actually play them these are like movies +of macaque monkeys and making facial + + align:start position:0% +of macaque monkeys and making facial + + + align:start position:0% +of macaque monkeys and making facial +movements of all different kinds face + + align:start position:0% +movements of all different kinds face + + + align:start position:0% +movements of all different kinds face +expressions and would then also have + + align:start position:0% +expressions and would then also have + + + align:start position:0% +expressions and would then also have +stills that are just changing from time + + align:start position:0% +stills that are just changing from time + + + align:start position:0% +stills that are just changing from time +to time and we have controls of toys + + align:start position:0% +to time and we have controls of toys + + + align:start position:0% +to time and we have controls of toys +that the animals also know that either + + align:start position:0% +that the animals also know that either + + + align:start position:0% +that the animals also know that either +moving or that are jumping every second + + align:start position:0% +moving or that are jumping every second + + + align:start position:0% +moving or that are jumping every second +from one state to the other and we would + + align:start position:0% +from one state to the other and we would + + + align:start position:0% +from one state to the other and we would +ask this wait in an earlier study this + + align:start position:0% +ask this wait in an earlier study this + + + align:start position:0% +ask this wait in an earlier study this +area's responding to this motion + + align:start position:0% +area's responding to this motion + + + align:start position:0% +area's responding to this motion +differently than to the static images so + + align:start position:0% +differently than to the static images so + + + align:start position:0% +differently than to the static images so +here's what he found he had six + + align:start position:0% +here's what he found he had six + + + align:start position:0% +here's what he found he had six +different faces he was looking at if you + + align:start position:0% +different faces he was looking at if you + + + align:start position:0% +different faces he was looking at if you +looking at aesthetic form selectivity + + align:start position:0% +looking at aesthetic form selectivity + + + align:start position:0% +looking at aesthetic form selectivity +we're just reproducing the way that the + + align:start position:0% +we're just reproducing the way that the + + + align:start position:0% +we're just reproducing the way that the +area was found just with the different + + align:start position:0% +area was found just with the different + + + align:start position:0% +area was found just with the different +stimulus set so all the 60s respond more + + align:start position:0% +stimulus set so all the 60s respond more + + + align:start position:0% +stimulus set so all the 60s respond more +to faces than to objects if we now + + align:start position:0% +to faces than to objects if we now + + + align:start position:0% +to faces than to objects if we now +compare moving faces to aesthetics so + + align:start position:0% +compare moving faces to aesthetics so + + + align:start position:0% +compare moving faces to aesthetics so +all the areas are responding more to the + + align:start position:0% +all the areas are responding more to the + + + align:start position:0% +all the areas are responding more to the +moving faces and aesthetic ones some + + align:start position:0% +moving faces and aesthetic ones some + + + align:start position:0% +moving faces and aesthetic ones some +quantitative differences but overall the + + align:start position:0% +quantitative differences but overall the + + + align:start position:0% +quantitative differences but overall the +same pattern more response to moving + + align:start position:0% +same pattern more response to moving + + + align:start position:0% +same pattern more response to moving +than static stimuli if you now compare + + align:start position:0% +than static stimuli if you now compare + + + align:start position:0% +than static stimuli if you now compare +the right hand side the modulation by + + align:start position:0% +the right hand side the modulation by + + + align:start position:0% +the right hand side the modulation by +moving objects to aesthetic objects you + + align:start position:0% +moving objects to aesthetic objects you + + + align:start position:0% +moving objects to aesthetic objects you +can see that also all the areas or + + align:start position:0% +can see that also all the areas or + + + align:start position:0% +can see that also all the areas or +almost all have a slight advantage of + + align:start position:0% +almost all have a slight advantage of + + + align:start position:0% +almost all have a slight advantage of +moving objects over static objects there + + align:start position:0% +moving objects over static objects there + + + align:start position:0% +moving objects over static objects there +seems to be a lack of general motion + + align:start position:0% +seems to be a lack of general motion + + + align:start position:0% +seems to be a lack of general motion +sensitivity there but if you do the + + align:start position:0% +sensitivity there but if you do the + + + align:start position:0% +sensitivity there but if you do the +interaction of shape and motion you can + + align:start position:0% +interaction of shape and motion you can + + + align:start position:0% +interaction of shape and motion you can +see that all the areas are selectively + + align:start position:0% +see that all the areas are selectively + + + align:start position:0% +see that all the areas are selectively +more enhanced by face motion than by non + + align:start position:0% +more enhanced by face motion than by non + + + align:start position:0% +more enhanced by face motion than by non +face motion okay but they all look + + align:start position:0% +face motion okay but they all look + + + align:start position:0% +face motion okay but they all look +pretty similar so now you can actually + + align:start position:0% +pretty similar so now you can actually + + + align:start position:0% +pretty similar so now you can actually +wonder if you have a conference like + + align:start position:0% +wonder if you have a conference like + + + align:start position:0% +wonder if you have a conference like +this like moving words are still there + + align:start position:0% +this like moving words are still there + + + align:start position:0% +this like moving words are still there +couple of things that are different so + + align:start position:0% +couple of things that are different so + + + align:start position:0% +couple of things that are different so +it's really about motion or is it just + + align:start position:0% +it's really about motion or is it just + + + align:start position:0% +it's really about motion or is it just +about the content if you just show like + + align:start position:0% +about the content if you just show like + + + align:start position:0% +about the content if you just show like +a picture every one second you can say + + align:start position:0% +a picture every one second you can say + + + align:start position:0% +a picture every one second you can say +well there's less content there + + align:start position:0% +well there's less content there + + + align:start position:0% +well there's less content there +therefore you might have more education + + align:start position:0% +therefore you might have more education + + + align:start position:0% +therefore you might have more education +therefore less response across the board + + align:start position:0% +therefore less response across the board + + + align:start position:0% +therefore less response across the board +is it about update frequency you know + + align:start position:0% +is it about update frequency you know + + + align:start position:0% +is it about update frequency you know +the first update versus a slow update so + + align:start position:0% +the first update versus a slow update so + + + align:start position:0% +the first update versus a slow update so +what and what Clark did was and this is + + align:start position:0% +what and what Clark did was and this is + + + align:start position:0% +what and what Clark did was and this is +normal playing he was creating another + + align:start position:0% +normal playing he was creating another + + + align:start position:0% +normal playing he was creating another +stimulus if you think about creepiness + + align:start position:0% +stimulus if you think about creepiness + + + align:start position:0% +stimulus if you think about creepiness +it's actually like a little bit creepy + + align:start position:0% +it's actually like a little bit creepy + + + align:start position:0% +it's actually like a little bit creepy +say like a scrambled version of a motion + + align:start position:0% +say like a scrambled version of a motion + + + align:start position:0% +say like a scrambled version of a motion +that it's shown here shows the same + + align:start position:0% +that it's shown here shows the same + + + align:start position:0% +that it's shown here shows the same +frames of the movie but just like + + align:start position:0% +frames of the movie but just like + + + align:start position:0% +frames of the movie but just like +randomly associated with each other + + align:start position:0% +randomly associated with each other + + + align:start position:0% +randomly associated with each other +so if anything now the motion energy and + + align:start position:0% +so if anything now the motion energy and + + + align:start position:0% +so if anything now the motion energy and +this thing is higher than in this one + + align:start position:0% +this thing is higher than in this one + + + align:start position:0% +this thing is higher than in this one +here and we can look now for the contras + + align:start position:0% +here and we can look now for the contras + + + align:start position:0% +here and we can look now for the contras +of those two and also the contest of two + + align:start position:0% +of those two and also the contest of two + + + align:start position:0% +of those two and also the contest of two +here and now what he finds is actually + + align:start position:0% +here and now what he finds is actually + + + align:start position:0% +here and now what he finds is actually +something where the phase errors are + + align:start position:0% +something where the phase errors are + + + align:start position:0% +something where the phase errors are +qualitatively different he finds two + + align:start position:0% +qualitatively different he finds two + + + align:start position:0% +qualitatively different he finds two +phase errors here which are responding + + align:start position:0% +phase errors here which are responding + + + align:start position:0% +phase errors here which are responding +more to the natural motion than the + + align:start position:0% +more to the natural motion than the + + + align:start position:0% +more to the natural motion than the +scramble motion and three phase errors + + align:start position:0% +scramble motion and three phase errors + + + align:start position:0% +scramble motion and three phase errors +that are spawning more to the scrambled + + align:start position:0% +that are spawning more to the scrambled + + + align:start position:0% +that are spawning more to the scrambled +motion than the natural motion so they + + align:start position:0% +motion than the natural motion so they + + + align:start position:0% +motion than the natural motion so they +should have opposite preferences what we + + align:start position:0% +should have opposite preferences what we + + + align:start position:0% +should have opposite preferences what we +think is going or is here that remember + + align:start position:0% +think is going or is here that remember + + + align:start position:0% +think is going or is here that remember +also the benefit for facial motion over + + align:start position:0% +also the benefit for facial motion over + + + align:start position:0% +also the benefit for facial motion over +static faces but they just like a fast + + align:start position:0% +static faces but they just like a fast + + + align:start position:0% +static faces but they just like a fast +update of content ideal in a way that's + + align:start position:0% +update of content ideal in a way that's + + + align:start position:0% +update of content ideal in a way that's +not predictable if you show me something + + align:start position:0% +not predictable if you show me something + + + align:start position:0% +not predictable if you show me something +new I'm going to respond and if it's + + align:start position:0% +new I'm going to respond and if it's + + + align:start position:0% +new I'm going to respond and if it's +something that I can predict even better + + align:start position:0% +something that I can predict even better + + + align:start position:0% +something that I can predict even better +so this is what these guys are doing but + + align:start position:0% +so this is what these guys are doing but + + + align:start position:0% +so this is what these guys are doing but +these ones here they seem to be really + + align:start position:0% +these ones here they seem to be really + + + align:start position:0% +these ones here they seem to be really +sensitive to facial movement and + + align:start position:0% +sensitive to facial movement and + + + align:start position:0% +sensitive to facial movement and +naturalness of facial movement + + align:start position:0% +naturalness of facial movement + + + align:start position:0% +naturalness of facial movement +and then was not smart and these areas + + align:start position:0% +and then was not smart and these areas + + + align:start position:0% +and then was not smart and these areas +are located more deep inside the STS + + align:start position:0% +are located more deep inside the STS + + + align:start position:0% +are located more deep inside the STS +more dorsally and these areas are + + align:start position:0% +more dorsally and these areas are + + + align:start position:0% +more dorsally and these areas are +located more ventrally so there's an + + align:start position:0% +located more ventrally so there's an + + + align:start position:0% +located more ventrally so there's an +organization and to discover the new + + align:start position:0% +organization and to discover the new + + + align:start position:0% +organization and to discover the new +face area didn't know before it's the + + align:start position:0% +face area didn't know before it's the + + + align:start position:0% +face area didn't know before it's the +seventh face area which we called MD + + align:start position:0% +seventh face area which we called MD + + + align:start position:0% +seventh face area which we called MD +which is really like a face motion area + + align:start position:0% +which is really like a face motion area + + + align:start position:0% +which is really like a face motion area +the lots of reasons we're excited about + + align:start position:0% +the lots of reasons we're excited about + + + align:start position:0% +the lots of reasons we're excited about +this I mention between face perception + + align:start position:0% +this I mention between face perception + + + align:start position:0% +this I mention between face perception +and agency interpretation this is one + + align:start position:0% +and agency interpretation this is one + + + align:start position:0% +and agency interpretation this is one +possible link that they're more it might + + align:start position:0% +possible link that they're more it might + + + align:start position:0% +possible link that they're more it might +be a second face processing system it + + align:start position:0% +be a second face processing system it + + + align:start position:0% +be a second face processing system it +cannot go through all the the evidence + + align:start position:0% +cannot go through all the the evidence + + + align:start position:0% +cannot go through all the the evidence +it's only indirect though that this area + + align:start position:0% +it's only indirect though that this area + + + align:start position:0% +it's only indirect though that this area +might not be connected to the other ones + + align:start position:0% +might not be connected to the other ones + + + align:start position:0% +might not be connected to the other ones +I told you before that the six face + + align:start position:0% +I told you before that the six face + + + align:start position:0% +I told you before that the six face +areas are intricately integrated to be + + align:start position:0% +areas are intricately integrated to be + + + align:start position:0% +areas are intricately integrated to be +like one network this area never showed + + align:start position:0% +like one network this area never showed + + + align:start position:0% +like one network this area never showed +up in areas therefore might be separate + + align:start position:0% +up in areas therefore might be separate + + + align:start position:0% +up in areas therefore might be separate +and this is kind of nice because it fits + + align:start position:0% +and this is kind of nice because it fits + + + align:start position:0% +and this is kind of nice because it fits +very nicely to the human situation so in + + align:start position:0% +very nicely to the human situation so in + + + align:start position:0% +very nicely to the human situation so in +human brain you have the posterior STS + + align:start position:0% +human brain you have the posterior STS + + + align:start position:0% +human brain you have the posterior STS +face area which is exquisitely sensitive + + align:start position:0% +face area which is exquisitely sensitive + + + align:start position:0% +face area which is exquisitely sensitive +to facial motion actually often don't + + align:start position:0% +to facial motion actually often don't + + + align:start position:0% +to facial motion actually often don't +even get it for static faces but very + + align:start position:0% +even get it for static faces but very + + + align:start position:0% +even get it for static faces but very +sensitive to that emotion and in ninety + + align:start position:0% +sensitive to that emotion and in ninety + + + align:start position:0% +sensitive to that emotion and in ninety +it's a beautiful study on that in this + + align:start position:0% +it's a beautiful study on that in this + + + align:start position:0% +it's a beautiful study on that in this +area by by several accounts the other + + align:start position:0% +area by by several accounts the other + + + align:start position:0% +area by by several accounts the other +face yes it seems to be like a separate + + align:start position:0% +face yes it seems to be like a separate + + + align:start position:0% +face yes it seems to be like a separate +specialization that's another thing + + align:start position:0% +specialization that's another thing + + + align:start position:0% +specialization that's another thing +another reason why we think that these + + align:start position:0% +another reason why we think that these + + + align:start position:0% +another reason why we think that these +systems might be might be connected to + + align:start position:0% +systems might be might be connected to + + + align:start position:0% +systems might be might be connected to +each other just a cool thing in the end + + align:start position:0% +each other just a cool thing in the end + + + align:start position:0% +each other just a cool thing in the end +who can recognize this actor here show + + align:start position:0% +who can recognize this actor here show + + + align:start position:0% +who can recognize this actor here show +of hands + + align:start position:0% +of hands + + + align:start position:0% +of hands +okay who can recognize now okay so a few + + align:start position:0% +okay who can recognize now okay so a few + + + align:start position:0% +okay who can recognize now okay so a few +more of the way a lot of things like + + align:start position:0% +more of the way a lot of things like + + + align:start position:0% +more of the way a lot of things like +identity technicals in there's a + + align:start position:0% +identity technicals in there's a + + + align:start position:0% +identity technicals in there's a +significant very typical a few movements + + align:start position:0% +significant very typical a few movements + + + align:start position:0% +significant very typical a few movements +so it's not just agency it's not just + + align:start position:0% +so it's not just agency it's not just + + + align:start position:0% +so it's not just agency it's not just +you know these expressions is also + + align:start position:0% +you know these expressions is also + + + align:start position:0% +you know these expressions is also +identity and lots of things that can go + + align:start position:0% +identity and lots of things that can go + + + align:start position:0% +identity and lots of things that can go +away so we if you don't know yet what + + align:start position:0% +away so we if you don't know yet what + + + align:start position:0% +away so we if you don't know yet what +these areas are doing okay so my summary + + align:start position:0% +these areas are doing okay so my summary + + + align:start position:0% +these areas are doing okay so my summary +and I'm sorry I'm lunch is this so we + + align:start position:0% +and I'm sorry I'm lunch is this so we + + + align:start position:0% +and I'm sorry I'm lunch is this so we +can be a from Ryan macaque monkeys + + align:start position:0% +can be a from Ryan macaque monkeys + + + align:start position:0% +can be a from Ryan macaque monkeys +roosters and humans what we find we he + + align:start position:0% +roosters and humans what we find we he + + + align:start position:0% +roosters and humans what we find we he +implied to lots of domains with an + + align:start position:0% +implied to lots of domains with an + + + align:start position:0% +implied to lots of domains with an +attention studies for new attention + + align:start position:0% +attention studies for new attention + + + align:start position:0% +attention studies for new attention +areas he will be applied to a face + + align:start position:0% +areas he will be applied to a face + + + align:start position:0% +areas he will be applied to a face +processing we find face selective areas + + align:start position:0% +processing we find face selective areas + + + align:start position:0% +processing we find face selective areas +of face processing recording their micro + + align:start position:0% +of face processing recording their micro + + + align:start position:0% +of face processing recording their micro +stimulate asourian activating these + + align:start position:0% +stimulate asourian activating these + + + align:start position:0% +stimulate asourian activating these +regions is supporting the notion that + + align:start position:0% +regions is supporting the notion that + + + align:start position:0% +regions is supporting the notion that +these are likely modules that are for + + align:start position:0% +these are likely modules that are for + + + align:start position:0% +these are likely modules that are for +processing faces and faces only + + align:start position:0% + + + + align:start position:0% + +beside interconnected into a face + + align:start position:0% +beside interconnected into a face + + + align:start position:0% +beside interconnected into a face +processing Network it looks like all + + align:start position:0% +processing Network it looks like all + + + align:start position:0% +processing Network it looks like all +these areas have different function + + align:start position:0% +these areas have different function + + + align:start position:0% +these areas have different function +specialization so my experiments are + + align:start position:0% +specialization so my experiments are + + + align:start position:0% +specialization so my experiments are +notoriously under powered in the head of + + align:start position:0% +notoriously under powered in the head of + + + align:start position:0% +notoriously under powered in the head of +number of different dimensions so if we + + align:start position:0% +number of different dimensions so if we + + + align:start position:0% +number of different dimensions so if we +call them face eros is not to say that + + align:start position:0% +call them face eros is not to say that + + + align:start position:0% +call them face eros is not to say that +they're all doing the same but they're + + align:start position:0% +they're all doing the same but they're + + + align:start position:0% +they're all doing the same but they're +likely all have different functions and + + align:start position:0% +likely all have different functions and + + + align:start position:0% +likely all have different functions and +make likely sub regions of these + + align:start position:0% +make likely sub regions of these + + + align:start position:0% +make likely sub regions of these +different functions so again there's no + + align:start position:0% +different functions so again there's no + + + align:start position:0% +different functions so again there's no +contradiction to the view of like a + + align:start position:0% +contradiction to the view of like a + + + align:start position:0% +contradiction to the view of like a +finds an organization then there's like + + align:start position:0% +finds an organization then there's like + + + align:start position:0% +finds an organization then there's like +a seventh face heir which doesn't seem + + align:start position:0% +a seventh face heir which doesn't seem + + + align:start position:0% +a seventh face heir which doesn't seem +to be clear that could be separate a + + align:start position:0% +to be clear that could be separate a + + + align:start position:0% +to be clear that could be separate a +separate face processing system we have + + align:start position:0% +separate face processing system we have + + + align:start position:0% +separate face processing system we have +evidence for racket processing that we + + align:start position:0% +evidence for racket processing that we + + + align:start position:0% +evidence for racket processing that we +can understand now in computational + + align:start position:0% +can understand now in computational + + + align:start position:0% +can understand now in computational +terms and this is like one way that you + + align:start position:0% +terms and this is like one way that you + + + align:start position:0% +terms and this is like one way that you +can link sometimes causally sometimes + + align:start position:0% +can link sometimes causally sometimes + + + align:start position:0% +can link sometimes causally sometimes +correlational II activity of single + + align:start position:0% +correlational II activity of single + + + align:start position:0% +correlational II activity of single +cells through different levels of + + align:start position:0% +cells through different levels of + + + align:start position:0% +cells through different levels of +organization to a very complex social + + align:start position:0% +organization to a very complex social + + + align:start position:0% +organization to a very complex social +behavior and that's again I think very + + align:start position:0% +behavior and that's again I think very + + + align:start position:0% +behavior and that's again I think very +cool opportunity to have in the domain + + align:start position:0% +cool opportunity to have in the domain + + + align:start position:0% +cool opportunity to have in the domain +of social cognition that you can + + align:start position:0% +of social cognition that you can + + + align:start position:0% +of social cognition that you can +actually control stimuli very well + + align:start position:0% +actually control stimuli very well + + + align:start position:0% +actually control stimuli very well +because faces are so powerful to getting + + align:start position:0% +because faces are so powerful to getting + + + align:start position:0% +because faces are so powerful to getting +to your social brain you can likely take + + align:start position:0% +to your social brain you can likely take + + + align:start position:0% +to your social brain you can likely take +this approach deeper and get instant to + + align:start position:0% +this approach deeper and get instant to + + + align:start position:0% +this approach deeper and get instant to +actual social intelligence beyond face + + align:start position:0% +actual social intelligence beyond face + + + align:start position:0% +actual social intelligence beyond face +perception this way + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/8YQf4xOEhag.txt b/8YQf4xOEhag.txt new file mode 100644 index 0000000000000000000000000000000000000000..824d34ec3daa838e1fc6ee36f3444b9a12947817 --- /dev/null +++ b/8YQf4xOEhag.txt @@ -0,0 +1,5595 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, welcome +everyone. + +It's 8:05, well, 9:05. + +So today's lecture and +discussion is about how to + +make good problems, whether +it's on homework problems, + +exams, even problems in class. + +Its general principles that +you can use constructing + +questions that you ask, so +problems broadly conceived. + +Now why problems? + +So problems are, I think, one +of the central ways of + +thinking about teaching. + +And I'll show you how problems +fit into the grand scheme of + +this course, of rethinking all +the aspects of teaching. + +So one way that I like to think +about teaching is called + +backward design. + +So this is a way of designing a +whole course, could even be + +for a curriculum. + +And doing problems is +one aspect of that. + +So why is it called +backward design? + +Well, it's backward from +the usual way. + +So I'll show you what backward +is and then show you what the + +usual way is. + +So in backward design the +highest-level thing you figure + +out-- not necessarily the first +thing you figure out, + +but the highest level thing-- +is your course goals. + +And that then feeds to OK, if +those are your course goals + +how do you know whether students +have reached them? + +And that's problems. + +Problems, tasks, projects, +whatever it may be, things + +that students are going to do. + +And so generally speaking, +things to do. + +And then given that you've +operationalized the goals in + +these problems what are you +going to do in class, so that + +students actually are able to +do these kind of things? + +OK, so that is backward +design because the + +usual way is the following. + +You say, OK, well, you have +a bunch of lecture notes. + +Where do you have those? + +Well, either the last person +who taught the course gives + +you their lecture notes. + +Or you just take the standard +book in the subject and you + +just do the lectures one per +chapter or one week per + +chapter, something like that. + +And you just go through +in the order. + +So in the usual way you +start with this. + +And then you think oh, whoops, +oh yeah, I've got to make some + +problem sets. + +And oh, some exams. + +Well, what have we done this +last couple weeks? + +OK, that's what we're +going to do. + +So the usual way is you +start with here. + +And then you get here. + +And you somehow never +get here. + +The course goals are, +basically, to + +get through the book. + +Right? + +That's the implicit +course goal. + +But it's never explicitly +planned. + +So that's a terrible way, +but the normal way + +of designing a course. + +So this is backward design. + +So this is due to Wiggins +and McTighe. + +OK, so here we're going to +be discussing this today. + +So we're doing this first. + +And then the next session +is this one. + +And I think the session after +that is, what do you do in + +class, interactive teaching +and things like that. + +So why am I doing it +in this order? + +Well, in the levels of +abstraction these + +are the most abstract. + +And this is the most concrete, +OK, what question I'm going to + +ask students in class now. + +And this is things like goals. + +I want them to really understand +conservation. + +They're really high level. + +So I think if you start here, by +trying to figure out course + +goals, I haven't found that +works very well for me because + +it's too high level. + +I can't think about course goals +in absence of actual + +problems and things I want +students to be able to do. + +So this has the right level +between concrete and abstract. + +So it's actually where +I start my thinking. + +Now, you may actually find you +want to start somewhere else + +on the continuum. + +But this is what I found +works quite well. + +You start here, you +operationalize what your goals + +are in the problems that you +think are interesting. + +And then you look +at the problems. + +And that sort of gives you an +idea of the course goals. + +And then you think about +the course goals. + +And that helps you think +of problems. + +But I start here. + +And then, once I have things +like that, then class time is + +actually much easier to plan. + +Because class often is going +to be problems like this, + +related to this, +maybe shorter. + +But it's easier to plan +here after that. + +Whereas we start here, you +don't know, you're + +back in the old way. + +So I don't want to start here. + +This is too abstract, +so I start here. + +So that's why we're +doing this now. + +And then next week we're +going to do this one. + +Question? + +AUDIENCE: So when you say +that you're setting + +goals for your class-- + +PROFESSOR: Pardon? + +AUDIENCE: So if you say that, +basically, setting the goals + +for your class, or for +your own course. + +So when you design your course, +basically you write + +out some kind of goals +you want to reach? + +So how do you then +do the problem? + +Do you go in detail +before you've even + +started the whole class? + +Or do you do it that on +a week-to-week basis? + +PROFESSOR: Oh, what do +I tell the students + +about the course goals? + +AUDIENCE: Yeah, I mean, if you +say, OK, basically, you have + +your goals and then you +design problems so you + +can reach the goals? + +But then do you also design +these problems before you even + +start the whole lecture? + +The whole semester? + +PROFESSOR: Oh, well, +it's pretty rough. + +I mean, usually the first time +you teach the thing it's too + +abstract to design-- + +I find-- + +everything in advance. + +Maybe that's my extrovert +nature, which is that I find + +it hard to design things for +people I don't know. + +If I don't know the audience I +don't even know what to say. + +So I want to actually teach the +course one time at least. + +So then the audience becomes +concrete for me. + +So really, the first time +through the course nothing is + +ever ideal. + +And you're doing everything +on the fly. + +But the second time through the +course, you can actually, + +basically, make all the problems +ahead of time. + +So the second time through the +course you actually refine + +your goals and your +problems together. + +So that shows you the structure +of where we are and + +where we're going to +go and then later. + +So this is two weeks from now. + +Today, here. + +So how do you make problems? + +Well, the fundamental principle +is, again, deduced + +by induction from what happens +with regular problems. + +So if you remember, I gave you +an example earlier of the + +results of standard +problem solving. + +And I'll just remind you that +we're putting up the + +percentages again. + +OK, so after doing lots +and lots of standard + +multiplication problems, +students were-- + +if you remember-- unable to +do the following problem. + +So these 13-year-Olds and +17-year-Olds were asked to + +estimate 3.04 times 5.3. + +So here were the answers. + +So they were given four +possible answers. + +And they could also +not answer. + +So this is no answer. + +So that's the age 13. + +So of the four possible +answers-- + +or let's say no answer is +possible as well-- so five, + +they're 1% over 1/5 will +get the correct answer. + +So that's a bit depressing. + +So you think, oh, OK, +the 17-year-olds + +are going to be better. + +And they are, but they only +have 37% correct. + +OK, so here is a serious +problem, + +which is rote learning. + +And that's the fundamental +thing to + +avoid when doing problems. + +So these students-- especially +the 17-year-olds-- + +were actually perfectly capable +of doing exactly + +multiplication. + +So on the same test they were +asked questions like multiply + +2.7 by 8.32 and given just empty +space on the page to + +multiply it out. + +About 80% did it right. + +So it's not that they don't +know how to multiply. + +They just don't know what +multiplication means, which is + +a far more serious problem. + +I'd rather they knew what +multiplication meant and + +didn't really understand, +didn't + +really know how to multiply. + +Because the algorithm you can +teach them later if they + +understand what it means. + +But if they don't even +understand what it means that + +basically it's 3 times 5, so +it's got to be somewhere + +around 16, they don't understand +what multiplication + +means or the number +system means. + +That's a far more +serious problem. + +And that's produced by the +traditional kind of problems. + +The traditional kinds of +problems are, generally + +speaking, too low level +and can be solved, + +to easily, by rote. + +Even the complicated traditional +problems can + +eventually be turned +into rote learning, + +and that's the danger. + +So the main goal in making +good problems is-- + +I would say-- + +how to make problems that +fight rote learning. + +OK? + +That produce long-lasting +actual conceptual + +understanding along with +whatever else you're trying to + +produce and teach. + +But really, fight the rote +learning because that is the + +fundamental problem. + +So a way of thinking about +this is to categorize the + +levels of thinking that you're +expecting of students when + +you're asking them +to do a problem. + +And for that there is work +from 50 years ago now-- + +which is still useful-- + +which is Bloom's Taxonomy. + +So Bloom's Taxonomy-- + +let's see, when was it? + +I think it was 1956. + +I think it was '56. + +I'll put a handout on the +website for you which + +summarizes in one page. + +But I'll summarize it +even shorter here. + +So what is it a taxonomy of? + +Well, when you read the title +the book, it's Bloom's + +Taxonomy of Educational +Objectives. + +And it's not really clear if +that's going to be useful for + +anything at all. + +Because you think, what +the hell is that? + +So the shortest way of +understanding it is that it's + +six levels. + +And each level is higher than +the one previous to it in + +terms of the level of thought +required of a student. + +So it's not really +a strict order. + +You can have really hard +questions that seem to be low + +level just because they address +misconceptions. + +But generally speaking, +it's a rough order. + +So the order is knowledge +questions. + +Those are things like define, +name, state, list, You know, + +it's basically almost rote. + +I mean, these are the kind of +problems that everyone would + +agree are rote, state +the definition of + +Newton's Second Law. + +The second is comprehension. + +So that's sort of like +knowledge but + +it's a higher level. + +So that's being able to grasp +the meaning of the material, + +not just recite the facts. + +But generally, that doesn't +include the idea of being able + +to transfer it to +new situations. + +That's where application +comes. + +So can you apply the material +to something? + +For example, often compute, +demonstrate, show that, those + +are typical verbs that +are used when you + +have application questions. + +The next level is analysis. + +So that's really trying to +understand the structure of + +the material. + +So things like diagram, +differentiate, infer, outline, + +point out, identify, +distinguish, discriminate, all + +those kinds of verbs com into +analysis kinds of questions. + +Synthesis-- + +so this is breaking +things apart. + +This is the ability +to put things back + +together in new ways. + +OK? + +So design, explain, categorize, +create, revise, + +rewrite, reorganize, devise. + +And the highest level +is evaluation. + +So judging the value of +material, for what purposes is + +this good versus that good? + +Explain, contrast, summarize, +support, recommend, evaluate, + +criticize, appraise, +so generally + +quite high-level skills. + +So this is the taxonomy and +this is a higher level. + +OK, so a useful exercise-- + +whenever you're thinking of +problems-- is to try to place + +them on this. + +Now it's not that you want +no-knowledge kind of questions + +and you want only to ask these +kind of questions. + +Because if you just ask these +kind of questions people will + +not be ready for them. + +And they're not prepared. + +It doesn't actually +teach anything. + +You want a mix of them. + +But generally speaking, what +happens to often, is that most + +of the questions that happen +are usually in this zone, + +maybe a few of those. + +And then only later in +people's careers do + +they get over here. + +For example, in engineering +curricula you learn a ton and + +ton of application, maybe +comprehension, Maxwell's + +equations, differentiation, +integration. + +Then we start to synthesize +stuff. + +You know, in your senior +year you do + +design and project classes. + +But you don't have to wait +all the way until then. + +You can actually start putting +stuff in much earlier. + +And it doesn't have to +be an entire class. + +You can have tasks that are like +that in a short time, on + +a problem set in the middle +of lecture time. + +OK? + +So questions about +Bloom's Taxonomy? + +OK, so what I'll do, is I'll +give you an example of + +questions that in freshman +physics mechanics-- + +on the topic of Newton's +laws-- + +that fit into each +of those levels. + +OK, so just to give you an +example, to make it concrete, + +to see what those kinds +of questions are. + +And some of the categorizations +I'm going to + +give you are debatable. + +But the rough idea is that +they go from high to low. + +So this is on the subject of +Newton's second and third law. + +So a knowledge question, state +Newton's second and third law. + +Newton's second law, state +Newton's third law, so you can + +see, just because people can +state it doesn't mean they can + +actually do anything with it. + +That's why this is way up just +at the knowledge end. + +Computers are actually +really good at this. + +Right? + +You can look it up on Google. + +But your computer can tell you +what Newton's second and third + +law are but you can't actually +do anything with them. + +So comprehension-- + +so give an example of Newton's +Second Law, using Newton's + +Second Law. + +OK, this next one is +an application. + +It turns out to be, actually, +quite a hard application. + +But it's still an application. + +So it's to apply Newton's second +and third law to show + +the following, which the +following is suppose I have a + +piece of chalk in my hand and +I stand on a weighing scale. + +I want the students to show that +the weight that the scale + +reads is equal to the sum of +the two individual weights. + +So I weigh myself. + +And then I put the chalk +on the scale. + +And I add up those +two weights. + +And that should be the +same as when I hold + +the chalk in my hand. + +OK? + +So I'll diagram that as-- + +OK, so that's me plus chalk +equals me plus chalk. + +So this is a scale. + +OK? + +So there is the piece +of chalk. + +So now this is an example of +where that's quite a hard + +application question, even +though it's kind of high up on + +the Bloom's list, so towards +the lower end. + +Because this is a serious +misconception + +that students have. + +Newton's second and Newton's +third law, people are + +completely confused about, +you'll find. + +They don't know when +to use which. + +And they think any time two +forces are equal it's sort of + +50-50, whether it's because of +Newton's third law or Newton's + +second law. + +So this-- if you're addressing +misconceptions-- + +makes the problem, actually, +all the much harder. + +So at analysis-- + +so the analysis comes out-- +oh, question sorry. + +AUDIENCE: What are Newton's +second and third laws? + +PROFESSOR: Ah, fair question. + +So Newton's Second Law says +force equals mass times + +acceleration. + +Third law is-- + +the way it's usually stated, +which it's terrible-- + +action equals reaction. + +Or for every action there's an +equal and opposite reaction. + +Oh, which reminds me, one of +the questions from before, + +which is what name +would I give? + +Because I said I slagged off the +reaction force as the name + +and the normal force +as a name. + +People ask me, what should +you call it? + +And I actually thought +about that. + +And I think the answer +is contact force. + +Because that tells you +what the thing is. + +It's a force of contact. + +So Newton's third law says +action equals reaction. + +So now, the problem is that +students have, is that + +whenever they see two forces +are equal they assume it's + +because the action +equals reaction. + +Or they think Newton's third +law is the reason for it. + +So for example, the +bouncing-ball question that we + +talked about last time. + +So in the bouncing ball the +question is, when it's + +stationary on the ground what +are the forces on it? + +And they'll often say, well, +there's a weight downwards. + +And there's the force upwards. + +And they'll often say, well, the +force upwards equals the + +weight downwards. + +These are both forces +on the ball because + +action equals reaction. + +And they won't realize that +action and reaction have to be + +on different objects. + +OK? + +So they're fundamentally +confused about the meaning of + +action and reaction, which you +can bring out with the + +following analysis question-- + +When two forces are equal in +magnitude how do you tell if + +it's Newton's two +or Newton three? + +So how do you know if it's +Newton two or Newton three? + +So just ask them that. + +Yes, question? + +AUDIENCE: This might be a little +bit off subject, but + +should we use Newton's +third law ever? + +It seems like it's a natural +consequence from + +saying a equals 0. + +PROFESSOR: Ah, oh, +OK, interesting. + +So OK, let me actually +explain that one. + +I'll put it over there because +I didn't do the + +boards right over here. + +So that is exactly the issue +brought out by this question. + +And let me show you +the difference. + +And then there was +another question. + +That reminds me of another whole +set of questions from + +the sheets, which was +how do you develop + +your physics intuition? + +So let me answer that +in a moment. + +After this and then we'll +have a break. + +OK, so the bouncing-ball +question-- + +actually let's not do +the bouncing ball. + +Let's just do an object +sitting on the ground. + +Oh, great, can you +pass them around? + +Oh, Leeann's just coming around +with a handout on + +Bloom's Taxonomy. + +And let's see, I'll do these +after the break. + +OK, suppose you have this object +sitting on the ground + +and it has Mass m. + +OK, let's look at what +the forces on it are. + +Well, there's mg down-- + +and actually, in this case, the +contact force, our normal + +force is equal to mg. + +OK, so now the question is, are +these two equal because of + +Newton's Second Law or +Newton's third law? + +That's what this +question asks. + +So it's actually worth +understanding + +the difference here. + +So these guys are equal +because a equals 0. + +So this thing's just sitting +on the ground, a equals 0. + +So the net force is +0, so these two + +forces have to cancel. + +OK, so that's Newton's +Second Law. + +So then the question is, where +does Newton's Third Law show + +up in this? + +Ah, Newton's Third Law +shows up here. + +Here is the Earth. + +And here is your object. + +Let's just separate them just so +you can see them separate, + +although this is sitting +on there. + +So this is mg. + +Well, this is the mg because +of gravity, right? + +The earth gravity is attracted +to mass, m. + +Well, the mass is also attracted +to the earth. + +So what's the force on the +earth from the mass? + +AUDIENCE: mg. + +PROFESSOR: mg, it has to be. + +Now this mg equals that mg. + +Call this f2 and this is f1. + +So f1 equals f2 by Newton's +third law. + +So that's a fundamentally +different set of forces. + +So are equal and opposite. + +They're an action/reaction +pair. + +So what Newton's third +law really says-- + +when you understand it-- is that +all forces in the world + +come in pairs. + +So if you ever see one force +you have to hunt around for + +his other half. + +And the other half +here is this. + +So actually, there's another +question you could use for + +Newton's third law. + +So I don't have it +on the list here. + +But I'll ask it right now, which +is suppose someone comes + +to you and proposes the +following gravitational law-- + +f gravity equals g m1 squared +m2 over r squared when the g + +is the proper units. + +So m1 squared times m2, +is that a legal + +force law for gravity? + +No, because when you switch m1 +and m2 as you're doing here-- + +you're switching the mass +and the earth-- + +you actually change the force. + +So then this would violate +Newton's third law. + +OK? + +So Newton's third law, it +actually is a constraint on + +the laws of physics. + +It's actually conservation +of momentum. + +And for momentum to be conserved +you can't have any + +arbitrary law of physics +that you want. + +Does that help clarify that? + +AUDIENCE: Come up with a better +set of taxonomy for + +describing it that doesn't lead +people-- it leads people + +into thinking about that. + +PROFESSOR: I know. + +I agree. + +So I think the terms +are very important. + +So that's why don't like this +form, action equals reaction. + +I actually would prefer it were +stated all forces come in + +pairs that are equal +and opposite. + +Right, and language does +have a powerful effect. + +Yes? + +AUDIENCE: The technical +[? route's ?] obvious, just in + +calling the novel force the +contact force, but that's not + +refined enough. + +Because both friction and +novel are contact force? + +PROFESSOR: Yeah. + +AUDIENCE: [INAUDIBLE] constraint +force because it + +could constrain into +the [INAUDIBLE]. + +PROFESSOR: Yeah, that's probably +a better name. + +Yeah, I agree with you. + +So the comment was that contact +force isn't quite + +right because there's friction +force as well. + +And that's also a +contact force. + +And maybe a better name +is constraint force. + +I think that is a better name. + +OK, so let me finish this list +of two more examples of + +Newton's Second and third law. + +And then we'll have a break. + +OK, synthesis. + +So creating a problem using +Newton's second and third law. + +So for example, this is +a problem like that. + +But here I'm asking the students +to make one up. + +And here is a very hard evaluate +question, which is + +what, if any, are the limits of +validity of Newton's Second + +and third law? + +So that's, actually, a very + +interesting historical question. + +Interesting historically because +Einstein thought about + +that question. + +He wanted to know whether +Newtonian gravitation and + +special relativity +were compatible. + +And basically, they can't be +because of Newton's third law. + +Because gravity should propagate +with some speed, not + +the speed of light. + +So you can't actually conserve +momentum right away. + +Suppose the sun does +something strange. + +Well, it takes a while +for the earth to + +actually respond to that. + +And it's in that intervening +time Newton's third law seems + +to be violated. + +So Einstein thought very +carefully about that question + +and came up with his theory +of gravitation. + +So this is quite a high-level +question. + +But it's to show the whole range +of things you can ask + +about the second and Newton's +third law as you + +climb Bloom's Taxonomy. + +OK, so what we're going to do +in the second part is we're + +going to actually practice + +rewriting a couple of questions. + +And I'll show you a couple +more examples. + +And seeing how we can make +questions worse and better, + +because I find that's actually +quite a good way to get + +practice with designing +questions is taking good + +questions, making them bad, +taking bad questions and + +making them good. + +Both ways are useful. + +OK, so we'll do that. + +Let's say it's 9:04, +9:10 let's say. + +So it's 904 on that clock. + +So see everyone, sorry it's +10:04 on that adjusted clock. + +So see everyone at +10:10 or 10:11. + +And meanwhile, here are +the feedback sheets. + +So I'll just put a bunch +in the two back things. + +So when you come back +just grab those. + +OK, so I'll just answer a +couple questions which I + +promised to answer. + +So the comment made by several +people about last week's + +examples, say, of the rock and +the rolling was that oh no, + +that showed me that my +physics intuition is + +quite off, and bummer. + +And so then if you're going to +teach it, how do you make + +sure, well, A, how do you learn +to think intuitively + +about these things? + +And B, if you're going +to teach it + +how do you make sure-- + +related to that-- + +you actually have the intuition +before you teach it. + +There's two answers to that. + +One is that it's very rare that +anyone ever achieved a + +goal that they didn't +set out to do. + +And then just happened +upon it. + +So I would say that's true, +also, with developing + +intuition in these areas. + +You have to make it your goal. + +So it's not going to just +happen by chance. + +So then questions, OK, if +it is your goal how do + +you go about it? + +One way is anytime you do a +calculation, at the end of the + +calculation ask yourself +this question. + +So John Wheeler-- who was +Feynman's adviser-- + +he recommended the following +question, which I think is a + +fantastic question. + +So the question is if you could +time travel back and + +talk to your earlier self what +one or two sentences would you + +tell your earlier self before +they started solving the + +problem that would make +the problem just + +sort of flow smoothly? + +OK? + +So what sentence would you tell +your earlier, pre-problem + +solved self? + +So this is after you +solved the problem. + +So that forces you to give a +insightful summary of what you + +learned from the problem. + +So it forces you towards the +intuitive way of reasoning. + +And you'll find it's quite +hard at first. + +Because you don't have the +intuitive library. + +But at least it points you in +the direction to be going. + +OK, now what else? + +Well, in chemistry there's +various books that help + +develop intuition. + +They have all kinds of +intuitive reasoning + +questions in them. + +And some are quite good. + +Some of the books +are quite good. + +So the one in chemistry that +I like is called Voyages in + +Conceptual Chemistry. + +And in physics one of the ones +I like is called Thinking + +Physics by Epstein. + +I think Epstein's like that. + +So what that is, is that's +basically, one + +question per page. + +And it's multiple-choice +intuitive reasoning question. + +And they're about all kinds of +interesting physics, like why + +do tea kettles whistle? + +If you shake bottle of soda +up, why does it explode? + +And so it's filled with really, +really fascinating + +puzzles and ways of thinking. + +And then with explanations. + +So just by thinking about them, +reading the explanation, + +trying to understand, OK, then +asking yourself Wheeler's + +question at the end of reading +the explanation, even if you + +didn't solve it, you can develop +a lot of intuition. + +I don't know a good one +for math or biology. + +And if anyone does, I definitely +appreciate any + +suggestions. + +OK? + +But there are resources +in some fields. + +And the other is just whenever +you find paradoxes go after + +them and share them +with everyone. + +And ask everyone you know,do +you know any + +paradoxes I can work on? + +That'll also developed +intuition. + +OK, and then related to that, +one comment was I've noticed + +that teaching is the best +way of learning. + +How can you incorporate +that into a course? + +So yeah, that's true. + +So sometimes you just have to +accept that the first time you + +teach the thing you're going +to be learning a lot. + +So that's fine. + +And the second time you teach +it, it'll be much better. + +So you'll actually develop a +lot of intuition the first + +time you teach a course. + +So for example, I found when I +was a graduate student, I was + +a teaching assistant for Physics +1A at Caltech, which + +was like 801. + +And I found I had +a huge number of + +misconceptions about tension. + +I just had no idea +what tension was. + +For example, I thought +tension was a force. + +And now that seems +ridiculous to me. + +And it doesn't seem ridiculous +to you that's because you're + +in exactly the same state I +was in before I was taught + +physics 1A. + +And I've got myself all in a +twist when I was trying to + +explain it. + +And I finally tracked it down +to actually, that particular + +misconception. + +So then I developed a bunch of +questions for myself, which I + +also asked students +about tension. + +So teaching is learning. + +And then how do you incorporate +that into a class + +for the students? + +Well, you can ask them to teach +each other and argue + +with each other. + +So we'll talk about that +in the session + +on interactive teaching. + +But yeah, it is the best +way of learning. + +And so if you can get the +students to do that as well + +you'll be increasing +their learning. + +And then the last question for +the moment was what's my + +response to the following +article-- so it was in the + +globe on February 15, 2009. + +And it said, don't +open with a joke. + +So it was summarizing a paper +called "Increased + +Interestingness of Extraneous +Details in a Multimedia + +Science Presentation Leads to +Decreased Learning." Journal + +of Experimental Psychology, +December, 2008. + +So they summarized that. + +So basically, what they found +is that if you start with a + +joke that's extraneous to the +material it actually decreases + +the learning. + +And that, I think, is +quite plausible. + +So I recommend that you start +with something interesting in + +the beginning. + +But it should be related +to the material. + +So the problem wasn't +the joke. + +The problem was that +the joke wasn't + +related to the material. + +So the thing should +be interesting. + +Because you want to +draw people in. + +You don't want to conclude from +that article that you + +shouldn't start with +some interesting. + +But you should start with +something interesting that's + +related to the material. + +OK, so redesigning questions. + +So here is an actual question +that we will redesign. + +And I've left up the Bloom's +Taxonomy there. + +So actually, I have a +bunch of questions. + +We'll do a couple of them. + +And we'll review, probably, one +of the questions we did + +earlier, which is +about the cones. + +OK, so the question to start +with-- and we're going to go + +that way and that way-- + +is find the eigenvalues +of this matrix. + +So for those whose linear +algebra is rusty, the + +eigenvalues of a matrix so +a matrix, m, times some + +eigenvector e is equal +to lambda times e. + +So if there's some vector that +the matrix just brings back to + +itself with some constant, +that's the eigenvalue. + +And this is the eigenvector. + +So eigen meaning +own in German. + +So somehow this vector belongs +to the matrix. + +It's said to be an eigenvector +of the matrix. + +It's preserved when you hit +it with the matrix. + +You get back the thing itself. + +And in that way it belongs +to the matrix. + +OK, so there are recipes +for computing it. + +And so here the question is, I'm +asking students to use the + +recipe for computing +the eigenvalue. + +OK, so now I'm going to ask you +the following question, + +which is to design-- + +well, first of all, where would +you say that guy goes? + +It's sort of comprehension. + +You know, it's basically +computing. + +Maybe it's a bit +of application. + +But it's basically +comprehension. + +OK, so can we go lower on the +taxonomy towards knowledge? + +Can we go higher towards the +higher-level reasoning? + +Let's try to construct questions +on this end. + +OK, so everyone understand +the thing to work out? + +I'm going to ask you to try to +think of stuff that could be + +put here and here. + +So this is lower level +and this is higher. + +Does anyone need +me to explain-- + +or want me to explain-- more +about eigenvalues or + +eigenvectors? + +OK, so find a neighbor or two. + +And try to think of stuff +that can go in + +this box or this box. + +And generally, the higher-level +questions + +requires more knowledge about +the material, which is one + +aspect of their being +higher level. + +You need a bigger margin of +safety when you're trying to + +design them. + +But don't let that bother you. + +See what you can construct. + +And you can use the levels on +Bloom's Taxonomy to try to + +create some kind of questions +around it. + +By the way, the answer to this +question, by the way, is i and + +minus i, just in case +you are curious. + +OK, so let's see what examples +you've come up with, so + +related to this question. + +Obviously, you'll change +it around some. + +Let's say either side, this +side or this side. + +Someone I haven't heard from? + +Yes, can you tell +me your name? + +AUDIENCE: Mike. + +PROFESSOR: Mike, yeah? + +AUDIENCE: What is +an eigenvalue? + +PROFESSOR: OK, so what +is an eigenvalue? + +Where would you put that? + +AUDIENCE: Lower. + +[INAUDIBLE]? + +PROFESSOR: Oh, yeah, +good question. + +It depends where you +put this one. + +This one is computing, which I +roughly put that somewhere + +between comprehension +and application. + +So right now I would say, we're +somewhere around there. + +So your question is to +define eigenvalue? + +OK. + +I'm just short-handing +it as defined lambda. + +OK, so that's one question. + +OK, another question. + +Can you tell me your name? + +AUDIENCE: Wendy. + +PROFESSOR: Wendy, yes? + +AUDIENCE: So related to that, +is that you could put that + +question higher. + +If you asked them, what does +an eigenvalue mean? + +If you word it differently +instead of [INAUDIBLE]. + +PROFESSOR: OK, which may have +been what you meant as well + +and I may have defined lambda. + +OK, so you're saying, well, you +can actually ask them to + +say, what does eigenvalue +mean? + +OK, so how would you if they +know what it means? + +So what would you look for +in something like that? + +AUDIENCE: If they could describe +it to you, or maybe + +tell you a problem in which it'd +be useful, in using it? + +PROFESSOR: OK, so yeah, +let me write that too. + +Create a problem that would +benefit from lambda, that + +would need lambda. + +OK, so for example +here, create. + +That's gone pretty far down +towards synthesis. + +I really should have flipped +the list around. + +But synthesis is quite high +on Bloom's taxonomy. + +So you're actually going +to create a problem. + +It's like the Newton's +law example. + +Yes? + +AUDIENCE: [INAUDIBLE] + +instead of saying, again, +what does lambda mean? + +You could say what do the +results from finding lambda? + +What are the results +of that solution? + +PROFESSOR: OK, so how does +it help you to know the + +eigenvalues? + +Is that the question? + +AUDIENCE: No, I'm just saying +instead of the general asking + +for the definition, what +does lambda mean? + +What is an eigenvalue? + +What does it mean? + +But after having solved the +problem saying, what does your + +answer mean? + +PROFESSOR: Ah, OK, so even if +you ask them this first you + +can say, OK, interpret +your answer. + +Yeah, and that's +a-- generally-- + +very good policy. + +So interpret. + +and where would I put that? + +Eh, interpret is somewhere +like analysis, + +maybe a bit of synthesis. + +But yeah, it's quite +high on the list. + +So interpret, that's another +really key word. + +In fact, it's often +neglected, right? + +We just ask students to +solve the problem. + +And wander, wander, wander. + +They get the thing that +looks like an answer. + +They put a box around +it and they're done. + +But actually, you can massively +increase the level + +of a problem just by adding +to the problem, + +interpret your answer. + +What does it mean, that +that's an eigenvalue? + +And maybe they would say +something like this. + +But even that would be better +than just having done the + +computational procedure and +got an answer out of it. + +Yes, can you tell +me your name? + +AUDIENCE: Ben. + +PROFESSOR: Ben, yes? + +AUDIENCE: I might ask, does +that matrix have any + +eigenvalues? + +PROFESSOR: OK, so yeah, so +let's put it over here. + +Right, so there what you're +doing is you're not presuming. + +You're not key-wording +what they should do. + +When you do this-- especially +if it's a + +linear algebra course-- + +they've probably seen a bunch +of things like this. + +Like in a calculus +course, integrate + +these things by parts. + +They just know I have to +integrate by parts, whereas + +here you're at least +one step higher. + +Because they don't know whether +there's an answer to + +the problem or not. + +And they have to think, well, +how do I know if they're + +eigenvalues? + +So there's actually one +intervening level of + +sophistication. + +Other suggestions? + +Yes, Adrian? + +AUDIENCE: Just give them two +numbers and say write a matrix + +that has these as +the eigenvalues? + +PROFESSOR: OK, so let me +continue the list over here. + +OK, so create a matrix which has +the following eigenvalues. + +So say lambda equals +2 comma 3. + +So create a matrix, +create a meaning. + +We're already high up in the +taxonomy toward synthesis. + +And actually, I would even use +a related one, which is-- + +so create a real matrix with +eigenvalues i comma minus i. + +So that one, is quite +related to this. + +And this is the answer. + +So it's quite a hard question. + +Even if people can do this and +find i comma minus i, this one + +is very hard because you're +asking to apply a constraint + +that the thing be real. + +So it's not just any matrix. + +But it's that the +thing be real. + +And then you have to really +understand quite a lot about + +matrices to do that. + +Yes, can you tell +me your name? + +AUDIENCE: Scott. + +PROFESSOR: Scott. + +AUDIENCE: So, I was thinking of +a synthesis question which + +would be is after multiplying +the item the eigenvector by + +the matrix how is it rotated? + +PROFESSOR: OK, so what is the +geometric effect on the + +eigenvector of the matrix +on the eigenvector? + +AUDIENCE: Right, but the +question is if they understand + +what an eigenvalue is. + +PROFESSOR: They should be able +to answer that right away. + +Right, but it really tests for +understanding of what the + +meaning is. + +So it's another way of +approaching the question of do + +they understand eigenvalue +means? + +What is the geometric effect +of the matrix on the + +eigenvector? + +And then hopefully, they'll be +able to say well, actually, it + +doesn't rotate it. + +It just scales it. + +And the eigenvalue is the +amount of scaling. + +OK, and that demonstrates +quite a high level of + +understanding too. + +And This is one reason that +oral exams, generally, are + +quite good ways of evaluating. + +Because you can ask these +kind of questions. + +And as soon as you see that they +understand you move on to + +something else. + +Which of the flip side is that's +why oral exams are very + +disconcerting for +the students. + +Because you spend no time on +the things they understand. + +Right? + +So as soon as you know they +understand it, you move on to + +something else. + +So the student just feels +like, what the + +hell happened to me? + +I was doing fine. + +And they asked me about +something else. + +Yeah, that's exactly right. + +That's why they asked you +about something else. + +They knew there was nothing +more here to find out. + +You understood it. + +But that's why oral exams +are such a good way-- so + +efficient-- + +for evaluating. + +So in Cambridge we used to do +oral exam interviews for + +admission for undergraduate. + +So people would be admitted +to the major right away. + +So we had two 20-minute +interviews. + +And we found those were much +more reliable than all the + +exams that they did in +high school, the + +equivalent of AP exams. + +Because you could really ask +questions that really probed + +understanding and right away see +what people could do and + +couldn't do. + +So geometric effective of m on e +creating a matrix, so you're + +asking, so what's the +geometric effect? + +It's not just comprehension. + +You're asking them to apply +it and maybe, in a + +bit in a new area. + +They hadn't really thought of +eigenvalues and eigenvectors + +as geometric at all. + +And now, all of sudden, you're +asking them that. + +You're asking them to transfer +their knowledge, which is one + +of the fundamental goals. + +Yes? + +AUDIENCE: Once you give them two +matrices that has the same + +eigenvalues you can ask them +to see if they are + +related in some ways. + +PROFESSOR: Right, so for +example, let's do this one. + +So how are those two +matrices related? + +So they both have eigenvalues +i and minus i. + +This one obviously does because +those are the diagonal + +values and there's +nothing else. + +And this one, you have to do +it by the magic procedure. + +You don't have to. + +And so how are they related? + +So that is some kind of +analysis question. + +And it's quite a difficult +analysis question. + +It tests for really, do they +understand what matrices mean? + +So that's why I've underlined +this word. + +The questions all in this column +are all somehow testing + +that they understand +what things mean. + +So that ties back to the point +I made earlier, which is that + +the whole fundamental point of +asking good questions is to + +avoid rote learning. + +Is that by asking good +questions you're + +fighting rote learning. + +And rote learning is the +bane of most education. + +Right? + +Rote learning is too often +the result of education. + +And it's the-- in my view-- + +fundamental problem +with education. + +So by asking questions that are +different you're actually + +starting to fight that +and break the habit. + +So for example, how does +rote learning show up? + +Well, in the bouncing-ball +question, so the force is-- in + +the instant that it's + +stationary, while it's bouncing-- + +people say mg. + +While this mg is right. + +The gravity, but the contact-- + +let's say the constraint +force-- + +in this case it is a very +full-contact force is mg. + +One of the reasons they say that +is the misconception that + +they think a equals 0 +because v equals 0. + +So that's one reason. + +But the other reason is that +they've done so many problems + +with books resting on tables, +balls resting on tables, where + +the force is mg. + +Right? + +So they've now induced a new +rule of physics, let's call it + +Newton's fourth law. + +That anytime you see a contact +force it is mg. + +So contact force equals mg maybe +times cosine of theta. + +[LAUGHTER] + +PROFESSOR: Right? + +or sine theta. + +I guess it's mg-- + +well, it depends how +you measure theta. + +But theta is the tilt +of the plane. + +So if the plane is tilted 0 +degrees just to ground, well + +it's then mg. + +So that kind of learning is the +result of rote learning + +because they've solved problems +without understanding + +what they mean. + +So instead of figuring out that +oh, actually, you could + +understand it from Newton's +Second Law and understanding + +acceleration, they think oh, +there's a new pattern here. + +Right? + +Oh, a new pattern is whenever +I see contact forces it's mg + +times maybe cos theta +or sine theta. + +Yes? + +AUDIENCE: What's the exact +question with that system and + +what's the normal [INAUDIBLE]? + +PROFESSOR: Yeah, so the question +was so you drop the + +ball, say from here. + +And when it bounces off the +steel table there's one + +instant when it's stationary +on steel table. + +And what are the forces +on it at that instant? + +AUDIENCE: I remember +from last week. + +PROFESSOR: Yeah, no, +fair enough. + +I should have stated the +question out again. + +So this is stationary +for an instant. + +All right, so actually the ball +is quite compressed here. + +Yes? + +AUDIENCE: Isn't it impossible +to give an exact answer for + +the force with the [INAUDIBLE] + +if you don't have +the duration? + +PROFESSOR: It is, right. + +So it is impossible to give +the exact answer. + +But what you ask them is, well, +how big is it roughly? + +So I always protect myself +by saying roughly. + +And then you can ask +anything you want. + +And because, really, all I'm +interested in is do they think + +it's 1 times mg or do +they realize it's 10 + +to the 4 times mg? + +And those are so far apart +that I don't care about + +factors of two or three +or even 10. + +Now, how can you know that it's +10 to the 4 times mg? + +Well, that is quite +a hard question. + +That's way down there. + +Even though you'll see some +lists of Bloom's Taxonomy say + +estimate is a low-level +skill, not that + +high in Bloom's Taxonomy. + +It's almost like computing +somewhere in comprehension. + +I don't agree with that. + +Because as you saw from the +example where students + +couldn't estimate 3.04 times +5.3, they're terrible at + +estimation. + +So estimation actually hits one +of the big misconceptions + +and reveals a lot of +the misconceptions. + +So I put estimation almost at +the level of synthesis because + +it forces you to really +synthesize your understanding. + +You can't hide behind +formulas. + +So the next thing I'll do is +say, OK, let's estimate this + +and see if you can do that. + +And if they really understand +the system they + +can estimate it. + +But it's quite hard. + +And I find almost no students +can do it on their own. + +But the method of estimation is, +as you say, you do need to + +know the contact time. + +So the acceleration is +not 0 as you say. + +But it's delta v over delta +t, where delta t + +is the contact time. + +Well, it's going v and then it's +pretty much going v up, + +so that's about 2v. + +But I don't care about +factors of 2. + +And then, what's the +contact time? + +Well, there's a couple methods +for doing the contact time. + +One is you listen +for the pitch. + +And whatever the highest +frequency in the pitch is-- + +suppose it's 10 to +the 4 hertz-- + +well, then 1 over that time, +1 over the frequency + +is roughly a time. + +So it's probably the +contact time. + +So that's one approach. + +The other approach is to say +well, actually, physically + +what's happening? + +The ball is hitting +the bottom. + +And this end compressing. + +But this end keeps going. + +Because it has no knowledge that +the bottom of the ball + +hit the ground. + +How's it going to +know about that? + +Well, the bottom of the +ball has to tell it. + +How's it going to tell it? + +Well, it has to send some +kind of signal. + +How does it send signal? + +Sound. + +So it sends a sound +wave upward. + +And the sound wave travels in +steel about 5 or 10 kilometers + +per second. + +So you suppose it's a +5-centimeter ball, then it's + +about 10 to the minus 5 seconds +is your contact time. + +So this is really short. + +So suppose v is something like a +meter per second, and divide + +it by 10 to the 5 seconds. + +You're talking about something +like 10 to the 5 meters per + +second squared, which is 10 to +the 4 times the acceleration + +due to gravity. + +OK? + +So I went through because I +think it's interesting but + +also to show that estimating +actually requires generally, + +very high-level skills. + +And it's quite hard +for the students. + +Therefore you should do it. + +So there are some people who +say, well, it's very hard for + +the students. + +Don't do it. + +But again, there's another rule +of thumb in teaching, + +which is nobody ever learned +anything that you didn't + +actually try to help +them with. + +Well, that's not quite true. + +But if you never teach something +they're not very + +likely to learn it. + +So if it's something hard but +valuable you have to start + +teaching at some point, +which is why I put + +up that graph earlier. + +Oh, it's gone now. + +Where in the earlier stages of +teaching you do things more + +approximately. + +And then in the later stages +you do it more exactly. + +So what I've told you +now is a slight lie. + +So this brings up the +question from last + +time, what about lying? + +Is it useful? + +Yes, it's essential because this +argument is simple enough + +that once you understand +it you can just + +keep it in your head. + +And it's a bit of a lie, the +reason being that the ball + +doesn't have a uniform +cross section. + +So as the ball compresses the +contact area changes, whereas + +if the ball were cube or a rod +the contact area would stay + +the same as it compressed. + +So there's a correction +factor because the + +contact area changes. + +Now, that correction factor +is not very big. + +It turns out to be the +fifth root of some + +dimensionless thing. + +And so this sound-wave argument +you put in to the 4/5 + +power and then you put in the +other thing to the 1/5 power. + +So it's almost correct for +this spherical ball. + +So in a later of course +it actually + +adjusts for that factor. + +And then in a much later course, +probably, what I would + +do is calculate the exact 2 pi +over whatever factor that + +shows up as well, by way of +increasing the symbolic + +complexity. + +But even this estimate, doing +that is conceptually hard. + +So I would say start +that early. + +AUDIENCE: I think the point +I was trying to + +make was that this-- + +I suspect that the students +answered that wrong because of + +real problem solving, and that +they expect there to be a + +solution given the data +that you [INAUDIBLE]. + +PROFESSOR: Well, if you've +worked with them a bit on + +estimating they know that +they're going to have to do + +some thinking. + +If you say compute the force +I agree with you for sure. + +They're going to think they have +to be able to do it from + +the data there. + +And they'll just say it's got +to be mg because that's the + +only other force I know. + +But if you say estimate then +there is a bit of a queue that + +they have to include some other +information which might + +not put in the problem. + +And so that mitigates +the rote learning. + +But what I find, even then, is +they usually still can't do it + +because their misconceptions +about acceleration are so deep + +and about equilibrium +and force. + +They think f equals +mv, basically. + +OK, so let's just look at +what we've done here. + +So I would say you can +define lambda. + +You can define eigenvector. + +You can even say state the +computational procedure. + +I'm not sure where +I would put that. + +Depending on how people learn +it, this could be purely a + +knowledge question. + +Because people could state the +procedure but not really + +understand it, not be +able to do anything. + +Or actually, you could say +program the procedure. + +Well, that would be something +over here probably. + +Because to program it you +probably have to understand + +what you're doing pretty well. + +So stating the procedure, it +depends how you ask them to + +state it, whether it's +a low-level or + +a high-level question. + +So I'll put program over here. + +OK, so we've gone down and up. + +And again, I want to remind you, +I'm not saying all your + +questions need to be here. + +But generally, the questions are +too much over here and not + +enough over here. + +So this gives you a recipe for +thinking of new questions. + +Yes? + +AUDIENCE: So throughout the +course do you basically, maybe + +start on the first three in +the beginning and then you + +move it more through until you +reach the end of the course? + +PROFESSOR: More fractal. + +The question was as the course +moves on do you move more + +towards synthesis? + +I actually try to +make it fractal. + +So within each unit and each day +even, I try to maybe have + +something, knowledge or +comprehension just to make + +sure everyone's tracking. + +But try to have something +interesting as + +well, all the time. + +So something synthesis, +analysis, maybe some evaluate. + +And so each problem set-- +for example-- + +I'll put, generally, +warm-up questions. + +So basically they're marked warm +up so that people know + +OK, those are going to be +knowledge and comprehension. + +And you need that. + +Because otherwise there's no +point trying to do synthesis + +if you don't have the +base knowledge. + +But just make sure you +understand those, + +just in your sleep. + +And then regular problems, which +tend to be somewhere in + +the middle, say application +or analysis. + +And then bonus problems which +are just optional. + +But they're for people who +either find all the other + +problems easy or are +really curious. + +For them I put either synthesis +or evaluation. + +For example, in the +approximation class the last + +problem set had design an +email indexing system. + +So that was the bonus problem. + +And there was a bunch of warm-up +and regular problems + +which were involving Unix +text processing. + +And then for the people who are +really curious actually, + +put it all together and make a +really fast email-indexing + +system so you can just find any +email that you want just + +by doing keyword search. + +Sort of like a web search but +just on your email inbox. + +Because I actually +use that myself. + +Because I find folders +are just hopeless. + +It just takes all my time. + +I have to figure out what +folder things are in. + +And that could be many. + +So I just keep it all in one +giant inbox with, I think, + +150,000 messages in it. + +And I just search +through that. + +And I have an index that's +rebuilt every week or so. + +And so I can search through +it really fast. + +So it's actually very practical +problem and it gives + +you an example of the levels +of things you can ask. + +So try to do it on +a fractal scale. + +Each class should have +something, mix the levels each + +homework, the exam. + +So the general rule is to +mix them up all the way. + +OK? + +So hopefully, from that, you +feel confident that you have + +tools that you can make +interesting questions. + +And this does have lots of +payoffs, which one of them is + +that questions that are +enjoyable and educational, + +students love them. + +So when I practiced what I +preached and made these kind + +of problems, mix of problems for +my classes, often students + +have said, oh, can you please +have more problems? + +Which is very rare. + +They said, oh, these are some +of the most interesting + +problems I'm likely +to get at MIT. + +And I used to read them +out in my living of my + +independent-living group just +so that other people could + +hear the interesting problems +and we'd try + +to solve them together. + +And then I've had several emails +after class finished, + +saying, oh, you promised to post +the optional problem set. + +Where is it? + +So it's because the problems, +actually, somehow connect to + +things that people find +real and interesting. + +So that's a mix of +the perceptual. + +Don't make it just purely +symbol manipulation. + +Try to connect to ways people +look at the world. + +But also, try to connect to +higher-level reasoning skills. + +Question? + +AUDIENCE: Do you always +use bonus problems? + +PROFESSOR: I do. + +I find that works really well. + +Because it's like a +pressure-escape valve. + +It caters for the diversity of +backgrounds in the class. + +The people who are feeling very +worried by the material, + +they can just skip +them, no problem. + +And they don't feel like +they have to do them. + +And they don't feel like, oh +my god, I can't do them. + +I'm going to get points off. + +And the people who find the +other stuff easy, they find + +something for them too. + +So yeah, I try to always +use bonus problems. + +And I learned that from Knuth's +book, called Concrete + +Mathematics. + +So actually, I think they have +five levels of problems at the + +end of every chapter. + +There's warm ups. + +There's homework problems. + +There's exam problems, +bonus problems, + +and research problems. + +So the research problems +were the ones + +that are not yet solved. + +So at least you know they're +not yet solved. + +So you're going to be spending +a while on them. + +And then in the second edition +I think some of them were + +actually solved. + +OK, so if everyone could just +take a one minute and fill out + +the feedback sheet? + +Oh yeah, and let me just say, +why I'm doing this now at + +10:50, of the questions on the +sheets before was the feedback + +sheet, the person said, I've +been using them in my class + +and they've been +really useful. + +But I find that the response +rate has been dropping. + +What do you do about that? + +And I have to say, that I +found the same thing. + +This year I found +the same thing. + +Not in this class but in my +other class, whereas I didn't + +find that last year. + +And I was trying to +figure out why. + +And theory I have is that I was +trying to put in too much + +material in the class and not +leaving the students time + +before the five-minute mark +to fill out the sheet. + +So one thing, I've been trying +to mend my ways and make sure + +I end class at 9:50 or 10 +minutes to the hour so the + +students have at least one or +two minutes to fill out the + +sheet without feeling +pressured to get + +to their new class. + +So I'll let you know how that +goes over the next week. + +So take a minute now and then +that'll maybe make you think + +of some questions which +we can answer in + +the next two minutes. + +And then while you're doing +that, just a couple + +announcements. + +So sorry I didn't say anything +before about what to do with + +the equation treatments that +you shared with each other. + +So just discuss them +with each other. + +You have a collaborator. + +And then revise your treatment +based on what + +that person told you. + +You don't have to turn in +your revised treatment. + +You guys are all graduate +students, or + +almost all of you. + +You're all taking the class +because you're interested. + +I'm not trying to +police everyone. + +But the goal here, and what +you should do, is take the + +benefit of the collaboration, +revise your equation + +treatment, and share +it with each other. + +And then just bring in your +original one next week. + +And then I'll also have a couple +of readings for you to + +do for next week. + +And also a short problem to work +on, things to think about + +to bring in next week as well. + +OK, so sheets and +then questions. + +Question? + +AUDIENCE: So I tried doing these +sheets for a class that + +I was teaching yesterday. + +In fact, I found that I got +a response rate of 15%. + +If your response rate from the +beginning's very low and + +[INAUDIBLE] to increase +that rate? + +PROFESSOR: Right, so 15%, yeah, +I find I'm getting that + +around now too. + +And I think what's happened is +that I've got people in the + +habit of not filling them out +because I wasn't giving them + +enough time. + +So I may be hosed because now +they're in the habit. + +So I'm trying to mend it. + +And I'll let you know if that +fixes it by giving people + +actual time before +they feel rushed. + +But it may be too late. + +And I worry that +it is too late. + +Because last year I was actually +more diligent about + +making sure they had time. + +And I found the response rate +stayed about 60%, 70%. + +But even I find the +15% very useful. + +And I found that-- + +people even in the past, when +the response rate was 30% in + +another class people said, +I didn't have a + +question all the time. + +But I knew when I did +I could ask it. + +So even the 15% isn't bad. + +It's still useful. + +But yeah, I would like +it to be higher. + +And I'll tell you +how that goes. + +Question? + +AUDIENCE: [INAUDIBLE]? + +Wiggins and-- + +PROFESSOR: McTighe, yeah. + +AUDIENCE: Oh, McTighe. + +Where are they based? + +PROFESSOR: So where are they? + +They're in New Jersey, and +they actually consult on + +educational course design and +run workshops and courses. + +And we actually invited +Wiggins last + +year to come and speak. + +So I'll put a short reading +selection from their book + +called Understanding By Design +for optional reading for + +people so then you can learn +more about that. + +I find the basic form that +they say very useful. + +I find applying it the way they +describe, sometimes I + +just can't square it. + +But it may resonate with +you quite well. + +And the overall approach +resonates very + +strongly with me. + +So hopefully you will +like it too. + +So I'll put that on the website +and some readings for + +next time about course design. + +Yes? + +AUDIENCE: Just a comment, +actually on your web page, + +where the response +sheet [INAUDIBLE] + +and situation where only a few +people were very dislike the + +current [INAUDIBLE]. + +They don't like it this way and +so they want to change it. + +But the 80% who don't +feel [INAUDIBLE] is + +actually OK with it. + +[INAUDIBLE] the change. + +It makes most people unhappy. + +PROFESSOR: Unhappy, right, +so that can happen. + +And so that's the silent +majority problem. + +So what I do when I get comments +like people saying, + +well, I wasn't happy +about this. + +Sometimes what I do is-- + +especially if it doesn't +resonate with my intuition + +about how things were +going, and I thought + +they were going well-- + +I'll say, well, there were a few +comments about this issue. + +What do people think? + +And just take an informal +straw pole + +before I make big changes. + +AUDIENCE: I think it helps to +have a positive question on + +[INAUDIBLE], like, +what did you take + +away from this lecture? + +Or what did you really +understand? + +PROFESSOR: Right, I think +that's right. + +It helps to have a positive +question. + +So that's why I say, either what +you take away, or what + +helped or hurt? + +So there's an opportunity to +say something helpful. + +And any other comments is also +interpreted in a positive way. + +Answers from Lecture +5 to questions + +generated in Lecture 4. + +PROFESSOR: OK, and questions +from last time. + +So they grouped into +several ones. + +One is how should you choose +your levels of your problems-- + +say, in class or in homeworks-- +among the + +different levels of +Bloom's Taxonomy? + +Should it be, for example all +towards the evaluation? + +So your side would be here, +sort of the high level. + +A Mix? + +A flat mix? + +Should it be peaked towards the +middle with some tails? + +So that depends, partly, +on your course design. + +So to answer that question, you +can't really answer that + +question until you figure out +what your course goals are. + +So in some ways there's an +argument for doing course + +design first and then working on +what problems to do and how + +to design problems. + +But actually, I like the +other way around. + +I like doing course +design second. + +Because actually, doing problems +is concrete enough to + +do something. + +And then it leads to questions +about course design, which + +we'll answer how to +mix the levels. + +OK, another one was several +people wanted to know, why is + +tension not a force? + +Or in fact, maybe is a force. + +So let me explain that. + +Because that actually gives you +another example of sorting + +out misconceptions. + +So it's always useful. + +So I'll show you the sequence +of questions I used with + +myself when I finally +convinced that + +tension wasn't a force. + +And here's how I did it. + +And then I used the same +sequence of questions with + +students to fight the +misconception that's been + +induced by many pictures of-- + +for example-- a pulley. + +And here's a rope and +there's tension. + +Sorry, this is actually +done the other way. + +So here's the rope. + +And there's a t labeled there. + +And then on the mass there's a +force labeled as t upward. + +So when you see that you think, +oh, tension's a force. + +So you see that a whole bunch +of times and you're pretty + +sure of it. + +So the sequence of questions +is as follows-- + +say OK, here's a tree. + +And I'm going to tie a rope to +the tree, rope or a string, + +it's a mass-less thing. + +And I put a force on it. + +OK, so I'm going to +pull that tree. + +The tree's not going +to go anywhere. + +We're going to pull +on the rope with + +100 newtons of force. + +OK, so you can try this +yourself too. + +What's the tension +in the string? + +OK, so take 30 seconds and +I'll take a tension. + +OK, a tension, anyone? + +AUDIENCE: 100 newtons. + +PROFESSOR: OK, so in fact +that is 100 newtons. + +And most people will +say 100 newtons. + +OK, so now the next +question is this-- + +here is a river and +here's a rope. + +And me and a friend each pull on +the rope with 100 newtons. + +OK? + +OK, so discuss with +your neighbor-- + +a, b, or c, what's the +tension in the rope? + +And we'll take a vote. + +OK, so take 10 seconds, +get your vote ready. + +We'll take a quick straw pole. + +Who votes for 0 newtons? + +Who votes for 100 newtons? + +Who votes for 200 newtons? + +OK, so now here, how do you know +what it's going to be? + +Well, you make a +force diagram. + +And there's a way to convince +yourself that there's no doubt + +about what it should be. + +And we just draw the forces +on the rope here. + +Oh, we've already done that. + +Let's draw the forces on +the rope up there. + +Well, what are the forces +on the rope here? + +Well, it's 100 newtons +from you. + +But there must also be 100 +newtons from the tree. + +All right? + +So in fact, these two situations +are identical. + +So yeah, 100 newtons seems +pretty clear here. + +So it has to be 100 newtons +up there too. + +OK, now that-- + +so far-- isn't the hard part. + +But now is when you actually +create the contradiction with + +the idea of it being a force. + +It can't be a force because if +it were a force you would just + +add up vectors. + +Right? + +So there's a couple answers +you get if it was a force. + +If you're a bit sloppy you'd +just add up the magnitudes and + +get 200 newtons. + +If it's really a vector-- + +you're putting two vectors +on it, two forces-- + +you should get 0 because they're +two opposite forces. + +But actually you get 100. + +The only way to get 100 is that +the tension has to be + +something completely different +from a force. + +So that's how you know +it's not a force. + +But how do what it is? + +Well, it turns out +to be a tensor. + +So it's not a vector. + +Forces are vectors. + +It adds differently +than vectors do. + +It adds like a tensor. + +So tension is more +like a pressure. + +It doesn't have a particular +direction. + +Pressure is in all directions. + +So things like that, they can't +be described by vectors. + +So you need something else. + +And that's why we introduced +tensors. + +So now, in freshman physics I +wouldn't give them a whole + +story about tensors. + +But I do actually teach this +much of it so that they know + +that is a different object. + +And then what do I +do about this? + +Well, I won't write t unless +it's for myself. + +But for the students I think +it's sloppy and it increases + +misconception. + +It's much better to write the +force sub t, which is the + +force due to tension. + +OK? + +So even a slight change like +that can mitigate the rote + +learning, where people think +oh, tension's a force. + +Because you always see it drawn +like every other force. + +There's mg down, There's t +up, must be a force too. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: What are the two +objects you hit it with to + +make a scalar? + +It's the two directions +that you're + +interested in, basically. + +So it would be the x direction +or the direction along the + +string and the direction +along the string. + +AUDIENCE: So it's the +two direction then? + +PROFESSOR: You can use the +same direction twice. + +So it's the direction +along the string + +and along the string. + +There's no cross direction. + +So it has no shear. + +So there's no cross direction. + +So it's some component, tension +is one component of + +the stress tensor. + +So now, again, freshman don't +need to know all the details. + +This is back to the subject of +lying they do need to not be + +told fundamental lies. + +Like for example, tension +is a force. + +OK, so now, how do you deal with +misconceptions that show + +up on problem sets? + +This is a good question. + +So the point was made well, in +class you can sort it out + +right then. + +Suppose you ask a question, say, +about the Ideal Gas Law. + +And you find that people have +confused the Ideal Gas Law and + +the Adiabatic Gas Law. + +Well, you can talk about it +right then, which is a good + +reason to do those +things in class. + +What happens on the problem +set if you find there's a + +bunch of misconceptions? + +Well, one thing is, the first +time you do the problem set, + +yeah it's a bit of a problem. + +Because you don't know what the +misconceptions are unless + +you've researched +ahead of time. + +But the second time you do the +class you know what they are. + +So you can address the +misconceptions in + +the solution set. + +So when I'm not totally sleep +deprived I always try to get + +the solution set out the exact +same day that the problem set + +is turned in. + +So the students can +right away see. + +They can turn in their problem +set, pick up a solution set or + +look at it online. + +So they can right away +get quick feedback. + +And they can sort out the +misconceptions that way. + +So that's a good question. + +So it is harder. + +Yes, question? + +AUDIENCE: What do you do about +the fact that a lot of people + +will just ignore the +solution sets? + +Or do you just consider +that their problem? + +PROFESSOR: So the question is, +what do I do about people who + +just ignore the solution sets? + +Because a lot of students +do that. + +Yeah, partly I consider +it their problem. + +Because look, that's there +for them to learn. + +But partly, to the extent that +they're ignoring the solution + +set because they only cared +about the grade. + +So one cause of that +is they really only + +care about the grade. + +So they just want to wait for +the grader to give them back + +their solutions, their problem +set with a mark on it. + +And they don't care what's +right and wrong. + +That, I think, partly, is our +responsibility that we've + +chosen boring problems. + +So to fix that, I think, one +of the key areas is to use + +more of the Bloom's Taxonomy and +make interesting problems. + +And the flip side is to +deemphasize the grading. + +So actually, I like the +PDF scale on homework. + +I think we are too +micromanaging, generally, + +about homework, you know, +grading it on a percentage + +scale, on A, B, C, D. P, +you did a reasonable. + +And D, you blew it off. + +You did something but +it was a joke. + +And F, you didn't turn it in. + +I think that scale puts the +right emphasis on the grading. + +Look, we just want you to +do the thing and try it. + +And if the problems are +interesting that allows people + +to actually get involved +in it. + +So there's lots of studies that +show that if you reward + +people for things they +already enjoy-- + +so you start paying them more +for doing things they really + +like-- they actually start +liking them less. + +So I'll talk about that as one +of the political barriers to + +educational change. + +Because that's completely +against the conventional + +psychology of this society, +where everything has to be + +rewarded, merit-based pay +and this and that. + +So how do you go against that? + +It's quite difficult. + +But one way, in general, in +those problem sets is to + +deemphasize the grading. + +Related method-- + +which I haven't tried yet +but I'm planning to-- + +is reading memos on +the solution set. + +So I talked about reading +memos before. + +And maybe one of you will try +it before me and can tell me + +how it works. + +A reading memo is-- + +I talked about-- where you +have the students take a + +reading and mark-- +either online or + +on a piece of paper-- + +things that were confusing or +things that were interesting + +and things they noticed. + +Well, you can do that with +the solution set too. + +You say, OK, your assignment, +homework 3A is to look at the + +solution set for homework +two and mark + +anything that's confusing. + +So that forces people to +read the solution set. + +And often what you'll find is +that they'll find mistakes in + +the solution set, which is good +to know because you can + +correct them right away. + +But you'll see what parts are +confusing to students or not. + +Did that help answer +your question? + +Great. + +Do I ever asked Wheeler's +question explicitly? + +Yes, sometimes. + +I should do it more in +class in lecture. + +But I do it a lot to myself. + +Whenever I solve a problem +I think oh, + +what was the key idea? + +And then once I see the key idea +happen many times I think + +oh, that's a very key idea. + +That should be taught +explicitly in class. + +So I do that. + +And I'm going to talk about +that principle of course + +design today, basically +organizing courses around + +large themes and principles, +which is one of the main + +[? cures. ?] + +OK, so what's wrong with +tension as a force? + +How far should I go +down the taxonomy? + +Basically, where in the +course should I be? + +Really low in the taxonomy +early and higher later? + +Well, I talked about that +a bit last time. + +The fractal picture +is not bad. + +So yeah, you have a few +low-level examples and + +higher-level examples. + +But you do that throughout +the course. + +So you don't wait until the end +of the course to get the + +reward of the really interesting +problems. + +And then related to that, what +about exams and homework? + +Should they be the same +or different? + +My view is they should be the +same given the constraint that + +maybe the exam is done +in a shorter time. + +So if anything, the +exam should be + +easier than the homework. + +Generally, homework people +will spend six + +or seven hours on. + +When I was an undergraduate +we had take-home exams. + +And we would spend +24 hours on them. + +You pick them up, you +signed it out. + +You'd turned it in +in 24 hours. + +So that was misery. + +And it was interesting. + +You learnt a lot. + +But it was kind of miserable +because it just wiped out a + +whole day from your quarter. + +And you had that for +four classes. + +So four days from your quarter +were just gone. + +So generally, exams are three +hours, maybe two hours. + +And so that's much less time +than a homework set. + +So if anything, exams +should be easier, + +definitely not harder. + +Student loath when the exam does +different things than the + +problem sets. + +And that is a general principle +of course design, + +that if you want to prepare +them for being able to do + +stuff-- for example +on the exam-- + +you have to prepare +them with things. + +You have to "teach to the test." +That's actually good. + +You want your homeworks +to be like the exam. + +And that's fine if +the test is good. + +If the test tests real-world, +interesting skills sure, then + +it's fine to teach the test +because they'll come out being + +able to do that, no problem. + +So the exam and homework-- as +a rough rule of function-- + +will be pretty much the same. + +Or if anything, the exam +should be easier. + +Oh yeah, the first time +you teach a class. + +So all this Bloom's Taxonomy +and designing questions, it + +takes a long time. + +And it's really hard to +make good questions. + +It's easy to make define +XYZ questions. + +But what about the higher-level +questions? + +What do you do to mitigate +that problem of a + +huge amount of time? + +Well, one of the cures is to +cooperate with other teachers. + +So you steal their +good problems. + +So I gave you the T.S. Eliot +saying before, that talent + +invents and genius steals. + +So be a genius. + +Whenever you see a good +problem just use it. + +And whenever someone wants +a good problem, if you + +have one, share it. + +And now, should you guard +your problems? + +I think those days of guarding +problems are gone. + +They've gone by because of +things like OpenCourseWare, + +putting problem sets online. + +It's just not possible anymore +to guard problems. + +I'm not sure it was +ever a good idea. + +But now it's not +even practical. + +So everything is online, all +from the previous year. + +So the problems can't +be guarded. + +And it's not practical to make +up a whole set of new good + +problems for the next year. + +You'll never sleep. + +So I just trust the students not +to cheat by looking at the + +old solution sets. + +And if you're grading, that's +yet another reason to minimize + +how strict the grading is. + +So if the grading is really, +just that they make an effort + +and try to learn something, +then there's no benefit to + +cheating and looking at +the old solution sets. + +So you actually make the +incentive structure so that + +they don't need to do all that. + +Question? + +AUDIENCE: Do you have to change +your problem to a + +certain extent in terms +of plagiarism? + +PROFESSOR: So the question is, +do I have to change the + +problems to a certain extent +to avoid plagiarism? + +I don't even care. + +I don't even change them. + +I think, again, it's sort of +what Adrian has said, is it + +their problem if they do it? + +And to some extent it +is their problem. + +If they're going to cheat and +look at the old solution set + +and not acknowledge it. + +There's only so much +you can do. + +And you then get in an +arms race with them. + +You change the problem +to some extent. + +But then someone +else makes it. + +So they can always +subvert that. + +One person can solve the new +problem and give it to + +everybody else. + +So you have no hope of actually +winning that war, + +even if it were a moral +war to try to win. + +So I don't even change them. + +And I say look, just +acknowledge, just like you + +would in science. + +I think it's Larry Lessig, +the copyright scholar, + +professor of law. + +He used to be at Harvard. + +Now it's Stanford. + +He founded Creative Commons +and various fantastic + +copyright projects. + +So he said, well, there's a +couple ways to get-- not + +compliance-- + +people to do things. + +One is you can do it +through rules. + +For example, this is illegal. + +You just can't do this. + +We'll punish you +if you do this. + +The other one is through norm. + +So this is just not done. + +In our community we just don't +do things like that. + +And generally, this kind +of-- not exhortation-- + +but push works much better +than the punishment kind. + +So I just tell them, look, in +science when you grow up and + +become a scientist of course you +acknowledge your peers and + +people you learn from. + +Because that's just polite. + +It's just how we are. + +We say, please. + +We don't say gimme, +gimme, gimme. + +I'm working on teaching my +daughter that right now. + +She says, daddy read. + +Daddy read. + +Mommy read. + +Elsa read. + +I'm like OK, I'm fine +with the Elsa read. + +But daddy read, mommy +read, that's nice. + +And we love reading. + +But how do you ask? + +And now she says mommy read +please, daddy read please. + +And so it's the start. + +So people already learnt +that from young. + +So you can tap into that. + +Look, how do you act as a +member of the community? + +We're social animals. + +So you don't have +to put too much + +pressure in that direction. + +Whereas if you try to do it +through a punishment you have + +to work much harder. + +The punishment one-- + +underneath-- + +has the idea that we don't +trust the students. + +Right? + +And in that way it's common with +changing the numbers on + +the problems set. + +It's that we don't trust you so +we're changing the numbers. + +So I try to avoid those things +as much as possible and try to + +go more towards this. + +Yes? + +AUDIENCE: Has anyone tried +to have problem + +sets without solutions? + +So then there's no grading. + +And then the problem sets +are just for practicing. + +PROFESSOR: Yeah, have problem +sets for practice with no + +solutions or no grading +on the problem sets? + +Have people tried that? + +So there's actually +whole educational + +systems based on that. + +Not so much in America, but +in England, the Oxford and + +Cambridge tutorial system. + +You're given problems +to work on. + +So I was on both sides +of that system. + +You're given problems to +work with your tutor. + +And they're not graded. + +I mean, your tutor helps +you make sure that + +you can do the problems. + +But everything that's graded +happens at the end. + +Well, when I was an +undergraduate it happened at + +the end of your entire degree. + +There was eight three-hour +exams that counted for + +everything. + +And nothing else counted. + +So it had some craziness. + +That time at the end was +pretty stressful. + +But before that your tutor +was actually your friend. + +And your tutor wasn't the +person doing the exams. + +So you would do problems because +you wanted to learn + +and your tutor would help you +so that you would do well on + +the exam that other people +were setting. + +So you had a nice alliance +with your tutor. + +AUDIENCE: Does that work well? + +PROFESSOR: I would say +it works well. + +At MIT it would work great. + +Given [INAUDIBLE] + +that people are too +overloaded. + +And they would say, oh well, if +there's not going to be any + +grading at all, I don't have +to do anything, while I'd + +really like to do this +problem set. + +But I have four other classes +that are making me work 20 + +hours a week. + +And I don't have any time. + +So then because of the +other pressures + +they might fall away. + +But they would like to do it. + +So that's why I compromise by +just saying, you have to do + +the thing and make an effort. + +And then I trust that once they +start trying it they'll + +enjoy doing it. + +So I tried to make it as light +as I think you can get away + +with at MIT, given the +pressures from + +all the other teachers. + +But in the ideal world I think +that's what we would do here. + +There wouldn't be +that pressure. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: Yeah, in Oxford and +Cambridge it works very well, + +provided you have +a good tutor. + +And there's many students who +are there just because it's a + +thing to do, to go to Oxford +and Cambridge. + +But if you factor out those +students who are just there + +for the stamp of the place, +for the other students it + +works fantastically well. + +I mean, the tutorials are +a great discussion time. + +You can really kindle people's +curiosity because it's really + +not based on grading, it's +based on helping. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: It's so hard to do. + +I mean, I don't know +of any comparative + +studies within one culture. + +And I don't think you could +really do them well between, + +say, the English universities +and the American just because + +there's so many other social +variables that are so + +different like the population +that goes to university, which + +universities are talking about +the exam system itself, so I + +don't know of any studies that +have been done across cultures + +and that I would trust. + +And within I don't +know of any. + +But it's a good question. + +I know studies in general about +rewards, which is that + +the more you reward people for +things that they like the less + +they like doing them. + +So I might give you some +readings for that for very + +last penultimate session. + +And for the reading that I'm +going to give you for the next + +session is going to be about +tutoring, actually. + +So I'll put that on +the website today. + +OK, questions? + +Yes? + +AUDIENCE: [INAUDIBLE] +of a question. + +So I was wondering, if you do +exams or homework problems + +throughout the semester, you +can, maybe, also better + +monitor how the students develop +compared to having one + +big exam on the end. + +And then maybe using [INAUDIBLE] +lectures. + +PROFESSOR: Right, so having +continuous assessment is one + +phrase for it. + +It allows you to monitor, make +sure things are going OK. + +So all of a sudden you don't +find, oh my god, the person + +didn't know anything. + +They got a third, which is +like straight D's in your + +whole undergraduate. + +So in Oxford and Cambridge +things are graded on first, + +second, third. + +And all of a sudden you had had +no idea the student was + +going to get a third, +or they were sick or + +something like that. + +So I think, yeah. + +So homework problems and exams +have a really good purpose in + +assessment and helping students +get feedback on how + +they're doing as well. + +So for that purpose, +grading is useful. + +And one solution to that +dilemma-- because I don't like + +to grade exactly because +it stresses them + +out with the grade-- + +is to give them the solution +set right away. + +So they can get feedback from +the solution set whether they + +understood things, not whether +they had a 90 or and 80, but + +whether it made sense to them. + +And that's, I think, a much +more important thing. + +But then the other part of +grading, which is that it's + +used publicly-- + +as part of your record and +written to other people-- + +that part of grading I +think is not right. + +I don't think it's morally right +to, basically, reveal + +information about students to +other people without their + +permission. + +I don't think that should be the +purpose of the university. + +But the other purpose of +grading, helping students know + +where they are. + +And helping us know where they +are so we can help them more, + +I think, is a completely +valid purpose. + +OK, so there was another +suggestion which was to use as + +many non-physics and math +examples as possible. + +So I'll try to reform my ways +for the non physicists and + +mathematicians. + +It's just those come most +naturally for me. + +OK, so I think that +was the main-- + +yes, question? + +AUDIENCE: [INAUDIBLE] + +for evaluating the students or +for teaching the students. + +PROFESSOR: Pardon? + +AUDIENCE: Homeworks? + +PROFESSOR: Yes, for evaluating +versus for teaching? + +AUDIENCE: Yes, because that's +one thing to evaluate, right? + +[INAUDIBLE]? + +PROFESSOR: It's both. + +So there's two, yeah. + +So the other purpose is that +they learn and they do things. + +That's for sure. + +So you want them to do that. + +And you can do that in +class and homework. + +And the take-home exams that +we had when I was an + +undergraduate had that +purpose too. + +You spent 24 hours really +learning stuff. + +So that purpose is +very valid too. + +But it's also very valid to know +where the students are. + +So for example, that basically +closes the feedback loop. + +You're doing all this stuff. + +And now you're seeing +the result of it. + +And you want to know, well, +did any of it take? + +Did any of it stick? + +And if none of it did, well, +maybe you want to change what + +you're doing. + +AUDIENCE: Oh, but you +cannot evaluate a + +person every week, right? + +And that's what drives students +to copy solutions + +because they care +about the grade. + +[INAUDIBLE]. + +PROFESSOR: That's +why distinguish + +two senses of evaluate. + +There's evaluate +for the purpose + +of helping the students. + +And there's evaluate for the +purpose of publishing their + +grades elsewhere. + +And it's the publishing +their grades elsewhere + +that worries them. + +So you want to minimize +that part. + +And you want to do as much +evaluation towards helping + +them as possible. + +So a solution set-- for example, +one thing you can do + +is say OK, here's the +solution set. + +Ask me about anything +that's confusing. + +And then you can put some of +the responsibility for this + +evaluation onto them so +it's self evaluation. + +But you're still using the +homework for evaluation. + +It's just you're not +trying to say look, + +that's the main thing. + +I'm going to use that to tell +everyone else about it. + +That's what worries them +and produces copying. + +So you want to minimize that +as much as possible. + +And it's hard. + +And that's the subject of the +political obstacles to + +educational change session +that'll be in the + +second-to-last lecture. + +OK, so yeah, I don't pretend +any of these have easy + +answers, unfortunately. + +Oh, there was another +suggestion, which is that I + +make a web forum where people +can ask questions afterwards. + +Because it's hard sometimes +think of a + +question on the fly. + +And that's true. + +And the problem is it's not easy +to make web forms on the + +MIT.edu site. + +So I'll try to figure out +a way to do that. + +But for security reasons you +can't really easily make web + +forms that just append to a +file or do something like + +that, although I'm going to +look into it and see what + +workarounds I can find. + +Yes? + +AUDIENCE: [INAUDIBLE] + +scripts? + +PROFESSOR: Yeah, you can +use scripts at MIT.edu. + +So I have to figure out +how to use that. + +But yeah, I had that in +the back of my mind. + +But thanks for pointing +that out. + +Yeah? + +AUDIENCE: What about forms? + +PROFESSOR: Pardon? + +AUDIENCE: Forms? + +PROFESSOR: Forms? + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: Yeah, so then +you get email. + +So the only problem with that is +that you get a ton of spam. + +So there are all these spam +bots that float around and + +just fill out forms and send +junk emails all the time. + +So maybe that can be filtered +out and it's not so bad. + +So but yeah, that's one of the +few things you can do on + +MIT.edu, directly on +the web.MIT.edu. + +So there's a very +solutions to it. + +I'll try to think of something +around that because it is a + +good suggestion. + +OK. \ No newline at end of file diff --git a/8jLy33vbtYM.txt b/8jLy33vbtYM.txt new file mode 100644 index 0000000000000000000000000000000000000000..45bf435b8d529010d3f0f82a0a11196ca4541641 --- /dev/null +++ b/8jLy33vbtYM.txt @@ -0,0 +1,8379 @@ +align:start position:0% + +so we're gonna get started this is this + + align:start position:0% +so we're gonna get started this is this + + + align:start position:0% +so we're gonna get started this is this +is a complicated lecture to choreograph + + align:start position:0% +is a complicated lecture to choreograph + + + align:start position:0% +is a complicated lecture to choreograph +but I'm gonna do my very very best + + align:start position:0% +but I'm gonna do my very very best + + + align:start position:0% +but I'm gonna do my very very best +because I think it's there's some pretty + + align:start position:0% +because I think it's there's some pretty + + + align:start position:0% +because I think it's there's some pretty +amazing stuff that we have to explain + + align:start position:0% +amazing stuff that we have to explain + + + align:start position:0% +amazing stuff that we have to explain +that is carried out in nature and one of + + align:start position:0% +that is carried out in nature and one of + + + align:start position:0% +that is carried out in nature and one of +those things is how do we replicate the + + align:start position:0% +those things is how do we replicate the + + + align:start position:0% +those things is how do we replicate the +entire genome of organisms in one fell + + align:start position:0% +entire genome of organisms in one fell + + + align:start position:0% +entire genome of organisms in one fell +swoop + + align:start position:0% +swoop + + + align:start position:0% +swoop +almost perfectly sometimes there are + + align:start position:0% +almost perfectly sometimes there are + + + align:start position:0% +almost perfectly sometimes there are +little errors and fast so we're gonna + + align:start position:0% +little errors and fast so we're gonna + + + align:start position:0% +little errors and fast so we're gonna +refer to these numbers in a moment but + + align:start position:0% +refer to these numbers in a moment but + + + align:start position:0% +refer to these numbers in a moment but +first of all I just want to get you back + + align:start position:0% +first of all I just want to get you back + + + align:start position:0% +first of all I just want to get you back +in the picture of where we were at the + + align:start position:0% +in the picture of where we were at the + + + align:start position:0% +in the picture of where we were at the +end of the last section the biochemistry + + align:start position:0% +end of the last section the biochemistry + + + align:start position:0% +end of the last section the biochemistry +section and in the next few classes + + align:start position:0% +section and in the next few classes + + + align:start position:0% +section and in the next few classes +we're going to address issues related to + + align:start position:0% +we're going to address issues related to + + + align:start position:0% +we're going to address issues related to +the central dogma and the use of nucleic + + align:start position:0% +the central dogma and the use of nucleic + + + align:start position:0% +the central dogma and the use of nucleic +acids for information storage and + + align:start position:0% +acids for information storage and + + + align:start position:0% +acids for information storage and +information transfer and before I do + + align:start position:0% +information transfer and before I do + + + align:start position:0% +information transfer and before I do +that I just want to highlight a couple + + align:start position:0% +that I just want to highlight a couple + + + align:start position:0% +that I just want to highlight a couple +of things just in terms that you should + + align:start position:0% +of things just in terms that you should + + + align:start position:0% +of things just in terms that you should +recall and recap from the biochemistry + + align:start position:0% +recall and recap from the biochemistry + + + align:start position:0% +recall and recap from the biochemistry +section about nucleic acids so nucleic + + align:start position:0% +section about nucleic acids so nucleic + + + align:start position:0% +section about nucleic acids so nucleic +acids form complimentary double strands + + align:start position:0% +acids form complimentary double strands + + + align:start position:0% +acids form complimentary double strands +through base pairing and that base + + align:start position:0% +through base pairing and that base + + + align:start position:0% +through base pairing and that base +pairing involves hydrogen bonding + + align:start position:0% +pairing involves hydrogen bonding + + + align:start position:0% +pairing involves hydrogen bonding +between the nucleobases one purine to + + align:start position:0% +between the nucleobases one purine to + + + align:start position:0% +between the nucleobases one purine to +one pyrimidine and the a T base pair is + + align:start position:0% +one pyrimidine and the a T base pair is + + + align:start position:0% +one pyrimidine and the a T base pair is +worth two hydrogen bonds the GC base + + align:start position:0% +worth two hydrogen bonds the GC base + + + align:start position:0% +worth two hydrogen bonds the GC base +pair is worth three hydrogen bonds and + + align:start position:0% +pair is worth three hydrogen bonds and + + + align:start position:0% +pair is worth three hydrogen bonds and +those are actually pretty useful facts + + align:start position:0% +those are actually pretty useful facts + + + align:start position:0% +those are actually pretty useful facts +to remember because they tell us about + + align:start position:0% +to remember because they tell us about + + + align:start position:0% +to remember because they tell us about +the stability of double-stranded DNA + + align:start position:0% +the stability of double-stranded DNA + + + align:start position:0% +the stability of double-stranded DNA +where it's easier to tease it apart and + + align:start position:0% +where it's easier to tease it apart and + + + align:start position:0% +where it's easier to tease it apart and +other characteristics so it's kind of a + + align:start position:0% +other characteristics so it's kind of a + + + align:start position:0% +other characteristics so it's kind of a +useful thing to keep in mind so the base + + align:start position:0% +useful thing to keep in mind so the base + + + align:start position:0% +useful thing to keep in mind so the base +pairing between what's the purine + + align:start position:0% +pairing between what's the purine + + + align:start position:0% +pairing between what's the purine +pyrimidine pair which sets the exact + + align:start position:0% +pyrimidine pair which sets the exact + + + align:start position:0% +pyrimidine pair which sets the exact +register down the double-stranded DNA + + align:start position:0% +register down the double-stranded DNA + + + align:start position:0% +register down the double-stranded DNA +that the backbone is the exact distance + + align:start position:0% +that the backbone is the exact distance + + + align:start position:0% +that the backbone is the exact distance +apart because you always combine a small + + align:start position:0% +apart because you always combine a small + + + align:start position:0% +apart because you always combine a small +pyrimidine with a much larger purine so + + align:start position:0% +pyrimidine with a much larger purine so + + + align:start position:0% +pyrimidine with a much larger purine so +that's something you should feel + + align:start position:0% +that's something you should feel + + + align:start position:0% +that's something you should feel +comfortable about the components are + + align:start position:0% +comfortable about the components are + + + align:start position:0% +comfortable about the components are +organized in an anti parallel + + align:start position:0% +organized in an anti parallel + + + align:start position:0% +organized in an anti parallel +orientation so one end is good runs 5 + + align:start position:0% +orientation so one end is good runs 5 + + + align:start position:0% +orientation so one end is good runs 5 +prime to 3 prime the other end runs 3 + + align:start position:0% +prime to 3 prime the other end runs 3 + + + align:start position:0% +prime to 3 prime the other end runs 3 +prime to 5 prime and I showed you last + + align:start position:0% +prime to 5 prime and I showed you last + + + align:start position:0% +prime to 5 prime and I showed you last +time an image + + align:start position:0% +time an image + + + align:start position:0% +time an image +that allows us to state quite clearly + + align:start position:0% +that allows us to state quite clearly + + + align:start position:0% +that allows us to state quite clearly +that the anti-parallel orientation is + + align:start position:0% +that the anti-parallel orientation is + + + align:start position:0% +that the anti-parallel orientation is +significantly more stable than the + + align:start position:0% +significantly more stable than the + + + align:start position:0% +significantly more stable than the +parallel orientation because you can't + + align:start position:0% +parallel orientation because you can't + + + align:start position:0% +parallel orientation because you can't +make all those great hydrogen bonds well + + align:start position:0% +make all those great hydrogen bonds well + + + align:start position:0% +make all those great hydrogen bonds well +in the parallel organization apart from + + align:start position:0% +in the parallel organization apart from + + + align:start position:0% +in the parallel organization apart from +everything else that becomes complicated + + align:start position:0% +everything else that becomes complicated + + + align:start position:0% +everything else that becomes complicated +another important thing that you're + + align:start position:0% +another important thing that you're + + + align:start position:0% +another important thing that you're +going to have to remember specially in + + align:start position:0% +going to have to remember specially in + + + align:start position:0% +going to have to remember specially in +this lecture is that we add new + + align:start position:0% +this lecture is that we add new + + + align:start position:0% +this lecture is that we add new +nucleotides to the 3 prime end of a + + align:start position:0% +nucleotides to the 3 prime end of a + + + align:start position:0% +nucleotides to the 3 prime end of a +nucleic acid and so I'm just gonna put + + align:start position:0% +nucleic acid and so I'm just gonna put + + + align:start position:0% +nucleic acid and so I'm just gonna put +this little guy in the corner here this + + align:start position:0% +this little guy in the corner here this + + + align:start position:0% +this little guy in the corner here this +is the ribose sugar that would be where + + align:start position:0% +is the ribose sugar that would be where + + + align:start position:0% +is the ribose sugar that would be where +the nuclear base is attached and it's a + + align:start position:0% +the nuclear base is attached and it's a + + + align:start position:0% +the nuclear base is attached and it's a +deoxy sugar so there's not no + + align:start position:0% +deoxy sugar so there's not no + + + align:start position:0% +deoxy sugar so there's not no +substituent at that carbon this is the + + align:start position:0% +substituent at that carbon this is the + + + align:start position:0% +substituent at that carbon this is the +one position where the base is the 2 + + align:start position:0% +one position where the base is the 2 + + + align:start position:0% +one position where the base is the 2 +position where it's deoxy the 3 position + + align:start position:0% +position where it's deoxy the 3 position + + + align:start position:0% +position where it's deoxy the 3 position +and these are all prime numbers remember + + align:start position:0% +and these are all prime numbers remember + + + align:start position:0% +and these are all prime numbers remember +the sugars have prime numbers the bases + + align:start position:0% +the sugars have prime numbers the bases + + + align:start position:0% +the sugars have prime numbers the bases +themselves have numbers without primes + + align:start position:0% +themselves have numbers without primes + + + align:start position:0% +themselves have numbers without primes +to distinguish what we're talking about + + align:start position:0% +to distinguish what we're talking about + + + align:start position:0% +to distinguish what we're talking about +so 3 4 5 and they're all prime and when + + align:start position:0% +so 3 4 5 and they're all prime and when + + + align:start position:0% +so 3 4 5 and they're all prime and when +we grow the the single strand of DNA we + + align:start position:0% +we grow the the single strand of DNA we + + + align:start position:0% +we grow the the single strand of DNA we +always add new basis to the 3 prime end + + align:start position:0% +always add new basis to the 3 prime end + + + align:start position:0% +always add new basis to the 3 prime end +that's a an import enum burring system + + align:start position:0% +that's a an import enum burring system + + + align:start position:0% +that's a an import enum burring system +so we have that piece of chalk so we + + align:start position:0% +so we have that piece of chalk so we + + + align:start position:0% +so we have that piece of chalk so we +always grow from 5 prime to 3 Prime oops + + align:start position:0% + + + + align:start position:0% + +and that will be important to you as we + + align:start position:0% +and that will be important to you as we + + + align:start position:0% +and that will be important to you as we +go through the discussion today and then + + align:start position:0% +go through the discussion today and then + + + align:start position:0% +go through the discussion today and then +finally a feature of DNA quite + + align:start position:0% +finally a feature of DNA quite + + + align:start position:0% +finally a feature of DNA quite +double-stranded DNA quite unlike + + align:start position:0% +double-stranded DNA quite unlike + + + align:start position:0% +double-stranded DNA quite unlike +proteins which sometimes you'll + + align:start position:0% +proteins which sometimes you'll + + + align:start position:0% +proteins which sometimes you'll +thermally or with pH melt out and will + + align:start position:0% +thermally or with pH melt out and will + + + align:start position:0% +thermally or with pH melt out and will +often have a problem reforming their + + align:start position:0% +often have a problem reforming their + + + align:start position:0% +often have a problem reforming their +reliable structure because instead of + + align:start position:0% +reliable structure because instead of + + + align:start position:0% +reliable structure because instead of +the structure refolding they aggregate + + align:start position:0% +the structure refolding they aggregate + + + align:start position:0% +the structure refolding they aggregate +double-stranded DNA doesn't aggregate + + align:start position:0% +double-stranded DNA doesn't aggregate + + + align:start position:0% +double-stranded DNA doesn't aggregate +because it's got all their negative + + align:start position:0% +because it's got all their negative + + + align:start position:0% +because it's got all their negative +charges that would be quite repulsive + + align:start position:0% +charges that would be quite repulsive + + + align:start position:0% +charges that would be quite repulsive +it would be very difficult for DNA + + align:start position:0% +it would be very difficult for DNA + + + align:start position:0% +it would be very difficult for DNA +strands to aggregate as such because + + align:start position:0% +strands to aggregate as such because + + + align:start position:0% +strands to aggregate as such because +there's too much of a concentration of + + align:start position:0% +there's too much of a concentration of + + + align:start position:0% +there's too much of a concentration of +negative charges that would be repulsion + + align:start position:0% +negative charges that would be repulsion + + + align:start position:0% +negative charges that would be repulsion +amongst the same type charges so DNA can + + align:start position:0% +amongst the same type charges so DNA can + + + align:start position:0% +amongst the same type charges so DNA can +be peeled apart with heat and it will + + align:start position:0% +be peeled apart with heat and it will + + + align:start position:0% +be peeled apart with heat and it will +really to its partner complementary + + align:start position:0% +really to its partner complementary + + + align:start position:0% +really to its partner complementary +strand once you get to six seven eight + + align:start position:0% +strand once you get to six seven eight + + + align:start position:0% +strand once you get to six seven eight +base pairs that is a nice interaction + + align:start position:0% +base pairs that is a nice interaction + + + align:start position:0% +base pairs that is a nice interaction +between the strands and it forms + + align:start position:0% +between the strands and it forms + + + align:start position:0% +between the strands and it forms +faithfully if we have a mistake in the + + align:start position:0% +faithfully if we have a mistake in the + + + align:start position:0% +faithfully if we have a mistake in the +strands the stability of the double + + align:start position:0% +strands the stability of the double + + + align:start position:0% +strands the stability of the double +strand would be a bit less and we can + + align:start position:0% +strand would be a bit less and we can + + + align:start position:0% +strand would be a bit less and we can +measure that through physical + + align:start position:0% +measure that through physical + + + align:start position:0% +measure that through physical +measurements that we carry out in the + + align:start position:0% +measurements that we carry out in the + + + align:start position:0% +measurements that we carry out in the +lab so we can measure the denaturation + + align:start position:0% +lab so we can measure the denaturation + + + align:start position:0% +lab so we can measure the denaturation +or the thermal melt temperature so we + + align:start position:0% +or the thermal melt temperature so we + + + align:start position:0% +or the thermal melt temperature so we +call this interaction we call this + + align:start position:0% +call this interaction we call this + + + align:start position:0% +call this interaction we call this +process rather after you separate + + align:start position:0% +process rather after you separate + + + align:start position:0% +process rather after you separate +double-stranded DNA we call it reeling + + align:start position:0% +double-stranded DNA we call it reeling + + + align:start position:0% +double-stranded DNA we call it reeling +or it's also designated as hybridization + + align:start position:0% +or it's also designated as hybridization + + + align:start position:0% +or it's also designated as hybridization +to form a hybrid which is the composite + + align:start position:0% +to form a hybrid which is the composite + + + align:start position:0% +to form a hybrid which is the composite +of the two structures those terms are + + align:start position:0% +of the two structures those terms are + + + align:start position:0% +of the two structures those terms are +used fairly interchangeably all right so + + align:start position:0% +used fairly interchangeably all right so + + + align:start position:0% +used fairly interchangeably all right so +the goals in the next four class is to + + align:start position:0% +the goals in the next four class is to + + + align:start position:0% +the goals in the next four class is to +show you how the structures of the + + align:start position:0% +show you how the structures of the + + + align:start position:0% +show you how the structures of the +nucleic acids really a purpose for the + + align:start position:0% +nucleic acids really a purpose for the + + + align:start position:0% +nucleic acids really a purpose for the +sorts of processes that they undergo so + + align:start position:0% +sorts of processes that they undergo so + + + align:start position:0% +sorts of processes that they undergo so +the replication of DNA the conversion of + + align:start position:0% +the replication of DNA the conversion of + + + align:start position:0% +the replication of DNA the conversion of +a strand of DNA into complimentary + + align:start position:0% +a strand of DNA into complimentary + + + align:start position:0% +a strand of DNA into complimentary +messenger RNA once the process of + + align:start position:0% +messenger RNA once the process of + + + align:start position:0% +messenger RNA once the process of +protein synthesis needs to be initiated + + align:start position:0% +protein synthesis needs to be initiated + + + align:start position:0% +protein synthesis needs to be initiated +that second step the first step is + + align:start position:0% +that second step the first step is + + + align:start position:0% +that second step the first step is +called replication the second step when + + align:start position:0% +called replication the second step when + + + align:start position:0% +called replication the second step when +you transcribe DNA into RNA is called + + align:start position:0% +you transcribe DNA into RNA is called + + + align:start position:0% +you transcribe DNA into RNA is called +transcription and then finally when you + + align:start position:0% +transcription and then finally when you + + + align:start position:0% +transcription and then finally when you +translate messenger RNA into proteins so + + align:start position:0% +translate messenger RNA into proteins so + + + align:start position:0% +translate messenger RNA into proteins so +going to a completely new language we + + align:start position:0% +going to a completely new language we + + + align:start position:0% +going to a completely new language we +call it a translation and that's the + + align:start position:0% +call it a translation and that's the + + + align:start position:0% +call it a translation and that's the +basis of these of these lectures there's + + align:start position:0% +basis of these of these lectures there's + + + align:start position:0% +basis of these of these lectures there's +a little bit of stuff in these lectures + + align:start position:0% +a little bit of stuff in these lectures + + + align:start position:0% +a little bit of stuff in these lectures +about more complicated issues in the + + align:start position:0% +about more complicated issues in the + + + align:start position:0% +about more complicated issues in the +mammalian cell where we have to process + + align:start position:0% +mammalian cell where we have to process + + + align:start position:0% +mammalian cell where we have to process +the messenger RNA a bit before we can + + align:start position:0% +the messenger RNA a bit before we can + + + align:start position:0% +the messenger RNA a bit before we can +have it leave the nucleus and I'll + + align:start position:0% +have it leave the nucleus and I'll + + + align:start position:0% +have it leave the nucleus and I'll +explain the time at there when it comes + + align:start position:0% +explain the time at there when it comes + + + align:start position:0% +explain the time at there when it comes +so this is the lineup for the four + + align:start position:0% +so this is the lineup for the four + + + align:start position:0% +so this is the lineup for the four +lectures all right so what I already + + align:start position:0% +lectures all right so what I already + + + align:start position:0% +lectures all right so what I already +talked to you how when you add I + + align:start position:0% +talked to you how when you add I + + + align:start position:0% +talked to you how when you add I +mentioned it + + align:start position:0% +mentioned it + + + align:start position:0% +mentioned it +here when you add sighted een + + align:start position:0% +here when you add sighted een + + + align:start position:0% +here when you add sighted een +triphosphate gtp ATP TTP these are the + + align:start position:0% +triphosphate gtp ATP TTP these are the + + + align:start position:0% +triphosphate gtp ATP TTP these are the +activated nucleobases + + align:start position:0% +activated nucleobases + + + align:start position:0% +activated nucleobases +so they're the deoxy nucleotide + + align:start position:0% +so they're the deoxy nucleotide + + + align:start position:0% +so they're the deoxy nucleotide +nucleoside triphosphates they are + + align:start position:0% +nucleoside triphosphates they are + + + align:start position:0% +nucleoside triphosphates they are +nucleotides because they include + + align:start position:0% +nucleotides because they include + + + align:start position:0% +nucleotides because they include +phosphate but when we describe them + + align:start position:0% +phosphate but when we describe them + + + align:start position:0% +phosphate but when we describe them +we'll call them nucleoside triphosphates + + align:start position:0% +we'll call them nucleoside triphosphates + + + align:start position:0% +we'll call them nucleoside triphosphates +if we're gonna mention the phosphate + + align:start position:0% +if we're gonna mention the phosphate + + + align:start position:0% +if we're gonna mention the phosphate +part and I know that probably doesn't + + align:start position:0% +part and I know that probably doesn't + + + align:start position:0% +part and I know that probably doesn't +make any sense at all right is everyone + + align:start position:0% +make any sense at all right is everyone + + + align:start position:0% +make any sense at all right is everyone +okay with that if you're just + + align:start position:0% +okay with that if you're just + + + align:start position:0% +okay with that if you're just +generically describing something with a + + align:start position:0% +generically describing something with a + + + align:start position:0% +generically describing something with a +phosphate in it you call it a nucleotide + + align:start position:0% +phosphate in it you call it a nucleotide + + + align:start position:0% +phosphate in it you call it a nucleotide +if you want to be a little bit more + + align:start position:0% +if you want to be a little bit more + + + align:start position:0% +if you want to be a little bit more +specific you say nucleoside and then you + + align:start position:0% +specific you say nucleoside and then you + + + align:start position:0% +specific you say nucleoside and then you +say how many phosphates alright and so + + align:start position:0% +say how many phosphates alright and so + + + align:start position:0% +say how many phosphates alright and so +for the building blocks it's a + + align:start position:0% +for the building blocks it's a + + + align:start position:0% +for the building blocks it's a +nucleoside triphosphate and believe me I + + align:start position:0% +nucleoside triphosphate and believe me I + + + align:start position:0% +nucleoside triphosphate and believe me I +get that wrong all the time and I my + + align:start position:0% +get that wrong all the time and I my + + + align:start position:0% +get that wrong all the time and I my +students correct me so I don't have a + + align:start position:0% +students correct me so I don't have a + + + align:start position:0% +students correct me so I don't have a +problem if you if you're not perfect + + align:start position:0% +problem if you if you're not perfect + + + align:start position:0% +problem if you if you're not perfect +with that nomenclature so these are the + + align:start position:0% +with that nomenclature so these are the + + + align:start position:0% +with that nomenclature so these are the +building blocks for DNA for + + align:start position:0% +building blocks for DNA for + + + align:start position:0% +building blocks for DNA for +polymerization and I just showed you how + + align:start position:0% +polymerization and I just showed you how + + + align:start position:0% +polymerization and I just showed you how +you grow from the 5 prime end that + + align:start position:0% +you grow from the 5 prime end that + + + align:start position:0% +you grow from the 5 prime end that +numbers not shown there but it's shown + + align:start position:0% +numbers not shown there but it's shown + + + align:start position:0% +numbers not shown there but it's shown +over here and you add to the 3 prime end + + align:start position:0% +over here and you add to the 3 prime end + + + align:start position:0% +over here and you add to the 3 prime end +and the convention remember when we + + align:start position:0% +and the convention remember when we + + + align:start position:0% +and the convention remember when we +describe a strand of DNA because we make + + align:start position:0% +describe a strand of DNA because we make + + + align:start position:0% +describe a strand of DNA because we make +it 5 prime to 3 prime we write it 5 + + align:start position:0% +it 5 prime to 3 prime we write it 5 + + + align:start position:0% +it 5 prime to 3 prime we write it 5 +prime to 3 prime just so that we're all + + align:start position:0% +prime to 3 prime just so that we're all + + + align:start position:0% +prime to 3 prime just so that we're all +consistent and we know what we're + + align:start position:0% +consistent and we know what we're + + + align:start position:0% +consistent and we know what we're +talking about now I want to talk about 2 + + align:start position:0% +talking about now I want to talk about 2 + + + align:start position:0% +talking about now I want to talk about 2 +experiments but enlist the use of + + align:start position:0% +experiments but enlist the use of + + + align:start position:0% +experiments but enlist the use of +isotopes + + align:start position:0% +isotopes + + + align:start position:0% +isotopes +because these were quite useful earlier + + align:start position:0% +because these were quite useful earlier + + + align:start position:0% +because these were quite useful earlier +early on to describe some of the + + align:start position:0% +early on to describe some of the + + + align:start position:0% +early on to describe some of the +characteristics of replications so some + + align:start position:0% +characteristics of replications so some + + + align:start position:0% +characteristics of replications so some +of the details of replication and also + + align:start position:0% +of the details of replication and also + + + align:start position:0% +of the details of replication and also +the fact the DNA was the genetic + + align:start position:0% +the fact the DNA was the genetic + + + align:start position:0% +the fact the DNA was the genetic +material okay so isotopes are elements + + align:start position:0% +material okay so isotopes are elements + + + align:start position:0% +material okay so isotopes are elements +that share the same number of protons + + align:start position:0% +that share the same number of protons + + + align:start position:0% +that share the same number of protons +and electrons but they differ in the + + align:start position:0% +and electrons but they differ in the + + + align:start position:0% +and electrons but they differ in the +number of neutrons okay so the common + + align:start position:0% +number of neutrons okay so the common + + + align:start position:0% +number of neutrons okay so the common +isotopes of the elements that are in all + + align:start position:0% +isotopes of the elements that are in all + + + align:start position:0% +isotopes of the elements that are in all +the covalent structures of the body are + + align:start position:0% +the covalent structures of the body are + + + align:start position:0% +the covalent structures of the body are +hydrogen + + align:start position:0% + + + + align:start position:0% + +carbon and what I'm putting is the + + align:start position:0% +carbon and what I'm putting is the + + + align:start position:0% +carbon and what I'm putting is the +number next to it is the common isotope + + align:start position:0% +number next to it is the common isotope + + + align:start position:0% +number next to it is the common isotope +so it's the number that number + + align:start position:0% +so it's the number that number + + + align:start position:0% +so it's the number that number +designates the sum of the number of + + align:start position:0% +designates the sum of the number of + + + align:start position:0% +designates the sum of the number of +neutrons and protons so carbon-12 + + align:start position:0% +neutrons and protons so carbon-12 + + + align:start position:0% +neutrons and protons so carbon-12 +phosphorus 31 I should have put nitrogen + + align:start position:0% +phosphorus 31 I should have put nitrogen + + + align:start position:0% +phosphorus 31 I should have put nitrogen +here let's see wait I mean I'm gonna put + + align:start position:0% +here let's see wait I mean I'm gonna put + + + align:start position:0% +here let's see wait I mean I'm gonna put +these in order because it makes more + + align:start position:0% +these in order because it makes more + + + align:start position:0% +these in order because it makes more +sense + + align:start position:0% +sense + + + align:start position:0% +sense +phosphorus 31 nitrogen 14 phosphorous 31 + + align:start position:0% +phosphorus 31 nitrogen 14 phosphorous 31 + + + align:start position:0% +phosphorus 31 nitrogen 14 phosphorous 31 +and sulfur + + align:start position:0% +and sulfur + + + align:start position:0% +and sulfur +what's the sulphur isotope 32 so these + + align:start position:0% +what's the sulphur isotope 32 so these + + + align:start position:0% +what's the sulphur isotope 32 so these +are the common isotopes that we that + + align:start position:0% +are the common isotopes that we that + + + align:start position:0% +are the common isotopes that we that +comprise the majority of those elements + + align:start position:0% +comprise the majority of those elements + + + align:start position:0% +comprise the majority of those elements +within the body but there are lots of + + align:start position:0% +within the body but there are lots of + + + align:start position:0% +within the body but there are lots of +experiments done that have different + + align:start position:0% +experiments done that have different + + + align:start position:0% +experiments done that have different +isotopes of these atoms that we can use + + align:start position:0% +isotopes of these atoms that we can use + + + align:start position:0% +isotopes of these atoms that we can use +as tracers or markers kind of the same + + align:start position:0% +as tracers or markers kind of the same + + + align:start position:0% +as tracers or markers kind of the same +thing but you'll see when I mentioned + + align:start position:0% +thing but you'll see when I mentioned + + + align:start position:0% +thing but you'll see when I mentioned +the word tracer to me it brings up the + + align:start position:0% +the word tracer to me it brings up the + + + align:start position:0% +the word tracer to me it brings up the +radioactive isotopes because we use very + + align:start position:0% +radioactive isotopes because we use very + + + align:start position:0% +radioactive isotopes because we use very +little of them so when we talk about + + align:start position:0% +little of them so when we talk about + + + align:start position:0% +little of them so when we talk about +these elements there are different + + align:start position:0% +these elements there are different + + + align:start position:0% +these elements there are different +isotopes that we use commonly there's + + align:start position:0% +isotopes that we use commonly there's + + + align:start position:0% +isotopes that we use commonly there's +the hydrogen that has an extra Neutron + + align:start position:0% +the hydrogen that has an extra Neutron + + + align:start position:0% +the hydrogen that has an extra Neutron +that's also called deuterium and then + + align:start position:0% +that's also called deuterium and then + + + align:start position:0% +that's also called deuterium and then +there's the hydrogen that is radioactive + + align:start position:0% +there's the hydrogen that is radioactive + + + align:start position:0% +there's the hydrogen that is radioactive +it's metastable it will decay and emit a + + align:start position:0% +it's metastable it will decay and emit a + + + align:start position:0% +it's metastable it will decay and emit a +radioactive particle so this one we + + align:start position:0% +radioactive particle so this one we + + + align:start position:0% +radioactive particle so this one we +would call it the heavy isotope and this + + align:start position:0% +would call it the heavy isotope and this + + + align:start position:0% +would call it the heavy isotope and this +one we would call the radioactive + + align:start position:0% +one we would call the radioactive + + + align:start position:0% +one we would call the radioactive +isotope so we could trace certain + + align:start position:0% +isotope so we could trace certain + + + align:start position:0% +isotope so we could trace certain +hydrogen's in biomolecules by either + + align:start position:0% +hydrogen's in biomolecules by either + + + align:start position:0% +hydrogen's in biomolecules by either +making those hydrogen's the heavier ones + + align:start position:0% +making those hydrogen's the heavier ones + + + align:start position:0% +making those hydrogen's the heavier ones +or making them the radioactive ones + + align:start position:0% +or making them the radioactive ones + + + align:start position:0% +or making them the radioactive ones +carbon also has useful isotopes carbon + + align:start position:0% +carbon also has useful isotopes carbon + + + align:start position:0% +carbon also has useful isotopes carbon +13 is the heavy isotope and carbon 14 is + + align:start position:0% +13 is the heavy isotope and carbon 14 is + + + align:start position:0% +13 is the heavy isotope and carbon 14 is +the radioactive isotope so they're used + + align:start position:0% +the radioactive isotope so they're used + + + align:start position:0% +the radioactive isotope so they're used +quite commonly and there + + align:start position:0% +quite commonly and there + + + align:start position:0% +quite commonly and there +things get a little bit different for + + align:start position:0% +things get a little bit different for + + + align:start position:0% +things get a little bit different for +nitrogen we use a heavy isotope of + + align:start position:0% +nitrogen we use a heavy isotope of + + + align:start position:0% +nitrogen we use a heavy isotope of +nitrogen which is n15 just one extra + + align:start position:0% +nitrogen which is n15 just one extra + + + align:start position:0% +nitrogen which is n15 just one extra +Neutron but while there is a radioactive + + align:start position:0% +Neutron but while there is a radioactive + + + align:start position:0% +Neutron but while there is a radioactive +isotope of nitrogen it's too short of a + + align:start position:0% +isotope of nitrogen it's too short of a + + + align:start position:0% +isotope of nitrogen it's too short of a +half-life to work with in the lab it's + + align:start position:0% +half-life to work with in the lab it's + + + align:start position:0% +half-life to work with in the lab it's +not useful to us so we never talk about + + align:start position:0% +not useful to us so we never talk about + + + align:start position:0% +not useful to us so we never talk about +it but we I will describe to you an + + align:start position:0% +it but we I will describe to you an + + + align:start position:0% +it but we I will describe to you an +experiment with the heavy n15 when we + + align:start position:0% +experiment with the heavy n15 when we + + + align:start position:0% +experiment with the heavy n15 when we +talk about the mechanism of replication + + align:start position:0% +talk about the mechanism of replication + + + align:start position:0% +talk about the mechanism of replication +and then for phosphorus and sulfur the + + align:start position:0% +and then for phosphorus and sulfur the + + + align:start position:0% +and then for phosphorus and sulfur the +most important ones are P 32 which is a + + align:start position:0% +most important ones are P 32 which is a + + + align:start position:0% +most important ones are P 32 which is a +radioactive phosphorus and s 35 which is + + align:start position:0% +radioactive phosphorus and s 35 which is + + + align:start position:0% +radioactive phosphorus and s 35 which is +a radioactive sulfur there's another + + align:start position:0% +a radioactive sulfur there's another + + + align:start position:0% +a radioactive sulfur there's another +radioactive phosphorus that's P 33 has a + + align:start position:0% +radioactive phosphorus that's P 33 has a + + + align:start position:0% +radioactive phosphorus that's P 33 has a +slightly longer half-life it's kind of + + align:start position:0% +slightly longer half-life it's kind of + + + align:start position:0% +slightly longer half-life it's kind of +handy to work with if you have certain + + align:start position:0% +handy to work with if you have certain + + + align:start position:0% +handy to work with if you have certain +experiments the half-life is very a lot + + align:start position:0% +experiments the half-life is very a lot + + + align:start position:0% +experiments the half-life is very a lot +but the half-life of tritium c14 a long + + align:start position:0% +but the half-life of tritium c14 a long + + + align:start position:0% +but the half-life of tritium c14 a long +that's why we do carbon dating the + + align:start position:0% +that's why we do carbon dating the + + + align:start position:0% +that's why we do carbon dating the +half-life of P 32 a short you know less + + align:start position:0% +half-life of P 32 a short you know less + + + align:start position:0% +half-life of P 32 a short you know less +day time frame and sulphur 35 is a + + align:start position:0% +day time frame and sulphur 35 is a + + + align:start position:0% +day time frame and sulphur 35 is a +little bit longer but those are nuances + + align:start position:0% +little bit longer but those are nuances + + + align:start position:0% +little bit longer but those are nuances +that you don't you don't need to worry + + align:start position:0% +that you don't you don't need to worry + + + align:start position:0% +that you don't you don't need to worry +about now how are these isotopes useful + + align:start position:0% +about now how are these isotopes useful + + + align:start position:0% +about now how are these isotopes useful +as tracers and markers to tell us about + + align:start position:0% +as tracers and markers to tell us about + + + align:start position:0% +as tracers and markers to tell us about +biology and details of biology so what + + align:start position:0% +biology and details of biology so what + + + align:start position:0% +biology and details of biology so what +I'm going to just show you here is a + + align:start position:0% +I'm going to just show you here is a + + + align:start position:0% +I'm going to just show you here is a +particular experiment that's carried out + + align:start position:0% +particular experiment that's carried out + + + align:start position:0% +particular experiment that's carried out +with what are known as baculovirus so + + align:start position:0% +with what are known as baculovirus so + + + align:start position:0% +with what are known as baculovirus so +viruses infect eukaryotic cells + + align:start position:0% +viruses infect eukaryotic cells + + + align:start position:0% +viruses infect eukaryotic cells +baculovirus --is infect bacteria so + + align:start position:0% +baculovirus --is infect bacteria so + + + align:start position:0% +baculovirus --is infect bacteria so +there's a commonality there and when + + align:start position:0% +there's a commonality there and when + + + align:start position:0% +there's a commonality there and when +baculovirus has infect bacteria just as + + align:start position:0% +baculovirus has infect bacteria just as + + + align:start position:0% +baculovirus has infect bacteria just as +the parallel with eukaryotic cells they + + align:start position:0% +the parallel with eukaryotic cells they + + + align:start position:0% +the parallel with eukaryotic cells they +deposit material into the bacteria so + + align:start position:0% +deposit material into the bacteria so + + + align:start position:0% +deposit material into the bacteria so +they can replicate so they can hijack + + align:start position:0% +they can replicate so they can hijack + + + align:start position:0% +they can replicate so they can hijack +the bacteria to make new viral new + + align:start position:0% +the bacteria to make new viral new + + + align:start position:0% +the bacteria to make new viral new +baculovirus so what an early experiment + + align:start position:0% +baculovirus so what an early experiment + + + align:start position:0% +baculovirus so what an early experiment +was done to ask what is the genetic + + align:start position:0% +was done to ask what is the genetic + + + align:start position:0% +was done to ask what is the genetic +material that transfers the information + + align:start position:0% +material that transfers the information + + + align:start position:0% +material that transfers the information +from the baculovirus to the to the + + align:start position:0% +from the baculovirus to the to the + + + align:start position:0% +from the baculovirus to the to the +bacterial cell in order to make more + + align:start position:0% +bacterial cell in order to make more + + + align:start position:0% +bacterial cell in order to make more +baculovirus right so they were able to + + align:start position:0% +baculovirus right so they were able to + + + align:start position:0% +baculovirus right so they were able to +demonstrate in this Hershey and chase + + align:start position:0% +demonstrate in this Hershey and chase + + + align:start position:0% +demonstrate in this Hershey and chase +experiment that you could raise + + align:start position:0% +experiment that you could raise + + + align:start position:0% +experiment that you could raise +you labor you could label protein and + + align:start position:0% +you labor you could label protein and + + + align:start position:0% +you labor you could label protein and +DNA with particular isotopes and find + + align:start position:0% +DNA with particular isotopes and find + + + align:start position:0% +DNA with particular isotopes and find +out what part of the baculovirus was + + align:start position:0% +out what part of the baculovirus was + + + align:start position:0% +out what part of the baculovirus was +important for transferring information + + align:start position:0% +important for transferring information + + + align:start position:0% +important for transferring information +for the production of new baculovirus so + + align:start position:0% +for the production of new baculovirus so + + + align:start position:0% +for the production of new baculovirus so +they wanted to label the capsid protein + + align:start position:0% +they wanted to label the capsid protein + + + align:start position:0% +they wanted to label the capsid protein +so the proteinaceous material that's on + + align:start position:0% +so the proteinaceous material that's on + + + align:start position:0% +so the proteinaceous material that's on +that's on the outside of this lunar + + align:start position:0% +that's on the outside of this lunar + + + align:start position:0% +that's on the outside of this lunar +lander this is a baculovirus it's um + + align:start position:0% +lander this is a baculovirus it's um + + + align:start position:0% +lander this is a baculovirus it's um +it's sort of amazing how it looks so I + + align:start position:0% +it's sort of amazing how it looks so I + + + align:start position:0% +it's sort of amazing how it looks so I +wanted to label the protein but they + + align:start position:0% +wanted to label the protein but they + + + align:start position:0% +wanted to label the protein but they +also wanted to label the contents of the + + align:start position:0% +also wanted to label the contents of the + + + align:start position:0% +also wanted to label the contents of the +baculovirus the DNA with tracer Radio + + align:start position:0% +baculovirus the DNA with tracer Radio + + + align:start position:0% +baculovirus the DNA with tracer Radio +isotopes so what would be the best + + align:start position:0% +isotopes so what would be the best + + + align:start position:0% +isotopes so what would be the best +isotopes to use if you wanted to + + align:start position:0% +isotopes to use if you wanted to + + + align:start position:0% +isotopes to use if you wanted to +differentiate between protein and + + align:start position:0% +differentiate between protein and + + + align:start position:0% +differentiate between protein and +nucleic acid and what you want to think + + align:start position:0% +nucleic acid and what you want to think + + + align:start position:0% +nucleic acid and what you want to think +about is what does protein have that + + align:start position:0% +about is what does protein have that + + + align:start position:0% +about is what does protein have that +nucleic acids don't have and what the + + align:start position:0% +nucleic acids don't have and what the + + + align:start position:0% +nucleic acids don't have and what the +nucleic acids have the proteins don't + + align:start position:0% +nucleic acids have the proteins don't + + + align:start position:0% +nucleic acids have the proteins don't +have which which are the elements that + + align:start position:0% +have which which are the elements that + + + align:start position:0% +have which which are the elements that +are important for differentiating yeah + + align:start position:0% +are important for differentiating yeah + + + align:start position:0% +are important for differentiating yeah +over there yes phosphorus going do you + + align:start position:0% +over there yes phosphorus going do you + + + align:start position:0% +over there yes phosphorus going do you +want to give a little bit more of a with + + align:start position:0% + + + + align:start position:0% + +okay so the answer is we use phosphorus + + align:start position:0% +okay so the answer is we use phosphorus + + + align:start position:0% +okay so the answer is we use phosphorus +to label nucleic acids because that + + align:start position:0% +to label nucleic acids because that + + + align:start position:0% +to label nucleic acids because that +phosphodiester backbone it's rich in + + align:start position:0% +phosphodiester backbone it's rich in + + + align:start position:0% +phosphodiester backbone it's rich in +phosphorus there are a few phosphates in + + align:start position:0% +phosphorus there are a few phosphates in + + + align:start position:0% +phosphorus there are a few phosphates in +proteins but they're very transient + + align:start position:0% +proteins but they're very transient + + + align:start position:0% +proteins but they're very transient +they're part of signaling but the boat + + align:start position:0% +they're part of signaling but the boat + + + align:start position:0% +they're part of signaling but the boat +you know every nucleotide has phosphorus + + align:start position:0% +you know every nucleotide has phosphorus + + + align:start position:0% +you know every nucleotide has phosphorus +in every building block and then in + + align:start position:0% +in every building block and then in + + + align:start position:0% +in every building block and then in +proteins they have sulfur in them where + + align:start position:0% +proteins they have sulfur in them where + + + align:start position:0% +proteins they have sulfur in them where +nucleic acids do not and the sulfur is + + align:start position:0% +nucleic acids do not and the sulfur is + + + align:start position:0% +nucleic acids do not and the sulfur is +in two amino acids cysteine and + + align:start position:0% +in two amino acids cysteine and + + + align:start position:0% +in two amino acids cysteine and +methionine so you can use those two + + align:start position:0% +methionine so you can use those two + + + align:start position:0% +methionine so you can use those two +traces for the building blocks and the + + align:start position:0% +traces for the building blocks and the + + + align:start position:0% +traces for the building blocks and the +way the experiment works is if you've + + align:start position:0% +way the experiment works is if you've + + + align:start position:0% +way the experiment works is if you've +labeled the protein with sulfur you + + align:start position:0% +labeled the protein with sulfur you + + + align:start position:0% +labeled the protein with sulfur you +infect a cell the virus replicates and + + align:start position:0% +infect a cell the virus replicates and + + + align:start position:0% +infect a cell the virus replicates and +what you're gonna do is then centrifuge + + align:start position:0% +what you're gonna do is then centrifuge + + + align:start position:0% +what you're gonna do is then centrifuge +the bacterial cells to see what's in the + + align:start position:0% +the bacterial cells to see what's in the + + + align:start position:0% +the bacterial cells to see what's in the +cell and then you can alternatively + + align:start position:0% +cell and then you can alternatively + + + align:start position:0% +cell and then you can alternatively +label the DNA and in this case I've + + align:start position:0% +label the DNA and in this case I've + + + align:start position:0% +label the DNA and in this case I've +shown it as green but that would be the + + align:start position:0% +shown it as green but that would be the + + + align:start position:0% +shown it as green but that would be the +other isotope let it infect the cell and + + align:start position:0% +other isotope let it infect the cell and + + + align:start position:0% +other isotope let it infect the cell and +deposit its contents in the cell + + align:start position:0% +deposit its contents in the cell + + + align:start position:0% +deposit its contents in the cell +centrifuge the cells out and you want to + + align:start position:0% +centrifuge the cells out and you want to + + + align:start position:0% +centrifuge the cells out and you want to +know where the radioactivity is and the + + align:start position:0% +know where the radioactivity is and the + + + align:start position:0% +know where the radioactivity is and the +radioactivity is strictly associated + + align:start position:0% +radioactivity is strictly associated + + + align:start position:0% +radioactivity is strictly associated +with phosphorus-32 because the genetic + + align:start position:0% +with phosphorus-32 because the genetic + + + align:start position:0% +with phosphorus-32 because the genetic +material that coded for the production + + align:start position:0% +material that coded for the production + + + align:start position:0% +material that coded for the production +of new baculovirus is the thing that + + align:start position:0% +of new baculovirus is the thing that + + + align:start position:0% +of new baculovirus is the thing that +stays associated with the bacterial cell + + align:start position:0% +stays associated with the bacterial cell + + + align:start position:0% +stays associated with the bacterial cell +in contrast there's no radioactivity + + align:start position:0% +in contrast there's no radioactivity + + + align:start position:0% +in contrast there's no radioactivity +associated when you label the cells with + + align:start position:0% +associated when you label the cells with + + + align:start position:0% +associated when you label the cells with +s 35 all right nice experiment easy way + + align:start position:0% +s 35 all right nice experiment easy way + + + align:start position:0% +s 35 all right nice experiment easy way +to do it quite a rather a nice way to do + + align:start position:0% +to do it quite a rather a nice way to do + + + align:start position:0% +to do it quite a rather a nice way to do +it the other experiment I want to + + align:start position:0% +it the other experiment I want to + + + align:start position:0% +it the other experiment I want to +describe to you very briefly because it + + align:start position:0% +describe to you very briefly because it + + + align:start position:0% +describe to you very briefly because it +relies on centrifugation technology + + align:start position:0% +relies on centrifugation technology + + + align:start position:0% +relies on centrifugation technology +that's very powerful and it's a method + + align:start position:0% +that's very powerful and it's a method + + + align:start position:0% +that's very powerful and it's a method +that utilizes in 15 very very nicely + + align:start position:0% +that utilizes in 15 very very nicely + + + align:start position:0% +that utilizes in 15 very very nicely +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let me tell you about that experiment + + align:start position:0% +so let me tell you about that experiment + + + align:start position:0% +so let me tell you about that experiment +there are things in the laboratory that + + align:start position:0% +there are things in the laboratory that + + + align:start position:0% +there are things in the laboratory that +we use every day Ultra centrifuges and + + align:start position:0% +we use every day Ultra centrifuges and + + + align:start position:0% +we use every day Ultra centrifuges and +regular centrifuges that spin at a very + + align:start position:0% +regular centrifuges that spin at a very + + + align:start position:0% +regular centrifuges that spin at a very +fast speed where we can really + + align:start position:0% +fast speed where we can really + + + align:start position:0% +fast speed where we can really +differentiate things by molecular mass + + align:start position:0% +differentiate things by molecular mass + + + align:start position:0% +differentiate things by molecular mass +which relates to this the sedimentation + + align:start position:0% +which relates to this the sedimentation + + + align:start position:0% +which relates to this the sedimentation +coefficients how fast does the particle + + align:start position:0% +coefficients how fast does the particle + + + align:start position:0% +coefficients how fast does the particle +spin to the bottom of the tube when it's + + align:start position:0% +spin to the bottom of the tube when it's + + + align:start position:0% +spin to the bottom of the tube when it's +under high centrifugal force the heavier + + align:start position:0% +under high centrifugal force the heavier + + + align:start position:0% +under high centrifugal force the heavier +it is the faster it will spin so the + + align:start position:0% +it is the faster it will spin so the + + + align:start position:0% +it is the faster it will spin so the +question that came up very early on it + + align:start position:0% +question that came up very early on it + + + align:start position:0% +question that came up very early on it +looks like a nonsense question now + + align:start position:0% +looks like a nonsense question now + + + align:start position:0% +looks like a nonsense question now +because it looks so obvious that we + + align:start position:0% +because it looks so obvious that we + + + align:start position:0% +because it looks so obvious that we +replicate DNA the way we do but + + align:start position:0% +replicate DNA the way we do but + + + align:start position:0% +replicate DNA the way we do but +originally wasn't absolutely certain + + align:start position:0% +originally wasn't absolutely certain + + + align:start position:0% +originally wasn't absolutely certain +where the DNA was replicated through a + + align:start position:0% +where the DNA was replicated through a + + + align:start position:0% +where the DNA was replicated through a +semi conservative mechanism where the + + align:start position:0% +semi conservative mechanism where the + + + align:start position:0% +semi conservative mechanism where the +strands came apart and you made two + + align:start position:0% +strands came apart and you made two + + + align:start position:0% +strands came apart and you made two +copies a copy of each strand to make two + + align:start position:0% +copies a copy of each strand to make two + + + align:start position:0% +copies a copy of each strand to make two +identical daughter new double-stranded + + align:start position:0% +identical daughter new double-stranded + + + align:start position:0% +identical daughter new double-stranded +DNA + + align:start position:0% +DNA + + + align:start position:0% +DNA +alternatively could you have a mechanism + + align:start position:0% +alternatively could you have a mechanism + + + align:start position:0% +alternatively could you have a mechanism +that was quite conservative you kept + + align:start position:0% +that was quite conservative you kept + + + align:start position:0% +that was quite conservative you kept +your DNA and somehow you made a copy of + + align:start position:0% +your DNA and somehow you made a copy of + + + align:start position:0% +your DNA and somehow you made a copy of +it a little harder for me to understand + + align:start position:0% +it a little harder for me to understand + + + align:start position:0% +it a little harder for me to understand +so your two new strands one would look + + align:start position:0% +so your two new strands one would look + + + align:start position:0% +so your two new strands one would look +like the original one but one would be + + align:start position:0% +like the original one but one would be + + + align:start position:0% +like the original one but one would be +very different and they're all + + align:start position:0% +very different and they're all + + + align:start position:0% +very different and they're all +dispersive where you're just copying + + align:start position:0% +dispersive where you're just copying + + + align:start position:0% +dispersive where you're just copying +bits of the DNA and somehow reassembling + + align:start position:0% +bits of the DNA and somehow reassembling + + + align:start position:0% +bits of the DNA and somehow reassembling +this gigantic jigsaw puzzle + + align:start position:0% +this gigantic jigsaw puzzle + + + align:start position:0% +this gigantic jigsaw puzzle +the centrifugation experiment allowed + + align:start position:0% +the centrifugation experiment allowed + + + align:start position:0% +the centrifugation experiment allowed +people to absolutely in clearly state + + align:start position:0% +people to absolutely in clearly state + + + align:start position:0% +people to absolutely in clearly state +that the rep + + align:start position:0% +that the rep + + + align:start position:0% +that the rep +occasion is via a semiconservative + + align:start position:0% +occasion is via a semiconservative + + + align:start position:0% +occasion is via a semiconservative +process so let's walk through it and + + align:start position:0% +process so let's walk through it and + + + align:start position:0% +process so let's walk through it and +what was done is that the nucleotides + + align:start position:0% +what was done is that the nucleotides + + + align:start position:0% +what was done is that the nucleotides +within the DNA were all labeled with + + align:start position:0% +within the DNA were all labeled with + + + align:start position:0% +within the DNA were all labeled with +heavy nitrogen so for every nucleic acid + + align:start position:0% +heavy nitrogen so for every nucleic acid + + + align:start position:0% +heavy nitrogen so for every nucleic acid +let's say for example when there's an + + align:start position:0% +let's say for example when there's an + + + align:start position:0% +let's say for example when there's an +adenine in the backbone there are five + + align:start position:0% +adenine in the backbone there are five + + + align:start position:0% +adenine in the backbone there are five +nitrogen's so that would be five atomic + + align:start position:0% +nitrogen's so that would be five atomic + + + align:start position:0% +nitrogen's so that would be five atomic +mass units heavier the nitrogen 14 in + + align:start position:0% +mass units heavier the nitrogen 14 in + + + align:start position:0% +mass units heavier the nitrogen 14 in +that nuclear base and 15 nuclear base + + align:start position:0% +that nuclear base and 15 nuclear base + + + align:start position:0% +that nuclear base and 15 nuclear base +five mass units heavier than n 14 + + align:start position:0% +five mass units heavier than n 14 + + + align:start position:0% +five mass units heavier than n 14 +nuclear base makes sense to everybody + + align:start position:0% +nuclear base makes sense to everybody + + + align:start position:0% +nuclear base makes sense to everybody +all right so it's heavier by some amount + + align:start position:0% +all right so it's heavier by some amount + + + align:start position:0% +all right so it's heavier by some amount +it's not a massive amount but it's + + align:start position:0% +it's not a massive amount but it's + + + align:start position:0% +it's not a massive amount but it's +enough to differentiate in a + + align:start position:0% +enough to differentiate in a + + + align:start position:0% +enough to differentiate in a +centrifugation experiment so the + + align:start position:0% +centrifugation experiment so the + + + align:start position:0% +centrifugation experiment so the +bacteria will first grown up in heavy + + align:start position:0% +bacteria will first grown up in heavy + + + align:start position:0% +bacteria will first grown up in heavy +nitrogen so all of the DNA sediments at + + align:start position:0% +nitrogen so all of the DNA sediments at + + + align:start position:0% +nitrogen so all of the DNA sediments at +a certain rate and place and it's all + + align:start position:0% +a certain rate and place and it's all + + + align:start position:0% +a certain rate and place and it's all +gone in 15 in it so it's as heavy as it + + align:start position:0% +gone in 15 in it so it's as heavy as it + + + align:start position:0% +gone in 15 in it so it's as heavy as it +can said iment and then they let the + + align:start position:0% +can said iment and then they let the + + + align:start position:0% +can said iment and then they let the +bacteria replicate in the presence of n + + align:start position:0% +bacteria replicate in the presence of n + + + align:start position:0% +bacteria replicate in the presence of n +14 the lighter isotope of nitrogen and + + align:start position:0% +14 the lighter isotope of nitrogen and + + + align:start position:0% +14 the lighter isotope of nitrogen and +what one would anticipate to happen is + + align:start position:0% +what one would anticipate to happen is + + + align:start position:0% +what one would anticipate to happen is +whenever you replicate you peel apart + + align:start position:0% +whenever you replicate you peel apart + + + align:start position:0% +whenever you replicate you peel apart +the two heavy strands and each one pairs + + align:start position:0% +the two heavy strands and each one pairs + + + align:start position:0% +the two heavy strands and each one pairs +with a light strand okay so you now have + + align:start position:0% +with a light strand okay so you now have + + + align:start position:0% +with a light strand okay so you now have +two copies two new identical copies of + + align:start position:0% +two copies two new identical copies of + + + align:start position:0% +two copies two new identical copies of +DNA where half of the straf of this one + + align:start position:0% +DNA where half of the straf of this one + + + align:start position:0% +DNA where half of the straf of this one +strand has n 15 one strand has N 14 so + + align:start position:0% +strand has n 15 one strand has N 14 so + + + align:start position:0% +strand has n 15 one strand has N 14 so +it will sediment less quickly because it + + align:start position:0% +it will sediment less quickly because it + + + align:start position:0% +it will sediment less quickly because it +is of a different density a lighter + + align:start position:0% +is of a different density a lighter + + + align:start position:0% +is of a different density a lighter +density than the all N 15 so you would + + align:start position:0% +density than the all N 15 so you would + + + align:start position:0% +density than the all N 15 so you would +get an intermediate weight band in this + + align:start position:0% +get an intermediate weight band in this + + + align:start position:0% +get an intermediate weight band in this +centrifuge tube when you're sedimenting + + align:start position:0% +centrifuge tube when you're sedimenting + + + align:start position:0% +centrifuge tube when you're sedimenting +if you peel those two strands apart + + align:start position:0% +if you peel those two strands apart + + + align:start position:0% +if you peel those two strands apart +again you've got a heavy and a light if + + align:start position:0% +again you've got a heavy and a light if + + + align:start position:0% +again you've got a heavy and a light if +you're growing in in 14 the light will + + align:start position:0% +you're growing in in 14 the light will + + + align:start position:0% +you're growing in in 14 the light will +combine with another light that and + + align:start position:0% +combine with another light that and + + + align:start position:0% +combine with another light that and +there are two of those and then the + + align:start position:0% +there are two of those and then the + + + align:start position:0% +there are two of those and then the +heavy will combine with the light so + + align:start position:0% +heavy will combine with the light so + + + align:start position:0% +heavy will combine with the light so +you'll get new sedimentation where you + + align:start position:0% +you'll get new sedimentation where you + + + align:start position:0% +you'll get new sedimentation where you +still have a band that's the combination + + align:start position:0% +still have a band that's the combination + + + align:start position:0% +still have a band that's the combination +of the light and heavy but then you + + align:start position:0% +of the light and heavy but then you + + + align:start position:0% +of the light and heavy but then you +start having some material that is all + + align:start position:0% +start having some material that is all + + + align:start position:0% +start having some material that is all +of the light so this would be this cycle + + align:start position:0% +of the light so this would be this cycle + + + align:start position:0% +of the light so this would be this cycle +so two that are still light plus heavy + + align:start position:0% +so two that are still light plus heavy + + + align:start position:0% +so two that are still light plus heavy +and then two that + + align:start position:0% +and then two that + + + align:start position:0% +and then two that +Sibley light you keep on replicating and + + align:start position:0% +Sibley light you keep on replicating and + + + align:start position:0% +Sibley light you keep on replicating and +your keep on diluting the heavy does + + align:start position:0% +your keep on diluting the heavy does + + + align:start position:0% +your keep on diluting the heavy does +that experiment make sense it's kind of + + align:start position:0% +that experiment make sense it's kind of + + + align:start position:0% +that experiment make sense it's kind of +a cool experiment you can hardly believe + + align:start position:0% +a cool experiment you can hardly believe + + + align:start position:0% +a cool experiment you can hardly believe +it's feasible but the centrifugation + + align:start position:0% +it's feasible but the centrifugation + + + align:start position:0% +it's feasible but the centrifugation +ability to differentiate with these + + align:start position:0% +ability to differentiate with these + + + align:start position:0% +ability to differentiate with these +isotopes is really valuable + + align:start position:0% +isotopes is really valuable + + + align:start position:0% +isotopes is really valuable +so I just want to put in a plug for the + + align:start position:0% +so I just want to put in a plug for the + + + align:start position:0% +so I just want to put in a plug for the +use of isotopes obviously they're used + + align:start position:0% +use of isotopes obviously they're used + + + align:start position:0% +use of isotopes obviously they're used +in nuclear physics we use a lot of the + + align:start position:0% +in nuclear physics we use a lot of the + + + align:start position:0% +in nuclear physics we use a lot of the +radioactive isotopes for different + + align:start position:0% +radioactive isotopes for different + + + align:start position:0% +radioactive isotopes for different +reasons but in biology they are + + align:start position:0% +reasons but in biology they are + + + align:start position:0% +reasons but in biology they are +indispensable for some of these + + align:start position:0% +indispensable for some of these + + + align:start position:0% +indispensable for some of these +experiments and even to this day you can + + align:start position:0% +experiments and even to this day you can + + + align:start position:0% +experiments and even to this day you can +do things with isotopes you can't do + + align:start position:0% +do things with isotopes you can't do + + + align:start position:0% +do things with isotopes you can't do +with a lot of that you can't do by other + + align:start position:0% +with a lot of that you can't do by other + + + align:start position:0% +with a lot of that you can't do by other +experiments either the radioactive are + + align:start position:0% +experiments either the radioactive are + + + align:start position:0% +experiments either the radioactive are +heavy there's a great deal of work done + + align:start position:0% +heavy there's a great deal of work done + + + align:start position:0% +heavy there's a great deal of work done +nowadays in proteomics using mass + + align:start position:0% +nowadays in proteomics using mass + + + align:start position:0% +nowadays in proteomics using mass +spectrometry and heavy isotopes where + + align:start position:0% +spectrometry and heavy isotopes where + + + align:start position:0% +spectrometry and heavy isotopes where +you can really track where things go and + + align:start position:0% +you can really track where things go and + + + align:start position:0% +you can really track where things go and +treat cancer cells differently from + + align:start position:0% +treat cancer cells differently from + + + align:start position:0% +treat cancer cells differently from +healthy cells but actually track what's + + align:start position:0% +healthy cells but actually track what's + + + align:start position:0% +healthy cells but actually track what's +happening by putting heavy isotopes in + + align:start position:0% +happening by putting heavy isotopes in + + + align:start position:0% +happening by putting heavy isotopes in +one of the growing dishes of cells okay + + align:start position:0% + + + + align:start position:0% + +so I like both of those experiments a + + align:start position:0% +so I like both of those experiments a + + + align:start position:0% +so I like both of those experiments a +lot even though they're I would put them + + align:start position:0% +lot even though they're I would put them + + + align:start position:0% +lot even though they're I would put them +in the category of oldies but goodies + + align:start position:0% +in the category of oldies but goodies + + + align:start position:0% +in the category of oldies but goodies +all right now I've got some details over + + align:start position:0% +all right now I've got some details over + + + align:start position:0% +all right now I've got some details over +here that we've got some explaining to + + align:start position:0% +here that we've got some explaining to + + + align:start position:0% +here that we've got some explaining to +do + + align:start position:0% +do + + + align:start position:0% +do +as we move forward and I just want to + + align:start position:0% +as we move forward and I just want to + + + align:start position:0% +as we move forward and I just want to +first of all start with a couple of + + align:start position:0% +first of all start with a couple of + + + align:start position:0% +first of all start with a couple of +details that I want to highlight on this + + align:start position:0% +details that I want to highlight on this + + + align:start position:0% +details that I want to highlight on this +screen on this board rather first of all + + align:start position:0% +screen on this board rather first of all + + + align:start position:0% +screen on this board rather first of all +bacteria and so prokaryotes such as + + align:start position:0% +bacteria and so prokaryotes such as + + + align:start position:0% +bacteria and so prokaryotes such as +bacteria E coli and eukaryote such as + + align:start position:0% +bacteria E coli and eukaryote such as + + + align:start position:0% +bacteria E coli and eukaryote such as +human cells have some differences in + + align:start position:0% +human cells have some differences in + + + align:start position:0% +human cells have some differences in +their DNA so the size of the bacterial + + align:start position:0% +their DNA so the size of the bacterial + + + align:start position:0% +their DNA so the size of the bacterial +genome is about five million base pairs + + align:start position:0% +genome is about five million base pairs + + + align:start position:0% +genome is about five million base pairs +the size of the human genome is a foul + + align:start position:0% +the size of the human genome is a foul + + + align:start position:0% +the size of the human genome is a foul +not quite a thousand times bigger but + + align:start position:0% +not quite a thousand times bigger but + + + align:start position:0% +not quite a thousand times bigger but +really a good deal bigger the DNA in + + align:start position:0% +really a good deal bigger the DNA in + + + align:start position:0% +really a good deal bigger the DNA in +bacteria is circular whereas the DNA in + + align:start position:0% +bacteria is circular whereas the DNA in + + + align:start position:0% +bacteria is circular whereas the DNA in +eukaryotic cells is linear and it's + + align:start position:0% +eukaryotic cells is linear and it's + + + align:start position:0% +eukaryotic cells is linear and it's +actually in the formula you see all + + align:start position:0% +actually in the formula you see all + + + align:start position:0% +actually in the formula you see all +these little images where you see the + + align:start position:0% +these little images where you see the + + + align:start position:0% +these little images where you see the +pairs of chromosomes are sort of stuck + + align:start position:0% +pairs of chromosomes are sort of stuck + + + align:start position:0% +pairs of chromosomes are sort of stuck +together at the same + + align:start position:0% +together at the same + + + align:start position:0% +together at the same +and that's linear DNA from one end to + + align:start position:0% +and that's linear DNA from one end to + + + align:start position:0% +and that's linear DNA from one end to +the other in bacteria the DNA is + + align:start position:0% +the other in bacteria the DNA is + + + align:start position:0% +the other in bacteria the DNA is +circular so it doesn't have an end so + + align:start position:0% +circular so it doesn't have an end so + + + align:start position:0% +circular so it doesn't have an end so +they're different all right + + align:start position:0% +they're different all right + + + align:start position:0% +they're different all right +so replicating circular DNA is a little + + align:start position:0% +so replicating circular DNA is a little + + + align:start position:0% +so replicating circular DNA is a little +bit different from replicating linear + + align:start position:0% +bit different from replicating linear + + + align:start position:0% +bit different from replicating linear +DNA all right now in both cases the DNA + + align:start position:0% +DNA all right now in both cases the DNA + + + align:start position:0% +DNA all right now in both cases the DNA +has to be packaged up so it will fit in + + align:start position:0% +has to be packaged up so it will fit in + + + align:start position:0% +has to be packaged up so it will fit in +the cell otherwise it's just too much of + + align:start position:0% +the cell otherwise it's just too much of + + + align:start position:0% +the cell otherwise it's just too much of +a disordered thing in the case of + + align:start position:0% +a disordered thing in the case of + + + align:start position:0% +a disordered thing in the case of +bacteria the circular DNA is wrapped up + + align:start position:0% +bacteria the circular DNA is wrapped up + + + align:start position:0% +bacteria the circular DNA is wrapped up +and super coiled with what are known as + + align:start position:0% +and super coiled with what are known as + + + align:start position:0% +and super coiled with what are known as +poly amines compounds that are very + + align:start position:0% +poly amines compounds that are very + + + align:start position:0% +poly amines compounds that are very +positively charged to neutralize all + + align:start position:0% +positively charged to neutralize all + + + align:start position:0% +positively charged to neutralize all +that negative charge in the DNA okay and + + align:start position:0% +that negative charge in the DNA okay and + + + align:start position:0% +that negative charge in the DNA okay and +in man and other eukaryotes the + + align:start position:0% +in man and other eukaryotes the + + + align:start position:0% +in man and other eukaryotes the +chromosomes are wrapped around very very + + align:start position:0% +chromosomes are wrapped around very very + + + align:start position:0% +chromosomes are wrapped around very very +positively charged proteins known as + + align:start position:0% +positively charged proteins known as + + + align:start position:0% +positively charged proteins known as +histones they're similar principles but + + align:start position:0% +histones they're similar principles but + + + align:start position:0% +histones they're similar principles but +they're different entities okay so when + + align:start position:0% +they're different entities okay so when + + + align:start position:0% +they're different entities okay so when +we start talking about replication of a + + align:start position:0% +we start talking about replication of a + + + align:start position:0% +we start talking about replication of a +prokaryotic cell here's the typical + + align:start position:0% +prokaryotic cell here's the typical + + + align:start position:0% +prokaryotic cell here's the typical +circular DNA so you can see the + + align:start position:0% +circular DNA so you can see the + + + align:start position:0% +circular DNA so you can see the +double-stranded DNA and I've put a + + align:start position:0% +double-stranded DNA and I've put a + + + align:start position:0% +double-stranded DNA and I've put a +little psy symbol here that I said that + + align:start position:0% +little psy symbol here that I said that + + + align:start position:0% +little psy symbol here that I said that +I call the Ori + + align:start position:0% + + + + align:start position:0% + +so that's origin of initiation so that + + align:start position:0% +so that's origin of initiation so that + + + align:start position:0% +so that's origin of initiation so that +is the place where you start copying + + align:start position:0% +is the place where you start copying + + + align:start position:0% +is the place where you start copying +your DNA and we're going to talk about + + align:start position:0% +your DNA and we're going to talk about + + + align:start position:0% +your DNA and we're going to talk about +how to spot these places in genomes in a + + align:start position:0% +how to spot these places in genomes in a + + + align:start position:0% +how to spot these places in genomes in a +moment and so the bacterial genome is + + align:start position:0% +moment and so the bacterial genome is + + + align:start position:0% +moment and so the bacterial genome is +copied bi-directionally so you can go in + + align:start position:0% +copied bi-directionally so you can go in + + + align:start position:0% +copied bi-directionally so you can go in +both directions copying you know in the + + align:start position:0% +both directions copying you know in the + + + align:start position:0% +both directions copying you know in the +appropriate direction we'll talk about + + align:start position:0% +appropriate direction we'll talk about + + + align:start position:0% +appropriate direction we'll talk about +that in a moment to make the entire + + align:start position:0% +that in a moment to make the entire + + + align:start position:0% +that in a moment to make the entire +circular DNA and a perfect copy of the + + align:start position:0% +circular DNA and a perfect copy of the + + + align:start position:0% +circular DNA and a perfect copy of the +DNA with bi-directional copying and + + align:start position:0% +DNA with bi-directional copying and + + + align:start position:0% +DNA with bi-directional copying and +that's not bad for small genomes because + + align:start position:0% +that's not bad for small genomes because + + + align:start position:0% +that's not bad for small genomes because +you've only got one origin of + + align:start position:0% +you've only got one origin of + + + align:start position:0% +you've only got one origin of +replication you've got to get all the + + align:start position:0% +replication you've got to get all the + + + align:start position:0% +replication you've got to get all the +way around the circular DNA all right + + align:start position:0% +way around the circular DNA all right + + + align:start position:0% +way around the circular DNA all right +it's quite a bit smaller than the human + + align:start position:0% +it's quite a bit smaller than the human + + + align:start position:0% +it's quite a bit smaller than the human +one but what you what do you do with + + align:start position:0% +one but what you what do you do with + + + align:start position:0% +one but what you what do you do with +gigantic genomes such as the one that's + + align:start position:0% +gigantic genomes such as the one that's + + + align:start position:0% +gigantic genomes such as the one that's +about you know + + align:start position:0% +about you know + + + align:start position:0% +about you know +thousand times bigger than the bacterial + + align:start position:0% +thousand times bigger than the bacterial + + + align:start position:0% +thousand times bigger than the bacterial +one how do you manage to still catalyze + + align:start position:0% +one how do you manage to still catalyze + + + align:start position:0% +one how do you manage to still catalyze +the replication of the entire genome + + align:start position:0% +the replication of the entire genome + + + align:start position:0% +the replication of the entire genome +quickly enough to make the copy of DNA + + align:start position:0% +quickly enough to make the copy of DNA + + + align:start position:0% +quickly enough to make the copy of DNA +in some reasonable amount of time and + + align:start position:0% +in some reasonable amount of time and + + + align:start position:0% +in some reasonable amount of time and +that is taken into taking also into + + align:start position:0% +that is taken into taking also into + + + align:start position:0% +that is taken into taking also into +consideration that the speed of + + align:start position:0% +consideration that the speed of + + + align:start position:0% +consideration that the speed of +bacterial replication is a thousand base + + align:start position:0% +bacterial replication is a thousand base + + + align:start position:0% +bacterial replication is a thousand base +pairs per second pretty impressive + + align:start position:0% +pairs per second pretty impressive + + + align:start position:0% +pairs per second pretty impressive +thousand of those bonds made every + + align:start position:0% +thousand of those bonds made every + + + align:start position:0% +thousand of those bonds made every +second + + align:start position:0% +second + + + align:start position:0% +second +whereas in eukaryotes it's somewhere + + align:start position:0% +whereas in eukaryotes it's somewhere + + + align:start position:0% +whereas in eukaryotes it's somewhere +down from 50 base pairs per second + + align:start position:0% +down from 50 base pairs per second + + + align:start position:0% +down from 50 base pairs per second +depending on conditions their numbers + + align:start position:0% +depending on conditions their numbers + + + align:start position:0% +depending on conditions their numbers +these are not very explicit numbers + + align:start position:0% +these are not very explicit numbers + + + align:start position:0% +these are not very explicit numbers +there's a little bit of variability so + + align:start position:0% +there's a little bit of variability so + + + align:start position:0% +there's a little bit of variability so +how would you do it if you had to if you + + align:start position:0% +how would you do it if you had to if you + + + align:start position:0% +how would you do it if you had to if you +had this massive chunk of gene and + + align:start position:0% +had this massive chunk of gene and + + + align:start position:0% +had this massive chunk of gene and +you've got a copy it just really pretty + + align:start position:0% +you've got a copy it just really pretty + + + align:start position:0% +you've got a copy it just really pretty +quickly in order to turnover replicate + + align:start position:0% +quickly in order to turnover replicate + + + align:start position:0% +quickly in order to turnover replicate +an entire cell contents in 8 hours what + + align:start position:0% +an entire cell contents in 8 hours what + + + align:start position:0% +an entire cell contents in 8 hours what +would you do how could you expect things + + align:start position:0% +would you do how could you expect things + + + align:start position:0% +would you do how could you expect things +yeah yes so the answer here is starting + + align:start position:0% +yeah yes so the answer here is starting + + + align:start position:0% +yeah yes so the answer here is starting +a lot of different places so there's a + + align:start position:0% +a lot of different places so there's a + + + align:start position:0% +a lot of different places so there's a +lot of collaborative work going on all + + align:start position:0% +lot of collaborative work going on all + + + align:start position:0% +lot of collaborative work going on all +along that large genome and so when the + + align:start position:0% +along that large genome and so when the + + + align:start position:0% +along that large genome and so when the +the replication of the long linear + + align:start position:0% +the replication of the long linear + + + align:start position:0% +the replication of the long linear +chromosomes that are in eukaryotic cells + + align:start position:0% +chromosomes that are in eukaryotic cells + + + align:start position:0% +chromosomes that are in eukaryotic cells +you end up with just a lot of origins of + + align:start position:0% +you end up with just a lot of origins of + + + align:start position:0% +you end up with just a lot of origins of +replication so you're basically starting + + align:start position:0% +replication so you're basically starting + + + align:start position:0% +replication so you're basically starting +all over the place so you can get the + + align:start position:0% +all over the place so you can get the + + + align:start position:0% +all over the place so you can get the +job done quickly enough for it to make + + align:start position:0% +job done quickly enough for it to make + + + align:start position:0% +job done quickly enough for it to make +sense does that make sense to everybody + + align:start position:0% +sense does that make sense to everybody + + + align:start position:0% +sense does that make sense to everybody +so starting a lot of places it's a + + align:start position:0% +so starting a lot of places it's a + + + align:start position:0% +so starting a lot of places it's a +pretty easy thing all right now I + + align:start position:0% +pretty easy thing all right now I + + + align:start position:0% +pretty easy thing all right now I +mentioned very briefly that when just + + align:start position:0% +mentioned very briefly that when just + + + align:start position:0% +mentioned very briefly that when just +before you can copy DNA you have to + + align:start position:0% +before you can copy DNA you have to + + + align:start position:0% +before you can copy DNA you have to +unpack it now we've got a lot of we + + align:start position:0% +unpack it now we've got a lot of we + + + align:start position:0% +unpack it now we've got a lot of we +think a lot about packaging DNA less + + align:start position:0% +think a lot about packaging DNA less + + + align:start position:0% +think a lot about packaging DNA less +about unpacking it but that's so I've + + align:start position:0% +about unpacking it but that's so I've + + + align:start position:0% +about unpacking it but that's so I've +got these pictures sort of in a reverse + + align:start position:0% +got these pictures sort of in a reverse + + + align:start position:0% +got these pictures sort of in a reverse +direction so it's only this form of DNA + + align:start position:0% +direction so it's only this form of DNA + + + align:start position:0% +direction so it's only this form of DNA +stretched out that can be copied whereas + + align:start position:0% +stretched out that can be copied whereas + + + align:start position:0% +stretched out that can be copied whereas +the DNA in your cells is bundled up very + + align:start position:0% +the DNA in your cells is bundled up very + + + align:start position:0% +the DNA in your cells is bundled up very +tightly into chromosomes how are they + + align:start position:0% +tightly into chromosomes how are they + + + align:start position:0% +tightly into chromosomes how are they +put together those chromosomes are made + + align:start position:0% +put together those chromosomes are made + + + align:start position:0% +put together those chromosomes are made +up of chromatin which is a bunch of + + align:start position:0% +up of chromatin which is a bunch of + + + align:start position:0% +up of chromatin which is a bunch of +balls which are histone protein + + align:start position:0% +balls which are histone protein + + + align:start position:0% +balls which are histone protein +with DNA wrapped around them + + align:start position:0% +with DNA wrapped around them + + + align:start position:0% +with DNA wrapped around them +chromatin that's compact chromatin oh + + align:start position:0% +chromatin that's compact chromatin oh + + + align:start position:0% +chromatin that's compact chromatin oh +sorry sorry ice whoops we go back not to + + align:start position:0% +sorry sorry ice whoops we go back not to + + + align:start position:0% +sorry sorry ice whoops we go back not to +go forwards so this is chromatin in a + + align:start position:0% +go forwards so this is chromatin in a + + + align:start position:0% +go forwards so this is chromatin in a +compact form + + align:start position:0% +compact form + + + align:start position:0% +compact form +this is chromatin now unraveled they + + align:start position:0% +this is chromatin now unraveled they + + + align:start position:0% +this is chromatin now unraveled they +look more like beads on a string DNA + + align:start position:0% +look more like beads on a string DNA + + + align:start position:0% +look more like beads on a string DNA +wrapped around each histone protein to + + align:start position:0% +wrapped around each histone protein to + + + align:start position:0% +wrapped around each histone protein to +form those nucleus own structures and + + align:start position:0% +form those nucleus own structures and + + + align:start position:0% +form those nucleus own structures and +then each nucleus own looks like this + + align:start position:0% +then each nucleus own looks like this + + + align:start position:0% +then each nucleus own looks like this +it's got a protein in the middle and DNA + + align:start position:0% +it's got a protein in the middle and DNA + + + align:start position:0% +it's got a protein in the middle and DNA +wrapped around it so in order to go + + align:start position:0% +wrapped around it so in order to go + + + align:start position:0% +wrapped around it so in order to go +forward and replicate we have to + + align:start position:0% +forward and replicate we have to + + + align:start position:0% +forward and replicate we have to +unpackage DNA there are lots of signals + + align:start position:0% +unpackage DNA there are lots of signals + + + align:start position:0% +unpackage DNA there are lots of signals +to unpackage the DNA that we will talk + + align:start position:0% +to unpackage the DNA that we will talk + + + align:start position:0% +to unpackage the DNA that we will talk +about later the nucleosomes look like + + align:start position:0% +about later the nucleosomes look like + + + align:start position:0% +about later the nucleosomes look like +this so you can see you can trace the + + align:start position:0% +this so you can see you can trace the + + + align:start position:0% +this so you can see you can trace the +DNA and the proteins bundled in the + + align:start position:0% +DNA and the proteins bundled in the + + + align:start position:0% +DNA and the proteins bundled in the +middle and if we have time at the end I + + align:start position:0% +middle and if we have time at the end I + + + align:start position:0% +middle and if we have time at the end I +will show you the video of the packaging + + align:start position:0% +will show you the video of the packaging + + + align:start position:0% +will show you the video of the packaging +of DNA and the video of the replication + + align:start position:0% +of DNA and the video of the replication + + + align:start position:0% +of DNA and the video of the replication +of DNA there about a minute and a half + + align:start position:0% +of DNA there about a minute and a half + + + align:start position:0% +of DNA there about a minute and a half +each so it's not a whole bunch later on + + align:start position:0% +each so it's not a whole bunch later on + + + align:start position:0% +each so it's not a whole bunch later on +we will talk about what happens when you + + align:start position:0% +we will talk about what happens when you + + + align:start position:0% +we will talk about what happens when you +make that there is a determination that + + align:start position:0% +make that there is a determination that + + + align:start position:0% +make that there is a determination that +a cell needs to replicate its genome a + + align:start position:0% +a cell needs to replicate its genome a + + + align:start position:0% +a cell needs to replicate its genome a +bunch of things have to happen a signals + + align:start position:0% +bunch of things have to happen a signals + + + align:start position:0% +bunch of things have to happen a signals +to do the unwrapping and one of those + + align:start position:0% +to do the unwrapping and one of those + + + align:start position:0% +to do the unwrapping and one of those +things is actually to alter the charged + + align:start position:0% +things is actually to alter the charged + + + align:start position:0% +things is actually to alter the charged +state of the histone proteins so you + + align:start position:0% +state of the histone proteins so you + + + align:start position:0% +state of the histone proteins so you +neutralize the positive charges so the + + align:start position:0% +neutralize the positive charges so the + + + align:start position:0% +neutralize the positive charges so the +DNA can unravel for it it makes sense + + align:start position:0% +DNA can unravel for it it makes sense + + + align:start position:0% +DNA can unravel for it it makes sense +it's still just a plain old + + align:start position:0% +it's still just a plain old + + + align:start position:0% +it's still just a plain old +electrostatic interaction so the + + align:start position:0% +electrostatic interaction so the + + + align:start position:0% +electrostatic interaction so the +synthesis of DNA is what's known as + + align:start position:0% +synthesis of DNA is what's known as + + + align:start position:0% +synthesis of DNA is what's known as +template driven polymerization + + align:start position:0% + + + + align:start position:0% + +okay so template driven deer + + align:start position:0% +okay so template driven deer + + + align:start position:0% +okay so template driven deer +polymerization you get a sense of + + align:start position:0% +polymerization you get a sense of + + + align:start position:0% +polymerization you get a sense of +exactly what that means we know the two + + align:start position:0% +exactly what that means we know the two + + + align:start position:0% +exactly what that means we know the two +strands are complementary and we're + + align:start position:0% +strands are complementary and we're + + + align:start position:0% +strands are complementary and we're +gonna use one strand as the code to make + + align:start position:0% +gonna use one strand as the code to make + + + align:start position:0% +gonna use one strand as the code to make +a new complementary strand so when we're + + align:start position:0% +a new complementary strand so when we're + + + align:start position:0% +a new complementary strand so when we're +making DNA we have one strand there + + align:start position:0% +making DNA we have one strand there + + + align:start position:0% +making DNA we have one strand there +that's the what's known as the template + + align:start position:0% +that's the what's known as the template + + + align:start position:0% +that's the what's known as the template +strand I want to make a complimentary + + align:start position:0% +strand I want to make a complimentary + + + align:start position:0% +strand I want to make a complimentary +copy of that strand + + align:start position:0% +copy of that strand + + + align:start position:0% +copy of that strand +so what I'm gonna do what the DNA + + align:start position:0% +so what I'm gonna do what the DNA + + + align:start position:0% +so what I'm gonna do what the DNA +polymerase is gonna do is systematically + + align:start position:0% +polymerase is gonna do is systematically + + + align:start position:0% +polymerase is gonna do is systematically +add bases + + align:start position:0% +add bases + + + align:start position:0% +add bases +sorry add nucleotides to the 3-prime Oh + + align:start position:0% +sorry add nucleotides to the 3-prime Oh + + + align:start position:0% +sorry add nucleotides to the 3-prime Oh +H of the ribose and then you keep + + align:start position:0% +H of the ribose and then you keep + + + align:start position:0% +H of the ribose and then you keep +growing but the base that gets put in is + + align:start position:0% +growing but the base that gets put in is + + + align:start position:0% +growing but the base that gets put in is +the one that's complementary to the base + + align:start position:0% +the one that's complementary to the base + + + align:start position:0% +the one that's complementary to the base +on the template strand so if it's I mean + + align:start position:0% +on the template strand so if it's I mean + + + align:start position:0% +on the template strand so if it's I mean +on the template strand its adenine + + align:start position:0% +on the template strand its adenine + + + align:start position:0% +on the template strand its adenine +puttin on the new strand and so on all + + align:start position:0% +puttin on the new strand and so on all + + + align:start position:0% +puttin on the new strand and so on all +right and just to get these numbers + + align:start position:0% +right and just to get these numbers + + + align:start position:0% +right and just to get these numbers +again the new strand is grown from 5 + + align:start position:0% +again the new strand is grown from 5 + + + align:start position:0% +again the new strand is grown from 5 +prime to 3 prime the old strand is red 3 + + align:start position:0% +prime to 3 prime the old strand is red 3 + + + align:start position:0% +prime to 3 prime the old strand is red 3 +prime to 5 prime so you're reading a + + align:start position:0% +prime to 5 prime so you're reading a + + + align:start position:0% +prime to 5 prime so you're reading a +strand and you're reading it's 3 to 5 + + align:start position:0% +strand and you're reading it's 3 to 5 + + + align:start position:0% +strand and you're reading it's 3 to 5 +and you're making 5 to 3 that's how you + + align:start position:0% +and you're making 5 to 3 that's how you + + + align:start position:0% +and you're making 5 to 3 that's how you +end up with complementary antiparallel + + align:start position:0% +end up with complementary antiparallel + + + align:start position:0% +end up with complementary antiparallel +strands all right ok with that + + align:start position:0% +strands all right ok with that + + + align:start position:0% +strands all right ok with that +everyone alright and when you form the + + align:start position:0% +everyone alright and when you form the + + + align:start position:0% +everyone alright and when you form the +bond you go in with nucleoside + + align:start position:0% +bond you go in with nucleoside + + + align:start position:0% +bond you go in with nucleoside +triphosphates you form a new phosphate + + align:start position:0% +triphosphates you form a new phosphate + + + align:start position:0% +triphosphates you form a new phosphate +diaster were just one of those + + align:start position:0% +diaster were just one of those + + + align:start position:0% +diaster were just one of those +phosphorous --is and you kick out + + align:start position:0% +phosphorous --is and you kick out + + + align:start position:0% +phosphorous --is and you kick out +phosphate phosphate which we would call + + align:start position:0% +phosphate phosphate which we would call + + + align:start position:0% +phosphate phosphate which we would call +pyrophosphate or diphosphate ok so here + + align:start position:0% +pyrophosphate or diphosphate ok so here + + + align:start position:0% +pyrophosphate or diphosphate ok so here +you could just sort of see just check + + align:start position:0% +you could just sort of see just check + + + align:start position:0% +you could just sort of see just check +what you think you know what you're + + align:start position:0% +what you think you know what you're + + + align:start position:0% +what you think you know what you're +doing I'm gonna just say it's this is + + align:start position:0% +doing I'm gonna just say it's this is + + + align:start position:0% +doing I'm gonna just say it's this is +really a pretty simple thing we're gonna + + align:start position:0% +really a pretty simple thing we're gonna + + + align:start position:0% +really a pretty simple thing we're gonna +put in a T then we're gonna put in an A + + align:start position:0% +put in a T then we're gonna put in an A + + + align:start position:0% +put in a T then we're gonna put in an A +then we're gonna put in a see because + + align:start position:0% +then we're gonna put in a see because + + + align:start position:0% +then we're gonna put in a see because +our template is telling us to put in the + + align:start position:0% +our template is telling us to put in the + + + align:start position:0% +our template is telling us to put in the +appropriate purine or pyrimidine that + + align:start position:0% +appropriate purine or pyrimidine that + + + align:start position:0% +appropriate purine or pyrimidine that +forms a nice base pair with that so + + align:start position:0% +forms a nice base pair with that so + + + align:start position:0% +forms a nice base pair with that so +there's a question here but that's I've + + align:start position:0% +there's a question here but that's I've + + + align:start position:0% +there's a question here but that's I've +already given you the answer to it so it + + align:start position:0% +already given you the answer to it so it + + + align:start position:0% +already given you the answer to it so it +should be very straightforward for you + + align:start position:0% +should be very straightforward for you + + + align:start position:0% +should be very straightforward for you +to look at a template strand and decide + + align:start position:0% +to look at a template strand and decide + + + align:start position:0% +to look at a template strand and decide +what would be on the complementary + + align:start position:0% +what would be on the complementary + + + align:start position:0% +what would be on the complementary +strand and also decide on the + + align:start position:0% +strand and also decide on the + + + align:start position:0% +strand and also decide on the +directionality of the complementary + + align:start position:0% +directionality of the complementary + + + align:start position:0% +directionality of the complementary +strand all right now origins of + + align:start position:0% +strand all right now origins of + + + align:start position:0% +strand all right now origins of +replication what do they look like we're + + align:start position:0% +replication what do they look like we're + + + align:start position:0% +replication what do they look like we're +in that big weird where is the old where + + align:start position:0% +in that big weird where is the old where + + + align:start position:0% +in that big weird where is the old where +do I start problem where do I start + + align:start position:0% +do I start problem where do I start + + + align:start position:0% +do I start problem where do I start +what's the best place to start someone + + align:start position:0% +what's the best place to start someone + + + align:start position:0% +what's the best place to start someone +not you not you anyone else want to + + align:start position:0% +not you not you anyone else want to + + + align:start position:0% +not you not you anyone else want to +answer here where I've got this whole + + align:start position:0% +answer here where I've got this whole + + + align:start position:0% +answer here where I've got this whole +genome I gotta get going I got to stop + + align:start position:0% +genome I gotta get going I got to stop + + + align:start position:0% +genome I gotta get going I got to stop +me + + align:start position:0% +me + + + align:start position:0% +me +copy of it where was the best place to + + align:start position:0% +copy of it where was the best place to + + + align:start position:0% +copy of it where was the best place to +break into it to start making copies + + align:start position:0% +break into it to start making copies + + + align:start position:0% +break into it to start making copies +yeah correct it's simple it's the + + align:start position:0% +yeah correct it's simple it's the + + + align:start position:0% +yeah correct it's simple it's the +difference between two and three if you + + align:start position:0% +difference between two and three if you + + + align:start position:0% +difference between two and three if you +go to the area where there's lots of G's + + align:start position:0% +go to the area where there's lots of G's + + + align:start position:0% +go to the area where there's lots of G's +and sees every GC has three hydrogen + + align:start position:0% +and sees every GC has three hydrogen + + + align:start position:0% +and sees every GC has three hydrogen +bonds if you go to a different area + + align:start position:0% +bonds if you go to a different area + + + align:start position:0% +bonds if you go to a different area +where there happened to be a lot of A's + + align:start position:0% +where there happened to be a lot of A's + + + align:start position:0% +where there happened to be a lot of A's +and T's in a row each pair is only worth + + align:start position:0% +and T's in a row each pair is only worth + + + align:start position:0% +and T's in a row each pair is only worth +two hydrogen bonds you're gonna pick the + + align:start position:0% +two hydrogen bonds you're gonna pick the + + + align:start position:0% +two hydrogen bonds you're gonna pick the +stretch that has the most days and T's + + align:start position:0% +stretch that has the most days and T's + + + align:start position:0% +stretch that has the most days and T's +because it's the place where the base + + align:start position:0% +because it's the place where the base + + + align:start position:0% +because it's the place where the base +pairing is weaker and it's a it's + + align:start position:0% +pairing is weaker and it's a it's + + + align:start position:0% +pairing is weaker and it's a it's +actually a very simple concept so it + + align:start position:0% +actually a very simple concept so it + + + align:start position:0% +actually a very simple concept so it +would be the 8e rich region is the place + + align:start position:0% +would be the 8e rich region is the place + + + align:start position:0% +would be the 8e rich region is the place +where origins of replication and the + + align:start position:0% +where origins of replication and the + + + align:start position:0% +where origins of replication and the +predominant okay so what we're gonna do + + align:start position:0% +predominant okay so what we're gonna do + + + align:start position:0% +predominant okay so what we're gonna do +now and this is going to be tricky but + + align:start position:0% +now and this is going to be tricky but + + + align:start position:0% +now and this is going to be tricky but +I'm gonna make this work is we're gonna + + align:start position:0% +I'm gonna make this work is we're gonna + + + align:start position:0% +I'm gonna make this work is we're gonna +talk about replicating an entire chunk + + align:start position:0% +talk about replicating an entire chunk + + + align:start position:0% +talk about replicating an entire chunk +of gene and what I've done here is I put + + align:start position:0% +of gene and what I've done here is I put + + + align:start position:0% +of gene and what I've done here is I put +the pieces that we're gonna discuss over + + align:start position:0% +the pieces that we're gonna discuss over + + + align:start position:0% +the pieces that we're gonna discuss over +here + + align:start position:0% +here + + + align:start position:0% +here +that's my menu and we're gonna work + + align:start position:0% +that's my menu and we're gonna work + + + align:start position:0% +that's my menu and we're gonna work +through what we need to copy a large + + align:start position:0% +through what we need to copy a large + + + align:start position:0% +through what we need to copy a large +chunk of DNA all right everybody with me + + align:start position:0% +chunk of DNA all right everybody with me + + + align:start position:0% +chunk of DNA all right everybody with me +so I redrew this this morning I promised + + align:start position:0% +so I redrew this this morning I promised + + + align:start position:0% +so I redrew this this morning I promised +myself I'm gonna be super tidy on this + + align:start position:0% +myself I'm gonna be super tidy on this + + + align:start position:0% +myself I'm gonna be super tidy on this +blackboard which is a far stretch from + + align:start position:0% +blackboard which is a far stretch from + + + align:start position:0% +blackboard which is a far stretch from +me + + align:start position:0% +me + + + align:start position:0% +me +so replication we know where replication + + align:start position:0% +so replication we know where replication + + + align:start position:0% +so replication we know where replication +starts a tea rich region we could pick + + align:start position:0% +starts a tea rich region we could pick + + + align:start position:0% +starts a tea rich region we could pick +those out in the genome we know that + + align:start position:0% +those out in the genome we know that + + + align:start position:0% +those out in the genome we know that +we've got to unwind the DNA to make a + + align:start position:0% +we've got to unwind the DNA to make a + + + align:start position:0% +we've got to unwind the DNA to make a +copy of it so we must have had to unwrap + + align:start position:0% +copy of it so we must have had to unwrap + + + align:start position:0% +copy of it so we must have had to unwrap +the DNA beforehand these are all known + + align:start position:0% +the DNA beforehand these are all known + + + align:start position:0% +the DNA beforehand these are all known +things so let's now take a look at + + align:start position:0% +things so let's now take a look at + + + align:start position:0% +things so let's now take a look at +double-stranded DNA and try and figure + + align:start position:0% +double-stranded DNA and try and figure + + + align:start position:0% +double-stranded DNA and try and figure +out how we use all the components such + + align:start position:0% +out how we use all the components such + + + align:start position:0% +out how we use all the components such +I'm going to bring this board down + + align:start position:0% +I'm going to bring this board down + + + align:start position:0% +I'm going to bring this board down +because I don't see it as well up there + + align:start position:0% +because I don't see it as well up there + + + align:start position:0% +because I don't see it as well up there +how do we make use of all these + + align:start position:0% +how do we make use of all these + + + align:start position:0% +how do we make use of all these +components that are part of the menu + + align:start position:0% +components that are part of the menu + + + align:start position:0% +components that are part of the menu +that we need to make the new strand of + + align:start position:0% +that we need to make the new strand of + + + align:start position:0% +that we need to make the new strand of +DNA so we have double stranded DNA + + align:start position:0% + + + + align:start position:0% + +and there are base pairs across so + + align:start position:0% +and there are base pairs across so + + + align:start position:0% +and there are base pairs across so +that's typical double-stranded DNA + + align:start position:0% +that's typical double-stranded DNA + + + align:start position:0% +that's typical double-stranded DNA +that's what we're starting from + + align:start position:0% +that's what we're starting from + + + align:start position:0% +that's what we're starting from +unwrapped I haven't made it helical + + align:start position:0% +unwrapped I haven't made it helical + + + align:start position:0% +unwrapped I haven't made it helical +because my Gila C's will get messy and + + align:start position:0% +because my Gila C's will get messy and + + + align:start position:0% +because my Gila C's will get messy and +so we need to start so what the first + + align:start position:0% +so we need to start so what the first + + + align:start position:0% +so we need to start so what the first +thing that will happen is that the the + + align:start position:0% +thing that will happen is that the the + + + align:start position:0% +thing that will happen is that the the +important enzymes like the helicase will + + align:start position:0% +important enzymes like the helicase will + + + align:start position:0% +important enzymes like the helicase will +scan to find an origin of replication so + + align:start position:0% +scan to find an origin of replication so + + + align:start position:0% +scan to find an origin of replication so +somewhere for the for the process to + + align:start position:0% +somewhere for the for the process to + + + align:start position:0% +somewhere for the for the process to +start cuz that's where they're gonna + + align:start position:0% +start cuz that's where they're gonna + + + align:start position:0% +start cuz that's where they're gonna +break in so David one of your TAS works + + align:start position:0% +break in so David one of your TAS works + + + align:start position:0% +break in so David one of your TAS works +for ste in Steve Bell's lab and they + + align:start position:0% +for ste in Steve Bell's lab and they + + + align:start position:0% +for ste in Steve Bell's lab and they +study the mammalian origin of + + align:start position:0% +study the mammalian origin of + + + align:start position:0% +study the mammalian origin of +replication complex which is this much + + align:start position:0% +replication complex which is this much + + + align:start position:0% +replication complex which is this much +more complicated situation than what I'm + + align:start position:0% +more complicated situation than what I'm + + + align:start position:0% +more complicated situation than what I'm +going to describe to you today but they + + align:start position:0% +going to describe to you today but they + + + align:start position:0% +going to describe to you today but they +do fabulous single molecule work to + + align:start position:0% +do fabulous single molecule work to + + + align:start position:0% +do fabulous single molecule work to +assemble to show how those pieces are + + align:start position:0% +assemble to show how those pieces are + + + align:start position:0% +assemble to show how those pieces are +assembled but I'll tell you the truth as + + align:start position:0% +assembled but I'll tell you the truth as + + + align:start position:0% +assembled but I'll tell you the truth as +dorky as I am the thing that I find the + + align:start position:0% +dorky as I am the thing that I find the + + + align:start position:0% +dorky as I am the thing that I find the +most cruel about the origin of + + align:start position:0% +most cruel about the origin of + + + align:start position:0% +most cruel about the origin of +replication complex is that the the + + align:start position:0% +replication complex is that the the + + + align:start position:0% +replication complex is that the the +expelled orc and if any of you are Lord + + align:start position:0% +expelled orc and if any of you are Lord + + + align:start position:0% +expelled orc and if any of you are Lord +of the Rings fans who can't be excited + + align:start position:0% +of the Rings fans who can't be excited + + + align:start position:0% +of the Rings fans who can't be excited +by a complex called the or complex + + align:start position:0% +by a complex called the or complex + + + align:start position:0% +by a complex called the or complex +alright so there's going to be the the + + align:start position:0% +alright so there's going to be the the + + + align:start position:0% +alright so there's going to be the the +screening of the genome for an Ori and I + + align:start position:0% +screening of the genome for an Ori and I + + + align:start position:0% +screening of the genome for an Ori and I +want you to remember that what is up + + align:start position:0% +want you to remember that what is up + + + align:start position:0% +want you to remember that what is up +here is the rest of the chromosome it's + + align:start position:0% +here is the rest of the chromosome it's + + + align:start position:0% +here is the rest of the chromosome it's +not just a fuzzy end it's something + + align:start position:0% +not just a fuzzy end it's something + + + align:start position:0% +not just a fuzzy end it's something +that's got a lot of stuff there that + + align:start position:0% +that's got a lot of stuff there that + + + align:start position:0% +that's got a lot of stuff there that +still be spared so the first thing that + + align:start position:0% +still be spared so the first thing that + + + align:start position:0% +still be spared so the first thing that +happens is that helicase needs to start + + align:start position:0% +happens is that helicase needs to start + + + align:start position:0% +happens is that helicase needs to start +unzippering the two of the + + align:start position:0% +unzippering the two of the + + + align:start position:0% +unzippering the two of the +double-stranded DNA so you get to a new + + align:start position:0% +double-stranded DNA so you get to a new + + + align:start position:0% +double-stranded DNA so you get to a new +intermediate we're gonna draw like this + + align:start position:0% + + + + align:start position:0% + +and the helicase is going to intercept + + align:start position:0% +and the helicase is going to intercept + + + align:start position:0% +and the helicase is going to intercept +to basically start separating those two + + align:start position:0% +to basically start separating those two + + + align:start position:0% +to basically start separating those two +strands of DNA in order to do the + + align:start position:0% +strands of DNA in order to do the + + + align:start position:0% +strands of DNA in order to do the +replication don't forget that these are + + align:start position:0% +replication don't forget that these are + + + align:start position:0% +replication don't forget that these are +still base paired and these now are + + align:start position:0% +still base paired and these now are + + + align:start position:0% +still base paired and these now are +single strands so I'm gonna need + + align:start position:0% +single strands so I'm gonna need + + + align:start position:0% +single strands so I'm gonna need +something from that menu I'm gonna need + + align:start position:0% +something from that menu I'm gonna need + + + align:start position:0% +something from that menu I'm gonna need +it quickly what do you think's the next + + align:start position:0% +it quickly what do you think's the next + + + align:start position:0% +it quickly what do you think's the next +thing we're really gonna need in order + + align:start position:0% +thing we're really gonna need in order + + + align:start position:0% +thing we're really gonna need in order +to be able to move forward in our job + + align:start position:0% +to be able to move forward in our job + + + align:start position:0% +to be able to move forward in our job +what do we need from over here we're + + align:start position:0% +what do we need from over here we're + + + align:start position:0% +what do we need from over here we're +we're already using the double-stranded + + align:start position:0% +we're already using the double-stranded + + + align:start position:0% +we're already using the double-stranded +DNA it's not gonna be too difficult to + + align:start position:0% +DNA it's not gonna be too difficult to + + + align:start position:0% +DNA it's not gonna be too difficult to +figure out that NT piece we're already + + align:start position:0% +figure out that NT piece we're already + + + align:start position:0% +figure out that NT piece we're already +using the unzip arrays the helicase what + + align:start position:0% +using the unzip arrays the helicase what + + + align:start position:0% +using the unzip arrays the helicase what +are we gonna need yeah primase ah + + align:start position:0% +are we gonna need yeah primase ah + + + align:start position:0% +are we gonna need yeah primase ah +primase shortly but we've really got to + + align:start position:0% +primase shortly but we've really got to + + + align:start position:0% +primase shortly but we've really got to +do something to stabilize our unzip and + + align:start position:0% +do something to stabilize our unzip and + + + align:start position:0% +do something to stabilize our unzip and +stuff anyone else so those two single + + align:start position:0% +stuff anyone else so those two single + + + align:start position:0% +stuff anyone else so those two single +strands are right near each other and + + align:start position:0% +strands are right near each other and + + + align:start position:0% +strands are right near each other and +they're complementary what's gonna stop + + align:start position:0% +they're complementary what's gonna stop + + + align:start position:0% +they're complementary what's gonna stop +them going straight back together again + + align:start position:0% +them going straight back together again + + + align:start position:0% +them going straight back together again +and not allowing replication so there + + align:start position:0% +and not allowing replication so there + + + align:start position:0% +and not allowing replication so there +are proteins that basically sit on the + + align:start position:0% +are proteins that basically sit on the + + + align:start position:0% +are proteins that basically sit on the +single-stranded parts of DNA that are + + align:start position:0% +single-stranded parts of DNA that are + + + align:start position:0% +single-stranded parts of DNA that are +known a single strand binding proteins + + align:start position:0% +known a single strand binding proteins + + + align:start position:0% +known a single strand binding proteins +that stabilize this transiently made + + align:start position:0% +that stabilize this transiently made + + + align:start position:0% +that stabilize this transiently made +complex long enough for it to be copied + + align:start position:0% +complex long enough for it to be copied + + + align:start position:0% +complex long enough for it to be copied +all right so we've so far we've used the + + align:start position:0% +all right so we've so far we've used the + + + align:start position:0% +all right so we've so far we've used the +helicase we've used the single strand + + align:start position:0% +helicase we've used the single strand + + + align:start position:0% +helicase we've used the single strand +binding proteins and i'm gonna draw them + + align:start position:0% +binding proteins and i'm gonna draw them + + + align:start position:0% +binding proteins and i'm gonna draw them +there all right still remembering that I + + align:start position:0% +there all right still remembering that I + + + align:start position:0% +there all right still remembering that I +have an entire chromosome up here now + + align:start position:0% +have an entire chromosome up here now + + + align:start position:0% +have an entire chromosome up here now +the heavy lifting has to start fairly + + align:start position:0% +the heavy lifting has to start fairly + + + align:start position:0% +the heavy lifting has to start fairly +soon so we need the enzyme that's going + + align:start position:0% +soon so we need the enzyme that's going + + + align:start position:0% +soon so we need the enzyme that's going +to start making a copy of one of those + + align:start position:0% +to start making a copy of one of those + + + align:start position:0% +to start making a copy of one of those +single strands + + align:start position:0% +single strands + + + align:start position:0% +single strands +that's going to be a DNA polymerase + + align:start position:0% +that's going to be a DNA polymerase + + + align:start position:0% +that's going to be a DNA polymerase +which is right here but DNA polymerase + + align:start position:0% +which is right here but DNA polymerase + + + align:start position:0% +which is right here but DNA polymerase +is kind of a finicky enzyme because it + + align:start position:0% +is kind of a finicky enzyme because it + + + align:start position:0% +is kind of a finicky enzyme because it +doesn't like to just start cold on the + + align:start position:0% +doesn't like to just start cold on the + + + align:start position:0% +doesn't like to just start cold on the +genome on the single strand and start + + align:start position:0% +genome on the single strand and start + + + align:start position:0% +genome on the single strand and start +making a copy DNA polymerase needs a + + align:start position:0% +making a copy DNA polymerase needs a + + + align:start position:0% +making a copy DNA polymerase needs a +primer of some kind all right so I'm + + align:start position:0% +primer of some kind all right so I'm + + + align:start position:0% +primer of some kind all right so I'm +gonna just put that as a note up here + + align:start position:0% +gonna just put that as a note up here + + + align:start position:0% +gonna just put that as a note up here +DNA polymerase needs what's called a + + align:start position:0% +DNA polymerase needs what's called a + + + align:start position:0% +DNA polymerase needs what's called a +primer and what is a primer a primer is + + align:start position:0% +primer and what is a primer a primer is + + + align:start position:0% +primer and what is a primer a primer is +a sequence I think I've got something up + + align:start position:0% +a sequence I think I've got something up + + + align:start position:0% +a sequence I think I've got something up +here a primer is a sequence that's + + align:start position:0% +here a primer is a sequence that's + + + align:start position:0% +here a primer is a sequence that's +complementary to a little bit of DNA so + + align:start position:0% +complementary to a little bit of DNA so + + + align:start position:0% +complementary to a little bit of DNA so +that when DNA polymerase comes along + + align:start position:0% +that when DNA polymerase comes along + + + align:start position:0% +that when DNA polymerase comes along +it's actually grabbing a double strand + + align:start position:0% +it's actually grabbing a double strand + + + align:start position:0% +it's actually grabbing a double strand +and then filling up the rest of the + + align:start position:0% +and then filling up the rest of the + + + align:start position:0% +and then filling up the rest of the +single strand so this would be a typical + + align:start position:0% +single strand so this would be a typical + + + align:start position:0% +single strand so this would be a typical +depiction of a prime a here's a strand + + align:start position:0% +depiction of a prime a here's a strand + + + align:start position:0% +depiction of a prime a here's a strand +we want to copy but the blue one is a + + align:start position:0% +we want to copy but the blue one is a + + + align:start position:0% +we want to copy but the blue one is a +primer strand giving you something + + align:start position:0% +primer strand giving you something + + + align:start position:0% +primer strand giving you something +double-stranded to hold on to and then + + align:start position:0% +double-stranded to hold on to and then + + + align:start position:0% +double-stranded to hold on to and then +in this situation DNA polymerase would + + align:start position:0% +in this situation DNA polymerase would + + + align:start position:0% +in this situation DNA polymerase would +be happy to fill in the rest of the + + align:start position:0% +be happy to fill in the rest of the + + + align:start position:0% +be happy to fill in the rest of the +sequence so for the purpose of this + + align:start position:0% +sequence so for the purpose of this + + + align:start position:0% +sequence so for the purpose of this +discussion to start we're just going to + + align:start position:0% +discussion to start we're just going to + + + align:start position:0% +discussion to start we're just going to +provide a primer that is complementary + + align:start position:0% +provide a primer that is complementary + + + align:start position:0% +provide a primer that is complementary +to the DNA just to give us a go we have + + align:start position:0% +to the DNA just to give us a go we have + + + align:start position:0% +to the DNA just to give us a go we have +an alternative in the cell where is to + + align:start position:0% +an alternative in the cell where is to + + + align:start position:0% +an alternative in the cell where is to +actually use a primase and RNA building + + align:start position:0% +actually use a primase and RNA building + + + align:start position:0% +actually use a primase and RNA building +blocks to build a primer but let's keep + + align:start position:0% +blocks to build a primer but let's keep + + + align:start position:0% +blocks to build a primer but let's keep +things simple for a minute and get on + + align:start position:0% +things simple for a minute and get on + + + align:start position:0% +things simple for a minute and get on +with a lot of the major work and then + + align:start position:0% +with a lot of the major work and then + + + align:start position:0% +with a lot of the major work and then +we'll come back to that in a second so + + align:start position:0% +we'll come back to that in a second so + + + align:start position:0% +we'll come back to that in a second so +this part is a primer and that primer if + + align:start position:0% +this part is a primer and that primer if + + + align:start position:0% +this part is a primer and that primer if +this is the 3 prime end that's five + + align:start position:0% +this is the 3 prime end that's five + + + align:start position:0% +this is the 3 prime end that's five +prime three prime so the primer is + + align:start position:0% +prime three prime so the primer is + + + align:start position:0% +prime three prime so the primer is +complementary to the DNA in that + + align:start position:0% +complementary to the DNA in that + + + align:start position:0% +complementary to the DNA in that +direction is anti parallel and then DNA + + align:start position:0% +direction is anti parallel and then DNA + + + align:start position:0% +direction is anti parallel and then DNA +polymerase can go along and fill in the + + align:start position:0% +polymerase can go along and fill in the + + + align:start position:0% +polymerase can go along and fill in the +Strand and I'm gonna draw it dashed and + + align:start position:0% +Strand and I'm gonna draw it dashed and + + + align:start position:0% +Strand and I'm gonna draw it dashed and +it's gonna keep on growing and what I + + align:start position:0% +it's gonna keep on growing and what I + + + align:start position:0% +it's gonna keep on growing and what I +want you to notice his DNA polymerase + + align:start position:0% +want you to notice his DNA polymerase + + + align:start position:0% +want you to notice his DNA polymerase +grows from five prime + + align:start position:0% + + + + align:start position:0% + +two three pride that is a cardinal rule + + align:start position:0% +two three pride that is a cardinal rule + + + align:start position:0% +two three pride that is a cardinal rule +the directionality that we grow the new + + align:start position:0% +the directionality that we grow the new + + + align:start position:0% +the directionality that we grow the new +DNA in so basically looking at this + + align:start position:0% +DNA in so basically looking at this + + + align:start position:0% +DNA in so basically looking at this +picture it's going in this direction + + align:start position:0% +picture it's going in this direction + + + align:start position:0% +picture it's going in this direction +alright because the 3-prime o H is free + + align:start position:0% +alright because the 3-prime o H is free + + + align:start position:0% +alright because the 3-prime o H is free +and you're building onto it so you use a + + align:start position:0% +and you're building onto it so you use a + + + align:start position:0% +and you're building onto it so you use a +primer first and then you use DNA + + align:start position:0% +primer first and then you use DNA + + + align:start position:0% +primer first and then you use DNA +polymerase plus deoxy nucleoside try + + align:start position:0% +polymerase plus deoxy nucleoside try + + + align:start position:0% +polymerase plus deoxy nucleoside try +phosphates + + align:start position:0% +phosphates + + + align:start position:0% +phosphates +so all those 80 CG building blocks so + + align:start position:0% +so all those 80 CG building blocks so + + + align:start position:0% +so all those 80 CG building blocks so +we've been using these we've used the + + align:start position:0% +we've been using these we've used the + + + align:start position:0% +we've been using these we've used the +single stranded binding proteins we've + + align:start position:0% +single stranded binding proteins we've + + + align:start position:0% +single stranded binding proteins we've +used a primer but there are an + + align:start position:0% +used a primer but there are an + + + align:start position:0% +used a primer but there are an +alternative I'll get to that in just a + + align:start position:0% +alternative I'll get to that in just a + + + align:start position:0% +alternative I'll get to that in just a +second but we now have a complex where + + align:start position:0% +second but we now have a complex where + + + align:start position:0% +second but we now have a complex where +I'm gonna briefly divert you to tell you + + align:start position:0% +I'm gonna briefly divert you to tell you + + + align:start position:0% +I'm gonna briefly divert you to tell you +about in the cell what else you could + + align:start position:0% +about in the cell what else you could + + + align:start position:0% +about in the cell what else you could +use as a primer and then we're gonna + + align:start position:0% +use as a primer and then we're gonna + + + align:start position:0% +use as a primer and then we're gonna +have to deal with copying this other + + align:start position:0% +have to deal with copying this other + + + align:start position:0% +have to deal with copying this other +strand + + align:start position:0% +strand + + + align:start position:0% +strand +but this first strand that is made is + + align:start position:0% +but this first strand that is made is + + + align:start position:0% +but this first strand that is made is +called the leading strand it's the one + + align:start position:0% +called the leading strand it's the one + + + align:start position:0% +called the leading strand it's the one +that's easy I peel apart the DNA I have + + align:start position:0% +that's easy I peel apart the DNA I have + + + align:start position:0% +that's easy I peel apart the DNA I have +a primer there and I can just build goes + + align:start position:0% +a primer there and I can just build goes + + + align:start position:0% +a primer there and I can just build goes +really smoothly I'm building in the + + align:start position:0% +really smoothly I'm building in the + + + align:start position:0% +really smoothly I'm building in the +right direction if you look over on the + + align:start position:0% +right direction if you look over on the + + + align:start position:0% +right direction if you look over on the +other side of the fence you've got a + + align:start position:0% +other side of the fence you've got a + + + align:start position:0% +other side of the fence you've got a +problem because I can't build on this + + align:start position:0% +problem because I can't build on this + + + align:start position:0% +problem because I can't build on this +side from here right why not yeah I'd be + + align:start position:0% +side from here right why not yeah I'd be + + + align:start position:0% +side from here right why not yeah I'd be +doing it the wrong direction I would be + + align:start position:0% +doing it the wrong direction I would be + + + align:start position:0% +doing it the wrong direction I would be +the total mess frankly there would be a + + align:start position:0% +the total mess frankly there would be a + + + align:start position:0% +the total mess frankly there would be a +crisis in the cell so we're gonna have + + align:start position:0% +crisis in the cell so we're gonna have + + + align:start position:0% +crisis in the cell so we're gonna have +to deal with that so let me just get you + + align:start position:0% +to deal with that so let me just get you + + + align:start position:0% +to deal with that so let me just get you +out of the primer just deal with this + + align:start position:0% +out of the primer just deal with this + + + align:start position:0% +out of the primer just deal with this +primer issue in the cell it's not like + + align:start position:0% +primer issue in the cell it's not like + + + align:start position:0% +primer issue in the cell it's not like +we can micro inject all these little + + align:start position:0% +we can micro inject all these little + + + align:start position:0% +we can micro inject all these little +primers to get our DNA synthesized so + + align:start position:0% +primers to get our DNA synthesized so + + + align:start position:0% +primers to get our DNA synthesized so +RNA polymerase believe it or not + + align:start position:0% + + + + align:start position:0% + +doesn't need a primer so you can build + + align:start position:0% +doesn't need a primer so you can build + + + align:start position:0% +doesn't need a primer so you can build +little bits of primer with RNA you don't + + align:start position:0% +little bits of primer with RNA you don't + + + align:start position:0% +little bits of primer with RNA you don't +build very much just build short + + align:start position:0% +build very much just build short + + + align:start position:0% +build very much just build short +segments and then once you've got sort + + align:start position:0% +segments and then once you've got sort + + + align:start position:0% +segments and then once you've got sort +of enough there DNA polymerase can start + + align:start position:0% +of enough there DNA polymerase can start + + + align:start position:0% +of enough there DNA polymerase can start +polymerizing so you you use RNA + + align:start position:0% +polymerizing so you you use RNA + + + align:start position:0% +polymerizing so you you use RNA +polymerize a nucleotide nucleoside + + align:start position:0% +polymerize a nucleotide nucleoside + + + align:start position:0% +polymerize a nucleotide nucleoside +triphosphates not the deoxy ones so + + align:start position:0% +triphosphates not the deoxy ones so + + + align:start position:0% +triphosphates not the deoxy ones so +later on we've got this piece here that + + align:start position:0% +later on we've got this piece here that + + + align:start position:0% +later on we've got this piece here that +might be made of RNA which is why coming + + align:start position:0% +might be made of RNA which is why coming + + + align:start position:0% +might be made of RNA which is why coming +over here to my menu do I have it yes we + + align:start position:0% +over here to my menu do I have it yes we + + + align:start position:0% +over here to my menu do I have it yes we +need an RNA RNA primase and we need RNAs + + align:start position:0% +need an RNA RNA primase and we need RNAs + + + align:start position:0% +need an RNA RNA primase and we need RNAs +to chop them out so that DNA polymerase + + align:start position:0% +to chop them out so that DNA polymerase + + + align:start position:0% +to chop them out so that DNA polymerase +can come back because now there is + + align:start position:0% +can come back because now there is + + + align:start position:0% +can come back because now there is +double-stranded material and fill in the + + align:start position:0% +double-stranded material and fill in the + + + align:start position:0% +double-stranded material and fill in the +gap and then we need one more enzyme to + + align:start position:0% +gap and then we need one more enzyme to + + + align:start position:0% +gap and then we need one more enzyme to +stitch together the gaps and that's the + + align:start position:0% +stitch together the gaps and that's the + + + align:start position:0% +stitch together the gaps and that's the +ligase the logic of this stuff is great + + align:start position:0% +ligase the logic of this stuff is great + + + align:start position:0% +ligase the logic of this stuff is great +I think it's just really amazing because + + align:start position:0% +I think it's just really amazing because + + + align:start position:0% +I think it's just really amazing because +all these moving parts have evolved to + + align:start position:0% +all these moving parts have evolved to + + + align:start position:0% +all these moving parts have evolved to +make all these functions fall into place + + align:start position:0% +make all these functions fall into place + + + align:start position:0% +make all these functions fall into place +now we need to talk about this pesky + + align:start position:0% +now we need to talk about this pesky + + + align:start position:0% +now we need to talk about this pesky +other strand okay so we have a problem + + align:start position:0% +other strand okay so we have a problem + + + align:start position:0% +other strand okay so we have a problem +here because we've got the wrong + + align:start position:0% +here because we've got the wrong + + + align:start position:0% +here because we've got the wrong +directionality so what happens in nature + + align:start position:0% +directionality so what happens in nature + + + align:start position:0% +directionality so what happens in nature +is a prime as soon as there's enough of + + align:start position:0% +is a prime as soon as there's enough of + + + align:start position:0% +is a prime as soon as there's enough of +a stretch a primer is put in place + + align:start position:0% +a stretch a primer is put in place + + + align:start position:0% +a stretch a primer is put in place +growing the DNA in the right direction + + align:start position:0% +growing the DNA in the right direction + + + align:start position:0% +growing the DNA in the right direction +that's from where the origin of + + align:start position:0% +that's from where the origin of + + + align:start position:0% +that's from where the origin of +replication zipping so we put in another + + align:start position:0% +replication zipping so we put in another + + + align:start position:0% +replication zipping so we put in another +primer and then DNA polymerase that's a + + align:start position:0% +primer and then DNA polymerase that's a + + + align:start position:0% +primer and then DNA polymerase that's a +white one can build its complementary + + align:start position:0% +white one can build its complementary + + + align:start position:0% +white one can build its complementary +strand building in the appropriate + + align:start position:0% +strand building in the appropriate + + + align:start position:0% +strand building in the appropriate +direction to be consistent so you + + align:start position:0% +direction to be consistent so you + + + align:start position:0% +direction to be consistent so you +basically fill in a chunk and then you + + align:start position:0% +basically fill in a chunk and then you + + + align:start position:0% +basically fill in a chunk and then you +have to wait awhile til more is on + + align:start position:0% +have to wait awhile til more is on + + + align:start position:0% +have to wait awhile til more is on +zippered put in another primer and then + + align:start position:0% +zippered put in another primer and then + + + align:start position:0% +zippered put in another primer and then +grow the DNA so in that other piece + + align:start position:0% +grow the DNA so in that other piece + + + align:start position:0% +grow the DNA so in that other piece +you're making little segments of DNA + + align:start position:0% +you're making little segments of DNA + + + align:start position:0% +you're making little segments of DNA +intervened by RNA primers later on those + + align:start position:0% +intervened by RNA primers later on those + + + align:start position:0% +intervened by RNA primers later on those +small primers are going to be chewed up + + align:start position:0% +small primers are going to be chewed up + + + align:start position:0% +small primers are going to be chewed up +by RNAs DNA polymerase is gonna fill + + align:start position:0% +by RNAs DNA polymerase is gonna fill + + + align:start position:0% +by RNAs DNA polymerase is gonna fill +them in and ligase is going to join them + + align:start position:0% +them in and ligase is going to join them + + + align:start position:0% +them in and ligase is going to join them +that makes sense it's a lot to grasp and + + align:start position:0% +that makes sense it's a lot to grasp and + + + align:start position:0% +that makes sense it's a lot to grasp and +this other side is called what's known + + align:start position:0% +this other side is called what's known + + + align:start position:0% +this other side is called what's known +as the lagging strand and there are + + align:start position:0% +as the lagging strand and there are + + + align:start position:0% +as the lagging strand and there are +pieces of short DNA that have + + align:start position:0% +pieces of short DNA that have + + + align:start position:0% +pieces of short DNA that have +transiently made that have had their own + + align:start position:0% +transiently made that have had their own + + + align:start position:0% +transiently made that have had their own +name you can remember it or not I just + + align:start position:0% +name you can remember it or not I just + + + align:start position:0% +name you can remember it or not I just +feel I'm not being complete if I don't + + align:start position:0% +feel I'm not being complete if I don't + + + align:start position:0% +feel I'm not being complete if I don't +describe mention their name they're + + align:start position:0% +describe mention their name they're + + + align:start position:0% +describe mention their name they're +called Okazaki fragments after the guy + + align:start position:0% +called Okazaki fragments after the guy + + + align:start position:0% +called Okazaki fragments after the guy +who discovered them and they're longer + + align:start position:0% +who discovered them and they're longer + + + align:start position:0% +who discovered them and they're longer +in bacteria than in humans so Okazaki + + align:start position:0% +in bacteria than in humans so Okazaki + + + align:start position:0% +in bacteria than in humans so Okazaki +fragments are the transient short + + align:start position:0% +fragments are the transient short + + + align:start position:0% +fragments are the transient short +stretches that are made of DNA that are + + align:start position:0% +stretches that are made of DNA that are + + + align:start position:0% +stretches that are made of DNA that are +made in the lagging strand and then they + + align:start position:0% +made in the lagging strand and then they + + + align:start position:0% +made in the lagging strand and then they +get zipped together so that's sort of + + align:start position:0% +get zipped together so that's sort of + + + align:start position:0% +get zipped together so that's sort of +the story for replicating the DNA I mean + + align:start position:0% +the story for replicating the DNA I mean + + + align:start position:0% +the story for replicating the DNA I mean +make sure I've described everything to + + align:start position:0% +make sure I've described everything to + + + align:start position:0% +make sure I've described everything to +you leading strand lagging strand + + align:start position:0% +you leading strand lagging strand + + + align:start position:0% +you leading strand lagging strand +oh I believe I almost got this all right + + align:start position:0% +oh I believe I almost got this all right + + + align:start position:0% +oh I believe I almost got this all right +now we got a problem so we've come all + + align:start position:0% +now we got a problem so we've come all + + + align:start position:0% +now we got a problem so we've come all +this way we've used all the pieces we + + align:start position:0% +this way we've used all the pieces we + + + align:start position:0% +this way we've used all the pieces we +haven't used one of the pieces all right + + align:start position:0% +haven't used one of the pieces all right + + + align:start position:0% +haven't used one of the pieces all right +so we're in a small bit of trouble + + align:start position:0% +so we're in a small bit of trouble + + + align:start position:0% +so we're in a small bit of trouble +because what's gonna happen when you're + + align:start position:0% +because what's gonna happen when you're + + + align:start position:0% +because what's gonna happen when you're +for example we're trying to peel apart + + align:start position:0% +for example we're trying to peel apart + + + align:start position:0% +for example we're trying to peel apart +your DNA what's what trouble are you + + align:start position:0% +your DNA what's what trouble are you + + + align:start position:0% +your DNA what's what trouble are you +gonna run into who wants to come up here + + align:start position:0% +gonna run into who wants to come up here + + + align:start position:0% +gonna run into who wants to come up here +and get involved in my demo and you've + + align:start position:0% +and get involved in my demo and you've + + + align:start position:0% +and get involved in my demo and you've +got to be aware that you're gonna be on + + align:start position:0% +got to be aware that you're gonna be on + + + align:start position:0% +got to be aware that you're gonna be on +screen you and you up there you got your + + align:start position:0% +screen you and you up there you got your + + + align:start position:0% +screen you and you up there you got your +hand up first okay I need someone who's + + align:start position:0% +hand up first okay I need someone who's + + + align:start position:0% +hand up first okay I need someone who's +going to hold on to this as if their + + align:start position:0% +going to hold on to this as if their + + + align:start position:0% +going to hold on to this as if their +life depends on it you can't let the + + align:start position:0% +life depends on it you can't let the + + + align:start position:0% +life depends on it you can't let the +yellow one slip out so you and the rest + + align:start position:0% +yellow one slip out so you and the rest + + + align:start position:0% +yellow one slip out so you and the rest +of the chromosome so make sure that + + align:start position:0% +of the chromosome so make sure that + + + align:start position:0% +of the chromosome so make sure that +you're really hold and you don't let + + align:start position:0% +you're really hold and you don't let + + + align:start position:0% +you're really hold and you don't let +things come apart now you are helicase + + align:start position:0% +things come apart now you are helicase + + + align:start position:0% +things come apart now you are helicase +okay okay so come on start HeLa casing + + align:start position:0% +okay okay so come on start HeLa casing + + + align:start position:0% +okay okay so come on start HeLa casing +and so I can get and really pull as hard + + align:start position:0% +and so I can get and really pull as hard + + + align:start position:0% +and so I can get and really pull as hard +as you can he's gonna hold it no I don't + + align:start position:0% +as you can he's gonna hold it no I don't + + + align:start position:0% +as you can he's gonna hold it no I don't +want you to unwind it because we're in + + align:start position:0% +want you to unwind it because we're in + + + align:start position:0% +want you to unwind it because we're in +the middle of a chromosome so you you've + + align:start position:0% +the middle of a chromosome so you you've + + + align:start position:0% +the middle of a chromosome so you you've +literally got to do what helicase does + + align:start position:0% +literally got to do what helicase does + + + align:start position:0% +literally got to do what helicase does +yeah keep on pulling come on you can do + + align:start position:0% +yeah keep on pulling come on you can do + + + align:start position:0% +yeah keep on pulling come on you can do +it + + align:start position:0% +it + + + align:start position:0% +it +can you go much further I mean a your + + align:start position:0% +can you go much further I mean a your + + + align:start position:0% +can you go much further I mean a your +arms lightly low but it's almost + + align:start position:0% +arms lightly low but it's almost + + + align:start position:0% +arms lightly low but it's almost +impossible right we get to a stage where + + align:start position:0% +impossible right we get to a stage where + + + align:start position:0% +impossible right we get to a stage where +we need hell + + align:start position:0% +we need hell + + + align:start position:0% +we need hell +the help we have coming just from + + align:start position:0% +the help we have coming just from + + + align:start position:0% +the help we have coming just from +topoisomerase topoisomerase does + + align:start position:0% +topoisomerase topoisomerase does + + + align:start position:0% +topoisomerase topoisomerase does +something so let's walk just one step + + align:start position:0% +something so let's walk just one step + + + align:start position:0% +something so let's walk just one step +this way so those yeah topoisomerase + + align:start position:0% +this way so those yeah topoisomerase + + + align:start position:0% +this way so those yeah topoisomerase +comes along and it cuts the DNA it holds + + align:start position:0% +comes along and it cuts the DNA it holds + + + align:start position:0% +comes along and it cuts the DNA it holds +the pieces in its hands if you will + + align:start position:0% +the pieces in its hands if you will + + + align:start position:0% +the pieces in its hands if you will +let's the supercoiling relax and then it + + align:start position:0% +let's the supercoiling relax and then it + + + align:start position:0% +let's the supercoiling relax and then it +joins them back again so topoisomerase + + align:start position:0% +joins them back again so topoisomerase + + + align:start position:0% +joins them back again so topoisomerase +thank you very much guys that's it + + align:start position:0% +thank you very much guys that's it + + + align:start position:0% +thank you very much guys that's it +chromosome helicase thank you we really + + align:start position:0% +chromosome helicase thank you we really + + + align:start position:0% +chromosome helicase thank you we really +have some tightly wound DNA here so + + align:start position:0% +have some tightly wound DNA here so + + + align:start position:0% +have some tightly wound DNA here so +topoisomerase is the + + align:start position:0% +topoisomerase is the + + + align:start position:0% +topoisomerase is the +get-out-of-jail-free card + + align:start position:0% +get-out-of-jail-free card + + + align:start position:0% +get-out-of-jail-free card +because it allows you to deal with all + + align:start position:0% +because it allows you to deal with all + + + align:start position:0% +because it allows you to deal with all +of this tension you got in place that + + align:start position:0% +of this tension you got in place that + + + align:start position:0% +of this tension you got in place that +you cannot unravel so you need someone + + align:start position:0% +you cannot unravel so you need someone + + + align:start position:0% +you cannot unravel so you need someone +who's literally gonna cut holes + + align:start position:0% +who's literally gonna cut holes + + + align:start position:0% +who's literally gonna cut holes +let the thing relax rejoin it and there + + align:start position:0% +let the thing relax rejoin it and there + + + align:start position:0% +let the thing relax rejoin it and there +also there are some topoisomerases + + align:start position:0% +also there are some topoisomerases + + + align:start position:0% +also there are some topoisomerases +called DNA gyrase is but the really cool + + align:start position:0% +called DNA gyrase is but the really cool + + + align:start position:0% +called DNA gyrase is but the really cool +thing about topoisomerase is that it's a + + align:start position:0% +thing about topoisomerase is that it's a + + + align:start position:0% +thing about topoisomerase is that it's a +wonderful drug target in both mammalian + + align:start position:0% +wonderful drug target in both mammalian + + + align:start position:0% +wonderful drug target in both mammalian +and bacterial cells because they're + + align:start position:0% +and bacterial cells because they're + + + align:start position:0% +and bacterial cells because they're +quite different in the two types of + + align:start position:0% +quite different in the two types of + + + align:start position:0% +quite different in the two types of +organisms so in bacteria the antibiotic + + align:start position:0% +organisms so in bacteria the antibiotic + + + align:start position:0% +organisms so in bacteria the antibiotic +ciprofloxacin is a topoisomerase + + align:start position:0% +ciprofloxacin is a topoisomerase + + + align:start position:0% +ciprofloxacin is a topoisomerase +inhibitor that actually stops your + + align:start position:0% +inhibitor that actually stops your + + + align:start position:0% +inhibitor that actually stops your +bacteria dividing because if topo + + align:start position:0% +bacteria dividing because if topo + + + align:start position:0% +bacteria dividing because if topo +doesn't work you can't go on and in + + align:start position:0% +doesn't work you can't go on and in + + + align:start position:0% +doesn't work you can't go on and in +human biology and cancer biology there + + align:start position:0% +human biology and cancer biology there + + + align:start position:0% +human biology and cancer biology there +are also topoisomerases there's one + + align:start position:0% +are also topoisomerases there's one + + + align:start position:0% +are also topoisomerases there's one +called contra Thiessen that does the + + align:start position:0% +called contra Thiessen that does the + + + align:start position:0% +called contra Thiessen that does the +same thing in the eukaryotic + + align:start position:0% +same thing in the eukaryotic + + + align:start position:0% +same thing in the eukaryotic +topoisomerase to stop cancer cells + + align:start position:0% +topoisomerase to stop cancer cells + + + align:start position:0% +topoisomerase to stop cancer cells +dividing rapidly so that those cannot be + + align:start position:0% +dividing rapidly so that those cannot be + + + align:start position:0% +dividing rapidly so that those cannot be +cannot go on and make larger tumors so I + + align:start position:0% +cannot go on and make larger tumors so I + + + align:start position:0% +cannot go on and make larger tumors so I +want to show you something and I am + + align:start position:0% +want to show you something and I am + + + align:start position:0% +want to show you something and I am +actually certain that I have time come + + align:start position:0% +actually certain that I have time come + + + align:start position:0% +actually certain that I have time come +on now I'm gonna show you in this + + align:start position:0% +on now I'm gonna show you in this + + + align:start position:0% +on now I'm gonna show you in this +animation we'll see the remarkable way + + align:start position:0% +animation we'll see the remarkable way + + + align:start position:0% +animation we'll see the remarkable way +our DNA is tightly packed up so that six + + align:start position:0% +our DNA is tightly packed up so that six + + + align:start position:0% +our DNA is tightly packed up so that six +feet of this long molecule fits into the + + align:start position:0% +feet of this long molecule fits into the + + + align:start position:0% +feet of this long molecule fits into the +microscopic nucleus of every cell + + align:start position:0% + + + + align:start position:0% + +the process starts when DNA is wrapped + + align:start position:0% +the process starts when DNA is wrapped + + + align:start position:0% +the process starts when DNA is wrapped +around special protein molecules called + + align:start position:0% +around special protein molecules called + + + align:start position:0% +around special protein molecules called +histones the combined loop of DNA and + + align:start position:0% +histones the combined loop of DNA and + + + align:start position:0% +histones the combined loop of DNA and +protein is called a nucleosome + + align:start position:0% + + + + align:start position:0% + +next the nucleosomes are packaged into a + + align:start position:0% +next the nucleosomes are packaged into a + + + align:start position:0% +next the nucleosomes are packaged into a +thread the end result is a fiber known + + align:start position:0% +thread the end result is a fiber known + + + align:start position:0% +thread the end result is a fiber known +as chromatin + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +this fiber is then looped and coiled yet + + align:start position:0% +this fiber is then looped and coiled yet + + + align:start position:0% +this fiber is then looped and coiled yet +again + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +leading finally to the familiar shapes + + align:start position:0% +leading finally to the familiar shapes + + + align:start position:0% +leading finally to the familiar shapes +known as chromosomes which can be seen + + align:start position:0% +known as chromosomes which can be seen + + + align:start position:0% +known as chromosomes which can be seen +in the nucleus of dividing cells I'm + + align:start position:0% +in the nucleus of dividing cells I'm + + + align:start position:0% +in the nucleus of dividing cells I'm +going to take you forward using computer + + align:start position:0% +going to take you forward using computer + + + align:start position:0% +going to take you forward using computer +animation based on molecular research we + + align:start position:0% +animation based on molecular research we + + + align:start position:0% +animation based on molecular research we +are now able to see how DNA is actually + + align:start position:0% +are now able to see how DNA is actually + + + align:start position:0% +are now able to see how DNA is actually +copied in living cells you are looking + + align:start position:0% +copied in living cells you are looking + + + align:start position:0% +copied in living cells you are looking +at an assembly line of amazing miniature + + align:start position:0% +at an assembly line of amazing miniature + + + align:start position:0% +at an assembly line of amazing miniature +biochemical machines that are pulling + + align:start position:0% +biochemical machines that are pulling + + + align:start position:0% +biochemical machines that are pulling +apart the DNA double helix and cranking + + align:start position:0% +apart the DNA double helix and cranking + + + align:start position:0% +apart the DNA double helix and cranking +out a copy of each strand the DNA to be + + align:start position:0% +out a copy of each strand the DNA to be + + + align:start position:0% +out a copy of each strand the DNA to be +copied enters the production line from + + align:start position:0% +copied enters the production line from + + + align:start position:0% +copied enters the production line from +bottom-left the whirling blue molecular + + align:start position:0% +bottom-left the whirling blue molecular + + + align:start position:0% +bottom-left the whirling blue molecular +machine is called helicase it spins the + + align:start position:0% +machine is called helicase it spins the + + + align:start position:0% +machine is called helicase it spins the +DNA as fast as a jet engine as it + + align:start position:0% +DNA as fast as a jet engine as it + + + align:start position:0% +DNA as fast as a jet engine as it +unwinds the double helix into two + + align:start position:0% +unwinds the double helix into two + + + align:start position:0% +unwinds the double helix into two +strands + + align:start position:0% +strands + + + align:start position:0% +strands +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +one strand is copied continuously and + + align:start position:0% +one strand is copied continuously and + + + align:start position:0% +one strand is copied continuously and +can be seen spooling off to the run + + align:start position:0% + + + + align:start position:0% + +things are not so simple for the other + + align:start position:0% +things are not so simple for the other + + + align:start position:0% +things are not so simple for the other +strand because it must be copied + + align:start position:0% +strand because it must be copied + + + align:start position:0% +strand because it must be copied +backwards it is drawn out repeatedly in + + align:start position:0% +backwards it is drawn out repeatedly in + + + align:start position:0% +backwards it is drawn out repeatedly in +loops and copied one section at a time + + align:start position:0% +loops and copied one section at a time + + + align:start position:0% +loops and copied one section at a time +the end result is two new DNA molecules + + align:start position:0% +the end result is two new DNA molecules + + + align:start position:0% +the end result is two new DNA molecules +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +all right okay that's what you saw today + + align:start position:0% +all right okay that's what you saw today + + + align:start position:0% +all right okay that's what you saw today +replication a lot of the mechanics a lot + + align:start position:0% +replication a lot of the mechanics a lot + + + align:start position:0% +replication a lot of the mechanics a lot +of the moving parts there's this tricky + + align:start position:0% +of the moving parts there's this tricky + + + align:start position:0% +of the moving parts there's this tricky +stuff with primers you'll get used to + + align:start position:0% +stuff with primers you'll get used to + + + align:start position:0% +stuff with primers you'll get used to +that + + align:start position:0% +that + + + align:start position:0% +that +but this is really the quintessential + + align:start position:0% +but this is really the quintessential + + + align:start position:0% +but this is really the quintessential +set of pieces to replicate DNA it is an + + align:start position:0% +set of pieces to replicate DNA it is an + + + align:start position:0% +set of pieces to replicate DNA it is an +amazing process + + align:start position:0% +amazing process + + + align:start position:0% +amazing process +look at the speed thousand base pairs a + + align:start position:0% +look at the speed thousand base pairs a + + + align:start position:0% +look at the speed thousand base pairs a +second can you even believe it + + align:start position:0% +second can you even believe it + + + align:start position:0% +second can you even believe it +a chromis entire cyclic circular + + align:start position:0% +a chromis entire cyclic circular + + + align:start position:0% +a chromis entire cyclic circular +chromosome copied in 20 minutes so these + + align:start position:0% +chromosome copied in 20 minutes so these + + + align:start position:0% +chromosome copied in 20 minutes so these +are really things to think about because + + align:start position:0% +are really things to think about because + + + align:start position:0% +are really things to think about because +they're so impressive that it's a + + align:start position:0% +they're so impressive that it's a + + + align:start position:0% +they're so impressive that it's a +delight to actually be able to teach + + align:start position:0% +delight to actually be able to teach + + + align:start position:0% +delight to actually be able to teach +them to you okay I'm done for today + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/9500J3lgu6U.txt b/9500J3lgu6U.txt new file mode 100644 index 0000000000000000000000000000000000000000..b14c52322332d036863eacf3b95b727682ab18f0 --- /dev/null +++ b/9500J3lgu6U.txt @@ -0,0 +1,9792 @@ +align:start position:0% + +Quiz 2 is this week on Friday from uh I + + align:start position:0% +Quiz 2 is this week on Friday from uh I + + + align:start position:0% +Quiz 2 is this week on Friday from uh I +hope that's correct whatever is on the + + align:start position:0% +hope that's correct whatever is on the + + + align:start position:0% +hope that's correct whatever is on the +web page is correct but I think it's + + align:start position:0% +web page is correct but I think it's + + + align:start position:0% +web page is correct but I think it's +lecture 9 through uh recitation number + + align:start position:0% +lecture 9 through uh recitation number + + + align:start position:0% +lecture 9 through uh recitation number +15 so in particular uh the log + + align:start position:0% +15 so in particular uh the log + + + align:start position:0% +15 so in particular uh the log +structured file system paper is not on + + align:start position:0% +structured file system paper is not on + + + align:start position:0% +structured file system paper is not on +the exam so some of you may have been + + align:start position:0% +the exam so some of you may have been + + + align:start position:0% +the exam so some of you may have been +told + + align:start position:0% +told + + + align:start position:0% +told +otherwise okay so what we're going to do + + align:start position:0% +otherwise okay so what we're going to do + + + align:start position:0% +otherwise okay so what we're going to do +today is continue our discussion of + + align:start position:0% +today is continue our discussion of + + + align:start position:0% +today is continue our discussion of +atomac + + align:start position:0% + + + + align:start position:0% + +city which as you'll recall is two + + align:start position:0% +city which as you'll recall is two + + + align:start position:0% +city which as you'll recall is two +properties that have to hold in order + + align:start position:0% +properties that have to hold in order + + + align:start position:0% +properties that have to hold in order +for atomos City to hold and the first + + align:start position:0% +for atomos City to hold and the first + + + align:start position:0% +for atomos City to hold and the first +property that + + align:start position:0% + + + + align:start position:0% + +we talked about was + + align:start position:0% +we talked about was + + + align:start position:0% +we talked about was +recoverability and the other property + + align:start position:0% +recoverability and the other property + + + align:start position:0% +recoverability and the other property +which is what we're going to spend most + + align:start position:0% +which is what we're going to spend most + + + align:start position:0% +which is what we're going to spend most +of our time on + + align:start position:0% +of our time on + + + align:start position:0% +of our time on +today is + + align:start position:0% + + + + align:start position:0% + +isolation Okay I guess I should just + + align:start position:0% +isolation Okay I guess I should just + + + align:start position:0% +isolation Okay I guess I should just +move it up a + + align:start position:0% + + + + align:start position:0% + +bit okay is that clear + + align:start position:0% + + + + align:start position:0% + +better + + align:start position:0% +better + + + align:start position:0% +better +okay so before we get into isolation I + + align:start position:0% +okay so before we get into isolation I + + + align:start position:0% +okay so before we get into isolation I +just want to wrap up U the discussion of + + align:start position:0% +just want to wrap up U the discussion of + + + align:start position:0% +just want to wrap up U the discussion of +recoverability because we left at a + + align:start position:0% +recoverability because we left at a + + + align:start position:0% +recoverability because we left at a +little bit of U 3/4s um point and didn't + + align:start position:0% +little bit of U 3/4s um point and didn't + + + align:start position:0% +little bit of U 3/4s um point and didn't +quite finish it so the story here was + + align:start position:0% +quite finish it so the story here was + + + align:start position:0% +quite finish it so the story here was +what we did + + align:start position:0% +what we did + + + align:start position:0% +what we did +first was talked about how to achieve a + + align:start position:0% +first was talked about how to achieve a + + + align:start position:0% +first was talked about how to achieve a +recoverable + + align:start position:0% +recoverable + + + align:start position:0% +recoverable +sector using two copies of the data and + + align:start position:0% +sector using two copies of the data and + + + align:start position:0% +sector using two copies of the data and +the Chooser sector to choose between + + align:start position:0% +the Chooser sector to choose between + + + align:start position:0% +the Chooser sector to choose between +them and then from here we went and + + align:start position:0% +them and then from here we went and + + + align:start position:0% +them and then from here we went and +talked about one way of achieving + + align:start position:0% +talked about one way of achieving + + + align:start position:0% +talked about one way of achieving +recoverability + + align:start position:0% +recoverability + + + align:start position:0% +recoverability +using version histories and we did um + + align:start position:0% +using version histories and we did um + + + align:start position:0% +using version histories and we did um +complete that discussion and then we + + align:start position:0% +complete that discussion and then we + + + align:start position:0% +complete that discussion and then we +started talking about a more efficient + + align:start position:0% +started talking about a more efficient + + + align:start position:0% +started talking about a more efficient +way of achieving recoverability in + + align:start position:0% +way of achieving recoverability in + + + align:start position:0% +way of achieving recoverability in +situations where you care a lot about + + align:start position:0% +situations where you care a lot about + + + align:start position:0% +situations where you care a lot about +performance using + + align:start position:0% + + + + align:start position:0% + +logging and the main idea in logging is + + align:start position:0% +logging and the main idea in logging is + + + align:start position:0% +logging and the main idea in logging is +this Pro for when you decide to write + + align:start position:0% +this Pro for when you decide to write + + + align:start position:0% +this Pro for when you decide to write +the log + + align:start position:0% +the log + + + align:start position:0% +the log +called the WR ahead logging protocol and + + align:start position:0% +called the WR ahead logging protocol and + + + align:start position:0% +called the WR ahead logging protocol and +the idea is very simple always write to + + align:start position:0% +the idea is very simple always write to + + + align:start position:0% +the idea is very simple always write to +the log before you update cell storage + + align:start position:0% +the log before you update cell storage + + + align:start position:0% +the log before you update cell storage +and that's the main discipline that if + + align:start position:0% +and that's the main discipline that if + + + align:start position:0% +and that's the main discipline that if +you always follow then you'll get things + + align:start position:0% +you always follow then you'll get things + + + align:start position:0% +you always follow then you'll get things +right but one of the consequences of + + align:start position:0% +right but one of the consequences of + + + align:start position:0% +right but one of the consequences of +logging you get two things from having + + align:start position:0% +logging you get two things from having + + + align:start position:0% +logging you get two things from having +this log the first is when an action + + align:start position:0% +this log the first is when an action + + + align:start position:0% +this log the first is when an action +abots independent of failure when you're + + align:start position:0% +abots independent of failure when you're + + + align:start position:0% +abots independent of failure when you're +running an atomic action and um the + + align:start position:0% +running an atomic action and um the + + + align:start position:0% +running an atomic action and um the +program calls a or the system abots that + + align:start position:0% +program calls a or the system abots that + + + align:start position:0% +program calls a or the system abots that +action what the log allows you to do is + + align:start position:0% +action what the log allows you to do is + + + align:start position:0% +action what the log allows you to do is +go back through the log scan the log + + align:start position:0% +go back through the log scan the log + + + align:start position:0% +go back through the log scan the log +backwards look at all of the steps that + + align:start position:0% +backwards look at all of the steps that + + + align:start position:0% +backwards look at all of the steps that +that action took and the action didn't + + align:start position:0% +that action took and the action didn't + + + align:start position:0% +that action took and the action didn't +quite commit so you have to back those + + align:start position:0% +quite commit so you have to back those + + + align:start position:0% +quite commit so you have to back those +changes out and the log helps you unroll + + align:start position:0% +changes out and the log helps you unroll + + + align:start position:0% +changes out and the log helps you unroll +backward so primarily um what you need + + align:start position:0% +backward so primarily um what you need + + + align:start position:0% +backward so primarily um what you need +in order to with the logging scheme in + + align:start position:0% +in order to with the logging scheme in + + + align:start position:0% +in order to with the logging scheme in +order to do aborts is the ability to + + align:start position:0% + + + + align:start position:0% + +undo which means that what you need in + + align:start position:0% +undo which means that what you need in + + + align:start position:0% +undo which means that what you need in +the log is uh to keep whenever you + + align:start position:0% +the log is uh to keep whenever you + + + align:start position:0% +the log is uh to keep whenever you +update cell store to something else you + + align:start position:0% +update cell store to something else you + + + align:start position:0% +update cell store to something else you +have to keep track of the old value and + + align:start position:0% +have to keep track of the old value and + + + align:start position:0% +have to keep track of the old value and +this is what we called in the log as an + + align:start position:0% +this is what we called in the log as an + + + align:start position:0% +this is what we called in the log as an +undo + + align:start position:0% + + + + align:start position:0% + +step but now failures also happen in + + align:start position:0% +step but now failures also happen in + + + align:start position:0% +step but now failures also happen in +addition uh to aborts + + align:start position:0% + + + + align:start position:0% + +and we need a little bit more U + + align:start position:0% +and we need a little bit more U + + + align:start position:0% +and we need a little bit more U +mechanism in addition to just the + + align:start position:0% +mechanism in addition to just the + + + align:start position:0% +mechanism in addition to just the +ability to undo and to understand why uh + + align:start position:0% +ability to undo and to understand why uh + + + align:start position:0% +ability to undo and to understand why uh +let's take a specific example where you + + align:start position:0% +let's take a specific example where you + + + align:start position:0% +let's take a specific example where you +have an application and it's writing + + align:start position:0% +have an application and it's writing + + + align:start position:0% +have an application and it's writing +data to a database that is on + + align:start position:0% + + + + align:start position:0% + +disk and um what we said was there was a + + align:start position:0% +disk and um what we said was there was a + + + align:start position:0% +disk and um what we said was there was a +log and the log is stored on disk as + + align:start position:0% +log and the log is stored on disk as + + + align:start position:0% +log and the log is stored on disk as +well and let's assume that the log's + + align:start position:0% +well and let's assume that the log's + + + align:start position:0% +well and let's assume that the log's +actually stored on a different disk now + + align:start position:0% +actually stored on a different disk now + + + align:start position:0% +actually stored on a different disk now +the right ahead log protocol basically + + align:start position:0% +the right ahead log protocol basically + + + align:start position:0% +the right ahead log protocol basically +says that whenever you update so you + + align:start position:0% +says that whenever you update so you + + + align:start position:0% +says that whenever you update so you +have an action which has things like + + align:start position:0% +have an action which has things like + + + align:start position:0% +have an action which has things like +reads and wrs of celles store and + + align:start position:0% +reads and wrs of celles store and + + + align:start position:0% +reads and wrs of celles store and +whenever there's a right to a celles + + align:start position:0% +whenever there's a right to a celles + + + align:start position:0% +whenever there's a right to a celles +store the right ahead log protocol says + + align:start position:0% +store the right ahead log protocol says + + + align:start position:0% +store the right ahead log protocol says +write to the log before you write to the + + align:start position:0% +write to the log before you write to the + + + align:start position:0% +write to the log before you write to the +database or to the cell + + align:start position:0% +database or to the cell + + + align:start position:0% +database or to the cell +store so two things can happen the first + + align:start position:0% +store so two things can happen the first + + + align:start position:0% +store so two things can happen the first +thing the simplest model here is that + + align:start position:0% +thing the simplest model here is that + + + align:start position:0% +thing the simplest model here is that +all rights are synchronous so what this + + align:start position:0% +all rights are synchronous so what this + + + align:start position:0% +all rights are synchronous so what this +means is that if you see a right um + + align:start position:0% +means is that if you see a right um + + + align:start position:0% +means is that if you see a right um +statement in an atomic action that write + + align:start position:0% +statement in an atomic action that write + + + align:start position:0% +statement in an atomic action that write +the first thing you have to do is to + + align:start position:0% +the first thing you have to do is to + + + align:start position:0% +the first thing you have to do is to +write to the log and then that returns + + align:start position:0% +write to the log and then that returns + + + align:start position:0% +write to the log and then that returns +and then you write to the + + align:start position:0% +and then you write to the + + + align:start position:0% +and then you write to the +database and then you run the next + + align:start position:0% +database and then you run the next + + + align:start position:0% +database and then you run the next +action the next step of the + + align:start position:0% +action the next step of the + + + align:start position:0% +action the next step of the +action so clearly by the time in this + + align:start position:0% +action so clearly by the time in this + + + align:start position:0% +action so clearly by the time in this +action if you ever get to the commit + + align:start position:0% +action if you ever get to the commit + + + align:start position:0% +action if you ever get to the commit +point and you're about to execute commit + + align:start position:0% +point and you're about to execute commit + + + align:start position:0% +point and you're about to execute commit +it means that all of the data has + + align:start position:0% +it means that all of the data has + + + align:start position:0% +it means that all of the data has +already been written to the database + + align:start position:0% +already been written to the database + + + align:start position:0% +already been written to the database +because by assumption we assume that all + + align:start position:0% +because by assumption we assume that all + + + align:start position:0% +because by assumption we assume that all +of the rights are synchronous and you + + align:start position:0% +of the rights are synchronous and you + + + align:start position:0% +of the rights are synchronous and you +know you write to the database and only + + align:start position:0% +know you write to the database and only + + + align:start position:0% +know you write to the database and only +then you go to the next you go to the + + align:start position:0% +then you go to the next you go to the + + + align:start position:0% +then you go to the next you go to the +next step and assuming there's only one + + align:start position:0% +next step and assuming there's only one + + + align:start position:0% +next step and assuming there's only one +thread of execution then in this simple + + align:start position:0% +thread of execution then in this simple + + + align:start position:0% +thread of execution then in this simple +model you always write to the database + + align:start position:0% +model you always write to the database + + + align:start position:0% +model you always write to the database +you first write to the log and then you + + align:start position:0% +you first write to the log and then you + + + align:start position:0% +you first write to the log and then you +write to this self store in the + + align:start position:0% +write to this self store in the + + + align:start position:0% +write to this self store in the +database but by construction when you + + align:start position:0% +database but by construction when you + + + align:start position:0% +database but by construction when you +get to the commit point you know for + + align:start position:0% +get to the commit point you know for + + + align:start position:0% +get to the commit point you know for +sure that all of the data has written to + + align:start position:0% +sure that all of the data has written to + + + align:start position:0% +sure that all of the data has written to +the + + align:start position:0% +the + + + align:start position:0% +the +database so if a failure happens now and + + align:start position:0% +database so if a failure happens now and + + + align:start position:0% +database so if a failure happens now and +you didn't get to commit and you and the + + align:start position:0% +you didn't get to commit and you and the + + + align:start position:0% +you didn't get to commit and you and the +system failed before the commit ran + + align:start position:0% +system failed before the commit ran + + + align:start position:0% +system failed before the commit ran +anytime in the middle of this + + align:start position:0% +anytime in the middle of this + + + align:start position:0% +anytime in the middle of this +action the only thing you really need to + + align:start position:0% +action the only thing you really need to + + + align:start position:0% +action the only thing you really need to +do is to roll back all of the changes + + align:start position:0% +do is to roll back all of the changes + + + align:start position:0% +do is to roll back all of the changes +made by actions that didn't get to + + align:start position:0% +made by actions that didn't get to + + + align:start position:0% +made by actions that didn't get to +commit which means that in this model as + + align:start position:0% +commit which means that in this model as + + + align:start position:0% +commit which means that in this model as +described so far the only thing you need + + align:start position:0% +described so far the only thing you need + + + align:start position:0% +described so far the only thing you need +to do is to undo actions that correspond + + align:start position:0% +to do is to undo actions that correspond + + + align:start position:0% +to do is to undo actions that correspond +to um actions that didn't commit + + align:start position:0% +to um actions that didn't commit + + + align:start position:0% +to um actions that didn't commit +any action that committed by + + align:start position:0% +any action that committed by + + + align:start position:0% +any action that committed by +construction must have written all of + + align:start position:0% +construction must have written all of + + + align:start position:0% +construction must have written all of +its data and installed that data into + + align:start position:0% +its data and installed that data into + + + align:start position:0% +its data and installed that data into +cell store because if an action gets to + + align:start position:0% +cell store because if an action gets to + + + align:start position:0% +cell store because if an action gets to +the statement to run commit and then + + align:start position:0% +the statement to run commit and then + + + align:start position:0% +the statement to run commit and then +finishes commit when it got to commit + + align:start position:0% +finishes commit when it got to commit + + + align:start position:0% +finishes commit when it got to commit +you know that because of all the rights + + align:start position:0% +you know that because of all the rights + + + align:start position:0% +you know that because of all the rights +being synchronous um to the cell store + + align:start position:0% +being synchronous um to the cell store + + + align:start position:0% +being synchronous um to the cell store +you know that that right got written and + + align:start position:0% +you know that that right got written and + + + align:start position:0% +you know that that right got written and +by the right ahead protocol's definition + + align:start position:0% +by the right ahead protocol's definition + + + align:start position:0% +by the right ahead protocol's definition +you know the log got written before that + + align:start position:0% +you know the log got written before that + + + align:start position:0% +you know the log got written before that +so you don't actually have to do + + align:start position:0% +so you don't actually have to do + + + align:start position:0% +so you don't actually have to do +anything even though the log contains + + align:start position:0% +anything even though the log contains + + + align:start position:0% +anything even though the log contains +the the results of these um actions that + + align:start position:0% +the the results of these um actions that + + + align:start position:0% +the the results of these um actions that +committed you don't have to do anything + + align:start position:0% +committed you don't have to do anything + + + align:start position:0% +committed you don't have to do anything +for the committed actions so in fact + + align:start position:0% +for the committed actions so in fact + + + align:start position:0% +for the committed actions so in fact +this undo log is enough to handle this + + align:start position:0% +this undo log is enough to handle this + + + align:start position:0% +this undo log is enough to handle this +simple database as well where um all of + + align:start position:0% +simple database as well where um all of + + + align:start position:0% +simple database as well where um all of +the rights are being done + + align:start position:0% +the rights are being done + + + align:start position:0% +the rights are being done +synchronously um in in in this by this + + align:start position:0% +synchronously um in in in this by this + + + align:start position:0% +synchronously um in in in this by this +application but there's a few things + + align:start position:0% +application but there's a few things + + + align:start position:0% +application but there's a few things +that can happen now one of the reasons + + align:start position:0% +that can happen now one of the reasons + + + align:start position:0% +that can happen now one of the reasons +we went we threw out version histories + + align:start position:0% +we went we threw out version histories + + + align:start position:0% +we went we threw out version histories +or discarded the idea to go to this more + + align:start position:0% +or discarded the idea to go to this more + + + align:start position:0% +or discarded the idea to go to this more +logging oriented model is for higher + + align:start position:0% +logging oriented model is for higher + + + align:start position:0% +logging oriented model is for higher +performance and one of the ways we got + + align:start position:0% +performance and one of the ways we got + + + align:start position:0% +performance and one of the ways we got +higher performance was we didn't have to + + align:start position:0% +higher performance was we didn't have to + + + align:start position:0% +higher performance was we didn't have to +do these link list reversals in order to + + align:start position:0% +do these link list reversals in order to + + + align:start position:0% +do these link list reversals in order to +read and write items + + align:start position:0% +read and write items + + + align:start position:0% +read and write items +but it's also going to be tempting and + + align:start position:0% +but it's also going to be tempting and + + + align:start position:0% +but it's also going to be tempting and +you've seen this before to not have to + + align:start position:0% +you've seen this before to not have to + + + align:start position:0% +you've seen this before to not have to +do not want to do synchronous rights to + + align:start position:0% +do not want to do synchronous rights to + + + align:start position:0% +do not want to do synchronous rights to +cell store on a database in order to get + + align:start position:0% +cell store on a database in order to get + + + align:start position:0% +cell store on a database in order to get +high performance you know you might have + + align:start position:0% +high performance you know you might have + + + align:start position:0% +high performance you know you might have +asynchronous rights happening to the + + align:start position:0% +asynchronous rights happening to the + + + align:start position:0% +asynchronous rights happening to the +database and you don't know when those + + align:start position:0% +database and you don't know when those + + + align:start position:0% +database and you don't know when those +rights complete um + + align:start position:0% +rights complete um + + + align:start position:0% +rights complete um +and what could happen as a result of + + align:start position:0% +and what could happen as a result of + + + align:start position:0% +and what could happen as a result of +that is you issue some rights to the + + align:start position:0% +that is you issue some rights to the + + + align:start position:0% +that is you issue some rights to the +database and then you go ahead and you + + align:start position:0% +database and then you go ahead and you + + + align:start position:0% +database and then you go ahead and you +commit the action but what could happen + + align:start position:0% +commit the action but what could happen + + + align:start position:0% +commit the action but what could happen +is the data um that was supposed to be + + align:start position:0% +is the data um that was supposed to be + + + align:start position:0% +is the data um that was supposed to be +written to this database cell store may + + align:start position:0% +written to this database cell store may + + + align:start position:0% +written to this database cell store may +not actually have gotten written because + + align:start position:0% +not actually have gotten written because + + + align:start position:0% +not actually have gotten written because +um there's some kind of a + + align:start position:0% +um there's some kind of a + + + align:start position:0% +um there's some kind of a +cache in memory that actually Returns + + align:start position:0% +cache in memory that actually Returns + + + align:start position:0% +cache in memory that actually Returns +the result of the return to you from the + + align:start position:0% +the result of the return to you from the + + + align:start position:0% +the result of the return to you from the +right but the right actually never made + + align:start position:0% +right but the right actually never made + + + align:start position:0% +right but the right actually never made +it to the + + align:start position:0% +it to the + + + align:start position:0% +it to the +database so in this system for higher + + align:start position:0% +database so in this system for higher + + + align:start position:0% +database so in this system for higher +performance if you stick a cach in here + + align:start position:0% +performance if you stick a cach in here + + + align:start position:0% +performance if you stick a cach in here +what could happen is that you might + + align:start position:0% +what could happen is that you might + + + align:start position:0% +what could happen is that you might +reach the commit + + align:start position:0% +reach the commit + + + align:start position:0% +reach the commit +point and finish commit but not be + + align:start position:0% +point and finish commit but not be + + + align:start position:0% +point and finish commit but not be +guaranteed that the cell store data + + align:start position:0% +guaranteed that the cell store data + + + align:start position:0% +guaranteed that the cell store data +actually got written to the database + + align:start position:0% +actually got written to the database + + + align:start position:0% +actually got written to the database +and if you fail now after commit you + + align:start position:0% +and if you fail now after commit you + + + align:start position:0% +and if you fail now after commit you +have to go through the log and redo the + + align:start position:0% +have to go through the log and redo the + + + align:start position:0% +have to go through the log and redo the +actions for all of those actions that + + align:start position:0% +actions for all of those actions that + + + align:start position:0% +actions for all of those actions that +committed because those actions some of + + align:start position:0% +committed because those actions some of + + + align:start position:0% +committed because those actions some of +those actions may not have made it into + + align:start position:0% +those actions may not have made it into + + + align:start position:0% +those actions may not have made it into +the cell storage in the + + align:start position:0% +the cell storage in the + + + align:start position:0% +the cell storage in the +database so what this means is that in + + align:start position:0% +database so what this means is that in + + + align:start position:0% +database so what this means is that in +general when you put a cache here and + + align:start position:0% +general when you put a cache here and + + + align:start position:0% +general when you put a cache here and +any memory cache here or if you have any + + align:start position:0% +any memory cache here or if you have any + + + align:start position:0% +any memory cache here or if you have any +situation where the rights are + + align:start position:0% +situation where the rights are + + + align:start position:0% +situation where the rights are +asynchronously being done to sell store + + align:start position:0% +asynchronously being done to sell store + + + align:start position:0% +asynchronously being done to sell store +um you need both an undo + + align:start position:0% +um you need both an undo + + + align:start position:0% +um you need both an undo +log um in order to handle aborts and to + + align:start position:0% +log um in order to handle aborts and to + + + align:start position:0% +log um in order to handle aborts and to +handle the simple case and you need the + + align:start position:0% +handle the simple case and you need the + + + align:start position:0% +handle the simple case and you need the +ability to + + align:start position:0% + + + + align:start position:0% + +redo the results of certain actions from + + align:start position:0% +redo the results of certain actions from + + + align:start position:0% +redo the results of certain actions from +the log and both of these are done so + + align:start position:0% +the log and both of these are done so + + + align:start position:0% +the log and both of these are done so +the system fails and then when you + + align:start position:0% +the system fails and then when you + + + align:start position:0% +the system fails and then when you +recover before you allow other actions + + align:start position:0% +recover before you allow other actions + + + align:start position:0% +recover before you allow other actions +um that might be ready to go to take + + align:start position:0% +um that might be ready to go to take + + + align:start position:0% +um that might be ready to go to take +over the database the system has to + + align:start position:0% +over the database the system has to + + + align:start position:0% +over the database the system has to +recover um running a recovery process + + align:start position:0% +recover um running a recovery process + + + align:start position:0% +recover um running a recovery process +and the recovery um happens from the + + align:start position:0% + + + + align:start position:0% + +log and the way the recovery works is + + align:start position:0% +log and the way the recovery works is + + + align:start position:0% +log and the way the recovery works is +and we went through the the last time + + align:start position:0% +and we went through the the last time + + + align:start position:0% +and we went through the the last time +you scan the log backwards um from the + + align:start position:0% +you scan the log backwards um from the + + + align:start position:0% +you scan the log backwards um from the +most recent entry entry in the + + align:start position:0% + + + + align:start position:0% + +log and while scanning the log backwards + + align:start position:0% +log and while scanning the log backwards + + + align:start position:0% +log and while scanning the log backwards +you make two lists you make a list of + + align:start position:0% +you make two lists you make a list of + + + align:start position:0% +you make two lists you make a list of +winners and and a list of losers and the + + align:start position:0% +winners and and a list of losers and the + + + align:start position:0% +winners and and a list of losers and the +winners are all of those actions that + + align:start position:0% +winners are all of those actions that + + + align:start position:0% +winners are all of those actions that +either committed or + + align:start position:0% +either committed or + + + align:start position:0% +either committed or +aborted and one there's one important + + align:start position:0% +aborted and one there's one important + + + align:start position:0% +aborted and one there's one important +Point uh in the aart step which is that + + align:start position:0% +Point uh in the aart step which is that + + + align:start position:0% +Point uh in the aart step which is that +when the system calls aot or when the + + align:start position:0% +when the system calls aot or when the + + + align:start position:0% +when the system calls aot or when the +application calls a bot and about + + align:start position:0% +application calls a bot and about + + + align:start position:0% +application calls a bot and about +Returns what the system does is goes + + align:start position:0% +Returns what the system does is goes + + + align:start position:0% +Returns what the system does is goes +through the log and looks at all the + + align:start position:0% +through the log and looks at all the + + + align:start position:0% +through the log and looks at all the +changes made by that action and undo all + + align:start position:0% +changes made by that action and undo all + + + align:start position:0% +changes made by that action and undo all +of them and then it writes a record + + align:start position:0% +of them and then it writes a record + + + align:start position:0% +of them and then it writes a record +called the abot record onto the log so + + align:start position:0% +called the abot record onto the log so + + + align:start position:0% +called the abot record onto the log so +when you recover you and you see an abot + + align:start position:0% +when you recover you and you see an abot + + + align:start position:0% +when you recover you and you see an abot +record you already know that those + + align:start position:0% +record you already know that those + + + align:start position:0% +record you already know that those +changes made by an aborted action have + + align:start position:0% +changes made by an aborted action have + + + align:start position:0% +changes made by an aborted action have +been + + align:start position:0% +been + + + align:start position:0% +been +undone so when you compose a list of + + align:start position:0% +undone so when you compose a list of + + + align:start position:0% +undone so when you compose a list of +winners that are committed actions and + + align:start position:0% +winners that are committed actions and + + + align:start position:0% +winners that are committed actions and +aborted actions the only things you + + align:start position:0% +aborted actions the only things you + + + align:start position:0% +aborted actions the only things you +really need to redo are the the steps + + align:start position:0% +really need to redo are the the steps + + + align:start position:0% +really need to redo are the the steps +corresponding to the committed actions + + align:start position:0% +corresponding to the committed actions + + + align:start position:0% +corresponding to the committed actions +you don't have to undo the steps + + align:start position:0% +you don't have to undo the steps + + + align:start position:0% +you don't have to undo the steps +corresponding to the aborted actions + + align:start position:0% +corresponding to the aborted actions + + + align:start position:0% +corresponding to the aborted actions +because they already got undone it was + + align:start position:0% +because they already got undone it was + + + align:start position:0% +because they already got undone it was +only after they got undone that the + + align:start position:0% +only after they got undone that the + + + align:start position:0% +only after they got undone that the +abort entry was written to the + + align:start position:0% +abort entry was written to the + + + align:start position:0% +abort entry was written to the +log so in addition to these + + align:start position:0% +log so in addition to these + + + align:start position:0% +log so in addition to these +committed and aborted actions that that + + align:start position:0% +committed and aborted actions that that + + + align:start position:0% +committed and aborted actions that that +are winners there are all other actions + + align:start position:0% +are winners there are all other actions + + + align:start position:0% +are winners there are all other actions +um that were pending or active at the + + align:start position:0% +um that were pending or active at the + + + align:start position:0% +um that were pending or active at the +time of the crash and those are + + align:start position:0% +time of the crash and those are + + + align:start position:0% +time of the crash and those are +losers and so what you have to do to the + + align:start position:0% +losers and so what you have to do to the + + + align:start position:0% +losers and so what you have to do to the +losers + + align:start position:0% +losers + + + align:start position:0% +losers +is to undo the action done by by losers + + align:start position:0% +is to undo the action done by by losers + + + align:start position:0% +is to undo the action done by by losers +so the actual step the recovery step + + align:start position:0% +so the actual step the recovery step + + + align:start position:0% +so the actual step the recovery step +runs after composing these winners and + + align:start position:0% +runs after composing these winners and + + + align:start position:0% +runs after composing these winners and +losers and it corresponds to redoing the + + align:start position:0% +losers and it corresponds to redoing the + + + align:start position:0% +losers and it corresponds to redoing the +committed + + align:start position:0% + + + + align:start position:0% + +winners and undoing the + + align:start position:0% + + + + align:start position:0% + +losers and any independent of crashes + + align:start position:0% +losers and any independent of crashes + + + align:start position:0% +losers and any independent of crashes +when you just independent of failures + + align:start position:0% +when you just independent of failures + + + align:start position:0% +when you just independent of failures +when you just have actions that might + + align:start position:0% +when you just have actions that might + + + align:start position:0% +when you just have actions that might +abart the only thing you really need is + + align:start position:0% +abart the only thing you really need is + + + align:start position:0% +abart the only thing you really need is +undo you don't need to redo anything if + + align:start position:0% +undo you don't need to redo anything if + + + align:start position:0% +undo you don't need to redo anything if +you don't ever have any failures but + + align:start position:0% +you don't ever have any failures but + + + align:start position:0% +you don't ever have any failures but +just actions aborting the only thing you + + align:start position:0% +just actions aborting the only thing you + + + align:start position:0% +just actions aborting the only thing you +need to do with the log is to undo um + + align:start position:0% +need to do with the log is to undo um + + + align:start position:0% +need to do with the log is to undo um +the results of the partially undo the + + align:start position:0% +the results of the partially undo the + + + align:start position:0% +the results of the partially undo the +results of uncommitted actions before + + align:start position:0% +results of uncommitted actions before + + + align:start position:0% +results of uncommitted actions before +aart + + align:start position:0% +aart + + + align:start position:0% +aart +returns now this procedure is okay + + align:start position:0% +returns now this procedure is okay + + + align:start position:0% +returns now this procedure is okay +failures happen rarely and and you're + + align:start position:0% +failures happen rarely and and you're + + + align:start position:0% +failures happen rarely and and you're +willing to take the time um you know + + align:start position:0% +willing to take the time um you know + + + align:start position:0% +willing to take the time um you know +take a substantial amount of time to + + align:start position:0% +take a substantial amount of time to + + + align:start position:0% +take a substantial amount of time to +recover from a failure then you know the + + align:start position:0% +recover from a failure then you know the + + + align:start position:0% +recover from a failure then you know the +log might be quite long if you know + + align:start position:0% +log might be quite long if you know + + + align:start position:0% +log might be quite long if you know +system phase once a week your log might + + align:start position:0% +system phase once a week your log might + + + align:start position:0% +system phase once a week your log might +be quite long and if you're willing to + + align:start position:0% +be quite long and if you're willing to + + + align:start position:0% +be quite long and if you're willing to +take the time to scan through the log + + align:start position:0% +take the time to scan through the log + + + align:start position:0% +take the time to scan through the log +you know entirely and build up these + + align:start position:0% +you know entirely and build up these + + + align:start position:0% +you know entirely and build up these +winners and losers lists then um this is + + align:start position:0% +winners and losers lists then um this is + + + align:start position:0% +winners and losers lists then um this is +fine this approach works just fine but + + align:start position:0% +fine this approach works just fine but + + + align:start position:0% +fine this approach works just fine but +people are often interested in + + align:start position:0% +people are often interested in + + + align:start position:0% +people are often interested in +optimizing the time it takes to recover + + align:start position:0% +optimizing the time it takes to recover + + + align:start position:0% +optimizing the time it takes to recover +from a crash and a common optimization + + align:start position:0% +from a crash and a common optimization + + + align:start position:0% +from a crash and a common optimization +that's done is um called a checkpoint + + align:start position:0% +that's done is um called a checkpoint + + + align:start position:0% +that's done is um called a checkpoint +and I believe you've seen this in system + + align:start position:0% +and I believe you've seen this in system + + + align:start position:0% +and I believe you've seen this in system +R and if you haven't seen it you'll + + align:start position:0% +R and if you haven't seen it you'll + + + align:start position:0% +R and if you haven't seen it you'll +probably see it on uh in tomorrow's + + align:start position:0% +probably see it on uh in tomorrow's + + + align:start position:0% +probably see it on uh in tomorrow's +recitation and the main idea and a + + align:start position:0% +recitation and the main idea and a + + + align:start position:0% +recitation and the main idea and a +checkpoint is it's an optimization that + + align:start position:0% +checkpoint is it's an optimization that + + + align:start position:0% +checkpoint is it's an optimization that +a lot this recovery process not to have + + align:start position:0% +a lot this recovery process not to have + + + align:start position:0% +a lot this recovery process not to have +to scan the log all the way back to Time + + align:start position:0% +to scan the log all the way back to Time + + + align:start position:0% +to scan the log all the way back to Time +Zero um that the system periodically + + align:start position:0% +Zero um that the system periodically + + + align:start position:0% +Zero um that the system periodically +while it's normally operating takes this + + align:start position:0% +while it's normally operating takes this + + + align:start position:0% +while it's normally operating takes this +checkpoint which is to write a special + + align:start position:0% +checkpoint which is to write a special + + + align:start position:0% +checkpoint which is to write a special +record into the log and that record + + align:start position:0% +record into the log and that record + + + align:start position:0% +record into the log and that record +basically says at this point in time + + align:start position:0% +basically says at this point in time + + + align:start position:0% +basically says at this point in time +here's all of the actions that have + + align:start position:0% +here's all of the actions that have + + + align:start position:0% +here's all of the actions that have +committed and whose results have already + + align:start position:0% +committed and whose results have already + + + align:start position:0% +committed and whose results have already +been installed into the celles + + align:start position:0% +been installed into the celles + + + align:start position:0% +been installed into the celles +store in other words they've committed + + align:start position:0% +store in other words they've committed + + + align:start position:0% +store in other words they've committed +and already been installed so when you + + align:start position:0% +and already been installed so when you + + + align:start position:0% +and already been installed so when you +recover you don't have to go and scan + + align:start position:0% +recover you don't have to go and scan + + + align:start position:0% +recover you don't have to go and scan +the log all the way back you just have + + align:start position:0% +the log all the way back you just have + + + align:start position:0% +the log all the way back you just have +to go back enough so you find all of the + + align:start position:0% +to go back enough so you find all of the + + + align:start position:0% +to go back enough so you find all of the +actions uh whose results haven't yet + + align:start position:0% +actions uh whose results haven't yet + + + align:start position:0% +actions uh whose results haven't yet +been installed uh completely which + + align:start position:0% +been installed uh completely which + + + align:start position:0% +been installed uh completely which +haven't been um which have been + + align:start position:0% +haven't been um which have been + + + align:start position:0% +haven't been um which have been +committed and the checkpoint also + + align:start position:0% +committed and the checkpoint also + + + align:start position:0% +committed and the checkpoint also +contains a list of all the actions that + + align:start position:0% +contains a list of all the actions that + + + align:start position:0% +contains a list of all the actions that +that are currently active so once you + + align:start position:0% +that are currently active so once you + + + align:start position:0% +that are currently active so once you +write a checkpoint record to the to the + + align:start position:0% +write a checkpoint record to the to the + + + align:start position:0% +write a checkpoint record to the to the +log during recovery you don't have to go + + align:start position:0% +log during recovery you don't have to go + + + align:start position:0% +log during recovery you don't have to go +all the way back in time there's a few + + align:start position:0% +all the way back in time there's a few + + + align:start position:0% +all the way back in time there's a few +other optimizations um that you can do + + align:start position:0% +other optimizations um that you can do + + + align:start position:0% +other optimizations um that you can do +with checkpoints that are not that + + align:start position:0% +with checkpoints that are not that + + + align:start position:0% +with checkpoints that are not that +interesting to get into here but the + + align:start position:0% +interesting to get into here but the + + + align:start position:0% +interesting to get into here but the +primary optimization that's done to uh + + align:start position:0% +primary optimization that's done to uh + + + align:start position:0% +primary optimization that's done to uh +speed up the recovery process is to use + + align:start position:0% +speed up the recovery process is to use + + + align:start position:0% +speed up the recovery process is to use +this checkpoint record and in most + + align:start position:0% +this checkpoint record and in most + + + align:start position:0% +this checkpoint record and in most +database U systems the checkpoint record + + align:start position:0% +database U systems the checkpoint record + + + align:start position:0% +database U systems the checkpoint record +is pretty small it's not like you're + + align:start position:0% +is pretty small it's not like you're + + + align:start position:0% +is pretty small it's not like you're +checkpointing the entire state of the + + align:start position:0% +checkpointing the entire state of the + + + align:start position:0% +checkpointing the entire state of the +database the main thing you're doing is + + align:start position:0% +database the main thing you're doing is + + + align:start position:0% +database the main thing you're doing is +it's a pretty small amount of State um + + align:start position:0% +it's a pretty small amount of State um + + + align:start position:0% +it's a pretty small amount of State um +that you're using to just um speed up + + align:start position:0% +that you're using to just um speed up + + + align:start position:0% +that you're using to just um speed up +recovery so it's you shouldn't be + + align:start position:0% +recovery so it's you shouldn't be + + + align:start position:0% +recovery so it's you shouldn't be +thinking that the checkpoint is + + align:start position:0% +thinking that the checkpoint is + + + align:start position:0% +thinking that the checkpoint is +something where you take the entire + + align:start position:0% +something where you take the entire + + + align:start position:0% +something where you take the entire +database and copy it over that's not + + align:start position:0% +database and copy it over that's not + + + align:start position:0% +database and copy it over that's not +what goes on it's a pretty lightweight + + align:start position:0% +what goes on it's a pretty lightweight + + + align:start position:0% +what goes on it's a pretty lightweight +small amount of State relative to the + + align:start position:0% +small amount of State relative to the + + + align:start position:0% +small amount of State relative to the +size um of all of the data in the + + align:start position:0% +size um of all of the data in the + + + align:start position:0% +size um of all of the data in the +system so that's the story behind um + + align:start position:0% +system so that's the story behind um + + + align:start position:0% +system so that's the story behind um +recoverability and we're actually going + + align:start position:0% +recoverability and we're actually going + + + align:start position:0% +recoverability and we're actually going +to come back to a piece of the story + + align:start position:0% +to come back to a piece of the story + + + align:start position:0% +to come back to a piece of the story +after we talk about isolation now + + align:start position:0% +after we talk about isolation now + + + align:start position:0% +after we talk about isolation now +because it'll turn out that the + + align:start position:0% +because it'll turn out that the + + + align:start position:0% +because it'll turn out that the +mechanisms for isolation and the + + align:start position:0% +mechanisms for isolation and the + + + align:start position:0% +mechanisms for isolation and the +mechanisms for recoverability using logs + + align:start position:0% +mechanisms for recoverability using logs + + + align:start position:0% +mechanisms for recoverability using logs +interact in certain ways so we'll have + + align:start position:0% +interact in certain ways so we'll have + + + align:start position:0% +interact in certain ways so we'll have +to come back to this um either later + + align:start position:0% +to come back to this um either later + + + align:start position:0% +to come back to this um either later +today or on + + align:start position:0% +today or on + + + align:start position:0% +today or on +Wednesday so now we're going to start + + align:start position:0% +Wednesday so now we're going to start + + + align:start position:0% +Wednesday so now we're going to start +talking about + + align:start position:0% + + + + align:start position:0% + +isolation so if you remember the idea + + align:start position:0% +isolation so if you remember the idea + + + align:start position:0% +isolation so if you remember the idea +behind isolation is when you have a set + + align:start position:0% +behind isolation is when you have a set + + + align:start position:0% +behind isolation is when you have a set +of actions that run concurrently what + + align:start position:0% +of actions that run concurrently what + + + align:start position:0% +of actions that run concurrently what +you would like is an equivalent ordering + + align:start position:0% +you would like is an equivalent ordering + + + align:start position:0% +you would like is an equivalent ordering +of the steps in an action that is + + align:start position:0% +of the steps in an action that is + + + align:start position:0% +of the steps in an action that is +equivalent an ordering of the steps of + + align:start position:0% +equivalent an ordering of the steps of + + + align:start position:0% +equivalent an ordering of the steps of +the different of the actions running + + align:start position:0% +the different of the actions running + + + align:start position:0% +the different of the actions running +concurrently such that the results are + + align:start position:0% +concurrently such that the results are + + + align:start position:0% +concurrently such that the results are +equivalent to some serial ordering of + + align:start position:0% +equivalent to some serial ordering of + + + align:start position:0% +equivalent to some serial ordering of +the actions so the simple way of + + align:start position:0% +the actions so the simple way of + + + align:start position:0% +the actions so the simple way of +describing isolation is do it all before + + align:start position:0% +describing isolation is do it all before + + + align:start position:0% +describing isolation is do it all before +or do it all after so if you have um + + align:start position:0% +or do it all after so if you have um + + + align:start position:0% +or do it all after so if you have um +actions let's say T1 T2 and so on + + align:start position:0% +actions let's say T1 T2 and so on + + + align:start position:0% +actions let's say T1 T2 and so on +running at the same time and they happen + + align:start position:0% +running at the same time and they happen + + + align:start position:0% +running at the same time and they happen +to be these act these actions might + + align:start position:0% +to be these act these actions might + + + align:start position:0% +to be these act these actions might +operate on some data that's in common + + align:start position:0% +operate on some data that's in common + + + align:start position:0% +operate on some data that's in common +they might act on data that's not at all + + align:start position:0% +they might act on data that's not at all + + + align:start position:0% +they might act on data that's not at all +in common and what you would like is an + + align:start position:0% +in common and what you would like is an + + + align:start position:0% +in common and what you would like is an +equivalent um the state of the system + + align:start position:0% +equivalent um the state of the system + + + align:start position:0% +equivalent um the state of the system +after running these concurrent actions + + align:start position:0% +after running these concurrent actions + + + align:start position:0% +after running these concurrent actions +should be equivalent to some serial + + align:start position:0% +should be equivalent to some serial + + + align:start position:0% +should be equivalent to some serial +ordering of the + + align:start position:0% +ordering of the + + + align:start position:0% +ordering of the +actions and it'll turn out that what's + + align:start position:0% +actions and it'll turn out that what's + + + align:start position:0% +actions and it'll turn out that what's +tricky about isolation is um that if you + + align:start position:0% +tricky about isolation is um that if you + + + align:start position:0% +tricky about isolation is um that if you +want isolation and you don't care about + + align:start position:0% +want isolation and you don't care about + + + align:start position:0% +want isolation and you don't care about +performance it's very very easy to do so + + align:start position:0% +performance it's very very easy to do so + + + align:start position:0% +performance it's very very easy to do so +it's very easy to get isolation if you + + align:start position:0% +it's very easy to get isolation if you + + + align:start position:0% +it's very easy to get isolation if you +don't care about performance it's very + + align:start position:0% +don't care about performance it's very + + + align:start position:0% +don't care about performance it's very +easy to run fast if you don't care about + + align:start position:0% +easy to run fast if you don't care about + + + align:start position:0% +easy to run fast if you don't care about +correctness so you know fast and correct + + align:start position:0% +correctness so you know fast and correct + + + align:start position:0% +correctness so you know fast and correct +is the hard problem it's fast and not + + align:start position:0% +is the hard problem it's fast and not + + + align:start position:0% +is the hard problem it's fast and not +correct is Trivial and correct and slow + + align:start position:0% +correct is Trivial and correct and slow + + + align:start position:0% +correct is Trivial and correct and slow +is also trivial I mean correct and slow + + align:start position:0% +is also trivial I mean correct and slow + + + align:start position:0% +is also trivial I mean correct and slow +is very easy because you could take all + + align:start position:0% +is very easy because you could take all + + + align:start position:0% +is very easy because you could take all +of these concurrent actions and just run + + align:start position:0% +of these concurrent actions and just run + + + align:start position:0% +of these concurrent actions and just run +them one after the other so you don't + + align:start position:0% +them one after the other so you don't + + + align:start position:0% +them one after the other so you don't +actually take advantage of any potential + + align:start position:0% +actually take advantage of any potential + + + align:start position:0% +actually take advantage of any potential +concurrency that that that might be uh + + align:start position:0% +concurrency that that that might be uh + + + align:start position:0% +concurrency that that that might be uh +possible so certainly slow and correct + + align:start position:0% +possible so certainly slow and correct + + + align:start position:0% +possible so certainly slow and correct +is very easy to do and we'll actually + + align:start position:0% +is very easy to do and we'll actually + + + align:start position:0% +is very easy to do and we'll actually +turn out we'll start with slow and + + align:start position:0% +turn out we'll start with slow and + + + align:start position:0% +turn out we'll start with slow and +correct and then optimize um + + align:start position:0% +correct and then optimize um + + + align:start position:0% +correct and then optimize um +um a simple + + align:start position:0% +um a simple + + + align:start position:0% +um a simple +scheme there's also a huge amount of + + align:start position:0% +scheme there's also a huge amount of + + + align:start position:0% +scheme there's also a huge amount of +work that's been done on Fast and + + align:start position:0% +work that's been done on Fast and + + + align:start position:0% +work that's been done on Fast and +correct schemes and um in the end they + + align:start position:0% +correct schemes and um in the end they + + + align:start position:0% +correct schemes and um in the end they +all boil down to this one basic idea + + align:start position:0% +all boil down to this one basic idea + + + align:start position:0% +all boil down to this one basic idea +that we'll talk about um toward the end + + align:start position:0% +that we'll talk about um toward the end + + + align:start position:0% +that we'll talk about um toward the end +of lecture + + align:start position:0% +of lecture + + + align:start position:0% +of lecture +today so let's take an example so let's + + align:start position:0% +today so let's take an example so let's + + + align:start position:0% +today so let's take an example so let's +say you have two actions I'm going to + + align:start position:0% +say you have two actions I'm going to + + + align:start position:0% +say you have two actions I'm going to +call them with T's because very often + + align:start position:0% +call them with T's because very often + + + align:start position:0% +call them with T's because very often +you know these are also these are + + align:start position:0% +you know these are also these are + + + align:start position:0% +you know these are also these are +intended to be transactions which add + + align:start position:0% +intended to be transactions which add + + + align:start position:0% +intended to be transactions which add +consistency and durability in addition + + align:start position:0% +consistency and durability in addition + + + align:start position:0% +consistency and durability in addition +to um isolation recover ility so I'm + + align:start position:0% +to um isolation recover ility so I'm + + + align:start position:0% +to um isolation recover ility so I'm +just going to use the word t to + + align:start position:0% +just going to use the word t to + + + align:start position:0% +just going to use the word t to +represent an + + align:start position:0% +represent an + + + align:start position:0% +represent an +action so let's say you have an action + + align:start position:0% +action so let's say you have an action + + + align:start position:0% +action so let's say you have an action +that does read of some variable X and it + + align:start position:0% +that does read of some variable X and it + + + align:start position:0% +that does read of some variable X and it +does right of a variable uh Y and you + + align:start position:0% +does right of a variable uh Y and you + + + align:start position:0% +does right of a variable uh Y and you +have transaction T2 that does WR X and + + align:start position:0% +have transaction T2 that does WR X and + + + align:start position:0% +have transaction T2 that does WR X and +it + + align:start position:0% +it + + + align:start position:0% +it +does right + + align:start position:0% +does right + + + align:start position:0% +does right +y so we're going to take a few examples + + align:start position:0% +y so we're going to take a few examples + + + align:start position:0% +y so we're going to take a few examples +like this in order to understand what it + + align:start position:0% +like this in order to understand what it + + + align:start position:0% +like this in order to understand what it +means for actions to run such that their + + align:start position:0% +means for actions to run such that their + + + align:start position:0% +means for actions to run such that their +steps are equivalent to some serial + + align:start position:0% +steps are equivalent to some serial + + + align:start position:0% +steps are equivalent to some serial +order so we're going to spend some time + + align:start position:0% +order so we're going to spend some time + + + align:start position:0% +order so we're going to spend some time +really understanding that and then once + + align:start position:0% +really understanding that and then once + + + align:start position:0% +really understanding that and then once +we understand what we want it turn out + + align:start position:0% +we understand what we want it turn out + + + align:start position:0% +we understand what we want it turn out +to be relatively easy to come up with + + align:start position:0% +to be relatively easy to come up with + + + align:start position:0% +to be relatively easy to come up with +schemes to achieve + + align:start position:0% + + + + align:start position:0% + +it so let's say that what happens here + + align:start position:0% +it so let's say that what happens here + + + align:start position:0% +it so let's say that what happens here +is that you you get the system gets + + align:start position:0% +is that you you get the system gets + + + align:start position:0% +is that you you get the system gets +presented with these concurrent actions + + align:start position:0% +presented with these concurrent actions + + + align:start position:0% +presented with these concurrent actions +um and let's assume each of these is an + + align:start position:0% +um and let's assume each of these is an + + + align:start position:0% +um and let's assume each of these is an +atomic step so there are four steps that + + align:start position:0% +atomic step so there are four steps that + + + align:start position:0% +atomic step so there are four steps that +can be interleaved in arbitrary ways in + + align:start position:0% +can be interleaved in arbitrary ways in + + + align:start position:0% +can be interleaved in arbitrary ways in +any number of ways so let's say that + + align:start position:0% +any number of ways so let's say that + + + align:start position:0% +any number of ways so let's say that +what happens is you run that first and + + align:start position:0% +what happens is you run that first and + + + align:start position:0% +what happens is you run that first and +then you run that second and then you + + align:start position:0% +then you run that second and then you + + + align:start position:0% +then you run that second and then you +run this third and then you run this + + align:start position:0% +run this third and then you run this + + + align:start position:0% +run this third and then you run this +fourth + + align:start position:0% +fourth + + + align:start position:0% +fourth +so what you get is I'm going to + + align:start position:0% +so what you get is I'm going to + + + align:start position:0% +so what you get is I'm going to +introduce a little bit of notation here + + align:start position:0% +introduce a little bit of notation here + + + align:start position:0% +introduce a little bit of notation here +I'm going to write these steps as R1 + + align:start position:0% +I'm going to write these steps as R1 + + + align:start position:0% +I'm going to write these steps as R1 +X W2 + + align:start position:0% +X W2 + + + align:start position:0% +X W2 +y W1 y I'm sorry w2x + + align:start position:0% +y W1 y I'm sorry w2x + + + align:start position:0% +y W1 y I'm sorry w2x +here and W2 + + align:start position:0% +here and W2 + + + align:start position:0% +here and W2 +Y what the r represents is a read W + + align:start position:0% +Y what the r represents is a read W + + + align:start position:0% +Y what the r represents is a read W +represents a right what the subscripts + + align:start position:0% +represents a right what the subscripts + + + align:start position:0% +represents a right what the subscripts +represent is the identifier of the + + align:start position:0% +represent is the identifier of the + + + align:start position:0% +represent is the identifier of the +action doing the read or right + + align:start position:0% +action doing the read or right + + + align:start position:0% +action doing the read or right +and what's in parenthesis is the + + align:start position:0% +and what's in parenthesis is the + + + align:start position:0% +and what's in parenthesis is the +variable that's being written so this + + align:start position:0% +variable that's being written so this + + + align:start position:0% +variable that's being written so this +says that action one does a read of X + + align:start position:0% +says that action one does a read of X + + + align:start position:0% +says that action one does a read of X +action two does a right of X action one + + align:start position:0% +action two does a right of X action one + + + align:start position:0% +action two does a right of X action one +does a a right of Y and action two does + + align:start position:0% +does a a right of Y and action two does + + + align:start position:0% +does a a right of Y and action two does +a right of Y + + align:start position:0% +a right of Y + + + align:start position:0% +a right of Y +okay so now if you look + + align:start position:0% +okay so now if you look + + + align:start position:0% +okay so now if you look +at um these different actions there's a + + align:start position:0% +at um these different actions there's a + + + align:start position:0% +at um these different actions there's a +few steps that conflict with each other + + align:start position:0% +few steps that conflict with each other + + + align:start position:0% +few steps that conflict with each other +and a few that don't so if you look at + + align:start position:0% +and a few that don't so if you look at + + + align:start position:0% +and a few that don't so if you look at +the read of X and a right of Y you're + + align:start position:0% +the read of X and a right of Y you're + + + align:start position:0% +the read of X and a right of Y you're +independent of everything else if you + + align:start position:0% +independent of everything else if you + + + align:start position:0% +independent of everything else if you +just have read X here and write y here + + align:start position:0% +just have read X here and write y here + + + align:start position:0% +just have read X here and write y here +they don't conflict with each other + + align:start position:0% +they don't conflict with each other + + + align:start position:0% +they don't conflict with each other +because those can happen in any order + + align:start position:0% +because those can happen in any order + + + align:start position:0% +because those can happen in any order +and the results are exactly the + + align:start position:0% +and the results are exactly the + + + align:start position:0% +and the results are exactly the +same similarly the right Y and the right + + align:start position:0% +same similarly the right Y and the right + + + align:start position:0% +same similarly the right Y and the right +X don't conflict with each other the + + align:start position:0% +X don't conflict with each other the + + + align:start position:0% +X don't conflict with each other the +only things that really conflict with + + align:start position:0% +only things that really conflict with + + + align:start position:0% +only things that really conflict with +each other are the read X and the right + + align:start position:0% +each other are the read X and the right + + + align:start position:0% +each other are the read X and the right +X in this example because the results + + align:start position:0% +X in this example because the results + + + align:start position:0% +X in this example because the results +depend on which goes + + align:start position:0% +depend on which goes + + + align:start position:0% +depend on which goes +first um right y conflicts with this + + align:start position:0% +first um right y conflicts with this + + + align:start position:0% +first um right y conflicts with this +right Y and those are basically the two + + align:start position:0% +right Y and those are basically the two + + + align:start position:0% +right Y and those are basically the two +things that um conflict with with each + + align:start position:0% +things that um conflict with with each + + + align:start position:0% +things that um conflict with with each +other in this example so so in general + + align:start position:0% +other in this example so so in general + + + align:start position:0% +other in this example so so in general +if you have + + align:start position:0% +if you have + + + align:start position:0% +if you have +um two actions conflict with one another + + align:start position:0% +um two actions conflict with one another + + + align:start position:0% +um two actions conflict with one another +if they both contain a read and a write + + align:start position:0% +if they both contain a read and a write + + + align:start position:0% +if they both contain a read and a write +of the same variable or a right and a + + align:start position:0% +of the same variable or a right and a + + + align:start position:0% +of the same variable or a right and a +right of the same variable so there's + + align:start position:0% +right of the same variable so there's + + + align:start position:0% +right of the same variable so there's +basically three things U that conflict + + align:start position:0% +basically three things U that conflict + + + align:start position:0% +basically three things U that conflict +if you have some variable call it Z if + + align:start position:0% +if you have some variable call it Z if + + + align:start position:0% +if you have some variable call it Z if +you have a read of Z and a right of Z in + + align:start position:0% +you have a read of Z and a right of Z in + + + align:start position:0% +you have a read of Z and a right of Z in +one action or the other if you have + + align:start position:0% +one action or the other if you have + + + align:start position:0% +one action or the other if you have +right of Z and read of Z or if you have + + align:start position:0% +right of Z and read of Z or if you have + + + align:start position:0% +right of Z and read of Z or if you have +a right of Z and a right of Z and those + + align:start position:0% +a right of Z and a right of Z and those + + + align:start position:0% +a right of Z and a right of Z and those +conflict with one another + + align:start position:0% +conflict with one another + + + align:start position:0% +conflict with one another +now a read and a read don't conflict + + align:start position:0% +now a read and a read don't conflict + + + align:start position:0% +now a read and a read don't conflict +because it doesn't matter what order + + align:start position:0% +because it doesn't matter what order + + + align:start position:0% +because it doesn't matter what order +they run in they're going to give you + + align:start position:0% +they run in they're going to give you + + + align:start position:0% +they run in they're going to give you +the same answer okay so if you look at + + align:start position:0% +the same answer okay so if you look at + + + align:start position:0% +the same answer okay so if you look at +this ordering of r1x + + align:start position:0% +this ordering of r1x + + + align:start position:0% +this ordering of r1x +w2x um W1 Y and W2 y the things that + + align:start position:0% +w2x um W1 Y and W2 y the things that + + + align:start position:0% +w2x um W1 Y and W2 y the things that +conflict are these + + align:start position:0% +conflict are these + + + align:start position:0% +conflict are these +two and these + + align:start position:0% + + + + align:start position:0% + +two now if you look at all of the + + align:start position:0% +two now if you look at all of the + + + align:start position:0% +two now if you look at all of the +conflicting the the two things that + + align:start position:0% +conflicting the the two things that + + + align:start position:0% +conflicting the the two things that +conflict and you draw arrows from + + align:start position:0% +conflict and you draw arrows from + + + align:start position:0% +conflict and you draw arrows from +which one happens before the other what + + align:start position:0% +which one happens before the other what + + + align:start position:0% +which one happens before the other what +you find is that for this x conflict one + + align:start position:0% +you find is that for this x conflict one + + + align:start position:0% +you find is that for this x conflict one +runs before two and for this y conflict + + align:start position:0% +runs before two and for this y conflict + + + align:start position:0% +runs before two and for this y conflict +one runs before two so the arrows if I + + align:start position:0% +one runs before two so the arrows if I + + + align:start position:0% +one runs before two so the arrows if I +were to draw them in time order would + + align:start position:0% +were to draw them in time order would + + + align:start position:0% +were to draw them in time order would +point this + + align:start position:0% +point this + + + align:start position:0% +point this +way and this ordering is basically the + + align:start position:0% +way and this ordering is basically the + + + align:start position:0% +way and this ordering is basically the +same as the same ordering you would get + + align:start position:0% +same as the same ordering you would get + + + align:start position:0% +same as the same ordering you would get +even though the steps run in different + + align:start position:0% +even though the steps run in different + + + align:start position:0% +even though the steps run in different +order it's exactly the same as if you + + align:start position:0% +order it's exactly the same as if you + + + align:start position:0% +order it's exactly the same as if you +ran T1 completely before T2 because + + align:start position:0% +ran T1 completely before T2 because + + + align:start position:0% +ran T1 completely before T2 because +running T1 completely before T2 says the + + align:start position:0% +running T1 completely before T2 says the + + + align:start position:0% +running T1 completely before T2 says the +ordering is is r1x W1 y w2x W2 y but the + + align:start position:0% +ordering is is r1x W1 y w2x W2 y but the + + + align:start position:0% +ordering is is r1x W1 y w2x W2 y but the +results exactly the same as this + + align:start position:0% +results exactly the same as this + + + align:start position:0% +results exactly the same as this +different inter leaving uh which does uh + + align:start position:0% +different inter leaving uh which does uh + + + align:start position:0% +different inter leaving uh which does uh +1 2 3 + + align:start position:0% +1 2 3 + + + align:start position:0% +1 2 3 +4 so what this says is that this Trace + + align:start position:0% +4 so what this says is that this Trace + + + align:start position:0% +4 so what this says is that this Trace +that you get we're going to use the word + + align:start position:0% +that you get we're going to use the word + + + align:start position:0% +that you get we're going to use the word +trace for this you know you you present + + align:start position:0% +trace for this you know you you present + + + align:start position:0% +trace for this you know you you present +these concurrent actions Each of which + + align:start position:0% +these concurrent actions Each of which + + + align:start position:0% +these concurrent actions Each of which +has one or more steps um and the system + + align:start position:0% +has one or more steps um and the system + + + align:start position:0% +has one or more steps um and the system +runs them and then the order in which + + align:start position:0% +runs them and then the order in which + + + align:start position:0% +runs them and then the order in which +the individual steps run produces a + + align:start position:0% +the individual steps run produces a + + + align:start position:0% +the individual steps run produces a +trace and then the question is whether + + align:start position:0% +trace and then the question is whether + + + align:start position:0% +trace and then the question is whether +that Trace is is what is called + + align:start position:0% +that Trace is is what is called + + + align:start position:0% +that Trace is is what is called +serializable a trace is serializable if + + align:start position:0% +serializable a trace is serializable if + + + align:start position:0% +serializable a trace is serializable if +the result of that if the trace results + + align:start position:0% +the result of that if the trace results + + + align:start position:0% +the result of that if the trace results +are identical to running the actions in + + align:start position:0% +are identical to running the actions in + + + align:start position:0% +are identical to running the actions in +some serial order one after the other + + align:start position:0% +some serial order one after the other + + + align:start position:0% +some serial order one after the other +and so what we're going to be trying to + + align:start position:0% +and so what we're going to be trying to + + + align:start position:0% +and so what we're going to be trying to +do is what we're trying to going to do + + align:start position:0% +do is what we're trying to going to do + + + align:start position:0% +do is what we're trying to going to do +today is to come up with schemes that + + align:start position:0% +today is to come up with schemes that + + + align:start position:0% +today is to come up with schemes that +which take these different steps + + align:start position:0% +which take these different steps + + + align:start position:0% +which take these different steps +corresponding to the actions and produce + + align:start position:0% +corresponding to the actions and produce + + + align:start position:0% +corresponding to the actions and produce +an order that turns out to be a + + align:start position:0% +an order that turns out to be a + + + align:start position:0% +an order that turns out to be a +serializable order and the challenge is + + align:start position:0% +serializable order and the challenge is + + + align:start position:0% +serializable order and the challenge is +to do it in a way that allows you to get + + align:start position:0% +to do it in a way that allows you to get + + + align:start position:0% +to do it in a way that allows you to get +reasonable performance + + align:start position:0% +reasonable performance + + + align:start position:0% +reasonable performance +so to give you an example of a non- + + align:start position:0% +so to give you an example of a non- + + + align:start position:0% +so to give you an example of a non- +serializable order if we did had the + + align:start position:0% +serializable order if we did had the + + + align:start position:0% +serializable order if we did had the +following Trace r1x followed by W2 y + + align:start position:0% +following Trace r1x followed by W2 y + + + align:start position:0% +following Trace r1x followed by W2 y +followed + + align:start position:0% +followed + + + align:start position:0% +followed +by + + align:start position:0% +by + + + align:start position:0% +by +w2x followed by W2 + + align:start position:0% +w2x followed by W2 + + + align:start position:0% +w2x followed by W2 +y followed + + align:start position:0% + + + + align:start position:0% + +by W1 Y what happens here is that these + + align:start position:0% +by W1 Y what happens here is that these + + + align:start position:0% +by W1 Y what happens here is that these +two guys conflict so you got an arrow + + align:start position:0% +two guys conflict so you got an arrow + + + align:start position:0% +two guys conflict so you got an arrow +from one to two going this + + align:start position:0% +from one to two going this + + + align:start position:0% +from one to two going this +way and similarly these two guys + + align:start position:0% +way and similarly these two guys + + + align:start position:0% +way and similarly these two guys +conflict but the arrow in time goes from + + align:start position:0% +conflict but the arrow in time goes from + + + align:start position:0% +conflict but the arrow in time goes from +two to + + align:start position:0% +two to + + + align:start position:0% +two to +one which means that if you drew drew + + align:start position:0% +one which means that if you drew drew + + + align:start position:0% +one which means that if you drew drew +the arrow one to two this way you would + + align:start position:0% +the arrow one to two this way you would + + + align:start position:0% +the arrow one to two this way you would +have an arrow going the opposite + + align:start position:0% +have an arrow going the opposite + + + align:start position:0% +have an arrow going the opposite +direction so this doesn't correspond to + + align:start position:0% +direction so this doesn't correspond to + + + align:start position:0% +direction so this doesn't correspond to +any serial order because per as far as + + align:start position:0% +any serial order because per as far as + + + align:start position:0% +any serial order because per as far as +this conflict is concerned this tray + + align:start position:0% +this conflict is concerned this tray + + + align:start position:0% +this conflict is concerned this tray +says that action one should run before + + align:start position:0% +says that action one should run before + + + align:start position:0% +says that action one should run before +action two and as far as this conflict + + align:start position:0% +action two and as far as this conflict + + + align:start position:0% +action two and as far as this conflict +is concerned it says that action two to + + align:start position:0% +is concerned it says that action two to + + + align:start position:0% +is concerned it says that action two to +should run before action + + align:start position:0% +should run before action + + + align:start position:0% +should run before action +one which means you're in trouble + + align:start position:0% +one which means you're in trouble + + + align:start position:0% +one which means you're in trouble +because there is really no serial um + + align:start position:0% +because there is really no serial um + + + align:start position:0% +because there is really no serial um +ordering here this Trace does not + + align:start position:0% +ordering here this Trace does not + + + align:start position:0% +ordering here this Trace does not +correspond to either T1 before T2 or T2 + + align:start position:0% +correspond to either T1 before T2 or T2 + + + align:start position:0% +correspond to either T1 before T2 or T2 +before + + align:start position:0% +before + + + align:start position:0% +before +T1 which means it this Trace if you have + + align:start position:0% +T1 which means it this Trace if you have + + + align:start position:0% +T1 which means it this Trace if you have +a scheme that runs your actions the + + align:start position:0% +a scheme that runs your actions the + + + align:start position:0% +a scheme that runs your actions the +steps of Your Action and produces the + + align:start position:0% +steps of Your Action and produces the + + + align:start position:0% +steps of Your Action and produces the +Stray it means that that scheme does not + + align:start position:0% +Stray it means that that scheme does not + + + align:start position:0% +Stray it means that that scheme does not +provide isolation Okay notice that we + + align:start position:0% +provide isolation Okay notice that we + + + align:start position:0% +provide isolation Okay notice that we +don't actually care whether T1 runs + + align:start position:0% +don't actually care whether T1 runs + + + align:start position:0% +don't actually care whether T1 runs +before T2 or T2 runs before T1 we're not + + align:start position:0% +before T2 or T2 runs before T1 we're not + + + align:start position:0% +before T2 or T2 runs before T1 we're not +worried about that we just worried about + + align:start position:0% +worried about that we just worried about + + + align:start position:0% +worried about that we just worried about +producing some equivalent serial order + + align:start position:0% +producing some equivalent serial order + + + align:start position:0% +producing some equivalent serial order +serial equivalent + + align:start position:0% + + + + align:start position:0% + +order so that's the definition of the + + align:start position:0% +order so that's the definition of the + + + align:start position:0% +order so that's the definition of the +property that we + + align:start position:0% + + + + align:start position:0% + +want is serializability and what it says + + align:start position:0% +want is serializability and what it says + + + align:start position:0% +want is serializability and what it says +is it's a trace whose conflict arrows uh + + align:start position:0% +is it's a trace whose conflict arrows uh + + + align:start position:0% +is it's a trace whose conflict arrows uh +these are these conflict arrows + + align:start position:0% +these are these conflict arrows + + + align:start position:0% +these are these conflict arrows +correspond to are equivalent to some + + align:start position:0% +correspond to are equivalent to some + + + align:start position:0% +correspond to are equivalent to some +serial ordering um of the steps of the + + align:start position:0% +serial ordering um of the steps of the + + + align:start position:0% +serial ordering um of the steps of the +action so what we want is the trace + + align:start position:0% +action so what we want is the trace + + + align:start position:0% +action so what we want is the trace +traces + + align:start position:0% + + + + align:start position:0% + +conflicts should be in the same + + align:start position:0% +conflicts should be in the same + + + align:start position:0% +conflicts should be in the same +order as some serial + + align:start position:0% +order as some serial + + + align:start position:0% +order as some serial +schedule or some serial order + + align:start position:0% + + + + align:start position:0% + +of of the + + align:start position:0% + + + + align:start position:0% + +actions so what we're going to do is in + + align:start position:0% +actions so what we're going to do is in + + + align:start position:0% +actions so what we're going to do is in +three + + align:start position:0% +three + + + align:start position:0% +three +parts the first part is to take we're + + align:start position:0% +parts the first part is to take we're + + + align:start position:0% +parts the first part is to take we're +going to look at one of these traces and + + align:start position:0% +going to look at one of these traces and + + + align:start position:0% +going to look at one of these traces and +given a trace the first problem is to + + align:start position:0% +given a trace the first problem is to + + + align:start position:0% +given a trace the first problem is to +figure out whether that Trace + + align:start position:0% +figure out whether that Trace + + + align:start position:0% +figure out whether that Trace +corresponds to some serial + + align:start position:0% +corresponds to some serial + + + align:start position:0% +corresponds to some serial +order and then we're going to derive a + + align:start position:0% +order and then we're going to derive a + + + align:start position:0% +order and then we're going to derive a +property that guarantees that if you you + + align:start position:0% +property that guarantees that if you you + + + align:start position:0% +property that guarantees that if you you +know if a certain property holds we'll + + align:start position:0% +know if a certain property holds we'll + + + align:start position:0% +know if a certain property holds we'll +be assured that a trace is in serial + + align:start position:0% +be assured that a trace is in serial + + + align:start position:0% +be assured that a trace is in serial +order and then the second part is we're + + align:start position:0% +order and then the second part is we're + + + align:start position:0% +order and then the second part is we're +going to come up with various schemes + + align:start position:0% +going to come up with various schemes + + + align:start position:0% +going to come up with various schemes +for achieving + + align:start position:0% +for achieving + + + align:start position:0% +for achieving +serializability and the third part is in + + align:start position:0% +serializability and the third part is in + + + align:start position:0% +serializability and the third part is in +order to prove Pro that those schemes + + align:start position:0% +order to prove Pro that those schemes + + + align:start position:0% +order to prove Pro that those schemes +are + + align:start position:0% +are + + + align:start position:0% +are +correct what we're going to do is to + + align:start position:0% +correct what we're going to do is to + + + align:start position:0% +correct what we're going to do is to +prove that this property um that all + + align:start position:0% +prove that this property um that all + + + align:start position:0% +prove that this property um that all +serial orderings should satisfy holds + + align:start position:0% +serial orderings should satisfy holds + + + align:start position:0% +serial orderings should satisfy holds +for the protocol or for the algorithm + + align:start position:0% +for the protocol or for the algorithm + + + align:start position:0% +for the protocol or for the algorithm +that we designed okay so that's that's + + align:start position:0% +that we designed okay so that's that's + + + align:start position:0% +that we designed okay so that's that's +the plan for for the rest of + + align:start position:0% +the plan for for the rest of + + + align:start position:0% +the plan for for the rest of +today so this property for + + align:start position:0% + + + + align:start position:0% + +serializability is going to use a data + + align:start position:0% +serializability is going to use a data + + + align:start position:0% +serializability is going to use a data +structure or a construction called an + + align:start position:0% +structure or a construction called an + + + align:start position:0% +structure or a construction called an +action graph okay and it turns out that + + align:start position:0% +action graph okay and it turns out that + + + align:start position:0% +action graph okay and it turns out that +what we're going to do is given one of + + align:start position:0% +what we're going to do is given one of + + + align:start position:0% +what we're going to do is given one of +these traces we're going to produce a + + align:start position:0% +these traces we're going to produce a + + + align:start position:0% +these traces we're going to produce a +graph out of those traces um called the + + align:start position:0% +graph out of those traces um called the + + + align:start position:0% +graph out of those traces um called the +action graph and then we're going to + + align:start position:0% +action graph and then we're going to + + + align:start position:0% +action graph and then we're going to +look to see whether a certain property + + align:start position:0% +look to see whether a certain property + + + align:start position:0% +look to see whether a certain property +holds for that action + + align:start position:0% +holds for that action + + + align:start position:0% +holds for that action +graph so let me show you what this + + align:start position:0% +graph so let me show you what this + + + align:start position:0% +graph so let me show you what this +action graph is by Example The the graph + + align:start position:0% +action graph is by Example The the graph + + + align:start position:0% +action graph is by Example The the graph +itself consists of nodes and edges and + + align:start position:0% +itself consists of nodes and edges and + + + align:start position:0% +itself consists of nodes and edges and +it's a directed graph and the nodes are + + align:start position:0% +it's a directed graph and the nodes are + + + align:start position:0% +it's a directed graph and the nodes are +not these r1s and W2s what the nodes are + + align:start position:0% +not these r1s and W2s what the nodes are + + + align:start position:0% +not these r1s and W2s what the nodes are +are the actions themselves so if you + + align:start position:0% +are the actions themselves so if you + + + align:start position:0% +are the actions themselves so if you +have you know four actions running you + + align:start position:0% +have you know four actions running you + + + align:start position:0% +have you know four actions running you +have four nodes in the graph and then + + align:start position:0% +have four nodes in the graph and then + + + align:start position:0% +have four nodes in the graph and then +there are edges between these nodes in + + align:start position:0% +there are edges between these nodes in + + + align:start position:0% +there are edges between these nodes in +the graph so let's do it by an example + + align:start position:0% +the graph so let's do it by an example + + + align:start position:0% +the graph so let's do it by an example +so let's say you + + align:start position:0% +so let's say you + + + align:start position:0% +so let's say you +have first trans first action T1 which + + align:start position:0% +have first trans first action T1 which + + + align:start position:0% +have first trans first action T1 which +has a read of X and a right of Y and + + align:start position:0% +has a read of X and a right of Y and + + + align:start position:0% +has a read of X and a right of Y and +just so we are sure that it's action one + + align:start position:0% +just so we are sure that it's action one + + + align:start position:0% +just so we are sure that it's action one +I'm going to draw one underneath as a + + align:start position:0% +I'm going to draw one underneath as a + + + align:start position:0% +I'm going to draw one underneath as a +subscript of course the just + + align:start position:0% +subscript of course the just + + + align:start position:0% +subscript of course the just +reads action two has a right of X and a + + align:start position:0% +reads action two has a right of X and a + + + align:start position:0% +reads action two has a right of X and a +right of + + align:start position:0% + + + + align:start position:0% + +y action three has a read of Y and a + + align:start position:0% +y action three has a read of Y and a + + + align:start position:0% +y action three has a read of Y and a +right of another variable + + align:start position:0% + + + + align:start position:0% + +Z and Action + + align:start position:0% +Z and Action + + + align:start position:0% +Z and Action +Four has a read of + + align:start position:0% + + + + align:start position:0% + +X so first of all given these + + align:start position:0% + + + + align:start position:0% + +actions which of the actions conflict + + align:start position:0% +actions which of the actions conflict + + + align:start position:0% +actions which of the actions conflict +with each other so let's first write for + + align:start position:0% +with each other so let's first write for + + + align:start position:0% +with each other so let's first write for +T1 does T2 conflict with + + align:start position:0% +T1 does T2 conflict with + + + align:start position:0% +T1 does T2 conflict with +T1 yes it does because the readex and I + + align:start position:0% +T1 yes it does because the readex and I + + + align:start position:0% +T1 yes it does because the readex and I +mean that's the same as that example so + + align:start position:0% +mean that's the same as that example so + + + align:start position:0% +mean that's the same as that example so +certainly T2 conflicts with + + align:start position:0% +certainly T2 conflicts with + + + align:start position:0% +certainly T2 conflicts with +T1 what about T3 does T3 conflict with + + align:start position:0% +T1 what about T3 does T3 conflict with + + + align:start position:0% +T1 what about T3 does T3 conflict with +T1 what that means is does the order + + align:start position:0% +T1 what that means is does the order + + + align:start position:0% +T1 what that means is does the order +matter does the interleaving of the + + align:start position:0% +matter does the interleaving of the + + + align:start position:0% +matter does the interleaving of the +individual steps matter as far as the + + align:start position:0% +individual steps matter as far as the + + + align:start position:0% +individual steps matter as far as the +final answer is + + align:start position:0% +final answer is + + + align:start position:0% +final answer is +concerned yeah it does because the right + + align:start position:0% +concerned yeah it does because the right + + + align:start position:0% +concerned yeah it does because the right +of Y and the read read of Y conflict so + + align:start position:0% +of Y and the read read of Y conflict so + + + align:start position:0% +of Y and the read read of Y conflict so +you got T1 and T3 that you have to worry + + align:start position:0% +you got T1 and T3 that you have to worry + + + align:start position:0% +you got T1 and T3 that you have to worry +about um does T1 conflict with + + align:start position:0% +about um does T1 conflict with + + + align:start position:0% +about um does T1 conflict with +T4 + + align:start position:0% +T4 + + + align:start position:0% +T4 +no it doesn't the read and the read + + align:start position:0% +no it doesn't the read and the read + + + align:start position:0% +no it doesn't the read and the read +don't conflict does T2 conflict with + + align:start position:0% +don't conflict does T2 conflict with + + + align:start position:0% +don't conflict does T2 conflict with +T3 yeah it does because you got the Y + + align:start position:0% +T3 yeah it does because you got the Y + + + align:start position:0% +T3 yeah it does because you got the Y +um okay um does T2 conflict with T4 it + + align:start position:0% + + + + align:start position:0% + +does and does T3 conflict with T4 it + + align:start position:0% +does and does T3 conflict with T4 it + + + align:start position:0% +does and does T3 conflict with T4 it +doesn't there's nothing that shared so + + align:start position:0% +doesn't there's nothing that shared so + + + align:start position:0% +doesn't there's nothing that shared so +out of the six part um or whatever four + + align:start position:0% +out of the six part um or whatever four + + + align:start position:0% +out of the six part um or whatever four +choose two possible conflicts conflicts + + align:start position:0% +choose two possible conflicts conflicts + + + align:start position:0% +choose two possible conflicts conflicts +you got four of them that you got to + + align:start position:0% +you got four of them that you got to + + + align:start position:0% +you got four of them that you got to +worry + + align:start position:0% +worry + + + align:start position:0% +worry +about + + align:start position:0% +about + + + align:start position:0% +about +okay so now we're going to draw this + + align:start position:0% +okay so now we're going to draw this + + + align:start position:0% +okay so now we're going to draw this +graph that has T1 T2 T3 and T4 and we're + + align:start position:0% +graph that has T1 T2 T3 and T4 and we're + + + align:start position:0% +graph that has T1 T2 T3 and T4 and we're +going to call this the action + + align:start position:0% + + + + align:start position:0% + +graph and what it's going to do is to + + align:start position:0% +graph and what it's going to do is to + + + align:start position:0% +graph and what it's going to do is to +draw arrows between + + align:start position:0% +draw arrows between + + + align:start position:0% +draw arrows between +actions that conflict with one another + + align:start position:0% +actions that conflict with one another + + + align:start position:0% +actions that conflict with one another +but of course the answer the arrows + + align:start position:0% +but of course the answer the arrows + + + align:start position:0% +but of course the answer the arrows +depend on the order in which these + + align:start position:0% +depend on the order in which these + + + align:start position:0% +depend on the order in which these +individual steps get scheduled by the + + align:start position:0% +individual steps get scheduled by the + + + align:start position:0% +individual steps get scheduled by the +system running these actions so we need + + align:start position:0% +system running these actions so we need + + + align:start position:0% +system running these actions so we need +an actual example for + + align:start position:0% +an actual example for + + + align:start position:0% +an actual example for +that so let's say that what happens is + + align:start position:0% +that so let's say that what happens is + + + align:start position:0% +that so let's say that what happens is +you present these concurrent actions and + + align:start position:0% +you present these concurrent actions and + + + align:start position:0% +you present these concurrent actions and +what happens is this guy runs + + align:start position:0% +what happens is this guy runs + + + align:start position:0% +what happens is this guy runs +first and then 2 3 + + align:start position:0% +first and then 2 3 + + + align:start position:0% +first and then 2 3 + + align:start position:0% + + + align:start position:0% +5 6 and S + + align:start position:0% +5 6 and S + + + align:start position:0% +5 6 and S +okay so that's the order in which the + + align:start position:0% +okay so that's the order in which the + + + align:start position:0% +okay so that's the order in which the +system runs the individual steps of this + + align:start position:0% +system runs the individual steps of this + + + align:start position:0% +system runs the individual steps of this +action so now we we're going to draw + + align:start position:0% +action so now we we're going to draw + + + align:start position:0% +action so now we we're going to draw +these arrows between actions if two + + align:start position:0% +these arrows between actions if two + + + align:start position:0% +these arrows between actions if two +actions share a conflicting + + align:start position:0% +actions share a conflicting + + + align:start position:0% +actions share a conflicting +operation and one of one of those that + + align:start position:0% +operation and one of one of those that + + + align:start position:0% +operation and one of one of those that +in the first action the conflicting + + align:start position:0% +in the first action the conflicting + + + align:start position:0% +in the first action the conflicting +operation occurs before the second + + align:start position:0% +operation occurs before the second + + + align:start position:0% +operation occurs before the second +action then you're going to draw an + + align:start position:0% +action then you're going to draw an + + + align:start position:0% +action then you're going to draw an +arrow from the first action to the + + align:start position:0% +arrow from the first action to the + + + align:start position:0% +arrow from the first action to the +second action so more generally there's + + align:start position:0% +second action so more generally there's + + + align:start position:0% +second action so more generally there's +an arrow from TI to + + align:start position:0% +an arrow from TI to + + + align:start position:0% +an arrow from TI to +TJ if I and J share a conflicting + + align:start position:0% +TJ if I and J share a conflicting + + + align:start position:0% +TJ if I and J share a conflicting +operation have a conflicting operation + + align:start position:0% +operation have a conflicting operation + + + align:start position:0% +operation have a conflicting operation +and that conflicting operation that + + align:start position:0% +and that conflicting operation that + + + align:start position:0% +and that conflicting operation that +individual step runs by this is run by + + align:start position:0% +individual step runs by this is run by + + + align:start position:0% +individual step runs by this is run by +the system for I first before + + align:start position:0% +the system for I first before + + + align:start position:0% +the system for I first before +J so if you look here at T1 to T2 + + align:start position:0% +J so if you look here at T1 to T2 + + + align:start position:0% +J so if you look here at T1 to T2 +there's an arrow between T1 and + + align:start position:0% +there's an arrow between T1 and + + + align:start position:0% +there's an arrow between T1 and +T2 because it ran r1x before it ran + + align:start position:0% +T2 because it ran r1x before it ran + + + align:start position:0% +T2 because it ran r1x before it ran +w2x if you look at um T1 and + + align:start position:0% +w2x if you look at um T1 and + + + align:start position:0% +w2x if you look at um T1 and +T3 this is a little subtle because it + + align:start position:0% +T3 this is a little subtle because it + + + align:start position:0% +T3 this is a little subtle because it +ran read of X before it ran R3 y but + + align:start position:0% +ran read of X before it ran R3 y but + + + align:start position:0% +ran read of X before it ran R3 y but +that doesn't matter because read of X + + align:start position:0% +that doesn't matter because read of X + + + align:start position:0% +that doesn't matter because read of X +there and read of Y there don't + + align:start position:0% +there and read of Y there don't + + + align:start position:0% +there and read of Y there don't +conflict but then it ran W1 y after it + + align:start position:0% +conflict but then it ran W1 y after it + + + align:start position:0% +conflict but then it ran W1 y after it +ran read 3 Y which means that the + + align:start position:0% +ran read 3 Y which means that the + + + align:start position:0% +ran read 3 Y which means that the +conflict is equivalent to running T that + + align:start position:0% +conflict is equivalent to running T that + + + align:start position:0% +conflict is equivalent to running T that +step of T3 before the step of T1 so you + + align:start position:0% +step of T3 before the step of T1 so you + + + align:start position:0% +step of T3 before the step of T1 so you +actually have an arrow going back from + + align:start position:0% +actually have an arrow going back from + + + align:start position:0% +actually have an arrow going back from +T3 to T1 okay okay so now what about T2 + + align:start position:0% +T3 to T1 okay okay so now what about T2 + + + align:start position:0% +T3 to T1 okay okay so now what about T2 +and + + align:start position:0% +and + + + align:start position:0% +and +T3 T2 and T3 same story w2x and R3 y + + align:start position:0% +T3 T2 and T3 same story w2x and R3 y + + + align:start position:0% +T3 T2 and T3 same story w2x and R3 y +don't conflict but R3 y runs before W2 + + align:start position:0% +don't conflict but R3 y runs before W2 + + + align:start position:0% +don't conflict but R3 y runs before W2 +W2 Y and that's the conflict so you have + + align:start position:0% +W2 Y and that's the conflict so you have + + + align:start position:0% +W2 Y and that's the conflict so you have +an arrow going this + + align:start position:0% +an arrow going this + + + align:start position:0% +an arrow going this +way so we got three of them we need a + + align:start position:0% +way so we got three of them we need a + + + align:start position:0% +way so we got three of them we need a +fourth one and that's between t and + + align:start position:0% +fourth one and that's between t and + + + align:start position:0% +fourth one and that's between t and +T4 between T2 and T4 w2x runs before r4x + + align:start position:0% +T4 between T2 and T4 w2x runs before r4x + + + align:start position:0% +T4 between T2 and T4 w2x runs before r4x +which means you have an arror going this + + align:start position:0% +which means you have an arror going this + + + align:start position:0% +which means you have an arror going this +way + + align:start position:0% +way + + + align:start position:0% +way +okay if you actually look at this + + align:start position:0% + + + + align:start position:0% + +picture and we'll see we'll come up with + + align:start position:0% +picture and we'll see we'll come up with + + + align:start position:0% +picture and we'll see we'll come up with +a method to systematically argue this + + align:start position:0% +a method to systematically argue this + + + align:start position:0% +a method to systematically argue this +point but if you look at that schedule + + align:start position:0% +point but if you look at that schedule + + + align:start position:0% +point but if you look at that schedule +as shown here where you run where the + + align:start position:0% +as shown here where you run where the + + + align:start position:0% +as shown here where you run where the +system runs the individual steps in that + + align:start position:0% +system runs the individual steps in that + + + align:start position:0% +system runs the individual steps in that +order this is actually equivalent to T3 + + align:start position:0% +order this is actually equivalent to T3 + + + align:start position:0% +order this is actually equivalent to T3 +running and then T1 running and then T2 + + align:start position:0% +running and then T1 running and then T2 + + + align:start position:0% +running and then T1 running and then T2 +running and then T4 running the order of + + align:start position:0% +running and then T4 running the order of + + + align:start position:0% +running and then T4 running the order of +interleaving these different steps in + + align:start position:0% +interleaving these different steps in + + + align:start position:0% +interleaving these different steps in +the way shown in that picture 1 2 3 4 5 + + align:start position:0% +the way shown in that picture 1 2 3 4 5 + + + align:start position:0% +the way shown in that picture 1 2 3 4 5 +6 7 is actually equivalent to the same + + align:start position:0% +6 7 is actually equivalent to the same + + + align:start position:0% +6 7 is actually equivalent to the same +result it's the same result that you get + + align:start position:0% +result it's the same result that you get + + + align:start position:0% +result it's the same result that you get +if you ran T3 completely and then T1 and + + align:start position:0% +if you ran T3 completely and then T1 and + + + align:start position:0% +if you ran T3 completely and then T1 and +then T2 and then T4 and fact if you + + align:start position:0% +then T2 and then T4 and fact if you + + + align:start position:0% +then T2 and then T4 and fact if you +think about it it's also + + align:start position:0% +think about it it's also + + + align:start position:0% +think about it it's also +equivalent to the same ordering that you + + align:start position:0% +equivalent to the same ordering that you + + + align:start position:0% +equivalent to the same ordering that you +get if you run T3 and then you run T1 + + align:start position:0% +get if you run T3 and then you run T1 + + + align:start position:0% +get if you run T3 and then you run T1 +and then you run T4 and then you run + + align:start position:0% + + + + align:start position:0% + +T2 that just says that for the ex exact + + align:start position:0% +T2 that just says that for the ex exact + + + align:start position:0% +T2 that just says that for the ex exact +same scheduling of individual steps in + + align:start position:0% +same scheduling of individual steps in + + + align:start position:0% +same scheduling of individual steps in +the concurrent actions you might find + + align:start position:0% +the concurrent actions you might find + + + align:start position:0% +the concurrent actions you might find +multiple equivalent serial orders that + + align:start position:0% +multiple equivalent serial orders that + + + align:start position:0% +multiple equivalent serial orders that +all give you the same + + align:start position:0% + + + + align:start position:0% + +answer is that clear + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +yeah T1 and + + align:start position:0% + + + + align:start position:0% + +T2 + + align:start position:0% + + + + align:start position:0% + +one Cal order or is there + + align:start position:0% + + + + align:start position:0% + +more no 34 doesn't + + align:start position:0% +more no 34 doesn't + + + align:start position:0% +more no 34 doesn't +work so I guess there is just + + align:start position:0% + + + + align:start position:0% + +one it's hard I could have sworn with + + align:start position:0% +one it's hard I could have sworn with + + + align:start position:0% +one it's hard I could have sworn with +two edges missing could be more but + + align:start position:0% + + + + align:start position:0% + +okay is the arrow from 2 to + + align:start position:0% + + + + align:start position:0% + +four the arrow from 2 to four is correct + + align:start position:0% +four the arrow from 2 to four is correct + + + align:start position:0% +four the arrow from 2 to four is correct +right right right of X runs before read + + align:start position:0% +right right right of X runs before read + + + align:start position:0% +right right right of X runs before read +of + + align:start position:0% + + + + align:start position:0% + +X so I think this is correct is there a + + align:start position:0% +X so I think this is correct is there a + + + align:start position:0% +X so I think this is correct is there a +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay so it isn't in this example it + + align:start position:0% +okay so it isn't in this example it + + + align:start position:0% +okay so it isn't in this example it +isn't multiple serial orders but in + + align:start position:0% +isn't multiple serial orders but in + + + align:start position:0% +isn't multiple serial orders but in +general it is the case that there are + + align:start position:0% +general it is the case that there are + + + align:start position:0% +general it is the case that there are +multiple serial orders + + align:start position:0% + + + + align:start position:0% + +possible + + align:start position:0% + + + + align:start position:0% + +okay so what does this action graph got + + align:start position:0% +okay so what does this action graph got + + + align:start position:0% +okay so what does this action graph got +to do with + + align:start position:0% +to do with + + + align:start position:0% +to do with +anything + + align:start position:0% +anything + + + align:start position:0% +anything +so it turns out and we'll prove + + align:start position:0% +so it turns out and we'll prove + + + align:start position:0% +so it turns out and we'll prove +this that if the action + + align:start position:0% + + + + align:start position:0% + +graph for any ordering of actions of of + + align:start position:0% +graph for any ordering of actions of of + + + align:start position:0% +graph for any ordering of actions of of +steps within an action if if the action + + align:start position:0% +steps within an action if if the action + + + align:start position:0% +steps within an action if if the action +graph does not have a + + align:start position:0% + + + + align:start position:0% + +cycle then the corresponding Trace from + + align:start position:0% +cycle then the corresponding Trace from + + + align:start position:0% +cycle then the corresponding Trace from +which the action graph was + + align:start position:0% +which the action graph was + + + align:start position:0% +which the action graph was +derived is serializable + + align:start position:0% + + + + align:start position:0% + +okay what that means is + + align:start position:0% + + + + align:start position:0% + +that what you have have to do given a + + align:start position:0% +that what you have have to do given a + + + align:start position:0% +that what you have have to do given a +certain ordering of steps you construct + + align:start position:0% +certain ordering of steps you construct + + + align:start position:0% +certain ordering of steps you construct +this action graph you look to see if it + + align:start position:0% +this action graph you look to see if it + + + align:start position:0% +this action graph you look to see if it +has any cycles and if it has any if + + align:start position:0% +has any cycles and if it has any if + + + align:start position:0% +has any cycles and if it has any if +doesn't have any Cycles then you know + + align:start position:0% +doesn't have any Cycles then you know + + + align:start position:0% +doesn't have any Cycles then you know +that the order is equivalent to some + + align:start position:0% +that the order is equivalent to some + + + align:start position:0% +that the order is equivalent to some +serial order of the steps of of the + + align:start position:0% +serial order of the steps of of the + + + align:start position:0% +serial order of the steps of of the +individual actions okay and it actually + + align:start position:0% +individual actions okay and it actually + + + align:start position:0% +individual actions okay and it actually +turns out the results a bit more + + align:start position:0% +turns out the results a bit more + + + align:start position:0% +turns out the results a bit more +powerful the opposite is also the + + align:start position:0% +powerful the opposite is also the + + + align:start position:0% +powerful the opposite is also the +converse is also true that if you have a + + align:start position:0% +converse is also true that if you have a + + + align:start position:0% +converse is also true that if you have a +serializable trace then the + + align:start position:0% +serializable trace then the + + + align:start position:0% +serializable trace then the +corresponding action graph has no cyles + + align:start position:0% +corresponding action graph has no cyles + + + align:start position:0% +corresponding action graph has no cyles +now it turn out the more interesting + + align:start position:0% +now it turn out the more interesting + + + align:start position:0% +now it turn out the more interesting +result for us is going to be the forward + + align:start position:0% +result for us is going to be the forward + + + align:start position:0% +result for us is going to be the forward +Direction Where um if the graph is AIC + + align:start position:0% +Direction Where um if the graph is AIC + + + align:start position:0% +Direction Where um if the graph is AIC +then the trace is serializable because + + align:start position:0% +then the trace is serializable because + + + align:start position:0% +then the trace is serializable because +what we're going to end up doing is + + align:start position:0% +what we're going to end up doing is + + + align:start position:0% +what we're going to end up doing is +inventing Proto one or two + + align:start position:0% +inventing Proto one or two + + + align:start position:0% +inventing Proto one or two +protocols for Pro for for achieving + + align:start position:0% +protocols for Pro for for achieving + + + align:start position:0% +protocols for Pro for for achieving +isolation for achieving serializability + + align:start position:0% +isolation for achieving serializability + + + align:start position:0% +isolation for achieving serializability +and we're going to prove that those + + align:start position:0% +and we're going to prove that those + + + align:start position:0% +and we're going to prove that those +Protocols are correct by proving that + + align:start position:0% +Protocols are correct by proving that + + + align:start position:0% +Protocols are correct by proving that +the corresponding action graph all of + + align:start position:0% +the corresponding action graph all of + + + align:start position:0% +the corresponding action graph all of +the possible action graphs produced by + + align:start position:0% +the possible action graphs produced by + + + align:start position:0% +the possible action graphs produced by +those protocols all have no Cycles okay + + align:start position:0% +those protocols all have no Cycles okay + + + align:start position:0% +those protocols all have no Cycles okay +so this direction is the direction + + align:start position:0% +so this direction is the direction + + + align:start position:0% +so this direction is the direction +that's actually more important um for us + + align:start position:0% +that's actually more important um for us + + + align:start position:0% +that's actually more important um for us +but the opposite is also true and not + + align:start position:0% +but the opposite is also true and not + + + align:start position:0% +but the opposite is also true and not +that hard to + + align:start position:0% +that hard to + + + align:start position:0% +that hard to +prove so what is the intuition behind + + align:start position:0% +prove so what is the intuition behind + + + align:start position:0% +prove so what is the intuition behind +why if you have an action graph that's + + align:start position:0% +why if you have an action graph that's + + + align:start position:0% +why if you have an action graph that's +serializable sorry that that doesn't + + align:start position:0% +serializable sorry that that doesn't + + + align:start position:0% +serializable sorry that that doesn't +have Cycles the trace is + + align:start position:0% +have Cycles the trace is + + + align:start position:0% +have Cycles the trace is +serializable well notice one thing about + + align:start position:0% +serializable well notice one thing about + + + align:start position:0% +serializable well notice one thing about +this which is uh to to draw a little bit + + align:start position:0% +this which is uh to to draw a little bit + + + align:start position:0% +this which is uh to to draw a little bit +of + + align:start position:0% +of + + + align:start position:0% +of +intuition suppose in fact what happened + + align:start position:0% +intuition suppose in fact what happened + + + align:start position:0% +intuition suppose in fact what happened +here was we didn't execute the actions + + align:start position:0% +here was we didn't execute the actions + + + align:start position:0% +here was we didn't execute the actions +uh the steps in that order but what we + + align:start position:0% +uh the steps in that order but what we + + + align:start position:0% +uh the steps in that order but what we +did was to + + align:start position:0% +did was to + + + align:start position:0% +did was to +run this at step five and that at step + + align:start position:0% +run this at step five and that at step + + + align:start position:0% +run this at step five and that at step +six okay what would happen in the + + align:start position:0% +six okay what would happen in the + + + align:start position:0% +six okay what would happen in the +resulting action graph is that you would + + align:start position:0% +resulting action graph is that you would + + + align:start position:0% +resulting action graph is that you would +actually have an arc from T2 to T1 going + + align:start position:0% +actually have an arc from T2 to T1 going + + + align:start position:0% +actually have an arc from T2 to T1 going +the other way as + + align:start position:0% + + + + align:start position:0% + +well cuz what this says is between T1 + + align:start position:0% +well cuz what this says is between T1 + + + align:start position:0% +well cuz what this says is between T1 +and T2 there's one conflicting operation + + align:start position:0% +and T2 there's one conflicting operation + + + align:start position:0% +and T2 there's one conflicting operation +that goes this way where the one action + + align:start position:0% +that goes this way where the one action + + + align:start position:0% +that goes this way where the one action +in one runs before two and these two + + align:start position:0% +in one runs before two and these two + + + align:start position:0% +in one runs before two and these two +guys conflict where the action where the + + align:start position:0% +guys conflict where the action where the + + + align:start position:0% +guys conflict where the action where the +step in two runs before the step in one + + align:start position:0% +step in two runs before the step in one + + + align:start position:0% +step in two runs before the step in one +and those two steps conflict with one + + align:start position:0% +and those two steps conflict with one + + + align:start position:0% +and those two steps conflict with one +another and this is actually the cycle + + align:start position:0% +another and this is actually the cycle + + + align:start position:0% +another and this is actually the cycle +here that causes the whole scheme to be + + align:start position:0% +here that causes the whole scheme to be + + + align:start position:0% +here that causes the whole scheme to be +not serializable + + align:start position:0% +not serializable + + + align:start position:0% +not serializable +anymore okay so that that's a little bit + + align:start position:0% +anymore okay so that that's a little bit + + + align:start position:0% +anymore okay so that that's a little bit +of intuition as to why this ayylic + + align:start position:0% +of intuition as to why this ayylic + + + align:start position:0% +of intuition as to why this ayylic +property is important but we really see + + align:start position:0% +property is important but we really see + + + align:start position:0% +property is important but we really see +um to prove this notice that if you have + + align:start position:0% +um to prove this notice that if you have + + + align:start position:0% +um to prove this notice that if you have +a directed a graph you could do + + align:start position:0% +a directed a graph you could do + + + align:start position:0% +a directed a graph you could do +something called a topological sort on + + align:start position:0% +something called a topological sort on + + + align:start position:0% +something called a topological sort on +the graph how many people know what a + + align:start position:0% +the graph how many people know what a + + + align:start position:0% +the graph how many people know what a +topological s is okay so for those who + + align:start position:0% +topological s is okay so for those who + + + align:start position:0% +topological s is okay so for those who +don't the idea is very + + align:start position:0% +don't the idea is very + + + align:start position:0% +don't the idea is very +simple in any directed asli + + align:start position:0% +simple in any directed asli + + + align:start position:0% +simple in any directed asli +graph there's going to be at least one + + align:start position:0% +graph there's going to be at least one + + + align:start position:0% +graph there's going to be at least one +node that has no no no arrows coming + + align:start position:0% +node that has no no no arrows coming + + + align:start position:0% +node that has no no no arrows coming +into it all of the arrows going out are + + align:start position:0% +into it all of the arrows going out are + + + align:start position:0% +into it all of the arrows going out are +only going out of the node and you can + + align:start position:0% +only going out of the node and you can + + + align:start position:0% +only going out of the node and you can +actually prove that by arguing by + + align:start position:0% +actually prove that by arguing by + + + align:start position:0% +actually prove that by arguing by +contradiction if it turns out that every + + align:start position:0% +contradiction if it turns out that every + + + align:start position:0% +contradiction if it turns out that every +node has an arc coming in and an arc + + align:start position:0% +node has an arc coming in and an arc + + + align:start position:0% +node has an arc coming in and an arc +going out then by traversing that chain + + align:start position:0% +going out then by traversing that chain + + + align:start position:0% +going out then by traversing that chain +of pointers you'll end up with a cycle + + align:start position:0% +of pointers you'll end up with a cycle + + + align:start position:0% +of pointers you'll end up with a cycle +so it's pretty easy to see that in any + + align:start position:0% +so it's pretty easy to see that in any + + + align:start position:0% +so it's pretty easy to see that in any +directed ayc graph you're going to have + + align:start position:0% +directed ayc graph you're going to have + + + align:start position:0% +directed ayc graph you're going to have +some node that has no arrows coming into + + align:start position:0% +some node that has no arrows coming into + + + align:start position:0% +some node that has no arrows coming into +it and only arrows going out of it so + + align:start position:0% +it and only arrows going out of it so + + + align:start position:0% +it and only arrows going out of it so +find that action in this picture it's D3 + + align:start position:0% +find that action in this picture it's D3 + + + align:start position:0% +find that action in this picture it's D3 +okay and take that action and put it in + + align:start position:0% +okay and take that action and put it in + + + align:start position:0% +okay and take that action and put it in +first okay so that's the first action + + align:start position:0% +first okay so that's the first action + + + align:start position:0% +first okay so that's the first action +that you wrong because it has no arrows + + align:start position:0% +that you wrong because it has no arrows + + + align:start position:0% +that you wrong because it has no arrows +coming into it and only arrows going out + + align:start position:0% +coming into it and only arrows going out + + + align:start position:0% +coming into it and only arrows going out +um what that means is that no other + + align:start position:0% +um what that means is that no other + + + align:start position:0% +um what that means is that no other +action in a Serial order runs before it + + align:start position:0% +action in a Serial order runs before it + + + align:start position:0% +action in a Serial order runs before it +because everybody every all of or at + + align:start position:0% +because everybody every all of or at + + + align:start position:0% +because everybody every all of or at +least there's no reason for any action + + align:start position:0% +least there's no reason for any action + + + align:start position:0% +least there's no reason for any action +to run before it because there are no + + align:start position:0% +to run before it because there are no + + + align:start position:0% +to run before it because there are no +arrows from any other action coming into + + align:start position:0% +arrows from any other action coming into + + + align:start position:0% +arrows from any other action coming into +this action so you put that in + + align:start position:0% +this action so you put that in + + + align:start position:0% +this action so you put that in +first now remove that node from the + + align:start position:0% +first now remove that node from the + + + align:start position:0% +first now remove that node from the +entire graph the resulting graph is a + + align:start position:0% +entire graph the resulting graph is a + + + align:start position:0% +entire graph the resulting graph is a +cyclic right you can't manufacture a + + align:start position:0% +cyclic right you can't manufacture a + + + align:start position:0% +cyclic right you can't manufacture a +cycle by removing a node so you + + align:start position:0% +cycle by removing a node so you + + + align:start position:0% +cycle by removing a node so you +recursively apply the same idea find + + align:start position:0% +recursively apply the same idea find + + + align:start position:0% +recursively apply the same idea find +some other node which has no other + + align:start position:0% +some other node which has no other + + + align:start position:0% +some other node which has no other +things coming into it and only things + + align:start position:0% +things coming into it and only things + + + align:start position:0% +things coming into it and only things +going out of it and and if there are + + align:start position:0% +going out of it and and if there are + + + align:start position:0% +going out of it and and if there are +ties just pick one at random and + + align:start position:0% +ties just pick one at random and + + + align:start position:0% +ties just pick one at random and +therefore construct an order and all + + align:start position:0% +therefore construct an order and all + + + align:start position:0% +therefore construct an order and all +such orders that you construct are + + align:start position:0% +such orders that you construct are + + + align:start position:0% +such orders that you construct are +topological s + + align:start position:0% + + + + align:start position:0% + +orders so this topological sort order by + + align:start position:0% +orders so this topological sort order by + + + align:start position:0% +orders so this topological sort order by +construction is a sequential order is a + + align:start position:0% +construction is a sequential order is a + + + align:start position:0% +construction is a sequential order is a +Serial order of the + + align:start position:0% +Serial order of the + + + align:start position:0% +Serial order of the +actions and this topological sort does + + align:start position:0% +actions and this topological sort does + + + align:start position:0% +actions and this topological sort does +not have you know if you now draw the + + align:start position:0% +not have you know if you now draw the + + + align:start position:0% +not have you know if you now draw the +arrows in the topological sort they're + + align:start position:0% +arrows in the topological sort they're + + + align:start position:0% +arrows in the topological sort they're +going to be the same arrows as in the + + align:start position:0% +going to be the same arrows as in the + + + align:start position:0% +going to be the same arrows as in the +original um um directed graph it's + + align:start position:0% +original um um directed graph it's + + + align:start position:0% +original um um directed graph it's +exactly the same graph and now you have + + align:start position:0% +exactly the same graph and now you have + + + align:start position:0% +exactly the same graph and now you have +a an equivalent serial + + align:start position:0% +a an equivalent serial + + + align:start position:0% +a an equivalent serial +order okay so that's the reason why this + + align:start position:0% +order okay so that's the reason why this + + + align:start position:0% +order okay so that's the reason why this +cyclic property is actually important as + + align:start position:0% +cyclic property is actually important as + + + align:start position:0% +cyclic property is actually important as +far as serializability is + + align:start position:0% + + + + align:start position:0% + +concerned okay so now we we can look at + + align:start position:0% +concerned okay so now we we can look at + + + align:start position:0% +concerned okay so now we we can look at +schemes that actually guarantee uh + + align:start position:0% +schemes that actually guarantee uh + + + align:start position:0% +schemes that actually guarantee uh +serializability and the schemes we're + + align:start position:0% +serializability and the schemes we're + + + align:start position:0% +serializability and the schemes we're +going to discuss all are in this system + + align:start position:0% +going to discuss all are in this system + + + align:start position:0% +going to discuss all are in this system +where you have cell storage and where + + align:start position:0% +where you have cell storage and where + + + align:start position:0% +where you have cell storage and where +you have loog logs for recovery and the + + align:start position:0% +you have loog logs for recovery and the + + + align:start position:0% +you have loog logs for recovery and the +logs are not going to matter for the + + align:start position:0% +logs are not going to matter for the + + + align:start position:0% +logs are not going to matter for the +most part um you can also do isolation + + align:start position:0% +most part um you can also do isolation + + + align:start position:0% +most part um you can also do isolation +inversion histories and uh one of the + + align:start position:0% +inversion histories and uh one of the + + + align:start position:0% +inversion histories and uh one of the +sections of the notes deals with that at + + align:start position:0% +sections of the notes deals with that at + + + align:start position:0% +sections of the notes deals with that at +length + + align:start position:0% +length + + + align:start position:0% +length +um I personally think it's not that + + align:start position:0% +um I personally think it's not that + + + align:start position:0% +um I personally think it's not that +important um it doesn't mean it's not on + + align:start position:0% +important um it doesn't mean it's not on + + + align:start position:0% +important um it doesn't mean it's not on +the + + align:start position:0% +the + + + align:start position:0% +the +quiz uh but I think you get a little bit + + align:start position:0% +quiz uh but I think you get a little bit + + + align:start position:0% +quiz uh but I think you get a little bit +more intuition reading that in addition + + align:start position:0% +more intuition reading that in addition + + + align:start position:0% +more intuition reading that in addition +to this discussion bulk of this + + align:start position:0% +to this discussion bulk of this + + + align:start position:0% +to this discussion bulk of this +discussion is actually not in the notes + + align:start position:0% +discussion is actually not in the notes + + + align:start position:0% +discussion is actually not in the notes +so it's just another way of looking at + + align:start position:0% +so it's just another way of looking at + + + align:start position:0% +so it's just another way of looking at +the problem okay so the mechanism we're + + align:start position:0% +the problem okay so the mechanism we're + + + align:start position:0% +the problem okay so the mechanism we're +going to build on is in fact described + + align:start position:0% +going to build on is in fact described + + + align:start position:0% +going to build on is in fact described +in in the notes as well and it's the + + align:start position:0% +in in the notes as well and it's the + + + align:start position:0% +in in the notes as well and it's the +mechanism you've seen before and it's + + align:start position:0% +mechanism you've seen before and it's + + + align:start position:0% +mechanism you've seen before and it's +called locks okay and if you as you + + align:start position:0% +called locks okay and if you as you + + + align:start position:0% +called locks okay and if you as you +recall if you have variable X or any + + align:start position:0% +recall if you have variable X or any + + + align:start position:0% +recall if you have variable X or any +chunk of data you could protect it using + + align:start position:0% +chunk of data you could protect it using + + + align:start position:0% +chunk of data you could protect it using +two calls acquire and release so you + + align:start position:0% +two calls acquire and release so you + + + align:start position:0% +two calls acquire and release so you +could do things like acquire lock of + + align:start position:0% +could do things like acquire lock of + + + align:start position:0% +could do things like acquire lock of +X and + + align:start position:0% +X and + + + align:start position:0% +X and +release lock of X and the lock protocol + + align:start position:0% +release lock of X and the lock protocol + + + align:start position:0% +release lock of X and the lock protocol +is that only one person can acquire a + + align:start position:0% +is that only one person can acquire a + + + align:start position:0% +is that only one person can acquire a +lock at a time and all other people + + align:start position:0% +lock at a time and all other people + + + align:start position:0% +lock at a time and all other people +wanting all other actions wishing to + + align:start position:0% +wanting all other actions wishing to + + + align:start position:0% +wanting all other actions wishing to +acquire the same lock will block um + + align:start position:0% +acquire the same lock will block um + + + align:start position:0% +acquire the same lock will block um +we'll wait until the locks is released + + align:start position:0% +we'll wait until the locks is released + + + align:start position:0% +we'll wait until the locks is released +and then they fight to acquire + + align:start position:0% +and then they fight to acquire + + + align:start position:0% +and then they fight to acquire +it and you know ultimately at the lowest + + align:start position:0% +it and you know ultimately at the lowest + + + align:start position:0% +it and you know ultimately at the lowest +level the lock has to be implemented + + align:start position:0% +level the lock has to be implemented + + + align:start position:0% +level the lock has to be implemented +with some lowlevel Atomic instruction + + align:start position:0% +with some lowlevel Atomic instruction + + + align:start position:0% +with some lowlevel Atomic instruction +for example something like a test and + + align:start position:0% +for example something like a test and + + + align:start position:0% +for example something like a test and +set lock instruction it's the same story + + align:start position:0% +set lock instruction it's the same story + + + align:start position:0% +set lock instruction it's the same story +as + + align:start position:0% +as + + + align:start position:0% +as +before now there's a few things to to + + align:start position:0% +before now there's a few things to to + + + align:start position:0% +before now there's a few things to to +worry about with locks the first one is + + align:start position:0% +worry about with locks the first one is + + + align:start position:0% +worry about with locks the first one is +the granularity of the lock now you + + align:start position:0% +the granularity of the lock now you + + + align:start position:0% +the granularity of the lock now you +could be very very + + align:start position:0% +could be very very + + + align:start position:0% +could be very very +conservative and decide that the + + align:start position:0% +conservative and decide that the + + + align:start position:0% +conservative and decide that the +granularity of the lock is your is your + + align:start position:0% +granularity of the lock is your is your + + + align:start position:0% +granularity of the lock is your is your +entire system so all of the data in the + + align:start position:0% +entire system so all of the data in the + + + align:start position:0% +entire system so all of the data in the +system gets protected with one with one + + align:start position:0% +system gets protected with one with one + + + align:start position:0% +system gets protected with one with one +lock which means that you're running + + align:start position:0% +lock which means that you're running + + + align:start position:0% +lock which means that you're running +this very slow slow scheme because what + + align:start position:0% +this very slow slow scheme because what + + + align:start position:0% +this very slow slow scheme because what +what you're guaranteeing is in fact um + + align:start position:0% +what you're guaranteeing is in fact um + + + align:start position:0% +what you're guaranteeing is in fact um +isolation but you're running essentially + + align:start position:0% +isolation but you're running essentially + + + align:start position:0% +isolation but you're running essentially +one action one action at a time and you + + align:start position:0% +one action one action at a time and you + + + align:start position:0% +one action one action at a time and you +have no concurrency at all at the Other + + align:start position:0% +have no concurrency at all at the Other + + + align:start position:0% +have no concurrency at all at the Other +Extreme you could be very very + + align:start position:0% +Extreme you could be very very + + + align:start position:0% +Extreme you could be very very +aggressive and every individual cell + + align:start position:0% +aggressive and every individual cell + + + align:start position:0% +aggressive and every individual cell +store item is protected with a lock and + + align:start position:0% +store item is protected with a lock and + + + align:start position:0% +store item is protected with a lock and +now you're trying to max out the degree + + align:start position:0% +now you're trying to max out the degree + + + align:start position:0% +now you're trying to max out the degree +of concurrency which means that although + + align:start position:0% +of concurrency which means that although + + + align:start position:0% +of concurrency which means that although +it could things could be fast you have + + align:start position:0% +it could things could be fast you have + + + align:start position:0% +it could things could be fast you have +to be a lot more careful if you want + + align:start position:0% +to be a lot more careful if you want + + + align:start position:0% +to be a lot more careful if you want +things to be correct and correct here + + align:start position:0% +things to be correct and correct here + + + align:start position:0% +things to be correct and correct here +means that you have an equivalent order + + align:start position:0% +means that you have an equivalent order + + + align:start position:0% +means that you have an equivalent order +that's an order that's equivalent to + + align:start position:0% +that's an order that's equivalent to + + + align:start position:0% +that's an order that's equivalent to +some serial + + align:start position:0% +some serial + + + align:start position:0% +some serial +order + + align:start position:0% +order + + + align:start position:0% +order +so why does the Locking protocol + + align:start position:0% +so why does the Locking protocol + + + align:start position:0% +so why does the Locking protocol +actually matter well let's go back to + + align:start position:0% +actually matter well let's go back to + + + align:start position:0% +actually matter well let's go back to +our example of of this these two action + + align:start position:0% +our example of of this these two action + + + align:start position:0% +our example of of this these two action +examples of r1x W1 Y and + + align:start position:0% +examples of r1x W1 Y and + + + align:start position:0% +examples of r1x W1 Y and +r2x I'm sorry to w2x + + align:start position:0% +r2x I'm sorry to w2x + + + align:start position:0% +r2x I'm sorry to w2x +and W2 y okay and let's just throw in an + + align:start position:0% +and W2 y okay and let's just throw in an + + + align:start position:0% +and W2 y okay and let's just throw in an +acquire a lock of X here and an + + align:start position:0% +acquire a lock of X here and an + + + align:start position:0% +acquire a lock of X here and an +acquire a lock of Y here and a + + align:start position:0% +acquire a lock of Y here and a + + + align:start position:0% +acquire a lock of Y here and a +release a lock of X + + align:start position:0% + + + + align:start position:0% + +here and in between here you have the + + align:start position:0% + + + + align:start position:0% + +read and here you do the release of the + + align:start position:0% +read and here you do the release of the + + + align:start position:0% +read and here you do the release of the +lock of Y and similarly you do an + + align:start position:0% +lock of Y and similarly you do an + + + align:start position:0% +lock of Y and similarly you do an +acquire LX here and you do an acquire l + + align:start position:0% +acquire LX here and you do an acquire l + + + align:start position:0% +acquire LX here and you do an acquire l +y here and then you + + align:start position:0% + + + + align:start position:0% + +release the locks at the end here so + + align:start position:0% +release the locks at the end here so + + + align:start position:0% +release the locks at the end here so +acquire lock X read X release lock X + + align:start position:0% +acquire lock X read X release lock X + + + align:start position:0% +acquire lock X read X release lock X +acquire lock y WR y release lock Y and + + align:start position:0% +acquire lock y WR y release lock Y and + + + align:start position:0% +acquire lock y WR y release lock Y and +acquire write acquire WR release + + align:start position:0% +acquire write acquire WR release + + + align:start position:0% +acquire write acquire WR release +release and on the face of it this kind + + align:start position:0% +release and on the face of it this kind + + + align:start position:0% +release and on the face of it this kind +of thing is actually reasonable for the + + align:start position:0% +of thing is actually reasonable for the + + + align:start position:0% +of thing is actually reasonable for the +old style um synchronization some of the + + align:start position:0% +old style um synchronization some of the + + + align:start position:0% +old style um synchronization some of the +old style synchronization things that we + + align:start position:0% +old style synchronization things that we + + + align:start position:0% +old style synchronization things that we +wanted because we didn't actually care + + align:start position:0% +wanted because we didn't actually care + + + align:start position:0% +wanted because we didn't actually care +about atomicity of full + + align:start position:0% +about atomicity of full + + + align:start position:0% +about atomicity of full +actions but if you look at what happens + + align:start position:0% +actions but if you look at what happens + + + align:start position:0% +actions but if you look at what happens +with this um kind of locking as shown + + align:start position:0% +with this um kind of locking as shown + + + align:start position:0% +with this um kind of locking as shown +here you might be a little bit in + + align:start position:0% +here you might be a little bit in + + + align:start position:0% +here you might be a little bit in +trouble because it could be that these + + align:start position:0% +trouble because it could be that these + + + align:start position:0% +trouble because it could be that these +three steps happen + + align:start position:0% + + + + align:start position:0% + +first and then this whole set of + + align:start position:0% +first and then this whole set of + + + align:start position:0% +first and then this whole set of +steps up to here happens + + align:start position:0% +steps up to here happens + + + align:start position:0% +steps up to here happens +second actually up to the end and then + + align:start position:0% +second actually up to the end and then + + + align:start position:0% +second actually up to the end and then +this + + align:start position:0% +this + + + align:start position:0% +this +chunk happens + + align:start position:0% +chunk happens + + + align:start position:0% +chunk happens +third and now you're in trouble because + + align:start position:0% +third and now you're in trouble because + + + align:start position:0% +third and now you're in trouble because +read X happens before right X and then + + align:start position:0% +read X happens before right X and then + + + align:start position:0% +read X happens before right X and then +right y happens before this right Y and + + align:start position:0% +right y happens before this right Y and + + + align:start position:0% +right y happens before this right Y and +now you haven't achieved isolation + + align:start position:0% +now you haven't achieved isolation + + + align:start position:0% +now you haven't achieved isolation +because now you have if you draw the + + align:start position:0% +because now you have if you draw the + + + align:start position:0% +because now you have if you draw the +conflict graph you'll get an arrow from + + align:start position:0% +conflict graph you'll get an arrow from + + + align:start position:0% +conflict graph you'll get an arrow from +T1 to T2 and an arrow coming back from + + align:start position:0% +T1 to T2 and an arrow coming back from + + + align:start position:0% +T1 to T2 and an arrow coming back from +T2 to T1 and you have a + + align:start position:0% +T2 to T1 and you have a + + + align:start position:0% +T2 to T1 and you have a +cycle which means that just throwing in + + align:start position:0% +cycle which means that just throwing in + + + align:start position:0% +cycle which means that just throwing in +the right acquires and releases isn't + + align:start position:0% +the right acquires and releases isn't + + + align:start position:0% +the right acquires and releases isn't +going to be sufficient to achieve um + + align:start position:0% +going to be sufficient to achieve um + + + align:start position:0% +going to be sufficient to achieve um +isolation so we're going to need a + + align:start position:0% +isolation so we're going to need a + + + align:start position:0% +isolation so we're going to need a +somewhat better set of schemes better + + align:start position:0% +somewhat better set of schemes better + + + align:start position:0% +somewhat better set of schemes better +scheme than just this you know throwing + + align:start position:0% +scheme than just this you know throwing + + + align:start position:0% +scheme than just this you know throwing +the right acquires and + + align:start position:0% +the right acquires and + + + align:start position:0% +the right acquires and +releases so the first scheme we're going + + align:start position:0% +releases so the first scheme we're going + + + align:start position:0% +releases so the first scheme we're going +to see is a simple scheme it's called + + align:start position:0% +to see is a simple scheme it's called + + + align:start position:0% +to see is a simple scheme it's called +Simple + + align:start position:0% + + + + align:start position:0% + +locking and the idea in simple locking + + align:start position:0% +locking and the idea in simple locking + + + align:start position:0% +locking and the idea in simple locking +is that every + + align:start position:0% +is that every + + + align:start position:0% +is that every +action knows beforehand all of the data + + align:start position:0% +action knows beforehand all of the data + + + align:start position:0% +action knows beforehand all of the data +items that it wants to read or write and + + align:start position:0% +items that it wants to read or write and + + + align:start position:0% +items that it wants to read or write and +it acquires all of the locks before it + + align:start position:0% +it acquires all of the locks before it + + + align:start position:0% +it acquires all of the locks before it +does anything before doing any reads or + + align:start position:0% +does anything before doing any reads or + + + align:start position:0% +does anything before doing any reads or +wres it acquires all of the locks so the + + align:start position:0% +wres it acquires all of the locks so the + + + align:start position:0% +wres it acquires all of the locks so the +idea would be here you would + + align:start position:0% +idea would be here you would + + + align:start position:0% +idea would be here you would +acquire the lock of X and acquire lock + + align:start position:0% +acquire the lock of X and acquire lock + + + align:start position:0% +acquire the lock of X and acquire lock +of Y and then you run the actions and + + align:start position:0% +of Y and then you run the actions and + + + align:start position:0% +of Y and then you run the actions and +similarly the other AC and then you run + + align:start position:0% +similarly the other AC and then you run + + + align:start position:0% +similarly the other AC and then you run +the steps and similarly the other action + + align:start position:0% +the steps and similarly the other action + + + align:start position:0% +the steps and similarly the other action +does the same thing and by construction + + align:start position:0% +does the same thing and by construction + + + align:start position:0% +does the same thing and by construction +if you have actions that that conflict + + align:start position:0% +if you have actions that that conflict + + + align:start position:0% +if you have actions that that conflict +with one another and one of the actions + + align:start position:0% +with one another and one of the actions + + + align:start position:0% +with one another and one of the actions +reaches the point where all of the + + align:start position:0% +reaches the point where all of the + + + align:start position:0% +reaches the point where all of the +locksets need all of the lockset needs + + align:start position:0% +locksets need all of the lockset needs + + + align:start position:0% +locksets need all of the lockset needs +have been acquired then by construction + + align:start position:0% +have been acquired then by construction + + + align:start position:0% +have been acquired then by construction +no other conflicting action could be in + + align:start position:0% +no other conflicting action could be in + + + align:start position:0% +no other conflicting action could be in +the same state right because if you have + + align:start position:0% +the same state right because if you have + + + align:start position:0% +the same state right because if you have +another action that conflicts then it + + align:start position:0% +another action that conflicts then it + + + align:start position:0% +another action that conflicts then it +means that there's at least one data + + align:start position:0% +means that there's at least one data + + + align:start position:0% +means that there's at least one data +item um common to them which means that + + align:start position:0% +item um common to them which means that + + + align:start position:0% +item um common to them which means that +only one of them could have reached this + + align:start position:0% +only one of them could have reached this + + + align:start position:0% +only one of them could have reached this +point because they both trying to + + align:start position:0% +point because they both trying to + + + align:start position:0% +point because they both trying to +acquire so this protocol where every + + align:start position:0% +acquire so this protocol where every + + + align:start position:0% +acquire so this protocol where every +action acquires all of the locks before + + align:start position:0% +action acquires all of the locks before + + + align:start position:0% +action acquires all of the locks before +running any step of the action will + + align:start position:0% +running any step of the action will + + + align:start position:0% +running any step of the action will +guarantee isolation and the isolation + + align:start position:0% +guarantee isolation and the isolation + + + align:start position:0% +guarantee isolation and the isolation +order the equivalent serial order that + + align:start position:0% +order the equivalent serial order that + + + align:start position:0% +order the equivalent serial order that +it guarantees is the order is the same + + align:start position:0% +it guarantees is the order is the same + + + align:start position:0% +it guarantees is the order is the same +as the order in which the different + + align:start position:0% +as the order in which the different + + + align:start position:0% +as the order in which the different +actions reach this point where they've + + align:start position:0% +actions reach this point where they've + + + align:start position:0% +actions reach this point where they've +acquired all of the locks and that point + + align:start position:0% +acquired all of the locks and that point + + + align:start position:0% +acquired all of the locks and that point +is also called the lock point the lock + + align:start position:0% +is also called the lock point the lock + + + align:start position:0% +is also called the lock point the lock +point of an action is defined as the + + align:start position:0% +point of an action is defined as the + + + align:start position:0% +point of an action is defined as the +point where all of the locks that it + + align:start position:0% +point where all of the locks that it + + + align:start position:0% +point where all of the locks that it +needs um or it wants to acquire have + + align:start position:0% +needs um or it wants to acquire have + + + align:start position:0% +needs um or it wants to acquire have +been acquired and because in this + + align:start position:0% +been acquired and because in this + + + align:start position:0% +been acquired and because in this +discipline where no no action does any + + align:start position:0% +discipline where no no action does any + + + align:start position:0% +discipline where no no action does any +operation until all of the locks that + + align:start position:0% +operation until all of the locks that + + + align:start position:0% +operation until all of the locks that +needs have been acquired you're + + align:start position:0% +needs have been acquired you're + + + align:start position:0% +needs have been acquired you're +guaranteed that the serial order of + + align:start position:0% +guaranteed that the serial order of + + + align:start position:0% +guaranteed that the serial order of +following every action following this + + align:start position:0% +following every action following this + + + align:start position:0% +following every action following this +protocol independent of knowledge of any + + align:start position:0% +protocol independent of knowledge of any + + + align:start position:0% +protocol independent of knowledge of any +other actions if everybody just blindly + + align:start position:0% +other actions if everybody just blindly + + + align:start position:0% +other actions if everybody just blindly +follows this protocol the serial order + + align:start position:0% +follows this protocol the serial order + + + align:start position:0% +follows this protocol the serial order +is the same as if the actions had run in + + align:start position:0% +is the same as if the actions had run in + + + align:start position:0% +is the same as if the actions had run in +the order of acquiring their lock points + + align:start position:0% +the order of acquiring their lock points + + + align:start position:0% +the order of acquiring their lock points +whatever that order might be okay so + + align:start position:0% +whatever that order might be okay so + + + align:start position:0% +whatever that order might be okay so +this actually provides um this is called + + align:start position:0% +this actually provides um this is called + + + align:start position:0% +this actually provides um this is called +Simple locking and it does provide + + align:start position:0% +Simple locking and it does provide + + + align:start position:0% +Simple locking and it does provide +isolation but the problem with simple + + align:start position:0% +isolation but the problem with simple + + + align:start position:0% +isolation but the problem with simple +locking where you acquire all of the + + align:start position:0% +locking where you acquire all of the + + + align:start position:0% +locking where you acquire all of the +locks before running anything is twofold + + align:start position:0% +locks before running anything is twofold + + + align:start position:0% +locks before running anything is twofold +the first problem is that this dictates + + align:start position:0% +the first problem is that this dictates + + + align:start position:0% +the first problem is that this dictates +that all of the actions know the + + align:start position:0% +that all of the actions know the + + + align:start position:0% +that all of the actions know the +different items that they want to read + + align:start position:0% +different items that they want to read + + + align:start position:0% +different items that they want to read +or write beforehand so which means that + + align:start position:0% +or write beforehand so which means that + + + align:start position:0% +or write beforehand so which means that +if you're deep inside some action + + align:start position:0% +if you're deep inside some action + + + align:start position:0% +if you're deep inside some action +there's all sorts of conditional + + align:start position:0% +there's all sorts of conditional + + + align:start position:0% +there's all sorts of conditional +statements uh you kind of have to know + + align:start position:0% +statements uh you kind of have to know + + + align:start position:0% +statements uh you kind of have to know +beforehand all of the data items you + + align:start position:0% +beforehand all of the data items you + + + align:start position:0% +beforehand all of the data items you +might be reading and writing and that + + align:start position:0% +might be reading and writing and that + + + align:start position:0% +might be reading and writing and that +could be pretty tricky so in practice if + + align:start position:0% +could be pretty tricky so in practice if + + + align:start position:0% +could be pretty tricky so in practice if +you want to adopt simple locking you + + align:start position:0% +you want to adopt simple locking you + + + align:start position:0% +you want to adopt simple locking you +might have to have to be very + + align:start position:0% +might have to have to be very + + + align:start position:0% +might have to have to be very +conservative and sort of try to lock + + align:start position:0% +conservative and sort of try to lock + + + align:start position:0% +conservative and sort of try to lock +everything or lock large amount of data + + align:start position:0% +everything or lock large amount of data + + + align:start position:0% +everything or lock large amount of data +uh which reduces performance and second + + align:start position:0% +uh which reduces performance and second + + + align:start position:0% +uh which reduces performance and second +it actually doesn't give you enough + + align:start position:0% +it actually doesn't give you enough + + + align:start position:0% +it actually doesn't give you enough +opportunity to get high performance even + + align:start position:0% +opportunity to get high performance even + + + align:start position:0% +opportunity to get high performance even +when you do know all of the data items + + align:start position:0% +when you do know all of the data items + + + align:start position:0% +when you do know all of the data items +beforehand so for example one thing you + + align:start position:0% +beforehand so for example one thing you + + + align:start position:0% +beforehand so for example one thing you +could do is acquire the lock of X and + + align:start position:0% +could do is acquire the lock of X and + + + align:start position:0% +could do is acquire the lock of X and +then read X and while you're off trying + + align:start position:0% +then read X and while you're off trying + + + align:start position:0% +then read X and while you're off trying +to read X um then you might um acquire a + + align:start position:0% +to read X um then you might um acquire a + + + align:start position:0% +to read X um then you might um acquire a +lock of Y and read why and so depending + + align:start position:0% +lock of Y and read why and so depending + + + align:start position:0% +lock of Y and read why and so depending +on how you've structured your system of + + align:start position:0% +on how you've structured your system of + + + align:start position:0% +on how you've structured your system of +scheme where you do some work maybe some + + align:start position:0% +scheme where you do some work maybe some + + + align:start position:0% +scheme where you do some work maybe some +computation as well in between before in + + align:start position:0% +computation as well in between before in + + + align:start position:0% +computation as well in between before in +between the lock acquisition steps U + + align:start position:0% +between the lock acquisition steps U + + + align:start position:0% +between the lock acquisition steps U +might give you higher + + align:start position:0% +might give you higher + + + align:start position:0% +might give you higher +performance + + align:start position:0% +performance + + + align:start position:0% +performance +so the question + + align:start position:0% +so the question + + + align:start position:0% +so the question +is can we be a little bit more + + align:start position:0% +is can we be a little bit more + + + align:start position:0% +is can we be a little bit more +aggressive than the simple locking + + align:start position:0% +aggressive than the simple locking + + + align:start position:0% +aggressive than the simple locking +scheme in order to get um isolation as + + align:start position:0% +scheme in order to get um isolation as + + + align:start position:0% +scheme in order to get um isolation as +well as a little bit higher + + align:start position:0% +well as a little bit higher + + + align:start position:0% +well as a little bit higher +performance and the answer is that there + + align:start position:0% +performance and the answer is that there + + + align:start position:0% +performance and the answer is that there +is such a scheme and it's called + + align:start position:0% +is such a scheme and it's called + + + align:start position:0% +is such a scheme and it's called +two-phase + + align:start position:0% + + + + align:start position:0% + +locking and although you know a lot of + + align:start position:0% +locking and although you know a lot of + + + align:start position:0% +locking and although you know a lot of +work has happened for you know more you + + align:start position:0% +work has happened for you know more you + + + align:start position:0% +work has happened for you know more you +maybe a couple of decades on very high + + align:start position:0% +maybe a couple of decades on very high + + + align:start position:0% +maybe a couple of decades on very high +performance locking schemes it turns out + + align:start position:0% +performance locking schemes it turns out + + + align:start position:0% +performance locking schemes it turns out +in the end they all or at least for a + + align:start position:0% +in the end they all or at least for a + + + align:start position:0% +in the end they all or at least for a +large class of schemes that use this + + align:start position:0% +large class of schemes that use this + + + align:start position:0% +large class of schemes that use this +kind of locking they all boil down to + + align:start position:0% +kind of locking they all boil down to + + + align:start position:0% +kind of locking they all boil down to +some variant of two-phase locking and + + align:start position:0% +some variant of two-phase locking and + + + align:start position:0% +some variant of two-phase locking and +the idea is very simple the two-phase + + align:start position:0% +the idea is very simple the two-phase + + + align:start position:0% +the idea is very simple the two-phase +Locking idea says there should be no + + align:start position:0% + + + + align:start position:0% + +release before all the acquires are + + align:start position:0% + + + + align:start position:0% + +done so don't release any lock until all + + align:start position:0% +done so don't release any lock until all + + + align:start position:0% +done so don't release any lock until all +of the locks that you need have been + + align:start position:0% +of the locks that you need have been + + + align:start position:0% +of the locks that you need have been +acquired + + align:start position:0% +acquired + + + align:start position:0% +acquired +so that's what happens here this scheme + + align:start position:0% +so that's what happens here this scheme + + + align:start position:0% +so that's what happens here this scheme +violates two-phase locking because you + + align:start position:0% +violates two-phase locking because you + + + align:start position:0% +violates two-phase locking because you +actually release lock X before you + + align:start position:0% +actually release lock X before you + + + align:start position:0% +actually release lock X before you +acquire lock Y and that violates + + align:start position:0% +acquire lock Y and that violates + + + align:start position:0% +acquire lock Y and that violates +two-phase + + align:start position:0% + + + + align:start position:0% + +locking and this idea that you don't + + align:start position:0% +locking and this idea that you don't + + + align:start position:0% +locking and this idea that you don't +release before all the acquires there's + + align:start position:0% +release before all the acquires there's + + + align:start position:0% +release before all the acquires there's +a little bit of a subtlety that happens + + align:start position:0% +a little bit of a subtlety that happens + + + align:start position:0% +a little bit of a subtlety that happens +because you want uh fault um um you want + + align:start position:0% +because you want uh fault um um you want + + + align:start position:0% +because you want uh fault um um you want +recoverability which is + + align:start position:0% +recoverability which is + + + align:start position:0% +recoverability which is +that that the action could at any stage + + align:start position:0% +that that the action could at any stage + + + align:start position:0% +that that the action could at any stage +abort and in order to abort an action + + align:start position:0% +abort and in order to abort an action + + + align:start position:0% +abort and in order to abort an action +you need to go back and unroll you know + + align:start position:0% +you need to go back and unroll you know + + + align:start position:0% +you need to go back and unroll you know +undo that variable the value to a + + align:start position:0% +undo that variable the value to a + + + align:start position:0% +undo that variable the value to a +previous value which means that in order + + align:start position:0% +previous value which means that in order + + + align:start position:0% +previous value which means that in order +to abort you need to hold on to the log + + align:start position:0% +to abort you need to hold on to the log + + + align:start position:0% +to abort you need to hold on to the log +you better make sure that in action in + + align:start position:0% +you better make sure that in action in + + + align:start position:0% +you better make sure that in action in +order to bought has the locks for all of + + align:start position:0% +order to bought has the locks for all of + + + align:start position:0% +order to bought has the locks for all of +the data items whose values it wishes to + + align:start position:0% +the data items whose values it wishes to + + + align:start position:0% +the data items whose values it wishes to +change to the original value which means + + align:start position:0% +change to the original value which means + + + align:start position:0% +change to the original value which means +that in practice at least for all the + + align:start position:0% +that in practice at least for all the + + + align:start position:0% +that in practice at least for all the +items that you're writing the locks that + + align:start position:0% +items that you're writing the locks that + + + align:start position:0% +items that you're writing the locks that +you hold shouldn't be released until um + + align:start position:0% +you hold shouldn't be released until um + + + align:start position:0% +you hold shouldn't be released until um +the commit point until the place where + + align:start position:0% +the commit point until the place where + + + align:start position:0% +the commit point until the place where +the action calls + + align:start position:0% +the action calls + + + align:start position:0% +the action calls +commit so + + align:start position:0% +commit so + + + align:start position:0% +commit so +no release before all acquires is + + align:start position:0% +no release before all acquires is + + + align:start position:0% +no release before all acquires is +basically equivalent to there should be + + align:start position:0% +basically equivalent to there should be + + + align:start position:0% +basically equivalent to there should be +no acquire statement after any release + + align:start position:0% +no acquire statement after any release + + + align:start position:0% +no acquire statement after any release +statement the moment you see a release + + align:start position:0% +statement the moment you see a release + + + align:start position:0% +statement the moment you see a release +statement and then acquire after that of + + align:start position:0% +statement and then acquire after that of + + + align:start position:0% +statement and then acquire after that of +anything then you know that this + + align:start position:0% +anything then you know that this + + + align:start position:0% +anything then you know that this +violates two-phase + + align:start position:0% +violates two-phase + + + align:start position:0% +violates two-phase +locking so it turns out that two-phase + + align:start position:0% +locking so it turns out that two-phase + + + align:start position:0% +locking so it turns out that two-phase +locking is correct that it provides + + align:start position:0% +locking is correct that it provides + + + align:start position:0% +locking is correct that it provides +isolation and to see + + align:start position:0% +isolation and to see + + + align:start position:0% +isolation and to see +why let's look at a + + align:start position:0% +why let's look at a + + + align:start position:0% +why let's look at a +picture we're going to go back to this + + align:start position:0% +picture we're going to go back to this + + + align:start position:0% +picture we're going to go back to this +action graph idea and look at a picture + + align:start position:0% + + + + align:start position:0% + +of what happens with two-phase locking + + align:start position:0% +of what happens with two-phase locking + + + align:start position:0% +of what happens with two-phase locking +so what we're going to prove is that if + + align:start position:0% +so what we're going to prove is that if + + + align:start position:0% +so what we're going to prove is that if +you use two-phase locking and you + + align:start position:0% +you use two-phase locking and you + + + align:start position:0% +you use two-phase locking and you +construct an action graph of what you + + align:start position:0% +construct an action graph of what you + + + align:start position:0% +construct an action graph of what you +get from running some sequence of steps + + align:start position:0% +get from running some sequence of steps + + + align:start position:0% +get from running some sequence of steps +that action graph has no cycles and we + + align:start position:0% +that action graph has no cycles and we + + + align:start position:0% +that action graph has no cycles and we +know that if you have no Cycles in the + + align:start position:0% +know that if you have no Cycles in the + + + align:start position:0% +know that if you have no Cycles in the +action graph you're guaranteed that it's + + align:start position:0% +action graph you're guaranteed that it's + + + align:start position:0% +action graph you're guaranteed that it's +equivalent to some serial order so we'll + + align:start position:0% +equivalent to some serial order so we'll + + + align:start position:0% +equivalent to some serial order so we'll +argue this by contradiction so let's say + + align:start position:0% +argue this by contradiction so let's say + + + align:start position:0% +argue this by contradiction so let's say +you have T1 and + + align:start position:0% +you have T1 and + + + align:start position:0% +you have T1 and +T2 all the way through some action TK + + align:start position:0% +T2 all the way through some action TK + + + align:start position:0% +T2 all the way through some action TK +and you have a cycle going back from TK + + align:start position:0% +and you have a cycle going back from TK + + + align:start position:0% +and you have a cycle going back from TK +to T1 okay in the action graph now if + + align:start position:0% +to T1 okay in the action graph now if + + + align:start position:0% +to T1 okay in the action graph now if +there's an arrow from T1 to T2 it means + + align:start position:0% +there's an arrow from T1 to T2 it means + + + align:start position:0% +there's an arrow from T1 to T2 it means +that there's some data item X1 in common + + align:start position:0% +that there's some data item X1 in common + + + align:start position:0% +that there's some data item X1 in common +between T1 and + + align:start position:0% +between T1 and + + + align:start position:0% +between T1 and +T2 and you know that T2 ran after T1 + + align:start position:0% +T2 and you know that T2 ran after T1 + + + align:start position:0% +T2 and you know that T2 ran after T1 +which means that in T1 there were there + + align:start position:0% +which means that in T1 there were there + + + align:start position:0% +which means that in T1 there were there +was a release dawn of + + align:start position:0% +was a release dawn of + + + align:start position:0% +was a release dawn of +L1 after which in the system there was + + align:start position:0% +L1 after which in the system there was + + + align:start position:0% +L1 after which in the system there was +an acquired + + align:start position:0% +an acquired + + + align:start position:0% +an acquired +done of + + align:start position:0% +done of + + + align:start position:0% +done of +L1 okay likewise between T2 and T3 + + align:start position:0% +L1 okay likewise between T2 and T3 + + + align:start position:0% +L1 okay likewise between T2 and T3 +there's some data item X2 such + + align:start position:0% +there's some data item X2 such + + + align:start position:0% +there's some data item X2 such +that a release was done of L2 by T2 and + + align:start position:0% +that a release was done of L2 by T2 and + + + align:start position:0% +that a release was done of L2 by T2 and +after that an acquire was + + align:start position:0% +after that an acquire was + + + align:start position:0% +after that an acquire was +done of L2 by T3 and the release has to + + align:start position:0% +done of L2 by T3 and the release has to + + + align:start position:0% +done of L2 by T3 and the release has to +have been done after the acquire of L1 + + align:start position:0% +have been done after the acquire of L1 + + + align:start position:0% +have been done after the acquire of L1 +because we're following two-phase + + align:start position:0% +because we're following two-phase + + + align:start position:0% +because we're following two-phase +locking so if you continue that down up + + align:start position:0% +locking so if you continue that down up + + + align:start position:0% +locking so if you continue that down up +to + + align:start position:0% +to + + + align:start position:0% +to +here out for TK + + align:start position:0% +here out for TK + + + align:start position:0% +here out for TK +TK did an + + align:start position:0% +TK did an + + + align:start position:0% +TK did an +acquire somewhere later in + + align:start position:0% +acquire somewhere later in + + + align:start position:0% +acquire somewhere later in +time of LK minus one and then it + + align:start position:0% +time of LK minus one and then it + + + align:start position:0% +time of LK minus one and then it +did a release of some data item a lock + + align:start position:0% +did a release of some data item a lock + + + align:start position:0% +did a release of some data item a lock +of LK where LK is actually some data + + align:start position:0% +of LK where LK is actually some data + + + align:start position:0% +of LK where LK is actually some data +item that shared between TK and T1 so + + align:start position:0% +item that shared between TK and T1 so + + + align:start position:0% +item that shared between TK and T1 so +there's actually some data item XK whose + + align:start position:0% +there's actually some data item XK whose + + + align:start position:0% +there's actually some data item XK whose +lock is LK and you know that TK did a + + align:start position:0% +lock is LK and you know that TK did a + + + align:start position:0% +lock is LK and you know that TK did a +release of LK before T1 did an acquire + + align:start position:0% +release of LK before T1 did an acquire + + + align:start position:0% +release of LK before T1 did an acquire +of + + align:start position:0% +of + + + align:start position:0% +of +LK but the t1s acquire of LK must have + + align:start position:0% +LK but the t1s acquire of LK must have + + + align:start position:0% +LK but the t1s acquire of LK must have +happened after the release for LK so it + + align:start position:0% +happened after the release for LK so it + + + align:start position:0% +happened after the release for LK so it +must have happened at some point here T1 + + align:start position:0% +must have happened at some point here T1 + + + align:start position:0% +must have happened at some point here T1 +must have done an acquire of LK at some + + align:start position:0% +must have done an acquire of LK at some + + + align:start position:0% +must have done an acquire of LK at some +point at the bottom here just going out + + align:start position:0% +point at the bottom here just going out + + + align:start position:0% +point at the bottom here just going out +in time you know with two-phase locking + + align:start position:0% +in time you know with two-phase locking + + + align:start position:0% +in time you know with two-phase locking +you get release of L1 then the other guy + + align:start position:0% +you get release of L1 then the other guy + + + align:start position:0% +you get release of L1 then the other guy +does an acquire of L1 release of L2 + + align:start position:0% +does an acquire of L1 release of L2 + + + align:start position:0% +does an acquire of L1 release of L2 +acquire of L2 all the way out and + + align:start position:0% +acquire of L2 all the way out and + + + align:start position:0% +acquire of L2 all the way out and +release of LK and then after that in + + align:start position:0% +release of LK and then after that in + + + align:start position:0% +release of LK and then after that in +time an acquire of LK so that must have + + align:start position:0% +time an acquire of LK so that must have + + + align:start position:0% +time an acquire of LK so that must have +happened later on in time but now this + + align:start position:0% +happened later on in time but now this + + + align:start position:0% +happened later on in time but now this +picture here violates two-phase locking + + align:start position:0% +picture here violates two-phase locking + + + align:start position:0% +picture here violates two-phase locking +because P1 for the cycle to hold has to + + align:start position:0% +because P1 for the cycle to hold has to + + + align:start position:0% +because P1 for the cycle to hold has to +have done an acquire of LK after release + + align:start position:0% +have done an acquire of LK after release + + + align:start position:0% +have done an acquire of LK after release +of L1 but that violates two-phase + + align:start position:0% +of L1 but that violates two-phase + + + align:start position:0% +of L1 but that violates two-phase +locking because you're not allowed to + + align:start position:0% +locking because you're not allowed to + + + align:start position:0% +locking because you're not allowed to +acquire anything after you've released + + align:start position:0% +acquire anything after you've released + + + align:start position:0% +acquire anything after you've released +something so two-phase locking therefore + + align:start position:0% +something so two-phase locking therefore + + + align:start position:0% +something so two-phase locking therefore +can't have a cycle in the action graph + + align:start position:0% +can't have a cycle in the action graph + + + align:start position:0% +can't have a cycle in the action graph +and from the previous story it means + + align:start position:0% +and from the previous story it means + + + align:start position:0% +and from the previous story it means +that it's equivalent to some serial + + align:start position:0% +that it's equivalent to some serial + + + align:start position:0% +that it's equivalent to some serial +order that corresponds to the + + align:start position:0% +order that corresponds to the + + + align:start position:0% +order that corresponds to the +topological sort um of that directed ay + + align:start position:0% +topological sort um of that directed ay + + + align:start position:0% +topological sort um of that directed ay +graph so I'm going to stop here we'll + + align:start position:0% +graph so I'm going to stop here we'll + + + align:start position:0% +graph so I'm going to stop here we'll +continue with this stuff and then talk + + align:start position:0% +continue with this stuff and then talk + + + align:start position:0% +continue with this stuff and then talk +about other aspects of transactions next + + align:start position:0% +about other aspects of transactions next + + + align:start position:0% +about other aspects of transactions next +time and and if there are any questions + + align:start position:0% +time and and if there are any questions + + + align:start position:0% +time and and if there are any questions +either send me email or ask me the next + + align:start position:0% + + + + align:start position:0% + +time \ No newline at end of file diff --git a/A0f4HUTooM4.txt b/A0f4HUTooM4.txt new file mode 100644 index 0000000000000000000000000000000000000000..8052a830f594f0f25514e9589510370e97bd84f1 --- /dev/null +++ b/A0f4HUTooM4.txt @@ -0,0 +1,3251 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu good morning uh my name is + + align:start position:0% +ocw.mit.edu good morning uh my name is + + + align:start position:0% +ocw.mit.edu good morning uh my name is +brown westrick and I'm going to be + + align:start position:0% +brown westrick and I'm going to be + + + align:start position:0% +brown westrick and I'm going to be +talking to you sorry about the uh Speech + + align:start position:0% +talking to you sorry about the uh Speech + + + align:start position:0% +talking to you sorry about the uh Speech +synthesis + + align:start position:0% +synthesis + + + align:start position:0% +synthesis +project + + align:start position:0% +project + + + align:start position:0% +project +uh our main goal for the speech + + align:start position:0% +uh our main goal for the speech + + + align:start position:0% +uh our main goal for the speech +synthesis project was to uh simulate uh + + align:start position:0% +synthesis project was to uh simulate uh + + + align:start position:0% +synthesis project was to uh simulate uh +to create simulated speech using a uh + + align:start position:0% +to create simulated speech using a uh + + + align:start position:0% +to create simulated speech using a uh +model of the vocal tract um in which we + + align:start position:0% +model of the vocal tract um in which we + + + align:start position:0% +model of the vocal tract um in which we +would uh model the flow of air over time + + align:start position:0% +would uh model the flow of air over time + + + align:start position:0% +would uh model the flow of air over time +um there is an existing there's existing + + align:start position:0% +um there is an existing there's existing + + + align:start position:0% +um there is an existing there's existing +software uh called new speech that + + align:start position:0% +software uh called new speech that + + + align:start position:0% +software uh called new speech that +already does this and we want to deport + + align:start position:0% +already does this and we want to deport + + + align:start position:0% +already does this and we want to deport +it to cell and then improve the speech + + align:start position:0% +it to cell and then improve the speech + + + align:start position:0% +it to cell and then improve the speech +quality that it would afford US by using + + align:start position:0% +quality that it would afford US by using + + + align:start position:0% +quality that it would afford US by using +additional computational + + align:start position:0% + + + + align:start position:0% + +Cycles so again + + align:start position:0% +Cycles so again + + + align:start position:0% +Cycles so again +um new speech was originally developed + + align:start position:0% +um new speech was originally developed + + + align:start position:0% +um new speech was originally developed +for Linguistics research but now it's + + align:start position:0% +for Linguistics research but now it's + + + align:start position:0% +for Linguistics research but now it's +available for free under the new public + + align:start position:0% +available for free under the new public + + + align:start position:0% +available for free under the new public +license uh it already models air flow in + + align:start position:0% +license uh it already models air flow in + + + align:start position:0% +license uh it already models air flow in +the vocal tract in real time uh what + + align:start position:0% +the vocal tract in real time uh what + + + align:start position:0% +the vocal tract in real time uh what +this means is that there are no + + align:start position:0% +this means is that there are no + + + align:start position:0% +this means is that there are no +pre-recorded sounds uh many speech + + align:start position:0% +pre-recorded sounds uh many speech + + + align:start position:0% +pre-recorded sounds uh many speech +synthesizers nowadays uh have very large + + align:start position:0% +synthesizers nowadays uh have very large + + + align:start position:0% +synthesizers nowadays uh have very large +dictionaries of of sounds that they just + + align:start position:0% +dictionaries of of sounds that they just + + + align:start position:0% +dictionaries of of sounds that they just +piece together and then try to smooth + + align:start position:0% +piece together and then try to smooth + + + align:start position:0% +piece together and then try to smooth +the transition between them uh however + + align:start position:0% +the transition between them uh however + + + align:start position:0% +the transition between them uh however +this model um attempts to uh actually do + + align:start position:0% +this model um attempts to uh actually do + + + align:start position:0% +this model um attempts to uh actually do +what the vocal tract is doing instead of + + align:start position:0% +what the vocal tract is doing instead of + + + align:start position:0% +what the vocal tract is doing instead of +just trying to imitate the end result uh + + align:start position:0% +just trying to imitate the end result uh + + + align:start position:0% +just trying to imitate the end result uh +this sort of the quality of the speech + + align:start position:0% +this sort of the quality of the speech + + + align:start position:0% +this sort of the quality of the speech +of this synthesizer the way that it + + align:start position:0% +of this synthesizer the way that it + + + align:start position:0% +of this synthesizer the way that it +exists uh is not as high as as the + + align:start position:0% +exists uh is not as high as as the + + + align:start position:0% +exists uh is not as high as as the +current ones that use the recorded + + align:start position:0% +current ones that use the recorded + + + align:start position:0% +current ones that use the recorded +libraries but it has potential to be + + align:start position:0% +libraries but it has potential to be + + + align:start position:0% +libraries but it has potential to be +much better because you have so much + + align:start position:0% +much better because you have so much + + + align:start position:0% +much better because you have so much +finer control over all the different + + align:start position:0% +finer control over all the different + + + align:start position:0% +finer control over all the different +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +um so our goal was although we have this + + align:start position:0% +um so our goal was although we have this + + + align:start position:0% +um so our goal was although we have this +software that would make an acceptable + + align:start position:0% +software that would make an acceptable + + + align:start position:0% +software that would make an acceptable +speech in real time we were hoping that + + align:start position:0% +speech in real time we were hoping that + + + align:start position:0% +speech in real time we were hoping that +we'd be able to take advantage of the + + align:start position:0% +we'd be able to take advantage of the + + + align:start position:0% +we'd be able to take advantage of the +additional computational power of cell + + align:start position:0% +additional computational power of cell + + + align:start position:0% +additional computational power of cell +to be able to get get an increase in + + align:start position:0% +to be able to get get an increase in + + + align:start position:0% +to be able to get get an increase in +speech quality um and I will turn it + + align:start position:0% +speech quality um and I will turn it + + + align:start position:0% +speech quality um and I will turn it +over to Drew who will tell you um about + + align:start position:0% +over to Drew who will tell you um about + + + align:start position:0% +over to Drew who will tell you um about +the new speech uh + + align:start position:0% + + + + align:start position:0% + +system + + align:start position:0% +system + + + align:start position:0% +system +so G speech is basically made up of + + align:start position:0% +so G speech is basically made up of + + + align:start position:0% +so G speech is basically made up of +three different major parts the first of + + align:start position:0% +three different major parts the first of + + + align:start position:0% +three different major parts the first of +which is just called the G speech engine + + align:start position:0% +which is just called the G speech engine + + + align:start position:0% +which is just called the G speech engine +second of which is is probably the + + align:start position:0% +second of which is is probably the + + + align:start position:0% +second of which is is probably the +largest part which is called Monae and + + align:start position:0% +largest part which is called Monae and + + + align:start position:0% +largest part which is called Monae and +then the tube resonance model which is + + align:start position:0% +then the tube resonance model which is + + + align:start position:0% +then the tube resonance model which is +the final part that actually outputs the + + align:start position:0% +the final part that actually outputs the + + + align:start position:0% +the final part that actually outputs the +sound and as the basic process is you + + align:start position:0% +sound and as the basic process is you + + + align:start position:0% +sound and as the basic process is you +take a text input standard string and + + align:start position:0% +take a text input standard string and + + + align:start position:0% +take a text input standard string and +the new speech engine will take care of + + align:start position:0% +the new speech engine will take care of + + + align:start position:0% +the new speech engine will take care of +that and transform into basic uh + + align:start position:0% +that and transform into basic uh + + + align:start position:0% +that and transform into basic uh +phonetic information which will then + + align:start position:0% +phonetic information which will then + + + align:start position:0% +phonetic information which will then +deal with and will take that string and + + align:start position:0% +deal with and will take that string and + + + align:start position:0% +deal with and will take that string and +eventually convert it into these what we + + align:start position:0% +eventually convert it into these what we + + + align:start position:0% +eventually convert it into these what we +call Vocal Track parameters which are + + align:start position:0% +call Vocal Track parameters which are + + + align:start position:0% +call Vocal Track parameters which are +basically uh parameters that can be sent + + align:start position:0% +basically uh parameters that can be sent + + + align:start position:0% +basically uh parameters that can be sent +to the tube resonance model and that and + + align:start position:0% +to the tube resonance model and that and + + + align:start position:0% +to the tube resonance model and that and +those parameters will Define exactly how + + align:start position:0% +those parameters will Define exactly how + + + align:start position:0% +those parameters will Define exactly how +this tube which represents the throat in + + align:start position:0% +this tube which represents the throat in + + + align:start position:0% +this tube which represents the throat in +the nasal tract changes over time to + + align:start position:0% +the nasal tract changes over time to + + + align:start position:0% +the nasal tract changes over time to +represent speech sounds and with those + + align:start position:0% +represent speech sounds and with those + + + align:start position:0% +represent speech sounds and with those +parameters you can send signal through + + align:start position:0% +parameters you can send signal through + + + align:start position:0% +parameters you can send signal through +it and create + + align:start position:0% +it and create + + + align:start position:0% +it and create +voice so the first part example we'll + + align:start position:0% +voice so the first part example we'll + + + align:start position:0% +voice so the first part example we'll +take a perfectly normal string like or + + align:start position:0% +take a perfectly normal string like or + + + align:start position:0% +take a perfectly normal string like or +your base belong to us and transform it + + align:start position:0% +your base belong to us and transform it + + + align:start position:0% +your base belong to us and transform it +into what we call the phonetic format of + + align:start position:0% +into what we call the phonetic format of + + + align:start position:0% +into what we call the phonetic format of +it where and you can see it highlighted + + align:start position:0% +it where and you can see it highlighted + + + align:start position:0% +it where and you can see it highlighted +the actual sounds are right there + + align:start position:0% +the actual sounds are right there + + + align:start position:0% +the actual sounds are right there +highlighted whereas various parameters + + align:start position:0% +highlighted whereas various parameters + + + align:start position:0% +highlighted whereas various parameters +are also included in the output string + + align:start position:0% +are also included in the output string + + + align:start position:0% +are also included in the output string +like slw where you can determine where + + align:start position:0% +like slw where you can determine where + + + align:start position:0% +like slw where you can determine where +words are and the patter sign as well as + + align:start position:0% +words are and the patter sign as well as + + + align:start position:0% +words are and the patter sign as well as +the SL which determine where sentences + + align:start position:0% +the SL which determine where sentences + + + align:start position:0% +the SL which determine where sentences +and various phrases end and basically + + align:start position:0% +and various phrases end and basically + + + align:start position:0% +and various phrases end and basically +new speech makes uses of uh dictionary + + align:start position:0% +new speech makes uses of uh dictionary + + + align:start position:0% +new speech makes uses of uh dictionary +files as well as some basic linguistic + + align:start position:0% +files as well as some basic linguistic + + + align:start position:0% +files as well as some basic linguistic +models in order to create this phonetic + + align:start position:0% +models in order to create this phonetic + + + align:start position:0% +models in order to create this phonetic +uh output from the basic input + + align:start position:0% + + + + align:start position:0% + +string so having created that uh + + align:start position:0% +string so having created that uh + + + align:start position:0% +string so having created that uh +phonetic model uh you can then send it + + align:start position:0% +phonetic model uh you can then send it + + + align:start position:0% +phonetic model uh you can then send it +to mon which is by far the largest part + + align:start position:0% +to mon which is by far the largest part + + + align:start position:0% +to mon which is by far the largest part +of the program which in turn will take + + align:start position:0% +of the program which in turn will take + + + align:start position:0% +of the program which in turn will take +the phonetic uh information and as I + + align:start position:0% +the phonetic uh information and as I + + + align:start position:0% +the phonetic uh information and as I +said use uh what a basic diones file + + align:start position:0% +said use uh what a basic diones file + + + align:start position:0% +said use uh what a basic diones file +which has takes uh a very large range of + + align:start position:0% +which has takes uh a very large range of + + + align:start position:0% +which has takes uh a very large range of +uh sounds and uh u sounds and uh + + align:start position:0% +uh sounds and uh u sounds and uh + + + align:start position:0% +uh sounds and uh u sounds and uh +characters and will then transform these + + align:start position:0% +characters and will then transform these + + + align:start position:0% +characters and will then transform these +phonetics into into direct parameters + + align:start position:0% +phonetics into into direct parameters + + + align:start position:0% +phonetics into into direct parameters +which can represent the changing of a + + align:start position:0% +which can represent the changing of a + + + align:start position:0% +which can represent the changing of a +throat and the nasal entire nasal tract + + align:start position:0% +throat and the nasal entire nasal tract + + + align:start position:0% +throat and the nasal entire nasal tract +as uh you voice your own speech so mono + + align:start position:0% +as uh you voice your own speech so mono + + + align:start position:0% +as uh you voice your own speech so mono +Mon Mon has to go through a long process + + align:start position:0% +Mon Mon has to go through a long process + + + align:start position:0% +Mon Mon has to go through a long process +of calculating these phrases given the + + align:start position:0% +of calculating these phrases given the + + + align:start position:0% +of calculating these phrases given the +whole the Rhythm and the ination of the + + align:start position:0% +whole the Rhythm and the ination of the + + + align:start position:0% +whole the Rhythm and the ination of the +phrase that's being given to Mon and + + align:start position:0% +phrase that's being given to Mon and + + + align:start position:0% +phrase that's being given to Mon and +also a very important part of the + + align:start position:0% +also a very important part of the + + + align:start position:0% +also a very important part of the +process is by taking each phrase and the + + align:start position:0% +process is by taking each phrase and the + + + align:start position:0% +process is by taking each phrase and the +postures is what we call them the output + + align:start position:0% +postures is what we call them the output + + + align:start position:0% +postures is what we call them the output +taking looking at the phrase and piece + + align:start position:0% +taking looking at the phrase and piece + + + align:start position:0% +taking looking at the phrase and piece +by piece + + align:start position:0% +by piece + + + align:start position:0% +by piece +um examining the sounds and realizing + + align:start position:0% +um examining the sounds and realizing + + + align:start position:0% +um examining the sounds and realizing +that as the postures of the throat + + align:start position:0% +that as the postures of the throat + + + align:start position:0% +that as the postures of the throat +change there are important things + + align:start position:0% +change there are important things + + + align:start position:0% +change there are important things +changes being made between there and + + align:start position:0% +changes being made between there and + + + align:start position:0% +changes being made between there and +basically having some sort of uh uh + + align:start position:0% +basically having some sort of uh uh + + + align:start position:0% +basically having some sort of uh uh +basically a + + align:start position:0% +basically a + + + align:start position:0% +basically a +uh a slow change between them not a + + align:start position:0% +uh a slow change between them not a + + + align:start position:0% +uh a slow change between them not a +gradual conversion as opposed to a + + align:start position:0% +gradual conversion as opposed to a + + + align:start position:0% +gradual conversion as opposed to a +sudden change in the actual shape so + + align:start position:0% +sudden change in the actual shape so + + + align:start position:0% +sudden change in the actual shape so +then having outputed the basic postures + + align:start position:0% +then having outputed the basic postures + + + align:start position:0% +then having outputed the basic postures +you finally send it to the tube + + align:start position:0% +you finally send it to the tube + + + align:start position:0% +you finally send it to the tube +resonance model or trm which will then + + align:start position:0% +resonance model or trm which will then + + + align:start position:0% +resonance model or trm which will then +take the vocal track which is divided + + align:start position:0% +take the vocal track which is divided + + + align:start position:0% +take the vocal track which is divided +into eight sections in this model and + + align:start position:0% +into eight sections in this model and + + + align:start position:0% +into eight sections in this model and +send a uh basically some sort of signal + + align:start position:0% +send a uh basically some sort of signal + + + align:start position:0% +send a uh basically some sort of signal +off in a sine wave through the modified + + align:start position:0% +off in a sine wave through the modified + + + align:start position:0% +off in a sine wave through the modified +uh tube resonance model and therefore + + align:start position:0% +uh tube resonance model and therefore + + + align:start position:0% +uh tube resonance model and therefore +all the changes that occur as time goes + + align:start position:0% +all the changes that occur as time goes + + + align:start position:0% +all the changes that occur as time goes +on and the posters which change the + + align:start position:0% +on and the posters which change the + + + align:start position:0% +on and the posters which change the +basically the widths of the tube in + + align:start position:0% +basically the widths of the tube in + + + align:start position:0% +basically the widths of the tube in +various stages will then cause uh + + align:start position:0% +various stages will then cause uh + + + align:start position:0% +various stages will then cause uh +different speech patterns to come out + + align:start position:0% +different speech patterns to come out + + + align:start position:0% +different speech patterns to come out +and basically create an actual uh Speech + + align:start position:0% +and basically create an actual uh Speech + + + align:start position:0% +and basically create an actual uh Speech +pattern which is usually recognized so + + align:start position:0% +pattern which is usually recognized so + + + align:start position:0% +pattern which is usually recognized so +basically you go through these three + + align:start position:0% +basically you go through these three + + + align:start position:0% +basically you go through these three +parts from a uh basic string to + + align:start position:0% +parts from a uh basic string to + + + align:start position:0% +parts from a uh basic string to +phonetics to throat postures until + + align:start position:0% +phonetics to throat postures until + + + align:start position:0% +phonetics to throat postures until +finally you get the actual speech + + align:start position:0% +finally you get the actual speech + + + align:start position:0% +finally you get the actual speech +output so now I'm heading it over + + align:start position:0% +output so now I'm heading it over + + + align:start position:0% +output so now I'm heading it over +to to Joyce to talk a little bit about + + align:start position:0% +to to Joyce to talk a little bit about + + + align:start position:0% +to to Joyce to talk a little bit about +the resources and + + align:start position:0% + + + + align:start position:0% + +algorithms well before I talk about the + + align:start position:0% +algorithms well before I talk about the + + + align:start position:0% +algorithms well before I talk about the +resources and algorithms I'll talk a + + align:start position:0% +resources and algorithms I'll talk a + + + align:start position:0% +resources and algorithms I'll talk a +little bit about the trm which is the + + align:start position:0% +little bit about the trm which is the + + + align:start position:0% +little bit about the trm which is the +tube resonance model so we talked about + + align:start position:0% +tube resonance model so we talked about + + + align:start position:0% +tube resonance model so we talked about +how Monet outputs like two parameters + + align:start position:0% +how Monet outputs like two parameters + + + align:start position:0% +how Monet outputs like two parameters +based on you know transitions between + + align:start position:0% +based on you know transitions between + + + align:start position:0% +based on you know transitions between +different words and postures and so on + + align:start position:0% +different words and postures and so on + + + align:start position:0% +different words and postures and so on +and the tube resonance model actually + + align:start position:0% +and the tube resonance model actually + + + align:start position:0% +and the tube resonance model actually +simulates the physics of the vocal tract + + align:start position:0% +simulates the physics of the vocal tract + + + align:start position:0% +simulates the physics of the vocal tract +first you have a glal source if you have + + align:start position:0% +first you have a glal source if you have + + + align:start position:0% +first you have a glal source if you have +done any you know Linguistics you might + + align:start position:0% +done any you know Linguistics you might + + + align:start position:0% +done any you know Linguistics you might +have heard the little clicking sound The + + align:start position:0% +have heard the little clicking sound The + + + align:start position:0% +have heard the little clicking sound The +glal Source makes there are different + + align:start position:0% +glal Source makes there are different + + + align:start position:0% +glal Source makes there are different +ways to simulate the GLaDOS Source now + + align:start position:0% +ways to simulate the GLaDOS Source now + + + align:start position:0% +ways to simulate the GLaDOS Source now +the ideally the way you have a good + + align:start position:0% +the ideally the way you have a good + + + align:start position:0% +the ideally the way you have a good +natural glal source is you have a + + align:start position:0% +natural glal source is you have a + + + align:start position:0% +natural glal source is you have a +simulation of physics between two + + align:start position:0% +simulation of physics between two + + + align:start position:0% +simulation of physics between two +oscillating masses as you know air + + align:start position:0% +oscillating masses as you know air + + + align:start position:0% +oscillating masses as you know air +passes through them now back in the days + + align:start position:0% +passes through them now back in the days + + + align:start position:0% +passes through them now back in the days +when say you know people were doing + + align:start position:0% +when say you know people were doing + + + align:start position:0% +when say you know people were doing +speech research on G speech actually + + align:start position:0% +speech research on G speech actually + + + align:start position:0% +speech research on G speech actually +simulating the physics of a a glaus was + + align:start position:0% +simulating the physics of a a glaus was + + + align:start position:0% +simulating the physics of a a glaus was +not possible so what they did instead + + align:start position:0% +not possible so what they did instead + + + align:start position:0% +not possible so what they did instead +was you know they would try a half sign + + align:start position:0% +was you know they would try a half sign + + + align:start position:0% +was you know they would try a half sign +wave or they would research the most + + align:start position:0% +wave or they would research the most + + + align:start position:0% +wave or they would research the most +natural sounding glottal pulse shape + + align:start position:0% +natural sounding glottal pulse shape + + + align:start position:0% +natural sounding glottal pulse shape +initialize a wave table and do table + + align:start position:0% +initialize a wave table and do table + + + align:start position:0% +initialize a wave table and do table +lookup on it updating it as you know + + align:start position:0% +lookup on it updating it as you know + + + align:start position:0% +lookup on it updating it as you know +with amplitude and so on to change it a + + align:start position:0% +with amplitude and so on to change it a + + + align:start position:0% +with amplitude and so on to change it a +little by little so one of our goals + + align:start position:0% +little by little so one of our goals + + + align:start position:0% +little by little so one of our goals +were was Pro possibly to because we + + align:start position:0% +were was Pro possibly to because we + + + align:start position:0% +were was Pro possibly to because we +harness the additional computational + + align:start position:0% +harness the additional computational + + + align:start position:0% +harness the additional computational +power and make more natural sounding + + align:start position:0% +power and make more natural sounding + + + align:start position:0% +power and make more natural sounding +speech and now I'll talk about um + + align:start position:0% +speech and now I'll talk about um + + + align:start position:0% +speech and now I'll talk about um +allocating the resources there's um for + + align:start position:0% +allocating the resources there's um for + + + align:start position:0% +allocating the resources there's um for +example new speech Monae there is not as + + align:start position:0% +example new speech Monae there is not as + + + align:start position:0% +example new speech Monae there is not as +much computation Monet has a lot of + + align:start position:0% +much computation Monet has a lot of + + + align:start position:0% +much computation Monet has a lot of +rules for example between postures and + + align:start position:0% +rules for example between postures and + + + align:start position:0% +rules for example between postures and +postures like different shapes of vocal + + align:start position:0% +postures like different shapes of vocal + + + align:start position:0% +postures like different shapes of vocal +tracks you can't just do an linear + + align:start position:0% +tracks you can't just do an linear + + + align:start position:0% +tracks you can't just do an linear +interpolation to smoothly change there + + align:start position:0% +interpolation to smoothly change there + + + align:start position:0% +interpolation to smoothly change there +are different rules in order to change + + align:start position:0% +are different rules in order to change + + + align:start position:0% +are different rules in order to change +between dep postures which greatly + + align:start position:0% +between dep postures which greatly + + + align:start position:0% +between dep postures which greatly +affects the + + align:start position:0% +affects the + + + align:start position:0% +affects the +speech um this was much harder to uh + + align:start position:0% +speech um this was much harder to uh + + + align:start position:0% +speech um this was much harder to uh +improve on like to + + align:start position:0% +improve on like to + + + align:start position:0% +improve on like to +paralize in the tube resonance module it + + align:start position:0% +paralize in the tube resonance module it + + + align:start position:0% +paralize in the tube resonance module it +had a lot more computation in fact the + + align:start position:0% +had a lot more computation in fact the + + + align:start position:0% +had a lot more computation in fact the +thing that took probably most + + align:start position:0% +thing that took probably most + + + align:start position:0% +thing that took probably most +computation was after we got our signal + + align:start position:0% +computation was after we got our signal + + + align:start position:0% +computation was after we got our signal +data from the mouth end of the + + align:start position:0% +data from the mouth end of the + + + align:start position:0% +data from the mouth end of the +simulation we would have to upsample or + + align:start position:0% +simulation we would have to upsample or + + + align:start position:0% +simulation we would have to upsample or +down sample it and that was something + + align:start position:0% +down sample it and that was something + + + align:start position:0% +down sample it and that was something +that had a lot of potential to be + + align:start position:0% +that had a lot of potential to be + + + align:start position:0% +that had a lot of potential to be +parallelized however when you were + + align:start position:0% +parallelized however when you were + + + align:start position:0% +parallelized however when you were +simulating two res model you could only + + align:start position:0% +simulating two res model you could only + + + align:start position:0% +simulating two res model you could only +update the signal inside the vocal track + + align:start position:0% +update the signal inside the vocal track + + + align:start position:0% +update the signal inside the vocal track +incrementally if you were to break it up + + align:start position:0% +incrementally if you were to break it up + + + align:start position:0% +incrementally if you were to break it up +there was um possibility that there + + align:start position:0% +there was um possibility that there + + + align:start position:0% +there was um possibility that there +would be like a lot of Pops in between + + align:start position:0% +would be like a lot of Pops in between + + + align:start position:0% +would be like a lot of Pops in between +if you when you try to space them + + align:start position:0% +if you when you try to space them + + + align:start position:0% +if you when you try to space them +together we thought about trying to + + align:start position:0% +together we thought about trying to + + + align:start position:0% +together we thought about trying to +resolve that with interpolation between + + align:start position:0% +resolve that with interpolation between + + + align:start position:0% +resolve that with interpolation between +forms um there were these there were + + align:start position:0% +forms um there were these there were + + + align:start position:0% +forms um there were these there were +nested Loops the main synthesize thing + + align:start position:0% +nested Loops the main synthesize thing + + + align:start position:0% +nested Loops the main synthesize thing +had two lested Loops you have a posture + + align:start position:0% +had two lested Loops you have a posture + + + align:start position:0% +had two lested Loops you have a posture +and then you simulate on the posture in + + align:start position:0% +and then you simulate on the posture in + + + align:start position:0% +and then you simulate on the posture in +between the postures and that took + + align:start position:0% +between the postures and that took + + + align:start position:0% +between the postures and that took +computation as well as updating the glal + + align:start position:0% +computation as well as updating the glal + + + align:start position:0% +computation as well as updating the glal +wave + + align:start position:0% +wave + + + align:start position:0% +wave +table all right now I'll hand it off to + + align:start position:0% +table all right now I'll hand it off to + + + align:start position:0% +table all right now I'll hand it off to +Omari to explain + + align:start position:0% + + + + align:start position:0% + +challenges okay so the trm algorithm U + + align:start position:0% +challenges okay so the trm algorithm U + + + align:start position:0% +challenges okay so the trm algorithm U +which is what you most focus on trying + + align:start position:0% +which is what you most focus on trying + + + align:start position:0% +which is what you most focus on trying +to + + align:start position:0% + + + + align:start position:0% + +uh so we most tried to focus on + + align:start position:0% +uh so we most tried to focus on + + + align:start position:0% +uh so we most tried to focus on +parallelizing the trm algorithm because + + align:start position:0% +parallelizing the trm algorithm because + + + align:start position:0% +parallelizing the trm algorithm because +both uh new speech and Monae were almost + + align:start position:0% +both uh new speech and Monae were almost + + + align:start position:0% +both uh new speech and Monae were almost +entirely just Dictionary lookups + + align:start position:0% +entirely just Dictionary lookups + + + align:start position:0% +entirely just Dictionary lookups +involving large amounts of memory with + + align:start position:0% +involving large amounts of memory with + + + align:start position:0% +involving large amounts of memory with +not that much computation so we didn't + + align:start position:0% +not that much computation so we didn't + + + align:start position:0% +not that much computation so we didn't +really Tred that there wasn't really + + align:start position:0% +really Tred that there wasn't really + + + align:start position:0% +really Tred that there wasn't really +that much potential for parallelizing + + align:start position:0% +that much potential for parallelizing + + + align:start position:0% +that much potential for parallelizing +those so we did + + align:start position:0% +those so we did + + + align:start position:0% +those so we did +uh uh looked at the tasks that were + + align:start position:0% +uh uh looked at the tasks that were + + + align:start position:0% +uh uh looked at the tasks that were +being done on trm profiled them and you + + align:start position:0% +being done on trm profiled them and you + + + align:start position:0% +being done on trm profiled them and you +can see the what took most of the time + + align:start position:0% +can see the what took most of the time + + + align:start position:0% +can see the what took most of the time +was the noise generator part like the + + align:start position:0% +was the noise generator part like the + + + align:start position:0% +was the noise generator part like the +attempted the glut source that was into + + align:start position:0% +attempted the glut source that was into + + + align:start position:0% +attempted the glut source that was into +that was in I mean that was being put + + align:start position:0% +that was in I mean that was being put + + + align:start position:0% +that was in I mean that was being put +into the tubes and the actual updates of + + align:start position:0% +into the tubes and the actual updates of + + + align:start position:0% +into the tubes and the actual updates of +where the tubes were supposed to be as + + align:start position:0% +where the tubes were supposed to be as + + + align:start position:0% +where the tubes were supposed to be as +they were shifting and so unfortunately + + align:start position:0% +they were shifting and so unfortunately + + + align:start position:0% +they were shifting and so unfortunately +um the main loop as this was updating + + align:start position:0% +um the main loop as this was updating + + + align:start position:0% +um the main loop as this was updating +was very very fast of about 15 + + align:start position:0% +was very very fast of about 15 + + + align:start position:0% +was very very fast of about 15 +microseconds + + align:start position:0% +microseconds + + + align:start position:0% +microseconds +so um it was it it would be pretty + + align:start position:0% +so um it was it it would be pretty + + + align:start position:0% +so um it was it it would be pretty +difficult to you know update um for + + align:start position:0% +difficult to you know update um for + + + align:start position:0% +difficult to you know update um for +example several spus for as fast as we + + align:start position:0% +example several spus for as fast as we + + + align:start position:0% +example several spus for as fast as we +needed them to like considering how um + + align:start position:0% +needed them to like considering how um + + + align:start position:0% +needed them to like considering how um +how communication costs affect + + align:start position:0% +how communication costs affect + + + align:start position:0% +how communication costs affect +that so the parallelism um was not + + align:start position:0% +that so the parallelism um was not + + + align:start position:0% +that so the parallelism um was not +very simple to use our main original + + align:start position:0% +very simple to use our main original + + + align:start position:0% +very simple to use our main original +idea for exploding parallelism was to + + align:start position:0% +idea for exploding parallelism was to + + + align:start position:0% +idea for exploding parallelism was to +make a pipeline of the various parts of + + align:start position:0% +make a pipeline of the various parts of + + + align:start position:0% +make a pipeline of the various parts of +the trm model maybe like using three or + + align:start position:0% +the trm model maybe like using three or + + + align:start position:0% +the trm model maybe like using three or +four spus like one for each part of the + + align:start position:0% +four spus like one for each part of the + + + align:start position:0% +four spus like one for each part of the +throat as the sound would go from one to + + align:start position:0% +throat as the sound would go from one to + + + align:start position:0% +throat as the sound would go from one to +the next so that all of them would be + + align:start position:0% +the next so that all of them would be + + + align:start position:0% +the next so that all of them would be +engaged simultaneously like going from + + align:start position:0% +engaged simultaneously like going from + + + align:start position:0% +engaged simultaneously like going from +one poster to the + + align:start position:0% +one poster to the + + + align:start position:0% +one poster to the +next in a like linear + + align:start position:0% +next in a like linear + + + align:start position:0% +next in a like linear +fashion but unfortunately the uh the + + align:start position:0% +fashion but unfortunately the uh the + + + align:start position:0% +fashion but unfortunately the uh the +loop the timing for this was very very + + align:start position:0% +loop the timing for this was very very + + + align:start position:0% +loop the timing for this was very very +fast in the order of about 70 khz which + + align:start position:0% +fast in the order of about 70 khz which + + + align:start position:0% +fast in the order of about 70 khz which +is like many times a second for spus to + + align:start position:0% +is like many times a second for spus to + + + align:start position:0% +is like many times a second for spus to +be transferring data back and forth to + + align:start position:0% +be transferring data back and forth to + + + align:start position:0% +be transferring data back and forth to +each other with mailboxes in + + align:start position:0% +each other with mailboxes in + + + align:start position:0% +each other with mailboxes in +memory + + align:start position:0% +memory + + + align:start position:0% +memory +so that was somewhat + + align:start position:0% + + + + align:start position:0% + +difficult + + align:start position:0% + + + + align:start position:0% + +um unfortunately with this Pro with this + + align:start position:0% +um unfortunately with this Pro with this + + + align:start position:0% +um unfortunately with this Pro with this +project we um faced a number of + + align:start position:0% +project we um faced a number of + + + align:start position:0% +project we um faced a number of +challenges the first and foremost being + + align:start position:0% +challenges the first and foremost being + + + align:start position:0% +challenges the first and foremost being +that uh new speech is written in a + + align:start position:0% +that uh new speech is written in a + + + align:start position:0% +that uh new speech is written in a +programming language most of us weren't + + align:start position:0% +programming language most of us weren't + + + align:start position:0% +programming language most of us weren't +familiar with and it's huge like um n + + align:start position:0% +familiar with and it's huge like um n + + + align:start position:0% +familiar with and it's huge like um n +for example is 30,000 lines it's hardly + + align:start position:0% +for example is 30,000 lines it's hardly + + + align:start position:0% +for example is 30,000 lines it's hardly +documented and yeah and it took uh a + + align:start position:0% +documented and yeah and it took uh a + + + align:start position:0% +documented and yeah and it took uh a +fair amount of time just like reading + + align:start position:0% +fair amount of time just like reading + + + align:start position:0% +fair amount of time just like reading +through and figuring out what was going + + align:start position:0% +through and figuring out what was going + + + align:start position:0% +through and figuring out what was going +on um additionally because it uses new + + align:start position:0% +on um additionally because it uses new + + + align:start position:0% +on um additionally because it uses new +Step which is sort of a gii + + align:start position:0% +Step which is sort of a gii + + + align:start position:0% +Step which is sort of a gii +library um the calls are asynchronous + + align:start position:0% +library um the calls are asynchronous + + + align:start position:0% +library um the calls are asynchronous +and it makes it tremendously difficult + + align:start position:0% +and it makes it tremendously difficult + + + align:start position:0% +and it makes it tremendously difficult +to to debug as + + align:start position:0% +to to debug as + + + align:start position:0% +to to debug as +well um I had tried to convert part of + + align:start position:0% +well um I had tried to convert part of + + + align:start position:0% +well um I had tried to convert part of +it to C+ plus to try to get the tube + + align:start position:0% +it to C+ plus to try to get the tube + + + align:start position:0% +it to C+ plus to try to get the tube +running on one of the spes and that took + + align:start position:0% +running on one of the spes and that took + + + align:start position:0% +running on one of the spes and that took +3 days in and of itself and I ended up + + align:start position:0% +3 days in and of itself and I ended up + + + align:start position:0% +3 days in and of itself and I ended up +having to toss that attempt out um + + align:start position:0% +having to toss that attempt out um + + + align:start position:0% +having to toss that attempt out um +another problem we had was Dynamic + + align:start position:0% +another problem we had was Dynamic + + + align:start position:0% +another problem we had was Dynamic +pointer alignment in Objective C most of + + align:start position:0% +pointer alignment in Objective C most of + + + align:start position:0% +pointer alignment in Objective C most of +the objects are stored as Dynamic + + align:start position:0% +the objects are stored as Dynamic + + + align:start position:0% +the objects are stored as Dynamic +pointers and + + align:start position:0% + + + + align:start position:0% + +um basically in in Objective C there's + + align:start position:0% +um basically in in Objective C there's + + + align:start position:0% +um basically in in Objective C there's +also no like malic align or anything of + + align:start position:0% +also no like malic align or anything of + + + align:start position:0% +also no like malic align or anything of +that nature so we couldn't really + + align:start position:0% +that nature so we couldn't really + + + align:start position:0% +that nature so we couldn't really +transfer any of the objects from The + + align:start position:0% +transfer any of the objects from The + + + align:start position:0% +transfer any of the objects from The +Objective + + align:start position:0% +Objective + + + align:start position:0% +Objective +C memory area I guess to the spus to + + align:start position:0% +C memory area I guess to the spus to + + + align:start position:0% +C memory area I guess to the spus to +work on the data and then send them back + + align:start position:0% +work on the data and then send them back + + + align:start position:0% +work on the data and then send them back +um so what is working now we are able to + + align:start position:0% +um so what is working now we are able to + + + align:start position:0% +um so what is working now we are able to +do line buffered text um in in the new + + align:start position:0% +do line buffered text um in in the new + + + align:start position:0% +do line buffered text um in in the new +speech engine um and translate that to + + align:start position:0% +speech engine um and translate that to + + + align:start position:0% +speech engine um and translate that to +utterances so the phonetic um + + align:start position:0% +utterances so the phonetic um + + + align:start position:0% +utterances so the phonetic um +pronunciations and get to the point + + align:start position:0% +pronunciations and get to the point + + + align:start position:0% +pronunciations and get to the point +where we + + align:start position:0% +where we + + + align:start position:0% +where we +would um execute the tube model + + align:start position:0% +would um execute the tube model + + + align:start position:0% +would um execute the tube model +unfortunately one of the like I gu a bug + + align:start position:0% +unfortunately one of the like I gu a bug + + + align:start position:0% +unfortunately one of the like I gu a bug +in new speech potentially is preventing + + align:start position:0% +in new speech potentially is preventing + + + align:start position:0% +in new speech potentially is preventing +us from properly executing the tube + + align:start position:0% +us from properly executing the tube + + + align:start position:0% +us from properly executing the tube +model right now + + align:start position:0% +model right now + + + align:start position:0% +model right now +so so that's one um thing we're having + + align:start position:0% +so so that's one um thing we're having + + + align:start position:0% +so so that's one um thing we're having +problems with additionally um the tube + + align:start position:0% +problems with additionally um the tube + + + align:start position:0% +problems with additionally um the tube +runs on the PPE we've been trying to get + + align:start position:0% +runs on the PPE we've been trying to get + + + align:start position:0% +runs on the PPE we've been trying to get +the tube to run on the S SP but it's not + + align:start position:0% +the tube to run on the S SP but it's not + + + align:start position:0% +the tube to run on the S SP but it's not +going well partly because of the um the + + align:start position:0% +going well partly because of the um the + + + align:start position:0% +going well partly because of the um the +dynamic pointer alignment issue and + + align:start position:0% +dynamic pointer alignment issue and + + + align:start position:0% +dynamic pointer alignment issue and +partly because of some other things + + align:start position:0% +partly because of some other things + + + align:start position:0% +partly because of some other things +we've run + + align:start position:0% +we've run + + + align:start position:0% +we've run +into um currently not + + align:start position:0% +into um currently not + + + align:start position:0% +into um currently not +working as um Drew had mentioned there + + align:start position:0% +working as um Drew had mentioned there + + + align:start position:0% +working as um Drew had mentioned there +is there are a lot of Dictionary lookups + + align:start position:0% +is there are a lot of Dictionary lookups + + + align:start position:0% +is there are a lot of Dictionary lookups +in the sort of the pre-processing + + align:start position:0% +in the sort of the pre-processing + + + align:start position:0% +in the sort of the pre-processing +pre-processing stage of the of the + + align:start position:0% +pre-processing stage of the of the + + + align:start position:0% +pre-processing stage of the of the +pipeline I guess and there's a bug in + + align:start position:0% +pipeline I guess and there's a bug in + + + align:start position:0% +pipeline I guess and there's a bug in +new Step where it won't recognize it + + align:start position:0% +new Step where it won't recognize it + + + align:start position:0% +new Step where it won't recognize it +won't parse the dictionary if it's above + + align:start position:0% +won't parse the dictionary if it's above + + + align:start position:0% +won't parse the dictionary if it's above +a certain size the dictionary has I + + align:start position:0% +a certain size the dictionary has I + + + align:start position:0% +a certain size the dictionary has I +believe 70,000 entries it takes up + + align:start position:0% +believe 70,000 entries it takes up + + + align:start position:0% +believe 70,000 entries it takes up +almost three Megs but + + align:start position:0% +almost three Megs but + + + align:start position:0% +almost three Megs but +if there are I believe more than like + + align:start position:0% +if there are I believe more than like + + + align:start position:0% +if there are I believe more than like +more than 3,000 entries in the + + align:start position:0% +more than 3,000 entries in the + + + align:start position:0% +more than 3,000 entries in the +dictionary it just doesn't parse and we + + align:start position:0% +dictionary it just doesn't parse and we + + + align:start position:0% +dictionary it just doesn't parse and we +have no idea + + align:start position:0% +have no idea + + + align:start position:0% +have no idea +why uh scoot past so um to + + align:start position:0% +why uh scoot past so um to + + + align:start position:0% +why uh scoot past so um to +conclude uh this was a tremendously + + align:start position:0% +conclude uh this was a tremendously + + + align:start position:0% +conclude uh this was a tremendously +difficult problem like there are a bunch + + align:start position:0% +difficult problem like there are a bunch + + + align:start position:0% +difficult problem like there are a bunch +of data + + align:start position:0% +of data + + + align:start position:0% +of data +dependencies and the synchronization is + + align:start position:0% +dependencies and the synchronization is + + + align:start position:0% +dependencies and the synchronization is +very very + + align:start position:0% +very very + + + align:start position:0% +very very +close um however we feel that with as + + align:start position:0% +close um however we feel that with as + + + align:start position:0% +close um however we feel that with as +with more time and with more experience + + align:start position:0% +with more time and with more experience + + + align:start position:0% +with more time and with more experience +with the code base we would have been + + align:start position:0% +with the code base we would have been + + + align:start position:0% +with the code base we would have been +able to parallelize it and um the + + align:start position:0% +able to parallelize it and um the + + + align:start position:0% +able to parallelize it and um the +parallelization can almost definitely + + align:start position:0% +parallelization can almost definitely + + + align:start position:0% +parallelization can almost definitely +help the vocal quality in terms of + + align:start position:0% +help the vocal quality in terms of + + + align:start position:0% +help the vocal quality in terms of +naturalness getting for example as Joyce + + align:start position:0% +naturalness getting for example as Joyce + + + align:start position:0% +naturalness getting for example as Joyce +mentioned a higher quality glottal + + align:start position:0% +mentioned a higher quality glottal + + + align:start position:0% +mentioned a higher quality glottal +source + + align:start position:0% +source + + + align:start position:0% +source +um speaker identification Val ident + + align:start position:0% +um speaker identification Val ident + + + align:start position:0% +um speaker identification Val ident +identification for example + + align:start position:0% +identification for example + + + align:start position:0% +identification for example +the when when you pronounce different + + align:start position:0% +the when when you pronounce different + + + align:start position:0% +the when when you pronounce different +vows sometimes the quality of the + + align:start position:0% +vows sometimes the quality of the + + + align:start position:0% +vows sometimes the quality of the +glottal Source changes and lastly it + + align:start position:0% +glottal Source changes and lastly it + + + align:start position:0% +glottal Source changes and lastly it +would be worth the time to rewrite the + + align:start position:0% +would be worth the time to rewrite the + + + align:start position:0% +would be worth the time to rewrite the +whole thing from scratch skipping new + + align:start position:0% +whole thing from scratch skipping new + + + align:start position:0% +whole thing from scratch skipping new +Step skipping Objective C and going with + + align:start position:0% +Step skipping Objective C and going with + + + align:start position:0% +Step skipping Objective C and going with +um C++ or most likely see for the whole + + align:start position:0% +um C++ or most likely see for the whole + + + align:start position:0% +um C++ or most likely see for the whole +thing um thank you any questions + + align:start position:0% + + + + align:start position:0% + +so it sounds sounds like you guys took a + + align:start position:0% +so it sounds sounds like you guys took a + + + align:start position:0% +so it sounds sounds like you guys took a +fine grain approach in which you're + + align:start position:0% +fine grain approach in which you're + + + align:start position:0% +fine grain approach in which you're +splitting the application across + + align:start position:0% +splitting the application across + + + align:start position:0% +splitting the application across +different looked at splitting the + + align:start position:0% +different looked at splitting the + + + align:start position:0% +different looked at splitting the +application across different units it + + align:start position:0% +application across different units it + + + align:start position:0% +application across different units it +seems since you're I mean you're + + align:start position:0% +seems since you're I mean you're + + + align:start position:0% +seems since you're I mean you're +synthesizing completely independent + + align:start position:0% +synthesizing completely independent + + + align:start position:0% +synthesizing completely independent +words let's say right could could you + + align:start position:0% +words let's say right could could you + + + align:start position:0% +words let's say right could could you +just run the whole application on an spu + + align:start position:0% +just run the whole application on an spu + + + align:start position:0% +just run the whole application on an spu +I mean there's engineering there but I + + align:start position:0% +I mean there's engineering there but I + + + align:start position:0% +I mean there's engineering there but I +mean from a from a paralyzation + + align:start position:0% +mean from a from a paralyzation + + + align:start position:0% +mean from a from a paralyzation +standpoint can you just take the whole + + align:start position:0% +standpoint can you just take the whole + + + align:start position:0% +standpoint can you just take the whole +application and run it for example on + + align:start position:0% +application and run it for example on + + + align:start position:0% +application and run it for example on +different words so the + + align:start position:0% +different words so the + + + align:start position:0% +different words so the +um so I believe you um you're suggesting + + align:start position:0% +um so I believe you um you're suggesting + + + align:start position:0% +um so I believe you um you're suggesting +we run the tube on different s spes and + + align:start position:0% +we run the tube on different s spes and + + + align:start position:0% +we run the tube on different s spes and +then like feed data to the separate + + align:start position:0% +then like feed data to the separate + + + align:start position:0% +then like feed data to the separate +instances of the tube from the pp uh + + align:start position:0% +instances of the tube from the pp uh + + + align:start position:0% +instances of the tube from the pp uh +well including well I guess the whole + + align:start position:0% +well including well I guess the whole + + + align:start position:0% +well including well I guess the whole +processing pipeline I mean all their + + align:start position:0% +processing pipeline I mean all their + + + align:start position:0% +processing pipeline I mean all their +dependences from one like One S to the + + align:start position:0% +dependences from one like One S to the + + + align:start position:0% +dependences from one like One S to the +next the big stumbling block for us was + + align:start position:0% +next the big stumbling block for us was + + + align:start position:0% +next the big stumbling block for us was +that there isn't currently an Objective + + align:start position:0% +that there isn't currently an Objective + + + align:start position:0% +that there isn't currently an Objective +C compile compiler for the spes so we + + align:start position:0% +C compile compiler for the spes so we + + + align:start position:0% +C compile compiler for the spes so we +can't run the SP code Run The Objective + + align:start position:0% +can't run the SP code Run The Objective + + + align:start position:0% +can't run the SP code Run The Objective +C code on the SPs at all if you did it + + align:start position:0% +C code on the SPs at all if you did it + + + align:start position:0% +C code on the SPs at all if you did it +from scratch to write your own + + align:start position:0% +from scratch to write your own + + + align:start position:0% +from scratch to write your own +you just throw away all the objectives + + align:start position:0% +you just throw away all the objectives + + + align:start position:0% +you just throw away all the objectives +here start from stretch would that be a + + align:start position:0% +here start from stretch would that be a + + + align:start position:0% +here start from stretch would that be a +better paralyzation strategy than a f + + align:start position:0% +better paralyzation strategy than a f + + + align:start position:0% +better paralyzation strategy than a f +GRE one + + align:start position:0% +GRE one + + + align:start position:0% +GRE one +um + + align:start position:0% +um + + + align:start position:0% +um +see possibly so one of the as + + align:start position:0% +see possibly so one of the as + + + align:start position:0% +see possibly so one of the as +disadvantages of sort of splitting up + + align:start position:0% +disadvantages of sort of splitting up + + + align:start position:0% +disadvantages of sort of splitting up +words is that um there is state that + + align:start position:0% +words is that um there is state that + + + align:start position:0% +words is that um there is state that +connects the different like it's + + align:start position:0% +connects the different like it's + + + align:start position:0% +connects the different like it's +continuous state that connects the + + align:start position:0% +continuous state that connects the + + + align:start position:0% +continuous state that connects the +different postures of the vocal tract + + align:start position:0% +different postures of the vocal tract + + + align:start position:0% +different postures of the vocal tract +all the way through the other s and so + + align:start position:0% +all the way through the other s and so + + + align:start position:0% +all the way through the other s and so +we would have to as do possibly some + + align:start position:0% +we would have to as do possibly some + + + align:start position:0% +we would have to as do possibly some +prediction possibly some interpolation + + align:start position:0% +prediction possibly some interpolation + + + align:start position:0% +prediction possibly some interpolation +to figure out how to connect the + + align:start position:0% +to figure out how to connect the + + + align:start position:0% +to figure out how to connect the +different separate utterances which + + align:start position:0% +different separate utterances which + + + align:start position:0% +different separate utterances which +should have been um produced maybe one + + align:start position:0% +should have been um produced maybe one + + + align:start position:0% +should have been um produced maybe one +sentence at a time or something yeah + + align:start position:0% +sentence at a time or something yeah + + + align:start position:0% +sentence at a time or something yeah +that might be in uh option + + align:start position:0% + + + + align:start position:0% + +yes \ No newline at end of file diff --git a/C_akTI3vnHQ.txt b/C_akTI3vnHQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..26cc4a5385bb389b80d6194d2d95d65eb2ea7220 --- /dev/null +++ b/C_akTI3vnHQ.txt @@ -0,0 +1,1011 @@ +align:start position:0% + +we've used the term social contract + + align:start position:0% +we've used the term social contract + + + align:start position:0% +we've used the term social contract +several times already so let's take a + + align:start position:0% +several times already so let's take a + + + align:start position:0% +several times already so let's take a +look at what did we mean by this post + + align:start position:0% +look at what did we mean by this post + + + align:start position:0% +look at what did we mean by this post +World War II social contract and why did + + align:start position:0% +World War II social contract and why did + + + align:start position:0% +World War II social contract and why did +it work so well for so many if you were + + align:start position:0% +it work so well for so many if you were + + + align:start position:0% +it work so well for so many if you were +born between 1946 and 1964 you're a + + align:start position:0% +born between 1946 and 1964 you're a + + + align:start position:0% +born between 1946 and 1964 you're a +member of what we call the baby boom + + align:start position:0% +member of what we call the baby boom + + + align:start position:0% +member of what we call the baby boom +generation and chances are you did quite + + align:start position:0% +generation and chances are you did quite + + + align:start position:0% +generation and chances are you did quite +well because you were able to follow + + align:start position:0% +well because you were able to follow + + + align:start position:0% +well because you were able to follow +your parents' advice of working hard + + align:start position:0% +your parents' advice of working hard + + + align:start position:0% +your parents' advice of working hard +staying in school and being able to + + align:start position:0% +staying in school and being able to + + + align:start position:0% +staying in school and being able to +improve on the standard of living you + + align:start position:0% +improve on the standard of living you + + + align:start position:0% +improve on the standard of living you +achieve for yourself and for your family + + align:start position:0% +achieve for yourself and for your family + + + align:start position:0% +achieve for yourself and for your family +compared to what your parents had so was + + align:start position:0% +compared to what your parents had so was + + + align:start position:0% +compared to what your parents had so was +this all just a matter of luck is there + + align:start position:0% +this all just a matter of luck is there + + + align:start position:0% +this all just a matter of luck is there +some iron law of Economics that achieved + + align:start position:0% +some iron law of Economics that achieved + + + align:start position:0% +some iron law of Economics that achieved +it well neither are true it took a lot + + align:start position:0% +it well neither are true it took a lot + + + align:start position:0% +it well neither are true it took a lot +of hard work and a lot of in invention + + align:start position:0% +of hard work and a lot of in invention + + + align:start position:0% +of hard work and a lot of in invention +on the part of Labor and management + + align:start position:0% +on the part of Labor and management + + + align:start position:0% +on the part of Labor and management +leaders of the time America came out of + + align:start position:0% +leaders of the time America came out of + + + align:start position:0% +leaders of the time America came out of +World War II with an enormous amount of + + align:start position:0% +World War II with an enormous amount of + + + align:start position:0% +World War II with an enormous amount of +pent up demand for consumer goods + + align:start position:0% +pent up demand for consumer goods + + + align:start position:0% +pent up demand for consumer goods +because we were focused on building the + + align:start position:0% +because we were focused on building the + + + align:start position:0% +because we were focused on building the +economy for the war so we had to convert + + align:start position:0% +economy for the war so we had to convert + + + align:start position:0% +economy for the war so we had to convert +from factories that made tanks and + + align:start position:0% +from factories that made tanks and + + + align:start position:0% +from factories that made tanks and +Military airplanes to factories that + + align:start position:0% +Military airplanes to factories that + + + align:start position:0% +Military airplanes to factories that +made cars and other kinds of goods and + + align:start position:0% +made cars and other kinds of goods and + + + align:start position:0% +made cars and other kinds of goods and +services that were in high demand in the + + align:start position:0% +services that were in high demand in the + + + align:start position:0% +services that were in high demand in the +postor War II economy and that created + + align:start position:0% +postor War II economy and that created + + + align:start position:0% +postor War II economy and that created +what we call the post-war social + + align:start position:0% +what we call the post-war social + + + align:start position:0% +what we call the post-war social +contract now you've seen this diagram + + align:start position:0% +contract now you've seen this diagram + + + align:start position:0% +contract now you've seen this diagram +before it shows that over the postor War + + align:start position:0% +before it shows that over the postor War + + + align:start position:0% +before it shows that over the postor War +II time period wages and and + + align:start position:0% +II time period wages and and + + + align:start position:0% +II time period wages and and +productivity moved in Tandem and so as + + align:start position:0% +productivity moved in Tandem and so as + + + align:start position:0% +productivity moved in Tandem and so as +the economy got better so too did wages + + align:start position:0% +the economy got better so too did wages + + + align:start position:0% +the economy got better so too did wages +and living conditions for the vast + + align:start position:0% +and living conditions for the vast + + + align:start position:0% +and living conditions for the vast +majority of families of that time so how + + align:start position:0% +majority of families of that time so how + + + align:start position:0% +majority of families of that time so how +did that work well as I said we've had + + align:start position:0% +did that work well as I said we've had + + + align:start position:0% +did that work well as I said we've had +an enormous amount of growth in + + align:start position:0% +an enormous amount of growth in + + + align:start position:0% +an enormous amount of growth in +construction in heavy industry in + + align:start position:0% +construction in heavy industry in + + + align:start position:0% +construction in heavy industry in +rebuilding the economy after World War + + align:start position:0% +rebuilding the economy after World War + + + align:start position:0% +rebuilding the economy after World War +II we had uh the rise of mass production + + align:start position:0% +II we had uh the rise of mass production + + + align:start position:0% +II we had uh the rise of mass production +we had automobiles coming out of our + + align:start position:0% +we had automobiles coming out of our + + + align:start position:0% +we had automobiles coming out of our +ears here's a picture of how Ford and + + align:start position:0% +ears here's a picture of how Ford and + + + align:start position:0% +ears here's a picture of how Ford and +General Motors and other companies were + + align:start position:0% +General Motors and other companies were + + + align:start position:0% +General Motors and other companies were +able to produce millions of vehicles for + + align:start position:0% +able to produce millions of vehicles for + + + align:start position:0% +able to produce millions of vehicles for +the mass Market largely similar kinds of + + align:start position:0% +the mass Market largely similar kinds of + + + align:start position:0% +the mass Market largely similar kinds of +of goods and services that people were + + align:start position:0% +of goods and services that people were + + + align:start position:0% +of goods and services that people were +were looking for so it was out of this + + align:start position:0% +were looking for so it was out of this + + + align:start position:0% +were looking for so it was out of this +time period that uh unions began to grow + + align:start position:0% +time period that uh unions began to grow + + + align:start position:0% +time period that uh unions began to grow +in the postor War II time period unions + + align:start position:0% +in the postor War II time period unions + + + align:start position:0% +in the postor War II time period unions +grew to about 30 to 35% but Union growth + + align:start position:0% +grew to about 30 to 35% but Union growth + + + align:start position:0% +grew to about 30 to 35% but Union growth +didn't come easily it took a lot of + + align:start position:0% +didn't come easily it took a lot of + + + align:start position:0% +didn't come easily it took a lot of +battles between labor and management in + + align:start position:0% +battles between labor and management in + + + align:start position:0% +battles between labor and management in +the steel industry in the Auto industry + + align:start position:0% +the steel industry in the Auto industry + + + align:start position:0% +the steel industry in the Auto industry +General Motors uh had to experience a + + align:start position:0% +General Motors uh had to experience a + + + align:start position:0% +General Motors uh had to experience a +sitdown strike in their plant in + + align:start position:0% +sitdown strike in their plant in + + + align:start position:0% +sitdown strike in their plant in +1937 before uh unionization uh was + + align:start position:0% +1937 before uh unionization uh was + + + align:start position:0% +1937 before uh unionization uh was +accepted by General Motors this is a uh + + align:start position:0% +accepted by General Motors this is a uh + + + align:start position:0% +accepted by General Motors this is a uh +an example of what's called the battle + + align:start position:0% +an example of what's called the battle + + + align:start position:0% +an example of what's called the battle +of the overpass where the Auto Workers + + align:start position:0% +of the overpass where the Auto Workers + + + align:start position:0% +of the overpass where the Auto Workers +leaders led by Walter Ruther who we're + + align:start position:0% +leaders led by Walter Ruther who we're + + + align:start position:0% +leaders led by Walter Ruther who we're +going to hear about a little bit more + + align:start position:0% +going to hear about a little bit more + + + align:start position:0% +going to hear about a little bit more +specifically in a moment had to fight + + align:start position:0% +specifically in a moment had to fight + + + align:start position:0% +specifically in a moment had to fight +with paid security guards hired by Ford + + align:start position:0% +with paid security guards hired by Ford + + + align:start position:0% +with paid security guards hired by Ford +motor to try to keep the union out so + + align:start position:0% +motor to try to keep the union out so + + + align:start position:0% +motor to try to keep the union out so +this was a a battle that went on not + + align:start position:0% +this was a a battle that went on not + + + align:start position:0% +this was a a battle that went on not +only in Autos but in steel and in many + + align:start position:0% +only in Autos but in steel and in many + + + align:start position:0% +only in Autos but in steel and in many +other Industries but once it was uh + + align:start position:0% +other Industries but once it was uh + + + align:start position:0% +other Industries but once it was uh +successful and once unions were or + + align:start position:0% +successful and once unions were or + + + align:start position:0% +successful and once unions were or +organized you + + align:start position:0% +organized you + + + align:start position:0% +organized you +got uh something called the post-war + + align:start position:0% +got uh something called the post-war + + + align:start position:0% +got uh something called the post-war +social contract this is an example of + + align:start position:0% +social contract this is an example of + + + align:start position:0% +social contract this is an example of +Walter Ruther here negotiating and + + align:start position:0% +Walter Ruther here negotiating and + + + align:start position:0% +Walter Ruther here negotiating and +signing an agreement with General Motors + + align:start position:0% +signing an agreement with General Motors + + + align:start position:0% +signing an agreement with General Motors +which was called the Treaty of Detroit + + align:start position:0% +which was called the Treaty of Detroit + + + align:start position:0% +which was called the Treaty of Detroit +where the parties agreed that they would + + align:start position:0% +where the parties agreed that they would + + + align:start position:0% +where the parties agreed that they would +increase wages by the rate of growth in + + align:start position:0% +increase wages by the rate of growth in + + + align:start position:0% +increase wages by the rate of growth in +the cost of living and the overall + + align:start position:0% +the cost of living and the overall + + + align:start position:0% +the cost of living and the overall +average rate of growth in productivity + + align:start position:0% +average rate of growth in productivity + + + align:start position:0% +average rate of growth in productivity +in the economy and it was that agreement + + align:start position:0% +in the economy and it was that agreement + + + align:start position:0% +in the economy and it was that agreement +that allowed wages then to grow and why + + align:start position:0% +that allowed wages then to grow and why + + + align:start position:0% +that allowed wages then to grow and why +we got this tandem movement of wages and + + align:start position:0% +we got this tandem movement of wages and + + + align:start position:0% +we got this tandem movement of wages and +productivity for so many years in the + + align:start position:0% +productivity for so many years in the + + + align:start position:0% +productivity for so many years in the +post-war time period but that was just + + align:start position:0% +post-war time period but that was just + + + align:start position:0% +post-war time period but that was just +the Auto industry how did we get this to + + align:start position:0% +the Auto industry how did we get this to + + + align:start position:0% +the Auto industry how did we get this to +spread across the country well to + + align:start position:0% +spread across the country well to + + + align:start position:0% +spread across the country well to +understand that we have to introduce + + align:start position:0% +understand that we have to introduce + + + align:start position:0% +understand that we have to introduce +another term something that in labor + + align:start position:0% +another term something that in labor + + + align:start position:0% +another term something that in labor +relations terminology is called pattern + + align:start position:0% +relations terminology is called pattern + + + align:start position:0% +relations terminology is called pattern +bargaining that is what would happen is + + align:start position:0% +bargaining that is what would happen is + + + align:start position:0% +bargaining that is what would happen is +you negotiated a wage agreement at let's + + align:start position:0% +you negotiated a wage agreement at let's + + + align:start position:0% +you negotiated a wage agreement at let's +say General Motors and then the Union + + align:start position:0% +say General Motors and then the Union + + + align:start position:0% +say General Motors and then the Union +would carry that same agreement to Ford + + align:start position:0% +would carry that same agreement to Ford + + + align:start position:0% +would carry that same agreement to Ford +and say if you don't want to strike then + + align:start position:0% +and say if you don't want to strike then + + + align:start position:0% +and say if you don't want to strike then +you should agree to the same wage and + + align:start position:0% +you should agree to the same wage and + + + align:start position:0% +you should agree to the same wage and +Ford would agree and the pattern would + + align:start position:0% +Ford would agree and the pattern would + + + align:start position:0% +Ford would agree and the pattern would +spread to price to Chrysler and others + + align:start position:0% +spread to price to Chrysler and others + + + align:start position:0% +spread to price to Chrysler and others +in the automobile industry while not + + align:start position:0% +in the automobile industry while not + + + align:start position:0% +in the automobile industry while not +perfect it then also spread to other + + align:start position:0% +perfect it then also spread to other + + + align:start position:0% +perfect it then also spread to other +Industries across the country at its own + + align:start position:0% +Industries across the country at its own + + + align:start position:0% +Industries across the country at its own +rate so you got oil and gas and + + align:start position:0% +rate so you got oil and gas and + + + align:start position:0% +rate so you got oil and gas and +household appliances and the steel + + align:start position:0% +household appliances and the steel + + + align:start position:0% +household appliances and the steel +industry and Aerospace rubber + + align:start position:0% +industry and Aerospace rubber + + + align:start position:0% +industry and Aerospace rubber +Electronics all of these growing + + align:start position:0% +Electronics all of these growing + + + align:start position:0% +Electronics all of these growing +Industries basically following a similar + + align:start position:0% +Industries basically following a similar + + + align:start position:0% +Industries basically following a similar +wage pattern not exactly copying but + + align:start position:0% +wage pattern not exactly copying but + + + align:start position:0% +wage pattern not exactly copying but +fitted to the economic circumstances of + + align:start position:0% +fitted to the economic circumstances of + + + align:start position:0% +fitted to the economic circumstances of +their particular setting and so this is + + align:start position:0% +their particular setting and so this is + + + align:start position:0% +their particular setting and so this is +what created that tandem movement of + + align:start position:0% +what created that tandem movement of + + + align:start position:0% +what created that tandem movement of +wages and productivity and as the + + align:start position:0% +wages and productivity and as the + + + align:start position:0% +wages and productivity and as the +economy got better so too did the + + align:start position:0% +economy got better so too did the + + + align:start position:0% +economy got better so too did the +average Workforce member and his or her + + align:start position:0% +average Workforce member and his or her + + + align:start position:0% +average Workforce member and his or her +families that's the kind of thing that + + align:start position:0% +families that's the kind of thing that + + + align:start position:0% +families that's the kind of thing that +we then lost since 1980 that's the kind + + align:start position:0% +we then lost since 1980 that's the kind + + + align:start position:0% +we then lost since 1980 that's the kind +of thing we have to find a new solution + + align:start position:0% +of thing we have to find a new solution + + + align:start position:0% +of thing we have to find a new solution +to create again but the key for us today + + align:start position:0% +to create again but the key for us today + + + align:start position:0% +to create again but the key for us today +is not to try to go back to the 1940s + + align:start position:0% +is not to try to go back to the 1940s + + + align:start position:0% +is not to try to go back to the 1940s +50s 60s or 70s but to ask how can we + + align:start position:0% +50s 60s or 70s but to ask how can we + + + align:start position:0% +50s 60s or 70s but to ask how can we +create wage Norms how can we create the + + align:start position:0% +create wage Norms how can we create the + + + align:start position:0% +create wage Norms how can we create the +bargaining power for workers so that we + + align:start position:0% +bargaining power for workers so that we + + + align:start position:0% +bargaining power for workers so that we +can once again start to get wages moving + + align:start position:0% +can once again start to get wages moving + + + align:start position:0% +can once again start to get wages moving +with the overall growth of the economy + + align:start position:0% +with the overall growth of the economy + + + align:start position:0% +with the overall growth of the economy +that's our challenge moving forward + + align:start position:0% +that's our challenge moving forward + + + align:start position:0% +that's our challenge moving forward +we'll talk about how to do that in + + align:start position:0% +we'll talk about how to do that in + + + align:start position:0% +we'll talk about how to do that in +future + + align:start position:0% +future + + + align:start position:0% +future +sessions e \ No newline at end of file diff --git a/DsSzQfejwMk.txt b/DsSzQfejwMk.txt new file mode 100644 index 0000000000000000000000000000000000000000..129d3540e1275788d4c1a6890e14ad0735cadcf6 --- /dev/null +++ b/DsSzQfejwMk.txt @@ -0,0 +1,11211 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +today we get to explore one of the use + + align:start position:0% +today we get to explore one of the use + + + align:start position:0% +today we get to explore one of the use +cases where there's actually a lot of + + align:start position:0% +cases where there's actually a lot of + + + align:start position:0% +cases where there's actually a lot of +activity going on in blockchain + + align:start position:0% +activity going on in blockchain + + + align:start position:0% +activity going on in blockchain +technology trade finance we also have I + + align:start position:0% +technology trade finance we also have I + + + align:start position:0% +technology trade finance we also have I +think at least two of the groups for + + align:start position:0% +think at least two of the groups for + + + align:start position:0% +think at least two of the groups for +final projects are doing things on trade + + align:start position:0% +final projects are doing things on trade + + + align:start position:0% +final projects are doing things on trade +finance there might be some that haven't + + align:start position:0% +finance there might be some that haven't + + + align:start position:0% +finance there might be some that haven't +disclosed that to me or after today + + align:start position:0% +disclosed that to me or after today + + + align:start position:0% +disclosed that to me or after today +might shift to it you never know and I + + align:start position:0% +might shift to it you never know and I + + + align:start position:0% +might shift to it you never know and I +think eight or ten of you actually wrote + + align:start position:0% +think eight or ten of you actually wrote + + + align:start position:0% +think eight or ten of you actually wrote +your individual pieces today so it's + + align:start position:0% +your individual pieces today so it's + + + align:start position:0% +your individual pieces today so it's +fifteen or twenty of you that have been + + align:start position:0% +fifteen or twenty of you that have been + + + align:start position:0% +fifteen or twenty of you that have been +spending a lot of time when trade + + align:start position:0% +spending a lot of time when trade + + + align:start position:0% +spending a lot of time when trade +finance and I think the reason is is + + align:start position:0% +finance and I think the reason is is + + + align:start position:0% +finance and I think the reason is is +that there's a lot of application of the + + align:start position:0% +that there's a lot of application of the + + + align:start position:0% +that there's a lot of application of the +underlying technology and that's what + + align:start position:0% +underlying technology and that's what + + + align:start position:0% +underlying technology and that's what +I'm going to try to do today is and then + + align:start position:0% +I'm going to try to do today is and then + + + align:start position:0% +I'm going to try to do today is and then +hopefully get the help from the two + + align:start position:0% +hopefully get the help from the two + + + align:start position:0% +hopefully get the help from the two +groups that have some final projects in + + align:start position:0% +groups that have some final projects in + + + align:start position:0% +groups that have some final projects in +this regard and and and so many of you + + align:start position:0% +this regard and and and so many of you + + + align:start position:0% +this regard and and and so many of you +that wrote on this today gonna go + + align:start position:0% +that wrote on this today gonna go + + + align:start position:0% +that wrote on this today gonna go +through readings and study guide what + + align:start position:0% +through readings and study guide what + + + align:start position:0% +through readings and study guide what +what is trade finance so we're gonna run + + align:start position:0% +what is trade finance so we're gonna run + + + align:start position:0% +what is trade finance so we're gonna run +through I want to give you a little + + align:start position:0% +through I want to give you a little + + + align:start position:0% +through I want to give you a little +sense of what trade finance is from my + + align:start position:0% +sense of what trade finance is from my + + + align:start position:0% +sense of what trade finance is from my +perspective and and then we're going to + + align:start position:0% +perspective and and then we're going to + + + align:start position:0% +perspective and and then we're going to +just go into the blockchain projects + + align:start position:0% +just go into the blockchain projects + + + align:start position:0% +just go into the blockchain projects +themselves so we'll skip through these + + align:start position:0% +themselves so we'll skip through these + + + align:start position:0% +themselves so we'll skip through these +because we're gonna be chatting about + + align:start position:0% +because we're gonna be chatting about + + + align:start position:0% +because we're gonna be chatting about +what attributes that trade finance + + align:start position:0% +what attributes that trade finance + + + align:start position:0% +what attributes that trade finance +really has well alpha you have a group + + align:start position:0% +really has well alpha you have a group + + + align:start position:0% +really has well alpha you have a group +what what attributes as trade fence what + + align:start position:0% +what what attributes as trade fence what + + + align:start position:0% +what what attributes as trade fence what +attracted you to this two things that I + + align:start position:0% +attracted you to this two things that I + + + align:start position:0% +attracted you to this two things that I +just heard multiple stakeholders + + align:start position:0% +just heard multiple stakeholders + + + align:start position:0% +just heard multiple stakeholders +transferring a lot of data anybody else + + align:start position:0% +transferring a lot of data anybody else + + + align:start position:0% +transferring a lot of data anybody else +what other attributes + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +stationary bangs so so not only is it + + align:start position:0% +stationary bangs so so not only is it + + + align:start position:0% +stationary bangs so so not only is it +data but it's still actually a lot of + + align:start position:0% +data but it's still actually a lot of + + + align:start position:0% +data but it's still actually a lot of +paperwork then actually often times + + align:start position:0% +paperwork then actually often times + + + align:start position:0% +paperwork then actually often times +actual physical favor work there are + + align:start position:0% +actual physical favor work there are + + + align:start position:0% +actual physical favor work there are +still companies I mean they they're not + + align:start position:0% +still companies I mean they they're not + + + align:start position:0% +still companies I mean they they're not +as persistent now than as they were + + align:start position:0% +as persistent now than as they were + + + align:start position:0% +as persistent now than as they were +years ago called document couriers + + align:start position:0% +years ago called document couriers + + + align:start position:0% +years ago called document couriers +they're literally brought the documents + + align:start position:0% +they're literally brought the documents + + + align:start position:0% +they're literally brought the documents +around the globe these weren't + + align:start position:0% +around the globe these weren't + + + align:start position:0% +around the globe these weren't +revelation some different countries hard + + align:start position:0% +revelation some different countries hard + + + align:start position:0% +revelation some different countries hard +to see it trust one central authority + + align:start position:0% +to see it trust one central authority + + + align:start position:0% +to see it trust one central authority +that it's going to give you all you need + + align:start position:0% +that it's going to give you all you need + + + align:start position:0% +that it's going to give you all you need +um so a lot of different regulatory + + align:start position:0% +um so a lot of different regulatory + + + align:start position:0% +um so a lot of different regulatory +regimes but also different countries so + + align:start position:0% +regimes but also different countries so + + + align:start position:0% +regimes but also different countries so +you have some information asymmetries + + align:start position:0% +you have some information asymmetries + + + align:start position:0% +you have some information asymmetries +and thus issues of trust across those + + align:start position:0% +and thus issues of trust across those + + + align:start position:0% +and thus issues of trust across those +jurisdictions so a lot of fraud and + + align:start position:0% +jurisdictions so a lot of fraud and + + + align:start position:0% +jurisdictions so a lot of fraud and +double spend or in trade finance it has + + align:start position:0% +double spend or in trade finance it has + + + align:start position:0% +double spend or in trade finance it has +another term actually anyway it's double + + align:start position:0% +another term actually anyway it's double + + + align:start position:0% +another term actually anyway it's double +financing but it's basically the same + + align:start position:0% +financing but it's basically the same + + + align:start position:0% +financing but it's basically the same +conceptual framework as a double spend + + align:start position:0% +conceptual framework as a double spend + + + align:start position:0% +conceptual framework as a double spend +can I fit finance one set of goods one + + align:start position:0% +can I fit finance one set of goods one + + + align:start position:0% +can I fit finance one set of goods one +one cargo being shipped across the + + align:start position:0% +one cargo being shipped across the + + + align:start position:0% +one cargo being shipped across the +Atlantic or Pacific and I fund it twice + + align:start position:0% + + + + align:start position:0% + +and so that's that's so do you think + + align:start position:0% +and so that's that's so do you think + + + align:start position:0% +and so that's that's so do you think +that small and medium-sized enterprises + + align:start position:0% +that small and medium-sized enterprises + + + align:start position:0% +that small and medium-sized enterprises +have a difficulty for the reasons you + + align:start position:0% +have a difficulty for the reasons you + + + align:start position:0% +have a difficulty for the reasons you +just said because if terrorist attacks + + align:start position:0% +just said because if terrorist attacks + + + align:start position:0% +just said because if terrorist attacks +and so forth there was there something + + align:start position:0% +and so forth there was there something + + + align:start position:0% +and so forth there was there something +more broadly that's going on maybe even + + align:start position:0% +more broadly that's going on maybe even + + + align:start position:0% +more broadly that's going on maybe even +four centuries new hand here like small + + align:start position:0% +four centuries new hand here like small + + + align:start position:0% +four centuries new hand here like small +financing that they don't have access to + + align:start position:0% + + + + align:start position:0% + +and I can't tell whether there's a hand + + align:start position:0% +and I can't tell whether there's a hand + + + align:start position:0% +and I can't tell whether there's a hand +up or you were fixing your hair + + align:start position:0% + + + + align:start position:0% + +so I'm I was gonna say it so small that + + align:start position:0% +so I'm I was gonna say it so small that + + + align:start position:0% +so I'm I was gonna say it so small that +this was often just like don't have the + + align:start position:0% +this was often just like don't have the + + + align:start position:0% +this was often just like don't have the +resources + + align:start position:0% +resources + + + align:start position:0% +resources +administrative way to deal with people + + align:start position:0% +administrative way to deal with people + + + align:start position:0% +administrative way to deal with people +paperwork so often the burden + + align:start position:0% +paperwork so often the burden + + + align:start position:0% +paperwork so often the burden +operational burden becomes also small + + align:start position:0% +operational burden becomes also small + + + align:start position:0% +operational burden becomes also small +businesses if you want to add I just + + align:start position:0% +businesses if you want to add I just + + + align:start position:0% +businesses if you want to add I just +want to put some numbers to make it + + align:start position:0% +want to put some numbers to make it + + + align:start position:0% +want to put some numbers to make it +clear to everybody I was looking at Tom + + align:start position:0% +clear to everybody I was looking at Tom + + + align:start position:0% +clear to everybody I was looking at Tom +a study for they should if I'm a bank is + + align:start position:0% +a study for they should if I'm a bank is + + + align:start position:0% +a study for they should if I'm a bank is +saying that small and medium-sized + + align:start position:0% +saying that small and medium-sized + + + align:start position:0% +saying that small and medium-sized +enterprises are the most credit + + align:start position:0% +enterprises are the most credit + + + align:start position:0% +enterprises are the most credit +constrained on 50 percent of their + + align:start position:0% +constrained on 50 percent of their + + + align:start position:0% +constrained on 50 percent of their +demands are being rejected by gangs + + align:start position:0% +demands are being rejected by gangs + + + align:start position:0% +demands are being rejected by gangs +portrait finance or as 7% to + + align:start position:0% +portrait finance or as 7% to + + + align:start position:0% +portrait finance or as 7% to +multinational corporation corporations + + align:start position:0% +multinational corporation corporations + + + align:start position:0% +multinational corporation corporations +smaller medium-sized enterprises also + + align:start position:0% +smaller medium-sized enterprises also + + + align:start position:0% +smaller medium-sized enterprises also +are smaller they're not as well-known + + align:start position:0% +are smaller they're not as well-known + + + align:start position:0% +are smaller they're not as well-known +and and your trade finance it but just + + align:start position:0% +and and your trade finance it but just + + + align:start position:0% +and and your trade finance it but just +by definition is cross-border it's + + align:start position:0% +by definition is cross-border it's + + + align:start position:0% +by definition is cross-border it's +across jurisdiction cross country how + + align:start position:0% +across jurisdiction cross country how + + + align:start position:0% +across jurisdiction cross country how +does somebody in the u.s. know a small + + align:start position:0% +does somebody in the u.s. know a small + + + align:start position:0% +does somebody in the u.s. know a small +business in Kenya or pick your countries + + align:start position:0% +business in Kenya or pick your countries + + + align:start position:0% +business in Kenya or pick your countries +China and Mexico so there's a lot of + + align:start position:0% +China and Mexico so there's a lot of + + + align:start position:0% +China and Mexico so there's a lot of +information challenges that's been the + + align:start position:0% +information challenges that's been the + + + align:start position:0% +information challenges that's been the +history of this business for a long time + + align:start position:0% + + + + align:start position:0% + +well we'll hold off on that you ongoing + + align:start position:0% +well we'll hold off on that you ongoing + + + align:start position:0% +well we'll hold off on that you ongoing +projects but we'll come back to that so + + align:start position:0% +projects but we'll come back to that so + + + align:start position:0% +projects but we'll come back to that so +we had a bunch of readings I updated + + align:start position:0% +we had a bunch of readings I updated + + + align:start position:0% +we had a bunch of readings I updated +this because it's it's ever-changing and + + align:start position:0% +this because it's it's ever-changing and + + + align:start position:0% +this because it's it's ever-changing and +I hope that if you had a chance to dig + + align:start position:0% +I hope that if you had a chance to dig + + + align:start position:0% +I hope that if you had a chance to dig +into the the bane bane review I thought + + align:start position:0% +into the the bane bane review I thought + + + align:start position:0% +into the the bane bane review I thought +as these writings go I was probably a + + align:start position:0% +as these writings go I was probably a + + + align:start position:0% +as these writings go I was probably a +little better than some of I'm sorry for + + align:start position:0% +little better than some of I'm sorry for + + + align:start position:0% +little better than some of I'm sorry for +any of you going into consultancy Tom + + align:start position:0% +any of you going into consultancy Tom + + + align:start position:0% +any of you going into consultancy Tom +you know but but but as these things go + + align:start position:0% +you know but but but as these things go + + + align:start position:0% +you know but but but as these things go +I thought it was better than some of the + + align:start position:0% +I thought it was better than some of the + + + align:start position:0% +I thought it was better than some of the +Deloitte papers and PwC papers that are + + align:start position:0% +Deloitte papers and PwC papers that are + + + align:start position:0% +Deloitte papers and PwC papers that are +still quite helpful but I thought this + + align:start position:0% +still quite helpful but I thought this + + + align:start position:0% +still quite helpful but I thought this +was a little bit more detailed so what + + align:start position:0% +was a little bit more detailed so what + + + align:start position:0% +was a little bit more detailed so what +is what is the background the economic + + align:start position:0% +is what is the background the economic + + + align:start position:0% +is what is the background the economic +background this is just from I think I + + align:start position:0% +background this is just from I think I + + + align:start position:0% +background this is just from I think I +pulled this from some World Bank figures + + align:start position:0% + + + + align:start position:0% + +worldwide exports of goods for 17 + + align:start position:0% +worldwide exports of goods for 17 + + + align:start position:0% +worldwide exports of goods for 17 +trillion dollars services are five or + + align:start position:0% +trillion dollars services are five or + + + align:start position:0% +trillion dollars services are five or +six trillion but trade finance is really + + align:start position:0% +six trillion but trade finance is really + + + align:start position:0% +six trillion but trade finance is really +around the exporting of goods more than + + align:start position:0% +around the exporting of goods more than + + + align:start position:0% +around the exporting of goods more than +services I'm not really familiar with it + + align:start position:0% +services I'm not really familiar with it + + + align:start position:0% +services I'm not really familiar with it +in the service context and manufacturers + + align:start position:0% +in the service context and manufacturers + + + align:start position:0% +in the service context and manufacturers +twelve trillion fuels agriculture you + + align:start position:0% +twelve trillion fuels agriculture you + + + align:start position:0% +twelve trillion fuels agriculture you +can see the so that's that's basically + + align:start position:0% +can see the so that's that's basically + + + align:start position:0% +can see the so that's that's basically +the the body of it and the financing + + align:start position:0% +the the body of it and the financing + + + align:start position:0% +the the body of it and the financing +international finance and I purposely + + align:start position:0% +international finance and I purposely + + + align:start position:0% +international finance and I purposely +use words this is the financing of + + align:start position:0% +use words this is the financing of + + + align:start position:0% +use words this is the financing of +international trade can come in two + + align:start position:0% +international trade can come in two + + + align:start position:0% +international trade can come in two +different ways one is if the bank is + + align:start position:0% +different ways one is if the bank is + + + align:start position:0% +different ways one is if the bank is +guaranteeing something or the bank is + + align:start position:0% +guaranteeing something or the bank is + + + align:start position:0% +guaranteeing something or the bank is +supporting it through the documents this + + align:start position:0% +supporting it through the documents this + + + align:start position:0% +supporting it through the documents this +is the traditional definition of trade + + align:start position:0% +is the traditional definition of trade + + + align:start position:0% +is the traditional definition of trade +finance is letters of credits and + + align:start position:0% +finance is letters of credits and + + + align:start position:0% +finance is letters of credits and +documentary collection anybody want to + + align:start position:0% +documentary collection anybody want to + + + align:start position:0% +documentary collection anybody want to +tell me what a letter of what the + + align:start position:0% +tell me what a letter of what the + + + align:start position:0% +tell me what a letter of what the +difference of these two things are since + + align:start position:0% +difference of these two things are since + + + align:start position:0% +difference of these two things are since +we've got a whole bunch of people laying + + align:start position:0% +we've got a whole bunch of people laying + + + align:start position:0% +we've got a whole bunch of people laying +out the terms but critically what is it + + align:start position:0% +out the terms but critically what is it + + + align:start position:0% +out the terms but critically what is it +doing removes counterparty risk it's + + align:start position:0% +doing removes counterparty risk it's + + + align:start position:0% +doing removes counterparty risk it's +guaranteeing payment but there is a + + align:start position:0% +guaranteeing payment but there is a + + + align:start position:0% +guaranteeing payment but there is a +second form that banks support this + + align:start position:0% +second form that banks support this + + + align:start position:0% +second form that banks support this +market in a very big way is document + + align:start position:0% +market in a very big way is document + + + align:start position:0% +market in a very big way is document +tere collection anybody familiar with + + align:start position:0% +tere collection anybody familiar with + + + align:start position:0% +tere collection anybody familiar with +DC's it's basically the banks are moving + + align:start position:0% +DC's it's basically the banks are moving + + + align:start position:0% +DC's it's basically the banks are moving +the paperwork this incredible paperwork + + align:start position:0% +the paperwork this incredible paperwork + + + align:start position:0% +the paperwork this incredible paperwork +around the globe and we'll get will dive + + align:start position:0% +around the globe and we'll get will dive + + + align:start position:0% +around the globe and we'll get will dive +into this a little bit and they're not + + align:start position:0% +into this a little bit and they're not + + + align:start position:0% +into this a little bit and they're not +they're not taking counterparty risk the + + align:start position:0% +they're not taking counterparty risk the + + + align:start position:0% +they're not taking counterparty risk the +banks themselves you're not guaranteeing + + align:start position:0% +banks themselves you're not guaranteeing + + + align:start position:0% +banks themselves you're not guaranteeing +the credit but they are performing + + align:start position:0% +the credit but they are performing + + + align:start position:0% +the credit but they are performing +enormous services in terms of the + + align:start position:0% +enormous services in terms of the + + + align:start position:0% +enormous services in terms of the +paperwork and and in essence its + + align:start position:0% +paperwork and and in essence its + + + align:start position:0% +paperwork and and in essence its +documents versus performance or + + align:start position:0% +documents versus performance or + + + align:start position:0% +documents versus performance or +documents versus authentication it goes + + align:start position:0% +documents versus authentication it goes + + + align:start position:0% +documents versus authentication it goes +in + + align:start position:0% +in + + + align:start position:0% +in +a bunch of different ways factoring in + + align:start position:0% +a bunch of different ways factoring in + + + align:start position:0% +a bunch of different ways factoring in +for fighting not that this is a quiz on + + align:start position:0% +for fighting not that this is a quiz on + + + align:start position:0% +for fighting not that this is a quiz on +these terms but these are different + + align:start position:0% +these terms but these are different + + + align:start position:0% +these terms but these are different +terms factoring is when you sell + + align:start position:0% +terms factoring is when you sell + + + align:start position:0% +terms factoring is when you sell +receivables short term receivables + + align:start position:0% +receivables short term receivables + + + align:start position:0% +receivables short term receivables +forfeiting is when they're longer term + + align:start position:0% +forfeiting is when they're longer term + + + align:start position:0% +forfeiting is when they're longer term +so they're kind of a little bit the same + + align:start position:0% +so they're kind of a little bit the same + + + align:start position:0% +so they're kind of a little bit the same +thing but one is short term receivables + + align:start position:0% +thing but one is short term receivables + + + align:start position:0% +thing but one is short term receivables +short term letters of credit 1 or + + align:start position:0% +short term letters of credit 1 or + + + align:start position:0% +short term letters of credit 1 or +longer-term you can actually take import + + align:start position:0% +longer-term you can actually take import + + + align:start position:0% +longer-term you can actually take import +and export loans out which which are + + align:start position:0% +and export loans out which which are + + + align:start position:0% +and export loans out which which are +longer-term and they're about a whole + + align:start position:0% +longer-term and they're about a whole + + + align:start position:0% +longer-term and they're about a whole +inventory and a whole supply chain you + + align:start position:0% +inventory and a whole supply chain you + + + align:start position:0% +inventory and a whole supply chain you +can get financing beforehand supplier + + align:start position:0% +can get financing beforehand supplier + + + align:start position:0% +can get financing beforehand supplier +credit and a new form of our court + + align:start position:0% +credit and a new form of our court + + + align:start position:0% +credit and a new form of our court +supply chain financing where you're + + align:start position:0% +supply chain financing where you're + + + align:start position:0% +supply chain financing where you're +really funding the whole supply chain + + align:start position:0% +really funding the whole supply chain + + + align:start position:0% +really funding the whole supply chain +but we're going to focus primarily on + + align:start position:0% +but we're going to focus primarily on + + + align:start position:0% +but we're going to focus primarily on +the first two and most of the blockchain + + align:start position:0% +the first two and most of the blockchain + + + align:start position:0% +the first two and most of the blockchain +projects in this space are focusing on + + align:start position:0% +projects in this space are focusing on + + + align:start position:0% +projects in this space are focusing on +the first two but international trade + + align:start position:0% +the first two but international trade + + + align:start position:0% +the first two but international trade +also has trade credit what's open + + align:start position:0% +also has trade credit what's open + + + align:start position:0% +also has trade credit what's open +account what does that mean in any + + align:start position:0% +account what does that mean in any + + + align:start position:0% +account what does that mean in any +business we're here it's slowing + + align:start position:0% +business we're here it's slowing + + + align:start position:0% +business we're here it's slowing +somebody's Elena call open account is + + align:start position:0% +somebody's Elena call open account is + + + align:start position:0% +somebody's Elena call open account is +what most businesses do if you just say + + align:start position:0% +what most businesses do if you just say + + + align:start position:0% +what most businesses do if you just say +I'm shipping something sent an invoice + + align:start position:0% +I'm shipping something sent an invoice + + + align:start position:0% +I'm shipping something sent an invoice +and it's the terms might be 2 and 30 you + + align:start position:0% +and it's the terms might be 2 and 30 you + + + align:start position:0% +and it's the terms might be 2 and 30 you +get a 2 percent discount if you pay + + align:start position:0% +get a 2 percent discount if you pay + + + align:start position:0% +get a 2 percent discount if you pay +prompt but 30 days just open account in + + align:start position:0% +prompt but 30 days just open account in + + + align:start position:0% +prompt but 30 days just open account in +domestic business that's how most + + align:start position:0% +domestic business that's how most + + + align:start position:0% +domestic business that's how most +services are provided and goods are + + align:start position:0% +services are provided and goods are + + + align:start position:0% +services are provided and goods are +shipped is open account it's the + + align:start position:0% +shipped is open account it's the + + + align:start position:0% +shipped is open account it's the +International export business that you + + align:start position:0% +International export business that you + + + align:start position:0% +International export business that you +find it different than cash in advance + + align:start position:0% +find it different than cash in advance + + + align:start position:0% +find it different than cash in advance +of course is what it sounds like and + + align:start position:0% +of course is what it sounds like and + + + align:start position:0% +of course is what it sounds like and +consignment is all the other way an + + align:start position:0% +consignment is all the other way an + + + align:start position:0% +consignment is all the other way an +exporter would actually ship you'd put + + align:start position:0% +exporter would actually ship you'd put + + + align:start position:0% +exporter would actually ship you'd put +it on your shelves you wouldn't have to + + align:start position:0% +it on your shelves you wouldn't have to + + + align:start position:0% +it on your shelves you wouldn't have to +pay and the exporter continues to have + + align:start position:0% +pay and the exporter continues to have + + + align:start position:0% +pay and the exporter continues to have +the risk of the sale not used a lot in + + align:start position:0% +the risk of the sale not used a lot in + + + align:start position:0% +the risk of the sale not used a lot in +international trade + + align:start position:0% + + + + align:start position:0% + +you can also get public guarantees or + + align:start position:0% +you can also get public guarantees or + + + align:start position:0% +you can also get public guarantees or +insurance so that's the whole world of + + align:start position:0% +insurance so that's the whole world of + + + align:start position:0% +insurance so that's the whole world of +these seventeen trillion dollars of + + align:start position:0% +these seventeen trillion dollars of + + + align:start position:0% +these seventeen trillion dollars of +trade only about five or six trillion is + + align:start position:0% +trade only about five or six trillion is + + + align:start position:0% +trade only about five or six trillion is +thought to be actually using trade + + align:start position:0% +thought to be actually using trade + + + align:start position:0% +thought to be actually using trade +credit letters of credit and documentary + + align:start position:0% +credit letters of credit and documentary + + + align:start position:0% +credit letters of credit and documentary +commitments these two main things + + align:start position:0% + + + + align:start position:0% + +so this ranges it this gives you a + + align:start position:0% +so this ranges it this gives you a + + + align:start position:0% +so this ranges it this gives you a +little bit of a flavor and and this you + + align:start position:0% +little bit of a flavor and and this you + + + align:start position:0% +little bit of a flavor and and this you +can think of is what's the most secure + + align:start position:0% +can think of is what's the most secure + + + align:start position:0% +can think of is what's the most secure +for the exporter is over here the + + align:start position:0% +for the exporter is over here the + + + align:start position:0% +for the exporter is over here the +exporter is going to have the most + + align:start position:0% +exporter is going to have the most + + + align:start position:0% +exporter is going to have the most +security if they get cash in advance but + + align:start position:0% +security if they get cash in advance but + + + align:start position:0% +security if they get cash in advance but +does an importer like that not really an + + align:start position:0% +does an importer like that not really an + + + align:start position:0% +does an importer like that not really an +importer really would rather have + + align:start position:0% +importer really would rather have + + + align:start position:0% +importer really would rather have +consignment having risk all the way on + + align:start position:0% +consignment having risk all the way on + + + align:start position:0% +consignment having risk all the way on +the other side + + align:start position:0% +the other side + + + align:start position:0% +the other side +consignment would say the exporter takes + + align:start position:0% +consignment would say the exporter takes + + + align:start position:0% +consignment would say the exporter takes +all the risk so it's all about + + align:start position:0% +all the risk so it's all about + + + align:start position:0% +all the risk so it's all about +commercial terms but you can think of it + + align:start position:0% +commercial terms but you can think of it + + + align:start position:0% +commercial terms but you can think of it +as as the other side of this is the the + + align:start position:0% +as as the other side of this is the the + + + align:start position:0% +as as the other side of this is the the +the least attractive for the importer is + + align:start position:0% +the least attractive for the importer is + + + align:start position:0% +the least attractive for the importer is +paying cash in advance the most + + align:start position:0% +paying cash in advance the most + + + align:start position:0% +paying cash in advance the most +attractive to the exporter is cash in + + align:start position:0% +attractive to the exporter is cash in + + + align:start position:0% +attractive to the exporter is cash in +advance and every one of these happens + + align:start position:0% +advance and every one of these happens + + + align:start position:0% +advance and every one of these happens +somewhere in a seventeen trillion dollar + + align:start position:0% +somewhere in a seventeen trillion dollar + + + align:start position:0% +somewhere in a seventeen trillion dollar +mark at seventeen trillion dollars of + + align:start position:0% +mark at seventeen trillion dollars of + + + align:start position:0% +mark at seventeen trillion dollars of +exports all of this is is open for + + align:start position:0% +exports all of this is is open for + + + align:start position:0% +exports all of this is is open for +negotiation but think of the exporter + + align:start position:0% +negotiation but think of the exporter + + + align:start position:0% +negotiation but think of the exporter +likes this curve and the importer likes + + align:start position:0% +likes this curve and the importer likes + + + align:start position:0% +likes this curve and the importer likes +this and as I will show in a second most + + align:start position:0% +this and as I will show in a second most + + + align:start position:0% +this and as I will show in a second most +of the market is in the middle so now + + align:start position:0% +of the market is in the middle so now + + + align:start position:0% +of the market is in the middle so now +trade finance exporters importers + + align:start position:0% +trade finance exporters importers + + + align:start position:0% +trade finance exporters importers +advising banks and issuing banks and + + align:start position:0% +advising banks and issuing banks and + + + align:start position:0% +advising banks and issuing banks and +what you're going to quickly sort of + + align:start position:0% +what you're going to quickly sort of + + + align:start position:0% +what you're going to quickly sort of +sense is there's a lot of room maybe for + + align:start position:0% +sense is there's a lot of room maybe for + + + align:start position:0% +sense is there's a lot of room maybe for +blockchain technology because there's a + + align:start position:0% +blockchain technology because there's a + + + align:start position:0% +blockchain technology because there's a +lot of moving ports by the way normally + + align:start position:0% +lot of moving ports by the way normally + + + align:start position:0% +lot of moving ports by the way normally +if you work at on a Wall Street or at a + + align:start position:0% +if you work at on a Wall Street or at a + + + align:start position:0% +if you work at on a Wall Street or at a +commercial bank you might never touch + + align:start position:0% +commercial bank you might never touch + + + align:start position:0% +commercial bank you might never touch +trade finance it's just like a depart + + align:start position:0% +trade finance it's just like a depart + + + align:start position:0% +trade finance it's just like a depart +that if you're on a trading floor you're + + align:start position:0% +that if you're on a trading floor you're + + + align:start position:0% +that if you're on a trading floor you're +not really thinking about a lot that + + align:start position:0% +not really thinking about a lot that + + + align:start position:0% +not really thinking about a lot that +who's worked on a trading floor here did + + align:start position:0% +who's worked on a trading floor here did + + + align:start position:0% +who's worked on a trading floor here did +you ever think about trade finance no + + align:start position:0% +you ever think about trade finance no + + + align:start position:0% +you ever think about trade finance no +but it's a big market it's a very big + + align:start position:0% +but it's a big market it's a very big + + + align:start position:0% +but it's a big market it's a very big +market but the basically the importer + + align:start position:0% +market but the basically the importer + + + align:start position:0% +market but the basically the importer +the exporter and importer sign a + + align:start position:0% +the exporter and importer sign a + + + align:start position:0% +the exporter and importer sign a +contract that's for the sale of goods it + + align:start position:0% +contract that's for the sale of goods it + + + align:start position:0% +contract that's for the sale of goods it +could be oil could be agriculture + + align:start position:0% +could be oil could be agriculture + + + align:start position:0% +could be oil could be agriculture +product or manufacturers importer then + + align:start position:0% +product or manufacturers importer then + + + align:start position:0% +product or manufacturers importer then +arranges with an issuing bank a letter + + align:start position:0% +arranges with an issuing bank a letter + + + align:start position:0% +arranges with an issuing bank a letter +of credit the letter of credit is sent + + align:start position:0% +of credit the letter of credit is sent + + + align:start position:0% +of credit the letter of credit is sent +to the exporters back sometimes the + + align:start position:0% +to the exporters back sometimes the + + + align:start position:0% +to the exporters back sometimes the +exporters bank puts a second guarantee + + align:start position:0% +exporters bank puts a second guarantee + + + align:start position:0% +exporters bank puts a second guarantee +on it the exporters bank might be + + align:start position:0% +on it the exporters bank might be + + + align:start position:0% +on it the exporters bank might be +actually guaranteeing the importers bank + + align:start position:0% +actually guaranteeing the importers bank + + + align:start position:0% +actually guaranteeing the importers bank +it's performance so there's hundreds of + + align:start position:0% +it's performance so there's hundreds of + + + align:start position:0% +it's performance so there's hundreds of +different arrangements but the classic + + align:start position:0% +different arrangements but the classic + + + align:start position:0% +different arrangements but the classic +thing is is that the importer gets a + + align:start position:0% +thing is is that the importer gets a + + + align:start position:0% +thing is is that the importer gets a +letter of credit to say look you don't + + align:start position:0% +letter of credit to say look you don't + + + align:start position:0% +letter of credit to say look you don't +know me but you can take the risk then I + + align:start position:0% +know me but you can take the risk then I + + + align:start position:0% +know me but you can take the risk then I +get this letter of credit you exporter + + align:start position:0% +get this letter of credit you exporter + + + align:start position:0% +get this letter of credit you exporter +will get your money based upon some + + align:start position:0% +will get your money based upon some + + + align:start position:0% +will get your money based upon some +documents when you put some documents + + align:start position:0% +documents when you put some documents + + + align:start position:0% +documents when you put some documents +together and send them to me that you've + + align:start position:0% +together and send them to me that you've + + + align:start position:0% +together and send them to me that you've +actually put your oil or agricultural + + align:start position:0% +actually put your oil or agricultural + + + align:start position:0% +actually put your oil or agricultural +products on a ship so shipping is a big + + align:start position:0% +products on a ship so shipping is a big + + + align:start position:0% +products on a ship so shipping is a big +part of it the second piece of this is + + align:start position:0% +part of it the second piece of this is + + + align:start position:0% +part of it the second piece of this is +how do the documents actually go the + + align:start position:0% +how do the documents actually go the + + + align:start position:0% +how do the documents actually go the +exporter then ships something + + align:start position:0% +exporter then ships something + + + align:start position:0% +exporter then ships something +the shipment usually leads to some + + align:start position:0% +the shipment usually leads to some + + + align:start position:0% +the shipment usually leads to some +documents and at the time of the + + align:start position:0% +documents and at the time of the + + + align:start position:0% +documents and at the time of the +shipping you see number six in this + + align:start position:0% +shipping you see number six in this + + + align:start position:0% +shipping you see number six in this +little box over here is the exporter + + align:start position:0% +little box over here is the exporter + + + align:start position:0% +little box over here is the exporter +when they ship something also sends some + + align:start position:0% +when they ship something also sends some + + + align:start position:0% +when they ship something also sends some +documents to their bank their bank sends + + align:start position:0% +documents to their bank their bank sends + + + align:start position:0% +documents to their bank their bank sends +it overseas to the bank in Kenya let's + + align:start position:0% +it overseas to the bank in Kenya let's + + + align:start position:0% +it overseas to the bank in Kenya let's +say even though that's doesn't have any + + align:start position:0% +say even though that's doesn't have any + + + align:start position:0% +say even though that's doesn't have any +ports if the OPA you have ports right + + align:start position:0% +ports if the OPA you have ports right + + + align:start position:0% +ports if the OPA you have ports right +yeah Pena has ports sorry you're + + align:start position:0% +yeah Pena has ports sorry you're + + + align:start position:0% +yeah Pena has ports sorry you're +landlocked + + align:start position:0% +landlocked + + + align:start position:0% +landlocked +all right sorry so I've got it right so + + align:start position:0% +all right sorry so I've got it right so + + + align:start position:0% +all right sorry so I've got it right so +Kenya I got it wrong but Kenya's got + + align:start position:0% +Kenya I got it wrong but Kenya's got + + + align:start position:0% +Kenya I got it wrong but Kenya's got +ports but the exporter at the same time + + align:start position:0% +ports but the exporter at the same time + + + align:start position:0% +ports but the exporter at the same time +their shipping will also send the + + align:start position:0% +their shipping will also send the + + + align:start position:0% +their shipping will also send the +documents but send the documents to + + align:start position:0% +documents but send the documents to + + + align:start position:0% +documents but send the documents to +their bank there + + align:start position:0% +their bank there + + + align:start position:0% +their bank there +sends it to the foreign bank the foreign + + align:start position:0% +sends it to the foreign bank the foreign + + + align:start position:0% +sends it to the foreign bank the foreign +bank says AHA that triggers the + + align:start position:0% +bank says AHA that triggers the + + + align:start position:0% +bank says AHA that triggers the +condition in the letter of credit + + align:start position:0% +condition in the letter of credit + + + align:start position:0% +condition in the letter of credit +payment will be made and payment can be + + align:start position:0% +payment will be made and payment can be + + + align:start position:0% +payment will be made and payment can be +made when you put the goods on the ship + + align:start position:0% +made when you put the goods on the ship + + + align:start position:0% +made when you put the goods on the ship +payment may be is made when the goods + + align:start position:0% +payment may be is made when the goods + + + align:start position:0% +payment may be is made when the goods +get to the foreign country all these + + align:start position:0% +get to the foreign country all these + + + align:start position:0% +get to the foreign country all these +arrangements can be different so this + + align:start position:0% +arrangements can be different so this + + + align:start position:0% +arrangements can be different so this +gives you a sense of the change letter + + align:start position:0% +gives you a sense of the change letter + + + align:start position:0% +gives you a sense of the change letter +credits were estimated in 1970 to be + + align:start position:0% +credits were estimated in 1970 to be + + + align:start position:0% +credits were estimated in 1970 to be +about half of all of trade now there are + + align:start position:0% +about half of all of trade now there are + + + align:start position:0% +about half of all of trade now there are +about 15% World Economic Forum Baine + + align:start position:0% +about 15% World Economic Forum Baine + + + align:start position:0% +about 15% World Economic Forum Baine +papers that you all had the pleasure of + + align:start position:0% +papers that you all had the pleasure of + + + align:start position:0% +papers that you all had the pleasure of +either reading or skimming or you'll + + align:start position:0% +either reading or skimming or you'll + + + align:start position:0% +either reading or skimming or you'll +read it tomorrow but but letters and + + align:start position:0% +read it tomorrow but but letters and + + + align:start position:0% +read it tomorrow but but letters and +credits a big piece of the market + + align:start position:0% +credits a big piece of the market + + + align:start position:0% +credits a big piece of the market +primary open account has widened as part + + align:start position:0% +primary open account has widened as part + + + align:start position:0% +primary open account has widened as part +of the market I think in part because + + align:start position:0% +of the market I think in part because + + + align:start position:0% +of the market I think in part because +international trade is probably more + + align:start position:0% +international trade is probably more + + + align:start position:0% +international trade is probably more +dominated by large companies now than in + + align:start position:0% +dominated by large companies now than in + + + align:start position:0% +dominated by large companies now than in +the past and in the 1970s even the large + + align:start position:0% +the past and in the 1970s even the large + + + align:start position:0% +the past and in the 1970s even the large +companies didn't know if they could + + align:start position:0% +companies didn't know if they could + + + align:start position:0% +companies didn't know if they could +trust each other the larger enterprises + + align:start position:0% +trust each other the larger enterprises + + + align:start position:0% +trust each other the larger enterprises +larger multinationals really would + + align:start position:0% +larger multinationals really would + + + align:start position:0% +larger multinationals really would +prefer just a trade on open account and + + align:start position:0% +prefer just a trade on open account and + + + align:start position:0% +prefer just a trade on open account and +extend each other's credit rather than + + align:start position:0% +extend each other's credit rather than + + + align:start position:0% +extend each other's credit rather than +using the banking system to guarantee + + align:start position:0% +using the banking system to guarantee + + + align:start position:0% +using the banking system to guarantee +their credit but trade finance is still + + align:start position:0% +their credit but trade finance is still + + + align:start position:0% +their credit but trade finance is still +a good call it 15 to 20 percent which + + align:start position:0% +a good call it 15 to 20 percent which + + + align:start position:0% +a good call it 15 to 20 percent which +would still be rather significant + + align:start position:0% +would still be rather significant + + + align:start position:0% +would still be rather significant +numbers so that's a little bit on the + + align:start position:0% +numbers so that's a little bit on the + + + align:start position:0% +numbers so that's a little bit on the +sort of questions about trade finance + + align:start position:0% +sort of questions about trade finance + + + align:start position:0% +sort of questions about trade finance +how it fits in before we start talking + + align:start position:0% +how it fits in before we start talking + + + align:start position:0% +how it fits in before we start talking +about blockchain projects I think I had + + align:start position:0% +about blockchain projects I think I had + + + align:start position:0% +about blockchain projects I think I had +one other thing was here are all the + + align:start position:0% +one other thing was here are all the + + + align:start position:0% +one other thing was here are all the +parties that can be involved and and + + align:start position:0% +parties that can be involved and and + + + align:start position:0% +parties that can be involved and and +just as sort of confuses aw here's a + + align:start position:0% +just as sort of confuses aw here's a + + + align:start position:0% +just as sort of confuses aw here's a +list of some of the documents and that's + + align:start position:0% +list of some of the documents and that's + + + align:start position:0% +list of some of the documents and that's +not even a complete list I went to a + + align:start position:0% +not even a complete list I went to a + + + align:start position:0% +not even a complete list I went to a +legal website to find out what all the + + align:start position:0% +legal website to find out what all the + + + align:start position:0% +legal website to find out what all the +different documents you might have + + align:start position:0% +different documents you might have + + + align:start position:0% +different documents you might have +anybody know what a bill of lading is so + + align:start position:0% +anybody know what a bill of lading is so + + + align:start position:0% +anybody know what a bill of lading is so +it's like a warehouse receipt remember + + align:start position:0% +it's like a warehouse receipt remember + + + align:start position:0% +it's like a warehouse receipt remember +we talked about some of the origins of + + align:start position:0% +we talked about some of the origins of + + + align:start position:0% +we talked about some of the origins of +money we're around warehouse receipts + + align:start position:0% +money we're around warehouse receipts + + + align:start position:0% +money we're around warehouse receipts +because I might put my corn or wheat or + + align:start position:0% +because I might put my corn or wheat or + + + align:start position:0% +because I might put my corn or wheat or +gold or bronze in a warehouse a bill of + + align:start position:0% +gold or bronze in a warehouse a bill of + + + align:start position:0% +gold or bronze in a warehouse a bill of +lading originally though the definition + + align:start position:0% +lading originally though the definition + + + align:start position:0% +lading originally though the definition +is moved on over the centuries the + + align:start position:0% +is moved on over the centuries the + + + align:start position:0% +is moved on over the centuries the +original definition it was it was like a + + align:start position:0% +original definition it was it was like a + + + align:start position:0% +original definition it was it was like a +warehouse receipt on a ship that you + + align:start position:0% +warehouse receipt on a ship that you + + + align:start position:0% +warehouse receipt on a ship that you +took your proto's or goods and placed it + + align:start position:0% +took your proto's or goods and placed it + + + align:start position:0% +took your proto's or goods and placed it +on a ship and you had a bill of lading + + align:start position:0% +on a ship and you had a bill of lading + + + align:start position:0% +on a ship and you had a bill of lading +because it was on the ship and you could + + align:start position:0% +because it was on the ship and you could + + + align:start position:0% +because it was on the ship and you could +actually just like those original forms + + align:start position:0% +actually just like those original forms + + + align:start position:0% +actually just like those original forms +of money warehouse receipts you could + + align:start position:0% +of money warehouse receipts you could + + + align:start position:0% +of money warehouse receipts you could +sell a bill of lading or discounted and + + align:start position:0% +sell a bill of lading or discounted and + + + align:start position:0% +sell a bill of lading or discounted and +get money for it so bills of lading have + + align:start position:0% +get money for it so bills of lading have + + + align:start position:0% +get money for it so bills of lading have +centuries old maybe thousands of years + + align:start position:0% +centuries old maybe thousands of years + + + align:start position:0% +centuries old maybe thousands of years +of history similar to warehouse receipts + + align:start position:0% +of history similar to warehouse receipts + + + align:start position:0% +of history similar to warehouse receipts +in it in essence you might think of a + + align:start position:0% +in it in essence you might think of a + + + align:start position:0% +in it in essence you might think of a +bill of lading a little bit as a form of + + align:start position:0% +bill of lading a little bit as a form of + + + align:start position:0% +bill of lading a little bit as a form of +money but what what did I list just for + + align:start position:0% +money but what what did I list just for + + + align:start position:0% +money but what what did I list just for +fun 50 different documents aleem how + + align:start position:0% +fun 50 different documents aleem how + + + align:start position:0% +fun 50 different documents aleem how +easy is it to fake one of these bills + + align:start position:0% +easy is it to fake one of these bills + + + align:start position:0% +easy is it to fake one of these bills +and claim someone else's good very good + + align:start position:0% +and claim someone else's good very good + + + align:start position:0% +and claim someone else's good very good +question so is it point earlier and + + align:start position:0% +question so is it point earlier and + + + align:start position:0% +question so is it point earlier and +again this goes back centuries that + + align:start position:0% +again this goes back centuries that + + + align:start position:0% +again this goes back centuries that +there's been a lot of fraud around + + align:start position:0% +there's been a lot of fraud around + + + align:start position:0% +there's been a lot of fraud around +faking a bill of lading or a bill of + + align:start position:0% +faking a bill of lading or a bill of + + + align:start position:0% +faking a bill of lading or a bill of +exchange a warehouse receipt in another + + align:start position:0% +exchange a warehouse receipt in another + + + align:start position:0% +exchange a warehouse receipt in another +effort so what you have is you have a + + align:start position:0% +effort so what you have is you have a + + + align:start position:0% +effort so what you have is you have a +lot of forms of notary well before + + align:start position:0% +lot of forms of notary well before + + + align:start position:0% +lot of forms of notary well before +cryptography a lot of forms of notary + + align:start position:0% +cryptography a lot of forms of notary + + + align:start position:0% +cryptography a lot of forms of notary +where various transport agents and + + align:start position:0% +where various transport agents and + + + align:start position:0% +where various transport agents and +shippers had to really have seals and + + align:start position:0% +shippers had to really have seals and + + + align:start position:0% +shippers had to really have seals and +forms of ways to say this was a + + align:start position:0% +forms of ways to say this was a + + + align:start position:0% +forms of ways to say this was a +committed Leonardo + + align:start position:0% + + + + align:start position:0% + +so those documents are easy to falsify + + align:start position:0% +so those documents are easy to falsify + + + align:start position:0% +so those documents are easy to falsify +that's why the system became so + + align:start position:0% +that's why the system became so + + + align:start position:0% +that's why the system became so +burdensome in terms of paperwork because + + align:start position:0% +burdensome in terms of paperwork because + + + align:start position:0% +burdensome in terms of paperwork because +they started to build a lot of steps to + + align:start position:0% +they started to build a lot of steps to + + + align:start position:0% +they started to build a lot of steps to +guarantee that you know you can track + + align:start position:0% +guarantee that you know you can track + + + align:start position:0% +guarantee that you know you can track +all those things and make sure you can + + align:start position:0% +all those things and make sure you can + + + align:start position:0% +all those things and make sure you can +reduce risk it's and it's why many + + align:start position:0% +reduce risk it's and it's why many + + + align:start position:0% +reduce risk it's and it's why many +people think this is actually one of the + + align:start position:0% +people think this is actually one of the + + + align:start position:0% +people think this is actually one of the +better use cases better ecosystems for a + + align:start position:0% +better use cases better ecosystems for a + + + align:start position:0% +better use cases better ecosystems for a +revised technology similar to blockchain + + align:start position:0% +revised technology similar to blockchain + + + align:start position:0% +revised technology similar to blockchain +or actually blockchain technology itself + + align:start position:0% +or actually blockchain technology itself + + + align:start position:0% +or actually blockchain technology itself +a lot of multiple parties and though I + + align:start position:0% +a lot of multiple parties and though I + + + align:start position:0% +a lot of multiple parties and though I +only listed seven you can have multiple + + align:start position:0% +only listed seven you can have multiple + + + align:start position:0% +only listed seven you can have multiple +banks you're gonna have the importers + + align:start position:0% +banks you're gonna have the importers + + + align:start position:0% +banks you're gonna have the importers +back the exporters back between them you + + align:start position:0% +back the exporters back between them you + + + align:start position:0% +back the exporters back between them you +can have a correspondent Bank right so + + align:start position:0% +can have a correspondent Bank right so + + + align:start position:0% +can have a correspondent Bank right so +at least three banks in the chain or + + align:start position:0% +at least three banks in the chain or + + + align:start position:0% +at least three banks in the chain or +sometimes even more freight forwarders + + align:start position:0% +sometimes even more freight forwarders + + + align:start position:0% +sometimes even more freight forwarders +shippers customs agents in both + + align:start position:0% +shippers customs agents in both + + + align:start position:0% +shippers customs agents in both +countries + + align:start position:0% +countries + + + align:start position:0% +countries +good question James so lots of parties + + align:start position:0% +good question James so lots of parties + + + align:start position:0% +good question James so lots of parties +lots of documents high chance of fraud + + align:start position:0% +lots of documents high chance of fraud + + + align:start position:0% +lots of documents high chance of fraud +and guaranteeing validation and + + align:start position:0% +and guaranteeing validation and + + + align:start position:0% +and guaranteeing validation and +verification is a big piece of this + + align:start position:0% +verification is a big piece of this + + + align:start position:0% +verification is a big piece of this +marketplace so then the question is can + + align:start position:0% +marketplace so then the question is can + + + align:start position:0% +marketplace so then the question is can +you put somebody in the middle see that + + align:start position:0% +you put somebody in the middle see that + + + align:start position:0% +you put somebody in the middle see that +little blockchain in the middle kind of + + align:start position:0% +little blockchain in the middle kind of + + + align:start position:0% +little blockchain in the middle kind of +cute + + align:start position:0% +cute + + + align:start position:0% +cute +all right and I got a laugh a little + + align:start position:0% +all right and I got a laugh a little + + + align:start position:0% +all right and I got a laugh a little +with me you know that's the question so + + align:start position:0% +with me you know that's the question so + + + align:start position:0% +with me you know that's the question so +multiple parties involved verification + + align:start position:0% +multiple parties involved verification + + + align:start position:0% +multiple parties involved verification +is critical to all the workflows in the + + align:start position:0% +is critical to all the workflows in the + + + align:start position:0% +is critical to all the workflows in the +economics and it relies on significant + + align:start position:0% +economics and it relies on significant + + + align:start position:0% +economics and it relies on significant +document flows that's the basic you know + + align:start position:0% +document flows that's the basic you know + + + align:start position:0% +document flows that's the basic you know +and it's what today's lecture is really + + align:start position:0% +and it's what today's lecture is really + + + align:start position:0% +and it's what today's lecture is really +to say well whether you're looking at + + align:start position:0% +to say well whether you're looking at + + + align:start position:0% +to say well whether you're looking at +healthcare records whether you're + + align:start position:0% +healthcare records whether you're + + + align:start position:0% +healthcare records whether you're +thinking about commercial real estate + + align:start position:0% +thinking about commercial real estate + + + align:start position:0% +thinking about commercial real estate +you're thinking about Internet of Things + + align:start position:0% +you're thinking about Internet of Things + + + align:start position:0% +you're thinking about Internet of Things +remind yourself of trade finance because + + align:start position:0% +remind yourself of trade finance because + + + align:start position:0% +remind yourself of trade finance because +this is probably one of the best use + + align:start position:0% +this is probably one of the best use + + + align:start position:0% +this is probably one of the best use +cases at least for permission + + align:start position:0% +cases at least for permission + + + align:start position:0% +cases at least for permission +blockchains you can debate whether it + + align:start position:0% +blockchains you can debate whether it + + + align:start position:0% +blockchains you can debate whether it +could be done on a traditional database + + align:start position:0% +could be done on a traditional database + + + align:start position:0% +could be done on a traditional database +but multiple parties + + align:start position:0% +but multiple parties + + + align:start position:0% +but multiple parties +lots of validation of verification is + + align:start position:0% +lots of validation of verification is + + + align:start position:0% +lots of validation of verification is +important an awful lot of different + + align:start position:0% +important an awful lot of different + + + align:start position:0% +important an awful lot of different +documents and there's property rights + + align:start position:0% +documents and there's property rights + + + align:start position:0% +documents and there's property rights +involved critically there's key property + + align:start position:0% +involved critically there's key property + + + align:start position:0% +involved critically there's key property +rights because when you're shipping oil + + align:start position:0% +rights because when you're shipping oil + + + align:start position:0% +rights because when you're shipping oil +in the high seeds or shipping any bits + + align:start position:0% +in the high seeds or shipping any bits + + + align:start position:0% +in the high seeds or shipping any bits +of that 17 trillion on the high seeds + + align:start position:0% +of that 17 trillion on the high seeds + + + align:start position:0% +of that 17 trillion on the high seeds +people want to finance against it how do + + align:start position:0% +people want to finance against it how do + + + align:start position:0% +people want to finance against it how do +you need ease from sending a good from + + align:start position:0% +you need ease from sending a good from + + + align:start position:0% +you need ease from sending a good from +San Francisco to Boston why is it a mark + + align:start position:0% +San Francisco to Boston why is it a mark + + + align:start position:0% +San Francisco to Boston why is it a mark +that we need all these documents and we + + align:start position:0% +that we need all these documents and we + + + align:start position:0% +that we need all these documents and we +need to put the documents on the + + align:start position:0% +need to put the documents on the + + + align:start position:0% +need to put the documents on the +blockchain or can we just get rid of the + + align:start position:0% +blockchain or can we just get rid of the + + + align:start position:0% +blockchain or can we just get rid of the +dog why don't we see the same thing in + + align:start position:0% +dog why don't we see the same thing in + + + align:start position:0% +dog why don't we see the same thing in +in try us a very good question though + + align:start position:0% +in try us a very good question though + + + align:start position:0% +in try us a very good question though +the word trade finance has come to mean + + align:start position:0% +the word trade finance has come to mean + + + align:start position:0% +the word trade finance has come to mean +for many decades maybe hundreds of years + + align:start position:0% +for many decades maybe hundreds of years + + + align:start position:0% +for many decades maybe hundreds of years +international trade the same can be true + + align:start position:0% +international trade the same can be true + + + align:start position:0% +international trade the same can be true +for domestic trade particularly as + + align:start position:0% +for domestic trade particularly as + + + align:start position:0% +for domestic trade particularly as +you're going as you said San Francisco + + align:start position:0% +you're going as you said San Francisco + + + align:start position:0% +you're going as you said San Francisco +to Boston you could use a letter of + + align:start position:0% +to Boston you could use a letter of + + + align:start position:0% +to Boston you could use a letter of +credit between a major domestic + + align:start position:0% +credit between a major domestic + + + align:start position:0% +credit between a major domestic +manufacturer and a small business in + + align:start position:0% +manufacturer and a small business in + + + align:start position:0% +manufacturer and a small business in +Boston so and they might say I don't + + align:start position:0% +Boston so and they might say I don't + + + align:start position:0% +Boston so and they might say I don't +want to take sorry Joe quit you know but + + align:start position:0% +want to take sorry Joe quit you know but + + + align:start position:0% +want to take sorry Joe quit you know but +you're you're you're that small + + align:start position:0% +you're you're you're that small + + + align:start position:0% +you're you're you're that small +manufacturer that small entity in Boston + + align:start position:0% +manufacturer that small entity in Boston + + + align:start position:0% +manufacturer that small entity in Boston +and Tom's not willing to take your + + align:start position:0% +and Tom's not willing to take your + + + align:start position:0% +and Tom's not willing to take your +credit risk you could still want to have + + align:start position:0% +credit risk you could still want to have + + + align:start position:0% +credit risk you could still want to have +a letter credit it wouldn't be caught + + align:start position:0% +a letter credit it wouldn't be caught + + + align:start position:0% +a letter credit it wouldn't be caught +technically a bill of lading if it's not + + align:start position:0% +technically a bill of lading if it's not + + + align:start position:0% +technically a bill of lading if it's not +on a ship even though that term + + align:start position:0% +on a ship even though that term + + + align:start position:0% +on a ship even though that term +sometimes is used but everything back + + align:start position:0% +sometimes is used but everything back + + + align:start position:0% +sometimes is used but everything back +here could happen in domestic trade but + + align:start position:0% +here could happen in domestic trade but + + + align:start position:0% +here could happen in domestic trade but +usually doesn't most of domestic trade + + align:start position:0% +usually doesn't most of domestic trade + + + align:start position:0% +usually doesn't most of domestic trade +has done on open account but some of its + + align:start position:0% +has done on open account but some of its + + + align:start position:0% +has done on open account but some of its +Donald letter of credit and especially + + align:start position:0% +Donald letter of credit and especially + + + align:start position:0% +Donald letter of credit and especially +if it's to small businesses that help + + align:start position:0% +if it's to small businesses that help + + + align:start position:0% +if it's to small businesses that help +yes I'm trying to think why do we need + + align:start position:0% +yes I'm trying to think why do we need + + + align:start position:0% +yes I'm trying to think why do we need +anyone there's more I think it's + + align:start position:0% +anyone there's more I think it's + + + align:start position:0% +anyone there's more I think it's +applicable in both it's more applicable + + align:start position:0% +applicable in both it's more applicable + + + align:start position:0% +applicable in both it's more applicable +and international trade because you have + + align:start position:0% +and international trade because you have + + + align:start position:0% +and international trade because you have +more more challenges of trust I would + + align:start position:0% +more more challenges of trust I would + + + align:start position:0% +more more challenges of trust I would +even say information asymmetries that if + + align:start position:0% +even say information asymmetries that if + + + align:start position:0% +even say information asymmetries that if +you're sitting in + + align:start position:0% +you're sitting in + + + align:start position:0% +you're sitting in +and you're exporting to Kenya you have + + align:start position:0% +and you're exporting to Kenya you have + + + align:start position:0% +and you're exporting to Kenya you have +less chance to actually know that local + + align:start position:0% +less chance to actually know that local + + + align:start position:0% +less chance to actually know that local +community and your look and your bank in + + align:start position:0% +community and your look and your bank in + + + align:start position:0% +community and your look and your bank in +China doesn't know them either and so + + align:start position:0% +China doesn't know them either and so + + + align:start position:0% +China doesn't know them either and so +what was built up to satisfy that those + + align:start position:0% +what was built up to satisfy that those + + + align:start position:0% +what was built up to satisfy that those +issues of trust is the banking sector + + align:start position:0% +issues of trust is the banking sector + + + align:start position:0% +issues of trust is the banking sector +largely picked up that either + + align:start position:0% +largely picked up that either + + + align:start position:0% +largely picked up that either +guaranteeing the documents we're + + align:start position:0% +guaranteeing the documents we're + + + align:start position:0% +guaranteeing the documents we're +actually guaranteeing the credit Hugo + + align:start position:0% +actually guaranteeing the credit Hugo + + + align:start position:0% +actually guaranteeing the credit Hugo +there's also say like border control + + align:start position:0% +there's also say like border control + + + align:start position:0% +there's also say like border control +right like I know in my lab we've had + + align:start position:0% +right like I know in my lab we've had + + + align:start position:0% +right like I know in my lab we've had +like waste materials shipped to us + + align:start position:0% +like waste materials shipped to us + + + align:start position:0% +like waste materials shipped to us +internationally and like customs agents + + align:start position:0% +internationally and like customs agents + + + align:start position:0% +internationally and like customs agents +really even care about that you have to + + align:start position:0% +really even care about that you have to + + + align:start position:0% +really even care about that you have to +put a price on that if you could just + + align:start position:0% +put a price on that if you could just + + + align:start position:0% +put a price on that if you could just +put something on a car and driving from + + align:start position:0% +put something on a car and driving from + + + align:start position:0% +put something on a car and driving from +San Francisco to Boston and maybe like + + align:start position:0% +San Francisco to Boston and maybe like + + + align:start position:0% +San Francisco to Boston and maybe like +yeah if you drive up in Canada to the US + + align:start position:0% +yeah if you drive up in Canada to the US + + + align:start position:0% +yeah if you drive up in Canada to the US +it would be different from group I'm + + align:start position:0% +it would be different from group I'm + + + align:start position:0% +it would be different from group I'm +shipping it from China to the US but I + + align:start position:0% +shipping it from China to the US but I + + + align:start position:0% +shipping it from China to the US but I +think the trust issue comes up a lot + + align:start position:0% +think the trust issue comes up a lot + + + align:start position:0% +think the trust issue comes up a lot +more when you're dealing with + + align:start position:0% +more when you're dealing with + + + align:start position:0% +more when you're dealing with +international and I'm not saying it + + align:start position:0% +international and I'm not saying it + + + align:start position:0% +international and I'm not saying it +doesn't exist in domestic trade it it + + align:start position:0% +doesn't exist in domestic trade it it + + + align:start position:0% +doesn't exist in domestic trade it it +definitely exists in domestic trade but + + align:start position:0% +definitely exists in domestic trade but + + + align:start position:0% +definitely exists in domestic trade but +international trade long ago created a + + align:start position:0% +international trade long ago created a + + + align:start position:0% +international trade long ago created a +system to address different languages + + align:start position:0% +system to address different languages + + + align:start position:0% +system to address different languages +different cultures different regulatory + + align:start position:0% +different cultures different regulatory + + + align:start position:0% +different cultures different regulatory +regimes taxing regimes and it was going + + align:start position:0% +regimes taxing regimes and it was going + + + align:start position:0% +regimes taxing regimes and it was going +on a ship you need to make sure that + + align:start position:0% +on a ship you need to make sure that + + + align:start position:0% +on a ship you need to make sure that +you're not breaking any regulation + + align:start position:0% +you're not breaking any regulation + + + align:start position:0% +you're not breaking any regulation +between different jurisdictions part of + + align:start position:0% +between different jurisdictions part of + + + align:start position:0% +between different jurisdictions part of +it will be ml as well for any CEO or + + align:start position:0% +it will be ml as well for any CEO or + + + align:start position:0% +it will be ml as well for any CEO or +whatever that question it's it seems + + align:start position:0% +whatever that question it's it seems + + + align:start position:0% +whatever that question it's it seems +like we are using a technology in this + + align:start position:0% +like we are using a technology in this + + + align:start position:0% +like we are using a technology in this +case blockchain to fit into the existing + + align:start position:0% +case blockchain to fit into the existing + + + align:start position:0% +case blockchain to fit into the existing +framework of how things work but + + align:start position:0% +framework of how things work but + + + align:start position:0% +framework of how things work but +shouldn't the question be flipped and + + align:start position:0% +shouldn't the question be flipped and + + + align:start position:0% +shouldn't the question be flipped and +say hang on a second do we need + + align:start position:0% +say hang on a second do we need + + + align:start position:0% +say hang on a second do we need +blockchain in his system that is better + + align:start position:0% +blockchain in his system that is better + + + align:start position:0% +blockchain in his system that is better +design under having 50 different + + align:start position:0% +design under having 50 different + + + align:start position:0% +design under having 50 different +documents and + + align:start position:0% +documents and + + + align:start position:0% +documents and +she's thinking about the actual problem + + align:start position:0% +she's thinking about the actual problem + + + align:start position:0% +she's thinking about the actual problem +I can see that when to the trust that + + align:start position:0% +I can see that when to the trust that + + + align:start position:0% +I can see that when to the trust that +which may need a blockchain solution but + + align:start position:0% +which may need a blockchain solution but + + + align:start position:0% +which may need a blockchain solution but +a lot of that be that truffle receipt + + align:start position:0% +a lot of that be that truffle receipt + + + align:start position:0% +a lot of that be that truffle receipt +Railway receipts forward karma receipts + + align:start position:0% +Railway receipts forward karma receipts + + + align:start position:0% +Railway receipts forward karma receipts +those are historical relics that surely + + align:start position:0% +those are historical relics that surely + + + align:start position:0% +those are historical relics that surely +there must be a technology other than + + align:start position:0% +there must be a technology other than + + + align:start position:0% +there must be a technology other than +watching that solve the problem + + align:start position:0% +watching that solve the problem + + + align:start position:0% +watching that solve the problem +well maybe or maybe blockchain + + align:start position:0% +well maybe or maybe blockchain + + + align:start position:0% +well maybe or maybe blockchain +technology is just the right technology + + align:start position:0% +technology is just the right technology + + + align:start position:0% +technology is just the right technology +that's come along in the 21st century to + + align:start position:0% +that's come along in the 21st century to + + + align:start position:0% +that's come along in the 21st century to +solve it better than initially pieces of + + align:start position:0% +solve it better than initially pieces of + + + align:start position:0% +solve it better than initially pieces of +paper and and literally document + + align:start position:0% +paper and and literally document + + + align:start position:0% +paper and and literally document +couriers that have to be trusted to do + + align:start position:0% +couriers that have to be trusted to do + + + align:start position:0% +couriers that have to be trusted to do +it well they haven't fully gone the way + + align:start position:0% +it well they haven't fully gone the way + + + align:start position:0% +it well they haven't fully gone the way +they dodo whilst I think that there's + + align:start position:0% +they dodo whilst I think that there's + + + align:start position:0% +they dodo whilst I think that there's +much to be said about blockchain that + + align:start position:0% +much to be said about blockchain that + + + align:start position:0% +much to be said about blockchain that +creates trust eating parties that may + + align:start position:0% +creates trust eating parties that may + + + align:start position:0% +creates trust eating parties that may +not naturally trust each other the + + align:start position:0% +not naturally trust each other the + + + align:start position:0% +not naturally trust each other the +problem seems to me is there's a lot of + + align:start position:0% +problem seems to me is there's a lot of + + + align:start position:0% +problem seems to me is there's a lot of +things that doesn't need to happen in + + align:start position:0% +things that doesn't need to happen in + + + align:start position:0% +things that doesn't need to happen in +this day and age as you mentioned + + align:start position:0% +this day and age as you mentioned + + + align:start position:0% +this day and age as you mentioned +domestic mail services it's between + + align:start position:0% +domestic mail services it's between + + + align:start position:0% +domestic mail services it's between +sender receiver what happens in between + + align:start position:0% +sender receiver what happens in between + + + align:start position:0% +sender receiver what happens in between +is tracked by UPS but what we don't + + align:start position:0% +is tracked by UPS but what we don't + + + align:start position:0% +is tracked by UPS but what we don't +Sonny don't seize all of that list of + + align:start position:0% +Sonny don't seize all of that list of + + + align:start position:0% +Sonny don't seize all of that list of +stuff whilst it's happening but it's an + + align:start position:0% +stuff whilst it's happening but it's an + + + align:start position:0% +stuff whilst it's happening but it's an +assistant well domestically you may be + + align:start position:0% +assistant well domestically you may be + + + align:start position:0% +assistant well domestically you may be +you might be right but what's happened + + align:start position:0% +you might be right but what's happened + + + align:start position:0% +you might be right but what's happened +well before blockchain technology came + + align:start position:0% +well before blockchain technology came + + + align:start position:0% +well before blockchain technology came +along as digitization but part of the + + align:start position:0% +along as digitization but part of the + + + align:start position:0% +along as digitization but part of the +trade can't be demoted materialized see + + align:start position:0% +trade can't be demoted materialized see + + + align:start position:0% +trade can't be demoted materialized see +in the securities business what we what + + align:start position:0% +in the securities business what we what + + + align:start position:0% +in the securities business what we what +we talked about when we talk about + + align:start position:0% +we talked about when we talk about + + + align:start position:0% +we talked about when we talk about +clearing and settling of securities the + + align:start position:0% +clearing and settling of securities the + + + align:start position:0% +clearing and settling of securities the +equity ownership has been dematerialized + + align:start position:0% +equity ownership has been dematerialized + + + align:start position:0% +equity ownership has been dematerialized +and it's started to happen in the 1970s + + align:start position:0% +and it's started to happen in the 1970s + + + align:start position:0% +and it's started to happen in the 1970s +the the legal right that you have this + + align:start position:0% +the the legal right that you have this + + + align:start position:0% +the the legal right that you have this +cash flow called an equity interest in + + align:start position:0% +cash flow called an equity interest in + + + align:start position:0% +cash flow called an equity interest in +an apple is all digitized part of this + + align:start position:0% +an apple is all digitized part of this + + + align:start position:0% +an apple is all digitized part of this +trade is not digitized 17 trillion + + align:start position:0% +trade is not digitized 17 trillion + + + align:start position:0% +trade is not digitized 17 trillion +dollars of physical goods on the high + + align:start position:0% +dollars of physical goods on the high + + + align:start position:0% +dollars of physical goods on the high +seas so I still think you're gonna need + + align:start position:0% +seas so I still think you're gonna need + + + align:start position:0% +seas so I still think you're gonna need +something that shows that there's the + + align:start position:0% +something that shows that there's the + + + align:start position:0% +something that shows that there's the +physical good has made it on a ship or + + align:start position:0% +physical good has made it on a ship or + + + align:start position:0% +physical good has made it on a ship or +on a cargo vessel of some sort so there + + align:start position:0% +on a cargo vessel of some sort so there + + + align:start position:0% +on a cargo vessel of some sort so there +are some differences Erik sounding her + + align:start position:0% +are some differences Erik sounding her + + + align:start position:0% +are some differences Erik sounding her +yes just to address a concern of James + + align:start position:0% +yes just to address a concern of James + + + align:start position:0% +yes just to address a concern of James +that many of the manual process the + + align:start position:0% +that many of the manual process the + + + align:start position:0% +that many of the manual process the +decision projects fail at the beginning + + align:start position:0% +decision projects fail at the beginning + + + align:start position:0% +decision projects fail at the beginning +because they actually did that they kind + + align:start position:0% +because they actually did that they kind + + + align:start position:0% +because they actually did that they kind +of try to reflect exactly what happened + + align:start position:0% +of try to reflect exactly what happened + + + align:start position:0% +of try to reflect exactly what happened +in the manual of line world into the + + align:start position:0% +in the manual of line world into the + + + align:start position:0% +in the manual of line world into the +digitized world which resulted in many + + align:start position:0% +digitized world which resulted in many + + + align:start position:0% +digitized world which resulted in many +inefficiencies and this is not the thing + + align:start position:0% +inefficiencies and this is not the thing + + + align:start position:0% +inefficiencies and this is not the thing +we're not actually trying to do exactly + + align:start position:0% +we're not actually trying to do exactly + + + align:start position:0% +we're not actually trying to do exactly +that offline process using blockchain + + align:start position:0% +that offline process using blockchain + + + align:start position:0% +that offline process using blockchain +technology that's not the alternative + + align:start position:0% +technology that's not the alternative + + + align:start position:0% +technology that's not the alternative +but that out that actually made me think + + align:start position:0% +but that out that actually made me think + + + align:start position:0% +but that out that actually made me think +it does I wanted to point out this did + + align:start position:0% +it does I wanted to point out this did + + + align:start position:0% +it does I wanted to point out this did +to your argument of the centralized + + align:start position:0% +to your argument of the centralized + + + align:start position:0% +to your argument of the centralized +databases and centralized databases have + + align:start position:0% +databases and centralized databases have + + + align:start position:0% +databases and centralized databases have +been around for more than 60 years + + align:start position:0% +been around for more than 60 years + + + align:start position:0% +been around for more than 60 years +they've been digitizing manual processes + + align:start position:0% +they've been digitizing manual processes + + + align:start position:0% +they've been digitizing manual processes +for a while that the question comes is + + align:start position:0% +for a while that the question comes is + + + align:start position:0% +for a while that the question comes is +why didn't they already digitized this + + align:start position:0% +why didn't they already digitized this + + + align:start position:0% +why didn't they already digitized this +sort of problems the answer is because + + align:start position:0% +sort of problems the answer is because + + + align:start position:0% +sort of problems the answer is because +this these trade finance issue has + + align:start position:0% +this these trade finance issue has + + + align:start position:0% +this these trade finance issue has +special characteristics that make it + + align:start position:0% +special characteristics that make it + + + align:start position:0% +special characteristics that make it +especially suitable for to be addressed + + align:start position:0% +especially suitable for to be addressed + + + align:start position:0% +especially suitable for to be addressed +by these specific technologies so that's + + align:start position:0% +by these specific technologies so that's + + + align:start position:0% +by these specific technologies so that's +why I would argue that what do you think + + align:start position:0% +why I would argue that what do you think + + + align:start position:0% +why I would argue that what do you think +that specialness is it's precisely the + + align:start position:0% +that specialness is it's precisely the + + + align:start position:0% +that specialness is it's precisely the +fact that we have multiple stakeholders + + align:start position:0% +fact that we have multiple stakeholders + + + align:start position:0% +fact that we have multiple stakeholders +dealing with information that goes about + + align:start position:0% +dealing with information that goes about + + + align:start position:0% +dealing with information that goes about +among these moving parts and you have a + + align:start position:0% +among these moving parts and you have a + + + align:start position:0% +among these moving parts and you have a +high cost of trust so what you're + + align:start position:0% +high cost of trust so what you're + + + align:start position:0% +high cost of trust so what you're +actually doing is you see blockchain + + align:start position:0% +actually doing is you see blockchain + + + align:start position:0% +actually doing is you see blockchain +technology permissioned or otherwise to + + align:start position:0% +technology permissioned or otherwise to + + + align:start position:0% +technology permissioned or otherwise to +address a specific challenge and you + + align:start position:0% +address a specific challenge and you + + + align:start position:0% +address a specific challenge and you +have a property right as well that + + align:start position:0% +have a property right as well that + + + align:start position:0% +have a property right as well that +people often want to borrow still + + align:start position:0% +people often want to borrow still + + + align:start position:0% +people often want to borrow still +against while it's on the high seas but + + align:start position:0% +against while it's on the high seas but + + + align:start position:0% +against while it's on the high seas but +I agree it may well be that that the + + align:start position:0% +I agree it may well be that that the + + + align:start position:0% +I agree it may well be that that the +blockchain technology is not the only + + align:start position:0% +blockchain technology is not the only + + + align:start position:0% +blockchain technology is not the only +solution to this but it does feel like + + align:start position:0% +solution to this but it does feel like + + + align:start position:0% +solution to this but it does feel like +it's a particularly fertile area and + + align:start position:0% +it's a particularly fertile area and + + + align:start position:0% +it's a particularly fertile area and +we're going to turn right now to some of + + align:start position:0% +we're going to turn right now to some of + + + align:start position:0% +we're going to turn right now to some of +the projects and there's a lot of + + align:start position:0% +the projects and there's a lot of + + + align:start position:0% +the projects and there's a lot of +projects in this space + + align:start position:0% +projects in this space + + + align:start position:0% +projects in this space +aleem and then we'll go in the back + + align:start position:0% + + + + align:start position:0% + +fix the product to fix the complexity + + align:start position:0% +fix the product to fix the complexity + + + align:start position:0% +fix the product to fix the complexity +list of higher goals well it's a really + + align:start position:0% +list of higher goals well it's a really + + + align:start position:0% +list of higher goals well it's a really +good question so those working on + + align:start position:0% +good question so those working on + + + align:start position:0% +good question so those working on +projects is it more about fraud or the + + align:start position:0% +projects is it more about fraud or the + + + align:start position:0% +projects is it more about fraud or the +complexity so they're so efficiency so + + align:start position:0% +complexity so they're so efficiency so + + + align:start position:0% +complexity so they're so efficiency so +you can you can drive a lot of + + align:start position:0% +you can you can drive a lot of + + + align:start position:0% +you can you can drive a lot of +efficiency which is to the complexity I + + align:start position:0% +efficiency which is to the complexity I + + + align:start position:0% +efficiency which is to the complexity I +think that's one of the overarching + + align:start position:0% +think that's one of the overarching + + + align:start position:0% +think that's one of the overarching +goals is driving efficiency but also to + + align:start position:0% +goals is driving efficiency but also to + + + align:start position:0% +goals is driving efficiency but also to +lower the the fraud or the loss to fraud + + align:start position:0% +lower the the fraud or the loss to fraud + + + align:start position:0% +lower the the fraud or the loss to fraud +it's it's both but I think it's driven + + align:start position:0% +it's it's both but I think it's driven + + + align:start position:0% +it's it's both but I think it's driven +more by the efficiency from my readings + + align:start position:0% +more by the efficiency from my readings + + + align:start position:0% +more by the efficiency from my readings +of this more by the efficiencies I don't + + align:start position:0% +of this more by the efficiencies I don't + + + align:start position:0% +of this more by the efficiencies I don't +know the front rate it's a good question + + align:start position:0% +know the front rate it's a good question + + + align:start position:0% +know the front rate it's a good question +we'll see if we can find it out vivo is + + align:start position:0% +we'll see if we can find it out vivo is + + + align:start position:0% +we'll see if we can find it out vivo is +going to be next + + align:start position:0% + + + + align:start position:0% + +it's more than the private blockchains + + align:start position:0% +it's more than the private blockchains + + + align:start position:0% +it's more than the private blockchains +event + + align:start position:0% + + + + align:start position:0% + +can I hold that because it's a it's a + + align:start position:0% +can I hold that because it's a it's a + + + align:start position:0% +can I hold that because it's a it's a +very good question that will come up + + align:start position:0% +very good question that will come up + + + align:start position:0% +very good question that will come up +when we talk a little bit about some of + + align:start position:0% +when we talk a little bit about some of + + + align:start position:0% +when we talk a little bit about some of +the IBM projects particularly with one + + align:start position:0% +the IBM projects particularly with one + + + align:start position:0% +the IBM projects particularly with one +of the Lords of shippers so I it's it's + + align:start position:0% +of the Lords of shippers so I it's it's + + + align:start position:0% +of the Lords of shippers so I it's it's +the right question but we're gonna chat + + align:start position:0% +the right question but we're gonna chat + + + align:start position:0% +the right question but we're gonna chat +about when we talk about can I talk + + align:start position:0% +about when we talk about can I talk + + + align:start position:0% +about when we talk about can I talk +about some of the projects or was there + + align:start position:0% +about some of the projects or was there + + + align:start position:0% +about some of the projects or was there +something all right so where are we well + + align:start position:0% +something all right so where are we well + + + align:start position:0% +something all right so where are we well +there's there's there's five big + + align:start position:0% +there's there's there's five big + + + align:start position:0% +there's there's there's five big +consortium two of them you can see are + + align:start position:0% +consortium two of them you can see are + + + align:start position:0% +consortium two of them you can see are +back on or working on the corridor that + + align:start position:0% +back on or working on the corridor that + + + align:start position:0% +back on or working on the corridor that +was the r3 corridor that we talked about + + align:start position:0% +was the r3 corridor that we talked about + + + align:start position:0% +was the r3 corridor that we talked about +earlier this semester two on IBM one + + align:start position:0% +earlier this semester two on IBM one + + + align:start position:0% +earlier this semester two on IBM one +that's on a on a ping and group is not + + align:start position:0% +that's on a on a ping and group is not + + + align:start position:0% +that's on a on a ping and group is not +we didn't talk about earlier this year + + align:start position:0% +we didn't talk about earlier this year + + + align:start position:0% +we didn't talk about earlier this year +and so let our credit approach + + align:start position:0% +and so let our credit approach + + + align:start position:0% +and so let our credit approach +receivables and payment guarantee + + align:start position:0% +receivables and payment guarantee + + + align:start position:0% +receivables and payment guarantee +financing which is a little bit + + align:start position:0% +financing which is a little bit + + + align:start position:0% +financing which is a little bit +different this is we already have + + align:start position:0% +different this is we already have + + + align:start position:0% +different this is we already have +receivables how do we fund them + + align:start position:0% + + + + align:start position:0% + +monitoring open transactions and letters + + align:start position:0% +monitoring open transactions and letters + + + align:start position:0% +monitoring open transactions and letters +of credit and then the Hongkong group is + + align:start position:0% +of credit and then the Hongkong group is + + + align:start position:0% +of credit and then the Hongkong group is +the supply chain record-keeping and just + + align:start position:0% +the supply chain record-keeping and just + + + align:start position:0% +the supply chain record-keeping and just +if you want to see it sort of visually + + align:start position:0% +if you want to see it sort of visually + + + align:start position:0% +if you want to see it sort of visually +this is all the backs that are involved + + align:start position:0% +this is all the backs that are involved + + + align:start position:0% +this is all the backs that are involved +in each of the consort + + align:start position:0% +in each of the consort + + + align:start position:0% +in each of the consort +and you'll see basically that there's + + align:start position:0% +and you'll see basically that there's + + + align:start position:0% +and you'll see basically that there's +some overlap I think unless unless I'm + + align:start position:0% +some overlap I think unless unless I'm + + + align:start position:0% +some overlap I think unless unless I'm +mistaken + + align:start position:0% +mistaken + + + align:start position:0% +mistaken +ing might be in a couple of them I think + + align:start position:0% +ing might be in a couple of them I think + + + align:start position:0% +ing might be in a couple of them I think +two of these consortia maybe have now + + align:start position:0% +two of these consortia maybe have now + + + align:start position:0% +two of these consortia maybe have now +merged but it goes a little bit it's not + + align:start position:0% +merged but it goes a little bit it's not + + + align:start position:0% +merged but it goes a little bit it's not +it's not fully gonna answer your + + align:start position:0% +it's not fully gonna answer your + + + align:start position:0% +it's not fully gonna answer your +question Aviva but even if there were + + align:start position:0% +question Aviva but even if there were + + + align:start position:0% +question Aviva but even if there were +five different consortium trying to + + align:start position:0% +five different consortium trying to + + + align:start position:0% +five different consortium trying to +figure this out amongst different groups + + align:start position:0% +figure this out amongst different groups + + + align:start position:0% +figure this out amongst different groups +of banks at some point in time to really + + align:start position:0% +of banks at some point in time to really + + + align:start position:0% +of banks at some point in time to really +gain a great deal more efficiency how do + + align:start position:0% +gain a great deal more efficiency how do + + + align:start position:0% +gain a great deal more efficiency how do +they operate how do they transact across + + align:start position:0% +they operate how do they transact across + + + align:start position:0% +they operate how do they transact across +their platforms now they each obviously + + align:start position:0% +their platforms now they each obviously + + + align:start position:0% +their platforms now they each obviously +don't want to give up economic rents + + align:start position:0% +don't want to give up economic rents + + + align:start position:0% +don't want to give up economic rents +they don't want to give up market power + + align:start position:0% +they don't want to give up market power + + + align:start position:0% +they don't want to give up market power +to somebody they don't want to all of a + + align:start position:0% +to somebody they don't want to all of a + + + align:start position:0% +to somebody they don't want to all of a +sudden find out that that some + + align:start position:0% +sudden find out that that some + + + align:start position:0% +sudden find out that that some +entrepreneur is charging them so much + + align:start position:0% +entrepreneur is charging them so much + + + align:start position:0% +entrepreneur is charging them so much +because they created a network because + + align:start position:0% +because they created a network because + + + align:start position:0% +because they created a network because +the one the one consortium that figures + + align:start position:0% +the one the one consortium that figures + + + align:start position:0% +the one the one consortium that figures +this out early on could price pretty + + align:start position:0% +this out early on could price pretty + + + align:start position:0% +this out early on could price pretty +close to their cost structure but later + + align:start position:0% +close to their cost structure but later + + + align:start position:0% +close to their cost structure but later +on could you know price a lot higher and + + align:start position:0% +on could you know price a lot higher and + + + align:start position:0% +on could you know price a lot higher and +collect a lot of monopoly or economic + + align:start position:0% +collect a lot of monopoly or economic + + + align:start position:0% +collect a lot of monopoly or economic +rents so I don't know where this will + + align:start position:0% +rents so I don't know where this will + + + align:start position:0% +rents so I don't know where this will +sort out and I don't even know that + + align:start position:0% +sort out and I don't even know that + + + align:start position:0% +sort out and I don't even know that +they're gonna want to solve the + + align:start position:0% +they're gonna want to solve the + + + align:start position:0% +they're gonna want to solve the +interoperability problem amongst + + align:start position:0% +interoperability problem amongst + + + align:start position:0% +interoperability problem amongst +themselves all of the listed up there a + + align:start position:0% +themselves all of the listed up there a + + + align:start position:0% +themselves all of the listed up there a +shipment or European fact none of the US + + align:start position:0% +shipment or European fact none of the US + + + align:start position:0% +shipment or European fact none of the US +banks are actually participating quite + + align:start position:0% +banks are actually participating quite + + + align:start position:0% +banks are actually participating quite +do you see JP Morgan Chase + + align:start position:0% + + + + align:start position:0% + +now who's the largest issue of trade + + align:start position:0% +now who's the largest issue of trade + + + align:start position:0% +now who's the largest issue of trade +finance in the world what's that it's + + align:start position:0% +finance in the world what's that it's + + + align:start position:0% +finance in the world what's that it's +not is it + + align:start position:0% +not is it + + + align:start position:0% +not is it +no no no I think it's fine I think it's + + align:start position:0% +no no no I think it's fine I think it's + + + align:start position:0% +no no no I think it's fine I think it's +a chance I'm not might be mistaken I + + align:start position:0% +a chance I'm not might be mistaken I + + + align:start position:0% +a chance I'm not might be mistaken I +think HSBC but but you're right the the + + align:start position:0% +think HSBC but but you're right the the + + + align:start position:0% +think HSBC but but you're right the the +five big Wells Fargo is not on there + + align:start position:0% +five big Wells Fargo is not on there + + + align:start position:0% +five big Wells Fargo is not on there +either are they that doesn't mean + + align:start position:0% +either are they that doesn't mean + + + align:start position:0% +either are they that doesn't mean +they're not working on other projects + + align:start position:0% +they're not working on other projects + + + align:start position:0% +they're not working on other projects +because here's some other projects and + + align:start position:0% +because here's some other projects and + + + align:start position:0% +because here's some other projects and +these aren't the consortium I'm just + + align:start position:0% +these aren't the consortium I'm just + + + align:start position:0% +these aren't the consortium I'm just +giving you a flavor there's a lot going + + align:start position:0% +giving you a flavor there's a lot going + + + align:start position:0% +giving you a flavor there's a lot going +on in this space and those of you who + + align:start position:0% +on in this space and those of you who + + + align:start position:0% +on in this space and those of you who +are doing final projects I challenge you + + align:start position:0% +are doing final projects I challenge you + + + align:start position:0% +are doing final projects I challenge you +to you know think about these projects + + align:start position:0% +to you know think about these projects + + + align:start position:0% +to you know think about these projects +and say well what are you recommending + + align:start position:0% +and say well what are you recommending + + + align:start position:0% +and say well what are you recommending +that it's different you know it's not + + align:start position:0% +that it's different you know it's not + + + align:start position:0% +that it's different you know it's not +just me - there's me - financial but + + align:start position:0% +just me - there's me - financial but + + + align:start position:0% +just me - there's me - financial but +India's in interesting to me there's + + align:start position:0% +India's in interesting to me there's + + + align:start position:0% +India's in interesting to me there's +there's another consortium it wasn't on + + align:start position:0% +there's another consortium it wasn't on + + + align:start position:0% +there's another consortium it wasn't on +that page and probably pronouncing wrong + + align:start position:0% +that page and probably pronouncing wrong + + + align:start position:0% +that page and probably pronouncing wrong +the final Kyle orphanet pal what's that + + align:start position:0% +the final Kyle orphanet pal what's that + + + align:start position:0% +the final Kyle orphanet pal what's that +are you familiar with that I needed it + + align:start position:0% +are you familiar with that I needed it + + + align:start position:0% +are you familiar with that I needed it +for validation documents and payment so + + align:start position:0% +for validation documents and payment so + + + align:start position:0% +for validation documents and payment so +they're not really saying we're just + + align:start position:0% +they're not really saying we're just + + + align:start position:0% +they're not really saying we're just +trade finance but we're gonna validate + + align:start position:0% +trade finance but we're gonna validate + + + align:start position:0% +trade finance but we're gonna validate +all the documents this is goes more to + + align:start position:0% +all the documents this is goes more to + + + align:start position:0% +all the documents this is goes more to +fraud Helene I think this project + + align:start position:0% +fraud Helene I think this project + + + align:start position:0% +fraud Helene I think this project +validating the documents saying yes + + align:start position:0% +validating the documents saying yes + + + align:start position:0% +validating the documents saying yes +they're true and good and you can lend + + align:start position:0% +they're true and good and you can lend + + + align:start position:0% +they're true and good and you can lend +against these documents and and a lot of + + align:start position:0% +against these documents and and a lot of + + + align:start position:0% +against these documents and and a lot of +time these documents are the bills of + + align:start position:0% +time these documents are the bills of + + + align:start position:0% +time these documents are the bills of +lading and Bills of exchange or left + + align:start position:0% +lading and Bills of exchange or left + + + align:start position:0% +lading and Bills of exchange or left +loan blendable and so forth so a lot of + + align:start position:0% +loan blendable and so forth so a lot of + + + align:start position:0% +loan blendable and so forth so a lot of +projects one I could only find now there + + align:start position:0% +projects one I could only find now there + + + align:start position:0% +projects one I could only find now there +may be others I could only find one with + + align:start position:0% +may be others I could only find one with + + + align:start position:0% +may be others I could only find one with +a token and I put it up there Lasky + + align:start position:0% +a token and I put it up there Lasky + + + align:start position:0% +a token and I put it up there Lasky +theory and based consensus the company + + align:start position:0% +theory and based consensus the company + + + align:start position:0% +theory and based consensus the company +that's run by Jo Lube and who who is the + + align:start position:0% +that's run by Jo Lube and who who is the + + + align:start position:0% +that's run by Jo Lube and who who is the +ventric Canadian venture capitalist who + + align:start position:0% +ventric Canadian venture capitalist who + + + align:start position:0% +ventric Canadian venture capitalist who +helped back the talaq booter Anna + + align:start position:0% +helped back the talaq booter Anna + + + align:start position:0% +helped back the talaq booter Anna +atheria + + align:start position:0% +atheria + + + align:start position:0% +atheria +consensus has three 400 people at least + + align:start position:0% +consensus has three 400 people at least + + + align:start position:0% +consensus has three 400 people at least +working in consensus doing a theory and + + align:start position:0% +working in consensus doing a theory and + + + align:start position:0% +working in consensus doing a theory and +based project so I was pleased to see I + + align:start position:0% +based project so I was pleased to see I + + + align:start position:0% +based project so I was pleased to see I +could find one native this token but to + + align:start position:0% +could find one native this token but to + + + align:start position:0% +could find one native this token but to +my knowledge all of the consortia and + + align:start position:0% +my knowledge all of the consortia and + + + align:start position:0% +my knowledge all of the consortia and +all of the ones I listed up there + + align:start position:0% +all of the ones I listed up there + + + align:start position:0% +all of the ones I listed up there +permissioned law chains can tell but I'm + + align:start position:0% +permissioned law chains can tell but I'm + + + align:start position:0% +permissioned law chains can tell but I'm +curious those of you who are working in + + align:start position:0% +curious those of you who are working in + + + align:start position:0% +curious those of you who are working in +this have you found any native token + + align:start position:0% +this have you found any native token + + + align:start position:0% +this have you found any native token +projects be verified which is a project + + align:start position:0% +projects be verified which is a project + + + align:start position:0% +projects be verified which is a project +from the Media Lab is not up doesn't + + align:start position:0% +from the Media Lab is not up doesn't + + + align:start position:0% +from the Media Lab is not up doesn't +happen if talking per se but uses + + align:start position:0% +happen if talking per se but uses + + + align:start position:0% +happen if talking per se but uses +permissionless blockchain existing block + + align:start position:0% +permissionless blockchain existing block + + + align:start position:0% +permissionless blockchain existing block +permissionless blockchain infrastructure + + align:start position:0% +permissionless blockchain infrastructure + + + align:start position:0% +permissionless blockchain infrastructure +to gain in the mutability of the lots of + + align:start position:0% +to gain in the mutability of the lots of + + + align:start position:0% +to gain in the mutability of the lots of +statements to build a warehouse resists + + align:start position:0% +statements to build a warehouse resists + + + align:start position:0% +statements to build a warehouse resists +use case so they're using transactions + + align:start position:0% +use case so they're using transactions + + + align:start position:0% +use case so they're using transactions +in the Bitcoin network right now to + + align:start position:0% +in the Bitcoin network right now to + + + align:start position:0% +in the Bitcoin network right now to +write it doesn't be there if I have a + + align:start position:0% +write it doesn't be there if I have a + + + align:start position:0% +write it doesn't be there if I have a +token note oh yeah + + align:start position:0% +token note oh yeah + + + align:start position:0% +token note oh yeah +what's Adaline our research Cecil okay + + align:start position:0% +what's Adaline our research Cecil okay + + + align:start position:0% +what's Adaline our research Cecil okay +Tina yes do is that your research that's + + align:start position:0% +Tina yes do is that your research that's + + + align:start position:0% +Tina yes do is that your research that's +right yeah it's terrific you're so + + align:start position:0% +right yeah it's terrific you're so + + + align:start position:0% +right yeah it's terrific you're so +you're glad to talk to Eric but you + + align:start position:0% +you're glad to talk to Eric but you + + + align:start position:0% +you're glad to talk to Eric but you +didn't have a token in that bitcoins out + + align:start position:0% +didn't have a token in that bitcoins out + + + align:start position:0% +didn't have a token in that bitcoins out +there it's a great system and you can + + align:start position:0% +there it's a great system and you can + + + align:start position:0% +there it's a great system and you can +build on top of it efficiently to + + align:start position:0% +build on top of it efficiently to + + + align:start position:0% +build on top of it efficiently to +provide immutability to any permission + + align:start position:0% +provide immutability to any permission + + + align:start position:0% +provide immutability to any permission +so don't start your smart contract + + align:start position:0% +so don't start your smart contract + + + align:start position:0% +so don't start your smart contract +necessarily unless it's not like digital + + align:start position:0% +necessarily unless it's not like digital + + + align:start position:0% +necessarily unless it's not like digital +identity for example but if you had put + + align:start position:0% +identity for example but if you had put + + + align:start position:0% +identity for example but if you had put +a token in and sold it right into this + + align:start position:0% +a token in and sold it right into this + + + align:start position:0% +a token in and sold it right into this +bull market I guess you wouldn't be + + align:start position:0% +bull market I guess you wouldn't be + + + align:start position:0% +bull market I guess you wouldn't be +sitting in this class + + align:start position:0% + + + + align:start position:0% + +I'm glad you didn't put a token I'm glad + + align:start position:0% +I'm glad you didn't put a token I'm glad + + + align:start position:0% +I'm glad you didn't put a token I'm glad +you're here but I mean that's part of + + align:start position:0% +you're here but I mean that's part of + + + align:start position:0% +you're here but I mean that's part of +like you're saying you didn't need it as + + align:start position:0% +like you're saying you didn't need it as + + + align:start position:0% +like you're saying you didn't need it as +a technological and commercial point is + + align:start position:0% +a technological and commercial point is + + + align:start position:0% +a technological and commercial point is +what you're saying + + align:start position:0% +what you're saying + + + align:start position:0% +what you're saying +Leonardo tell us something about it yeah + + align:start position:0% +Leonardo tell us something about it yeah + + + align:start position:0% +Leonardo tell us something about it yeah +so I have to dig a little bit into the + + align:start position:0% +so I have to dig a little bit into the + + + align:start position:0% +so I have to dig a little bit into the +native token that you mention but most + + align:start position:0% +native token that you mention but most + + + align:start position:0% +native token that you mention but most +of the trading friends there are funding + + align:start position:0% +of the trading friends there are funding + + + align:start position:0% +of the trading friends there are funding +based query over very large shippers of + + align:start position:0% +based query over very large shippers of + + + align:start position:0% +based query over very large shippers of +paternal and back to your point view of + + align:start position:0% +paternal and back to your point view of + + + align:start position:0% +paternal and back to your point view of +ladings in the commodity space that + + align:start position:0% +ladings in the commodity space that + + + align:start position:0% +ladings in the commodity space that +petroleum lanes are the ones that were + + align:start position:0% +petroleum lanes are the ones that were + + + align:start position:0% +petroleum lanes are the ones that were +most actively traded and they change + + align:start position:0% +most actively traded and they change + + + align:start position:0% +most actively traded and they change +hands very often while the best is that + + align:start position:0% +hands very often while the best is that + + + align:start position:0% +hands very often while the best is that +then if I can add to this because I + + align:start position:0% +then if I can add to this because I + + + align:start position:0% +then if I can add to this because I +learned a little bit about this when I + + align:start position:0% +learned a little bit about this when I + + + align:start position:0% +learned a little bit about this when I +was in the US Commodity Futures Trading + + align:start position:0% +was in the US Commodity Futures Trading + + + align:start position:0% +was in the US Commodity Futures Trading +Commission of the Bill of Lading + + align:start position:0% +Commission of the Bill of Lading + + + align:start position:0% +Commission of the Bill of Lading +before oil on the high seeds can trade + + align:start position:0% +before oil on the high seeds can trade + + + align:start position:0% +before oil on the high seeds can trade +hands hundreds if not thousands of time + + align:start position:0% +hands hundreds if not thousands of time + + + align:start position:0% +hands hundreds if not thousands of time +oil coming from the the Strait of Hormuz + + align:start position:0% +oil coming from the the Strait of Hormuz + + + align:start position:0% +oil coming from the the Strait of Hormuz +to Houston might change ownership in a I + + align:start position:0% +to Houston might change ownership in a I + + + align:start position:0% +to Houston might change ownership in a I +don't know how long that takes a fifteen + + align:start position:0% +don't know how long that takes a fifteen + + + align:start position:0% +don't know how long that takes a fifteen +or thirty day trip twenty day trip they + + align:start position:0% +or thirty day trip twenty day trip they + + + align:start position:0% +or thirty day trip twenty day trip they +can change the ownership hundreds of + + align:start position:0% +can change the ownership hundreds of + + + align:start position:0% +can change the ownership hundreds of +times so those documents become tradable + + align:start position:0% +times so those documents become tradable + + + align:start position:0% +times so those documents become tradable +goods and it's not just in theory it's + + align:start position:0% +goods and it's not just in theory it's + + + align:start position:0% +goods and it's not just in theory it's +it's very much in practice so I suspect + + align:start position:0% +it's very much in practice so I suspect + + + align:start position:0% +it's very much in practice so I suspect +they may be talking that must be some + + align:start position:0% +they may be talking that must be some + + + align:start position:0% +they may be talking that must be some +kind of authorization against those + + align:start position:0% + + + + align:start position:0% + +so alpha who I'm sure remember everybody + + align:start position:0% +so alpha who I'm sure remember everybody + + + align:start position:0% +so alpha who I'm sure remember everybody +in your group what what can you tell us + + align:start position:0% +in your group what what can you tell us + + + align:start position:0% +in your group what what can you tell us +about what you're what you're working on + + align:start position:0% +about what you're what you're working on + + + align:start position:0% +about what you're what you're working on +how are you gonna beat all these + + align:start position:0% +how are you gonna beat all these + + + align:start position:0% +how are you gonna beat all these +consortia I'm thinking you're you know + + align:start position:0% +consortia I'm thinking you're you know + + + align:start position:0% +consortia I'm thinking you're you know +your final projects do better than these + + align:start position:0% +your final projects do better than these + + + align:start position:0% +your final projects do better than these +right I did give these two groups the + + align:start position:0% +right I did give these two groups the + + + align:start position:0% +right I did give these two groups the +heads up and I was gonna call on them so + + align:start position:0% +heads up and I was gonna call on them so + + + align:start position:0% +heads up and I was gonna call on them so +this is just but yeah what we're + + align:start position:0% +this is just but yeah what we're + + + align:start position:0% +this is just but yeah what we're +thinking that budget is being very + + align:start position:0% +thinking that budget is being very + + + align:start position:0% +thinking that budget is being very +specific so we're focusing on the narrow + + align:start position:0% +specific so we're focusing on the narrow + + + align:start position:0% +specific so we're focusing on the narrow +corridor thirteen Chinese exports coming + + align:start position:0% +corridor thirteen Chinese exports coming + + + align:start position:0% +corridor thirteen Chinese exports coming +to you yeah and so one there are many + + align:start position:0% +to you yeah and so one there are many + + + align:start position:0% +to you yeah and so one there are many +people obviously looking at that space + + align:start position:0% +people obviously looking at that space + + + align:start position:0% +people obviously looking at that space +at least not yet + + align:start position:0% +at least not yet + + + align:start position:0% +at least not yet +and is it through the trade finance side + + align:start position:0% +and is it through the trade finance side + + + align:start position:0% +and is it through the trade finance side +or what I'll call the supply chain saw + + align:start position:0% +or what I'll call the supply chain saw + + + align:start position:0% +or what I'll call the supply chain saw +yeah and so we think it's particularly + + align:start position:0% +yeah and so we think it's particularly + + + align:start position:0% +yeah and so we think it's particularly +interesting around not just the geogi + + align:start position:0% +interesting around not just the geogi + + + align:start position:0% +interesting around not just the geogi +but all of the sort developing countries + + align:start position:0% +but all of the sort developing countries + + + align:start position:0% +but all of the sort developing countries +in that region because credit and + + align:start position:0% +in that region because credit and + + + align:start position:0% +in that region because credit and +Finance is already so limited and so the + + align:start position:0% +Finance is already so limited and so the + + + align:start position:0% +Finance is already so limited and so the +best banking system ever developed + + align:start position:0% +best banking system ever developed + + + align:start position:0% +best banking system ever developed +domestic banks system in Ethiopia pretty + + align:start position:0% +domestic banks system in Ethiopia pretty + + + align:start position:0% +domestic banks system in Ethiopia pretty +quickly in across the south of Elysee so + + align:start position:0% +quickly in across the south of Elysee so + + + align:start position:0% +quickly in across the south of Elysee so +their reliance on trade finance in those + + align:start position:0% +their reliance on trade finance in those + + + align:start position:0% +their reliance on trade finance in those +import heavy economies I think it's even + + align:start position:0% +import heavy economies I think it's even + + + align:start position:0% +import heavy economies I think it's even +higher so the pain point I think is even + + align:start position:0% +higher so the pain point I think is even + + + align:start position:0% +higher so the pain point I think is even +stronger there James did you have a + + align:start position:0% +stronger there James did you have a + + + align:start position:0% +stronger there James did you have a +question for their group anybody has + + align:start position:0% +question for their group anybody has + + + align:start position:0% +question for their group anybody has +question for the group pile in will + + align:start position:0% +question for the group pile in will + + + align:start position:0% +question for the group pile in will +they'll take the advice not specifically + + align:start position:0% +they'll take the advice not specifically + + + align:start position:0% +they'll take the advice not specifically +on this one but more clarification so I + + align:start position:0% +on this one but more clarification so I + + + align:start position:0% +on this one but more clarification so I +think clearly see the trade finance + + align:start position:0% +think clearly see the trade finance + + + align:start position:0% +think clearly see the trade finance +requires different parties in the + + align:start position:0% +requires different parties in the + + + align:start position:0% +requires different parties in the +ownership of the goods at any point in + + align:start position:0% +ownership of the goods at any point in + + + align:start position:0% +ownership of the goods at any point in +time or the supply chain is important + + align:start position:0% +time or the supply chain is important + + + align:start position:0% +time or the supply chain is important +but particularly when it becomes + + align:start position:0% +but particularly when it becomes + + + align:start position:0% +but particularly when it becomes +commoditize like warrior and so forth + + align:start position:0% +commoditize like warrior and so forth + + + align:start position:0% +commoditize like warrior and so forth +like over time a lot of the times I hear + + align:start position:0% +like over time a lot of the times I hear + + + align:start position:0% +like over time a lot of the times I hear +about people saying blockchain using in + + align:start position:0% +about people saying blockchain using in + + + align:start position:0% +about people saying blockchain using in +this scenario it's mostly on supply + + align:start position:0% +this scenario it's mostly on supply + + + align:start position:0% +this scenario it's mostly on supply +chain given that they're not really + + align:start position:0% +chain given that they're not really + + + align:start position:0% +chain given that they're not really +exchanging it for money are there + + align:start position:0% +exchanging it for money are there + + + align:start position:0% +exchanging it for money are there +actually any commercial cases of use + + align:start position:0% +actually any commercial cases of use + + + align:start position:0% +actually any commercial cases of use +cases of genuine useful points about + + align:start position:0% +cases of genuine useful points about + + + align:start position:0% +cases of genuine useful points about +supply chain being on the blockchain + + align:start position:0% +supply chain being on the blockchain + + + align:start position:0% +supply chain being on the blockchain +I mean tracing where my coffee bean came + + align:start position:0% +I mean tracing where my coffee bean came + + + align:start position:0% +I mean tracing where my coffee bean came +from on a block chaining + + align:start position:0% +from on a block chaining + + + align:start position:0% +from on a block chaining +pretty useless to me that people seem to + + align:start position:0% +pretty useless to me that people seem to + + + align:start position:0% +pretty useless to me that people seem to +like all about it there's a great + + align:start position:0% +like all about it there's a great + + + align:start position:0% +like all about it there's a great +I can trace my thinking for you a coffee + + align:start position:0% +I can trace my thinking for you a coffee + + + align:start position:0% +I can trace my thinking for you a coffee +drinker yes yes not because of your + + align:start position:0% +drinker yes yes not because of your + + + align:start position:0% +drinker yes yes not because of your +clothes no you could turn tea to stay + + align:start position:0% +clothes no you could turn tea to stay + + + align:start position:0% +clothes no you could turn tea to stay +awake in my class to see but I just and + + align:start position:0% +awake in my class to see but I just and + + + align:start position:0% +awake in my class to see but I just and +people keep talking about supply chain + + align:start position:0% +people keep talking about supply chain + + + align:start position:0% +people keep talking about supply chain +needing to be on the blockchain I just + + align:start position:0% +needing to be on the blockchain I just + + + align:start position:0% +needing to be on the blockchain I just +don't understand why I think this + + align:start position:0% +don't understand why I think this + + + align:start position:0% +don't understand why I think this +treatment that's absolutely alright + + align:start position:0% +treatment that's absolutely alright + + + align:start position:0% +treatment that's absolutely alright +you're sold is wait before everybody + + align:start position:0% +you're sold is wait before everybody + + + align:start position:0% +you're sold is wait before everybody +Paulson is it anybody have advice for + + align:start position:0% +Paulson is it anybody have advice for + + + align:start position:0% +Paulson is it anybody have advice for +China Ethiopia trade finance I'm gonna + + align:start position:0% +China Ethiopia trade finance I'm gonna + + + align:start position:0% +China Ethiopia trade finance I'm gonna +give everybody a chance to pile into + + align:start position:0% +give everybody a chance to pile into + + + align:start position:0% +give everybody a chance to pile into +James's question your you're into China + + align:start position:0% +James's question your you're into China + + + align:start position:0% +James's question your you're into China +Ethiopia trade finance I mean what's the + + align:start position:0% + + + + align:start position:0% + +these open firms just have to basically + + align:start position:0% +these open firms just have to basically + + + align:start position:0% +these open firms just have to basically +buy into whatever system firms debates + + align:start position:0% +buy into whatever system firms debates + + + align:start position:0% +buy into whatever system firms debates +have to use letters of credit so now + + align:start position:0% +have to use letters of credit so now + + + align:start position:0% +have to use letters of credit so now +that's a regulation so everything is + + align:start position:0% +that's a regulation so everything is + + + align:start position:0% +that's a regulation so everything is +done completely vandalized right now so + + align:start position:0% +done completely vandalized right now so + + + align:start position:0% +done completely vandalized right now so +we would offer to something very very + + align:start position:0% +we would offer to something very very + + + align:start position:0% +we would offer to something very very +specific like my impressions that would + + align:start position:0% +specific like my impressions that would + + + align:start position:0% +specific like my impressions that would +be easier to get the Ethiopian firms to + + align:start position:0% +be easier to get the Ethiopian firms to + + + align:start position:0% +be easier to get the Ethiopian firms to +buy into this new system where if the + + align:start position:0% +buy into this new system where if the + + + align:start position:0% +buy into this new system where if the +transfer may have multiple options + + align:start position:0% +transfer may have multiple options + + + align:start position:0% +transfer may have multiple options +absolutely both systems of how would you + + align:start position:0% +absolutely both systems of how would you + + + align:start position:0% +absolutely both systems of how would you +approach getting them onto your system + + align:start position:0% +approach getting them onto your system + + + align:start position:0% +approach getting them onto your system +specifically or being able to utilize a + + align:start position:0% +specifically or being able to utilize a + + + align:start position:0% +specifically or being able to utilize a +sewer system so yeah so we agree so + + align:start position:0% +sewer system so yeah so we agree so + + + align:start position:0% +sewer system so yeah so we agree so +would have to get just EQ in businesses + + align:start position:0% +would have to get just EQ in businesses + + + align:start position:0% +would have to get just EQ in businesses +and banks onto the system and so they + + align:start position:0% +and banks onto the system and so they + + + align:start position:0% +and banks onto the system and so they +would be sort of our initial customers + + align:start position:0% +would be sort of our initial customers + + + align:start position:0% +would be sort of our initial customers +and for any Chinese think I want to do + + align:start position:0% +and for any Chinese think I want to do + + + align:start position:0% +and for any Chinese think I want to do +business or export you yoga they have to + + align:start position:0% +business or export you yoga they have to + + + align:start position:0% +business or export you yoga they have to +go through you in May so so it sounds + + align:start position:0% +go through you in May so so it sounds + + + align:start position:0% +go through you in May so so it sounds +like you're trying to build a solution + + align:start position:0% +like you're trying to build a solution + + + align:start position:0% +like you're trying to build a solution +your adoption it's through the importer + + align:start position:0% +your adoption it's through the importer + + + align:start position:0% +your adoption it's through the importer +side through the Ethiopian side + + align:start position:0% +side through the Ethiopian side + + + align:start position:0% +side through the Ethiopian side +initially and then the Chinese exporters + + align:start position:0% +initially and then the Chinese exporters + + + align:start position:0% +initially and then the Chinese exporters +would say well this is how I get into + + align:start position:0% +would say well this is how I get into + + + align:start position:0% +would say well this is how I get into +the Ethiopian market and a more secure + + align:start position:0% +the Ethiopian market and a more secure + + + align:start position:0% +the Ethiopian market and a more secure +maybe more efficient but certainly more + + align:start position:0% +maybe more efficient but certainly more + + + align:start position:0% +maybe more efficient but certainly more +secure way other thoughts on this + + align:start position:0% +secure way other thoughts on this + + + align:start position:0% +secure way other thoughts on this +project + + align:start position:0% + + + + align:start position:0% + +and container companies that wasn't on + + align:start position:0% +and container companies that wasn't on + + + align:start position:0% +and container companies that wasn't on +that it's not this it's not the first + + align:start position:0% +that it's not this it's not the first + + + align:start position:0% +that it's not this it's not the first +one the people no no this is this is one + + align:start position:0% +one the people no no this is this is one + + + align:start position:0% +one the people no no this is this is one +of the most active and it's remained + + align:start position:0% +of the most active and it's remained + + + align:start position:0% +of the most active and it's remained +active mostly permission blockchain + + align:start position:0% +active mostly permission blockchain + + + align:start position:0% +active mostly permission blockchain +technology it's the most active and very + + align:start position:0% +technology it's the most active and very + + + align:start position:0% +technology it's the most active and very +vibrant and you know if you have to say + + align:start position:0% +vibrant and you know if you have to say + + + align:start position:0% +vibrant and you know if you have to say +probability weighted there'll be + + align:start position:0% +probability weighted there'll be + + + align:start position:0% +probability weighted there'll be +something successful in this space more + + align:start position:0% +something successful in this space more + + + align:start position:0% +something successful in this space more +than maybe some of the other spaces so + + align:start position:0% +than maybe some of the other spaces so + + + align:start position:0% +than maybe some of the other spaces so +who wants to chime in to this James's + + align:start position:0% +who wants to chime in to this James's + + + align:start position:0% +who wants to chime in to this James's +supply cherry this unit you're gonna + + align:start position:0% +supply cherry this unit you're gonna + + + align:start position:0% +supply cherry this unit you're gonna +jump in so I just want to tell the + + align:start position:0% +jump in so I just want to tell the + + + align:start position:0% +jump in so I just want to tell the +here's are just two example of some + + align:start position:0% +here's are just two example of some + + + align:start position:0% +here's are just two example of some +shipping and I just pulled up five quick + + align:start position:0% +shipping and I just pulled up five quick + + + align:start position:0% +shipping and I just pulled up five quick +examples of supply chain projects but + + align:start position:0% +examples of supply chain projects but + + + align:start position:0% +examples of supply chain projects but +Eric you want to address James says + + align:start position:0% +Eric you want to address James says + + + align:start position:0% +Eric you want to address James says +caught you like coffee more than James + + align:start position:0% + + + + align:start position:0% + +suddenly you have reports of a sudden + + align:start position:0% +suddenly you have reports of a sudden + + + align:start position:0% +suddenly you have reports of a sudden +infection of equality in a specific + + align:start position:0% +infection of equality in a specific + + + align:start position:0% +infection of equality in a specific +route can you sell us responsible + + align:start position:0% +route can you sell us responsible + + + align:start position:0% +route can you sell us responsible +measure you have to follow dog actually + + align:start position:0% +measure you have to follow dog actually + + + align:start position:0% +measure you have to follow dog actually +has to know which apart which lot of + + align:start position:0% +has to know which apart which lot of + + + align:start position:0% +has to know which apart which lot of +through this is the one affected so + + align:start position:0% +through this is the one affected so + + + align:start position:0% +through this is the one affected so +since the whole process of you don't + + align:start position:0% +since the whole process of you don't + + + align:start position:0% +since the whole process of you don't +begin the huge file of a forward six + + align:start position:0% +begin the huge file of a forward six + + + align:start position:0% +begin the huge file of a forward six +weeks these guys will have to hold up a + + align:start position:0% +weeks these guys will have to hold up a + + + align:start position:0% +weeks these guys will have to hold up a +big bunch of food that eventually I get + + align:start position:0% +big bunch of food that eventually I get + + + align:start position:0% +big bunch of food that eventually I get +most with the you know economical + + align:start position:0% +most with the you know economical + + + align:start position:0% +most with the you know economical +implications of that supply chain for me + + align:start position:0% +implications of that supply chain for me + + + align:start position:0% +implications of that supply chain for me +to a block chain you can allow you + + align:start position:0% +to a block chain you can allow you + + + align:start position:0% +to a block chain you can allow you +quickly get the information + + align:start position:0% +quickly get the information + + + align:start position:0% +quickly get the information +hours and immediately identifies which + + align:start position:0% +hours and immediately identifies which + + + align:start position:0% +hours and immediately identifies which +is the love is being affected take it + + align:start position:0% +is the love is being affected take it + + + align:start position:0% +is the love is being affected take it +out with a decreased you can only cost + + align:start position:0% +out with a decreased you can only cost + + + align:start position:0% +out with a decreased you can only cost +so we've got at least three other hands + + align:start position:0% +so we've got at least three other hands + + + align:start position:0% +so we've got at least three other hands +will go yes James so what I could + + align:start position:0% +will go yes James so what I could + + + align:start position:0% +will go yes James so what I could +critiques of using blockchain for supply + + align:start position:0% +critiques of using blockchain for supply + + + align:start position:0% +critiques of using blockchain for supply +chains for things like blood diamonds or + + align:start position:0% +chains for things like blood diamonds or + + + align:start position:0% +chains for things like blood diamonds or +yeah preventing counterfeit goods or + + align:start position:0% +yeah preventing counterfeit goods or + + + align:start position:0% +yeah preventing counterfeit goods or +whatever diamonds we have to we have to + + align:start position:0% +whatever diamonds we have to we have to + + + align:start position:0% +whatever diamonds we have to we have to +be revived yeah so now these guys if I + + align:start position:0% +be revived yeah so now these guys if I + + + align:start position:0% +be revived yeah so now these guys if I +know these guys for doing that but the + + align:start position:0% +know these guys for doing that but the + + + align:start position:0% +know these guys for doing that but the +criticism I fear this is because these + + align:start position:0% +criticism I fear this is because these + + + align:start position:0% +criticism I fear this is because these +aren't digital native Goods it has to be + + align:start position:0% +aren't digital native Goods it has to be + + + align:start position:0% +aren't digital native Goods it has to be +nice to placed between the real world + + align:start position:0% +nice to placed between the real world + + + align:start position:0% +nice to placed between the real world +and the blockchain to the digital and + + align:start position:0% +and the blockchain to the digital and + + + align:start position:0% +and the blockchain to the digital and +what I've heard from critics is that + + align:start position:0% +what I've heard from critics is that + + + align:start position:0% +what I've heard from critics is that +it's at the point of origin that this + + align:start position:0% +it's at the point of origin that this + + + align:start position:0% +it's at the point of origin that this +fraud or counterfeiting or whatever + + align:start position:0% +fraud or counterfeiting or whatever + + + align:start position:0% +fraud or counterfeiting or whatever +takes place and it's the point of origin + + align:start position:0% +takes place and it's the point of origin + + + align:start position:0% +takes place and it's the point of origin +where that died are introduced to be + + align:start position:0% +where that died are introduced to be + + + align:start position:0% +where that died are introduced to be +takes place anyway so it's garbage in + + align:start position:0% +takes place anyway so it's garbage in + + + align:start position:0% +takes place anyway so it's garbage in +garbage yeah frankly put a counterfeit + + align:start position:0% +garbage yeah frankly put a counterfeit + + + align:start position:0% +garbage yeah frankly put a counterfeit +thing that's but then that passes + + align:start position:0% +thing that's but then that passes + + + align:start position:0% +thing that's but then that passes +through the supply chain so my god I + + align:start position:0% +through the supply chain so my god I + + + align:start position:0% +through the supply chain so my god I +need somebody on the other side of James + + align:start position:0% + + + + align:start position:0% + +Randi zaqqum for example David many etc + + align:start position:0% +Randi zaqqum for example David many etc + + + align:start position:0% +Randi zaqqum for example David many etc +but basically if we were just said like + + align:start position:0% +but basically if we were just said like + + + align:start position:0% +but basically if we were just said like +so there's basically they're using IBM + + align:start position:0% +so there's basically they're using IBM + + + align:start position:0% +so there's basically they're using IBM +infrastructure right if they went to + + align:start position:0% +infrastructure right if they went to + + + align:start position:0% +infrastructure right if they went to +their supply chain and said look guys we + + align:start position:0% +their supply chain and said look guys we + + + align:start position:0% +their supply chain and said look guys we +hired IBM okay now you're gonna send + + align:start position:0% +hired IBM okay now you're gonna send + + + align:start position:0% +hired IBM okay now you're gonna send +every time this this good can transfer + + align:start position:0% +every time this this good can transfer + + + align:start position:0% +every time this this good can transfer +hands you're gonna send that information + + align:start position:0% +hands you're gonna send that information + + + align:start position:0% +hands you're gonna send that information +to IBM that's it I mean basically that's + + align:start position:0% +to IBM that's it I mean basically that's + + + align:start position:0% +to IBM that's it I mean basically that's +what happens because it's being stored + + align:start position:0% +what happens because it's being stored + + + align:start position:0% +what happens because it's being stored +on a server that I'd be like what is + + align:start position:0% +on a server that I'd be like what is + + + align:start position:0% +on a server that I'd be like what is +blockchain about well like I heard them + + align:start position:0% +blockchain about well like I heard them + + + align:start position:0% +blockchain about well like I heard them +how this is about you but I read on + + align:start position:0% +how this is about you but I read on + + + align:start position:0% +how this is about you but I read on +sterling to see what that what what is + + align:start position:0% +sterling to see what that what what is + + + align:start position:0% +sterling to see what that what what is +blockchain e about it I mean she's + + align:start position:0% +blockchain e about it I mean she's + + + align:start position:0% +blockchain e about it I mean she's +basically who wants to take you one sec + + align:start position:0% +basically who wants to take you one sec + + + align:start position:0% +basically who wants to take you one sec +the other side Brahim I know James + + align:start position:0% +the other side Brahim I know James + + + align:start position:0% +the other side Brahim I know James +you're not taking the other side of + + align:start position:0% +you're not taking the other side of + + + align:start position:0% +you're not taking the other side of +James I think this is bit controversial + + align:start position:0% +James I think this is bit controversial + + + align:start position:0% +James I think this is bit controversial +but one of the UK couple years ago there + + align:start position:0% +but one of the UK couple years ago there + + + align:start position:0% +but one of the UK couple years ago there +was some activists talking about the + + align:start position:0% +was some activists talking about the + + + align:start position:0% +was some activists talking about the +origin of weapons and some areas where + + align:start position:0% +origin of weapons and some areas where + + + align:start position:0% +origin of weapons and some areas where +weapons have been smuggled in some war + + align:start position:0% +weapons have been smuggled in some war + + + align:start position:0% +weapons have been smuggled in some war +zones the point of origin in this case + + align:start position:0% +zones the point of origin in this case + + + align:start position:0% +zones the point of origin in this case +would be the developed world which is + + align:start position:0% + + + + align:start position:0% + +and you can trust the data entry not not + + align:start position:0% +and you can trust the data entry not not + + + align:start position:0% +and you can trust the data entry not not +trusted it will be trusted because there + + align:start position:0% +trusted it will be trusted because there + + + align:start position:0% +trusted it will be trusted because there +will be manufacturers and most of the + + align:start position:0% +will be manufacturers and most of the + + + align:start position:0% +will be manufacturers and most of the +manufacturer would be an office I want + + align:start position:0% +manufacturer would be an office I want + + + align:start position:0% +manufacturer would be an office I want +to get Tom and I'm gonna give you + + align:start position:0% +to get Tom and I'm gonna give you + + + align:start position:0% +to get Tom and I'm gonna give you +required yeah I think it works and it + + align:start position:0% +required yeah I think it works and it + + + align:start position:0% +required yeah I think it works and it +sort of goes back to the original + + align:start position:0% +sort of goes back to the original + + + align:start position:0% +sort of goes back to the original +question whether or not this is about + + align:start position:0% +question whether or not this is about + + + align:start position:0% +question whether or not this is about +addressing fraud or addressing the + + align:start position:0% +addressing fraud or addressing the + + + align:start position:0% +addressing fraud or addressing the +efficiency of the system the data entry + + align:start position:0% +efficiency of the system the data entry + + + align:start position:0% +efficiency of the system the data entry +is the same I mean if the data entry + + align:start position:0% +is the same I mean if the data entry + + + align:start position:0% +is the same I mean if the data entry +from a paper system or a non-locking + + align:start position:0% +from a paper system or a non-locking + + + align:start position:0% +from a paper system or a non-locking +digital system or a blockchain system is + + align:start position:0% +digital system or a blockchain system is + + + align:start position:0% +digital system or a blockchain system is +bad then it's always gonna be bad but if + + align:start position:0% +bad then it's always gonna be bad but if + + + align:start position:0% +bad then it's always gonna be bad but if +it's good it's as good as it is right + + align:start position:0% +it's good it's as good as it is right + + + align:start position:0% +it's good it's as good as it is right +now and probably as good as it's going + + align:start position:0% +now and probably as good as it's going + + + align:start position:0% +now and probably as good as it's going +to be short of like RFID chipping every + + align:start position:0% +to be short of like RFID chipping every + + + align:start position:0% +to be short of like RFID chipping every +individual product then what it does is + + align:start position:0% +individual product then what it does is + + + align:start position:0% +individual product then what it does is +allow that same record to go through the + + align:start position:0% +allow that same record to go through the + + + align:start position:0% +allow that same record to go through the +entire supply chain so what is deemed by + + align:start position:0% +entire supply chain so what is deemed by + + + align:start position:0% +entire supply chain so what is deemed by +whatever data input system to be a + + align:start position:0% +whatever data input system to be a + + + align:start position:0% +whatever data input system to be a +conflict diamond is seen by De Beers the + + align:start position:0% +conflict diamond is seen by De Beers the + + + align:start position:0% +conflict diamond is seen by De Beers the +exporter or the producer the the port + + align:start position:0% +exporter or the producer the the port + + + align:start position:0% +exporter or the producer the the port +the ultimate importer of the good and so + + align:start position:0% +the ultimate importer of the good and so + + + align:start position:0% +the ultimate importer of the good and so +you can save what are now verification + + align:start position:0% +you can save what are now verification + + + align:start position:0% +you can save what are now verification +costs in terms of time by processing of + + align:start position:0% +costs in terms of time by processing of + + + align:start position:0% +costs in terms of time by processing of +railway receive fracking receives a + + align:start position:0% +railway receive fracking receives a + + + align:start position:0% +railway receive fracking receives a +shipping receipt forwarding exchange + + align:start position:0% +shipping receipt forwarding exchange + + + align:start position:0% +shipping receipt forwarding exchange +received by making that same document + + align:start position:0% +received by making that same document + + + align:start position:0% +received by making that same document +viewable and immutable to all of the + + align:start position:0% +viewable and immutable to all of the + + + align:start position:0% +viewable and immutable to all of the +partners and shamar's question I think + + align:start position:0% +partners and shamar's question I think + + + align:start position:0% +partners and shamar's question I think +you frame the right question basically + + align:start position:0% +you frame the right question basically + + + align:start position:0% +you frame the right question basically +well why not just a traditional database + + align:start position:0% +well why not just a traditional database + + + align:start position:0% +well why not just a traditional database +iBM is the software provider of hyper + + align:start position:0% +iBM is the software provider of hyper + + + align:start position:0% +iBM is the software provider of hyper +ledger fabric why not just give the + + align:start position:0% +ledger fabric why not just give the + + + align:start position:0% +ledger fabric why not just give the +information to IBM and in fact maybe + + align:start position:0% +information to IBM and in fact maybe + + + align:start position:0% +information to IBM and in fact maybe +that's what Walmart is doing it's now I + + align:start position:0% +that's what Walmart is doing it's now I + + + align:start position:0% +that's what Walmart is doing it's now I +I haven't dog deeply enough and often + + align:start position:0% +I haven't dog deeply enough and often + + + align:start position:0% +I haven't dog deeply enough and often +when you dig into these websites and the + + align:start position:0% +when you dig into these websites and the + + + align:start position:0% +when you dig into these websites and the +news articles and the white papers you + + align:start position:0% +news articles and the white papers you + + + align:start position:0% +news articles and the white papers you +can't quite tell how they're using IBM + + align:start position:0% +can't quite tell how they're using IBM + + + align:start position:0% +can't quite tell how they're using IBM +IBM I think has 1500 people in their + + align:start position:0% +IBM I think has 1500 people in their + + + align:start position:0% +IBM I think has 1500 people in their +division that does hyper ledger + + align:start position:0% +division that does hyper ledger + + + align:start position:0% +division that does hyper ledger +Jax so they they're out there iBM is + + align:start position:0% +Jax so they they're out there iBM is + + + align:start position:0% +Jax so they they're out there iBM is +marketing this but I think the theory at + + align:start position:0% +marketing this but I think the theory at + + + align:start position:0% +marketing this but I think the theory at +least because I'm not going to be able + + align:start position:0% +least because I'm not going to be able + + + align:start position:0% +least because I'm not going to be able +to answer what more Walmart's really + + align:start position:0% +to answer what more Walmart's really + + + align:start position:0% +to answer what more Walmart's really +doing the theory is is it's more + + align:start position:0% +doing the theory is is it's more + + + align:start position:0% +doing the theory is is it's more +censorship resistant that the data is + + align:start position:0% +censorship resistant that the data is + + + align:start position:0% +censorship resistant that the data is +actually shared on multiple nodes even + + align:start position:0% +actually shared on multiple nodes even + + + align:start position:0% +actually shared on multiple nodes even +if it's permissioned even if there's + + align:start position:0% +if it's permissioned even if there's + + + align:start position:0% +if it's permissioned even if there's +only 15 or 20 nodes or 30 nodes that + + align:start position:0% +only 15 or 20 nodes or 30 nodes that + + + align:start position:0% +only 15 or 20 nodes or 30 nodes that +it's more censorship resistant than if + + align:start position:0% +it's more censorship resistant than if + + + align:start position:0% +it's more censorship resistant than if +it's all stored on an IBM server and I + + align:start position:0% +it's all stored on an IBM server and I + + + align:start position:0% +it's all stored on an IBM server and I +don't know the answer whether the + + align:start position:0% +don't know the answer whether the + + + align:start position:0% +don't know the answer whether the +Walmart is actually stored on 30 + + align:start position:0% +Walmart is actually stored on 30 + + + align:start position:0% +Walmart is actually stored on 30 +different nodes but if it were then then + + align:start position:0% +different nodes but if it were then then + + + align:start position:0% +different nodes but if it were then then +arguably then even though it's + + align:start position:0% +arguably then even though it's + + + align:start position:0% +arguably then even though it's +permission and private it's more + + align:start position:0% +permission and private it's more + + + align:start position:0% +permission and private it's more +censorship resistant you can have more + + align:start position:0% +censorship resistant you can have more + + + align:start position:0% +censorship resistant you can have more +assurance around this one of the + + align:start position:0% +assurance around this one of the + + + align:start position:0% +assurance around this one of the +challenges of Viva left the room when + + align:start position:0% +challenges of Viva left the room when + + + align:start position:0% +challenges of Viva left the room when +interoperability is this this number to + + align:start position:0% +interoperability is this this number to + + + align:start position:0% +interoperability is this this number to +translate trade lends the IBM and Marx + + align:start position:0% +translate trade lends the IBM and Marx + + + align:start position:0% +translate trade lends the IBM and Marx +mercs what's how do you pronounce that + + align:start position:0% +mercs what's how do you pronounce that + + + align:start position:0% +mercs what's how do you pronounce that +company mercs it's one of the largest + + align:start position:0% +company mercs it's one of the largest + + + align:start position:0% +company mercs it's one of the largest +it's one of the two or three largest + + align:start position:0% +it's one of the two or three largest + + + align:start position:0% +it's one of the two or three largest +shipping companies in the entire world + + align:start position:0% +shipping companies in the entire world + + + align:start position:0% +shipping companies in the entire world +they come up with a project they + + align:start position:0% +they come up with a project they + + + align:start position:0% +they come up with a project they +announce it tout it is over a year and a + + align:start position:0% +announce it tout it is over a year and a + + + align:start position:0% +announce it tout it is over a year and a +half ago + + align:start position:0% +half ago + + + align:start position:0% +half ago +there's no adoption because the other + + align:start position:0% +there's no adoption because the other + + + align:start position:0% +there's no adoption because the other +shipping companies are saying why do I + + align:start position:0% +shipping companies are saying why do I + + + align:start position:0% +shipping companies are saying why do I +want to adopt something with you + + align:start position:0% +want to adopt something with you + + + align:start position:0% +want to adopt something with you +that'd be one thing if some neutral + + align:start position:0% +that'd be one thing if some neutral + + + align:start position:0% +that'd be one thing if some neutral +standard setter almost like in the + + align:start position:0% +standard setter almost like in the + + + align:start position:0% +standard setter almost like in the +internet the ICANN or something but some + + align:start position:0% +internet the ICANN or something but some + + + align:start position:0% +internet the ICANN or something but some +neutral standard setter came up with a + + align:start position:0% +neutral standard setter came up with a + + + align:start position:0% +neutral standard setter came up with a +consortium but all the other shippers in + + align:start position:0% +consortium but all the other shippers in + + + align:start position:0% +consortium but all the other shippers in +the world say I don't want to give up + + align:start position:0% +the world say I don't want to give up + + + align:start position:0% +the world say I don't want to give up +timorese my data my information and what + + align:start position:0% +timorese my data my information and what + + + align:start position:0% +timorese my data my information and what +might be also market power + + align:start position:0% +might be also market power + + + align:start position:0% +might be also market power +so interoperability works there as well + + align:start position:0% +so interoperability works there as well + + + align:start position:0% +so interoperability works there as well +all right James wants to have a reply + + align:start position:0% +all right James wants to have a reply + + + align:start position:0% +all right James wants to have a reply +but you are holding off all right so + + align:start position:0% +but you are holding off all right so + + + align:start position:0% +but you are holding off all right so +we'll take two from my rug there's + + align:start position:0% +we'll take two from my rug there's + + + align:start position:0% +we'll take two from my rug there's +another issue which is more about the + + align:start position:0% +another issue which is more about the + + + align:start position:0% +another issue which is more about the +economics of it which is okay you + + align:start position:0% +economics of it which is okay you + + + align:start position:0% +economics of it which is okay you +basically right now we can force a lot + + align:start position:0% +basically right now we can force a lot + + + align:start position:0% +basically right now we can force a lot +of budget + + align:start position:0% +of budget + + + align:start position:0% +of budget +and there's real question about and what + + align:start position:0% +and there's real question about and what + + + align:start position:0% +and there's real question about and what +they're gonna do with that data right + + align:start position:0% +they're gonna do with that data right + + + align:start position:0% +they're gonna do with that data right +because essentially what it does it + + align:start position:0% +because essentially what it does it + + + align:start position:0% +because essentially what it does it +allows them access to the end producer + + align:start position:0% +allows them access to the end producer + + + align:start position:0% +allows them access to the end producer +so the production of mangoes is very + + align:start position:0% +so the production of mangoes is very + + + align:start position:0% +so the production of mangoes is very +fragmented right but then you get + + align:start position:0% +fragmented right but then you get + + + align:start position:0% +fragmented right but then you get +consolidated so so there are the + + align:start position:0% +consolidated so so there are the + + + align:start position:0% +consolidated so so there are the +multiple steps along the chain that + + align:start position:0% +multiple steps along the chain that + + + align:start position:0% +multiple steps along the chain that +actually extract economic value not the + + align:start position:0% +actually extract economic value not the + + + align:start position:0% +actually extract economic value not the +growers I mean that kind of screwed + + align:start position:0% +growers I mean that kind of screwed + + + align:start position:0% +growers I mean that kind of screwed +right and but if now Walmart can go + + align:start position:0% +right and but if now Walmart can go + + + align:start position:0% +right and but if now Walmart can go +directly to the growers because now they + + align:start position:0% +directly to the growers because now they + + + align:start position:0% +directly to the growers because now they +have access to the data who the grower + + align:start position:0% +have access to the data who the grower + + + align:start position:0% +have access to the data who the grower +is what the productivity is how much + + align:start position:0% +is what the productivity is how much + + + align:start position:0% +is what the productivity is how much +they produce at what time of the year + + align:start position:0% +they produce at what time of the year + + + align:start position:0% +they produce at what time of the year +that et cetera + + align:start position:0% +that et cetera + + + align:start position:0% +that et cetera +well there's a question about whether + + align:start position:0% +well there's a question about whether + + + align:start position:0% +well there's a question about whether +whether I want to cooperate with that or + + align:start position:0% +whether I want to cooperate with that or + + + align:start position:0% +whether I want to cooperate with that or +how much much I want to share with that + + align:start position:0% +how much much I want to share with that + + + align:start position:0% +how much much I want to share with that +if I'm in the middle and I make sure + + align:start position:0% +if I'm in the middle and I make sure + + + align:start position:0% +if I'm in the middle and I make sure +extracting economic rent right now right + + align:start position:0% +extracting economic rent right now right + + + align:start position:0% +extracting economic rent right now right +so the whole supply chain is that's + + align:start position:0% +so the whole supply chain is that's + + + align:start position:0% +so the whole supply chain is that's +right the data just like Facebook + + align:start position:0% +right the data just like Facebook + + + align:start position:0% +right the data just like Facebook +collects data or visa collects data that + + align:start position:0% +collects data or visa collects data that + + + align:start position:0% +collects data or visa collects data that +maybe Walmart would collect data my + + align:start position:0% +maybe Walmart would collect data my + + + align:start position:0% +maybe Walmart would collect data my +question takes the Walmart example a + + align:start position:0% +question takes the Walmart example a + + + align:start position:0% +question takes the Walmart example a +little bit further I'm curious to + + align:start position:0% +little bit further I'm curious to + + + align:start position:0% +little bit further I'm curious to +understand do you put a supplier early + + align:start position:0% +understand do you put a supplier early + + + align:start position:0% +understand do you put a supplier early +on in the process say a farm or + + align:start position:0% +on in the process say a farm or + + + align:start position:0% +on in the process say a farm or +something selling to Walmart do they + + align:start position:0% +something selling to Walmart do they + + + align:start position:0% +something selling to Walmart do they +even have exposure in terms of the user + + align:start position:0% +even have exposure in terms of the user + + + align:start position:0% +even have exposure in terms of the user +experience that they are on blockchain + + align:start position:0% +experience that they are on blockchain + + + align:start position:0% +experience that they are on blockchain +or does this just become the backend + + align:start position:0% +or does this just become the backend + + + align:start position:0% +or does this just become the backend +no okay I guess I duck been in terms of + + align:start position:0% +no okay I guess I duck been in terms of + + + align:start position:0% +no okay I guess I duck been in terms of +private keys for digital currency I'm + + align:start position:0% +private keys for digital currency I'm + + + align:start position:0% +private keys for digital currency I'm +trying to connect how that ties to the + + align:start position:0% +trying to connect how that ties to the + + + align:start position:0% +trying to connect how that ties to the +user experiment only they have like the + + align:start position:0% +user experiment only they have like the + + + align:start position:0% +user experiment only they have like the +scanners that the Missy scan phones or + + align:start position:0% +scanners that the Missy scan phones or + + + align:start position:0% +scanners that the Missy scan phones or +whatever right so you have third parties + + align:start position:0% +whatever right so you have third parties + + + align:start position:0% +whatever right so you have third parties +using these linkages they don't know + + align:start position:0% +using these linkages they don't know + + + align:start position:0% +using these linkages they don't know +basically where this data is going so + + align:start position:0% +basically where this data is going so + + + align:start position:0% +basically where this data is going so +I'm not gonna take Sherman's description + + align:start position:0% +I'm not gonna take Sherman's description + + + align:start position:0% +I'm not gonna take Sherman's description +of it I'm not as close to the Walmart I + + align:start position:0% +of it I'm not as close to the Walmart I + + + align:start position:0% +of it I'm not as close to the Walmart I +think in the trade finance side that + + align:start position:0% +think in the trade finance side that + + + align:start position:0% +think in the trade finance side that +consortium that these and these the + + align:start position:0% +consortium that these and these the + + + align:start position:0% +consortium that these and these the +importer the export or the bank's the + + align:start position:0% +importer the export or the bank's the + + + align:start position:0% +importer the export or the bank's the +shippers in the best of in the best of + + align:start position:0% +shippers in the best of in the best of + + + align:start position:0% +shippers in the best of in the best of +these are meant to have a lot of + + align:start position:0% +these are meant to have a lot of + + + align:start position:0% +these are meant to have a lot of +involvement and exposure because even + + align:start position:0% +involvement and exposure because even + + + align:start position:0% +involvement and exposure because even +even though this looks pretty + + align:start position:0% +even though this looks pretty + + + align:start position:0% +even though this looks pretty +complicated and that is their large + + align:start position:0% +complicated and that is their large + + + align:start position:0% +complicated and that is their large +institution their bank + + align:start position:0% +institution their bank + + + align:start position:0% +institution their bank +they're shippers their freight + + align:start position:0% +they're shippers their freight + + + align:start position:0% +they're shippers their freight +forwarders except for maybe the small + + align:start position:0% +forwarders except for maybe the small + + + align:start position:0% +forwarders except for maybe the small +medium-sized enterprises in Ethiopia but + + align:start position:0% +medium-sized enterprises in Ethiopia but + + + align:start position:0% +medium-sized enterprises in Ethiopia but +then there are an importer that needs to + + align:start position:0% +then there are an importer that needs to + + + align:start position:0% +then there are an importer that needs to +have involvement I think on the supply + + align:start position:0% +have involvement I think on the supply + + + align:start position:0% +have involvement I think on the supply +chain side the Walmart an individual + + align:start position:0% +chain side the Walmart an individual + + + align:start position:0% +chain side the Walmart an individual +grower of mango I you're saying from + + align:start position:0% +grower of mango I you're saying from + + + align:start position:0% +grower of mango I you're saying from +your understanding Walmart's not looking + + align:start position:0% +your understanding Walmart's not looking + + + align:start position:0% +your understanding Walmart's not looking +for you I guess because I'm - proud of + + align:start position:0% +for you I guess because I'm - proud of + + + align:start position:0% +for you I guess because I'm - proud of +that as proud of the fact that they can + + align:start position:0% +that as proud of the fact that they can + + + align:start position:0% +that as proud of the fact that they can +actually influence the reason why you + + align:start position:0% +actually influence the reason why you + + + align:start position:0% +actually influence the reason why you +know because they have sort of their + + align:start position:0% +know because they have sort of their + + + align:start position:0% +know because they have sort of their +last mile is very simple but they would + + align:start position:0% +last mile is very simple but they would + + + align:start position:0% +last mile is very simple but they would +have to have some way to do with Tom + + align:start position:0% +have to have some way to do with Tom + + + align:start position:0% +have to have some way to do with Tom +said they have to be able to put into + + align:start position:0% +said they have to be able to put into + + + align:start position:0% +said they have to be able to put into +digital form the physical asset the + + align:start position:0% +digital form the physical asset the + + + align:start position:0% +digital form the physical asset the +mangos are from this James you want to + + align:start position:0% +mangos are from this James you want to + + + align:start position:0% +mangos are from this James you want to +reply and then we'll go back to you I + + align:start position:0% +reply and then we'll go back to you I + + + align:start position:0% +reply and then we'll go back to you I +think are you best yet mutability + + align:start position:0% +think are you best yet mutability + + + align:start position:0% +think are you best yet mutability +whether it's a blockchain or a very + + align:start position:0% +whether it's a blockchain or a very + + + align:start position:0% +whether it's a blockchain or a very +secure standard I expanded traditional + + align:start position:0% +secure standard I expanded traditional + + + align:start position:0% +secure standard I expanded traditional +database they are going to be the same + + align:start position:0% +database they are going to be the same + + + align:start position:0% +database they are going to be the same +the digital records is it's fine but in + + align:start position:0% +the digital records is it's fine but in + + + align:start position:0% +the digital records is it's fine but in +the physical world as in in the context + + align:start position:0% +the physical world as in in the context + + + align:start position:0% +the physical world as in in the context +supply chain whether it's from the + + align:start position:0% +supply chain whether it's from the + + + align:start position:0% +supply chain whether it's from the +origin or any other individuals and on + + align:start position:0% +origin or any other individuals and on + + + align:start position:0% +origin or any other individuals and on +the chain all it takes is one bad actor + + align:start position:0% +the chain all it takes is one bad actor + + + align:start position:0% +the chain all it takes is one bad actor +to do something so that this is good but + + align:start position:0% +to do something so that this is good but + + + align:start position:0% +to do something so that this is good but +while traditional record is immutable + + align:start position:0% +while traditional record is immutable + + + align:start position:0% +while traditional record is immutable +your link between the physical and of + + align:start position:0% +your link between the physical and of + + + align:start position:0% +your link between the physical and of +digital is not guaranteed so I still + + align:start position:0% +digital is not guaranteed so I still + + + align:start position:0% +digital is not guaranteed so I still +don't see how a physical commodity can + + align:start position:0% +don't see how a physical commodity can + + + align:start position:0% +don't see how a physical commodity can +be guaranteed to go from one end to the + + align:start position:0% +be guaranteed to go from one end to the + + + align:start position:0% +be guaranteed to go from one end to the +other of the supply chain without ever + + align:start position:0% +other of the supply chain without ever + + + align:start position:0% +other of the supply chain without ever +being tampered or altered that is still + + align:start position:0% +being tampered or altered that is still + + + align:start position:0% +being tampered or altered that is still +a it's like if you take diamonds right + + align:start position:0% +a it's like if you take diamonds right + + + align:start position:0% +a it's like if you take diamonds right +and as long as you like what people care + + align:start position:0% +and as long as you like what people care + + + align:start position:0% +and as long as you like what people care +about when they're buying their diner + + align:start position:0% +about when they're buying their diner + + + align:start position:0% +about when they're buying their diner +just the Argent right but my point is it + + align:start position:0% +just the Argent right but my point is it + + + align:start position:0% +just the Argent right but my point is it +doesn't stop anyone a long supply change + + align:start position:0% +doesn't stop anyone a long supply change + + + align:start position:0% +doesn't stop anyone a long supply change +makes it more expensive + + align:start position:0% + + + + align:start position:0% + +see I think you're holding it up to up + + align:start position:0% +see I think you're holding it up to up + + + align:start position:0% +see I think you're holding it up to up +to higher standard because even the oil + + align:start position:0% +to higher standard because even the oil + + + align:start position:0% +to higher standard because even the oil +let's go back and up diamonds but oil + + align:start position:0% +let's go back and up diamonds but oil + + + align:start position:0% +let's go back and up diamonds but oil +for quite some time you could have a + + align:start position:0% +for quite some time you could have a + + + align:start position:0% +for quite some time you could have a +bill of lading and then sell it and as I + + align:start position:0% +bill of lading and then sell it and as I + + + align:start position:0% +bill of lading and then sell it and as I +mentioned earlier for the twenty days + + align:start position:0% +mentioned earlier for the twenty days + + + align:start position:0% +mentioned earlier for the twenty days +that things are coming from the Mideast + + align:start position:0% +that things are coming from the Mideast + + + align:start position:0% +that things are coming from the Mideast +Houston that might transact twenty times + + align:start position:0% +Houston that might transact twenty times + + + align:start position:0% +Houston that might transact twenty times +a hundred times today in 2018 markets + + align:start position:0% +a hundred times today in 2018 markets + + + align:start position:0% +a hundred times today in 2018 markets +and nobody's actually looking to see + + align:start position:0% +and nobody's actually looking to see + + + align:start position:0% +and nobody's actually looking to see +whether the oil has been somehow + + align:start position:0% +whether the oil has been somehow + + + align:start position:0% +whether the oil has been somehow +siphoned off the ship and it's no longer + + align:start position:0% +siphoned off the ship and it's no longer + + + align:start position:0% +siphoned off the ship and it's no longer +there so there are aspects of trust that + + align:start position:0% +there so there are aspects of trust that + + + align:start position:0% +there so there are aspects of trust that +would still be in the system with + + align:start position:0% +would still be in the system with + + + align:start position:0% +would still be in the system with +somebody certifying when when the ship + + align:start position:0% +somebody certifying when when the ship + + + align:start position:0% +somebody certifying when when the ship +is remember the word but on board when + + align:start position:0% +is remember the word but on board when + + + align:start position:0% +is remember the word but on board when +the oil is put on the ship and it comes + + align:start position:0% +the oil is put on the ship and it comes + + + align:start position:0% +the oil is put on the ship and it comes +off and there's there's validations at + + align:start position:0% +off and there's there's validations at + + + align:start position:0% +off and there's there's validations at +those moments that would then + + align:start position:0% +those moments that would then + + + align:start position:0% +those moments that would then +communicate to the digital records and + + align:start position:0% +communicate to the digital records and + + + align:start position:0% +communicate to the digital records and +you could do that through inspections of + + align:start position:0% +you could do that through inspections of + + + align:start position:0% +you could do that through inspections of +diamonds I don't think you're gonna + + align:start position:0% +diamonds I don't think you're gonna + + + align:start position:0% +diamonds I don't think you're gonna +change that I think that's still gonna + + align:start position:0% +change that I think that's still gonna + + + align:start position:0% +change that I think that's still gonna +be poor but what you can do is leaves + + align:start position:0% +be poor but what you can do is leaves + + + align:start position:0% +be poor but what you can do is leaves +earlier point you can lower a lot of the + + align:start position:0% +earlier point you can lower a lot of the + + + align:start position:0% +earlier point you can lower a lot of the +cost you can drive a lot of efficiency + + align:start position:0% +cost you can drive a lot of efficiency + + + align:start position:0% +cost you can drive a lot of efficiency +and you can probably lower the fraud + + align:start position:0% +and you can probably lower the fraud + + + align:start position:0% +and you can probably lower the fraud +around the documents yeah so I guess + + align:start position:0% +around the documents yeah so I guess + + + align:start position:0% +around the documents yeah so I guess +what I'm saying is the trust isn't there + + align:start position:0% +what I'm saying is the trust isn't there + + + align:start position:0% +what I'm saying is the trust isn't there +in the first place you have to rely on + + align:start position:0% +in the first place you have to rely on + + + align:start position:0% +in the first place you have to rely on +some other trust and what exactly is + + align:start position:0% +some other trust and what exactly is + + + align:start position:0% +some other trust and what exactly is +blockchain adding in terms of the + + align:start position:0% +blockchain adding in terms of the + + + align:start position:0% +blockchain adding in terms of the +physical and the digital records but + + align:start position:0% +physical and the digital records but + + + align:start position:0% +physical and the digital records but +that's what I'm finding difficult online + + align:start position:0% +that's what I'm finding difficult online + + + align:start position:0% +that's what I'm finding difficult online +but I think I finished off with a quick + + align:start position:0% +but I think I finished off with a quick + + + align:start position:0% +but I think I finished off with a quick +point on I speak to someone at the + + align:start position:0% +point on I speak to someone at the + + + align:start position:0% +point on I speak to someone at the +conference of personal mobile since + + align:start position:0% +conference of personal mobile since + + + align:start position:0% +conference of personal mobile since +we're talking oil and he does the supply + + align:start position:0% +we're talking oil and he does the supply + + + align:start position:0% +we're talking oil and he does the supply +chain in implementation of blockchain + + align:start position:0% +chain in implementation of blockchain + + + align:start position:0% +chain in implementation of blockchain +and I challenged him why not users + + align:start position:0% +and I challenged him why not users + + + align:start position:0% +and I challenged him why not users +standardized database and he said well + + align:start position:0% +standardized database and he said well + + + align:start position:0% +standardized database and he said well +it's because if you're gonna get + + align:start position:0% +it's because if you're gonna get + + + align:start position:0% +it's because if you're gonna get +everyone along the chain to upgrade to a + + align:start position:0% +everyone along the chain to upgrade to a + + + align:start position:0% +everyone along the chain to upgrade to a +new system it's far easier by telling + + align:start position:0% +new system it's far easier by telling + + + align:start position:0% +new system it's far easier by telling +them always blockchain rather than + + align:start position:0% +them always blockchain rather than + + + align:start position:0% +them always blockchain rather than +saying + + align:start position:0% +saying + + + align:start position:0% +saying +I'm gonna hold that point oh I'm a great + + align:start position:0% +I'm gonna hold that point oh I'm a great + + + align:start position:0% +I'm gonna hold that point oh I'm a great +at that point but with dam Jake yeah I + + align:start position:0% +at that point but with dam Jake yeah I + + + align:start position:0% +at that point but with dam Jake yeah I +just wanted to say I mean I think this + + align:start position:0% +just wanted to say I mean I think this + + + align:start position:0% +just wanted to say I mean I think this +is weight work feasible for smaller kind + + align:start position:0% +is weight work feasible for smaller kind + + + align:start position:0% +is weight work feasible for smaller kind +of pretty vertical integrated vertically + + align:start position:0% +of pretty vertical integrated vertically + + + align:start position:0% +of pretty vertical integrated vertically +integrated supply chains where like for + + align:start position:0% +integrated supply chains where like for + + + align:start position:0% +integrated supply chains where like for +the beers where like they own every kind + + align:start position:0% +the beers where like they own every kind + + + align:start position:0% +the beers where like they own every kind +of step in the process and therefore you + + align:start position:0% +of step in the process and therefore you + + + align:start position:0% +of step in the process and therefore you +kind of you can you can really trust and + + align:start position:0% +kind of you can you can really trust and + + + align:start position:0% +kind of you can you can really trust and +trace the flow of the product but + + align:start position:0% +trace the flow of the product but + + + align:start position:0% +trace the flow of the product but +something for like a groceries where you + + align:start position:0% +something for like a groceries where you + + + align:start position:0% +something for like a groceries where you +have kind of farmers all over the world + + align:start position:0% +have kind of farmers all over the world + + + align:start position:0% +have kind of farmers all over the world +and either seasonality right changing so + + align:start position:0% +and either seasonality right changing so + + + align:start position:0% +and either seasonality right changing so +there's just so many smaller shops that + + align:start position:0% +there's just so many smaller shops that + + + align:start position:0% +there's just so many smaller shops that +like I can't ever see it being feasible + + align:start position:0% +like I can't ever see it being feasible + + + align:start position:0% +like I can't ever see it being feasible +for them to adopt kind of a high level + + align:start position:0% +for them to adopt kind of a high level + + + align:start position:0% +for them to adopt kind of a high level +technology you might well be right + + align:start position:0% +technology you might well be right + + + align:start position:0% +technology you might well be right +though QR codes have been adopted in + + align:start position:0% +though QR codes have been adopted in + + + align:start position:0% +though QR codes have been adopted in +millions of retail establishments when + + align:start position:0% +millions of retail establishments when + + + align:start position:0% +millions of retail establishments when +twenty years ago it was kind of like + + align:start position:0% +twenty years ago it was kind of like + + + align:start position:0% +twenty years ago it was kind of like +what's this all about + + align:start position:0% +what's this all about + + + align:start position:0% +what's this all about +in fact thirty years ago he's in the + + align:start position:0% +in fact thirty years ago he's in the + + + align:start position:0% +in fact thirty years ago he's in the +news because he just passed away but + + align:start position:0% +news because he just passed away but + + + align:start position:0% +news because he just passed away but +President George Herbert Walker Bush + + align:start position:0% +President George Herbert Walker Bush + + + align:start position:0% +President George Herbert Walker Bush +once some people say part of the reason + + align:start position:0% +once some people say part of the reason + + + align:start position:0% +once some people say part of the reason +he lost the election in 1992 was that he + + align:start position:0% +he lost the election in 1992 was that he + + + align:start position:0% +he lost the election in 1992 was that he +didn't know what a scanner was in a + + align:start position:0% +didn't know what a scanner was in a + + + align:start position:0% +didn't know what a scanner was in a +grocery store and he was president + + align:start position:0% +grocery store and he was president + + + align:start position:0% +grocery store and he was president +United States can you imagine that but + + align:start position:0% +United States can you imagine that but + + + align:start position:0% +United States can you imagine that but +he didn't because he grew up in an era + + align:start position:0% +he didn't because he grew up in an era + + + align:start position:0% +he didn't because he grew up in an era +and it was happening while he was in the + + align:start position:0% +and it was happening while he was in the + + + align:start position:0% +and it was happening while he was in the +White House and now you you couldn't + + align:start position:0% +White House and now you you couldn't + + + align:start position:0% +White House and now you you couldn't +imagine not knowing what a scanner is so + + align:start position:0% +imagine not knowing what a scanner is so + + + align:start position:0% +imagine not knowing what a scanner is so +a dot I agree with you but what's + + align:start position:0% +a dot I agree with you but what's + + + align:start position:0% +a dot I agree with you but what's +happening in 20 years is sometimes hard + + align:start position:0% +happening in 20 years is sometimes hard + + + align:start position:0% +happening in 20 years is sometimes hard +to predict yeah to build on that a + + align:start position:0% +to predict yeah to build on that a + + + align:start position:0% +to predict yeah to build on that a +little bit I think if you are completely + + align:start position:0% +little bit I think if you are completely + + + align:start position:0% +little bit I think if you are completely +vertical then you don't really be + + align:start position:0% +vertical then you don't really be + + + align:start position:0% +vertical then you don't really be +launching in the first place because you + + align:start position:0% +launching in the first place because you + + + align:start position:0% +launching in the first place because you +have your own database you're tracking + + align:start position:0% +have your own database you're tracking + + + align:start position:0% +have your own database you're tracking +everything as it goes through that the + + align:start position:0% +everything as it goes through that the + + + align:start position:0% +everything as it goes through that the +reason you'd bought changes for the + + align:start position:0% +reason you'd bought changes for the + + + align:start position:0% +reason you'd bought changes for the +traceability when you have twenty + + align:start position:0% +traceability when you have twenty + + + align:start position:0% +traceability when you have twenty +different gardens but also when once you + + align:start position:0% +different gardens but also when once you + + + align:start position:0% +different gardens but also when once you +digitize this whole thing I mean right + + align:start position:0% +digitize this whole thing I mean right + + + align:start position:0% +digitize this whole thing I mean right +now it's all paperwork so you you bring + + align:start position:0% +now it's all paperwork so you you bring + + + align:start position:0% +now it's all paperwork so you you bring +it like the doodle ization is and allow + + align:start position:0% +it like the doodle ization is and allow + + + align:start position:0% +it like the doodle ization is and allow +you to use other tools like IOT so you + + align:start position:0% +you to use other tools like IOT so you + + + align:start position:0% +you to use other tools like IOT so you +can maybe use to take the diamond + + align:start position:0% +can maybe use to take the diamond + + + align:start position:0% +can maybe use to take the diamond +example use computer vision to actually + + align:start position:0% +example use computer vision to actually + + + align:start position:0% +example use computer vision to actually +like tell that you have the exact time + + align:start position:0% +like tell that you have the exact time + + + align:start position:0% +like tell that you have the exact time +and you started with at the end of the + + align:start position:0% +and you started with at the end of the + + + align:start position:0% +and you started with at the end of the +supply chain or food + + align:start position:0% +supply chain or food + + + align:start position:0% +supply chain or food +the temperature food and things like + + align:start position:0% +the temperature food and things like + + + align:start position:0% +the temperature food and things like +that you can use remember that stuff + + align:start position:0% +that you can use remember that stuff + + + align:start position:0% +that you can use remember that stuff +that broccoli at the beginning you can + + align:start position:0% +that broccoli at the beginning you can + + + align:start position:0% +that broccoli at the beginning you can +use cryptographic hash is also to take + + align:start position:0% +use cryptographic hash is also to take + + + align:start position:0% +use cryptographic hash is also to take +pictures to take other data about the + + align:start position:0% +pictures to take other data about the + + + align:start position:0% +pictures to take other data about the +diamond other data about the foods + + align:start position:0% + + + + align:start position:0% + +article because we all know to be really + + align:start position:0% +article because we all know to be really + + + align:start position:0% +article because we all know to be really +like what they're the best marketers you + + align:start position:0% +like what they're the best marketers you + + + align:start position:0% +like what they're the best marketers you +know in the world they convinced every + + align:start position:0% +know in the world they convinced every + + + align:start position:0% +know in the world they convinced every +woman that they needed diamonds so I + + align:start position:0% +woman that they needed diamonds so I + + + align:start position:0% +woman that they needed diamonds so I +think like this is the perfect marketing + + align:start position:0% +think like this is the perfect marketing + + + align:start position:0% +think like this is the perfect marketing +ploy to say they needed blockchain for + + align:start position:0% +ploy to say they needed blockchain for + + + align:start position:0% +ploy to say they needed blockchain for +diamonds like the entire like De Beers + + align:start position:0% +diamonds like the entire like De Beers + + + align:start position:0% +diamonds like the entire like De Beers +the entire diamond like industry and how + + align:start position:0% +the entire diamond like industry and how + + + align:start position:0% +the entire diamond like industry and how +they now receive diamonds already + + align:start position:0% +they now receive diamonds already + + + align:start position:0% +they now receive diamonds already +completely regulated and like they + + align:start position:0% +completely regulated and like they + + + align:start position:0% +completely regulated and like they +brought it all in-house and controlled + + align:start position:0% +brought it all in-house and controlled + + + align:start position:0% +brought it all in-house and controlled +by them because the originated diamond + + align:start position:0% +by them because the originated diamond + + + align:start position:0% +by them because the originated diamond +so for me it just seems like a big + + align:start position:0% +so for me it just seems like a big + + + align:start position:0% +so for me it just seems like a big +marketing scheme that you know they + + align:start position:0% +marketing scheme that you know they + + + align:start position:0% +marketing scheme that you know they +already feel like they have this under + + align:start position:0% +already feel like they have this under + + + align:start position:0% +already feel like they have this under +control + + align:start position:0% +control + + + align:start position:0% +control +but in order to they're using you you + + align:start position:0% +but in order to they're using you you + + + align:start position:0% +but in order to they're using you you +land upon a point about marketing and + + align:start position:0% +land upon a point about marketing and + + + align:start position:0% +land upon a point about marketing and +James has said it earlier a little bit + + align:start position:0% +James has said it earlier a little bit + + + align:start position:0% +James has said it earlier a little bit +at all these insure it oil executives + + align:start position:0% +at all these insure it oil executives + + + align:start position:0% +at all these insure it oil executives +says well it's the only way I'm gonna + + align:start position:0% +says well it's the only way I'm gonna + + + align:start position:0% +says well it's the only way I'm gonna +get broad adoption as if I call this + + align:start position:0% +get broad adoption as if I call this + + + align:start position:0% +get broad adoption as if I call this +blockchain and that might be true even + + align:start position:0% +blockchain and that might be true even + + + align:start position:0% +blockchain and that might be true even +of the Australian Stock Exchange even + + align:start position:0% +of the Australian Stock Exchange even + + + align:start position:0% +of the Australian Stock Exchange even +though I think there's a real use case + + align:start position:0% +though I think there's a real use case + + + align:start position:0% +though I think there's a real use case +there but but it's about adoption now De + + align:start position:0% +there but but it's about adoption now De + + + align:start position:0% +there but but it's about adoption now De +Beers might be doing it because they + + align:start position:0% +Beers might be doing it because they + + + align:start position:0% +Beers might be doing it because they +want to sell more diamonds the oil + + align:start position:0% +want to sell more diamonds the oil + + + align:start position:0% +want to sell more diamonds the oil +executive might be doing it because he + + align:start position:0% +executive might be doing it because he + + + align:start position:0% +executive might be doing it because he +just wants to get rid of a legacy system + + align:start position:0% +just wants to get rid of a legacy system + + + align:start position:0% +just wants to get rid of a legacy system +or the Australian Stock Exchange might + + align:start position:0% +or the Australian Stock Exchange might + + + align:start position:0% +or the Australian Stock Exchange might +say this is the only way I can get + + align:start position:0% +say this is the only way I can get + + + align:start position:0% +say this is the only way I can get +investment in in getting rid of a legacy + + align:start position:0% +investment in in getting rid of a legacy + + + align:start position:0% +investment in in getting rid of a legacy +system because I can either scare my + + align:start position:0% +system because I can either scare my + + + align:start position:0% +system because I can either scare my +board of directors and say we have to do + + align:start position:0% +board of directors and say we have to do + + + align:start position:0% +board of directors and say we have to do +blockchain or I can inspire my board of + + align:start position:0% +blockchain or I can inspire my board of + + + align:start position:0% +blockchain or I can inspire my board of +directors by saying I have to use + + align:start position:0% +directors by saying I have to use + + + align:start position:0% +directors by saying I have to use +blockchain but nonetheless blockchain + + align:start position:0% +blockchain but nonetheless blockchain + + + align:start position:0% +blockchain but nonetheless blockchain +technology will have some adoption and I + + align:start position:0% +technology will have some adoption and I + + + align:start position:0% +technology will have some adoption and I +think it will have more adoption so it's + + align:start position:0% +think it will have more adoption so it's + + + align:start position:0% +think it will have more adoption so it's +more ripe for adoption and I'm going to + + align:start position:0% +more ripe for adoption and I'm going to + + + align:start position:0% +more ripe for adoption and I'm going to +turn to this again you know where I'm + + align:start position:0% +turn to this again you know where I'm + + + align:start position:0% +turn to this again you know where I'm +going + + align:start position:0% +going + + + align:start position:0% +going +like yeah yep you know cost and benefits + + align:start position:0% +like yeah yep you know cost and benefits + + + align:start position:0% +like yeah yep you know cost and benefits +these are yeah I'm doing this as a favor + + align:start position:0% +these are yeah I'm doing this as a favor + + + align:start position:0% +these are yeah I'm doing this as a favor +for all of you too because you're all + + align:start position:0% +for all of you too because you're all + + + align:start position:0% +for all of you too because you're all +writing your final projects but it's + + align:start position:0% +writing your final projects but it's + + + align:start position:0% +writing your final projects but it's +really about it's going to be where + + align:start position:0% +really about it's going to be where + + + align:start position:0% +really about it's going to be where +there's multiple parties involved in + + align:start position:0% +there's multiple parties involved in + + + align:start position:0% +there's multiple parties involved in +data and that that data represents some + + align:start position:0% +data and that that data represents some + + + align:start position:0% +data and that that data represents some +property right some either money in addy + + align:start position:0% +property right some either money in addy + + + align:start position:0% +property right some either money in addy +materialized way it's easier to envision + + align:start position:0% +materialized way it's easier to envision + + + align:start position:0% +materialized way it's easier to envision +if it's money versus Security monies + + align:start position:0% +if it's money versus Security monies + + + align:start position:0% +if it's money versus Security monies +versus something dematerialized it's a + + align:start position:0% +versus something dematerialized it's a + + + align:start position:0% +versus something dematerialized it's a +little harder as we've done today on the + + align:start position:0% +little harder as we've done today on the + + + align:start position:0% +little harder as we've done today on the +supply chain when it's against a + + align:start position:0% +supply chain when it's against a + + + align:start position:0% +supply chain when it's against a +physical asset but if there's multiple + + align:start position:0% +physical asset but if there's multiple + + + align:start position:0% +physical asset but if there's multiple +parties and we're verification matters + + align:start position:0% +parties and we're verification matters + + + align:start position:0% +parties and we're verification matters +no verification costs you can probably + + align:start position:0% +no verification costs you can probably + + + align:start position:0% +no verification costs you can probably +drive some efficiency with a blockchain + + align:start position:0% +drive some efficiency with a blockchain + + + align:start position:0% +drive some efficiency with a blockchain +technology solution + + align:start position:0% +technology solution + + + align:start position:0% +technology solution +good question Shimon raises we'll wait a + + align:start position:0% +good question Shimon raises we'll wait a + + + align:start position:0% +good question Shimon raises we'll wait a +minute maybe you're just shipping the + + align:start position:0% +minute maybe you're just shipping the + + + align:start position:0% +minute maybe you're just shipping the +data to IBM are you really shipping it + + align:start position:0% +data to IBM are you really shipping it + + + align:start position:0% +data to IBM are you really shipping it +to just well that's called a traditional + + align:start position:0% +to just well that's called a traditional + + + align:start position:0% +to just well that's called a traditional +database a distributed database or do + + align:start position:0% +database a distributed database or do + + + align:start position:0% +database a distributed database or do +you get something out of censorship + + align:start position:0% +you get something out of censorship + + + align:start position:0% +you get something out of censorship +resistance and if it's truly shared in + + align:start position:0% +resistance and if it's truly shared in + + + align:start position:0% +resistance and if it's truly shared in +twenty thirty fifty or a hundred places + + align:start position:0% +twenty thirty fifty or a hundred places + + + align:start position:0% +twenty thirty fifty or a hundred places +do you lower as the Australian Stock + + align:start position:0% +do you lower as the Australian Stock + + + align:start position:0% +do you lower as the Australian Stock +Exchange really does believe they'll do + + align:start position:0% +Exchange really does believe they'll do + + + align:start position:0% +Exchange really does believe they'll do +lower reconciliation cost which is again + + align:start position:0% +lower reconciliation cost which is again + + + align:start position:0% +lower reconciliation cost which is again +a way to drive efficiency but they're I + + align:start position:0% +a way to drive efficiency but they're I + + + align:start position:0% +a way to drive efficiency but they're I +can't remember the number there seventy + + align:start position:0% +can't remember the number there seventy + + + align:start position:0% +can't remember the number there seventy +seven member companies can all have a + + align:start position:0% +seven member companies can all have a + + + align:start position:0% +seven member companies can all have a +shared ledger and then lower the cost of + + align:start position:0% +shared ledger and then lower the cost of + + + align:start position:0% +shared ledger and then lower the cost of +reconciliation it's still what somewhat + + align:start position:0% +reconciliation it's still what somewhat + + + align:start position:0% +reconciliation it's still what somewhat +controlled those seventy-seven it's not + + align:start position:0% +controlled those seventy-seven it's not + + + align:start position:0% +controlled those seventy-seven it's not +a public blockchain like Bitcoin so + + align:start position:0% +a public blockchain like Bitcoin so + + + align:start position:0% +a public blockchain like Bitcoin so +whether it's the two groups that are + + align:start position:0% +whether it's the two groups that are + + + align:start position:0% +whether it's the two groups that are +that are here today that are doing trade + + align:start position:0% +that are here today that are doing trade + + + align:start position:0% +that are here today that are doing trade +finance and you have a Tartar challenge + + align:start position:0% +finance and you have a Tartar challenge + + + align:start position:0% +finance and you have a Tartar challenge +by the way because you've got to go + + align:start position:0% +by the way because you've got to go + + + align:start position:0% +by the way because you've got to go +beyond this lecture right yeah alpha is + + align:start position:0% +beyond this lecture right yeah alpha is + + + align:start position:0% +beyond this lecture right yeah alpha is +going yeah sure but where if you're + + align:start position:0% +going yeah sure but where if you're + + + align:start position:0% +going yeah sure but where if you're +doing commercial or consumer finance or + + align:start position:0% +doing commercial or consumer finance or + + + align:start position:0% +doing commercial or consumer finance or +real estate or whatever there were some + + align:start position:0% +real estate or whatever there were some + + + align:start position:0% +real estate or whatever there were some +really interesting projects and once you + + align:start position:0% +really interesting projects and once you + + + align:start position:0% +really interesting projects and once you +just thinking about where is that value + + align:start position:0% +just thinking about where is that value + + + align:start position:0% +just thinking about where is that value +add + + align:start position:0% +add + + + align:start position:0% +add +what verification and networking costs + + align:start position:0% +what verification and networking costs + + + align:start position:0% +what verification and networking costs +are going to be lowered what's the + + align:start position:0% +are going to be lowered what's the + + + align:start position:0% +are going to be lowered what's the +competition doing figure out if there's + + align:start position:0% +competition doing figure out if there's + + + align:start position:0% +competition doing figure out if there's +any consortium doing whatever you're + + align:start position:0% +any consortium doing whatever you're + + + align:start position:0% +any consortium doing whatever you're +proposing to do or is there any of the + + align:start position:0% +proposing to do or is there any of the + + + align:start position:0% +proposing to do or is there any of the +three to five thousand white papers we + + align:start position:0% +three to five thousand white papers we + + + align:start position:0% +three to five thousand white papers we +or any ico token and then if you want to + + align:start position:0% +or any ico token and then if you want to + + + align:start position:0% +or any ico token and then if you want to +do a slap down and say why what they're + + align:start position:0% +do a slap down and say why what they're + + + align:start position:0% +do a slap down and say why what they're +doing is foolish and doesn't work and + + align:start position:0% +doing is foolish and doesn't work and + + + align:start position:0% +doing is foolish and doesn't work and +you're doing something better or you + + align:start position:0% +you're doing something better or you + + + align:start position:0% +you're doing something better or you +just want to learn just please don't + + align:start position:0% +just want to learn just please don't + + + align:start position:0% +just want to learn just please don't +plagiarize but just you know look at + + align:start position:0% +plagiarize but just you know look at + + + align:start position:0% +plagiarize but just you know look at +what the competition's doing as well and + + align:start position:0% +what the competition's doing as well and + + + align:start position:0% +what the competition's doing as well and +why isn't a pen only log you know the + + align:start position:0% +why isn't a pen only log you know the + + + align:start position:0% +why isn't a pen only log you know the +right way to go absolutely so you're + + align:start position:0% +right way to go absolutely so you're + + + align:start position:0% +right way to go absolutely so you're +still doing the mortgage product right I + + align:start position:0% +still doing the mortgage product right I + + + align:start position:0% +still doing the mortgage product right I +didn't know if you changed yeah what's + + align:start position:0% +didn't know if you changed yeah what's + + + align:start position:0% +didn't know if you changed yeah what's +happening in the mortgage market how + + align:start position:0% +happening in the mortgage market how + + + align:start position:0% +happening in the mortgage market how +how's it being whether it's securitized + + align:start position:0% +how's it being whether it's securitized + + + align:start position:0% +how's it being whether it's securitized +or or underwritten and whether it's + + align:start position:0% +or or underwritten and whether it's + + + align:start position:0% +or or underwritten and whether it's +traditional database management but but + + align:start position:0% +traditional database management but but + + + align:start position:0% +traditional database management but but +it's also interesting to know if anyone + + align:start position:0% +it's also interesting to know if anyone + + + align:start position:0% +it's also interesting to know if anyone +else is trying to look at either + + align:start position:0% +else is trying to look at either + + + align:start position:0% +else is trying to look at either +permission or permissionless systems and + + align:start position:0% +permission or permissionless systems and + + + align:start position:0% +permission or permissionless systems and +where you fit in to that because you're + + align:start position:0% +where you fit in to that because you're + + + align:start position:0% +where you fit in to that because you're +actually trying to raise money on this + + align:start position:0% +actually trying to raise money on this + + + align:start position:0% +actually trying to raise money on this +if I remember yeah so so to the extent + + align:start position:0% +if I remember yeah so so to the extent + + + align:start position:0% +if I remember yeah so so to the extent +you're gonna raise money those venture + + align:start position:0% +you're gonna raise money those venture + + + align:start position:0% +you're gonna raise money those venture +capitalists are gonna be asking tougher + + align:start position:0% +capitalists are gonna be asking tougher + + + align:start position:0% +capitalists are gonna be asking tougher +questions that I'll ever be asking yeah + + align:start position:0% +questions that I'll ever be asking yeah + + + align:start position:0% +questions that I'll ever be asking yeah +I got it you want cheap money you want + + align:start position:0% +I got it you want cheap money you want + + + align:start position:0% +I got it you want cheap money you want +me to be the Tuffy yeah all right and + + align:start position:0% +me to be the Tuffy yeah all right and + + + align:start position:0% +me to be the Tuffy yeah all right and +you know what are the trade-offs + + align:start position:0% +you know what are the trade-offs + + + align:start position:0% +you know what are the trade-offs +I'm not asking any of you to solve + + align:start position:0% +I'm not asking any of you to solve + + + align:start position:0% +I'm not asking any of you to solve +scalability and performance some of the + + align:start position:0% +scalability and performance some of the + + + align:start position:0% +scalability and performance some of the +scalability performance issues won't be + + align:start position:0% +scalability performance issues won't be + + + align:start position:0% +scalability performance issues won't be +solved for five or ten years but at + + align:start position:0% +solved for five or ten years but at + + + align:start position:0% +solved for five or ten years but at +least note though let me say hey this + + align:start position:0% +least note though let me say hey this + + + align:start position:0% +least note though let me say hey this +won't work until this is solved or + + align:start position:0% +won't work until this is solved or + + + align:start position:0% +won't work until this is solved or +something like that Thursday we're gonna + + align:start position:0% +something like that Thursday we're gonna + + + align:start position:0% +something like that Thursday we're gonna +do identity I can't remember is anybody + + align:start position:0% +do identity I can't remember is anybody + + + align:start position:0% +do identity I can't remember is anybody +doing projects on identity that's you're + + align:start position:0% +doing projects on identity that's you're + + + align:start position:0% +doing projects on identity that's you're +together right you're yeah all right be + + align:start position:0% +together right you're yeah all right be + + + align:start position:0% +together right you're yeah all right be +ready to chat on Thursday and share + + align:start position:0% +ready to chat on Thursday and share + + + align:start position:0% +ready to chat on Thursday and share +share where you are Kelly's looking like + + align:start position:0% +share where you are Kelly's looking like + + + align:start position:0% +share where you are Kelly's looking like +you're gonna be sick on Thursday + + align:start position:0% +you're gonna be sick on Thursday + + + align:start position:0% +you're gonna be sick on Thursday +and yo we here and how many of you are + + align:start position:0% +and yo we here and how many of you are + + + align:start position:0% +and yo we here and how many of you are +going to get your MIT diploma on a + + align:start position:0% +going to get your MIT diploma on a + + + align:start position:0% +going to get your MIT diploma on a +blockchain oh you mean you think you + + align:start position:0% +blockchain oh you mean you think you + + + align:start position:0% +blockchain oh you mean you think you +have to so it's done for you all right + + align:start position:0% +have to so it's done for you all right + + + align:start position:0% +have to so it's done for you all right +there you go + + align:start position:0% +there you go + + + align:start position:0% +there you go +what's that you excited by that do you + + align:start position:0% +what's that you excited by that do you + + + align:start position:0% +what's that you excited by that do you +think you can finance off of it though + + align:start position:0% +think you can finance off of it though + + + align:start position:0% +think you can finance off of it though +so trade finance 17 trillion dollars + + align:start position:0% +so trade finance 17 trillion dollars + + + align:start position:0% +so trade finance 17 trillion dollars +it's a real very significant role that + + align:start position:0% +it's a real very significant role that + + + align:start position:0% +it's a real very significant role that +financing this 17 trillion dollars of + + align:start position:0% +financing this 17 trillion dollars of + + + align:start position:0% +financing this 17 trillion dollars of +trade lots of people involved sort of + + align:start position:0% +trade lots of people involved sort of + + + align:start position:0% +trade lots of people involved sort of +ripe for blockchain technology a lot of + + align:start position:0% +ripe for blockchain technology a lot of + + + align:start position:0% +ripe for blockchain technology a lot of +consortiums and projects under the way + + align:start position:0% +consortiums and projects under the way + + + align:start position:0% +consortiums and projects under the way +underway but they're almost all + + align:start position:0% +underway but they're almost all + + + align:start position:0% +underway but they're almost all +permission systems with a couple of + + align:start position:0% +permission systems with a couple of + + + align:start position:0% +permission systems with a couple of +exceptions but it feels like it's a + + align:start position:0% +exceptions but it feels like it's a + + + align:start position:0% +exceptions but it feels like it's a +catalyst for change I think that even if + + align:start position:0% +catalyst for change I think that even if + + + align:start position:0% +catalyst for change I think that even if +it's just simply because it's the way to + + align:start position:0% +it's just simply because it's the way to + + + align:start position:0% +it's just simply because it's the way to +get adoption and I'm talking about trade + + align:start position:0% +get adoption and I'm talking about trade + + + align:start position:0% +get adoption and I'm talking about trade +finance and then there's this related + + align:start position:0% +finance and then there's this related + + + align:start position:0% +finance and then there's this related +part of the supply chain management and + + align:start position:0% +part of the supply chain management and + + + align:start position:0% +part of the supply chain management and +so forth any other questions are we + + align:start position:0% +so forth any other questions are we + + + align:start position:0% +so forth any other questions are we +breaking early but you want anything all + + align:start position:0% +breaking early but you want anything all + + + align:start position:0% +breaking early but you want anything all +right we'll break early great + + align:start position:0% +right we'll break early great + + + align:start position:0% +right we'll break early great +[Applause] \ No newline at end of file diff --git a/Eqom7VcaEKI.txt b/Eqom7VcaEKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..999924764139dfd21a4caa4878e2b76a9da0de0d --- /dev/null +++ b/Eqom7VcaEKI.txt @@ -0,0 +1,1445 @@ +Today is my last class with you. Awe, I'm sorry, too. You guys are + +a lot of fun. This has actually been the most interactive 7. + +1 I've ever had. Usually there are a couple of people who perk up and + +say things, but you guys are great because all sorts of people are + +willing to contribute. So, I've had a wonderful time and + +it certainly seems like you guys have learned a lot. + +What I'd like to do for my last lecture is pick up again a little + +bit like I did with genomics and try to give you a sense of where + +things are going. I always like doing this because I + +get to talk about things that are in none of the textbooks that, + +well, I mean, it's just stuff that many people working in the field + +don't necessarily know. And that's what's so much fun about + +teaching introductory biology is because it only takes a semester for + +you guys to get up to the point of at least being able to understand + +what's getting done on the cutting-edge. + +Even if you might not yet be able to go off and practice it, + +you might need a little more experience for that, + +but you'd be surprised, it's not that much more. + +Take maybe Project Lab and you'll be able to start doing it already. + +It's really wonderful that it's possible to grasp what's going on. + +And, in many ways, you guys may have an advantage in grasping what's + +going on because, as I've already hinted, + +biology's undergoing this remarkable transformation from being a purely + +laboratory-based science where each individual works on his or her own + +project to being an information-based science that + +involves an integration of vast amounts of data across the whole + +world and trying to learn things from this tremendous dataset. + +And, in that sense, I think the new students coming into + +the field have a distinct advantage over those who have been in it. + +And certainly the students who know mathematical and physical and + +chemical and other sorts of things, and aren't scared to write computer + +code when they need to write computer code have a really + +great advantage. So, anyway, all that by way of + +introduction. I want to talk about two subjects today of great interest + +to me. One is DNA variation and one is RNA variation. + +The variation of DNA sequence between individuals within a + +population, and in particular our population, and the other is RNA + +variation, the variation in RNA expression between different cell + +types, different tissues. And the work I'm going to talk + +about today is work that I, and my colleagues, have all been + +involved in. And it's stuff I know and love. + +So, feel free to ask questions about it. I may know the answers, + +but what's reasonably fun about these lectures is if I don't know + +the answers it's probably the case that the answers aren't known. + +So, that's good fun because it's stuff I really do know well, + +and I love. So, anyway, here's some DNA sequence. It's pretty boring. + +This is a chunk of sequence from, let's say, the human genome. + +How much does this differ between any two individuals? + +If I were to sequence any two chromosomes, any two copies of the + +chromosome from an individual in this class or two individuals on + +this planet, how much would they differ? The answer is that much. + +That's the average amount of difference between any two people on + +this planet. Not a lot. If you counted up, it is on average + +one nucleotide difference out of 1, 00 nucleotides on average, somewhat + +less than one part in 1, 00 or better than 99.9% identity + +between any two individuals. Now, that is a very small amount, + +not just in absolute terms, 99.9% identity is a lot, + +but in comparative terms with other species. If I take two chimpanzees + +in Africa, on average they will differ by about twice as much as any + +two random humans. And if I take two orangutans in + +Southeast Asia, they will on average differ by about + +eight times as much as any two humans on this planet. + +You guys think the orangutans all look the same. + +They think you all look the same, and they're right. So, why is this? + + Why are humans amongst mammalian + +species relatively limited in the amount of variation? + +Well, it's a direct result of our population history. + +It turns out that the amount of variation that can be sustained in a + +population depends on two things. At equilibrium, if population has + +constant size N for a very long time and a certain mutation rate, + +Mu, you can just write a piece of arithmetic that says, + +well, mutations are always arising due to new mutations in the + +population and mutations are being lost by genetic drift, + +just by random sampling from generation to generation. + +And those two processes, the creation of new mutations and + +the loss of mutations just due to random sampling in each generation, + +sets up an equilibrium, and the equilibrium defines an equation + +there, Pi equals one over one plus four and Mu reciprocal which + +equation you have no need to memorize whatsoever and possibly + +even no need to write down. The important point is the concept, + +that if you know the number of organisms in the population and you + +know the mutation rate, those set up the bounds of mutation + +and drift, and you can write down how polymorphic, + +how heterozygous random individuals should be at equilibrium. + +That is if the population has been at size N for a very long time. + +Well, the expected amount of heterozygosity for the + +human population -- Sorry. For a population of size 10, + +00 would be about one nucleotide in 1300. We have exactly the amount of + +heterozygosity you would expect for a population of about 10, + +00 individuals. Yeah, but wait, we're not a population of 10,000 + +individuals. Why do we have the heterozygosity you would expect from + +a population of 10, 00 individuals? We're six billion. + + It's a reflection of our history. + +Because remember I said that was the statement about what the + +population heterozygosity should be at equilibrium? + +We haven't been six billion people except very recently. + +The human population has undergone an exponential expansion. + +It used to be a relatively small size, and then it very recently + +underwent this huge exponential expansion. If you actually write + +down the equations, the amount of variation in our + +population was determined by that constant size for a very long time. + +And then a rapid exponential expansion that's basically taken + +place in a mere 3, 00 generations, it's much too rapid + +to have any affect on the real variation in our population. + +What do I mean by that? What's the mutation rate per nucleotide in the + +human genome? It's on the order of two times ten to the minus eighth + +per generation. In a mere 3,000 generations, + +a tiny mutation rate like two times ten to the minus eighth is not going + +to be able to build up much more variation. + +So you might as well ignore the last 100,000 years or so. + +They're irrelevant to how much variation we have. + +The variation we have was set by our ancestral population size. + +Now, don't get me wrong. Eventually it will equilibrate. + +A couple million years from now we will have a much higher variation in + +the human population as a function of our size, but the population + +variation we have today is set by the fact that humans derive from a + +founding population of about 10, 00 individuals or so. + +And that means that the variation that you see in the human population + +is mostly ancestral variations, the variation that we all walked + +around with in Africa. And, in fact, that makes a + +prediction. That would say that if most of the variation in the human + +population is from the ancestral African founding population then if + +I go to any two villages around this world, in Japan or in Sweden or in + +Nigeria, the variance that I see will largely be identical. + +And that prediction has been well satisfied. + +Because when you go and look and you collect variation in Japan or Sweden + +or Africa and you compare it, 90% of the variance are common + +across the entire world. Most variation is common ancestral + +variation around the world, and only a minority of the variance + +are new local mutations restricted to individual populations. + +This is so contrary to what people think because there's a natural + +tendency to kind of xenophobia, to imagine that world populations + +are very different in their genetic background. + +But, in point of fact, they're extremely similar. + +So, anyway, there's a limited amount of variation. + +That's why we have such little variation in the human population. + +Now, that variation, humans have a low rate of genetic variation. + +Most of the variance that are out there are due to common genetic + +variance, not rare variance. If I take your genome and I find a + +site of genetic variation at the point of heterozygosity in your + +genome, what's the probability that somebody else in this class also is + +heterozygous for that spot? It turns out that the odds are about + +95% that someone else in this class will also share that variance. + +So that the variance are not mostly rare, they're mostly common. + +And it turns out that some of this common variation, + +that is most of this variation is likely to be important in the risk + +of human genetic diseases. So human geneticists have gotten + +very excited about the following paradigm. + +If there's only a limited amount of genetic variation in the human + +population, actually, if you do the arithmetic, + +there are only about ten million sites of common variation in the + +human population, where common might be defined as + +more than about 1% in the population. There are only ten million sites. + +Folks are saying, well, why not enumerate them all? + +Let's just know them all, and then let's test each one for its + +risk of, say, confirming susceptibility of diabetes or heart + +disease or whatever? After all, ten million is not as + +big a number as it used to be. We now have the whole sequence of + +the human genome. Why not layer on the sequence of + +the human genome all common human genetic polymorphism? + +Now, that's a fairly outrageous idea but could be a very useful one. + +Some of these variance are important, by the way. + +We know that there are two nucleotides that vary in the gene + +apolipoprotein E on chromosome number 19. Apolipoprotein E is also + +an apolipoprotein like we talked about before with familiar + +hypercholesterolemia. But, in fact, it turns out that + +apolipoprotein E is expressed in the brain. And it turns out, + +amongst other tissues, that it comes in three variances, + +the spelling T-T, T-C and C-C at those two particular spots. + +And if you happen to be homozygous for the E4 variant, + +homozygous for the E4 variant, you have about a 60% to 70% lifetime + +risk of Alzheimer's disease. In this class 13 of you are + +homozygous for E4 and have a high lifetime risk of Alzheimer's. + +And it would be fairly trivial to go across the street to anybody's + +lab and test that. Now, I don't particular recommend + +it, and I haven't tested myself for this variant because there happens + +to be no particular therapy available today to delay the onset + +of Alzheimer's disease. And, therefore, + +I don't recommend finding out about that. But a number of + +pharmaceutical companies, knowing that this is a very + +important gene in the pathogenesis of Alzheimer's disease, + +are working on drugs to try to delay the pathogenesis using this + +information. And it may be the case that five or ten years from now + +people will begin to offer drugs that will delay the onset of + +Alzheimer's disease by delaying the interaction of apolipoprotein E with + +a target protein called towe, etc. So, this is an example of where a + +common variant in the population points us to the basis of a common + +disease and has important therapeutic implications. + +There are some other ones, for example. 5% of you carry a + +particular variant in your factor 5 gene which is the clotting cascade. + +It's called the leiden variant. Those 5% of you are going to account + +for 50% of the admissions to emergency rooms for deep venous + +clots, for example. The much higher risk of deep venous + +clots. And, in particular, + +there are significant issues if you have that variant and you are a + +woman with taking birth control pills. Some of you were at higher + +risk for diabetes, type 2 adult onset diabetes. + +There's a particular variant in the population that increased your risk + +for type 2 diabetes by about 30%. 85% of you have the high-risk + +factor, so you might as well figure you do. + +15% of you have a lower risk, et cetera. And one I'm particularly + +interested in here, it turns out that HIV virus gets + +into cells with a co-receptor encoded by a gene called CCR5. + +Well, it turns out that if we go across the European population, + +10% of all chromosomes of European ancestry have a deletion + +within the CCR5 gene. If 10% of all chromosomes have that + +deletion then 10% times 10%, 1% of all individuals are homozygous + +for that deletion. Those individuals are essentially + +immune to infection from HIV. They are not susceptible. It's not + +through immunity, it's through lack of a receptor. + +Yes? You certainly can. It's not hard. It's a specific known variant. + +You could test for it. Absolutely. + +Now, of course, that only helps the 1% of people who + +have that variant. But what it did do was point to the + +pharmaceutical industry that the interaction between the virus and + +that variant is essential. And now companies are developing + +drugs to block the interaction with that particular protein. + +And that tells you that it's an important protein. Yes? + + Over the whole world? + +I just specified European population for that one. + +That one, interestingly, is not found at as high a frequency + +outside of Europe, and no one knows why, + +whether that might have been due to an ancient selective event or a + +genetic drift. By contrast, the apolipoprotein E + +variant, at that frequency of about 3% of people being homozygous and + +being at risk for Alzheimer's, is about the same frequency + +everywhere in the world. So, there's a little bit of + +population variation in frequency. Now, the HIV variant is found + +elsewhere but at considerably lower frequencies there. + +And that's an interesting question as to what causes that variation. + +So the notion would be, I've given you a couple of interesting examples, + +but, look, there's only ten million variants. Just write them all down. + +Make one big Excel spreadsheet with ten million variants along the top + +and all the diseases along the rows, and let's just fill in the matrix + +and then we'll really, you know, this is the way people + +think in a post-genomic era. Now, could you do something like + +that? You would have to enumerate all of the single nucleotide + +polymorphisms, or SNPs we call them, + +single nucleotide polymorphisms. Now, to give you an idea of the + +magnitude of this problem, as recently as 1998, the number of + +SNPs that were known in the human genome was a couple hundred. + +But then a project has taken off. In 1998 an initial SNP map of the + +human genome was built here at MIT that had about 4, + +00 of these variants. Then within the next year or so an + +international consortium was organized here and elsewhere to + +begin to collect more of these genetic variants. + +The goal was going to be to find 300, 00 of them within a period of two + +years. In fact, that goal was blown away and within + +three years two million of the SNPs in the human population were found. + +And as of today, if you go on the Web, you'll find the database with + +about 7.8 million of the roughly ten million SNPs in the human population + +already known. Now, that isn't all ten million. + +And it takes a while to collect the last ones, you know, + +collecting the last ones are hard, but we're already the hump of + +knowing the majority of common variation in the human population. + +Not just a sequence of the genome, but a database that already contains + +more than half of all common variation in the population. + +So, we could start building that Excel spreadsheet. + +Now, it turns out that it's even a little bit better than that because + +if we look at many chromosomes in the population, + +here are chromosomes in the population, it turns out that the + +common variance on each of those chromosomes tend to be correlated + +with each other. If I know your genotype at one + +variant, like over at this locus, I know your genotype at the next + +locus with reasonably high probability. There's a lot of local + +correlation. So, instead of looking like a scattered + +picture like that, it's more like this. + +If I know that you're red, red, red you're probably red, + +red, red over here. In other words, these variations occur in blocks + +that we called haplotypes. Here's real data. + +Across 111 kilobases of DNA there's a bunch of variants, + +but it turns out that the variants come in two basic flavors. + +98% of all chromosomes are either this, this, this, + +this, this or this, this, this, this, this. + +Then there tends to be sites of recombination that are actually + +hotspots of recombination where most of the recombination of the + +population is concentrated. And you get a couple of + +possibilities here. So, the human genome can kind of be + +broken up into these haplotypes. Blocks that might be 20, + +30, 40, sometimes 100 kilobases long in which within the block you tend + +to have a small number of haplotypes, or flavors as you might think of + +them, that define most of the chromosomes in the population. + +So, in fact, I don't actually need to know all the variants. + +If they're so well correlated within a block, + +if I knew this block structure I would be able to pick a small number + +of SNPs that would serve as a proxy for that entire block of inheritance + +in the population. So, what you might want to do is + +determine that entire haplotype block structure of hwo they're + +related to each other, and pick out tag snips. + +And it turns out that in theory, a mere 300,000 or so of them would + +suffice to proxy for most of the genome. So, you might want to + +declare an international project, and international haplotype map + +project to create a haplotype map of the human genome. + +And indeed, such a project was declared about a year and a half ago + +through some instigation of scientists and a number of places, + +including here. And this is $100 million project + +involving six different countries. And, it is already more than + +halfway done with the task, and it's very likely that by the + +middle of next year, we will have a pretty good haplotype + +map, not just knowing all the variation, but knowing the + +correlation between that variation, being able to break up the genome + +into these blocks. By the next time I teach 701, + +I should be able to show a haplotype map of the whole human genome + +already. That will allow you to start undertaking systematic studies + +of inheritance for different diseases across populations. + +And in fact, people are already doing things like that. + +Here's an example of a study done here at MIT like this, + +where to study inflammatory bowel disease, there was evidence that + +there might be a particular region of the genome that contained it, + +and haplotypes were determined across this, and blah, + +blah, blah, blah, blah, blah, blah. And this red haplotype + +here turns out to confer high risk, about a two and a half or higher + +risk of inflammatory bowel disease. + +And it sits over some genes involved in immune responses, + +certain cytokine genes and all that. And, things like this have been + +done for type 2 diabetes, schizophrenia, cardiovascular + +disease, just right now at the moment, a dozen or two examples. + +But I think we're set for an explosion in this kind of work. + +In addition, you can use this information to do things beyond + +medical genetics. You can use it for history and + +anthropology as well. It turns out rather interestingly, + +that since the human population originated in Africa and spread out + +from Africa all the way around the world arriving at different places + +in different times, you can trace those migrations by + +virtue of rare genetic variants that arose along the way, + +and let you, like a trail of break crumbs, see the migrations. + +So, for example, there are certain rare genetic variants that we can + +see in a South American Indian tribe, and we can actually see that they + +came along this route because we can see that residual of that. + +In fact, we can do things with this like take a look at Native American + +individuals and determine that they cluster into three distinct genetic + +groups that represent three distinct migrations over the land bridge. + +And, you can assign them to these different migrations. + +You can do this on the basis of mitochondrial genotype, + +etc. You can also, for example, determine when people talk about the + +out of Africa migration, there's now increasing evidence that + +there really were two, one that went this way over the land, + +and one that went this way following along the coast into southeast Asia. + +And, it looks like we're now beginning to get enough evidence of + +these two separate migrations by virtue of the genetic breadcrumbs + +that they have left along the way. + +So, it's really a very fascinating thing of how much you can + +reconstruct from looking at genetic variation, both the common variation + +that allows us to recognize medical risk, and the rare genetic variation + +that provides much more individual trails of things. + +None of this is perfect yet. There's lots to learn. But I think + +anthropologists are finding that the existing human population has a + +tremendous amount of its own history embedded in pattern of genetic + +variation across the world. You can do other things. + +I won't spend much time on this. Well, I'll take a moment on this, + +right? There's some very interesting work of a post-doctoral + +fellow here at MIT named Pardese Sebetti who has been trying to ask, + +can we see in the genetic variation in the population, + +signatures, patterns of ancient selection, or even recent selection + +in the human population? Now, hang onto your seats, + +because this will get just slightly tricky. + +But, hang on. It's only a couple of slides. Here was her idea. + +You see, when a mutation arises in the population, + +it usually dies out, right? Any new mutation just + +typically dies out. But, sometimes by chance it drifts + +up to a high frequency. Random events happen. But it + +usually takes a long time to do that. If some random mutation happens, + +and it happens to drift up to high frequency with no selection on it, + +then on average it takes a long time to do so. + +If you want, I could write a stochastic differential equation + +that would say that, but just take your gut feeling that + +if something has no selection on it and it's a rare event that'll drift + +up, when it drifts up it's kind of a slow process. It was a slow process. + +Then over the course of time that it took to drift to high frequency, + +a lot of genetic recombination would have had to have occurred many + +generations. And the correlation between the genotype at that spot + +and genotypes at other loci would break down. + +And there would only be short-range correlation. So, + +in other words, the amount of correlation between knowing the + +genotype here and the genotype here, maybe allele A here and a C here. + +That is an indication of time. It's a clock almost. It's like + +radioactive decay, right, that genetic recombination + +scrambles up the correlations. And, if something's old, the + +correlations go over short distances. But suppose that something happened. + +Some mutation happened that was very advantageous. + +Then, it would have risen to high frequency quickly because it was + +under selection. If it did so quickly, + +then the long-range correlations would not have had time to break + +down, and we'd have a smoking gun. A smoking gun would be that there + +would be a long-range correlation around that locus, + +much longer than you would expect across the genome. + +Things even out of this distance would show correlation with that, + +indicating that this was a recent event. + +So, we just measure across the genome, and look for this telltale + +sign of common variance that have very long range correlation that + +indicate that they're very recent. So, a plot of the allele frequency, + +common variance, sorry, if something has a common high frequency and + +long-range correlation, you wouldn't expect that by chance. + + So, something that was common in its + +frequency and had long-range correlation would be a signature of + +positive selection. So anyway, Pardise had this idea, + +and she tried it out with some interesting mutations, + +some mutations that confer resistance to malaria, + +one well-known mutation causing resistance to malaria called G6 PD + +and another one that she herself had proposed as a mutation causing + +resistance to malaria, variants in the CD4 ligand gene. + +And to make a long story short, both the known and her newly + +predicted variant showed this telltale property of having a high + +frequency and very long range correlation. + +Well that's very interesting because she was able to show that each of + +these mutations probably were the result of positive selection. + +But what you could do in principle is test every variant in the human + +genome this way: take any variant, look at its frequency, and compare + +it to the long range correlation around it, and test every single + +variant in the human population to see which ones might be the result + +of long range correlation. Now, when she proposed this, + +this was about a year and a half ago or two years ago, + +this was a pretty nutty idea because you would need all the variants in + +the human population, and you would need all this + +correlation information. But in fact, as I say, that + +information's almost upon us, and I believed that this experiment, + +this analysis to look for all strong positive selection in the human + +genome will in fact be done in the course of the next 12 months. + +So, I'm hoping by next year I can actually report on a genome-wide + +search for all the signatures of positive selection. + +Now, this doesn't detect all positive selection. + +It will detect sufficiently strong positive selection going back pretty + +much only over the 10, 00 years. When you do the + +arithmetic, that's how much power you have. Of course, + +10,000 years has been a pretty interesting time for the human + +population, right? The time of civilization and + +population density, and infectious diseases, + +and all that, and I think we'll have an interesting window into + +the change in diet. All of that should come out of + +something like this. So, there's a lot of really cool + +information in DNA variation to be had. All right, + +that's one half. The other half of what I would like to talk about is + +totally different. It's not about inherited DNA + +variation. It's about somatic differences between tissues in RNA + +variation. So, let's shift gears. + +RNA variation: let me start by giving you an example here. + +These are cells from two different patients with acute leukemia. + +Can you spot the difference between these? Yep? More like bunches of + +grapes and all that. Yeah, it turns out that's just a + +reflection of the field of view you have if you move over + +to look like that. But I mean, that's good. + +It's just that it turns out that that isn't actually a distinction + +when you look at more fields. Anything else? Yep? White blood + +cells like different. They look broken. There's more of + +them in this field of view. But you look at 100 fields of view + +and it turns out that's not either. Well, the reason you're having + +trouble spotting any difference is that highly trained pathologists + +can't find any difference either. I generally agree there's no + +difference between these two if you look at enough fields of view. + +But you can convince yourself if you look that you see things there. + +But these actually are two very different kinds of leukemia. + +And, these patients have to be treated very differently. + +But, pathologists cannot determine which leukemia it is just by looking + +at the microscope, it turns out. This is the work of this man, + +Sydney Farber, namesake of the Dana Farber Cancer Institute here in + +Boston, who in the 1950s began noticing that patients with + +leukemias, some of them seemed different in the way they responded + +to a certain treatment, and he said, look, I think there's + +some underlying classification of these leukemias, + +but I can't get any reliable way to tell it in the microscope. + +And he put many years into working this out, first by noticing certain + +difference in enzymes in the cells, and then people noticed certain + +things in cell surface markers, and some chromosomal rearrangements. + +And nowadays, there are a bunch of test that can be done by a + +pathologist when a patient comes in with acute leukemia to determine + +whether they have AML or ALL. But it turns out that you can't do + +it by looking. You have to do some kind of + +immunohystochemical test of some sort in order to do that. + +So this is a triumph of diagnosis. After 40 years of work, we can now + +correctly classify patients as AML or ALL. And they get the + +appropriate treatment. And if they don't get the right + +treatment, they have a much higher chance of dying. + +And if they do get the right treatment, they have a much higher + +chance of living. So, this is great. + +There's only one problem with the story. It took 40 years, + +40 years to sort this out. That's a long time. Couldn't we do + +better? Surely these cells know what they are. + +Surely we could just ask them if they are. Well, here's the idea. + +Suppose we could ask each cell, please tell us every gene that you + +have turned on, and the level to which you have that + +gene expressed. In other words, + +let us summarize each cell, each tumor by a description of its + +complete pattern of gene expression to 22,000 genes on the human genome. + +Let's write down the level of expression, X1 up to X22, + +00 for each of the 22,000 genes of the genome. So, + +ever tumor becomes a point in 22, 00 dimensional space, right? + +Now clearly, if we had every tumor described as a point in 22, + +00 dimensional space, we ought to be able to sort out which tumors are + +similar to each other, right? Well, it turns out you can + +do that now. These are gene chips, one of several technologies by which + +on a piece of glass are put little spots, each of which contains a + +piece of DNA, a unique DNA sequence. Actually, many copies of that DNA + +sequence are there. Each of these is a 25 base long DNA + +sequence, and I can design this so whatever DNA sequence you + +want is in each spot. The way that's done is with the same + +photolithographic techniques that are used to make microprocessors. + +People have worked out a chemistry where through a mask, + +you shine a light, photodeprotect certain pixels; the pixels that are + +photodeprotected you can chemically attach an A, then re-protect the + +surface. Use a light. Chemically photodeprotect certain + +spots. Wash on a C. And in this fashion, + +since you can randomly address the spots by light, + +and then chemically add bases to whatever spots are deprotected, + +you can simultaneously construct hundreds of thousands of spots each + +containing its own unique specified oligonucleotide sequence. + +And you can get them in little plastic chips. + +And then if you want, all you do is you take a tumor. + +You grind it up. You prepare RNA. You fluorescently label the RNA + +with some appropriate fluorescent dye. You squirt it into the chip. + +You wash it back and forth. You rock it back and forth, + +wash it out, and stick it in a laser scanner. And it'll see how much + +fluorescence is stuck to each spot. And bingo: you get a readout of the + +level of gene expression. I guess each spot, you should + +design it so that this spot has an oligonucleotide complementary to + +gene number one. And the next one, + +an oligonucleotide matching by Crick-Watson base pairing + +complementary to gene number two and gene number three. + +So, if I knew all the genes in the genome, I could make a detector spot + +for each gene in the genome. And of course we know essentially + +all the genes in the genome. So you can make those detector + +spots and you can buy them. So, you can now get a readout of + +all the, I mean, this is like so cool because when I + +started teaching 701, which wasn't that long ago because I + +ain't (sic) that old still, the way people did an analysis of + +gene expression is they used primitive technologies where they + +would analyze one gene at a time, certain things called northern blots + +and things like that, right? And, you know, + +you'd put in a lot of work and you get the expression level of a gene, + +whereas now you can get the expression of all the genes + +simultaneously, and it's pretty mind boggling that + +you can do that. How do you analyze data like that? + +So, we still use northern blots. It's true. So, + +every tumor becomes a vector, and we get a vector corresponding to + +each tumor. So, this line here is the first tumor, + +the second tumor, the third tumor, the fourth tumor. + +The columns here correspond to genes. There are 22, + +00 columns in this matrix, and I've shown a certain subset of + +the columns because these genes here have the interesting property that + +they tend to be high red in the ALL tumors, and they tend to be low blue + +in the AML tumors, whereas these genes here have the + +opposite property. They tend to be low blue in the ALL + +tumors and high red in the AML tumors. These genes do a pretty + +good job of telling apart these tumors. + +So, here's a new tumor. Patient came in. We analyzed the + +RNA, squirted it on the chip. Can somebody classify that? Louder? + +AML. Next? Next? Congratulations, you're + +pathologists. Very good. That's right, you can do that. + +It works. And in fact, in the study that was done that was + +published about this, the computer was able to get it + +right 100% of the time. Not bad. So now you say, + +wait, wait, wait, but you're cheating. + +You're giving it a whole bunch of knowns. Once I have a whole bunch + +of knowns it's not so hard to classify a new tumor. + +What Sydney Farber did was he discovered in the first place that + +there existed two subtypes. Surely that's harder than + +classifying when you're given a bunch of knowns. And + +that's true. So, suppose instead, + +I didn't tell you in advance which were AML's and which were ALL's, + +and I just gave you vectors corresponding to a large number of + +tumors, do you think you would be able to sort out that they actually + +fell into two clusters? + +Could you by computer tell that there's one class and the other + +class? Turns out that you can. Now, I've made it a little easier + +by not listing most of the 22,000 columns here. + +But think about it. Every tumor is a point in 22, + +00 dimensional space. If some of the tumors are similar, + +what can you say about those points in 22,000 dimensional space? + +They're going to be clumped together. They're near each other. + +So, just plot every tumor as a point in 22,000 dimensional space, + +and your question is, do the points tend to lie in two clumps up in 22, + +00 dimensional space? And there's simple arithmetic you + +can learn using linear algebra to get some separating hyperplane and + +ask, do tumors lie on one side or the other? And, + +it turns out the procedures like that will quickly tell you that + +these tumors clump into two very clear clumps. They're not randomly + +distributed. And so, if you get these tumors, + +and you do gene expression on them and put the data into a computer, + +the amount of time it takes the computer to discover that there were + +actually two types of acute leukemia is about three seconds marked down + +from 40 years. That's good. So, you can reproduce the discovery + +of AML and ALL in three seconds. Now you know what the pathologists + +say about this. They say, oh, give me a break. + +It's shooting fish in a barrel. We know there was a distinction. + +Big deal that the computer can find the distinction. + +We knew that there was distinction there. I know the computer didn't + +know it and all that. Tell us something we don't know. + +That's a fair question. So it turns out that you can ask + +some more questions. You can say, suppose I take now + +just the ALL's. Are they a homogeneous class, + +or did they fall into two classes? It turns out that extending this + +work, folks here were able to show that we can further split that ALL + +class. There was a hint that you might be able to do so because + +there's some ALL patients who have disruptions of a gene called MLL. + +And this tends to be a little more common in infants, + +and tends to be associated with a poor prognosis. + +But it was really very unclear whether this was simply one of a + +zillion factoids about some leukemia patients, whether this was a + +fundamental distinction. So, what happened was folks took a + +lot of ALL patients, got their expression profiles, + +and lo and behold it turned out that ALL itself broke into two very + +different clusters. This is an artist's rendition of a + +22,000 dimensional space. We can't afford a 22,000 + +dimensional projector here, so we're just using two dimensions. + +But, the two forms of ALL were quite distinct from each other, + +and so actually ALL itself should be split up into two classes, + +ALL plus and minus, or ALL one and two, or MLL and ALL. + +And it turns out that these forms are quite different. + +They have different outcomes and should be treated differently. + +It also turns out that a particularly good distinction + +between these two subtypes of ALL is found by looking at this particular + +gene called the flit-3 kinase. The flit-3 kinase gene, whatever + +that is, was of great interest because people know that they can + +make inhibitors against certain kinases. And so, + +it turned out that an inhibitor against flit-3 kinases, + +against this flit-3 kinase gene product. + +If you treat cells with that inhibitor, cells of this type die, + +and cells of this type are not affected. So in fact, + +there's a potential drug use of flit-3 kinases in the MLL class of + +these leukemias, and folks are trying some clinical + +trials now. So, not only did the analysis of the + +gene expression point to two important sub-types of leukemias, + +but the analysis of the gene expression even suggested potential + +targets for therapy. So, I'll give you a bunch more + +examples. I have a bunch more examples like that there. + +They are examples of taking lymphomas and showing that they can + +be split into two different categories, examples of taking + +breast cancers into several categories, colon cancers. + +Basically what's going on right now is an attempt to reclassify cancers + +based not on what they look like in the microscope, + +and based not on what organ in the body they affect, + +but based on, molecularly, what their description is, because + +the molecular description, as Bob talked to you about with CML + +and with Gleveck, turns out to be a tremendously + +powerful way of classifying cancers because you're able to see what is + +the molecular defect and can make a molecular targeted therapy. + +So, these sorts of tools are quite cool, and I've got to say, + +in the last year we've begun using these expression tools not just to + +classify cancers, but to classify drugs. + +We've begun an interesting and somewhat crazy project to take all + +the FDA approved drugs, put them onto cell types, + +and see what they do, that is, get a signature, a fingerprint, + +a gene expression description of the action of a drug. + +And then we hope, here's the nutty idea, + +that we can look up in the computer which drugs do which things and + +might be useful for which diseases, because we'd put the diseases and + +the drugs on an equal footing. All of them would be described in + +terms of their gene expression patterns. So, + +I'll tell you one interesting example, OK? This is an interesting + +enough example. I don't even have slides for it yet. + +It turns out that these patients with ALL that I've been talking + +about, some of the patients with ALL will respond to the drug + +dexamethasone. Some won't. If you take patients + +who respond to dexamethasone, and patients who are resistant to + +dexamethasone, and you get their gene expression + +patterns, you can ask are there some genes that explain the difference? + +And you can get a certain gene signature, a list of, + +say, a dozen or so genes that do a pretty good job of classifying who's + +sensitive and who's resistant. Then you can go to this database I + +was telling you about of the action of many drugs and say, + +do we see any drugs whose effect would be to produce a signature + +of sensitivity? If we found a drug X, + +which when we put it on cells turned on those genes that correlate with + +being sensitive to dexamethasone, you could hallucinate the following + +really happy possibility that when you added that drug together with + +dexamethasone, you might be able to treat resistant + +patients because that drug could make them sensitive to dexamethasone, + +and that you could find that drug just by looking it up in + +a computer database. So, we tried it and we hit a drug. + +There was a certain drug that came up on the screen, + +yes? That's very much in the idea too. We found a drug that produced + +the signature sensitivity, and tested it in vitro. In vitro, + +if you take cells that are resistant and you add dexamethasone, + +nothing happens because they're resistant. If you add drug X, + +nothing happens. But if you add both drug X plus dexamethasone, + +the cells drop dead. It's now going into clinical trials + +in human patients. It turns out drug X is already a + +well FDA approved drug, so it can be tested in human + +patients right away, so it's going to be tested. + +So, the gene expression pattern was able to tell us to use a drug which + +actually had nothing to do with cancer uses in a cancer setting + +because it might do something helpful. + +Now, what's the point of all this? We can turn up the lights because I + +think I'm going to stop the slides there. The point of all of this, + +which is what I've made again, and I will make again, + +because you are the generation that's going to really live this, + +is that biology is becoming information. Now, + +don't get me wrong. It's not stopping being + +biochemistry. It's going to be biochemistry. It's not stopping + +being molecular biology. It's not stopping any of the things + +it was before. 45:57 But it is also becoming + +information, that for the first time we're entering a world where we can + +collect vast amounts of information: all the genetic variants in a + +patient, all of the gene expression pattern in a cell, + +or all of the gene expression pattern induced by a drug, + +and that whatever question you're asking will be informed by being + +able to access that whole database. In no way does it decrease the role + +of the individual smart scientist working on his or her problem. + +To the contrary, the goal is to empower the + +individual smart scientist so that you have all of that information at + +your fingertips. There are databases scattered + +around the web that have sequences from different species, + +variations from the human population, all of these drug database, + +etc., etc., etc., etc. It's a time of tremendous ferment, + +a little bit of chaos. You talk to people in the field, + +they say, we're getting deluged by data. We're getting crushed by the + +amount of data. I don't' know what to do with all + +the data. There's only one solution for a + +field in that condition, and that is young scientists because + +the young scientists who come into the field are the ones who take for + +granted, of course we're going to have all these data. + +We love having all these data. This is just great, couldn't be + +happier to have all these data. We're not put off by it in the + +least. That's what's going on. That's what's so important about + +your generation, and that's why I think it's really + +important that even though it's 701 and we're supposed to be teaching + +you the basics, it's important that you see this + +stuff because this is the change that's going on, + +and we're counting on this very much to drive a revolution in health, + +a revolution in biomedical research, and we're counting on you guys very + +much to drive that revolution. It has been a pleasure to teach you + +this term. I hope many of you will stay in touch, + +and some of you will go into biology, and even those of you who don't will + +know lots about it and enjoy it. Thank you very much. [APPLAUSE] \ No newline at end of file diff --git a/Ew4VqTsP2js.txt b/Ew4VqTsP2js.txt new file mode 100644 index 0000000000000000000000000000000000000000..7734487ce3e5283e66acc8548874e0a11eb2a674 --- /dev/null +++ b/Ew4VqTsP2js.txt @@ -0,0 +1,10275 @@ +align:start position:0% + +okayy ready for lecture 7 uh and the + + align:start position:0% +okayy ready for lecture 7 uh and the + + + align:start position:0% +okayy ready for lecture 7 uh and the +topics then would be the first time + + align:start position:0% +topics then would be the first time + + + align:start position:0% +topics then would be the first time +we're seeing differential equations uh + + align:start position:0% +we're seeing differential equations uh + + + align:start position:0% +we're seeing differential equations uh +let me copy that equation up here and I + + align:start position:0% + + + + align:start position:0% + +hope you might guess that it's + + align:start position:0% +hope you might guess that it's + + + align:start position:0% +hope you might guess that it's +completely analogous to our Matrix + + align:start position:0% +completely analogous to our Matrix + + + align:start position:0% +completely analogous to our Matrix +equation so this is going to be a + + align:start position:0% +equation so this is going to be a + + + align:start position:0% +equation so this is going to be a +transpose minus d by DX this you + + align:start position:0% +transpose minus d by DX this you + + + align:start position:0% +transpose minus d by DX this you +remember we had the diagonal matrix C + + align:start position:0% +remember we had the diagonal matrix C + + + align:start position:0% +remember we had the diagonal matrix C +well now we've got with with a discrete + + align:start position:0% +well now we've got with with a discrete + + + align:start position:0% +well now we've got with with a discrete +set of uh spring constants now we have + + align:start position:0% +set of uh spring constants now we have + + + align:start position:0% +set of uh spring constants now we have +an elastic constant all along the bar so + + align:start position:0% +an elastic constant all along the bar so + + + align:start position:0% +an elastic constant all along the bar so +I'm thinking instead of before we had a + + align:start position:0% +I'm thinking instead of before we had a + + + align:start position:0% +I'm thinking instead of before we had a +line of + + align:start position:0% +line of + + + align:start position:0% +line of +Springs with + + align:start position:0% +Springs with + + + align:start position:0% +Springs with +masses and now so this + + align:start position:0% +masses and now so this + + + align:start position:0% +masses and now so this +is for a transpose C a u equal F that + + align:start position:0% +is for a transpose C a u equal F that + + + align:start position:0% +is for a transpose C a u equal F that +was the discrete one The Continuous one + + align:start position:0% +was the discrete one The Continuous one + + + align:start position:0% +was the discrete one The Continuous one +will + + align:start position:0% +will + + + align:start position:0% +will +be if we want to so you can tell part of + + align:start position:0% +be if we want to so you can tell part of + + + align:start position:0% +be if we want to so you can tell part of +the point here is to get the analogies + + align:start position:0% +the point here is to get the analogies + + + align:start position:0% +the point here is to get the analogies +because I think that's sort of a part + + align:start position:0% +because I think that's sort of a part + + + align:start position:0% +because I think that's sort of a part +something that mathematics can + + align:start position:0% +something that mathematics can + + + align:start position:0% +something that mathematics can +contribute to see the same pattern + + align:start position:0% +contribute to see the same pattern + + + align:start position:0% +contribute to see the same pattern +appearing in different places and here + + align:start position:0% +appearing in different places and here + + + align:start position:0% +appearing in different places and here +we have uh the pattern appearing in the + + align:start position:0% +we have uh the pattern appearing in the + + + align:start position:0% +we have uh the pattern appearing in the +a discrete problem and in a continuous + + align:start position:0% +a discrete problem and in a continuous + + + align:start position:0% +a discrete problem and in a continuous +problem so I'm thinking here of an + + align:start position:0% +problem so I'm thinking here of an + + + align:start position:0% +problem so I'm thinking here of an +elastic bar you could + + align:start position:0% +elastic bar you could + + + align:start position:0% +elastic bar you could +say of length so we make the length one + + align:start position:0% +say of length so we make the length one + + + align:start position:0% +say of length so we make the length one +so we'll run from X = 0 to xal + + align:start position:0% +so we'll run from X = 0 to xal + + + align:start position:0% +so we'll run from X = 0 to xal +1 and then we've + + align:start position:0% +1 and then we've + + + align:start position:0% +1 and then we've +got we'll end up with this differential + + align:start position:0% +got we'll end up with this differential + + + align:start position:0% +got we'll end up with this differential +equation so again we have this + + align:start position:0% +equation so again we have this + + + align:start position:0% +equation so again we have this +displacements but now the displacements + + align:start position:0% +displacements but now the displacements + + + align:start position:0% +displacements but now the displacements +are function of X so this is a + + align:start position:0% +are function of X so this is a + + + align:start position:0% +are function of X so this is a +displacement When Gravity Acts or when + + align:start position:0% +displacement When Gravity Acts or when + + + align:start position:0% +displacement When Gravity Acts or when +we put some weights on the bar for + + align:start position:0% +we put some weights on the bar for + + + align:start position:0% +we put some weights on the bar for +example I might uh put on a weight tack + + align:start position:0% +example I might uh put on a weight tack + + + align:start position:0% +example I might uh put on a weight tack +on a weight right there at at a point x + + align:start position:0% +on a weight right there at at a point x + + + align:start position:0% +on a weight right there at at a point x +equal a I might tack on a weight + + align:start position:0% +equal a I might tack on a weight + + + align:start position:0% +equal a I might tack on a weight +w so that would pull you it's worth + + align:start position:0% +w so that would pull you it's worth + + + align:start position:0% +w so that would pull you it's worth +really thinking I mean these are these + + align:start position:0% +really thinking I mean these are these + + + align:start position:0% +really thinking I mean these are these +are problems where even if we're not uh + + align:start position:0% +are problems where even if we're not uh + + + align:start position:0% +are problems where even if we're not uh +mechanics specialists in mechanics we + + align:start position:0% +mechanics specialists in mechanics we + + + align:start position:0% +mechanics specialists in mechanics we +can see what that will do to the what + + align:start position:0% +can see what that will do to the what + + + align:start position:0% +can see what that will do to the what +displacement that might produce so + + align:start position:0% +displacement that might produce so + + + align:start position:0% +displacement that might produce so +there'll be a function U of X there will + + align:start position:0% +there'll be a function U of X there will + + + align:start position:0% +there'll be a function U of X there will +be uh a + + align:start position:0% + + + + align:start position:0% + +stretching and what will that be well + + align:start position:0% +stretching and what will that be well + + + align:start position:0% +stretching and what will that be well +this is the operator + + align:start position:0% +this is the operator + + + align:start position:0% +this is the operator +a and the stretching is + + align:start position:0% +a and the stretching is + + + align:start position:0% +a and the stretching is +DX is the + + align:start position:0% +DX is the + + + align:start position:0% +DX is the +derivative and that's uh sort of right I + + align:start position:0% +derivative and that's uh sort of right I + + + align:start position:0% +derivative and that's uh sort of right I +mean the in this in this case the + + align:start position:0% +mean the in this in this case the + + + align:start position:0% +mean the in this in this case the +stretching was you remember what the + + align:start position:0% +stretching was you remember what the + + + align:start position:0% +stretching was you remember what the +operator a did the stretching was uh the + + align:start position:0% +operator a did the stretching was uh the + + + align:start position:0% +operator a did the stretching was uh the +E so this is e if we keep that same + + align:start position:0% +E so this is e if we keep that same + + + align:start position:0% +E so this is e if we keep that same +symbol uh the E here in the discret case + + align:start position:0% +symbol uh the E here in the discret case + + + align:start position:0% +symbol uh the E here in the discret case +what was what was E this one dropped by + + align:start position:0% +what was what was E this one dropped by + + + align:start position:0% +what was what was E this one dropped by +U1 and this point well either didn't + + align:start position:0% +U1 and this point well either didn't + + + align:start position:0% +U1 and this point well either didn't +move or moved by u0o so e was U1 minus + + align:start position:0% +move or moved by u0o so e was U1 minus + + + align:start position:0% +move or moved by u0o so e was U1 minus +u0 it was a difference + + align:start position:0% +u0 it was a difference + + + align:start position:0% +u0 it was a difference +operator now in the continuous case we + + align:start position:0% +operator now in the continuous case we + + + align:start position:0% +operator now in the continuous case we +would just expect and it happens that + + align:start position:0% +would just expect and it happens that + + + align:start position:0% +would just expect and it happens that +the difference operator turns into a + + align:start position:0% +the difference operator turns into a + + + align:start position:0% +the difference operator turns into a +derivative it was a first difference and + + align:start position:0% +derivative it was a first difference and + + + align:start position:0% +derivative it was a first difference and +it turns into a first derivative and + + align:start position:0% +it turns into a first derivative and + + + align:start position:0% +it turns into a first derivative and +then comes Hook's law the constitutive + + align:start position:0% +then comes Hook's law the constitutive + + + align:start position:0% +then comes Hook's law the constitutive +law and that's a multiplication by C ofx + + align:start position:0% +law and that's a multiplication by C ofx + + + align:start position:0% +law and that's a multiplication by C ofx +and produces W of X the internal Force + + align:start position:0% +and produces W of X the internal Force + + + align:start position:0% +and produces W of X the internal Force +this is this is like internal + + align:start position:0% +this is this is like internal + + + align:start position:0% +this is this is like internal +Force so these + + align:start position:0% +Force so these + + + align:start position:0% +Force so these +e the the U up here and the W down there + + align:start position:0% +e the the U up here and the W down there + + + align:start position:0% +e the the U up here and the W down there +are still the principal + + align:start position:0% +are still the principal + + + align:start position:0% +are still the principal +unknowns and uh then there's so then + + align:start position:0% +unknowns and uh then there's so then + + + align:start position:0% +unknowns and uh then there's so then +there's going to be an a + + align:start position:0% +there's going to be an a + + + align:start position:0% +there's going to be an a +transpose and there's going to be an + + align:start position:0% +transpose and there's going to be an + + + align:start position:0% +transpose and there's going to be an +equation minus + + align:start position:0% +equation minus + + + align:start position:0% +equation minus +DW DX = + + align:start position:0% +DW DX = + + + align:start position:0% +DW DX = +F and what will that equation + + align:start position:0% + + + + align:start position:0% + +represent so as + + align:start position:0% +represent so as + + + align:start position:0% +represent so as +before + + align:start position:0% +before + + + align:start position:0% +before +uh we have sort of a + + align:start position:0% +uh we have sort of a + + + align:start position:0% +uh we have sort of a +geometry you know we if we know the + + align:start position:0% +geometry you know we if we know the + + + align:start position:0% +geometry you know we if we know the +displacements then we can see how much a + + align:start position:0% +displacements then we can see how much a + + + align:start position:0% +displacements then we can see how much a +little piece is being + + align:start position:0% +little piece is being + + + align:start position:0% +little piece is being +stretched that's the derivative then we + + align:start position:0% +stretched that's the derivative then we + + + align:start position:0% +stretched that's the derivative then we +multiply by C to connect to the force + + align:start position:0% +multiply by C to connect to the force + + + align:start position:0% +multiply by C to connect to the force +that does that stret in so that's the + + align:start position:0% +that does that stret in so that's the + + + align:start position:0% +that does that stret in so that's the +internal + + align:start position:0% +internal + + + align:start position:0% +internal +force uh W and then what does that + + align:start position:0% +force uh W and then what does that + + + align:start position:0% +force uh W and then what does that +equation indic tell + + align:start position:0% +equation indic tell + + + align:start position:0% +equation indic tell +us something about sorry yeah that we + + align:start position:0% +us something about sorry yeah that we + + + align:start position:0% +us something about sorry yeah that we +have the exactly the internal balance is + + align:start position:0% +have the exactly the internal balance is + + + align:start position:0% +have the exactly the internal balance is +the external it's a force balance force + + align:start position:0% +the external it's a force balance force + + + align:start position:0% +the external it's a force balance force +balance + + align:start position:0% + + + + align:start position:0% + +exactly okay and by the way I I've + + align:start position:0% +exactly okay and by the way I I've + + + align:start position:0% +exactly okay and by the way I I've +mentioned Delta function there on my my + + align:start position:0% +mentioned Delta function there on my my + + + align:start position:0% +mentioned Delta function there on my my +uh General outline let me put + + align:start position:0% +uh General outline let me put + + + align:start position:0% +uh General outline let me put +in the this where where is the we we + + align:start position:0% +in the this where where is the we we + + + align:start position:0% +in the this where where is the we we +have to S like get it's worth getting + + align:start position:0% +have to S like get it's worth getting + + + align:start position:0% +have to S like get it's worth getting +familiar with the Delta + + align:start position:0% +familiar with the Delta + + + align:start position:0% +familiar with the Delta +function and it it's in my picture here + + align:start position:0% +function and it it's in my picture here + + + align:start position:0% +function and it it's in my picture here +it's going to come up right up right + + align:start position:0% +it's going to come up right up right + + + align:start position:0% +it's going to come up right up right +away what's the external force in this + + align:start position:0% +away what's the external force in this + + + align:start position:0% +away what's the external force in this +picture I I we may have some weight from + + align:start position:0% +picture I I we may have some weight from + + + align:start position:0% +picture I I we may have some weight from +the bar that would contribute an F ofx + + align:start position:0% +the bar that would contribute an F ofx + + + align:start position:0% +the bar that would contribute an F ofx +all + + align:start position:0% +all + + + align:start position:0% +all +along a force uh write the length of the + + align:start position:0% +along a force uh write the length of the + + + align:start position:0% +along a force uh write the length of the +bar but what would be the contribution + + align:start position:0% +bar but what would be the contribution + + + align:start position:0% +bar but what would be the contribution +from this point load this is a point + + align:start position:0% +from this point load this is a point + + + align:start position:0% +from this point load this is a point +load and I'm I think it's uh really + + align:start position:0% + + + + align:start position:0% + +worth getting the hang it's almost a + + align:start position:0% +worth getting the hang it's almost a + + + align:start position:0% +worth getting the hang it's almost a +punt but getting the idea of a point + + align:start position:0% +punt but getting the idea of a point + + + align:start position:0% +punt but getting the idea of a point +load and so that point load in in in + + align:start position:0% +load and so that point load in in in + + + align:start position:0% +load and so that point load in in in +math terms here would be w you the the + + align:start position:0% +math terms here would be w you the the + + + align:start position:0% +math terms here would be w you the the +the weight to get the units right and + + align:start position:0% +the weight to get the units right and + + + align:start position:0% +the weight to get the units right and +then the fact of being a point load I + + align:start position:0% +then the fact of being a point load I + + + align:start position:0% +then the fact of being a point load I +use this Delta function and it's a Delta + + align:start position:0% +use this Delta function and it's a Delta + + + align:start position:0% +use this Delta function and it's a Delta +function that has a has its Spike at at + + align:start position:0% +function that has a has its Spike at at + + + align:start position:0% +function that has a has its Spike at at +a at that particular point so Delta of X + + align:start position:0% +a at that particular point so Delta of X + + + align:start position:0% +a at that particular point so Delta of X +so let's can + + align:start position:0% +so let's can + + + align:start position:0% +so let's can +I can I go with this Delta function idea + + align:start position:0% +I can I go with this Delta function idea + + + align:start position:0% +I can I go with this Delta function idea +a little bit while we're + + align:start position:0% +a little bit while we're + + + align:start position:0% +a little bit while we're +fresh um + + align:start position:0% +fresh um + + + align:start position:0% +fresh um +so just a discussion about Delta + + align:start position:0% +so just a discussion about Delta + + + align:start position:0% +so just a discussion about Delta +functions and step + + align:start position:0% + + + + align:start position:0% + +functions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +cuz well what what I want to show is if + + align:start position:0% +cuz well what what I want to show is if + + + align:start position:0% +cuz well what what I want to show is if +we can deal with right hand sides being + + align:start position:0% +we can deal with right hand sides being + + + align:start position:0% +we can deal with right hand sides being +Delta functions then that's sort of like + + align:start position:0% +Delta functions then that's sort of like + + + align:start position:0% +Delta functions then that's sort of like +the + + align:start position:0% +the + + + align:start position:0% +the +basic uh right hand side that's your + + align:start position:0% +basic uh right hand side that's your + + + align:start position:0% +basic uh right hand side that's your +basic right hand side is the Delta + + align:start position:0% +basic right hand side is the Delta + + + align:start position:0% +basic right hand side is the Delta +function at different points if we could + + align:start position:0% +function at different points if we could + + + align:start position:0% +function at different points if we could +deal with those we can deal with any F + + align:start position:0% +deal with those we can deal with any F + + + align:start position:0% +deal with those we can deal with any F +ofx somehow any f ofx is + + align:start position:0% +ofx somehow any f ofx is + + + align:start position:0% +ofx somehow any f ofx is +somehow an integral of Delta function so + + align:start position:0% +somehow an integral of Delta function so + + + align:start position:0% +somehow an integral of Delta function so +it's the Delta function that's the most + + align:start position:0% +it's the Delta function that's the most + + + align:start position:0% +it's the Delta function that's the most +basic now the basic Delta function is + + align:start position:0% +basic now the basic Delta function is + + + align:start position:0% +basic now the basic Delta function is +Delta of + + align:start position:0% + + + + align:start position:0% + +X and what is it I don't know it's um + + align:start position:0% +X and what is it I don't know it's um + + + align:start position:0% +X and what is it I don't know it's um +often described as an Impulse here we're + + align:start position:0% +often described as an Impulse here we're + + + align:start position:0% +often described as an Impulse here we're +using the word Point + + align:start position:0% +using the word Point + + + align:start position:0% +using the word Point +load uh Spike I sometimes use it's if I + + align:start position:0% +load uh Spike I sometimes use it's if I + + + align:start position:0% +load uh Spike I sometimes use it's if I +try to graph + + align:start position:0% +try to graph + + + align:start position:0% +try to graph +it I can't do justice to it but let me + + align:start position:0% +it I can't do justice to it but let me + + + align:start position:0% +it I can't do justice to it but let me +try it's it's it's if I graph the + + align:start position:0% +try it's it's it's if I graph the + + + align:start position:0% +try it's it's it's if I graph the +function it's + + align:start position:0% +function it's + + + align:start position:0% +function it's +zero until the origin until I hit that + + align:start position:0% +zero until the origin until I hit that + + + align:start position:0% +zero until the origin until I hit that +particular point and then it well it's + + align:start position:0% +particular point and then it well it's + + + align:start position:0% +particular point and then it well it's +something amazing at that + + align:start position:0% +something amazing at that + + + align:start position:0% +something amazing at that +point and zero after that so so it's + + align:start position:0% +point and zero after that so so it's + + + align:start position:0% +point and zero after that so so it's +like everything is happening at that + + align:start position:0% +like everything is happening at that + + + align:start position:0% +like everything is happening at that +point and of course everybody sees Delta + + align:start position:0% +point and of course everybody sees Delta + + + align:start position:0% +point and of course everybody sees Delta +of x minus a what's the effect of of uh + + align:start position:0% +of x minus a what's the effect of of uh + + + align:start position:0% +of x minus a what's the effect of of uh +translating Shifting the + + align:start position:0% +translating Shifting the + + + align:start position:0% +translating Shifting the +variable uh what what would the so now + + align:start position:0% +variable uh what what would the so now + + + align:start position:0% +variable uh what what would the so now +if I tried to graph Delta of x minus a + + align:start position:0% +if I tried to graph Delta of x minus a + + + align:start position:0% +if I tried to graph Delta of x minus a +what would change in the + + align:start position:0% +what would change in the + + + align:start position:0% +what would change in the +graph the spike would be at a right + + align:start position:0% +graph the spike would be at a right + + + align:start position:0% +graph the spike would be at a right +because it's wherever this this thing is + + align:start position:0% +because it's wherever this this thing is + + + align:start position:0% +because it's wherever this this thing is +zero and it's zero at a so that would be + + align:start position:0% +zero and it's zero at a so that would be + + + align:start position:0% +zero and it's zero at a so that would be +Delta of xus a no problem okay often so + + align:start position:0% +Delta of xus a no problem okay often so + + + align:start position:0% +Delta of xus a no problem okay often so +so if we understand Delta of X we no no + + align:start position:0% +so if we understand Delta of X we no no + + + align:start position:0% +so if we understand Delta of X we no no +difficulty with the sh the shifting of + + align:start position:0% +difficulty with the sh the shifting of + + + align:start position:0% +difficulty with the sh the shifting of +it okay so that's a Delta function and + + align:start position:0% +it okay so that's a Delta function and + + + align:start position:0% +it okay so that's a Delta function and +oh but now I didn't say the main point + + align:start position:0% +oh but now I didn't say the main point + + + align:start position:0% +oh but now I didn't say the main point +right what's the main point about that + + align:start position:0% +right what's the main point about that + + + align:start position:0% +right what's the main point about that +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +function it's well + + align:start position:0% +function it's well + + + align:start position:0% +function it's well +so + + align:start position:0% +so + + + align:start position:0% +so +it's it it's + + align:start position:0% +it's it it's + + + align:start position:0% +it's it it's +so powerful at that one point that its + + align:start position:0% +so powerful at that one point that its + + + align:start position:0% +so powerful at that one point that its +integral + + align:start position:0% +integral + + + align:start position:0% +integral +is one it has a I mean it's an Impulse + + align:start position:0% +is one it has a I mean it's an Impulse + + + align:start position:0% +is one it has a I mean it's an Impulse +it it happens in an instant so it so no + + align:start position:0% +it it happens in an instant so it so no + + + align:start position:0% +it it happens in an instant so it so no +true function can do it it happens in an + + align:start position:0% +true function can do it it happens in an + + + align:start position:0% +true function can do it it happens in an +instant but what it does in that instant + + align:start position:0% +instant but what it does in that instant + + + align:start position:0% +instant but what it does in that instant +is the integral jumps to one and the + + align:start position:0% +is the integral jumps to one and the + + + align:start position:0% +is the integral jumps to one and the +integral is the step function let me put + + align:start position:0% +integral is the step function let me put + + + align:start position:0% +integral is the step function let me put +this back to zero or well I can leave it + + align:start position:0% +this back to zero or well I can leave it + + + align:start position:0% +this back to zero or well I can leave it +at a the step so what's the graph of its + + align:start position:0% +at a the step so what's the graph of its + + + align:start position:0% +at a the step so what's the graph of its +integral this is the integral of the + + align:start position:0% +integral this is the integral of the + + + align:start position:0% +integral this is the integral of the +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +function is that + + align:start position:0% +function is that + + + align:start position:0% +function is that +right yes the integral of the Delta + + align:start position:0% +right yes the integral of the Delta + + + align:start position:0% +right yes the integral of the Delta +function okay so the Delta function is + + align:start position:0% +function okay so the Delta function is + + + align:start position:0% +function okay so the Delta function is +it's worse than a step function + + align:start position:0% +it's worse than a step function + + + align:start position:0% +it's worse than a step function +integration always Smooths + + align:start position:0% +integration always Smooths + + + align:start position:0% +integration always Smooths +things differentiation always + + align:start position:0% +things differentiation always + + + align:start position:0% +things differentiation always +makes + + align:start position:0% +makes + + + align:start position:0% +makes +them noisier so here we're going in the + + align:start position:0% +them noisier so here we're going in the + + + align:start position:0% +them noisier so here we're going in the +smooth Direction so what happens then if + + align:start position:0% +smooth Direction so what happens then if + + + align:start position:0% +smooth Direction so what happens then if +I integrate this function so I so I + + align:start position:0% +I integrate this function so I so I + + + align:start position:0% +I integrate this function so I so I +integrate Delta of x minus + + align:start position:0% +integrate Delta of x minus + + + align:start position:0% +integrate Delta of x minus +a say integral of Delta of x - A DX from + + align:start position:0% +a say integral of Delta of x - A DX from + + + align:start position:0% +a say integral of Delta of x - A DX from +let's say I could start at minus + + align:start position:0% +let's say I could start at minus + + + align:start position:0% +let's say I could start at minus +infinity because nothing's going to + + align:start position:0% +infinity because nothing's going to + + + align:start position:0% +infinity because nothing's going to +happen back here and let me go to an + + align:start position:0% +happen back here and let me go to an + + + align:start position:0% +happen back here and let me go to an +arbitary Point say capital X + + align:start position:0% +arbitary Point say capital X + + + align:start position:0% +arbitary Point say capital X +so this is so can I graph that + + align:start position:0% +so this is so can I graph that + + + align:start position:0% +so this is so can I graph that +now so now it's a function of capital + + align:start position:0% +now so now it's a function of capital + + + align:start position:0% +now so now it's a function of capital +x we can the choice of variable isn't + + align:start position:0% +x we can the choice of variable isn't + + + align:start position:0% +x we can the choice of variable isn't +too crucial okay what's the integral + + align:start position:0% +too crucial okay what's the integral + + + align:start position:0% +too crucial okay what's the integral +then of the Delta function you you know + + align:start position:0% +then of the Delta function you you know + + + align:start position:0% +then of the Delta function you you know +it but just to see it so the integral as + + align:start position:0% +it but just to see it so the integral as + + + align:start position:0% +it but just to see it so the integral as +I'm coming along here is zero so I'm + + align:start position:0% +I'm coming along here is zero so I'm + + + align:start position:0% +I'm coming along here is zero so I'm +coming along and then I hit oh good I + + align:start position:0% +coming along and then I hit oh good I + + + align:start position:0% +coming along and then I hit oh good I +hit the crack in the Blackboard that's a + + align:start position:0% +hit the crack in the Blackboard that's a + + + align:start position:0% +hit the crack in the Blackboard that's a +and after that the integral jumps up to + + align:start position:0% +and after that the integral jumps up to + + + align:start position:0% +and after that the integral jumps up to +one right and then doesn't change after + + align:start position:0% +one right and then doesn't change after + + + align:start position:0% +one right and then doesn't change after +that so it jumps up to one okay so the + + align:start position:0% +that so it jumps up to one okay so the + + + align:start position:0% +that so it jumps up to one okay so the +integral of this + + align:start position:0% +integral of this + + + align:start position:0% +integral of this +function not a true function it's it's + + align:start position:0% +function not a true function it's it's + + + align:start position:0% +function not a true function it's it's +it sort of it I guess it's Associated + + align:start position:0% +it sort of it I guess it's Associated + + + align:start position:0% +it sort of it I guess it's Associated +first of all with the name of heavy side + + align:start position:0% +first of all with the name of heavy side + + + align:start position:0% +first of all with the name of heavy side +h e a v Sid Oliver heaviside who was + + align:start position:0% +h e a v Sid Oliver heaviside who was + + + align:start position:0% +h e a v Sid Oliver heaviside who was +among the first to do what we're really + + align:start position:0% +among the first to do what we're really + + + align:start position:0% +among the first to do what we're really +going to do just deal with + + align:start position:0% +going to do just deal with + + + align:start position:0% +going to do just deal with +it uh it was sort of + + align:start position:0% +it uh it was sort of + + + align:start position:0% +it uh it was sort of +legitimized as and given a new name a + + align:start position:0% +legitimized as and given a new name a + + + align:start position:0% +legitimized as and given a new name a +distribution uh by schz L schz so the + + align:start position:0% +distribution uh by schz L schz so the + + + align:start position:0% +distribution uh by schz L schz so the +theory of distributions is the theory of + + align:start position:0% +theory of distributions is the theory of + + + align:start position:0% +theory of distributions is the theory of +dealing with functions like the Delta + + align:start position:0% +dealing with functions like the Delta + + + align:start position:0% +dealing with functions like the Delta +function and worse than that the + + align:start position:0% +function and worse than that the + + + align:start position:0% +function and worse than that the +derivative of the Delta function what so + + align:start position:0% +derivative of the Delta function what so + + + align:start position:0% +derivative of the Delta function what so +if I go in the other direction to take + + align:start position:0% +if I go in the other direction to take + + + align:start position:0% +if I go in the other direction to take +derivatives I'm really getting stranger + + align:start position:0% +derivatives I'm really getting stranger + + + align:start position:0% +derivatives I'm really getting stranger +and stranger functions uh for the moment + + align:start position:0% +and stranger functions uh for the moment + + + align:start position:0% +and stranger functions uh for the moment +let's go that that way + + align:start position:0% +let's go that that way + + + align:start position:0% +let's go that that way +okay so that I would like to be able to + + align:start position:0% +okay so that I would like to be able to + + + align:start position:0% +okay so that I would like to be able to +put that on the right hand side + + align:start position:0% +put that on the right hand side + + + align:start position:0% +put that on the right hand side +so so so let me here will be the the + + align:start position:0% +so so so let me here will be the the + + + align:start position:0% +so so so let me here will be the the +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +examples which we can solve in + + align:start position:0% +examples which we can solve in + + + align:start position:0% +examples which we can solve in +detail I'll take C of x to be + + align:start position:0% +detail I'll take C of x to be + + + align:start position:0% +detail I'll take C of x to be +identically one in these examples so + + align:start position:0% +identically one in these examples so + + + align:start position:0% +identically one in these examples so +it's like it's like C is the identity + + align:start position:0% +it's like it's like C is the identity + + + align:start position:0% +it's like it's like C is the identity +Matrix and I'm back to my nicest case a + + align:start position:0% +Matrix and I'm back to my nicest case a + + + align:start position:0% +Matrix and I'm back to my nicest case a +transpose a I mean a transpose a is so + + align:start position:0% +transpose a I mean a transpose a is so + + + align:start position:0% +transpose a I mean a transpose a is so +really got the guts of the problem in it + + align:start position:0% +really got the guts of the problem in it + + + align:start position:0% +really got the guts of the problem in it +and uh C of X or the Matrix C just is a + + align:start position:0% +and uh C of X or the Matrix C just is a + + + align:start position:0% +and uh C of X or the Matrix C just is a +necessary General is a useful + + align:start position:0% +necessary General is a useful + + + align:start position:0% +necessary General is a useful +generalization but but the heart of the + + align:start position:0% +generalization but but the heart of the + + + align:start position:0% +generalization but but the heart of the +problem is in a transpose a okay so + + align:start position:0% +problem is in a transpose a okay so + + + align:start position:0% +problem is in a transpose a okay so +examples if C of X is 1 then my equation + + align:start position:0% +examples if C of X is 1 then my equation + + + align:start position:0% +examples if C of X is 1 then my equation +becomes simpler it's just minus the + + align:start position:0% +becomes simpler it's just minus the + + + align:start position:0% +becomes simpler it's just minus the +second + + align:start position:0% +second + + + align:start position:0% +second +derivative of U equals and now let me + + align:start position:0% +derivative of U equals and now let me + + + align:start position:0% +derivative of U equals and now let me +take a Delta function at a let me I'll + + align:start position:0% +take a Delta function at a let me I'll + + + align:start position:0% +take a Delta function at a let me I'll +take I'll even let W be one just because + + align:start position:0% +take I'll even let W be one just because + + + align:start position:0% +take I'll even let W be one just because +no use to make it more complicated than + + align:start position:0% +no use to make it more complicated than + + + align:start position:0% +no use to make it more complicated than +necessary so that's my differential + + align:start position:0% +necessary so that's my differential + + + align:start position:0% +necessary so that's my differential +equation and now + + align:start position:0% +equation and now + + + align:start position:0% +equation and now +now so two or three things coming to my + + align:start position:0% +now so two or three things coming to my + + + align:start position:0% +now so two or three things coming to my +mind here we've got to have boundary + + align:start position:0% +mind here we've got to have boundary + + + align:start position:0% +mind here we've got to have boundary +conditions we've got to have we would + + align:start position:0% +conditions we've got to have we would + + + align:start position:0% +conditions we've got to have we would +expect two boundary + + align:start position:0% +expect two boundary + + + align:start position:0% +expect two boundary +conditions because we have a second + + align:start position:0% +conditions because we have a second + + + align:start position:0% +conditions because we have a second +order + + align:start position:0% +order + + + align:start position:0% +order +equation and we'd expect a boundary + + align:start position:0% +equation and we'd expect a boundary + + + align:start position:0% +equation and we'd expect a boundary +condition at one end and a boundary + + align:start position:0% +condition at one end and a boundary + + + align:start position:0% +condition at one end and a boundary +condition at the other end this is a + + align:start position:0% +condition at the other end this is a + + + align:start position:0% +condition at the other end this is a +boundary value + + align:start position:0% +boundary value + + + align:start position:0% +boundary value +problem that's very different from an + + align:start position:0% +problem that's very different from an + + + align:start position:0% +problem that's very different from an +initial IAL value problem initial value + + align:start position:0% +initial IAL value problem initial value + + + align:start position:0% +initial IAL value problem initial value +means we give everything at time zero + + align:start position:0% +means we give everything at time zero + + + align:start position:0% +means we give everything at time zero +and + + align:start position:0% +and + + + align:start position:0% +and +go in that problem the igen values + + align:start position:0% +go in that problem the igen values + + + align:start position:0% +go in that problem the igen values +appeared we saw some of those last time + + align:start position:0% +appeared we saw some of those last time + + + align:start position:0% +appeared we saw some of those last time +and we'll see more for partial + + align:start position:0% +and we'll see more for partial + + + align:start position:0% +and we'll see more for partial +differential equations heat equation + + align:start position:0% +differential equations heat equation + + + align:start position:0% +differential equations heat equation +wave equation things happen in time here + + align:start position:0% +wave equation things happen in time here + + + align:start position:0% +wave equation things happen in time here +there's no time steady state it's + + align:start position:0% +there's no time steady state it's + + + align:start position:0% +there's no time steady state it's +equilibrium it's a boundary value + + align:start position:0% +equilibrium it's a boundary value + + + align:start position:0% +equilibrium it's a boundary value +problem it would in in partial differen + + align:start position:0% +problem it would in in partial differen + + + align:start position:0% +problem it would in in partial differen +equations we would refer to an elliptic + + align:start position:0% +equations we would refer to an elliptic + + + align:start position:0% +equations we would refer to an elliptic +a partial differential equation of + + align:start position:0% +a partial differential equation of + + + align:start position:0% +a partial differential equation of +elliptic type and my second lecture + + align:start position:0% +elliptic type and my second lecture + + + align:start position:0% +elliptic type and my second lecture +today will be about the L equation which + + align:start position:0% +today will be about the L equation which + + + align:start position:0% +today will be about the L equation which +is the absolute sort of prototype of + + align:start position:0% +is the absolute sort of prototype of + + + align:start position:0% +is the absolute sort of prototype of +boundary value problems for pdes here we + + align:start position:0% +boundary value problems for pdes here we + + + align:start position:0% +boundary value problems for pdes here we +have boundary value problems for Odes so + + align:start position:0% +have boundary value problems for Odes so + + + align:start position:0% +have boundary value problems for Odes so +we I'm I'm expecting a boundary + + align:start position:0% +we I'm I'm expecting a boundary + + + align:start position:0% +we I'm I'm expecting a boundary +condition at at the top and expecting a + + align:start position:0% +condition at at the top and expecting a + + + align:start position:0% +condition at at the top and expecting a +boundary condition at the bottom at x + + align:start position:0% +boundary condition at the bottom at x + + + align:start position:0% +boundary condition at the bottom at x +equals 0 and at x equal 1 why don't we + + align:start position:0% +equals 0 and at x equal 1 why don't we + + + align:start position:0% +equals 0 and at x equal 1 why don't we +put in the boundary conditions that are + + align:start position:0% +put in the boundary conditions that are + + + align:start position:0% +put in the boundary conditions that are +appropriate for that physical model so + + align:start position:0% +appropriate for that physical model so + + + align:start position:0% +appropriate for that physical model so +what's the boundary condition at the + + align:start position:0% +what's the boundary condition at the + + + align:start position:0% +what's the boundary condition at the +top U equals z right U at this point is + + align:start position:0% +top U equals z right U at this point is + + + align:start position:0% +top U equals z right U at this point is +zero so the boundary condition that I'm + + align:start position:0% +zero so the boundary condition that I'm + + + align:start position:0% +zero so the boundary condition that I'm +seeing here is U of 0 equals z let me + + align:start position:0% +seeing here is U of 0 equals z let me + + + align:start position:0% +seeing here is U of 0 equals z let me +copy that over here U + + align:start position:0% +copy that over here U + + + align:start position:0% +copy that over here U +of0 equals z okay and now what boundary + + align:start position:0% +of0 equals z okay and now what boundary + + + align:start position:0% +of0 equals z okay and now what boundary +condition that's + + align:start position:0% +condition that's + + + align:start position:0% +condition that's +fine + + align:start position:0% +fine + + + align:start position:0% +fine +and uh what boundary condition am I + + align:start position:0% +and uh what boundary condition am I + + + align:start position:0% +and uh what boundary condition am I +going to see at the bottom end in this + + align:start position:0% +going to see at the bottom end in this + + + align:start position:0% +going to see at the bottom end in this +picture W is zero right W is zero the + + align:start position:0% +picture W is zero right W is zero the + + + align:start position:0% +picture W is zero right W is zero the +the boundary conditions are on U or on + + align:start position:0% +the boundary conditions are on U or on + + + align:start position:0% +the boundary conditions are on U or on +W and so let so it's w at the point one + + align:start position:0% +W and so let so it's w at the point one + + + align:start position:0% +W and so let so it's w at the point one +is zero so that would be uh W of one is + + align:start position:0% +is zero so that would be uh W of one is + + + align:start position:0% +is zero so that would be uh W of one is +zero and of course I can write in what w + + align:start position:0% +zero and of course I can write in what w + + + align:start position:0% +zero and of course I can write in what w +of one is it's C + + align:start position:0% +of one is it's C + + + align:start position:0% +of one is it's C +DX at + + align:start position:0% +DX at + + + align:start position:0% +DX at +one is zero is zero + + align:start position:0% +one is zero is zero + + + align:start position:0% +one is zero is zero +okay good we could solve that equation + + align:start position:0% +okay good we could solve that equation + + + align:start position:0% +okay good we could solve that equation +it's kind of fun actually to solve that + + align:start position:0% +it's kind of fun actually to solve that + + + align:start position:0% +it's kind of fun actually to solve that +equation and we + + align:start position:0% +equation and we + + + align:start position:0% +equation and we +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +can um + + align:start position:0% +can um + + + align:start position:0% +can um +so let's do + + align:start position:0% +so let's do + + + align:start position:0% +so let's do +it + + align:start position:0% +it + + + align:start position:0% +it +um and we can uh make the analogies with + + align:start position:0% +um and we can uh make the analogies with + + + align:start position:0% +um and we can uh make the analogies with +the with the discret problem with the + + align:start position:0% +the with the discret problem with the + + + align:start position:0% +the with the discret problem with the +discret problem where we had maybe like + + align:start position:0% +discret problem where we had maybe like + + + align:start position:0% +discret problem where we had maybe like +two masses and two + + align:start position:0% +two masses and two + + + align:start position:0% +two masses and two +Springs and that mass was hanging free + + align:start position:0% +Springs and that mass was hanging free + + + align:start position:0% +Springs and that mass was hanging free +just the way that's hanging free why was + + align:start position:0% +just the way that's hanging free why was + + + align:start position:0% +just the way that's hanging free why was +the answer W equals z here I + + align:start position:0% +the answer W equals z here I + + + align:start position:0% +the answer W equals z here I +always if you tell me the right answer I + + align:start position:0% +always if you tell me the right answer I + + + align:start position:0% +always if you tell me the right answer I +write it down right away and I don't uh + + align:start position:0% +write it down right away and I don't uh + + + align:start position:0% +write it down right away and I don't uh +always remember to say more + + align:start position:0% +always remember to say more + + + align:start position:0% +always remember to say more +yeah because there's + + align:start position:0% +yeah because there's + + + align:start position:0% +yeah because there's +nothing right equilibrium at that point + + align:start position:0% +nothing right equilibrium at that point + + + align:start position:0% +nothing right equilibrium at that point +there's nobody here right there's no + + align:start position:0% +there's nobody here right there's no + + + align:start position:0% +there's nobody here right there's no +Force here + + align:start position:0% +Force here + + + align:start position:0% +Force here +so uh and and the force is w and the and + + align:start position:0% +so uh and and the force is w and the and + + + align:start position:0% +so uh and and the force is w and the and +the force is yeah so the force has to be + + align:start position:0% +the force is yeah so the force has to be + + + align:start position:0% +the force is yeah so the force has to be +there there's nothing pulling on that + + align:start position:0% +there there's nothing pulling on that + + + align:start position:0% +there there's nothing pulling on that +nothing pulling on that bottom of the + + align:start position:0% +nothing pulling on that bottom of the + + + align:start position:0% +nothing pulling on that bottom of the +bar the bottom of the bar is hanging + + align:start position:0% +bar the bottom of the bar is hanging + + + align:start position:0% +bar the bottom of the bar is hanging +free so it's we're speaking here about + + align:start position:0% +free so it's we're speaking here about + + + align:start position:0% +free so it's we're speaking here about +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +free boundary conditions of course you + + align:start position:0% +free boundary conditions of course you + + + align:start position:0% +free boundary conditions of course you +know that I'm going to when I've said + + align:start position:0% +know that I'm going to when I've said + + + align:start position:0% +know that I'm going to when I've said +examples another another one is going to + + align:start position:0% +examples another another one is going to + + + align:start position:0% +examples another another one is going to +be what another one of interest is going + + align:start position:0% +be what another one of interest is going + + + align:start position:0% +be what another one of interest is going +to be + + align:start position:0% +to be + + + align:start position:0% +to be +or + + align:start position:0% +or + + + align:start position:0% +or +or U of 0 equals 0 and and what and U of + + align:start position:0% +or U of 0 equals 0 and and what and U of + + + align:start position:0% +or U of 0 equals 0 and and what and U of +one equals z fixed + + align:start position:0% + + + + align:start position:0% + +fixed fixed at both ends that would be a + + align:start position:0% +fixed fixed at both ends that would be a + + + align:start position:0% +fixed fixed at both ends that would be a +different + + align:start position:0% +different + + + align:start position:0% +different +example to be solved in a different way + + align:start position:0% +example to be solved in a different way + + + align:start position:0% +example to be solved in a different way +actually so those are the two sort of + + align:start position:0% +actually so those are the two sort of + + + align:start position:0% +actually so those are the two sort of +model examples I'm I'm sort of inclined + + align:start position:0% +model examples I'm I'm sort of inclined + + + align:start position:0% +model examples I'm I'm sort of inclined +to jump into + + align:start position:0% +to jump into + + + align:start position:0% +to jump into +those uh to say how would we let's we + + align:start position:0% +those uh to say how would we let's we + + + align:start position:0% +those uh to say how would we let's we +actually find those Solutions + + align:start position:0% +actually find those Solutions + + + align:start position:0% +actually find those Solutions +okay before I jump + + align:start position:0% +okay before I jump + + + align:start position:0% +okay before I jump +in I'm I'm always open to questions and + + align:start position:0% +in I'm I'm always open to questions and + + + align:start position:0% +in I'm I'm always open to questions and +I have a question for + + align:start position:0% +I have a question for + + + align:start position:0% +I have a question for +myself um and that + + align:start position:0% +myself um and that + + + align:start position:0% +myself um and that +is I wrote down this + + align:start position:0% +is I wrote down this + + + align:start position:0% +is I wrote down this +framework and this differential + + align:start position:0% +framework and this differential + + + align:start position:0% +framework and this differential +equation well I so I without much + + align:start position:0% +equation well I so I without much + + + align:start position:0% +equation well I so I without much +discussion right and in particular I + + align:start position:0% +discussion right and in particular I + + + align:start position:0% +discussion right and in particular I +didn't discuss this this little + + align:start position:0% +didn't discuss this this little + + + align:start position:0% +didn't discuss this this little +surprising business here that a is now + + align:start position:0% +surprising business here that a is now + + + align:start position:0% +surprising business here that a is now +the + + align:start position:0% + + + + align:start position:0% + +derivative so that Au U the derivative + + align:start position:0% +derivative so that Au U the derivative + + + align:start position:0% +derivative so that Au U the derivative +of U is e the next + + align:start position:0% +of U is e the next + + + align:start position:0% +of U is e the next +step and what's a transpose that's + + align:start position:0% +step and what's a transpose that's + + + align:start position:0% +step and what's a transpose that's +that's the that's what I realized wow + + align:start position:0% +that's the that's what I realized wow + + + align:start position:0% +that's the that's what I realized wow +how did where did that come from and + + align:start position:0% +how did where did that come from and + + + align:start position:0% +how did where did that come from and +what what is a transpose in this analogy + + align:start position:0% +what what is a transpose in this analogy + + + align:start position:0% +what what is a transpose in this analogy +and it's only an analogy right now is is + + align:start position:0% +and it's only an analogy right now is is + + + align:start position:0% +and it's only an analogy right now is is +minus the derivative + + align:start position:0% +minus the derivative + + + align:start position:0% +minus the derivative +so what's up so a transposes minus the + + align:start position:0% + + + + align:start position:0% + +derivative these I would use maybe the + + align:start position:0% +derivative these I would use maybe the + + + align:start position:0% +derivative these I would use maybe the +word operator for something like the + + align:start position:0% +word operator for something like the + + + align:start position:0% +word operator for something like the +derivative where I where this was a + + align:start position:0% +derivative where I where this was a + + + align:start position:0% +derivative where I where this was a +where a a was here was a difference + + align:start position:0% +where a a was here was a difference + + + align:start position:0% +where a a was here was a difference +Matrix It multiplied U and produced e it + + align:start position:0% +Matrix It multiplied U and produced e it + + + align:start position:0% +Matrix It multiplied U and produced e it +acted on U matrices act that's really + + align:start position:0% +acted on U matrices act that's really + + + align:start position:0% +acted on U matrices act that's really +the point matrices act operators act + + align:start position:0% +the point matrices act operators act + + + align:start position:0% +the point matrices act operators act +they you give them an input U and they + + align:start position:0% +they you give them an input U and they + + + align:start position:0% +they you give them an input U and they +give you back an output + + align:start position:0% +give you back an output + + + align:start position:0% +give you back an output +e it's it's you know a matrix a m a + + align:start position:0% +e it's it's you know a matrix a m a + + + align:start position:0% +e it's it's you know a matrix a m a +matrix in particular we use it kind of + + align:start position:0% +matrix in particular we use it kind of + + + align:start position:0% +matrix in particular we use it kind of +in two ways we think of a matrix as kind + + align:start position:0% +in two ways we think of a matrix as kind + + + align:start position:0% +in two ways we think of a matrix as kind +of maybe just a storage of n of a of an + + align:start position:0% +of maybe just a storage of n of a of an + + + align:start position:0% +of maybe just a storage of n of a of an +array of numbers it's just like sitting + + align:start position:0% +array of numbers it's just like sitting + + + align:start position:0% +array of numbers it's just like sitting +there that's not so much what we're + + align:start position:0% +there that's not so much what we're + + + align:start position:0% +there that's not so much what we're +doing here I mean that's convenient to + + align:start position:0% +doing here I mean that's convenient to + + + align:start position:0% +doing here I mean that's convenient to +have + + align:start position:0% +have + + + align:start position:0% +have +bunch of numbers stored in a rectangular + + align:start position:0% +bunch of numbers stored in a rectangular + + + align:start position:0% +bunch of numbers stored in a rectangular +array here our a is and the a over here + + align:start position:0% +array here our a is and the a over here + + + align:start position:0% +array here our a is and the a over here +is operating it's acting it's taking an + + align:start position:0% +is operating it's acting it's taking an + + + align:start position:0% +is operating it's acting it's taking an +input and producing an + + align:start position:0% +input and producing an + + + align:start position:0% +input and producing an +output and for some + + align:start position:0% +output and for some + + + align:start position:0% +output and for some +reason the derivative is so the + + align:start position:0% +reason the derivative is so the + + + align:start position:0% +reason the derivative is so the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +is the first derivative is somehow + + align:start position:0% +is the first derivative is somehow + + + align:start position:0% +is the first derivative is somehow +anti-symmetric right that's what if this + + align:start position:0% +anti-symmetric right that's what if this + + + align:start position:0% +anti-symmetric right that's what if this +is true and I haven't so this I reason I + + align:start position:0% +is true and I haven't so this I reason I + + + align:start position:0% +is true and I haven't so this I reason I +circled those is to come back to that + + align:start position:0% +circled those is to come back to that + + + align:start position:0% +circled those is to come back to that +but for some + + align:start position:0% +but for some + + + align:start position:0% +but for some +reason the first derivative is we're + + align:start position:0% +reason the first derivative is we're + + + align:start position:0% +reason the first derivative is we're +seeing that if if the first derivative + + align:start position:0% +seeing that if if the first derivative + + + align:start position:0% +seeing that if if the first derivative +is a then the transpose is the negative + + align:start position:0% +is a then the transpose is the negative + + + align:start position:0% +is a then the transpose is the negative +is minus well I is minus + + align:start position:0% +is minus well I is minus + + + align:start position:0% +is minus well I is minus +a I'm I'm I'm uh so morally speaking uh + + align:start position:0% +a I'm I'm I'm uh so morally speaking uh + + + align:start position:0% +a I'm I'm I'm uh so morally speaking uh +the derivative the first derivative is + + align:start position:0% +the derivative the first derivative is + + + align:start position:0% +the derivative the first derivative is +anti symmetric sometimes I would use the + + align:start position:0% +anti symmetric sometimes I would use the + + + align:start position:0% +anti symmetric sometimes I would use the +word skew symmetric just meaning the + + align:start position:0% +word skew symmetric just meaning the + + + align:start position:0% +word skew symmetric just meaning the +transpose is minus + + align:start position:0% +transpose is minus + + + align:start position:0% +transpose is minus +now I caught myself as I said that and + + align:start position:0% +now I caught myself as I said that and + + + align:start position:0% +now I caught myself as I said that and +why did I catch myself + + align:start position:0% +why did I catch myself + + + align:start position:0% +why did I catch myself +because inside in the op in in the + + align:start position:0% +because inside in the op in in the + + + align:start position:0% +because inside in the op in in the +definition of the operator come the + + align:start position:0% +definition of the operator come the + + + align:start position:0% +definition of the operator come the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +conditions + + align:start position:0% +conditions + + + align:start position:0% +conditions +so um so so to speak in the middle of + + align:start position:0% +so um so so to speak in the middle of + + + align:start position:0% +so um so so to speak in the middle of +the interval + + align:start position:0% +the interval + + + align:start position:0% +the interval +I'm I'm totally happy to say that + + align:start position:0% +I'm I'm totally happy to say that + + + align:start position:0% +I'm I'm totally happy to say that +derivative is anti-symmetric and its + + align:start position:0% +derivative is anti-symmetric and its + + + align:start position:0% +derivative is anti-symmetric and its +transpose is minus the derivative but I + + align:start position:0% +transpose is minus the derivative but I + + + align:start position:0% +transpose is minus the derivative but I +I have + + align:start position:0% +I have + + + align:start position:0% +I have +to pay attention also to the boundary + + align:start position:0% +to pay attention also to the boundary + + + align:start position:0% +to pay attention also to the boundary +conditions and the boundary conditions + + align:start position:0% +conditions and the boundary conditions + + + align:start position:0% +conditions and the boundary conditions +these are these go with a the boundary + + align:start position:0% +these are these go with a the boundary + + + align:start position:0% +these are these go with a the boundary +conditions on + + align:start position:0% +conditions on + + + align:start position:0% +conditions on +U are are part of the definition of a a + + align:start position:0% +U are are part of the definition of a a + + + align:start position:0% +U are are part of the definition of a a +is the derivative and it acts on + + align:start position:0% +is the derivative and it acts on + + + align:start position:0% +is the derivative and it acts on +functions + + align:start position:0% +functions + + + align:start position:0% +functions +that satisfy the the U the boundary + + align:start position:0% +that satisfy the the U the boundary + + + align:start position:0% +that satisfy the the U the boundary +conditions functions U of X that satisfy + + align:start position:0% +conditions functions U of X that satisfy + + + align:start position:0% +conditions functions U of X that satisfy +the boundary conditions on u a + + align:start position:0% +the boundary conditions on u a + + + align:start position:0% +the boundary conditions on u a +transpose is minus the derivative and it + + align:start position:0% +transpose is minus the derivative and it + + + align:start position:0% +transpose is minus the derivative and it +acts on functions W that satisfy any + + align:start position:0% +acts on functions W that satisfy any + + + align:start position:0% +acts on functions W that satisfy any +boundary conditions on W so maybe I just + + align:start position:0% +boundary conditions on W so maybe I just + + + align:start position:0% +boundary conditions on W so maybe I just +make the point + + align:start position:0% +make the point + + + align:start position:0% +make the point +here here I've got two boundary + + align:start position:0% +here here I've got two boundary + + + align:start position:0% +here here I've got two boundary +conditions on U and none on + + align:start position:0% +conditions on U and none on + + + align:start position:0% +conditions on U and none on +W so I I so it's not really quite + + align:start position:0% +W so I I so it's not really quite + + + align:start position:0% +W so I I so it's not really quite +legitimate for me to say say that a is + + align:start position:0% +legitimate for me to say say that a is + + + align:start position:0% +legitimate for me to say say that a is +anti- symmetric it's it's pretty + + align:start position:0% +anti- symmetric it's it's pretty + + + align:start position:0% +anti- symmetric it's it's pretty +anti-symmetric the derivative except the + + align:start position:0% +anti-symmetric the derivative except the + + + align:start position:0% +anti-symmetric the derivative except the +the functions it's acting on are + + align:start position:0% +the functions it's acting on are + + + align:start position:0% +the functions it's acting on are +different and and also here we have a + + align:start position:0% +different and and also here we have a + + + align:start position:0% +different and and also here we have a +boundary condition at one end on U and a + + align:start position:0% +boundary condition at one end on U and a + + + align:start position:0% +boundary condition at one end on U and a +boundary condition at the other end on W + + align:start position:0% +boundary condition at the other end on W + + + align:start position:0% +boundary condition at the other end on W +what I what I really want to emphasize + + align:start position:0% +what I what I really want to emphasize + + + align:start position:0% +what I what I really want to emphasize +is that boundary conditions + + align:start position:0% +is that boundary conditions + + + align:start position:0% +is that boundary conditions +are part of the problem and often the + + align:start position:0% +are part of the problem and often the + + + align:start position:0% +are part of the problem and often the +hardest + + align:start position:0% +hardest + + + align:start position:0% +hardest +part I really have learned in + + align:start position:0% +part I really have learned in + + + align:start position:0% +part I really have learned in +uh many years of leaving my office door + + align:start position:0% +uh many years of leaving my office door + + + align:start position:0% +uh many years of leaving my office door +open and people come in and they always + + align:start position:0% +open and people come in and they always + + + align:start position:0% +open and people come in and they always +say I just have a little question okay I + + align:start position:0% +say I just have a little question okay I + + + align:start position:0% +say I just have a little question okay I +know um in trouble and I hope you'll say + + align:start position:0% +know um in trouble and I hope you'll say + + + align:start position:0% +know um in trouble and I hope you'll say +that too because uh I don't mean trouble + + align:start position:0% +that too because uh I don't mean trouble + + + align:start position:0% +that too because uh I don't mean trouble +I mean it's good I know it's not going + + align:start position:0% +I mean it's good I know it's not going + + + align:start position:0% +I mean it's good I know it's not going +to be a little question and I won't know + + align:start position:0% +to be a little question and I won't know + + + align:start position:0% +to be a little question and I won't know +the answer but it's very very often + + align:start position:0% +the answer but it's very very often + + + align:start position:0% +the answer but it's very very often +about boundary conditions you know their + + align:start position:0% +about boundary conditions you know their + + + align:start position:0% +about boundary conditions you know their +thesis is buzzing along they've got the + + align:start position:0% +thesis is buzzing along they've got the + + + align:start position:0% +thesis is buzzing along they've got the +differential equation and oh if it was + + align:start position:0% +differential equation and oh if it was + + + align:start position:0% +differential equation and oh if it was +just a little bit clearer what are the + + align:start position:0% +just a little bit clearer what are the + + + align:start position:0% +just a little bit clearer what are the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +conditions + + align:start position:0% +conditions + + + align:start position:0% +conditions +and often they're doing it + + align:start position:0% +and often they're doing it + + + align:start position:0% +and often they're doing it +numerically they're replacing this + + align:start position:0% +numerically they're replacing this + + + align:start position:0% +numerically they're replacing this +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation by finite + + align:start position:0% +equation by finite + + + align:start position:0% +equation by finite +differences and + + align:start position:0% +differences and + + + align:start position:0% +differences and +then what do they do what's the finite + + align:start position:0% +then what do they do what's the finite + + + align:start position:0% +then what do they do what's the finite +difference what finite differ difference + + align:start position:0% +difference what finite differ difference + + + align:start position:0% +difference what finite differ difference +what's the what's the discrete form of + + align:start position:0% +what's the what's the discrete form of + + + align:start position:0% +what's the what's the discrete form of +the boundary condition that's that's + + align:start position:0% +the boundary condition that's that's + + + align:start position:0% +the boundary condition that's that's +like a real + + align:start position:0% +like a real + + + align:start position:0% +like a real +issue still more to be learned not not + + align:start position:0% +issue still more to be learned not not + + + align:start position:0% +issue still more to be learned not not +everything is known about that topic and + + align:start position:0% +everything is known about that topic and + + + align:start position:0% +everything is known about that topic and +of course the point is there's not just + + align:start position:0% +of course the point is there's not just + + + align:start position:0% +of course the point is there's not just +one discrete form if I have a boundary + + align:start position:0% +one discrete form if I have a boundary + + + align:start position:0% +one discrete form if I have a boundary +condition like derivative equals + + align:start position:0% +condition like derivative equals + + + align:start position:0% +condition like derivative equals +zero + + align:start position:0% +zero + + + align:start position:0% +zero +well how do I replace that by finite + + align:start position:0% +well how do I replace that by finite + + + align:start position:0% +well how do I replace that by finite +differences a lot of possibilities every + + align:start position:0% +differences a lot of possibilities every + + + align:start position:0% +differences a lot of possibilities every +possibility + + align:start position:0% +possibility + + + align:start position:0% +possibility +uh do you see that these boundary where + + align:start position:0% +uh do you see that these boundary where + + + align:start position:0% +uh do you see that these boundary where +are these boundary conditions going to + + align:start position:0% +are these boundary conditions going to + + + align:start position:0% +are these boundary conditions going to +show up in our + + align:start position:0% +show up in our + + + align:start position:0% +show up in our +matrices I'm I'm making you think back + + align:start position:0% +matrices I'm I'm making you think back + + + align:start position:0% +matrices I'm I'm making you think back +back to the matrices that we saw from + + align:start position:0% +back to the matrices that we saw from + + + align:start position:0% +back to the matrices that we saw from +the very first day in fact and keep + + align:start position:0% +the very first day in fact and keep + + + align:start position:0% +the very first day in fact and keep +those in mind at the same time as + + align:start position:0% +those in mind at the same time as + + + align:start position:0% +those in mind at the same time as +dealing with the new + + align:start position:0% +dealing with the new + + + align:start position:0% +dealing with the new +problem so where did we see boundary + + align:start position:0% +problem so where did we see boundary + + + align:start position:0% +problem so where did we see boundary +conditions showing + + align:start position:0% +conditions showing + + + align:start position:0% +conditions showing +up we I don't know if we even use the + + align:start position:0% +up we I don't know if we even use the + + + align:start position:0% +up we I don't know if we even use the +word in our matrices you remember our + + align:start position:0% +word in our matrices you remember our + + + align:start position:0% +word in our matrices you remember our +matrices were can I I so I'll just + + align:start position:0% +matrices were can I I so I'll just + + + align:start position:0% +matrices were can I I so I'll just +follow up that discussion one of our + + align:start position:0% +follow up that discussion one of our + + + align:start position:0% +follow up that discussion one of our +matrices our favorite + + align:start position:0% +matrices our favorite + + + align:start position:0% +matrices our favorite +almost favorite of some was though that + + align:start position:0% +almost favorite of some was though that + + + align:start position:0% +almost favorite of some was though that +that + + align:start position:0% +that + + + align:start position:0% +that +K and we discovered that that was an a + + align:start position:0% +K and we discovered that that was an a + + + align:start position:0% +K and we discovered that that was an a +transpose + + align:start position:0% + + + + align:start position:0% + +a and + + align:start position:0% +a and + + + align:start position:0% +a and +what's so I want to talk about that + + align:start position:0% +what's so I want to talk about that + + + align:start position:0% +what's so I want to talk about that +again while we're fresh I'm I'm jump on + + align:start position:0% +again while we're fresh I'm I'm jump on + + + align:start position:0% +again while we're fresh I'm I'm jump on +to that one the the boundary conditions + + align:start position:0% +to that one the the boundary conditions + + + align:start position:0% +to that one the the boundary conditions +are somehow part of a and a transpose + + align:start position:0% +are somehow part of a and a transpose + + + align:start position:0% +are somehow part of a and a transpose +and we can't we don't deeply understand + + align:start position:0% +and we can't we don't deeply understand + + + align:start position:0% +and we can't we don't deeply understand +a and a transpose until we got a h got a + + align:start position:0% +a and a transpose until we got a h got a + + + align:start position:0% +a and a transpose until we got a h got a +hang on those boundary conditions yeah + + align:start position:0% +hang on those boundary conditions yeah + + + align:start position:0% +hang on those boundary conditions yeah +so uh so this was the operator we called + + align:start position:0% +so uh so this was the operator we called + + + align:start position:0% +so uh so this was the operator we called +K + + align:start position:0% +K + + + align:start position:0% +K +right and what uh do you see what what + + align:start position:0% +right and what uh do you see what what + + + align:start position:0% +right and what uh do you see what what +do you remember from the Springs what + + align:start position:0% +do you remember from the Springs what + + + align:start position:0% +do you remember from the Springs what +boundary conditions which of our are two + + align:start position:0% +boundary conditions which of our are two + + + align:start position:0% +boundary conditions which of our are two +problems that that's going to come + + align:start position:0% +problems that that's going to come + + + align:start position:0% +problems that that's going to come +from it's going to come from fixed and + + align:start position:0% +from it's going to come from fixed and + + + align:start position:0% +from it's going to come from fixed and +fixed somehow the minus one that ought + + align:start position:0% +fixed somehow the minus one that ought + + + align:start position:0% +fixed somehow the minus one that ought +to be over here that multiplied u0 you + + align:start position:0% +to be over here that multiplied u0 you + + + align:start position:0% +to be over here that multiplied u0 you +remember this multiplied like a U1 and + + align:start position:0% +remember this multiplied like a U1 and + + + align:start position:0% +remember this multiplied like a U1 and +U2 and a u3 and then there was a u4 that + + align:start position:0% +U2 and a u3 and then there was a u4 that + + + align:start position:0% +U2 and a u3 and then there was a u4 that +was these were zero it was it was this + + align:start position:0% +was these were zero it was it was this + + + align:start position:0% +was these were zero it was it was this +problem it was this problem that led to + + align:start position:0% +problem it was this problem that led to + + + align:start position:0% +problem it was this problem that led to +I'll put it in + + align:start position:0% + + + + align:start position:0% + +K and and now come I'll come back in a + + align:start position:0% +K and and now come I'll come back in a + + + align:start position:0% +K and and now come I'll come back in a +second to that problem do do you see + + align:start position:0% +second to that problem do do you see + + + align:start position:0% +second to that problem do do you see +that here the we have so what are the + + align:start position:0% +that here the we have so what are the + + + align:start position:0% +that here the we have so what are the +analogies that I that I want to make + + align:start position:0% +analogies that I that I want to make + + + align:start position:0% +analogies that I that I want to make +here I want to indicate that by dropping + + align:start position:0% +here I want to indicate that by dropping + + + align:start position:0% +here I want to indicate that by dropping +this this uh + + align:start position:0% +this this uh + + + align:start position:0% +this this uh +uo by by taking it as zero we + + align:start position:0% +uo by by taking it as zero we + + + align:start position:0% +uo by by taking it as zero we +were in a simple way applying the + + align:start position:0% +were in a simple way applying the + + + align:start position:0% +were in a simple way applying the +boundary condition and at the bottom end + + align:start position:0% +boundary condition and at the bottom end + + + align:start position:0% +boundary condition and at the bottom end +where we have the same picture there's a + + align:start position:0% +where we have the same picture there's a + + + align:start position:0% +where we have the same picture there's a +minus one not not uh neglected thrown + + align:start position:0% +minus one not not uh neglected thrown + + + align:start position:0% +minus one not not uh neglected thrown +away because it would multiply you see + + align:start position:0% +away because it would multiply you see + + + align:start position:0% +away because it would multiply you see +that when I do that multiplication that + + align:start position:0% +that when I do that multiplication that + + + align:start position:0% +that when I do that multiplication that +minus one would hit u4 and it's being + + align:start position:0% +minus one would hit u4 and it's being + + + align:start position:0% +minus one would hit u4 and it's being +taken as zero so in some + + align:start position:0% +taken as zero so in some + + + align:start position:0% +taken as zero so in some +way the boundary condition so the answer + + align:start position:0% +way the boundary condition so the answer + + + align:start position:0% +way the boundary condition so the answer +to my question + + align:start position:0% +to my question + + + align:start position:0% +to my question +was the boundary conditions come in the + + align:start position:0% +was the boundary conditions come in the + + + align:start position:0% +was the boundary conditions come in the +first row and last row of the + + align:start position:0% +first row and last row of the + + + align:start position:0% +first row and last row of the +Matrix when we had the matrices we had + + align:start position:0% +Matrix when we had the matrices we had + + + align:start position:0% +Matrix when we had the matrices we had +different first rows and sometimes + + align:start position:0% +different first rows and sometimes + + + align:start position:0% +different first rows and sometimes +different last rows so what would you + + align:start position:0% +different last rows so what would you + + + align:start position:0% +different last rows so what would you +remember our other our next uh example + + align:start position:0% +remember our other our next uh example + + + align:start position:0% +remember our other our next uh example +was like + + align:start position:0% + + + + align:start position:0% + +that so what's what's up there again + + align:start position:0% +that so what's what's up there again + + + align:start position:0% +that so what's what's up there again +here is a u equals + + align:start position:0% +here is a u equals + + + align:start position:0% +here is a u equals +z because we're dropping a minus one + + align:start position:0% +z because we're dropping a minus one + + + align:start position:0% +z because we're dropping a minus one +what boundary condition is being + + align:start position:0% +what boundary condition is being + + + align:start position:0% +what boundary condition is being +reflected in that first row of the + + align:start position:0% + + + + align:start position:0% + +Matrix U Prime is zero that first row is + + align:start position:0% +Matrix U Prime is zero that first row is + + + align:start position:0% +Matrix U Prime is zero that first row is +telling us somehow we've we've thrown + + align:start position:0% +telling us somehow we've we've thrown + + + align:start position:0% +telling us somehow we've we've thrown +away you see what have we thrown away + + align:start position:0% +away you see what have we thrown away + + + align:start position:0% +away you see what have we thrown away +out of the Min if we if we really had a + + align:start position:0% +out of the Min if we if we really had a + + + align:start position:0% +out of the Min if we if we really had a +minus one 2 minus one then we've said to + + align:start position:0% +minus one 2 minus one then we've said to + + + align:start position:0% +minus one 2 minus one then we've said to +ourselves this guy is the same as this + + align:start position:0% +ourselves this guy is the same as this + + + align:start position:0% +ourselves this guy is the same as this +guy so I've really taken you you have + + align:start position:0% +guy so I've really taken you you have + + + align:start position:0% +guy so I've really taken you you have +the the boundary condition that led led + + align:start position:0% +the the boundary condition that led led + + + align:start position:0% +the the boundary condition that led led +me to this row was really that U of Z u0 + + align:start position:0% +me to this row was really that U of Z u0 + + + align:start position:0% +me to this row was really that U of Z u0 +was the same as U1 the slope was zero so + + align:start position:0% +was the same as U1 the slope was zero so + + + align:start position:0% +was the same as U1 the slope was zero so +this this one leads to ah I almost Drew + + align:start position:0% +this this one leads to ah I almost Drew + + + align:start position:0% +this this one leads to ah I almost Drew +an arrow to that but why is why is this + + align:start position:0% +an arrow to that but why is why is this + + + align:start position:0% +an arrow to that but why is why is this +not not matching that one + + align:start position:0% +not not matching that one + + + align:start position:0% +not not matching that one +perfectly because it's a wrong end wrong + + align:start position:0% +perfectly because it's a wrong end wrong + + + align:start position:0% +perfectly because it's a wrong end wrong +end so if I if I wanted it to match + + align:start position:0% +end so if I if I wanted it to match + + + align:start position:0% +end so if I if I wanted it to match +perfectly I should put put the no slope + + align:start position:0% +perfectly I should put put the no slope + + + align:start position:0% +perfectly I should put put the no slope +the free end down here so now I've got + + align:start position:0% +the free end down here so now I've got + + + align:start position:0% +the free end down here so now I've got +at this end I'm looking at w equals 0 + + align:start position:0% +at this end I'm looking at w equals 0 + + + align:start position:0% +at this end I'm looking at w equals 0 +and up at this end I'm now looking at as + + align:start position:0% +and up at this end I'm now looking at as + + + align:start position:0% +and up at this end I'm now looking at as +always at U equals z so U equals z at + + align:start position:0% +always at U equals z so U equals z at + + + align:start position:0% +always at U equals z so U equals z at +top and W equals z at the + + align:start position:0% + + + + align:start position:0% + +bottom + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay oh I could let me go a little + + align:start position:0% +okay oh I could let me go a little + + + align:start position:0% +okay oh I could let me go a little +further with these let me go a little + + align:start position:0% +further with these let me go a little + + + align:start position:0% +further with these let me go a little +further with + + align:start position:0% +further with + + + align:start position:0% +further with +these + + align:start position:0% +these + + + align:start position:0% +these +um maybe I better take them one at a + + align:start position:0% +um maybe I better take them one at a + + + align:start position:0% +um maybe I better take them one at a +time and I guess this was our our K that + + align:start position:0% +time and I guess this was our our K that + + + align:start position:0% +time and I guess this was our our K that +we that we started with so let me start + + align:start position:0% +we that we started with so let me start + + + align:start position:0% +we that we started with so let me start +let me deal with that one first I would + + align:start position:0% +let me deal with that one first I would + + + align:start position:0% +let me deal with that one first I would +like to see + + align:start position:0% +like to see + + + align:start position:0% +like to see +K as a transpose a so I'll I'll put this + + align:start position:0% +K as a transpose a so I'll I'll put this + + + align:start position:0% +K as a transpose a so I'll I'll put this +example back up when when we're finished + + align:start position:0% +example back up when when we're finished + + + align:start position:0% +example back up when when we're finished +with this guy okay I would like to see + + align:start position:0% +with this guy okay I would like to see + + + align:start position:0% +with this guy okay I would like to see +this K which is the fixed fixed right + + align:start position:0% +this K which is the fixed fixed right + + + align:start position:0% +this K which is the fixed fixed right +this is fixed fixed K is + + align:start position:0% +this is fixed fixed K is + + + align:start position:0% +this is fixed fixed K is +fixed + + align:start position:0% + + + + align:start position:0% + +fixed it's it's it's this problem in the + + align:start position:0% +fixed it's it's it's this problem in the + + + align:start position:0% +fixed it's it's it's this problem in the +discret case it's the the bottom spring + + align:start position:0% +discret case it's the the bottom spring + + + align:start position:0% +discret case it's the the bottom spring +is there's another spring attached + + align:start position:0% +is there's another spring attached + + + align:start position:0% +is there's another spring attached +to + + align:start position:0% +to + + + align:start position:0% +to +ground there's a there's a that one's + + align:start position:0% +ground there's a there's a that one's + + + align:start position:0% +ground there's a there's a that one's +fixed okay I I'm going to stay with + + align:start position:0% +fixed okay I I'm going to stay with + + + align:start position:0% +fixed okay I I'm going to stay with +these analogies just a little longer to + + align:start position:0% +these analogies just a little longer to + + + align:start position:0% +these analogies just a little longer to +to get because it's it's all coming now + + align:start position:0% +to get because it's it's all coming now + + + align:start position:0% +to get because it's it's all coming now +and then I'm going + + align:start position:0% +and then I'm going + + + align:start position:0% +and then I'm going +to solve these equations with the Delta + + align:start position:0% +to solve these equations with the Delta + + + align:start position:0% +to solve these equations with the Delta +functions so that's my two + + align:start position:0% +functions so that's my two + + + align:start position:0% +functions so that's my two +principal tasks in uh now is first of + + align:start position:0% +principal tasks in uh now is first of + + + align:start position:0% +principal tasks in uh now is first of +all to to make this + + align:start position:0% +all to to make this + + + align:start position:0% +all to to make this +analogy continue with the analogy + + align:start position:0% +analogy continue with the analogy + + + align:start position:0% +analogy continue with the analogy +and then to then to say okay on with a + + align:start position:0% +and then to then to say okay on with a + + + align:start position:0% +and then to then to say okay on with a +differential equation let's solve it + + align:start position:0% +differential equation let's solve it + + + align:start position:0% +differential equation let's solve it +okay so what was the a do you remember + + align:start position:0% +okay so what was the a do you remember + + + align:start position:0% +okay so what was the a do you remember +we actually had an a this was an a + + align:start position:0% +we actually had an a this was an a + + + align:start position:0% +we actually had an a this was an a +transpose a what was the a let's + + align:start position:0% +transpose a what was the a let's + + + align:start position:0% +transpose a what was the a let's +see result is + + align:start position:0% + + + + align:start position:0% + +3x3 but there were four Springs right + + align:start position:0% +3x3 but there were four Springs right + + + align:start position:0% +3x3 but there were four Springs right +when it was fixed fixed right with three + + align:start position:0% +when it was fixed fixed right with three + + + align:start position:0% +when it was fixed fixed right with three +masses there were four Springs so it was + + align:start position:0% +masses there were four Springs so it was + + + align:start position:0% +masses there were four Springs so it was +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +3X3 came from an A transpose which was + + align:start position:0% +3X3 came from an A transpose which was + + + align:start position:0% +3X3 came from an A transpose which was +3x4 and an a which was + + align:start position:0% + + + + align:start position:0% + +4x3 and what were they let me just + + align:start position:0% +4x3 and what were they let me just + + + align:start position:0% +4x3 and what were they let me just +remember them + + align:start position:0% +remember them + + + align:start position:0% +remember them +a was 4x3 I think there was let's see it + + align:start position:0% +a was 4x3 I think there was let's see it + + + align:start position:0% +a was 4x3 I think there was let's see it +it involved oh gosh can you remember + + align:start position:0% +it involved oh gosh can you remember + + + align:start position:0% +it involved oh gosh can you remember +back yeah okay you got it all right good + + align:start position:0% +back yeah okay you got it all right good + + + align:start position:0% +back yeah okay you got it all right good +to okay fine all right so ones there's a + + align:start position:0% +to okay fine all right so ones there's a + + + align:start position:0% +to okay fine all right so ones there's a +it's a it's a first difference there's a + + align:start position:0% +it's a it's a first difference there's a + + + align:start position:0% +it's a it's a first difference there's a +one minus this guy but that's U zero and + + align:start position:0% +one minus this guy but that's U zero and + + + align:start position:0% +one minus this guy but that's U zero and +it's not there and then there was a U2 - + + align:start position:0% +it's not there and then there was a U2 - + + + align:start position:0% +it's not there and then there was a U2 - +U1 and a u3 - U2 and a u4 - u3 + + align:start position:0% +U1 and a u3 - U2 and a u4 - u3 + + + align:start position:0% +U1 and a u3 - U2 and a u4 - u3 +whoops those were the that was our + + align:start position:0% +whoops those were the that was our + + + align:start position:0% +whoops those were the that was our +Matrix you don't have the + + align:start position:0% +Matrix you don't have the + + + align:start position:0% +Matrix you don't have the +last + + align:start position:0% +last + + + align:start position:0% +last +isow true have I got a fourth row you + + align:start position:0% +isow true have I got a fourth row you + + + align:start position:0% +isow true have I got a fourth row you +have I do and why is that wrong it's + + align:start position:0% +have I do and why is that wrong it's + + + align:start position:0% +have I do and why is that wrong it's +wrong yeah and why shouldn't that row be + + align:start position:0% +wrong yeah and why shouldn't that row be + + + align:start position:0% +wrong yeah and why shouldn't that row be +there you're right totally right + + align:start position:0% +there you're right totally right + + + align:start position:0% +there you're right totally right +because I'm doing fixed fixed and u4 is + + align:start position:0% +because I'm doing fixed fixed and u4 is + + + align:start position:0% +because I'm doing fixed fixed and u4 is +zero right good okay and now for its + + align:start position:0% +zero right good okay and now for its + + + align:start position:0% +zero right good okay and now for its +transpose so am I able to transpose that + + align:start position:0% +transpose so am I able to transpose that + + + align:start position:0% +transpose so am I able to transpose that +one minus one one minus one one minus + + align:start position:0% +one minus one one minus one one minus + + + align:start position:0% +one minus one one minus one one minus +one oh you're seeing + + align:start position:0% +one oh you're seeing + + + align:start position:0% +one oh you're seeing +those H actually we're seeing it all do + + align:start position:0% +those H actually we're seeing it all do + + + align:start position:0% +those H actually we're seeing it all do +you do you see do you see that 1 minus + + align:start position:0% +you do you see do you see that 1 minus + + + align:start position:0% +you do you see do you see that 1 minus +one as being a finite difference of + + align:start position:0% +one as being a finite difference of + + + align:start position:0% +one as being a finite difference of +course you do it's the U2 minus U1 or u3 + + align:start position:0% +course you do it's the U2 minus U1 or u3 + + + align:start position:0% +course you do it's the U2 minus U1 or u3 +minus + + align:start position:0% +minus + + + align:start position:0% +minus +U2 + + align:start position:0% +U2 + + + align:start position:0% +U2 +and do are you happy if I don't put in + + align:start position:0% +and do are you happy if I don't put in + + + align:start position:0% +and do are you happy if I don't put in +all the zeros yeah and do you see + + align:start position:0% +all the zeros yeah and do you see + + + align:start position:0% +all the zeros yeah and do you see +somehow morally this minus sign showing + + align:start position:0% +somehow morally this minus sign showing + + + align:start position:0% +somehow morally this minus sign showing +up in the + + align:start position:0% +up in the + + + align:start position:0% +up in the +transpose you see it right because in + + align:start position:0% +transpose you see it right because in + + + align:start position:0% +transpose you see it right because in +the transpose + + align:start position:0% +the transpose + + + align:start position:0% +the transpose +it's it's it's somehow yeah it's + + align:start position:0% +it's it's it's somehow yeah it's + + + align:start position:0% +it's it's it's somehow yeah it's +reversed the signs are reversed it's a + + align:start position:0% +reversed the signs are reversed it's a + + + align:start position:0% +reversed the signs are reversed it's a +it's a difference and yeah it may be one + + align:start position:0% +it's a difference and yeah it may be one + + + align:start position:0% +it's a difference and yeah it may be one +and when we have differences we might be + + align:start position:0% +and when we have differences we might be + + + align:start position:0% +and when we have differences we might be +like forward in the difference U Beyond + + align:start position:0% +like forward in the difference U Beyond + + + align:start position:0% +like forward in the difference U Beyond +minus U here or we might be doing U here + + align:start position:0% +minus U here or we might be doing U here + + + align:start position:0% +minus U here or we might be doing U here +minus U earlier those are both okay for + + align:start position:0% +minus U earlier those are both okay for + + + align:start position:0% +minus U earlier those are both okay for +differences or or we might have a center + + align:start position:0% +differences or or we might have a center + + + align:start position:0% +differences or or we might have a center +difference U Beyond minus U earlier + + align:start position:0% +difference U Beyond minus U earlier + + + align:start position:0% +difference U Beyond minus U earlier +that's that has a lot of value that + + align:start position:0% +that's that has a lot of value that + + + align:start position:0% +that's that has a lot of value that +centered one but these are not centered + + align:start position:0% +centered one but these are not centered + + + align:start position:0% +centered one but these are not centered +this is but the point I'm everybody's + + align:start position:0% +this is but the point I'm everybody's + + + align:start position:0% +this is but the point I'm everybody's +seeing the point that sort of when I + + align:start position:0% +seeing the point that sort of when I + + + align:start position:0% +seeing the point that sort of when I +transpose that Matrix this was a four + + align:start position:0% +transpose that Matrix this was a four + + + align:start position:0% +transpose that Matrix this was a four +this was a a difference and this was the + + align:start position:0% +this was a a difference and this was the + + + align:start position:0% +this was a a difference and this was the +difference as a minus sign + + align:start position:0% +difference as a minus sign + + + align:start position:0% +difference as a minus sign +because it's because it's well you see + + align:start position:0% +because it's because it's well you see + + + align:start position:0% +because it's because it's well you see +it okay and and what so again + + align:start position:0% +it okay and and what so again + + + align:start position:0% +it okay and and what so again +the you see why I was only able to say + + align:start position:0% +the you see why I was only able to say + + + align:start position:0% +the you see why I was only able to say +that that + + align:start position:0% +that that + + + align:start position:0% +that that +morally the transpose produced a minus + + align:start position:0% +morally the transpose produced a minus + + + align:start position:0% +morally the transpose produced a minus +sign because it did something more it + + align:start position:0% +sign because it did something more it + + + align:start position:0% +sign because it did something more it +changed the shape of the Matrix from 4x3 + + align:start position:0% +changed the shape of the Matrix from 4x3 + + + align:start position:0% +changed the shape of the Matrix from 4x3 +we change to 3x4 so we don't strictly + + align:start position:0% +we change to 3x4 so we don't strictly + + + align:start position:0% +we change to 3x4 so we don't strictly +speaking have here an anti-symmetric + + align:start position:0% +speaking have here an anti-symmetric + + + align:start position:0% +speaking have here an anti-symmetric +Matrix just I'm I'm just being picky + + align:start position:0% +Matrix just I'm I'm just being picky + + + align:start position:0% +Matrix just I'm I'm just being picky +about this point that we don't have an + + align:start position:0% +about this point that we don't have an + + + align:start position:0% +about this point that we don't have an +antisymmetric Matrix because when we + + align:start position:0% +antisymmetric Matrix because when we + + + align:start position:0% +antisymmetric Matrix because when we +transpose it we we do get a s reversal + + align:start position:0% +transpose it we we do get a s reversal + + + align:start position:0% +transpose it we we do get a s reversal +but we also + + align:start position:0% +but we also + + + align:start position:0% +but we also +get the other shape but the point was + + align:start position:0% +get the other shape but the point was + + + align:start position:0% +get the other shape but the point was +that when we multiply everybody's done + + align:start position:0% +that when we multiply everybody's done + + + align:start position:0% +that when we multiply everybody's done +this multiplication now we got the two + + align:start position:0% +this multiplication now we got the two + + + align:start position:0% +this multiplication now we got the two +and the minus ones and the two and the + + align:start position:0% +and the minus ones and the two and the + + + align:start position:0% +and the minus ones and the two and the +minus ones + + align:start position:0% +minus ones + + + align:start position:0% +minus ones +and and we all remember the good + + align:start position:0% +and and we all remember the good + + + align:start position:0% +and and we all remember the good +properties of + + align:start position:0% +properties of + + + align:start position:0% +properties of +K it's certainly symmetric of course + + align:start position:0% +K it's certainly symmetric of course + + + align:start position:0% +K it's certainly symmetric of course +because it's a transpose a and it's + + align:start position:0% +because it's a transpose a and it's + + + align:start position:0% +because it's a transpose a and it's +positive definite why is that now a + + align:start position:0% +positive definite why is that now a + + + align:start position:0% +positive definite why is that now a +transpose a is always positive definite + + align:start position:0% +transpose a is always positive definite + + + align:start position:0% +transpose a is always positive definite +or at least semidefinite and what was + + align:start position:0% +or at least semidefinite and what was + + + align:start position:0% +or at least semidefinite and what was +the point + + align:start position:0% +the point + + + align:start position:0% +the point +about why was it why do why is it + + align:start position:0% +about why was it why do why is it + + + align:start position:0% +about why was it why do why is it +actually definite it's non this is non- + + align:start position:0% +actually definite it's non this is non- + + + align:start position:0% +actually definite it's non this is non- +singular we're we're pushed up from zero + + align:start position:0% +singular we're we're pushed up from zero + + + align:start position:0% +singular we're we're pushed up from zero +because yeah because the test was that + + align:start position:0% +because yeah because the test was that + + + align:start position:0% +because yeah because the test was that +this a had no null space there were no + + align:start position:0% +this a had no null space there were no + + + align:start position:0% +this a had no null space there were no +combinations of those three columns that + + align:start position:0% +combinations of those three columns that + + + align:start position:0% +combinations of those three columns that +gave the zero + + align:start position:0% +gave the zero + + + align:start position:0% +gave the zero +column except of course to take zero of + + align:start position:0% +column except of course to take zero of + + + align:start position:0% +column except of course to take zero of +every column that's always possible but + + align:start position:0% +every column that's always possible but + + + align:start position:0% +every column that's always possible but +but those three columns are independent + + align:start position:0% +but those three columns are independent + + + align:start position:0% +but those three columns are independent +the rank is three so the rank of this + + align:start position:0% +the rank is three so the rank of this + + + align:start position:0% +the rank is three so the rank of this +thing is three it's non singular + + align:start position:0% +thing is three it's non singular + + + align:start position:0% +thing is three it's non singular +everything positive definite all good + + align:start position:0% +everything positive definite all good + + + align:start position:0% +everything positive definite all good +yeah okay and if we wanted + + align:start position:0% +yeah okay and if we wanted + + + align:start position:0% +yeah okay and if we wanted +to + + align:start position:0% +to + + + align:start position:0% +to +um yeah to + + align:start position:0% + + + + align:start position:0% + +uh I could I could do the same + + align:start position:0% +uh I could I could do the same + + + align:start position:0% +uh I could I could do the same +analogy I could do the yeah let me do + + align:start position:0% +analogy I could do the yeah let me do + + + align:start position:0% +analogy I could do the yeah let me do +the same analogy can I do it with the + + align:start position:0% +the same analogy can I do it with the + + + align:start position:0% +the same analogy can I do it with the +with the second problem just while we're + + align:start position:0% +with the second problem just while we're + + + align:start position:0% +with the second problem just while we're +doing doing these things what will be up + + align:start position:0% +doing doing these things what will be up + + + align:start position:0% +doing doing these things what will be up +with the second problem so the or rather + + align:start position:0% +with the second problem so the or rather + + + align:start position:0% +with the second problem so the or rather +the first as I've written it here the + + align:start position:0% +the first as I've written it here the + + + align:start position:0% +the first as I've written it here the +fix free problem how could I get fixed + + align:start position:0% +fix free problem how could I get fixed + + + align:start position:0% +fix free problem how could I get fixed +and free + + align:start position:0% +and free + + + align:start position:0% +and free +here I think + + align:start position:0% +here I think + + + align:start position:0% +here I think +I get fixed and free just by do I get it + + align:start position:0% +I get fixed and free just by do I get it + + + align:start position:0% +I get fixed and free just by do I get it +by just throwing away that fourth Spring + + align:start position:0% +by just throwing away that fourth Spring + + + align:start position:0% +by just throwing away that fourth Spring +right the fourth spring was the was was + + align:start position:0% +right the fourth spring was the was was + + + align:start position:0% +right the fourth spring was the was was +hooking me to the bottom if I throw that + + align:start position:0% +hooking me to the bottom if I throw that + + + align:start position:0% +hooking me to the bottom if I throw that +away that means I throw away the fourth + + align:start position:0% +away that means I throw away the fourth + + + align:start position:0% +away that means I throw away the fourth +row this now becomes + + align:start position:0% + + + + align:start position:0% + +3x3 this is that right now I throw away + + align:start position:0% +3x3 this is that right now I throw away + + + align:start position:0% +3x3 this is that right now I throw away +the fourth column + + align:start position:0% +the fourth column + + + align:start position:0% +the fourth column +here because I'm transposing it's 3x3 + + align:start position:0% +here because I'm transposing it's 3x3 + + + align:start position:0% +here because I'm transposing it's 3x3 +and now what is a transpose a it now has + + align:start position:0% +and now what is a transpose a it now has + + + align:start position:0% +and now what is a transpose a it now has +the new + + align:start position:0% +the new + + + align:start position:0% +the new +name uh but now what's it what's changed + + align:start position:0% +name uh but now what's it what's changed + + + align:start position:0% +name uh but now what's it what's changed +in this + + align:start position:0% +in this + + + align:start position:0% +in this +Matrix this guy has become a one right + + align:start position:0% +Matrix this guy has become a one right + + + align:start position:0% +Matrix this guy has become a one right +when I multiply Row three by column 3 it + + align:start position:0% +when I multiply Row three by column 3 it + + + align:start position:0% +when I multiply Row three by column 3 it +you're I'll make it look a little + + align:start position:0% +you're I'll make it look a little + + + align:start position:0% +you're I'll make it look a little +cleaner there's only a one there to + + align:start position:0% +cleaner there's only a one there to + + + align:start position:0% +cleaner there's only a one there to +multiply the one yeah and I'm getting + + align:start position:0% +multiply the one yeah and I'm getting + + + align:start position:0% +multiply the one yeah and I'm getting +the right now + + align:start position:0% +the right now + + + align:start position:0% +the right now +actually there's some something else to + + align:start position:0% +actually there's some something else to + + + align:start position:0% +actually there's some something else to +recognize about there's another + + align:start position:0% +recognize about there's another + + + align:start position:0% +recognize about there's another +difference to recognize about these two + + align:start position:0% + + + + align:start position:0% + +problems and it's in the fact that this + + align:start position:0% +problems and it's in the fact that this + + + align:start position:0% +problems and it's in the fact that this +one gave us Square + + align:start position:0% +one gave us Square + + + align:start position:0% +one gave us Square +matrices where the other problem gave us + + align:start position:0% +matrices where the other problem gave us + + + align:start position:0% +matrices where the other problem gave us +rectangular + + align:start position:0% +rectangular + + + align:start position:0% +rectangular +matrices so let me try to write that let + + align:start position:0% +matrices so let me try to write that let + + + align:start position:0% +matrices so let me try to write that let +me try to write that point down because + + align:start position:0% +me try to write that point down because + + + align:start position:0% +me try to write that point down because +it's kind of important kind it's kind of + + align:start position:0% +it's kind of important kind it's kind of + + + align:start position:0% +it's kind of important kind it's kind of +satisfying I think okay so so so the the + + align:start position:0% +satisfying I think okay so so so the the + + + align:start position:0% +satisfying I think okay so so so the the +point I'm trying to I'm just pointing it + + align:start position:0% +point I'm trying to I'm just pointing it + + + align:start position:0% +point I'm trying to I'm just pointing it +out that the fixed + + align:start position:0% + + + + align:start position:0% + +free that led to square + + align:start position:0% +free that led to square + + + align:start position:0% +free that led to square +matrices square + + align:start position:0% +matrices square + + + align:start position:0% +matrices square +a and in this + + align:start position:0% +a and in this + + + align:start position:0% +a and in this +um what it means is what's good about + + align:start position:0% +um what it means is what's good about + + + align:start position:0% +um what it means is what's good about +having the a square Matrix a see + + align:start position:0% +having the a square Matrix a see + + + align:start position:0% +having the a square Matrix a see +normally we have a rectangular + + align:start position:0% +normally we have a rectangular + + + align:start position:0% +normally we have a rectangular +and and that's what we have for fixed + + align:start position:0% +and and that's what we have for fixed + + + align:start position:0% +and and that's what we have for fixed +fixed fixed + + align:start position:0% +fixed fixed + + + align:start position:0% +fixed fixed +fixed we have uh rectangular + + align:start position:0% +fixed we have uh rectangular + + + align:start position:0% +fixed we have uh rectangular +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +a and in practice what difference does + + align:start position:0% +a and in practice what difference does + + + align:start position:0% +a and in practice what difference does +it make well in this Square + + align:start position:0% +it make well in this Square + + + align:start position:0% +it make well in this Square +case we + + align:start position:0% +case we + + + align:start position:0% +case we +can solve first for w we can we can the + + align:start position:0% +can solve first for w we can we can the + + + align:start position:0% +can solve first for w we can we can the +inverse of this Matrix we can inverse + + align:start position:0% +inverse of this Matrix we can inverse + + + align:start position:0% +inverse of this Matrix we can inverse +that one and that one of course they go + + align:start position:0% +that one and that one of course they go + + + align:start position:0% +that one and that one of course they go +would go in the opposite order so in + + align:start position:0% +would go in the opposite order so in + + + align:start position:0% +would go in the opposite order so in +the in the Square + + align:start position:0% +the in the Square + + + align:start position:0% +the in the Square +case uh K + + align:start position:0% +case uh K + + + align:start position:0% +case uh K +inverse is so K was a transpose a so K + + align:start position:0% +inverse is so K was a transpose a so K + + + align:start position:0% +inverse is so K was a transpose a so K +inverse will be a inverse a transpose + + align:start position:0% +inverse will be a inverse a transpose + + + align:start position:0% +inverse will be a inverse a transpose +inverse and that makes good + + align:start position:0% +inverse and that makes good + + + align:start position:0% +inverse and that makes good +sense a transpose has got an inverse + + align:start position:0% +sense a transpose has got an inverse + + + align:start position:0% +sense a transpose has got an inverse +this has an inverse those are we can + + align:start position:0% +this has an inverse those are we can + + + align:start position:0% +this has an inverse those are we can +invert separately where in the + + align:start position:0% +invert separately where in the + + + align:start position:0% +invert separately where in the +rectangular case we + + align:start position:0% +rectangular case we + + + align:start position:0% +rectangular case we +can't split apart the + + align:start position:0% + + + + align:start position:0% + +inverses and so the the conclusion is I + + align:start position:0% +inverses and so the the conclusion is I + + + align:start position:0% +inverses and so the the conclusion is I +must Sol I must keep it all together and + + align:start position:0% +must Sol I must keep it all together and + + + align:start position:0% +must Sol I must keep it all together and +solve for U solve KU equal F first for + + align:start position:0% +solve for U solve KU equal F first for + + + align:start position:0% +solve for U solve KU equal F first for +you to give me U and then later w + + align:start position:0% +you to give me U and then later w + + + align:start position:0% +you to give me U and then later w +I'm really using every corner of the + + align:start position:0% +I'm really using every corner of the + + + align:start position:0% +I'm really using every corner of the +board here do do you see what I'm saying + + align:start position:0% +board here do do you see what I'm saying + + + align:start position:0% +board here do do you see what I'm saying +that in this case we we it means that I + + align:start position:0% +that in this case we we it means that I + + + align:start position:0% +that in this case we we it means that I +can first W and then U it's it's + + align:start position:0% +can first W and then U it's it's + + + align:start position:0% +can first W and then U it's it's +exceptional this is the exceptional case + + align:start position:0% +exceptional this is the exceptional case + + + align:start position:0% +exceptional this is the exceptional case +exceptionally + + align:start position:0% +exceptionally + + + align:start position:0% +exceptionally +easy it's because the factors uh allow + + align:start position:0% +easy it's because the factors uh allow + + + align:start position:0% +easy it's because the factors uh allow +us to in other words what I'm saying + + align:start position:0% +us to in other words what I'm saying + + + align:start position:0% +us to in other words what I'm saying +what I want to say is that this problem + + align:start position:0% +what I want to say is that this problem + + + align:start position:0% +what I want to say is that this problem +with these boundary conditions this is + + align:start position:0% +with these boundary conditions this is + + + align:start position:0% +with these boundary conditions this is +the easier + + align:start position:0% +the easier + + + align:start position:0% +the easier +one we can find W first and then find + + align:start position:0% +one we can find W first and then find + + + align:start position:0% +one we can find W first and then find +U whereas this + + align:start position:0% +U whereas this + + + align:start position:0% +U whereas this +problem we're going to have to go for + + align:start position:0% +problem we're going to have to go for + + + align:start position:0% +problem we're going to have to go for +you straight + + align:start position:0% +you straight + + + align:start position:0% +you straight +off okay I I'm ready now to do that to + + align:start position:0% +off okay I I'm ready now to do that to + + + align:start position:0% +off okay I I'm ready now to do that to +to solve those two example + + align:start position:0% + + + + align:start position:0% + +problems and uh this is oh I I let me + + align:start position:0% +problems and uh this is oh I I let me + + + align:start position:0% +problems and uh this is oh I I let me +mention where we are in the textbook + + align:start position:0% +mention where we are in the textbook + + + align:start position:0% +mention where we are in the textbook +we're in in section 3.1 and there's a + + align:start position:0% +we're in in section 3.1 and there's a + + + align:start position:0% +we're in in section 3.1 and there's a +lot in that + + align:start position:0% +lot in that + + + align:start position:0% +lot in that +section but I'm picking here the heart + + align:start position:0% +section but I'm picking here the heart + + + align:start position:0% +section but I'm picking here the heart +of it which is + + align:start position:0% +of it which is + + + align:start position:0% +of it which is +the now the new framework that for the + + align:start position:0% +the now the new framework that for the + + + align:start position:0% +the now the new framework that for the +first time includes + + align:start position:0% +first time includes + + + align:start position:0% +first time includes +derivatives the boundary + + align:start position:0% +derivatives the boundary + + + align:start position:0% +derivatives the boundary +conditions the showing up of a Delta + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% +function + + + align:start position:0% +function +the uh solution of the equations with + + align:start position:0% +the uh solution of the equations with + + + align:start position:0% +the uh solution of the equations with +that Delta function so can we go for + + align:start position:0% +that Delta function so can we go for + + + align:start position:0% +that Delta function so can we go for +that now let me solve these two problems + + align:start position:0% +that now let me solve these two problems + + + align:start position:0% +that now let me solve these two problems +they're different + + align:start position:0% +they're different + + + align:start position:0% +they're different +problems same + + align:start position:0% +problems same + + + align:start position:0% +problems same +equation but that set of boundary + + align:start position:0% +equation but that set of boundary + + + align:start position:0% +equation but that set of boundary +conditions let me do that one + + align:start position:0% +conditions let me do that one + + + align:start position:0% +conditions let me do that one +first and then let me do this one second + + align:start position:0% +first and then let me do this one second + + + align:start position:0% +first and then let me do this one second +okay so first I'm tackling the the + + align:start position:0% +okay so first I'm tackling the the + + + align:start position:0% +okay so first I'm tackling the the +hanging + + align:start position:0% + + + + align:start position:0% + +bar with a weight that I've now called + + align:start position:0% +bar with a weight that I've now called + + + align:start position:0% +bar with a weight that I've now called +one it's now a unit weight so I won't + + align:start position:0% +one it's now a unit weight so I won't + + + align:start position:0% +one it's now a unit weight so I won't +write a an amount at a point x equal a + + align:start position:0% +write a an amount at a point x equal a + + + align:start position:0% +write a an amount at a point x equal a +tell me physically first before + + align:start position:0% +tell me physically first before + + + align:start position:0% +tell me physically first before +we deal with the deal with a + + align:start position:0% +we deal with the deal with a + + + align:start position:0% +we deal with the deal with a +differential equation what's going to + + align:start position:0% +differential equation what's going to + + + align:start position:0% +differential equation what's going to +happen if I take a bar it's a light bar + + align:start position:0% +happen if I take a bar it's a light bar + + + align:start position:0% +happen if I take a bar it's a light bar +so its own weight is not significant + + align:start position:0% +so its own weight is not significant + + + align:start position:0% +so its own weight is not significant +here I hang a load a unit load at some + + align:start position:0% +here I hang a load a unit load at some + + + align:start position:0% +here I hang a load a unit load at some +Midway point partway point + + align:start position:0% + + + + align:start position:0% + +what do you expect what will tell me + + align:start position:0% +what do you expect what will tell me + + + align:start position:0% +what do you expect what will tell me +something about the internal forces that + + align:start position:0% +something about the internal forces that + + + align:start position:0% +something about the internal forces that +those are the W's and then I'll ask you + + align:start position:0% +those are the W's and then I'll ask you + + + align:start position:0% +those are the W's and then I'll ask you +about the displacements U all right what + + align:start position:0% +about the displacements U all right what + + + align:start position:0% +about the displacements U all right what +about internal forces W what will be the + + align:start position:0% +about internal forces W what will be the + + + align:start position:0% +about internal forces W what will be the +internal Force below the + + align:start position:0% +internal Force below the + + + align:start position:0% +internal Force below the +load right zero zero right because we're + + align:start position:0% +load right zero zero right because we're + + + align:start position:0% +load right zero zero right because we're +we're assuming this thing is weightless + + align:start position:0% +we're assuming this thing is weightless + + + align:start position:0% +we're assuming this thing is weightless +so there's nothing happening down here + + align:start position:0% +so there's nothing happening down here + + + align:start position:0% +so there's nothing happening down here +and it's just hanging where above the + + align:start position:0% +and it's just hanging where above the + + + align:start position:0% +and it's just hanging where above the +load the internal force will + + align:start position:0% +load the internal force will + + + align:start position:0% +load the internal force will +be will be that weight w or which I'm + + align:start position:0% +be will be that weight w or which I'm + + + align:start position:0% +be will be that weight w or which I'm +just setting for convenience to be one + + align:start position:0% +just setting for convenience to be one + + + align:start position:0% +just setting for convenience to be one +I'm expecting so now I'm ready I'm we + + align:start position:0% +I'm expecting so now I'm ready I'm we + + + align:start position:0% +I'm expecting so now I'm ready I'm we +just solved that differential + + align:start position:0% +just solved that differential + + + align:start position:0% +just solved that differential +equation so let's put let's draw the + + align:start position:0% +equation so let's put let's draw the + + + align:start position:0% +equation so let's put let's draw the +solution I think it's drawing graphing + + align:start position:0% +solution I think it's drawing graphing + + + align:start position:0% +solution I think it's drawing graphing +these so this is the fix + + align:start position:0% +these so this is the fix + + + align:start position:0% +these so this is the fix +free so this is fixed free just so we + + align:start position:0% +free so this is fixed free just so we + + + align:start position:0% +free so this is fixed free just so we +keep straight which which one we're + + align:start position:0% +keep straight which which one we're + + + align:start position:0% +keep straight which which one we're +solving this is that means U of0 is zero + + align:start position:0% +solving this is that means U of0 is zero + + + align:start position:0% +solving this is that means U of0 is zero +and W of one is + + align:start position:0% +and W of one is + + + align:start position:0% +and W of one is +zero okay and we just found + + align:start position:0% +zero okay and we just found + + + align:start position:0% +zero okay and we just found +W and what was it as as a function of + + align:start position:0% +W and what was it as as a function of + + + align:start position:0% +W and what was it as as a function of +X it changed at x equal + + align:start position:0% +X it changed at x equal + + + align:start position:0% +X it changed at x equal +a and beyond x equal a it was + + align:start position:0% +a and beyond x equal a it was + + + align:start position:0% +a and beyond x equal a it was +zero beyond x equal a below below the + + align:start position:0% +zero beyond x equal a below below the + + + align:start position:0% +zero beyond x equal a below below the +load nothing's happening it's zero all + + align:start position:0% +load nothing's happening it's zero all + + + align:start position:0% +load nothing's happening it's zero all +the way out to + + align:start position:0% +the way out to + + + align:start position:0% +the way out to +one and above above the load PRI for X + + align:start position:0% +one and above above the load PRI for X + + + align:start position:0% +one and above above the load PRI for X +less than a + + align:start position:0% +less than a + + + align:start position:0% +less than a +the the um Force + + align:start position:0% +the the um Force + + + align:start position:0% +the the um Force +is is one it's the load which we've + + align:start position:0% +is is one it's the load which we've + + + align:start position:0% +is is one it's the load which we've +normalized to be one so there's our it's + + align:start position:0% +normalized to be one so there's our it's + + + align:start position:0% +normalized to be one so there's our it's +a step function or + + align:start position:0% + + + + align:start position:0% + +and now is is is that true does that + + align:start position:0% +and now is is is that true does that + + + align:start position:0% +and now is is is that true does that +actually solve the differential equation + + align:start position:0% +actually solve the differential equation + + + align:start position:0% +actually solve the differential equation +what's the differential equation for w + + align:start position:0% +what's the differential equation for w + + + align:start position:0% +what's the differential equation for w +it's that's the equilibrium equation and + + align:start position:0% +it's that's the equilibrium equation and + + + align:start position:0% +it's that's the equilibrium equation and +here's the right hand side and there is + + align:start position:0% +here's the right hand side and there is + + + align:start position:0% +here's the right hand side and there is +a minus did that get + + align:start position:0% +a minus did that get + + + align:start position:0% +a minus did that get +lost don't let don't let let's not lose + + align:start position:0% +lost don't let don't let let's not lose + + + align:start position:0% +lost don't let don't let let's not lose +that yeah there's a minus dwdx so do do + + align:start position:0% +that yeah there's a minus dwdx so do do + + + align:start position:0% +that yeah there's a minus dwdx so do do +you see minus dwdx equal step function + + align:start position:0% +you see minus dwdx equal step function + + + align:start position:0% +you see minus dwdx equal step function +with those B with the boundary condition + + align:start position:0% +with those B with the boundary condition + + + align:start position:0% +with those B with the boundary condition +W of 1 equals z so again right minus + + align:start position:0% +W of 1 equals z so again right minus + + + align:start position:0% +W of 1 equals z so again right minus +dwdx yeah let's write that in here's the + + align:start position:0% +dwdx yeah let's write that in here's the + + + align:start position:0% +dwdx yeah let's write that in here's the +differential equation minus DW DX is the + + align:start position:0% +differential equation minus DW DX is the + + + align:start position:0% +differential equation minus DW DX is the +step function at + + align:start position:0% +step function at + + + align:start position:0% +step function at +a and why do we step down instead of + + align:start position:0% + + + + align:start position:0% + +up because of the minus sign right + + align:start position:0% +up because of the minus sign right + + + align:start position:0% +up because of the minus sign right +because of the minus sign + + align:start position:0% +because of the minus sign + + + align:start position:0% +because of the minus sign +so so the solution is a step + + align:start position:0% +so so the solution is a step + + + align:start position:0% +so so the solution is a step +down and and of course it has to be + + align:start position:0% +down and and of course it has to be + + + align:start position:0% +down and and of course it has to be +adjusted to match the boundary condition + + align:start position:0% +adjusted to match the boundary condition + + + align:start position:0% +adjusted to match the boundary condition +and we because we wanted to end up with + + align:start position:0% +and we because we wanted to end up with + + + align:start position:0% +and we because we wanted to end up with +W of one to be + + align:start position:0% +W of one to be + + + align:start position:0% +W of one to be +zero we had to we had to end up here and + + align:start position:0% +zero we had to we had to end up here and + + + align:start position:0% +zero we had to we had to end up here and +therefore we had to start from + + align:start position:0% +therefore we had to start from + + + align:start position:0% +therefore we had to start from +there really I'm just working + + align:start position:0% +there really I'm just working + + + align:start position:0% +there really I'm just working +upwards I'm doing like it's like back + + align:start position:0% +upwards I'm doing like it's like back + + + align:start position:0% +upwards I'm doing like it's like back +substitution working up the bar + + align:start position:0% +substitution working up the bar + + + align:start position:0% +substitution working up the bar +nothing's happening here nothing's + + align:start position:0% +nothing's happening here nothing's + + + align:start position:0% +nothing's happening here nothing's +happening nothing's happening W is zero + + align:start position:0% +happening nothing's happening W is zero + + + align:start position:0% +happening nothing's happening W is zero +all there's no internal force and then + + align:start position:0% +all there's no internal force and then + + + align:start position:0% +all there's no internal force and then +at that point something happens and from + + align:start position:0% +at that point something happens and from + + + align:start position:0% +at that point something happens and from +there on the internal force is equal to + + align:start position:0% +there on the internal force is equal to + + + align:start position:0% +there on the internal force is equal to +that weight which I'm taking to be one + + align:start position:0% +that weight which I'm taking to be one + + + align:start position:0% +that weight which I'm taking to be one +okay tell me you tell me U of X + + align:start position:0% +okay tell me you tell me U of X + + + align:start position:0% +okay tell me you tell me U of X +now what's the what's + + align:start position:0% +now what's the what's + + + align:start position:0% +now what's the what's +the what's the + + align:start position:0% +the what's the + + + align:start position:0% +the what's the +displacement X going here expecting + + align:start position:0% +displacement X going here expecting + + + align:start position:0% +displacement X going here expecting +something to change at a and ending at + + align:start position:0% +something to change at a and ending at + + + align:start position:0% +something to change at a and ending at +one okay what what do you expect for + + align:start position:0% +one okay what what do you expect for + + + align:start position:0% +one okay what what do you expect for +displacement let's do just uh Common + + align:start position:0% +displacement let's do just uh Common + + + align:start position:0% +displacement let's do just uh Common +Sense + + align:start position:0% +Sense + + + align:start position:0% +Sense +first Common Sense what's what's + + align:start position:0% +first Common Sense what's what's + + + align:start position:0% +first Common Sense what's what's +happening + + align:start position:0% +happening + + + align:start position:0% +happening +here I'm I'm giving a great big pull at + + align:start position:0% +here I'm I'm giving a great big pull at + + + align:start position:0% +here I'm I'm giving a great big pull at +that + + align:start position:0% +that + + + align:start position:0% +that +point and not below so what do you let's + + align:start position:0% +point and not below so what do you let's + + + align:start position:0% +point and not below so what do you let's +take below first what's happening below + + align:start position:0% +take below first what's happening below + + + align:start position:0% +take below first what's happening below +U is a constant yeah the whole thing is + + align:start position:0% +U is a constant yeah the whole thing is + + + align:start position:0% +U is a constant yeah the whole thing is +going to like + + align:start position:0% +going to like + + + align:start position:0% +going to like +drop down rigidly so I'm expecting you + + align:start position:0% +drop down rigidly so I'm expecting you + + + align:start position:0% +drop down rigidly so I'm expecting you +to be a constant here but not not + + align:start position:0% +to be a constant here but not not + + + align:start position:0% +to be a constant here but not not +zero just it's going to drop and what + + align:start position:0% +zero just it's going to drop and what + + + align:start position:0% +zero just it's going to drop and what +about in + + align:start position:0% + + + + align:start position:0% + +here it's going + + align:start position:0% +here it's going + + + align:start position:0% +here it's going +to yeah what's it going to what's the + + align:start position:0% +to yeah what's it going to what's the + + + align:start position:0% +to yeah what's it going to what's the +displacement going to + + align:start position:0% +displacement going to + + + align:start position:0% +displacement going to +be yeah be linear a an ax that's right + + align:start position:0% +be yeah be linear a an ax that's right + + + align:start position:0% +be yeah be linear a an ax that's right +because it starts at zero but you know + + align:start position:0% +because it starts at zero but you know + + + align:start position:0% +because it starts at zero but you know +it's the whole thing the stretching is + + align:start position:0% +it's the whole thing the stretching is + + + align:start position:0% +it's the whole thing the stretching is +uniform but the displacement of course + + align:start position:0% +uniform but the displacement of course + + + align:start position:0% +uniform but the displacement of course +then is linear so actually we could draw + + align:start position:0% +then is linear so actually we could draw + + + align:start position:0% +then is linear so actually we could draw +it here we're + + align:start position:0% +it here we're + + + align:start position:0% +it here we're +expecting to go + + align:start position:0% + + + + align:start position:0% + +up and then to stay constant + + align:start position:0% +up and then to stay constant + + + align:start position:0% +up and then to stay constant +right now just just put do I have + + align:start position:0% +right now just just put do I have + + + align:start position:0% +right now just just put do I have +anything else to so that that's my U of + + align:start position:0% +anything else to so that that's my U of + + + align:start position:0% +anything else to so that that's my U of +X and and like it has the both W and U + + align:start position:0% +X and and like it has the both W and U + + + align:start position:0% +X and and like it has the both W and U +are best written in two + + align:start position:0% +are best written in two + + + align:start position:0% +are best written in two +parts um before a and after a I I don't + + align:start position:0% +parts um before a and after a I I don't + + + align:start position:0% +parts um before a and after a I I don't +think we want to write one function that + + align:start position:0% +think we want to write one function that + + + align:start position:0% +think we want to write one function that +that does that does this but do so this + + align:start position:0% +that does that does this but do so this + + + align:start position:0% +that does that does this but do so this +what are the pieces here the pieces + + align:start position:0% +what are the pieces here the pieces + + + align:start position:0% +what are the pieces here the pieces +are U of X let's see what's the + + align:start position:0% +are U of X let's see what's the + + + align:start position:0% +are U of X let's see what's the +differential equation + + align:start position:0% +differential equation + + + align:start position:0% +differential equation +there H and here U of X is a constant so + + align:start position:0% +there H and here U of X is a constant so + + + align:start position:0% +there H and here U of X is a constant so +okay that's what are these what are + + align:start position:0% +okay that's what are these what are + + + align:start position:0% +okay that's what are these what are +these amounts let's to to get it all + + align:start position:0% +these amounts let's to to get it all + + + align:start position:0% +these amounts let's to to get it all +straight let's see everybody knows it + + align:start position:0% +straight let's see everybody knows it + + + align:start position:0% +straight let's see everybody knows it +had to start there + + align:start position:0% +had to start there + + + align:start position:0% +had to start there +why because the boundary condition said + + align:start position:0% +why because the boundary condition said + + + align:start position:0% +why because the boundary condition said +so and then from that point I just + + align:start position:0% +so and then from that point I just + + + align:start position:0% +so and then from that point I just +looked at the differential equation what + + align:start position:0% +looked at the differential equation what + + + align:start position:0% +looked at the differential equation what +is the differential + + align:start position:0% +is the differential + + + align:start position:0% +is the differential +equation let's see what what's the + + align:start position:0% +equation let's see what what's the + + + align:start position:0% +equation let's see what what's the +differential equation for you if I know + + align:start position:0% +differential equation for you if I know + + + align:start position:0% +differential equation for you if I know +W which I do that that's the that's the + + align:start position:0% +W which I do that that's the that's the + + + align:start position:0% +W which I do that that's the that's the +beauty of this fix free problem I could + + align:start position:0% +beauty of this fix free problem I could + + + align:start position:0% +beauty of this fix free problem I could +find W straight off before finding youu + + align:start position:0% +find W straight off before finding youu + + + align:start position:0% +find W straight off before finding youu +so so like I inte ated + + align:start position:0% +so so like I inte ated + + + align:start position:0% +so so like I inte ated +once to find W and then I integrate + + align:start position:0% +once to find W and then I integrate + + + align:start position:0% +once to find W and then I integrate +again to find U because U is so what's U + + align:start position:0% +again to find U because U is so what's U + + + align:start position:0% +again to find U because U is so what's U +what's the equation for u u is getting + + align:start position:0% +what's the equation for u u is getting + + + align:start position:0% +what's the equation for u u is getting +the derivative is e but then C is one so + + align:start position:0% +the derivative is e but then C is one so + + + align:start position:0% +the derivative is e but then C is one so +so U is + + align:start position:0% +so U is + + + align:start position:0% +so U is +just + + align:start position:0% +just + + + align:start position:0% +just +D what is + + align:start position:0% +D what is + + + align:start position:0% +D what is +U what's the equation yeah that DX is W + + align:start position:0% +U what's the equation yeah that DX is W + + + align:start position:0% +U what's the equation yeah that DX is W +right DX is is e but that's the same as + + align:start position:0% +right DX is is e but that's the same as + + + align:start position:0% +right DX is is e but that's the same as +W here because I took C to be one so one + + align:start position:0% +W here because I took C to be one so one + + + align:start position:0% +W here because I took C to be one so one +integration and I've got + + align:start position:0% +integration and I've got + + + align:start position:0% +integration and I've got +one boundary value so that's like + + align:start position:0% +one boundary value so that's like + + + align:start position:0% +one boundary value so that's like +perfect I just integrate in other words + + align:start position:0% +perfect I just integrate in other words + + + align:start position:0% +perfect I just integrate in other words +I'm integrating this function gosh I'm + + align:start position:0% +I'm integrating this function gosh I'm + + + align:start position:0% +I'm integrating this function gosh I'm +making a lot of work out of that I've + + align:start position:0% +making a lot of work out of that I've + + + align:start position:0% +making a lot of work out of that I've +integrated this function and got that + + align:start position:0% +integrated this function and got that + + + align:start position:0% +integrated this function and got that +one so U of X this was one there because + + align:start position:0% +one so U of X this was one there because + + + align:start position:0% +one so U of X this was one there because +we made it a unit load so U of X will + + align:start position:0% +we made it a unit load so U of X will + + + align:start position:0% +we made it a unit load so U of X will +just be X it's integral and what will + + align:start position:0% +just be X it's integral and what will + + + align:start position:0% +just be X it's integral and what will +U of X what's the constant in this + + align:start position:0% +U of X what's the constant in this + + + align:start position:0% +U of X what's the constant in this +range it's reached the height a and it + + align:start position:0% +range it's reached the height a and it + + + align:start position:0% +range it's reached the height a and it +stays there + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +okay that's the that's the solution to + + align:start position:0% +okay that's the that's the solution to + + + align:start position:0% +okay that's the that's the solution to +the fixed free + + align:start position:0% +the fixed free + + + align:start position:0% +the fixed free +problem it it does it let's look at so + + align:start position:0% +problem it it does it let's look at so + + + align:start position:0% +problem it it does it let's look at so +we took it in two steps CU because this + + align:start position:0% +we took it in two steps CU because this + + + align:start position:0% +we took it in two steps CU because this +this particular fixed free with one + + align:start position:0% +this particular fixed free with one + + + align:start position:0% +this particular fixed free with one +boundary condition on W allowed us to + + align:start position:0% +boundary condition on W allowed us to + + + align:start position:0% +boundary condition on W allowed us to +get to W right away and then + + align:start position:0% +get to W right away and then + + + align:start position:0% +get to W right away and then +subsequently use the one boundary + + align:start position:0% +subsequently use the one boundary + + + align:start position:0% +subsequently use the one boundary +condition on U to get to U of + + align:start position:0% +condition on U to get to U of + + + align:start position:0% +condition on U to get to U of +X but what's the what's the uh so if I + + align:start position:0% +X but what's the what's the uh so if I + + + align:start position:0% +X but what's the what's the uh so if I +put those together now the the the the + + align:start position:0% +put those together now the the the the + + + align:start position:0% +put those together now the the the the +complete differential equation is this + + align:start position:0% +complete differential equation is this + + + align:start position:0% +complete differential equation is this +one and and do you see that this + + align:start position:0% +one and and do you see that this + + + align:start position:0% +one and and do you see that this +satisfies + + align:start position:0% +satisfies + + + align:start position:0% +satisfies +that + + align:start position:0% + + + + align:start position:0% + +equation uh what let's see what are we + + align:start position:0% +equation uh what let's see what are we + + + align:start position:0% +equation uh what let's see what are we +going to call this type of a point here + + align:start position:0% +going to call this type of a point here + + + align:start position:0% +going to call this type of a point here +that's a very important point it's not a + + align:start position:0% +that's a very important point it's not a + + + align:start position:0% +that's a very important point it's not a +Delta function of course it's not a jump + + align:start position:0% +Delta function of course it's not a jump + + + align:start position:0% +Delta function of course it's not a jump +it's not a step we need a name + + align:start position:0% +it's not a step we need a name + + + align:start position:0% +it's not a step we need a name +for what what's going on at that point a + + align:start position:0% +for what what's going on at that point a + + + align:start position:0% +for what what's going on at that point a +ramp might be a good word we could use + + align:start position:0% +ramp might be a good word we could use + + + align:start position:0% +ramp might be a good word we could use +the word ramp because that certainly + + align:start position:0% +the word ramp because that certainly + + + align:start position:0% +the word ramp because that certainly +reminds us of of a + + align:start position:0% +reminds us of of a + + + align:start position:0% +reminds us of of a +ramp or a corner in the problem and + + align:start position:0% +ramp or a corner in the problem and + + + align:start position:0% +ramp or a corner in the problem and +what's happening at a corner what what + + align:start position:0% +what's happening at a corner what what + + + align:start position:0% +what's happening at a corner what what +do I mean + + align:start position:0% +do I mean + + + align:start position:0% +do I mean +by the derivative is is taking a jump + + align:start position:0% +by the derivative is is taking a jump + + + align:start position:0% +by the derivative is is taking a jump +right the derivative the slope is + + align:start position:0% +right the derivative the slope is + + + align:start position:0% +right the derivative the slope is +jumping right jump in + + align:start position:0% +jumping right jump in + + + align:start position:0% +jumping right jump in +slope + + align:start position:0% +slope + + + align:start position:0% +slope +jump in + + align:start position:0% +jump in + + + align:start position:0% +jump in +slope right and that's is is is that + + align:start position:0% +slope right and that's is is is that + + + align:start position:0% +slope right and that's is is is that +what the differential equation would + + align:start position:0% +what the differential equation would + + + align:start position:0% +what the differential equation would +like us to have sure the + + align:start position:0% +like us to have sure the + + + align:start position:0% +like us to have sure the +the the second derivative of this + + align:start position:0% +the the second derivative of this + + + align:start position:0% +the the second derivative of this +function well with the minus is supposed + + align:start position:0% +function well with the minus is supposed + + + align:start position:0% +function well with the minus is supposed +to be a Delta so the first derivative is + + align:start position:0% +to be a Delta so the first derivative is + + + align:start position:0% +to be a Delta so the first derivative is +supposed to be a step so the function + + align:start position:0% +supposed to be a step so the function + + + align:start position:0% +supposed to be a step so the function +itself is supposed to be a ramp and the + + align:start position:0% +itself is supposed to be a ramp and the + + + align:start position:0% +itself is supposed to be a ramp and the +equation is + + align:start position:0% +equation is + + + align:start position:0% +equation is +saying it's telling us something about + + align:start position:0% +saying it's telling us something about + + + align:start position:0% +saying it's telling us something about +what happens at that at that corner it's + + align:start position:0% +what happens at that at that corner it's + + + align:start position:0% +what happens at that at that corner it's +saying what is it saying is happening at + + align:start position:0% +saying what is it saying is happening at + + + align:start position:0% +saying what is it saying is happening at +that corner the it's a there's a jump in + + align:start position:0% +that corner the it's a there's a jump in + + + align:start position:0% +that corner the it's a there's a jump in +the delt in the slope and what's the + + align:start position:0% +the delt in the slope and what's the + + + align:start position:0% +the delt in the slope and what's the +amount of the + + align:start position:0% +amount of the + + + align:start position:0% +amount of the +jump what does the slope Jump + + align:start position:0% +jump what does the slope Jump + + + align:start position:0% +jump what does the slope Jump +by it jumps + + align:start position:0% +by it jumps + + + align:start position:0% +by it jumps +by it jumps down by one it's a i well + + align:start position:0% +by it jumps down by one it's a i well + + + align:start position:0% +by it jumps down by one it's a i well +let's call it a jump of minus one + + align:start position:0% +let's call it a jump of minus one + + + align:start position:0% +let's call it a jump of minus one +because the slope here is one and here + + align:start position:0% +because the slope here is one and here + + + align:start position:0% +because the slope here is one and here +it's zero so the slope dropped and here + + align:start position:0% +it's zero so the slope dropped and here + + + align:start position:0% +it's zero so the slope dropped and here +of course here's our picture there's + + align:start position:0% +of course here's our picture there's + + + align:start position:0% +of course here's our picture there's +there's the slope it dropped from one to + + align:start position:0% +there's the slope it dropped from one to + + + align:start position:0% +there's the slope it dropped from one to +zero so it's and the reason why was this + + align:start position:0% +zero so it's and the reason why was this + + + align:start position:0% +zero so it's and the reason why was this +minus sign the minus sign made it a drop + + align:start position:0% +minus sign the minus sign made it a drop + + + align:start position:0% +minus sign the minus sign made it a drop +instead of a instead of a increase in + + align:start position:0% +instead of a instead of a increase in + + + align:start position:0% +instead of a instead of a increase in +the in the + + align:start position:0% +the in the + + + align:start position:0% +the in the +slope do you do you see that uh picture + + align:start position:0% +slope do you do you see that uh picture + + + align:start position:0% +slope do you do you see that uh picture +and I believe that we could I mean if we + + align:start position:0% +and I believe that we could I mean if we + + + align:start position:0% +and I believe that we could I mean if we +wrote If we kept those matrices that + + align:start position:0% +wrote If we kept those matrices that + + + align:start position:0% +wrote If we kept those matrices that +were + + align:start position:0% +were + + + align:start position:0% +were +there the The Matrix the The Matrix with + + align:start position:0% +there the The Matrix the The Matrix with + + + align:start position:0% +there the The Matrix the The Matrix with +the with the uh two in one corner and a + + align:start position:0% +the with the uh two in one corner and a + + + align:start position:0% +the with the uh two in one corner and a +one in the other corner + + align:start position:0% +one in the other corner + + + align:start position:0% +one in the other corner +and and the A's that a and a transpose + + align:start position:0% +and and the A's that a and a transpose + + + align:start position:0% +and and the A's that a and a transpose +have produced it we could do the same in + + align:start position:0% +have produced it we could do the same in + + + align:start position:0% +have produced it we could do the same in +the discret + + align:start position:0% +the discret + + + align:start position:0% +the discret +case I I would like to spend the + + align:start position:0% +case I I would like to spend the + + + align:start position:0% +case I I would like to spend the +remaining + + align:start position:0% +remaining + + + align:start position:0% +remaining +moments minutes + + align:start position:0% +moments minutes + + + align:start position:0% +moments minutes +hours uh solving the second + + align:start position:0% +hours uh solving the second + + + align:start position:0% +hours uh solving the second +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay which I guess may not be as easy so + + align:start position:0% +okay which I guess may not be as easy so + + + align:start position:0% +okay which I guess may not be as easy so +what's up with the second problem the + + align:start position:0% +what's up with the second problem the + + + align:start position:0% +what's up with the second problem the +physics is I'm now fixing the bottom as + + align:start position:0% + + + + align:start position:0% + +well so physically what are you + + align:start position:0% +well so physically what are you + + + align:start position:0% +well so physically what are you +expecting it's I mean it's fun to at + + align:start position:0% +expecting it's I mean it's fun to at + + + align:start position:0% +expecting it's I mean it's fun to at +least visualize what's happening so we + + align:start position:0% +least visualize what's happening so we + + + align:start position:0% +least visualize what's happening so we +have this + + align:start position:0% +have this + + + align:start position:0% +have this +bar like a like a uh column in a + + align:start position:0% +bar like a like a uh column in a + + + align:start position:0% +bar like a like a uh column in a +building and then we hang a load at a + + align:start position:0% +building and then we hang a load at a + + + align:start position:0% +building and then we hang a load at a +point and what what will happen + + align:start position:0% +point and what what will happen + + + align:start position:0% +point and what what will happen +that's right it'll stretch as before + + align:start position:0% +that's right it'll stretch as before + + + align:start position:0% +that's right it'll stretch as before +some there'll be stretching uniform + + align:start position:0% +some there'll be stretching uniform + + + align:start position:0% +some there'll be stretching uniform +stretching above and uniform compression + + align:start position:0% +stretching above and uniform compression + + + align:start position:0% +stretching above and uniform compression +below I'm expecting so are are you + + align:start position:0% +below I'm expecting so are are you + + + align:start position:0% +below I'm expecting so are are you +expecting a a w to look + + align:start position:0% +expecting a a w to look + + + align:start position:0% +expecting a a w to look +like now we don't have this boundary + + align:start position:0% +like now we don't have this boundary + + + align:start position:0% +like now we don't have this boundary +condition W 1 equals z anymore in fact + + align:start position:0% +condition W 1 equals z anymore in fact + + + align:start position:0% +condition W 1 equals z anymore in fact +we don't have any boundary condition on + + align:start position:0% +we don't have any boundary condition on + + + align:start position:0% +we don't have any boundary condition on +W and I think just based on common sense + + align:start position:0% +W and I think just based on common sense + + + align:start position:0% +W and I think just based on common sense +we would expect the uh that's a positive + + align:start position:0% +we would expect the uh that's a positive + + + align:start position:0% +we would expect the uh that's a positive +W so that's a + + align:start position:0% +W so that's a + + + align:start position:0% +W so that's a +compression and then I sorry that's a + + align:start position:0% +compression and then I sorry that's a + + + align:start position:0% +compression and then I sorry that's a +tension the bar is in in tension here + + align:start position:0% +tension the bar is in in tension here + + + align:start position:0% +tension the bar is in in tension here +tension + + align:start position:0% +tension + + + align:start position:0% +tension +above and that's W positive and + + align:start position:0% +above and that's W positive and + + + align:start position:0% +above and that's W positive and +compression + + align:start position:0% +compression + + + align:start position:0% +compression +below and that's W negative and I think + + align:start position:0% +below and that's W negative and I think + + + align:start position:0% +below and that's W negative and I think +that's what the graph is going to look + + align:start position:0% +that's what the graph is going to look + + + align:start position:0% +that's what the graph is going to look +like and constant in each piece because + + align:start position:0% +like and constant in each piece because + + + align:start position:0% +like and constant in each piece because +there's no no force acting no external + + align:start position:0% +there's no no force acting no external + + + align:start position:0% +there's no no force acting no external +force acting within the piece and the + + align:start position:0% +force acting within the piece and the + + + align:start position:0% +force acting within the piece and the +drop will be at a and what will be the + + align:start position:0% +drop will be at a and what will be the + + + align:start position:0% +drop will be at a and what will be the +amount of the + + align:start position:0% + + + + align:start position:0% + +drop between the + + align:start position:0% +drop between the + + + align:start position:0% +drop between the +W the positive W uh above the load and + + align:start position:0% +W the positive W uh above the load and + + + align:start position:0% +W the positive W uh above the load and +the negative + + align:start position:0% +the negative + + + align:start position:0% +the negative +W what's this + + align:start position:0% +W what's this + + + align:start position:0% +W what's this +amount it's the weight which I've taken + + align:start position:0% +amount it's the weight which I've taken + + + align:start position:0% +amount it's the weight which I've taken +to be one I mean right I if if I put in + + align:start position:0% +to be one I mean right I if if I put in + + + align:start position:0% +to be one I mean right I if if I put in +a I hate to use another letter W that I + + align:start position:0% +a I hate to use another letter W that I + + + align:start position:0% +a I hate to use another letter W that I +should do better uh but anyway we've + + align:start position:0% +should do better uh but anyway we've + + + align:start position:0% +should do better uh but anyway we've +taken it to be one that drop will be + + align:start position:0% +taken it to be one that drop will be + + + align:start position:0% +taken it to be one that drop will be +one I mean what is w it's the integral + + align:start position:0% +one I mean what is w it's the integral + + + align:start position:0% +one I mean what is w it's the integral +of the Delta + + align:start position:0% +of the Delta + + + align:start position:0% +of the Delta +function it's the integral of the Delta + + align:start position:0% +function it's the integral of the Delta + + + align:start position:0% +function it's the integral of the Delta +function with a minus sign so it's a + + align:start position:0% +function with a minus sign so it's a + + + align:start position:0% +function with a minus sign so it's a +drop and it's the Delta function's been + + align:start position:0% +drop and it's the Delta function's been + + + align:start position:0% +drop and it's the Delta function's been +centered at a so the drop occurs at a + + align:start position:0% +centered at a so the drop occurs at a + + + align:start position:0% +centered at a so the drop occurs at a +but now what's up here I've got that's + + align:start position:0% +but now what's up here I've got that's + + + align:start position:0% +but now what's up here I've got that's +what it'll look like + + align:start position:0% +what it'll look like + + + align:start position:0% +what it'll look like +but there's an arbitrary constant + + align:start position:0% +but there's an arbitrary constant + + + align:start position:0% +but there's an arbitrary constant +there's a constant here I mean I I + + align:start position:0% +there's a constant here I mean I I + + + align:start position:0% +there's a constant here I mean I I +haven't + + align:start position:0% +haven't + + + align:start position:0% +haven't +settled this I've settled that this + + align:start position:0% +settled this I've settled that this + + + align:start position:0% +settled this I've settled that this +distance is a one but I don't know these + + align:start position:0% +distance is a one but I don't know these + + + align:start position:0% +distance is a one but I don't know these +numbers yet there's a I and I can't find + + align:start position:0% +numbers yet there's a I and I can't find + + + align:start position:0% +numbers yet there's a I and I can't find +them out from the W equation because I + + align:start position:0% +them out from the W equation because I + + + align:start position:0% +them out from the W equation because I +haven't got any boundary condition on W + + align:start position:0% +haven't got any boundary condition on W + + + align:start position:0% +haven't got any boundary condition on W +previously fixed now I'm I'm now I'm + + align:start position:0% +previously fixed now I'm I'm now I'm + + + align:start position:0% +previously fixed now I'm I'm now I'm +doing fixed fix so let me get the let me + + align:start position:0% +doing fixed fix so let me get the let me + + + align:start position:0% +doing fixed fix so let me get the let me +get the the the black Blackboard up to + + align:start position:0% +get the the the black Blackboard up to + + + align:start position:0% +get the the the black Blackboard up to +date now I'm doing fixed + + align:start position:0% +date now I'm doing fixed + + + align:start position:0% +date now I'm doing fixed +fixed I've got two boundary conditions + + align:start position:0% +fixed I've got two boundary conditions + + + align:start position:0% +fixed I've got two boundary conditions +on U and none on + + align:start position:0% +on U and none on + + + align:start position:0% +on U and none on +W my Matrix a is + + align:start position:0% +W my Matrix a is + + + align:start position:0% +W my Matrix a is +rectangular I can't invert to find W my + + align:start position:0% +rectangular I can't invert to find W my + + + align:start position:0% +rectangular I can't invert to find W my +my operator is morally speaking + + align:start position:0% +my operator is morally speaking + + + align:start position:0% +my operator is morally speaking +rectangular I I can't there's a there's + + align:start position:0% +rectangular I I can't there's a there's + + + align:start position:0% +rectangular I I can't there's a there's +an known constant here the thing has a + + align:start position:0% +an known constant here the thing has a + + + align:start position:0% +an known constant here the thing has a +null + + align:start position:0% +null + + + align:start position:0% +null +space this a transpose has a null space + + align:start position:0% +space this a transpose has a null space + + + align:start position:0% +space this a transpose has a null space +the null space is W if I have a solution + + align:start position:0% +the null space is W if I have a solution + + + align:start position:0% +the null space is W if I have a solution +W I can add a constant and I've still + + align:start position:0% +W I can add a constant and I've still + + + align:start position:0% +W I can add a constant and I've still +got a solution and that constant I don't + + align:start position:0% +got a solution and that constant I don't + + + align:start position:0% +got a solution and that constant I don't +have any boundary condition condition to + + align:start position:0% +have any boundary condition condition to + + + align:start position:0% +have any boundary condition condition to +make it go away so in other + + align:start position:0% +make it go away so in other + + + align:start position:0% +make it go away so in other +words the only way I can figure out the + + align:start position:0% +words the only way I can figure out the + + + align:start position:0% +words the only way I can figure out the +numbers here is to get on to + + align:start position:0% +numbers here is to get on to + + + align:start position:0% +numbers here is to get on to +you so this is going to be some slope + + align:start position:0% +you so this is going to be some slope + + + align:start position:0% +you so this is going to be some slope +some what shall I call this that'll be S + + align:start position:0% +some what shall I call this that'll be S + + + align:start position:0% +some what shall I call this that'll be S +the original slope and this will be S + + align:start position:0% +the original slope and this will be S + + + align:start position:0% +the original slope and this will be S +minus one can I is that all right but I + + align:start position:0% +minus one can I is that all right but I + + + align:start position:0% +minus one can I is that all right but I +don't know s + + align:start position:0% +don't know s + + + align:start position:0% +don't know s +it I don't know it until I come over + + align:start position:0% +it I don't know it until I come over + + + align:start position:0% +it I don't know it until I come over +here and figure out you okay so tell me + + align:start position:0% +here and figure out you okay so tell me + + + align:start position:0% +here and figure out you okay so tell me +what you looks like and then we're we've + + align:start position:0% +what you looks like and then we're we've + + + align:start position:0% +what you looks like and then we're we've +got this + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% +thing + + + align:start position:0% +thing +okay so tell me what U is like + + align:start position:0% + + + + align:start position:0% + +start starts at zero and ends at zero + + align:start position:0% +start starts at zero and ends at zero + + + align:start position:0% +start starts at zero and ends at zero +that's the one thing we definitely + + align:start position:0% +that's the one thing we definitely + + + align:start position:0% +that's the one thing we definitely +know and it does something at a and and + + align:start position:0% +know and it does something at a and and + + + align:start position:0% +know and it does something at a and and +what will it do at + + align:start position:0% +what will it do at + + + align:start position:0% +what will it do at +a it + + align:start position:0% +a it + + + align:start position:0% +a it +changes it's slope changes sign because + + align:start position:0% +changes it's slope changes sign because + + + align:start position:0% +changes it's slope changes sign because +in fact this is the picture of the slope + + align:start position:0% +in fact this is the picture of the slope + + + align:start position:0% +in fact this is the picture of the slope +right and the slope drops by + + align:start position:0% +right and the slope drops by + + + align:start position:0% +right and the slope drops by +one so we we've got it we've got it here + + align:start position:0% +one so we we've got it we've got it here + + + align:start position:0% +one so we we've got it we've got it here +it's it goes up so + + align:start position:0% +it's it goes up so + + + align:start position:0% +it's it goes up so +the slope is constant so the slope is + + align:start position:0% +the slope is constant so the slope is + + + align:start position:0% +the slope is constant so the slope is +constant slope s so it's + + align:start position:0% +constant slope s so it's + + + align:start position:0% +constant slope s so it's +SX reaching some point + + align:start position:0% +SX reaching some point + + + align:start position:0% +SX reaching some point +sa and then it's + + align:start position:0% +sa and then it's + + + align:start position:0% +sa and then it's +dropping at what slope what's the slope + + align:start position:0% + + + + align:start position:0% + +here s minus + + align:start position:0% + + + + align:start position:0% + +one and so what's the + + align:start position:0% + + + + align:start position:0% + +function let's see somehow out of this + + align:start position:0% +function let's see somehow out of this + + + align:start position:0% +function let's see somehow out of this +is going + + align:start position:0% +is going + + + align:start position:0% +is going +appear the number s this has to + + align:start position:0% + + + + align:start position:0% + +magically so I guess let's see how + + align:start position:0% +magically so I guess let's see how + + + align:start position:0% +magically so I guess let's see how +should we do it we started for this for + + align:start position:0% +should we do it we started for this for + + + align:start position:0% +should we do it we started for this for +this linear function here I don't know + + align:start position:0% +this linear function here I don't know + + + align:start position:0% +this linear function here I don't know +how you would like + + align:start position:0% +how you would like + + + align:start position:0% +how you would like +to everybody's everybody for himself at + + align:start position:0% +to everybody's everybody for himself at + + + align:start position:0% +to everybody's everybody for himself at +this point uh you all I want to know is + + align:start position:0% +this point uh you all I want to know is + + + align:start position:0% +this point uh you all I want to know is +the slope here is is 1 minus + + align:start position:0% +the slope here is is 1 minus + + + align:start position:0% +the slope here is is 1 minus +s and I want to choose the number s just + + align:start position:0% +s and I want to choose the number s just + + + align:start position:0% +s and I want to choose the number s just +right so that if it goes up with slope s + + align:start position:0% +right so that if it goes up with slope s + + + align:start position:0% +right so that if it goes up with slope s +to the point a and then comes down with + + align:start position:0% +to the point a and then comes down with + + + align:start position:0% +to the point a and then comes down with +slope 1 minus s what I want it to hit + + align:start position:0% +slope 1 minus s what I want it to hit + + + align:start position:0% +slope 1 minus s what I want it to hit +zero s minus one would be + + align:start position:0% + + + + align:start position:0% + +better + + align:start position:0% + + + + align:start position:0% + +okay should I leave that one or should + + align:start position:0% +okay should I leave that one or should + + + align:start position:0% +okay should I leave that one or should +do you want to any suggestion on what s + + align:start position:0% +do you want to any suggestion on what s + + + align:start position:0% +do you want to any suggestion on what s +is here let's + + align:start position:0% +is here let's + + + align:start position:0% +is here let's +see we should be able to do this + + align:start position:0% +see we should be able to do this + + + align:start position:0% +see we should be able to do this +right + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +right + + align:start position:0% +right + + + align:start position:0% +right +and I want to make those things match + + align:start position:0% +and I want to make those things match + + + align:start position:0% +and I want to make those things match +well okay at this point I want I don't + + align:start position:0% +well okay at this point I want I don't + + + align:start position:0% +well okay at this point I want I don't +want the bar to break we could say at + + align:start position:0% +want the bar to break we could say at + + + align:start position:0% +want the bar to break we could say at +this point you should be the same from + + align:start position:0% +this point you should be the same from + + + align:start position:0% +this point you should be the same from +both sides okay so the're same from both + + align:start position:0% +both sides okay so the're same from both + + + align:start position:0% +both sides okay so the're same from both +sides all right you on the + + align:start position:0% +sides all right you on the + + + align:start position:0% +sides all right you on the +left side If U minus is s is + + align:start position:0% +left side If U minus is s is + + + align:start position:0% +left side If U minus is s is +sa and what is youu coming from the + + align:start position:0% +sa and what is youu coming from the + + + align:start position:0% +sa and what is youu coming from the +right side that's what we haven't really + + align:start position:0% +right side that's what we haven't really + + + align:start position:0% +right side that's what we haven't really +pinned down let's see it starts at zero + + align:start position:0% +pinned down let's see it starts at zero + + + align:start position:0% +pinned down let's see it starts at zero +and I want to I'm looking for a straight + + align:start position:0% +and I want to I'm looking for a straight + + + align:start position:0% +and I want to I'm looking for a straight +line that goes through zero at x equal 1 + + align:start position:0% +line that goes through zero at x equal 1 + + + align:start position:0% +line that goes through zero at x equal 1 +and has that slope okay let's see how + + align:start position:0% +and has that slope okay let's see how + + + align:start position:0% +and has that slope okay let's see how +about s + + align:start position:0% +about s + + + align:start position:0% +about s +-1 * x - one would that do + + align:start position:0% + + + + align:start position:0% + +it I said as everybody for himself here + + align:start position:0% +it I said as everybody for himself here + + + align:start position:0% +it I said as everybody for himself here +so you may you may have a different + + align:start position:0% +so you may you may have a different + + + align:start position:0% +so you may you may have a different +smarter way to look at it but I've at + + align:start position:0% +smarter way to look at it but I've at + + + align:start position:0% +smarter way to look at it but I've at +least I found a function whose + + align:start position:0% +least I found a function whose + + + align:start position:0% +least I found a function whose +derivative is s minus one good and at + + align:start position:0% +derivative is s minus one good and at + + + align:start position:0% +derivative is s minus one good and at +xal 1 it's gone is that okay so that's + + align:start position:0% +xal 1 it's gone is that okay so that's + + + align:start position:0% +xal 1 it's gone is that okay so that's +what that function is so maybe I should + + align:start position:0% +what that function is so maybe I should + + + align:start position:0% +what that function is so maybe I should +have left the X + + align:start position:0% +have left the X + + + align:start position:0% +have left the X +here U coming on the left is SX U coming + + align:start position:0% +here U coming on the left is SX U coming + + + align:start position:0% +here U coming on the left is SX U coming +on the right is s -1 * x -1 that has the + + align:start position:0% +on the right is s -1 * x -1 that has the + + + align:start position:0% +on the right is s -1 * x -1 that has the +right slope and and the right boundary + + align:start position:0% +right slope and and the right boundary + + + align:start position:0% +right slope and and the right boundary +condition and then at a they're supposed + + align:start position:0% +condition and then at a they're supposed + + + align:start position:0% +condition and then at a they're supposed +to meet so that finally does it at a + + align:start position:0% +to meet so that finally does it at a + + + align:start position:0% +to meet so that finally does it at a +this sa from the left is supposed to + + align:start position:0% +this sa from the left is supposed to + + + align:start position:0% +this sa from the left is supposed to +agree with s -1 a minus one from the + + align:start position:0% +agree with s -1 a minus one from the + + + align:start position:0% +agree with s -1 a minus one from the +right that's the magic equation then + + align:start position:0% +right that's the magic equation then + + + align:start position:0% +right that's the magic equation then +that has to determine s and it easier + + align:start position:0% +that has to determine s and it easier + + + align:start position:0% +that has to determine s and it easier +than it looks because an sa is going to + + align:start position:0% +than it looks because an sa is going to + + + align:start position:0% +than it looks because an sa is going to +be on both sides and cancel out so I'll + + align:start position:0% +be on both sides and cancel out so I'll + + + align:start position:0% +be on both sides and cancel out so I'll +get a expression for s for the slope let + + align:start position:0% +get a expression for s for the slope let + + + align:start position:0% +get a expression for s for the slope let +me because I I want to keep that idea + + align:start position:0% +me because I I want to keep that idea + + + align:start position:0% +me because I I want to keep that idea +foremost rather than the the + + align:start position:0% + + + + align:start position:0% + +algebra that's what happens in calculus + + align:start position:0% +algebra that's what happens in calculus + + + align:start position:0% +algebra that's what happens in calculus +courses algebra like takes over you + + align:start position:0% +courses algebra like takes over you + + + align:start position:0% +courses algebra like takes over you +become become just like a demon + + align:start position:0% +become become just like a demon + + + align:start position:0% +become become just like a demon +factorization problem but that's not + + align:start position:0% +factorization problem but that's not + + + align:start position:0% +factorization problem but that's not +what mathematics is about about is about + + align:start position:0% +what mathematics is about about is about + + + align:start position:0% +what mathematics is about about is about +what's going on here and what's going on + + align:start position:0% +what's going on here and what's going on + + + align:start position:0% +what's going on here and what's going on +is a continuity condition we expected + + align:start position:0% +is a continuity condition we expected + + + align:start position:0% +is a continuity condition we expected +the slope to jump the function to have a + + align:start position:0% +the slope to jump the function to have a + + + align:start position:0% +the slope to jump the function to have a +corner that's a corner you'd have to + + align:start position:0% +corner that's a corner you'd have to + + + align:start position:0% +corner that's a corner you'd have to +call it a ramp too and the slope Changed + + align:start position:0% +call it a ramp too and the slope Changed + + + align:start position:0% +call it a ramp too and the slope Changed +by one and the boundary conditions sort + + align:start position:0% +by one and the boundary conditions sort + + + align:start position:0% +by one and the boundary conditions sort +of sent them both up from the sides and + + align:start position:0% +of sent them both up from the sides and + + + align:start position:0% +of sent them both up from the sides and +the continuity condition that U is a + + align:start position:0% +the continuity condition that U is a + + + align:start position:0% +the continuity condition that U is a +continuous function you see if the + + align:start position:0% +continuous function you see if the + + + align:start position:0% +continuous function you see if the +displacement wasn't continuous the bar + + align:start position:0% +displacement wasn't continuous the bar + + + align:start position:0% +displacement wasn't continuous the bar +would break apart there if we had two + + align:start position:0% +would break apart there if we had two + + + align:start position:0% +would break apart there if we had two +different values of U it's the same + + align:start position:0% +different values of U it's the same + + + align:start position:0% +different values of U it's the same +value of + + align:start position:0% +value of + + + align:start position:0% +value of +U positive value it drops all right so U + + align:start position:0% +U positive value it drops all right so U + + + align:start position:0% +U positive value it drops all right so U +the displacement is positive everything + + align:start position:0% +the displacement is positive everything + + + align:start position:0% +the displacement is positive everything +in this bar goes + + align:start position:0% +in this bar goes + + + align:start position:0% +in this bar goes +down but it goes down most at + + align:start position:0% +down but it goes down most at + + + align:start position:0% +down but it goes down most at +a goes down most at a okay so that leads + + align:start position:0% +a goes down most at a okay so that leads + + + align:start position:0% +a goes down most at a okay so that leads +to equation for s + + align:start position:0% +to equation for s + + + align:start position:0% +to equation for s +so you see that + + align:start position:0% +so you see that + + + align:start position:0% +so you see that +as uh expected the fixed fixed problem + + align:start position:0% +as uh expected the fixed fixed problem + + + align:start position:0% +as uh expected the fixed fixed problem +was a little + + align:start position:0% +was a little + + + align:start position:0% +was a little +tougher the fixed free we could find W + + align:start position:0% +tougher the fixed free we could find W + + + align:start position:0% +tougher the fixed free we could find W +and then just one more integral gave us + + align:start position:0% +and then just one more integral gave us + + + align:start position:0% +and then just one more integral gave us +U this the fixed fixed we found uh we + + align:start position:0% +U this the fixed fixed we found uh we + + + align:start position:0% +U this the fixed fixed we found uh we +found W but with an unknown constant and + + align:start position:0% +found W but with an unknown constant and + + + align:start position:0% +found W but with an unknown constant and +then we couldn't resolve that constant + + align:start position:0% +then we couldn't resolve that constant + + + align:start position:0% +then we couldn't resolve that constant +until we got to + + align:start position:0% +until we got to + + + align:start position:0% +until we got to +U okay so quick recap then we're + + align:start position:0% +U okay so quick recap then we're + + + align:start position:0% +U okay so quick recap then we're +speaking about our our familiar + + align:start position:0% +speaking about our our familiar + + + align:start position:0% +speaking about our our familiar +framework but now derivatives have + + align:start position:0% +framework but now derivatives have + + + align:start position:0% +framework but now derivatives have +entered and somehow we still have to + + align:start position:0% +entered and somehow we still have to + + + align:start position:0% +entered and somehow we still have to +discuss more this idea of the transpose + + align:start position:0% +discuss more this idea of the transpose + + + align:start position:0% +discuss more this idea of the transpose +being minus the derivative so more to + + align:start position:0% +being minus the derivative so more to + + + align:start position:0% +being minus the derivative so more to +say about + + align:start position:0% +say about + + + align:start position:0% +say about +that what does transpose mean for + + align:start position:0% +that what does transpose mean for + + + align:start position:0% +that what does transpose mean for +derivatives anyway then we got the Delta + + align:start position:0% +derivatives anyway then we got the Delta + + + align:start position:0% +derivatives anyway then we got the Delta +function into the problem as a point + + align:start position:0% +function into the problem as a point + + + align:start position:0% +function into the problem as a point +source and solved the two principal + + align:start position:0% +source and solved the two principal + + + align:start position:0% +source and solved the two principal +examples and the to just to finally end + + align:start position:0% +examples and the to just to finally end + + + align:start position:0% +examples and the to just to finally end +with the what have we + + align:start position:0% +with the what have we + + + align:start position:0% +with the what have we +found when the right hand side is a + + align:start position:0% +found when the right hand side is a + + + align:start position:0% +found when the right hand side is a +Delta function the solution is called + + align:start position:0% +Delta function the solution is called + + + align:start position:0% +Delta function the solution is called +the greens function for the problem so + + align:start position:0% +the greens function for the problem so + + + align:start position:0% +the greens function for the problem so +we have found the greens function for + + align:start position:0% +we have found the greens function for + + + align:start position:0% +we have found the greens function for +this fix fixed boundary condition this U + + align:start position:0% +this fix fixed boundary condition this U + + + align:start position:0% +this fix fixed boundary condition this U +of X is the greens function named after + + align:start position:0% +of X is the greens function named after + + + align:start position:0% +of X is the greens function named after +this U guy who did a lot of the central + + align:start position:0% +this U guy who did a lot of the central + + + align:start position:0% +this U guy who did a lot of the central +formulas for + + align:start position:0% +formulas for + + + align:start position:0% +formulas for +um for calculus in one and several + + align:start position:0% +um for calculus in one and several + + + align:start position:0% +um for calculus in one and several +variables okay so that's that's uh um + + align:start position:0% +variables okay so that's that's uh um + + + align:start position:0% +variables okay so that's that's uh um +that really is then the the simple + + align:start position:0% +that really is then the the simple + + + align:start position:0% +that really is then the the simple +differential + + align:start position:0% +differential + + + align:start position:0% +differential +equation the boundary conditions you saw + + align:start position:0% +equation the boundary conditions you saw + + + align:start position:0% +equation the boundary conditions you saw +produce all the all the interest and now + + align:start position:0% +produce all the all the interest and now + + + align:start position:0% +produce all the all the interest and now +we've got the solution okay so that's uh + + align:start position:0% +we've got the solution okay so that's uh + + + align:start position:0% +we've got the solution okay so that's uh +lecture seven lecture eight we'll see + + align:start position:0% +lecture seven lecture eight we'll see + + + align:start position:0% +lecture seven lecture eight we'll see +partial differential equations coming so + + align:start position:0% +partial differential equations coming so + + + align:start position:0% +partial differential equations coming so +we're really moving along Okay so \ No newline at end of file diff --git a/EzeYI7p9MjU.txt b/EzeYI7p9MjU.txt new file mode 100644 index 0000000000000000000000000000000000000000..854820bab2556772f714acad1e2ae466dcc11b8b --- /dev/null +++ b/EzeYI7p9MjU.txt @@ -0,0 +1,13395 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right good morning + + align:start position:0% +ocw.mit.edu all right good morning + + + align:start position:0% +ocw.mit.edu all right good morning +everyone let's get + + align:start position:0% +everyone let's get + + + align:start position:0% +everyone let's get +started so we're going to start + + align:start position:0% +started so we're going to start + + + align:start position:0% +started so we're going to start +6046 in Earnest today uh we're going to + + align:start position:0% +6046 in Earnest today uh we're going to + + + align:start position:0% +6046 in Earnest today uh we're going to +start with our first module on divide + + align:start position:0% +start with our first module on divide + + + align:start position:0% +start with our first module on divide +and conquer uh you've all seen divide + + align:start position:0% +and conquer uh you've all seen divide + + + align:start position:0% +and conquer uh you've all seen divide +and conquer algorithms before merge s is + + align:start position:0% +and conquer algorithms before merge s is + + + align:start position:0% +and conquer algorithms before merge s is +a classic divide and conquer algorithm + + align:start position:0% +a classic divide and conquer algorithm + + + align:start position:0% +a classic divide and conquer algorithm +I'm going to spend just a couple of + + align:start position:0% +I'm going to spend just a couple of + + + align:start position:0% +I'm going to spend just a couple of +minutes talking about the + + align:start position:0% +minutes talking about the + + + align:start position:0% +minutes talking about the +Paradigm give you a slightly more + + align:start position:0% +Paradigm give you a slightly more + + + align:start position:0% +Paradigm give you a slightly more +general setting than merge sort and then + + align:start position:0% +general setting than merge sort and then + + + align:start position:0% +general setting than merge sort and then +we'll get into two really cool divide + + align:start position:0% +we'll get into two really cool divide + + + align:start position:0% +we'll get into two really cool divide +and + + align:start position:0% +and + + + align:start position:0% +and +conquer uh uh problems in the sense that + + align:start position:0% +conquer uh uh problems in the sense that + + + align:start position:0% +conquer uh uh problems in the sense that +these are problems for which divid and + + align:start position:0% +these are problems for which divid and + + + align:start position:0% +these are problems for which divid and +Conquer works very well namely convex + + align:start position:0% +Conquer works very well namely convex + + + align:start position:0% +Conquer works very well namely convex +Hull and median + + align:start position:0% +Hull and median + + + align:start position:0% +Hull and median +finding so before I get started on the + + align:start position:0% +finding so before I get started on the + + + align:start position:0% +finding so before I get started on the +material uh let me remind you that uh + + align:start position:0% +material uh let me remind you that uh + + + align:start position:0% +material uh let me remind you that uh +you should be signing up for a + + align:start position:0% +you should be signing up for a + + + align:start position:0% +you should be signing up for a +registation section on stellar and + + align:start position:0% +registation section on stellar and + + + align:start position:0% +registation section on stellar and +please do that even if you don't plan on + + align:start position:0% +please do that even if you don't plan on + + + align:start position:0% +please do that even if you don't plan on +attending sections because we need that + + align:start position:0% +attending sections because we need that + + + align:start position:0% +attending sections because we need that +uh so we can assign your problem sets to + + align:start position:0% +uh so we can assign your problem sets to + + + align:start position:0% +uh so we can assign your problem sets to +be graded okay so that's our way of uh + + align:start position:0% +be graded okay so that's our way of uh + + + align:start position:0% +be graded okay so that's our way of uh +partitioning problem sets as well uh and + + align:start position:0% +partitioning problem sets as well uh and + + + align:start position:0% +partitioning problem sets as well uh and +then the other thing is uh problem set + + align:start position:0% +then the other thing is uh problem set + + + align:start position:0% +then the other thing is uh problem set +one is going to go out today and uh it's + + align:start position:0% +one is going to go out today and uh it's + + + align:start position:0% +one is going to go out today and uh it's +a onewe problem set all problem sets are + + align:start position:0% +a onewe problem set all problem sets are + + + align:start position:0% +a onewe problem set all problem sets are +going to be a a week in duration U + + align:start position:0% +going to be a a week in duration U + + + align:start position:0% +going to be a a week in duration U +please read these problem sets the day + + align:start position:0% +please read these problem sets the day + + + align:start position:0% +please read these problem sets the day +they they come out spend 5 10 minutes + + align:start position:0% +they they come out spend 5 10 minutes + + + align:start position:0% +they they come out spend 5 10 minutes +reading them um some things are going to + + align:start position:0% +reading them um some things are going to + + + align:start position:0% +reading them um some things are going to +look like they're magic that they're uh + + align:start position:0% +look like they're magic that they're uh + + + align:start position:0% +look like they're magic that they're uh +you know how could I possibly prove this + + align:start position:0% +you know how could I possibly prove this + + + align:start position:0% +you know how could I possibly prove this +uh if you think about it for a bit it'll + + align:start position:0% +uh if you think about it for a bit it'll + + + align:start position:0% +uh if you think about it for a bit it'll +become obvious we promise you that but + + align:start position:0% +become obvious we promise you that but + + + align:start position:0% +become obvious we promise you that but +get started early don't get started uh + + align:start position:0% +get started early don't get started uh + + + align:start position:0% +get started early don't get started uh +you know at 700 p.m. when we have a + + align:start position:0% +you know at 700 p.m. when we have a + + + align:start position:0% +you know at 700 p.m. when we have a +11:59 p.m. deadline on Thursday right + + align:start position:0% +11:59 p.m. deadline on Thursday right + + + align:start position:0% +11:59 p.m. deadline on Thursday right +the that 4 hours or 5 hours of time may + + align:start position:0% +the that 4 hours or 5 hours of time may + + + align:start position:0% +the that 4 hours or 5 hours of time may +not be enough to go from magical to + + align:start position:0% +not be enough to go from magical to + + + align:start position:0% +not be enough to go from magical to +obvious okay so um let's get started + + align:start position:0% +obvious okay so um let's get started + + + align:start position:0% +obvious okay so um let's get started +with the + + align:start position:0% +with the + + + align:start position:0% +with the +Paradigm associated with divide and + + align:start position:0% +Paradigm associated with divide and + + + align:start position:0% +Paradigm associated with divide and +conquer it's just a + + align:start position:0% +conquer it's just a + + + align:start position:0% +conquer it's just a +beautiful + + align:start position:0% +beautiful + + + align:start position:0% +beautiful +notion that you can break up a + + align:start position:0% +notion that you can break up a + + + align:start position:0% +notion that you can break up a +problem into smaller parts and somehow + + align:start position:0% +problem into smaller parts and somehow + + + align:start position:0% +problem into smaller parts and somehow +compose the solutions to the smaller + + align:start position:0% +compose the solutions to the smaller + + + align:start position:0% +compose the solutions to the smaller +parts and of course the details are + + align:start position:0% +parts and of course the details are + + + align:start position:0% +parts and of course the details are +going to be what's important when we + + align:start position:0% +going to be what's important when we + + + align:start position:0% +going to be what's important when we +take a particular problem instance but + + align:start position:0% +take a particular problem instance but + + + align:start position:0% +take a particular problem instance but +let's say we given a problem of size + + align:start position:0% +let's say we given a problem of size + + + align:start position:0% +let's say we given a problem of size +n we're going to divide + + align:start position:0% +n we're going to divide + + + align:start position:0% +n we're going to divide +it into a sub problems I'll put that in + + align:start position:0% +it into a sub problems I'll put that in + + + align:start position:0% +it into a sub problems I'll put that in +quotes so you know it's uh a + + align:start position:0% +quotes so you know it's uh a + + + align:start position:0% +quotes so you know it's uh a +symbol + + align:start position:0% +symbol + + + align:start position:0% +symbol +uh a sub problems of + + align:start position:0% +uh a sub problems of + + + align:start position:0% +uh a sub problems of +size n / + + align:start position:0% +size n / + + + align:start position:0% +size n / +B and here a could is is an integer and + + align:start position:0% +B and here a could is is an integer and + + + align:start position:0% +B and here a could is is an integer and +a is going to be greater than or equal + + align:start position:0% +a is going to be greater than or equal + + + align:start position:0% +a is going to be greater than or equal +to one it could be two it could be three + + align:start position:0% +to one it could be two it could be three + + + align:start position:0% +to one it could be two it could be three +it could be four this is the + + align:start position:0% +it could be four this is the + + + align:start position:0% +it could be four this is the +generalization I alluded to and B does + + align:start position:0% +generalization I alluded to and B does + + + align:start position:0% +generalization I alluded to and B does +not have to be too + + align:start position:0% +not have to be too + + + align:start position:0% +not have to be too +or even an integer but it has to be + + align:start position:0% +or even an integer but it has to be + + + align:start position:0% +or even an integer but it has to be +strictly greater than one otherwise you + + align:start position:0% +strictly greater than one otherwise you + + + align:start position:0% +strictly greater than one otherwise you +know there's no notion of uh divide and + + align:start position:0% +know there's no notion of uh divide and + + + align:start position:0% +know there's no notion of uh divide and +conquer you're not breaking things up + + align:start position:0% +conquer you're not breaking things up + + + align:start position:0% +conquer you're not breaking things up +into smaller problems so B should be + + align:start position:0% +into smaller problems so B should be + + + align:start position:0% +into smaller problems so B should be +strictly greater than one right so + + align:start position:0% +strictly greater than one right so + + + align:start position:0% +strictly greater than one right so +that's the the general setting and then + + align:start position:0% +that's the the general setting and then + + + align:start position:0% +that's the the general setting and then +you + + align:start position:0% +you + + + align:start position:0% +you +solve each sub problem + + align:start position:0% +solve each sub problem + + + align:start position:0% +solve each sub problem +recursively and the idea here is that + + align:start position:0% +recursively and the idea here is that + + + align:start position:0% +recursively and the idea here is that +once the sub problems become + + align:start position:0% +once the sub problems become + + + align:start position:0% +once the sub problems become +really small they become constant size + + align:start position:0% +really small they become constant size + + + align:start position:0% +really small they become constant size +It's relatively easy to solve them you + + align:start position:0% +It's relatively easy to solve them you + + + align:start position:0% +It's relatively easy to solve them you +can just do exhaustive search uh if you + + align:start position:0% +can just do exhaustive search uh if you + + + align:start position:0% +can just do exhaustive search uh if you +have 10 elements uh and uh you're doing + + align:start position:0% +have 10 elements uh and uh you're doing + + + align:start position:0% +have 10 elements uh and uh you're doing +effectively a cubic search well 10 cubed + + align:start position:0% +effectively a cubic search well 10 cubed + + + align:start position:0% +effectively a cubic search well 10 cubed +is a, that's a constant you're in great + + align:start position:0% +is a, that's a constant you're in great + + + align:start position:0% +is a, that's a constant you're in great +shape right as long as the constants are + + align:start position:0% +shape right as long as the constants are + + + align:start position:0% +shape right as long as the constants are +small enough and so you're going to + + align:start position:0% +small enough and so you're going to + + + align:start position:0% +small enough and so you're going to +recurse until these problems get small + + align:start position:0% +recurse until these problems get small + + + align:start position:0% +recurse until these problems get small +and then typically this is not true for + + align:start position:0% +and then typically this is not true for + + + align:start position:0% +and then typically this is not true for +all divide and concer approaches but for + + align:start position:0% +all divide and concer approaches but for + + + align:start position:0% +all divide and concer approaches but for +most of them and certainly the ones + + align:start position:0% +most of them and certainly the ones + + + align:start position:0% +most of them and certainly the ones +we're going to cover uh today the smarts + + align:start position:0% +we're going to cover uh today the smarts + + + align:start position:0% +we're going to cover uh today the smarts +is going to be in the combination step + + align:start position:0% +is going to be in the combination step + + + align:start position:0% +is going to be in the combination step +when you combine these + + align:start position:0% +when you combine these + + + align:start position:0% +when you combine these +problems uh the solutions of these sub + + align:start position:0% +problems uh the solutions of these sub + + + align:start position:0% +problems uh the solutions of these sub +problems into the overall solution + + align:start position:0% + + + + align:start position:0% + +and so that's uh the story um typically + + align:start position:0% +and so that's uh the story um typically + + + align:start position:0% +and so that's uh the story um typically +what happens in terms of + + align:start position:0% +what happens in terms of + + + align:start position:0% +what happens in terms of +efficiency is that you can write a + + align:start position:0% +efficiency is that you can write a + + + align:start position:0% +efficiency is that you can write a +recurrence that's associated + + align:start position:0% +recurrence that's associated + + + align:start position:0% +recurrence that's associated +with this divide and conquer algorithm + + align:start position:0% +with this divide and conquer algorithm + + + align:start position:0% +with this divide and conquer algorithm +and you say t of n which is the running + + align:start position:0% +and you say t of n which is the running + + + align:start position:0% +and you say t of n which is the running +time for a problem of size n is going to + + align:start position:0% +time for a problem of size n is going to + + + align:start position:0% +time for a problem of size n is going to +be a * T ofn / B + + align:start position:0% +be a * T ofn / B + + + align:start position:0% +be a * T ofn / B +and this is a recurrence plus the + + align:start position:0% +and this is a recurrence plus the + + + align:start position:0% +and this is a recurrence plus the +work that you need to do for the merge + + align:start position:0% +work that you need to do for the merge + + + align:start position:0% +work that you need to do for the merge +operation are the combine this is the + + align:start position:0% +operation are the combine this is the + + + align:start position:0% +operation are the combine this is the +same as + + align:start position:0% + + + + align:start position:0% + +merge um and so you get a recurrence and + + align:start position:0% +merge um and so you get a recurrence and + + + align:start position:0% +merge um and so you get a recurrence and +you're not quite done yet in terms + + align:start position:0% +you're not quite done yet in terms + + + align:start position:0% +you're not quite done yet in terms +of the analysis because once you have + + align:start position:0% +of the analysis because once you have + + + align:start position:0% +of the analysis because once you have +the recurrence you do have to solve the + + align:start position:0% +the recurrence you do have to solve the + + + align:start position:0% +the recurrence you do have to solve the +recurrence and it's usually not that + + align:start position:0% +recurrence and it's usually not that + + + align:start position:0% +recurrence and it's usually not that +hard and certainly it's not going to be + + align:start position:0% +hard and certainly it's not going to be + + + align:start position:0% +hard and certainly it's not going to be +particularly difficult for the divide + + align:start position:0% +particularly difficult for the divide + + + align:start position:0% +particularly difficult for the divide +and + + align:start position:0% +and + + + align:start position:0% +and +conquer examples that we're going to + + align:start position:0% +conquer examples that we're going to + + + align:start position:0% +conquer examples that we're going to +look at at least today but we also have + + align:start position:0% +look at at least today but we also have + + + align:start position:0% +look at at least today but we also have +this theorem that's called the master + + align:start position:0% +this theorem that's called the master + + + align:start position:0% +this theorem that's called the master +theorem that uh is essentially something + + align:start position:0% +theorem that uh is essentially something + + + align:start position:0% +theorem that uh is essentially something +where you can fairly + + align:start position:0% +where you can fairly + + + align:start position:0% +where you can fairly +mechanically plug + + align:start position:0% +mechanically plug + + + align:start position:0% +mechanically plug +in the A's and the B's and whatever you + + align:start position:0% +in the A's and the B's and whatever you + + + align:start position:0% +in the A's and the B's and whatever you +have there maybe it's Theta n maybe it's + + align:start position:0% +have there maybe it's Theta n maybe it's + + + align:start position:0% +have there maybe it's Theta n maybe it's +Theta n square and get the solution to + + align:start position:0% +Theta n square and get the solution to + + + align:start position:0% +Theta n square and get the solution to +the recurrence I'm actually not going to + + align:start position:0% +the recurrence I'm actually not going to + + + align:start position:0% +the recurrence I'm actually not going to +do that today but you'll here once again + + align:start position:0% +do that today but you'll here once again + + + align:start position:0% +do that today but you'll here once again +about the master theorem uh tomorrow in + + align:start position:0% +about the master theorem uh tomorrow in + + + align:start position:0% +about the master theorem uh tomorrow in +in section and it's a fairly + + align:start position:0% +in section and it's a fairly + + + align:start position:0% +in section and it's a fairly +straightforward template that you can + + align:start position:0% +straightforward template that you can + + + align:start position:0% +straightforward template that you can +use for most of the divid and Concor + + align:start position:0% +use for most of the divid and Concor + + + align:start position:0% +use for most of the divid and Concor +examples we're going to look at in 046 + + align:start position:0% +examples we're going to look at in 046 + + + align:start position:0% +examples we're going to look at in 046 +with one exception uh that we'll look at + + align:start position:0% +with one exception uh that we'll look at + + + align:start position:0% +with one exception uh that we'll look at +in median finding today that will simply + + align:start position:0% +in median finding today that will simply + + + align:start position:0% +in median finding today that will simply +give you the solution to the recurrence + + align:start position:0% +give you the solution to the recurrence + + + align:start position:0% +give you the solution to the recurrence +okay so you've seen most of these things + + align:start position:0% +okay so you've seen most of these things + + + align:start position:0% +okay so you've seen most of these things +before that's a little bit of setup and + + align:start position:0% +before that's a little bit of setup and + + + align:start position:0% +before that's a little bit of setup and +so let's Dive Right In into convex Hull + + align:start position:0% +so let's Dive Right In into convex Hull + + + align:start position:0% +so let's Dive Right In into convex Hull +which is + + align:start position:0% +which is + + + align:start position:0% +which is +uh my + + align:start position:0% +uh my + + + align:start position:0% +uh my +favorite problem when it comes to using + + align:start position:0% +favorite problem when it comes to using + + + align:start position:0% +favorite problem when it comes to using +divide and concer so convex Hall I got a + + align:start position:0% +divide and concer so convex Hall I got a + + + align:start position:0% +divide and concer so convex Hall I got a +little prop here uh which will save me + + align:start position:0% +little prop here uh which will save me + + + align:start position:0% +little prop here uh which will save me +from writing on the board and hopefully + + align:start position:0% +from writing on the board and hopefully + + + align:start position:0% +from writing on the board and hopefully +be more more understandable but the idea + + align:start position:0% +be more more understandable but the idea + + + align:start position:0% +be more more understandable but the idea +here is that um in this case we have a a + + align:start position:0% +here is that um in this case we have a a + + + align:start position:0% +here is that um in this case we have a a +two-dimensional problem problem with uh + + align:start position:0% +two-dimensional problem problem with uh + + + align:start position:0% +two-dimensional problem problem with uh +a bunch of points in a two-dimensional + + align:start position:0% +a bunch of points in a two-dimensional + + + align:start position:0% +a bunch of points in a two-dimensional +plane uh you can certainly do convex + + align:start position:0% +plane uh you can certainly do convex + + + align:start position:0% +plane uh you can certainly do convex +Hull for three dimensions many + + align:start position:0% +Hull for three dimensions many + + + align:start position:0% +Hull for three dimensions many +dimensions and uh convexity is something + + align:start position:0% +dimensions and uh convexity is something + + + align:start position:0% +dimensions and uh convexity is something +that is a fundamental notion in + + align:start position:0% +that is a fundamental notion in + + + align:start position:0% +that is a fundamental notion in +optimization and maybe we'll get to that + + align:start position:0% +optimization and maybe we'll get to that + + + align:start position:0% +optimization and maybe we'll get to that +in 6046 in advanced topics maybe not but + + align:start position:0% +in 6046 in advanced topics maybe not but + + + align:start position:0% +in 6046 in advanced topics maybe not but +in the context of today's lecture what + + align:start position:0% +in the context of today's lecture what + + + align:start position:0% +in the context of today's lecture what +we're interested in doing is essentially + + align:start position:0% +we're interested in doing is essentially + + + align:start position:0% +we're interested in doing is essentially +finding an envelope or a hull associated + + align:start position:0% +finding an envelope or a hull associated + + + align:start position:0% +finding an envelope or a hull associated +with the collection of points on a + + align:start position:0% +with the collection of points on a + + + align:start position:0% +with the collection of points on a +two-dimensional plane and this Hull + + align:start position:0% +two-dimensional plane and this Hull + + + align:start position:0% +two-dimensional plane and this Hull +obviously is going to be something as + + align:start position:0% +obviously is going to be something as + + + align:start position:0% +obviously is going to be something as +you can guess um that + + align:start position:0% +you can guess um that + + + align:start position:0% +you can guess um that +encloses all of these points okay so uh + + align:start position:0% +encloses all of these points okay so uh + + + align:start position:0% +encloses all of these points okay so uh +what I have here uh if I make this + + align:start position:0% +what I have here uh if I make this + + + align:start position:0% +what I have here uh if I make this +string taught enough this is not working + + align:start position:0% +string taught enough this is not working + + + align:start position:0% +string taught enough this is not working +out so well but I think you get the + + align:start position:0% +out so well but I think you get the + + + align:start position:0% +out so well but I think you get the +picture uh + + align:start position:0% + + + + align:start position:0% + +all right so that's not a convex Hull + + align:start position:0% +all right so that's not a convex Hull + + + align:start position:0% +all right so that's not a convex Hull +okay this this is not a convex Hull for + + align:start position:0% +okay this this is not a convex Hull for + + + align:start position:0% +okay this this is not a convex Hull for +the reason that I have a bunch of points + + align:start position:0% +the reason that I have a bunch of points + + + align:start position:0% +the reason that I have a bunch of points +outside of the hull all right so let me + + align:start position:0% +outside of the hull all right so let me + + + align:start position:0% +outside of the hull all right so let me +just that is a convex H okay um and now + + align:start position:0% +just that is a convex H okay um and now + + + align:start position:0% +just that is a convex H okay um and now +if I start stretching like that or like + + align:start position:0% +if I start stretching like that or like + + + align:start position:0% +if I start stretching like that or like +this or like that that's still a convex + + align:start position:0% +this or like that that's still a convex + + + align:start position:0% +this or like that that's still a convex +Hall okay so that's the game we have to + + align:start position:0% +Hall okay so that's the game we have to + + + align:start position:0% +Hall okay so that's the game we have to +uh find an algorithm and we'll look at a + + align:start position:0% +uh find an algorithm and we'll look at a + + + align:start position:0% +uh find an algorithm and we'll look at a +couple of different ones that will find + + align:start position:0% +couple of different ones that will find + + + align:start position:0% +couple of different ones that will find +all of these segments that are + + align:start position:0% +all of these segments that are + + + align:start position:0% +all of these segments that are +associated with this convex Hall okay so + + align:start position:0% +associated with this convex Hall okay so + + + align:start position:0% +associated with this convex Hall okay so +this is a segment that's part of the + + align:start position:0% +this is a segment that's part of the + + + align:start position:0% +this is a segment that's part of the +convex Hall that's a segment that's part + + align:start position:0% +convex Hall that's a segment that's part + + + align:start position:0% +convex Hall that's a segment that's part +of the convex Hull if in fact I had + + align:start position:0% +of the convex Hull if in fact I had + + + align:start position:0% +of the convex Hull if in fact I had +something like + + align:start position:0% +something like + + + align:start position:0% +something like +this this and and this was stretched out + + align:start position:0% +this this and and this was stretched out + + + align:start position:0% +this this and and this was stretched out +because I have those two points outside + + align:start position:0% +because I have those two points outside + + + align:start position:0% +because I have those two points outside +the convex H this may still be + + align:start position:0% +the convex H this may still be + + + align:start position:0% +the convex H this may still be +a segment that's part of the correct + + align:start position:0% +a segment that's part of the correct + + + align:start position:0% +a segment that's part of the correct +convex Hull but this one was is not + + align:start position:0% +convex Hull but this one was is not + + + align:start position:0% +convex Hull but this one was is not +right so so that's the the game here is + + align:start position:0% +right so so that's the the game here is + + + align:start position:0% +right so so that's the the game here is +to find these segments so if you're + + align:start position:0% +to find these segments so if you're + + + align:start position:0% +to find these segments so if you're +going to be working with segments or + + align:start position:0% +going to be working with segments or + + + align:start position:0% +going to be working with segments or +tangents uh they're going to be used + + align:start position:0% +tangents uh they're going to be used + + + align:start position:0% +tangents uh they're going to be used +synonymously that are all of the + + align:start position:0% +synonymously that are all of the + + + align:start position:0% +synonymously that are all of the +tangents or segments associated with the + + align:start position:0% +tangents or segments associated with the + + + align:start position:0% +tangents or segments associated with the +entirety of the convex Hull and we have + + align:start position:0% +entirety of the convex Hull and we have + + + align:start position:0% +entirety of the convex Hull and we have +to discover them and the only input that + + align:start position:0% +to discover them and the only input that + + + align:start position:0% +to discover them and the only input that +we have is the set of points X I Yi + + align:start position:0% +we have is the set of points X I Yi + + + align:start position:0% +we have is the set of points X I Yi +coordinates okay and there's just a + + align:start position:0% +coordinates okay and there's just a + + + align:start position:0% +coordinates okay and there's just a +variety of algorithms that you can use + + align:start position:0% +variety of algorithms that you can use + + + align:start position:0% +variety of algorithms that you can use +to do this the the the one that I I wish + + align:start position:0% +to do this the the the one that I I wish + + + align:start position:0% +to do this the the the one that I I wish +I had time to explain but I'll just + + align:start position:0% +I had time to explain but I'll just + + + align:start position:0% +I had time to explain but I'll just +mention is what's called a gift wrapping + + align:start position:0% +mention is what's called a gift wrapping + + + align:start position:0% +mention is what's called a gift wrapping +algorithm where I you might not have + + align:start position:0% +algorithm where I you might not have + + + align:start position:0% +algorithm where I you might not have +done this but I guarantee you uh that + + align:start position:0% +done this but I guarantee you uh that + + + align:start position:0% +done this but I guarantee you uh that +you probably have taken a misshapen gift + + align:start position:0% +you probably have taken a misshapen gift + + + align:start position:0% +you probably have taken a misshapen gift +right and try to wrap it in gift + + align:start position:0% +right and try to wrap it in gift + + + align:start position:0% +right and try to wrap it in gift +wrapping paper and when you're doing + + align:start position:0% +wrapping paper and when you're doing + + + align:start position:0% +wrapping paper and when you're doing +that you're essentially if you're doing + + align:start position:0% +that you're essentially if you're doing + + + align:start position:0% +that you're essentially if you're doing +it right you're essentially trying to + + align:start position:0% +it right you're essentially trying to + + + align:start position:0% +it right you're essentially trying to +find the convex Hull of this + + align:start position:0% +find the convex Hull of this + + + align:start position:0% +find the convex Hull of this +three-dimensional structure you're + + align:start position:0% +three-dimensional structure you're + + + align:start position:0% +three-dimensional structure you're +trying to tighten it up you're trying to + + align:start position:0% +trying to tighten it up you're trying to + + + align:start position:0% +trying to tighten it up you're trying to +find the minimum amount of graph of gift + + align:start position:0% +find the minimum amount of graph of gift + + + align:start position:0% +find the minimum amount of graph of gift +wrapping paper I'm not sure you ever + + align:start position:0% +wrapping paper I'm not sure you ever + + + align:start position:0% +wrapping paper I'm not sure you ever +thought about minimizing gift wrap paper + + align:start position:0% +thought about minimizing gift wrap paper + + + align:start position:0% +thought about minimizing gift wrap paper +but you should have um and uh that's the + + align:start position:0% +but you should have um and uh that's the + + + align:start position:0% +but you should have um and uh that's the +convex Hull of this three-dimensional + + align:start position:0% +convex Hull of this three-dimensional + + + align:start position:0% +convex Hull of this three-dimensional +shape right but we'll stick to two + + align:start position:0% +shape right but we'll stick to two + + + align:start position:0% +shape right but we'll stick to two +Dimensions because we'll have to draw + + align:start position:0% +Dimensions because we'll have to draw + + + align:start position:0% +Dimensions because we'll have to draw +things on the + + align:start position:0% +things on the + + + align:start position:0% +things on the +board so um let me just uh spec this out + + align:start position:0% +board so um let me just uh spec this out + + + align:start position:0% +board so um let me just uh spec this out +a bit uh we're given + + align:start position:0% +a bit uh we're given + + + align:start position:0% +a bit uh we're given +end + + align:start position:0% + + + + align:start position:0% + +points in a + + align:start position:0% +points in a + + + align:start position:0% +points in a +plane and those set of points are + + align:start position:0% +plane and those set of points are + + + align:start position:0% +plane and those set of points are +s x i + + align:start position:0% +s x i + + + align:start position:0% +s x i +Yi such that I equals 1 2 to n and we're + + align:start position:0% +Yi such that I equals 1 2 to n and we're + + + align:start position:0% +Yi such that I equals 1 2 to n and we're +just going to assume + + align:start position:0% +just going to assume + + + align:start position:0% +just going to assume +here just to make things easy because we + + align:start position:0% +here just to make things easy because we + + + align:start position:0% +here just to make things easy because we +don't want to have segments that are uh + + align:start position:0% +don't want to have segments that are uh + + + align:start position:0% +don't want to have segments that are uh +uh null or segments that are uh that are + + align:start position:0% +uh null or segments that are uh that are + + + align:start position:0% +uh null or segments that are uh that are +a little bit different because they're + + align:start position:0% +a little bit different because they're + + + align:start position:0% +a little bit different because they're +disc continuous but we're going to + + align:start position:0% +disc continuous but we're going to + + + align:start position:0% +disc continuous but we're going to +assume that no + + align:start position:0% +assume that no + + + align:start position:0% +assume that no +two have the same x + + align:start position:0% +two have the same x + + + align:start position:0% +two have the same x +coordinate this is just a matter of + + align:start position:0% + + + + align:start position:0% + +convenience and + + align:start position:0% +convenience and + + + align:start position:0% +convenience and +no two have the same + + align:start position:0% + + + + align:start position:0% + +y-coordinate and then finally no three + + align:start position:0% +y-coordinate and then finally no three + + + align:start position:0% +y-coordinate and then finally no three +in a + + align:start position:0% +in a + + + align:start position:0% +in a +line okay because we want to be able to + + align:start position:0% +line okay because we want to be able to + + + align:start position:0% +line okay because we want to be able to +look at pairs of of points and find + + align:start position:0% +look at pairs of of points and find + + + align:start position:0% +look at pairs of of points and find +these segments and it just gets kind of + + align:start position:0% +these segments and it just gets kind of + + + align:start position:0% +these segments and it just gets kind of +inconvenient and you have to deal + + align:start position:0% +inconvenient and you have to deal + + + align:start position:0% +inconvenient and you have to deal +special cases if if no if three of them + + align:start position:0% +special cases if if no if three of them + + + align:start position:0% +special cases if if no if three of them +are on a + + align:start position:0% +are on a + + + align:start position:0% +are on a +line and so the convex Hull + + align:start position:0% + + + + align:start position:0% + +itself is the + + align:start position:0% + + + + align:start position:0% + +smallest + + align:start position:0% + + + + align:start position:0% + +polygon + + align:start position:0% + + + + align:start position:0% + +containing all points + + align:start position:0% +containing all points + + + align:start position:0% +containing all points +in s and we're going to call that + + align:start position:0% +in s and we're going to call that + + + align:start position:0% +in s and we're going to call that +CH of s okay convex Hull of + + align:start position:0% + + + + align:start position:0% + +s as small as convex polygon thank + + align:start position:0% + + + + align:start position:0% + +you and so just as + + align:start position:0% +you and so just as + + + align:start position:0% +you and so just as +uh an example on the board when you have + + align:start position:0% +uh an example on the board when you have + + + align:start position:0% +uh an example on the board when you have +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +you're going to have your convex Hull + + align:start position:0% +you're going to have your convex Hull + + + align:start position:0% +you're going to have your convex Hull +being + + align:start position:0% + + + + align:start position:0% + +that this one is inside of it these two + + align:start position:0% +that this one is inside of it these two + + + align:start position:0% +that this one is inside of it these two +points are inside of it and all of the + + align:start position:0% +points are inside of it and all of the + + + align:start position:0% +points are inside of it and all of the +other ones form the from the hull so we + + align:start position:0% +other ones form the from the hull so we + + + align:start position:0% +other ones form the from the hull so we +might have p + + align:start position:0% +might have p + + + align:start position:0% +might have p +q r s + + align:start position:0% +q r s + + + align:start position:0% +q r s +Tu and V and X are inside of the hull + + align:start position:0% +Tu and V and X are inside of the hull + + + align:start position:0% +Tu and V and X are inside of the hull +they're not they're not part of the + + align:start position:0% +they're not they're not part of the + + + align:start position:0% +they're not they're not part of the +specification of CH of s which I haven't + + align:start position:0% +specification of CH of s which I haven't + + + align:start position:0% +specification of CH of s which I haven't +quite told you how we're going to + + align:start position:0% +quite told you how we're going to + + + align:start position:0% +quite told you how we're going to +specify that but the way we're going to + + align:start position:0% +specify that but the way we're going to + + + align:start position:0% +specify that but the way we're going to +specify that uh is simply by + + align:start position:0% +specify that uh is simply by + + + align:start position:0% +specify that uh is simply by +representing it as a + + align:start position:0% +representing it as a + + + align:start position:0% +representing it as a +sequence of + + align:start position:0% +sequence of + + + align:start position:0% +sequence of +points that are on the + + align:start position:0% +points that are on the + + + align:start position:0% +points that are on the +boundary on the + + align:start position:0% + + + + align:start position:0% + +hull in clockwise + + align:start position:0% + + + + align:start position:0% + +order and you can think of this as being + + align:start position:0% +order and you can think of this as being + + + align:start position:0% +order and you can think of this as being +a doubly link list in terms of the data + + align:start position:0% +a doubly link list in terms of the data + + + align:start position:0% +a doubly link list in terms of the data +structure that you'd use if you coded + + align:start position:0% +structure that you'd use if you coded + + + align:start position:0% +structure that you'd use if you coded +this up so in this case it would be + + align:start position:0% +this up so in this case it would be + + + align:start position:0% +this up so in this case it would be +P to + + align:start position:0% +P to + + + align:start position:0% +P to +Q to + + align:start position:0% +Q to + + + align:start position:0% +Q to +R to S you're going to start with with P + + align:start position:0% +R to S you're going to start with with P + + + align:start position:0% +R to S you're going to start with with P +in this case it's a w link list + + align:start position:0% +in this case it's a w link list + + + align:start position:0% +in this case it's a w link list +so you could conceivably start with + + align:start position:0% +so you could conceivably start with + + + align:start position:0% +so you could conceivably start with +anything but that's + + align:start position:0% +anything but that's + + + align:start position:0% +anything but that's +the the representation of the convex + + align:start position:0% +the the representation of the convex + + + align:start position:0% +the the representation of the convex +hall right and we're going to use + + align:start position:0% +hall right and we're going to use + + + align:start position:0% +hall right and we're going to use +clockwise just because uh we want to be + + align:start position:0% +clockwise just because uh we want to be + + + align:start position:0% +clockwise just because uh we want to be +clear um as to what order we're + + align:start position:0% +clear um as to what order we're + + + align:start position:0% +clear um as to what order we're +enumerating these points it's going to + + align:start position:0% +enumerating these points it's going to + + + align:start position:0% +enumerating these points it's going to +become important when we do the divide + + align:start position:0% +become important when we do the divide + + + align:start position:0% +become important when we do the divide +and conquer algorithm so let's say that + + align:start position:0% +and conquer algorithm so let's say that + + + align:start position:0% +and conquer algorithm so let's say that +we didn't care about divide and conquer + + align:start position:0% +we didn't care about divide and conquer + + + align:start position:0% +we didn't care about divide and conquer +just for the heck of it and I gave you a + + align:start position:0% +just for the heck of it and I gave you a + + + align:start position:0% +just for the heck of it and I gave you a +bunch of + + align:start position:0% + + + + align:start position:0% + +points over + + align:start position:0% + + + + align:start position:0% + +here can you think of + + align:start position:0% + + + + align:start position:0% + +a simple figet efficiency for just a + + align:start position:0% +a simple figet efficiency for just a + + + align:start position:0% +a simple figet efficiency for just a +couple of + + align:start position:0% +couple of + + + align:start position:0% +couple of +minutes can you think of a simple + + align:start position:0% +minutes can you think of a simple + + + align:start position:0% +minutes can you think of a simple +algorithm that would generate the + + align:start position:0% +algorithm that would generate the + + + align:start position:0% +algorithm that would generate the +segments of the convex Hull for example + + align:start position:0% +segments of the convex Hull for example + + + align:start position:0% +segments of the convex Hull for example +I do not want to generate this segment + + align:start position:0% +I do not want to generate this segment + + + align:start position:0% +I do not want to generate this segment +VX if I think of a segment as being + + align:start position:0% +VX if I think of a segment as being + + + align:start position:0% +VX if I think of a segment as being +something that is defined by two points + + align:start position:0% +something that is defined by two points + + + align:start position:0% +something that is defined by two points +then I don't want to generate the + + align:start position:0% +then I don't want to generate the + + + align:start position:0% +then I don't want to generate the +segment X because clearly the segment is + + align:start position:0% +segment X because clearly the segment is + + + align:start position:0% +segment X because clearly the segment is +not part of the convex Hull but whereas + + align:start position:0% +not part of the convex Hull but whereas + + + align:start position:0% +not part of the convex Hull but whereas +the segment PQ QR RS Etc they're all + + align:start position:0% +the segment PQ QR RS Etc they're all + + + align:start position:0% +the segment PQ QR RS Etc they're all +part of the convex Hull right so what is + + align:start position:0% +part of the convex Hull right so what is + + + align:start position:0% +part of the convex Hull right so what is +the obvious Brute Force algorithm + + align:start position:0% +the obvious Brute Force algorithm + + + align:start position:0% +the obvious Brute Force algorithm +forgetting efficiency that given this + + align:start position:0% +forgetting efficiency that given this + + + align:start position:0% +forgetting efficiency that given this +set of points will generate One By One + + align:start position:0% +set of points will generate One By One + + + align:start position:0% +set of points will generate One By One +The segments of the convex + + align:start position:0% +The segments of the convex + + + align:start position:0% +The segments of the convex +Hull + + align:start position:0% +Hull + + + align:start position:0% +Hull +anybody did you have your hand + + align:start position:0% +anybody did you have your hand + + + align:start position:0% +anybody did you have your hand +up no + + align:start position:0% +up no + + + align:start position:0% +up no +go ahead + + align:start position:0% + + + + align:start position:0% + +yeah draw the line and check how many + + align:start position:0% +yeah draw the line and check how many + + + align:start position:0% +yeah draw the line and check how many +lines it intersects with um is there I I + + align:start position:0% +lines it intersects with um is there I I + + + align:start position:0% +lines it intersects with um is there I I +think you got you draw the line that's + + align:start position:0% +think you got you draw the line that's + + + align:start position:0% +think you got you draw the line that's +good right + + align:start position:0% +good right + + + align:start position:0% +good right +um well uh but you want to do a little + + align:start position:0% +um well uh but you want to do a little + + + align:start position:0% +um well uh but you want to do a little +bit more yeah go ahead go ahead yeah + + align:start position:0% + + + + align:start position:0% + +ah so that's good that's good that's + + align:start position:0% +ah so that's good that's good that's + + + align:start position:0% +ah so that's good that's good that's +good all right so uh you know the the + + align:start position:0% +good all right so uh you know the the + + + align:start position:0% +good all right so uh you know the the +first person who who breaks the ice here + + align:start position:0% +first person who who breaks the ice here + + + align:start position:0% +first person who who breaks the ice here +always gets a frisbe sorry man at least + + align:start position:0% +always gets a frisbe sorry man at least + + + align:start position:0% +always gets a frisbe sorry man at least +I only hit the lecturer right no + + align:start position:0% +I only hit the lecturer right no + + + align:start position:0% +I only hit the lecturer right no +liability considerations here okay now + + align:start position:0% +liability considerations here okay now + + + align:start position:0% +liability considerations here okay now +now I'm getting scared um so uh right so + + align:start position:0% +now I'm getting scared um so uh right so + + + align:start position:0% +now I'm getting scared um so uh right so +I think there's a certain amount of when + + align:start position:0% +I think there's a certain amount of when + + + align:start position:0% +I think there's a certain amount of when +I throw this you know am I going to + + align:start position:0% +I throw this you know am I going to + + + align:start position:0% +I throw this you know am I going to +choke or not right but uh it's going to + + align:start position:0% +choke or not right but uh it's going to + + + align:start position:0% +choke or not right but uh it's going to +get harder and one of you guys at the + + align:start position:0% +get harder and one of you guys at the + + + align:start position:0% +get harder and one of you guys at the +back uh answers a question so you're + + align:start position:0% +back uh answers a question so you're + + + align:start position:0% +back uh answers a question so you're +exactly right and uh you draw a + + align:start position:0% +exactly right and uh you draw a + + + align:start position:0% +exactly right and uh you draw a +line and then you just look at it and + + align:start position:0% +line and then you just look at it and + + + align:start position:0% +line and then you just look at it and +you look at the half plane and if all + + align:start position:0% +you look at the half plane and if all + + + align:start position:0% +you look at the half plane and if all +the points are to one side it is a + + align:start position:0% +the points are to one side it is a + + + align:start position:0% +the points are to one side it is a +segment of the convex Hall if it's if if + + align:start position:0% +segment of the convex Hall if it's if if + + + align:start position:0% +segment of the convex Hall if it's if if +if they're not it's not a segment + + align:start position:0% +if they're not it's not a segment + + + align:start position:0% +if they're not it's not a segment +beautiful right are we done can we go + + align:start position:0% +beautiful right are we done can we go + + + align:start position:0% +beautiful right are we done can we go +enjoy the good weather outside right no + + align:start position:0% +enjoy the good weather outside right no + + + align:start position:0% +enjoy the good weather outside right no +we got a waste to go here right so this + + align:start position:0% +we got a waste to go here right so this + + + align:start position:0% +we got a waste to go here right so this +is not a segment whereas this one let me + + align:start position:0% +is not a segment whereas this one let me + + + align:start position:0% +is not a segment whereas this one let me +draw + + align:start position:0% +draw + + + align:start position:0% +draw +that little I should draw these in + + align:start position:0% +that little I should draw these in + + + align:start position:0% +that little I should draw these in +dotted way this is not a segment this is + + align:start position:0% +dotted way this is not a segment this is + + + align:start position:0% +dotted way this is not a segment this is +not a + + align:start position:0% +not a + + + align:start position:0% +not a +segment this is a segment and I violated + + align:start position:0% +segment this is a segment and I violated + + + align:start position:0% +segment this is a segment and I violated +my rule of these three uh not being in a + + align:start position:0% +my rule of these three uh not being in a + + + align:start position:0% +my rule of these three uh not being in a +straight line so I'll move this over + + align:start position:0% +straight line so I'll move this over + + + align:start position:0% +straight line so I'll move this over +here and then that's a segment and so on + + align:start position:0% +here and then that's a segment and so on + + + align:start position:0% +here and then that's a segment and so on +and so forth okay + + align:start position:0% +and so forth okay + + + align:start position:0% +and so forth okay +right I'm + + align:start position:0% + + + + align:start position:0% + +sorry oh you're right that's a good + + align:start position:0% +sorry oh you're right that's a good + + + align:start position:0% +sorry oh you're right that's a good +point that's an excellent point so what + + align:start position:0% +point that's an excellent point so what + + + align:start position:0% +point that's an excellent point so what +happened here was when I move that out + + align:start position:0% +happened here was when I move that out + + + align:start position:0% +happened here was when I move that out +you're exactly right thank you this is + + align:start position:0% +you're exactly right thank you this is + + + align:start position:0% +you're exactly right thank you this is +good uh and so uh when I when I moved + + align:start position:0% +good uh and so uh when I when I moved + + + align:start position:0% +good uh and so uh when I when I moved +this out here what happened was and I + + align:start position:0% +this out here what happened was and I + + + align:start position:0% +this out here what happened was and I +drew this well this one here my convex + + align:start position:0% +drew this well this one here my convex + + + align:start position:0% +drew this well this one here my convex +Hal changed the problem specification + + align:start position:0% +Hal changed the problem specification + + + align:start position:0% +Hal changed the problem specification +changed on me it was it was my fault but + + align:start position:0% +changed on me it was it was my fault but + + + align:start position:0% +changed on me it was it was my fault but +then what what would happen of course is + + align:start position:0% +then what what would happen of course is + + + align:start position:0% +then what what would happen of course is +as I move this that would become the uh + + align:start position:0% +as I move this that would become the uh + + + align:start position:0% +as I move this that would become the uh +the the segment that was part of the + + align:start position:0% +the the segment that was part of the + + + align:start position:0% +the the segment that was part of the +convex Sol + + align:start position:0% +convex Sol + + + align:start position:0% +convex Sol +okay so sorry to confuse people but what + + align:start position:0% +okay so sorry to confuse people but what + + + align:start position:0% +okay so sorry to confuse people but what +we have here in terms of an algorithm if + + align:start position:0% +we have here in terms of an algorithm if + + + align:start position:0% +we have here in terms of an algorithm if +I leave the points the same Works PR + + align:start position:0% +I leave the points the same Works PR + + + align:start position:0% +I leave the points the same Works PR +perfectly well right so let me just + + align:start position:0% +perfectly well right so let me just + + + align:start position:0% +perfectly well right so let me just +leave the points the same + + align:start position:0% +leave the points the same + + + align:start position:0% +leave the points the same +and just quickly recap which is I'm + + align:start position:0% +and just quickly recap which is I'm + + + align:start position:0% +and just quickly recap which is I'm +going to take a pair of points and I'm + + align:start position:0% +going to take a pair of points and I'm + + + align:start position:0% +going to take a pair of points and I'm +going to draw and let me just draw this + + align:start position:0% +going to draw and let me just draw this + + + align:start position:0% +going to draw and let me just draw this +in a dotted fashion first uh and I'm + + align:start position:0% +in a dotted fashion first uh and I'm + + + align:start position:0% +in a dotted fashion first uh and I'm +going to say that's the segment now I'm + + align:start position:0% +going to say that's the segment now I'm + + + align:start position:0% +going to say that's the segment now I'm +going to take a look at that line and + + align:start position:0% +going to take a look at that line and + + + align:start position:0% +going to take a look at that line and +say this breaks up + + align:start position:0% +say this breaks up + + + align:start position:0% +say this breaks up +uh uh the plane into two half planes are + + align:start position:0% +uh uh the plane into two half planes are + + + align:start position:0% +uh uh the plane into two half planes are +all the points on one side and if the + + align:start position:0% +all the points on one side and if the + + + align:start position:0% +all the points on one side and if the +answer is yes I'm going to go ahead and + + align:start position:0% +answer is yes I'm going to go ahead and + + + align:start position:0% +answer is yes I'm going to go ahead and +boom say that is a segment of my convex + + align:start position:0% +boom say that is a segment of my convex + + + align:start position:0% +boom say that is a segment of my convex +Hull if the answer is is no like in this + + align:start position:0% +Hull if the answer is is no like in this + + + align:start position:0% +Hull if the answer is is no like in this +case I'm going to drop that segment okay + + align:start position:0% +case I'm going to drop that segment okay + + + align:start position:0% +case I'm going to drop that segment okay +so now let's talk about + + align:start position:0% +so now let's talk about + + + align:start position:0% +so now let's talk about +complexity um let's say that there are + + align:start position:0% +complexity um let's say that there are + + + align:start position:0% +complexity um let's say that there are +end points + + align:start position:0% + + + + align:start position:0% + +here and how many segments do I + + align:start position:0% +here and how many segments do I + + + align:start position:0% +here and how many segments do I +have I have uh order n Square Theta n + + align:start position:0% +have I have uh order n Square Theta n + + + align:start position:0% +have I have uh order n Square Theta n +Square segments and what is the + + align:start position:0% +Square segments and what is the + + + align:start position:0% +Square segments and what is the +complexity of the test what is the + + align:start position:0% +complexity of the test what is the + + + align:start position:0% +complexity of the test what is the +complexity of the test that's associated + + align:start position:0% +complexity of the test that's associated + + + align:start position:0% +complexity of the test that's associated +with once I've drawn the segments + + align:start position:0% +with once I've drawn the segments + + + align:start position:0% +with once I've drawn the segments +deciding whether the segment is going to + + align:start position:0% +deciding whether the segment is going to + + + align:start position:0% +deciding whether the segment is going to +be a tangent which is part of the convex + + align:start position:0% +be a tangent which is part of the convex + + + align:start position:0% +be a tangent which is part of the convex +hall or not what is the complexity o n + + align:start position:0% +hall or not what is the complexity o n + + + align:start position:0% +hall or not what is the complexity o n +exactly right so o n test + + align:start position:0% +exactly right so o n test + + + align:start position:0% +exactly right so o n test +complexity and so we + + align:start position:0% +complexity and so we + + + align:start position:0% +complexity and so we +got overall Theta n cubed complexity + + align:start position:0% +got overall Theta n cubed complexity + + + align:start position:0% +got overall Theta n cubed complexity +okay so it makes sense to do divide and + + align:start position:0% +okay so it makes sense to do divide and + + + align:start position:0% +okay so it makes sense to do divide and +conquer if you can do better than this + + align:start position:0% +conquer if you can do better than this + + + align:start position:0% +conquer if you can do better than this +because this is a really simple + + align:start position:0% +because this is a really simple + + + align:start position:0% +because this is a really simple +algorithm right the good news is we will + + align:start position:0% +algorithm right the good news is we will + + + align:start position:0% +algorithm right the good news is we will +be able to do better than that + + align:start position:0% +be able to do better than that + + + align:start position:0% +be able to do better than that +and now that we + + align:start position:0% +and now that we + + + align:start position:0% +and now that we +have a particular algorithm uh I'm not + + align:start position:0% +have a particular algorithm uh I'm not + + + align:start position:0% +have a particular algorithm uh I'm not +quite ready to show you that yet um now + + align:start position:0% +quite ready to show you that yet um now + + + align:start position:0% +quite ready to show you that yet um now +that we have a particular algorithm we + + align:start position:0% +that we have a particular algorithm we + + + align:start position:0% +that we have a particular algorithm we +can think about how we can improve + + align:start position:0% +can think about how we can improve + + + align:start position:0% +can think about how we can improve +things and of course we're going to use + + align:start position:0% +things and of course we're going to use + + + align:start position:0% +things and of course we're going to use +uh divide and + + align:start position:0% +uh divide and + + + align:start position:0% +uh divide and +concer so let's go ahead and do that and + + align:start position:0% +concer so let's go ahead and do that and + + + align:start position:0% +concer so let's go ahead and do that and +so generally with divide and concer as I + + align:start position:0% +so generally with divide and concer as I + + + align:start position:0% +so generally with divide and concer as I +mentioned + + align:start position:0% +mentioned + + + align:start position:0% +mentioned +before in most cases the division is + + align:start position:0% +before in most cases the division is + + + align:start position:0% +before in most cases the division is +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +straightforward and that's the case here + + align:start position:0% +straightforward and that's the case here + + + align:start position:0% +straightforward and that's the case here +as well all the fun is going to be in + + align:start position:0% +as well all the fun is going to be in + + + align:start position:0% +as well all the fun is going to be in +the merge step right so what we're going + + align:start position:0% +the merge step right so what we're going + + + align:start position:0% +the merge step right so what we're going +to do as you can imagine is we're going + + align:start position:0% +to do as you can imagine is we're going + + + align:start position:0% +to do as you can imagine is we're going +to take these points and we're going to + + align:start position:0% +to take these points and we're going to + + + align:start position:0% +to take these points and we're going to +break them up right and uh the way we + + align:start position:0% +break them up right and uh the way we + + + align:start position:0% +break them up right and uh the way we +going to break them up is by dividing + + align:start position:0% +going to break them up is by dividing + + + align:start position:0% +going to break them up is by dividing +them into half planes we're going to + + align:start position:0% +them into half planes we're going to + + + align:start position:0% +them into half planes we're going to +just draw a line and we're going to say + + align:start position:0% +just draw a line and we're going to say + + + align:start position:0% +just draw a line and we're going to say +everything to the left of the line is + + align:start position:0% +everything to the left of the line is + + + align:start position:0% +everything to the left of the line is +one sub problem everything to the right + + align:start position:0% +one sub problem everything to the right + + + align:start position:0% +one sub problem everything to the right +of the line is another sub problem go + + align:start position:0% +of the line is another sub problem go + + + align:start position:0% +of the line is another sub problem go +off and find the convex Hull for each of + + align:start position:0% +off and find the convex Hull for each of + + + align:start position:0% +off and find the convex Hull for each of +the sub problems if you have uh two + + align:start position:0% +the sub problems if you have uh two + + + align:start position:0% +the sub problems if you have uh two +points you're done obviously it's + + align:start position:0% +points you're done obviously it's + + + align:start position:0% +points you're done obviously it's +trivial and at some point you can say + + align:start position:0% +trivial and at some point you can say + + + align:start position:0% +trivial and at some point you can say +I'm just going to deal with Brute Force + + align:start position:0% +I'm just going to deal with Brute Force + + + align:start position:0% +I'm just going to deal with Brute Force +we can go down to order n cubed if if n + + align:start position:0% +we can go down to order n cubed if if n + + + align:start position:0% +we can go down to order n cubed if if n +is small I can just apply that algorithm + + align:start position:0% +is small I can just apply that algorithm + + + align:start position:0% +is small I can just apply that algorithm +so it doesn't have even have to be the + + align:start position:0% +so it doesn't have even have to be the + + + align:start position:0% +so it doesn't have even have to be the +base case of n 1 or nals 2 that's a + + align:start position:0% +base case of n 1 or nals 2 that's a + + + align:start position:0% +base case of n 1 or nals 2 that's a +perfectly fine thing to do but you can + + align:start position:0% +perfectly fine thing to do but you can + + + align:start position:0% +perfectly fine thing to do but you can +certainly go with n equals 10 as I + + align:start position:0% +certainly go with n equals 10 as I + + + align:start position:0% +certainly go with n equals 10 as I +mentioned before and run this Brute + + align:start position:0% +mentioned before and run this Brute + + + align:start position:0% +mentioned before and run this Brute +Force algorithm and so at that point you + + align:start position:0% +Force algorithm and so at that point you + + + align:start position:0% +Force algorithm and so at that point you +know that you can get down to small + + align:start position:0% +know that you can get down to small + + + align:start position:0% +know that you can get down to small +enough size sub problems for which you + + align:start position:0% +enough size sub problems for which you + + + align:start position:0% +enough size sub problems for which you +can find the convex Hall efficiently and + + align:start position:0% +can find the convex Hall efficiently and + + + align:start position:0% +can find the convex Hall efficiently and +uh then you got these two convex Halls + + align:start position:0% +uh then you got these two convex Halls + + + align:start position:0% +uh then you got these two convex Halls +right which are clearly on on well two + + align:start position:0% +right which are clearly on on well two + + + align:start position:0% +right which are clearly on on well two +different half planes because that's the + + align:start position:0% +different half planes because that's the + + + align:start position:0% +different half planes because that's the +way you define them and now you got to + + align:start position:0% +way you define them and now you got to + + + align:start position:0% +way you define them and now you got to +merge them right and that's where all + + align:start position:0% +merge them right and that's where all + + + align:start position:0% +merge them right and that's where all +the fun is okay so let's just write this + + align:start position:0% +the fun is okay so let's just write this + + + align:start position:0% +the fun is okay so let's just write this +out + + align:start position:0% +out + + + align:start position:0% +out +again uh we're going to sort the + + align:start position:0% + + + + align:start position:0% + +points by x + + align:start position:0% +points by x + + + align:start position:0% +points by x +coordinates and we're going to do this + + align:start position:0% +coordinates and we're going to do this + + + align:start position:0% +coordinates and we're going to do this +once and for all we don't have to keep + + align:start position:0% +once and for all we don't have to keep + + + align:start position:0% +once and for all we don't have to keep +sorting here because we're just going to + + align:start position:0% +sorting here because we're just going to + + + align:start position:0% +sorting here because we're just going to +be partitioning based on x coordinates + + align:start position:0% +be partitioning based on x coordinates + + + align:start position:0% +be partitioning based on x coordinates +and we can keep splitting based on x + + align:start position:0% +and we can keep splitting based on x + + + align:start position:0% +and we can keep splitting based on x +coordinates because we want to generate + + align:start position:0% +coordinates because we want to generate + + + align:start position:0% +coordinates because we want to generate +these half planes right so so we can do + + align:start position:0% +these half planes right so so we can do + + + align:start position:0% +these half planes right so so we can do +this once and for + + align:start position:0% + + + + align:start position:0% + +all and for the input set + + align:start position:0% + + + + align:start position:0% + +s we're going to + + align:start position:0% +s we're going to + + + align:start position:0% +s we're going to +divide into the left + + align:start position:0% +divide into the left + + + align:start position:0% +divide into the left +half a and right half + + align:start position:0% + + + + align:start position:0% + +B by the x coordinates + + align:start position:0% + + + + align:start position:0% + +and then we're going to + + align:start position:0% +and then we're going to + + + align:start position:0% +and then we're going to +compute CH of a and CH of B + + align:start position:0% +compute CH of a and CH of B + + + align:start position:0% +compute CH of a and CH of B +recursively and then we're going to + + align:start position:0% +recursively and then we're going to + + + align:start position:0% +recursively and then we're going to +combine so the + + align:start position:0% +combine so the + + + align:start position:0% +combine so the +only difference here from what we had + + align:start position:0% +only difference here from what we had + + + align:start position:0% +only difference here from what we had +before is the specification of the + + align:start position:0% +before is the specification of the + + + align:start position:0% +before is the specification of the +division um it looks pretty generic it's + + align:start position:0% +division um it looks pretty generic it's + + + align:start position:0% +division um it looks pretty generic it's +similar to the Paradigm that I wrote + + align:start position:0% +similar to the Paradigm that I wrote + + + align:start position:0% +similar to the Paradigm that I wrote +before but I've specified exactly how + + align:start position:0% +before but I've specified exactly how + + + align:start position:0% +before but I've specified exactly how +I'm going to break this up all + + align:start position:0% +I'm going to break this up all + + + align:start position:0% +I'm going to break this up all +right um so let's start + + align:start position:0% + + + + align:start position:0% + +with uh the merge operation and we're + + align:start position:0% +with uh the merge operation and we're + + + align:start position:0% +with uh the merge operation and we're +going to spend most of our time specking + + align:start position:0% +going to spend most of our time specking + + + align:start position:0% +going to spend most of our time specking +that and again there's many ways you + + align:start position:0% +that and again there's many ways you + + + align:start position:0% +that and again there's many ways you +could do the + + align:start position:0% + + + + align:start position:0% + +merge and we want the most efficient way + + align:start position:0% +merge and we want the most efficient way + + + align:start position:0% +merge and we want the most efficient way +that's obviously going to + + align:start position:0% +that's obviously going to + + + align:start position:0% +that's obviously going to +determine + + align:start position:0% +determine + + + align:start position:0% +determine +complexity so big question how to + + align:start position:0% + + + + align:start position:0% + +merge right so what I have here if I + + align:start position:0% +merge right so what I have here if I + + + align:start position:0% +merge right so what I have here if I +look at the merge step + + align:start position:0% +look at the merge step + + + align:start position:0% +look at the merge step +is I've created my two sub problems + + align:start position:0% +is I've created my two sub problems + + + align:start position:0% +is I've created my two sub problems +corresponding to these two half planes + + align:start position:0% +corresponding to these two half planes + + + align:start position:0% +corresponding to these two half planes +and uh what I have here is let's say I + + align:start position:0% +and uh what I have here is let's say I + + + align:start position:0% +and uh what I have here is let's say I +have I've generated at this point a + + align:start position:0% +have I've generated at this point a + + + align:start position:0% +have I've generated at this point a +convex + + align:start position:0% +convex + + + align:start position:0% +convex +Hull associated with each of these sub + + align:start position:0% +Hull associated with each of these sub + + + align:start position:0% +Hull associated with each of these sub +problems okay so what I have here is uh + + align:start position:0% +problems okay so what I have here is uh + + + align:start position:0% +problems okay so what I have here is uh +A1 A2 I'm going to go clockwise to + + align:start position:0% +A1 A2 I'm going to go clockwise to + + + align:start position:0% +A1 A2 I'm going to go clockwise to +specify the the the convex Hull + + align:start position:0% +specify the the the convex Hull + + + align:start position:0% +specify the the the convex Hull +and the other thing that I'm going to do + + align:start position:0% +and the other thing that I'm going to do + + + align:start position:0% +and the other thing that I'm going to do +is um in the sub problem case my + + align:start position:0% +is um in the sub problem case my + + + align:start position:0% +is um in the sub problem case my +starting point is going to be for the + + align:start position:0% +starting point is going to be for the + + + align:start position:0% +starting point is going to be for the +left sub problem the coordinate that is + + align:start position:0% +left sub problem the coordinate that is + + + align:start position:0% +left sub problem the coordinate that is +uh that has the highest x value okay so + + align:start position:0% +uh that has the highest x value okay so + + + align:start position:0% +uh that has the highest x value okay so +that's A1 in this case the highest x + + align:start position:0% +that's A1 in this case the highest x + + + align:start position:0% +that's A1 in this case the highest x +value going over X is increasing to the + + align:start position:0% +value going over X is increasing to the + + + align:start position:0% +value going over X is increasing to the +right and um in the for the right half + + align:start position:0% +right and um in the for the right half + + + align:start position:0% +right and um in the for the right half +of the problem um it's going to be the + + align:start position:0% +of the problem um it's going to be the + + + align:start position:0% +of the problem um it's going to be the +coordinate that has the lowest x value + + align:start position:0% +coordinate that has the lowest x value + + + align:start position:0% +coordinate that has the lowest x value +and I'm going to go clockwise in both of + + align:start position:0% +and I'm going to go clockwise in both of + + + align:start position:0% +and I'm going to go clockwise in both of +these cases so when you when you see an + + align:start position:0% +these cases so when you when you see an + + + align:start position:0% +these cases so when you when you see an +ordering here associated with the + + align:start position:0% +ordering here associated with the + + + align:start position:0% +ordering here associated with the +subscripts for these U these points + + align:start position:0% +subscripts for these U these points + + + align:start position:0% +subscripts for these U these points +start with uh A1 or B1 and then go + + align:start position:0% +start with uh A1 or B1 and then go + + + align:start position:0% +start with uh A1 or B1 and then go +clockwise and that's how we number this + + align:start position:0% +clockwise and that's how we number this + + + align:start position:0% +clockwise and that's how we number this +right so just nutational not nothing + + align:start position:0% +right so just nutational not nothing + + + align:start position:0% +right so just nutational not nothing +profound here so um I got I got these + + align:start position:0% +profound here so um I got I got these + + + align:start position:0% +profound here so um I got I got these +two convex hulls these sub hulls if you + + align:start position:0% +two convex hulls these sub hulls if you + + + align:start position:0% +two convex hulls these sub hulls if you +will and what I need to do now is merge + + align:start position:0% +will and what I need to do now is merge + + + align:start position:0% +will and what I need to do now is merge +them together and you can obviously look + + align:start position:0% +them together and you can obviously look + + + align:start position:0% +them together and you can obviously look +at this and it's kind of obvious you + + align:start position:0% +at this and it's kind of obvious you + + + align:start position:0% +at this and it's kind of obvious you +know what the overall convex Hull is + + align:start position:0% +know what the overall convex Hull is + + + align:start position:0% +know what the overall convex Hull is +right um so but the but the key thing is + + align:start position:0% +right um so but the but the key thing is + + + align:start position:0% +right um so but the but the key thing is +I'm going to have to look + + align:start position:0% +I'm going to have to look + + + align:start position:0% +I'm going to have to look +at um each of the the pairs of points + + align:start position:0% +at um each of the the pairs of points + + + align:start position:0% +at um each of the the pairs of points +that are associated with this and that + + align:start position:0% +that are associated with this and that + + + align:start position:0% +that are associated with this and that +and try to to generate the tangents the + + align:start position:0% +and try to to generate the tangents the + + + align:start position:0% +and try to to generate the tangents the +new tangents that are not part of the + + align:start position:0% +new tangents that are not part of the + + + align:start position:0% +new tangents that are not part of the +sub huls but they're part of the overall + + align:start position:0% +sub huls but they're part of the overall + + + align:start position:0% +sub huls but they're part of the overall +Hull right and so in this case uh you + + align:start position:0% +Hull right and so in this case uh you + + + align:start position:0% +Hull right and so in this case uh you +can + + align:start position:0% +can + + + align:start position:0% +can +imagine an an algorithm that is going to + + align:start position:0% +imagine an an algorithm that is going to + + + align:start position:0% +imagine an an algorithm that is going to +kind of do what this Brute Force + + align:start position:0% +kind of do what this Brute Force + + + align:start position:0% +kind of do what this Brute Force +algorithm does uh except that uh it's + + align:start position:0% +algorithm does uh except that uh it's + + + align:start position:0% +algorithm does uh except that uh it's +looking at a point from here and a point + + align:start position:0% +looking at a point from here and a point + + + align:start position:0% +looking at a point from here and a point +from here right so you can imagine that + + align:start position:0% +from here right so you can imagine that + + + align:start position:0% +from here right so you can imagine that +I'm going to do a + + align:start position:0% +I'm going to do a + + + align:start position:0% +I'm going to do a +pairwise a generation of segments I'm + + align:start position:0% +pairwise a generation of segments I'm + + + align:start position:0% +pairwise a generation of segments I'm +going to check to see whether these + + align:start position:0% +going to check to see whether these + + + align:start position:0% +going to check to see whether these +segments are actually tangents they're + + align:start position:0% +segments are actually tangents they're + + + align:start position:0% +segments are actually tangents they're +part of the overall convex Hull or not + + align:start position:0% +part of the overall convex Hull or not + + + align:start position:0% +part of the overall convex Hull or not +okay so what what I would do here is I'd + + align:start position:0% +okay so what what I would do here is I'd + + + align:start position:0% +okay so what what I would do here is I'd +look at this and um is that going to be + + align:start position:0% +look at this and um is that going to be + + + align:start position:0% +look at this and um is that going to be +part of the overall + + align:start position:0% +part of the overall + + + align:start position:0% +part of the overall +Hall no and precisely why not someone + + align:start position:0% +Hall no and precisely why not someone + + + align:start position:0% +Hall no and precisely why not someone +tell me why this segment A1 B1 is not + + align:start position:0% +tell me why this segment A1 B1 is not + + + align:start position:0% +tell me why this segment A1 B1 is not +part of the overall + + align:start position:0% +part of the overall + + + align:start position:0% +part of the overall +Hall yeah go + + align:start position:0% + + + + align:start position:0% + +ahead exactly right that's exactly right + + align:start position:0% +ahead exactly right that's exactly right + + + align:start position:0% +ahead exactly right that's exactly right +so here you + + align:start position:0% +so here you + + + align:start position:0% +so here you +go um so so that's not part of it uh now + + align:start position:0% +go um so so that's not part of it uh now + + + align:start position:0% +go um so so that's not part of it uh now +if I look at + + align:start position:0% +if I look at + + + align:start position:0% +if I look at +this well same reason that's not part of + + align:start position:0% +this well same reason that's not part of + + + align:start position:0% +this well same reason that's not part of +it in this case and this is a fairly + + align:start position:0% +it in this case and this is a fairly + + + align:start position:0% +it in this case and this is a fairly +obvious example I'm going to do + + align:start position:0% +obvious example I'm going to do + + + align:start position:0% +obvious example I'm going to do +something that's slightly less obvious + + align:start position:0% +something that's slightly less obvious + + + align:start position:0% +something that's slightly less obvious +in case you get your hopes up that we + + align:start position:0% +in case you get your hopes up that we + + + align:start position:0% +in case you get your hopes up that we +have this trivial algorithm okay this is + + align:start position:0% +have this trivial algorithm okay this is + + + align:start position:0% +have this trivial algorithm okay this is +looking good + + align:start position:0% +looking good + + + align:start position:0% +looking good +right um that's supposed to be a + + align:start position:0% +right um that's supposed to be a + + + align:start position:0% +right um that's supposed to be a +straight line by the way okay um so so + + align:start position:0% +straight line by the way okay um so so + + + align:start position:0% +straight line by the way okay um so so +A4 B2 I mean that's looking good right + + align:start position:0% +A4 B2 I mean that's looking good right + + + align:start position:0% +A4 B2 I mean that's looking good right +because all the points are on one side + + align:start position:0% +because all the points are on one side + + + align:start position:0% +because all the points are on one side +so A4 + + align:start position:0% +so A4 + + + align:start position:0% +so A4 +B2 is our upper + + align:start position:0% +B2 is our upper + + + align:start position:0% +B2 is our upper +tangent right so our upper tangent is + + align:start position:0% +tangent right so our upper tangent is + + + align:start position:0% +tangent right so our upper tangent is +something that we're going to Define + + align:start position:0% +something that we're going to Define + + + align:start position:0% +something that we're going to Define +as if I look at uh each of these things + + align:start position:0% +as if I look at uh each of these things + + + align:start position:0% +as if I look at uh each of these things +I'm going to say they have a Yi J okay + + align:start position:0% +I'm going to say they have a Yi J okay + + + align:start position:0% +I'm going to say they have a Yi J okay +what is Yi J Yi J is the y coordinate of + + align:start position:0% +what is Yi J Yi J is the y coordinate of + + + align:start position:0% +what is Yi J Yi J is the y coordinate of +the of the + + align:start position:0% +the of the + + + align:start position:0% +the of the +segment that I'm looking at + + align:start position:0% +segment that I'm looking at + + + align:start position:0% +segment that I'm looking at +the i j segment so this yig J is for AI + + align:start position:0% +the i j segment so this yig J is for AI + + + align:start position:0% +the i j segment so this yig J is for AI +and BJ so what I have here is U + + align:start position:0% +and BJ so what I have here is U + + + align:start position:0% +and BJ so what I have here is U +y42 out here and this is for the upper + + align:start position:0% +y42 out here and this is for the upper + + + align:start position:0% +y42 out here and this is for the upper +tangent Yi J is going to be maximum + + align:start position:0% +tangent Yi J is going to be maximum + + + align:start position:0% +tangent Yi J is going to be maximum +right because uh uh that's essentially + + align:start position:0% +right because uh uh that's essentially + + + align:start position:0% +right because uh uh that's essentially +something which would ensure me that + + align:start position:0% +something which would ensure me that + + + align:start position:0% +something which would ensure me that +there are no points higher than that + + align:start position:0% +there are no points higher than that + + + align:start position:0% +there are no points higher than that +right so if I go up all the way and I + + align:start position:0% +right so if I go up all the way and I + + + align:start position:0% +right so if I go up all the way and I +and I find this that has the maximum Yi + + align:start position:0% +and I find this that has the maximum Yi + + + align:start position:0% +and I find this that has the maximum Yi +J that is going to be my upper tangent + + align:start position:0% +J that is going to be my upper tangent + + + align:start position:0% +J that is going to be my upper tangent +because because only for that will I + + align:start position:0% +because because only for that will I + + + align:start position:0% +because because only for that will I +have no points ahead of that okay so so + + align:start position:0% +have no points ahead of that okay so so + + + align:start position:0% +have no points ahead of that okay so so +y j is upper tangent this is going to be + + align:start position:0% +y j is upper tangent this is going to be + + + align:start position:0% +y j is upper tangent this is going to be +maximum and I'm not going to write this + + align:start position:0% +maximum and I'm not going to write this + + + align:start position:0% +maximum and I'm not going to write this +down but it makes sense that um the + + align:start position:0% +down but it makes sense that um the + + + align:start position:0% +down but it makes sense that um the +lower tangent is going to have the + + align:start position:0% +lower tangent is going to have the + + + align:start position:0% +lower tangent is going to have the +lowest Yi J all right are we are are we + + align:start position:0% +lowest Yi J all right are we are are we + + + align:start position:0% +lowest Yi J all right are we are are we +all good + + align:start position:0% +all good + + + align:start position:0% +all good +here yeah + + align:start position:0% + + + + align:start position:0% + +question okay so good I let me uh the + + align:start position:0% +question okay so good I let me uh the + + + align:start position:0% +question okay so good I let me uh the +reason we moved out A1 B1 is because if + + align:start position:0% +reason we moved out A1 B1 is because if + + + align:start position:0% +reason we moved out A1 B1 is because if +I just drew A1 B1 like this and I'm + + align:start position:0% +I just drew A1 B1 like this and I'm + + + align:start position:0% +I just drew A1 B1 like this and I'm +extrapolating this this is again + + align:start position:0% +extrapolating this this is again + + + align:start position:0% +extrapolating this this is again +supposed to be a straight line um then + + align:start position:0% +supposed to be a straight line um then + + + align:start position:0% +supposed to be a straight line um then +you clearly see that there points on + + align:start position:0% +you clearly see that there points on + + + align:start position:0% +you clearly see that there points on +either side of the A1 B1 segment when + + align:start position:0% +either side of the A1 B1 segment when + + + align:start position:0% +either side of the A1 B1 segment when +you look at the overall problem correct + + align:start position:0% +you look at the overall problem correct + + + align:start position:0% +you look at the overall problem correct +you see that on A1 B1 B2 is on this side + + align:start position:0% +you see that on A1 B1 B2 is on this side + + + align:start position:0% +you see that on A1 B1 B2 is on this side +B3 is on this side if I just extend this + + align:start position:0% +B3 is on this side if I just extend this + + + align:start position:0% +B3 is on this side if I just extend this +line all the way to Infinity in both + + align:start position:0% +line all the way to Infinity in both + + + align:start position:0% +line all the way to Infinity in both +directions and that violates the + + align:start position:0% +directions and that violates the + + + align:start position:0% +directions and that violates the +requirement that this segment be part of + + align:start position:0% +requirement that this segment be part of + + + align:start position:0% +requirement that this segment be part of +the overall Hull okay that Mak sense + + align:start position:0% +the overall Hull okay that Mak sense + + + align:start position:0% +the overall Hull okay that Mak sense +good so everybody with me so clearly + + align:start position:0% +good so everybody with me so clearly + + + align:start position:0% +good so everybody with me so clearly +there is a trivial uh merge algorithm + + align:start position:0% +there is a trivial uh merge algorithm + + + align:start position:0% +there is a trivial uh merge algorithm +here and uh the trivial merge algorithm + + align:start position:0% +here and uh the trivial merge algorithm + + + align:start position:0% +here and uh the trivial merge algorithm +is to look at uh every pair of + + align:start position:0% +is to look at uh every pair of + + + align:start position:0% +is to look at uh every pair of +points every a pair right every AI BJ + + align:start position:0% +points every a pair right every AI BJ + + + align:start position:0% +points every a pair right every AI BJ +pair and so what is the complexity of uh + + align:start position:0% +pair and so what is the complexity of uh + + + align:start position:0% +pair and so what is the complexity of uh +of of of doing + + align:start position:0% +of of of doing + + + align:start position:0% +of of of doing +that um if I have n total points the + + align:start position:0% +that um if I have n total points the + + + align:start position:0% +that um if I have n total points the +complexity would be which would be n + + align:start position:0% +complexity would be which would be n + + + align:start position:0% +complexity would be which would be n +square right because maybe I'd have half + + align:start position:0% +square right because maybe I'd have half + + + align:start position:0% +square right because maybe I'd have half +here and half + + align:start position:0% +here and half + + + align:start position:0% +here and half +there ignore constants and you could say + + align:start position:0% +there ignore constants and you could say + + + align:start position:0% +there ignore constants and you could say +well it's going to be n Square divided + + align:start position:0% +well it's going to be n Square divided + + + align:start position:0% +well it's going to be n Square divided +by four but you know that's Theta n + + align:start position:0% +by four but you know that's Theta n + + + align:start position:0% +by four but you know that's Theta n +square right so there's a there's a + + align:start position:0% +square right so there's a there's a + + + align:start position:0% +square right so there's a there's a +there's an + + align:start position:0% +there's an + + + align:start position:0% +there's an +obvious merge + + align:start position:0% +obvious merge + + + align:start position:0% +obvious merge +algorithm that is Theta n s looking at + + align:start position:0% +algorithm that is Theta n s looking at + + + align:start position:0% +algorithm that is Theta n s looking at +all + + align:start position:0% +all + + + align:start position:0% +all +pairs um of points and when I mean all + + align:start position:0% +pairs um of points and when I mean all + + + align:start position:0% +pairs um of points and when I mean all +pairs of points I mean I like an A and A + + align:start position:0% +pairs of points I mean I like an A and A + + + align:start position:0% +pairs of points I mean I like an A and A +B because I want to pick a a pair where + + align:start position:0% +B because I want to pick a a pair where + + + align:start position:0% +B because I want to pick a a pair where +I go left of that that dividing line and + + align:start position:0% +I go left of that that dividing line and + + + align:start position:0% +I go left of that that dividing line and +then right of the dividing line but + + align:start position:0% +then right of the dividing line but + + + align:start position:0% +then right of the dividing line but +either way it's Theta and square okay so + + align:start position:0% +either way it's Theta and square okay so + + + align:start position:0% +either way it's Theta and square okay so +now you look at that and you go huh you + + align:start position:0% +now you look at that and you go huh you + + + align:start position:0% +now you look at that and you go huh you +know can I do better what if I just went + + align:start position:0% +know can I do better what if I just went + + + align:start position:0% +know can I do better what if I just went +for the highest a point and the highest + + align:start position:0% +for the highest a point and the highest + + + align:start position:0% +for the highest a point and the highest +B + + align:start position:0% +B + + + align:start position:0% +B +point and I just no that's it I'm done + + align:start position:0% +point and I just no that's it I'm done + + + align:start position:0% +point and I just no that's it I'm done +constant time wouldn't that be + + align:start position:0% +constant time wouldn't that be + + + align:start position:0% +constant time wouldn't that be +wonderful yeah wonderful but incorrect + + align:start position:0% +wonderful yeah wonderful but incorrect + + + align:start position:0% +wonderful yeah wonderful but incorrect +okay right so so what is an example and + + align:start position:0% +okay right so so what is an example and + + + align:start position:0% +okay right so so what is an example and +so this is something that I that I I + + align:start position:0% +so this is something that I that I I + + + align:start position:0% +so this is something that I that I I +spent a little bit of time uh last night + + align:start position:0% +spent a little bit of time uh last night + + + align:start position:0% +spent a little bit of time uh last night +concocting so I'm like you guys too I do + + align:start position:0% +concocting so I'm like you guys too I do + + + align:start position:0% +concocting so I'm like you guys too I do +my problem set the night + + align:start position:0% +my problem set the night + + + align:start position:0% +my problem set the night +before well don't don't do as I do do as + + align:start position:0% +before well don't don't do as I do do as + + + align:start position:0% +before well don't don't do as I do do as +I say right + + align:start position:0% +I say right + + + align:start position:0% +I say right +um but but I've done this before so + + align:start position:0% +um but but I've done this before so + + + align:start position:0% +um but but I've done this before so +that's that's the difference uh but this + + align:start position:0% +that's that's the difference uh but this + + + align:start position:0% +that's that's the difference uh but this +particular example is is is is new so uh + + align:start position:0% +particular example is is is is new so uh + + + align:start position:0% +particular example is is is is new so uh +so what I have here is I'm going to show + + align:start position:0% +so what I have here is I'm going to show + + + align:start position:0% +so what I have here is I'm going to show +you why there's not a trivial + + align:start position:0% +you why there's not a trivial + + + align:start position:0% +you why there's not a trivial +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +okay uh + + align:start position:0% + + + + align:start position:0% + +that I got to get these uh angles right + + align:start position:0% +that I got to get these uh angles right + + + align:start position:0% +that I got to get these uh angles right +uh that that you can't just pick the the + + align:start position:0% +uh that that you can't just pick the the + + + align:start position:0% +uh that that you can't just pick the the +highest points + + align:start position:0% +highest points + + + align:start position:0% +highest points +and uh keep going right and then that + + align:start position:0% +and uh keep going right and then that + + + align:start position:0% +and uh keep going right and then that +would be constant time so that's my a + + align:start position:0% +would be constant time so that's my a + + + align:start position:0% +would be constant time so that's my a +over here and let's assume that I + + align:start position:0% +over here and let's assume that I + + + align:start position:0% +over here and let's assume that I +have uh my dividing line like that and + + align:start position:0% +have uh my dividing line like that and + + + align:start position:0% +have uh my dividing line like that and +then what I'm going to do here and I + + align:start position:0% +then what I'm going to do here and I + + + align:start position:0% +then what I'm going to do here and I +hope I get this right um is I'm going to + + align:start position:0% +hope I get this right um is I'm going to + + + align:start position:0% +hope I get this right um is I'm going to +have something like like + + align:start position:0% +have something like like + + + align:start position:0% +have something like like +this like that and then I'm going to + + align:start position:0% +this like that and then I'm going to + + + align:start position:0% +this like that and then I'm going to +have B1 here clockwise so B2 B3 and B4 + + align:start position:0% +have B1 here clockwise so B2 B3 and B4 + + + align:start position:0% +have B1 here clockwise so B2 B3 and B4 +Okay so so as you can see here if I look + + align:start position:0% +Okay so so as you can see here if I look + + + align:start position:0% +Okay so so as you can see here if I look +at U uh + + align:start position:0% +at U uh + + + align:start position:0% +at U uh +A4 + + align:start position:0% +A4 + + + align:start position:0% +A4 +uh little adjustment + + align:start position:0% + + + + align:start position:0% + +necessary okay so if I look at that um + + align:start position:0% +necessary okay so if I look at that um + + + align:start position:0% +necessary okay so if I look at that um +A4 to + + align:start position:0% +A4 to + + + align:start position:0% +A4 to +B1 versus I mean just eyeball it A3 to + + align:start position:0% +B1 versus I mean just eyeball it A3 to + + + align:start position:0% +B1 versus I mean just eyeball it A3 to +B1 right is is A4 to B1 going to be the + + align:start position:0% +B1 right is is A4 to B1 going to be the + + + align:start position:0% +B1 right is is A4 to B1 going to be the +upper + + align:start position:0% +upper + + + align:start position:0% +upper +tangent no right so so now A3 is lower + + align:start position:0% +tangent no right so so now A3 is lower + + + align:start position:0% +tangent no right so so now A3 is lower +than A4 you guys see that and and B1 is + + align:start position:0% +than A4 you guys see that and and B1 is + + + align:start position:0% +than A4 you guys see that and and B1 is +lower than B2 right so it's clear that + + align:start position:0% +lower than B2 right so it's clear that + + + align:start position:0% +lower than B2 right so it's clear that +if I if I just took A4 to B2 that it + + align:start position:0% +if I if I just took A4 to B2 that it + + + align:start position:0% +if I if I just took A4 to B2 that it +would not be an upper tangent everybody + + align:start position:0% +would not be an upper tangent everybody + + + align:start position:0% +would not be an upper tangent everybody +see that yep all right good so so what + + align:start position:0% +see that yep all right good so so what + + + align:start position:0% +see that yep all right good so so what +so we kind of have a constant time + + align:start position:0% +so we kind of have a constant time + + + align:start position:0% +so we kind of have a constant time +algorithm we have the Theta n Square in + + align:start position:0% +algorithm we have the Theta n Square in + + + align:start position:0% +algorithm we have the Theta n Square in +the bag right so you know is there + + align:start position:0% +the bag right so you know is there + + + align:start position:0% +the bag right so you know is there +something maybe Theta + + align:start position:0% +something maybe Theta + + + align:start position:0% +something maybe Theta +n how would we do uh this merge and find + + align:start position:0% +n how would we do uh this merge and find + + + align:start position:0% +n how would we do uh this merge and find +the upper tangent by being a little + + align:start position:0% +the upper tangent by being a little + + + align:start position:0% +the upper tangent by being a little +smarter about searching for pairs of + + align:start position:0% +smarter about searching for pairs of + + + align:start position:0% +smarter about searching for pairs of +points that uh will give us this maximum + + align:start position:0% +points that uh will give us this maximum + + + align:start position:0% +points that uh will give us this maximum +yig J right I mean the goal here is + + align:start position:0% +yig J right I mean the goal here is + + + align:start position:0% +yig J right I mean the goal here is +simple it's uh at some level if you + + align:start position:0% +simple it's uh at some level if you + + + align:start position:0% +simple it's uh at some level if you +looked at the Brute Force I would + + align:start position:0% +looked at the Brute Force I would + + + align:start position:0% +looked at the Brute Force I would +generate each of these things I'd find + + align:start position:0% +generate each of these things I'd find + + + align:start position:0% +generate each of these things I'd find +the Y J intercepts associated with this + + align:start position:0% +the Y J intercepts associated with this + + + align:start position:0% +the Y J intercepts associated with this +line and i' just pick the maximum right + + align:start position:0% +line and i' just pick the maximum right + + + align:start position:0% +line and i' just pick the maximum right +and I the constant time algorithm + + align:start position:0% +and I the constant time algorithm + + + align:start position:0% +and I the constant time algorithm +doesn't work the Theta n Square + + align:start position:0% +doesn't work the Theta n Square + + + align:start position:0% +doesn't work the Theta n Square +algorithm definitely works but we don't + + align:start position:0% +algorithm definitely works but we don't + + + align:start position:0% +algorithm definitely works but we don't +like it so there's something there has + + align:start position:0% +like it so there's something there has + + + align:start position:0% +like it so there's something there has +to be something in between right so any + + align:start position:0% +to be something in between right so any + + + align:start position:0% +to be something in between right so any +ideas yeah back + + align:start position:0% +ideas yeah back + + + align:start position:0% +ideas yeah back +there + + align:start position:0% + + + + align:start position:0% + +yeah no you're just finding no you're + + align:start position:0% +yeah no you're just finding no you're + + + align:start position:0% +yeah no you're just finding no you're +maximizing the yig J so for once you + + align:start position:0% +maximizing the yig J so for once you + + + align:start position:0% +maximizing the yig J so for once you +have the segment so that the question + + align:start position:0% +have the segment so that the question + + + align:start position:0% +have the segment so that the question +was isn't the obvious merge algorithm + + align:start position:0% +was isn't the obvious merge algorithm + + + align:start position:0% +was isn't the obvious merge algorithm +Theta n cubed right and and my answer is + + align:start position:0% +Theta n cubed right and and my answer is + + + align:start position:0% +Theta n cubed right and and my answer is +no because uh the Theta n extra Factor + + align:start position:0% +no because uh the Theta n extra Factor + + + align:start position:0% +no because uh the Theta n extra Factor +was came from the fact that you had to + + align:start position:0% +was came from the fact that you had to + + + align:start position:0% +was came from the fact that you had to +check every point every end point to see + + align:start position:0% +check every point every end point to see + + + align:start position:0% +check every point every end point to see +on which side of the plane it was + + align:start position:0% +on which side of the plane it was + + + align:start position:0% +on which side of the plane it was +whereas here what I'm doing is I got + + align:start position:0% +whereas here what I'm doing is I got + + + align:start position:0% +whereas here what I'm doing is I got +this one line here that is basically y + + align:start position:0% +this one line here that is basically y + + + align:start position:0% +this one line here that is basically y +equals Zer if you like right or y equals + + align:start position:0% +equals Zer if you like right or y equals + + + align:start position:0% +equals Zer if you like right or y equals +some uh I'm sorry x equals z or or x + + align:start position:0% +some uh I'm sorry x equals z or or x + + + align:start position:0% +some uh I'm sorry x equals z or or x +equals some value and I just need to + + align:start position:0% +equals some value and I just need to + + + align:start position:0% +equals some value and I just need to +once I have the the the equation for the + + align:start position:0% +once I have the the the equation for the + + + align:start position:0% +once I have the the the equation for the +line associated with A4 B1 or A4 B2 I + + align:start position:0% +line associated with A4 B1 or A4 B2 I + + + align:start position:0% +line associated with A4 B1 or A4 B2 I +just have to find the intercept of it + + align:start position:0% +just have to find the intercept of it + + + align:start position:0% +just have to find the intercept of it +which is constant time + + align:start position:0% +which is constant time + + + align:start position:0% +which is constant time +right and then once I find The Intercept + + align:start position:0% +right and then once I find The Intercept + + + align:start position:0% +right and then once I find The Intercept +of it I I just maximize that intercept + + align:start position:0% +of it I I just maximize that intercept + + + align:start position:0% +of it I I just maximize that intercept +to get my Yi J so I'm good okay so it's + + align:start position:0% +to get my Yi J so I'm good okay so it's + + + align:start position:0% +to get my Yi J so I'm good okay so it's +only Theta n square right good + + align:start position:0% +only Theta n square right good + + + align:start position:0% +only Theta n square right good +question um so uh so this is actually + + align:start position:0% +question um so uh so this is actually + + + align:start position:0% +question um so uh so this is actually +quite uh very very clever this + + align:start position:0% +quite uh very very clever this + + + align:start position:0% +quite uh very very clever this +particular algorithm is called the + + align:start position:0% +particular algorithm is called the + + + align:start position:0% +particular algorithm is called the +two-finger algorithm and I do have + + align:start position:0% +two-finger algorithm and I do have + + + align:start position:0% +two-finger algorithm and I do have +multiple fingers but uh it's going to + + align:start position:0% +multiple fingers but uh it's going to + + + align:start position:0% +multiple fingers but uh it's going to +work out better if I borrow Eric's + + align:start position:0% +work out better if I borrow Eric's + + + align:start position:0% +work out better if I borrow Eric's +finger um and we're going to demonstrate + + align:start position:0% +finger um and we're going to demonstrate + + + align:start position:0% +finger um and we're going to demonstrate +to you the the two-finger algorithm for + + align:start position:0% +to you the the two-finger algorithm for + + + align:start position:0% +to you the the two-finger algorithm for +uh for uh merging these two convex halls + + align:start position:0% +uh for uh merging these two convex halls + + + align:start position:0% +uh for uh merging these two convex halls +and uh then we'll talk about the + + align:start position:0% +and uh then we'll talk about the + + + align:start position:0% +and uh then we'll talk about the +complexity of it okay and my Innovation + + align:start position:0% +complexity of it okay and my Innovation + + + align:start position:0% +complexity of it okay and my Innovation +again last night was to turn this from a + + align:start position:0% +again last night was to turn this from a + + + align:start position:0% +again last night was to turn this from a +two-finger algorithm not only did I have + + align:start position:0% +two-finger algorithm not only did I have + + + align:start position:0% +two-finger algorithm not only did I have +the bright idea of using Eric I decided + + align:start position:0% +the bright idea of using Eric I decided + + + align:start position:0% +the bright idea of using Eric I decided +was it was going to become the + + align:start position:0% +was it was going to become the + + + align:start position:0% +was it was going to become the +two-finger and string algorithm okay so + + align:start position:0% +two-finger and string algorithm okay so + + + align:start position:0% +two-finger and string algorithm okay so +this is wild this this is my + + align:start position:0% +this is wild this this is my + + + align:start position:0% +this is wild this this is my +contribution to 046 lore come on + + align:start position:0% +contribution to 046 lore come on + + + align:start position:0% +contribution to 046 lore come on +right so so the way the two-finger + + align:start position:0% +right so so the way the two-finger + + + align:start position:0% +right so so the way the two-finger +algorithm works and this pseudo code + + align:start position:0% +algorithm works and this pseudo code + + + align:start position:0% +algorithm works and this pseudo code +should be + + align:start position:0% +should be + + + align:start position:0% +should be +incomprehensible okay if you just look + + align:start position:0% +incomprehensible okay if you just look + + + align:start position:0% +incomprehensible okay if you just look +at it and you go what right but this + + align:start position:0% +at it and you go what right but this + + + align:start position:0% +at it and you go what right but this +demo is going to clear everything up + + align:start position:0% +demo is going to clear everything up + + + align:start position:0% +demo is going to clear everything up +right so here's what you do so now we're + + align:start position:0% +right so here's what you do so now we're + + + align:start position:0% +right so here's what you do so now we're +going to do a demo of the merge + + align:start position:0% +going to do a demo of the merge + + + align:start position:0% +going to do a demo of the merge +algorithm that uh is uh a clever merge + + align:start position:0% +algorithm that uh is uh a clever merge + + + align:start position:0% +algorithm that uh is uh a clever merge +algorithm than the one that uses order n + + align:start position:0% +algorithm than the one that uses order n + + + align:start position:0% +algorithm than the one that uses order n +Square time and it's correct um it's + + align:start position:0% +Square time and it's correct um it's + + + align:start position:0% +Square time and it's correct um it's +going to get you the correct upper + + align:start position:0% +going to get you the correct upper + + + align:start position:0% +going to get you the correct upper +tangent and what we're starting at here + + align:start position:0% +tangent and what we're starting at here + + + align:start position:0% +tangent and what we're starting at here +is with Eric's left finger on A1 which + + align:start position:0% +is with Eric's left finger on A1 which + + + align:start position:0% +is with Eric's left finger on A1 which +is defined to be + + align:start position:0% +is defined to be + + + align:start position:0% +is defined to be +the point that's + + align:start position:0% +the point that's + + + align:start position:0% +the point that's +closest to the vertical line that you + + align:start position:0% +closest to the vertical line that you + + + align:start position:0% +closest to the vertical line that you +see here the one that has the highest x + + align:start position:0% +see here the one that has the highest x + + + align:start position:0% +see here the one that has the highest x +coordinate and my finger is on B1 which + + align:start position:0% +coordinate and my finger is on B1 which + + + align:start position:0% +coordinate and my finger is on B1 which +is the point that has the smallest x + + align:start position:0% +is the point that has the smallest x + + + align:start position:0% +is the point that has the smallest x +coordinate on the right hand side sub + + align:start position:0% +coordinate on the right hand side sub + + + align:start position:0% +coordinate on the right hand side sub +Hull and what we do is we compute + + align:start position:0% +Hull and what we do is we compute + + + align:start position:0% +Hull and what we do is we compute +for the segment A1 B1 we compute Yi J in + + align:start position:0% +for the segment A1 B1 we compute Yi J in + + + align:start position:0% +for the segment A1 B1 we compute Yi J in +this case y11 which is The Intercept on + + align:start position:0% +this case y11 which is The Intercept on + + + align:start position:0% +this case y11 which is The Intercept on +the vertical line that you see here that + + align:start position:0% +the vertical line that you see here that + + + align:start position:0% +the vertical line that you see here that +Eric just marked with the Red Dot and um + + align:start position:0% +Eric just marked with the Red Dot and um + + + align:start position:0% +Eric just marked with the Red Dot and um +you can look at the pseudo code over on + + align:start position:0% +you can look at the pseudo code over on + + + align:start position:0% +you can look at the pseudo code over on +to my uh right if I face the board and + + align:start position:0% +to my uh right if I face the board and + + + align:start position:0% +to my uh right if I face the board and +what happens now is I'm going to move + + align:start position:0% +what happens now is I'm going to move + + + align:start position:0% +what happens now is I'm going to move +clockwise and I'm going to go from B1 to + + align:start position:0% +clockwise and I'm going to go from B1 to + + + align:start position:0% +clockwise and I'm going to go from B1 to +B4 and what happened here did the Yi J + + align:start position:0% +B4 and what happened here did the Yi J + + + align:start position:0% +B4 and what happened here did the Yi J +increase or decrease well as you can see + + align:start position:0% +increase or decrease well as you can see + + + align:start position:0% +increase or decrease well as you can see +it decreased and so I'm going to go back + + align:start position:0% +it decreased and so I'm going to go back + + + align:start position:0% +it decreased and so I'm going to go back +to B1 and we're not quite done with this + + align:start position:0% +to B1 and we're not quite done with this + + + align:start position:0% +to B1 and we're not quite done with this +step here Eric's going to go + + align:start position:0% +step here Eric's going to go + + + align:start position:0% +step here Eric's going to go +counterclockwise over to A4 and we're + + align:start position:0% +counterclockwise over to A4 and we're + + + align:start position:0% +counterclockwise over to A4 and we're +going to check again yeah keep the + + align:start position:0% +going to check again yeah keep the + + + align:start position:0% +going to check again yeah keep the +string t uh check again whether y + + align:start position:0% +string t uh check again whether y + + + align:start position:0% +string t uh check again whether y +increased or decreased and as is clear + + align:start position:0% +increased or decreased and as is clear + + + align:start position:0% +increased or decreased and as is clear +from here YJ increased so now we move to + + align:start position:0% +from here YJ increased so now we move to + + + align:start position:0% +from here YJ increased so now we move to +this point and as of this moment um we + + align:start position:0% +this point and as of this moment um we + + + align:start position:0% +this point and as of this moment um we +think that A4 B1 has the highest yig J + + align:start position:0% +think that A4 B1 has the highest yig J + + + align:start position:0% +think that A4 B1 has the highest yig J +but we have a while loop we're going to + + align:start position:0% +but we have a while loop we're going to + + + align:start position:0% +but we have a while loop we're going to +have to continue with this while loop + + align:start position:0% +have to continue with this while loop + + + align:start position:0% +have to continue with this while loop +and now what happens is I'm going to go + + align:start position:0% +and now what happens is I'm going to go + + + align:start position:0% +and now what happens is I'm going to go +from B1 counter clockwise again to B4 + + align:start position:0% +from B1 counter clockwise again to B4 + + + align:start position:0% +from B1 counter clockwise again to B4 +and when this happens did YJ increase or + + align:start position:0% +and when this happens did YJ increase or + + + align:start position:0% +and when this happens did YJ increase or +decrease well it decreased so I'm going + + align:start position:0% +decrease well it decreased so I'm going + + + align:start position:0% +decrease well it decreased so I'm going +to go back to B1 and um Eric now is + + align:start position:0% +to go back to B1 and um Eric now is + + + align:start position:0% +to go back to B1 and um Eric now is +going to go counterclockwise to + + align:start position:0% +going to go counterclockwise to + + + align:start position:0% +going to go counterclockwise to +A3 and as you can see + + align:start position:0% + + + + align:start position:0% + +y31 increased a little bit so we're + + align:start position:0% +y31 increased a little bit so we're + + + align:start position:0% +y31 increased a little bit so we're +going to now stop uh this iteration of + + align:start position:0% +going to now stop uh this iteration of + + + align:start position:0% +going to now stop uh this iteration of +the algorithm and we're at A3 B1 which + + align:start position:0% +the algorithm and we're at A3 B1 which + + + align:start position:0% +the algorithm and we're at A3 B1 which +we think at this point is our upper + + align:start position:0% +we think at this point is our upper + + + align:start position:0% +we think at this point is our upper +tangent but let's check that um start + + align:start position:0% +tangent but let's check that um start + + + align:start position:0% +tangent but let's check that um start +over again on my side B1 to B4 what + + align:start position:0% +over again on my side B1 to B4 what + + + align:start position:0% +over again on my side B1 to B4 what +happened well YJ decreased so I'm going + + align:start position:0% +happened well YJ decreased so I'm going + + + align:start position:0% +happened well YJ decreased so I'm going +to go back to B1 and then Eric's going + + align:start position:0% +to go back to B1 and then Eric's going + + + align:start position:0% +to go back to B1 and then Eric's going +to try he's is going counterclockwise + + align:start position:0% +to try he's is going counterclockwise + + + align:start position:0% +to try he's is going counterclockwise +he's going to go A3 to A2 and well big + + align:start position:0% +he's going to go A3 to A2 and well big + + + align:start position:0% +he's going to go A3 to A2 and well big +decrease in y j now Eric goes back to A3 + + align:start position:0% +decrease in y j now Eric goes back to A3 + + + align:start position:0% +decrease in y j now Eric goes back to A3 +at this point we've tried both moves my + + align:start position:0% +at this point we've tried both moves my + + + align:start position:0% +at this point we've tried both moves my +clockwise move and Eric's + + align:start position:0% +clockwise move and Eric's + + + align:start position:0% +clockwise move and Eric's +counterclockwise move my move from B1 to + + align:start position:0% +counterclockwise move my move from B1 to + + + align:start position:0% +counterclockwise move my move from B1 to +B4 and Eric's move from A3 to A2 so + + align:start position:0% +B4 and Eric's move from A3 to A2 so + + + align:start position:0% +B4 and Eric's move from A3 to A2 so +we've converged we're out of the wild + + align:start position:0% +we've converged we're out of the wild + + + align:start position:0% +we've converged we're out of the wild +Loop A3 B1 for this example is our upper + + align:start position:0% +Loop A3 B1 for this example is our upper + + + align:start position:0% +Loop A3 B1 for this example is our upper +tangent all right you can have your + + align:start position:0% +tangent all right you can have your + + + align:start position:0% +tangent all right you can have your +finger back + + align:start position:0% +finger back + + + align:start position:0% +finger back +Eric um so the reason this works is + + align:start position:0% +Eric um so the reason this works is + + + align:start position:0% +Eric um so the reason this works is +because we have a convex Hull here and a + + align:start position:0% +because we have a convex Hull here and a + + + align:start position:0% +because we have a convex Hull here and a +convex Hull here we're starting + + align:start position:0% +convex Hull here we're starting + + + align:start position:0% +convex Hull here we're starting +with the points that are closest to each + + align:start position:0% +with the points that are closest to each + + + align:start position:0% +with the points that are closest to each +other in terms of A1 being the closest + + align:start position:0% +other in terms of A1 being the closest + + + align:start position:0% +other in terms of A1 being the closest +to this vertical line B1 being the + + align:start position:0% +to this vertical line B1 being the + + + align:start position:0% +to this vertical line B1 being the +closest to this vertical line and we're + + align:start position:0% +closest to this vertical line and we're + + + align:start position:0% +closest to this vertical line and we're +moving upward + + align:start position:0% +moving upward + + + align:start position:0% +moving upward +in both directions because I went + + align:start position:0% +in both directions because I went + + + align:start position:0% +in both directions because I went +clockwise and Eric went counterclockwise + + align:start position:0% +clockwise and Eric went counterclockwise + + + align:start position:0% +clockwise and Eric went counterclockwise +and that's the intuition of why this + + align:start position:0% +and that's the intuition of why this + + + align:start position:0% +and that's the intuition of why this +algorithm Works we're not going to do a + + align:start position:0% +algorithm Works we're not going to do a + + + align:start position:0% +algorithm Works we're not going to do a +formal proof of this algorithm but the + + align:start position:0% +formal proof of this algorithm but the + + + align:start position:0% +formal proof of this algorithm but the +monotonicity property corresponding to + + align:start position:0% +monotonicity property corresponding to + + + align:start position:0% +monotonicity property corresponding to +the convexity of this sub hul and the + + align:start position:0% +the convexity of this sub hul and the + + + align:start position:0% +the convexity of this sub hul and the +convexity of this sub hul essentially + + align:start position:0% +convexity of this sub hul essentially + + + align:start position:0% +convexity of this sub hul essentially +can give you a formal proof of + + align:start position:0% +can give you a formal proof of + + + align:start position:0% +can give you a formal proof of +correctness of this algorithm but as I + + align:start position:0% +correctness of this algorithm but as I + + + align:start position:0% +correctness of this algorithm but as I +said we won't cover that in 046 + + align:start position:0% +said we won't cover that in 046 + + + align:start position:0% +said we won't cover that in 046 +so All That Remains now is to look at + + align:start position:0% +so All That Remains now is to look at + + + align:start position:0% +so All That Remains now is to look at +our pseudo code which matches the + + align:start position:0% +our pseudo code which matches the + + + align:start position:0% +our pseudo code which matches the +execution that you just saw and talk + + align:start position:0% +execution that you just saw and talk + + + align:start position:0% +execution that you just saw and talk +about the complexity of the pseudo + + align:start position:0% +about the complexity of the pseudo + + + align:start position:0% +about the complexity of the pseudo +code what is the complexity of this + + align:start position:0% +code what is the complexity of this + + + align:start position:0% +code what is the complexity of this +algorithm it's order n right so what has + + align:start position:0% +algorithm it's order n right so what has + + + align:start position:0% +algorithm it's order n right so what has +happened here if you look at this while + + align:start position:0% +happened here if you look at this while + + + align:start position:0% +happened here if you look at this while +loop is that while I have two counters + + align:start position:0% +loop is that while I have two counters + + + align:start position:0% +loop is that while I have two counters +um I I'm essentially looking at uh two + + align:start position:0% +um I I'm essentially looking at uh two + + + align:start position:0% +um I I'm essentially looking at uh two +operations per Loop and uh the + + align:start position:0% +operations per Loop and uh the + + + align:start position:0% +operations per Loop and uh the +either one of those counters is + + align:start position:0% +either one of those counters is + + + align:start position:0% +either one of those counters is +guaranteed to increment through the loop + + align:start position:0% +guaranteed to increment through the loop + + + align:start position:0% +guaranteed to increment through the loop +and so since I have in this case P + + align:start position:0% +and so since I have in this case P + + + align:start position:0% +and so since I have in this case P +points in in one case P plus Q equals n + + align:start position:0% +points in in one case P plus Q equals n + + + align:start position:0% +points in in one case P plus Q equals n +so let's say I had P points + + align:start position:0% +so let's say I had P points + + + align:start position:0% +so let's say I had P points +here and I have uh Q points + + align:start position:0% +here and I have uh Q points + + + align:start position:0% +here and I have uh Q points +here and I got P plus Q let's say equals + + align:start position:0% +here and I got P plus Q let's say equals + + + align:start position:0% +here and I got P plus Q let's say equals +n uh then I got a Theta n merge simply + + align:start position:0% +n uh then I got a Theta n merge simply + + + align:start position:0% +n uh then I got a Theta n merge simply +because I'm going to be running through + + align:start position:0% +because I'm going to be running through + + + align:start position:0% +because I'm going to be running through +and + + align:start position:0% +and + + + align:start position:0% +and +incrementing as long as I'm in the loop + + align:start position:0% +incrementing as long as I'm in the loop + + + align:start position:0% +incrementing as long as I'm in the loop +I'm going to be incrementing uh uh + + align:start position:0% +I'm going to be incrementing uh uh + + + align:start position:0% +I'm going to be incrementing uh uh +either the I or the J and the maximum + + align:start position:0% +either the I or the J and the maximum + + + align:start position:0% +either the I or the J and the maximum +that can go to our our our p and Q + + align:start position:0% +that can go to our our our p and Q + + + align:start position:0% +that can go to our our our p and Q +before I bounce out of the loop or + + align:start position:0% +before I bounce out of the loop or + + + align:start position:0% +before I bounce out of the loop or +before I rotate around and so that's why + + align:start position:0% +before I rotate around and so that's why + + + align:start position:0% +before I rotate around and so that's why +this is Theta n um and so you put it all + + align:start position:0% +this is Theta n um and so you put it all + + + align:start position:0% +this is Theta n um and so you put it all +together uh in terms of what the what + + align:start position:0% +together uh in terms of what the what + + + align:start position:0% +together uh in terms of what the what +the merge corresponds to in terms of + + align:start position:0% +the merge corresponds to in terms of + + + align:start position:0% +the merge corresponds to in terms of +complexity and put that together with uh + + align:start position:0% +complexity and put that together with uh + + + align:start position:0% +complexity and put that together with uh +with the overall divid and + + align:start position:0% +with the overall divid and + + + align:start position:0% +with the overall divid and +Conquer we have a case + + align:start position:0% +Conquer we have a case + + + align:start position:0% +Conquer we have a case +where this is looking like a recurrence + + align:start position:0% +where this is looking like a recurrence + + + align:start position:0% +where this is looking like a recurrence +that you've seen many a Time T of n I've + + align:start position:0% +that you've seen many a Time T of n I've + + + align:start position:0% +that you've seen many a Time T of n I've +broken it up into two sub problems so I + + align:start position:0% +broken it up into two sub problems so I + + + align:start position:0% +broken it up into two sub problems so I +have two + + align:start position:0% +have two + + + align:start position:0% +have two +and I could certainly + + align:start position:0% +and I could certainly + + + align:start position:0% +and I could certainly +choose this uh L over here that's uh + + align:start position:0% +choose this uh L over here that's uh + + + align:start position:0% +choose this uh L over here that's uh +that's my line L uh to be such that I + + align:start position:0% +that's my line L uh to be such that I + + + align:start position:0% +that's my line L uh to be such that I +have a good partition between the two + + align:start position:0% +have a good partition between the two + + + align:start position:0% +have a good partition between the two +sets of points right now if I choose L + + align:start position:0% +sets of points right now if I choose L + + + align:start position:0% +sets of points right now if I choose L +to be all the way on the right hand side + + align:start position:0% +to be all the way on the right hand side + + + align:start position:0% +to be all the way on the right hand side +then I have this large sub problem makes + + align:start position:0% +then I have this large sub problem makes + + + align:start position:0% +then I have this large sub problem makes +no sense what whatsoever so what I can + + align:start position:0% +no sense what whatsoever so what I can + + + align:start position:0% +no sense what whatsoever so what I can +do there's nothing that's stopping me + + align:start position:0% +do there's nothing that's stopping me + + + align:start position:0% +do there's nothing that's stopping me +when I've sorted these points by the x + + align:start position:0% +when I've sorted these points by the x + + + align:start position:0% +when I've sorted these points by the x +coordinates to do the division such that + + align:start position:0% +coordinates to do the division such that + + + align:start position:0% +coordinates to do the division such that +there's exactly the same number assuming + + align:start position:0% +there's exactly the same number assuming + + + align:start position:0% +there's exactly the same number assuming +an even number of points n exactly the + + align:start position:0% +an even number of points n exactly the + + + align:start position:0% +an even number of points n exactly the +same number on the left hand side or the + + align:start position:0% +same number on the left hand side or the + + + align:start position:0% +same number on the left hand side or the +right hand side but I can get that right + + align:start position:0% +right hand side but I can get that right + + + align:start position:0% +right hand side but I can get that right +roughly certainly within one one very + + align:start position:0% +roughly certainly within one one very + + + align:start position:0% +roughly certainly within one one very +easily so that's where the N /2 comes + + align:start position:0% +easily so that's where the N /2 comes + + + align:start position:0% +easily so that's where the N /2 comes +from okay um in the next problem that + + align:start position:0% +from okay um in the next problem that + + + align:start position:0% +from okay um in the next problem that +we'll look at the median finding problem + + align:start position:0% +we'll look at the median finding problem + + + align:start position:0% +we'll look at the median finding problem +we'll find that trying to get the sub + + align:start position:0% +we'll find that trying to get the sub + + + align:start position:0% +we'll find that trying to get the sub +problems to be of roughly equal size is + + align:start position:0% +problems to be of roughly equal size is + + + align:start position:0% +problems to be of roughly equal size is +actually a little difficult okay but I + + align:start position:0% +actually a little difficult okay but I + + + align:start position:0% +actually a little difficult okay but I +want to point out that in this + + align:start position:0% +want to point out that in this + + + align:start position:0% +want to point out that in this +particular case it's easy to get sub + + align:start position:0% +particular case it's easy to get sub + + + align:start position:0% +particular case it's easy to get sub +problems that are half the size because + + align:start position:0% +problems that are half the size because + + + align:start position:0% +problems that are half the size because +you've done the sorting and then you + + align:start position:0% +you've done the sorting and then you + + + align:start position:0% +you've done the sorting and then you +just choose the uh the the line the + + align:start position:0% +just choose the uh the the line the + + + align:start position:0% +just choose the uh the the line the +vertical line such that you got a bunch + + align:start position:0% +vertical line such that you got a bunch + + + align:start position:0% +vertical line such that you got a bunch +of points that uh on either side and + + align:start position:0% +of points that uh on either side and + + + align:start position:0% +of points that uh on either side and +then in terms of the merge operation we + + align:start position:0% +then in terms of the merge operation we + + + align:start position:0% +then in terms of the merge operation we +have 2 TN /2 plus Theta n people + + align:start position:0% +have 2 TN /2 plus Theta n people + + + align:start position:0% +have 2 TN /2 plus Theta n people +recognize this uh + + align:start position:0% +recognize this uh + + + align:start position:0% +recognize this uh +recurrence it's the old merge sort + + align:start position:0% +recurrence it's the old merge sort + + + align:start position:0% +recurrence it's the old merge sort +recurrence uh so we did all of this and + + align:start position:0% +recurrence uh so we did all of this and + + + align:start position:0% +recurrence uh so we did all of this and +well it's not merged sort clearly the + + align:start position:0% +well it's not merged sort clearly the + + + align:start position:0% +well it's not merged sort clearly the +the algorithm is not merged sort but we + + align:start position:0% +the algorithm is not merged sort but we + + + align:start position:0% +the algorithm is not merged sort but we +got the same recurrence and so this is + + align:start position:0% +got the same recurrence and so this is + + + align:start position:0% +got the same recurrence and so this is +Theta n log n so a lot better than uh + + align:start position:0% +Theta n log n so a lot better than uh + + + align:start position:0% +Theta n log n so a lot better than uh +than Theta n Cub okay and uh there's no + + align:start position:0% +than Theta n Cub okay and uh there's no + + + align:start position:0% +than Theta n Cub okay and uh there's no +convex Hol algorithm that's um uh in the + + align:start position:0% +convex Hol algorithm that's um uh in the + + + align:start position:0% +convex Hol algorithm that's um uh in the +general case better than this even the + + align:start position:0% +general case better than this even the + + + align:start position:0% +general case better than this even the +gift wrapping algorithm that I mentioned + + align:start position:0% +gift wrapping algorithm that I mentioned + + + align:start position:0% +gift wrapping algorithm that I mentioned +to you with the right data structures it + + align:start position:0% +to you with the right data structures it + + + align:start position:0% +to you with the right data structures it +it gets down to that in terms of theta n + + align:start position:0% +it gets down to that in terms of theta n + + + align:start position:0% +it gets down to that in terms of theta n +log n but uh but no better okay so good + + align:start position:0% +log n but uh but no better okay so good + + + align:start position:0% +log n but uh but no better okay so good +uh that's pretty much what I had here uh + + align:start position:0% +uh that's pretty much what I had here uh + + + align:start position:0% +uh that's pretty much what I had here uh +again like I said happy to answer + + align:start position:0% +again like I said happy to answer + + + align:start position:0% +again like I said happy to answer +questions about uh the correctness of + + align:start position:0% +questions about uh the correctness of + + + align:start position:0% +questions about uh the correctness of +the of this Loop algorithm for merge + + align:start position:0% +the of this Loop algorithm for merge + + + align:start position:0% +the of this Loop algorithm for merge +later any other questions associated + + align:start position:0% +later any other questions associated + + + align:start position:0% +later any other questions associated +with this + + align:start position:0% +with this + + + align:start position:0% +with this +yeah back + + align:start position:0% + + + + align:start position:0% + +there uh no you you can't because uh I + + align:start position:0% +there uh no you you can't because uh I + + + align:start position:0% +there uh no you you can't because uh I +mean that n log n for the pre sorting I + + align:start position:0% +mean that n log n for the pre sorting I + + + align:start position:0% +mean that n log n for the pre sorting I +mean there's another Theta n logn for + + align:start position:0% +mean there's another Theta n logn for + + + align:start position:0% +mean there's another Theta n logn for +the Sorting at the top level um and we + + align:start position:0% +the Sorting at the top level um and we + + + align:start position:0% +the Sorting at the top level um and we +didn't actually use that right so the + + align:start position:0% +didn't actually use that right so the + + + align:start position:0% +didn't actually use that right so the +question was uh can we do better if the + + align:start position:0% +question was uh can we do better if the + + + align:start position:0% +question was uh can we do better if the +input was pre-sorted and I actually did + + align:start position:0% +input was pre-sorted and I actually did + + + align:start position:0% +input was pre-sorted and I actually did +not even use uh the the complexity of + + align:start position:0% +not even use uh the the complexity of + + + align:start position:0% +not even use uh the the complexity of +the sort we just matched it in this case + + align:start position:0% +the sort we just matched it in this case + + + align:start position:0% +the sort we just matched it in this case +right so Theta n log n and you can + + align:start position:0% +right so Theta n log n and you can + + + align:start position:0% +right so Theta n log n and you can +imagine maybe that you could do a Theta + + align:start position:0% +imagine maybe that you could do a Theta + + + align:start position:0% +imagine maybe that you could do a Theta +n sort if these points were small enough + + align:start position:0% +n sort if these points were small enough + + + align:start position:0% +n sort if these points were small enough +and you rounded them up then you could + + align:start position:0% +and you rounded them up then you could + + + align:start position:0% +and you rounded them up then you could +use a bucket sort or a counting sort and + + align:start position:0% +use a bucket sort or a counting sort and + + + align:start position:0% +use a bucket sort or a counting sort and +lower that right so this Theta n log n + + align:start position:0% +lower that right so this Theta n log n + + + align:start position:0% +lower that right so this Theta n log n +is is kind of fundamental to the divide + + align:start position:0% +is is kind of fundamental to the divide + + + align:start position:0% +is is kind of fundamental to the divide +and conquer algorithm it's the only way + + align:start position:0% +and conquer algorithm it's the only way + + + align:start position:0% +and conquer algorithm it's the only way +you can improve that is by making a + + align:start position:0% +you can improve that is by making a + + + align:start position:0% +you can improve that is by making a +merge process that's even faster okay + + align:start position:0% +merge process that's even faster okay + + + align:start position:0% +merge process that's even faster okay +and we uh obviously tried to cook up a + + align:start position:0% +and we uh obviously tried to cook up a + + + align:start position:0% +and we uh obviously tried to cook up a +Theta one merge process but that didn't + + align:start position:0% +Theta one merge process but that didn't + + + align:start position:0% +Theta one merge process but that didn't +work out + + align:start position:0% + + + + align:start position:0% + +okay for if you assume certain things + + align:start position:0% +okay for if you assume certain things + + + align:start position:0% +okay for if you assume certain things +about the input uh you absolutely right + + align:start position:0% +about the input uh you absolutely right + + + align:start position:0% +about the input uh you absolutely right +so one thing you'll discover in in + + align:start position:0% +so one thing you'll discover in in + + + align:start position:0% +so one thing you'll discover in in +algorithms and in 6046 as well is that + + align:start position:0% +algorithms and in 6046 as well is that + + + align:start position:0% +algorithms and in 6046 as well is that +we're never satisfied okay so I just + + align:start position:0% +we're never satisfied okay so I just + + + align:start position:0% +we're never satisfied okay so I just +said oh you can't do better than Theta n + + align:start position:0% +said oh you can't do better than Theta n + + + align:start position:0% +said oh you can't do better than Theta n +log n but that's in the general case and + + align:start position:0% +log n but that's in the general case and + + + align:start position:0% +log n but that's in the general case and +I think I mentioned that um you you're + + align:start position:0% +I think I mentioned that um you you're + + + align:start position:0% +I think I mentioned that um you you're +on the right track if the input is + + align:start position:0% +on the right track if the input is + + + align:start position:0% +on the right track if the input is +pre-sorted and and uh you can take that + + align:start position:0% +pre-sorted and and uh you can take that + + + align:start position:0% +pre-sorted and and uh you can take that +away uh well it doesn't help in that + + align:start position:0% +away uh well it doesn't help in that + + + align:start position:0% +away uh well it doesn't help in that +particular instance if the you have + + align:start position:0% +particular instance if the you have + + + align:start position:0% +particular instance if the you have +general settings but uh um if you um the + + align:start position:0% +general settings but uh um if you um the + + + align:start position:0% +general settings but uh um if you um the +two-dimensional case uh if if if you you + + align:start position:0% +two-dimensional case uh if if if you you + + + align:start position:0% +two-dimensional case uh if if if you you +know the hull uh all the segments are uh + + align:start position:0% +know the hull uh all the segments are uh + + + align:start position:0% +know the hull uh all the segments are uh +um have a certain characteristic uh not + + align:start position:0% +um have a certain characteristic uh not + + + align:start position:0% +um have a certain characteristic uh not +quite pler but uh something that's a + + align:start position:0% +quite pler but uh something that's a + + + align:start position:0% +quite pler but uh something that's a +little more stringent than that you know + + align:start position:0% +little more stringent than that you know + + + align:start position:0% +little more stringent than that you know +you can imagine that you can do + + align:start position:0% +you can imagine that you can do + + + align:start position:0% +you can imagine that you can do +improvements I don't know of any + + align:start position:0% +improvements I don't know of any + + + align:start position:0% +improvements I don't know of any +compelling uh special case input for + + align:start position:0% +compelling uh special case input for + + + align:start position:0% +compelling uh special case input for +convex Hull for which you can do do + + align:start position:0% +convex Hull for which you can do do + + + align:start position:0% +convex Hull for which you can do do +better than Theta n log n but that's a + + align:start position:0% +better than Theta n log n but that's a + + + align:start position:0% +better than Theta n log n but that's a +fine exercise for you which is you know + + align:start position:0% +fine exercise for you which is you know + + + align:start position:0% +fine exercise for you which is you know +in what cases given some structure on + + align:start position:0% +in what cases given some structure on + + + align:start position:0% +in what cases given some structure on +the points can I do better than Theta n + + align:start position:0% +the points can I do better than Theta n + + + align:start position:0% +the points can I do better than Theta n +log n right so that's something that + + align:start position:0% +log n right so that's something that + + + align:start position:0% +log n right so that's something that +keeps coming up in the algorithm + + align:start position:0% +keeps coming up in the algorithm + + + align:start position:0% +keeps coming up in the algorithm +literature uh if you can use that okay + + align:start position:0% +literature uh if you can use that okay + + + align:start position:0% +literature uh if you can use that okay +so yeah back there + + align:start position:0% + + + + align:start position:0% + +question ah great Point uh and uh you're + + align:start position:0% +question ah great Point uh and uh you're + + + align:start position:0% +question ah great Point uh and uh you're +exactly absolutely right and I just + + align:start position:0% +exactly absolutely right and I just + + + align:start position:0% +exactly absolutely right and I just +realized that I skipped that step right + + align:start position:0% +realized that I skipped that step right + + + align:start position:0% +realized that I skipped that step right +thank you so much so the question was um + + align:start position:0% +thank you so much so the question was um + + + align:start position:0% +thank you so much so the question was um +how do I remove the lines and it's + + align:start position:0% +how do I remove the lines and it's + + + align:start position:0% +how do I remove the lines and it's +actually fairly straightforward let's + + align:start position:0% +actually fairly straightforward let's + + + align:start position:0% +actually fairly straightforward let's +keep this up here uh and uh we don't + + align:start position:0% +keep this up here uh and uh we don't + + + align:start position:0% +keep this up here uh and uh we don't +need this incomprehensible pseudo code + + align:start position:0% +need this incomprehensible pseudo code + + + align:start position:0% +need this incomprehensible pseudo code +right uh so let's let's erase that and + + align:start position:0% +right uh so let's let's erase that and + + + align:start position:0% +right uh so let's let's erase that and +uh thank you for asking that question so + + align:start position:0% +uh thank you for asking that question so + + + align:start position:0% +uh thank you for asking that question so +uh it's it's a little simple cut and + + align:start position:0% +uh it's it's a little simple cut and + + + align:start position:0% +uh it's it's a little simple cut and +paste approach where let's say that uh + + align:start position:0% +paste approach where let's say that uh + + + align:start position:0% +paste approach where let's say that uh +uh I find + + align:start position:0% +uh I find + + + align:start position:0% +uh I find +the upper tangent um a + + align:start position:0% +the upper tangent um a + + + align:start position:0% +the upper tangent um a +i + + align:start position:0% +i + + + align:start position:0% +i +BJ okay um and I I find the lower + + align:start position:0% +BJ okay um and I I find the lower + + + align:start position:0% +BJ okay um and I I find the lower +tangent uh let's call it AK + + align:start position:0% +tangent uh let's call it AK + + + align:start position:0% +tangent uh let's call it AK +BM and uh in this particular instance um + + align:start position:0% +BM and uh in this particular instance um + + + align:start position:0% +BM and uh in this particular instance um +what do I have I have A1 A2 A3 + + align:start position:0% + + + + align:start position:0% + +A4 uh as being one of my uh sub hulls + + align:start position:0% +A4 uh as being one of my uh sub hulls + + + align:start position:0% +A4 uh as being one of my uh sub hulls +and then I have B1 B2 B3 B4 as the other + + align:start position:0% +and then I have B1 B2 B3 B4 as the other + + + align:start position:0% +and then I have B1 B2 B3 B4 as the other +one right now what did we determine to + + align:start position:0% +one right now what did we determine to + + + align:start position:0% +one right now what did we determine to +be the uh upper tangent was it A3 + + align:start position:0% +be the uh upper tangent was it A3 + + + align:start position:0% +be the uh upper tangent was it A3 +B1 right A3 B1 so A3 B1 was my upper + + align:start position:0% +B1 right A3 B1 so A3 B1 was my upper + + + align:start position:0% +B1 right A3 B1 so A3 B1 was my upper +tangent and uh uh I guess it was + + align:start position:0% +tangent and uh uh I guess it was + + + align:start position:0% +tangent and uh uh I guess it was +A1 A1 + + align:start position:0% +A1 A1 + + + align:start position:0% +A1 A1 +B4 um A1 B4 was my lower + + align:start position:0% +B4 um A1 B4 was my lower + + + align:start position:0% +B4 um A1 B4 was my lower +tangent so so the big question is now + + align:start position:0% +tangent so so the big question is now + + + align:start position:0% +tangent so so the big question is now +that I have found these two um how do I + + align:start position:0% +that I have found these two um how do I + + + align:start position:0% +that I have found these two um how do I +generate the correct representation of + + align:start position:0% +generate the correct representation of + + + align:start position:0% +generate the correct representation of +the overall convex Hall all right and so + + align:start position:0% +the overall convex Hall all right and so + + + align:start position:0% +the overall convex Hall all right and so +it turns out that you have to do this + + align:start position:0% +it turns out that you have to do this + + + align:start position:0% +it turns out that you have to do this +you want and and the complexity of this + + align:start position:0% +you want and and the complexity of this + + + align:start position:0% +you want and and the complexity of this +is important as well and you need to do + + align:start position:0% +is important as well and you need to do + + + align:start position:0% +is important as well and you need to do +what's called a cut and paste um that's + + align:start position:0% +what's called a cut and paste um that's + + + align:start position:0% +what's called a cut and paste um that's +associated with this where we're going + + align:start position:0% +associated with this where we're going + + + align:start position:0% +associated with this where we're going +to just look at this and that right so + + align:start position:0% +to just look at this and that right so + + + align:start position:0% +to just look at this and that right so +we're going to have these two things and + + align:start position:0% +we're going to have these two things and + + + align:start position:0% +we're going to have these two things and +we got to generate a list of points now + + align:start position:0% +we got to generate a list of points now + + + align:start position:0% +we got to generate a list of points now +clearly A4 is not going to be part of + + align:start position:0% +clearly A4 is not going to be part of + + + align:start position:0% +clearly A4 is not going to be part of +that right uh uh A4 is not going to be + + align:start position:0% +that right uh uh A4 is not going to be + + + align:start position:0% +that right uh uh A4 is not going to be +part of the overall Hull what is it that + + align:start position:0% +part of the overall Hull what is it that + + + align:start position:0% +part of the overall Hull what is it that +we want we want something like um A1 A2 + + align:start position:0% +we want we want something like um A1 A2 + + + align:start position:0% +we want we want something like um A1 A2 +A3 um B1 B2 B3 uh B4 right but this this + + align:start position:0% +A3 um B1 B2 B3 uh B4 right but this this + + + align:start position:0% +A3 um B1 B2 B3 uh B4 right but this this +a point that we have to discard here + + align:start position:0% +a point that we have to discard here + + + align:start position:0% +a point that we have to discard here +agreed um and so the way we do this is U + + align:start position:0% +agreed um and so the way we do this is U + + + align:start position:0% +agreed um and so the way we do this is U +is is very uh mechanical that's the good + + align:start position:0% +is is very uh mechanical that's the good + + + align:start position:0% +is is very uh mechanical that's the good +news here I mean you don't have to look + + align:start position:0% +news here I mean you don't have to look + + + align:start position:0% +news here I mean you don't have to look +at it pictorially I just made that up + + align:start position:0% +at it pictorially I just made that up + + + align:start position:0% +at it pictorially I just made that up +looking at eyeballing it + + align:start position:0% +looking at eyeballing it + + + align:start position:0% +looking at eyeballing it +clearly the computer you doesn't have + + align:start position:0% +clearly the computer you doesn't have + + + align:start position:0% +clearly the computer you doesn't have +eyeballs right um and so so what we're + + align:start position:0% +eyeballs right um and so so what we're + + + align:start position:0% +eyeballs right um and so so what we're +going to do is we're going to say the + + align:start position:0% +going to do is we're going to say the + + + align:start position:0% +going to do is we're going to say the +first link in general the first link is + + align:start position:0% +first link in general the first link is + + + align:start position:0% +first link in general the first link is +AI to BJ because that's my upper + + align:start position:0% +AI to BJ because that's my upper + + + align:start position:0% +AI to BJ because that's my upper +tangent okay um and in this case it's + + align:start position:0% +tangent okay um and in this case it's + + + align:start position:0% +tangent okay um and in this case it's +going to be um A3 B1 okay uh and then + + align:start position:0% +going to be um A3 B1 okay uh and then + + + align:start position:0% +going to be um A3 B1 okay uh and then +I'm going to go + + align:start position:0% +I'm going to go + + + align:start position:0% +I'm going to go +down the the b + + align:start position:0% +down the the b + + + align:start position:0% +down the the b +list till till I + + align:start position:0% + + + + align:start position:0% + +see + + align:start position:0% +see + + + align:start position:0% +see +um till you + + align:start position:0% +um till you + + + align:start position:0% +um till you +see uh BM which is the lower tangent + + align:start position:0% +see uh BM which is the lower tangent + + + align:start position:0% +see uh BM which is the lower tangent +you're on the b list so you're looking + + align:start position:0% +you're on the b list so you're looking + + + align:start position:0% +you're on the b list so you're looking +for the lower tangent point and and then + + align:start position:0% +for the lower tangent point and and then + + + align:start position:0% +for the lower tangent point and and then +you're going to jump um till you see BM + + align:start position:0% +you're going to jump um till you see BM + + + align:start position:0% +you're going to jump um till you see BM +you link it to + + align:start position:0% +you link it to + + + align:start position:0% +you link it to +AK okay you link it to AK and + + align:start position:0% + + + + align:start position:0% + +continue uh + + align:start position:0% +continue uh + + + align:start position:0% +continue uh +till you return to + + align:start position:0% +till you return to + + + align:start position:0% +till you return to +AI right and then you have your your + + align:start position:0% +AI right and then you have your your + + + align:start position:0% +AI right and then you have your your +circular list okay so um what you see + + align:start position:0% +circular list okay so um what you see + + + align:start position:0% +circular list okay so um what you see +here is um you have A3 here so I'm going + + align:start position:0% +here is um you have A3 here so I'm going + + + align:start position:0% +here is um you have A3 here so I'm going +to go ahead and and write + + align:start position:0% + + + + align:start position:0% + +out the execution of what I just wrote + + align:start position:0% +out the execution of what I just wrote + + + align:start position:0% +out the execution of what I just wrote +here so I have A3 and I'm going to go + + align:start position:0% +here so I have A3 and I'm going to go + + + align:start position:0% +here so I have A3 and I'm going to go +jump over to B1 so I'm going to write + + align:start position:0% +jump over to B1 so I'm going to write + + + align:start position:0% +jump over to B1 so I'm going to write +down B1 then I'm going to walk along the + + align:start position:0% +down B1 then I'm going to walk along the + + + align:start position:0% +down B1 then I'm going to walk along the +B's until I get to B4 in this case I'm + + align:start position:0% +B's until I get to B4 in this case I'm + + + align:start position:0% +B's until I get to B4 in this case I'm +going to include all of the B's so I got + + align:start position:0% +going to include all of the B's so I got + + + align:start position:0% +going to include all of the B's so I got +B1 B2 B3 B4 and then I'm going to jump + + align:start position:0% +B1 B2 B3 B4 and then I'm going to jump + + + align:start position:0% +B1 B2 B3 B4 and then I'm going to jump +from B4 to A1 because that's part of my + + align:start position:0% +from B4 to A1 because that's part of my + + + align:start position:0% +from B4 to A1 because that's part of my +um uh lower + + align:start position:0% +um uh lower + + + align:start position:0% +um uh lower +tangent and I got uh A1 here + + align:start position:0% +tangent and I got uh A1 here + + + align:start position:0% +tangent and I got uh A1 here +A2 and uh then I'm back to A3 which is + + align:start position:0% +A2 and uh then I'm back to A3 which is + + + align:start position:0% +A2 and uh then I'm back to A3 which is +great because then I'm + + align:start position:0% +great because then I'm + + + align:start position:0% +great because then I'm +done okay and so exactly what I said + + align:start position:0% +done okay and so exactly what I said + + + align:start position:0% +done okay and so exactly what I said +happened thank + + align:start position:0% +happened thank + + + align:start position:0% +happened thank +goodness which is we dropped A4 but we + + align:start position:0% +goodness which is we dropped A4 but we + + + align:start position:0% +goodness which is we dropped A4 but we +kept all the other points all right so + + align:start position:0% +kept all the other points all right so + + + align:start position:0% +kept all the other points all right so +answer your + + align:start position:0% +answer your + + + align:start position:0% +answer your +question good what is the complexity of + + align:start position:0% +question good what is the complexity of + + + align:start position:0% +question good what is the complexity of +cut and + + align:start position:0% +cut and + + + align:start position:0% +cut and +paste it's orderan I'm just walking + + align:start position:0% +paste it's orderan I'm just walking + + + align:start position:0% +paste it's orderan I'm just walking +through these lists so there's no hidden + + align:start position:0% +through these lists so there's no hidden + + + align:start position:0% +through these lists so there's no hidden +complexity here okay good good thank you + + align:start position:0% +complexity here okay good good thank you + + + align:start position:0% +complexity here okay good good thank you +um you desperately deserve a frisbee in + + align:start position:0% +um you desperately deserve a frisbee in + + + align:start position:0% +um you desperately deserve a frisbee in +fact you deserve two right where are you + + align:start position:0% +fact you deserve two right where are you + + + align:start position:0% +fact you deserve two right where are you +I + + align:start position:0% +I + + + align:start position:0% +I +oh could you stand up yeah right two two + + align:start position:0% +oh could you stand up yeah right two two + + + align:start position:0% +oh could you stand up yeah right two two +colors all + + align:start position:0% + + + + align:start position:0% + +right oh so well you can give it to him + + align:start position:0% +right oh so well you can give it to him + + + align:start position:0% +right oh so well you can give it to him +if you like + + align:start position:0% +if you like + + + align:start position:0% +if you like +but so uh good thank you so are we done + + align:start position:0% +but so uh good thank you so are we done + + + align:start position:0% +but so uh good thank you so are we done +are we done with convex + + align:start position:0% +are we done with convex + + + align:start position:0% +are we done with convex +Hall okay good so let's uh let's go on + + align:start position:0% +Hall okay good so let's uh let's go on + + + align:start position:0% +Hall okay good so let's uh let's go on +and do median finding I very different + + align:start position:0% +and do median finding I very different + + + align:start position:0% +and do median finding I very different +very different uh set of uh issues here + + align:start position:0% +very different uh set of uh issues here + + + align:start position:0% +very different uh set of uh issues here +I still a divid and + + align:start position:0% +I still a divid and + + + align:start position:0% +I still a divid and +coner but a very different set of + + align:start position:0% + + + + align:start position:0% + +issues the specification here is of + + align:start position:0% +issues the specification here is of + + + align:start position:0% +issues the specification here is of +course uh straightforward uh you can + + align:start position:0% +course uh straightforward uh you can + + + align:start position:0% +course uh straightforward uh you can +think of it as I just want a better + + align:start position:0% +think of it as I just want a better + + + align:start position:0% +think of it as I just want a better +algorithm than sorting and looking for + + align:start position:0% +algorithm than sorting and looking for + + + align:start position:0% +algorithm than sorting and looking for +the median at a particular position n/2 + + align:start position:0% +the median at a particular position n/2 + + + align:start position:0% +the median at a particular position n/2 +position uh for + + align:start position:0% +position uh for + + + align:start position:0% +position uh for +example let's say n is + + align:start position:0% +example let's say n is + + + align:start position:0% +example let's say n is +um n is odd and uh it's floor of n /2 + + align:start position:0% +um n is odd and uh it's floor of n /2 + + + align:start position:0% +um n is odd and uh it's floor of n /2 +you can find that median right so it's + + align:start position:0% +you can find that median right so it's + + + align:start position:0% +you can find that median right so it's +it's pretty easy if you can do sorting + + align:start position:0% +it's pretty easy if you can do sorting + + + align:start position:0% +it's pretty easy if you can do sorting +uh but we're we're never satisfied with + + align:start position:0% +uh but we're we're never satisfied with + + + align:start position:0% +uh but we're we're never satisfied with +uh uh with using a standard algorithm uh + + align:start position:0% +uh uh with using a standard algorithm uh + + + align:start position:0% +uh uh with using a standard algorithm uh +if we think that we can do better than + + align:start position:0% +if we think that we can do better than + + + align:start position:0% +if we think that we can do better than +that so the whole game here is going to + + align:start position:0% +that so the whole game here is going to + + + align:start position:0% +that so the whole game here is going to +be I want to find the + + align:start position:0% +be I want to find the + + + align:start position:0% +be I want to find the +median a and um I want to do it in + + align:start position:0% +median a and um I want to do it in + + + align:start position:0% +median a and um I want to do it in +better than Theta n log n time + + align:start position:0% + + + + align:start position:0% + +okay so that's what median finding is + + align:start position:0% +okay so that's what median finding is + + + align:start position:0% +okay so that's what median finding is +all about we're going to use divide and + + align:start position:0% +all about we're going to use divide and + + + align:start position:0% +all about we're going to use divide and +conquer for + + align:start position:0% +conquer for + + + align:start position:0% +conquer for +this um and so in general um we're going + + align:start position:0% +this um and so in general um we're going + + + align:start position:0% +this um and so in general um we're going +to Define + + align:start position:0% +to Define + + + align:start position:0% +to Define +given um a set of n + + align:start position:0% + + + + align:start position:0% + +numbers + + align:start position:0% +numbers + + + align:start position:0% +numbers +Define rank of + + align:start position:0% +Define rank of + + + align:start position:0% +Define rank of +X as + + align:start position:0% + + + + align:start position:0% + +the numbers in the + + align:start position:0% + + + + align:start position:0% + +set that are greater than I'm sorry less + + align:start position:0% +set that are greater than I'm sorry less + + + align:start position:0% +set that are greater than I'm sorry less +than or equal to X I mean you could have + + align:start position:0% +than or equal to X I mean you could have + + + align:start position:0% +than or equal to X I mean you could have +defined it differently we're going to go + + align:start position:0% +defined it differently we're going to go + + + align:start position:0% +defined it differently we're going to go +with less than or equal to so in general + + align:start position:0% +with less than or equal to so in general + + + align:start position:0% +with less than or equal to so in general +uh uh the rank of course is U something + + align:start position:0% +uh uh the rank of course is U something + + + align:start position:0% +uh uh the rank of course is U something +that you could be used very easily to + + align:start position:0% +that you could be used very easily to + + + align:start position:0% +that you could be used very easily to +find the median so if you want to find + + align:start position:0% +find the median so if you want to find + + + align:start position:0% +find the median so if you want to find +the + + align:start position:0% +the + + + align:start position:0% +the +element of + + align:start position:0% +element of + + + align:start position:0% +element of +rank n + 1 divided by two floor that's + + align:start position:0% +rank n + 1 divided by two floor that's + + + align:start position:0% +rank n + 1 divided by two floor that's +what we call the lower + + align:start position:0% +what we call the lower + + + align:start position:0% +what we call the lower +median and uh n + 1 divided by two + + align:start position:0% +median and uh n + 1 divided by two + + + align:start position:0% +median and uh n + 1 divided by two +ceiling is the upper median and they may + + align:start position:0% +ceiling is the upper median and they may + + + align:start position:0% +ceiling is the upper median and they may +be the + + align:start position:0% +be the + + + align:start position:0% +be the +same if n is + + align:start position:0% +same if n is + + + align:start position:0% +same if n is +odd but that's what we want so you can + + align:start position:0% +odd but that's what we want so you can + + + align:start position:0% +odd but that's what we want so you can +think of it as not median finding but + + align:start position:0% +think of it as not median finding but + + + align:start position:0% +think of it as not median finding but +finding elements with a certain Rank and + + align:start position:0% +finding elements with a certain Rank and + + + align:start position:0% +finding elements with a certain Rank and +we want to do this in linear time + + align:start position:0% +we want to do this in linear time + + + align:start position:0% +we want to do this in linear time +okay um so we got to apply divide and + + align:start position:0% +okay um so we got to apply divide and + + + align:start position:0% +okay um so we got to apply divide and +conquer here and uh as always the + + align:start position:0% +conquer here and uh as always the + + + align:start position:0% +conquer here and uh as always the +template can be instantiated and the + + align:start position:0% +template can be instantiated and the + + + align:start position:0% +template can be instantiated and the +devil is in the details of either + + align:start position:0% +devil is in the details of either + + + align:start position:0% +devil is in the details of either +division or merge and we had uh most of + + align:start position:0% +division or merge and we had uh most of + + + align:start position:0% +division or merge and we had uh most of +our fun with convex Hull on the merge + + align:start position:0% +our fun with convex Hull on the merge + + + align:start position:0% +our fun with convex Hull on the merge +operation it turns out most of the fun + + align:start position:0% +operation it turns out most of the fun + + + align:start position:0% +operation it turns out most of the fun +here with respect to median finding is + + align:start position:0% +here with respect to median finding is + + + align:start position:0% +here with respect to median finding is +in the Divide okay uh so + + align:start position:0% + + + + align:start position:0% + +what I want + + align:start position:0% +what I want + + + align:start position:0% +what I want +is the definition of a select + + align:start position:0% +is the definition of a select + + + align:start position:0% +is the definition of a select +routine that takes a set of numbers + + align:start position:0% +routine that takes a set of numbers + + + align:start position:0% +routine that takes a set of numbers +s and this is the + + align:start position:0% +s and this is the + + + align:start position:0% +s and this is the +rank so I want a rank + + align:start position:0% +rank so I want a rank + + + align:start position:0% +rank so I want a rank +I and that I might be n / two uh well + + align:start position:0% +I and that I might be n / two uh well + + + align:start position:0% +I and that I might be n / two uh well +floor of n plus one over two whatever um + + align:start position:0% +floor of n plus one over two whatever um + + + align:start position:0% +floor of n plus one over two whatever um +and so what does the divide and conquer + + align:start position:0% +and so what does the divide and conquer + + + align:start position:0% +and so what does the divide and conquer +look like well the first thing you need + + align:start position:0% +look like well the first thing you need + + + align:start position:0% +look like well the first thing you need +do is divide and as of now we're just + + align:start position:0% +do is divide and as of now we're just + + + align:start position:0% +do is divide and as of now we're just +going to say we're going to pick some + + align:start position:0% +going to say we're going to pick some + + + align:start position:0% +going to say we're going to pick some +element X belonging to S and this choice + + align:start position:0% +element X belonging to S and this choice + + + align:start position:0% +element X belonging to S and this choice +is going to be crucial but at this point + + align:start position:0% +is going to be crucial but at this point + + + align:start position:0% +is going to be crucial but at this point +I'm not ready to specify this Choice yet + + align:start position:0% +I'm not ready to specify this Choice yet + + + align:start position:0% +I'm not ready to specify this Choice yet +okay so we're going to have to do this + + align:start position:0% +okay so we're going to have to do this + + + align:start position:0% +okay so we're going to have to do this +cleverly and then what we're going to do + + align:start position:0% +cleverly and then what we're going to do + + + align:start position:0% +cleverly and then what we're going to do +is we're going to + + align:start position:0% +is we're going to + + + align:start position:0% +is we're going to +compute um K which is the + + align:start position:0% +compute um K which is the + + + align:start position:0% +compute um K which is the +rank of X and generate + + align:start position:0% +rank of X and generate + + + align:start position:0% +rank of X and generate +two sub arrays such + + align:start position:0% +two sub arrays such + + + align:start position:0% +two sub arrays such +that I want to find the fifth highest + + align:start position:0% +that I want to find the fifth highest + + + align:start position:0% +that I want to find the fifth highest +element I want to find the median + + align:start position:0% +element I want to find the median + + + align:start position:0% +element I want to find the median +element I want to find the 10th highest + + align:start position:0% +element I want to find the 10th highest + + + align:start position:0% +element I want to find the 10th highest +element so I have to I have to keep + + align:start position:0% +element so I have to I have to keep + + + align:start position:0% +element so I have to I have to keep +track of what happens in the sub + + align:start position:0% +track of what happens in the sub + + + align:start position:0% +track of what happens in the sub +problems because the the sub problems + + align:start position:0% +problems because the the sub problems + + + align:start position:0% +problems because the the sub problems +are going to determine depending on how + + align:start position:0% +are going to determine depending on how + + + align:start position:0% +are going to determine depending on how +many elements are inside those sub + + align:start position:0% +many elements are inside those sub + + + align:start position:0% +many elements are inside those sub +problems which I can only determine + + align:start position:0% +problems which I can only determine + + + align:start position:0% +problems which I can only determine +after I've solved those sub problems I'm + + align:start position:0% +after I've solved those sub problems I'm + + + align:start position:0% +after I've solved those sub problems I'm +going to have to collect that + + align:start position:0% +going to have to collect that + + + align:start position:0% +going to have to collect that +information and put it together in the + + align:start position:0% +information and put it together in the + + + align:start position:0% +information and put it together in the +merge operation um so if I want to find + + align:start position:0% +merge operation um so if I want to find + + + align:start position:0% +merge operation um so if I want to find +the 10th highest element and I've broken + + align:start position:0% +the 10th highest element and I've broken + + + align:start position:0% +the 10th highest element and I've broken +it up at relatively arbitrarily it's + + align:start position:0% +it up at relatively arbitrarily it's + + + align:start position:0% +it up at relatively arbitrarily it's +quite possible that the 10th highest + + align:start position:0% +quite possible that the 10th highest + + + align:start position:0% +quite possible that the 10th highest +element uh is going to be discovered in + + align:start position:0% +element uh is going to be discovered in + + + align:start position:0% +element uh is going to be discovered in +the left one or the right one uh and I + + align:start position:0% +the left one or the right one uh and I + + + align:start position:0% +the left one or the right one uh and I +have to show that it's the 10th highest + + align:start position:0% +have to show that it's the 10th highest + + + align:start position:0% +have to show that it's the 10th highest +and it might be that there's four + + align:start position:0% +and it might be that there's four + + + align:start position:0% +and it might be that there's four +elements in the left and five on the + + align:start position:0% +elements in the left and five on the + + + align:start position:0% +elements in the left and five on the +right that are + + align:start position:0% +right that are + + + align:start position:0% +right that are +um that are um uh let's see if I Define + + align:start position:0% +um that are um uh let's see if I Define + + + align:start position:0% +um that are um uh let's see if I Define +the rank as less than or equal to X + + align:start position:0% +the rank as less than or equal to X + + + align:start position:0% +the rank as less than or equal to X +there's four on the left and five on the + + align:start position:0% +there's four on the left and five on the + + + align:start position:0% +there's four on the left and five on the +right that are smaller and that's why + + align:start position:0% +right that are smaller and that's why + + + align:start position:0% +right that are smaller and that's why +this is the 10th highest element uh and + + align:start position:0% +this is the 10th highest element uh and + + + align:start position:0% +this is the 10th highest element uh and +that's that's essentially what we have + + align:start position:0% +that's that's essentially what we have + + + align:start position:0% +that's that's essentially what we have +to look at so B and C are going to + + align:start position:0% +to look at so B and C are going to + + + align:start position:0% +to look at so B and C are going to +correspond to um the subarrays that you + + align:start position:0% +correspond to um the subarrays that you + + + align:start position:0% +correspond to um the subarrays that you +can uh clearly eliminate one of them uh + + align:start position:0% +can uh clearly eliminate one of them uh + + + align:start position:0% +can uh clearly eliminate one of them uh +you can count the number of elements in + + align:start position:0% +you can count the number of elements in + + + align:start position:0% +you can count the number of elements in +B count the number of elements in C and + + align:start position:0% +B count the number of elements in C and + + + align:start position:0% +B count the number of elements in C and +uh you can eliminate one of them + + align:start position:0% +uh you can eliminate one of them + + + align:start position:0% +uh you can eliminate one of them +in this uh in this recursion as you're + + align:start position:0% +in this uh in this recursion as you're + + + align:start position:0% +in this uh in this recursion as you're +discovering this uh element with the + + align:start position:0% +discovering this uh element with the + + + align:start position:0% +discovering this uh element with the +correct rank in this case I so let me + + align:start position:0% +correct rank in this case I so let me + + + align:start position:0% +correct rank in this case I so let me +write the rest of this out and U make + + align:start position:0% +write the rest of this out and U make + + + align:start position:0% +write the rest of this out and U make +sure U we're all on the same page uh + + align:start position:0% +sure U we're all on the same page uh + + + align:start position:0% +sure U we're all on the same page uh +what I have here + + align:start position:0% +what I have here + + + align:start position:0% +what I have here +pictorially is I've + + align:start position:0% + + + + align:start position:0% + +generated B + + align:start position:0% +generated B + + + align:start position:0% +generated B +here and C so this is all of B and + + align:start position:0% +here and C so this is all of B and + + + align:start position:0% +here and C so this is all of B and +that's all of C I have K minus one + + align:start position:0% +that's all of C I have K minus one + + + align:start position:0% +that's all of C I have K minus one +elements here in + + align:start position:0% +elements here in + + + align:start position:0% +elements here in +B and let's say I have n minus + + align:start position:0% +B and let's say I have n minus + + + align:start position:0% +B and let's say I have n minus +K + + align:start position:0% +K + + + align:start position:0% +K +elements in C and uh I'm going to uh + + align:start position:0% +elements in C and uh I'm going to uh + + + align:start position:0% +elements in C and uh I'm going to uh +essentially um uh take once I've + + align:start position:0% +essentially um uh take once I've + + + align:start position:0% +essentially um uh take once I've +selected a particular element I'm going + + align:start position:0% +selected a particular element I'm going + + + align:start position:0% +selected a particular element I'm going +to look at all of the elements that are + + align:start position:0% +to look at all of the elements that are + + + align:start position:0% +to look at all of the elements that are +less than it and put it into the array B + + align:start position:0% +less than it and put it into the array B + + + align:start position:0% +less than it and put it into the array B +I'm going to look at all the elements + + align:start position:0% +I'm going to look at all the elements + + + align:start position:0% +I'm going to look at all the elements +that are greater than it let's assume + + align:start position:0% +that are greater than it let's assume + + + align:start position:0% +that are greater than it let's assume +all elements are unique I'm going to put + + align:start position:0% +all elements are unique I'm going to put + + + align:start position:0% +all elements are unique I'm going to put +all of them into C and I'm going to + + align:start position:0% +all of them into C and I'm going to + + + align:start position:0% +all of them into C and I'm going to +recur on B and C that's uh those two are + + align:start position:0% +recur on B and C that's uh those two are + + + align:start position:0% +recur on B and C that's uh those two are +my sub problems uh but what I have to + + align:start position:0% +my sub problems uh but what I have to + + + align:start position:0% +my sub problems uh but what I have to +do is once I recur and + + align:start position:0% +do is once I recur and + + + align:start position:0% +do is once I recur and +I've + + align:start position:0% +I've + + + align:start position:0% +I've +discovered the the ranks of the sub + + align:start position:0% +discovered the the ranks of the sub + + + align:start position:0% +discovered the the ranks of the sub +problems I have to put them together so + + align:start position:0% +problems I have to put them together so + + + align:start position:0% +problems I have to put them together so +what I have here is if k equals I if + + align:start position:0% +what I have here is if k equals I if + + + align:start position:0% +what I have here is if k equals I if +I've computed the rank and I I realize + + align:start position:0% +I've computed the rank and I I realize + + + align:start position:0% +I've computed the rank and I I realize +that if k equals equals I I should say + + align:start position:0% +that if k equals equals I I should say + + + align:start position:0% +that if k equals equals I I should say +uh if k equals I then I'm going to just + + align:start position:0% +uh if k equals I then I'm going to just + + + align:start position:0% +uh if k equals I then I'm going to just +return X I'm done at this point I got + + align:start position:0% +return X I'm done at this point I got + + + align:start position:0% +return X I'm done at this point I got +lucky I picked an element X and it + + align:start position:0% +lucky I picked an element X and it + + + align:start position:0% +lucky I picked an element X and it +magically ended up having the correct + + align:start position:0% +magically ended up having the correct + + + align:start position:0% +magically ended up having the correct +rank okay uh not always going to happen + + align:start position:0% +rank okay uh not always going to happen + + + align:start position:0% +rank okay uh not always going to happen +uh and so in other case if K is greater + + align:start position:0% +uh and so in other case if K is greater + + + align:start position:0% +uh and so in other case if K is greater +than + + align:start position:0% +than + + + align:start position:0% +than +I then I'm going to + + align:start position:0% +I then I'm going to + + + align:start position:0% +I then I'm going to +return select + + align:start position:0% +return select + + + align:start position:0% +return select +bi + + align:start position:0% +bi + + + align:start position:0% +bi +I so uh what I've done here is uh I'm if + + align:start position:0% +I so uh what I've done here is uh I'm if + + + align:start position:0% +I so uh what I've done here is uh I'm if +if K is is greater than I then I'm going + + align:start position:0% +if K is is greater than I then I'm going + + + align:start position:0% +if K is is greater than I then I'm going +to say oh so now I'm going to have to + + align:start position:0% +to say oh so now I'm going to have to + + + align:start position:0% +to say oh so now I'm going to have to +find the element in B I know that it's + + align:start position:0% +find the element in B I know that it's + + + align:start position:0% +find the element in B I know that it's +going to be in B Because K is greater + + align:start position:0% +going to be in B Because K is greater + + + align:start position:0% +going to be in B Because K is greater +than I and I got to find the exact + + align:start position:0% +than I and I got to find the exact + + + align:start position:0% +than I and I got to find the exact +position depending on what what i is + + align:start position:0% +position depending on what what i is + + + align:start position:0% +position depending on what what i is +over here but it's going to be you know + + align:start position:0% +over here but it's going to be you know + + + align:start position:0% +over here but it's going to be you know +somewhere between um between one and K + + align:start position:0% +somewhere between um between one and K + + + align:start position:0% +somewhere between um between one and K +minus one okay and then uh the last case + + align:start position:0% +minus one okay and then uh the last case + + + align:start position:0% +minus one okay and then uh the last case +is + + align:start position:0% +is + + + align:start position:0% +is +um if uh K is less than I then uh this + + align:start position:0% +um if uh K is less than I then uh this + + + align:start position:0% +um if uh K is less than I then uh this +is a little more tricky I'm going to + + align:start position:0% +is a little more tricky I'm going to + + + align:start position:0% +is a little more tricky I'm going to +return C of I minus K okay so what what + + align:start position:0% +return C of I minus K okay so what what + + + align:start position:0% +return C of I minus K okay so what what +happens here is that um my K uh is uh + + align:start position:0% +happens here is that um my K uh is uh + + + align:start position:0% +happens here is that um my K uh is uh +that the the rank for the X that I've + + align:start position:0% +that the the rank for the X that I've + + + align:start position:0% +that the the rank for the X that I've +looked at over here is less than I so + + align:start position:0% +looked at over here is less than I so + + + align:start position:0% +looked at over here is less than I so +I'm going to look I know that I'm going + + align:start position:0% +I'm going to look I know that I'm going + + + align:start position:0% +I'm going to look I know that I'm going +to find this element that I'm looking + + align:start position:0% +to find this element that I'm looking + + + align:start position:0% +to find this element that I'm looking +for in C but if I just look at c um I + + align:start position:0% +for in C but if I just look at c um I + + + align:start position:0% +for in C but if I just look at c um I +don't want to look at C and look for an + + align:start position:0% +don't want to look at C and look for an + + + align:start position:0% +don't want to look at C and look for an +element of rank I within C right that + + align:start position:0% +element of rank I within C right that + + + align:start position:0% +element of rank I within C right that +that doesn't make sense because I'm + + align:start position:0% +that doesn't make sense because I'm + + + align:start position:0% +that doesn't make sense because I'm +looking for an element of rank I in the + + align:start position:0% +looking for an element of rank I in the + + + align:start position:0% +looking for an element of rank I in the +overall array that was given to me so I + + align:start position:0% +overall array that was given to me so I + + + align:start position:0% +overall array that was given to me so I +have to subtract out uh the K elements + + align:start position:0% +have to subtract out uh the K elements + + + align:start position:0% +have to subtract out uh the K elements +uh that correspond to X and all of the K + + align:start position:0% +uh that correspond to X and all of the K + + + align:start position:0% +uh that correspond to X and all of the K +minus one elements that are in B to go + + align:start position:0% +minus one elements that are in B to go + + + align:start position:0% +minus one elements that are in B to go +figure out exactly what position or rank + + align:start position:0% +figure out exactly what position or rank + + + align:start position:0% +figure out exactly what position or rank +I'm looking for in the subarray + + align:start position:0% +I'm looking for in the subarray + + + align:start position:0% +I'm looking for in the subarray +corresponding to see okay so people buy + + align:start position:0% +corresponding to see okay so people buy + + + align:start position:0% +corresponding to see okay so people buy +that so that's just a small little thing + + align:start position:0% +that so that's just a small little thing + + + align:start position:0% +that so that's just a small little thing +that you have to keep in mind as you do + + align:start position:0% +that you have to keep in mind as you do + + + align:start position:0% +that you have to keep in mind as you do +this right so that's uh pretty + + align:start position:0% +this right so that's uh pretty + + + align:start position:0% +this right so that's uh pretty +straightforward looking pretty good uh + + align:start position:0% +straightforward looking pretty good uh + + + align:start position:0% +straightforward looking pretty good uh +and you say well am I done here and uh + + align:start position:0% +and you say well am I done here and uh + + + align:start position:0% +and you say well am I done here and uh +as you can imagine the answer is no + + align:start position:0% +as you can imagine the answer is no + + + align:start position:0% +as you can imagine the answer is no +because we haven't + + align:start position:0% +because we haven't + + + align:start position:0% +because we haven't +specified uh this this value now can + + align:start position:0% +specified uh this this value now can + + + align:start position:0% +specified uh this this value now can +someone tell + + align:start position:0% +someone tell + + + align:start position:0% +someone tell +me um at least from an efficiency + + align:start position:0% +me um at least from an efficiency + + + align:start position:0% +me um at least from an efficiency +standpoint + + align:start position:0% +standpoint + + + align:start position:0% +standpoint +um what might happen what we're looking + + align:start position:0% +um what might happen what we're looking + + + align:start position:0% +um what might happen what we're looking +for here as you can imagine we want to + + align:start position:0% +for here as you can imagine we want to + + + align:start position:0% +for here as you can imagine we want to +improve on Theta n log n and so you you + + align:start position:0% +improve on Theta n log n and so you you + + + align:start position:0% +improve on Theta n log n and so you you +could say well I'm happy with Theta n + + align:start position:0% +could say well I'm happy with Theta n + + + align:start position:0% +could say well I'm happy with Theta n +Theta n a Theta n complexity algorithm + + align:start position:0% +Theta n a Theta n complexity algorithm + + + align:start position:0% +Theta n a Theta n complexity algorithm +is better than a Theta n log n + + align:start position:0% +is better than a Theta n log n + + + align:start position:0% +is better than a Theta n log n +complexity algorithm which is kind of in + + align:start position:0% +complexity algorithm which is kind of in + + + align:start position:0% +complexity algorithm which is kind of in +the bag because we know how to sort and + + align:start position:0% +the bag because we know how to sort and + + + align:start position:0% +the bag because we know how to sort and +we know how to Index right so we want a + + align:start position:0% +we know how to Index right so we want a + + + align:start position:0% +we know how to Index right so we want a +Theta n algorithm now if you take this + + align:start position:0% +Theta n algorithm now if you take this + + + align:start position:0% +Theta n algorithm now if you take this +and um if I just uh I picked let's say + + align:start position:0% +and um if I just uh I picked let's say + + + align:start position:0% +and um if I just uh I picked let's say +the the the biggest element or I I kept + + align:start position:0% +the the the biggest element or I I kept + + + align:start position:0% +the the the biggest element or I I kept +picking X to be n or n n minus one or + + align:start position:0% +picking X to be n or n n minus one or + + + align:start position:0% +picking X to be n or n n minus one or +just pick a constant value I picked X to + + align:start position:0% +just pick a constant value I picked X to + + + align:start position:0% +just pick a constant value I picked X to +be in the middle right I picked the + + align:start position:0% +be in the middle right I picked the + + + align:start position:0% +be in the middle right I picked the +index uh uh because I can always pick a + + align:start position:0% +index uh uh because I can always pick a + + + align:start position:0% +index uh uh because I can always pick a +pick an element based on its index I can + + align:start position:0% +pick an element based on its index I can + + + align:start position:0% +pick an element based on its index I can +always go for the middle one right so + + align:start position:0% +always go for the middle one right so + + + align:start position:0% +always go for the middle one right so +what is the worst case complexity of + + align:start position:0% +what is the worst case complexity of + + + align:start position:0% +what is the worst case complexity of +this algorithm for uh if I don't + + align:start position:0% +this algorithm for uh if I don't + + + align:start position:0% +this algorithm for uh if I don't +specify or I give you this arbitrary + + align:start position:0% +specify or I give you this arbitrary + + + align:start position:0% +specify or I give you this arbitrary +selection corresponding to X belonging + + align:start position:0% +selection corresponding to X belonging + + + align:start position:0% +selection corresponding to X belonging +to S what is the worst case comp + + align:start position:0% +to S what is the worst case comp + + + align:start position:0% +to S what is the worst case comp +complexity of this algorithm right yeah + + align:start position:0% +complexity of this algorithm right yeah + + + align:start position:0% +complexity of this algorithm right yeah +go ahead n Square why is + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +yeah exactly right that's exactly right + + align:start position:0% +yeah exactly right that's exactly right + + + align:start position:0% +yeah exactly right that's exactly right +um so what happens here is that you're + + align:start position:0% +um so what happens here is that you're + + + align:start position:0% +um so what happens here is that you're +doing a bunch of work here with is Theta + + align:start position:0% +doing a bunch of work here with is Theta + + + align:start position:0% +doing a bunch of work here with is Theta +n work right right here this is Theta n + + align:start position:0% +n work right right here this is Theta n + + + align:start position:0% +n work right right here this is Theta n +work okay so given that you're doing + + align:start position:0% +work okay so given that you're doing + + + align:start position:0% +work okay so given that you're doing +Theta n work here uh uh you have to be + + align:start position:0% +Theta n work here uh uh you have to be + + + align:start position:0% +Theta n work here uh uh you have to be +really careful um as to how you pick the + + align:start position:0% +really careful um as to how you pick the + + + align:start position:0% +really careful um as to how you pick the +the the X element so what might happen + + align:start position:0% +the the X element so what might happen + + + align:start position:0% +the the X element so what might happen +is that you end up picking the X over + + align:start position:0% +is that you end up picking the X over + + + align:start position:0% +is that you end up picking the X over +here and uh given the particular rank + + align:start position:0% +here and uh given the particular rank + + + align:start position:0% +here and uh given the particular rank +you're looking for you have to now + + align:start position:0% +you're looking for you have to now + + + align:start position:0% +you're looking for you have to now +you're left with a large array that has + + align:start position:0% +you're left with a large array that has + + + align:start position:0% +you're left with a large array that has +n minus one elements in the worst case + + align:start position:0% +n minus one elements in the worst case + + + align:start position:0% +n minus one elements in the worst case +you started with n you do not go to n /2 + + align:start position:0% +you started with n you do not go to n /2 + + + align:start position:0% +you started with n you do not go to n /2 +n n /2 which is what divide and conquer + + align:start position:0% +n n /2 which is what divide and conquer + + + align:start position:0% +n n /2 which is what divide and conquer +is all about or even n / B okay you went + + align:start position:0% +is all about or even n / B okay you went + + + align:start position:0% +is all about or even n / B okay you went +to n minus one and then you go to n + + align:start position:0% +to n minus one and then you go to n + + + align:start position:0% +to n minus one and then you go to n +minus 2 then you go to n minus 3 because + + align:start position:0% +minus 2 then you go to n minus 3 because + + + align:start position:0% +minus 2 then you go to n minus 3 because +you're constantly picking this is worst + + align:start position:0% +you're constantly picking this is worst + + + align:start position:0% +you're constantly picking this is worst +case analysis you're constantly picking + + align:start position:0% +case analysis you're constantly picking + + + align:start position:0% +case analysis you're constantly picking +these subarrays to be extremely + + align:start position:0% +these subarrays to be extremely + + + align:start position:0% +these subarrays to be extremely +unbalanced right so when the sub arrays + + align:start position:0% +unbalanced right so when the sub arrays + + + align:start position:0% +unbalanced right so when the sub arrays +are extremely unbalanced you're you end + + align:start position:0% +are extremely unbalanced you're you end + + + align:start position:0% +are extremely unbalanced you're you end +up doing Theta n work in each level of + + align:start position:0% +up doing Theta n work in each level of + + + align:start position:0% +up doing Theta n work in each level of +the recursion and those Theta NS because + + align:start position:0% +the recursion and those Theta NS because + + + align:start position:0% +the recursion and those Theta NS because +you're going down all the way to from n + + align:start position:0% +you're going down all the way to from n + + + align:start position:0% +you're going down all the way to from n +to one are going to be Theta n Square + + align:start position:0% +to one are going to be Theta n Square + + + align:start position:0% +to one are going to be Theta n Square +when you keep doing that okay so uh good + + align:start position:0% +when you keep doing that okay so uh good + + + align:start position:0% +when you keep doing that okay so uh good +thanks for that + + align:start position:0% + + + + align:start position:0% + +analysis and so this is Theta n s if you + + align:start position:0% +analysis and so this is Theta n s if you + + + align:start position:0% +analysis and so this is Theta n s if you +uh + + align:start position:0% +uh + + + align:start position:0% +uh +if you have a bad + + align:start position:0% +if you have a bad + + + align:start position:0% +if you have a bad +selection + + align:start position:0% +selection + + + align:start position:0% +selection +okay so we will talk about randomized + + align:start position:0% +okay so we will talk about randomized + + + align:start position:0% +okay so we will talk about randomized +algorithms uh but the problem with + + align:start position:0% +algorithms uh but the problem with + + + align:start position:0% +algorithms uh but the problem with +randomized algorithms is that um the + + align:start position:0% +randomized algorithms is that um the + + + align:start position:0% +randomized algorithms is that um the +analysis will be uh given a probability + + align:start position:0% +analysis will be uh given a probability + + + align:start position:0% +analysis will be uh given a probability +distribution uh uh and it'll be expected + + align:start position:0% +distribution uh uh and it'll be expected + + + align:start position:0% +distribution uh uh and it'll be expected +time what we want here is a + + align:start position:0% +time what we want here is a + + + align:start position:0% +time what we want here is a +deterministic algorithm that is + + align:start position:0% +deterministic algorithm that is + + + align:start position:0% +deterministic algorithm that is +guaranteed to run in worse case Theta n + + align:start position:0% +guaranteed to run in worse case Theta n + + + align:start position:0% +guaranteed to run in worse case Theta n +right so we want a deterministic way of + + align:start position:0% +right so we want a deterministic way of + + + align:start position:0% +right so we want a deterministic way of +picking + + align:start position:0% +picking + + + align:start position:0% +picking +X belonging to S such that um all of + + align:start position:0% +X belonging to S such that um all of + + + align:start position:0% +X belonging to S such that um all of +this works out and when we get our + + align:start position:0% +this works out and when we get our + + + align:start position:0% +this works out and when we get our +recurrence and we solve it somehow + + align:start position:0% +recurrence and we solve it somehow + + + align:start position:0% +recurrence and we solve it somehow +magically we're getting fairly balanced + + align:start position:0% +magically we're getting fairly balanced + + + align:start position:0% +magically we're getting fairly balanced +partitions fairly balanced sub problems + + align:start position:0% +partitions fairly balanced sub problems + + + align:start position:0% +partitions fairly balanced sub problems +in the sense that it's not n minus one + + align:start position:0% +in the sense that it's not n minus one + + + align:start position:0% +in the sense that it's not n minus one +and one it's something like it could + + align:start position:0% +and one it's something like it could + + + align:start position:0% +and one it's something like it could +even be n / 10 and 9 N / 10 but as long + + align:start position:0% +even be n / 10 and 9 N / 10 but as long + + + align:start position:0% +even be n / 10 and 9 N / 10 but as long +as you guarantee that you are shrinking + + align:start position:0% +as you guarantee that you are shrinking + + + align:start position:0% +as you guarantee that you are shrinking +things down geometrically and the + + align:start position:0% +things down geometrically and the + + + align:start position:0% +things down geometrically and the +asymptotics is going to work out okay + + align:start position:0% +asymptotics is going to work out okay + + + align:start position:0% +asymptotics is going to work out okay +but that's the determinism is what we + + align:start position:0% +but that's the determinism is what we + + + align:start position:0% +but that's the determinism is what we +need um and so um we're going to pick X + + align:start position:0% +need um and so um we're going to pick X + + + align:start position:0% +need um and so um we're going to pick X +cleverly + + align:start position:0% +cleverly + + + align:start position:0% +cleverly +right and um we don't want the rank X to + + align:start position:0% +right and um we don't want the rank X to + + + align:start position:0% +right and um we don't want the rank X to +be extreme so this is uh not the only + + align:start position:0% +be extreme so this is uh not the only + + + align:start position:0% +be extreme so this is uh not the only +way you could do it uh but this is + + align:start position:0% +way you could do it uh but this is + + + align:start position:0% +way you could do it uh but this is +really very + + align:start position:0% +really very + + + align:start position:0% +really very +clever this deterministic way + + align:start position:0% +clever this deterministic way + + + align:start position:0% +clever this deterministic way +and you're going to see some constants + + align:start position:0% +and you're going to see some constants + + + align:start position:0% +and you're going to see some constants +here and we'll we'll talk about them + + align:start position:0% +here and we'll we'll talk about them + + + align:start position:0% +here and we'll we'll talk about them +once I've described it but what we're + + align:start position:0% +once I've described it but what we're + + + align:start position:0% +once I've described it but what we're +going to do is we're going to arrange s + + align:start position:0% +going to do is we're going to arrange s + + + align:start position:0% +going to do is we're going to arrange s +into Columns of size five right we're + + align:start position:0% +into Columns of size five right we're + + + align:start position:0% +into Columns of size five right we're +going to take this uh single array and + + align:start position:0% +going to take this uh single array and + + + align:start position:0% +going to take this uh single array and +we're going to make it a two-dimensional + + align:start position:0% +we're going to make it a two-dimensional + + + align:start position:0% +we're going to make it a two-dimensional +array where um the number of rows is + + align:start position:0% +array where um the number of rows is + + + align:start position:0% +array where um the number of rows is +five and the number of columns that you + + align:start position:0% +five and the number of columns that you + + + align:start position:0% +five and the number of columns that you +have is n over five uh ceiling in this + + align:start position:0% +have is n over five uh ceiling in this + + + align:start position:0% +have is n over five uh ceiling in this +case um and then we're going to sort + + align:start position:0% +case um and then we're going to sort + + + align:start position:0% +case um and then we're going to sort +each + + align:start position:0% +each + + + align:start position:0% +each +column big elements on + + align:start position:0% + + + + align:start position:0% + +top and we're going to do this in linear + + align:start position:0% +top and we're going to do this in linear + + + align:start position:0% +top and we're going to do this in linear +time and you might say you know how did + + align:start position:0% +time and you might say you know how did + + + align:start position:0% +time and you might say you know how did +that happen well there's only five + + align:start position:0% +that happen well there's only five + + + align:start position:0% +that happen well there's only five +elements so it's linear right um you + + align:start position:0% +elements so it's linear right um you + + + align:start position:0% +elements so it's linear right um you +could do whatever you wanted you know + + align:start position:0% +could do whatever you wanted you know + + + align:start position:0% +could do whatever you wanted you know +you could do n raised to 4 but it's 5 + + align:start position:0% +you could do n raised to 4 but it's 5 + + + align:start position:0% +you could do n raised to 4 but it's 5 +rais to 4 and it's constants don't you + + align:start position:0% +rais to 4 and it's constants don't you + + + align:start position:0% +rais to 4 and it's constants don't you +love + + align:start position:0% +love + + + align:start position:0% +love +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +um so then we're going to find + + align:start position:0% +um so then we're going to find + + + align:start position:0% +um so then we're going to find +what we're going to call the median of + + align:start position:0% +what we're going to call the median of + + + align:start position:0% +what we're going to call the median of +medians so I'm going to explain this + + align:start position:0% +medians so I'm going to explain this + + + align:start position:0% +medians so I'm going to explain this +this works for arbitrary rank but it's a + + align:start position:0% +this works for arbitrary rank but it's a + + + align:start position:0% +this works for arbitrary rank but it's a +little easier to focus in on the median + + align:start position:0% +little easier to focus in on the median + + + align:start position:0% +little easier to focus in on the median +to just explain the particular example + + align:start position:0% +to just explain the particular example + + + align:start position:0% +to just explain the particular example +because as you can see there's some uh + + align:start position:0% +because as you can see there's some uh + + + align:start position:0% +because as you can see there's some uh +intricacy here um associated with + + align:start position:0% +intricacy here um associated with + + + align:start position:0% +intricacy here um associated with +the uh with with the + + align:start position:0% +the uh with with the + + + align:start position:0% +the uh with with the +breakup and so here we go I'm going to + + align:start position:0% +breakup and so here we go I'm going to + + + align:start position:0% +breakup and so here we go I'm going to +draw out a picture and you're going to + + align:start position:0% +draw out a picture and you're going to + + + align:start position:0% +draw out a picture and you're going to +try and argue that this deterministic + + align:start position:0% +try and argue that this deterministic + + + align:start position:0% +try and argue that this deterministic +strategy that I'll specify gives you + + align:start position:0% +strategy that I'll specify gives you + + + align:start position:0% +strategy that I'll specify gives you +fairly balanced partitions in all cases + + align:start position:0% +fairly balanced partitions in all cases + + + align:start position:0% +fairly balanced partitions in all cases +okay so what we see here is we see + + align:start position:0% +okay so what we see here is we see + + + align:start position:0% +okay so what we see here is we see +pictorially you + + align:start position:0% +pictorially you + + + align:start position:0% +pictorially you +see + + align:start position:0% + + + + align:start position:0% + +Columns of length five right each of + + align:start position:0% +Columns of length five right each of + + + align:start position:0% +Columns of length five right each of +these dots corresponds to a number this + + align:start position:0% +these dots corresponds to a number this + + + align:start position:0% +these dots corresponds to a number this +one-dimensional array got turned into a + + align:start position:0% +one-dimensional array got turned into a + + + align:start position:0% +one-dimensional array got turned into a +two-dimensional array + + align:start position:0% + + + + align:start position:0% + +right so I got four full columns and + + align:start position:0% +right so I got four full columns and + + + align:start position:0% +right so I got four full columns and +it's certainly possible given + + align:start position:0% +it's certainly possible given + + + align:start position:0% +it's certainly possible given +n that my fifth column uh is not full + + align:start position:0% +n that my fifth column uh is not full + + + align:start position:0% +n that my fifth column uh is not full +right so that's certainly possible so + + align:start position:0% +right so that's certainly possible so + + + align:start position:0% +right so that's certainly possible so +that's why I have that up here + + align:start position:0% +that's why I have that up here + + + align:start position:0% +that's why I have that up here +um so what I have here is I'm going to + + align:start position:0% +um so what I have here is I'm going to + + + align:start position:0% +um so what I have here is I'm going to +lay them out this way and I'm going to + + align:start position:0% +lay them out this way and I'm going to + + + align:start position:0% +lay them out this way and I'm going to +look + + align:start position:0% +look + + + align:start position:0% +look +at that + + align:start position:0% +at that + + + align:start position:0% +at that +I'm going to look at the middle elements + + align:start position:0% +I'm going to look at the middle elements + + + align:start position:0% +I'm going to look at the middle elements +of each of these n over five columns + + align:start position:0% +of each of these n over five columns + + + align:start position:0% +of each of these n over five columns +right that's exactly what I'm going to + + align:start position:0% +right that's exactly what I'm going to + + + align:start position:0% +right that's exactly what I'm going to +look + + align:start position:0% +look + + + align:start position:0% +look +at + + align:start position:0% + + + + align:start position:0% + +um now if I look at what I want what I + + align:start position:0% +um now if I look at what I want what I + + + align:start position:0% +um now if I look at what I want what I +want over here is this x if I want to + + align:start position:0% +want over here is this x if I want to + + + align:start position:0% +want over here is this x if I want to +find uh um I'm going to find the median + + align:start position:0% +find uh um I'm going to find the median + + + align:start position:0% +find uh um I'm going to find the median +of medians so uh this is uh is is is is + + align:start position:0% +of medians so uh this is uh is is is is + + + align:start position:0% +of medians so uh this is uh is is is is +is X now it it is true the first that uh + + align:start position:0% +is X now it it is true the first that uh + + + align:start position:0% +is X now it it is true the first that uh +um these columns I'm just putting that + + align:start position:0% +um these columns I'm just putting that + + + align:start position:0% +um these columns I'm just putting that +up here imagining that that's X it's not + + align:start position:0% +up here imagining that that's X it's not + + + align:start position:0% +up here imagining that that's X it's not +guaranteed to be X because the columns + + align:start position:0% +guaranteed to be X because the columns + + + align:start position:0% +guaranteed to be X because the columns +themselves uh aren't U + + align:start position:0% +themselves uh aren't U + + + align:start position:0% +themselves uh aren't U +uh the well each of these columns is + + align:start position:0% +uh the well each of these columns is + + + align:start position:0% +uh the well each of these columns is +sorted and uh what I'm going to have to + + align:start position:0% +sorted and uh what I'm going to have to + + + align:start position:0% +sorted and uh what I'm going to have to +guarantee of course is that when I go uh + + align:start position:0% +guarantee of course is that when I go uh + + + align:start position:0% +guarantee of course is that when I go uh +find this median of medians um is that + + align:start position:0% +find this median of medians um is that + + + align:start position:0% +find this median of medians um is that +it ends up being something that gives me + + align:start position:0% +it ends up being something that gives me + + + align:start position:0% +it ends up being something that gives me +balanced partitions right so let me say + + align:start position:0% +balanced partitions right so let me say + + + align:start position:0% +balanced partitions right so let me say +a little bit more before I explain + + align:start position:0% +a little bit more before I explain + + + align:start position:0% +a little bit more before I explain +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +um each of these columns is sorted and + + align:start position:0% +um each of these columns is sorted and + + + align:start position:0% +um each of these columns is sorted and +uh s is arranged into Columns of of size + + align:start position:0% +uh s is arranged into Columns of of size + + + align:start position:0% +uh s is arranged into Columns of of size +five like I just said here um the these + + align:start position:0% +five like I just said here um the these + + + align:start position:0% +five like I just said here um the these +are the + + align:start position:0% +are the + + + align:start position:0% +are the +medians okay um if I look at if if I + + align:start position:0% +medians okay um if I look at if if I + + + align:start position:0% +medians okay um if I look at if if I +look at determining the medians and I + + align:start position:0% +look at determining the medians and I + + + align:start position:0% +look at determining the medians and I +say that once I've determined this x + + align:start position:0% +say that once I've determined this x + + + align:start position:0% +say that once I've determined this x +which I've discovered that it's the + + align:start position:0% +which I've discovered that it's the + + + align:start position:0% +which I've discovered that it's the +median then uh this is right there in + + align:start position:0% +median then uh this is right there in + + + align:start position:0% +median then uh this is right there in +the middle there's going to be a bunch + + align:start position:0% +the middle there's going to be a bunch + + + align:start position:0% +the middle there's going to be a bunch +of columns to the left of it bunch of + + align:start position:0% +of columns to the left of it bunch of + + + align:start position:0% +of columns to the left of it bunch of +elements to the left of it and a bunch + + align:start position:0% +elements to the left of it and a bunch + + + align:start position:0% +elements to the left of it and a bunch +of elements to the right of it and in + + align:start position:0% +of elements to the right of it and in + + + align:start position:0% +of elements to the right of it and in +this case I have five columns I could + + align:start position:0% +this case I have five columns I could + + + align:start position:0% +this case I have five columns I could +have had more uh it happens to be the + + align:start position:0% +have had more uh it happens to be the + + + align:start position:0% +have had more uh it happens to be the +third one so the idea is that once I + + align:start position:0% +third one so the idea is that once I + + + align:start position:0% +third one so the idea is that once I +find this median of medians which + + align:start position:0% +find this median of medians which + + + align:start position:0% +find this median of medians which +corresponds to this x number I can I can + + align:start position:0% +corresponds to this x number I can I can + + + align:start position:0% +corresponds to this x number I can I can +say that um all of the columns these are + + align:start position:0% +say that um all of the columns these are + + + align:start position:0% +say that um all of the columns these are +all uh uh correspond to columns that + + align:start position:0% +all uh uh correspond to columns that + + + align:start position:0% +all uh uh correspond to columns that +have their median element greater than x + + align:start position:0% +have their median element greater than x + + + align:start position:0% +have their median element greater than x +these correspond to columns that have + + align:start position:0% +these correspond to columns that have + + + align:start position:0% +these correspond to columns that have +their median element less than x okay so + + align:start position:0% +their median element less than x okay so + + + align:start position:0% +their median element less than x okay so +what I have here in this picture is that + + align:start position:0% +what I have here in this picture is that + + + align:start position:0% +what I have here in this picture is that +these elements + + align:start position:0% +these elements + + + align:start position:0% +these elements +here are going to be greater than + + align:start position:0% +here are going to be greater than + + + align:start position:0% +here are going to be greater than +x okay and these elements + + align:start position:0% + + + + align:start position:0% + +here not that are going to be less than + + align:start position:0% +here not that are going to be less than + + + align:start position:0% +here not that are going to be less than +x right so let me be clear what's + + align:start position:0% +x right so let me be clear what's + + + align:start position:0% +x right so let me be clear what's +happened here is we've not only sorted + + align:start position:0% +happened here is we've not only sorted + + + align:start position:0% +happened here is we've not only sorted +all of the + + align:start position:0% +all of the + + + align:start position:0% +all of the +columns such that you have larger + + align:start position:0% +columns such that you have larger + + + align:start position:0% +columns such that you have larger +elements up + + align:start position:0% +elements up + + + align:start position:0% +elements up +here each of these five columns has been + + align:start position:0% +here each of these five columns has been + + + align:start position:0% +here each of these five columns has been +sorted that way on top of that I've + + align:start position:0% +sorted that way on top of that I've + + + align:start position:0% +sorted that way on top of that I've +discovered the particular column that + + align:start position:0% +discovered the particular column that + + + align:start position:0% +discovered the particular column that +corresponds to the median of of medians + + align:start position:0% +corresponds to the median of of medians + + + align:start position:0% +corresponds to the median of of medians +and and this is my X over here and it + + align:start position:0% +and and this is my X over here and it + + + align:start position:0% +and and this is my X over here and it +may be the case that you know these + + align:start position:0% +may be the case that you know these + + + align:start position:0% +may be the case that you know these +columns aren't sorted this one may be + + align:start position:0% +columns aren't sorted this one may be + + + align:start position:0% +columns aren't sorted this one may be +larger than that or vice versa same + + align:start position:0% +larger than that or vice versa same + + + align:start position:0% +larger than that or vice versa same +thing over there I have no idea but it's + + align:start position:0% +thing over there I have no idea but it's + + + align:start position:0% +thing over there I have no idea but it's +guaranteed that once I find this median + + align:start position:0% +guaranteed that once I find this median + + + align:start position:0% +guaranteed that once I find this median +that that I I do know uh all of the + + align:start position:0% +that that I I do know uh all of the + + + align:start position:0% +that that I I do know uh all of the +columns that have elements uh that uh in + + align:start position:0% +columns that have elements uh that uh in + + + align:start position:0% +columns that have elements uh that uh in +this position that are uh less than this + + align:start position:0% +this position that are uh less than this + + + align:start position:0% +this position that are uh less than this +X and I know columns uh that uh in this + + align:start position:0% +X and I know columns uh that uh in this + + + align:start position:0% +X and I know columns uh that uh in this +position have elements that are greater + + align:start position:0% +position have elements that are greater + + + align:start position:0% +position have elements that are greater +than x okay y + + align:start position:0% + + + + align:start position:0% + +you're exactly + + align:start position:0% + + + + align:start position:0% + +right I would have probably been able to + + align:start position:0% +right I would have probably been able to + + + align:start position:0% +right I would have probably been able to +U get the same asmic complexity if I + + align:start position:0% +U get the same asmic complexity if I + + + align:start position:0% +U get the same asmic complexity if I +dropped those because I had a constant + + align:start position:0% +dropped those because I had a constant + + + align:start position:0% +dropped those because I had a constant +number but you're absolutely exactly + + align:start position:0% +number but you're absolutely exactly + + + align:start position:0% +number but you're absolutely exactly +right right so the point that uh the + + align:start position:0% +right right so the point that uh the + + + align:start position:0% +right right so the point that uh the +question was I I just redrew it these + + align:start position:0% +question was I I just redrew it these + + + align:start position:0% +question was I I just redrew it these +two are clearly less than x as well + + align:start position:0% +two are clearly less than x as well + + + align:start position:0% +two are clearly less than x as well +because they're part of the Sorting + + align:start position:0% +because they're part of the Sorting + + + align:start position:0% +because they're part of the Sorting +right um and I that's essentially what I + + align:start position:0% +right um and I that's essentially what I + + + align:start position:0% +right um and I that's essentially what I +have here now my goal here and you can + + align:start position:0% +have here now my goal here and you can + + + align:start position:0% +have here now my goal here and you can +kind of see from here as to where we + + align:start position:0% +kind of see from here as to where we + + + align:start position:0% +kind of see from here as to where we +headed right what I've done here by this + + align:start position:0% +headed right what I've done here by this + + + align:start position:0% +headed right what I've done here by this +process of sorting each column and + + align:start position:0% +process of sorting each column and + + + align:start position:0% +process of sorting each column and +finding the median of medians is that I + + align:start position:0% +finding the median of medians is that I + + + align:start position:0% +finding the median of medians is that I +found this median of medians such that + + align:start position:0% +found this median of medians such that + + + align:start position:0% +found this median of medians such that +there's a bunch of columns on the left + + align:start position:0% +there's a bunch of columns on the left + + + align:start position:0% +there's a bunch of columns on the left +and and roughly half of those elements + + align:start position:0% +and and roughly half of those elements + + + align:start position:0% +and and roughly half of those elements +in those columns are less than x and + + align:start position:0% +in those columns are less than x and + + + align:start position:0% +in those columns are less than x and +then there are a bunch of columns on the + + align:start position:0% +then there are a bunch of columns on the + + + align:start position:0% +then there are a bunch of columns on the +right and roughly you know half of those + + align:start position:0% +right and roughly you know half of those + + + align:start position:0% +right and roughly you know half of those +columns have have elements that are + + align:start position:0% +columns have have elements that are + + + align:start position:0% +columns have have elements that are +greater than x um so what I now have to + + align:start position:0% +greater than x um so what I now have to + + + align:start position:0% +greater than x um so what I now have to +do is to do a little bit of math to show + + align:start position:0% +do is to do a little bit of math to show + + + align:start position:0% +do is to do a little bit of math to show +you exactly what the recurrences and let + + align:start position:0% +you exactly what the recurrences and let + + + align:start position:0% +you exactly what the recurrences and let +me do that over here so that's the last + + align:start position:0% +me do that over here so that's the last + + + align:start position:0% +me do that over here so that's the last +thing that we have to do um I probably + + align:start position:0% +thing that we have to do um I probably + + + align:start position:0% +thing that we have to do um I probably +won't solve the recurrence but that can + + align:start position:0% +won't solve the recurrence but that can + + + align:start position:0% +won't solve the recurrence but that can +wait till tomorrow that recurrence will + + align:start position:0% +wait till tomorrow that recurrence will + + + align:start position:0% +wait till tomorrow that recurrence will +be U something that's uh not not + + align:start position:0% +be U something that's uh not not + + + align:start position:0% +be U something that's uh not not +particularly difficult to to + + align:start position:0% +particularly difficult to to + + + align:start position:0% +particularly difficult to to +solve so I want to now make a a more + + align:start position:0% +solve so I want to now make a a more + + + align:start position:0% +solve so I want to now make a a more +quantitative + + align:start position:0% +quantitative + + + align:start position:0% +quantitative +argument that uh the variable being n as + + align:start position:0% +argument that uh the variable being n as + + + align:start position:0% +argument that uh the variable being n as +to how how many elements are + + align:start position:0% + + + + align:start position:0% + +guaranteed to be greater than + + align:start position:0% +guaranteed to be greater than + + + align:start position:0% +guaranteed to be greater than +x + + align:start position:0% +x + + + align:start position:0% +x +and essentially what I'm saying which is + + align:start position:0% +and essentially what I'm saying which is + + + align:start position:0% +and essentially what I'm saying which is +I'm writing out what I have on that + + align:start position:0% +I'm writing out what I have on that + + + align:start position:0% +I'm writing out what I have on that +picture there half of the N over + + align:start position:0% +picture there half of the N over + + + align:start position:0% +picture there half of the N over +five + + align:start position:0% +five + + + align:start position:0% +five +groups + + align:start position:0% + + + + align:start position:0% + +contribute at + + align:start position:0% +contribute at + + + align:start position:0% +contribute at +least three elements + + align:start position:0% +least three elements + + + align:start position:0% +least three elements +greater than x + + align:start position:0% + + + + align:start position:0% + +except for one + + align:start position:0% +except for one + + + align:start position:0% +except for one +group with possibly less than uh five + + align:start position:0% +group with possibly less than uh five + + + align:start position:0% +group with possibly less than uh five +elements which is the one that I have + + align:start position:0% +elements which is the one that I have + + + align:start position:0% +elements which is the one that I have +all the way to the + + align:start position:0% + + + + align:start position:0% + +right and one + + align:start position:0% + + + + align:start position:0% + +group um that contains X + + align:start position:0% + + + + align:start position:0% + +so for all the other columns I'm going + + align:start position:0% +so for all the other columns I'm going + + + align:start position:0% +so for all the other columns I'm going +to get three elements that are greater + + align:start position:0% +to get three elements that are greater + + + align:start position:0% +to get three elements that are greater +than + + align:start position:0% +than + + + align:start position:0% +than +x um and so if you write that out this + + align:start position:0% +x um and so if you write that out this + + + align:start position:0% +x um and so if you write that out this +says there at + + align:start position:0% +says there at + + + align:start position:0% +says there at +least + + align:start position:0% +least + + + align:start position:0% +least +three n / 10 because I have half of all + + align:start position:0% +three n / 10 because I have half of all + + + align:start position:0% +three n / 10 because I have half of all +of those groups minus 2 and I'm not + + align:start position:0% +of those groups minus 2 and I'm not + + + align:start position:0% +of those groups minus 2 and I'm not +counting uh perfectly accurately here + + align:start position:0% +counting uh perfectly accurately here + + + align:start position:0% +counting uh perfectly accurately here +but I I have an at least so this should + + align:start position:0% +but I I have an at least so this should + + + align:start position:0% +but I I have an at least so this should +should all be fine + + align:start position:0% +should all be fine + + + align:start position:0% +should all be fine +3 n / 10 uh 3 * n / 10 minus 2 elements + + align:start position:0% +3 n / 10 uh 3 * n / 10 minus 2 elements + + + align:start position:0% +3 n / 10 uh 3 * n / 10 minus 2 elements +are strictly greater than x right and + + align:start position:0% +are strictly greater than x right and + + + align:start position:0% +are strictly greater than x right and +that comes from that + + align:start position:0% +that comes from that + + + align:start position:0% +that comes from that +picture um I'm going to be able to say + + align:start position:0% +picture um I'm going to be able to say + + + align:start position:0% +picture um I'm going to be able to say +the same + + align:start position:0% +the same + + + align:start position:0% +the same +thing um + + align:start position:0% +thing um + + + align:start position:0% +thing um +for less than x as well I can't count + + align:start position:0% +for less than x as well I can't count + + + align:start position:0% +for less than x as well I can't count +the one uh uh depending on how things go + + align:start position:0% +the one uh uh depending on how things go + + + align:start position:0% +the one uh uh depending on how things go +maybe I could have uh played around and + + align:start position:0% +maybe I could have uh played around and + + + align:start position:0% +maybe I could have uh played around and +and subtracted a one instead of a two in + + align:start position:0% +and subtracted a one instead of a two in + + + align:start position:0% +and subtracted a one instead of a two in +the latter case but I'm just being + + align:start position:0% +the latter case but I'm just being + + + align:start position:0% +the latter case but I'm just being +conservative here it is clear that uh + + align:start position:0% +conservative here it is clear that uh + + + align:start position:0% +conservative here it is clear that uh +I'm going to have a bunch of columns + + align:start position:0% +I'm going to have a bunch of columns + + + align:start position:0% +I'm going to have a bunch of columns +that are full columns uh that have going + + align:start position:0% +that are full columns uh that have going + + + align:start position:0% +that are full columns uh that have going +to be contributing three elements that + + align:start position:0% +to be contributing three elements that + + + align:start position:0% +to be contributing three elements that +are greater than x and in this case I + + align:start position:0% +are greater than x and in this case I + + + align:start position:0% +are greater than x and in this case I +have well two of them here for the less + + align:start position:0% +have well two of them here for the less + + + align:start position:0% +have well two of them here for the less +than x and I got uh one for the greater + + align:start position:0% +than x and I got uh one for the greater + + + align:start position:0% +than x and I got uh one for the greater +than x right so that's all that I'm + + align:start position:0% +than x right so that's all that I'm + + + align:start position:0% +than x right so that's all that I'm +saying over here with respect to the + + align:start position:0% +saying over here with respect to the + + + align:start position:0% +saying over here with respect to the +balance of the partitions and it turns + + align:start position:0% +balance of the partitions and it turns + + + align:start position:0% +balance of the partitions and it turns +out that's enough H it it turns out um + + align:start position:0% +out that's enough H it it turns out um + + + align:start position:0% +out that's enough H it it turns out um +all I have to + + align:start position:0% +all I have to + + + align:start position:0% +all I have to +do with this observation is to go off + + align:start position:0% +do with this observation is to go off + + + align:start position:0% +do with this observation is to go off +and write the recurrence and uh we're + + align:start position:0% +and write the recurrence and uh we're + + + align:start position:0% +and write the recurrence and uh we're +going to get uh a an efficient + + align:start position:0% + + + + align:start position:0% + +algorithm yeah + + align:start position:0% +algorithm yeah + + + align:start position:0% +algorithm yeah +not or equal um no there's nothing + + align:start position:0% +not or equal um no there's nothing + + + align:start position:0% +not or equal um no there's nothing +that's equal yeah all unique yeah yeah I + + align:start position:0% +that's equal yeah all unique yeah yeah I + + + align:start position:0% +that's equal yeah all unique yeah yeah I +I assume that so convenience yeah + + align:start position:0% +I assume that so convenience yeah + + + align:start position:0% +I assume that so convenience yeah +there's always a little bit of + + align:start position:0% +there's always a little bit of + + + align:start position:0% +there's always a little bit of +convenience thrown in here uh we will + + align:start position:0% +convenience thrown in here uh we will + + + align:start position:0% +convenience thrown in here uh we will +assume that uh that the the array is is + + align:start position:0% +assume that uh that the the array is is + + + align:start position:0% +assume that uh that the the array is is +uh has unique elements so there's + + align:start position:0% +uh has unique elements so there's + + + align:start position:0% +uh has unique elements so there's +nothing that's X okay good um so uh the + + align:start position:0% +nothing that's X okay good um so uh the + + + align:start position:0% +nothing that's X okay good um so uh the +recurrence once you do + + align:start position:0% +recurrence once you do + + + align:start position:0% +recurrence once you do +that um is T of + + align:start position:0% +that um is T of + + + align:start position:0% +that um is T of +n + + align:start position:0% +n + + + align:start position:0% +n +equals we're going to just say it's + + align:start position:0% +equals we're going to just say it's + + + align:start position:0% +equals we're going to just say it's +order one for + + align:start position:0% +order one for + + + align:start position:0% +order one for +n less than or equal to 140 where did + + align:start position:0% +n less than or equal to 140 where did + + + align:start position:0% +n less than or equal to 140 where did +that come from well I like 140 uh it's + + align:start position:0% +that come from well I like 140 uh it's + + + align:start position:0% +that come from well I like 140 uh it's +it's just a large number uh it it came + + align:start position:0% +it's just a large number uh it it came + + + align:start position:0% +it's just a large number uh it it came +from the fact that you're going to see + + align:start position:0% +from the fact that you're going to see + + + align:start position:0% +from the fact that you're going to see +uh 10 minus 3 which is 7 and then you + + align:start position:0% +uh 10 minus 3 which is 7 and then you + + + align:start position:0% +uh 10 minus 3 which is 7 and then you +want to multiply that by two so some + + align:start position:0% +want to multiply that by two so some + + + align:start position:0% +want to multiply that by two so some +reasonably large number we're going to + + align:start position:0% +reasonably large number we're going to + + + align:start position:0% +reasonably large number we're going to +go off and we're going to assume that's + + align:start position:0% +go off and we're going to assume that's + + + align:start position:0% +go off and we're going to assume that's +a constant so you could sort those 140 + + align:start position:0% +a constant so you could sort those 140 + + + align:start position:0% +a constant so you could sort those 140 +numbers and find the median or whatever + + align:start position:0% +numbers and find the median or whatever + + + align:start position:0% +numbers and find the median or whatever +rank uh it's all constant time once you + + align:start position:0% +rank uh it's all constant time once you + + + align:start position:0% +rank uh it's all constant time once you +get down to the base case right so you + + align:start position:0% +get down to the base case right so you + + + align:start position:0% +get down to the base case right so you +just want it to be large enough such + + align:start position:0% +just want it to be large enough such + + + align:start position:0% +just want it to be large enough such +that you can break it up and you have + + align:start position:0% +that you can break it up and you have + + + align:start position:0% +that you can break it up and you have +something interesting going on with + + align:start position:0% +something interesting going on with + + + align:start position:0% +something interesting going on with +respect to the number of columns right + + align:start position:0% +respect to the number of columns right + + + align:start position:0% +respect to the number of columns right +so don't worry too much about that + + align:start position:0% +so don't worry too much about that + + + align:start position:0% +so don't worry too much about that +number uh the the key thing here is the + + align:start position:0% +number uh the the key thing here is the + + + align:start position:0% +number uh the the key thing here is the +recurrence right and this is what we + + align:start position:0% +recurrence right and this is what we + + + align:start position:0% +recurrence right and this is what we +have to spend the rest of our time on + + align:start position:0% +have to spend the rest of our time on + + + align:start position:0% +have to spend the rest of our time on +and + + align:start position:0% +and + + + align:start position:0% +and +um I'll just write this out and explain + + align:start position:0% +um I'll just write this out and explain + + + align:start position:0% +um I'll just write this out and explain +where these these numbers came + + align:start position:0% + + + + align:start position:0% + +from all right so um that's our + + align:start position:0% +from all right so um that's our + + + align:start position:0% +from all right so um that's our +recurrence uh if for n less than or + + align:start position:0% +recurrence uh if for n less than or + + + align:start position:0% +recurrence uh if for n less than or +equal to 140 and else you're going to do + + align:start position:0% +equal to 140 and else you're going to do + + + align:start position:0% +equal to 140 and else you're going to do +do this so what is going on here what + + align:start position:0% +do this so what is going on here what + + + align:start position:0% +do this so what is going on here what +are all of these components SC + + align:start position:0% +are all of these components SC + + + align:start position:0% +are all of these components SC +responding to this recurrence um really + + align:start position:0% +responding to this recurrence um really + + + align:start position:0% +responding to this recurrence um really +quickly this is um simply something that + + align:start position:0% +quickly this is um simply something that + + + align:start position:0% +quickly this is um simply something that +says I'm finding the median of medians + + align:start position:0% +says I'm finding the median of medians + + + align:start position:0% +says I'm finding the median of medians +I'm finding some element that has a + + align:start position:0% +I'm finding some element that has a + + + align:start position:0% +I'm finding some element that has a +certain rank so this median of medians + + align:start position:0% +certain rank so this median of medians + + + align:start position:0% +certain rank so this median of medians +is going to be running on N over five + + align:start position:0% +is going to be running on N over five + + + align:start position:0% +is going to be running on N over five +columns so I'm going these are there + + align:start position:0% +columns so I'm going these are there + + + align:start position:0% +columns so I'm going these are there +there n over five columns here and I'm + + align:start position:0% +there n over five columns here and I'm + + + align:start position:0% +there n over five columns here and I'm +going to be calling this algorithm uh + + align:start position:0% +going to be calling this algorithm uh + + + align:start position:0% +going to be calling this algorithm uh +recursively the median finding algorithm + + align:start position:0% +recursively the median finding algorithm + + + align:start position:0% +recursively the median finding algorithm +uh to to do that finding the median of + + align:start position:0% +uh to to do that finding the median of + + + align:start position:0% +uh to to do that finding the median of +medians + + align:start position:0% +medians + + + align:start position:0% +medians +okay um this thing over here is uh I'm + + align:start position:0% +okay um this thing over here is uh I'm + + + align:start position:0% +okay um this thing over here is uh I'm +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +discarding at least depending regardless + + align:start position:0% +discarding at least depending regardless + + + align:start position:0% +discarding at least depending regardless +of what I do because I have these two + + align:start position:0% +of what I do because I have these two + + + align:start position:0% +of what I do because I have these two +statements here um I take the overall uh + + align:start position:0% +statements here um I take the overall uh + + + align:start position:0% +statements here um I take the overall uh +n and I'm going to + + align:start position:0% +n and I'm going to + + + align:start position:0% +n and I'm going to +discard uh in my uh Paradigm over here + + align:start position:0% +discard uh in my uh Paradigm over here + + + align:start position:0% +discard uh in my uh Paradigm over here +I'm either going to go with b or I'm + + align:start position:0% +I'm either going to go with b or I'm + + + align:start position:0% +I'm either going to go with b or I'm +either going to go with C depending on + + align:start position:0% +either going to go with C depending on + + + align:start position:0% +either going to go with C depending on +what I'm looking for uh and given that B + + align:start position:0% +what I'm looking for uh and given that B + + + align:start position:0% +what I'm looking for uh and given that B +and C are not completely unbalanced I'm + + align:start position:0% +and C are not completely unbalanced I'm + + + align:start position:0% +and C are not completely unbalanced I'm +going to be discarding um 3 n / 10us six + + align:start position:0% +going to be discarding um 3 n / 10us six + + + align:start position:0% +going to be discarding um 3 n / 10us six +elements which simply corresponds to me + + align:start position:0% +elements which simply corresponds to me + + + align:start position:0% +elements which simply corresponds to me +ignoring the ceiling here and + + align:start position:0% +ignoring the ceiling here and + + + align:start position:0% +ignoring the ceiling here and +multiplying the three out so that's 3 n + + align:start position:0% +multiplying the three out so that's 3 n + + + align:start position:0% +multiplying the three out so that's 3 n +/ 10 - 6 so then I have 7n / 10 + 6 + + align:start position:0% +/ 10 - 6 so then I have 7n / 10 + 6 + + + align:start position:0% +/ 10 - 6 so then I have 7n / 10 + 6 +that's the maximum size uh partition + + align:start position:0% +that's the maximum size uh partition + + + align:start position:0% +that's the maximum size uh partition +that I'm going to recur on it's only + + align:start position:0% +that I'm going to recur on it's only + + + align:start position:0% +that I'm going to recur on it's only +going to be exactly one of them as you + + align:start position:0% +going to be exactly one of them as you + + + align:start position:0% +going to be exactly one of them as you +can see from that it's either else it's + + align:start position:0% +can see from that it's either else it's + + + align:start position:0% +can see from that it's either else it's +not recurring on both of them is + + align:start position:0% +not recurring on both of them is + + + align:start position:0% +not recurring on both of them is +recurring on one of them so that's where + + align:start position:0% +recurring on one of them so that's where + + + align:start position:0% +recurring on one of them so that's where +the 7n / 10 + 6 comes from and then you + + align:start position:0% +the 7n / 10 + 6 comes from and then you + + + align:start position:0% +the 7n / 10 + 6 comes from and then you +ask where does this Theta n come from + + align:start position:0% +ask where does this Theta n come from + + + align:start position:0% +ask where does this Theta n come from +well the Theta n comes from the fact + + align:start position:0% +well the Theta n comes from the fact + + + align:start position:0% +well the Theta n comes from the fact +that I do have to do some sorting it's + + align:start position:0% +that I do have to do some sorting it's + + + align:start position:0% +that I do have to do some sorting it's +constant time sorting for every column + + align:start position:0% +constant time sorting for every column + + + align:start position:0% +constant time sorting for every column +okay because there's only five elements + + align:start position:0% +okay because there's only five elements + + + align:start position:0% +okay because there's only five elements +so I'm going to do constant time sorting + + align:start position:0% +so I'm going to do constant time sorting + + + align:start position:0% +so I'm going to do constant time sorting +but there's order n columns right + + align:start position:0% +but there's order n columns right + + + align:start position:0% +but there's order n columns right +because there that it's n/ five columns + + align:start position:0% +because there that it's n/ five columns + + + align:start position:0% +because there that it's n/ five columns +so this is the + + align:start position:0% +so this is the + + + align:start position:0% +so this is the +Sorting of all of the columns + + align:start position:0% +Sorting of all of the columns + + + align:start position:0% +Sorting of all of the columns +all + + align:start position:0% +all + + + align:start position:0% +all +right so that's it and I'll just leave + + align:start position:0% +right so that's it and I'll just leave + + + align:start position:0% +right so that's it and I'll just leave +you with um you cannot apply the master + + align:start position:0% +you with um you cannot apply the master + + + align:start position:0% +you with um you cannot apply the master +theorem uh for solving this particular + + align:start position:0% +theorem uh for solving this particular + + + align:start position:0% +theorem uh for solving this particular +recurrence but if you make the + + align:start position:0% +recurrence but if you make the + + + align:start position:0% +recurrence but if you make the +observation and you'll see this in + + align:start position:0% +observation and you'll see this in + + + align:start position:0% +observation and you'll see this in +section you make the observation that n + + align:start position:0% +section you make the observation that n + + + align:start position:0% +section you make the observation that n +/ 5 + 7n / 10 is actually less than n + + align:start position:0% +/ 5 + 7n / 10 is actually less than n + + + align:start position:0% +/ 5 + 7n / 10 is actually less than n +right so you get you know 2 N here and 7 + + align:start position:0% +right so you get you know 2 N here and 7 + + + align:start position:0% +right so you get you know 2 N here and 7 +n there that's actually less than n this + + align:start position:0% +n there that's actually less than n this + + + align:start position:0% +n there that's actually less than n this +thing runs in linear time and you'll see + + align:start position:0% +thing runs in linear time and you'll see + + + align:start position:0% +thing runs in linear time and you'll see +that in in section tomorrow so this + + align:start position:0% +that in in section tomorrow so this + + + align:start position:0% +that in in section tomorrow so this +whole thing is Theta n + + align:start position:0% +whole thing is Theta n + + + align:start position:0% +whole thing is Theta n +time see you next time \ No newline at end of file diff --git a/FNOfxJxceIM.txt b/FNOfxJxceIM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c3d3f3699677d186175aea83147fd9711a04b318 --- /dev/null +++ b/FNOfxJxceIM.txt @@ -0,0 +1,1619 @@ +align:start position:0% + +let's look at an typical application of + + align:start position:0% +let's look at an typical application of + + + align:start position:0% +let's look at an typical application of +Newton's second law for a system of + + align:start position:0% +Newton's second law for a system of + + + align:start position:0% +Newton's second law for a system of +objects so what I want to consider is a + + align:start position:0% +objects so what I want to consider is a + + + align:start position:0% +objects so what I want to consider is a +system of pulleys and Ma and masses so + + align:start position:0% +system of pulleys and Ma and masses so + + + align:start position:0% +system of pulleys and Ma and masses so +I'll have a fixed surface here a ceiling + + align:start position:0% +I'll have a fixed surface here a ceiling + + + align:start position:0% +I'll have a fixed surface here a ceiling +and from the ceiling will hang a pulley + + align:start position:0% +and from the ceiling will hang a pulley + + + align:start position:0% +and from the ceiling will hang a pulley +which I'm going to call pulley a and + + align:start position:0% +which I'm going to call pulley a and + + + align:start position:0% +which I'm going to call pulley a and +this pulley will have a rope attached to + + align:start position:0% +this pulley will have a rope attached to + + + align:start position:0% +this pulley will have a rope attached to +it wrapped around it and here we have + + align:start position:0% +it wrapped around it and here we have + + + align:start position:0% +it wrapped around it and here we have +object one and the Rope goes around the + + align:start position:0% +object one and the Rope goes around the + + + align:start position:0% +object one and the Rope goes around the +pulley and now it's going to go around + + align:start position:0% +pulley and now it's going to go around + + + align:start position:0% +pulley and now it's going to go around +another pulley + + align:start position:0% + + + + align:start position:0% + +B and fixed to the ceiling so that's + + align:start position:0% +B and fixed to the ceiling so that's + + + align:start position:0% +B and fixed to the ceiling so that's +fixed and hanging from pulley b is + + align:start position:0% +fixed and hanging from pulley b is + + + align:start position:0% +fixed and hanging from pulley b is +another Mass two and our goal in + + align:start position:0% +another Mass two and our goal in + + + align:start position:0% +another Mass two and our goal in +applying Newton Second Law is to find + + align:start position:0% +applying Newton Second Law is to find + + + align:start position:0% +applying Newton Second Law is to find +the accelerations of objects one and two + + align:start position:0% +the accelerations of objects one and two + + + align:start position:0% +the accelerations of objects one and two +now how how do we approach this well the + + align:start position:0% +now how how do we approach this well the + + + align:start position:0% +now how how do we approach this well the +first thing we have to do is decide if + + align:start position:0% +first thing we have to do is decide if + + + align:start position:0% +first thing we have to do is decide if +we're going to apply Newton's Second Law + + align:start position:0% +we're going to apply Newton's Second Law + + + align:start position:0% +we're going to apply Newton's Second Law +what is the system that will apply it to + + align:start position:0% +what is the system that will apply it to + + + align:start position:0% +what is the system that will apply it to +and there's many different ways to + + align:start position:0% +and there's many different ways to + + + align:start position:0% +and there's many different ways to +choose a system when we look at this + + align:start position:0% +choose a system when we look at this + + + align:start position:0% +choose a system when we look at this +problem um we'll have several different + + align:start position:0% +problem um we'll have several different + + + align:start position:0% +problem um we'll have several different +systems so let's consider the ones that + + align:start position:0% +systems so let's consider the ones that + + + align:start position:0% +systems so let's consider the ones that +we're going to look at and the first one + + align:start position:0% +we're going to look at and the first one + + + align:start position:0% +we're going to look at and the first one +is very simple it will be block + + align:start position:0% +is very simple it will be block + + + align:start position:0% +is very simple it will be block +one and the second system that we look + + align:start position:0% +one and the second system that we look + + + align:start position:0% +one and the second system that we look +at we'll call that a b is pulley a + + align:start position:0% +at we'll call that a b is pulley a + + + align:start position:0% +at we'll call that a b is pulley a +now that brings us to an interesting + + align:start position:0% +now that brings us to an interesting + + + align:start position:0% +now that brings us to an interesting +question about B pulley B and block two + + align:start position:0% +question about B pulley B and block two + + + align:start position:0% +question about B pulley B and block two +because we could separately look at + + align:start position:0% +because we could separately look at + + + align:start position:0% +because we could separately look at +pulley B and we could separately + + align:start position:0% +pulley B and we could separately + + + align:start position:0% +pulley B and we could separately +consider block two or we consider them + + align:start position:0% +consider block two or we consider them + + + align:start position:0% +consider block two or we consider them +together and I want to First consider + + align:start position:0% +together and I want to First consider + + + align:start position:0% +together and I want to First consider +separately pulley + + align:start position:0% +separately pulley + + + align:start position:0% +separately pulley +B + + align:start position:0% +B + + + align:start position:0% +B +and block two now in some ways when + + align:start position:0% +and block two now in some ways when + + + align:start position:0% +and block two now in some ways when +you're looking at a system of compound a + + align:start position:0% +you're looking at a system of compound a + + + align:start position:0% +you're looking at a system of compound a +compound system and it has four object + + align:start position:0% +compound system and it has four object + + + align:start position:0% +compound system and it has four object +it makes sense to apply Newton's Second + + align:start position:0% +it makes sense to apply Newton's Second + + + align:start position:0% +it makes sense to apply Newton's Second +Law to each object separately but we'll + + align:start position:0% +Law to each object separately but we'll + + + align:start position:0% +Law to each object separately but we'll +pay careful attention to the fact that + + align:start position:0% +pay careful attention to the fact that + + + align:start position:0% +pay careful attention to the fact that +object two is connected to pulley B and + + align:start position:0% +object two is connected to pulley B and + + + align:start position:0% +object two is connected to pulley B and +eventually we'll see that we can combine + + align:start position:0% +eventually we'll see that we can combine + + + align:start position:0% +eventually we'll see that we can combine +these two things so the next step is + + align:start position:0% +these two things so the next step is + + + align:start position:0% +these two things so the next step is +once we've identified our object is to + + align:start position:0% +once we've identified our object is to + + + align:start position:0% +once we've identified our object is to +draw free body Force diagrams for each + + align:start position:0% +draw free body Force diagrams for each + + + align:start position:0% +draw free body Force diagrams for each +of the objects so in order to do that + + align:start position:0% +of the objects so in order to do that + + + align:start position:0% +of the objects so in order to do that +let's start with object + + align:start position:0% +let's start with object + + + align:start position:0% +let's start with object +one and + + align:start position:0% +one and + + + align:start position:0% +one and +we want to consider the forces on object + + align:start position:0% +we want to consider the forces on object + + + align:start position:0% +we want to consider the forces on object +one now that brings us to our first + + align:start position:0% +one now that brings us to our first + + + align:start position:0% +one now that brings us to our first +issue about what types of assumptions + + align:start position:0% +issue about what types of assumptions + + + align:start position:0% +issue about what types of assumptions +we're making in our system for instance + + align:start position:0% +we're making in our system for instance + + + align:start position:0% +we're making in our system for instance +we have a rope that's wrapped around + + align:start position:0% +we have a rope that's wrapped around + + + align:start position:0% +we have a rope that's wrapped around +this pulley and we have two pulleys that + + align:start position:0% +this pulley and we have two pulleys that + + + align:start position:0% +this pulley and we have two pulleys that +in principle could be rotating but what + + align:start position:0% +in principle could be rotating but what + + + align:start position:0% +in principle could be rotating but what +we'd like to do to simplify our analysis + + align:start position:0% +we'd like to do to simplify our analysis + + + align:start position:0% +we'd like to do to simplify our analysis +so let's keep track of some assumptions + + align:start position:0% +so let's keep track of some assumptions + + + align:start position:0% +so let's keep track of some assumptions +here our first + + align:start position:0% +here our first + + + align:start position:0% +here our first +assumption will be that the mass + + align:start position:0% +assumption will be that the mass + + + align:start position:0% +assumption will be that the mass +MP of pulley a and the mass of pulley B + + align:start position:0% +MP of pulley a and the mass of pulley B + + + align:start position:0% +MP of pulley a and the mass of pulley B +are approximately zero now the reason + + align:start position:0% +are approximately zero now the reason + + + align:start position:0% +are approximately zero now the reason +for that is that we're not going to + + align:start position:0% +for that is that we're not going to + + + align:start position:0% +for that is that we're not going to +consider any of the fact that these + + align:start position:0% +consider any of the fact that these + + + align:start position:0% +consider any of the fact that these +objects have to be put into rotational + + align:start position:0% +objects have to be put into rotational + + + align:start position:0% +objects have to be put into rotational +motion later on in the course we'll see + + align:start position:0% +motion later on in the course we'll see + + + align:start position:0% +motion later on in the course we'll see +that this will give us a more + + align:start position:0% +that this will give us a more + + + align:start position:0% +that this will give us a more +complicated analysis we're also going to + + align:start position:0% +complicated analysis we're also going to + + + align:start position:0% +complicated analysis we're also going to +assume that our rope is not slipping so + + align:start position:0% +assume that our rope is not slipping so + + + align:start position:0% +assume that our rope is not slipping so +the + + align:start position:0% +the + + + align:start position:0% +the +Rope is actually is just slipping on the + + align:start position:0% +Rope is actually is just slipping on the + + + align:start position:0% +Rope is actually is just slipping on the +pulleys so with that means is it's just + + align:start position:0% +pulleys so with that means is it's just + + + align:start position:0% +pulleys so with that means is it's just +the Rope is sliding as the objects move + + align:start position:0% +the Rope is sliding as the objects move + + + align:start position:0% +the Rope is sliding as the objects move +now again what this is going to + + align:start position:0% +now again what this is going to + + + align:start position:0% +now again what this is going to +imply is that the tension in the Rope + + align:start position:0% +imply is that the tension in the Rope + + + align:start position:0% +imply is that the tension in the Rope +this rope is also is slipping and the + + align:start position:0% +this rope is also is slipping and the + + + align:start position:0% +this rope is also is slipping and the +Rope + + align:start position:0% +Rope + + + align:start position:0% +Rope +is massless as well it's very light rope + + align:start position:0% +is massless as well it's very light rope + + + align:start position:0% +is massless as well it's very light rope +and all of these assumptions we've seen + + align:start position:0% +and all of these assumptions we've seen + + + align:start position:0% +and all of these assumptions we've seen +when we analyze ropes tell us that the + + align:start position:0% +when we analyze ropes tell us that the + + + align:start position:0% +when we analyze ropes tell us that the +tension + + align:start position:0% +tension + + + align:start position:0% +tension +T is uniform in the Rope so that's our + + align:start position:0% +T is uniform in the Rope so that's our + + + align:start position:0% +T is uniform in the Rope so that's our +first assumption and we need to think + + align:start position:0% +first assumption and we need to think + + + align:start position:0% +first assumption and we need to think +about this before we even begin to think + + align:start position:0% +about this before we even begin to think + + + align:start position:0% +about this before we even begin to think +about the forces on the object and now + + align:start position:0% +about the forces on the object and now + + + align:start position:0% +about the forces on the object and now +we can draw our forces what do we have + + align:start position:0% +we can draw our forces what do we have + + + align:start position:0% +we can draw our forces what do we have +we have the gravitational force on + + align:start position:0% +we have the gravitational force on + + + align:start position:0% +we have the gravitational force on +object one and now we can identify the + + align:start position:0% +object one and now we can identify the + + + align:start position:0% +object one and now we can identify the +tension pulling in the string pulling + + align:start position:0% +tension pulling in the string pulling + + + align:start position:0% +tension pulling in the string pulling +object one up now for every time we + + align:start position:0% +object one up now for every time we + + + align:start position:0% +object one up now for every time we +introduce a free body diagram recall + + align:start position:0% +introduce a free body diagram recall + + + align:start position:0% +introduce a free body diagram recall +that we have to choose what we mean by + + align:start position:0% +that we have to choose what we mean by + + + align:start position:0% +that we have to choose what we mean by +Positive Directions and in this case I'm + + align:start position:0% +Positive Directions and in this case I'm + + + align:start position:0% +Positive Directions and in this case I'm +going to pick a unit Vector down J hat + + align:start position:0% +going to pick a unit Vector down J hat + + + align:start position:0% +going to pick a unit Vector down J hat +one down so that's my positive direction + + align:start position:0% +one down so that's my positive direction + + + align:start position:0% +one down so that's my positive direction +for Force now before I write down all of + + align:start position:0% +for Force now before I write down all of + + + align:start position:0% +for Force now before I write down all of +Newton's Laws I'll just write down our + + align:start position:0% +Newton's Laws I'll just write down our + + + align:start position:0% +Newton's Laws I'll just write down our +various Force + + align:start position:0% +various Force + + + align:start position:0% +various Force +diagrams so for pulley + + align:start position:0% +diagrams so for pulley + + + align:start position:0% +diagrams so for pulley +a I have two strings that are pulling it + + align:start position:0% +a I have two strings that are pulling it + + + align:start position:0% +a I have two strings that are pulling it +downwards so I have tension and tension + + align:start position:0% +downwards so I have tension and tension + + + align:start position:0% +downwards so I have tension and tension +and this string I'm going to call that + + align:start position:0% +and this string I'm going to call that + + + align:start position:0% +and this string I'm going to call that +T2 is pulling is holding that pulley up + + align:start position:0% +T2 is pulling is holding that pulley up + + + align:start position:0% +T2 is pulling is holding that pulley up +so we have the force diagram now I could + + align:start position:0% +so we have the force diagram now I could + + + align:start position:0% +so we have the force diagram now I could +write M A but we've assumed that the + + align:start position:0% +write M A but we've assumed that the + + + align:start position:0% +write M A but we've assumed that the +pulley is + + align:start position:0% +pulley is + + + align:start position:0% +pulley is +massless and again I'll call J hat a + + align:start position:0% +massless and again I'll call J hat a + + + align:start position:0% +massless and again I'll call J hat a +down for object two let's do pulley B + + align:start position:0% +down for object two let's do pulley B + + + align:start position:0% +down for object two let's do pulley B +first now what are the forces on pully B + + align:start position:0% +first now what are the forces on pully B + + + align:start position:0% +first now what are the forces on pully B +I have strings on both sides + + align:start position:0% +I have strings on both sides + + + align:start position:0% +I have strings on both sides +T pulley B is mes so I'm not putting + + align:start position:0% +T pulley B is mes so I'm not putting + + + align:start position:0% +T pulley B is mes so I'm not putting +gravitational force and I'm + + align:start position:0% +gravitational force and I'm + + + align:start position:0% +gravitational force and I'm +pulling this string is pulling B + + align:start position:0% +pulling this string is pulling B + + + align:start position:0% +pulling this string is pulling B +downwards so that's T3 and again we'll + + align:start position:0% +downwards so that's T3 and again we'll + + + align:start position:0% +downwards so that's T3 and again we'll +write jat B + + align:start position:0% +write jat B + + + align:start position:0% +write jat B +downwards and finally I have block two + + align:start position:0% +downwards and finally I have block two + + + align:start position:0% +downwards and finally I have block two +so I'll draw that over here I'll write + + align:start position:0% +so I'll draw that over here I'll write + + + align:start position:0% +so I'll draw that over here I'll write +block two in fact let's save a little + + align:start position:0% +block two in fact let's save a little + + + align:start position:0% +block two in fact let's save a little +space here we'll have J Hat B downwards + + align:start position:0% +space here we'll have J Hat B downwards + + + align:start position:0% +space here we'll have J Hat B downwards +now block two what do we have there we + + align:start position:0% +now block two what do we have there we + + + align:start position:0% +now block two what do we have there we +have the string pulling up block two + + align:start position:0% +have the string pulling up block two + + + align:start position:0% +have the string pulling up block two +which we've identified as + + align:start position:0% +which we've identified as + + + align:start position:0% +which we've identified as +T3 and we have the gravitational force + + align:start position:0% +T3 and we have the gravitational force + + + align:start position:0% +T3 and we have the gravitational force +on block two downward + + align:start position:0% +on block two downward + + + align:start position:0% +on block two downward +m2g and there we have J had 2 so I've + + align:start position:0% +m2g and there we have J had 2 so I've + + + align:start position:0% +m2g and there we have J had 2 so I've +now drawn the free body diagrams on the + + align:start position:0% +now drawn the free body diagrams on the + + + align:start position:0% +now drawn the free body diagrams on the +various objects and that enables me to + + align:start position:0% +various objects and that enables me to + + + align:start position:0% +various objects and that enables me to +apply Newton Second Law for each of + + align:start position:0% +apply Newton Second Law for each of + + + align:start position:0% +apply Newton Second Law for each of +these objects so let's begin we'll start + + align:start position:0% +these objects so let's begin we'll start + + + align:start position:0% +these objects so let's begin we'll start +with object one we have remember in all + + align:start position:0% +with object one we have remember in all + + + align:start position:0% +with object one we have remember in all +cases we're going to apply FAL + + align:start position:0% +cases we're going to apply FAL + + + align:start position:0% +cases we're going to apply FAL +Ma so for object one we have + + align:start position:0% +Ma so for object one we have + + + align:start position:0% +Ma so for object one we have +m1g positive downward minus t is equal + + align:start position:0% +m1g positive downward minus t is equal + + + align:start position:0% +m1g positive downward minus t is equal +to M1 + + align:start position:0% +to M1 + + + align:start position:0% +to M1 +A1 and that's our fals Ma on object one + + align:start position:0% +A1 and that's our fals Ma on object one + + + align:start position:0% +A1 and that's our fals Ma on object one +so sometimes we'll divide distinguish + + align:start position:0% +so sometimes we'll divide distinguish + + + align:start position:0% +so sometimes we'll divide distinguish +that the forces we're getting from our + + align:start position:0% +that the forces we're getting from our + + + align:start position:0% +that the forces we're getting from our +free body diagrams and a is a + + align:start position:0% +free body diagrams and a is a + + + align:start position:0% +free body diagrams and a is a +mathematical description of the + + align:start position:0% +mathematical description of the + + + align:start position:0% +mathematical description of the +motion for Block two we have + + align:start position:0% +motion for Block two we have + + + align:start position:0% +motion for Block two we have +m2g minus T3 is equal to M2 + + align:start position:0% +m2g minus T3 is equal to M2 + + + align:start position:0% +m2g minus T3 is equal to M2 +A2 and now for pulley + + align:start position:0% +A2 and now for pulley + + + align:start position:0% +A2 and now for pulley +a we have 2 T pointing + + align:start position:0% +a we have 2 T pointing + + + align:start position:0% +a we have 2 T pointing +downwards minus T2 going upwards and + + align:start position:0% +downwards minus T2 going upwards and + + + align:start position:0% +downwards minus T2 going upwards and +because pulley a is + + align:start position:0% +because pulley a is + + + align:start position:0% +because pulley a is +massless this is + + align:start position:0% +massless this is + + + align:start position:0% +massless this is +zero even though pulley a May B this is + + align:start position:0% +zero even though pulley a May B this is + + + align:start position:0% +zero even though pulley a May B this is +it's actually fixed too so it's not even + + align:start position:0% +it's actually fixed too so it's not even + + + align:start position:0% +it's actually fixed too so it's not even +accelerating and what we see here is + + align:start position:0% +accelerating and what we see here is + + + align:start position:0% +accelerating and what we see here is +this equation I'm going to quickly note + + align:start position:0% +this equation I'm going to quickly note + + + align:start position:0% +this equation I'm going to quickly note +that it tells us that the + + align:start position:0% +that it tells us that the + + + align:start position:0% +that it tells us that the +string holding poly 2 up T2 is equal to + + align:start position:0% +string holding poly 2 up T2 is equal to + + + align:start position:0% +string holding poly 2 up T2 is equal to +2T now um so we can think of if we want + + align:start position:0% +2T now um so we can think of if we want + + + align:start position:0% +2T now um so we can think of if we want +to know what T2 is we need to calculate + + align:start position:0% +to know what T2 is we need to calculate + + + align:start position:0% +to know what T2 is we need to calculate +T and finally we have + + align:start position:0% +T and finally we have + + + align:start position:0% +T and finally we have +B and what is the forces on B we have + + align:start position:0% +B and what is the forces on B we have + + + align:start position:0% +B and what is the forces on B we have +T3 minus 2T and again pulley B is zero + + align:start position:0% +T3 minus 2T and again pulley B is zero + + + align:start position:0% +T3 minus 2T and again pulley B is zero +and so we see that T3 is equal to 2 + + align:start position:0% +and so we see that T3 is equal to 2 + + + align:start position:0% +and so we see that T3 is equal to 2 +T now now if you think about what I said + + align:start position:0% +T now now if you think about what I said + + + align:start position:0% +T now now if you think about what I said +before about combining systems if we + + align:start position:0% +before about combining systems if we + + + align:start position:0% +before about combining systems if we +combine pulley B and block two visually + + align:start position:0% +combine pulley B and block two visually + + + align:start position:0% +combine pulley B and block two visually +what we're doing is we're just adding + + align:start position:0% +what we're doing is we're just adding + + + align:start position:0% +what we're doing is we're just adding +these two free body diagrams together + + align:start position:0% +these two free body diagrams together + + + align:start position:0% +these two free body diagrams together +when we have a system + + align:start position:0% +when we have a system + + + align:start position:0% +when we have a system +B and block two let's call this J hat + + align:start position:0% +B and block two let's call this J hat + + + align:start position:0% +B and block two let's call this J hat +downwards and when we add these free + + align:start position:0% +downwards and when we add these free + + + align:start position:0% +downwards and when we add these free +body diagrams together you see that the + + align:start position:0% +body diagrams together you see that the + + + align:start position:0% +body diagrams together you see that the +T3 is now internal Force to the system + + align:start position:0% +T3 is now internal Force to the system + + + align:start position:0% +T3 is now internal Force to the system +it cancels in Pair by Newton's Second + + align:start position:0% +it cancels in Pair by Newton's Second + + + align:start position:0% +it cancels in Pair by Newton's Second +Law and all we have is the two strings + + align:start position:0% +Law and all we have is the two strings + + + align:start position:0% +Law and all we have is the two strings +going up so we have T and T and we have + + align:start position:0% +going up so we have T and T and we have + + + align:start position:0% +going up so we have T and T and we have +the gravitational force + + align:start position:0% +the gravitational force + + + align:start position:0% +the gravitational force +downward and separately when we saw that + + align:start position:0% +downward and separately when we saw that + + + align:start position:0% +downward and separately when we saw that +T3 = + + align:start position:0% +T3 = + + + align:start position:0% +T3 = +2T and we apply it there then if we + + align:start position:0% +2T and we apply it there then if we + + + align:start position:0% +2T and we apply it there then if we +consider a system + + align:start position:0% +consider a system + + + align:start position:0% +consider a system +B2 and look at our free body diagram we + + align:start position:0% +B2 and look at our free body diagram we + + + align:start position:0% +B2 and look at our free body diagram we +have + + align:start position:0% +have + + + align:start position:0% +have +m2g minus 2T and notice we have the same + + align:start position:0% +m2g minus 2T and notice we have the same + + + align:start position:0% +m2g minus 2T and notice we have the same +result there 2T = M2 + + align:start position:0% +result there 2T = M2 + + + align:start position:0% +result there 2T = M2 +A2 so in principle now and I'll outline + + align:start position:0% +A2 so in principle now and I'll outline + + + align:start position:0% +A2 so in principle now and I'll outline +our equations we have equation one + + align:start position:0% +our equations we have equation one + + + align:start position:0% +our equations we have equation one +we have equation + + align:start position:0% +we have equation + + + align:start position:0% +we have equation +two and in these two equations we have + + align:start position:0% +two and in these two equations we have + + + align:start position:0% +two and in these two equations we have +three unknowns T A1 and A2 but only two + + align:start position:0% +three unknowns T A1 and A2 but only two + + + align:start position:0% +three unknowns T A1 and A2 but only two +equations and so you might think what + + align:start position:0% +equations and so you might think what + + + align:start position:0% +equations and so you might think what +about this missing third equation here + + align:start position:0% +about this missing third equation here + + + align:start position:0% +about this missing third equation here +however in this equation we have a + + align:start position:0% +however in this equation we have a + + + align:start position:0% +however in this equation we have a +fourth unknown T3 and this equation is + + align:start position:0% +fourth unknown T3 and this equation is + + + align:start position:0% +fourth unknown T3 and this equation is +just relating to T and T3 so in + + align:start position:0% +just relating to T and T3 so in + + + align:start position:0% +just relating to T and T3 so in +principle we would have four unknowns in + + align:start position:0% +principle we would have four unknowns in + + + align:start position:0% +principle we would have four unknowns in +three equations or if we restrict our + + align:start position:0% +three equations or if we restrict our + + + align:start position:0% +three equations or if we restrict our +attention to these two equations we have + + align:start position:0% +attention to these two equations we have + + + align:start position:0% +attention to these two equations we have +two unknowns three unknowns and two + + align:start position:0% +two unknowns three unknowns and two + + + align:start position:0% +two unknowns three unknowns and two +equations our unknowns are T A1 and + + align:start position:0% +equations our unknowns are T A1 and + + + align:start position:0% +equations our unknowns are T A1 and +A2 these are our unknowns and now our + + align:start position:0% +A2 these are our unknowns and now our + + + align:start position:0% +A2 these are our unknowns and now our +next step is to try to figure out what + + align:start position:0% +next step is to try to figure out what + + + align:start position:0% +next step is to try to figure out what +is the missing condition that's relating + + align:start position:0% +is the missing condition that's relating + + + align:start position:0% +is the missing condition that's relating +this some of these unknowns and that + + align:start position:0% +this some of these unknowns and that + + + align:start position:0% +this some of these unknowns and that +will be a constraint condition that + + align:start position:0% +will be a constraint condition that + + + align:start position:0% +will be a constraint condition that +we'll analyze next \ No newline at end of file diff --git a/HA4undazeF0.txt b/HA4undazeF0.txt new file mode 100644 index 0000000000000000000000000000000000000000..2077ea15bee488d2afd0e2de02b0927addeffe71 --- /dev/null +++ b/HA4undazeF0.txt @@ -0,0 +1,5811 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +I'll just be brief today but you can + + align:start position:0% +I'll just be brief today but you can + + + align:start position:0% +I'll just be brief today but you can +check out some of my stuff at the + + align:start position:0% +check out some of my stuff at the + + + align:start position:0% +check out some of my stuff at the +website up there if you're confused by + + align:start position:0% +website up there if you're confused by + + + align:start position:0% +website up there if you're confused by +my appearance if you've met me before + + align:start position:0% +my appearance if you've met me before + + + align:start position:0% +my appearance if you've met me before +yes I used to look like that but at a + + align:start position:0% +yes I used to look like that but at a + + + align:start position:0% +yes I used to look like that but at a +deeper level really I look like this + + align:start position:0% +deeper level really I look like this + + + align:start position:0% +deeper level really I look like this +this is me and you look like that too + + align:start position:0% +this is me and you look like that too + + + align:start position:0% +this is me and you look like that too +inside and these are parts of showing + + align:start position:0% +inside and these are parts of showing + + + align:start position:0% +inside and these are parts of showing +you these are parts of my brain that + + align:start position:0% +you these are parts of my brain that + + + align:start position:0% +you these are parts of my brain that +we've mapped with functional MRI that + + align:start position:0% +we've mapped with functional MRI that + + + align:start position:0% +we've mapped with functional MRI that +were either discovered in my lab or that + + align:start position:0% +were either discovered in my lab or that + + + align:start position:0% +were either discovered in my lab or that +my colleagues discovered and that we + + align:start position:0% +my colleagues discovered and that we + + + align:start position:0% +my colleagues discovered and that we +then ran their kinds of scans in my lab + + align:start position:0% +then ran their kinds of scans in my lab + + + align:start position:0% +then ran their kinds of scans in my lab +these are all regions that do very + + align:start position:0% +these are all regions that do very + + + align:start position:0% +these are all regions that do very +specific things and that to me are a big + + align:start position:0% +specific things and that to me are a big + + + align:start position:0% +specific things and that to me are a big +part of the story of how we are so smart + + align:start position:0% +part of the story of how we are so smart + + + align:start position:0% +part of the story of how we are so smart +so my interests at a very general level + + align:start position:0% +so my interests at a very general level + + + align:start position:0% +so my interests at a very general level +are to answer things like you know what + + align:start position:0% +are to answer things like you know what + + + align:start position:0% +are to answer things like you know what +are what is the architecture of the + + align:start position:0% +are what is the architecture of the + + + align:start position:0% +are what is the architecture of the +human mind what are its fundamental + + align:start position:0% +human mind what are its fundamental + + + align:start position:0% +human mind what are its fundamental +components and there are lots and lots + + align:start position:0% +components and there are lots and lots + + + align:start position:0% +components and there are lots and lots +of ways to find those fundamental + + align:start position:0% +of ways to find those fundamental + + + align:start position:0% +of ways to find those fundamental +components functional MRI which is how + + align:start position:0% +components functional MRI which is how + + + align:start position:0% +components functional MRI which is how +we made this picture is just one of a + + align:start position:0% +we made this picture is just one of a + + + align:start position:0% +we made this picture is just one of a +huge number + + align:start position:0% +huge number + + + align:start position:0% +huge number +I loved Patrick's comment that you + + align:start position:0% +I loved Patrick's comment that you + + + align:start position:0% +I loved Patrick's comment that you +should find questions not hammers I kind + + align:start position:0% +should find questions not hammers I kind + + + align:start position:0% +should find questions not hammers I kind +of like my hammer I have to confess but + + align:start position:0% +of like my hammer I have to confess but + + + align:start position:0% +of like my hammer I have to confess but +there are but questions are more + + align:start position:0% +there are but questions are more + + + align:start position:0% +there are but questions are more +important and there are lots of ways to + + align:start position:0% +important and there are lots of ways to + + + align:start position:0% +important and there are lots of ways to +approach this question of the basic + + align:start position:0% +approach this question of the basic + + + align:start position:0% +approach this question of the basic +architecture of the human mind I also + + align:start position:0% +architecture of the human mind I also + + + align:start position:0% +architecture of the human mind I also +want to know how this structure which is + + align:start position:0% +want to know how this structure which is + + + align:start position:0% +want to know how this structure which is +present in every normal person I could + + align:start position:0% +present in every normal person I could + + + align:start position:0% +present in every normal person I could +pop any of you in the scanner and make a + + align:start position:0% +pop any of you in the scanner and make a + + + align:start position:0% +pop any of you in the scanner and make a +picture like this of your brain ok take + + align:start position:0% +picture like this of your brain ok take + + + align:start position:0% +picture like this of your brain ok take +a little while but um but wouldn't take + + align:start position:0% +a little while but um but wouldn't take + + + align:start position:0% +a little while but um but wouldn't take +that long how does that structure a rise + + align:start position:0% +that long how does that structure a rise + + + align:start position:0% +that long how does that structure a rise +over development how does your how does + + align:start position:0% +over development how does your how does + + + align:start position:0% +over development how does your how does +your genetic code and your experience + + align:start position:0% +your genetic code and your experience + + + align:start position:0% +your genetic code and your experience +work together to wire that up when + + align:start position:0% +work together to wire that up when + + + align:start position:0% +work together to wire that up when +you're an infant and a child how did it + + align:start position:0% +you're an infant and a child how did it + + + align:start position:0% +you're an infant and a child how did it +evolve over human evolution what this is + + align:start position:0% +evolve over human evolution what this is + + + align:start position:0% +evolve over human evolution what this is +sort of what's sometimes called a meso + + align:start position:0% +sort of what's sometimes called a meso + + + align:start position:0% +sort of what's sometimes called a meso +scale this really Makris + + align:start position:0% +scale this really Makris + + + align:start position:0% +scale this really Makris +EPIK picture of the major components of + + align:start position:0% +EPIK picture of the major components of + + + align:start position:0% +EPIK picture of the major components of +the human mind and brain but of course + + align:start position:0% +the human mind and brain but of course + + + align:start position:0% +the human mind and brain but of course +we also want to know how each of those + + align:start position:0% +we also want to know how each of those + + + align:start position:0% +we also want to know how each of those +bits work what are the representations + + align:start position:0% +bits work what are the representations + + + align:start position:0% +bits work what are the representations +that live in each of those regions and + + align:start position:0% +that live in each of those regions and + + + align:start position:0% +that live in each of those regions and +how are they computed and what are the + + align:start position:0% +how are they computed and what are the + + + align:start position:0% +how are they computed and what are the +neural circuits that implement those + + align:start position:0% +neural circuits that implement those + + + align:start position:0% +neural circuits that implement those +computations and of course cognition + + align:start position:0% +computations and of course cognition + + + align:start position:0% +computations and of course cognition +doesn't happen in just one little + + align:start position:0% +doesn't happen in just one little + + + align:start position:0% +doesn't happen in just one little +machine in there it's the product of all + + align:start position:0% +machine in there it's the product of all + + + align:start position:0% +machine in there it's the product of all +of these bits working together we want + + align:start position:0% +of these bits working together we want + + + align:start position:0% +of these bits working together we want +to understand how all of that works too + + align:start position:0% +to understand how all of that works too + + + align:start position:0% +to understand how all of that works too +and how all of that goes together to + + align:start position:0% +and how all of that goes together to + + + align:start position:0% +and how all of that goes together to +make us so smart and that's related to a + + align:start position:0% +make us so smart and that's related to a + + + align:start position:0% +make us so smart and that's related to a +question that I'm deeply interested in + + align:start position:0% +question that I'm deeply interested in + + + align:start position:0% +question that I'm deeply interested in +which is what is so special about this + + align:start position:0% +which is what is so special about this + + + align:start position:0% +which is what is so special about this +machine it looks a lot like a rodent + + align:start position:0% +machine it looks a lot like a rodent + + + align:start position:0% +machine it looks a lot like a rodent +brain and it's smaller than a whale + + align:start position:0% +brain and it's smaller than a whale + + + align:start position:0% +brain and it's smaller than a whale +brain or a Neanderthal brain so it's not + + align:start position:0% +brain or a Neanderthal brain so it's not + + + align:start position:0% +brain or a Neanderthal brain so it's not +just that we have more of it what is so + + align:start position:0% +just that we have more of it what is so + + + align:start position:0% +just that we have more of it what is so +special about thing this thing that has + + align:start position:0% +special about thing this thing that has + + + align:start position:0% +special about thing this thing that has +put all of us here interacting with each + + align:start position:0% +put all of us here interacting with each + + + align:start position:0% +put all of us here interacting with each +other and studying this thing something + + align:start position:0% +other and studying this thing something + + + align:start position:0% +other and studying this thing something +that no other brain is doing no other + + align:start position:0% +that no other brain is doing no other + + + align:start position:0% +that no other brain is doing no other +species brain so are there special bits + + align:start position:0% +species brain so are there special bits + + + align:start position:0% +species brain so are there special bits +to those bits work differently are there + + align:start position:0% +to those bits work differently are there + + + align:start position:0% +to those bits work differently are there +special kinds of neurons I don't think + + align:start position:0% +special kinds of neurons I don't think + + + align:start position:0% +special kinds of neurons I don't think +so some people do what is it about this + + align:start position:0% +so some people do what is it about this + + + align:start position:0% +so some people do what is it about this +that that has brought us all right here + + align:start position:0% +that that has brought us all right here + + + align:start position:0% +that that has brought us all right here +ok so that at a top level er is some of + + align:start position:0% +ok so that at a top level er is some of + + + align:start position:0% +ok so that at a top level er is some of +the questions I would most like to + + align:start position:0% +the questions I would most like to + + + align:start position:0% +the questions I would most like to +answer not that I know how to approach + + align:start position:0% +answer not that I know how to approach + + + align:start position:0% +answer not that I know how to approach +any of them but I think it's important + + align:start position:0% +any of them but I think it's important + + + align:start position:0% +any of them but I think it's important +to keep an eye on those goals even when + + align:start position:0% +to keep an eye on those goals even when + + + align:start position:0% +to keep an eye on those goals even when +you don't quite see how you're going to + + align:start position:0% +you don't quite see how you're going to + + + align:start position:0% +you don't quite see how you're going to +get there my particular focus in the + + align:start position:0% +get there my particular focus in the + + + align:start position:0% +get there my particular focus in the +CBMM project is to look at social + + align:start position:0% +CBMM project is to look at social + + + align:start position:0% +CBMM project is to look at social +intelligence which is one piece of that + + align:start position:0% +intelligence which is one piece of that + + + align:start position:0% +intelligence which is one piece of that +puzzle and so why social intelligence + + align:start position:0% +puzzle and so why social intelligence + + + align:start position:0% +puzzle and so why social intelligence +well just briefly I think social + + align:start position:0% +well just briefly I think social + + + align:start position:0% +well just briefly I think social +cognition is in many ways the crux of + + align:start position:0% +cognition is in many ways the crux of + + + align:start position:0% +cognition is in many ways the crux of +human intelligence ok this is a crux in + + align:start position:0% +human intelligence ok this is a crux in + + + align:start position:0% +human intelligence ok this is a crux in +a whole bunch of different senses one is + + align:start position:0% +a whole bunch of different senses one is + + + align:start position:0% +a whole bunch of different senses one is +it's just the source of how we're so + + align:start position:0% +it's just the source of how we're so + + + align:start position:0% +it's just the source of how we're so +smart like if you think about all the + + align:start position:0% +smart like if you think about all the + + + align:start position:0% +smart like if you think about all the +stuff you know ok do a quick mental + + align:start position:0% +stuff you know ok do a quick mental + + + align:start position:0% +stuff you know ok do a quick mental +inventory people told us stuff you know + + align:start position:0% +inventory people told us stuff you know + + + align:start position:0% +inventory people told us stuff you know +make a little taxonomy there's this kind + + align:start position:0% +make a little taxonomy there's this kind + + + align:start position:0% +make a little taxonomy there's this kind +of stuff it's all lots of different + + align:start position:0% +of stuff it's all lots of different + + + align:start position:0% +of stuff it's all lots of different +kinds of stuff you know ok now how much + + align:start position:0% +kinds of stuff you know ok now how much + + + align:start position:0% +kinds of stuff you know ok now how much +of that stuff that you know would you + + align:start position:0% +of that stuff that you know would you + + + align:start position:0% +of that stuff that you know would you +know if you had never interacted with + + align:start position:0% +know if you had never interacted with + + + align:start position:0% +know if you had never interacted with +another person a lot of it you wouldn't + + align:start position:0% +another person a lot of it you wouldn't + + + align:start position:0% +another person a lot of it you wouldn't +know right so a lot of the stuff we know + + align:start position:0% +know right so a lot of the stuff we know + + + align:start position:0% +know right so a lot of the stuff we know +and a lot of the ways that were smart + + align:start position:0% +and a lot of the ways that were smart + + + align:start position:0% +and a lot of the ways that were smart +are things that we get from interacting + + align:start position:0% +are things that we get from interacting + + + align:start position:0% +are things that we get from interacting +with other people that's social + + align:start position:0% +with other people that's social + + + align:start position:0% +with other people that's social +cognition + + align:start position:0% +cognition + + + align:start position:0% +cognition +okay another sense in which social + + align:start position:0% +okay another sense in which social + + + align:start position:0% +okay another sense in which social +cognition is the crux of human + + align:start position:0% +cognition is the crux of human + + + align:start position:0% +cognition is the crux of human +intelligence is many people think that + + align:start position:0% +intelligence is many people think that + + + align:start position:0% +intelligence is many people think that +the primary driver of the evolution of + + align:start position:0% +the primary driver of the evolution of + + + align:start position:0% +the primary driver of the evolution of +the human brain has been the requirement + + align:start position:0% +the human brain has been the requirement + + + align:start position:0% +the human brain has been the requirement +to interact with other people who are + + align:start position:0% +to interact with other people who are + + + align:start position:0% +to interact with other people who are +after all very complex entities and to + + align:start position:0% +after all very complex entities and to + + + align:start position:0% +after all very complex entities and to +be able to understand how to work with + + align:start position:0% +be able to understand how to work with + + + align:start position:0% +be able to understand how to work with +them and what they're doing and what + + align:start position:0% +them and what they're doing and what + + + align:start position:0% +them and what they're doing and what +they'll do next is very cognitively + + align:start position:0% +they'll do next is very cognitively + + + align:start position:0% +they'll do next is very cognitively +demanding and so that that may be one of + + align:start position:0% +demanding and so that that may be one of + + + align:start position:0% +demanding and so that that may be one of +the major forces that has driven the + + align:start position:0% +the major forces that has driven the + + + align:start position:0% +the major forces that has driven the +evolution of our brain another sense in + + align:start position:0% +evolution of our brain another sense in + + + align:start position:0% +evolution of our brain another sense in +which social intelligence is the crux of + + align:start position:0% +which social intelligence is the crux of + + + align:start position:0% +which social intelligence is the crux of +human intelligence is that it's just + + align:start position:0% +human intelligence is that it's just + + + align:start position:0% +human intelligence is that it's just +plain a large percent of human cognition + + align:start position:0% +plain a large percent of human cognition + + + align:start position:0% +plain a large percent of human cognition +okay so we do versions of social + + align:start position:0% +okay so we do versions of social + + + align:start position:0% +okay so we do versions of social +cognition much of every day right now + + align:start position:0% +cognition much of every day right now + + + align:start position:0% +cognition much of every day right now +I'm having these thoughts in my head god + + align:start position:0% +I'm having these thoughts in my head god + + + align:start position:0% +I'm having these thoughts in my head god +knows what that looks like neroli I'm + + align:start position:0% +knows what that looks like neroli I'm + + + align:start position:0% +knows what that looks like neroli I'm +translating that into some noises that + + align:start position:0% +translating that into some noises that + + + align:start position:0% +translating that into some noises that +are coming out of my mouth you're + + align:start position:0% +are coming out of my mouth you're + + + align:start position:0% +are coming out of my mouth you're +hearing those noises and you're getting + + align:start position:0% +hearing those noises and you're getting + + + align:start position:0% +hearing those noises and you're getting +let's hope kind of similar thoughts in + + align:start position:0% +let's hope kind of similar thoughts in + + + align:start position:0% +let's hope kind of similar thoughts in +your head that is a miracle nobody has + + align:start position:0% +your head that is a miracle nobody has + + + align:start position:0% +your head that is a miracle nobody has +the foggiest idea how that works at a + + align:start position:0% +the foggiest idea how that works at a + + + align:start position:0% +the foggiest idea how that works at a +neural level nobody can even like make + + align:start position:0% +neural level nobody can even like make + + + align:start position:0% +neural level nobody can even like make +up a sketch of a hypothesis of a bunch + + align:start position:0% +up a sketch of a hypothesis of a bunch + + + align:start position:0% +up a sketch of a hypothesis of a bunch +of neural circuits that might be able to + + align:start position:0% +of neural circuits that might be able to + + + align:start position:0% +of neural circuits that might be able to +make that happen right that's a + + align:start position:0% +make that happen right that's a + + + align:start position:0% +make that happen right that's a +fascinating puzzle and it's also of the + + align:start position:0% +fascinating puzzle and it's also of the + + + align:start position:0% +fascinating puzzle and it's also of the +essence and human intelligence and we do + + align:start position:0% +essence and human intelligence and we do + + + align:start position:0% +essence and human intelligence and we do +it all the time not just speaking per se + + align:start position:0% +it all the time not just speaking per se + + + align:start position:0% +it all the time not just speaking per se +but all the other ways that we share + + align:start position:0% +but all the other ways that we share + + + align:start position:0% +but all the other ways that we share +information with each other so one + + align:start position:0% +information with each other so one + + + align:start position:0% +information with each other so one +social social cognition is just what we + + align:start position:0% +social social cognition is just what we + + + align:start position:0% +social social cognition is just what we +do all day long every day it's also a + + align:start position:0% +do all day long every day it's also a + + + align:start position:0% +do all day long every day it's also a +big part of the surface area of the + + align:start position:0% +big part of the surface area of the + + + align:start position:0% +big part of the surface area of the +cortex so this cartoon here shows with + + align:start position:0% +cortex so this cartoon here shows with + + + align:start position:0% +cortex so this cartoon here shows with +some major poetic license brain regions + + align:start position:0% +some major poetic license brain regions + + + align:start position:0% +some major poetic license brain regions +that are involved in different aspects + + align:start position:0% +that are involved in different aspects + + + align:start position:0% +that are involved in different aspects +of social cognition and it's just a big + + align:start position:0% +of social cognition and it's just a big + + + align:start position:0% +of social cognition and it's just a big +part of the cortical area as well + + align:start position:0% +part of the cortical area as well + + + align:start position:0% +part of the cortical area as well +okay another sense in which social + + align:start position:0% +okay another sense in which social + + + align:start position:0% +okay another sense in which social +cognition is of the essence in human + + align:start position:0% +cognition is of the essence in human + + + align:start position:0% +cognition is of the essence in human +intelligence is that many of the + + align:start position:0% +intelligence is that many of the + + + align:start position:0% +intelligence is that many of the +greatest things that humanity has + + align:start position:0% +greatest things that humanity has + + + align:start position:0% +greatest things that humanity has +accomplished our products of people + + align:start position:0% +accomplished our products of people + + + align:start position:0% +accomplished our products of people +working together so all of that is the + + align:start position:0% +working together so all of that is the + + + align:start position:0% +working together so all of that is the +big picture on why social cognition is + + align:start position:0% +big picture on why social cognition is + + + align:start position:0% +big picture on why social cognition is +cool and important and fundamental the + + align:start position:0% +cool and important and fundamental the + + + align:start position:0% +cool and important and fundamental the +part of it that we're focusing on in our + + align:start position:0% +part of it that we're focusing on in our + + + align:start position:0% +part of it that we're focusing on in our +thrust within this NSF grant is + + align:start position:0% +thrust within this NSF grant is + + + align:start position:0% +thrust within this NSF grant is +something I call social perception + + align:start position:0% +something I call social perception + + + align:start position:0% +something I call social perception +okay so bye social perception I mean + + align:start position:0% +okay so bye social perception I mean + + + align:start position:0% +okay so bye social perception I mean +this spectacularly impressive human + + align:start position:0% +this spectacularly impressive human + + + align:start position:0% +this spectacularly impressive human +ability to extract rich + + align:start position:0% +ability to extract rich + + + align:start position:0% +ability to extract rich +multi-dimensional social information + + align:start position:0% +multi-dimensional social information + + + align:start position:0% +multi-dimensional social information +from a brief glimpse of a scene from a + + align:start position:0% +from a brief glimpse of a scene from a + + + align:start position:0% +from a brief glimpse of a scene from a +brief glimpse at a person you can tell + + align:start position:0% +brief glimpse at a person you can tell + + + align:start position:0% +brief glimpse at a person you can tell +not just who that person is + + align:start position:0% +not just who that person is + + + align:start position:0% +not just who that person is +you can tell what they're trying to do + + align:start position:0% +you can tell what they're trying to do + + + align:start position:0% +you can tell what they're trying to do +you can tell how they feel you can tell + + align:start position:0% +you can tell how they feel you can tell + + + align:start position:0% +you can tell how they feel you can tell +what they're paying attention to hmm you + + align:start position:0% +what they're paying attention to hmm you + + + align:start position:0% +what they're paying attention to hmm you +can tell what they know and who they + + align:start position:0% +can tell what they know and who they + + + align:start position:0% +can tell what they know and who they +like okay and that's just a beginning + + align:start position:0% +like okay and that's just a beginning + + + align:start position:0% +like okay and that's just a beginning +okay so the work in our thrusts tries to + + align:start position:0% +okay so the work in our thrusts tries to + + + align:start position:0% +okay so the work in our thrusts tries to +approach all of these different kinds of + + align:start position:0% +approach all of these different kinds of + + + align:start position:0% +approach all of these different kinds of +questions that that we are calling as + + align:start position:0% +questions that that we are calling as + + + align:start position:0% +questions that that we are calling as +part of our you know PR of this NSF + + align:start position:0% +part of our you know PR of this NSF + + + align:start position:0% +part of our you know PR of this NSF +grant it's kind of an organizing + + align:start position:0% +grant it's kind of an organizing + + + align:start position:0% +grant it's kind of an organizing +principle the Turing questions these + + align:start position:0% +principle the Turing questions these + + + align:start position:0% +principle the Turing questions these +these kind of demanding difficult + + align:start position:0% +these kind of demanding difficult + + + align:start position:0% +these kind of demanding difficult +computational problems of social + + align:start position:0% +computational problems of social + + + align:start position:0% +computational problems of social +perception who is that person what are + + align:start position:0% +perception who is that person what are + + + align:start position:0% +perception who is that person what are +they paying attention to what are they + + align:start position:0% +they paying attention to what are they + + + align:start position:0% +they paying attention to what are they +feeling + + align:start position:0% +feeling + + + align:start position:0% +feeling +what are they like are they interacting + + align:start position:0% +what are they like are they interacting + + + align:start position:0% +what are they like are they interacting +with somebody what is the nature of that + + align:start position:0% +with somebody what is the nature of that + + + align:start position:0% +with somebody what is the nature of that +interaction and so on okay + + align:start position:0% +interaction and so on okay + + + align:start position:0% +interaction and so on okay +so the general plan of action and how to + + align:start position:0% +so the general plan of action and how to + + + align:start position:0% +so the general plan of action and how to +approach this and our thrust is first to + + align:start position:0% +approach this and our thrust is first to + + + align:start position:0% +approach this and our thrust is first to +study these abilities in the + + align:start position:0% +study these abilities in the + + + align:start position:0% +study these abilities in the +computational system that's best at them + + align:start position:0% +computational system that's best at them + + + align:start position:0% +computational system that's best at them +namely this one and those they're yours + + align:start position:0% +namely this one and those they're yours + + + align:start position:0% +namely this one and those they're yours +to the human brain and so the roadmap + + align:start position:0% +to the human brain and so the roadmap + + + align:start position:0% +to the human brain and so the roadmap +here is to first do psychophysics + + align:start position:0% +here is to first do psychophysics + + + align:start position:0% +here is to first do psychophysics +characterized what you know simple + + align:start position:0% +characterized what you know simple + + + align:start position:0% +characterized what you know simple +behavioral measurements what can people + + align:start position:0% +behavioral measurements what can people + + + align:start position:0% +behavioral measurements what can people +do what can't they do from simple + + align:start position:0% +do what can't they do from simple + + + align:start position:0% +do what can't they do from simple +stimuli and quantify that in detail ask + + align:start position:0% +stimuli and quantify that in detail ask + + + align:start position:0% +stimuli and quantify that in detail ask +how good are we at it maybe some of + + align:start position:0% +how good are we at it maybe some of + + + align:start position:0% +how good are we at it maybe some of +these things that we think we can do + + align:start position:0% +these things that we think we can do + + + align:start position:0% +these things that we think we can do +like size up somebody's personality in + + align:start position:0% +like size up somebody's personality in + + + align:start position:0% +like size up somebody's personality in +three seconds when we first meet them + + align:start position:0% +three seconds when we first meet them + + + align:start position:0% +three seconds when we first meet them +feels like you can do that or at least + + align:start position:0% +feels like you can do that or at least + + + align:start position:0% +feels like you can do that or at least +you get a read on them I mean is that + + align:start position:0% +you get a read on them I mean is that + + + align:start position:0% +you get a read on them I mean is that +based on anything is that just garbage + + align:start position:0% +based on anything is that just garbage + + + align:start position:0% +based on anything is that just garbage +right a service or anything or are we + + align:start position:0% +right a service or anything or are we + + + align:start position:0% +right a service or anything or are we +actually tapping into real information + + align:start position:0% +actually tapping into real information + + + align:start position:0% +actually tapping into real information +there what cues are we using we when we + + align:start position:0% +there what cues are we using we when we + + + align:start position:0% +there what cues are we using we when we +make those high level social inferences + + align:start position:0% +make those high level social inferences + + + align:start position:0% +make those high level social inferences +what is the input that we get that we + + align:start position:0% +what is the input that we get that we + + + align:start position:0% +what is the input that we get that we +use as a basis for you know analyzing + + align:start position:0% +use as a basis for you know analyzing + + + align:start position:0% +use as a basis for you know analyzing +this particular percept or throughout + + align:start position:0% +this particular percept or throughout + + + align:start position:0% +this particular percept or throughout +life that is that we've used to train up + + align:start position:0% +life that is that we've used to train up + + + align:start position:0% +life that is that we've used to train up +our brains to be able to do this + + align:start position:0% +our brains to be able to do this + + + align:start position:0% +our brains to be able to do this +so the second approach is once we have + + align:start position:0% +so the second approach is once we have + + + align:start position:0% +so the second approach is once we have +some kind of sense of what are those + + align:start position:0% +some kind of sense of what are those + + + align:start position:0% +some kind of sense of what are those +abilities that's like sometimes called + + align:start position:0% +abilities that's like sometimes called + + + align:start position:0% +abilities that's like sometimes called +Mars theory level kind of characterizing + + align:start position:0% +Mars theory level kind of characterizing + + + align:start position:0% +Mars theory level kind of characterizing +what can we do right as we can then try + + align:start position:0% +what can we do right as we can then try + + + align:start position:0% +what can we do right as we can then try +to computationally model this and so + + align:start position:0% +to computationally model this and so + + + align:start position:0% +to computationally model this and so +there's lots of different ways to do + + align:start position:0% +there's lots of different ways to do + + + align:start position:0% +there's lots of different ways to do +this and many of the other thrusts that + + align:start position:0% +this and many of the other thrusts that + + + align:start position:0% +this and many of the other thrusts that +you'll hear about are really tackling + + align:start position:0% +you'll hear about are really tackling + + + align:start position:0% +you'll hear about are really tackling +that problem another thing we can do is + + align:start position:0% +that problem another thing we can do is + + + align:start position:0% +that problem another thing we can do is +of course characterize the brain basis + + align:start position:0% +of course characterize the brain basis + + + align:start position:0% +of course characterize the brain basis +of these abilities and we can do that + + align:start position:0% +of these abilities and we can do that + + + align:start position:0% +of these abilities and we can do that +with all kinds of methods we're using in + + align:start position:0% +with all kinds of methods we're using in + + + align:start position:0% +with all kinds of methods we're using in +our thrust functional MRI intracranial + + align:start position:0% +our thrust functional MRI intracranial + + + align:start position:0% +our thrust functional MRI intracranial +recordings something called Neer's this + + align:start position:0% +recordings something called Neer's this + + + align:start position:0% +recordings something called Neer's this +is the ability to make measurements of + + align:start position:0% +is the ability to make measurements of + + + align:start position:0% +is the ability to make measurements of +blood flow changes in very young infants + + align:start position:0% +blood flow changes in very young infants + + + align:start position:0% +blood flow changes in very young infants +and so we can characterize these brain + + align:start position:0% +and so we can characterize these brain + + + align:start position:0% +and so we can characterize these brain +systems in adults and infants and that's + + align:start position:0% +systems in adults and infants and that's + + + align:start position:0% +systems in adults and infants and that's +gives you a leg up and understanding + + align:start position:0% +gives you a leg up and understanding + + + align:start position:0% +gives you a leg up and understanding +these other broader questions about how + + align:start position:0% +these other broader questions about how + + + align:start position:0% +these other broader questions about how +the whole system works in a number of + + align:start position:0% +the whole system works in a number of + + + align:start position:0% +the whole system works in a number of +different ways just seeing how the brain + + align:start position:0% +different ways just seeing how the brain + + + align:start position:0% +different ways just seeing how the brain +carves up the problem of social + + align:start position:0% +carves up the problem of social + + + align:start position:0% +carves up the problem of social +perception into pieces already gives you + + align:start position:0% +perception into pieces already gives you + + + align:start position:0% +perception into pieces already gives you +some clues about the kinds of + + align:start position:0% +some clues about the kinds of + + + align:start position:0% +some clues about the kinds of +computations that may go on in each of + + align:start position:0% +computations that may go on in each of + + + align:start position:0% +computations that may go on in each of +those pieces okay okay so that's the + + align:start position:0% +those pieces okay okay so that's the + + + align:start position:0% +those pieces okay okay so that's the +overview there's many many ways you can + + align:start position:0% +overview there's many many ways you can + + + align:start position:0% +overview there's many many ways you can +do this and of course people all over + + align:start position:0% +do this and of course people all over + + + align:start position:0% +do this and of course people all over +the place are doing this there's nothing + + align:start position:0% +the place are doing this there's nothing + + + align:start position:0% +the place are doing this there's nothing +all that you know unique about it this + + align:start position:0% +all that you know unique about it this + + + align:start position:0% +all that you know unique about it this +is just our our framework here some of + + align:start position:0% +is just our our framework here some of + + + align:start position:0% +is just our our framework here some of +the specific projects that are going on + + align:start position:0% +the specific projects that are going on + + + align:start position:0% +the specific projects that are going on +include some work on face recognition + + align:start position:0% +include some work on face recognition + + + align:start position:0% +include some work on face recognition +which of course are really classic + + align:start position:0% +which of course are really classic + + + align:start position:0% +which of course are really classic +question that many people have been + + align:start position:0% +question that many people have been + + + align:start position:0% +question that many people have been +approaching my postdoc Matt Peterson + + align:start position:0% +approaching my postdoc Matt Peterson + + + align:start position:0% +approaching my postdoc Matt Peterson +here has done some very lovely work + + align:start position:0% +here has done some very lovely work + + + align:start position:0% +here has done some very lovely work +where he's shown that actually where you + + align:start position:0% +where he's shown that actually where you + + + align:start position:0% +where he's shown that actually where you +look on a face is very systematic you + + align:start position:0% +look on a face is very systematic you + + + align:start position:0% +look on a face is very systematic you +don't just kind of look anywhere right + + align:start position:0% +don't just kind of look anywhere right + + + align:start position:0% +don't just kind of look anywhere right +when you first make a saccade into a + + align:start position:0% +when you first make a saccade into a + + + align:start position:0% +when you first make a saccade into a +face somebody appears in your visual + + align:start position:0% +face somebody appears in your visual + + + align:start position:0% +face somebody appears in your visual +periphery right of course all that the + + align:start position:0% +periphery right of course all that the + + + align:start position:0% +periphery right of course all that the +high-resolution visual abilities are all + + align:start position:0% +high-resolution visual abilities are all + + + align:start position:0% +high-resolution visual abilities are all +right near the center of gaze around the + + align:start position:0% +right near the center of gaze around the + + + align:start position:0% +right near the center of gaze around the +fovea where you have a high density of + + align:start position:0% +fovea where you have a high density of + + + align:start position:0% +fovea where you have a high density of +photoreceptors and a shitload of cortex + + align:start position:0% +photoreceptors and a shitload of cortex + + + align:start position:0% +photoreceptors and a shitload of cortex +to be technical about it + + align:start position:0% +to be technical about it + + + align:start position:0% +to be technical about it +devoted to allocating the center of gaze + + align:start position:0% +devoted to allocating the center of gaze + + + align:start position:0% +devoted to allocating the center of gaze +right back here in primary visual cortex + + align:start position:0% +right back here in primary visual cortex + + + align:start position:0% +right back here in primary visual cortex +you have and with the first few + + align:start position:0% +you have and with the first few + + + align:start position:0% +you have and with the first few +retinotopic regions you have 20 square + + align:start position:0% +retinotopic regions you have 20 square + + + align:start position:0% +retinotopic regions you have 20 square +centimeters that's like that of cortex + + align:start position:0% +centimeters that's like that of cortex + + + align:start position:0% +centimeters that's like that of cortex +allocated to just the central 2 degrees + + align:start position:0% +allocated to just the central 2 degrees + + + align:start position:0% +allocated to just the central 2 degrees +of vision right so you have a lot of + + align:start position:0% +of vision right so you have a lot of + + + align:start position:0% +of vision right so you have a lot of +computational machinery doing just that + + align:start position:0% +computational machinery doing just that + + + align:start position:0% +computational machinery doing just that +bit right there + + align:start position:0% +bit right there + + + align:start position:0% +bit right there +well when you when a face appears in + + align:start position:0% +well when you when a face appears in + + + align:start position:0% +well when you when a face appears in +your periphery you move that bit of your + + align:start position:0% +your periphery you move that bit of your + + + align:start position:0% +your periphery you move that bit of your +cortex boom right on top of it so you + + align:start position:0% +cortex boom right on top of it so you + + + align:start position:0% +cortex boom right on top of it so you +have all that computational machinery to + + align:start position:0% +have all that computational machinery to + + + align:start position:0% +have all that computational machinery to +dig in on the face right okay so what + + align:start position:0% +dig in on the face right okay so what + + + align:start position:0% +dig in on the face right okay so what +matt has shown is that the particular + + align:start position:0% +matt has shown is that the particular + + + align:start position:0% +matt has shown is that the particular +way that you allocate that computational + + align:start position:0% +way that you allocate that computational + + + align:start position:0% +way that you allocate that computational +machinery namely by making an eye + + align:start position:0% +machinery namely by making an eye + + + align:start position:0% +machinery namely by making an eye +movement to put that stimulus right on + + align:start position:0% +movement to put that stimulus right on + + + align:start position:0% +movement to put that stimulus right on +your phobia people do that slightly + + align:start position:0% +your phobia people do that slightly + + + align:start position:0% +your phobia people do that slightly +differently + + align:start position:0% +differently + + + align:start position:0% +differently +some people fixate on a face up here + + align:start position:0% +some people fixate on a face up here + + + align:start position:0% +some people fixate on a face up here +some people fixate on a face down there + + align:start position:0% +some people fixate on a face down there + + + align:start position:0% +some people fixate on a face down there +and most people fixate someplace in the + + align:start position:0% +and most people fixate someplace in the + + + align:start position:0% +and most people fixate someplace in the +middle okay well so why is that + + align:start position:0% +middle okay well so why is that + + + align:start position:0% +middle okay well so why is that +interesting here's why it's interesting + + align:start position:0% +interesting here's why it's interesting + + + align:start position:0% +interesting here's why it's interesting +people do that in very systematic ways + + align:start position:0% +people do that in very systematic ways + + + align:start position:0% +people do that in very systematic ways +and if you look up here you pretty much + + align:start position:0% +and if you look up here you pretty much + + + align:start position:0% +and if you look up here you pretty much +always look up there and if you look + + align:start position:0% +always look up there and if you look + + + align:start position:0% +always look up there and if you look +down there you pretty much always look + + align:start position:0% +down there you pretty much always look + + + align:start position:0% +down there you pretty much always look +down there + + align:start position:0% +down there + + + align:start position:0% +down there +and this has computational consequences + + align:start position:0% +and this has computational consequences + + + align:start position:0% +and this has computational consequences +if we brought you guys into the lab and + + align:start position:0% +if we brought you guys into the lab and + + + align:start position:0% +if we brought you guys into the lab and +ran you on an eye tracker for 15 minutes + + align:start position:0% +ran you on an eye tracker for 15 minutes + + + align:start position:0% +ran you on an eye tracker for 15 minutes +we'd find out which if you look up there + + align:start position:0% +we'd find out which if you look up there + + + align:start position:0% +we'd find out which if you look up there +and which if you look down there and if + + align:start position:0% +and which if you look down there and if + + + align:start position:0% +and which if you look down there and if +we took the those of you who look up + + align:start position:0% +we took the those of you who look up + + + align:start position:0% +we took the those of you who look up +here and we presented a face by flashing + + align:start position:0% +here and we presented a face by flashing + + + align:start position:0% +here and we presented a face by flashing +it briefly while you're fixating so that + + align:start position:0% +it briefly while you're fixating so that + + + align:start position:0% +it briefly while you're fixating so that +the face landed in you're not preferred + + align:start position:0% +the face landed in you're not preferred + + + align:start position:0% +the face landed in you're not preferred +looking position your accuracy at + + align:start position:0% +looking position your accuracy at + + + align:start position:0% +looking position your accuracy at +recognizing that face would be much + + align:start position:0% +recognizing that face would be much + + + align:start position:0% +recognizing that face would be much +lower and vice-versa if you're one of + + align:start position:0% +lower and vice-versa if you're one of + + + align:start position:0% +lower and vice-versa if you're one of +the people who looks down there we flash + + align:start position:0% +the people who looks down there we flash + + + align:start position:0% +the people who looks down there we flash +up a face so that it lands right there + + align:start position:0% +up a face so that it lands right there + + + align:start position:0% +up a face so that it lands right there +on your retina you're much worse at + + align:start position:0% +on your retina you're much worse at + + + align:start position:0% +on your retina you're much worse at +recognizing it and what that means is + + align:start position:0% +recognizing it and what that means is + + + align:start position:0% +recognizing it and what that means is +that this fundamental problem that + + align:start position:0% +that this fundamental problem that + + + align:start position:0% +that this fundamental problem that +you'll hear about in the course that + + align:start position:0% +you'll hear about in the course that + + + align:start position:0% +you'll hear about in the course that +Tommy has worked at and many people it's + + align:start position:0% +Tommy has worked at and many people it's + + + align:start position:0% +Tommy has worked at and many people it's +one of the central problems of vision + + align:start position:0% +one of the central problems of vision + + + align:start position:0% +one of the central problems of vision +research of how we deal with the many + + align:start position:0% +research of how we deal with the many + + + align:start position:0% +research of how we deal with the many +different ways an object the many + + align:start position:0% +different ways an object the many + + + align:start position:0% +different ways an object the many +different kinds of images an object can + + align:start position:0% +different kinds of images an object can + + + align:start position:0% +different kinds of images an object can +make on our retina by where it lands on + + align:start position:0% +make on our retina by where it lands on + + + align:start position:0% +make on our retina by where it lands on +the retina how close it is to you the + + align:start position:0% +the retina how close it is to you the + + + align:start position:0% +the retina how close it is to you the +orientation the lighting all these + + align:start position:0% +orientation the lighting all these + + + align:start position:0% +orientation the lighting all these +things that that create the central + + align:start position:0% +things that that create the central + + + align:start position:0% +things that that create the central +problem and vision of the variable ways + + align:start position:0% +problem and vision of the variable ways + + + align:start position:0% +problem and vision of the variable ways +an object can look a big part of how we + + align:start position:0% +an object can look a big part of how we + + + align:start position:0% +an object can look a big part of how we +solve that for face recognition is we + + align:start position:0% +solve that for face recognition is we + + + align:start position:0% +solve that for face recognition is we +just move our eyes to the same place + + align:start position:0% +just move our eyes to the same place + + + align:start position:0% +just move our eyes to the same place +position invariance problem solved + + align:start position:0% +position invariance problem solved + + + align:start position:0% +position invariance problem solved +mostly it's kind of a low-tech solution + + align:start position:0% +mostly it's kind of a low-tech solution + + + align:start position:0% +mostly it's kind of a low-tech solution +it's a good one okay anyway so mat has + + align:start position:0% +it's a good one okay anyway so mat has + + + align:start position:0% +it's a good one okay anyway so mat has +been working on that for a while + + align:start position:0% +been working on that for a while + + + align:start position:0% +been working on that for a while +and so now most of that is lab studies + + align:start position:0% +and so now most of that is lab studies + + + align:start position:0% +and so now most of that is lab studies +now what he's done is he's using mobile + + align:start position:0% +now what he's done is he's using mobile + + + align:start position:0% +now what he's done is he's using mobile +eye trackers which looked like this and + + align:start position:0% +eye trackers which looked like this and + + + align:start position:0% +eye trackers which looked like this and +a little GoPro attached to his head + + align:start position:0% +a little GoPro attached to his head + + + align:start position:0% +a little GoPro attached to his head +because the mobile eye trackers don't + + align:start position:0% +because the mobile eye trackers don't + + + align:start position:0% +because the mobile eye trackers don't +have very good image resolution and so + + align:start position:0% +have very good image resolution and so + + + align:start position:0% +have very good image resolution and so +he's sending people + + align:start position:0% +he's sending people + + + align:start position:0% +he's sending people +the world and he's finding that first of + + align:start position:0% +the world and he's finding that first of + + + align:start position:0% +the world and he's finding that first of +all yes in fact when you're walking + + align:start position:0% +all yes in fact when you're walking + + + align:start position:0% +all yes in fact when you're walking +around in the world not just when you're + + align:start position:0% +around in the world not just when you're + + + align:start position:0% +around in the world not just when you're +you know on a bike bar and a lab with a + + align:start position:0% +you know on a bike bar and a lab with a + + + align:start position:0% +you know on a bike bar and a lab with a +you know with the tracker and a screen + + align:start position:0% +you know with the tracker and a screen + + + align:start position:0% +you know with the tracker and a screen +the people who look up here also look up + + align:start position:0% +the people who look up here also look up + + + align:start position:0% +the people who look up here also look up +there in the world right so that's just + + align:start position:0% +there in the world right so that's just + + + align:start position:0% +there in the world right so that's just +a reality check shows that our + + align:start position:0% +a reality check shows that our + + + align:start position:0% +a reality check shows that our +technology is working and now Matt is + + align:start position:0% +technology is working and now Matt is + + + align:start position:0% +technology is working and now Matt is +using this to ask all kinds of questions + + align:start position:0% +using this to ask all kinds of questions + + + align:start position:0% +using this to ask all kinds of questions +for example social interactions where do + + align:start position:0% +for example social interactions where do + + + align:start position:0% +for example social interactions where do +people look in social interactions can + + align:start position:0% +people look in social interactions can + + + align:start position:0% +people look in social interactions can +you tell stuff about what they think + + align:start position:0% +you tell stuff about what they think + + + align:start position:0% +you tell stuff about what they think +about each other based on where they + + align:start position:0% +about each other based on where they + + + align:start position:0% +about each other based on where they +look on faces right we want to run this + + align:start position:0% +look on faces right we want to run this + + + align:start position:0% +look on faces right we want to run this +is fruit even we haven't set it up yet + + align:start position:0% +is fruit even we haven't set it up yet + + + align:start position:0% +is fruit even we haven't set it up yet +but we want to run speed dating + + align:start position:0% +but we want to run speed dating + + + align:start position:0% +but we want to run speed dating +experiments in the lab with people + + align:start position:0% +experiments in the lab with people + + + align:start position:0% +experiments in the lab with people +wearing eye trackers I bet in the first + + align:start position:0% +wearing eye trackers I bet in the first + + + align:start position:0% +wearing eye trackers I bet in the first +few fixation positions you can tell + + align:start position:0% +few fixation positions you can tell + + + align:start position:0% +few fixation positions you can tell +who's gonna want to recontact to I don't + + align:start position:0% +who's gonna want to recontact to I don't + + + align:start position:0% +who's gonna want to recontact to I don't +know we haven't done that yet okay + + align:start position:0% +know we haven't done that yet okay + + + align:start position:0% +know we haven't done that yet okay +that's a little trashy but it's kind of + + align:start position:0% +that's a little trashy but it's kind of + + + align:start position:0% +that's a little trashy but it's kind of +interesting some interesting scientific + + align:start position:0% +interesting some interesting scientific + + + align:start position:0% +interesting some interesting scientific +questions are a little bit thrashing you + + align:start position:0% +questions are a little bit thrashing you + + + align:start position:0% +questions are a little bit thrashing you +know some trashy questions are not + + align:start position:0% +know some trashy questions are not + + + align:start position:0% +know some trashy questions are not +scientifically interesting I think + + align:start position:0% +scientifically interesting I think + + + align:start position:0% +scientifically interesting I think +that's one of those rare that's actually + + align:start position:0% +that's one of those rare that's actually + + + align:start position:0% +that's one of those rare that's actually +both anyway we also want to characterize + + align:start position:0% +both anyway we also want to characterize + + + align:start position:0% +both anyway we also want to characterize +a whole other part of this is is this + + align:start position:0% +a whole other part of this is is this + + + align:start position:0% +a whole other part of this is is this +question that people have been + + align:start position:0% +question that people have been + + + align:start position:0% +question that people have been +considering for a few decades now of + + align:start position:0% +considering for a few decades now of + + + align:start position:0% +considering for a few decades now of +natural image statistics right so people + + align:start position:0% +natural image statistics right so people + + + align:start position:0% +natural image statistics right so people +have done all this stuff collecting + + align:start position:0% +have done all this stuff collecting + + + align:start position:0% +have done all this stuff collecting +images and at first they did it you know + + align:start position:0% +images and at first they did it you know + + + align:start position:0% +images and at first they did it you know +really low-tech and then the web + + align:start position:0% +really low-tech and then the web + + + align:start position:0% +really low-tech and then the web +appeared it's like oh now there's like a + + align:start position:0% +appeared it's like oh now there's like a + + + align:start position:0% +appeared it's like oh now there's like a +lot of images out there we can just + + align:start position:0% +lot of images out there we can just + + + align:start position:0% +lot of images out there we can just +collect them easily and let's + + align:start position:0% +collect them easily and let's + + + align:start position:0% +collect them easily and let's +characterize them what are natural + + align:start position:0% +characterize them what are natural + + + align:start position:0% +characterize them what are natural +images like so it's a whole set of math + + align:start position:0% +images like so it's a whole set of math + + + align:start position:0% +images like so it's a whole set of math +where people have looked at those + + align:start position:0% +where people have looked at those + + + align:start position:0% +where people have looked at those +natural images and characterized them + + align:start position:0% +natural images and characterized them + + + align:start position:0% +natural images and characterized them +and tried to ask how the statistical + + align:start position:0% +and tried to ask how the statistical + + + align:start position:0% +and tried to ask how the statistical +properties of natural images have how we + + align:start position:0% +properties of natural images have how we + + + align:start position:0% +properties of natural images have how we +have adjusted our visual systems to deal + + align:start position:0% +have adjusted our visual systems to deal + + + align:start position:0% +have adjusted our visual systems to deal +with the images that we confront and + + align:start position:0% +with the images that we confront and + + + align:start position:0% +with the images that we confront and +that's a cool and important area of + + align:start position:0% +that's a cool and important area of + + + align:start position:0% +that's a cool and important area of +research but in all of that work + + align:start position:0% +research but in all of that work + + + align:start position:0% +research but in all of that work +nobody's actually asked nobody's + + align:start position:0% +nobody's actually asked nobody's + + + align:start position:0% +nobody's actually asked nobody's +actually used real natural images right + + align:start position:0% +actually used real natural images right + + + align:start position:0% +actually used real natural images right +the image is on the web somebody stuck a + + align:start position:0% +the image is on the web somebody stuck a + + + align:start position:0% +the image is on the web somebody stuck a +camera and put it there and then they + + align:start position:0% +camera and put it there and then they + + + align:start position:0% +camera and put it there and then they +threw away you know most of the pictures + + align:start position:0% +threw away you know most of the pictures + + + align:start position:0% +threw away you know most of the pictures +they took the ones that land on the web + + align:start position:0% +they took the ones that land on the web + + + align:start position:0% +they took the ones that land on the web +are the ones that you know have good + + align:start position:0% +are the ones that you know have good + + + align:start position:0% +are the ones that you know have good +resolution where people weren't moving + + align:start position:0% +resolution where people weren't moving + + + align:start position:0% +resolution where people weren't moving +in and out of frame things weren't + + align:start position:0% +in and out of frame things weren't + + + align:start position:0% +in and out of frame things weren't +occluded they're not at all like the + + align:start position:0% +occluded they're not at all like the + + + align:start position:0% +occluded they're not at all like the +actual images that land on your retina + + align:start position:0% +actual images that land on your retina + + + align:start position:0% +actual images that land on your retina +so we're collecting the actual images + + align:start position:0% +so we're collecting the actual images + + + align:start position:0% +so we're collecting the actual images +that ran lead on your retina and we're + + align:start position:0% +that ran lead on your retina and we're + + + align:start position:0% +that ran lead on your retina and we're +doing with mobile eye trackers sending + + align:start position:0% +doing with mobile eye trackers sending + + + align:start position:0% +doing with mobile eye trackers sending +people around in the world using these + + align:start position:0% +people around in the world using these + + + align:start position:0% +people around in the world using these +nice GoPro system to give us high-res + + align:start position:0% +nice GoPro system to give us high-res + + + align:start position:0% +nice GoPro system to give us high-res +and importantly not only are we + + align:start position:0% +and importantly not only are we + + + align:start position:0% +and importantly not only are we +collecting real natural image statistics + + align:start position:0% +collecting real natural image statistics + + + align:start position:0% +collecting real natural image statistics +from these real natural images we know + + align:start position:0% +from these real natural images we know + + + align:start position:0% +from these real natural images we know +for each frame where the person was + + align:start position:0% +for each frame where the person was + + + align:start position:0% +for each frame where the person was +looking and that's important for the + + align:start position:0% +looking and that's important for the + + + align:start position:0% +looking and that's important for the +reason I mentioned a while ago that most + + align:start position:0% +reason I mentioned a while ago that most + + + align:start position:0% +reason I mentioned a while ago that most +of your high resolution information is + + align:start position:0% +of your high resolution information is + + + align:start position:0% +of your high resolution information is +right at the center of gaze and your you + + align:start position:0% +right at the center of gaze and your you + + + align:start position:0% +right at the center of gaze and your you +know the information out in the + + align:start position:0% +know the information out in the + + + align:start position:0% +know the information out in the +periphery is pretty lousy okay so that's + + align:start position:0% +periphery is pretty lousy okay so that's + + + align:start position:0% +periphery is pretty lousy okay so that's +one project that I described too long so + + align:start position:0% +one project that I described too long so + + + align:start position:0% +one project that I described too long so +I'll whip through the others more + + align:start position:0% +I'll whip through the others more + + + align:start position:0% +I'll whip through the others more +briefly we want to know where how well + + align:start position:0% +briefly we want to know where how well + + + align:start position:0% +briefly we want to know where how well +people can read each other's direction + + align:start position:0% +people can read each other's direction + + + align:start position:0% +people can read each other's direction +of attention okay so when I'm lecturing + + align:start position:0% +of attention okay so when I'm lecturing + + + align:start position:0% +of attention okay so when I'm lecturing +now if you guys get bored and look at + + align:start position:0% +now if you guys get bored and look at + + + align:start position:0% +now if you guys get bored and look at +the clock I will see it right and that's + + align:start position:0% +the clock I will see it right and that's + + + align:start position:0% +the clock I will see it right and that's +just one of these things you know we're + + align:start position:0% +just one of these things you know we're + + + align:start position:0% +just one of these things you know we're +very attuned to where each other are + + align:start position:0% +very attuned to where each other are + + + align:start position:0% +very attuned to where each other are +looking and that's very useful + + align:start position:0% +looking and that's very useful + + + align:start position:0% +looking and that's very useful +information you meet somebody at a + + align:start position:0% +information you meet somebody at a + + + align:start position:0% +information you meet somebody at a +conference and you see them make a + + align:start position:0% +conference and you see them make a + + + align:start position:0% +conference and you see them make a +saccade down to your named hang it's + + align:start position:0% +saccade down to your named hang it's + + + align:start position:0% +saccade down to your named hang it's +like Danny doesn't this person Remember + + align:start position:0% +like Danny doesn't this person Remember + + + align:start position:0% +like Danny doesn't this person Remember +Who I am you know I'm very aware of this + + align:start position:0% +Who I am you know I'm very aware of this + + + align:start position:0% +Who I am you know I'm very aware of this +because I'm mildly prosopagnosia so if + + align:start position:0% +because I'm mildly prosopagnosia so if + + + align:start position:0% +because I'm mildly prosopagnosia so if +I've met you before and I'm like slow to + + align:start position:0% +I've met you before and I'm like slow to + + + align:start position:0% +I've met you before and I'm like slow to +register don't take it personally I'm + + align:start position:0% +register don't take it personally I'm + + + align:start position:0% +register don't take it personally I'm +just lousy it takes me a long time to + + align:start position:0% +just lousy it takes me a long time to + + + align:start position:0% +just lousy it takes me a long time to +encode a face anyway we're very attuned + + align:start position:0% +encode a face anyway we're very attuned + + + align:start position:0% +encode a face anyway we're very attuned +at where each other are looking and so + + align:start position:0% +at where each other are looking and so + + + align:start position:0% +at where each other are looking and so +there's been a lot of work on how + + align:start position:0% +there's been a lot of work on how + + + align:start position:0% +there's been a lot of work on how +precisely we can tell whether somebody's + + align:start position:0% +precisely we can tell whether somebody's + + + align:start position:0% +precisely we can tell whether somebody's +looking right at you versus off to the + + align:start position:0% +looking right at you versus off to the + + + align:start position:0% +looking right at you versus off to the +side try this at lunch when you're in + + align:start position:0% +side try this at lunch when you're in + + + align:start position:0% +side try this at lunch when you're in +the middle of a conversation with + + align:start position:0% +the middle of a conversation with + + + align:start position:0% +the middle of a conversation with +somebody fixate on just the side of + + align:start position:0% +somebody fixate on just the side of + + + align:start position:0% +somebody fixate on just the side of +their face not way off to the side just + + align:start position:0% +their face not way off to the side just + + + align:start position:0% +their face not way off to the side just +like here and just do that for a few + + align:start position:0% +like here and just do that for a few + + + align:start position:0% +like here and just do that for a few +seconds it's deeply weird the person + + align:start position:0% +seconds it's deeply weird the person + + + align:start position:0% +seconds it's deeply weird the person +you're talking to will detect it + + align:start position:0% +you're talking to will detect it + + + align:start position:0% +you're talking to will detect it +immediately will feel uncomfortable + + align:start position:0% +immediately will feel uncomfortable + + + align:start position:0% +immediately will feel uncomfortable +until they realize what you're doing and + + align:start position:0% +until they realize what you're doing and + + + align:start position:0% +until they realize what you're doing and +then you guys will have a good laugh and + + align:start position:0% +then you guys will have a good laugh and + + + align:start position:0% +then you guys will have a good laugh and +that will show you how exquisitely + + align:start position:0% +that will show you how exquisitely + + + align:start position:0% +that will show you how exquisitely +precise your ability to read another + + align:start position:0% +precise your ability to read another + + + align:start position:0% +precise your ability to read another +person's gaze is it's really very + + align:start position:0% +person's gaze is it's really very + + + align:start position:0% +person's gaze is it's really very +precisely tuned okay so there's a lot of + + align:start position:0% +precisely tuned okay so there's a lot of + + + align:start position:0% +precisely tuned okay so there's a lot of +work on that but there's less work on + + align:start position:0% +work on that but there's less work on + + + align:start position:0% +work on that but there's less work on +how well I can tell a what exactly + + align:start position:0% +how well I can tell a what exactly + + + align:start position:0% +how well I can tell a what exactly +you're looking at if it's not me that is + + align:start position:0% +you're looking at if it's not me that is + + + align:start position:0% +you're looking at if it's not me that is +I can tell if you're looking at me or + + align:start position:0% +I can tell if you're looking at me or + + + align:start position:0% +I can tell if you're looking at me or +off to the side or this side or that + + align:start position:0% +off to the side or this side or that + + + align:start position:0% +off to the side or this side or that +side but what we're looking at is how + + align:start position:0% +side but what we're looking at is how + + + align:start position:0% +side but what we're looking at is how +well can I tell what object you're + + align:start position:0% +well can I tell what object you're + + + align:start position:0% +well can I tell what object you're +looking at and that's an important + + align:start position:0% +looking at and that's an important + + + align:start position:0% +looking at and that's an important +question because many people have + + align:start position:0% +question because many people have + + + align:start position:0% +question because many people have +pointed out that a kind of central + + align:start position:0% +pointed out that a kind of central + + + align:start position:0% +pointed out that a kind of central +little microcosm kind of unit of social + + align:start position:0% +little microcosm kind of unit of social + + + align:start position:0% +little microcosm kind of unit of social +interaction is something called joint + + align:start position:0% +interaction is something called joint + + + align:start position:0% +interaction is something called joint +attention joint attention is when you're + + align:start position:0% +attention joint attention is when you're + + + align:start position:0% +attention joint attention is when you're +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +this thing and I'm looking at it and I + + align:start position:0% +this thing and I'm looking at it and I + + + align:start position:0% +this thing and I'm looking at it and I +know you're looking at it and you know + + align:start position:0% +know you're looking at it and you know + + + align:start position:0% +know you're looking at it and you know +I'm looking at it that's a cosmic little + + align:start position:0% +I'm looking at it that's a cosmic little + + + align:start position:0% +I'm looking at it that's a cosmic little +thing like we can have this little + + align:start position:0% +thing like we can have this little + + + align:start position:0% +thing like we can have this little +moment right joint attention okay and + + align:start position:0% +moment right joint attention okay and + + + align:start position:0% +moment right joint attention okay and +people have argued that that's of the + + align:start position:0% +people have argued that that's of the + + + align:start position:0% +people have argued that that's of the +essence in children learning language + + align:start position:0% +essence in children learning language + + + align:start position:0% +essence in children learning language +it's of the essence of all kinds of + + align:start position:0% +it's of the essence of all kinds of + + + align:start position:0% +it's of the essence of all kinds of +social interactions and by most accounts + + align:start position:0% +social interactions and by most accounts + + + align:start position:0% +social interactions and by most accounts +no other species has it not even chimps + + align:start position:0% +no other species has it not even chimps + + + align:start position:0% +no other species has it not even chimps +okay I mean there's still some debate + + align:start position:0% +okay I mean there's still some debate + + + align:start position:0% +okay I mean there's still some debate +about this and people niggle and stuff + + align:start position:0% +about this and people niggle and stuff + + + align:start position:0% +about this and people niggle and stuff +but basically they don't have it in + + align:start position:0% +but basically they don't have it in + + + align:start position:0% +but basically they don't have it in +anything like the way we have it so we + + align:start position:0% +anything like the way we have it so we + + + align:start position:0% +anything like the way we have it so we +want to know what is the acuity of joint + + align:start position:0% +want to know what is the acuity of joint + + + align:start position:0% +want to know what is the acuity of joint +attention okay so I'm supposed to do + + align:start position:0% +attention okay so I'm supposed to do + + + align:start position:0% +attention okay so I'm supposed to do +that briefly I can't seem to like be + + align:start position:0% +that briefly I can't seem to like be + + + align:start position:0% +that briefly I can't seem to like be +brief okay + + align:start position:0% +brief okay + + + align:start position:0% +brief okay +so that's a whole project that's going + + align:start position:0% +so that's a whole project that's going + + + align:start position:0% +so that's a whole project that's going +on with Danny Harare and tau Gow we're + + align:start position:0% +on with Danny Harare and tau Gow we're + + + align:start position:0% +on with Danny Harare and tau Gow we're +also asking how well people can predict + + align:start position:0% +also asking how well people can predict + + + align:start position:0% +also asking how well people can predict +the target of another person's action + + align:start position:0% +the target of another person's action + + + align:start position:0% +the target of another person's action +right so if I go out to reach this at + + align:start position:0% +right so if I go out to reach this at + + + align:start position:0% +right so if I go out to reach this at +one point what was only one thing there + + align:start position:0% +one point what was only one thing there + + + align:start position:0% +one point what was only one thing there +but if we had a whole array of things at + + align:start position:0% +but if we had a whole array of things at + + + align:start position:0% +but if we had a whole array of things at +one point when I'm reaching for an + + align:start position:0% +one point when I'm reaching for an + + + align:start position:0% +one point when I'm reaching for an +object can you extrapolate my trajectory + + align:start position:0% +object can you extrapolate my trajectory + + + align:start position:0% +object can you extrapolate my trajectory +look at my eye gaze and use all of those + + align:start position:0% +look at my eye gaze and use all of those + + + align:start position:0% +look at my eye gaze and use all of those +cues to figure out what I what is the + + align:start position:0% +cues to figure out what I what is the + + + align:start position:0% +cues to figure out what I what is the +goal of my action here's a cool way to + + align:start position:0% +goal of my action here's a cool way to + + + align:start position:0% +goal of my action here's a cool way to +look at at how well people can predict + + align:start position:0% +look at at how well people can predict + + + align:start position:0% +look at at how well people can predict +each other's actions this is work by + + align:start position:0% +each other's actions this is work by + + + align:start position:0% +each other's actions this is work by +Miriam Weiser a posh comb shown here + + align:start position:0% +Miriam Weiser a posh comb shown here + + + align:start position:0% +Miriam Weiser a posh comb shown here +who's a postdoc at Harvard working with + + align:start position:0% +who's a postdoc at Harvard working with + + + align:start position:0% +who's a postdoc at Harvard working with +Ken Nakayama who will give a lecture + + align:start position:0% +Ken Nakayama who will give a lecture + + + align:start position:0% +Ken Nakayama who will give a lecture +later in the course and what they are + + align:start position:0% +later in the course and what they are + + + align:start position:0% +later in the course and what they are +trying to do is get an online read of + + align:start position:0% +trying to do is get an online read of + + + align:start position:0% +trying to do is get an online read of +how well people can predict each other's + + align:start position:0% +how well people can predict each other's + + + align:start position:0% +how well people can predict each other's +actions and so obviously this happens in + + align:start position:0% +actions and so obviously this happens in + + + align:start position:0% +actions and so obviously this happens in +all kinds of situations especially in + + align:start position:0% +all kinds of situations especially in + + + align:start position:0% +all kinds of situations especially in +sports right if if you're playing + + align:start position:0% +sports right if if you're playing + + + align:start position:0% +sports right if if you're playing +basketball or Ultimate Frisbee it's all + + align:start position:0% +basketball or Ultimate Frisbee it's all + + + align:start position:0% +basketball or Ultimate Frisbee it's all +about predicting who's gonna go where + + align:start position:0% +about predicting who's gonna go where + + + align:start position:0% +about predicting who's gonna go where +win and try to take that into account + + align:start position:0% +win and try to take that into account + + + align:start position:0% +win and try to take that into account +with your actions so they've set this up + + align:start position:0% +with your actions so they've set this up + + + align:start position:0% +with your actions so they've set this up +in the lab and they have a piece of + + align:start position:0% +in the lab and they have a piece of + + + align:start position:0% +in the lab and they have a piece of +glass here and there's two post-its on + + align:start position:0% +glass here and there's two post-its on + + + align:start position:0% +glass here and there's two post-its on +this piece of glass and one person's + + align:start position:0% +this piece of glass and one person's + + + align:start position:0% +this piece of glass and one person's +task is to reach out and touch one of + + align:start position:0% +task is to reach out and touch one of + + + align:start position:0% +task is to reach out and touch one of +those targets quickly and the other + + align:start position:0% +those targets quickly and the other + + + align:start position:0% +those targets quickly and the other +person who's goalie watches them through + + align:start position:0% +person who's goalie watches them through + + + align:start position:0% +person who's goalie watches them through +the glass and tries to touch that target + + align:start position:0% +the glass and tries to touch that target + + + align:start position:0% +the glass and tries to touch that target +as soon as possible after the first one + + align:start position:0% +as soon as possible after the first one + + + align:start position:0% +as soon as possible after the first one +does okay and so it's just like a basic + + align:start position:0% +does okay and so it's just like a basic + + + align:start position:0% +does okay and so it's just like a basic +little game and so they have little + + align:start position:0% +little game and so they have little + + + align:start position:0% +little game and so they have little +sensors on the each person's finger so + + align:start position:0% +sensors on the each person's finger so + + + align:start position:0% +sensors on the each person's finger so +they can track the exact trajectories + + align:start position:0% +they can track the exact trajectories + + + align:start position:0% +they can track the exact trajectories +and get reaction times they're just + + align:start position:0% +and get reaction times they're just + + + align:start position:0% +and get reaction times they're just +behavioral measurements but they're very + + align:start position:0% +behavioral measurements but they're very + + + align:start position:0% +behavioral measurements but they're very +cool so what they find first of all is + + align:start position:0% +cool so what they find first of all is + + + align:start position:0% +cool so what they find first of all is +that the goalie the person + + align:start position:0% +that the goalie the person + + + align:start position:0% +that the goalie the person +to reach to respond to the other person + + align:start position:0% +to reach to respond to the other person + + + align:start position:0% +to reach to respond to the other person +can do that extremely fast right they + + align:start position:0% +can do that extremely fast right they + + + align:start position:0% +can do that extremely fast right they +launched their hand to the correct + + align:start position:0% +launched their hand to the correct + + + align:start position:0% +launched their hand to the correct +target within a hundred and fifty + + align:start position:0% +target within a hundred and fifty + + + align:start position:0% +target within a hundred and fifty +milliseconds you should immediately + + align:start position:0% +milliseconds you should immediately + + + align:start position:0% +milliseconds you should immediately +realize that something's fishy you can't + + align:start position:0% +realize that something's fishy you can't + + + align:start position:0% +realize that something's fishy you can't +do that it takes about a hundred + + align:start position:0% +do that it takes about a hundred + + + align:start position:0% +do that it takes about a hundred +milliseconds just to get to v1 it takes + + align:start position:0% +milliseconds just to get to v1 it takes + + + align:start position:0% +milliseconds just to get to v1 it takes +I forget how long but a few tens of + + align:start position:0% +I forget how long but a few tens of + + + align:start position:0% +I forget how long but a few tens of +milliseconds to send the the signal out + + align:start position:0% +milliseconds to send the the signal out + + + align:start position:0% +milliseconds to send the the signal out +you know from your brain out your arm to + + align:start position:0% +you know from your brain out your arm to + + + align:start position:0% +you know from your brain out your arm to +initiate the movement so how could you + + align:start position:0% +initiate the movement so how could you + + + align:start position:0% +initiate the movement so how could you +possibly do all of that in that in that + + align:start position:0% +possibly do all of that in that in that + + + align:start position:0% +possibly do all of that in that in that +time + + align:start position:0% +time + + + align:start position:0% +time +well you can't and what that means is + + align:start position:0% +well you can't and what that means is + + + align:start position:0% +well you can't and what that means is +that people are actually launching there + + align:start position:0% +that people are actually launching there + + + align:start position:0% +that people are actually launching there +were the the hand action the goalie is + + align:start position:0% +were the the hand action the goalie is + + + align:start position:0% +were the the hand action the goalie is +launching the action before the other + + align:start position:0% +launching the action before the other + + + align:start position:0% +launching the action before the other +person has actually started moving their + + align:start position:0% +person has actually started moving their + + + align:start position:0% +person has actually started moving their +finger they've started processing it + + align:start position:0% +finger they've started processing it + + + align:start position:0% +finger they've started processing it +before and the way they've done that is + + align:start position:0% +before and the way they've done that is + + + align:start position:0% +before and the way they've done that is +before this person starts before their + + align:start position:0% +before this person starts before their + + + align:start position:0% +before this person starts before their +hand moves at all + + align:start position:0% +hand moves at all + + + align:start position:0% +hand moves at all +they've subtly change their body + + align:start position:0% +they've subtly change their body + + + align:start position:0% +they've subtly change their body +configuration in ways that the other + + align:start position:0% +configuration in ways that the other + + + align:start position:0% +configuration in ways that the other +person can read okay now on the one hand + + align:start position:0% +person can read okay now on the one hand + + + align:start position:0% +person can read okay now on the one hand +okay you're playing this game you learn + + align:start position:0% +okay you're playing this game you learn + + + align:start position:0% +okay you're playing this game you learn +to exploit cues we're really great at + + align:start position:0% +to exploit cues we're really great at + + + align:start position:0% +to exploit cues we're really great at +figuring out cues quickly and using them + + align:start position:0% +figuring out cues quickly and using them + + + align:start position:0% +figuring out cues quickly and using them +and learning to use them but here's the + + align:start position:0% +and learning to use them but here's the + + + align:start position:0% +and learning to use them but here's the +one second here's the cool thing about + + align:start position:0% +one second here's the cool thing about + + + align:start position:0% +one second here's the cool thing about +this task is that this immediate ultra + + align:start position:0% +this task is that this immediate ultra + + + align:start position:0% +this task is that this immediate ultra +fast reaction time happens on the very + + align:start position:0% +fast reaction time happens on the very + + + align:start position:0% +fast reaction time happens on the very +first few trials so the ability that + + align:start position:0% +first few trials so the ability that + + + align:start position:0% +first few trials so the ability that +this task is tapping into is not that + + align:start position:0% +this task is tapping into is not that + + + align:start position:0% +this task is tapping into is not that +the goalie can learn what cues are + + align:start position:0% +the goalie can learn what cues are + + + align:start position:0% +the goalie can learn what cues are +predictive given enough trials and + + align:start position:0% +predictive given enough trials and + + + align:start position:0% +predictive given enough trials and +feedback know they do it right off the + + align:start position:0% +feedback know they do it right off the + + + align:start position:0% +feedback know they do it right off the +bat this task is tapping into an ability + + align:start position:0% +bat this task is tapping into an ability + + + align:start position:0% +bat this task is tapping into an ability +that we all have already right now to + + align:start position:0% +that we all have already right now to + + + align:start position:0% +that we all have already right now to +read each other's actions and prick to + + align:start position:0% +read each other's actions and prick to + + + align:start position:0% +read each other's actions and prick to +predict each other's behavior and so + + align:start position:0% +predict each other's behavior and so + + + align:start position:0% +predict each other's behavior and so +people with no instruction and no + + align:start position:0% +people with no instruction and no + + + align:start position:0% +people with no instruction and no +experience whatsoever in this novel task + + align:start position:0% +experience whatsoever in this novel task + + + align:start position:0% +experience whatsoever in this novel task +know that this subtle little cue of the + + align:start position:0% +know that this subtle little cue of the + + + align:start position:0% +know that this subtle little cue of the +way the body is moving a little bit + + align:start position:0% +way the body is moving a little bit + + + align:start position:0% +way the body is moving a little bit +before the person's finger even starts + + align:start position:0% +before the person's finger even starts + + + align:start position:0% +before the person's finger even starts +to move they can tell what its + + align:start position:0% +to move they can tell what its + + + align:start position:0% +to move they can tell what its +predictive of so that's just another way + + align:start position:0% +predictive of so that's just another way + + + align:start position:0% +predictive of so that's just another way +to get to characterize people's + + align:start position:0% +to get to characterize people's + + + align:start position:0% +to get to characterize people's +abilities in social perceptions so some + + align:start position:0% +abilities in social perceptions so some + + + align:start position:0% +abilities in social perceptions so some +of the many different things that we + + align:start position:0% +of the many different things that we + + + align:start position:0% +of the many different things that we +just see really well in other people's + + align:start position:0% +just see really well in other people's + + + align:start position:0% +just see really well in other people's +actions okay that's what I just said + + align:start position:0% +actions okay that's what I just said + + + align:start position:0% +actions okay that's what I just said +all right all right I'm gonna skip over + + align:start position:0% +all right all right I'm gonna skip over + + + align:start position:0% +all right all right I'm gonna skip over +some stuff we're looking at perception + + align:start position:0% +some stuff we're looking at perception + + + align:start position:0% +some stuff we're looking at perception +of emotional expressions almost the + + align:start position:0% +of emotional expressions almost the + + + align:start position:0% +of emotional expressions almost the +entire literature is based on + + align:start position:0% +entire literature is based on + + + align:start position:0% +entire literature is based on +aged emotional expressions on faces huge + + align:start position:0% +aged emotional expressions on faces huge + + + align:start position:0% +aged emotional expressions on faces huge +literature with neuroimaging and + + align:start position:0% +literature with neuroimaging and + + + align:start position:0% +literature with neuroimaging and +behavior and it goes back forever but my + + align:start position:0% +behavior and it goes back forever but my + + + align:start position:0% +behavior and it goes back forever but my +colleague Eleanor McCone has pointed out + + align:start position:0% +colleague Eleanor McCone has pointed out + + + align:start position:0% +colleague Eleanor McCone has pointed out +that actually Nate you know it would be + + align:start position:0% +that actually Nate you know it would be + + + align:start position:0% +that actually Nate you know it would be +important to look at real real emotional + + align:start position:0% +important to look at real real emotional + + + align:start position:0% +important to look at real real emotional +expressions on faces maybe that's + + align:start position:0% +expressions on faces maybe that's + + + align:start position:0% +expressions on faces maybe that's +different the Haverly turns out it's + + align:start position:0% +different the Haverly turns out it's + + + align:start position:0% +different the Haverly turns out it's +very different behaviorally one you can + + align:start position:0% +very different behaviorally one you can + + + align:start position:0% +very different behaviorally one you can +tell somebody's faking an emotional + + align:start position:0% +tell somebody's faking an emotional + + + align:start position:0% +tell somebody's faking an emotional +expression or if it's a real one like + + align:start position:0% +expression or if it's a real one like + + + align:start position:0% +expression or if it's a real one like +okay which of these is real fear and + + align:start position:0% +okay which of these is real fear and + + + align:start position:0% +okay which of these is real fear and +which of these is staged fear duh okay + + align:start position:0% +which of these is staged fear duh okay + + + align:start position:0% +which of these is staged fear duh okay +so one we're really attuned to that I + + align:start position:0% +so one we're really attuned to that I + + + align:start position:0% +so one we're really attuned to that I +think that's really interesting just as + + align:start position:0% +think that's really interesting just as + + + align:start position:0% +think that's really interesting just as +a social perceptual ability we spend a + + align:start position:0% +a social perceptual ability we spend a + + + align:start position:0% +a social perceptual ability we spend a +lot of time trying to figure out who's + + align:start position:0% +lot of time trying to figure out who's + + + align:start position:0% +lot of time trying to figure out who's +sincere who's genuine who's faking + + align:start position:0% +sincere who's genuine who's faking + + + align:start position:0% +sincere who's genuine who's faking +something what's for real right you know + + align:start position:0% +something what's for real right you know + + + align:start position:0% +something what's for real right you know +there's all kinds of shades of that and + + align:start position:0% +there's all kinds of shades of that and + + + align:start position:0% +there's all kinds of shades of that and +here's one little piece of it right so I + + align:start position:0% +here's one little piece of it right so I + + + align:start position:0% +here's one little piece of it right so I +think that's very interesting and + + align:start position:0% +think that's very interesting and + + + align:start position:0% +think that's very interesting and +they've shown that behaviorally these + + align:start position:0% +they've shown that behaviorally these + + + align:start position:0% +they've shown that behaviorally these +phenomenon are very different just one + + align:start position:0% +phenomenon are very different just one + + + align:start position:0% +phenomenon are very different just one +example a prior literature had shown + + align:start position:0% +example a prior literature had shown + + + align:start position:0% +example a prior literature had shown +that people with schizophrenia are + + align:start position:0% +that people with schizophrenia are + + + align:start position:0% +that people with schizophrenia are +particularly bad at reading facial + + align:start position:0% +particularly bad at reading facial + + + align:start position:0% +particularly bad at reading facial +expressions using the standard measures + + align:start position:0% +expressions using the standard measures + + + align:start position:0% +expressions using the standard measures +a standard stimuli the Ekman six facial + + align:start position:0% +a standard stimuli the Ekman six facial + + + align:start position:0% +a standard stimuli the Ekman six facial +expressions these guys replicated that + + align:start position:0% +expressions these guys replicated that + + + align:start position:0% +expressions these guys replicated that +finding and then showed that when you + + align:start position:0% +finding and then showed that when you + + + align:start position:0% +finding and then showed that when you +run the same experiment but using not + + align:start position:0% +run the same experiment but using not + + + align:start position:0% +run the same experiment but using not +staged but real emotional expressions + + align:start position:0% +staged but real emotional expressions + + + align:start position:0% +staged but real emotional expressions +schizophrenics are better than everyone + + align:start position:0% +schizophrenics are better than everyone + + + align:start position:0% +schizophrenics are better than everyone +else okay so it matters behaviorally and + + align:start position:0% +else okay so it matters behaviorally and + + + align:start position:0% +else okay so it matters behaviorally and +it's interesting okay all right + + align:start position:0% +it's interesting okay all right + + + align:start position:0% +it's interesting okay all right +other things that we're doing right + + align:start position:0% +other things that we're doing right + + + align:start position:0% +other things that we're doing right +Leila your TA here who's done beautiful + + align:start position:0% +Leila your TA here who's done beautiful + + + align:start position:0% +Leila your TA here who's done beautiful +work on her thesis work with Tommy using + + align:start position:0% +work on her thesis work with Tommy using + + + align:start position:0% +work on her thesis work with Tommy using +energy and other methods is now working + + align:start position:0% +energy and other methods is now working + + + align:start position:0% +energy and other methods is now working +with me and Gabrielle using some of this + + align:start position:0% +with me and Gabrielle using some of this + + + align:start position:0% +with me and Gabrielle using some of this +magnificent data that Gabrielle has + + align:start position:0% +magnificent data that Gabrielle has + + + align:start position:0% +magnificent data that Gabrielle has +collected over a bunch of years when + + align:start position:0% +collected over a bunch of years when + + + align:start position:0% +collected over a bunch of years when +he's got intracranial recordings from + + align:start position:0% +he's got intracranial recordings from + + + align:start position:0% +he's got intracranial recordings from +human brains while people watch movies + + align:start position:0% +human brains while people watch movies + + + align:start position:0% +human brains while people watch movies +this is so precious these data are like + + align:start position:0% +this is so precious these data are like + + + align:start position:0% +this is so precious these data are like +you know a dream to me if somebody who's + + align:start position:0% +you know a dream to me if somebody who's + + + align:start position:0% +you know a dream to me if somebody who's +been using functional MRI for as my main + + align:start position:0% +been using functional MRI for as my main + + + align:start position:0% +been using functional MRI for as my main +hammer for the last 15 years functional + + align:start position:0% +hammer for the last 15 years functional + + + align:start position:0% +hammer for the last 15 years functional +MRI is magnificent it's wonderful it's + + align:start position:0% +MRI is magnificent it's wonderful it's + + + align:start position:0% +MRI is magnificent it's wonderful it's +fun but it has fundamental limits one it + + align:start position:0% +fun but it has fundamental limits one it + + + align:start position:0% +fun but it has fundamental limits one it +has no time information or at the dam + + align:start position:0% +has no time information or at the dam + + + align:start position:0% +has no time information or at the dam +and and the computations that make up + + align:start position:0% +and and the computations that make up + + + align:start position:0% +and and the computations that make up +perception including + + align:start position:0% +perception including + + + align:start position:0% +perception including +social perception and language + + align:start position:0% +social perception and language + + + align:start position:0% +social perception and language +processing and most of the interesting + + align:start position:0% +processing and most of the interesting + + + align:start position:0% +processing and most of the interesting +aspects of cognition happened on the + + align:start position:0% +aspects of cognition happened on the + + + align:start position:0% +aspects of cognition happened on the +order of tens of milliseconds we can't + + align:start position:0% +order of tens of milliseconds we can't + + + align:start position:0% +order of tens of milliseconds we can't +see any of that it's all just squashed + + align:start position:0% +see any of that it's all just squashed + + + align:start position:0% +see any of that it's all just squashed +together like a pancake right with + + align:start position:0% +together like a pancake right with + + + align:start position:0% +together like a pancake right with +functional MRI with intracranial + + align:start position:0% +functional MRI with intracranial + + + align:start position:0% +functional MRI with intracranial +recordings you have exquisite time + + align:start position:0% +recordings you have exquisite time + + + align:start position:0% +recordings you have exquisite time +information and you can see computations + + align:start position:0% +information and you can see computations + + + align:start position:0% +information and you can see computations +unfold over time that's very precious + + align:start position:0% +unfold over time that's very precious + + + align:start position:0% +unfold over time that's very precious +second of all in principle with + + align:start position:0% +second of all in principle with + + + align:start position:0% +second of all in principle with +intracranial electrodes you can test + + align:start position:0% +intracranial electrodes you can test + + + align:start position:0% +intracranial electrodes you can test +causality something you can't do with + + align:start position:0% +causality something you can't do with + + + align:start position:0% +causality something you can't do with +functional MRI you can stimulate and ask + + align:start position:0% +functional MRI you can stimulate and ask + + + align:start position:0% +functional MRI you can stimulate and ask +what what tasks are disrupted right so + + align:start position:0% +what what tasks are disrupted right so + + + align:start position:0% +what what tasks are disrupted right so +there's a huge number of cool things you + + align:start position:0% +there's a huge number of cool things you + + + align:start position:0% +there's a huge number of cool things you +can do with intracranial recordings + + align:start position:0% +can do with intracranial recordings + + + align:start position:0% +can do with intracranial recordings +Leila is looking at some of the data + + align:start position:0% +Leila is looking at some of the data + + + align:start position:0% +Leila is looking at some of the data +that Gabriele has been collecting with + + align:start position:0% +that Gabriele has been collecting with + + + align:start position:0% +that Gabriele has been collecting with +intracranial recordings of people + + align:start position:0% +intracranial recordings of people + + + align:start position:0% +intracranial recordings of people +watching movies it's and because these + + align:start position:0% +watching movies it's and because these + + + align:start position:0% +watching movies it's and because these +are rich complex social stimuli she's + + align:start position:0% +are rich complex social stimuli she's + + + align:start position:0% +are rich complex social stimuli she's +gonna look at all kinds of things that + + align:start position:0% +gonna look at all kinds of things that + + + align:start position:0% +gonna look at all kinds of things that +we can try to extract from those data + + align:start position:0% +we can try to extract from those data + + + align:start position:0% +we can try to extract from those data +like can you tell the identity of the + + align:start position:0% +like can you tell the identity of the + + + align:start position:0% +like can you tell the identity of the +person who's on the screen right now can + + align:start position:0% +person who's on the screen right now can + + + align:start position:0% +person who's on the screen right now can +you tell from their fate at their face + + align:start position:0% +you tell from their fate at their face + + + align:start position:0% +you tell from their fate at their face +their voice their body can you tell what + + align:start position:0% +their voice their body can you tell what + + + align:start position:0% +their voice their body can you tell what +action they're carrying out can you tell + + align:start position:0% +action they're carrying out can you tell + + + align:start position:0% +action they're carrying out can you tell +if the person on the screen right now + + align:start position:0% +if the person on the screen right now + + + align:start position:0% +if the person on the screen right now +was a good guy or a bad guy right can + + align:start position:0% +was a good guy or a bad guy right can + + + align:start position:0% +was a good guy or a bad guy right can +you tell what kind of social + + align:start position:0% +you tell what kind of social + + + align:start position:0% +you tell what kind of social +interactions are going on so we know all + + align:start position:0% +interactions are going on so we know all + + + align:start position:0% +interactions are going on so we know all +of this stuff all this information is + + align:start position:0% +of this stuff all this information is + + + align:start position:0% +of this stuff all this information is +extracted in the brain because people + + align:start position:0% +extracted in the brain because people + + + align:start position:0% +extracted in the brain because people +are good at it but to get a handle on + + align:start position:0% +are good at it but to get a handle on + + + align:start position:0% +are good at it but to get a handle on +the actual neural basis of how we carry + + align:start position:0% +the actual neural basis of how we carry + + + align:start position:0% +the actual neural basis of how we carry +out those perceptual processes this will + + align:start position:0% +out those perceptual processes this will + + + align:start position:0% +out those perceptual processes this will +be a really cool tool so that project is + + align:start position:0% +be a really cool tool so that project is + + + align:start position:0% +be a really cool tool so that project is +just starting now + + align:start position:0% +just starting now + + + align:start position:0% +just starting now +and in other projects going on Lindsey + + align:start position:0% +and in other projects going on Lindsey + + + align:start position:0% +and in other projects going on Lindsey +Powell shown here who's working with + + align:start position:0% +Powell shown here who's working with + + + align:start position:0% +Powell shown here who's working with +Rebecca Saxe + + align:start position:0% +Rebecca Saxe + + + align:start position:0% +Rebecca Saxe +and Liz spelke and others is using this + + align:start position:0% +and Liz spelke and others is using this + + + align:start position:0% +and Liz spelke and others is using this +Neer's method to look at blood flow + + align:start position:0% +Neer's method to look at blood flow + + + align:start position:0% +Neer's method to look at blood flow +changes in response to neural activity + + align:start position:0% +changes in response to neural activity + + + align:start position:0% +changes in response to neural activity +in infant brains she's looking at some + + align:start position:0% +in infant brains she's looking at some + + + align:start position:0% +in infant brains she's looking at some +of those specializations that I showed + + align:start position:0% +of those specializations that I showed + + + align:start position:0% +of those specializations that I showed +you in my brain at the beginning and + + align:start position:0% +you in my brain at the beginning and + + + align:start position:0% +you in my brain at the beginning and +asking which of those are present in + + align:start position:0% +asking which of those are present in + + + align:start position:0% +asking which of those are present in +infancy a totally cool question and Ben + + align:start position:0% +infancy a totally cool question and Ben + + + align:start position:0% +infancy a totally cool question and Ben +Dean and Rebecca Saxe and me and a bunch + + align:start position:0% +Dean and Rebecca Saxe and me and a bunch + + + align:start position:0% +Dean and Rebecca Saxe and me and a bunch +of others are looking at a big chunk of + + align:start position:0% +of others are looking at a big chunk of + + + align:start position:0% +of others are looking at a big chunk of +the human brain that was one of my + + align:start position:0% +the human brain that was one of my + + + align:start position:0% +the human brain that was one of my +colored patches before this whole dark + + align:start position:0% +colored patches before this whole dark + + + align:start position:0% +colored patches before this whole dark +gray region here it's called the + + align:start position:0% +gray region here it's called the + + + align:start position:0% +gray region here it's called the +superior + + align:start position:0% +superior + + + align:start position:0% +superior +temporal sulcus this is an inflated + + align:start position:0% +temporal sulcus this is an inflated + + + align:start position:0% +temporal sulcus this is an inflated +picture of the brain that means you + + align:start position:0% +picture of the brain that means you + + + align:start position:0% +picture of the brain that means you +usually the cortexes or fold it up + + align:start position:0% +usually the cortexes or fold it up + + + align:start position:0% +usually the cortexes or fold it up +inside the head you have to do that to + + align:start position:0% +inside the head you have to do that to + + + align:start position:0% +inside the head you have to do that to +fit it in there + + align:start position:0% +fit it in there + + + align:start position:0% +fit it in there +but if you want to see the whole thing + + align:start position:0% +but if you want to see the whole thing + + + align:start position:0% +but if you want to see the whole thing +you can mathematically inflate it so + + align:start position:0% +you can mathematically inflate it so + + + align:start position:0% +you can mathematically inflate it so +that's what's happened here and the dark + + align:start position:0% +that's what's happened here and the dark + + + align:start position:0% +that's what's happened here and the dark +bits are the bits that were inside a + + align:start position:0% +bits are the bits that were inside a + + + align:start position:0% +bits are the bits that were inside a +fold before it was inflated so they're + + align:start position:0% +fold before it was inflated so they're + + + align:start position:0% +fold before it was inflated so they're +inside a sulcus but now shown on blown + + align:start position:0% +inside a sulcus but now shown on blown + + + align:start position:0% +inside a sulcus but now shown on blown +out to the surface so this superior + + align:start position:0% +out to the surface so this superior + + + align:start position:0% +out to the surface so this superior +temporal sulcus running down here is one + + align:start position:0% +temporal sulcus running down here is one + + + align:start position:0% +temporal sulcus running down here is one +of the longest salsa in the human brain + + align:start position:0% +of the longest salsa in the human brain + + + align:start position:0% +of the longest salsa in the human brain +and one of the coolest and an awful lot + + align:start position:0% +and one of the coolest and an awful lot + + + align:start position:0% +and one of the coolest and an awful lot +of social perception goes on right there + + align:start position:0% +of social perception goes on right there + + + align:start position:0% +of social perception goes on right there +Ben Dean has a paper in press and some + + align:start position:0% +Ben Dean has a paper in press and some + + + align:start position:0% +Ben Dean has a paper in press and some +ongoing work where he shows that lots of + + align:start position:0% +ongoing work where he shows that lots of + + + align:start position:0% +ongoing work where he shows that lots of +different kinds of social cognitive and + + align:start position:0% +different kinds of social cognitive and + + + align:start position:0% +different kinds of social cognitive and +perceptual abilities actually inhabit + + align:start position:0% +perceptual abilities actually inhabit + + + align:start position:0% +perceptual abilities actually inhabit +somewhat distinct regions along the + + align:start position:0% +somewhat distinct regions along the + + + align:start position:0% +somewhat distinct regions along the +superior temporal sulcus they're not + + align:start position:0% +superior temporal sulcus they're not + + + align:start position:0% +superior temporal sulcus they're not +perfectly discrete nothing as a neat + + align:start position:0% +perfectly discrete nothing as a neat + + + align:start position:0% +perfectly discrete nothing as a neat +little oval in the brain actually they + + align:start position:0% +little oval in the brain actually they + + + align:start position:0% +little oval in the brain actually they +somewhat overlap but there's a lot of + + align:start position:0% +somewhat overlap but there's a lot of + + + align:start position:0% +somewhat overlap but there's a lot of +organization in there and that's cool + + align:start position:0% +organization in there and that's cool + + + align:start position:0% +organization in there and that's cool +because it gives us a lever to try to + + align:start position:0% +because it gives us a lever to try to + + + align:start position:0% +because it gives us a lever to try to +understand this whole big space of + + align:start position:0% +understand this whole big space of + + + align:start position:0% +understand this whole big space of +cognition + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Hdi8zAUZJ4Q.txt b/Hdi8zAUZJ4Q.txt new file mode 100644 index 0000000000000000000000000000000000000000..15c54ed5bc959915f80cacafba93ebce0365fddd --- /dev/null +++ b/Hdi8zAUZJ4Q.txt @@ -0,0 +1,659 @@ +align:start position:0% + +Episode + + align:start position:0% + + + + align:start position:0% + +8. Are you sure that's a risk? + + align:start position:0% +8. Are you sure that's a risk? + + + align:start position:0% +8. Are you sure that's a risk? +If something can go wrong, it will go + + align:start position:0% +If something can go wrong, it will go + + + align:start position:0% +If something can go wrong, it will go +wrong. This is what's known as Murphy's + + align:start position:0% +wrong. This is what's known as Murphy's + + + align:start position:0% +wrong. This is what's known as Murphy's +law, and it is one of those awkward + + align:start position:0% +law, and it is one of those awkward + + + align:start position:0% +law, and it is one of those awkward +rules of thumb that every engineer has + + align:start position:0% +rules of thumb that every engineer has + + + align:start position:0% +rules of thumb that every engineer has +had to wrestle with. Just keep it in + + align:start position:0% +had to wrestle with. Just keep it in + + + align:start position:0% +had to wrestle with. Just keep it in +mind for now. The common advice given to + + align:start position:0% +mind for now. The common advice given to + + + align:start position:0% +mind for now. The common advice given to +innovators and entrepreneurs is that you + + align:start position:0% +innovators and entrepreneurs is that you + + + align:start position:0% +innovators and entrepreneurs is that you +should focus. You're told to pick one + + align:start position:0% +should focus. You're told to pick one + + + align:start position:0% +should focus. You're told to pick one +idea or one market or one user, + + align:start position:0% +idea or one market or one user, + + + align:start position:0% +idea or one market or one user, +whatever, and work on it. The advice + + align:start position:0% +whatever, and work on it. The advice + + + align:start position:0% +whatever, and work on it. The advice +makes it seem like this is only your + + align:start position:0% +makes it seem like this is only your + + + align:start position:0% +makes it seem like this is only your +choice to make. The more focused you + + align:start position:0% +choice to make. The more focused you + + + align:start position:0% +choice to make. The more focused you +are, the lower the risk. But you are not + + align:start position:0% +are, the lower the risk. But you are not + + + align:start position:0% +are, the lower the risk. But you are not +being advised to focus per se. Rather, + + align:start position:0% +being advised to focus per se. Rather, + + + align:start position:0% +being advised to focus per se. Rather, +you're being told to narrow your + + align:start position:0% +you're being told to narrow your + + + align:start position:0% +you're being told to narrow your +options. There is a difference. Remember + + align:start position:0% +options. There is a difference. Remember + + + align:start position:0% +options. There is a difference. Remember +the analogy we drew between working on + + align:start position:0% +the analogy we drew between working on + + + align:start position:0% +the analogy we drew between working on +the problem and what Chris Hatfield said + + align:start position:0% +the problem and what Chris Hatfield said + + + align:start position:0% +the problem and what Chris Hatfield said +about the way astronauts prepare for + + align:start position:0% +about the way astronauts prepare for + + + align:start position:0% +about the way astronauts prepare for +missions to the International Space + + align:start position:0% +missions to the International Space + + + align:start position:0% +missions to the International Space +Station. The way you were being asked to + + align:start position:0% +Station. The way you were being asked to + + + align:start position:0% +Station. The way you were being asked to +focus is similar to telling astronauts + + align:start position:0% +focus is similar to telling astronauts + + + align:start position:0% +focus is similar to telling astronauts +to pay attention only to problems in + + align:start position:0% +to pay attention only to problems in + + + align:start position:0% +to pay attention only to problems in +some part of the rocket and ignore + + align:start position:0% +some part of the rocket and ignore + + + align:start position:0% +some part of the rocket and ignore +everything else. The problem with that + + align:start position:0% +everything else. The problem with that + + + align:start position:0% +everything else. The problem with that +advice is Murphy's law. It always stands + + align:start position:0% +advice is Murphy's law. It always stands + + + align:start position:0% +advice is Murphy's law. It always stands +in the way. If something can go wrong, + + align:start position:0% +in the way. If something can go wrong, + + + align:start position:0% +in the way. If something can go wrong, +it will. And as Chris Hatfield put it, + + align:start position:0% +it will. And as Chris Hatfield put it, + + + align:start position:0% +it will. And as Chris Hatfield put it, +you just decided to not pay attention to + + align:start position:0% +you just decided to not pay attention to + + + align:start position:0% +you just decided to not pay attention to +many things that can kill you. The same + + align:start position:0% +many things that can kill you. The same + + + align:start position:0% +many things that can kill you. The same +might be true for your innovating. + + align:start position:0% +might be true for your innovating. + + + align:start position:0% +might be true for your innovating. +Narrowing your options at the start to + + align:start position:0% +Narrowing your options at the start to + + + align:start position:0% +Narrowing your options at the start to +just the one idea increases your risk + + align:start position:0% +just the one idea increases your risk + + + align:start position:0% +just the one idea increases your risk +and gives you a false sense of + + align:start position:0% +and gives you a false sense of + + + align:start position:0% +and gives you a false sense of +certainty. That's exactly the opposite + + align:start position:0% +certainty. That's exactly the opposite + + + align:start position:0% +certainty. That's exactly the opposite +of what you want. Focusing and narrowing + + align:start position:0% +of what you want. Focusing and narrowing + + + align:start position:0% +of what you want. Focusing and narrowing +are not the same thing. This is easy to + + align:start position:0% +are not the same thing. This is easy to + + + align:start position:0% +are not the same thing. This is easy to +see in a camera. When you zoom, you + + align:start position:0% +see in a camera. When you zoom, you + + + align:start position:0% +see in a camera. When you zoom, you +narrow the field of view. When you focus + + align:start position:0% +narrow the field of view. When you focus + + + align:start position:0% +narrow the field of view. When you focus +the image, the image gains sharpness and + + align:start position:0% +the image, the image gains sharpness and + + + align:start position:0% +the image, the image gains sharpness and +clarity, but the field of view stays the + + align:start position:0% +clarity, but the field of view stays the + + + align:start position:0% +clarity, but the field of view stays the +same. Whether you are the innovator or + + align:start position:0% +same. Whether you are the innovator or + + + align:start position:0% +same. Whether you are the innovator or +the capital, you want to reduce risk by + + align:start position:0% +the capital, you want to reduce risk by + + + align:start position:0% +the capital, you want to reduce risk by +increasing clarity around what you are + + align:start position:0% +increasing clarity around what you are + + + align:start position:0% +increasing clarity around what you are +doing. Narrowing your options only + + align:start position:0% +doing. Narrowing your options only + + + align:start position:0% +doing. Narrowing your options only +increases risks. Like Murphy's law and + + align:start position:0% +increases risks. Like Murphy's law and + + + align:start position:0% +increases risks. Like Murphy's law and +the distinction between focus and + + align:start position:0% +the distinction between focus and + + + align:start position:0% +the distinction between focus and +narrowing, in the new mindset, we avail + + align:start position:0% +narrowing, in the new mindset, we avail + + + align:start position:0% +narrowing, in the new mindset, we avail +ourselves of several finance and general + + align:start position:0% +ourselves of several finance and general + + + align:start position:0% +ourselves of several finance and general +engineering principles like preventing + + align:start position:0% +engineering principles like preventing + + + align:start position:0% +engineering principles like preventing +error accumulation, diversification, the + + align:start position:0% +error accumulation, diversification, the + + + align:start position:0% +error accumulation, diversification, the +difference between precision and + + align:start position:0% +difference between precision and + + + align:start position:0% +difference between precision and +accuracy, and many more that fall beyond + + align:start position:0% +accuracy, and many more that fall beyond + + + align:start position:0% +accuracy, and many more that fall beyond +the scope of this introductory course. + + align:start position:0% +the scope of this introductory course. + + + align:start position:0% +the scope of this introductory course. +Those principles help innovators make + + align:start position:0% +Those principles help innovators make + + + align:start position:0% +Those principles help innovators make +informed decisions without wasting time + + align:start position:0% +informed decisions without wasting time + + + align:start position:0% +informed decisions without wasting time +or inadvertently increasing risk. In the + + align:start position:0% +or inadvertently increasing risk. In the + + + align:start position:0% +or inadvertently increasing risk. In the +MIT mindset, students do this by keeping + + align:start position:0% +MIT mindset, students do this by keeping + + + align:start position:0% +MIT mindset, students do this by keeping +at least three distinct options open + + align:start position:0% +at least three distinct options open + + + align:start position:0% +at least three distinct options open +throughout their explorations. They + + align:start position:0% +throughout their explorations. They + + + align:start position:0% +throughout their explorations. They +focus on coming up with next steps and + + align:start position:0% +focus on coming up with next steps and + + + align:start position:0% +focus on coming up with next steps and +actions that will help them advance in + + align:start position:0% +actions that will help them advance in + + + align:start position:0% +actions that will help them advance in +all three at the same time. Which three + + align:start position:0% +all three at the same time. Which three + + + align:start position:0% +all three at the same time. Which three +they focus on might change as they gain + + align:start position:0% +they focus on might change as they gain + + + align:start position:0% +they focus on might change as they gain +understanding of the problem, but + + align:start position:0% +understanding of the problem, but + + + align:start position:0% +understanding of the problem, but +keeping three options open helps them + + align:start position:0% +keeping three options open helps them + + + align:start position:0% +keeping three options open helps them +keep Murphy's law at bay. Chances are + + align:start position:0% +keep Murphy's law at bay. Chances are + + + align:start position:0% +keep Murphy's law at bay. Chances are +this is not the first time you heard + + align:start position:0% +this is not the first time you heard + + + align:start position:0% +this is not the first time you heard +about Murphy's law, but it might be the + + align:start position:0% +about Murphy's law, but it might be the + + + align:start position:0% +about Murphy's law, but it might be the +first time you hear it connected with + + align:start position:0% +first time you hear it connected with + + + align:start position:0% +first time you hear it connected with +innovation. We hear so many things about + + align:start position:0% +innovation. We hear so many things about + + + align:start position:0% +innovation. We hear so many things about +innovation that sometimes we forget what + + align:start position:0% +innovation that sometimes we forget what + + + align:start position:0% +innovation that sometimes we forget what +should be obvious. The way I typically + + align:start position:0% +should be obvious. The way I typically + + + align:start position:0% +should be obvious. The way I typically +summarize this for my students is that + + align:start position:0% +summarize this for my students is that + + + align:start position:0% +summarize this for my students is that +there's a lot of things you need to + + align:start position:0% +there's a lot of things you need to + + + align:start position:0% +there's a lot of things you need to +unlearn about innovation so you can + + align:start position:0% +unlearn about innovation so you can + + + align:start position:0% +unlearn about innovation so you can +actually use the skills you already + + align:start position:0% +actually use the skills you already + + + align:start position:0% +actually use the skills you already +have. The next video tell you all there + + align:start position:0% +have. The next video tell you all there + + + align:start position:0% +have. The next video tell you all there +is to unlearn so you can actually truly + + align:start position:0% +is to unlearn so you can actually truly + + + align:start position:0% +is to unlearn so you can actually truly +start innovating. + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/HnRoq5Pc8Z4.txt b/HnRoq5Pc8Z4.txt new file mode 100644 index 0000000000000000000000000000000000000000..90094d2c0cb00e0c0c2f354f41da603f352320e0 --- /dev/null +++ b/HnRoq5Pc8Z4.txt @@ -0,0 +1,2171 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +so we continue our discussion now of + + align:start position:0% +so we continue our discussion now of + + + align:start position:0% +so we continue our discussion now of +electron and proton scattering + + align:start position:0% +electron and proton scattering + + + align:start position:0% +electron and proton scattering +and we dive deep into this structure + + align:start position:0% +and we dive deep into this structure + + + align:start position:0% +and we dive deep into this structure +using + + align:start position:0% +using + + + align:start position:0% +using +deep inelastic scattering inelastic here + + align:start position:0% +deep inelastic scattering inelastic here + + + align:start position:0% +deep inelastic scattering inelastic here +means that we are destroying the + + align:start position:0% +means that we are destroying the + + + align:start position:0% +means that we are destroying the +structure of the proton in the + + align:start position:0% +structure of the proton in the + + + align:start position:0% +structure of the proton in the +scattering process + + align:start position:0% +scattering process + + + align:start position:0% +scattering process +so we have a way to look at the remnant + + align:start position:0% +so we have a way to look at the remnant + + + align:start position:0% +so we have a way to look at the remnant +of the proton + + align:start position:0% +of the proton + + + align:start position:0% +of the proton +and also of the scattered electron and + + align:start position:0% +and also of the scattered electron and + + + align:start position:0% +and also of the scattered electron and +then + + align:start position:0% +then + + + align:start position:0% +then +compare our theoretical expectation for + + align:start position:0% +compare our theoretical expectation for + + + align:start position:0% +compare our theoretical expectation for +the cross-sections with the finding in + + align:start position:0% +the cross-sections with the finding in + + + align:start position:0% +the cross-sections with the finding in +experiments + + align:start position:0% +experiments + + + align:start position:0% +experiments +let me just talk about this in more + + align:start position:0% +let me just talk about this in more + + + align:start position:0% +let me just talk about this in more +general terms + + align:start position:0% +general terms + + + align:start position:0% +general terms +the energy of the probing electron or + + align:start position:0% +the energy of the probing electron or + + + align:start position:0% +the energy of the probing electron or +the photon and the scattering process + + align:start position:0% +the photon and the scattering process + + + align:start position:0% +the photon and the scattering process +allows us to look at the proton with + + align:start position:0% +allows us to look at the proton with + + + align:start position:0% +allows us to look at the proton with +varying resolution + + align:start position:0% +varying resolution + + + align:start position:0% +varying resolution +so at very low energies we basically see + + align:start position:0% +so at very low energies we basically see + + + align:start position:0% +so at very low energies we basically see +a point like particle and then the + + align:start position:0% +a point like particle and then the + + + align:start position:0% +a point like particle and then the +scattering process looks very much like + + align:start position:0% +scattering process looks very much like + + + align:start position:0% +scattering process looks very much like +the scattering of an electron with a + + align:start position:0% +the scattering of an electron with a + + + align:start position:0% +the scattering of an electron with a +mirror + + align:start position:0% +mirror + + + align:start position:0% +mirror +if we increase the energy of the + + align:start position:0% +if we increase the energy of the + + + align:start position:0% +if we increase the energy of the +electron we can see + + align:start position:0% +electron we can see + + + align:start position:0% +electron we can see +that there's an extended charge + + align:start position:0% +that there's an extended charge + + + align:start position:0% +that there's an extended charge +distribution in the proton + + align:start position:0% +distribution in the proton + + + align:start position:0% +distribution in the proton +further increase and allows us to + + align:start position:0% +further increase and allows us to + + + align:start position:0% +further increase and allows us to +resolve the fact that the proton is made + + align:start position:0% +resolve the fact that the proton is made + + + align:start position:0% +resolve the fact that the proton is made +out of three quarks and if you increase + + align:start position:0% +out of three quarks and if you increase + + + align:start position:0% +out of three quarks and if you increase +the energy further + + align:start position:0% +the energy further + + + align:start position:0% +the energy further +we see a lot of new particles appearing + + align:start position:0% +we see a lot of new particles appearing + + + align:start position:0% +we see a lot of new particles appearing +quarks and antiquarks and gluons + + align:start position:0% +quarks and antiquarks and gluons + + + align:start position:0% +quarks and antiquarks and gluons +which make up the structure of the + + align:start position:0% +which make up the structure of the + + + align:start position:0% +which make up the structure of the +proton + + align:start position:0% + + + + align:start position:0% + +the picture here is i like this very + + align:start position:0% +the picture here is i like this very + + + align:start position:0% +the picture here is i like this very +much i drew this myself some years ago + + align:start position:0% +much i drew this myself some years ago + + + align:start position:0% +much i drew this myself some years ago +um is what i would like to you know + + align:start position:0% +um is what i would like to you know + + + align:start position:0% +um is what i would like to you know +have you remember so in deep inelastic + + align:start position:0% +have you remember so in deep inelastic + + + align:start position:0% +have you remember so in deep inelastic +scattering experiments we basically use + + align:start position:0% +scattering experiments we basically use + + + align:start position:0% +scattering experiments we basically use +the photon scattered + + align:start position:0% +the photon scattered + + + align:start position:0% +the photon scattered +radiated off the electron as a + + align:start position:0% +radiated off the electron as a + + + align:start position:0% +radiated off the electron as a +magnifying glass for the proton + + align:start position:0% +magnifying glass for the proton + + + align:start position:0% +magnifying glass for the proton +so we can look into the structure of the + + align:start position:0% +so we can look into the structure of the + + + align:start position:0% +so we can look into the structure of the +proton here and we see the distribution + + align:start position:0% +proton here and we see the distribution + + + align:start position:0% +proton here and we see the distribution +of the charged particles + + align:start position:0% +of the charged particles + + + align:start position:0% +of the charged particles +in the proton only the electrically + + align:start position:0% +in the proton only the electrically + + + align:start position:0% +in the proton only the electrically +charged particles we don't + + align:start position:0% +charged particles we don't + + + align:start position:0% +charged particles we don't +have scattering between four direct + + align:start position:0% +have scattering between four direct + + + align:start position:0% +have scattering between four direct +scattering between photons and lawns + + align:start position:0% +scattering between photons and lawns + + + align:start position:0% +scattering between photons and lawns +so in measurements what we can do is we + + align:start position:0% +so in measurements what we can do is we + + + align:start position:0% +so in measurements what we can do is we +can test a scattered electron + + align:start position:0% +can test a scattered electron + + + align:start position:0% +can test a scattered electron +and we can look for the remnant of the + + align:start position:0% +and we can look for the remnant of the + + + align:start position:0% +and we can look for the remnant of the +proton in our measurement and then we do + + align:start position:0% +proton in our measurement and then we do + + + align:start position:0% +proton in our measurement and then we do +differential cross-section + + align:start position:0% +differential cross-section + + + align:start position:0% +differential cross-section +measurements compare with our theory and + + align:start position:0% +measurements compare with our theory and + + + align:start position:0% +measurements compare with our theory and +can infer + + align:start position:0% +can infer + + + align:start position:0% +can infer +information about the structure of the + + align:start position:0% +information about the structure of the + + + align:start position:0% +information about the structure of the +proton + + align:start position:0% +proton + + + align:start position:0% +proton +to do this we have special kinematic + + align:start position:0% +to do this we have special kinematic + + + align:start position:0% +to do this we have special kinematic +variables which + + align:start position:0% +variables which + + + align:start position:0% +variables which +turn out to be very useful the most + + align:start position:0% +turn out to be very useful the most + + + align:start position:0% +turn out to be very useful the most +important one is probably this x here + + align:start position:0% +important one is probably this x here + + + align:start position:0% +important one is probably this x here +which is called the bjergen + + align:start position:0% +which is called the bjergen + + + align:start position:0% +which is called the bjergen +scaling x of broken x which + + align:start position:0% +scaling x of broken x which + + + align:start position:0% +scaling x of broken x which +you can think about so this is q square + + align:start position:0% +you can think about so this is q square + + + align:start position:0% +you can think about so this is q square +as a momentum transfer of the photon + + align:start position:0% +as a momentum transfer of the photon + + + align:start position:0% +as a momentum transfer of the photon +p is the momentum of the proton q is the + + align:start position:0% +p is the momentum of the proton q is the + + + align:start position:0% +p is the momentum of the proton q is the +momentum transfer is q here + + align:start position:0% +momentum transfer is q here + + + align:start position:0% +momentum transfer is q here +factor of two and what this is is + + align:start position:0% +factor of two and what this is is + + + align:start position:0% +factor of two and what this is is +basically the fraction of the momentum + + align:start position:0% +basically the fraction of the momentum + + + align:start position:0% +basically the fraction of the momentum +carried by the part on + + align:start position:0% +carried by the part on + + + align:start position:0% +carried by the part on +here in the scattering process there's a + + align:start position:0% +here in the scattering process there's a + + + align:start position:0% +here in the scattering process there's a +few other useful variables but i don't + + align:start position:0% +few other useful variables but i don't + + + align:start position:0% +few other useful variables but i don't +want to go into any of the details here + + align:start position:0% +want to go into any of the details here + + + align:start position:0% +want to go into any of the details here +so there's a number of very important + + align:start position:0% +so there's a number of very important + + + align:start position:0% +so there's a number of very important +scattering experiments + + align:start position:0% +scattering experiments + + + align:start position:0% +scattering experiments +um the first one i mentioned before is a + + align:start position:0% +um the first one i mentioned before is a + + + align:start position:0% +um the first one i mentioned before is a +slag mit experiment + + align:start position:0% +slag mit experiment + + + align:start position:0% +slag mit experiment +which led to the discovery that the + + align:start position:0% +which led to the discovery that the + + + align:start position:0% +which led to the discovery that the +proton is made out of quarks + + align:start position:0% +proton is made out of quarks + + + align:start position:0% +proton is made out of quarks +and the nobel prize in physics 1990 to + + align:start position:0% +and the nobel prize in physics 1990 to + + + align:start position:0% +and the nobel prize in physics 1990 to +jerry friedman henry kendall + + align:start position:0% +jerry friedman henry kendall + + + align:start position:0% +jerry friedman henry kendall +and taylor and what they did is they + + align:start position:0% +and taylor and what they did is they + + + align:start position:0% +and taylor and what they did is they +basically had a beam + + align:start position:0% +basically had a beam + + + align:start position:0% +basically had a beam +um at slack of electrons of 5 to 20 gev + + align:start position:0% +um at slack of electrons of 5 to 20 gev + + + align:start position:0% +um at slack of electrons of 5 to 20 gev +and they scattered this beam of a + + align:start position:0% +and they scattered this beam of a + + + align:start position:0% +and they scattered this beam of a +hydrogen target protons + + align:start position:0% +hydrogen target protons + + + align:start position:0% +hydrogen target protons +and they use this spectrometer here in + + align:start position:0% +and they use this spectrometer here in + + + align:start position:0% +and they use this spectrometer here in +order to then make a differential + + align:start position:0% +order to then make a differential + + + align:start position:0% +order to then make a differential +measurement of the scattered electrons + + align:start position:0% +measurement of the scattered electrons + + + align:start position:0% +measurement of the scattered electrons +so that's very cool um even higher + + align:start position:0% +so that's very cool um even higher + + + align:start position:0% +so that's very cool um even higher +energies were available at hera + + align:start position:0% +energies were available at hera + + + align:start position:0% +energies were available at hera +um the electron positron collider where + + align:start position:0% +um the electron positron collider where + + + align:start position:0% +um the electron positron collider where +the energies of the electrons were in + + align:start position:0% +the energies of the electrons were in + + + align:start position:0% +the energies of the electrons were in +the order of 30 gb + + align:start position:0% +the order of 30 gb + + + align:start position:0% +the order of 30 gb +of the protons up to 3 830 gb + + align:start position:0% +of the protons up to 3 830 gb + + + align:start position:0% +of the protons up to 3 830 gb +um and so what we find then in those + + align:start position:0% +um and so what we find then in those + + + align:start position:0% +um and so what we find then in those +collisions of differential cross-section + + align:start position:0% +collisions of differential cross-section + + + align:start position:0% +collisions of differential cross-section +measurement is shown here and it's a + + align:start position:0% +measurement is shown here and it's a + + + align:start position:0% +measurement is shown here and it's a +very it's not an easy plot to read + + align:start position:0% +very it's not an easy plot to read + + + align:start position:0% +very it's not an easy plot to read +so you see our structure function here + + align:start position:0% +so you see our structure function here + + + align:start position:0% +so you see our structure function here +in the logarithmic plot + + align:start position:0% +in the logarithmic plot + + + align:start position:0% +in the logarithmic plot +remember this is a log template here + + align:start position:0% +remember this is a log template here + + + align:start position:0% +remember this is a log template here +and you see here q square the momentum + + align:start position:0% +and you see here q square the momentum + + + align:start position:0% +and you see here q square the momentum +transfer of the photon so the energy + + align:start position:0% +transfer of the photon so the energy + + + align:start position:0% +transfer of the photon so the energy +used in the scattering process + + align:start position:0% +used in the scattering process + + + align:start position:0% +used in the scattering process +when we try to read this here we can + + align:start position:0% +when we try to read this here we can + + + align:start position:0% +when we try to read this here we can +look at a fixed q square for example + + align:start position:0% +look at a fixed q square for example + + + align:start position:0% +look at a fixed q square for example +and at a fixed q square you see that + + align:start position:0% +and at a fixed q square you see that + + + align:start position:0% +and at a fixed q square you see that +um if you if you + + align:start position:0% +um if you if you + + + align:start position:0% +um if you if you +probe if you're testing for a fixed + + align:start position:0% +probe if you're testing for a fixed + + + align:start position:0% +probe if you're testing for a fixed +fraction of the patterns taking away + + align:start position:0% +fraction of the patterns taking away + + + align:start position:0% +fraction of the patterns taking away +patons fraction of the partner's + + align:start position:0% +patons fraction of the partner's + + + align:start position:0% +patons fraction of the partner's +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +of the proton you see that the lower the + + align:start position:0% +of the proton you see that the lower the + + + align:start position:0% +of the proton you see that the lower the +fractions the more particles you see + + align:start position:0% +fractions the more particles you see + + + align:start position:0% +fractions the more particles you see +so at a fixed energy you see + + align:start position:0% +so at a fixed energy you see + + + align:start position:0% +so at a fixed energy you see +many many more particles the lower you + + align:start position:0% +many many more particles the lower you + + + align:start position:0% +many many more particles the lower you +go in the fraction so there seem to be + + align:start position:0% +go in the fraction so there seem to be + + + align:start position:0% +go in the fraction so there seem to be +like an + + align:start position:0% +like an + + + align:start position:0% +like an +increase of particles um the lower the + + align:start position:0% +increase of particles um the lower the + + + align:start position:0% +increase of particles um the lower the +fraction + + align:start position:0% +fraction + + + align:start position:0% +fraction +is if you then check for + + align:start position:0% +is if you then check for + + + align:start position:0% +is if you then check for +a fixed fraction let's say 0.4 + + align:start position:0% +a fixed fraction let's say 0.4 + + + align:start position:0% +a fixed fraction let's say 0.4 +um so it means that the pattern carries + + align:start position:0% +um so it means that the pattern carries + + + align:start position:0% +um so it means that the pattern carries +forty percent of the protons + + align:start position:0% +forty percent of the protons + + + align:start position:0% +forty percent of the protons +energy you see that it's almost flat as + + align:start position:0% +energy you see that it's almost flat as + + + align:start position:0% +energy you see that it's almost flat as +a function of q + + align:start position:0% +a function of q + + + align:start position:0% +a function of q +square so it seems like there's you know + + align:start position:0% +square so it seems like there's you know + + + align:start position:0% +square so it seems like there's you know +forty percent + + align:start position:0% +forty percent + + + align:start position:0% +forty percent +uh the number of particles you see at 40 + + align:start position:0% +uh the number of particles you see at 40 + + + align:start position:0% +uh the number of particles you see at 40 +percent of the momentum fraction is + + align:start position:0% +percent of the momentum fraction is + + + align:start position:0% +percent of the momentum fraction is +constant with key square however + + align:start position:0% +constant with key square however + + + align:start position:0% +constant with key square however +if you look at smaller energies oh sorry + + align:start position:0% +if you look at smaller energies oh sorry + + + align:start position:0% +if you look at smaller energies oh sorry +smaller momentum fractions + + align:start position:0% +smaller momentum fractions + + + align:start position:0% +smaller momentum fractions +you see that higher energies seem to + + align:start position:0% +you see that higher energies seem to + + + align:start position:0% +you see that higher energies seem to +show even more particles at this + + align:start position:0% +show even more particles at this + + + align:start position:0% +show even more particles at this +momentum fraction + + align:start position:0% +momentum fraction + + + align:start position:0% +momentum fraction +and the ways to understand this is these + + align:start position:0% +and the ways to understand this is these + + + align:start position:0% +and the ways to understand this is these +two + + align:start position:0% +two + + + align:start position:0% +two +diagrams so the first one is this one + + align:start position:0% +diagrams so the first one is this one + + + align:start position:0% +diagrams so the first one is this one +here + + align:start position:0% +here + + + align:start position:0% +here +where you see a quark radiating clone + + align:start position:0% + + + + align:start position:0% + +and so what you see is that you know the + + align:start position:0% +and so what you see is that you know the + + + align:start position:0% +and so what you see is that you know the +deeper you look + + align:start position:0% + + + + align:start position:0% + +you're able to then resolve this part + + align:start position:0% +you're able to then resolve this part + + + align:start position:0% +you're able to then resolve this part +here + + align:start position:0% +here + + + align:start position:0% +here +and so you see more quarks and gluons + + align:start position:0% +and so you see more quarks and gluons + + + align:start position:0% +and so you see more quarks and gluons +which carry even smaller momentum + + align:start position:0% +which carry even smaller momentum + + + align:start position:0% +which carry even smaller momentum +fraction than the initial quark here + + align:start position:0% +fraction than the initial quark here + + + align:start position:0% +fraction than the initial quark here +you also see diagrams like this which is + + align:start position:0% +you also see diagrams like this which is + + + align:start position:0% +you also see diagrams like this which is +called a blue one splitting with the + + align:start position:0% +called a blue one splitting with the + + + align:start position:0% +called a blue one splitting with the +gluon splits in the clock and the cork + + align:start position:0% +gluon splits in the clock and the cork + + + align:start position:0% +gluon splits in the clock and the cork +pair + + align:start position:0% +pair + + + align:start position:0% +pair +and you start resolving those and those + + align:start position:0% +and you start resolving those and those + + + align:start position:0% +and you start resolving those and those +also carry + + align:start position:0% +also carry + + + align:start position:0% +also carry +lower momentum the evolution of our + + align:start position:0% +lower momentum the evolution of our + + + align:start position:0% +lower momentum the evolution of our +of this pattern distribution function or + + align:start position:0% +of this pattern distribution function or + + + align:start position:0% +of this pattern distribution function or +the the structure functions + + align:start position:0% +the the structure functions + + + align:start position:0% +the the structure functions +can be calculated and described in the + + align:start position:0% +can be calculated and described in the + + + align:start position:0% +can be calculated and described in the +so-called decline + + align:start position:0% + + + + align:start position:0% + +equations and all you do here is + + align:start position:0% +equations and all you do here is + + + align:start position:0% +equations and all you do here is +calculate the contributions from the + + align:start position:0% +calculate the contributions from the + + + align:start position:0% +calculate the contributions from the +so-called + + align:start position:0% +so-called + + + align:start position:0% +so-called +um work and glue and splitting so you + + align:start position:0% +um work and glue and splitting so you + + + align:start position:0% +um work and glue and splitting so you +calculate those splitting functions as + + align:start position:0% +calculate those splitting functions as + + + align:start position:0% +calculate those splitting functions as +higher order corrections + + align:start position:0% +higher order corrections + + + align:start position:0% +higher order corrections +to a very simple quark model + + align:start position:0% +to a very simple quark model + + + align:start position:0% +to a very simple quark model +and you find um that you can actually + + align:start position:0% +and you find um that you can actually + + + align:start position:0% +and you find um that you can actually +very nicely describe those curves here + + align:start position:0% +very nicely describe those curves here + + + align:start position:0% +very nicely describe those curves here +so you see this yellowing level here is + + align:start position:0% +so you see this yellowing level here is + + + align:start position:0% +so you see this yellowing level here is +a qcd fit + + align:start position:0% +a qcd fit + + + align:start position:0% +a qcd fit +which basically uses those splitting + + align:start position:0% +which basically uses those splitting + + + align:start position:0% +which basically uses those splitting +functions as + + align:start position:0% +functions as + + + align:start position:0% +functions as +input all right so we learned quite a + + align:start position:0% +input all right so we learned quite a + + + align:start position:0% +input all right so we learned quite a +bit about + + align:start position:0% +bit about + + + align:start position:0% +bit about +the proton already if we want to now + + align:start position:0% +the proton already if we want to now + + + align:start position:0% +the proton already if we want to now +calculate a cross section of a proton + + align:start position:0% +calculate a cross section of a proton + + + align:start position:0% +calculate a cross section of a proton +scattering with a proton + + align:start position:0% +scattering with a proton + + + align:start position:0% +scattering with a proton +we are actually interested in the energy + + align:start position:0% +we are actually interested in the energy + + + align:start position:0% +we are actually interested in the energy +distributions or the momentum + + align:start position:0% +distributions or the momentum + + + align:start position:0% +distributions or the momentum +distributions of the particles in the + + align:start position:0% +distributions of the particles in the + + + align:start position:0% +distributions of the particles in the +protons + + align:start position:0% +protons + + + align:start position:0% +protons +and so we come back to how we use this + + align:start position:0% +and so we come back to how we use this + + + align:start position:0% +and so we come back to how we use this +later but i want to introduce part-time + + align:start position:0% +later but i want to introduce part-time + + + align:start position:0% +later but i want to introduce part-time +distribution functions which do exactly + + align:start position:0% +distribution functions which do exactly + + + align:start position:0% +distribution functions which do exactly +that + + align:start position:0% +that + + + align:start position:0% +that +they're defined as a probability to find + + align:start position:0% +they're defined as a probability to find + + + align:start position:0% +they're defined as a probability to find +a part on in the proton that carries + + align:start position:0% +a part on in the proton that carries + + + align:start position:0% +a part on in the proton that carries +energy between + + align:start position:0% +energy between + + + align:start position:0% +energy between +x and x plus dx you can write them + + align:start position:0% +x and x plus dx you can write them + + + align:start position:0% +x and x plus dx you can write them +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +using the structure functions before but + + align:start position:0% +using the structure functions before but + + + align:start position:0% +using the structure functions before but +they literally describe + + align:start position:0% +they literally describe + + + align:start position:0% +they literally describe +this probability and so what you find + + align:start position:0% +this probability and so what you find + + + align:start position:0% +this probability and so what you find +inside the protons are now the valence + + align:start position:0% +inside the protons are now the valence + + + align:start position:0% +inside the protons are now the valence +clock + + align:start position:0% +clock + + + align:start position:0% +clock +the down clock and the up quarks c + + align:start position:0% +the down clock and the up quarks c + + + align:start position:0% +the down clock and the up quarks c +quarks and antiquarks + + align:start position:0% +quarks and antiquarks + + + align:start position:0% +quarks and antiquarks +influence so you want to describe those + + align:start position:0% +influence so you want to describe those + + + align:start position:0% +influence so you want to describe those +momentum + + align:start position:0% +momentum + + + align:start position:0% +momentum +distributions or energy distributions of + + align:start position:0% +distributions or energy distributions of + + + align:start position:0% +distributions or energy distributions of +those particles + + align:start position:0% +those particles + + + align:start position:0% +those particles +there's a number of sum rules uh if you + + align:start position:0% +there's a number of sum rules uh if you + + + align:start position:0% +there's a number of sum rules uh if you +integrate momentum fractions from zero + + align:start position:0% +integrate momentum fractions from zero + + + align:start position:0% +integrate momentum fractions from zero +to one + + align:start position:0% +to one + + + align:start position:0% +to one +one being the momentum of the proton if + + align:start position:0% +one being the momentum of the proton if + + + align:start position:0% +one being the momentum of the proton if +you integrate them all together you have + + align:start position:0% +you integrate them all together you have + + + align:start position:0% +you integrate them all together you have +to find one + + align:start position:0% +to find one + + + align:start position:0% +to find one +because that is the momentum of the + + align:start position:0% +because that is the momentum of the + + + align:start position:0% +because that is the momentum of the +proton to start with + + align:start position:0% +proton to start with + + + align:start position:0% +proton to start with +if you integrate the down quarks in the + + align:start position:0% +if you integrate the down quarks in the + + + align:start position:0% +if you integrate the down quarks in the +up quarks you find + + align:start position:0% +up quarks you find + + + align:start position:0% +up quarks you find +one or two meaning that those are the + + align:start position:0% +one or two meaning that those are the + + + align:start position:0% +one or two meaning that those are the +number of valence corks we have + + align:start position:0% +number of valence corks we have + + + align:start position:0% +number of valence corks we have +available + + align:start position:0% +available + + + align:start position:0% +available +if you integrate the distributions of + + align:start position:0% +if you integrate the distributions of + + + align:start position:0% +if you integrate the distributions of +strange and anti-strange and charm and + + align:start position:0% +strange and anti-strange and charm and + + + align:start position:0% +strange and anti-strange and charm and +anti-charm + + align:start position:0% +anti-charm + + + align:start position:0% +anti-charm +you get zero well because there needs to + + align:start position:0% +you get zero well because there needs to + + + align:start position:0% +you get zero well because there needs to +be the same number of + + align:start position:0% +be the same number of + + + align:start position:0% +be the same number of +uh strange and anti-strange and charming + + align:start position:0% +uh strange and anti-strange and charming + + + align:start position:0% +uh strange and anti-strange and charming +anti-strange + + align:start position:0% +anti-strange + + + align:start position:0% +anti-strange +um and because of energy conservation + + align:start position:0% +um and because of energy conservation + + + align:start position:0% +um and because of energy conservation +the sum needs to this sum so sums need + + align:start position:0% +the sum needs to this sum so sums need + + + align:start position:0% +the sum needs to this sum so sums need +to be zero + + align:start position:0% +to be zero + + + align:start position:0% +to be zero +and then we can look at those so what's + + align:start position:0% +and then we can look at those so what's + + + align:start position:0% +and then we can look at those so what's +shown here is x + + align:start position:0% +shown here is x + + + align:start position:0% +shown here is x +times the pattern distribution functions + + align:start position:0% +times the pattern distribution functions + + + align:start position:0% +times the pattern distribution functions +the pdf + + align:start position:0% +the pdf + + + align:start position:0% +the pdf +as a function of f and what you see here + + align:start position:0% +as a function of f and what you see here + + + align:start position:0% +as a function of f and what you see here +for our valence quarks you see a + + align:start position:0% +for our valence quarks you see a + + + align:start position:0% +for our valence quarks you see a +distribution which is kind of what you + + align:start position:0% +distribution which is kind of what you + + + align:start position:0% +distribution which is kind of what you +expect + + align:start position:0% +expect + + + align:start position:0% +expect +it almost peaks at 0.3 a third um and + + align:start position:0% +it almost peaks at 0.3 a third um and + + + align:start position:0% +it almost peaks at 0.3 a third um and +has a distributions because there's + + align:start position:0% +has a distributions because there's + + + align:start position:0% +has a distributions because there's +kinematics involved + + align:start position:0% +kinematics involved + + + align:start position:0% +kinematics involved +and also um interactions because of the + + align:start position:0% +and also um interactions because of the + + + align:start position:0% +and also um interactions because of the +interactions with + + align:start position:0% +interactions with + + + align:start position:0% +interactions with +the clones and then you see + + align:start position:0% +the clones and then you see + + + align:start position:0% +the clones and then you see +the the c quarks and antiquarks and you + + align:start position:0% +the the c quarks and antiquarks and you + + + align:start position:0% +the the c quarks and antiquarks and you +see them + + align:start position:0% +see them + + + align:start position:0% +see them +increasing in numbers quite + + align:start position:0% +increasing in numbers quite + + + align:start position:0% +increasing in numbers quite +significantly as you go to small + + align:start position:0% +significantly as you go to small + + + align:start position:0% +significantly as you go to small +fraction of the momentum carriage + + align:start position:0% +fraction of the momentum carriage + + + align:start position:0% +fraction of the momentum carriage +it's exactly what we just discussed in + + align:start position:0% +it's exactly what we just discussed in + + + align:start position:0% +it's exactly what we just discussed in +the previous plot already + + align:start position:0% +the previous plot already + + + align:start position:0% +the previous plot already +an interesting way to look at this very + + align:start position:0% +an interesting way to look at this very + + + align:start position:0% +an interesting way to look at this very +same distribution function is if you + + align:start position:0% +same distribution function is if you + + + align:start position:0% +same distribution function is if you +plot them proportional to the momentum + + align:start position:0% +plot them proportional to the momentum + + + align:start position:0% +plot them proportional to the momentum +fractions or the area proportional to + + align:start position:0% +fractions or the area proportional to + + + align:start position:0% +fractions or the area proportional to +the momentum function and what you see + + align:start position:0% +the momentum function and what you see + + + align:start position:0% +the momentum function and what you see +there + + align:start position:0% +there + + + align:start position:0% +there +is that very significant part of the + + align:start position:0% +is that very significant part of the + + + align:start position:0% +is that very significant part of the +momentum of the proton is carried by the + + align:start position:0% +momentum of the proton is carried by the + + + align:start position:0% +momentum of the proton is carried by the +gluon + + align:start position:0% +gluon + + + align:start position:0% +gluon +um so you see here again our valence + + align:start position:0% +um so you see here again our valence + + + align:start position:0% +um so you see here again our valence +quarks our c + + align:start position:0% +quarks our c + + + align:start position:0% +quarks our c +quarks and the gluons itself so that's + + align:start position:0% +quarks and the gluons itself so that's + + + align:start position:0% +quarks and the gluons itself so that's +all i wanted to say on the structure of + + align:start position:0% +all i wanted to say on the structure of + + + align:start position:0% +all i wanted to say on the structure of +the proton + + align:start position:0% +the proton + + + align:start position:0% +the proton +we later in the lecture see how we can + + align:start position:0% +we later in the lecture see how we can + + + align:start position:0% +we later in the lecture see how we can +use those pdfs those pattern + + align:start position:0% +use those pdfs those pattern + + + align:start position:0% +use those pdfs those pattern +distribution functions in order to + + align:start position:0% +distribution functions in order to + + + align:start position:0% +distribution functions in order to +calculate a cross section in portrait + + align:start position:0% + + + + align:start position:0% + +protons + + align:start position:0% +protons + + + align:start position:0% +protons +you \ No newline at end of file diff --git a/HyqBcD_e_Uw.txt b/HyqBcD_e_Uw.txt new file mode 100644 index 0000000000000000000000000000000000000000..cc6b6fccc04c12d3e3914b2b905e3ac9f4100f0d --- /dev/null +++ b/HyqBcD_e_Uw.txt @@ -0,0 +1,1706 @@ +align:start position:0% + +hi welcome back to recitation in lecture + + align:start position:0% +hi welcome back to recitation in lecture + + + align:start position:0% +hi welcome back to recitation in lecture +you've been learning about how to solve + + align:start position:0% +you've been learning about how to solve + + + align:start position:0% +you've been learning about how to solve +multivariable optimization problems + + align:start position:0% +multivariable optimization problems + + + align:start position:0% +multivariable optimization problems +using the method of lrange multipliers + + align:start position:0% +using the method of lrange multipliers + + + align:start position:0% +using the method of lrange multipliers +and I have a nice problem here for you + + align:start position:0% +and I have a nice problem here for you + + + align:start position:0% +and I have a nice problem here for you +that can be solved that way so um in + + align:start position:0% +that can be solved that way so um in + + + align:start position:0% +that can be solved that way so um in +this problem we've got an ellipse the + + align:start position:0% +this problem we've got an ellipse the + + + align:start position:0% +this problem we've got an ellipse the +ellipse with equation x^2 + 4 y^2 equal + + align:start position:0% +ellipse with equation x^2 + 4 y^2 equal + + + align:start position:0% +ellipse with equation x^2 + 4 y^2 equal +4 so that's this ellipse and we want to + + align:start position:0% +4 so that's this ellipse and we want to + + + align:start position:0% +4 so that's this ellipse and we want to +inscribe a rectangle in it so here um I + + align:start position:0% +inscribe a rectangle in it so here um I + + + align:start position:0% +inscribe a rectangle in it so here um I +mean actually a rectangle whose whose + + align:start position:0% +mean actually a rectangle whose whose + + + align:start position:0% +mean actually a rectangle whose whose +edges are parallel to the to the axes so + + align:start position:0% +edges are parallel to the to the axes so + + + align:start position:0% +edges are parallel to the to the axes so +I want to inscribe a rectangle in this + + align:start position:0% +I want to inscribe a rectangle in this + + + align:start position:0% +I want to inscribe a rectangle in this +ellipse and I want to find the re among + + align:start position:0% +ellipse and I want to find the re among + + + align:start position:0% +ellipse and I want to find the re among +all such rectangles I want to find the + + align:start position:0% +all such rectangles I want to find the + + + align:start position:0% +all such rectangles I want to find the +one with the largest perimeter so I want + + align:start position:0% +one with the largest perimeter so I want + + + align:start position:0% +one with the largest perimeter so I want +to find the maximal perimeter of a + + align:start position:0% +to find the maximal perimeter of a + + + align:start position:0% +to find the maximal perimeter of a +rectangle that can be inscribed in this + + align:start position:0% +rectangle that can be inscribed in this + + + align:start position:0% +rectangle that can be inscribed in this +ellipse so why don't you have a go at + + align:start position:0% +ellipse so why don't you have a go at + + + align:start position:0% +ellipse so why don't you have a go at +solving this problem uh pause the video + + align:start position:0% +solving this problem uh pause the video + + + align:start position:0% +solving this problem uh pause the video +Work It Out come back and we can uh work + + align:start position:0% +Work It Out come back and we can uh work + + + align:start position:0% +Work It Out come back and we can uh work +it out together + + align:start position:0% + + + + align:start position:0% + +so hopefully you've had some luck + + align:start position:0% +so hopefully you've had some luck + + + align:start position:0% +so hopefully you've had some luck +working on this problem let's get + + align:start position:0% +working on this problem let's get + + + align:start position:0% +working on this problem let's get +started on it um so one thing uh we need + + align:start position:0% +started on it um so one thing uh we need + + + align:start position:0% +started on it um so one thing uh we need +to start is we need to figure out a way + + align:start position:0% +to start is we need to figure out a way + + + align:start position:0% +to start is we need to figure out a way +to sort of describe these rectangles and + + align:start position:0% +to sort of describe these rectangles and + + + align:start position:0% +to sort of describe these rectangles and +then in a way that will let us describe + + align:start position:0% +then in a way that will let us describe + + + align:start position:0% +then in a way that will let us describe +their perimeter write down what their + + align:start position:0% +their perimeter write down what their + + + align:start position:0% +their perimeter write down what their +perimeter is so a so a natural way to do + + align:start position:0% +perimeter is so a so a natural way to do + + + align:start position:0% +perimeter is so a so a natural way to do +that is to call this upper right hand + + align:start position:0% +that is to call this upper right hand + + + align:start position:0% +that is to call this upper right hand +corner of the rectangle to call it the + + align:start position:0% +corner of the rectangle to call it the + + + align:start position:0% +corner of the rectangle to call it the +point x y um so XY is going to be that + + align:start position:0% +point x y um so XY is going to be that + + + align:start position:0% +point x y um so XY is going to be that +upper right hand corner of the rectangle + + align:start position:0% +upper right hand corner of the rectangle + + + align:start position:0% +upper right hand corner of the rectangle +and it's going to be ranging over the + + align:start position:0% +and it's going to be ranging over the + + + align:start position:0% +and it's going to be ranging over the +region from this this topmost point on + + align:start position:0% +region from this this topmost point on + + + align:start position:0% +region from this this topmost point on +the ellipse down to this uh rightmost + + align:start position:0% +the ellipse down to this uh rightmost + + + align:start position:0% +the ellipse down to this uh rightmost +point on the ellipse on this on this + + align:start position:0% +point on the ellipse on this on this + + + align:start position:0% +point on the ellipse on this on this +quarter Arc of the ellipse so if that + + align:start position:0% +quarter Arc of the ellipse so if that + + + align:start position:0% +quarter Arc of the ellipse so if that +point is XY we need to figure out what + + align:start position:0% +point is XY we need to figure out what + + + align:start position:0% +point is XY we need to figure out what +is the perimeter that we're we're trying + + align:start position:0% +is the perimeter that we're we're trying + + + align:start position:0% +is the perimeter that we're we're trying +to optimize so the perimeter + + align:start position:0% +to optimize so the perimeter + + + align:start position:0% +to optimize so the perimeter +here P which is a function of X and Y + + align:start position:0% +here P which is a function of X and Y + + + align:start position:0% +here P which is a function of X and Y +well so X is this distance so the length + + align:start position:0% +well so X is this distance so the length + + + align:start position:0% +well so X is this distance so the length +of the horizontal edge of the rectangle + + align:start position:0% +of the horizontal edge of the rectangle + + + align:start position:0% +of the horizontal edge of the rectangle +is 2X and we've got two of those so + + align:start position:0% +is 2X and we've got two of those so + + + align:start position:0% +is 2X and we've got two of those so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +4X from the horizontal sides and then + + align:start position:0% +4X from the horizontal sides and then + + + align:start position:0% +4X from the horizontal sides and then +this height is y so the the length of + + align:start position:0% +this height is y so the the length of + + + align:start position:0% +this height is y so the the length of +the vertical side of the rectangle is 2 + + align:start position:0% +the vertical side of the rectangle is 2 + + + align:start position:0% +the vertical side of the rectangle is 2 +y so the the perimeter um is going to be + + align:start position:0% +y so the the perimeter um is going to be + + + align:start position:0% +y so the the perimeter um is going to be +4X plus 4 y so that's the function + + align:start position:0% +4X plus 4 y so that's the function + + + align:start position:0% +4X plus 4 y so that's the function +that's our objective function that we're + + align:start position:0% +that's our objective function that we're + + + align:start position:0% +that's our objective function that we're +trying to optimize that we're trying to + + align:start position:0% +trying to optimize that we're trying to + + + align:start position:0% +trying to optimize that we're trying to +to find the maximum of and we also have + + align:start position:0% +to find the maximum of and we also have + + + align:start position:0% +to find the maximum of and we also have +the constraint function G + + align:start position:0% + + + + align:start position:0% + +which is x^2 + 4 y^2 and the constraint + + align:start position:0% +which is x^2 + 4 y^2 and the constraint + + + align:start position:0% +which is x^2 + 4 y^2 and the constraint +is that that g is equal to 4 so we have + + align:start position:0% +is that that g is equal to 4 so we have + + + align:start position:0% +is that that g is equal to 4 so we have +we have the objective function p p of XY + + align:start position:0% +we have the objective function p p of XY + + + align:start position:0% +we have the objective function p p of XY +and we have this uh this constraint + + align:start position:0% +and we have this uh this constraint + + + align:start position:0% +and we have this uh this constraint +function G and so we want to write down + + align:start position:0% +function G and so we want to write down + + + align:start position:0% +function G and so we want to write down +some equations using lrange multipliers + + align:start position:0% +some equations using lrange multipliers + + + align:start position:0% +some equations using lrange multipliers +whose Solutions will will correspond to + + align:start position:0% +whose Solutions will will correspond to + + + align:start position:0% +whose Solutions will will correspond to +the to the possible uh maximum points of + + align:start position:0% +the to the possible uh maximum points of + + + align:start position:0% +the to the possible uh maximum points of +P so what are those equations well we + + align:start position:0% +P so what are those equations well we + + + align:start position:0% +P so what are those equations well we +need that the that the that the gradient + + align:start position:0% +need that the that the that the gradient + + + align:start position:0% +need that the that the that the gradient +of p is parallel to the gradient of G so + + align:start position:0% +of p is parallel to the gradient of G so + + + align:start position:0% +of p is parallel to the gradient of G so +that means that we need + + align:start position:0% +that means that we need + + + align:start position:0% +that means that we need +PX is equal to Lambda * GX and py is + + align:start position:0% +PX is equal to Lambda * GX and py is + + + align:start position:0% +PX is equal to Lambda * GX and py is +equal to Lambda * gy for some value of + + align:start position:0% +equal to Lambda * gy for some value of + + + align:start position:0% +equal to Lambda * gy for some value of +Lambda we need to find a value of Lambda + + align:start position:0% +Lambda we need to find a value of Lambda + + + align:start position:0% +Lambda we need to find a value of Lambda +that makes this true and then also our + + align:start position:0% +that makes this true and then also our + + + align:start position:0% +that makes this true and then also our +third equation is is the constraint + + align:start position:0% +third equation is is the constraint + + + align:start position:0% +third equation is is the constraint +equation that g is equal to four so what + + align:start position:0% +equation that g is equal to four so what + + + align:start position:0% +equation that g is equal to four so what +does PX equal Lambda GX translate to in + + align:start position:0% +does PX equal Lambda GX translate to in + + + align:start position:0% +does PX equal Lambda GX translate to in +our case just draw a line here um so our + + align:start position:0% +our case just draw a line here um so our + + + align:start position:0% +our case just draw a line here um so our +case PX is the the xth partial + + align:start position:0% +case PX is the the xth partial + + + align:start position:0% +case PX is the the xth partial +derivative of of 4x + 4 y so that's just + + align:start position:0% +derivative of of 4x + 4 y so that's just + + + align:start position:0% +derivative of of 4x + 4 y so that's just +4 and GX is we take the partial + + align:start position:0% +4 and GX is we take the partial + + + align:start position:0% +4 and GX is we take the partial +derivative with respect to X of x^2 + 4 + + align:start position:0% +derivative with respect to X of x^2 + 4 + + + align:start position:0% +derivative with respect to X of x^2 + 4 +y^2 and that's equal to 2x so 4 is equal + + align:start position:0% +y^2 and that's equal to 2x so 4 is equal + + + align:start position:0% +y^2 and that's equal to 2x so 4 is equal +to Lambda * 2X and from taking the Y + + align:start position:0% +to Lambda * 2X and from taking the Y + + + align:start position:0% +to Lambda * 2X and from taking the Y +partial derivatives we have that the Y + + align:start position:0% +partial derivatives we have that the Y + + + align:start position:0% +partial derivatives we have that the Y +partial derivative of p is four py is + + align:start position:0% +partial derivative of p is four py is + + + align:start position:0% +partial derivative of p is four py is +four and gy is going to be the Y partial + + align:start position:0% +four and gy is going to be the Y partial + + + align:start position:0% +four and gy is going to be the Y partial +derivative of x^2 + 4 y^2 so that's 8 y + + align:start position:0% +derivative of x^2 + 4 y^2 so that's 8 y + + + align:start position:0% +derivative of x^2 + 4 y^2 so that's 8 y +so 4al Lambda time 8 Y and we also have + + align:start position:0% +so 4al Lambda time 8 Y and we also have + + + align:start position:0% +so 4al Lambda time 8 Y and we also have +the equation the the constraint equation + + align:start position:0% +the equation the the constraint equation + + + align:start position:0% +the equation the the constraint equation +x^2 + 4 y^2 = 4 so we need to solve + + align:start position:0% +x^2 + 4 y^2 = 4 so we need to solve + + + align:start position:0% +x^2 + 4 y^2 = 4 so we need to solve +these three equations and we need to + + align:start position:0% +these three equations and we need to + + + align:start position:0% +these three equations and we need to +figure out which values of X and Y are + + align:start position:0% +figure out which values of X and Y are + + + align:start position:0% +figure out which values of X and Y are +are the are the solutions um so I think + + align:start position:0% +are the are the solutions um so I think + + + align:start position:0% +are the are the solutions um so I think +the the simplest way to proceed here is + + align:start position:0% +the the simplest way to proceed here is + + + align:start position:0% +the the simplest way to proceed here is +to note that from the from the first + + align:start position:0% +to note that from the from the first + + + align:start position:0% +to note that from the from the first +equation and the second equation we can + + align:start position:0% +equation and the second equation we can + + + align:start position:0% +equation and the second equation we can +eliminate Lambda between them and what + + align:start position:0% +eliminate Lambda between them and what + + + align:start position:0% +eliminate Lambda between them and what +we'll see is that X has to be exactly + + align:start position:0% +we'll see is that X has to be exactly + + + align:start position:0% +we'll see is that X has to be exactly +four times as large as y for this to be + + align:start position:0% +four times as large as y for this to be + + + align:start position:0% +four times as large as y for this to be +true okay for both of these equations to + + align:start position:0% +true okay for both of these equations to + + + align:start position:0% +true okay for both of these equations to +be true at the same time so we need X to + + align:start position:0% +be true at the same time so we need X to + + + align:start position:0% +be true at the same time so we need X to +be equal to 4 y + + align:start position:0% + + + + align:start position:0% + +so so from the first + + align:start position:0% +so so from the first + + + align:start position:0% +so so from the first +two equations we have that X is equal to + + align:start position:0% +two equations we have that X is equal to + + + align:start position:0% +two equations we have that X is equal to +4 Y and now we can substitute that in to + + align:start position:0% +4 Y and now we can substitute that in to + + + align:start position:0% +4 Y and now we can substitute that in to +the to the constraint equation so if x + + align:start position:0% +the to the constraint equation so if x + + + align:start position:0% +the to the constraint equation so if x +is 4 y then x^2 is 16 y^2 so x^2 + 4 y^2 + + align:start position:0% +is 4 y then x^2 is 16 y^2 so x^2 + 4 y^2 + + + align:start position:0% +is 4 y then x^2 is 16 y^2 so x^2 + 4 y^2 +is 20 + + align:start position:0% +is 20 + + + align:start position:0% +is 20 +y^2 so we have 20 y^2 is equal to 4 and + + align:start position:0% +y^2 so we have 20 y^2 is equal to 4 and + + + align:start position:0% +y^2 so we have 20 y^2 is equal to 4 and +okay so we can solve this for y we can + + align:start position:0% +okay so we can solve this for y we can + + + align:start position:0% +okay so we can solve this for y we can +divide by 20 and take a square root so + + align:start position:0% +divide by 20 and take a square root so + + + align:start position:0% +divide by 20 and take a square root so +we get that y well so y^2 is equal to5 + + align:start position:0% +we get that y well so y^2 is equal to5 + + + align:start position:0% +we get that y well so y^2 is equal to5 +so so Y is equal to plus or- 1 over the + + align:start position:0% +so so Y is equal to plus or- 1 over the + + + align:start position:0% +so so Y is equal to plus or- 1 over the +< TK 5 but remember it come back over + + align:start position:0% +< TK 5 but remember it come back over + + + align:start position:0% +< TK 5 but remember it come back over +here we've taken XY to be the upper + + align:start position:0% +here we've taken XY to be the upper + + + align:start position:0% +here we've taken XY to be the upper +right hand corner this first quadrant + + align:start position:0% +right hand corner this first quadrant + + + align:start position:0% +right hand corner this first quadrant +corner of our rectangle so Y is always + + align:start position:0% +corner of our rectangle so Y is always + + + align:start position:0% +corner of our rectangle so Y is always +positive so we had that y^2 = 1/5 and Y + + align:start position:0% +positive so we had that y^2 = 1/5 and Y + + + align:start position:0% +positive so we had that y^2 = 1/5 and Y +is positive so there's actually only one + + align:start position:0% +is positive so there's actually only one + + + align:start position:0% +is positive so there's actually only one +root we don't need to consider the + + align:start position:0% +root we don't need to consider the + + + align:start position:0% +root we don't need to consider the +negative root so over here we know that + + align:start position:0% +negative root so over here we know that + + + align:start position:0% +negative root so over here we know that +Y is 1 / the < TK of 5 + + align:start position:0% +Y is 1 / the < TK of 5 + + + align:start position:0% +Y is 1 / the < TK of 5 +okay so that's y now what's X well okay + + align:start position:0% +okay so that's y now what's X well okay + + + align:start position:0% +okay so that's y now what's X well okay +so we solved for X in terms of Y so X is + + align:start position:0% +so we solved for X in terms of Y so X is + + + align:start position:0% +so we solved for X in terms of Y so X is +equal to 4 over theun of 5 so lrange + + align:start position:0% +equal to 4 over theun of 5 so lrange + + + align:start position:0% +equal to 4 over theun of 5 so lrange +multipliers um when we when we use the + + align:start position:0% +multipliers um when we when we use the + + + align:start position:0% +multipliers um when we when we use the +method of LR multipliers we get this one + + align:start position:0% +method of LR multipliers we get this one + + + align:start position:0% +method of LR multipliers we get this one +possible point for for at at which we + + align:start position:0% +possible point for for at at which we + + + align:start position:0% +possible point for for at at which we +have to check to be the maximum but + + align:start position:0% +have to check to be the maximum but + + + align:start position:0% +have to check to be the maximum but +remember that when you're using lrange + + align:start position:0% +remember that when you're using lrange + + + align:start position:0% +remember that when you're using lrange +multipliers you also have to worry about + + align:start position:0% +multipliers you also have to worry about + + + align:start position:0% +multipliers you also have to worry about +the boundary of the region that you're + + align:start position:0% +the boundary of the region that you're + + + align:start position:0% +the boundary of the region that you're +interested in so let's go look at our + + align:start position:0% +interested in so let's go look at our + + + align:start position:0% +interested in so let's go look at our +picture again um so over on our picture + + align:start position:0% +picture again um so over on our picture + + + align:start position:0% +picture again um so over on our picture +this point XY moved along the + + align:start position:0% +this point XY moved along the + + + align:start position:0% +this point XY moved along the +arc from connecting the topmost point of + + align:start position:0% +arc from connecting the topmost point of + + + align:start position:0% +arc from connecting the topmost point of +the ellipse to the rightmost point of + + align:start position:0% +the ellipse to the rightmost point of + + + align:start position:0% +the ellipse to the rightmost point of +the ellipse so we also have to look at + + align:start position:0% +the ellipse so we also have to look at + + + align:start position:0% +the ellipse so we also have to look at +the perimeters when the when the point + + align:start position:0% +the perimeters when the when the point + + + align:start position:0% +the perimeters when the when the point +is the topmost point and when the point + + align:start position:0% +is the topmost point and when the point + + + align:start position:0% +is the topmost point and when the point +is the rightmost point now in those two + + align:start position:0% +is the rightmost point now in those two + + + align:start position:0% +is the rightmost point now in those two +cases the rectangle is a sort of + + align:start position:0% +cases the rectangle is a sort of + + + align:start position:0% +cases the rectangle is a sort of +degenerate rectangle and when the when + + align:start position:0% +degenerate rectangle and when the when + + + align:start position:0% +degenerate rectangle and when the when +the when XY is is this 01 it's sort of + + align:start position:0% +the when XY is is this 01 it's sort of + + + align:start position:0% +the when XY is is this 01 it's sort of +two two copies of this vertical uh line + + align:start position:0% +two two copies of this vertical uh line + + + align:start position:0% +two two copies of this vertical uh line +this this minor axis and when XY is the + + align:start position:0% +this this minor axis and when XY is the + + + align:start position:0% +this this minor axis and when XY is the +point two Z then then our rectangle just + + align:start position:0% +point two Z then then our rectangle just + + + align:start position:0% +point two Z then then our rectangle just +looks like the the the major axis just + + align:start position:0% +looks like the the the major axis just + + + align:start position:0% +looks like the the the major axis just +that horizontal line U but we still have + + align:start position:0% +that horizontal line U but we still have + + + align:start position:0% +that horizontal line U but we still have +to check those cases because to to see + + align:start position:0% +to check those cases because to to see + + + align:start position:0% +to check those cases because to to see +whether our function has a maximum and + + align:start position:0% +whether our function has a maximum and + + + align:start position:0% +whether our function has a maximum and +what it is so we need to compute the + + align:start position:0% +what it is so we need to compute the + + + align:start position:0% +what it is so we need to compute the +function the objective function value at + + align:start position:0% +function the objective function value at + + + align:start position:0% +function the objective function value at +this point and we need to compute it at + + align:start position:0% +this point and we need to compute it at + + + align:start position:0% +this point and we need to compute it at +at those end points so we need to look + + align:start position:0% +at those end points so we need to look + + + align:start position:0% +at those end points so we need to look +we need to look at P of so this is our 4 + + align:start position:0% +we need to look at P of so this is our 4 + + + align:start position:0% +we need to look at P of so this is our 4 +over < TK 5A 1 over < TK 5 and we know + + align:start position:0% +over < TK 5A 1 over < TK 5 and we know + + + align:start position:0% +over < TK 5A 1 over < TK 5 and we know +that P of X Y is 4x + 4 y so that's + + align:start position:0% +that P of X Y is 4x + 4 y so that's + + + align:start position:0% +that P of X Y is 4x + 4 y so that's +equal to 20 over < TK 5 which we can + + align:start position:0% +equal to 20 over < TK 5 which we can + + + align:start position:0% +equal to 20 over < TK 5 which we can +also write as 4 * the < TK 5 and we also + + align:start position:0% +also write as 4 * the < TK 5 and we also + + + align:start position:0% +also write as 4 * the < TK 5 and we also +need to check those two end points so we + + align:start position:0% +need to check those two end points so we + + + align:start position:0% +need to check those two end points so we +need to check the points P of 01 so + + align:start position:0% +need to check the points P of 01 so + + + align:start position:0% +need to check the points P of 01 so +that's four and we need to check the + + align:start position:0% +that's four and we need to check the + + + align:start position:0% +that's four and we need to check the +point P of 20 so that's eight so in + + align:start position:0% +point P of 20 so that's eight so in + + + align:start position:0% +point P of 20 so that's eight so in +order to find out what the max imum + + align:start position:0% +order to find out what the max imum + + + align:start position:0% +order to find out what the max imum +value of p is we need to compare the + + align:start position:0% +value of p is we need to compare the + + + align:start position:0% +value of p is we need to compare the +value of P at the fun at the points + + align:start position:0% +value of P at the fun at the points + + + align:start position:0% +value of P at the fun at the points +given to us by LR multipliers and at the + + align:start position:0% +given to us by LR multipliers and at the + + + align:start position:0% +given to us by LR multipliers and at the +the the boundary points of the region um + + align:start position:0% +the the boundary points of the region um + + + align:start position:0% +the the boundary points of the region um +which in this case are the end points of + + align:start position:0% +which in this case are the end points of + + + align:start position:0% +which in this case are the end points of +the arc so we need to Compare the + + align:start position:0% +the arc so we need to Compare the + + + align:start position:0% +the arc so we need to Compare the +numbers 4un of 5 four and8 and indeed + + align:start position:0% +numbers 4un of 5 four and8 and indeed + + + align:start position:0% +numbers 4un of 5 four and8 and indeed +four Ro 5 is the largest of these so + + align:start position:0% +four Ro 5 is the largest of these so + + + align:start position:0% +four Ro 5 is the largest of these so +this is the largest so this is actually + + align:start position:0% +this is the largest so this is actually + + + align:start position:0% +this is the largest so this is actually +the maximum value okay so the so maximum + + align:start position:0% +the maximum value okay so the so maximum + + + align:start position:0% +the maximum value okay so the so maximum +perimeter + + align:start position:0% + + + + align:start position:0% + +is four S + + align:start position:0% +is four S + + + align:start position:0% +is four S + + align:start position:0% + + + + align:start position:0% + +when + + align:start position:0% +when + + + align:start position:0% +when +rectangle has its upper rightmost vertex + + align:start position:0% +rectangle has its upper rightmost vertex + + + align:start position:0% +rectangle has its upper rightmost vertex +at the point uh this this point 4 over + + align:start position:0% +at the point uh this this point 4 over + + + align:start position:0% +at the point uh this this point 4 over +Square < TK of 5 comma 1 over < TK 5 so + + align:start position:0% +Square < TK of 5 comma 1 over < TK 5 so + + + align:start position:0% +Square < TK of 5 comma 1 over < TK 5 so +the maximum so our our rectangle Max + + align:start position:0% +the maximum so our our rectangle Max + + + align:start position:0% +the maximum so our our rectangle Max +maal perimeter is 4un 5 and that occurs + + align:start position:0% +maal perimeter is 4un 5 and that occurs + + + align:start position:0% +maal perimeter is 4un 5 and that occurs +when the upper right hand vertex is at + + align:start position:0% +when the upper right hand vertex is at + + + align:start position:0% +when the upper right hand vertex is at +the point 4 overun 5 1 overun 5 so to + + align:start position:0% +the point 4 overun 5 1 overun 5 so to + + + align:start position:0% +the point 4 overun 5 1 overun 5 so to +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +recap we had we wanted to apply the + + align:start position:0% +recap we had we wanted to apply the + + + align:start position:0% +recap we had we wanted to apply the +method of lrange multipliers to this + + align:start position:0% +method of lrange multipliers to this + + + align:start position:0% +method of lrange multipliers to this +problem so we we chose to to keep track + + align:start position:0% +problem so we we chose to to keep track + + + align:start position:0% +problem so we we chose to to keep track +of our rectangles by their upper right + + align:start position:0% +of our rectangles by their upper right + + + align:start position:0% +of our rectangles by their upper right +hand corner and then that gave us the + + align:start position:0% +hand corner and then that gave us the + + + align:start position:0% +hand corner and then that gave us the +perimeter uh was 4X plus 4 y that was + + align:start position:0% +perimeter uh was 4X plus 4 y that was + + + align:start position:0% +perimeter uh was 4X plus 4 y that was +our objective function and the + + align:start position:0% +our objective function and the + + + align:start position:0% +our objective function and the +constraint was that that upper right + + align:start position:0% +constraint was that that upper right + + + align:start position:0% +constraint was that that upper right +hand corner actually had to lie on the + + align:start position:0% +hand corner actually had to lie on the + + + align:start position:0% +hand corner actually had to lie on the +ellipse so then + + align:start position:0% +ellipse so then + + + align:start position:0% +ellipse so then +we needed so we set the gradients of the + + align:start position:0% +we needed so we set the gradients of the + + + align:start position:0% +we needed so we set the gradients of the +two functions equal and solved the + + align:start position:0% +two functions equal and solved the + + + align:start position:0% +two functions equal and solved the +system of equations that we get um by + + align:start position:0% +system of equations that we get um by + + + align:start position:0% +system of equations that we get um by +having those those uh sorry the + + align:start position:0% +having those those uh sorry the + + + align:start position:0% +having those those uh sorry the +gradients not to be equal but to be + + align:start position:0% +gradients not to be equal but to be + + + align:start position:0% +gradients not to be equal but to be +parallel there's some some constant + + align:start position:0% +parallel there's some some constant + + + align:start position:0% +parallel there's some some constant +multiple Lambda that appears so we set + + align:start position:0% +multiple Lambda that appears so we set + + + align:start position:0% +multiple Lambda that appears so we set +the gradients to be parallel to each + + align:start position:0% +the gradients to be parallel to each + + + align:start position:0% +the gradients to be parallel to each +other and the constraint equation to + + align:start position:0% +other and the constraint equation to + + + align:start position:0% +other and the constraint equation to +hold and we solved those three uh those + + align:start position:0% +hold and we solved those three uh those + + + align:start position:0% +hold and we solved those three uh those +three equations simultaneously for X and + + align:start position:0% +three equations simultaneously for X and + + + align:start position:0% +three equations simultaneously for X and +Y um um and those equations gave us one + + align:start position:0% +Y um um and those equations gave us one + + + align:start position:0% +Y um um and those equations gave us one +uh point that we had to check to be the + + align:start position:0% +uh point that we had to check to be the + + + align:start position:0% +uh point that we had to check to be the +maximum and we also needed to check + + align:start position:0% +maximum and we also needed to check + + + align:start position:0% +maximum and we also needed to check +points on the boundary of the region in + + align:start position:0% +points on the boundary of the region in + + + align:start position:0% +points on the boundary of the region in +question so here those were just the two + + align:start position:0% +question so here those were just the two + + + align:start position:0% +question so here those were just the two +points 01 and + + align:start position:0% +points 01 and + + + align:start position:0% +points 01 and +two so I'll end there \ No newline at end of file diff --git a/IPDZFNh73Kw.txt b/IPDZFNh73Kw.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d71af46a61e1bd7b7ad61828ddc68e8e8ea073c --- /dev/null +++ b/IPDZFNh73Kw.txt @@ -0,0 +1,715 @@ +align:start position:0% + +regard to Market segmentation let me + + align:start position:0% +regard to Market segmentation let me + + + align:start position:0% +regard to Market segmentation let me +give you a very concrete example uh one + + align:start position:0% +give you a very concrete example uh one + + + align:start position:0% +give you a very concrete example uh one +of the companies um that I started with + + align:start position:0% +of the companies um that I started with + + + align:start position:0% +of the companies um that I started with +Thomas Massie it was actually his + + align:start position:0% +Thomas Massie it was actually his + + + align:start position:0% +Thomas Massie it was actually his +technology it started about sensible + + align:start position:0% +technology it started about sensible + + + align:start position:0% +technology it started about sensible +devices then we created sensible + + align:start position:0% +devices then we created sensible + + + align:start position:0% +devices then we created sensible +Technologies was a revolutionary 3D um + + align:start position:0% +Technologies was a revolutionary 3D um + + + align:start position:0% +Technologies was a revolutionary 3D um +interface into the computer basically it + + align:start position:0% +interface into the computer basically it + + + align:start position:0% +interface into the computer basically it +was a robot um that allowed you to feel + + align:start position:0% +was a robot um that allowed you to feel + + + align:start position:0% +was a robot um that allowed you to feel +things in the computer it's like a 3D + + align:start position:0% +things in the computer it's like a 3D + + + align:start position:0% +things in the computer it's like a 3D +Mouse next to it but I could feel it as + + align:start position:0% +Mouse next to it but I could feel it as + + + align:start position:0% +Mouse next to it but I could feel it as +I moved in here I could feel what I saw + + align:start position:0% +I moved in here I could feel what I saw + + + align:start position:0% +I moved in here I could feel what I saw +and I could lift it up and down I could + + align:start position:0% +and I could lift it up and down I could + + + align:start position:0% +and I could lift it up and down I could +twist it around I could move it + + align:start position:0% +twist it around I could move it + + + align:start position:0% +twist it around I could move it +extraordinary technology and I could + + align:start position:0% +extraordinary technology and I could + + + align:start position:0% +extraordinary technology and I could +actually deform what I saw there so uh + + align:start position:0% +actually deform what I saw there so uh + + + align:start position:0% +actually deform what I saw there so uh +for the first time people could they + + align:start position:0% +for the first time people could they + + + align:start position:0% +for the first time people could they +could see things in the computer they + + align:start position:0% +could see things in the computer they + + + align:start position:0% +could see things in the computer they +could hear things in the computer but + + align:start position:0% +could hear things in the computer but + + + align:start position:0% +could hear things in the computer but +for the first time they could touch it + + align:start position:0% +for the first time they could touch it + + + align:start position:0% +for the first time they could touch it +as well extraordinary + + align:start position:0% +as well extraordinary + + + align:start position:0% +as well extraordinary +breakthrough um it allowed all types of + + align:start position:0% +breakthrough um it allowed all types of + + + align:start position:0% +breakthrough um it allowed all types of +things to happen you could now play + + align:start position:0% +things to happen you could now play + + + align:start position:0% +things to happen you could now play +games we could feel things you could do + + align:start position:0% +games we could feel things you could do + + + align:start position:0% +games we could feel things you could do +medical simulations you could do + + align:start position:0% +medical simulations you could do + + + align:start position:0% +medical simulations you could do +interact with 3D objects in ways that + + align:start position:0% +interact with 3D objects in ways that + + + align:start position:0% +interact with 3D objects in ways that +people couldn't imag have imagined + + align:start position:0% +people couldn't imag have imagined + + + align:start position:0% +people couldn't imag have imagined +before uh blind people could now use it + + align:start position:0% +before uh blind people could now use it + + + align:start position:0% +before uh blind people could now use it +there was just it was a target-rich + + align:start position:0% +there was just it was a target-rich + + + align:start position:0% +there was just it was a target-rich +environment of things that we could do + + align:start position:0% +environment of things that we could do + + + align:start position:0% +environment of things that we could do +and we made a list of all the things we + + align:start position:0% +and we made a list of all the things we + + + align:start position:0% +and we made a list of all the things we +could do it was extraordinarily long + + align:start position:0% +could do it was extraordinarily long + + + align:start position:0% +could do it was extraordinarily long +crazy ideas um ideas that were + + align:start position:0% +crazy ideas um ideas that were + + + align:start position:0% +crazy ideas um ideas that were +inappropriate um but we had to come up + + align:start position:0% +inappropriate um but we had to come up + + + align:start position:0% +inappropriate um but we had to come up +with a way to move forward that was + + align:start position:0% +with a way to move forward that was + + + align:start position:0% +with a way to move forward that was +aligned with our p passions and our + + align:start position:0% +aligned with our p passions and our + + + align:start position:0% +aligned with our p passions and our +values so what we did is we made a + + align:start position:0% +values so what we did is we made a + + + align:start position:0% +values so what we did is we made a +matrix that that listed at the very top + + align:start position:0% +matrix that that listed at the very top + + + align:start position:0% +matrix that that listed at the very top +you know the top markets that we were + + align:start position:0% +you know the top markets that we were + + + align:start position:0% +you know the top markets that we were +going to be involved with and for + + align:start position:0% +going to be involved with and for + + + align:start position:0% +going to be involved with and for +instance one of them + + align:start position:0% +instance one of them + + + align:start position:0% +instance one of them +was uh an animator that was the customer + + align:start position:0% +was uh an animator that was the customer + + + align:start position:0% +was uh an animator that was the customer +so in this it was the the industry was + + align:start position:0% +so in this it was the the industry was + + + align:start position:0% +so in this it was the the industry was +the entertainment + + align:start position:0% + + + + align:start position:0% + +industry and I apologize for this being + + align:start position:0% +industry and I apologize for this being + + + align:start position:0% +industry and I apologize for this being +too small but we we we'll we'll put + + align:start position:0% +too small but we we we'll we'll put + + + align:start position:0% +too small but we we we'll we'll put +online an example of this of this Matrix + + align:start position:0% +online an example of this of this Matrix + + + align:start position:0% +online an example of this of this Matrix +cuz it's going to be very detailed but + + align:start position:0% +cuz it's going to be very detailed but + + + align:start position:0% +cuz it's going to be very detailed but +while the industry entertainment was + + align:start position:0% +while the industry entertainment was + + + align:start position:0% +while the industry entertainment was +relevant what was much more relevant was + + align:start position:0% +relevant what was much more relevant was + + + align:start position:0% +relevant what was much more relevant was +who was the end + + align:start position:0% +who was the end + + + align:start position:0% +who was the end +user who was the end user and in this + + align:start position:0% +user who was the end user and in this + + + align:start position:0% +user who was the end user and in this +case the end user was an animator be it + + align:start position:0% +case the end user was an animator be it + + + align:start position:0% +case the end user was an animator be it +a Pixar be it industrial Light and Magic + + align:start position:0% +a Pixar be it industrial Light and Magic + + + align:start position:0% +a Pixar be it industrial Light and Magic +you know these you know being at Disney + + align:start position:0% +you know these you know being at Disney + + + align:start position:0% +you know these you know being at Disney +all these people had a real need to to + + align:start position:0% +all these people had a real need to to + + + align:start position:0% +all these people had a real need to to +move three-dimensional object around and + + align:start position:0% +move three-dimensional object around and + + + align:start position:0% +move three-dimensional object around and +we decided not to focus on the 2D but + + align:start position:0% +we decided not to focus on the 2D but + + + align:start position:0% +we decided not to focus on the 2D but +strictly the 3D So within that we had to + + align:start position:0% +strictly the 3D So within that we had to + + + align:start position:0% +strictly the 3D So within that we had to +say that's the end user what exactly are + + align:start position:0% +say that's the end user what exactly are + + + align:start position:0% +say that's the end user what exactly are +they doing and in three dimensions what + + align:start position:0% +they doing and in three dimensions what + + + align:start position:0% +they doing and in three dimensions what +they were doing was what was the + + align:start position:0% +they were doing was what was the + + + align:start position:0% +they were doing was what was the +application that they were + + align:start position:0% + + + + align:start position:0% + +doing and the application was they were + + align:start position:0% + + + + align:start position:0% + +sculpting they were + + align:start position:0% +sculpting they were + + + align:start position:0% +sculpting they were +painting and there might be some + + align:start position:0% + + + + align:start position:0% + +Dynamics so you've seen 3D movies so + + align:start position:0% +Dynamics so you've seen 3D movies so + + + align:start position:0% +Dynamics so you've seen 3D movies so +they have to create the shapes they have + + align:start position:0% +they have to create the shapes they have + + + align:start position:0% +they have to create the shapes they have +to sculpt them they then paint them to + + align:start position:0% +to sculpt them they then paint them to + + + align:start position:0% +to sculpt them they then paint them to +be a certain color and they paint them + + align:start position:0% +be a certain color and they paint them + + + align:start position:0% +be a certain color and they paint them +in three dimensions um and then they + + align:start position:0% +in three dimensions um and then they + + + align:start position:0% +in three dimensions um and then they +move them around and so all of these + + align:start position:0% +move them around and so all of these + + + align:start position:0% +move them around and so all of these +things were things that were animators + + align:start position:0% +things were things that were animators + + + align:start position:0% +things were things that were animators +were doing in a very non-intuitive way + + align:start position:0% +were doing in a very non-intuitive way + + + align:start position:0% +were doing in a very non-intuitive way +but as soon as they could have our 3D + + align:start position:0% +but as soon as they could have our 3D + + + align:start position:0% +but as soon as they could have our 3D +device they could do that and so as we + + align:start position:0% +device they could do that and so as we + + + align:start position:0% +device they could do that and so as we +go down to what was they we were going + + align:start position:0% +go down to what was they we were going + + + align:start position:0% +go down to what was they we were going +to use it for now we could have the + + align:start position:0% +to use it for now we could have the + + + align:start position:0% +to use it for now we could have the +specific benefits that they were going + + align:start position:0% +specific benefits that they were going + + + align:start position:0% +specific benefits that they were going +to achieve from this as + + align:start position:0% + + + + align:start position:0% + +well and we could we gave a detailed + + align:start position:0% +well and we could we gave a detailed + + + align:start position:0% +well and we could we gave a detailed +description of the benefits that they + + align:start position:0% +description of the benefits that they + + + align:start position:0% +description of the benefits that they +would get from this then we would say + + align:start position:0% +would get from this then we would say + + + align:start position:0% +would get from this then we would say +what does the market look like Market + + align:start position:0% +what does the market look like Market + + + align:start position:0% +what does the market look like Market +characteristics then we talk about who + + align:start position:0% +characteristics then we talk about who + + + align:start position:0% +characteristics then we talk about who +are the current players that are out + + align:start position:0% +are the current players that are out + + + align:start position:0% +are the current players that are out +there doing that so we can see the Asis + + align:start position:0% +there doing that so we can see the Asis + + + align:start position:0% +there doing that so we can see the Asis +States so why we're better and you can + + align:start position:0% +States so why we're better and you can + + + align:start position:0% +States so why we're better and you can +see through this whole Matrix that we + + align:start position:0% +see through this whole Matrix that we + + + align:start position:0% +see through this whole Matrix that we +lay out \ No newline at end of file diff --git a/IZ405_YLKJQ.txt b/IZ405_YLKJQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..81877c536c4181221901399665ffa995d99cc37d --- /dev/null +++ b/IZ405_YLKJQ.txt @@ -0,0 +1,6715 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +ok so this is going to be a fun lecture + + align:start position:0% +ok so this is going to be a fun lecture + + + align:start position:0% +ok so this is going to be a fun lecture +because it's mostly pictures and + + align:start position:0% +because it's mostly pictures and + + + align:start position:0% +because it's mostly pictures and +language and it's also an area of + + align:start position:0% +language and it's also an area of + + + align:start position:0% +language and it's also an area of +physical chemistry which is pretty much + + align:start position:0% +physical chemistry which is pretty much + + + align:start position:0% +physical chemistry which is pretty much +I mean there's three areas of physical + + align:start position:0% +I mean there's three areas of physical + + + align:start position:0% +I mean there's three areas of physical +chemistry that where people have trouble + + align:start position:0% +chemistry that where people have trouble + + + align:start position:0% +chemistry that where people have trouble +talking to each other there's + + align:start position:0% +talking to each other there's + + + align:start position:0% +talking to each other there's +statistical mechanics + + align:start position:0% +statistical mechanics + + + align:start position:0% +statistical mechanics +there's quantum mechanics and there's + + align:start position:0% +there's quantum mechanics and there's + + + align:start position:0% +there's quantum mechanics and there's +the time-dependent time independent + + align:start position:0% +the time-dependent time independent + + + align:start position:0% +the time-dependent time independent +forms of quantum mechanics and these + + align:start position:0% +forms of quantum mechanics and these + + + align:start position:0% +forms of quantum mechanics and these +three communities have to learn how to + + align:start position:0% +three communities have to learn how to + + + align:start position:0% +three communities have to learn how to +talk to each other and I'm hoping that I + + align:start position:0% +talk to each other and I'm hoping that I + + + align:start position:0% +talk to each other and I'm hoping that I +will help to bridge that gap ok so last + + align:start position:0% +will help to bridge that gap ok so last + + + align:start position:0% +will help to bridge that gap ok so last +time we talked about the time-dependent + + align:start position:0% +time we talked about the time-dependent + + + align:start position:0% +time we talked about the time-dependent +schrodinger equation it's a simple + + align:start position:0% +schrodinger equation it's a simple + + + align:start position:0% +schrodinger equation it's a simple +looking little thing remember though + + align:start position:0% +looking little thing remember though + + + align:start position:0% +looking little thing remember though +it's an extra level of complexity on + + align:start position:0% +it's an extra level of complexity on + + + align:start position:0% +it's an extra level of complexity on +what you already understand now in the + + align:start position:0% +what you already understand now in the + + + align:start position:0% +what you already understand now in the +special case where the Hamiltonian is + + align:start position:0% +special case where the Hamiltonian is + + + align:start position:0% +special case where the Hamiltonian is +time independent then if you know all of + + align:start position:0% +time independent then if you know all of + + + align:start position:0% +time independent then if you know all of +the energy levels and wave functions for + + align:start position:0% +the energy levels and wave functions for + + + align:start position:0% +the energy levels and wave functions for +the time independent Hamiltonian you can + + align:start position:0% +the time independent Hamiltonian you can + + + align:start position:0% +the time independent Hamiltonian you can +immediately write down the solution to + + align:start position:0% +immediately write down the solution to + + + align:start position:0% +immediately write down the solution to +the time-dependent Hamiltonian and so + + align:start position:0% +the time-dependent Hamiltonian and so + + + align:start position:0% +the time-dependent Hamiltonian and so +you have a complete set of wave + + align:start position:0% +you have a complete set of wave + + + align:start position:0% +you have a complete set of wave +functions and you have a complete set of + + align:start position:0% +functions and you have a complete set of + + + align:start position:0% +functions and you have a complete set of +energy levels and with that you can + + align:start position:0% +energy levels and with that you can + + + align:start position:0% +energy levels and with that you can +basically describe something that + + align:start position:0% +basically describe something that + + + align:start position:0% +basically describe something that +satisfies this thing now the set of + + align:start position:0% +satisfies this thing now the set of + + + align:start position:0% +satisfies this thing now the set of +coefficients is often something that you + + align:start position:0% +coefficients is often something that you + + + align:start position:0% +coefficients is often something that you +that you arrange for simplicity or for + + align:start position:0% +that you arrange for simplicity or for + + + align:start position:0% +that you arrange for simplicity or for +insight and I want to understand I want + + align:start position:0% +insight and I want to understand I want + + + align:start position:0% +insight and I want to understand I want +to talk about that ok and so in the + + align:start position:0% +to talk about that ok and so in the + + + align:start position:0% +to talk about that ok and so in the +previous lecture we talked about the + + align:start position:0% +previous lecture we talked about the + + + align:start position:0% +previous lecture we talked about the +total probability the probability + + align:start position:0% +total probability the probability + + + align:start position:0% +total probability the probability +density which is psy star psy and that + + align:start position:0% +density which is psy star psy and that + + + align:start position:0% +density which is psy star psy and that +can move and that can move + + align:start position:0% +can move and that can move + + + align:start position:0% +can move and that can move +in two ways if there are in the + + align:start position:0% +in two ways if there are in the + + + align:start position:0% +in two ways if there are in the +wavefunction if there are two or more + + align:start position:0% +wavefunction if there are two or more + + + align:start position:0% +wavefunction if there are two or more +states blowing to two or more different + + align:start position:0% +states blowing to two or more different + + + align:start position:0% +states blowing to two or more different +energies then you can have motion and + + align:start position:0% +energies then you can have motion and + + + align:start position:0% +energies then you can have motion and +you can have motion like breathing where + + align:start position:0% +you can have motion like breathing where + + + align:start position:0% +you can have motion like breathing where +probability moves towards the extremes + + align:start position:0% +probability moves towards the extremes + + + align:start position:0% +probability moves towards the extremes +or motion where there's actually wave + + align:start position:0% +or motion where there's actually wave + + + align:start position:0% +or motion where there's actually wave +packet going from one side to another so + + align:start position:0% +packet going from one side to another so + + + align:start position:0% +packet going from one side to another so +it required for anything interesting to + + align:start position:0% +it required for anything interesting to + + + align:start position:0% +it required for anything interesting to +happen this probability density has to + + align:start position:0% +happen this probability density has to + + + align:start position:0% +happen this probability density has to +include to at least two different + + align:start position:0% +include to at least two different + + + align:start position:0% +include to at least two different +eigenstates belonging to two different + + align:start position:0% +eigenstates belonging to two different + + + align:start position:0% +eigenstates belonging to two different +energy levels now the total probability + + align:start position:0% +energy levels now the total probability + + + align:start position:0% +energy levels now the total probability +is just the integral over all + + align:start position:0% +is just the integral over all + + + align:start position:0% +is just the integral over all +coordinates of the probability density + + align:start position:0% +coordinates of the probability density + + + align:start position:0% +coordinates of the probability density +and probability is conserved so one of + + align:start position:0% +and probability is conserved so one of + + + align:start position:0% +and probability is conserved so one of +the things that happens when you do an + + align:start position:0% +the things that happens when you do an + + + align:start position:0% +the things that happens when you do an +integral the wave functions go away and + + align:start position:0% +integral the wave functions go away and + + + align:start position:0% +integral the wave functions go away and +in this particular case integral psystar + + align:start position:0% +in this particular case integral psystar + + + align:start position:0% +in this particular case integral psystar +sigh all you get is 1 or you get a + + align:start position:0% +sigh all you get is 1 or you get a + + + align:start position:0% +sigh all you get is 1 or you get a +constant depending on how you normalize + + align:start position:0% +constant depending on how you normalize + + + align:start position:0% +constant depending on how you normalize +things but it doesn't it's not + + align:start position:0% +things but it doesn't it's not + + + align:start position:0% +things but it doesn't it's not +time-dependent now - in understanding + + align:start position:0% +time-dependent now - in understanding + + + align:start position:0% +time-dependent now - in understanding +motion from classical mechanics we know + + align:start position:0% +motion from classical mechanics we know + + + align:start position:0% +motion from classical mechanics we know +Newton's equations we know how the + + align:start position:0% +Newton's equations we know how the + + + align:start position:0% +Newton's equations we know how the +coordinate and the momentum depends on + + align:start position:0% +coordinate and the momentum depends on + + + align:start position:0% +coordinate and the momentum depends on +time and and so if we calculate the + + align:start position:0% +time and and so if we calculate the + + + align:start position:0% +time and and so if we calculate the +expectation value of the coordinate or + + align:start position:0% +expectation value of the coordinate or + + + align:start position:0% +expectation value of the coordinate or +the expectation value of the momentum we + + align:start position:0% +the expectation value of the momentum we + + + align:start position:0% +the expectation value of the momentum we +get some results and it turns out that + + align:start position:0% +get some results and it turns out that + + + align:start position:0% +get some results and it turns out that +these things describe the motion of the + + align:start position:0% +these things describe the motion of the + + + align:start position:0% +these things describe the motion of the +center of a wave packet web packet is + + align:start position:0% +center of a wave packet web packet is + + + align:start position:0% +center of a wave packet web packet is +anything that's not just a single + + align:start position:0% +anything that's not just a single + + + align:start position:0% +anything that's not just a single +eigenstate so it moves and so the the + + align:start position:0% +eigenstate so it moves and so the the + + + align:start position:0% +eigenstate so it moves and so the the +motion of a single eigenstate a motion + + align:start position:0% +motion of a single eigenstate a motion + + + align:start position:0% +motion of a single eigenstate a motion +of a wave packet is described by + + align:start position:0% +of a wave packet is described by + + + align:start position:0% +of a wave packet is described by +Newton's laws and this is ehrenfest + + align:start position:0% +Newton's laws and this is ehrenfest + + + align:start position:0% +Newton's laws and this is ehrenfest +theorem and it can easily be proven so + + align:start position:0% +theorem and it can easily be proven so + + + align:start position:0% +theorem and it can easily be proven so +but we're not going to prove it we're + + align:start position:0% +but we're not going to prove it we're + + + align:start position:0% +but we're not going to prove it we're +just going to use it so we are very + + align:start position:0% +just going to use it so we are very + + + align:start position:0% +just going to use it so we are very +interested in expectation values of the + + align:start position:0% +interested in expectation values of the + + + align:start position:0% +interested in expectation values of the +ordinate and the momentum and for a + + align:start position:0% +ordinate and the momentum and for a + + + align:start position:0% +ordinate and the momentum and for a +harmonic oscillator this is duck soup + + align:start position:0% +harmonic oscillator this is duck soup + + + align:start position:0% +harmonic oscillator this is duck soup +and we have nothing about trivial + + align:start position:0% +and we have nothing about trivial + + + align:start position:0% +and we have nothing about trivial +integrals involving the A's and a + + align:start position:0% +integrals involving the A's and a + + + align:start position:0% +integrals involving the A's and a +daggers and so even though in some ways + + align:start position:0% +daggers and so even though in some ways + + + align:start position:0% +daggers and so even though in some ways +the harmonic oscillator is a more + + align:start position:0% +the harmonic oscillator is a more + + + align:start position:0% +the harmonic oscillator is a more +complicated problem than the particle in + + align:start position:0% +complicated problem than the particle in + + + align:start position:0% +complicated problem than the particle in +a box the harmonic oscillator is the + + align:start position:0% +a box the harmonic oscillator is the + + + align:start position:0% +a box the harmonic oscillator is the +problem of choice for dealing with + + align:start position:0% +problem of choice for dealing with + + + align:start position:0% +problem of choice for dealing with +motion and developing insight is another + + align:start position:0% +motion and developing insight is another + + + align:start position:0% +motion and developing insight is another +useful okay we have this wave function + + align:start position:0% +useful okay we have this wave function + + + align:start position:0% +useful okay we have this wave function +here there's a huge amount of + + align:start position:0% +here there's a huge amount of + + + align:start position:0% +here there's a huge amount of +information embedded in it + + align:start position:0% +information embedded in it + + + align:start position:0% +information embedded in it +too much to just look at we need to have + + align:start position:0% +too much to just look at we need to have + + + align:start position:0% +too much to just look at we need to have +ways of reducing that information and + + align:start position:0% +ways of reducing that information and + + + align:start position:0% +ways of reducing that information and +one of the nice ways is this survival + + align:start position:0% +one of the nice ways is this survival + + + align:start position:0% +one of the nice ways is this survival +probability the survival probability + + align:start position:0% +probability the survival probability + + + align:start position:0% +probability the survival probability +tells you how fast does the initial + + align:start position:0% +tells you how fast does the initial + + + align:start position:0% +tells you how fast does the initial +state move away from itself and this is + + align:start position:0% +state move away from itself and this is + + + align:start position:0% +state move away from itself and this is +very revealing another very revealing + + align:start position:0% +very revealing another very revealing + + + align:start position:0% +very revealing another very revealing +thing is if this survival probability + + align:start position:0% +thing is if this survival probability + + + align:start position:0% +thing is if this survival probability +which is a function of time and nothing + + align:start position:0% +which is a function of time and nothing + + + align:start position:0% +which is a function of time and nothing +else because we've integrated over the + + align:start position:0% +else because we've integrated over the + + + align:start position:0% +else because we've integrated over the +wave functions if this survival + + align:start position:0% +wave functions if this survival + + + align:start position:0% +wave functions if this survival +probability goes up and down and up and + + align:start position:0% +probability goes up and down and up and + + + align:start position:0% +probability goes up and down and up and +down there are recurrences so at a + + align:start position:0% +down there are recurrences so at a + + + align:start position:0% +down there are recurrences so at a +maximum which is usually a maximum at T + + align:start position:0% +maximum which is usually a maximum at T + + + align:start position:0% +maximum which is usually a maximum at T +equals 0 because the wave function is it + + align:start position:0% +equals 0 because the wave function is it + + + align:start position:0% +equals 0 because the wave function is it +at its birthplace the the survival + + align:start position:0% +at its birthplace the the survival + + + align:start position:0% +at its birthplace the the survival +probability will will start high and go + + align:start position:0% +probability will will start high and go + + + align:start position:0% +probability will will start high and go +down and come up go down and there's all + + align:start position:0% +down and come up go down and there's all + + + align:start position:0% +down and come up go down and there's all +sorts of information about recurrences + + align:start position:0% +sorts of information about recurrences + + + align:start position:0% +sorts of information about recurrences +as the wave function returns to its + + align:start position:0% +as the wave function returns to its + + + align:start position:0% +as the wave function returns to its +birthplace it might not return + + align:start position:0% +birthplace it might not return + + + align:start position:0% +birthplace it might not return +completely and so we get partial + + align:start position:0% +completely and so we get partial + + + align:start position:0% +completely and so we get partial +recurrences and these tell us something + + align:start position:0% +recurrences and these tell us something + + + align:start position:0% +recurrences and these tell us something +and the the times at which the Maxima in + + align:start position:0% +and the the times at which the Maxima in + + + align:start position:0% +and the the times at which the Maxima in +the survival probability occur tell us a + + align:start position:0% +the survival probability occur tell us a + + + align:start position:0% +the survival probability occur tell us a +lot about the potential and there are + + align:start position:0% +lot about the potential and there are + + + align:start position:0% +lot about the potential and there are +some grand recurrences where because all + + align:start position:0% +some grand recurrences where because all + + + align:start position:0% +some grand recurrences where because all +of the energy level differences are an + + align:start position:0% +of the energy level differences are an + + + align:start position:0% +of the energy level differences are an +integer multiple of a common factor then + + align:start position:0% +integer multiple of a common factor then + + + align:start position:0% +integer multiple of a common factor then +you get a perfect recurrence and these + + align:start position:0% +you get a perfect recurrence and these + + + align:start position:0% +you get a perfect recurrence and these +are wonderful for making draw + + align:start position:0% +are wonderful for making draw + + + align:start position:0% +are wonderful for making draw +pictures now you really want to + + align:start position:0% +pictures now you really want to + + + align:start position:0% +pictures now you really want to +understand the concepts of + + align:start position:0% +understand the concepts of + + + align:start position:0% +understand the concepts of +time-dependent quantum mechanics + + align:start position:0% +time-dependent quantum mechanics + + + align:start position:0% +time-dependent quantum mechanics +pictorially and to develop a language + + align:start position:0% +pictorially and to develop a language + + + align:start position:0% +pictorially and to develop a language +that describes it and there are a lot of + + align:start position:0% +that describes it and there are a lot of + + + align:start position:0% +that describes it and there are a lot of +little pieces here that you need to + + align:start position:0% +little pieces here that you need to + + + align:start position:0% +little pieces here that you need to +convince yourself you understand and so + + align:start position:0% +convince yourself you understand and so + + + align:start position:0% +convince yourself you understand and so +you can use the language okay okay one + + align:start position:0% +you can use the language okay okay one + + + align:start position:0% +you can use the language okay okay one +of the things I said at the beginning of + + align:start position:0% +of the things I said at the beginning of + + + align:start position:0% +of the things I said at the beginning of +the course is the central object in + + align:start position:0% +the course is the central object in + + + align:start position:0% +the course is the central object in +quantum mechanics is the wave function + + align:start position:0% +quantum mechanics is the wave function + + + align:start position:0% +quantum mechanics is the wave function +or we could have generalized to this + + align:start position:0% +or we could have generalized to this + + + align:start position:0% +or we could have generalized to this +this is actually this is the truth + + align:start position:0% +this is actually this is the truth + + + align:start position:0% +this is actually this is the truth +this is a partial truth this is + + align:start position:0% +this is a partial truth this is + + + align:start position:0% +this is a partial truth this is +everything that we can possibly know but + + align:start position:0% +everything that we can possibly know but + + + align:start position:0% +everything that we can possibly know but +we can't know this we can never observe + + align:start position:0% +we can't know this we can never observe + + + align:start position:0% +we can't know this we can never observe +the wave function however we do + + align:start position:0% +the wave function however we do + + + align:start position:0% +the wave function however we do +observations and we construct a picture + + align:start position:0% +observations and we construct a picture + + + align:start position:0% +observations and we construct a picture +which is what we call the effective + + align:start position:0% +which is what we call the effective + + + align:start position:0% +which is what we call the effective +Hamiltonian this effective Hamiltonian + + align:start position:0% +Hamiltonian this effective Hamiltonian + + + align:start position:0% +Hamiltonian this effective Hamiltonian +describes everything we know mostly + + align:start position:0% +describes everything we know mostly + + + align:start position:0% +describes everything we know mostly +energy levels we have formulas for the + + align:start position:0% +energy levels we have formulas for the + + + align:start position:0% +energy levels we have formulas for the +energy levels we determine the constants + + align:start position:0% +energy levels we determine the constants + + + align:start position:0% +energy levels we determine the constants +there's all sorts of stuff that we + + align:start position:0% +there's all sorts of stuff that we + + + align:start position:0% +there's all sorts of stuff that we +collect by experiment and so we create + + align:start position:0% +collect by experiment and so we create + + + align:start position:0% +collect by experiment and so we create +an object which we think is like the + + align:start position:0% +an object which we think is like the + + + align:start position:0% +an object which we think is like the +true Hamiltonian and by having the + + align:start position:0% +true Hamiltonian and by having the + + + align:start position:0% +true Hamiltonian and by having the +effective Hamiltonian we can get these + + align:start position:0% +effective Hamiltonian we can get these + + + align:start position:0% +effective Hamiltonian we can get these +things so we observe we make some + + align:start position:0% +things so we observe we make some + + + align:start position:0% +things so we observe we make some +observations and then this is a kind of + + align:start position:0% +observations and then this is a kind of + + + align:start position:0% +observations and then this is a kind of +a reduced version of the truth and we + + align:start position:0% +a reduced version of the truth and we + + + align:start position:0% +a reduced version of the truth and we +can get a pretty good representation of + + align:start position:0% +can get a pretty good representation of + + + align:start position:0% +can get a pretty good representation of +the thing that is supposedly hidden from + + align:start position:0% +the thing that is supposedly hidden from + + + align:start position:0% +the thing that is supposedly hidden from +us + + align:start position:0% + + + + align:start position:0% + +okay so let's start now at T equals zero + + align:start position:0% +okay so let's start now at T equals zero + + + align:start position:0% +okay so let's start now at T equals zero +at T equals zero which I like to call + + align:start position:0% +at T equals zero which I like to call + + + align:start position:0% +at T equals zero which I like to call +the pluck and it really makes it contact + + align:start position:0% +the pluck and it really makes it contact + + + align:start position:0% +the pluck and it really makes it contact +with those of you who are musicians that + + align:start position:0% +with those of you who are musicians that + + + align:start position:0% +with those of you who are musicians that +you know how to create a particular kind + + align:start position:0% +you know how to create a particular kind + + + align:start position:0% +you know how to create a particular kind +of sound which will evolve in time and + + align:start position:0% +of sound which will evolve in time and + + + align:start position:0% +of sound which will evolve in time and +it depends on details of how you handle + + align:start position:0% +it depends on details of how you handle + + + align:start position:0% +it depends on details of how you handle +the instrument so at t equals zero we + + align:start position:0% +the instrument so at t equals zero we + + + align:start position:0% +the instrument so at t equals zero we +have this thing which if we have a + + align:start position:0% +have this thing which if we have a + + + align:start position:0% +have this thing which if we have a +complete set of eigenfunctions of the + + align:start position:0% +complete set of eigenfunctions of the + + + align:start position:0% +complete set of eigenfunctions of the +hamiltonian of the time independent + + align:start position:0% +hamiltonian of the time independent + + + align:start position:0% +hamiltonian of the time independent +Hamiltonian we know we can write this as + + align:start position:0% +Hamiltonian we know we can write this as + + + align:start position:0% +Hamiltonian we know we can write this as +CJ psy K of X now often we don't need an + + align:start position:0% +CJ psy K of X now often we don't need an + + + align:start position:0% +CJ psy K of X now often we don't need an +infinite number of terms but we know + + align:start position:0% +infinite number of terms but we know + + + align:start position:0% +infinite number of terms but we know +that there are lots of different kinds + + align:start position:0% +that there are lots of different kinds + + + align:start position:0% +that there are lots of different kinds +of plucks + + align:start position:0% +of plucks + + + align:start position:0% +of plucks +and you could find out what the what the + + align:start position:0% +and you could find out what the what the + + + align:start position:0% +and you could find out what the what the +these coefficients are by just + + align:start position:0% +these coefficients are by just + + + align:start position:0% +these coefficients are by just +calculating an overlap integral of these + + align:start position:0% +calculating an overlap integral of these + + + align:start position:0% +calculating an overlap integral of these +functions with this initial state okay + + align:start position:0% +functions with this initial state okay + + + align:start position:0% +functions with this initial state okay +so this is telling you what happens at T + + align:start position:0% +so this is telling you what happens at T + + + align:start position:0% +so this is telling you what happens at T +equals 0 and if you can write the + + align:start position:0% +equals 0 and if you can write the + + + align:start position:0% +equals 0 and if you can write the +initial state as a superposition of + + align:start position:0% +initial state as a superposition of + + + align:start position:0% +initial state as a superposition of +eigen states then you can immediately + + align:start position:0% +eigen states then you can immediately + + + align:start position:0% +eigen states then you can immediately +write the time evolving object + + align:start position:0% + + + + align:start position:0% + +this way now we have a - I well why do + + align:start position:0% +this way now we have a - I well why do + + + align:start position:0% +this way now we have a - I well why do +we need a - I well because we're going + + align:start position:0% +we need a - I well because we're going + + + align:start position:0% +we need a - I well because we're going +to take the time derivative of the + + align:start position:0% +to take the time derivative of the + + + align:start position:0% +to take the time derivative of the +Hamiltonian and multiply it by IH bar + + align:start position:0% +Hamiltonian and multiply it by IH bar + + + align:start position:0% +Hamiltonian and multiply it by IH bar +we're going to want to get we're going + + align:start position:0% +we're going to want to get we're going + + + align:start position:0% +we're going to want to get we're going +to want to get the energy not minus the + + align:start position:0% +to want to get the energy not minus the + + + align:start position:0% +to want to get the energy not minus the +energy and so we need a - I here and we + + align:start position:0% +energy and so we need a - I here and we + + + align:start position:0% +energy and so we need a - I here and we +need a divided by h-bar here in order to + + align:start position:0% +need a divided by h-bar here in order to + + + align:start position:0% +need a divided by h-bar here in order to +satisfy the time-independent equation + + align:start position:0% +satisfy the time-independent equation + + + align:start position:0% +satisfy the time-independent equation +time dependence varies so this always + + align:start position:0% +time dependence varies so this always + + + align:start position:0% +time dependence varies so this always +bothers bothers people why should there + + align:start position:0% +bothers bothers people why should there + + + align:start position:0% +bothers bothers people why should there +be an eye here and why should it be - I + + align:start position:0% +be an eye here and why should it be - I + + + align:start position:0% +be an eye here and why should it be - I +and I recommend not trying to memorize + + align:start position:0% +and I recommend not trying to memorize + + + align:start position:0% +and I recommend not trying to memorize +it but to just convince yourself I need + + align:start position:0% +it but to just convince yourself I need + + + align:start position:0% +it but to just convince yourself I need +the - I because I'm going to bring down + + align:start position:0% +the - I because I'm going to bring down + + + align:start position:0% +the - I because I'm going to bring down +a minus I over H bar times e and we have + + align:start position:0% +a minus I over H bar times e and we have + + + align:start position:0% +a minus I over H bar times e and we have +this IH bar that - I times I gives less + + align:start position:0% +this IH bar that - I times I gives less + + + align:start position:0% +this IH bar that - I times I gives less +one okay so now in understanding how + + align:start position:0% +one okay so now in understanding how + + + align:start position:0% +one okay so now in understanding how +time the time-dependent Hamiltonian can + + align:start position:0% +time the time-dependent Hamiltonian can + + + align:start position:0% +time the time-dependent Hamiltonian can +be sampled we build these superposition + + align:start position:0% +be sampled we build these superposition + + + align:start position:0% +be sampled we build these superposition +states with the minimum number of terms + + align:start position:0% +states with the minimum number of terms + + + align:start position:0% +states with the minimum number of terms +like two or three even though in order + + align:start position:0% +like two or three even though in order + + + align:start position:0% +like two or three even though in order +to create a very very sharply localized + + align:start position:0% +to create a very very sharply localized + + + align:start position:0% +to create a very very sharply localized +state it needs a huge number of terms + + align:start position:0% +state it needs a huge number of terms + + + align:start position:0% +state it needs a huge number of terms +here but you always build your insight + + align:start position:0% +here but you always build your insight + + + align:start position:0% +here but you always build your insight +with something you can do in your head + + align:start position:0% +with something you can do in your head + + + align:start position:0% +with something you can do in your head +and so for some problems you need only + + align:start position:0% +and so for some problems you need only + + + align:start position:0% +and so for some problems you need only +two states and for others you need three + + align:start position:0% +two states and for others you need three + + + align:start position:0% +two states and for others you need three +and those are the ones you want to kill + + align:start position:0% +and those are the ones you want to kill + + + align:start position:0% +and those are the ones you want to kill +you want to understand everything you + + align:start position:0% +you want to understand everything you + + + align:start position:0% +you want to understand everything you +can build with two and three states or + + align:start position:0% +can build with two and three states or + + + align:start position:0% +can build with two and three states or +four positions + + align:start position:0% + + + + align:start position:0% + +okay so there's two classes of problems + + align:start position:0% + + + + align:start position:0% + +okay so for 1/2 harmonic oscillator so + + align:start position:0% +okay so for 1/2 harmonic oscillator so + + + align:start position:0% +okay so for 1/2 harmonic oscillator so +for 1/2 harmonic oscillator we start + + align:start position:0% +for 1/2 harmonic oscillator we start + + + align:start position:0% +for 1/2 harmonic oscillator we start +with a harmonic oscillator and divided + + align:start position:0% +with a harmonic oscillator and divided + + + align:start position:0% +with a harmonic oscillator and divided +in half and say this is this goes to + + align:start position:0% +in half and say this is this goes to + + + align:start position:0% +in half and say this is this goes to +infinity and so this side is not + + align:start position:0% +infinity and so this side is not + + + align:start position:0% +infinity and so this side is not +accessible and so if the wave if the + + align:start position:0% +accessible and so if the wave if the + + + align:start position:0% +accessible and so if the wave if the +potential is 1/2 of a harmonic + + align:start position:0% +potential is 1/2 of a harmonic + + + align:start position:0% +potential is 1/2 of a harmonic +oscillator potential then we know + + align:start position:0% +oscillator potential then we know + + + align:start position:0% +oscillator potential then we know +immediately what the eigenvalues and + + align:start position:0% +immediately what the eigenvalues and + + + align:start position:0% +immediately what the eigenvalues and +eigenfunctions are they are the harmonic + + align:start position:0% +eigenfunctions are they are the harmonic + + + align:start position:0% +eigenfunctions are they are the harmonic +oscillator functions that have a node in + + align:start position:0% +oscillator functions that have a node in + + + align:start position:0% +oscillator functions that have a node in +the middle so we know that we have V + + align:start position:0% +the middle so we know that we have V + + + align:start position:0% +the middle so we know that we have V +equals 1 V equals 3 know V equals 0 to I + + align:start position:0% +equals 1 V equals 3 know V equals 0 to I + + + align:start position:0% +equals 1 V equals 3 know V equals 0 to I +mean this corresponds to the lowest + + align:start position:0% +mean this corresponds to the lowest + + + align:start position:0% +mean this corresponds to the lowest +level V equals 0 for the half oscillator + + align:start position:0% +level V equals 0 for the half oscillator + + + align:start position:0% +level V equals 0 for the half oscillator +but this is basically now what we're + + align:start position:0% +but this is basically now what we're + + + align:start position:0% +but this is basically now what we're +going to do is we create some state of + + align:start position:0% +going to do is we create some state of + + + align:start position:0% +going to do is we create some state of +the half oscillator and then we take + + align:start position:0% +the half oscillator and then we take + + + align:start position:0% +the half oscillator and then we take +away the barrier so that's a cheap way + + align:start position:0% +away the barrier so that's a cheap way + + + align:start position:0% +away the barrier so that's a cheap way +of creating localization of course we + + align:start position:0% +of creating localization of course we + + + align:start position:0% +of creating localization of course we +can't do this experimentally but you + + align:start position:0% +can't do this experimentally but you + + + align:start position:0% +can't do this experimentally but you +could in principle do it and so + + align:start position:0% +could in principle do it and so + + + align:start position:0% +could in principle do it and so +basically you want an initial state + + align:start position:0% + + + + align:start position:0% + +which is a superposition of vibrational + + align:start position:0% +which is a superposition of vibrational + + + align:start position:0% +which is a superposition of vibrational +levels okay and this initial state needs + + align:start position:0% +levels okay and this initial state needs + + + align:start position:0% +levels okay and this initial state needs +to have zero and the wave function be + + align:start position:0% +to have zero and the wave function be + + + align:start position:0% +to have zero and the wave function be +zero at the barrier so since we're going + + align:start position:0% +zero at the barrier so since we're going + + + align:start position:0% +zero at the barrier so since we're going +to be looking at the full potential + + align:start position:0% +to be looking at the full potential + + + align:start position:0% +to be looking at the full potential +we're taking away the barrier we're + + align:start position:0% +we're taking away the barrier we're + + + align:start position:0% +we're taking away the barrier we're +allowed to use the even and odd States + + align:start position:0% +allowed to use the even and odd States + + + align:start position:0% +allowed to use the even and odd States +and so let's take the three lowest + + align:start position:0% +and so let's take the three lowest + + + align:start position:0% +and so let's take the three lowest +states and so we have C 0 sy 0 plus C 1 + + align:start position:0% +states and so we have C 0 sy 0 plus C 1 + + + align:start position:0% +states and so we have C 0 sy 0 plus C 1 +Phi 1 plus C 2 sigh - ok this guy is ok + + align:start position:0% +Phi 1 plus C 2 sigh - ok this guy is ok + + + align:start position:0% +Phi 1 plus C 2 sigh - ok this guy is ok +yes yes yes yes we play fast and loose + + align:start position:0% +yes yes yes yes we play fast and loose + + + align:start position:0% +yes yes yes yes we play fast and loose +with normalization constants we already + + align:start position:0% +with normalization constants we already + + + align:start position:0% +with normalization constants we already +always know that whenever you want to + + align:start position:0% +always know that whenever you want to + + + align:start position:0% +always know that whenever you want to +calculate anything you're going to + + align:start position:0% +calculate anything you're going to + + + align:start position:0% +calculate anything you're going to +divide by the normalization integral + + align:start position:0% +divide by the normalization integral + + + align:start position:0% +divide by the normalization integral +however it's ok because we're going to + + align:start position:0% +however it's ok because we're going to + + + align:start position:0% +however it's ok because we're going to +be using the full harmonic oscillator + + align:start position:0% +be using the full harmonic oscillator + + + align:start position:0% +be using the full harmonic oscillator +functions which do exist over here it's + + align:start position:0% +functions which do exist over here it's + + + align:start position:0% +functions which do exist over here it's +just and then it's fine once we remove + + align:start position:0% +just and then it's fine once we remove + + + align:start position:0% +just and then it's fine once we remove +the barrier but you know we want to + + align:start position:0% +the barrier but you know we want to + + + align:start position:0% +the barrier but you know we want to +choose a problem which is as simple as + + align:start position:0% +choose a problem which is as simple as + + + align:start position:0% +choose a problem which is as simple as +possible ok now this guy is not 0 at the + + align:start position:0% +possible ok now this guy is not 0 at the + + + align:start position:0% +possible ok now this guy is not 0 at the +at x equals 0 and this guy is not 0 at x + + align:start position:0% +at x equals 0 and this guy is not 0 at x + + + align:start position:0% +at x equals 0 and this guy is not 0 at x +equals 0 but you can say 0 is equal to C + + align:start position:0% +equals 0 but you can say 0 is equal to C + + + align:start position:0% +equals 0 but you can say 0 is equal to C +0 sy 0 of 0 plus C 2 so I 2 of 0 we + + align:start position:0% +0 sy 0 of 0 plus C 2 so I 2 of 0 we + + + align:start position:0% +0 sy 0 of 0 plus C 2 so I 2 of 0 we +choose the coefficients so that these + + align:start position:0% +choose the coefficients so that these + + + align:start position:0% +choose the coefficients so that these +two guys together make 0 at the boundary + + align:start position:0% +two guys together make 0 at the boundary + + + align:start position:0% +two guys together make 0 at the boundary +and why do we do this we're going to be + + align:start position:0% +and why do we do this we're going to be + + + align:start position:0% +and why do we do this we're going to be +calculating expectation values of X and + + align:start position:0% +calculating expectation values of X and + + + align:start position:0% +calculating expectation values of X and +T if we only have odd if we only have + + align:start position:0% +T if we only have odd if we only have + + + align:start position:0% +T if we only have odd if we only have +half of the energy levels + + align:start position:0% +half of the energy levels + + + align:start position:0% +half of the energy levels +all of the integrals are going to be 0 + + align:start position:0% +all of the integrals are going to be 0 + + + align:start position:0% +all of the integrals are going to be 0 +so we have to have three consecutive + + align:start position:0% +so we have to have three consecutive + + + align:start position:0% +so we have to have three consecutive +levels to have anything interesting okay + + align:start position:0% +levels to have anything interesting okay + + + align:start position:0% +levels to have anything interesting okay +so so the artifice of making these two + + align:start position:0% +so so the artifice of making these two + + + align:start position:0% +so so the artifice of making these two +arranging the coefficients so that you + + align:start position:0% +arranging the coefficients so that you + + + align:start position:0% +arranging the coefficients so that you +get a temporary note at x equals 0 + + align:start position:0% +get a temporary note at x equals 0 + + + align:start position:0% +get a temporary note at x equals 0 +it won't stay anode because we let + + align:start position:0% +it won't stay anode because we let + + + align:start position:0% +it won't stay anode because we let +things oscillate with time these two + + align:start position:0% +things oscillate with time these two + + + align:start position:0% +things oscillate with time these two +will oscillate differently and the node + + align:start position:0% +will oscillate differently and the node + + + align:start position:0% +will oscillate differently and the node +will go away but that's how you do it + + align:start position:0% +will go away but that's how you do it + + + align:start position:0% +will go away but that's how you do it +that's how you build a superposition ok + + align:start position:0% + + + + align:start position:0% + +ok now what we want to do is to be able + + align:start position:0% +ok now what we want to do is to be able + + + align:start position:0% +ok now what we want to do is to be able +to draw pictures of what's happening and + + align:start position:0% +to draw pictures of what's happening and + + + align:start position:0% +to draw pictures of what's happening and +also to calculate what's going on and + + align:start position:0% +also to calculate what's going on and + + + align:start position:0% +also to calculate what's going on and +one of the things we use for our + + align:start position:0% +one of the things we use for our + + + align:start position:0% +one of the things we use for our +pictures is the expectation value of x + + align:start position:0% +pictures is the expectation value of x + + + align:start position:0% +pictures is the expectation value of x +and the expectation value of P so you + + align:start position:0% +and the expectation value of P so you + + + align:start position:0% +and the expectation value of P so you +notic calculate the expectation value of + + align:start position:0% +notic calculate the expectation value of + + + align:start position:0% +notic calculate the expectation value of +x we have this capital upside star X + + align:start position:0% +x we have this capital upside star X + + + align:start position:0% +x we have this capital upside star X +capital psystar Capital upside integrate + + align:start position:0% +capital psystar Capital upside integrate + + + align:start position:0% +capital psystar Capital upside integrate +over X and so we get 2 C 0 C 1 X 0 1 + + align:start position:0% +over X and so we get 2 C 0 C 1 X 0 1 + + + align:start position:0% +over X and so we get 2 C 0 C 1 X 0 1 +cosine Omega T plus 2 C 1 C 2 X 1 2 + + align:start position:0% +cosine Omega T plus 2 C 1 C 2 X 1 2 + + + align:start position:0% +cosine Omega T plus 2 C 1 C 2 X 1 2 +cosine Omega T now how did I do that oh + + align:start position:0% + + + + align:start position:0% + +come on you could do it too so what is + + align:start position:0% +come on you could do it too so what is + + + align:start position:0% +come on you could do it too so what is +this X 0 well X 0 1 is the integral ty0 + + align:start position:0% +this X 0 well X 0 1 is the integral ty0 + + + align:start position:0% +this X 0 well X 0 1 is the integral ty0 +star tax it's not 1/x and we know we can + + align:start position:0% +star tax it's not 1/x and we know we can + + + align:start position:0% +star tax it's not 1/x and we know we can +replace X by a plus a dagger times a + + align:start position:0% +replace X by a plus a dagger times a + + + align:start position:0% +replace X by a plus a dagger times a +constant we always like to forget that + + align:start position:0% +constant we always like to forget that + + + align:start position:0% +constant we always like to forget that +constant we only bring it in at the end + + align:start position:0% +constant we only bring it in at the end + + + align:start position:0% +constant we only bring it in at the end +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +and so well this has value is a constant + + align:start position:0% +and so well this has value is a constant + + + align:start position:0% +and so well this has value is a constant +the constant that we're forgetting x one + + align:start position:0% +the constant that we're forgetting x one + + + align:start position:0% +the constant that we're forgetting x one +square root right and 2x 0 1 and X 1 2 + + align:start position:0% +square root right and 2x 0 1 and X 1 2 + + + align:start position:0% +square root right and 2x 0 1 and X 1 2 +is the same sort of thing it's going to + + align:start position:0% +is the same sort of thing it's going to + + + align:start position:0% +is the same sort of thing it's going to +be the same constant x 2 square root + + align:start position:0% +be the same constant x 2 square root + + + align:start position:0% +be the same constant x 2 square root +this is easy + + align:start position:0% +this is easy + + + align:start position:0% +this is easy +so getting from this symbol to this that + + align:start position:0% +so getting from this symbol to this that + + + align:start position:0% +so getting from this symbol to this that +just requires a little practice and then + + align:start position:0% +just requires a little practice and then + + + align:start position:0% +just requires a little practice and then +simplifying further to to know what + + align:start position:0% +simplifying further to to know what + + + align:start position:0% +simplifying further to to know what +these X's are and then the constraint on + + align:start position:0% +these X's are and then the constraint on + + + align:start position:0% +these X's are and then the constraint on +C 2 and C 0 we have all that stuff ok + + align:start position:0% +C 2 and C 0 we have all that stuff ok + + + align:start position:0% +C 2 and C 0 we have all that stuff ok +and now we can draw a picture what's + + align:start position:0% +and now we can draw a picture what's + + + align:start position:0% +and now we can draw a picture what's +going to happen so here we have the full + + align:start position:0% +going to happen so here we have the full + + + align:start position:0% +going to happen so here we have the full +oscillator and let's just draw some + + align:start position:0% +oscillator and let's just draw some + + + align:start position:0% +oscillator and let's just draw some +energy which is now that's complicated + + align:start position:0% +energy which is now that's complicated + + + align:start position:0% +energy which is now that's complicated +we have a time-dependent wave function + + align:start position:0% +we have a time-dependent wave function + + + align:start position:0% +we have a time-dependent wave function +which is composed of several different + + align:start position:0% +which is composed of several different + + + align:start position:0% +which is composed of several different +energy eigenstates so what of it what is + + align:start position:0% +energy eigenstates so what of it what is + + + align:start position:0% +energy eigenstates so what of it what is +its energy well you can evaluate what + + align:start position:0% +its energy well you can evaluate what + + + align:start position:0% +its energy well you can evaluate what +the energy is by taking the expectation + + align:start position:0% +the energy is by taking the expectation + + + align:start position:0% +the energy is by taking the expectation +value of the Hamiltonian and so you can + + align:start position:0% +value of the Hamiltonian and so you can + + + align:start position:0% +value of the Hamiltonian and so you can +do that so what we've made at T equals + + align:start position:0% +do that so what we've made at T equals + + + align:start position:0% +do that so what we've made at T equals +zero is something that looks like this + + align:start position:0% + + + + align:start position:0% + +it's localized on the left side or it's + + align:start position:0% +it's localized on the left side or it's + + + align:start position:0% +it's localized on the left side or it's +more localized on the left side now + + align:start position:0% +more localized on the left side now + + + align:start position:0% +more localized on the left side now +sometimes you're going to worry about + + align:start position:0% +sometimes you're going to worry about + + + align:start position:0% +sometimes you're going to worry about +phase and so many times when you're when + + align:start position:0% +phase and so many times when you're when + + + align:start position:0% +phase and so many times when you're when +you're working symbolically rather than + + align:start position:0% +you're working symbolically rather than + + + align:start position:0% +you're working symbolically rather than +actually evaluating integrals + + align:start position:0% +actually evaluating integrals + + + align:start position:0% +actually evaluating integrals +there are symbolic phase choices which + + align:start position:0% +there are symbolic phase choices which + + + align:start position:0% +there are symbolic phase choices which +what you're using has made and for + + align:start position:0% +what you're using has made and for + + + align:start position:0% +what you're using has made and for +example for the harmonic oscillator if + + align:start position:0% +example for the harmonic oscillator if + + + align:start position:0% +example for the harmonic oscillator if +you look in the book you'll see that for + + align:start position:0% +you look in the book you'll see that for + + + align:start position:0% +you look in the book you'll see that for +for all of the harmonic oscillator + + align:start position:0% +for all of the harmonic oscillator + + + align:start position:0% +for all of the harmonic oscillator +functions the outer lobe is always + + align:start position:0% +functions the outer lobe is always + + + align:start position:0% +functions the outer lobe is always +positive + + align:start position:0% +positive + + + align:start position:0% +positive +and the inner lobe is alternating with + + align:start position:0% +and the inner lobe is alternating with + + + align:start position:0% +and the inner lobe is alternating with +with with quantum number so that's a + + align:start position:0% +with with quantum number so that's a + + + align:start position:0% +with with quantum number so that's a +phase convention that's implicit in + + align:start position:0% +phase convention that's implicit in + + + align:start position:0% +phase convention that's implicit in +everything that people have derived and + + align:start position:0% +everything that people have derived and + + + align:start position:0% +everything that people have derived and +as long as the different things you + + align:start position:0% +as long as the different things you + + + align:start position:0% +as long as the different things you +combine in doing a calculation involve + + align:start position:0% +combine in doing a calculation involve + + + align:start position:0% +combine in doing a calculation involve +the same phase Convention which is + + align:start position:0% +the same phase Convention which is + + + align:start position:0% +the same phase Convention which is +implicit we don't want to look at wave + + align:start position:0% +implicit we don't want to look at wave + + + align:start position:0% +implicit we don't want to look at wave +functions we want to look at these X I + + align:start position:0% +functions we want to look at these X I + + + align:start position:0% +functions we want to look at these X I +J's okay and the and so those those + + align:start position:0% +J's okay and the and so those those + + + align:start position:0% +J's okay and the and so those those +things that we're manipulating have a + + align:start position:0% +things that we're manipulating have a + + + align:start position:0% +things that we're manipulating have a +phase implicit in how you define them + + align:start position:0% +phase implicit in how you define them + + + align:start position:0% +phase implicit in how you define them +but that's gone in your manipulation so + + align:start position:0% +but that's gone in your manipulation so + + + align:start position:0% +but that's gone in your manipulation so +you want to be a little careful okay so + + align:start position:0% +you want to be a little careful okay so + + + align:start position:0% +you want to be a little careful okay so +we start out and the wave function or + + align:start position:0% +we start out and the wave function or + + + align:start position:0% +we start out and the wave function or +the expectation value is on this side + + align:start position:0% +the expectation value is on this side + + + align:start position:0% +the expectation value is on this side +and the the size darkside is localized + + align:start position:0% +and the the size darkside is localized + + + align:start position:0% +and the the size darkside is localized +on this side mostly and at a later time + + align:start position:0% +on this side mostly and at a later time + + + align:start position:0% +on this side mostly and at a later time +so this is a later time I shouldn't make + + align:start position:0% +so this is a later time I shouldn't make + + + align:start position:0% +so this is a later time I shouldn't make +it bigger in a later time this thing has + + align:start position:0% +it bigger in a later time this thing has + + + align:start position:0% +it bigger in a later time this thing has +moved to the other turning point back + + align:start position:0% +moved to the other turning point back + + + align:start position:0% +moved to the other turning point back +and forth back and forth now since we + + align:start position:0% +and forth back and forth now since we + + + align:start position:0% +and forth back and forth now since we +have three energy levels and well + + align:start position:0% +have three energy levels and well + + + align:start position:0% +have three energy levels and well +actually we have a coherence term which + + align:start position:0% +actually we have a coherence term which + + + align:start position:0% +actually we have a coherence term which +involves the product of size zero and + + align:start position:0% +involves the product of size zero and + + + align:start position:0% +involves the product of size zero and +sigh one and one in situ they differ in + + align:start position:0% +sigh one and one in situ they differ in + + + align:start position:0% +sigh one and one in situ they differ in +energy both by Omega so these two things + + align:start position:0% +energy both by Omega so these two things + + + align:start position:0% +energy both by Omega so these two things +have the same oscillation frequency and + + align:start position:0% +have the same oscillation frequency and + + + align:start position:0% +have the same oscillation frequency and +so what's going to happen is the wave + + align:start position:0% +so what's going to happen is the wave + + + align:start position:0% +so what's going to happen is the wave +function the wave packet is going to + + align:start position:0% +function the wave packet is going to + + + align:start position:0% +function the wave packet is going to +move from this side to that side back + + align:start position:0% +move from this side to that side back + + + align:start position:0% +move from this side to that side back +and forth always forever at the same + + align:start position:0% +and forth always forever at the same + + + align:start position:0% +and forth always forever at the same +frequency no D phasing in the middle I + + align:start position:0% +frequency no D phasing in the middle I + + + align:start position:0% +frequency no D phasing in the middle I +can't tell you what it's going to look + + align:start position:0% +can't tell you what it's going to look + + + align:start position:0% +can't tell you what it's going to look +like I don't want to tell you because + + align:start position:0% +like I don't want to tell you because + + + align:start position:0% +like I don't want to tell you because +you don't care you care + + align:start position:0% +you don't care you care + + + align:start position:0% +you don't care you care +mostly about what's it going to look + + align:start position:0% +mostly about what's it going to look + + + align:start position:0% +mostly about what's it going to look +like at a turning point or what is it + + align:start position:0% +like at a turning point or what is it + + + align:start position:0% +like at a turning point or what is it +going to look like when it returns to + + align:start position:0% +going to look like when it returns to + + + align:start position:0% +going to look like when it returns to +home base and all sorts of insights come + + align:start position:0% +home base and all sorts of insights come + + + align:start position:0% +home base and all sorts of insights come +from that okay now I said well if we + + align:start position:0% +from that okay now I said well if we + + + align:start position:0% +from that okay now I said well if we +want to know the energy of this wave + + align:start position:0% +want to know the energy of this wave + + + align:start position:0% +want to know the energy of this wave +packet well we take the expectation + + align:start position:0% +packet well we take the expectation + + + align:start position:0% +packet well we take the expectation +value of the Hamiltonian and the + + align:start position:0% +value of the Hamiltonian and the + + + align:start position:0% +value of the Hamiltonian and the +expectation of the Hamiltonian is c0 + + align:start position:0% +expectation of the Hamiltonian is c0 + + + align:start position:0% +expectation of the Hamiltonian is c0 +squared + + align:start position:0% +squared + + + align:start position:0% +squared +sy 0 I'm not sighs 0 e 0 plus C 1 plus C + + align:start position:0% +sy 0 I'm not sighs 0 e 0 plus C 1 plus C + + + align:start position:0% +sy 0 I'm not sighs 0 e 0 plus C 1 plus C +2 2 e 2 these things are easy once + + align:start position:0% +2 2 e 2 these things are easy once + + + align:start position:0% +2 2 e 2 these things are easy once +you've gone through it a couple of times + + align:start position:0% +you've gone through it a couple of times + + + align:start position:0% +you've gone through it a couple of times +because what's happening is you have + + align:start position:0% +because what's happening is you have + + + align:start position:0% +because what's happening is you have +these factors e to the minus i e i ej T + + align:start position:0% +these factors e to the minus i e i ej T + + + align:start position:0% +these factors e to the minus i e i ej T +over H bar and they cancel when you do + + align:start position:0% +over H bar and they cancel when you do + + + align:start position:0% +over H bar and they cancel when you do +as Phi star side or they generate a + + align:start position:0% +as Phi star side or they generate a + + + align:start position:0% +as Phi star side or they generate a +difference Omega H bar Omega when you + + align:start position:0% +difference Omega H bar Omega when you + + + align:start position:0% +difference Omega H bar Omega when you +have different values of the energy so + + align:start position:0% +have different values of the energy so + + + align:start position:0% +have different values of the energy so +this is something that you can derive + + align:start position:0% +this is something that you can derive + + + align:start position:0% +this is something that you can derive +really quickly and the fact that this + + align:start position:0% +really quickly and the fact that this + + + align:start position:0% +really quickly and the fact that this +your eigenfunctions the basis of the + + align:start position:0% +your eigenfunctions the basis of the + + + align:start position:0% +your eigenfunctions the basis of the +size in your linear combination up there + + align:start position:0% +size in your linear combination up there + + + align:start position:0% +size in your linear combination up there +are eigenfunctions the Hamiltonian so + + align:start position:0% +are eigenfunctions the Hamiltonian so + + + align:start position:0% +are eigenfunctions the Hamiltonian so +every time the Hamiltonian operates on a + + align:start position:0% +every time the Hamiltonian operates on a + + + align:start position:0% +every time the Hamiltonian operates on a +wave function it gives the energy times + + align:start position:0% +wave function it gives the energy times + + + align:start position:0% +wave function it gives the energy times +that wave function and then you're + + align:start position:0% +that wave function and then you're + + + align:start position:0% +that wave function and then you're +taking the expectation value and so we + + align:start position:0% +taking the expectation value and so we + + + align:start position:0% +taking the expectation value and so we +have the wave function time times itself + + align:start position:0% +have the wave function time times itself + + + align:start position:0% +have the wave function time times itself +integrated and that goes away so after + + align:start position:0% +integrated and that goes away so after + + + align:start position:0% +integrated and that goes away so after +doing this a few times you don't need to + + align:start position:0% +doing this a few times you don't need to + + + align:start position:0% +doing this a few times you don't need to +write the intermediate steps and you + + align:start position:0% +write the intermediate steps and you + + + align:start position:0% +write the intermediate steps and you +shouldn't because you will they get lost + + align:start position:0% +shouldn't because you will they get lost + + + align:start position:0% +shouldn't because you will they get lost +in the forest of notation because one of + + align:start position:0% +in the forest of notation because one of + + + align:start position:0% +in the forest of notation because one of +the things you probably noticed in the + + align:start position:0% +the things you probably noticed in the + + + align:start position:0% +the things you probably noticed in the +last lecture is the equations got really + + align:start position:0% +last lecture is the equations got really + + + align:start position:0% +last lecture is the equations got really +big and then we + + align:start position:0% +big and then we + + + align:start position:0% +big and then we +something else and it gets twice as big + + align:start position:0% +something else and it gets twice as big + + + align:start position:0% +something else and it gets twice as big +and then all of a sudden it all goes + + align:start position:0% +and then all of a sudden it all goes + + + align:start position:0% +and then all of a sudden it all goes +away and that's what you want to be able + + align:start position:0% +away and that's what you want to be able + + + align:start position:0% +away and that's what you want to be able +to anticipate okay so you can really + + align:start position:0% +to anticipate okay so you can really + + + align:start position:0% +to anticipate okay so you can really +kill this half oscillator problem that + + align:start position:0% +kill this half oscillator problem that + + + align:start position:0% +kill this half oscillator problem that +there's nothing much happening except + + align:start position:0% +there's nothing much happening except + + + align:start position:0% +there's nothing much happening except +you create a localization and when you + + align:start position:0% +you create a localization and when you + + + align:start position:0% +you create a localization and when you +take away the other when you restore the + + align:start position:0% +take away the other when you restore the + + + align:start position:0% +take away the other when you restore the +full oscillator everything oscillates at + + align:start position:0% +full oscillator everything oscillates at + + + align:start position:0% +full oscillator everything oscillates at +Omega and so you have a whole bunch of + + align:start position:0% +Omega and so you have a whole bunch of + + + align:start position:0% +Omega and so you have a whole bunch of +terms contributing to the motion of the + + align:start position:0% +terms contributing to the motion of the + + + align:start position:0% +terms contributing to the motion of the +wave packet and they're all very simple + + align:start position:0% +wave packet and they're all very simple + + + align:start position:0% +wave packet and they're all very simple +because they're all oscillating at the + + align:start position:0% +because they're all oscillating at the + + + align:start position:0% +because they're all oscillating at the +same frequency now as an aside that I I + + align:start position:0% +same frequency now as an aside that I I + + + align:start position:0% +same frequency now as an aside that I I +want to say there's a huge number of + + align:start position:0% +want to say there's a huge number of + + + align:start position:0% +want to say there's a huge number of +stuff it's up in this lecture that's + + align:start position:0% +stuff it's up in this lecture that's + + + align:start position:0% +stuff it's up in this lecture that's +going to be on the exam a huge amount so + + align:start position:0% +going to be on the exam a huge amount so + + + align:start position:0% +going to be on the exam a huge amount so +if for example you wanted to calculate + + align:start position:0% +if for example you wanted to calculate + + + align:start position:0% +if for example you wanted to calculate +something like x squared well fine you + + align:start position:0% +something like x squared well fine you + + + align:start position:0% +something like x squared well fine you +know what the selection rule for x + + align:start position:0% +know what the selection rule for x + + + align:start position:0% +know what the selection rule for x +squared is it's Delta V of 0 plus of + + align:start position:0% +squared is it's Delta V of 0 plus of + + + align:start position:0% +squared is it's Delta V of 0 plus of +minus 2 and so this thing is going to + + align:start position:0% +minus 2 and so this thing is going to + + + align:start position:0% +minus 2 and so this thing is going to +generate some constant terms and some + + align:start position:0% +generate some constant terms and some + + + align:start position:0% +generate some constant terms and some +terms at 2 Omega okay so there are a lot + + align:start position:0% +terms at 2 Omega okay so there are a lot + + + align:start position:0% +terms at 2 Omega okay so there are a lot +of things about the harmonic oscillator + + align:start position:0% +of things about the harmonic oscillator + + + align:start position:0% +of things about the harmonic oscillator +that make it really wonderful to + + align:start position:0% +that make it really wonderful to + + + align:start position:0% +that make it really wonderful to +consider a problem even a complicated + + align:start position:0% +consider a problem even a complicated + + + align:start position:0% +consider a problem even a complicated +problem which is not explicitly a + + align:start position:0% +problem which is not explicitly a + + + align:start position:0% +problem which is not explicitly a +harmonic oscillator problem because you + + align:start position:0% +harmonic oscillator problem because you + + + align:start position:0% +harmonic oscillator problem because you +can get everything so quickly without + + align:start position:0% +can get everything so quickly without + + + align:start position:0% +can get everything so quickly without +any thought after a little bit of + + align:start position:0% +any thought after a little bit of + + + align:start position:0% +any thought after a little bit of +investment ok now we haven't talked + + align:start position:0% +investment ok now we haven't talked + + + align:start position:0% +investment ok now we haven't talked +about electronic transitions and + + align:start position:0% +about electronic transitions and + + + align:start position:0% +about electronic transitions and +potential energy curves but we will so + + align:start position:0% +potential energy curves but we will so + + + align:start position:0% +potential energy curves but we will so +and I think you know about them and so + + align:start position:0% +and I think you know about them and so + + + align:start position:0% +and I think you know about them and so +we have some electronic ground state and + + align:start position:0% +we have some electronic ground state and + + + align:start position:0% +we have some electronic ground state and +we have some electronically excited + + align:start position:0% +we have some electronically excited + + + align:start position:0% +we have some electronically excited +state and so each of these states + + align:start position:0% +state and so each of these states + + + align:start position:0% +state and so each of these states +as a vibrational coordinate and we can + + align:start position:0% +as a vibrational coordinate and we can + + + align:start position:0% +as a vibrational coordinate and we can +pretend that it's harmonic even if it's + + align:start position:0% +pretend that it's harmonic even if it's + + + align:start position:0% +pretend that it's harmonic even if it's +not because we built a framework + + align:start position:0% +not because we built a framework + + + align:start position:0% +not because we built a framework +treating them as harmonic and then + + align:start position:0% +treating them as harmonic and then + + + align:start position:0% +treating them as harmonic and then +discover that there's discrepancies + + align:start position:0% +discover that there's discrepancies + + + align:start position:0% +discover that there's discrepancies +which we can fit to a a model and we can + + align:start position:0% +which we can fit to a a model and we can + + + align:start position:0% +which we can fit to a a model and we can +determine from the time dependence what + + align:start position:0% +determine from the time dependence what + + + align:start position:0% +determine from the time dependence what +that model is okay so we start out with + + align:start position:0% +that model is okay so we start out with + + + align:start position:0% +that model is okay so we start out with +the molecule in V equals zero and + + align:start position:0% + + + + align:start position:0% + +there's a much repeated truism electrons + + align:start position:0% +there's a much repeated truism electrons + + + align:start position:0% +there's a much repeated truism electrons +move fast nuclei slow transition is + + align:start position:0% +move fast nuclei slow transition is + + + align:start position:0% +move fast nuclei slow transition is +instantaneous or nearly instantaneous + + align:start position:0% +instantaneous or nearly instantaneous + + + align:start position:0% +instantaneous or nearly instantaneous +because it involves the electrons so + + align:start position:0% +because it involves the electrons so + + + align:start position:0% +because it involves the electrons so +what ends up happening is you draw a + + align:start position:0% +what ends up happening is you draw a + + + align:start position:0% +what ends up happening is you draw a +vertical line and now you transfer this + + align:start position:0% +vertical line and now you transfer this + + + align:start position:0% +vertical line and now you transfer this +wave function to the upper state you + + align:start position:0% +wave function to the upper state you + + + align:start position:0% +wave function to the upper state you +just move this is the probability + + align:start position:0% +just move this is the probability + + + align:start position:0% +just move this is the probability +amplitude distribution of the the the + + align:start position:0% +amplitude distribution of the the the + + + align:start position:0% +amplitude distribution of the the the +vibration we transfer that to the + + align:start position:0% +vibration we transfer that to the + + + align:start position:0% +vibration we transfer that to the +excited state and that's not an + + align:start position:0% +excited state and that's not an + + + align:start position:0% +excited state and that's not an +eigenstate of the excited state it's a + + align:start position:0% +eigenstate of the excited state it's a + + + align:start position:0% +eigenstate of the excited state it's a +localized state localized at a turning + + align:start position:0% +localized state localized at a turning + + + align:start position:0% +localized state localized at a turning +point now you want to know so the + + align:start position:0% +point now you want to know so the + + + align:start position:0% +point now you want to know so the +there's a franck-condon principle that + + align:start position:0% +there's a franck-condon principle that + + + align:start position:0% +there's a franck-condon principle that +is just another way of saying electrons + + align:start position:0% +is just another way of saying electrons + + + align:start position:0% +is just another way of saying electrons +move fast nuclei slow and there is delta + + align:start position:0% +move fast nuclei slow and there is delta + + + align:start position:0% +move fast nuclei slow and there is delta +x equals zero Delta P equals zero yes + + align:start position:0% +x equals zero Delta P equals zero yes + + + align:start position:0% +x equals zero Delta P equals zero yes +the nuclear state can't change while the + + align:start position:0% +the nuclear state can't change while the + + + align:start position:0% +the nuclear state can't change while the +electron is jumping then the coordinate + + align:start position:0% +electron is jumping then the coordinate + + + align:start position:0% +electron is jumping then the coordinate +and the momentum are both constant so + + align:start position:0% +and the momentum are both constant so + + + align:start position:0% +and the momentum are both constant so +you're creating a wave packet and the + + align:start position:0% +you're creating a wave packet and the + + + align:start position:0% +you're creating a wave packet and the +best place to create it is near a + + align:start position:0% +best place to create it is near a + + + align:start position:0% +best place to create it is near a +turning point because then you can match + + align:start position:0% +turning point because then you can match + + + align:start position:0% +turning point because then you can match +the momentum of this guy to that that + + align:start position:0% +the momentum of this guy to that that + + + align:start position:0% +the momentum of this guy to that that +zero point momentum which you can + + align:start position:0% +zero point momentum which you can + + + align:start position:0% +zero point momentum which you can +calculate you know how to calculate this + + align:start position:0% +calculate you know how to calculate this + + + align:start position:0% +calculate you know how to calculate this +because the the the potential energy + + align:start position:0% +because the the the potential energy + + + align:start position:0% +because the the the potential energy +curve + + align:start position:0% +curve + + + align:start position:0% +curve +is 1/2 K x-squared and the momentum is + + align:start position:0% +is 1/2 K x-squared and the momentum is + + + align:start position:0% +is 1/2 K x-squared and the momentum is +is given by this energy difference here + + align:start position:0% +is given by this energy difference here + + + align:start position:0% +is given by this energy difference here +and so you can work at that out it's in + + align:start position:0% +and so you can work at that out it's in + + + align:start position:0% +and so you can work at that out it's in +the notes I don't want to write it down + + align:start position:0% +the notes I don't want to write it down + + + align:start position:0% +the notes I don't want to write it down +so you're going to create something + + align:start position:0% +so you're going to create something + + + align:start position:0% +so you're going to create something +which is vertical and it's not quite + + align:start position:0% +which is vertical and it's not quite + + + align:start position:0% +which is vertical and it's not quite +exactly at the turning point because you + + align:start position:0% +exactly at the turning point because you + + + align:start position:0% +exactly at the turning point because you +have to have a little bit of momentum to + + align:start position:0% +have to have a little bit of momentum to + + + align:start position:0% +have to have a little bit of momentum to +match this zero point oh man I'm here so + + align:start position:0% +match this zero point oh man I'm here so + + + align:start position:0% +match this zero point oh man I'm here so +you know everything about the initial + + align:start position:0% +you know everything about the initial + + + align:start position:0% +you know everything about the initial +state and so you can calculate what it + + align:start position:0% +state and so you can calculate what it + + + align:start position:0% +state and so you can calculate what it +is by taking the overlap of V equals + + align:start position:0% +is by taking the overlap of V equals + + + align:start position:0% +is by taking the overlap of V equals +zero of the ground state with all of the + + align:start position:0% +zero of the ground state with all of the + + + align:start position:0% +zero of the ground state with all of the +vibration levels of the excited state + + align:start position:0% +vibration levels of the excited state + + + align:start position:0% +vibration levels of the excited state +and so we have the coefficients of each + + align:start position:0% +and so we have the coefficients of each + + + align:start position:0% +and so we have the coefficients of each +of those vibrational levels in the + + align:start position:0% +of those vibrational levels in the + + + align:start position:0% +of those vibrational levels in the +excited state that makes this wave + + align:start position:0% +excited state that makes this wave + + + align:start position:0% +excited state that makes this wave +packet now of course this wave packet is + + align:start position:0% +packet now of course this wave packet is + + + align:start position:0% +packet now of course this wave packet is +going to move back and forth back and + + align:start position:0% +going to move back and forth back and + + + align:start position:0% +going to move back and forth back and +forth and if this were a harmonic + + align:start position:0% +forth and if this were a harmonic + + + align:start position:0% +forth and if this were a harmonic +oscillator it would move harmonically + + align:start position:0% +oscillator it would move harmonically + + + align:start position:0% +oscillator it would move harmonically +and so the only thing that would appear + + align:start position:0% +and so the only thing that would appear + + + align:start position:0% +and so the only thing that would appear +in the expectation value of x is going + + align:start position:0% +in the expectation value of x is going + + + align:start position:0% +in the expectation value of x is going +to be this motion at Omega now this is + + align:start position:0% +to be this motion at Omega now this is + + + align:start position:0% +to be this motion at Omega now this is +usually a relatively high vibrational + + align:start position:0% +usually a relatively high vibrational + + + align:start position:0% +usually a relatively high vibrational +level and the molecule is not being + + align:start position:0% +level and the molecule is not being + + + align:start position:0% +level and the molecule is not being +harmonic here so there are correction + + align:start position:0% +harmonic here so there are correction + + + align:start position:0% +harmonic here so there are correction +terms called anharmonicity terms which + + align:start position:0% +terms called anharmonicity terms which + + + align:start position:0% +terms called anharmonicity terms which +are which so we have the energy level + + align:start position:0% +are which so we have the energy level + + + align:start position:0% +are which so we have the energy level +expression plus h-bar omega e x e that's + + align:start position:0% +expression plus h-bar omega e x e that's + + + align:start position:0% +expression plus h-bar omega e x e that's +one number E Plus 1/2 squared so we have + + align:start position:0% +one number E Plus 1/2 squared so we have + + + align:start position:0% +one number E Plus 1/2 squared so we have +a linear term in a quadratic term and + + align:start position:0% +a linear term in a quadratic term and + + + align:start position:0% +a linear term in a quadratic term and +this Omega e XE is on the order of 0.02 + + align:start position:0% +this Omega e XE is on the order of 0.02 + + + align:start position:0% +this Omega e XE is on the order of 0.02 +times your Iggy 2% so it's a small thing + + align:start position:0% +times your Iggy 2% so it's a small thing + + + align:start position:0% +times your Iggy 2% so it's a small thing +but if you're going to be allowing a + + align:start position:0% +but if you're going to be allowing a + + + align:start position:0% +but if you're going to be allowing a +wave packet + + align:start position:0% +wave packet + + + align:start position:0% +wave packet +to be built out of many vibrational + + align:start position:0% +to be built out of many vibrational + + + align:start position:0% +to be built out of many vibrational +levels this guy is going to deface a + + align:start position:0% +levels this guy is going to deface a + + + align:start position:0% +levels this guy is going to deface a +little bit as you go around and come + + align:start position:0% +little bit as you go around and come + + + align:start position:0% +little bit as you go around and come +back and you can't quite have everybody + + align:start position:0% +back and you can't quite have everybody + + + align:start position:0% +back and you can't quite have everybody +back where they started and so you'll + + align:start position:0% +back where they started and so you'll + + + align:start position:0% +back where they started and so you'll +see a a decreasing amplitude here and + + align:start position:0% +see a a decreasing amplitude here and + + + align:start position:0% +see a a decreasing amplitude here and +that's best looked at by the probability + + align:start position:0% +that's best looked at by the probability + + + align:start position:0% +that's best looked at by the probability +the survival probability and you'll see + + align:start position:0% +the survival probability and you'll see + + + align:start position:0% +the survival probability and you'll see +characteristic behavior in their + + align:start position:0% +characteristic behavior in their + + + align:start position:0% +characteristic behavior in their +survival probability okay but let's + + align:start position:0% +survival probability okay but let's + + + align:start position:0% +survival probability okay but let's +let's go a little bit deeper before I + + align:start position:0% +let's go a little bit deeper before I + + + align:start position:0% +let's go a little bit deeper before I +move on to okay so let's just say our + + align:start position:0% +move on to okay so let's just say our + + + align:start position:0% +move on to okay so let's just say our +superposition state the electronically + + align:start position:0% +superposition state the electronically + + + align:start position:0% +superposition state the electronically +excited state is a combination of V + + align:start position:0% +excited state is a combination of V + + + align:start position:0% +excited state is a combination of V +equals 10 and V equals 11 so we know + + align:start position:0% +equals 10 and V equals 11 so we know + + + align:start position:0% +equals 10 and V equals 11 so we know +immediately it's AI star P sy this + + align:start position:0% +immediately it's AI star P sy this + + + align:start position:0% +immediately it's AI star P sy this +probability amplitude probability yes + + align:start position:0% +probability amplitude probability yes + + + align:start position:0% +probability amplitude probability yes +this probability is C 10 squared side 2 + + align:start position:0% +this probability is C 10 squared side 2 + + + align:start position:0% +this probability is C 10 squared side 2 +squared plus C 11 bird I 11 squared plus + + align:start position:0% +squared plus C 11 bird I 11 squared plus + + + align:start position:0% +squared plus C 11 bird I 11 squared plus +2 c10 c11 sy 1011 cosine Omega T + + align:start position:0% + + + + align:start position:0% + +now I'm playing fast and loose here + + align:start position:0% +now I'm playing fast and loose here + + + align:start position:0% +now I'm playing fast and loose here +because I've done this before I know + + align:start position:0% +because I've done this before I know + + + align:start position:0% +because I've done this before I know +what disappears and I know if it's + + align:start position:0% +what disappears and I know if it's + + + align:start position:0% +what disappears and I know if it's +harmonic you just get this well there's + + align:start position:0% +harmonic you just get this well there's + + + align:start position:0% +harmonic you just get this well there's +two states this this thing is really + + align:start position:0% +two states this this thing is really + + + align:start position:0% +two states this this thing is really +this the the the frequency associated + + align:start position:0% +this the the the frequency associated + + + align:start position:0% +this the the the frequency associated +with these two levels okay now once we + + align:start position:0% +with these two levels okay now once we + + + align:start position:0% +with these two levels okay now once we +have this we can also generate the + + align:start position:0% +have this we can also generate the + + + align:start position:0% +have this we can also generate the +problem survival probability the + + align:start position:0% +problem survival probability the + + + align:start position:0% +problem survival probability the +survival probability capital P of T + + align:start position:0% +survival probability capital P of T + + + align:start position:0% +survival probability capital P of T +that's defined as the square modulus of + + align:start position:0% +that's defined as the square modulus of + + + align:start position:0% +that's defined as the square modulus of +Phi star pecks P Phi X zero the X okay + + align:start position:0% + + + + align:start position:0% + +and you can immediately write that's + + align:start position:0% +and you can immediately write that's + + + align:start position:0% +and you can immediately write that's +good what that is going to be it's going + + align:start position:0% +good what that is going to be it's going + + + align:start position:0% +good what that is going to be it's going +to be C ten squared and we've integrated + + align:start position:0% +to be C ten squared and we've integrated + + + align:start position:0% +to be C ten squared and we've integrated +so the wave functions go away and so we + + align:start position:0% +so the wave functions go away and so we + + + align:start position:0% +so the wave functions go away and so we +have C ten e to the I h-bar 10.5 Omega + + align:start position:0% +have C ten e to the I h-bar 10.5 Omega + + + align:start position:0% +have C ten e to the I h-bar 10.5 Omega +if I T divided by H bar plus C eleven + + align:start position:0% +if I T divided by H bar plus C eleven + + + align:start position:0% +if I T divided by H bar plus C eleven +eat them as hot plus h bar 11.5 Omega + + align:start position:0% + + + + align:start position:0% + +okay why did I make the mistake here + + align:start position:0% + + + + align:start position:0% + +well we have a sigh star and so we're + + align:start position:0% +well we have a sigh star and so we're + + + align:start position:0% +well we have a sigh star and so we're +going to get the complex + + align:start position:0% +going to get the complex + + + align:start position:0% +going to get the complex +you get of the e to the minus I Omega + + align:start position:0% +you get of the e to the minus I Omega + + + align:start position:0% +you get of the e to the minus I Omega +Emmett + + align:start position:0% +Emmett + + + align:start position:0% +Emmett +so any you end up getting this practice + + align:start position:0% +so any you end up getting this practice + + + align:start position:0% +so any you end up getting this practice +that yes I have to him right exactly so + + align:start position:0% + + + + align:start position:0% + +and now lo and behold we know what to do + + align:start position:0% +and now lo and behold we know what to do + + + align:start position:0% +and now lo and behold we know what to do +with this too and so we're going to get + + align:start position:0% +with this too and so we're going to get + + + align:start position:0% +with this too and so we're going to get +c1 0 to the fourth let's see + + align:start position:0% +c1 0 to the fourth let's see + + + align:start position:0% +c1 0 to the fourth let's see +now 1 0 10 c11 to the 4th + 2 c1 0 of 10 + + align:start position:0% +now 1 0 10 c11 to the 4th + 2 c1 0 of 10 + + + align:start position:0% +now 1 0 10 c11 to the 4th + 2 c1 0 of 10 +squared c11 spurred cosine Omega T and + + align:start position:0% +squared c11 spurred cosine Omega T and + + + align:start position:0% +squared c11 spurred cosine Omega T and +then neat so we've got a whole bunch of + + align:start position:0% +then neat so we've got a whole bunch of + + + align:start position:0% +then neat so we've got a whole bunch of +constant terms this is constant because + + align:start position:0% +constant terms this is constant because + + + align:start position:0% +constant terms this is constant because +of its square modulus and it's to the + + align:start position:0% +of its square modulus and it's to the + + + align:start position:0% +of its square modulus and it's to the +fourth R and so all of these + + align:start position:0% +fourth R and so all of these + + + align:start position:0% +fourth R and so all of these +coefficients are constant are positive + + align:start position:0% +coefficients are constant are positive + + + align:start position:0% +coefficients are constant are positive +at T equals 0 this is 1 and so at T + + align:start position:0% +at T equals 0 this is 1 and so at T + + + align:start position:0% +at T equals 0 this is 1 and so at T +equals 0 the probability the survival + + align:start position:0% +equals 0 the probability the survival + + + align:start position:0% +equals 0 the probability the survival +probability is at a maximum and at some + + align:start position:0% +probability is at a maximum and at some + + + align:start position:0% +probability is at a maximum and at some +later time that survival probability + + align:start position:0% +later time that survival probability + + + align:start position:0% +later time that survival probability +will be at a minimum okay and so you can + + align:start position:0% +will be at a minimum okay and so you can + + + align:start position:0% +will be at a minimum okay and so you can +say the maximum will occur at integer + + align:start position:0% +say the maximum will occur at integer + + + align:start position:0% +say the maximum will occur at integer +when Omega T when Omega T is equal to + + align:start position:0% + + + + align:start position:0% + +and I 2 n pi + + align:start position:0% + + + + align:start position:0% + +so then the exponential factor is always + + align:start position:0% +so then the exponential factor is always + + + align:start position:0% +so then the exponential factor is always +1 and we have a minimum at when Omega T + + align:start position:0% +1 and we have a minimum at when Omega T + + + align:start position:0% +1 and we have a minimum at when Omega T +is an odd multiple of Pi and all the + + align:start position:0% +is an odd multiple of Pi and all the + + + align:start position:0% +is an odd multiple of Pi and all the +exponential factors are minus 1 so we + + align:start position:0% +exponential factors are minus 1 so we + + + align:start position:0% +exponential factors are minus 1 so we +can also now look at the expectation + + align:start position:0% +can also now look at the expectation + + + align:start position:0% +can also now look at the expectation +value for X of T and P of T and I'm + + align:start position:0% +value for X of T and P of T and I'm + + + align:start position:0% +value for X of T and P of T and I'm +going to just draw sketches so for X of + + align:start position:0% +going to just draw sketches so for X of + + + align:start position:0% +going to just draw sketches so for X of +T we have something that looks like this + + align:start position:0% +T we have something that looks like this + + + align:start position:0% +T we have something that looks like this +this is at the left turning point this + + align:start position:0% +this is at the left turning point this + + + align:start position:0% +this is at the left turning point this +is the right turning point or near the + + align:start position:0% +is the right turning point or near the + + + align:start position:0% +is the right turning point or near the +right turning point and this is at PI + + align:start position:0% +right turning point and this is at PI + + + align:start position:0% +right turning point and this is at PI +over 2 Omega this is at PI over Omega so + + align:start position:0% +over 2 Omega this is at PI over Omega so + + + align:start position:0% +over 2 Omega this is at PI over Omega so +that's the half point now it starts out + + align:start position:0% +that's the half point now it starts out + + + align:start position:0% +that's the half point now it starts out +and the expectation value is at the left + + align:start position:0% +and the expectation value is at the left + + + align:start position:0% +and the expectation value is at the left +turning point and it's not changing the + + align:start position:0% +turning point and it's not changing the + + + align:start position:0% +turning point and it's not changing the +derivative of the expectation value with + + align:start position:0% +derivative of the expectation value with + + + align:start position:0% +derivative of the expectation value with +respect to T is 0 the momentum which has + + align:start position:0% +respect to T is 0 the momentum which has + + + align:start position:0% +respect to T is 0 the momentum which has +a different it has a different phase + + align:start position:0% +a different it has a different phase + + + align:start position:0% +a different it has a different phase +starts out the momentum starts out at 0 + + align:start position:0% +starts out the momentum starts out at 0 + + + align:start position:0% +starts out the momentum starts out at 0 +also and at PI over 2 Omega it reaches a + + align:start position:0% +also and at PI over 2 Omega it reaches a + + + align:start position:0% +also and at PI over 2 Omega it reaches a +maximum and at the at PI over Omega it + + align:start position:0% +maximum and at the at PI over Omega it + + + align:start position:0% +maximum and at the at PI over Omega it +reaches 0 again but the important thing + + align:start position:0% +reaches 0 again but the important thing + + + align:start position:0% +reaches 0 again but the important thing +here is at T equals 0 the derivative of + + align:start position:0% +here is at T equals 0 the derivative of + + + align:start position:0% +here is at T equals 0 the derivative of +the momentum is as big as it can get so + + align:start position:0% +the momentum is as big as it can get so + + + align:start position:0% +the momentum is as big as it can get so +what's that telling you it's telling you + + align:start position:0% +what's that telling you it's telling you + + + align:start position:0% +what's that telling you it's telling you +this wave packet as far as coordinate + + align:start position:0% +this wave packet as far as coordinate + + + align:start position:0% +this wave packet as far as coordinate +space is concerned it's not moving at T + + align:start position:0% +space is concerned it's not moving at T + + + align:start position:0% +space is concerned it's not moving at T +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +as far as momentum is consumer concerned + + align:start position:0% +as far as momentum is consumer concerned + + + align:start position:0% +as far as momentum is consumer concerned +it's moving like crazy and so this + + align:start position:0% +it's moving like crazy and so this + + + align:start position:0% +it's moving like crazy and so this +probability survival probability is + + align:start position:0% +probability survival probability is + + + align:start position:0% +probability survival probability is +changing entirely dominated by the + + align:start position:0% +changing entirely dominated by the + + + align:start position:0% +changing entirely dominated by the +change in momentum which is encoded in + + align:start position:0% +change in momentum which is encoded in + + + align:start position:0% +change in momentum which is encoded in +the wave function which is neat because + + align:start position:0% +the wave function which is neat because + + + align:start position:0% +the wave function which is neat because +Newton's equation says that the time + + align:start position:0% +Newton's equation says that the time + + + align:start position:0% +Newton's equation says that the time +derivative of the momentum is equal to + + align:start position:0% +derivative of the momentum is equal to + + + align:start position:0% +derivative of the momentum is equal to +that's the mass times the time to you + + align:start position:0% +that's the mass times the time to you + + + align:start position:0% +that's the mass times the time to you +know at mass times acceleration is equal + + align:start position:0% +know at mass times acceleration is equal + + + align:start position:0% +know at mass times acceleration is equal +to the force which is minus the gradient + + align:start position:0% +to the force which is minus the gradient + + + align:start position:0% +to the force which is minus the gradient +of the potential the function of time + + align:start position:0% +of the potential the function of time + + + align:start position:0% +of the potential the function of time +and for a harmonic oscillator the grainy + + align:start position:0% +and for a harmonic oscillator the grainy + + + align:start position:0% +and for a harmonic oscillator the grainy +of the potential is X KX and so it's + + align:start position:0% +of the potential is X KX and so it's + + + align:start position:0% +of the potential is X KX and so it's +telling you that that the the we have + + align:start position:0% +telling you that that the the we have + + + align:start position:0% +telling you that that the the we have +this relationship between X and and T + + align:start position:0% +this relationship between X and and T + + + align:start position:0% +this relationship between X and and T +and P and the we know what the momentum + + align:start position:0% +and P and the we know what the momentum + + + align:start position:0% +and P and the we know what the momentum +is and I'm sorry and so the change in + + align:start position:0% +is and I'm sorry and so the change in + + + align:start position:0% +is and I'm sorry and so the change in +the momentum which is responsible for + + align:start position:0% +the momentum which is responsible for + + + align:start position:0% +the momentum which is responsible for +the change in the survival probability + + align:start position:0% +the change in the survival probability + + + align:start position:0% +the change in the survival probability +at T equals zero is due to the gradient + + align:start position:0% +at T equals zero is due to the gradient + + + align:start position:0% +at T equals zero is due to the gradient +of the potential so we're actually + + align:start position:0% +of the potential so we're actually + + + align:start position:0% +of the potential so we're actually +sampling what is the gradient the + + align:start position:0% +sampling what is the gradient the + + + align:start position:0% +sampling what is the gradient the +potential at the left turning point and + + align:start position:0% +potential at the left turning point and + + + align:start position:0% +potential at the left turning point and +often for any kind of a problem we want + + align:start position:0% +often for any kind of a problem we want + + + align:start position:0% +often for any kind of a problem we want +to know what kind of force is acting on + + align:start position:0% +to know what kind of force is acting on + + + align:start position:0% +to know what kind of force is acting on +the wave packet there it is + + align:start position:0% +the wave packet there it is + + + align:start position:0% +the wave packet there it is +classical mechanics embedded in quantum + + align:start position:0% +classical mechanics embedded in quantum + + + align:start position:0% +classical mechanics embedded in quantum +mechanics it's really amazing so if you + + align:start position:0% +mechanics it's really amazing so if you + + + align:start position:0% +mechanics it's really amazing so if you +have some way of measuring the survival + + align:start position:0% +have some way of measuring the survival + + + align:start position:0% +have some way of measuring the survival +probability at near T equals zero it's + + align:start position:0% +probability at near T equals zero it's + + + align:start position:0% +probability at near T equals zero it's +telling you + + align:start position:0% +telling you + + + align:start position:0% +telling you +what the the slope of the potential is + + align:start position:0% +what the the slope of the potential is + + + align:start position:0% +what the the slope of the potential is +at the turning point okay well if we + + align:start position:0% +at the turning point okay well if we + + + align:start position:0% +at the turning point okay well if we +have a initial state which involves many + + align:start position:0% +have a initial state which involves many + + + align:start position:0% +have a initial state which involves many +eigenstates of the Hamiltonian we still + + align:start position:0% +eigenstates of the Hamiltonian we still + + + align:start position:0% +eigenstates of the Hamiltonian we still +know that there's going to be some + + align:start position:0% +know that there's going to be some + + + align:start position:0% +know that there's going to be some +complicated behavior which is modulated + + align:start position:0% +complicated behavior which is modulated + + + align:start position:0% +complicated behavior which is modulated +by Omega so we have a cosine Omega T + + align:start position:0% +by Omega so we have a cosine Omega T + + + align:start position:0% +by Omega so we have a cosine Omega T +always and so no matter what kind of a + + align:start position:0% +always and so no matter what kind of a + + + align:start position:0% +always and so no matter what kind of a +wave function we make if we start out at + + align:start position:0% +wave function we make if we start out at + + + align:start position:0% +wave function we make if we start out at +one turning point it's going to go to + + align:start position:0% +one turning point it's going to go to + + + align:start position:0% +one turning point it's going to go to +the other turning point and it'll keep + + align:start position:0% +the other turning point and it'll keep + + + align:start position:0% +the other turning point and it'll keep +coming back and back and back and and so + + align:start position:0% +coming back and back and back and and so + + + align:start position:0% +coming back and back and back and and so +one could imagine doing an experiment + + align:start position:0% +one could imagine doing an experiment + + + align:start position:0% +one could imagine doing an experiment +where let's let's just draw the excited + + align:start position:0% +where let's let's just draw the excited + + + align:start position:0% +where let's let's just draw the excited +state and some other repulsive state so + + align:start position:0% +state and some other repulsive state so + + + align:start position:0% +state and some other repulsive state so +at this turning point vertical + + align:start position:0% +at this turning point vertical + + + align:start position:0% +at this turning point vertical +transition to that repulsive state is + + align:start position:0% +transition to that repulsive state is + + + align:start position:0% +transition to that repulsive state is +within the range of your laser and this + + align:start position:0% +within the range of your laser and this + + + align:start position:0% +within the range of your laser and this +turning point its way high and so what + + align:start position:0% +turning point its way high and so what + + + align:start position:0% +turning point its way high and so what +you can imagine doing is probing where + + align:start position:0% +you can imagine doing is probing where + + + align:start position:0% +you can imagine doing is probing where +this wave packet is as a function of + + align:start position:0% +this wave packet is as a function of + + + align:start position:0% +this wave packet is as a function of +time by having a probe pulse which + + align:start position:0% +time by having a probe pulse which + + + align:start position:0% +time by having a probe pulse which +creates dissociating fragments and now + + align:start position:0% +creates dissociating fragments and now + + + align:start position:0% +creates dissociating fragments and now +now you that is what Abed's oil did he + + align:start position:0% +now you that is what Abed's oil did he + + + align:start position:0% +now you that is what Abed's oil did he +talked about real dynamics in real time + + align:start position:0% +talked about real dynamics in real time + + + align:start position:0% +talked about real dynamics in real time +so when the wave packet is here it can't + + align:start position:0% +so when the wave packet is here it can't + + + align:start position:0% +so when the wave packet is here it can't +be dissociated but it's here it can and + + align:start position:0% +be dissociated but it's here it can and + + + align:start position:0% +be dissociated but it's here it can and +you look at the fragments very simple so + + align:start position:0% +you look at the fragments very simple so + + + align:start position:0% +you look at the fragments very simple so +there are lots of ways of taking these + + align:start position:0% +there are lots of ways of taking these + + + align:start position:0% +there are lots of ways of taking these +simple pictures of + + align:start position:0% +simple pictures of + + + align:start position:0% +simple pictures of +packets moving and and saying okay I can + + align:start position:0% +packets moving and and saying okay I can + + + align:start position:0% +packets moving and and saying okay I can +use them to set up an experiment where I + + align:start position:0% +use them to set up an experiment where I + + + align:start position:0% +use them to set up an experiment where I +ask a very specific question and I get + + align:start position:0% +ask a very specific question and I get + + + align:start position:0% +ask a very specific question and I get +answers and I know what to do with the + + align:start position:0% +answers and I know what to do with the + + + align:start position:0% +answers and I know what to do with the +answers now if it's not harmonic you can + + align:start position:0% +answers now if it's not harmonic you can + + + align:start position:0% +answers now if it's not harmonic you can +still do the Wales experiment or some + + align:start position:0% +still do the Wales experiment or some + + + align:start position:0% +still do the Wales experiment or some +other experiment and you can ask okay + + align:start position:0% +other experiment and you can ask okay + + + align:start position:0% +other experiment and you can ask okay +the wave packet moved over here and + + align:start position:0% +the wave packet moved over here and + + + align:start position:0% +the wave packet moved over here and +there's some dynamics that occurs it + + align:start position:0% +there's some dynamics that occurs it + + + align:start position:0% +there's some dynamics that occurs it +dissociates or do you do something and + + align:start position:0% +dissociates or do you do something and + + + align:start position:0% +dissociates or do you do something and +when it comes back it's not at the same + + align:start position:0% +when it comes back it's not at the same + + + align:start position:0% +when it comes back it's not at the same +amplitude and so you can yeah you can + + align:start position:0% +amplitude and so you can yeah you can + + + align:start position:0% +amplitude and so you can yeah you can +use the the time history of this these + + align:start position:0% +use the the time history of this these + + + align:start position:0% +use the the time history of this these +recurrences if it's harmonic if it's not + + align:start position:0% +recurrences if it's harmonic if it's not + + + align:start position:0% +recurrences if it's harmonic if it's not +harmonic then they recursive recurrences + + align:start position:0% +harmonic then they recursive recurrences + + + align:start position:0% +harmonic then they recursive recurrences +even if nothing happens over here + + align:start position:0% +even if nothing happens over here + + + align:start position:0% +even if nothing happens over here +the recurrences will be increasingly + + align:start position:0% +the recurrences will be increasingly + + + align:start position:0% +the recurrences will be increasingly +less perfect and so you measure the and + + align:start position:0% +less perfect and so you measure the and + + + align:start position:0% +less perfect and so you measure the and +harmonicity + + align:start position:0% + + + + align:start position:0% + +okay five minutes tunneling is a quantum + + align:start position:0% +okay five minutes tunneling is a quantum + + + align:start position:0% +okay five minutes tunneling is a quantum +mechanical phenomena and again you want + + align:start position:0% +mechanical phenomena and again you want + + + align:start position:0% +mechanical phenomena and again you want +to use the simplest possible picture to + + align:start position:0% +to use the simplest possible picture to + + + align:start position:0% +to use the simplest possible picture to +understand the signature of tunneling + + align:start position:0% +understand the signature of tunneling + + + align:start position:0% +understand the signature of tunneling +and so what do you do well the simplest + + align:start position:0% +and so what do you do well the simplest + + + align:start position:0% +and so what do you do well the simplest +thing you can do is start with a + + align:start position:0% +thing you can do is start with a + + + align:start position:0% +thing you can do is start with a +harmonic oscillator the next thing you + + align:start position:0% +harmonic oscillator the next thing you + + + align:start position:0% +harmonic oscillator the next thing you +do is you put a barrier in the middle + + align:start position:0% +do is you put a barrier in the middle + + + align:start position:0% +do is you put a barrier in the middle +and you make it really thin thin is + + align:start position:0% +and you make it really thin thin is + + + align:start position:0% +and you make it really thin thin is +because you don't want to calculate an + + align:start position:0% +because you don't want to calculate an + + + align:start position:0% +because you don't want to calculate an +integral you wanted to say oh yeah I + + align:start position:0% +integral you wanted to say oh yeah I + + + align:start position:0% +integral you wanted to say oh yeah I +know that the wave function forget about + + align:start position:0% +know that the wave function forget about + + + align:start position:0% +know that the wave function forget about +the barrier we know them the the + + align:start position:0% +the barrier we know them the the + + + align:start position:0% +the barrier we know them the the +magnitude of the wave function at the + + align:start position:0% +magnitude of the wave function at the + + + align:start position:0% +magnitude of the wave function at the +barrier okay and so if you have us a + + align:start position:0% +barrier okay and so if you have us a + + + align:start position:0% +barrier okay and so if you have us a +state which has a maximum here well that + + align:start position:0% +state which has a maximum here well that + + + align:start position:0% +state which has a maximum here well that +means that it's feeling the barrier and + + align:start position:0% +means that it's feeling the barrier and + + + align:start position:0% +means that it's feeling the barrier and +so you you you know what to do if there + + align:start position:0% +so you you you know what to do if there + + + align:start position:0% +so you you you know what to do if there +is a node here it doesn't know about the + + align:start position:0% +is a node here it doesn't know about the + + + align:start position:0% +is a node here it doesn't know about the +barrier so you can do all sorts of + + align:start position:0% +barrier so you can do all sorts of + + + align:start position:0% +barrier so you can do all sorts of +things really fast okay so and it's + + align:start position:0% +things really fast okay so and it's + + + align:start position:0% +things really fast okay so and it's +harmonic because you're gonna what you + + align:start position:0% +harmonic because you're gonna what you + + + align:start position:0% +harmonic because you're gonna what you +want to use A's and a daggers so equals + + align:start position:0% +want to use A's and a daggers so equals + + + align:start position:0% +want to use A's and a daggers so equals +one three five they have nodes here they + + align:start position:0% +one three five they have nodes here they + + + align:start position:0% +one three five they have nodes here they +don't know about the barrier or if they + + align:start position:0% +don't know about the barrier or if they + + + align:start position:0% +don't know about the barrier or if they +do it's a very modest effect if you make + + align:start position:0% +do it's a very modest effect if you make + + + align:start position:0% +do it's a very modest effect if you make +this thin enough and they won't know + + align:start position:0% +this thin enough and they won't know + + + align:start position:0% +this thin enough and they won't know +about it at all and and then V equals + + align:start position:0% +about it at all and and then V equals + + + align:start position:0% +about it at all and and then V equals +zero two more etc well their maximum + + align:start position:0% +zero two more etc well their maximum + + + align:start position:0% +zero two more etc well their maximum +well they have a local maximum here now + + align:start position:0% +well they have a local maximum here now + + + align:start position:0% +well they have a local maximum here now +remember this is a harmonic oscillator + + align:start position:0% +remember this is a harmonic oscillator + + + align:start position:0% +remember this is a harmonic oscillator +so the big lobes are on the extremes the + + align:start position:0% +so the big lobes are on the extremes the + + + align:start position:0% +so the big lobes are on the extremes the +smallest lobe is in the middle + + align:start position:0% +smallest lobe is in the middle + + + align:start position:0% +smallest lobe is in the middle +but it's not zero okay there are also + + align:start position:0% +but it's not zero okay there are also + + + align:start position:0% +but it's not zero okay there are also +symmetry restrictions this is a problem + + align:start position:0% +symmetry restrictions this is a problem + + + align:start position:0% +symmetry restrictions this is a problem +that has symmetry we have even functions + + align:start position:0% +that has symmetry we have even functions + + + align:start position:0% +that has symmetry we have even functions +and odd functions and for the even + + align:start position:0% +and odd functions and for the even + + + align:start position:0% +and odd functions and for the even +functions deep sigh the X is equal to + + align:start position:0% +functions deep sigh the X is equal to + + + align:start position:0% +functions deep sigh the X is equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +and for the odd functions sigh of zero + + align:start position:0% +and for the odd functions sigh of zero + + + align:start position:0% +and for the odd functions sigh of zero +is equal to zero okay so this is + + align:start position:0% +is equal to zero okay so this is + + + align:start position:0% +is equal to zero okay so this is +something that you know you choose the + + align:start position:0% +something that you know you choose the + + + align:start position:0% +something that you know you choose the +simplest problem and you use symmetry + + align:start position:0% +simplest problem and you use symmetry + + + align:start position:0% +simplest problem and you use symmetry +and bang all of a sudden you get + + align:start position:0% +and bang all of a sudden you get + + + align:start position:0% +and bang all of a sudden you get +fantastic insights so so let's look at + + align:start position:0% +fantastic insights so so let's look at + + + align:start position:0% +fantastic insights so so let's look at +what happens to the even functions so + + align:start position:0% +what happens to the even functions so + + + align:start position:0% +what happens to the even functions so +let's just draw a picture of their + + align:start position:0% +let's just draw a picture of their + + + align:start position:0% +let's just draw a picture of their +harmonic oscillator energy levels and we + + align:start position:0% +harmonic oscillator energy levels and we + + + align:start position:0% +harmonic oscillator energy levels and we +have a barrier which we say maybe goes + + align:start position:0% +have a barrier which we say maybe goes + + + align:start position:0% +have a barrier which we say maybe goes +that high and so we have one and we have + + align:start position:0% +that high and so we have one and we have + + + align:start position:0% +that high and so we have one and we have +three and we have five they're basically + + align:start position:0% +three and we have five they're basically + + + align:start position:0% +three and we have five they're basically +not affected by the very because they + + align:start position:0% +not affected by the very because they + + + align:start position:0% +not affected by the very because they +have a node at the barrier and then we + + align:start position:0% +have a node at the barrier and then we + + + align:start position:0% +have a node at the barrier and then we +have V equals zero what happens to V + + align:start position:0% +have V equals zero what happens to V + + + align:start position:0% +have V equals zero what happens to V +equals zero well wants to it hits this + + align:start position:0% +equals zero well wants to it hits this + + + align:start position:0% +equals zero well wants to it hits this +barrier and it's got a large amplitude + + align:start position:0% +barrier and it's got a large amplitude + + + align:start position:0% +barrier and it's got a large amplitude +and it can't it can't accrue more phase + + align:start position:0% +and it can't it can't accrue more phase + + + align:start position:0% +and it can't it can't accrue more phase +as you go through the barrier so when it + + align:start position:0% +as you go through the barrier so when it + + + align:start position:0% +as you go through the barrier so when it +hits the other turning point it doesn't + + align:start position:0% +hits the other turning point it doesn't + + + align:start position:0% +hits the other turning point it doesn't +satisfy the boundary conditions it'll go + + align:start position:0% +satisfy the boundary conditions it'll go + + + align:start position:0% +satisfy the boundary conditions it'll go +to infinity at x equals positive + + align:start position:0% +to infinity at x equals positive + + + align:start position:0% +to infinity at x equals positive +infinity so it has to be shifted so that + + align:start position:0% +infinity so it has to be shifted so that + + + align:start position:0% +infinity so it has to be shifted so that +the boundary conditions at the turning + + align:start position:0% +the boundary conditions at the turning + + + align:start position:0% +the boundary conditions at the turning +points are met and the only way that can + + align:start position:0% +points are met and the only way that can + + + align:start position:0% +points are met and the only way that can +happen is it gets shifted up in energy a + + align:start position:0% +happen is it gets shifted up in energy a + + + align:start position:0% +happen is it gets shifted up in energy a +lot + + align:start position:0% +lot + + + align:start position:0% +lot +so it equals zero is here now it can't + + align:start position:0% +so it equals zero is here now it can't + + + align:start position:0% +so it equals zero is here now it can't +be shifted above equals one because that + + align:start position:0% +be shifted above equals one because that + + + align:start position:0% +be shifted above equals one because that +would violate the node rule and if you + + align:start position:0% +would violate the node rule and if you + + + align:start position:0% +would violate the node rule and if you +draw a picture of the wave function for + + align:start position:0% +draw a picture of the wave function for + + + align:start position:0% +draw a picture of the wave function for +V equals zero in the boundary region the + + align:start position:0% +V equals zero in the boundary region the + + + align:start position:0% +V equals zero in the boundary region the +wave function has to look something well + + align:start position:0% +wave function has to look something well + + + align:start position:0% +wave function has to look something well +it has to look something like that so we + + align:start position:0% +it has to look something like that so we + + + align:start position:0% +it has to look something like that so we +have two lobes and it's trying to make a + + align:start position:0% +have two lobes and it's trying to make a + + + align:start position:0% +have two lobes and it's trying to make a +node but it can't + + align:start position:0% +node but it can't + + + align:start position:0% +node but it can't +it's a decreasing exponential I mean if + + align:start position:0% +it's a decreasing exponential I mean if + + + align:start position:0% +it's a decreasing exponential I mean if +you have a wave going into this region + + align:start position:0% +you have a wave going into this region + + + align:start position:0% +you have a wave going into this region +of the barrier you can have an + + align:start position:0% +of the barrier you can have an + + + align:start position:0% +of the barrier you can have an +increasing exponential or a decreasing + + align:start position:0% +increasing exponential or a decreasing + + + align:start position:0% +increasing exponential or a decreasing +exponential you can never satisfy + + align:start position:0% +exponential you can never satisfy + + + align:start position:0% +exponential you can never satisfy +continuity of the wave function with the + + align:start position:0% +continuity of the wave function with the + + + align:start position:0% +continuity of the wave function with the +increasing exponential but you can with + + align:start position:0% +increasing exponential but you can with + + + align:start position:0% +increasing exponential but you can with +a decreasing exponential and so the + + align:start position:0% +a decreasing exponential and so the + + + align:start position:0% +a decreasing exponential and so the +height of the barrier determines how + + align:start position:0% +height of the barrier determines how + + + align:start position:0% +height of the barrier determines how +close this guy comes to having a node it + + align:start position:0% +close this guy comes to having a node it + + + align:start position:0% +close this guy comes to having a node it +never will and how does this compare to + + align:start position:0% +never will and how does this compare to + + + align:start position:0% +never will and how does this compare to +the wave function for vehicles one well + + align:start position:0% +the wave function for vehicles one well + + + align:start position:0% +the wave function for vehicles one well +the wave function for vehicles one looks + + align:start position:0% +the wave function for vehicles one looks + + + align:start position:0% +the wave function for vehicles one looks +like this the amplitude in this lobe and + + align:start position:0% +like this the amplitude in this lobe and + + + align:start position:0% +like this the amplitude in this lobe and +the amplitude in that lobe are the same + + align:start position:0% +the amplitude in that lobe are the same + + + align:start position:0% +the amplitude in that lobe are the same +but the sine is reversed and so + + align:start position:0% +but the sine is reversed and so + + + align:start position:0% +but the sine is reversed and so +basically this picture tells you that + + align:start position:0% +basically this picture tells you that + + + align:start position:0% +basically this picture tells you that +these two levels have almost exactly the + + align:start position:0% +these two levels have almost exactly the + + + align:start position:0% +these two levels have almost exactly the +same energy so the equal zero is shifted + + align:start position:0% +same energy so the equal zero is shifted + + + align:start position:0% +same energy so the equal zero is shifted +up the equals two is shifted up but not + + align:start position:0% +up the equals two is shifted up but not + + + align:start position:0% +up the equals two is shifted up but not +quite so much and B equals three IB + + align:start position:0% +quite so much and B equals three IB + + + align:start position:0% +quite so much and B equals three IB +equals four is shifted up hardly at all + + align:start position:0% +equals four is shifted up hardly at all + + + align:start position:0% +equals four is shifted up hardly at all +and so you get what's called level + + align:start position:0% +and so you get what's called level + + + align:start position:0% +and so you get what's called level +snacker and this levels gas sag is + + align:start position:0% +snacker and this levels gas sag is + + + align:start position:0% +snacker and this levels gas sag is +staggering is the signature of tunneling + + align:start position:0% +staggering is the signature of tunneling + + + align:start position:0% +staggering is the signature of tunneling +this is how we know about tunneling the + + align:start position:0% +this is how we know about tunneling the + + + align:start position:0% +this is how we know about tunneling the +only way we know about tunneling so we + + align:start position:0% +only way we know about tunneling so we + + + align:start position:0% +only way we know about tunneling so we +measured the energy levels and it tells + + align:start position:0% +measured the energy levels and it tells + + + align:start position:0% +measured the energy levels and it tells +us how how is our the wave function + + align:start position:0% +us how how is our the wave function + + + align:start position:0% +us how how is our the wave function +sampling this barrier now this is a + + align:start position:0% +sampling this barrier now this is a + + + align:start position:0% +sampling this barrier now this is a +childish barrier and there's a real + + align:start position:0% +childish barrier and there's a real + + + align:start position:0% +childish barrier and there's a real +barriers and you know molecules + + align:start position:0% +barriers and you know molecules + + + align:start position:0% +barriers and you know molecules +isomerize and they isomerize over a + + align:start position:0% +isomerize and they isomerize over a + + + align:start position:0% +isomerize and they isomerize over a +barrier and the barrier isn't + + align:start position:0% +barrier and the barrier isn't + + + align:start position:0% +barrier and the barrier isn't +necessarily at x equals zero but if you + + align:start position:0% +necessarily at x equals zero but if you + + + align:start position:0% +necessarily at x equals zero but if you +understand this + + align:start position:0% +understand this + + + align:start position:0% +understand this +problem you can deal with isomerization + + align:start position:0% +problem you can deal with isomerization + + + align:start position:0% +problem you can deal with isomerization +now I'm a author of a paper that's just + + align:start position:0% +now I'm a author of a paper that's just + + + align:start position:0% +now I'm a author of a paper that's just +appearing in science than the next few + + align:start position:0% +appearing in science than the next few + + + align:start position:0% +appearing in science than the next few +weeks on the isomerization from vanilla + + align:start position:0% +weeks on the isomerization from vanilla + + + align:start position:0% +weeks on the isomerization from vanilla +diene to acetylene there's a barrier + + align:start position:0% +diene to acetylene there's a barrier + + + align:start position:0% +diene to acetylene there's a barrier +involved so these sorts of pictures are + + align:start position:0% +involved so these sorts of pictures are + + + align:start position:0% +involved so these sorts of pictures are +important for understanding those sorts + + align:start position:0% +important for understanding those sorts + + + align:start position:0% +important for understanding those sorts +of phenomena now so I'm done really so + + align:start position:0% +of phenomena now so I'm done really so + + + align:start position:0% +of phenomena now so I'm done really so +what we are now encountering with the + + align:start position:0% +what we are now encountering with the + + + align:start position:0% +what we are now encountering with the +time dependent Schrodinger equation is + + align:start position:0% +time dependent Schrodinger equation is + + + align:start position:0% +time dependent Schrodinger equation is +discovering how dynamics like tunneling + + align:start position:0% +discovering how dynamics like tunneling + + + align:start position:0% +discovering how dynamics like tunneling +is encoded in an eigenstate spectrum + + align:start position:0% +is encoded in an eigenstate spectrum + + + align:start position:0% +is encoded in an eigenstate spectrum +because the encoding is level staggering + + align:start position:0% +because the encoding is level staggering + + + align:start position:0% +because the encoding is level staggering +eigenstates so people normally have this + + align:start position:0% +eigenstates so people normally have this + + + align:start position:0% +eigenstates so people normally have this +this naive idea that eigenstates time + + align:start position:0% +this naive idea that eigenstates time + + + align:start position:0% +this naive idea that eigenstates time +independent Hamiltonian spectroscopy + + align:start position:0% +independent Hamiltonian spectroscopy + + + align:start position:0% +independent Hamiltonian spectroscopy +does not sample dynamics because it's + + align:start position:0% +does not sample dynamics because it's + + + align:start position:0% +does not sample dynamics because it's +only measuring energy levels real + + align:start position:0% +only measuring energy levels real + + + align:start position:0% +only measuring energy levels real +dynamical processes are time dependent + + align:start position:0% +dynamical processes are time dependent + + + align:start position:0% +dynamical processes are time dependent +but the dynamics is encoded in energy + + align:start position:0% +but the dynamics is encoded in energy + + + align:start position:0% +but the dynamics is encoded in energy +level patterns and that is actually sort + + align:start position:0% +level patterns and that is actually sort + + + align:start position:0% +level patterns and that is actually sort +of the the the my signature in + + align:start position:0% +of the the the my signature in + + + align:start position:0% +of the the the my signature in +experimental spectroscopy I've looked + + align:start position:0% +experimental spectroscopy I've looked + + + align:start position:0% +experimental spectroscopy I've looked +for ways in which dynamics is encoded in + + align:start position:0% +for ways in which dynamics is encoded in + + + align:start position:0% +for ways in which dynamics is encoded in +eigenstate spectra and chemists are + + align:start position:0% +eigenstate spectra and chemists are + + + align:start position:0% +eigenstate spectra and chemists are +interested in dynamics much more than in + + align:start position:0% +interested in dynamics much more than in + + + align:start position:0% +interested in dynamics much more than in +structure so that's that's it for today + + align:start position:0% +structure so that's that's it for today + + + align:start position:0% +structure so that's that's it for today +I will see you on Wednesday \ No newline at end of file diff --git a/Ih0cPR745fM.txt b/Ih0cPR745fM.txt new file mode 100644 index 0000000000000000000000000000000000000000..d8f56993238d20ca3074ccdcea630232973081c0 --- /dev/null +++ b/Ih0cPR745fM.txt @@ -0,0 +1,14011 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right uh today we have + + align:start position:0% +ocw.mit.edu all right uh today we have + + + align:start position:0% +ocw.mit.edu all right uh today we have +lecture guest lecture two of two by C + + align:start position:0% +lecture guest lecture two of two by C + + + align:start position:0% +lecture guest lecture two of two by C +scalak all right uh glad to be back so + + align:start position:0% +scalak all right uh glad to be back so + + + align:start position:0% +scalak all right uh glad to be back so +let's continue on the path we followed + + align:start position:0% +let's continue on the path we followed + + + align:start position:0% +let's continue on the path we followed +last time um let me remind you what we + + align:start position:0% +last time um let me remind you what we + + + align:start position:0% +last time um let me remind you what we +did last time first of all so I talked + + align:start position:0% +did last time first of all so I talked + + + align:start position:0% +did last time first of all so I talked +about uh interesting theorems in + + align:start position:0% +about uh interesting theorems in + + + align:start position:0% +about uh interesting theorems in +topology Nash uh sperner and + + align:start position:0% +topology Nash uh sperner and + + + align:start position:0% +topology Nash uh sperner and +Brower and + + align:start position:0% +Brower and + + + align:start position:0% +Brower and +I uh you know defined the corresponding + + align:start position:0% +I uh you know defined the corresponding + + + align:start position:0% +I uh you know defined the corresponding +so these were theorems in topology I + + align:start position:0% +so these were theorems in topology I + + + align:start position:0% +so these were theorems in topology I +Define the corresponding + + align:start position:0% +Define the corresponding + + + align:start position:0% +Define the corresponding +problems uh and uh because of this + + align:start position:0% +problems uh and uh because of this + + + align:start position:0% +problems uh and uh because of this +existing theorems the corresponding + + align:start position:0% +existing theorems the corresponding + + + align:start position:0% +existing theorems the corresponding +search problems were + + align:start position:0% +search problems were + + + align:start position:0% +search problems were +total and then I looked + + align:start position:0% +total and then I looked + + + align:start position:0% +total and then I looked +into the problems in NP that are total + + align:start position:0% +into the problems in NP that are total + + + align:start position:0% +into the problems in NP that are total +and + + align:start position:0% +and + + + align:start position:0% +and +um I tried to identify what what in + + align:start position:0% +um I tried to identify what what in + + + align:start position:0% +um I tried to identify what what in +these problems make them total and try + + align:start position:0% +these problems make them total and try + + + align:start position:0% +these problems make them total and try +to identify a combinatorial argument + + align:start position:0% +to identify a combinatorial argument + + + align:start position:0% +to identify a combinatorial argument +that guarantees the existence of + + align:start position:0% +that guarantees the existence of + + + align:start position:0% +that guarantees the existence of +Solutions in these problems motivated by + + align:start position:0% +Solutions in these problems motivated by + + + align:start position:0% +Solutions in these problems motivated by +that argument which turned out to be a + + align:start position:0% +that argument which turned out to be a + + + align:start position:0% +that argument which turned out to be a +parity argument on directed graphs I + + align:start position:0% +parity argument on directed graphs I + + + align:start position:0% +parity argument on directed graphs I +defined the class + + align:start position:0% +defined the class + + + align:start position:0% +defined the class +PPD and I introduced the problem + + align:start position:0% +PPD and I introduced the problem + + + align:start position:0% +PPD and I introduced the problem +arithmetic circuit + + align:start position:0% +arithmetic circuit + + + align:start position:0% +arithmetic circuit +Set uh from which uh which which is PPD + + align:start position:0% +Set uh from which uh which which is PPD + + + align:start position:0% +Set uh from which uh which which is PPD +complete and uh you know from which I + + align:start position:0% +complete and uh you know from which I + + + align:start position:0% +complete and uh you know from which I +promised to show a bunch of PPD hardness + + align:start position:0% +promised to show a bunch of PPD hardness + + + align:start position:0% +promised to show a bunch of PPD hardness +reductions this time so let me remind + + align:start position:0% +reductions this time so let me remind + + + align:start position:0% +reductions this time so let me remind +you the you know silent points uh from + + align:start position:0% +you the you know silent points uh from + + + align:start position:0% +you the you know silent points uh from +this + + align:start position:0% +this + + + align:start position:0% +this +uh + + align:start position:0% +uh + + + align:start position:0% +uh +list before I keep going so first of all + + align:start position:0% +list before I keep going so first of all + + + align:start position:0% +list before I keep going so first of all +the PPD class has combinatorial flavor + + align:start position:0% +the PPD class has combinatorial flavor + + + align:start position:0% +the PPD class has combinatorial flavor +in the definition of the class what I'm + + align:start position:0% +in the definition of the class what I'm + + + align:start position:0% +in the definition of the class what I'm +doing is I'm defining a graph uh on all + + align:start position:0% +doing is I'm defining a graph uh on all + + + align:start position:0% +doing is I'm defining a graph uh on all +possible end bit strings so an + + align:start position:0% +possible end bit strings so an + + + align:start position:0% +possible end bit strings so an +exponentially large + + align:start position:0% +exponentially large + + + align:start position:0% +exponentially large +Set uh by providing two circuits p and n + + align:start position:0% +Set uh by providing two circuits p and n + + + align:start position:0% +Set uh by providing two circuits p and n +p is the circuit of + + align:start position:0% +p is the circuit of + + + align:start position:0% +p is the circuit of +possible uh + + align:start position:0% +possible uh + + + align:start position:0% +possible uh +father and uh n is the circuit of + + align:start position:0% +father and uh n is the circuit of + + + align:start position:0% +father and uh n is the circuit of +possible child and given these two + + align:start position:0% +possible child and given these two + + + align:start position:0% +possible child and given these two +circuits I establish a directed Edge + + align:start position:0% +circuits I establish a directed Edge + + + align:start position:0% +circuits I establish a directed Edge +between between string V1 and string V2 + + align:start position:0% +between between string V1 and string V2 + + + align:start position:0% +between between string V1 and string V2 +if they agree on their Parenthood + + align:start position:0% +if they agree on their Parenthood + + + align:start position:0% +if they agree on their Parenthood +relationship meaning V2 believes V1 is + + align:start position:0% +relationship meaning V2 believes V1 is + + + align:start position:0% +relationship meaning V2 believes V1 is +his father and uh also V1 believes V2 is + + align:start position:0% +his father and uh also V1 believes V2 is + + + align:start position:0% +his father and uh also V1 believes V2 is +its child in that case if this condition + + align:start position:0% +its child in that case if this condition + + + align:start position:0% +its child in that case if this condition +is true I establish a net between these + + align:start position:0% +is true I establish a net between these + + + align:start position:0% +is true I establish a net between these +two pair of notes and I do the same for + + align:start position:0% +two pair of notes and I do the same for + + + align:start position:0% +two pair of notes and I do the same for +all pairs of strings and in the end I + + align:start position:0% +all pairs of strings and in the end I + + + align:start position:0% +all pairs of strings and in the end I +get a + + align:start position:0% +get a + + + align:start position:0% +get a +graph and the problem end of the line is + + align:start position:0% +graph and the problem end of the line is + + + align:start position:0% +graph and the problem end of the line is +given these two circuits and the + + align:start position:0% +given these two circuits and the + + + align:start position:0% +given these two circuits and the +corresponding graph that they Define on + + align:start position:0% +corresponding graph that they Define on + + + align:start position:0% +corresponding graph that they Define on +this set if the AL zero string is + + align:start position:0% +this set if the AL zero string is + + + align:start position:0% +this set if the AL zero string is +unbalanced uh meaning different in and + + align:start position:0% +unbalanced uh meaning different in and + + + align:start position:0% +unbalanced uh meaning different in and +out degree then uh I want you to find + + align:start position:0% +out degree then uh I want you to find + + + align:start position:0% +out degree then uh I want you to find +another unbalanced uh node string okay + + align:start position:0% +another unbalanced uh node string okay + + + align:start position:0% +another unbalanced uh node string okay +uh which is guaranteed to Exist by the + + align:start position:0% +uh which is guaranteed to Exist by the + + + align:start position:0% +uh which is guaranteed to Exist by the +parity + + align:start position:0% +parity + + + align:start position:0% +parity +argument and PPD is the class of all + + align:start position:0% +argument and PPD is the class of all + + + align:start position:0% +argument and PPD is the class of all +search problems in FNP that are + + align:start position:0% +search problems in FNP that are + + + align:start position:0% +search problems in FNP that are +reducible polinomial time reducible to + + align:start position:0% +reducible polinomial time reducible to + + + align:start position:0% +reducible polinomial time reducible to +this problem I remind you I'll remind + + align:start position:0% +this problem I remind you I'll remind + + + align:start position:0% +this problem I remind you I'll remind +you also of the structure of the graph + + align:start position:0% +you also of the structure of the graph + + + align:start position:0% +you also of the structure of the graph +defined by this two circuits it's easy + + align:start position:0% +defined by this two circuits it's easy + + + align:start position:0% +defined by this two circuits it's easy +to verify that uh uh if my Edge + + align:start position:0% +to verify that uh uh if my Edge + + + align:start position:0% +to verify that uh uh if my Edge +definition is this then every vertex has + + align:start position:0% +definition is this then every vertex has + + + align:start position:0% +definition is this then every vertex has +in degree and out degree at most one so + + align:start position:0% +in degree and out degree at most one so + + + align:start position:0% +in degree and out degree at most one so +uh the graph that's induced by these two + + align:start position:0% +uh the graph that's induced by these two + + + align:start position:0% +uh the graph that's induced by these two +circuits will have this form and + + align:start position:0% +circuits will have this form and + + + align:start position:0% +circuits will have this form and +basically I'm looking for all red points + + align:start position:0% +basically I'm looking for all red points + + + align:start position:0% +basically I'm looking for all red points +I mean for any of these points any of + + align:start position:0% +I mean for any of these points any of + + + align:start position:0% +I mean for any of these points any of +these red Point strings are solutions + + align:start position:0% +these red Point strings are solutions + + + align:start position:0% +these red Point strings are solutions +any unbalanced string except for the all + + align:start position:0% +any unbalanced string except for the all + + + align:start position:0% +any unbalanced string except for the all +zero string okay if the all zero string + + align:start position:0% +zero string okay if the all zero string + + + align:start position:0% +zero string okay if the all zero string +is not unbal Balan then I don't want you + + align:start position:0% +is not unbal Balan then I don't want you + + + align:start position:0% +is not unbal Balan then I don't want you +to do anything if it is unbalanced then + + align:start position:0% +to do anything if it is unbalanced then + + + align:start position:0% +to do anything if it is unbalanced then +I'm looking for any of these red + + align:start position:0% +I'm looking for any of these red + + + align:start position:0% +I'm looking for any of these red +vertices so that's the class PPD and it + + align:start position:0% +vertices so that's the class PPD and it + + + align:start position:0% +vertices so that's the class PPD and it +has a combinatorial flavor okay so I'm + + align:start position:0% +has a combinatorial flavor okay so I'm + + + align:start position:0% +has a combinatorial flavor okay so I'm +defining a huge graph via these two + + align:start position:0% +defining a huge graph via these two + + + align:start position:0% +defining a huge graph via these two +circuits and I'm asking you to find any + + align:start position:0% +circuits and I'm asking you to find any + + + align:start position:0% +circuits and I'm asking you to find any +of these red points okay + + align:start position:0% +of these red points okay + + + align:start position:0% +of these red points okay +so uh on the other hand sort of like the + + align:start position:0% +so uh on the other hand sort of like the + + + align:start position:0% +so uh on the other hand sort of like the +the problems we were targeting nilium + + align:start position:0% +the problems we were targeting nilium + + + align:start position:0% +the problems we were targeting nilium +and BR s were you know had a more + + align:start position:0% +and BR s were you know had a more + + + align:start position:0% +and BR s were you know had a more +continuous flavor so uh instead of uh uh + + align:start position:0% +continuous flavor so uh instead of uh uh + + + align:start position:0% +continuous flavor so uh instead of uh uh +working directly with this problem with + + align:start position:0% +working directly with this problem with + + + align:start position:0% +working directly with this problem with +end of the line and trying to reduce the + + align:start position:0% +end of the line and trying to reduce the + + + align:start position:0% +end of the line and trying to reduce the +this problem to Nash and to Brower to + + align:start position:0% +this problem to Nash and to Brower to + + + align:start position:0% +this problem to Nash and to Brower to +establish PPD hardness reductions I + + align:start position:0% +establish PPD hardness reductions I + + + align:start position:0% +establish PPD hardness reductions I +actually introduced a problem that's + + align:start position:0% +actually introduced a problem that's + + + align:start position:0% +actually introduced a problem that's +actually that's closer to these problem + + align:start position:0% +actually that's closer to these problem + + + align:start position:0% +actually that's closer to these problem +which is has a continuous flavor and it + + align:start position:0% +which is has a continuous flavor and it + + + align:start position:0% +which is has a continuous flavor and it +was the problem arithmetic circuit + + align:start position:0% +was the problem arithmetic circuit + + + align:start position:0% +was the problem arithmetic circuit +side uh there were a bunch of problems + + align:start position:0% +side uh there were a bunch of problems + + + align:start position:0% +side uh there were a bunch of problems +last time about uh the definition of the + + align:start position:0% +last time about uh the definition of the + + + align:start position:0% +last time about uh the definition of the +problem so I decided to uh be more + + align:start position:0% +problem so I decided to uh be more + + + align:start position:0% +problem so I decided to uh be more +explicit about what it is so basically + + align:start position:0% +explicit about what it is so basically + + + align:start position:0% +explicit about what it is so basically +I'm giving a circuit that has two types + + align:start position:0% +I'm giving a circuit that has two types + + + align:start position:0% +I'm giving a circuit that has two types +of nodes variable nodes V1 through VN + + align:start position:0% +of nodes variable nodes V1 through VN + + + align:start position:0% +of nodes variable nodes V1 through VN +and gate nodes G1 through GM now every + + align:start position:0% +and gate nodes G1 through GM now every + + + align:start position:0% +and gate nodes G1 through GM now every +gate node has one of uh six possible + + align:start position:0% +gate node has one of uh six possible + + + align:start position:0% +gate node has one of uh six possible +flavors okay it can be an assignment + + align:start position:0% +flavors okay it can be an assignment + + + align:start position:0% +flavors okay it can be an assignment +assignment gate an addition gate + + align:start position:0% +assignment gate an addition gate + + + align:start position:0% +assignment gate an addition gate +subtraction gate set equal to a constant + + align:start position:0% +subtraction gate set equal to a constant + + + align:start position:0% +subtraction gate set equal to a constant +gate multiply by a constant gate and + + align:start position:0% +gate multiply by a constant gate and + + + align:start position:0% +gate multiply by a constant gate and +comparison + + align:start position:0% +comparison + + + align:start position:0% +comparison +gate um depending on the type it's going + + align:start position:0% +gate um depending on the type it's going + + + align:start position:0% +gate um depending on the type it's going +to have uh from 0 to 3 inputs to two + + align:start position:0% +to have uh from 0 to 3 inputs to two + + + align:start position:0% +to have uh from 0 to 3 inputs to two +inputs and it always has one output now + + align:start position:0% +inputs and it always has one output now + + + align:start position:0% +inputs and it always has one output now +what I wanted to emphasize is that this + + align:start position:0% +what I wanted to emphasize is that this + + + align:start position:0% +what I wanted to emphasize is that this +uh graph doesn't have inputs input + + align:start position:0% +uh graph doesn't have inputs input + + + align:start position:0% +uh graph doesn't have inputs input +variables okay it Loops are + + align:start position:0% +variables okay it Loops are + + + align:start position:0% +variables okay it Loops are +allowed and uh what I want to emphasize + + align:start position:0% +allowed and uh what I want to emphasize + + + align:start position:0% +allowed and uh what I want to emphasize +which I didn't emphasize last time is + + align:start position:0% +which I didn't emphasize last time is + + + align:start position:0% +which I didn't emphasize last time is +that variable nodes have in degree + + align:start position:0% +that variable nodes have in degree + + + align:start position:0% +that variable nodes have in degree +one uh and Gates have Zer one or two + + align:start position:0% +one uh and Gates have Zer one or two + + + align:start position:0% +one uh and Gates have Zer one or two +inputs depending on their type other + + align:start position:0% +inputs depending on their type other + + + align:start position:0% +inputs depending on their type other +wise uh you know for instance the out + + align:start position:0% +wise uh you know for instance the out + + + align:start position:0% +wise uh you know for instance the out +degree of a note could be arbitrary the + + align:start position:0% +degree of a note could be arbitrary the + + + align:start position:0% +degree of a note could be arbitrary the +fun out could be arbitrary doesn't + + align:start position:0% +fun out could be arbitrary doesn't + + + align:start position:0% +fun out could be arbitrary doesn't +matter okay but you have to respect this + + align:start position:0% +matter okay but you have to respect this + + + align:start position:0% +matter okay but you have to respect this +every no every variable node has inte + + align:start position:0% +every no every variable node has inte + + + align:start position:0% +every no every variable node has inte +degree + + align:start position:0% +degree + + + align:start position:0% +degree +one uh every gate node has Z one or two + + align:start position:0% +one uh every gate node has Z one or two + + + align:start position:0% +one uh every gate node has Z one or two +inputs depending on the + + align:start position:0% +inputs depending on the + + + align:start position:0% +inputs depending on the +type uh there are no edges between uh + + align:start position:0% +type uh there are no edges between uh + + + align:start position:0% +type uh there are no edges between uh +Gates and Gates and variables and + + align:start position:0% +Gates and Gates and variables and + + + align:start position:0% +Gates and Gates and variables and +variables that only edges between + + align:start position:0% +variables that only edges between + + + align:start position:0% +variables that only edges between +variables and Gates and gates to + + align:start position:0% +variables and Gates and gates to + + + align:start position:0% +variables and Gates and gates to +variables okay that's the input input is + + align:start position:0% +variables okay that's the input input is + + + align:start position:0% +variables okay that's the input input is +a circuit that has this + + align:start position:0% +a circuit that has this + + + align:start position:0% +a circuit that has this +form and what I want you to do is I want + + align:start position:0% +form and what I want you to do is I want + + + align:start position:0% +form and what I want you to do is I want +you to find an assignment + + align:start position:0% +you to find an assignment + + + align:start position:0% +you to find an assignment +of real 01 values to the variables of + + align:start position:0% +of real 01 values to the variables of + + + align:start position:0% +of real 01 values to the variables of +the circuit such that the the the the + + align:start position:0% +the circuit such that the the the the + + + align:start position:0% +the circuit such that the the the the +constraints of the gates are + + align:start position:0% +constraints of the gates are + + + align:start position:0% +constraints of the gates are +satisfied and here are the constraints + + align:start position:0% +satisfied and here are the constraints + + + align:start position:0% +satisfied and here are the constraints +of the gates okay so if the gate is an + + align:start position:0% +of the gates okay so if the gate is an + + + align:start position:0% +of the gates okay so if the gate is an +assignment gate I want that the output + + align:start position:0% +assignment gate I want that the output + + + align:start position:0% +assignment gate I want that the output +node the node who's connected to the + + align:start position:0% +node the node who's connected to the + + + align:start position:0% +node the node who's connected to the +output of that gate uh has equal value + + align:start position:0% +output of that gate uh has equal value + + + align:start position:0% +output of that gate uh has equal value +to the node that's fitting into that + + align:start position:0% +to the node that's fitting into that + + + align:start position:0% +to the node that's fitting into that +gate if the gate is addition gate I want + + align:start position:0% +gate if the gate is addition gate I want + + + align:start position:0% +gate if the gate is addition gate I want +that the variable node who uh the output + + align:start position:0% +that the variable node who uh the output + + + align:start position:0% +that the variable node who uh the output +of the connected to the output of the + + align:start position:0% +of the connected to the output of the + + + align:start position:0% +of the connected to the output of the +gate to be basically the sum of the + + align:start position:0% +gate to be basically the sum of the + + + align:start position:0% +gate to be basically the sum of the +values of the inputs to the addition + + align:start position:0% +values of the inputs to the addition + + + align:start position:0% +values of the inputs to the addition +gate except I'm also going to threshold + + align:start position:0% +gate except I'm also going to threshold + + + align:start position:0% +gate except I'm also going to threshold +it I'm not going to allow it going above + + align:start position:0% +it I'm not going to allow it going above + + + align:start position:0% +it I'm not going to allow it going above +one and so on so forth so these are the + + align:start position:0% +one and so on so forth so these are the + + + align:start position:0% +one and so on so forth so these are the +gate + + align:start position:0% +gate + + + align:start position:0% +gate +conditions okay so now uh what I said + + align:start position:0% +conditions okay so now uh what I said + + + align:start position:0% +conditions okay so now uh what I said +last time is that a satisfying + + align:start position:0% +last time is that a satisfying + + + align:start position:0% +last time is that a satisfying +assignment always exists for this + + align:start position:0% +assignment always exists for this + + + align:start position:0% +assignment always exists for this +problem it's not a pror obuse so it + + align:start position:0% +problem it's not a pror obuse so it + + + align:start position:0% +problem it's not a pror obuse so it +requires work and actually it is going + + align:start position:0% +requires work and actually it is going + + + align:start position:0% +requires work and actually it is going +through a fix point to argue that there + + align:start position:0% +through a fix point to argue that there + + + align:start position:0% +through a fix point to argue that there +is a always a solution to this problem + + align:start position:0% +is a always a solution to this problem + + + align:start position:0% +is a always a solution to this problem +uh what I also claimed last time is that + + align:start position:0% +uh what I also claimed last time is that + + + align:start position:0% +uh what I also claimed last time is that +uh it's PPD complete to find a + + align:start position:0% +uh it's PPD complete to find a + + + align:start position:0% +uh it's PPD complete to find a +satisfying assignment so it's a natural + + align:start position:0% +satisfying assignment so it's a natural + + + align:start position:0% +satisfying assignment so it's a natural +starting point for + + align:start position:0% +starting point for + + + align:start position:0% +starting point for +reductions what I also said last time is + + align:start position:0% +reductions what I also said last time is + + + align:start position:0% +reductions what I also said last time is +that in fact I can allow some noise in + + align:start position:0% +that in fact I can allow some noise in + + + align:start position:0% +that in fact I can allow some noise in +the error in the uh gate constraints so + + align:start position:0% +the error in the uh gate constraints so + + + align:start position:0% +the error in the uh gate constraints so +I can allow plus minus + + align:start position:0% +I can allow plus minus + + + align:start position:0% +I can allow plus minus +Epsilon uh deviation from the gate + + align:start position:0% +Epsilon uh deviation from the gate + + + align:start position:0% +Epsilon uh deviation from the gate +constraints uh and uh okay so this + + align:start position:0% +constraints uh and uh okay so this + + + align:start position:0% +constraints uh and uh okay so this +should be a minus Epsilon sorry about + + align:start position:0% +should be a minus Epsilon sorry about + + + align:start position:0% +should be a minus Epsilon sorry about +that uh and this Epsilon is part of the + + align:start position:0% +that uh and this Epsilon is part of the + + + align:start position:0% +that uh and this Epsilon is part of the +input okay so I can I can I can uh sort + + align:start position:0% +input okay so I can I can I can uh sort + + + align:start position:0% +input okay so I can I can I can uh sort +of like I can give us input both a + + align:start position:0% +of like I can give us input both a + + + align:start position:0% +of like I can give us input both a +circuit and an Epsilon and I will ask + + align:start position:0% +circuit and an Epsilon and I will ask + + + align:start position:0% +circuit and an Epsilon and I will ask +you to satisfy the gate constraints + + align:start position:0% +you to satisfy the gate constraints + + + align:start position:0% +you to satisfy the gate constraints +within Epsilon + + align:start position:0% +within Epsilon + + + align:start position:0% +within Epsilon +now last time I also showed you the + + align:start position:0% +now last time I also showed you the + + + align:start position:0% +now last time I also showed you the +structure of the hardness proof for Nash + + align:start position:0% +structure of the hardness proof for Nash + + + align:start position:0% +structure of the hardness proof for Nash +which basically took the generic PPD end + + align:start position:0% +which basically took the generic PPD end + + + align:start position:0% +which basically took the generic PPD end +of the line problem generic PPD complete + + align:start position:0% +of the line problem generic PPD complete + + + align:start position:0% +of the line problem generic PPD complete +problem end of the line it embedded it + + align:start position:0% +problem end of the line it embedded it + + + align:start position:0% +problem end of the line it embedded it +into geometry into uh the 3D cube then + + align:start position:0% +into geometry into uh the 3D cube then + + + align:start position:0% +into geometry into uh the 3D cube then +it uh defined a version of spers LMA + + align:start position:0% +it uh defined a version of spers LMA + + + align:start position:0% +it uh defined a version of spers LMA +which then it reduced to arithmetic + + align:start position:0% +which then it reduced to arithmetic + + + align:start position:0% +which then it reduced to arithmetic +circuit set and I didn't show this part + + align:start position:0% +circuit set and I didn't show this part + + + align:start position:0% +circuit set and I didn't show this part +of the reduction and I'm not going to + + align:start position:0% +of the reduction and I'm not going to + + + align:start position:0% +of the reduction and I'm not going to +show it because that's the complicated + + align:start position:0% +show it because that's the complicated + + + align:start position:0% +show it because that's the complicated +part but what I'm going to show is how + + align:start position:0% +part but what I'm going to show is how + + + align:start position:0% +part but what I'm going to show is how +to go from this problem the arithmetic + + align:start position:0% +to go from this problem the arithmetic + + + align:start position:0% +to go from this problem the arithmetic +circuits set to Nash equilibrium okay + + align:start position:0% +circuits set to Nash equilibrium okay + + + align:start position:0% +circuits set to Nash equilibrium okay +just to show how easy it is to uh work + + align:start position:0% +just to show how easy it is to uh work + + + align:start position:0% +just to show how easy it is to uh work +with this problem reduce to other + + align:start position:0% +with this problem reduce to other + + + align:start position:0% +with this problem reduce to other +problems uh okay so that's what I want + + align:start position:0% +problems uh okay so that's what I want + + + align:start position:0% +problems uh okay so that's what I want +to focus on so okay so that was the + + align:start position:0% +to focus on so okay so that was the + + + align:start position:0% +to focus on so okay so that was the +that's the review from last time and + + align:start position:0% +that's the review from last time and + + + align:start position:0% +that's the review from last time and +this time I want to talk about I want to + + align:start position:0% +this time I want to talk about I want to + + + align:start position:0% +this time I want to talk about I want to +show the PPD completeness of Nash + + align:start position:0% +show the PPD completeness of Nash + + + align:start position:0% +show the PPD completeness of Nash +equilibrium I'm going to briefly uh + + align:start position:0% +equilibrium I'm going to briefly uh + + + align:start position:0% +equilibrium I'm going to briefly uh +give two other + + align:start position:0% +give two other + + + align:start position:0% +give two other +examples that uh have um that that come + + align:start position:0% +examples that uh have um that that come + + + align:start position:0% +examples that uh have um that that come +from combinatorics and then lastly I'm + + align:start position:0% +from combinatorics and then lastly I'm + + + align:start position:0% +from combinatorics and then lastly I'm +going to talk about other existence + + align:start position:0% +going to talk about other existence + + + align:start position:0% +going to talk about other existence +arguments and the complexity classes + + align:start position:0% +arguments and the complexity classes + + + align:start position:0% +arguments and the complexity classes +that they Define uh so I'm going to + + align:start position:0% +that they Define uh so I'm going to + + + align:start position:0% +that they Define uh so I'm going to +introduce this classes PPA PPP and PLS + + align:start position:0% +introduce this classes PPA PPP and PLS + + + align:start position:0% +introduce this classes PPA PPP and PLS +uh before I do that also that was a + + align:start position:0% +uh before I do that also that was a + + + align:start position:0% +uh before I do that also that was a +question from last time PPD stands from + + align:start position:0% +question from last time PPD stands from + + + align:start position:0% +question from last time PPD stands from +polinomial parity argument in directed + + align:start position:0% +polinomial parity argument in directed + + + align:start position:0% +polinomial parity argument in directed +graphs okay corresponding to the fact + + align:start position:0% +graphs okay corresponding to the fact + + + align:start position:0% +graphs okay corresponding to the fact +that this classes defined with this + + align:start position:0% +that this classes defined with this + + + align:start position:0% +that this classes defined with this +parity argument on directed graphs in + + align:start position:0% +parity argument on directed graphs in + + + align:start position:0% +parity argument on directed graphs in +mind okay cool so let's focus on this + + align:start position:0% +mind okay cool so let's focus on this + + + align:start position:0% +mind okay cool so let's focus on this +reduction from circuit to Nash I want to + + align:start position:0% +reduction from circuit to Nash I want to + + + align:start position:0% +reduction from circuit to Nash I want to +introduce a uh a concept before I show + + align:start position:0% +introduce a uh a concept before I show + + + align:start position:0% +introduce a uh a concept before I show +the reduction uh that concept is + + align:start position:0% +the reduction uh that concept is + + + align:start position:0% +the reduction uh that concept is +graphical games and polymatrix games a + + align:start position:0% +graphical games and polymatrix games a + + + align:start position:0% +graphical games and polymatrix games a +special case of graphical games so + + align:start position:0% +special case of graphical games so + + + align:start position:0% +special case of graphical games so +graphical games were introduced in 2001 + + align:start position:0% +graphical games were introduced in 2001 + + + align:start position:0% +graphical games were introduced in 2001 +by kence Litman and sing is something + + align:start position:0% +by kence Litman and sing is something + + + align:start position:0% +by kence Litman and sing is something +very natural uh uh basically they tried + + align:start position:0% +very natural uh uh basically they tried + + + align:start position:0% +very natural uh uh basically they tried +to capture situations where the payoff + + align:start position:0% +to capture situations where the payoff + + + align:start position:0% +to capture situations where the payoff +of a player only depends on the actions + + align:start position:0% +of a player only depends on the actions + + + align:start position:0% +of a player only depends on the actions +of uh a few other players because of you + + align:start position:0% +of uh a few other players because of you + + + align:start position:0% +of uh a few other players because of you +know geographical communication or other + + align:start position:0% +know geographical communication or other + + + align:start position:0% +know geographical communication or other +constraints so in a graphical game uh + + align:start position:0% +constraints so in a graphical game uh + + + align:start position:0% +constraints so in a graphical game uh +the players are nodes in a graph in a + + align:start position:0% +the players are nodes in a graph in a + + + align:start position:0% +the players are nodes in a graph in a +directed + + align:start position:0% +directed + + + align:start position:0% +directed +graph and uh a player's payoff only + + align:start position:0% +graph and uh a player's payoff only + + + align:start position:0% +graph and uh a player's payoff only +depends on her own strategy as well as + + align:start position:0% +depends on her own strategy as well as + + + align:start position:0% +depends on her own strategy as well as +the strategies of the players that point + + align:start position:0% +the strategies of the players that point + + + align:start position:0% +the strategies of the players that point +to + + align:start position:0% +to + + + align:start position:0% +to +him okay uh for example this guy's + + align:start position:0% +him okay uh for example this guy's + + + align:start position:0% +him okay uh for example this guy's +payoff depends on this guys this guys + + align:start position:0% +payoff depends on this guys this guys + + + align:start position:0% +payoff depends on this guys this guys +and this gu's action because all of + + align:start position:0% +and this gu's action because all of + + + align:start position:0% +and this gu's action because all of +these guys point to him as well as his + + align:start position:0% +these guys point to him as well as his + + + align:start position:0% +these guys point to him as well as his +own + + align:start position:0% + + + + align:start position:0% + +action uh a special case of these games + + align:start position:0% +action uh a special case of these games + + + align:start position:0% +action uh a special case of these games +was + + align:start position:0% +was + + + align:start position:0% +was +actually uh introduced much + + align:start position:0% +actually uh introduced much + + + align:start position:0% +actually uh introduced much +earlier um so polymetric games are + + align:start position:0% +earlier um so polymetric games are + + + align:start position:0% +earlier um so polymetric games are +graphical games where the pay of + + align:start position:0% +graphical games where the pay of + + + align:start position:0% +graphical games where the pay of +functions of the nodes are actually + + align:start position:0% +functions of the nodes are actually + + + align:start position:0% +functions of the nodes are actually +edgewise separable so for instance the + + align:start position:0% +edgewise separable so for instance the + + + align:start position:0% +edgewise separable so for instance the +payoff of this guy + + align:start position:0% +payoff of this guy + + + align:start position:0% +payoff of this guy +uh as a function of everybody's mixed + + align:start position:0% +uh as a function of everybody's mixed + + + align:start position:0% +uh as a function of everybody's mixed +strategy is just separable over all + + align:start position:0% +strategy is just separable over all + + + align:start position:0% +strategy is just separable over all +edges that point to him of some pairwise + + align:start position:0% +edges that point to him of some pairwise + + + align:start position:0% +edges that point to him of some pairwise +pay of function that has to do with v + + align:start position:0% +pay of function that has to do with v + + + align:start position:0% +pay of function that has to do with v +action and his neighbor's action okay + + align:start position:0% +action and his neighbor's action okay + + + align:start position:0% +action and his neighbor's action okay +that's what's written here and it's not + + align:start position:0% +that's what's written here and it's not + + + align:start position:0% +that's what's written here and it's not +very hard to see that + + align:start position:0% +very hard to see that + + + align:start position:0% +very hard to see that +any + + align:start position:0% +any + + + align:start position:0% +any +um uh so this is a utility function that + + align:start position:0% +um uh so this is a utility function that + + + align:start position:0% +um uh so this is a utility function that +depends on uh + + align:start position:0% +depends on uh + + + align:start position:0% +depends on uh +uh the two mixed strategies right and + + align:start position:0% +uh the two mixed strategies right and + + + align:start position:0% +uh the two mixed strategies right and +you know by assumption these players + + align:start position:0% +you know by assumption these players + + + align:start position:0% +you know by assumption these players +randomized independently of each other + + align:start position:0% +randomized independently of each other + + + align:start position:0% +randomized independently of each other +so any such expectation over a pair of + + align:start position:0% +so any such expectation over a pair of + + + align:start position:0% +so any such expectation over a pair of +player + + align:start position:0% +player + + + align:start position:0% +player +strategies uh that are a product can + + align:start position:0% +strategies uh that are a product can + + + align:start position:0% +strategies uh that are a product can +actually be written as a quadratic + + align:start position:0% +actually be written as a quadratic + + + align:start position:0% +actually be written as a quadratic +form right do you see that so if um um + + align:start position:0% +form right do you see that so if um um + + + align:start position:0% +form right do you see that so if um um +let me write it on the board so again so + + align:start position:0% +let me write it on the board so again so + + + align:start position:0% +let me write it on the board so again so +so XU is the uh x v is the mixed + + align:start position:0% + + + + align:start position:0% + +strategy of player v x w is the mix + + align:start position:0% + + + + align:start position:0% + +strategy of w what I mean by + + align:start position:0% +strategy of w what I mean by + + + align:start position:0% +strategy of w what I mean by +u w v XU comma XV x w is basically Bally + + align:start position:0% +u w v XU comma XV x w is basically Bally + + + align:start position:0% +u w v XU comma XV x w is basically Bally +an expectation over an + + align:start position:0% +an expectation over an + + + align:start position:0% +an expectation over an +action Su drawn from XU and action s w + + align:start position:0% +action Su drawn from XU and action s w + + + align:start position:0% +action Su drawn from XU and action s w +sorry SV drawn from XV s w drawn from xw + + align:start position:0% +sorry SV drawn from XV s w drawn from xw + + + align:start position:0% +sorry SV drawn from XV s w drawn from xw +independently of + + align:start position:0% + + + + align:start position:0% + +uh and that's a just the sum right + + align:start position:0% +uh and that's a just the sum right + + + align:start position:0% +uh and that's a just the sum right +overall s 's and overall + + align:start position:0% +overall s 's and overall + + + align:start position:0% +overall s 's and overall +s W's of uh uh you know u + + align:start position:0% +s W's of uh uh you know u + + + align:start position:0% +s W's of uh uh you know u +w s v + + align:start position:0% +w s v + + + align:start position:0% +w s v +w and then the + + align:start position:0% + + + + align:start position:0% + +probabilities and that's a quadratic + + align:start position:0% +probabilities and that's a quadratic + + + align:start position:0% +probabilities and that's a quadratic +form if I right so uh that's what I mean + + align:start position:0% +form if I right so uh that's what I mean + + + align:start position:0% +form if I right so uh that's what I mean +by this line + + align:start position:0% +by this line + + + align:start position:0% +by this line +right because players play independently + + align:start position:0% +right because players play independently + + + align:start position:0% +right because players play independently +from each other any + + align:start position:0% +from each other any + + + align:start position:0% +from each other any +expectation with respect to that product + + align:start position:0% +expectation with respect to that product + + + align:start position:0% +expectation with respect to that product +distribution is a quadratic + + align:start position:0% +distribution is a quadratic + + + align:start position:0% +distribution is a quadratic +form I'm not saying something + + align:start position:0% +form I'm not saying something + + + align:start position:0% +form I'm not saying something +interesting okay good okay so uh then a + + align:start position:0% +interesting okay good okay so uh then a + + + align:start position:0% +interesting okay good okay so uh then a +polymatrix game is really because of + + align:start position:0% +polymatrix game is really because of + + + align:start position:0% +polymatrix game is really because of +this is defined by a directed graph and + + align:start position:0% +this is defined by a directed graph and + + + align:start position:0% +this is defined by a directed graph and +then for every directed + + align:start position:0% +then for every directed + + + align:start position:0% +then for every directed +Edge uh and every + + align:start position:0% +Edge uh and every + + + align:start position:0% +Edge uh and every +uh uh there is a + + align:start position:0% +uh uh there is a + + + align:start position:0% +uh uh there is a +matrix uh that defines the quadratic + + align:start position:0% +matrix uh that defines the quadratic + + + align:start position:0% +matrix uh that defines the quadratic +form for that edge okay so polymatrix + + align:start position:0% +form for that edge okay so polymatrix + + + align:start position:0% +form for that edge okay so polymatrix +game is is easily described it's uh you + + align:start position:0% +game is is easily described it's uh you + + + align:start position:0% +game is is easily described it's uh you +can you can describe by specifying the + + align:start position:0% +can you can describe by specifying the + + + align:start position:0% +can you can describe by specifying the +graph and then giving a matrix for every + + align:start position:0% +graph and then giving a matrix for every + + + align:start position:0% +graph and then giving a matrix for every +directed + + align:start position:0% +directed + + + align:start position:0% +directed +Edge so B Matrix Game is two are two + + align:start position:0% +Edge so B Matrix Game is two are two + + + align:start position:0% +Edge so B Matrix Game is two are two +player games so that's why these are + + align:start position:0% +player games so that's why these are + + + align:start position:0% +player games so that's why these are +called polymatrix because you have many + + align:start position:0% +called polymatrix because you have many + + + align:start position:0% +called polymatrix because you have many +matrices okay in a two- player game you + + align:start position:0% +matrices okay in a two- player game you + + + align:start position:0% +matrices okay in a two- player game you +only need to give two Matrix is one for + + align:start position:0% +only need to give two Matrix is one for + + + align:start position:0% +only need to give two Matrix is one for +uh a two- player game is uh just uh + + align:start position:0% +uh a two- player game is uh just uh + + + align:start position:0% +uh a two- player game is uh just uh +player + + align:start position:0% +player + + + align:start position:0% +player +one player two and you give one Matrix + + align:start position:0% +one player two and you give one Matrix + + + align:start position:0% +one player two and you give one Matrix +for this direction and one Matrix for + + align:start position:0% +for this direction and one Matrix for + + + align:start position:0% +for this direction and one Matrix for +that direction so that's a batrix game + + align:start position:0% +that direction so that's a batrix game + + + align:start position:0% +that direction so that's a batrix game +this is a polymatrix game okay okay good + + align:start position:0% +this is a polymatrix game okay okay good + + + align:start position:0% +this is a polymatrix game okay okay good +uh now what I want to do is I want + + align:start position:0% +uh now what I want to do is I want + + + align:start position:0% +uh now what I want to do is I want +to uh before sort of in order to reduce + + align:start position:0% +to uh before sort of in order to reduce + + + align:start position:0% +to uh before sort of in order to reduce +arithmetic circuits out to Nash instead + + align:start position:0% +arithmetic circuits out to Nash instead + + + align:start position:0% +arithmetic circuits out to Nash instead +what I'm going to do first is I'm going + + align:start position:0% +what I'm going to do first is I'm going + + + align:start position:0% +what I'm going to do first is I'm going +to reduce arithmetic circuit uh set to + + align:start position:0% +to reduce arithmetic circuit uh set to + + + align:start position:0% +to reduce arithmetic circuit uh set to +finding a Nash equilibrium in a + + align:start position:0% +finding a Nash equilibrium in a + + + align:start position:0% +finding a Nash equilibrium in a +polymetric + + align:start position:0% +polymetric + + + align:start position:0% +polymetric +game that's what I want to do first + + align:start position:0% +game that's what I want to do first + + + align:start position:0% +game that's what I want to do first +after I do that then I want I'm going to + + align:start position:0% +after I do that then I want I'm going to + + + align:start position:0% +after I do that then I want I'm going to +reduce it to so here I have many players + + align:start position:0% +reduce it to so here I have many players + + + align:start position:0% +reduce it to so here I have many players +I want to go down to two + + align:start position:0% +I want to go down to two + + + align:start position:0% +I want to go down to two +players but the first step is to just go + + align:start position:0% +players but the first step is to just go + + + align:start position:0% +players but the first step is to just go +to multiplayer Nash equilibrium then + + align:start position:0% +to multiplayer Nash equilibrium then + + + align:start position:0% +to multiplayer Nash equilibrium then +that reduction is the easy + + align:start position:0% +that reduction is the easy + + + align:start position:0% +that reduction is the easy +part Al also this is an easy part the + + align:start position:0% +part Al also this is an easy part the + + + align:start position:0% +part Al also this is an easy part the +hard part happened + + align:start position:0% +hard part happened + + + align:start position:0% +hard part happened +before okay + + align:start position:0% +before okay + + + align:start position:0% +before okay +uh okay so now how do we how can we + + align:start position:0% +uh okay so now how do we how can we + + + align:start position:0% +uh okay so now how do we how can we +reduce uh an Ari arithmetic circuit set + + align:start position:0% +reduce uh an Ari arithmetic circuit set + + + align:start position:0% +reduce uh an Ari arithmetic circuit set +problem into a polymetric game Nash + + align:start position:0% +problem into a polymetric game Nash + + + align:start position:0% +problem into a polymetric game Nash +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +problem like in NP completeness uh like + + align:start position:0% +problem like in NP completeness uh like + + + align:start position:0% +problem like in NP completeness uh like +uh you know in reductions for NP NP + + align:start position:0% +uh you know in reductions for NP NP + + + align:start position:0% +uh you know in reductions for NP NP +hardness proofs you have to uh give + + align:start position:0% +hardness proofs you have to uh give + + + align:start position:0% +hardness proofs you have to uh give +gadgets right you have to + + align:start position:0% +gadgets right you have to + + + align:start position:0% +gadgets right you have to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +objects uh in polymetric games that + + align:start position:0% +objects uh in polymetric games that + + + align:start position:0% +objects uh in polymetric games that +simulate uh the operations that happen + + align:start position:0% +simulate uh the operations that happen + + + align:start position:0% +simulate uh the operations that happen +in your circuit over here so what I want + + align:start position:0% +in your circuit over here so what I want + + + align:start position:0% +in your circuit over here so what I want +to introduce I want to introduce what is + + align:start position:0% +to introduce I want to introduce what is + + + align:start position:0% +to introduce I want to introduce what is +called the game Gadget these are small + + align:start position:0% +called the game Gadget these are small + + + align:start position:0% +called the game Gadget these are small +polymatrix games that do various + + align:start position:0% +polymatrix games that do various + + + align:start position:0% +polymatrix games that do various +arithmetic operations which I can then + + align:start position:0% +arithmetic operations which I can then + + + align:start position:0% +arithmetic operations which I can then +put together to simulate an arithmetic + + align:start position:0% +put together to simulate an arithmetic + + + align:start position:0% +put together to simulate an arithmetic +circuit side + + align:start position:0% +circuit side + + + align:start position:0% +circuit side +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay so what I want to do is I'm going + + align:start position:0% +okay so what I want to do is I'm going + + + align:start position:0% +okay so what I want to do is I'm going +to give you you know a flavor of these + + align:start position:0% +to give you you know a flavor of these + + + align:start position:0% +to give you you know a flavor of these +gadgets so I'm going to give you the + + align:start position:0% +gadgets so I'm going to give you the + + + align:start position:0% +gadgets so I'm going to give you the +addition Gadget so I want to give you a + + align:start position:0% +addition Gadget so I want to give you a + + + align:start position:0% +addition Gadget so I want to give you a +polymatrix game that does + + align:start position:0% + + + + align:start position:0% + +addition so it's going to have this game + + align:start position:0% +addition so it's going to have this game + + + align:start position:0% +addition so it's going to have this game +is going to have four players every + + align:start position:0% +is going to have four players every + + + align:start position:0% +is going to have four players every +player will have just two strategies + + align:start position:0% +player will have just two strategies + + + align:start position:0% +player will have just two strategies +zero and one two pure strategies hence + + align:start position:0% +zero and one two pure strategies hence + + + align:start position:0% +zero and one two pure strategies hence +the mixed strategy of that player is + + align:start position:0% +the mixed strategy of that player is + + + align:start position:0% +the mixed strategy of that player is +going to be a real number in 01 which + + align:start position:0% +going to be a real number in 01 which + + + align:start position:0% +going to be a real number in 01 which +corresponds to the probability by which + + align:start position:0% +corresponds to the probability by which + + + align:start position:0% +corresponds to the probability by which +this player plays one + + align:start position:0% +this player plays one + + + align:start position:0% +this player plays one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so here's the structure of the gadget + + align:start position:0% +um so here's the structure of the gadget + + + align:start position:0% +um so here's the structure of the gadget +okay so this gadget I'm showing it here + + align:start position:0% +okay so this gadget I'm showing it here + + + align:start position:0% +okay so this gadget I'm showing it here +embedded into potentially bigger + + align:start position:0% +embedded into potentially bigger + + + align:start position:0% +embedded into potentially bigger +polymatrix game but uh uh the gadget + + align:start position:0% +polymatrix game but uh uh the gadget + + + align:start position:0% +polymatrix game but uh uh the gadget +itself is going to have four players x y + + align:start position:0% +itself is going to have four players x y + + + align:start position:0% +itself is going to have four players x y +w and z now XY are What's called the + + align:start position:0% +w and z now XY are What's called the + + + align:start position:0% +w and z now XY are What's called the +input to the gadget so these are players + + align:start position:0% +input to the gadget so these are players + + + align:start position:0% +input to the gadget so these are players +who point to W but don't depend on the + + align:start position:0% +who point to W but don't depend on the + + + align:start position:0% +who point to W but don't depend on the +actions of w and z because there are no + + align:start position:0% +actions of w and z because there are no + + + align:start position:0% +actions of w and z because there are no +directions going the other way so these + + align:start position:0% +directions going the other way so these + + + align:start position:0% +directions going the other way so these +guys are don't care about what these + + align:start position:0% +guys are don't care about what these + + + align:start position:0% +guys are don't care about what these +players are doing doing right and they + + align:start position:0% +players are doing doing right and they + + + align:start position:0% +players are doing doing right and they +serve as an input to the + + align:start position:0% +serve as an input to the + + + align:start position:0% +serve as an input to the +gadget now this player W uh gets us + + align:start position:0% +gadget now this player W uh gets us + + + align:start position:0% +gadget now this player W uh gets us +input all you know player strategies in + + align:start position:0% +input all you know player strategies in + + + align:start position:0% +input all you know player strategies in +this gadget while Z only cares about + + align:start position:0% +this gadget while Z only cares about + + + align:start position:0% +this gadget while Z only cares about +what w is + + align:start position:0% +what w is + + + align:start position:0% +what w is +doing okay so X and Y are going to be + + align:start position:0% +doing okay so X and Y are going to be + + + align:start position:0% +doing okay so X and Y are going to be +called the input players to the gadget Z + + align:start position:0% +called the input players to the gadget Z + + + align:start position:0% +called the input players to the gadget Z +is going to be the out is going to be + + align:start position:0% +is going to be the out is going to be + + + align:start position:0% +is going to be the out is going to be +called the output player to the gadget + + align:start position:0% +called the output player to the gadget + + + align:start position:0% +called the output player to the gadget +and W is going to be called the + + align:start position:0% +and W is going to be called the + + + align:start position:0% +and W is going to be called the +auxiliary + + align:start position:0% +auxiliary + + + align:start position:0% +auxiliary +player now what I want to do is I want + + align:start position:0% +player now what I want to do is I want + + + align:start position:0% +player now what I want to do is I want +to Define so what the only thing I'm + + align:start position:0% +to Define so what the only thing I'm + + + align:start position:0% +to Define so what the only thing I'm +going to Define is the pay of function + + align:start position:0% +going to Define is the pay of function + + + align:start position:0% +going to Define is the pay of function +of w and the pay of function of Z and + + align:start position:0% +of w and the pay of function of Z and + + + align:start position:0% +of w and the pay of function of Z and +I'm going to Define these pay of + + align:start position:0% +I'm going to Define these pay of + + + align:start position:0% +I'm going to Define these pay of +functions in a way that addition somehow + + align:start position:0% +functions in a way that addition somehow + + + align:start position:0% +functions in a way that addition somehow +happens AR anash equilibrium of this + + align:start position:0% +happens AR anash equilibrium of this + + + align:start position:0% +happens AR anash equilibrium of this +little + + align:start position:0% +little + + + align:start position:0% +little +game um so I'm going to define the pay + + align:start position:0% +game um so I'm going to define the pay + + + align:start position:0% +game um so I'm going to define the pay +of suly but then I'm going to convince + + align:start position:0% +of suly but then I'm going to convince + + + align:start position:0% +of suly but then I'm going to convince +you that these really correspond to + + align:start position:0% +you that these really correspond to + + + align:start position:0% +you that these really correspond to +tables so I'm going to say that W is + + align:start position:0% +tables so I'm going to say that W is + + + align:start position:0% +tables so I'm going to say that W is +paid an + + align:start position:0% +paid an + + + align:start position:0% +paid an +expected uh depending on what he plays + + align:start position:0% +expected uh depending on what he plays + + + align:start position:0% +expected uh depending on what he plays +so if he plays zero he gets paid an + + align:start position:0% +so if he plays zero he gets paid an + + + align:start position:0% +so if he plays zero he gets paid an +expected probability X = $1 plus + + align:start position:0% +expected probability X = $1 plus + + + align:start position:0% +expected probability X = $1 plus +probability X = Y = + + align:start position:0% +probability X = Y = + + + align:start position:0% +probability X = Y = +$1 uh if he plays zero but if he plays + + align:start position:0% +$1 uh if he plays zero but if he plays + + + align:start position:0% +$1 uh if he plays zero but if he plays +one he he only gets paid probability is + + align:start position:0% +one he he only gets paid probability is + + + align:start position:0% +one he he only gets paid probability is +equals $1 okay so in some sense if he + + align:start position:0% +equals $1 okay so in some sense if he + + + align:start position:0% +equals $1 okay so in some sense if he +plays zero he looks to the left if he + + align:start position:0% +plays zero he looks to the left if he + + + align:start position:0% +plays zero he looks to the left if he +plays one he looks to the right his + + align:start position:0% +plays one he looks to the right his + + + align:start position:0% +plays one he looks to the right his +payoffs are uh the sum of these two guys + + align:start position:0% +payoffs are uh the sum of these two guys + + + align:start position:0% +payoffs are uh the sum of these two guys +probabilities of playing one in one case + + align:start position:0% +probabilities of playing one in one case + + + align:start position:0% +probabilities of playing one in one case +and one and and and this prob this guy's + + align:start position:0% +and one and and and this prob this guy's + + + align:start position:0% +and one and and and this prob this guy's +probability of playing one in the other + + align:start position:0% +probability of playing one in the other + + + align:start position:0% +probability of playing one in the other +case so that's that's the pay function + + align:start position:0% +case so that's that's the pay function + + + align:start position:0% +case so that's that's the pay function +to W now you would ask me you know maybe + + align:start position:0% +to W now you would ask me you know maybe + + + align:start position:0% +to W now you would ask me you know maybe +um you know how can you implement this + + align:start position:0% +um you know how can you implement this + + + align:start position:0% +um you know how can you implement this +pay of functions uh and uh that that's + + align:start position:0% +pay of functions uh and uh that that's + + + align:start position:0% +pay of functions uh and uh that that's +actually very easy so here's the table + + align:start position:0% +actually very easy so here's the table + + + align:start position:0% +actually very easy so here's the table +for player W so when w plays one plays + + align:start position:0% +for player W so when w plays one plays + + + align:start position:0% +for player W so when w plays one plays +zero I'm going to his pay off depending + + align:start position:0% +zero I'm going to his pay off depending + + + align:start position:0% +zero I'm going to his pay off depending +on the strategies of + + align:start position:0% +on the strategies of + + + align:start position:0% +on the strategies of +X and Y + + align:start position:0% + + + + align:start position:0% + +I'm going to Define it to be 0 1 1 and + + align:start position:0% +I'm going to Define it to be 0 1 1 and + + + align:start position:0% +I'm going to Define it to be 0 1 1 and +two now notice that in expectation over + + align:start position:0% +two now notice that in expectation over + + + align:start position:0% +two now notice that in expectation over +these over x's and Y + + align:start position:0% +these over x's and Y + + + align:start position:0% +these over x's and Y +strategies his payoff he so if he plays + + align:start position:0% +strategies his payoff he so if he plays + + + align:start position:0% +strategies his payoff he so if he plays +zero his expected payoff over X and Y + + align:start position:0% +zero his expected payoff over X and Y + + + align:start position:0% +zero his expected payoff over X and Y +strategies is just uh the probability + + align:start position:0% +strategies is just uh the probability + + + align:start position:0% +strategies is just uh the probability +that X play one plus the probability + + align:start position:0% +that X play one plus the probability + + + align:start position:0% +that X play one plus the probability +that uh y Place one do you see this from + + align:start position:0% +that uh y Place one do you see this from + + + align:start position:0% +that uh y Place one do you see this from +this Matrix + + align:start position:0% +this Matrix + + + align:start position:0% +this Matrix +so what's the expected + + align:start position:0% +so what's the expected + + + align:start position:0% +so what's the expected +payoff to + + align:start position:0% +payoff to + + + align:start position:0% +payoff to +W when he plays + + align:start position:0% +W when he plays + + + align:start position:0% +W when he plays +zero well this is one if uh y plays + + align:start position:0% +zero well this is one if uh y plays + + + align:start position:0% +zero well this is one if uh y plays +one but uh X plays + + align:start position:0% + + + + align:start position:0% + +zero and it's one if uh X plays one but + + align:start position:0% +zero and it's one if uh X plays one but + + + align:start position:0% +zero and it's one if uh X plays one but +y plays + + align:start position:0% +y plays + + + align:start position:0% +y plays +zero and it's two if they both play one + + align:start position:0% + + + + align:start position:0% + +one and I claim that if you + + align:start position:0% +one and I claim that if you + + + align:start position:0% +one and I claim that if you +appropriately correct collect the terms + + align:start position:0% +appropriately correct collect the terms + + + align:start position:0% +appropriately correct collect the terms +this is just equal to probability y 1 + + align:start position:0% +this is just equal to probability y 1 + + + align:start position:0% +this is just equal to probability y 1 +and X+ + + align:start position:0% +and X+ + + + align:start position:0% +and X+ +one okay so that's that's what I claim + + align:start position:0% +one okay so that's that's what I claim + + + align:start position:0% +one okay so that's that's what I claim +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so uh okay so I covered this line this + + align:start position:0% +so uh okay so I covered this line this + + + align:start position:0% +so uh okay so I covered this line this +line is also easy to cover by saying + + align:start position:0% +line is also easy to cover by saying + + + align:start position:0% +line is also easy to cover by saying +that when w plays zero his pay just + + align:start position:0% +that when w plays zero his pay just + + + align:start position:0% +that when w plays zero his pay just +depends on what uh C is + + align:start position:0% +depends on what uh C is + + + align:start position:0% +depends on what uh C is +doing and it's going to be like + + align:start position:0% +doing and it's going to be like + + + align:start position:0% +doing and it's going to be like +this oops so when w plays one his + + align:start position:0% +this oops so when w plays one his + + + align:start position:0% +this oops so when w plays one his +expected payoff is exactly the + + align:start position:0% +expected payoff is exactly the + + + align:start position:0% +expected payoff is exactly the +probability Z plays + + align:start position:0% + + + + align:start position:0% + +one right so what I've written here is + + align:start position:0% +one right so what I've written here is + + + align:start position:0% +one right so what I've written here is +actually consistent with some + + align:start position:0% +actually consistent with some + + + align:start position:0% +actually consistent with some +tables that I'm hiding from this + + align:start position:0% +tables that I'm hiding from this + + + align:start position:0% +tables that I'm hiding from this +slide uh okay so that's I guess that's + + align:start position:0% +slide uh okay so that's I guess that's + + + align:start position:0% +slide uh okay so that's I guess that's +what + + align:start position:0% +what + + + align:start position:0% +what +I what I want to write and then + + align:start position:0% +I what I want to write and then + + + align:start position:0% +I what I want to write and then +similarly Z is paid to play the opposite + + align:start position:0% +similarly Z is paid to play the opposite + + + align:start position:0% +similarly Z is paid to play the opposite +of w what do I mean by that I mean + + align:start position:0% +of w what do I mean by that I mean + + + align:start position:0% +of w what do I mean by that I mean +that this payoff when he plays zero is + + align:start position:0% +that this payoff when he plays zero is + + + align:start position:0% +that this payoff when he plays zero is +exactly 1 half no matter what w does but + + align:start position:0% +exactly 1 half no matter what w does but + + + align:start position:0% +exactly 1 half no matter what w does but +if he plays one his payoff is one + + align:start position:0% +if he plays one his payoff is one + + + align:start position:0% +if he plays one his payoff is one +minus uh W plays one which again you + + align:start position:0% +minus uh W plays one which again you + + + align:start position:0% +minus uh W plays one which again you +should be able to see that there is a + + align:start position:0% +should be able to see that there is a + + + align:start position:0% +should be able to see that there is a +table little table implement menting + + align:start position:0% +table little table implement menting + + + align:start position:0% +table little table implement menting +this pay of + + align:start position:0% +this pay of + + + align:start position:0% +this pay of +functions okay now that sounds weird why + + align:start position:0% +functions okay now that sounds weird why + + + align:start position:0% +functions okay now that sounds weird why +did I Define it this way here's my + + align:start position:0% +did I Define it this way here's my + + + align:start position:0% +did I Define it this way here's my +claim in any Nash equilibrium of a game + + align:start position:0% +claim in any Nash equilibrium of a game + + + align:start position:0% +claim in any Nash equilibrium of a game +that contains this little + + align:start position:0% + + + + align:start position:0% + +Gadget the probability that the output + + align:start position:0% +Gadget the probability that the output + + + align:start position:0% +Gadget the probability that the output +player plays one is basically the sum of + + align:start position:0% +player plays one is basically the sum of + + + align:start position:0% +player plays one is basically the sum of +the probabilities that the input players + + align:start position:0% +the probabilities that the input players + + + align:start position:0% +the probabilities that the input players +play + + align:start position:0% +play + + + align:start position:0% +play +one threshold it at one of course okay + + align:start position:0% +one threshold it at one of course okay + + + align:start position:0% +one threshold it at one of course okay +so if this little Gadget that you find + + align:start position:0% +so if this little Gadget that you find + + + align:start position:0% +so if this little Gadget that you find +here is part of a a bigger + + align:start position:0% +here is part of a a bigger + + + align:start position:0% +here is part of a a bigger +game now what does the bigger game what + + align:start position:0% +game now what does the bigger game what + + + align:start position:0% +game now what does the bigger game what +can the bigger game do so it can fit Stu + + align:start position:0% +can the bigger game do so it can fit Stu + + + align:start position:0% +can the bigger game do so it can fit Stu +it can fit something into + + align:start position:0% +it can fit something into + + + align:start position:0% +it can fit something into +X and it can take the value of Z and use + + align:start position:0% +X and it can take the value of Z and use + + + align:start position:0% +X and it can take the value of Z and use +it in some other way potentially looping + + align:start position:0% +it in some other way potentially looping + + + align:start position:0% +it in some other way potentially looping +around doing anything it wants except + + align:start position:0% +around doing anything it wants except + + + align:start position:0% +around doing anything it wants except +you know the only inputs to W's payoff + + align:start position:0% +you know the only inputs to W's payoff + + + align:start position:0% +you know the only inputs to W's payoff +are X Y and Z and the only inputs to Z's + + align:start position:0% +are X Y and Z and the only inputs to Z's + + + align:start position:0% +are X Y and Z and the only inputs to Z's +payoff is W but otherwise the game can't + + align:start position:0% +payoff is W but otherwise the game can't + + + align:start position:0% +payoff is W but otherwise the game can't +be arbitrary okay so if this game that I + + align:start position:0% +be arbitrary okay so if this game that I + + + align:start position:0% +be arbitrary okay so if this game that I +defined here is embedded within a bigger + + align:start position:0% +defined here is embedded within a bigger + + + align:start position:0% +defined here is embedded within a bigger +game then in any n of that bigger game + + align:start position:0% +game then in any n of that bigger game + + + align:start position:0% +game then in any n of that bigger game +the probability that this guy plays one + + align:start position:0% +the probability that this guy plays one + + + align:start position:0% +the probability that this guy plays one +is exactly the sum of the probabilities + + align:start position:0% +is exactly the sum of the probabilities + + + align:start position:0% +is exactly the sum of the probabilities +that these two guys play one thresholded + + align:start position:0% +that these two guys play one thresholded + + + align:start position:0% +that these two guys play one thresholded +at + + align:start position:0% +at + + + align:start position:0% +at +one now how can we see this why is that + + align:start position:0% +one now how can we see this why is that + + + align:start position:0% +one now how can we see this why is that +true it's a little uh case analysis it's + + align:start position:0% +true it's a little uh case analysis it's + + + align:start position:0% +true it's a little uh case analysis it's +very simple let's try to do + + align:start position:0% + + + + align:start position:0% + +it uh let's say that uh + + align:start position:0% +it uh let's say that uh + + + align:start position:0% +it uh let's say that uh +so suppose that probability that Z Place + + align:start position:0% +so suppose that probability that Z Place + + + align:start position:0% +so suppose that probability that Z Place +one is + + align:start position:0% +one is + + + align:start position:0% +one is +smaller than the probability X Play 1 + + align:start position:0% +smaller than the probability X Play 1 + + + align:start position:0% +smaller than the probability X Play 1 +plus probability y Play + + align:start position:0% +plus probability y Play + + + align:start position:0% +plus probability y Play +1 actually let's do something + + align:start position:0% +1 actually let's do something + + + align:start position:0% +1 actually let's do something +else it's smaller than the let's see the + + align:start position:0% +else it's smaller than the let's see the + + + align:start position:0% +else it's smaller than the let's see the +minan between this and + + align:start position:0% +minan between this and + + + align:start position:0% +minan between this and +one what happens in this case so what if + + align:start position:0% +one what happens in this case so what if + + + align:start position:0% +one what happens in this case so what if +so what happens if Z is smaller than the + + align:start position:0% +so what happens if Z is smaller than the + + + align:start position:0% +so what happens if Z is smaller than the +minimum of these two + + align:start position:0% +minimum of these two + + + align:start position:0% +minimum of these two +values what is w going to do in that + + align:start position:0% +values what is w going to do in that + + + align:start position:0% +values what is w going to do in that +case yeah is it going to play Zero yeah + + align:start position:0% +case yeah is it going to play Zero yeah + + + align:start position:0% +case yeah is it going to play Zero yeah +because zero gives him a much higher + + align:start position:0% +because zero gives him a much higher + + + align:start position:0% +because zero gives him a much higher +payoff it gives him higher payoff than + + align:start position:0% +payoff it gives him higher payoff than + + + align:start position:0% +payoff it gives him higher payoff than +this guy right because of that + + align:start position:0% +this guy right because of that + + + align:start position:0% +this guy right because of that +condition right so this + + align:start position:0% + + + + align:start position:0% + +implies that uh + + align:start position:0% +implies that uh + + + align:start position:0% +implies that uh +W is going to play Zero with probability + + align:start position:0% +W is going to play Zero with probability + + + align:start position:0% +W is going to play Zero with probability +one + + align:start position:0% +one + + + align:start position:0% +one +now what does this + + align:start position:0% + + + + align:start position:0% + +imply if W plays Zer with probability + + align:start position:0% +imply if W plays Zer with probability + + + align:start position:0% +imply if W plays Zer with probability +one what does Z + + align:start position:0% +one what does Z + + + align:start position:0% +one what does Z +do if he play here he get5 what if he + + align:start position:0% +do if he play here he get5 what if he + + + align:start position:0% +do if he play here he get5 what if he +plays one how much this he + + align:start position:0% +plays one how much this he + + + align:start position:0% +plays one how much this he +get I gets one right because of that + + align:start position:0% +get I gets one right because of that + + + align:start position:0% +get I gets one right because of that +condition so he's going to play what one + + align:start position:0% +condition so he's going to play what one + + + align:start position:0% +condition so he's going to play what one +right so this implies that uh + + align:start position:0% + + + + align:start position:0% + +but how can one be smaller than the + + align:start position:0% +but how can one be smaller than the + + + align:start position:0% +but how can one be smaller than the +minimum of one and something else it's + + align:start position:0% +minimum of one and something else it's + + + align:start position:0% +minimum of one and something else it's +can't be right so this is impossible is + + align:start position:0% +can't be right so this is impossible is + + + align:start position:0% +can't be right so this is impossible is +but so let's do the other side or maybe + + align:start position:0% +but so let's do the other side or maybe + + + align:start position:0% +but so let's do the other side or maybe +you already trust me that it's + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh let's try to argue that this cannot + + align:start position:0% +uh let's try to argue that this cannot + + + align:start position:0% +uh let's try to argue that this cannot +be the case I don't need to do the mean + + align:start position:0% +be the case I don't need to do the mean + + + align:start position:0% +be the case I don't need to do the mean +anymore because uh it can't possibly be + + align:start position:0% +anymore because uh it can't possibly be + + + align:start position:0% +anymore because uh it can't possibly be +that this guy plays more than one + + align:start position:0% +that this guy plays more than one + + + align:start position:0% +that this guy plays more than one +probability so this is the only case I + + align:start position:0% +probability so this is the only case I + + + align:start position:0% +probability so this is the only case I +want to consider + + align:start position:0% + + + + align:start position:0% + +now okay so what happens in this + + align:start position:0% + + + + align:start position:0% + +case the same + + align:start position:0% +case the same + + + align:start position:0% +case the same +logic uh what does w + + align:start position:0% +logic uh what does w + + + align:start position:0% +logic uh what does w +do play one has to play one cuz that's + + align:start position:0% +do play one has to play one cuz that's + + + align:start position:0% +do play one has to play one cuz that's +the better + + align:start position:0% +the better + + + align:start position:0% +the better +straty and what does it + + align:start position:0% +straty and what does it + + + align:start position:0% +straty and what does it +do + + align:start position:0% + + + + align:start position:0% + +Z but zero can't be bigger than two the + + align:start position:0% +Z but zero can't be bigger than two the + + + align:start position:0% +Z but zero can't be bigger than two the +sum of two our probabilities so this and + + align:start position:0% +sum of two our probabilities so this and + + + align:start position:0% +sum of two our probabilities so this and +that can't happen hence the only case + + align:start position:0% +that can't happen hence the only case + + + align:start position:0% +that can't happen hence the only case +that's possible is uh this + + align:start position:0% +that's possible is uh this + + + align:start position:0% +that's possible is uh this +one + + align:start position:0% +one + + + align:start position:0% +one +yeah okay so it's very simple okay so + + align:start position:0% +yeah okay so it's very simple okay so + + + align:start position:0% +yeah okay so it's very simple okay so +the only realization one had to do is + + align:start position:0% +the only realization one had to do is + + + align:start position:0% +the only realization one had to do is +that uh you know like you know so like + + align:start position:0% +that uh you know like you know so like + + + align:start position:0% +that uh you know like you know so like +where the arithmetic happens right and + + align:start position:0% +where the arithmetic happens right and + + + align:start position:0% +where the arithmetic happens right and +it happens in the mixed strategies + + align:start position:0% +it happens in the mixed strategies + + + align:start position:0% +it happens in the mixed strategies +chosen by the players that's where the + + align:start position:0% +chosen by the players that's where the + + + align:start position:0% +chosen by the players that's where the +arithmetic + + align:start position:0% + + + + align:start position:0% + +happens so + + align:start position:0% +happens so + + + align:start position:0% +happens so +then uh okay so this is the addition + + align:start position:0% +then uh okay so this is the addition + + + align:start position:0% +then uh okay so this is the addition +Gadget similarly one can Define other + + align:start position:0% +Gadget similarly one can Define other + + + align:start position:0% +Gadget similarly one can Define other +gadgets for example the subtraction + + align:start position:0% +gadgets for example the subtraction + + + align:start position:0% +gadgets for example the subtraction +Gadget is really really similar to this + + align:start position:0% +Gadget is really really similar to this + + + align:start position:0% +Gadget is really really similar to this +except with one change I replace this + + align:start position:0% +except with one change I replace this + + + align:start position:0% +except with one change I replace this +plus with a minus okay that's the only + + align:start position:0% +plus with a minus okay that's the only + + + align:start position:0% +plus with a minus okay that's the only +change I need to do in other words uh uh + + align:start position:0% +change I need to do in other words uh uh + + + align:start position:0% +change I need to do in other words uh uh +I'm not sure I want to do it but in + + align:start position:0% +I'm not sure I want to do it but in + + + align:start position:0% +I'm not sure I want to do it but in +other words + + align:start position:0% +other words + + + align:start position:0% +other words +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh this + + align:start position:0% +uh this + + + align:start position:0% +uh this +table for for I only change this + + align:start position:0% +table for for I only change this + + + align:start position:0% +table for for I only change this +table to have um zero here and minus one + + align:start position:0% +table to have um zero here and minus one + + + align:start position:0% +table to have um zero here and minus one +here and I'm exactly implementing that + + align:start position:0% +here and I'm exactly implementing that + + + align:start position:0% +here and I'm exactly implementing that +the + + align:start position:0% +the + + + align:start position:0% +the +subtraction and the the the proof is + + align:start position:0% +subtraction and the the the proof is + + + align:start position:0% +subtraction and the the the proof is +exactly the same you can argue that in + + align:start position:0% +exactly the same you can argue that in + + + align:start position:0% +exactly the same you can argue that in +any Nash equilibrium of a game that + + align:start position:0% +any Nash equilibrium of a game that + + + align:start position:0% +any Nash equilibrium of a game that +contains this gadget the probability + + align:start position:0% +contains this gadget the probability + + + align:start position:0% +contains this gadget the probability +that this guy plays one is actually the + + align:start position:0% +that this guy plays one is actually the + + + align:start position:0% +that this guy plays one is actually the +difference of the probabilities that X + + align:start position:0% +difference of the probabilities that X + + + align:start position:0% +difference of the probabilities that X +plays one and Y Place one uh + + align:start position:0% +plays one and Y Place one uh + + + align:start position:0% +plays one and Y Place one uh +appropriately trated at + + align:start position:0% + + + + align:start position:0% + +zero any questions about what's taking + + align:start position:0% +zero any questions about what's taking + + + align:start position:0% +zero any questions about what's taking +place here what we're trying to do is + + align:start position:0% +place here what we're trying to do is + + + align:start position:0% +place here what we're trying to do is +we're going to want to take a arithmetic + + align:start position:0% +we're going to want to take a arithmetic + + + align:start position:0% +we're going to want to take a arithmetic +circuit side instance and we want to + + align:start position:0% +circuit side instance and we want to + + + align:start position:0% +circuit side instance and we want to +create a polymatrix game that simulates + + align:start position:0% +create a polymatrix game that simulates + + + align:start position:0% +create a polymatrix game that simulates +that circuit side instance and what we + + align:start position:0% +that circuit side instance and what we + + + align:start position:0% +that circuit side instance and what we +need for that is gadgets so + + align:start position:0% +need for that is gadgets so + + + align:start position:0% +need for that is gadgets so +little uh polymatrix games that + + align:start position:0% +little uh polymatrix games that + + + align:start position:0% +little uh polymatrix games that +Implement various + + align:start position:0% + + + + align:start position:0% + +operations uh and I showed you addition + + align:start position:0% +operations uh and I showed you addition + + + align:start position:0% +operations uh and I showed you addition +and subtraction but uh I + + align:start position:0% +and subtraction but uh I + + + align:start position:0% +and subtraction but uh I +claim uh that you can Implement Buns of + + align:start position:0% +claim uh that you can Implement Buns of + + + align:start position:0% +claim uh that you can Implement Buns of +other Gates so + + align:start position:0% +other Gates so + + + align:start position:0% +other Gates so +to uh you know sort of like give my not + + align:start position:0% +to uh you know sort of like give my not + + + align:start position:0% +to uh you know sort of like give my not +to have a more succinct notation I'm + + align:start position:0% +to have a more succinct notation I'm + + + align:start position:0% +to have a more succinct notation I'm +going to use probability that some node + + align:start position:0% +going to use probability that some node + + + align:start position:0% +going to use probability that some node +plays + + align:start position:0% +plays + + + align:start position:0% +plays +one uh I'm not going to differentiate + + align:start position:0% +one uh I'm not going to differentiate + + + align:start position:0% +one uh I'm not going to differentiate +done within X and the probability that + + align:start position:0% +done within X and the probability that + + + align:start position:0% +done within X and the probability that +X+ one okay so with this notation I + + align:start position:0% +X+ one okay so with this notation I + + + align:start position:0% +X+ one okay so with this notation I +claim that we can Implement all the + + align:start position:0% +claim that we can Implement all the + + + align:start position:0% +claim that we can Implement all the +gadgets that we need to simulate a + + align:start position:0% +gadgets that we need to simulate a + + + align:start position:0% +gadgets that we need to simulate a +circuit s + + align:start position:0% +circuit s + + + align:start position:0% +circuit s +instance okay so let's look at this + + align:start position:0% +instance okay so let's look at this + + + align:start position:0% +instance okay so let's look at this +table so in all these lines of this + + align:start position:0% +table so in all these lines of this + + + align:start position:0% +table so in all these lines of this +table Z is the output player of the + + align:start position:0% +table Z is the output player of the + + + align:start position:0% +table Z is the output player of the +gadget X and Y are the input players of + + align:start position:0% +gadget X and Y are the input players of + + + align:start position:0% +gadget X and Y are the input players of +the gadget and potentially the gadgets + + align:start position:0% +the gadget and potentially the gadgets + + + align:start position:0% +the gadget and potentially the gadgets +implementing each of these Gates use + + align:start position:0% +implementing each of these Gates use + + + align:start position:0% +implementing each of these Gates use +auxiliary players like uh in the + + align:start position:0% +auxiliary players like uh in the + + + align:start position:0% +auxiliary players like uh in the +addition case I was using one + + align:start position:0% +addition case I was using one + + + align:start position:0% +addition case I was using one +intermediate player he was the auxiliary + + align:start position:0% +intermediate player he was the auxiliary + + + align:start position:0% +intermediate player he was the auxiliary +player and uh the claim is that um you + + align:start position:0% +player and uh the claim is that um you + + + align:start position:0% +player and uh the claim is that um you +know you can Implement gadgets such that + + align:start position:0% +know you can Implement gadgets such that + + + align:start position:0% +know you can Implement gadgets such that +if any of these Gadget is contained in a + + align:start position:0% +if any of these Gadget is contained in a + + + align:start position:0% +if any of these Gadget is contained in a +bigger polymetric + + align:start position:0% +bigger polymetric + + + align:start position:0% +bigger polymetric +game then any Nash equilibrium of this + + align:start position:0% +game then any Nash equilibrium of this + + + align:start position:0% +game then any Nash equilibrium of this +bigger polymetric + + align:start position:0% +bigger polymetric + + + align:start position:0% +bigger polymetric +G the these conditions are satisfied uh + + align:start position:0% +G the these conditions are satisfied uh + + + align:start position:0% +G the these conditions are satisfied uh +by the uh output and input players of + + align:start position:0% +by the uh output and input players of + + + align:start position:0% +by the uh output and input players of +the gadget + + align:start position:0% +the gadget + + + align:start position:0% +the gadget +okay and this is as long as you don't + + align:start position:0% +okay and this is as long as you don't + + + align:start position:0% +okay and this is as long as you don't +mess up with the gadgets meaning that uh + + align:start position:0% +mess up with the gadgets meaning that uh + + + align:start position:0% +mess up with the gadgets meaning that uh +the bigger game can have edges into the + + align:start position:0% +the bigger game can have edges into the + + + align:start position:0% +the bigger game can have edges into the +input players of the gadgets and edges + + align:start position:0% +input players of the gadgets and edges + + + align:start position:0% +input players of the gadgets and edges +out of the output players of the + + align:start position:0% + + + + align:start position:0% + +gadget but I claim that you can + + align:start position:0% +gadget but I claim that you can + + + align:start position:0% +gadget but I claim that you can +Implement all of the gadgets that you + + align:start position:0% +Implement all of the gadgets that you + + + align:start position:0% +Implement all of the gadgets that you +need so in particular if you have an + + align:start position:0% +need so in particular if you have an + + + align:start position:0% +need so in particular if you have an +instance for arithmetic circuit set you + + align:start position:0% +instance for arithmetic circuit set you + + + align:start position:0% +instance for arithmetic circuit set you +can create a poly Matrix Game by + + align:start position:0% +can create a poly Matrix Game by + + + align:start position:0% +can create a poly Matrix Game by +composing + + align:start position:0% + + + + align:start position:0% + +gadgets uh for each of these + + align:start position:0% +gadgets uh for each of these + + + align:start position:0% +gadgets uh for each of these +Gates so that at any n equilibrium of + + align:start position:0% +Gates so that at any n equilibrium of + + + align:start position:0% +Gates so that at any n equilibrium of +this polymetric game all uh gate + + align:start position:0% +this polymetric game all uh gate + + + align:start position:0% +this polymetric game all uh gate +conditions are satisfied so in + + align:start position:0% +conditions are satisfied so in + + + align:start position:0% +conditions are satisfied so in +particular uh you are uh by by finding a + + align:start position:0% +particular uh you are uh by by finding a + + + align:start position:0% +particular uh you are uh by by finding a +n equilibrium of this game you are + + align:start position:0% +n equilibrium of this game you are + + + align:start position:0% +n equilibrium of this game you are +solving the instance of of arithmetic + + align:start position:0% +solving the instance of of arithmetic + + + align:start position:0% +solving the instance of of arithmetic +circuit set you started with so that's + + align:start position:0% +circuit set you started with so that's + + + align:start position:0% +circuit set you started with so that's +the + + align:start position:0% +the + + + align:start position:0% +the +idea any questions about what what what + + align:start position:0% +idea any questions about what what what + + + align:start position:0% +idea any questions about what what what +happened so far in the + + align:start position:0% +happened so far in the + + + align:start position:0% +happened so far in the +lecture questions about this reduction + + align:start position:0% +lecture questions about this reduction + + + align:start position:0% +lecture questions about this reduction +or or how the gadgets + + align:start position:0% +or or how the gadgets + + + align:start position:0% +or or how the gadgets +work yeah does this give a valid proof + + align:start position:0% +work yeah does this give a valid proof + + + align:start position:0% +work yeah does this give a valid proof +that um every instance in arithmetic + + align:start position:0% +that um every instance in arithmetic + + + align:start position:0% +that um every instance in arithmetic +circuit at has a satisfying assignment + + align:start position:0% +circuit at has a satisfying assignment + + + align:start position:0% +circuit at has a satisfying assignment +yeah that's circular that's correct uh + + align:start position:0% +yeah that's circular that's correct uh + + + align:start position:0% +yeah that's circular that's correct uh +because this is a game so by NIS theorem + + align:start position:0% +because this is a game so by NIS theorem + + + align:start position:0% +because this is a game so by NIS theorem +there is a n equilibrium hence uh there + + align:start position:0% +there is a n equilibrium hence uh there + + + align:start position:0% +there is a n equilibrium hence uh there +is a solution to that because n is the + + align:start position:0% +is a solution to that because n is the + + + align:start position:0% +is a solution to that because n is the +solution to that that's a exactly right + + align:start position:0% +solution to that that's a exactly right + + + align:start position:0% +solution to that that's a exactly right +so actually that's how we get + + align:start position:0% + + + + align:start position:0% + +it um one thing that's not exactly + + align:start position:0% +it um one thing that's not exactly + + + align:start position:0% +it um one thing that's not exactly +obvious but you can argue that it's true + + align:start position:0% +obvious but you can argue that it's true + + + align:start position:0% +obvious but you can argue that it's true +is that actually not only there is + + align:start position:0% +is that actually not only there is + + + align:start position:0% +is that actually not only there is +always a solution but there is a + + align:start position:0% +always a solution but there is a + + + align:start position:0% +always a solution but there is a +solution in rational + + align:start position:0% +solution in rational + + + align:start position:0% +solution in rational +numbers uh with polinomial description + + align:start position:0% +numbers uh with polinomial description + + + align:start position:0% +numbers uh with polinomial description +complexity in the input size so that + + align:start position:0% +complexity in the input size so that + + + align:start position:0% +complexity in the input size so that +requires some linear + + align:start position:0% +requires some linear + + + align:start position:0% +requires some linear +programming uh techniques but uh that's + + align:start position:0% +programming uh techniques but uh that's + + + align:start position:0% +programming uh techniques but uh that's +also easy to show so you know a priori n + + align:start position:0% +also easy to show so you know a priori n + + + align:start position:0% +also easy to show so you know a priori n +theorem will give you that a solution + + align:start position:0% +theorem will give you that a solution + + + align:start position:0% +theorem will give you that a solution +exists it wouldn't give guarantees about + + align:start position:0% +exists it wouldn't give guarantees about + + + align:start position:0% +exists it wouldn't give guarantees about +the description complex of that solution + + align:start position:0% +the description complex of that solution + + + align:start position:0% +the description complex of that solution +but using linear programming you can + + align:start position:0% +but using linear programming you can + + + align:start position:0% +but using linear programming you can +argue that there is always a rational + + align:start position:0% +argue that there is always a rational + + + align:start position:0% +argue that there is always a rational +solution with polinomial description + + align:start position:0% +solution with polinomial description + + + align:start position:0% +solution with polinomial description +complexity are you interested in seeing + + align:start position:0% +complexity are you interested in seeing + + + align:start position:0% +complexity are you interested in seeing +any of these + + align:start position:0% + + + + align:start position:0% + +gadgets you I've only showed addition do + + align:start position:0% +gadgets you I've only showed addition do + + + align:start position:0% +gadgets you I've only showed addition do +you want to see anything else or you + + align:start position:0% +you want to see anything else or you + + + align:start position:0% +you want to see anything else or you +believe me that I can actually do that + + align:start position:0% +believe me that I can actually do that + + + align:start position:0% +believe me that I can actually do that +the compare someone that has arbitrary + + align:start position:0% +the compare someone that has arbitrary + + + align:start position:0% +the compare someone that has arbitrary +output for certain conditions seems + + align:start position:0% +output for certain conditions seems + + + align:start position:0% +output for certain conditions seems +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +okay I can show that uh so let me try to + + align:start position:0% +okay I can show that uh so let me try to + + + align:start position:0% +okay I can show that uh so let me try to +do the comparison Gadget they actually + + align:start position:0% +do the comparison Gadget they actually + + + align:start position:0% +do the comparison Gadget they actually +simpler than the addition + + align:start position:0% + + + + align:start position:0% + +Gadget uh so yeah so I want to implement + + align:start position:0% +Gadget uh so yeah so I want to implement + + + align:start position:0% +Gadget uh so yeah so I want to implement +a comparison so I'm going going to have + + align:start position:0% +a comparison so I'm going going to have + + + align:start position:0% +a comparison so I'm going going to have +the input + + align:start position:0% +the input + + + align:start position:0% +the input +players and the output + + align:start position:0% +players and the output + + + align:start position:0% +players and the output +player and the payoff of the and the + + align:start position:0% +player and the payoff of the and the + + + align:start position:0% +player and the payoff of the and the +payoffs of the output player are let's + + align:start position:0% +payoffs of the output player are let's + + + align:start position:0% +payoffs of the output player are let's +see right so if he plays zero then his + + align:start position:0% +see right so if he plays zero then his + + + align:start position:0% +see right so if he plays zero then his +payoff is uh only depends on + + align:start position:0% + + + + align:start position:0% + +X and it looks like this if you place + + align:start position:0% +X and it looks like this if you place + + + align:start position:0% +X and it looks like this if you place +uh one let's see let's see if it works I + + align:start position:0% +uh one let's see let's see if it works I + + + align:start position:0% +uh one let's see let's see if it works I +haven't I haven't prepared it but it's + + align:start position:0% +haven't I haven't prepared it but it's + + + align:start position:0% +haven't I haven't prepared it but it's +easy to cons okay + + align:start position:0% +easy to cons okay + + + align:start position:0% +easy to cons okay +so worst case + + align:start position:0% +so worst case + + + align:start position:0% +so worst case +backtrack uh okay so now what I want to + + align:start position:0% +backtrack uh okay so now what I want to + + + align:start position:0% +backtrack uh okay so now what I want to +argue is that + + align:start position:0% +argue is that + + + align:start position:0% +argue is that +uh uh let's bring up the conditions that + + align:start position:0% +uh uh let's bring up the conditions that + + + align:start position:0% +uh uh let's bring up the conditions that +I need to + + align:start position:0% + + + + align:start position:0% + +satisfy okay so I want to satisfy those + + align:start position:0% +satisfy okay so I want to satisfy those + + + align:start position:0% +satisfy okay so I want to satisfy those +conditions so let's see if I do satisfy + + align:start position:0% +conditions so let's see if I do satisfy + + + align:start position:0% +conditions so let's see if I do satisfy +this conditions okay so I messed it up a + + align:start position:0% +this conditions okay so I messed it up a + + + align:start position:0% +this conditions okay so I messed it up a +little bit I guess so I have to replace + + align:start position:0% +little bit I guess so I have to replace + + + align:start position:0% +little bit I guess so I have to replace +X + + align:start position:0% +X + + + align:start position:0% +X +here and Y + + align:start position:0% +here and Y + + + align:start position:0% +here and Y +here okay now let's see if that's true + + align:start position:0% +here okay now let's see if that's true + + + align:start position:0% +here okay now let's see if that's true +so I claim that if probability X is + + align:start position:0% +so I claim that if probability X is + + + align:start position:0% +so I claim that if probability X is +bigger than + + align:start position:0% +bigger than + + + align:start position:0% +bigger than +probability y + + align:start position:0% + + + + align:start position:0% + +then what I what what do I prefer to + + align:start position:0% +then what I what what do I prefer to + + + align:start position:0% +then what I what what do I prefer to +play I prefer to play Z + + align:start position:0% + + + + align:start position:0% + +right similarly for the other case when + + align:start position:0% +right similarly for the other case when + + + align:start position:0% +right similarly for the other case when +they're equal anything is + + align:start position:0% +they're equal anything is + + + align:start position:0% +they're equal anything is +possible so that's that's simple there's + + align:start position:0% +possible so that's that's simple there's + + + align:start position:0% +possible so that's that's simple there's +no not much Trier going on + + align:start position:0% +no not much Trier going on + + + align:start position:0% +no not much Trier going on +here + + align:start position:0% +here + + + align:start position:0% +here +okay cool so I've established that uh + + align:start position:0% +okay cool so I've established that uh + + + align:start position:0% +okay cool so I've established that uh +this direction of the this this part of + + align:start position:0% +this direction of the this this part of + + + align:start position:0% +this direction of the this this part of +the reduction I want to go down from a + + align:start position:0% +the reduction I want to go down from a + + + align:start position:0% +the reduction I want to go down from a +polymatrix game to a two player + + align:start position:0% + + + + align:start position:0% + +game that's the next part of the lecture + + align:start position:0% +game that's the next part of the lecture + + + align:start position:0% +game that's the next part of the lecture +how do you go down to two + + align:start position:0% +how do you go down to two + + + align:start position:0% +how do you go down to two +players well the first thing to note is + + align:start position:0% +players well the first thing to note is + + + align:start position:0% +players well the first thing to note is +that + + align:start position:0% + + + + align:start position:0% + +uh uh all the GES can be implemented + + align:start position:0% +uh uh all the GES can be implemented + + + align:start position:0% +uh uh all the GES can be implemented +with bipartite graphs okay so if you + + align:start position:0% +with bipartite graphs okay so if you + + + align:start position:0% +with bipartite graphs okay so if you +remember my addition + + align:start position:0% +remember my addition + + + align:start position:0% +remember my addition +Gadget uh if you remember my addition + + align:start position:0% +Gadget uh if you remember my addition + + + align:start position:0% +Gadget uh if you remember my addition +Gadget it had uh the input and the + + align:start position:0% +Gadget it had uh the input and the + + + align:start position:0% +Gadget it had uh the input and the +output players on one side and the + + align:start position:0% +output players on one side and the + + + align:start position:0% +output players on one side and the +auxiliary player on one side my + + align:start position:0% +auxiliary player on one side my + + + align:start position:0% +auxiliary player on one side my +comparison Gadget does not satisfy this + + align:start position:0% +comparison Gadget does not satisfy this + + + align:start position:0% +comparison Gadget does not satisfy this +property because the input players and + + align:start position:0% +property because the input players and + + + align:start position:0% +property because the input players and +the output players are on different + + align:start position:0% +the output players are on different + + + align:start position:0% +the output players are on different +sides but I claim that you can Implement + + align:start position:0% +sides but I claim that you can Implement + + + align:start position:0% +sides but I claim that you can Implement +actually comparison by adding an next an + + align:start position:0% +actually comparison by adding an next an + + + align:start position:0% +actually comparison by adding an next an +additional step with a bipartite gage so + + align:start position:0% +additional step with a bipartite gage so + + + align:start position:0% +additional step with a bipartite gage so +I claim that all Gates can be + + align:start position:0% +I claim that all Gates can be + + + align:start position:0% +I claim that all Gates can be +implemented with polymetric game that + + align:start position:0% +implemented with polymetric game that + + + align:start position:0% +implemented with polymetric game that +have input and output players on one + + align:start position:0% +have input and output players on one + + + align:start position:0% +have input and output players on one +side and auxiliary vertices on on one on + + align:start position:0% +side and auxiliary vertices on on one on + + + align:start position:0% +side and auxiliary vertices on on one on +the other side okay so I claim that um + + align:start position:0% +the other side okay so I claim that um + + + align:start position:0% +the other side okay so I claim that um +all my gadgets are actually + + align:start position:0% +all my gadgets are actually + + + align:start position:0% +all my gadgets are actually +bipartite so in particular I can color + + align:start position:0% +bipartite so in particular I can color + + + align:start position:0% +bipartite so in particular I can color +this graph with two colors blue and + + align:start position:0% +this graph with two colors blue and + + + align:start position:0% +this graph with two colors blue and +red and what I want to do is I want to + + align:start position:0% +red and what I want to do is I want to + + + align:start position:0% +red and what I want to do is I want to +uh uh create these Super Players I'm + + align:start position:0% +uh uh create these Super Players I'm + + + align:start position:0% +uh uh create these Super Players I'm +going to call them lawyers I'm going to + + align:start position:0% +going to call them lawyers I'm going to + + + align:start position:0% +going to call them lawyers I'm going to +have a I'm going to have a red lawyer + + align:start position:0% +have a I'm going to have a red lawyer + + + align:start position:0% +have a I'm going to have a red lawyer +and a blue lawyer okay and the red + + align:start position:0% +and a blue lawyer okay and the red + + + align:start position:0% +and a blue lawyer okay and the red +player is going to represent all the + + align:start position:0% +player is going to represent all the + + + align:start position:0% +player is going to represent all the +nodes that are color red in here while + + align:start position:0% +nodes that are color red in here while + + + align:start position:0% +nodes that are color red in here while +the blue lawyer is going to uh represent + + align:start position:0% +the blue lawyer is going to uh represent + + + align:start position:0% +the blue lawyer is going to uh represent +all blue + + align:start position:0% +all blue + + + align:start position:0% +all blue +nodes right um and what I want to do is + + align:start position:0% +nodes right um and what I want to do is + + + align:start position:0% +nodes right um and what I want to do is +I want to define the lower game in the + + align:start position:0% +I want to define the lower game in the + + + align:start position:0% +I want to define the lower game in the +next + + align:start position:0% +next + + + align:start position:0% +next +slide Okay so every lawyer so the red + + align:start position:0% +slide Okay so every lawyer so the red + + + align:start position:0% +slide Okay so every lawyer so the red +lawyer his strategy set is the union not + + align:start position:0% +lawyer his strategy set is the union not + + + align:start position:0% +lawyer his strategy set is the union not +the product the union of the that's + + align:start position:0% +the product the union of the that's + + + align:start position:0% +the product the union of the that's +important otherwise my reduction would + + align:start position:0% +important otherwise my reduction would + + + align:start position:0% +important otherwise my reduction would +be exponentially large my reduction + + align:start position:0% +be exponentially large my reduction + + + align:start position:0% +be exponentially large my reduction +wouldn't be polinomial so every lawyer + + align:start position:0% +wouldn't be polinomial so every lawyer + + + align:start position:0% +wouldn't be polinomial so every lawyer +and that poses actually technicalities + + align:start position:0% +and that poses actually technicalities + + + align:start position:0% +and that poses actually technicalities +in the construction that I'm about to + + align:start position:0% +in the construction that I'm about to + + + align:start position:0% +in the construction that I'm about to +present but every lawyer will have as + + align:start position:0% +present but every lawyer will have as + + + align:start position:0% +present but every lawyer will have as +strategy set pure strategy set the union + + align:start position:0% +strategy set pure strategy set the union + + + align:start position:0% +strategy set pure strategy set the union +of the pure strategy sets of the clients + + align:start position:0% +of the pure strategy sets of the clients + + + align:start position:0% +of the pure strategy sets of the clients +that he represents so the the red lawyer + + align:start position:0% +that he represents so the the red lawyer + + + align:start position:0% +that he represents so the the red lawyer +has one strategy for every strategy of + + align:start position:0% +has one strategy for every strategy of + + + align:start position:0% +has one strategy for every strategy of +every red node the blue lawyer has one + + align:start position:0% +every red node the blue lawyer has one + + + align:start position:0% +every red node the blue lawyer has one +strategy for every strategy of every + + align:start position:0% +strategy for every strategy of every + + + align:start position:0% +strategy for every strategy of every +blue + + align:start position:0% +blue + + + align:start position:0% +blue +note okay now what I want to do is I + + align:start position:0% +note okay now what I want to do is I + + + align:start position:0% +note okay now what I want to do is I +want to define the payoffs in the lawyer + + align:start position:0% +want to define the payoffs in the lawyer + + + align:start position:0% +want to define the payoffs in the lawyer +game what are the payoffs in the lawyer + + align:start position:0% +game what are the payoffs in the lawyer + + + align:start position:0% +game what are the payoffs in the lawyer +game well what happens if the red lawyer + + align:start position:0% +game well what happens if the red lawyer + + + align:start position:0% +game well what happens if the red lawyer +decides to play strategy I of red client + + align:start position:0% +decides to play strategy I of red client + + + align:start position:0% +decides to play strategy I of red client +U + + align:start position:0% +U + + + align:start position:0% +U +and what if at the the blue lawyer plays + + align:start position:0% +and what if at the the blue lawyer plays + + + align:start position:0% +and what if at the the blue lawyer plays +strategy J of blue node V what are the + + align:start position:0% +strategy J of blue node V what are the + + + align:start position:0% +strategy J of blue node V what are the +pay of of the two lawyers in that choice + + align:start position:0% +pay of of the two lawyers in that choice + + + align:start position:0% +pay of of the two lawyers in that choice +of strategies well it's going to be + + align:start position:0% +of strategies well it's going to be + + + align:start position:0% +of strategies well it's going to be +exactly the corresponding payoffs of the + + align:start position:0% +exactly the corresponding payoffs of the + + + align:start position:0% +exactly the corresponding payoffs of the +nodes of the polymatrix game if so the + + align:start position:0% +nodes of the polymatrix game if so the + + + align:start position:0% +nodes of the polymatrix game if so the +red ler will get will get the payoff + + align:start position:0% +red ler will get will get the payoff + + + align:start position:0% +red ler will get will get the payoff +that you would have gotten in the + + align:start position:0% +that you would have gotten in the + + + align:start position:0% +that you would have gotten in the +polymetric game if the if the two these + + align:start position:0% +polymetric game if the if the two these + + + align:start position:0% +polymetric game if the if the two these +two players play played I and J and uh + + align:start position:0% +two players play played I and J and uh + + + align:start position:0% +two players play played I and J and uh +the blue lawyer is going to get his + + align:start position:0% +the blue lawyer is going to get his + + + align:start position:0% +the blue lawyer is going to get his +client's value so V value under the same + + align:start position:0% +client's value so V value under the same + + + align:start position:0% +client's value so V value under the same +the same choice of strategies so in + + align:start position:0% +the same choice of strategies so in + + + align:start position:0% +the same choice of strategies so in +particular if there's no Edge between + + align:start position:0% +particular if there's no Edge between + + + align:start position:0% +particular if there's no Edge between +these two nodes that blue and red + + align:start position:0% +these two nodes that blue and red + + + align:start position:0% +these two nodes that blue and red +lawyers chose to play uh the nobody gets + + align:start position:0% +lawyers chose to play uh the nobody gets + + + align:start position:0% +lawyers chose to play uh the nobody gets +anything that's the the pay of here is + + align:start position:0% +anything that's the the pay of here is + + + align:start position:0% +anything that's the the pay of here is +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +zero um you know if there is a directed + + align:start position:0% +zero um you know if there is a directed + + + align:start position:0% +zero um you know if there is a directed +Edge from uh V to U then this is going + + align:start position:0% +Edge from uh V to U then this is going + + + align:start position:0% +Edge from uh V to U then this is going +to be zero and that's not going you know + + align:start position:0% +to be zero and that's not going you know + + + align:start position:0% +to be zero and that's not going you know +that's whatever it is and vice versa but + + align:start position:0% +that's whatever it is and vice versa but + + + align:start position:0% +that's whatever it is and vice versa but +uh you get the idea if if the blue + + align:start position:0% +uh you get the idea if if the blue + + + align:start position:0% +uh you get the idea if if the blue +lawyer decides to represent a client and + + align:start position:0% +lawyer decides to represent a client and + + + align:start position:0% +lawyer decides to represent a client and +the red lawyer decides to + + align:start position:0% +the red lawyer decides to + + + align:start position:0% +the red lawyer decides to +represent another client then the + + align:start position:0% +represent another client then the + + + align:start position:0% +represent another client then the +payoffs of the lawyers are the + + align:start position:0% +payoffs of the lawyers are the + + + align:start position:0% +payoffs of the lawyers are the +corresponding payoffs that the clients + + align:start position:0% +corresponding payoffs that the clients + + + align:start position:0% +corresponding payoffs that the clients +would have gotten had they played the + + align:start position:0% +would have gotten had they played the + + + align:start position:0% +would have gotten had they played the +strategies that the lawyers decided to + + align:start position:0% +strategies that the lawyers decided to + + + align:start position:0% +strategies that the lawyers decided to +play for them that's the definition of + + align:start position:0% +play for them that's the definition of + + + align:start position:0% +play for them that's the definition of +the lower game is it clear + + align:start position:0% + + + + align:start position:0% + +Now The Wishful Thinking + + align:start position:0% +Now The Wishful Thinking + + + align:start position:0% +Now The Wishful Thinking +is that if X and Y is a ntion + + align:start position:0% +is that if X and Y is a ntion + + + align:start position:0% +is that if X and Y is a ntion +equilibrium of the lawyer + + align:start position:0% +equilibrium of the lawyer + + + align:start position:0% +equilibrium of the lawyer +game then if I look at the marginal + + align:start position:0% +game then if I look at the marginal + + + align:start position:0% +game then if I look at the marginal +probability + + align:start position:0% + + + + align:start position:0% + +distributions uh on the different + + align:start position:0% +distributions uh on the different + + + align:start position:0% +distributions uh on the different +nodes on the different clients by their + + align:start position:0% +nodes on the different clients by their + + + align:start position:0% +nodes on the different clients by their +lawyer then these marginal probability + + align:start position:0% +lawyer then these marginal probability + + + align:start position:0% +lawyer then these marginal probability +distributions are an as equilibrium + + align:start position:0% + + + + align:start position:0% + +so The Wishful Thinking is + + align:start position:0% +so The Wishful Thinking is + + + align:start position:0% +so The Wishful Thinking is +that if I start with the Nash + + align:start position:0% +that if I start with the Nash + + + align:start position:0% +that if I start with the Nash +equilibrium of the lower game then if I + + align:start position:0% +equilibrium of the lower game then if I + + + align:start position:0% +equilibrium of the lower game then if I +look + + align:start position:0% +look + + + align:start position:0% +look +at uh the distribution that uh the red + + align:start position:0% +at uh the distribution that uh the red + + + align:start position:0% +at uh the distribution that uh the red +lawyer the marginal probability + + align:start position:0% +lawyer the marginal probability + + + align:start position:0% +lawyer the marginal probability +distribution that the red lawyer places + + align:start position:0% +distribution that the red lawyer places + + + align:start position:0% +distribution that the red lawyer places +on every red node separately and the + + align:start position:0% +on every red node separately and the + + + align:start position:0% +on every red node separately and the +marginal probability distributions that + + align:start position:0% +marginal probability distributions that + + + align:start position:0% +marginal probability distributions that +the blue lawyer places on all blue nodes + + align:start position:0% +the blue lawyer places on all blue nodes + + + align:start position:0% +the blue lawyer places on all blue nodes +separately so all this collection of + + align:start position:0% +separately so all this collection of + + + align:start position:0% +separately so all this collection of +marginal probability + + align:start position:0% +marginal probability + + + align:start position:0% +marginal probability +distributions that this collection is a + + align:start position:0% +distributions that this collection is a + + + align:start position:0% +distributions that this collection is a +natur equilibrium of the polymatrix game + + align:start position:0% +natur equilibrium of the polymatrix game + + + align:start position:0% +natur equilibrium of the polymatrix game +that's a whistful + + align:start position:0% + + + + align:start position:0% + +thinking + + align:start position:0% +thinking + + + align:start position:0% +thinking +okay uh questions about what the whistle + + align:start position:0% +okay uh questions about what the whistle + + + align:start position:0% +okay uh questions about what the whistle +thinking + + align:start position:0% + + + + align:start position:0% + +is okay okay of course this that's + + align:start position:0% +is okay okay of course this that's + + + align:start position:0% +is okay okay of course this that's +whistful thinking because we know how + + align:start position:0% +whistful thinking because we know how + + + align:start position:0% +whistful thinking because we know how +lawyers + + align:start position:0% +lawyers + + + align:start position:0% +lawyers +behave they only represent the lucrative + + align:start position:0% +behave they only represent the lucrative + + + align:start position:0% +behave they only represent the lucrative +clients right and the you know a + + align:start position:0% +clients right and the you know a + + + align:start position:0% +clients right and the you know a +priority there's no reason that the red + + align:start position:0% +priority there's no reason that the red + + + align:start position:0% +priority there's no reason that the red +lawyer would have incentive to uh + + align:start position:0% +lawyer would have incentive to uh + + + align:start position:0% +lawyer would have incentive to uh +choose at least some strategy for you + + align:start position:0% +choose at least some strategy for you + + + align:start position:0% +choose at least some strategy for you +know to place positive probability Mass + + align:start position:0% +know to place positive probability Mass + + + align:start position:0% +know to place positive probability Mass +on every node he represents maybe in a n + + align:start position:0% +on every node he represents maybe in a n + + + align:start position:0% +on every node he represents maybe in a n +equilibrium of this lawyer game uh some + + align:start position:0% +equilibrium of this lawyer game uh some + + + align:start position:0% +equilibrium of this lawyer game uh some +of these marginal distributions are + + align:start position:0% +of these marginal distributions are + + + align:start position:0% +of these marginal distributions are +actually undefined because the lawyers + + align:start position:0% +actually undefined because the lawyers + + + align:start position:0% +actually undefined because the lawyers +are are IL defined because the lawyers + + align:start position:0% +are are IL defined because the lawyers + + + align:start position:0% +are are IL defined because the lawyers +Place zero probability Mass on the + + align:start position:0% +Place zero probability Mass on the + + + align:start position:0% +Place zero probability Mass on the +strategy of those nodes okay so that + + align:start position:0% +strategy of those nodes okay so that + + + align:start position:0% +strategy of those nodes okay so that +whistful thinking isn't going through + + align:start position:0% +whistful thinking isn't going through + + + align:start position:0% +whistful thinking isn't going through +but there is some truth to that so there + + align:start position:0% +but there is some truth to that so there + + + align:start position:0% +but there is some truth to that so there +is a way to fix it so here's how we're + + align:start position:0% +is a way to fix it so here's how we're + + + align:start position:0% +is a way to fix it so here's how we're +going to fix the lawyer + + align:start position:0% +going to fix the lawyer + + + align:start position:0% +going to fix the lawyer +game so we're going to we know what + + align:start position:0% +game so we're going to we know what + + + align:start position:0% +game so we're going to we know what +lawyers like they like money okay so + + align:start position:0% +lawyers like they like money okay so + + + align:start position:0% +lawyers like they like money okay so +we're going to define a high stakes + + align:start position:0% +we're going to define a high stakes + + + align:start position:0% +we're going to define a high stakes +game that the lowers are going to play + + align:start position:0% +game that the lowers are going to play + + + align:start position:0% +game that the lowers are going to play +on the + + align:start position:0% +on the + + + align:start position:0% +on the +side at the same time as the actual game + + align:start position:0% +side at the same time as the actual game + + + align:start position:0% +side at the same time as the actual game +that we're interested in okay so for a + + align:start position:0% +that we're interested in okay so for a + + + align:start position:0% +that we're interested in okay so for a +lot of cash okay so these are the Stakes + + align:start position:0% +lot of cash okay so these are the Stakes + + + align:start position:0% +lot of cash okay so these are the Stakes +of that + + align:start position:0% +of that + + + align:start position:0% +of that +game uh we're going to do the following + + align:start position:0% +game uh we're going to do the following + + + align:start position:0% +game uh we're going to do the following +so uh some uh terminology first so + + align:start position:0% +so uh some uh terminology first so + + + align:start position:0% +so uh some uh terminology first so +suppose that without loss of generality + + align:start position:0% +suppose that without loss of generality + + + align:start position:0% +suppose that without loss of generality +suppose that every lawyer has n clients + + align:start position:0% +suppose that every lawyer has n clients + + + align:start position:0% +suppose that every lawyer has n clients +he represents okay so uh and let's label + + align:start position:0% +he represents okay so uh and let's label + + + align:start position:0% +he represents okay so uh and let's label +the the red lawyer clients 1 through n + + align:start position:0% +the the red lawyer clients 1 through n + + + align:start position:0% +the the red lawyer clients 1 through n +and the blue lawyer clients one through + + align:start position:0% +and the blue lawyer clients one through + + + align:start position:0% +and the blue lawyer clients one through +n if you know one of the two lawyers + + align:start position:0% +n if you know one of the two lawyers + + + align:start position:0% +n if you know one of the two lawyers +have fewer clients then we can pad this + + align:start position:0% +have fewer clients then we can pad this + + + align:start position:0% +have fewer clients then we can pad this +with you know dummy players and that + + align:start position:0% +with you know dummy players and that + + + align:start position:0% +with you know dummy players and that +doesn't change the polymetric games + + align:start position:0% +doesn't change the polymetric games + + + align:start position:0% +doesn't change the polymetric games +equilibria um so suppose that both + + align:start position:0% +equilibria um so suppose that both + + + align:start position:0% +equilibria um so suppose that both +lawyers represent the same number of + + align:start position:0% +lawyers represent the same number of + + + align:start position:0% +lawyers represent the same number of +players clients and let's label both + + align:start position:0% +players clients and let's label both + + + align:start position:0% +players clients and let's label both +lawyers' clients one through n in an + + align:start position:0% +lawyers' clients one through n in an + + + align:start position:0% +lawyers' clients one through n in an +arbitrary way okay now + + align:start position:0% +arbitrary way okay now + + + align:start position:0% +arbitrary way okay now +uh the high stes and and the strategies + + align:start position:0% +uh the high stes and and the strategies + + + align:start position:0% +uh the high stes and and the strategies +of the High stes game are exactly the + + align:start position:0% +of the High stes game are exactly the + + + align:start position:0% +of the High stes game are exactly the +same as the strategies of the game that + + align:start position:0% +same as the strategies of the game that + + + align:start position:0% +same as the strategies of the game that +I showed in the previous slide in + + align:start position:0% +I showed in the previous slide in + + + align:start position:0% +I showed in the previous slide in +particular the redler has the union of + + align:start position:0% +particular the redler has the union of + + + align:start position:0% +particular the redler has the union of +the strategies of all blue nodes the red + + align:start position:0% +the strategies of all blue nodes the red + + + align:start position:0% +the strategies of all blue nodes the red +and the and red lawyer has the union of + + align:start position:0% +and the and red lawyer has the union of + + + align:start position:0% +and the and red lawyer has the union of +the Strat of the red nodes now what's + + align:start position:0% +the Strat of the red nodes now what's + + + align:start position:0% +the Strat of the red nodes now what's +the high St + + align:start position:0% +the high St + + + align:start position:0% +the high St +game uh suppose that the red ler plays + + align:start position:0% +game uh suppose that the red ler plays + + + align:start position:0% +game uh suppose that the red ler plays +any strategy of client J and the blue + + align:start position:0% +any strategy of client J and the blue + + + align:start position:0% +any strategy of client J and the blue +ler plays any strategy of client k then + + align:start position:0% +ler plays any strategy of client k then + + + align:start position:0% +ler plays any strategy of client k then +if they choose the they choose different + + align:start position:0% +if they choose the they choose different + + + align:start position:0% +if they choose the they choose different +clients they both get zero doar but if + + align:start position:0% +clients they both get zero doar but if + + + align:start position:0% +clients they both get zero doar but if +they get choose the same client that I + + align:start position:0% +they get choose the same client that I + + + align:start position:0% +they get choose the same client that I +mean it's not the same client it's the + + align:start position:0% +mean it's not the same client it's the + + + align:start position:0% +mean it's not the same client it's the +same label of a client right CU they + + align:start position:0% +same label of a client right CU they + + + align:start position:0% +same label of a client right CU they +each represent different clients right + + align:start position:0% +each represent different clients right + + + align:start position:0% +each represent different clients right +but if they choose different labels then + + align:start position:0% +but if they choose different labels then + + + align:start position:0% +but if they choose different labels then +they both get zero if they choose the + + align:start position:0% +they both get zero if they choose the + + + align:start position:0% +they both get zero if they choose the +same + + align:start position:0% +same + + + align:start position:0% +same +label uh the whoever it was the red + + align:start position:0% +label uh the whoever it was the red + + + align:start position:0% +label uh the whoever it was the red +lawyer gets a lot of cash and the blue + + align:start position:0% +lawyer gets a lot of cash and the blue + + + align:start position:0% +lawyer gets a lot of cash and the blue +lawyer loses a lot of + + align:start position:0% + + + + align:start position:0% + +cash + + align:start position:0% +cash + + + align:start position:0% +cash +okay okay again so this game has the + + align:start position:0% +okay okay again so this game has the + + + align:start position:0% +okay okay again so this game has the +same strategy is as the uh lawyer game + + align:start position:0% +same strategy is as the uh lawyer game + + + align:start position:0% +same strategy is as the uh lawyer game +that I showed in the previous + + align:start position:0% +that I showed in the previous + + + align:start position:0% +that I showed in the previous +slide except now in this game all the + + align:start position:0% +slide except now in this game all the + + + align:start position:0% +slide except now in this game all the +lawyers care about is the labels of the + + align:start position:0% +lawyers care about is the labels of the + + + align:start position:0% +lawyers care about is the labels of the +CL of the uh clients whose strategies + + align:start position:0% +CL of the uh clients whose strategies + + + align:start position:0% +CL of the uh clients whose strategies +they choose so if the uh choose a + + align:start position:0% +they choose so if the uh choose a + + + align:start position:0% +they choose so if the uh choose a +strategy of a client that has the same + + align:start position:0% +strategy of a client that has the same + + + align:start position:0% +strategy of a client that has the same +label then the red lawyer gains a lot of + + align:start position:0% +label then the red lawyer gains a lot of + + + align:start position:0% +label then the red lawyer gains a lot of +money and the blue lawyer loses a lot of + + align:start position:0% +money and the blue lawyer loses a lot of + + + align:start position:0% +money and the blue lawyer loses a lot of +money but if they choose strategies of + + align:start position:0% +money but if they choose strategies of + + + align:start position:0% +money but if they choose strategies of +clients with different labels then they + + align:start position:0% +clients with different labels then they + + + align:start position:0% +clients with different labels then they +both get + + align:start position:0% +both get + + + align:start position:0% +both get +zero in other words in some sense the + + align:start position:0% +zero in other words in some sense the + + + align:start position:0% +zero in other words in some sense the +blue L is trying to + + align:start position:0% +blue L is trying to + + + align:start position:0% +blue L is trying to +avoid the red lawyer and the red lawyer + + align:start position:0% +avoid the red lawyer and the red lawyer + + + align:start position:0% +avoid the red lawyer and the red lawyer +trying to catch the blue lawyer okay if + + align:start position:0% +trying to catch the blue lawyer okay if + + + align:start position:0% +trying to catch the blue lawyer okay if +you want so now this is a simple zero s + + align:start position:0% +you want so now this is a simple zero s + + + align:start position:0% +you want so now this is a simple zero s +game and it's not hard to see to see + + align:start position:0% +game and it's not hard to see to see + + + align:start position:0% +game and it's not hard to see to see +that in any Nash equilibrium of this + + align:start position:0% +that in any Nash equilibrium of this + + + align:start position:0% +that in any Nash equilibrium of this +game uh so the unique Nash I mean in any + + align:start position:0% +game uh so the unique Nash I mean in any + + + align:start position:0% +game uh so the unique Nash I mean in any +Nash of this game the loyer + + align:start position:0% +Nash of this game the loyer + + + align:start position:0% +Nash of this game the loyer +is going to are going to + + align:start position:0% +is going to are going to + + + align:start position:0% +is going to are going to +represent every client with the same + + align:start position:0% +represent every client with the same + + + align:start position:0% +represent every client with the same +probability + + align:start position:0% +probability + + + align:start position:0% +probability +so each lawyer assigns probability + + align:start position:0% +so each lawyer assigns probability + + + align:start position:0% +so each lawyer assigns probability +exactly one / n to the set of his + + align:start position:0% +exactly one / n to the set of his + + + align:start position:0% +exactly one / n to the set of his +strategies corresponding to each of his + + align:start position:0% +strategies corresponding to each of his + + + align:start position:0% +strategies corresponding to each of his +clients so the highx game has the + + align:start position:0% +clients so the highx game has the + + + align:start position:0% +clients so the highx game has the +property that the lawyers represent all + + align:start position:0% +property that the lawyers represent all + + + align:start position:0% +property that the lawyers represent all +their clients with the same probability + + align:start position:0% +their clients with the same probability + + + align:start position:0% +their clients with the same probability +distribution and you can divide that + + align:start position:0% +distribution and you can divide that + + + align:start position:0% +distribution and you can divide that +probility distribution in an arbitrary + + align:start position:0% +probility distribution in an arbitrary + + + align:start position:0% +probility distribution in an arbitrary +way within the strategies of each of + + align:start position:0% +way within the strategies of each of + + + align:start position:0% +way within the strategies of each of +their clients in this + + align:start position:0% +their clients in this + + + align:start position:0% +their clients in this +game that's easy to + + align:start position:0% +game that's easy to + + + align:start position:0% +game that's easy to +see just by the symmetry of the game + + align:start position:0% +see just by the symmetry of the game + + + align:start position:0% +see just by the symmetry of the game +this has to be true right and with these + + align:start position:0% +this has to be true right and with these + + + align:start position:0% +this has to be true right and with these +two + + align:start position:0% +two + + + align:start position:0% +two +definitions the game really the game + + align:start position:0% +definitions the game really the game + + + align:start position:0% +definitions the game really the game +that I'm going to do for my reduction + + align:start position:0% +that I'm going to do for my reduction + + + align:start position:0% +that I'm going to do for my reduction +from polymatrix games to two player + + align:start position:0% +from polymatrix games to two player + + + align:start position:0% +from polymatrix games to two player +games is going to be this the sum of + + align:start position:0% +games is going to be this the sum of + + + align:start position:0% +games is going to be this the sum of +these two games Okay so this is the game + + align:start position:0% +these two games Okay so this is the game + + + align:start position:0% +these two games Okay so this is the game +that I defined earlier right and this is + + align:start position:0% +that I defined earlier right and this is + + + align:start position:0% +that I defined earlier right and this is +a this Matrix is a block Matrix so this + + align:start position:0% +a this Matrix is a block Matrix so this + + + align:start position:0% +a this Matrix is a block Matrix so this +is a block of Strat is corresponding to + + align:start position:0% +is a block of Strat is corresponding to + + + align:start position:0% +is a block of Strat is corresponding to +this Matrix is a matrix that has is a + + align:start position:0% +this Matrix is a matrix that has is a + + + align:start position:0% +this Matrix is a matrix that has is a +constant Matrix where everything is + + align:start position:0% +constant Matrix where everything is + + + align:start position:0% +constant Matrix where everything is +big and uh this block corresponds to + + align:start position:0% +big and uh this block corresponds to + + + align:start position:0% +big and uh this block corresponds to +these are the strategies of client with + + align:start position:0% +these are the strategies of client with + + + align:start position:0% +these are the strategies of client with +label one for the red lawyer and this is + + align:start position:0% +label one for the red lawyer and this is + + + align:start position:0% +label one for the red lawyer and this is +the the strategist of the uh uh client + + align:start position:0% +the the strategist of the uh uh client + + + align:start position:0% +the the strategist of the uh uh client +of the pl lawyer with label one and so + + align:start position:0% +of the pl lawyer with label one and so + + + align:start position:0% +of the pl lawyer with label one and so +on so forth so this is a block Matrix + + align:start position:0% +on so forth so this is a block Matrix + + + align:start position:0% +on so forth so this is a block Matrix +and there are M's and minus M's in this + + align:start position:0% +and there are M's and minus M's in this + + + align:start position:0% +and there are M's and minus M's in this +diagonal blocks and everything else is + + align:start position:0% +diagonal blocks and everything else is + + + align:start position:0% +diagonal blocks and everything else is +zero so that's the high stakes game it's + + align:start position:0% +zero so that's the high stakes game it's + + + align:start position:0% +zero so that's the high stakes game it's +played among blocks of uh strategies CU + + align:start position:0% +played among blocks of uh strategies CU + + + align:start position:0% +played among blocks of uh strategies CU +all I carry to is the label of the + + align:start position:0% +all I carry to is the label of the + + + align:start position:0% +all I carry to is the label of the +client I'm choosing uh for each of these + + align:start position:0% +client I'm choosing uh for each of these + + + align:start position:0% +client I'm choosing uh for each of these +lawyers well this is a more fine grained + + align:start position:0% +lawyers well this is a more fine grained + + + align:start position:0% +lawyers well this is a more fine grained +game where I not only care about which + + align:start position:0% +game where I not only care about which + + + align:start position:0% +game where I not only care about which +clients I'm choosing but also which + + align:start position:0% +clients I'm choosing but also which + + + align:start position:0% +clients I'm choosing but also which +strategies of these clients I'm choosing + + align:start position:0% +strategies of these clients I'm choosing + + + align:start position:0% +strategies of these clients I'm choosing +and I'm going to choose an M that + + align:start position:0% +and I'm going to choose an M that + + + align:start position:0% +and I'm going to choose an M that +overwhelms uh the payoffs in this game + + align:start position:0% +overwhelms uh the payoffs in this game + + + align:start position:0% +overwhelms uh the payoffs in this game +so this condition is okay for what I'm + + align:start position:0% +so this condition is okay for what I'm + + + align:start position:0% +so this condition is okay for what I'm +about to say but think of M as huge + + align:start position:0% +about to say but think of M as huge + + + align:start position:0% +about to say but think of M as huge +compared to the maximum utility in this + + align:start position:0% +compared to the maximum utility in this + + + align:start position:0% +compared to the maximum utility in this +game times the number of of clients in + + align:start position:0% +game times the number of of clients in + + + align:start position:0% +game times the number of of clients in +that + + align:start position:0% + + + + align:start position:0% + +game yeah just make sure I'm + + align:start position:0% +game yeah just make sure I'm + + + align:start position:0% +game yeah just make sure I'm +understanding this so far so in the + + align:start position:0% +understanding this so far so in the + + + align:start position:0% +understanding this so far so in the +naive game if the two if the red guy + + align:start position:0% +naive game if the two if the red guy + + + align:start position:0% +naive game if the two if the red guy +chooses strategy and the blue guy + + align:start position:0% +chooses strategy and the blue guy + + + align:start position:0% +chooses strategy and the blue guy +chooses a strategy and the two vertices + + align:start position:0% +chooses a strategy and the two vertices + + + align:start position:0% +chooses a strategy and the two vertices +they choose from are not connected by an + + align:start position:0% +they choose from are not connected by an + + + align:start position:0% +they choose from are not connected by an +edge then they just both get zero yeah + + align:start position:0% +edge then they just both get zero yeah + + + align:start position:0% +edge then they just both get zero yeah +okay and if they're connected they get + + align:start position:0% +okay and if they're connected they get + + + align:start position:0% +okay and if they're connected they get +the pays that the corresponding nodes + + align:start position:0% +the pays that the corresponding nodes + + + align:start position:0% +the pays that the corresponding nodes +would have gotten with this Edge one the + + align:start position:0% +would have gotten with this Edge one the + + + align:start position:0% +would have gotten with this Edge one the +one on the outgoing ver ver still get + + align:start position:0% +one on the outgoing ver ver still get + + + align:start position:0% +one on the outgoing ver ver still get +zero exact + + align:start position:0% + + + + align:start position:0% + +yeah uh cool any other questions about + + align:start position:0% +yeah uh cool any other questions about + + + align:start position:0% +yeah uh cool any other questions about +yeah uh even with a really large choice + + align:start position:0% +yeah uh even with a really large choice + + + align:start position:0% +yeah uh even with a really large choice +of M did still like mess up the values a + + align:start position:0% +of M did still like mess up the values a + + + align:start position:0% +of M did still like mess up the values a +little bit yeah it will mess it up a + + align:start position:0% +little bit yeah it will mess it up a + + + align:start position:0% +little bit yeah it will mess it up a +little bit so the Nash equilibria of + + align:start position:0% +little bit so the Nash equilibria of + + + align:start position:0% +little bit so the Nash equilibria of +this game the addition of these two + + align:start position:0% +this game the addition of these two + + + align:start position:0% +this game the addition of these two +games is not going to have the property + + align:start position:0% +games is not going to have the property + + + align:start position:0% +games is not going to have the property +that this game by itself had but it's + + align:start position:0% +that this game by itself had but it's + + + align:start position:0% +that this game by itself had but it's +going to be very close and I'm going to + + align:start position:0% +going to be very close and I'm going to + + + align:start position:0% +going to be very close and I'm going to +be specific about it so the of M is so + + align:start position:0% +be specific about it so the of M is so + + + align:start position:0% +be specific about it so the of M is so +that the the fudging isn't that big uh + + align:start position:0% +that the the fudging isn't that big uh + + + align:start position:0% +that the the fudging isn't that big uh +even for arbitrary large M I can't + + align:start position:0% +even for arbitrary large M I can't + + + align:start position:0% +even for arbitrary large M I can't +actually quite show that the lawyers + + align:start position:0% +actually quite show that the lawyers + + + align:start position:0% +actually quite show that the lawyers +represent their clients exactly equally + + align:start position:0% +represent their clients exactly equally + + + align:start position:0% +represent their clients exactly equally +but they come really close and the + + align:start position:0% +but they come really close and the + + + align:start position:0% +but they come really close and the +larger m is the closer they come so in + + align:start position:0% +larger m is the closer they come so in + + + align:start position:0% +larger m is the closer they come so in +particular I can show the following + + align:start position:0% +particular I can show the following + + + align:start position:0% +particular I can show the following +statement that uh in any Nash + + align:start position:0% +statement that uh in any Nash + + + align:start position:0% +statement that uh in any Nash +equilibrium of the combined + + align:start position:0% +equilibrium of the combined + + + align:start position:0% +equilibrium of the combined +game uh if x use the total mass that uh + + align:start position:0% +game uh if x use the total mass that uh + + + align:start position:0% +game uh if x use the total mass that uh +the blue the red lawyer places on the + + align:start position:0% +the blue the red lawyer places on the + + + align:start position:0% +the blue the red lawyer places on the +sum of on the on the union of strategies + + align:start position:0% +sum of on the on the union of strategies + + + align:start position:0% +sum of on the on the union of strategies +of node U then that's about 1 /n but + + align:start position:0% +of node U then that's about 1 /n but + + + align:start position:0% +of node U then that's about 1 /n but +there is some error that decays with + + align:start position:0% +there is some error that decays with + + + align:start position:0% +there is some error that decays with +them and similarly for the blue + + align:start position:0% +them and similarly for the blue + + + align:start position:0% +them and similarly for the blue +lawyer right so + + align:start position:0% +lawyer right so + + + align:start position:0% +lawyer right so +approximately they're representing all + + align:start position:0% +approximately they're representing all + + + align:start position:0% +approximately they're representing all +their clients and if I choose M huge + + align:start position:0% +their clients and if I choose M huge + + + align:start position:0% +their clients and if I choose M huge +then at least my marginals are well + + align:start position:0% +then at least my marginals are well + + + align:start position:0% +then at least my marginals are well +defined now right so the there is + + align:start position:0% +defined now right so the there is + + + align:start position:0% +defined now right so the there is +probability Mass on every client and I + + align:start position:0% +probability Mass on every client and I + + + align:start position:0% +probability Mass on every client and I +can Define this marginal distributions + + align:start position:0% +can Define this marginal distributions + + + align:start position:0% +can Define this marginal distributions +now whether these distributions are + + align:start position:0% +now whether these distributions are + + + align:start position:0% +now whether these distributions are +useful or not we're about to + + align:start position:0% +useful or not we're about to + + + align:start position:0% +useful or not we're about to +see okay but what I'm saying here is + + align:start position:0% +see okay but what I'm saying here is + + + align:start position:0% +see okay but what I'm saying here is +that as far as deciding how to split + + align:start position:0% +that as far as deciding how to split + + + align:start position:0% +that as far as deciding how to split +the pie into my + + align:start position:0% +the pie into my + + + align:start position:0% +the pie into my +clients really the large game is what + + align:start position:0% +clients really the large game is what + + + align:start position:0% +clients really the large game is what +matters the high stakes game is what + + align:start position:0% +matters the high stakes game is what + + + align:start position:0% +matters the high stakes game is what +matters because if I make a + + align:start position:0% +matters because if I make a + + + align:start position:0% +matters because if I make a +mistake um you know m is huge so I'm + + align:start position:0% +mistake um you know m is huge so I'm + + + align:start position:0% +mistake um you know m is huge so I'm +hugely punished so for splitting for + + align:start position:0% +hugely punished so for splitting for + + + align:start position:0% +hugely punished so for splitting for +decide how to split my total unit of ma + + align:start position:0% +decide how to split my total unit of ma + + + align:start position:0% +decide how to split my total unit of ma +of probability Mass into my clients only + + align:start position:0% +of probability Mass into my clients only + + + align:start position:0% +of probability Mass into my clients only +the high stakes games M essentially only + + align:start position:0% +the high stakes games M essentially only + + + align:start position:0% +the high stakes games M essentially only +the high stakes games + + align:start position:0% +the high stakes games + + + align:start position:0% +the high stakes games +matter on on the other + + align:start position:0% +matter on on the other + + + align:start position:0% +matter on on the other +hand uh when it comes to + + align:start position:0% +hand uh when it comes to + + + align:start position:0% +hand uh when it comes to +you know having decided how how much + + align:start position:0% +you know having decided how how much + + + align:start position:0% +you know having decided how how much +mass to put on the union of a particular + + align:start position:0% +mass to put on the union of a particular + + + align:start position:0% +mass to put on the union of a particular +node strategies deciding you know about + + align:start position:0% +node strategies deciding you know about + + + align:start position:0% +node strategies deciding you know about +the fine grain you know the fine grain + + align:start position:0% +the fine grain you know the fine grain + + + align:start position:0% +the fine grain you know the fine grain +decision of how to allocate that + + align:start position:0% +decision of how to allocate that + + + align:start position:0% +decision of how to allocate that +uh uh XU into the different strategies + + align:start position:0% +uh uh XU into the different strategies + + + align:start position:0% +uh uh XU into the different strategies +of that node U then actually only the + + align:start position:0% +of that node U then actually only the + + + align:start position:0% +of that node U then actually only the +small game + + align:start position:0% +small game + + + align:start position:0% +small game +matters and the reason is that the pay + + align:start position:0% +matters and the reason is that the pay + + + align:start position:0% +matters and the reason is that the pay +of difference of the red let's say red + + align:start position:0% +of difference of the red let's say red + + + align:start position:0% +of difference of the red let's say red +lawyer + + align:start position:0% +lawyer + + + align:start position:0% +lawyer +uh uh from strategies UI and UJ so to + + align:start position:0% +uh uh from strategies UI and UJ so to + + + align:start position:0% +uh uh from strategies UI and UJ so to +distinguish between strategies I and J + + align:start position:0% +distinguish between strategies I and J + + + align:start position:0% +distinguish between strategies I and J +of node U the pay of difference between + + align:start position:0% +of node U the pay of difference between + + + align:start position:0% +of node U the pay of difference between +these two + + align:start position:0% +these two + + + align:start position:0% +these two +choices doesn't have m in it if you if + + align:start position:0% +choices doesn't have m in it if you if + + + align:start position:0% +choices doesn't have m in it if you if +you actually look at it m goes away + + align:start position:0% +you actually look at it m goes away + + + align:start position:0% +you actually look at it m goes away +there's no m in the pay of difference + + align:start position:0% +there's no m in the pay of difference + + + align:start position:0% +there's no m in the pay of difference +between this two + + align:start position:0% +between this two + + + align:start position:0% +between this two +options so which one is better doesn't + + align:start position:0% +options so which one is better doesn't + + + align:start position:0% +options so which one is better doesn't +have m in it okay um essentially it + + align:start position:0% +have m in it okay um essentially it + + + align:start position:0% +have m in it okay um essentially it +doesn't have m in it there is some m in + + align:start position:0% +doesn't have m in it there is some m in + + + align:start position:0% +doesn't have m in it there is some m in +here I mean cuz + + align:start position:0% +here I mean cuz + + + align:start position:0% +here I mean cuz +this uh you know I'm summing over all + + align:start position:0% +this uh you know I'm summing over all + + + align:start position:0% +this uh you know I'm summing over all +nodes and different nodes uh + + align:start position:0% +nodes and different nodes uh + + + align:start position:0% +nodes and different nodes uh +have different + + align:start position:0% +have different + + + align:start position:0% +have different +uh sum of uh probabilities + + align:start position:0% +uh sum of uh probabilities + + + align:start position:0% +uh sum of uh probabilities +but I'm going to get to that okay but + + align:start position:0% +but I'm going to get to that okay but + + + align:start position:0% +but I'm going to get to that okay but +trust me that uh when the red lawyer is + + align:start position:0% +trust me that uh when the red lawyer is + + + align:start position:0% +trust me that uh when the red lawyer is +trying to decide how to + + align:start position:0% +trying to decide how to + + + align:start position:0% +trying to decide how to +allocate uh uh this + + align:start position:0% +allocate uh uh this + + + align:start position:0% +allocate uh uh this +XU probability that he has decided to + + align:start position:0% +XU probability that he has decided to + + + align:start position:0% +XU probability that he has decided to +allocate on uh the different strategies + + align:start position:0% +allocate on uh the different strategies + + + align:start position:0% +allocate on uh the different strategies +of node U he looks at this difference + + align:start position:0% +of node U he looks at this difference + + + align:start position:0% +of node U he looks at this difference +that's the difference in the two payos + + align:start position:0% +that's the difference in the two payos + + + align:start position:0% +that's the difference in the two payos +and essentially there's no m in this + + align:start position:0% +and essentially there's no m in this + + + align:start position:0% +and essentially there's no m in this +equation so we're going to see where M + + align:start position:0% +equation so we're going to see where M + + + align:start position:0% +equation so we're going to see where M +gets into the picture and + + align:start position:0% +gets into the picture and + + + align:start position:0% +gets into the picture and +why but this is just from the definition + + align:start position:0% +why but this is just from the definition + + + align:start position:0% +why but this is just from the definition +of the game I claim this is exactly true + + align:start position:0% +of the game I claim this is exactly true + + + align:start position:0% +of the game I claim this is exactly true +the difference of the two payos is + + align:start position:0% +the difference of the two payos is + + + align:start position:0% +the difference of the two payos is +exactly this + + align:start position:0% + + + + align:start position:0% + +now from that equation it follows that + + align:start position:0% +now from that equation it follows that + + + align:start position:0% +now from that equation it follows that +if the lawyer decides to put positive + + align:start position:0% +if the lawyer decides to put positive + + + align:start position:0% +if the lawyer decides to put positive +probability Mass on a particular + + align:start position:0% +probability Mass on a particular + + + align:start position:0% +probability Mass on a particular +strategy I of that node then this for + + align:start position:0% +strategy I of that node then this for + + + align:start position:0% +strategy I of that node then this for +all JS for all alternative strategies of + + align:start position:0% +all JS for all alternative strategies of + + + align:start position:0% +all JS for all alternative strategies of +that note that he could choose it better + + align:start position:0% +that note that he could choose it better + + + align:start position:0% +that note that he could choose it better +be that this pay of difference is + + align:start position:0% +be that this pay of difference is + + + align:start position:0% +be that this pay of difference is +positive and that is really really looks + + align:start position:0% +positive and that is really really looks + + + align:start position:0% +positive and that is really really looks +like the condition of the the N + + align:start position:0% +like the condition of the the N + + + align:start position:0% +like the condition of the the N +equilibrium condition for the + + align:start position:0% +equilibrium condition for the + + + align:start position:0% +equilibrium condition for the +client if you think about it + + align:start position:0% +client if you think about it + + + align:start position:0% +client if you think about it +because if I Define you know the + + align:start position:0% +because if I Define you know the + + + align:start position:0% +because if I Define you know the +marginal + + align:start position:0% +marginal + + + align:start position:0% +marginal +probabilities of node you on these two + + align:start position:0% +probabilities of node you on these two + + + align:start position:0% +probabilities of node you on these two +strategies on on these + + align:start position:0% +strategies on on these + + + align:start position:0% +strategies on on these +strategies then this is really the Nash + + align:start position:0% +strategies then this is really the Nash + + + align:start position:0% +strategies then this is really the Nash +equ then you know the Nash equilibrium + + align:start position:0% +equ then you know the Nash equilibrium + + + align:start position:0% +equ then you know the Nash equilibrium +condition for that node + + align:start position:0% +condition for that node + + + align:start position:0% +condition for that node +U and the only the only problem is to go + + align:start position:0% +U and the only the only problem is to go + + + align:start position:0% +U and the only the only problem is to go +from this equation for the unmarinated + + align:start position:0% + + + + align:start position:0% + +the problem is that uh these xvs are not + + align:start position:0% +the problem is that uh these xvs are not + + + align:start position:0% +the problem is that uh these xvs are not +all + + align:start position:0% +all + + + align:start position:0% +all +equal y y vs are not all equal so I + + align:start position:0% +equal y y vs are not all equal so I + + + align:start position:0% +equal y y vs are not all equal so I +cannot just divide by 1 /n and claim + + align:start position:0% +cannot just divide by 1 /n and claim + + + align:start position:0% +cannot just divide by 1 /n and claim +that the equation is still true but + + align:start position:0% +that the equation is still true but + + + align:start position:0% +that the equation is still true but +because but the point is that this uh + + align:start position:0% +because but the point is that this uh + + + align:start position:0% +because but the point is that this uh +error doesn't create too much problems + + align:start position:0% +error doesn't create too much problems + + + align:start position:0% +error doesn't create too much problems +in the equilibrium conditions and okay + + align:start position:0% +in the equilibrium conditions and okay + + + align:start position:0% +in the equilibrium conditions and okay +it's not going to be an exact NCH + + align:start position:0% +it's not going to be an exact NCH + + + align:start position:0% +it's not going to be an exact NCH +equilibrium for the polymetric game but + + align:start position:0% +equilibrium for the polymetric game but + + + align:start position:0% +equilibrium for the polymetric game but +it's going to be an approximate one and + + align:start position:0% +it's going to be an approximate one and + + + align:start position:0% +it's going to be an approximate one and +um because I can take M to be as large + + align:start position:0% +um because I can take M to be as large + + + align:start position:0% +um because I can take M to be as large +as I want I can make this approximation + + align:start position:0% +as I want I can make this approximation + + + align:start position:0% +as I want I can make this approximation +go to zero as as fast as I want and you + + align:start position:0% +go to zero as as fast as I want and you + + + align:start position:0% +go to zero as as fast as I want and you +know remember this arithmetic circuit + + align:start position:0% +know remember this arithmetic circuit + + + align:start position:0% +know remember this arithmetic circuit +side problem allowed some error in it so + + align:start position:0% +side problem allowed some error in it so + + + align:start position:0% +side problem allowed some error in it so +what effectively is going to happen here + + align:start position:0% +what effectively is going to happen here + + + align:start position:0% +what effectively is going to happen here +is that okay so I'm going to get an + + align:start position:0% +is that okay so I'm going to get an + + + align:start position:0% +is that okay so I'm going to get an +approximate equilibrium of the + + align:start position:0% +approximate equilibrium of the + + + align:start position:0% +approximate equilibrium of the +polymetric game so that would correspond + + align:start position:0% +polymetric game so that would correspond + + + align:start position:0% +polymetric game so that would correspond +to an approximate equilibrium of the + + align:start position:0% +to an approximate equilibrium of the + + + align:start position:0% +to an approximate equilibrium of the +arithmetic s problem I started with but + + align:start position:0% +arithmetic s problem I started with but + + + align:start position:0% +arithmetic s problem I started with but +this approximation can be accommodated + + align:start position:0% +this approximation can be accommodated + + + align:start position:0% +this approximation can be accommodated +and the problem is still ppad + + align:start position:0% +and the problem is still ppad + + + align:start position:0% +and the problem is still ppad +hard so that's approximately how the + + align:start position:0% +hard so that's approximately how the + + + align:start position:0% +hard so that's approximately how the +argument works so this uh you + + align:start position:0% +argument works so this uh you + + + align:start position:0% +argument works so this uh you +know the fact that the distributions + + align:start position:0% +know the fact that the distributions + + + align:start position:0% +know the fact that the distributions +aren't uniform doesn't really matter as + + align:start position:0% +aren't uniform doesn't really matter as + + + align:start position:0% +aren't uniform doesn't really matter as +long as m is chosen large + + align:start position:0% +long as m is chosen large + + + align:start position:0% +long as m is chosen large +enough I went a bit too fast so I want + + align:start position:0% +enough I went a bit too fast so I want + + + align:start position:0% +enough I went a bit too fast so I want +to I I didn't mean this to be sort of + + align:start position:0% +to I I didn't mean this to be sort of + + + align:start position:0% +to I I didn't mean this to be sort of +like uh very detailed but I meant to + + align:start position:0% +like uh very detailed but I meant to + + + align:start position:0% +like uh very detailed but I meant to +convey the you know bigger picture and + + align:start position:0% +convey the you know bigger picture and + + + align:start position:0% +convey the you know bigger picture and +the bigger picture basically says that + + align:start position:0% +the bigger picture basically says that + + + align:start position:0% +the bigger picture basically says that +you can analyze what happens in this + + align:start position:0% +you can analyze what happens in this + + + align:start position:0% +you can analyze what happens in this +lower game + + align:start position:0% +lower game + + + align:start position:0% +lower game +in two steps in one step you argue that + + align:start position:0% +in two steps in one step you argue that + + + align:start position:0% +in two steps in one step you argue that +the lawyers approximately represent all + + align:start position:0% +the lawyers approximately represent all + + + align:start position:0% +the lawyers approximately represent all +their + + align:start position:0% +their + + + align:start position:0% +their +clients in the other step you have to + + align:start position:0% +clients in the other step you have to + + + align:start position:0% +clients in the other step you have to +decide how these lawyers + + align:start position:0% +decide how these lawyers + + + align:start position:0% +decide how these lawyers +allocate uh their uh probabilities to + + align:start position:0% +allocate uh their uh probabilities to + + + align:start position:0% +allocate uh their uh probabilities to +the different strategies of a particular + + align:start position:0% +the different strategies of a particular + + + align:start position:0% +the different strategies of a particular +node so that leads you to write down + + align:start position:0% +node so that leads you to write down + + + align:start position:0% +node so that leads you to write down +this difference of payoffs that the + + align:start position:0% +this difference of payoffs that the + + + align:start position:0% +this difference of payoffs that the +lawyer is experiencing when he switches + + align:start position:0% +lawyer is experiencing when he switches + + + align:start position:0% +lawyer is experiencing when he switches +uh the the you know + + align:start position:0% +uh the the you know + + + align:start position:0% +uh the the you know +this is tracking how much better the + + align:start position:0% +this is tracking how much better the + + + align:start position:0% +this is tracking how much better the +expected payoff from this strategy is + + align:start position:0% +expected payoff from this strategy is + + + align:start position:0% +expected payoff from this strategy is +compared to that + + align:start position:0% +compared to that + + + align:start position:0% +compared to that +strategy and by the equilibrium + + align:start position:0% +strategy and by the equilibrium + + + align:start position:0% +strategy and by the equilibrium +conditions of the lower game you get the + + align:start position:0% +conditions of the lower game you get the + + + align:start position:0% +conditions of the lower game you get the +inequality I showed in the next slide uh + + align:start position:0% +inequality I showed in the next slide uh + + + align:start position:0% +inequality I showed in the next slide uh +that if the lawyer decides to place + + align:start position:0% +that if the lawyer decides to place + + + align:start position:0% +that if the lawyer decides to place +positive probability Mass to a strategy + + align:start position:0% +positive probability Mass to a strategy + + + align:start position:0% +positive probability Mass to a strategy +I of node du then it must be that there + + align:start position:0% +I of node du then it must be that there + + + align:start position:0% +I of node du then it must be that there +is no alternative + + align:start position:0% +is no alternative + + + align:start position:0% +is no alternative +strategy uh UJ that would give him the + + align:start position:0% +strategy uh UJ that would give him the + + + align:start position:0% +strategy uh UJ that would give him the +better payoff so you get get this + + align:start position:0% +better payoff so you get get this + + + align:start position:0% +better payoff so you get get this +condition and that's essentially what + + align:start position:0% +condition and that's essentially what + + + align:start position:0% +condition and that's essentially what +that's essentially the equilibrium + + align:start position:0% +that's essentially the equilibrium + + + align:start position:0% +that's essentially the equilibrium +condition for the polymatrix game except + + align:start position:0% +condition for the polymatrix game except + + + align:start position:0% +condition for the polymatrix game except +that you need to normalize these guys + + align:start position:0% +that you need to normalize these guys + + + align:start position:0% +that you need to normalize these guys +and when you try to normalize these guys + + align:start position:0% +and when you try to normalize these guys + + + align:start position:0% +and when you try to normalize these guys +you run into the problem that uh you you + + align:start position:0% +you run into the problem that uh you you + + + align:start position:0% +you run into the problem that uh you you +know the lawers don't don't don't play + + align:start position:0% +know the lawers don't don't don't play + + + align:start position:0% +know the lawers don't don't don't play +uh uniform strategies over their clients + + align:start position:0% +uh uniform strategies over their clients + + + align:start position:0% +uh uniform strategies over their clients +but they approxim but they play + + align:start position:0% +but they approxim but they play + + + align:start position:0% +but they approxim but they play +approximately uniform distribution of + + align:start position:0% +approximately uniform distribution of + + + align:start position:0% +approximately uniform distribution of +their clients so this inequality gets + + align:start position:0% +their clients so this inequality gets + + + align:start position:0% +their clients so this inequality gets +messed up a little bit so effectively + + align:start position:0% +messed up a little bit so effectively + + + align:start position:0% +messed up a little bit so effectively +that means that the players are almost + + align:start position:0% +that means that the players are almost + + + align:start position:0% +that means that the players are almost +best + + align:start position:0% +best + + + align:start position:0% +best +responding the marginal distributions + + align:start position:0% +responding the marginal distributions + + + align:start position:0% +responding the marginal distributions +are an approximate Nas equilibrium of + + align:start position:0% +are an approximate Nas equilibrium of + + + align:start position:0% +are an approximate Nas equilibrium of +the polymatrix game hence uh you know + + align:start position:0% +the polymatrix game hence uh you know + + + align:start position:0% +the polymatrix game hence uh you know +also because the polymatrix game came + + align:start position:0% +also because the polymatrix game came + + + align:start position:0% +also because the polymatrix game came +from a arithmetic circuit s problem an + + align:start position:0% +from a arithmetic circuit s problem an + + + align:start position:0% +from a arithmetic circuit s problem an +approximate evaluation of that problem + + align:start position:0% +approximate evaluation of that problem + + + align:start position:0% +approximate evaluation of that problem +but the these are all PP hard as I + + align:start position:0% +but the these are all PP hard as I + + + align:start position:0% +but the these are all PP hard as I +pointed out earlier that's the high + + align:start position:0% +pointed out earlier that's the high + + + align:start position:0% +pointed out earlier that's the high +level + + align:start position:0% +level + + + align:start position:0% +level +idea and you know trust me the details + + align:start position:0% +idea and you know trust me the details + + + align:start position:0% +idea and you know trust me the details +are not hard at all okay so uh you just + + align:start position:0% +are not hard at all okay so uh you just + + + align:start position:0% +are not hard at all okay so uh you just +have to trust me that you know uh + + align:start position:0% +have to trust me that you know uh + + + align:start position:0% +have to trust me that you know uh +approximate uniform distributions the + + align:start position:0% +approximate uniform distributions the + + + align:start position:0% +approximate uniform distributions the +approximate uniform distributions that I + + align:start position:0% +approximate uniform distributions that I + + + align:start position:0% +approximate uniform distributions that I +claim are true and that dividing you + + align:start position:0% +claim are true and that dividing you + + + align:start position:0% +claim are true and that dividing you +know dividing by you know approximately + + align:start position:0% +know dividing by you know approximately + + + align:start position:0% +know dividing by you know approximately +one over and here doesn't mess up this + + align:start position:0% +one over and here doesn't mess up this + + + align:start position:0% +one over and here doesn't mess up this +condition too + + align:start position:0% + + + + align:start position:0% + +much so this was this was the end of the + + align:start position:0% +much so this was this was the end of the + + + align:start position:0% +much so this was this was the end of the +proof basically that's that's basically + + align:start position:0% +proof basically that's that's basically + + + align:start position:0% +proof basically that's that's basically +how the proof goes so if you + + align:start position:0% +how the proof goes so if you + + + align:start position:0% +how the proof goes so if you +have if you have this it's easy to to do + + align:start position:0% +have if you have this it's easy to to do + + + align:start position:0% +have if you have this it's easy to to do +do this and then it's easy to go here + + align:start position:0% +do this and then it's easy to go here + + + align:start position:0% +do this and then it's easy to go here +now um any + + align:start position:0% +now um any + + + align:start position:0% +now um any +questions now the reduction of show you + + align:start position:0% +questions now the reduction of show you + + + align:start position:0% +questions now the reduction of show you +was not from the original paper it was + + align:start position:0% +was not from the original paper it was + + + align:start position:0% +was not from the original paper it was +from uh it was established by followup + + align:start position:0% +from uh it was established by followup + + + align:start position:0% +from uh it was established by followup +paper by Chen and Deng in our original + + align:start position:0% +paper by Chen and Deng in our original + + + align:start position:0% +paper by Chen and Deng in our original +paper we actually reduc took this + + align:start position:0% +paper we actually reduc took this + + + align:start position:0% +paper we actually reduc took this +problem and reduced it to four player + + align:start position:0% +problem and reduced it to four player + + + align:start position:0% +problem and reduced it to four player +Nash uh and the only reason the proof is + + align:start position:0% +Nash uh and the only reason the proof is + + + align:start position:0% +Nash uh and the only reason the proof is +identical to the one I showed you the + + align:start position:0% +identical to the one I showed you the + + + align:start position:0% +identical to the one I showed you the +only reason that we went to four players + + align:start position:0% +only reason that we went to four players + + + align:start position:0% +only reason that we went to four players +instead of two players is that but uh we + + align:start position:0% +instead of two players is that but uh we + + + align:start position:0% +instead of two players is that but uh we +had uh our our gadgets were four partite + + align:start position:0% +had uh our our gadgets were four partite + + + align:start position:0% +had uh our our gadgets were four partite +instead of bipartite so we had four + + align:start position:0% +instead of bipartite so we had four + + + align:start position:0% +instead of bipartite so we had four +colors and four lawyers now what do we + + align:start position:0% +colors and four lawyers now what do we + + + align:start position:0% +colors and four lawyers now what do we +have four P parte gadgets where we were + + align:start position:0% +have four P parte gadgets where we were + + + align:start position:0% +have four P parte gadgets where we were +being a bit silly okay so uh we had uh + + align:start position:0% +being a bit silly okay so uh we had uh + + + align:start position:0% +being a bit silly okay so uh we had uh +in our arithmetic circuit we had an + + align:start position:0% +in our arithmetic circuit we had an + + + align:start position:0% +in our arithmetic circuit we had an +extra gate which was multiplication not + + align:start position:0% +extra gate which was multiplication not + + + align:start position:0% +extra gate which was multiplication not +by constant but multiplication of two + + align:start position:0% +by constant but multiplication of two + + + align:start position:0% +by constant but multiplication of two +numbers and you can show that this but + + align:start position:0% +numbers and you can show that this but + + + align:start position:0% +numbers and you can show that this but +but we didn't use it so we're being a + + align:start position:0% +but we didn't use it so we're being a + + + align:start position:0% +but we didn't use it so we're being a +bit silly Okay so + + align:start position:0% +bit silly Okay so + + + align:start position:0% +bit silly Okay so +we had this uh Gadget here that we + + align:start position:0% +we had this uh Gadget here that we + + + align:start position:0% +we had this uh Gadget here that we +weren't using and it was hard to mop it + + align:start position:0% +weren't using and it was hard to mop it + + + align:start position:0% +weren't using and it was hard to mop it +down it was actually it's impossible to + + align:start position:0% +down it was actually it's impossible to + + + align:start position:0% +down it was actually it's impossible to +make it into a bipartite gadget okay so + + align:start position:0% +make it into a bipartite gadget okay so + + + align:start position:0% +make it into a bipartite gadget okay so +you know in our original paper we made + + align:start position:0% +you know in our original paper we made + + + align:start position:0% +you know in our original paper we made +it into a four partide Gadget and then + + align:start position:0% +it into a four partide Gadget and then + + + align:start position:0% +it into a four partide Gadget and then +in a followup paper we actually managed + + align:start position:0% +in a followup paper we actually managed + + + align:start position:0% +in a followup paper we actually managed +to reduce it to a three partite Gadget + + align:start position:0% +to reduce it to a three partite Gadget + + + align:start position:0% +to reduce it to a three partite Gadget +but then this multiplication Gadget + + align:start position:0% +but then this multiplication Gadget + + + align:start position:0% +but then this multiplication Gadget +actually you can show cannot be reduced + + align:start position:0% +actually you can show cannot be reduced + + + align:start position:0% +actually you can show cannot be reduced +to bipartite so these guys observe that + + align:start position:0% +to bipartite so these guys observe that + + + align:start position:0% +to bipartite so these guys observe that +actually we are not using multiplication + + align:start position:0% +actually we are not using multiplication + + + align:start position:0% +actually we are not using multiplication +so uh you know you can Implement all + + align:start position:0% +so uh you know you can Implement all + + + align:start position:0% +so uh you know you can Implement all +gadgets that we actually use with bipar + + align:start position:0% +gadgets that we actually use with bipar + + + align:start position:0% +gadgets that we actually use with bipar +grow so you can go down to two two + + align:start position:0% +grow so you can go down to two two + + + align:start position:0% +grow so you can go down to two two +lawyers instead of three lawyers okay so + + align:start position:0% +lawyers instead of three lawyers okay so + + + align:start position:0% +lawyers instead of three lawyers okay so +you know it was uh you know it felt like + + align:start position:0% +you know it was uh you know it felt like + + + align:start position:0% +you know it was uh you know it felt like +leaving money on the table but uh it's + + align:start position:0% +leaving money on the table but uh it's + + + align:start position:0% +leaving money on the table but uh it's +okay + + align:start position:0% +okay + + + align:start position:0% +okay +cool uh okay that's my discussion of the + + align:start position:0% +cool uh okay that's my discussion of the + + + align:start position:0% +cool uh okay that's my discussion of the +pbd completeness of + + align:start position:0% +pbd completeness of + + + align:start position:0% +pbd completeness of +Nash yeah obviously uh zero some games + + align:start position:0% +Nash yeah obviously uh zero some games + + + align:start position:0% +Nash yeah obviously uh zero some games +it's easy to find an equilibrium um is + + align:start position:0% +it's easy to find an equilibrium um is + + + align:start position:0% +it's easy to find an equilibrium um is +is there something in between zero some + + align:start position:0% +is there something in between zero some + + + align:start position:0% +is there something in between zero some +games and general two player games for + + align:start position:0% +games and general two player games for + + + align:start position:0% +games and general two player games for +which any hardness result is + + align:start position:0% + + + + align:start position:0% + +known uh yeah so a natural way to uh + + align:start position:0% +known uh yeah so a natural way to uh + + + align:start position:0% +known uh yeah so a natural way to uh +interpolate between Zero Sum games and + + align:start position:0% +interpolate between Zero Sum games and + + + align:start position:0% +interpolate between Zero Sum games and +um General two-player games is the + + align:start position:0% +um General two-player games is the + + + align:start position:0% +um General two-player games is the +following so in a in a zero sum games + + align:start position:0% +following so in a in a zero sum games + + + align:start position:0% +following so in a in a zero sum games +let's call R and see the pay of matrices + + align:start position:0% +let's call R and see the pay of matrices + + + align:start position:0% +let's call R and see the pay of matrices +of the two players the game is zero sum + + align:start position:0% +of the two players the game is zero sum + + + align:start position:0% +of the two players the game is zero sum +if r plus C the sum of these two + + align:start position:0% +if r plus C the sum of these two + + + align:start position:0% +if r plus C the sum of these two +matrices is identically zero as as I + + align:start position:0% +matrices is identically zero as as I + + + align:start position:0% +matrices is identically zero as as I +showed as I claimed in the very first + + align:start position:0% +showed as I claimed in the very first + + + align:start position:0% +showed as I claimed in the very first +slide I gave last time now uh you can + + align:start position:0% +slide I gave last time now uh you can + + + align:start position:0% +slide I gave last time now uh you can +call a game + + align:start position:0% +call a game + + + align:start position:0% +call a game +rank + + align:start position:0% +rank + + + align:start position:0% +rank +R if r + C has + + align:start position:0% + + + + align:start position:0% + +rank + + align:start position:0% +rank + + + align:start position:0% +rank +R okay now what is known is that rank + + align:start position:0% +R okay now what is known is that rank + + + align:start position:0% +R okay now what is known is that rank +one game + + align:start position:0% +one game + + + align:start position:0% +one game +can be solved in + + align:start position:0% + + + + align:start position:0% + +p uh I believe that it's known that rank + + align:start position:0% +p uh I believe that it's known that rank + + + align:start position:0% +p uh I believe that it's known that rank +three + + align:start position:0% + + + + align:start position:0% + +games are PPD + + align:start position:0% + + + + align:start position:0% + +hard and you should look at the paper by + + align:start position:0% +hard and you should look at the paper by + + + align:start position:0% +hard and you should look at the paper by +rout Sorry by met rout + + align:start position:0% +rout Sorry by met rout + + + align:start position:0% +rout Sorry by met rout +meta in 14 I + + align:start position:0% +meta in 14 I + + + align:start position:0% +meta in 14 I +believe where she shows that she might + + align:start position:0% +believe where she shows that she might + + + align:start position:0% +believe where she shows that she might +might even be showing two rank two but + + align:start position:0% +might even be showing two rank two but + + + align:start position:0% +might even be showing two rank two but +I'm not sure maybe there is some uh Gap + + align:start position:0% +I'm not sure maybe there is some uh Gap + + + align:start position:0% +I'm not sure maybe there is some uh Gap +there maybe maybe it's even + + align:start position:0% +there maybe maybe it's even + + + align:start position:0% +there maybe maybe it's even +uh okay you know so there is a constant + + align:start position:0% +uh okay you know so there is a constant + + + align:start position:0% +uh okay you know so there is a constant +where it's already pretty + + align:start position:0% +where it's already pretty + + + align:start position:0% +where it's already pretty +hard um + + align:start position:0% +hard um + + + align:start position:0% +hard um +right and and you know while I'm here I + + align:start position:0% +right and and you know while I'm here I + + + align:start position:0% +right and and you know while I'm here I +mean if you're interested in interest I + + align:start position:0% +mean if you're interested in interest I + + + align:start position:0% +mean if you're interested in interest I +mean an interesting open question + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +uh approximate equilibria so interesting + + align:start position:0% +uh approximate equilibria so interesting + + + align:start position:0% +uh approximate equilibria so interesting +open + + align:start position:0% + + + + align:start position:0% + +problem so approximate Nash + + align:start position:0% + + + + align:start position:0% + +equilibria uh even in two- player games + + align:start position:0% +equilibria uh even in two- player games + + + align:start position:0% +equilibria uh even in two- player games +we don't know how to find them so let me + + align:start position:0% +we don't know how to find them so let me + + + align:start position:0% +we don't know how to find them so let me +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh remind you what this is so a Nal + + align:start position:0% +uh remind you what this is so a Nal + + + align:start position:0% +uh remind you what this is so a Nal +equilibrium is a pair of strategies such + + align:start position:0% +equilibrium is a pair of strategies such + + + align:start position:0% +equilibrium is a pair of strategies such +that no one has an incentive to change + + align:start position:0% +that no one has an incentive to change + + + align:start position:0% +that no one has an incentive to change +his randomization given uh what the + + align:start position:0% +his randomization given uh what the + + + align:start position:0% +his randomization given uh what the +other player is doing and Epsilon n + + align:start position:0% +other player is doing and Epsilon n + + + align:start position:0% +other player is doing and Epsilon n +equilibrium is + + align:start position:0% +equilibrium is + + + align:start position:0% +equilibrium is +uh uh when these conditions are true to + + align:start position:0% +uh uh when these conditions are true to + + + align:start position:0% +uh uh when these conditions are true to +within an addtive Epsilon okay so no + + align:start position:0% +within an addtive Epsilon okay so no + + + align:start position:0% +within an addtive Epsilon okay so no +player has incentive to to more than + + align:start position:0% +player has incentive to to more than + + + align:start position:0% +player has incentive to to more than +Epsilon additive Epsilon incentive to + + align:start position:0% +Epsilon additive Epsilon incentive to + + + align:start position:0% +Epsilon additive Epsilon incentive to +change his + + align:start position:0% +change his + + + align:start position:0% +change his +strategies now + + align:start position:0% +strategies now + + + align:start position:0% +strategies now +uh okay so atmost + + align:start position:0% + + + + align:start position:0% + +additive Epsilon incentive to + + align:start position:0% + + + + align:start position:0% + +change now what do we know about uh this + + align:start position:0% +change now what do we know about uh this + + + align:start position:0% +change now what do we know about uh this +problems well if if uh you know if the + + align:start position:0% +problems well if if uh you know if the + + + align:start position:0% +problems well if if uh you know if the +input to your problem is a game and an + + align:start position:0% +input to your problem is a game and an + + + align:start position:0% +input to your problem is a game and an +Epsilon then it follows from the those + + align:start position:0% +Epsilon then it follows from the those + + + align:start position:0% +Epsilon then it follows from the those +results that that's PPD complete + + align:start position:0% +results that that's PPD complete + + + align:start position:0% +results that that's PPD complete +okay uh now it's even true that if your + + align:start position:0% +okay uh now it's even true that if your + + + align:start position:0% +okay uh now it's even true that if your +input is a game and you have a predeter + + align:start position:0% +input is a game and you have a predeter + + + align:start position:0% +input is a game and you have a predeter +pre-specified Epsilon that's inverse + + align:start position:0% +pre-specified Epsilon that's inverse + + + align:start position:0% +pre-specified Epsilon that's inverse +polinomial in the size of the game so + + align:start position:0% +polinomial in the size of the game so + + + align:start position:0% +polinomial in the size of the game so +the the G the input is a game and there + + align:start position:0% +the the G the input is a game and there + + + align:start position:0% +the the G the input is a game and there +is a um an inverse polinomial function + + align:start position:0% +is a um an inverse polinomial function + + + align:start position:0% +is a um an inverse polinomial function +and that's your Epsilon and you want to + + align:start position:0% +and that's your Epsilon and you want to + + + align:start position:0% +and that's your Epsilon and you want to +find an inverse polinomial n equilibrium + + align:start position:0% +find an inverse polinomial n equilibrium + + + align:start position:0% +find an inverse polinomial n equilibrium +of this given game that's still pbd + + align:start position:0% +of this given game that's still pbd + + + align:start position:0% +of this given game that's still pbd +complete but what is not known is + + align:start position:0% +complete but what is not known is + + + align:start position:0% +complete but what is not known is +Epsilon + + align:start position:0% + + + + align:start position:0% + +constant how hard is it to find find + + align:start position:0% +constant how hard is it to find find + + + align:start position:0% +constant how hard is it to find find +equilibria when Epsilon is a + + align:start position:0% +equilibria when Epsilon is a + + + align:start position:0% +equilibria when Epsilon is a +constant and if your + + align:start position:0% +constant and if your + + + align:start position:0% +constant and if your +matrices have entries in uh + + align:start position:0% + + + + align:start position:0% + +01 then we know how to do this in time n + + align:start position:0% +01 then we know how to do this in time n + + + align:start position:0% +01 then we know how to do this in time n +to the order log + + align:start position:0% +to the order log + + + align:start position:0% +to the order log +n over Epsilon + + align:start position:0% + + + + align:start position:0% + +s we know that there is no fptas for the + + align:start position:0% +s we know that there is no fptas for the + + + align:start position:0% +s we know that there is no fptas for the +problem uh because uh of uh actually + + align:start position:0% +problem uh because uh of uh actually + + + align:start position:0% +problem uh because uh of uh actually +this results + + align:start position:0% +this results + + + align:start position:0% +this results +uh followup results to this results what + + align:start position:0% +uh followup results to this results what + + + align:start position:0% +uh followup results to this results what +I what I claimed earlier about inverse + + align:start position:0% +I what I claimed earlier about inverse + + + align:start position:0% +I what I claimed earlier about inverse +polinomial accuracy prohibits an fpas + + align:start position:0% +polinomial accuracy prohibits an fpas + + + align:start position:0% +polinomial accuracy prohibits an fpas +for the + + align:start position:0% +for the + + + align:start position:0% +for the +problem uh but a pasas is possible what + + align:start position:0% +problem uh but a pasas is possible what + + + align:start position:0% +problem uh but a pasas is possible what +we have is a quasi pasas so if you have + + align:start position:0% +we have is a quasi pasas so if you have + + + align:start position:0% +we have is a quasi pasas so if you have +an nend strategy game and you're + + align:start position:0% +an nend strategy game and you're + + + align:start position:0% +an nend strategy game and you're +interested in some constant Epsilon then + + align:start position:0% +interested in some constant Epsilon then + + + align:start position:0% +interested in some constant Epsilon then +we can get you an Epsilon n equilibrium + + align:start position:0% +we can get you an Epsilon n equilibrium + + + align:start position:0% +we can get you an Epsilon n equilibrium +n to the log over Epsilon squ time and + + align:start position:0% +n to the log over Epsilon squ time and + + + align:start position:0% +n to the log over Epsilon squ time and +because I'm looking at additive epsilons + + align:start position:0% +because I'm looking at additive epsilons + + + align:start position:0% +because I'm looking at additive epsilons +I'm also normalizing my payoffs to be 01 + + align:start position:0% +I'm also normalizing my payoffs to be 01 + + + align:start position:0% +I'm also normalizing my payoffs to be 01 +so that Epsilon is related to the + + align:start position:0% +so that Epsilon is related to the + + + align:start position:0% +so that Epsilon is related to the +maximum payoff of the + + align:start position:0% +maximum payoff of the + + + align:start position:0% +maximum payoff of the +game so that's what we have and it's a + + align:start position:0% +game so that's what we have and it's a + + + align:start position:0% +game so that's what we have and it's a +you know great open problem if you can + + align:start position:0% +you know great open problem if you can + + + align:start position:0% +you know great open problem if you can +improve + + align:start position:0% +improve + + + align:start position:0% +improve +this um or or you know or show a lower + + align:start position:0% +this um or or you know or show a lower + + + align:start position:0% +this um or or you know or show a lower +bound okay that's a great open + + align:start position:0% +bound okay that's a great open + + + align:start position:0% +bound okay that's a great open +problem uh speaking of which uh if the + + align:start position:0% +problem uh speaking of which uh if the + + + align:start position:0% +problem uh speaking of which uh if the +rank of this game is up to I believe + + align:start position:0% +rank of this game is up to I believe + + + align:start position:0% +rank of this game is up to I believe +logarithmic we know how to get a + + align:start position:0% + + + + align:start position:0% + +pasas + + align:start position:0% +pasas + + + align:start position:0% +pasas +okay now I don't have too much time left + + align:start position:0% +okay now I don't have too much time left + + + align:start position:0% +okay now I don't have too much time left +so uh I guess I had two options uh for + + align:start position:0% +so uh I guess I had two options uh for + + + align:start position:0% +so uh I guess I had two options uh for +today one was to talk about uh different + + align:start position:0% +today one was to talk about uh different + + + align:start position:0% +today one was to talk about uh different +problems that you can show PPD + + align:start position:0% +problems that you can show PPD + + + align:start position:0% +problems that you can show PPD +hard um + + align:start position:0% +hard um + + + align:start position:0% +hard um +or to talk about other existence + + align:start position:0% +or to talk about other existence + + + align:start position:0% +or to talk about other existence +arguments and I think I only have time + + align:start position:0% +arguments and I think I only have time + + + align:start position:0% +arguments and I think I only have time +for one of the two so you know uh right + + align:start position:0% +for one of the two so you know uh right + + + align:start position:0% +for one of the two so you know uh right +so one is + + align:start position:0% +so one is + + + align:start position:0% +so one is +to uh the other option is to show other + + align:start position:0% +to uh the other option is to show other + + + align:start position:0% +to uh the other option is to show other +arguments of existence in tfmp so two + + align:start position:0% +arguments of existence in tfmp so two + + + align:start position:0% +arguments of existence in tfmp so two +examples or other + + align:start position:0% +examples or other + + + align:start position:0% +examples or other +arguments what do you guys + + align:start position:0% + + + + align:start position:0% + +vote so who wants two other + + align:start position:0% +vote so who wants two other + + + align:start position:0% +vote so who wants two other +examples okay who's keeping the + + align:start position:0% +examples okay who's keeping the + + + align:start position:0% +examples okay who's keeping the +count Okay who wants other exist + + align:start position:0% + + + + align:start position:0% + +arguments okay so I think there's uh a + + align:start position:0% +arguments okay so I think there's uh a + + + align:start position:0% +arguments okay so I think there's uh a +slight majority for other existence + + align:start position:0% +slight majority for other existence + + + align:start position:0% +slight majority for other existence +arguments so I'm going to show + + align:start position:0% +arguments so I'm going to show + + + align:start position:0% +arguments so I'm going to show +that okay + + align:start position:0% +that okay + + + align:start position:0% +that okay +so uh cool so PPD is founded on the + + align:start position:0% +so uh cool so PPD is founded on the + + + align:start position:0% +so uh cool so PPD is founded on the +directed parity + + align:start position:0% +directed parity + + + align:start position:0% +directed parity +argument other natural arguments of + + align:start position:0% +argument other natural arguments of + + + align:start position:0% +argument other natural arguments of +existence uh in combinatorics are the + + align:start position:0% +existence uh in combinatorics are the + + + align:start position:0% +existence uh in combinatorics are the +following and each of them is going to + + align:start position:0% +following and each of them is going to + + + align:start position:0% +following and each of them is going to +correspond to a different complexity + + align:start position:0% +correspond to a different complexity + + + align:start position:0% +correspond to a different complexity +class + + align:start position:0% +class + + + align:start position:0% +class +this is a parity argument on an + + align:start position:0% +this is a parity argument on an + + + align:start position:0% +this is a parity argument on an +undirected graph if an undirected graph + + align:start position:0% +undirected graph if an undirected graph + + + align:start position:0% +undirected graph if an undirected graph +has a node of odd degree then it must + + align:start position:0% +has a node of odd degree then it must + + + align:start position:0% +has a node of odd degree then it must +have another node of degree also also + + align:start position:0% +have another node of degree also also + + + align:start position:0% +have another node of degree also also +known as the handshaking L I + + align:start position:0% +known as the handshaking L I + + + align:start position:0% +known as the handshaking L I +believe + + align:start position:0% +believe + + + align:start position:0% +believe +um well this is another simple one if a + + align:start position:0% +um well this is another simple one if a + + + align:start position:0% +um well this is another simple one if a +dag you know any dag has a + + align:start position:0% +dag you know any dag has a + + + align:start position:0% +dag you know any dag has a +sync that's going to give rise to the + + align:start position:0% +sync that's going to give rise to the + + + align:start position:0% +sync that's going to give rise to the +class + + align:start position:0% +class + + + align:start position:0% +class +PS uh and that's the pigeon hole + + align:start position:0% +PS uh and that's the pigeon hole + + + align:start position:0% +PS uh and that's the pigeon hole +principle if you have a function mapping + + align:start position:0% +principle if you have a function mapping + + + align:start position:0% +principle if you have a function mapping +n elements to n minus one elements then + + align:start position:0% +n elements to n minus one elements then + + + align:start position:0% +n elements to n minus one elements then +there is a collision that's going to + + align:start position:0% +there is a collision that's going to + + + align:start position:0% +there is a collision that's going to +give rise to PPP so PPA stands for + + align:start position:0% +give rise to PPP so PPA stands for + + + align:start position:0% +give rise to PPP so PPA stands for +polinomial parity on undirected graphs + + align:start position:0% +polinomial parity on undirected graphs + + + align:start position:0% +polinomial parity on undirected graphs +PLS polinomial local search PPP + + align:start position:0% +PLS polinomial local search PPP + + + align:start position:0% +PLS polinomial local search PPP +polinomial pigion + + align:start position:0% +polinomial pigion + + + align:start position:0% +polinomial pigion +principle and uh I'm going to Define + + align:start position:0% +principle and uh I'm going to Define + + + align:start position:0% +principle and uh I'm going to Define +them formally in the next few slides + + align:start position:0% +them formally in the next few slides + + + align:start position:0% +them formally in the next few slides +okay so I'm going to start with PPA just + + align:start position:0% +okay so I'm going to start with PPA just + + + align:start position:0% +okay so I'm going to start with PPA just +because it's very similar to ppad except + + align:start position:0% +because it's very similar to ppad except + + + align:start position:0% +because it's very similar to ppad except +there's no + + align:start position:0% +there's no + + + align:start position:0% +there's no +Direction uh and um + + align:start position:0% +Direction uh and um + + + align:start position:0% +Direction uh and um +uh the input to the problem is uh a + + align:start position:0% +uh the input to the problem is uh a + + + align:start position:0% +uh the input to the problem is uh a +circuit that induces a graph over all n + + align:start position:0% +circuit that induces a graph over all n + + + align:start position:0% +circuit that induces a graph over all n +bit strings so the circuit gets us input + + align:start position:0% +bit strings so the circuit gets us input + + + align:start position:0% +bit strings so the circuit gets us input +a node and it + + align:start position:0% +a node and it + + + align:start position:0% +a node and it +outputs two + + align:start position:0% +outputs two + + + align:start position:0% +outputs two +strings it one string outputs two + + align:start position:0% +strings it one string outputs two + + + align:start position:0% +strings it one string outputs two +strings now this circuit induces an + + align:start position:0% +strings now this circuit induces an + + + align:start position:0% +strings now this circuit induces an +undirected graph over all possible + + align:start position:0% +undirected graph over all possible + + + align:start position:0% +undirected graph over all possible +strings in the following way there is a + + align:start position:0% +strings in the following way there is a + + + align:start position:0% +strings in the following way there is a +Nets between string one and string two + + align:start position:0% +Nets between string one and string two + + + align:start position:0% +Nets between string one and string two +if V1 is in the output list of V2 and V2 + + align:start position:0% +if V1 is in the output list of V2 and V2 + + + align:start position:0% +if V1 is in the output list of V2 and V2 +is in the output list of + + align:start position:0% +is in the output list of + + + align:start position:0% +is in the output list of +V1 okay so this circuit gets n Bits as + + align:start position:0% +V1 okay so this circuit gets n Bits as + + + align:start position:0% +V1 okay so this circuit gets n Bits as +input and has 2 n Bits as output and no + + align:start position:0% +input and has 2 n Bits as output and no + + + align:start position:0% +input and has 2 n Bits as output and no +matter what it is it does induce a graph + + align:start position:0% +matter what it is it does induce a graph + + + align:start position:0% +matter what it is it does induce a graph +over + + align:start position:0% +over + + + align:start position:0% +over +strings uh that uh places an edge + + align:start position:0% +strings uh that uh places an edge + + + align:start position:0% +strings uh that uh places an edge +between these two + + align:start position:0% +between these two + + + align:start position:0% +between these two +strings if uh V1 is in the output list + + align:start position:0% +strings if uh V1 is in the output list + + + align:start position:0% +strings if uh V1 is in the output list +of V2 and vice versa + + align:start position:0% +of V2 and vice versa + + + align:start position:0% +of V2 and vice versa +now in the same reasoning as last time + + align:start position:0% +now in the same reasoning as last time + + + align:start position:0% +now in the same reasoning as last time +in The Same Spirit as last time any + + align:start position:0% +in The Same Spirit as last time any + + + align:start position:0% +in The Same Spirit as last time any +input C is going to reduce a graph with + + align:start position:0% +input C is going to reduce a graph with + + + align:start position:0% +input C is going to reduce a graph with +a particular structure what's that + + align:start position:0% +a particular structure what's that + + + align:start position:0% +a particular structure what's that +structure the out degree of every node + + align:start position:0% +structure the out degree of every node + + + align:start position:0% +structure the out degree of every node +is what at most + + align:start position:0% +is what at most + + + align:start position:0% +is what at most +two hence the graph that is induced By + + align:start position:0% +two hence the graph that is induced By + + + align:start position:0% +two hence the graph that is induced By +Any Given circuit is going to be a + + align:start position:0% +Any Given circuit is going to be a + + + align:start position:0% +Any Given circuit is going to be a +collection of isolated vertices cycles + + align:start position:0% +collection of isolated vertices cycles + + + align:start position:0% +collection of isolated vertices cycles +and + + align:start position:0% + + + + align:start position:0% + +paths uh the O degree node problem is + + align:start position:0% +paths uh the O degree node problem is + + + align:start position:0% +paths uh the O degree node problem is +the following if the zero string is has + + align:start position:0% +the following if the zero string is has + + + align:start position:0% +the following if the zero string is has +odd degree then I want you to find me + + align:start position:0% +odd degree then I want you to find me + + + align:start position:0% +odd degree then I want you to find me +another node with odd degree which we + + align:start position:0% +another node with odd degree which we + + + align:start position:0% +another node with odd degree which we +know exists by the handshaking LMA + + align:start position:0% +know exists by the handshaking LMA + + + align:start position:0% +know exists by the handshaking LMA +otherwise if 0 to the end has even + + align:start position:0% +otherwise if 0 to the end has even + + + align:start position:0% +otherwise if 0 to the end has even +degree you know just say yes and you + + align:start position:0% +degree you know just say yes and you + + + align:start position:0% +degree you know just say yes and you +know call it a day right now PPA is the + + align:start position:0% +know call it a day right now PPA is the + + + align:start position:0% +know call it a day right now PPA is the +class of search problems in um n p that + + align:start position:0% +class of search problems in um n p that + + + align:start position:0% +class of search problems in um n p that +are reducible poly time reducible to + + align:start position:0% +are reducible poly time reducible to + + + align:start position:0% +are reducible poly time reducible to +this problem to the odd degree node + + align:start position:0% +this problem to the odd degree node + + + align:start position:0% +this problem to the odd degree node +problem whose graph structure is you + + align:start position:0% +problem whose graph structure is you + + + align:start position:0% +problem whose graph structure is you +know like very similar to PPD except + + align:start position:0% +know like very similar to PPD except + + + align:start position:0% +know like very similar to PPD except +there are no + + align:start position:0% +there are no + + + align:start position:0% +there are no +directions so any circuit C defines a + + align:start position:0% +directions so any circuit C defines a + + + align:start position:0% +directions so any circuit C defines a +graph of this form except the graph is + + align:start position:0% +graph of this form except the graph is + + + align:start position:0% +graph of this form except the graph is +over exponentially many vertices so we + + align:start position:0% +over exponentially many vertices so we + + + align:start position:0% +over exponentially many vertices so we +can not just go and uh check every + + align:start position:0% +can not just go and uh check every + + + align:start position:0% +can not just go and uh check every +node uh every node's degree so the + + align:start position:0% +node uh every node's degree so the + + + align:start position:0% +node uh every node's degree so the +question is if 0 to the N is has OD + + align:start position:0% +question is if 0 to the N is has OD + + + align:start position:0% +question is if 0 to the N is has OD +degree then there must be another node + + align:start position:0% +degree then there must be another node + + + align:start position:0% +degree then there must be another node +of odd degree any of the nodes is a + + align:start position:0% +of odd degree any of the nodes is a + + + align:start position:0% +of odd degree any of the nodes is a +valid solution to the + + align:start position:0% +valid solution to the + + + align:start position:0% +valid solution to the +problem uh something that um I didn't + + align:start position:0% +problem uh something that um I didn't + + + align:start position:0% +problem uh something that um I didn't +mention before for PPD but it's useful + + align:start position:0% +mention before for PPD but it's useful + + + align:start position:0% +mention before for PPD but it's useful +to mention and I'm also going to mention + + align:start position:0% +to mention and I'm also going to mention + + + align:start position:0% +to mention and I'm also going to mention +it for + + align:start position:0% +it for + + + align:start position:0% +it for +PPA if I insist on finding the other end + + align:start position:0% +PPA if I insist on finding the other end + + + align:start position:0% +PPA if I insist on finding the other end +of this path of this specific path that + + align:start position:0% +of this path of this specific path that + + + align:start position:0% +of this path of this specific path that +start at zero the problem is not in + + align:start position:0% +start at zero the problem is not in + + + align:start position:0% +start at zero the problem is not in +FNP + + align:start position:0% +FNP + + + align:start position:0% +FNP +okay right so it's crucial that given + + align:start position:0% +okay right so it's crucial that given + + + align:start position:0% +okay right so it's crucial that given +the balancedness or the odd degree of + + align:start position:0% +the balancedness or the odd degree of + + + align:start position:0% +the balancedness or the odd degree of +this node allow you to return any other + + align:start position:0% +this node allow you to return any other + + + align:start position:0% +this node allow you to return any other +unbalanced any other OD degree node + + align:start position:0% +unbalanced any other OD degree node + + + align:start position:0% +unbalanced any other OD degree node +that's very crucial if I insisted on you + + align:start position:0% +that's very crucial if I insisted on you + + + align:start position:0% +that's very crucial if I insisted on you +returning me the uh other end point of + + align:start position:0% +returning me the uh other end point of + + + align:start position:0% +returning me the uh other end point of +the path that starts at zero that's + + align:start position:0% +the path that starts at zero that's + + + align:start position:0% +the path that starts at zero that's +above NP basically because there's no + + align:start position:0% +above NP basically because there's no + + + align:start position:0% +above NP basically because there's no +sord + + align:start position:0% +sord + + + align:start position:0% +sord +certificate that this nde is in the + + align:start position:0% +certificate that this nde is in the + + + align:start position:0% +certificate that this nde is in the +other end of the path starting at zero + + align:start position:0% +other end of the path starting at zero + + + align:start position:0% +other end of the path starting at zero +okay so it's very crucial that allow you + + align:start position:0% +okay so it's very crucial that allow you + + + align:start position:0% +okay so it's very crucial that allow you +to return any OD degree node okay + + align:start position:0% +to return any OD degree node okay + + + align:start position:0% +to return any OD degree node okay +now an interesting problem that is in + + align:start position:0% +now an interesting problem that is in + + + align:start position:0% +now an interesting problem that is in +this class and as far as we know not in + + align:start position:0% +this class and as far as we know not in + + + align:start position:0% +this class and as far as we know not in +ppad is the problem Smith which is given + + align:start position:0% +ppad is the problem Smith which is given + + + align:start position:0% +ppad is the problem Smith which is given +a hamiltonian circuit in a three regular + + align:start position:0% +a hamiltonian circuit in a three regular + + + align:start position:0% +a hamiltonian circuit in a three regular +graph find me another hamiltonian + + align:start position:0% +graph find me another hamiltonian + + + align:start position:0% +graph find me another hamiltonian +circuit in this graph now this graph is + + align:start position:0% +circuit in this graph now this graph is + + + align:start position:0% +circuit in this graph now this graph is +not exponentially big it's actually a + + align:start position:0% +not exponentially big it's actually a + + + align:start position:0% +not exponentially big it's actually a +graph that you can write down okay so I + + align:start position:0% +graph that you can write down okay so I + + + align:start position:0% +graph that you can write down okay so I +give you a graph explicitly and I also + + align:start position:0% +give you a graph explicitly and I also + + + align:start position:0% +give you a graph explicitly and I also +give you hamiltonian circuit in this + + align:start position:0% +give you hamiltonian circuit in this + + + align:start position:0% +give you hamiltonian circuit in this +graph I claim that there is another + + align:start position:0% +graph I claim that there is another + + + align:start position:0% +graph I claim that there is another +hamiltonian + + align:start position:0% +hamiltonian + + + align:start position:0% +hamiltonian +circuit okay the question is find + + align:start position:0% + + + + align:start position:0% + +it now why is there always a hon circuit + + align:start position:0% +it now why is there always a hon circuit + + + align:start position:0% +it now why is there always a hon circuit +well that follows from a theorem by + + align:start position:0% +well that follows from a theorem by + + + align:start position:0% +well that follows from a theorem by +Smith uh saying that uh you know a + + align:start position:0% +Smith uh saying that uh you know a + + + align:start position:0% +Smith uh saying that uh you know a +theorem by Smith implies that there's + + align:start position:0% +theorem by Smith implies that there's + + + align:start position:0% +theorem by Smith implies that there's +always another Honan path and let me + + align:start position:0% +always another Honan path and let me + + + align:start position:0% +always another Honan path and let me +actually show it to you it's very simple + + align:start position:0% +actually show it to you it's very simple + + + align:start position:0% +actually show it to you it's very simple +so here's actually a copy from papus 94 + + align:start position:0% +so here's actually a copy from papus 94 + + + align:start position:0% +so here's actually a copy from papus 94 +VOR uh uh I guess there is a missing + + align:start position:0% +VOR uh uh I guess there is a missing + + + align:start position:0% +VOR uh uh I guess there is a missing +apostrophe here in any so here's the + + align:start position:0% +apostrophe here in any so here's the + + + align:start position:0% +apostrophe here in any so here's the +input graph + + align:start position:0% +input graph + + + align:start position:0% +input graph +okay and obviously um mean uh obviously + + align:start position:0% +okay and obviously um mean uh obviously + + + align:start position:0% +okay and obviously um mean uh obviously +this is a hamiltonian circuit + + align:start position:0% +this is a hamiltonian circuit + + + align:start position:0% +this is a hamiltonian circuit +right okay so I'm I'm I'm following the + + align:start position:0% +right okay so I'm I'm I'm following the + + + align:start position:0% +right okay so I'm I'm I'm following the +outer boundary here going + + align:start position:0% +outer boundary here going + + + align:start position:0% +outer boundary here going +inside and then coming back here okay + + align:start position:0% +inside and then coming back here okay + + + align:start position:0% +inside and then coming back here okay +that's the hamiltonian circuit and here + + align:start position:0% +that's the hamiltonian circuit and here + + + align:start position:0% +that's the hamiltonian circuit and here +is the same circuit except I've removed + + align:start position:0% +is the same circuit except I've removed + + + align:start position:0% +is the same circuit except I've removed +one Edge + + align:start position:0% +one Edge + + + align:start position:0% +one Edge +X and + + align:start position:0% +X and + + + align:start position:0% +X and +Y and here I'm I'm showing a bunch of + + align:start position:0% +Y and here I'm I'm showing a bunch of + + + align:start position:0% +Y and here I'm I'm showing a bunch of +operations you can do to this hilon path + + align:start position:0% +operations you can do to this hilon path + + + align:start position:0% +operations you can do to this hilon path +circuit I me this is a hamiltonian path + + align:start position:0% +circuit I me this is a hamiltonian path + + + align:start position:0% +circuit I me this is a hamiltonian path +um to create another hamiltonian path + + align:start position:0% +um to create another hamiltonian path + + + align:start position:0% +um to create another hamiltonian path +with a same Edge missing hence adding + + align:start position:0% +with a same Edge missing hence adding + + + align:start position:0% +with a same Edge missing hence adding +that edge you get another hon + + align:start position:0% +that edge you get another hon + + + align:start position:0% +that edge you get another hon +circuit and the series of operations is + + align:start position:0% +circuit and the series of operations is + + + align:start position:0% +circuit and the series of operations is +very simple so what you do is the + + align:start position:0% +very simple so what you do is the + + + align:start position:0% +very simple so what you do is the +following so you know so you start with + + align:start position:0% +following so you know so you start with + + + align:start position:0% +following so you know so you start with +you know it doesn't matter they're going + + align:start position:0% +you know it doesn't matter they're going + + + align:start position:0% +you know it doesn't matter they're going +to start with an arbitrary nodes but uh + + align:start position:0% +to start with an arbitrary nodes but uh + + + align:start position:0% +to start with an arbitrary nodes but uh +all this all this all the circuits all + + align:start position:0% +all this all this all the circuits all + + + align:start position:0% +all this all this all the circuits all +the circuits I'm going to be + + align:start position:0% +the circuits I'm going to be + + + align:start position:0% +the circuits I'm going to be +defining that uh um we'll have X as one + + align:start position:0% +defining that uh um we'll have X as one + + + align:start position:0% +defining that uh um we'll have X as one +of the two end points but the other end + + align:start position:0% +of the two end points but the other end + + + align:start position:0% +of the two end points but the other end +point is going to be moving + + align:start position:0% +point is going to be moving + + + align:start position:0% +point is going to be moving +around and in the end it's going to get + + align:start position:0% +around and in the end it's going to get + + + align:start position:0% +around and in the end it's going to get +back to the this vertex hence I canot + + align:start position:0% +back to the this vertex hence I canot + + + align:start position:0% +back to the this vertex hence I canot +that Ed back and get the circuit okay so + + align:start position:0% +that Ed back and get the circuit okay so + + + align:start position:0% +that Ed back and get the circuit okay so +I start with the circuit I remove one NS + + align:start position:0% +I start with the circuit I remove one NS + + + align:start position:0% +I start with the circuit I remove one NS +X and Y + + align:start position:0% +X and Y + + + align:start position:0% +X and Y +and I'm about to show you that there is + + align:start position:0% +and I'm about to show you that there is + + + align:start position:0% +and I'm about to show you that there is +another hamiltonian C path that misses + + align:start position:0% +another hamiltonian C path that misses + + + align:start position:0% +another hamiltonian C path that misses +the same Edge but is different than this + + align:start position:0% +the same Edge but is different than this + + + align:start position:0% +the same Edge but is different than this +one so it's going to be that one okay + + align:start position:0% +one so it's going to be that one okay + + + align:start position:0% +one so it's going to be that one okay +now let me try to argue that there is + + align:start position:0% +now let me try to argue that there is + + + align:start position:0% +now let me try to argue that there is +another hamiltonian path that is missing + + align:start position:0% +another hamiltonian path that is missing + + + align:start position:0% +another hamiltonian path that is missing +the same Edge how am I going to do that + + align:start position:0% +the same Edge how am I going to do that + + + align:start position:0% +the same Edge how am I going to do that +well in the sequence of hamiltonian uh + + align:start position:0% +well in the sequence of hamiltonian uh + + + align:start position:0% +well in the sequence of hamiltonian uh +path I'm going to Define X is going to + + align:start position:0% +path I'm going to Define X is going to + + + align:start position:0% +path I'm going to Define X is going to +stay fixed Y is going to be moving + + align:start position:0% +stay fixed Y is going to be moving + + + align:start position:0% +stay fixed Y is going to be moving +around now let's land somewhere in the + + align:start position:0% +around now let's land somewhere in the + + + align:start position:0% +around now let's land somewhere in the +middle here + + align:start position:0% +middle here + + + align:start position:0% +middle here +okay so now why is this + + align:start position:0% +okay so now why is this + + + align:start position:0% +okay so now why is this +guy why because the graph is three + + align:start position:0% +guy why because the graph is three + + + align:start position:0% +guy why because the graph is three +regular and why is an end point there is + + align:start position:0% +regular and why is an end point there is + + + align:start position:0% +regular and why is an end point there is +exactly one Edge that's used in the + + align:start position:0% +exactly one Edge that's used in the + + + align:start position:0% +exactly one Edge that's used in the +hamiltonian path and there are two edges + + align:start position:0% +hamiltonian path and there are two edges + + + align:start position:0% +hamiltonian path and there are two edges +that are + + align:start position:0% +that are + + + align:start position:0% +that are +missing I'm going to try to add both of + + align:start position:0% +missing I'm going to try to add both of + + + align:start position:0% +missing I'm going to try to add both of +them and have and get a + + align:start position:0% +them and have and get a + + + align:start position:0% +them and have and get a +circuit and get a path a hamiltonian + + align:start position:0% +circuit and get a path a hamiltonian + + + align:start position:0% +circuit and get a path a hamiltonian +path okay what would happen if I try to + + align:start position:0% +path okay what would happen if I try to + + + align:start position:0% +path okay what would happen if I try to +brought this Edge into this path well + + align:start position:0% +brought this Edge into this path well + + + align:start position:0% +brought this Edge into this path well +that wouldn't be a PA path + + align:start position:0% +that wouldn't be a PA path + + + align:start position:0% +that wouldn't be a PA path +anymore uh so because this guy would + + align:start position:0% +anymore uh so because this guy would + + + align:start position:0% +anymore uh so because this guy would +have degree three if I haded that edge + + align:start position:0% +have degree three if I haded that edge + + + align:start position:0% +have degree three if I haded that edge +now I have to kill one of the two edges + + align:start position:0% +now I have to kill one of the two edges + + + align:start position:0% +now I have to kill one of the two edges +adjacent to this node and I'm going to + + align:start position:0% +adjacent to this node and I'm going to + + + align:start position:0% +adjacent to this node and I'm going to +kill the one that maintains the fact + + align:start position:0% +kill the one that maintains the fact + + + align:start position:0% +kill the one that maintains the fact +that the graph is + + align:start position:0% +that the graph is + + + align:start position:0% +that the graph is +connected right so if I add this Edge + + align:start position:0% +connected right so if I add this Edge + + + align:start position:0% +connected right so if I add this Edge +and I kill this Edge I'm + + align:start position:0% +and I kill this Edge I'm + + + align:start position:0% +and I kill this Edge I'm +screwed the path is not the graph is not + + align:start position:0% +screwed the path is not the graph is not + + + align:start position:0% +screwed the path is not the graph is not +connect anymore so I'm going to K that + + align:start position:0% +connect anymore so I'm going to K that + + + align:start position:0% +connect anymore so I'm going to K that +edge so what happens here I added that + + align:start position:0% +edge so what happens here I added that + + + align:start position:0% +edge so what happens here I added that +edge and I kill that edge and this what + + align:start position:0% +edge and I kill that edge and this what + + + align:start position:0% +edge and I kill that edge and this what +I + + align:start position:0% +I + + + align:start position:0% +I +got if I try to add this + + align:start position:0% +got if I try to add this + + + align:start position:0% +got if I try to add this +Edge then this node will have degree + + align:start position:0% +Edge then this node will have degree + + + align:start position:0% +Edge then this node will have degree +three I have to kill either that edge or + + align:start position:0% +three I have to kill either that edge or + + + align:start position:0% +three I have to kill either that edge or +that edge I can kill exactly one to + + align:start position:0% +that edge I can kill exactly one to + + + align:start position:0% +that edge I can kill exactly one to +avoid disconnecting My Graph and I'm + + align:start position:0% +avoid disconnecting My Graph and I'm + + + align:start position:0% +avoid disconnecting My Graph and I'm +going to be killing that one and that's + + align:start position:0% +going to be killing that one and that's + + + align:start position:0% +going to be killing that one and that's +going to bring me here so every + + align:start position:0% +going to bring me here so every + + + align:start position:0% +going to bring me here so every +hamiltonan + + align:start position:0% +hamiltonan + + + align:start position:0% +hamiltonan +path uh + + align:start position:0% +path uh + + + align:start position:0% +path uh +uh has exactly two neighbors + + align:start position:0% +uh has exactly two neighbors + + + align:start position:0% +uh has exactly two neighbors +corresponding + + align:start position:0% +corresponding + + + align:start position:0% +corresponding +to um + + align:start position:0% +to um + + + align:start position:0% +to um +adding uh one of the two + + align:start position:0% +adding uh one of the two + + + align:start position:0% +adding uh one of the two +missing uh uh edges from the Y end point + + align:start position:0% +missing uh uh edges from the Y end point + + + align:start position:0% +missing uh uh edges from the Y end point +of that + + align:start position:0% +of that + + + align:start position:0% +of that +path and there's only one way this thing + + align:start position:0% +path and there's only one way this thing + + + align:start position:0% +path and there's only one way this thing +can stop what you know by arriving at y + + align:start position:0% +can stop what you know by arriving at y + + + align:start position:0% +can stop what you know by arriving at y +okay which will give me if I don't + + align:start position:0% +okay which will give me if I don't + + + align:start position:0% +okay which will give me if I don't +arrive if I don't get end point Y to + + align:start position:0% +arrive if I don't get end point Y to + + + align:start position:0% +arrive if I don't get end point Y to +come back to its original position I'll + + align:start position:0% +come back to its original position I'll + + + align:start position:0% +come back to its original position I'll +keep + + align:start position:0% +keep + + + align:start position:0% +keep +going okay so this this this um in other + + align:start position:0% +going okay so this this this um in other + + + align:start position:0% +going okay so this this this um in other +words like uh my proof of sperner what I + + align:start position:0% +words like uh my proof of sperner what I + + + align:start position:0% +words like uh my proof of sperner what I +did here is I defined a neighborhood + + align:start position:0% +did here is I defined a neighborhood + + + align:start position:0% +did here is I defined a neighborhood +relationship between hamiltonian paths + + align:start position:0% +relationship between hamiltonian paths + + + align:start position:0% +relationship between hamiltonian paths +which was adding an + + align:start position:0% +which was adding an + + + align:start position:0% +which was adding an +edge one of the two missing edges from + + align:start position:0% +edge one of the two missing edges from + + + align:start position:0% +edge one of the two missing edges from +the end points and I know that the only + + align:start position:0% +the end points and I know that the only + + + align:start position:0% +the end points and I know that the only +stopping condition is if I get here and + + align:start position:0% +stopping condition is if I get here and + + + align:start position:0% +stopping condition is if I get here and +that's why Smith is in PPA now it's a + + align:start position:0% +that's why Smith is in PPA now it's a + + + align:start position:0% +that's why Smith is in PPA now it's a +very interesting problem to show that + + align:start position:0% +very interesting problem to show that + + + align:start position:0% +very interesting problem to show that +this is PPA + + align:start position:0% +this is PPA + + + align:start position:0% +this is PPA +complete + + align:start position:0% +complete + + + align:start position:0% +complete +okay uh let me Define the class + + align:start position:0% +okay uh let me Define the class + + + align:start position:0% +okay uh let me Define the class +PLS uh that was defined earlier by um + + align:start position:0% +PLS uh that was defined earlier by um + + + align:start position:0% +PLS uh that was defined earlier by um +Johnson papar yanakakis + + align:start position:0% +Johnson papar yanakakis + + + align:start position:0% +Johnson papar yanakakis +uh now I want to implement a class that + + align:start position:0% +uh now I want to implement a class that + + + align:start position:0% +uh now I want to implement a class that +uh exploits this argument that every dck + + align:start position:0% +uh exploits this argument that every dck + + + align:start position:0% +uh exploits this argument that every dck +has a sync the way I'm going to do that + + align:start position:0% +has a sync the way I'm going to do that + + + align:start position:0% +has a sync the way I'm going to do that +is I'm going to give you two + + align:start position:0% +is I'm going to give you two + + + align:start position:0% +is I'm going to give you two +functions function C is going to take a + + align:start position:0% +functions function C is going to take a + + + align:start position:0% +functions function C is going to take a +both of them are have n Bits as inputs + + align:start position:0% +both of them are have n Bits as inputs + + + align:start position:0% +both of them are have n Bits as inputs +this guy C is uh will output a list of + + align:start position:0% +this guy C is uh will output a list of + + + align:start position:0% +this guy C is uh will output a list of +strings of list of CAS strings okay so + + align:start position:0% +strings of list of CAS strings okay so + + + align:start position:0% +strings of list of CAS strings okay so +it has n Bits as input and k n Bits as + + align:start position:0% +it has n Bits as input and k n Bits as + + + align:start position:0% +it has n Bits as input and k n Bits as +output while this guy is outputting uh + + align:start position:0% +output while this guy is outputting uh + + + align:start position:0% +output while this guy is outputting uh +you know some real + + align:start position:0% +you know some real + + + align:start position:0% +you know some real +number I mean some rational number + + align:start position:0% +number I mean some rational number + + + align:start position:0% +number I mean some rational number +whatever so but I interpret the output + + align:start position:0% +whatever so but I interpret the output + + + align:start position:0% +whatever so but I interpret the output +of this circuit as a number I interpret + + align:start position:0% +of this circuit as a number I interpret + + + align:start position:0% +of this circuit as a number I interpret +the output of this circuit as a list of + + align:start position:0% +the output of this circuit as a list of + + + align:start position:0% +the output of this circuit as a list of +other + + align:start position:0% +other + + + align:start position:0% +other +strings + + align:start position:0% +strings + + + align:start position:0% +strings +now as an edge between given these two + + align:start position:0% +now as an edge between given these two + + + align:start position:0% +now as an edge between given these two +circuits uh that induces a Doug I claim + + align:start position:0% +circuits uh that induces a Doug I claim + + + align:start position:0% +circuits uh that induces a Doug I claim +in the following way I add an edge from + + align:start position:0% +in the following way I add an edge from + + + align:start position:0% +in the following way I add an edge from +V1 to V2 if V2 is in the adjacency list + + align:start position:0% +V1 to V2 if V2 is in the adjacency list + + + align:start position:0% +V1 to V2 if V2 is in the adjacency list +of + + align:start position:0% +of + + + align:start position:0% +of +V1 + + align:start position:0% +V1 + + + align:start position:0% +V1 +and the score of + + align:start position:0% +and the score of + + + align:start position:0% +and the score of +V2 is better than the score of V1 that's + + align:start position:0% +V2 is better than the score of V1 that's + + + align:start position:0% +V2 is better than the score of V1 that's +and only then then and only then I add + + align:start position:0% +and only then then and only then I add + + + align:start position:0% +and only then then and only then I add +an edge from V1 to + + align:start position:0% +an edge from V1 to + + + align:start position:0% +an edge from V1 to +V2 and obviously this is a dug now + + align:start position:0% +V2 and obviously this is a dug now + + + align:start position:0% +V2 and obviously this is a dug now +because uh I'm increasing my score as I + + align:start position:0% +because uh I'm increasing my score as I + + + align:start position:0% +because uh I'm increasing my score as I +go along right so I cannot come back to + + align:start position:0% +go along right so I cannot come back to + + + align:start position:0% +go along right so I cannot come back to +where I + + align:start position:0% +where I + + + align:start position:0% +where I +started so the problem that uh I want to + + align:start position:0% +started so the problem that uh I want to + + + align:start position:0% +started so the problem that uh I want to +Define is the find sync problem which is + + align:start position:0% +Define is the find sync problem which is + + + align:start position:0% +Define is the find sync problem which is +given two circuits as + + align:start position:0% +given two circuits as + + + align:start position:0% +given two circuits as +above find an + + align:start position:0% +above find an + + + align:start position:0% +above find an +X + + align:start position:0% +X + + + align:start position:0% +X +that uh has better + + align:start position:0% +that uh has better + + + align:start position:0% +that uh has better +score than any of the adjacent + + align:start position:0% +score than any of the adjacent + + + align:start position:0% +score than any of the adjacent +vertices and such a thing has to exist + + align:start position:0% +vertices and such a thing has to exist + + + align:start position:0% +vertices and such a thing has to exist +because if I Define this graph and find + + align:start position:0% +because if I Define this graph and find + + + align:start position:0% +because if I Define this graph and find +any sync of this graph this will satisfy + + align:start position:0% +any sync of this graph this will satisfy + + + align:start position:0% +any sync of this graph this will satisfy +this + + align:start position:0% +this + + + align:start position:0% +this +property the class PLS are all search + + align:start position:0% +property the class PLS are all search + + + align:start position:0% +property the class PLS are all search +problems in NP that are polinomial time + + align:start position:0% +problems in NP that are polinomial time + + + align:start position:0% +problems in NP that are polinomial time +reducible to this problem find + + align:start position:0% +reducible to this problem find + + + align:start position:0% +reducible to this problem find +sync the picture for this problem is + + align:start position:0% +sync the picture for this problem is + + + align:start position:0% +sync the picture for this problem is +this exponentially large graph but there + + align:start position:0% +this exponentially large graph but there + + + align:start position:0% +this exponentially large graph but there +is a Doug that's implicitly defined by + + align:start position:0% +is a Doug that's implicitly defined by + + + align:start position:0% +is a Doug that's implicitly defined by +these two vertices but this two circuits + + align:start position:0% +these two vertices but this two circuits + + + align:start position:0% +these two vertices but this two circuits +and all of these are solutions + + align:start position:0% + + + + align:start position:0% + +uh interesting problem in this class an + + align:start position:0% +uh interesting problem in this class an + + + align:start position:0% +uh interesting problem in this class an +interesting problem in this class is the + + align:start position:0% +interesting problem in this class is the + + + align:start position:0% +interesting problem in this class is the +local Max cut problem a relative of the + + align:start position:0% +local Max cut problem a relative of the + + + align:start position:0% +local Max cut problem a relative of the +well-known Max cut problem which is NP + + align:start position:0% +well-known Max cut problem which is NP + + + align:start position:0% +well-known Max cut problem which is NP +complete in the local Max cut problem + + align:start position:0% +complete in the local Max cut problem + + + align:start position:0% +complete in the local Max cut problem +I'm giving you a weighted graph and I + + align:start position:0% +I'm giving you a weighted graph and I + + + align:start position:0% +I'm giving you a weighted graph and I +want a partition that's not globally + + align:start position:0% +want a partition that's not globally + + + align:start position:0% +want a partition that's not globally +optimal but locally optimal meaning + + align:start position:0% +optimal but locally optimal meaning + + + align:start position:0% +optimal but locally optimal meaning +there is no single node I can move from + + align:start position:0% +there is no single node I can move from + + + align:start position:0% +there is no single node I can move from +one to the other side of the cut to + + align:start position:0% +one to the other side of the cut to + + + align:start position:0% +one to the other side of the cut to +improve the cut value + + align:start position:0% + + + + align:start position:0% + +now if the weights were bounded and + + align:start position:0% +now if the weights were bounded and + + + align:start position:0% +now if the weights were bounded and +integral this wouldn't be a hard + + align:start position:0% +integral this wouldn't be a hard + + + align:start position:0% +integral this wouldn't be a hard +problem but for arbitrary weights is + + align:start position:0% +problem but for arbitrary weights is + + + align:start position:0% +problem but for arbitrary weights is +actually PLS complete to + + align:start position:0% +actually PLS complete to + + + align:start position:0% +actually PLS complete to +find uh a local maximum + + align:start position:0% + + + + align:start position:0% + +cut + + align:start position:0% +cut + + + align:start position:0% +cut +okay final problem and I'm + + align:start position:0% +okay final problem and I'm + + + align:start position:0% +okay final problem and I'm +concluding is uh final class is the + + align:start position:0% +concluding is uh final class is the + + + align:start position:0% +concluding is uh final class is the +class PPP that's trying to implement the + + align:start position:0% +class PPP that's trying to implement the + + + align:start position:0% +class PPP that's trying to implement the +pigeonhole + + align:start position:0% +pigeonhole + + + align:start position:0% +pigeonhole +principle here I'm giving you a circuit + + align:start position:0% +principle here I'm giving you a circuit + + + align:start position:0% +principle here I'm giving you a circuit +that has n Bits And nbit inputs and N + + align:start position:0% +that has n Bits And nbit inputs and N + + + align:start position:0% +that has n Bits And nbit inputs and N +bit + + align:start position:0% + + + + align:start position:0% + +outputs + + align:start position:0% + + + + align:start position:0% + +and uh the Collision problem that I want + + align:start position:0% +and uh the Collision problem that I want + + + align:start position:0% +and uh the Collision problem that I want +to Define is given such a + + align:start position:0% +to Define is given such a + + + align:start position:0% +to Define is given such a +circuit either find me an X that maps to + + align:start position:0% +circuit either find me an X that maps to + + + align:start position:0% +circuit either find me an X that maps to +the zero + + align:start position:0% +the zero + + + align:start position:0% +the zero +string or find me a pair X and Y that + + align:start position:0% +string or find me a pair X and Y that + + + align:start position:0% +string or find me a pair X and Y that +map to the same + + align:start position:0% +map to the same + + + align:start position:0% +map to the same +string now clearly by the pigeon hole + + align:start position:0% +string now clearly by the pigeon hole + + + align:start position:0% +string now clearly by the pigeon hole +principle if no body goes to zero there + + align:start position:0% +principle if no body goes to zero there + + + align:start position:0% +principle if no body goes to zero there +must be two guys that Collide okay so + + align:start position:0% +must be two guys that Collide okay so + + + align:start position:0% +must be two guys that Collide okay so +this problem is also total by the P + + align:start position:0% +this problem is also total by the P + + + align:start position:0% +this problem is also total by the P +principle so it always has a solution no + + align:start position:0% +principle so it always has a solution no + + + align:start position:0% +principle so it always has a solution no +matter what the circuit is and the class + + align:start position:0% +matter what the circuit is and the class + + + align:start position:0% +matter what the circuit is and the class +PPP is all problems in n p that are + + align:start position:0% +PPP is all problems in n p that are + + + align:start position:0% +PPP is all problems in n p that are +reducible to this + + align:start position:0% + + + + align:start position:0% + +problem uh finally the hierarchy of + + align:start position:0% +problem uh finally the hierarchy of + + + align:start position:0% +problem uh finally the hierarchy of +problems that def finded is + + align:start position:0% +problems that def finded is + + + align:start position:0% +problems that def finded is +this P FNP so this total FNP somewhere + + align:start position:0% +this P FNP so this total FNP somewhere + + + align:start position:0% +this P FNP so this total FNP somewhere +here which I don't show + + align:start position:0% +here which I don't show + + + align:start position:0% +here which I don't show +and these are the relationships of these + + align:start position:0% +and these are the relationships of these + + + align:start position:0% +and these are the relationships of these +problems I haven't shown that these + + align:start position:0% +problems I haven't shown that these + + + align:start position:0% +problems I haven't shown that these +arrows are true that this is a subass + + align:start position:0% +arrows are true that this is a subass + + + align:start position:0% +arrows are true that this is a subass +PPD is a subass of these two classes + + align:start position:0% +PPD is a subass of these two classes + + + align:start position:0% +PPD is a subass of these two classes +this is easy this is a simple exercise + + align:start position:0% +this is easy this is a simple exercise + + + align:start position:0% +this is easy this is a simple exercise +you can think about it okay uh this is + + align:start position:0% +you can think about it okay uh this is + + + align:start position:0% +you can think about it okay uh this is +basically my introduction to PPA PP and + + align:start position:0% +basically my introduction to PPA PP and + + + align:start position:0% +basically my introduction to PPA PP and +related + + align:start position:0% +related + + + align:start position:0% +related +classes um the final thing that I wanted + + align:start position:0% +classes um the final thing that I wanted + + + align:start position:0% +classes um the final thing that I wanted +to point out is uh answering a question + + align:start position:0% +to point out is uh answering a question + + + align:start position:0% +to point out is uh answering a question +that was asked after the previous + + align:start position:0% +that was asked after the previous + + + align:start position:0% +that was asked after the previous +lecture which was why did you define + + align:start position:0% +lecture which was why did you define + + + align:start position:0% +lecture which was why did you define +these classes and not just a uh tfmp + + align:start position:0% +these classes and not just a uh tfmp + + + align:start position:0% +these classes and not just a uh tfmp +complete problem why did you have + + align:start position:0% +complete problem why did you have + + + align:start position:0% +complete problem why did you have +to pay special attention to the precise + + align:start position:0% +to pay special attention to the precise + + + align:start position:0% +to pay special attention to the precise +existence argument that gives rise to + + align:start position:0% +existence argument that gives rise to + + + align:start position:0% +existence argument that gives rise to +the total like The guarantee that your + + align:start position:0% +the total like The guarantee that your + + + align:start position:0% +the total like The guarantee that your +problems are total and the reason for + + align:start position:0% +problems are total and the reason for + + + align:start position:0% +problems are total and the reason for +that is that actually um uh tfn is not + + align:start position:0% +that is that actually um uh tfn is not + + + align:start position:0% +that is that actually um uh tfn is not +what is called a syntactic class in + + align:start position:0% +what is called a syntactic class in + + + align:start position:0% +what is called a syntactic class in +other + + align:start position:0% +other + + + align:start position:0% +other +words if I give you problem with TF + + align:start position:0% +words if I give you problem with TF + + + align:start position:0% +words if I give you problem with TF +andp um um if I give you a language if I + + align:start position:0% +andp um um if I give you a language if I + + + align:start position:0% +andp um um if I give you a language if I +give you a um a teing machine you cannot + + align:start position:0% +give you a um a teing machine you cannot + + + align:start position:0% +give you a um a teing machine you cannot +decide whether that is Computing a total + + align:start position:0% +decide whether that is Computing a total + + + align:start position:0% +decide whether that is Computing a total +problem that no matter what input to + + align:start position:0% +problem that no matter what input to + + + align:start position:0% +problem that no matter what input to +that machine is there is always an + + align:start position:0% +that machine is there is always an + + + align:start position:0% +that machine is there is always an +output okay so I had to pay attention to + + align:start position:0% +output okay so I had to pay attention to + + + align:start position:0% +output okay so I had to pay attention to +the specialized existence arguments + + align:start position:0% +the specialized existence arguments + + + align:start position:0% +the specialized existence arguments +because for specialized existence + + align:start position:0% +because for specialized existence + + + align:start position:0% +because for specialized existence +argument I know a priority that the the + + align:start position:0% +argument I know a priority that the the + + + align:start position:0% +argument I know a priority that the the +problem is total so in particular no + + align:start position:0% +problem is total so in particular no + + + align:start position:0% +problem is total so in particular no +matter what circuit I give you here I + + align:start position:0% +matter what circuit I give you here I + + + align:start position:0% +matter what circuit I give you here I +know I don't even have to check anything + + align:start position:0% +know I don't even have to check anything + + + align:start position:0% +know I don't even have to check anything +no matter what input you give me I know + + align:start position:0% +no matter what input you give me I know + + + align:start position:0% +no matter what input you give me I know +there is a solution no matter what uh + + align:start position:0% +there is a solution no matter what uh + + + align:start position:0% +there is a solution no matter what uh +pairs of circuits you give me here I + + align:start position:0% +pairs of circuits you give me here I + + + align:start position:0% +pairs of circuits you give me here I +don't need to do to check anything I + + align:start position:0% +don't need to do to check anything I + + + align:start position:0% +don't need to do to check anything I +know that the answer to this problem + + align:start position:0% +know that the answer to this problem + + + align:start position:0% +know that the answer to this problem +there Al there's always an answer to + + align:start position:0% +there Al there's always an answer to + + + align:start position:0% +there Al there's always an answer to +this problem and so on so forth right + + align:start position:0% +this problem and so on so forth right + + + align:start position:0% +this problem and so on so forth right +this no matter what you give to me as + + align:start position:0% +this no matter what you give to me as + + + align:start position:0% +this no matter what you give to me as +input is important to Define uh + + align:start position:0% +input is important to Define uh + + + align:start position:0% +input is important to Define uh +complexity classes for which you can + + align:start position:0% +complexity classes for which you can + + + align:start position:0% +complexity classes for which you can +show hardness results to find complete + + align:start position:0% +show hardness results to find complete + + + align:start position:0% +show hardness results to find complete +problems um otherwise you would have you + + align:start position:0% +problems um otherwise you would have you + + + align:start position:0% +problems um otherwise you would have you +know sort of like what is called Promise + + align:start position:0% +know sort of like what is called Promise + + + align:start position:0% +know sort of like what is called Promise +classes which are not amable to showing + + align:start position:0% +classes which are not amable to showing + + + align:start position:0% +classes which are not amable to showing +uh completeness results okay and with + + align:start position:0% +uh completeness results okay and with + + + align:start position:0% +uh completeness results okay and with +that brief note I want to stop thanks a + + align:start position:0% +that brief note I want to stop thanks a + + + align:start position:0% +that brief note I want to stop thanks a +lot \ No newline at end of file diff --git a/K-8nCXY-iSI.txt b/K-8nCXY-iSI.txt new file mode 100644 index 0000000000000000000000000000000000000000..ea2daba034b5442790c2cc49131a563dd500397f --- /dev/null +++ b/K-8nCXY-iSI.txt @@ -0,0 +1,498 @@ +align:start position:0% + +kul's Force law can be the basis for + + align:start position:0% +kul's Force law can be the basis for + + + align:start position:0% +kul's Force law can be the basis for +estimating the net charge on an + + align:start position:0% +estimating the net charge on an + + + align:start position:0% +estimating the net charge on an +object conservation of charge and + + align:start position:0% +object conservation of charge and + + + align:start position:0% +object conservation of charge and +gauss's law are also the basis for the + + align:start position:0% +gauss's law are also the basis for the + + + align:start position:0% +gauss's law are also the basis for the +measurement of + + align:start position:0% + + + + align:start position:0% + +charge in this demonstration the + + align:start position:0% +charge in this demonstration the + + + align:start position:0% +charge in this demonstration the +particles are airfill + + align:start position:0% +particles are airfill + + + align:start position:0% +particles are airfill +balloons of the variety used at + + align:start position:0% + + + + align:start position:0% + +parties they can be charged by rubbing + + align:start position:0% +parties they can be charged by rubbing + + + align:start position:0% +parties they can be charged by rubbing +them with a dry + + align:start position:0% + + + + align:start position:0% + +cloth they repel each other because + + align:start position:0% +cloth they repel each other because + + + align:start position:0% +cloth they repel each other because +they've been charged to the same + + align:start position:0% + + + + align:start position:0% + +polarity let's use measurements of the + + align:start position:0% +polarity let's use measurements of the + + + align:start position:0% +polarity let's use measurements of the +separation distance and the weight of + + align:start position:0% +separation distance and the weight of + + + align:start position:0% +separation distance and the weight of +the balloon to approximate the charge + + align:start position:0% +the balloon to approximate the charge + + + align:start position:0% +the balloon to approximate the charge +that's been left on one of the + + align:start position:0% + + + + align:start position:0% + +balloons the threads that have been used + + align:start position:0% +balloons the threads that have been used + + + align:start position:0% +balloons the threads that have been used +to suspend them are tied at a common + + align:start position:0% + + + + align:start position:0% + +point the spacing between balloon + + align:start position:0% +point the spacing between balloon + + + align:start position:0% +point the spacing between balloon +centers is about 50 cm it's not possible + + align:start position:0% +centers is about 50 cm it's not possible + + + align:start position:0% +centers is about 50 cm it's not possible +to to put the meter stick close to the + + align:start position:0% +to to put the meter stick close to the + + + align:start position:0% +to to put the meter stick close to the +balloons without they being attracted to + + align:start position:0% +balloons without they being attracted to + + + align:start position:0% +balloons without they being attracted to +Professor Zan his body's a good + + align:start position:0% +Professor Zan his body's a good + + + align:start position:0% +Professor Zan his body's a good +conductor the charges on the balloons + + align:start position:0% +conductor the charges on the balloons + + + align:start position:0% +conductor the charges on the balloons +induce image charges of opposite + + align:start position:0% +induce image charges of opposite + + + align:start position:0% +induce image charges of opposite +polarity on conducting surfaces to which + + align:start position:0% +polarity on conducting surfaces to which + + + align:start position:0% +polarity on conducting surfaces to which +they're + + align:start position:0% + + + + align:start position:0% + +attracted this image charge is just that + + align:start position:0% +attracted this image charge is just that + + + align:start position:0% +attracted this image charge is just that +responsible for attracting the balloons + + align:start position:0% +responsible for attracting the balloons + + + align:start position:0% +responsible for attracting the balloons +to any essentially grounded conductor in + + align:start position:0% +to any essentially grounded conductor in + + + align:start position:0% +to any essentially grounded conductor in +its vicinity + + align:start position:0% + + + + align:start position:0% + +by now one of our balloons is broken but + + align:start position:0% +by now one of our balloons is broken but + + + align:start position:0% +by now one of our balloons is broken but +with new balloons and A Renewed charge + + align:start position:0% +with new balloons and A Renewed charge + + + align:start position:0% +with new balloons and A Renewed charge +the spacing looks to be about what we + + align:start position:0% +the spacing looks to be about what we + + + align:start position:0% +the spacing looks to be about what we +had + + align:start position:0% +had + + + align:start position:0% +had +before here's what happens when we + + align:start position:0% +before here's what happens when we + + + align:start position:0% +before here's what happens when we +insert the balloon in the Faraday + + align:start position:0% + + + + align:start position:0% + +cage watch the meter + + align:start position:0% + + + + align:start position:0% + +too our char conservation statement can + + align:start position:0% +too our char conservation statement can + + + align:start position:0% +too our char conservation statement can +be used to see that it makes no + + align:start position:0% +be used to see that it makes no + + + align:start position:0% +be used to see that it makes no +difference to the measurement whether + + align:start position:0% +difference to the measurement whether + + + align:start position:0% +difference to the measurement whether +the balloon makes physical and + + align:start position:0% +the balloon makes physical and + + + align:start position:0% +the balloon makes physical and +electrical contact with the inner + + align:start position:0% +electrical contact with the inner + + + align:start position:0% +electrical contact with the inner +box from the dial settings on the top + + align:start position:0% +box from the dial settings on the top + + + align:start position:0% +box from the dial settings on the top +scale a full scale deflection is a + + align:start position:0% +scale a full scale deflection is a + + + align:start position:0% +scale a full scale deflection is a +charge of minus 1,000 + + align:start position:0% +charge of minus 1,000 + + + align:start position:0% +charge of minus 1,000 +nanocs the measured charge is 220 or + + align:start position:0% +nanocs the measured charge is 220 or + + + align:start position:0% +nanocs the measured charge is 220 or + + align:start position:0% + + + + align:start position:0% + +nanocs let's see what we get for the + + align:start position:0% +nanocs let's see what we get for the + + + align:start position:0% +nanocs let's see what we get for the +other balloon + + align:start position:0% + + + + align:start position:0% + +the readings about the same about 220 + + align:start position:0% + + + + align:start position:0% + +nanoc when the balloon is removed the + + align:start position:0% +nanoc when the balloon is removed the + + + align:start position:0% +nanoc when the balloon is removed the +meter reading almost goes back to + + align:start position:0% + + + + align:start position:0% + +zero parent ly the charge is essentially + + align:start position:0% +zero parent ly the charge is essentially + + + align:start position:0% +zero parent ly the charge is essentially +removed with the + + align:start position:0% + + + + align:start position:0% + +balloon what happens to the charge on + + align:start position:0% +balloon what happens to the charge on + + + align:start position:0% +balloon what happens to the charge on +the balloon if it's broken while in the + + align:start position:0% +the balloon if it's broken while in the + + + align:start position:0% +the balloon if it's broken while in the +Faraday cage and then + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +removed we've used Scotch tape to hold + + align:start position:0% +removed we've used Scotch tape to hold + + + align:start position:0% +removed we've used Scotch tape to hold +the balloon together + + align:start position:0% + + + + align:start position:0% + +Professor Zan feels that most of the + + align:start position:0% +Professor Zan feels that most of the + + + align:start position:0% +Professor Zan feels that most of the +balloon was removed the charge was not \ No newline at end of file diff --git a/KUuxdk_V7To.txt b/KUuxdk_V7To.txt new file mode 100644 index 0000000000000000000000000000000000000000..52deb060fd2a3fe2d91459cdda188e2dbf7ef80a --- /dev/null +++ b/KUuxdk_V7To.txt @@ -0,0 +1,987 @@ +align:start position:0% + +hi today we're gonna do a problem about + + align:start position:0% +hi today we're gonna do a problem about + + + align:start position:0% +hi today we're gonna do a problem about +similar matrices the problem is right + + align:start position:0% +similar matrices the problem is right + + + align:start position:0% +similar matrices the problem is right +here so the question asks which of the + + align:start position:0% +here so the question asks which of the + + + align:start position:0% +here so the question asks which of the +following statements are true and it + + align:start position:0% +following statements are true and it + + + align:start position:0% +following statements are true and it +asks you to explain why the first + + align:start position:0% +asks you to explain why the first + + + align:start position:0% +asks you to explain why the first +statement is if a and B are similar + + align:start position:0% +statement is if a and B are similar + + + align:start position:0% +statement is if a and B are similar +matrices then 2a cubed plus a minus 3 + + align:start position:0% +matrices then 2a cubed plus a minus 3 + + + align:start position:0% +matrices then 2a cubed plus a minus 3 +times the identity is similar to 2 times + + align:start position:0% +times the identity is similar to 2 times + + + align:start position:0% +times the identity is similar to 2 times +B cubed plus B minus 3 times the + + align:start position:0% +B cubed plus B minus 3 times the + + + align:start position:0% +B cubed plus B minus 3 times the +identity the second question asks if a + + align:start position:0% +identity the second question asks if a + + + align:start position:0% +identity the second question asks if a +and B are 3x3 matrices with eigenvalues + + align:start position:0% +and B are 3x3 matrices with eigenvalues + + + align:start position:0% +and B are 3x3 matrices with eigenvalues +1 0 and negative 1 then they're similar + + align:start position:0% +1 0 and negative 1 then they're similar + + + align:start position:0% +1 0 and negative 1 then they're similar +and the third part asks you whether + + align:start position:0% +and the third part asks you whether + + + align:start position:0% +and the third part asks you whether +these 2 j matrices are similar ok I'll + + align:start position:0% +these 2 j matrices are similar ok I'll + + + align:start position:0% +these 2 j matrices are similar ok I'll +give you a moment to hit pause and try + + align:start position:0% +give you a moment to hit pause and try + + + align:start position:0% +give you a moment to hit pause and try +it on your own I'll be back in just a + + align:start position:0% +it on your own I'll be back in just a + + + align:start position:0% +it on your own I'll be back in just a +moment and we can do it together + + align:start position:0% + + + + align:start position:0% + +okay and we're back let's start with + + align:start position:0% +okay and we're back let's start with + + + align:start position:0% +okay and we're back let's start with +Part A Part A is true why well what does + + align:start position:0% +Part A Part A is true why well what does + + + align:start position:0% +Part A Part A is true why well what does +it mean for a and B to be similar right + + align:start position:0% +it mean for a and B to be similar right + + + align:start position:0% +it mean for a and B to be similar right +we know there's some matrix M such that + + align:start position:0% +we know there's some matrix M such that + + + align:start position:0% +we know there's some matrix M such that +that's what s T means when I multiply M + + align:start position:0% +that's what s T means when I multiply M + + + align:start position:0% +that's what s T means when I multiply M +on the left or a on the left by M and + + align:start position:0% +on the left or a on the left by M and + + + align:start position:0% +on the left or a on the left by M and +the right by M inverse I get B okay so + + align:start position:0% +the right by M inverse I get B okay so + + + align:start position:0% +the right by M inverse I get B okay so +let's take that same matrix M and + + align:start position:0% +let's take that same matrix M and + + + align:start position:0% +let's take that same matrix M and +multiply it and multiply it on the left + + align:start position:0% +multiply it and multiply it on the left + + + align:start position:0% +multiply it and multiply it on the left +and the right of 2 a cubed plus a minus + + align:start position:0% +and the right of 2 a cubed plus a minus + + + align:start position:0% +and the right of 2 a cubed plus a minus +3 times the identity okay what are we + + align:start position:0% +3 times the identity okay what are we + + + align:start position:0% +3 times the identity okay what are we +get here well the point is what M times + + align:start position:0% +get here well the point is what M times + + + align:start position:0% +get here well the point is what M times +a cubed times M inverse we can just + + align:start position:0% +a cubed times M inverse we can just + + + align:start position:0% +a cubed times M inverse we can just +write that as 3m am inverses similarly + + align:start position:0% +write that as 3m am inverses similarly + + + align:start position:0% +write that as 3m am inverses similarly +we have an M a M inverse and an M times + + align:start position:0% +we have an M a M inverse and an M times + + + align:start position:0% +we have an M a M inverse and an M times +the identity times M inverse good and so + + align:start position:0% +the identity times M inverse good and so + + + align:start position:0% +the identity times M inverse good and so +remember that M times a times M inverse + + align:start position:0% +remember that M times a times M inverse + + + align:start position:0% +remember that M times a times M inverse +is B so we just get 2b cubed right three + + align:start position:0% +is B so we just get 2b cubed right three + + + align:start position:0% +is B so we just get 2b cubed right three +B's plus B minus well M times the + + align:start position:0% +B's plus B minus well M times the + + + align:start position:0% +B's plus B minus well M times the +identity is just M so we just get the + + align:start position:0% +identity is just M so we just get the + + + align:start position:0% +identity is just M so we just get the +identity back and we have three times + + align:start position:0% +identity back and we have three times + + + align:start position:0% +identity back and we have three times +the identity good and this is sort of a + + align:start position:0% +the identity good and this is sort of a + + + align:start position:0% +the identity good and this is sort of a +general remark that if you have matrices + + align:start position:0% +general remark that if you have matrices + + + align:start position:0% +general remark that if you have matrices +a and B that are similar than any + + align:start position:0% +a and B that are similar than any + + + align:start position:0% +a and B that are similar than any +polynomials in these matrices a and B + + align:start position:0% +polynomials in these matrices a and B + + + align:start position:0% +polynomials in these matrices a and B +will be similar it's the exact same + + align:start position:0% +will be similar it's the exact same + + + align:start position:0% +will be similar it's the exact same +justification okay now let's go on to + + align:start position:0% +justification okay now let's go on to + + + align:start position:0% +justification okay now let's go on to +Part B okay so now a and B are 3x3 + + align:start position:0% +Part B okay so now a and B are 3x3 + + + align:start position:0% +Part B okay so now a and B are 3x3 +similar matrix + + align:start position:0% +similar matrix + + + align:start position:0% +similar matrix +with the same eigenvalues and their + + align:start position:0% +with the same eigenvalues and their + + + align:start position:0% +with the same eigenvalues and their +eigenvalues are distinct so it turns out + + align:start position:0% +eigenvalues are distinct so it turns out + + + align:start position:0% +eigenvalues are distinct so it turns out +that B is true as well okay and well why + + align:start position:0% +that B is true as well okay and well why + + + align:start position:0% +that B is true as well okay and well why +is that well a matrix with distinct + + align:start position:0% +is that well a matrix with distinct + + + align:start position:0% +is that well a matrix with distinct +eigenvalues is diagonalizable so we can + + align:start position:0% +eigenvalues is diagonalizable so we can + + + align:start position:0% +eigenvalues is diagonalizable so we can +write a as s lambda s inverse where + + align:start position:0% +write a as s lambda s inverse where + + + align:start position:0% +write a as s lambda s inverse where +lambda is just this eigenvalue matrix + + align:start position:0% +lambda is just this eigenvalue matrix + + + align:start position:0% +lambda is just this eigenvalue matrix +okay we can also write B as T lambda T + + align:start position:0% +okay we can also write B as T lambda T + + + align:start position:0% +okay we can also write B as T lambda T +inverse where lambda is the same in both + + align:start position:0% +inverse where lambda is the same in both + + + align:start position:0% +inverse where lambda is the same in both +cases because they have the same eigen + + align:start position:0% +cases because they have the same eigen + + + align:start position:0% +cases because they have the same eigen +values good now I'll let you you uh so + + align:start position:0% +values good now I'll let you you uh so + + + align:start position:0% +values good now I'll let you you uh so +before we check it let's just say the + + align:start position:0% +before we check it let's just say the + + + align:start position:0% +before we check it let's just say the +point the point is if two matrices are + + align:start position:0% +point the point is if two matrices are + + + align:start position:0% +point the point is if two matrices are +similar to the same matrix then they're + + align:start position:0% +similar to the same matrix then they're + + + align:start position:0% +similar to the same matrix then they're +similar to each other similarity is a + + align:start position:0% +similar to each other similarity is a + + + align:start position:0% +similar to each other similarity is a +transitive relation and I'll just let + + align:start position:0% +transitive relation and I'll just let + + + align:start position:0% +transitive relation and I'll just let +you you a check that you can take TS + + align:start position:0% +you you a check that you can take TS + + + align:start position:0% +you you a check that you can take TS +inverse a times T s inverse inverse and + + align:start position:0% +inverse a times T s inverse inverse and + + + align:start position:0% +inverse a times T s inverse inverse and +you'll get be good this this follows + + align:start position:0% +you'll get be good this this follows + + + align:start position:0% +you'll get be good this this follows +directly from just these two relations + + align:start position:0% +directly from just these two relations + + + align:start position:0% +directly from just these two relations +good now let's take on Part C so Part C + + align:start position:0% +good now let's take on Part C so Part C + + + align:start position:0% +good now let's take on Part C so Part C +is false let's come back over here and + + align:start position:0% +is false let's come back over here and + + + align:start position:0% +is false let's come back over here and +look at these two matrices J 1 and J 2 + + align:start position:0% +look at these two matrices J 1 and J 2 + + + align:start position:0% +look at these two matrices J 1 and J 2 +well the first thing you should see is + + align:start position:0% +well the first thing you should see is + + + align:start position:0% +well the first thing you should see is +that these two are Jordan blocks and + + align:start position:0% +that these two are Jordan blocks and + + + align:start position:0% +that these two are Jordan blocks and +they're different or they're sorry not + + align:start position:0% +they're different or they're sorry not + + + align:start position:0% +they're different or they're sorry not +Jordan blocks there are matrices in + + align:start position:0% +Jordan blocks there are matrices in + + + align:start position:0% +Jordan blocks there are matrices in +Jordan normal form and they're different + + align:start position:0% +Jordan normal form and they're different + + + align:start position:0% +Jordan normal form and they're different +matrices in Jordan normal form so they + + align:start position:0% +matrices in Jordan normal form so they + + + align:start position:0% +matrices in Jordan normal form so they +will not be similar but but let's + + align:start position:0% +will not be similar but but let's + + + align:start position:0% +will not be similar but but let's +actually see why okay so let's look at + + align:start position:0% +actually see why okay so let's look at + + + align:start position:0% +actually see why okay so let's look at +remember one of the things that + + align:start position:0% +remember one of the things that + + + align:start position:0% +remember one of the things that +similarity preserves our eigenvectors + + align:start position:0% +similarity preserves our eigenvectors + + + align:start position:0% +similarity preserves our eigenvectors +and eigenvalues + + align:start position:0% +and eigenvalues + + + align:start position:0% +and eigenvalues +so let's look at the eigenspace with + + align:start position:0% +so let's look at the eigenspace with + + + align:start position:0% +so let's look at the eigenspace with +eigenvalue - one with these two matrices + + align:start position:0% +eigenvalue - one with these two matrices + + + align:start position:0% +eigenvalue - one with these two matrices +so j1 plus the identity let's let's look + + align:start position:0% +so j1 plus the identity let's let's look + + + align:start position:0% +so j1 plus the identity let's let's look +at the null space of this matrix so this + + align:start position:0% +at the null space of this matrix so this + + + align:start position:0% +at the null space of this matrix so this +is just 0 + + align:start position:0% + + + + align:start position:0% + +it's just 0s on the diagonal and ones + + align:start position:0% +it's just 0s on the diagonal and ones + + + align:start position:0% +it's just 0s on the diagonal and ones +right above the diagonal and j2 plus the + + align:start position:0% +right above the diagonal and j2 plus the + + + align:start position:0% +right above the diagonal and j2 plus the +identity well this is just 0 1 0 0 good + + align:start position:0% +identity well this is just 0 1 0 0 good + + + align:start position:0% +identity well this is just 0 1 0 0 good +so the point is that the null space of + + align:start position:0% +so the point is that the null space of + + + align:start position:0% +so the point is that the null space of +this of this matrix is just one + + align:start position:0% +this of this matrix is just one + + + align:start position:0% +this of this matrix is just one +dimensional so there's only one + + align:start position:0% +dimensional so there's only one + + + align:start position:0% +dimensional so there's only one +independent eigenvector of j1 with + + align:start position:0% +independent eigenvector of j1 with + + + align:start position:0% +independent eigenvector of j1 with +eigenvalue minus 1 whereas the null + + align:start position:0% +eigenvalue minus 1 whereas the null + + + align:start position:0% +eigenvalue minus 1 whereas the null +space of this matrix is 2 dimensional + + align:start position:0% +space of this matrix is 2 dimensional + + + align:start position:0% +space of this matrix is 2 dimensional +the there are two independent + + align:start position:0% +the there are two independent + + + align:start position:0% +the there are two independent +eigenvectors with eigenvalue minus 1 so + + align:start position:0% +eigenvectors with eigenvalue minus 1 so + + + align:start position:0% +eigenvectors with eigenvalue minus 1 so +the dimension of the null space of j1 + + align:start position:0% +the dimension of the null space of j1 + + + align:start position:0% +the dimension of the null space of j1 +plus the identity this is 1 and this is + + align:start position:0% +plus the identity this is 1 and this is + + + align:start position:0% +plus the identity this is 1 and this is +2 so they cannot possibly be similar + + align:start position:0% + + + + align:start position:0% + +good good so that completes the problem + + align:start position:0% +good good so that completes the problem + + + align:start position:0% +good good so that completes the problem +it's a nice exercise to do this more + + align:start position:0% +it's a nice exercise to do this more + + + align:start position:0% +it's a nice exercise to do this more +generally and you can use these + + align:start position:0% +generally and you can use these + + + align:start position:0% +generally and you can use these +techniques not just looking at the the + + align:start position:0% +techniques not just looking at the the + + + align:start position:0% +techniques not just looking at the the +number of independent eigen vectors and + + align:start position:0% +number of independent eigen vectors and + + + align:start position:0% +number of independent eigen vectors and +the null space of your J matrix your J + + align:start position:0% +the null space of your J matrix your J + + + align:start position:0% +the null space of your J matrix your J +minus lambda I matrix but also powers of + + align:start position:0% +minus lambda I matrix but also powers of + + + align:start position:0% +minus lambda I matrix but also powers of +J minus lambda I and their null spaces + + align:start position:0% +J minus lambda I and their null spaces + + + align:start position:0% +J minus lambda I and their null spaces +you can use this to show that any two + + align:start position:0% +you can use this to show that any two + + + align:start position:0% +you can use this to show that any two +matrices in Jordan normal form that are + + align:start position:0% +matrices in Jordan normal form that are + + + align:start position:0% +matrices in Jordan normal form that are +different are not similar the same + + align:start position:0% +different are not similar the same + + + align:start position:0% +different are not similar the same +method works and that's a nice exercise + + align:start position:0% +method works and that's a nice exercise + + + align:start position:0% +method works and that's a nice exercise +if you want to go a little further with + + align:start position:0% +if you want to go a little further with + + + align:start position:0% +if you want to go a little further with +similar matrices anyway let's let's just + + align:start position:0% +similar matrices anyway let's let's just + + + align:start position:0% +similar matrices anyway let's let's just +recap the properties we we saw here we + + align:start position:0% +recap the properties we we saw here we + + + align:start position:0% +recap the properties we we saw here we +saw that if we had two similar matrices + + align:start position:0% +saw that if we had two similar matrices + + + align:start position:0% +saw that if we had two similar matrices +then + + align:start position:0% +then + + + align:start position:0% +then +polynomials in those matrices were + + align:start position:0% +polynomials in those matrices were + + + align:start position:0% +polynomials in those matrices were +similar and we saw that if we have two + + align:start position:0% +similar and we saw that if we have two + + + align:start position:0% +similar and we saw that if we have two +matrices that have the same distinct + + align:start position:0% +matrices that have the same distinct + + + align:start position:0% +matrices that have the same distinct +eigenvalues then they're some then + + align:start position:0% +eigenvalues then they're some then + + + align:start position:0% +eigenvalues then they're some then +they're similar and we saw that in a + + align:start position:0% +they're similar and we saw that in a + + + align:start position:0% +they're similar and we saw that in a +special case we saw that two matrices in + + align:start position:0% +special case we saw that two matrices in + + + align:start position:0% +special case we saw that two matrices in +jordan normal form that are different + + align:start position:0% +jordan normal form that are different + + + align:start position:0% +jordan normal form that are different +are not similar thanks \ No newline at end of file diff --git a/KWaGHCjsSAM.txt b/KWaGHCjsSAM.txt new file mode 100644 index 0000000000000000000000000000000000000000..e70d0347f901b71615605a191a7b8a4fd1ba3fc2 --- /dev/null +++ b/KWaGHCjsSAM.txt @@ -0,0 +1,6851 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +well it's promises we're gonna cover no + + align:start position:0% +well it's promises we're gonna cover no + + + align:start position:0% +well it's promises we're gonna cover no +new material today we've just hit the + + align:start position:0% +new material today we've just hit the + + + align:start position:0% +new material today we've just hit the +end of part 2 of the course which I + + align:start position:0% +end of part 2 of the course which I + + + align:start position:0% +end of part 2 of the course which I +think you'll agree with me was probably + + align:start position:0% +think you'll agree with me was probably + + + align:start position:0% +think you'll agree with me was probably +the most technically challenging part + + align:start position:0% +the most technically challenging part + + + align:start position:0% +the most technically challenging part +who would disagree I wonder I didn't + + align:start position:0% +who would disagree I wonder I didn't + + + align:start position:0% +who would disagree I wonder I didn't +think so so I wanted a bit of review and + + align:start position:0% +think so so I wanted a bit of review and + + + align:start position:0% +think so so I wanted a bit of review and +help you guys out with problem set seven + + align:start position:0% +help you guys out with problem set seven + + + align:start position:0% +help you guys out with problem set seven +since I've got a couple of fun problems + + align:start position:0% +since I've got a couple of fun problems + + + align:start position:0% +since I've got a couple of fun problems +I think they're fun because they're + + align:start position:0% +I think they're fun because they're + + + align:start position:0% +I think they're fun because they're +actually fairly realistic like the last + + align:start position:0% +actually fairly realistic like the last + + + align:start position:0% +actually fairly realistic like the last +one will it blend the ap1000 edition + + align:start position:0% +one will it blend the ap1000 edition + + + align:start position:0% +one will it blend the ap1000 edition +well you'll actually analyze if we've + + align:start position:0% +well you'll actually analyze if we've + + + align:start position:0% +well you'll actually analyze if we've +given the actual specification sheet of + + align:start position:0% +given the actual specification sheet of + + + align:start position:0% +given the actual specification sheet of +an ap1000 reactor which is a modern + + align:start position:0% +an ap1000 reactor which is a modern + + + align:start position:0% +an ap1000 reactor which is a modern +reactor that's being built now can you + + align:start position:0% +reactor that's being built now can you + + + align:start position:0% +reactor that's being built now can you +determine its k effective using the to + + align:start position:0% +determine its k effective using the to + + + align:start position:0% +determine its k effective using the to +group the two energy group approximation + + align:start position:0% +group the two energy group approximation + + + align:start position:0% +group the two energy group approximation +and just to show you guys that this + + align:start position:0% +and just to show you guys that this + + + align:start position:0% +and just to show you guys that this +isn't crazy I've got the ap1000 spec + + align:start position:0% +isn't crazy I've got the ap1000 spec + + + align:start position:0% +isn't crazy I've got the ap1000 spec +sheet up here so who got a chance to + + align:start position:0% +sheet up here so who got a chance to + + + align:start position:0% +sheet up here so who got a chance to +take a look at pset seven good that's a + + align:start position:0% +take a look at pset seven good that's a + + + align:start position:0% +take a look at pset seven good that's a +lot of hands alright I I highly + + align:start position:0% +lot of hands alright I I highly + + + align:start position:0% +lot of hands alright I I highly +recommend everyone look at it ahead of + + align:start position:0% +recommend everyone look at it ahead of + + + align:start position:0% +recommend everyone look at it ahead of +time because it is the doozy and it will + + align:start position:0% +time because it is the doozy and it will + + + align:start position:0% +time because it is the doozy and it will +be the last doozy of this course so part + + align:start position:0% +be the last doozy of this course so part + + + align:start position:0% +be the last doozy of this course so part +three of the course is lighter because + + align:start position:0% +three of the course is lighter because + + + align:start position:0% +three of the course is lighter because +most your other courses are gonna go + + align:start position:0% +most your other courses are gonna go + + + align:start position:0% +most your other courses are gonna go +nuts after Thanksgiving as far as I know + + align:start position:0% +nuts after Thanksgiving as far as I know + + + align:start position:0% +nuts after Thanksgiving as far as I know +right yeah this one's not so doing my + + align:start position:0% +right yeah this one's not so doing my + + + align:start position:0% +right yeah this one's not so doing my +best to equalize your total course load + + align:start position:0% +best to equalize your total course load + + + align:start position:0% +best to equalize your total course load +this semester by making this course + + align:start position:0% +this semester by making this course + + + align:start position:0% +this semester by making this course +crazy now and lighten up when final + + align:start position:0% +crazy now and lighten up when final + + + align:start position:0% +crazy now and lighten up when final +season comes so I've got the spec sheet + + align:start position:0% +season comes so I've got the spec sheet + + + align:start position:0% +season comes so I've got the spec sheet +for the ap1000 right here that actually + + align:start position:0% +for the ap1000 right here that actually + + + align:start position:0% +for the ap1000 right here that actually +goes over a description of what the core + + align:start position:0% +goes over a description of what the core + + + align:start position:0% +goes over a description of what the core +is like the materials that are used how + + align:start position:0% +is like the materials that are used how + + + align:start position:0% +is like the materials that are used how +many fuel rods there are how many + + align:start position:0% +many fuel rods there are how many + + + align:start position:0% +many fuel rods there are how many +assemblies there are basically what the + + align:start position:0% +assemblies there are basically what the + + + align:start position:0% +assemblies there are basically what the +core is made of and what I want to do is + + align:start position:0% +core is made of and what I want to do is + + + align:start position:0% +core is made of and what I want to do is +jump to the end where they actually talk + + align:start position:0% +jump to the end where they actually talk + + + align:start position:0% +jump to the end where they actually talk +about the analytical techniques used in + + align:start position:0% +about the analytical techniques used in + + + align:start position:0% +about the analytical techniques used in +the core design what I want to show you + + align:start position:0% +the core design what I want to show you + + + align:start position:0% +the core design what I want to show you +is for nuclear design of the core to get + + align:start position:0% +is for nuclear design of the core to get + + + align:start position:0% +is for nuclear design of the core to get +axial power distributions look at that + + align:start position:0% +axial power distributions look at that + + + align:start position:0% +axial power distributions look at that +to group diffusion Theory the same stuff + + align:start position:0% +to group diffusion Theory the same stuff + + + align:start position:0% +to group diffusion Theory the same stuff +that we just learned right here for + + align:start position:0% +that we just learned right here for + + + align:start position:0% +that we just learned right here for +axial power distribution control rod + + align:start position:0% +axial power distribution control rod + + + align:start position:0% +axial power distribution control rod +Worth's one-dimensional to group + + align:start position:0% +Worth's one-dimensional to group + + + align:start position:0% +Worth's one-dimensional to group +diffusion theory these are problems that + + align:start position:0% +diffusion theory these are problems that + + + align:start position:0% +diffusion theory these are problems that +you can solve with the stuff that we've + + align:start position:0% +you can solve with the stuff that we've + + + align:start position:0% +you can solve with the stuff that we've +done over the past week and a half they + + align:start position:0% +done over the past week and a half they + + + align:start position:0% +done over the past week and a half they +have a little more complexity and that + + align:start position:0% +have a little more complexity and that + + + align:start position:0% +have a little more complexity and that +they keep all the spatial variance in + + align:start position:0% +they keep all the spatial variance in + + + align:start position:0% +they keep all the spatial variance in +there + + align:start position:0% +there + + + align:start position:0% +there +so probably done with computers however + + align:start position:0% +so probably done with computers however + + + align:start position:0% +so probably done with computers however +when they make the same equations that + + align:start position:0% +when they make the same equations that + + + align:start position:0% +when they make the same equations that +you do so Westinghouse is making the + + align:start position:0% +you do so Westinghouse is making the + + + align:start position:0% +you do so Westinghouse is making the +same assumptions that we made in this + + align:start position:0% +same assumptions that we made in this + + + align:start position:0% +same assumptions that we made in this +course they have a lot more complexity + + align:start position:0% +course they have a lot more complexity + + + align:start position:0% +course they have a lot more complexity +in that there you know we just had cross + + align:start position:0% +in that there you know we just had cross + + + align:start position:0% +in that there you know we just had cross +sections or macroscopic cross sections + + align:start position:0% +sections or macroscopic cross sections + + + align:start position:0% +sections or macroscopic cross sections +as a function of energy but you may also + + align:start position:0% +as a function of energy but you may also + + + align:start position:0% +as a function of energy but you may also +think about it as a function of position + + align:start position:0% +think about it as a function of position + + + align:start position:0% +think about it as a function of position +and a function of temperature since as + + align:start position:0% +and a function of temperature since as + + + align:start position:0% +and a function of temperature since as +we started alluding to on what was today + + align:start position:0% +we started alluding to on what was today + + + align:start position:0% +we started alluding to on what was today +it's on Wednesday know Tuesday what day + + align:start position:0% +it's on Wednesday know Tuesday what day + + + align:start position:0% +it's on Wednesday know Tuesday what day +is it now + + align:start position:0% +is it now + + + align:start position:0% +is it now +it's Thursday thank you so definitely on + + align:start position:0% +it's Thursday thank you so definitely on + + + align:start position:0% +it's Thursday thank you so definitely on +Tuesday we started talking about how + + align:start position:0% +Tuesday we started talking about how + + + align:start position:0% +Tuesday we started talking about how +cross sections change with temperature + + align:start position:0% +cross sections change with temperature + + + align:start position:0% +cross sections change with temperature +and so really if we want to go crazy on + + align:start position:0% +and so really if we want to go crazy on + + + align:start position:0% +and so really if we want to go crazy on +that neutron transport equation these + + align:start position:0% +that neutron transport equation these + + + align:start position:0% +that neutron transport equation these +cross sections will be functions of + + align:start position:0% +cross sections will be functions of + + + align:start position:0% +cross sections will be functions of +energy temperature and position and so + + align:start position:0% +energy temperature and position and so + + + align:start position:0% +energy temperature and position and so +that's how this reactor would have + + align:start position:0% +that's how this reactor would have + + + align:start position:0% +that's how this reactor would have +actually been designed but you're going + + align:start position:0% +actually been designed but you're going + + + align:start position:0% +actually been designed but you're going +to do a simpler approximation and take + + align:start position:0% +to do a simpler approximation and take + + + align:start position:0% +to do a simpler approximation and take +all of the information about the core + + align:start position:0% +all of the information about the core + + + align:start position:0% +all of the information about the core +and an ap1000 blend it so homogenized it + + align:start position:0% +and an ap1000 blend it so homogenized it + + + align:start position:0% +and an ap1000 blend it so homogenized it +figure out what the average atomic + + align:start position:0% +figure out what the average atomic + + + align:start position:0% +figure out what the average atomic +fractions of all the different things in + + align:start position:0% +fractions of all the different things in + + + align:start position:0% +fractions of all the different things in +it are and calculate is K effective so I + + align:start position:0% +it are and calculate is K effective so I + + + align:start position:0% +it are and calculate is K effective so I +think is a pretty cool problem to do I + + align:start position:0% +think is a pretty cool problem to do I + + + align:start position:0% +think is a pretty cool problem to do I +haven't seen it done in the courses here + + align:start position:0% +haven't seen it done in the courses here + + + align:start position:0% +haven't seen it done in the courses here +but I want to see how you how it turns + + align:start position:0% +but I want to see how you how it turns + + + align:start position:0% +but I want to see how you how it turns +out and you might find it's surprisingly + + align:start position:0% +out and you might find it's surprisingly + + + align:start position:0% +out and you might find it's surprisingly +different from one because we make a lot + + align:start position:0% +different from one because we make a lot + + + align:start position:0% +different from one because we make a lot +a lot of simplifications that actually + + align:start position:0% +a lot of simplifications that actually + + + align:start position:0% +a lot of simplifications that actually +matter quite a bit but to help you parse + + align:start position:0% +matter quite a bit but to help you parse + + + align:start position:0% +matter quite a bit but to help you parse +this spec sheet well actually why don't + + align:start position:0% +this spec sheet well actually why don't + + + align:start position:0% +this spec sheet well actually why don't +I show you the problem first we'll go + + align:start position:0% +I show you the problem first we'll go + + + align:start position:0% +I show you the problem first we'll go +through a few of the different things + + align:start position:0% +through a few of the different things + + + align:start position:0% +through a few of the different things +that I've simplified the problem to make + + align:start position:0% +that I've simplified the problem to make + + + align:start position:0% +that I've simplified the problem to make +it not so tedious but I also want to + + align:start position:0% +it not so tedious but I also want to + + + align:start position:0% +it not so tedious but I also want to +make sure you understand what to do so + + align:start position:0% +make sure you understand what to do so + + + align:start position:0% +make sure you understand what to do so +the simple the simple statement is + + align:start position:0% +the simple the simple statement is + + + align:start position:0% +the simple the simple statement is +calculate K effective of the ap1000 + + align:start position:0% +calculate K effective of the ap1000 + + + align:start position:0% +calculate K effective of the ap1000 +using two group diffusion theory which + + align:start position:0% +using two group diffusion theory which + + + align:start position:0% +using two group diffusion theory which +means you've got a criticality condition + + align:start position:0% +means you've got a criticality condition + + + align:start position:0% +means you've got a criticality condition +from the two group approximation and I'd + + align:start position:0% +from the two group approximation and I'd + + + align:start position:0% +from the two group approximation and I'd +like to go over what that is right now + + align:start position:0% +like to go over what that is right now + + + align:start position:0% +like to go over what that is right now +let's so let's write out if we had a two + + align:start position:0% +let's so let's write out if we had a two + + + align:start position:0% +let's so let's write out if we had a two +group so there are two Energy Group + + align:start position:0% +group so there are two Energy Group + + + align:start position:0% +group so there are two Energy Group +equations for gains and losses of + + align:start position:0% +equations for gains and losses of + + + align:start position:0% +equations for gains and losses of +neutrons in the fast and thermal group + + align:start position:0% +neutrons in the fast and thermal group + + + align:start position:0% +neutrons in the fast and thermal group +what would it look like what are the + + align:start position:0% +what would it look like what are the + + + align:start position:0% +what would it look like what are the +gain terms + + align:start position:0% + + + + align:start position:0% + +yep there's gonna be some average new + + align:start position:0% +yep there's gonna be some average new + + + align:start position:0% +yep there's gonna be some average new +times Sigma fission fast times flux fast + + align:start position:0% +times Sigma fission fast times flux fast + + + align:start position:0% +times Sigma fission fast times flux fast +plus Sigma fission thermal times flux + + align:start position:0% +plus Sigma fission thermal times flux + + + align:start position:0% +plus Sigma fission thermal times flux +Thermal any other sources of neutrons + + align:start position:0% +Thermal any other sources of neutrons + + + align:start position:0% +Thermal any other sources of neutrons +into the fast group I don't think so + + align:start position:0% +into the fast group I don't think so + + + align:start position:0% +into the fast group I don't think so +what about sinks + + align:start position:0% +what about sinks + + + align:start position:0% +what about sinks +how do neutrons leave the fast group yep + + align:start position:0% +how do neutrons leave the fast group yep + + + align:start position:0% +how do neutrons leave the fast group yep +by absorption how else yep + + align:start position:0% +by absorption how else yep + + + align:start position:0% +by absorption how else yep +scattering from the fast to the thermal + + align:start position:0% +scattering from the fast to the thermal + + + align:start position:0% +scattering from the fast to the thermal +group how else + + align:start position:0% +group how else + + + align:start position:0% +group how else +leakage so there'll be some diffusion + + align:start position:0% +leakage so there'll be some diffusion + + + align:start position:0% +leakage so there'll be some diffusion +constant fast times some fast geometric + + align:start position:0% +constant fast times some fast geometric + + + align:start position:0% +constant fast times some fast geometric +buckling squared and yeah I think that's + + align:start position:0% +buckling squared and yeah I think that's + + + align:start position:0% +buckling squared and yeah I think that's +it no that needs a Phi as well fast okay + + align:start position:0% +it no that needs a Phi as well fast okay + + + align:start position:0% +it no that needs a Phi as well fast okay +cool + + align:start position:0% +cool + + + align:start position:0% +cool +what about the thermal group what are + + align:start position:0% +what about the thermal group what are + + + align:start position:0% +what about the thermal group what are +the sources of thermal neutrons yep + + align:start position:0% +the sources of thermal neutrons yep + + + align:start position:0% +the sources of thermal neutrons yep +scattering from the fast group so this + + align:start position:0% +scattering from the fast group so this + + + align:start position:0% +scattering from the fast group so this +same term right here fast a thermal + + align:start position:0% +same term right here fast a thermal + + + align:start position:0% +same term right here fast a thermal +times Phi fast and what are the losses + + align:start position:0% + + + + align:start position:0% + +leakage and absorption they look pretty + + align:start position:0% +leakage and absorption they look pretty + + + align:start position:0% +leakage and absorption they look pretty +familiar thermal by thermal plus the + + align:start position:0% +familiar thermal by thermal plus the + + + align:start position:0% +familiar thermal by thermal plus the +thermal BG squared by thermal and that's + + align:start position:0% +thermal BG squared by thermal and that's + + + align:start position:0% +thermal BG squared by thermal and that's +C T okay the hard part in this problem + + align:start position:0% +C T okay the hard part in this problem + + + align:start position:0% +C T okay the hard part in this problem +is going to be doing these averages this + + align:start position:0% +is going to be doing these averages this + + + align:start position:0% +is going to be doing these averages this +is the part that we haven't explicitly + + align:start position:0% +is the part that we haven't explicitly + + + align:start position:0% +is the part that we haven't explicitly +done on the board and I want to show you + + align:start position:0% +done on the board and I want to show you + + + align:start position:0% +done on the board and I want to show you +yeah this one top equation that should + + align:start position:0% +yeah this one top equation that should + + + align:start position:0% +yeah this one top equation that should +be a I'll make the apps really curly + + align:start position:0% +be a I'll make the apps really curly + + + align:start position:0% +be a I'll make the apps really curly +curve and those are straight T's these + + align:start position:0% +curve and those are straight T's these + + + align:start position:0% +curve and those are straight T's these +are curly FS + + align:start position:0% +are curly FS + + + align:start position:0% +are curly FS +okay great thank you so the hard part is + + align:start position:0% +okay great thank you so the hard part is + + + align:start position:0% +okay great thank you so the hard part is +going to be doing cross section averages + + align:start position:0% +going to be doing cross section averages + + + align:start position:0% +going to be doing cross section averages +we've just kind of written them as hey + + align:start position:0% +we've just kind of written them as hey + + + align:start position:0% +we've just kind of written them as hey +they're average cross sections in an + + align:start position:0% +they're average cross sections in an + + + align:start position:0% +they're average cross sections in an +average cross section would look + + align:start position:0% +average cross section would look + + + align:start position:0% +average cross section would look +something like the integral from a + + align:start position:0% +something like the integral from a + + + align:start position:0% +something like the integral from a +minimum to a maximum of the cross + + align:start position:0% +minimum to a maximum of the cross + + + align:start position:0% +minimum to a maximum of the cross +section as a function of energy times + + align:start position:0% +section as a function of energy times + + + align:start position:0% +section as a function of energy times +the flux over the same integral without + + align:start position:0% +the flux over the same integral without + + + align:start position:0% +the flux over the same integral without +the cross section + + align:start position:0% + + + + align:start position:0% + +this is where I want to point out + + align:start position:0% +this is where I want to point out + + + align:start position:0% +this is where I want to point out +something that I want you to remember + + align:start position:0% +something that I want you to remember + + + align:start position:0% +something that I want you to remember +for the rest of this course and the rest + + align:start position:0% +for the rest of this course and the rest + + + align:start position:0% +for the rest of this course and the rest +of your life you don't have to do things + + align:start position:0% +of your life you don't have to do things + + + align:start position:0% +of your life you don't have to do things +analytically if you don't want to unless + + align:start position:0% +analytically if you don't want to unless + + + align:start position:0% +analytically if you don't want to unless +it's explicitly stated that you have to + + align:start position:0% +it's explicitly stated that you have to + + + align:start position:0% +it's explicitly stated that you have to +so part of this pset is to drill in the + + align:start position:0% +so part of this pset is to drill in the + + + align:start position:0% +so part of this pset is to drill in the +idea that it's the future we have + + align:start position:0% +idea that it's the future we have + + + align:start position:0% +idea that it's the future we have +computers and you can do numerical + + align:start position:0% +computers and you can do numerical + + + align:start position:0% +computers and you can do numerical +integration with data remember on one of + + align:start position:0% +integration with data remember on one of + + + align:start position:0% +integration with data remember on one of +the second problem sets I showed you + + align:start position:0% +the second problem sets I showed you + + + align:start position:0% +the second problem sets I showed you +guys the web plot digitizer how you can + + align:start position:0% +guys the web plot digitizer how you can + + + align:start position:0% +guys the web plot digitizer how you can +extract information from a printed graph + + align:start position:0% +extract information from a printed graph + + + align:start position:0% +extract information from a printed graph +well a lot of times what you already + + align:start position:0% +well a lot of times what you already + + + align:start position:0% +well a lot of times what you already +have is that data and you'll have to + + align:start position:0% +have is that data and you'll have to + + + align:start position:0% +have is that data and you'll have to +then integrate that numerically in + + align:start position:0% +then integrate that numerically in + + + align:start position:0% +then integrate that numerically in +something as simple as Excel or as + + align:start position:0% +something as simple as Excel or as + + + align:start position:0% +something as simple as Excel or as +complicated as MATLAB or something worse + + align:start position:0% +complicated as MATLAB or something worse + + + align:start position:0% +complicated as MATLAB or something worse +whatever tool you choose to use I'll be + + align:start position:0% +whatever tool you choose to use I'll be + + + align:start position:0% +whatever tool you choose to use I'll be +using excel because it's kind of the + + align:start position:0% +using excel because it's kind of the + + + align:start position:0% +using excel because it's kind of the +lowest common denominator and so to show + + align:start position:0% +lowest common denominator and so to show + + + align:start position:0% +lowest common denominator and so to show +you guys you don't need to know any + + align:start position:0% +you guys you don't need to know any + + + align:start position:0% +you guys you don't need to know any +fancy software to actually solve these + + align:start position:0% +fancy software to actually solve these + + + align:start position:0% +fancy software to actually solve these +problems so let's go through getting + + align:start position:0% +problems so let's go through getting + + + align:start position:0% +problems so let's go through getting +some of this data right now let's say + + align:start position:0% +some of this data right now let's say + + + align:start position:0% +some of this data right now let's say +that the cutoff between fast and thermal + + align:start position:0% +that the cutoff between fast and thermal + + + align:start position:0% +that the cutoff between fast and thermal +so if we were doing a fast cross section + + align:start position:0% +so if we were doing a fast cross section + + + align:start position:0% +so if we were doing a fast cross section +the cutoff would be at one Evie and our + + align:start position:0% +the cutoff would be at one Evie and our + + + align:start position:0% +the cutoff would be at one Evie and our +max would be let's say 10 MeV which + + align:start position:0% +max would be let's say 10 MeV which + + + align:start position:0% +max would be let's say 10 MeV which +would be the top of the fission birth + + align:start position:0% +would be the top of the fission birth + + + align:start position:0% +would be the top of the fission birth +spectrum or the Chi spectrum one UV that + + align:start position:0% +spectrum or the Chi spectrum one UV that + + + align:start position:0% +spectrum or the Chi spectrum one UV that +would be 10 MeV so all that's left is + + align:start position:0% +would be 10 MeV so all that's left is + + + align:start position:0% +would be 10 MeV so all that's left is +you need tabulated values for the cross + + align:start position:0% +you need tabulated values for the cross + + + align:start position:0% +you need tabulated values for the cross +sections and the fluxes and then you can + + align:start position:0% +sections and the fluxes and then you can + + + align:start position:0% +sections and the fluxes and then you can +perform this numerical integral I've + + align:start position:0% +perform this numerical integral I've + + + align:start position:0% +perform this numerical integral I've +given you tabulated values for the + + align:start position:0% +given you tabulated values for the + + + align:start position:0% +given you tabulated values for the +fluxes wherever that is yep use the + + align:start position:0% +fluxes wherever that is yep use the + + + align:start position:0% +fluxes wherever that is yep use the +attached ap1000 tabulated Neutron flux + + align:start position:0% +attached ap1000 tabulated Neutron flux + + + align:start position:0% +attached ap1000 tabulated Neutron flux +profile which opens that's awesome so + + align:start position:0% +profile which opens that's awesome so + + + align:start position:0% +profile which opens that's awesome so +I've given you the approximate Neutron + + align:start position:0% +I've given you the approximate Neutron + + + align:start position:0% +I've given you the approximate Neutron +flux in neutrons per centimeter squared + + align:start position:0% +flux in neutrons per centimeter squared + + + align:start position:0% +flux in neutrons per centimeter squared +per second as a function of neutron + + align:start position:0% +per second as a function of neutron + + + align:start position:0% +per second as a function of neutron +energy and so you can tell for a low + + align:start position:0% +energy and so you can tell for a low + + + align:start position:0% +energy and so you can tell for a low +Neutron energy there aren't any ultra + + align:start position:0% +Neutron energy there aren't any ultra + + + align:start position:0% +Neutron energy there aren't any ultra +cold neutrons in this problem though + + align:start position:0% +cold neutrons in this problem though + + + align:start position:0% +cold neutrons in this problem though +there are in the problem right before + + align:start position:0% +there are in the problem right before + + + align:start position:0% +there are in the problem right before +because remember the we'll see now is + + align:start position:0% +because remember the we'll see now is + + + align:start position:0% +because remember the we'll see now is +when we'll see but if we scale down we + + align:start position:0% +when we'll see but if we scale down we + + + align:start position:0% +when we'll see but if we scale down we +get down to the thermal regions where + + align:start position:0% +get down to the thermal regions where + + + align:start position:0% +get down to the thermal regions where +it's in the EVM levels you start to see + + align:start position:0% +it's in the EVM levels you start to see + + + align:start position:0% +it's in the EVM levels you start to see +pretty significant Neutron fluxes on the + + align:start position:0% +pretty significant Neutron fluxes on the + + + align:start position:0% +pretty significant Neutron fluxes on the +rail + + align:start position:0% +rail + + + align:start position:0% +rail +of 10 to the 14th neutrons for + + align:start position:0% +of 10 to the 14th neutrons for + + + align:start position:0% +of 10 to the 14th neutrons for +centimeter squared per second so that + + align:start position:0% +centimeter squared per second so that + + + align:start position:0% +centimeter squared per second so that +value of 10 to the 14th for flux that + + align:start position:0% +value of 10 to the 14th for flux that + + + align:start position:0% +value of 10 to the 14th for flux that +we've been using in all our previous + + align:start position:0% +we've been using in all our previous + + + align:start position:0% +we've been using in all our previous +problem sets it's because that's what we + + align:start position:0% +problem sets it's because that's what we + + + align:start position:0% +problem sets it's because that's what we +actually get this flux spectrum and the + + align:start position:0% +actually get this flux spectrum and the + + + align:start position:0% +actually get this flux spectrum and the +picture of it that we have here was + + align:start position:0% +picture of it that we have here was + + + align:start position:0% +picture of it that we have here was +taken from the MIT reactor because it's + + align:start position:0% +taken from the MIT reactor because it's + + + align:start position:0% +taken from the MIT reactor because it's +representative of a pressurized water + + align:start position:0% +representative of a pressurized water + + + align:start position:0% +representative of a pressurized water +reactor + + align:start position:0% +reactor + + + align:start position:0% +reactor +the only difference here is this is the + + align:start position:0% +the only difference here is this is the + + + align:start position:0% +the only difference here is this is the +spectrum from the fast flux trap you + + align:start position:0% +spectrum from the fast flux trap you + + + align:start position:0% +spectrum from the fast flux trap you +don't usually see that fast to thermal + + align:start position:0% +don't usually see that fast to thermal + + + align:start position:0% +don't usually see that fast to thermal +ratio in a thermal reactor but it's the + + align:start position:0% +ratio in a thermal reactor but it's the + + + align:start position:0% +ratio in a thermal reactor but it's the +closest spectrum that I was even easily + + align:start position:0% +closest spectrum that I was even easily + + + align:start position:0% +closest spectrum that I was even easily +able to get my hands on and it's not + + align:start position:0% +able to get my hands on and it's not + + + align:start position:0% +able to get my hands on and it's not +that unrepresentative and the reaction + + align:start position:0% +that unrepresentative and the reaction + + + align:start position:0% +that unrepresentative and the reaction +rates for things aren't gonna be that + + align:start position:0% +rates for things aren't gonna be that + + + align:start position:0% +rates for things aren't gonna be that +different because most of the reaction + + align:start position:0% +different because most of the reaction + + + align:start position:0% +different because most of the reaction +rates the cross-sections down here are + + align:start position:0% +rates the cross-sections down here are + + + align:start position:0% +rates the cross-sections down here are +in the like thousands of barns level and + + align:start position:0% +in the like thousands of barns level and + + + align:start position:0% +in the like thousands of barns level and +the cross-sections here are in the one + + align:start position:0% +the cross-sections here are in the one + + + align:start position:0% +the cross-sections here are in the one +barn level it's pretty much any fast + + align:start position:0% +barn level it's pretty much any fast + + + align:start position:0% +barn level it's pretty much any fast +cross-section for anything about a barn + + align:start position:0% +cross-section for anything about a barn + + + align:start position:0% +cross-section for anything about a barn +that's a good rule of thumb so it's not + + align:start position:0% +that's a good rule of thumb so it's not + + + align:start position:0% +that's a good rule of thumb so it's not +going to change total reaction rates + + align:start position:0% +going to change total reaction rates + + + align:start position:0% +going to change total reaction rates +that much and that's why I'm not worried + + align:start position:0% +that much and that's why I'm not worried + + + align:start position:0% +that much and that's why I'm not worried +about making a taking the fast flux + + align:start position:0% +about making a taking the fast flux + + + align:start position:0% +about making a taking the fast flux +spectrum from the MIT reactor and + + align:start position:0% +spectrum from the MIT reactor and + + + align:start position:0% +spectrum from the MIT reactor and +pretending like it's the ap1000 it's not + + align:start position:0% +pretending like it's the ap1000 it's not + + + align:start position:0% +pretending like it's the ap1000 it's not +horribly that far off and it's at the + + align:start position:0% +horribly that far off and it's at the + + + align:start position:0% +horribly that far off and it's at the +right order of magnitude which is + + align:start position:0% +right order of magnitude which is + + + align:start position:0% +right order of magnitude which is +important so that data I give you let's + + align:start position:0% +important so that data I give you let's + + + align:start position:0% +important so that data I give you let's +talk about how to get this data the + + align:start position:0% +talk about how to get this data the + + + align:start position:0% +talk about how to get this data the +macroscopic cross-sections + + align:start position:0% + + + + align:start position:0% + +so if you remember a macroscopic + + align:start position:0% +so if you remember a macroscopic + + + align:start position:0% +so if you remember a macroscopic +cross-section is a microscopic + + align:start position:0% +cross-section is a microscopic + + + align:start position:0% +cross-section is a microscopic +cross-section times a number density and + + align:start position:0% +cross-section times a number density and + + + align:start position:0% +cross-section times a number density and +that's for one single isotope if you + + align:start position:0% +that's for one single isotope if you + + + align:start position:0% +that's for one single isotope if you +have a mix of isotopes then your total + + align:start position:0% +have a mix of isotopes then your total + + + align:start position:0% +have a mix of isotopes then your total +averaged cross-section for all different + + align:start position:0% +averaged cross-section for all different + + + align:start position:0% +averaged cross-section for all different +types of atoms is going to be a sum and + + align:start position:0% +types of atoms is going to be a sum and + + + align:start position:0% +types of atoms is going to be a sum and +make it very different over all of your + + align:start position:0% +make it very different over all of your + + + align:start position:0% +make it very different over all of your +isotopic possible ores all your possible + + align:start position:0% +isotopic possible ores all your possible + + + align:start position:0% +isotopic possible ores all your possible +isotopes of the atom fraction of that + + align:start position:0% +isotopes of the atom fraction of that + + + align:start position:0% +isotopes of the atom fraction of that +isotope times the number density of that + + align:start position:0% +isotope times the number density of that + + + align:start position:0% +isotope times the number density of that +isotope times the microscopic + + align:start position:0% +isotope times the microscopic + + + align:start position:0% +isotope times the microscopic +cross-section of that reaction for that + + align:start position:0% +cross-section of that reaction for that + + + align:start position:0% +cross-section of that reaction for that +isotope I'm sorry the atom fraction is + + align:start position:0% +isotope I'm sorry the atom fraction is + + + align:start position:0% +isotope I'm sorry the atom fraction is +included in the number density let's + + align:start position:0% +included in the number density let's + + + align:start position:0% +included in the number density let's +just simplify this a little bit + + align:start position:0% +just simplify this a little bit + + + align:start position:0% +just simplify this a little bit +the total number density of that isotope + + align:start position:0% +the total number density of that isotope + + + align:start position:0% +the total number density of that isotope +that'll be in atoms per cubic centimeter + + align:start position:0% +that'll be in atoms per cubic centimeter + + + align:start position:0% +that'll be in atoms per cubic centimeter +times the cross-section for that + + align:start position:0% +times the cross-section for that + + + align:start position:0% +times the cross-section for that +particular isotope which is in + + align:start position:0% +particular isotope which is in + + + align:start position:0% +particular isotope which is in +centimeters squared which leads you to a + + align:start position:0% + + + + align:start position:0% + +one over centimeter macroscopic cross + + align:start position:0% +one over centimeter macroscopic cross + + + align:start position:0% +one over centimeter macroscopic cross +section and so let's say we were summing + + align:start position:0% +section and so let's say we were summing + + + align:start position:0% +section and so let's say we were summing +up something like stainless steel which + + align:start position:0% +up something like stainless steel which + + + align:start position:0% +up something like stainless steel which +happened to be iron 18 chrome 10 nickel + + align:start position:0% +happened to be iron 18 chrome 10 nickel + + + align:start position:0% +happened to be iron 18 chrome 10 nickel +not only would you have to then get the + + align:start position:0% +not only would you have to then get the + + + align:start position:0% +not only would you have to then get the +number densities of iron chrome and + + align:start position:0% +number densities of iron chrome and + + + align:start position:0% +number densities of iron chrome and +nickel but you have to look at which + + align:start position:0% +nickel but you have to look at which + + + align:start position:0% +nickel but you have to look at which +isotopes there are so if we want it to + + align:start position:0% +isotopes there are so if we want it to + + + align:start position:0% +isotopes there are so if we want it to +get the macroscopic cross section for + + align:start position:0% +get the macroscopic cross section for + + + align:start position:0% +get the macroscopic cross section for +stainless steel we'd have to split this + + align:start position:0% +stainless steel we'd have to split this + + + align:start position:0% +stainless steel we'd have to split this +into the stable isotopes of iron the + + align:start position:0% +into the stable isotopes of iron the + + + align:start position:0% +into the stable isotopes of iron the +stable isotopes of chrome and the stable + + align:start position:0% +stable isotopes of chrome and the stable + + + align:start position:0% +stable isotopes of chrome and the stable +isotopes of nickel and then say it's + + align:start position:0% +isotopes of nickel and then say it's + + + align:start position:0% +isotopes of nickel and then say it's +this number density times of + + align:start position:0% +this number density times of + + + align:start position:0% +this number density times of +cross-section Plus this number density + + align:start position:0% +cross-section Plus this number density + + + align:start position:0% +cross-section Plus this number density +times a cross-section and so on and so + + align:start position:0% +times a cross-section and so on and so + + + align:start position:0% +times a cross-section and so on and so +on and so on the easy way to do get + + align:start position:0% +on and so on the easy way to do get + + + align:start position:0% +on and so on the easy way to do get +those number densities if you take the + + align:start position:0% +those number densities if you take the + + + align:start position:0% +those number densities if you take the +number density of your stainless steel + + align:start position:0% +number density of your stainless steel + + + align:start position:0% +number density of your stainless steel +times the atom fraction of that isotope + + align:start position:0% +times the atom fraction of that isotope + + + align:start position:0% +times the atom fraction of that isotope +that should give you the number density + + align:start position:0% +that should give you the number density + + + align:start position:0% +that should give you the number density +of that isotope this makes sense to + + align:start position:0% +of that isotope this makes sense to + + + align:start position:0% +of that isotope this makes sense to +everybody + + align:start position:0% + + + + align:start position:0% + +does anyone not know how to get a number + + align:start position:0% +does anyone not know how to get a number + + + align:start position:0% +does anyone not know how to get a number +density of a material from its basic + + align:start position:0% +density of a material from its basic + + + align:start position:0% +density of a material from its basic +chemical properties okay + + align:start position:0% +chemical properties okay + + + align:start position:0% +chemical properties okay +so a number density is in atoms per + + align:start position:0% +so a number density is in atoms per + + + align:start position:0% +so a number density is in atoms per +cubic centimeter and usually we would + + align:start position:0% +cubic centimeter and usually we would + + + align:start position:0% +cubic centimeter and usually we would +have something like its density which + + align:start position:0% +have something like its density which + + + align:start position:0% +have something like its density which +would be grams per cubic centimeter so + + align:start position:0% +would be grams per cubic centimeter so + + + align:start position:0% +would be grams per cubic centimeter so +if we take density in grams per + + align:start position:0% +if we take density in grams per + + + align:start position:0% +if we take density in grams per +centimeter cubed and x Avogadro's number + + align:start position:0% +centimeter cubed and x Avogadro's number + + + align:start position:0% +centimeter cubed and x Avogadro's number +and divide by I'll just put a / symbol + + align:start position:0% +and divide by I'll just put a / symbol + + + align:start position:0% +and divide by I'll just put a / symbol +here the molar mass of a god rose number + + align:start position:0% +here the molar mass of a god rose number + + + align:start position:0% +here the molar mass of a god rose number +is given in atoms per mole and divided + + align:start position:0% +is given in atoms per mole and divided + + + align:start position:0% +is given in atoms per mole and divided +by molar mass units are given in what is + + align:start position:0% +by molar mass units are given in what is + + + align:start position:0% +by molar mass units are given in what is +it grams per mole so that's going to be + + align:start position:0% +it grams per mole so that's going to be + + + align:start position:0% +it grams per mole so that's going to be +like moles per gram the grams cancel the + + align:start position:0% +like moles per gram the grams cancel the + + + align:start position:0% +like moles per gram the grams cancel the +moles cancel and you get atoms per cubic + + align:start position:0% +moles cancel and you get atoms per cubic + + + align:start position:0% +moles cancel and you get atoms per cubic +centimeter so to get a number density + + align:start position:0% +centimeter so to get a number density + + + align:start position:0% +centimeter so to get a number density +you can take the density of the material + + align:start position:0% +you can take the density of the material + + + align:start position:0% +you can take the density of the material +you know for stainless steel it's like + + align:start position:0% +you know for stainless steel it's like + + + align:start position:0% +you know for stainless steel it's like +eight grams per cubic centimeter times + + align:start position:0% +eight grams per cubic centimeter times + + + align:start position:0% +eight grams per cubic centimeter times +Avogadro's number say 6 times 10 to the + + align:start position:0% +Avogadro's number say 6 times 10 to the + + + align:start position:0% +Avogadro's number say 6 times 10 to the +23rd this would be like 8 grams per + + align:start position:0% +23rd this would be like 8 grams per + + + align:start position:0% +23rd this would be like 8 grams per +centimeter cubed or so time or divided + + align:start position:0% +centimeter cubed or so time or divided + + + align:start position:0% +centimeter cubed or so time or divided +by the molar mass or the average molar + + align:start position:0% +by the molar mass or the average molar + + + align:start position:0% +by the molar mass or the average molar +mass of stainless steel I'm guessing + + align:start position:0% +mass of stainless steel I'm guessing + + + align:start position:0% +mass of stainless steel I'm guessing +that's around 56 grams per mole and then + + align:start position:0% +that's around 56 grams per mole and then + + + align:start position:0% +that's around 56 grams per mole and then +you'll get a number density and typical + + align:start position:0% +you'll get a number density and typical + + + align:start position:0% +you'll get a number density and typical +solid number densities tend to range + + align:start position:0% +solid number densities tend to range + + + align:start position:0% +solid number densities tend to range +from like 10 to the 26 to 10 to the 28 + + align:start position:0% +from like 10 to the 26 to 10 to the 28 + + + align:start position:0% +from like 10 to the 26 to 10 to the 28 +it'll be atoms per meter cube so it's + + align:start position:0% +it'll be atoms per meter cube so it's + + + align:start position:0% +it'll be atoms per meter cube so it's +gonna be around like 21 to 23 atoms per + + align:start position:0% +gonna be around like 21 to 23 atoms per + + + align:start position:0% +gonna be around like 21 to 23 atoms per +centimeter cubed so if you end up with + + align:start position:0% +centimeter cubed so if you end up with + + + align:start position:0% +centimeter cubed so if you end up with +something way outside those bounds + + align:start position:0% +something way outside those bounds + + + align:start position:0% +something way outside those bounds +you've probably got some sort of unit or + + align:start position:0% +you've probably got some sort of unit or + + + align:start position:0% +you've probably got some sort of unit or +power error so that'll help you check + + align:start position:0% +power error so that'll help you check + + + align:start position:0% +power error so that'll help you check +your math to make sure you get the + + align:start position:0% +your math to make sure you get the + + + align:start position:0% +your math to make sure you get the +number densities right if you get the + + align:start position:0% +number densities right if you get the + + + align:start position:0% +number densities right if you get the +number densities right and you know the + + align:start position:0% +number densities right and you know the + + + align:start position:0% +number densities right and you know the +atom fraction + + align:start position:0% +atom fraction + + + align:start position:0% +atom fraction +and you have the number density of each + + align:start position:0% +and you have the number density of each + + + align:start position:0% +and you have the number density of each +isotope in the number of atoms of that + + align:start position:0% +isotope in the number of atoms of that + + + align:start position:0% +isotope in the number of atoms of that +isotope cubic centimeter and then you + + align:start position:0% +isotope cubic centimeter and then you + + + align:start position:0% +isotope cubic centimeter and then you +multiply by your cross-section your + + align:start position:0% +multiply by your cross-section your + + + align:start position:0% +multiply by your cross-section your +microscopic cross-section and you get + + align:start position:0% +microscopic cross-section and you get + + + align:start position:0% +microscopic cross-section and you get +your macroscopic cross-section yeah yep + + align:start position:0% +your macroscopic cross-section yeah yep + + + align:start position:0% +your macroscopic cross-section yeah yep +atom fraction is a fraction between zero + + align:start position:0% +atom fraction is a fraction between zero + + + align:start position:0% +atom fraction is a fraction between zero +and one of what proportion of the atoms + + align:start position:0% +and one of what proportion of the atoms + + + align:start position:0% +and one of what proportion of the atoms +in your material are that isotope so + + align:start position:0% +in your material are that isotope so + + + align:start position:0% +in your material are that isotope so +again if your atom fractions are outside + + align:start position:0% +again if your atom fractions are outside + + + align:start position:0% +again if your atom fractions are outside +the bounds of zero to one that's not + + align:start position:0% +the bounds of zero to one that's not + + + align:start position:0% +the bounds of zero to one that's not +physically significant if you're number + + align:start position:0% +physically significant if you're number + + + align:start position:0% +physically significant if you're number +densities are around to really far from + + align:start position:0% +densities are around to really far from + + + align:start position:0% +densities are around to really far from +those bounds then they're probably not + + align:start position:0% +those bounds then they're probably not + + + align:start position:0% +those bounds then they're probably not +right unless you're talking about a gas + + align:start position:0% +right unless you're talking about a gas + + + align:start position:0% +right unless you're talking about a gas +or a neutron star but solid matter tends + + align:start position:0% +or a neutron star but solid matter tends + + + align:start position:0% +or a neutron star but solid matter tends +to have approximately those number + + align:start position:0% +to have approximately those number + + + align:start position:0% +to have approximately those number +densities + + align:start position:0% + + + + align:start position:0% + +good question you'll determine those + + align:start position:0% +good question you'll determine those + + + align:start position:0% +good question you'll determine those +fractions from the ap1000 spec sheet so + + align:start position:0% +fractions from the ap1000 spec sheet so + + + align:start position:0% +fractions from the ap1000 spec sheet so +in the ap1000 spec sheet it tells you + + align:start position:0% +in the ap1000 spec sheet it tells you + + + align:start position:0% +in the ap1000 spec sheet it tells you +things like total weight of the fuel as + + align:start position:0% +things like total weight of the fuel as + + + align:start position:0% +things like total weight of the fuel as +uranium dioxide and so you can go from + + align:start position:0% +uranium dioxide and so you can go from + + + align:start position:0% +uranium dioxide and so you can go from +total weight of the fuel to let's say + + align:start position:0% +total weight of the fuel to let's say + + + align:start position:0% +total weight of the fuel to let's say +molar or atom fraction of the fuel if + + align:start position:0% +molar or atom fraction of the fuel if + + + align:start position:0% +molar or atom fraction of the fuel if +you know the weight of the fuel it's + + align:start position:0% +you know the weight of the fuel it's + + + align:start position:0% +you know the weight of the fuel it's +nice they give you the way to the fuel + + align:start position:0% +nice they give you the way to the fuel + + + align:start position:0% +nice they give you the way to the fuel +they gave you the way to the clad and + + align:start position:0% +they gave you the way to the clad and + + + align:start position:0% +they gave you the way to the clad and +what let's see which materials did we + + align:start position:0% +what let's see which materials did we + + + align:start position:0% +what let's see which materials did we +say you have to talk think about said + + align:start position:0% +say you have to talk think about said + + + align:start position:0% +say you have to talk think about said +you have to talk about four materials + + align:start position:0% +you have to talk about four materials + + + align:start position:0% +you have to talk about four materials +the coolant of the moderator water the + + align:start position:0% +the coolant of the moderator water the + + + align:start position:0% +the coolant of the moderator water the +fuel you owe to the clotting where you + + align:start position:0% +fuel you owe to the clotting where you + + + align:start position:0% +fuel you owe to the clotting where you +can assume piers or cone iam forget all + + align:start position:0% +can assume piers or cone iam forget all + + + align:start position:0% +can assume piers or cone iam forget all +the crazy Zircaloy because that's just + + align:start position:0% +the crazy Zircaloy because that's just + + + align:start position:0% +the crazy Zircaloy because that's just +busywork + + align:start position:0% +busywork + + + align:start position:0% +busywork +and structural materials assume pure + + align:start position:0% +and structural materials assume pure + + + align:start position:0% +and structural materials assume pure +iron and so on this spec sheet luckily + + align:start position:0% +iron and so on this spec sheet luckily + + + align:start position:0% +iron and so on this spec sheet luckily +they just tell you the mass of the fuel + + align:start position:0% +they just tell you the mass of the fuel + + + align:start position:0% +they just tell you the mass of the fuel +they tell you the mass of the clad I do + + align:start position:0% +they tell you the mass of the clad I do + + + align:start position:0% +they tell you the mass of the clad I do +not believe they give you the mass of + + align:start position:0% +not believe they give you the mass of + + + align:start position:0% +not believe they give you the mass of +the water but they do give you the + + align:start position:0% +the water but they do give you the + + + align:start position:0% +the water but they do give you the +volume of the core and so you can figure + + align:start position:0% +volume of the core and so you can figure + + + align:start position:0% +volume of the core and so you can figure +out if you've got a core and you + + align:start position:0% +out if you've got a core and you + + + align:start position:0% +out if you've got a core and you +subtract off the volume of the fuel and + + align:start position:0% +subtract off the volume of the fuel and + + + align:start position:0% +subtract off the volume of the fuel and +the weight and the cladding and the + + align:start position:0% +the weight and the cladding and the + + + align:start position:0% +the weight and the cladding and the +structural materials all you're left + + align:start position:0% +structural materials all you're left + + + align:start position:0% +structural materials all you're left +with this volume of the water in the + + align:start position:0% +with this volume of the water in the + + + align:start position:0% +with this volume of the water in the +core and that'll give you your total + + align:start position:0% +core and that'll give you your total + + + align:start position:0% +core and that'll give you your total +weight of water and once you have all + + align:start position:0% +weight of water and once you have all + + + align:start position:0% +weight of water and once you have all +the weights then you can go to atom + + align:start position:0% +the weights then you can go to atom + + + align:start position:0% +the weights then you can go to atom +fractions and then you've got all the + + align:start position:0% +fractions and then you've got all the + + + align:start position:0% +fractions and then you've got all the +information you need to get the + + align:start position:0% +information you need to get the + + + align:start position:0% +information you need to get the +macroscopic cross-sections is that + + align:start position:0% +macroscopic cross-sections is that + + + align:start position:0% +macroscopic cross-sections is that +unclear to anybody cool so we talked + + align:start position:0% +unclear to anybody cool so we talked + + + align:start position:0% +unclear to anybody cool so we talked +about how to get the ends let's show you + + align:start position:0% +about how to get the ends let's show you + + + align:start position:0% +about how to get the ends let's show you +how to get the Sigma's so there was a + + align:start position:0% +how to get the Sigma's so there was a + + + align:start position:0% +how to get the Sigma's so there was a +comment that came in that said please + + align:start position:0% +comment that came in that said please + + + align:start position:0% +comment that came in that said please +teach us how to use these databases we + + align:start position:0% +teach us how to use these databases we + + + align:start position:0% +teach us how to use these databases we +just kind of throw them around well I + + align:start position:0% +just kind of throw them around well I + + + align:start position:0% +just kind of throw them around well I +want to teach you how to use this + + align:start position:0% +want to teach you how to use this + + + align:start position:0% +want to teach you how to use this +database let's say we're going to get + + align:start position:0% +database let's say we're going to get + + + align:start position:0% +database let's say we're going to get +the cross-sections for oxygen in uranium + + align:start position:0% +the cross-sections for oxygen in uranium + + + align:start position:0% +the cross-sections for oxygen in uranium +dioxide that's nice it easy because + + align:start position:0% +dioxide that's nice it easy because + + + align:start position:0% +dioxide that's nice it easy because +there's only one stable isotope of + + align:start position:0% +there's only one stable isotope of + + + align:start position:0% +there's only one stable isotope of +oxygen you have to consider is oxygen 16 + + align:start position:0% +oxygen you have to consider is oxygen 16 + + + align:start position:0% +oxygen you have to consider is oxygen 16 +I highly recommend using the java + + align:start position:0% +I highly recommend using the java + + + align:start position:0% +I highly recommend using the java +version of Janus because it is a lot + + align:start position:0% +version of Janus because it is a lot + + + align:start position:0% +version of Janus because it is a lot +easier to use less clunky and more + + align:start position:0% +easier to use less clunky and more + + + align:start position:0% +easier to use less clunky and more +intuitive so if you don't have + + align:start position:0% +intuitive so if you don't have + + + align:start position:0% +intuitive so if you don't have +on your machine first of all it runs on + + align:start position:0% +on your machine first of all it runs on + + + align:start position:0% +on your machine first of all it runs on +everything like phones tablets Linux Mac + + align:start position:0% +everything like phones tablets Linux Mac + + + align:start position:0% +everything like phones tablets Linux Mac +Windows whatever and second of all it'll + + align:start position:0% +Windows whatever and second of all it'll + + + align:start position:0% +Windows whatever and second of all it'll +just make your life easier so a little + + align:start position:0% +just make your life easier so a little + + + align:start position:0% +just make your life easier so a little +time investment now will make the piece + + align:start position:0% +time investment now will make the piece + + + align:start position:0% +time investment now will make the piece +that take less so once you have Java it + + align:start position:0% +that take less so once you have Java it + + + align:start position:0% +that take less so once you have Java it +should just open cleanly and it may show + + align:start position:0% +should just open cleanly and it may show + + + align:start position:0% +should just open cleanly and it may show +up with nothing it may show up something + + align:start position:0% +up with nothing it may show up something + + + align:start position:0% +up with nothing it may show up something +depending on what you last looked at in + + align:start position:0% +depending on what you last looked at in + + + align:start position:0% +depending on what you last looked at in +this case it's looking at whatever last + + align:start position:0% +this case it's looking at whatever last + + + align:start position:0% +this case it's looking at whatever last +library I looked at so let's pretend + + align:start position:0% +library I looked at so let's pretend + + + align:start position:0% +library I looked at so let's pretend +we're starting over so sometimes you may + + align:start position:0% +we're starting over so sometimes you may + + + align:start position:0% +we're starting over so sometimes you may +just see this database as NEA + + align:start position:0% +just see this database as NEA + + + align:start position:0% +just see this database as NEA +that's the that's all the databases that + + align:start position:0% +that's the that's all the databases that + + + align:start position:0% +that's the that's all the databases that +come with Janis we expand this make sure + + align:start position:0% +come with Janis we expand this make sure + + + align:start position:0% +come with Janis we expand this make sure +that you go to incident Neutron data + + align:start position:0% +that you go to incident Neutron data + + + align:start position:0% +that you go to incident Neutron data +because these are cross-sections for + + align:start position:0% +because these are cross-sections for + + + align:start position:0% +because these are cross-sections for +Neutron reactions that we want to go for + + align:start position:0% +Neutron reactions that we want to go for + + + align:start position:0% +Neutron reactions that we want to go for +and there are a lot of databases in here + + align:start position:0% +and there are a lot of databases in here + + + align:start position:0% +and there are a lot of databases in here +and in the problem set specifically say + + align:start position:0% +and in the problem set specifically say + + + align:start position:0% +and in the problem set specifically say +to use the most recent en d.f or + + align:start position:0% +to use the most recent en d.f or + + + align:start position:0% +to use the most recent en d.f or +evaluated nuclear data file just to make + + align:start position:0% +evaluated nuclear data file just to make + + + align:start position:0% +evaluated nuclear data file just to make +sure that we're all using the same data + + align:start position:0% +sure that we're all using the same data + + + align:start position:0% +sure that we're all using the same data +set you'll notice that there are + + align:start position:0% +set you'll notice that there are + + + align:start position:0% +set you'll notice that there are +discrepancies between the data so + + align:start position:0% +discrepancies between the data so + + + align:start position:0% +discrepancies between the data so +different groups have measured things + + align:start position:0% +different groups have measured things + + + align:start position:0% +different groups have measured things +with different uncertainties and + + align:start position:0% +with different uncertainties and + + + align:start position:0% +with different uncertainties and +different values and so these + + align:start position:0% +different values and so these + + + align:start position:0% +different values and so these +cross-sections are necessarily + + align:start position:0% +cross-sections are necessarily + + + align:start position:0% +cross-sections are necessarily +fundamental constants of nature they're + + align:start position:0% +fundamental constants of nature they're + + + align:start position:0% +fundamental constants of nature they're +measurements of those constants with + + align:start position:0% +measurements of those constants with + + + align:start position:0% +measurements of those constants with +whatever uncertainty and error which are + + align:start position:0% +whatever uncertainty and error which are + + + align:start position:0% +whatever uncertainty and error which are +two separate things that could be in + + align:start position:0% +two separate things that could be in + + + align:start position:0% +two separate things that could be in +there so let's open up the most recent + + align:start position:0% +there so let's open up the most recent + + + align:start position:0% +there so let's open up the most recent +endif library and click on + + align:start position:0% +endif library and click on + + + align:start position:0% +endif library and click on +cross-sections and now whatever you see + + align:start position:0% +cross-sections and now whatever you see + + + align:start position:0% +cross-sections and now whatever you see +here the green squares are the elements + + align:start position:0% +here the green squares are the elements + + + align:start position:0% +here the green squares are the elements +that have tabulated cross-sections just + + align:start position:0% +that have tabulated cross-sections just + + + align:start position:0% +that have tabulated cross-sections just +to make sure that we only have to + + align:start position:0% +to make sure that we only have to + + + align:start position:0% +to make sure that we only have to +consider oxygen-16 + + align:start position:0% +consider oxygen-16 + + + align:start position:0% +consider oxygen-16 +let's go to the table of nuclides we'll + + align:start position:0% +let's go to the table of nuclides we'll + + + align:start position:0% +let's go to the table of nuclides we'll +never stop using this table it's like + + align:start position:0% +never stop using this table it's like + + + align:start position:0% +never stop using this table it's like +the most useful thing in this class and + + align:start position:0% +the most useful thing in this class and + + + align:start position:0% +the most useful thing in this class and +check to make sure that there's no other + + align:start position:0% +check to make sure that there's no other + + + align:start position:0% +check to make sure that there's no other +stable isotopes of oxygen that we have + + align:start position:0% +stable isotopes of oxygen that we have + + + align:start position:0% +stable isotopes of oxygen that we have +to worry about as long as the Internet's + + align:start position:0% +to worry about as long as the Internet's + + + align:start position:0% +to worry about as long as the Internet's +working + + align:start position:0% + + + + align:start position:0% + +did they immigrate to Korea website + + align:start position:0% +did they immigrate to Korea website + + + align:start position:0% +did they immigrate to Korea website +crashed to + + align:start position:0% +crashed to + + + align:start position:0% +crashed to +interesting well we'll let that load for + + align:start position:0% +interesting well we'll let that load for + + + align:start position:0% +interesting well we'll let that load for +a bit and let's start looking at + + align:start position:0% +a bit and let's start looking at + + + align:start position:0% +a bit and let's start looking at +oxygen-16 + + align:start position:0% +oxygen-16 + + + align:start position:0% +oxygen-16 +so if you double-click on the element of + + align:start position:0% +so if you double-click on the element of + + + align:start position:0% +so if you double-click on the element of +interest it'll usually take a little + + align:start position:0% +interest it'll usually take a little + + + align:start position:0% +interest it'll usually take a little +while because it's Java it's loading + + align:start position:0% +while because it's Java it's loading + + + align:start position:0% +while because it's Java it's loading +cross-sections and then you can pick the + + align:start position:0% +cross-sections and then you can pick the + + + align:start position:0% +cross-sections and then you can pick the +nuclear reaction of choice from here and + + align:start position:0% +nuclear reaction of choice from here and + + + align:start position:0% +nuclear reaction of choice from here and +unfortunately I can't easily make this + + align:start position:0% +unfortunately I can't easily make this + + + align:start position:0% +unfortunately I can't easily make this +bigger I will take a very quick detour + + align:start position:0% +bigger I will take a very quick detour + + + align:start position:0% +bigger I will take a very quick detour +and see if I can make these things a bit + + align:start position:0% +and see if I can make these things a bit + + + align:start position:0% +and see if I can make these things a bit +larger so you can see them but if not + + align:start position:0% +larger so you can see them but if not + + + align:start position:0% +larger so you can see them but if not +then whatever no no oh well so let's say + + align:start position:0% +then whatever no no oh well so let's say + + + align:start position:0% +then whatever no no oh well so let's say +you wanted to get the elastic scattering + + align:start position:0% +you wanted to get the elastic scattering + + + align:start position:0% +you wanted to get the elastic scattering +cross-section for oxygen the first the + + align:start position:0% +cross-section for oxygen the first the + + + align:start position:0% +cross-section for oxygen the first the +first letter before the comma is going + + align:start position:0% +first letter before the comma is going + + + align:start position:0% +first letter before the comma is going +to be the incident particle notice that + + align:start position:0% +to be the incident particle notice that + + + align:start position:0% +to be the incident particle notice that +sometimes it says N and sometimes it + + align:start position:0% +sometimes it says N and sometimes it + + + align:start position:0% +sometimes it says N and sometimes it +says Z and specifically means neutrons z + + align:start position:0% +says Z and specifically means neutrons z + + + align:start position:0% +says Z and specifically means neutrons z +means whatever incident particle you + + align:start position:0% +means whatever incident particle you + + + align:start position:0% +means whatever incident particle you +chose so we know that here Z means + + align:start position:0% +chose so we know that here Z means + + + align:start position:0% +chose so we know that here Z means +neutrons coming in and elastic that's + + align:start position:0% +neutrons coming in and elastic that's + + + align:start position:0% +neutrons coming in and elastic that's +elastic scattering so we can then click + + align:start position:0% +elastic scattering so we can then click + + + align:start position:0% +elastic scattering so we can then click +on cross-section if you want to see what + + align:start position:0% +on cross-section if you want to see what + + + align:start position:0% +on cross-section if you want to see what +it looks like you can check P for plot + + align:start position:0% +it looks like you can check P for plot + + + align:start position:0% +it looks like you can check P for plot +and this will give you a logarithmic + + align:start position:0% +and this will give you a logarithmic + + + align:start position:0% +and this will give you a logarithmic +plot of the scattering cross-section as + + align:start position:0% +plot of the scattering cross-section as + + + align:start position:0% +plot of the scattering cross-section as +a function of energy you can see that + + align:start position:0% +a function of energy you can see that + + + align:start position:0% +a function of energy you can see that +it's pretty boring for oxygen there + + align:start position:0% +it's pretty boring for oxygen there + + + align:start position:0% +it's pretty boring for oxygen there +aren't a lot of nucleons there aren't a + + align:start position:0% +aren't a lot of nucleons there aren't a + + + align:start position:0% +aren't a lot of nucleons there aren't a +lot of different energy levels there are + + align:start position:0% +lot of different energy levels there are + + + align:start position:0% +lot of different energy levels there are +not that many resonances or things going + + align:start position:0% +not that many resonances or things going + + + align:start position:0% +not that many resonances or things going +on so I wouldn't be that upset if you + + align:start position:0% +on so I wouldn't be that upset if you + + + align:start position:0% +on so I wouldn't be that upset if you +just approximated the fast scattering + + align:start position:0% +just approximated the fast scattering + + + align:start position:0% +just approximated the fast scattering +cross-section for argon as that value + + align:start position:0% +cross-section for argon as that value + + + align:start position:0% +cross-section for argon as that value +whatever it is but let's do this + + align:start position:0% +whatever it is but let's do this + + + align:start position:0% +whatever it is but let's do this +completely let's tabulate this so if you + + align:start position:0% +completely let's tabulate this so if you + + + align:start position:0% +completely let's tabulate this so if you +click on T you actually get a table of + + align:start position:0% +click on T you actually get a table of + + + align:start position:0% +click on T you actually get a table of +data and you can choose how much data + + align:start position:0% +data and you can choose how much data + + + align:start position:0% +data and you can choose how much data +you export by default you get like + + align:start position:0% +you export by default you get like + + + align:start position:0% +you export by default you get like +thousands upon thousands of entries + + align:start position:0% +thousands upon thousands of entries + + + align:start position:0% +thousands upon thousands of entries +which is just gonna make your life + + align:start position:0% +which is just gonna make your life + + + align:start position:0% +which is just gonna make your life +horrible so what you can do is either + + align:start position:0% +horrible so what you can do is either + + + align:start position:0% +horrible so what you can do is either +pick the original values starting at one + + align:start position:0% +pick the original values starting at one + + + align:start position:0% +pick the original values starting at one +evey and we know we only have to go up + + align:start position:0% +evey and we know we only have to go up + + + align:start position:0% +evey and we know we only have to go up +to ten MeV so you can pick your bounds + + align:start position:0% +to ten MeV so you can pick your bounds + + + align:start position:0% +to ten MeV so you can pick your bounds +and all of a sudden there is + + align:start position:0% +and all of a sudden there is + + + align:start position:0% +and all of a sudden there is +only a few thousands worth of data or + + align:start position:0% +only a few thousands worth of data or + + + align:start position:0% +only a few thousands worth of data or +you can interpolate them you can + + align:start position:0% +you can interpolate them you can + + + align:start position:0% +you can interpolate them you can +interpolate values either linearly or + + align:start position:0% +interpolate values either linearly or + + + align:start position:0% +interpolate values either linearly or +logarithmically I recommend logarithmic + + align:start position:0% +logarithmically I recommend logarithmic + + + align:start position:0% +logarithmically I recommend logarithmic +because this is such a large energy + + align:start position:0% +because this is such a large energy + + + align:start position:0% +because this is such a large energy +range and get maybe five values per + + align:start position:0% +range and get maybe five values per + + + align:start position:0% +range and get maybe five values per +decade so between one and ten MeV you + + align:start position:0% +decade so between one and ten MeV you + + + align:start position:0% +decade so between one and ten MeV you +only need five numbers that's still + + align:start position:0% +only need five numbers that's still + + + align:start position:0% +only need five numbers that's still +pretty intense oh I didn't uncheck the + + align:start position:0% +pretty intense oh I didn't uncheck the + + + align:start position:0% +pretty intense oh I didn't uncheck the +original values ah isn't that better + + align:start position:0% +original values ah isn't that better + + + align:start position:0% +original values ah isn't that better +so now there's only 20 or 30 entries it + + align:start position:0% +so now there's only 20 or 30 entries it + + + align:start position:0% +so now there's only 20 or 30 entries it +glosses over the residences it sure does + + align:start position:0% +glosses over the residences it sure does + + + align:start position:0% +glosses over the residences it sure does +but are they that important that's up to + + align:start position:0% +but are they that important that's up to + + + align:start position:0% +but are they that important that's up to +you guys to decide you can try doing one + + align:start position:0% +you guys to decide you can try doing one + + + align:start position:0% +you guys to decide you can try doing one +of these calculations with the original + + align:start position:0% +of these calculations with the original + + + align:start position:0% +of these calculations with the original +values and with the interpolated values + + align:start position:0% +values and with the interpolated values + + + align:start position:0% +values and with the interpolated values +and see just how different they really + + align:start position:0% +and see just how different they really + + + align:start position:0% +and see just how different they really +are in to group theory and hint is not + + align:start position:0% +are in to group theory and hint is not + + + align:start position:0% +are in to group theory and hint is not +very much so then you can actually + + align:start position:0% +very much so then you can actually + + + align:start position:0% +very much so then you can actually +export that data so either you can just + + align:start position:0% +export that data so either you can just + + + align:start position:0% +export that data so either you can just +copy paste it so I just highlighted + + align:start position:0% +copy paste it so I just highlighted + + + align:start position:0% +copy paste it so I just highlighted +copied start Excel and in it comes and + + align:start position:0% +copied start Excel and in it comes and + + + align:start position:0% +copied start Excel and in it comes and +right there's the data that you can + + align:start position:0% +right there's the data that you can + + + align:start position:0% +right there's the data that you can +start to use to do your numerical + + align:start position:0% +start to use to do your numerical + + + align:start position:0% +start to use to do your numerical +integration and I don't want to give + + align:start position:0% +integration and I don't want to give + + + align:start position:0% +integration and I don't want to give +away how to do the numerical integration + + align:start position:0% +away how to do the numerical integration + + + align:start position:0% +away how to do the numerical integration +though I kind of did symbolically I'd + + align:start position:0% +though I kind of did symbolically I'd + + + align:start position:0% +though I kind of did symbolically I'd +like you guys how to figure out how to + + align:start position:0% +like you guys how to figure out how to + + + align:start position:0% +like you guys how to figure out how to +do this numerical integration + + align:start position:0% +do this numerical integration + + + align:start position:0% +do this numerical integration +mathematically given that you can get + + align:start position:0% +mathematically given that you can get + + + align:start position:0% +mathematically given that you can get +the data now so is there any step here + + align:start position:0% +the data now so is there any step here + + + align:start position:0% +the data now so is there any step here +that's unclear to anyone yeah + + align:start position:0% + + + + align:start position:0% + +every single material yes you are sounds + + align:start position:0% +every single material yes you are sounds + + + align:start position:0% +every single material yes you are sounds +horrible isn't it that's why I made some + + align:start position:0% +horrible isn't it that's why I made some + + + align:start position:0% +horrible isn't it that's why I made some +simplifications so if you notice we are + + align:start position:0% +simplifications so if you notice we are + + + align:start position:0% +simplifications so if you notice we are +simplifying the cladding as Zr and we're + + align:start position:0% +simplifying the cladding as Zr and we're + + + align:start position:0% +simplifying the cladding as Zr and we're +simplifying stainless steel as pure iron + + align:start position:0% +simplifying stainless steel as pure iron + + + align:start position:0% +simplifying stainless steel as pure iron +I don't want you guys to just do tons + + align:start position:0% +I don't want you guys to just do tons + + + align:start position:0% +I don't want you guys to just do tons +and tons of repetitive stuff but I do + + align:start position:0% +and tons of repetitive stuff but I do + + + align:start position:0% +and tons of repetitive stuff but I do +want you to get roughly the right answer + + align:start position:0% + + + + align:start position:0% + +I want you to answer that question so + + align:start position:0% +I want you to answer that question so + + + align:start position:0% +I want you to answer that question so +how would you consider the isotopes of + + align:start position:0% +how would you consider the isotopes of + + + align:start position:0% +how would you consider the isotopes of +uranium in this question that's right + + align:start position:0% +uranium in this question that's right + + + align:start position:0% +uranium in this question that's right +it's not the natural values it's the + + align:start position:0% +it's not the natural values it's the + + + align:start position:0% +it's not the natural values it's the +enriched values so they will say in the + + align:start position:0% +enriched values so they will say in the + + + align:start position:0% +enriched values so they will say in the +spec sheet + + align:start position:0% + + + + align:start position:0% + +you wanna don't want to be on a list you + + align:start position:0% +you wanna don't want to be on a list you + + + align:start position:0% +you wanna don't want to be on a list you +don't have to look up and rich to + + align:start position:0% +don't have to look up and rich to + + + align:start position:0% +don't have to look up and rich to +uranium on Google you can look it up on + + align:start position:0% +uranium on Google you can look it up on + + + align:start position:0% +uranium on Google you can look it up on +Janus so if you go to Janus right are + + align:start position:0% +Janus so if you go to Janus right are + + + align:start position:0% +Janus so if you go to Janus right are +you looking for what the enrichment + + align:start position:0% +you looking for what the enrichment + + + align:start position:0% +you looking for what the enrichment +level is yeah oh that's in the ap1000 + + align:start position:0% +level is yeah oh that's in the ap1000 + + + align:start position:0% +level is yeah oh that's in the ap1000 +spec sheet where'd it go we search for + + align:start position:0% +spec sheet where'd it go we search for + + + align:start position:0% +spec sheet where'd it go we search for +enrichment fuel enrichment first cycle + + align:start position:0% +enrichment fuel enrichment first cycle + + + align:start position:0% +enrichment fuel enrichment first cycle +weight percent + + align:start position:0% + + + + align:start position:0% + +you can either average these or just + + align:start position:0% +you can either average these or just + + + align:start position:0% +you can either average these or just +pretend it's five because that's that's + + align:start position:0% +pretend it's five because that's that's + + + align:start position:0% +pretend it's five because that's that's +a pretty pretty typical enrichment level + + align:start position:0% +a pretty pretty typical enrichment level + + + align:start position:0% +a pretty pretty typical enrichment level +is 5% atomic fraction u-235 or if you + + align:start position:0% +is 5% atomic fraction u-235 or if you + + + align:start position:0% +is 5% atomic fraction u-235 or if you +want to get really technical you can + + align:start position:0% +want to get really technical you can + + + align:start position:0% +want to get really technical you can +average these noting how many fuel + + align:start position:0% +average these noting how many fuel + + + align:start position:0% +average these noting how many fuel +assemblies are in each of the regions + + align:start position:0% +assemblies are in each of the regions + + + align:start position:0% +assemblies are in each of the regions +but I don't really care if you do that + + align:start position:0% + + + + align:start position:0% + +you 238 yep so there's only two isotopes + + align:start position:0% +you 238 yep so there's only two isotopes + + + align:start position:0% +you 238 yep so there's only two isotopes +of uranium one of oxygen however many of + + align:start position:0% +of uranium one of oxygen however many of + + + align:start position:0% +of uranium one of oxygen however many of +iron and zirconium hint there's not that + + align:start position:0% +iron and zirconium hint there's not that + + + align:start position:0% +iron and zirconium hint there's not that +many and then there is h2o and there's + + align:start position:0% +many and then there is h2o and there's + + + align:start position:0% +many and then there is h2o and there's +only one hydrogen and one oxygen so it's + + align:start position:0% +only one hydrogen and one oxygen so it's + + + align:start position:0% +only one hydrogen and one oxygen so it's +not really that much busy work it's just + + align:start position:0% +not really that much busy work it's just + + + align:start position:0% +not really that much busy work it's just +enough for you to get to the right + + align:start position:0% +enough for you to get to the right + + + align:start position:0% +enough for you to get to the right +answer so I wouldn't even call it busy + + align:start position:0% +answer so I wouldn't even call it busy + + + align:start position:0% +answer so I wouldn't even call it busy +work because there's a point to it so in + + align:start position:0% +work because there's a point to it so in + + + align:start position:0% +work because there's a point to it so in +that way you can determine all of these + + align:start position:0% +that way you can determine all of these + + + align:start position:0% +that way you can determine all of these +cross sections we give you these fluxes + + align:start position:0% +cross sections we give you these fluxes + + + align:start position:0% +cross sections we give you these fluxes +these new values you can also get from + + align:start position:0% +these new values you can also get from + + + align:start position:0% +these new values you can also get from +Janus they're not labeled as new but + + align:start position:0% +Janus they're not labeled as new but + + + align:start position:0% +Janus they're not labeled as new but +they are labeled as Neutron + + align:start position:0% +they are labeled as Neutron + + + align:start position:0% +they are labeled as Neutron +multiplication factor and they're + + align:start position:0% +multiplication factor and they're + + + align:start position:0% +multiplication factor and they're +usually way down here and we probably + + align:start position:0% +usually way down here and we probably + + + align:start position:0% +usually way down here and we probably +need to find a fissile isotope for that + + align:start position:0% +need to find a fissile isotope for that + + + align:start position:0% +need to find a fissile isotope for that +so let's ditch oxygen for now go up to + + align:start position:0% +so let's ditch oxygen for now go up to + + + align:start position:0% +so let's ditch oxygen for now go up to +uranium + + align:start position:0% + + + + align:start position:0% + +okay so let's do you 235 it'll pull up + + align:start position:0% +okay so let's do you 235 it'll pull up + + + align:start position:0% +okay so let's do you 235 it'll pull up +the data and then near the bottom + + align:start position:0% +the data and then near the bottom + + + align:start position:0% +the data and then near the bottom +noubar total neutron production check it + + align:start position:0% +noubar total neutron production check it + + + align:start position:0% +noubar total neutron production check it +out for pretty much all energies until + + align:start position:0% +out for pretty much all energies until + + + align:start position:0% +out for pretty much all energies until +you get to the fast region it's the + + align:start position:0% +you get to the fast region it's the + + + align:start position:0% +you get to the fast region it's the +value we talked about two point four + + align:start position:0% +value we talked about two point four + + + align:start position:0% +value we talked about two point four +four and then in the fast region you + + align:start position:0% +four and then in the fast region you + + + align:start position:0% +four and then in the fast region you +suddenly can get more neutrons from + + align:start position:0% +suddenly can get more neutrons from + + + align:start position:0% +suddenly can get more neutrons from +fission why do you guys think that is + + align:start position:0% + + + + align:start position:0% + +well what sort of additional things + + align:start position:0% +well what sort of additional things + + + align:start position:0% +well what sort of additional things +happen when you're incident particle + + align:start position:0% +happen when you're incident particle + + + align:start position:0% +happen when you're incident particle +energy increases let's think back to + + align:start position:0% +energy increases let's think back to + + + align:start position:0% +energy increases let's think back to +binding energy and all the stuff at the + + align:start position:0% +binding energy and all the stuff at the + + + align:start position:0% +binding energy and all the stuff at the +beginning of the course there's more + + align:start position:0% +beginning of the course there's more + + + align:start position:0% +beginning of the course there's more +different kinds of fission products that + + align:start position:0% +different kinds of fission products that + + + align:start position:0% +different kinds of fission products that +can be made because you're increasing + + align:start position:0% +can be made because you're increasing + + + align:start position:0% +can be made because you're increasing +the Q value of this reaction by + + align:start position:0% +the Q value of this reaction by + + + align:start position:0% +the Q value of this reaction by +increasing the initial kinetic energy so + + align:start position:0% +increasing the initial kinetic energy so + + + align:start position:0% +increasing the initial kinetic energy so +there are more fission products that can + + align:start position:0% +there are more fission products that can + + + align:start position:0% +there are more fission products that can +be made and some of them let's say give + + align:start position:0% +be made and some of them let's say give + + + align:start position:0% +be made and some of them let's say give +off more neutrons than others so you'll + + align:start position:0% +off more neutrons than others so you'll + + + align:start position:0% +off more neutrons than others so you'll +be able to get your noubar total from + + align:start position:0% +be able to get your noubar total from + + + align:start position:0% +be able to get your noubar total from +this one near the bottom and everything + + align:start position:0% +this one near the bottom and everything + + + align:start position:0% +this one near the bottom and everything +else will be near the top they'll either + + align:start position:0% +else will be near the top they'll either + + + align:start position:0% +else will be near the top they'll either +be a fission cross-section an absorption + + align:start position:0% +be a fission cross-section an absorption + + + align:start position:0% +be a fission cross-section an absorption +cross-section a scattering cross-section + + align:start position:0% +cross-section a scattering cross-section + + + align:start position:0% +cross-section a scattering cross-section +how do you get your diffusion + + align:start position:0% +how do you get your diffusion + + + align:start position:0% +how do you get your diffusion +coefficients + + align:start position:0% + + + + align:start position:0% + +they're not tabulated but they're close + + align:start position:0% + + + + align:start position:0% + +yep exactly + + align:start position:0% +yep exactly + + + align:start position:0% +yep exactly +so let's render this nicely the + + align:start position:0% +so let's render this nicely the + + + align:start position:0% +so let's render this nicely the +diffusion constant is one over three + + align:start position:0% +diffusion constant is one over three + + + align:start position:0% +diffusion constant is one over three +times the total cross-section minus mu + + align:start position:0% +times the total cross-section minus mu + + + align:start position:0% +times the total cross-section minus mu +not scattering average average average + + align:start position:0% +not scattering average average average + + + align:start position:0% +not scattering average average average +and this average cosine is sorry about + + align:start position:0% +and this average cosine is sorry about + + + align:start position:0% +and this average cosine is sorry about +two-thirds times the atomic mass so you + + align:start position:0% +two-thirds times the atomic mass so you + + + align:start position:0% +two-thirds times the atomic mass so you +can get these diffusion coefficients + + align:start position:0% +can get these diffusion coefficients + + + align:start position:0% +can get these diffusion coefficients +from tabulated data the total cross + + align:start position:0% +from tabulated data the total cross + + + align:start position:0% +from tabulated data the total cross +section is found at the top better wise + + align:start position:0% +section is found at the top better wise + + + align:start position:0% +section is found at the top better wise +better known as well it's just as total + + align:start position:0% +better known as well it's just as total + + + align:start position:0% +better known as well it's just as total +so you can get total cross-sections here + + align:start position:0% +so you can get total cross-sections here + + + align:start position:0% +so you can get total cross-sections here +the only one that might be a little + + align:start position:0% +the only one that might be a little + + + align:start position:0% +the only one that might be a little +tricky for you to find from notation is + + align:start position:0% +tricky for you to find from notation is + + + align:start position:0% +tricky for you to find from notation is +absorption you're not going to see + + align:start position:0% +absorption you're not going to see + + + align:start position:0% +absorption you're not going to see +something labeled absorption in this + + align:start position:0% +something labeled absorption in this + + + align:start position:0% +something labeled absorption in this +database however you will see this gamma + + align:start position:0% +database however you will see this gamma + + + align:start position:0% +database however you will see this gamma +reaction or how else do you get it if + + align:start position:0% +reaction or how else do you get it if + + + align:start position:0% +reaction or how else do you get it if +you take the total - fission + + align:start position:0% +you take the total - fission + + + align:start position:0% +you take the total - fission +- scattering you're left with absorption + + align:start position:0% +- scattering you're left with absorption + + + align:start position:0% +- scattering you're left with absorption +if you don't count end-to-end reactions + + align:start position:0% +if you don't count end-to-end reactions + + + align:start position:0% +if you don't count end-to-end reactions +or really esoteric high-energy things so + + align:start position:0% +or really esoteric high-energy things so + + + align:start position:0% +or really esoteric high-energy things so +if you can't find it that's okay because + + align:start position:0% +if you can't find it that's okay because + + + align:start position:0% +if you can't find it that's okay because +you can calculate it because we know + + align:start position:0% +you can calculate it because we know + + + align:start position:0% +you can calculate it because we know +Sigma absorption is Sigma total minus + + align:start position:0% +Sigma absorption is Sigma total minus + + + align:start position:0% +Sigma absorption is Sigma total minus +Sigma scattering minus Sigma fission - + + align:start position:0% +Sigma scattering minus Sigma fission - + + + align:start position:0% +Sigma scattering minus Sigma fission - +others that we don't care about and + + align:start position:0% +others that we don't care about and + + + align:start position:0% +others that we don't care about and +since you're getting these anyway + + align:start position:0% +since you're getting these anyway + + + align:start position:0% +since you're getting these anyway +tabulating Sigma absorption should be + + align:start position:0% +tabulating Sigma absorption should be + + + align:start position:0% +tabulating Sigma absorption should be +trivial it's just an Excel subtraction + + align:start position:0% +trivial it's just an Excel subtraction + + + align:start position:0% +trivial it's just an Excel subtraction +yep + + align:start position:0% + + + + align:start position:0% + +yep inelastic scattering is not + + align:start position:0% +yep inelastic scattering is not + + + align:start position:0% +yep inelastic scattering is not +considered absorption so inelastic + + align:start position:0% +considered absorption so inelastic + + + align:start position:0% +considered absorption so inelastic +scattering means one neutron goes in one + + align:start position:0% +scattering means one neutron goes in one + + + align:start position:0% +scattering means one neutron goes in one +neutron comes out but at a very + + align:start position:0% +neutron comes out but at a very + + + align:start position:0% +neutron comes out but at a very +different energy level so I guess we + + align:start position:0% +different energy level so I guess we + + + align:start position:0% +different energy level so I guess we +would also say minus Sigma in elastic + + align:start position:0% +would also say minus Sigma in elastic + + + align:start position:0% +would also say minus Sigma in elastic +and inelastic does happen for just about + + align:start position:0% +and inelastic does happen for just about + + + align:start position:0% +and inelastic does happen for just about +every other element but the nice thing + + align:start position:0% +every other element but the nice thing + + + align:start position:0% +every other element but the nice thing +is those don't turn on until about one + + align:start position:0% +is those don't turn on until about one + + + align:start position:0% +is those don't turn on until about one +MeV so it's not going to matter much but + + align:start position:0% +MeV so it's not going to matter much but + + + align:start position:0% +MeV so it's not going to matter much but +you can quantify how much it matters and + + align:start position:0% +you can quantify how much it matters and + + + align:start position:0% +you can quantify how much it matters and +just check so if you can make a + + align:start position:0% +just check so if you can make a + + + align:start position:0% +just check so if you can make a +justified assumption to say here's the + + align:start position:0% +justified assumption to say here's the + + + align:start position:0% +justified assumption to say here's the +one of the calyx with and without + + align:start position:0% +one of the calyx with and without + + + align:start position:0% +one of the calyx with and without +inelastic scattering and if they don't + + align:start position:0% +inelastic scattering and if they don't + + + align:start position:0% +inelastic scattering and if they don't +differ by much then forget it + + align:start position:0% +differ by much then forget it + + + align:start position:0% +differ by much then forget it +as long as you show me your math so + + align:start position:0% +as long as you show me your math so + + + align:start position:0% +as long as you show me your math so +let's say we've got news we have + + align:start position:0% +let's say we've got news we have + + + align:start position:0% +let's say we've got news we have +cross-sections I give you fluxes we have + + align:start position:0% +cross-sections I give you fluxes we have + + + align:start position:0% +cross-sections I give you fluxes we have +DS you can calculate buckling from the + + align:start position:0% +DS you can calculate buckling from the + + + align:start position:0% +DS you can calculate buckling from the +geometry of the reactor which is given + + align:start position:0% +geometry of the reactor which is given + + + align:start position:0% +geometry of the reactor which is given +in the ap1000 spec sheet the only other + + align:start position:0% +in the ap1000 spec sheet the only other + + + align:start position:0% +in the ap1000 spec sheet the only other +trick will be what's Sigma scattering + + align:start position:0% +trick will be what's Sigma scattering + + + align:start position:0% +trick will be what's Sigma scattering +from fast to thermal so you'll have to + + align:start position:0% +from fast to thermal so you'll have to + + + align:start position:0% +from fast to thermal so you'll have to +figure out what is the cross section not + + align:start position:0% +figure out what is the cross section not + + + align:start position:0% +figure out what is the cross section not +just of scattering total but the cross + + align:start position:0% +just of scattering total but the cross + + + align:start position:0% +just of scattering total but the cross +section or the probability that a fast + + align:start position:0% +section or the probability that a fast + + + align:start position:0% +section or the probability that a fast +Neutron enters the thermal group and I + + align:start position:0% +Neutron enters the thermal group and I + + + align:start position:0% +Neutron enters the thermal group and I +don't want to give that away either but + + align:start position:0% +don't want to give that away either but + + + align:start position:0% +don't want to give that away either but +it's not terribly mathematical yep + + align:start position:0% + + + + align:start position:0% + +not quite so even if you only have one + + align:start position:0% +not quite so even if you only have one + + + align:start position:0% +not quite so even if you only have one +isotope for each material if you have + + align:start position:0% +isotope for each material if you have + + + align:start position:0% +isotope for each material if you have +more than one material you've got to + + align:start position:0% +more than one material you've got to + + + align:start position:0% +more than one material you've got to +average those cross sections because + + align:start position:0% +average those cross sections because + + + align:start position:0% +average those cross sections because +this criticality criterion is for the + + align:start position:0% +this criticality criterion is for the + + + align:start position:0% +this criticality criterion is for the +entire reactor and all the stuff in it + + align:start position:0% +entire reactor and all the stuff in it + + + align:start position:0% +entire reactor and all the stuff in it +that's why it's like in a blender so + + align:start position:0% +that's why it's like in a blender so + + + align:start position:0% +that's why it's like in a blender so +even if iron has one isotope and + + align:start position:0% +even if iron has one isotope and + + + align:start position:0% +even if iron has one isotope and +zirconium as one isotope and uranium has + + align:start position:0% +zirconium as one isotope and uranium has + + + align:start position:0% +zirconium as one isotope and uranium has +one isotope which wouldn't really be a + + align:start position:0% +one isotope which wouldn't really be a + + + align:start position:0% +one isotope which wouldn't really be a +reactor then you'd still have to take + + align:start position:0% +reactor then you'd still have to take + + + align:start position:0% +reactor then you'd still have to take +atom fractions of those to get the total + + align:start position:0% +atom fractions of those to get the total + + + align:start position:0% +atom fractions of those to get the total +criticality condition speaking of which + + align:start position:0% +criticality condition speaking of which + + + align:start position:0% +criticality condition speaking of which +I forgot to write where the K is and + + align:start position:0% +I forgot to write where the K is and + + + align:start position:0% +I forgot to write where the K is and +since everything else here will be + + align:start position:0% +since everything else here will be + + + align:start position:0% +since everything else here will be +tabulated you can solve for K effective + + align:start position:0% +tabulated you can solve for K effective + + + align:start position:0% +tabulated you can solve for K effective +so K effective is the only variable + + align:start position:0% +so K effective is the only variable + + + align:start position:0% +so K effective is the only variable +unknown in this whole equation + + align:start position:0% +unknown in this whole equation + + + align:start position:0% +unknown in this whole equation +yep that's right + + align:start position:0% +yep that's right + + + align:start position:0% +yep that's right +so yeah let's go to the rest of the + + align:start position:0% +so yeah let's go to the rest of the + + + align:start position:0% +so yeah let's go to the rest of the +problem set since you mentioned it for + + align:start position:0% +problem set since you mentioned it for + + + align:start position:0% +problem set since you mentioned it for +one of the other questions North Korean + + align:start position:0% +one of the other questions North Korean + + + align:start position:0% +one of the other questions North Korean +nuclear weapons why is it that just + + align:start position:0% +nuclear weapons why is it that just + + + align:start position:0% +nuclear weapons why is it that just +putting together a super critical mass + + align:start position:0% +putting together a super critical mass + + + align:start position:0% +putting together a super critical mass +of plutonium does not constitute an + + align:start position:0% +of plutonium does not constitute an + + + align:start position:0% +of plutonium does not constitute an +effective bomb we're lucky for that too + + align:start position:0% +effective bomb we're lucky for that too + + + align:start position:0% +effective bomb we're lucky for that too +that making nuclear weapons is a lot + + align:start position:0% +that making nuclear weapons is a lot + + + align:start position:0% +that making nuclear weapons is a lot +harder than just getting nuclear + + align:start position:0% +harder than just getting nuclear + + + align:start position:0% +harder than just getting nuclear +material and this is a lot of the reason + + align:start position:0% +material and this is a lot of the reason + + + align:start position:0% +material and this is a lot of the reason +why there's a been you know 500 tonne + + align:start position:0% +why there's a been you know 500 tonne + + + align:start position:0% +why there's a been you know 500 tonne +yield or kiloton yields duds it's really + + align:start position:0% +yield or kiloton yields duds it's really + + + align:start position:0% +yield or kiloton yields duds it's really +really really really hard and I want you + + align:start position:0% +really really really hard and I want you + + + align:start position:0% +really really really hard and I want you +to think about what would you need to do + + align:start position:0% +to think about what would you need to do + + + align:start position:0% +to think about what would you need to do +to turn a super critical mass of nuclear + + align:start position:0% +to turn a super critical mass of nuclear + + + align:start position:0% +to turn a super critical mass of nuclear +material into an effective weapon and + + align:start position:0% +material into an effective weapon and + + + align:start position:0% +material into an effective weapon and +why is it that it's so difficult to do + + align:start position:0% +why is it that it's so difficult to do + + + align:start position:0% +why is it that it's so difficult to do +and actually really glad it's so + + align:start position:0% +and actually really glad it's so + + + align:start position:0% +and actually really glad it's so +difficult to do it's one of the reasons + + align:start position:0% +difficult to do it's one of the reasons + + + align:start position:0% +difficult to do it's one of the reasons +that a lot of folks don't have them but + + align:start position:0% +that a lot of folks don't have them but + + + align:start position:0% +that a lot of folks don't have them but +yeah if you only have one isotope like + + align:start position:0% +yeah if you only have one isotope like + + + align:start position:0% +yeah if you only have one isotope like +you do in this problem you don't have to + + align:start position:0% +you do in this problem you don't have to + + + align:start position:0% +you do in this problem you don't have to +do atom fractions you just take number + + align:start position:0% +do atom fractions you just take number + + + align:start position:0% +do atom fractions you just take number +density times microscopic cross-section + + align:start position:0% +density times microscopic cross-section + + + align:start position:0% +density times microscopic cross-section +from Janus and you get the macro + + align:start position:0% +from Janus and you get the macro + + + align:start position:0% +from Janus and you get the macro +cross-sections that's why it's one of + + align:start position:0% +cross-sections that's why it's one of + + + align:start position:0% +cross-sections that's why it's one of +the skill building problems where it's + + align:start position:0% +the skill building problems where it's + + + align:start position:0% +the skill building problems where it's +it shouldn't be that hard so you'll have + + align:start position:0% +it shouldn't be that hard so you'll have + + + align:start position:0% +it shouldn't be that hard so you'll have +a criticality condition you'll be able + + align:start position:0% +a criticality condition you'll be able + + + align:start position:0% +a criticality condition you'll be able +to get cross-sections and number + + align:start position:0% +to get cross-sections and number + + + align:start position:0% +to get cross-sections and number +densities and you'll be able to tell + + align:start position:0% +densities and you'll be able to tell + + + align:start position:0% +densities and you'll be able to tell +what that radius of the sphere is given + + align:start position:0% +what that radius of the sphere is given + + + align:start position:0% +what that radius of the sphere is given +the form of buckling for a sphere which + + align:start position:0% +the form of buckling for a sphere which + + + align:start position:0% +the form of buckling for a sphere which +would be in your reading yep + + align:start position:0% + + + + align:start position:0% + +that's being sent to you today so + + align:start position:0% +that's being sent to you today so + + + align:start position:0% +that's being sent to you today so +everyone oh so you guys all did power + + align:start position:0% +everyone oh so you guys all did power + + + align:start position:0% +everyone oh so you guys all did power +manipulations from the reactor I wanted + + align:start position:0% +manipulations from the reactor I wanted + + + align:start position:0% +manipulations from the reactor I wanted +to get him from Monday the guys were + + align:start position:0% +to get him from Monday the guys were + + + align:start position:0% +to get him from Monday the guys were +busy doing an in core experiment + + align:start position:0% +busy doing an in core experiment + + + align:start position:0% +busy doing an in core experiment +installed they've promised me the data + + align:start position:0% +installed they've promised me the data + + + align:start position:0% +installed they've promised me the data +today so you guys will be able to take a + + align:start position:0% +today so you guys will be able to take a + + + align:start position:0% +today so you guys will be able to take a +look at it and using the transient stuff + + align:start position:0% +look at it and using the transient stuff + + + align:start position:0% +look at it and using the transient stuff +that we talked about Tuesday explain why + + align:start position:0% +that we talked about Tuesday explain why + + + align:start position:0% +that we talked about Tuesday explain why +it doesn't look the linear feedback or + + align:start position:0% +it doesn't look the linear feedback or + + + align:start position:0% +it doesn't look the linear feedback or +intuitive yep so we'll also I'll be + + align:start position:0% +intuitive yep so we'll also I'll be + + + align:start position:0% +intuitive yep so we'll also I'll be +giving each of you that data today we + + align:start position:0% +giving each of you that data today we + + + align:start position:0% +giving each of you that data today we +talked about nuclear weapons there's top + + align:start position:0% +talked about nuclear weapons there's top + + + align:start position:0% +talked about nuclear weapons there's top +one I want you to do on your own because + + align:start position:0% +one I want you to do on your own because + + + align:start position:0% +one I want you to do on your own because +it's other repetitions of the intuitive + + align:start position:0% +it's other repetitions of the intuitive + + + align:start position:0% +it's other repetitions of the intuitive +criticality examples that we did on + + align:start position:0% +criticality examples that we did on + + + align:start position:0% +criticality examples that we did on +Tuesday the last one we haven't talked + + align:start position:0% +Tuesday the last one we haven't talked + + + align:start position:0% +Tuesday the last one we haven't talked +about is the ultra cold nuclear reactor + + align:start position:0% +about is the ultra cold nuclear reactor + + + align:start position:0% +about is the ultra cold nuclear reactor +or the will see problem so here I want + + align:start position:0% +or the will see problem so here I want + + + align:start position:0% +or the will see problem so here I want +you to actually get a criticality + + align:start position:0% +you to actually get a criticality + + + align:start position:0% +you to actually get a criticality +condition for the case where you can + + align:start position:0% +condition for the case where you can + + + align:start position:0% +condition for the case where you can +have ultra cold neutrons where your + + align:start position:0% +have ultra cold neutrons where your + + + align:start position:0% +have ultra cold neutrons where your +moderator is let's say liquid hydrogen + + align:start position:0% +moderator is let's say liquid hydrogen + + + align:start position:0% +moderator is let's say liquid hydrogen +really really cold way below the thermal + + align:start position:0% +really really cold way below the thermal + + + align:start position:0% +really really cold way below the thermal +level and you have to split your reactor + + align:start position:0% +level and you have to split your reactor + + + align:start position:0% +level and you have to split your reactor +into three energy groups fast thermal + + align:start position:0% +into three energy groups fast thermal + + + align:start position:0% +into three energy groups fast thermal +and ultra cooled and the trick to this + + align:start position:0% +and ultra cooled and the trick to this + + + align:start position:0% +and ultra cooled and the trick to this +here is somebody asked can you ever have + + align:start position:0% +here is somebody asked can you ever have + + + align:start position:0% +here is somebody asked can you ever have +ultra up scattering why yes if you have + + align:start position:0% +ultra up scattering why yes if you have + + + align:start position:0% +ultra up scattering why yes if you have +an ultra cold moderator but you've got + + align:start position:0% +an ultra cold moderator but you've got + + + align:start position:0% +an ultra cold moderator but you've got +hot fuel you can actually scatter up in + + align:start position:0% +hot fuel you can actually scatter up in + + + align:start position:0% +hot fuel you can actually scatter up in +energy where the surrounding atoms could + + align:start position:0% +energy where the surrounding atoms could + + + align:start position:0% +energy where the surrounding atoms could +be hotter than some of the neutrons + + align:start position:0% +be hotter than some of the neutrons + + + align:start position:0% +be hotter than some of the neutrons +hitting it and will impart energy to + + align:start position:0% +hitting it and will impart energy to + + + align:start position:0% +hitting it and will impart energy to +those neutrons and send it up the energy + + align:start position:0% +those neutrons and send it up the energy + + + align:start position:0% +those neutrons and send it up the energy +spectrum yep + + align:start position:0% + + + + align:start position:0% + +mmm well how do you get old for cold + + align:start position:0% +mmm well how do you get old for cold + + + align:start position:0% +mmm well how do you get old for cold +neutrons mm-hmm but some of them might + + align:start position:0% +neutrons mm-hmm but some of them might + + + align:start position:0% +neutrons mm-hmm but some of them might +scatter up yeah they can scatter about + + align:start position:0% +scatter up yeah they can scatter about + + + align:start position:0% +scatter up yeah they can scatter about +they can scatter down by hitting + + align:start position:0% +they can scatter down by hitting + + + align:start position:0% +they can scatter down by hitting +something cold and scatter back up by + + align:start position:0% +something cold and scatter back up by + + + align:start position:0% +something cold and scatter back up by +getting knocked by a hot item yeah so + + align:start position:0% +getting knocked by a hot item yeah so + + + align:start position:0% +getting knocked by a hot item yeah so +it's all gonna be in the formulation of + + align:start position:0% +it's all gonna be in the formulation of + + + align:start position:0% +it's all gonna be in the formulation of +the equations for this problem like 80 + + align:start position:0% +the equations for this problem like 80 + + + align:start position:0% +the equations for this problem like 80 +or 85 percent of the credit is did you + + align:start position:0% +or 85 percent of the credit is did you + + + align:start position:0% +or 85 percent of the credit is did you +formulate the three group equations + + align:start position:0% +formulate the three group equations + + + align:start position:0% +formulate the three group equations +correctly so I want you to think about + + align:start position:0% +correctly so I want you to think about + + + align:start position:0% +correctly so I want you to think about +what are the actual sources and sinks in + + align:start position:0% +what are the actual sources and sinks in + + + align:start position:0% +what are the actual sources and sinks in +each case what are the fractions of + + align:start position:0% +each case what are the fractions of + + + align:start position:0% +each case what are the fractions of +prompt and delayed neutrons where do + + align:start position:0% +prompt and delayed neutrons where do + + + align:start position:0% +prompt and delayed neutrons where do +they go and what terms matter where so + + align:start position:0% +they go and what terms matter where so + + + align:start position:0% +they go and what terms matter where so +it's doing this but for the case that + + align:start position:0% +it's doing this but for the case that + + + align:start position:0% +it's doing this but for the case that +we've given you here solving it is a lot + + align:start position:0% +we've given you here solving it is a lot + + + align:start position:0% +we've given you here solving it is a lot +of algebra and therefore not a lot of + + align:start position:0% +of algebra and therefore not a lot of + + + align:start position:0% +of algebra and therefore not a lot of +credit so is that clear to everybody + + align:start position:0% +credit so is that clear to everybody + + + align:start position:0% +credit so is that clear to everybody +figured this piece up with worth + + align:start position:0% +figured this piece up with worth + + + align:start position:0% +figured this piece up with worth +explaining and not just saying have fun + + align:start position:0% +explaining and not just saying have fun + + + align:start position:0% +explaining and not just saying have fun +you know I'll see you on Piazza Sunday + + align:start position:0% +you know I'll see you on Piazza Sunday + + + align:start position:0% +you know I'll see you on Piazza Sunday +night yeah that's why I check it yeah + + align:start position:0% +night yeah that's why I check it yeah + + + align:start position:0% +night yeah that's why I check it yeah +cool I've also got problem set four for + + align:start position:0% +cool I've also got problem set four for + + + align:start position:0% +cool I've also got problem set four for +everybody here I want to mention a + + align:start position:0% +everybody here I want to mention a + + + align:start position:0% +everybody here I want to mention a +couple of quick things please when you + + align:start position:0% +couple of quick things please when you + + + align:start position:0% +couple of quick things please when you +if you handwrite your psets which is + + align:start position:0% +if you handwrite your psets which is + + + align:start position:0% +if you handwrite your psets which is +fine please make sure to scan them + + align:start position:0% +fine please make sure to scan them + + + align:start position:0% +fine please make sure to scan them +legibly and to write legibly + + align:start position:0% +legibly and to write legibly + + + align:start position:0% +legibly and to write legibly +we can't give partial credit for things + + align:start position:0% +we can't give partial credit for things + + + align:start position:0% +we can't give partial credit for things +we can't read and so this will be a + + align:start position:0% +we can't read and so this will be a + + + align:start position:0% +we can't read and so this will be a +lesson to some of you guys so depending + + align:start position:0% +lesson to some of you guys so depending + + + align:start position:0% +lesson to some of you guys so depending +on who got what grade there are times + + align:start position:0% +on who got what grade there are times + + + align:start position:0% +on who got what grade there are times +when you may have written stuff for + + align:start position:0% +when you may have written stuff for + + + align:start position:0% +when you may have written stuff for +partial credit but we just honestly + + align:start position:0% +partial credit but we just honestly + + + align:start position:0% +partial credit but we just honestly +couldn't make it out so please do make + + align:start position:0% +couldn't make it out so please do make + + + align:start position:0% +couldn't make it out so please do make +sure that your submissions are legible + + align:start position:0% +sure that your submissions are legible + + + align:start position:0% +sure that your submissions are legible +and for things like these these are + + align:start position:0% +and for things like these these are + + + align:start position:0% +and for things like these these are +handwritten problem sets but they were + + align:start position:0% +handwritten problem sets but they were + + + align:start position:0% +handwritten problem sets but they were +scanned with either a scanner which does + + align:start position:0% +scanned with either a scanner which does + + + align:start position:0% +scanned with either a scanner which does +the correct contrast or writing them on + + align:start position:0% +the correct contrast or writing them on + + + align:start position:0% +the correct contrast or writing them on +one note which apparently works pretty + + align:start position:0% +one note which apparently works pretty + + + align:start position:0% +one note which apparently works pretty +well or apps like cam scanner + + align:start position:0% +well or apps like cam scanner + + + align:start position:0% +well or apps like cam scanner +there's an app on your phone you can get + + align:start position:0% +there's an app on your phone you can get + + + align:start position:0% +there's an app on your phone you can get +that scans pieces of paper and + + align:start position:0% +that scans pieces of paper and + + + align:start position:0% +that scans pieces of paper and +automatically contrast enhances them it + + align:start position:0% +automatically contrast enhances them it + + + align:start position:0% +automatically contrast enhances them it +knows the paper should be white and the + + align:start position:0% +knows the paper should be white and the + + + align:start position:0% +knows the paper should be white and the +writing should be black and it also does + + align:start position:0% +writing should be black and it also does + + + align:start position:0% +writing should be black and it also does +it in color so if you do color graphs it + + align:start position:0% +it in color so if you do color graphs it + + + align:start position:0% +it in color so if you do color graphs it +recognizes that there are multiple + + align:start position:0% +recognizes that there are multiple + + + align:start position:0% +recognizes that there are multiple +colors and will take care of that for + + align:start position:0% +colors and will take care of that for + + + align:start position:0% +colors and will take care of that for +you + + align:start position:0% +you + + + align:start position:0% +you +it only takes an additional minute but I + + align:start position:0% +it only takes an additional minute but I + + + align:start position:0% +it only takes an additional minute but I +can give you you know double the points + + align:start position:0% +can give you you know double the points + + + align:start position:0% +can give you you know double the points +and a problem set because we can read + + align:start position:0% +and a problem set because we can read + + + align:start position:0% +and a problem set because we can read +stuff so I'll give back pset for now + + align:start position:0% +stuff so I'll give back pset for now + + + align:start position:0% +stuff so I'll give back pset for now +we're working on five and six + + align:start position:0% +we're working on five and six + + + align:start position:0% +we're working on five and six +the big delay in grading there was I + + align:start position:0% +the big delay in grading there was I + + + align:start position:0% +the big delay in grading there was I +went to Russia and Russia doesn't have + + align:start position:0% +went to Russia and Russia doesn't have + + + align:start position:0% +went to Russia and Russia doesn't have +as much internet as we do at least not + + align:start position:0% +as much internet as we do at least not + + + align:start position:0% +as much internet as we do at least not +where I was and it was busy so working + + align:start position:0% +where I was and it was busy so working + + + align:start position:0% +where I was and it was busy so working +on those solutions now yeah yep oh okay + + align:start position:0% +on those solutions now yeah yep oh okay + + + align:start position:0% +on those solutions now yeah yep oh okay +yeah good question so problem one + + align:start position:0% +yeah good question so problem one + + + align:start position:0% +yeah good question so problem one +throwing quarters into the directly into + + align:start position:0% +throwing quarters into the directly into + + + align:start position:0% +throwing quarters into the directly into +the core like a wishing well it used to + + align:start position:0% +the core like a wishing well it used to + + + align:start position:0% +the core like a wishing well it used to +be that back in the day they would take + + align:start position:0% +be that back in the day they would take + + + align:start position:0% +be that back in the day they would take +folks on reactor tours to look down into + + align:start position:0% +folks on reactor tours to look down into + + + align:start position:0% +folks on reactor tours to look down into +the core because when the lid is off you + + align:start position:0% +the core because when the lid is off you + + + align:start position:0% +the core because when the lid is off you +can see it you can see the Cherenkov + + align:start position:0% +can see it you can see the Cherenkov + + + align:start position:0% +can see it you can see the Cherenkov +radiation the nice blue light you can + + align:start position:0% +radiation the nice blue light you can + + + align:start position:0% +radiation the nice blue light you can +actually see the fuel elements because + + align:start position:0% +actually see the fuel elements because + + + align:start position:0% +actually see the fuel elements because +the water is sufficient shielding for + + align:start position:0% +the water is sufficient shielding for + + + align:start position:0% +the water is sufficient shielding for +you and the distance is sufficient + + align:start position:0% +you and the distance is sufficient + + + align:start position:0% +you and the distance is sufficient +shielding to keep you away from the + + align:start position:0% +shielding to keep you away from the + + + align:start position:0% +shielding to keep you away from the +gammas not to mention the reactor is + + align:start position:0% +gammas not to mention the reactor is + + + align:start position:0% +gammas not to mention the reactor is +usually off when the lid is off so it's + + align:start position:0% +usually off when the lid is off so it's + + + align:start position:0% +usually off when the lid is off so it's +not that hot problem is you can't watch + + align:start position:0% +not that hot problem is you can't watch + + + align:start position:0% +not that hot problem is you can't watch +what everyone's doing all the time and + + align:start position:0% +what everyone's doing all the time and + + + align:start position:0% +what everyone's doing all the time and +someone he dropped a quarter into the + + align:start position:0% +someone he dropped a quarter into the + + + align:start position:0% +someone he dropped a quarter into the +reactor they were like oh it's a wishing + + align:start position:0% +reactor they were like oh it's a wishing + + + align:start position:0% +reactor they were like oh it's a wishing +well well it took something like six + + align:start position:0% +well well it took something like six + + + align:start position:0% +well well it took something like six +dive robots to go into the core and fish + + align:start position:0% +dive robots to go into the core and fish + + + align:start position:0% +dive robots to go into the core and fish +it out because each of those robots + + align:start position:0% +it out because each of those robots + + + align:start position:0% +it out because each of those robots +lasts you know 10 minutes before the + + align:start position:0% +lasts you know 10 minutes before the + + + align:start position:0% +lasts you know 10 minutes before the +intense radiation fries it and if you + + align:start position:0% +intense radiation fries it and if you + + + align:start position:0% +intense radiation fries it and if you +didn't find the corridor you got to take + + align:start position:0% +didn't find the corridor you got to take + + + align:start position:0% +didn't find the corridor you got to take +into out put down another one and these + + align:start position:0% +into out put down another one and these + + + align:start position:0% +into out put down another one and these +are like radiation hard you know narrow + + align:start position:0% +are like radiation hard you know narrow + + + align:start position:0% +are like radiation hard you know narrow +whatever diving robots this story was + + align:start position:0% +whatever diving robots this story was + + + align:start position:0% +whatever diving robots this story was +relayed to me through someone that + + align:start position:0% +relayed to me through someone that + + + align:start position:0% +relayed to me through someone that +related to them through whatever so it's + + align:start position:0% +related to them through whatever so it's + + + align:start position:0% +related to them through whatever so it's +been through the telephone chain but I + + align:start position:0% +been through the telephone chain but I + + + align:start position:0% +been through the telephone chain but I +dunno that's one of the big reasons you + + align:start position:0% +dunno that's one of the big reasons you + + + align:start position:0% +dunno that's one of the big reasons you +can't look down on the core anymore it's + + align:start position:0% +can't look down on the core anymore it's + + + align:start position:0% +can't look down on the core anymore it's +because folks abused the privileges of + + align:start position:0% +because folks abused the privileges of + + + align:start position:0% +because folks abused the privileges of +torus yeah + + align:start position:0% + + + + align:start position:0% + +yep interesting then you could use the + + align:start position:0% +yep interesting then you could use the + + + align:start position:0% +yep interesting then you could use the +web version which is just through the + + align:start position:0% +web version which is just through the + + + align:start position:0% +web version which is just through the +blah browser and no plugins required + + align:start position:0% +blah browser and no plugins required + + + align:start position:0% +blah browser and no plugins required +yeah cool any other questions about the + + align:start position:0% +yeah cool any other questions about the + + + align:start position:0% +yeah cool any other questions about the +pset that we didn't cover together does + + align:start position:0% +pset that we didn't cover together does + + + align:start position:0% +pset that we didn't cover together does +looking a little more doable + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/KqAYOtPNtN8.txt b/KqAYOtPNtN8.txt new file mode 100644 index 0000000000000000000000000000000000000000..844dea89053915308721ce943c89ba2c3882d7d2 --- /dev/null +++ b/KqAYOtPNtN8.txt @@ -0,0 +1,1139 @@ +align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +from your practice you should now be + + align:start position:0% +from your practice you should now be + + + align:start position:0% +from your practice you should now be +familiar + + align:start position:0% +familiar + + + align:start position:0% +familiar +with the following dna rules + + align:start position:0% +with the following dna rules + + + align:start position:0% +with the following dna rules +you should understand base pairing and + + align:start position:0% +you should understand base pairing and + + + align:start position:0% +you should understand base pairing and +be able to + + align:start position:0% +be able to + + + align:start position:0% +be able to +put in the opposite complementary strand + + align:start position:0% +put in the opposite complementary strand + + + align:start position:0% +put in the opposite complementary strand +relative to a piece of dna you + + align:start position:0% +relative to a piece of dna you + + + align:start position:0% +relative to a piece of dna you +should understand polarity that we + + align:start position:0% +should understand polarity that we + + + align:start position:0% +should understand polarity that we +talked about before + + align:start position:0% +talked about before + + + align:start position:0% +talked about before +the five prime and the three prime ends + + align:start position:0% +the five prime and the three prime ends + + + align:start position:0% +the five prime and the three prime ends +of nucleic acid + + align:start position:0% +of nucleic acid + + + align:start position:0% +of nucleic acid +and you should understand the concept of + + align:start position:0% +and you should understand the concept of + + + align:start position:0% +and you should understand the concept of +antiparallel strands + + align:start position:0% +antiparallel strands + + + align:start position:0% +antiparallel strands +where one strand goes five prime to + + align:start position:0% +where one strand goes five prime to + + + align:start position:0% +where one strand goes five prime to +three prime + + align:start position:0% +three prime + + + align:start position:0% +three prime +and the other three prime to five prime + + align:start position:0% +and the other three prime to five prime + + + align:start position:0% +and the other three prime to five prime +this will set you up for the next thing + + align:start position:0% +this will set you up for the next thing + + + align:start position:0% +this will set you up for the next thing +that we're going to talk about + + align:start position:0% +that we're going to talk about + + + align:start position:0% +that we're going to talk about +which is dna replication + + align:start position:0% +which is dna replication + + + align:start position:0% +which is dna replication +what do we mean by dna replication we + + align:start position:0% +what do we mean by dna replication we + + + align:start position:0% +what do we mean by dna replication we +mean + + align:start position:0% +mean + + + align:start position:0% +mean +that dna is produced by copying + + align:start position:0% +that dna is produced by copying + + + align:start position:0% +that dna is produced by copying +a dna template dna replication + + align:start position:0% +a dna template dna replication + + + align:start position:0% +a dna template dna replication +produces dna + + align:start position:0% +produces dna + + + align:start position:0% +produces dna +from a dna + + align:start position:0% +from a dna + + + align:start position:0% +from a dna +template this is a process + + align:start position:0% +template this is a process + + + align:start position:0% +template this is a process +that takes place in the nucleus of the + + align:start position:0% +that takes place in the nucleus of the + + + align:start position:0% +that takes place in the nucleus of the +cell and it is the mechanism + + align:start position:0% +cell and it is the mechanism + + + align:start position:0% +cell and it is the mechanism +by which dna the genes + + align:start position:0% +by which dna the genes + + + align:start position:0% +by which dna the genes +make more of themselves before + + align:start position:0% +make more of themselves before + + + align:start position:0% +make more of themselves before +they undergo cell division mitosis + + align:start position:0% +they undergo cell division mitosis + + + align:start position:0% +they undergo cell division mitosis +or meiosis what do we mean + + align:start position:0% +or meiosis what do we mean + + + align:start position:0% +or meiosis what do we mean +by dna replication let us start + + align:start position:0% +by dna replication let us start + + + align:start position:0% +by dna replication let us start +by looking at a piece of double-stranded + + align:start position:0% +by looking at a piece of double-stranded + + + align:start position:0% +by looking at a piece of double-stranded +dna + + align:start position:0% +dna + + + align:start position:0% +dna +and i'm not going to put in the exact + + align:start position:0% +and i'm not going to put in the exact + + + align:start position:0% +and i'm not going to put in the exact +nucleotides i'm just going to put some + + align:start position:0% +nucleotides i'm just going to put some + + + align:start position:0% +nucleotides i'm just going to put some +dots and things to represent the + + align:start position:0% +dots and things to represent the + + + align:start position:0% +dots and things to represent the +nucleotides + + align:start position:0% +nucleotides + + + align:start position:0% +nucleotides +so here is one strand + + align:start position:0% +so here is one strand + + + align:start position:0% +so here is one strand +and here is the antiparallel strand + + align:start position:0% +and here is the antiparallel strand + + + align:start position:0% +and here is the antiparallel strand +with the complementary bases + + align:start position:0% +with the complementary bases + + + align:start position:0% +with the complementary bases +dna is replicated + + align:start position:0% +dna is replicated + + + align:start position:0% +dna is replicated +firstly by separating the strands + + align:start position:0% +firstly by separating the strands + + + align:start position:0% +firstly by separating the strands +so a process of strand separation + + align:start position:0% +so a process of strand separation + + + align:start position:0% +so a process of strand separation +leads to two strands the top one + + align:start position:0% +leads to two strands the top one + + + align:start position:0% +leads to two strands the top one +five prime plus the bottom one + + align:start position:0% +five prime plus the bottom one + + + align:start position:0% +five prime plus the bottom one +that goes three prime to five prime + + align:start position:0% +that goes three prime to five prime + + + align:start position:0% +that goes three prime to five prime +these two separated strands + + align:start position:0% +these two separated strands + + + align:start position:0% +these two separated strands +now serve as templates something to copy + + align:start position:0% +now serve as templates something to copy + + + align:start position:0% +now serve as templates something to copy +in order to make more dna so each strand + + align:start position:0% +in order to make more dna so each strand + + + align:start position:0% +in order to make more dna so each strand +is a template that + + align:start position:0% +is a template that + + + align:start position:0% +is a template that +is then copied to make the complementary + + align:start position:0% +is then copied to make the complementary + + + align:start position:0% +is then copied to make the complementary +dna + + align:start position:0% +dna + + + align:start position:0% +dna +and the outcome will be that this top + + align:start position:0% +and the outcome will be that this top + + + align:start position:0% +and the outcome will be that this top +strand + + align:start position:0% +strand + + + align:start position:0% +strand +five prime to three prime will be + + align:start position:0% +five prime to three prime will be + + + align:start position:0% +five prime to three prime will be +filled in with its complement the + + align:start position:0% +filled in with its complement the + + + align:start position:0% +filled in with its complement the +matching other strand + + align:start position:0% +matching other strand + + + align:start position:0% +matching other strand +and the bottom template that went three + + align:start position:0% +and the bottom template that went three + + + align:start position:0% +and the bottom template that went three +prime to five + + align:start position:0% +prime to five + + + align:start position:0% +prime to five +prime will be filled in + + align:start position:0% +prime will be filled in + + + align:start position:0% +prime will be filled in +with its matching complementary strand + + align:start position:0% +with its matching complementary strand + + + align:start position:0% +with its matching complementary strand +so out of this one dna template + + align:start position:0% +so out of this one dna template + + + align:start position:0% +so out of this one dna template +or this one double stranded piece of dna + + align:start position:0% +or this one double stranded piece of dna + + + align:start position:0% +or this one double stranded piece of dna +there are two single stranded templates + + align:start position:0% +there are two single stranded templates + + + align:start position:0% +there are two single stranded templates +that then lead to + + align:start position:0% +that then lead to + + + align:start position:0% +that then lead to +two new dna molecules + + align:start position:0% +two new dna molecules + + + align:start position:0% +two new dna molecules +that are identical to the one + + align:start position:0% +that are identical to the one + + + align:start position:0% +that are identical to the one +that you started with so you've doubled + + align:start position:0% +that you started with so you've doubled + + + align:start position:0% +that you started with so you've doubled +the amount of dna + + align:start position:0% +the amount of dna + + + align:start position:0% +the amount of dna +and made identical new molecules + + align:start position:0% +and made identical new molecules + + + align:start position:0% +and made identical new molecules +starting with this parental dna template + + align:start position:0% +starting with this parental dna template + + + align:start position:0% +starting with this parental dna template +this is dna replication it is how your + + align:start position:0% +this is dna replication it is how your + + + align:start position:0% +this is dna replication it is how your +genes are replicated from + + align:start position:0% +genes are replicated from + + + align:start position:0% +genes are replicated from +cell division to cell division from + + align:start position:0% +cell division to cell division from + + + align:start position:0% +cell division to cell division from +parent + + align:start position:0% +parent + + + align:start position:0% +parent +to offspring it the process + + align:start position:0% +to offspring it the process + + + align:start position:0% +to offspring it the process +is absolutely dependent on base pairing + + align:start position:0% +is absolutely dependent on base pairing + + + align:start position:0% +is absolutely dependent on base pairing +without base pairing you wouldn't know + + align:start position:0% +without base pairing you wouldn't know + + + align:start position:0% +without base pairing you wouldn't know +which the right strand was it would be a + + align:start position:0% +which the right strand was it would be a + + + align:start position:0% +which the right strand was it would be a +mess + + align:start position:0% +mess + + + align:start position:0% +mess +but because of base pairing because of + + align:start position:0% +but because of base pairing because of + + + align:start position:0% +but because of base pairing because of +complementarity + + align:start position:0% +complementarity + + + align:start position:0% +complementarity +you can take the two strands fill them + + align:start position:0% +you can take the two strands fill them + + + align:start position:0% +you can take the two strands fill them +in + + align:start position:0% +in + + + align:start position:0% +in +and come up with dna that is identical + + align:start position:0% +and come up with dna that is identical + + + align:start position:0% +and come up with dna that is identical +to the parent so here is your parent dna + + align:start position:0% +to the parent so here is your parent dna + + + align:start position:0% +to the parent so here is your parent dna +and here is your new dna + + align:start position:0% +and here is your new dna + + + align:start position:0% +and here is your new dna +and they are identical very + + align:start position:0% +and they are identical very + + + align:start position:0% +and they are identical very +profound let's take a look at a couple + + align:start position:0% +profound let's take a look at a couple + + + align:start position:0% +profound let's take a look at a couple +of slides + + align:start position:0% +of slides + + + align:start position:0% +of slides +so here is a double-stranded dna + + align:start position:0% +so here is a double-stranded dna + + + align:start position:0% +so here is a double-stranded dna +template i put in just some of the + + align:start position:0% +template i put in just some of the + + + align:start position:0% +template i put in just some of the +nucleotides the strands separate + + align:start position:0% +nucleotides the strands separate + + + align:start position:0% +nucleotides the strands separate +dna replication occurs from + + align:start position:0% +dna replication occurs from + + + align:start position:0% +dna replication occurs from +each three prime end + + align:start position:0% +each three prime end + + + align:start position:0% +each three prime end +now there's a little wrinkle here + + align:start position:0% +now there's a little wrinkle here + + + align:start position:0% +now there's a little wrinkle here +that you need to know dna replication + + align:start position:0% +that you need to know dna replication + + + align:start position:0% +that you need to know dna replication +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +exactly occur the way i drew it on the + + align:start position:0% +exactly occur the way i drew it on the + + + align:start position:0% +exactly occur the way i drew it on the +board + + align:start position:0% +board + + + align:start position:0% +board +it occurs with a running start + + align:start position:0% +it occurs with a running start + + + align:start position:0% +it occurs with a running start +it needs a little tiny piece of dna + + align:start position:0% +it needs a little tiny piece of dna + + + align:start position:0% +it needs a little tiny piece of dna +called a primer + + align:start position:0% +called a primer + + + align:start position:0% +called a primer +that allows the dna then to elongate + + align:start position:0% +that allows the dna then to elongate + + + align:start position:0% +that allows the dna then to elongate +from that three prime end so there's + + align:start position:0% +from that three prime end so there's + + + align:start position:0% +from that three prime end so there's +something called an + + align:start position:0% +something called an + + + align:start position:0% +something called an +rna primer which matches a little bit of + + align:start position:0% +rna primer which matches a little bit of + + + align:start position:0% +rna primer which matches a little bit of +the dna + + align:start position:0% +the dna + + + align:start position:0% +the dna +and that then gets elongated + + align:start position:0% + + + + align:start position:0% + +okay what is really really crucial here + + align:start position:0% +okay what is really really crucial here + + + align:start position:0% +okay what is really really crucial here +is that using the rules of + + align:start position:0% +is that using the rules of + + + align:start position:0% +is that using the rules of +complementarity + + align:start position:0% +complementarity + + + align:start position:0% +complementarity +and adding on to the three prime end we + + align:start position:0% +and adding on to the three prime end we + + + align:start position:0% +and adding on to the three prime end we +make + + align:start position:0% +make + + + align:start position:0% +make +two identical dna molecules that are + + align:start position:0% +two identical dna molecules that are + + + align:start position:0% +two identical dna molecules that are +identical to the parent + + align:start position:0% +identical to the parent + + + align:start position:0% +identical to the parent +okay and i see here on the board + + align:start position:0% +okay and i see here on the board + + + align:start position:0% +okay and i see here on the board +i must add a three prime n there + + align:start position:0% +i must add a three prime n there + + + align:start position:0% +i must add a three prime n there +okay if we look + + align:start position:0% +okay if we look + + + align:start position:0% +okay if we look +at a representation of the double helix + + align:start position:0% +at a representation of the double helix + + + align:start position:0% +at a representation of the double helix +this is what it looks like more in the + + align:start position:0% +this is what it looks like more in the + + + align:start position:0% +this is what it looks like more in the +cell the dna has the spiral helical form + + align:start position:0% +cell the dna has the spiral helical form + + + align:start position:0% +cell the dna has the spiral helical form +it unwinds so that you get two single + + align:start position:0% +it unwinds so that you get two single + + + align:start position:0% +it unwinds so that you get two single +strands in part of the + + align:start position:0% +strands in part of the + + + align:start position:0% +strands in part of the +helix and then those single strands get + + align:start position:0% +helix and then those single strands get + + + align:start position:0% +helix and then those single strands get +filled in with new dna there's some + + align:start position:0% +filled in with new dna there's some + + + align:start position:0% +filled in with new dna there's some +various nuances that we're not + + align:start position:0% +various nuances that we're not + + + align:start position:0% +various nuances that we're not +discussing here + + align:start position:0% +discussing here + + + align:start position:0% +discussing here +i threw out the notion of a primer to + + align:start position:0% +i threw out the notion of a primer to + + + align:start position:0% +i threw out the notion of a primer to +you all that means is that there's a + + align:start position:0% +you all that means is that there's a + + + align:start position:0% +you all that means is that there's a +three prime end you can add on to + + align:start position:0% +three prime end you can add on to + + + align:start position:0% +three prime end you can add on to +but the notion is as we have put it on + + align:start position:0% +but the notion is as we have put it on + + + align:start position:0% +but the notion is as we have put it on +the board + + align:start position:0% +the board + + + align:start position:0% +the board +single strands filled in with the + + align:start position:0% +single strands filled in with the + + + align:start position:0% +single strands filled in with the +complementary + + align:start position:0% +complementary + + + align:start position:0% +complementary +bases and voila you have dna replication + + align:start position:0% +bases and voila you have dna replication + + + align:start position:0% +bases and voila you have dna replication +take a look at assign the next + + align:start position:0% +take a look at assign the next + + + align:start position:0% +take a look at assign the next +assignment the next class exercise + + align:start position:0% +assignment the next class exercise + + + align:start position:0% +assignment the next class exercise +and see if you can replicate dna + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Kv7eOsMVx6E.txt b/Kv7eOsMVx6E.txt new file mode 100644 index 0000000000000000000000000000000000000000..a969056b95d0cbc11fd12b7534d7de39bbe1db8b --- /dev/null +++ b/Kv7eOsMVx6E.txt @@ -0,0 +1,7107 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license + + align:start position:0% +a Creative Commons license + + + align:start position:0% +a Creative Commons license +your support will help MIT + + align:start position:0% +your support will help MIT + + + align:start position:0% +your support will help MIT +OpenCourseWare continue to offer high + + align:start position:0% +OpenCourseWare continue to offer high + + + align:start position:0% +OpenCourseWare continue to offer high +quality educational resources for free + + align:start position:0% +quality educational resources for free + + + align:start position:0% +quality educational resources for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +ok thank you for coming today + + align:start position:0% +ok thank you for coming today + + + align:start position:0% +ok thank you for coming today +the day before Thanksgiving day before + + align:start position:0% +the day before Thanksgiving day before + + + align:start position:0% +the day before Thanksgiving day before +my birthday actually it's so on it's a + + align:start position:0% +my birthday actually it's so on it's a + + + align:start position:0% +my birthday actually it's so on it's a +special day + + align:start position:0% +special day + + + align:start position:0% +special day +everybody gets an a first even you ok so + + align:start position:0% +everybody gets an a first even you ok so + + + align:start position:0% +everybody gets an a first even you ok so +let's see last time I wrote down these + + align:start position:0% +let's see last time I wrote down these + + + align:start position:0% +let's see last time I wrote down these +formulas for the Fourier integral + + align:start position:0% +formulas for the Fourier integral + + + align:start position:0% +formulas for the Fourier integral +transform and I thought I'd just write + + align:start position:0% +transform and I thought I'd just write + + + align:start position:0% +transform and I thought I'd just write +them again so you kind of photograph + + align:start position:0% +them again so you kind of photograph + + + align:start position:0% +them again so you kind of photograph +them and and remember them they're easy + + align:start position:0% +them and and remember them they're easy + + + align:start position:0% +them and and remember them they're easy +to remember as always you take the + + align:start position:0% +to remember as always you take the + + + align:start position:0% +to remember as always you take the +function you multiply by e to the minus + + align:start position:0% +function you multiply by e to the minus + + + align:start position:0% +function you multiply by e to the minus +ikx and you integrate to get the amount + + align:start position:0% +ikx and you integrate to get the amount + + + align:start position:0% +ikx and you integrate to get the amount +so K is my frequency variable like it + + align:start position:0% +so K is my frequency variable like it + + + align:start position:0% +so K is my frequency variable like it +could well have been Omega or some other + + align:start position:0% +could well have been Omega or some other + + + align:start position:0% +could well have been Omega or some other +variable I stayed with K because it was + + align:start position:0% +variable I stayed with K because it was + + + align:start position:0% +variable I stayed with K because it was +K in the Fourier series so that's the + + align:start position:0% +K in the Fourier series so that's the + + + align:start position:0% +K in the Fourier series so that's the +calculation which oh as always I mean + + align:start position:0% +calculation which oh as always I mean + + + align:start position:0% +calculation which oh as always I mean +these are integrals that we may be able + + align:start position:0% +these are integrals that we may be able + + + align:start position:0% +these are integrals that we may be able +to do if the function is especially nice + + align:start position:0% +to do if the function is especially nice + + + align:start position:0% +to do if the function is especially nice +or or we may not but that's the that's + + align:start position:0% +or or we may not but that's the that's + + + align:start position:0% +or or we may not but that's the that's +the formula and then to reconstruct the + + align:start position:0% +the formula and then to reconstruct the + + + align:start position:0% +the formula and then to reconstruct the +function we combine all the e to the ikx + + align:start position:0% +function we combine all the e to the ikx + + + align:start position:0% +function we combine all the e to the ikx +is in that amount to get f of X back ok + + align:start position:0% +is in that amount to get f of X back ok + + + align:start position:0% +is in that amount to get f of X back ok +nice formulas ok so I did one example + + align:start position:0% +nice formulas ok so I did one example + + + align:start position:0% +nice formulas ok so I did one example +last time and now could I just double it + + align:start position:0% +last time and now could I just double it + + + align:start position:0% +last time and now could I just double it +up this is also in the textbook and it's + + align:start position:0% +up this is also in the textbook and it's + + + align:start position:0% +up this is also in the textbook and it's +a it's so this is now going to be an + + align:start position:0% +a it's so this is now going to be an + + + align:start position:0% +a it's so this is now going to be an +even function last time the example I + + align:start position:0% +even function last time the example I + + + align:start position:0% +even function last time the example I +did was zero on the up to up to x equals + + align:start position:0% +did was zero on the up to up to x equals + + + align:start position:0% +did was zero on the up to up to x equals +zero this time I'll make it symmetric + + align:start position:0% +zero this time I'll make it symmetric + + + align:start position:0% +zero this time I'll make it symmetric +make the function even and then I have + + align:start position:0% +make the function even and then I have + + + align:start position:0% +make the function even and then I have +two pieces in the + + align:start position:0% +two pieces in the + + + align:start position:0% +two pieces in the +integral and if you remember what it was + + align:start position:0% +integral and if you remember what it was + + + align:start position:0% +integral and if you remember what it was +do you remember that this I'll just + + align:start position:0% +do you remember that this I'll just + + + align:start position:0% +do you remember that this I'll just +remind you what we did we we wrote that + + align:start position:0% +remind you what we did we we wrote that + + + align:start position:0% +remind you what we did we we wrote that +as e to the minus a plus I K times X + + align:start position:0% +as e to the minus a plus I K times X + + + align:start position:0% +as e to the minus a plus I K times X +that was clear and then when we + + align:start position:0% +that was clear and then when we + + + align:start position:0% +that was clear and then when we +integrated we got that same function + + align:start position:0% +integrated we got that same function + + + align:start position:0% +integrated we got that same function +divided by minus a plus I K and then we + + align:start position:0% +divided by minus a plus I K and then we + + + align:start position:0% +divided by minus a plus I K and then we +put in the limits and the answer was let + + align:start position:0% +put in the limits and the answer was let + + + align:start position:0% +put in the limits and the answer was let +me maybe write the answer down here was + + align:start position:0% +me maybe write the answer down here was + + + align:start position:0% +me maybe write the answer down here was +just at X equal infinity the limit was + + align:start position:0% +just at X equal infinity the limit was + + + align:start position:0% +just at X equal infinity the limit was +zero because this thing is tailing off + + align:start position:0% +zero because this thing is tailing off + + + align:start position:0% +zero because this thing is tailing off +at x equals zero this is one it comes in + + align:start position:0% +at x equals zero this is one it comes in + + + align:start position:0% +at x equals zero this is one it comes in +with a minus because that's the lower + + align:start position:0% +with a minus because that's the lower + + + align:start position:0% +with a minus because that's the lower +limit so it was 1 over a plus okay for + + align:start position:0% +limit so it was 1 over a plus okay for + + + align:start position:0% +limit so it was 1 over a plus okay for +the first half and and we were not + + align:start position:0% +the first half and and we were not + + + align:start position:0% +the first half and and we were not +surprised to see this 1 over K because + + align:start position:0% +surprised to see this 1 over K because + + + align:start position:0% +surprised to see this 1 over K because +for the first half all by itself has + + align:start position:0% +for the first half all by itself has + + + align:start position:0% +for the first half all by itself has +that jump from 0 to 1 so we we see that + + align:start position:0% +that jump from 0 to 1 so we we see that + + + align:start position:0% +that jump from 0 to 1 so we we see that +jump reflected in slow decay alright but + + align:start position:0% +jump reflected in slow decay alright but + + + align:start position:0% +jump reflected in slow decay alright but +now I'm putting in making it even what + + align:start position:0% +now I'm putting in making it even what + + + align:start position:0% +now I'm putting in making it even what +are you going to guess for the rate of + + align:start position:0% +are you going to guess for the rate of + + + align:start position:0% +are you going to guess for the rate of +decay of the of F hat of K for this this + + align:start position:0% +decay of the of F hat of K for this this + + + align:start position:0% +decay of the of F hat of K for this this +function this function no longer has a + + align:start position:0% +function this function no longer has a + + + align:start position:0% +function this function no longer has a +jump but it does have I don't know what + + align:start position:0% +jump but it does have I don't know what + + + align:start position:0% +jump but it does have I don't know what +were we saying ramp or corner it's this + + align:start position:0% +were we saying ramp or corner it's this + + + align:start position:0% +were we saying ramp or corner it's this +is not a not a smooth point here because + + align:start position:0% +is not a not a smooth point here because + + + align:start position:0% +is not a not a smooth point here because +the derivative going up is plus a so so + + align:start position:0% +the derivative going up is plus a so so + + + align:start position:0% +the derivative going up is plus a so so +I'll just put a circle right the + + align:start position:0% +I'll just put a circle right the + + + align:start position:0% +I'll just put a circle right the +derivative is a e to the ax and at x + + align:start position:0% +derivative is a e to the ax and at x + + + align:start position:0% +derivative is a e to the ax and at x +equals 0 that would be plus a going up + + align:start position:0% +equals 0 that would be plus a going up + + + align:start position:0% +equals 0 that would be plus a going up +and here the derivative is minus a e to + + align:start position:0% +and here the derivative is minus a e to + + + align:start position:0% +and here the derivative is minus a e to +the minus ax put in X equal 0 and the + + align:start position:0% +the minus ax put in X equal 0 and the + + + align:start position:0% +the minus ax put in X equal 0 and the +derivative coming down is minus X so + + align:start position:0% +derivative coming down is minus X so + + + align:start position:0% +derivative coming down is minus X so +there's a jump in the derivative so what + + align:start position:0% +there's a jump in the derivative so what + + + align:start position:0% +there's a jump in the derivative so what +just before we see it what will you + + align:start position:0% +just before we see it what will you + + + align:start position:0% +just before we see it what will you +expect for the rate of decay of the of + + align:start position:0% +expect for the rate of decay of the of + + + align:start position:0% +expect for the rate of decay of the of +the of the transform 1 over K to what + + align:start position:0% +the of the transform 1 over K to what + + + align:start position:0% +the of the transform 1 over K to what +power + + align:start position:0% +power + + + align:start position:0% +power +now so it didn't have a jump a jump was + + align:start position:0% +now so it didn't have a jump a jump was + + + align:start position:0% +now so it didn't have a jump a jump was +1 over K this has a jump in the + + align:start position:0% +1 over K this has a jump in the + + + align:start position:0% +1 over K this has a jump in the +derivative so we're expecting 1 over K + + align:start position:0% +derivative so we're expecting 1 over K + + + align:start position:0% +derivative so we're expecting 1 over K +squared K squared + + align:start position:0% +squared K squared + + + align:start position:0% +squared K squared +it'll be ones order smoother okay and + + align:start position:0% +it'll be ones order smoother okay and + + + align:start position:0% +it'll be ones order smoother okay and +we'll you can easily see that happen + + align:start position:0% +we'll you can easily see that happen + + + align:start position:0% +we'll you can easily see that happen +because this part well this is just e to + + align:start position:0% +because this part well this is just e to + + + align:start position:0% +because this part well this is just e to +the a a minus I K X which I'm going to + + align:start position:0% +the a a minus I K X which I'm going to + + + align:start position:0% +the a a minus I K X which I'm going to +integrate to get this thing over a minus + + align:start position:0% +integrate to get this thing over a minus + + + align:start position:0% +integrate to get this thing over a minus +I K and I'm going to plug in the limits + + align:start position:0% +I K and I'm going to plug in the limits + + + align:start position:0% +I K and I'm going to plug in the limits +minus infinity and 0 and at minus + + align:start position:0% +minus infinity and 0 and at minus + + + align:start position:0% +minus infinity and 0 and at minus +infinity I'll get nothing this e to the + + align:start position:0% +infinity I'll get nothing this e to the + + + align:start position:0% +infinity I'll get nothing this e to the +ax at minus infinity will be 0 where the + + align:start position:0% +ax at minus infinity will be 0 where the + + + align:start position:0% +ax at minus infinity will be 0 where the +function starts way down at 0 so and at + + align:start position:0% +function starts way down at 0 so and at + + + align:start position:0% +function starts way down at 0 so and at +x equals zero this is a 1 so I just get + + align:start position:0% +x equals zero this is a 1 so I just get + + + align:start position:0% +x equals zero this is a 1 so I just get +1 over a plus okay / - thank you + + align:start position:0% +1 over a plus okay / - thank you + + + align:start position:0% +1 over a plus okay / - thank you +oh right over a minus I K okay yeah and + + align:start position:0% +oh right over a minus I K okay yeah and + + + align:start position:0% +oh right over a minus I K okay yeah and +you know somehow it can't be an accident + + align:start position:0% +you know somehow it can't be an accident + + + align:start position:0% +you know somehow it can't be an accident +that this is the complex conjugate of + + align:start position:0% +that this is the complex conjugate of + + + align:start position:0% +that this is the complex conjugate of +that somehow that's not a surprise okay + + align:start position:0% +that somehow that's not a surprise okay + + + align:start position:0% +that somehow that's not a surprise okay +so let's put those together into a + + align:start position:0% +so let's put those together into a + + + align:start position:0% +so let's put those together into a +single fraction and see what we have so + + align:start position:0% +single fraction and see what we have so + + + align:start position:0% +single fraction and see what we have so +the denominator of that fraction will be + + align:start position:0% +the denominator of that fraction will be + + + align:start position:0% +the denominator of that fraction will be +this times this and that's the most + + align:start position:0% +this times this and that's the most + + + align:start position:0% +this times this and that's the most +basic multiplication of complex numbers + + align:start position:0% +basic multiplication of complex numbers + + + align:start position:0% +basic multiplication of complex numbers +that one times its conjugate gives me + + align:start position:0% +that one times its conjugate gives me + + + align:start position:0% +that one times its conjugate gives me +what it gives me an a squared and what + + align:start position:0% +what it gives me an a squared and what + + + align:start position:0% +what it gives me an a squared and what +else a plus K squared because I times + + align:start position:0% +else a plus K squared because I times + + + align:start position:0% +else a plus K squared because I times +minus I is plus K squared and nothing + + align:start position:0% +minus I is plus K squared and nothing + + + align:start position:0% +minus I is plus K squared and nothing +and it's and no no in no imaginary part + + align:start position:0% +and it's and no no in no imaginary part + + + align:start position:0% +and it's and no no in no imaginary part +there's a plus ika and a minus a ika all + + align:start position:0% +there's a plus ika and a minus a ika all + + + align:start position:0% +there's a plus ika and a minus a ika all +we're seeing here is the sum of squares + + align:start position:0% +we're seeing here is the sum of squares + + + align:start position:0% +we're seeing here is the sum of squares +the usual Z times Z bar and on the in + + align:start position:0% +the usual Z times Z bar and on the in + + + align:start position:0% +the usual Z times Z bar and on the in +the numerator let's see when I put it + + align:start position:0% +the numerator let's see when I put it + + + align:start position:0% +the numerator let's see when I put it +over this so this was putting it over + + align:start position:0% +over this so this was putting it over + + + align:start position:0% +over this so this was putting it over +this common denominator so I should have + + align:start position:0% +this common denominator so I should have + + + align:start position:0% +this common denominator so I should have +an + + align:start position:0% +an + + + align:start position:0% +an +a minus I K going up on top there and an + + align:start position:0% +a minus I K going up on top there and an + + + align:start position:0% +a minus I K going up on top there and an +A plus I K going up on top here right + + align:start position:0% +A plus I K going up on top here right + + + align:start position:0% +A plus I K going up on top here right +those are my two fractions that over + + align:start position:0% +those are my two fractions that over + + + align:start position:0% +those are my two fractions that over +this and that over this and now that + + align:start position:0% +this and that over this and now that + + + align:start position:0% +this and that over this and now that +numerator simplifies oh look it's great + + align:start position:0% +numerator simplifies oh look it's great + + + align:start position:0% +numerator simplifies oh look it's great +I'm getting a real answer and because + + align:start position:0% +I'm getting a real answer and because + + + align:start position:0% +I'm getting a real answer and because +the I minus I K and the plus I cancel + + align:start position:0% +the I minus I K and the plus I cancel + + + align:start position:0% +the I minus I K and the plus I cancel +and it's just the two way and probably + + align:start position:0% +and it's just the two way and probably + + + align:start position:0% +and it's just the two way and probably +no surprise or somehow that that's the + + align:start position:0% +no surprise or somehow that that's the + + + align:start position:0% +no surprise or somehow that that's the +jump in the slope that must have + + align:start position:0% +jump in the slope that must have + + + align:start position:0% +jump in the slope that must have +something to do with that two way so we + + align:start position:0% +something to do with that two way so we + + + align:start position:0% +something to do with that two way so we +got a real even for a f hat from my real + + align:start position:0% +got a real even for a f hat from my real + + + align:start position:0% +got a real even for a f hat from my real +even F and it decays like K squared okay + + align:start position:0% +even F and it decays like K squared okay + + + align:start position:0% +even F and it decays like K squared okay +so that's another good example a very + + align:start position:0% +so that's another good example a very + + + align:start position:0% +so that's another good example a very +useful example right + + align:start position:0% +useful example right + + + align:start position:0% +useful example right +I could add other examples one quite + + align:start position:0% +I could add other examples one quite + + + align:start position:0% +I could add other examples one quite +yeah before I use that in application + + align:start position:0% +yeah before I use that in application + + + align:start position:0% +yeah before I use that in application +let me just well let's do let's do just + + align:start position:0% +let me just well let's do let's do just + + + align:start position:0% +let me just well let's do let's do just +a few more examples suppose f of X is + + align:start position:0% +a few more examples suppose f of X is + + + align:start position:0% +a few more examples suppose f of X is +the Delta function what's F hat of K + + align:start position:0% +the Delta function what's F hat of K + + + align:start position:0% +the Delta function what's F hat of K +that's can you can you just can you just + + align:start position:0% +that's can you can you just can you just + + + align:start position:0% +that's can you can you just can you just +plug in f of X equal Delta of X here do + + align:start position:0% +plug in f of X equal Delta of X here do + + + align:start position:0% +plug in f of X equal Delta of X here do +that integration and what does F hat of + + align:start position:0% +that integration and what does F hat of + + + align:start position:0% +that integration and what does F hat of +K come out to be 1 because if it's a + + align:start position:0% +K come out to be 1 because if it's a + + + align:start position:0% +K come out to be 1 because if it's a +delta function there at x at x equals 0 + + align:start position:0% +delta function there at x at x equals 0 + + + align:start position:0% +delta function there at x at x equals 0 +the spike is that x equals 0 so i plug + + align:start position:0% +the spike is that x equals 0 so i plug + + + align:start position:0% +the spike is that x equals 0 so i plug +in x equals 0 i get 1 so that's what + + align:start position:0% +in x equals 0 i get 1 so that's what + + + align:start position:0% +in x equals 0 i get 1 so that's what +we're kind of we'd be surprised if it + + align:start position:0% +we're kind of we'd be surprised if it + + + align:start position:0% +we're kind of we'd be surprised if it +wasn't a constant right the delta + + align:start position:0% +wasn't a constant right the delta + + + align:start position:0% +wasn't a constant right the delta +function in one in physical space goes + + align:start position:0% +function in one in physical space goes + + + align:start position:0% +function in one in physical space goes +in has all frequencies in equal amounts + + align:start position:0% +in has all frequencies in equal amounts + + + align:start position:0% +in has all frequencies in equal amounts +and it's a constant in in frequency + + align:start position:0% +and it's a constant in in frequency + + + align:start position:0% +and it's a constant in in frequency +space then there's one more that i'm + + align:start position:0% +space then there's one more that i'm + + + align:start position:0% +space then there's one more that i'm +that the there's it takes a little trick + + align:start position:0% +that the there's it takes a little trick + + + align:start position:0% +that the there's it takes a little trick +to do but it's a very neat one f of X + + align:start position:0% +to do but it's a very neat one f of X + + + align:start position:0% +to do but it's a very neat one f of X +is e to the minus x squared over 2 you + + align:start position:0% +is e to the minus x squared over 2 you + + + align:start position:0% +is e to the minus x squared over 2 you +recognize that as an important function + + align:start position:0% +recognize that as an important function + + + align:start position:0% +recognize that as an important function +e to the minus x squared or it usually + + align:start position:0% +e to the minus x squared or it usually + + + align:start position:0% +e to the minus x squared or it usually +has that e to the minus x squared over 2 + + align:start position:0% +has that e to the minus x squared over 2 + + + align:start position:0% +has that e to the minus x squared over 2 +or sometimes an e to the minus x squared + + align:start position:0% +or sometimes an e to the minus x squared + + + align:start position:0% +or sometimes an e to the minus x squared +over 2 Sigma squared a rescaling but + + align:start position:0% +over 2 Sigma squared a rescaling but + + + align:start position:0% +over 2 Sigma squared a rescaling but +that this would be the the bell-shaped + + align:start position:0% +that this would be the the bell-shaped + + + align:start position:0% +that this would be the the bell-shaped +curve the bell-shaped curve it decays + + align:start position:0% +curve the bell-shaped curve it decays + + + align:start position:0% +curve the bell-shaped curve it decays +very quickly the variance because I + + align:start position:0% +very quickly the variance because I + + + align:start position:0% +very quickly the variance because I +because that's a 2 are not a 2 Sigma + + align:start position:0% +because that's a 2 are not a 2 Sigma + + + align:start position:0% +because that's a 2 are not a 2 Sigma +squared the the standard deviation is 1 + + align:start position:0% +squared the the standard deviation is 1 + + + align:start position:0% +squared the the standard deviation is 1 +here the variance is 1 so it's a + + align:start position:0% +here the variance is 1 so it's a + + + align:start position:0% +here the variance is 1 so it's a +bell-shaped curve that has about 2/3 of + + align:start position:0% +bell-shaped curve that has about 2/3 of + + + align:start position:0% +bell-shaped curve that has about 2/3 of +its area between minus 1 and 1 this is + + align:start position:0% +its area between minus 1 and 1 this is + + + align:start position:0% +its area between minus 1 and 1 this is +the it all important function for + + align:start position:0% +the it all important function for + + + align:start position:0% +the it all important function for +probability the normal distribution the + + align:start position:0% +probability the normal distribution the + + + align:start position:0% +probability the normal distribution the +Gaussian both of those words are used + + align:start position:0% +Gaussian both of those words are used + + + align:start position:0% +Gaussian both of those words are used +it's the most important probability + + align:start position:0% +it's the most important probability + + + align:start position:0% +it's the most important probability +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +I need a 1 over square root of 2 pi to + + align:start position:0% +I need a 1 over square root of 2 pi to + + + align:start position:0% +I need a 1 over square root of 2 pi to +to make the total probability be 1 but + + align:start position:0% +to make the total probability be 1 but + + + align:start position:0% +to make the total probability be 1 but +let me just leave it there that's a very + + align:start position:0% +let me just leave it there that's a very + + + align:start position:0% +let me just leave it there that's a very +very important function it's also going + + align:start position:0% +very important function it's also going + + + align:start position:0% +very important function it's also going +to be important in the heat equation + + align:start position:0% +to be important in the heat equation + + + align:start position:0% +to be important in the heat equation +just in in math finance shows up all + + align:start position:0% +just in in math finance shows up all + + + align:start position:0% +just in in math finance shows up all +over the place and and it's integral + + align:start position:0% +over the place and and it's integral + + + align:start position:0% +over the place and and it's integral +would not be easy to do from 0 to 1 from + + align:start position:0% +would not be easy to do from 0 to 1 from + + + align:start position:0% +would not be easy to do from 0 to 1 from +the integral of that function from 0 to + + align:start position:0% +the integral of that function from 0 to + + + align:start position:0% +the integral of that function from 0 to +1 we have tables of it you know to the + + align:start position:0% +1 we have tables of it you know to the + + + align:start position:0% +1 we have tables of it you know to the +enth place but so but there's no simple + + align:start position:0% +enth place but so but there's no simple + + + align:start position:0% +enth place but so but there's no simple +elementary function whose derivative is + + align:start position:0% +elementary function whose derivative is + + + align:start position:0% +elementary function whose derivative is +this that x squared is what's making the + + align:start position:0% +this that x squared is what's making the + + + align:start position:0% +this that x squared is what's making the +integral tricky so from 0 to 1 we just + + align:start position:0% +integral tricky so from 0 to 1 we just + + + align:start position:0% +integral tricky so from 0 to 1 we just +have to give it a name so error function + + align:start position:0% +have to give it a name so error function + + + align:start position:0% +have to give it a name so error function +this would be e RF error function the + + align:start position:0% +this would be e RF error function the + + + align:start position:0% +this would be e RF error function the +integral of that thing correctly + + align:start position:0% +integral of that thing correctly + + + align:start position:0% +integral of that thing correctly +normalized just I'm just saying + + align:start position:0% +normalized just I'm just saying + + + align:start position:0% +normalized just I'm just saying +important important function but and + + align:start position:0% +important important function but and + + + align:start position:0% +important important function but and +their turns out that integrals from + + align:start position:0% +their turns out that integrals from + + + align:start position:0% +their turns out that integrals from +minus infinity + + align:start position:0% +minus infinity + + + align:start position:0% +minus infinity +to infinity can be done so beautifully + + align:start position:0% +to infinity can be done so beautifully + + + align:start position:0% +to infinity can be done so beautifully +by some trickery we can find the + + align:start position:0% +by some trickery we can find the + + + align:start position:0% +by some trickery we can find the +transform of this thing we can find the + + align:start position:0% +transform of this thing we can find the + + + align:start position:0% +transform of this thing we can find the +transform of this we can do this + + align:start position:0% +transform of this we can do this + + + align:start position:0% +transform of this we can do this +integral from minus infinity to infinity + + align:start position:0% +integral from minus infinity to infinity + + + align:start position:0% +integral from minus infinity to infinity +where we could not do it from 0 to 1 for + + align:start position:0% +where we could not do it from 0 to 1 for + + + align:start position:0% +where we could not do it from 0 to 1 for +example so I'll just write down the + + align:start position:0% +example so I'll just write down the + + + align:start position:0% +example so I'll just write down the +answer for this guy only because it's + + align:start position:0% +answer for this guy only because it's + + + align:start position:0% +answer for this guy only because it's +such a key example it's some constant + + align:start position:0% +such a key example it's some constant + + + align:start position:0% +such a key example it's some constant +that involves 2 pi times e to the minus + + align:start position:0% +that involves 2 pi times e to the minus + + + align:start position:0% +that involves 2 pi times e to the minus +K squared over 2 boy that's pretty + + align:start position:0% +K squared over 2 boy that's pretty + + + align:start position:0% +K squared over 2 boy that's pretty +amazing right the fourier integral has + + align:start position:0% +amazing right the fourier integral has + + + align:start position:0% +amazing right the fourier integral has +the same one the Fourier integral + + align:start position:0% +the same one the Fourier integral + + + align:start position:0% +the same one the Fourier integral +transform F hat of K has the same form + + align:start position:0% +transform F hat of K has the same form + + + align:start position:0% +transform F hat of K has the same form +as the function that's and of course + + align:start position:0% +as the function that's and of course + + + align:start position:0% +as the function that's and of course +this function is infinitely smooth so + + align:start position:0% +this function is infinitely smooth so + + + align:start position:0% +this function is infinitely smooth so +it's transform decay is infinitely fast + + align:start position:0% +it's transform decay is infinitely fast + + + align:start position:0% +it's transform decay is infinitely fast +yeah there's no no no problems like 1 + + align:start position:0% +yeah there's no no no problems like 1 + + + align:start position:0% +yeah there's no no no problems like 1 +over K squared error there no there are + + align:start position:0% +over K squared error there no there are + + + align:start position:0% +over K squared error there no there are +no bumps in the in the bell-shaped curve + + align:start position:0% +no bumps in the in the bell-shaped curve + + + align:start position:0% +no bumps in the in the bell-shaped curve +so I won't push that example except bell + + align:start position:0% +so I won't push that example except bell + + + align:start position:0% +so I won't push that example except bell +music what else should I say just like + + align:start position:0% +music what else should I say just like + + + align:start position:0% +music what else should I say just like +emphasize that this is such an important + + align:start position:0% +emphasize that this is such an important + + + align:start position:0% +emphasize that this is such an important +distribution in probability why is it + + align:start position:0% +distribution in probability why is it + + + align:start position:0% +distribution in probability why is it +important at probability that's that's + + align:start position:0% +important at probability that's that's + + + align:start position:0% +important at probability that's that's +the question why is why does everybody + + align:start position:0% +the question why is why does everybody + + + align:start position:0% +the question why is why does everybody +assume if you don't get it if you can + + align:start position:0% +assume if you don't get it if you can + + + align:start position:0% +assume if you don't get it if you can +get away with it and don't have any any + + align:start position:0% +get away with it and don't have any any + + + align:start position:0% +get away with it and don't have any any +other any natural alternative everybody + + align:start position:0% +other any natural alternative everybody + + + align:start position:0% +other any natural alternative everybody +assumes that noise whatever is coming + + align:start position:0% +assumes that noise whatever is coming + + + align:start position:0% +assumes that noise whatever is coming +with a normal distribution so in other + + align:start position:0% +with a normal distribution so in other + + + align:start position:0% +with a normal distribution so in other +words the width with a Sigma squared in + + align:start position:0% +words the width with a Sigma squared in + + + align:start position:0% +words the width with a Sigma squared in +there so so a normal distribution that + + align:start position:0% +there so so a normal distribution that + + + align:start position:0% +there so so a normal distribution that +has mean zero because it's absolutely + + align:start position:0% +has mean zero because it's absolutely + + + align:start position:0% +has mean zero because it's absolutely +centered at the origin and it has + + align:start position:0% +centered at the origin and it has + + + align:start position:0% +centered at the origin and it has +variance one but I could change the + + align:start position:0% +variance one but I could change the + + + align:start position:0% +variance one but I could change the +variance and that would just spread out + + align:start position:0% +variance and that would just spread out + + + align:start position:0% +variance and that would just spread out +or or or tighten bell the bell-shaped + + align:start position:0% +or or or tighten bell the bell-shaped + + + align:start position:0% +or or or tighten bell the bell-shaped +curve why is the bell shaped curve so + + align:start position:0% +curve why is the bell shaped curve so + + + align:start position:0% +curve why is the bell shaped curve so +important that's certainly we're not + + align:start position:0% +important that's certainly we're not + + + align:start position:0% +important that's certainly we're not +going to + + align:start position:0% +going to + + + align:start position:0% +going to +launched into theory of probability but + + align:start position:0% +launched into theory of probability but + + + align:start position:0% +launched into theory of probability but +it's the central limit theorem so let me + + align:start position:0% +it's the central limit theorem so let me + + + align:start position:0% +it's the central limit theorem so let me +just use those words the central limit + + align:start position:0% +just use those words the central limit + + + align:start position:0% +just use those words the central limit +theorem that says that if I start with + + align:start position:0% +theorem that says that if I start with + + + align:start position:0% +theorem that says that if I start with +other probability distributions like I'm + + align:start position:0% +other probability distributions like I'm + + + align:start position:0% +other probability distributions like I'm +flipping the coin flip a coin in a + + align:start position:0% +flipping the coin flip a coin in a + + + align:start position:0% +flipping the coin flip a coin in a +million times then the mean and let's + + align:start position:0% +million times then the mean and let's + + + align:start position:0% +million times then the mean and let's +say zero for tails one for heads okay so + + align:start position:0% +say zero for tails one for heads okay so + + + align:start position:0% +say zero for tails one for heads okay so +I flip flip flip well the mean of that + + align:start position:0% +I flip flip flip well the mean of that + + + align:start position:0% +I flip flip flip well the mean of that +the expected mean is what half a million + + align:start position:0% +the expected mean is what half a million + + + align:start position:0% +the expected mean is what half a million +right half half tails half heads so the + + align:start position:0% +right half half tails half heads so the + + + align:start position:0% +right half half tails half heads so the +so if I give zero for tails one's for + + align:start position:0% +so if I give zero for tails one's for + + + align:start position:0% +so if I give zero for tails one's for +heads and flip a million times the mean + + align:start position:0% +heads and flip a million times the mean + + + align:start position:0% +heads and flip a million times the mean +would be about half a million and then + + align:start position:0% +would be about half a million and then + + + align:start position:0% +would be about half a million and then +so let me take let me Center the mean oh + + align:start position:0% +so let me take let me Center the mean oh + + + align:start position:0% +so let me take let me Center the mean oh +yeah I could have centered it by taking + + align:start position:0% +yeah I could have centered it by taking + + + align:start position:0% +yeah I could have centered it by taking +minus one and one that would have been + + align:start position:0% +minus one and one that would have been + + + align:start position:0% +minus one and one that would have been +smarter minus 1 and 1 minus 1 for tails + + align:start position:0% +smarter minus 1 and 1 minus 1 for tails + + + align:start position:0% +smarter minus 1 and 1 minus 1 for tails +one for heads would have had a mean of + + align:start position:0% +one for heads would have had a mean of + + + align:start position:0% +one for heads would have had a mean of +zero and then I it would be natural if I + + align:start position:0% +zero and then I it would be natural if I + + + align:start position:0% +zero and then I it would be natural if I +have a million of these to divide by a + + align:start position:0% +have a million of these to divide by a + + + align:start position:0% +have a million of these to divide by a +thousand I think I'll count of course + + align:start position:0% +thousand I think I'll count of course + + + align:start position:0% +thousand I think I'll count of course +the answer won't be zero right if I do a + + align:start position:0% +the answer won't be zero right if I do a + + + align:start position:0% +the answer won't be zero right if I do a +million flips it's not going to come out + + align:start position:0% +million flips it's not going to come out + + + align:start position:0% +million flips it's not going to come out +exactly half a million and half a + + align:start position:0% +exactly half a million and half a + + + align:start position:0% +exactly half a million and half a +million I'm remembering I used to have a + + align:start position:0% +million I'm remembering I used to have a + + + align:start position:0% +million I'm remembering I used to have a +long discussion with a nice guy in + + align:start position:0% +long discussion with a nice guy in + + + align:start position:0% +long discussion with a nice guy in +college he ran for mayor of Boston + + align:start position:0% +college he ran for mayor of Boston + + + align:start position:0% +college he ran for mayor of Boston +actually but he had a he had the idea + + align:start position:0% +actually but he had a he had the idea + + + align:start position:0% +actually but he had a he had the idea +that after a million flips suppose the + + align:start position:0% +that after a million flips suppose the + + + align:start position:0% +that after a million flips suppose the +suppose the there had been more heads + + align:start position:0% +suppose the there had been more heads + + + align:start position:0% +suppose the there had been more heads +than tails then the next flip he figured + + align:start position:0% +than tails then the next flip he figured + + + align:start position:0% +than tails then the next flip he figured +was more likely to be tails I couldn't + + align:start position:0% +was more likely to be tails I couldn't + + + align:start position:0% +was more likely to be tails I couldn't +convince him that this was not + + align:start position:0% +convince him that this was not + + + align:start position:0% +convince him that this was not +mathematically the right thing to think + + align:start position:0% +mathematically the right thing to think + + + align:start position:0% +mathematically the right thing to think +about and I all I did was say don't go + + align:start position:0% +about and I all I did was say don't go + + + align:start position:0% +about and I all I did was say don't go +to Las Vegas I mean if you're if you're + + align:start position:0% +to Las Vegas I mean if you're if you're + + + align:start position:0% +to Las Vegas I mean if you're if you're +thinking that way save your money so + + align:start position:0% +thinking that way save your money so + + + align:start position:0% +thinking that way save your money so +right so anyway but this is much study + + align:start position:0% +right so anyway but this is much study + + + align:start position:0% +right so anyway but this is much study +the the variation what that curve looked + + align:start position:0% +the the variation what that curve looked + + + align:start position:0% +the the variation what that curve looked +like it's quite interesting but my point + + align:start position:0% +like it's quite interesting but my point + + + align:start position:0% +like it's quite interesting but my point +is that + + align:start position:0% +is that + + + align:start position:0% +is that +the number gets bigger and bigger and we + + align:start position:0% +the number gets bigger and bigger and we + + + align:start position:0% +the number gets bigger and bigger and we +scale it properly the distribution will + + align:start position:0% +scale it properly the distribution will + + + align:start position:0% +scale it properly the distribution will +approach the normal all sorts of + + align:start position:0% +approach the normal all sorts of + + + align:start position:0% +approach the normal all sorts of +distributions if I just repeat and + + align:start position:0% +distributions if I just repeat and + + + align:start position:0% +distributions if I just repeat and +repeat experiments and we can scale it + + align:start position:0% +repeat experiments and we can scale it + + + align:start position:0% +repeat experiments and we can scale it +the the central limit theorem says + + align:start position:0% +the the central limit theorem says + + + align:start position:0% +the the central limit theorem says +you're always going to the normal + + align:start position:0% +you're always going to the normal + + + align:start position:0% +you're always going to the normal +distribution so that's highly important + + align:start position:0% +distribution so that's highly important + + + align:start position:0% +distribution so that's highly important +okay and it just it comes up different + + align:start position:0% +okay and it just it comes up different + + + align:start position:0% +okay and it just it comes up different +places and it's quite a neat function + + align:start position:0% +places and it's quite a neat function + + + align:start position:0% +places and it's quite a neat function +okay so that's some examples now let me + + align:start position:0% +okay so that's some examples now let me + + + align:start position:0% +okay so that's some examples now let me +you every topic that I introduce I want + + align:start position:0% +you every topic that I introduce I want + + + align:start position:0% +you every topic that I introduce I want +to find a use for so now can I start on + + align:start position:0% +to find a use for so now can I start on + + + align:start position:0% +to find a use for so now can I start on +that on this one constant coefficient + + align:start position:0% +that on this one constant coefficient + + + align:start position:0% +that on this one constant coefficient +differential equation so I'm gonna write + + align:start position:0% +differential equation so I'm gonna write + + + align:start position:0% +differential equation so I'm gonna write +down a differential equation which will + + align:start position:0% +down a differential equation which will + + + align:start position:0% +down a differential equation which will +look pretty much like the ones we + + align:start position:0% +look pretty much like the ones we + + + align:start position:0% +look pretty much like the ones we +started this course with and I could + + align:start position:0% +started this course with and I could + + + align:start position:0% +started this course with and I could +well let's let me write it down - ii u + + align:start position:0% +well let's let me write it down - ii u + + + align:start position:0% +well let's let me write it down - ii u +DX squared we're used to that now let me + + align:start position:0% +DX squared we're used to that now let me + + + align:start position:0% +DX squared we're used to that now let me +put in an a squared u which is a lower + + align:start position:0% +put in an a squared u which is a lower + + + align:start position:0% +put in an a squared u which is a lower +order term we could deal with that + + align:start position:0% +order term we could deal with that + + + align:start position:0% +order term we could deal with that +equals some f of X and now because I + + align:start position:0% +equals some f of X and now because I + + + align:start position:0% +equals some f of X and now because I +want to do Fourier integrals I'm thinkin + + align:start position:0% +want to do Fourier integrals I'm thinkin + + + align:start position:0% +want to do Fourier integrals I'm thinkin +all X we're on the whole line instead of + + align:start position:0% +all X we're on the whole line instead of + + + align:start position:0% +all X we're on the whole line instead of +the interval 0 1 where I might use + + align:start position:0% +the interval 0 1 where I might use + + + align:start position:0% +the interval 0 1 where I might use +Fourier series and have sine series or + + align:start position:0% +Fourier series and have sine series or + + + align:start position:0% +Fourier series and have sine series or +cosine series depending on the boundary + + align:start position:0% +cosine series depending on the boundary + + + align:start position:0% +cosine series depending on the boundary +conditions here the boundary condition + + align:start position:0% +conditions here the boundary condition + + + align:start position:0% +conditions here the boundary condition +is just everything drops off at infinity + + align:start position:0% +is just everything drops off at infinity + + + align:start position:0% +is just everything drops off at infinity +and minus infinity so so all these + + align:start position:0% +and minus infinity so so all these + + + align:start position:0% +and minus infinity so so all these +functions we can we can do these + + align:start position:0% +functions we can we can do these + + + align:start position:0% +functions we can we can do these +integrals okay + + align:start position:0% +integrals okay + + + align:start position:0% +integrals okay +so there's a question what's the + + align:start position:0% +so there's a question what's the + + + align:start position:0% +so there's a question what's the +solution okay we could work we could + + align:start position:0% +solution okay we could work we could + + + align:start position:0% +solution okay we could work we could +tackle it but I want to suggest to use + + align:start position:0% +tackle it but I want to suggest to use + + + align:start position:0% +tackle it but I want to suggest to use +for you so it's not the only way but + + align:start position:0% +for you so it's not the only way but + + + align:start position:0% +for you so it's not the only way but +it's one way to see so now if I use what + + align:start position:0% +it's one way to see so now if I use what + + + align:start position:0% +it's one way to see so now if I use what +do I mean by using for you it means I'm + + align:start position:0% +do I mean by using for you it means I'm + + + align:start position:0% +do I mean by using for you it means I'm +going to take the Fourier transform of + + align:start position:0% +going to take the Fourier transform of + + + align:start position:0% +going to take the Fourier transform of +every term + + align:start position:0% +every term + + + align:start position:0% +every term +so when I take the Fourier transform of + + align:start position:0% +so when I take the Fourier transform of + + + align:start position:0% +so when I take the Fourier transform of +the right-hand side I'm gonna get F hat + + align:start position:0% +the right-hand side I'm gonna get F hat + + + align:start position:0% +the right-hand side I'm gonna get F hat +okay whatever this is known of course + + align:start position:0% +okay whatever this is known of course + + + align:start position:0% +okay whatever this is known of course +this guy is given that's the source and + + align:start position:0% +this guy is given that's the source and + + + align:start position:0% +this guy is given that's the source and +year was the unknown okay so so I'm + + align:start position:0% +year was the unknown okay so so I'm + + + align:start position:0% +year was the unknown okay so so I'm +gonna take them Fourier transform of + + align:start position:0% +gonna take them Fourier transform of + + + align:start position:0% +gonna take them Fourier transform of +every term well this is a is a constant + + align:start position:0% +every term well this is a is a constant + + + align:start position:0% +every term well this is a is a constant +this is yeah + + align:start position:0% +this is yeah + + + align:start position:0% +this is yeah +hey had to be a constant or I couldn't + + align:start position:0% +hey had to be a constant or I couldn't + + + align:start position:0% +hey had to be a constant or I couldn't +do you know if a depended on X this + + align:start position:0% +do you know if a depended on X this + + + align:start position:0% +do you know if a depended on X this +would be some multiplication and it + + align:start position:0% +would be some multiplication and it + + + align:start position:0% +would be some multiplication and it +would that the the transform would be a + + align:start position:0% +would that the the transform would be a + + + align:start position:0% +would that the the transform would be a +mess at Fourier applies when you've got + + align:start position:0% +mess at Fourier applies when you've got + + + align:start position:0% +mess at Fourier applies when you've got +constant coefficients and nice boundary + + align:start position:0% +constant coefficients and nice boundary + + + align:start position:0% +constant coefficients and nice boundary +conditions and here we're here our + + align:start position:0% +conditions and here we're here our + + + align:start position:0% +conditions and here we're here our +boundary conditions are nice they just + + align:start position:0% +boundary conditions are nice they just + + + align:start position:0% +boundary conditions are nice they just +go to 0 fast okay so the transform of + + align:start position:0% +go to 0 fast okay so the transform of + + + align:start position:0% +go to 0 fast okay so the transform of +this is a that's a constant you had of K + + align:start position:0% +this is a that's a constant you had of K + + + align:start position:0% +this is a that's a constant you had of K +and what's the transform of that so this + + align:start position:0% +and what's the transform of that so this + + + align:start position:0% +and what's the transform of that so this +is our chance to use probably the most + + align:start position:0% +is our chance to use probably the most + + + align:start position:0% +is our chance to use probably the most +important rule for Fourier integrals if + + align:start position:0% +important rule for Fourier integrals if + + + align:start position:0% +important rule for Fourier integrals if +if if so I maybe you'll tell me what it + + align:start position:0% +if if so I maybe you'll tell me what it + + + align:start position:0% +if if so I maybe you'll tell me what it +is you should think what it is if I take + + align:start position:0% +is you should think what it is if I take + + + align:start position:0% +is you should think what it is if I take +a derivative that's the rule if I if I + + align:start position:0% +a derivative that's the rule if I if I + + + align:start position:0% +a derivative that's the rule if I if I +take a derivative of the function what + + align:start position:0% +take a derivative of the function what + + + align:start position:0% +take a derivative of the function what +is what's happening in frequency space + + align:start position:0% +is what's happening in frequency space + + + align:start position:0% +is what's happening in frequency space +and you I could make that happen here if + + align:start position:0% +and you I could make that happen here if + + + align:start position:0% +and you I could make that happen here if +I took the derivative yeah so well maybe + + align:start position:0% +I took the derivative yeah so well maybe + + + align:start position:0% +I took the derivative yeah so well maybe +if I take the derivative here so so + + align:start position:0% +if I take the derivative here so so + + + align:start position:0% +if I take the derivative here so so +here's just remembering the rule suppose + + align:start position:0% +here's just remembering the rule suppose + + + align:start position:0% +here's just remembering the rule suppose +I take the derivative of this equation I + + align:start position:0% +I take the derivative of this equation I + + + align:start position:0% +I take the derivative of this equation I +get this integral and what would F prime + + align:start position:0% +get this integral and what would F prime + + + align:start position:0% +get this integral and what would F prime +be what would that hat sorry if I take + + align:start position:0% +be what would that hat sorry if I take + + + align:start position:0% +be what would that hat sorry if I take +the the X derivative of this yeah if I + + align:start position:0% +the the X derivative of this yeah if I + + + align:start position:0% +the the X derivative of this yeah if I +take the X derivative of this equation + + align:start position:0% +take the X derivative of this equation + + + align:start position:0% +take the X derivative of this equation +what happens on the right hand side when + + align:start position:0% +what happens on the right hand side when + + + align:start position:0% +what happens on the right hand side when +I take the X derivative down comes I K + + align:start position:0% +I take the X derivative down comes I K + + + align:start position:0% +I take the X derivative down comes I K +down comes I K so so when I K is coming + + align:start position:0% +down comes I K so so when I K is coming + + + align:start position:0% +down comes I K so so when I K is coming +down I won't even finish that equation + + align:start position:0% +down I won't even finish that equation + + + align:start position:0% +down I won't even finish that equation +and ika is coming down when I take the + + align:start position:0% +and ika is coming down when I take the + + + align:start position:0% +and ika is coming down when I take the +derivative so the derivative the + + align:start position:0% +derivative so the derivative the + + + align:start position:0% +derivative so the derivative the +transform is multiplied by I K higher + + align:start position:0% +transform is multiplied by I K higher + + + align:start position:0% +transform is multiplied by I K higher +frequencies are + + align:start position:0% +frequencies are + + + align:start position:0% +frequencies are +are emphasized now because of that K + + align:start position:0% +are emphasized now because of that K + + + align:start position:0% +are emphasized now because of that K +factor and now if I take two derivatives + + align:start position:0% +factor and now if I take two derivatives + + + align:start position:0% +factor and now if I take two derivatives +I bring I K twice so it's I squared K + + align:start position:0% +I bring I K twice so it's I squared K + + + align:start position:0% +I bring I K twice so it's I squared K +squared the I squared and the minus give + + align:start position:0% +squared the I squared and the minus give + + + align:start position:0% +squared the I squared and the minus give +me a plus so that's just K squared you + + align:start position:0% +me a plus so that's just K squared you + + + align:start position:0% +me a plus so that's just K squared you +had okay okay with that and now we get + + align:start position:0% +had okay okay with that and now we get + + + align:start position:0% +had okay okay with that and now we get +an immediate formula for the for you how + + align:start position:0% +an immediate formula for the for you how + + + align:start position:0% +an immediate formula for the for you how +to K the solution well it's the solution + + align:start position:0% +to K the solution well it's the solution + + + align:start position:0% +to K the solution well it's the solution +but it's in frequency space if we wanted + + align:start position:0% +but it's in frequency space if we wanted + + + align:start position:0% +but it's in frequency space if we wanted +to know at an x space as we do we've got + + align:start position:0% +to know at an x space as we do we've got + + + align:start position:0% +to know at an x space as we do we've got +to transform back but what do we get + + align:start position:0% +to transform back but what do we get + + + align:start position:0% +to transform back but what do we get +here it's just F hat of K divided by + + align:start position:0% +here it's just F hat of K divided by + + + align:start position:0% +here it's just F hat of K divided by +this is just multiplied by a squared + + align:start position:0% +this is just multiplied by a squared + + + align:start position:0% +this is just multiplied by a squared +plus K squared okay so that's the answer + + align:start position:0% +plus K squared okay so that's the answer + + + align:start position:0% +plus K squared okay so that's the answer +in frequency space that was simple and + + align:start position:0% +in frequency space that was simple and + + + align:start position:0% +in frequency space that was simple and +then if I wanted it in X space I take + + align:start position:0% +then if I wanted it in X space I take + + + align:start position:0% +then if I wanted it in X space I take +the reverse transform notice that this + + align:start position:0% +the reverse transform notice that this + + + align:start position:0% +the reverse transform notice that this +is hidden here are the same three steps + + align:start position:0% +is hidden here are the same three steps + + + align:start position:0% +is hidden here are the same three steps +that I emphasize all the time about + + align:start position:0% +that I emphasize all the time about + + + align:start position:0% +that I emphasize all the time about +using eigenvectors and eigenvalues do + + align:start position:0% +using eigenvectors and eigenvalues do + + + align:start position:0% +using eigenvectors and eigenvalues do +you remember those three steps for + + align:start position:0% +you remember those three steps for + + + align:start position:0% +you remember those three steps for +solving differential equations + + align:start position:0% +solving differential equations + + + align:start position:0% +solving differential equations +difference equations linear equations + + align:start position:0% +difference equations linear equations + + + align:start position:0% +difference equations linear equations +whatever the three steps were right find + + align:start position:0% +whatever the three steps were right find + + + align:start position:0% +whatever the three steps were right find +the coefficients expand everything in + + align:start position:0% +the coefficients expand everything in + + + align:start position:0% +the coefficients expand everything in +Augen functions it's just I won't write + + align:start position:0% +Augen functions it's just I won't write + + + align:start position:0% +Augen functions it's just I won't write +out talk the three steps were expand and + + align:start position:0% +out talk the three steps were expand and + + + align:start position:0% +out talk the three steps were expand and +eigen functions follow each eigen + + align:start position:0% +eigen functions follow each eigen + + + align:start position:0% +eigen functions follow each eigen +function separately that was the trivial + + align:start position:0% +function separately that was the trivial + + + align:start position:0% +function separately that was the trivial +step with just a division like this + + align:start position:0% +step with just a division like this + + + align:start position:0% +step with just a division like this +division and then use those coefficients + + align:start position:0% +division and then use those coefficients + + + align:start position:0% +division and then use those coefficients +of the eigen functions combine them all + + align:start position:0% +of the eigen functions combine them all + + + align:start position:0% +of the eigen functions combine them all +back to get the answer right step one + + align:start position:0% +back to get the answer right step one + + + align:start position:0% +back to get the answer right step one +write it in the right bases step two + + align:start position:0% +write it in the right bases step two + + + align:start position:0% +write it in the right bases step two +easy in that basis + + align:start position:0% +easy in that basis + + + align:start position:0% +easy in that basis +step three go back to your your physical + + align:start position:0% +step three go back to your your physical + + + align:start position:0% +step three go back to your your physical +space we're doing exactly the same thing + + align:start position:0% +space we're doing exactly the same thing + + + align:start position:0% +space we're doing exactly the same thing +here these e to the ikx s are the + + align:start position:0% +here these e to the ikx s are the + + + align:start position:0% +here these e to the ikx s are the +eigenfunction + + align:start position:0% +eigenfunction + + + align:start position:0% +eigenfunction +of this thing they're the eigenfunctions + + align:start position:0% +of this thing they're the eigenfunctions + + + align:start position:0% +of this thing they're the eigenfunctions +and here the eigenvalue of this stuff is + + align:start position:0% +and here the eigenvalue of this stuff is + + + align:start position:0% +and here the eigenvalue of this stuff is +K squared plus I squared and we that's + + align:start position:0% +K squared plus I squared and we that's + + + align:start position:0% +K squared plus I squared and we that's +what we divided by and then the final + + align:start position:0% +what we divided by and then the final + + + align:start position:0% +what we divided by and then the final +job of going back from U hat to you + + align:start position:0% +job of going back from U hat to you + + + align:start position:0% +job of going back from U hat to you +bye-bye + + align:start position:0% +bye-bye + + + align:start position:0% +bye-bye +so right you there can I like this F now + + align:start position:0% +so right you there can I like this F now + + + align:start position:0% +so right you there can I like this F now +I'm it's really you that I'm wanting to + + align:start position:0% +I'm it's really you that I'm wanting to + + + align:start position:0% +I'm it's really you that I'm wanting to +bring back to physical space so so what + + align:start position:0% +bring back to physical space so so what + + + align:start position:0% +bring back to physical space so so what +just for the for the sake of your eye + + align:start position:0% +just for the for the sake of your eye + + + align:start position:0% +just for the for the sake of your eye +seeing it let me let me put it you in + + align:start position:0% +seeing it let me let me put it you in + + + align:start position:0% +seeing it let me let me put it you in +okay so that that's the answer in a way + + align:start position:0% +okay so that that's the answer in a way + + + align:start position:0% +okay so that that's the answer in a way +it's the answer it's a formula for the + + align:start position:0% +it's the answer it's a formula for the + + + align:start position:0% +it's the answer it's a formula for the +answer + + align:start position:0% +answer + + + align:start position:0% +answer +it did depend on our being able to do + + align:start position:0% +it did depend on our being able to do + + + align:start position:0% +it did depend on our being able to do +two integrals by the integral from F to + + align:start position:0% +two integrals by the integral from F to + + + align:start position:0% +two integrals by the integral from F to +F hat may not have been easy and then + + align:start position:0% +F hat may not have been easy and then + + + align:start position:0% +F hat may not have been easy and then +the integral from u hat back to you this + + align:start position:0% +the integral from u hat back to you this + + + align:start position:0% +the integral from u hat back to you this +integral might not have been easy so + + align:start position:0% +integral might not have been easy so + + + align:start position:0% +integral might not have been easy so +it's a formula okay now I want to go + + align:start position:0% +it's a formula okay now I want to go + + + align:start position:0% +it's a formula okay now I want to go +with it a little longer because I want + + align:start position:0% +with it a little longer because I want + + + align:start position:0% +with it a little longer because I want +to show you how the Delta function pays + + align:start position:0% +to show you how the Delta function pays + + + align:start position:0% +to show you how the Delta function pays +off so let me do the example where f of + + align:start position:0% +off so let me do the example where f of + + + align:start position:0% +off so let me do the example where f of +X is the Delta function so now we have + + align:start position:0% +X is the Delta function so now we have + + + align:start position:0% +X is the Delta function so now we have +where now we're really close to where + + align:start position:0% +where now we're really close to where + + + align:start position:0% +where now we're really close to where +this course began differential equation + + align:start position:0% +this course began differential equation + + + align:start position:0% +this course began differential equation +with a delta function the only new thing + + align:start position:0% +with a delta function the only new thing + + + align:start position:0% +with a delta function the only new thing +is we're not on an interval we're on the + + align:start position:0% +is we're not on an interval we're on the + + + align:start position:0% +is we're not on an interval we're on the +whole life okay so I take transforms so + + align:start position:0% +whole life okay so I take transforms so + + + align:start position:0% +whole life okay so I take transforms so +what's the transform now of the new of + + align:start position:0% +what's the transform now of the new of + + + align:start position:0% +what's the transform now of the new of +this specific f of X is one we just saw + + align:start position:0% +this specific f of X is one we just saw + + + align:start position:0% +this specific f of X is one we just saw +okay so now we got a one there now we + + align:start position:0% +okay so now we got a one there now we + + + align:start position:0% +okay so now we got a one there now we +just divide by here and we've got a one + + align:start position:0% +just divide by here and we've got a one + + + align:start position:0% +just divide by here and we've got a one +here so we were able to go this was an + + align:start position:0% +here so we were able to go this was an + + + align:start position:0% +here so we were able to go this was an +integral we could easily do to get from + + align:start position:0% +integral we could easily do to get from + + + align:start position:0% +integral we could easily do to get from +Delta to its 2 Delta hat which was just + + align:start position:0% +Delta to its 2 Delta hat which was just + + + align:start position:0% +Delta to its 2 Delta hat which was just +1 and fantastically this is an integral + + align:start position:0% +1 and fantastically this is an integral + + + align:start position:0% +1 and fantastically this is an integral +to go back to U of X to go back to you + + align:start position:0% +to go back to U of X to go back to you + + + align:start position:0% +to go back to U of X to go back to you +of X that's an integral we can do well + + align:start position:0% +of X that's an integral we can do well + + + align:start position:0% +of X that's an integral we can do well +you may ask how can we do it how can how + + align:start position:0% +you may ask how can we do it how can how + + + align:start position:0% +you may ask how can we do it how can how +do I find the U of X that has this + + align:start position:0% +do I find the U of X that has this + + + align:start position:0% +do I find the U of X that has this +transform well I either use complex + + align:start position:0% +transform well I either use complex + + + align:start position:0% +transform well I either use complex +variables to do integrals like this + + align:start position:0% +variables to do integrals like this + + + align:start position:0% +variables to do integrals like this +residue methods that are in Chapter five + + align:start position:0% +residue methods that are in Chapter five + + + align:start position:0% +residue methods that are in Chapter five +or I look in a table or I look at the + + align:start position:0% +or I look in a table or I look at the + + + align:start position:0% +or I look in a table or I look at the +blackboard over there I think that's the + + align:start position:0% +blackboard over there I think that's the + + + align:start position:0% +blackboard over there I think that's the +best way look at this blackboard right + + align:start position:0% +best way look at this blackboard right + + + align:start position:0% +best way look at this blackboard right +because this is the answer we got we got + + align:start position:0% +because this is the answer we got we got + + + align:start position:0% +because this is the answer we got we got +that same answer apart from a constant + + align:start position:0% +that same answer apart from a constant + + + align:start position:0% +that same answer apart from a constant +factor to a so this is our function this + + align:start position:0% +factor to a so this is our function this + + + align:start position:0% +factor to a so this is our function this +is our solution U of X is this what am I + + align:start position:0% +is our solution U of X is this what am I + + + align:start position:0% +is our solution U of X is this what am I +going to call that two-sided pulse I'll + + align:start position:0% +going to call that two-sided pulse I'll + + + align:start position:0% +going to call that two-sided pulse I'll +call that the two-sided pulse maybe yeah + + align:start position:0% +call that the two-sided pulse maybe yeah + + + align:start position:0% +call that the two-sided pulse maybe yeah +maybe I should give it a name but I'll + + align:start position:0% +maybe I should give it a name but I'll + + + align:start position:0% +maybe I should give it a name but I'll +just write out those words two-sided + + align:start position:0% +just write out those words two-sided + + + align:start position:0% +just write out those words two-sided +pulse that's the that's it divided by 2 + + align:start position:0% +pulse that's the that's it divided by 2 + + + align:start position:0% +pulse that's the that's it divided by 2 +a so now so we get the answer let me + + align:start position:0% +a so now so we get the answer let me + + + align:start position:0% +a so now so we get the answer let me +just make a little more space here this + + align:start position:0% +just make a little more space here this + + + align:start position:0% +just make a little more space here this +was 1 over a squared plus K squared and + + align:start position:0% +was 1 over a squared plus K squared and + + + align:start position:0% +was 1 over a squared plus K squared and +now having seen that already I just say + + align:start position:0% +now having seen that already I just say + + + align:start position:0% +now having seen that already I just say +yep that must be it it's the two-sided + + align:start position:0% +yep that must be it it's the two-sided + + + align:start position:0% +yep that must be it it's the two-sided +pulse and I have to divide by 2a do you + + align:start position:0% +pulse and I have to divide by 2a do you + + + align:start position:0% +pulse and I have to divide by 2a do you +see that that's that's the correct + + align:start position:0% +see that that's that's the correct + + + align:start position:0% +see that that's that's the correct +answer we can substitute that in the + + align:start position:0% +answer we can substitute that in the + + + align:start position:0% +answer we can substitute that in the +equation and see that it works I mean it + + align:start position:0% +equation and see that it works I mean it + + + align:start position:0% +equation and see that it works I mean it +so we have solved the problem we have + + align:start position:0% +so we have solved the problem we have + + + align:start position:0% +so we have solved the problem we have +solved the problem when the right side + + align:start position:0% +solved the problem when the right side + + + align:start position:0% +solved the problem when the right side +was Delta let's put it into the equation + + align:start position:0% +was Delta let's put it into the equation + + + align:start position:0% +was Delta let's put it into the equation +so this is just because we did this it's + + align:start position:0% +so this is just because we did this it's + + + align:start position:0% +so this is just because we did this it's +nice to do it again after all this time + + align:start position:0% +nice to do it again after all this time + + + align:start position:0% +nice to do it again after all this time +so I put it in the equation this + + align:start position:0% +so I put it in the equation this + + + align:start position:0% +so I put it in the equation this +two-sided pulse over 2a so what's my + + align:start position:0% +two-sided pulse over 2a so what's my + + + align:start position:0% +two-sided pulse over 2a so what's my +equation well this is 0 most of the time + + align:start position:0% +equation well this is 0 most of the time + + + align:start position:0% +equation well this is 0 most of the time +so I believe that if I plug in this + + align:start position:0% +so I believe that if I plug in this + + + align:start position:0% +so I believe that if I plug in this +function it will give me the zero yeah + + align:start position:0% +function it will give me the zero yeah + + + align:start position:0% +function it will give me the zero yeah +do you want to just plug it in I believe + + align:start position:0% +do you want to just plug it in I believe + + + align:start position:0% +do you want to just plug it in I believe +that if I plug in a to the minus X or E + + align:start position:0% +that if I plug in a to the minus X or E + + + align:start position:0% +that if I plug in a to the minus X or E +or a + + align:start position:0% +or a + + + align:start position:0% +or a +the ax either one can you kind of just + + align:start position:0% +the ax either one can you kind of just + + + align:start position:0% +the ax either one can you kind of just +check that you try u equal e to the + + align:start position:0% +check that you try u equal e to the + + + align:start position:0% +check that you try u equal e to the +minus ax put it in and just see that I + + align:start position:0% +minus ax put it in and just see that I + + + align:start position:0% +minus ax put it in and just see that I +get zero because yeah two two + + align:start position:0% +get zero because yeah two two + + + align:start position:0% +get zero because yeah two two +derivatives bring down a squared with a + + align:start position:0% +derivatives bring down a squared with a + + + align:start position:0% +derivatives bring down a squared with a +minus and there's a squared with a plus + + align:start position:0% +minus and there's a squared with a plus + + + align:start position:0% +minus and there's a squared with a plus +it's it works right two derivatives of + + align:start position:0% +it's it works right two derivatives of + + + align:start position:0% +it's it works right two derivatives of +this function bring down - a twice so + + align:start position:0% +this function bring down - a twice so + + + align:start position:0% +this function bring down - a twice so +that's a squared so it's minus a squared + + align:start position:0% +that's a squared so it's minus a squared + + + align:start position:0% +that's a squared so it's minus a squared +plus a squared works and then of course + + align:start position:0% +plus a squared works and then of course + + + align:start position:0% +plus a squared works and then of course +the important point is x equals zero + + align:start position:0% +the important point is x equals zero + + + align:start position:0% +the important point is x equals zero +where the spike is what's the what's the + + align:start position:0% +where the spike is what's the what's the + + + align:start position:0% +where the spike is what's the what's the +what happens at the spike going back to + + align:start position:0% +what happens at the spike going back to + + + align:start position:0% +what happens at the spike going back to +the beginning of the course this term is + + align:start position:0% +the beginning of the course this term is + + + align:start position:0% +the beginning of the course this term is +going to be unimportant compared to this + + align:start position:0% +going to be unimportant compared to this + + + align:start position:0% +going to be unimportant compared to this +term what what do I see with with minus + + align:start position:0% +term what what do I see with with minus + + + align:start position:0% +term what what do I see with with minus +u double prime equal a spike what what + + align:start position:0% +u double prime equal a spike what what + + + align:start position:0% +u double prime equal a spike what what +was the solution to two that you had a + + align:start position:0% +was the solution to two that you had a + + + align:start position:0% +was the solution to two that you had a +corner right the slope of you what did + + align:start position:0% +corner right the slope of you what did + + + align:start position:0% +corner right the slope of you what did +the slope of you do it dropped by one + + align:start position:0% +the slope of you do it dropped by one + + + align:start position:0% +the slope of you do it dropped by one +was that right the slope of you dropped + + align:start position:0% +was that right the slope of you dropped + + + align:start position:0% +was that right the slope of you dropped +by one we used to have corners going up + + align:start position:0% +by one we used to have corners going up + + + align:start position:0% +by one we used to have corners going up +and down and the difference between the + + align:start position:0% +and down and the difference between the + + + align:start position:0% +and down and the difference between the +slopes was one and here the difference + + align:start position:0% +slopes was one and here the difference + + + align:start position:0% +slopes was one and here the difference +between the slopes ah look their slope + + align:start position:0% +between the slopes ah look their slope + + + align:start position:0% +between the slopes ah look their slope +has dropped by 2a and when we divided by + + align:start position:0% +has dropped by 2a and when we divided by + + + align:start position:0% +has dropped by 2a and when we divided by +that when we divided by the two way it + + align:start position:0% +that when we divided by the two way it + + + align:start position:0% +that when we divided by the two way it +was just right now this this when I + + align:start position:0% +was just right now this this when I + + + align:start position:0% +was just right now this this when I +divide by the two way this has a slope + + align:start position:0% +divide by the two way this has a slope + + + align:start position:0% +divide by the two way this has a slope +of 1/2 this has a slope of minus 1/2 the + + align:start position:0% +of 1/2 this has a slope of minus 1/2 the + + + align:start position:0% +of 1/2 this has a slope of minus 1/2 the +drop is one and and we're right it + + align:start position:0% +drop is one and and we're right it + + + align:start position:0% +drop is one and and we're right it +solves the equation nobody doubted that + + align:start position:0% +solves the equation nobody doubted that + + + align:start position:0% +solves the equation nobody doubted that +ok so that's great + + align:start position:0% +ok so that's great + + + align:start position:0% +ok so that's great +we have found the solution to this + + align:start position:0% +we have found the solution to this + + + align:start position:0% +we have found the solution to this +equation when the right side is Delta + + align:start position:0% +equation when the right side is Delta + + + align:start position:0% +equation when the right side is Delta +good now can I ask you do you remember + + align:start position:0% +good now can I ask you do you remember + + + align:start position:0% +good now can I ask you do you remember +the name there's a special name for the + + align:start position:0% +the name there's a special name for the + + + align:start position:0% +the name there's a special name for the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +when the right side as a delta function + + align:start position:0% +when the right side as a delta function + + + align:start position:0% +when the right side as a delta function +whose whose name is associated with that + + align:start position:0% +whose whose name is associated with that + + + align:start position:0% +whose whose name is associated with that +so that this particular you I'm gonna + + align:start position:0% +so that this particular you I'm gonna + + + align:start position:0% +so that this particular you I'm gonna +give it another letter it's the + + align:start position:0% +give it another letter it's the + + + align:start position:0% +give it another letter it's the +particular you the special you when the + + align:start position:0% +particular you the special you when the + + + align:start position:0% +particular you the special you when the +right side is Delta and whose name is + + align:start position:0% +right side is Delta and whose name is + + + align:start position:0% +right side is Delta and whose name is +associated with that with that solution + + align:start position:0% +associated with that with that solution + + + align:start position:0% +associated with that with that solution +green green it's the greens function + + align:start position:0% +green green it's the greens function + + + align:start position:0% +green green it's the greens function +greens function the famous greens + + align:start position:0% +greens function the famous greens + + + align:start position:0% +greens function the famous greens +function greens function is just like an + + align:start position:0% +function greens function is just like an + + + align:start position:0% +function greens function is just like an +inverse to the problem this is like + + align:start position:0% +inverse to the problem this is like + + + align:start position:0% +inverse to the problem this is like +having an identity on the right hand + + align:start position:0% +having an identity on the right hand + + + align:start position:0% +having an identity on the right hand +side in fact there there it is so let me + + align:start position:0% +side in fact there there it is so let me + + + align:start position:0% +side in fact there there it is so let me +just use G for green function so that's + + align:start position:0% +just use G for green function so that's + + + align:start position:0% +just use G for green function so that's +the Fourier transform of the greens + + align:start position:0% +the Fourier transform of the greens + + + align:start position:0% +the Fourier transform of the greens +function and this is the greens function + + align:start position:0% +function and this is the greens function + + + align:start position:0% +function and this is the greens function +that's this is the green phone but now + + align:start position:0% +that's this is the green phone but now + + + align:start position:0% +that's this is the green phone but now +now I can give it it it's its name + + align:start position:0% +now I can give it it it's its name + + + align:start position:0% +now I can give it it it's its name +greens function when I divide by the 2a + + align:start position:0% +greens function when I divide by the 2a + + + align:start position:0% +greens function when I divide by the 2a +and now the slope is 1/2 going up and + + align:start position:0% +and now the slope is 1/2 going up and + + + align:start position:0% +and now the slope is 1/2 going up and +minus 1/2 coming down and it's alright + + align:start position:0% +minus 1/2 coming down and it's alright + + + align:start position:0% +minus 1/2 coming down and it's alright +ok so we found the greens function we + + align:start position:0% +ok so we found the greens function we + + + align:start position:0% +ok so we found the greens function we +found the fundamental solution to the + + align:start position:0% +found the fundamental solution to the + + + align:start position:0% +found the fundamental solution to the +equation and this is it you know it's + + align:start position:0% +equation and this is it you know it's + + + align:start position:0% +equation and this is it you know it's +just that it's that it was straight + + align:start position:0% +just that it's that it was straight + + + align:start position:0% +just that it's that it was straight +lines right it was straight lines in the + + align:start position:0% +lines right it was straight lines in the + + + align:start position:0% +lines right it was straight lines in the +in the first weeks of the course but now + + align:start position:0% +in the first weeks of the course but now + + + align:start position:0% +in the first weeks of the course but now +it's there's an exponential drop off + + align:start position:0% +it's there's an exponential drop off + + + align:start position:0% +it's there's an exponential drop off +caused by this additional term right ok + + align:start position:0% + + + + align:start position:0% + +good so that's straightforward depending + + align:start position:0% +good so that's straightforward depending + + + align:start position:0% +good so that's straightforward depending +on our being able to recognize or do the + + align:start position:0% +on our being able to recognize or do the + + + align:start position:0% +on our being able to recognize or do the +transform back to the X space ok now + + align:start position:0% +transform back to the X space ok now + + + align:start position:0% +transform back to the X space ok now +comes the question what about the + + align:start position:0% +comes the question what about the + + + align:start position:0% +comes the question what about the +original f of X can I you how can the + + align:start position:0% +original f of X can I you how can the + + + align:start position:0% +original f of X can I you how can the +greens function be used so you're seeing + + align:start position:0% +greens function be used so you're seeing + + + align:start position:0% +greens function be used so you're seeing +now how the greens fund what what uses + + align:start position:0% +now how the greens fund what what uses + + + align:start position:0% +now how the greens fund what what uses +this greens function with that right + + align:start position:0% +this greens function with that right + + + align:start position:0% +this greens function with that right +hand side when the right hand side is + + align:start position:0% +hand side when the right hand side is + + + align:start position:0% +hand side when the right hand side is +something different when the right hand + + align:start position:0% +something different when the right hand + + + align:start position:0% +something different when the right hand +side is some different f of X so let me + + align:start position:0% +side is some different f of X so let me + + + align:start position:0% +side is some different f of X so let me +go back to + + align:start position:0% +go back to + + + align:start position:0% +go back to +- an F of X on the right and then + + align:start position:0% +- an F of X on the right and then + + + align:start position:0% +- an F of X on the right and then +there's an F hat of K after the + + align:start position:0% +there's an F hat of K after the + + + align:start position:0% +there's an F hat of K after the +transform how can I use the greens + + align:start position:0% +transform how can I use the greens + + + align:start position:0% +transform how can I use the greens +function for a general source the + + align:start position:0% +function for a general source the + + + align:start position:0% +function for a general source the +general source term a general load right + + align:start position:0% +general source term a general load right + + + align:start position:0% +general source term a general load right +that's this is a fundamental idea it's + + align:start position:0% +that's this is a fundamental idea it's + + + align:start position:0% +that's this is a fundamental idea it's +yeah I would say fundamental how do you + + align:start position:0% +yeah I would say fundamental how do you + + + align:start position:0% +yeah I would say fundamental how do you +use the greens function and remember the + + align:start position:0% +use the greens function and remember the + + + align:start position:0% +use the greens function and remember the +greens function is like telling you the + + align:start position:0% +greens function is like telling you the + + + align:start position:0% +greens function is like telling you the +inverse matrix so it can't be too hard + + align:start position:0% +inverse matrix so it can't be too hard + + + align:start position:0% +inverse matrix so it can't be too hard +you're it's like solving a linear system + + align:start position:0% +you're it's like solving a linear system + + + align:start position:0% +you're it's like solving a linear system +when you know the inverse matrix and + + align:start position:0% +when you know the inverse matrix and + + + align:start position:0% +when you know the inverse matrix and +here so that's the analogy but but let's + + align:start position:0% +here so that's the analogy but but let's + + + align:start position:0% +here so that's the analogy but but let's +just focus on the particular question + + align:start position:0% +just focus on the particular question + + + align:start position:0% +just focus on the particular question +okay I think the intuition yeah it's you + + align:start position:0% +okay I think the intuition yeah it's you + + + align:start position:0% +okay I think the intuition yeah it's you +should have an intuition for how the + + align:start position:0% +should have an intuition for how the + + + align:start position:0% +should have an intuition for how the +greens function works so the greens + + align:start position:0% +greens function works so the greens + + + align:start position:0% +greens function works so the greens +function was the solution when the + + align:start position:0% +function was the solution when the + + + align:start position:0% +function was the solution when the +source term was a delta and here's the + + align:start position:0% +source term was a delta and here's the + + + align:start position:0% +source term was a delta and here's the +intuition it's it's it's rough but it's + + align:start position:0% +intuition it's it's it's rough but it's + + + align:start position:0% +intuition it's it's it's rough but it's +it works any source term f of X is in + + align:start position:0% +it works any source term f of X is in + + + align:start position:0% +it works any source term f of X is in +some way a combination of deltas if f of + + align:start position:0% +some way a combination of deltas if f of + + + align:start position:0% +some way a combination of deltas if f of +X is a combination of deltas then our + + align:start position:0% +X is a combination of deltas then our + + + align:start position:0% +X is a combination of deltas then our +answer U of X is the same combination of + + align:start position:0% +answer U of X is the same combination of + + + align:start position:0% +answer U of X is the same combination of +the greens function right if if f of X + + align:start position:0% +the greens function right if if f of X + + + align:start position:0% +the greens function right if if f of X +if the right hand side is some + + align:start position:0% +if the right hand side is some + + + align:start position:0% +if the right hand side is some +combination of this special Delta then + + align:start position:0% +combination of this special Delta then + + + align:start position:0% +combination of this special Delta then +the solution will be the same comment + + align:start position:0% +the solution will be the same comment + + + align:start position:0% +the solution will be the same comment +this is just linearity superposition + + align:start position:0% +this is just linearity superposition + + + align:start position:0% +this is just linearity superposition +whatever short or a long word you you + + align:start position:0% +whatever short or a long word you you + + + align:start position:0% +whatever short or a long word you you +you like to use so so if I can make + + align:start position:0% +you like to use so so if I can make + + + align:start position:0% +you like to use so so if I can make +sense of that statement that f of X is a + + align:start position:0% +sense of that statement that f of X is a + + + align:start position:0% +sense of that statement that f of X is a +combination of deltas then I'm I'm in + + align:start position:0% +combination of deltas then I'm I'm in + + + align:start position:0% +combination of deltas then I'm I'm in +now what do I mean by a combination of + + align:start position:0% +now what do I mean by a combination of + + + align:start position:0% +now what do I mean by a combination of +deltas I mean + + align:start position:0% +deltas I mean + + + align:start position:0% +deltas I mean +well those deltas are going to be + + align:start position:0% +well those deltas are going to be + + + align:start position:0% +well those deltas are going to be +shifted deltas obviously the the the + + align:start position:0% +shifted deltas obviously the the the + + + align:start position:0% +shifted deltas obviously the the the +single Delta Delta of X is spiked in the + + align:start position:0% +single Delta Delta of X is spiked in the + + + align:start position:0% +single Delta Delta of X is spiked in the +origin that's only one point I want to + + align:start position:0% +origin that's only one point I want to + + + align:start position:0% +origin that's only one point I want to +combine the Delta of X and it shifts so + + align:start position:0% +combine the Delta of X and it shifts so + + + align:start position:0% +combine the Delta of X and it shifts so +I'm going to have to expect to be using + + align:start position:0% +I'm going to have to expect to be using + + + align:start position:0% +I'm going to have to expect to be using +G of X and it's shift right okay so if + + align:start position:0% +G of X and it's shift right okay so if + + + align:start position:0% +G of X and it's shift right okay so if +now I'll just say this again I'm + + align:start position:0% +now I'll just say this again I'm + + + align:start position:0% +now I'll just say this again I'm +thinking of f of X as a combination of + + align:start position:0% +thinking of f of X as a combination of + + + align:start position:0% +thinking of f of X as a combination of +Delta and it shifts and then the + + align:start position:0% +Delta and it shifts and then the + + + align:start position:0% +Delta and it shifts and then the +solution u will be the same combination + + align:start position:0% +solution u will be the same combination + + + align:start position:0% +solution u will be the same combination +of G of X and it's shifts so now you + + align:start position:0% +of G of X and it's shifts so now you + + + align:start position:0% +of G of X and it's shifts so now you +just have to tell me what combination + + align:start position:0% +just have to tell me what combination + + + align:start position:0% +just have to tell me what combination +what combination of of Delta and it + + align:start position:0% +what combination of of Delta and it + + + align:start position:0% +what combination of of Delta and it +shifts maybe you'll allow me let me just + + align:start position:0% +shifts maybe you'll allow me let me just + + + align:start position:0% +shifts maybe you'll allow me let me just +do this on this on this maybe on that + + align:start position:0% +do this on this on this maybe on that + + + align:start position:0% +do this on this on this maybe on that +board it's it's I just can't help + + align:start position:0% +board it's it's I just can't help + + + align:start position:0% +board it's it's I just can't help +writing down the discrete case so in the + + align:start position:0% +writing down the discrete case so in the + + + align:start position:0% +writing down the discrete case so in the +discrete case the Delta vector + + align:start position:0% +discrete case the Delta vector + + + align:start position:0% +discrete case the Delta vector +corresponds to something like one zero + + align:start position:0% +corresponds to something like one zero + + + align:start position:0% +corresponds to something like one zero +zero zero + + align:start position:0% +zero zero + + + align:start position:0% +zero zero +right that was a typical Delta vector + + align:start position:0% +right that was a typical Delta vector + + + align:start position:0% +right that was a typical Delta vector +with a 1 in the 0th position then it + + align:start position:0% +with a 1 in the 0th position then it + + + align:start position:0% +with a 1 in the 0th position then it +shifts would be 0 1 0 0 that would be a + + align:start position:0% +shifts would be 0 1 0 0 that would be a + + + align:start position:0% +shifts would be 0 1 0 0 that would be a +shift and another shift would be 0 0 1 0 + + align:start position:0% +shift and another shift would be 0 0 1 0 + + + align:start position:0% +shift and another shift would be 0 0 1 0 +and another shift would be 0 0 0 1 ok so + + align:start position:0% +and another shift would be 0 0 0 1 ok so + + + align:start position:0% +and another shift would be 0 0 0 1 ok so +now there's the Delta vector and it + + align:start position:0% +now there's the Delta vector and it + + + align:start position:0% +now there's the Delta vector and it +shifts just four guys okay now suppose + + align:start position:0% +shifts just four guys okay now suppose + + + align:start position:0% +shifts just four guys okay now suppose +my F my right-hand side is 1 2 3 + + align:start position:0% +my F my right-hand side is 1 2 3 + + + align:start position:0% +my F my right-hand side is 1 2 3 +except I want to write that as a + + align:start position:0% +except I want to write that as a + + + align:start position:0% +except I want to write that as a +combination of those deltas this would + + align:start position:0% +combination of those deltas this would + + + align:start position:0% +combination of those deltas this would +be in the in the case when I if I know + + align:start position:0% +be in the in the case when I if I know + + + align:start position:0% +be in the in the case when I if I know +the solution for each of these guys the + + align:start position:0% +the solution for each of these guys the + + + align:start position:0% +the solution for each of these guys the +greens function the inverse matrix you + + align:start position:0% +greens function the inverse matrix you + + + align:start position:0% +greens function the inverse matrix you +everybody sees that if I know the + + align:start position:0% +everybody sees that if I know the + + + align:start position:0% +everybody sees that if I know the +solution to those four I know the + + align:start position:0% +solution to those four I know the + + + align:start position:0% +solution to those four I know the +inverse matrix right because if I can + + align:start position:0% +inverse matrix right because if I can + + + align:start position:0% +inverse matrix right because if I can +solve with those four right-hand sides + + align:start position:0% +solve with those four right-hand sides + + + align:start position:0% +solve with those four right-hand sides +those four solutions are the columns of + + align:start position:0% +those four solutions are the columns of + + + align:start position:0% +those four solutions are the columns of +the inverse matrix right you remember + + align:start position:0% +the inverse matrix right you remember + + + align:start position:0% +the inverse matrix right you remember +that if I had a matrix a and I was + + align:start position:0% +that if I had a matrix a and I was + + + align:start position:0% +that if I had a matrix a and I was +looking for its inverse + + align:start position:0% +looking for its inverse + + + align:start position:0% +looking for its inverse +I solved a inverse equal I and I is just + + align:start position:0% +I solved a inverse equal I and I is just + + + align:start position:0% +I solved a inverse equal I and I is just +these four guys so so a inverse is the + + align:start position:0% +these four guys so so a inverse is the + + + align:start position:0% +these four guys so so a inverse is the +solution from these four guys right okay + + align:start position:0% +solution from these four guys right okay + + + align:start position:0% +solution from these four guys right okay +now everybody gotta tell me what's the + + align:start position:0% +now everybody gotta tell me what's the + + + align:start position:0% +now everybody gotta tell me what's the +solution for this right-hand side one + + align:start position:0% +solution for this right-hand side one + + + align:start position:0% +solution for this right-hand side one +two three seven suppose this guy has + + align:start position:0% +two three seven suppose this guy has + + + align:start position:0% +two three seven suppose this guy has +solution so a inverse the columns of a + + align:start position:0% +solution so a inverse the columns of a + + + align:start position:0% +solution so a inverse the columns of a +inverse are these are this greens + + align:start position:0% +inverse are these are this greens + + + align:start position:0% +inverse are these are this greens +function this greens function with a + + align:start position:0% +function this greens function with a + + + align:start position:0% +function this greens function with a +shift may be SG for greens greens + + align:start position:0% +shift may be SG for greens greens + + + align:start position:0% +shift may be SG for greens greens +function with a ship SS s square G + + align:start position:0% +function with a ship SS s square G + + + align:start position:0% +function with a ship SS s square G +greens function with a double shift s + + align:start position:0% +greens function with a double shift s + + + align:start position:0% +greens function with a double shift s +cube G I'm just cooking up I never used + + align:start position:0% +cube G I'm just cooking up I never used + + + align:start position:0% +cube G I'm just cooking up I never used +these levees before but yeah what's the + + align:start position:0% +these levees before but yeah what's the + + + align:start position:0% +these levees before but yeah what's the +answer then U is what it's 1 times the + + align:start position:0% +answer then U is what it's 1 times the + + + align:start position:0% +answer then U is what it's 1 times the +the greens function and it's 2 times the + + align:start position:0% +the greens function and it's 2 times the + + + align:start position:0% +the greens function and it's 2 times the +guy right this F is just this F just is + + align:start position:0% +guy right this F is just this F just is + + + align:start position:0% +guy right this F is just this F just is +1 times the greens function 2 times the + + align:start position:0% +1 times the greens function 2 times the + + + align:start position:0% +1 times the greens function 2 times the +shifted 3 times the double shifted and 7 + + align:start position:0% +shifted 3 times the double shifted and 7 + + + align:start position:0% +shifted 3 times the double shifted and 7 +times the triple shift right just taking + + align:start position:0% +times the triple shift right just taking + + + align:start position:0% +times the triple shift right just taking +four minutes to do something simple + + align:start position:0% +four minutes to do something simple + + + align:start position:0% +four minutes to do something simple +because over there when I write when I + + align:start position:0% +because over there when I write when I + + + align:start position:0% +because over there when I write when I +use the continuous case it'll look you + + align:start position:0% +use the continuous case it'll look you + + + align:start position:0% +use the continuous case it'll look you +know a little little strange and right + + align:start position:0% +know a little little strange and right + + + align:start position:0% +know a little little strange and right +here it's so easy that'll involve + + align:start position:0% +here it's so easy that'll involve + + + align:start position:0% +here it's so easy that'll involve +integrals this involves a sum so what is + + align:start position:0% +integrals this involves a sum so what is + + + align:start position:0% +integrals this involves a sum so what is +it I have G twice the shift of G three + + align:start position:0% +it I have G twice the shift of G three + + + align:start position:0% +it I have G twice the shift of G three +times the double shift of G and seven + + align:start position:0% +times the double shift of G and seven + + + align:start position:0% +times the double shift of G and seven +times the triple shift of G right by + + align:start position:0% +times the triple shift of G right by + + + align:start position:0% +times the triple shift of G right by +linearity by superposition if this is my + + align:start position:0% +linearity by superposition if this is my + + + align:start position:0% +linearity by superposition if this is my +F this is my U everybody's with me here + + align:start position:0% +F this is my U everybody's with me here + + + align:start position:0% +F this is my U everybody's with me here +right if I take a combination of F's the + + align:start position:0% +right if I take a combination of F's the + + + align:start position:0% +right if I take a combination of F's the +answer is this corresponding combination + + align:start position:0% +answer is this corresponding combination + + + align:start position:0% +answer is this corresponding combination +of G's okay good + + align:start position:0% +of G's okay good + + + align:start position:0% +of G's okay good +okay ah did I didn't mean this that + + align:start position:0% +okay ah did I didn't mean this that + + + align:start position:0% +okay ah did I didn't mean this that +wasn't so great this that shouldn't have + + align:start position:0% +wasn't so great this that shouldn't have + + + align:start position:0% +wasn't so great this that shouldn't have +been caught I didn't mean to call those + + align:start position:0% +been caught I didn't mean to call those + + + align:start position:0% +been caught I didn't mean to call those +the Greens functions I meant to call + + align:start position:0% +the Greens functions I meant to call + + + align:start position:0% +the Greens functions I meant to call +those the deltas right and the Greens + + align:start position:0% +those the deltas right and the Greens + + + align:start position:0% +those the deltas right and the Greens +functions were the answers so this is a + + align:start position:0% +functions were the answers so this is a + + + align:start position:0% +functions were the answers so this is a +shift of Delta this is a doubly shifted + + align:start position:0% +shift of Delta this is a doubly shifted + + + align:start position:0% +shift of Delta this is a doubly shifted +Delta this is a triply shifted Delta and + + align:start position:0% +Delta this is a triply shifted Delta and + + + align:start position:0% +Delta this is a triply shifted Delta and +now this is one of the Delta two of the + + align:start position:0% +now this is one of the Delta two of the + + + align:start position:0% +now this is one of the Delta two of the +shifted Delta 3 of the doubly shifted + + align:start position:0% +shifted Delta 3 of the doubly shifted + + + align:start position:0% +shifted Delta 3 of the doubly shifted +Delta the F the F is a combination of + + align:start position:0% +Delta the F the F is a combination of + + + align:start position:0% +Delta the F the F is a combination of +deltas and it shifts the U is a + + align:start position:0% +deltas and it shifts the U is a + + + align:start position:0% +deltas and it shifts the U is a +combination of green functions and it + + align:start position:0% +combination of green functions and it + + + align:start position:0% +combination of green functions and it +shifts yeah apologies for making that + + align:start position:0% +shifts yeah apologies for making that + + + align:start position:0% +shifts yeah apologies for making that +mistake but maybe it brought us back to + + align:start position:0% +mistake but maybe it brought us back to + + + align:start position:0% +mistake but maybe it brought us back to +the point so the point is the point is + + align:start position:0% +the point so the point is the point is + + + align:start position:0% +the point so the point is the point is +express your function f your source as I + + align:start position:0% +express your function f your source as I + + + align:start position:0% +express your function f your source as I +come as a combination of deltas just + + align:start position:0% +come as a combination of deltas just + + + align:start position:0% +come as a combination of deltas just +exactly our plan then U is the same + + align:start position:0% +exactly our plan then U is the same + + + align:start position:0% +exactly our plan then U is the same +combination of the G's with the same + + align:start position:0% +combination of the G's with the same + + + align:start position:0% +combination of the G's with the same +shift all right now back here how do i + + align:start position:0% +shift all right now back here how do i + + + align:start position:0% +shift all right now back here how do i +express f f of X as what in what way is + + align:start position:0% +express f f of X as what in what way is + + + align:start position:0% +express f f of X as what in what way is +f of X a combination of deltas let me + + align:start position:0% +f of X a combination of deltas let me + + + align:start position:0% +f of X a combination of deltas let me +slow down a moment just to see that + + align:start position:0% +slow down a moment just to see that + + + align:start position:0% +slow down a moment just to see that +point how much of Delta at of the spike + + align:start position:0% +point how much of Delta at of the spike + + + align:start position:0% +point how much of Delta at of the spike +at X equal 3 how much of Delta of X + + align:start position:0% +at X equal 3 how much of Delta of X + + + align:start position:0% +at X equal 3 how much of Delta of X +minus 3 so that's a spike at 3 right how + + align:start position:0% +minus 3 so that's a spike at 3 right how + + + align:start position:0% +minus 3 so that's a spike at 3 right how +much of that do you think I need in f of + + align:start position:0% +much of that do you think I need in f of + + + align:start position:0% +much of that do you think I need in f of +X F of 3 F of 3 whatever F is at that + + align:start position:0% +X F of 3 F of 3 whatever F is at that + + + align:start position:0% +X F of 3 F of 3 whatever F is at that +point x equals 3 that's the amount I + + align:start position:0% +point x equals 3 that's the amount I + + + align:start position:0% +point x equals 3 that's the amount I +need there so this would be F of 3 so + + align:start position:0% +need there so this would be F of 3 so + + + align:start position:0% +need there so this would be F of 3 so +that part would that little that part + + align:start position:0% +that part would that little that part + + + align:start position:0% +that part would that little that part +would sort of have the right pep the + + align:start position:0% +would sort of have the right pep the + + + align:start position:0% +would sort of have the right pep the +right punch + + align:start position:0% +right punch + + + align:start position:0% +right punch +the point three now three could be any + + align:start position:0% +the point three now three could be any + + + align:start position:0% +the point three now three could be any +point that's that's any point along the + + align:start position:0% +point that's that's any point along the + + + align:start position:0% +point that's that's any point along the +line let me I can't use X for other + + align:start position:0% +line let me I can't use X for other + + + align:start position:0% +line let me I can't use X for other +points on the line because I've got an X + + align:start position:0% +points on the line because I've got an X + + + align:start position:0% +points on the line because I've got an X +in the formula let me use T so this was + + align:start position:0% +in the formula let me use T so this was + + + align:start position:0% +in the formula let me use T so this was +T equal to three now I want to do it at + + align:start position:0% +T equal to three now I want to do it at + + + align:start position:0% +T equal to three now I want to do it at +all points I want to take F at 2 and F + + align:start position:0% +all points I want to take F at 2 and F + + + align:start position:0% +all points I want to take F at 2 and F +at PI and F at everything and put them + + align:start position:0% +at PI and F at everything and put them + + + align:start position:0% +at PI and F at everything and put them +together and of course putting them + + align:start position:0% +together and of course putting them + + + align:start position:0% +together and of course putting them +together in the continuous case means + + align:start position:0% +together in the continuous case means + + + align:start position:0% +together in the continuous case means +not sum as I did there but integrate so + + align:start position:0% +not sum as I did there but integrate so + + + align:start position:0% +not sum as I did there but integrate so +I have to now I'm going to change 3 to a + + align:start position:0% +I have to now I'm going to change 3 to a + + + align:start position:0% +I have to now I'm going to change 3 to a +t because I'm doing because this is the + + align:start position:0% +t because I'm doing because this is the + + + align:start position:0% +t because I'm doing because this is the +amount of f of so that's the that's the + + align:start position:0% +amount of f of so that's the that's the + + + align:start position:0% +amount of f of so that's the that's the +amount that's the Delta functions with + + align:start position:0% +amount that's the Delta functions with + + + align:start position:0% +amount that's the Delta functions with +Spike at T multiplied by F of T and now + + align:start position:0% +Spike at T multiplied by F of T and now + + + align:start position:0% +Spike at T multiplied by F of T and now +how do I get f of X out of this I can + + align:start position:0% +how do I get f of X out of this I can + + + align:start position:0% +how do I get f of X out of this I can +put them together DT I add up this is + + align:start position:0% +put them together DT I add up this is + + + align:start position:0% +put them together DT I add up this is +the combination I've been talking about + + align:start position:0% +the combination I've been talking about + + + align:start position:0% +the combination I've been talking about +the so this is like any F this is like + + align:start position:0% +the so this is like any F this is like + + + align:start position:0% +the so this is like any F this is like +this is like a crazy Delta function + + align:start position:0% +this is like a crazy Delta function + + + align:start position:0% +this is like a crazy Delta function +identity actually it's not crazy it's a + + align:start position:0% +identity actually it's not crazy it's a + + + align:start position:0% +identity actually it's not crazy it's a +fun it's the identity we view as though + + align:start position:0% +fun it's the identity we view as though + + + align:start position:0% +fun it's the identity we view as though +our whole lives or at least our whole + + align:start position:0% +our whole lives or at least our whole + + + align:start position:0% +our whole lives or at least our whole +1808 five lives which is all that + + align:start position:0% +1808 five lives which is all that + + + align:start position:0% +1808 five lives which is all that +matters right okay so because right I do + + align:start position:0% +matters right okay so because right I do + + + align:start position:0% +matters right okay so because right I do +I'm integrating a delta function and I + + align:start position:0% +I'm integrating a delta function and I + + + align:start position:0% +I'm integrating a delta function and I +want to see that do I get that answer + + align:start position:0% +want to see that do I get that answer + + + align:start position:0% +want to see that do I get that answer +and you're gonna say absolutely clearly + + align:start position:0% +and you're gonna say absolutely clearly + + + align:start position:0% +and you're gonna say absolutely clearly +you get that answer no everybody knows + + align:start position:0% +you get that answer no everybody knows + + + align:start position:0% +you get that answer no everybody knows +that if I integrate something times a + + align:start position:0% +that if I integrate something times a + + + align:start position:0% +that if I integrate something times a +delta function that I plug in at the + + align:start position:0% +delta function that I plug in at the + + + align:start position:0% +delta function that I plug in at the +point t equal X where the spike happens + + align:start position:0% +point t equal X where the spike happens + + + align:start position:0% +point t equal X where the spike happens +I put t equal X I get f of X correct so + + align:start position:0% +I put t equal X I get f of X correct so + + + align:start position:0% +I put t equal X I get f of X correct so +that's like any that's an identity or + + align:start position:0% +that's like any that's an identity or + + + align:start position:0% +that's like any that's an identity or +whatever you would like to call it and + + align:start position:0% +whatever you would like to call it and + + + align:start position:0% +whatever you would like to call it and +now just tell me the final answer + + align:start position:0% +now just tell me the final answer + + + align:start position:0% +now just tell me the final answer +let me put it on the board above now so + + align:start position:0% +let me put it on the board above now so + + + align:start position:0% +let me put it on the board above now so +this was this expressed my f of X as a + + align:start position:0% +this was this expressed my f of X as a + + + align:start position:0% +this was this expressed my f of X as a +combination of Delta's just the way over + + align:start position:0% +combination of Delta's just the way over + + + align:start position:0% +combination of Delta's just the way over +here I expressed one two three seven as + + align:start position:0% +here I expressed one two three seven as + + + align:start position:0% +here I expressed one two three seven as +a combination of deltas now what's the + + align:start position:0% +a combination of deltas now what's the + + + align:start position:0% +a combination of deltas now what's the +you what's the function you this is the + + align:start position:0% +you what's the function you this is the + + + align:start position:0% +you what's the function you this is the +solution that comes from f of X just + + align:start position:0% +solution that comes from f of X just + + + align:start position:0% +solution that comes from f of X just +erase here so that I can put this all + + align:start position:0% +erase here so that I can put this all + + + align:start position:0% +erase here so that I can put this all +the point of the whole example now is + + align:start position:0% +the point of the whole example now is + + + align:start position:0% +the point of the whole example now is +for you to tell me what's u of X can you + + align:start position:0% +for you to tell me what's u of X can you + + + align:start position:0% +for you to tell me what's u of X can you +do it you see what u of X is going to + + align:start position:0% +do it you see what u of X is going to + + + align:start position:0% +do it you see what u of X is going to +come out it's going to come out nicely + + align:start position:0% +come out it's going to come out nicely + + + align:start position:0% +come out it's going to come out nicely +I've written the right-hand side F as a + + align:start position:0% +I've written the right-hand side F as a + + + align:start position:0% +I've written the right-hand side F as a +combination of deltas I know the answer + + align:start position:0% +combination of deltas I know the answer + + + align:start position:0% +combination of deltas I know the answer +for Delta its G what's the answer when + + align:start position:0% +for Delta its G what's the answer when + + + align:start position:0% +for Delta its G what's the answer when +the Delta is shifted along + + align:start position:0% +the Delta is shifted along + + + align:start position:0% +the Delta is shifted along +what's the greens function when the + + align:start position:0% +what's the greens function when the + + + align:start position:0% +what's the greens function when the +spike is moved along to a point T just + + align:start position:0% +spike is moved along to a point T just + + + align:start position:0% +spike is moved along to a point T just +because this constant coefficient + + align:start position:0% +because this constant coefficient + + + align:start position:0% +because this constant coefficient +translation invariant LTI problem is + + align:start position:0% +translation invariant LTI problem is + + + align:start position:0% +translation invariant LTI problem is +shift invariant the answer when this + + align:start position:0% +shift invariant the answer when this + + + align:start position:0% +shift invariant the answer when this +bike has moved along is just the answer + + align:start position:0% +bike has moved along is just the answer + + + align:start position:0% +bike has moved along is just the answer +G moved along so here's my answer all + + align:start position:0% +G moved along so here's my answer all + + + align:start position:0% +G moved along so here's my answer all +this this is my my my input and my + + align:start position:0% +this this is my my my input and my + + + align:start position:0% +this this is my my my input and my +output is the same integral this from + + align:start position:0% +output is the same integral this from + + + align:start position:0% +output is the same integral this from +minus infinity to infinity of where it + + align:start position:0% +minus infinity to infinity of where it + + + align:start position:0% +minus infinity to infinity of where it +was f now it's G oh no what do I want no + + align:start position:0% +was f now it's G oh no what do I want no + + + align:start position:0% +was f now it's G oh no what do I want no +help me out here no F of T is just the + + align:start position:0% +help me out here no F of T is just the + + + align:start position:0% +help me out here no F of T is just the +amount of the Delta but now what's the + + align:start position:0% +amount of the Delta but now what's the + + + align:start position:0% +amount of the Delta but now what's the +solution if what do I write now G of X + + align:start position:0% +solution if what do I write now G of X + + + align:start position:0% +solution if what do I write now G of X +minus T yeah + + align:start position:0% + + + + align:start position:0% + +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +you see why that works because this was + + align:start position:0% +you see why that works because this was + + + align:start position:0% +you see why that works because this was +the input geez the output the problem + + align:start position:0% +the input geez the output the problem + + + align:start position:0% +the input geez the output the problem +was shift invariant so if I shifted the + + align:start position:0% +was shift invariant so if I shifted the + + + align:start position:0% +was shift invariant so if I shifted the +input I shifted the output it was linear + + align:start position:0% +input I shifted the output it was linear + + + align:start position:0% +input I shifted the output it was linear +so if I add up a bunch of a bunch of + + align:start position:0% +so if I add up a bunch of a bunch of + + + align:start position:0% +so if I add up a bunch of a bunch of +deltas the solution is the bunt is add + + align:start position:0% +deltas the solution is the bunt is add + + + align:start position:0% +deltas the solution is the bunt is add +up a bunch of G's that's that's that's + + align:start position:0% +up a bunch of G's that's that's that's + + + align:start position:0% +up a bunch of G's that's that's that's +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +oh I could just say one thing more but + + align:start position:0% +oh I could just say one thing more but + + + align:start position:0% +oh I could just say one thing more but +you've got it if you've seen that so + + align:start position:0% +you've got it if you've seen that so + + + align:start position:0% +you've got it if you've seen that so +that's the point that if you know the + + align:start position:0% +that's the point that if you know the + + + align:start position:0% +that's the point that if you know the +greens function well yeah baby + + align:start position:0% +greens function well yeah baby + + + align:start position:0% +greens function well yeah baby +from a practical point of view what have + + align:start position:0% +from a practical point of view what have + + + align:start position:0% +from a practical point of view what have +we done we have the original way we did + + align:start position:0% +we done we have the original way we did + + + align:start position:0% +we done we have the original way we did +it involved are computing two integrals + + align:start position:0% +it involved are computing two integrals + + + align:start position:0% +it involved are computing two integrals +we had two if we were given an f of X we + + align:start position:0% +we had two if we were given an f of X we + + + align:start position:0% +we had two if we were given an f of X we +had to find its transform F hat of K + + align:start position:0% +had to find its transform F hat of K + + + align:start position:0% +had to find its transform F hat of K +that we weren't sure we could do with + + align:start position:0% +that we weren't sure we could do with + + + align:start position:0% +that we weren't sure we could do with +pencil and paper and then we got an + + align:start position:0% +pencil and paper and then we got an + + + align:start position:0% +pencil and paper and then we got an +answer with an F hat of K up here and + + align:start position:0% +answer with an F hat of K up here and + + + align:start position:0% +answer with an F hat of K up here and +then we had to transform back step one + + align:start position:0% +then we had to transform back step one + + + align:start position:0% +then we had to transform back step one +in step three we had to do now this this + + align:start position:0% +in step three we had to do now this this + + + align:start position:0% +in step three we had to do now this this +is like better this is like better + + align:start position:0% +is like better this is like better + + + align:start position:0% +is like better this is like better +because because we were able to do + + align:start position:0% +because because we were able to do + + + align:start position:0% +because because we were able to do +without any we were able to get us + + align:start position:0% +without any we were able to get us + + + align:start position:0% +without any we were able to get us +explicit answer G when this was a delta + + align:start position:0% +explicit answer G when this was a delta + + + align:start position:0% +explicit answer G when this was a delta +you could say I've got it down to one + + align:start position:0% +you could say I've got it down to one + + + align:start position:0% +you could say I've got it down to one +integral yeah well for whatever that's + + align:start position:0% +integral yeah well for whatever that's + + + align:start position:0% +integral yeah well for whatever that's +worth I probably well I was gonna say I + + align:start position:0% +worth I probably well I was gonna say I + + + align:start position:0% +worth I probably well I was gonna say I +probably can't do that one either + + align:start position:0% +probably can't do that one either + + + align:start position:0% +probably can't do that one either +depending what f of X is but this is + + align:start position:0% +depending what f of X is but this is + + + align:start position:0% +depending what f of X is but this is +that's a nice way to see the answer you + + align:start position:0% +that's a nice way to see the answer you + + + align:start position:0% +that's a nice way to see the answer you +have to admit that that and it's because + + align:start position:0% +have to admit that that and it's because + + + align:start position:0% +have to admit that that and it's because +the problem is is shift invariant and I + + align:start position:0% +the problem is is shift invariant and I + + + align:start position:0% +the problem is is shift invariant and I +can write the answer that way okay and + + align:start position:0% +can write the answer that way okay and + + + align:start position:0% +can write the answer that way okay and +now one more thing about this and I've + + align:start position:0% +now one more thing about this and I've + + + align:start position:0% +now one more thing about this and I've +written the word the key word down here + + align:start position:0% +written the word the key word down here + + + align:start position:0% +written the word the key word down here +convolution + + align:start position:0% + + + + align:start position:0% + +do you see with a nice way to write that + + align:start position:0% +do you see with a nice way to write that + + + align:start position:0% +do you see with a nice way to write that +answer + + align:start position:0% +answer + + + align:start position:0% +answer +it's the convolution of F with G that's + + align:start position:0% +it's the convolution of F with G that's + + + align:start position:0% +it's the convolution of F with G that's +what we didn't do + + align:start position:0% +what we didn't do + + + align:start position:0% +what we didn't do +integral convolutions we just did the + + align:start position:0% +integral convolutions we just did the + + + align:start position:0% +integral convolutions we just did the +discrete sums but I mentioned that in + + align:start position:0% +discrete sums but I mentioned that in + + + align:start position:0% +discrete sums but I mentioned that in +the integral case you have this same + + align:start position:0% +the integral case you have this same + + + align:start position:0% +the integral case you have this same +thing T and X minus T adding up to X + + align:start position:0% +thing T and X minus T adding up to X + + + align:start position:0% +thing T and X minus T adding up to X +just the way we had K and n minus K + + align:start position:0% +just the way we had K and n minus K + + + align:start position:0% +just the way we had K and n minus K +adding up to n in other words this is + + align:start position:0% +adding up to n in other words this is + + + align:start position:0% +adding up to n in other words this is +just notation but I'm just gonna write + + align:start position:0% +just notation but I'm just gonna write + + + align:start position:0% +just notation but I'm just gonna write +the answer in a nice way yeah so after + + align:start position:0% +the answer in a nice way yeah so after + + + align:start position:0% +the answer in a nice way yeah so after +all that lecture the answer to the + + align:start position:0% +all that lecture the answer to the + + + align:start position:0% +all that lecture the answer to the +differential equation is in three + + align:start position:0% +differential equation is in three + + + align:start position:0% +differential equation is in three +symbols F star G yeah where this is + + align:start position:0% +symbols F star G yeah where this is + + + align:start position:0% +symbols F star G yeah where this is +where this just simply means this this + + align:start position:0% +where this just simply means this this + + + align:start position:0% +where this just simply means this this +is the this is the continuous + + align:start position:0% +is the this is the continuous + + + align:start position:0% +is the this is the continuous +convolution not cyclic and there's the + + align:start position:0% +convolution not cyclic and there's the + + + align:start position:0% +convolution not cyclic and there's the +answer okay and and yeah oh I'll allow + + align:start position:0% +answer okay and and yeah oh I'll allow + + + align:start position:0% +answer okay and and yeah oh I'll allow +myself one more thing what's the here we + + align:start position:0% +myself one more thing what's the here we + + + align:start position:0% +myself one more thing what's the here we +had a convolution for the right hand + + align:start position:0% +had a convolution for the right hand + + + align:start position:0% +had a convolution for the right hand +side for the we started with this this + + align:start position:0% +side for the we started with this this + + + align:start position:0% +side for the we started with this this +is a convolution now what what are the + + align:start position:0% +is a convolution now what what are the + + + align:start position:0% +is a convolution now what what are the +three symbols that I write down to for + + align:start position:0% +three symbols that I write down to for + + + align:start position:0% +three symbols that I write down to for +the shorthand for this equation so this + + align:start position:0% +the shorthand for this equation so this + + + align:start position:0% +the shorthand for this equation so this +was to be true for any F and now can I + + align:start position:0% +was to be true for any F and now can I + + + align:start position:0% +was to be true for any F and now can I +write down how do I write f of X is + + align:start position:0% +write down how do I write f of X is + + + align:start position:0% +write down how do I write f of X is +equal to what is this right hand side + + align:start position:0% + + + + align:start position:0% + +it's f convolved with Delta so any F is + + align:start position:0% +it's f convolved with Delta so any F is + + + align:start position:0% +it's f convolved with Delta so any F is +the same have involved with Delta that's + + align:start position:0% + + + + align:start position:0% + +Delta in convolution Delta is one + + align:start position:0% +Delta in convolution Delta is one + + + align:start position:0% +Delta in convolution Delta is one +because when I go to the other space and + + align:start position:0% +because when I go to the other space and + + + align:start position:0% +because when I go to the other space and +I get a multiplication it really is one + + align:start position:0% +I get a multiplication it really is one + + + align:start position:0% +I get a multiplication it really is one +right in the other space so in the other + + align:start position:0% +right in the other space so in the other + + + align:start position:0% +right in the other space so in the other +space so convent is convolution in X + + align:start position:0% +space so convent is convolution in X + + + align:start position:0% +space so convent is convolution in X +space turns into multiplication in + + align:start position:0% +space turns into multiplication in + + + align:start position:0% +space turns into multiplication in +frequency space and it just tells me + + align:start position:0% +frequency space and it just tells me + + + align:start position:0% +frequency space and it just tells me +that F hat is f hat times 1 so this is + + align:start position:0% +that F hat is f hat times 1 so this is + + + align:start position:0% +that F hat is f hat times 1 so this is +that's the way to look at it in in + + align:start position:0% +that's the way to look at it in in + + + align:start position:0% +that's the way to look at it in in +physical space and this is the way to + + align:start position:0% +physical space and this is the way to + + + align:start position:0% +physical space and this is the way to +look at it in look at the solution so + + align:start position:0% +look at it in look at the solution so + + + align:start position:0% +look at it in look at the solution so +one more thought and I'll come back to + + align:start position:0% +one more thought and I'll come back to + + + align:start position:0% +one more thought and I'll come back to +that this so this G the greens function + + align:start position:0% +that this so this G the greens function + + + align:start position:0% +that this so this G the greens function +this is what a cat-scan does what a what + + align:start position:0% +this is what a cat-scan does what a what + + + align:start position:0% +this is what a cat-scan does what a what +an x-ray telescope does what all sorts + + align:start position:0% +an x-ray telescope does what all sorts + + + align:start position:0% +an x-ray telescope does what all sorts +of physical things do provided we can + + align:start position:0% +of physical things do provided we can + + + align:start position:0% +of physical things do provided we can +assume this translation invariance which + + align:start position:0% +assume this translation invariance which + + + align:start position:0% +assume this translation invariance which +is never perfectly true because the + + align:start position:0% +is never perfectly true because the + + + align:start position:0% +is never perfectly true because the +telescope is finite but a telescope + + align:start position:0% +telescope is finite but a telescope + + + align:start position:0% +telescope is finite but a telescope +takes the star takes the light signal + + align:start position:0% +takes the star takes the light signal + + + align:start position:0% +takes the star takes the light signal +convolve zit with the telescopes own + + align:start position:0% +convolve zit with the telescopes own + + + align:start position:0% +convolve zit with the telescopes own +little green's function it blurs it it's + + align:start position:0% +little green's function it blurs it it's + + + align:start position:0% +little green's function it blurs it it's +the it's a point spread function it's + + align:start position:0% +the it's a point spread function it's + + + align:start position:0% +the it's a point spread function it's +the blurring function G the green's + + align:start position:0% +the blurring function G the green's + + + align:start position:0% +the blurring function G the green's +function on a telescope is somehow + + align:start position:0% +function on a telescope is somehow + + + align:start position:0% +function on a telescope is somehow +that's what your convolving with and if + + align:start position:0% +that's what your convolving with and if + + + align:start position:0% +that's what your convolving with and if +you want to find that star as a bright + + align:start position:0% +you want to find that star as a bright + + + align:start position:0% +you want to find that star as a bright +single point you've got to deke do + + align:start position:0% +single point you've got to deke do + + + align:start position:0% +single point you've got to deke do +deconvolution you got to do a division + + align:start position:0% +deconvolution you got to do a division + + + align:start position:0% +deconvolution you got to do a division +to get the G out so may I just say those + + align:start position:0% +to get the G out so may I just say those + + + align:start position:0% +to get the G out so may I just say those +words and then it's Thanksgiving that a + + align:start position:0% +words and then it's Thanksgiving that a + + + align:start position:0% +words and then it's Thanksgiving that a +machine a sensor which is translation + + align:start position:0% +machine a sensor which is translation + + + align:start position:0% +machine a sensor which is translation +invariant or you could say close enough + + align:start position:0% +invariant or you could say close enough + + + align:start position:0% +invariant or you could say close enough +to pretend it is because nothing is + + align:start position:0% +to pretend it is because nothing is + + + align:start position:0% +to pretend it is because nothing is +going to be perfectly translation + + align:start position:0% +going to be perfectly translation + + + align:start position:0% +going to be perfectly translation +invariant all the way out to infinity + + align:start position:0% +invariant all the way out to infinity + + + align:start position:0% +invariant all the way out to infinity +but if it's if near the star so so I + + align:start position:0% +but if it's if near the star so so I + + + align:start position:0% +but if it's if near the star so so I +look at this point star in the telescope + + align:start position:0% +look at this point star in the telescope + + + align:start position:0% +look at this point star in the telescope +I see a blur that's big + + align:start position:0% +I see a blur that's big + + + align:start position:0% +I see a blur that's big +the telescope has convolve the correct + + align:start position:0% +the telescope has convolve the correct + + + align:start position:0% +the telescope has convolve the correct +the correct thing that I should have + + align:start position:0% +the correct thing that I should have + + + align:start position:0% +the correct thing that I should have +seen with G with its own it's it's + + align:start position:0% +seen with G with its own it's it's + + + align:start position:0% +seen with G with its own it's it's +blurted by its point spread function so + + align:start position:0% +blurted by its point spread function so + + + align:start position:0% +blurted by its point spread function so +what if the person the the factory where + + align:start position:0% +what if the person the the factory where + + + align:start position:0% +what if the person the the factory where +the telescope was built can test this + + align:start position:0% +the telescope was built can test this + + + align:start position:0% +the telescope was built can test this +whole thing on points and it can find + + align:start position:0% +whole thing on points and it can find + + + align:start position:0% +whole thing on points and it can find +the point spread function and if I knew + + align:start position:0% +the point spread function and if I knew + + + align:start position:0% +the point spread function and if I knew +G then I could undo it and get a clearer + + align:start position:0% +G then I could undo it and get a clearer + + + align:start position:0% +G then I could undo it and get a clearer +picture so it's that that step that that + + align:start position:0% +picture so it's that that step that that + + + align:start position:0% +picture so it's that that step that that +won the Nobel Prize for the cat scan and + + align:start position:0% +won the Nobel Prize for the cat scan and + + + align:start position:0% +won the Nobel Prize for the cat scan and +I'm sure is winning Nobel prizes for + + align:start position:0% +I'm sure is winning Nobel prizes for + + + align:start position:0% +I'm sure is winning Nobel prizes for +astronomers okay have a great + + align:start position:0% +astronomers okay have a great + + + align:start position:0% +astronomers okay have a great +Thanksgiving I'll see you Monday good \ No newline at end of file diff --git a/LaP0Ut84GzI.txt b/LaP0Ut84GzI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f6296df44622461bf433d87f8cee87f44767c54f --- /dev/null +++ b/LaP0Ut84GzI.txt @@ -0,0 +1,16640 @@ +align:start position:0% + +welcome back + + align:start position:0% +welcome back + + + align:start position:0% +welcome back +to fintech + + align:start position:0% +to fintech + + + align:start position:0% +to fintech +we're getting together for our fourth + + align:start position:0% +we're getting together for our fourth + + + align:start position:0% +we're getting together for our fourth +class + + align:start position:0% +class + + + align:start position:0% +class +and we're going to get going now i thank + + align:start position:0% +and we're going to get going now i thank + + + align:start position:0% +and we're going to get going now i thank +you for tying in online + + align:start position:0% +you for tying in online + + + align:start position:0% +you for tying in online +and by this modern technology + + align:start position:0% +and by this modern technology + + + align:start position:0% +and by this modern technology +today we're going to move to uh + + align:start position:0% +today we're going to move to uh + + + align:start position:0% +today we're going to move to uh +important customer interfaces + + align:start position:0% +important customer interfaces + + + align:start position:0% +important customer interfaces +user interfaces and user experiences + + align:start position:0% +user interfaces and user experiences + + + align:start position:0% +user interfaces and user experiences +that would have been greatly enhanced + + align:start position:0% +that would have been greatly enhanced + + + align:start position:0% +that would have been greatly enhanced +by open application program interfaces + + align:start position:0% +by open application program interfaces + + + align:start position:0% +by open application program interfaces +now application to program interfaces is + + align:start position:0% +now application to program interfaces is + + + align:start position:0% +now application to program interfaces is +not new to finance + + align:start position:0% +not new to finance + + + align:start position:0% +not new to finance +and it didn't start and emanate finance + + align:start position:0% +and it didn't start and emanate finance + + + align:start position:0% +and it didn't start and emanate finance +it's a basic concept of how + + align:start position:0% +it's a basic concept of how + + + align:start position:0% +it's a basic concept of how +one computer is talking to another + + align:start position:0% +one computer is talking to another + + + align:start position:0% +one computer is talking to another +computer and again this is not a + + align:start position:0% +computer and again this is not a + + + align:start position:0% +computer and again this is not a +computer science class but we're going + + align:start position:0% +computer science class but we're going + + + align:start position:0% +computer science class but we're going +to spend a little bit of time + + align:start position:0% +to spend a little bit of time + + + align:start position:0% +to spend a little bit of time +on what application program interfaces + + align:start position:0% +on what application program interfaces + + + align:start position:0% +on what application program interfaces +are + + align:start position:0% +are + + + align:start position:0% +are +and what this concept of open api is + + align:start position:0% +and what this concept of open api is + + + align:start position:0% +and what this concept of open api is +and some of the companies around it and + + align:start position:0% +and some of the companies around it and + + + align:start position:0% +and some of the companies around it and +how companies have organized themselves + + align:start position:0% +how companies have organized themselves + + + align:start position:0% +how companies have organized themselves +both in terms of finance and a little + + align:start position:0% +both in terms of finance and a little + + + align:start position:0% +both in terms of finance and a little +bit even outside of finance + + align:start position:0% +bit even outside of finance + + + align:start position:0% +bit even outside of finance +and some of the challenges with regard + + align:start position:0% +and some of the challenges with regard + + + align:start position:0% +and some of the challenges with regard +to that + + align:start position:0% +to that + + + align:start position:0% +to that +what open apis also led to is a movement + + align:start position:0% +what open apis also led to is a movement + + + align:start position:0% +what open apis also led to is a movement +of + + align:start position:0% +of + + + align:start position:0% +of +and a greater concentration around + + align:start position:0% +and a greater concentration around + + + align:start position:0% +and a greater concentration around +companies called data aggregators and + + align:start position:0% +companies called data aggregators and + + + align:start position:0% +companies called data aggregators and +we'll get into that + + align:start position:0% +we'll get into that + + + align:start position:0% +we'll get into that +as well as i sort of + + align:start position:0% +as well as i sort of + + + align:start position:0% +as well as i sort of +worked through with the class already + + align:start position:0% +worked through with the class already + + + align:start position:0% +worked through with the class already +it's my thought that certain + + align:start position:0% +it's my thought that certain + + + align:start position:0% +it's my thought that certain +technologies have been moving into + + align:start position:0% +technologies have been moving into + + + align:start position:0% +technologies have been moving into +the finance technology stack and are + + align:start position:0% +the finance technology stack and are + + + align:start position:0% +the finance technology stack and are +really + + align:start position:0% +really + + + align:start position:0% +really +part and parcel of what finance is in + + align:start position:0% +part and parcel of what finance is in + + + align:start position:0% +part and parcel of what finance is in +2020 and i think + + align:start position:0% +2020 and i think + + + align:start position:0% +2020 and i think +open api well it's a movement around the + + align:start position:0% +open api well it's a movement around the + + + align:start position:0% +open api well it's a movement around the +globe and some countries have moved + + align:start position:0% +globe and some countries have moved + + + align:start position:0% +globe and some countries have moved +further in it + + align:start position:0% +further in it + + + align:start position:0% +further in it +some countries have moved less some + + align:start position:0% +some countries have moved less some + + + align:start position:0% +some countries have moved less some +companies have moved further some + + align:start position:0% +companies have moved further some + + + align:start position:0% +companies have moved further some +companies have moved less + + align:start position:0% +companies have moved less + + + align:start position:0% +companies have moved less +that that this is a trend that will be + + align:start position:0% +that that this is a trend that will be + + + align:start position:0% +that that this is a trend that will be +fully incorporated into the technology + + align:start position:0% +fully incorporated into the technology + + + align:start position:0% +fully incorporated into the technology +stack of finance country by country if + + align:start position:0% +stack of finance country by country if + + + align:start position:0% +stack of finance country by country if +it hasn't already been south + + align:start position:0% +it hasn't already been south + + + align:start position:0% +it hasn't already been south +but it's been a major disrupter in the + + align:start position:0% +but it's been a major disrupter in the + + + align:start position:0% +but it's been a major disrupter in the +last five seven years + + align:start position:0% +last five seven years + + + align:start position:0% +last five seven years +and it will continue to be a bit of a + + align:start position:0% +and it will continue to be a bit of a + + + align:start position:0% +and it will continue to be a bit of a +disrupter for the next handful of years + + align:start position:0% +disrupter for the next handful of years + + + align:start position:0% +disrupter for the next handful of years +by the end of this decade we'll look + + align:start position:0% +by the end of this decade we'll look + + + align:start position:0% +by the end of this decade we'll look +back and we'll say that + + align:start position:0% +back and we'll say that + + + align:start position:0% +back and we'll say that +that sort of probably already happened + + align:start position:0% +that sort of probably already happened + + + align:start position:0% +that sort of probably already happened +and there'll be enhancements around it + + align:start position:0% +and there'll be enhancements around it + + + align:start position:0% +and there'll be enhancements around it +but it will be fully + + align:start position:0% +but it will be fully + + + align:start position:0% +but it will be fully +inside of it maybe not as dramatic + + align:start position:0% +inside of it maybe not as dramatic + + + align:start position:0% +inside of it maybe not as dramatic +artificial intelligence and machine + + align:start position:0% +artificial intelligence and machine + + + align:start position:0% +artificial intelligence and machine +learning to our minds thinking of + + align:start position:0% +learning to our minds thinking of + + + align:start position:0% +learning to our minds thinking of +machines + + align:start position:0% +machines + + + align:start position:0% +machines +extracting correlations better than we + + align:start position:0% +extracting correlations better than we + + + align:start position:0% +extracting correlations better than we +can + + align:start position:0% +can + + + align:start position:0% +can +but i think fairly dramatic in terms of + + align:start position:0% +but i think fairly dramatic in terms of + + + align:start position:0% +but i think fairly dramatic in terms of +the + + align:start position:0% +the + + + align:start position:0% +the +advancement of finance and all that we + + align:start position:0% +advancement of finance and all that we + + + align:start position:0% +advancement of finance and all that we +have uh + + align:start position:0% +have uh + + + align:start position:0% +have uh +in front of us so that's why i decided + + align:start position:0% +in front of us so that's why i decided + + + align:start position:0% +in front of us so that's why i decided +to take a + + align:start position:0% +to take a + + + align:start position:0% +to take a +one one class and one lecture on it um i + + align:start position:0% +one one class and one lecture on it um i + + + align:start position:0% +one one class and one lecture on it um i +also want to thank everybody romaine + + align:start position:0% +also want to thank everybody romaine + + + align:start position:0% +also want to thank everybody romaine +put out a survey about a third of you uh + + align:start position:0% +put out a survey about a third of you uh + + + align:start position:0% +put out a survey about a third of you uh +took it it was a voluntary survey and + + align:start position:0% +took it it was a voluntary survey and + + + align:start position:0% +took it it was a voluntary survey and +it's helpful + + align:start position:0% +it's helpful + + + align:start position:0% +it's helpful +and and what i took back from the uh + + align:start position:0% +and and what i took back from the uh + + + align:start position:0% +and and what i took back from the uh +uh desires of students are um + + align:start position:0% +uh desires of students are um + + + align:start position:0% +uh desires of students are um +could i do a little bit more talking + + align:start position:0% +could i do a little bit more talking + + + align:start position:0% +could i do a little bit more talking +about the companies in the fintech space + + align:start position:0% +about the companies in the fintech space + + + align:start position:0% +about the companies in the fintech space +uh and maybe uh uh + + align:start position:0% +uh and maybe uh uh + + + align:start position:0% +uh and maybe uh uh +if i might say a little last feather + + align:start position:0% +if i might say a little last feather + + + align:start position:0% +if i might say a little last feather +it's on the broader + + align:start position:0% +it's on the broader + + + align:start position:0% +it's on the broader +technology or broader policy side um + + align:start position:0% +technology or broader policy side um + + + align:start position:0% +technology or broader policy side um +i'll do my best but i also want to share + + align:start position:0% +i'll do my best but i also want to share + + + align:start position:0% +i'll do my best but i also want to share +with you why + + align:start position:0% +with you why + + + align:start position:0% +with you why +i think there's a reason to have some + + align:start position:0% +i think there's a reason to have some + + + align:start position:0% +i think there's a reason to have some +foundation some foundation of + + align:start position:0% +foundation some foundation of + + + align:start position:0% +foundation some foundation of +of what the technologies are or even + + align:start position:0% +of what the technologies are or even + + + align:start position:0% +of what the technologies are or even +some foundation on the public policy + + align:start position:0% +some foundation on the public policy + + + align:start position:0% +some foundation on the public policy +side as we move + + align:start position:0% +side as we move + + + align:start position:0% +side as we move +into the latter part of this class the + + align:start position:0% +into the latter part of this class the + + + align:start position:0% +into the latter part of this class the +latter part of this class is really to + + align:start position:0% +latter part of this class is really to + + + align:start position:0% +latter part of this class is really to +talk sector by sector + + align:start position:0% +talk sector by sector + + + align:start position:0% +talk sector by sector +what the competitive landscape is which + + align:start position:0% +what the competitive landscape is which + + + align:start position:0% +what the competitive landscape is which +companies are up which companies are + + align:start position:0% +companies are up which companies are + + + align:start position:0% +companies are up which companies are +down and so forth + + align:start position:0% +down and so forth + + + align:start position:0% +down and so forth +um but as we've already talked about a + + align:start position:0% +um but as we've already talked about a + + + align:start position:0% +um but as we've already talked about a +bit + + align:start position:0% +bit + + + align:start position:0% +bit +uh today the companies really matter + + align:start position:0% +uh today the companies really matter + + + align:start position:0% +uh today the companies really matter +and i'll sort of interject that more as + + align:start position:0% +and i'll sort of interject that more as + + + align:start position:0% +and i'll sort of interject that more as +we go + + align:start position:0% +we go + + + align:start position:0% +we go +forward during this semester one other + + align:start position:0% +forward during this semester one other + + + align:start position:0% +forward during this semester one other +request is whether we could have some + + align:start position:0% +request is whether we could have some + + + align:start position:0% +request is whether we could have some +guest speakers + + align:start position:0% +guest speakers + + + align:start position:0% +guest speakers +i'm kind of gonna have to apologize in + + align:start position:0% +i'm kind of gonna have to apologize in + + + align:start position:0% +i'm kind of gonna have to apologize in +advance + + align:start position:0% +advance + + + align:start position:0% +advance +uh this is kind of what you get but uh + + align:start position:0% +uh this is kind of what you get but uh + + + align:start position:0% +uh this is kind of what you get but uh +over the next uh handful of sessions if + + align:start position:0% +over the next uh handful of sessions if + + + align:start position:0% +over the next uh handful of sessions if +if i + + align:start position:0% +if i + + + align:start position:0% +if i +come up with somebody to bring in it's a + + align:start position:0% +come up with somebody to bring in it's a + + + align:start position:0% +come up with somebody to bring in it's a +little hard + + align:start position:0% +little hard + + + align:start position:0% +little hard +at this juncture to bring in uh guest + + align:start position:0% +at this juncture to bring in uh guest + + + align:start position:0% +at this juncture to bring in uh guest +speakers um + + align:start position:0% +speakers um + + + align:start position:0% +speakers um +but i certainly appreciate the request + + align:start position:0% +but i certainly appreciate the request + + + align:start position:0% +but i certainly appreciate the request +and + + align:start position:0% +and + + + align:start position:0% +and +and uh four weeks to go you never know + + align:start position:0% +and uh four weeks to go you never know + + + align:start position:0% +and uh four weeks to go you never know +um + + align:start position:0% +um + + + align:start position:0% +um +but with that i'm going to um uh uh + + align:start position:0% +but with that i'm going to um uh uh + + + align:start position:0% +but with that i'm going to um uh uh +uh start to share some slides i don't + + align:start position:0% +uh start to share some slides i don't + + + align:start position:0% +uh start to share some slides i don't +know + + align:start position:0% +know + + + align:start position:0% +know +romaine if you have anything you took + + align:start position:0% +romaine if you have anything you took + + + align:start position:0% +romaine if you have anything you took +from from + + align:start position:0% +from from + + + align:start position:0% +from from +that uh the feedback which was very + + align:start position:0% +that uh the feedback which was very + + + align:start position:0% +that uh the feedback which was very +helpful + + align:start position:0% +helpful + + + align:start position:0% +helpful +well thank you thank you very much for + + align:start position:0% +well thank you thank you very much for + + + align:start position:0% +well thank you thank you very much for +filling out this survey that was great + + align:start position:0% +filling out this survey that was great + + + align:start position:0% +filling out this survey that was great +just two small announcements from my + + align:start position:0% +just two small announcements from my + + + align:start position:0% +just two small announcements from my +side one + + align:start position:0% +side one + + + align:start position:0% +side one +a reminder for your team formation + + align:start position:0% +a reminder for your team formation + + + align:start position:0% +a reminder for your team formation +friday is the deadline + + align:start position:0% +friday is the deadline + + + align:start position:0% +friday is the deadline +please register your teams in canvas in + + align:start position:0% +please register your teams in canvas in + + + align:start position:0% +please register your teams in canvas in +the people's tab + + align:start position:0% +the people's tab + + + align:start position:0% +the people's tab +using the groups function if you don't + + align:start position:0% +using the groups function if you don't + + + align:start position:0% +using the groups function if you don't +know how to do that i'll be happy to + + align:start position:0% +know how to do that i'll be happy to + + + align:start position:0% +know how to do that i'll be happy to +show you + + align:start position:0% +show you + + + align:start position:0% +show you +so please register your teams to of + + align:start position:0% +so please register your teams to of + + + align:start position:0% +so please register your teams to of +three to four students for the group + + align:start position:0% +three to four students for the group + + + align:start position:0% +three to four students for the group +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +and then second reminder as per the + + align:start position:0% +and then second reminder as per the + + + align:start position:0% +and then second reminder as per the +syllabus have one of your team members + + align:start position:0% +syllabus have one of your team members + + + align:start position:0% +syllabus have one of your team members +just send me an email + + align:start position:0% +just send me an email + + + align:start position:0% +just send me an email +saying what is the topic that you wish + + align:start position:0% +saying what is the topic that you wish + + + align:start position:0% +saying what is the topic that you wish +to study for your group assignment + + align:start position:0% +to study for your group assignment + + + align:start position:0% +to study for your group assignment +right please don't forget to do that the + + align:start position:0% +right please don't forget to do that the + + + align:start position:0% +right please don't forget to do that the +deadline is also friday april the + + align:start position:0% +deadline is also friday april the + + + align:start position:0% +deadline is also friday april the +10th thank you thank you and part of + + align:start position:0% +10th thank you thank you and part of + + + align:start position:0% +10th thank you thank you and part of +that is just to + + align:start position:0% +that is just to + + + align:start position:0% +that is just to +really help you engage in this subject + + align:start position:0% +really help you engage in this subject + + + align:start position:0% +really help you engage in this subject +it doesn't + + align:start position:0% +it doesn't + + + align:start position:0% +it doesn't +to remain in myself doesn't matter which + + align:start position:0% +to remain in myself doesn't matter which + + + align:start position:0% +to remain in myself doesn't matter which +sector you pick + + align:start position:0% +sector you pick + + + align:start position:0% +sector you pick +or whether you choose to sort of write + + align:start position:0% +or whether you choose to sort of write + + + align:start position:0% +or whether you choose to sort of write +your paper from the perspective of + + align:start position:0% +your paper from the perspective of + + + align:start position:0% +your paper from the perspective of +incumbents to big tech or to a venture + + align:start position:0% +incumbents to big tech or to a venture + + + align:start position:0% +incumbents to big tech or to a venture +capitalist + + align:start position:0% +capitalist + + + align:start position:0% +capitalist +but it's really to help you sort of + + align:start position:0% +but it's really to help you sort of + + + align:start position:0% +but it's really to help you sort of +engage in the world of + + align:start position:0% +engage in the world of + + + align:start position:0% +engage in the world of +fintech that which we're studying and to + + align:start position:0% +fintech that which we're studying and to + + + align:start position:0% +fintech that which we're studying and to +pick one sector + + align:start position:0% +pick one sector + + + align:start position:0% +pick one sector +and are you taking it from the + + align:start position:0% +and are you taking it from the + + + align:start position:0% +and are you taking it from the +entrepreneurial strategy of the + + align:start position:0% +entrepreneurial strategy of the + + + align:start position:0% +entrepreneurial strategy of the +disruptor are you taking it from + + align:start position:0% +disruptor are you taking it from + + + align:start position:0% +disruptor are you taking it from +a big firm either incumbent or tech + + align:start position:0% +a big firm either incumbent or tech + + + align:start position:0% +a big firm either incumbent or tech +firm's perspective + + align:start position:0% +firm's perspective + + + align:start position:0% +firm's perspective +in this regard so + + align:start position:0% +in this regard so + + + align:start position:0% +in this regard so +as i said we're going to talk a little + + align:start position:0% +as i said we're going to talk a little + + + align:start position:0% +as i said we're going to talk a little +bit about application program interface + + align:start position:0% +bit about application program interface + + + align:start position:0% +bit about application program interface +how this fits into the history of + + align:start position:0% +how this fits into the history of + + + align:start position:0% +how this fits into the history of +finance + + align:start position:0% +finance + + + align:start position:0% +finance +deep deeper dive and open api and open + + align:start position:0% +deep deeper dive and open api and open + + + align:start position:0% +deep deeper dive and open api and open +banking + + align:start position:0% +banking + + + align:start position:0% +banking +uh you were all asked to prepare and + + align:start position:0% +uh you were all asked to prepare and + + + align:start position:0% +uh you were all asked to prepare and +sort of look at the bank of + + align:start position:0% +sort of look at the bank of + + + align:start position:0% +sort of look at the bank of +international settlement + + align:start position:0% +international settlement + + + align:start position:0% +international settlement +reports so i'm not going to dive in i'm + + align:start position:0% +reports so i'm not going to dive in i'm + + + align:start position:0% +reports so i'm not going to dive in i'm +going to hopefully assume that + + align:start position:0% +going to hopefully assume that + + + align:start position:0% +going to hopefully assume that +you've had a chance to engage with that + + align:start position:0% +you've had a chance to engage with that + + + align:start position:0% +you've had a chance to engage with that +and then talk a little bit also about + + align:start position:0% +and then talk a little bit also about + + + align:start position:0% +and then talk a little bit also about +data aggregators + + align:start position:0% +data aggregators + + + align:start position:0% +data aggregators +and a movement amongst many large + + align:start position:0% +and a movement amongst many large + + + align:start position:0% +and a movement amongst many large +financial firms to have + + align:start position:0% +financial firms to have + + + align:start position:0% +financial firms to have +a standard setting group the financial + + align:start position:0% +a standard setting group the financial + + + align:start position:0% +a standard setting group the financial +data exchange on open api + + align:start position:0% +data exchange on open api + + + align:start position:0% +data exchange on open api +on apis and then try to close out a + + align:start position:0% +on apis and then try to close out a + + + align:start position:0% +on apis and then try to close out a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +on robotic process automation so a lot + + align:start position:0% +on robotic process automation so a lot + + + align:start position:0% +on robotic process automation so a lot +to cover + + align:start position:0% +to cover + + + align:start position:0% +to cover +but i think we'll we'll keep it going + + align:start position:0% +but i think we'll we'll keep it going + + + align:start position:0% +but i think we'll we'll keep it going +and i ask again + + align:start position:0% +and i ask again + + + align:start position:0% +and i ask again +use the participate button to raise the + + align:start position:0% +use the participate button to raise the + + + align:start position:0% +use the participate button to raise the +blue hands + + align:start position:0% +blue hands + + + align:start position:0% +blue hands +use the chat function uh romaine's going + + align:start position:0% +use the chat function uh romaine's going + + + align:start position:0% +use the chat function uh romaine's going +to keep interrupting me + + align:start position:0% +to keep interrupting me + + + align:start position:0% +to keep interrupting me +and we'll have hopefully a good uh + + align:start position:0% +and we'll have hopefully a good uh + + + align:start position:0% +and we'll have hopefully a good uh +session together + + align:start position:0% +session together + + + align:start position:0% +session together +so the the the readings again bank of + + align:start position:0% +so the the the readings again bank of + + + align:start position:0% +so the the the readings again bank of +international settlement this consortium + + align:start position:0% +international settlement this consortium + + + align:start position:0% +international settlement this consortium +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +60 or so central banks around the globe + + align:start position:0% +60 or so central banks around the globe + + + align:start position:0% +60 or so central banks around the globe +stands up reports and studies from time + + align:start position:0% +stands up reports and studies from time + + + align:start position:0% +stands up reports and studies from time +to time one + + align:start position:0% +to time one + + + align:start position:0% +to time one +new challenges that they're saying so + + align:start position:0% +new challenges that they're saying so + + + align:start position:0% +new challenges that they're saying so +just that they + + align:start position:0% +just that they + + + align:start position:0% +just that they +pick this topic to write a report that + + align:start position:0% +pick this topic to write a report that + + + align:start position:0% +pick this topic to write a report that +came out this past november of 2019 + + align:start position:0% +came out this past november of 2019 + + + align:start position:0% +came out this past november of 2019 +is indicative right there in and of + + align:start position:0% +is indicative right there in and of + + + align:start position:0% +is indicative right there in and of +itself + + align:start position:0% +itself + + + align:start position:0% +itself +that it's a movement around the globe + + align:start position:0% +that it's a movement around the globe + + + align:start position:0% +that it's a movement around the globe +that they thought they needed to study + + align:start position:0% +that they thought they needed to study + + + align:start position:0% +that they thought they needed to study +and an important uh aspect i picked one + + align:start position:0% +and an important uh aspect i picked one + + + align:start position:0% +and an important uh aspect i picked one +article out of the many articles that + + align:start position:0% +article out of the many articles that + + + align:start position:0% +article out of the many articles that +you can grab + + align:start position:0% +you can grab + + + align:start position:0% +you can grab +off the internet about fintech for the + + align:start position:0% +off the internet about fintech for the + + + align:start position:0% +off the internet about fintech for the +next decade and this was one article + + align:start position:0% +next decade and this was one article + + + align:start position:0% +next decade and this was one article +that i thought was relevant because it + + align:start position:0% +that i thought was relevant because it + + + align:start position:0% +that i thought was relevant because it +really did + + align:start position:0% +really did + + + align:start position:0% +really did +also include this concept of of the + + align:start position:0% +also include this concept of of the + + + align:start position:0% +also include this concept of of the +interface the customer user interface + + align:start position:0% +interface the customer user interface + + + align:start position:0% +interface the customer user interface +and what was going on with regard to + + align:start position:0% +and what was going on with regard to + + + align:start position:0% +and what was going on with regard to +apis and then one article again + + align:start position:0% +apis and then one article again + + + align:start position:0% +apis and then one article again +just to give you a sort of a a primer on + + align:start position:0% +just to give you a sort of a a primer on + + + align:start position:0% +just to give you a sort of a a primer on +robotic process automation that + + align:start position:0% +robotic process automation that + + + align:start position:0% +robotic process automation that +i think is relevant as well + + align:start position:0% +i think is relevant as well + + + align:start position:0% +i think is relevant as well +um so + + align:start position:0% + + + + align:start position:0% + +again just if anybody wants to give a + + align:start position:0% +again just if anybody wants to give a + + + align:start position:0% +again just if anybody wants to give a +little short brief as to + + align:start position:0% +little short brief as to + + + align:start position:0% +little short brief as to +what are the major trends on the + + align:start position:0% +what are the major trends on the + + + align:start position:0% +what are the major trends on the +marketing side + + align:start position:0% +marketing side + + + align:start position:0% +marketing side +that's affecting financial services + + align:start position:0% +that's affecting financial services + + + align:start position:0% +that's affecting financial services +right now and we can go broader than api + + align:start position:0% +right now and we can go broader than api + + + align:start position:0% +right now and we can go broader than api +of course but uh romaine anybody want to + + align:start position:0% +of course but uh romaine anybody want to + + + align:start position:0% +of course but uh romaine anybody want to +sort of contribute now let's see who + + align:start position:0% +sort of contribute now let's see who + + + align:start position:0% +sort of contribute now let's see who +will be our first volunteer of the day + + align:start position:0% + + + + align:start position:0% + +michael + + align:start position:0% + + + + align:start position:0% + +um not sure if this is exactly marketing + + align:start position:0% +um not sure if this is exactly marketing + + + align:start position:0% +um not sure if this is exactly marketing +side but + + align:start position:0% +side but + + + align:start position:0% +side but +um i think customer processes may be + + align:start position:0% +um i think customer processes may be + + + align:start position:0% +um i think customer processes may be +more + + align:start position:0% +more + + + align:start position:0% +more +out of trust in connecting + + align:start position:0% +out of trust in connecting + + + align:start position:0% +out of trust in connecting +your personal data to a third party i'm + + align:start position:0% +your personal data to a third party i'm + + + align:start position:0% +your personal data to a third party i'm +thinking something like + + align:start position:0% +thinking something like + + + align:start position:0% +thinking something like +into it like mint.com where i have my + + align:start position:0% +into it like mint.com where i have my + + + align:start position:0% +into it like mint.com where i have my +bank account i can + + align:start position:0% +bank account i can + + + align:start position:0% +bank account i can +connect and feel comfortable giving that + + align:start position:0% +connect and feel comfortable giving that + + + align:start position:0% +connect and feel comfortable giving that +information to + + align:start position:0% +information to + + + align:start position:0% +information to +a site that's not necessarily my bank or + + align:start position:0% +a site that's not necessarily my bank or + + + align:start position:0% +a site that's not necessarily my bank or +my credit card + + align:start position:0% +my credit card + + + align:start position:0% +my credit card +absolutely absolutely so one of the + + align:start position:0% +absolutely absolutely so one of the + + + align:start position:0% +absolutely absolutely so one of the +major changes and this is + + align:start position:0% +major changes and this is + + + align:start position:0% +major changes and this is +this has been a number of years as + + align:start position:0% +this has been a number of years as + + + align:start position:0% +this has been a number of years as +companies like mint and others + + align:start position:0% +companies like mint and others + + + align:start position:0% +companies like mint and others +well you'll give your data to a company + + align:start position:0% +well you'll give your data to a company + + + align:start position:0% +well you'll give your data to a company +that you've + + align:start position:0% +that you've + + + align:start position:0% +that you've +personally never met a human being if + + align:start position:0% +personally never met a human being if + + + align:start position:0% +personally never met a human being if +you've downloaded an + + align:start position:0% +you've downloaded an + + + align:start position:0% +you've downloaded an +app and you're giving your data to that + + align:start position:0% +app and you're giving your data to that + + + align:start position:0% +app and you're giving your data to that +company to give you advice + + align:start position:0% +company to give you advice + + + align:start position:0% +company to give you advice +or to give you a better rate have you + + align:start position:0% +or to give you a better rate have you + + + align:start position:0% +or to give you a better rate have you +used menta by the way + + align:start position:0% +used menta by the way + + + align:start position:0% +used menta by the way +and do you mind just saying what what + + align:start position:0% +and do you mind just saying what what + + + align:start position:0% +and do you mind just saying what what +product were you shopping for or what + + align:start position:0% +product were you shopping for or what + + + align:start position:0% +product were you shopping for or what +service were you looking for + + align:start position:0% +service were you looking for + + + align:start position:0% +service were you looking for +i was just trying to track my spending + + align:start position:0% +i was just trying to track my spending + + + align:start position:0% +i was just trying to track my spending +because i was spending way too much + + align:start position:0% +because i was spending way too much + + + align:start position:0% +because i was spending way too much +all right so there there are also sites + + align:start position:0% +all right so there there are also sites + + + align:start position:0% +all right so there there are also sites +where it can help you + + align:start position:0% +where it can help you + + + align:start position:0% +where it can help you +keep your personal budget if you wish + + align:start position:0% +keep your personal budget if you wish + + + align:start position:0% +keep your personal budget if you wish +personal uh accounting and so forth and + + align:start position:0% +personal uh accounting and so forth and + + + align:start position:0% +personal uh accounting and so forth and +you give them permission + + align:start position:0% +you give them permission + + + align:start position:0% +you give them permission +to look into your bank account but this + + align:start position:0% +to look into your bank account but this + + + align:start position:0% +to look into your bank account but this +trend + + align:start position:0% +trend + + + align:start position:0% +trend +of using and there are many competitors + + align:start position:0% +of using and there are many competitors + + + align:start position:0% +of using and there are many competitors +to meant that we'll dive into + + align:start position:0% +to meant that we'll dive into + + + align:start position:0% +to meant that we'll dive into +in the next couple weeks but their many + + align:start position:0% +in the next couple weeks but their many + + + align:start position:0% +in the next couple weeks but their many +competitors + + align:start position:0% +competitors + + + align:start position:0% +competitors +is basically saying all right i am going + + align:start position:0% +is basically saying all right i am going + + + align:start position:0% +is basically saying all right i am going +to permission + + align:start position:0% +to permission + + + align:start position:0% +to permission +a website a data service provider + + align:start position:0% +a website a data service provider + + + align:start position:0% +a website a data service provider +fintech company i'm going to permission + + align:start position:0% +fintech company i'm going to permission + + + align:start position:0% +fintech company i'm going to permission +them + + align:start position:0% +them + + + align:start position:0% +them +to look inside my bank account + + align:start position:0% +to look inside my bank account + + + align:start position:0% +to look inside my bank account +i have to give them my password and my + + align:start position:0% +i have to give them my password and my + + + align:start position:0% +i have to give them my password and my +username in some way + + align:start position:0% +username in some way + + + align:start position:0% +username in some way +and have them linked in big change + + align:start position:0% +and have them linked in big change + + + align:start position:0% +and have them linked in big change +it takes away a little of the + + align:start position:0% +it takes away a little of the + + + align:start position:0% +it takes away a little of the +comparative advantage possibly + + align:start position:0% +comparative advantage possibly + + + align:start position:0% +comparative advantage possibly +of the big incumbents because you and i + + align:start position:0% +of the big incumbents because you and i + + + align:start position:0% +of the big incumbents because you and i +can give somebody else permission + + align:start position:0% +can give somebody else permission + + + align:start position:0% +can give somebody else permission +to go in and look at that data + + align:start position:0% +to go in and look at that data + + + align:start position:0% +to go in and look at that data +iqbal hi + + align:start position:0% +iqbal hi + + + align:start position:0% +iqbal hi +morning professor i just want to + + align:start position:0% +morning professor i just want to + + + align:start position:0% +morning professor i just want to +highlight that + + align:start position:0% +highlight that + + + align:start position:0% +highlight that +there's an avenue for um to + + align:start position:0% +there's an avenue for um to + + + align:start position:0% +there's an avenue for um to +market or to showcase financial services + + align:start position:0% +market or to showcase financial services + + + align:start position:0% +market or to showcase financial services +uh it's starting to be on uh lifestyle + + align:start position:0% +uh it's starting to be on uh lifestyle + + + align:start position:0% +uh it's starting to be on uh lifestyle +platform so + + align:start position:0% +platform so + + + align:start position:0% +platform so +if you look at for example uh alipay + + align:start position:0% +if you look at for example uh alipay + + + align:start position:0% +if you look at for example uh alipay +it's all about + + align:start position:0% +it's all about + + + align:start position:0% +it's all about +access to taobao or online shopping + + align:start position:0% +access to taobao or online shopping + + + align:start position:0% +access to taobao or online shopping +and which are paid access to its gaming + + align:start position:0% +and which are paid access to its gaming + + + align:start position:0% +and which are paid access to its gaming +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +there's a lot of this uh uh conflicting + + align:start position:0% +there's a lot of this uh uh conflicting + + + align:start position:0% +there's a lot of this uh uh conflicting +with the financial services and + + align:start position:0% +with the financial services and + + + align:start position:0% +with the financial services and +and uh and uh key services that people + + align:start position:0% +and uh and uh key services that people + + + align:start position:0% +and uh and uh key services that people +want + + align:start position:0% +want + + + align:start position:0% +want +so it's nothing new uh in fact now + + align:start position:0% +so it's nothing new uh in fact now + + + align:start position:0% +so it's nothing new uh in fact now +walmart and even now stock market has + + align:start position:0% +walmart and even now stock market has + + + align:start position:0% +walmart and even now stock market has +banks opened up within its grocery + + align:start position:0% +banks opened up within its grocery + + + align:start position:0% +banks opened up within its grocery +stores + + align:start position:0% +stores + + + align:start position:0% +stores +so uh i think there will be a trend that + + align:start position:0% +so uh i think there will be a trend that + + + align:start position:0% +so uh i think there will be a trend that +will be further + + align:start position:0% +will be further + + + align:start position:0% +will be further +and so what is raised is not know + + align:start position:0% +and so what is raised is not know + + + align:start position:0% +and so what is raised is not know +decades old that even big retailers + + align:start position:0% +decades old that even big retailers + + + align:start position:0% +decades old that even big retailers +bricks and mortar retailers thought well + + align:start position:0% +bricks and mortar retailers thought well + + + align:start position:0% +bricks and mortar retailers thought well +should we have a counter for you to do + + align:start position:0% +should we have a counter for you to do + + + align:start position:0% +should we have a counter for you to do +some finance should we embed finance + + align:start position:0% +some finance should we embed finance + + + align:start position:0% +some finance should we embed finance +into the retailing business + + align:start position:0% +into the retailing business + + + align:start position:0% +into the retailing business +with the trends with in-store and + + align:start position:0% +with the trends with in-store and + + + align:start position:0% +with the trends with in-store and +branded credit cards for decades + + align:start position:0% +branded credit cards for decades + + + align:start position:0% +branded credit cards for decades +but now online embedded finance + + align:start position:0% +but now online embedded finance + + + align:start position:0% +but now online embedded finance +inside of alipay which was mentioned + + align:start position:0% +inside of alipay which was mentioned + + + align:start position:0% +inside of alipay which was mentioned +just that in other companies + + align:start position:0% +just that in other companies + + + align:start position:0% +just that in other companies +to embed the financial aspects right in + + align:start position:0% +to embed the financial aspects right in + + + align:start position:0% +to embed the financial aspects right in +their product offerings + + align:start position:0% +their product offerings + + + align:start position:0% +their product offerings +and some of that embedded finance is an + + align:start position:0% +and some of that embedded finance is an + + + align:start position:0% +and some of that embedded finance is an +amazon + + align:start position:0% +amazon + + + align:start position:0% +amazon +credit card or an alipay payment + + align:start position:0% +credit card or an alipay payment + + + align:start position:0% +credit card or an alipay payment +mechanism + + align:start position:0% +mechanism + + + align:start position:0% +mechanism +some of the embedded finance can even be + + align:start position:0% +some of the embedded finance can even be + + + align:start position:0% +some of the embedded finance can even be +that if + + align:start position:0% +that if + + + align:start position:0% +that if +you're buying a mattress from casper i + + align:start position:0% +you're buying a mattress from casper i + + + align:start position:0% +you're buying a mattress from casper i +think i may have referenced this already + + align:start position:0% +think i may have referenced this already + + + align:start position:0% +think i may have referenced this already +but if you're buying a mattress from + + align:start position:0% +but if you're buying a mattress from + + + align:start position:0% +but if you're buying a mattress from +casper online + + align:start position:0% +casper online + + + align:start position:0% +casper online +that they might offer what's called + + align:start position:0% +that they might offer what's called + + + align:start position:0% +that they might offer what's called +point-of-sale + + align:start position:0% +point-of-sale + + + align:start position:0% +point-of-sale +financing now you and i don't think of + + align:start position:0% +financing now you and i don't think of + + + align:start position:0% +financing now you and i don't think of +it that way they just say you can pay + + align:start position:0% +it that way they just say you can pay + + + align:start position:0% +it that way they just say you can pay +over four + + align:start position:0% +over four + + + align:start position:0% +over four +installments but in fact they're lending + + align:start position:0% +installments but in fact they're lending + + + align:start position:0% +installments but in fact they're lending +you money for those four installments + + align:start position:0% +you money for those four installments + + + align:start position:0% +you money for those four installments +and it's embedded right in the product + + align:start position:0% +and it's embedded right in the product + + + align:start position:0% +and it's embedded right in the product +and uber and lyft actually embed + + align:start position:0% +and uber and lyft actually embed + + + align:start position:0% +and uber and lyft actually embed +some finance right in their app + + align:start position:0% +some finance right in their app + + + align:start position:0% +some finance right in their app +now they build it on top of credit card + + align:start position:0% +now they build it on top of credit card + + + align:start position:0% +now they build it on top of credit card +companies but they could choose to build + + align:start position:0% +companies but they could choose to build + + + align:start position:0% +companies but they could choose to build +it on top of their + + align:start position:0% +it on top of their + + + align:start position:0% +it on top of their +own sort of financing mechanism with + + align:start position:0% +own sort of financing mechanism with + + + align:start position:0% +own sort of financing mechanism with +their drivers and the like + + align:start position:0% +their drivers and the like + + + align:start position:0% +their drivers and the like +so big change embedded finance + + align:start position:0% +so big change embedded finance + + + align:start position:0% +so big change embedded finance +multi decades incoming but now it's + + align:start position:0% +multi decades incoming but now it's + + + align:start position:0% +multi decades incoming but now it's +embedded finance in a technological way + + align:start position:0% +embedded finance in a technological way + + + align:start position:0% +embedded finance in a technological way +that + + align:start position:0% +that + + + align:start position:0% +that +it looks seamless to the user or can + + align:start position:0% +it looks seamless to the user or can + + + align:start position:0% +it looks seamless to the user or can +look seamless + + align:start position:0% + + + + align:start position:0% + +um nikita other piece that i thought was + + align:start position:0% +um nikita other piece that i thought was + + + align:start position:0% +um nikita other piece that i thought was +interesting was + + align:start position:0% +interesting was + + + align:start position:0% +interesting was +uh the articles talk about first the + + align:start position:0% +uh the articles talk about first the + + + align:start position:0% +uh the articles talk about first the +uncoupling of financial services so + + align:start position:0% +uncoupling of financial services so + + + align:start position:0% +uncoupling of financial services so +a lot of fintech incumbents like + + align:start position:0% +a lot of fintech incumbents like + + + align:start position:0% +a lot of fintech incumbents like +decouple the product offerings but then + + align:start position:0% +decouple the product offerings but then + + + align:start position:0% +decouple the product offerings but then +there's a resurgence of + + align:start position:0% +there's a resurgence of + + + align:start position:0% +there's a resurgence of +funding products again so when you work + + align:start position:0% +funding products again so when you work + + + align:start position:0% +funding products again so when you work +at wealthfront they started with just + + align:start position:0% +at wealthfront they started with just + + + align:start position:0% +at wealthfront they started with just +asset management but now they're + + align:start position:0% +asset management but now they're + + + align:start position:0% +asset management but now they're +offering cash management robinhood the + + align:start position:0% +offering cash management robinhood the + + + align:start position:0% +offering cash management robinhood the +same way with + + align:start position:0% +same way with + + + align:start position:0% +same way with +came up for trading but again they're + + align:start position:0% +came up for trading but again they're + + + align:start position:0% +came up for trading but again they're +trying to pivot to cash management so + + align:start position:0% +trying to pivot to cash management so + + + align:start position:0% +trying to pivot to cash management so +and they focus on various niche products + + align:start position:0% +and they focus on various niche products + + + align:start position:0% +and they focus on various niche products +to begin with but there seems to be + + align:start position:0% +to begin with but there seems to be + + + align:start position:0% +to begin with but there seems to be +bundling + + align:start position:0% +bundling + + + align:start position:0% +bundling +happening again right and i think this + + align:start position:0% +happening again right and i think this + + + align:start position:0% +happening again right and i think this +this + + align:start position:0% +this + + + align:start position:0% +this +unbundling and and rebundling happens in + + align:start position:0% +unbundling and and rebundling happens in + + + align:start position:0% +unbundling and and rebundling happens in +many industries + + align:start position:0% +many industries + + + align:start position:0% +many industries +uh some of the + + align:start position:0% +uh some of the + + + align:start position:0% +uh some of the +the proponents and the most optimistic + + align:start position:0% +the proponents and the most optimistic + + + align:start position:0% +the proponents and the most optimistic +side + + align:start position:0% +side + + + align:start position:0% +side +of financial technology say we can have + + align:start position:0% +of financial technology say we can have + + + align:start position:0% +of financial technology say we can have +a flattening of finance we can have a + + align:start position:0% +a flattening of finance we can have a + + + align:start position:0% +a flattening of finance we can have a +full + + align:start position:0% +full + + + align:start position:0% +full +unbundling where you can get each of + + align:start position:0% +unbundling where you can get each of + + + align:start position:0% +unbundling where you can get each of +your products separately + + align:start position:0% +your products separately + + + align:start position:0% +your products separately +and while the technology can and does + + align:start position:0% +and while the technology can and does + + + align:start position:0% +and while the technology can and does +facilitate that + + align:start position:0% +facilitate that + + + align:start position:0% +facilitate that +i think our tendencies in markets + + align:start position:0% +i think our tendencies in markets + + + align:start position:0% +i think our tendencies in markets +and as humans and our behavioral science + + align:start position:0% +and as humans and our behavioral science + + + align:start position:0% +and as humans and our behavioral science +tells us that bundling happens so + + align:start position:0% +tells us that bundling happens so + + + align:start position:0% +tells us that bundling happens so +even if this is transitional period of + + align:start position:0% +even if this is transitional period of + + + align:start position:0% +even if this is transitional period of +time even if this this + + align:start position:0% +time even if this this + + + align:start position:0% +time even if this this +late 20 teens and early 2020s + + align:start position:0% +late 20 teens and early 2020s + + + align:start position:0% +late 20 teens and early 2020s +allows for a lot of unbundling + + align:start position:0% +allows for a lot of unbundling + + + align:start position:0% +allows for a lot of unbundling +i believe that a lot of this will stay + + align:start position:0% +i believe that a lot of this will stay + + + align:start position:0% +i believe that a lot of this will stay +bundled and rebundled + + align:start position:0% +bundled and rebundled + + + align:start position:0% +bundled and rebundled +within particular websites particularly + + align:start position:0% +within particular websites particularly + + + align:start position:0% +within particular websites particularly +product offerings + + align:start position:0% +product offerings + + + align:start position:0% +product offerings +i don't know if leonore is trying to + + align:start position:0% +i don't know if leonore is trying to + + + align:start position:0% +i don't know if leonore is trying to +speak because your + + align:start position:0% +speak because your + + + align:start position:0% +speak because your +name's popping up here on the screen but + + align:start position:0% +name's popping up here on the screen but + + + align:start position:0% +name's popping up here on the screen but +if not + + align:start position:0% +if not + + + align:start position:0% +if not +how um how would open api initiatives + + align:start position:0% +how um how would open api initiatives + + + align:start position:0% +how um how would open api initiatives +influence all of this i've sort of said + + align:start position:0% +influence all of this i've sort of said + + + align:start position:0% +influence all of this i've sort of said +it a little bit myself but anybody want + + align:start position:0% +it a little bit myself but anybody want + + + align:start position:0% +it a little bit myself but anybody want +to + + align:start position:0% +to + + + align:start position:0% +to +chime in + + align:start position:0% +chime in + + + align:start position:0% +chime in +gita yeah i think um + + align:start position:0% +gita yeah i think um + + + align:start position:0% +gita yeah i think um +i'll speak from the incumbent side i + + align:start position:0% +i'll speak from the incumbent side i + + + align:start position:0% +i'll speak from the incumbent side i +think open apis have + + align:start position:0% +think open apis have + + + align:start position:0% +think open apis have +made it so easy from a banking + + align:start position:0% +made it so easy from a banking + + + align:start position:0% +made it so easy from a banking +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +terms of ability to + + align:start position:0% +terms of ability to + + + align:start position:0% +terms of ability to +track uh what is being accessed of + + align:start position:0% +track uh what is being accessed of + + + align:start position:0% +track uh what is being accessed of +customer data + + align:start position:0% +customer data + + + align:start position:0% +customer data +because before apis and before some of + + align:start position:0% +because before apis and before some of + + + align:start position:0% +because before apis and before some of +the standards like oauth and oidc + + align:start position:0% +the standards like oauth and oidc + + + align:start position:0% +the standards like oauth and oidc +they were pretty much uh dependent on + + align:start position:0% +they were pretty much uh dependent on + + + align:start position:0% +they were pretty much uh dependent on +screen scraping + + align:start position:0% +screen scraping + + + align:start position:0% +screen scraping +and it was very difficult for us to + + align:start position:0% +and it was very difficult for us to + + + align:start position:0% +and it was very difficult for us to +track + + align:start position:0% +track + + + align:start position:0% +track +and the customers pretty much gave their + + align:start position:0% +and the customers pretty much gave their + + + align:start position:0% +and the customers pretty much gave their +user id and password to these vendors + + align:start position:0% +user id and password to these vendors + + + align:start position:0% +user id and password to these vendors +and they could pretty much log in and + + align:start position:0% +and they could pretty much log in and + + + align:start position:0% +and they could pretty much log in and +screen scrape anything and we won't even + + align:start position:0% +screen scrape anything and we won't even + + + align:start position:0% +screen scrape anything and we won't even +know + + align:start position:0% +know + + + align:start position:0% +know +yeah so api so you're saying from the + + align:start position:0% +yeah so api so you're saying from the + + + align:start position:0% +yeah so api so you're saying from the +incumbent side from the big financial + + align:start position:0% +incumbent side from the big financial + + + align:start position:0% +incumbent side from the big financial +firm side + + align:start position:0% +firm side + + + align:start position:0% +firm side +these new startups the mints of the + + align:start position:0% +these new startups the mints of the + + + align:start position:0% +these new startups the mints of the +world so to speak + + align:start position:0% +world so to speak + + + align:start position:0% +world so to speak +we're able to get folks usernames and + + align:start position:0% +we're able to get folks usernames and + + + align:start position:0% +we're able to get folks usernames and +passwords + + align:start position:0% +passwords + + + align:start position:0% +passwords +and come into the incumbent systems + + align:start position:0% +and come into the incumbent systems + + + align:start position:0% +and come into the incumbent systems +and grab the data through a method + + align:start position:0% +and grab the data through a method + + + align:start position:0% +and grab the data through a method +called screen scraping + + align:start position:0% +called screen scraping + + + align:start position:0% +called screen scraping +or even through robotic process + + align:start position:0% +or even through robotic process + + + align:start position:0% +or even through robotic process +automation which we're going to chat + + align:start position:0% +automation which we're going to chat + + + align:start position:0% +automation which we're going to chat +about + + align:start position:0% +about + + + align:start position:0% +about +yeah and you're saying you feel from an + + align:start position:0% +yeah and you're saying you feel from an + + + align:start position:0% +yeah and you're saying you feel from an +incumbent side + + align:start position:0% +incumbent side + + + align:start position:0% +incumbent side +it's better to manage all of that + + align:start position:0% +it's better to manage all of that + + + align:start position:0% +it's better to manage all of that +those interfaces which could be + + align:start position:0% +those interfaces which could be + + + align:start position:0% +those interfaces which could be +disruptive + + align:start position:0% +disruptive + + + align:start position:0% +disruptive +you'd have more more awareness and more + + align:start position:0% +you'd have more more awareness and more + + + align:start position:0% +you'd have more more awareness and more +security around that + + align:start position:0% +security around that + + + align:start position:0% +security around that +interface correct + + align:start position:0% + + + + align:start position:0% + +and how's it influence it from the + + align:start position:0% +and how's it influence it from the + + + align:start position:0% +and how's it influence it from the +consumer side anybody want to throw an + + align:start position:0% +consumer side anybody want to throw an + + + align:start position:0% +consumer side anybody want to throw an +idea in from the + + align:start position:0% +idea in from the + + + align:start position:0% +idea in from the +customer side i agree with what gita's + + align:start position:0% +customer side i agree with what gita's + + + align:start position:0% +customer side i agree with what gita's +saying + + align:start position:0% +saying + + + align:start position:0% +saying +so i'm not sure it will be related but + + align:start position:0% +so i'm not sure it will be related but + + + align:start position:0% +so i'm not sure it will be related but +yi had his handle + + align:start position:0% +yi had his handle + + + align:start position:0% +yi had his handle +sure yeah i think the benefits is more + + align:start position:0% +sure yeah i think the benefits is more + + + align:start position:0% +sure yeah i think the benefits is more +for the fiend type company rather than + + align:start position:0% +for the fiend type company rather than + + + align:start position:0% +for the fiend type company rather than +the in cubans because + + align:start position:0% +the in cubans because + + + align:start position:0% +the in cubans because +uh it basically lowered the end uh the + + align:start position:0% +uh it basically lowered the end uh the + + + align:start position:0% +uh it basically lowered the end uh the +entry barriers + + align:start position:0% +entry barriers + + + align:start position:0% +entry barriers +so i guess like from the the consumer + + align:start position:0% +so i guess like from the the consumer + + + align:start position:0% +so i guess like from the the consumer +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +now you have many more options uh + + align:start position:0% +now you have many more options uh + + + align:start position:0% +now you have many more options uh +previously you you can only work with + + align:start position:0% +previously you you can only work with + + + align:start position:0% +previously you you can only work with +those like + + align:start position:0% +those like + + + align:start position:0% +those like +large banks but now you can work with + + align:start position:0% +large banks but now you can work with + + + align:start position:0% +large banks but now you can work with +like many more companies + + align:start position:0% +like many more companies + + + align:start position:0% +like many more companies +that are there so it's more the market + + align:start position:0% +that are there so it's more the market + + + align:start position:0% +that are there so it's more the market +is more competitive + + align:start position:0% +is more competitive + + + align:start position:0% +is more competitive +basically so if i permission a company + + align:start position:0% +basically so if i permission a company + + + align:start position:0% +basically so if i permission a company +like + + align:start position:0% +like + + + align:start position:0% +like +mint mint can give me advice around my + + align:start position:0% +mint mint can give me advice around my + + + align:start position:0% +mint mint can give me advice around my +cash flow management if i permission a + + align:start position:0% +cash flow management if i permission a + + + align:start position:0% +cash flow management if i permission a +company like + + align:start position:0% +company like + + + align:start position:0% +company like +sofi which is frankly competing with the + + align:start position:0% +sofi which is frankly competing with the + + + align:start position:0% +sofi which is frankly competing with the +banks competing with + + align:start position:0% +banks competing with + + + align:start position:0% +banks competing with +with lending products but if i + + align:start position:0% +with lending products but if i + + + align:start position:0% +with lending products but if i +permission so far to see my accounts + + align:start position:0% +permission so far to see my accounts + + + align:start position:0% +permission so far to see my accounts +then i get more options as a consumer so + + align:start position:0% +then i get more options as a consumer so + + + align:start position:0% +then i get more options as a consumer so +if i might compete with the banks but + + align:start position:0% +if i might compete with the banks but + + + align:start position:0% +if i might compete with the banks but +also + + align:start position:0% +also + + + align:start position:0% +also +give me a better user interface user + + align:start position:0% +give me a better user interface user + + + align:start position:0% +give me a better user interface user +experience as well + + align:start position:0% +experience as well + + + align:start position:0% +experience as well +so it's far broadened out the the world + + align:start position:0% +so it's far broadened out the the world + + + align:start position:0% +so it's far broadened out the the world +for the consumers + + align:start position:0% +for the consumers + + + align:start position:0% +for the consumers +and then i i put a couple of readings in + + align:start position:0% +and then i i put a couple of readings in + + + align:start position:0% +and then i i put a couple of readings in +about robotic process automation + + align:start position:0% +about robotic process automation + + + align:start position:0% +about robotic process automation +and screen scraping gita's already + + align:start position:0% +and screen scraping gita's already + + + align:start position:0% +and screen scraping gita's already +raised uh this + + align:start position:0% +raised uh this + + + align:start position:0% +raised uh this +uh a bit and it's being used + + align:start position:0% +uh a bit and it's being used + + + align:start position:0% +uh a bit and it's being used +it's it's also being used by the + + align:start position:0% +it's it's also being used by the + + + align:start position:0% +it's it's also being used by the +financial sector so + + align:start position:0% +financial sector so + + + align:start position:0% +financial sector so +what anybody want to add how how you + + align:start position:0% +what anybody want to add how how you + + + align:start position:0% +what anybody want to add how how you +think about + + align:start position:0% +think about + + + align:start position:0% +think about +robotic process automation in a positive + + align:start position:0% +robotic process automation in a positive + + + align:start position:0% +robotic process automation in a positive +way in a way + + align:start position:0% +way in a way + + + align:start position:0% +way in a way +from from the incumbents and the + + align:start position:0% +from from the incumbents and the + + + align:start position:0% +from from the incumbents and the +financial firms how they're using it + + align:start position:0% +financial firms how they're using it + + + align:start position:0% +financial firms how they're using it +it's certainly also being used by the + + align:start position:0% +it's certainly also being used by the + + + align:start position:0% +it's certainly also being used by the +disruptors + + align:start position:0% +disruptors + + + align:start position:0% +disruptors +trying to get information out of the + + align:start position:0% +trying to get information out of the + + + align:start position:0% +trying to get information out of the +incumbents + + align:start position:0% +incumbents + + + align:start position:0% +incumbents +they're using it as sort of an automated + + align:start position:0% +they're using it as sort of an automated + + + align:start position:0% +they're using it as sort of an automated +screen scraping to grab + + align:start position:0% +screen scraping to grab + + + align:start position:0% +screen scraping to grab +information from the incumbents but does + + align:start position:0% +information from the incumbents but does + + + align:start position:0% +information from the incumbents but does +anybody want to sort of say how maybe + + align:start position:0% +anybody want to sort of say how maybe + + + align:start position:0% +anybody want to sort of say how maybe +the + + align:start position:0% +the + + + align:start position:0% +the +incumbents are using it in their + + align:start position:0% +incumbents are using it in their + + + align:start position:0% +incumbents are using it in their +business models + + align:start position:0% + + + + align:start position:0% + +hi professor yeah i just have um + + align:start position:0% + + + + align:start position:0% + +i mean a question about the apis i don't + + align:start position:0% +i mean a question about the apis i don't + + + align:start position:0% +i mean a question about the apis i don't +actually + + align:start position:0% +actually + + + align:start position:0% +actually +talk to understand what are the i mean + + align:start position:0% +talk to understand what are the i mean + + + align:start position:0% +talk to understand what are the i mean +is it like an operating system + + align:start position:0% +is it like an operating system + + + align:start position:0% +is it like an operating system +i mean what's an api exactly i'll try to + + align:start position:0% +i mean what's an api exactly i'll try to + + + align:start position:0% +i mean what's an api exactly i'll try to +google it but i had not quite + + align:start position:0% +google it but i had not quite + + + align:start position:0% +google it but i had not quite +understood it so i'm gonna i'm gonna + + align:start position:0% +understood it so i'm gonna i'm gonna + + + align:start position:0% +understood it so i'm gonna i'm gonna +dive into can i can i hold that hassan + + align:start position:0% +dive into can i can i hold that hassan + + + align:start position:0% +dive into can i can i hold that hassan +just for a minute because i'm gonna dive + + align:start position:0% +just for a minute because i'm gonna dive + + + align:start position:0% +just for a minute because i'm gonna dive +into it in the + + align:start position:0% +into it in the + + + align:start position:0% +into it in the +next six minutes but fundamentally + + align:start position:0% +next six minutes but fundamentally + + + align:start position:0% +next six minutes but fundamentally +fundamentally an application program + + align:start position:0% +fundamentally an application program + + + align:start position:0% +fundamentally an application program +interface is a is a method that two + + align:start position:0% +interface is a is a method that two + + + align:start position:0% +interface is a is a method that two +computers can speak to + + align:start position:0% +computers can speak to + + + align:start position:0% +computers can speak to +and the traditional way in the old way + + align:start position:0% +and the traditional way in the old way + + + align:start position:0% +and the traditional way in the old way +was just + + align:start position:0% +was just + + + align:start position:0% +was just +how one system can go in + + align:start position:0% +how one system can go in + + + align:start position:0% +how one system can go in +and get information get objects + + align:start position:0% +and get information get objects + + + align:start position:0% +and get information get objects +out of the other system and it and then + + align:start position:0% +out of the other system and it and then + + + align:start position:0% +out of the other system and it and then +we'll we'll do a little + + align:start position:0% +we'll we'll do a little + + + align:start position:0% +we'll we'll do a little +uh cursory dive into what it looks like + + align:start position:0% +uh cursory dive into what it looks like + + + align:start position:0% +uh cursory dive into what it looks like +today because it's moved a lot from that + + align:start position:0% +today because it's moved a lot from that + + + align:start position:0% +today because it's moved a lot from that +traditional + + align:start position:0% +traditional + + + align:start position:0% +traditional +method uh on in a web-based api system + + align:start position:0% +method uh on in a web-based api system + + + align:start position:0% +method uh on in a web-based api system +uh you can actually sort of almost it + + align:start position:0% +uh you can actually sort of almost it + + + align:start position:0% +uh you can actually sort of almost it +feels like on your computer + + align:start position:0% +feels like on your computer + + + align:start position:0% +feels like on your computer +on your laptop so to speak that you're + + align:start position:0% +on your laptop so to speak that you're + + + align:start position:0% +on your laptop so to speak that you're +actually + + align:start position:0% +actually + + + align:start position:0% +actually +operating that system that's at a + + align:start position:0% +operating that system that's at a + + + align:start position:0% +operating that system that's at a +distance + + align:start position:0% +distance + + + align:start position:0% +distance +so you sort of think of it like it's not + + align:start position:0% +so you sort of think of it like it's not + + + align:start position:0% +so you sort of think of it like it's not +only just grabbing some data or + + align:start position:0% +only just grabbing some data or + + + align:start position:0% +only just grabbing some data or +objects or records but it's actually + + align:start position:0% +objects or records but it's actually + + + align:start position:0% +objects or records but it's actually +sort of grabbing some + + align:start position:0% +sort of grabbing some + + + align:start position:0% +sort of grabbing some +uh uh application as if + + align:start position:0% +uh uh application as if + + + align:start position:0% +uh uh application as if +it feels like you're really operating it + + align:start position:0% +it feels like you're really operating it + + + align:start position:0% +it feels like you're really operating it +on your system + + align:start position:0% +on your system + + + align:start position:0% +on your system +open api open api is this conceptual + + align:start position:0% +open api open api is this conceptual + + + align:start position:0% +open api open api is this conceptual +framework + + align:start position:0% +framework + + + align:start position:0% +framework +that it's a public interface rather than + + align:start position:0% +that it's a public interface rather than + + + align:start position:0% +that it's a public interface rather than +a private interface + + align:start position:0% +a private interface + + + align:start position:0% +a private interface +and if you think that you could you + + align:start position:0% +and if you think that you could you + + + align:start position:0% +and if you think that you could you +could literally have just a restricted + + align:start position:0% +could literally have just a restricted + + + align:start position:0% +could literally have just a restricted +private interface + + align:start position:0% +private interface + + + align:start position:0% +private interface +that you give one other computer whether + + align:start position:0% +that you give one other computer whether + + + align:start position:0% +that you give one other computer whether +it's an affiliate of yours or a customer + + align:start position:0% +it's an affiliate of yours or a customer + + + align:start position:0% +it's an affiliate of yours or a customer +of yours + + align:start position:0% +of yours + + + align:start position:0% +of yours +a contractual private interface + + align:start position:0% +a contractual private interface + + + align:start position:0% +a contractual private interface +to do that which they wish to do + + align:start position:0% +to do that which they wish to do + + + align:start position:0% +to do that which they wish to do +or is it a public interface where + + align:start position:0% +or is it a public interface where + + + align:start position:0% +or is it a public interface where +broadly it can be + + align:start position:0% +broadly it can be + + + align:start position:0% +broadly it can be +uh interfaced and so + + align:start position:0% +uh interfaced and so + + + align:start position:0% +uh interfaced and so +that's sort of the thumbnail but let me + + align:start position:0% +that's sort of the thumbnail but let me + + + align:start position:0% +that's sort of the thumbnail but let me +let me sort of develop that a little bit + + align:start position:0% +let me sort of develop that a little bit + + + align:start position:0% +let me sort of develop that a little bit +more + + align:start position:0% +more + + + align:start position:0% +more +over the next half hour does that help + + align:start position:0% +over the next half hour does that help + + + align:start position:0% +over the next half hour does that help +yeah i did thank you very much so to + + align:start position:0% +yeah i did thank you very much so to + + + align:start position:0% +yeah i did thank you very much so to +answer your question gary we have ivy + + align:start position:0% +answer your question gary we have ivy + + + align:start position:0% +answer your question gary we have ivy +and then andrea + + align:start position:0% +and then andrea + + + align:start position:0% +and then andrea +okay and then i'll move away thanks ivy + + align:start position:0% + + + + align:start position:0% + +yeah i just wanted to answer the + + align:start position:0% +yeah i just wanted to answer the + + + align:start position:0% +yeah i just wanted to answer the +question cause i thought the medium + + align:start position:0% +question cause i thought the medium + + + align:start position:0% +question cause i thought the medium +article + + align:start position:0% +article + + + align:start position:0% +article +did a good job of talking about you know + + align:start position:0% +did a good job of talking about you know + + + align:start position:0% +did a good job of talking about you know +the different ways that + + align:start position:0% +the different ways that + + + align:start position:0% +the different ways that +um are banking use cases um and i've + + align:start position:0% +um are banking use cases um and i've + + + align:start position:0% +um are banking use cases um and i've +actually + + align:start position:0% +actually + + + align:start position:0% +actually +like gone through a lot in terms of just + + align:start position:0% +like gone through a lot in terms of just + + + align:start position:0% +like gone through a lot in terms of just +on the banking side like actually having + + align:start position:0% +on the banking side like actually having + + + align:start position:0% +on the banking side like actually having +to do + + align:start position:0% +to do + + + align:start position:0% +to do +customer onboarding kyc and um + + align:start position:0% +customer onboarding kyc and um + + + align:start position:0% +customer onboarding kyc and um +like we actually have what's called like + + align:start position:0% +like we actually have what's called like + + + align:start position:0% +like we actually have what's called like +um kyc analyst so all of this + + align:start position:0% +um kyc analyst so all of this + + + align:start position:0% +um kyc analyst so all of this +is actually very very manual typically + + align:start position:0% +is actually very very manual typically + + + align:start position:0% +is actually very very manual typically +and + + align:start position:0% +and + + + align:start position:0% +and +going through compliance checks like + + align:start position:0% +going through compliance checks like + + + align:start position:0% +going through compliance checks like +we'll be + + align:start position:0% +we'll be + + + align:start position:0% +we'll be +working on a deal and at the very last + + align:start position:0% +working on a deal and at the very last + + + align:start position:0% +working on a deal and at the very last +minute it's like you can't get + + align:start position:0% +minute it's like you can't get + + + align:start position:0% +minute it's like you can't get +compliance checks through and + + align:start position:0% +compliance checks through and + + + align:start position:0% +compliance checks through and +it's usually a huge pain so i was + + align:start position:0% +it's usually a huge pain so i was + + + align:start position:0% +it's usually a huge pain so i was +excited to see + + align:start position:0% +excited to see + + + align:start position:0% +excited to see +that there could potentially change the + + align:start position:0% +that there could potentially change the + + + align:start position:0% +that there could potentially change the +system because it ends up + + align:start position:0% +system because it ends up + + + align:start position:0% +system because it ends up +being a huge headache for everyone um i + + align:start position:0% +being a huge headache for everyone um i + + + align:start position:0% +being a huge headache for everyone um i +think my question though is + + align:start position:0% +think my question though is + + + align:start position:0% +think my question though is +like when i read about this obviously it + + align:start position:0% +like when i read about this obviously it + + + align:start position:0% +like when i read about this obviously it +seems like i'm sure the technology + + align:start position:0% +seems like i'm sure the technology + + + align:start position:0% +seems like i'm sure the technology +is there but i i think about just like + + align:start position:0% +is there but i i think about just like + + + align:start position:0% +is there but i i think about just like +any bulge bracket banks like + + align:start position:0% +any bulge bracket banks like + + + align:start position:0% +any bulge bracket banks like +these are like their it infrastructure + + align:start position:0% +these are like their it infrastructure + + + align:start position:0% +these are like their it infrastructure +has been placed + + align:start position:0% +has been placed + + + align:start position:0% +has been placed +um you know for like 50 plus years and + + align:start position:0% +um you know for like 50 plus years and + + + align:start position:0% +um you know for like 50 plus years and +changing that so changing that + + align:start position:0% +changing that so changing that + + + align:start position:0% +changing that so changing that +technology is like removing one piece of + + align:start position:0% +technology is like removing one piece of + + + align:start position:0% +technology is like removing one piece of +a really big complicated puzzle + + align:start position:0% +a really big complicated puzzle + + + align:start position:0% +a really big complicated puzzle +so i almost like just like question um + + align:start position:0% +so i almost like just like question um + + + align:start position:0% +so i almost like just like question um +how feasible that is like + + align:start position:0% +how feasible that is like + + + align:start position:0% +how feasible that is like +the the article does a really good job + + align:start position:0% +the the article does a really good job + + + align:start position:0% +the the article does a really good job +of laying out + + align:start position:0% +of laying out + + + align:start position:0% +of laying out +um what we can actually automate but i + + align:start position:0% +um what we can actually automate but i + + + align:start position:0% +um what we can actually automate but i +guess i + + align:start position:0% +guess i + + + align:start position:0% +guess i +am a little bit skeptical as to like + + align:start position:0% +am a little bit skeptical as to like + + + align:start position:0% +am a little bit skeptical as to like +when that time will come + + align:start position:0% +when that time will come + + + align:start position:0% +when that time will come +and ivy may ask which banker what + + align:start position:0% +and ivy may ask which banker what + + + align:start position:0% +and ivy may ask which banker what +country you were working in that was + + align:start position:0% +country you were working in that was + + + align:start position:0% +country you were working in that was +doing i worked at merrell and um + + align:start position:0% +doing i worked at merrell and um + + + align:start position:0% +doing i worked at merrell and um +barclays + + align:start position:0% +barclays + + + align:start position:0% +barclays +so a merrill lynch or barclays you're + + align:start position:0% +so a merrill lynch or barclays you're + + + align:start position:0% +so a merrill lynch or barclays you're +right they're incumbents and they can + + align:start position:0% +right they're incumbents and they can + + + align:start position:0% +right they're incumbents and they can +automate many things the technology + + align:start position:0% +automate many things the technology + + + align:start position:0% +automate many things the technology +is an advance of what they are actually + + align:start position:0% +is an advance of what they are actually + + + align:start position:0% +is an advance of what they are actually +doing right now + + align:start position:0% +doing right now + + + align:start position:0% +doing right now +but robotic process automation can + + align:start position:0% +but robotic process automation can + + + align:start position:0% +but robotic process automation can +provide + + align:start position:0% +provide + + + align:start position:0% +provide +both incumbents and disruptors but the + + align:start position:0% +both incumbents and disruptors but the + + + align:start position:0% +both incumbents and disruptors but the +mayorals and barclays + + align:start position:0% +mayorals and barclays + + + align:start position:0% +mayorals and barclays +are already using it to some extent to + + align:start position:0% +are already using it to some extent to + + + align:start position:0% +are already using it to some extent to +automate that which + + align:start position:0% +automate that which + + + align:start position:0% +automate that which +humans are doing some of it as we'll + + align:start position:0% +humans are doing some of it as we'll + + + align:start position:0% +humans are doing some of it as we'll +dive into later on + + align:start position:0% +dive into later on + + + align:start position:0% +dive into later on +is about reading documents just + + align:start position:0% +is about reading documents just + + + align:start position:0% +is about reading documents just +literally + + align:start position:0% +literally + + + align:start position:0% +literally +object you know reading a document + + align:start position:0% +object you know reading a document + + + align:start position:0% +object you know reading a document +you could say that one form of robotic + + align:start position:0% +you could say that one form of robotic + + + align:start position:0% +you could say that one form of robotic +process automation that we already have + + align:start position:0% +process automation that we already have + + + align:start position:0% +process automation that we already have +is is when we can deposit a check by + + align:start position:0% +is is when we can deposit a check by + + + align:start position:0% +is is when we can deposit a check by +using our mobile phone + + align:start position:0% +using our mobile phone + + + align:start position:0% +using our mobile phone +now that also use natural language + + align:start position:0% +now that also use natural language + + + align:start position:0% +now that also use natural language +processing and it sort of reads that + + align:start position:0% +processing and it sort of reads that + + + align:start position:0% +processing and it sort of reads that +into the computer and so forth but + + align:start position:0% +into the computer and so forth but + + + align:start position:0% +into the computer and so forth but +you're absolutely right that each + + align:start position:0% +you're absolutely right that each + + + align:start position:0% +you're absolutely right that each +incumbent + + align:start position:0% +incumbent + + + align:start position:0% +incumbent +is dedicated to ensuring that if they're + + align:start position:0% +is dedicated to ensuring that if they're + + + align:start position:0% +is dedicated to ensuring that if they're +moving from a legacy system to a new + + align:start position:0% +moving from a legacy system to a new + + + align:start position:0% +moving from a legacy system to a new +system that they do that in in their own + + align:start position:0% +system that they do that in in their own + + + align:start position:0% +system that they do that in in their own +way so that it doesn't break in the + + align:start position:0% +way so that it doesn't break in the + + + align:start position:0% +way so that it doesn't break in the +middle + + align:start position:0% +middle + + + align:start position:0% +middle +and that they actually do save money and + + align:start position:0% +and that they actually do save money and + + + align:start position:0% +and that they actually do save money and +they have to schedule it + + align:start position:0% +they have to schedule it + + + align:start position:0% +they have to schedule it +and they might not get to that project + + align:start position:0% +and they might not get to that project + + + align:start position:0% +and they might not get to that project +for 18 months or even five or seven + + align:start position:0% +for 18 months or even five or seven + + + align:start position:0% +for 18 months or even five or seven +years and + + align:start position:0% +years and + + + align:start position:0% +years and +sometimes that's what gives the fintech + + align:start position:0% +sometimes that's what gives the fintech + + + align:start position:0% +sometimes that's what gives the fintech +disruptor the opportunity + + align:start position:0% +disruptor the opportunity + + + align:start position:0% +disruptor the opportunity +that the incumbent can use + + align:start position:0% +that the incumbent can use + + + align:start position:0% +that the incumbent can use +a new technology in this case rpa they + + align:start position:0% +a new technology in this case rpa they + + + align:start position:0% +a new technology in this case rpa they +can use that technology but they can't + + align:start position:0% +can use that technology but they can't + + + align:start position:0% +can use that technology but they can't +schedule it for three years + + align:start position:0% +schedule it for three years + + + align:start position:0% +schedule it for three years +or even longer or if they're scheduling + + align:start position:0% +or even longer or if they're scheduling + + + align:start position:0% +or even longer or if they're scheduling +it they have to do it in a very + + align:start position:0% +it they have to do it in a very + + + align:start position:0% +it they have to do it in a very +controlled way and then disrupter then + + align:start position:0% +controlled way and then disrupter then + + + align:start position:0% +controlled way and then disrupter then +is coming along and having an + + align:start position:0% +is coming along and having an + + + align:start position:0% +is coming along and having an +opportunity in the meantime + + align:start position:0% +opportunity in the meantime + + + align:start position:0% +opportunity in the meantime +to attack that business model so i thank + + align:start position:0% +to attack that business model so i thank + + + align:start position:0% +to attack that business model so i thank +you + + align:start position:0% +you + + + align:start position:0% +you +um romaine are there others or should i + + align:start position:0% +um romaine are there others or should i + + + align:start position:0% +um romaine are there others or should i +move on we finally had andrea + + align:start position:0% +move on we finally had andrea + + + align:start position:0% +move on we finally had andrea +who i believe has experience in this + + align:start position:0% +who i believe has experience in this + + + align:start position:0% +who i believe has experience in this +topic so could all benefit from it + + align:start position:0% +topic so could all benefit from it + + + align:start position:0% +topic so could all benefit from it +yeah but i wanted to touch a point uh a + + align:start position:0% +yeah but i wanted to touch a point uh a + + + align:start position:0% +yeah but i wanted to touch a point uh a +similar points that + + align:start position:0% +similar points that + + + align:start position:0% +similar points that +uh we just discussed with ivy so we can + + align:start position:0% +uh we just discussed with ivy so we can + + + align:start position:0% +uh we just discussed with ivy so we can +move on definitely + + align:start position:0% +move on definitely + + + align:start position:0% +move on definitely +but what i appreciate about the rpa in + + align:start position:0% +but what i appreciate about the rpa in + + + align:start position:0% +but what i appreciate about the rpa in +in the incumbents is that + + align:start position:0% +in the incumbents is that + + + align:start position:0% +in the incumbents is that +it helps them to increase the efficiency + + align:start position:0% +it helps them to increase the efficiency + + + align:start position:0% +it helps them to increase the efficiency +and operations + + align:start position:0% +and operations + + + align:start position:0% +and operations +but at the same time um you know it also + + align:start position:0% +but at the same time um you know it also + + + align:start position:0% +but at the same time um you know it also +brings in the the standardization and uh + + align:start position:0% +brings in the the standardization and uh + + + align:start position:0% +brings in the the standardization and uh +people + + align:start position:0% +people + + + align:start position:0% +people +can uh can focus or like the the the + + align:start position:0% +can uh can focus or like the the the + + + align:start position:0% +can uh can focus or like the the the +employees of the bank can focus on more + + align:start position:0% +employees of the bank can focus on more + + + align:start position:0% +employees of the bank can focus on more +evaluating services for example + + align:start position:0% +evaluating services for example + + + align:start position:0% +evaluating services for example +um the advisory to the clients when it + + align:start position:0% +um the advisory to the clients when it + + + align:start position:0% +um the advisory to the clients when it +comes to + + align:start position:0% +comes to + + + align:start position:0% +comes to +more difficult products such as + + align:start position:0% +more difficult products such as + + + align:start position:0% +more difficult products such as +mortgages or or consumer loans + + align:start position:0% +mortgages or or consumer loans + + + align:start position:0% +mortgages or or consumer loans +but at the same time as you mentioned + + align:start position:0% +but at the same time as you mentioned + + + align:start position:0% +but at the same time as you mentioned +the the time + + align:start position:0% +the the time + + + align:start position:0% +the the time +and the and the resources that you need + + align:start position:0% +and the and the resources that you need + + + align:start position:0% +and the and the resources that you need +especially in huge incumbents like + + align:start position:0% +especially in huge incumbents like + + + align:start position:0% +especially in huge incumbents like +merrill or berkeley's + + align:start position:0% +merrill or berkeley's + + + align:start position:0% +merrill or berkeley's +um it takes a lot of time to get there + + align:start position:0% +um it takes a lot of time to get there + + + align:start position:0% +um it takes a lot of time to get there +right and so what's interesting about + + align:start position:0% +right and so what's interesting about + + + align:start position:0% +right and so what's interesting about +each of these technologies and this is + + align:start position:0% +each of these technologies and this is + + + align:start position:0% +each of these technologies and this is +true if we broaden it out open api + + align:start position:0% +true if we broaden it out open api + + + align:start position:0% +true if we broaden it out open api +robotic process automation they're both + + align:start position:0% +robotic process automation they're both + + + align:start position:0% +robotic process automation they're both +a tool for the disruptors + + align:start position:0% +a tool for the disruptors + + + align:start position:0% +a tool for the disruptors +to produce services and new business + + align:start position:0% +to produce services and new business + + + align:start position:0% +to produce services and new business +models to + + align:start position:0% +models to + + + align:start position:0% +models to +the consuming public and there are also + + align:start position:0% +the consuming public and there are also + + + align:start position:0% +the consuming public and there are also +tools to the incumbents depending upon + + align:start position:0% +tools to the incumbents depending upon + + + align:start position:0% +tools to the incumbents depending upon +how they can invest in those tools how + + align:start position:0% +how they can invest in those tools how + + + align:start position:0% +how they can invest in those tools how +they can + + align:start position:0% +they can + + + align:start position:0% +they can +update their business models and the + + align:start position:0% +update their business models and the + + + align:start position:0% +update their business models and the +like and in particularly in open api + + align:start position:0% +like and in particularly in open api + + + align:start position:0% +like and in particularly in open api +we'll see there's a real challenge + + align:start position:0% +we'll see there's a real challenge + + + align:start position:0% +we'll see there's a real challenge +that the large incumbents the the the jp + + align:start position:0% +that the large incumbents the the the jp + + + align:start position:0% +that the large incumbents the the the jp +morgan chases and + + align:start position:0% +morgan chases and + + + align:start position:0% +morgan chases and +and the pnc banks and so forth are + + align:start position:0% +and the pnc banks and so forth are + + + align:start position:0% +and the pnc banks and so forth are +sharing data now with a lot of the + + align:start position:0% +sharing data now with a lot of the + + + align:start position:0% +sharing data now with a lot of the +disruptors they're + + align:start position:0% +disruptors they're + + + align:start position:0% +disruptors they're +providing greater services to their + + align:start position:0% +providing greater services to their + + + align:start position:0% +providing greater services to their +ultimate end users and customers + + align:start position:0% +ultimate end users and customers + + + align:start position:0% +ultimate end users and customers +but then also they're they're concerned + + align:start position:0% +but then also they're they're concerned + + + align:start position:0% +but then also they're they're concerned +about are they giving up some of their + + align:start position:0% +about are they giving up some of their + + + align:start position:0% +about are they giving up some of their +inherent competitive advantage of + + align:start position:0% +inherent competitive advantage of + + + align:start position:0% +inherent competitive advantage of +controlling that data + + align:start position:0% +controlling that data + + + align:start position:0% +controlling that data +and so there's some real trade-offs + + align:start position:0% +and so there's some real trade-offs + + + align:start position:0% +and so there's some real trade-offs +particularly in the open api + + align:start position:0% +particularly in the open api + + + align:start position:0% +particularly in the open api +world as to how banks look at this so i + + align:start position:0% +world as to how banks look at this so i + + + align:start position:0% +world as to how banks look at this so i +wanted to go back to the question of + + align:start position:0% +wanted to go back to the question of + + + align:start position:0% +wanted to go back to the question of +like what is + + align:start position:0% +like what is + + + align:start position:0% +like what is +api i just i was able to find a slide + + align:start position:0% +api i just i was able to find a slide + + + align:start position:0% +api i just i was able to find a slide +off of tech target that i thought was + + align:start position:0% +off of tech target that i thought was + + + align:start position:0% +off of tech target that i thought was +helpful uh + + align:start position:0% +helpful uh + + + align:start position:0% +helpful uh +just to think about this an api just + + align:start position:0% +just to think about this an api just + + + align:start position:0% +just to think about this an api just +think of two + + align:start position:0% +think of two + + + align:start position:0% +think of two +two systems that are linking together + + align:start position:0% +two systems that are linking together + + + align:start position:0% +two systems that are linking together +and sort of the original apis was just a + + align:start position:0% +and sort of the original apis was just a + + + align:start position:0% +and sort of the original apis was just a +local + + align:start position:0% +local + + + align:start position:0% +local +application program interface that sort + + align:start position:0% +application program interface that sort + + + align:start position:0% +application program interface that sort +of could connect + + align:start position:0% +of could connect + + + align:start position:0% +of could connect +uh two two computers together web-based + + align:start position:0% +uh two two computers together web-based + + + align:start position:0% +uh two two computers together web-based +api + + align:start position:0% +api + + + align:start position:0% +api +which went further and web-based apis + + align:start position:0% +which went further and web-based apis + + + align:start position:0% +which went further and web-based apis +have been around for 30 years this is + + align:start position:0% +have been around for 30 years this is + + + align:start position:0% +have been around for 30 years this is +not a new technology but web-based + + align:start position:0% +not a new technology but web-based + + + align:start position:0% +not a new technology but web-based +are designed really to represent uh such + + align:start position:0% +are designed really to represent uh such + + + align:start position:0% +are designed really to represent uh such +that + + align:start position:0% +that + + + align:start position:0% +that +they could be widely used html and later + + align:start position:0% +they could be widely used html and later + + + align:start position:0% +they could be widely used html and later +something called rest api which is more + + align:start position:0% +something called rest api which is more + + + align:start position:0% +something called rest api which is more +recently + + align:start position:0% +recently + + + align:start position:0% +recently +these are protocols these are protocols + + align:start position:0% +these are protocols these are protocols + + + align:start position:0% +these are protocols these are protocols +that + + align:start position:0% +that + + + align:start position:0% +that +multiple parties on the web can come + + align:start position:0% +multiple parties on the web can come + + + align:start position:0% +multiple parties on the web can come +into your service + + align:start position:0% +into your service + + + align:start position:0% +into your service +in some way in some way + + align:start position:0% +in some way in some way + + + align:start position:0% +in some way in some way +and then we talk about public apis which + + align:start position:0% +and then we talk about public apis which + + + align:start position:0% +and then we talk about public apis which +really sort of broadens + + align:start position:0% +really sort of broadens + + + align:start position:0% +really sort of broadens +broadens it out further so thinking of + + align:start position:0% +broadens it out further so thinking of + + + align:start position:0% +broadens it out further so thinking of +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +and you could even think of this as sort + + align:start position:0% +and you could even think of this as sort + + + align:start position:0% +and you could even think of this as sort +of private + + align:start position:0% +of private + + + align:start position:0% +of private +registered apis to broadly publicly + + align:start position:0% +registered apis to broadly publicly + + + align:start position:0% +registered apis to broadly publicly +available apis + + align:start position:0% +available apis + + + align:start position:0% +available apis +and what many businesses are trying to + + align:start position:0% +and what many businesses are trying to + + + align:start position:0% +and what many businesses are trying to +use and they manage it and it's a very + + align:start position:0% +use and they manage it and it's a very + + + align:start position:0% +use and they manage it and it's a very +active part of strategy is to manage + + align:start position:0% +active part of strategy is to manage + + + align:start position:0% +active part of strategy is to manage +that interface + + align:start position:0% +that interface + + + align:start position:0% +that interface +to allow the developer community + + align:start position:0% +to allow the developer community + + + align:start position:0% +to allow the developer community +to interface with your platform facebook + + align:start position:0% +to interface with your platform facebook + + + align:start position:0% +to interface with your platform facebook +needs to do it instagram needs to do it + + align:start position:0% +needs to do it instagram needs to do it + + + align:start position:0% +needs to do it instagram needs to do it +any network based or platform based + + align:start position:0% +any network based or platform based + + + align:start position:0% +any network based or platform based +service actually wants to encourage + + align:start position:0% +service actually wants to encourage + + + align:start position:0% +service actually wants to encourage +developers to build + + align:start position:0% +developers to build + + + align:start position:0% +developers to build +applications on top of a platform + + align:start position:0% +applications on top of a platform + + + align:start position:0% +applications on top of a platform +so now you bring this to phineas does jp + + align:start position:0% +so now you bring this to phineas does jp + + + align:start position:0% +so now you bring this to phineas does jp +morgan chase does bank of america does + + align:start position:0% +morgan chase does bank of america does + + + align:start position:0% +morgan chase does bank of america does +barclays does merrill + + align:start position:0% +barclays does merrill + + + align:start position:0% +barclays does merrill +want to do the same encourage + + align:start position:0% +want to do the same encourage + + + align:start position:0% +want to do the same encourage +development of applications on back + + align:start position:0% +development of applications on back + + + align:start position:0% +development of applications on back +on top of their platform recognizing + + align:start position:0% +on top of their platform recognizing + + + align:start position:0% +on top of their platform recognizing +that they make a lot on their platform + + align:start position:0% +that they make a lot on their platform + + + align:start position:0% +that they make a lot on their platform +their balance sheet their funding models + + align:start position:0% +their balance sheet their funding models + + + align:start position:0% +their balance sheet their funding models +their data + + align:start position:0% +their data + + + align:start position:0% +their data +their analytics do they want to + + align:start position:0% +their analytics do they want to + + + align:start position:0% +their analytics do they want to +encourage the development of + + align:start position:0% +encourage the development of + + + align:start position:0% +encourage the development of +applications on top + + align:start position:0% +applications on top + + + align:start position:0% +applications on top +and it and it's a little bit of a push + + align:start position:0% +and it and it's a little bit of a push + + + align:start position:0% +and it and it's a little bit of a push +and pull because they're also + + align:start position:0% +and pull because they're also + + + align:start position:0% +and pull because they're also +encouraging development of applications + + align:start position:0% +encouraging development of applications + + + align:start position:0% +encouraging development of applications +that might compete with them + + align:start position:0% +that might compete with them + + + align:start position:0% +that might compete with them +but also enhance what they're doing + + align:start position:0% + + + + align:start position:0% + +so i sort of found this other spaghetti + + align:start position:0% +so i sort of found this other spaghetti + + + align:start position:0% +so i sort of found this other spaghetti +slide that i thought was really helpful + + align:start position:0% +slide that i thought was really helpful + + + align:start position:0% +slide that i thought was really helpful +is + + align:start position:0% +is + + + align:start position:0% +is +now if you would think about thousands + + align:start position:0% +now if you would think about thousands + + + align:start position:0% +now if you would think about thousands +of financial firms dealing with + + align:start position:0% +of financial firms dealing with + + + align:start position:0% +of financial firms dealing with +thousands of + + align:start position:0% +thousands of + + + align:start position:0% +thousands of +public this spaghetti wire gets even + + align:start position:0% +public this spaghetti wire gets even + + + align:start position:0% +public this spaghetti wire gets even +worse + + align:start position:0% +worse + + + align:start position:0% +worse +but application program interface is a + + align:start position:0% +but application program interface is a + + + align:start position:0% +but application program interface is a +classic + + align:start position:0% +classic + + + align:start position:0% +classic +problem of math is that if you only have + + align:start position:0% +problem of math is that if you only have + + + align:start position:0% +problem of math is that if you only have +two computers by two computers you might + + align:start position:0% +two computers by two computers you might + + + align:start position:0% +two computers by two computers you might +need + + align:start position:0% +need + + + align:start position:0% +need +four lines of connections but all of a + + align:start position:0% +four lines of connections but all of a + + + align:start position:0% +four lines of connections but all of a +sudden when you have thousands + + align:start position:0% +sudden when you have thousands + + + align:start position:0% +sudden when you have thousands +you could have this spaghetti wire of + + align:start position:0% +you could have this spaghetti wire of + + + align:start position:0% +you could have this spaghetti wire of +interfaces + + align:start position:0% +interfaces + + + align:start position:0% +interfaces +so what's happened in the midst of this + + align:start position:0% +so what's happened in the midst of this + + + align:start position:0% +so what's happened in the midst of this +in sector by sector + + align:start position:0% +in sector by sector + + + align:start position:0% +in sector by sector +is that there have been companies that + + align:start position:0% +is that there have been companies that + + + align:start position:0% +is that there have been 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+providers in the middle +and here are some examples in + + align:start position:0% +and here are some examples in + + + align:start position:0% +and here are some examples in +non-finance + + align:start position:0% +non-finance + + + align:start position:0% +non-finance +and and whether you know + + align:start position:0% +and and whether you know + + + align:start position:0% +and and whether you know +underneath the hood about twilio + + align:start position:0% +underneath the hood about twilio + + + align:start position:0% +underneath the hood about twilio +or others twilio probably has i'm told + + align:start position:0% +or others twilio probably has i'm told + + + align:start position:0% +or others twilio probably has i'm told +something close to an + + align:start position:0% +something close to an + + + align:start position:0% +something close to an +80 market share in voice + + align:start position:0% +80 market share in voice + + + align:start position:0% +80 market share in voice +and messaging that they're sort of the + + align:start position:0% +and messaging that they're sort of the + + + align:start position:0% +and messaging that they're sort of the +that + + align:start position:0% +that + + + align:start position:0% +that +layer in between the disruptors + + align:start position:0% +layer in between the disruptors + + + align:start position:0% +layer in between the disruptors +and the service providers and and the + + align:start position:0% +and the service providers and and the + + + align:start position:0% +and the service providers and and the +classic companies providing it as + + align:start position:0% +classic companies providing it as + + + align:start position:0% +classic companies providing it as +a layer in the middle a layer in the + + align:start position:0% +a layer in the middle a layer in the + + + align:start position:0% +a layer in the middle a layer in the +middle + + align:start position:0% +middle + + + align:start position:0% +middle +a check r does it on employment checks + + align:start position:0% +a check r does it on employment checks + + + align:start position:0% +a check r does it on employment checks +you know + + align:start position:0% +you know + + + align:start position:0% +you know +when when we want to check each one of + + align:start position:0% +when when we want to check each one of + + + align:start position:0% +when when we want to check each one of +these companies were startups over the + + align:start position:0% +these companies were startups over the + + + align:start position:0% +these companies were startups over the +last 20 years + + align:start position:0% +last 20 years + + + align:start position:0% +last 20 years +sales forces a little bit earlier and + + align:start position:0% +sales forces a little bit earlier and + + + align:start position:0% +sales forces a little bit earlier and +they really + + align:start position:0% +they really + + + align:start position:0% +they really +took even if they didn't know it at the + + align:start position:0% +took even if they didn't know it at the + + + align:start position:0% +took even if they didn't know it at the +time + + align:start position:0% +time + + + align:start position:0% +time +they took the concept of open api + + align:start position:0% +they took the concept of open api + + + align:start position:0% +they took the concept of open api +and api and they built it + + align:start position:0% +and api and they built it + + + align:start position:0% +and api and they built it +and in fact there's there's these words + + align:start position:0% +and in fact there's there's these words + + + align:start position:0% +and in fact there's there's these words +that called + + align:start position:0% +that called + + + align:start position:0% +that called +api first that you can build a strategy + + align:start position:0% +api first that you can build a strategy + + + align:start position:0% +api first that you can build a strategy +saying + + align:start position:0% +saying + + + align:start position:0% +saying +we're going to be the best providing + + align:start position:0% +we're going to be the best providing + + + align:start position:0% +we're going to be the best providing +apis now who's done this in finance + + align:start position:0% +apis now who's done this in finance + + + align:start position:0% +apis now who's done this in finance +who's done this advanced one company + + align:start position:0% +who's done this advanced one company + + + align:start position:0% +who's done this advanced one company +that you might think of as a payment + + align:start position:0% +that you might think of as a payment + + + align:start position:0% +that you might think of as a payment +service provider stripe did it very well + + align:start position:0% +service provider stripe did it very well + + + align:start position:0% +service provider stripe did it very well +stripe basically said we will be that + + align:start position:0% +stripe basically said we will be that + + + align:start position:0% +stripe basically said we will be that +api + + align:start position:0% +api + + + align:start position:0% +api +provider in the payment space + + align:start position:0% +provider in the payment space + + + align:start position:0% +provider in the payment space +what company did it really well most + + align:start position:0% +what company did it really well most + + + align:start position:0% +what company did it really well most +recently that we talked about + + align:start position:0% +recently that we talked about + + + align:start position:0% +recently that we talked about +last uh class was plaid and we're going + + align:start position:0% +last uh class was plaid and we're going + + + align:start position:0% +last uh class was plaid and we're going +to come back into plaid as well + + align:start position:0% +to come back into plaid as well + + + align:start position:0% +to come back into plaid as well +the plaid did this very well now they + + align:start position:0% +the plaid did this very well now they + + + align:start position:0% +the plaid did this very well now they +didn't start by saying we're going to be + + align:start position:0% +didn't start by saying we're going to be + + + align:start position:0% +didn't start by saying we're going to be +only an api company but they did start + + align:start position:0% +only an api company but they did start + + + align:start position:0% +only an api company but they did start +with being an api company it was two + + align:start position:0% +with being an api company it was two + + + align:start position:0% +with being an api company it was two +entrepreneurs in plaid's case about + + align:start position:0% +entrepreneurs in plaid's case about + + + align:start position:0% +entrepreneurs in plaid's case about +six or seven years ago that said there + + align:start position:0% +six or seven years ago that said there + + + align:start position:0% +six or seven years ago that said there +really isn't a good api + + align:start position:0% +really isn't a good api + + + align:start position:0% +really isn't a good api +in the payment space now there was + + align:start position:0% +in the payment space now there was + + + align:start position:0% +in the payment space now there was +stripe + + align:start position:0% +stripe + + + align:start position:0% +stripe +and i'm not sure about their + + align:start position:0% +and i'm not sure about their + + + align:start position:0% +and i'm not sure about their +foundational stories why + + align:start position:0% +foundational stories why + + + align:start position:0% +foundational stories why +uh they didn't feel that the stripe uh + + align:start position:0% +uh they didn't feel that the stripe uh + + + align:start position:0% +uh they didn't feel that the stripe uh +apis were good enough + + align:start position:0% +apis were good enough + + + align:start position:0% +apis were good enough +but they created an api and of course + + align:start position:0% +but they created an api and of course + + + align:start position:0% +but they created an api and of course +plaid just recently sold + + align:start position:0% +plaid just recently sold + + + align:start position:0% +plaid just recently sold +for five billion dollars plus the visa + + align:start position:0% +for five billion dollars plus the visa + + + align:start position:0% +for five billion dollars plus the visa +or announced the sale + + align:start position:0% +or announced the sale + + + align:start position:0% +or announced the sale +um so we talked a little bit about + + align:start position:0% +um so we talked a little bit about + + + align:start position:0% +um so we talked a little bit about +finance and this history this stack + + align:start position:0% +finance and this history this stack + + + align:start position:0% +finance and this history this stack +and i'm going back to the customer + + align:start position:0% +and i'm going back to the customer + + + align:start position:0% +and i'm going back to the customer +interface stack + + align:start position:0% +interface stack + + + align:start position:0% +interface stack +we don't need to go back to bricks and + + align:start position:0% +we don't need to go back to bricks and + + + align:start position:0% +we don't need to go back to bricks and +mortars and electronic payments + + align:start position:0% +mortars and electronic payments + + + align:start position:0% +mortars and electronic payments +but again sort of the conceptual + + align:start position:0% +but again sort of the conceptual + + + align:start position:0% +but again sort of the conceptual +framework of this + + align:start position:0% +framework of this + + + align:start position:0% +framework of this +class and how i think about it the most + + align:start position:0% +class and how i think about it the most + + + align:start position:0% +class and how i think about it the most +recent things added to the stack the + + align:start position:0% +recent things added to the stack the + + + align:start position:0% +recent things added to the stack the +internet + + align:start position:0% +internet + + + align:start position:0% +internet +mobile phones contact cards and the like + + align:start position:0% +mobile phones contact cards and the like + + + align:start position:0% +mobile phones contact cards and the like +those are all fully engaged and part + + align:start position:0% +those are all fully engaged and part + + + align:start position:0% +those are all fully engaged and part +of the finance technology stack and now + + align:start position:0% +of the finance technology stack and now + + + align:start position:0% +of the finance technology stack and now +we're adding + + align:start position:0% +we're adding + + + align:start position:0% +we're adding +open api and chat bots which we talked + + align:start position:0% +open api and chat bots which we talked + + + align:start position:0% +open api and chat bots which we talked +about last class + + align:start position:0% +about last class + + + align:start position:0% +about last class +and natural language processing robotic + + align:start position:0% +and natural language processing robotic + + + align:start position:0% +and natural language processing robotic +processing + + align:start position:0% +processing + + + align:start position:0% +processing +we're adding that to the finance + + align:start position:0% +we're adding that to the finance + + + align:start position:0% +we're adding that to the finance +technology stack and that's sort of the + + align:start position:0% +technology stack and that's sort of the + + + align:start position:0% +technology stack and that's sort of the +conceptual framework + + align:start position:0% +conceptual framework + + + align:start position:0% +conceptual framework +and i think those are where the + + align:start position:0% +and i think those are where the + + + align:start position:0% +and i think those are where the +opportunities are + + align:start position:0% +opportunities are + + + align:start position:0% +opportunities are +and five or eight or ten years from now + + align:start position:0% +and five or eight or ten years from now + + + align:start position:0% +and five or eight or ten years from now +it will be taken for granted + + align:start position:0% +it will be taken for granted + + + align:start position:0% +it will be taken for granted +of course there'll be enhancements and + + align:start position:0% +of course there'll be enhancements and + + + align:start position:0% +of course there'll be enhancements and +every change there's an enhancement that + + align:start position:0% +every change there's an enhancement that + + + align:start position:0% +every change there's an enhancement that +creates some opportunities as well + + align:start position:0% +creates some opportunities as well + + + align:start position:0% +creates some opportunities as well +so what do we mean by open api to + + align:start position:0% +so what do we mean by open api to + + + align:start position:0% +so what do we mean by open api to +iqbal's + + align:start position:0% +iqbal's + + + align:start position:0% +iqbal's +earlier question open application + + align:start position:0% +earlier question open application + + + align:start position:0% +earlier question open application +program interface + + align:start position:0% +program interface + + + align:start position:0% +program interface +provides developers access to an ability + + align:start position:0% +provides developers access to an ability + + + align:start position:0% +provides developers access to an ability +to get permission customer data that + + align:start position:0% +to get permission customer data that + + + align:start position:0% +to get permission customer data that +means you and i give a password you and + + align:start position:0% +means you and i give a password you and + + + align:start position:0% +means you and i give a password you and +i give + + align:start position:0% +i give + + + align:start position:0% +i give +a username + + align:start position:0% +a username + + + align:start position:0% +a username +open banking initiatives open banking is + + align:start position:0% +open banking initiatives open banking is + + + align:start position:0% +open banking initiatives open banking is +unique to the financial world or + + align:start position:0% +unique to the financial world or + + + align:start position:0% +unique to the financial world or +initiatives usually promoted + + align:start position:0% +initiatives usually promoted + + + align:start position:0% +initiatives usually promoted +by the official sector usually promoted + + align:start position:0% +by the official sector usually promoted + + + align:start position:0% +by the official sector usually promoted +either by the central banks + + align:start position:0% +either by the central banks + + + align:start position:0% +either by the central banks +or by the banking regulators and + + align:start position:0% +or by the banking regulators and + + + align:start position:0% +or by the banking regulators and +sometimes promoted by competition + + align:start position:0% +sometimes promoted by competition + + + align:start position:0% +sometimes promoted by competition +authority + + align:start position:0% +authority + + + align:start position:0% +authority +to say you must share certain data or + + align:start position:0% +to say you must share certain data or + + + align:start position:0% +to say you must share certain data or +you must + + align:start position:0% +you must + + + align:start position:0% +you must +create some standards for these open + + align:start position:0% +create some standards for these open + + + align:start position:0% +create some standards for these open +apis + + align:start position:0% +apis + + + align:start position:0% +apis +again as i just mentioned open apis are + + align:start position:0% +again as i just mentioned open apis are + + + align:start position:0% +again as i just mentioned open apis are +in + + align:start position:0% +in + + + align:start position:0% +in +every field of online services + + align:start position:0% +every field of online services + + + align:start position:0% +every field of online services +from voice to employment to retail and + + align:start position:0% +from voice to employment to retail and + + + align:start position:0% +from voice to employment to retail and +but + + align:start position:0% +but + + + align:start position:0% +but +the competition authorities and the + + align:start position:0% +the competition authorities and the + + + align:start position:0% +the competition authorities and the +central banks around the globe said well + + align:start position:0% +central banks around the globe said well + + + align:start position:0% +central banks around the globe said well +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +maybe we should lean into this + + align:start position:0% +maybe we should lean into this + + + align:start position:0% +maybe we should lean into this +the official sector lean in and promote + + align:start position:0% +the official sector lean in and promote + + + align:start position:0% +the official sector lean in and promote +competition for this + + align:start position:0% +competition for this + + + align:start position:0% +competition for this +sharing of data and these initiatives + + align:start position:0% +sharing of data and these initiatives + + + align:start position:0% +sharing of data and these initiatives +which + + align:start position:0% +which + + + align:start position:0% +which +you got a chance to read about do have + + align:start position:0% +you got a chance to read about do have + + + align:start position:0% +you got a chance to read about do have +policy trade-offs + + align:start position:0% +policy trade-offs + + + align:start position:0% +policy trade-offs +and why i focus on these policy + + align:start position:0% +and why i focus on these policy + + + align:start position:0% +and why i focus on these policy +trade-offs is they're also + + align:start position:0% +trade-offs is they're also + + + align:start position:0% +trade-offs is they're also +about competition incumbents + + align:start position:0% +about competition incumbents + + + align:start position:0% +about competition incumbents +are not going to really want to embrace + + align:start position:0% +are not going to really want to embrace + + + align:start position:0% +are not going to really want to embrace +competition like this + + align:start position:0% + + + + align:start position:0% + +having said that many of the incumbents + + align:start position:0% +having said that many of the incumbents + + + align:start position:0% +having said that many of the incumbents +recognize + + align:start position:0% +recognize + + + align:start position:0% +recognize +that it might be that they're shifting + + align:start position:0% +that it might be that they're shifting + + + align:start position:0% +that it might be that they're shifting +right now that their business models are + + align:start position:0% +right now that their business models are + + + align:start position:0% +right now that their business models are +shifting and they have to think + + align:start position:0% +shifting and they have to think + + + align:start position:0% +shifting and they have to think +like platform companies and to the + + align:start position:0% +like platform companies and to the + + + align:start position:0% +like platform companies and to the +extent that the jp morgans or the + + align:start position:0% +extent that the jp morgans or the + + + align:start position:0% +extent that the jp morgans or the +barclays think more like platform + + align:start position:0% +barclays think more like platform + + + align:start position:0% +barclays think more like platform +companies + + align:start position:0% +companies + + + align:start position:0% +companies +they want to encourage the developer + + align:start position:0% +they want to encourage the developer + + + align:start position:0% +they want to encourage the developer +community to develop + + align:start position:0% +community to develop + + + align:start position:0% +community to develop +applications on top of their platforms + + align:start position:0% +applications on top of their platforms + + + align:start position:0% +applications on top of their platforms +if they think it's simply losing + + align:start position:0% +if they think it's simply losing + + + align:start position:0% +if they think it's simply losing +market share to the sofis and to the new + + align:start position:0% +market share to the sofis and to the new + + + align:start position:0% +market share to the sofis and to the new +banks + + align:start position:0% +banks + + + align:start position:0% +banks +then they're going to be more close to + + align:start position:0% +then they're going to be more close to + + + align:start position:0% +then they're going to be more close to +open api + + align:start position:0% +open api + + + align:start position:0% +open api +if they think more like platform + + align:start position:0% +if they think more like platform + + + align:start position:0% +if they think more like platform +companies they're going to want to + + align:start position:0% +companies they're going to want to + + + align:start position:0% +companies they're going to want to +promote it + + align:start position:0% +promote it + + + align:start position:0% +promote it +but there are also trade-offs there are + + align:start position:0% +but there are also trade-offs there are + + + align:start position:0% +but there are also trade-offs there are +also trade-offs that the big incumbents + + align:start position:0% +also trade-offs that the big incumbents + + + align:start position:0% +also trade-offs that the big incumbents +would say about + + align:start position:0% +would say about + + + align:start position:0% +would say about +cyber security if we just let anybody + + align:start position:0% +cyber security if we just let anybody + + + align:start position:0% +cyber security if we just let anybody +into our platform + + align:start position:0% +into our platform + + + align:start position:0% +into our platform +they can also bring down that platform + + align:start position:0% +they can also bring down that platform + + + align:start position:0% +they can also bring down that platform +possibly + + align:start position:0% +possibly + + + align:start position:0% +possibly +and so these are real public policy + + align:start position:0% +and so these are real public policy + + + align:start position:0% +and so these are real public policy +trade-offs but they're + + align:start position:0% +trade-offs but they're + + + align:start position:0% +trade-offs but they're +also commercial trade-offs as well + + align:start position:0% +also commercial trade-offs as well + + + align:start position:0% +also commercial trade-offs as well +um romaine i don't know if there is a + + align:start position:0% +um romaine i don't know if there is a + + + align:start position:0% +um romaine i don't know if there is a +question i see some activity in the chat + + align:start position:0% +question i see some activity in the chat + + + align:start position:0% +question i see some activity in the chat +we have a question from gita please + + align:start position:0% +we have a question from gita please + + + align:start position:0% +we have a question from gita please +um gary i've been thinking a lot about + + align:start position:0% +um gary i've been thinking a lot about + + + align:start position:0% +um gary i've been thinking a lot about +uh incumbents becoming platforms + + align:start position:0% +uh incumbents becoming platforms + + + align:start position:0% +uh incumbents becoming platforms +other than ability to allow + + align:start position:0% +other than ability to allow + + + align:start position:0% +other than ability to allow +access to their customer data to vendors + + align:start position:0% +access to their customer data to vendors + + + align:start position:0% +access to their customer data to vendors +um i'm not able to think of + + align:start position:0% +um i'm not able to think of + + + align:start position:0% +um i'm not able to think of +examples of what kind of platforms + + align:start position:0% +examples of what kind of platforms + + + align:start position:0% +examples of what kind of platforms +incumbents can be like they are not a + + align:start position:0% +incumbents can be like they are not a + + + align:start position:0% +incumbents can be like they are not a +specific payment company they are only + + align:start position:0% +specific payment company they are only + + + align:start position:0% +specific payment company they are only +servicing their own customers + + align:start position:0% +servicing their own customers + + + align:start position:0% +servicing their own customers +so i wonder if you have any examples of + + align:start position:0% +so i wonder if you have any examples of + + + align:start position:0% +so i wonder if you have any examples of +so i think i think many of the major + + align:start position:0% +so i think i think many of the major + + + align:start position:0% +so i think i think many of the major +banks are already platforms + + align:start position:0% +banks are already platforms + + + align:start position:0% +banks are already platforms +uh they they don't necessarily think of + + align:start position:0% +uh they they don't necessarily think of + + + align:start position:0% +uh they they don't necessarily think of +themselves this way + + align:start position:0% +themselves this way + + + align:start position:0% +themselves this way +but they are bringing together + + align:start position:0% +but they are bringing together + + + align:start position:0% +but they are bringing together +in in this troop for centuries they are + + align:start position:0% +in in this troop for centuries they are + + + align:start position:0% +in in this troop for centuries they are +bringing together + + align:start position:0% +bringing together + + + align:start position:0% +bringing together +borrowers and lenders or savers so they + + align:start position:0% +borrowers and lenders or savers so they + + + align:start position:0% +borrowers and lenders or savers so they +have a balance sheet that brings + + align:start position:0% +have a balance sheet that brings + + + align:start position:0% +have a balance sheet that brings +together + + align:start position:0% +together + + + align:start position:0% +together +in some cases millions of savers + + align:start position:0% +in some cases millions of savers + + + align:start position:0% +in some cases millions of savers +and tens of thousands or hundreds of + + align:start position:0% +and tens of thousands or hundreds of + + + align:start position:0% +and tens of thousands or hundreds of +thousands of borrowers and they're + + align:start position:0% +thousands of borrowers and they're + + + align:start position:0% +thousands of borrowers and they're +bringing that together + + align:start position:0% +bringing that together + + + align:start position:0% +bringing that together +and we consider that sort of the modern + + align:start position:0% +and we consider that sort of the modern + + + align:start position:0% +and we consider that sort of the modern +large financial firm with the trillion + + align:start position:0% +large financial firm with the trillion + + + align:start position:0% +large financial firm with the trillion +or two trillion dollar balance sheet + + align:start position:0% +or two trillion dollar balance sheet + + + align:start position:0% +or two trillion dollar balance sheet +many of the largest world + + align:start position:0% +many of the largest world + + + align:start position:0% +many of the largest world +and and so forth and so they're bringing + + align:start position:0% +and and so forth and so they're bringing + + + align:start position:0% +and and so forth and so they're bringing +that together + + align:start position:0% +that together + + + align:start position:0% +that together +and they're managing risk and and and + + align:start position:0% +and they're managing risk and and and + + + align:start position:0% +and they're managing risk and and and +they're + + align:start position:0% +they're + + + align:start position:0% +they're +they're very good or some of them are + + align:start position:0% +they're very good or some of them are + + + align:start position:0% +they're very good or some of them are +very good at that risk management + + align:start position:0% +very good at that risk management + + + align:start position:0% +very good at that risk management +of of those millions of depositors + + align:start position:0% +of of those millions of depositors + + + align:start position:0% +of of those millions of depositors +and tens or hundreds of thousands of + + align:start position:0% +and tens or hundreds of thousands of + + + align:start position:0% +and tens or hundreds of thousands of +borrowers that in itself + + align:start position:0% +borrowers that in itself + + + align:start position:0% +borrowers that in itself +is a platform that creates a data + + align:start position:0% +is a platform that creates a data + + + align:start position:0% +is a platform that creates a data +advantage that they have about risk + + align:start position:0% +advantage that they have about risk + + + align:start position:0% +advantage that they have about risk +management + + align:start position:0% +management + + + align:start position:0% +management +and and it could be a real one and they + + align:start position:0% +and and it could be a real one and they + + + align:start position:0% +and and it could be a real one and they +can offer activities and + + align:start position:0% +can offer activities and + + + align:start position:0% +can offer activities and +products on top of that the fintech + + align:start position:0% +products on top of that the fintech + + + align:start position:0% +products on top of that the fintech +startups can be in a sense + + align:start position:0% +startups can be in a sense + + + align:start position:0% +startups can be in a sense +a front-end distribution channel to + + align:start position:0% +a front-end distribution channel to + + + align:start position:0% +a front-end distribution channel to +bring more + + align:start position:0% +bring more + + + align:start position:0% +bring more +in because a lot of the fintech startups + + align:start position:0% +in because a lot of the fintech startups + + + align:start position:0% +in because a lot of the fintech startups +don't have that same + + align:start position:0% +don't have that same + + + align:start position:0% +don't have that same +balance sheet capability that same + + align:start position:0% +balance sheet capability that same + + + align:start position:0% +balance sheet capability that same +ability to + + align:start position:0% +ability to + + + align:start position:0% +ability to +in essence earn a spread between + + align:start position:0% +in essence earn a spread between + + + align:start position:0% +in essence earn a spread between +savers and borrowers now + + align:start position:0% +savers and borrowers now + + + align:start position:0% +savers and borrowers now +you might contend well but no they're + + align:start position:0% +you might contend well but no they're + + + align:start position:0% +you might contend well but no they're +losing their competitive advantage + + align:start position:0% +losing their competitive advantage + + + align:start position:0% +losing their competitive advantage +because those startups are + + align:start position:0% +because those startups are + + + align:start position:0% +because those startups are +are sort of have that customer interface + + align:start position:0% +are sort of have that customer interface + + + align:start position:0% +are sort of have that customer interface +that direct + + align:start position:0% +that direct + + + align:start position:0% +that direct +one might consider it the last mile + + align:start position:0% +one might consider it the last mile + + + align:start position:0% +one might consider it the last mile +with that customer but the technology + + align:start position:0% +with that customer but the technology + + + align:start position:0% +with that customer but the technology +companies taking another approach and + + align:start position:0% +companies taking another approach and + + + align:start position:0% +companies taking another approach and +saying we like developers developing + + align:start position:0% +saying we like developers developing + + + align:start position:0% +saying we like developers developing +applications on top of our platforms we + + align:start position:0% +applications on top of our platforms we + + + align:start position:0% +applications on top of our platforms we +think it brings more activities + + align:start position:0% +think it brings more activities + + + align:start position:0% +think it brings more activities +we think it brings more interface more + + align:start position:0% +we think it brings more interface more + + + align:start position:0% +we think it brings more interface more +data and so they're they're sort of + + align:start position:0% +data and so they're they're sort of + + + align:start position:0% +data and so they're they're sort of +a network that is bringing data and + + align:start position:0% +a network that is bringing data and + + + align:start position:0% +a network that is bringing data and +activity + + align:start position:0% +activity + + + align:start position:0% +activity +on the platform but i agree with you + + align:start position:0% +on the platform but i agree with you + + + align:start position:0% +on the platform but i agree with you +it's a real strategic trade-off it's a + + align:start position:0% +it's a real strategic trade-off it's a + + + align:start position:0% +it's a real strategic trade-off it's a +real strategic challenge + + align:start position:0% +real strategic challenge + + + align:start position:0% +real strategic challenge +and the incumbents are still sorting it + + align:start position:0% +and the incumbents are still sorting it + + + align:start position:0% +and the incumbents are still sorting it +out + + align:start position:0% +out + + + align:start position:0% +out +camilo um + + align:start position:0% +camilo um + + + align:start position:0% +camilo um +yeah hi i just wanted to ask um + + align:start position:0% +yeah hi i just wanted to ask um + + + align:start position:0% +yeah hi i just wanted to ask um +uh in the in one of the on the lectures + + align:start position:0% +uh in the in one of the on the lectures + + + align:start position:0% +uh in the in one of the on the lectures +they tried to classify the open banking + + align:start position:0% +they tried to classify the open banking + + + align:start position:0% +they tried to classify the open banking +between + + align:start position:0% +between + + + align:start position:0% +between +prescriptive facilities market market + + align:start position:0% +prescriptive facilities market market + + + align:start position:0% +prescriptive facilities market market +driven and in process + + align:start position:0% +driven and in process + + + align:start position:0% +driven and in process +but there were many countries as for + + align:start position:0% +but there were many countries as for + + + align:start position:0% +but there were many countries as for +example colombia who didn't have any + + align:start position:0% +example colombia who didn't have any + + + align:start position:0% +example colombia who didn't have any +classification + + align:start position:0% +classification + + + align:start position:0% +classification +uh what's the meaning of that it means + + align:start position:0% +uh what's the meaning of that it means + + + align:start position:0% +uh what's the meaning of that it means +that um is it + + align:start position:0% +that um is it + + + align:start position:0% +that um is it +forbidden i mean is it impossible to + + align:start position:0% +forbidden i mean is it impossible to + + + align:start position:0% +forbidden i mean is it impossible to +scrap the data from + + align:start position:0% +scrap the data from + + + align:start position:0% +scrap the data from +from the from the bank + + align:start position:0% +from the from the bank + + + align:start position:0% +from the from the bank +so it's a good question the bank of + + align:start position:0% +so it's a good question the bank of + + + align:start position:0% +so it's a good question the bank of +international settlement paper i think + + align:start position:0% +international settlement paper i think + + + align:start position:0% +international settlement paper i think +is + + align:start position:0% +is + + + align:start position:0% +is +to which you refer and what what they + + align:start position:0% +to which you refer and what what they + + + align:start position:0% +to which you refer and what what they +did was country by country review + + align:start position:0% +did was country by country review + + + align:start position:0% +did was country by country review +where it is and and uh in fact uh that's + + align:start position:0% +where it is and and uh in fact uh that's + + + align:start position:0% +where it is and and uh in fact uh that's +probably a good + + align:start position:0% +probably a good + + + align:start position:0% +probably a good +leading to to the the map that + + align:start position:0% +leading to to the the map that + + + align:start position:0% +leading to to the the map that +that was in that report that i'll show + + align:start position:0% +that was in that report that i'll show + + + align:start position:0% +that was in that report that i'll show +in many countries the central bank + + align:start position:0% +in many countries the central bank + + + align:start position:0% +in many countries the central bank +bank regulators and competition + + align:start position:0% +bank regulators and competition + + + align:start position:0% +bank regulators and competition +authorities have not said much + + align:start position:0% +authorities have not said much + + + align:start position:0% +authorities have not said much +i'm not close enough to colombia to know + + align:start position:0% +i'm not close enough to colombia to know + + + align:start position:0% +i'm not close enough to colombia to know +but in those countries you can still + + align:start position:0% +but in those countries you can still + + + align:start position:0% +but in those countries you can still +technologically + + align:start position:0% +technologically + + + align:start position:0% +technologically +go in and spray an alternative as i lay + + align:start position:0% +go in and spray an alternative as i lay + + + align:start position:0% +go in and spray an alternative as i lay +out here is actually scraping from the + + align:start position:0% +out here is actually scraping from the + + + align:start position:0% +out here is actually scraping from the +screen + + align:start position:0% +screen + + + align:start position:0% +screen +and so i think actually it's the next i + + align:start position:0% +and so i think actually it's the next i + + + align:start position:0% +and so i think actually it's the next i +i grabbed this slide + + align:start position:0% +i grabbed this slide + + + align:start position:0% +i grabbed this slide +from the bank of international + + align:start position:0% +from the bank of international + + + align:start position:0% +from the bank of international +settlement report so thank you it's a + + align:start position:0% +settlement report so thank you it's a + + + align:start position:0% +settlement report so thank you it's a +great setup + + align:start position:0% +great setup + + + align:start position:0% +great setup +that europe passed something called the + + align:start position:0% +that europe passed something called the + + + align:start position:0% +that europe passed something called the +payment system + + align:start position:0% +payment system + + + align:start position:0% +payment system +directive and it was actually the second + + align:start position:0% +directive and it was actually the second + + + align:start position:0% +directive and it was actually the second +time that europe came together the + + align:start position:0% +time that europe came together the + + + align:start position:0% +time that europe came together the +european parliament came together + + align:start position:0% +european parliament came together + + + align:start position:0% +european parliament came together +and said we need to promote in the + + align:start position:0% +and said we need to promote in the + + + align:start position:0% +and said we need to promote in the +payment space not + + align:start position:0% +payment space not + + + align:start position:0% +payment space not +necessarily in the lending space but in + + align:start position:0% +necessarily in the lending space but in + + + align:start position:0% +necessarily in the lending space but in +the payment space + + align:start position:0% +the payment space + + + align:start position:0% +the payment space +that there's more availability from + + align:start position:0% +that there's more availability from + + + align:start position:0% +that there's more availability from +merchants and from fintech startups + + align:start position:0% +merchants and from fintech startups + + + align:start position:0% +merchants and from fintech startups +to access your data and move money + + align:start position:0% +to access your data and move money + + + align:start position:0% +to access your data and move money +that's europe + + align:start position:0% +that's europe + + + align:start position:0% +that's europe +and and it's it's as as the bank of + + align:start position:0% +and and it's it's as as the bank of + + + align:start position:0% +and and it's it's as as the bank of +international says it + + align:start position:0% +international says it + + + align:start position:0% +international says it +says more prescriptive in the countries + + align:start position:0% +says more prescriptive in the countries + + + align:start position:0% +says more prescriptive in the countries +that are gray on this map + + align:start position:0% +that are gray on this map + + + align:start position:0% +that are gray on this map +most of africa uh many parts of the + + align:start position:0% +most of africa uh many parts of the + + + align:start position:0% +most of africa uh many parts of the +mideast + + align:start position:0% +mideast + + + align:start position:0% +mideast +and so forth parts of latin america + + align:start position:0% +and so forth parts of latin america + + + align:start position:0% +and so forth parts of latin america +the bank of international settlement i + + align:start position:0% +the bank of international settlement i + + + align:start position:0% +the bank of international settlement i +should say is only covers about 60 + + align:start position:0% +should say is only covers about 60 + + + align:start position:0% +should say is only covers about 60 +countries so many of the parts that are + + align:start position:0% +countries so many of the parts that are + + + align:start position:0% +countries so many of the parts that are +gray are countries that the bank + + align:start position:0% +gray are countries that the bank + + + align:start position:0% +gray are countries that the bank +national settlement didn't survey but + + align:start position:0% +national settlement didn't survey but + + + align:start position:0% +national settlement didn't survey but +those countries + + align:start position:0% +those countries + + + align:start position:0% +those countries +are probably like the u.s technically + + align:start position:0% +are probably like the u.s technically + + + align:start position:0% +are probably like the u.s technically +market driven + + align:start position:0% +market driven + + + align:start position:0% +market driven +there is no federal law in the u.s and + + align:start position:0% +there is no federal law in the u.s and + + + align:start position:0% +there is no federal law in the u.s and +there's no banking rule + + align:start position:0% +there's no banking rule + + + align:start position:0% +there's no banking rule +that prescribes that you must have open + + align:start position:0% +that prescribes that you must have open + + + align:start position:0% +that prescribes that you must have open +api in the u.s + + align:start position:0% +api in the u.s + + + align:start position:0% +api in the u.s +so i think that in colombia it might be + + align:start position:0% +so i think that in colombia it might be + + + align:start position:0% +so i think that in colombia it might be +technically market driven + + align:start position:0% +technically market driven + + + align:start position:0% +technically market driven +where the startups are using some form + + align:start position:0% +where the startups are using some form + + + align:start position:0% +where the startups are using some form +of screen scraping and some form of + + align:start position:0% +of screen scraping and some form of + + + align:start position:0% +of screen scraping and some form of +robotic process automation + + align:start position:0% +robotic process automation + + + align:start position:0% +robotic process automation +but what we found in the u.s is + + align:start position:0% +but what we found in the u.s is + + + align:start position:0% +but what we found in the u.s is +companies like stripe + + align:start position:0% +companies like stripe + + + align:start position:0% +companies like stripe +companies like plaid others that i'm + + align:start position:0% +companies like plaid others that i'm + + + align:start position:0% +companies like plaid others that i'm +going to list in a moment like yodlee + + align:start position:0% +going to list in a moment like yodlee + + + align:start position:0% +going to list in a moment like yodlee +and + + align:start position:0% +and + + + align:start position:0% +and +and others just built a business model + + align:start position:0% +and others just built a business model + + + align:start position:0% +and others just built a business model +out of creating public apis and the + + align:start position:0% +out of creating public apis and the + + + align:start position:0% +out of creating public apis and the +incumbents possibly in colombia are + + align:start position:0% +incumbents possibly in colombia are + + + align:start position:0% +incumbents possibly in colombia are +dealing with the same + + align:start position:0% +dealing with the same + + + align:start position:0% +dealing with the same +i don't know um + + align:start position:0% +i don't know um + + + align:start position:0% +i don't know um +yeah well i don't know in colombia the + + align:start position:0% +yeah well i don't know in colombia the + + + align:start position:0% +yeah well i don't know in colombia the +banks are happy to + + align:start position:0% +banks are happy to + + + align:start position:0% +banks are happy to +not let um create apis because they they + + align:start position:0% +not let um create apis because they they + + + align:start position:0% +not let um create apis because they they +don't + + align:start position:0% +don't + + + align:start position:0% +don't +believe themselves as platforms they + + align:start position:0% +believe themselves as platforms they + + + align:start position:0% +believe themselves as platforms they +prefer to charge any type of fees for + + align:start position:0% +prefer to charge any type of fees for + + + align:start position:0% +prefer to charge any type of fees for +whatever they can do it in the + + align:start position:0% +whatever they can do it in the + + + align:start position:0% +whatever they can do it in the +small print letter so they they got more + + align:start position:0% +small print letter so they they got more + + + align:start position:0% +small print letter so they they got more +defensive approach + + align:start position:0% +defensive approach + + + align:start position:0% +defensive approach +rather than what you're saying seeing + + align:start position:0% +rather than what you're saying seeing + + + align:start position:0% +rather than what you're saying seeing +themselves in a platform and monetizing + + align:start position:0% +themselves in a platform and monetizing + + + align:start position:0% +themselves in a platform and monetizing +over + + align:start position:0% +over + + + align:start position:0% +over +you know many layers of applications so + + align:start position:0% +you know many layers of applications so + + + align:start position:0% +you know many layers of applications so +uh it's it's + + align:start position:0% +uh it's it's + + + align:start position:0% +uh it's it's +yeah no no i think that i think in many + + align:start position:0% +yeah no no i think that i think in many + + + align:start position:0% +yeah no no i think that i think in many +countries + + align:start position:0% +countries + + + align:start position:0% +countries +and in many incumbents they're taking a + + align:start position:0% +and in many incumbents they're taking a + + + align:start position:0% +and in many incumbents they're taking a +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +guarded approach and sort of saying no + + align:start position:0% +guarded approach and sort of saying no + + + align:start position:0% +guarded approach and sort of saying no +no no this is this is good this is + + align:start position:0% +no no this is this is good this is + + + align:start position:0% +no no this is this is good this is +dangerous for our business model + + align:start position:0% +dangerous for our business model + + + align:start position:0% +dangerous for our business model +um this is dangerous for a business + + align:start position:0% +um this is dangerous for a business + + + align:start position:0% +um this is dangerous for a business +model but to that incumbent that does + + align:start position:0% +model but to that incumbent that does + + + align:start position:0% +model but to that incumbent that does +that often they lose out + + align:start position:0% +that often they lose out + + + align:start position:0% +that often they lose out +it sometimes takes years to lose out but + + align:start position:0% +it sometimes takes years to lose out but + + + align:start position:0% +it sometimes takes years to lose out but +it's + + align:start position:0% +it's + + + align:start position:0% +it's +you know that somebody finds a way to + + align:start position:0% +you know that somebody finds a way to + + + align:start position:0% +you know that somebody finds a way to +encroach on that business model + + align:start position:0% +encroach on that business model + + + align:start position:0% +encroach on that business model +and what we're finding around the globe + + align:start position:0% +and what we're finding around the globe + + + align:start position:0% +and what we're finding around the globe +is that more and more countries are + + align:start position:0% +is that more and more countries are + + + align:start position:0% +is that more and more countries are +promoting this brazil for instance is + + align:start position:0% +promoting this brazil for instance is + + + align:start position:0% +promoting this brazil for instance is +taking it to their national legislature + + align:start position:0% +taking it to their national legislature + + + align:start position:0% +taking it to their national legislature +now with the corona crisis i don't i + + align:start position:0% +now with the corona crisis i don't i + + + align:start position:0% +now with the corona crisis i don't i +haven't stayed closely enough it was + + align:start position:0% +haven't stayed closely enough it was + + + align:start position:0% +haven't stayed closely enough it was +gonna + + align:start position:0% +gonna + + + align:start position:0% +gonna +it looked like it was gonna pass this + + align:start position:0% +it looked like it was gonna pass this + + + align:start position:0% +it looked like it was gonna pass this +spring and maybe one of the students + + align:start position:0% +spring and maybe one of the students + + + align:start position:0% +spring and maybe one of the students +knows whether + + align:start position:0% +knows whether + + + align:start position:0% +knows whether +uh they did but the central bank was + + align:start position:0% +uh they did but the central bank was + + + align:start position:0% +uh they did but the central bank was +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +in essence insert more competition so + + align:start position:0% +in essence insert more competition so + + + align:start position:0% +in essence insert more competition so +that e2o and others in brazil + + align:start position:0% +that e2o and others in brazil + + + align:start position:0% +that e2o and others in brazil +had to sort of take a little bit more + + align:start position:0% +had to sort of take a little bit more + + + align:start position:0% +had to sort of take a little bit more +competition in that + + align:start position:0% +competition in that + + + align:start position:0% +competition in that +environment um so + + align:start position:0% +environment um so + + + align:start position:0% +environment um so +my prediction would be even in colombia + + align:start position:0% +my prediction would be even in colombia + + + align:start position:0% +my prediction would be even in colombia +it would be hard to guard against this + + align:start position:0% +it would be hard to guard against this + + + align:start position:0% +it would be hard to guard against this +for + + align:start position:0% +for + + + align:start position:0% +for +multiple years maybe a few more years + + align:start position:0% +multiple years maybe a few more years + + + align:start position:0% +multiple years maybe a few more years +but they'll be guarding a business model + + align:start position:0% +but they'll be guarding a business model + + + align:start position:0% +but they'll be guarding a business model +that will + + align:start position:0% +that will + + + align:start position:0% +that will +have some encroachment on it um the bank + + align:start position:0% +have some encroachment on it um the bank + + + align:start position:0% +have some encroachment on it um the bank +of international settlement also sort of + + align:start position:0% +of international settlement also sort of + + + align:start position:0% +of international settlement also sort of +did this chart which sort of said what's + + align:start position:0% +did this chart which sort of said what's + + + align:start position:0% +did this chart which sort of said what's +mandatory australia and europe is fuller + + align:start position:0% +mandatory australia and europe is fuller + + + align:start position:0% +mandatory australia and europe is fuller +to the mandatory that's why they're at + + align:start position:0% +to the mandatory that's why they're at + + + align:start position:0% +to the mandatory that's why they're at +the top of this chart + + align:start position:0% +the top of this chart + + + align:start position:0% +the top of this chart +and you see the us china argentina + + align:start position:0% +and you see the us china argentina + + + align:start position:0% +and you see the us china argentina +probably colombia is technically market + + align:start position:0% +probably colombia is technically market + + + align:start position:0% +probably colombia is technically market +driven towards the bottom + + align:start position:0% +driven towards the bottom + + + align:start position:0% +driven towards the bottom +it's also what products is it all about + + align:start position:0% +it's also what products is it all about + + + align:start position:0% +it's also what products is it all about +just funds transfer + + align:start position:0% +just funds transfer + + + align:start position:0% +just funds transfer +europe was more about payments was it + + align:start position:0% +europe was more about payments was it + + + align:start position:0% +europe was more about payments was it +also about the underlying product + + align:start position:0% +also about the underlying product + + + align:start position:0% +also about the underlying product +information because + + align:start position:0% +information because + + + align:start position:0% +information because +if it's forced upon the banks from the + + align:start position:0% +if it's forced upon the banks from the + + + align:start position:0% +if it's forced upon the banks from the +from the official sector in the u.s it's + + align:start position:0% +from the official sector in the u.s it's + + + align:start position:0% +from the official sector in the u.s it's +not but in europe in australia hong kong + + align:start position:0% +not but in europe in australia hong kong + + + align:start position:0% +not but in europe in australia hong kong +and has been + + align:start position:0% +and has been + + + align:start position:0% +and has been +if it's sort of by the official sector + + align:start position:0% +if it's sort of by the official sector + + + align:start position:0% +if it's sort of by the official sector +then it might well be that you have to + + align:start position:0% +then it might well be that you have to + + + align:start position:0% +then it might well be that you have to +include the product information as well + + align:start position:0% +include the product information as well + + + align:start position:0% +include the product information as well +as the information underneath it + + align:start position:0% +as the information underneath it + + + align:start position:0% +as the information underneath it +um so back to the market-driven side + + align:start position:0% +um so back to the market-driven side + + + align:start position:0% +um so back to the market-driven side +to the market-driven side is what's + + align:start position:0% +to the market-driven side is what's + + + align:start position:0% +to the market-driven side is what's +happened here in the u.s + + align:start position:0% +happened here in the u.s + + + align:start position:0% +happened here in the u.s +and what's happened here in the u.s and + + align:start position:0% +and what's happened here in the u.s and + + + align:start position:0% +and what's happened here in the u.s and +i list this is not just the us but also + + align:start position:0% +i list this is not just the us but also + + + align:start position:0% +i list this is not just the us but also +europe + + align:start position:0% +europe + + + align:start position:0% +europe +australia and some places i list about a + + align:start position:0% +australia and some places i list about a + + + align:start position:0% +australia and some places i list about a +dozen firms + + align:start position:0% +dozen firms + + + align:start position:0% +dozen firms +that are very active in this place this + + align:start position:0% +that are very active in this place this + + + align:start position:0% +that are very active in this place this +is not forced by the official sector + + align:start position:0% +is not forced by the official sector + + + align:start position:0% +is not forced by the official sector +this is basically the private sector + + align:start position:0% +this is basically the private sector + + + align:start position:0% +this is basically the private sector +saying + + align:start position:0% +saying + + + align:start position:0% +saying +let's avoid that spaghetti wire these + + align:start position:0% +let's avoid that spaghetti wire these + + + align:start position:0% +let's avoid that spaghetti wire these +are companies that are going + + align:start position:0% +are companies that are going + + + align:start position:0% +are companies that are going +in between all the startups + + align:start position:0% +in between all the startups + + + align:start position:0% +in between all the startups +and the financial firms and saying we + + align:start position:0% +and the financial firms and saying we + + + align:start position:0% +and the financial firms and saying we +can provide + + align:start position:0% +can provide + + + align:start position:0% +can provide +a standard a way to do these + + align:start position:0% +a standard a way to do these + + + align:start position:0% +a standard a way to do these +interfaces plaid that i've talked about + + align:start position:0% +interfaces plaid that i've talked about + + + align:start position:0% +interfaces plaid that i've talked about +just announced it's being sold to visa + + align:start position:0% +just announced it's being sold to visa + + + align:start position:0% +just announced it's being sold to visa +for 5.3 billion dollars + + align:start position:0% +for 5.3 billion dollars + + + align:start position:0% +for 5.3 billion dollars +what do these firms compete on + + align:start position:0% +what do these firms compete on + + + align:start position:0% +what do these firms compete on +they compete on a lot of things + + align:start position:0% +they compete on a lot of things + + + align:start position:0% +they compete on a lot of things +first is coverage if i'm plaid do i + + align:start position:0% +first is coverage if i'm plaid do i + + + align:start position:0% +first is coverage if i'm plaid do i +cover + + align:start position:0% +cover + + + align:start position:0% +cover +all the banks that you need if if i'm a + + align:start position:0% +all the banks that you need if if i'm a + + + align:start position:0% +all the banks that you need if if i'm a +new startup and i'm thinking should i + + align:start position:0% +new startup and i'm thinking should i + + + align:start position:0% +new startup and i'm thinking should i +use plaid or yodley and yogli and plaid + + align:start position:0% +use plaid or yodley and yogli and plaid + + + align:start position:0% +use plaid or yodley and yogli and plaid +are deep competitors maybe one you'd say + + align:start position:0% +are deep competitors maybe one you'd say + + + align:start position:0% +are deep competitors maybe one you'd say +just as competitive + + align:start position:0% +just as competitive + + + align:start position:0% +just as competitive +each each other as goldman sachs and + + align:start position:0% +each each other as goldman sachs and + + + align:start position:0% +each each other as goldman sachs and +morgan stanley + + align:start position:0% +morgan stanley + + + align:start position:0% +morgan stanley +yodlee was acquired years ago by a + + align:start position:0% +yodlee was acquired years ago by a + + + align:start position:0% +yodlee was acquired years ago by a +company called + + align:start position:0% +company called + + + align:start position:0% +company called +investnet but yodlee and plaid + + align:start position:0% +investnet but yodlee and plaid + + + align:start position:0% +investnet but yodlee and plaid +deep competitors each other well first + + align:start position:0% +deep competitors each other well first + + + align:start position:0% +deep competitors each other well first +what coverage do they have + + align:start position:0% +what coverage do they have + + + align:start position:0% +what coverage do they have +can if as a startup if i use plaid + + align:start position:0% +can if as a startup if i use plaid + + + align:start position:0% +can if as a startup if i use plaid +instead of yodlee can i get to all of + + align:start position:0% +instead of yodlee can i get to all of + + + align:start position:0% +instead of yodlee can i get to all of +them + + align:start position:0% +them + + + align:start position:0% +them +all of the banks what services do they + + align:start position:0% +all of the banks what services do they + + + align:start position:0% +all of the banks what services do they +give me as a developer + + align:start position:0% +give me as a developer + + + align:start position:0% +give me as a developer +obviously what price are they reliable + + align:start position:0% +obviously what price are they reliable + + + align:start position:0% +obviously what price are they reliable +what's their security + + align:start position:0% +what's their security + + + align:start position:0% +what's their security +and the like so all of these are + + align:start position:0% +and the like so all of these are + + + align:start position:0% +and the like so all of these are +important and one of the + + align:start position:0% +important and one of the + + + align:start position:0% +important and one of the +sort of incumbents in this space fist + + align:start position:0% +sort of incumbents in this space fist + + + align:start position:0% +sort of incumbents in this space fist +serve + + align:start position:0% +serve + + + align:start position:0% +serve +bought cash edge and plaid was being + + align:start position:0% +bought cash edge and plaid was being + + + align:start position:0% +bought cash edge and plaid was being +bought by + + align:start position:0% +bought by + + + align:start position:0% +bought by +visa so some of these get caught up + + align:start position:0% +visa so some of these get caught up + + + align:start position:0% +visa so some of these get caught up +sought edges in 55 countries + + align:start position:0% +sought edges in 55 countries + + + align:start position:0% +sought edges in 55 countries +and then i did a little research on a + + align:start position:0% +and then i did a little research on a + + + align:start position:0% +and then i did a little research on a +paper that was written three years ago + + align:start position:0% +paper that was written three years ago + + + align:start position:0% +paper that was written three years ago +or it's it's really a website that keeps + + align:start position:0% +or it's it's really a website that keeps + + + align:start position:0% +or it's it's really a website that keeps +a list + + align:start position:0% +a list + + + align:start position:0% +a list +and i sort of put together this list is + + align:start position:0% +and i sort of put together this list is + + + align:start position:0% +and i sort of put together this list is +three years old these + + align:start position:0% +three years old these + + + align:start position:0% +three years old these +are the account aggregators in + + align:start position:0% +are the account aggregators in + + + align:start position:0% +are the account aggregators in +all of these countries and i'm sorry + + align:start position:0% +all of these countries and i'm sorry + + + align:start position:0% +all of these countries and i'm sorry +camilo i don't see one for + + align:start position:0% +camilo i don't see one for + + + align:start position:0% +camilo i don't see one for +for uh colombia but + + align:start position:0% +for uh colombia but + + + align:start position:0% +for uh colombia but +all of these companies all of these + + align:start position:0% +all of these companies all of these + + + align:start position:0% +all of these companies all of these +companies in some way + + align:start position:0% +companies in some way + + + align:start position:0% +companies in some way +built up a business model to say we will + + align:start position:0% +built up a business model to say we will + + + align:start position:0% +built up a business model to say we will +serve + + align:start position:0% +serve + + + align:start position:0% +serve +in these various countries to be between + + align:start position:0% +in these various countries to be between + + + align:start position:0% +in these various countries to be between +the incumbents + + align:start position:0% +the incumbents + + + align:start position:0% +the incumbents +and the and the startups we will build + + align:start position:0% +and the and the startups we will build + + + align:start position:0% +and the and the startups we will build +some business model in between + + align:start position:0% + + + + align:start position:0% + +now what can you do once you do that you + + align:start position:0% +now what can you do once you do that you + + + align:start position:0% +now what can you do once you do that you +get a lot of data + + align:start position:0% +get a lot of data + + + align:start position:0% +get a lot of data +and so what used to be just a software + + align:start position:0% +and so what used to be just a software + + + align:start position:0% +and so what used to be just a software +company + + align:start position:0% +company + + + align:start position:0% +company +clad for instance started as + + align:start position:0% +clad for instance started as + + + align:start position:0% +clad for instance started as +in essence we can provide this software + + align:start position:0% +in essence we can provide this software + + + align:start position:0% +in essence we can provide this software +started to have remarkable amounts of + + align:start position:0% +started to have remarkable amounts of + + + align:start position:0% +started to have remarkable amounts of +data + + align:start position:0% +data + + + align:start position:0% +data +and that remarkable amount of data + + align:start position:0% +and that remarkable amount of data + + + align:start position:0% +and that remarkable amount of data +in clad founded in 2013 sells for 5.3 + + align:start position:0% +in clad founded in 2013 sells for 5.3 + + + align:start position:0% +in clad founded in 2013 sells for 5.3 +billion a visa or announces the sale + + align:start position:0% +billion a visa or announces the sale + + + align:start position:0% +billion a visa or announces the sale +only 450 employees and forbes estimates + + align:start position:0% +only 450 employees and forbes estimates + + + align:start position:0% +only 450 employees and forbes estimates +it's only had 109 million in revenues + + align:start position:0% +it's only had 109 million in revenues + + + align:start position:0% +it's only had 109 million in revenues +so that's nearly 50 times revenues quite + + align:start position:0% +so that's nearly 50 times revenues quite + + + align:start position:0% +so that's nearly 50 times revenues quite +a + + align:start position:0% +a + + + align:start position:0% +a +multiple you might want to wonder why + + align:start position:0% +multiple you might want to wonder why + + + align:start position:0% +multiple you might want to wonder why +visa is doing this this is from the visa + + align:start position:0% +visa is doing this this is from the visa + + + align:start position:0% +visa is doing this this is from the visa +slides that visa announced in january + + align:start position:0% +slides that visa announced in january + + + align:start position:0% +slides that visa announced in january +this is how they + + align:start position:0% +this is how they + + + align:start position:0% +this is how they +they they sort of picture + + align:start position:0% +they they sort of picture + + + align:start position:0% +they they sort of picture +they look at plaid they say plaid + + align:start position:0% +they look at plaid they say plaid + + + align:start position:0% +they look at plaid they say plaid +is connected to two thousand + + align:start position:0% +is connected to two thousand + + + align:start position:0% +is connected to two thousand +six hundred fintech firms that's 2600 + + align:start position:0% +six hundred fintech firms that's 2600 + + + align:start position:0% +six hundred fintech firms that's 2600 +fintech firms + + align:start position:0% +fintech firms + + + align:start position:0% +fintech firms +connect into plaid and then plat on the + + align:start position:0% +connect into plaid and then plat on the + + + align:start position:0% +connect into plaid and then plat on the +other side provides an api + + align:start position:0% +other side provides an api + + + align:start position:0% +other side provides an api +into eleven thousand data sources + + align:start position:0% +into eleven thousand data sources + + + align:start position:0% +into eleven thousand data sources +eleven thousand financial firms twenty + + align:start position:0% +eleven thousand financial firms twenty + + + align:start position:0% +eleven thousand financial firms twenty +six hundred fintech firms connected to + + align:start position:0% +six hundred fintech firms connected to + + + align:start position:0% +six hundred fintech firms connected to +plaid + + align:start position:0% +plaid + + + align:start position:0% +plaid +plaid connects to eleven thousand again + + align:start position:0% +plaid connects to eleven thousand again + + + align:start position:0% +plaid connects to eleven thousand again +that's the classic place you wanna be + + align:start position:0% +that's the classic place you wanna be + + + align:start position:0% +that's the classic place you wanna be +platt is at the bottleneck plat is at + + align:start position:0% +platt is at the bottleneck plat is at + + + align:start position:0% +platt is at the bottleneck plat is at +the gateway you would say + + align:start position:0% +the gateway you would say + + + align:start position:0% +the gateway you would say +and they can collect data on 200 million + + align:start position:0% +and they can collect data on 200 million + + + align:start position:0% +and they can collect data on 200 million +users + + align:start position:0% + + + + align:start position:0% + +visa thinks there's a value in that + + align:start position:0% +visa thinks there's a value in that + + + align:start position:0% +visa thinks there's a value in that +we'll have to see we'll have to see + + align:start position:0% +we'll have to see we'll have to see + + + align:start position:0% +we'll have to see we'll have to see +whether that + + align:start position:0% +whether that + + + align:start position:0% +whether that +ends up being a good acquisition for + + align:start position:0% +ends up being a good acquisition for + + + align:start position:0% +ends up being a good acquisition for +visa or not + + align:start position:0% +visa or not + + + align:start position:0% +visa or not +but these these companies in the middle + + align:start position:0% +but these these companies in the middle + + + align:start position:0% +but these these companies in the middle +the plaids the yodlees + + align:start position:0% +the plaids the yodlees + + + align:start position:0% +the plaids the yodlees +have right in the middle created value + + align:start position:0% +have right in the middle created value + + + align:start position:0% +have right in the middle created value +uh romaine i'm gonna pause there and see + + align:start position:0% +uh romaine i'm gonna pause there and see + + + align:start position:0% +uh romaine i'm gonna pause there and see +if there's some + + align:start position:0% +if there's some + + + align:start position:0% +if there's some +discussion that we can get going + + align:start position:0% + + + + align:start position:0% + +yeah professor can you share + + align:start position:0% +yeah professor can you share + + + align:start position:0% +yeah professor can you share +some insight as to the relationship + + align:start position:0% +some insight as to the relationship + + + align:start position:0% +some insight as to the relationship +between platt and the financial + + align:start position:0% +between platt and the financial + + + align:start position:0% +between platt and the financial +institutions what's he need for the + + align:start position:0% +institutions what's he need for the + + + align:start position:0% +institutions what's he need for the +finance institutions to + + align:start position:0% +finance institutions to + + + align:start position:0% +finance institutions to +face pla in reality what was it were + + align:start position:0% +face pla in reality what was it were + + + align:start position:0% +face pla in reality what was it were +there fees involved + + align:start position:0% +there fees involved + + + align:start position:0% +there fees involved +you know because in the example we + + align:start position:0% +you know because in the example we + + + align:start position:0% +you know because in the example we +looked at for some latin american + + align:start position:0% +looked at for some latin american + + + align:start position:0% +looked at for some latin american +countries + + align:start position:0% +countries + + + align:start position:0% +countries +such as brazil the incumbents are + + align:start position:0% +such as brazil the incumbents are + + + align:start position:0% +such as brazil the incumbents are +reluctant uh + + align:start position:0% +reluctant uh + + + align:start position:0% +reluctant uh +to participate in open api and they + + align:start position:0% +to participate in open api and they + + + align:start position:0% +to participate in open api and they +probably reinvent themselves + + align:start position:0% +probably reinvent themselves + + + align:start position:0% +probably reinvent themselves +it's a terrific question initially + + align:start position:0% +it's a terrific question initially + + + align:start position:0% +it's a terrific question initially +and and i'm going to apologize but i'm + + align:start position:0% +and and i'm going to apologize but i'm + + + align:start position:0% +and and i'm going to apologize but i'm +going to slide back here + + align:start position:0% +going to slide back here + + + align:start position:0% +going to slide back here +uh on the slides uh a bit to go back to + + align:start position:0% +uh on the slides uh a bit to go back to + + + align:start position:0% +uh on the slides uh a bit to go back to +something + + align:start position:0% +something + + + align:start position:0% +something +uh this is what they want to avoid + + align:start position:0% +uh this is what they want to avoid + + + align:start position:0% +uh this is what they want to avoid +this is even the incumbents don't want + + align:start position:0% +this is even the incumbents don't want + + + align:start position:0% +this is even the incumbents don't want +thousands of folks to enter into + + align:start position:0% +thousands of folks to enter into + + + align:start position:0% +thousands of folks to enter into +contractual arrangements enter into + + align:start position:0% +contractual arrangements enter into + + + align:start position:0% +contractual arrangements enter into +secure + + align:start position:0% +secure + + + align:start position:0% +secure +private apis even the incumbents want to + + align:start position:0% +private apis even the incumbents want to + + + align:start position:0% +private apis even the incumbents want to +sort of avoid this spaghetti wire of + + align:start position:0% +sort of avoid this spaghetti wire of + + + align:start position:0% +sort of avoid this spaghetti wire of +mess + + align:start position:0% +mess + + + align:start position:0% +mess +now it might have been it might have + + align:start position:0% +now it might have been it might have + + + align:start position:0% +now it might have been it might have +been + + align:start position:0% +been + + + align:start position:0% +been +less strategic and more incremental + + align:start position:0% +less strategic and more incremental + + + align:start position:0% +less strategic and more incremental +that when you think about + + align:start position:0% + + + + align:start position:0% + +thinking about all these companies on + + align:start position:0% +thinking about all these companies on + + + align:start position:0% +thinking about all these companies on +this list these + + align:start position:0% +this list these + + + align:start position:0% +this list these +10 or 12 that have built up these + + align:start position:0% +10 or 12 that have built up these + + + align:start position:0% +10 or 12 that have built up these +remarkable businesses + + align:start position:0% +remarkable businesses + + + align:start position:0% +remarkable businesses +or around the globe all these that many + + align:start position:0% +or around the globe all these that many + + + align:start position:0% +or around the globe all these that many +of these started as small + + align:start position:0% +of these started as small + + + align:start position:0% +of these started as small +software providers and they were saying + + align:start position:0% +software providers and they were saying + + + align:start position:0% +software providers and they were saying +to the big incumbents + + align:start position:0% +to the big incumbents + + + align:start position:0% +to the big incumbents +we can we can handle that spaghetti wire + + align:start position:0% +we can we can handle that spaghetti wire + + + align:start position:0% +we can we can handle that spaghetti wire +we can ensure that people aren't just + + align:start position:0% +we can ensure that people aren't just + + + align:start position:0% +we can ensure that people aren't just +screen scraping + + align:start position:0% +screen scraping + + + align:start position:0% +screen scraping +and using rpa it's going to happen + + align:start position:0% +and using rpa it's going to happen + + + align:start position:0% +and using rpa it's going to happen +anyway you need somebody to help manage + + align:start position:0% +anyway you need somebody to help manage + + + align:start position:0% +anyway you need somebody to help manage +and so every modern online company + + align:start position:0% +and so every modern online company + + + align:start position:0% +and so every modern online company +in finance and outside of finance has to + + align:start position:0% +in finance and outside of finance has to + + + align:start position:0% +in finance and outside of finance has to +have an ap + + align:start position:0% +have an ap + + + align:start position:0% +have an ap +management strategy you don't normally + + align:start position:0% +management strategy you don't normally + + + align:start position:0% +management strategy you don't normally +think about something + + align:start position:0% +think about something + + + align:start position:0% +think about something +you would sort of in the ceo suite this + + align:start position:0% +you would sort of in the ceo suite this + + + align:start position:0% +you would sort of in the ceo suite this +chief executive officer is managing this + + align:start position:0% +chief executive officer is managing this + + + align:start position:0% +chief executive officer is managing this +but here we are at mit i'd like to bring + + align:start position:0% +but here we are at mit i'd like to bring + + + align:start position:0% +but here we are at mit i'd like to bring +this technology this is an important + + align:start position:0% +this technology this is an important + + + align:start position:0% +this technology this is an important +technology question that you need to be + + align:start position:0% +technology question that you need to be + + + align:start position:0% +technology question that you need to be +asking is + + align:start position:0% +asking is + + + align:start position:0% +asking is +how are we managing our developer + + align:start position:0% +how are we managing our developer + + + align:start position:0% +how are we managing our developer +community + + align:start position:0% +community + + + align:start position:0% +community +our public interface are we gonna + + align:start position:0% +our public interface are we gonna + + + align:start position:0% +our public interface are we gonna +do it internally are we gonna hire a + + align:start position:0% +do it internally are we gonna hire a + + + align:start position:0% +do it internally are we gonna hire a +plaid + + align:start position:0% +plaid + + + align:start position:0% +plaid +and and i can tell you that the banks + + align:start position:0% +and and i can tell you that the banks + + + align:start position:0% +and and i can tell you that the banks +now this is + + align:start position:0% +now this is + + + align:start position:0% +now this is +this has happened in the last four to + + align:start position:0% +this has happened in the last four to + + + align:start position:0% +this has happened in the last four to +seven years + + align:start position:0% +seven years + + + align:start position:0% +seven years +and many of the banks are sort of saying + + align:start position:0% +and many of the banks are sort of saying + + + align:start position:0% +and many of the banks are sort of saying +is this gotten out of hand + + align:start position:0% +is this gotten out of hand + + + align:start position:0% +is this gotten out of hand +has this gotten out of control is this + + align:start position:0% +has this gotten out of control is this + + + align:start position:0% +has this gotten out of control is this +something that we really want to + + align:start position:0% +something that we really want to + + + align:start position:0% +something that we really want to +allow the plaids and the yodlees and + + align:start position:0% +allow the plaids and the yodlees and + + + align:start position:0% +allow the plaids and the yodlees and +others to commercialize our data + + align:start position:0% + + + + align:start position:0% + +but i think that in part it was + + align:start position:0% +but i think that in part it was + + + align:start position:0% +but i think that in part it was +incrementally decisions about how to + + align:start position:0% +incrementally decisions about how to + + + align:start position:0% +incrementally decisions about how to +manage + + align:start position:0% +manage + + + align:start position:0% +manage +broadly this interface and + + align:start position:0% +broadly this interface and + + + align:start position:0% +broadly this interface and +it it's also possible that it wasn't far + + align:start position:0% +it it's also possible that it wasn't far + + + align:start position:0% +it it's also possible that it wasn't far +enough + + align:start position:0% +enough + + + align:start position:0% +enough +up the in the c-suite and it was sort of + + align:start position:0% +up the in the c-suite and it was sort of + + + align:start position:0% +up the in the c-suite and it was sort of +managed down in some regards + + align:start position:0% +managed down in some regards + + + align:start position:0% +managed down in some regards +um but one one reaction + + align:start position:0% +um but one one reaction + + + align:start position:0% +um but one one reaction +is this financial data exchange that's + + align:start position:0% +is this financial data exchange that's + + + align:start position:0% +is this financial data exchange that's +happened here + + align:start position:0% +happened here + + + align:start position:0% +happened here +and there i've listed the major founders + + align:start position:0% +and there i've listed the major founders + + + align:start position:0% +and there i've listed the major founders +of fdx + + align:start position:0% +of fdx + + + align:start position:0% +of fdx +but financial data exchange and this is + + align:start position:0% +but financial data exchange and this is + + + align:start position:0% +but financial data exchange and this is +straight from their + + align:start position:0% +straight from their + + + align:start position:0% +straight from their +their own white paper they want to + + align:start position:0% +their own white paper they want to + + + align:start position:0% +their own white paper they want to +create this group of remarkably large + + align:start position:0% +create this group of remarkably large + + + align:start position:0% +create this group of remarkably large +banks i think the members of + + align:start position:0% +banks i think the members of + + + align:start position:0% +banks i think the members of +fdx have two trillion dollars + + align:start position:0% +fdx have two trillion dollars + + + align:start position:0% +fdx have two trillion dollars +of of market value if i remember + + align:start position:0% +of of market value if i remember + + + align:start position:0% +of of market value if i remember +um because many of these actually uh + + align:start position:0% +um because many of these actually uh + + + align:start position:0% +um because many of these actually uh +have + + align:start position:0% +have + + + align:start position:0% +have +uh two trillion dollar balance sheets + + align:start position:0% +uh two trillion dollar balance sheets + + + align:start position:0% +uh two trillion dollar balance sheets +it's + + align:start position:0% +it's + + + align:start position:0% +it's +when you add up all of these companies + + align:start position:0% +when you add up all of these companies + + + align:start position:0% +when you add up all of these companies +they've come together and say we want to + + align:start position:0% +they've come together and say we want to + + + align:start position:0% +they've come together and say we want to +create standards for financial data + + align:start position:0% +create standards for financial data + + + align:start position:0% +create standards for financial data +sharing + + align:start position:0% +sharing + + + align:start position:0% +sharing +and secure apis we want to basically + + align:start position:0% +and secure apis we want to basically + + + align:start position:0% +and secure apis we want to basically +not sort of have the plaids and the + + align:start position:0% +not sort of have the plaids and the + + + align:start position:0% +not sort of have the plaids and the +others commercialize their data + + align:start position:0% +others commercialize their data + + + align:start position:0% +others commercialize their data +even though that's not in their the + + align:start position:0% +even though that's not in their the + + + align:start position:0% +even though that's not in their the +fdx's + + align:start position:0% +fdx's + + + align:start position:0% +fdx's +mandate + + align:start position:0% + + + + align:start position:0% + +but in some regards the cat's already + + align:start position:0% +but in some regards the cat's already + + + align:start position:0% +but in some regards the cat's already +out of the board + + align:start position:0% +out of the board + + + align:start position:0% +out of the board +and now they're grappling with it but + + align:start position:0% +and now they're grappling with it but + + + align:start position:0% +and now they're grappling with it but +but the jp morgan's + + align:start position:0% +but the jp morgan's + + + align:start position:0% +but the jp morgan's +and the pnc actually i believe + + align:start position:0% +and the pnc actually i believe + + + align:start position:0% +and the pnc actually i believe +which is a large uh mid-sized bank in + + align:start position:0% +which is a large uh mid-sized bank in + + + align:start position:0% +which is a large uh mid-sized bank in +the us + + align:start position:0% +the us + + + align:start position:0% +the us +has stopped having plaid have access + + align:start position:0% +has stopped having plaid have access + + + align:start position:0% +has stopped having plaid have access +if i'm not mistaken so it's sort of an + + align:start position:0% +if i'm not mistaken so it's sort of an + + + align:start position:0% +if i'm not mistaken so it's sort of an +interesting challenge back and forth + + align:start position:0% +interesting challenge back and forth + + + align:start position:0% +interesting challenge back and forth +you now have gita and then lin + + align:start position:0% +you now have gita and then lin + + + align:start position:0% +you now have gita and then lin +from the incumbent side to tell us why + + align:start position:0% +from the incumbent side to tell us why + + + align:start position:0% +from the incumbent side to tell us why +they're using the plaids + + align:start position:0% +they're using the plaids + + + align:start position:0% +they're using the plaids +yeah i just wanted to make a comment on + + align:start position:0% +yeah i just wanted to make a comment on + + + align:start position:0% +yeah i just wanted to make a comment on +plant specifically + + align:start position:0% +plant specifically + + + align:start position:0% +plant specifically +um we allow access to a number of + + align:start position:0% +um we allow access to a number of + + + align:start position:0% +um we allow access to a number of +fintech vendors + + align:start position:0% +fintech vendors + + + align:start position:0% +fintech vendors +uh to our data because and then we have + + align:start position:0% +uh to our data because and then we have + + + align:start position:0% +uh to our data because and then we have +no choice because + + align:start position:0% +no choice because + + + align:start position:0% +no choice because +the customer is providing access to + + align:start position:0% +the customer is providing access to + + + align:start position:0% +the customer is providing access to +their data and we have to allow them to + + align:start position:0% +their data and we have to allow them to + + + align:start position:0% +their data and we have to allow them to +access it + + align:start position:0% +access it + + + align:start position:0% +access it +uh the biggest to somebody's question + + align:start position:0% +uh the biggest to somebody's question + + + align:start position:0% +uh the biggest to somebody's question +earlier the biggest problem with plaid + + align:start position:0% +earlier the biggest problem with plaid + + + align:start position:0% +earlier the biggest problem with plaid +and i'll probably send some articles on + + align:start position:0% +and i'll probably send some articles on + + + align:start position:0% +and i'll probably send some articles on +kind of issues between platinum capital + + align:start position:0% +kind of issues between platinum capital + + + align:start position:0% +kind of issues between platinum capital +one + + align:start position:0% +one + + + align:start position:0% +one +there was a period of time when we + + align:start position:0% +there was a period of time when we + + + align:start position:0% +there was a period of time when we +stopped access giving access to plaid + + align:start position:0% +stopped access giving access to plaid + + + align:start position:0% +stopped access giving access to plaid +because + + align:start position:0% +because + + + align:start position:0% +because +plaid wouldn't comply with any of the + + align:start position:0% +plaid wouldn't comply with any of the + + + align:start position:0% +plaid wouldn't comply with any of the +standards that we imposed + + align:start position:0% +standards that we imposed + + + align:start position:0% +standards that we imposed +for example we needed fintech vendors to + + align:start position:0% +for example we needed fintech vendors to + + + align:start position:0% +for example we needed fintech vendors to +come from certain ips because they look + + align:start position:0% +come from certain ips because they look + + + align:start position:0% +come from certain ips because they look +like bots right because they do + + align:start position:0% +like bots right because they do + + + align:start position:0% +like bots right because they do +all these batch accesses and they look + + align:start position:0% +all these batch accesses and they look + + + align:start position:0% +all these batch accesses and they look +like bots but plaid wouldn't comply with + + align:start position:0% +like bots but plaid wouldn't comply with + + + align:start position:0% +like bots but plaid wouldn't comply with +those + + align:start position:0% +those + + + align:start position:0% +those +those standards and it became very + + align:start position:0% +those standards and it became very + + + align:start position:0% +those standards and it became very +difficult for us to + + align:start position:0% +difficult for us to + + + align:start position:0% +difficult for us to +differentiate clad from a bot + + align:start position:0% +differentiate clad from a bot + + + align:start position:0% +differentiate clad from a bot +um and even though we had apis they + + align:start position:0% +um and even though we had apis they + + + align:start position:0% +um and even though we had apis they +would do screen scraping sometimes they + + align:start position:0% +would do screen scraping sometimes they + + + align:start position:0% +would do screen scraping sometimes they +would come through + + align:start position:0% +would come through + + + align:start position:0% +would come through +our mobile channels sometimes they would + + align:start position:0% +our mobile channels sometimes they would + + + align:start position:0% +our mobile channels sometimes they would +come through our web channels they would + + align:start position:0% +come through our web channels they would + + + align:start position:0% +come through our web channels they would +come through any api + + align:start position:0% +come through any api + + + align:start position:0% +come through any api +it became really hard for us to + + align:start position:0% +it became really hard for us to + + + align:start position:0% +it became really hard for us to +differentiate plan from + + align:start position:0% +differentiate plan from + + + align:start position:0% +differentiate plan from +uh fraudsters so there was a period of + + align:start position:0% +uh fraudsters so there was a period of + + + align:start position:0% +uh fraudsters so there was a period of +time when we blocked pled + + align:start position:0% +time when we blocked pled + + + align:start position:0% +time when we blocked pled +and and then they came to the table we + + align:start position:0% +and and then they came to the table we + + + align:start position:0% +and and then they came to the table we +had conversations and then let them in + + align:start position:0% + + + + align:start position:0% + +and you were cap one yes + + align:start position:0% +and you were cap one yes + + + align:start position:0% +and you were cap one yes +yeah so for those who might not be + + align:start position:0% +yeah so for those who might not be + + + align:start position:0% +yeah so for those who might not be +familiar cap one is + + align:start position:0% +familiar cap one is + + + align:start position:0% +familiar cap one is +one of the largest credit card banks in + + align:start position:0% +one of the largest credit card banks in + + + align:start position:0% +one of the largest credit card banks in +the u.s competing + + align:start position:0% +the u.s competing + + + align:start position:0% +the u.s competing +head-to-head with bank of america and + + align:start position:0% +head-to-head with bank of america and + + + align:start position:0% +head-to-head with bank of america and +city and chase + + align:start position:0% +city and chase + + + align:start position:0% +city and chase +uh discover and uh american express and + + align:start position:0% +uh discover and uh american express and + + + align:start position:0% +uh discover and uh american express and +so forth i sort of call it the big seven + + align:start position:0% +so forth i sort of call it the big seven + + + align:start position:0% +so forth i sort of call it the big seven +um and and cap one's the largest + + align:start position:0% +um and and cap one's the largest + + + align:start position:0% +um and and cap one's the largest +that isn't in and of itself one of the + + align:start position:0% +that isn't in and of itself one of the + + + align:start position:0% +that isn't in and of itself one of the +big + + align:start position:0% +big + + + align:start position:0% +big +four banks in the u.s um + + align:start position:0% + + + + align:start position:0% + +so it's a remarkable organization and + + align:start position:0% +so it's a remarkable organization and + + + align:start position:0% +so it's a remarkable organization and +it's cut out a + + align:start position:0% +it's cut out a + + + align:start position:0% +it's cut out a +big chunk of its business model + + align:start position:0% +big chunk of its business model + + + align:start position:0% +big chunk of its business model +around serving customers in the credit + + align:start position:0% +around serving customers in the credit + + + align:start position:0% +around serving customers in the credit +card space + + align:start position:0% +card space + + + align:start position:0% +card space +uh and here you're hearing gita say but + + align:start position:0% +uh and here you're hearing gita say but + + + align:start position:0% +uh and here you're hearing gita say but +we didn't really have a choice + + align:start position:0% +we didn't really have a choice + + + align:start position:0% +we didn't really have a choice +um we is what you're saying + + align:start position:0% +um we is what you're saying + + + align:start position:0% +um we is what you're saying +yeah um + + align:start position:0% + + + + align:start position:0% + +romaine others let's go with lin and + + align:start position:0% +romaine others let's go with lin and + + + align:start position:0% +romaine others let's go with lin and +then + + align:start position:0% +then + + + align:start position:0% +then +carlos if we have time please um yeah so + + align:start position:0% +carlos if we have time please um yeah so + + + align:start position:0% +carlos if we have time please um yeah so +in the example for plaid + + align:start position:0% +in the example for plaid + + + align:start position:0% +in the example for plaid +uh it seems like most of the data if not + + align:start position:0% +uh it seems like most of the data if not + + + align:start position:0% +uh it seems like most of the data if not +all of the data + + align:start position:0% +all of the data + + + align:start position:0% +all of the data +is financial data coming from financial + + align:start position:0% +is financial data coming from financial + + + align:start position:0% +is financial data coming from financial +institutions i'm just curious to hear + + align:start position:0% +institutions i'm just curious to hear + + + align:start position:0% +institutions i'm just curious to hear +your thoughts on um the market moving + + align:start position:0% +your thoughts on um the market moving + + + align:start position:0% +your thoughts on um the market moving +towards using non-financial data + + align:start position:0% +towards using non-financial data + + + align:start position:0% +towards using non-financial data +so uh customer data in the retail health + + align:start position:0% +so uh customer data in the retail health + + + align:start position:0% +so uh customer data in the retail health +sector to + + align:start position:0% +sector to + + + align:start position:0% +sector to +inform or build um financial services + + align:start position:0% +inform or build um financial services + + + align:start position:0% +inform or build um financial services +upon and whether + + align:start position:0% +upon and whether + + + align:start position:0% +upon and whether +there are any people doing that at the + + align:start position:0% +there are any people doing that at the + + + align:start position:0% +there are any people doing that at the +moment you know it's a really good + + align:start position:0% +moment you know it's a really good + + + align:start position:0% +moment you know it's a really good +uh observation that + + align:start position:0% +uh observation that + + + align:start position:0% +uh observation that +the data aggregators uh i'll go back uh + + align:start position:0% +the data aggregators uh i'll go back uh + + + align:start position:0% +the data aggregators uh i'll go back uh +aside this whole cacophony + + align:start position:0% +aside this whole cacophony + + + align:start position:0% +aside this whole cacophony +from three years ago around the globe or + + align:start position:0% +from three years ago around the globe or + + + align:start position:0% +from three years ago around the globe or +the data aggregators here in the u.s the + + align:start position:0% +the data aggregators here in the u.s the + + + align:start position:0% +the data aggregators here in the u.s the +these big eight or ten in the us and + + align:start position:0% +these big eight or ten in the us and + + + align:start position:0% +these big eight or ten in the us and +europe + + align:start position:0% +europe + + + align:start position:0% +europe +these data aggregators are largely about + + align:start position:0% +these data aggregators are largely about + + + align:start position:0% +these data aggregators are largely about +financial data + + align:start position:0% +financial data + + + align:start position:0% +financial data +for now so their their + + align:start position:0% +for now so their their + + + align:start position:0% +for now so their their +their business strategy these this dozen + + align:start position:0% +their business strategy these this dozen + + + align:start position:0% +their business strategy these this dozen +companies their business strategies was + + align:start position:0% +companies their business strategies was + + + align:start position:0% +companies their business strategies was +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +api first they built an api + + align:start position:0% +api first they built an api + + + align:start position:0% +api first they built an api +upon which they got a network advantage + + align:start position:0% +upon which they got a network advantage + + + align:start position:0% +upon which they got a network advantage +to get a lot of financial data + + align:start position:0% +to get a lot of financial data + + + align:start position:0% +to get a lot of financial data +but it is also true that they could add + + align:start position:0% +but it is also true that they could add + + + align:start position:0% +but it is also true that they could add +other data + + align:start position:0% +other data + + + align:start position:0% +other data +and in fact plaid gets bought by visa + + align:start position:0% +and in fact plaid gets bought by visa + + + align:start position:0% +and in fact plaid gets bought by visa +yodlee got bought by envestnet and + + align:start position:0% +yodlee got bought by envestnet and + + + align:start position:0% +yodlee got bought by envestnet and +envestnet is also + + align:start position:0% +envestnet is also + + + align:start position:0% +envestnet is also +in uh asset management and fund + + align:start position:0% +in uh asset management and fund + + + align:start position:0% +in uh asset management and fund +management + + align:start position:0% +management + + + align:start position:0% +management +and so forth i believe you're right your + + align:start position:0% +and so forth i believe you're right your + + + align:start position:0% +and so forth i believe you're right your +observation is right is a lot of these + + align:start position:0% +observation is right is a lot of these + + + align:start position:0% +observation is right is a lot of these +api first data aggregator second + + align:start position:0% +api first data aggregator second + + + align:start position:0% +api first data aggregator second +are also going to be adding other + + align:start position:0% +are also going to be adding other + + + align:start position:0% +are also going to be adding other +non-financial + + align:start position:0% +non-financial + + + align:start position:0% +non-financial +data alternative data as we've talked + + align:start position:0% +data alternative data as we've talked + + + align:start position:0% +data alternative data as we've talked +about + + align:start position:0% +about + + + align:start position:0% +about +can come from finance like whether + + align:start position:0% +can come from finance like whether + + + align:start position:0% +can come from finance like whether +you're paying your utility bill or not + + align:start position:0% +you're paying your utility bill or not + + + align:start position:0% +you're paying your utility bill or not +it can come from finance and building + + align:start position:0% +it can come from finance and building + + + align:start position:0% +it can come from finance and building +full cash flow + + align:start position:0% +full cash flow + + + align:start position:0% +full cash flow +underwriting models but it also can be + + align:start position:0% +underwriting models but it also can be + + + align:start position:0% +underwriting models but it also can be +your social media + + align:start position:0% +your social media + + + align:start position:0% +your social media +footprint and often is alternative data + + align:start position:0% +footprint and often is alternative data + + + align:start position:0% +footprint and often is alternative data +is about your social media input + + align:start position:0% +is about your social media input + + + align:start position:0% +is about your social media input +and and and your footprint i should say + + align:start position:0% +and and and your footprint i should say + + + align:start position:0% +and and and your footprint i should say +your footprint + + align:start position:0% +your footprint + + + align:start position:0% +your footprint +so i think you're right uh their + + align:start position:0% +so i think you're right uh their + + + align:start position:0% +so i think you're right uh their +comparative advantage + + align:start position:0% +comparative advantage + + + align:start position:0% +comparative advantage +is around this financial data plaid + + align:start position:0% +is around this financial data plaid + + + align:start position:0% +is around this financial data plaid +uh that's that's their that's their + + align:start position:0% +uh that's that's their that's their + + + align:start position:0% +uh that's that's their that's their +their uh advantage i want to know one + + align:start position:0% +their uh advantage i want to know one + + + align:start position:0% +their uh advantage i want to know one +company uh that's on this + + align:start position:0% +company uh that's on this + + + align:start position:0% +company uh that's on this +uh list here i think i included was + + align:start position:0% +uh list here i think i included was + + + align:start position:0% +uh list here i think i included was +galileo + + align:start position:0% +galileo + + + align:start position:0% +galileo +did i yeah i included galileo galileo's + + align:start position:0% +did i yeah i included galileo galileo's + + + align:start position:0% +did i yeah i included galileo galileo's +done a recent fundraising round + + align:start position:0% +done a recent fundraising round + + + align:start position:0% +done a recent fundraising round +in the middle of 2019. it's still + + align:start position:0% +in the middle of 2019. it's still + + + align:start position:0% +in the middle of 2019. it's still +private + + align:start position:0% +private + + + align:start position:0% +private +i think their valuation was 1.2 billion + + align:start position:0% +i think their valuation was 1.2 billion + + + align:start position:0% +i think their valuation was 1.2 billion +might have been a little higher if i + + align:start position:0% +might have been a little higher if i + + + align:start position:0% +might have been a little higher if i +can't recall the figure so it's a + + align:start position:0% +can't recall the figure so it's a + + + align:start position:0% +can't recall the figure so it's a +unicorn not many of us have heard of + + align:start position:0% +unicorn not many of us have heard of + + + align:start position:0% +unicorn not many of us have heard of +galileo + + align:start position:0% +galileo + + + align:start position:0% +galileo +but two of their big customers chime + + align:start position:0% +but two of their big customers chime + + + align:start position:0% +but two of their big customers chime +uh is what well i'll just say chime is + + align:start position:0% +uh is what well i'll just say chime is + + + align:start position:0% +uh is what well i'll just say chime is +one + + align:start position:0% +one + + + align:start position:0% +one +fintech company that's one of their big + + align:start position:0% +fintech company that's one of their big + + + align:start position:0% +fintech company that's one of their big +customers last year galileo had a glitch + + align:start position:0% +customers last year galileo had a glitch + + + align:start position:0% +customers last year galileo had a glitch +and chime went down for 24 hours because + + align:start position:0% +and chime went down for 24 hours because + + + align:start position:0% +and chime went down for 24 hours because +galileo's standards and api + + align:start position:0% +galileo's standards and api + + + align:start position:0% +galileo's standards and api +had a glitch so tom sometimes you're + + align:start position:0% +had a glitch so tom sometimes you're + + + align:start position:0% +had a glitch so tom sometimes you're +that fintech startup + + align:start position:0% +that fintech startup + + + align:start position:0% +that fintech startup +relying upon a galileo in that instance + + align:start position:0% +relying upon a galileo in that instance + + + align:start position:0% +relying upon a galileo in that instance +and if galileo's software has a problem + + align:start position:0% +and if galileo's software has a problem + + + align:start position:0% +and if galileo's software has a problem +you have a problem + + align:start position:0% +you have a problem + + + align:start position:0% +you have a problem +so there's there's there's that uh + + align:start position:0% +so there's there's there's that uh + + + align:start position:0% +so there's there's there's that uh +challenge too + + align:start position:0% +challenge too + + + align:start position:0% +challenge too +in in the midst of this uh marquetta has + + align:start position:0% +in in the midst of this uh marquetta has + + + align:start position:0% +in in the midst of this uh marquetta has +done a + + align:start position:0% +done a + + + align:start position:0% +done a +fundraising round i think its valuation + + align:start position:0% +fundraising round i think its valuation + + + align:start position:0% +fundraising round i think its valuation +is about two billion + + align:start position:0% +is about two billion + + + align:start position:0% +is about two billion +dollars uh again still private still in + + align:start position:0% +dollars uh again still private still in + + + align:start position:0% +dollars uh again still private still in +the venture + + align:start position:0% +the venture + + + align:start position:0% +the venture +uh land and so forth so there's there's + + align:start position:0% +uh land and so forth so there's there's + + + align:start position:0% +uh land and so forth so there's there's +significant value that has been built + + align:start position:0% + + + + align:start position:0% + +api first data aggregation second and + + align:start position:0% +api first data aggregation second and + + + align:start position:0% +api first data aggregation second and +these companies are all + + align:start position:0% +these companies are all + + + align:start position:0% +these companies are all +somewhere between the incumbents and the + + align:start position:0% +somewhere between the incumbents and the + + + align:start position:0% +somewhere between the incumbents and the +developer community and the startups + + align:start position:0% +developer community and the startups + + + align:start position:0% +developer community and the startups +back to the class romain carlos is up + + align:start position:0% +back to the class romain carlos is up + + + align:start position:0% +back to the class romain carlos is up +hi so i just wanted to give an example + + align:start position:0% +hi so i just wanted to give an example + + + align:start position:0% +hi so i just wanted to give an example +of a shout out to plaid really + + align:start position:0% +of a shout out to plaid really + + + align:start position:0% +of a shout out to plaid really +for something they're doing at the + + align:start position:0% +for something they're doing at the + + + align:start position:0% +for something they're doing at the +moment so as part of the sba + + align:start position:0% +moment so as part of the sba + + + align:start position:0% +moment so as part of the sba +ppp program for emergency funding to + + align:start position:0% +ppp program for emergency funding to + + + align:start position:0% +ppp program for emergency funding to +small businesses with the whole coronet + + align:start position:0% +small businesses with the whole coronet + + + align:start position:0% +small businesses with the whole coronet +crisis + + align:start position:0% +crisis + + + align:start position:0% +crisis +you know there's 300 billion dollars + + align:start position:0% +you know there's 300 billion dollars + + + align:start position:0% +you know there's 300 billion dollars +being disbursed over the course of three + + align:start position:0% +being disbursed over the course of three + + + align:start position:0% +being disbursed over the course of three +months and actually + + align:start position:0% +months and actually + + + align:start position:0% +months and actually +probably there's thursday there's gonna + + align:start position:0% +probably there's thursday there's gonna + + + align:start position:0% +probably there's thursday there's gonna +be an additional 200 billion approved + + align:start position:0% +be an additional 200 billion approved + + + align:start position:0% +be an additional 200 billion approved +so 250 sorry so what plat is doing is + + align:start position:0% +so 250 sorry so what plat is doing is + + + align:start position:0% +so 250 sorry so what plat is doing is +they're actually helping + + align:start position:0% +they're actually helping + + + align:start position:0% +they're actually helping +because of the the rosa data aggregator + + align:start position:0% +because of the the rosa data aggregator + + + align:start position:0% +because of the the rosa data aggregator +to populate the payroll portion of these + + align:start position:0% +to populate the payroll portion of these + + + align:start position:0% +to populate the payroll portion of these +loans + + align:start position:0% +loans + + + align:start position:0% +loans +of these loan applications sorry because + + align:start position:0% +of these loan applications sorry because + + + align:start position:0% +of these loan applications sorry because +a lot of banks are trying to do it + + align:start position:0% +a lot of banks are trying to do it + + + align:start position:0% +a lot of banks are trying to do it +manually + + align:start position:0% +manually + + + align:start position:0% +manually +which is completely feasible given the + + align:start position:0% +which is completely feasible given the + + + align:start position:0% +which is completely feasible given the +the massive size of the role that + + align:start position:0% +the massive size of the role that + + + align:start position:0% +the massive size of the role that +they're proposing + + align:start position:0% +they're proposing + + + align:start position:0% +they're proposing +so thanks to plaid and what they're + + align:start position:0% +so thanks to plaid and what they're + + + align:start position:0% +so thanks to plaid and what they're +trying to do at least like a lot of + + align:start position:0% +trying to do at least like a lot of + + + align:start position:0% +trying to do at least like a lot of +loans can be approved + + align:start position:0% +loans can be approved + + + align:start position:0% +loans can be approved +or at least application submitted + + align:start position:0% +or at least application submitted + + + align:start position:0% +or at least application submitted +exponentially faster and that can make a + + align:start position:0% +exponentially faster and that can make a + + + align:start position:0% +exponentially faster and that can make a +huge difference for businesses to + + align:start position:0% +huge difference for businesses to + + + align:start position:0% +huge difference for businesses to +survive + + align:start position:0% +survive + + + align:start position:0% +survive +and and uh i thank you for bringing that + + align:start position:0% +and and uh i thank you for bringing that + + + align:start position:0% +and and uh i thank you for bringing that +information + + align:start position:0% +information + + + align:start position:0% +information +in do you uh work with plaid or have you + + align:start position:0% +in do you uh work with plaid or have you + + + align:start position:0% +in do you uh work with plaid or have you +worked there or this something you're + + align:start position:0% +worked there or this something you're + + + align:start position:0% +worked there or this something you're +reading about + + align:start position:0% +reading about + + + align:start position:0% +reading about +uh online so i've been following because + + align:start position:0% +uh online so i've been following because + + + align:start position:0% +uh online so i've been following because +i work for + + align:start position:0% +i work for + + + align:start position:0% +i work for +for a fintech focus vc that actually + + align:start position:0% +for a fintech focus vc that actually + + + align:start position:0% +for a fintech focus vc that actually +invested in kobo which was acquired by + + align:start position:0% +invested in kobo which was acquired by + + + align:start position:0% +invested in kobo which was acquired by +plaid so + + align:start position:0% +plaid so + + + align:start position:0% +plaid so +so i know the model pretty well these + + align:start position:0% +so i know the model pretty well these + + + align:start position:0% +so i know the model pretty well these +companies + + align:start position:0% +companies + + + align:start position:0% +companies +have brought a great deal more financial + + align:start position:0% +have brought a great deal more financial + + + align:start position:0% +have brought a great deal more financial +inclusion + + align:start position:0% +inclusion + + + align:start position:0% +inclusion +these companies have opened up the + + align:start position:0% +these companies have opened up the + + + align:start position:0% +these companies have opened up the +banking sector to some extent and now + + align:start position:0% +banking sector to some extent and now + + + align:start position:0% +banking sector to some extent and now +the banking sector was probably + + align:start position:0% +the banking sector was probably + + + align:start position:0% +the banking sector was probably +going to be opened up by competitive + + align:start position:0% +going to be opened up by competitive + + + align:start position:0% +going to be opened up by competitive +pressures in any + + align:start position:0% +pressures in any + + + align:start position:0% +pressures in any +regard but with the plaids + + align:start position:0% +regard but with the plaids + + + align:start position:0% +regard but with the plaids +earlier stripe the gala galileos and the + + align:start position:0% +earlier stripe the gala galileos and the + + + align:start position:0% +earlier stripe the gala galileos and the +yogli's and others what they've done is + + align:start position:0% +yogli's and others what they've done is + + + align:start position:0% +yogli's and others what they've done is +they've brought some standardization + + align:start position:0% +they've brought some standardization + + + align:start position:0% +they've brought some standardization +to that spaghetti wire that i put + + align:start position:0% +to that spaghetti wire that i put + + + align:start position:0% +to that spaghetti wire that i put +earlier this these + + align:start position:0% +earlier this these + + + align:start position:0% +earlier this these +these interfaces these sort of they're + + align:start position:0% +these interfaces these sort of they're + + + align:start position:0% +these interfaces these sort of they're +they're in the weeds they're just + + align:start position:0% +they're in the weeds they're just + + + align:start position:0% +they're in the weeds they're just +to some of us it might just be mundane + + align:start position:0% +to some of us it might just be mundane + + + align:start position:0% +to some of us it might just be mundane +uh + + align:start position:0% +uh + + + align:start position:0% +uh +connections but they're not they're + + align:start position:0% +connections but they're not they're + + + align:start position:0% +connections but they're not they're +really really + + align:start position:0% +really really + + + align:start position:0% +really really +important connections and i would say if + + align:start position:0% +important connections and i would say if + + + align:start position:0% +important connections and i would say if +you take anything out of this lecture + + align:start position:0% +you take anything out of this lecture + + + align:start position:0% +you take anything out of this lecture +moving forward if you're at an incumbent + + align:start position:0% +moving forward if you're at an incumbent + + + align:start position:0% +moving forward if you're at an incumbent +or you're at a start-off + + align:start position:0% +or you're at a start-off + + + align:start position:0% +or you're at a start-off +that you sort of think about your api + + align:start position:0% +that you sort of think about your api + + + align:start position:0% +that you sort of think about your api +strategy + + align:start position:0% +strategy + + + align:start position:0% +strategy +what is it you might not manage it but + + align:start position:0% +what is it you might not manage it but + + + align:start position:0% +what is it you might not manage it but +it's good to know what it is + + align:start position:0% +it's good to know what it is + + + align:start position:0% +it's good to know what it is +you might know what's your competitor's + + align:start position:0% +you might know what's your competitor's + + + align:start position:0% +you might know what's your competitor's +uh uh + + align:start position:0% +uh uh + + + align:start position:0% +uh uh +view of it but i agree with carlos that + + align:start position:0% +view of it but i agree with carlos that + + + align:start position:0% +view of it but i agree with carlos that +that + + align:start position:0% +that + + + align:start position:0% +that +in this time of crisis the corona crisis + + align:start position:0% +in this time of crisis the corona crisis + + + align:start position:0% +in this time of crisis the corona crisis +in the + + align:start position:0% +in the + + + align:start position:0% +in the +in the us the program that he's + + align:start position:0% +in the us the program that he's + + + align:start position:0% +in the us the program that he's +referencing was of this two trillion + + align:start position:0% +referencing was of this two trillion + + + align:start position:0% +referencing was of this two trillion +dollar + + align:start position:0% +dollar + + + align:start position:0% +dollar +uh uh package that congress just passed + + align:start position:0% +uh uh package that congress just passed + + + align:start position:0% +uh uh package that congress just passed +there was 350 billion dollars to fund + + align:start position:0% +there was 350 billion dollars to fund + + + align:start position:0% +there was 350 billion dollars to fund +small businesses they have to be 500 + + align:start position:0% +small businesses they have to be 500 + + + align:start position:0% +small businesses they have to be 500 +employees or less but + + align:start position:0% +employees or less but + + + align:start position:0% +employees or less but +small businesses to it's called the + + align:start position:0% +small businesses to it's called the + + + align:start position:0% +small businesses to it's called the +payroll protection + + align:start position:0% +payroll protection + + + align:start position:0% +payroll protection +uh program ppp + + align:start position:0% +uh program ppp + + + align:start position:0% +uh program ppp +and through the small business + + align:start position:0% +and through the small business + + + align:start position:0% +and through the small business +administration + + align:start position:0% +administration + + + align:start position:0% +administration +guarantees the banking sector can make + + align:start position:0% +guarantees the banking sector can make + + + align:start position:0% +guarantees the banking sector can make +loans that are forgiven so they're + + align:start position:0% +loans that are forgiven so they're + + + align:start position:0% +loans that are forgiven so they're +forgivable loans up to 10 million + + align:start position:0% +forgivable loans up to 10 million + + + align:start position:0% +forgivable loans up to 10 million +dollars a piece + + align:start position:0% +dollars a piece + + + align:start position:0% +dollars a piece +they're alone but they're really a grant + + align:start position:0% +they're alone but they're really a grant + + + align:start position:0% +they're alone but they're really a grant +if you can show in your application that + + align:start position:0% +if you can show in your application that + + + align:start position:0% +if you can show in your application that +the money is going to support + + align:start position:0% +the money is going to support + + + align:start position:0% +the money is going to support +employment and there's a various uh + + align:start position:0% +employment and there's a various uh + + + align:start position:0% +employment and there's a various uh +conditions and conditionality and so + + align:start position:0% +conditions and conditionality and so + + + align:start position:0% +conditions and conditionality and so +what carlos is talking about is in the + + align:start position:0% +what carlos is talking about is in the + + + align:start position:0% +what carlos is talking about is in the +loan + + align:start position:0% +loan + + + align:start position:0% +loan +applications that were the loan + + align:start position:0% +applications that were the loan + + + align:start position:0% +applications that were the loan +applications were first being fought i + + align:start position:0% +applications were first being fought i + + + align:start position:0% +applications were first being fought i +think last friday but it might have been + + align:start position:0% +think last friday but it might have been + + + align:start position:0% +think last friday but it might have been +over the weekend + + align:start position:0% +over the weekend + + + align:start position:0% +over the weekend +and these loan applications had to go + + align:start position:0% +and these loan applications had to go + + + align:start position:0% +and these loan applications had to go +through your employment and show + + align:start position:0% +through your employment and show + + + align:start position:0% +through your employment and show +who you had uh earning less than a + + align:start position:0% +who you had uh earning less than a + + + align:start position:0% +who you had uh earning less than a +certain amount of dollar per employee + + align:start position:0% +certain amount of dollar per employee + + + align:start position:0% +certain amount of dollar per employee +so a lot of data a lot of data and it + + align:start position:0% +so a lot of data a lot of data and it + + + align:start position:0% +so a lot of data a lot of data and it +sounds like + + align:start position:0% +sounds like + + + align:start position:0% +sounds like +plaid is actually helping facilitate + + align:start position:0% +plaid is actually helping facilitate + + + align:start position:0% +plaid is actually helping facilitate +that in some regard + + align:start position:0% +that in some regard + + + align:start position:0% +that in some regard +so thank you + + align:start position:0% + + + + align:start position:0% + +romaine i think i'm getting close to + + align:start position:0% +romaine i think i'm getting close to + + + align:start position:0% +romaine i think i'm getting close to +that 15-minute warning time but + + align:start position:0% +that 15-minute warning time but + + + align:start position:0% +that 15-minute warning time but +is there another question or i was just + + align:start position:0% +is there another question or i was just + + + align:start position:0% +is there another question or i was just +going to move on to robotic process + + align:start position:0% +going to move on to robotic process + + + align:start position:0% +going to move on to robotic process +automation for a minute + + align:start position:0% +automation for a minute + + + align:start position:0% +automation for a minute +i think we can move on and indeed we + + align:start position:0% +i think we can move on and indeed we + + + align:start position:0% +i think we can move on and indeed we +have 17 minutes left + + align:start position:0% +have 17 minutes left + + + align:start position:0% +have 17 minutes left +all right so let me just pause for a + + align:start position:0% +all right so let me just pause for a + + + align:start position:0% +all right so let me just pause for a +minute again on financial data exchange + + align:start position:0% +minute again on financial data exchange + + + align:start position:0% +minute again on financial data exchange +i'm not close enough to it + + align:start position:0% +i'm not close enough to it + + + align:start position:0% +i'm not close enough to it +to know where they are in their + + align:start position:0% +to know where they are in their + + + align:start position:0% +to know where they are in their +development but basically + + align:start position:0% +development but basically + + + align:start position:0% +development but basically +a large set of big incumbents and i've + + align:start position:0% +a large set of big incumbents and i've + + + align:start position:0% +a large set of big incumbents and i've +just put a + + align:start position:0% +just put a + + + align:start position:0% +just put a +visual of their principal members but + + align:start position:0% +visual of their principal members but + + + align:start position:0% +visual of their principal members but +then they have behind this another 50 or + + align:start position:0% +then they have behind this another 50 or + + + align:start position:0% +then they have behind this another 50 or + + align:start position:0% + + + align:start position:0% +second-tier members and by a second tier + + align:start position:0% +second-tier members and by a second tier + + + align:start position:0% +second-tier members and by a second tier +they they + + align:start position:0% +they they + + + align:start position:0% +they they +this is the group that's that's + + align:start position:0% +this is the group that's that's + + + align:start position:0% +this is the group that's that's +primarily + + align:start position:0% +primarily + + + align:start position:0% +primarily +running its board of directors and sort + + align:start position:0% +running its board of directors and sort + + + align:start position:0% +running its board of directors and sort +of coordinating + + align:start position:0% +of coordinating + + + align:start position:0% +of coordinating +and it has all the big u.s banks uh on + + align:start position:0% +and it has all the big u.s banks uh on + + + align:start position:0% +and it has all the big u.s banks uh on +here the largest + + align:start position:0% +here the largest + + + align:start position:0% +here the largest +and quicken loans which is the largest + + align:start position:0% +and quicken loans which is the largest + + + align:start position:0% +and quicken loans which is the largest +in mortgage lending + + align:start position:0% +in mortgage lending + + + align:start position:0% +in mortgage lending +in the us and siffa which is the trade + + align:start position:0% +in the us and siffa which is the trade + + + align:start position:0% +in the us and siffa which is the trade +association + + align:start position:0% +association + + + align:start position:0% +association +they're coming together to say we need + + align:start position:0% +they're coming together to say we need + + + align:start position:0% +they're coming together to say we need +to standardize financial data sharing + + align:start position:0% +to standardize financial data sharing + + + align:start position:0% +to standardize financial data sharing +standards for secure authentication + + align:start position:0% +standards for secure authentication + + + align:start position:0% +standards for secure authentication +and how this user experience works + + align:start position:0% +and how this user experience works + + + align:start position:0% +and how this user experience works +but part of it but part of it is the + + align:start position:0% +but part of it but part of it is the + + + align:start position:0% +but part of it but part of it is the +incumbent's sort of trying to reclaim a + + align:start position:0% +incumbent's sort of trying to reclaim a + + + align:start position:0% +incumbent's sort of trying to reclaim a +little bit of the territory + + align:start position:0% +little bit of the territory + + + align:start position:0% +little bit of the territory +i don't think the cat's going to be able + + align:start position:0% +i don't think the cat's going to be able + + + align:start position:0% +i don't think the cat's going to be able +to be pushed back into the barn so to + + align:start position:0% +to be pushed back into the barn so to + + + align:start position:0% +to be pushed back into the barn so to +speak but + + align:start position:0% +speak but + + + align:start position:0% +speak but +or you might say the horse is out of the + + align:start position:0% +or you might say the horse is out of the + + + align:start position:0% +or you might say the horse is out of the +barn and i won't use a cat + + align:start position:0% +barn and i won't use a cat + + + align:start position:0% +barn and i won't use a cat +but i think that this is an interesting + + align:start position:0% +but i think that this is an interesting + + + align:start position:0% +but i think that this is an interesting +dynamic that's going on + + align:start position:0% +dynamic that's going on + + + align:start position:0% +dynamic that's going on +right now now you put that in the + + align:start position:0% +right now now you put that in the + + + align:start position:0% +right now now you put that in the +context of what we + + align:start position:0% +context of what we + + + align:start position:0% +context of what we +talked about robotic process automation + + align:start position:0% +talked about robotic process automation + + + align:start position:0% +talked about robotic process automation +robotic process automation + + align:start position:0% +robotic process automation + + + align:start position:0% +robotic process automation +can be used in a positive way by the + + align:start position:0% +can be used in a positive way by the + + + align:start position:0% +can be used in a positive way by the +incumbents + + align:start position:0% +incumbents + + + align:start position:0% +incumbents +and by the startups to do account + + align:start position:0% +and by the startups to do account + + + align:start position:0% +and by the startups to do account +opening + + align:start position:0% +opening + + + align:start position:0% +opening +onboarding as we talked about earlier + + align:start position:0% +onboarding as we talked about earlier + + + align:start position:0% +onboarding as we talked about earlier +loan processing + + align:start position:0% +loan processing + + + align:start position:0% +loan processing +anything that you can take and automate + + align:start position:0% +anything that you can take and automate + + + align:start position:0% +anything that you can take and automate +that which humans are doing + + align:start position:0% +that which humans are doing + + + align:start position:0% +that which humans are doing +and i'm not sure moving into chat bots + + align:start position:0% +and i'm not sure moving into chat bots + + + align:start position:0% +and i'm not sure moving into chat bots +and the + + align:start position:0% +and the + + + align:start position:0% +and the +conversational interfaces that we've + + align:start position:0% +conversational interfaces that we've + + + align:start position:0% +conversational interfaces that we've +already spoken about + + align:start position:0% +already spoken about + + + align:start position:0% +already spoken about +i'm talking about the more standardized + + align:start position:0% +i'm talking about the more standardized + + + align:start position:0% +i'm talking about the more standardized +documents reading the documents + + align:start position:0% +documents reading the documents + + + align:start position:0% +documents reading the documents +and opening the accounts and and + + align:start position:0% +and opening the accounts and and + + + align:start position:0% +and opening the accounts and and +uh as was mentioned earlier and i maybe + + align:start position:0% +uh as was mentioned earlier and i maybe + + + align:start position:0% +uh as was mentioned earlier and i maybe +should have put on this list + + align:start position:0% +should have put on this list + + + align:start position:0% +should have put on this list +also compliance for + + align:start position:0% +also compliance for + + + align:start position:0% +also compliance for +any money laundering and and know your + + align:start position:0% +any money laundering and and know your + + + align:start position:0% +any money laundering and and know your +customer those are very positive ways + + align:start position:0% +customer those are very positive ways + + + align:start position:0% +customer those are very positive ways +but it's also a way that challenger + + align:start position:0% +but it's also a way that challenger + + + align:start position:0% +but it's also a way that challenger +banks + + align:start position:0% +banks + + + align:start position:0% +banks +and challengers can use it to scrape the + + align:start position:0% +and challengers can use it to scrape the + + + align:start position:0% +and challengers can use it to scrape the +data + + align:start position:0% +data + + + align:start position:0% +data +and pull the data out of the incumbents + + align:start position:0% +and pull the data out of the incumbents + + + align:start position:0% +and pull the data out of the incumbents +as long as + + align:start position:0% +as long as + + + align:start position:0% +as long as +a customer permissions it so it's sort + + align:start position:0% +a customer permissions it so it's sort + + + align:start position:0% +a customer permissions it so it's sort +of + + align:start position:0% +of + + + align:start position:0% +of +both of those sides in a very positive + + align:start position:0% +both of those sides in a very positive + + + align:start position:0% +both of those sides in a very positive +way + + align:start position:0% +way + + + align:start position:0% +way +uh across across the entire field of + + align:start position:0% +uh across across the entire field of + + + align:start position:0% +uh across across the entire field of +finance a very positive way that we can + + align:start position:0% +finance a very positive way that we can + + + align:start position:0% +finance a very positive way that we can +automate that which humans are doing in + + align:start position:0% +automate that which humans are doing in + + + align:start position:0% +automate that which humans are doing in +the past + + align:start position:0% +the past + + + align:start position:0% +the past +this is frankly just the same as when + + align:start position:0% +this is frankly just the same as when + + + align:start position:0% +this is frankly just the same as when +uh the tractor came along and we were + + align:start position:0% +uh the tractor came along and we were + + + align:start position:0% +uh the tractor came along and we were +automating what humans and the horse and + + align:start position:0% +automating what humans and the horse and + + + align:start position:0% +automating what humans and the horse and +the cow and the oxen were doing in the + + align:start position:0% +the cow and the oxen were doing in the + + + align:start position:0% +the cow and the oxen were doing in the +field + + align:start position:0% +field + + + align:start position:0% +field +we can automate that which the human + + align:start position:0% +we can automate that which the human + + + align:start position:0% +we can automate that which the human +does but it + + align:start position:0% +does but it + + + align:start position:0% +does but it +changes the way that uh the sort of the + + align:start position:0% +changes the way that uh the sort of the + + + align:start position:0% +changes the way that uh the sort of the +dynamic between + + align:start position:0% +dynamic between + + + align:start position:0% +dynamic between +uh incumbents and startups + + align:start position:0% +uh incumbents and startups + + + align:start position:0% +uh incumbents and startups +um and then um + + align:start position:0% +um and then um + + + align:start position:0% +um and then um +i wanna i wanna pause and see if there + + align:start position:0% +i wanna i wanna pause and see if there + + + align:start position:0% +i wanna i wanna pause and see if there +are questions and then i wanted to say + + align:start position:0% +are questions and then i wanted to say + + + align:start position:0% +are questions and then i wanted to say +a bit on assignments and then close we + + align:start position:0% +a bit on assignments and then close we + + + align:start position:0% +a bit on assignments and then close we +have a question in the chat for you + + align:start position:0% +have a question in the chat for you + + + align:start position:0% +have a question in the chat for you +from alex a sloan fellow who tells us + + align:start position:0% +from alex a sloan fellow who tells us + + + align:start position:0% +from alex a sloan fellow who tells us +that in one of the readings you know + + align:start position:0% +that in one of the readings you know + + + align:start position:0% +that in one of the readings you know +one of the authors ends with consumer + + align:start position:0% +one of the authors ends with consumer + + + align:start position:0% +one of the authors ends with consumer +will access financial services from + + align:start position:0% +will access financial services from + + + align:start position:0% +will access financial services from +one central hub but then another author + + align:start position:0% +one central hub but then another author + + + align:start position:0% +one central hub but then another author +in another reading + + align:start position:0% +in another reading + + + align:start position:0% +in another reading +speaks of another other trend of + + align:start position:0% +speaks of another other trend of + + + align:start position:0% +speaks of another other trend of +embedded fintech + + align:start position:0% +embedded fintech + + + align:start position:0% +embedded fintech +and so which ones of these perspectives + + align:start position:0% +and so which ones of these perspectives + + + align:start position:0% +and so which ones of these perspectives +would you tend to agree with + + align:start position:0% +would you tend to agree with + + + align:start position:0% +would you tend to agree with +well alex i think that's the debate and + + align:start position:0% +well alex i think that's the debate and + + + align:start position:0% +well alex i think that's the debate and +and + + align:start position:0% +and + + + align:start position:0% +and +um i think you probably uh + + align:start position:0% +um i think you probably uh + + + align:start position:0% +um i think you probably uh +could guess that i'm at neither end i + + align:start position:0% +could guess that i'm at neither end i + + + align:start position:0% +could guess that i'm at neither end i +i i don't think that we'll + + align:start position:0% +i i don't think that we'll + + + align:start position:0% +i i don't think that we'll +end up with truly + + align:start position:0% + + + + align:start position:0% + +decentralized and we can sort of uh + + align:start position:0% +decentralized and we can sort of uh + + + align:start position:0% +decentralized and we can sort of uh +disaggregate we had this discussion a + + align:start position:0% +disaggregate we had this discussion a + + + align:start position:0% +disaggregate we had this discussion a +little earlier will it be completely + + align:start position:0% +little earlier will it be completely + + + align:start position:0% +little earlier will it be completely +unbundled + + align:start position:0% +unbundled + + + align:start position:0% +unbundled +i don't think so i think there's still + + align:start position:0% +i don't think so i think there's still + + + align:start position:0% +i don't think so i think there's still +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +economic benefits to scale + + align:start position:0% +economic benefits to scale + + + align:start position:0% +economic benefits to scale +sometimes that's driven by balance sheet + + align:start position:0% +sometimes that's driven by balance sheet + + + align:start position:0% +sometimes that's driven by balance sheet +that the the balance sheet financing + + align:start position:0% +that the the balance sheet financing + + + align:start position:0% +that the the balance sheet financing +side + + align:start position:0% +side + + + align:start position:0% +side +leads to scale though + + align:start position:0% +leads to scale though + + + align:start position:0% +leads to scale though +securitization and asset securitization + + align:start position:0% +securitization and asset securitization + + + align:start position:0% +securitization and asset securitization +is a way to rent somebody else's balance + + align:start position:0% +is a way to rent somebody else's balance + + + align:start position:0% +is a way to rent somebody else's balance +sheet and to + + align:start position:0% +sheet and to + + + align:start position:0% +sheet and to +sort of lay off that risk to somebody + + align:start position:0% +sort of lay off that risk to somebody + + + align:start position:0% +sort of lay off that risk to somebody +else but i think that there's a lot of + + align:start position:0% +else but i think that there's a lot of + + + align:start position:0% +else but i think that there's a lot of +reasons + + align:start position:0% +reasons + + + align:start position:0% +reasons +that scale and network effects balance + + align:start position:0% +that scale and network effects balance + + + align:start position:0% +that scale and network effects balance +shipping one of the network effects + + align:start position:0% +shipping one of the network effects + + + align:start position:0% +shipping one of the network effects +data being another network effect + + align:start position:0% +data being another network effect + + + align:start position:0% +data being another network effect +customer user interface + + align:start position:0% +customer user interface + + + align:start position:0% +customer user interface +another network effect that there's + + align:start position:0% +another network effect that there's + + + align:start position:0% +another network effect that there's +benefits to some + + align:start position:0% +benefits to some + + + align:start position:0% +benefits to some +scale that there will be some + + align:start position:0% +scale that there will be some + + + align:start position:0% +scale that there will be some +concentration + + align:start position:0% +concentration + + + align:start position:0% +concentration +will there be one portal will we go all + + align:start position:0% +will there be one portal will we go all + + + align:start position:0% +will there be one portal will we go all +the way to one portal will be + + align:start position:0% +the way to one portal will be + + + align:start position:0% +the way to one portal will be +will it be uh that amazon will + + align:start position:0% +will it be uh that amazon will + + + align:start position:0% +will it be uh that amazon will +sort of be the one place i go to for all + + align:start position:0% +sort of be the one place i go to for all + + + align:start position:0% +sort of be the one place i go to for all +of my + + align:start position:0% +of my + + + align:start position:0% +of my +online financial needs uh jeff bezos + + align:start position:0% +online financial needs uh jeff bezos + + + align:start position:0% +online financial needs uh jeff bezos +might have a strategy that way you might + + align:start position:0% +might have a strategy that way you might + + + align:start position:0% +might have a strategy that way you might +write papers that way + + align:start position:0% +write papers that way + + + align:start position:0% +write papers that way +i would caution that i think that there + + align:start position:0% +i would caution that i think that there + + + align:start position:0% +i would caution that i think that there +will be some + + align:start position:0% +will be some + + + align:start position:0% +will be some +competitive pressures and economic + + align:start position:0% +competitive pressures and economic + + + align:start position:0% +competitive pressures and economic +pressures on the other side that will + + align:start position:0% +pressures on the other side that will + + + align:start position:0% +pressures on the other side that will +still have some disaggregation + + align:start position:0% +still have some disaggregation + + + align:start position:0% +still have some disaggregation +for instance in country after country + + align:start position:0% +for instance in country after country + + + align:start position:0% +for instance in country after country +for decades there's been the debate + + align:start position:0% +for decades there's been the debate + + + align:start position:0% +for decades there's been the debate +whether + + align:start position:0% +whether + + + align:start position:0% +whether +insurance products will be sold by banks + + align:start position:0% +insurance products will be sold by banks + + + align:start position:0% +insurance products will be sold by banks +and banking products by insurance firms + + align:start position:0% +and banking products by insurance firms + + + align:start position:0% +and banking products by insurance firms +and for some reason around the globe by + + align:start position:0% +and for some reason around the globe by + + + align:start position:0% +and for some reason around the globe by +and large + + align:start position:0% +and large + + + align:start position:0% +and large +we still see this separation some of + + align:start position:0% +we still see this separation some of + + + align:start position:0% +we still see this separation some of +it's uh just + + align:start position:0% +it's uh just + + + align:start position:0% +it's uh just +legacy and history some of it is + + align:start position:0% +legacy and history some of it is + + + align:start position:0% +legacy and history some of it is +regulation + + align:start position:0% +regulation + + + align:start position:0% +regulation +but it's also how we think of the + + align:start position:0% +but it's also how we think of the + + + align:start position:0% +but it's also how we think of the +products that we think of buying our + + align:start position:0% +products that we think of buying our + + + align:start position:0% +products that we think of buying our +life insurance + + align:start position:0% +life insurance + + + align:start position:0% +life insurance +or our household insurance or auto + + align:start position:0% +or our household insurance or auto + + + align:start position:0% +or our household insurance or auto +insurance a little differently than we + + align:start position:0% +insurance a little differently than we + + + align:start position:0% +insurance a little differently than we +think about + + align:start position:0% +think about + + + align:start position:0% +think about +funding the same things funding our + + align:start position:0% +funding the same things funding our + + + align:start position:0% +funding the same things funding our +house which is called a mortgage + + align:start position:0% +house which is called a mortgage + + + align:start position:0% +house which is called a mortgage +and funding our cars which is called an + + align:start position:0% +and funding our cars which is called an + + + align:start position:0% +and funding our cars which is called an +auto loan + + align:start position:0% +auto loan + + + align:start position:0% +auto loan +we tend to uh now it's true in some + + align:start position:0% +we tend to uh now it's true in some + + + align:start position:0% +we tend to uh now it's true in some +countries it's + + align:start position:0% +countries it's + + + align:start position:0% +countries it's +it's come together but by and large it's + + align:start position:0% +it's come together but by and large it's + + + align:start position:0% +it's come together but by and large it's +not one portal + + align:start position:0% +not one portal + + + align:start position:0% +not one portal +so but alex you're you do you have a + + align:start position:0% +so but alex you're you do you have a + + + align:start position:0% +so but alex you're you do you have a +point of view did you + + align:start position:0% +point of view did you + + + align:start position:0% +point of view did you +did you feel strongly one way or the + + align:start position:0% +did you feel strongly one way or the + + + align:start position:0% +did you feel strongly one way or the +other if you're there still + + align:start position:0% +other if you're there still + + + align:start position:0% +other if you're there still +i i think the um + + align:start position:0% +i i think the um + + + align:start position:0% +i i think the um +the embedded fintech is quite insightful + + align:start position:0% +the embedded fintech is quite insightful + + + align:start position:0% +the embedded fintech is quite insightful +because nowadays that people talk about + + align:start position:0% +because nowadays that people talk about + + + align:start position:0% +because nowadays that people talk about +customer-centric + + align:start position:0% +customer-centric + + + align:start position:0% +customer-centric +idea even more than before because we + + align:start position:0% +idea even more than before because we + + + align:start position:0% +idea even more than before because we +have more data to provide + + align:start position:0% +have more data to provide + + + align:start position:0% +have more data to provide +relevant services but the thing is that + + align:start position:0% +relevant services but the thing is that + + + align:start position:0% +relevant services but the thing is that +when we talk about the jobs to be done + + align:start position:0% +when we talk about the jobs to be done + + + align:start position:0% +when we talk about the jobs to be done +financial service is that + + align:start position:0% +financial service is that + + + align:start position:0% +financial service is that +not actually the job the ultimate or the + + align:start position:0% +not actually the job the ultimate or the + + + align:start position:0% +not actually the job the ultimate or the +ultimate job you want to + + align:start position:0% +ultimate job you want to + + + align:start position:0% +ultimate job you want to +get done you want to buy a hot you want + + align:start position:0% +get done you want to buy a hot you want + + + align:start position:0% +get done you want to buy a hot you want +to buy a house so you need it long + + align:start position:0% +to buy a house so you need it long + + + align:start position:0% +to buy a house so you need it long +so which means that maybe it makes sense + + align:start position:0% +so which means that maybe it makes sense + + + align:start position:0% +so which means that maybe it makes sense +some of the services will be the second + + align:start position:0% +some of the services will be the second + + + align:start position:0% +some of the services will be the second +layer i mean + + align:start position:0% +layer i mean + + + align:start position:0% +layer i mean +be embedded into those jobs really need + + align:start position:0% +be embedded into those jobs really need + + + align:start position:0% +be embedded into those jobs really need +to be done by the customers + + align:start position:0% +to be done by the customers + + + align:start position:0% +to be done by the customers +i want to say this about embedded + + align:start position:0% +i want to say this about embedded + + + align:start position:0% +i want to say this about embedded +finance and this concept that was in the + + align:start position:0% +finance and this concept that was in the + + + align:start position:0% +finance and this concept that was in the +article + + align:start position:0% +article + + + align:start position:0% +article +and i'm glad you reminded me of this + + align:start position:0% +and i'm glad you reminded me of this + + + align:start position:0% +and i'm glad you reminded me of this +alex + + align:start position:0% +alex + + + align:start position:0% +alex +i do think that we're going to see more + + align:start position:0% +i do think that we're going to see more + + + align:start position:0% +i do think that we're going to see more +what's called embedded finance and by + + align:start position:0% +what's called embedded finance and by + + + align:start position:0% +what's called embedded finance and by +that term + + align:start position:0% +that term + + + align:start position:0% +that term +what i take from it it's not a + + align:start position:0% +what i take from it it's not a + + + align:start position:0% +what i take from it it's not a +well-defined term you can't look at + + align:start position:0% +well-defined term you can't look at + + + align:start position:0% +well-defined term you can't look at +a webster's dictionary and say what's + + align:start position:0% +a webster's dictionary and say what's + + + align:start position:0% +a webster's dictionary and say what's +embedded finance + + align:start position:0% +embedded finance + + + align:start position:0% +embedded finance +but what i take from that term is that + + align:start position:0% +but what i take from that term is that + + + align:start position:0% +but what i take from that term is that +non-financial firms will embed + + align:start position:0% +non-financial firms will embed + + + align:start position:0% +non-financial firms will embed +some aspect of finance in their product + + align:start position:0% +some aspect of finance in their product + + + align:start position:0% +some aspect of finance in their product +offering + + align:start position:0% +offering + + + align:start position:0% +offering +not a new concept even the local grocery + + align:start position:0% +not a new concept even the local grocery + + + align:start position:0% +not a new concept even the local grocery +store in the 19th century was saying + + align:start position:0% +store in the 19th century was saying + + + align:start position:0% +store in the 19th century was saying +you can buy your groceries and pay + + align:start position:0% +you can buy your groceries and pay + + + align:start position:0% +you can buy your groceries and pay +tomorrow + + align:start position:0% +tomorrow + + + align:start position:0% +tomorrow +you know that local merchant and that + + align:start position:0% +you know that local merchant and that + + + align:start position:0% +you know that local merchant and that +led over + + align:start position:0% +led over + + + align:start position:0% +led over +50 or 70 years to the modern credit card + + align:start position:0% +50 or 70 years to the modern credit card + + + align:start position:0% +50 or 70 years to the modern credit card +being invented in the 1940s and taking + + align:start position:0% +being invented in the 1940s and taking + + + align:start position:0% +being invented in the 1940s and taking +off by the 1960s + + align:start position:0% +off by the 1960s + + + align:start position:0% +off by the 1960s +so we've had some concepts of embedded + + align:start position:0% +so we've had some concepts of embedded + + + align:start position:0% +so we've had some concepts of embedded +finance but i think that + + align:start position:0% +finance but i think that + + + align:start position:0% +finance but i think that +that the modern technology will provide + + align:start position:0% +that the modern technology will provide + + + align:start position:0% +that the modern technology will provide +more alternatives to embed + + align:start position:0% +more alternatives to embed + + + align:start position:0% +more alternatives to embed +a payment mechanism or a lending + + align:start position:0% +a payment mechanism or a lending + + + align:start position:0% +a payment mechanism or a lending +mechanism and those would be the two + + align:start position:0% +mechanism and those would be the two + + + align:start position:0% +mechanism and those would be the two +principal things + + align:start position:0% +principal things + + + align:start position:0% +principal things +some aspect of a loan or some aspect of + + align:start position:0% +some aspect of a loan or some aspect of + + + align:start position:0% +some aspect of a loan or some aspect of +payment + + align:start position:0% +payment + + + align:start position:0% +payment +right in an app in a sense like uber + + align:start position:0% +right in an app in a sense like uber + + + align:start position:0% +right in an app in a sense like uber +and lyft does in a sense like + + align:start position:0% +and lyft does in a sense like + + + align:start position:0% +and lyft does in a sense like +point-of-sale lending point-of-sale + + align:start position:0% +point-of-sale lending point-of-sale + + + align:start position:0% +point-of-sale lending point-of-sale +lending that i can buy something online + + align:start position:0% +lending that i can buy something online + + + align:start position:0% +lending that i can buy something online +and pay an installment + + align:start position:0% +and pay an installment + + + align:start position:0% +and pay an installment +uh over four or six payments maybe over + + align:start position:0% +uh over four or six payments maybe over + + + align:start position:0% +uh over four or six payments maybe over +multiple months + + align:start position:0% +multiple months + + + align:start position:0% +multiple months +i i think embedded finance is a is a + + align:start position:0% +i i think embedded finance is a is a + + + align:start position:0% +i i think embedded finance is a is a +trend + + align:start position:0% +trend + + + align:start position:0% +trend +i also do think that + + align:start position:0% +i also do think that + + + align:start position:0% +i also do think that +because of this api movement and this is + + align:start position:0% +because of this api movement and this is + + + align:start position:0% +because of this api movement and this is +a way to close on apis + + align:start position:0% +a way to close on apis + + + align:start position:0% +a way to close on apis +that startups can provide services in a + + align:start position:0% +that startups can provide services in a + + + align:start position:0% +that startups can provide services in a +way they couldn't in the past + + align:start position:0% +way they couldn't in the past + + + align:start position:0% +way they couldn't in the past +that a robin hood could come along and + + align:start position:0% +that a robin hood could come along and + + + align:start position:0% +that a robin hood could come along and +we'll talk about robin hood more when we + + align:start position:0% +we'll talk about robin hood more when we + + + align:start position:0% +we'll talk about robin hood more when we +talk about capital markets but a robin + + align:start position:0% +talk about capital markets but a robin + + + align:start position:0% +talk about capital markets but a robin +hood could come along and say + + align:start position:0% +hood could come along and say + + + align:start position:0% +hood could come along and say +we offer that you can open brokerage + + align:start position:0% +we offer that you can open brokerage + + + align:start position:0% +we offer that you can open brokerage +accounts + + align:start position:0% +accounts + + + align:start position:0% +accounts +on this handheld device + + align:start position:0% +on this handheld device + + + align:start position:0% +on this handheld device +you can scan your documents using + + align:start position:0% +you can scan your documents using + + + align:start position:0% +you can scan your documents using +robotic process automation and natural + + align:start position:0% +robotic process automation and natural + + + align:start position:0% +robotic process automation and natural +language processing you can scan your + + align:start position:0% +language processing you can scan your + + + align:start position:0% +language processing you can scan your +documents + + align:start position:0% +documents + + + align:start position:0% +documents +by taking a picture from your phone + + align:start position:0% +by taking a picture from your phone + + + align:start position:0% +by taking a picture from your phone +open a brokerage account and trade + + align:start position:0% +open a brokerage account and trade + + + align:start position:0% +open a brokerage account and trade +automatically + + align:start position:0% +automatically + + + align:start position:0% +automatically +interfacing there's there's probably + + align:start position:0% +interfacing there's there's probably + + + align:start position:0% +interfacing there's there's probably +dozens of apis that stand between your + + align:start position:0% +dozens of apis that stand between your + + + align:start position:0% +dozens of apis that stand between your +robinhood app + + align:start position:0% +robinhood app + + + align:start position:0% +robinhood app +and the new york stock exchange and it's + + align:start position:0% +and the new york stock exchange and it's + + + align:start position:0% +and the new york stock exchange and it's +not just robinhood directly to the new + + align:start position:0% +not just robinhood directly to the new + + + align:start position:0% +not just robinhood directly to the new +york stock exchange there's + + align:start position:0% +york stock exchange there's + + + align:start position:0% +york stock exchange there's +multiple interfaces in between + + align:start position:0% +multiple interfaces in between + + + align:start position:0% +multiple interfaces in between +so i think it's facilitated a remarkable + + align:start position:0% +so i think it's facilitated a remarkable + + + align:start position:0% +so i think it's facilitated a remarkable +shift in finance that we can do those + + align:start position:0% +shift in finance that we can do those + + + align:start position:0% +shift in finance that we can do those +things + + align:start position:0% +things + + + align:start position:0% +things +right on our cell phones and embedded + + align:start position:0% +right on our cell phones and embedded + + + align:start position:0% +right on our cell phones and embedded +finance + + align:start position:0% +finance + + + align:start position:0% +finance +and these apis relate to it + + align:start position:0% +and these apis relate to it + + + align:start position:0% +and these apis relate to it +i'm just not quite there that it will + + align:start position:0% +i'm just not quite there that it will + + + align:start position:0% +i'm just not quite there that it will +all be bundled up + + align:start position:0% +all be bundled up + + + align:start position:0% +all be bundled up +into one service provider or that it + + align:start position:0% +into one service provider or that it + + + align:start position:0% +into one service provider or that it +will all be fragmented + + align:start position:0% +will all be fragmented + + + align:start position:0% +will all be fragmented +i think we'll have a little bit in + + align:start position:0% +i think we'll have a little bit in + + + align:start position:0% +i think we'll have a little bit in +between so + + align:start position:0% +between so + + + align:start position:0% +between so +um i just want to mention something on + + align:start position:0% +um i just want to mention something on + + + align:start position:0% +um i just want to mention something on +assignments because + + align:start position:0% +assignments because + + + align:start position:0% +assignments because +the april 8th again assignments + + align:start position:0% +the april 8th again assignments + + + align:start position:0% +the april 8th again assignments +particularly + + align:start position:0% +particularly + + + align:start position:0% +particularly +at this stage where we're past emergency + + align:start position:0% +at this stage where we're past emergency + + + align:start position:0% +at this stage where we're past emergency +no + + align:start position:0% +no + + + align:start position:0% +no +credit emergency or sort of colloquially + + align:start position:0% +credit emergency or sort of colloquially + + + align:start position:0% +credit emergency or sort of colloquially +pass fail + + align:start position:0% +pass fail + + + align:start position:0% +pass fail +assignments are a great way to engage in + + align:start position:0% +assignments are a great way to engage in + + + align:start position:0% +assignments are a great way to engage in +the subject i + + align:start position:0% +the subject i + + + align:start position:0% +the subject i +think of that even when we have a's and + + align:start position:0% +think of that even when we have a's and + + + align:start position:0% +think of that even when we have a's and +b's and things like that + + align:start position:0% +b's and things like that + + + align:start position:0% +b's and things like that +i i just really ask you to engage in the + + align:start position:0% +i i just really ask you to engage in the + + + align:start position:0% +i i just really ask you to engage in the +subject pick + + align:start position:0% +subject pick + + + align:start position:0% +subject pick +some subject that interests you that + + align:start position:0% +some subject that interests you that + + + align:start position:0% +some subject that interests you that +excites you + + align:start position:0% +excites you + + + align:start position:0% +excites you +and you want to write to an incumbent to + + align:start position:0% +and you want to write to an incumbent to + + + align:start position:0% +and you want to write to an incumbent to +a big tech firm like + + align:start position:0% +a big tech firm like + + + align:start position:0% +a big tech firm like +amazon or andreessen horowitz which + + align:start position:0% +amazon or andreessen horowitz which + + + align:start position:0% +amazon or andreessen horowitz which +andreessen horowitz owns a slice of a + + align:start position:0% +andreessen horowitz owns a slice of a + + + align:start position:0% +andreessen horowitz owns a slice of a +lot of the companies we've been talking + + align:start position:0% +lot of the companies we've been talking + + + align:start position:0% +lot of the companies we've been talking +about already + + align:start position:0% +about already + + + align:start position:0% +about already +i mean they're a remarkable venture + + align:start position:0% +i mean they're a remarkable venture + + + align:start position:0% +i mean they're a remarkable venture +capital firm + + align:start position:0% +capital firm + + + align:start position:0% +capital firm +and and just think of some sort of + + align:start position:0% +and and just think of some sort of + + + align:start position:0% +and and just think of some sort of +strategy around it the individual papers + + align:start position:0% +strategy around it the individual papers + + + align:start position:0% +strategy around it the individual papers +are just a way to break up the + + align:start position:0% +are just a way to break up the + + + align:start position:0% +are just a way to break up the +assignment in a way + + align:start position:0% +assignment in a way + + + align:start position:0% +assignment in a way +that one person would write about it + + align:start position:0% +that one person would write about it + + + align:start position:0% +that one person would write about it +overall market analysis + + align:start position:0% +overall market analysis + + + align:start position:0% +overall market analysis +somebody doing the technological trends + + align:start position:0% +somebody doing the technological trends + + + align:start position:0% +somebody doing the technological trends +if you pick that you're writing to + + align:start position:0% +if you pick that you're writing to + + + align:start position:0% +if you pick that you're writing to +amazon + + align:start position:0% +amazon + + + align:start position:0% +amazon +about uh + + align:start position:0% +about uh + + + align:start position:0% +about uh +let's say the lending space the consumer + + align:start position:0% +let's say the lending space the consumer + + + align:start position:0% +let's say the lending space the consumer +lending space + + align:start position:0% +lending space + + + align:start position:0% +lending space +what are the technological trends really + + align:start position:0% +what are the technological trends really + + + align:start position:0% +what are the technological trends really +you know do + + align:start position:0% +you know do + + + align:start position:0% +you know do +to doing to that space who are the + + align:start position:0% +to doing to that space who are the + + + align:start position:0% +to doing to that space who are the +traditional competitors and who are the + + align:start position:0% +traditional competitors and who are the + + + align:start position:0% +traditional competitors and who are the +big tech competitors + + align:start position:0% +big tech competitors + + + align:start position:0% +big tech competitors +and just breaking it off three or four + + align:start position:0% +and just breaking it off three or four + + + align:start position:0% +and just breaking it off three or four +pages + + align:start position:0% +pages + + + align:start position:0% +pages +900 to 1200 words again we're we're just + + align:start position:0% +900 to 1200 words again we're we're just + + + align:start position:0% +900 to 1200 words again we're we're just +helping you kind of engage in a subject + + align:start position:0% +helping you kind of engage in a subject + + + align:start position:0% +helping you kind of engage in a subject +perhaps you can answer another question + + align:start position:0% +perhaps you can answer another question + + + align:start position:0% +perhaps you can answer another question +i received from a student who does not + + align:start position:0% +i received from a student who does not + + + align:start position:0% +i received from a student who does not +understand how played makes money + + align:start position:0% +understand how played makes money + + + align:start position:0% +understand how played makes money +what is the business model + + align:start position:0% +what is the business model + + + align:start position:0% +what is the business model +uh well with only 110 million in + + align:start position:0% +uh well with only 110 million in + + + align:start position:0% +uh well with only 110 million in +revenues now that's a forbes + + align:start position:0% +revenues now that's a forbes + + + align:start position:0% +revenues now that's a forbes +estimate you sort of go wait a minute + + align:start position:0% +estimate you sort of go wait a minute + + + align:start position:0% +estimate you sort of go wait a minute +how's this + + align:start position:0% +how's this + + + align:start position:0% +how's this +work but how how the space makes money + + align:start position:0% +work but how how the space makes money + + + align:start position:0% +work but how how the space makes money +how + + align:start position:0% +how + + + align:start position:0% +how +not just plaid but how + + align:start position:0% +not just plaid but how + + + align:start position:0% +not just plaid but how +api companies make money + + align:start position:0% +api companies make money + + + align:start position:0% +api companies make money +in finance and outside of finance is + + align:start position:0% +in finance and outside of finance is + + + align:start position:0% +in finance and outside of finance is +they do charge fees i i apologize i + + align:start position:0% +they do charge fees i i apologize i + + + align:start position:0% +they do charge fees i i apologize i +don't know if it's a penny a transaction + + align:start position:0% +don't know if it's a penny a transaction + + + align:start position:0% +don't know if it's a penny a transaction +or what + + align:start position:0% +or what + + + align:start position:0% +or what +it is and maybe somebody on this call + + align:start position:0% +it is and maybe somebody on this call + + + align:start position:0% +it is and maybe somebody on this call +actually knows gita or others know their + + align:start position:0% +actually knows gita or others know their + + + align:start position:0% +actually knows gita or others know their +actual revenue model + + align:start position:0% +actual revenue model + + + align:start position:0% +actual revenue model +but charging a very small a + + align:start position:0% +but charging a very small a + + + align:start position:0% +but charging a very small a +fraction of money per trade and then + + align:start position:0% +fraction of money per trade and then + + + align:start position:0% +fraction of money per trade and then +what they do + + align:start position:0% +what they do + + + align:start position:0% +what they do +is data aggregation and with that data + + align:start position:0% +is data aggregation and with that data + + + align:start position:0% +is data aggregation and with that data +in other fields then you try to see how + + align:start position:0% +in other fields then you try to see how + + + align:start position:0% +in other fields then you try to see how +you can commercialize that data + + align:start position:0% +you can commercialize that data + + + align:start position:0% +you can commercialize that data +by cross-selling to + + align:start position:0% +by cross-selling to + + + align:start position:0% +by cross-selling to +either directly or remember + + align:start position:0% +either directly or remember + + + align:start position:0% +either directly or remember +a lot of these companies like plaid and + + align:start position:0% +a lot of these companies like plaid and + + + align:start position:0% +a lot of these companies like plaid and +galileo and others + + align:start position:0% +galileo and others + + + align:start position:0% +galileo and others +are are in between they're behind the + + align:start position:0% +are are in between they're behind the + + + align:start position:0% +are are in between they're behind the +scenes between + + align:start position:0% +scenes between + + + align:start position:0% +scenes between +one side of a market and another side of + + align:start position:0% +one side of a market and another side of + + + align:start position:0% +one side of a market and another side of +the market but when you create that + + align:start position:0% +the market but when you create that + + + align:start position:0% +the market but when you create that +that like twilio twilio + + align:start position:0% +that like twilio twilio + + + align:start position:0% +that like twilio twilio +is an 80 market share between + + align:start position:0% +is an 80 market share between + + + align:start position:0% +is an 80 market share between +voice and messaging and things like that + + align:start position:0% +voice and messaging and things like that + + + align:start position:0% +voice and messaging and things like that +in the us at least + + align:start position:0% +in the us at least + + + align:start position:0% +in the us at least +so all of a sudden then you can either + + align:start position:0% +so all of a sudden then you can either + + + align:start position:0% +so all of a sudden then you can either +enhance your fee structure + + align:start position:0% +enhance your fee structure + + + align:start position:0% +enhance your fee structure +because you're such a dominant + + align:start position:0% +because you're such a dominant + + + align:start position:0% +because you're such a dominant +oligopolist sort of + + align:start position:0% +oligopolist sort of + + + align:start position:0% +oligopolist sort of +uh you can collect economic rents or you + + align:start position:0% +uh you can collect economic rents or you + + + align:start position:0% +uh you can collect economic rents or you +commercialize the data and it's the data + + align:start position:0% +commercialize the data and it's the data + + + align:start position:0% +commercialize the data and it's the data +aggregation side + + align:start position:0% +aggregation side + + + align:start position:0% +aggregation side +i think visas paying what might be 25 or + + align:start position:0% +i think visas paying what might be 25 or + + + align:start position:0% +i think visas paying what might be 25 or +50 times revenues for that data + + align:start position:0% +50 times revenues for that data + + + align:start position:0% +50 times revenues for that data +aggregation side \ No newline at end of file diff --git a/LoXGM05lqKc.txt b/LoXGM05lqKc.txt new file mode 100644 index 0000000000000000000000000000000000000000..26aea1e6ff1c7fbdcc7628acf29e0666b9cd6900 --- /dev/null +++ b/LoXGM05lqKc.txt @@ -0,0 +1,13429 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu let's do a + + align:start position:0% +ocw.mit.edu let's do a + + + align:start position:0% +ocw.mit.edu let's do a +little general discussion of some of the + + align:start position:0% +little general discussion of some of the + + + align:start position:0% +little general discussion of some of the +political issues that we will encounter + + align:start position:0% +political issues that we will encounter + + + align:start position:0% +political issues that we will encounter +this is a + + align:start position:0% + + + + align:start position:0% + +um if you if you read why there are + + align:start position:0% +um if you if you read why there are + + + align:start position:0% +um if you if you read why there are +governments if you read what governments + + align:start position:0% +governments if you read what governments + + + align:start position:0% +governments if you read what governments +say + + align:start position:0% +say + + + align:start position:0% +say +about why they are established you get + + align:start position:0% +about why they are established you get + + + align:start position:0% +about why they are established you get +very high flown language this is the + + align:start position:0% +very high flown language this is the + + + align:start position:0% +very high flown language this is the +Declaration of Independence life liberty + + align:start position:0% +Declaration of Independence life liberty + + + align:start position:0% +Declaration of Independence life liberty +and the pursuit of happiness governments + + align:start position:0% +and the pursuit of happiness governments + + + align:start position:0% +and the pursuit of happiness governments +are to assure those rights + + align:start position:0% +are to assure those rights + + + align:start position:0% +are to assure those rights +this is the Constitution a little less + + align:start position:0% +this is the Constitution a little less + + + align:start position:0% +this is the Constitution a little less +highflying established Justice ensure + + align:start position:0% +highflying established Justice ensure + + + align:start position:0% +highflying established Justice ensure +domestic tranquility provide for the + + align:start position:0% +domestic tranquility provide for the + + + align:start position:0% +domestic tranquility provide for the +common defense promote the general + + align:start position:0% +common defense promote the general + + + align:start position:0% +common defense promote the general +welfare and secure the blessings of + + align:start position:0% +welfare and secure the blessings of + + + align:start position:0% +welfare and secure the blessings of +liberty you will notice that we have + + align:start position:0% +liberty you will notice that we have + + + align:start position:0% +liberty you will notice that we have +domestic tranquility common defense + + align:start position:0% +domestic tranquility common defense + + + align:start position:0% +domestic tranquility common defense +things that have things that are a + + align:start position:0% +things that have things that are a + + + align:start position:0% +things that have things that are a +little less High flowing than life + + align:start position:0% +little less High flowing than life + + + align:start position:0% +little less High flowing than life +liberty and the pursuit of + + align:start position:0% +liberty and the pursuit of + + + align:start position:0% +liberty and the pursuit of +happiness does anybody know where this + + align:start position:0% +happiness does anybody know where this + + + align:start position:0% +happiness does anybody know where this +comes from + + align:start position:0% + + + + align:start position:0% + +this is the this is the law that um It's + + align:start position:0% +this is the this is the law that um It's + + + align:start position:0% +this is the this is the law that um It's +actually an act of English the English + + align:start position:0% +actually an act of English the English + + + align:start position:0% +actually an act of English the English +government that sets up Canada as a + + align:start position:0% +government that sets up Canada as a + + + align:start position:0% +government that sets up Canada as a +separate as a separate State peace order + + align:start position:0% +separate as a separate State peace order + + + align:start position:0% +separate as a separate State peace order +and good government somewhat different + + align:start position:0% +and good government somewhat different + + + align:start position:0% +and good government somewhat different +emphasis than life liberty in the + + align:start position:0% +emphasis than life liberty in the + + + align:start position:0% +emphasis than life liberty in the +pursuit of + + align:start position:0% +pursuit of + + + align:start position:0% +pursuit of +happiness um if you look + + align:start position:0% +happiness um if you look + + + align:start position:0% +happiness um if you look +at lots of other governments don't write + + align:start position:0% +at lots of other governments don't write + + + align:start position:0% +at lots of other governments don't write +down or lots of other countries lots of + + align:start position:0% +down or lots of other countries lots of + + + align:start position:0% +down or lots of other countries lots of +regimes + + align:start position:0% +regimes + + + align:start position:0% +regimes +post-revolutionary Henry VII Ivan the + + align:start position:0% +post-revolutionary Henry VII Ivan the + + + align:start position:0% +post-revolutionary Henry VII Ivan the +Terrible k Rouge Joseph Stalin Adolf + + align:start position:0% +Terrible k Rouge Joseph Stalin Adolf + + + align:start position:0% +Terrible k Rouge Joseph Stalin Adolf +Hitler would not write statements like + + align:start position:0% +Hitler would not write statements like + + + align:start position:0% +Hitler would not write statements like +that um but they had goals they have + + align:start position:0% +that um but they had goals they have + + + align:start position:0% +that um but they had goals they have +goals a key + + align:start position:0% +goals a key + + + align:start position:0% +goals a key +element of a functioning government is a + + align:start position:0% +element of a functioning government is a + + + align:start position:0% +element of a functioning government is a +is a near Monopoly on the use of + + align:start position:0% +is a near Monopoly on the use of + + + align:start position:0% +is a near Monopoly on the use of +force if you think about it when you + + align:start position:0% +force if you think about it when you + + + align:start position:0% +force if you think about it when you +think about um Somalia as a failed + + align:start position:0% +think about um Somalia as a failed + + + align:start position:0% +think about um Somalia as a failed +state or Libya is a failing State not + + align:start position:0% +state or Libya is a failing State not + + + align:start position:0% +state or Libya is a failing State not +that long a ago what broke was the + + align:start position:0% +that long a ago what broke was the + + + align:start position:0% +that long a ago what broke was the +Monopoly on the use of deadly force near + + align:start position:0% +Monopoly on the use of deadly force near + + + align:start position:0% +Monopoly on the use of deadly force near +Monopoly near Monopoly has Syria a + + align:start position:0% +Monopoly near Monopoly has Syria a + + + align:start position:0% +Monopoly near Monopoly has Syria a +failed state yet probably + + align:start position:0% +failed state yet probably + + + align:start position:0% +failed state yet probably +not is it on Route + + align:start position:0% +not is it on Route + + + align:start position:0% +not is it on Route +maybe but + + align:start position:0% +maybe but + + + align:start position:0% +maybe but +that's every every government that's + + align:start position:0% +that's every every government that's + + + align:start position:0% +that's every every government that's +really a + + align:start position:0% +really a + + + align:start position:0% +really a +government really a government has a + + align:start position:0% +government really a government has a + + + align:start position:0% +government really a government has a +monopoly on the use of + + align:start position:0% +monopoly on the use of + + + align:start position:0% +monopoly on the use of +force it also + + align:start position:0% +force it also + + + align:start position:0% +force it also +has governments tend to have legitimacy + + align:start position:0% +has governments tend to have legitimacy + + + align:start position:0% +has governments tend to have legitimacy +that is to say even in North Korea + + align:start position:0% +that is to say even in North Korea + + + align:start position:0% +that is to say even in North Korea +people aren't followed around by a man + + align:start position:0% +people aren't followed around by a man + + + align:start position:0% +people aren't followed around by a man +with a gun people follow + + align:start position:0% +with a gun people follow + + + align:start position:0% +with a gun people follow +orders without the use of + + align:start position:0% +orders without the use of + + + align:start position:0% +orders without the use of +force generally + + align:start position:0% +force generally + + + align:start position:0% +force generally +generally legitimacy comes from can come + + align:start position:0% +generally legitimacy comes from can come + + + align:start position:0% +generally legitimacy comes from can come +from a number of sources again you think + + align:start position:0% +from a number of sources again you think + + + align:start position:0% +from a number of sources again you think +about it in the + + align:start position:0% +about it in the + + + align:start position:0% +about it in the +abstract the US government probably its + + align:start position:0% +abstract the US government probably its + + + align:start position:0% +abstract the US government probably its +legitimacy from the fact that most + + align:start position:0% +legitimacy from the fact that most + + + align:start position:0% +legitimacy from the fact that most +people think the processes followed are + + align:start position:0% +people think the processes followed are + + + align:start position:0% +people think the processes followed are +reasonably fair you might not like have + + align:start position:0% +reasonably fair you might not like have + + + align:start position:0% +reasonably fair you might not like have +liked the decision in Bush versus Gore + + align:start position:0% +liked the decision in Bush versus Gore + + + align:start position:0% +liked the decision in Bush versus Gore +that gave the election to Bush but it + + align:start position:0% +that gave the election to Bush but it + + + align:start position:0% +that gave the election to Bush but it +followed a certain process and yeah you + + align:start position:0% +followed a certain process and yeah you + + + align:start position:0% +followed a certain process and yeah you +didn't like it but fundamentally the + + align:start position:0% +didn't like it but fundamentally the + + + align:start position:0% +didn't like it but fundamentally the +process was okay you don't like the + + align:start position:0% +process was okay you don't like the + + + align:start position:0% +process was okay you don't like the +bills that come out of Congress but you + + align:start position:0% +bills that come out of Congress but you + + + align:start position:0% +bills that come out of Congress but you +know how people are elected blah blah + + align:start position:0% +know how people are elected blah blah + + + align:start position:0% +know how people are elected blah blah +blah um in the days of the divine right + + align:start position:0% +blah um in the days of the divine right + + + align:start position:0% +blah um in the days of the divine right +of King legitimacy came from someplace + + align:start position:0% +of King legitimacy came from someplace + + + align:start position:0% +of King legitimacy came from someplace +else legitimacy came from the fact that + + align:start position:0% +else legitimacy came from the fact that + + + align:start position:0% +else legitimacy came from the fact that +the King was the king and God in said + + align:start position:0% +the King was the king and God in said + + + align:start position:0% +the King was the king and God in said +he's the king do what he says that's a + + align:start position:0% +he's the king do what he says that's a + + + align:start position:0% +he's the king do what he says that's a +pretty good source of legitimacy or you + + align:start position:0% +pretty good source of legitimacy or you + + + align:start position:0% +pretty good source of legitimacy or you +can have a government that's + + align:start position:0% + + + + align:start position:0% + +arbitrary uh doesn't have Divine rights + + align:start position:0% +arbitrary uh doesn't have Divine rights + + + align:start position:0% +arbitrary uh doesn't have Divine rights +but is doing things that people like you + + align:start position:0% +but is doing things that people like you + + + align:start position:0% +but is doing things that people like you +might ask why was the Hitler government + + align:start position:0% +might ask why was the Hitler government + + + align:start position:0% +might ask why was the Hitler government +leg why did it have legitimacy in + + align:start position:0% +leg why did it have legitimacy in + + + align:start position:0% +leg why did it have legitimacy in +Germany because a variety of the goals + + align:start position:0% +Germany because a variety of the goals + + + align:start position:0% +Germany because a variety of the goals +it was pursuing were popular + + align:start position:0% +it was pursuing were popular + + + align:start position:0% +it was pursuing were popular +goals was the process that put it in + + align:start position:0% +goals was the process that put it in + + + align:start position:0% +goals was the process that put it in +office fair not + + align:start position:0% +office fair not + + + align:start position:0% +office fair not +really was Adolf Hitler divinely + + align:start position:0% +really was Adolf Hitler divinely + + + align:start position:0% +really was Adolf Hitler divinely +endorsed not + + align:start position:0% +endorsed not + + + align:start position:0% +endorsed not +really but restoring German self-respect + + align:start position:0% +really but restoring German self-respect + + + align:start position:0% +really but restoring German self-respect +ex expanding the territory of the + + align:start position:0% +ex expanding the territory of the + + + align:start position:0% +ex expanding the territory of the +country making it a power again etc etc + + align:start position:0% +country making it a power again etc etc + + + align:start position:0% +country making it a power again etc etc +those were popular goals + + align:start position:0% + + + + align:start position:0% + +and sometimes North Korea you have + + align:start position:0% +and sometimes North Korea you have + + + align:start position:0% +and sometimes North Korea you have +legitimacy because the + + align:start position:0% +legitimacy because the + + + align:start position:0% +legitimacy because the +consequences of not following orders are + + align:start position:0% +consequences of not following orders are + + + align:start position:0% +consequences of not following orders are +pretty terrible so you follow + + align:start position:0% +pretty terrible so you follow + + + align:start position:0% +pretty terrible so you follow +orders uh governments also have policies + + align:start position:0% +orders uh governments also have policies + + + align:start position:0% +orders uh governments also have policies +and a process uh for changing + + align:start position:0% +and a process uh for changing + + + align:start position:0% +and a process uh for changing +them I want to spend just a couple of + + align:start position:0% +them I want to spend just a couple of + + + align:start position:0% +them I want to spend just a couple of +minutes about how the the market system + + align:start position:0% +minutes about how the the market system + + + align:start position:0% +minutes about how the the market system +the mar the market which you all studied + + align:start position:0% +the mar the market which you all studied + + + align:start position:0% +the mar the market which you all studied +in economics differs from the political + + align:start position:0% +in economics differs from the political + + + align:start position:0% +in economics differs from the political +world which we will be spending some + + align:start position:0% +world which we will be spending some + + + align:start position:0% +world which we will be spending some +time on + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +in the market we think of individuals or + + align:start position:0% +in the market we think of individuals or + + + align:start position:0% +in the market we think of individuals or +firms pursuing the pursuing + + align:start position:0% +firms pursuing the pursuing + + + align:start position:0% +firms pursuing the pursuing +self-interest that happens in the + + align:start position:0% +self-interest that happens in the + + + align:start position:0% +self-interest that happens in the +political + + align:start position:0% +political + + + align:start position:0% +political +world but what also happens in the + + align:start position:0% +world but what also happens in the + + + align:start position:0% +world but what also happens in the +political world is a groups are involved + + align:start position:0% +political world is a groups are involved + + + align:start position:0% +political world is a groups are involved +not just + + align:start position:0% +not just + + + align:start position:0% +not just +individuals parties interest groups + + align:start position:0% +individuals parties interest groups + + + align:start position:0% +individuals parties interest groups +trade associations Industries acting + + align:start position:0% + + + + align:start position:0% + +together and you see the pursuit both of + + align:start position:0% +together and you see the pursuit both of + + + align:start position:0% +together and you see the pursuit both of +self-interest and have different views + + align:start position:0% +self-interest and have different views + + + align:start position:0% +self-interest and have different views +of the public + + align:start position:0% +of the public + + + align:start position:0% +of the public +interest because in the in + + align:start position:0% +interest because in the in + + + align:start position:0% +interest because in the in +the market right you make decisions for + + align:start position:0% +the market right you make decisions for + + + align:start position:0% +the market right you make decisions for +yourself firm makes decisions for itself + + align:start position:0% +yourself firm makes decisions for itself + + + align:start position:0% +yourself firm makes decisions for itself +in the political + + align:start position:0% +in the political + + + align:start position:0% +in the political +world most decisions are for the + + align:start position:0% +world most decisions are for the + + + align:start position:0% +world most decisions are for the +community so the question is not only + + align:start position:0% +community so the question is not only + + + align:start position:0% +community so the question is not only +what's good for for me that matters + + align:start position:0% +what's good for for me that matters + + + align:start position:0% +what's good for for me that matters +obviously but what's good for the + + align:start position:0% +obviously but what's good for the + + + align:start position:0% +obviously but what's good for the +community how do I think a government + + align:start position:0% +community how do I think a government + + + align:start position:0% +community how do I think a government +should work how do I think a community a + + align:start position:0% +should work how do I think a community a + + + align:start position:0% +should work how do I think a community a +state a country should be organized what + + align:start position:0% +state a country should be organized what + + + align:start position:0% +state a country should be organized what +goals should it should it + + align:start position:0% +goals should it should it + + + align:start position:0% +goals should it should it +pursue that gets + + align:start position:0% + + + + align:start position:0% + +us to the question of + + align:start position:0% + + + + align:start position:0% + +ideology I in the market individual + + align:start position:0% +ideology I in the market individual + + + align:start position:0% +ideology I in the market individual +decisions are driven by individual + + align:start position:0% +decisions are driven by individual + + + align:start position:0% +decisions are driven by individual +references in the political world + + align:start position:0% +references in the political world + + + align:start position:0% +references in the political world +ideology matters different views of how + + align:start position:0% +ideology matters different views of how + + + align:start position:0% +ideology matters different views of how +the state should + + align:start position:0% +the state should + + + align:start position:0% +the state should +operate uh how Society should work and + + align:start position:0% +operate uh how Society should work and + + + align:start position:0% +operate uh how Society should work and +what + + align:start position:0% +what + + + align:start position:0% +what +Arrangements uh it should be adopted so + + align:start position:0% +Arrangements uh it should be adopted so + + + align:start position:0% +Arrangements uh it should be adopted so +you and I might for instance + + align:start position:0% +you and I might for instance + + + align:start position:0% +you and I might for instance +agree that uh Society should take care + + align:start position:0% +agree that uh Society should take care + + + align:start position:0% +agree that uh Society should take care +of poor + + align:start position:0% +of poor + + + align:start position:0% +of poor +people or that poor people should be + + align:start position:0% +people or that poor people should be + + + align:start position:0% +people or that poor people should be +taken care of people on the market side + + align:start position:0% +taken care of people on the market side + + + align:start position:0% +taken care of people on the market side +might might say yeah that's what + + align:start position:0% +might might say yeah that's what + + + align:start position:0% +might might say yeah that's what +families are + + align:start position:0% +families are + + + align:start position:0% +families are +for that's how the state should be + + align:start position:0% +for that's how the state should be + + + align:start position:0% +for that's how the state should be +organized to achieve that goal is + + align:start position:0% +organized to achieve that goal is + + + align:start position:0% +organized to achieve that goal is +families should understand that that's + + align:start position:0% +families should understand that that's + + + align:start position:0% +families should understand that that's +their duty to take care of poor + + align:start position:0% +their duty to take care of poor + + + align:start position:0% +their duty to take care of poor +relatives and poor + + align:start position:0% +relatives and poor + + + align:start position:0% +relatives and poor +friends people on the state side might + + align:start position:0% +friends people on the state side might + + + align:start position:0% +friends people on the state side might +say well that's all well and good but it + + align:start position:0% +say well that's all well and good but it + + + align:start position:0% +say well that's all well and good but it +that won't + + align:start position:0% +that won't + + + align:start position:0% +that won't +work that won't work you might have + + align:start position:0% +work that won't work you might have + + + align:start position:0% +work that won't work you might have +different different goals of + + align:start position:0% +different different goals of + + + align:start position:0% +different different goals of +course people on the market side might + + align:start position:0% +course people on the market side might + + + align:start position:0% +course people on the market side might +say the notion that the POR should be + + align:start position:0% +say the notion that the POR should be + + + align:start position:0% +say the notion that the POR should be +taken care of is a bad idea it'll Rob + + align:start position:0% +taken care of is a bad idea it'll Rob + + + align:start position:0% +taken care of is a bad idea it'll Rob +them of incentives and if the poor don't + + align:start position:0% +them of incentives and if the poor don't + + + align:start position:0% +them of incentives and if the poor don't +have incentives they'll be a burden on + + align:start position:0% +have incentives they'll be a burden on + + + align:start position:0% +have incentives they'll be a burden on +the rest of us and we just shouldn't + + align:start position:0% +the rest of us and we just shouldn't + + + align:start position:0% +the rest of us and we just shouldn't +have that people on the state side might + + align:start position:0% +have that people on the state side might + + + align:start position:0% +have that people on the state side might +say no no no you got to take care of the + + align:start position:0% +say no no no you got to take care of the + + + align:start position:0% +say no no no you got to take care of the +poor it's simple Humanity forget all the + + align:start position:0% +poor it's simple Humanity forget all the + + + align:start position:0% +poor it's simple Humanity forget all the +incentives those are ideological + + align:start position:0% +incentives those are ideological + + + align:start position:0% +incentives those are ideological +statements those are statements about + + align:start position:0% +statements those are statements about + + + align:start position:0% +statements those are statements about +how the government how the society how + + align:start position:0% +how the government how the society how + + + align:start position:0% +how the government how the society how +the + + align:start position:0% +the + + + align:start position:0% +the +community what should it work to do and + + align:start position:0% +community what should it work to do and + + + align:start position:0% +community what should it work to do and +how best to get there + + align:start position:0% +how best to get there + + + align:start position:0% +how best to get there +they don't arise those kinds of issues + + align:start position:0% +they don't arise those kinds of issues + + + align:start position:0% +they don't arise those kinds of issues +don't arise in the + + align:start position:0% +don't arise in the + + + align:start position:0% +don't arise in the +market right market economy you're + + align:start position:0% +market right market economy you're + + + align:start position:0% +market right market economy you're +buying you're selling you're pursuing + + align:start position:0% +buying you're selling you're pursuing + + + align:start position:0% +buying you're selling you're pursuing +your interest you're maximizing profit + + align:start position:0% +your interest you're maximizing profit + + + align:start position:0% +your interest you're maximizing profit +none of this stuff comes up it may come + + align:start position:0% +none of this stuff comes up it may come + + + align:start position:0% +none of this stuff comes up it may come +up but it's not + + align:start position:0% +up but it's not + + + align:start position:0% +up but it's not +Central it's not Central in the + + align:start position:0% +Central it's not Central in the + + + align:start position:0% +Central it's not Central in the +political system it's Central so if I + + align:start position:0% +political system it's Central so if I + + + align:start position:0% +political system it's Central so if I +can do this let me just for + + align:start position:0% +can do this let me just for + + + align:start position:0% +can do this let me just for +fun if I've still got it + + align:start position:0% +fun if I've still got it + + + align:start position:0% +fun if I've still got it +um no I don't still have it it uh wait a + + align:start position:0% +um no I don't still have it it uh wait a + + + align:start position:0% +um no I don't still have it it uh wait a +sec yeah I + + align:start position:0% +sec yeah I + + + align:start position:0% +sec yeah I +do just for + + align:start position:0% + + + + align:start position:0% + +humor let's + + align:start position:0% +humor let's + + + align:start position:0% +humor let's +do Howard + + align:start position:0% + + + + align:start position:0% + +roor this is a statement of + + align:start position:0% +roor this is a statement of + + + align:start position:0% +roor this is a statement of +ideology I shall call no Witnesses this + + align:start position:0% +ideology I shall call no Witnesses this + + + align:start position:0% +ideology I shall call no Witnesses this +will be my testimony and my + + align:start position:0% +will be my testimony and my + + + align:start position:0% +will be my testimony and my +take you swear to tell the truth the + + align:start position:0% +take you swear to tell the truth the + + + align:start position:0% +take you swear to tell the truth the +whole truth are nothing but the truth I + + align:start position:0% + + + + align:start position:0% + +do thousands of years ago the first man + + align:start position:0% +do thousands of years ago the first man + + + align:start position:0% +do thousands of years ago the first man +discovered how to make fire he was + + align:start position:0% +discovered how to make fire he was + + + align:start position:0% +discovered how to make fire he was +probably burned at the stake he had + + align:start position:0% +probably burned at the stake he had + + + align:start position:0% +probably burned at the stake he had +taught his brothers to light but he left + + align:start position:0% +taught his brothers to light but he left + + + align:start position:0% +taught his brothers to light but he left +them a gift they had not conceived and + + align:start position:0% +them a gift they had not conceived and + + + align:start position:0% +them a gift they had not conceived and +he lifted Darkness off the Earth + + align:start position:0% +he lifted Darkness off the Earth + + + align:start position:0% +he lifted Darkness off the Earth +throughout the centuries there were men + + align:start position:0% +throughout the centuries there were men + + + align:start position:0% +throughout the centuries there were men +who took first steps down New Roads + + align:start position:0% +who took first steps down New Roads + + + align:start position:0% +who took first steps down New Roads +armed with nothing but their own Vision + + align:start position:0% +armed with nothing but their own Vision + + + align:start position:0% +armed with nothing but their own Vision +the great creators the thinkers the + + align:start position:0% +the great creators the thinkers the + + + align:start position:0% +the great creators the thinkers the +artists the scientists the inventors + + align:start position:0% +artists the scientists the inventors + + + align:start position:0% +artists the scientists the inventors +stood alone against the men of their + + align:start position:0% +stood alone against the men of their + + + align:start position:0% +stood alone against the men of their +time time every new thought was opposed + + align:start position:0% +time time every new thought was opposed + + + align:start position:0% +time time every new thought was opposed +every new invention was denounced but + + align:start position:0% +every new invention was denounced but + + + align:start position:0% +every new invention was denounced but +the men of unborrowed vision went ahead + + align:start position:0% +the men of unborrowed vision went ahead + + + align:start position:0% +the men of unborrowed vision went ahead +they fought they suffered and they paid + + align:start position:0% +they fought they suffered and they paid + + + align:start position:0% +they fought they suffered and they paid +but they won no Creator was prompted by + + align:start position:0% +but they won no Creator was prompted by + + + align:start position:0% +but they won no Creator was prompted by +a desire to please his + + align:start position:0% +a desire to please his + + + align:start position:0% +a desire to please his +brothers his brothers hated the gift he + + align:start position:0% +brothers his brothers hated the gift he + + + align:start position:0% +brothers his brothers hated the gift he +offered his truth was his only motive + + align:start position:0% +offered his truth was his only motive + + + align:start position:0% +offered his truth was his only motive +his work was his only goal this is a + + align:start position:0% +his work was his only goal this is a + + + align:start position:0% +his work was his only goal this is a +model of progress not those come from + + align:start position:0% +model of progress not those come from + + + align:start position:0% +model of progress not those come from +his creation not the benefits others + + align:start position:0% +his creation not the benefits others + + + align:start position:0% +his creation not the benefits others +derive from it the creation which gave + + align:start position:0% +derive from it the creation which gave + + + align:start position:0% +derive from it the creation which gave +form to his truth he held his truth + + align:start position:0% +form to his truth he held his truth + + + align:start position:0% +form to his truth he held his truth +above all things and against all + + align:start position:0% +above all things and against all + + + align:start position:0% +above all things and against all +men he went ahead whether others agreed + + align:start position:0% +men he went ahead whether others agreed + + + align:start position:0% +men he went ahead whether others agreed +with him or not with his Integrity as + + align:start position:0% +with him or not with his Integrity as + + + align:start position:0% +with him or not with his Integrity as +his only Banner he served nothing and no + + align:start position:0% +his only Banner he served nothing and no + + + align:start position:0% +his only Banner he served nothing and no +one he lived for + + align:start position:0% +one he lived for + + + align:start position:0% +one he lived for +himself and only by living for himself + + align:start position:0% +himself and only by living for himself + + + align:start position:0% +himself and only by living for himself +was he able to achieve the things which + + align:start position:0% +was he able to achieve the things which + + + align:start position:0% +was he able to achieve the things which +are the glory of mankind such is the + + align:start position:0% +are the glory of mankind such is the + + + align:start position:0% +are the glory of mankind such is the +nature of + + align:start position:0% +nature of + + + align:start position:0% +nature of +achievement man cannot survive except + + align:start position:0% +achievement man cannot survive except + + + align:start position:0% +achievement man cannot survive except +through his mind he comes on Earth + + align:start position:0% +through his mind he comes on Earth + + + align:start position:0% +through his mind he comes on Earth +unarmed his brain is his only weapon but + + align:start position:0% +unarmed his brain is his only weapon but + + + align:start position:0% +unarmed his brain is his only weapon but +the mind is an attribute of the + + align:start position:0% +the mind is an attribute of the + + + align:start position:0% +the mind is an attribute of the +individual there is no such thing as a + + align:start position:0% +individual there is no such thing as a + + + align:start position:0% +individual there is no such thing as a +collective brain the man who thinks must + + align:start position:0% +collective brain the man who thinks must + + + align:start position:0% +collective brain the man who thinks must +think and act on his own the reasoning + + align:start position:0% +think and act on his own the reasoning + + + align:start position:0% +think and act on his own the reasoning +mind cannot work under any form of + + align:start position:0% +mind cannot work under any form of + + + align:start position:0% +mind cannot work under any form of +compulsion it cannot be subordinated to + + align:start position:0% +compulsion it cannot be subordinated to + + + align:start position:0% +compulsion it cannot be subordinated to +to the needs opinions or wishes of + + align:start position:0% +to the needs opinions or wishes of + + + align:start position:0% +to the needs opinions or wishes of +others it is not an object of + + align:start position:0% +others it is not an object of + + + align:start position:0% +others it is not an object of +sacrifice the Creator stands on his own + + align:start position:0% +sacrifice the Creator stands on his own + + + align:start position:0% +sacrifice the Creator stands on his own +judgment the parasite follows the + + align:start position:0% +judgment the parasite follows the + + + align:start position:0% +judgment the parasite follows the +opinions of others the Creator thinks + + align:start position:0% +opinions of others the Creator thinks + + + align:start position:0% +opinions of others the Creator thinks +the parasite copies the Creator produces + + align:start position:0% +the parasite copies the Creator produces + + + align:start position:0% +the parasite copies the Creator produces +the parasite loots the Creator's concern + + align:start position:0% +the parasite loots the Creator's concern + + + align:start position:0% +the parasite loots the Creator's concern +is the conquest of nature the parasite's + + align:start position:0% +is the conquest of nature the parasite's + + + align:start position:0% +is the conquest of nature the parasite's +concern is the conquest of man the cre + + align:start position:0% +concern is the conquest of man the cre + + + align:start position:0% +concern is the conquest of man the cre +Creator requires Independence he he + + align:start position:0% +Creator requires Independence he he + + + align:start position:0% +Creator requires Independence he he +neither serves nor rules he deals with + + align:start position:0% +neither serves nor rules he deals with + + + align:start position:0% +neither serves nor rules he deals with +men by free exchange and voluntary + + align:start position:0% +men by free exchange and voluntary + + + align:start position:0% +men by free exchange and voluntary +Choice the parasite seeks power he wants + + align:start position:0% +Choice the parasite seeks power he wants + + + align:start position:0% +Choice the parasite seeks power he wants +to bind all men together in common + + align:start position:0% +to bind all men together in common + + + align:start position:0% +to bind all men together in common +action and common slavery he he claims + + align:start position:0% +action and common slavery he he claims + + + align:start position:0% +action and common slavery he he claims +is only a tool for the use of others + + align:start position:0% +is only a tool for the use of others + + + align:start position:0% +is only a tool for the use of others +that he must think as they think act as + + align:start position:0% +that he must think as they think act as + + + align:start position:0% +that he must think as they think act as +they act and live in selfless joyless + + align:start position:0% +they act and live in selfless joyless + + + align:start position:0% +they act and live in selfless joyless +servitude to any need but his own look + + align:start position:0% +servitude to any need but his own look + + + align:start position:0% +servitude to any need but his own look +at history everything we have every + + align:start position:0% +at history everything we have every + + + align:start position:0% +at history everything we have every +great achievement has come from the + + align:start position:0% +great achievement has come from the + + + align:start position:0% +great achievement has come from the +Independent work of some independent + + align:start position:0% +Independent work of some independent + + + align:start position:0% +Independent work of some independent +mind every horror and destruction came + + align:start position:0% +mind every horror and destruction came + + + align:start position:0% +mind every horror and destruction came +from attempts to force men into a herd + + align:start position:0% +from attempts to force men into a herd + + + align:start position:0% +from attempts to force men into a herd +of brainless soulless robots without + + align:start position:0% +of brainless soulless robots without + + + align:start position:0% +of brainless soulless robots without +personal rights without personal + + align:start position:0% +personal rights without personal + + + align:start position:0% +personal rights without personal +ambition without will hope or dignity it + + align:start position:0% +ambition without will hope or dignity it + + + align:start position:0% +ambition without will hope or dignity it +is an ancient conflict it has another + + align:start position:0% +is an ancient conflict it has another + + + align:start position:0% +is an ancient conflict it has another +name the individual against the + + align:start position:0% + + + + align:start position:0% + +collective our country country in the + + align:start position:0% +collective our country country in the + + + align:start position:0% +collective our country country in the +history of men was based on the + + align:start position:0% +history of men was based on the + + + align:start position:0% +history of men was based on the +principle of individualism the principle + + align:start position:0% +principle of individualism the principle + + + align:start position:0% +principle of individualism the principle +of man's inalienable + + align:start position:0% +of man's inalienable + + + align:start position:0% +of man's inalienable +rights it was a country where a man was + + align:start position:0% +rights it was a country where a man was + + + align:start position:0% +rights it was a country where a man was +free to seek his own happiness to gain + + align:start position:0% +free to seek his own happiness to gain + + + align:start position:0% +free to seek his own happiness to gain +and produce not to give up and renounce + + align:start position:0% +and produce not to give up and renounce + + + align:start position:0% +and produce not to give up and renounce +to prosper not to starve to + + align:start position:0% +to prosper not to starve to + + + align:start position:0% +to prosper not to starve to +achieve not to + + align:start position:0% +achieve not to + + + align:start position:0% +achieve not to +plunder to hold as His Highest + + align:start position:0% +plunder to hold as His Highest + + + align:start position:0% +plunder to hold as His Highest +possession a sense of his personal value + + align:start position:0% +possession a sense of his personal value + + + align:start position:0% +possession a sense of his personal value +and as His Highest virtue his + + align:start position:0% +and as His Highest virtue his + + + align:start position:0% +and as His Highest virtue his +self-respect + + align:start position:0% +self-respect + + + align:start position:0% +self-respect +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +results that is what the collectivists + + align:start position:0% +results that is what the collectivists + + + align:start position:0% +results that is what the collectivists +are now asking you to destroy as much of + + align:start position:0% +are now asking you to destroy as much of + + + align:start position:0% +are now asking you to destroy as much of +the Earth has been + + align:start position:0% +the Earth has been + + + align:start position:0% +the Earth has been +destroy I am an architect I know what is + + align:start position:0% +destroy I am an architect I know what is + + + align:start position:0% +destroy I am an architect I know what is +to come by the principle on which it is + + align:start position:0% +to come by the principle on which it is + + + align:start position:0% +to come by the principle on which it is +built we are approaching a world in + + align:start position:0% +built we are approaching a world in + + + align:start position:0% +built we are approaching a world in +which I cannot permit myself to live my + + align:start position:0% +which I cannot permit myself to live my + + + align:start position:0% +which I cannot permit myself to live my +ideas are my property they were taken + + align:start position:0% +ideas are my property they were taken + + + align:start position:0% +ideas are my property they were taken +from me by force by breach of + + align:start position:0% +from me by force by breach of + + + align:start position:0% +from me by force by breach of +contract no appeal was left to me it + + align:start position:0% +contract no appeal was left to me it + + + align:start position:0% +contract no appeal was left to me it +believed that my work belonged to others + + align:start position:0% +believed that my work belonged to others + + + align:start position:0% +believed that my work belonged to others +to do with as they pleased they had a + + align:start position:0% +to do with as they pleased they had a + + + align:start position:0% +to do with as they pleased they had a +claim upon me without my consent that it + + align:start position:0% +claim upon me without my consent that it + + + align:start position:0% +claim upon me without my consent that it +was my duty to serve them without choice + + align:start position:0% +was my duty to serve them without choice + + + align:start position:0% +was my duty to serve them without choice +or reward now you know why I Dynamite at + + align:start position:0% +or reward now you know why I Dynamite at + + + align:start position:0% +or reward now you know why I Dynamite at +courland I designed courland I made it + + align:start position:0% +courland I designed courland I made it + + + align:start position:0% +courland I designed courland I made it +possible I destroyed it I agreed to + + align:start position:0% +possible I destroyed it I agreed to + + + align:start position:0% +possible I destroyed it I agreed to +design it for the purpose of seeing it + + align:start position:0% +design it for the purpose of seeing it + + + align:start position:0% +design it for the purpose of seeing it +built as I wished that was the price I + + align:start position:0% +built as I wished that was the price I + + + align:start position:0% +built as I wished that was the price I +set for my work I was not paid my + + align:start position:0% +set for my work I was not paid my + + + align:start position:0% +set for my work I was not paid my +building was disfigured at a whim of + + align:start position:0% +building was disfigured at a whim of + + + align:start position:0% +building was disfigured at a whim of +others who took all the benefit me of my + + align:start position:0% +others who took all the benefit me of my + + + align:start position:0% +others who took all the benefit me of my +work and gave me nothing in + + align:start position:0% +work and gave me nothing in + + + align:start position:0% +work and gave me nothing in +return I came here to say that I do not + + align:start position:0% +return I came here to say that I do not + + + align:start position:0% +return I came here to say that I do not +recognize anyone's right to one minute + + align:start position:0% +recognize anyone's right to one minute + + + align:start position:0% +recognize anyone's right to one minute +of my life nor to any part of my energy + + align:start position:0% +of my life nor to any part of my energy + + + align:start position:0% +of my life nor to any part of my energy +nor to any achievement of mine no matter + + align:start position:0% +nor to any achievement of mine no matter + + + align:start position:0% +nor to any achievement of mine no matter +who makes the claim it had to be said + + align:start position:0% +who makes the claim it had to be said + + + align:start position:0% +who makes the claim it had to be said +the world is perishing from an orgy of + + align:start position:0% +the world is perishing from an orgy of + + + align:start position:0% +the world is perishing from an orgy of +self-sacrificing I came here to be heard + + align:start position:0% +self-sacrificing I came here to be heard + + + align:start position:0% +self-sacrificing I came here to be heard +in the name of every man of Independence + + align:start position:0% +in the name of every man of Independence + + + align:start position:0% +in the name of every man of Independence +still left in the world I wanted to + + align:start position:0% +still left in the world I wanted to + + + align:start position:0% +still left in the world I wanted to +State my terms I do not care to work or + + align:start position:0% +State my terms I do not care to work or + + + align:start position:0% +State my terms I do not care to work or +live on any others + + align:start position:0% +live on any others + + + align:start position:0% +live on any others +my terms are a man's right to exist for + + align:start position:0% +my terms are a man's right to exist for + + + align:start position:0% +my terms are a man's right to exist for +his own + + align:start position:0% + + + + align:start position:0% + +sake so I'm + + align:start position:0% +sake so I'm + + + align:start position:0% +sake so I'm +not I'm not going to ask for a + + align:start position:0% +not I'm not going to ask for a + + + align:start position:0% +not I'm not going to ask for a +vote but you see that is an ideological + + align:start position:0% +vote but you see that is an ideological + + + align:start position:0% +vote but you see that is an ideological +statement it is about how the world must + + align:start position:0% +statement it is about how the world must + + + align:start position:0% +statement it is about how the world must +be organized should be organized to + + align:start position:0% +be organized should be organized to + + + align:start position:0% +be organized should be organized to +permit + + align:start position:0% +permit + + + align:start position:0% +permit +progress the inventors have to be free + + align:start position:0% +progress the inventors have to be free + + + align:start position:0% +progress the inventors have to be free +to invent the parasites have to be + + align:start position:0% +to invent the parasites have to be + + + align:start position:0% +to invent the parasites have to be +suppressed it's an ideological statement + + align:start position:0% +suppressed it's an ideological statement + + + align:start position:0% +suppressed it's an ideological statement +it's not just how he wants to live but + + align:start position:0% +it's not just how he wants to live but + + + align:start position:0% +it's not just how he wants to live but +how others should live how the + + align:start position:0% +how others should live how the + + + align:start position:0% +how others should live how the +government how the how the society + + align:start position:0% +government how the how the society + + + align:start position:0% +government how the how the society +should be organized there's another + + align:start position:0% +should be organized there's another + + + align:start position:0% +should be organized there's another +example on the on the list which was + + align:start position:0% +example on the on the list which was + + + align:start position:0% +example on the on the list which was +long and tedious and optional so I + + align:start position:0% +long and tedious and optional so I + + + align:start position:0% +long and tedious and optional so I +assume nobody read it um uh but uh I + + align:start position:0% +assume nobody read it um uh but uh I + + + align:start position:0% +assume nobody read it um uh but uh I +will I will um give you the story it's + + align:start position:0% +will I will um give you the story it's + + + align:start position:0% +will I will um give you the story it's +kind of an amazing story + + align:start position:0% +kind of an amazing story + + + align:start position:0% +kind of an amazing story +it's um a description of the London + + align:start position:0% +it's um a description of the London + + + align:start position:0% +it's um a description of the London +electrical system the Hughes reading + + align:start position:0% +electrical system the Hughes reading + + + align:start position:0% +electrical system the Hughes reading +before the first world war Now by say + + align:start position:0% +before the first world war Now by say + + + align:start position:0% +before the first world war Now by say +1914 was lots of electricity in Chicago + + align:start position:0% +1914 was lots of electricity in Chicago + + + align:start position:0% +1914 was lots of electricity in Chicago +Chicago was electrified there were + + align:start position:0% +Chicago was electrified there were + + + align:start position:0% +Chicago was electrified there were +trolleys there was a company that + + align:start position:0% +trolleys there was a company that + + + align:start position:0% +trolleys there was a company that +spanned the city there was a lot of + + align:start position:0% +spanned the city there was a lot of + + + align:start position:0% +spanned the city there was a lot of +electricity had penetrated a good deal + + align:start position:0% +electricity had penetrated a good deal + + + align:start position:0% +electricity had penetrated a good deal +in Berlin again a single system modern + + align:start position:0% +in Berlin again a single system modern + + + align:start position:0% +in Berlin again a single system modern +by the standards of the day in + + align:start position:0% +by the standards of the day in + + + align:start position:0% +by the standards of the day in +London there there were what's it say 65 + + align:start position:0% +London there there were what's it say 65 + + + align:start position:0% +London there there were what's it say 65 +utilities operating on 10 different + + align:start position:0% +utilities operating on 10 different + + + align:start position:0% +utilities operating on 10 different +frequencies with 24 different voltages + + align:start position:0% +frequencies with 24 different voltages + + + align:start position:0% +frequencies with 24 different voltages +delivered to + + align:start position:0% +delivered to + + + align:start position:0% +delivered to +customers now and it's not like London + + align:start position:0% +customers now and it's not like London + + + align:start position:0% +customers now and it's not like London +was populated by idiots or there weren't + + align:start position:0% +was populated by idiots or there weren't + + + align:start position:0% +was populated by idiots or there weren't +Engineers there were plenty of Engineers + + align:start position:0% +Engineers there were plenty of Engineers + + + align:start position:0% +Engineers there were plenty of Engineers +they had societies of electrical + + align:start position:0% +they had societies of electrical + + + align:start position:0% +they had societies of electrical +engineers just like the Germans did and + + align:start position:0% +engineers just like the Germans did and + + + align:start position:0% +engineers just like the Germans did and +the Americans did and commissions + + align:start position:0% +the Americans did and commissions + + + align:start position:0% +the Americans did and commissions +regularly said is insane this is crazy + + align:start position:0% +regularly said is insane this is crazy + + + align:start position:0% +regularly said is insane this is crazy +Appliance makers said this is nuts we + + align:start position:0% +Appliance makers said this is nuts we + + + align:start position:0% +Appliance makers said this is nuts we +can't we can't sell the same appliances + + align:start position:0% +can't we can't sell the same appliances + + + align:start position:0% +can't we can't sell the same appliances +in this part of London that we sell in + + align:start position:0% +in this part of London that we sell in + + + align:start position:0% +in this part of London that we sell in +that part of London the US has a + + align:start position:0% +that part of London the US has a + + + align:start position:0% +that part of London the US has a +standard Germany has a standard London + + align:start position:0% +standard Germany has a standard London + + + align:start position:0% +standard Germany has a standard London +has 10 frequencies and 24 voltages and + + align:start position:0% +has 10 frequencies and 24 voltages and + + + align:start position:0% +has 10 frequencies and 24 voltages and + + align:start position:0% + + + align:start position:0% +companies so + + align:start position:0% +companies so + + + align:start position:0% +companies so +why well since nobody read it but me + + align:start position:0% +why well since nobody read it but me + + + align:start position:0% +why well since nobody read it but me +I'll tell you why um because London was + + align:start position:0% +I'll tell you why um because London was + + + align:start position:0% +I'll tell you why um because London was +divided into a set of local governments + + align:start position:0% +divided into a set of local governments + + + align:start position:0% +divided into a set of local governments +that had since the Middle Ages authority + + align:start position:0% +that had since the Middle Ages authority + + + align:start position:0% +that had since the Middle Ages authority +over the their + + align:start position:0% +over the their + + + align:start position:0% +over the their +domains and the ideology was this is + + align:start position:0% +domains and the ideology was this is + + + align:start position:0% +domains and the ideology was this is +local it goes to residences it goes to + + align:start position:0% +local it goes to residences it goes to + + + align:start position:0% +local it goes to residences it goes to +BU to factories it's the domain of local + + align:start position:0% +BU to factories it's the domain of local + + + align:start position:0% +BU to factories it's the domain of local +government that was the ideology that's + + align:start position:0% +government that was the ideology that's + + + align:start position:0% +government that was the ideology that's +the statement about how that Society + + align:start position:0% +the statement about how that Society + + + align:start position:0% +the statement about how that Society +should be organized local governments + + align:start position:0% +should be organized local governments + + + align:start position:0% +should be organized local governments +should no matter maximization Here Local + + align:start position:0% +should no matter maximization Here Local + + + align:start position:0% +should no matter maximization Here Local +Government should have control over + + align:start position:0% +Government should have control over + + + align:start position:0% +Government should have control over +local + + align:start position:0% +local + + + align:start position:0% +local +utilities it took them a long time to + + align:start position:0% +utilities it took them a long time to + + + align:start position:0% +utilities it took them a long time to +get past + + align:start position:0% +get past + + + align:start position:0% +get past +that and you say wait couldn't you just + + align:start position:0% +that and you say wait couldn't you just + + + align:start position:0% +that and you say wait couldn't you just +say that that's all fine that's a nice + + align:start position:0% +say that that's all fine that's a nice + + + align:start position:0% +say that that's all fine that's a nice +ideology + + align:start position:0% +ideology + + + align:start position:0% +ideology +but why don't we just get the electrical + + align:start position:0% +but why don't we just get the electrical + + + align:start position:0% +but why don't we just get the electrical +system right it was the biggest richest + + align:start position:0% +system right it was the biggest richest + + + align:start position:0% +system right it was the biggest richest +city in the world and it had a terrible + + align:start position:0% +city in the world and it had a terrible + + + align:start position:0% +city in the world and it had a terrible +electrical system because of this + + align:start position:0% +electrical system because of this + + + align:start position:0% +electrical system because of this +ideology how could they Poss POS L have + + align:start position:0% +ideology how could they Poss POS L have + + + align:start position:0% +ideology how could they Poss POS L have +gone with + + align:start position:0% +gone with + + + align:start position:0% +gone with +it well you will see in the course of + + align:start position:0% +it well you will see in the course of + + + align:start position:0% +it well you will see in the course of +human events as you as you read and uh + + align:start position:0% +human events as you as you read and uh + + + align:start position:0% +human events as you as you read and uh +as you read the paper and as you read + + align:start position:0% +as you read the paper and as you read + + + align:start position:0% +as you read the paper and as you read +other things this kind of thing happens + + align:start position:0% +other things this kind of thing happens + + + align:start position:0% +other things this kind of thing happens +all the + + align:start position:0% +all the + + + align:start position:0% +all the +time beliefs about how things should be + + align:start position:0% +time beliefs about how things should be + + + align:start position:0% +time beliefs about how things should be +organized beliefs about the right way + + align:start position:0% +organized beliefs about the right way + + + align:start position:0% +organized beliefs about the right way +for a community to organize are very + + align:start position:0% +for a community to organize are very + + + align:start position:0% +for a community to organize are very +strong they don't change + + align:start position:0% +strong they don't change + + + align:start position:0% +strong they don't change +rapidly we have a federal system + + align:start position:0% +rapidly we have a federal system + + + align:start position:0% +rapidly we have a federal system +uh I will discuss later on how we + + align:start position:0% +uh I will discuss later on how we + + + align:start position:0% +uh I will discuss later on how we +regulate the electric power system in + + align:start position:0% +regulate the electric power system in + + + align:start position:0% +regulate the electric power system in +this country and we do a lot of + + align:start position:0% +this country and we do a lot of + + + align:start position:0% +this country and we do a lot of +pretending that electrons don't cross + + align:start position:0% +pretending that electrons don't cross + + + align:start position:0% +pretending that electrons don't cross +state + + align:start position:0% +state + + + align:start position:0% +state +lines but of course they do but the + + align:start position:0% +lines but of course they do but the + + + align:start position:0% +lines but of course they do but the +ideology is that's a state + + align:start position:0% +ideology is that's a state + + + align:start position:0% +ideology is that's a state +function and if you stand up and say why + + align:start position:0% +function and if you stand up and say why + + + align:start position:0% +function and if you stand up and say why +in Heaven's name I mean we we do have + + align:start position:0% +in Heaven's name I mean we we do have + + + align:start position:0% +in Heaven's name I mean we we do have +national standards it's not not like + + align:start position:0% +national standards it's not not like + + + align:start position:0% +national standards it's not not like +London but if you stand up and say this + + align:start position:0% +London but if you stand up and say this + + + align:start position:0% +London but if you stand up and say this +ought to be a federal + + align:start position:0% +ought to be a federal + + + align:start position:0% +ought to be a federal +function you get shot I mean it's just + + align:start position:0% +function you get shot I mean it's just + + + align:start position:0% +function you get shot I mean it's just +it's just not on the table you can't + + align:start position:0% +it's just not on the table you can't + + + align:start position:0% +it's just not on the table you can't +have a technical debate about would it + + align:start position:0% +have a technical debate about would it + + + align:start position:0% +have a technical debate about would it +be good or bad because of the strength + + align:start position:0% +be good or bad because of the strength + + + align:start position:0% +be good or bad because of the strength +of the of the ideologies now I don't say + + align:start position:0% +of the of the ideologies now I don't say + + + align:start position:0% +of the of the ideologies now I don't say +that as a as an indictment of human + + align:start position:0% +that as a as an indictment of human + + + align:start position:0% +that as a as an indictment of human +society you have to have beliefs about + + align:start position:0% +society you have to have beliefs about + + + align:start position:0% +society you have to have beliefs about +how the world should be organized how do + + align:start position:0% +how the world should be organized how do + + + align:start position:0% +how the world should be organized how do +you function without them just like you + + align:start position:0% +you function without them just like you + + + align:start position:0% +you function without them just like you +have to have preferences about you know + + align:start position:0% +have to have preferences about you know + + + align:start position:0% +have to have preferences about you know +do you like tacos or burritos I mean you + + align:start position:0% +do you like tacos or burritos I mean you + + + align:start position:0% +do you like tacos or burritos I mean you +have to get through life you have to + + align:start position:0% +have to get through life you have to + + + align:start position:0% +have to get through life you have to +have views of the world should be + + align:start position:0% +have views of the world should be + + + align:start position:0% +have views of the world should be +organized and how people how the the + + align:start position:0% +organized and how people how the the + + + align:start position:0% +organized and how people how the the +government should pursue certain goals + + align:start position:0% +government should pursue certain goals + + + align:start position:0% +government should pursue certain goals +those beliefs might want to occasionally + + align:start position:0% +those beliefs might want to occasionally + + + align:start position:0% +those beliefs might want to occasionally +brush up against facts just like you + + align:start position:0% +brush up against facts just like you + + + align:start position:0% +brush up against facts just like you +know your preferences for ice cream + + align:start position:0% +know your preferences for ice cream + + + align:start position:0% +know your preferences for ice cream +might occasionally want to brush up + + align:start position:0% +might occasionally want to brush up + + + align:start position:0% +might occasionally want to brush up +against facts about colesterol but uh + + align:start position:0% +against facts about colesterol but uh + + + align:start position:0% +against facts about colesterol but uh +fundamentally just like you you need + + align:start position:0% +fundamentally just like you you need + + + align:start position:0% +fundamentally just like you you need +preferences and habits to get through + + align:start position:0% +preferences and habits to get through + + + align:start position:0% +preferences and habits to get through +the day individuals in the political + + align:start position:0% +the day individuals in the political + + + align:start position:0% +the day individuals in the political +world need + + align:start position:0% +world need + + + align:start position:0% +world need +ideologies so this that's not a that's + + align:start position:0% +ideologies so this that's not a that's + + + align:start position:0% +ideologies so this that's not a that's +not a pejorative statement the other the + + align:start position:0% +not a pejorative statement the other the + + + align:start position:0% +not a pejorative statement the other the +other point I want to make a difference + + align:start position:0% +other point I want to make a difference + + + align:start position:0% +other point I want to make a difference +between uh the market and the um the + + align:start position:0% +between uh the market and the um the + + + align:start position:0% +between uh the market and the um the +polus the political world is we + + align:start position:0% +polus the political world is we + + + align:start position:0% +polus the political world is we +generally assume in economics that + + align:start position:0% +generally assume in economics that + + + align:start position:0% +generally assume in economics that +individuals at some point in time at + + align:start position:0% +individuals at some point in time at + + + align:start position:0% +individuals at some point in time at +least have relatively well-defined + + align:start position:0% +least have relatively well-defined + + + align:start position:0% +least have relatively well-defined +preferences well-defined preferences + + align:start position:0% +preferences well-defined preferences + + + align:start position:0% +preferences well-defined preferences +basically just means you're + + align:start position:0% +basically just means you're + + + align:start position:0% +basically just means you're +consistent you know if you you don't you + + align:start position:0% +consistent you know if you you don't you + + + align:start position:0% +consistent you know if you you don't you +don't behave in a way way that that's + + align:start position:0% +don't behave in a way way that that's + + + align:start position:0% +don't behave in a way way that that's +obviously evidence of of an unsound mind + + align:start position:0% +obviously evidence of of an unsound mind + + + align:start position:0% +obviously evidence of of an unsound mind +uh political judgments can be + + align:start position:0% +uh political judgments can be + + + align:start position:0% +uh political judgments can be +inconsistent in that sense let me just + + align:start position:0% +inconsistent in that sense let me just + + + align:start position:0% +inconsistent in that sense let me just +give you the simplest case of the + + align:start position:0% +give you the simplest case of the + + + align:start position:0% +give you the simplest case of the +condray + + align:start position:0% +condray + + + align:start position:0% +condray +Paradox uh which a very bright Frenchman + + align:start position:0% +Paradox uh which a very bright Frenchman + + + align:start position:0% +Paradox uh which a very bright Frenchman +discovered in + + align:start position:0% +discovered in + + + align:start position:0% +discovered in +1785 and it it's a special case of a + + align:start position:0% +1785 and it it's a special case of a + + + align:start position:0% +1785 and it it's a special case of a +general rule that + + align:start position:0% +general rule that + + + align:start position:0% +general rule that +says for which K Aro got a Nobel Prize + + align:start position:0% +says for which K Aro got a Nobel Prize + + + align:start position:0% +says for which K Aro got a Nobel Prize +that says + + align:start position:0% +that says + + + align:start position:0% +that says +basically any regime without a dictator + + align:start position:0% +basically any regime without a dictator + + + align:start position:0% +basically any regime without a dictator +will behave inconsistently in roughly + + align:start position:0% +will behave inconsistently in roughly + + + align:start position:0% +will behave inconsistently in roughly +the following + + align:start position:0% +the following + + + align:start position:0% +the following +sense let me be let me say I've got + + align:start position:0% +sense let me be let me say I've got + + + align:start position:0% +sense let me be let me say I've got +three individuals three + + align:start position:0% + + + + align:start position:0% + +voters this is what the slide says but + + align:start position:0% +voters this is what the slide says but + + + align:start position:0% +voters this is what the slide says but +I'm going to unpack it a little bit one + + align:start position:0% +I'm going to unpack it a little bit one + + + align:start position:0% +I'm going to unpack it a little bit one +two and three and there are three + + align:start position:0% +two and three and there are three + + + align:start position:0% +two and three and there are three +Alternatives a b and c so individual one + + align:start position:0% +Alternatives a b and c so individual one + + + align:start position:0% +Alternatives a b and c so individual one +prefers a to B and prefers B to + + align:start position:0% +prefers a to B and prefers B to + + + align:start position:0% +prefers a to B and prefers B to +C individual two prefers C that's that's + + align:start position:0% +C individual two prefers C that's that's + + + align:start position:0% +C individual two prefers C that's that's +her first choice C to + + align:start position:0% +her first choice C to + + + align:start position:0% +her first choice C to +A and A to + + align:start position:0% +A and A to + + + align:start position:0% +A and A to +B individual three prefers + + align:start position:0% +B individual three prefers + + + align:start position:0% +B individual three prefers +B to + + align:start position:0% +B to + + + align:start position:0% +B to +C to + + align:start position:0% + + + + align:start position:0% + +a okay so suppose I I have a vote + + align:start position:0% +a okay so suppose I I have a vote + + + align:start position:0% +a okay so suppose I I have a vote +between A and B if I have a vote between + + align:start position:0% +between A and B if I have a vote between + + + align:start position:0% +between A and B if I have a vote between +A and B one prefers A to B two prefers A + + align:start position:0% +A and B one prefers A to B two prefers A + + + align:start position:0% +A and B one prefers A to B two prefers A +to B so if I + + align:start position:0% + + + + align:start position:0% + +vote a is preferred to + + align:start position:0% +vote a is preferred to + + + align:start position:0% +vote a is preferred to +B now let me do B versus + + align:start position:0% +B now let me do B versus + + + align:start position:0% +B now let me do B versus +c one prefers B to C three prefers B to + + align:start position:0% +c one prefers B to C three prefers B to + + + align:start position:0% +c one prefers B to C three prefers B to +C so the vote tells me that b is + + align:start position:0% +C so the vote tells me that b is + + + align:start position:0% +C so the vote tells me that b is +preferred to C + + align:start position:0% + + + + align:start position:0% + +now let me do a and + + align:start position:0% +now let me do a and + + + align:start position:0% +now let me do a and +C two prefers C to a three prefers C to + + align:start position:0% +C two prefers C to a three prefers C to + + + align:start position:0% +C two prefers C to a three prefers C to +a c is preferred to + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% + + + + align:start position:0% + +that is inconsistent + + align:start position:0% +that is inconsistent + + + align:start position:0% +that is inconsistent +Behavior right if an if an individual + + align:start position:0% +Behavior right if an if an individual + + + align:start position:0% +Behavior right if an if an individual +behaved in that fashion and said you + + align:start position:0% +behaved in that fashion and said you + + + align:start position:0% +behaved in that fashion and said you +know I I I I prefer chocolate to + + align:start position:0% +know I I I I prefer chocolate to + + + align:start position:0% +know I I I I prefer chocolate to +Strawberry Berry I prefer strawberry to + + align:start position:0% +Strawberry Berry I prefer strawberry to + + + align:start position:0% +Strawberry Berry I prefer strawberry to +vanilla but I prefer vanilla to + + align:start position:0% +vanilla but I prefer vanilla to + + + align:start position:0% +vanilla but I prefer vanilla to +Chocolate you'd say I'm sorry wait a + + align:start position:0% +Chocolate you'd say I'm sorry wait a + + + align:start position:0% +Chocolate you'd say I'm sorry wait a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +what but in voting that can happen all + + align:start position:0% +what but in voting that can happen all + + + align:start position:0% +what but in voting that can happen all +the + + align:start position:0% +the + + + align:start position:0% +the +time and it also says for + + align:start position:0% +time and it also says for + + + align:start position:0% +time and it also says for +instance if you'd like to you'd really + + align:start position:0% +instance if you'd like to you'd really + + + align:start position:0% +instance if you'd like to you'd really +like to be the chairman of this + + align:start position:0% +like to be the chairman of this + + + align:start position:0% +like to be the chairman of this +committee because if you're the chairman + + align:start position:0% +committee because if you're the chairman + + + align:start position:0% +committee because if you're the chairman +of this committee what what what whoever + + align:start position:0% +of this committee what what what whoever + + + align:start position:0% +of this committee what what what whoever +you are you can set the agenda to get + + align:start position:0% +you are you can set the agenda to get + + + align:start position:0% +you are you can set the agenda to get +the outcome you + + align:start position:0% +the outcome you + + + align:start position:0% +the outcome you +want + + align:start position:0% +want + + + align:start position:0% +want +suppose suppose you're number one you + + align:start position:0% +suppose suppose you're number one you + + + align:start position:0% +suppose suppose you're number one you +want + + align:start position:0% +want + + + align:start position:0% +want +a so what do you do you first have a + + align:start position:0% +a so what do you do you first have a + + + align:start position:0% +a so what do you do you first have a +vote between B and C B wins then you say + + align:start position:0% +vote between B and C B wins then you say + + + align:start position:0% +vote between B and C B wins then you say +okay let's try A and B A + + align:start position:0% +okay let's try A and B A + + + align:start position:0% +okay let's try A and B A +wins of course if you're number + + align:start position:0% +wins of course if you're number + + + align:start position:0% +wins of course if you're number +two then what you'd like to do is start + + align:start position:0% +two then what you'd like to do is start + + + align:start position:0% +two then what you'd like to do is start +with the ab vote a wins and then do the + + align:start position:0% +with the ab vote a wins and then do the + + + align:start position:0% +with the ab vote a wins and then do the +AC vote C + + align:start position:0% + + + + align:start position:0% + +wins the the kind of consistency + + align:start position:0% +wins the the kind of consistency + + + align:start position:0% +wins the the kind of consistency +that we expect when we talk about + + align:start position:0% +that we expect when we talk about + + + align:start position:0% +that we expect when we talk about +individual + + align:start position:0% +individual + + + align:start position:0% +individual +behavior is not a necessary feature in + + align:start position:0% +behavior is not a necessary feature in + + + align:start position:0% +behavior is not a necessary feature in +of political behavior of collective + + align:start position:0% +of political behavior of collective + + + align:start position:0% +of political behavior of collective +Behavior with a dictator okay + + align:start position:0% +Behavior with a dictator okay + + + align:start position:0% +Behavior with a dictator okay +sure with a voting system a parli you + + align:start position:0% +sure with a voting system a parli you + + + align:start position:0% +sure with a voting system a parli you +name your + + align:start position:0% +name your + + + align:start position:0% +name your +system it is capable of that kind of + + align:start position:0% +system it is capable of that kind of + + + align:start position:0% +system it is capable of that kind of +inconsistency even if it's not even if + + align:start position:0% +inconsistency even if it's not even if + + + align:start position:0% +inconsistency even if it's not even if +it's not voting so let me do just a have + + align:start position:0% +it's not voting so let me do just a have + + + align:start position:0% +it's not voting so let me do just a have +a couple more remarks + + align:start position:0% +a couple more remarks + + + align:start position:0% +a couple more remarks +before we get to the + + align:start position:0% +before we get to the + + + align:start position:0% +before we get to the +case in the market + + align:start position:0% +case in the market + + + align:start position:0% +case in the market +system the main process is competition + + align:start position:0% +system the main process is competition + + + align:start position:0% +system the main process is competition +there may be other things going on + + align:start position:0% +there may be other things going on + + + align:start position:0% +there may be other things going on +depending on the system is competition + + align:start position:0% +depending on the system is competition + + + align:start position:0% +depending on the system is competition +perfect is it not perfect is their + + align:start position:0% +perfect is it not perfect is their + + + align:start position:0% +perfect is it not perfect is their +Monopoly but but the central feature of + + align:start position:0% +Monopoly but but the central feature of + + + align:start position:0% +Monopoly but but the central feature of +a market system is competition + + align:start position:0% +a market system is competition + + + align:start position:0% +a market system is competition +competition happens in + + align:start position:0% + + + + align:start position:0% + +politics but it's not the only process + + align:start position:0% +politics but it's not the only process + + + align:start position:0% +politics but it's not the only process +think about think about about what we're + + align:start position:0% +think about think about about what we're + + + align:start position:0% +think about think about about what we're +going through now in in the Republican + + align:start position:0% +going through now in in the Republican + + + align:start position:0% +going through now in in the Republican +primary uh process there's a ton spent + + align:start position:0% +primary uh process there's a ton spent + + + align:start position:0% +primary uh process there's a ton spent +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +influence that happens in politics it + + align:start position:0% +influence that happens in politics it + + + align:start position:0% +influence that happens in politics it +happens through TV ads it also happens + + align:start position:0% +happens through TV ads it also happens + + + align:start position:0% +happens through TV ads it also happens +in parliaments and legislates when + + align:start position:0% +in parliaments and legislates when + + + align:start position:0% +in parliaments and legislates when +people try to persuade other people you + + align:start position:0% +people try to persuade other people you + + + align:start position:0% +people try to persuade other people you +try to persuade them to act in ways that + + align:start position:0% +try to persuade them to act in ways that + + + align:start position:0% +try to persuade them to act in ways that +benefit you and you try to persuade them + + align:start position:0% +benefit you and you try to persuade them + + + align:start position:0% +benefit you and you try to persuade them +that in fact it benefits them to do so + + align:start position:0% +that in fact it benefits them to do so + + + align:start position:0% +that in fact it benefits them to do so +influence + + align:start position:0% + + + + align:start position:0% + +cooperation + + align:start position:0% +cooperation + + + align:start position:0% +cooperation +again what are political parties all + + align:start position:0% +again what are political parties all + + + align:start position:0% +again what are political parties all +about they're a group of people working + + align:start position:0% +about they're a group of people working + + + align:start position:0% +about they're a group of people working +together for a common end typically or + + align:start position:0% +together for a common end typically or + + + align:start position:0% +together for a common end typically or +or a team or a set of folks in A + + align:start position:0% +or a team or a set of folks in A + + + align:start position:0% +or a team or a set of folks in A +legislature trying to get something done + + align:start position:0% +legislature trying to get something done + + + align:start position:0% +legislature trying to get something done +groups act + + align:start position:0% +groups act + + + align:start position:0% +groups act +politically sometimes for you listen to + + align:start position:0% +politically sometimes for you listen to + + + align:start position:0% +politically sometimes for you listen to +um you read descriptions of of Japanese + + align:start position:0% +um you read descriptions of of Japanese + + + align:start position:0% +um you read descriptions of of Japanese +politics and it's all about this faction + + align:start position:0% +politics and it's all about this faction + + + align:start position:0% +politics and it's all about this faction +and that faction it's all about + + align:start position:0% +and that faction it's all about + + + align:start position:0% +and that faction it's all about +cooperating groups in the same party but + + align:start position:0% +cooperating groups in the same party but + + + align:start position:0% +cooperating groups in the same party but +pursuing different + + align:start position:0% +pursuing different + + + align:start position:0% +pursuing different +ends and + + align:start position:0% +ends and + + + align:start position:0% +ends and +loyalty changing your position a lot in + + align:start position:0% +loyalty changing your position a lot in + + + align:start position:0% +loyalty changing your position a lot in +politics cost you friends cost you + + align:start position:0% +politics cost you friends cost you + + + align:start position:0% +politics cost you friends cost you +influence so a lot of what happens is + + align:start position:0% +influence so a lot of what happens is + + + align:start position:0% +influence so a lot of what happens is +you know Democrats hold their noses and + + align:start position:0% +you know Democrats hold their noses and + + + align:start position:0% +you know Democrats hold their noses and +vote for a Democrat they don't really + + align:start position:0% +vote for a Democrat they don't really + + + align:start position:0% +vote for a Democrat they don't really +like because she's a Democrat + + align:start position:0% +like because she's a Democrat + + + align:start position:0% +like because she's a Democrat +Republicans do the same thing we'll see + + align:start position:0% +Republicans do the same thing we'll see + + + align:start position:0% +Republicans do the same thing we'll see +that in the fall I'm I'm loyal this is + + align:start position:0% +that in the fall I'm I'm loyal this is + + + align:start position:0% +that in the fall I'm I'm loyal this is +what I believe it's not perfect I'm + + align:start position:0% +what I believe it's not perfect I'm + + + align:start position:0% +what I believe it's not perfect I'm +going there there's nothing like that in + + align:start position:0% +going there there's nothing like that in + + + align:start position:0% +going there there's nothing like that in +the + + align:start position:0% +the + + + align:start position:0% +the +marketplace I you may be loyal to + + align:start position:0% +marketplace I you may be loyal to + + + align:start position:0% +marketplace I you may be loyal to +Chevrolet even though it produces a + + align:start position:0% +Chevrolet even though it produces a + + + align:start position:0% +Chevrolet even though it produces a +lousy car but this is not a common event + + align:start position:0% +lousy car but this is not a common event + + + align:start position:0% +lousy car but this is not a common event +loyalty in politics is more important + + align:start position:0% +loyalty in politics is more important + + + align:start position:0% +loyalty in politics is more important +cooperation is more important and + + align:start position:0% +cooperation is more important and + + + align:start position:0% +cooperation is more important and +influence yeah there's influence in the + + align:start position:0% +influence yeah there's influence in the + + + align:start position:0% +influence yeah there's influence in the +market of course people advertise but + + align:start position:0% +market of course people advertise but + + + align:start position:0% +market of course people advertise but +influence is sort of central to politics + + align:start position:0% +influence is sort of central to politics + + + align:start position:0% +influence is sort of central to politics +it's there's no influ there's not much + + align:start position:0% +it's there's no influ there's not much + + + align:start position:0% +it's there's no influ there's not much +influence in the wheat Market + + align:start position:0% +influence in the wheat Market + + + align:start position:0% +influence in the wheat Market +but there's a lot of influence in the + + align:start position:0% +but there's a lot of influence in the + + + align:start position:0% +but there's a lot of influence in the +Republican primary + + align:start position:0% +Republican primary + + + align:start position:0% +Republican primary +Market all right so when you think about + + align:start position:0% +Market all right so when you think about + + + align:start position:0% +Market all right so when you think about +there's competition people try to win + + align:start position:0% +there's competition people try to win + + + align:start position:0% +there's competition people try to win +people want to advance and so + + align:start position:0% +people want to advance and so + + + align:start position:0% +people want to advance and so +on but it's + + align:start position:0% +on but it's + + + align:start position:0% +on but it's +different + + align:start position:0% +different + + + align:start position:0% +different +finally when you think about + + align:start position:0% +finally when you think about + + + align:start position:0% +finally when you think about +politics you think about the + + align:start position:0% +politics you think about the + + + align:start position:0% +politics you think about the +market the goals you think about are + + align:start position:0% +market the goals you think about are + + + align:start position:0% +market the goals you think about are +utility or wealth and I just said wealth + + align:start position:0% +utility or wealth and I just said wealth + + + align:start position:0% +utility or wealth and I just said wealth +to save space but you you think of folks + + align:start position:0% +to save space but you you think of folks + + + align:start position:0% +to save space but you you think of folks +as self-interested in a in a + + align:start position:0% +as self-interested in a in a + + + align:start position:0% +as self-interested in a in a +particularly narrow way in politics of + + align:start position:0% +particularly narrow way in politics of + + + align:start position:0% +particularly narrow way in politics of +course people pursue + + align:start position:0% +course people pursue + + + align:start position:0% +course people pursue +wealth of course but they also pursue + + align:start position:0% +wealth of course but they also pursue + + + align:start position:0% +wealth of course but they also pursue +power and power is different power is + + align:start position:0% + + + + align:start position:0% + +sometimes sometimes is conferred by an + + align:start position:0% +sometimes sometimes is conferred by an + + + align:start position:0% +sometimes sometimes is conferred by an +office you're a president the system has + + align:start position:0% +office you're a president the system has + + + align:start position:0% +office you're a president the system has +legitimacy therefore you have power + + align:start position:0% +legitimacy therefore you have power + + + align:start position:0% +legitimacy therefore you have power +power means you can get others to act + + align:start position:0% +power means you can get others to act + + + align:start position:0% +power means you can get others to act +against their self-interest you can get + + align:start position:0% +against their self-interest you can get + + + align:start position:0% +against their self-interest you can get +them to pay taxes + + align:start position:0% +them to pay taxes + + + align:start position:0% +them to pay taxes +for instance uh you can get them to uh + + align:start position:0% +for instance uh you can get them to uh + + + align:start position:0% +for instance uh you can get them to uh +uh put their lives on the line in a + + align:start position:0% +uh put their lives on the line in a + + + align:start position:0% +uh put their lives on the line in a +war you have the ability to do a variety + + align:start position:0% +war you have the ability to do a variety + + + align:start position:0% +war you have the ability to do a variety +of things against to get people to do a + + align:start position:0% +of things against to get people to do a + + + align:start position:0% +of things against to get people to do a +variety of things against their + + align:start position:0% +variety of things against their + + + align:start position:0% +variety of things against their +self-interest either for + + align:start position:0% +self-interest either for + + + align:start position:0% +self-interest either for +you or for your view of the public + + align:start position:0% +you or for your view of the public + + + align:start position:0% +you or for your view of the public +interest so the important coin of the + + align:start position:0% +interest so the important coin of the + + + align:start position:0% +interest so the important coin of the +realm in politics and again there's + + align:start position:0% +realm in politics and again there's + + + align:start position:0% +realm in politics and again there's +nothing quite like it in the market + + align:start position:0% +nothing quite like it in the market + + + align:start position:0% +nothing quite like it in the market +system is power + + align:start position:0% +system is power + + + align:start position:0% +system is power +is power you know power comes from + + align:start position:0% +is power you know power comes from + + + align:start position:0% +is power you know power comes from +influence cooperation loyalty sometimes + + align:start position:0% +influence cooperation loyalty sometimes + + + align:start position:0% +influence cooperation loyalty sometimes +Force also comes from the legitimacy of + + align:start position:0% +Force also comes from the legitimacy of + + + align:start position:0% +Force also comes from the legitimacy of +the government you're in you hear + + align:start position:0% +the government you're in you hear + + + align:start position:0% +the government you're in you hear +occasionally about people in + + align:start position:0% +occasionally about people in + + + align:start position:0% +occasionally about people in +legislatures being + + align:start position:0% +legislatures being + + + align:start position:0% +legislatures being +powerful not necessarily because they + + align:start position:0% +powerful not necessarily because they + + + align:start position:0% +powerful not necessarily because they +have some office that makes them + + align:start position:0% +have some office that makes them + + + align:start position:0% +have some office that makes them +powerful but because they've managed to + + align:start position:0% +powerful but because they've managed to + + + align:start position:0% +powerful but because they've managed to +attract a set of followers because they + + align:start position:0% +attract a set of followers because they + + + align:start position:0% +attract a set of followers because they +have some ability to confirm favors + + align:start position:0% +have some ability to confirm favors + + + align:start position:0% +have some ability to confirm favors +because because + + align:start position:0% +because because + + + align:start position:0% +because because +because when I was in + + align:start position:0% +because when I was in + + + align:start position:0% +because when I was in +Washington John Dingle the congressman + + align:start position:0% +Washington John Dingle the congressman + + + align:start position:0% +Washington John Dingle the congressman +from Michigan was legendarily powerful + + align:start position:0% +from Michigan was legendarily powerful + + + align:start position:0% +from Michigan was legendarily powerful +he was chairman of a committee he was a + + align:start position:0% +he was chairman of a committee he was a + + + align:start position:0% +he was chairman of a committee he was a +congressman he was chairman of a + + align:start position:0% +congressman he was chairman of a + + + align:start position:0% +congressman he was chairman of a +committee the committee had a lot of + + align:start position:0% +committee the committee had a lot of + + + align:start position:0% +committee the committee had a lot of +jurisdiction Dingle also had a very + + align:start position:0% +jurisdiction Dingle also had a very + + + align:start position:0% +jurisdiction Dingle also had a very +smart staff Dingle also knew everybody + + align:start position:0% +smart staff Dingle also knew everybody + + + align:start position:0% +smart staff Dingle also knew everybody +in + + align:start position:0% +in + + + align:start position:0% +in +town Dingle would send letters to people + + align:start position:0% +town Dingle would send letters to people + + + align:start position:0% +town Dingle would send letters to people +in the executive branch called Dingle + + align:start position:0% +in the executive branch called Dingle + + + align:start position:0% +in the executive branch called Dingle +grams that would consist of four pages + + align:start position:0% +grams that would consist of four pages + + + align:start position:0% +grams that would consist of four pages +of detailed questions written by his + + align:start position:0% +of detailed questions written by his + + + align:start position:0% +of detailed questions written by his +staff that needed to be answered within + + align:start position:0% +staff that needed to be answered within + + + align:start position:0% +staff that needed to be answered within +a week you get a letter from that like + + align:start position:0% +a week you get a letter from that like + + + align:start position:0% +a week you get a letter from that like +that from anybody else you'd say yeah + + align:start position:0% +that from anybody else you'd say yeah + + + align:start position:0% +that from anybody else you'd say yeah +right you got a letter like that from + + align:start position:0% +right you got a letter like that from + + + align:start position:0% +right you got a letter like that from +Dingle you got you answered it you put + + align:start position:0% +Dingle you got you answered it you put + + + align:start position:0% +Dingle you got you answered it you put +people on it and you answered it because + + align:start position:0% +people on it and you answered it because + + + align:start position:0% +people on it and you answered it because +Dingle had power Dingle had power hard + + align:start position:0% +Dingle had power Dingle had power hard + + + align:start position:0% +Dingle had power Dingle had power hard +to exactly describe why Dingle had power + + align:start position:0% +to exactly describe why Dingle had power + + + align:start position:0% +to exactly describe why Dingle had power +but Dingle had power he could move votes + + align:start position:0% +but Dingle had power he could move votes + + + align:start position:0% +but Dingle had power he could move votes +he could build coalitions + + align:start position:0% +he could build coalitions + + + align:start position:0% +he could build coalitions +he could operate he had power + + align:start position:0% + + + + align:start position:0% + +okay we we now have our introduction to + + align:start position:0% +okay we we now have our introduction to + + + align:start position:0% +okay we we now have our introduction to +political science and political + + align:start position:0% +political science and political + + + align:start position:0% +political science and political +philosophy let's do a little bit of + + align:start position:0% +philosophy let's do a little bit of + + + align:start position:0% +philosophy let's do a little bit of +Carter + + align:start position:0% +Carter + + + align:start position:0% +Carter +Cole uh some of the background which we + + align:start position:0% +Cole uh some of the background which we + + + align:start position:0% +Cole uh some of the background which we +didn't quite give you but let me just do + + align:start position:0% +didn't quite give you but let me just do + + + align:start position:0% +didn't quite give you but let me just do +a little bit of that to get to it + + align:start position:0% +a little bit of that to get to it + + + align:start position:0% +a little bit of that to get to it +um this is the new deal period and + + align:start position:0% +um this is the new deal period and + + + align:start position:0% +um this is the new deal period and +Roosevelt is + + align:start position:0% +Roosevelt is + + + align:start position:0% +Roosevelt is +doing has gotten a democratic Congress + + align:start position:0% +doing has gotten a democratic Congress + + + align:start position:0% +doing has gotten a democratic Congress +to pass a variety of laws that extend + + align:start position:0% +to pass a variety of laws that extend + + + align:start position:0% +to pass a variety of laws that extend +the power of government in an attempt to + + align:start position:0% +the power of government in an attempt to + + + align:start position:0% +the power of government in an attempt to +use the power of government in a variety + + align:start position:0% +use the power of government in a variety + + + align:start position:0% +use the power of government in a variety +of ways to deal with the + + align:start position:0% +of ways to deal with the + + + align:start position:0% +of ways to deal with the +depression in early beginning in early + + align:start position:0% +depression in early beginning in early + + + align:start position:0% +depression in early beginning in early +1935 the Supreme Court was striking + + align:start position:0% +1935 the Supreme Court was striking + + + align:start position:0% +1935 the Supreme Court was striking +these down regularly as unconstitutional + + align:start position:0% +these down regularly as unconstitutional + + + align:start position:0% +these down regularly as unconstitutional +there's a fairly long list of things + + align:start position:0% +there's a fairly long list of things + + + align:start position:0% +there's a fairly long list of things +struck + + align:start position:0% +struck + + + align:start position:0% +struck +down um they' struck down an earlier an + + align:start position:0% +down um they' struck down an earlier an + + + align:start position:0% +down um they' struck down an earlier an +earlier um + + align:start position:0% +earlier um + + + align:start position:0% +earlier um +piece of legislation in the um oh I'm + + align:start position:0% +piece of legislation in the um oh I'm + + + align:start position:0% +piece of legislation in the um oh I'm +forgetting it now the um it's one of the + + align:start position:0% +forgetting it now the um it's one of the + + + align:start position:0% +forgetting it now the um it's one of the +uh sheor the sheor decision sheor + + align:start position:0% +uh sheor the sheor decision sheor + + + align:start position:0% +uh sheor the sheor decision sheor +poultry uh struck + + align:start position:0% +poultry uh struck + + + align:start position:0% +poultry uh struck +down basically uh an industry regulatory + + align:start position:0% +down basically uh an industry regulatory + + + align:start position:0% +down basically uh an industry regulatory +statute that like the coal statute the + + align:start position:0% +statute that like the coal statute the + + + align:start position:0% +statute that like the coal statute the +binus coal conservation Act was an + + align:start position:0% +binus coal conservation Act was an + + + align:start position:0% +binus coal conservation Act was an +attempt to raise prices and raise wages + + align:start position:0% +attempt to raise prices and raise wages + + + align:start position:0% +attempt to raise prices and raise wages +the theory was uh we have ruinous + + align:start position:0% +the theory was uh we have ruinous + + + align:start position:0% +the theory was uh we have ruinous +competition so we're going to deal with + + align:start position:0% +competition so we're going to deal with + + + align:start position:0% +competition so we're going to deal with +the depression by getting prices up + + align:start position:0% +the depression by getting prices up + + + align:start position:0% +the depression by getting prices up +which will get wages up which will get + + align:start position:0% +which will get wages up which will get + + + align:start position:0% +which will get wages up which will get +people spending which will get us out of + + align:start position:0% +people spending which will get us out of + + + align:start position:0% +people spending which will get us out of +this mess that's not the best economics + + align:start position:0% +this mess that's not the best economics + + + align:start position:0% +this mess that's not the best economics +but you know that was that was the that + + align:start position:0% +but you know that was that was the that + + + align:start position:0% +but you know that was that was the that +was the deal he was trying to do and + + align:start position:0% +was the deal he was trying to do and + + + align:start position:0% +was the deal he was trying to do and +this act which just focused on the coal + + align:start position:0% +this act which just focused on the coal + + + align:start position:0% +this act which just focused on the coal +industry uh attempted to raise prices + + align:start position:0% +industry uh attempted to raise prices + + + align:start position:0% +industry uh attempted to raise prices +and wages and was drafted to get around + + align:start position:0% +and wages and was drafted to get around + + + align:start position:0% +and wages and was drafted to get around +sheor so they' thrown out an earlier law + + align:start position:0% +sheor so they' thrown out an earlier law + + + align:start position:0% +sheor so they' thrown out an earlier law +in the sheor decision so somebody said + + align:start position:0% +in the sheor decision so somebody said + + + align:start position:0% +in the sheor decision so somebody said +all right let's write this so that it + + align:start position:0% +all right let's write this so that it + + + align:start position:0% +all right let's write this so that it +under the standards of Shear it's + + align:start position:0% +under the standards of Shear it's + + + align:start position:0% +under the standards of Shear it's +legal uh it + + align:start position:0% +legal uh it + + + align:start position:0% +legal uh it +involved getting people to getting a + + align:start position:0% +involved getting people to getting a + + + align:start position:0% +involved getting people to getting a +coal manufacturers to obey the law by + + align:start position:0% +coal manufacturers to obey the law by + + + align:start position:0% +coal manufacturers to obey the law by +imposing a tax on them most of which was + + align:start position:0% +imposing a tax on them most of which was + + + align:start position:0% +imposing a tax on them most of which was +refunded if they pay if they followed + + align:start position:0% +refunded if they pay if they followed + + + align:start position:0% +refunded if they pay if they followed +the practices laid out in the + + align:start position:0% +the practices laid out in the + + + align:start position:0% +the practices laid out in the +ACT it's Carter versus Carter Cole I + + align:start position:0% +ACT it's Carter versus Carter Cole I + + + align:start position:0% +ACT it's Carter versus Carter Cole I +love this this gu board of directors + + align:start position:0% +love this this gu board of directors + + + align:start position:0% +love this this gu board of directors +votes to pay the tax the CEO sues them + + align:start position:0% +votes to pay the tax the CEO sues them + + + align:start position:0% +votes to pay the tax the CEO sues them +this is an odd + + align:start position:0% +this is an odd + + + align:start position:0% +this is an odd +action the law says you have to pay the + + align:start position:0% +action the law says you have to pay the + + + align:start position:0% +action the law says you have to pay the +tax the bo the board says yeah we'll pay + + align:start position:0% +tax the bo the board says yeah we'll pay + + + align:start position:0% +tax the bo the board says yeah we'll pay +the tax the CEO says the hell we will + + align:start position:0% +the tax the CEO says the hell we will + + + align:start position:0% +the tax the CEO says the hell we will +and sues the + + align:start position:0% +and sues the + + + align:start position:0% +and sues the +board oky dooke + + align:start position:0% +board oky dooke + + + align:start position:0% +board oky dooke +um and as as you have recognized and as + + align:start position:0% +um and as as you have recognized and as + + + align:start position:0% +um and as as you have recognized and as +youve discussed last + + align:start position:0% +youve discussed last + + + align:start position:0% +youve discussed last +week this + + align:start position:0% +week this + + + align:start position:0% +week this +case on its + + align:start position:0% +case on its + + + align:start position:0% +case on its +face is a technical exercise in legal + + align:start position:0% +face is a technical exercise in legal + + + align:start position:0% +face is a technical exercise in legal +analysis this is how Court decisions are + + align:start position:0% +analysis this is how Court decisions are + + + align:start position:0% +analysis this is how Court decisions are +always + + align:start position:0% +always + + + align:start position:0% +always +written um that that it's fascinating + + align:start position:0% +written um that that it's fascinating + + + align:start position:0% +written um that that it's fascinating +judges never say well there's this + + align:start position:0% +judges never say well there's this + + + align:start position:0% +judges never say well there's this +consideration and there's this + + align:start position:0% +consideration and there's this + + + align:start position:0% +consideration and there's this +consideration and in the balance I think + + align:start position:0% +consideration and in the balance I think + + + align:start position:0% +consideration and in the balance I think +I should go this way they all almost + + align:start position:0% +I should go this way they all almost + + + align:start position:0% +I should go this way they all almost +always say there's this consideration + + align:start position:0% +always say there's this consideration + + + align:start position:0% +always say there's this consideration +and people have made this argument but + + align:start position:0% +and people have made this argument but + + + align:start position:0% +and people have made this argument but +it's junk so we should go this way uh + + align:start position:0% +it's junk so we should go this way uh + + + align:start position:0% +it's junk so we should go this way uh +and you've seen and those tend to + + align:start position:0% +and you've seen and those tend to + + + align:start position:0% +and you've seen and those tend to +be reflect differences in + + align:start position:0% +be reflect differences in + + + align:start position:0% +be reflect differences in +ideology right it's clear that + + align:start position:0% +ideology right it's clear that + + + align:start position:0% +ideology right it's clear that +Southerland and cardoo talk briefly + + align:start position:0% +Southerland and cardoo talk briefly + + + align:start position:0% +Southerland and cardoo talk briefly +about Hughes but southernland and and + + align:start position:0% +about Hughes but southernland and and + + + align:start position:0% +about Hughes but southernland and and +cardoo have a different view of how the + + align:start position:0% +cardoo have a different view of how the + + + align:start position:0% +cardoo have a different view of how the +United States should be + + align:start position:0% +United States should be + + + align:start position:0% +United States should be +organized and how the government should + + align:start position:0% +organized and how the government should + + + align:start position:0% +organized and how the government should +be run so let's do + + align:start position:0% +be run so let's do + + + align:start position:0% +be run so let's do +this what are the two Provisions at at + + align:start position:0% +this what are the two Provisions at at + + + align:start position:0% +this what are the two Provisions at at +issue + + align:start position:0% +issue + + + align:start position:0% +issue +here + + align:start position:0% +here + + + align:start position:0% +here +anybody Brendan you've got a great sign + + align:start position:0% +anybody Brendan you've got a great sign + + + align:start position:0% +anybody Brendan you've got a great sign +other people will have a great sign but + + align:start position:0% +other people will have a great sign but + + + align:start position:0% +other people will have a great sign but +I can read yours what are the two + + align:start position:0% +I can read yours what are the two + + + align:start position:0% +I can read yours what are the two +Provisions in this the binous col act + + align:start position:0% +Provisions in this the binous col act + + + align:start position:0% +Provisions in this the binous col act +that the court is dealing with well + + align:start position:0% +that the court is dealing with well + + + align:start position:0% +that the court is dealing with well +first like the Commerce Clause like + + align:start position:0% +first like the Commerce Clause like + + + align:start position:0% +first like the Commerce Clause like +whether not that's the that's the uh + + align:start position:0% +whether not that's the that's the uh + + + align:start position:0% +whether not that's the that's the uh +that's the issue in terms of + + align:start position:0% +that's the issue in terms of + + + align:start position:0% +that's the issue in terms of +constitutionality but what are two + + align:start position:0% +constitutionality but what are two + + + align:start position:0% +constitutionality but what are two +things that the ACT did that are + + align:start position:0% +things that the ACT did that are + + + align:start position:0% +things that the ACT did that are +challenged + + align:start position:0% + + + + align:start position:0% + +here for price like this is what the + + align:start position:0% +here for price like this is what the + + + align:start position:0% +here for price like this is what the +price has it set it set the a price for + + align:start position:0% +price has it set it set the a price for + + + align:start position:0% +price has it set it set the a price for +coal okay anything else Scott what else + + align:start position:0% +coal okay anything else Scott what else + + + align:start position:0% +coal okay anything else Scott what else +did it do tax the tax yeah yeah but that + + align:start position:0% +did it do tax the tax yeah yeah but that + + + align:start position:0% +did it do tax the tax yeah yeah but that +was an enforcement mechanism + + align:start position:0% +was an enforcement mechanism + + + align:start position:0% +was an enforcement mechanism +what did it do in terms of Sam wage for + + align:start position:0% +what did it do in terms of Sam wage for + + + align:start position:0% +what did it do in terms of Sam wage for +the workers wage for the workers so you + + align:start position:0% +the workers wage for the workers so you + + + align:start position:0% +the workers wage for the workers so you +got a price control and a wage control + + align:start position:0% +got a price control and a wage control + + + align:start position:0% +got a price control and a wage control +provision let's talk about southernland + + align:start position:0% +provision let's talk about southernland + + + align:start position:0% +provision let's talk about southernland +those of you over here must know what + + align:start position:0% +those of you over here must know what + + + align:start position:0% +those of you over here must know what +southernland why did southernland say + + align:start position:0% +southernland why did southernland say + + + align:start position:0% +southernland why did southernland say +both of them were + + align:start position:0% +both of them were + + + align:start position:0% +both of them were +unconstitutional yeah says that the of + + align:start position:0% +unconstitutional yeah says that the of + + + align:start position:0% +unconstitutional yeah says that the of +the co + + align:start position:0% +the co + + + align:start position:0% +the co +isly production and doesn't deal with + + align:start position:0% + + + + align:start position:0% + +so the production is not Commerce mining + + align:start position:0% +so the production is not Commerce mining + + + align:start position:0% +so the production is not Commerce mining +the coal making the machine is not + + align:start position:0% +the coal making the machine is not + + + align:start position:0% +the coal making the machine is not +Commerce and the federal government has + + align:start position:0% +Commerce and the federal government has + + + align:start position:0% +Commerce and the federal government has +the power to regulate commerce but it + + align:start position:0% +the power to regulate commerce but it + + + align:start position:0% +the power to regulate commerce but it +doesn't have the power to + + align:start position:0% +doesn't have the power to + + + align:start position:0% +doesn't have the power to +regulate uh + + align:start position:0% +regulate uh + + + align:start position:0% +regulate uh +production unless of course it's + + align:start position:0% +production unless of course it's + + + align:start position:0% +production unless of course it's +directly involved in Commerce and what + + align:start position:0% +directly involved in Commerce and what + + + align:start position:0% +directly involved in Commerce and what +did he say about + + align:start position:0% +did he say about + + + align:start position:0% +did he say about +that whatever the heck that means it's + + align:start position:0% +that whatever the heck that means it's + + + align:start position:0% +that whatever the heck that means it's +it's indirect it's not Direct + + align:start position:0% +it's indirect it's not Direct + + + align:start position:0% +it's indirect it's not Direct +okay what did he say about the other + + align:start position:0% +okay what did he say about the other + + + align:start position:0% +okay what did he say about the other +provision Rachel he said they dep + + align:start position:0% + + + + align:start position:0% + +on it's an interesting opinion right + + align:start position:0% +on it's an interesting opinion right + + + align:start position:0% +on it's an interesting opinion right +they wrote the law in the law they + + align:start position:0% +they wrote the law in the law they + + + align:start position:0% +they wrote the law in the law they +said invalidation of any part of this + + align:start position:0% +said invalidation of any part of this + + + align:start position:0% +said invalidation of any part of this +law will not affect the validity of the + + align:start position:0% +law will not affect the validity of the + + + align:start position:0% +law will not affect the validity of the +others and Southerland said yeah I know + + align:start position:0% +others and Southerland said yeah I know + + + align:start position:0% +others and Southerland said yeah I know +they said that but they passed them both + + align:start position:0% +they said that but they passed them both + + + align:start position:0% +they said that but they passed them both +so clearly they're linked so if one's + + align:start position:0% +so clearly they're linked so if one's + + + align:start position:0% +so clearly they're linked so if one's +bad others bad + + align:start position:0% +bad others bad + + + align:start position:0% +bad others bad +goodbye that was interesting reasoning + + align:start position:0% +goodbye that was interesting reasoning + + + align:start position:0% +goodbye that was interesting reasoning +right it's that was one where you say + + align:start position:0% +right it's that was one where you say + + + align:start position:0% +right it's that was one where you say +that's not + + align:start position:0% +that's not + + + align:start position:0% +that's not +technical that's ideology that's his + + align:start position:0% +technical that's ideology that's his + + + align:start position:0% +technical that's ideology that's his +statement about I don't like that either + + align:start position:0% +statement about I don't like that either + + + align:start position:0% +statement about I don't like that either +and since they're in the same bill you + + align:start position:0% +and since they're in the same bill you + + + align:start position:0% +and since they're in the same bill you +wonder what if they if they' just gone + + align:start position:0% +wonder what if they if they' just gone + + + align:start position:0% +wonder what if they if they' just gone +on and done the second bill + + align:start position:0% + + + + align:start position:0% + +so group a what's southernland saying + + align:start position:0% +so group a what's southernland saying + + + align:start position:0% +so group a what's southernland saying +about the proper role of government + + align:start position:0% + + + + align:start position:0% + +yeah yep so that's that's a great line + + align:start position:0% +yeah yep so that's that's a great line + + + align:start position:0% +yeah yep so that's that's a great line +isn't it the the slippery slope single + + align:start position:0% +isn't it the the slippery slope single + + + align:start position:0% +isn't it the the slippery slope single +step + + align:start position:0% +step + + + align:start position:0% +step +um that was one of his one of his better + + align:start position:0% +um that was one of his one of his better + + + align:start position:0% +um that was one of his one of his better +lines it is exactly every journey to a + + align:start position:0% +lines it is exactly every journey to a + + + align:start position:0% +lines it is exactly every journey to a +forbidden end begins with the first step + + align:start position:0% +forbidden end begins with the first step + + + align:start position:0% +forbidden end begins with the first step +The Forbidden end so southerland's view + + align:start position:0% +The Forbidden end so southerland's view + + + align:start position:0% +The Forbidden end so southerland's view +is we got to be very strict about what + + align:start position:0% +is we got to be very strict about what + + + align:start position:0% +is we got to be very strict about what +we let the federal government do because + + align:start position:0% +we let the federal government do because + + + align:start position:0% +we let the federal government do because +once it starts + + align:start position:0% +once it starts + + + align:start position:0% +once it starts +expanding we're we're toast uh but + + align:start position:0% +expanding we're we're toast uh but + + + align:start position:0% +expanding we're we're toast uh but +what's the Forbidden end that he worries + + align:start position:0% +what's the Forbidden end that he worries + + + align:start position:0% +what's the Forbidden end that he worries +about where does he not want to go + + align:start position:0% +about where does he not want to go + + + align:start position:0% +about where does he not want to go +anybody over here + + align:start position:0% +anybody over here + + + align:start position:0% +anybody over here +Jad you've made it black I can read it + + align:start position:0% +Jad you've made it black I can read it + + + align:start position:0% +Jad you've made it black I can read it +that's great we'll get you we'll get you + + align:start position:0% +that's great we'll get you we'll get you + + + align:start position:0% +that's great we'll get you we'll get you +better one soon so I think that + + align:start position:0% + + + + align:start position:0% + +okay what's your definition of + + align:start position:0% + + + + align:start position:0% + +tyranny okay suppose they they still had + + align:start position:0% +tyranny okay suppose they they still had + + + align:start position:0% +tyranny okay suppose they they still had +elections they still had elections but + + align:start position:0% +elections they still had elections but + + + align:start position:0% +elections they still had elections but +the government had a much broader role + + align:start position:0% +the government had a much broader role + + + align:start position:0% +the government had a much broader role +is that + + align:start position:0% +is that + + + align:start position:0% +is that +tyranny it depends it depends there's an + + align:start position:0% +tyranny it depends it depends there's an + + + align:start position:0% +tyranny it depends it depends there's an +interesting I I'm reading this + + align:start position:0% +interesting I I'm reading this + + + align:start position:0% +interesting I I'm reading this +monstrously thick biography of Hamilton + + align:start position:0% +monstrously thick biography of Hamilton + + + align:start position:0% +monstrously thick biography of Hamilton +and this was exactly the debate over the + + align:start position:0% +and this was exactly the debate over the + + + align:start position:0% +and this was exactly the debate over the +Constitution uh and it was the debate + + align:start position:0% +Constitution uh and it was the debate + + + align:start position:0% +Constitution uh and it was the debate +over Hamilton's extending executive + + align:start position:0% +over Hamilton's extending executive + + + align:start position:0% +over Hamilton's extending executive +powers that it's going to be a tyranny + + align:start position:0% +powers that it's going to be a tyranny + + + align:start position:0% +powers that it's going to be a tyranny +unless there's a + + align:start position:0% +unless there's a + + + align:start position:0% +unless there's a +check unless there's a check got a + + align:start position:0% +check unless there's a check got a + + + align:start position:0% +check unless there's a check got a +comment yes to to degree argue that when + + align:start position:0% +comment yes to to degree argue that when + + + align:start position:0% +comment yes to to degree argue that when +the government would begin to impose the + + align:start position:0% +the government would begin to impose the + + + align:start position:0% +the government would begin to impose the +tyranny of the majority on a + + align:start position:0% +tyranny of the majority on a + + + align:start position:0% +tyranny of the majority on a +um that would be when + + align:start position:0% +um that would be when + + + align:start position:0% +um that would be when +they and southernland wouldn't agree + + align:start position:0% +they and southernland wouldn't agree + + + align:start position:0% +they and southernland wouldn't agree +would he that the Bill of Rights is a + + align:start position:0% +would he that the Bill of Rights is a + + + align:start position:0% +would he that the Bill of Rights is a +sufficient check on that Southerland + + align:start position:0% +sufficient check on that Southerland + + + align:start position:0% +sufficient check on that Southerland +would + + align:start position:0% +would + + + align:start position:0% +would +say the Constitution says the federal + + align:start position:0% +say the Constitution says the federal + + + align:start position:0% +say the Constitution says the federal +government has limited powers once you + + align:start position:0% +government has limited powers once you + + + align:start position:0% +government has limited powers once you +go beyond them where where do you + + align:start position:0% +go beyond them where where do you + + + align:start position:0% +go beyond them where where do you +stop okay I mean the Bill of Rights + + align:start position:0% +stop okay I mean the Bill of Rights + + + align:start position:0% +stop okay I mean the Bill of Rights +stops uh stops you at some point but + + align:start position:0% +stops uh stops you at some point but + + + align:start position:0% +stops uh stops you at some point but +there's a lot of ground between yeah + + align:start position:0% +there's a lot of ground between yeah + + + align:start position:0% +there's a lot of ground between yeah +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +doesn't think the states should just + + align:start position:0% +doesn't think the states should just + + + align:start position:0% +doesn't think the states should just +become divisions thinks it's important + + align:start position:0% +become divisions thinks it's important + + + align:start position:0% +become divisions thinks it's important +that they have their own identity where + + align:start position:0% +that they have their own identity where + + + align:start position:0% +that they have their own identity where +they can determine what's happening so + + align:start position:0% +they can determine what's happening so + + + align:start position:0% +they can determine what's happening so +even if the federal federal government + + align:start position:0% +even if the federal federal government + + + align:start position:0% +even if the federal federal government +wasn't a tyranny wasn't um taking + + align:start position:0% +wasn't a tyranny wasn't um taking + + + align:start position:0% +wasn't a tyranny wasn't um taking +control of the people per se if they + + align:start position:0% +control of the people per se if they + + + align:start position:0% +control of the people per se if they +undermined the state's own laws that's + + align:start position:0% +undermined the state's own laws that's + + + align:start position:0% +undermined the state's own laws that's +what so + + align:start position:0% +what so + + + align:start position:0% +what so +he's he's what we now call a federalist + + align:start position:0% +he's he's what we now call a federalist + + + align:start position:0% +he's he's what we now call a federalist +what back in the day they called a + + align:start position:0% +what back in the day they called a + + + align:start position:0% +what back in the day they called a +republican he believes the Constitution + + align:start position:0% +republican he believes the Constitution + + + align:start position:0% +republican he believes the Constitution +says the states should be strong the + + align:start position:0% +says the states should be strong the + + + align:start position:0% +says the states should be strong the +stat should have a lot of power + + align:start position:0% +stat should have a lot of power + + + align:start position:0% +stat should have a lot of power +maybe States could regulate wages if + + align:start position:0% +maybe States could regulate wages if + + + align:start position:0% +maybe States could regulate wages if +they wanted to but the federal + + align:start position:0% +they wanted to but the federal + + + align:start position:0% +they wanted to but the federal +government can't okay so this is a + + align:start position:0% +government can't okay so this is a + + + align:start position:0% +government can't okay so this is a +limited government point of + + align:start position:0% +limited government point of + + + align:start position:0% +limited government point of +view was Southerland + + align:start position:0% +view was Southerland + + + align:start position:0% +view was Southerland +right T let's hear a stirring + + align:start position:0% +right T let's hear a stirring + + + align:start position:0% +right T let's hear a stirring +presentation from Team a somebody + + align:start position:0% +presentation from Team a somebody + + + align:start position:0% +presentation from Team a somebody +somebody revved up + + align:start position:0% +somebody revved up + + + align:start position:0% +somebody revved up +here oh come on Matthew you ready to go + + align:start position:0% +here oh come on Matthew you ready to go + + + align:start position:0% +here oh come on Matthew you ready to go +get yourself psyched up over the weekend + + align:start position:0% +get yourself psyched up over the weekend + + + align:start position:0% +get yourself psyched up over the weekend +okay based on the results of the case + + align:start position:0% +okay based on the results of the case + + + align:start position:0% +okay based on the results of the case +yes he was right why um why is that the + + align:start position:0% +yes he was right why um why is that the + + + align:start position:0% +yes he was right why um why is that the +right view of the role of + + align:start position:0% +right view of the role of + + + align:start position:0% +right view of the role of +government you could quote Howard RoR + + align:start position:0% +government you could quote Howard RoR + + + align:start position:0% +government you could quote Howard RoR +right Howard RoR would have like this + + align:start position:0% +right Howard RoR would have like this + + + align:start position:0% +right Howard RoR would have like this +regulate wages anyway yeah I mean they + + align:start position:0% +regulate wages anyway yeah I mean they + + + align:start position:0% +regulate wages anyway yeah I mean they +were trying to regulate something that + + align:start position:0% +were trying to regulate something that + + + align:start position:0% +were trying to regulate something that +was not defined in the Constitution for + + align:start position:0% +was not defined in the Constitution for + + + align:start position:0% +was not defined in the Constitution for +that government to do which was the + + align:start position:0% +that government to do which was the + + + align:start position:0% +that government to do which was the +production of + + align:start position:0% + + + + align:start position:0% + +the so put aside the legal + + align:start position:0% +the so put aside the legal + + + align:start position:0% +the so put aside the legal +argument how about the philosophical or + + align:start position:0% +argument how about the philosophical or + + + align:start position:0% +argument how about the philosophical or +ideological argument + + align:start position:0% +ideological argument + + + align:start position:0% +ideological argument +why would you if you would agree with + + align:start position:0% +why would you if you would agree with + + + align:start position:0% +why would you if you would agree with +him absent the legal + + align:start position:0% +him absent the legal + + + align:start position:0% +him absent the legal +background I + + align:start position:0% +background I + + + align:start position:0% +background I +mean what's your view about how team a + + align:start position:0% +mean what's your view about how team a + + + align:start position:0% +mean what's your view about how team a +about how Society should be organized + + align:start position:0% +about how Society should be organized + + + align:start position:0% +about how Society should be organized +and about how it should function because + + align:start position:0% +and about how it should function because + + + align:start position:0% +and about how it should function because +sou souland has a view is that a view + + align:start position:0% +sou souland has a view is that a view + + + align:start position:0% +sou souland has a view is that a view +you share if so why is that a good + + align:start position:0% + + + + align:start position:0% + +view I don't mean to push you there we + + align:start position:0% +view I don't mean to push you there we + + + align:start position:0% +view I don't mean to push you there we +go interesting analogy + + align:start position:0% +go interesting analogy + + + align:start position:0% +go interesting analogy +would be that we're we're being recorded + + align:start position:0% +would be that we're we're being recorded + + + align:start position:0% +would be that we're we're being recorded +here recorded here and this say Crossing + + align:start position:0% +here recorded here and this say Crossing + + + align:start position:0% +here recorded here and this say Crossing +National lines and I can say something + + align:start position:0% +National lines and I can say something + + + align:start position:0% +National lines and I can say something +which might be censored in other + + align:start position:0% +which might be censored in other + + + align:start position:0% +which might be censored in other +countries what this law I know it's an + + align:start position:0% +countries what this law I know it's an + + + align:start position:0% +countries what this law I know it's an +analogy and you should take it that way + + align:start position:0% +analogy and you should take it that way + + + align:start position:0% +analogy and you should take it that way +but what this law would want to do is + + align:start position:0% +but what this law would want to do is + + + align:start position:0% +but what this law would want to do is +censor me as opposed to censor the + + align:start position:0% + + + + align:start position:0% + +broadcast because they're trying to they + + align:start position:0% +broadcast because they're trying to they + + + align:start position:0% +broadcast because they're trying to they +are trying to change production not + + align:start position:0% +are trying to change production not + + + align:start position:0% +are trying to change production not +Commerce so what they're saying is let + + align:start position:0% +Commerce so what they're saying is let + + + align:start position:0% +Commerce so what they're saying is let +us produce what we have and and then + + align:start position:0% +us produce what we have and and then + + + align:start position:0% +us produce what we have and and then +once it crosses state lines if you want + + align:start position:0% +once it crosses state lines if you want + + + align:start position:0% +once it crosses state lines if you want +to regulate it at that point that's + + align:start position:0% +to regulate it at that point that's + + + align:start position:0% +to regulate it at that point that's +Commerce but don't change + + align:start position:0% +Commerce but don't change + + + align:start position:0% +Commerce but don't change +production could would would you agree + + align:start position:0% +production could would would you agree + + + align:start position:0% +production could would would you agree +that it would would be appropriate for + + align:start position:0% +that it would would be appropriate for + + + align:start position:0% +that it would would be appropriate for +the state of West Virginia to set wages + + align:start position:0% +the state of West Virginia to set wages + + + align:start position:0% +the state of West Virginia to set wages +for coal mines if the federal government + + align:start position:0% +for coal mines if the federal government + + + align:start position:0% +for coal mines if the federal government +can't because a + + align:start position:0% +can't because a + + + align:start position:0% +can't because a +southernland person a good team a person + + align:start position:0% +southernland person a good team a person + + + align:start position:0% +southernland person a good team a person +would say yeah yeah yeah there's a + + align:start position:0% +would say yeah yeah yeah there's a + + + align:start position:0% +would say yeah yeah yeah there's a +constitutional reason why the FED + + align:start position:0% +constitutional reason why the FED + + + align:start position:0% +constitutional reason why the FED +shouldn't do it but I'm not happy with + + align:start position:0% +shouldn't do it but I'm not happy with + + + align:start position:0% +shouldn't do it but I'm not happy with +the State's doing it + + align:start position:0% + + + + align:start position:0% + +yeah should be not the government to + + align:start position:0% +yeah should be not the government to + + + align:start position:0% +yeah should be not the government to +step in and do it for the market so you + + align:start position:0% +step in and do it for the market so you + + + align:start position:0% +step in and do it for the market so you +think this is overruling individual + + align:start position:0% +think this is overruling individual + + + align:start position:0% +think this is overruling individual +choice in a way that's inappropriate + + align:start position:0% +choice in a way that's inappropriate + + + align:start position:0% +choice in a way that's inappropriate +yeah um in my opinion I think in this + + align:start position:0% +yeah um in my opinion I think in this + + + align:start position:0% +yeah um in my opinion I think in this +case it's saying that the central + + align:start position:0% +case it's saying that the central + + + align:start position:0% +case it's saying that the central +government or I guess if you want to + + align:start position:0% +government or I guess if you want to + + + align:start position:0% +government or I guess if you want to +push it to state governments they're + + align:start position:0% +push it to state governments they're + + + align:start position:0% +push it to state governments they're +taking over like too much power and + + align:start position:0% +taking over like too much power and + + + align:start position:0% +taking over like too much power and +they're basically dictating how a person + + align:start position:0% +they're basically dictating how a person + + + align:start position:0% +they're basically dictating how a person +should run their company by saying okay + + align:start position:0% +should run their company by saying okay + + + align:start position:0% +should run their company by saying okay +you have to sell it at this price you + + align:start position:0% +you have to sell it at this price you + + + align:start position:0% +you have to sell it at this price you +have to give this amount of wages this + + align:start position:0% +have to give this amount of wages this + + + align:start position:0% +have to give this amount of wages this +is like they're setting the guidelines + + align:start position:0% +is like they're setting the guidelines + + + align:start position:0% +is like they're setting the guidelines +and instructions on like how to run your + + align:start position:0% +and instructions on like how to run your + + + align:start position:0% +and instructions on like how to run your +company whereas in this where as coal in + + align:start position:0% +company whereas in this where as coal in + + + align:start position:0% +company whereas in this where as coal in +this case says I don't want to follow + + align:start position:0% +this case says I don't want to follow + + + align:start position:0% +this case says I don't want to follow +these rules I want to run my company how + + align:start position:0% +these rules I want to run my company how + + + align:start position:0% +these rules I want to run my company how +I run how I want to run my company I + + align:start position:0% +I run how I want to run my company I + + + align:start position:0% +I run how I want to run my company I +have a vision of how I want to sell coal + + align:start position:0% +have a vision of how I want to sell coal + + + align:start position:0% +have a vision of how I want to sell coal +how I want to make the lifestyle for the + + align:start position:0% +how I want to make the lifestyle for the + + + align:start position:0% +how I want to make the lifestyle for the +workers here and if it's my company I + + align:start position:0% +workers here and if it's my company I + + + align:start position:0% +workers here and if it's my company I +should be able to do that is that the + + align:start position:0% +should be able to do that is that the + + + align:start position:0% +should be able to do that is that the +right way for society to be organized + + align:start position:0% +right way for society to be organized + + + align:start position:0% +right way for society to be organized +that's a statement about that's an + + align:start position:0% +that's a statement about that's an + + + align:start position:0% +that's a statement about that's an +ideological statement that not only is + + align:start position:0% +ideological statement that not only is + + + align:start position:0% +ideological statement that not only is +that what he's saying but that's the + + align:start position:0% +that what he's saying but that's the + + + align:start position:0% +that what he's saying but that's the +right thing to say because that's the + + align:start position:0% +right thing to say because that's the + + + align:start position:0% +right thing to say because that's the +right way to organize Society let me go + + align:start position:0% +right way to organize Society let me go + + + align:start position:0% +right way to organize Society let me go +back to the back yeah yeah I think on + + align:start position:0% +back to the back yeah yeah I think on + + + align:start position:0% +back to the back yeah yeah I think on +the philosophical side like you want if + + align:start position:0% +the philosophical side like you want if + + + align:start position:0% +the philosophical side like you want if +you put the federal govern puts a lot of + + align:start position:0% +you put the federal govern puts a lot of + + + align:start position:0% +you put the federal govern puts a lot of +regulations + + align:start position:0% +regulations + + + align:start position:0% +regulations +wages then you like Ste just saying you + + align:start position:0% +wages then you like Ste just saying you + + + align:start position:0% +wages then you like Ste just saying you +take away all the + + align:start position:0% +take away all the + + + align:start position:0% +take away all the +entrepreneur OPP out of situation so + + align:start position:0% +entrepreneur OPP out of situation so + + + align:start position:0% +entrepreneur OPP out of situation so +that it's just + + align:start position:0% +that it's just + + + align:start position:0% +that it's just +of so it's a bad way to organize society + + align:start position:0% +of so it's a bad way to organize society + + + align:start position:0% +of so it's a bad way to organize society +when there's too much government because + + align:start position:0% +when there's too much government because + + + align:start position:0% +when there's too much government because +you restrict as Howard work would say + + align:start position:0% +you restrict as Howard work would say + + + align:start position:0% +you restrict as Howard work would say +the the entrepreneurial energies the + + align:start position:0% +the the entrepreneurial energies the + + + align:start position:0% +the the entrepreneurial energies the +creativity Etc and of course the ability + + align:start position:0% +creativity Etc and of course the ability + + + align:start position:0% +creativity Etc and of course the ability +of Carter to squeeze his workers + + align:start position:0% +of Carter to squeeze his workers + + + align:start position:0% +of Carter to squeeze his workers +and I was going to say Yeah in general + + align:start position:0% +and I was going to say Yeah in general + + + align:start position:0% +and I was going to say Yeah in general +thinking about markets I would think + + align:start position:0% +thinking about markets I would think + + + align:start position:0% +thinking about markets I would think +that they're they may not be fair per + + align:start position:0% +that they're they may not be fair per + + + align:start position:0% +that they're they may not be fair per +say in whatever wait a minute you're on + + align:start position:0% +say in whatever wait a minute you're on + + + align:start position:0% +say in whatever wait a minute you're on +team a now hold on + + align:start position:0% + + + + align:start position:0% + +here give you reward based on the effort + + align:start position:0% +here give you reward based on the effort + + + align:start position:0% +here give you reward based on the effort +you put and at the end of the day they + + align:start position:0% +you put and at the end of the day they + + + align:start position:0% +you put and at the end of the day they +are the same like as brutal as they are + + align:start position:0% +are the same like as brutal as they are + + + align:start position:0% +are the same like as brutal as they are +person a they're going to be the person + + align:start position:0% +person a they're going to be the person + + + align:start position:0% +person a they're going to be the person +be not they have no Prejudice and like + + align:start position:0% +be not they have no Prejudice and like + + + align:start position:0% +be not they have no Prejudice and like +if you were if I would trust that + + align:start position:0% +if you were if I would trust that + + + align:start position:0% +if you were if I would trust that +markets would be more consistent and in + + align:start position:0% +markets would be more consistent and in + + + align:start position:0% +markets would be more consistent and in +that sense more fair than than the + + align:start position:0% +that sense more fair than than the + + + align:start position:0% +that sense more fair than than the +government so I think that it makes + + align:start position:0% +government so I think that it makes + + + align:start position:0% +government so I think that it makes +sense for for to have a system where you + + align:start position:0% +sense for for to have a system where you + + + align:start position:0% +sense for for to have a system where you +have markets dictating the rules and + + align:start position:0% +have markets dictating the rules and + + + align:start position:0% +have markets dictating the rules and +when you have externalities or problems + + align:start position:0% +when you have externalities or problems + + + align:start position:0% +when you have externalities or problems +then you might think about having state + + align:start position:0% +then you might think about having state + + + align:start position:0% +then you might think about having state +or or fedal government stepping in but + + align:start position:0% +or or fedal government stepping in but + + + align:start position:0% +or or fedal government stepping in but +in general I would assume I would think + + align:start position:0% +in general I would assume I would think + + + align:start position:0% +in general I would assume I would think +that nicer rule to is look at the cases + + align:start position:0% +that nicer rule to is look at the cases + + + align:start position:0% +that nicer rule to is look at the cases +where markets do not work well then you + + align:start position:0% +where markets do not work well then you + + + align:start position:0% +where markets do not work well then you +would have to go into the debate where + + align:start position:0% +would have to go into the debate where + + + align:start position:0% +would have to go into the debate where +where the market not work and that's + + align:start position:0% +where the market not work and that's + + + align:start position:0% +where the market not work and that's +another debate by itself but what I'm + + align:start position:0% +another debate by itself but what I'm + + + align:start position:0% +another debate by itself but what I'm +saying is that markets I think are are + + align:start position:0% +saying is that markets I think are are + + + align:start position:0% +saying is that markets I think are are +fair in that sense well suppose suppose + + align:start position:0% +fair in that sense well suppose suppose + + + align:start position:0% +fair in that sense well suppose suppose +I told you that I knew that all coal + + align:start position:0% +I told you that I knew that all coal + + + align:start position:0% +I told you that I knew that all coal +mine all owners of coal miners were + + align:start position:0% +mine all owners of coal miners were + + + align:start position:0% +mine all owners of coal miners were +terrible racists and that in fact just + + align:start position:0% +terrible racists and that in fact just + + + align:start position:0% +terrible racists and that in fact just +out of prejudice they paid half uh uh as + + align:start position:0% +out of prejudice they paid half uh uh as + + + align:start position:0% +out of prejudice they paid half uh uh as +much to Black workers as the white + + align:start position:0% +much to Black workers as the white + + + align:start position:0% +much to Black workers as the white +workers + + align:start position:0% +workers + + + align:start position:0% +workers +what would happen was probably you would + + align:start position:0% +what would happen was probably you would + + + align:start position:0% +what would happen was probably you would +have like another another another + + align:start position:0% +have like another another another + + + align:start position:0% +have like another another another +company that would come out with would + + align:start position:0% +company that would come out with would + + + align:start position:0% +company that would come out with would +pay like uh better wages and could + + align:start position:0% +pay like uh better wages and could + + + align:start position:0% +pay like uh better wages and could +probably uh could hire away good black + + align:start position:0% +probably uh could hire away good black + + + align:start position:0% +probably uh could hire away good black +workers for cheap wages okay okay so the + + align:start position:0% +workers for cheap wages okay okay so the + + + align:start position:0% +workers for cheap wages okay okay so the +market does have a tendency to be + + align:start position:0% +market does have a tendency to be + + + align:start position:0% +market does have a tendency to be +self-correcting so let me let me let me + + align:start position:0% +self-correcting so let me let me let me + + + align:start position:0% +self-correcting so let me let me let me +move on we'll we we'll get to the + + align:start position:0% +move on we'll we we'll get to the + + + align:start position:0% +move on we'll we we'll get to the +Socialists over here in a minute + + align:start position:0% +Socialists over here in a minute + + + align:start position:0% +Socialists over here in a minute +but + + align:start position:0% +but + + + align:start position:0% +but +uh I we didn't ass sign Hughes but did + + align:start position:0% +uh I we didn't ass sign Hughes but did + + + align:start position:0% +uh I we didn't ass sign Hughes but did +you notice + + align:start position:0% +you notice + + + align:start position:0% +you notice +what Hughes said in + + align:start position:0% + + + + align:start position:0% + +descent Hughes was a Hughes was the + + align:start position:0% +descent Hughes was a Hughes was the + + + align:start position:0% +descent Hughes was a Hughes was the +chief justice he had a yeah + + align:start position:0% + + + + align:start position:0% + +Rory yeah he just said how can you + + align:start position:0% +Rory yeah he just said how can you + + + align:start position:0% +Rory yeah he just said how can you +possibly staple these together when the + + align:start position:0% +possibly staple these together when the + + + align:start position:0% +possibly staple these together when the +terms of the law says they're not that I + + align:start position:0% +terms of the law says they're not that I + + + align:start position:0% +terms of the law says they're not that I +don't get that um which is a pretty + + align:start position:0% +don't get that um which is a pretty + + + align:start position:0% +don't get that um which is a pretty +narrow technical argument and that's why + + align:start position:0% +narrow technical argument and that's why + + + align:start position:0% +narrow technical argument and that's why +we're not going to talk about him how + + align:start position:0% +we're not going to talk about him how + + + align:start position:0% +we're not going to talk about him how +about + + align:start position:0% +about + + + align:start position:0% +about +cardoo Casey so he said in regards to + + align:start position:0% +cardoo Casey so he said in regards to + + + align:start position:0% +cardoo Casey so he said in regards to +price fixing provision of the ACT that + + align:start position:0% +price fixing provision of the ACT that + + + align:start position:0% +price fixing provision of the ACT that +it was legal um because of the Commerce + + align:start position:0% +it was legal um because of the Commerce + + + align:start position:0% +it was legal um because of the Commerce +car uh Commerce Clause because the price + + align:start position:0% +car uh Commerce Clause because the price + + + align:start position:0% +car uh Commerce Clause because the price +of cold definitely affects interstate + + align:start position:0% +of cold definitely affects interstate + + + align:start position:0% +of cold definitely affects interstate +commerce um and then he didn't make a + + align:start position:0% +commerce um and then he didn't make a + + + align:start position:0% +commerce um and then he didn't make a +decision necessarily with the + + align:start position:0% + + + + align:start position:0% + +other it's a little obscure did anybody + + align:start position:0% +other it's a little obscure did anybody + + + align:start position:0% +other it's a little obscure did anybody +C anybody see something that he said + + align:start position:0% +C anybody see something that he said + + + align:start position:0% +C anybody see something that he said +that related to the other provision as + + align:start position:0% +that related to the other provision as + + + align:start position:0% +that related to the other provision as +well he he didn't say it directly you're + + align:start position:0% +well he he didn't say it directly you're + + + align:start position:0% +well he he didn't say it directly you're +right + + align:start position:0% +right + + + align:start position:0% +right +um but he did + + align:start position:0% +um but he did + + + align:start position:0% +um but he did +say yeah anybody the collectivists over + + align:start position:0% +say yeah anybody the collectivists over + + + align:start position:0% +say yeah anybody the collectivists over +here no he he + + align:start position:0% + + + + align:start position:0% + +said + + align:start position:0% + + + + align:start position:0% + +um he he comes on + + align:start position:0% +um he he comes on + + + align:start position:0% +um he he comes on +to this distinction by southernland of + + align:start position:0% +to this distinction by southernland of + + + align:start position:0% +to this distinction by southernland of +direct and indirect + + align:start position:0% +direct and indirect + + + align:start position:0% +direct and indirect +effects um and he says um the question + + align:start position:0% +effects um and he says um the question + + + align:start position:0% +effects um and he says um the question +remains whether comes within that power + + align:start position:0% +remains whether comes within that power + + + align:start position:0% +remains whether comes within that power +is applied to Interstate sales where + + align:start position:0% +is applied to Interstate sales where + + + align:start position:0% +is applied to Interstate sales where +Interstate prices are directly or + + align:start position:0% +Interstate prices are directly or + + + align:start position:0% +Interstate prices are directly or +intimately affected Mining and + + align:start position:0% +intimately affected Mining and + + + align:start position:0% +intimately affected Mining and +agriculture uh Mining and man + + align:start position:0% +agriculture uh Mining and man + + + align:start position:0% +agriculture uh Mining and man +Agriculture and manufacturer are not + + align:start position:0% +Agriculture and manufacturer are not + + + align:start position:0% +Agriculture and manufacturer are not +interstate commerce yet their relation + + align:start position:0% +interstate commerce yet their relation + + + align:start position:0% +interstate commerce yet their relation +may be such that for the protection of + + align:start position:0% +may be such that for the protection of + + + align:start position:0% +may be such that for the protection of +the one there is need to regulate the + + align:start position:0% +the one there is need to regulate the + + + align:start position:0% +the one there is need to regulate the +other and he goes on and says at all + + align:start position:0% +other and he goes on and says at all + + + align:start position:0% +other and he goes on and says at all +events direct and indirect even if + + align:start position:0% +events direct and indirect even if + + + align:start position:0% +events direct and indirect even if +accepted as sufficient that is to say + + align:start position:0% +accepted as sufficient that is to say + + + align:start position:0% +accepted as sufficient that is to say +even if you buy southerland's + + align:start position:0% +even if you buy southerland's + + + align:start position:0% +even if you buy southerland's +distinction must not be read read too + + align:start position:0% +distinction must not be read read too + + + align:start position:0% +distinction must not be read read too +narrowly in fact I don't know how + + align:start position:0% +narrowly in fact I don't know how + + + align:start position:0% +narrowly in fact I don't know how +anybody can tell the difference or what + + align:start position:0% +anybody can tell the difference or what + + + align:start position:0% +anybody can tell the difference or what +the difference means you can read I read + + align:start position:0% +the difference means you can read I read + + + align:start position:0% +the difference means you can read I read +southernland several times and it made + + align:start position:0% +southernland several times and it made + + + align:start position:0% +southernland several times and it made +no sense to me but so cardoo as you + + align:start position:0% +no sense to me but so cardoo as you + + + align:start position:0% +no sense to me but so cardoo as you +point out it's very clear look it's + + align:start position:0% +point out it's very clear look it's + + + align:start position:0% +point out it's very clear look it's +interstate commerce we can fix prices of + + align:start position:0% +interstate commerce we can fix prices of + + + align:start position:0% +interstate commerce we can fix prices of +coal and Interstate Commerce for + + align:start position:0% +coal and Interstate Commerce for + + + align:start position:0% +coal and Interstate Commerce for +heaven's sakes and then he kind of + + align:start position:0% +heaven's sakes and then he kind of + + + align:start position:0% +heaven's sakes and then he kind of +waffles around and says and you + + align:start position:0% +waffles around and says and you + + + align:start position:0% +waffles around and says and you +know to say that wages don't affect + + align:start position:0% +know to say that wages don't affect + + + align:start position:0% +know to say that wages don't affect +prices + + align:start position:0% +prices + + + align:start position:0% +prices +directly kind of + + align:start position:0% +directly kind of + + + align:start position:0% +directly kind of +God uh you'd have to read it kind of + + align:start position:0% +God uh you'd have to read it kind of + + + align:start position:0% +God uh you'd have to read it kind of +narrowly that's a that may be the that + + align:start position:0% +narrowly that's a that may be the that + + + align:start position:0% +narrowly that's a that may be the that +may be the Criterion southernland may + + align:start position:0% +may be the Criterion southernland may + + + align:start position:0% +may be the Criterion southernland may +have the Criterion but to say to to + + align:start position:0% +have the Criterion but to say to to + + + align:start position:0% +have the Criterion but to say to to +treat directly + + align:start position:0% + + + + align:start position:0% + +narrowly is is inappropriate so what is + + align:start position:0% +narrowly is is inappropriate so what is + + + align:start position:0% +narrowly is is inappropriate so what is +cardozo's view of the proper + + align:start position:0% + + + + align:start position:0% + +role Erica what do you say what does + + align:start position:0% +role Erica what do you say what does + + + align:start position:0% +role Erica what do you say what does +cardoo think the government should be + + align:start position:0% +cardoo think the government should be + + + align:start position:0% +cardoo think the government should be +able to do + + align:start position:0% + + + + align:start position:0% + +so he he he says the government should + + align:start position:0% +so he he he says the government should + + + align:start position:0% +so he he he says the government should +be able to regulate + + align:start position:0% +be able to regulate + + + align:start position:0% +be able to regulate +it more or less um does he is + + align:start position:0% +it more or less um does he is + + + align:start position:0% +it more or less um does he is +there where is he versus Southerland on + + align:start position:0% +there where is he versus Southerland on + + + align:start position:0% +there where is he versus Southerland on +in general terms the role of + + align:start position:0% +in general terms the role of + + + align:start position:0% +in general terms the role of +government the role of the Federal + + align:start position:0% +government the role of the Federal + + + align:start position:0% +government the role of the Federal +Government let's start there Rory it + + align:start position:0% +Government let's start there Rory it + + + align:start position:0% +Government let's start there Rory it +seems to be able to do that that it + + align:start position:0% +seems to be able to do that that it + + + align:start position:0% +seems to be able to do that that it +should be allowed to regulate it because + + align:start position:0% +should be allowed to regulate it because + + + align:start position:0% +should be allowed to regulate it because +given the checks and balances you have + + align:start position:0% +given the checks and balances you have + + + align:start position:0% +given the checks and balances you have +in the system while you may create a + + align:start position:0% +in the system while you may create a + + + align:start position:0% +in the system while you may create a +rule the rule can have degrees and so I + + align:start position:0% +rule the rule can have degrees and so I + + + align:start position:0% +rule the rule can have degrees and so I +think he talks about the fact that you + + align:start position:0% +think he talks about the fact that you + + + align:start position:0% +think he talks about the fact that you +know he says something along the lines + + align:start position:0% +know he says something along the lines + + + align:start position:0% +know he says something along the lines +of the law isn't stupid you know it can + + align:start position:0% +of the law isn't stupid you know it can + + + align:start position:0% +of the law isn't stupid you know it can +work out when one thing is a direct + + align:start position:0% +work out when one thing is a direct + + + align:start position:0% +work out when one thing is a direct +action one an + + align:start position:0% +action one an + + + align:start position:0% +action one an +indect I didn't get the word stupid but + + align:start position:0% +indect I didn't get the word stupid but + + + align:start position:0% +indect I didn't get the word stupid but +uh but yeah yeah yeah yeah + + align:start position:0% + + + + align:start position:0% + +yeah well that's his that's is don't + + align:start position:0% +yeah well that's his that's is don't + + + align:start position:0% +yeah well that's his that's is don't +Define them too narrowly a survey of the + + align:start position:0% +Define them too narrowly a survey of the + + + align:start position:0% +Define them too narrowly a survey of the +cases shows that the words direct and + + align:start position:0% +cases shows that the words direct and + + + align:start position:0% +cases shows that the words direct and +indirect have been interpreted with + + align:start position:0% +indirect have been interpreted with + + + align:start position:0% +indirect have been interpreted with +suppleness of adaption and flexibility + + align:start position:0% +suppleness of adaption and flexibility + + + align:start position:0% +suppleness of adaption and flexibility +of meaning the power is as broad as the + + align:start position:0% +of meaning the power is as broad as the + + + align:start position:0% +of meaning the power is as broad as the +need that evokes it that's a nice little + + align:start position:0% +need that evokes it that's a nice little + + + align:start position:0% +need that evokes it that's a nice little +phrase too that's that kind of matches + + align:start position:0% +phrase too that's that kind of matches + + + align:start position:0% +phrase too that's that kind of matches +southerland's journey toward a forbidden + + align:start position:0% +southerland's journey toward a forbidden + + + align:start position:0% +southerland's journey toward a forbidden +end the power is as broad as the need + + align:start position:0% +end the power is as broad as the need + + + align:start position:0% +end the power is as broad as the need +that evokes + + align:start position:0% +that evokes + + + align:start position:0% +that evokes +it that's a that's a statement thank you + + align:start position:0% +it that's a that's a statement thank you + + + align:start position:0% +it that's a that's a statement thank you +for reminding me of that lovely phrase + + align:start position:0% +for reminding me of that lovely phrase + + + align:start position:0% +for reminding me of that lovely phrase +that's a statement about the role of + + align:start position:0% +that's a statement about the role of + + + align:start position:0% +that's a statement about the role of +government that's a statement about how + + align:start position:0% +government that's a statement about how + + + align:start position:0% +government that's a statement about how +Society should be organized right what + + align:start position:0% +Society should be organized right what + + + align:start position:0% +Society should be organized right what +government should be able to + + align:start position:0% + + + + align:start position:0% + +do it says if you have a representative + + align:start position:0% +do it says if you have a representative + + + align:start position:0% +do it says if you have a representative +government which is kind of assumed here + + align:start position:0% +government which is kind of assumed here + + + align:start position:0% +government which is kind of assumed here +and the government says there is a need + + align:start position:0% +and the government says there is a need + + + align:start position:0% +and the government says there is a need +then the government can act + + align:start position:0% +then the government can act + + + align:start position:0% +then the government can act +I don't see a forbidden end here I don't + + align:start position:0% +I don't see a forbidden end here I don't + + + align:start position:0% +I don't see a forbidden end here I don't +see a concern for the sovereignty of the + + align:start position:0% +see a concern for the sovereignty of the + + + align:start position:0% +see a concern for the sovereignty of the +states I see a government concerned with + + align:start position:0% +states I see a government concerned with + + + align:start position:0% +states I see a government concerned with +meeting + + align:start position:0% + + + + align:start position:0% + +needs Team B you like + + align:start position:0% +needs Team B you like + + + align:start position:0% +needs Team B you like +that why is that + + align:start position:0% +that why is that + + + align:start position:0% +that why is that +good Jackie I think it sense for the + + align:start position:0% +good Jackie I think it sense for the + + + align:start position:0% +good Jackie I think it sense for the +government as the RO of the protector um + + align:start position:0% +government as the RO of the protector um + + + align:start position:0% +government as the RO of the protector um +especially like during the era of the + + align:start position:0% +especially like during the era of the + + + align:start position:0% +especially like during the era of the +new deal when it's all about recovery + + align:start position:0% +new deal when it's all about recovery + + + align:start position:0% +new deal when it's all about recovery +makes sense that the government saying + + align:start position:0% +makes sense that the government saying + + + align:start position:0% +makes sense that the government saying +what's going + + align:start position:0% + + + + align:start position:0% + +on decisions + + align:start position:0% + + + + align:start position:0% + +ofen solve for something that's AAL + + align:start position:0% +ofen solve for something that's AAL + + + align:start position:0% +ofen solve for something that's AAL +issue one of the reasons why like in + + align:start position:0% +issue one of the reasons why like in + + + align:start position:0% +issue one of the reasons why like in +ancient Rome people were willing to + + align:start position:0% +ancient Rome people were willing to + + + align:start position:0% +ancient Rome people were willing to +accept the role of the dictator during + + align:start position:0% +accept the role of the dictator during + + + align:start position:0% +accept the role of the dictator during +of War because learn from democracy + + align:start position:0% + + + + align:start position:0% + +bealing so of course they also had they + + align:start position:0% +bealing so of course they also had they + + + align:start position:0% +bealing so of course they also had they +also accepted Emperors in times of Peace + + align:start position:0% +also accepted Emperors in times of Peace + + + align:start position:0% +also accepted Emperors in times of Peace +after a little while but hey + + align:start position:0% +after a little while but hey + + + align:start position:0% +after a little while but hey +but hey but that's that's an interesting + + align:start position:0% +but hey but that's that's an interesting + + + align:start position:0% +but hey but that's that's an interesting +example of sources of legitimacy right + + align:start position:0% +example of sources of legitimacy right + + + align:start position:0% +example of sources of legitimacy right +as long as the Empire is growing and + + align:start position:0% +as long as the Empire is growing and + + + align:start position:0% +as long as the Empire is growing and +people are + + align:start position:0% +people are + + + align:start position:0% +people are +prosperous do I really care that the + + align:start position:0% +prosperous do I really care that the + + + align:start position:0% +prosperous do I really care that the +petorian guard put the emperor in his + + align:start position:0% +petorian guard put the emperor in his + + + align:start position:0% +petorian guard put the emperor in his +place as long as things are going well + + align:start position:0% +place as long as things are going well + + + align:start position:0% +place as long as things are going well +I'll play along so so you think with + + align:start position:0% +I'll play along so so you think with + + + align:start position:0% +I'll play along so so you think with +cardoo that if a + + align:start position:0% +cardoo that if a + + + align:start position:0% +cardoo that if a +legitimately installed + + align:start position:0% +legitimately installed + + + align:start position:0% +legitimately installed +government finds a real need + + align:start position:0% +government finds a real need + + + align:start position:0% +government finds a real need +the government should be able to deal + + align:start position:0% +the government should be able to deal + + + align:start position:0% +the government should be able to deal +with + + align:start position:0% +with + + + align:start position:0% +with +it + + align:start position:0% +it + + + align:start position:0% +it +yeah this is Morris Smith's opinion + + align:start position:0% +yeah this is Morris Smith's opinion + + + align:start position:0% +yeah this is Morris Smith's opinion +because it doesn't necessarily + + align:start position:0% +because it doesn't necessarily + + + align:start position:0% +because it doesn't necessarily +completely contradict with what cardoo + + align:start position:0% +completely contradict with what cardoo + + + align:start position:0% +completely contradict with what cardoo +says he says uh for example if you think + + align:start position:0% +says he says uh for example if you think + + + align:start position:0% +says he says uh for example if you think +of like the RO of policy is supposed to + + align:start position:0% +of like the RO of policy is supposed to + + + align:start position:0% +of like the RO of policy is supposed to +uh deal account for any externality that + + align:start position:0% +uh deal account for any externality that + + + align:start position:0% +uh deal account for any externality that +the free market uh usually wouldn't + + align:start position:0% +the free market uh usually wouldn't + + + align:start position:0% +the free market uh usually wouldn't +consider it's Miss says you know the the + + align:start position:0% +consider it's Miss says you know the the + + + align:start position:0% +consider it's Miss says you know the the +the best representative would be the + + align:start position:0% +the best representative would be the + + + align:start position:0% +the best representative would be the +person who truly understands the local + + align:start position:0% +person who truly understands the local + + + align:start position:0% +person who truly understands the local +population the climate the geography all + + align:start position:0% +population the climate the geography all + + + align:start position:0% +population the climate the geography all +that is specific area so he what he says + + align:start position:0% +that is specific area so he what he says + + + align:start position:0% +that is specific area so he what he says +is there's nothing wrong with policy but + + align:start position:0% +is there's nothing wrong with policy but + + + align:start position:0% +is there's nothing wrong with policy but +it's who should be the the the the + + align:start position:0% +it's who should be the the the the + + + align:start position:0% +it's who should be the the the the +people making that decision he basically + + align:start position:0% +people making that decision he basically + + + align:start position:0% +people making that decision he basically +he's U against the government making a + + align:start position:0% +he's U against the government making a + + + align:start position:0% +he's U against the government making a +decision for all the states but he's not + + align:start position:0% +decision for all the states but he's not + + + align:start position:0% +decision for all the states but he's not +necessarily against uh you know some + + align:start position:0% +necessarily against uh you know some + + + align:start position:0% +necessarily against uh you know some +sort of policy for directing um but + + align:start position:0% +sort of policy for directing um but + + + align:start position:0% +sort of policy for directing um but +suppose you know your real + + align:start position:0% +suppose you know your real + + + align:start position:0% +suppose you know your real +concern is terrible poverty in coal + + align:start position:0% +concern is terrible poverty in coal + + + align:start position:0% +concern is terrible poverty in coal +mining areas which was pretty brutal + + align:start position:0% +mining areas which was pretty brutal + + + align:start position:0% +mining areas which was pretty brutal +actually in the 30s and you say well + + align:start position:0% +actually in the 30s and you say well + + + align:start position:0% +actually in the 30s and you say well +here's what we're going to do we're + + align:start position:0% +here's what we're going to do we're + + + align:start position:0% +here's what we're going to do we're +going to let West Virginia a poor State + + align:start position:0% +going to let West Virginia a poor State + + + align:start position:0% +going to let West Virginia a poor State +deal with poverty in West + + align:start position:0% +deal with poverty in West + + + align:start position:0% +deal with poverty in West +Virginia and West Virginia doesn't have + + align:start position:0% +Virginia and West Virginia doesn't have + + + align:start position:0% +Virginia and West Virginia doesn't have +the money it could try to fix wages + + align:start position:0% +the money it could try to fix wages + + + align:start position:0% +the money it could try to fix wages +maybe it maybe that would be the way for + + align:start position:0% +maybe it maybe that would be the way for + + + align:start position:0% +maybe it maybe that would be the way for +West Virginia to go + + align:start position:0% + + + + align:start position:0% + +forward + + align:start position:0% +forward + + + align:start position:0% +forward +but maybe not maybe West Virginia has a + + align:start position:0% +but maybe not maybe West Virginia has a + + + align:start position:0% +but maybe not maybe West Virginia has a +government that isn't concerned with + + align:start position:0% +government that isn't concerned with + + + align:start position:0% +government that isn't concerned with +poverty in poor areas because it was put + + align:start position:0% +poverty in poor areas because it was put + + + align:start position:0% +poverty in poor areas because it was put +in place by the coal + + align:start position:0% +in place by the coal + + + align:start position:0% +in place by the coal +miners maybe that system broke down I + + align:start position:0% +miners maybe that system broke down I + + + align:start position:0% +miners maybe that system broke down I +don't know + + align:start position:0% +don't know + + + align:start position:0% +don't know +Rory if I only do it in West Virginia + + align:start position:0% +Rory if I only do it in West Virginia + + + align:start position:0% +Rory if I only do it in West Virginia +then the companies move to somewhere + + align:start position:0% +then the companies move to somewhere + + + align:start position:0% +then the companies move to somewhere +else and those prices get forced down + + align:start position:0% +else and those prices get forced down + + + align:start position:0% +else and those prices get forced down +you create the problem there and then + + align:start position:0% +you create the problem there and then + + + align:start position:0% +you create the problem there and then +only eventually do move back to West vir + + align:start position:0% +only eventually do move back to West vir + + + align:start position:0% +only eventually do move back to West vir +so you worry about this is something the + + align:start position:0% +so you worry about this is something the + + + align:start position:0% +so you worry about this is something the +European Union worries about a lot you + + align:start position:0% +European Union worries about a lot you + + + align:start position:0% +European Union worries about a lot you +worry + + align:start position:0% +worry + + + align:start position:0% +worry +about stay or in the European case + + align:start position:0% +about stay or in the European case + + + align:start position:0% +about stay or in the European case +countries uh racing to the bottom + + align:start position:0% +countries uh racing to the bottom + + + align:start position:0% +countries uh racing to the bottom +subsidizing Industries regulating + + align:start position:0% +subsidizing Industries regulating + + + align:start position:0% +subsidizing Industries regulating +lightly in know in a way that attracts + + align:start position:0% +lightly in know in a way that attracts + + + align:start position:0% +lightly in know in a way that attracts +jobs but takes them away from somebody + + align:start position:0% +jobs but takes them away from somebody + + + align:start position:0% +jobs but takes them away from somebody +else that's part of the same Club so you + + align:start position:0% +else that's part of the same Club so you + + + align:start position:0% +else that's part of the same Club so you +say the federal government uh should be + + align:start position:0% +say the federal government uh should be + + + align:start position:0% +say the federal government uh should be +able to act on problems like this + + align:start position:0% +able to act on problems like this + + + align:start position:0% +able to act on problems like this +because you'll get competition among the + + align:start position:0% +because you'll get competition among the + + + align:start position:0% +because you'll get competition among the +states that might be + + align:start position:0% +states that might be + + + align:start position:0% +states that might be +destructive in essence anybody else from + + align:start position:0% +destructive in essence anybody else from + + + align:start position:0% +destructive in essence anybody else from +the the left wing + + align:start position:0% +the the left wing + + + align:start position:0% +the the left wing +yeah the Depression was like a a + + align:start position:0% +yeah the Depression was like a a + + + align:start position:0% +yeah the Depression was like a a +national problem that you're going to + + align:start position:0% +national problem that you're going to + + + align:start position:0% +national problem that you're going to +need like a national lawmaker + + align:start position:0% +need like a national lawmaker + + + align:start position:0% +need like a national lawmaker +to bring it back up and um coal prices + + align:start position:0% +to bring it back up and um coal prices + + + align:start position:0% +to bring it back up and um coal prices +well yeah coal is also you know + + align:start position:0% +well yeah coal is also you know + + + align:start position:0% +well yeah coal is also you know +something that affects a lot more you + + align:start position:0% +something that affects a lot more you + + + align:start position:0% +something that affects a lot more you +prices will affect areas all over around + + align:start position:0% +prices will affect areas all over around + + + align:start position:0% +prices will affect areas all over around +it so I guess I think the federal + + align:start position:0% +it so I guess I think the federal + + + align:start position:0% +it so I guess I think the federal +government feel so you would expand + + align:start position:0% +government feel so you would expand + + + align:start position:0% +government feel so you would expand +powers in times of depression just like + + align:start position:0% +powers in times of depression just like + + + align:start position:0% +powers in times of depression just like +they have tended historically to be + + align:start position:0% +they have tended historically to be + + + align:start position:0% +they have tended historically to be +expanded in times of War right Lincoln + + align:start position:0% +expanded in times of War right Lincoln + + + align:start position:0% +expanded in times of War right Lincoln +expanded the power of the federal + + align:start position:0% +expanded the power of the federal + + + align:start position:0% +expanded the power of the federal +government enormously during the Civil + + align:start position:0% +government enormously during the Civil + + + align:start position:0% +government enormously during the Civil +War do they get rolled + + align:start position:0% + + + + align:start position:0% + +back once you once you've built the + + align:start position:0% +back once you once you've built the + + + align:start position:0% +back once you once you've built the +agency and put the law in place do they + + align:start position:0% +agency and put the law in place do they + + + align:start position:0% +agency and put the law in place do they +roll back Jessica yeah I'm sitting here + + align:start position:0% +roll back Jessica yeah I'm sitting here + + + align:start position:0% +roll back Jessica yeah I'm sitting here +thinking um because I'm a refugee from + + align:start position:0% +thinking um because I'm a refugee from + + + align:start position:0% +thinking um because I'm a refugee from +Cuba so I'm definitely not a socialist + + align:start position:0% +Cuba so I'm definitely not a socialist + + + align:start position:0% +Cuba so I'm definitely not a socialist +but when you opened with but you're on + + align:start position:0% +but when you opened with but you're on + + + align:start position:0% +but when you opened with but you're on +Team B here I mean I'm sorry we need + + align:start position:0% +Team B here I mean I'm sorry we need + + + align:start position:0% +Team B here I mean I'm sorry we need +that we need you with okay when you open + + align:start position:0% +that we need you with okay when you open + + + align:start position:0% +that we need you with okay when you open +support cardoo I was joking you don't + + align:start position:0% +support cardoo I was joking you don't + + + align:start position:0% +support cardoo I was joking you don't +have + + align:start position:0% +have + + + align:start position:0% +have +I was like Wow there are more + + align:start position:0% +I was like Wow there are more + + + align:start position:0% +I was like Wow there are more +correlations than I than I realized at + + align:start position:0% +correlations than I than I realized at + + + align:start position:0% +correlations than I than I realized at +first and there's a joke that um when + + align:start position:0% +first and there's a joke that um when + + + align:start position:0% +first and there's a joke that um when +costro was asking for when costro was + + align:start position:0% +costro was asking for when costro was + + + align:start position:0% +costro was asking for when costro was +asking for an economist CH heard + + align:start position:0% +asking for an economist CH heard + + + align:start position:0% +asking for an economist CH heard +communist and that's why he signed up so + + align:start position:0% +communist and that's why he signed up so + + + align:start position:0% +communist and that's why he signed up so +there opposite sort of implication which + + align:start position:0% +there opposite sort of implication which + + + align:start position:0% +there opposite sort of implication which +is where markets took over and they were + + align:start position:0% +is where markets took over and they were + + + align:start position:0% +is where markets took over and they were +so bad for the people that they just + + align:start position:0% +so bad for the people that they just + + + align:start position:0% +so bad for the people that they just +needed a government to take over the + + align:start position:0% +needed a government to take over the + + + align:start position:0% +needed a government to take over the +markets and that's when they turned to + + align:start position:0% +markets and that's when they turned to + + + align:start position:0% +markets and that's when they turned to +let's be let's give everything to this + + align:start position:0% +let's be let's give everything to this + + + align:start position:0% +let's be let's give everything to this +one guy + + align:start position:0% +one guy + + + align:start position:0% +one guy +so it might also be a prehensive attack + + align:start position:0% +so it might also be a prehensive attack + + + align:start position:0% +so it might also be a prehensive attack +this is you're talking about about Cuba + + align:start position:0% +this is you're talking about about Cuba + + + align:start position:0% +this is you're talking about about Cuba +before the Revolution when the the + + align:start position:0% +before the Revolution when the the + + + align:start position:0% +before the Revolution when the the +Baptista government was corrupt was + + align:start position:0% +Baptista government was corrupt was + + + align:start position:0% +Baptista government was corrupt was +basically an oligarchy and gave really + + align:start position:0% +basically an oligarchy and gave really + + + align:start position:0% +basically an oligarchy and gave really +nice parties in Havana and great + + align:start position:0% +nice parties in Havana and great + + + align:start position:0% +nice parties in Havana and great +nightlife in Havana for visiting + + align:start position:0% +nightlife in Havana for visiting + + + align:start position:0% +nightlife in Havana for visiting +Americans and immense poverty for much + + align:start position:0% +Americans and immense poverty for much + + + align:start position:0% +Americans and immense poverty for much +of + + align:start position:0% +of + + + align:start position:0% +of +Cuba and that government lost + + align:start position:0% +Cuba and that government lost + + + align:start position:0% +Cuba and that government lost +legitimacy and you got Central + + align:start position:0% +legitimacy and you got Central + + + align:start position:0% +legitimacy and you got Central +action which + + align:start position:0% +action which + + + align:start position:0% +action which +brought a lot of literacy to the Cuban + + align:start position:0% +brought a lot of literacy to the Cuban + + + align:start position:0% +brought a lot of literacy to the Cuban +people improved Medical + + align:start position:0% +people improved Medical + + + align:start position:0% +people improved Medical +Care and well better than it was and of + + align:start position:0% +Care and well better than it was and of + + + align:start position:0% +Care and well better than it was and of +course now we're back to grinding + + align:start position:0% +course now we're back to grinding + + + align:start position:0% +course now we're back to grinding +poverty but again now now that now that + + align:start position:0% +poverty but again now now that now that + + + align:start position:0% +poverty but again now now that now that +the Soviet support is gone but system of + + align:start position:0% +the Soviet support is gone but system of + + + align:start position:0% +the Soviet support is gone but system of +checks and balances having that + + align:start position:0% +checks and balances having that + + + align:start position:0% +checks and balances having that +flexibility to like open to give + + align:start position:0% +flexibility to like open to give + + + align:start position:0% +flexibility to like open to give +government more power when it's needed + + align:start position:0% +government more power when it's needed + + + align:start position:0% +government more power when it's needed +and less when it's when it's not needed + + align:start position:0% +and less when it's when it's not needed + + + align:start position:0% +and less when it's when it's not needed +might be a preemptive strategy to to + + align:start position:0% +might be a preemptive strategy to to + + + align:start position:0% +might be a preemptive strategy to to +make it radical in One Direction + + align:start position:0% +make it radical in One Direction + + + align:start position:0% +make it radical in One Direction +any any other U uh defense of cord Doo's + + align:start position:0% +any any other U uh defense of cord Doo's + + + align:start position:0% +any any other U uh defense of cord Doo's +view the the power let me read that read + + align:start position:0% +view the the power let me read that read + + + align:start position:0% +view the the power let me read that read +that one sentence + + align:start position:0% +that one sentence + + + align:start position:0% +that one sentence +again uh the power is as broad as the + + align:start position:0% +again uh the power is as broad as the + + + align:start position:0% +again uh the power is as broad as the +need that evokes it + + align:start position:0% +need that evokes it + + + align:start position:0% +need that evokes it +yeah here is I when + + align:start position:0% +yeah here is I when + + + align:start position:0% +yeah here is I when +weiz wages and prices the people who + + align:start position:0% +weiz wages and prices the people who + + + align:start position:0% +weiz wages and prices the people who +would be affected is the the general + + align:start position:0% +would be affected is the the general + + + align:start position:0% +would be affected is the the general +public and when the argument is between + + align:start position:0% +public and when the argument is between + + + align:start position:0% +public and when the argument is between +the market and the Poli makers but the + + align:start position:0% +the market and the Poli makers but the + + + align:start position:0% +the market and the Poli makers but the +people who are really going to be aded + + align:start position:0% +people who are really going to be aded + + + align:start position:0% +people who are really going to be aded +are the general public so let's think if + + align:start position:0% +are the general public so let's think if + + + align:start position:0% +are the general public so let's think if +we had this debate or if we had this if + + align:start position:0% +we had this debate or if we had this if + + + align:start position:0% +we had this debate or if we had this if +we go back to the general public and see + + align:start position:0% +we go back to the general public and see + + + align:start position:0% +we go back to the general public and see +what's their opinion about this point + + align:start position:0% +what's their opinion about this point + + + align:start position:0% +what's their opinion about this point +most probably most people will just they + + align:start position:0% +most probably most people will just they + + + align:start position:0% +most probably most people will just they +want to have a regular prices and they + + align:start position:0% +want to have a regular prices and they + + + align:start position:0% +want to have a regular prices and they +want have regular wages they don't want + + align:start position:0% +want have regular wages they don't want + + + align:start position:0% +want have regular wages they don't want +to like the price to depend only on the + + align:start position:0% +to like the price to depend only on the + + + align:start position:0% +to like the price to depend only on the +decision of people who own these + + align:start position:0% +decision of people who own these + + + align:start position:0% +decision of people who own these +companies or people who are in the + + align:start position:0% +companies or people who are in the + + + align:start position:0% +companies or people who are in the +market so most people you think would + + align:start position:0% +market so most people you think would + + + align:start position:0% +market so most people you think would +would in fact if you put this Pro if you + + align:start position:0% +would in fact if you put this Pro if you + + + align:start position:0% +would in fact if you put this Pro if you +put this to a vote put the Constitution + + align:start position:0% +put this to a vote put the Constitution + + + align:start position:0% +put this to a vote put the Constitution +to one side if you put it to a vote and + + align:start position:0% +to one side if you put it to a vote and + + + align:start position:0% +to one side if you put it to a vote and +you + + align:start position:0% +you + + + align:start position:0% +you +said and by the way there's another + + align:start position:0% +said and by the way there's another + + + align:start position:0% +said and by the way there's another +reading uh uh that's that's optional + + align:start position:0% +reading uh uh that's that's optional + + + align:start position:0% +reading uh uh that's that's optional +that gives you a sense of how really + + align:start position:0% +that gives you a sense of how really + + + align:start position:0% +that gives you a sense of how really +awful it was to be a coal miner in this + + align:start position:0% +awful it was to be a coal miner in this + + + align:start position:0% +awful it was to be a coal miner in this +period uh and Beyond perhaps if you put + + align:start position:0% +period uh and Beyond perhaps if you put + + + align:start position:0% +period uh and Beyond perhaps if you put +it to a vote and you said these people + + align:start position:0% +it to a vote and you said these people + + + align:start position:0% +it to a vote and you said these people +have terrible jobs they die young + + align:start position:0% +have terrible jobs they die young + + + align:start position:0% +have terrible jobs they die young +they're dirt poor things have gotten + + align:start position:0% +they're dirt poor things have gotten + + + align:start position:0% +they're dirt poor things have gotten +worse how about we pay them a living + + align:start position:0% +worse how about we pay them a living + + + align:start position:0% +worse how about we pay them a living +wage and the cost of coal goes up a + + align:start position:0% +wage and the cost of coal goes up a + + + align:start position:0% +wage and the cost of coal goes up a +little bit you think that would pass and + + align:start position:0% +little bit you think that would pass and + + + align:start position:0% +little bit you think that would pass and +that that ought to be enough + + align:start position:0% +that that ought to be enough + + + align:start position:0% +that that ought to be enough +the Constitution saying maybe you can't + + align:start position:0% +the Constitution saying maybe you can't + + + align:start position:0% +the Constitution saying maybe you can't +do it maybe you can that the fact that + + align:start position:0% +do it maybe you can that the fact that + + + align:start position:0% +do it maybe you can that the fact that +you could get a vote on it which you + + align:start position:0% +you could get a vote on it which you + + + align:start position:0% +you could get a vote on it which you +probably could you probably could have + + align:start position:0% +probably could you probably could have + + + align:start position:0% +probably could you probably could have +in the in the uh in the depression there + + align:start position:0% +in the in the uh in the depression there + + + align:start position:0% +in the in the uh in the depression there +was a a 1933 case called Appalachian + + align:start position:0% +was a a 1933 case called Appalachian + + + align:start position:0% +was a a 1933 case called Appalachian +Kohl's an anti trust case that went to + + align:start position:0% +Kohl's an anti trust case that went to + + + align:start position:0% +Kohl's an anti trust case that went to +the same Supreme Court two years earlier + + align:start position:0% +the same Supreme Court two years earlier + + + align:start position:0% +the same Supreme Court two years earlier +and Appalachian Kohl's was an attempt by + + align:start position:0% +and Appalachian Kohl's was an attempt by + + + align:start position:0% +and Appalachian Kohl's was an attempt by +a group of coal + + align:start position:0% +a group of coal + + + align:start position:0% +a group of coal +miners they colluded they fixed the + + align:start position:0% +miners they colluded they fixed the + + + align:start position:0% +miners they colluded they fixed the +price they set a minimum price of coal + + align:start position:0% +price they set a minimum price of coal + + + align:start position:0% +price they set a minimum price of coal +which by all the Edy trust law precedent + + align:start position:0% +which by all the Edy trust law precedent + + + align:start position:0% +which by all the Edy trust law precedent +up to that point was just flat illegal + + align:start position:0% +up to that point was just flat illegal + + + align:start position:0% +up to that point was just flat illegal +was just no question about it go to jail + + align:start position:0% +was just no question about it go to jail + + + align:start position:0% +was just no question about it go to jail +well yeah go to jail illegal the Supreme + + align:start position:0% +well yeah go to jail illegal the Supreme + + + align:start position:0% +well yeah go to jail illegal the Supreme +Court managed to find it legal in one of + + align:start position:0% +Court managed to find it legal in one of + + + align:start position:0% +Court managed to find it legal in one of +the most bizarre opinions you'll ever + + align:start position:0% +the most bizarre opinions you'll ever + + + align:start position:0% +the most bizarre opinions you'll ever +read because it was the 30s it was coal + + align:start position:0% +read because it was the 30s it was coal + + + align:start position:0% +read because it was the 30s it was coal +miners these people were in terrible + + align:start position:0% +miners these people were in terrible + + + align:start position:0% +miners these people were in terrible +shape so you would say if it's such a + + align:start position:0% +shape so you would say if it's such a + + + align:start position:0% +shape so you would say if it's such a +terrible + + align:start position:0% +terrible + + + align:start position:0% +terrible +problem you there's clear clear popular + + align:start position:0% +problem you there's clear clear popular + + + align:start position:0% +problem you there's clear clear popular +will just do it forget about the + + align:start position:0% +will just do it forget about the + + + align:start position:0% +will just do it forget about the +Forbidden Place forget about the + + align:start position:0% +Forbidden Place forget about the + + + align:start position:0% +Forbidden Place forget about the +states + + align:start position:0% +states + + + align:start position:0% +states +okay we got that rebuttal te you've + + align:start position:0% +okay we got that rebuttal te you've + + + align:start position:0% +okay we got that rebuttal te you've +heard what they + + align:start position:0% +heard what they + + + align:start position:0% +heard what they +said the the power is as broad as the + + align:start position:0% +said the the power is as broad as the + + + align:start position:0% +said the the power is as broad as the +need that evokes it you're right in the + + align:start position:0% +need that evokes it you're right in the + + + align:start position:0% +need that evokes it you're right in the +middle remind me which team you're + + align:start position:0% +middle remind me which team you're + + + align:start position:0% +middle remind me which team you're +you're on okay um you're a right winger + + align:start position:0% +you're on okay um you're a right winger + + + align:start position:0% +you're on okay um you're a right winger +all right so I think that like so I + + align:start position:0% +all right so I think that like so I + + + align:start position:0% +all right so I think that like so I +personally probably agree with the + + align:start position:0% +personally probably agree with the + + + align:start position:0% +personally probably agree with the +statement that the coal miners were in + + align:start position:0% +statement that the coal miners were in + + + align:start position:0% +statement that the coal miners were in +horrible conditions and by putting it + + align:start position:0% +horrible conditions and by putting it + + + align:start position:0% +horrible conditions and by putting it +that to a vote you could pass it but I + + align:start position:0% +that to a vote you could pass it but I + + + align:start position:0% +that to a vote you could pass it but I +don't I think that southerland's + + align:start position:0% +don't I think that southerland's + + + align:start position:0% +don't I think that southerland's +position is yeah maybe that's true but + + align:start position:0% +position is yeah maybe that's true but + + + align:start position:0% +position is yeah maybe that's true but +in many Supreme Court cases the basis of + + align:start position:0% +in many Supreme Court cases the basis of + + + align:start position:0% +in many Supreme Court cases the basis of +the decision is what has been said in + + align:start position:0% +the decision is what has been said in + + + align:start position:0% +the decision is what has been said in +the past and so if you pass if you made + + align:start position:0% +the past and so if you pass if you made + + + align:start position:0% +the past and so if you pass if you made +this legal for this case then in future + + align:start position:0% +this legal for this case then in future + + + align:start position:0% +this legal for this case then in future +cases it would like you know baby steps + + align:start position:0% +cases it would like you know baby steps + + + align:start position:0% +cases it would like you know baby steps +to that um the government having full + + align:start position:0% +to that um the government having full + + + align:start position:0% +to that um the government having full +control over everything so maybe like it + + align:start position:0% +control over everything so maybe like it + + + align:start position:0% +control over everything so maybe like it +would have been right in that case but + + align:start position:0% +would have been right in that case but + + + align:start position:0% +would have been right in that case but +considering the big p picture you might + + align:start position:0% +considering the big p picture you might + + + align:start position:0% +considering the big p picture you might +be going down a road that you don't want + + align:start position:0% +be going down a road that you don't want + + + align:start position:0% +be going down a road that you don't want +to take any further and the reason you + + align:start position:0% +to take any further and the reason you + + + align:start position:0% +to take any further and the reason you +don't want to take it is because in + + align:start position:0% +don't want to take it is because in + + + align:start position:0% +don't want to take it is because in +1793 the Constitution was ratified by a + + align:start position:0% +1793 the Constitution was ratified by a + + + align:start position:0% +1793 the Constitution was ratified by a +bunch of guys in breaches and powdered + + align:start position:0% +bunch of guys in breaches and powdered + + + align:start position:0% +bunch of guys in breaches and powdered +wigs and because you don't want to + + align:start position:0% +wigs and because you don't want to + + + align:start position:0% +wigs and because you don't want to +disrespect the you know the different + + align:start position:0% +disrespect the you know the different + + + align:start position:0% +disrespect the you know the different +corporations own entrepreneurial + + align:start position:0% +corporations own entrepreneurial + + + align:start position:0% +corporations own entrepreneurial +creativity + + align:start position:0% +creativity + + + align:start position:0% +creativity +okay any answer from this side we're a + + align:start position:0% +okay any answer from this side we're a + + + align:start position:0% +okay any answer from this side we're a +little unbalanced here we've got a lot + + align:start position:0% +little unbalanced here we've got a lot + + + align:start position:0% +little unbalanced here we've got a lot +of Market lovers not a lot of Rory stand + + align:start position:0% +of Market lovers not a lot of Rory stand + + + align:start position:0% +of Market lovers not a lot of Rory stand +up for the + + align:start position:0% +up for the + + + align:start position:0% +up for the +uh the poor the poor suffering minors um + + align:start position:0% +uh the poor the poor suffering minors um + + + align:start position:0% +uh the poor the poor suffering minors um +well if you go back you've got a + + align:start position:0% +well if you go back you've got a + + + align:start position:0% +well if you go back you've got a +forbidden Place argument there a + + align:start position:0% +forbidden Place argument there a + + + align:start position:0% +forbidden Place argument there a +slippery slope take one step got to draw + + align:start position:0% +slippery slope take one step got to draw + + + align:start position:0% +slippery slope take one step got to draw +the line someplace we're going to draw + + align:start position:0% +the line someplace we're going to draw + + + align:start position:0% +the line someplace we're going to draw +it here for my very poor knowledge of + + align:start position:0% +it here for my very poor knowledge of + + + align:start position:0% +it here for my very poor knowledge of +the Constitution I think it like has + + align:start position:0% +the Constitution I think it like has + + + align:start position:0% +the Constitution I think it like has +Clauses on eminent domain and you could + + align:start position:0% +Clauses on eminent domain and you could + + + align:start position:0% +Clauses on eminent domain and you could +argue that the government at certain + + align:start position:0% +argue that the government at certain + + + align:start position:0% +argue that the government at certain +times has the right to take property + + align:start position:0% +times has the right to take property + + + align:start position:0% +times has the right to take property +from you and I think recently they even + + align:start position:0% +from you and I think recently they even + + + align:start position:0% +from you and I think recently they even +took it from private people to give to + + align:start position:0% +took it from private people to give to + + + align:start position:0% +took it from private people to give to +other private people and the Supreme + + align:start position:0% +other private people and the Supreme + + + align:start position:0% +other private people and the Supreme +Court said that was okay so things are + + align:start position:0% +Court said that was okay so things are + + + align:start position:0% +Court said that was okay so things are +different now than they were in 193 + + align:start position:0% +different now than they were in 193 + + + align:start position:0% +different now than they were in 193 +let me just say boy was that + + align:start position:0% +let me just say boy was that + + + align:start position:0% +let me just say boy was that +controversial okay so example would be + + align:start position:0% +controversial okay so example would be + + + align:start position:0% +controversial okay so example would be +police laws are pretty tyrannical in + + align:start position:0% +police laws are pretty tyrannical in + + + align:start position:0% +police laws are pretty tyrannical in +their own way but they're appropriate to + + align:start position:0% +their own way but they're appropriate to + + + align:start position:0% +their own way but they're appropriate to +the crime and so in the same way you + + align:start position:0% +the crime and so in the same way you + + + align:start position:0% +the crime and so in the same way you +could create tyranical laws in business + + align:start position:0% +could create tyranical laws in business + + + align:start position:0% +could create tyranical laws in business +if they're appropriate to the crime and + + align:start position:0% +if they're appropriate to the crime and + + + align:start position:0% +if they're appropriate to the crime and +that would come from Emin domain which I + + align:start position:0% +that would come from Emin domain which I + + + align:start position:0% +that would come from Emin domain which I +think is one of the early amendments em + + align:start position:0% +think is one of the early amendments em + + + align:start position:0% +think is one of the early amendments em +domain is a provision I'm not sure it's + + align:start position:0% +domain is a provision I'm not sure it's + + + align:start position:0% +domain is a provision I'm not sure it's +in the federal well I think it comes out + + align:start position:0% +in the federal well I think it comes out + + + align:start position:0% +in the federal well I think it comes out +of the common law it's the ability of a + + align:start position:0% +of the common law it's the ability of a + + + align:start position:0% +of the common law it's the ability of a +government to take property private + + align:start position:0% +government to take property private + + + align:start position:0% +government to take property private +property for public purpose and pay Fair + + align:start position:0% +property for public purpose and pay Fair + + + align:start position:0% +property for public purpose and pay Fair +compensation there is a fair + + align:start position:0% +compensation there is a fair + + + align:start position:0% +compensation there is a fair +compensation requirement um which is the + + align:start position:0% +compensation requirement um which is the + + + align:start position:0% +compensation requirement um which is the +only way you get power lines built or + + align:start position:0% +only way you get power lines built or + + + align:start position:0% +only way you get power lines built or +railroads or lots of other things you + + align:start position:0% +railroads or lots of other things you + + + align:start position:0% +railroads or lots of other things you +have you have to assemble Parcels yeah I + + align:start position:0% +have you have to assemble Parcels yeah I + + + align:start position:0% +have you have to assemble Parcels yeah I +think um fundament sorry I like been + + align:start position:0% +think um fundament sorry I like been + + + align:start position:0% +think um fundament sorry I like been +sick um fundamentally there is a + + align:start position:0% +sick um fundamentally there is a + + + align:start position:0% +sick um fundamentally there is a +tradeoff between yeah I think I'm + + align:start position:0% +tradeoff between yeah I think I'm + + + align:start position:0% +tradeoff between yeah I think I'm +getting better so I don't think I'm + + align:start position:0% +getting better so I don't think I'm + + + align:start position:0% +getting better so I don't think I'm +contagious anymore okay + + align:start position:0% +contagious anymore okay + + + align:start position:0% +contagious anymore okay +um fundamentally everybody now inhales + + align:start position:0% +um fundamentally everybody now inhales + + + align:start position:0% +um fundamentally everybody now inhales +go ahead um sorry there's always going + + align:start position:0% +go ahead um sorry there's always going + + + align:start position:0% +go ahead um sorry there's always going +to be a tradeoff between freedom and + + align:start position:0% +to be a tradeoff between freedom and + + + align:start position:0% +to be a tradeoff between freedom and +equality and I think that like all of + + align:start position:0% +equality and I think that like all of + + + align:start position:0% +equality and I think that like all of +this conversation is about where do you + + align:start position:0% +this conversation is about where do you + + + align:start position:0% +this conversation is about where do you +want to fall on that scale um personally + + align:start position:0% +want to fall on that scale um personally + + + align:start position:0% +want to fall on that scale um personally +and I think souland would agree that + + align:start position:0% +and I think souland would agree that + + + align:start position:0% +and I think souland would agree that +it's not okay to take away other + + align:start position:0% +it's not okay to take away other + + + align:start position:0% +it's not okay to take away other +people's freedoms to make them more + + align:start position:0% +people's freedoms to make them more + + + align:start position:0% +people's freedoms to make them more +equal you know it would be nice if in + + align:start position:0% +equal you know it would be nice if in + + + align:start position:0% +equal you know it would be nice if in +the whole world everyone was fine and + + align:start position:0% +the whole world everyone was fine and + + + align:start position:0% +the whole world everyone was fine and +had the same amount of money and it was + + align:start position:0% +had the same amount of money and it was + + + align:start position:0% +had the same amount of money and it was +immaterial because there was enough food + + align:start position:0% +immaterial because there was enough food + + + align:start position:0% +immaterial because there was enough food +and everyone had equal access but but + + align:start position:0% +and everyone had equal access but but + + + align:start position:0% +and everyone had equal access but but +that's not the case but that doesn't + + align:start position:0% +that's not the case but that doesn't + + + align:start position:0% +that's not the case but that doesn't +mean that you get to go around taking + + align:start position:0% +mean that you get to go around taking + + + align:start position:0% +mean that you get to go around taking +away people's freedoms and freedoms that + + align:start position:0% +away people's freedoms and freedoms that + + + align:start position:0% +away people's freedoms and freedoms that +have been guaranteed to them just to + + align:start position:0% +have been guaranteed to them just to + + + align:start position:0% +have been guaranteed to them just to +make other people better off you you + + align:start position:0% +make other people better off you you + + + align:start position:0% +make other people better off you you +point + + align:start position:0% +point + + + align:start position:0% +point +to um two different conceptions of + + align:start position:0% +to um two different conceptions of + + + align:start position:0% +to um two different conceptions of +Justice there's Justice in terms of fair + + align:start position:0% +Justice there's Justice in terms of fair + + + align:start position:0% +Justice there's Justice in terms of fair +outcomes and there's Justice in terms of + + align:start position:0% +outcomes and there's Justice in terms of + + + align:start position:0% +outcomes and there's Justice in terms of +fair + + align:start position:0% +fair + + + align:start position:0% +fair +process and if + + align:start position:0% +process and if + + + align:start position:0% +process and if +people they're fundamentally different + + align:start position:0% +people they're fundamentally different + + + align:start position:0% +people they're fundamentally different +Notions what you're saying is I don't + + align:start position:0% +Notions what you're saying is I don't + + + align:start position:0% +Notions what you're saying is I don't +want trample with a process that I think + + align:start position:0% +want trample with a process that I think + + + align:start position:0% +want trample with a process that I think +is fair in order to produce say more + + align:start position:0% +is fair in order to produce say more + + + align:start position:0% +is fair in order to produce say more +equality than that process would produce + + align:start position:0% +equality than that process would produce + + + align:start position:0% +equality than that process would produce +other people might say well I'm really + + align:start position:0% +other people might say well I'm really + + + align:start position:0% +other people might say well I'm really +concerned with inequality say in the + + align:start position:0% +concerned with inequality say in the + + + align:start position:0% +concerned with inequality say in the +United States today where inequality has + + align:start position:0% +United States today where inequality has + + + align:start position:0% +United States today where inequality has +been growing by any measure and I yeah + + align:start position:0% +been growing by any measure and I yeah + + + align:start position:0% +been growing by any measure and I yeah +maybe everything's competitive and + + align:start position:0% +maybe everything's competitive and + + + align:start position:0% +maybe everything's competitive and +everything's swell but I don't like that + + align:start position:0% +everything's swell but I don't like that + + + align:start position:0% +everything's swell but I don't like that +outcome so I'll I'll fiddle with it with + + align:start position:0% +outcome so I'll I'll fiddle with it with + + + align:start position:0% +outcome so I'll I'll fiddle with it with +taxes so I'm just saying there are these + + align:start position:0% +taxes so I'm just saying there are these + + + align:start position:0% +taxes so I'm just saying there are these +two different views I'm not saying + + align:start position:0% +two different views I'm not saying + + + align:start position:0% +two different views I'm not saying +either one's necessarily right you're + + align:start position:0% +either one's necessarily right you're + + + align:start position:0% +either one's necessarily right you're +more of a process person you like a fair + + align:start position:0% +more of a process person you like a fair + + + align:start position:0% +more of a process person you like a fair +process and the outcome of a fair + + align:start position:0% +process and the outcome of a fair + + + align:start position:0% +process and the outcome of a fair +process is fair others might say take + + align:start position:0% +process is fair others might say take + + + align:start position:0% +process is fair others might say take +executive salaries nobody's forcing + + align:start position:0% +executive salaries nobody's forcing + + + align:start position:0% +executive salaries nobody's forcing +Boards of directors to pay high salaries + + align:start position:0% +Boards of directors to pay high salaries + + + align:start position:0% +Boards of directors to pay high salaries +they're very high should we do something + + align:start position:0% +they're very high should we do something + + + align:start position:0% +they're very high should we do something +about it process people say no outcome + + align:start position:0% +about it process people say no outcome + + + align:start position:0% +about it process people say no outcome +people say + + align:start position:0% + + + + align:start position:0% + +yes thank + + align:start position:0% +yes thank + + + align:start position:0% +yes thank +you other + + align:start position:0% +you other + + + align:start position:0% +you other +comments yeah I think going back to what + + align:start position:0% +comments yeah I think going back to what + + + align:start position:0% +comments yeah I think going back to what +Rory said while I symp to the minors and + + align:start position:0% +Rory said while I symp to the minors and + + + align:start position:0% +Rory said while I symp to the minors and +I understand that it's difficult to be + + align:start position:0% +I understand that it's difficult to be + + + align:start position:0% +I understand that it's difficult to be +impoverished especially in impoverished + + align:start position:0% +impoverished especially in impoverished + + + align:start position:0% +impoverished especially in impoverished +States these tyrannical laws that TV is + + align:start position:0% +States these tyrannical laws that TV is + + + align:start position:0% +States these tyrannical laws that TV is +suggesting are still just a short-term + + align:start position:0% +suggesting are still just a short-term + + + align:start position:0% +suggesting are still just a short-term +solution and because the markets are + + align:start position:0% +solution and because the markets are + + + align:start position:0% +solution and because the markets are +self correcting and because both + + align:start position:0% +self correcting and because both + + + align:start position:0% +self correcting and because both +participants are voluntary in the end in + + align:start position:0% +participants are voluntary in the end in + + + align:start position:0% +participants are voluntary in the end in +the long term maybe after a few + + align:start position:0% +the long term maybe after a few + + + align:start position:0% +the long term maybe after a few +Generations everything will solve itself + + align:start position:0% +Generations everything will solve itself + + + align:start position:0% +Generations everything will solve itself +without these tyrannical laws that are + + align:start position:0% +without these tyrannical laws that are + + + align:start position:0% +without these tyrannical laws that are +just inappropriate in the situation + + align:start position:0% +just inappropriate in the situation + + + align:start position:0% +just inappropriate in the situation +minimum wage law is a tyrannical law + + align:start position:0% +minimum wage law is a tyrannical law + + + align:start position:0% +minimum wage law is a tyrannical law +Okie do I'm with you I'm with you I got + + align:start position:0% +Okie do I'm with you I'm with you I got + + + align:start position:0% +Okie do I'm with you I'm with you I got +it no no you play the role yeah um I'm + + align:start position:0% +it no no you play the role yeah um I'm + + + align:start position:0% +it no no you play the role yeah um I'm +kind of a right winger in enemy + + align:start position:0% +kind of a right winger in enemy + + + align:start position:0% +kind of a right winger in enemy +territory over here um but I'd say like + + align:start position:0% +territory over here um but I'd say like + + + align:start position:0% +territory over here um but I'd say like +I don't like really the idea of like the + + align:start position:0% +I don't like really the idea of like the + + + align:start position:0% +I don't like really the idea of like the +government you know ideologically being + + align:start position:0% +government you know ideologically being + + + align:start position:0% +government you know ideologically being +able to step on the toes of private + + align:start position:0% +able to step on the toes of private + + + align:start position:0% +able to step on the toes of private +Enterprise uh just the you know ideology + + align:start position:0% +Enterprise uh just the you know ideology + + + align:start position:0% +Enterprise uh just the you know ideology +of it but I mean I don't know if this is + + align:start position:0% +of it but I mean I don't know if this is + + + align:start position:0% +of it but I mean I don't know if this is +so much an opinion or hindsight + + align:start position:0% +so much an opinion or hindsight + + + align:start position:0% +so much an opinion or hindsight +suggestion but uh as far as the plight + + align:start position:0% +suggestion but uh as far as the plight + + + align:start position:0% +suggestion but uh as far as the plight +of the workers I mean they have just as + + align:start position:0% +of the workers I mean they have just as + + + align:start position:0% +of the workers I mean they have just as +much right to deny to work and so if + + align:start position:0% +much right to deny to work and so if + + + align:start position:0% +much right to deny to work and so if +you're the federal government I don't + + align:start position:0% +you're the federal government I don't + + + align:start position:0% +you're the federal government I don't +know how much you know union labor laws + + align:start position:0% +know how much you know union labor laws + + + align:start position:0% +know how much you know union labor laws +you can pass but I think you know Pro + + align:start position:0% +you can pass but I think you know Pro + + + align:start position:0% +you can pass but I think you know Pro +union labor laws for coal miners I think + + align:start position:0% +union labor laws for coal miners I think + + + align:start position:0% +union labor laws for coal miners I think +would be a more effective way if you + + align:start position:0% +would be a more effective way if you + + + align:start position:0% +would be a more effective way if you +wanted to do it without stepping on the + + align:start position:0% +wanted to do it without stepping on the + + + align:start position:0% +wanted to do it without stepping on the +toes of the Constitution or anything + + align:start position:0% +toes of the Constitution or anything + + + align:start position:0% +toes of the Constitution or anything +like that they in fact moved in that + + align:start position:0% +like that they in fact moved in that + + + align:start position:0% +like that they in fact moved in that +direction the Wagner Act and the + + align:start position:0% +direction the Wagner Act and the + + + align:start position:0% +direction the Wagner Act and the +National Labor Relations Act I believe + + align:start position:0% +National Labor Relations Act I believe + + + align:start position:0% +National Labor Relations Act I believe +came after this legislation which + + align:start position:0% +came after this legislation which + + + align:start position:0% +came after this legislation which +strengthened the ability of unions the + + align:start position:0% +strengthened the ability of unions the + + + align:start position:0% +strengthened the ability of unions the +the only thing since the left wing is + + align:start position:0% +the only thing since the left wing is + + + align:start position:0% +the only thing since the left wing is +being very timid over here the the only + + align:start position:0% +being very timid over here the the only + + + align:start position:0% +being very timid over here the the only +thing I would say is these little towns + + align:start position:0% +thing I would say is these little towns + + + align:start position:0% +thing I would say is these little towns +in West + + align:start position:0% +in West + + + align:start position:0% +in West +Virginia if you're a minor and the mind + + align:start position:0% +Virginia if you're a minor and the mind + + + align:start position:0% +Virginia if you're a minor and the mind +goes bust and you own a home it's + + align:start position:0% +goes bust and you own a home it's + + + align:start position:0% +goes bust and you own a home it's +worthless so you got no job and you've + + align:start position:0% +worthless so you got no job and you've + + + align:start position:0% +worthless so you got no job and you've +got no asset to sell to + + align:start position:0% +got no asset to sell to + + + align:start position:0% +got no asset to sell to +move yeah you can withhold your labor + + align:start position:0% +move yeah you can withhold your labor + + + align:start position:0% +move yeah you can withhold your labor +but I mean you don't have a lot of + + align:start position:0% +but I mean you don't have a lot of + + + align:start position:0% +but I mean you don't have a lot of +options it's not a frictionless it's not + + align:start position:0% +options it's not a frictionless it's not + + + align:start position:0% +options it's not a frictionless it's not +a frictionless plane um I I was involved + + align:start position:0% +a frictionless plane um I I was involved + + + align:start position:0% +a frictionless plane um I I was involved +in Washington in the uh Northern spotted + + align:start position:0% +in Washington in the uh Northern spotted + + + align:start position:0% +in Washington in the uh Northern spotted +owl debate in the around + + align:start position:0% +owl debate in the around + + + align:start position:0% +owl debate in the around +1990 and the issue there one of the + + align:start position:0% +1990 and the issue there one of the + + + align:start position:0% +1990 and the issue there one of the +factors in that debate turned on people + + align:start position:0% +factors in that debate turned on people + + + align:start position:0% +factors in that debate turned on people +in small town in Oregon who made their + + align:start position:0% +in small town in Oregon who made their + + + align:start position:0% +in small town in Oregon who made their +living cutting down + + align:start position:0% +living cutting down + + + align:start position:0% +living cutting down +trees if you regulated + + align:start position:0% +trees if you regulated + + + align:start position:0% +trees if you regulated +logging sharply they had worthless homes + + align:start position:0% +logging sharply they had worthless homes + + + align:start position:0% +logging sharply they had worthless homes +and their skill was cutting down trees + + align:start position:0% +and their skill was cutting down trees + + + align:start position:0% +and their skill was cutting down trees +and they got no place to go so unless + + align:start position:0% +and they got no place to go so unless + + + align:start position:0% +and they got no place to go so unless +you did something to compensate + + align:start position:0% +you did something to compensate + + + align:start position:0% +you did something to compensate +them uh for that situation that was a + + align:start position:0% +them uh for that situation that was a + + + align:start position:0% +them uh for that situation that was a +case where it was government regulation + + align:start position:0% +case where it was government regulation + + + align:start position:0% +case where it was government regulation +but it could easily have been a market + + align:start position:0% +but it could easily have been a market + + + align:start position:0% +but it could easily have been a market +they're just stuck and you get + + align:start position:0% +they're just stuck and you get + + + align:start position:0% +they're just stuck and you get +alcoholism child abuse and spousal abuse + + align:start position:0% +alcoholism child abuse and spousal abuse + + + align:start position:0% +alcoholism child abuse and spousal abuse +and all of the things that happen when + + align:start position:0% +and all of the things that happen when + + + align:start position:0% +and all of the things that happen when +communities break down so it's not it's + + align:start position:0% +communities break down so it's not it's + + + align:start position:0% +communities break down so it's not it's +not pretty I'm trying to help the left + + align:start position:0% +not pretty I'm trying to help the left + + + align:start position:0% +not pretty I'm trying to help the left +over here with a little tear jerking + + align:start position:0% +over here with a little tear jerking + + + align:start position:0% +over here with a little tear jerking +argument but uh + + align:start position:0% +argument but uh + + + align:start position:0% +argument but uh +yeah I was say just for the leftwing + + align:start position:0% +yeah I was say just for the leftwing + + + align:start position:0% +yeah I was say just for the leftwing +side I was going to say back into the + + align:start position:0% +side I was going to say back into the + + + align:start position:0% +side I was going to say back into the +argument that you know electricity does + + align:start position:0% +argument that you know electricity does + + + align:start position:0% +argument that you know electricity does +cross Interstate lines so Congress does + + align:start position:0% +cross Interstate lines so Congress does + + + align:start position:0% +cross Interstate lines so Congress does +have the power to regulate this laws + + align:start position:0% +have the power to regulate this laws + + + align:start position:0% +have the power to regulate this laws +regardless of you know how ideologically + + align:start position:0% +regardless of you know how ideologically + + + align:start position:0% +regardless of you know how ideologically +you feel about it constitutionally you + + align:start position:0% +you feel about it constitutionally you + + + align:start position:0% +you feel about it constitutionally you +know this should be allowed so You' say + + align:start position:0% +know this should be allowed so You' say + + + align:start position:0% +know this should be allowed so You' say +that this whole direct indirect thing + + align:start position:0% +that this whole direct indirect thing + + + align:start position:0% +that this whole direct indirect thing +that Southerland was writing uh which he + + align:start position:0% +that Southerland was writing uh which he + + + align:start position:0% +that Southerland was writing uh which he +couldn't Define other than to Mush + + align:start position:0% +couldn't Define other than to Mush + + + align:start position:0% +couldn't Define other than to Mush +around for a couple Pages uh is really + + align:start position:0% +around for a couple Pages uh is really + + + align:start position:0% +around for a couple Pages uh is really +not a distinction that if it affects it + + align:start position:0% +not a distinction that if it affects it + + + align:start position:0% +not a distinction that if it affects it +affects and there's no direct indirect + + align:start position:0% +affects and there's no direct indirect + + + align:start position:0% +affects and there's no direct indirect +sensible distinction and wages affect + + align:start position:0% +sensible distinction and wages affect + + + align:start position:0% +sensible distinction and wages affect +prices of coal yeah um sir I'm like Fair + + align:start position:0% +prices of coal yeah um sir I'm like Fair + + + align:start position:0% +prices of coal yeah um sir I'm like Fair +believer in the market but I'm sitting + + align:start position:0% +believer in the market but I'm sitting + + + align:start position:0% +believer in the market but I'm sitting +on this side so I figured I'd job yeah + + align:start position:0% +on this side so I figured I'd job yeah + + + align:start position:0% +on this side so I figured I'd job yeah +um and it was pertaining to the um to + + align:start position:0% +um and it was pertaining to the um to + + + align:start position:0% +um and it was pertaining to the um to +having a fair process and uh I mean I + + align:start position:0% +having a fair process and uh I mean I + + + align:start position:0% +having a fair process and uh I mean I +believe in a fair process but it's uh + + align:start position:0% +believe in a fair process but it's uh + + + align:start position:0% +believe in a fair process but it's uh +it's always like the uh kind of + + align:start position:0% +it's always like the uh kind of + + + align:start position:0% +it's always like the uh kind of +recursive uh nature in the sense that + + align:start position:0% +recursive uh nature in the sense that + + + align:start position:0% +recursive uh nature in the sense that +you have to establish a fair playground + + align:start position:0% +you have to establish a fair playground + + + align:start position:0% +you have to establish a fair playground +in order for the outcome of a fair + + align:start position:0% +in order for the outcome of a fair + + + align:start position:0% +in order for the outcome of a fair +process to be fair and perhaps in this + + align:start position:0% +process to be fair and perhaps in this + + + align:start position:0% +process to be fair and perhaps in this +case when shit's hitting the fan you + + align:start position:0% +case when shit's hitting the fan you + + + align:start position:0% +case when shit's hitting the fan you +really need to try and you know have the + + align:start position:0% +really need to try and you know have the + + + align:start position:0% +really need to try and you know have the +government interfere and create somewhat + + align:start position:0% +government interfere and create somewhat + + + align:start position:0% +government interfere and create somewhat +equality so that the process is then + + align:start position:0% +equality so that the process is then + + + align:start position:0% +equality so that the process is then +fair and from then on you can then say + + align:start position:0% +fair and from then on you can then say + + + align:start position:0% +fair and from then on you can then say +well you know we've allowed everyone + + align:start position:0% +well you know we've allowed everyone + + + align:start position:0% +well you know we've allowed everyone +with the same or we tried to give + + align:start position:0% +with the same or we tried to give + + + align:start position:0% +with the same or we tried to give +everyone the same kind of benefits or + + align:start position:0% +everyone the same kind of benefits or + + + align:start position:0% +everyone the same kind of benefits or +the same opportunities and from here + + align:start position:0% +the same opportunities and from here + + + align:start position:0% +the same opportunities and from here +whoever takes it well you know is then a + + align:start position:0% +whoever takes it well you know is then a + + + align:start position:0% +whoever takes it well you know is then a +CEO and is making money and who who + + align:start position:0% +CEO and is making money and who who + + + align:start position:0% +CEO and is making money and who who +doesn't is and what are the folks on + + align:start position:0% +doesn't is and what are the folks on + + + align:start position:0% +doesn't is and what are the folks on +this side say in response to that + + align:start position:0% +this side say in response to that + + + align:start position:0% +this side say in response to that +somebody who hasn't spoken Max I think + + align:start position:0% +somebody who hasn't spoken Max I think + + + align:start position:0% +somebody who hasn't spoken Max I think +it's a big issue with conflict of + + align:start position:0% +it's a big issue with conflict of + + + align:start position:0% +it's a big issue with conflict of +interest um + + align:start position:0% +interest um + + + align:start position:0% +interest um +in this situation you have a government + + align:start position:0% +in this situation you have a government + + + align:start position:0% +in this situation you have a government +that may have been trying to act in uh + + align:start position:0% +that may have been trying to act in uh + + + align:start position:0% +that may have been trying to act in uh +in the interest of workers in labor + + align:start position:0% +in the interest of workers in labor + + + align:start position:0% +in the interest of workers in labor +rights uh things of that nature but that + + align:start position:0% +rights uh things of that nature but that + + + align:start position:0% +rights uh things of that nature but that +might not always be the case we've been + + align:start position:0% +might not always be the case we've been + + + align:start position:0% +might not always be the case we've been +looking at the government as kind of + + align:start position:0% +looking at the government as kind of + + + align:start position:0% +looking at the government as kind of +this uh benevolent power that's trying + + align:start position:0% +this uh benevolent power that's trying + + + align:start position:0% +this uh benevolent power that's trying +to improve workers rights but in the + + align:start position:0% +to improve workers rights but in the + + + align:start position:0% +to improve workers rights but in the +future you have all these uh congressmen + + align:start position:0% +future you have all these uh congressmen + + + align:start position:0% +future you have all these uh congressmen +from different states and legislation + + align:start position:0% +from different states and legislation + + + align:start position:0% +from different states and legislation +passed might not be in the interest of + + align:start position:0% +passed might not be in the interest of + + + align:start position:0% +passed might not be in the interest of +one state it might be in the interest of + + align:start position:0% +one state it might be in the interest of + + + align:start position:0% +one state it might be in the interest of +another state and if there's a majority + + align:start position:0% +another state and if there's a majority + + + align:start position:0% +another state and if there's a majority +you end up affecting one state the + + align:start position:0% +you end up affecting one state the + + + align:start position:0% +you end up affecting one state the +interest of many others and so that's + + align:start position:0% +interest of many others and so that's + + + align:start position:0% +interest of many others and so that's +where the if it doesn't affect + + align:start position:0% +where the if it doesn't affect + + + align:start position:0% +where the if it doesn't affect +interstate commerce and in this case the + + align:start position:0% +interstate commerce and in this case the + + + align:start position:0% +interstate commerce and in this case the +argument was that production does not + + align:start position:0% +argument was that production does not + + + align:start position:0% +argument was that production does not +affect interstate commerce the federal + + align:start position:0% +affect interstate commerce the federal + + + align:start position:0% +affect interstate commerce the federal +government shouldn't have shouldn't have + + align:start position:0% +government shouldn't have shouldn't have + + + align:start position:0% +government shouldn't have shouldn't have +the power to regulate it because of that + + align:start position:0% +the power to regulate it because of that + + + align:start position:0% +the power to regulate it because of that +conflict of interest so you think we + + align:start position:0% +conflict of interest so you think we + + + align:start position:0% +conflict of interest so you think we +draw a simple clear bright line there's + + align:start position:0% +draw a simple clear bright line there's + + + align:start position:0% +draw a simple clear bright line there's +a lot of good stuff on the other side of + + align:start position:0% +a lot of good stuff on the other side of + + + align:start position:0% +a lot of good stuff on the other side of +that line but there's a lot of bad stuff + + align:start position:0% +that line but there's a lot of bad stuff + + + align:start position:0% +that line but there's a lot of bad stuff +there's a The southerland's Forbidden + + align:start position:0% +there's a The southerland's Forbidden + + + align:start position:0% +there's a The southerland's Forbidden +places on that on that side I think one + + align:start position:0% +places on that on that side I think one + + + align:start position:0% +places on that on that side I think one +of the comments was the necessary evil + + align:start position:0% +of the comments was the necessary evil + + + align:start position:0% +of the comments was the necessary evil +of an open market where while the + + align:start position:0% +of an open market where while the + + + align:start position:0% +of an open market where while the +government has to accept that there are + + align:start position:0% +government has to accept that there are + + + align:start position:0% +government has to accept that there are +some evils maybe uh unfair labor + + align:start position:0% +some evils maybe uh unfair labor + + + align:start position:0% +some evils maybe uh unfair labor +standards that they can't deal with but + + align:start position:0% +standards that they can't deal with but + + + align:start position:0% +standards that they can't deal with but +to have a truly fair and open market you + + align:start position:0% +to have a truly fair and open market you + + + align:start position:0% +to have a truly fair and open market you +need to let those evils exist and let + + align:start position:0% +need to let those evils exist and let + + + align:start position:0% +need to let those evils exist and let +the states deal with them if they think + + align:start position:0% +the states deal with them if they think + + + align:start position:0% +the states deal with them if they think +it's proper and if I were Southerland I + + align:start position:0% +it's proper and if I were Southerland I + + + align:start position:0% +it's proper and if I were Southerland I +might say look uh today it's the poor + + align:start position:0% +might say look uh today it's the poor + + + align:start position:0% +might say look uh today it's the poor +the poor coal miners tomorrow it's the + + align:start position:0% +the poor coal miners tomorrow it's the + + + align:start position:0% +the poor coal miners tomorrow it's the +poor investment bankers and and the we + + align:start position:0% +poor investment bankers and and the we + + + align:start position:0% +poor investment bankers and and the we +get votes in Congress God knows how that + + align:start position:0% +get votes in Congress God knows how that + + + align:start position:0% +get votes in Congress God knows how that +investment bankers wages are too low and + + align:start position:0% +investment bankers wages are too low and + + + align:start position:0% +investment bankers wages are too low and +they need to be increased and if you let + + align:start position:0% +they need to be increased and if you let + + + align:start position:0% +they need to be increased and if you let +me fix a wage for coal miners I'll fix a + + align:start position:0% +me fix a wage for coal miners I'll fix a + + + align:start position:0% +me fix a wage for coal miners I'll fix a +wage for investment bankers tomorrow and + + align:start position:0% +wage for investment bankers tomorrow and + + + align:start position:0% +wage for investment bankers tomorrow and +we know that's nuts and we need a wall + + align:start position:0% +we know that's nuts and we need a wall + + + align:start position:0% +we know that's nuts and we need a wall +okay let me let me bring it to a close + + align:start position:0% +okay let me let me bring it to a close + + + align:start position:0% +okay let me let me bring it to a close +thank you all this was good you aired a + + align:start position:0% +thank you all this was good you aired a + + + align:start position:0% +thank you all this was good you aired a +lot of the a lot of the main issues um + + align:start position:0% +lot of the a lot of the main issues um + + + align:start position:0% +lot of the a lot of the main issues um +let me just tell you what happened uh + + align:start position:0% +let me just tell you what happened uh + + + align:start position:0% +let me just tell you what happened uh +after this Roosevelt found this string + + align:start position:0% +after this Roosevelt found this string + + + align:start position:0% +after this Roosevelt found this string +of defeats this was just another defeat + + align:start position:0% +of defeats this was just another defeat + + + align:start position:0% +of defeats this was just another defeat +for the New Deal very frustrating and in + + align:start position:0% +for the New Deal very frustrating and in + + + align:start position:0% +for the New Deal very frustrating and in + + align:start position:0% + + + align:start position:0% +7 he issued a bill which would have let + + align:start position:0% +7 he issued a bill which would have let + + + align:start position:0% +7 he issued a bill which would have let +him appoint more justices to the Supreme + + align:start position:0% +him appoint more justices to the Supreme + + + align:start position:0% +him appoint more justices to the Supreme +Court the so-called Court packing bill + + align:start position:0% +Court the so-called Court packing bill + + + align:start position:0% +Court the so-called Court packing bill +um in February uh two months later the + + align:start position:0% +um in February uh two months later the + + + align:start position:0% +um in February uh two months later the +court reversed itself on the federal + + align:start position:0% +court reversed itself on the federal + + + align:start position:0% +court reversed itself on the federal +government's ability to to regulate + + align:start position:0% +government's ability to to regulate + + + align:start position:0% +government's ability to to regulate +wages one judge switched Carter versus + + align:start position:0% +wages one judge switched Carter versus + + + align:start position:0% +wages one judge switched Carter versus +Carter Cole was a 5 to4 decision um in + + align:start position:0% +Carter Cole was a 5 to4 decision um in + + + align:start position:0% +Carter Cole was a 5 to4 decision um in +1937 they switched this was referred to + + align:start position:0% +1937 they switched this was referred to + + + align:start position:0% +1937 they switched this was referred to +as the switch in time that saved nine + + align:start position:0% +as the switch in time that saved nine + + + align:start position:0% +as the switch in time that saved nine +nine justices in the Supreme Court + + align:start position:0% +nine justices in the Supreme Court + + + align:start position:0% +nine justices in the Supreme Court +clever language the court says however + + align:start position:0% +clever language the court says however + + + align:start position:0% +clever language the court says however +they'd taken the vote earlier um this + + align:start position:0% +they'd taken the vote earlier um this + + + align:start position:0% +they'd taken the vote earlier um this +the bill died in any case in the senate + + align:start position:0% +the bill died in any case in the senate + + + align:start position:0% +the bill died in any case in the senate +in July which is why we still have nine + + align:start position:0% +in July which is why we still have nine + + + align:start position:0% +in July which is why we still have nine +justices on the Supreme Court + + align:start position:0% +justices on the Supreme Court + + + align:start position:0% +justices on the Supreme Court +um who has won historically southernland + + align:start position:0% +um who has won historically southernland + + + align:start position:0% +um who has won historically southernland +or + + align:start position:0% + + + + align:start position:0% + +cardoo cardoo do we have a federal + + align:start position:0% +cardoo cardoo do we have a federal + + + align:start position:0% +cardoo cardoo do we have a federal +minimum wage yeah yes + + align:start position:0% +minimum wage yeah yes + + + align:start position:0% +minimum wage yeah yes +Scott because the minimum + + align:start position:0% + + + + align:start position:0% + +W but but the the fundamental question + + align:start position:0% +W but but the the fundamental question + + + align:start position:0% +W but but the the fundamental question +of does the Commerce Clause stop that + + align:start position:0% +of does the Commerce Clause stop that + + + align:start position:0% +of does the Commerce Clause stop that +fundamental question stop the federal + + align:start position:0% +fundamental question stop the federal + + + align:start position:0% +fundamental question stop the federal +government from regulating things that + + align:start position:0% +government from regulating things that + + + align:start position:0% +government from regulating things that +occur inside States like paying wages or + + align:start position:0% +occur inside States like paying wages or + + + align:start position:0% +occur inside States like paying wages or +setting safety conditions for this room + + align:start position:0% +setting safety conditions for this room + + + align:start position:0% +setting safety conditions for this room +or lots of other things cardoo one + + align:start position:0% + + + + align:start position:0% + +uh the the view at least until + + align:start position:0% +uh the the view at least until + + + align:start position:0% +uh the the view at least until +recently was that if you could find an + + align:start position:0% +recently was that if you could find an + + + align:start position:0% +recently was that if you could find an +impact on interstate commerce the + + align:start position:0% +impact on interstate commerce the + + + align:start position:0% +impact on interstate commerce the +federal government could regulate + + align:start position:0% +federal government could regulate + + + align:start position:0% +federal government could regulate +it that's disputed now and we have a + + align:start position:0% +it that's disputed now and we have a + + + align:start position:0% +it that's disputed now and we have a +supreme court that is tilting the other + + align:start position:0% +supreme court that is tilting the other + + + align:start position:0% +supreme court that is tilting the other +direction but the Run of + + align:start position:0% +direction but the Run of + + + align:start position:0% +direction but the Run of +decisions from the 30s forward has + + align:start position:0% +decisions from the 30s forward has + + + align:start position:0% +decisions from the 30s forward has +largely been in cardozo's Direction at + + align:start position:0% +largely been in cardozo's Direction at + + + align:start position:0% +largely been in cardozo's Direction at +least as regards the Commerce + + align:start position:0% +least as regards the Commerce + + + align:start position:0% +least as regards the Commerce +Clause um + + align:start position:0% +Clause um + + + align:start position:0% +Clause um +but issues like this don't get settled + + align:start position:0% +but issues like this don't get settled + + + align:start position:0% +but issues like this don't get settled +permanently the pendulum may swing + + align:start position:0% +permanently the pendulum may swing + + + align:start position:0% +permanently the pendulum may swing +there's a lot more concern with State's + + align:start position:0% +there's a lot more concern with State's + + + align:start position:0% +there's a lot more concern with State's +rights and as I say to actually say the + + align:start position:0% +rights and as I say to actually say the + + + align:start position:0% +rights and as I say to actually say the +federal government should just fix the + + align:start position:0% +federal government should just fix the + + + align:start position:0% +federal government should just fix the +Electric + + align:start position:0% +Electric + + + align:start position:0% +Electric +System is to get laughed out of town + + align:start position:0% +System is to get laughed out of town + + + align:start position:0% +System is to get laughed out of town +it's it's a state function full + + align:start position:0% +it's it's a state function full + + + align:start position:0% +it's it's a state function full +stop okay I think we've covered what + + align:start position:0% +stop okay I think we've covered what + + + align:start position:0% +stop okay I think we've covered what +there was to cover questions comments + + align:start position:0% + + + + align:start position:0% + +reactions thank you I'll see you all + + align:start position:0% +reactions thank you I'll see you all + + + align:start position:0% +reactions thank you I'll see you all +tomorrow believe it or not \ No newline at end of file diff --git a/LuJFPVY1Nzo.txt b/LuJFPVY1Nzo.txt new file mode 100644 index 0000000000000000000000000000000000000000..1411abe0ea528593ea0933f30e12850a8849c8c7 --- /dev/null +++ b/LuJFPVY1Nzo.txt @@ -0,0 +1,15971 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu I presume everyone has an + + align:start position:0% +ocw.mit.edu I presume everyone has an + + + align:start position:0% +ocw.mit.edu I presume everyone has an +urgent question to ask + + align:start position:0% + + + + align:start position:0% + +maybe I'll have to point to + + align:start position:0% +maybe I'll have to point to + + + align:start position:0% +maybe I'll have to point to +someone + + align:start position:0% +someone + + + align:start position:0% +someone +there oh good + + align:start position:0% +there oh good + + + align:start position:0% +there oh good +so that's exactly what said but you said + + align:start position:0% +so that's exactly what said but you said + + + align:start position:0% +so that's exactly what said but you said +that maybe like the G light are + + align:start position:0% +that maybe like the G light are + + + align:start position:0% +that maybe like the G light are +associated to the Gia cell is that + + align:start position:0% +associated to the Gia cell is that + + + align:start position:0% +associated to the Gia cell is that +right oh I don't want to speculate on + + align:start position:0% +right oh I don't want to speculate on + + + align:start position:0% +right oh I don't want to speculate on +how the brain + + align:start position:0% +how the brain + + + align:start position:0% +how the brain +works because + + align:start position:0% + + + + align:start position:0% + +because there's this huge community of + + align:start position:0% +because there's this huge community of + + + align:start position:0% +because there's this huge community of +neuroscientists who write papers + + align:start position:0% +neuroscientists who write papers + + + align:start position:0% +neuroscientists who write papers +about they're very strange papers + + align:start position:0% +about they're very strange papers + + + align:start position:0% +about they're very strange papers +because they talk about how maybe it's + + align:start position:0% +because they talk about how maybe it's + + + align:start position:0% +because they talk about how maybe it's +not the neuron and I just downloaded a + + align:start position:0% +not the neuron and I just downloaded a + + + align:start position:0% +not the neuron and I just downloaded a +long paper by someone whose name I won't + + align:start position:0% +long paper by someone whose name I won't + + + align:start position:0% +long paper by someone whose name I won't +mention about the idea that a typical + + align:start position:0% +mention about the idea that a typical + + + align:start position:0% +mention about the idea that a typical +neuron has 100,000 connections and so + + align:start position:0% +neuron has 100,000 connections and so + + + align:start position:0% +neuron has 100,000 connections and so +some something awesomely important must + + align:start position:0% +some something awesomely important must + + + align:start position:0% +some something awesomely important must +go on inside the neuron's body and it's + + align:start position:0% +go on inside the neuron's body and it's + + + align:start position:0% +go on inside the neuron's body and it's +got all these little fibers and things + + align:start position:0% +got all these little fibers and things + + + align:start position:0% +got all these little fibers and things +and presumably if it's dealing with + + align:start position:0% +and presumably if it's dealing with + + + align:start position:0% +and presumably if it's dealing with +100,000 signals or something then it + + align:start position:0% +100,000 signals or something then it + + + align:start position:0% +100,000 signals or something then it +must be very complicated so maybe the + + align:start position:0% +must be very complicated so maybe the + + + align:start position:0% +must be very complicated so maybe the +neuron isn't smart enough to do that so + + align:start position:0% +neuron isn't smart enough to do that so + + + align:start position:0% +neuron isn't smart enough to do that so +maybe the other cells nearby that + + align:start position:0% +maybe the other cells nearby that + + + align:start position:0% +maybe the other cells nearby that +support the neurons and feed them and + + align:start position:0% +support the neurons and feed them and + + + align:start position:0% +support the neurons and feed them and +send chemicals to and fro around their + + align:start position:0% +send chemicals to and fro around their + + + align:start position:0% +send chemicals to and fro around their +have some something to do with it how + + align:start position:0% +have some something to do with it how + + + align:start position:0% +have some something to do with it how +many of you have read such + + align:start position:0% +many of you have read such + + + align:start position:0% +many of you have read such +articles uh it's a very strange + + align:start position:0% +articles uh it's a very strange + + + align:start position:0% +articles uh it's a very strange +Community + + align:start position:0% +Community + + + align:start position:0% +Community +because + + align:start position:0% +because + + + align:start position:0% +because +um I think the problem is that + + align:start position:0% +um I think the problem is that + + + align:start position:0% +um I think the problem is that +history of that + + align:start position:0% + + + + align:start position:0% + +science + + align:start position:0% +science + + + align:start position:0% +science +started first there was the it was + + align:start position:0% +started first there was the it was + + + align:start position:0% +started first there was the it was +generally thought that all the neurons + + align:start position:0% +generally thought that all the neurons + + + align:start position:0% +generally thought that all the neurons +were connected and then around + + align:start position:0% + + + + align:start position:0% + +1890 was the first clear idea that nerve + + align:start position:0% +1890 was the first clear idea that nerve + + + align:start position:0% +1890 was the first clear idea that nerve +cells weren't arranged in a continuous + + align:start position:0% +cells weren't arranged in a continuous + + + align:start position:0% +cells weren't arranged in a continuous +network uh I think it was generally + + align:start position:0% +network uh I think it was generally + + + align:start position:0% +network uh I think it was generally +believed that they were all connected to + + align:start position:0% +believed that they were all connected to + + + align:start position:0% +believed that they were all connected to +each other because as far as you could + + align:start position:0% +each other because as far as you could + + + align:start position:0% +each other because as far as you could +tell with the microscopes of the + + align:start position:0% +tell with the microscopes of the + + + align:start position:0% +tell with the microscopes of the +time + + align:start position:0% + + + + align:start position:0% + +um um didn't show enough and + + align:start position:0% +um um didn't show enough and + + + align:start position:0% +um um didn't show enough and +then the hypothesis that the neurons are + + align:start position:0% +then the hypothesis that the neurons are + + + align:start position:0% +then the hypothesis that the neurons are +separate and there are little gaps + + align:start position:0% +separate and there are little gaps + + + align:start position:0% +separate and there are little gaps +called synapses as far as I can tell uh + + align:start position:0% +called synapses as far as I can tell uh + + + align:start position:0% +called synapses as far as I can tell uh +started around the + + align:start position:0% +started around the + + + align:start position:0% +started around the +1890s + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +um from then on as far as I can + + align:start position:0% +um from then on as far as I can + + + align:start position:0% +um from then on as far as I can +see neurology and psychology became more + + align:start position:0% +see neurology and psychology became more + + + align:start position:0% +see neurology and psychology became more +and more separate and the + + align:start position:0% +and more separate and the + + + align:start position:0% +and more separate and the +uh neurologists got obsessed with + + align:start position:0% +uh neurologists got obsessed with + + + align:start position:0% +uh neurologists got obsessed with +chemicals hormones epinephrine and uh + + align:start position:0% +chemicals hormones epinephrine and uh + + + align:start position:0% +chemicals hormones epinephrine and uh +there are about a + + align:start position:0% +there are about a + + + align:start position:0% +there are about a +dozen chemicals involved that gets that + + align:start position:0% +dozen chemicals involved that gets that + + + align:start position:0% +dozen chemicals involved that gets that +you can detect when parts of the brain + + align:start position:0% +you can detect when parts of the brain + + + align:start position:0% +you can detect when parts of the brain +are + + align:start position:0% +are + + + align:start position:0% +are +activated and so uh a whole bunch of + + align:start position:0% +activated and so uh a whole bunch of + + + align:start position:0% +activated and so uh a whole bunch of +folklore grew up over the about the + + align:start position:0% +folklore grew up over the about the + + + align:start position:0% +folklore grew up over the about the +roles of these chemicals and one fot of + + align:start position:0% +roles of these chemicals and one fot of + + + align:start position:0% +roles of these chemicals and one fot of +some chemical as inhibitory and + + align:start position:0% +some chemical as inhibitory and + + + align:start position:0% +some chemical as inhibitory and +excitatory and that idea still spreads + + align:start position:0% +excitatory and that idea still spreads + + + align:start position:0% +excitatory and that idea still spreads +although uh what we know about the + + align:start position:0% +although uh what we know about the + + + align:start position:0% +although uh what we know about the +nervous system now and I think I + + align:start position:0% +nervous system now and I think I + + + align:start position:0% +nervous system now and I think I +mentioned this before is that in general + + align:start position:0% +mentioned this before is that in general + + + align:start position:0% +mentioned this before is that in general +if you trace a neural pathway from one + + align:start position:0% +if you trace a neural pathway from one + + + align:start position:0% +if you trace a neural pathway from one +part of the brain to + + align:start position:0% +part of the brain to + + + align:start position:0% +part of the brain to +another what happens is that the + + align:start position:0% +another what happens is that the + + + align:start position:0% +another what happens is that the +connections tend to alternate not always + + align:start position:0% +connections tend to alternate not always + + + align:start position:0% +connections tend to alternate not always +but frequently so that this connection + + align:start position:0% +but frequently so that this connection + + + align:start position:0% +but frequently so that this connection +might inhibit this neuron and then you + + align:start position:0% +might inhibit this neuron and then you + + + align:start position:0% +might inhibit this neuron and then you +look at the output of that neuron and + + align:start position:0% +look at the output of that neuron and + + + align:start position:0% +look at the output of that neuron and +that might tend to excite neurons in the + + align:start position:0% +that might tend to excite neurons in the + + + align:start position:0% +that might tend to excite neurons in the +next brain Center and uh then most of + + align:start position:0% +next brain Center and uh then most of + + + align:start position:0% +next brain Center and uh then most of +those cells will tend to + + align:start position:0% +those cells will tend to + + + align:start position:0% +those cells will tend to +inhibit uh I mean each brain Center gets + + align:start position:0% +inhibit uh I mean each brain Center gets + + + align:start position:0% +inhibit uh I mean each brain Center gets +inputs from several others and so it's + + align:start position:0% +inputs from several others and so it's + + + align:start position:0% +inputs from several others and so it's +not that a brain Center is excitatory or + + align:start position:0% +not that a brain Center is excitatory or + + + align:start position:0% +not that a brain Center is excitatory or +inhibitory but the connections from one + + align:start position:0% +inhibitory but the connections from one + + + align:start position:0% +inhibitory but the connections from one +brain Center to another tend to have + + align:start position:0% +brain Center to another tend to have + + + align:start position:0% +brain Center to another tend to have +this effect and that's probably + + align:start position:0% +this effect and that's probably + + + align:start position:0% +this effect and that's probably +uh necessary from A System's Dynamic + + align:start position:0% +uh necessary from A System's Dynamic + + + align:start position:0% +uh necessary from A System's Dynamic +point of view because if all neurons + + align:start position:0% +point of view because if all neurons + + + align:start position:0% +point of view because if all neurons +tended to either do nothing or excite + + align:start position:0% +tended to either do nothing or excite + + + align:start position:0% +tended to either do nothing or excite +the next brain Center then what would + + align:start position:0% +the next brain Center then what would + + + align:start position:0% +the next brain Center then what would +happen uh as soon as you got a certain + + align:start position:0% +happen uh as soon as you got a certain + + + align:start position:0% +happen uh as soon as you got a certain +level of excitement then more and more + + align:start position:0% +level of excitement then more and more + + + align:start position:0% +level of excitement then more and more +brain centers would get activated and + + align:start position:0% +brain centers would get activated and + + + align:start position:0% +brain centers would get activated and +the whole thing would explode and that's + + align:start position:0% +the whole thing would explode and that's + + + align:start position:0% +the whole thing would explode and that's +more or less what happens in an + + align:start position:0% +more or less what happens in an + + + align:start position:0% +more or less what happens in an +epileptic seizure where if you get + + align:start position:0% +epileptic seizure where if you get + + + align:start position:0% +epileptic seizure where if you get +enough electrical and chemical activity + + align:start position:0% +enough electrical and chemical activity + + + align:start position:0% +enough electrical and chemical activity +of one kind or another mostly electrical + + align:start position:0% +of one kind or another mostly electrical + + + align:start position:0% +of one kind or another mostly electrical +I think but I don't know uh then whole + + align:start position:0% +I think but I don't know uh then whole + + + align:start position:0% +I think but I don't know uh then whole +large parts of the brain start to Fire + + align:start position:0% +large parts of the brain start to Fire + + + align:start position:0% +large parts of the brain start to Fire +synchronously and the thing spreads like + + align:start position:0% +synchronously and the thing spreads like + + + align:start position:0% +synchronously and the thing spreads like +a very much like a forest fire + + align:start position:0% + + + + align:start position:0% + +so that's a long + + align:start position:0% +so that's a long + + + align:start position:0% +so that's a long +rant I guess I've repeated it several + + align:start position:0% +rant I guess I've repeated it several + + + align:start position:0% +rant I guess I've repeated it several +times but it's hard to communicate with + + align:start position:0% +times but it's hard to communicate with + + + align:start position:0% +times but it's hard to communicate with +that Community because + + align:start position:0% +that Community because + + + align:start position:0% +that Community because +they really want to find the secret of + + align:start position:0% +they really want to find the secret of + + + align:start position:0% +they really want to find the secret of +thinking and knowledge in the brain + + align:start position:0% +thinking and knowledge in the brain + + + align:start position:0% +thinking and knowledge in the brain +cells rather than in the architecture of + + align:start position:0% +cells rather than in the architecture of + + + align:start position:0% +cells rather than in the architecture of +the + + align:start position:0% +the + + + align:start position:0% +the +interconnections so my inclination is to + + align:start position:0% +interconnections so my inclination is to + + + align:start position:0% +interconnections so my inclination is to +find an intermediate + + align:start position:0% +find an intermediate + + + align:start position:0% +find an intermediate +level uh such as at + + align:start position:0% +level uh such as at + + + align:start position:0% +level uh such as at +least in the cortex which is what + + align:start position:0% +least in the cortex which is what + + + align:start position:0% +least in the cortex which is what +distinguishes + + align:start position:0% + + + + align:start position:0% + +the does it start in + + align:start position:0% +the does it start in + + + align:start position:0% +the does it start in +mammals think so uh I think if + + align:start position:0% +mammals think so uh I think if + + + align:start position:0% +mammals think so uh I think if +I rather than a neurology book I'm + + align:start position:0% +I rather than a neurology book I'm + + + align:start position:0% +I rather than a neurology book I'm +thinking of Carl Sean's book which uh + + align:start position:0% +thinking of Carl Sean's book which uh + + + align:start position:0% +thinking of Carl Sean's book which uh +there's a sort of Triune Theory that's + + align:start position:0% +there's a sort of Triune Theory that's + + + align:start position:0% +there's a sort of Triune Theory that's +very popular which is that the brain + + align:start position:0% +very popular which is that the brain + + + align:start position:0% +very popular which is that the brain +consists of three major divisions and + + align:start position:0% +consists of three major divisions and + + + align:start position:0% +consists of three major divisions and +the I forget what the lowest level one + + align:start position:0% +the I forget what the lowest level one + + + align:start position:0% +the I forget what the lowest level one +is called but the middle level is sort + + align:start position:0% +is called but the middle level is sort + + + align:start position:0% +is called but the middle level is sort +of the amphibian and uh + + align:start position:0% + + + + align:start position:0% + +and then uh the Mamon + + align:start position:0% +and then uh the Mamon + + + align:start position:0% +and then uh the Mamon +and it's in the + + align:start position:0% +and it's in the + + + align:start position:0% +and it's in the +Mamon development that most of the that + + align:start position:0% +Mamon development that most of the that + + + align:start position:0% +Mamon development that most of the that +large parts of the brain are cortex and + + align:start position:0% +large parts of the brain are cortex and + + + align:start position:0% +large parts of the brain are cortex and +the + + align:start position:0% +the + + + align:start position:0% +the +cortex isn't so much like a tangled + + align:start position:0% +cortex isn't so much like a tangled + + + align:start position:0% +cortex isn't so much like a tangled +neural net but it's divided mainly into + + align:start position:0% +neural net but it's divided mainly into + + + align:start position:0% +neural net but it's divided mainly into +columns so and each column these + + align:start position:0% +columns so and each column these + + + align:start position:0% +columns so and each column these +vertical columns tend to have six or + + align:start position:0% +vertical columns tend to have six or + + + align:start position:0% +vertical columns tend to have six or +seven layers I think six is the + + align:start position:0% +seven layers I think six is the + + + align:start position:0% +seven layers I think six is the +standard and the whole thing + + align:start position:0% +standard and the whole thing + + + align:start position:0% +standard and the whole thing +is what is it about four millimet four + + align:start position:0% +is what is it about four millimet four + + + align:start position:0% +is what is it about four millimet four +or five millimeters + + align:start position:0% + + + + align:start position:0% + +thick maybe a little + + align:start position:0% + + + + align:start position:0% + +more and in each of these columns there + + align:start position:0% +more and in each of these columns there + + + align:start position:0% +more and in each of these columns there +there's major columns which have about a + + align:start position:0% +there's major columns which have about a + + + align:start position:0% +there's major columns which have about a +thousand neurons and one of these + + align:start position:0% +thousand neurons and one of these + + + align:start position:0% +thousand neurons and one of these +columns is made of maybe 10 or 20 of + + align:start position:0% +columns is made of maybe 10 or 20 of + + + align:start position:0% +columns is made of maybe 10 or 20 of +these mini columns that are have 50 + + align:start position:0% +these mini columns that are have 50 + + + align:start position:0% +these mini columns that are have 50 +or or 100 or + + align:start position:0% +or or 100 or + + + align:start position:0% +or or 100 or +whatever and so my inclination is to + + align:start position:0% +whatever and so my inclination is to + + + align:start position:0% +whatever and so my inclination is to +suspect that since these are the animals + + align:start position:0% +suspect that since these are the animals + + + align:start position:0% +suspect that since these are the animals +that think and plan many steps ahead and + + align:start position:0% +that think and plan many steps ahead and + + + align:start position:0% +that think and plan many steps ahead and +uh do all the sorts of things we take + + align:start position:0% +uh do all the sorts of things we take + + + align:start position:0% +uh do all the sorts of things we take +for granted in + + align:start position:0% +for granted in + + + align:start position:0% +for granted in +humans that we want to look there for + + align:start position:0% +humans that we want to look there for + + + align:start position:0% +humans that we want to look there for +the architecture of of + + align:start position:0% +the architecture of of + + + align:start position:0% +the architecture of of +U memory and problem solving systems + + align:start position:0% +U memory and problem solving systems + + + align:start position:0% +U memory and problem solving systems +in the animals without cortexes you can + + align:start position:0% +in the animals without cortexes you can + + + align:start position:0% +in the animals without cortexes you can +account for most of their behavior in + + align:start position:0% +account for most of their behavior in + + + align:start position:0% +account for most of their behavior in +terms of Fairly low-level immediate + + align:start position:0% +terms of Fairly low-level immediate + + + align:start position:0% +terms of Fairly low-level immediate +stimulus response reflexes and large + + align:start position:0% +stimulus response reflexes and large + + + align:start position:0% +stimulus response reflexes and large +major States like turning on some parts + + align:start position:0% +major States like turning on some parts + + + align:start position:0% +major States like turning on some parts +of some big blocks of these reflexes + + align:start position:0% +of some big blocks of these reflexes + + + align:start position:0% +of some big blocks of these reflexes +when it's hungry and turn on other + + align:start position:0% +when it's hungry and turn on other + + + align:start position:0% +when it's hungry and turn on other +blocks when there's a environmental + + align:start position:0% +blocks when there's a environmental + + + align:start position:0% +blocks when there's a environmental +threat and so forth or or + + align:start position:0% +threat and so forth or or + + + align:start position:0% +threat and so forth or or +whatever um + + align:start position:0% +whatever um + + + align:start position:0% +whatever um +anyway I forget what yes so in chapter + + align:start position:0% +anyway I forget what yes so in chapter + + + align:start position:0% +anyway I forget what yes so in chapter +three you talked about um like the + + align:start position:0% +three you talked about um like the + + + align:start position:0% +three you talked about um like the +stages we go through when we Face + + align:start position:0% +stages we go through when we Face + + + align:start position:0% +stages we go through when we Face +something like your car breaks down and + + align:start position:0% +something like your car breaks down and + + + align:start position:0% +something like your car breaks down and +you can go work that's the example given + + align:start position:0% +you can go work that's the example given + + + align:start position:0% +you can go work that's the example given +the book I'm wondering how do you decide + + align:start position:0% +the book I'm wondering how do you decide + + + align:start position:0% +the book I'm wondering how do you decide +that we you know transition from one + + align:start position:0% +that we you know transition from one + + + align:start position:0% +that we you know transition from one +state to another and why do we um go + + align:start position:0% +state to another and why do we um go + + + align:start position:0% +state to another and why do we um go +through stages of um denial bargaining + + align:start position:0% +through stages of um denial bargaining + + + align:start position:0% +through stages of um denial bargaining +like + + align:start position:0% +like + + + align:start position:0% +like +frustration depression and then like um + + align:start position:0% +frustration depression and then like um + + + align:start position:0% +frustration depression and then like um +only like the last stage seems + + align:start position:0% +only like the last stage seems + + + align:start position:0% +only like the last stage seems +productive I guess I my main question is + + align:start position:0% +productive I guess I my main question is + + + align:start position:0% +productive I guess I my main question is +how do we decide that we should + + align:start position:0% +how do we decide that we should + + + align:start position:0% +how do we decide that we should +transition from one to another what + + align:start position:0% +transition from one to another what + + + align:start position:0% +transition from one to another what +marks the end and why do + + align:start position:0% +marks the end and why do + + + align:start position:0% +marks the end and why do +we that's a beautiful + + align:start position:0% +we that's a beautiful + + + align:start position:0% +we that's a beautiful +question uh + + align:start position:0% + + + + align:start position:0% + +I think it's fairly well understood in + + align:start position:0% +I think it's fairly well understood in + + + align:start position:0% +I think it's fairly well understood in +the + + align:start position:0% +the + + + align:start position:0% +the +invertebrates that there are different + + align:start position:0% +invertebrates that there are different + + + align:start position:0% +invertebrates that there are different +centers in the brain for different + + align:start position:0% +centers in the brain for different + + + align:start position:0% +centers in the brain for different +activities + + align:start position:0% +activities + + + align:start position:0% +activities +and I'm not sure how much is how much is + + align:start position:0% +and I'm not sure how much is how much is + + + align:start position:0% +and I'm not sure how much is how much is +known about how these things + + align:start position:0% +known about how these things + + + align:start position:0% +known about how these things +switch uh how does an animal decide + + align:start position:0% +switch uh how does an animal decide + + + align:start position:0% +switch uh how does an animal decide +whether it's time + + align:start position:0% +whether it's time + + + align:start position:0% +whether it's time +to for example most animals are either + + align:start position:0% +to for example most animals are either + + + align:start position:0% +to for example most animals are either +dial or nocturnal so some + + align:start position:0% +dial or nocturnal so some + + + align:start position:0% +dial or nocturnal so some +stimulus uh comes along like it's + + align:start position:0% +stimulus uh comes along like it's + + + align:start position:0% +stimulus uh comes along like it's +getting + + align:start position:0% +getting + + + align:start position:0% +getting +dark and a nocturnal animal might then + + align:start position:0% +dark and a nocturnal animal might then + + + align:start position:0% +dark and a nocturnal animal might then +start waking up and it turns on some + + align:start position:0% +start waking up and it turns on some + + + align:start position:0% +start waking up and it turns on some +part of the brain and it uh turns off + + align:start position:0% +part of the brain and it uh turns off + + + align:start position:0% +part of the brain and it uh turns off +some other parts and it starts to sneak + + align:start position:0% +some other parts and it starts to sneak + + + align:start position:0% +some other parts and it starts to sneak +around looking for food or whatever it + + align:start position:0% +around looking for food or whatever it + + + align:start position:0% +around looking for food or whatever it +does at night whereas a d a daily + + align:start position:0% +does at night whereas a d a daily + + + align:start position:0% +does at night whereas a d a daily +animal um when it starts to get dark + + align:start position:0% +animal um when it starts to get dark + + + align:start position:0% +animal um when it starts to get dark +that might trigger uh + + align:start position:0% +that might trigger uh + + + align:start position:0% +that might trigger uh +some brain Center to turn on and it + + align:start position:0% +some brain Center to turn on and it + + + align:start position:0% +some brain Center to turn on and it +looks for its place to sleep and goes + + align:start position:0% +looks for its place to sleep and goes + + + align:start position:0% +looks for its place to sleep and goes +and + + align:start position:0% +and + + + align:start position:0% +and +hides so some of these are due to + + align:start position:0% +hides so some of these are due to + + + align:start position:0% +hides so some of these are due to +external things then of course they're + + align:start position:0% +external things then of course they're + + + align:start position:0% +external things then of course they're +internal + + align:start position:0% +internal + + + align:start position:0% +internal +clocks so for lots of animals if you put + + align:start position:0% +clocks so for lots of animals if you put + + + align:start position:0% +clocks so for lots of animals if you put +it in a box that's dimly + + align:start position:0% +it in a box that's dimly + + + align:start position:0% +it in a box that's dimly +illuminated + + align:start position:0% +illuminated + + + align:start position:0% +illuminated +um and it has a 24-hour cycle of some + + align:start position:0% +um and it has a 24-hour cycle of some + + + align:start position:0% +um and it has a 24-hour cycle of some +sort it might persist in that cycle for + + align:start position:0% +sort it might persist in that cycle for + + + align:start position:0% +sort it might persist in that cycle for +for quite a few days and go to sleep + + align:start position:0% +for quite a few days and go to sleep + + + align:start position:0% +for quite a few days and go to sleep +every 24 hours for half the time and so + + align:start position:0% +every 24 hours for half the time and so + + + align:start position:0% +every 24 hours for half the time and so +on a friend of mine once decided he + + align:start position:0% +on a friend of mine once decided he + + + align:start position:0% +on a friend of mine once decided he +would he would see about this + + align:start position:0% +would he would see about this + + + align:start position:0% +would he would see about this +and it's a famous uh AI theorist named + + align:start position:0% +and it's a famous uh AI theorist named + + + align:start position:0% +and it's a famous uh AI theorist named +Ray + + align:start position:0% +Ray + + + align:start position:0% +Ray +solomonov and he um put black paint on + + align:start position:0% +solomonov and he um put black paint on + + + align:start position:0% +solomonov and he um put black paint on +all his windows and found that he had a + + align:start position:0% +all his windows and found that he had a + + + align:start position:0% +all his windows and found that he had a +25 or 26h hour natural cycle which + + align:start position:0% + + + + align:start position:0% + +was very + + align:start position:0% +was very + + + align:start position:0% +was very +nice + + align:start position:0% +nice + + + align:start position:0% +nice +and this persisted for several months uh + + align:start position:0% +and this persisted for several months uh + + + align:start position:0% +and this persisted for several months uh +I had another friend who lived in the + + align:start position:0% +I had another friend who lived in the + + + align:start position:0% +I had another friend who lived in the +New York subways because + + align:start position:0% +New York subways because + + + align:start position:0% +New York subways because +his his apartment was in a building that + + align:start position:0% +his his apartment was in a building that + + + align:start position:0% +his his apartment was in a building that +had an entrance to the subway and he + + align:start position:0% +had an entrance to the subway and he + + + align:start position:0% +had an entrance to the subway and he +stayed uh out of daylight for 6 months + + align:start position:0% +stayed uh out of daylight for 6 months + + + align:start position:0% +stayed uh out of daylight for 6 months +but + + align:start position:0% +but + + + align:start position:0% +but +uh anyway he too found that he preferred + + align:start position:0% +uh anyway he too found that he preferred + + + align:start position:0% +uh anyway he too found that he preferred +to be on a 25 or 26 hour day than + + align:start position:0% +to be on a 25 or 26 hour day than + + + align:start position:0% +to be on a 25 or 26 hour day than +24 I'm rambling but uh so uh we + + align:start position:0% +24 I'm rambling but uh so uh we + + + align:start position:0% +24 I'm rambling but uh so uh we +apparently have several different + + align:start position:0% +apparently have several different + + + align:start position:0% +apparently have several different +systems so there's dead reckoning system + + align:start position:0% +systems so there's dead reckoning system + + + align:start position:0% +systems so there's dead reckoning system +where some internal clocks are + + align:start position:0% +where some internal clocks are + + + align:start position:0% +where some internal clocks are +regulating your behavior and then uh + + align:start position:0% +regulating your behavior and then uh + + + align:start position:0% +regulating your behavior and then uh +there are other systems where you're + + align:start position:0% +there are other systems where you're + + + align:start position:0% +there are other systems where you're +people are very much affected by the + + align:start position:0% +people are very much affected by the + + + align:start position:0% +people are very much affected by the +amount of light and + + align:start position:0% +amount of light and + + + align:start position:0% +amount of light and +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +forth so we probably have four or five + + align:start position:0% +forth so we probably have four or five + + + align:start position:0% +forth so we probably have four or five +ways of doing almost everything that's + + align:start position:0% +ways of doing almost everything that's + + + align:start position:0% +ways of doing almost everything that's +important and um then people get various + + align:start position:0% +important and um then people get various + + + align:start position:0% +important and um then people get various +disorders where some of these system + + align:start position:0% +disorders where some of these system + + + align:start position:0% +disorders where some of these system +fail and uh person uh doesn't have a + + align:start position:0% +fail and uh person uh doesn't have a + + + align:start position:0% +fail and uh person uh doesn't have a +regular sleep cycle and um + + align:start position:0% +regular sleep cycle and um + + + align:start position:0% +regular sleep cycle and um +there disorders where uh people fall as + + align:start position:0% +there disorders where uh people fall as + + + align:start position:0% +there disorders where uh people fall as +what's it called when when you fall + + align:start position:0% +what's it called when when you fall + + + align:start position:0% +what's it called when when you fall +asleep every few minutes narcolepsy + + align:start position:0% +asleep every few minutes narcolepsy + + + align:start position:0% +asleep every few minutes narcolepsy +narcolepsy and uh all sorts of wonderful + + align:start position:0% +narcolepsy and uh all sorts of wonderful + + + align:start position:0% +narcolepsy and uh all sorts of wonderful +disorders just because the brain has + + align:start position:0% +disorders just because the brain has + + + align:start position:0% +disorders just because the brain has +evolved so many uh different ways of + + align:start position:0% +evolved so many uh different ways of + + + align:start position:0% +evolved so many uh different ways of +doing anything that's very + + align:start position:0% + + + + align:start position:0% + +important + + align:start position:0% +important + + + align:start position:0% +important +yeah uh can you describe like the best + + align:start position:0% +yeah uh can you describe like the best + + + align:start position:0% +yeah uh can you describe like the best +piece of criticism for the Society of + + align:start position:0% +piece of criticism for the Society of + + + align:start position:0% +piece of criticism for the Society of +Mind Theory best piece of what the best + + align:start position:0% +Mind Theory best piece of what the best + + + align:start position:0% +Mind Theory best piece of what the best +criticism + + align:start position:0% + + + + align:start position:0% + +oh it reminds me + + align:start position:0% +oh it reminds me + + + align:start position:0% +oh it reminds me +of an article I recent read + + align:start position:0% +of an article I recent read + + + align:start position:0% +of an article I recent read +about + + align:start position:0% +about + + + align:start position:0% +about +um the possibility of a virus + + align:start position:0% +um the possibility of a virus + + + align:start position:0% +um the possibility of a virus +for what's the disorder we're + + align:start position:0% + + + + align:start position:0% + +no the + + align:start position:0% + + + + align:start position:0% + +uh actually there isn't any uh generally + + align:start position:0% +uh actually there isn't any uh generally + + + align:start position:0% +uh actually there isn't any uh generally +accepted cause for + + align:start position:0% +accepted cause for + + + align:start position:0% +accepted cause for +Alzheimer's as far as I know is + + align:start position:0% +Alzheimer's as far as I know is + + + align:start position:0% +Alzheimer's as far as I know is +it somebody just did an experiment where + + align:start position:0% +it somebody just did an experiment where + + + align:start position:0% +it somebody just did an experiment where +they injected Alzheimer infected matter + + align:start position:0% +they injected Alzheimer infected matter + + + align:start position:0% +they injected Alzheimer infected matter +into someone and they got the same La + + align:start position:0% +into someone and they got the same La + + + align:start position:0% +into someone and they got the same La +than oh well U + + align:start position:0% +than oh well U + + + align:start position:0% +than oh well U +right I'm I'm I wonder wonder if that's + + align:start position:0% +right I'm I'm I wonder wonder if that's + + + align:start position:0% +right I'm I'm I wonder wonder if that's +a popular + + align:start position:0% + + + + align:start position:0% + +Theory no what's the one where people + + align:start position:0% + + + + align:start position:0% + +uh say it again fibro my yes right + + align:start position:0% +uh say it again fibro my yes right + + + align:start position:0% +uh say it again fibro my yes right +that's right which is not recognized by + + align:start position:0% +that's right which is not recognized by + + + align:start position:0% +that's right which is not recognized by +most theorists to be a definite + + align:start position:0% +most theorists to be a definite + + + align:start position:0% +most theorists to be a definite +disease uh but + + align:start position:0% +disease uh but + + + align:start position:0% +disease uh but +uh there's been an episode in which + + align:start position:0% +uh there's been an episode in which + + + align:start position:0% +uh there's been an episode in which +somebody I forget what her name is uh + + align:start position:0% +somebody I forget what her name is uh + + + align:start position:0% +somebody I forget what her name is uh +was pretty sure that she had found a + + align:start position:0% +was pretty sure that she had found a + + + align:start position:0% +was pretty sure that she had found a +virus for it and um every now and then + + align:start position:0% +virus for it and um every now and then + + + align:start position:0% +virus for it and um every now and then +somebody uh revives that theory and uh + + align:start position:0% +somebody uh revives that theory and uh + + + align:start position:0% +somebody uh revives that theory and uh +tries to get more evidence for it anyway + + align:start position:0% +tries to get more evidence for it anyway + + + align:start position:0% +tries to get more evidence for it anyway +uh there must be disorders where the + + align:start position:0% +uh there must be disorders where the + + + align:start position:0% +uh there must be disorders where the +programming is bad rather than a + + align:start position:0% +programming is bad rather than a + + + align:start position:0% +programming is bad rather than a +biochemical + + align:start position:0% +biochemical + + + align:start position:0% +biochemical +disorder because uh + + align:start position:0% +disorder because uh + + + align:start position:0% +disorder because uh +whatever the brain is it's it's uh the + + align:start position:0% +whatever the brain is it's it's uh the + + + align:start position:0% +whatever the brain is it's it's uh the +adult brain is certainly uh has a very + + align:start position:0% +adult brain is certainly uh has a very + + + align:start position:0% +adult brain is certainly uh has a very +large component of what we would in any + + align:start position:0% +large component of what we would in any + + + align:start position:0% +large component of what we would in any +other case consider to be software + + align:start position:0% +other case consider to be software + + + align:start position:0% +other case consider to be software +namely lots of things that you've + + align:start position:0% +namely lots of things that you've + + + align:start position:0% +namely lots of things that you've +learned including ways for one part of + + align:start position:0% +learned including ways for one part of + + + align:start position:0% +learned including ways for one part of +the brain to discover how to modulate or + + align:start position:0% +the brain to discover how to modulate or + + + align:start position:0% +the brain to discover how to modulate or +turn on or turn off other parts of the + + align:start position:0% +turn on or turn off other parts of the + + + align:start position:0% +turn on or turn off other parts of the +brain and uh since we're only we've only + + align:start position:0% +brain and uh since we're only we've only + + + align:start position:0% +brain and uh since we're only we've only +only had this kind of Cortex for four or + + align:start position:0% +only had this kind of Cortex for four or + + + align:start position:0% +only had this kind of Cortex for four or +five million years it's probably still + + align:start position:0% +five million years it's probably still + + + align:start position:0% +five million years it's probably still +got lots of + + align:start position:0% +got lots of + + + align:start position:0% +got lots of +bugs Evolution never knows what when it + + align:start position:0% +bugs Evolution never knows what when it + + + align:start position:0% +bugs Evolution never knows what when it +when you make a new innovation you don't + + align:start position:0% +when you make a new innovation you don't + + + align:start position:0% +when you make a new innovation you don't +know what's going to come after that + + align:start position:0% +know what's going to come after that + + + align:start position:0% +know what's going to come after that +that might uh find bugs and ways to get + + align:start position:0% +that might uh find bugs and ways to get + + + align:start position:0% +that might uh find bugs and ways to get +short range advantages short-term + + align:start position:0% +short range advantages short-term + + + align:start position:0% +short range advantages short-term +advantages at the expense of longer term + + align:start position:0% +advantages at the expense of longer term + + + align:start position:0% +advantages at the expense of longer term +advantages so lots of mental diseases + + align:start position:0% +advantages so lots of mental diseases + + + align:start position:0% +advantages so lots of mental diseases +might might be software bugs uh and a + + align:start position:0% +might might be software bugs uh and a + + + align:start position:0% +might might be software bugs uh and a +few of them are known to be connected to + + align:start position:0% +few of them are known to be connected to + + + align:start position:0% +few of them are known to be connected to +uh you + + align:start position:0% +uh you + + + align:start position:0% +uh you +know um abnormal secretions of chemicals + + align:start position:0% +know um abnormal secretions of chemicals + + + align:start position:0% +know um abnormal secretions of chemicals +and so forth but even in those cases + + align:start position:0% +and so forth but even in those cases + + + align:start position:0% +and so forth but even in those cases +it's hard to be sure that the over + + align:start position:0% +it's hard to be sure that the over + + + align:start position:0% +it's hard to be sure that the over +production or underproduction of a + + align:start position:0% +production or underproduction of a + + + align:start position:0% +production or underproduction of a +neurologically important + + align:start position:0% +neurologically important + + + align:start position:0% +neurologically important +chemical + + align:start position:0% +chemical + + + align:start position:0% +chemical +uh is a + + align:start position:0% +uh is a + + + align:start position:0% +uh is a +uh which I call it a biological disorder + + align:start position:0% +uh which I call it a biological disorder + + + align:start position:0% +uh which I call it a biological disorder +or a functional disorder because some + + align:start position:0% +or a functional disorder because some + + + align:start position:0% +or a functional disorder because some +part of the nervous system might have + + align:start position:0% +part of the nervous system might have + + + align:start position:0% +part of the nervous system might have +found some trick to cause um abnormal + + align:start position:0% +found some trick to cause um abnormal + + + align:start position:0% +found some trick to cause um abnormal +secretions of of some + + align:start position:0% + + + + align:start position:0% + +substance that's the sort of thing that + + align:start position:0% +substance that's the sort of thing that + + + align:start position:0% +substance that's the sort of thing that +we can expect + + align:start position:0% +we can expect + + + align:start position:0% +we can expect +to learn a great deal more about in the + + align:start position:0% +to learn a great deal more about in the + + + align:start position:0% +to learn a great deal more about in the +Next + + align:start position:0% +Next + + + align:start position:0% +Next +Generation because of the lower cost C + + align:start position:0% +Generation because of the lower cost C + + + align:start position:0% +Generation because of the lower cost C +and greater resolution of of brain + + align:start position:0% +and greater resolution of of brain + + + align:start position:0% +and greater resolution of of brain +scanning techniques + + align:start position:0% +scanning techniques + + + align:start position:0% +scanning techniques +and what's his name the and new + + align:start position:0% +and what's his name the and new + + + align:start position:0% +and what's his name the and new +synthetic ways of of uh putting + + align:start position:0% +synthetic ways of of uh putting + + + align:start position:0% +synthetic ways of of uh putting +inflorescent chemicals into a normal + + align:start position:0% +inflorescent chemicals into a normal + + + align:start position:0% +inflorescent chemicals into a normal +brain without injuring it much uh so + + align:start position:0% +brain without injuring it much uh so + + + align:start position:0% +brain without injuring it much uh so +that you can now + + align:start position:0% +that you can now + + + align:start position:0% +that you can now +do sort of macrochemical + + align:start position:0% +do sort of macrochemical + + + align:start position:0% +do sort of macrochemical +experiments seeing what chemicals are uh + + align:start position:0% +experiments seeing what chemicals are uh + + + align:start position:0% +experiments seeing what chemicals are uh +being secreted in the brain uh with new + + align:start position:0% +being secreted in the brain uh with new + + + align:start position:0% +being secreted in the brain uh with new +kinds of scanning techniques so uh + + align:start position:0% +kinds of scanning techniques so uh + + + align:start position:0% +kinds of scanning techniques so uh +Neuroscience is going to be very + + align:start position:0% +Neuroscience is going to be very + + + align:start position:0% +Neuroscience is going to be very +exciting in the + + align:start position:0% +exciting in the + + + align:start position:0% +exciting in the +Next Generation with all the great new + + align:start position:0% + + + + align:start position:0% + +instruments as you know my complaint is + + align:start position:0% +instruments as you know my complaint is + + + align:start position:0% +instruments as you know my complaint is +that + + align:start position:0% +that + + + align:start position:0% +that +somehow introduction to the I'm not + + align:start position:0% +somehow introduction to the I'm not + + + align:start position:0% +somehow introduction to the I'm not +saying any of the present AI theories + + align:start position:0% +saying any of the present AI theories + + + align:start position:0% +saying any of the present AI theories +have been confirmed to to tell you that + + align:start position:0% +have been confirmed to to tell you that + + + align:start position:0% +have been confirmed to to tell you that +the brain works + + align:start position:0% +the brain works + + + align:start position:0% +the brain works +as such and such a rule-based system or + + align:start position:0% +as such and such a rule-based system or + + + align:start position:0% +as such and such a rule-based system or +such and such a or use uh Winston type + + align:start position:0% +such and such a or use uh Winston type + + + align:start position:0% +such and such a or use uh Winston type +representations or Roger shank type + + align:start position:0% +representations or Roger shank type + + + align:start position:0% +representations or Roger shank type +representations or scripts or frames or + + align:start position:0% +representations or scripts or frames or + + + align:start position:0% +representations or scripts or frames or +whatever and the U next to last chapter + + align:start position:0% +whatever and the U next to last chapter + + + align:start position:0% +whatever and the U next to last chapter +of the emotion machine sort of + + align:start position:0% +of the emotion machine sort of + + + align:start position:0% +of the emotion machine sort of +summarizes I think uh almost a dozen + + align:start position:0% +summarizes I think uh almost a dozen + + + align:start position:0% +summarizes I think uh almost a dozen +different um AI theories of of ways to + + align:start position:0% +different um AI theories of of ways to + + + align:start position:0% +different um AI theories of of ways to +represent knowledge uh nobody has + + align:start position:0% +represent knowledge uh nobody has + + + align:start position:0% +represent knowledge uh nobody has +confirmed that any of those particular + + align:start position:0% +confirmed that any of those particular + + + align:start position:0% +confirmed that any of those particular +ideas + + align:start position:0% +ideas + + + align:start position:0% +ideas +are uh represent what happens in a Maman + + align:start position:0% +are uh represent what happens in a Maman + + + align:start position:0% +are uh represent what happens in a Maman +brain and the problem is that + + align:start position:0% + + + + align:start position:0% + +the to me is that the Neuroscience + + align:start position:0% +the to me is that the Neuroscience + + + align:start position:0% +the to me is that the Neuroscience +Community just doesn't read that stuff + + align:start position:0% +Community just doesn't read that stuff + + + align:start position:0% +Community just doesn't read that stuff +and doesn't design experiments to to + + align:start position:0% +and doesn't design experiments to to + + + align:start position:0% +and doesn't design experiments to to +look for + + align:start position:0% + + + + align:start position:0% + +them David is been moving from computer + + align:start position:0% +them David is been moving from computer + + + align:start position:0% +them David is been moving from computer +science and AI into uh into that so he's + + align:start position:0% +science and AI into uh into that so he's + + + align:start position:0% +science and AI into uh into that so he's +he's my current source of knowledge + + align:start position:0% +he's my current source of knowledge + + + align:start position:0% +he's my current source of knowledge +about what's happening + + align:start position:0% +about what's happening + + + align:start position:0% +about what's happening +there have any of you been following + + align:start position:0% +there have any of you been following + + + align:start position:0% +there have any of you been following +contemporary + + align:start position:0% + + + + align:start position:0% + +Neuroscience that's + + align:start position:0% +Neuroscience that's + + + align:start position:0% +Neuroscience that's +strange + + align:start position:0% + + + + align:start position:0% + +yeah so uh you will talk about software + + align:start position:0% +yeah so uh you will talk about software + + + align:start position:0% +yeah so uh you will talk about software +a little bit like so they I think they + + align:start position:0% +a little bit like so they I think they + + + align:start position:0% +a little bit like so they I think they +they like analyze I brain and realized + + align:start position:0% +they like analyze I brain and realized + + + align:start position:0% +they like analyze I brain and realized +like that's why I talk about Thea cells + + align:start position:0% +like that's why I talk about Thea cells + + + align:start position:0% +like that's why I talk about Thea cells +and maybe like he had a lot of like a + + align:start position:0% +and maybe like he had a lot of like a + + + align:start position:0% +and maybe like he had a lot of like a +lot more G cells than than normal humans + + align:start position:0% +lot more G cells than than normal humans + + + align:start position:0% +lot more G cells than than normal humans +and uh so do you believe that uh the + + align:start position:0% +and uh so do you believe that uh the + + + align:start position:0% +and uh so do you believe that uh the +intelligence of humans is like more on + + align:start position:0% +intelligence of humans is like more on + + + align:start position:0% +intelligence of humans is like more on +the sof side side or on the hardware + + align:start position:0% +the sof side side or on the hardware + + + align:start position:0% +the sof side side or on the hardware +side like we have computers that are + + align:start position:0% +side like we have computers that are + + + align:start position:0% +side like we have computers that are +very very powerful could we create + + align:start position:0% +very very powerful could we create + + + align:start position:0% +very very powerful could we create +software that like we can run these + + align:start position:0% +software that like we can run these + + + align:start position:0% +software that like we can run these +machines that we produce in uh like + + align:start position:0% +machines that we produce in uh like + + + align:start position:0% +machines that we produce in uh like +humans + + align:start position:0% + + + + align:start position:0% + +like I don't see any uh reason to doubt + + align:start position:0% + + + + align:start position:0% + +it as far as we know computers can + + align:start position:0% +it as far as we know computers can + + + align:start position:0% +it as far as we know computers can +simulate anything + + align:start position:0% +simulate anything + + + align:start position:0% +simulate anything +uh what they can't do yet I suppose is + + align:start position:0% +uh what they can't do yet I suppose is + + + align:start position:0% +uh what they can't do yet I suppose is +simulate large scale Quantum phenomenon + + align:start position:0% + + + + align:start position:0% + +because if you know the theing theory of + + align:start position:0% +because if you know the theing theory of + + + align:start position:0% +because if you know the theing theory of +quantum + + align:start position:0% +quantum + + + align:start position:0% +quantum +mechanics is + + align:start position:0% + + + + align:start position:0% + +that if you have a network of physical + + align:start position:0% +that if you have a network of physical + + + align:start position:0% +that if you have a network of physical +systems that are + + align:start position:0% +systems that are + + + align:start position:0% +systems that are +connected then it's in the nature of + + align:start position:0% +connected then it's in the nature of + + + align:start position:0% +connected then it's in the nature of +physics that whatever + + align:start position:0% +physics that whatever + + + align:start position:0% +physics that whatever +happens from one state to + + align:start position:0% +happens from one state to + + + align:start position:0% +happens from one state to +another + + align:start position:0% +another + + + align:start position:0% +another +uh in the real + + align:start position:0% +uh in the real + + + align:start position:0% +uh in the real +Universe + + align:start position:0% +Universe + + + align:start position:0% +Universe +uh whatever happens actually happens by + + align:start position:0% +uh whatever happens actually happens by + + + align:start position:0% +uh whatever happens actually happens by +the way function the way function + + align:start position:0% +the way function the way function + + + align:start position:0% +the way function the way function +represents the sum of of the activities + + align:start position:0% +represents the sum of of the activities + + + align:start position:0% +represents the sum of of the activities +propagating through all possible + + align:start position:0% +propagating through all possible + + + align:start position:0% +propagating through all possible +paths so in some sense uh that's that's + + align:start position:0% +paths so in some sense uh that's that's + + + align:start position:0% +paths so in some sense uh that's that's +too exponential to simulate our computer + + align:start position:0% +too exponential to simulate our computer + + + align:start position:0% +too exponential to simulate our computer +in other words we can I believe + + align:start position:0% +in other words we can I believe + + + align:start position:0% +in other words we can I believe +the the biggest + + align:start position:0% +the the biggest + + + align:start position:0% +the the biggest +supercomputers can simulate a helium at + + align:start position:0% +supercomputers can simulate a helium at + + + align:start position:0% +supercomputers can simulate a helium at +today very + + align:start position:0% +today very + + + align:start position:0% +today very +well but they can't simulate a lithium + + align:start position:0% +well but they can't simulate a lithium + + + align:start position:0% +well but they can't simulate a lithium +out because it's sort of four or five + + align:start position:0% +out because it's sort of four or five + + + align:start position:0% +out because it's sort of four or five +layers of + + align:start position:0% + + + + align:start position:0% + +exponation two to the two the two to the + + align:start position:0% +exponation two to the two the two to the + + + align:start position:0% +exponation two to the two the two to the +two and four to the four to four to the + + align:start position:0% +two and four to the four to four to the + + + align:start position:0% +two and four to the four to four to the +four + + align:start position:0% +four + + + align:start position:0% +four +get those numbers get out of hand but I + + align:start position:0% +get those numbers get out of hand but I + + + align:start position:0% +get those numbers get out of hand but I +suspect that the reason the brain works + + align:start position:0% +suspect that the reason the brain works + + + align:start position:0% +suspect that the reason the brain works +is that it's evolved to prevent Quantum + + align:start position:0% +is that it's evolved to prevent Quantum + + + align:start position:0% +is that it's evolved to prevent Quantum +effects from uh making things + + align:start position:0% +effects from uh making things + + + align:start position:0% +effects from uh making things +complicated the reason the great thing + + align:start position:0% +complicated the reason the great thing + + + align:start position:0% +complicated the reason the great thing +about a neuron is that generally + + align:start position:0% +about a neuron is that generally + + + align:start position:0% +about a neuron is that generally +speaking a neuron fires all or none and + + align:start position:0% +speaking a neuron fires all or none and + + + align:start position:0% +speaking a neuron fires all or none and +you get this + + align:start position:0% +you get this + + + align:start position:0% +you get this +point you actually get a full half bol + + align:start position:0% +point you actually get a full half bol + + + align:start position:0% +point you actually get a full half bol +of potential between the + + align:start position:0% +of potential between the + + + align:start position:0% +of potential between the +neurons fiber surrounding fluid and + + align:start position:0% +neurons fiber surrounding fluid and + + + align:start position:0% +neurons fiber surrounding fluid and +that's a half a vol is a a + + align:start position:0% + + + + align:start position:0% + +big so like do you believe that the + + align:start position:0% +big so like do you believe that the + + + align:start position:0% +big so like do you believe that the +software that we have right now is + + align:start position:0% +software that we have right now is + + + align:start position:0% +software that we have right now is +equivalent to for example uh the + + align:start position:0% +equivalent to for example uh the + + + align:start position:0% +equivalent to for example uh the +intelligence that we have like in dogs + + align:start position:0% +intelligence that we have like in dogs + + + align:start position:0% +intelligence that we have like in dogs +or for example simple animals is like + + align:start position:0% +or for example simple animals is like + + + align:start position:0% +or for example simple animals is like +the + + align:start position:0% +the + + + align:start position:0% +the +difference that like do we just need to + + align:start position:0% +difference that like do we just need to + + + align:start position:0% +difference that like do we just need to +implement the software like modify the + + align:start position:0% +implement the software like modify the + + + align:start position:0% +implement the software like modify the +software or somehow we need to create a + + align:start position:0% +software or somehow we need to create a + + + align:start position:0% +software or somehow we need to create a +whole different software that no there + + align:start position:0% +whole different software that no there + + + align:start position:0% +whole different software that no there +doesn't seem to be much difference in + + align:start position:0% +doesn't seem to be much difference in + + + align:start position:0% +doesn't seem to be much difference in +the architecture of in the local + + align:start position:0% +the architecture of in the local + + + align:start position:0% +the architecture of in the local +architecture of the + + align:start position:0% +architecture of the + + + align:start position:0% +architecture of the +microphone you want po oh can I turn it + + align:start position:0% +microphone you want po oh can I turn it + + + align:start position:0% +microphone you want po oh can I turn it +off + + align:start position:0% +off + + + align:start position:0% +off +yes it's not green yeah so throw throw + + align:start position:0% +yes it's not green yeah so throw throw + + + align:start position:0% +yes it's not green yeah so throw throw +the switch is it green now now it's + + align:start position:0% +the switch is it green now now it's + + + align:start position:0% +the switch is it green now now it's +green okay + + align:start position:0% +green okay + + + align:start position:0% +green okay +good + + align:start position:0% +good + + + align:start position:0% +good +um the difference between the dog and a + + align:start position:0% +um the difference between the dog and a + + + align:start position:0% +um the difference between the dog and a +person is the the huge frontal + + align:start position:0% +person is the the huge frontal + + + align:start position:0% +person is the the huge frontal +cortex uh I think the rest of it is + + align:start position:0% +cortex uh I think the rest of it is + + + align:start position:0% +cortex uh I think the rest of it is +fairly similar and I presume the + + align:start position:0% +fairly similar and I presume the + + + align:start position:0% +fairly similar and I presume the +hippocampus and amydala and the + + align:start position:0% +hippocampus and amydala and the + + + align:start position:0% +hippocampus and amydala and the +structures that control which parts of + + align:start position:0% +structures that control which parts of + + + align:start position:0% +structures that control which parts of +the cortex are used used for what are + + align:start position:0% +the cortex are used used for what are + + + align:start position:0% +the cortex are used used for what are +somewhat different but + + align:start position:0% +somewhat different but + + + align:start position:0% +somewhat different but +the the small details of the all Mion + + align:start position:0% +the the small details of the all Mion + + + align:start position:0% +the the small details of the all Mion +brains are practically the same I mean + + align:start position:0% +brains are practically the same I mean + + + align:start position:0% +brains are practically the same I mean +basically you can't you can't make a an + + align:start position:0% +basically you can't you can't make a an + + + align:start position:0% +basically you can't you can't make a an +early genetic change in how neurons work + + align:start position:0% +early genetic change in how neurons work + + + align:start position:0% +early genetic change in how neurons work +or all the brain cells of the offspring + + align:start position:0% +or all the brain cells of the offspring + + + align:start position:0% +or all the brain cells of the offspring +would be somewhat different and the + + align:start position:0% +would be somewhat different and the + + + align:start position:0% +would be somewhat different and the +thing would be + + align:start position:0% +thing would be + + + align:start position:0% +thing would be +dead so Evolution has this property that + + align:start position:0% +dead so Evolution has this property that + + + align:start position:0% +dead so Evolution has this property that +generally there are only two places in + + align:start position:0% +generally there are only two places in + + + align:start position:0% +generally there are only two places in +the development of an embryo that + + align:start position:0% +the development of an embryo that + + + align:start position:0% +the development of an embryo that +Evolution can uh operate namely in the + + align:start position:0% +Evolution can uh operate namely in the + + + align:start position:0% +Evolution can uh operate namely in the +pre placental + + align:start position:0% +pre placental + + + align:start position:0% +pre placental +stage you can change the way the egg egg + + align:start position:0% +stage you can change the way the egg egg + + + align:start position:0% +stage you can change the way the egg egg +breaks up and evolves and you can have + + align:start position:0% +breaks up and evolves and you can have + + + align:start position:0% +breaks up and evolves and you can have +amazing things like identical twins + + align:start position:0% +amazing things like identical twins + + + align:start position:0% +amazing things like identical twins +happen without any effect on the nature + + align:start position:0% +happen without any effect on the nature + + + align:start position:0% +happen without any effect on the nature +of the adult Offspring or you can change + + align:start position:0% +of the adult Offspring or you can change + + + align:start position:0% +of the adult Offspring or you can change +the things that happened most recently + + align:start position:0% +the things that happened most recently + + + align:start position:0% +the things that happened most recently +in evolution like uh little tweaks in + + align:start position:0% +in evolution like uh little tweaks in + + + align:start position:0% +in evolution like uh little tweaks in +how uh some part of the nervous system + + align:start position:0% +how uh some part of the nervous system + + + align:start position:0% +how uh some part of the nervous system +works uh if it doesn't change earlier + + align:start position:0% +works uh if it doesn't change earlier + + + align:start position:0% +works uh if it doesn't change earlier +stages what + + align:start position:0% +stages what + + + align:start position:0% +stages what +you however mutations that operate in + + align:start position:0% +you however mutations that operate in + + + align:start position:0% +you however mutations that operate in +the middle of all that and change the + + align:start position:0% +the middle of all that and change the + + + align:start position:0% +the middle of all that and change the +number of segments in the + + align:start position:0% +number of segments in the + + + align:start position:0% +number of segments in the +embryo I guess you could have a longer + + align:start position:0% +embryo I guess you could have a longer + + + align:start position:0% +embryo I guess you could have a longer +tail or a shorter tail and that won't + + align:start position:0% +tail or a shorter tail and that won't + + + align:start position:0% +tail or a shorter tail and that won't +affect much but if you change the the 12 + + align:start position:0% +affect much but if you change the the 12 + + + align:start position:0% +affect much but if you change the the 12 +segments of the spine that the brain + + align:start position:0% +segments of the spine that the brain + + + align:start position:0% +segments of the spine that the brain +develops from you'd get a huge + + align:start position:0% +develops from you'd get a huge + + + align:start position:0% +develops from you'd get a huge +alteration in + + align:start position:0% +alteration in + + + align:start position:0% +alteration in +the how that animal will think so we're + + align:start position:0% +the how that animal will think so we're + + + align:start position:0% +the how that animal will think so we're +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of in other words + + align:start position:0% +of in other words + + + align:start position:0% +of in other words +Evolution cannot + + align:start position:0% +Evolution cannot + + + align:start position:0% +Evolution cannot +change intermediate structures very much + + align:start position:0% +change intermediate structures very much + + + align:start position:0% +change intermediate structures very much +or uh the animal won't + + align:start position:0% +or uh the animal won't + + + align:start position:0% +or uh the animal won't +live Bob ler if if one thinks of + + align:start position:0% +live Bob ler if if one thinks of + + + align:start position:0% +live Bob ler if if one thinks of +comparing a person to a dog would it not + + align:start position:0% +comparing a person to a dog would it not + + + align:start position:0% +comparing a person to a dog would it not +be most appropriate to think of those + + align:start position:0% +be most appropriate to think of those + + + align:start position:0% +be most appropriate to think of those +persons who are like the Wild Boy of + + align:start position:0% +persons who are like the Wild Boy of + + + align:start position:0% +persons who are like the Wild Boy of +Southern France who who grew up in the + + align:start position:0% +Southern France who who grew up in the + + + align:start position:0% +Southern France who who grew up in the +woods without any language I would say + + align:start position:0% +woods without any language I would say + + + align:start position:0% +woods without any language I would say +that if you're going to look at an + + align:start position:0% +that if you're going to look at an + + + align:start position:0% +that if you're going to look at an +individual's intelligence that would be + + align:start position:0% +individual's intelligence that would be + + + align:start position:0% +individual's intelligence that would be +a fair comparison with a dog whereas + + align:start position:0% +a fair comparison with a dog whereas + + + align:start position:0% +a fair comparison with a dog whereas +what we have when we think of people + + align:start position:0% +what we have when we think of people + + + align:start position:0% +what we have when we think of people +today is people who have learned so much + + align:start position:0% +today is people who have learned so much + + + align:start position:0% +today is people who have learned so much +through interaction with other people + + align:start position:0% +through interaction with other people + + + align:start position:0% +through interaction with other people +the the transmission of culture is it + + align:start position:0% +the the transmission of culture is it + + + align:start position:0% +the the transmission of culture is it +not essentially ways of thinking that + + align:start position:0% +not essentially ways of thinking that + + + align:start position:0% +not essentially ways of thinking that +have been learned throughout the history + + align:start position:0% +have been learned throughout the history + + + align:start position:0% +have been learned throughout the history +of civilization and some of us are able + + align:start position:0% +of civilization and some of us are able + + + align:start position:0% +of civilization and some of us are able +to pass on to others uh sure uh + + align:start position:0% +to pass on to others uh sure uh + + + align:start position:0% +to pass on to others uh sure uh +although uh if you expose a dog to + + align:start position:0% +although uh if you expose a dog to + + + align:start position:0% +although uh if you expose a dog to +humans it doesn't learn language so uh + + align:start position:0% +humans it doesn't learn language so uh + + + align:start position:0% +humans it doesn't learn language so uh +not + + align:start position:0% +not + + + align:start position:0% +not +come right so + + align:start position:0% +come right so + + + align:start position:0% +come right so +there but presumably + + align:start position:0% +there but presumably + + + align:start position:0% +there but presumably +language + + align:start position:0% + + + + align:start position:0% + +uh is fairly recent so you could have + + align:start position:0% +uh is fairly recent so you could have + + + align:start position:0% +uh is fairly recent so you could have +mutations in + + align:start position:0% +mutations in + + + align:start position:0% +mutations in +the uh structure of of the language + + align:start position:0% +the uh structure of of the language + + + align:start position:0% +the uh structure of of the language +centers and still have a human that's + + align:start position:0% +centers and still have a human that's + + + align:start position:0% +centers and still have a human that's +alive and it might be better at language + + align:start position:0% +alive and it might be better at language + + + align:start position:0% +alive and it might be better at language +than most other people or somewhat worse + + align:start position:0% +than most other people or somewhat worse + + + align:start position:0% +than most other people or somewhat worse +so we could have lots of small mutations + + align:start position:0% +so we could have lots of small mutations + + + align:start position:0% +so we could have lots of small mutations +in anything that's been recently + + align:start position:0% +in anything that's been recently + + + align:start position:0% +in anything that's been recently +evolved but + + align:start position:0% + + + + align:start position:0% + +uh but the frontal cortex is uh + + align:start position:0% +uh but the frontal cortex is uh + + + align:start position:0% +uh but the frontal cortex is uh +and the the human cortex is is really + + align:start position:0% +and the the human cortex is is really + + + align:start position:0% +and the the human cortex is is really +very large compared to the rest of the + + align:start position:0% +very large compared to the rest of the + + + align:start position:0% +very large compared to the rest of the +brain uh same in dolphins and a couple + + align:start position:0% +brain uh same in dolphins and a couple + + + align:start position:0% +brain uh same in dolphins and a couple +of other animals I + + align:start position:0% +of other animals I + + + align:start position:0% +of other animals I +forget + + align:start position:0% +forget + + + align:start position:0% +forget +whales yeah so the reason why I asked + + align:start position:0% +whales yeah so the reason why I asked + + + align:start position:0% +whales yeah so the reason why I asked +that is that it seems to me that we have + + align:start position:0% +that is that it seems to me that we have + + + align:start position:0% +that is that it seems to me that we have +some quality like some kind of we can + + align:start position:0% +some quality like some kind of we can + + + align:start position:0% +some quality like some kind of we can +see the word like add some qualities the + + align:start position:0% +see the word like add some qualities the + + + align:start position:0% +see the word like add some qualities the +world and like this is what I would call + + align:start position:0% +world and like this is what I would call + + + align:start position:0% +world and like this is what I would call +Consciousness and like for me it seems + + align:start position:0% +Consciousness and like for me it seems + + + align:start position:0% +Consciousness and like for me it seems +that dogs also have this quality of + + align:start position:0% +that dogs also have this quality of + + + align:start position:0% +that dogs also have this quality of +like uh seeing the word and like adding + + align:start position:0% +like uh seeing the word and like adding + + + align:start position:0% +like uh seeing the word and like adding +qualities to the word so like maybe all + + align:start position:0% +qualities to the word so like maybe all + + + align:start position:0% +qualities to the word so like maybe all +uh this is good this is bad like there + + align:start position:0% +uh this is good this is bad like there + + + align:start position:0% +uh this is good this is bad like there +are different qualities for different uh + + align:start position:0% +are different qualities for different uh + + + align:start position:0% +are different qualities for different uh +beings and like the software that we + + align:start position:0% +beings and like the software that we + + + align:start position:0% +beings and like the software that we +produce right now seems to be made maybe + + align:start position:0% +produce right now seems to be made maybe + + + align:start position:0% +produce right now seems to be made maybe +faster and like maybe do more tasks than + + align:start position:0% +faster and like maybe do more tasks than + + + align:start position:0% +faster and like maybe do more tasks than +what maybe a dog does + + align:start position:0% +what maybe a dog does + + + align:start position:0% +what maybe a dog does +but + + align:start position:0% +but + + + align:start position:0% +but +uh for me it doesn't seem that it has + + align:start position:0% +uh for me it doesn't seem that it has + + + align:start position:0% +uh for me it doesn't seem that it has +essential this like quality uh thing + + align:start position:0% +essential this like quality uh thing + + + align:start position:0% +essential this like quality uh thing +like it doesn't have Consciousness in + + align:start position:0% +like it doesn't have Consciousness in + + + align:start position:0% +like it doesn't have Consciousness in +the sense it doesn't like aggregate + + align:start position:0% +the sense it doesn't like aggregate + + + align:start position:0% +the sense it doesn't like aggregate +quality to the things in the world maybe + + align:start position:0% +quality to the things in the world maybe + + + align:start position:0% +quality to the things in the world maybe +well + + align:start position:0% +well + + + align:start position:0% +well +I I think I know what you're getting at + + align:start position:0% +I I think I know what you're getting at + + + align:start position:0% +I I think I know what you're getting at +but + + align:start position:0% +but + + + align:start position:0% +but +uh but you're using that word + + align:start position:0% +uh but you're using that word + + + align:start position:0% +uh but you're using that word +Consciousness which + + align:start position:0% +Consciousness which + + + align:start position:0% +Consciousness which +uh which I've decided to abandon because + + align:start position:0% +uh which I've decided to abandon because + + + align:start position:0% +uh which I've decided to abandon because +because it's 36 different things and + + align:start position:0% +because it's 36 different things and + + + align:start position:0% +because it's 36 different things and +probably uh a dog has five or six of + + align:start position:0% +probably uh a dog has five or six of + + + align:start position:0% +probably uh a dog has five or six of +them or 31 I don't + + align:start position:0% +them or 31 I don't + + + align:start position:0% +them or 31 I don't +know but uh + + align:start position:0% + + + + align:start position:0% + +one question + + align:start position:0% + + + + align:start position:0% + +is do you think a dog can think several + + align:start position:0% +is do you think a dog can think several + + + align:start position:0% +is do you think a dog can think several +steps ahead and consider two + + align:start position:0% + + + + align:start position:0% + +alternative that's + + align:start position:0% + + + + align:start position:0% + +funny oh let's make this abstract so + + align:start position:0% +funny oh let's make this abstract so + + + align:start position:0% +funny oh let's make this abstract so +here here's a world and the dog is here + + align:start position:0% +here here's a world and the dog is here + + + align:start position:0% +here here's a world and the dog is here +and it wants to get here and there are + + align:start position:0% +and it wants to get here and there are + + + align:start position:0% +and it wants to get here and there are +all sorts of obstacles in it so can the + + align:start position:0% +all sorts of obstacles in it so can the + + + align:start position:0% +all sorts of obstacles in it so can the +dog say well if I went this way uh I'd + + align:start position:0% +dog say well if I went this way uh I'd + + + align:start position:0% +dog say well if I went this way uh I'd +have such and such difficulty whereas if + + align:start position:0% +have such and such difficulty whereas if + + + align:start position:0% +have such and such difficulty whereas if +I went this way I'd have this difficulty + + align:start position:0% +I went this way I'd have this difficulty + + + align:start position:0% +I went this way I'd have this difficulty +well I think this one looks + + align:start position:0% +well I think this one looks + + + align:start position:0% +well I think this one looks +better do you think your dog considers + + align:start position:0% +better do you think your dog considers + + + align:start position:0% +better do you think your dog considers +two or three Alternatives and makes + + align:start position:0% +two or three Alternatives and makes + + + align:start position:0% +two or three Alternatives and makes +plans I have no idea but + + align:start position:0% +plans I have no idea but + + + align:start position:0% +plans I have no idea but +uh the Curious Thing about a person is + + align:start position:0% +uh the Curious Thing about a person is + + + align:start position:0% +uh the Curious Thing about a person is +uh you can decide that you're going to + + align:start position:0% +uh you can decide that you're going to + + + align:start position:0% +uh you can decide that you're going to +not uh not act in the situation until + + align:start position:0% +not uh not act in the situation until + + + align:start position:0% +not uh not act in the situation until +you've considered 16 plans and then one + + align:start position:0% +you've considered 16 plans and then one + + + align:start position:0% +you've considered 16 plans and then one +part of your brain is making these + + align:start position:0% +part of your brain is making these + + + align:start position:0% +part of your brain is making these +different uh approaches to the problem + + align:start position:0% +different uh approaches to the problem + + + align:start position:0% +different uh approaches to the problem +is and another part of your brain is + + align:start position:0% +is and another part of your brain is + + + align:start position:0% +is and another part of your brain is +saying well now I've made five plans and + + align:start position:0% +saying well now I've made five plans and + + + align:start position:0% +saying well now I've made five plans and +I'm beginning to forget the first one so + + align:start position:0% +I'm beginning to forget the first one so + + + align:start position:0% +I'm beginning to forget the first one so +uh I better reformulate it + + align:start position:0% +uh I better reformulate it + + + align:start position:0% +uh I better reformulate it +and you're doing all of + + align:start position:0% +and you're doing all of + + + align:start position:0% +and you're doing all of +these self-conscious in the sense that + + align:start position:0% +these self-conscious in the sense that + + + align:start position:0% +these self-conscious in the sense that +uh you're making plans that involve + + align:start position:0% +uh you're making plans that involve + + + align:start position:0% +uh you're making plans that involve +predicting what decisions you will make + + align:start position:0% +predicting what decisions you will make + + + align:start position:0% +predicting what decisions you will make +and instead of making them you make the + + align:start position:0% +and instead of making them you make the + + + align:start position:0% +and instead of making them you make the +decision to say I'm going to follow out + + align:start position:0% +decision to say I'm going to follow out + + + align:start position:0% +decision to say I'm going to follow out +these two plans and uh use the result of + + align:start position:0% +these two plans and uh use the result of + + + align:start position:0% +these two plans and uh use the result of +that to decide which one + + align:start position:0% +that to decide which one + + + align:start position:0% +that to decide which one +do you think a dog does any of that does + + align:start position:0% +do you think a dog does any of that does + + + align:start position:0% +do you think a dog does any of that does +it look around and say well I could go + + align:start position:0% +it look around and say well I could go + + + align:start position:0% +it look around and say well I could go +that way or this way + + align:start position:0% + + + + align:start position:0% + +h i + + align:start position:0% +h i + + + align:start position:0% +h i +remember our dog was good at uh if you + + align:start position:0% +remember our dog was good at uh if you + + + align:start position:0% +remember our dog was good at uh if you +throw a ball it would go and get it and + + align:start position:0% +throw a ball it would go and get it and + + + align:start position:0% +throw a ball it would go and get it and +if you threw two ballls it would go and + + align:start position:0% +if you threw two ballls it would go and + + + align:start position:0% +if you threw two ballls it would go and +get both of them and sometimes if you + + align:start position:0% +get both of them and sometimes if you + + + align:start position:0% +get both of them and sometimes if you +threw three bowls it would uh go and get + + align:start position:0% +threw three bowls it would uh go and get + + + align:start position:0% +threw three bowls it would uh go and get +them all and some sometimes if a ball + + align:start position:0% +them all and some sometimes if a ball + + + align:start position:0% +them all and some sometimes if a ball +would roll under a couch that it + + align:start position:0% +would roll under a couch that it + + + align:start position:0% +would roll under a couch that it +couldn't + + align:start position:0% +couldn't + + + align:start position:0% +couldn't +reach it would get the other two and it + + align:start position:0% +reach it would get the other two and it + + + align:start position:0% +reach it would get the other two and it +would think and then it would run back + + align:start position:0% +would think and then it would run back + + + align:start position:0% +would think and then it would run back +to the kitchen where that ball is + + align:start position:0% +to the kitchen where that ball is + + + align:start position:0% +to the kitchen where that ball is +usually found and then it would come + + align:start position:0% +usually found and then it would come + + + align:start position:0% +usually found and then it would come +back disappointed so what does that mean + + align:start position:0% +back disappointed so what does that mean + + + align:start position:0% +back disappointed so what does that mean +did it have parallel plans or + + align:start position:0% +did it have parallel plans or + + + align:start position:0% +did it have parallel plans or +uh does it make a new one when the + + align:start position:0% +uh does it make a new one when the + + + align:start position:0% +uh does it make a new one when the +previous one fails and they're not + + align:start position:0% +previous one fails and they're not + + + align:start position:0% +previous one fails and they're not +actually parallel + + align:start position:0% + + + + align:start position:0% + +what's your + + align:start position:0% +what's your + + + align:start position:0% +what's your +gu how far ahead does a dog think do you + + align:start position:0% +gu how far ahead does a dog think do you + + + align:start position:0% +gu how far ahead does a dog think do you +have a dog yeah I do have a dog but + + align:start position:0% +have a dog yeah I do have a dog but + + + align:start position:0% +have a dog yeah I do have a dog but +like I don't believe that's the + + align:start position:0% +like I don't believe that's the + + + align:start position:0% +like I don't believe that's the +essential part of like beings that have + + align:start position:0% +essential part of like beings that have + + + align:start position:0% +essential part of like beings that have +some kind of Advanced Brain like we can + + align:start position:0% +some kind of Advanced Brain like we can + + + align:start position:0% +some kind of Advanced Brain like we can +plan ahead humans can plan ahead I don't + + align:start position:0% + + + + align:start position:0% + +think they like are the fundamental part + + align:start position:0% +think they like are the fundamental part + + + align:start position:0% +think they like are the fundamental part +of + + align:start position:0% +of + + + align:start position:0% +of +intelligence like humans uh I think Wist + + align:start position:0% +intelligence like humans uh I think Wist + + + align:start position:0% +intelligence like humans uh I think Wist +say that humans are better than primates + + align:start position:0% +say that humans are better than primates + + + align:start position:0% +say that humans are better than primates +in like they can understand stories and + + align:start position:0% +in like they can understand stories and + + + align:start position:0% +in like they can understand stories and +they can join together stories + + align:start position:0% +they can join together stories + + + align:start position:0% +they can join together stories +but somehow uh I like I don't buy the + + align:start position:0% +but somehow uh I like I don't buy the + + + align:start position:0% +but somehow uh I like I don't buy the +story + + align:start position:0% +story + + + align:start position:0% +story +that uh primates are just like uh + + align:start position:0% +that uh primates are just like uh + + + align:start position:0% +that uh primates are just like uh +planners like I believe somehow we can + + align:start position:0% +planners like I believe somehow we can + + + align:start position:0% +planners like I believe somehow we can +we have some uh quality machine of the + + align:start position:0% +we have some uh quality machine of the + + + align:start position:0% +we have some uh quality machine of the +word and like somehow we're not writing + + align:start position:0% +word and like somehow we're not writing + + + align:start position:0% +word and like somehow we're not writing +a software that but you know it's funny + + align:start position:0% +a software that but you know it's funny + + + align:start position:0% +a software that but you know it's funny +uh computer science teaches us things + + align:start position:0% +uh computer science teaches us things + + + align:start position:0% +uh computer science teaches us things +that that weren't obvious before like it + + align:start position:0% +that that weren't obvious before like it + + + align:start position:0% +that that weren't obvious before like it +might turn out + + align:start position:0% +might turn out + + + align:start position:0% +might turn out +that if you're a computer and you only + + align:start position:0% +that if you're a computer and you only + + + align:start position:0% +that if you're a computer and you only +have two registers + + align:start position:0% +have two registers + + + align:start position:0% +have two registers +then well in principle you could do + + align:start position:0% +then well in principle you could do + + + align:start position:0% +then well in principle you could do +anything but that's that's another + + align:start position:0% +anything but that's that's another + + + align:start position:0% +anything but that's that's another +matter uh but it might turn out that + + align:start position:0% +matter uh but it might turn out that + + + align:start position:0% +matter uh but it might turn out that +maybe a dog has only two registers and a + + align:start position:0% +maybe a dog has only two registers and a + + + align:start position:0% +maybe a dog has only two registers and a +person has four and a trivial thing like + + align:start position:0% +person has four and a trivial thing like + + + align:start position:0% +person has four and a trivial thing like +that makes it possible to have two plans + + align:start position:0% +that makes it possible to have two plans + + + align:start position:0% +that makes it possible to have two plans +and put them in suspense and think about + + align:start position:0% +and put them in suspense and think about + + + align:start position:0% +and put them in suspense and think about +the strategy and come back and change + + align:start position:0% +the strategy and come back and change + + + align:start position:0% +the strategy and come back and change +one whereas if you only had two + + align:start position:0% +one whereas if you only had two + + + align:start position:0% +one whereas if you only had two +registers uh your mind would be much + + align:start position:0% +registers uh your mind would be much + + + align:start position:0% +registers uh your mind would be much +lower order and there's no big + + align:start position:0% +lower order and there's no big + + + align:start position:0% +lower order and there's no big +difference so computer + + align:start position:0% +difference so computer + + + align:start position:0% +difference so computer +science tells us that the usual way of + + align:start position:0% +science tells us that the usual way of + + + align:start position:0% +science tells us that the usual way of +thinking about + + align:start position:0% +thinking about + + + align:start position:0% +thinking about +abilities might be wrong before computer + + align:start position:0% +abilities might be wrong before computer + + + align:start position:0% +abilities might be wrong before computer +science people didn't really have that + + align:start position:0% +science people didn't really have that + + + align:start position:0% +science people didn't really have that +kind + + align:start position:0% +kind + + + align:start position:0% +kind +of + + align:start position:0% +of + + + align:start position:0% +of +idea uh many years ago I was in a + + align:start position:0% +idea uh many years ago I was in a + + + align:start position:0% +idea uh many years ago I was in a +contest I mean you know a + + align:start position:0% +contest I mean you know a + + + align:start position:0% +contest I mean you know a +science because us + + align:start position:0% +science because us + + + align:start position:0% +science because us +uh some of our friends showed that you + + align:start position:0% +uh some of our friends showed that you + + + align:start position:0% +uh some of our friends showed that you +could make a universal computer with + + align:start position:0% +could make a universal computer with + + + align:start position:0% +could make a universal computer with +four + + align:start position:0% +four + + + align:start position:0% +four +registers and + + align:start position:0% +registers and + + + align:start position:0% +registers and +uh I had discovered some other things + + align:start position:0% +uh I had discovered some other things + + + align:start position:0% +uh I had discovered some other things +and I managed to uh show that you could + + align:start position:0% +and I managed to uh show that you could + + + align:start position:0% +and I managed to uh show that you could +make a universal computer with just two + + align:start position:0% +make a universal computer with just two + + + align:start position:0% +make a universal computer with just two +registers and + + align:start position:0% +registers and + + + align:start position:0% +registers and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that that was a big surprise to a lot of + + align:start position:0% +that that was a big surprise to a lot of + + + align:start position:0% +that that was a big surprise to a lot of +people but there wasn't there aren't + + align:start position:0% +people but there wasn't there aren't + + + align:start position:0% +people but there wasn't there aren't +anything in there never was anything in + + align:start position:0% +anything in there never was anything in + + + align:start position:0% +anything in there never was anything in +the history of + + align:start position:0% +the history of + + + align:start position:0% +the history of +psychology uh of that nature so there + + align:start position:0% +psychology uh of that nature so there + + + align:start position:0% +psychology uh of that nature so there +never were + + align:start position:0% +never were + + + align:start position:0% +never were +really technical theories + + align:start position:0% +really technical theories + + + align:start position:0% +really technical theories +of of it's really computational + + align:start position:0% +of of it's really computational + + + align:start position:0% +of of it's really computational +complexity what does it take to solve + + align:start position:0% +complexity what does it take to solve + + + align:start position:0% +complexity what does it take to solve +certain kinds of problems and until the + + align:start position:0% +certain kinds of problems and until the + + + align:start position:0% +certain kinds of problems and until the +1960s there weren't any theories of that + + align:start position:0% +1960s there weren't any theories of that + + + align:start position:0% +1960s there weren't any theories of that +and I'm not sure that + + align:start position:0% +and I'm not sure that + + + align:start position:0% +and I'm not sure that +uh that aspect of computer science has + + align:start position:0% +uh that aspect of computer science has + + + align:start position:0% +uh that aspect of computer science has +actually reached many psychologists or + + align:start position:0% +actually reached many psychologists or + + + align:start position:0% +actually reached many psychologists or +neuroscientists I'm not even sure that + + align:start position:0% +neuroscientists I'm not even sure that + + + align:start position:0% +neuroscientists I'm not even sure that +it's relevant but it's it's really + + align:start position:0% +it's relevant but it's it's really + + + align:start position:0% +it's relevant but it's it's really +interesting that the difference between + + align:start position:0% +interesting that the difference between + + + align:start position:0% +interesting that the difference between +two and three registers could make an + + align:start position:0% +two and three registers could make an + + + align:start position:0% +two and three registers could make an +exponential difference in how fast you + + align:start position:0% +exponential difference in how fast you + + + align:start position:0% +exponential difference in how fast you +could solve certain kinds of problems + + align:start position:0% +could solve certain kinds of problems + + + align:start position:0% +could solve certain kinds of problems +and not + + align:start position:0% + + + + align:start position:0% + +others so maybe there'll be a little a + + align:start position:0% +others so maybe there'll be a little a + + + align:start position:0% +others so maybe there'll be a little a +little more mathematical psychology in + + align:start position:0% +little more mathematical psychology in + + + align:start position:0% +little more mathematical psychology in +the next couple of + + align:start position:0% +the next couple of + + + align:start position:0% +the next couple of +decades + + align:start position:0% +decades + + + align:start position:0% +decades +yeah um so in artificial intelligence + + align:start position:0% +yeah um so in artificial intelligence + + + align:start position:0% +yeah um so in artificial intelligence +how much of the effort should be um how + + align:start position:0% +how much of the effort should be um how + + + align:start position:0% +how much of the effort should be um how +much of our effort should be devoted to + + align:start position:0% +much of our effort should be devoted to + + + align:start position:0% +much of our effort should be devoted to +like kind of reflecting on our own + + align:start position:0% +like kind of reflecting on our own + + + align:start position:0% +like kind of reflecting on our own +thinking as humans and trying to figure + + align:start position:0% +thinking as humans and trying to figure + + + align:start position:0% +thinking as humans and trying to figure +out what's really going on inside our + + align:start position:0% +out what's really going on inside our + + + align:start position:0% +out what's really going on inside our +brains and then trying to kind of + + align:start position:0% +brains and then trying to kind of + + + align:start position:0% +brains and then trying to kind of +implement that versus uh observing and + + align:start position:0% +implement that versus uh observing and + + + align:start position:0% +implement that versus uh observing and +identifying what kinds of problems we as + + align:start position:0% +identifying what kinds of problems we as + + + align:start position:0% +identifying what kinds of problems we as +humans can solve and then come up with + + align:start position:0% +humans can solve and then come up with + + + align:start position:0% +humans can solve and then come up with +any sort of way for a computer to uh + + align:start position:0% +any sort of way for a computer to uh + + + align:start position:0% +any sort of way for a computer to uh +kind of in a humanlike way solve these + + align:start position:0% +kind of in a humanlike way solve these + + + align:start position:0% +kind of in a humanlike way solve these +problems well there are a lot of nice + + align:start position:0% +problems well there are a lot of nice + + + align:start position:0% +problems well there are a lot of nice +questions I don't + + align:start position:0% +questions I don't + + + align:start position:0% +questions I don't +think it doesn't make any sense to + + align:start position:0% +think it doesn't make any sense to + + + align:start position:0% +think it doesn't make any sense to +say to suggest that we think about + + align:start position:0% +say to suggest that we think about + + + align:start position:0% +say to suggest that we think about +what's happening in our brains because + + align:start position:0% +what's happening in our brains because + + + align:start position:0% +what's happening in our brains because +uh that takes scientific instruments + + align:start position:0% +uh that takes scientific instruments + + + align:start position:0% +uh that takes scientific instruments +but it certainly makes sense to go over + + align:start position:0% +but it certainly makes sense to go over + + + align:start position:0% +but it certainly makes sense to go over +older theories of psychology and ask + + align:start position:0% +older theories of psychology and ask + + + align:start position:0% +older theories of psychology and ask +what kinds of + + align:start position:0% +what kinds of + + + align:start position:0% +what kinds of +procedures + + align:start position:0% + + + + align:start position:0% + +uh to solve a certain kind of problem + + align:start position:0% +uh to solve a certain kind of problem + + + align:start position:0% +uh to solve a certain kind of problem +what kind of procedures are absolutely + + align:start position:0% +what kind of procedures are absolutely + + + align:start position:0% +what kind of procedures are absolutely +necessary and you could find some like + + align:start position:0% +necessary and you could find some like + + + align:start position:0% +necessary and you could find some like +that like like how many registers would + + align:start position:0% +that like like how many registers would + + + align:start position:0% +that like like how many registers would +you need and what kinds of conditionals + + align:start position:0% +you need and what kinds of conditionals + + + align:start position:0% +you need and what kinds of conditionals +and uh what kind of + + align:start position:0% +and uh what kind of + + + align:start position:0% +and uh what kind of +addressing um + + align:start position:0% + + + + align:start position:0% + +so I think a lot of cognitive psychology + + align:start position:0% +so I think a lot of cognitive psychology + + + align:start position:0% +so I think a lot of cognitive psychology +modern cognitive + + align:start position:0% +modern cognitive + + + align:start position:0% +modern cognitive +psychology is is of that character + + align:start position:0% +psychology is is of that character + + + align:start position:0% +psychology is is of that character +but + + align:start position:0% +but + + + align:start position:0% +but +um I don't see any way to + + align:start position:0% +um I don't see any way to + + + align:start position:0% +um I don't see any way to +introspect + + align:start position:0% +introspect + + + align:start position:0% +introspect +and well enough to to guess how your + + align:start position:0% +and well enough to to guess how your + + + align:start position:0% +and well enough to to guess how your +brain does something because uh we're + + align:start position:0% +brain does something because uh we're + + + align:start position:0% +brain does something because uh we're +just not that + + align:start position:0% +just not that + + + align:start position:0% +just not that +conscious we don't have access to + + align:start position:0% +conscious we don't have access to + + + align:start position:0% +conscious we don't have access to +you could think for 10 years about how + + align:start position:0% +you could think for 10 years about how + + + align:start position:0% +you could think for 10 years about how +do I think of the next word to + + align:start position:0% +do I think of the next word to + + + align:start position:0% +do I think of the next word to +speak and uh unlikely that you would you + + align:start position:0% +speak and uh unlikely that you would you + + + align:start position:0% +speak and uh unlikely that you would you +might get some new ideas about how this + + align:start position:0% +might get some new ideas about how this + + + align:start position:0% +might get some new ideas about how this +might have happened in + + align:start position:0% +might have happened in + + + align:start position:0% +might have happened in +fact uh but you couldn't be + + align:start position:0% +fact uh but you couldn't be + + + align:start position:0% +fact uh but you couldn't be +sure well I take it back + + align:start position:0% + + + + align:start position:0% + +probably + + align:start position:0% + + + + align:start position:0% + +people you could probably get some + + align:start position:0% +people you could probably get some + + + align:start position:0% +people you could probably get some +correct theories by being lucky and + + align:start position:0% +correct theories by being lucky and + + + align:start position:0% +correct theories by being lucky and +clever and then you'd have to find a + + align:start position:0% +clever and then you'd have to find a + + + align:start position:0% +clever and then you'd have to find a +neuroscientist + + align:start position:0% +neuroscientist + + + align:start position:0% +neuroscientist +to uh design an experiment to see if + + align:start position:0% +to uh design an experiment to see if + + + align:start position:0% +to uh design an experiment to see if +there's any evidence for that in + + align:start position:0% +there's any evidence for that in + + + align:start position:0% +there's any evidence for that in +particular I'd like to convince some + + align:start position:0% +particular I'd like to convince some + + + align:start position:0% +particular I'd like to convince some +neurologist + + align:start position:0% +neurologist + + + align:start position:0% +neurologist +to consider the idea of klines that's um + + align:start position:0% +to consider the idea of klines that's um + + + align:start position:0% +to consider the idea of klines that's um +described I think in both of my + + align:start position:0% +described I think in both of my + + + align:start position:0% +described I think in both of my +books and uh think of think of + + align:start position:0% +books and uh think of think of + + + align:start position:0% +books and uh think of think of +experiments as see if you could get them + + align:start position:0% +experiments as see if you could get them + + + align:start position:0% +experiments as see if you could get them +to light up or uh otherwise localize and + + align:start position:0% +to light up or uh otherwise localize and + + + align:start position:0% +to light up or uh otherwise localize and +uh once you have in your mind the idea + + align:start position:0% +uh once you have in your mind the idea + + + align:start position:0% +uh once you have in your mind the idea +that maybe the way one brain connects + + align:start position:0% +that maybe the way one brain connects + + + align:start position:0% +that maybe the way one brain connects +sends information to another is over + + align:start position:0% +sends information to another is over + + + align:start position:0% +sends information to another is over +something like Kines which uh I think I + + align:start position:0% +something like Kines which uh I think I + + + align:start position:0% +something like Kines which uh I think I +talked about that the other day random + + align:start position:0% +talked about that the other day random + + + align:start position:0% +talked about that the other day random +superimposed coding on Parallel wires + + align:start position:0% +superimposed coding on Parallel wires + + + align:start position:0% +superimposed coding on Parallel wires +then maybe you could think of + + align:start position:0% +then maybe you could think of + + + align:start position:0% +then maybe you could think of +experiments that uh even present brain + + align:start position:0% +experiments that uh even present brain + + + align:start position:0% +experiments that uh even present brain +scanning techniques could use to to + + align:start position:0% +scanning techniques could use to to + + + align:start position:0% +scanning techniques could use to to +localize these uh my main concern is + + align:start position:0% +localize these uh my main concern is + + + align:start position:0% +localize these uh my main concern is +that uh the way they do brain scanning + + align:start position:0% +that uh the way they do brain scanning + + + align:start position:0% +that uh the way they do brain scanning +now is to set thresholds to see which + + align:start position:0% +now is to set thresholds to see which + + + align:start position:0% +now is to set thresholds to see which +brain centers light up uh and which go + + align:start position:0% +brain centers light up uh and which go + + + align:start position:0% +brain centers light up uh and which go +turn off and then they say oh I see this + + align:start position:0% +turn off and then they say oh I see this + + + align:start position:0% +turn off and then they say oh I see this +activity looks like it happen in the + + align:start position:0% +activity looks like it happen in the + + + align:start position:0% +activity looks like it happen in the +lateral hippocampus and because you see + + align:start position:0% +lateral hippocampus and because you see + + + align:start position:0% +lateral hippocampus and because you see +that light up I think that there should + + align:start position:0% +that light up I think that there should + + + align:start position:0% +that light up I think that there should +be an at least a couple + + align:start position:0% +be an at least a couple + + + align:start position:0% +be an at least a couple +of um neuroscientist groups who do the + + align:start position:0% +of um neuroscientist groups who do the + + + align:start position:0% +of um neuroscientist groups who do the +opposite which is to reduce the contrast + + align:start position:0% +opposite which is to reduce the contrast + + + align:start position:0% +opposite which is to reduce the contrast +and when there are several brain centers + + align:start position:0% +and when there are several brain centers + + + align:start position:0% +and when there are several brain centers +that seem to be involved in an activity + + align:start position:0% +that seem to be involved in an activity + + + align:start position:0% +that seem to be involved in an activity +then say something to the patient and + + align:start position:0% +then say something to the patient and + + + align:start position:0% +then say something to the patient and +look for one area to get 2% d dimer and + + align:start position:0% +look for one area to get 2% d dimer and + + + align:start position:0% +look for one area to get 2% d dimer and +another to look 4% brighter and say that + + align:start position:0% +another to look 4% brighter and say that + + + align:start position:0% +another to look 4% brighter and say that +might mean that there's a K line going + + align:start position:0% +might mean that there's a K line going + + + align:start position:0% +might mean that there's a K line going +from this one to that one with an + + align:start position:0% +from this one to that one with an + + + align:start position:0% +from this one to that one with an +inhibitory effect on this or that uh but + + align:start position:0% +inhibitory effect on this or that uh but + + + align:start position:0% +inhibitory effect on this or that uh but +as far as I know right now every paper + + align:start position:0% +as far as I know right now every paper + + + align:start position:0% +as far as I know right now every paper +I've ever seen published showing brain + + align:start position:0% +I've ever seen published showing brain + + + align:start position:0% +I've ever seen published showing brain +centers lighting up has high contrast + + align:start position:0% +centers lighting up has high contrast + + + align:start position:0% +centers lighting up has high contrast +and so they're missing all the small + + align:start position:0% +and so they're missing all the small + + + align:start position:0% +and so they're missing all the small +things and maybe maybe they're only + + align:start position:0% +things and maybe maybe they're only + + + align:start position:0% +things and maybe maybe they're only +seeing the end result of the process + + align:start position:0% +seeing the end result of the process + + + align:start position:0% +seeing the end result of the process +where a little thinking has gone on with + + align:start position:0% +where a little thinking has gone on with + + + align:start position:0% +where a little thinking has gone on with +all these intricate + + align:start position:0% +all these intricate + + + align:start position:0% +all these intricate +uh low intensity + + align:start position:0% +uh low intensity + + + align:start position:0% +uh low intensity +interactions and then the thing decides + + align:start position:0% +interactions and then the thing decides + + + align:start position:0% +interactions and then the thing decides +oh okay I'm going to do this and you + + align:start position:0% +oh okay I'm going to do this and you + + + align:start position:0% +oh okay I'm going to do this and you +conclude that that brain Center which + + align:start position:0% +conclude that that brain Center which + + + align:start position:0% +conclude that that brain Center which +lit up is the one that decided to do + + align:start position:0% +lit up is the one that decided to do + + + align:start position:0% +lit up is the one that decided to do +this + + align:start position:0% + + + + align:start position:0% + +whereas it's a result of a very small + + align:start position:0% +whereas it's a result of a very small + + + align:start position:0% +whereas it's a result of a very small +fast Avalanche + + align:start position:0% + + + + align:start position:0% + +have you seen the one a couple weeks ago + + align:start position:0% +have you seen the one a couple weeks ago + + + align:start position:0% +have you seen the one a couple weeks ago +about reading out the visual in real + + align:start position:0% +about reading out the visual in real + + + align:start position:0% +about reading out the visual in real +time from the visual cortex yes quite + + align:start position:0% +time from the visual cortex yes quite + + + align:start position:0% +time from the visual cortex yes quite +quite a nice hack they aren't actually + + align:start position:0% +quite a nice hack they aren't actually + + + align:start position:0% +quite a nice hack they aren't actually +reading out the visual field they for + + align:start position:0% +reading out the visual field they for + + + align:start position:0% +reading out the visual field they for +each subject they do a massive amount of + + align:start position:0% +each subject they do a massive amount of + + + align:start position:0% +each subject they do a massive amount of +training where they + + align:start position:0% +training where they + + + align:start position:0% +training where they +flash thousands of one second video + + align:start position:0% +flash thousands of one second video + + + align:start position:0% +flash thousands of one second video +clips and assemble a database of uh a + + align:start position:0% +clips and assemble a database of uh a + + + align:start position:0% +clips and assemble a database of uh a +very small perations in different parts + + align:start position:0% +very small perations in different parts + + + align:start position:0% +very small perations in different parts +of the visual cortex lighting up and + + align:start position:0% +of the visual cortex lighting up and + + + align:start position:0% +of the visual cortex lighting up and +then they they show a novel video to + + align:start position:0% +then they they show a novel video to + + + align:start position:0% +then they they show a novel video to +each of the the subjects and uh + + align:start position:0% +each of the the subjects and uh + + + align:start position:0% +each of the the subjects and uh +basically uh just do a linear + + align:start position:0% +basically uh just do a linear + + + align:start position:0% +basically uh just do a linear +combination of all of the videos that + + align:start position:0% +combination of all of the videos that + + + align:start position:0% +combination of all of the videos that +they have done in the training phase + + align:start position:0% +they have done in the training phase + + + align:start position:0% +they have done in the training phase +weighted by how closely things line up + + align:start position:0% +weighted by how closely things line up + + + align:start position:0% +weighted by how closely things line up +in the brain and you can you can sort of + + align:start position:0% +in the brain and you can you can sort of + + + align:start position:0% +in the brain and you can you can sort of +see what's going on it's it's quite + + align:start position:0% +see what's going on it's it's quite + + + align:start position:0% +see what's going on it's it's quite +striking can you tell what they're + + align:start position:0% +striking can you tell what they're + + + align:start position:0% +striking can you tell what they're +thinking or you can only tell what + + align:start position:0% +thinking or you can only tell what + + + align:start position:0% +thinking or you can only tell what +they're seeing um and but I think yeah + + align:start position:0% +they're seeing um and but I think yeah + + + align:start position:0% +they're seeing um and but I think yeah +if your eyes are closed what is your + + align:start position:0% +if your eyes are closed what is your + + + align:start position:0% +if your eyes are closed what is your +your primary visual cortex probably + + align:start position:0% +your primary visual cortex probably + + + align:start position:0% +your primary visual cortex probably +doesn't do anything does I think it's + + align:start position:0% +doesn't do anything does I think it's + + + align:start position:0% +doesn't do anything does I think it's +just yeah but the secondary one might + + align:start position:0% +just yeah but the secondary one might + + + align:start position:0% +just yeah but the secondary one might +be representing things that you that + + align:start position:0% +be representing things that you that + + + align:start position:0% +be representing things that you that +might be there yes so the the goal of + + align:start position:0% +might be there yes so the the goal of + + + align:start position:0% +might be there yes so the the goal of +the authors of this paper is eventually + + align:start position:0% +the authors of this paper is eventually + + + align:start position:0% +the authors of this paper is eventually +to literally make movies out of + + align:start position:0% +to literally make movies out of + + + align:start position:0% +to literally make movies out of +dreams but that's a long way + + align:start position:0% +dreams but that's a long way + + + align:start position:0% +dreams but that's a long way +off it's an old idea in science fiction + + align:start position:0% + + + + align:start position:0% + +M how many of you read science + + align:start position:0% + + + + align:start position:0% + +fiction + + align:start position:0% +fiction + + + align:start position:0% +fiction +wow that's a + + align:start position:0% + + + + align:start position:0% + +majority who's the best new + + align:start position:0% +majority who's the best new + + + align:start position:0% +majority who's the best new +writer Neil + + align:start position:0% +writer Neil + + + align:start position:0% +writer Neil +Stevenson he's been writing a long + + align:start position:0% +Stevenson he's been writing a long + + + align:start position:0% +Stevenson he's been writing a long +time do compared to + + align:start position:0% + + + + align:start position:0% + +yes I had dinner with Stephenson at the + + align:start position:0% +yes I had dinner with Stephenson at the + + + align:start position:0% +yes I had dinner with Stephenson at the +hilles a couple of years + + align:start position:0% + + + + align:start position:0% + +ago yeah ask so from what I understood + + align:start position:0% +ago yeah ask so from what I understood + + + align:start position:0% +ago yeah ask so from what I understood +it seems that you're you're saying that + + align:start position:0% +it seems that you're you're saying that + + + align:start position:0% +it seems that you're you're saying that +the difference between us and like for + + align:start position:0% +the difference between us and like for + + + align:start position:0% +the difference between us and like for +example dogs is just a confrontation of + + align:start position:0% +example dogs is just a confrontation of + + + align:start position:0% +example dogs is just a confrontation of +like + + align:start position:0% +like + + + align:start position:0% +like +power + + align:start position:0% +power + + + align:start position:0% +power +so do you believe that the difference + + align:start position:0% +so do you believe that the difference + + + align:start position:0% +so do you believe that the difference +between dogs and computers is also just + + align:start position:0% +between dogs and computers is also just + + + align:start position:0% +between dogs and computers is also just +computational like what what what would + + align:start position:0% +computational like what what what would + + + align:start position:0% +computational like what what what would +be the difference + + align:start position:0% +be the difference + + + align:start position:0% +be the difference +between dogs and like touring + + align:start position:0% + + + + align:start position:0% + +machine well there is no difference it's + + align:start position:0% +machine well there is no difference it's + + + align:start position:0% +machine well there is no difference it's +just it might be that only humans + + align:start position:0% +just it might be that only humans + + + align:start position:0% +just it might be that only humans +and maybe some of their closest rela + + align:start position:0% +and maybe some of their closest rela + + + align:start position:0% +and maybe some of their closest rela +atives can imagine a + + align:start position:0% + + + + align:start position:0% + +sequence in other words + + align:start position:0% +sequence in other words + + + align:start position:0% +sequence in other words +the the simplest oldest theories in + + align:start position:0% +the the simplest oldest theories in + + + align:start position:0% +the the simplest oldest theories in +psychology + + align:start position:0% +psychology + + + align:start position:0% +psychology +were uh the theory of like David Hume + + align:start position:0% +were uh the theory of like David Hume + + + align:start position:0% +were uh the theory of like David Hume +had the idea of Association one idea in + + align:start position:0% +had the idea of Association one idea in + + + align:start position:0% +had the idea of Association one idea in +the mind or brain would + + align:start position:0% +the mind or brain would + + + align:start position:0% +the mind or brain would +uh causes another idea to appear in + + align:start position:0% +uh causes another idea to appear in + + + align:start position:0% +uh causes another idea to appear in +another so that means that uh a brain + + align:start position:0% +another so that means that uh a brain + + + align:start position:0% +another so that means that uh a brain +that's learned associations or learn if + + align:start position:0% +that's learned associations or learn if + + + align:start position:0% +that's learned associations or learn if +then rule Bas systems can make chains of + + align:start position:0% +then rule Bas systems can make chains of + + + align:start position:0% +then rule Bas systems can make chains of +things but the question is uh can any + + align:start position:0% +things but the question is uh can any + + + align:start position:0% +things but the question is uh can any +animal other than humans imagine two + + align:start position:0% +animal other than humans imagine two + + + align:start position:0% +animal other than humans imagine two +different + + align:start position:0% +different + + + align:start position:0% +different +situations and then compare them and say + + align:start position:0% +situations and then compare them and say + + + align:start position:0% +situations and then compare them and say +if I did this and then that how would + + align:start position:0% +if I did this and then that how would + + + align:start position:0% +if I did this and then that how would +the result differ from doing that and + + align:start position:0% +the result differ from doing that and + + + align:start position:0% +the result differ from doing that and +then this + + align:start position:0% +then this + + + align:start position:0% +then this +if you look at Jerry susman's + + align:start position:0% +if you look at Jerry susman's + + + align:start position:0% +if you look at Jerry susman's +thesis if you're at + + align:start position:0% +thesis if you're at + + + align:start position:0% +thesis if you're at +MIT a good thing to do is to read the + + align:start position:0% +MIT a good thing to do is to read the + + + align:start position:0% +MIT a good thing to do is to read the +and you're taking a course you should + + align:start position:0% +and you're taking a course you should + + + align:start position:0% +and you're taking a course you should +read the PHD thesis of your + + align:start position:0% + + + + align:start position:0% + +professor + + align:start position:0% +professor + + + align:start position:0% +professor +uh it not only will help you understand + + align:start position:0% +uh it not only will help you understand + + + align:start position:0% +uh it not only will help you understand +better uh what the professor said uh + + align:start position:0% +better uh what the professor said uh + + + align:start position:0% +better uh what the professor said uh +you'll get a higher grade if you care + + align:start position:0% +you'll get a higher grade if you care + + + align:start position:0% +you'll get a higher grade if you care +and many other advantages like you'll + + align:start position:0% +and many other advantages like you'll + + + align:start position:0% +and many other advantages like you'll +actually be able to talk to him and his + + align:start position:0% +actually be able to talk to him and his + + + align:start position:0% +actually be able to talk to him and his +mind won't throw + + align:start position:0% + + + + align:start position:0% + +up so uh you know I don't know if a dog + + align:start position:0% +up so uh you know I don't know if a dog + + + align:start position:0% +up so uh you know I don't know if a dog +can recapitulate + + align:start position:0% +can recapitulate + + + align:start position:0% +can recapitulate +as can the dog think I think I'll go + + align:start position:0% +as can the dog think I think I'll go + + + align:start position:0% +as can the dog think I think I'll go +around this fence and when I get to this + + align:start position:0% +around this fence and when I get to this + + + align:start position:0% +around this fence and when I get to this +tree I'll do this I'll pee on it that's + + align:start position:0% +tree I'll do this I'll pee on it that's + + + align:start position:0% +tree I'll do this I'll pee on it that's +what what dogs do and then I'll + + align:start position:0% +what what dogs do and then I'll + + + align:start position:0% +what what dogs do and then I'll +uh whereas if I go this way something + + align:start position:0% +uh whereas if I go this way something + + + align:start position:0% +uh whereas if I go this way something +else will happen it might be that you uh + + align:start position:0% +else will happen it might be that you uh + + + align:start position:0% +else will happen it might be that you uh +that + + align:start position:0% +that + + + align:start position:0% +that +pre pre uh primates can't do much of + + align:start position:0% +pre pre uh primates can't do much of + + + align:start position:0% +pre pre uh primates can't do much of +that on the other hand I just if you ask + + align:start position:0% +that on the other hand I just if you ask + + + align:start position:0% +that on the other hand I just if you ask +what is the what is the song of the + + align:start position:0% +what is the what is the song of the + + + align:start position:0% +what is the what is the song of the +whale what's the whale that has this 20 + + align:start position:0% +whale what's the whale that has this 20 + + + align:start position:0% +whale what's the whale that has this 20 +minute song + + align:start position:0% + + + + align:start position:0% + +uh I think my conjecture is that uh you + + align:start position:0% +uh I think my conjecture is that uh you + + + align:start position:0% +uh I think my conjecture is that uh you +know a whale has to swim a thousand + + align:start position:0% +know a whale has to swim a thousand + + + align:start position:0% +know a whale has to swim a thousand +miles or several hundred miles sometimes + + align:start position:0% +miles or several hundred miles sometimes + + + align:start position:0% +miles or several hundred miles sometimes +to get the food it wants because things + + align:start position:0% +to get the food it wants because things + + + align:start position:0% +to get the food it wants because things +change and uh each group of + + align:start position:0% + + + + align:start position:0% + +whales humpback whales I guess sing this + + align:start position:0% +whales humpback whales I guess sing this + + + align:start position:0% +whales humpback whales I guess sing this +song that's about 20 minutes long and + + align:start position:0% +song that's about 20 minutes long and + + + align:start position:0% +song that's about 20 minutes long and +nobody has made a good + + align:start position:0% +nobody has made a good + + + align:start position:0% +nobody has made a good +conjecture about what's the content of + + align:start position:0% +conjecture about what's the content of + + + align:start position:0% +conjecture about what's the content of +that song but it's shared among the + + align:start position:0% +that song but it's shared among the + + + align:start position:0% +that song but it's shared among the +animals and it goes you know they can + + align:start position:0% +animals and it goes you know they can + + + align:start position:0% +animals and it goes you know they can +hear it 20 or 50 miles away and repeat + + align:start position:0% +hear it 20 or 50 miles away and repeat + + + align:start position:0% +hear it 20 or 50 miles away and repeat +it and it changes every season so I + + align:start position:0% +it and it changes every season so I + + + align:start position:0% +it and it changes every season so I +suspect that the obvious thing that it + + align:start position:0% +suspect that the obvious thing that it + + + align:start position:0% +suspect that the obvious thing that it +should be about is where's the food + + align:start position:0% +should be about is where's the food + + + align:start position:0% +should be about is where's the food +these days we're the best flocks of fish + + align:start position:0% +these days we're the best flocks of fish + + + align:start position:0% +these days we're the best flocks of fish +to eat because + + align:start position:0% +to eat because + + + align:start position:0% +to eat because +a whale can't afford to swim 200 miles + + align:start position:0% +a whale can't afford to swim 200 miles + + + align:start position:0% +a whale can't afford to swim 200 miles +uh to the place where the the its + + align:start position:0% +uh to the place where the the its + + + align:start position:0% +uh to the place where the the its +favorite fish were last year and find it + + align:start position:0% +favorite fish were last year and find it + + + align:start position:0% +favorite fish were last year and find it +empty it takes a lot of energy + + align:start position:0% +empty it takes a lot of energy + + + align:start position:0% +empty it takes a lot of energy +to to cross the + + align:start position:0% +to to cross the + + + align:start position:0% +to to cross the +ocean so maybe those animals have + + align:start position:0% +ocean so maybe those animals have + + + align:start position:0% +ocean so maybe those animals have +the ability to remember very long + + align:start position:0% +the ability to remember very long + + + align:start position:0% +the ability to remember very long +sequences and even some semantics + + align:start position:0% +sequences and even some semantics + + + align:start position:0% +sequences and even some semantics +connected with it + + align:start position:0% +connected with it + + + align:start position:0% +connected with it +I don't know if dogs have anything like + + align:start position:0% +I don't know if dogs have anything like + + + align:start position:0% +I don't know if dogs have anything like +that do dogs ever seem to be talking to + + align:start position:0% +that do dogs ever seem to be talking to + + + align:start position:0% +that do dogs ever seem to be talking to +each + + align:start position:0% +each + + + align:start position:0% +each +other or are they + + align:start position:0% +other or are they + + + align:start position:0% +other or are they +just a story about dogs so apparently in + + align:start position:0% +just a story about dogs so apparently in + + + align:start position:0% +just a story about dogs so apparently in +Moscow um not all dogs but a very small + + align:start position:0% +Moscow um not all dogs but a very small + + + align:start position:0% +Moscow um not all dogs but a very small +fraction of the stray dogs um in the in + + align:start position:0% +fraction of the stray dogs um in the in + + + align:start position:0% +fraction of the stray dogs um in the in +the city have learned how to ride the + + align:start position:0% +the city have learned how to ride the + + + align:start position:0% +the city have learned how to ride the +Metro um they live out in the suburbs + + align:start position:0% +Metro um they live out in the suburbs + + + align:start position:0% +Metro um they live out in the suburbs +because I guess people give them less + + align:start position:0% +because I guess people give them less + + + align:start position:0% +because I guess people give them less +trouble when they're out in the suburbs + + align:start position:0% +trouble when they're out in the suburbs + + + align:start position:0% +trouble when they're out in the suburbs +and then they take the subway each day + + align:start position:0% +and then they take the subway each day + + + align:start position:0% +and then they take the subway each day +into the city center where there are + + align:start position:0% +into the city center where there are + + + align:start position:0% +into the city center where there are +more people and they have various + + align:start position:0% +more people and they have various + + + align:start position:0% +more people and they have various +strategies for begging in the city + + align:start position:0% +strategies for begging in the city + + + align:start position:0% +strategies for begging in the city +center so for instance they find some + + align:start position:0% +center so for instance they find some + + + align:start position:0% +center so for instance they find some +guy with a sandwich and they bark really + + align:start position:0% +guy with a sandwich and they bark really + + + align:start position:0% +guy with a sandwich and they bark really +loudly behind the guy and the guy would + + align:start position:0% +loudly behind the guy and the guy would + + + align:start position:0% +loudly behind the guy and the guy would +drop the sandwich and then they steal + + align:start position:0% +drop the sandwich and then they steal + + + align:start position:0% +drop the sandwich and then they steal +it or they have a pack of them and they + + align:start position:0% +it or they have a pack of them and they + + + align:start position:0% +it or they have a pack of them and they +all know each other and they send out a + + align:start position:0% +all know each other and they send out a + + + align:start position:0% +all know each other and they send out a +really cute one to beg for food and so + + align:start position:0% +really cute one to beg for food and so + + + align:start position:0% +really cute one to beg for food and so +they'll give the cute one food and the + + align:start position:0% +they'll give the cute one food and the + + + align:start position:0% +they'll give the cute one food and the +cute one brings it back to everyone else + + align:start position:0% +cute one brings it back to everyone else + + + align:start position:0% +cute one brings it back to everyone else +and simply navigating the subway is + + align:start position:0% +and simply navigating the subway is + + + align:start position:0% +and simply navigating the subway is +actually a bit complicated for a dog um + + align:start position:0% +actually a bit complicated for a dog um + + + align:start position:0% +actually a bit complicated for a dog um +but somehow like a very small group of + + align:start position:0% +but somehow like a very small group of + + + align:start position:0% +but somehow like a very small group of +dogs in Moscow have learned how to do it + + align:start position:0% +dogs in Moscow have learned how to do it + + + align:start position:0% +dogs in Moscow have learned how to do it +like figure out where their stop is get + + align:start position:0% +like figure out where their stop is get + + + align:start position:0% +like figure out where their stop is get +on get + + align:start position:0% +on get + + + align:start position:0% +on get +off yeah our dog once popped on the + + align:start position:0% +off yeah our dog once popped on the + + + align:start position:0% +off yeah our dog once popped on the +green line and got off at Park Street so + + align:start position:0% +green line and got off at Park Street so + + + align:start position:0% +green line and got off at Park Street so +she was missing for a while and somebody + + align:start position:0% +she was missing for a while and somebody + + + align:start position:0% +she was missing for a while and somebody +at Park street called up and said your + + align:start position:0% +at Park street called up and said your + + + align:start position:0% +at Park street called up and said your +dog is here so I went down and got + + align:start position:0% +dog is here so I went down and got + + + align:start position:0% +dog is here so I went down and got +her and the the agent + + align:start position:0% +her and the the agent + + + align:start position:0% +her and the the agent +said you know we had a dog that came to + + align:start position:0% +said you know we had a dog that came to + + + align:start position:0% +said you know we had a dog that came to +Park Street every + + align:start position:0% +Park Street every + + + align:start position:0% +Park Street every +day and changed trains and took the red + + align:start position:0% +day and changed trains and took the red + + + align:start position:0% +day and changed trains and took the red +line to + + align:start position:0% +line to + + + align:start position:0% +line to +somewhere + + align:start position:0% +somewhere + + + align:start position:0% +somewhere +and finally we found out that its Master + + align:start position:0% +and finally we found out that its Master + + + align:start position:0% +and finally we found out that its Master +had it used to go to work with its + + align:start position:0% +had it used to go to work with its + + + align:start position:0% +had it used to go to work with its +owner every day and he + + align:start position:0% +owner every day and he + + + align:start position:0% +owner every day and he +died and the dog took the same trip + + align:start position:0% +died and the dog took the same trip + + + align:start position:0% +died and the dog took the same trip +every day and + + align:start position:0% + + + + align:start position:0% + +the uh tea people understood that he + + align:start position:0% +the uh tea people understood that he + + + align:start position:0% +the uh tea people understood that he +shouldn't be bothered with + + align:start position:0% +shouldn't be bothered with + + + align:start position:0% +shouldn't be bothered with +it our dog chased cars was it Jenny and + + align:start position:0% +it our dog chased cars was it Jenny and + + + align:start position:0% +it our dog chased cars was it Jenny and +uh that was terrible because we knew she + + align:start position:0% +uh that was terrible because we knew she + + + align:start position:0% +uh that was terrible because we knew she +was going to get hurt and we finally a + + align:start position:0% +was going to get hurt and we finally a + + + align:start position:0% +was going to get hurt and we finally a +car squashed her leg and she was uh laid + + align:start position:0% +car squashed her leg and she was uh laid + + + align:start position:0% +car squashed her leg and she was uh laid +up for a while with a somewhat broken + + align:start position:0% +up for a while with a somewhat broken + + + align:start position:0% +up for a while with a somewhat broken +leg and I thought well she won't Chase + + align:start position:0% +leg and I thought well she won't Chase + + + align:start position:0% +leg and I thought well she won't Chase +cars + + align:start position:0% +cars + + + align:start position:0% +cars +anymore but she did but she didn't what + + align:start position:0% +anymore but she did but she didn't what + + + align:start position:0% +anymore but she did but she didn't what +she wouldn't do is go to the + + align:start position:0% +she wouldn't do is go to the + + + align:start position:0% +she wouldn't do is go to the +intersection of Carlton and Ivy Street + + align:start position:0% +intersection of Carlton and Ivy Street + + + align:start position:0% +intersection of Carlton and Ivy Street +anymore which + + align:start position:0% +anymore which + + + align:start position:0% +anymore which +is so she had learned + + align:start position:0% + + + + align:start position:0% + +something but it wasn't the right thing + + align:start position:0% + + + + align:start position:0% + +I'm not sure I answered + + align:start position:0% + + + + align:start position:0% + +your well actually according to so + + align:start position:0% +your well actually according to so + + + align:start position:0% +your well actually according to so +there's the story that you gave um in + + align:start position:0% +there's the story that you gave um in + + + align:start position:0% +there's the story that you gave um in +chapter two about the girl who's digging + + align:start position:0% +chapter two about the girl who's digging + + + align:start position:0% +chapter two about the girl who's digging +dirt and um so in the case where um she + + align:start position:0% +dirt and um so in the case where um she + + + align:start position:0% +dirt and um so in the case where um she +learns whether digging dirt is a good or + + align:start position:0% +learns whether digging dirt is a good or + + + align:start position:0% +learns whether digging dirt is a good or +bad activity is when there's somebody + + align:start position:0% +bad activity is when there's somebody + + + align:start position:0% +bad activity is when there's somebody +with that with wh she has attachment + + align:start position:0% +with that with wh she has attachment + + + align:start position:0% +with that with wh she has attachment +bond with pres who's telling her whether + + align:start position:0% +bond with pres who's telling her whether + + + align:start position:0% +bond with pres who's telling her whether +it's good or bad and in the case where + + align:start position:0% +it's good or bad and in the case where + + + align:start position:0% +it's good or bad and in the case where +she learns to avoid that spot is when + + align:start position:0% +she learns to avoid that spot is when + + + align:start position:0% +she learns to avoid that spot is when +something bad happens to her in the spot + + align:start position:0% +something bad happens to her in the spot + + + align:start position:0% +something bad happens to her in the spot +so in a sense the the dog is behaving + + align:start position:0% +so in a sense the the dog is behaving + + + align:start position:0% +so in a sense the the dog is behaving +just like that logic yes the + + align:start position:0% +just like that logic yes the + + + align:start position:0% +just like that logic yes the +dog except that the dog is oriented + + align:start position:0% +dog except that the dog is oriented + + + align:start position:0% +dog except that the dog is oriented +toward location rather than something + + align:start position:0% +toward location rather than something + + + align:start position:0% +toward location rather than something +else so uh + + align:start position:0% + + + + align:start position:0% + +as talk about uh possible hierarchy of + + align:start position:0% +as talk about uh possible hierarchy of + + + align:start position:0% +as talk about uh possible hierarchy of +higher + + align:start position:0% +higher + + + align:start position:0% +higher +or representation schemes of knowledge + + align:start position:0% +or representation schemes of knowledge + + + align:start position:0% +or representation schemes of knowledge +with like um semantic Nets on top at the + + align:start position:0% +with like um semantic Nets on top at the + + + align:start position:0% +with like um semantic Nets on top at the +bottom there's like NE in the middle of + + align:start position:0% +bottom there's like NE in the middle of + + + align:start position:0% +bottom there's like NE in the middle of +K lines on the bottom there's things up + + align:start position:0% +K lines on the bottom there's things up + + + align:start position:0% +K lines on the bottom there's things up +there um so the way I thought about the + + align:start position:0% +there um so the way I thought about the + + + align:start position:0% +there um so the way I thought about the +questions I were just asked that humans + + align:start position:0% +questions I were just asked that humans + + + align:start position:0% +questions I were just asked that humans +it seems natural to me that you need all + + align:start position:0% +it seems natural to me that you need all + + + align:start position:0% +it seems natural to me that you need all +the intermediate um representations in + + align:start position:0% +the intermediate um representations in + + + align:start position:0% +the intermediate um representations in +order to support like something like + + align:start position:0% +order to support like something like + + + align:start position:0% +order to support like something like +semantic Nets it seems natural to me to + + align:start position:0% +semantic Nets it seems natural to me to + + + align:start position:0% +semantic Nets it seems natural to me to +think that humans of all these the whole + + align:start position:0% +think that humans of all these the whole + + + align:start position:0% +think that humans of all these the whole +hierarchy of representations that dogs + + align:start position:0% +hierarchy of representations that dogs + + + align:start position:0% +hierarchy of representations that dogs +might have something um only in the + + align:start position:0% +might have something um only in the + + + align:start position:0% +might have something um only in the +middle like might have something like + + align:start position:0% +middle like might have something like + + + align:start position:0% +middle like might have something like +neur or something um so my question is + + align:start position:0% +neur or something um so my question is + + + align:start position:0% +neur or something um so my question is +what behaviors that you could observe in + + align:start position:0% +what behaviors that you could observe in + + + align:start position:0% +what behaviors that you could observe in +real life + + align:start position:0% +real life + + + align:start position:0% +real life +um could only be done with one of these + + align:start position:0% +um could only be done with one of these + + + align:start position:0% +um could only be done with one of these +intermediate representations of + + align:start position:0% +intermediate representations of + + + align:start position:0% +intermediate representations of +knowledge um that can't be done with + + align:start position:0% +knowledge um that can't be done with + + + align:start position:0% +knowledge um that can't be done with +something like machine + + align:start position:0% + + + + align:start position:0% + +learning you mean machine learning of + + align:start position:0% +learning you mean machine learning of + + + align:start position:0% +learning you mean machine learning of +what of some particular + + align:start position:0% +what of some particular + + + align:start position:0% +what of some particular +kind the kind that's currently + + align:start position:0% +kind the kind that's currently + + + align:start position:0% +kind the kind that's currently +fashionable I + + align:start position:0% +fashionable I + + + align:start position:0% +fashionable I +think kind of like with like H data set + + align:start position:0% +think kind of like with like H data set + + + align:start position:0% +think kind of like with like H data set +Ro force sort of uh calibration of some + + align:start position:0% +Ro force sort of uh calibration of some + + + align:start position:0% +Ro force sort of uh calibration of some +parameter + + align:start position:0% + + + + align:start position:0% + +to me that if you recognize a behavior + + align:start position:0% +to me that if you recognize a behavior + + + align:start position:0% +to me that if you recognize a behavior +like that it might be a worthy + + align:start position:0% +like that it might be a worthy + + + align:start position:0% +like that it might be a worthy +intermediate goal to be able to model + + align:start position:0% +intermediate goal to be able to model + + + align:start position:0% +intermediate goal to be able to model +that instead of trying to model + + align:start position:0% +that instead of trying to model + + + align:start position:0% +that instead of trying to model +something like natural language which is + + align:start position:0% +something like natural language which is + + + align:start position:0% +something like natural language which is +you might need the first part to get the + + align:start position:0% +you might need the first part to get the + + + align:start position:0% +you might need the first part to get the +second + + align:start position:0% +second + + + align:start position:0% +second +part well it would be nice to + + align:start position:0% + + + + align:start position:0% + +know I wonder how much is known about + + align:start position:0% +know I wonder how much is known about + + + align:start position:0% +know I wonder how much is known about +elephants which + + align:start position:0% + + + + align:start position:0% + +are awfully smart compared + + align:start position:0% + + + + align:start position:0% + +to I suspect that they are very good at + + align:start position:0% +to I suspect that they are very good at + + + align:start position:0% +to I suspect that they are very good at +making plans + + align:start position:0% +making plans + + + align:start position:0% +making plans +because it's so easy for an elephant to + + align:start position:0% +because it's so easy for an elephant to + + + align:start position:0% +because it's so easy for an elephant to +make a fatal + + align:start position:0% +make a fatal + + + align:start position:0% +make a fatal +mistake + + align:start position:0% +mistake + + + align:start position:0% +mistake +so unfortunately it probably U nobody no + + align:start position:0% +so unfortunately it probably U nobody no + + + align:start position:0% +so unfortunately it probably U nobody no +research group has enough + + align:start position:0% +research group has enough + + + align:start position:0% +research group has enough +budget + + align:start position:0% +budget + + + align:start position:0% +budget +to to study that kind of animal because + + align:start position:0% +to to study that kind of animal because + + + align:start position:0% +to to study that kind of animal because +it's just too expensive + + align:start position:0% +it's just too expensive + + + align:start position:0% +it's just too expensive +how smart are elephant + + align:start position:0% + + + + align:start position:0% + +anybody I've never interacted with + + align:start position:0% + + + + align:start position:0% + +one I'm not sure if you have a + + align:start position:0% + + + + align:start position:0% + +question the question is are there + + align:start position:0% +question the question is are there + + + align:start position:0% +question the question is are there +behaviors that you you need an + + align:start position:0% +behaviors that you you need an + + + align:start position:0% +behaviors that you you need an +intermediate level of the repetition of + + align:start position:0% +intermediate level of the repetition of + + + align:start position:0% +intermediate level of the repetition of +knowledge in order to perform that uh + + align:start position:0% +knowledge in order to perform that uh + + + align:start position:0% +knowledge in order to perform that uh +you don't need like the highest level + + align:start position:0% +you don't need like the highest level + + + align:start position:0% +you don't need like the highest level +like the semantic like basically natural + + align:start position:0% +like the semantic like basically natural + + + align:start position:0% +like the semantic like basically natural +language are to do so you could say that + + align:start position:0% +language are to do so you could say that + + + align:start position:0% +language are to do so you could say that +if I saw an animal doing this Behavior I + + align:start position:0% +if I saw an animal doing this Behavior I + + + align:start position:0% +if I saw an animal doing this Behavior I +know that it has some intermediate level + + align:start position:0% +know that it has some intermediate level + + + align:start position:0% +know that it has some intermediate level +of uh representation of knowledge that's + + align:start position:0% +of uh representation of knowledge that's + + + align:start position:0% +of uh representation of knowledge that's +more than kind of a Brute Force machine + + align:start position:0% +more than kind of a Brute Force machine + + + align:start position:0% +more than kind of a Brute Force machine +learning approach because like like was + + align:start position:0% +learning approach because like like was + + + align:start position:0% +learning approach because like like was +discussed before a computer can do pathf + + align:start position:0% +discussed before a computer can do pathf + + + align:start position:0% +discussed before a computer can do pathf +finding and with just like a Brute Force + + align:start position:0% +finding and with just like a Brute Force + + + align:start position:0% +finding and with just like a Brute Force +approach but I don't think that's how + + align:start position:0% +approach but I don't think that's how + + + align:start position:0% +approach but I don't think that's how +humans do it or animals do + + align:start position:0% + + + + align:start position:0% + +it I can't think of a good EX + + align:start position:0% + + + + align:start position:0% + +it's just hard to think of any + + align:start position:0% +it's just hard to think of any + + + align:start position:0% +it's just hard to think of any +animals besides us that + + align:start position:0% + + + + align:start position:0% + +have really elaborate semantic + + align:start position:0% +have really elaborate semantic + + + align:start position:0% +have really elaborate semantic +networks there's coko + + align:start position:0% +networks there's coko + + + align:start position:0% +networks there's coko +who's a Gilla that apparently had + + align:start position:0% +who's a Gilla that apparently had + + + align:start position:0% +who's a Gilla that apparently had +hundreds of + + align:start position:0% +hundreds of + + + align:start position:0% +hundreds of +words but + + align:start position:0% + + + + align:start position:0% + +uh the question is to find something + + align:start position:0% +uh the question is to find something + + + align:start position:0% +uh the question is to find something +like maybe Betty the + + align:start position:0% +like maybe Betty the + + + align:start position:0% +like maybe Betty the +crow with that stick + + align:start position:0% + + + + align:start position:0% + +yeah how many have you seen the Crow + + align:start position:0% +yeah how many have you seen the Crow + + + align:start position:0% +yeah how many have you seen the Crow +movie she she bends the she has a wire + + align:start position:0% +movie she she bends the she has a wire + + + align:start position:0% +movie she she bends the she has a wire +that she bends and pulls something out + + align:start position:0% +that she bends and pulls something out + + + align:start position:0% +that she bends and pulls something out +of a + + align:start position:0% + + + + align:start position:0% + +tube but + + align:start position:0% + + + + align:start position:0% + +uh I don't think machine learning can do + + align:start position:0% +uh I don't think machine learning can do + + + align:start position:0% +uh I don't think machine learning can do +that think you + + align:start position:0% +that think you + + + align:start position:0% +that think you +need I have a parrot who lives in a + + align:start position:0% +need I have a parrot who lives in a + + + align:start position:0% +need I have a parrot who lives in a +three-dimensional + + align:start position:0% +three-dimensional + + + align:start position:0% +three-dimensional +cage and she knows how to get from any + + align:start position:0% +cage and she knows how to get from any + + + align:start position:0% +cage and she knows how to get from any +place to another and if she's in a hurry + + align:start position:0% +place to another and if she's in a hurry + + + align:start position:0% +place to another and if she's in a hurry +she'll find a new + + align:start position:0% +she'll find a new + + + align:start position:0% +she'll find a new +way uh at the risk of injuring a wing + + align:start position:0% +way uh at the risk of injuring a wing + + + align:start position:0% +way uh at the risk of injuring a wing +because there a lot of sticks in the way + + align:start position:0% +because there a lot of sticks in the way + + + align:start position:0% +because there a lot of sticks in the way +so flying is risky but + + align:start position:0% + + + + align:start position:0% + +U our + + align:start position:0% +U our + + + align:start position:0% +U our +our daughter Julie once visited coko the + + align:start position:0% +our daughter Julie once visited coko the + + + align:start position:0% +our daughter Julie once visited coko the +gorilla + + align:start position:0% +gorilla + + + align:start position:0% +gorilla +and + + align:start position:0% +and + + + align:start position:0% +and +uh she was introduced Coco's in a + + align:start position:0% +uh she was introduced Coco's in a + + + align:start position:0% +uh she was introduced Coco's in a +cage + + align:start position:0% +cage + + + align:start position:0% +cage +and + + align:start position:0% +and + + + align:start position:0% +and +uh Penny who is Coco's + + align:start position:0% +uh Penny who is Coco's + + + align:start position:0% +uh Penny who is Coco's +owner introduces Julie in Sign Language + + align:start position:0% +owner introduces Julie in Sign Language + + + align:start position:0% +owner introduces Julie in Sign Language +Coco it's not words I it's not uh spoken + + align:start position:0% +Coco it's not words I it's not uh spoken + + + align:start position:0% +Coco it's not words I it's not uh spoken +its sign language + + align:start position:0% +its sign language + + + align:start position:0% +its sign language +and + + align:start position:0% +and + + + align:start position:0% +and +uh so Julie gets some + + align:start position:0% +uh so Julie gets some + + + align:start position:0% +uh so Julie gets some +name + + align:start position:0% +name + + + align:start position:0% +name +and she's introduced to coko and coko + + align:start position:0% +and she's introduced to coko and coko + + + align:start position:0% +and she's introduced to coko and coko +likes Julie so coko says let me + + align:start position:0% +likes Julie so coko says let me + + + align:start position:0% +likes Julie so coko says let me +out and + + align:start position:0% +out and + + + align:start position:0% +out and +Penny says no you can't get out and coko + + align:start position:0% +Penny says no you can't get out and coko + + + align:start position:0% +Penny says no you can't get out and coko +says then let Julie + + align:start position:0% +says then let Julie + + + align:start position:0% +says then let Julie +in + + align:start position:0% +in + + + align:start position:0% +in +and I thought that showed some fairly + + align:start position:0% +and I thought that showed some fairly + + + align:start position:0% +and I thought that showed some fairly +abstract reasoning or + + align:start position:0% + + + + align:start position:0% + +representation and Penny didn't let Co + + align:start position:0% +representation and Penny didn't let Co + + + align:start position:0% +representation and Penny didn't let Co +let Julie + + align:start position:0% + + + + align:start position:0% + +in but + + align:start position:0% +in but + + + align:start position:0% +in but +uh coko seemed to have + + align:start position:0% +uh coko seemed to have + + + align:start position:0% +uh coko seemed to have +a a fair amount + + align:start position:0% +a a fair amount + + + align:start position:0% +a a fair amount +of of + + align:start position:0% +of of + + + align:start position:0% +of of +uh declarative + + align:start position:0% +uh declarative + + + align:start position:0% +uh declarative +syntax I don't know if she could do + + align:start position:0% +syntax I don't know if she could do + + + align:start position:0% +syntax I don't know if she could do +passives or anything like that if you're + + align:start position:0% +passives or anything like that if you're + + + align:start position:0% +passives or anything like that if you're +interested you probably can look it up + + align:start position:0% +interested you probably can look it up + + + align:start position:0% +interested you probably can look it up +on the + + align:start position:0% +on the + + + align:start position:0% +on the +web uh Penny's owner I mean Penny Penny + + align:start position:0% +web uh Penny's owner I mean Penny Penny + + + align:start position:0% +web uh Penny's owner I mean Penny Penny +thought that coko knew six or 700 words + + align:start position:0% +thought that coko knew six or 700 words + + + align:start position:0% +thought that coko knew six or 700 words +and a friend of ours was a teenager who + + align:start position:0% +and a friend of ours was a teenager who + + + align:start position:0% +and a friend of ours was a teenager who +worked for her and uh what's his + + align:start position:0% + + + + align:start position:0% + +name and he was convinced that uh that + + align:start position:0% +name and he was convinced that uh that + + + align:start position:0% +name and he was convinced that uh that +coko knew more than a thousand words + + align:start position:0% +coko knew more than a thousand words + + + align:start position:0% +coko knew more than a thousand words +words but he said you see I'm a teenager + + align:start position:0% +words but he said you see I'm a teenager + + + align:start position:0% +words but he said you see I'm a teenager +and I'm still good at picking + + align:start position:0% +and I'm still good at picking + + + align:start position:0% +and I'm still good at picking +up gestures and clues better than the + + align:start position:0% +up gestures and clues better than the + + + align:start position:0% +up gestures and clues better than the +adults + + align:start position:0% +adults + + + align:start position:0% +adults +here + + align:start position:0% +here + + + align:start position:0% +here +but anyway I gather coko is still there + + align:start position:0% +but anyway I gather coko is still there + + + align:start position:0% +but anyway I gather coko is still there +and I don't know if she's still learning + + align:start position:0% +and I don't know if she's still learning + + + align:start position:0% +and I don't know if she's still learning +more + + align:start position:0% +more + + + align:start position:0% +more +words but every now and then we get a + + align:start position:0% +words but every now and then we get a + + + align:start position:0% +words but every now and then we get a +letter asking to send more money + + align:start position:0% + + + + align:start position:0% + +oh in the last + + align:start position:0% + + + + align:start position:0% + +lecture I couldn't think of + + align:start position:0% + + + + align:start position:0% + +a the right Crypt + + align:start position:0% +a the right Crypt + + + align:start position:0% +a the right Crypt +cryptarithmetic example + + align:start position:0% + + + + align:start position:0% + +I think that's the one that the new old + + align:start position:0% +I think that's the one that the new old + + + align:start position:0% +I think that's the one that the new old +Simon book starts out + + align:start position:0% +Simon book starts out + + + align:start position:0% +Simon book starts out +with so obviously m is + + align:start position:0% +with so obviously m is + + + align:start position:0% +with so obviously m is +one and + + align:start position:0% + + + + align:start position:0% + +then I bet some of you could figure that + + align:start position:0% +then I bet some of you could figure that + + + align:start position:0% +then I bet some of you could figure that +out in four or five + + align:start position:0% + + + + align:start position:0% + +minutes has anybody figured it out yet + + align:start position:0% + + + + align:start position:0% + +help send more + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +yeah I have an example for instance I go + + align:start position:0% +yeah I have an example for instance I go + + + align:start position:0% +yeah I have an example for instance I go +out to a restaurant of this and of this + + align:start position:0% +out to a restaurant of this and of this + + + align:start position:0% +out to a restaurant of this and of this +type of exotic food that I've never ever + + align:start position:0% +type of exotic food that I've never ever + + + align:start position:0% +type of exotic food that I've never ever +had before and I end up getting sick + + align:start position:0% +had before and I end up getting sick + + + align:start position:0% +had before and I end up getting sick +from it so what determines whether um + + align:start position:0% +from it so what determines whether um + + + align:start position:0% +from it so what determines whether um +what I learn from this because there are + + align:start position:0% +what I learn from this because there are + + + align:start position:0% +what I learn from this because there are +many different possibilities here + + align:start position:0% +many different possibilities here + + + align:start position:0% +many different possibilities here +there's the one possibility of I learn + + align:start position:0% +there's the one possibility of I learn + + + align:start position:0% +there's the one possibility of I learn +to avoid the specific food I ate another + + align:start position:0% +to avoid the specific food I ate another + + + align:start position:0% +to avoid the specific food I ate another +possibility is like I learn to avoid + + align:start position:0% +possibility is like I learn to avoid + + + align:start position:0% +possibility is like I learn to avoid +that type of food because it might + + align:start position:0% +that type of food because it might + + + align:start position:0% +that type of food because it might +contain some sort of spice that I react + + align:start position:0% +contain some sort of spice that I react + + + align:start position:0% +contain some sort of spice that I react +too badly and the third possibility + + align:start position:0% +too badly and the third possibility + + + align:start position:0% +too badly and the third possibility +there might be more is like I learned to + + align:start position:0% +there might be more is like I learned to + + + align:start position:0% +there might be more is like I learned to +avoid that restaurant because that just + + align:start position:0% +avoid that restaurant because that just + + + align:start position:0% +avoid that restaurant because that just +might be a bad restaurant so in this + + align:start position:0% +might be a bad restaurant so in this + + + align:start position:0% +might be a bad restaurant so in this +case it's not entirely clear which one + + align:start position:0% +case it's not entirely clear which one + + + align:start position:0% +case it's not entirely clear which one +you ought to pick um and of course maybe + + align:start position:0% +you ought to pick um and of course maybe + + + align:start position:0% +you ought to pick um and of course maybe +in real life I I might go there again + + align:start position:0% +in real life I I might go there again + + + align:start position:0% +in real life I I might go there again +and empirically try another food or try + + align:start position:0% +and empirically try another food or try + + + align:start position:0% +and empirically try another food or try +the same food at the different + + align:start position:0% +the same food at the different + + + align:start position:0% +the same food at the different +restaurants but what do you think about + + align:start position:0% +restaurants but what do you think about + + + align:start position:0% +restaurants but what do you think about +just on that scenario what causes people + + align:start position:0% +just on that scenario what causes people + + + align:start position:0% +just on that scenario what causes people +to pick which one the trouble is we keep + + align:start position:0% +to pick which one the trouble is we keep + + + align:start position:0% +to pick which one the trouble is we keep +thinking of ourselves as people and what + + align:start position:0% +thinking of ourselves as people and what + + + align:start position:0% +thinking of ourselves as people and what +you really should you should think of + + align:start position:0% +you really should you should think of + + + align:start position:0% +you really should you should think of +yourself as a sort of petri dish with uh + + align:start position:0% +yourself as a sort of petri dish with uh + + + align:start position:0% +yourself as a sort of petri dish with uh +a trillion bacteria in it and it's + + align:start position:0% +a trillion bacteria in it and it's + + + align:start position:0% +a trillion bacteria in it and it's +really not important to you what you eat + + align:start position:0% +really not important to you what you eat + + + align:start position:0% +really not important to you what you eat +but your intestinal bacteria are the + + align:start position:0% +but your intestinal bacteria are the + + + align:start position:0% +but your intestinal bacteria are the +ones who are really going to suffer + + align:start position:0% +ones who are really going to suffer + + + align:start position:0% +ones who are really going to suffer +because they're not used to anything + + align:start position:0% +because they're not used to anything + + + align:start position:0% +because they're not used to anything +new so I I don't know what conclusion to + + align:start position:0% +new so I I don't know what conclusion to + + + align:start position:0% +new so I I don't know what conclusion to +draw from + + align:start position:0% +draw from + + + align:start position:0% +draw from +that + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +mention David Hume got that now might + + align:start position:0% +mention David Hume got that now might + + + align:start position:0% +mention David Hume got that now might +represented as uh + + align:start position:0% +represented as uh + + + align:start position:0% +represented as uh +associations and uh that occurred to me + + align:start position:0% +associations and uh that occurred to me + + + align:start position:0% +associations and uh that occurred to me +as being some sort of like a Wiki + + align:start position:0% +as being some sort of like a Wiki + + + align:start position:0% +as being some sort of like a Wiki +structure where uh entries have tags so + + align:start position:0% +structure where uh entries have tags so + + + align:start position:0% +structure where uh entries have tags so +um uh an entry might be defined by what + + align:start position:0% +um uh an entry might be defined by what + + + align:start position:0% +um uh an entry might be defined by what +tags it has or what associations it has + + align:start position:0% +tags it has or what associations it has + + + align:start position:0% +tags it has or what associations it has +I'm wondering if that structure has been + + align:start position:0% +I'm wondering if that structure has been + + + align:start position:0% +I'm wondering if that structure has been +uh somebody has attempted to code that + + align:start position:0% +uh somebody has attempted to code that + + + align:start position:0% +uh somebody has attempted to code that +into some kind of virtual structure has + + align:start position:0% +into some kind of virtual structure has + + + align:start position:0% +into some kind of virtual structure has +there been any success with Ting that + + align:start position:0% +there been any success with Ting that + + + align:start position:0% +there been any success with Ting that +idea into a potential + + align:start position:0% + + + + align:start position:0% + +AI I don't know how to answer + + align:start position:0% + + + + align:start position:0% + +that do any psychologists use semantic + + align:start position:0% +that do any psychologists use semantic + + + align:start position:0% +that do any psychologists use semantic +networks as representations Pat do you + + align:start position:0% +networks as representations Pat do you + + + align:start position:0% +networks as representations Pat do you +know has + + align:start position:0% +know has + + + align:start position:0% +know has +anybody I + + align:start position:0% +anybody I + + + align:start position:0% +anybody I +know is + + align:start position:0% +know is + + + align:start position:0% +know is +anyone building an AI system with with + + align:start position:0% +anyone building an AI system with with + + + align:start position:0% +anyone building an AI system with with +semantic represent ations or semantic + + align:start position:0% +semantic represent ations or semantic + + + align:start position:0% +semantic represent ations or semantic +networks anymore or is it all everything + + align:start position:0% +networks anymore or is it all everything + + + align:start position:0% +networks anymore or is it all everything +I've seen has gone probabilistic in the + + align:start position:0% +I've seen has gone probabilistic in the + + + align:start position:0% +I've seen has gone probabilistic in the +last few + + align:start position:0% +last few + + + align:start position:0% +last few +years me your your project do you have + + align:start position:0% +years me your your project do you have + + + align:start position:0% +years me your your project do you have +any + + align:start position:0% +any + + + align:start position:0% +any +competitors no any idea what the + + align:start position:0% +competitors no any idea what the + + + align:start position:0% +competitors no any idea what the +um the IBM people are + + align:start position:0% +um the IBM people are + + + align:start position:0% +um the IBM people are +using I saw a long article that I didn't + + align:start position:0% +using I saw a long article that I didn't + + + align:start position:0% +using I saw a long article that I didn't +read yet but is traditional information + + align:start position:0% +read yet but is traditional information + + + align:start position:0% +read yet but is traditional information +retrieval + + align:start position:0% +retrieval + + + align:start position:0% +retrieval +plus 100 hacks plus machine + + align:start position:0% +plus 100 hacks plus machine + + + align:start position:0% +plus 100 hacks plus machine +learning they seem to have a whole lot + + align:start position:0% +learning they seem to have a whole lot + + + align:start position:0% +learning they seem to have a whole lot +of different slightly different + + align:start position:0% +of different slightly different + + + align:start position:0% +of different slightly different +representations that they switch among + + align:start position:0% + + + + align:start position:0% + +but none of them are very + + align:start position:0% + + + + align:start position:0% + +stic well they probably have I don't + + align:start position:0% +stic well they probably have I don't + + + align:start position:0% +stic well they probably have I don't +know does anybody know what the answer + + align:start position:0% +know does anybody know what the answer + + + align:start position:0% +know does anybody know what the answer +is but they must have little frame like + + align:start position:0% +is but they must have little frame like + + + align:start position:0% +is but they must have little frame like +things yeah for the T for the standard + + align:start position:0% +things yeah for the T for the standard + + + align:start position:0% +things yeah for the T for the standard +questions of course the thing doesn't + + align:start position:0% +questions of course the thing doesn't + + + align:start position:0% +questions of course the thing doesn't +answer any + + align:start position:0% +answer any + + + align:start position:0% +answer any +it doesn't do any reasoning as far as + + align:start position:0% +it doesn't do any reasoning as far as + + + align:start position:0% +it doesn't do any reasoning as far as +you can tell so + + align:start position:0% +you can tell so + + + align:start position:0% +you can tell so +it's it's trying to match sentences in + + align:start position:0% +it's it's trying to match sentences in + + + align:start position:0% +it's it's trying to match sentences in +the database with the + + align:start position:0% + + + + align:start position:0% + +question well what's your theory of why + + align:start position:0% +question well what's your theory of why + + + align:start position:0% +question well what's your theory of why +there are't other groups working on what + + align:start position:0% +there are't other groups working on what + + + align:start position:0% +there are't other groups working on what +we used to and you + + align:start position:0% +we used to and you + + + align:start position:0% +we used to and you +are well those are Computing is a + + align:start position:0% +are well those are Computing is a + + + align:start position:0% +are well those are Computing is a +fed and if you can do better and less + + align:start position:0% +fed and if you can do better and less + + + align:start position:0% +fed and if you can do better and less +time that way then figuring out figuring + + align:start position:0% +time that way then figuring out figuring + + + align:start position:0% +time that way then figuring out figuring +out how it really works then that's what + + align:start position:0% +out how it really works then that's what + + + align:start position:0% +out how it really works then that's what +you + + align:start position:0% +you + + + align:start position:0% +you +do I mean no one no one no one does + + align:start position:0% +do I mean no one no one no one does + + + align:start position:0% +do I mean no one no one no one does +research on + + align:start position:0% +research on + + + align:start position:0% +research on +chess no one does any research on how + + align:start position:0% +chess no one does any research on how + + + align:start position:0% +chess no one does any research on how +humans might play chess because we bu + + align:start position:0% +humans might play chess because we bu + + + align:start position:0% +humans might play chess because we bu +those are computers of one right there + + align:start position:0% +those are computers of one right there + + + align:start position:0% +those are computers of one right there +were there were some articles on chess + + align:start position:0% +were there were some articles on chess + + + align:start position:0% +were there were some articles on chess +and checkers early in the game + + align:start position:0% +and checkers early in the game + + + align:start position:0% +and checkers early in the game +but nothing recent as far as I + + align:start position:0% + + + + align:start position:0% + +know so it's a local in many ways it's a + + align:start position:0% +know so it's a local in many ways it's a + + + align:start position:0% +know so it's a local in many ways it's a +local maximum + + align:start position:0% +local maximum + + + align:start position:0% +local maximum +phenomenon the bulldozer Computing stuff + + align:start position:0% +phenomenon the bulldozer Computing stuff + + + align:start position:0% +phenomenon the bulldozer Computing stuff +has got up on a certain local Maxima + + align:start position:0% +has got up on a certain local Maxima + + + align:start position:0% +has got up on a certain local Maxima +until you can do better than that some + + align:start position:0% +until you can do better than that some + + + align:start position:0% +until you can do better than that some +other way they were too + + align:start position:0% +other way they were too + + + align:start position:0% +other way they were too +fastic well I wonder if we could invent + + align:start position:0% +fastic well I wonder if we could invent + + + align:start position:0% +fastic well I wonder if we could invent +a new TV + + align:start position:0% +a new TV + + + align:start position:0% +a new TV +show where the questions are + + align:start position:0% + + + + align:start position:0% + +interesting like I'm obsessed with the + + align:start position:0% +interesting like I'm obsessed with the + + + align:start position:0% +interesting like I'm obsessed with the +question of why you can pull something + + align:start position:0% +question of why you can pull something + + + align:start position:0% +question of why you can pull something +with a string but you can't push it and + + align:start position:0% +with a string but you can't push it and + + + align:start position:0% +with a string but you can't push it and +in + + align:start position:0% +in + + + align:start position:0% +in +fact what was this we had a student who + + align:start position:0% +fact what was this we had a student who + + + align:start position:0% +fact what was this we had a student who +actually did something with that a long + + align:start position:0% +actually did something with that a long + + + align:start position:0% +actually did something with that a long +time ago but I've lost track of + + align:start position:0% +time ago but I've lost track of + + + align:start position:0% +time ago but I've lost track of +him but how could you make a TV + + align:start position:0% +him but how could you make a TV + + + align:start position:0% +him but how could you make a TV +how could you make a TV show that had + + align:start position:0% +how could you make a TV show that had + + + align:start position:0% +how could you make a TV show that had +common sense + + align:start position:0% +common sense + + + align:start position:0% +common sense +questions rather than ones about sports + + align:start position:0% +questions rather than ones about sports + + + align:start position:0% +questions rather than ones about sports +and + + align:start position:0% + + + + align:start position:0% + +actors well you imagine what happen when + + align:start position:0% +actors well you imagine what happen when + + + align:start position:0% +actors well you imagine what happen when +you push with a screen it's hard to + + align:start position:0% +you push with a screen it's hard to + + + align:start position:0% +you push with a screen it's hard to +explain that in words it's easy to + + align:start position:0% +explain that in words it's easy to + + + align:start position:0% +explain that in words it's easy to +imagine yeah so you can simulate it + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +so I have a question so suppose in the + + align:start position:0% +so I have a question so suppose in the + + + align:start position:0% +so I have a question so suppose in the +future we can create a robot which is as + + align:start position:0% +future we can create a robot which is as + + + align:start position:0% +future we can create a robot which is as +intelligent as human as smart and how we + + align:start position:0% +intelligent as human as smart and how we + + + align:start position:0% +intelligent as human as smart and how we +should evaluate it when do we know that + + align:start position:0% +should evaluate it when do we know that + + + align:start position:0% +should evaluate it when do we know that +we reach like certain thing like which + + align:start position:0% +we reach like certain thing like which + + + align:start position:0% +we reach like certain thing like which +test it should pass or which should um I + + align:start position:0% +test it should pass or which should um I + + + align:start position:0% +test it should pass or which should um I +don't know so for example Watson right + + align:start position:0% +don't know so for example Watson right + + + align:start position:0% +don't know so for example Watson right +it can answer pretty um hard questions + + align:start position:0% +it can answer pretty um hard questions + + + align:start position:0% +it can answer pretty um hard questions +and seem to be intelligent but what what + + align:start position:0% +and seem to be intelligent but what what + + + align:start position:0% +and seem to be intelligent but what what +all it is doing is doing some algorithms + + align:start position:0% +all it is doing is doing some algorithms + + + align:start position:0% +all it is doing is doing some algorithms +and then calculating some probabilities + + align:start position:0% +and then calculating some probabilities + + + align:start position:0% +and then calculating some probabilities +and stuff humans don't do that they try + + align:start position:0% +and stuff humans don't do that they try + + + align:start position:0% +and stuff humans don't do that they try +to understand questions and they look + + align:start position:0% +to understand questions and they look + + + align:start position:0% +to understand questions and they look +for the answer right but then suppose + + align:start position:0% +for the answer right but then suppose + + + align:start position:0% +for the answer right but then suppose +you can create a robot that can behave + + align:start position:0% +you can create a robot that can behave + + + align:start position:0% +you can create a robot that can behave +as it is like I don't know how would you + + align:start position:0% +as it is like I don't know how would you + + + align:start position:0% +as it is like I don't know how would you +evaluate like when do you know that you + + align:start position:0% +evaluate like when do you know that you + + + align:start position:0% +evaluate like when do you know that you +reach + + align:start position:0% + + + + align:start position:0% + +something that's sort of funny + + align:start position:0% +something that's sort of funny + + + align:start position:0% +something that's sort of funny +because + + align:start position:0% + + + + align:start position:0% + +uh because you if it's any good you + + align:start position:0% +uh because you if it's any good you + + + align:start position:0% +uh because you if it's any good you +wouldn't you wouldn't have that question + + align:start position:0% +wouldn't you wouldn't have that question + + + align:start position:0% +wouldn't you wouldn't have that question +you + + align:start position:0% +you + + + align:start position:0% +you +you'd say well what can't it do and why + + align:start position:0% +you'd say well what can't it do and why + + + align:start position:0% +you'd say well what can't it do and why +not and you'd argue with + + align:start position:0% + + + + align:start position:0% + +it in other words people people talk + + align:start position:0% +it in other words people people talk + + + align:start position:0% +it in other words people people talk +about passing the touring test or + + align:start position:0% +about passing the touring test or + + + align:start position:0% +about passing the touring test or +whatever + + align:start position:0% + + + + align:start position:0% + +and it's hard to imagine a machine that + + align:start position:0% +and it's hard to imagine a machine that + + + align:start position:0% +and it's hard to imagine a machine that +uh that you converse with for a while + + align:start position:0% +uh that you converse with for a while + + + align:start position:0% +uh that you converse with for a while +and + + align:start position:0% +and + + + align:start position:0% +and +uh then when you're told it's a machine + + align:start position:0% +uh then when you're told it's a machine + + + align:start position:0% +uh then when you're told it's a machine +you you're + + align:start position:0% + + + + align:start position:0% + +surprised I think that for example you + + align:start position:0% +surprised I think that for example you + + + align:start position:0% +surprised I think that for example you +can make a machine to say some very + + align:start position:0% +can make a machine to say some very + + + align:start position:0% +can make a machine to say some very +intelligent and smart things because + + align:start position:0% +intelligent and smart things because + + + align:start position:0% +intelligent and smart things because +like it may know like all this like text + + align:start position:0% +like it may know like all this like text + + + align:start position:0% +like it may know like all this like text +information from different books and all + + align:start position:0% +information from different books and all + + + align:start position:0% +information from different books and all +this information it has somewhere + + align:start position:0% +this information it has somewhere + + + align:start position:0% +this information it has somewhere +right but then like when people speak + + align:start position:0% +right but then like when people speak + + + align:start position:0% +right but then like when people speak +they kind of understand what they're + + align:start position:0% +they kind of understand what they're + + + align:start position:0% +they kind of understand what they're +speaking how would do you know like + + align:start position:0% +speaking how would do you know like + + + align:start position:0% +speaking how would do you know like +understand something it doesn't + + align:start position:0% +understand something it doesn't + + + align:start position:0% +understand something it doesn't +understand or does it have to understand + + align:start position:0% +understand or does it have to understand + + + align:start position:0% +understand or does it have to understand +at all well I would ask you questions + + align:start position:0% +at all well I would ask you questions + + + align:start position:0% +at all well I would ask you questions +like uh why can't you push something + + align:start position:0% +like uh why can't you push something + + + align:start position:0% +like uh why can't you push something +with a + + align:start position:0% +with a + + + align:start position:0% +with a +string + + align:start position:0% +string + + + align:start position:0% +string +and + + align:start position:0% +and + + + align:start position:0% +and +uh well anyone have a Google + + align:start position:0% +uh well anyone have a Google + + + align:start position:0% +uh well anyone have a Google +working what what does Google say if you + + align:start position:0% +working what what does Google say if you + + + align:start position:0% +working what what does Google say if you +ask it that + + align:start position:0% +ask it that + + + align:start position:0% +ask it that +maybe maybe it'll quote + + align:start position:0% + + + + align:start position:0% + +me or someone who's yeah how would you + + align:start position:0% +me or someone who's yeah how would you + + + align:start position:0% +me or someone who's yeah how would you +answer that + + align:start position:0% + + + + align:start position:0% + +question I'd say well it would buckle + + align:start position:0% +question I'd say well it would buckle + + + align:start position:0% +question I'd say well it would buckle +and then they would say what do you mean + + align:start position:0% +and then they would say what do you mean + + + align:start position:0% +and then they would say what do you mean +by Buckle and then I'd say oh it would + + align:start position:0% +by Buckle and then I'd say oh it would + + + align:start position:0% +by Buckle and then I'd say oh it would +fold up so that it got shorter + + align:start position:0% +fold up so that it got shorter + + + align:start position:0% +fold up so that it got shorter +without exerting any Force at the end or + + align:start position:0% +without exerting any Force at the end or + + + align:start position:0% +without exerting any Force at the end or +blah blah I don't know there are lots of + + align:start position:0% +blah blah I don't know there are lots of + + + align:start position:0% +blah blah I don't know there are lots of +answers how would you answer + + align:start position:0% + + + + align:start position:0% + +it a uh a physicist might say if you got + + align:start position:0% +it a uh a physicist might say if you got + + + align:start position:0% +it a uh a physicist might say if you got +it really very very very straight you + + align:start position:0% +it really very very very straight you + + + align:start position:0% +it really very very very straight you +could push it with a + + align:start position:0% + + + + align:start position:0% + +string but quantum mechanics would say + + align:start position:0% +string but quantum mechanics would say + + + align:start position:0% +string but quantum mechanics would say +you can't yeah + + align:start position:0% +you can't yeah + + + align:start position:0% +you can't yeah +I feel like if you like a difficult or + + align:start position:0% +I feel like if you like a difficult or + + + align:start position:0% +I feel like if you like a difficult or +like an interesting show would be have + + align:start position:0% +like an interesting show would be have + + + align:start position:0% +like an interesting show would be have +like an alternate cooking show or + + align:start position:0% +like an alternate cooking show or + + + align:start position:0% +like an alternate cooking show or +something where you have to use objects + + align:start position:0% +something where you have to use objects + + + align:start position:0% +something where you have to use objects +that's like not normally um found to + + align:start position:0% +that's like not normally um found to + + + align:start position:0% +that's like not normally um found to +have that use so you want to paint a + + align:start position:0% +have that use so you want to paint a + + + align:start position:0% +have that use so you want to paint a +room but you're not given a brush you're + + align:start position:0% +room but you're not given a brush you're + + + align:start position:0% +room but you're not given a brush you're +given like say a + + align:start position:0% +given like say a + + + align:start position:0% +given like say a +sponge a piece of cloth and like + + align:start position:0% +sponge a piece of cloth and like + + + align:start position:0% +sponge a piece of cloth and like +eggplants put in + + align:start position:0% +eggplants put in + + + align:start position:0% +eggplants put in +so it has to represent the thing in a + + align:start position:0% +so it has to represent the thing in a + + + align:start position:0% +so it has to represent the thing in a +different way other than like you know + + align:start position:0% +different way other than like you know + + + align:start position:0% +different way other than like you know +words + + align:start position:0% +words + + + align:start position:0% +words +yeah that's + + align:start position:0% +yeah that's + + + align:start position:0% +yeah that's +interesting when I was in graduate + + align:start position:0% +interesting when I was in graduate + + + align:start position:0% +interesting when I was in graduate +school I took a course in not + + align:start position:0% +school I took a course in not + + + align:start position:0% +school I took a course in not +Theory and in fact you couldn't talk + + align:start position:0% +Theory and in fact you couldn't talk + + + align:start position:0% +Theory and in fact you couldn't talk +about them and if anybody had a question + + align:start position:0% +about them and if anybody had a question + + + align:start position:0% +about them and if anybody had a question +they'd have to run up to the board + + align:start position:0% +they'd have to run up to the board + + + align:start position:0% +they'd have to run up to the board +and you + + align:start position:0% +and you + + + align:start position:0% +and you +know they'd have to do something like + + align:start position:0% +know they'd have to do something like + + + align:start position:0% +know they'd have to do something like +this + + align:start position:0% + + + + align:start position:0% + +is that a + + align:start position:0% + + + + align:start position:0% + +knot + + align:start position:0% +knot + + + align:start position:0% +knot +no no that's just a + + align:start position:0% +no no that's just a + + + align:start position:0% +no no that's just a +loop + + align:start position:0% + + + + align:start position:0% + +words but if you were restricted to + + align:start position:0% +words but if you were restricted to + + + align:start position:0% +words but if you were restricted to +words it would take a half hour to + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +Yeah you mentioned solving the string + + align:start position:0% +Yeah you mentioned solving the string + + + align:start position:0% +Yeah you mentioned solving the string +puzzle by imagining the result and I + + align:start position:0% +puzzle by imagining the result and I + + + align:start position:0% +puzzle by imagining the result and I +think I heard someone else say computers + + align:start position:0% +think I heard someone else say computers + + + align:start position:0% +think I heard someone else say computers +can do that in some way you can simulate + + align:start position:0% +can do that in some way you can simulate + + + align:start position:0% +can do that in some way you can simulate +a string and we know in a physics that + + align:start position:0% +a string and we know in a physics that + + + align:start position:0% +a string and we know in a physics that +you could give a reasonable + + align:start position:0% +you could give a reasonable + + + align:start position:0% +you could give a reasonable +approximation to the string but I find + + align:start position:0% +approximation to the string but I find + + + align:start position:0% +approximation to the string but I find +that uh the question that is often not + + align:start position:0% +that uh the question that is often not + + + align:start position:0% +that uh the question that is often not +asked in AI is or by computers is how + + align:start position:0% +asked in AI is or by computers is how + + + align:start position:0% +asked in AI is or by computers is how +does one choose the correct model with + + align:start position:0% +does one choose the correct model with + + + align:start position:0% +does one choose the correct model with +which to answer questions there's a lot + + align:start position:0% +which to answer questions there's a lot + + + align:start position:0% +which to answer questions there's a lot +of questions were really good at + + align:start position:0% +of questions were really good at + + + align:start position:0% +of questions were really good at +answering of computers and some of them + + align:start position:0% +answering of computers and some of them + + + align:start position:0% +answering of computers and some of them +you know genetic algorithms are good for + + align:start position:0% +you know genetic algorithms are good for + + + align:start position:0% +you know genetic algorithms are good for +some of them basing statistics some of + + align:start position:0% +some of them basing statistics some of + + + align:start position:0% +some of them basing statistics some of +them formal logic some of them physics + + align:start position:0% +them formal logic some of them physics + + + align:start position:0% +them formal logic some of them physics +simulation but this is all to me this is + + align:start position:0% +simulation but this is all to me this is + + + align:start position:0% +simulation but this is all to me this is +the core question because this is what + + align:start position:0% +the core question because this is what + + + align:start position:0% +the core question because this is what +people decide and no one seems to have + + align:start position:0% +people decide and no one seems to have + + + align:start position:0% +people decide and no one seems to have +ever ever tackled an a well for instance + + align:start position:0% +ever ever tackled an a well for instance + + + align:start position:0% +ever ever tackled an a well for instance +you have to if somebody asks the + + align:start position:0% +you have to if somebody asks the + + + align:start position:0% +you have to if somebody asks the +question you have to make up a biography + + align:start position:0% +question you have to make up a biography + + + align:start position:0% +question you have to make up a biography +of that + + align:start position:0% +of that + + + align:start position:0% +of that +person so that because the same question + + align:start position:0% +person so that because the same question + + + align:start position:0% +person so that because the same question +question from different people would get + + align:start position:0% +question from different people would get + + + align:start position:0% +question from different people would get +really different + + align:start position:0% + + + + align:start position:0% + +answers why does a kettle make a noise + + align:start position:0% +answers why does a kettle make a noise + + + align:start position:0% +answers why does a kettle make a noise +when the water + + align:start position:0% +when the water + + + align:start position:0% +when the water +boils uh if you know that the other + + align:start position:0% +boils uh if you know that the other + + + align:start position:0% +boils uh if you know that the other +person is a + + align:start position:0% +person is a + + + align:start position:0% +person is a +physicist and it's easy to think of + + align:start position:0% +physicist and it's easy to think of + + + align:start position:0% +physicist and it's easy to think of +things to say + + align:start position:0% + + + + align:start position:0% + +but not a very not a very good example + + align:start position:0% + + + + align:start position:0% + +what what's the context of that how do + + align:start position:0% + + + + align:start position:0% + +you in a human conversation How does + + align:start position:0% +you in a human conversation How does + + + align:start position:0% +you in a human conversation How does +each person know what to say + + align:start position:0% +each person know what to say + + + align:start position:0% +each person know what to say +next I guess you know one question is + + align:start position:0% +next I guess you know one question is + + + align:start position:0% +next I guess you know one question is +how do people decide what AI methods to + + align:start position:0% +how do people decide what AI methods to + + + align:start position:0% +how do people decide what AI methods to +use to tackle a problem and I guess the + + align:start position:0% +use to tackle a problem and I guess the + + + align:start position:0% +use to tackle a problem and I guess the +more fundamental question is when people + + align:start position:0% +more fundamental question is when people + + + align:start position:0% +more fundamental question is when people +are solving problems how do they decide + + align:start position:0% +are solving problems how do they decide + + + align:start position:0% +are solving problems how do they decide +how they're going to think about the + + align:start position:0% +how they're going to think about the + + + align:start position:0% +how they're going to think about the +problem are they going to think about it + + align:start position:0% +problem are they going to think about it + + + align:start position:0% +problem are they going to think about it +by visualizing it think about it by + + align:start position:0% +by visualizing it think about it by + + + align:start position:0% +by visualizing it think about it by +trying different thing think about it by + + align:start position:0% +trying different thing think about it by + + + align:start position:0% +trying different thing think about it by +analogy or form of logic of all the + + align:start position:0% +analogy or form of logic of all the + + + align:start position:0% +analogy or form of logic of all the +tools we have why do we pick the ones we + + align:start position:0% + + + + align:start position:0% + +do yeah well that goes back to + + align:start position:0% +do yeah well that goes back to + + + align:start position:0% +do yeah well that goes back to +the if you make a list of the 50 most + + align:start position:0% +the if you make a list of the 50 most + + + align:start position:0% +the if you make a list of the 50 most +common ways to + + align:start position:0% +common ways to + + + align:start position:0% +common ways to +think um and somebody asks you a + + align:start position:0% +think um and somebody asks you a + + + align:start position:0% +think um and somebody asks you a +question uh + + align:start position:0% +question uh + + + align:start position:0% +question uh +or ask why does such and such happen uh + + align:start position:0% +or ask why does such and such happen uh + + + align:start position:0% +or ask why does such and such happen uh +how do you decide which of your ways to + + align:start position:0% +how do you decide which of your ways to + + + align:start position:0% +how do you decide which of your ways to +think about it and I suspect that + + align:start position:0% + + + + align:start position:0% + +uh that's another knowledge base so we + + align:start position:0% +uh that's another knowledge base so we + + + align:start position:0% +uh that's another knowledge base so we +have common sense knowledge + + align:start position:0% +have common sense knowledge + + + align:start position:0% +have common sense knowledge +about you know if you let go of an + + align:start position:0% +about you know if you let go of an + + + align:start position:0% +about you know if you let go of an +object it will + + align:start position:0% +object it will + + + align:start position:0% +object it will +fall and then we + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% +have + + + align:start position:0% +have +um more General knowledge about what + + align:start position:0% +um more General knowledge about what + + + align:start position:0% +um more General knowledge about what +happens when an object falls Why didn't + + align:start position:0% +happens when an object falls Why didn't + + + align:start position:0% +happens when an object falls Why didn't +it + + align:start position:0% +it + + + align:start position:0% +it +break well it actually + + align:start position:0% +break well it actually + + + align:start position:0% +break well it actually +did because here's a little little white + + align:start position:0% +did because here's a little little white + + + align:start position:0% +did because here's a little little white +thing which turned into + + align:start position:0% +thing which turned into + + + align:start position:0% +thing which turned into +dust and so that's why I think you need + + align:start position:0% +dust and so that's why I think you need + + + align:start position:0% +dust and so that's why I think you need +to have five or six or how many + + align:start position:0% +to have five or six or how many + + + align:start position:0% +to have five or six or how many +different levels of + + align:start position:0% +different levels of + + + align:start position:0% +different levels of +representation so uh as soon as somebody + + align:start position:0% +representation so uh as soon as somebody + + + align:start position:0% +representation so uh as soon as somebody +asks a question one part of your brain + + align:start position:0% +asks a question one part of your brain + + + align:start position:0% +asks a question one part of your brain +is coming up with a with your first + + align:start position:0% +is coming up with a with your first + + + align:start position:0% +is coming up with a with your first +idea another part of your brain is + + align:start position:0% +idea another part of your brain is + + + align:start position:0% +idea another part of your brain is +saying is this a question about physics + + align:start position:0% +saying is this a question about physics + + + align:start position:0% +saying is this a question about physics +or philosophy or uh is it a social + + align:start position:0% +or philosophy or uh is it a social + + + align:start position:0% +or philosophy or uh is it a social +question uh did this person ask it + + align:start position:0% +question uh did this person ask it + + + align:start position:0% +question uh did this person ask it +because they actually want to know or + + align:start position:0% +because they actually want to know or + + + align:start position:0% +because they actually want to know or +they want to trap me + + align:start position:0% + + + + align:start position:0% + +or + + align:start position:0% +or + + + align:start position:0% +or +um so I think you that + + align:start position:0% +um so I think you that + + + align:start position:0% +um so I think you that +generally this idea of + + align:start position:0% +generally this idea of + + + align:start position:0% +generally this idea of +a there must be many kinds of Society of + + align:start position:0% +a there must be many kinds of Society of + + + align:start position:0% +a there must be many kinds of Society of +Mind models that people have in each + + align:start position:0% +Mind models that people have in each + + + align:start position:0% +Mind models that people have in each +person whenever you talking to somebody + + align:start position:0% +person whenever you talking to somebody + + + align:start position:0% +person whenever you talking to somebody +you're you have + + align:start position:0% +you're you have + + + align:start position:0% +you're you have +some you choose some model of what is + + align:start position:0% +some you choose some model of what is + + + align:start position:0% +some you choose some model of what is +this conversation about am I trying to + + align:start position:0% +this conversation about am I trying to + + + align:start position:0% +this conversation about am I trying to +accomplish something by this discussion + + align:start position:0% +accomplish something by this discussion + + + align:start position:0% +accomplish something by this discussion +am I is it really an interesting + + align:start position:0% +am I is it really an interesting + + + align:start position:0% +am I is it really an interesting +question uh through I not want to offend + + align:start position:0% +question uh through I not want to offend + + + align:start position:0% +question uh through I not want to offend +with person or do I want to make him go + + align:start position:0% +with person or do I want to make him go + + + align:start position:0% +with person or do I want to make him go +away forever + + align:start position:0% +away forever + + + align:start position:0% +away forever +or and little parts of your brain are + + align:start position:0% +or and little parts of your brain are + + + align:start position:0% +or and little parts of your brain are +making all these decisions for + + align:start position:0% +making all these decisions for + + + align:start position:0% +making all these decisions for +you I'd like to introduce Bob ller + + align:start position:0% +you I'd like to introduce Bob ller + + + align:start position:0% +you I'd like to introduce Bob ller +who's visiting one of my favorite + + align:start position:0% +who's visiting one of my favorite + + + align:start position:0% +who's visiting one of my favorite +stories U one of my favorite stories + + align:start position:0% +stories U one of my favorite stories + + + align:start position:0% +stories U one of my favorite stories +about finan was U comes from asking of a + + align:start position:0% +about finan was U comes from asking of a + + + align:start position:0% +about finan was U comes from asking of a +dinner one night + + align:start position:0% +dinner one night + + + align:start position:0% +dinner one night +um I asked him how he got to be so smart + + align:start position:0% +um I asked him how he got to be so smart + + + align:start position:0% +um I asked him how he got to be so smart +and + + align:start position:0% +and + + + align:start position:0% +and +and and he said that when when he was an + + align:start position:0% +and and he said that when when he was an + + + align:start position:0% +and and he said that when when he was an +undergraduate here he uh you know he + + align:start position:0% +undergraduate here he uh you know he + + + align:start position:0% +undergraduate here he uh you know he +would consider every Tommy was able to + + align:start position:0% +would consider every Tommy was able to + + + align:start position:0% +would consider every Tommy was able to +solve a problem just the beginning step + + align:start position:0% +solve a problem just the beginning step + + + align:start position:0% +solve a problem just the beginning step +of how to exploit that and what he would + + align:start position:0% +of how to exploit that and what he would + + + align:start position:0% +of how to exploit that and what he would +then do would be to try to reformulate + + align:start position:0% +then do would be to try to reformulate + + + align:start position:0% +then do would be to try to reformulate +the problem in as different rep many + + align:start position:0% +the problem in as different rep many + + + align:start position:0% +the problem in as different rep many +different representations as he could + + align:start position:0% +different representations as he could + + + align:start position:0% +different representations as he could +and then use his solution of the first + + align:start position:0% +and then use his solution of the first + + + align:start position:0% +and then use his solution of the first +problem as a guide in working out + + align:start position:0% +problem as a guide in working out + + + align:start position:0% +problem as a guide in working out +alternate representations and procedures + + align:start position:0% +alternate representations and procedures + + + align:start position:0% +alternate representations and procedures +in them the consequence according to him + + align:start position:0% +in them the consequence according to him + + + align:start position:0% +in them the consequence according to him +was that he became very good at knowing + + align:start position:0% +was that he became very good at knowing + + + align:start position:0% +was that he became very good at knowing +which was the most fit representation to + + align:start position:0% +which was the most fit representation to + + + align:start position:0% +which was the most fit representation to +use in solving any particular problem + + align:start position:0% +use in solving any particular problem + + + align:start position:0% +use in solving any particular problem +that he encountered and he said that + + align:start position:0% +that he encountered and he said that + + + align:start position:0% +that he encountered and he said that +that's where his legendary capability of + + align:start position:0% +that's where his legendary capability of + + + align:start position:0% +that's where his legendary capability of +being so quick with good Solutions and + + align:start position:0% +being so quick with good Solutions and + + + align:start position:0% +being so quick with good Solutions and +good methods the solutions came from so + + align:start position:0% +good methods the solutions came from so + + + align:start position:0% +good methods the solutions came from so +maybe a Criterion for an intelligent + + align:start position:0% +maybe a Criterion for an intelligent + + + align:start position:0% +maybe a Criterion for an intelligent +machine would be one that had a number + + align:start position:0% +machine would be one that had a number + + + align:start position:0% +machine would be one that had a number +of 15 different ways of thinking and + + align:start position:0% +of 15 different ways of thinking and + + + align:start position:0% +of 15 different ways of thinking and +applied them regularly to develop + + align:start position:0% +applied them regularly to develop + + + align:start position:0% +applied them regularly to develop +alternative information about the + + align:start position:0% +alternative information about the + + + align:start position:0% +alternative information about the +different methods of problem solving you + + align:start position:0% +different methods of problem solving you + + + align:start position:0% +different methods of problem solving you +would expect it then to be have some + + align:start position:0% +would expect it then to be have some + + + align:start position:0% +would expect it then to be have some +facility and choosing based on its + + align:start position:0% +facility and choosing based on its + + + align:start position:0% +facility and choosing based on its +experience yeah you wrote something + + align:start position:0% + + + + align:start position:0% + +about cu + + align:start position:0% +about cu + + + align:start position:0% +about cu +the other physicist would argue about + + align:start position:0% +the other physicist would argue about + + + align:start position:0% +the other physicist would argue about +whether to use Heisenberg matrices or + + align:start position:0% +whether to use Heisenberg matrices or + + + align:start position:0% +whether to use Heisenberg matrices or +Schrodinger's equation and he thought he + + align:start position:0% +Schrodinger's equation and he thought he + + + align:start position:0% +Schrodinger's equation and he thought he +was the only one who knew how to solve + + align:start position:0% +was the only one who knew how to solve + + + align:start position:0% +was the only one who knew how to solve +each problem both ways + + align:start position:0% +each problem both ways + + + align:start position:0% +each problem both ways +because most of the other physicists + + align:start position:0% +because most of the other physicists + + + align:start position:0% +because most of the other physicists +would get very good at one or the + + align:start position:0% + + + + align:start position:0% + +other he had another feature which was + + align:start position:0% +other he had another feature which was + + + align:start position:0% +other he had another feature which was +that if you argued with + + align:start position:0% +that if you argued with + + + align:start position:0% +that if you argued with +him uh + + align:start position:0% + + + + align:start position:0% + +sometimes he would say oh you're right I + + align:start position:0% +sometimes he would say oh you're right I + + + align:start position:0% +sometimes he would say oh you're right I +was + + align:start position:0% +was + + + align:start position:0% +was +wrong + + align:start position:0% + + + + align:start position:0% + +which like he was once arguing with + + align:start position:0% +which like he was once arguing with + + + align:start position:0% +which like he was once arguing with +fredkin + + align:start position:0% +fredkin + + + align:start position:0% +fredkin +about could you have clocks all over the + + align:start position:0% +about could you have clocks all over the + + + align:start position:0% +about could you have clocks all over the +universe that were + + align:start position:0% +universe that were + + + align:start position:0% +universe that were +synchronized + + align:start position:0% + + + + align:start position:0% + +and the standard ideas you couldn't + + align:start position:0% +and the standard ideas you couldn't + + + align:start position:0% +and the standard ideas you couldn't +because of + + align:start position:0% +because of + + + align:start position:0% +because of +Relativity and fredin said well suppose + + align:start position:0% +Relativity and fredin said well suppose + + + align:start position:0% +Relativity and fredin said well suppose +you start out on Earth and you send + + align:start position:0% +you start out on Earth and you send + + + align:start position:0% +you start out on Earth and you send +a huge Army of little bacteria siiz + + align:start position:0% +a huge Army of little bacteria siiz + + + align:start position:0% +a huge Army of little bacteria siiz +clocks and send them through all + + align:start position:0% +clocks and send them through all + + + align:start position:0% +clocks and send them through all +possible routs to every place and + + align:start position:0% +possible routs to every place and + + + align:start position:0% +possible routs to every place and +uh figure + + align:start position:0% +uh figure + + + align:start position:0% +uh figure +out and compensate for all the + + align:start position:0% +out and compensate for all the + + + align:start position:0% +out and compensate for all the +accelerations they had experienced on + + align:start position:0% +accelerations they had experienced on + + + align:start position:0% +accelerations they had experienced on +the path then wouldn't you get a + + align:start position:0% +the path then wouldn't you get a + + + align:start position:0% +the path then wouldn't you get a +synchronous time everywhere and find + + align:start position:0% +synchronous time everywhere and find + + + align:start position:0% +synchronous time everywhere and find +said uh you're right I was + + align:start position:0% +said uh you're right I was + + + align:start position:0% +said uh you're right I was +wrong without + + align:start position:0% + + + + align:start position:0% + +blinking he may have been + + align:start position:0% + + + + align:start position:0% + +wrong but uh + + align:start position:0% + + + + align:start position:0% + +more + + align:start position:0% + + + + align:start position:0% + +questions along the same Lin his + + align:start position:0% +questions along the same Lin his + + + align:start position:0% +questions along the same Lin his +question about how do we know what + + align:start position:0% +question about how do we know what + + + align:start position:0% +question about how do we know what +method to use for solving problem I'm + + align:start position:0% +method to use for solving problem I'm + + + align:start position:0% +method to use for solving problem I'm +kind of curious how we know what data + + align:start position:0% +kind of curious how we know what data + + + align:start position:0% +kind of curious how we know what data +set or what data to use when solving + + align:start position:0% +set or what data to use when solving + + + align:start position:0% +set or what data to use when solving +problems CU like we have so much sensory + + align:start position:0% +problems CU like we have so much sensory + + + align:start position:0% +problems CU like we have so much sensory +input into moment and so much data that + + align:start position:0% +input into moment and so much data that + + + align:start position:0% +input into moment and so much data that +we have from experience but like when + + align:start position:0% +we have from experience but like when + + + align:start position:0% +we have from experience but like when +you get a problem you instantly and I + + align:start position:0% +you get a problem you instantly and I + + + align:start position:0% +you get a problem you instantly and I +guess kin is sort of a solution for that + + align:start position:0% +guess kin is sort of a solution for that + + + align:start position:0% +guess kin is sort of a solution for that +um but it be curious how you could + + align:start position:0% +um but it be curious how you could + + + align:start position:0% +um but it be curious how you could +possibly represent good data + + align:start position:0% +possibly represent good data + + + align:start position:0% +possibly represent good data +relationships in a way that a computer + + align:start position:0% +relationships in a way that a computer + + + align:start position:0% +relationships in a way that a computer +might be able to use because like right + + align:start position:0% +might be able to use because like right + + + align:start position:0% +might be able to use because like right +now the problem is that we always have + + align:start position:0% +now the problem is that we always have + + + align:start position:0% +now the problem is that we always have +to very narrowly Define problem for a + + align:start position:0% +to very narrowly Define problem for a + + + align:start position:0% +to very narrowly Define problem for a +machine to be able to solve it but I + + align:start position:0% +machine to be able to solve it but I + + + align:start position:0% +machine to be able to solve it but I +feel like we could come up with good + + align:start position:0% +feel like we could come up with good + + + align:start position:0% +feel like we could come up with good +methods for filtering know massive data + + align:start position:0% +methods for filtering know massive data + + + align:start position:0% +methods for filtering know massive data +sets to just what might be relevant it + + align:start position:0% +sets to just what might be relevant it + + + align:start position:0% +sets to just what might be relevant it +doesn't involve like trial and error + + align:start position:0% +doesn't involve like trial and error + + + align:start position:0% +doesn't involve like trial and error +yes + + align:start position:0% + + + + align:start position:0% + +uh so the thing must be + + align:start position:0% + + + + align:start position:0% + +that if you have a + + align:start position:0% +that if you have a + + + align:start position:0% +that if you have a +problem how do you characterize + + align:start position:0% +problem how do you characterize + + + align:start position:0% +problem how do you characterize +it how do you think what kind of problem + + align:start position:0% +it how do you think what kind of problem + + + align:start position:0% +it how do you think what kind of problem +is this and what method is good for that + + align:start position:0% +is this and what method is good for that + + + align:start position:0% +is this and what method is good for that +kind of problem so I suppose that people + + align:start position:0% +kind of problem so I suppose that people + + + align:start position:0% +kind of problem so I suppose that people +vary a lot and + + align:start position:0% + + + + align:start position:0% + +um it's a great question + + align:start position:0% +um it's a great question + + + align:start position:0% +um it's a great question +uh that's what the critics do they say + + align:start position:0% +uh that's what the critics do they say + + + align:start position:0% +uh that's what the critics do they say +uh what kind of problem is this how do I + + align:start position:0% +uh what kind of problem is this how do I + + + align:start position:0% +uh what kind of problem is this how do I +recognize this particular + + align:start position:0% +recognize this particular + + + align:start position:0% +recognize this particular +predicament and + + align:start position:0% + + + + align:start position:0% + +uh I wish there were some psychologists + + align:start position:0% +uh I wish there were some psychologists + + + align:start position:0% +uh I wish there were some psychologists +who thought about that the way new and + + align:start position:0% +who thought about that the way new and + + + align:start position:0% +who thought about that the way new and +Simon did God in the + + align:start position:0% +Simon did God in the + + + align:start position:0% +Simon did God in the +1960s it's 50 years ago how many of you + + align:start position:0% +1960s it's 50 years ago how many of you + + + align:start position:0% +1960s it's 50 years ago how many of you +have seen that book called human problem + + align:start position:0% +have seen that book called human problem + + + align:start position:0% +have seen that book called human problem +solving it's a big thick book and it's + + align:start position:0% +solving it's a big thick book and it's + + + align:start position:0% +solving it's a big thick book and it's +uh got all sorts of chapters that's the + + align:start position:0% +uh got all sorts of chapters that's the + + + align:start position:0% +uh got all sorts of chapters that's the +one I mentioned the other day where they + + align:start position:0% +one I mentioned the other day where they + + + align:start position:0% +one I mentioned the other day where they +actually had some theories of human + + align:start position:0% +actually had some theories of human + + + align:start position:0% +actually had some theories of human +problem solving and + + align:start position:0% +problem solving and + + + align:start position:0% +problem solving and +simulated + + align:start position:0% +simulated + + + align:start position:0% +simulated +uh there + + align:start position:0% + + + + align:start position:0% + +they give they gave subjects problems + + align:start position:0% +they give they gave subjects problems + + + align:start position:0% +they give they gave subjects problems +like this and said + + align:start position:0% +like this and said + + + align:start position:0% +like this and said +uh we want you to figure out what + + align:start position:0% +uh we want you to figure out what + + + align:start position:0% +uh we want you to figure out what +numbers those are and they lied to the + + align:start position:0% +numbers those are and they lied to the + + + align:start position:0% +numbers those are and they lied to the +subjects and said this is an important + + align:start position:0% +subjects and said this is an important + + + align:start position:0% +subjects and said this is an important +kind of problem in + + align:start position:0% +kind of problem in + + + align:start position:0% +kind of problem in +cryptography the uh the secret agents + + align:start position:0% +cryptography the uh the secret agents + + + align:start position:0% +cryptography the uh the secret agents +need to know how to uh decode + + align:start position:0% +need to know how to uh decode + + + align:start position:0% +need to know how to uh decode +cryptograms of this sort where uh + + align:start position:0% +cryptograms of this sort where uh + + + align:start position:0% +cryptograms of this sort where uh +usually it's the other way around the + + align:start position:0% +usually it's the other way around the + + + align:start position:0% +usually it's the other way around the +numbers stand for letters and there's + + align:start position:0% +numbers stand for letters and there's + + + align:start position:0% +numbers stand for letters and there's +some complicated coding but these are + + align:start position:0% +some complicated coding but these are + + + align:start position:0% +some complicated coding but these are +simple cases so you have to figure + + align:start position:0% +simple cases so you have to figure + + + align:start position:0% +simple cases so you have to figure +out that sort of thing and then the book + + align:start position:0% +out that sort of thing and then the book + + + align:start position:0% +out that sort of thing and then the book +is has various chapters on theories of + + align:start position:0% +is has various chapters on theories of + + + align:start position:0% +is has various chapters on theories of +how you recognize different kinds of + + align:start position:0% +how you recognize different kinds of + + + align:start position:0% +how you recognize different kinds of +problems and and uh select strategies + + align:start position:0% +problems and and uh select strategies + + + align:start position:0% +problems and and uh select strategies +and of course some people are better + + align:start position:0% +and of course some people are better + + + align:start position:0% +and of course some people are better +than others and believe it or not at + + align:start position:0% +than others and believe it or not at + + + align:start position:0% +than others and believe it or not at +MIT there was a almost a Whole Decade of + + align:start position:0% +MIT there was a almost a Whole Decade of + + + align:start position:0% +MIT there was a almost a Whole Decade of +psychologists here who were studying the + + align:start position:0% +psychologists here who were studying the + + + align:start position:0% +psychologists here who were studying the +psychology of five person + + align:start position:0% +psychology of five person + + + align:start position:0% +psychology of five person +groups it became uh suppose you take + + align:start position:0% +groups it became uh suppose you take + + + align:start position:0% +groups it became uh suppose you take +five people and put them in a room and + + align:start position:0% +five people and put them in a room and + + + align:start position:0% +five people and put them in a room and +give them problems like this or not the + + align:start position:0% +give them problems like this or not the + + + align:start position:0% +give them problems like this or not the +same crypto but you know little uh + + align:start position:0% +same crypto but you know little uh + + + align:start position:0% +same crypto but you know little uh +puzzles that require some cleverness to + + align:start position:0% +puzzles that require some cleverness to + + + align:start position:0% +puzzles that require some cleverness to +solve and uh you record and video they + + align:start position:0% +solve and uh you record and video they + + + align:start position:0% +solve and uh you record and video they +didn't have video in those days so it + + align:start position:0% +didn't have video in those days so it + + + align:start position:0% +didn't have video in those days so it +was actual film + + align:start position:0% +was actual film + + + align:start position:0% +was actual film +look and + + align:start position:0% +look and + + + align:start position:0% +look and +uh there are many there's a whole + + align:start position:0% +uh there are many there's a whole + + + align:start position:0% +uh there are many there's a whole +generation of + + align:start position:0% +generation of + + + align:start position:0% +generation of +Publications about the social be and and + + align:start position:0% +Publications about the social be and and + + + align:start position:0% +Publications about the social be and and +cognitive behavior of these little + + align:start position:0% +cognitive behavior of these little + + + align:start position:0% +cognitive behavior of these little +groups of people they zeroed in on five + + align:start position:0% +groups of people they zeroed in on five + + + align:start position:0% +groups of people they zeroed in on five +person groups for reasons I don't + + align:start position:0% +person groups for reasons I don't + + + align:start position:0% +person groups for reasons I don't +remember but it turned out that almost + + align:start position:0% +remember but it turned out that almost + + + align:start position:0% +remember but it turned out that almost +always when you had + + align:start position:0% +always when you had + + + align:start position:0% +always when you had +that the group divided into two + + align:start position:0% +that the group divided into two + + + align:start position:0% +that the group divided into two +competitive groups with two and three + + align:start position:0% +competitive groups with two and three + + + align:start position:0% +competitive groups with two and three +and uh every now and then they would + + align:start position:0% +and uh every now and then they would + + + align:start position:0% +and uh every now and then they would +reorganize but it was more a study in + + align:start position:0% +reorganize but it was more a study in + + + align:start position:0% +reorganize but it was more a study in +Social relations than in cognitive + + align:start position:0% +Social relations than in cognitive + + + align:start position:0% +Social relations than in cognitive +psychology but + + align:start position:0% +psychology but + + + align:start position:0% +psychology but +uh it's an interesting book and I + + align:start position:0% +uh it's an interesting book and I + + + align:start position:0% +uh it's an interesting book and I +don't there must be uh contemporary + + align:start position:0% +don't there must be uh contemporary + + + align:start position:0% +don't there must be uh contemporary +studies like that of how people + + align:start position:0% +studies like that of how people + + + align:start position:0% +studies like that of how people +cooperate but um I just haven't been in + + align:start position:0% +cooperate but um I just haven't been in + + + align:start position:0% +cooperate but um I just haven't been in +that environment any of you taken a + + align:start position:0% +that environment any of you taken a + + + align:start position:0% +that environment any of you taken a +psychology course + + align:start position:0% +psychology course + + + align:start position:0% +psychology course +recently not a + + align:start position:0% +recently not a + + + align:start position:0% +recently not a +one just what hap wonder what's happened + + align:start position:0% +one just what hap wonder what's happened + + + align:start position:0% +one just what hap wonder what's happened +to General + + align:start position:0% +to General + + + align:start position:0% +to General +psychology I used to sit in on Tober and + + align:start position:0% +psychology I used to sit in on Tober and + + + align:start position:0% +psychology I used to sit in on Tober and +a couple of other lecturers here and + + align:start position:0% +a couple of other lecturers here and + + + align:start position:0% +a couple of other lecturers here and +psychology course was it was sort of + + align:start position:0% +psychology course was it was sort of + + + align:start position:0% +psychology course was it was sort of +like 20% optical illusions and yeah they + + align:start position:0% +like 20% optical illusions and yeah they + + + align:start position:0% +like 20% optical illusions and yeah they +still do that stuff like that they also + + align:start position:0% +still do that stuff like that they also + + + align:start position:0% +still do that stuff like that they also +concentrate a lot on U developmental + + align:start position:0% +concentrate a lot on U developmental + + + align:start position:0% +concentrate a lot on U developmental +psychology well that's that's nice to + + align:start position:0% +psychology well that's that's nice to + + + align:start position:0% +psychology well that's that's nice to +hear because + + align:start position:0% +hear because + + + align:start position:0% +hear because +uh I don't believe there was any of that + + align:start position:0% +uh I don't believe there was any of that + + + align:start position:0% +uh I don't believe there was any of that +in troyer's + + align:start position:0% +in troyer's + + + align:start position:0% +in troyer's +class I think Professor gabrieli now + + align:start position:0% +class I think Professor gabrieli now + + + align:start position:0% +class I think Professor gabrieli now +teaches the introductory psychology and + + align:start position:0% +teaches the introductory psychology and + + + align:start position:0% +teaches the introductory psychology and +he do they still believe P or do they + + align:start position:0% +he do they still believe P or do they + + + align:start position:0% +he do they still believe P or do they +think think that he was + + align:start position:0% +think think that he was + + + align:start position:0% +think think that he was +wrong uh I think they probably take the + + align:start position:0% +wrong uh I think they probably take the + + + align:start position:0% +wrong uh I think they probably take the +same approaches with like Freud they + + align:start position:0% +same approaches with like Freud they + + + align:start position:0% +same approaches with like Freud they +would say you know great ideas in a + + align:start position:0% +would say you know great ideas in a + + + align:start position:0% +would say you know great ideas in a +revolution + + align:start position:0% +revolution + + + align:start position:0% +revolution +but they also don't think he the + + align:start position:0% + + + + align:start position:0% + +end well he got + + align:start position:0% +end well he got + + + align:start position:0% +end well he got +uh I know like the child childhood + + align:start position:0% +uh I know like the child childhood + + + align:start position:0% +uh I know like the child childhood +development class you read pH + + align:start position:0% +development class you read pH + + + align:start position:0% +development class you read pH +like yeah in ph's later years he + + align:start position:0% +like yeah in ph's later years he + + + align:start position:0% +like yeah in ph's later years he +got algebra envy and uh + + align:start position:0% +got algebra envy and uh + + + align:start position:0% +got algebra envy and uh +he wanted to be more scientific + + align:start position:0% +he wanted to be more scientific + + + align:start position:0% +he wanted to be more scientific +and studied logic and uh few things like + + align:start position:0% +and studied logic and uh few things like + + + align:start position:0% +and studied logic and uh few things like +that and became less scientific was sort + + align:start position:0% +that and became less scientific was sort + + + align:start position:0% +that and became less scientific was sort +of sad + + align:start position:0% +of sad + + + align:start position:0% +of sad +to I can + + align:start position:0% +to I can + + + align:start position:0% +to I can +imagine being browbeaten by + + align:start position:0% +imagine being browbeaten by + + + align:start position:0% +imagine being browbeaten by +mathematicians because they're the ones + + align:start position:0% +mathematicians because they're the ones + + + align:start position:0% +mathematicians because they're the ones +who were getting published + + align:start position:0% +who were getting published + + + align:start position:0% +who were getting published +and he only had how many books did + + align:start position:0% +and he only had how many books did + + + align:start position:0% +and he only had how many books did +P + + align:start position:0% +P + + + align:start position:0% +P +Inc if I may add a comment about PJ here + + align:start position:0% +Inc if I may add a comment about PJ here + + + align:start position:0% +Inc if I may add a comment about PJ here +that uh really comes from an old friend + + align:start position:0% +that uh really comes from an old friend + + + align:start position:0% +that uh really comes from an old friend +of many of us + + align:start position:0% +of many of us + + + align:start position:0% +of many of us +Seymour as you know he was of course + + align:start position:0% +Seymour as you know he was of course + + + align:start position:0% +Seymour as you know he was of course +PJ's mathematician for many years we got + + align:start position:0% +PJ's mathematician for many years we got + + + align:start position:0% +PJ's mathematician for many years we got +Pete pord from P's + + align:start position:0% +Pete pord from P's + + + align:start position:0% +Pete pord from P's +lab but uh Seymour said that he felt + + align:start position:0% +lab but uh Seymour said that he felt + + + align:start position:0% +lab but uh Seymour said that he felt +that ph's best work was his early work + + align:start position:0% +that ph's best work was his early work + + + align:start position:0% +that ph's best work was his early work +especially build around his case studies + + align:start position:0% +especially build around his case studies + + + align:start position:0% +especially build around his case studies +and one time when we were talking about + + align:start position:0% +and one time when we were talking about + + + align:start position:0% +and one time when we were talking about +the issue of focusing from the AI lab + + align:start position:0% +the issue of focusing from the AI lab + + + align:start position:0% +the issue of focusing from the AI lab +worked on in Psychology here sour said + + align:start position:0% +worked on in Psychology here sour said + + + align:start position:0% +worked on in Psychology here sour said +he felt that was less + + align:start position:0% +he felt that was less + + + align:start position:0% +he felt that was less +necessary than more of a concentration + + align:start position:0% +necessary than more of a concentration + + + align:start position:0% +necessary than more of a concentration +on an AI because he expected in the + + align:start position:0% +on an AI because he expected in the + + + align:start position:0% +on an AI because he expected in the +future the the world of study of the + + align:start position:0% +future the the world of study of the + + + align:start position:0% +future the the world of study of the +mind would separate into two individual + + align:start position:0% +mind would separate into two individual + + + align:start position:0% +mind would separate into two individual +studies one much more biological like + + align:start position:0% +studies one much more biological like + + + align:start position:0% +studies one much more biological like +the neurosciences of today and the other + + align:start position:0% +the neurosciences of today and the other + + + align:start position:0% +the neurosciences of today and the other +focused more on the structure of + + align:start position:0% +focused more on the structure of + + + align:start position:0% +focused more on the structure of +knowledge and on representations and in + + align:start position:0% +knowledge and on representations and in + + + align:start position:0% +knowledge and on representations and in +effect the genetic epistemology of P + + align:start position:0% +effect the genetic epistemology of P + + + align:start position:0% +effect the genetic epistemology of P +then he added that uh something that was + + align:start position:0% +then he added that uh something that was + + + align:start position:0% +then he added that uh something that was +a quote later he made was that even if + + align:start position:0% +a quote later he made was that even if + + + align:start position:0% +a quote later he made was that even if +PJ's marvelous theory of today proved to + + align:start position:0% +PJ's marvelous theory of today proved to + + + align:start position:0% +PJ's marvelous theory of today proved to +be wrong he would sure that whatever + + align:start position:0% +be wrong he would sure that whatever + + + align:start position:0% +be wrong he would sure that whatever +replaced it would be his theory of the + + align:start position:0% +replaced it would be his theory of the + + + align:start position:0% +replaced it would be his theory of the +same sort one of the development of + + align:start position:0% +same sort one of the development of + + + align:start position:0% +same sort one of the development of +knowledge and all its + + align:start position:0% +knowledge and all its + + + align:start position:0% +knowledge and all its +changes so uh I don't think people will + + align:start position:0% +changes so uh I don't think people will + + + align:start position:0% +changes so uh I don't think people will +get away from puj however much they want + + align:start position:0% +get away from puj however much they want + + + align:start position:0% +get away from puj however much they want +to I don't think so + + align:start position:0% +to I don't think so + + + align:start position:0% +to I don't think so +either I meant to + + align:start position:0% +either I meant to + + + align:start position:0% +either I meant to +introduce our visitor + + align:start position:0% +introduce our visitor + + + align:start position:0% +introduce our visitor +here + + align:start position:0% + + + + align:start position:0% + +because Bob ller here has + + align:start position:0% +because Bob ller here has + + + align:start position:0% +because Bob ller here has +reproduced a good many of the kinds of + + align:start position:0% +reproduced a good many of the kinds of + + + align:start position:0% +reproduced a good many of the kinds of +studies that P did in the 1930s and 40s + + align:start position:0% +studies that P did in the 1930s and 40s + + + align:start position:0% +studies that P did in the 1930s and 40s +and if you look him up on the web + + align:start position:0% +and if you look him up on the web + + + align:start position:0% +and if you look him up on the web +you'll you must have a few papers + + align:start position:0% +you'll you must have a few papers + + + align:start position:0% +you'll you must have a few papers +actually I I better tell you what the + + align:start position:0% +actually I I better tell you what the + + + align:start position:0% +actually I I better tell you what the +website is because it's still hidden oh + + align:start position:0% +website is because it's still hidden oh + + + align:start position:0% +website is because it's still hidden oh +from + + align:start position:0% +from + + + align:start position:0% +from +web it's + + align:start position:0% +web it's + + + align:start position:0% +web it's +nlcsa Donnet that would be hard too + + align:start position:0% +nlcsa Donnet that would be hard too + + + align:start position:0% +nlcsa Donnet that would be hard too +natural learning case study + + align:start position:0% +natural learning case study + + + align:start position:0% +natural learning case study +archive.net + + align:start position:0% + + + + align:start position:0% + +it's still in process still in + + align:start position:0% +it's still in process still in + + + align:start position:0% +it's still in process still in +development but it's worth looking at + + align:start position:0% +development but it's worth looking at + + + align:start position:0% +development but it's worth looking at +that how many children did P have well P + + align:start position:0% +that how many children did P have well P + + + align:start position:0% +that how many children did P have well P +had three children development he + + align:start position:0% +had three children development he + + + align:start position:0% +had three children development he +studied but uh you know what he did was + + align:start position:0% +studied but uh you know what he did was + + + align:start position:0% +studied but uh you know what he did was +to mix together the information from all + + align:start position:0% +to mix together the information from all + + + align:start position:0% +to mix together the information from all +three studies and supported the ideas + + align:start position:0% +three studies and supported the ideas + + + align:start position:0% +three studies and supported the ideas +with which he began so was illustrations + + align:start position:0% +with which he began so was illustrations + + + align:start position:0% +with which he began so was illustrations +of his + + align:start position:0% +of his + + + align:start position:0% +of his +theories anyway Bob has quite a lot of + + align:start position:0% +theories anyway Bob has quite a lot of + + + align:start position:0% +theories anyway Bob has quite a lot of +studies about how his + + align:start position:0% +studies about how his + + + align:start position:0% +studies about how his +children uh developed concepts of number + + align:start position:0% +children uh developed concepts of number + + + align:start position:0% +children uh developed concepts of number +and geometry and things like that and I + + align:start position:0% +and geometry and things like that and I + + + align:start position:0% +and geometry and things like that and I +don't know of anyone else since PJ who's + + align:start position:0% +don't know of anyone else since PJ who's + + + align:start position:0% +don't know of anyone else since PJ who's +continued to do those sorts of + + align:start position:0% +continued to do those sorts of + + + align:start position:0% +continued to do those sorts of +experiments there were there were quite + + align:start position:0% +experiments there were there were quite + + + align:start position:0% +experiments there were there were quite +a lot at PJ's Institute in + + align:start position:0% +a lot at PJ's Institute in + + + align:start position:0% +a lot at PJ's Institute in +Geneva for some years after P was gone + + align:start position:0% +Geneva for some years after P was gone + + + align:start position:0% +Geneva for some years after P was gone +but I think it's pretty much closed now + + align:start position:0% +but I think it's pretty much closed now + + + align:start position:0% +but I think it's pretty much closed now +hasn't it the the last psychologist that + + align:start position:0% +hasn't it the the last psychologist that + + + align:start position:0% +hasn't it the the last psychologist that +P hired was + + align:start position:0% +P hired was + + + align:start position:0% +P hired was +jaes who + + align:start position:0% +jaes who + + + align:start position:0% +jaes who +was no longer at the + + align:start position:0% +was no longer at the + + + align:start position:0% +was no longer at the +University he retired and uh it has been + + align:start position:0% +University he retired and uh it has been + + + align:start position:0% +University he retired and uh it has been +taken over by the neopians who are doing + + align:start position:0% +taken over by the neopians who are doing + + + align:start position:0% +taken over by the neopians who are doing +something different is there any other + + align:start position:0% +something different is there any other + + + align:start position:0% +something different is there any other +place well there was + + align:start position:0% +place well there was + + + align:start position:0% +place well there was +uh oh there are people there was + + align:start position:0% +uh oh there are people there was + + + align:start position:0% +uh oh there are people there was +yoichi's lab on children in Japan there + + align:start position:0% +yoichi's lab on children in Japan there + + + align:start position:0% +yoichi's lab on children in Japan there +are many people who take PJ seriously + + align:start position:0% +are many people who take PJ seriously + + + align:start position:0% +are many people who take PJ seriously +and + + align:start position:0% +and + + + align:start position:0% +and +uh in this country as well as + + align:start position:0% + + + + align:start position:0% + +others so Robert mentioned that + + align:start position:0% +others so Robert mentioned that + + + align:start position:0% +others so Robert mentioned that +fan had like more representations of the + + align:start position:0% +fan had like more representations of the + + + align:start position:0% +fan had like more representations of the +cour than like usual people the like + + align:start position:0% +cour than like usual people the like + + + align:start position:0% +cour than like usual people the like +when I talked about I and the g c I + + align:start position:0% +when I talked about I and the g c I + + + align:start position:0% +when I talked about I and the g c I +refer to that because I believe K lines + + align:start position:0% +refer to that because I believe K lines + + + align:start position:0% +refer to that because I believe K lines +is a way of representing the world and + + align:start position:0% +is a way of representing the world and + + + align:start position:0% +is a way of representing the world and +maybe e had like better ways of + + align:start position:0% +maybe e had like better ways of + + + align:start position:0% +maybe e had like better ways of +representing the world and I believe + + align:start position:0% +representing the world and I believe + + + align:start position:0% +representing the world and I believe +that for example agents and + + align:start position:0% +that for example agents and + + + align:start position:0% +that for example agents and +resources are not different from touring + + align:start position:0% +resources are not different from touring + + + align:start position:0% +resources are not different from touring +Machin you can create a very simple like + + align:start position:0% +Machin you can create a very simple like + + + align:start position:0% +Machin you can create a very simple like +T machine that act like agents and you + + align:start position:0% +T machine that act like agents and you + + + align:start position:0% +T machine that act like agents and you +have some mental States + + align:start position:0% +have some mental States + + + align:start position:0% +have some mental States +but + + align:start position:0% +but + + + align:start position:0% +but +uh there is no I believe good way + + align:start position:0% +uh there is no I believe good way + + + align:start position:0% +uh there is no I believe good way +of uh right now of representing the + + align:start position:0% +of uh right now of representing the + + + align:start position:0% +of uh right now of representing the +world and like updating this + + align:start position:0% +world and like updating this + + + align:start position:0% +world and like updating this +representation of the world like it + + align:start position:0% +representation of the world like it + + + align:start position:0% +representation of the world like it +seems to me that + + align:start position:0% +seems to me that + + + align:start position:0% +seems to me that +uh when you grow up you're learning + + align:start position:0% +uh when you grow up you're learning + + + align:start position:0% +uh when you grow up you're learning +like how to represent the word better + + align:start position:0% +like how to represent the word better + + + align:start position:0% +like how to represent the word better +and better and you have some layers and + + align:start position:0% +and better and you have some layers and + + + align:start position:0% +and better and you have some layers and +that's all about K lines and + + align:start position:0% +that's all about K lines and + + + align:start position:0% +that's all about K lines and +if if clear cells are actually like + + align:start position:0% +if if clear cells are actually like + + + align:start position:0% +if if clear cells are actually like +related to K lines so it means that I + + align:start position:0% +related to K lines so it means that I + + + align:start position:0% +related to K lines so it means that I +like + + align:start position:0% +like + + + align:start position:0% +like +had like a better Hardware in + + align:start position:0% +had like a better Hardware in + + + align:start position:0% +had like a better Hardware in +representing the word and that's why he + + align:start position:0% +representing the word and that's why he + + + align:start position:0% +representing the word and that's why he +would be smarter than other + + align:start position:0% +would be smarter than other + + + align:start position:0% +would be smarter than other +people well it's hard + + align:start position:0% + + + + align:start position:0% + +to I'm I'm sure that that's right that + + align:start position:0% +to I'm I'm sure that that's right that + + + align:start position:0% +to I'm I'm sure that that's right that +uh you have a + + align:start position:0% +uh you have a + + + align:start position:0% +uh you have a +certain amount of Hardware but but you + + align:start position:0% +certain amount of Hardware but but you + + + align:start position:0% +certain amount of Hardware but but you +can + + align:start position:0% +can + + + align:start position:0% +can +reconfigure some of it uh + + align:start position:0% +reconfigure some of it uh + + + align:start position:0% +reconfigure some of it uh +nobody really knows but some brain + + align:start position:0% +nobody really knows but some brain + + + align:start position:0% +nobody really knows but some brain +centers may have only a few neurons and + + align:start position:0% +centers may have only a few neurons and + + + align:start position:0% +centers may have only a few neurons and +maybe if they're + + align:start position:0% +maybe if they're + + + align:start position:0% +maybe if they're +uh maybe there's some retrograde signals + + align:start position:0% +uh maybe there's some retrograde signals + + + align:start position:0% +uh maybe there's some retrograde signals +so that if two brain centers are are + + align:start position:0% +so that if two brain centers are are + + + align:start position:0% +so that if two brain centers are are +simultaneously + + align:start position:0% +simultaneously + + + align:start position:0% +simultaneously +activated uh then uh usually + + align:start position:0% +activated uh then uh usually + + + align:start position:0% +activated uh then uh usually +the signals only go one way from one to + + align:start position:0% +the signals only go one way from one to + + + align:start position:0% +the signals only go one way from one to +the other have to go through a third one + + align:start position:0% +the other have to go through a third one + + + align:start position:0% +the other have to go through a third one +to get back but um it could be that the + + align:start position:0% +to get back but um it could be that the + + + align:start position:0% +to get back but um it could be that the +brain uh that the neurons have a + + align:start position:0% +brain uh that the neurons have a + + + align:start position:0% +brain uh that the neurons have a +property that if two centers are + + align:start position:0% +property that if two centers are + + + align:start position:0% +property that if two centers are +activated maybe uh that causes more + + align:start position:0% +activated maybe uh that causes more + + + align:start position:0% +activated maybe uh that causes more +connections to be made between them that + + align:start position:0% +connections to be made between them that + + + align:start position:0% +connections to be made between them that +can then be programmed more I don't + + align:start position:0% +can then be programmed more I don't + + + align:start position:0% +can then be programmed more I don't +think anybody really has a clear idea + + align:start position:0% +think anybody really has a clear idea + + + align:start position:0% +think anybody really has a clear idea +of of whether you can grow new + + align:start position:0% +of of whether you can grow new + + + align:start position:0% +of of whether you can grow new +connections between brain centers that + + align:start position:0% +connections between brain centers that + + + align:start position:0% +connections between brain centers that +that are far apart does anybody know is + + align:start position:0% +that are far apart does anybody know is + + + align:start position:0% +that are far apart does anybody know is +there anything + + align:start position:0% +there anything + + + align:start position:0% +there anything +uh used to on the knowledge that there + + align:start position:0% +uh used to on the knowledge that there + + + align:start position:0% +uh used to on the knowledge that there +was no such thing as adult neurogenesis + + align:start position:0% +was no such thing as adult neurogenesis + + + align:start position:0% +was no such thing as adult neurogenesis +and now it is known that it exists in + + align:start position:0% +and now it is known that it exists in + + + align:start position:0% +and now it is known that it exists in +certain limited regions of the brain so + + align:start position:0% +certain limited regions of the brain so + + + align:start position:0% +certain limited regions of the brain so +in the future it may be known that it + + align:start position:0% +in the future it may be known that it + + + align:start position:0% +in the future it may be known that it +exists everywhere right or else that the + + align:start position:0% +exists everywhere right or else that the + + + align:start position:0% +exists everywhere right or else that the +those experiments were wrong + + align:start position:0% +those experiments were wrong + + + align:start position:0% +those experiments were wrong +and and they were in a frog rather than + + align:start position:0% +and and they were in a frog rather than + + + align:start position:0% +and and they were in a frog rather than +a + + align:start position:0% + + + + align:start position:0% + +person doesn't claim that you could take + + align:start position:0% +person doesn't claim that you could take + + + align:start position:0% +person doesn't claim that you could take +a frog brain out stick it in backwards + + align:start position:0% +a frog brain out stick it in backwards + + + align:start position:0% +a frog brain out stick it in backwards +and pretty soon it would behave just + + align:start position:0% +and pretty soon it would behave just + + + align:start position:0% +and pretty soon it would behave just +like it used + + align:start position:0% +like it used + + + align:start position:0% +like it used +to myin head yeah of course I don't know + + align:start position:0% +to myin head yeah of course I don't know + + + align:start position:0% +to myin head yeah of course I don't know +if he was kidding or not you never could + + align:start position:0% +if he was kidding or not you never could + + + align:start position:0% +if he was kidding or not you never could +tell you could never could never tell + + align:start position:0% +tell you could never could never tell + + + align:start position:0% +tell you could never could never tell +when he was + + align:start position:0% + + + + align:start position:0% + +kidding lein was a neuroscientist here + + align:start position:0% +kidding lein was a neuroscientist here + + + align:start position:0% +kidding lein was a neuroscientist here +who was so one of + + align:start position:0% +who was so one of + + + align:start position:0% +who was so one of +the Great alltime neuroscientists + + align:start position:0% +the Great alltime neuroscientists + + + align:start position:0% +the Great alltime neuroscientists +he was also one of + + align:start position:0% +he was also one of + + + align:start position:0% +he was also one of +the first scientists to use transistors + + align:start position:0% +the first scientists to use transistors + + + align:start position:0% +the first scientists to use transistors +for uh biological purposes and made + + align:start position:0% +for uh biological purposes and made + + + align:start position:0% +for uh biological purposes and made +circuits that are still used in every + + align:start position:0% +circuits that are still used in every + + + align:start position:0% +circuits that are still used in every +laboratory + + align:start position:0% +laboratory + + + align:start position:0% +laboratory +so he was very colorful figure and + + align:start position:0% +so he was very colorful figure and + + + align:start position:0% +so he was very colorful figure and +everyone should read some of his older + + align:start position:0% +everyone should read some of his older + + + align:start position:0% +everyone should read some of his older +papers I don't I don't know that there + + align:start position:0% +papers I don't I don't know that there + + + align:start position:0% +papers I don't I don't know that there +were any recent ones but he had an army + + align:start position:0% +were any recent ones but he had an army + + + align:start position:0% +were any recent ones but he had an army +of students + + align:start position:0% + + + + align:start position:0% + +who and he was extremely + + align:start position:0% + + + + align:start position:0% + +funny what + + align:start position:0% + + + + align:start position:0% + +else sort of uh continuing on the idea + + align:start position:0% +else sort of uh continuing on the idea + + + align:start position:0% +else sort of uh continuing on the idea +of Hardware versus software uh what do + + align:start position:0% +of Hardware versus software uh what do + + + align:start position:0% +of Hardware versus software uh what do +you think about the idea that um like + + align:start position:0% +you think about the idea that um like + + + align:start position:0% +you think about the idea that um like +intelligences or humans may need strong + + align:start position:0% +intelligences or humans may need strong + + + align:start position:0% +intelligences or humans may need strong +instincts uh as when they're born in + + align:start position:0% +instincts uh as when they're born in + + + align:start position:0% +instincts uh as when they're born in +order like and the interplay between + + align:start position:0% +order like and the interplay between + + + align:start position:0% +order like and the interplay between +their instincts like they know to cry + + align:start position:0% +their instincts like they know to cry + + + align:start position:0% +their instincts like they know to cry +when they're hungry or to look for their + + align:start position:0% +when they're hungry or to look for their + + + align:start position:0% +when they're hungry or to look for their +mother they need these instincts in + + align:start position:0% +mother they need these instincts in + + + align:start position:0% +mother they need these instincts in +order to develop um higher orders of + + align:start position:0% +order to develop um higher orders of + + + align:start position:0% +order to develop um higher orders of +knowledge you'd have to ask elron hubber + + align:start position:0% + + + + align:start position:0% + +for I don't recall + + align:start position:0% +for I don't recall + + + align:start position:0% +for I don't recall +any real attempts + + align:start position:0% + + + + align:start position:0% + +to I don't think I've ever run across + + align:start position:0% +to I don't think I've ever run across + + + align:start position:0% +to I don't think I've ever run across +any + + align:start position:0% +any + + + align:start position:0% +any +uh body claiming to have correlations + + align:start position:0% +uh body claiming to have correlations + + + align:start position:0% +uh body claiming to have correlations +between prenatal experience and the + + align:start position:0% +between prenatal experience and the + + + align:start position:0% +between prenatal experience and the +development of + + align:start position:0% +development of + + + align:start position:0% +development of +intelligence that's not what I'm talking + + align:start position:0% +intelligence that's not what I'm talking + + + align:start position:0% +intelligence that's not what I'm talking +about I'm talking about when uh before + + align:start position:0% +about I'm talking about when uh before + + + align:start position:0% +about I'm talking about when uh before +intelligence is really developed like + + align:start position:0% +intelligence is really developed like + + + align:start position:0% +intelligence is really developed like +you learn language before you learn + + align:start position:0% +you learn language before you learn + + + align:start position:0% +you learn language before you learn +language you need to have motivation to + + align:start position:0% +language you need to have motivation to + + + align:start position:0% +language you need to have motivation to +do something so you need to have + + align:start position:0% +do something so you need to have + + + align:start position:0% +do something so you need to have +Instinct instinctual reactions to things + + align:start position:0% +Instinct instinctual reactions to things + + + align:start position:0% +Instinct instinctual reactions to things +and by accumulation of experiential + + align:start position:0% +and by accumulation of experiential + + + align:start position:0% +and by accumulation of experiential +knowledge after you're born children + + align:start position:0% +knowledge after you're born children + + + align:start position:0% +knowledge after you're born children +learn language you know 12 to 18 + + align:start position:0% +learn language you know 12 to 18 + + + align:start position:0% +learn language you know 12 to 18 +months what are you saying that they + + align:start position:0% +months what are you saying that they + + + align:start position:0% +months what are you saying that they +need some + + align:start position:0% + + + + align:start position:0% + +preparation I'm not sure what you're + + align:start position:0% +preparation I'm not sure what you're + + + align:start position:0% +preparation I'm not sure what you're +asking so take it from an engineering + + align:start position:0% +asking so take it from an engineering + + + align:start position:0% +asking so take it from an engineering +point you if you were to uh build like a + + align:start position:0% +point you if you were to uh build like a + + + align:start position:0% +point you if you were to uh build like a +robot would you need to program it with + + align:start position:0% +robot would you need to program it with + + + align:start position:0% +robot would you need to program it with +some instincts um some like Ru thumb + + align:start position:0% +some instincts um some like Ru thumb + + + align:start position:0% +some instincts um some like Ru thumb +algorithms in order to get it started in + + align:start position:0% +algorithms in order to get it started in + + + align:start position:0% +algorithms in order to get it started in +the world in order to build experiential + + align:start position:0% +the world in order to build experiential + + + align:start position:0% +the world in order to build experiential +knowledge you might want to build + + align:start position:0% +knowledge you might want to build + + + align:start position:0% +knowledge you might want to build +something like a Difference Engine so + + align:start position:0% +something like a Difference Engine so + + + align:start position:0% +something like a Difference Engine so +that you can represent a goal and it + + align:start position:0% +that you can represent a goal and it + + + align:start position:0% +that you can represent a goal and it +will try to achieve it so you need some + + align:start position:0% +will try to achieve it so you need some + + + align:start position:0% +will try to achieve it so you need some +engine for for producing any Behavior at + + align:start position:0% +engine for for producing any Behavior at + + + align:start position:0% +engine for for producing any Behavior at +all so like if you take the approach + + align:start position:0% +all so like if you take the approach + + + align:start position:0% +all so like if you take the approach +that like maybe to build an AI you + + align:start position:0% +that like maybe to build an AI you + + + align:start position:0% +that like maybe to build an AI you +should build like like an infant robot + + align:start position:0% +should build like like an infant robot + + + align:start position:0% +should build like like an infant robot +and then you teach it um as you would + + align:start position:0% +and then you teach it um as you would + + + align:start position:0% +and then you teach it um as you would +like a human child then would it be + + align:start position:0% +like a human child then would it be + + + align:start position:0% +like a human child then would it be +useful to make it dependent on like some + + align:start position:0% +useful to make it dependent on like some + + + align:start position:0% +useful to make it dependent on like some +mother figure in order to help it learn + + align:start position:0% +mother figure in order to help it learn + + + align:start position:0% +mother figure in order to help it learn +how to do things like a human + + align:start position:0% + + + + align:start position:0% + +childwood well in order to learn you + + align:start position:0% +childwood well in order to learn you + + + align:start position:0% +childwood well in order to learn you +have to learn from + + align:start position:0% +have to learn from + + + align:start position:0% +have to learn from +something and one way to learn is + + align:start position:0% +something and one way to learn is + + + align:start position:0% +something and one way to learn is +is in isolation just to have some you + + align:start position:0% +is in isolation just to have some you + + + align:start position:0% +is in isolation just to have some you +could build a goal to to predict what + + align:start position:0% +could build a goal to to predict what + + + align:start position:0% +could build a goal to to predict what +will + + align:start position:0% +will + + + align:start position:0% +will +happen and the best way to predict as + + align:start position:0% +happen and the best way to predict as + + + align:start position:0% +happen and the best way to predict as +Alan Kay put it once the best way to + + align:start position:0% +Alan Kay put it once the best way to + + + align:start position:0% +Alan Kay put it once the best way to +predict the future is to invent + + align:start position:0% +predict the future is to invent + + + align:start position:0% +predict the future is to invent +it so you could make a + + align:start position:0% +it so you could make a + + + align:start position:0% +it so you could make a +uh or you + + align:start position:0% +uh or you + + + align:start position:0% +uh or you +could or you could put a model of an + + align:start position:0% +could or you could put a model of an + + + align:start position:0% +could or you could put a model of an +adult in it to start with so that + + align:start position:0% + + + + align:start position:0% + +other words one way to make a very smart + + align:start position:0% +other words one way to make a very smart + + + align:start position:0% +other words one way to make a very smart +child is to copy its mother's brain into + + align:start position:0% +child is to copy its mother's brain into + + + align:start position:0% +child is to copy its mother's brain into +a little subb brain when it's born and + + align:start position:0% +a little subb brain when it's born and + + + align:start position:0% +a little subb brain when it's born and +then it could learn from that instead of + + align:start position:0% +then it could learn from that instead of + + + align:start position:0% +then it could learn from that instead of +depending on anybody else I'm not + + align:start position:0% +depending on anybody else I'm not + + + align:start position:0% +depending on anybody else I'm not +sure it you have to start with something + + align:start position:0% + + + + align:start position:0% + +of course + + align:start position:0% +of course + + + align:start position:0% +of course +humans as Bob mentioned or someone + + align:start position:0% +humans as Bob mentioned or someone + + + align:start position:0% +humans as Bob mentioned or someone +mentioned + + align:start position:0% +mentioned + + + align:start position:0% +mentioned +uh a if you take a human baby and + + align:start position:0% +uh a if you take a human baby and + + + align:start position:0% +uh a if you take a human baby and +isolate + + align:start position:0% +isolate + + + align:start position:0% +isolate +it it looks like it won't + + align:start position:0% +it it looks like it won't + + + align:start position:0% +it it looks like it won't +develop + + align:start position:0% +develop + + + align:start position:0% +develop +Language by itself because I don't know + + align:start position:0% +Language by itself because I don't know + + + align:start position:0% +Language by itself because I don't know +what because + + align:start position:0% + + + + align:start position:0% + +but I I remember one of our children who + + align:start position:0% +but I I remember one of our children who + + + align:start position:0% +but I I remember one of our children who +had just learning to talk and she said + + align:start position:0% +had just learning to talk and she said + + + align:start position:0% +had just learning to talk and she said +something came up and she said what + + align:start position:0% +something came up and she said what + + + align:start position:0% +something came up and she said what +because is + + align:start position:0% +because is + + + align:start position:0% +because is +that + + align:start position:0% +that + + + align:start position:0% +that +and do you remember took a while to get + + align:start position:0% +and do you remember took a while to get + + + align:start position:0% +and do you remember took a while to get +her to say + + align:start position:0% +her to say + + + align:start position:0% +her to say +why so so when she she she would come up + + align:start position:0% +why so so when she she she would come up + + + align:start position:0% +why so so when she she she would come up +and say what because and I I would say + + align:start position:0% +and say what because and I I would say + + + align:start position:0% +and say what because and I I would say +you're asking why I did + + align:start position:0% +you're asking why I did + + + align:start position:0% +you're asking why I did +this after a long time she got the hint + + align:start position:0% + + + + align:start position:0% + +but why do all wh words start with + + align:start position:0% +but why do all wh words start with + + + align:start position:0% +but why do all wh words start with +wh one of them doesn't how + + align:start position:0% +wh one of them doesn't how + + + align:start position:0% +wh one of them doesn't how +how could you say + + align:start position:0% + + + + align:start position:0% + +wow + + align:start position:0% +wow + + + align:start position:0% +wow +how is there a + + align:start position:0% + + + + align:start position:0% + +theory it's a basic sound telling that + + align:start position:0% +theory it's a basic sound telling that + + + align:start position:0% +theory it's a basic sound telling that +you're making a query before you can do + + align:start position:0% +you're making a query before you can do + + + align:start position:0% +you're making a query before you can do +the + + align:start position:0% +the + + + align:start position:0% +the +Rising + + align:start position:0% +Rising + + + align:start position:0% +Rising +inflection it's interesting is it true + + align:start position:0% +inflection it's interesting is it true + + + align:start position:0% +inflection it's interesting is it true +in + + align:start position:0% +in + + + align:start position:0% +in +French qua or the the land of the silent + + align:start position:0% + + + + align:start position:0% + +letter anybody know what's the + + align:start position:0% +letter anybody know what's the + + + align:start position:0% +letter anybody know what's the +equivalent of wh words in a in your + + align:start position:0% +equivalent of wh words in a in your + + + align:start position:0% +equivalent of wh words in a in your +native language n what n n yeah in what + + align:start position:0% +native language n what n n yeah in what + + + align:start position:0% +native language n what n n yeah in what +really + + align:start position:0% +really + + + align:start position:0% +really +they all start with n + + align:start position:0% + + + + align:start position:0% + +wow + + align:start position:0% + + + + align:start position:0% + +interesting maybe the infants have a + + align:start position:0% +interesting maybe the infants have a + + + align:start position:0% +interesting maybe the infants have a +effect on + + align:start position:0% +effect on + + + align:start position:0% +effect on +something do questions in + + align:start position:0% +something do questions in + + + align:start position:0% +something do questions in +Turkish and with a rise yeah is it rise + + align:start position:0% +Turkish and with a rise yeah is it rise + + + align:start position:0% +Turkish and with a rise yeah is it rise +well so um only the only the wh + + align:start position:0% +well so um only the only the wh + + + align:start position:0% +well so um only the only the wh +questions um okay all questions end in a + + align:start position:0% +questions um okay all questions end in a + + + align:start position:0% +questions um okay all questions end in a +kind of an inflection but normally you + + align:start position:0% +kind of an inflection but normally you + + + align:start position:0% +kind of an inflection but normally you +have a um little kind of little word + + align:start position:0% +have a um little kind of little word + + + align:start position:0% +have a um little kind of little word +that you would put at the end of any + + align:start position:0% +that you would put at the end of any + + + align:start position:0% +that you would put at the end of any +sentence to make it into a question uhuh + + align:start position:0% +sentence to make it into a question uhuh + + + align:start position:0% +sentence to make it into a question uhuh +except for the the wh questions which + + align:start position:0% +except for the the wh questions which + + + align:start position:0% +except for the the wh questions which +are standal you don't need + + align:start position:0% +are standal you don't need + + + align:start position:0% +are standal you don't need +them yes you say this is + + align:start position:0% +them yes you say this is + + + align:start position:0% +them yes you say this is +expensive they don't need the wh if you + + align:start position:0% +expensive they don't need the wh if you + + + align:start position:0% +expensive they don't need the wh if you +do enough of + + align:start position:0% +do enough of + + + align:start position:0% +do enough of +that huh + + align:start position:0% + + + + align:start position:0% + +so question is that in the brain at + + align:start position:0% + + + + align:start position:0% + +Birth is that pattern mired in English + + align:start position:0% +Birth is that pattern mired in English + + + align:start position:0% +Birth is that pattern mired in English +where you can say is this expensive but + + align:start position:0% +where you can say is this expensive but + + + align:start position:0% +where you can say is this expensive but +you can say how expensive is this + + align:start position:0% +you can say how expensive is this + + + align:start position:0% +you can say how expensive is this +without that Rising + + align:start position:0% +without that Rising + + + align:start position:0% +without that Rising +ination mirr the using the separate word + + align:start position:0% +ination mirr the using the separate word + + + align:start position:0% +ination mirr the using the separate word +but you don't need that separate word if + + align:start position:0% +but you don't need that separate word if + + + align:start position:0% +but you don't need that separate word if +it's any word but but if you're saying + + align:start position:0% +it's any word but but if you're saying + + + align:start position:0% +it's any word but but if you're saying +how expensive is this without the + + align:start position:0% +how expensive is this without the + + + align:start position:0% +how expensive is this without the +question of flection it almost sounds + + align:start position:0% +question of flection it almost sounds + + + align:start position:0% +question of flection it almost sounds +like you're making a statement about + + align:start position:0% +like you're making a statement about + + + align:start position:0% +like you're making a statement about +just how ridiculous the expensive it you + + align:start position:0% +just how ridiculous the expensive it you + + + align:start position:0% +just how ridiculous the expensive it you +know like you're going how expensive is + + align:start position:0% +know like you're going how expensive is + + + align:start position:0% +know like you're going how expensive is +this how expensive is this + + align:start position:0% + + + + align:start position:0% + +well I should let you go \ No newline at end of file diff --git a/MsJ31I9umCM.txt b/MsJ31I9umCM.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e285b4e0a0e6f82687bb5e83f190973b809d38a --- /dev/null +++ b/MsJ31I9umCM.txt @@ -0,0 +1,15544 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +opencourseware under a creative commons + + align:start position:0% +opencourseware under a creative commons + + + align:start position:0% +opencourseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit opencourseware in general is + + align:start position:0% +and mit opencourseware in general is + + + align:start position:0% +and mit opencourseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +well i want to talk about four things um + + align:start position:0% +well i want to talk about four things um + + + align:start position:0% +well i want to talk about four things um +and as i thought about it i was going to + + align:start position:0% +and as i thought about it i was going to + + + align:start position:0% +and as i thought about it i was going to +put number four last but i've decided to + + align:start position:0% +put number four last but i've decided to + + + align:start position:0% +put number four last but i've decided to +put it first + + align:start position:0% +put it first + + + align:start position:0% +put it first +because i think + + align:start position:0% + + + + align:start position:0% + +move some stuff out of the way and and + + align:start position:0% +move some stuff out of the way and and + + + align:start position:0% +move some stuff out of the way and and +that fourth + + align:start position:0% +that fourth + + + align:start position:0% +that fourth +fourth thing i think is + + align:start position:0% +fourth thing i think is + + + align:start position:0% +fourth thing i think is +don't be cynical + + align:start position:0% +don't be cynical + + + align:start position:0% +don't be cynical +there are a lot of people who grow + + align:start position:0% +there are a lot of people who grow + + + align:start position:0% +there are a lot of people who grow +around life thinking that every + + align:start position:0% +around life thinking that every + + + align:start position:0% +around life thinking that every +organization they work with is corrupt + + align:start position:0% +organization they work with is corrupt + + + align:start position:0% +organization they work with is corrupt +every you know society is corrupt + + align:start position:0% +every you know society is corrupt + + + align:start position:0% +every you know society is corrupt +and and i think that's very debilitating + + align:start position:0% +and and i think that's very debilitating + + + align:start position:0% +and and i think that's very debilitating +and i think it keeps them from + + align:start position:0% +and i think it keeps them from + + + align:start position:0% +and i think it keeps them from +really latching on to what i think are + + align:start position:0% +really latching on to what i think are + + + align:start position:0% +really latching on to what i think are +very important + + align:start position:0% +very important + + + align:start position:0% +very important +and valuable ideas ideas that i consider + + align:start position:0% +and valuable ideas ideas that i consider + + + align:start position:0% +and valuable ideas ideas that i consider +are extremely pragmatic i mean i'm an + + align:start position:0% +are extremely pragmatic i mean i'm an + + + align:start position:0% +are extremely pragmatic i mean i'm an +engineer and and i think the whole + + align:start position:0% +engineer and and i think the whole + + + align:start position:0% +engineer and and i think the whole +question of ethics and values + + align:start position:0% +question of ethics and values + + + align:start position:0% +question of ethics and values +is an extremely pragmatic + + align:start position:0% +is an extremely pragmatic + + + align:start position:0% +is an extremely pragmatic +set of tools + + align:start position:0% +set of tools + + + align:start position:0% +set of tools +and + + align:start position:0% +and + + + align:start position:0% +and +so i think that's why i started out + + align:start position:0% +so i think that's why i started out + + + align:start position:0% +so i think that's why i started out +saying you know don't be a cynic be a + + align:start position:0% +saying you know don't be a cynic be a + + + align:start position:0% +saying you know don't be a cynic be a +person for whom the glass is half full + + align:start position:0% +person for whom the glass is half full + + + align:start position:0% +person for whom the glass is half full +and always try to be the person who + + align:start position:0% +and always try to be the person who + + + align:start position:0% +and always try to be the person who +urges on your friends your organization + + align:start position:0% +urges on your friends your organization + + + align:start position:0% +urges on your friends your organization +your society to higher goals + + align:start position:0% +your society to higher goals + + + align:start position:0% +your society to higher goals +because again in the end that's + + align:start position:0% +because again in the end that's + + + align:start position:0% +because again in the end that's +pragmatic and all we have to do is look + + align:start position:0% +pragmatic and all we have to do is look + + + align:start position:0% +pragmatic and all we have to do is look +around the world + + align:start position:0% +around the world + + + align:start position:0% +around the world +and see the usefulness + + align:start position:0% +and see the usefulness + + + align:start position:0% +and see the usefulness +of these ideas that we're talking about + + align:start position:0% +of these ideas that we're talking about + + + align:start position:0% +of these ideas that we're talking about +so the other three ideas i want to talk + + align:start position:0% +so the other three ideas i want to talk + + + align:start position:0% +so the other three ideas i want to talk +about + + align:start position:0% +about + + + align:start position:0% +about +are + + align:start position:0% +are + + + align:start position:0% +are +individual values + + align:start position:0% +individual values + + + align:start position:0% +individual values +professional values + + align:start position:0% +professional values + + + align:start position:0% +professional values +and institutional values + + align:start position:0% +and institutional values + + + align:start position:0% +and institutional values +now to talk about individual values i + + align:start position:0% +now to talk about individual values i + + + align:start position:0% +now to talk about individual values i +brought along the united states air + + align:start position:0% +brought along the united states air + + + align:start position:0% +brought along the united states air +force little blue book on core values + + align:start position:0% +force little blue book on core values + + + align:start position:0% +force little blue book on core values +when i was secretary of the air force i + + align:start position:0% +when i was secretary of the air force i + + + align:start position:0% +when i was secretary of the air force i +really felt the need and i and i was was + + align:start position:0% +really felt the need and i and i was was + + + align:start position:0% +really felt the need and i and i was was +not an original idea i was getting this + + align:start position:0% +not an original idea i was getting this + + + align:start position:0% +not an original idea i was getting this +from people in the air force + + align:start position:0% +from people in the air force + + + align:start position:0% +from people in the air force +that what the air force needed was a + + align:start position:0% +that what the air force needed was a + + + align:start position:0% +that what the air force needed was a +statement of + + align:start position:0% +statement of + + + align:start position:0% +statement of +fundamental statement of core values + + align:start position:0% +fundamental statement of core values + + + align:start position:0% +fundamental statement of core values +so that people could internalize + + align:start position:0% +so that people could internalize + + + align:start position:0% +so that people could internalize +the values that they and their fellow + + align:start position:0% +the values that they and their fellow + + + align:start position:0% +the values that they and their fellow +hold + + align:start position:0% +hold + + + align:start position:0% +hold +i saw it as actually a psychic reward + + align:start position:0% +i saw it as actually a psychic reward + + + align:start position:0% +i saw it as actually a psychic reward +yeah we couldn't give money + + align:start position:0% +yeah we couldn't give money + + + align:start position:0% +yeah we couldn't give money +but we could give them core values + + align:start position:0% +but we could give them core values + + + align:start position:0% +but we could give them core values +you know and think about it you know + + align:start position:0% +you know and think about it you know + + + align:start position:0% +you know and think about it you know +where what we were doing is telling them + + align:start position:0% +where what we were doing is telling them + + + align:start position:0% +where what we were doing is telling them +how good they were + + align:start position:0% +how good they were + + + align:start position:0% +how good they were +not to mention the fact that this is a + + align:start position:0% +not to mention the fact that this is a + + + align:start position:0% +not to mention the fact that this is a +very pragmatic thing to do from all + + align:start position:0% +very pragmatic thing to do from all + + + align:start position:0% +very pragmatic thing to do from all +sorts of reasons + + align:start position:0% +sorts of reasons + + + align:start position:0% +sorts of reasons +it builds trust + + align:start position:0% +it builds trust + + + align:start position:0% +it builds trust +you know the guys working next to you + + align:start position:0% +you know the guys working next to you + + + align:start position:0% +you know the guys working next to you +shares the same values + + align:start position:0% +shares the same values + + + align:start position:0% +shares the same values +i can't tell you the number of times + + align:start position:0% +i can't tell you the number of times + + + align:start position:0% +i can't tell you the number of times +well i mean it's an organization like + + align:start position:0% +well i mean it's an organization like + + + align:start position:0% +well i mean it's an organization like +the air force that espouses high values + + align:start position:0% +the air force that espouses high values + + + align:start position:0% +the air force that espouses high values +is under the microscope of the media + + align:start position:0% +is under the microscope of the media + + + align:start position:0% +is under the microscope of the media +and all you have to do is just move a + + align:start position:0% +and all you have to do is just move a + + + align:start position:0% +and all you have to do is just move a +little bit in a direction that probably + + align:start position:0% +little bit in a direction that probably + + + align:start position:0% +little bit in a direction that probably +most institutions would get away with in + + align:start position:0% +most institutions would get away with in + + + align:start position:0% +most institutions would get away with in +our society and all hell breaks loose + + align:start position:0% +our society and all hell breaks loose + + + align:start position:0% +our society and all hell breaks loose +and that's fine + + align:start position:0% +and that's fine + + + align:start position:0% +and that's fine +we espouse high values and when we + + align:start position:0% +we espouse high values and when we + + + align:start position:0% +we espouse high values and when we +let them down let the people down + + align:start position:0% +let them down let the people down + + + align:start position:0% +let them down let the people down +we get hammered and i never had a + + align:start position:0% +we get hammered and i never had a + + + align:start position:0% +we get hammered and i never had a +problem with that i thought that + + align:start position:0% +problem with that i thought that + + + align:start position:0% +problem with that i thought that +you know we needed to explain ourselves + + align:start position:0% +you know we needed to explain ourselves + + + align:start position:0% +you know we needed to explain ourselves +and + + align:start position:0% +and + + + align:start position:0% +and +let the chips fall where they may + + align:start position:0% +let the chips fall where they may + + + align:start position:0% +let the chips fall where they may +so anyway we established a program + + align:start position:0% +so anyway we established a program + + + align:start position:0% +so anyway we established a program +of core values and i'll just tell you + + align:start position:0% +of core values and i'll just tell you + + + align:start position:0% +of core values and i'll just tell you +what those values are you know i don't + + align:start position:0% +what those values are you know i don't + + + align:start position:0% +what those values are you know i don't +believe there's a unique set of core + + align:start position:0% +believe there's a unique set of core + + + align:start position:0% +believe there's a unique set of core +values but there's a lot of overlap and + + align:start position:0% +values but there's a lot of overlap and + + + align:start position:0% +values but there's a lot of overlap and +a lot of commonality and + + align:start position:0% +a lot of commonality and + + + align:start position:0% +a lot of commonality and +the core values of the air force are + + align:start position:0% +the core values of the air force are + + + align:start position:0% +the core values of the air force are +integrity first + + align:start position:0% +integrity first + + + align:start position:0% +integrity first +service before self + + align:start position:0% +service before self + + + align:start position:0% +service before self +and excellence in all you do + + align:start position:0% +and excellence in all you do + + + align:start position:0% +and excellence in all you do +that works for me + + align:start position:0% +that works for me + + + align:start position:0% +that works for me +i think that + + align:start position:0% +i think that + + + align:start position:0% +i think that +and and i believe those values also work + + align:start position:0% +and and i believe those values also work + + + align:start position:0% +and and i believe those values also work +at mit + + align:start position:0% +at mit + + + align:start position:0% +at mit +i think those are also the mit values + + align:start position:0% + + + + align:start position:0% + +the phrase service before itself has a + + align:start position:0% +the phrase service before itself has a + + + align:start position:0% +the phrase service before itself has a +little different meaning in a military + + align:start position:0% +little different meaning in a military + + + align:start position:0% +little different meaning in a military +organization because it means that you + + align:start position:0% +organization because it means that you + + + align:start position:0% +organization because it means that you +could put your life on the line + + align:start position:0% +could put your life on the line + + + align:start position:0% +could put your life on the line +you would be expected to put your life + + align:start position:0% +you would be expected to put your life + + + align:start position:0% +you would be expected to put your life +on the line that's what service really + + align:start position:0% +on the line that's what service really + + + align:start position:0% +on the line that's what service really +means in a military + + align:start position:0% +means in a military + + + align:start position:0% +means in a military +organization i think at an institution + + align:start position:0% +organization i think at an institution + + + align:start position:0% +organization i think at an institution +like mit + + align:start position:0% +like mit + + + align:start position:0% +like mit +we think of public service + + align:start position:0% +we think of public service + + + align:start position:0% +we think of public service +we think of all the values that mit + + align:start position:0% +we think of all the values that mit + + + align:start position:0% +we think of all the values that mit +brings to the table which serve the + + align:start position:0% +brings to the table which serve the + + + align:start position:0% +brings to the table which serve the +public + + align:start position:0% +public + + + align:start position:0% +public +making + + align:start position:0% +making + + + align:start position:0% +making +admissions to mit possible for + + align:start position:0% +admissions to mit possible for + + + align:start position:0% +admissions to mit possible for +low-income people not evaluating people + + align:start position:0% +low-income people not evaluating people + + + align:start position:0% +low-income people not evaluating people +for financial aid on the basis of what + + align:start position:0% +for financial aid on the basis of what + + + align:start position:0% +for financial aid on the basis of what +score they got on the sat + + align:start position:0% +score they got on the sat + + + align:start position:0% +score they got on the sat +being willing to do certain kinds of + + align:start position:0% +being willing to do certain kinds of + + + align:start position:0% +being willing to do certain kinds of +research for the government even though + + align:start position:0% +research for the government even though + + + align:start position:0% +research for the government even though +it creates a level of difficulty that + + align:start position:0% +it creates a level of difficulty that + + + align:start position:0% +it creates a level of difficulty that +maybe we wouldn't want to be involved in + + align:start position:0% +maybe we wouldn't want to be involved in + + + align:start position:0% +maybe we wouldn't want to be involved in +but we've done it since world war ii and + + align:start position:0% +but we've done it since world war ii and + + + align:start position:0% +but we've done it since world war ii and +it's been an important part of what we + + align:start position:0% +it's been an important part of what we + + + align:start position:0% +it's been an important part of what we +do so the public service part is is just + + align:start position:0% +do so the public service part is is just + + + align:start position:0% +do so the public service part is is just +really very much + + align:start position:0% +really very much + + + align:start position:0% +really very much +front center at mit + + align:start position:0% +front center at mit + + + align:start position:0% +front center at mit +and obviously excellence but they need + + align:start position:0% +and obviously excellence but they need + + + align:start position:0% +and obviously excellence but they need +to say no more about excellence so i'm + + align:start position:0% +to say no more about excellence so i'm + + + align:start position:0% +to say no more about excellence so i'm +going to pass this around um + + align:start position:0% +going to pass this around um + + + align:start position:0% +going to pass this around um +and as i understand it um these uh + + align:start position:0% +and as i understand it um these uh + + + align:start position:0% +and as i understand it um these uh +everybody gets this little blue book + + align:start position:0% +everybody gets this little blue book + + + align:start position:0% +everybody gets this little blue book +when they you know sort of + + align:start position:0% +when they you know sort of + + + align:start position:0% +when they you know sort of +get into the air force either as an + + align:start position:0% +get into the air force either as an + + + align:start position:0% +get into the air force either as an +enlisted person or + + align:start position:0% +enlisted person or + + + align:start position:0% +enlisted person or +as an officer and i actually don't know + + align:start position:0% +as an officer and i actually don't know + + + align:start position:0% +as an officer and i actually don't know +whether you get it if you're in rotc i + + align:start position:0% +whether you get it if you're in rotc i + + + align:start position:0% +whether you get it if you're in rotc i +actually have to check that out with the + + align:start position:0% +actually have to check that out with the + + + align:start position:0% +actually have to check that out with the +commander here but + + align:start position:0% +commander here but + + + align:start position:0% +commander here but +you know i think the basic idea is that + + align:start position:0% +you know i think the basic idea is that + + + align:start position:0% +you know i think the basic idea is that +that that is what we and and when i go + + align:start position:0% +that that is what we and and when i go + + + align:start position:0% +that that is what we and and when i go +to a briefing you know of air force + + align:start position:0% +to a briefing you know of air force + + + align:start position:0% +to a briefing you know of air force +officers i mean they may be talking + + align:start position:0% +officers i mean they may be talking + + + align:start position:0% +officers i mean they may be talking +about + + align:start position:0% +about + + + align:start position:0% +about +how do you connect the satellite up but + + align:start position:0% +how do you connect the satellite up but + + + align:start position:0% +how do you connect the satellite up but +down at the bottom + + align:start position:0% +down at the bottom + + + align:start position:0% +down at the bottom +on the master slide it says integrity + + align:start position:0% +on the master slide it says integrity + + + align:start position:0% +on the master slide it says integrity +service before itself and excellence + + align:start position:0% +service before itself and excellence + + + align:start position:0% +service before itself and excellence +it has nothing to do well sort of with + + align:start position:0% +it has nothing to do well sort of with + + + align:start position:0% +it has nothing to do well sort of with +organizing a satellite how you put it + + align:start position:0% +organizing a satellite how you put it + + + align:start position:0% +organizing a satellite how you put it +together but it is a statement about the + + align:start position:0% +together but it is a statement about the + + + align:start position:0% +together but it is a statement about the +air force + + align:start position:0% +air force + + + align:start position:0% +air force +and about their commitment their public + + align:start position:0% +and about their commitment their public + + + align:start position:0% +and about their commitment their public +commitment + + align:start position:0% +commitment + + + align:start position:0% +commitment +and most the time the people in the room + + align:start position:0% +and most the time the people in the room + + + align:start position:0% +and most the time the people in the room +have no idea that i had anything to do + + align:start position:0% +have no idea that i had anything to do + + + align:start position:0% +have no idea that i had anything to do +with this + + align:start position:0% +with this + + + align:start position:0% +with this +so they're lecturing me on you know core + + align:start position:0% +so they're lecturing me on you know core + + + align:start position:0% +so they're lecturing me on you know core +values and how important they are and i + + align:start position:0% +values and how important they are and i + + + align:start position:0% +values and how important they are and i +say it's wonderful + + align:start position:0% +say it's wonderful + + + align:start position:0% +say it's wonderful +how did this happen you know never say + + align:start position:0% +how did this happen you know never say + + + align:start position:0% +how did this happen you know never say +anything okay so that's + + align:start position:0% +anything okay so that's + + + align:start position:0% +anything okay so that's +uh i think that's that's basic that's + + align:start position:0% +uh i think that's that's basic that's + + + align:start position:0% +uh i think that's that's basic that's +core + + align:start position:0% +core + + + align:start position:0% +core +that's that's where we all begin + + align:start position:0% +that's that's where we all begin + + + align:start position:0% +that's that's where we all begin +um + + align:start position:0% +um + + + align:start position:0% +um +then the other thing that i wanted to + + align:start position:0% +then the other thing that i wanted to + + + align:start position:0% +then the other thing that i wanted to +talk about are professional + + align:start position:0% +talk about are professional + + + align:start position:0% +talk about are professional +values and i think that's probably a + + align:start position:0% +values and i think that's probably a + + + align:start position:0% +values and i think that's probably a +subject that you've spent a lot of time + + align:start position:0% +subject that you've spent a lot of time + + + align:start position:0% +subject that you've spent a lot of time +at but + + align:start position:0% +at but + + + align:start position:0% +at but +you know what i would say is that + + align:start position:0% +you know what i would say is that + + + align:start position:0% +you know what i would say is that +integrity is basic to the scientific and + + align:start position:0% +integrity is basic to the scientific and + + + align:start position:0% +integrity is basic to the scientific and +engineering profession + + align:start position:0% +engineering profession + + + align:start position:0% +engineering profession +and i brought along uh the report of a + + align:start position:0% +and i brought along uh the report of a + + + align:start position:0% +and i brought along uh the report of a +committee that i chaired + + align:start position:0% +committee that i chaired + + + align:start position:0% +committee that i chaired +and it's called fostering academic + + align:start position:0% +and it's called fostering academic + + + align:start position:0% +and it's called fostering academic +integrity + + align:start position:0% +integrity + + + align:start position:0% +integrity +and the year was + + align:start position:0% +and the year was + + + align:start position:0% +and the year was + + align:start position:0% + + + align:start position:0% +actually before i went to the pentagon + + align:start position:0% +actually before i went to the pentagon + + + align:start position:0% +actually before i went to the pentagon +these were the years of controversy over + + align:start position:0% +these were the years of controversy over + + + align:start position:0% +these were the years of controversy over +allegations of scientific misconduct in + + align:start position:0% +allegations of scientific misconduct in + + + align:start position:0% +allegations of scientific misconduct in +our nation's universities and we had + + align:start position:0% +our nation's universities and we had + + + align:start position:0% +our nation's universities and we had +some major problems here at mit + + align:start position:0% +some major problems here at mit + + + align:start position:0% +some major problems here at mit +involving david baltimore and charges + + align:start position:0% +involving david baltimore and charges + + + align:start position:0% +involving david baltimore and charges +that uh data had been by one of his + + align:start position:0% +that uh data had been by one of his + + + align:start position:0% +that uh data had been by one of his +co-authors had been falsified + + align:start position:0% +co-authors had been falsified + + + align:start position:0% +co-authors had been falsified +it literally took 20 years to unscramble + + align:start position:0% +it literally took 20 years to unscramble + + + align:start position:0% +it literally took 20 years to unscramble +that + + align:start position:0% +that + + + align:start position:0% +that +i mean and he paid an enormous price for + + align:start position:0% +i mean and he paid an enormous price for + + + align:start position:0% +i mean and he paid an enormous price for +it mit paid an enormous price for not + + align:start position:0% +it mit paid an enormous price for not + + + align:start position:0% +it mit paid an enormous price for not +you know for what i would say brushing + + align:start position:0% +you know for what i would say brushing + + + align:start position:0% +you know for what i would say brushing +it off + + align:start position:0% +it off + + + align:start position:0% +it off +fairly early in the game saying oh well + + align:start position:0% +fairly early in the game saying oh well + + + align:start position:0% +fairly early in the game saying oh well +i know david he wouldn't be responsible + + align:start position:0% +i know david he wouldn't be responsible + + + align:start position:0% +i know david he wouldn't be responsible +so uh and in fact in the end he wasn't + + align:start position:0% +so uh and in fact in the end he wasn't + + + align:start position:0% +so uh and in fact in the end he wasn't +but you know not taking the allegations + + align:start position:0% +but you know not taking the allegations + + + align:start position:0% +but you know not taking the allegations +seriously + + align:start position:0% +seriously + + + align:start position:0% +seriously +congress + + align:start position:0% +congress + + + align:start position:0% +congress +congress went + + align:start position:0% +congress went + + + align:start position:0% +congress went +into high gear + + align:start position:0% +into high gear + + + align:start position:0% +into high gear +david testified in front of the dingle + + align:start position:0% +david testified in front of the dingle + + + align:start position:0% +david testified in front of the dingle +committee + + align:start position:0% + + + + align:start position:0% + +universities were you're under the gun + + align:start position:0% +universities were you're under the gun + + + align:start position:0% +universities were you're under the gun +federal agencies were + + align:start position:0% +federal agencies were + + + align:start position:0% +federal agencies were +in instituting policies with respect to + + align:start position:0% +in instituting policies with respect to + + + align:start position:0% +in instituting policies with respect to +issues of academic integrity + + align:start position:0% +issues of academic integrity + + + align:start position:0% +issues of academic integrity +uh and i think we had always taken the + + align:start position:0% +uh and i think we had always taken the + + + align:start position:0% +uh and i think we had always taken the +view that science was + + align:start position:0% +view that science was + + + align:start position:0% +view that science was +sort of self-checking + + align:start position:0% +sort of self-checking + + + align:start position:0% +sort of self-checking +and i believe that science is + + align:start position:0% +and i believe that science is + + + align:start position:0% +and i believe that science is +self-checking and so that was kind of + + align:start position:0% +self-checking and so that was kind of + + + align:start position:0% +self-checking and so that was kind of +the stance in the community + + align:start position:0% +the stance in the community + + + align:start position:0% +the stance in the community +but i think what we learned from from + + align:start position:0% +but i think what we learned from from + + + align:start position:0% +but i think what we learned from from +this from the government and this this + + align:start position:0% +this from the government and this this + + + align:start position:0% +this from the government and this this +thing is that + + align:start position:0% +thing is that + + + align:start position:0% +thing is that +we all we have to develop a process that + + align:start position:0% +we all we have to develop a process that + + + align:start position:0% +we all we have to develop a process that +takes these initial allegations + + align:start position:0% +takes these initial allegations + + + align:start position:0% +takes these initial allegations +seriously + + align:start position:0% +seriously + + + align:start position:0% +seriously +even though we believe that ultimately + + align:start position:0% +even though we believe that ultimately + + + align:start position:0% +even though we believe that ultimately +it is self-checking and you know you saw + + align:start position:0% +it is self-checking and you know you saw + + + align:start position:0% +it is self-checking and you know you saw +it in the case of the korean + + align:start position:0% +it in the case of the korean + + + align:start position:0% +it in the case of the korean +example of cloning and you know and it + + align:start position:0% +example of cloning and you know and it + + + align:start position:0% +example of cloning and you know and it +happens here at mit and it works + + align:start position:0% +happens here at mit and it works + + + align:start position:0% +happens here at mit and it works +you know we do in fact but + + align:start position:0% +you know we do in fact but + + + align:start position:0% +you know we do in fact but +the national academy set up a committee + + align:start position:0% +the national academy set up a committee + + + align:start position:0% +the national academy set up a committee +on academic integrity i was a member of + + align:start position:0% +on academic integrity i was a member of + + + align:start position:0% +on academic integrity i was a member of +that committee mit set up a committee on + + align:start position:0% +that committee mit set up a committee on + + + align:start position:0% +that committee mit set up a committee on +academic integrity and asked me to chair + + align:start position:0% +academic integrity and asked me to chair + + + align:start position:0% +academic integrity and asked me to chair +it + + align:start position:0% +it + + + align:start position:0% +it +this is a characteristic of mit we tend + + align:start position:0% +this is a characteristic of mit we tend + + + align:start position:0% +this is a characteristic of mit we tend +to get in early + + align:start position:0% +to get in early + + + align:start position:0% +to get in early +so mit finished their report + + align:start position:0% +so mit finished their report + + + align:start position:0% +so mit finished their report +in time for it to be an appendix in the + + align:start position:0% +in time for it to be an appendix in the + + + align:start position:0% +in time for it to be an appendix in the +national academy of sciences report + + align:start position:0% +national academy of sciences report + + + align:start position:0% +national academy of sciences report +which i think gave us + + align:start position:0% +which i think gave us + + + align:start position:0% +which i think gave us +you know kind of extra visibility extra + + align:start position:0% +you know kind of extra visibility extra + + + align:start position:0% +you know kind of extra visibility extra +prominence + + align:start position:0% +prominence + + + align:start position:0% +prominence +and + + align:start position:0% +and + + + align:start position:0% +and +you know + + align:start position:0% +you know + + + align:start position:0% +you know +i just think it was + + align:start position:0% +i just think it was + + + align:start position:0% +i just think it was +an opportunity for us to make this + + align:start position:0% +an opportunity for us to make this + + + align:start position:0% +an opportunity for us to make this +not only statement at mit but very + + align:start position:0% +not only statement at mit but very + + + align:start position:0% +not only statement at mit but very +visible + + align:start position:0% + + + + align:start position:0% + +in in + + align:start position:0% +in in + + + align:start position:0% +in in +academic integrity i mean the key words + + align:start position:0% +academic integrity i mean the key words + + + align:start position:0% +academic integrity i mean the key words +and i hope i get them right are + + align:start position:0% +and i hope i get them right are + + + align:start position:0% +and i hope i get them right are +falsification + + align:start position:0% +falsification + + + align:start position:0% +falsification +fabrication and plagiarism it is those + + align:start position:0% +fabrication and plagiarism it is those + + + align:start position:0% +fabrication and plagiarism it is those +three words + + align:start position:0% +three words + + + align:start position:0% +three words +which are the technical terms associated + + align:start position:0% +which are the technical terms associated + + + align:start position:0% +which are the technical terms associated +with academic integrity and let me pass + + align:start position:0% +with academic integrity and let me pass + + + align:start position:0% +with academic integrity and let me pass +this report around this is again another + + align:start position:0% +this report around this is again another + + + align:start position:0% +this report around this is again another +very famous document + + align:start position:0% +very famous document + + + align:start position:0% +very famous document +um + + align:start position:0% + + + + align:start position:0% + +now and also that's on the mit website + + align:start position:0% +now and also that's on the mit website + + + align:start position:0% +now and also that's on the mit website +and in fact we had it + + align:start position:0% +and in fact we had it + + + align:start position:0% +and in fact we had it +we had an incident this year i think + + align:start position:0% +we had an incident this year i think + + + align:start position:0% +we had an incident this year i think +we're uh i'm not trying to remember the + + align:start position:0% +we're uh i'm not trying to remember the + + + align:start position:0% +we're uh i'm not trying to remember the +details i think a graduate student came + + align:start position:0% +details i think a graduate student came + + + align:start position:0% +details i think a graduate student came +forward and made an allegation against + + align:start position:0% +forward and made an allegation against + + + align:start position:0% +forward and made an allegation against +his professor i think that's what it was + + align:start position:0% +his professor i think that's what it was + + + align:start position:0% +his professor i think that's what it was +and so there was an investigation along + + align:start position:0% +and so there was an investigation along + + + align:start position:0% +and so there was an investigation along +the lines of the procedures laid out + + align:start position:0% +the lines of the procedures laid out + + + align:start position:0% +the lines of the procedures laid out +i mean it's confidential there's no + + align:start position:0% +i mean it's confidential there's no + + + align:start position:0% +i mean it's confidential there's no +assumption of guilt you know it's arm's + + align:start position:0% +assumption of guilt you know it's arm's + + + align:start position:0% +assumption of guilt you know it's arm's +length it's two stages it's very very + + align:start position:0% +length it's two stages it's very very + + + align:start position:0% +length it's two stages it's very very +careful to protect + + align:start position:0% +careful to protect + + + align:start position:0% +careful to protect +the rights of everybody and the + + align:start position:0% +the rights of everybody and the + + + align:start position:0% +the rights of everybody and the +confidentiality of everybody but to sort + + align:start position:0% +confidentiality of everybody but to sort + + + align:start position:0% +confidentiality of everybody but to sort +of get on with + + align:start position:0% +of get on with + + + align:start position:0% +of get on with +the process to determine whether there + + align:start position:0% +the process to determine whether there + + + align:start position:0% +the process to determine whether there +is an issue that does not meet mit + + align:start position:0% +is an issue that does not meet mit + + + align:start position:0% +is an issue that does not meet mit +standards + + align:start position:0% +standards + + + align:start position:0% +standards +so that's + + align:start position:0% + + + + align:start position:0% + +that's an important set and i would + + align:start position:0% +that's an important set and i would + + + align:start position:0% +that's an important set and i would +would characterize that as + + align:start position:0% +would characterize that as + + + align:start position:0% +would characterize that as +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +professional values + + align:start position:0% +professional values + + + align:start position:0% +professional values +and you know a similar set of values + + align:start position:0% +and you know a similar set of values + + + align:start position:0% +and you know a similar set of values +is + + align:start position:0% +is + + + align:start position:0% +is +is involved in engineering engineering + + align:start position:0% +is involved in engineering engineering + + + align:start position:0% +is involved in engineering engineering +is more complex + + align:start position:0% +is more complex + + + align:start position:0% +is more complex +the responsibilities to the public + + align:start position:0% +the responsibilities to the public + + + align:start position:0% +the responsibilities to the public +are more complex + + align:start position:0% +are more complex + + + align:start position:0% +are more complex +than the responsibilities of say an + + align:start position:0% +than the responsibilities of say an + + + align:start position:0% +than the responsibilities of say an +individual scientist in their lab but + + align:start position:0% +individual scientist in their lab but + + + align:start position:0% +individual scientist in their lab but +they are no less compelling and + + align:start position:0% +they are no less compelling and + + + align:start position:0% +they are no less compelling and +important + + align:start position:0% +important + + + align:start position:0% +important +and i know you've talked about the + + align:start position:0% +and i know you've talked about the + + + align:start position:0% +and i know you've talked about the +challenger + + align:start position:0% +challenger + + + align:start position:0% +challenger +i guess all of you know that i was on + + align:start position:0% +i guess all of you know that i was on + + + align:start position:0% +i guess all of you know that i was on +the columbia accent investigation board + + align:start position:0% +the columbia accent investigation board + + + align:start position:0% +the columbia accent investigation board +you know in some sense as i reflect on + + align:start position:0% +you know in some sense as i reflect on + + + align:start position:0% +you know in some sense as i reflect on +the difference between those two + + align:start position:0% +the difference between those two + + + align:start position:0% +the difference between those two +situations it seems to me in the + + align:start position:0% +situations it seems to me in the + + + align:start position:0% +situations it seems to me in the +challenger + + align:start position:0% +challenger + + + align:start position:0% +challenger +investigation the + + align:start position:0% + + + + align:start position:0% + +behavior with individuals + + align:start position:0% +behavior with individuals + + + align:start position:0% +behavior with individuals +was more prominent in other words i + + align:start position:0% +was more prominent in other words i + + + align:start position:0% +was more prominent in other words i +think we all know the story of roger + + align:start position:0% +think we all know the story of roger + + + align:start position:0% +think we all know the story of roger +beaujolais an individual + + align:start position:0% +beaujolais an individual + + + align:start position:0% +beaujolais an individual +raising issues against an organization + + align:start position:0% +raising issues against an organization + + + align:start position:0% +raising issues against an organization +i think in the case of the columbia it + + align:start position:0% +i think in the case of the columbia it + + + align:start position:0% +i think in the case of the columbia it +was almost reversed + + align:start position:0% +was almost reversed + + + align:start position:0% +was almost reversed +it was a band of engineers who were + + align:start position:0% +it was a band of engineers who were + + + align:start position:0% +it was a band of engineers who were +attempting to raise issues and these + + align:start position:0% +attempting to raise issues and these + + + align:start position:0% +attempting to raise issues and these +were tamped down by individual people in + + align:start position:0% +were tamped down by individual people in + + + align:start position:0% +were tamped down by individual people in +the organization + + align:start position:0% +the organization + + + align:start position:0% +the organization +at management level + + align:start position:0% +at management level + + + align:start position:0% +at management level +and so in some sense the situation was a + + align:start position:0% +and so in some sense the situation was a + + + align:start position:0% +and so in some sense the situation was a +little reversed but the issue is + + align:start position:0% +little reversed but the issue is + + + align:start position:0% +little reversed but the issue is +obviously no + + align:start position:0% +obviously no + + + align:start position:0% +obviously no +no less compelling + + align:start position:0% +no less compelling + + + align:start position:0% +no less compelling +i think we made + + align:start position:0% +i think we made + + + align:start position:0% +i think we made +we made a + + align:start position:0% +we made a + + + align:start position:0% +we made a +number of recommendations of an + + align:start position:0% +number of recommendations of an + + + align:start position:0% +number of recommendations of an +organizational and + + align:start position:0% +organizational and + + + align:start position:0% +organizational and +cultural sort that um + + align:start position:0% +cultural sort that um + + + align:start position:0% +cultural sort that um +i think had great impact and still + + align:start position:0% +i think had great impact and still + + + align:start position:0% +i think had great impact and still +having + + align:start position:0% +having + + + align:start position:0% +having +still having great impact on on the + + align:start position:0% +still having great impact on on the + + + align:start position:0% +still having great impact on on the +organization + + align:start position:0% + + + + align:start position:0% + +so that's another you know theme and + + align:start position:0% +so that's another you know theme and + + + align:start position:0% +so that's another you know theme and +obviously for people at mit the whole + + align:start position:0% +obviously for people at mit the whole + + + align:start position:0% +obviously for people at mit the whole +question of engineering professional + + align:start position:0% +question of engineering professional + + + align:start position:0% +question of engineering professional +ethics scientific + + align:start position:0% +ethics scientific + + + align:start position:0% +ethics scientific +ethics are just extremely important and + + align:start position:0% +ethics are just extremely important and + + + align:start position:0% +ethics are just extremely important and +that's why i'm glad you're doing what + + align:start position:0% +that's why i'm glad you're doing what + + + align:start position:0% +that's why i'm glad you're doing what +you're doing + + align:start position:0% +you're doing + + + align:start position:0% +you're doing +so uh you know i'll just pass this + + align:start position:0% +so uh you know i'll just pass this + + + align:start position:0% +so uh you know i'll just pass this +around i don't expect you to read it + + align:start position:0% +around i don't expect you to read it + + + align:start position:0% +around i don't expect you to read it +but if you look at the table of contents + + align:start position:0% +but if you look at the table of contents + + + align:start position:0% +but if you look at the table of contents +i think you'll see that + + align:start position:0% +i think you'll see that + + + align:start position:0% +i think you'll see that +in addition to talking about what broke + + align:start position:0% +in addition to talking about what broke + + + align:start position:0% +in addition to talking about what broke +we also had chapters + + align:start position:0% +we also had chapters + + + align:start position:0% +we also had chapters +that dealt with organizational culture + + align:start position:0% +that dealt with organizational culture + + + align:start position:0% +that dealt with organizational culture +how do you develop a safety culture in a + + align:start position:0% +how do you develop a safety culture in a + + + align:start position:0% +how do you develop a safety culture in a +large organization like that + + align:start position:0% +large organization like that + + + align:start position:0% +large organization like that +and what were our recommendations + + align:start position:0% +and what were our recommendations + + + align:start position:0% +and what were our recommendations +for for doing that + + align:start position:0% + + + + align:start position:0% + +okay so that's um + + align:start position:0% +okay so that's um + + + align:start position:0% +okay so that's um +that's kind of that topic + + align:start position:0% + + + + align:start position:0% + +uh i think the third thing i wanted to + + align:start position:0% +uh i think the third thing i wanted to + + + align:start position:0% +uh i think the third thing i wanted to +talk about was what i would call + + align:start position:0% +talk about was what i would call + + + align:start position:0% +talk about was what i would call +institutional ethics + + align:start position:0% +institutional ethics + + + align:start position:0% +institutional ethics +and i brought a couple of things along + + align:start position:0% + + + + align:start position:0% + +this is a report again i do a lot of + + align:start position:0% +this is a report again i do a lot of + + + align:start position:0% +this is a report again i do a lot of +committee chairing + + align:start position:0% + + + + align:start position:0% + +this is a report that deals with + + align:start position:0% +this is a report that deals with + + + align:start position:0% +this is a report that deals with +research at mit + + align:start position:0% +research at mit + + + align:start position:0% +research at mit +and what are our policies + + align:start position:0% +and what are our policies + + + align:start position:0% +and what are our policies +with respect to accepting money from the + + align:start position:0% +with respect to accepting money from the + + + align:start position:0% +with respect to accepting money from the +government + + align:start position:0% +government + + + align:start position:0% +government +and what are our values and you know + + align:start position:0% +and what are our values and you know + + + align:start position:0% +and what are our values and you know +these are complex issues + + align:start position:0% +these are complex issues + + + align:start position:0% +these are complex issues +but i would summarize the report in this + + align:start position:0% +but i would summarize the report in this + + + align:start position:0% +but i would summarize the report in this +way and mit again we were the first to + + align:start position:0% +way and mit again we were the first to + + + align:start position:0% +way and mit again we were the first to +publish + + align:start position:0% +publish + + + align:start position:0% +publish +there is no other university that has + + align:start position:0% +there is no other university that has + + + align:start position:0% +there is no other university that has +published + + align:start position:0% +published + + + align:start position:0% +published +a report like this + + align:start position:0% +a report like this + + + align:start position:0% +a report like this +certainly as quickly as we did i mean we + + align:start position:0% +certainly as quickly as we did i mean we + + + align:start position:0% +certainly as quickly as we did i mean we +were out of the box + + align:start position:0% +were out of the box + + + align:start position:0% +were out of the box +i mean obviously a lot of this was + + align:start position:0% +i mean obviously a lot of this was + + + align:start position:0% +i mean obviously a lot of this was +driven by 911 and we were out of the box + + align:start position:0% +driven by 911 and we were out of the box + + + align:start position:0% +driven by 911 and we were out of the box +in january and we had the report done by + + align:start position:0% +in january and we had the report done by + + + align:start position:0% +in january and we had the report done by +may + + align:start position:0% +may + + + align:start position:0% +may +and it's you know it's widely publicized + + align:start position:0% +and it's you know it's widely publicized + + + align:start position:0% +and it's you know it's widely publicized +i love the title it came to me while i + + align:start position:0% +i love the title it came to me while i + + + align:start position:0% +i love the title it came to me while i +was riding my bike the title of the + + align:start position:0% +was riding my bike the title of the + + + align:start position:0% +was riding my bike the title of the +report is in the public interest + + align:start position:0% +report is in the public interest + + + align:start position:0% +report is in the public interest +and i think that that says a lot about + + align:start position:0% +and i think that that says a lot about + + + align:start position:0% +and i think that that says a lot about +what a place like mcq is trying to do + + align:start position:0% +what a place like mcq is trying to do + + + align:start position:0% +what a place like mcq is trying to do +but + + align:start position:0% +but + + + align:start position:0% +but +i think what we recommended you know + + align:start position:0% +i think what we recommended you know + + + align:start position:0% +i think what we recommended you know +it's a big long report and there are + + align:start position:0% +it's a big long report and there are + + + align:start position:0% +it's a big long report and there are +lots of complexities to it but something + + align:start position:0% +lots of complexities to it but something + + + align:start position:0% +lots of complexities to it but something +like this + + align:start position:0% +like this + + + align:start position:0% +like this +that everything on our campus should be + + align:start position:0% +that everything on our campus should be + + + align:start position:0% +that everything on our campus should be +open to every student + + align:start position:0% +open to every student + + + align:start position:0% +open to every student +and we don't want any + + align:start position:0% +and we don't want any + + + align:start position:0% +and we don't want any +material on our campus that cannot be + + align:start position:0% +material on our campus that cannot be + + + align:start position:0% +material on our campus that cannot be +shared + + align:start position:0% +shared + + + align:start position:0% +shared +now you know it seems fairly + + align:start position:0% +now you know it seems fairly + + + align:start position:0% +now you know it seems fairly +straightforward but + + align:start position:0% +straightforward but + + + align:start position:0% +straightforward but +with people who do government contract + + align:start position:0% +with people who do government contract + + + align:start position:0% +with people who do government contract +oh and also that includes + + align:start position:0% +oh and also that includes + + + align:start position:0% +oh and also that includes +no restrictions on publication + + align:start position:0% +no restrictions on publication + + + align:start position:0% +no restrictions on publication +that our faculty and students should be + + align:start position:0% +that our faculty and students should be + + + align:start position:0% +that our faculty and students should be +able to publish their research without + + align:start position:0% +able to publish their research without + + + align:start position:0% +able to publish their research without +restrictions + + align:start position:0% +restrictions + + + align:start position:0% +restrictions +uh that sounds fairly straightforward + + align:start position:0% +uh that sounds fairly straightforward + + + align:start position:0% +uh that sounds fairly straightforward +but there are lots of forces who would + + align:start position:0% +but there are lots of forces who would + + + align:start position:0% +but there are lots of forces who would +want to change that and i can just give + + align:start position:0% +want to change that and i can just give + + + align:start position:0% +want to change that and i can just give +you some examples + + align:start position:0% +you some examples + + + align:start position:0% +you some examples +for example in the federal government + + align:start position:0% +for example in the federal government + + + align:start position:0% +for example in the federal government +there's this category of information + + align:start position:0% +there's this category of information + + + align:start position:0% +there's this category of information +called + + align:start position:0% +called + + + align:start position:0% +called +sensitive but unclassified + + align:start position:0% +sensitive but unclassified + + + align:start position:0% +sensitive but unclassified +one of the problems is that nobody has + + align:start position:0% +one of the problems is that nobody has + + + align:start position:0% +one of the problems is that nobody has +any idea what that means + + align:start position:0% +any idea what that means + + + align:start position:0% +any idea what that means +you know there are 35 different + + align:start position:0% +you know there are 35 different + + + align:start position:0% +you know there are 35 different +definitions of this in fact i just got + + align:start position:0% +definitions of this in fact i just got + + + align:start position:0% +definitions of this in fact i just got +back from the national academy science + + align:start position:0% +back from the national academy science + + + align:start position:0% +back from the national academy science +and law panel last week and that was you + + align:start position:0% +and law panel last week and that was you + + + align:start position:0% +and law panel last week and that was you +know a big issue we had big we have a + + align:start position:0% +know a big issue we had big we have a + + + align:start position:0% +know a big issue we had big we have a +committee step up on it we're trying to + + align:start position:0% +committee step up on it we're trying to + + + align:start position:0% +committee step up on it we're trying to +work with federal agencies to really + + align:start position:0% +work with federal agencies to really + + + align:start position:0% +work with federal agencies to really +understand you know what in the world + + align:start position:0% +understand you know what in the world + + + align:start position:0% +understand you know what in the world +are you guys worried about i mean can we + + align:start position:0% +are you guys worried about i mean can we + + + align:start position:0% +are you guys worried about i mean can we +help you + + align:start position:0% +help you + + + align:start position:0% +help you +without having you just just lay all + + align:start position:0% +without having you just just lay all + + + align:start position:0% +without having you just just lay all +over us + + align:start position:0% +over us + + + align:start position:0% +over us +the problem + + align:start position:0% +the problem + + + align:start position:0% +the problem +is even worse because a lot of the + + align:start position:0% +is even worse because a lot of the + + + align:start position:0% +is even worse because a lot of the +decisions are made fairly low in the + + align:start position:0% +decisions are made fairly low in the + + + align:start position:0% +decisions are made fairly low in the +agency and + + align:start position:0% +agency and + + + align:start position:0% +agency and +but anyway mit says we will not accept a + + align:start position:0% +but anyway mit says we will not accept a + + + align:start position:0% +but anyway mit says we will not accept a +contract + + align:start position:0% +contract + + + align:start position:0% +contract +that contains a clause relating to this + + align:start position:0% +that contains a clause relating to this + + + align:start position:0% +that contains a clause relating to this +issue + + align:start position:0% +issue + + + align:start position:0% +issue +and it's just a flat + + align:start position:0% +and it's just a flat + + + align:start position:0% +and it's just a flat +prohibition against this + + align:start position:0% +prohibition against this + + + align:start position:0% +prohibition against this +that is not true at all universities + + align:start position:0% +that is not true at all universities + + + align:start position:0% +that is not true at all universities +other universities is kind of a slippery + + align:start position:0% +other universities is kind of a slippery + + + align:start position:0% +other universities is kind of a slippery +slope that they + + align:start position:0% +slope that they + + + align:start position:0% +slope that they +do this + + align:start position:0% +do this + + + align:start position:0% +do this +uh restrictions on publications uh i + + align:start position:0% +uh restrictions on publications uh i + + + align:start position:0% +uh restrictions on publications uh i +mean we felt that it was extremely + + align:start position:0% +mean we felt that it was extremely + + + align:start position:0% +mean we felt that it was extremely +important that we not + + align:start position:0% +important that we not + + + align:start position:0% +important that we not +put restrictions on the federal + + align:start position:0% +put restrictions on the federal + + + align:start position:0% +put restrictions on the federal +government that we were not willing to + + align:start position:0% +government that we were not willing to + + + align:start position:0% +government that we were not willing to +put on industry + + align:start position:0% +put on industry + + + align:start position:0% +put on industry +and i mean that would be a conflict of + + align:start position:0% +and i mean that would be a conflict of + + + align:start position:0% +and i mean that would be a conflict of +interest on our part so we said okay + + align:start position:0% +interest on our part so we said okay + + + align:start position:0% +interest on our part so we said okay +in industry when we do contracting with + + align:start position:0% +in industry when we do contracting with + + + align:start position:0% +in industry when we do contracting with +industry we will allow them to review a + + align:start position:0% +industry we will allow them to review a + + + align:start position:0% +industry we will allow them to review a +paper for 30 days 60 days some number + + align:start position:0% +paper for 30 days 60 days some number + + + align:start position:0% +paper for 30 days 60 days some number +like that to see whether there are + + align:start position:0% +like that to see whether there are + + + align:start position:0% +like that to see whether there are +patentable + + align:start position:0% +patentable + + + align:start position:0% +patentable +inventions within this paper + + align:start position:0% +inventions within this paper + + + align:start position:0% +inventions within this paper +but + + align:start position:0% +but + + + align:start position:0% +but +we control the time and we control the + + align:start position:0% +we control the time and we control the + + + align:start position:0% +we control the time and we control the +decision + + align:start position:0% +decision + + + align:start position:0% +decision +we say okay well you know let us know + + align:start position:0% +we say okay well you know let us know + + + align:start position:0% +we say okay well you know let us know +your concerns + + align:start position:0% +your concerns + + + align:start position:0% +your concerns +and at the end of 60 days we will make a + + align:start position:0% +and at the end of 60 days we will make a + + + align:start position:0% +and at the end of 60 days we will make a +decision + + align:start position:0% +decision + + + align:start position:0% +decision +as to whether your concerns are valid + + align:start position:0% +as to whether your concerns are valid + + + align:start position:0% +as to whether your concerns are valid +when you work with the federal + + align:start position:0% +when you work with the federal + + + align:start position:0% +when you work with the federal +government it's exactly the opposite + + align:start position:0% +government it's exactly the opposite + + + align:start position:0% +government it's exactly the opposite +they control the time and they control + + align:start position:0% +they control the time and they control + + + align:start position:0% +they control the time and they control +the output + + align:start position:0% +the output + + + align:start position:0% +the output +and there have been many examples + + align:start position:0% +and there have been many examples + + + align:start position:0% +and there have been many examples +where you know it has seriously it + + align:start position:0% +where you know it has seriously it + + + align:start position:0% +where you know it has seriously it +impacted the career of a student + + align:start position:0% +impacted the career of a student + + + align:start position:0% +impacted the career of a student +or a faculty member because of delays + + align:start position:0% +or a faculty member because of delays + + + align:start position:0% +or a faculty member because of delays +now + + align:start position:0% +now + + + align:start position:0% +now +there are always issues that have to be + + align:start position:0% +there are always issues that have to be + + + align:start position:0% +there are always issues that have to be +fought in this the there are um certain + + align:start position:0% +fought in this the there are um certain + + + align:start position:0% +fought in this the there are um certain +marching rights for extremely serious + + align:start position:0% +marching rights for extremely serious + + + align:start position:0% +marching rights for extremely serious +things that need to be classified and + + align:start position:0% +things that need to be classified and + + + align:start position:0% +things that need to be classified and +you know but these are these are the + + align:start position:0% +you know but these are these are the + + + align:start position:0% +you know but these are these are the +rare events these are the less than one + + align:start position:0% +rare events these are the less than one + + + align:start position:0% +rare events these are the less than one +percent + + align:start position:0% +percent + + + align:start position:0% +percent +so so i think you know we've been very + + align:start position:0% +so so i think you know we've been very + + + align:start position:0% +so so i think you know we've been very +open very public and very firm about + + align:start position:0% +open very public and very firm about + + + align:start position:0% +open very public and very firm about +these issues + + align:start position:0% +these issues + + + align:start position:0% +these issues +there are issues having to do with + + align:start position:0% + + + + align:start position:0% + +contract monitors and and these are more + + align:start position:0% +contract monitors and and these are more + + + align:start position:0% +contract monitors and and these are more +this is more gray not from the point of + + align:start position:0% +this is more gray not from the point of + + + align:start position:0% +this is more gray not from the point of +view of mit but because we don't always + + align:start position:0% +view of mit but because we don't always + + + align:start position:0% +view of mit but because we don't always +have visibility into these issues + + align:start position:0% +have visibility into these issues + + + align:start position:0% +have visibility into these issues +there are some contract monitors who say + + align:start position:0% +there are some contract monitors who say + + + align:start position:0% +there are some contract monitors who say +well you know we would prefer if you + + align:start position:0% +well you know we would prefer if you + + + align:start position:0% +well you know we would prefer if you +didn't hire any international graduate + + align:start position:0% +didn't hire any international graduate + + + align:start position:0% +didn't hire any international graduate +students on this + + align:start position:0% +students on this + + + align:start position:0% +students on this +and you know we have no way of knowing + + align:start position:0% +and you know we have no way of knowing + + + align:start position:0% +and you know we have no way of knowing +how mit faculty respond to that but it + + align:start position:0% +how mit faculty respond to that but it + + + align:start position:0% +how mit faculty respond to that but it +certainly is not + + align:start position:0% +certainly is not + + + align:start position:0% +certainly is not +does not line up with mit + + align:start position:0% +does not line up with mit + + + align:start position:0% +does not line up with mit +he's policy + + align:start position:0% +he's policy + + + align:start position:0% +he's policy +on the other hand mit is + + align:start position:0% + + + + align:start position:0% + +very active + + align:start position:0% +very active + + + align:start position:0% +very active +you know working in the federal + + align:start position:0% +you know working in the federal + + + align:start position:0% +you know working in the federal +government to ensure that there are no + + align:start position:0% +government to ensure that there are no + + + align:start position:0% +government to ensure that there are no +unreasonable restrictions on visas + + align:start position:0% +unreasonable restrictions on visas + + + align:start position:0% +unreasonable restrictions on visas +for international students so i mean + + align:start position:0% +for international students so i mean + + + align:start position:0% +for international students so i mean +again this is all part of the same + + align:start position:0% +again this is all part of the same + + + align:start position:0% +again this is all part of the same +picture + + align:start position:0% +picture + + + align:start position:0% +picture +but on the other hand what what this + + align:start position:0% +but on the other hand what what this + + + align:start position:0% +but on the other hand what what this +report talks about is the important + + align:start position:0% +report talks about is the important + + + align:start position:0% +report talks about is the important +public service dimension that mit + + align:start position:0% +public service dimension that mit + + + align:start position:0% +public service dimension that mit +performs when it engages in classified + + align:start position:0% +performs when it engages in classified + + + align:start position:0% +performs when it engages in classified +research + + align:start position:0% +research + + + align:start position:0% +research +and if we actually recommend that + + align:start position:0% +and if we actually recommend that + + + align:start position:0% +and if we actually recommend that +mit faculty get security clearances so + + align:start position:0% +mit faculty get security clearances so + + + align:start position:0% +mit faculty get security clearances so +they can + + align:start position:0% +they can + + + align:start position:0% +they can +serve on federal advisory committees + + align:start position:0% +serve on federal advisory committees + + + align:start position:0% +serve on federal advisory committees +that evaluate the quality + + align:start position:0% +that evaluate the quality + + + align:start position:0% +that evaluate the quality +of research because research that is + + align:start position:0% +of research because research that is + + + align:start position:0% +of research because research that is +done + + align:start position:0% +done + + + align:start position:0% +done +you know behind the block + + align:start position:0% +you know behind the block + + + align:start position:0% +you know behind the block +door + + align:start position:0% +door + + + align:start position:0% +door +is not necessarily of very high quality + + align:start position:0% +is not necessarily of very high quality + + + align:start position:0% +is not necessarily of very high quality +so how do we + + align:start position:0% +so how do we + + + align:start position:0% +so how do we +how do we ensure that the nation gets + + align:start position:0% +how do we ensure that the nation gets + + + align:start position:0% +how do we ensure that the nation gets +its money's worth from classified + + align:start position:0% +its money's worth from classified + + + align:start position:0% +its money's worth from classified +research + + align:start position:0% +research + + + align:start position:0% +research +one answer to that is to have mit + + align:start position:0% +one answer to that is to have mit + + + align:start position:0% +one answer to that is to have mit +faculty involved and we have many + + align:start position:0% +faculty involved and we have many + + + align:start position:0% +faculty involved and we have many +faculty involved in + + align:start position:0% +faculty involved in + + + align:start position:0% +faculty involved in +government advisory boards + + align:start position:0% +government advisory boards + + + align:start position:0% +government advisory boards +special + + align:start position:0% +special + + + align:start position:0% +special +report review + + align:start position:0% +report review + + + align:start position:0% +report review +program evaluation + + align:start position:0% +program evaluation + + + align:start position:0% +program evaluation +plus lincoln lab which you know we see + + align:start position:0% +plus lincoln lab which you know we see + + + align:start position:0% +plus lincoln lab which you know we see +lincoln + + align:start position:0% +lincoln + + + align:start position:0% +lincoln +as as a public service that this gives + + align:start position:0% +as as a public service that this gives + + + align:start position:0% +as as a public service that this gives +the defense department access to + + align:start position:0% +the defense department access to + + + align:start position:0% +the defense department access to +excellent people with very high + + align:start position:0% +excellent people with very high + + + align:start position:0% +excellent people with very high +standards of integrity and of course + + align:start position:0% +standards of integrity and of course + + + align:start position:0% +standards of integrity and of course +you're probably all familiar with the + + align:start position:0% +you're probably all familiar with the + + + align:start position:0% +you're probably all familiar with the +flap that's going on now and mit is + + align:start position:0% +flap that's going on now and mit is + + + align:start position:0% +flap that's going on now and mit is +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +determined to carry that through to the + + align:start position:0% +determined to carry that through to the + + + align:start position:0% +determined to carry that through to the +end + + align:start position:0% +end + + + align:start position:0% +end +to get to the bottom of allegations + + align:start position:0% +to get to the bottom of allegations + + + align:start position:0% +to get to the bottom of allegations +again of scientific misconduct actually + + align:start position:0% +again of scientific misconduct actually + + + align:start position:0% +again of scientific misconduct actually +using that framework that is laid out in + + align:start position:0% +using that framework that is laid out in + + + align:start position:0% +using that framework that is laid out in +that report to determine the truth of + + align:start position:0% +that report to determine the truth of + + + align:start position:0% +that report to determine the truth of +those allegations so that's + + align:start position:0% +those allegations so that's + + + align:start position:0% +those allegations so that's +that's one example of of + + align:start position:0% +that's one example of of + + + align:start position:0% +that's one example of of +institutional values the other one just + + align:start position:0% +institutional values the other one just + + + align:start position:0% +institutional values the other one just +i just happen to get this + + align:start position:0% +i just happen to get this + + + align:start position:0% +i just happen to get this +uh i'm on a corporate board + + align:start position:0% +uh i'm on a corporate board + + + align:start position:0% +uh i'm on a corporate board +and this this corporation builds rocket + + align:start position:0% +and this this corporation builds rocket + + + align:start position:0% +and this this corporation builds rocket +engines my favorite thing + + align:start position:0% +engines my favorite thing + + + align:start position:0% +engines my favorite thing +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and + + align:start position:0% +and + + + align:start position:0% +and +anybody who works for the federal + + align:start position:0% +anybody who works for the federal + + + align:start position:0% +anybody who works for the federal +government has to really maintain a very + + align:start position:0% +government has to really maintain a very + + + align:start position:0% +government has to really maintain a very +high standard of integrity + + align:start position:0% +high standard of integrity + + + align:start position:0% +high standard of integrity +and the costs are enormous + + align:start position:0% +and the costs are enormous + + + align:start position:0% +and the costs are enormous +for failing in this responsibility i can + + align:start position:0% +for failing in this responsibility i can + + + align:start position:0% +for failing in this responsibility i can +just give you a little example i don't + + align:start position:0% +just give you a little example i don't + + + align:start position:0% +just give you a little example i don't +know you know if you if you follow + + align:start position:0% +know you know if you if you follow + + + align:start position:0% +know you know if you if you follow +aerospace then you would know that a + + align:start position:0% +aerospace then you would know that a + + + align:start position:0% +aerospace then you would know that a +boeing vice boeing senior executive + + align:start position:0% +boeing vice boeing senior executive + + + align:start position:0% +boeing vice boeing senior executive +i i think he was higher than a vice + + align:start position:0% +i i think he was higher than a vice + + + align:start position:0% +i i think he was higher than a vice +president might have been president of + + align:start position:0% +president might have been president of + + + align:start position:0% +president might have been president of +the division a boeing + + align:start position:0% +the division a boeing + + + align:start position:0% +the division a boeing +senior executive made an inappropriate + + align:start position:0% +senior executive made an inappropriate + + + align:start position:0% +senior executive made an inappropriate +job offer to a + + align:start position:0% +job offer to a + + + align:start position:0% +job offer to a +high official in the defense department + + align:start position:0% +high official in the defense department + + + align:start position:0% +high official in the defense department +and it cost boeing + + align:start position:0% +and it cost boeing + + + align:start position:0% +and it cost boeing +five billion dollars + + align:start position:0% +five billion dollars + + + align:start position:0% +five billion dollars +and it landed + + align:start position:0% +and it landed + + + align:start position:0% +and it landed +this woman in jail for nine months and i + + align:start position:0% +this woman in jail for nine months and i + + + align:start position:0% +this woman in jail for nine months and i +think it landed the senior executive in + + align:start position:0% +think it landed the senior executive in + + + align:start position:0% +think it landed the senior executive in +jail for six months something like that + + align:start position:0% +jail for six months something like that + + + align:start position:0% +jail for six months something like that +so who was served by that + + align:start position:0% +so who was served by that + + + align:start position:0% +so who was served by that +behavior nobody nobody was served the + + align:start position:0% +behavior nobody nobody was served the + + + align:start position:0% +behavior nobody nobody was served the +company was not served + + align:start position:0% +company was not served + + + align:start position:0% +company was not served +the individuals involved who were not + + align:start position:0% +the individuals involved who were not + + + align:start position:0% +the individuals involved who were not +served the nation was sponsored the air + + align:start position:0% +served the nation was sponsored the air + + + align:start position:0% +served the nation was sponsored the air +force just landed on its backside + + align:start position:0% +force just landed on its backside + + + align:start position:0% +force just landed on its backside +so i mean you know that's why when i say + + align:start position:0% +so i mean you know that's why when i say + + + align:start position:0% +so i mean you know that's why when i say +that i believe that values are pragmatic + + align:start position:0% +that i believe that values are pragmatic + + + align:start position:0% +that i believe that values are pragmatic +it's that sort of thing i'm talking + + align:start position:0% +it's that sort of thing i'm talking + + + align:start position:0% +it's that sort of thing i'm talking +about that rightly so the consequences + + align:start position:0% +about that rightly so the consequences + + + align:start position:0% +about that rightly so the consequences +for + + align:start position:0% +for + + + align:start position:0% +for +what one + + align:start position:0% +what one + + + align:start position:0% +what one +might be able to rationalize + + align:start position:0% +might be able to rationalize + + + align:start position:0% +might be able to rationalize +as regional behavior at some early stage + + align:start position:0% +as regional behavior at some early stage + + + align:start position:0% +as regional behavior at some early stage +in the process simply becomes + + align:start position:0% +in the process simply becomes + + + align:start position:0% +in the process simply becomes +extraordinary at some later stage + + align:start position:0% +extraordinary at some later stage + + + align:start position:0% +extraordinary at some later stage +this is a code of business conduct which + + align:start position:0% +this is a code of business conduct which + + + align:start position:0% +this is a code of business conduct which +is i i was at the board meeting and and + + align:start position:0% +is i i was at the board meeting and and + + + align:start position:0% +is i i was at the board meeting and and +you know it just lays it all out + + align:start position:0% +you know it just lays it all out + + + align:start position:0% +you know it just lays it all out +business entertainment timekeeping + + align:start position:0% +business entertainment timekeeping + + + align:start position:0% +business entertainment timekeeping +bribes and kickbacks dealing with + + align:start position:0% +bribes and kickbacks dealing with + + + align:start position:0% +bribes and kickbacks dealing with +suppliers use of company resources + + align:start position:0% +suppliers use of company resources + + + align:start position:0% +suppliers use of company resources +conflict of interest + + align:start position:0% +conflict of interest + + + align:start position:0% +conflict of interest +export control political contributions + + align:start position:0% +export control political contributions + + + align:start position:0% +export control political contributions +corporate citizenships reporting + + align:start position:0% +corporate citizenships reporting + + + align:start position:0% +corporate citizenships reporting +you know they have a hotline that's + + align:start position:0% +you know they have a hotline that's + + + align:start position:0% +you know they have a hotline that's +anonymous + + align:start position:0% +anonymous + + + align:start position:0% +anonymous +any employee who has a concern about + + align:start position:0% +any employee who has a concern about + + + align:start position:0% +any employee who has a concern about +anything that they observe + + align:start position:0% +anything that they observe + + + align:start position:0% +anything that they observe +going on in the corporation calls the + + align:start position:0% +going on in the corporation calls the + + + align:start position:0% +going on in the corporation calls the +hotline + + align:start position:0% +hotline + + + align:start position:0% +hotline +and the hotline goes directly to the + + align:start position:0% +and the hotline goes directly to the + + + align:start position:0% +and the hotline goes directly to the +board of directors + + align:start position:0% +board of directors + + + align:start position:0% +board of directors +and i believe it's the corporate + + align:start position:0% +and i believe it's the corporate + + + align:start position:0% +and i believe it's the corporate +governance committee + + align:start position:0% +governance committee + + + align:start position:0% +governance committee +and the matter is taken very seriously + + align:start position:0% +and the matter is taken very seriously + + + align:start position:0% +and the matter is taken very seriously +and is reported so and and this is not + + align:start position:0% +and is reported so and and this is not + + + align:start position:0% +and is reported so and and this is not +unusual just the one i happened to pick + + align:start position:0% +unusual just the one i happened to pick + + + align:start position:0% +unusual just the one i happened to pick +up last week when i was in california so + + align:start position:0% +up last week when i was in california so + + + align:start position:0% +up last week when i was in california so +let me + + align:start position:0% +let me + + + align:start position:0% +let me +let me + + align:start position:0% +let me + + + align:start position:0% +let me +pass that out + + align:start position:0% +pass that out + + + align:start position:0% +pass that out +now it may be true that since the + + align:start position:0% +now it may be true that since the + + + align:start position:0% +now it may be true that since the +defense department has in fact a whole + + align:start position:0% +defense department has in fact a whole + + + align:start position:0% +defense department has in fact a whole +set of governing regulations it may be + + align:start position:0% +set of governing regulations it may be + + + align:start position:0% +set of governing regulations it may be +that companies who do business with + + align:start position:0% +that companies who do business with + + + align:start position:0% +that companies who do business with +defense and maybe more generally the + + align:start position:0% +defense and maybe more generally the + + + align:start position:0% +defense and maybe more generally the +government i suspect that anybody who + + align:start position:0% +government i suspect that anybody who + + + align:start position:0% +government i suspect that anybody who +does business with the government has to + + align:start position:0% +does business with the government has to + + + align:start position:0% +does business with the government has to +be quite explicit + + align:start position:0% +be quite explicit + + + align:start position:0% +be quite explicit +about their corporate values + + align:start position:0% +about their corporate values + + + align:start position:0% +about their corporate values +because uh it is it is in fact required + + align:start position:0% +because uh it is it is in fact required + + + align:start position:0% +because uh it is it is in fact required +this kind of uh behavior is required and + + align:start position:0% +this kind of uh behavior is required and + + + align:start position:0% +this kind of uh behavior is required and +if if there's a slip up + + align:start position:0% +if if there's a slip up + + + align:start position:0% +if if there's a slip up +all hell breaks loose you know i mean it + + align:start position:0% +all hell breaks loose you know i mean it + + + align:start position:0% +all hell breaks loose you know i mean it +just it goes from bad to worse very + + align:start position:0% +just it goes from bad to worse very + + + align:start position:0% +just it goes from bad to worse very +quickly and large + + align:start position:0% +quickly and large + + + align:start position:0% +quickly and large +large amounts of resources are at stake + + align:start position:0% +large amounts of resources are at stake + + + align:start position:0% +large amounts of resources are at stake +and people's individual careers are + + align:start position:0% +and people's individual careers are + + + align:start position:0% +and people's individual careers are +devastated + + align:start position:0% +devastated + + + align:start position:0% +devastated +so + + align:start position:0% +so + + + align:start position:0% +so +anyway that's all i plan to talk about + + align:start position:0% +anyway that's all i plan to talk about + + + align:start position:0% +anyway that's all i plan to talk about +so i guess we could throw the class the + + align:start position:0% +so i guess we could throw the class the + + + align:start position:0% +so i guess we could throw the class the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the field open for questions + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +um + + align:start position:0% + + + + align:start position:0% + +i'd like to ask a couple of questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh back in 1986 + + align:start position:0% +uh back in 1986 + + + align:start position:0% +uh back in 1986 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i got a letter and a manuscript + + align:start position:0% +i got a letter and a manuscript + + + align:start position:0% +i got a letter and a manuscript +from hans mom + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and what he said in that letter was + + align:start position:0% +and what he said in that letter was + + + align:start position:0% +and what he said in that letter was +that he had the final authority in nasa + + align:start position:0% +that he had the final authority in nasa + + + align:start position:0% +that he had the final authority in nasa +to okay + + align:start position:0% +to okay + + + align:start position:0% +to okay +a flight that shall flight + + align:start position:0% +a flight that shall flight + + + align:start position:0% +a flight that shall flight +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and he said that he in his years of + + align:start position:0% +and he said that he in his years of + + + align:start position:0% +and he said that he in his years of +experience that every time he gave the + + align:start position:0% +experience that every time he gave the + + + align:start position:0% +experience that every time he gave the +located fly + + align:start position:0% +located fly + + + align:start position:0% +located fly +it was over the objections of some + + align:start position:0% +it was over the objections of some + + + align:start position:0% +it was over the objections of some +engineers who said + + align:start position:0% +engineers who said + + + align:start position:0% +engineers who said +that's what he exploded yeah + + align:start position:0% +that's what he exploded yeah + + + align:start position:0% +that's what he exploded yeah +he had the rationale that will never get + + align:start position:0% +he had the rationale that will never get + + + align:start position:0% +he had the rationale that will never get +to the movement + + align:start position:0% +to the movement + + + align:start position:0% +to the movement +right right without risk yeah i don't + + align:start position:0% +right right without risk yeah i don't + + + align:start position:0% +right right without risk yeah i don't +think it was really a risk issue + + align:start position:0% +think it was really a risk issue + + + align:start position:0% +think it was really a risk issue +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +i just want to know what kind of + + align:start position:0% +i just want to know what kind of + + + align:start position:0% +i just want to know what kind of +principle yes right + + align:start position:0% +principle yes right + + + align:start position:0% +principle yes right +i got it + + align:start position:0% +i got it + + + align:start position:0% +i got it +now i have the answer to that question + + align:start position:0% +now i have the answer to that question + + + align:start position:0% +now i have the answer to that question +yeah now i have the answer that question + + align:start position:0% +yeah now i have the answer that question + + + align:start position:0% +yeah now i have the answer that question +um of course i think yeah i mean once + + align:start position:0% +um of course i think yeah i mean once + + + align:start position:0% +um of course i think yeah i mean once +one answer is that's why we need + + align:start position:0% +one answer is that's why we need + + + align:start position:0% +one answer is that's why we need +leadership that's too simple an answer + + align:start position:0% +leadership that's too simple an answer + + + align:start position:0% +leadership that's too simple an answer +i've served on a lot of + + align:start position:0% +i've served on a lot of + + + align:start position:0% +i've served on a lot of +what i would call a mission review + + align:start position:0% +what i would call a mission review + + + align:start position:0% +what i would call a mission review +boards + + align:start position:0% +boards + + + align:start position:0% +boards +i did the mission review for the first + + align:start position:0% +i did the mission review for the first + + + align:start position:0% +i did the mission review for the first +flight of boeing's delta iv launch + + align:start position:0% +flight of boeing's delta iv launch + + + align:start position:0% +flight of boeing's delta iv launch +vehicle + + align:start position:0% +vehicle + + + align:start position:0% +vehicle +uh i did + + align:start position:0% +uh i did + + + align:start position:0% +uh i did +i chaired + + align:start position:0% +i chaired + + + align:start position:0% +i chaired +the what was called the return to flight + + align:start position:0% +the what was called the return to flight + + + align:start position:0% +the what was called the return to flight +there was a time in our nation's history + + align:start position:0% +there was a time in our nation's history + + + align:start position:0% +there was a time in our nation's history +where + + align:start position:0% +where + + + align:start position:0% +where +i'm more on the launch vehicle side as + + align:start position:0% +i'm more on the launch vehicle side as + + + align:start position:0% +i'm more on the launch vehicle side as +opposed to nasa i hadn't done a lot with + + align:start position:0% +opposed to nasa i hadn't done a lot with + + + align:start position:0% +opposed to nasa i hadn't done a lot with +nasa but + + align:start position:0% +nasa but + + + align:start position:0% +nasa but +on the launch vehicle side we went + + align:start position:0% +on the launch vehicle side we went + + + align:start position:0% +on the launch vehicle side we went +through a period where we lost + + align:start position:0% +through a period where we lost + + + align:start position:0% +through a period where we lost +something like four launch vehicles in a + + align:start position:0% +something like four launch vehicles in a + + + align:start position:0% +something like four launch vehicles in a +row from all sorts of ridiculous + + align:start position:0% +row from all sorts of ridiculous + + + align:start position:0% +row from all sorts of ridiculous +accidents + + align:start position:0% +accidents + + + align:start position:0% +accidents +you know just failure to do certain + + align:start position:0% +you know just failure to do certain + + + align:start position:0% +you know just failure to do certain +things and so + + align:start position:0% +things and so + + + align:start position:0% +things and so +we kind of shut everything down and we + + align:start position:0% +we kind of shut everything down and we + + + align:start position:0% +we kind of shut everything down and we +began looking across + + align:start position:0% +began looking across + + + align:start position:0% +began looking across +at processes + + align:start position:0% +at processes + + + align:start position:0% +at processes +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so what i would say + + align:start position:0% +so what i would say + + + align:start position:0% +so what i would say +you know an answer to that is that + + align:start position:0% +you know an answer to that is that + + + align:start position:0% +you know an answer to that is that +engineers must put their concerns in + + align:start position:0% +engineers must put their concerns in + + + align:start position:0% +engineers must put their concerns in +actionable form + + align:start position:0% +actionable form + + + align:start position:0% +actionable form +you know don't tell me what keeps you + + align:start position:0% +you know don't tell me what keeps you + + + align:start position:0% +you know don't tell me what keeps you +awake at night + + align:start position:0% +awake at night + + + align:start position:0% +awake at night +tell me what you want me to do + + align:start position:0% +tell me what you want me to do + + + align:start position:0% +tell me what you want me to do +and i actually looked at the challenger + + align:start position:0% +and i actually looked at the challenger + + + align:start position:0% +and i actually looked at the challenger +thing the other night because there's a + + align:start position:0% +thing the other night because there's a + + + align:start position:0% +thing the other night because there's a +tv tv thing you know one of those old + + align:start position:0% +tv tv thing you know one of those old + + + align:start position:0% +tv tv thing you know one of those old +things the history channel um + + align:start position:0% +things the history channel um + + + align:start position:0% +things the history channel um +so i think the way to distinguish + + align:start position:0% +so i think the way to distinguish + + + align:start position:0% +so i think the way to distinguish +between the the concerns of engineers + + align:start position:0% +between the the concerns of engineers + + + align:start position:0% +between the the concerns of engineers +that that are just always there you know + + align:start position:0% +that that are just always there you know + + + align:start position:0% +that that are just always there you know +and and you know sometimes i wish i + + align:start position:0% +and and you know sometimes i wish i + + + align:start position:0% +and and you know sometimes i wish i +could just take these guys line them up + + align:start position:0% +could just take these guys line them up + + + align:start position:0% +could just take these guys line them up +and shoot them + + align:start position:0% +and shoot them + + + align:start position:0% +and shoot them +you know because + + align:start position:0% +you know because + + + align:start position:0% +you know because +they're just not giving me what i need + + align:start position:0% +they're just not giving me what i need + + + align:start position:0% +they're just not giving me what i need +in order to take the next step + + align:start position:0% +in order to take the next step + + + align:start position:0% +in order to take the next step +uh it is not useful if you tell me + + align:start position:0% +uh it is not useful if you tell me + + + align:start position:0% +uh it is not useful if you tell me +you're worried + + align:start position:0% +you're worried + + + align:start position:0% +you're worried +you've got to tell me what you want me + + align:start position:0% +you've got to tell me what you want me + + + align:start position:0% +you've got to tell me what you want me +to do what test do you want me to run + + align:start position:0% +to do what test do you want me to run + + + align:start position:0% +to do what test do you want me to run +why are you worried what's the data + + align:start position:0% +why are you worried what's the data + + + align:start position:0% +why are you worried what's the data +what's the analysis what's the next step + + align:start position:0% +what's the analysis what's the next step + + + align:start position:0% +what's the analysis what's the next step +how can i + + align:start position:0% +how can i + + + align:start position:0% +how can i +take the next step in order to to + + align:start position:0% +take the next step in order to to + + + align:start position:0% +take the next step in order to to +understand whether i share your concern + + align:start position:0% +understand whether i share your concern + + + align:start position:0% +understand whether i share your concern +or i'm about to dismiss your concern and + + align:start position:0% +or i'm about to dismiss your concern and + + + align:start position:0% +or i'm about to dismiss your concern and +it seems to me in the case of + + align:start position:0% +it seems to me in the case of + + + align:start position:0% +it seems to me in the case of +roger beaujolais he did all of those + + align:start position:0% +roger beaujolais he did all of those + + + align:start position:0% +roger beaujolais he did all of those +things + + align:start position:0% +things + + + align:start position:0% +things +he had the data + + align:start position:0% +he had the data + + + align:start position:0% +he had the data +the data i think validated his concern + + align:start position:0% +the data i think validated his concern + + + align:start position:0% +the data i think validated his concern +about the + + align:start position:0% +about the + + + align:start position:0% +about the +opening the envelope + + align:start position:0% +opening the envelope + + + align:start position:0% +opening the envelope +in terms of of temperature external + + align:start position:0% +in terms of of temperature external + + + align:start position:0% +in terms of of temperature external +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +he had the previous flight data which + + align:start position:0% +he had the previous flight data which + + + align:start position:0% +he had the previous flight data which +indicated a concern + + align:start position:0% +indicated a concern + + + align:start position:0% +indicated a concern +so i think he + + align:start position:0% +so i think he + + + align:start position:0% +so i think he +he met my barrier + + align:start position:0% +he met my barrier + + + align:start position:0% +he met my barrier +for an engineer who should be taken + + align:start position:0% +for an engineer who should be taken + + + align:start position:0% +for an engineer who should be taken +seriously + + align:start position:0% +seriously + + + align:start position:0% +seriously +he also had support from i guess his his + + align:start position:0% +he also had support from i guess his his + + + align:start position:0% +he also had support from i guess his his +counterpart slightly other part of the + + align:start position:0% +counterpart slightly other part of the + + + align:start position:0% +counterpart slightly other part of the +organization but two of the major senior + + align:start position:0% +organization but two of the major senior + + + align:start position:0% +organization but two of the major senior +engineers + + align:start position:0% +engineers + + + align:start position:0% +engineers +i think expressed their concerns + + align:start position:0% +i think expressed their concerns + + + align:start position:0% +i think expressed their concerns +in an actionable form which i believe + + align:start position:0% +in an actionable form which i believe + + + align:start position:0% +in an actionable form which i believe +needs to be taken seriously so i think + + align:start position:0% +needs to be taken seriously so i think + + + align:start position:0% +needs to be taken seriously so i think +that's my threshold + + align:start position:0% +that's my threshold + + + align:start position:0% +that's my threshold +and and i've told that to engineers you + + align:start position:0% +and and i've told that to engineers you + + + align:start position:0% +and and i've told that to engineers you +know when i'm + + align:start position:0% +know when i'm + + + align:start position:0% +know when i'm +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +these issues you know on the columbiax + + align:start position:0% +these issues you know on the columbiax + + + align:start position:0% +these issues you know on the columbiax +investigation board and other things so + + align:start position:0% +investigation board and other things so + + + align:start position:0% +investigation board and other things so +for me that's the threshold + + align:start position:0% + + + + align:start position:0% + +and i think so that's one threshold i + + align:start position:0% +and i think so that's one threshold i + + + align:start position:0% +and i think so that's one threshold i +think there's another threshold in + + align:start position:0% +think there's another threshold in + + + align:start position:0% +think there's another threshold in +what i would call the collective + + align:start position:0% +what i would call the collective + + + align:start position:0% +what i would call the collective +processes of + + align:start position:0% +processes of + + + align:start position:0% +processes of +of + + align:start position:0% +of + + + align:start position:0% +of +the + + align:start position:0% +the + + + align:start position:0% +the +well whatever safety program an agency + + align:start position:0% +well whatever safety program an agency + + + align:start position:0% +well whatever safety program an agency +is using in the case of space + + align:start position:0% +is using in the case of space + + + align:start position:0% +is using in the case of space +there are some really fundamental rules + + align:start position:0% +there are some really fundamental rules + + + align:start position:0% +there are some really fundamental rules +that you do not break + + align:start position:0% +that you do not break + + + align:start position:0% +that you do not break +and one of those rules is test as you + + align:start position:0% +and one of those rules is test as you + + + align:start position:0% +and one of those rules is test as you +fly + + align:start position:0% +fly + + + align:start position:0% +fly +resolve anomalies + + align:start position:0% +resolve anomalies + + + align:start position:0% +resolve anomalies +those are the two rules + + align:start position:0% +those are the two rules + + + align:start position:0% +those are the two rules +i think in the case of columbia and + + align:start position:0% +i think in the case of columbia and + + + align:start position:0% +i think in the case of columbia and +maybe challenger 2 i think there might + + align:start position:0% +maybe challenger 2 i think there might + + + align:start position:0% +maybe challenger 2 i think there might +have been a little bit of this + + align:start position:0% +have been a little bit of this + + + align:start position:0% +have been a little bit of this +is you do not use a successful flight to + + align:start position:0% +is you do not use a successful flight to + + + align:start position:0% +is you do not use a successful flight to +expand the envelope of operations + + align:start position:0% +expand the envelope of operations + + + align:start position:0% +expand the envelope of operations +when you start the program you have an + + align:start position:0% +when you start the program you have an + + + align:start position:0% +when you start the program you have an +initial requirement + + align:start position:0% +initial requirement + + + align:start position:0% +initial requirement +when something happens that goes outside + + align:start position:0% +when something happens that goes outside + + + align:start position:0% +when something happens that goes outside +that busts that requirement you do not + + align:start position:0% +that busts that requirement you do not + + + align:start position:0% +that busts that requirement you do not +use that as justification for expanding + + align:start position:0% +use that as justification for expanding + + + align:start position:0% +use that as justification for expanding +the envelope + + align:start position:0% +the envelope + + + align:start position:0% +the envelope +and in the case of of the columbia + + align:start position:0% + + + + align:start position:0% + +foam was coming off the shuttle from the + + align:start position:0% +foam was coming off the shuttle from the + + + align:start position:0% +foam was coming off the shuttle from the +beginning of the program + + align:start position:0% +beginning of the program + + + align:start position:0% +beginning of the program +okay you go back to the test as you fly + + align:start position:0% +okay you go back to the test as you fly + + + align:start position:0% +okay you go back to the test as you fly +rule + + align:start position:0% +rule + + + align:start position:0% +rule +so + + align:start position:0% +so + + + align:start position:0% +so +and that oh yeah that's kind of a cute + + align:start position:0% +and that oh yeah that's kind of a cute + + + align:start position:0% +and that oh yeah that's kind of a cute +play on words if you think about it + + align:start position:0% +play on words if you think about it + + + align:start position:0% +play on words if you think about it +test as you fly means + + align:start position:0% +test as you fly means + + + align:start position:0% +test as you fly means +you identify flight conditions you test + + align:start position:0% +you identify flight conditions you test + + + align:start position:0% +you identify flight conditions you test +every component + + align:start position:0% + + + + align:start position:0% + +according to or exceeding those flight + + align:start position:0% +according to or exceeding those flight + + + align:start position:0% +according to or exceeding those flight +conditions + + align:start position:0% +conditions + + + align:start position:0% +conditions +it does not mean you run the test as you + + align:start position:0% +it does not mean you run the test as you + + + align:start position:0% +it does not mean you run the test as you +fly + + align:start position:0% +fly + + + align:start position:0% +fly +which is + + align:start position:0% +which is + + + align:start position:0% +which is +in some sense the way nasa and it took + + align:start position:0% +in some sense the way nasa and it took + + + align:start position:0% +in some sense the way nasa and it took +me a long time to you know to think a + + align:start position:0% +me a long time to you know to think a + + + align:start position:0% +me a long time to you know to think a +little bit about that play on word so + + align:start position:0% +little bit about that play on word so + + + align:start position:0% +little bit about that play on word so +that i was a little more careful + + align:start position:0% +that i was a little more careful + + + align:start position:0% +that i was a little more careful +saying test as you fly but you know and + + align:start position:0% +saying test as you fly but you know and + + + align:start position:0% +saying test as you fly but you know and +the the test that we ran in the columbia + + align:start position:0% +the the test that we ran in the columbia + + + align:start position:0% +the the test that we ran in the columbia +accent investigation board was to take a + + align:start position:0% +accent investigation board was to take a + + + align:start position:0% +accent investigation board was to take a +large chunk of foam + + align:start position:0% +large chunk of foam + + + align:start position:0% +large chunk of foam +put it in a foam gun 800 feet per second + + align:start position:0% +put it in a foam gun 800 feet per second + + + align:start position:0% +put it in a foam gun 800 feet per second +and blasted out the leading edge + + align:start position:0% +and blasted out the leading edge + + + align:start position:0% +and blasted out the leading edge +well if you back up a little bit and say + + align:start position:0% +well if you back up a little bit and say + + + align:start position:0% +well if you back up a little bit and say +now the fundamental real space flight is + + align:start position:0% +now the fundamental real space flight is + + + align:start position:0% +now the fundamental real space flight is +test as you fly + + align:start position:0% +test as you fly + + + align:start position:0% +test as you fly +once nasa determined that foam was + + align:start position:0% +once nasa determined that foam was + + + align:start position:0% +once nasa determined that foam was +coming off the shuttle they should have + + align:start position:0% +coming off the shuttle they should have + + + align:start position:0% +coming off the shuttle they should have +run that test they should have run it a + + align:start position:0% +run that test they should have run it a + + + align:start position:0% +run that test they should have run it a +long time ago + + align:start position:0% +long time ago + + + align:start position:0% +long time ago +so i would say those are those are kind + + align:start position:0% +so i would say those are those are kind + + + align:start position:0% +so i would say those are those are kind +of the things that that the fundamental + + align:start position:0% +of the things that that the fundamental + + + align:start position:0% +of the things that that the fundamental +responsibility of engineers is to + + align:start position:0% +responsibility of engineers is to + + + align:start position:0% +responsibility of engineers is to +express their concern in a form that is + + align:start position:0% +express their concern in a form that is + + + align:start position:0% +express their concern in a form that is +actionable that's a that's a general + + align:start position:0% +actionable that's a that's a general + + + align:start position:0% +actionable that's a that's a general +rule then i would say the second rules + + align:start position:0% +rule then i would say the second rules + + + align:start position:0% +rule then i would say the second rules +have to do with the particular + + align:start position:0% +have to do with the particular + + + align:start position:0% +have to do with the particular +field or discipline that you're working + + align:start position:0% +field or discipline that you're working + + + align:start position:0% +field or discipline that you're working +in but certainly in space which is a + + align:start position:0% +in but certainly in space which is a + + + align:start position:0% +in but certainly in space which is a +very hostile environment which + + align:start position:0% +very hostile environment which + + + align:start position:0% +very hostile environment which +because of successful + + align:start position:0% +because of successful + + + align:start position:0% +because of successful +missions has developed this this set of + + align:start position:0% +missions has developed this this set of + + + align:start position:0% +missions has developed this this set of +rules about + + align:start position:0% +rules about + + + align:start position:0% +rules about +test as you fly and uh resolving + + align:start position:0% +test as you fly and uh resolving + + + align:start position:0% +test as you fly and uh resolving +anomalies the the thing the specific + + align:start position:0% +anomalies the the thing the specific + + + align:start position:0% +anomalies the the thing the specific +thing about colombia is that they had + + align:start position:0% +thing about colombia is that they had + + + align:start position:0% +thing about colombia is that they had +actually taken + + align:start position:0% +actually taken + + + align:start position:0% +actually taken +that particular anomaly had really + + align:start position:0% +that particular anomaly had really + + + align:start position:0% +that particular anomaly had really +become very serious + + align:start position:0% +become very serious + + + align:start position:0% +become very serious +and it almost systematically happened + + align:start position:0% +and it almost systematically happened + + + align:start position:0% +and it almost systematically happened +and they actually + + align:start position:0% +and they actually + + + align:start position:0% +and they actually +took it off the table and they put it in + + align:start position:0% +took it off the table and they put it in + + + align:start position:0% +took it off the table and they put it in +a category + + align:start position:0% +a category + + + align:start position:0% +a category +we're working on that so they actually + + align:start position:0% +we're working on that so they actually + + + align:start position:0% +we're working on that so they actually +didn't they paid less attention to it at + + align:start position:0% +didn't they paid less attention to it at + + + align:start position:0% +didn't they paid less attention to it at +the beginning of the columbia mission + + align:start position:0% +the beginning of the columbia mission + + + align:start position:0% +the beginning of the columbia mission +assurance review than they had on some + + align:start position:0% +assurance review than they had on some + + + align:start position:0% +assurance review than they had on some +of the previous reviews not that it + + align:start position:0% +of the previous reviews not that it + + + align:start position:0% +of the previous reviews not that it +would have made a difference i think + + align:start position:0% +would have made a difference i think + + + align:start position:0% +would have made a difference i think +their fundamental process for + + align:start position:0% +their fundamental process for + + + align:start position:0% +their fundamental process for +getting to flight is is broken and they + + align:start position:0% +getting to flight is is broken and they + + + align:start position:0% +getting to flight is is broken and they +need to re-examine and that's what we + + align:start position:0% +need to re-examine and that's what we + + + align:start position:0% +need to re-examine and that's what we +basically recommended to + + align:start position:0% +basically recommended to + + + align:start position:0% +basically recommended to +and hopefully that will happen + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% + + + + align:start position:0% + +um i have a question about the in the + + align:start position:0% +um i have a question about the in the + + + align:start position:0% +um i have a question about the in the +public industry yes right the policies + + align:start position:0% +public industry yes right the policies + + + align:start position:0% +public industry yes right the policies +on um + + align:start position:0% +on um + + + align:start position:0% +on um +accepting federal funding + + align:start position:0% +accepting federal funding + + + align:start position:0% +accepting federal funding +how how are professors at mit bound to + + align:start position:0% +how how are professors at mit bound to + + + align:start position:0% +how how are professors at mit bound to +those policies + + align:start position:0% +those policies + + + align:start position:0% +those policies +are they bound + + align:start position:0% +are they bound + + + align:start position:0% +are they bound +to accepting research according to it + + align:start position:0% +to accepting research according to it + + + align:start position:0% +to accepting research according to it +well first of all + + align:start position:0% + + + + align:start position:0% + +i want to i kind of want to turn your + + align:start position:0% +i want to i kind of want to turn your + + + align:start position:0% +i want to i kind of want to turn your +question around + + align:start position:0% +question around + + + align:start position:0% +question around +mit's policies will not let money come + + align:start position:0% +mit's policies will not let money come + + + align:start position:0% +mit's policies will not let money come +through the door all the contracts that + + align:start position:0% +through the door all the contracts that + + + align:start position:0% +through the door all the contracts that +mit has are with + + align:start position:0% +mit has are with + + + align:start position:0% +mit has are with +mit not individual faculty okay so an + + align:start position:0% +mit not individual faculty okay so an + + + align:start position:0% +mit not individual faculty okay so an +individual faculty member might be + + align:start position:0% +individual faculty member might be + + + align:start position:0% +individual faculty member might be +willing to accept + + align:start position:0% +willing to accept + + + align:start position:0% +willing to accept +a contract that specifically said no + + align:start position:0% +a contract that specifically said no + + + align:start position:0% +a contract that specifically said no +international graduate students + + align:start position:0% +international graduate students + + + align:start position:0% +international graduate students +or + + align:start position:0% +or + + + align:start position:0% +or +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you must + + align:start position:0% +you must + + + align:start position:0% +you must +obtain + + align:start position:0% +obtain + + + align:start position:0% +obtain +permission to publish + + align:start position:0% +permission to publish + + + align:start position:0% +permission to publish +mit would not allow such a contract to + + align:start position:0% +mit would not allow such a contract to + + + align:start position:0% +mit would not allow such a contract to +be + + align:start position:0% +be + + + align:start position:0% +be +signed + + align:start position:0% +signed + + + align:start position:0% +signed +now i'm not saying there aren't under + + align:start position:0% +now i'm not saying there aren't under + + + align:start position:0% +now i'm not saying there aren't under +the table winks and nods but + + align:start position:0% +the table winks and nods but + + + align:start position:0% +the table winks and nods but +these don't satisfy my definition of + + align:start position:0% +these don't satisfy my definition of + + + align:start position:0% +these don't satisfy my definition of +ethical behavior + + align:start position:0% +ethical behavior + + + align:start position:0% +ethical behavior +uh so so that is that is so that's + + align:start position:0% +uh so so that is that is so that's + + + align:start position:0% +uh so so that is that is so that's +basically the way it's done is that all + + align:start position:0% +basically the way it's done is that all + + + align:start position:0% +basically the way it's done is that all +contracts are with mit + + align:start position:0% +contracts are with mit + + + align:start position:0% +contracts are with mit +and that ensures this openness that we + + align:start position:0% +and that ensures this openness that we + + + align:start position:0% +and that ensures this openness that we +insist on that + + align:start position:0% +insist on that + + + align:start position:0% +insist on that +you know open + + align:start position:0% +you know open + + + align:start position:0% +you know open +information in the classroom open + + align:start position:0% +information in the classroom open + + + align:start position:0% +information in the classroom open +information freedom to publish + + align:start position:0% +information freedom to publish + + + align:start position:0% +information freedom to publish +and all of that those are the things + + align:start position:0% +and all of that those are the things + + + align:start position:0% +and all of that those are the things +that we think are really + + align:start position:0% +that we think are really + + + align:start position:0% +that we think are really +important so then does that mean that + + align:start position:0% +important so then does that mean that + + + align:start position:0% +important so then does that mean that +there there are no mit contracts that + + align:start position:0% +there there are no mit contracts that + + + align:start position:0% +there there are no mit contracts that +include classified research + + align:start position:0% +include classified research + + + align:start position:0% +include classified research +not on campus okay + + align:start position:0% +not on campus okay + + + align:start position:0% +not on campus okay +in fact that that's kind of historically + + align:start position:0% +in fact that that's kind of historically + + + align:start position:0% +in fact that that's kind of historically +very interesting because we used to have + + align:start position:0% +very interesting because we used to have + + + align:start position:0% +very interesting because we used to have +contracts on campus that include + + align:start position:0% +contracts on campus that include + + + align:start position:0% +contracts on campus that include +classified research and you know during + + align:start position:0% +classified research and you know during + + + align:start position:0% +classified research and you know during +the vietnam unrest + + align:start position:0% +the vietnam unrest + + + align:start position:0% +the vietnam unrest +you were probably too at that point + + align:start position:0% +you were probably too at that point + + + align:start position:0% +you were probably too at that point +if that + + align:start position:0% +if that + + + align:start position:0% +if that +we we basically made a decision that + + align:start position:0% +we we basically made a decision that + + + align:start position:0% +we we basically made a decision that +that we would not do classified research + + align:start position:0% +that we would not do classified research + + + align:start position:0% +that we would not do classified research +and and and when we got this committee + + align:start position:0% +and and and when we got this committee + + + align:start position:0% +and and and when we got this committee +together you know because we had + + align:start position:0% +together you know because we had + + + align:start position:0% +together you know because we had +recommended that mit faculty get + + align:start position:0% +recommended that mit faculty get + + + align:start position:0% +recommended that mit faculty get +clearances and they do serve on + + align:start position:0% +clearances and they do serve on + + + align:start position:0% +clearances and they do serve on +government advisory boards and they are + + align:start position:0% +government advisory boards and they are + + + align:start position:0% +government advisory boards and they are +in a position to + + align:start position:0% +in a position to + + + align:start position:0% +in a position to +oversee the + + align:start position:0% +oversee the + + + align:start position:0% +oversee the +the quality of classified research we + + align:start position:0% +the quality of classified research we + + + align:start position:0% +the quality of classified research we +gave some brief thought to thinking well + + align:start position:0% +gave some brief thought to thinking well + + + align:start position:0% +gave some brief thought to thinking well +should we have + + align:start position:0% +should we have + + + align:start position:0% +should we have +a reading room on campus for the + + align:start position:0% + + + + align:start position:0% + +convenience of such faculty which where + + align:start position:0% +convenience of such faculty which where + + + align:start position:0% +convenience of such faculty which where +they could go and read these documents + + align:start position:0% +they could go and read these documents + + + align:start position:0% +they could go and read these documents +that that are part of what they need to + + align:start position:0% +that that are part of what they need to + + + align:start position:0% +that that are part of what they need to +do + + align:start position:0% +do + + + align:start position:0% +do +and in the end we said no we won't do + + align:start position:0% +and in the end we said no we won't do + + + align:start position:0% +and in the end we said no we won't do +that + + align:start position:0% +that + + + align:start position:0% +that +we just said that you know it's much + + align:start position:0% +we just said that you know it's much + + + align:start position:0% +we just said that you know it's much +much better if we just say there's in + + align:start position:0% +much better if we just say there's in + + + align:start position:0% +much better if we just say there's in +fact we got that particular um + + align:start position:0% +fact we got that particular um + + + align:start position:0% +fact we got that particular um +advice from ernie moniz ernie + + align:start position:0% +advice from ernie moniz ernie + + + align:start position:0% +advice from ernie moniz ernie +was well he's a major figure around here + + align:start position:0% +was well he's a major figure around here + + + align:start position:0% +was well he's a major figure around here +but he was head of the physics + + align:start position:0% +but he was head of the physics + + + align:start position:0% +but he was head of the physics +department he was under secretary in the + + align:start position:0% +department he was under secretary in the + + + align:start position:0% +department he was under secretary in the +department of energy + + align:start position:0% +department of energy + + + align:start position:0% +department of energy +physicists um + + align:start position:0% +physicists um + + + align:start position:0% +physicists um +they they work a lot with classified + + align:start position:0% +they they work a lot with classified + + + align:start position:0% +they they work a lot with classified +mature because of the nuclear + + align:start position:0% +mature because of the nuclear + + + align:start position:0% +mature because of the nuclear +issue and so he'd been very close to + + align:start position:0% +issue and so he'd been very close to + + + align:start position:0% +issue and so he'd been very close to +that and and he just he said you know + + align:start position:0% +that and and he just he said you know + + + align:start position:0% +that and and he just he said you know +really don't do it + + align:start position:0% +really don't do it + + + align:start position:0% +really don't do it +so + + align:start position:0% +so + + + align:start position:0% +so +i think you know if if mit faculty and + + align:start position:0% +i think you know if if mit faculty and + + + align:start position:0% +i think you know if if mit faculty and +and you know when you're serving in a + + align:start position:0% +and you know when you're serving in a + + + align:start position:0% +and you know when you're serving in a +situation like that you need to review + + align:start position:0% +situation like that you need to review + + + align:start position:0% +situation like that you need to review +materials + + align:start position:0% +materials + + + align:start position:0% +materials +so i typically go out to hand scope + + align:start position:0% +so i typically go out to hand scope + + + align:start position:0% +so i typically go out to hand scope +when i have to review materials and i + + align:start position:0% +when i have to review materials and i + + + align:start position:0% +when i have to review materials and i +can get access to a classified web out + + align:start position:0% +can get access to a classified web out + + + align:start position:0% +can get access to a classified web out +there and do it there's also draper lab + + align:start position:0% +there and do it there's also draper lab + + + align:start position:0% +there and do it there's also draper lab +we have a kind of a relationship with + + align:start position:0% +we have a kind of a relationship with + + + align:start position:0% +we have a kind of a relationship with +draper lab and so if an mit faculty + + align:start position:0% +draper lab and so if an mit faculty + + + align:start position:0% +draper lab and so if an mit faculty +member was serving on a government + + align:start position:0% +member was serving on a government + + + align:start position:0% +member was serving on a government +advisory panel and needed + + align:start position:0% +advisory panel and needed + + + align:start position:0% +advisory panel and needed +to be able to read a report and make + + align:start position:0% +to be able to read a report and make + + + align:start position:0% +to be able to read a report and make +comments on it and stuff like that they + + align:start position:0% +comments on it and stuff like that they + + + align:start position:0% +comments on it and stuff like that they +could conceivably do that at draper + + align:start position:0% +could conceivably do that at draper + + + align:start position:0% +could conceivably do that at draper +lincoln is a great facility + + align:start position:0% +lincoln is a great facility + + + align:start position:0% +lincoln is a great facility +so there's lots of possibilities but we + + align:start position:0% +so there's lots of possibilities but we + + + align:start position:0% +so there's lots of possibilities but we +do not have classified material + + align:start position:0% +do not have classified material + + + align:start position:0% +do not have classified material +during the vietnam unrest when that + + align:start position:0% +during the vietnam unrest when that + + + align:start position:0% +during the vietnam unrest when that +decision was made was it because of the + + align:start position:0% +decision was made was it because of the + + + align:start position:0% +decision was made was it because of the +desire to to enable every student to + + align:start position:0% +desire to to enable every student to + + + align:start position:0% +desire to to enable every student to +access everything you know it's really + + align:start position:0% +access everything you know it's really + + + align:start position:0% +access everything you know it's really +hard for me to remember i was a young + + align:start position:0% +hard for me to remember i was a young + + + align:start position:0% +hard for me to remember i was a young +faculty member at that time and you know + + align:start position:0% +faculty member at that time and you know + + + align:start position:0% +faculty member at that time and you know +there was just so much turmoil involved + + align:start position:0% + + + + align:start position:0% + +i think it was more a matter of + + align:start position:0% +i think it was more a matter of + + + align:start position:0% +i think it was more a matter of +principle + + align:start position:0% +principle + + + align:start position:0% +principle +you know obviously if you had a little + + align:start position:0% +you know obviously if you had a little + + + align:start position:0% +you know obviously if you had a little +room somewhere that doesn't really + + align:start position:0% +room somewhere that doesn't really + + + align:start position:0% +room somewhere that doesn't really +interfere with the right of students + + align:start position:0% +interfere with the right of students + + + align:start position:0% +interfere with the right of students +yeah you know i mean that's you know a + + align:start position:0% +yeah you know i mean that's you know a + + + align:start position:0% +yeah you know i mean that's you know a +little room in the basement that and + + align:start position:0% +little room in the basement that and + + + align:start position:0% +little room in the basement that and +that from a pragmatic point of view + + align:start position:0% +that from a pragmatic point of view + + + align:start position:0% +that from a pragmatic point of view +would be okay i think it was a matter of + + align:start position:0% +would be okay i think it was a matter of + + + align:start position:0% +would be okay i think it was a matter of +principle i just i just think that mit + + align:start position:0% +principle i just i just think that mit + + + align:start position:0% +principle i just i just think that mit +at that point uh divested draper and + + align:start position:0% +at that point uh divested draper and + + + align:start position:0% +at that point uh divested draper and +i think we just made the decision i mean + + align:start position:0% +i think we just made the decision i mean + + + align:start position:0% +i think we just made the decision i mean +for example uh + + align:start position:0% +for example uh + + + align:start position:0% +for example uh +there can be no classified student + + align:start position:0% +there can be no classified student + + + align:start position:0% +there can be no classified student +theses + + align:start position:0% +theses + + + align:start position:0% +theses +uh now + + align:start position:0% +uh now + + + align:start position:0% +uh now +the people at draper we have a lot of + + align:start position:0% +the people at draper we have a lot of + + + align:start position:0% +the people at draper we have a lot of +air force officers at draper they have + + align:start position:0% +air force officers at draper they have + + + align:start position:0% +air force officers at draper they have +access to classified material uh they're + + align:start position:0% +access to classified material uh they're + + + align:start position:0% +access to classified material uh they're +probably doing work that involves + + align:start position:0% +probably doing work that involves + + + align:start position:0% +probably doing work that involves +classified but when they get around to + + align:start position:0% +classified but when they get around to + + + align:start position:0% +classified but when they get around to +writing their thesis + + align:start position:0% +writing their thesis + + + align:start position:0% +writing their thesis +their thesis is a public document + + align:start position:0% +their thesis is a public document + + + align:start position:0% +their thesis is a public document +the thesis committee does not need + + align:start position:0% +the thesis committee does not need + + + align:start position:0% +the thesis committee does not need +classification to serve + + align:start position:0% +classification to serve + + + align:start position:0% +classification to serve +on a thesis committee so you know we + + align:start position:0% +on a thesis committee so you know we + + + align:start position:0% +on a thesis committee so you know we +really do maintain + + align:start position:0% +really do maintain + + + align:start position:0% +really do maintain +a kind of a + + align:start position:0% +a kind of a + + + align:start position:0% +a kind of a +totally open educational campus program + + align:start position:0% +totally open educational campus program + + + align:start position:0% +totally open educational campus program +that's kind of how we emerged and i + + align:start position:0% +that's kind of how we emerged and i + + + align:start position:0% +that's kind of how we emerged and i +remember when i was a graduate student + + align:start position:0% +remember when i was a graduate student + + + align:start position:0% +remember when i was a graduate student +we had block file cabinets and + + align:start position:0% +we had block file cabinets and + + + align:start position:0% +we had block file cabinets and +you know i can hardly remember i think i + + align:start position:0% +you know i can hardly remember i think i + + + align:start position:0% +you know i can hardly remember i think i +had a confidential clearance it's all + + align:start position:0% +had a confidential clearance it's all + + + align:start position:0% +had a confidential clearance it's all +very fuzzy it means very little + + align:start position:0% +very fuzzy it means very little + + + align:start position:0% +very fuzzy it means very little +confidential is i don't even know if + + align:start position:0% +confidential is i don't even know if + + + align:start position:0% +confidential is i don't even know if +anybody uses it anymore it's a fairly + + align:start position:0% +anybody uses it anymore it's a fairly + + + align:start position:0% +anybody uses it anymore it's a fairly +low level + + align:start position:0% +low level + + + align:start position:0% +low level +of + + align:start position:0% +of + + + align:start position:0% +of +security clearance but um + + align:start position:0% +security clearance but um + + + align:start position:0% +security clearance but um +when you know when i got my last + + align:start position:0% +when you know when i got my last + + + align:start position:0% +when you know when i got my last +security clearance i asked him what what + + align:start position:0% +security clearance i asked him what what + + + align:start position:0% +security clearance i asked him what what +level is this and they say we can't tell + + align:start position:0% +level is this and they say we can't tell + + + align:start position:0% +level is this and they say we can't tell +you + + align:start position:0% + + + + align:start position:0% + +yeah i have a question you talked about + + align:start position:0% +yeah i have a question you talked about + + + align:start position:0% +yeah i have a question you talked about +personal ethics first and i was + + align:start position:0% +personal ethics first and i was + + + align:start position:0% +personal ethics first and i was +wondering + + align:start position:0% +wondering + + + align:start position:0% +wondering +if at any point in your + + align:start position:0% +if at any point in your + + + align:start position:0% +if at any point in your +academic or government career you sort + + align:start position:0% +academic or government career you sort + + + align:start position:0% +academic or government career you sort +of came up to a situation where + + align:start position:0% +of came up to a situation where + + + align:start position:0% +of came up to a situation where +your personal ethics were really + + align:start position:0% +your personal ethics were really + + + align:start position:0% +your personal ethics were really +challenged + + align:start position:0% +challenged + + + align:start position:0% +challenged +maybe there was a mismatch between + + align:start position:0% +maybe there was a mismatch between + + + align:start position:0% +maybe there was a mismatch between +the institution you were affiliated + + align:start position:0% + + + + align:start position:0% + +no i mean i don't don't mean to sound + + align:start position:0% +no i mean i don't don't mean to sound + + + align:start position:0% +no i mean i don't don't mean to sound +pollyannish but i actually can't + + align:start position:0% +pollyannish but i actually can't + + + align:start position:0% +pollyannish but i actually can't +remember a situation that really + + align:start position:0% +remember a situation that really + + + align:start position:0% +remember a situation that really +it's probably those nuns + + align:start position:0% +it's probably those nuns + + + align:start position:0% +it's probably those nuns +they raised me + + align:start position:0% + + + + align:start position:0% + +i see sister albertine standing behind + + align:start position:0% +i see sister albertine standing behind + + + align:start position:0% +i see sister albertine standing behind +me every time i get in a tight situation + + align:start position:0% +me every time i get in a tight situation + + + align:start position:0% +me every time i get in a tight situation +no i mean i you know again because i + + align:start position:0% +no i mean i you know again because i + + + align:start position:0% +no i mean i you know again because i +think because i think the um + + align:start position:0% +think because i think the um + + + align:start position:0% +think because i think the um +the value structure is very pragmatic + + align:start position:0% +the value structure is very pragmatic + + + align:start position:0% +the value structure is very pragmatic +you know and i'm a pragmatic person i've + + align:start position:0% +you know and i'm a pragmatic person i've + + + align:start position:0% +you know and i'm a pragmatic person i've +simply seen too many examples of the + + align:start position:0% +simply seen too many examples of the + + + align:start position:0% +simply seen too many examples of the +slippery slope + + align:start position:0% +slippery slope + + + align:start position:0% +slippery slope +um the big explosion + + align:start position:0% +um the big explosion + + + align:start position:0% +um the big explosion +you know + + align:start position:0% +you know + + + align:start position:0% +you know +the penalty for + + align:start position:0% +the penalty for + + + align:start position:0% +the penalty for +um for letting up in some sense + + align:start position:0% +um for letting up in some sense + + + align:start position:0% +um for letting up in some sense +issue so i you know i can't really + + align:start position:0% +issue so i you know i can't really + + + align:start position:0% +issue so i you know i can't really +remember + + align:start position:0% +remember + + + align:start position:0% +remember +a situation + + align:start position:0% +a situation + + + align:start position:0% +a situation +that that would have been + + align:start position:0% +that that would have been + + + align:start position:0% +that that would have been +stark i don't think i'm dodging + + align:start position:0% + + + + align:start position:0% + +i don't maybe i can make the comment + + align:start position:0% +i don't maybe i can make the comment + + + align:start position:0% +i don't maybe i can make the comment +that i + + align:start position:0% +that i + + + align:start position:0% +that i +think about organization + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +based on what you said do you think that + + align:start position:0% +based on what you said do you think that + + + align:start position:0% +based on what you said do you think that +maybe that speaks to the importance of + + align:start position:0% +maybe that speaks to the importance of + + + align:start position:0% +maybe that speaks to the importance of +being affiliated or + + align:start position:0% +being affiliated or + + + align:start position:0% +being affiliated or +becoming involved with organizations + + align:start position:0% +becoming involved with organizations + + + align:start position:0% +becoming involved with organizations +since maybe cultures kind of match yours + + align:start position:0% +since maybe cultures kind of match yours + + + align:start position:0% +since maybe cultures kind of match yours +because i think in + + align:start position:0% +because i think in + + + align:start position:0% +because i think in +your case + + align:start position:0% + + + + align:start position:0% + +yeah no i think it's extremely important + + align:start position:0% +yeah no i think it's extremely important + + + align:start position:0% +yeah no i think it's extremely important +i'm actually glad you raised the issue + + align:start position:0% +i'm actually glad you raised the issue + + + align:start position:0% +i'm actually glad you raised the issue +um + + align:start position:0% +um + + + align:start position:0% +um +you know you + + align:start position:0% +you know you + + + align:start position:0% +you know you +will all be faced with the issue of + + align:start position:0% +will all be faced with the issue of + + + align:start position:0% +will all be faced with the issue of +deciding what organizations to be a part + + align:start position:0% +deciding what organizations to be a part + + + align:start position:0% +deciding what organizations to be a part +of + + align:start position:0% +of + + + align:start position:0% +of +you know if you leave here go out and + + align:start position:0% +you know if you leave here go out and + + + align:start position:0% +you know if you leave here go out and +get a job you know join + + align:start position:0% +get a job you know join + + + align:start position:0% +get a job you know join +some other organization how do you make + + align:start position:0% +some other organization how do you make + + + align:start position:0% +some other organization how do you make +that choice what do you need to know + + align:start position:0% +that choice what do you need to know + + + align:start position:0% +that choice what do you need to know +about an organization + + align:start position:0% +about an organization + + + align:start position:0% +about an organization +when you see something within that other + + align:start position:0% +when you see something within that other + + + align:start position:0% +when you see something within that other +organization that gives you concern + + align:start position:0% +organization that gives you concern + + + align:start position:0% +organization that gives you concern +does the organization support your + + align:start position:0% +does the organization support your + + + align:start position:0% +does the organization support your +concern + + align:start position:0% +concern + + + align:start position:0% +concern +and you know i doubt very much that + + align:start position:0% +and you know i doubt very much that + + + align:start position:0% +and you know i doubt very much that +people + + align:start position:0% +people + + + align:start position:0% +people +think about those things you know as + + align:start position:0% +think about those things you know as + + + align:start position:0% +think about those things you know as +they're thinking about organizations + + align:start position:0% +they're thinking about organizations + + + align:start position:0% +they're thinking about organizations +but you know organizations are very + + align:start position:0% +but you know organizations are very + + + align:start position:0% +but you know organizations are very +complicated things you know for example + + align:start position:0% +complicated things you know for example + + + align:start position:0% +complicated things you know for example +i + + align:start position:0% +i + + + align:start position:0% +i +i consider myself a real fan boeing + + align:start position:0% +i consider myself a real fan boeing + + + align:start position:0% +i consider myself a real fan boeing +you know i worked for them when i was + + align:start position:0% +you know i worked for them when i was + + + align:start position:0% +you know i worked for them when i was +undergraduate + + align:start position:0% +undergraduate + + + align:start position:0% +undergraduate +in seattle + + align:start position:0% +in seattle + + + align:start position:0% +in seattle +and and every time one of these things + + align:start position:0% +and and every time one of these things + + + align:start position:0% +and and every time one of these things +comes up i feel like a dagger is going + + align:start position:0% +comes up i feel like a dagger is going + + + align:start position:0% +comes up i feel like a dagger is going +into my heart + + align:start position:0% +into my heart + + + align:start position:0% +into my heart +because these complexities + + align:start position:0% +because these complexities + + + align:start position:0% +because these complexities +i don't believe are representative of + + align:start position:0% +i don't believe are representative of + + + align:start position:0% +i don't believe are representative of +the entire company + + align:start position:0% + + + + align:start position:0% + +but they have a devastating effect + + align:start position:0% +but they have a devastating effect + + + align:start position:0% +but they have a devastating effect +on on the company on its + + align:start position:0% +on on the company on its + + + align:start position:0% +on on the company on its +uh business line its profits its its + + align:start position:0% +uh business line its profits its its + + + align:start position:0% +uh business line its profits its its +image + + align:start position:0% +image + + + align:start position:0% +image +and i just you know i say oh god there + + align:start position:0% +and i just you know i say oh god there + + + align:start position:0% +and i just you know i say oh god there +they go again you know something got + + align:start position:0% +they go again you know something got + + + align:start position:0% +they go again you know something got +away + + align:start position:0% +away + + + align:start position:0% +away +from them um + + align:start position:0% +from them um + + + align:start position:0% +from them um +so + + align:start position:0% +so + + + align:start position:0% +so +you know i still believe um that they + + align:start position:0% +you know i still believe um that they + + + align:start position:0% +you know i still believe um that they +are a great company and i just + + align:start position:0% +are a great company and i just + + + align:start position:0% +are a great company and i just +i anguish every time + + align:start position:0% +i anguish every time + + + align:start position:0% +i anguish every time +you know i see one of these things so i + + align:start position:0% +you know i see one of these things so i + + + align:start position:0% +you know i see one of these things so i +don't think + + align:start position:0% +don't think + + + align:start position:0% +don't think +i think in order to understand a company + + align:start position:0% +i think in order to understand a company + + + align:start position:0% +i think in order to understand a company +you have to understand them at you know + + align:start position:0% +you have to understand them at you know + + + align:start position:0% +you have to understand them at you know +the inner layers as opposed to kind of + + align:start position:0% +the inner layers as opposed to kind of + + + align:start position:0% +the inner layers as opposed to kind of +let's see what's in the paper not that + + align:start position:0% +let's see what's in the paper not that + + + align:start position:0% +let's see what's in the paper not that +that's any easier + + align:start position:0% + + + + align:start position:0% + +and and i think i think any company + + align:start position:0% +and and i think i think any company + + + align:start position:0% +and and i think i think any company +needs + + align:start position:0% +needs + + + align:start position:0% +needs +people who are able to contribute in a + + align:start position:0% +people who are able to contribute in a + + + align:start position:0% +people who are able to contribute in a +positive way to the uh to the culture + + align:start position:0% + + + + align:start position:0% + +his background to some of this + + align:start position:0% +his background to some of this + + + align:start position:0% +his background to some of this +discussion + + align:start position:0% +discussion + + + align:start position:0% +discussion +i had told stoops at uh back in the + + align:start position:0% +i had told stoops at uh back in the + + + align:start position:0% +i had told stoops at uh back in the +early 70s + + align:start position:0% +early 70s + + + align:start position:0% +early 70s +when engineering ethnics was forming + + align:start position:0% +when engineering ethnics was forming + + + align:start position:0% +when engineering ethnics was forming +itself as a field + + align:start position:0% + + + + align:start position:0% + +one of the great hopes of all the + + align:start position:0% +one of the great hopes of all the + + + align:start position:0% +one of the great hopes of all the +philosophers + + align:start position:0% + + + + align:start position:0% + +was that they would get their names + + align:start position:0% +was that they would get their names + + + align:start position:0% +was that they would get their names +written up with aristotle and plato by + + align:start position:0% +written up with aristotle and plato by + + + align:start position:0% +written up with aristotle and plato by +discovering a new ethic + + align:start position:0% + + + + align:start position:0% + +and one of their specific hopes in those + + align:start position:0% +and one of their specific hopes in those + + + align:start position:0% +and one of their specific hopes in those +days + + align:start position:0% +days + + + align:start position:0% +days +was to break away from the reconditioned + + align:start position:0% +was to break away from the reconditioned + + + align:start position:0% +was to break away from the reconditioned +tradition + + align:start position:0% +tradition + + + align:start position:0% +tradition +that holds that only uh + + align:start position:0% +that holds that only uh + + + align:start position:0% +that holds that only uh +only an individual can be a moral agent + + align:start position:0% +only an individual can be a moral agent + + + align:start position:0% +only an individual can be a moral agent +and the hope was that the ethicist would + + align:start position:0% +and the hope was that the ethicist would + + + align:start position:0% +and the hope was that the ethicist would +be able to do like the lawyers where a + + align:start position:0% +be able to do like the lawyers where a + + + align:start position:0% +be able to do like the lawyers where a +corporation is has personhood + + align:start position:0% +corporation is has personhood + + + align:start position:0% +corporation is has personhood +in law + + align:start position:0% +in law + + + align:start position:0% +in law +can commit a crime + + align:start position:0% +can commit a crime + + + align:start position:0% +can commit a crime +independently + + align:start position:0% +independently + + + align:start position:0% +independently +they wanted to see if they could come up + + align:start position:0% +they wanted to see if they could come up + + + align:start position:0% +they wanted to see if they could come up +with an ethic where a corporation could + + align:start position:0% +with an ethic where a corporation could + + + align:start position:0% +with an ethic where a corporation could +be ethical + + align:start position:0% +be ethical + + + align:start position:0% +be ethical +and then + + align:start position:0% +and then + + + align:start position:0% +and then +the um + + align:start position:0% +the um + + + align:start position:0% +the um +with the uh colombia + + align:start position:0% +with the uh colombia + + + align:start position:0% +with the uh colombia +there was this big conclusion coming out + + align:start position:0% +there was this big conclusion coming out + + + align:start position:0% +there was this big conclusion coming out +that there was something that had + + align:start position:0% +that there was something that had + + + align:start position:0% +that there was something that had +to be + + align:start position:0% +to be + + + align:start position:0% +to be +that particular organization yes yes + + align:start position:0% +that particular organization yes yes + + + align:start position:0% +that particular organization yes yes +and then we uh uh + + align:start position:0% +and then we uh uh + + + align:start position:0% +and then we uh uh +are saying the same thing about enron + + align:start position:0% +are saying the same thing about enron + + + align:start position:0% +are saying the same thing about enron +yeah it wasn't just a couple of them bad + + align:start position:0% +yeah it wasn't just a couple of them bad + + + align:start position:0% +yeah it wasn't just a couple of them bad +people no yeah + + align:start position:0% +people no yeah + + + align:start position:0% +people no yeah +something that something right when all + + align:start position:0% +something that something right when all + + + align:start position:0% +something that something right when all +through the culture yeah + + align:start position:0% +through the culture yeah + + + align:start position:0% +through the culture yeah +so um + + align:start position:0% +so um + + + align:start position:0% +so um +i'm thinking that there's this + + align:start position:0% +i'm thinking that there's this + + + align:start position:0% +i'm thinking that there's this +unavoidable + + align:start position:0% +unavoidable + + + align:start position:0% +unavoidable +uh inclination for leaders + + align:start position:0% +uh inclination for leaders + + + align:start position:0% +uh inclination for leaders +talking about people who are in + + align:start position:0% +talking about people who are in + + + align:start position:0% +talking about people who are in +positions that you have + + align:start position:0% +positions that you have + + + align:start position:0% +positions that you have +occupied and have these experiences + + align:start position:0% +occupied and have these experiences + + + align:start position:0% +occupied and have these experiences +there's something that's unavoidable + + align:start position:0% +there's something that's unavoidable + + + align:start position:0% +there's something that's unavoidable +inescapable to think about the + + align:start position:0% +inescapable to think about the + + + align:start position:0% +inescapable to think about the +culture + + align:start position:0% +culture + + + align:start position:0% +culture +as + + align:start position:0% +as + + + align:start position:0% +as +being good or bad + + align:start position:0% +being good or bad + + + align:start position:0% +being good or bad +and the organization being a moral agent + + align:start position:0% +and the organization being a moral agent + + + align:start position:0% +and the organization being a moral agent +no matter what the philosopher's + + align:start position:0% +no matter what the philosopher's + + + align:start position:0% +no matter what the philosopher's +is there something how do you + + align:start position:0% +is there something how do you + + + align:start position:0% +is there something how do you +think about + + align:start position:0% +think about + + + align:start position:0% +think about +an organization in terms of being good + + align:start position:0% +an organization in terms of being good + + + align:start position:0% +an organization in terms of being good +or bad and if you judge it to be bad in + + align:start position:0% +or bad and if you judge it to be bad in + + + align:start position:0% +or bad and if you judge it to be bad in +some sort of way how do you go about + + align:start position:0% +some sort of way how do you go about + + + align:start position:0% +some sort of way how do you go about +correcting it yeah and and of course + + align:start position:0% +correcting it yeah and and of course + + + align:start position:0% +correcting it yeah and and of course +we've already talked about how we can + + align:start position:0% +we've already talked about how we can + + + align:start position:0% +we've already talked about how we can +deal with codes + + align:start position:0% +deal with codes + + + align:start position:0% +deal with codes +of conduct + + align:start position:0% +of conduct + + + align:start position:0% +of conduct +well yeah i guess + + align:start position:0% +well yeah i guess + + + align:start position:0% +well yeah i guess +well i guess i do believe + + align:start position:0% +well i guess i do believe + + + align:start position:0% +well i guess i do believe +um + + align:start position:0% +um + + + align:start position:0% +um +that there are organizations + + align:start position:0% +that there are organizations + + + align:start position:0% +that there are organizations +that are good + + align:start position:0% +that are good + + + align:start position:0% +that are good +and not so good + + align:start position:0% +and not so good + + + align:start position:0% +and not so good +and you know for me + + align:start position:0% +and you know for me + + + align:start position:0% +and you know for me +i i guess i look at it primarily as an + + align:start position:0% +i i guess i look at it primarily as an + + + align:start position:0% +i i guess i look at it primarily as an +issue of leadership + + align:start position:0% +issue of leadership + + + align:start position:0% +issue of leadership +and i'm and i mean + + align:start position:0% +and i'm and i mean + + + align:start position:0% +and i'm and i mean +leadership active leadership + + align:start position:0% +leadership active leadership + + + align:start position:0% +leadership active leadership +i don't mean people who just talk a good + + align:start position:0% +i don't mean people who just talk a good + + + align:start position:0% +i don't mean people who just talk a good +game i mean really active leadership and + + align:start position:0% +game i mean really active leadership and + + + align:start position:0% +game i mean really active leadership and +i would have to say that i believe mit + + align:start position:0% +i would have to say that i believe mit + + + align:start position:0% +i would have to say that i believe mit +is a good organization + + align:start position:0% +is a good organization + + + align:start position:0% +is a good organization +i mean i've been + + align:start position:0% +i mean i've been + + + align:start position:0% +i mean i've been +involved with mit + + align:start position:0% +involved with mit + + + align:start position:0% +involved with mit +for a very long time since 56 when i + + align:start position:0% +for a very long time since 56 when i + + + align:start position:0% +for a very long time since 56 when i +came as a freshman + + align:start position:0% +came as a freshman + + + align:start position:0% +came as a freshman +but + + align:start position:0% +but + + + align:start position:0% +but +the typical pattern of mit + + align:start position:0% +the typical pattern of mit + + + align:start position:0% +the typical pattern of mit +is to get in early + + align:start position:0% +is to get in early + + + align:start position:0% +is to get in early +and do the right thing + + align:start position:0% +and do the right thing + + + align:start position:0% +and do the right thing +and i could just think of so many + + align:start position:0% +and i could just think of so many + + + align:start position:0% +and i could just think of so many +examples of that um + + align:start position:0% +examples of that um + + + align:start position:0% +examples of that um +when affirmative action came came in + + align:start position:0% +when affirmative action came came in + + + align:start position:0% +when affirmative action came came in +uh and this was like 72 or 70 and this + + align:start position:0% +uh and this was like 72 or 70 and this + + + align:start position:0% +uh and this was like 72 or 70 and this +was a very long time ago + + align:start position:0% +was a very long time ago + + + align:start position:0% +was a very long time ago +um + + align:start position:0% +um + + + align:start position:0% +um +many universities + + align:start position:0% +many universities + + + align:start position:0% +many universities +gamed it you know they said well we + + align:start position:0% +gamed it you know they said well we + + + align:start position:0% +gamed it you know they said well we +could figure out a way to you know sort + + align:start position:0% +could figure out a way to you know sort + + + align:start position:0% +could figure out a way to you know sort +of deflect this stuff + + align:start position:0% +of deflect this stuff + + + align:start position:0% +of deflect this stuff +and mit said we're going to do it and + + align:start position:0% +and mit said we're going to do it and + + + align:start position:0% +and mit said we're going to do it and +we're going to do it next year + + align:start position:0% +we're going to do it next year + + + align:start position:0% +we're going to do it next year +i mean it couldn't have been different + + align:start position:0% +i mean it couldn't have been different + + + align:start position:0% +i mean it couldn't have been different +it could have been more different + + align:start position:0% +it could have been more different + + + align:start position:0% +it could have been more different +i mean howard happened to be howard + + align:start position:0% +i mean howard happened to be howard + + + align:start position:0% +i mean howard happened to be howard +johnson + + align:start position:0% +johnson + + + align:start position:0% +johnson +basically said you know we're going to + + align:start position:0% +basically said you know we're going to + + + align:start position:0% +basically said you know we're going to +do this + + align:start position:0% +do this + + + align:start position:0% +do this +and and you know we're going to hire + + align:start position:0% +and and you know we're going to hire + + + align:start position:0% +and and you know we're going to hire +women factor with our minority faculty + + align:start position:0% +women factor with our minority faculty + + + align:start position:0% +women factor with our minority faculty +we're going to move on and we're going + + align:start position:0% +we're going to move on and we're going + + + align:start position:0% +we're going to move on and we're going +to do this we're going to make this + + align:start position:0% +to do this we're going to make this + + + align:start position:0% +to do this we're going to make this +happen + + align:start position:0% +happen + + + align:start position:0% +happen +and i i + + align:start position:0% +and i i + + + align:start position:0% +and i i +i just think of so many examples where + + align:start position:0% +i just think of so many examples where + + + align:start position:0% +i just think of so many examples where +that's true + + align:start position:0% +that's true + + + align:start position:0% +that's true +mit was sued by the federal government + + align:start position:0% +mit was sued by the federal government + + + align:start position:0% +mit was sued by the federal government +over the issue of + + align:start position:0% + + + + align:start position:0% + +merit-based statement + + align:start position:0% +merit-based statement + + + align:start position:0% +merit-based statement +i always get this extent that you know + + align:start position:0% +i always get this extent that you know + + + align:start position:0% +i always get this extent that you know +it's the basic issue of + + align:start position:0% +it's the basic issue of + + + align:start position:0% +it's the basic issue of +need-based financial aid + + align:start position:0% +need-based financial aid + + + align:start position:0% +need-based financial aid +all the ivs just kind of + + align:start position:0% +all the ivs just kind of + + + align:start position:0% +all the ivs just kind of +withered away + + align:start position:0% +withered away + + + align:start position:0% +withered away +from the issue leaving us standing all + + align:start position:0% +from the issue leaving us standing all + + + align:start position:0% +from the issue leaving us standing all +by ourselves we won the place + + align:start position:0% +by ourselves we won the place + + + align:start position:0% +by ourselves we won the place +so + + align:start position:0% + + + + align:start position:0% + +and and it's been it's been leadership + + align:start position:0% +and and it's been it's been leadership + + + align:start position:0% +and and it's been it's been leadership +it's been top leadership it's been + + align:start position:0% +it's been top leadership it's been + + + align:start position:0% +it's been top leadership it's been +passed over from leader to leader + + align:start position:0% +passed over from leader to leader + + + align:start position:0% +passed over from leader to leader +there's been howard johnson it's been + + align:start position:0% +there's been howard johnson it's been + + + align:start position:0% +there's been howard johnson it's been +jerry wiesner it's been paul gray it's + + align:start position:0% +jerry wiesner it's been paul gray it's + + + align:start position:0% +jerry wiesner it's been paul gray it's +been chuck fest + + align:start position:0% +been chuck fest + + + align:start position:0% +been chuck fest +and the + + align:start position:0% +and the + + + align:start position:0% +and the +there's been a passover in leadership + + align:start position:0% +there's been a passover in leadership + + + align:start position:0% +there's been a passover in leadership +from + + align:start position:0% +from + + + align:start position:0% +from +from these different leaders and a + + align:start position:0% +from these different leaders and a + + + align:start position:0% +from these different leaders and a +highly visible statement + + align:start position:0% +highly visible statement + + + align:start position:0% +highly visible statement +followed by action mit is a very + + align:start position:0% +followed by action mit is a very + + + align:start position:0% +followed by action mit is a very +action-oriented place + + align:start position:0% +action-oriented place + + + align:start position:0% +action-oriented place +and these guys just don't talk a good + + align:start position:0% +and these guys just don't talk a good + + + align:start position:0% +and these guys just don't talk a good +game they + + align:start position:0% +game they + + + align:start position:0% +game they +put in place + + align:start position:0% +put in place + + + align:start position:0% +put in place +the + + align:start position:0% +the + + + align:start position:0% +the +organizational + + align:start position:0% +organizational + + + align:start position:0% +organizational +culture and and policies and dynamics + + align:start position:0% +culture and and policies and dynamics + + + align:start position:0% +culture and and policies and dynamics +that would actually make + + align:start position:0% +that would actually make + + + align:start position:0% +that would actually make +these things happen so i mean i think + + align:start position:0% +these things happen so i mean i think + + + align:start position:0% +these things happen so i mean i think +you know as i look around + + align:start position:0% +you know as i look around + + + align:start position:0% +you know as i look around +mit i think is a fine example + + align:start position:0% +mit i think is a fine example + + + align:start position:0% +mit i think is a fine example +of an organization probably one of the + + align:start position:0% +of an organization probably one of the + + + align:start position:0% +of an organization probably one of the +best i can think of + + align:start position:0% + + + + align:start position:0% + +and then you know there are other + + align:start position:0% +and then you know there are other + + + align:start position:0% +and then you know there are other +organizations and + + align:start position:0% +organizations and + + + align:start position:0% +organizations and +they and then there's some really bad + + align:start position:0% +they and then there's some really bad + + + align:start position:0% +they and then there's some really bad +ones like + + align:start position:0% +ones like + + + align:start position:0% +ones like +so + + align:start position:0% +so + + + align:start position:0% +so +somehow totally corrupt + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +you know one's in the middle that you + + align:start position:0% +you know one's in the middle that you + + + align:start position:0% +you know one's in the middle that you +know + + align:start position:0% +know + + + align:start position:0% +know +i think are fundamentally good but every + + align:start position:0% +i think are fundamentally good but every + + + align:start position:0% +i think are fundamentally good but every +once in a while individuals who somehow + + align:start position:0% +once in a while individuals who somehow + + + align:start position:0% +once in a while individuals who somehow +haven't gotten the message and that's + + align:start position:0% +haven't gotten the message and that's + + + align:start position:0% +haven't gotten the message and that's +responsibility of leadership + + align:start position:0% +responsibility of leadership + + + align:start position:0% +responsibility of leadership +is to just to get that message out and + + align:start position:0% +is to just to get that message out and + + + align:start position:0% +is to just to get that message out and +if leadership doesn't do it well shame + + align:start position:0% +if leadership doesn't do it well shame + + + align:start position:0% +if leadership doesn't do it well shame +on them i mean it's their responsibility + + align:start position:0% +on them i mean it's their responsibility + + + align:start position:0% +on them i mean it's their responsibility +to + + align:start position:0% +to + + + align:start position:0% +to +i think the air force is a very good + + align:start position:0% +i think the air force is a very good + + + align:start position:0% +i think the air force is a very good +organization + + align:start position:0% +organization + + + align:start position:0% +organization +um + + align:start position:0% +um + + + align:start position:0% +um +i didn't have i mean obviously we had + + align:start position:0% +i didn't have i mean obviously we had + + + align:start position:0% +i didn't have i mean obviously we had +challenges + + align:start position:0% +challenges + + + align:start position:0% +challenges +big challenges but + + align:start position:0% +big challenges but + + + align:start position:0% +big challenges but +uh the organization responds to + + align:start position:0% +uh the organization responds to + + + align:start position:0% +uh the organization responds to +leadership it is a leadership org it's a + + align:start position:0% +leadership it is a leadership org it's a + + + align:start position:0% +leadership it is a leadership org it's a +leadership focused organization within + + align:start position:0% +leadership focused organization within + + + align:start position:0% +leadership focused organization within +good civic core values so + + align:start position:0% +good civic core values so + + + align:start position:0% +good civic core values so +those are the tools + + align:start position:0% +those are the tools + + + align:start position:0% +those are the tools +that you use + + align:start position:0% +that you use + + + align:start position:0% +that you use +in order to motivate people to + + align:start position:0% +in order to motivate people to + + + align:start position:0% +in order to motivate people to +you know aim high that's basically what + + align:start position:0% +you know aim high that's basically what + + + align:start position:0% +you know aim high that's basically what +would say is aim high + + align:start position:0% +would say is aim high + + + align:start position:0% +would say is aim high +so no i agree with you that + + align:start position:0% +so no i agree with you that + + + align:start position:0% +so no i agree with you that +organizational ethics is an extremely + + align:start position:0% +organizational ethics is an extremely + + + align:start position:0% +organizational ethics is an extremely +important + + align:start position:0% +important + + + align:start position:0% +important +issue + + align:start position:0% + + + + align:start position:0% + +and i think that's + + align:start position:0% +and i think that's + + + align:start position:0% +and i think that's +you know i would have maybe not called + + align:start position:0% +you know i would have maybe not called + + + align:start position:0% +you know i would have maybe not called +the nasa thing organizational ethics but + + align:start position:0% +the nasa thing organizational ethics but + + + align:start position:0% +the nasa thing organizational ethics but +the fact matter is it is + + align:start position:0% +the fact matter is it is + + + align:start position:0% +the fact matter is it is +because nasa's responsibility is + + align:start position:0% +because nasa's responsibility is + + + align:start position:0% +because nasa's responsibility is +is to spend the nation's resources + + align:start position:0% +is to spend the nation's resources + + + align:start position:0% +is to spend the nation's resources +wisely + + align:start position:0% +wisely + + + align:start position:0% +wisely +and to protect the people that they're + + align:start position:0% +and to protect the people that they're + + + align:start position:0% +and to protect the people that they're +involved in human spaceflight and those + + align:start position:0% +involved in human spaceflight and those + + + align:start position:0% +involved in human spaceflight and those +are those are high ethical responses + + align:start position:0% + + + + align:start position:0% + +that brings up um something that's been + + align:start position:0% +that brings up um something that's been + + + align:start position:0% +that brings up um something that's been +challenging for me in this class which + + align:start position:0% +challenging for me in this class which + + + align:start position:0% +challenging for me in this class which +is the tension between + + align:start position:0% +is the tension between + + + align:start position:0% +is the tension between +when you're when you're considering an + + align:start position:0% +when you're when you're considering an + + + align:start position:0% +when you're when you're considering an +organization or a company the tension + + align:start position:0% +organization or a company the tension + + + align:start position:0% +organization or a company the tension +between the bottom line + + align:start position:0% +between the bottom line + + + align:start position:0% +between the bottom line +the needs is to stay on the ground + + align:start position:0% +the needs is to stay on the ground + + + align:start position:0% +the needs is to stay on the ground +financially and the well-being + + align:start position:0% +financially and the well-being + + + align:start position:0% +financially and the well-being +so i guess there's three things + + align:start position:0% +so i guess there's three things + + + align:start position:0% +so i guess there's three things +finances the well-being of employees and + + align:start position:0% +finances the well-being of employees and + + + align:start position:0% +finances the well-being of employees and +the well-being of the public being + + align:start position:0% +the well-being of the public being + + + align:start position:0% +the well-being of the public being +served + + align:start position:0% +served + + + align:start position:0% +served +i i wonder what + + align:start position:0% + + + + align:start position:0% + +challenges you face in managing that + + align:start position:0% +challenges you face in managing that + + + align:start position:0% +challenges you face in managing that +tension + + align:start position:0% +tension + + + align:start position:0% +tension +how you approach well of course most of + + align:start position:0% +how you approach well of course most of + + + align:start position:0% +how you approach well of course most of +the + + align:start position:0% +the + + + align:start position:0% +the +well i guess no + + align:start position:0% +well i guess no + + + align:start position:0% +well i guess no +i can see organizations i've been + + align:start position:0% +i can see organizations i've been + + + align:start position:0% +i can see organizations i've been +involved in you know really do worry + + align:start position:0% +involved in you know really do worry + + + align:start position:0% +involved in you know really do worry +about the bottom line i mean even though + + align:start position:0% +about the bottom line i mean even though + + + align:start position:0% +about the bottom line i mean even though +we we get money from the taxpayers in + + align:start position:0% +we we get money from the taxpayers in + + + align:start position:0% +we we get money from the taxpayers in +one form or another the fact of the + + align:start position:0% +one form or another the fact of the + + + align:start position:0% +one form or another the fact of the +matter is that you spend most of your + + align:start position:0% +matter is that you spend most of your + + + align:start position:0% +matter is that you spend most of your +time a leader will spend most of their + + align:start position:0% +time a leader will spend most of their + + + align:start position:0% +time a leader will spend most of their +time arguing for resources + + align:start position:0% +time arguing for resources + + + align:start position:0% +time arguing for resources +that's basically what you have to do + + align:start position:0% + + + + align:start position:0% + +but in + + align:start position:0% +but in + + + align:start position:0% +but in +in both of the organizations that i've + + align:start position:0% +in both of the organizations that i've + + + align:start position:0% +in both of the organizations that i've +been involved in + + align:start position:0% + + + + align:start position:0% + +there is no benefit and considerable + + align:start position:0% +there is no benefit and considerable + + + align:start position:0% +there is no benefit and considerable +risk + + align:start position:0% +risk + + + align:start position:0% +risk +for what i would call taking the side + + align:start position:0% +for what i would call taking the side + + + align:start position:0% +for what i would call taking the side +door i mean if you just look at the + + align:start position:0% +door i mean if you just look at the + + + align:start position:0% +door i mean if you just look at the +things that have been going on in + + align:start position:0% +things that have been going on in + + + align:start position:0% +things that have been going on in +washington with lobbyists + + align:start position:0% + + + + align:start position:0% + +there is no benefit say to an + + align:start position:0% +there is no benefit say to an + + + align:start position:0% +there is no benefit say to an +institution like mit or the air force + + align:start position:0% +institution like mit or the air force + + + align:start position:0% +institution like mit or the air force +ever trying + + align:start position:0% +ever trying + + + align:start position:0% +ever trying +that kind + + align:start position:0% +that kind + + + align:start position:0% +that kind +the + + align:start position:0% +the + + + align:start position:0% +the +costs of doing that are extraordinary + + align:start position:0% +costs of doing that are extraordinary + + + align:start position:0% +costs of doing that are extraordinary +so + + align:start position:0% + + + + align:start position:0% + +so in that kind of organization where + + align:start position:0% +so in that kind of organization where + + + align:start position:0% +so in that kind of organization where +where you do in fact spend most of your + + align:start position:0% +where you do in fact spend most of your + + + align:start position:0% +where you do in fact spend most of your +time + + align:start position:0% +time + + + align:start position:0% +time +arguing for resources + + align:start position:0% + + + + align:start position:0% + +you will be most successful if you argue + + align:start position:0% +you will be most successful if you argue + + + align:start position:0% +you will be most successful if you argue +for resources from a high plain + + align:start position:0% +for resources from a high plain + + + align:start position:0% +for resources from a high plain +i mean you know mit is always looking + + align:start position:0% +i mean you know mit is always looking + + + align:start position:0% +i mean you know mit is always looking +for resources it looks from alumni it + + align:start position:0% +for resources it looks from alumni it + + + align:start position:0% +for resources it looks from alumni it +looks from corporations + + align:start position:0% +looks from corporations + + + align:start position:0% +looks from corporations +friends benefactors + + align:start position:0% +friends benefactors + + + align:start position:0% +friends benefactors +but the story + + align:start position:0% +but the story + + + align:start position:0% +but the story +is a consistent story + + align:start position:0% +is a consistent story + + + align:start position:0% +is a consistent story +of excellence in public service + + align:start position:0% +of excellence in public service + + + align:start position:0% +of excellence in public service +and that's about all you can do + + align:start position:0% +and that's about all you can do + + + align:start position:0% +and that's about all you can do +that's about all you can do + + align:start position:0% +that's about all you can do + + + align:start position:0% +that's about all you can do +to to depart from that i think is + + align:start position:0% +to to depart from that i think is + + + align:start position:0% +to to depart from that i think is +is sort of self-defeating + + align:start position:0% +is sort of self-defeating + + + align:start position:0% +is sort of self-defeating +because that begins + + align:start position:0% +because that begins + + + align:start position:0% +because that begins +uh you know it slippery slope + + align:start position:0% +uh you know it slippery slope + + + align:start position:0% +uh you know it slippery slope +anybody's ever able to point to an + + align:start position:0% +anybody's ever able to point to an + + + align:start position:0% +anybody's ever able to point to an +organization like mit or like the air + + align:start position:0% +organization like mit or like the air + + + align:start position:0% +organization like mit or like the air +force for some + + align:start position:0% +force for some + + + align:start position:0% +force for some +inappropriate act + + align:start position:0% +inappropriate act + + + align:start position:0% +inappropriate act +it all just goes away + + align:start position:0% + + + + align:start position:0% + +i guess i believe you know enough in the + + align:start position:0% +i guess i believe you know enough in the + + + align:start position:0% +i guess i believe you know enough in the +sort of adam smith theory of economics + + align:start position:0% +sort of adam smith theory of economics + + + align:start position:0% +sort of adam smith theory of economics +to believe that there are corporations + + align:start position:0% +to believe that there are corporations + + + align:start position:0% +to believe that there are corporations +that + + align:start position:0% +that + + + align:start position:0% +that +definitely provide a benefit to our + + align:start position:0% +definitely provide a benefit to our + + + align:start position:0% +definitely provide a benefit to our +society + + align:start position:0% +society + + + align:start position:0% +society +by their inventiveness + + align:start position:0% +by their inventiveness + + + align:start position:0% +by their inventiveness +by getting talented and excellent people + + align:start position:0% +by getting talented and excellent people + + + align:start position:0% +by getting talented and excellent people +together by producing products which you + + align:start position:0% +together by producing products which you + + + align:start position:0% +together by producing products which you +know produces jobs i do believe that + + align:start position:0% +know produces jobs i do believe that + + + align:start position:0% +know produces jobs i do believe that +those organizations provide a net + + align:start position:0% +those organizations provide a net + + + align:start position:0% +those organizations provide a net +benefit to our society do they have + + align:start position:0% +benefit to our society do they have + + + align:start position:0% +benefit to our society do they have +challenges of course of course they have + + align:start position:0% +challenges of course of course they have + + + align:start position:0% +challenges of course of course they have +challenges but i i think that there are + + align:start position:0% +challenges but i i think that there are + + + align:start position:0% +challenges but i i think that there are +many companies that one will be very + + align:start position:0% +many companies that one will be very + + + align:start position:0% +many companies that one will be very +proud to be associated with because they + + align:start position:0% +proud to be associated with because they + + + align:start position:0% +proud to be associated with because they +do in fact + + align:start position:0% +do in fact + + + align:start position:0% +do in fact +provide a benefit to our society + + align:start position:0% +provide a benefit to our society + + + align:start position:0% +provide a benefit to our society +actually + + align:start position:0% +actually + + + align:start position:0% +actually +you hate my channel + + align:start position:0% +you hate my channel + + + align:start position:0% +you hate my channel +well actually i think if if we bring + + align:start position:0% +well actually i think if if we bring + + + align:start position:0% +well actually i think if if we bring +this the conversation into the students + + align:start position:0% +this the conversation into the students + + + align:start position:0% +this the conversation into the students +you've got a bottom line + + align:start position:0% +you've got a bottom line + + + align:start position:0% +you've got a bottom line +of grades and graduation + + align:start position:0% + + + + align:start position:0% + +and i haven't been here quite a calendar + + align:start position:0% +and i haven't been here quite a calendar + + + align:start position:0% +and i haven't been here quite a calendar +a year yet but i've + + align:start position:0% +a year yet but i've + + + align:start position:0% +a year yet but i've +i've been invited to give nether's talk + + align:start position:0% +i've been invited to give nether's talk + + + align:start position:0% +i've been invited to give nether's talk +before the graduate student and they + + align:start position:0% +before the graduate student and they + + + align:start position:0% +before the graduate student and they +brought us some issues + + align:start position:0% +brought us some issues + + + align:start position:0% +brought us some issues +uh + + align:start position:0% +uh + + + align:start position:0% +uh +and + + align:start position:0% +and + + + align:start position:0% +and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +one student said it was kind of hard + + align:start position:0% +one student said it was kind of hard + + + align:start position:0% +one student said it was kind of hard +it's really it's just kind of hard + + align:start position:0% +it's really it's just kind of hard + + + align:start position:0% +it's really it's just kind of hard +to be working real hard in a class + + align:start position:0% +to be working real hard in a class + + + align:start position:0% +to be working real hard in a class +so i'm just getting over there chief + + align:start position:0% +so i'm just getting over there chief + + + align:start position:0% +so i'm just getting over there chief +gets an a plus + + align:start position:0% +gets an a plus + + + align:start position:0% +gets an a plus +and i get an a minus turn him in + + align:start position:0% +and i get an a minus turn him in + + + align:start position:0% +and i get an a minus turn him in +dad's bathroom all right + + align:start position:0% +dad's bathroom all right + + + align:start position:0% +dad's bathroom all right +you got the same problem + + align:start position:0% +you got the same problem + + + align:start position:0% +you got the same problem +what are you going to do yeah and i + + align:start position:0% +what are you going to do yeah and i + + + align:start position:0% +what are you going to do yeah and i +think that the that that the classroom + + align:start position:0% +think that the that that the classroom + + + align:start position:0% +think that the that that the classroom +and research lab for students + + align:start position:0% +and research lab for students + + + align:start position:0% +and research lab for students +uh is more than a training ground it's a + + align:start position:0% +uh is more than a training ground it's a + + + align:start position:0% +uh is more than a training ground it's a +it's a case endpoint of the kind of + + align:start position:0% +it's a case endpoint of the kind of + + + align:start position:0% +it's a case endpoint of the kind of +thing + + align:start position:0% +thing + + + align:start position:0% +thing +you get out but but + + align:start position:0% +you get out but but + + + align:start position:0% +you get out but but +apart from that lecture um i just want + + align:start position:0% +apart from that lecture um i just want + + + align:start position:0% +apart from that lecture um i just want +to go back to dr mcnaught + + align:start position:0% + + + + align:start position:0% + +when mit has a personality + + align:start position:0% +when mit has a personality + + + align:start position:0% +when mit has a personality +really get it on be first + + align:start position:0% +really get it on be first + + + align:start position:0% +really get it on be first +really get it + + align:start position:0% +really get it + + + align:start position:0% +really get it +to be a leader + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +where does the student share it all it + + align:start position:0% +where does the student share it all it + + + align:start position:0% +where does the student share it all it +seems like it's a faculty and high + + align:start position:0% +seems like it's a faculty and high + + + align:start position:0% +seems like it's a faculty and high +administration + + align:start position:0% +administration + + + align:start position:0% +administration +no i guess i don't yeah no i don't think + + align:start position:0% +no i guess i don't yeah no i don't think + + + align:start position:0% +no i guess i don't yeah no i don't think +so first of all i i guess i think the + + align:start position:0% +so first of all i i guess i think the + + + align:start position:0% +so first of all i i guess i think the +students i was a student at mit + + align:start position:0% +students i was a student at mit + + + align:start position:0% +students i was a student at mit +i think the students benefit enormously + + align:start position:0% +i think the students benefit enormously + + + align:start position:0% +i think the students benefit enormously +i mean there's lots of different ways to + + align:start position:0% +i mean there's lots of different ways to + + + align:start position:0% +i mean there's lots of different ways to +to put it but uh first of all at the + + align:start position:0% +to put it but uh first of all at the + + + align:start position:0% +to put it but uh first of all at the +undergraduate level there's europe + + align:start position:0% +undergraduate level there's europe + + + align:start position:0% +undergraduate level there's europe +other universities have dried europe and + + align:start position:0% +other universities have dried europe and + + + align:start position:0% +other universities have dried europe and +not been successful + + align:start position:0% +not been successful + + + align:start position:0% +not been successful +primarily i think you know we sort of + + align:start position:0% +primarily i think you know we sort of + + + align:start position:0% +primarily i think you know we sort of +have some lucky numbers and faculty + + align:start position:0% +have some lucky numbers and faculty + + + align:start position:0% +have some lucky numbers and faculty +student ratio + + align:start position:0% +student ratio + + + align:start position:0% +student ratio +i mean that makes it possible yeah right + + align:start position:0% +i mean that makes it possible yeah right + + + align:start position:0% +i mean that makes it possible yeah right +uh you know the other part is i used to + + align:start position:0% +uh you know the other part is i used to + + + align:start position:0% +uh you know the other part is i used to +tell students you know + + align:start position:0% +tell students you know + + + align:start position:0% +tell students you know +knock on the door + + align:start position:0% +knock on the door + + + align:start position:0% +knock on the door +you know + + align:start position:0% +you know + + + align:start position:0% +you know +99 of the time you will see a friendly + + align:start position:0% +99 of the time you will see a friendly + + + align:start position:0% +99 of the time you will see a friendly +face + + align:start position:0% +face + + + align:start position:0% +face +on the other side of that door + + align:start position:0% +on the other side of that door + + + align:start position:0% +on the other side of that door +uh + + align:start position:0% +uh + + + align:start position:0% +uh +students benefit + + align:start position:0% +students benefit + + + align:start position:0% +students benefit +i think enormously from the volume and + + align:start position:0% +i think enormously from the volume and + + + align:start position:0% +i think enormously from the volume and +the in the quality of the research + + align:start position:0% +the in the quality of the research + + + align:start position:0% +the in the quality of the research +that's going on in this place i mean it + + align:start position:0% +that's going on in this place i mean it + + + align:start position:0% +that's going on in this place i mean it +just + + align:start position:0% +just + + + align:start position:0% +just +it it's very exciting it drives the + + align:start position:0% +it it's very exciting it drives the + + + align:start position:0% +it it's very exciting it drives the +place nobody has time + + align:start position:0% +place nobody has time + + + align:start position:0% +place nobody has time +to + + align:start position:0% +to + + + align:start position:0% +to +get all the benefits + + align:start position:0% +get all the benefits + + + align:start position:0% +get all the benefits +i guess the other thing i wanted to say + + align:start position:0% +i guess the other thing i wanted to say + + + align:start position:0% +i guess the other thing i wanted to say +in + + align:start position:0% +in + + + align:start position:0% +in +in + + align:start position:0% +in + + + align:start position:0% +in +connection with your comment is that i + + align:start position:0% +connection with your comment is that i + + + align:start position:0% +connection with your comment is that i +do believe it is + + align:start position:0% +do believe it is + + + align:start position:0% +do believe it is +the responsibility of the faculty + + align:start position:0% +the responsibility of the faculty + + + align:start position:0% +the responsibility of the faculty +to ensure that students can benefit from + + align:start position:0% +to ensure that students can benefit from + + + align:start position:0% +to ensure that students can benefit from +ethical behavior + + align:start position:0% + + + + align:start position:0% + +i think faculty fews are casual and + + align:start position:0% +i think faculty fews are casual and + + + align:start position:0% +i think faculty fews are casual and +careless about + + align:start position:0% +careless about + + + align:start position:0% +careless about +the structuring of exams + + align:start position:0% + + + + align:start position:0% + +so that students + + align:start position:0% +so that students + + + align:start position:0% +so that students +who take inappropriate measures can + + align:start position:0% +who take inappropriate measures can + + + align:start position:0% +who take inappropriate measures can +benefit i think that that's unethical + + align:start position:0% +benefit i think that that's unethical + + + align:start position:0% +benefit i think that that's unethical +behavior + + align:start position:0% + + + + align:start position:0% + +so i you know i think that the faculty + + align:start position:0% +so i you know i think that the faculty + + + align:start position:0% +so i you know i think that the faculty +have a responsibility to + + align:start position:0% +have a responsibility to + + + align:start position:0% +have a responsibility to +structure the educational and research + + align:start position:0% +structure the educational and research + + + align:start position:0% +structure the educational and research +program in such a way that students + + align:start position:0% +program in such a way that students + + + align:start position:0% +program in such a way that students +get the most out of it and also are not + + align:start position:0% +get the most out of it and also are not + + + align:start position:0% +get the most out of it and also are not +disadvantaged from somebody else's + + align:start position:0% +disadvantaged from somebody else's + + + align:start position:0% +disadvantaged from somebody else's +unethical behavior and i say that as the + + align:start position:0% +unethical behavior and i say that as the + + + align:start position:0% +unethical behavior and i say that as the +former chairman of the discipline + + align:start position:0% +former chairman of the discipline + + + align:start position:0% +former chairman of the discipline +committee + + align:start position:0% + + + + align:start position:0% + +because we you know we we're the ones + + align:start position:0% +because we you know we we're the ones + + + align:start position:0% +because we you know we we're the ones +that + + align:start position:0% +that + + + align:start position:0% +that +heard the cases about + + align:start position:0% +heard the cases about + + + align:start position:0% +heard the cases about +but you know you hope it never gets to + + align:start position:0% +but you know you hope it never gets to + + + align:start position:0% +but you know you hope it never gets to +that + + align:start position:0% +that + + + align:start position:0% +that +you know you hope it never gets to that + + align:start position:0% +you know you hope it never gets to that + + + align:start position:0% +you know you hope it never gets to that +we hope that + + align:start position:0% +we hope that + + + align:start position:0% +we hope that +you know that the rules are clear and + + align:start position:0% +you know that the rules are clear and + + + align:start position:0% +you know that the rules are clear and +that the system is set up in such a way + + align:start position:0% +that the system is set up in such a way + + + align:start position:0% +that the system is set up in such a way +so that the students + + align:start position:0% +so that the students + + + align:start position:0% +so that the students +you know get the benefit from it in + + align:start position:0% +you know get the benefit from it in + + + align:start position:0% +you know get the benefit from it in +proportion to + + align:start position:0% +proportion to + + + align:start position:0% +proportion to +their talents and the uh + + align:start position:0% +their talents and the uh + + + align:start position:0% +their talents and the uh +energy that they put into + + align:start position:0% +energy that they put into + + + align:start position:0% +energy that they put into +into the endeavor + + align:start position:0% +into the endeavor + + + align:start position:0% +into the endeavor +and that's really what it's all about + + align:start position:0% +and that's really what it's all about + + + align:start position:0% +and that's really what it's all about +because that's where the true education + + align:start position:0% +because that's where the true education + + + align:start position:0% +because that's where the true education +comes from + + align:start position:0% +comes from + + + align:start position:0% +comes from +you had a question right i saw you with + + align:start position:0% +you had a question right i saw you with + + + align:start position:0% +you had a question right i saw you with +your hand up some questions + + align:start position:0% +your hand up some questions + + + align:start position:0% +your hand up some questions +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um + + align:start position:0% + + + + align:start position:0% + +when you encounter + + align:start position:0% +when you encounter + + + align:start position:0% +when you encounter +situations that are gray yeah + + align:start position:0% +situations that are gray yeah + + + align:start position:0% +situations that are gray yeah +i mean if it's black and white you know + + align:start position:0% +i mean if it's black and white you know + + + align:start position:0% +i mean if it's black and white you know +often here's the thing it's not right + + align:start position:0% +often here's the thing it's not right + + + align:start position:0% +often here's the thing it's not right +there might be things that are grey it's + + align:start position:0% +there might be things that are grey it's + + + align:start position:0% +there might be things that are grey it's +the appropriate course of action then to + + align:start position:0% + + + + align:start position:0% + +yeah i you know i i think i think sort + + align:start position:0% +yeah i you know i i think i think sort + + + align:start position:0% +yeah i you know i i think i think sort +of + + align:start position:0% +of + + + align:start position:0% +of +talking to somebody is is is the right + + align:start position:0% +talking to somebody is is is the right + + + align:start position:0% +talking to somebody is is is the right +thing you if you have questions uh it + + align:start position:0% +thing you if you have questions uh it + + + align:start position:0% +thing you if you have questions uh it +seems to me it probably isn't just a + + align:start position:0% +seems to me it probably isn't just a + + + align:start position:0% +seems to me it probably isn't just a +single individual it probably is case + + align:start position:0% +single individual it probably is case + + + align:start position:0% +single individual it probably is case +dependent + + align:start position:0% +dependent + + + align:start position:0% +dependent +you know it could be a faculty colleague + + align:start position:0% +you know it could be a faculty colleague + + + align:start position:0% +you know it could be a faculty colleague +it could be + + align:start position:0% +it could be + + + align:start position:0% +it could be +you know somebody in your department it + + align:start position:0% +you know somebody in your department it + + + align:start position:0% +you know somebody in your department it +could be somebody in the provost you + + align:start position:0% +could be somebody in the provost you + + + align:start position:0% +could be somebody in the provost you +know it depends an awful lot on + + align:start position:0% +know it depends an awful lot on + + + align:start position:0% +know it depends an awful lot on +on what the situation is + + align:start position:0% +on what the situation is + + + align:start position:0% +on what the situation is +but yeah i would think i would think to + + align:start position:0% +but yeah i would think i would think to + + + align:start position:0% +but yeah i would think i would think to +have a dialogue about these things is + + align:start position:0% +have a dialogue about these things is + + + align:start position:0% +have a dialogue about these things is +very healthy + + align:start position:0% +very healthy + + + align:start position:0% +very healthy +for an institution + + align:start position:0% +for an institution + + + align:start position:0% +for an institution +and + + align:start position:0% +and + + + align:start position:0% +and +you know it probably strengthens + + align:start position:0% +you know it probably strengthens + + + align:start position:0% +you know it probably strengthens +everybody who gets involved + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +yeah right right right right + + align:start position:0% + + + + align:start position:0% + +when it's critical for them to say do a + + align:start position:0% +when it's critical for them to say do a + + + align:start position:0% +when it's critical for them to say do a +particular action + + align:start position:0% + + + + align:start position:0% + +yeah there are extreme conditions yeah + + align:start position:0% +yeah there are extreme conditions yeah + + + align:start position:0% +yeah there are extreme conditions yeah +there aren't right there are extreme + + align:start position:0% +there aren't right there are extreme + + + align:start position:0% +there aren't right there are extreme +conditions i i think that is probably a + + align:start position:0% +conditions i i think that is probably a + + + align:start position:0% +conditions i i think that is probably a +very complex situation um + + align:start position:0% +very complex situation um + + + align:start position:0% +very complex situation um +it's a little like your question about + + align:start position:0% +it's a little like your question about + + + align:start position:0% +it's a little like your question about +engineers + + align:start position:0% +engineers + + + align:start position:0% +engineers +you know + + align:start position:0% +you know + + + align:start position:0% +you know +what is the i mean if engineers just + + align:start position:0% +what is the i mean if engineers just + + + align:start position:0% +what is the i mean if engineers just +worry about everything that are not + + align:start position:0% +worry about everything that are not + + + align:start position:0% +worry about everything that are not +expressing their concerns in actionable + + align:start position:0% +expressing their concerns in actionable + + + align:start position:0% +expressing their concerns in actionable +form + + align:start position:0% +form + + + align:start position:0% +form +that would tend to bring an organization + + align:start position:0% +that would tend to bring an organization + + + align:start position:0% +that would tend to bring an organization +to a halt and i think the same thing is + + align:start position:0% +to a halt and i think the same thing is + + + align:start position:0% +to a halt and i think the same thing is +probably true in the military + + align:start position:0% +probably true in the military + + + align:start position:0% +probably true in the military +if you know say you're going to get a + + align:start position:0% +if you know say you're going to get a + + + align:start position:0% +if you know say you're going to get a +group of guys and you're going to get in + + align:start position:0% +group of guys and you're going to get in + + + align:start position:0% +group of guys and you're going to get in +this humvee and you're going to drive + + align:start position:0% +this humvee and you're going to drive + + + align:start position:0% +this humvee and you're going to drive +out to the center of the city you know i + + align:start position:0% +out to the center of the city you know i + + + align:start position:0% +out to the center of the city you know i +mean the last thing that that could + + align:start position:0% +mean the last thing that that could + + + align:start position:0% +mean the last thing that that could +happen at that point is people arguing + + align:start position:0% +happen at that point is people arguing + + + align:start position:0% +happen at that point is people arguing +about whether that was a good idea + + align:start position:0% +about whether that was a good idea + + + align:start position:0% +about whether that was a good idea +so i think + + align:start position:0% +so i think + + + align:start position:0% +so i think +it seems to me and i'm not an expert on + + align:start position:0% +it seems to me and i'm not an expert on + + + align:start position:0% +it seems to me and i'm not an expert on +this it seems to me there have to be + + align:start position:0% +this it seems to me there have to be + + + align:start position:0% +this it seems to me there have to be +kind of a set of ground rules about what + + align:start position:0% +kind of a set of ground rules about what + + + align:start position:0% +kind of a set of ground rules about what +is reasonable to object to + + align:start position:0% +is reasonable to object to + + + align:start position:0% +is reasonable to object to +you know i think it's very clear in the + + align:start position:0% +you know i think it's very clear in the + + + align:start position:0% +you know i think it's very clear in the +abba grave situation that it would be + + align:start position:0% +abba grave situation that it would be + + + align:start position:0% +abba grave situation that it would be +very reasonable to object to that + + align:start position:0% +very reasonable to object to that + + + align:start position:0% +very reasonable to object to that +there's a bright line there + + align:start position:0% + + + + align:start position:0% + +but as i understand the structure of the + + align:start position:0% +but as i understand the structure of the + + + align:start position:0% +but as i understand the structure of the +military i don't think you can do it the + + align:start position:0% +military i don't think you can do it the + + + align:start position:0% +military i don't think you can do it the +morning that you've been told to go out + + align:start position:0% +morning that you've been told to go out + + + align:start position:0% +morning that you've been told to go out +in a in a humvee i mean but but there is + + align:start position:0% +in a in a humvee i mean but but there is + + + align:start position:0% +in a in a humvee i mean but but there is +a general + + align:start position:0% +a general + + + align:start position:0% +a general +jag corps + + align:start position:0% +jag corps + + + align:start position:0% +jag corps +military justice system that is sort of + + align:start position:0% +military justice system that is sort of + + + align:start position:0% +military justice system that is sort of +attached + + align:start position:0% +attached + + + align:start position:0% +attached +to + + align:start position:0% +to + + + align:start position:0% +to +the command at some level + + align:start position:0% +the command at some level + + + align:start position:0% +the command at some level +and you know these people are for all + + align:start position:0% +and you know these people are for all + + + align:start position:0% +and you know these people are for all +practical purposes lawyers + + align:start position:0% +practical purposes lawyers + + + align:start position:0% +practical purposes lawyers +and + + align:start position:0% +and + + + align:start position:0% +and +it would not be unreasonable i think to + + align:start position:0% +it would not be unreasonable i think to + + + align:start position:0% +it would not be unreasonable i think to +bring concerns of a kind of global + + align:start position:0% +bring concerns of a kind of global + + + align:start position:0% +bring concerns of a kind of global +nature + + align:start position:0% +nature + + + align:start position:0% +nature +to such people and certainly + + align:start position:0% + + + + align:start position:0% + +you know in the case of things like abu + + align:start position:0% +you know in the case of things like abu + + + align:start position:0% +you know in the case of things like abu +ghraib + + align:start position:0% +ghraib + + + align:start position:0% +ghraib +those those things were so obviously + + align:start position:0% +those those things were so obviously + + + align:start position:0% +those those things were so obviously +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +that that + + align:start position:0% +that that + + + align:start position:0% +that that +individuals must have felt + + align:start position:0% +individuals must have felt + + + align:start position:0% +individuals must have felt +you know like there was a boundary there + + align:start position:0% +you know like there was a boundary there + + + align:start position:0% +you know like there was a boundary there +that they were crossing + + align:start position:0% +that they were crossing + + + align:start position:0% +that they were crossing +so i think there are um + + align:start position:0% +so i think there are um + + + align:start position:0% +so i think there are um +there are opportunities and i'm also + + align:start position:0% +there are opportunities and i'm also + + + align:start position:0% +there are opportunities and i'm also +assuming and i don't i don't know this + + align:start position:0% +assuming and i don't i don't know this + + + align:start position:0% +assuming and i don't i don't know this +for a fact but i'm assuming you know in + + align:start position:0% +for a fact but i'm assuming you know in + + + align:start position:0% +for a fact but i'm assuming you know in +officer training + + align:start position:0% +officer training + + + align:start position:0% +officer training +you know either through like the air + + align:start position:0% +you know either through like the air + + + align:start position:0% +you know either through like the air +force academy or officer training school + + align:start position:0% +force academy or officer training school + + + align:start position:0% +force academy or officer training school +or something + + align:start position:0% +or something + + + align:start position:0% +or something +that these kinds of issues come up and + + align:start position:0% +that these kinds of issues come up and + + + align:start position:0% +that these kinds of issues come up and +that officers discuss + + align:start position:0% +that officers discuss + + + align:start position:0% +that officers discuss +what would you do in a situation where + + align:start position:0% +what would you do in a situation where + + + align:start position:0% +what would you do in a situation where +you had concern about + + align:start position:0% +you had concern about + + + align:start position:0% +you had concern about +an order given by a superior officer and + + align:start position:0% +an order given by a superior officer and + + + align:start position:0% +an order given by a superior officer and +just as a corporation has a hotline + + align:start position:0% +just as a corporation has a hotline + + + align:start position:0% +just as a corporation has a hotline +sort of making the assumption that there + + align:start position:0% +sort of making the assumption that there + + + align:start position:0% +sort of making the assumption that there +are avenues that younger officers + + align:start position:0% +are avenues that younger officers + + + align:start position:0% +are avenues that younger officers +or enlisted + + align:start position:0% +or enlisted + + + align:start position:0% +or enlisted +personnel + + align:start position:0% +personnel + + + align:start position:0% +personnel +could use to + + align:start position:0% +could use to + + + align:start position:0% +could use to +again talk with somebody and + + align:start position:0% +again talk with somebody and + + + align:start position:0% +again talk with somebody and +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +get a sense + + align:start position:0% +get a sense + + + align:start position:0% +get a sense +or what the boundaries are + + align:start position:0% +or what the boundaries are + + + align:start position:0% +or what the boundaries are +other i mean otherwise i + + align:start position:0% +other i mean otherwise i + + + align:start position:0% +other i mean otherwise i +i think people are going to be + + align:start position:0% +i think people are going to be + + + align:start position:0% +i think people are going to be +kind of lonely if they're not if they + + align:start position:0% +kind of lonely if they're not if they + + + align:start position:0% +kind of lonely if they're not if they +don't have an opportunity to really talk + + align:start position:0% +don't have an opportunity to really talk + + + align:start position:0% +don't have an opportunity to really talk +about this + + align:start position:0% +about this + + + align:start position:0% +about this +i was in the army doing vietnam + + align:start position:0% + + + + align:start position:0% + +it was a big scare for us culturally + + align:start position:0% +it was a big scare for us culturally + + + align:start position:0% +it was a big scare for us culturally +before the milan + + align:start position:0% + + + + align:start position:0% + +uh you were very comfortable in + + align:start position:0% +uh you were very comfortable in + + + align:start position:0% +uh you were very comfortable in +following your office because right if + + align:start position:0% +following your office because right if + + + align:start position:0% +following your office because right if +the order was a bad order the person who + + align:start position:0% +the order was a bad order the person who + + + align:start position:0% +the order was a bad order the person who +gave it to you + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +right changed all of this yeah no i + + align:start position:0% +right changed all of this yeah no i + + + align:start position:0% +right changed all of this yeah no i +think so uh + + align:start position:0% +think so uh + + + align:start position:0% +think so uh +but i think + + align:start position:0% +but i think + + + align:start position:0% +but i think +uh and i + + align:start position:0% +uh and i + + + align:start position:0% +uh and i +i really would like to know what you + + align:start position:0% +i really would like to know what you + + + align:start position:0% +i really would like to know what you +think about this because i + + align:start position:0% +think about this because i + + + align:start position:0% +think about this because i +don't have a clue + + align:start position:0% +don't have a clue + + + align:start position:0% +don't have a clue +that there was this move i can't + + align:start position:0% +that there was this move i can't + + + align:start position:0% +that there was this move i can't +remember the name + + align:start position:0% +remember the name + + + align:start position:0% +remember the name +star gene hackman hackman + + align:start position:0% +star gene hackman hackman + + + align:start position:0% +star gene hackman hackman +in disney or washington + + align:start position:0% +in disney or washington + + + align:start position:0% +in disney or washington +uh one of them was central + + align:start position:0% +uh one of them was central + + + align:start position:0% +uh one of them was central +was it the submarine submarine yeah + + align:start position:0% + + + + align:start position:0% + +you get like me + + align:start position:0% +you get like me + + + align:start position:0% +you get like me +yeah i know i have these problems well + + align:start position:0% +yeah i know i have these problems well + + + align:start position:0% +yeah i know i have these problems well +the issue was + + align:start position:0% +the issue was + + + align:start position:0% +the issue was +that + + align:start position:0% +that + + + align:start position:0% +that +a lower ranking officer + + align:start position:0% +a lower ranking officer + + + align:start position:0% +a lower ranking officer +didn't want to follow him oh yeah right + + align:start position:0% +didn't want to follow him oh yeah right + + + align:start position:0% +didn't want to follow him oh yeah right +right + + align:start position:0% +right + + + align:start position:0% +right +because + + align:start position:0% +because + + + align:start position:0% +because +the stakes in the game have lifted so + + align:start position:0% +the stakes in the game have lifted so + + + align:start position:0% +the stakes in the game have lifted so +hard you're talking about a nuclear + + align:start position:0% +hard you're talking about a nuclear + + + align:start position:0% +hard you're talking about a nuclear +weapon yes right right right okay + + align:start position:0% +weapon yes right right right okay + + + align:start position:0% +weapon yes right right right okay +even if we lie yeah i had to be little + + align:start position:0% +even if we lie yeah i had to be little + + + align:start position:0% +even if we lie yeah i had to be little +yeah but the worst that happened was the + + align:start position:0% +yeah but the worst that happened was the + + + align:start position:0% +yeah but the worst that happened was the +killing of a lot of women and children + + align:start position:0% +killing of a lot of women and children + + + align:start position:0% +killing of a lot of women and children +yeah in a village + + align:start position:0% +yeah in a village + + + align:start position:0% +yeah in a village +a nuclear weapon that's a whole + + align:start position:0% +a nuclear weapon that's a whole + + + align:start position:0% +a nuclear weapon that's a whole +different thing + + align:start position:0% +different thing + + + align:start position:0% +different thing +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +no i i mean that's why we have movies + + align:start position:0% +no i i mean that's why we have movies + + + align:start position:0% +no i i mean that's why we have movies +but i + + align:start position:0% +but i + + + align:start position:0% +but i +yeah no i mean i + + align:start position:0% +yeah no i mean i + + + align:start position:0% +yeah no i mean i +i vaguely remember the movie but um + + align:start position:0% +i vaguely remember the movie but um + + + align:start position:0% +i vaguely remember the movie but um +i i guess what i remember about it was + + align:start position:0% +i i guess what i remember about it was + + + align:start position:0% +i i guess what i remember about it was +not unreasonable for a younger officer + + align:start position:0% +not unreasonable for a younger officer + + + align:start position:0% +not unreasonable for a younger officer +to challenge + + align:start position:0% +to challenge + + + align:start position:0% +to challenge +senior officer and + + align:start position:0% +senior officer and + + + align:start position:0% +senior officer and +and there are evidently uh situations + + align:start position:0% +and there are evidently uh situations + + + align:start position:0% +and there are evidently uh situations +under which he could have been declared + + align:start position:0% +under which he could have been declared + + + align:start position:0% +under which he could have been declared +unfit for command at that moment + + align:start position:0% +unfit for command at that moment + + + align:start position:0% +unfit for command at that moment +and and it's possible to imagine + + align:start position:0% +and and it's possible to imagine + + + align:start position:0% +and and it's possible to imagine +that happening + + align:start position:0% +that happening + + + align:start position:0% +that happening +getting agreement from the crew that + + align:start position:0% +getting agreement from the crew that + + + align:start position:0% +getting agreement from the crew that +that was in fact the appropriate thing + + align:start position:0% +that was in fact the appropriate thing + + + align:start position:0% +that was in fact the appropriate thing +to do + + align:start position:0% +to do + + + align:start position:0% +to do +and + + align:start position:0% +and + + + align:start position:0% +and +coming back is sure to have it + + align:start position:0% +coming back is sure to have it + + + align:start position:0% +coming back is sure to have it +adjudicated and found that that was in + + align:start position:0% +adjudicated and found that that was in + + + align:start position:0% +adjudicated and found that that was in +fact appropriate + + align:start position:0% +fact appropriate + + + align:start position:0% +fact appropriate +appropriate action given the + + align:start position:0% +appropriate action given the + + + align:start position:0% +appropriate action given the +circumstances given the risk + + align:start position:0% +circumstances given the risk + + + align:start position:0% +circumstances given the risk +given the judgments that were being made + + align:start position:0% +given the judgments that were being made + + + align:start position:0% +given the judgments that were being made +it sounds to me like a very doable + + align:start position:0% +it sounds to me like a very doable + + + align:start position:0% +it sounds to me like a very doable +a doable thing + + align:start position:0% +a doable thing + + + align:start position:0% +a doable thing +i mean i do consider the military to be + + align:start position:0% +i mean i do consider the military to be + + + align:start position:0% +i mean i do consider the military to be +an extremely ethical + + align:start position:0% +an extremely ethical + + + align:start position:0% +an extremely ethical +organization + + align:start position:0% +organization + + + align:start position:0% +organization +there's just been so i've you know + + align:start position:0% +there's just been so i've you know + + + align:start position:0% +there's just been so i've you know +following upon my experience as chairman + + align:start position:0% +following upon my experience as chairman + + + align:start position:0% +following upon my experience as chairman +of the discipline committee uh i really + + align:start position:0% +of the discipline committee uh i really + + + align:start position:0% +of the discipline committee uh i really +took a great interest in the military + + align:start position:0% +took a great interest in the military + + + align:start position:0% +took a great interest in the military +justice system and i pursued every case + + align:start position:0% +justice system and i pursued every case + + + align:start position:0% +justice system and i pursued every case +i had to sign off on all officer cases + + align:start position:0% +i had to sign off on all officer cases + + + align:start position:0% +i had to sign off on all officer cases +and so i + + align:start position:0% +and so i + + + align:start position:0% +and so i +you know i went through the history of + + align:start position:0% +you know i went through the history of + + + align:start position:0% +you know i went through the history of +every case very carefully + + align:start position:0% +every case very carefully + + + align:start position:0% +every case very carefully +and i could see + + align:start position:0% +and i could see + + + align:start position:0% +and i could see +you know the response the actions that + + align:start position:0% +you know the response the actions that + + + align:start position:0% +you know the response the actions that +were taken by various + + align:start position:0% +were taken by various + + + align:start position:0% +were taken by various +officers + + align:start position:0% +officers + + + align:start position:0% +officers +along the way during the incident itself + + align:start position:0% +along the way during the incident itself + + + align:start position:0% +along the way during the incident itself +and sort of getting it into + + align:start position:0% +and sort of getting it into + + + align:start position:0% +and sort of getting it into +the system and the decisions that were + + align:start position:0% +the system and the decisions that were + + + align:start position:0% +the system and the decisions that were +made until it finally + + align:start position:0% +made until it finally + + + align:start position:0% +made until it finally +reached my desk + + align:start position:0% +reached my desk + + + align:start position:0% +reached my desk +i guess all i can say about that is that + + align:start position:0% +i guess all i can say about that is that + + + align:start position:0% +i guess all i can say about that is that +it gave me a very good feeling + + align:start position:0% +it gave me a very good feeling + + + align:start position:0% +it gave me a very good feeling +about the + + align:start position:0% +about the + + + align:start position:0% +about the +about the integrity and about the + + align:start position:0% +about the integrity and about the + + + align:start position:0% +about the integrity and about the +excellence of the officers + + align:start position:0% +excellence of the officers + + + align:start position:0% +excellence of the officers +let me give you a simple somewhat + + align:start position:0% +let me give you a simple somewhat + + + align:start position:0% +let me give you a simple somewhat +humorous example um + + align:start position:0% +humorous example um + + + align:start position:0% +humorous example um +and this happens + + align:start position:0% +and this happens + + + align:start position:0% +and this happens +people get mid-life crises but we had a + + align:start position:0% +people get mid-life crises but we had a + + + align:start position:0% +people get mid-life crises but we had a +general + + align:start position:0% +general + + + align:start position:0% +general +maybe he was a colonel but i think he + + align:start position:0% +maybe he was a colonel but i think he + + + align:start position:0% +maybe he was a colonel but i think he +was the general + + align:start position:0% +was the general + + + align:start position:0% +was the general +who you know is that that + + align:start position:0% +who you know is that that + + + align:start position:0% +who you know is that that +tender age for men + + align:start position:0% +tender age for men + + + align:start position:0% +tender age for men +uh 45 50 something like that and he's + + align:start position:0% +uh 45 50 something like that and he's + + + align:start position:0% +uh 45 50 something like that and he's +got this absolute + + align:start position:0% +got this absolute + + + align:start position:0% +got this absolute +attraction for this young airman + + align:start position:0% +attraction for this young airman + + + align:start position:0% +attraction for this young airman +now just couldn't live without her well + + align:start position:0% +now just couldn't live without her well + + + align:start position:0% +now just couldn't live without her well +she would have none of it + + align:start position:0% +she would have none of it + + + align:start position:0% +she would have none of it +so + + align:start position:0% +so + + + align:start position:0% +so +anyway he had her transferred with him + + align:start position:0% +anyway he had her transferred with him + + + align:start position:0% +anyway he had her transferred with him +when he moved from europe to + + align:start position:0% +when he moved from europe to + + + align:start position:0% +when he moved from europe to +the united states and you know he + + align:start position:0% +the united states and you know he + + + align:start position:0% +the united states and you know he +just tried to + + align:start position:0% +just tried to + + + align:start position:0% +just tried to +you know get her alone with him and he + + align:start position:0% +you know get her alone with him and he + + + align:start position:0% +you know get her alone with him and he +just she just kept resisting + + align:start position:0% +just she just kept resisting + + + align:start position:0% +just she just kept resisting +finally + + align:start position:0% +finally + + + align:start position:0% +finally +he chased her around the desk + + align:start position:0% +he chased her around the desk + + + align:start position:0% +he chased her around the desk +and she ran out into the hall and ran + + align:start position:0% +and she ran out into the hall and ran + + + align:start position:0% +and she ran out into the hall and ran +into this canadian major + + align:start position:0% +into this canadian major + + + align:start position:0% +into this canadian major +and told him what had happened the guy + + align:start position:0% +and told him what had happened the guy + + + align:start position:0% +and told him what had happened the guy +turned him in immediately + + align:start position:0% +turned him in immediately + + + align:start position:0% +turned him in immediately +just like that it was no question + + align:start position:0% +just like that it was no question + + + align:start position:0% +just like that it was no question +and and and i saw that constantly i mean + + align:start position:0% +and and and i saw that constantly i mean + + + align:start position:0% +and and and i saw that constantly i mean +it was nobody in the air force + + align:start position:0% +it was nobody in the air force + + + align:start position:0% +it was nobody in the air force +who was engaging in bad activity could + + align:start position:0% +who was engaging in bad activity could + + + align:start position:0% +who was engaging in bad activity could +have any confidence that they wouldn't + + align:start position:0% +have any confidence that they wouldn't + + + align:start position:0% +have any confidence that they wouldn't +be turned in just like that + + align:start position:0% +be turned in just like that + + + align:start position:0% +be turned in just like that +it was the culture of the organization + + align:start position:0% +it was the culture of the organization + + + align:start position:0% +it was the culture of the organization +that + + align:start position:0% +that + + + align:start position:0% +that +people would simply not put up with + + align:start position:0% +people would simply not put up with + + + align:start position:0% +people would simply not put up with +bad behavior this was not a + + align:start position:0% +bad behavior this was not a + + + align:start position:0% +bad behavior this was not a +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it was you know all the things your + + align:start position:0% +it was you know all the things your + + + align:start position:0% +it was you know all the things your +mother told you about don't tattle on + + align:start position:0% +mother told you about don't tattle on + + + align:start position:0% +mother told you about don't tattle on +your friends this was not an operative + + align:start position:0% +your friends this was not an operative + + + align:start position:0% +your friends this was not an operative +principle in the air force people moved + + align:start position:0% +principle in the air force people moved + + + align:start position:0% +principle in the air force people moved +very quickly + + align:start position:0% +very quickly + + + align:start position:0% +very quickly +to uh to take appropriate action so + + align:start position:0% +to uh to take appropriate action so + + + align:start position:0% +to uh to take appropriate action so +i i know i felt really good about things + + align:start position:0% +i i know i felt really good about things + + + align:start position:0% +i i know i felt really good about things +like that + + align:start position:0% +like that + + + align:start position:0% +like that +because it said that the organization + + align:start position:0% +because it said that the organization + + + align:start position:0% +because it said that the organization +um + + align:start position:0% +um + + + align:start position:0% +um +the the fundamental loyalty of people + + align:start position:0% +the the fundamental loyalty of people + + + align:start position:0% +the the fundamental loyalty of people +was to the organization not to + + align:start position:0% +was to the organization not to + + + align:start position:0% +was to the organization not to +you know some kind of underground + + align:start position:0% +you know some kind of underground + + + align:start position:0% +you know some kind of underground +buddy system + + align:start position:0% + + + + align:start position:0% + +what's that i've never experienced an + + align:start position:0% +what's that i've never experienced an + + + align:start position:0% +what's that i've never experienced an +organization like that where it's so + + align:start position:0% +organization like that where it's so + + + align:start position:0% +organization like that where it's so +clear it's so clear + + align:start position:0% +clear it's so clear + + + align:start position:0% +clear it's so clear +you just turn people in + + align:start position:0% +you just turn people in + + + align:start position:0% +you just turn people in +well it's hard because most of the + + align:start position:0% +well it's hard because most of the + + + align:start position:0% +well it's hard because most of the +organizations have been affiliated with + + align:start position:0% +organizations have been affiliated with + + + align:start position:0% +organizations have been affiliated with +our schools + + align:start position:0% +our schools + + + align:start position:0% +our schools +is very important + + align:start position:0% +is very important + + + align:start position:0% +is very important +well yeah i mean you know i've we don't + + align:start position:0% +well yeah i mean you know i've we don't + + + align:start position:0% +well yeah i mean you know i've we don't +have an honor code here at mit but + + align:start position:0% +have an honor code here at mit but + + + align:start position:0% +have an honor code here at mit but +there's an honor code at the air force + + align:start position:0% +there's an honor code at the air force + + + align:start position:0% +there's an honor code at the air force +academy and there's also an honor code + + align:start position:0% +academy and there's also an honor code + + + align:start position:0% +academy and there's also an honor code +out at owen college and i've basically + + align:start position:0% +out at owen college and i've basically + + + align:start position:0% +out at owen college and i've basically +been involved in those systems and the + + align:start position:0% +been involved in those systems and the + + + align:start position:0% +been involved in those systems and the +thing you get into is this constant + + align:start position:0% +thing you get into is this constant + + + align:start position:0% +thing you get into is this constant +tension between loyalty to your friends + + align:start position:0% +tension between loyalty to your friends + + + align:start position:0% +tension between loyalty to your friends +and loyalty to the institution + + align:start position:0% +and loyalty to the institution + + + align:start position:0% +and loyalty to the institution +and the notion of turning someone in is + + align:start position:0% +and the notion of turning someone in is + + + align:start position:0% +and the notion of turning someone in is +a tough thing for most young people to + + align:start position:0% +a tough thing for most young people to + + + align:start position:0% +a tough thing for most young people to +deal with + + align:start position:0% +deal with + + + align:start position:0% +deal with +it takes a long time + + align:start position:0% +it takes a long time + + + align:start position:0% +it takes a long time +to rise to a level i think where you see + + align:start position:0% +to rise to a level i think where you see + + + align:start position:0% +to rise to a level i think where you see +that clearly + + align:start position:0% + + + + align:start position:0% + +and you know if you if your friend + + align:start position:0% +and you know if you if your friend + + + align:start position:0% +and you know if you if your friend +cheats on + + align:start position:0% +cheats on + + + align:start position:0% +cheats on +some exam or something um + + align:start position:0% +some exam or something um + + + align:start position:0% +some exam or something um +you probably + + align:start position:0% +you probably + + + align:start position:0% +you probably +would you know not turn them in + + align:start position:0% +would you know not turn them in + + + align:start position:0% +would you know not turn them in +it's when you get like me you know and i + + align:start position:0% +it's when you get like me you know and i + + + align:start position:0% +it's when you get like me you know and i +you get to a certain level and you just + + align:start position:0% +you get to a certain level and you just + + + align:start position:0% +you get to a certain level and you just +be turn them in + + align:start position:0% + + + + align:start position:0% + +well before you ask your question i just + + align:start position:0% +well before you ask your question i just + + + align:start position:0% +well before you ask your question i just +want to make one observation and that is + + align:start position:0% +want to make one observation and that is + + + align:start position:0% +want to make one observation and that is +that we have not discussed women's + + align:start position:0% +that we have not discussed women's + + + align:start position:0% +that we have not discussed women's +issues + + align:start position:0% + + + + align:start position:0% + +i was hoping that you would bring one up + + align:start position:0% +i was hoping that you would bring one up + + + align:start position:0% +i was hoping that you would bring one up +and say that now from this point + + align:start position:0% +and say that now from this point + + + align:start position:0% +and say that now from this point +right now + + align:start position:0% +right now + + + align:start position:0% +right now +on in the class with his issues + + align:start position:0% +on in the class with his issues + + + align:start position:0% +on in the class with his issues +our legitimate father for this class + + align:start position:0% +our legitimate father for this class + + + align:start position:0% +our legitimate father for this class +and i want y'all to + + align:start position:0% +and i want y'all to + + + align:start position:0% +and i want y'all to +really gain from dr whitnell's + + align:start position:0% +really gain from dr whitnell's + + + align:start position:0% +really gain from dr whitnell's +experience because this engineering game + + align:start position:0% +experience because this engineering game + + + align:start position:0% +experience because this engineering game +can be pretty uh + + align:start position:0% +can be pretty uh + + + align:start position:0% +can be pretty uh +yeah i mean it's + + align:start position:0% +yeah i mean it's + + + align:start position:0% +yeah i mean it's +yeah oh very yeah very much so it's uh + + align:start position:0% +yeah oh very yeah very much so it's uh + + + align:start position:0% +yeah oh very yeah very much so it's uh +but you know there are lots of humorous + + align:start position:0% +but you know there are lots of humorous + + + align:start position:0% +but you know there are lots of humorous +things that happen you have to have a + + align:start position:0% +things that happen you have to have a + + + align:start position:0% +things that happen you have to have a +good sense of humor in a situation like + + align:start position:0% +good sense of humor in a situation like + + + align:start position:0% +good sense of humor in a situation like +this but you know again getting back to + + align:start position:0% +this but you know again getting back to + + + align:start position:0% +this but you know again getting back to +mit back in 1970 + + align:start position:0% +mit back in 1970 + + + align:start position:0% +mit back in 1970 +mit began to take this issue seriously + + align:start position:0% +mit began to take this issue seriously + + + align:start position:0% +mit began to take this issue seriously +and we had + + align:start position:0% + + + + align:start position:0% + +you know a women's faculty group it was + + align:start position:0% +you know a women's faculty group it was + + + align:start position:0% +you know a women's faculty group it was +a mentoring group we met with + + align:start position:0% +a mentoring group we met with + + + align:start position:0% +a mentoring group we met with +the senior administration of mit they + + align:start position:0% +the senior administration of mit they + + + align:start position:0% +the senior administration of mit they +said we are going to take this seriously + + align:start position:0% +said we are going to take this seriously + + + align:start position:0% +said we are going to take this seriously +um + + align:start position:0% +um + + + align:start position:0% +um +and we said you're lucky to have us + + align:start position:0% +and we said you're lucky to have us + + + align:start position:0% +and we said you're lucky to have us +because we're really good and we will + + align:start position:0% +because we're really good and we will + + + align:start position:0% +because we're really good and we will +help you solve this problem + + align:start position:0% +help you solve this problem + + + align:start position:0% +help you solve this problem +you know so we didn't want mit to lower + + align:start position:0% +you know so we didn't want mit to lower + + + align:start position:0% +you know so we didn't want mit to lower +its standards but + + align:start position:0% +its standards but + + + align:start position:0% +its standards but +no it is it's a comp i mean it's very + + align:start position:0% +no it is it's a comp i mean it's very + + + align:start position:0% +no it is it's a comp i mean it's very +very complex issue um + + align:start position:0% +very complex issue um + + + align:start position:0% +very complex issue um +because it it + + align:start position:0% +because it it + + + align:start position:0% +because it it +it's so culturally + + align:start position:0% +it's so culturally + + + align:start position:0% +it's so culturally +you know related + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +you know at at some level of course i'm + + align:start position:0% +you know at at some level of course i'm + + + align:start position:0% +you know at at some level of course i'm +so far beyond all of this now i'll just + + align:start position:0% +so far beyond all of this now i'll just + + + align:start position:0% +so far beyond all of this now i'll just +i come out swinging you know i mean + + align:start position:0% +i come out swinging you know i mean + + + align:start position:0% +i come out swinging you know i mean +every time i get in a situation where + + align:start position:0% +every time i get in a situation where + + + align:start position:0% +every time i get in a situation where +this becomes an issue so i you know i + + align:start position:0% +this becomes an issue so i you know i + + + align:start position:0% +this becomes an issue so i you know i +come out swinging + + align:start position:0% +come out swinging + + + align:start position:0% +come out swinging +not everybody can do that + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% +you know + + + align:start position:0% +you know +you as you move through your life you + + align:start position:0% +you as you move through your life you + + + align:start position:0% +you as you move through your life you +you know i always tell people i only + + align:start position:0% +you know i always tell people i only + + + align:start position:0% +you know i always tell people i only +pick battles i can win + + align:start position:0% +pick battles i can win + + + align:start position:0% +pick battles i can win +so i don't + + align:start position:0% +so i don't + + + align:start position:0% +so i don't +react to every slight + + align:start position:0% +react to every slight + + + align:start position:0% +react to every slight +you know i just you know most of them i + + align:start position:0% +you know i just you know most of them i + + + align:start position:0% +you know i just you know most of them i +just kind of go but of course as i've + + align:start position:0% +just kind of go but of course as i've + + + align:start position:0% +just kind of go but of course as i've +gotten more senior the more i can win so + + align:start position:0% +gotten more senior the more i can win so + + + align:start position:0% +gotten more senior the more i can win so +if i take take on more of them but um + + align:start position:0% +if i take take on more of them but um + + + align:start position:0% +if i take take on more of them but um +i think society is changing in a + + align:start position:0% +i think society is changing in a + + + align:start position:0% +i think society is changing in a +dramatic way + + align:start position:0% +dramatic way + + + align:start position:0% +dramatic way +and of course i think mit is a very + + align:start position:0% +and of course i think mit is a very + + + align:start position:0% +and of course i think mit is a very +special place our high percentage of + + align:start position:0% +special place our high percentage of + + + align:start position:0% +special place our high percentage of +women students + + align:start position:0% +women students + + + align:start position:0% +women students +our + + align:start position:0% +our + + + align:start position:0% +our +real commitment to women faculty the + + align:start position:0% +real commitment to women faculty the + + + align:start position:0% +real commitment to women faculty the +sheer numbers the critical mass the + + align:start position:0% +sheer numbers the critical mass the + + + align:start position:0% +sheer numbers the critical mass the +momentum all of that has changed this + + align:start position:0% +momentum all of that has changed this + + + align:start position:0% +momentum all of that has changed this +place dramatically + + align:start position:0% +place dramatically + + + align:start position:0% +place dramatically +uh the question i have is what is it + + align:start position:0% +uh the question i have is what is it + + + align:start position:0% +uh the question i have is what is it +like when you get out + + align:start position:0% +like when you get out + + + align:start position:0% +like when you get out +you know to the outside world + + align:start position:0% +you know to the outside world + + + align:start position:0% +you know to the outside world +i + + align:start position:0% +i + + + align:start position:0% +i +i don't know much about that but you + + align:start position:0% +i don't know much about that but you + + + align:start position:0% +i don't know much about that but you +know i suspect it's different in + + align:start position:0% +know i suspect it's different in + + + align:start position:0% +know i suspect it's different in +different fields nuclear engineering + + align:start position:0% +different fields nuclear engineering + + + align:start position:0% +different fields nuclear engineering +construction + + align:start position:0% +construction + + + align:start position:0% +construction +environmental probably great you know + + align:start position:0% +environmental probably great you know + + + align:start position:0% +environmental probably great you know +there's certain obvious places you could + + align:start position:0% +there's certain obvious places you could + + + align:start position:0% +there's certain obvious places you could +go where you would find a high + + align:start position:0% +go where you would find a high + + + align:start position:0% +go where you would find a high +percentage of women but there are + + align:start position:0% +percentage of women but there are + + + align:start position:0% +percentage of women but there are +certain other places where it's really + + align:start position:0% +certain other places where it's really + + + align:start position:0% +certain other places where it's really +quite an old boys + + align:start position:0% +quite an old boys + + + align:start position:0% +quite an old boys +network and + + align:start position:0% +network and + + + align:start position:0% +network and +you know i do think it's changing just + + align:start position:0% +you know i do think it's changing just + + + align:start position:0% +you know i do think it's changing just +changing very dramatically + + align:start position:0% + + + + align:start position:0% + +i think we have time for one more and + + align:start position:0% +i think we have time for one more and + + + align:start position:0% +i think we have time for one more and +then you've got the last word okay + + align:start position:0% +then you've got the last word okay + + + align:start position:0% +then you've got the last word okay +i + + align:start position:0% +i + + + align:start position:0% +i +i was just interested in the previous + + align:start position:0% +i was just interested in the previous + + + align:start position:0% +i was just interested in the previous +three or four questions they were more + + align:start position:0% +three or four questions they were more + + + align:start position:0% +three or four questions they were more +of the + + align:start position:0% +of the + + + align:start position:0% +of the +hierarchical issues + + align:start position:0% +hierarchical issues + + + align:start position:0% +hierarchical issues +with authority and ethics and and i + + align:start position:0% +with authority and ethics and and i + + + align:start position:0% +with authority and ethics and and i +think a situation we find ourselves in + + align:start position:0% +think a situation we find ourselves in + + + align:start position:0% +think a situation we find ourselves in +is also sort of the lateral + + align:start position:0% +is also sort of the lateral + + + align:start position:0% +is also sort of the lateral +collaborative issues where international + + align:start position:0% +collaborative issues where international + + + align:start position:0% +collaborative issues where international +or gender + + align:start position:0% +or gender + + + align:start position:0% +or gender +challenges present themselves + + align:start position:0% +challenges present themselves + + + align:start position:0% +challenges present themselves +and that i was just wondering if you + + align:start position:0% +and that i was just wondering if you + + + align:start position:0% +and that i was just wondering if you +could comment anything about sort of + + align:start position:0% +could comment anything about sort of + + + align:start position:0% +could comment anything about sort of +where you draw the line + + align:start position:0% +where you draw the line + + + align:start position:0% +where you draw the line +in terms of trying to influence your + + align:start position:0% +in terms of trying to influence your + + + align:start position:0% +in terms of trying to influence your +ethical standards with somebody else's + + align:start position:0% + + + + align:start position:0% + +well i don't know if i'd be too coherent + + align:start position:0% +well i don't know if i'd be too coherent + + + align:start position:0% +well i don't know if i'd be too coherent +on that i i + + align:start position:0% + + + + align:start position:0% + +i certainly have great concern on a + + align:start position:0% +i certainly have great concern on a + + + align:start position:0% +i certainly have great concern on a +global scale about + + align:start position:0% +global scale about + + + align:start position:0% +global scale about +you know the various ethical + + align:start position:0% +you know the various ethical + + + align:start position:0% +you know the various ethical +positions that various groups take + + align:start position:0% +positions that various groups take + + + align:start position:0% +positions that various groups take +um + + align:start position:0% + + + + align:start position:0% + +i'm obviously concerned about women in + + align:start position:0% +i'm obviously concerned about women in + + + align:start position:0% +i'm obviously concerned about women in +the large when you talk about the global + + align:start position:0% +the large when you talk about the global + + + align:start position:0% +the large when you talk about the global +the global ethics + + align:start position:0% +the global ethics + + + align:start position:0% +the global ethics +um + + align:start position:0% +um + + + align:start position:0% +um +you know with respect + + align:start position:0% +you know with respect + + + align:start position:0% +you know with respect +i mean the the environments that i've + + align:start position:0% +i mean the the environments that i've + + + align:start position:0% +i mean the the environments that i've +been in have been very comfortable + + align:start position:0% +been in have been very comfortable + + + align:start position:0% +been in have been very comfortable +environments you know i've hardly ever + + align:start position:0% +environments you know i've hardly ever + + + align:start position:0% +environments you know i've hardly ever +had to really challenge anybody + + align:start position:0% + + + + align:start position:0% + +very much um + + align:start position:0% + + + + align:start position:0% + +you know i think + + align:start position:0% +you know i think + + + align:start position:0% +you know i think +most people around here you know if + + align:start position:0% +most people around here you know if + + + align:start position:0% +most people around here you know if +there's a need for a challenge it's a + + align:start position:0% +there's a need for a challenge it's a + + + align:start position:0% +there's a need for a challenge it's a +little push + + align:start position:0% +little push + + + align:start position:0% +little push +just a little push + + align:start position:0% +just a little push + + + align:start position:0% +just a little push +is all it takes + + align:start position:0% + + + + align:start position:0% + +and i'm trying to think of situations + + align:start position:0% +and i'm trying to think of situations + + + align:start position:0% +and i'm trying to think of situations +where that + + align:start position:0% +where that + + + align:start position:0% +where that +comes about for example imagine hiring + + align:start position:0% +comes about for example imagine hiring + + + align:start position:0% +comes about for example imagine hiring +faculty you know you're in a search + + align:start position:0% +faculty you know you're in a search + + + align:start position:0% +faculty you know you're in a search +committee and you're hiring faculty and + + align:start position:0% +committee and you're hiring faculty and + + + align:start position:0% +committee and you're hiring faculty and +you're looking at women and minorities + + align:start position:0% +you're looking at women and minorities + + + align:start position:0% +you're looking at women and minorities +and sometimes you have to push a group + + align:start position:0% +and sometimes you have to push a group + + + align:start position:0% +and sometimes you have to push a group +like that a little bit + + align:start position:0% +like that a little bit + + + align:start position:0% +like that a little bit +to get them to think more globally to + + align:start position:0% +to get them to think more globally to + + + align:start position:0% +to get them to think more globally to +get them to not make assumptions about + + align:start position:0% +get them to not make assumptions about + + + align:start position:0% +get them to not make assumptions about +people based on + + align:start position:0% +people based on + + + align:start position:0% +people based on +on you know race or gender just a little + + align:start position:0% +on you know race or gender just a little + + + align:start position:0% +on you know race or gender just a little +push + + align:start position:0% +push + + + align:start position:0% +push +because this institution i think really + + align:start position:0% +because this institution i think really + + + align:start position:0% +because this institution i think really +does respond + + align:start position:0% +does respond + + + align:start position:0% +does respond +so i think in a situation like that you + + align:start position:0% +so i think in a situation like that you + + + align:start position:0% +so i think in a situation like that you +know it is an issue you're conscious of + + align:start position:0% +know it is an issue you're conscious of + + + align:start position:0% +know it is an issue you're conscious of +but just + + align:start position:0% +but just + + + align:start position:0% +but just +just a little pushes is really all it + + align:start position:0% +just a little pushes is really all it + + + align:start position:0% +just a little pushes is really all it +takes to + + align:start position:0% +takes to + + + align:start position:0% +takes to +move it + + align:start position:0% +move it + + + align:start position:0% +move it +then there are obviously other issues + + align:start position:0% +then there are obviously other issues + + + align:start position:0% +then there are obviously other issues +in which there's no compromise + + align:start position:0% +in which there's no compromise + + + align:start position:0% +in which there's no compromise +and i would say the issue of academic + + align:start position:0% +and i would say the issue of academic + + + align:start position:0% +and i would say the issue of academic +integrity is one for which there is no + + align:start position:0% +integrity is one for which there is no + + + align:start position:0% +integrity is one for which there is no +compromise + + align:start position:0% +compromise + + + align:start position:0% +compromise +and + + align:start position:0% +and + + + align:start position:0% +and +so you know you would just just + + align:start position:0% +so you know you would just just + + + align:start position:0% +so you know you would just just +basically lay out those basic principles + + align:start position:0% +basically lay out those basic principles + + + align:start position:0% +basically lay out those basic principles +and just make sure that people + + align:start position:0% +and just make sure that people + + + align:start position:0% +and just make sure that people +understood + + align:start position:0% +understood + + + align:start position:0% +understood +because i think the + + align:start position:0% +because i think the + + + align:start position:0% +because i think the +i think the importance of an issue like + + align:start position:0% +i think the importance of an issue like + + + align:start position:0% +i think the importance of an issue like +that is if you present it properly it is + + align:start position:0% +that is if you present it properly it is + + + align:start position:0% +that is if you present it properly it is +so obviously right + + align:start position:0% +so obviously right + + + align:start position:0% +so obviously right +you know it's it's not a matter for + + align:start position:0% +you know it's it's not a matter for + + + align:start position:0% +you know it's it's not a matter for +discussion if you present it right + + align:start position:0% + + + + align:start position:0% + +and so you know this this issue + + align:start position:0% +and so you know this this issue + + + align:start position:0% +and so you know this this issue +this organization will respond uh i've + + align:start position:0% +this organization will respond uh i've + + + align:start position:0% +this organization will respond uh i've +just not been in situations where people + + align:start position:0% +just not been in situations where people + + + align:start position:0% +just not been in situations where people +were cheating or stealing or + + align:start position:0% +were cheating or stealing or + + + align:start position:0% +were cheating or stealing or +you know that sort of thing + + align:start position:0% +you know that sort of thing + + + align:start position:0% +you know that sort of thing +not likely to be at this point because + + align:start position:0% +not likely to be at this point because + + + align:start position:0% +not likely to be at this point because +they everybody knows i'll turn them in + + align:start position:0% +they everybody knows i'll turn them in + + + align:start position:0% +they everybody knows i'll turn them in +so + + align:start position:0% +so + + + align:start position:0% +so +you know it's just not not an issue \ No newline at end of file diff --git a/Mx0uXIBD-yA.txt b/Mx0uXIBD-yA.txt new file mode 100644 index 0000000000000000000000000000000000000000..346ac4fdea1cf02caa68c922cdbc146fb0d193b9 --- /dev/null +++ b/Mx0uXIBD-yA.txt @@ -0,0 +1,1933 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: For those of you who +are unaccustomed to seeing + +it, that blue stuff through +the window is called sky. + +OK. + +I left you last time +with a question. + +I'd shown you a bisection search +implementation, or I + +should say putative +implementation of the square + +root, and told you that it was +flawed, and asked you to think + +about what was wrong with it. + +So first, I'd just like +to take a poll. + +How many of you know what the +problem is, or at least what a + +problem is? + +OK well that's a good start. + +And I won't ask how many of +you don't know, because I + +presume that's the +rest of you. + +So let's look at it now. + +I'm not going to ask you the +answer, because I want to show + +people how to find it. + +So here's a slightly simplified +version of it. + +Just get rid of this stuff here, +so it doesn't confuse + +the picture. + +So this is roughly the one we +looked at on Tuesday, but I + +just took out some print +statements and things and + +simplified it. + +And let's just run it. + +And we'll run it with +trying to find the + +square root of 0.5. + +See what happens +when we run it. + +Well, not much happens +when we run it. + +Actually quite a lot +is happening. + +We just can't see it. + +So this program is running +longer than I expected it to. + +So if you go to the keyboard and +you hit Control and C. It + +will interrupt the program. + +It generates what's called +a keyboard interrupt, + +and it stops it. + +And it tells us where it +happened to stop it. + +It happened to stop +it in line seven-- + +the test of the while loop. + +And the problem is, the program +just seemed to be + +running forever. + +So despite my, perhaps +persuasive, argument last time + +about the decrementing function, +there's clearly a + +flaw in my logic. + +And, in fact, it does not +always terminate. + +So what do we do about it? + +Well this is the main trick. + +And one of the things I need +you to understand this + +semester is perhaps the most +important thing you'll learn + +is how to debug programs. + +Too many people think the hard +part is done when they write + +the code the first time. + +No, that's actually +the easy part. + +The hard part is actually +getting it to work. + +So the thing you need to learn +is how to debug code, and the + +nice thing is it's a +transferable skill. + +It's also fine for debugging +lab experiences or family + +members or anything else that +can be seriously awry. + +So the way I do it when I +program is typically with + +print statements. + +So the fact that the program was +running forever, suggests + +that I'm not exiting +the while loop. + +So clearly, I need to print +something in the while loop. + +And the only three variables +it seems to be using are + +answer, low, and high. + +Those are the three +that change. + +So let's see what +the value is. + +Notice, by the way, that I +actually went to the trouble + +to type ans equals ans, low +equals low, et cetera. + +A lot of people would just say, +OK I'm going to print and + +they'll ans comma +low comma high. + +And then when they run +the code they'll + +forget which is which. + +The most common problem that +people have in debugging + +programs is that +they are lazy. + +They think they're saving +themselves work, and in fact + +they're creating work. + +So my first piece of +advice to you as + +debuggers is don't be lazy. + +Maybe you heard this from your +mother at some point in life, + +or your father. + +But now you're hearing +it from me. + +Try and just do it right +the first time. + +So let's run it and see +what happens now. + +Well at least it's printing +some output. + +And it's chugging away +and chug-- uh-oh-- + +so now, we see we have +a real problem. + +We've reached a fixed point, +where every time through the + +loop, nothing is changing. + +Well the first time we go +through the loop and nothing + +changes we know we're in +trouble, because nothing's + +going to ever change. + +And therefore, we're going to +be in the loop forever. + +So we see, I've gone +to a stage where + +everything equals 0.5. + +And now if I go back and look at +the code, and I ask myself + +the question well what happens +when everything is 0.5, and I + +can see the problem. + +It's this statement here. + +Yep, turn it around maybe. + +But that's never going to change +now, because it's 0.5 + +plus 0.5, divided by 2 is 0.5. + +And it'll just stay +there forever. + +So that's my problem. + +I have to somehow change +my code now, so that + +this doesn't happen. + +So what is the problem? + +Now somebody can tell +me, simply. + +What is the problem here? + +What was the flaw in my +reasoning when I first set + +this program up? + +Yeah? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Louder please? + +AUDIENCE: You don't have a high +minus low is less than or + +equal to epsilon. + +PROFESSOR: So the comment was I +don't have a high minus low + +is less than or equal +to epsilon. + +True, but that's not really +the real flaw. + +Yeah? + +AUDIENCE: The fraction is +greater than the original + +fraction, so the solution is +not in the search space. + +PROFESSOR: Exactly. + +So the answer is the problem was +that I did a search in a + +region, and the answer wasn't +in that region. + +Because the square root +of 0.5 does not lie + +between 0 and 0.5. + +Silly me, when I thought about +it, I didn't think of finding + +the square root of numbers +less than 1. + +So what's a simple fix? + +Well what I can do is the +following: I'll go back and + +say high is going to be +the max of x and 1. + +So now I'm going to ensure that +the square root actually + +does lie in the region +I'm searching. + +I hope. + +Let's run it. + +Ah. + +All right, well I got to some +stuff at the end which you + +shouldn't worry about, but it +found something that I guess + +is a good enough answer. + +We'll get rid of that code I +put in this morning which + +we'll get to this later. + +OK so I've now fixed +the program. + +Everyone with me on that? + +Any questions? + +And the thing to understand is +conceptually what was wrong + +with my reasoning, that I'm +doing a search in a region + +where the answer doesn't lie. + +So I'm not going to find it. + +And the other thing to +understand is my systematic + +way of finding the bug. + +Now I confess I knew the bug +was there when I wrote the + +code, so I kind of cheated +with the debugging. + +But even if I hadn't +known, this is what + +I would have done. + +I would have put in that +print statement. + +All right, so now we have +actually a pretty good piece + +of code for finding +square roots. + +And as we looked at on Tuesday, +I can use the same + +piece of code. + +I can modify it to get cube +roots, or fourth roots, or + +fifth roots. + +And so I have a general +framework for doing things. + +But it's pretty unsatisfying in +that sense, because let's + +look at it. + +If I wanted to find the square +root of some number other than + +0.5, I have to go and edit the +code, replace the assignment + +to x by whatever I'm +trying to do. + +If I want to do cube roots I +have to cut and paste and edit + +and do things. + +There's no very good way to now +embed this piece of code + +inside a larger computation. + +Imagine that I've got some +10,000 line program that needs + +to find the square root six or +seven times, well now I'm + +going to have six or seven +copies of this code in my + +program, for every time I +need the square root. + +Clearly not what +you want to do. + +In general, having more +code is a bad thing. + +So it's not like you're given an +essay to write and someone + +tells you it's got to be 5,000 +words, and you just sweat + +blood trying to figure out how +to stretch it to be that long. + +In code, it's the other +way around. + +Most of the time we want to make +it shorter not longer. + +And the reason we want to do +that is the difficulty of + +getting code to work grows, +maybe even grows + +quadratically, or worse but +the size of the code. + +So the more code you have, +the harder it is + +to get it to work. + +So one of the things good +programmers learn to do is + +write less code. + +And so we don't measure +productivity of a programmer + +by the number of lines of code +they produce each day, but we + +measure it by the amount +of functionality they + +produce each day. + +And we give them bonus points +if they achieve the desired + +functionality with less code. + +So let's talk about how +we can write less code + +and accomplish more. + +Well to do that, we're going +to look at a new language + +mechanism-- + +actually not new, but +new to this class-- + +called a function. + +But before we do that, I want +to pull back and talk about + +what it is we hope to accomplish +by introducing + +functions into our programming +language. + +We want to provide a mechanism +that provides for two things: + +decomposition and abstraction. + +What decomposition does, is +it creates structure. + +It allows us to break our +program up into something + +called modules. + +And the module we'll focus on +today is function, but later + +we'll see there's another +important kind of module in + +Python called the class. + +And the advantage of a module is +it should be self-contained + +and reusable. + +So it's a self-contained unit +of functionality that can be + +used in multiple contexts. + +Abstraction suppresses +details. + +It allows us to use a piece +of code as if it + +were a black box. + +That is, something whose +interior details we can't see, + +don't need to see, and shouldn't +even want to see. + +We only need to understand +what it does, + +not how it does it. + +And that lets us use code +that other people + +have written easily. + +And, in fact, use code that +we have written easily. + +It's one of those few occasions +where I think Thomas + +Gray was right, when he said, +"ignorance is bliss." + +Sometimes knowing +less is better. + +All right, so let's look at +the way functions work. + +The functions let us +break code into + +reusable, coherent pieces. + +Now we've already looked at +similar kinds of things. + +When we looked at say floating +point numbers, and we wrote + +operations like plus or divide, +whatever, we didn't + +worry about how they +were actually + +implemented in the machine. + +We said OK they do something, +they're kind of like dividing + +real numbers, let's not worry +about the details. + +We do that with a +lot of things. + +We looked at strings. + +We concatenated strings. + +Well we didn't worry about +how did Python + +go about doing that. + +We just assumed it did it, +and it had the meaning + +we wanted it to. + +What functions let us do is +extend the language in some + +sense by adding new primitives +that we can use just the way + +we used the built-in +primitives. + +So let's look at an +example here. + +I've written a very +simple function. + +Does something that we actually +did already when we + +looked at square roots. + +It's a function called +within epsilon. + +And let me comment this out +while I'm thinking about it, + +so we don't have to live +with it later. + +And I now want to walk you, +slowly, through what this + +function does. + +So at the start, it uses the +keyword Def, short for define. + +Following that is a name. + +I chose the name +within epsilon. + +You can choose any name you +want for a function. + +I'm strongly encourage you to +choose mnemonic names, that is + +to say names that +have a meaning. + +So in some sense you see it says +within epsilon, and you + +know what it does already. + +Following that, it has three +things called formal + +parameters. + +I'll come back to in a minute, +what that means. + +And then after that, it's +got something called + +the function body. + +So we see that a function has a +name, it has parameters, and + +it has a body. + +The body is the code that's +part of the function. + +In the body, you can write +any code you want. + +Plus, there's something you +can't write outside of a + +function, called return. + +That's a special command that +says whoever calls me has + +called me to have me +compute a value. + +I'm going to return the value +that this person would want. + +And then here we see something +that's very important. + +This is where we get +abstraction, and that's the + +specification of the function. + +And it says here, there +are two pieces to it. + +One that its parameters x, y, +and epsilon, are all floats. + +And furthermore, epsilon +is greater than 0. + +You can imagine this is +important, and it returns true + +if x is within epsilon of y. + +Otherwise it will +return false. + +If I want to use within epsilon, +I don't need to look + +at the code. + +I look instead at the +specification. + +Now here where the code is one +line, maybe I haven't gained a + +lot by looking at the +specification + +instead of the code. + +But you can imagine if the code +were 1,000 lines, I'd + +much rather read the +specification than the code. + +We'll also see for other reasons +later why it's in fact + +dangerous to look at the code. + +How do I use it? + +I use it by invoking it. + +So I could, for example write +something like print within + +epsilon, of two, three, one. + +What's it going to print? + +Pardon? + +Why is it going to print +an error do you think? + +AUDIENCE: Because you +haven't put epsilon. + +PROFESSOR: Ah, typed it wrong. + +Thank you. + +You're correct. + +It would have printed +an error. + +Now what will it print? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Sure enough. + +I could also, if I chose, +write something like val + +equals that, then if I want +I could print val. + +Now it's going to print false. + +So within epsilon is just like +plus or something else, does + +some computation, +returns a value. + +I can use that value any place +I could have used an + +expression. + +Now one more thing to +look at with this. + +Suppose I don't return +anything. + +Anyone want to guess what +it's going to do now? + +I point this out, because this +is a very common error. + +People write lots of code, +calculate some wonderful value + +and then forget to return it. + +What's it going to do now? + +Well let's run it and see. + +That, by the way, is a good +habit to get into. + +It's going to return the +special value none. + +Remember we looked at that +earlier, meaning I + +don't have a value. + +So if you see in your code some +none popping up where you + +don't expect it to, it's +probably because you forgot to + +return a value. + +So just keep that in mind. + +All right, now there's a +big advantage of this. + +Once I've written this code I +can now anywhere I want call + +within epsilon, and I don't have +to duplicate the code. + +I only do it once. + +As I said earlier maybe I'm not +gaining much, because the + +body is so short. + +On the other hand, I'm still +gaining something. + +Notice that when I look at the +code down here, it's easy to + +read, I'm printing within +epsilon two, three, and one. + +And I don't have to decode this +and tell me that that's + +what that's doing. + +So if I have a function and I +choose the names properly, + +code that uses the function +is much easier to read. + +And that can be a big value. + +All right, let's look +at another example. + +So here I've got this +function, f. + +I've chose a non-mnemonic name, +because there isn't much + +meaning to this function. + +What f does, it is a +formal parameter x. + +It sets x to x plus 1. + +Then it prints x +and returns x-- + +pretty boring. + +So let's see what +it does here. + +So now I'm going to set x to +three, set z, or zed if you + +happen to be Canadian, +to f of x. + +And then print the values +of z and x. + +Also in f, before I return +x, I'm going to print it. + +So let's see what happens +when I run this one. + +It prints four, four, +and then three. + +All right, what's going on? + +Why did it do that? + +Well it's pretty easy to see +why it printed four here, + +because I called f of x with +an x equal to 3, and then I + +incremented it by one, and +then I printed it. + +It's probably also easy to +understand why z was four, + +because I returned the value of +x here, which was four and + +it printed it. + +But why is this x three? + +And the answer is this x and +that x have nothing to do with + +each other. + +Right? + +I could just as easily have +chosen some other value for + +the formal parameter, say +George, and said George is + +equal to George plus 1, print +George, return George. + +There is no relation between the +name of the formal and, in + +this case, x defined in the +calling environment. + +So now let's think about that +by working slowly and + +carefully through what happens +when we call a function. + +So the first thing that happens +at the call, and I'll + +just work it through this one, +is the formal parameter, x in + +this case, is bound-- + +and I'll come back to what +binding means, that's a + +critical concept here-- + +to the value of the +actual parameter. + +So these are important terms, +actual and formal, which in + +this case, also happens +to be called x. + +But what's happening here, is +upon entry of a function, a + +new scope is created. + +What's a scope? + +A scope is a mapping from +names to objects. + +So if we look at what's going +on over here, we can draw a + +little picture. + +Well before I draw a picture, +I'm going to look at a + +slightly more complicated +example. + +Well, yeah let's do that. + +This one is not in your +handout, but it is + +illustrative of, I think, what's +really going on here. + +Here I've got another +beautifully named function, in + +this case f1, and inside it, +I've defined another function, + +called g, which takes +no arguments. + +I've set x to abc. + +Then I haven't shown you these +assert statements yet, or + +haven't talked about them. + +Assert is a command in which the +keyword assert is followed + +by an expression that +evaluates to + +either true or false. + +If it evaluates to true, +it does nothing. + +It just continues. + +If it evaluates to false, +it stops your + +program dead in its tracks. + +So I've just used it here as a +trick to make my program stop + +when I run it. + +In general, you'll find that +I use asserts quite a lot. + +So for example, in the next +piece of code, which + +is called find root. + +It takes the root, is it square, +or cube, whatever, the + +value, and epsilon. + +It assumes that powers, and +int, and val, and epsilon + +float, in the specification. + +And then you'll notice, I +start by putting in an + +assertion here. + +And what I'm asserting is that +the actuals to which these + +formals are bound, have the +properties the specification + +says they do. + +This is what's called defensive +programming. + +In principle, I shouldn't have +to do that, because in + +principle, nobody should call +this with incorrect values. + +But, in fact, it can happen. + +Programmers occasionally +make mistakes. + +And so I'm protecting myself +by checking that the + +assumptions are met, and +if they're not, my + +program will just stop. + +Then I can go hunt down the fool +that called it with the + +wrong parameters-- + +probably myself. + +So asserts are good for that, +and I'll use them a lot for + +these kinds of things. + +I'll also use them when I +think I know what value + +something should be in a program +at some point, and I'm + +not sure it really is. + +I'll assert that it has the +value I think it is. + +I'll assert that x is six, if I +think it's going to be six. + +And then my program will +conveniently stop for me if + +it's not true. + +All right so that's assert. + +Other than that, I think there's +nothing here you + +haven't seen before. + +So what's going to happen, we're +going to step through + +this piece by piece. + +So initially, as we look at it, +we enter the main body of + +the program, which is not +wrapped in a function. + +So what IDLE will do, or the +interpreter will do, is it + +will start by executing +each def. + +But executing a def doesn't do +anything, but put some names + +in the environment. + +Then it will go and start +actually running and + +interpreting the code that's not +nested inside a function. + +So the first thing that will +happen is the interpreter will + +build for me what's +called the scope. + +I've already mentioned, +that's a mapping + +from names to objects. + +So in the outermost scope, it +will first find the name f1. + +F1 it will tell me that f1 maps +to an object that happens + +to be a function. + +So it will come over here-- + +and I'm just going to draw some +picture, we'll assume + +that's the memory of +the computer-- + +and it will map to something +that happens to be a bunch of + +code, if you will. + +All right? + +It will then stop. + +It will then notice that it's +got, at the outermost level a + +variable called x. + +And that will map to an integer, +which will initially + +have no value in it. + +And then after the assignment, +it will now be bound to the + +object three. + +It will then create another +object z, but before it can + +bind a value to it, it will +invoke the function f1. + +Now the interpreter starts +to execute f1. + +When it does that, it will +create another scope. + +So this is the main scope. + +It will next create a scope +called the f1 scope. + +In that, it will have another +name g, which will be + +bound to some code. + +It will have a name x, which +will be initially + +bound to the actual. + +So in this case, it will be +bound to the object three. + +We'll then eventually +do a print. + +It will involve g, which will +now create the g scope. + +And the g scope will create a +name x, which in this case + +will be bound to +the string abc. + +It will then start executing +g, and it will stop. + +So let's see what +that looks like. + +Sure enough, it got an +assert false, gave + +an assertion error. + +What I can do now is go up to +this debug here, and go to + +what's called a stack viewer. + +Each of these scopes is what's +called a stack frame. + +Now why are they called +stack frames? + +Because when we do it, we begin +with the main scope. + +We call f, and we +get the scope. + +f calls g and we get +the g scope. + +When g completes, which alas +it doesn't because of the + +error, it pops the stack, and +gets rid of the g scope. + +And now the stack is the f and +the main, and then when f + +completes, it will have +just the main. + +So it's last in, first out, +which is typically called a + +stack in computing-- + +or a LIFO, if you're a course +15 major, and do accounting. + +So let's look at the +stack viewer. + +And I apologize for the small +type font, but I was unable to + +make it look bigger. + +So it says at the top we've +got an assertion error. + +And then you'll note it's got +three stacks: the main, the f1 + +stack, and the g stack. + +I forgot I called +it f1, not f. + +Then I can inspect +them further. + +So the g stack has local +and global variables. + +The local variables include +x, which is equal to abc. + +Globals we'll get to later. + +If I look at f1, it also has a +local called x, but its value + +is now four, not abc. + +And it has a value called +g, which is a + +function, as we discussed. + +And if I look at main, it has a +bunch of things, but it has + +everything that's available in +the interpreter, which because + +we've looked at within +epsilon it's there. + +But you'll notice it's x is 3. + +All right? + +So the stack viewer can be very +handy, to look at what + +you've got, when you've +got a bunch of calls. + +Now if we go back to our code +here, and we'll take this out. + +And suppose what we do is +we assert false here. + +Now if we look at the stack +viewer, we see that we have f1 + +in main, but g is +no longer there. + +It's gone. + +All those variables don't exist +anymore, because I'm no + +longer in g. + +This is the nice thing, because +it means if you call + +something 1,000 times, +it doesn't + +use up all your memory. + +Every time it's finished, +it gets rid of what + +it no longer needs. + +All right? + +Does that make sense? + +This is an important +thing to get-- + +yeah, thank you, question. + +AUDIENCE: --the assertion. + +PROFESSOR: Where did I-- + +AUDIENCE: Where did you put this +other assertion, when you + +just changed-- + +PROFESSOR: Ah, where did I +put the other assertion? + +If we look at the code, you'll +see I put it after I call g, + +and g is by now returned, but +before I left f1, which is why + +the f1 stack is still present. + +That makes sense to you? + +Which stacks exist, which stack +frames exist, depends + +upon which functions +are still active. + +Yeah? + +AUDIENCE: How come +you don't need a + +return under the g function? + +PROFESSOR: Oh, because there's +not going to be anything + +interesting. + +It's useless. + +Right? + +Why don't I need a +return under g? + +Well if I wanted it to do +something useful, I would need + +to return something. + +But I'd probably also want to +pass it some arguments, rather + +than have it take no +arguments, as well. + +So it's here just to be the +simplest thing I could put + +that created a stack frame. + +But don't try and interpre it as +being anything meaningful. + +Yeah? + +AUDIENCE: Would you run into +problems assuming that g did + +something to x and +then returned it? + +Would you run into any problems +that you named the + +variable the same? + +You know, that you +used x twice? + +Would you want to-- + +PROFESSOR: No. + +If an x exists, or any variable +exists within a + +function body, when you leave +that function, that variable + +is gone forever. + +These are just names. + +They have no intrinsic +meaning. + +So one of the ways to think +about it, and we'll see this + +later when we get to classes-- + +a lot later. + +You could, if you wanted, think +about this as really the + +name g.x, and you could really +think of this as the name of + +f1.x, and you could think of +this as the name of main.x, + +indicating that they're +really not the same. + +But it would be kind of a pain +to write them all that way. + +OK? + +So different scopes have +different names + +available to them. + +You can use the names in the +scope, and you have to keep + +track of what they mean. + +OK? + +Any other questions? + +These are great questions, and +I really do appreciate them. + +Yeah? + +AUDIENCE: Does this also +happen with four loops? + +Like if you say 4x in +range something, + +can you use x later? + +Or is it x-- + +PROFESSOR: You can +use x later. + +AUDIENCE: Okay so-- + +PROFESSOR: x will be available +outside the loop. + +This was if you said for x in +something, is x available + +outside the loop? + +Yes. + +And in fact, you'll often want +to test what the final value + +of x is, when you +leave the loop. + +OK, the next thing on your +handout, and I'm not going to + +go over it, is using functions +to implement something that + +finds roots. + +There's no real point in +my walking you through + +this code in class. + +I did include it +in the handout. + +And by the way, the handouts +are all available after + +lecture, online. + +Is that, I think you should work +through in your own, and + +make sure you understand it, +to get a sense of how + +functions work. + +And it's certainly related to +the current problem set, which + +would be another good reason +to work through it-- + +the problem set that will +be posted today-- + +the new problem set, PS 2. + +Note again how careful I am +about the specifications. + +And I should point out something +interesting, if I + +type find root, open para-- +well let's do this here. + +Let's clear things up. + +Let's get rid of things +that will cause + +the program to halt. + +Notice that when I type find +root open, open paren, it's + +given me the values-- + +the names of the formal +parameters, which I've chosen + +in such way that will remind me +what their value should be. + +And it's also given me part of +the specification, the piece + +in the triple quotation marks +to tell me the rules I'm + +supposed to be following +here on these things. + +So it's a very handy thing. + +And as you use IDLE, you'll get +used to the fact that this + +is a convenience. + +All right, work your way +through that code. + +Make sure you know +what it does. + +Finally, today I want to switch +gears, and talk about + +something else. + +Up till now, all of the programs +we've looked at have + +been numeric-- + +they've played with numbers. + +And I've done that, because I +assumed you guys all had some + +intuition about numbers. + +I've use strings as a primitive +data element to + +print things, but we haven't +done anything very interesting + +with strings. + +However strings are indeed quite +interesting, in that + +they're the first non-scalar +value we've looked at. + +You'll recall non-scalar values +are values that can be + +decomposed. + +So if we now look at the code +again, I've got this little + +piece of code called +sumDigits. + +So before, the for statement +we looked at + +was for x in range. + +Well you can apply it to a for +statement to any type that has + +a way to enumerate +its elements. + +So for c in STR, actually of +1952, so I've taken the number + +1952 and converted it to a +string so it will now be quote + +one nine five two, I can now +do something to every + +character in that string. + +And what I'm doing is converting +it back to an int, + +and then adding it. + +So this will give me the +sum of the digits. + +17. + +This is a very convenient +mechanism, and you'll use for + +a lot, this way. + +You'll use it in fact more for +this sort of thing then you + +will for ints. + +Now I can also select values. + +So if I look at-- + +I don't know what's +going on here. + +Every once in while when you go +back and forth between the + +editor and the shell, the shell +hangs and you have to go + +try it again. + +If I go to s equals abc, I can +look at individual elements of + +s, for example s sub +0, which will be a. + +I can also look at +slices of s. + +So for example s +from 0 to one. + +That's interesting. + +What is it doing? + +Now try and infer. + +I'll give you another example. + +So you'll remember when we +did range from x to y, it + +went y minus 1. + +Same kind of thing is +happening here. + +So that's why s from 0 to one +gives me only one character, + +but s from 0 to two gives me +the character string ab. + +This is what's called slicing, +and it's very common. + +What a slice does, is it +makes a new copy-- + +makes a new object, in this +case-- which is a sub-string + +of the original string. + +There are many other things +I can do on strings. + +I can do something like s.find, +and it will tell me + +that b is at position +number one in s. + +So use Google, whatever you use, +to find the Python web + +page that describe strings, and +it will give you all of + +the operations you can do. + +And they're quite convenient. + +One other scalar type that +you're going to need for the + +problem set is tuples, and +that will be discussed in + +recitation tomorrow. + +OK, thanks a lot. \ No newline at end of file diff --git a/NbXDgm7UyVM.txt b/NbXDgm7UyVM.txt new file mode 100644 index 0000000000000000000000000000000000000000..6a47a756b788f5388ee48b96fa41075ebebdabac --- /dev/null +++ b/NbXDgm7UyVM.txt @@ -0,0 +1,355 @@ +align:start position:0% + +let's consider the motion of a symmetric + + align:start position:0% +let's consider the motion of a symmetric + + + align:start position:0% +let's consider the motion of a symmetric +object that's rotating about a fixed + + align:start position:0% +object that's rotating about a fixed + + + align:start position:0% +object that's rotating about a fixed +axis so we could take some object and we + + align:start position:0% +axis so we could take some object and we + + + align:start position:0% +axis so we could take some object and we +can imagine this is sort of what + + align:start position:0% +can imagine this is sort of what + + + align:start position:0% +can imagine this is sort of what +sometimes people refer to as a spinning + + align:start position:0% +sometimes people refer to as a spinning + + + align:start position:0% +sometimes people refer to as a spinning +top and it's rotating about this + + align:start position:0% +top and it's rotating about this + + + align:start position:0% +top and it's rotating about this +symmetry axis K and we know that the + + align:start position:0% +symmetry axis K and we know that the + + + align:start position:0% +symmetry axis K and we know that the +angular velocity of the object we can + + align:start position:0% +angular velocity of the object we can + + + align:start position:0% +angular velocity of the object we can +write as Omega ZK hat and the angular + + align:start position:0% +write as Omega ZK hat and the angular + + + align:start position:0% +write as Omega ZK hat and the angular +momentum about this symmetry axis we + + align:start position:0% +momentum about this symmetry axis we + + + align:start position:0% +momentum about this symmetry axis we +just showed that was equal to the moment + + align:start position:0% +just showed that was equal to the moment + + + align:start position:0% +just showed that was equal to the moment +of inertia about this axis times the + + align:start position:0% +of inertia about this axis times the + + + align:start position:0% +of inertia about this axis times the +angular velocity and in particular the + + align:start position:0% +angular velocity and in particular the + + + align:start position:0% +angular velocity and in particular the +magnitude of the angular momentum I'll + + align:start position:0% +magnitude of the angular momentum I'll + + + align:start position:0% +magnitude of the angular momentum I'll +just write that L about that axis is I + + align:start position:0% +just write that L about that axis is I + + + align:start position:0% +just write that L about that axis is I +axis times the magnitude of the angular + + align:start position:0% +axis times the magnitude of the angular + + + align:start position:0% +axis times the magnitude of the angular +velocity now we've seen separately that + + align:start position:0% +velocity now we've seen separately that + + + align:start position:0% +velocity now we've seen separately that +the kinetic energy about this axis which + + align:start position:0% +the kinetic energy about this axis which + + + align:start position:0% +the kinetic energy about this axis which +we'll call the rotational kinetic energy + + align:start position:0% +we'll call the rotational kinetic energy + + + align:start position:0% +we'll call the rotational kinetic energy +was one-half times the moment of inertia + + align:start position:0% +was one-half times the moment of inertia + + + align:start position:0% +was one-half times the moment of inertia +about that axis times the angular + + align:start position:0% +about that axis times the angular + + + align:start position:0% +about that axis times the angular +velocity squared but here we see that + + align:start position:0% +velocity squared but here we see that + + + align:start position:0% +velocity squared but here we see that +Omega squared is equal to L over I so if + + align:start position:0% +Omega squared is equal to L over I so if + + + align:start position:0% +Omega squared is equal to L over I so if +we substitute that in we get L squared + + align:start position:0% +we substitute that in we get L squared + + + align:start position:0% +we substitute that in we get L squared +about that axis over I axis squared and + + align:start position:0% +about that axis over I axis squared and + + + align:start position:0% +about that axis over I axis squared and +so we have a nice expression for the + + align:start position:0% +so we have a nice expression for the + + + align:start position:0% +so we have a nice expression for the +kinetic rotational kinetic energy is l + + align:start position:0% +kinetic rotational kinetic energy is l + + + align:start position:0% +kinetic rotational kinetic energy is l +squared about that axis over to moment + + align:start position:0% +squared about that axis over to moment + + + align:start position:0% +squared about that axis over to moment +of inertia about that axis and this we + + align:start position:0% +of inertia about that axis and this we + + + align:start position:0% +of inertia about that axis and this we +can describe is the kinetic energy of a + + align:start position:0% +can describe is the kinetic energy of a + + + align:start position:0% +can describe is the kinetic energy of a +symmetric body about a fixed axis it is + + align:start position:0% +symmetric body about a fixed axis it is + + + align:start position:0% +symmetric body about a fixed axis it is +nice to notice the angular the linear + + align:start position:0% +nice to notice the angular the linear + + + align:start position:0% +nice to notice the angular the linear +analogy to this when we wrote that the + + align:start position:0% +analogy to this when we wrote that the + + + align:start position:0% +analogy to this when we wrote that the +momentum of an object was MV so the + + align:start position:0% +momentum of an object was MV so the + + + align:start position:0% +momentum of an object was MV so the +magnitude of the momentum is just M + + align:start position:0% +magnitude of the momentum is just M + + + align:start position:0% +magnitude of the momentum is just M +times V and when we write kinetic energy + + align:start position:0% +times V and when we write kinetic energy + + + align:start position:0% +times V and when we write kinetic energy +translation as one-half MV squared we + + align:start position:0% +translation as one-half MV squared we + + + align:start position:0% +translation as one-half MV squared we +can write that as a translational + + align:start position:0% +can write that as a translational + + + align:start position:0% +can write that as a translational +kinetic energy as P squared + + align:start position:0% +kinetic energy as P squared + + + align:start position:0% +kinetic energy as P squared +over 2m so once again we see this nice + + align:start position:0% +over 2m so once again we see this nice + + + align:start position:0% +over 2m so once again we see this nice +analogy for rotational motion where we + + align:start position:0% +analogy for rotational motion where we + + + align:start position:0% +analogy for rotational motion where we +describe it in terms of the angular + + align:start position:0% +describe it in terms of the angular + + + align:start position:0% +describe it in terms of the angular +momentum and the moment of inertia and + + align:start position:0% +momentum and the moment of inertia and + + + align:start position:0% +momentum and the moment of inertia and +the linear motion we describe in terms + + align:start position:0% +the linear motion we describe in terms + + + align:start position:0% +the linear motion we describe in terms +of momentum and the mass \ No newline at end of file diff --git a/OMdmcfA1MDU.txt b/OMdmcfA1MDU.txt new file mode 100644 index 0000000000000000000000000000000000000000..ac2e86fdb9da4a081a4685e000c8f264d4d5ed99 --- /dev/null +++ b/OMdmcfA1MDU.txt @@ -0,0 +1,859 @@ +align:start position:0% + +richard duffel again the previous + + align:start position:0% +richard duffel again the previous + + + align:start position:0% +richard duffel again the previous +segment that i prepared for you is to + + align:start position:0% +segment that i prepared for you is to + + + align:start position:0% +segment that i prepared for you is to +describe what the flaw of averages is + + align:start position:0% +describe what the flaw of averages is + + + align:start position:0% +describe what the flaw of averages is +but now we're talking about why it is + + align:start position:0% +but now we're talking about why it is + + + align:start position:0% +but now we're talking about why it is +important + + align:start position:0% +important + + + align:start position:0% +important +and it's important because the standard + + align:start position:0% +and it's important because the standard + + + align:start position:0% +and it's important because the standard +practice that evaluates the performance + + align:start position:0% +practice that evaluates the performance + + + align:start position:0% +practice that evaluates the performance +of a system under the most likely of the + + align:start position:0% +of a system under the most likely of the + + + align:start position:0% +of a system under the most likely of the +average conditions gives you the wrong + + align:start position:0% +average conditions gives you the wrong + + + align:start position:0% +average conditions gives you the wrong +answer if you do that the result is the + + align:start position:0% +answer if you do that the result is the + + + align:start position:0% +answer if you do that the result is the +wrong estimates of the performance of + + align:start position:0% +wrong estimates of the performance of + + + align:start position:0% +wrong estimates of the performance of +any particular design + + align:start position:0% +any particular design + + + align:start position:0% +any particular design +consequently the wrong ranking of the + + align:start position:0% +consequently the wrong ranking of the + + + align:start position:0% +consequently the wrong ranking of the +alternatives and consequently the wrong + + align:start position:0% +alternatives and consequently the wrong + + + align:start position:0% +alternatives and consequently the wrong +choice of design that is unless you + + align:start position:0% +choice of design that is unless you + + + align:start position:0% +choice of design that is unless you +really look at how the system + + align:start position:0% +really look at how the system + + + align:start position:0% +really look at how the system +performance + + align:start position:0% +performance + + + align:start position:0% +performance +occurs over the range of possibilities + + align:start position:0% +occurs over the range of possibilities + + + align:start position:0% +occurs over the range of possibilities +the ranges of demands the ranges of + + align:start position:0% +the ranges of demands the ranges of + + + align:start position:0% +the ranges of demands the ranges of +performance and ranges of prices unless + + align:start position:0% +performance and ranges of prices unless + + + align:start position:0% +performance and ranges of prices unless +you do that you get the wrong answers + + align:start position:0% +you do that you get the wrong answers + + + align:start position:0% +you do that you get the wrong answers +mathematically to be correct but they're + + align:start position:0% +mathematically to be correct but they're + + + align:start position:0% +mathematically to be correct but they're +not what's going to happen and you get + + align:start position:0% +not what's going to happen and you get + + + align:start position:0% +not what's going to happen and you get +the wrong choice of design that's why + + align:start position:0% +the wrong choice of design that's why + + + align:start position:0% +the wrong choice of design that's why +you should care about it that's why you + + align:start position:0% +you should care about it that's why you + + + align:start position:0% +you should care about it that's why you +should not be a victim of the flaw of + + align:start position:0% +should not be a victim of the flaw of + + + align:start position:0% +should not be a victim of the flaw of +averages + + align:start position:0% +averages + + + align:start position:0% +averages +so just let me put it in to show you how + + align:start position:0% +so just let me put it in to show you how + + + align:start position:0% +so just let me put it in to show you how +this works to give you a concrete a + + align:start position:0% +this works to give you a concrete a + + + align:start position:0% +this works to give you a concrete a +specific example let's suppose we have a + + align:start position:0% +specific example let's suppose we have a + + + align:start position:0% +specific example let's suppose we have a +very simple uh measure of performance + + align:start position:0% +very simple uh measure of performance + + + align:start position:0% +very simple uh measure of performance +which is that this f of x is equal to x + + align:start position:0% +which is that this f of x is equal to x + + + align:start position:0% +which is that this f of x is equal to x +squared plus two and that x can have + + align:start position:0% +squared plus two and that x can have + + + align:start position:0% +squared plus two and that x can have +with equal probability it can be 1 + + align:start position:0% +with equal probability it can be 1 + + + align:start position:0% +with equal probability it can be 1 +2 or 3. + + align:start position:0% +2 or 3. + + + align:start position:0% +2 or 3. +so so on average the average value of x + + align:start position:0% +so so on average the average value of x + + + align:start position:0% +so so on average the average value of x +is + + align:start position:0% +is + + + align:start position:0% +is +2. + + align:start position:0% +2. + + + align:start position:0% +2. +if we evaluate this function using that + + align:start position:0% +if we evaluate this function using that + + + align:start position:0% +if we evaluate this function using that +average value we get x squared is equal + + align:start position:0% +average value we get x squared is equal + + + align:start position:0% +average value we get x squared is equal +to four plus two + + align:start position:0% +to four plus two + + + align:start position:0% +to four plus two +result six + + align:start position:0% +result six + + + align:start position:0% +result six +but that's not what the + + align:start position:0% +but that's not what the + + + align:start position:0% +but that's not what the +what the average value of that is + + align:start position:0% +what the average value of that is + + + align:start position:0% +what the average value of that is +if we calculate it with x is equal to + + align:start position:0% +if we calculate it with x is equal to + + + align:start position:0% +if we calculate it with x is equal to +one we have one plus two is equal to + + align:start position:0% +one we have one plus two is equal to + + + align:start position:0% +one we have one plus two is equal to +three if x is equal to two it's six + + align:start position:0% +three if x is equal to two it's six + + + align:start position:0% +three if x is equal to two it's six +but if x is equal to three it's nine + + align:start position:0% +but if x is equal to three it's nine + + + align:start position:0% +but if x is equal to three it's nine +plus two eleven + + align:start position:0% +plus two eleven + + + align:start position:0% +plus two eleven +all with equal probability and the + + align:start position:0% +all with equal probability and the + + + align:start position:0% +all with equal probability and the +average value of this is three plus six + + align:start position:0% +average value of this is three plus six + + + align:start position:0% +average value of this is three plus six +plus eleven divide by three which is six + + align:start position:0% +plus eleven divide by three which is six + + + align:start position:0% +plus eleven divide by three which is six +and two thirds and it's not the six that + + align:start position:0% +and two thirds and it's not the six that + + + align:start position:0% +and two thirds and it's not the six that +is the value we calculated using the + + align:start position:0% +is the value we calculated using the + + + align:start position:0% +is the value we calculated using the +average + + align:start position:0% +average + + + align:start position:0% +average +so the point is very simple that + + align:start position:0% +so the point is very simple that + + + align:start position:0% +so the point is very simple that +if you don't use the whole distribution + + align:start position:0% +if you don't use the whole distribution + + + align:start position:0% +if you don't use the whole distribution +you get the wrong answer + + align:start position:0% +you get the wrong answer + + + align:start position:0% +you get the wrong answer +now + + align:start position:0% +now + + + align:start position:0% +now +to be fair there is an example a contour + + align:start position:0% +to be fair there is an example a contour + + + align:start position:0% +to be fair there is an example a contour +example that is if the situation is + + align:start position:0% +example that is if the situation is + + + align:start position:0% +example that is if the situation is +totally linear so i have an equation + + align:start position:0% +totally linear so i have an equation + + + align:start position:0% +totally linear so i have an equation +like the function is x plus 2 and you + + align:start position:0% +like the function is x plus 2 and you + + + align:start position:0% +like the function is x plus 2 and you +have + + align:start position:0% +have + + + align:start position:0% +have +1 2 or 3 with equal probability in that + + align:start position:0% +1 2 or 3 with equal probability in that + + + align:start position:0% +1 2 or 3 with equal probability in that +case they are the same + + align:start position:0% +case they are the same + + + align:start position:0% +case they are the same +but the world is not linear the world is + + align:start position:0% +but the world is not linear the world is + + + align:start position:0% +but the world is not linear the world is +in fact on our systems are almost always + + align:start position:0% +in fact on our systems are almost always + + + align:start position:0% +in fact on our systems are almost always +guaranteed to be non-linear they are + + align:start position:0% +guaranteed to be non-linear they are + + + align:start position:0% +guaranteed to be non-linear they are +step functions that is we build uh one + + align:start position:0% +step functions that is we build uh one + + + align:start position:0% +step functions that is we build uh one +up one plan and then we build another + + align:start position:0% +up one plan and then we build another + + + align:start position:0% +up one plan and then we build another +plan so the capacity goes from this + + align:start position:0% +plan so the capacity goes from this + + + align:start position:0% +plan so the capacity goes from this +level in a step function to another + + align:start position:0% +level in a step function to another + + + align:start position:0% +level in a step function to another +level there are changes in prices there + + align:start position:0% +level there are changes in prices there + + + align:start position:0% +level there are changes in prices there +are economies of scale there's all kinds + + align:start position:0% +are economies of scale there's all kinds + + + align:start position:0% +are economies of scale there's all kinds +of things that happen the world is not + + align:start position:0% +of things that happen the world is not + + + align:start position:0% +of things that happen the world is not +linear so in general the + + align:start position:0% +linear so in general the + + + align:start position:0% +linear so in general the +flaw of averages holds and you get the + + align:start position:0% +flaw of averages holds and you get the + + + align:start position:0% +flaw of averages holds and you get the +wrong answer if you use you base your + + align:start position:0% +wrong answer if you use you base your + + + align:start position:0% +wrong answer if you use you base your +calculations on the average or most + + align:start position:0% +calculations on the average or most + + + align:start position:0% +calculations on the average or most +likely value + + align:start position:0% +likely value + + + align:start position:0% +likely value +so what are the practical consequences + + align:start position:0% +so what are the practical consequences + + + align:start position:0% +so what are the practical consequences +since the world is not linear unless you + + align:start position:0% +since the world is not linear unless you + + + align:start position:0% +since the world is not linear unless you +work with a distribution you get the + + align:start position:0% +work with a distribution you get the + + + align:start position:0% +work with a distribution you get the +wrong answer it's as simple as that any + + align:start position:0% +wrong answer it's as simple as that any + + + align:start position:0% +wrong answer it's as simple as that any +calculation done based on a single uh + + align:start position:0% +calculation done based on a single uh + + + align:start position:0% +calculation done based on a single uh +expected + + align:start position:0% +expected + + + align:start position:0% +expected +trajectory of demand or costs or + + align:start position:0% +trajectory of demand or costs or + + + align:start position:0% +trajectory of demand or costs or +performance + + align:start position:0% +performance + + + align:start position:0% +performance +rather than the distribution gives you + + align:start position:0% +rather than the distribution gives you + + + align:start position:0% +rather than the distribution gives you +the wrong answer + + align:start position:0% +the wrong answer + + + align:start position:0% +the wrong answer +the answer from a realistically + + align:start position:0% +the answer from a realistically + + + align:start position:0% +the answer from a realistically +distribution of what might happen + + align:start position:0% +distribution of what might happen + + + align:start position:0% +distribution of what might happen +differs from the result you get from the + + align:start position:0% +differs from the result you get from the + + + align:start position:0% +differs from the result you get from the +averages + + align:start position:0% +averages + + + align:start position:0% +averages +so why is that because very often the + + align:start position:0% +so why is that because very often the + + + align:start position:0% +so why is that because very often the +gains when things go well do not balance + + align:start position:0% +gains when things go well do not balance + + + align:start position:0% +gains when things go well do not balance +off the losses when things do not + + align:start position:0% +off the losses when things do not + + + align:start position:0% +off the losses when things do not +i have a visual example here that may be + + align:start position:0% +i have a visual example here that may be + + + align:start position:0% +i have a visual example here that may be +interesting to you here is a story of + + align:start position:0% +interesting to you here is a story of + + + align:start position:0% +interesting to you here is a story of +the drunk walking down the middle of the + + align:start position:0% +the drunk walking down the middle of the + + + align:start position:0% +the drunk walking down the middle of the +road + + align:start position:0% +road + + + align:start position:0% +road +on average he's in the middle of the + + align:start position:0% +on average he's in the middle of the + + + align:start position:0% +on average he's in the middle of the +road the cars pass and don't hit him but + + align:start position:0% +road the cars pass and don't hit him but + + + align:start position:0% +road the cars pass and don't hit him but +on average he is hit by a car in fact + + align:start position:0% +on average he is hit by a car in fact + + + align:start position:0% +on average he is hit by a car in fact +and is dead do not be a victim of the + + align:start position:0% +and is dead do not be a victim of the + + + align:start position:0% +and is dead do not be a victim of the +flaw of averages + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/OlQie93CwLY.txt b/OlQie93CwLY.txt new file mode 100644 index 0000000000000000000000000000000000000000..6d5e5fde1ee0df1d61a7b15b4894cae530f3d258 --- /dev/null +++ b/OlQie93CwLY.txt @@ -0,0 +1,6547 @@ +align:start position:0% + +quick introduction I know hardly anybody + + align:start position:0% +quick introduction I know hardly anybody + + + align:start position:0% +quick introduction I know hardly anybody +says they care about helicopters but as + + align:start position:0% +says they care about helicopters but as + + + align:start position:0% +says they care about helicopters but as +God is my witness I'm gonna change that + + align:start position:0% +God is my witness I'm gonna change that + + + align:start position:0% +God is my witness I'm gonna change that +if I can reach one of you airplane + + align:start position:0% +if I can reach one of you airplane + + + align:start position:0% +if I can reach one of you airplane +obsessed folks I will do my best okay so + + align:start position:0% +obsessed folks I will do my best okay so + + + align:start position:0% +obsessed folks I will do my best okay so +what is cool about a helicopter here + + align:start position:0% +what is cool about a helicopter here + + + align:start position:0% +what is cool about a helicopter here +it's a view so let's start first and + + align:start position:0% +it's a view so let's start first and + + + align:start position:0% +it's a view so let's start first and +foremost it's a view so these are some + + align:start position:0% +foremost it's a view so these are some + + + align:start position:0% +foremost it's a view so these are some +pictures that I snapped on a trip from + + align:start position:0% +pictures that I snapped on a trip from + + + align:start position:0% +pictures that I snapped on a trip from +the Robinson factory in Los Angeles back + + align:start position:0% +the Robinson factory in Los Angeles back + + + align:start position:0% +the Robinson factory in Los Angeles back +to Boston who recognizes the city in the + + align:start position:0% +to Boston who recognizes the city in the + + + align:start position:0% +to Boston who recognizes the city in the +middle ooh + + align:start position:0% + + + + align:start position:0% + +some Midwesterners here Chicago indeed + + align:start position:0% + + + + align:start position:0% + +all right of course this is the Stata + + align:start position:0% +all right of course this is the Stata + + + align:start position:0% +all right of course this is the Stata +Center where we will be tomorrow + + align:start position:0% +Center where we will be tomorrow + + + align:start position:0% +Center where we will be tomorrow +remember that 30 to 141 all right one of + + align:start position:0% +remember that 30 to 141 all right one of + + + align:start position:0% +remember that 30 to 141 all right one of +the parts of the helicopter if you're + + align:start position:0% +the parts of the helicopter if you're + + + align:start position:0% +the parts of the helicopter if you're +between ages three and five it's + + align:start position:0% +between ages three and five it's + + + align:start position:0% +between ages three and five it's +acceptable to call the thing on the top + + align:start position:0% +acceptable to call the thing on the top + + + align:start position:0% +acceptable to call the thing on the top +the propeller but older than that it's + + align:start position:0% +the propeller but older than that it's + + + align:start position:0% +the propeller but older than that it's +better to say main rotor system tail + + align:start position:0% +better to say main rotor system tail + + + align:start position:0% +better to say main rotor system tail +rotor is in the back we'll talk about + + align:start position:0% +rotor is in the back we'll talk about + + + align:start position:0% +rotor is in the back we'll talk about +why we need that in a minute you got to + + align:start position:0% +why we need that in a minute you got to + + + align:start position:0% +why we need that in a minute you got to +have transmissions in helicopters the + + align:start position:0% +have transmissions in helicopters the + + + align:start position:0% +have transmissions in helicopters the +speed of the engine is never the speed + + align:start position:0% +speed of the engine is never the speed + + + align:start position:0% +speed of the engine is never the speed +that you want + + align:start position:0% +that you want + + + align:start position:0% +that you want +I don't think and landing gear is kind + + align:start position:0% +I don't think and landing gear is kind + + + align:start position:0% +I don't think and landing gear is kind +of nice although for record-setting + + align:start position:0% +of nice although for record-setting + + + align:start position:0% +of nice although for record-setting +flights sometimes people have taken them + + align:start position:0% +flights sometimes people have taken them + + + align:start position:0% +flights sometimes people have taken them +off to try to get a little higher a + + align:start position:0% +off to try to get a little higher a + + + align:start position:0% +off to try to get a little higher a +little faster and they just land very + + align:start position:0% +little faster and they just land very + + + align:start position:0% +little faster and they just land very +gently okay so your typical helicopter + + align:start position:0% +gently okay so your typical helicopter + + + align:start position:0% +gently okay so your typical helicopter +drivetrain will have transmissions + + align:start position:0% +drivetrain will have transmissions + + + align:start position:0% +drivetrain will have transmissions +in both for both the main rotor and + + align:start position:0% +in both for both the main rotor and + + + align:start position:0% +in both for both the main rotor and +they'll have another transmission to + + align:start position:0% +they'll have another transmission to + + + align:start position:0% +they'll have another transmission to +adjust the speed of the tail maybe your + + align:start position:0% +adjust the speed of the tail maybe your + + + align:start position:0% +adjust the speed of the tail maybe your +back up a little bit this unfortunately + + align:start position:0% +back up a little bit this unfortunately + + + align:start position:0% +back up a little bit this unfortunately +does introduce another source of + + align:start position:0% +does introduce another source of + + + align:start position:0% +does introduce another source of +unreliability so in the airplane you + + align:start position:0% +unreliability so in the airplane you + + + align:start position:0% +unreliability so in the airplane you +know you've got your engine it's bolted + + align:start position:0% +know you've got your engine it's bolted + + + align:start position:0% +know you've got your engine it's bolted +to the propeller as long as the engines + + align:start position:0% +to the propeller as long as the engines + + + align:start position:0% +to the propeller as long as the engines +turning you really it's hard to have a + + align:start position:0% +turning you really it's hard to have a + + + align:start position:0% +turning you really it's hard to have a +problem that propellers don't generally + + align:start position:0% +problem that propellers don't generally + + + align:start position:0% +problem that propellers don't generally +just come apart in flight but here with + + align:start position:0% +just come apart in flight but here with + + + align:start position:0% +just come apart in flight but here with +the helicopter you might have a working + + align:start position:0% +the helicopter you might have a working + + + align:start position:0% +the helicopter you might have a working +engine and working main rotor + + align:start position:0% +engine and working main rotor + + + align:start position:0% +engine and working main rotor +and the transmission all the oil might + + align:start position:0% +and the transmission all the oil might + + + align:start position:0% +and the transmission all the oil might +come out in the gear seized up so you've + + align:start position:0% +come out in the gear seized up so you've + + + align:start position:0% +come out in the gear seized up so you've +got a there's a couple warning lights in + + align:start position:0% +got a there's a couple warning lights in + + + align:start position:0% +got a there's a couple warning lights in +there for when you're having a + + align:start position:0% +there for when you're having a + + + align:start position:0% +there for when you're having a +transmission problem this is the rubber + + align:start position:0% +transmission problem this is the rubber + + + align:start position:0% +transmission problem this is the rubber +belt system that's used in some piston + + align:start position:0% +belt system that's used in some piston + + + align:start position:0% +belt system that's used in some piston +helicopters I think this is probably a + + align:start position:0% +helicopters I think this is probably a + + + align:start position:0% +helicopters I think this is probably a +drawing off of a Robinson but basically + + align:start position:0% +drawing off of a Robinson but basically + + + align:start position:0% +drawing off of a Robinson but basically +you have pulleys on the engine side and + + align:start position:0% +you have pulleys on the engine side and + + + align:start position:0% +you have pulleys on the engine side and +on the drivetrain side and you have + + align:start position:0% +on the drivetrain side and you have + + + align:start position:0% +on the drivetrain side and you have +these rubber belts connecting them so + + align:start position:0% +these rubber belts connecting them so + + + align:start position:0% +these rubber belts connecting them so +you can start your engine with the belts + + align:start position:0% +you can start your engine with the belts + + + align:start position:0% +you can start your engine with the belts +loose and then tighten them up when you + + align:start position:0% +loose and then tighten them up when you + + + align:start position:0% +loose and then tighten them up when you +want the engine to begin driving the + + align:start position:0% +want the engine to begin driving the + + + align:start position:0% +want the engine to begin driving the +rotor system that way you don't have to + + align:start position:0% +rotor system that way you don't have to + + + align:start position:0% +rotor system that way you don't have to +have the little starter motor actually + + align:start position:0% +have the little starter motor actually + + + align:start position:0% +have the little starter motor actually +turn all the rotors and stuff all right + + align:start position:0% +turn all the rotors and stuff all right + + + align:start position:0% +turn all the rotors and stuff all right +how does it work + + align:start position:0% +how does it work + + + align:start position:0% +how does it work +so Tina is a hard act to follow + + align:start position:0% +so Tina is a hard act to follow + + + align:start position:0% +so Tina is a hard act to follow +with my cave-person computer programmers + + align:start position:0% +with my cave-person computer programmers + + + align:start position:0% +with my cave-person computer programmers +understanding of lift but if you assume + + align:start position:0% +understanding of lift but if you assume + + + align:start position:0% +understanding of lift but if you assume +that lift is a combination of Newton's + + align:start position:0% +that lift is a combination of Newton's + + + align:start position:0% +that lift is a combination of Newton's +third law and their Bernoulli principle + + align:start position:0% +third law and their Bernoulli principle + + + align:start position:0% +third law and their Bernoulli principle +the the sped up air has more kinetic + + align:start position:0% +the the sped up air has more kinetic + + + align:start position:0% +the the sped up air has more kinetic +energy therefore it has to have for + + align:start position:0% +energy therefore it has to have for + + + align:start position:0% +energy therefore it has to have for +conservation of energy has to have less + + align:start position:0% +conservation of energy has to have less + + + align:start position:0% +conservation of energy has to have less +of something else it's going to have + + align:start position:0% +of something else it's going to have + + + align:start position:0% +of something else it's going to have +lower static pressure so here's one of + + align:start position:0% +lower static pressure so here's one of + + + align:start position:0% +lower static pressure so here's one of +the F phase diagrams here right you have + + align:start position:0% +the F phase diagrams here right you have + + + align:start position:0% +the F phase diagrams here right you have +velocity and pressure that are equal + + align:start position:0% +velocity and pressure that are equal + + + align:start position:0% +velocity and pressure that are equal +they go into the venturi the velocity is + + align:start position:0% +they go into the venturi the velocity is + + + align:start position:0% +they go into the venturi the velocity is +higher the pressure is lower so the + + align:start position:0% +higher the pressure is lower so the + + + align:start position:0% +higher the pressure is lower so the +energy of the air is still the same and + + align:start position:0% +energy of the air is still the same and + + + align:start position:0% +energy of the air is still the same and +it comes out again at the same velocity + + align:start position:0% +it comes out again at the same velocity + + + align:start position:0% +it comes out again at the same velocity +and pressure so you're getting lift from + + align:start position:0% +and pressure so you're getting lift from + + + align:start position:0% +and pressure so you're getting lift from +the wing from both Newton's third law + + align:start position:0% +the wing from both Newton's third law + + + align:start position:0% +the wing from both Newton's third law +just pushing air down makes the wing go + + align:start position:0% +just pushing air down makes the wing go + + + align:start position:0% +just pushing air down makes the wing go +up and there Bernoulli principle of + + align:start position:0% +up and there Bernoulli principle of + + + align:start position:0% +up and there Bernoulli principle of +generating some low pressure this is the + + align:start position:0% +generating some low pressure this is the + + + align:start position:0% +generating some low pressure this is the +same drawing you saw earlier of how when + + align:start position:0% +same drawing you saw earlier of how when + + + align:start position:0% +same drawing you saw earlier of how when +you exceed a certain critical angle of + + align:start position:0% +you exceed a certain critical angle of + + + align:start position:0% +you exceed a certain critical angle of +attack depending on the airfoil your + + align:start position:0% +attack depending on the airfoil your + + + align:start position:0% +attack depending on the airfoil your +lift your lift party comes to a quick + + align:start position:0% +lift your lift party comes to a quick + + + align:start position:0% +lift your lift party comes to a quick +end it doesn't go away completely but + + align:start position:0% +end it doesn't go away completely but + + + align:start position:0% +end it doesn't go away completely but +it's a sudden drop angle of attack so + + align:start position:0% +it's a sudden drop angle of attack so + + + align:start position:0% +it's a sudden drop angle of attack so +remember there's your chord line there's + + align:start position:0% +remember there's your chord line there's + + + align:start position:0% +remember there's your chord line there's +your relative wind four degree angle of + + align:start position:0% +your relative wind four degree angle of + + + align:start position:0% +your relative wind four degree angle of +attack and a reasonable amount of + + align:start position:0% +attack and a reasonable amount of + + + align:start position:0% +attack and a reasonable amount of +forward speed remember the lift series + + align:start position:0% +forward speed remember the lift series + + + align:start position:0% +forward speed remember the lift series +is the speed squared will have you going + + align:start position:0% +is the speed squared will have you going + + + align:start position:0% +is the speed squared will have you going +and if you want to fly slowly you just + + align:start position:0% +and if you want to fly slowly you just + + + align:start position:0% +and if you want to fly slowly you just +go to higher and higher angles + + align:start position:0% +go to higher and higher angles + + + align:start position:0% +go to higher and higher angles +attack so why not hover in your system + + align:start position:0% +attack so why not hover in your system + + + align:start position:0% +attack so why not hover in your system +172 and save yourself the trouble of + + align:start position:0% +172 and save yourself the trouble of + + + align:start position:0% +172 and save yourself the trouble of +getting a helicopter rating it's because + + align:start position:0% +getting a helicopter rating it's because + + + align:start position:0% +getting a helicopter rating it's because +you know off the right end of this chart + + align:start position:0% +you know off the right end of this chart + + + align:start position:0% +you know off the right end of this chart +you quickly get to the stalling angle of + + align:start position:0% +you quickly get to the stalling angle of + + + align:start position:0% +you quickly get to the stalling angle of +attack and the plane doesn't fly anymore + + align:start position:0% +attack and the plane doesn't fly anymore + + + align:start position:0% +attack and the plane doesn't fly anymore +so there's an F a drawing I think from + + align:start position:0% +so there's an F a drawing I think from + + + align:start position:0% +so there's an F a drawing I think from +the pilots handbook where the air flow + + align:start position:0% +the pilots handbook where the air flow + + + align:start position:0% +the pilots handbook where the air flow +becomes turbulent somewhere between 12 + + align:start position:0% +becomes turbulent somewhere between 12 + + + align:start position:0% +becomes turbulent somewhere between 12 +and 16 degrees angle of attack depending + + align:start position:0% +and 16 degrees angle of attack depending + + + align:start position:0% +and 16 degrees angle of attack depending +on the airfoil and that's why the Cessna + + align:start position:0% +on the airfoil and that's why the Cessna + + + align:start position:0% +on the airfoil and that's why the Cessna +can't be used for hovering operations + + align:start position:0% +can't be used for hovering operations + + + align:start position:0% +can't be used for hovering operations +all right what if you saw the wing off + + align:start position:0% +all right what if you saw the wing off + + + align:start position:0% +all right what if you saw the wing off +the Cessna and spin it around so if you + + align:start position:0% +the Cessna and spin it around so if you + + + align:start position:0% +the Cessna and spin it around so if you +do that the wing will always have + + align:start position:0% +do that the wing will always have + + + align:start position:0% +do that the wing will always have +airspeed even if the fuselage is not + + align:start position:0% +airspeed even if the fuselage is not + + + align:start position:0% +airspeed even if the fuselage is not +moving and that was an idea that was + + align:start position:0% +moving and that was an idea that was + + + align:start position:0% +moving and that was an idea that was +first reduced to practice in 1907 so + + align:start position:0% +first reduced to practice in 1907 so + + + align:start position:0% +first reduced to practice in 1907 so +only four years after the Wright + + align:start position:0% +only four years after the Wright + + + align:start position:0% +only four years after the Wright +brothers flew a couple guys in France + + align:start position:0% +brothers flew a couple guys in France + + + align:start position:0% +brothers flew a couple guys in France +were actually hovering a little bit in + + align:start position:0% +were actually hovering a little bit in + + + align:start position:0% +were actually hovering a little bit in +the helicopter the first helicopters + + align:start position:0% +the helicopter the first helicopters + + + align:start position:0% +the helicopter the first helicopters +that could be flown and controlled and + + align:start position:0% +that could be flown and controlled and + + + align:start position:0% +that could be flown and controlled and +you know actually operated as you know a + + align:start position:0% +you know actually operated as you know a + + + align:start position:0% +you know actually operated as you know a +practical aircraft I think you know mid + + align:start position:0% +practical aircraft I think you know mid + + + align:start position:0% +practical aircraft I think you know mid +30s in Germany and then Sikorsky is + + align:start position:0% +30s in Germany and then Sikorsky is + + + align:start position:0% +30s in Germany and then Sikorsky is +famous for being the first mass producer + + align:start position:0% +famous for being the first mass producer + + + align:start position:0% +famous for being the first mass producer +of helicopters with the Sikorsky r4 it + + align:start position:0% +of helicopters with the Sikorsky r4 it + + + align:start position:0% +of helicopters with the Sikorsky r4 it +was briefly it was used for a few + + align:start position:0% +was briefly it was used for a few + + + align:start position:0% +was briefly it was used for a few +operational purposes in World War two + + align:start position:0% +operational purposes in World War two + + + align:start position:0% +operational purposes in World War two +search-and-rescue type stuff but really + + align:start position:0% +search-and-rescue type stuff but really + + + align:start position:0% +search-and-rescue type stuff but really +you know Korea the Korean War was the + + align:start position:0% +you know Korea the Korean War was the + + + align:start position:0% +you know Korea the Korean War was the +first time that helicopters were widely + + align:start position:0% +first time that helicopters were widely + + + align:start position:0% +first time that helicopters were widely +used by the military alright let's talk + + align:start position:0% +used by the military alright let's talk + + + align:start position:0% +used by the military alright let's talk +about a very simple qualitative physics + + align:start position:0% +about a very simple qualitative physics + + + align:start position:0% +about a very simple qualitative physics +here we're spinning on the ramp and + + align:start position:0% +here we're spinning on the ramp and + + + align:start position:0% +here we're spinning on the ramp and +we're hovering we're sorry we're + + align:start position:0% +we're hovering we're sorry we're + + + align:start position:0% +we're hovering we're sorry we're +spinning on the ramp so we spin the + + align:start position:0% +spinning on the ramp so we spin the + + + align:start position:0% +spinning on the ramp so we spin the +rotor system up to 400 rpm but we're + + align:start position:0% +rotor system up to 400 rpm but we're + + + align:start position:0% +rotor system up to 400 rpm but we're +still on the ramp so does anybody have a + + align:start position:0% +still on the ramp so does anybody have a + + + align:start position:0% +still on the ramp so does anybody have a +brilliant idea for how do we get up into + + align:start position:0% +brilliant idea for how do we get up into + + + align:start position:0% +brilliant idea for how do we get up into +the air where we want to be is there + + align:start position:0% + + + + align:start position:0% + +okay excellent so what's your name sorry + + align:start position:0% +okay excellent so what's your name sorry + + + align:start position:0% +okay excellent so what's your name sorry +Aziz has a correct observation that if + + align:start position:0% +Aziz has a correct observation that if + + + align:start position:0% +Aziz has a correct observation that if +you want to get the same lift out of a + + align:start position:0% +you want to get the same lift out of a + + + align:start position:0% +you want to get the same lift out of a +wing without changing the speed we don't + + align:start position:0% +wing without changing the speed we don't + + + align:start position:0% +wing without changing the speed we don't +want to have this we don't want to speed + + align:start position:0% +want to have this we don't want to speed + + + align:start position:0% +want to have this we don't want to speed +up too much because the tips will go + + align:start position:0% +up too much because the tips will go + + + align:start position:0% +up too much because the tips will go +supersonic and the neighbors will begin + + align:start position:0% +supersonic and the neighbors will begin + + + align:start position:0% +supersonic and the neighbors will begin +to complain so we just twist the blades + + align:start position:0% +to complain so we just twist the blades + + + align:start position:0% +to complain so we just twist the blades +up a little bit and as they're twisted + + align:start position:0% +up a little bit and as they're twisted + + + align:start position:0% +up a little bit and as they're twisted +up they'll bite more air generate more + + align:start position:0% +up they'll bite more air generate more + + + align:start position:0% +up they'll bite more air generate more +lift and the helicopter will begin + + align:start position:0% +lift and the helicopter will begin + + + align:start position:0% +lift and the helicopter will begin +rising up what will happen to the speed + + align:start position:0% +rising up what will happen to the speed + + + align:start position:0% +rising up what will happen to the speed +let's hear from one of these Aero + + align:start position:0% +let's hear from one of these Aero + + + align:start position:0% +let's hear from one of these Aero +engineering heroes as we generate more + + align:start position:0% +engineering heroes as we generate more + + + align:start position:0% +engineering heroes as we generate more +lift what happens more lift more drag + + align:start position:0% +lift what happens more lift more drag + + + align:start position:0% +lift what happens more lift more drag +so without adding more power the engine + + align:start position:0% +so without adding more power the engine + + + align:start position:0% +so without adding more power the engine +well without adding more power the + + align:start position:0% +well without adding more power the + + + align:start position:0% +well without adding more power the +blades will slow down so you want a + + align:start position:0% +blades will slow down so you want a + + + align:start position:0% +blades will slow down so you want a +correlator as you're lifting the + + align:start position:0% +correlator as you're lifting the + + + align:start position:0% +correlator as you're lifting the +collective control on a helicopter the + + align:start position:0% +collective control on a helicopter the + + + align:start position:0% +collective control on a helicopter the +correlator is opening the throttle and + + align:start position:0% +correlator is opening the throttle and + + + align:start position:0% +correlator is opening the throttle and +adding more power automatically and + + align:start position:0% +adding more power automatically and + + + align:start position:0% +adding more power automatically and +there's also an electronic governor that + + align:start position:0% +there's also an electronic governor that + + + align:start position:0% +there's also an electronic governor that +I'll just touch that up a little bit by + + align:start position:0% +I'll just touch that up a little bit by + + + align:start position:0% +I'll just touch that up a little bit by +watching the RPM turbine helicopters all + + align:start position:0% +watching the RPM turbine helicopters all + + + align:start position:0% +watching the RPM turbine helicopters all +have governor's most piston Robinsons + + align:start position:0% +have governor's most piston Robinsons + + + align:start position:0% +have governor's most piston Robinsons +have governor's as well all right so + + align:start position:0% +have governor's as well all right so + + + align:start position:0% +have governor's as well all right so +what if we are parked on ice has anybody + + align:start position:0% +what if we are parked on ice has anybody + + + align:start position:0% +what if we are parked on ice has anybody +here seen my favorite movie blades of + + align:start position:0% +here seen my favorite movie blades of + + + align:start position:0% +here seen my favorite movie blades of +glory + + align:start position:0% +glory + + + align:start position:0% +glory +so when Will Ferrell and his partner + + align:start position:0% +so when Will Ferrell and his partner + + + align:start position:0% +so when Will Ferrell and his partner +what if they're on the ice and they + + align:start position:0% +what if they're on the ice and they + + + align:start position:0% +what if they're on the ice and they +pushed each other what happens both go + + align:start position:0% +pushed each other what happens both go + + + align:start position:0% +pushed each other what happens both go +backwards right the pusher and the pushy + + align:start position:0% +backwards right the pusher and the pushy + + + align:start position:0% +backwards right the pusher and the pushy +so keeping in mind blades of glory an + + align:start position:0% +so keeping in mind blades of glory an + + + align:start position:0% +so keeping in mind blades of glory an +important physics work + + align:start position:0% +important physics work + + + align:start position:0% +important physics work +what if we're parked on the ice what + + align:start position:0% +what if we're parked on the ice what + + + align:start position:0% +what if we're parked on the ice what +happens to our helicopter after we start + + align:start position:0% +happens to our helicopter after we start + + + align:start position:0% +happens to our helicopter after we start +the engine and start the blades spinning + + align:start position:0% + + + + align:start position:0% + +helicopter students the other way + + align:start position:0% +helicopter students the other way + + + align:start position:0% +helicopter students the other way +excellent yeah so that's Newton's third + + align:start position:0% +excellent yeah so that's Newton's third + + + align:start position:0% +excellent yeah so that's Newton's third +law once again right for every action + + align:start position:0% +law once again right for every action + + + align:start position:0% +law once again right for every action +there's an equal and opposite reaction + + align:start position:0% +there's an equal and opposite reaction + + + align:start position:0% +there's an equal and opposite reaction +you're not going to see that as + + align:start position:0% +you're not going to see that as + + + align:start position:0% +you're not going to see that as +dramatically if you're parked on + + align:start position:0% +dramatically if you're parked on + + + align:start position:0% +dramatically if you're parked on +pavement because of the friction so what + + align:start position:0% +pavement because of the friction so what + + + align:start position:0% +pavement because of the friction so what +do we do we Oh we add the tail rotor so + + align:start position:0% +do we do we Oh we add the tail rotor so + + + align:start position:0% +do we do we Oh we add the tail rotor so +yeah here the forces up here there's the + + align:start position:0% +yeah here the forces up here there's the + + + align:start position:0% +yeah here the forces up here there's the +blade rotation + + align:start position:0% +blade rotation + + + align:start position:0% +blade rotation +there's the torque to counteract the + + align:start position:0% +there's the torque to counteract the + + + align:start position:0% +there's the torque to counteract the +torque we've got the tail rotor thrust + + align:start position:0% +torque we've got the tail rotor thrust + + + align:start position:0% +torque we've got the tail rotor thrust +to blow the tail back into position and + + align:start position:0% +to blow the tail back into position and + + + align:start position:0% +to blow the tail back into position and +the only thing here that's not corrected + + align:start position:0% +the only thing here that's not corrected + + + align:start position:0% +the only thing here that's not corrected +you'll notice is the tail rotor thrust + + align:start position:0% +you'll notice is the tail rotor thrust + + + align:start position:0% +you'll notice is the tail rotor thrust +so if you set everything up the way you + + align:start position:0% +so if you set everything up the way you + + + align:start position:0% +so if you set everything up the way you +would think obvious like put the rotor + + align:start position:0% +would think obvious like put the rotor + + + align:start position:0% +would think obvious like put the rotor +mass straight up and put the tail rotor + + align:start position:0% +mass straight up and put the tail rotor + + + align:start position:0% +mass straight up and put the tail rotor +on it the whole helicopter with the + + align:start position:0% +on it the whole helicopter with the + + + align:start position:0% +on it the whole helicopter with the +controls neutral would drift to the + + align:start position:0% +controls neutral would drift to the + + + align:start position:0% +controls neutral would drift to the +right from the tail rotor thrust so + + align:start position:0% +right from the tail rotor thrust so + + + align:start position:0% +right from the tail rotor thrust so +right because it's pushing the tail the + + align:start position:0% +right because it's pushing the tail the + + + align:start position:0% +right because it's pushing the tail the +helicopter wants to rotate the + + align:start position:0% +helicopter wants to rotate the + + + align:start position:0% +helicopter wants to rotate the +helicopter wants to rotate that way the + + align:start position:0% +helicopter wants to rotate that way the + + + align:start position:0% +helicopter wants to rotate that way the +tail rotor blows it back this way + + align:start position:0% +tail rotor blows it back this way + + + align:start position:0% +tail rotor blows it back this way +and that would blow the whole machine + + align:start position:0% +and that would blow the whole machine + + + align:start position:0% +and that would blow the whole machine +off the side of the ramp if the pilot + + align:start position:0% +off the side of the ramp if the pilot + + + align:start position:0% +off the side of the ramp if the pilot +didn't hold a lot of left cyclic so to + + align:start position:0% +didn't hold a lot of left cyclic so to + + + align:start position:0% +didn't hold a lot of left cyclic so to +counteract that the helicopters are + + align:start position:0% +counteract that the helicopters are + + + align:start position:0% +counteract that the helicopters are +rigged with the mast at a slight left + + align:start position:0% +rigged with the mast at a slight left + + + align:start position:0% +rigged with the mast at a slight left +angle so that they don't have this + + align:start position:0% +angle so that they don't have this + + + align:start position:0% +angle so that they don't have this +tendency to go off to their right the + + align:start position:0% +tendency to go off to their right the + + + align:start position:0% +tendency to go off to their right the +governor okay yeah so let me reinforce + + align:start position:0% +governor okay yeah so let me reinforce + + + align:start position:0% +governor okay yeah so let me reinforce +that so yes as you generate lift you get + + align:start position:0% +that so yes as you generate lift you get + + + align:start position:0% +that so yes as you generate lift you get +more drag which will cause the blades to + + align:start position:0% +more drag which will cause the blades to + + + align:start position:0% +more drag which will cause the blades to +slow down so there's a mechanical + + align:start position:0% +slow down so there's a mechanical + + + align:start position:0% +slow down so there's a mechanical +correlation as you're raising the + + align:start position:0% +correlation as you're raising the + + + align:start position:0% +correlation as you're raising the +collective the throttles being opened + + align:start position:0% +collective the throttles being opened + + + align:start position:0% +collective the throttles being opened +just kind of blindly and the governor is + + align:start position:0% +just kind of blindly and the governor is + + + align:start position:0% +just kind of blindly and the governor is +touching that up the governor is + + align:start position:0% +touching that up the governor is + + + align:start position:0% +touching that up the governor is +watching and maybe twisting the throttle + + align:start position:0% +watching and maybe twisting the throttle + + + align:start position:0% +watching and maybe twisting the throttle +control slightly to fine tune the + + align:start position:0% +control slightly to fine tune the + + + align:start position:0% +control slightly to fine tune the +throttle to keep the blades exactly at + + align:start position:0% +throttle to keep the blades exactly at + + + align:start position:0% +throttle to keep the blades exactly at +400 rpm let's say that's the 100 for a + + align:start position:0% +400 rpm let's say that's the 100 for a + + + align:start position:0% +400 rpm let's say that's the 100 for a +pilot pilots are you know you don't want + + align:start position:0% +pilot pilots are you know you don't want + + + align:start position:0% +pilot pilots are you know you don't want +to distract the pilot too much so the + + align:start position:0% +to distract the pilot too much so the + + + align:start position:0% +to distract the pilot too much so the +gauge is just calibrated in percent it's + + align:start position:0% +gauge is just calibrated in percent it's + + + align:start position:0% +gauge is just calibrated in percent it's +a 100 percent rpm that's good that's all + + align:start position:0% +a 100 percent rpm that's good that's all + + + align:start position:0% +a 100 percent rpm that's good that's all +you need to know about your helicopter + + align:start position:0% +you need to know about your helicopter + + + align:start position:0% +you need to know about your helicopter +it you know I think in the Robinson it + + align:start position:0% +it you know I think in the Robinson it + + + align:start position:0% +it you know I think in the Robinson it +works out to pretty close to 400 rpm + + align:start position:0% +works out to pretty close to 400 rpm + + + align:start position:0% +works out to pretty close to 400 rpm +all right forward flight + + align:start position:0% +all right forward flight + + + align:start position:0% +all right forward flight +so we're hovering and we want to go + + align:start position:0% +so we're hovering and we want to go + + + align:start position:0% +so we're hovering and we want to go +forward so it seems obvious that we want + + align:start position:0% +forward so it seems obvious that we want + + + align:start position:0% +forward so it seems obvious that we want +to tilt the fan right we want to push + + align:start position:0% +to tilt the fan right we want to push + + + align:start position:0% +to tilt the fan right we want to push +the fan down this way and that way we'll + + align:start position:0% +the fan down this way and that way we'll + + + align:start position:0% +the fan down this way and that way we'll +get some horizontal vector of thrust and + + align:start position:0% +get some horizontal vector of thrust and + + + align:start position:0% +get some horizontal vector of thrust and +we'll be going forward but where do we + + align:start position:0% +we'll be going forward but where do we + + + align:start position:0% +we'll be going forward but where do we +push it from right from according to + + align:start position:0% +push it from right from according to + + + align:start position:0% +push it from right from according to +it's a spinning gyro so it has a lot of + + align:start position:0% +it's a spinning gyro so it has a lot of + + + align:start position:0% +it's a spinning gyro so it has a lot of +stability if we're really strong and we + + align:start position:0% +stability if we're really strong and we + + + align:start position:0% +stability if we're really strong and we +reach up from our pilot seat and try to + + align:start position:0% +reach up from our pilot seat and try to + + + align:start position:0% +reach up from our pilot seat and try to +nudge the rotor system why wouldn't that + + align:start position:0% +nudge the rotor system why wouldn't that + + + align:start position:0% +nudge the rotor system why wouldn't that +just cause the helicopter fuselage to + + align:start position:0% +just cause the helicopter fuselage to + + + align:start position:0% +just cause the helicopter fuselage to +move underneath the fixed rotor system + + align:start position:0% +move underneath the fixed rotor system + + + align:start position:0% +move underneath the fixed rotor system +instead of moving the rotor system + + align:start position:0% +instead of moving the rotor system + + + align:start position:0% +instead of moving the rotor system +there's nothing to fix unless we can + + align:start position:0% +there's nothing to fix unless we can + + + align:start position:0% +there's nothing to fix unless we can +call up you know an incredibly strong + + align:start position:0% +call up you know an incredibly strong + + + align:start position:0% +call up you know an incredibly strong +friend and say hey who's you mind + + align:start position:0% +friend and say hey who's you mind + + + align:start position:0% +friend and say hey who's you mind +holding the helicopter and fix position + + align:start position:0% +holding the helicopter and fix position + + + align:start position:0% +holding the helicopter and fix position +we don't have anything to push against + + align:start position:0% +we don't have anything to push against + + + align:start position:0% +we don't have anything to push against +in order to tilt the rotor does that + + align:start position:0% +in order to tilt the rotor does that + + + align:start position:0% +in order to tilt the rotor does that +make sense + + align:start position:0% +make sense + + + align:start position:0% +make sense +you got this gyro on top of you and + + align:start position:0% +you got this gyro on top of you and + + + align:start position:0% +you got this gyro on top of you and +disturbing and it's gonna take a lot of + + align:start position:0% +disturbing and it's gonna take a lot of + + + align:start position:0% +disturbing and it's gonna take a lot of +power and even if you had the strength + + align:start position:0% +power and even if you had the strength + + + align:start position:0% +power and even if you had the strength +you don't have anywhere to stand rigidly + + align:start position:0% +you don't have anywhere to stand rigidly + + + align:start position:0% +you don't have anywhere to stand rigidly +and push so what do you think could the + + align:start position:0% +and push so what do you think could the + + + align:start position:0% +and push so what do you think could the +rotor just fly itself into a new + + align:start position:0% +rotor just fly itself into a new + + + align:start position:0% +rotor just fly itself into a new +position and how would that work like + + align:start position:0% +position and how would that work like + + + align:start position:0% +position and how would that work like +how could you use the spinning wing + + align:start position:0% +how could you use the spinning wing + + + align:start position:0% +how could you use the spinning wing +itself to fly itself into a new tilted + + align:start position:0% +itself to fly itself into a new tilted + + + align:start position:0% +itself to fly itself into a new tilted +down position anybody have any brilliant + + align:start position:0% +down position anybody have any brilliant + + + align:start position:0% +down position anybody have any brilliant +ideas john has a good idea so John says + + align:start position:0% +ideas john has a good idea so John says + + + align:start position:0% +ideas john has a good idea so John says +increase the angle of attack and + + align:start position:0% +increase the angle of attack and + + + align:start position:0% +increase the angle of attack and +decrease it as the blade moves around + + align:start position:0% +decrease it as the blade moves around + + + align:start position:0% +decrease it as the blade moves around +the disc so if you can increase the lift + + align:start position:0% +the disc so if you can increase the lift + + + align:start position:0% +the disc so if you can increase the lift +on part of the disc compared to another + + align:start position:0% +on part of the disc compared to another + + + align:start position:0% +on part of the disc compared to another +part of the disc it will naturally tilt + + align:start position:0% +part of the disc it will naturally tilt + + + align:start position:0% +part of the disc it will naturally tilt +itself so if you want to go forward + + align:start position:0% +itself so if you want to go forward + + + align:start position:0% +itself so if you want to go forward +let's ignore gyroscopic precession for a + + align:start position:0% +let's ignore gyroscopic precession for a + + + align:start position:0% +let's ignore gyroscopic precession for a +moment because I think we've proven that + + align:start position:0% +moment because I think we've proven that + + + align:start position:0% +moment because I think we've proven that +nobody understands it let's just say + + align:start position:0% +nobody understands it let's just say + + + align:start position:0% +nobody understands it let's just say +that we could make the angle of attack + + align:start position:0% +that we could make the angle of attack + + + align:start position:0% +that we could make the angle of attack +higher on the back of the disc compared + + align:start position:0% +higher on the back of the disc compared + + + align:start position:0% +higher on the back of the disc compared +to the front then the back of the disc + + align:start position:0% +to the front then the back of the disc + + + align:start position:0% +to the front then the back of the disc +would have more lift it would rise it + + align:start position:0% +would have more lift it would rise it + + + align:start position:0% +would have more lift it would rise it +rise up and the front would go lower and + + align:start position:0% +rise up and the front would go lower and + + + align:start position:0% +rise up and the front would go lower and +then you would see this flight path that + + align:start position:0% +then you would see this flight path that + + + align:start position:0% +then you would see this flight path that +you do see that makes sense so basically + + align:start position:0% +you do see that makes sense so basically + + + align:start position:0% +you do see that makes sense so basically +you're controlling you're basically + + align:start position:0% +you're controlling you're basically + + + align:start position:0% +you're controlling you're basically +flying the rotor system you're not + + align:start position:0% +flying the rotor system you're not + + + align:start position:0% +flying the rotor system you're not +flying the helicopter the helicopters is + + align:start position:0% +flying the helicopter the helicopters is + + + align:start position:0% +flying the helicopter the helicopters is +hanging from the rotor system that's a + + align:start position:0% +hanging from the rotor system that's a + + + align:start position:0% +hanging from the rotor system that's a +good mental model and all the power is + + align:start position:0% +good mental model and all the power is + + + align:start position:0% +good mental model and all the power is +you know from the engine to the rotor + + align:start position:0% +you know from the engine to the rotor + + + align:start position:0% +you know from the engine to the rotor +system so that's a natural place to do + + align:start position:0% +system so that's a natural place to do + + + align:start position:0% +system so that's a natural place to do +it just by tweaking the blade angle as + + align:start position:0% +it just by tweaking the blade angle as + + + align:start position:0% +it just by tweaking the blade angle as +it rotates around so left hand is + + align:start position:0% +it rotates around so left hand is + + + align:start position:0% +it rotates around so left hand is +collective moving the blades angle + + align:start position:0% +collective moving the blades angle + + + align:start position:0% +collective moving the blades angle +regardless of where they are on the disc + + align:start position:0% +regardless of where they are on the disc + + + align:start position:0% +regardless of where they are on the disc +and the cyclic which is changing the + + align:start position:0% +and the cyclic which is changing the + + + align:start position:0% +and the cyclic which is changing the +pitch cyclically as is suggested all + + align:start position:0% +pitch cyclically as is suggested all + + + align:start position:0% +pitch cyclically as is suggested all +right Andy what's the magic this design + + align:start position:0% +right Andy what's the magic this design + + + align:start position:0% +right Andy what's the magic this design +I'm not sure it's really changed at all + + align:start position:0% +I'm not sure it's really changed at all + + + align:start position:0% +I'm not sure it's really changed at all +since the very first helicopters maybe + + align:start position:0% +since the very first helicopters maybe + + + align:start position:0% +since the very first helicopters maybe +those brothers in Paris didn't have one + + align:start position:0% +those brothers in Paris didn't have one + + + align:start position:0% +those brothers in Paris didn't have one +in 1907 but I'm pretty sure that every + + align:start position:0% +in 1907 but I'm pretty sure that every + + + align:start position:0% +in 1907 but I'm pretty sure that every +helicopter since then has had this + + align:start position:0% +helicopter since then has had this + + + align:start position:0% +helicopter since then has had this +there's a swash plate oh watch this so + + align:start position:0% +there's a swash plate oh watch this so + + + align:start position:0% +there's a swash plate oh watch this so +the lower part of the swash plate here + + align:start position:0% +the lower part of the swash plate here + + + align:start position:0% +the lower part of the swash plate here +is fixed and connected to the flight + + align:start position:0% +is fixed and connected to the flight + + + align:start position:0% +is fixed and connected to the flight +controls and then there's a bearing and + + align:start position:0% +controls and then there's a bearing and + + + align:start position:0% +controls and then there's a bearing and +the upper swash plate rotates with the + + align:start position:0% +the upper swash plate rotates with the + + + align:start position:0% +the upper swash plate rotates with the +Blaz + + align:start position:0% +Blaz + + + align:start position:0% +Blaz +does that make sense so if you lift a + + align:start position:0% +does that make sense so if you lift a + + + align:start position:0% +does that make sense so if you lift a +lower swash plate up that pushes the + + align:start position:0% +lower swash plate up that pushes the + + + align:start position:0% +lower swash plate up that pushes the +upper swash plate up which pushes these + + align:start position:0% +upper swash plate up which pushes these + + + align:start position:0% +upper swash plate up which pushes these +rods that are connected to a corner of + + align:start position:0% +rods that are connected to a corner of + + + align:start position:0% +rods that are connected to a corner of +the blade and that'll cause the blades + + align:start position:0% +the blade and that'll cause the blades + + + align:start position:0% +the blade and that'll cause the blades +to tilt that makes sense so you have + + align:start position:0% +to tilt that makes sense so you have + + + align:start position:0% +to tilt that makes sense so you have +this rotating swash plate that's + + align:start position:0% +this rotating swash plate that's + + + align:start position:0% +this rotating swash plate that's +connected to a corner of the blade and + + align:start position:0% +connected to a corner of the blade and + + + align:start position:0% +connected to a corner of the blade and +if you push the whole thing up by + + align:start position:0% +if you push the whole thing up by + + + align:start position:0% +if you push the whole thing up by +yanking up on the collective then you + + align:start position:0% +yanking up on the collective then you + + + align:start position:0% +yanking up on the collective then you +can see the blades actually twist you + + align:start position:0% +can see the blades actually twist you + + + align:start position:0% +can see the blades actually twist you +can do that in the hangar and see the + + align:start position:0% +can do that in the hangar and see the + + + align:start position:0% +can do that in the hangar and see the +effect of this at the same time in your + + align:start position:0% +effect of this at the same time in your + + + align:start position:0% +effect of this at the same time in your +right hand is the cyclic and with the + + align:start position:0% +right hand is the cyclic and with the + + + align:start position:0% +right hand is the cyclic and with the +cyclic you're tilting the swash plate so + + align:start position:0% +cyclic you're tilting the swash plate so + + + align:start position:0% +cyclic you're tilting the swash plate so +with the tilted swash plate that will + + align:start position:0% +with the tilted swash plate that will + + + align:start position:0% +with the tilted swash plate that will +just cause the blades to tilt up sorry + + align:start position:0% +just cause the blades to tilt up sorry + + + align:start position:0% +just cause the blades to tilt up sorry +the it'll cause the blades to twist up + + align:start position:0% +the it'll cause the blades to twist up + + + align:start position:0% +the it'll cause the blades to twist up +and twist down as they rotate so it's a + + align:start position:0% +and twist down as they rotate so it's a + + + align:start position:0% +and twist down as they rotate so it's a +pretty elegant solution this is not + + align:start position:0% +pretty elegant solution this is not + + + align:start position:0% +pretty elegant solution this is not +carrying much of the load of the + + align:start position:0% +carrying much of the load of the + + + align:start position:0% +carrying much of the load of the +helicopter you know there's still a mast + + align:start position:0% +helicopter you know there's still a mast + + + align:start position:0% +helicopter you know there's still a mast +holding the whole thing up this is + + align:start position:0% +holding the whole thing up this is + + + align:start position:0% +holding the whole thing up this is +really just + + align:start position:0% +really just + + + align:start position:0% +really just +has to carry enough force to twist the + + align:start position:0% +has to carry enough force to twist the + + + align:start position:0% +has to carry enough force to twist the +blades up and down up and down up and + + align:start position:0% +blades up and down up and down up and + + + align:start position:0% +blades up and down up and down up and +down + + align:start position:0% +down + + + align:start position:0% +down +so that's your engineering design + + align:start position:0% + + + + align:start position:0% + +everybody appreciates that okay do we + + align:start position:0% +everybody appreciates that okay do we + + + align:start position:0% +everybody appreciates that okay do we +want to take off straight up like in a + + align:start position:0% +want to take off straight up like in a + + + align:start position:0% +want to take off straight up like in a +Hollywood movie well if you have one or + + align:start position:0% +Hollywood movie well if you have one or + + + align:start position:0% +Hollywood movie well if you have one or +two people in a helicopter design for + + align:start position:0% +two people in a helicopter design for + + + align:start position:0% +two people in a helicopter design for +four or five that you actually do have + + align:start position:0% +four or five that you actually do have + + + align:start position:0% +four or five that you actually do have +enough power to do that however there's + + align:start position:0% +enough power to do that however there's + + + align:start position:0% +enough power to do that however there's +something over here on the right called + + align:start position:0% +something over here on the right called + + + align:start position:0% +something over here on the right called +the height velocity diagram and you can + + align:start position:0% +the height velocity diagram and you can + + + align:start position:0% +the height velocity diagram and you can +see it says avoid operation in shaded + + align:start position:0% +see it says avoid operation in shaded + + + align:start position:0% +see it says avoid operation in shaded +areas so they're saying we'll talk about + + align:start position:0% +areas so they're saying we'll talk about + + + align:start position:0% +areas so they're saying we'll talk about +this maybe a little later if people are + + align:start position:0% +this maybe a little later if people are + + + align:start position:0% +this maybe a little later if people are +interested but if you are let's say up + + align:start position:0% +interested but if you are let's say up + + + align:start position:0% +interested but if you are let's say up +at 200 feet at zero airspeed so you're + + align:start position:0% +at 200 feet at zero airspeed so you're + + + align:start position:0% +at 200 feet at zero airspeed so you're +just parked hovering 200 feet above the + + align:start position:0% +just parked hovering 200 feet above the + + + align:start position:0% +just parked hovering 200 feet above the +ground you don't have huge stores of + + align:start position:0% +ground you don't have huge stores of + + + align:start position:0% +ground you don't have huge stores of +forward speed which is a kinetic energy + + align:start position:0% +forward speed which is a kinetic energy + + + align:start position:0% +forward speed which is a kinetic energy +or potential energy because you're only + + align:start position:0% +or potential energy because you're only + + + align:start position:0% +or potential energy because you're only +up 200 feet so it's gonna be hard to do + + align:start position:0% +up 200 feet so it's gonna be hard to do + + + align:start position:0% +up 200 feet so it's gonna be hard to do +an auto rotation that's perfect and + + align:start position:0% +an auto rotation that's perfect and + + + align:start position:0% +an auto rotation that's perfect and +doesn't bend anything especially because + + align:start position:0% +doesn't bend anything especially because + + + align:start position:0% +doesn't bend anything especially because +the FAA says if you're up high like that + + align:start position:0% +the FAA says if you're up high like that + + + align:start position:0% +the FAA says if you're up high like that +and the engine quits in test piloting + + align:start position:0% +and the engine quits in test piloting + + + align:start position:0% +and the engine quits in test piloting +you have to sit there with your arms + + align:start position:0% +you have to sit there with your arms + + + align:start position:0% +you have to sit there with your arms +folded for one second and do nothing + + align:start position:0% +folded for one second and do nothing + + + align:start position:0% +folded for one second and do nothing +because that's what would probably + + align:start position:0% +because that's what would probably + + + align:start position:0% +because that's what would probably +happen in real life you know you'd be + + align:start position:0% +happen in real life you know you'd be + + + align:start position:0% +happen in real life you know you'd be +surprised people can do Auto rotations + + align:start position:0% +surprised people can do Auto rotations + + + align:start position:0% +surprised people can do Auto rotations +from 200 feet and land perfectly but + + align:start position:0% +from 200 feet and land perfectly but + + + align:start position:0% +from 200 feet and land perfectly but +they know it's coming they chop the + + align:start position:0% +they know it's coming they chop the + + + align:start position:0% +they know it's coming they chop the +throttle themselves they immediately put + + align:start position:0% +throttle themselves they immediately put + + + align:start position:0% +throttle themselves they immediately put +the collective down and they do the auto + + align:start position:0% +the collective down and they do the auto + + + align:start position:0% +the collective down and they do the auto +rotation so but basically if you're a + + align:start position:0% +rotation so but basically if you're a + + + align:start position:0% +rotation so but basically if you're a +pilot of average skill and you don't do + + align:start position:0% +pilot of average skill and you don't do + + + align:start position:0% +pilot of average skill and you don't do +anything for about a second after the + + align:start position:0% +anything for about a second after the + + + align:start position:0% +anything for about a second after the +engine quits then this is supposed to + + align:start position:0% +engine quits then this is supposed to + + + align:start position:0% +engine quits then this is supposed to +keep you safe by you either fly 50 knots + + align:start position:0% +keep you safe by you either fly 50 knots + + + align:start position:0% +keep you safe by you either fly 50 knots +or faster or you fly you know 400 feet + + align:start position:0% +or faster or you fly you know 400 feet + + + align:start position:0% +or faster or you fly you know 400 feet +or higher at sea level and higher than + + align:start position:0% +or higher at sea level and higher than + + + align:start position:0% +or higher at sea level and higher than +that at high altitude alright so what + + align:start position:0% +that at high altitude alright so what + + + align:start position:0% +that at high altitude alright so what +we're actually recommended to do see + + align:start position:0% +we're actually recommended to do see + + + align:start position:0% +we're actually recommended to do see +this recommended takeoff profile is skim + + align:start position:0% +this recommended takeoff profile is skim + + + align:start position:0% +this recommended takeoff profile is skim +along the ground until we get up to + + align:start position:0% +along the ground until we get up to + + + align:start position:0% +along the ground until we get up to +about 45 knots and then what the hell + + align:start position:0% +about 45 knots and then what the hell + + + align:start position:0% +about 45 knots and then what the hell +top to climb I think this is the curve + + align:start position:0% +top to climb I think this is the curve + + + align:start position:0% +top to climb I think this is the curve +for a Robinson r44 why would you want to + + align:start position:0% +for a Robinson r44 why would you want to + + + align:start position:0% +for a Robinson r44 why would you want to +do that aside from safety well another + + align:start position:0% +do that aside from safety well another + + + align:start position:0% +do that aside from safety well another +good reason to do that is you watch + + align:start position:0% +good reason to do that is you watch + + + align:start position:0% +good reason to do that is you watch +these drag versus speed curves and you + + align:start position:0% +these drag versus speed curves and you + + + align:start position:0% +these drag versus speed curves and you +see that you reach kind of a minimum + + align:start position:0% +see that you reach kind of a minimum + + + align:start position:0% +see that you reach kind of a minimum +this is this is some generic helicopter + + align:start position:0% +this is this is some generic helicopter + + + align:start position:0% +this is this is some generic helicopter +from an F a book it's actually 55 knots + + align:start position:0% +from an F a book it's actually 55 knots + + + align:start position:0% +from an F a book it's actually 55 knots +for the Robinson but if you can go 55 + + align:start position:0% +for the Robinson but if you can go 55 + + + align:start position:0% +for the Robinson but if you can go 55 +knots you need less energy than any + + align:start position:0% +knots you need less energy than any + + + align:start position:0% +knots you need less energy than any +other airspeed so the idea for takeoff + + align:start position:0% +other airspeed so the idea for takeoff + + + align:start position:0% +other airspeed so the idea for takeoff +is you nudge the helicopter forward a + + align:start position:0% +is you nudge the helicopter forward a + + + align:start position:0% +is you nudge the helicopter forward a +little bit if you can build up two knots + + align:start position:0% +little bit if you can build up two knots + + + align:start position:0% +little bit if you can build up two knots +of speed that gives you excess power you + + align:start position:0% +of speed that gives you excess power you + + + align:start position:0% +of speed that gives you excess power you +can use that excess power to climb up + + align:start position:0% +can use that excess power to climb up + + + align:start position:0% +can use that excess power to climb up +three inches or you can use that excess + + align:start position:0% +three inches or you can use that excess + + + align:start position:0% +three inches or you can use that excess +power to accelerate maybe to three or + + align:start position:0% +power to accelerate maybe to three or + + + align:start position:0% +power to accelerate maybe to three or +four knots and if you just keep + + align:start position:0% +four knots and if you just keep + + + align:start position:0% +four knots and if you just keep +accelerating using your extra power to + + align:start position:0% +accelerating using your extra power to + + + align:start position:0% +accelerating using your extra power to +accelerate the faster you go the less + + align:start position:0% +accelerate the faster you go the less + + + align:start position:0% +accelerate the faster you go the less +power you need so even if you've never + + align:start position:0% +power you need so even if you've never + + + align:start position:0% +power you need so even if you've never +touched a collective or drawn any more + + align:start position:0% +touched a collective or drawn any more + + + align:start position:0% +touched a collective or drawn any more +horsepower as long as you have an open + + align:start position:0% +horsepower as long as you have an open + + + align:start position:0% +horsepower as long as you have an open +area in front of you you'll accelerate + + align:start position:0% +area in front of you you'll accelerate + + + align:start position:0% +area in front of you you'll accelerate +and once you hit 45 or 55 knots you now + + align:start position:0% +and once you hit 45 or 55 knots you now + + + align:start position:0% +and once you hit 45 or 55 knots you now +have your hover power turns into + + align:start position:0% +have your hover power turns into + + + align:start position:0% +have your hover power turns into +significant excess power that you can + + align:start position:0% +significant excess power that you can + + + align:start position:0% +significant excess power that you can +use for a climb so that's why you often + + align:start position:0% +use for a climb so that's why you often + + + align:start position:0% +use for a climb so that's why you often +see helicopters at airports taking off + + align:start position:0% +see helicopters at airports taking off + + + align:start position:0% +see helicopters at airports taking off +kind of like a short field airplane and + + align:start position:0% +kind of like a short field airplane and + + + align:start position:0% +kind of like a short field airplane and +also landing a bit like a short filler + + align:start position:0% +also landing a bit like a short filler + + + align:start position:0% +also landing a bit like a short filler +airplane all right + + align:start position:0% +airplane all right + + + align:start position:0% +airplane all right +straight and level it's very similar to + + align:start position:0% +straight and level it's very similar to + + + align:start position:0% +straight and level it's very similar to +an airplane the performance is all is a + + align:start position:0% +an airplane the performance is all is a + + + align:start position:0% +an airplane the performance is all is a +function of the attitude that the + + align:start position:0% +function of the attitude that the + + + align:start position:0% +function of the attitude that the +aircraft is in is it pitched up or down + + align:start position:0% +aircraft is in is it pitched up or down + + + align:start position:0% +aircraft is in is it pitched up or down +and how much power is being applied and + + align:start position:0% +and how much power is being applied and + + + align:start position:0% +and how much power is being applied and +that's an indirect function of the + + align:start position:0% +that's an indirect function of the + + + align:start position:0% +that's an indirect function of the +collective position so as with an + + align:start position:0% +collective position so as with an + + + align:start position:0% +collective position so as with an +airplane remember your pitch controls + + align:start position:0% +airplane remember your pitch controls + + + align:start position:0% +airplane remember your pitch controls +your speed and the amount of power + + align:start position:0% +your speed and the amount of power + + + align:start position:0% +your speed and the amount of power +throttle and the airplane collective and + + align:start position:0% +throttle and the airplane collective and + + + align:start position:0% +throttle and the airplane collective and +the helicopter determines whether you're + + align:start position:0% +the helicopter determines whether you're + + + align:start position:0% +the helicopter determines whether you're +climbing or descending at that airspeed + + align:start position:0% +climbing or descending at that airspeed + + + align:start position:0% +climbing or descending at that airspeed +your attitude indicator in a VFR + + align:start position:0% +your attitude indicator in a VFR + + + align:start position:0% +your attitude indicator in a VFR +helicopter is the horizon so you're + + align:start position:0% +helicopter is the horizon so you're + + + align:start position:0% +helicopter is the horizon so you're +watching horizon carefully the reason + + align:start position:0% +watching horizon carefully the reason + + + align:start position:0% +watching horizon carefully the reason +why people people who are instrument + + align:start position:0% +why people people who are instrument + + + align:start position:0% +why people people who are instrument +rated airplane pilots they jump into the + + align:start position:0% +rated airplane pilots they jump into the + + + align:start position:0% +rated airplane pilots they jump into the +helicopter and they can fly it + + align:start position:0% +helicopter and they can fly it + + + align:start position:0% +helicopter and they can fly it +immediately and people who've never + + align:start position:0% +immediately and people who've never + + + align:start position:0% +immediately and people who've never +flown have a tough time it takes them + + align:start position:0% +flown have a tough time it takes them + + + align:start position:0% +flown have a tough time it takes them +you know 10 hours and the reason is that + + align:start position:0% +you know 10 hours and the reason is that + + + align:start position:0% +you know 10 hours and the reason is that +people who are instrument rated airplane + + align:start position:0% +people who are instrument rated airplane + + + align:start position:0% +people who are instrument rated airplane +pilots they become very sensitive to + + align:start position:0% +pilots they become very sensitive to + + + align:start position:0% +pilots they become very sensitive to +watching for small changes + + align:start position:0% +watching for small changes + + + align:start position:0% +watching for small changes +in attitude alright the anti-torque + + align:start position:0% +in attitude alright the anti-torque + + + align:start position:0% +in attitude alright the anti-torque +pedals remember we had that tail rotor + + align:start position:0% +pedals remember we had that tail rotor + + + align:start position:0% +pedals remember we had that tail rotor +and we adjust it so that the tail + + align:start position:0% +and we adjust it so that the tail + + + align:start position:0% +and we adjust it so that the tail +doesn't spin around on the ground in the + + align:start position:0% +doesn't spin around on the ground in the + + + align:start position:0% +doesn't spin around on the ground in the +air we adjusted so that the helicopters + + align:start position:0% +air we adjusted so that the helicopters + + + align:start position:0% +air we adjusted so that the helicopters +streamlined into the wind we don't + + align:start position:0% +streamlined into the wind we don't + + + align:start position:0% +streamlined into the wind we don't +actually have to use them to make turns + + align:start position:0% +actually have to use them to make turns + + + align:start position:0% +actually have to use them to make turns +there's no adverse yaw as in some + + align:start position:0% +there's no adverse yaw as in some + + + align:start position:0% +there's no adverse yaw as in some +airplanes where I'll start skidding or + + align:start position:0% +airplanes where I'll start skidding or + + + align:start position:0% +airplanes where I'll start skidding or +there's none of that + + align:start position:0% +there's none of that + + + align:start position:0% +there's none of that +so basically or slipping all we do is to + + align:start position:0% +so basically or slipping all we do is to + + + align:start position:0% +so basically or slipping all we do is to +make a turn is we put the helicopter + + align:start position:0% +make a turn is we put the helicopter + + + align:start position:0% +make a turn is we put the helicopter +using the cyclic into a little bit of a + + align:start position:0% +using the cyclic into a little bit of a + + + align:start position:0% +using the cyclic into a little bit of a +bank and then we wait so if we have you + + align:start position:0% +bank and then we wait so if we have you + + + align:start position:0% +bank and then we wait so if we have you +know let's say a 10 degree Bank the + + align:start position:0% +know let's say a 10 degree Bank the + + + align:start position:0% +know let's say a 10 degree Bank the +helicopter in one minute will make a 180 + + align:start position:0% +helicopter in one minute will make a 180 + + + align:start position:0% +helicopter in one minute will make a 180 +degree turn landing with power so again + + align:start position:0% +degree turn landing with power so again + + + align:start position:0% +degree turn landing with power so again +like an airplane if you see the spot in + + align:start position:0% +like an airplane if you see the spot in + + + align:start position:0% +like an airplane if you see the spot in +the ground + + align:start position:0% +the ground + + + align:start position:0% +the ground +you adjust the power so you don't over + + align:start position:0% +you adjust the power so you don't over + + + align:start position:0% +you adjust the power so you don't over +fly the spot or under fly the spot if + + align:start position:0% +fly the spot or under fly the spot if + + + align:start position:0% +fly the spot or under fly the spot if +the spots rising up in the windshield + + align:start position:0% +the spots rising up in the windshield + + + align:start position:0% +the spots rising up in the windshield +from your perspective that means you're + + align:start position:0% +from your perspective that means you're + + + align:start position:0% +from your perspective that means you're +gonna land short so you add power raised + + align:start position:0% +gonna land short so you add power raised + + + align:start position:0% +gonna land short so you add power raised +collective in the helicopter if the spot + + align:start position:0% +collective in the helicopter if the spot + + + align:start position:0% +collective in the helicopter if the spot +is descending then you're over flying + + align:start position:0% +is descending then you're over flying + + + align:start position:0% +is descending then you're over flying +the spot so you have to reduce power + + align:start position:0% +the spot so you have to reduce power + + + align:start position:0% +the spot so you have to reduce power +it's a purely physical it's a purely + + align:start position:0% +it's a purely physical it's a purely + + + align:start position:0% +it's a purely physical it's a purely +visual maneuver except when you're + + align:start position:0% +visual maneuver except when you're + + + align:start position:0% +visual maneuver except when you're +landing on a pinnacle and the reason for + + align:start position:0% +landing on a pinnacle and the reason for + + + align:start position:0% +landing on a pinnacle and the reason for +that is if you're landing on a pinnacle + + align:start position:0% +that is if you're landing on a pinnacle + + + align:start position:0% +that is if you're landing on a pinnacle +you don't get a sensation of your + + align:start position:0% +you don't get a sensation of your + + + align:start position:0% +you don't get a sensation of your +forward speed from the ground rushing by + + align:start position:0% +forward speed from the ground rushing by + + + align:start position:0% +forward speed from the ground rushing by +so the ideal the idea and the helicopter + + align:start position:0% +so the ideal the idea and the helicopter + + + align:start position:0% +so the ideal the idea and the helicopter +is to land unlike with the airplane it's + + align:start position:0% +is to land unlike with the airplane it's + + + align:start position:0% +is to land unlike with the airplane it's +actually a little bit it's a little bit + + align:start position:0% +actually a little bit it's a little bit + + + align:start position:0% +actually a little bit it's a little bit +less unnerving than an airplane some + + align:start position:0% +less unnerving than an airplane some + + + align:start position:0% +less unnerving than an airplane some +people get a little bit ground shy in + + align:start position:0% +people get a little bit ground shy in + + + align:start position:0% +people get a little bit ground shy in +the airplane like they're happy flying + + align:start position:0% +the airplane like they're happy flying + + + align:start position:0% +the airplane like they're happy flying +80 knots in the pattern but they're not + + align:start position:0% +80 knots in the pattern but they're not + + + align:start position:0% +80 knots in the pattern but they're not +that happy flying 70 knots you know 10 + + align:start position:0% +that happy flying 70 knots you know 10 + + + align:start position:0% +that happy flying 70 knots you know 10 +feet above the runway which makes sense + + align:start position:0% +feet above the runway which makes sense + + + align:start position:0% +feet above the runway which makes sense +because you don't want to slam into the + + align:start position:0% +because you don't want to slam into the + + + align:start position:0% +because you don't want to slam into the +ground going really fast well the good + + align:start position:0% +ground going really fast well the good + + + align:start position:0% +ground going really fast well the good +news is in the helicopter you never get + + align:start position:0% +news is in the helicopter you never get + + + align:start position:0% +news is in the helicopter you never get +to that phase where you're going fast + + align:start position:0% +to that phase where you're going fast + + + align:start position:0% +to that phase where you're going fast +close to the ground because when you're + + align:start position:0% +close to the ground because when you're + + + align:start position:0% +close to the ground because when you're +landing you just say you know how in my + + align:start position:0% +landing you just say you know how in my + + + align:start position:0% +landing you just say you know how in my +peripheral vision how fast is the ground + + align:start position:0% +peripheral vision how fast is the ground + + + align:start position:0% +peripheral vision how fast is the ground +rushing by and + + align:start position:0% +rushing by and + + + align:start position:0% +rushing by and +just kind of keep that constant whatever + + align:start position:0% +just kind of keep that constant whatever + + + align:start position:0% +just kind of keep that constant whatever +it was up at 500 feet above the ground + + align:start position:0% +it was up at 500 feet above the ground + + + align:start position:0% +it was up at 500 feet above the ground +that's what you want when you're 5 feet + + align:start position:0% +that's what you want when you're 5 feet + + + align:start position:0% +that's what you want when you're 5 feet +above the ground and you'll very + + align:start position:0% +above the ground and you'll very + + + align:start position:0% +above the ground and you'll very +naturally slow down you'll do the right + + align:start position:0% +naturally slow down you'll do the right + + + align:start position:0% +naturally slow down you'll do the right +your natural instinct to slow down as + + align:start position:0% +your natural instinct to slow down as + + + align:start position:0% +your natural instinct to slow down as +the ground begins rushing is a helpful + + align:start position:0% +the ground begins rushing is a helpful + + + align:start position:0% +the ground begins rushing is a helpful +one in the helicopter so your peripheral + + align:start position:0% +one in the helicopter so your peripheral + + + align:start position:0% +one in the helicopter so your peripheral +vision is used for speed reference and + + align:start position:0% +vision is used for speed reference and + + + align:start position:0% +vision is used for speed reference and +the spot moving up or down is used for a + + align:start position:0% +the spot moving up or down is used for a + + + align:start position:0% +the spot moving up or down is used for a +descent rate reference and that's you + + align:start position:0% +descent rate reference and that's you + + + align:start position:0% +descent rate reference and that's you +never have to look inside at the gauges + + align:start position:0% +never have to look inside at the gauges + + + align:start position:0% +never have to look inside at the gauges +except when you're landing on top of an + + align:start position:0% +except when you're landing on top of an + + + align:start position:0% +except when you're landing on top of an +office building or something all right + + align:start position:0% +office building or something all right + + + align:start position:0% +office building or something all right +can you land the helicopter without + + align:start position:0% +can you land the helicopter without + + + align:start position:0% +can you land the helicopter without +power it turns out the answer is yes you + + align:start position:0% +power it turns out the answer is yes you + + + align:start position:0% +power it turns out the answer is yes you +have these three buckets of energy that + + align:start position:0% +have these three buckets of energy that + + + align:start position:0% +have these three buckets of energy that +I alluded to earlier kinetic from your + + align:start position:0% +I alluded to earlier kinetic from your + + + align:start position:0% +I alluded to earlier kinetic from your +forward airspeed potential from being up + + align:start position:0% +forward airspeed potential from being up + + + align:start position:0% +forward airspeed potential from being up +high and then another form of kinetic + + align:start position:0% +high and then another form of kinetic + + + align:start position:0% +high and then another form of kinetic +which we'll call blade inertia from + + align:start position:0% +which we'll call blade inertia from + + + align:start position:0% +which we'll call blade inertia from +their relatively heavy blades spinning + + align:start position:0% +their relatively heavy blades spinning + + + align:start position:0% +their relatively heavy blades spinning +so raise your hand if you think the + + align:start position:0% +so raise your hand if you think the + + + align:start position:0% +so raise your hand if you think the +forward air speed is number one in terms + + align:start position:0% +forward air speed is number one in terms + + + align:start position:0% +forward air speed is number one in terms +of size let's rank these what's what's + + align:start position:0% +of size let's rank these what's what's + + + align:start position:0% +of size let's rank these what's what's +the biggest air speed going a heavy + + align:start position:0% +the biggest air speed going a heavy + + + align:start position:0% +the biggest air speed going a heavy +helicopter going 100 knots potential + + align:start position:0% +helicopter going 100 knots potential + + + align:start position:0% +helicopter going 100 knots potential +energy the helicopter having been lifted + + align:start position:0% +energy the helicopter having been lifted + + + align:start position:0% +energy the helicopter having been lifted +up off the ground or the blades whipping + + align:start position:0% +up off the ground or the blades whipping + + + align:start position:0% +up off the ground or the blades whipping +around near the speed of sound okay who + + align:start position:0% +around near the speed of sound okay who + + + align:start position:0% +around near the speed of sound okay who +votes for one forward airspeed a few who + + align:start position:0% +votes for one forward airspeed a few who + + + align:start position:0% +votes for one forward airspeed a few who +votes for potential a fair number who + + align:start position:0% +votes for potential a fair number who + + + align:start position:0% +votes for potential a fair number who +votes for blade inertia the blades + + align:start position:0% +votes for blade inertia the blades + + + align:start position:0% +votes for blade inertia the blades +whipping around all right good we got a + + align:start position:0% +whipping around all right good we got a + + + align:start position:0% +whipping around all right good we got a +good distribution okay well let me give + + align:start position:0% +good distribution okay well let me give + + + align:start position:0% +good distribution okay well let me give +you I'll tell you about I think it was a + + align:start position:0% +you I'll tell you about I think it was a + + + align:start position:0% +you I'll tell you about I think it was a +crazy French guy who got into your + + align:start position:0% +crazy French guy who got into your + + + align:start position:0% +crazy French guy who got into your +what's now called a gyro copter and + + align:start position:0% +what's now called a gyro copter and + + + align:start position:0% +what's now called a gyro copter and +Alouette and went up to 40,000 feet to + + align:start position:0% +Alouette and went up to 40,000 feet to + + + align:start position:0% +Alouette and went up to 40,000 feet to +set an altitude record the record was + + align:start position:0% +set an altitude record the record was + + + align:start position:0% +set an altitude record the record was +set when the engines flamed out that's + + align:start position:0% +set when the engines flamed out that's + + + align:start position:0% +set when the engines flamed out that's +why it's you know 40,000 and change not + + align:start position:0% +why it's you know 40,000 and change not + + + align:start position:0% +why it's you know 40,000 and change not +41,000 and change and then Auto rotated + + align:start position:0% +41,000 and change and then Auto rotated + + + align:start position:0% +41,000 and change and then Auto rotated +all the way down to the ground so + + align:start position:0% +all the way down to the ground so + + + align:start position:0% +all the way down to the ground so +whatever energy bucket that was there + + align:start position:0% +whatever energy bucket that was there + + + align:start position:0% +whatever energy bucket that was there +had to be sufficient to make it all the + + align:start position:0% +had to be sufficient to make it all the + + + align:start position:0% +had to be sufficient to make it all the +way the ground so what does that tell + + align:start position:0% +way the ground so what does that tell + + + align:start position:0% +way the ground so what does that tell +you the biggest one is it's got to be + + align:start position:0% +you the biggest one is it's got to be + + + align:start position:0% +you the biggest one is it's got to be +something that scales up to 40,000 feet + + align:start position:0% +something that scales up to 40,000 feet + + + align:start position:0% +something that scales up to 40,000 feet +potential yeah so potential energy is a + + align:start position:0% +potential yeah so potential energy is a + + + align:start position:0% +potential yeah so potential energy is a +good candidate for the biggest because + + align:start position:0% +good candidate for the biggest because + + + align:start position:0% +good candidate for the biggest because +again if you you know you got to keep + + align:start position:0% +again if you you know you got to keep + + + align:start position:0% +again if you you know you got to keep +the rotor spinning for longer if you're + + align:start position:0% +the rotor spinning for longer if you're + + + align:start position:0% +the rotor spinning for longer if you're +Auto rotating from ten thousand feet or + + align:start position:0% +Auto rotating from ten thousand feet or + + + align:start position:0% +Auto rotating from ten thousand feet or +fifty thousand feet or whoever I don't + + align:start position:0% +fifty thousand feet or whoever I don't + + + align:start position:0% +fifty thousand feet or whoever I don't +think that records been broken actually + + align:start position:0% +think that records been broken actually + + + align:start position:0% +think that records been broken actually +it was set in the 70s okay so number two + + align:start position:0% +it was set in the 70s okay so number two + + + align:start position:0% +it was set in the 70s okay so number two +is the forward air speed of the + + align:start position:0% +is the forward air speed of the + + + align:start position:0% +is the forward air speed of the +helicopter the blade inertia isn't good + + align:start position:0% +helicopter the blade inertia isn't good + + + align:start position:0% +helicopter the blade inertia isn't good +for much except for cushioning your fall + + align:start position:0% +for much except for cushioning your fall + + + align:start position:0% +for much except for cushioning your fall +from five or ten feet above the ground + + align:start position:0% +from five or ten feet above the ground + + + align:start position:0% +from five or ten feet above the ground +so what you do in the helicopter would + + align:start position:0% +so what you do in the helicopter would + + + align:start position:0% +so what you do in the helicopter would +if the engine were to fail number one + + align:start position:0% +if the engine were to fail number one + + + align:start position:0% +if the engine were to fail number one +reason is fuel starvation from failing + + align:start position:0% +reason is fuel starvation from failing + + + align:start position:0% +reason is fuel starvation from failing +to top it off + + align:start position:0% +to top it off + + + align:start position:0% +to top it off +helicopters are often short on payload + + align:start position:0% +helicopters are often short on payload + + + align:start position:0% +helicopters are often short on payload +so people will say well I want to take + + align:start position:0% +so people will say well I want to take + + + align:start position:0% +so people will say well I want to take +these seven people somewhere and I'd be + + align:start position:0% +these seven people somewhere and I'd be + + + align:start position:0% +these seven people somewhere and I'd be +overweight if I fell to the fuel tank so + + align:start position:0% +overweight if I fell to the fuel tank so + + + align:start position:0% +overweight if I fell to the fuel tank so +I'll put an you know half an hour of + + align:start position:0% +I'll put an you know half an hour of + + + align:start position:0% +I'll put an you know half an hour of +fuel for this 15 minute trip actually + + align:start position:0% +fuel for this 15 minute trip actually + + + align:start position:0% +fuel for this 15 minute trip actually +that would be illegal twenty minutes is + + align:start position:0% +that would be illegal twenty minutes is + + + align:start position:0% +that would be illegal twenty minutes is +the minimum reserve so I'll put in half + + align:start position:0% +the minimum reserve so I'll put in half + + + align:start position:0% +the minimum reserve so I'll put in half +an hour if you offered this ten minute + + align:start position:0% +an hour if you offered this ten minute + + + align:start position:0% +an hour if you offered this ten minute +trip and then you know there's a bit of + + align:start position:0% +trip and then you know there's a bit of + + + align:start position:0% +trip and then you know there's a bit of +a delay and you run out of fuel there's + + align:start position:0% +a delay and you run out of fuel there's + + + align:start position:0% +a delay and you run out of fuel there's +a warning might at ten minutes all right + + align:start position:0% +a warning might at ten minutes all right + + + align:start position:0% +a warning might at ten minutes all right +and the good news is you can land in the + + align:start position:0% +and the good news is you can land in the + + + align:start position:0% +and the good news is you can land in the +field you know baseball field pretty + + align:start position:0% +field you know baseball field pretty + + + align:start position:0% +field you know baseball field pretty +easily alright so the engine quits for + + align:start position:0% +easily alright so the engine quits for + + + align:start position:0% +easily alright so the engine quits for +whatever reason let's say you've run out + + align:start position:0% +whatever reason let's say you've run out + + + align:start position:0% +whatever reason let's say you've run out +of fuel you want to get to 60 or 70 + + align:start position:0% +of fuel you want to get to 60 or 70 + + + align:start position:0% +of fuel you want to get to 60 or 70 +knots some reasonable air speed and then + + align:start position:0% +knots some reasonable air speed and then + + + align:start position:0% +knots some reasonable air speed and then +the challenge is to hold that air speed + + align:start position:0% +the challenge is to hold that air speed + + + align:start position:0% +the challenge is to hold that air speed +even as the ground is rushing up at you + + align:start position:0% +even as the ground is rushing up at you + + + align:start position:0% +even as the ground is rushing up at you +you hold it right till you're at + + align:start position:0% +you hold it right till you're at + + + align:start position:0% +you hold it right till you're at +treetops height about forty feet above + + align:start position:0% +treetops height about forty feet above + + + align:start position:0% +treetops height about forty feet above +the ground then you begin to flare just + + align:start position:0% +the ground then you begin to flare just + + + align:start position:0% +the ground then you begin to flare just +like in an airplane flaring for landing + + align:start position:0% +like in an airplane flaring for landing + + + align:start position:0% +like in an airplane flaring for landing +you scrub off that forward speed and + + align:start position:0% +you scrub off that forward speed and + + + align:start position:0% +you scrub off that forward speed and +that reduces your descent rate so you + + align:start position:0% +that reduces your descent rate so you + + + align:start position:0% +that reduces your descent rate so you +can reduce your descent rate to zero by + + align:start position:0% +can reduce your descent rate to zero by + + + align:start position:0% +can reduce your descent rate to zero by +bleeding off all that energy from the + + align:start position:0% +bleeding off all that energy from the + + + align:start position:0% +bleeding off all that energy from the +forward air speed and the kinetic energy + + align:start position:0% +forward air speed and the kinetic energy + + + align:start position:0% +forward air speed and the kinetic energy +remember is MV squared so it's very + + align:start position:0% +remember is MV squared so it's very + + + align:start position:0% +remember is MV squared so it's very +important there's twice as much energy + + align:start position:0% +important there's twice as much energy + + + align:start position:0% +important there's twice as much energy +at 70 knots compared to 50 knots + + align:start position:0% +at 70 knots compared to 50 knots + + + align:start position:0% +at 70 knots compared to 50 knots +so once you've scrubbed off all your + + align:start position:0% +so once you've scrubbed off all your + + + align:start position:0% +so once you've scrubbed off all your +descent rate and all your forward speed + + align:start position:0% +descent rate and all your forward speed + + + align:start position:0% +descent rate and all your forward speed +you're like this so your tails will be + + align:start position:0% +you're like this so your tails will be + + + align:start position:0% +you're like this so your tails will be +low and now you're gonna just follow the + + align:start position:0% +low and now you're gonna just follow the + + + align:start position:0% +low and now you're gonna just follow the +ground and hit the tail first so it's + + align:start position:0% +ground and hit the tail first so it's + + + align:start position:0% +ground and hit the tail first so it's +not going to be an FAA quality you're + + align:start position:0% +not going to be an FAA quality you're + + + align:start position:0% +not going to be an FAA quality you're +gonna walk away but it's not going to be + + align:start position:0% +gonna walk away but it's not going to be + + + align:start position:0% +gonna walk away but it's not going to be +an FAA quality landing so what you can + + align:start position:0% +an FAA quality landing so what you can + + + align:start position:0% +an FAA quality landing so what you can +do is stick forward and settle by + + align:start position:0% +do is stick forward and settle by + + + align:start position:0% +do is stick forward and settle by +pulling up on the collective so you + + align:start position:0% +pulling up on the collective so you + + + align:start position:0% +pulling up on the collective so you +stick forward to level the skids + + align:start position:0% +stick forward to level the skids + + + align:start position:0% +stick forward to level the skids +and then when you're about five feet + + align:start position:0% +and then when you're about five feet + + + align:start position:0% +and then when you're about five feet +above the ground or maybe two feet above + + align:start position:0% +above the ground or maybe two feet above + + + align:start position:0% +above the ground or maybe two feet above +the ground you start pulling up on the + + align:start position:0% +the ground you start pulling up on the + + + align:start position:0% +the ground you start pulling up on the +collective to cushion your fall that + + align:start position:0% +collective to cushion your fall that + + + align:start position:0% +collective to cushion your fall that +last few feet so you've used up + + align:start position:0% +last few feet so you've used up + + + align:start position:0% +last few feet so you've used up +potential energy keeping the blades + + align:start position:0% +potential energy keeping the blades + + + align:start position:0% +potential energy keeping the blades +windmilling + + align:start position:0% +windmilling + + + align:start position:0% +windmilling +if you just flatten the collective the + + align:start position:0% +if you just flatten the collective the + + + align:start position:0% +if you just flatten the collective the +blades will have a relatively normal + + align:start position:0% +blades will have a relatively normal + + + align:start position:0% +blades will have a relatively normal +angle of attack to the air that's now + + align:start position:0% +angle of attack to the air that's now + + + align:start position:0% +angle of attack to the air that's now +coming from below you've kept up your + + align:start position:0% +coming from below you've kept up your + + + align:start position:0% +coming from below you've kept up your +forward speed and you bleed that off at + + align:start position:0% +forward speed and you bleed that off at + + + align:start position:0% +forward speed and you bleed that off at +the end to reduce your vertical speed + + align:start position:0% +the end to reduce your vertical speed + + + align:start position:0% +the end to reduce your vertical speed +and then finally you go + + align:start position:0% + + + + align:start position:0% + +I think I cheated + + align:start position:0% +I think I cheated + + + align:start position:0% +I think I cheated +what's the cheat and I'm gonna I'm + + align:start position:0% +what's the cheat and I'm gonna I'm + + + align:start position:0% +what's the cheat and I'm gonna I'm +telling you the cheat is you can hear it + + align:start position:0% +telling you the cheat is you can hear it + + + align:start position:0% +telling you the cheat is you can hear it +you could hear the cheating going on he + + align:start position:0% +you could hear the cheating going on he + + + align:start position:0% +you could hear the cheating going on he +landed with zero forward air speed why + + align:start position:0% + + + + align:start position:0% + +what enabled that and like I said you + + align:start position:0% +what enabled that and like I said you + + + align:start position:0% +what enabled that and like I said you +could hear it it's not from the engine + + align:start position:0% +could hear it it's not from the engine + + + align:start position:0% +could hear it it's not from the engine +running the engine was presumably at + + align:start position:0% +running the engine was presumably at + + + align:start position:0% +running the engine was presumably at +idle okay so what was the cheat nobody + + align:start position:0% +idle okay so what was the cheat nobody + + + align:start position:0% +idle okay so what was the cheat nobody +hurt wind exactly yes what's your name + + align:start position:0% +hurt wind exactly yes what's your name + + + align:start position:0% +hurt wind exactly yes what's your name +messin figured this out so basically he + + align:start position:0% +messin figured this out so basically he + + + align:start position:0% +messin figured this out so basically he +landed with probably it's very hard to + + align:start position:0% +landed with probably it's very hard to + + + align:start position:0% +landed with probably it's very hard to +kill all of your vertical speed and all + + align:start position:0% +kill all of your vertical speed and all + + + align:start position:0% +kill all of your vertical speed and all +of your forward speed so if you go out + + align:start position:0% +of your forward speed so if you go out + + + align:start position:0% +of your forward speed so if you go out +and it's 15 knots down the runway if you + + align:start position:0% +and it's 15 knots down the runway if you + + + align:start position:0% +and it's 15 knots down the runway if you +can just get down to 15 knots and + + align:start position:0% +can just get down to 15 knots and + + + align:start position:0% +can just get down to 15 knots and +instead of sliding and gone down the + + align:start position:0% +instead of sliding and gone down the + + + align:start position:0% +instead of sliding and gone down the +runway which is common and not not + + align:start position:0% +runway which is common and not not + + + align:start position:0% +runway which is common and not not +harmful to the helicopter you'll have a + + align:start position:0% +harmful to the helicopter you'll have a + + + align:start position:0% +harmful to the helicopter you'll have a +perfect how it looks like a perfect + + align:start position:0% +perfect how it looks like a perfect + + + align:start position:0% +perfect how it looks like a perfect +landing it's very hard and the big + + align:start position:0% +landing it's very hard and the big + + + align:start position:0% +landing it's very hard and the big +helicopters like a Huey or something + + align:start position:0% +helicopters like a Huey or something + + + align:start position:0% +helicopters like a Huey or something +it's practical to do a zero-zero landing + + align:start position:0% +it's practical to do a zero-zero landing + + + align:start position:0% +it's practical to do a zero-zero landing +out of an auto all the time and in + + align:start position:0% +out of an auto all the time and in + + + align:start position:0% +out of an auto all the time and in +Robinson it can be tough but the wind + + align:start position:0% +Robinson it can be tough but the wind + + + align:start position:0% +Robinson it can be tough but the wind +helps hugely and the like I said the + + align:start position:0% +helps hugely and the like I said the + + + align:start position:0% +helps hugely and the like I said the +throttle was down at idle so the engines + + align:start position:0% +throttle was down at idle so the engines + + + align:start position:0% +throttle was down at idle so the engines +not really doing anything question + + align:start position:0% + + + + align:start position:0% + +it is yes great great question so + + align:start position:0% +it is yes great great question so + + + align:start position:0% +it is yes great great question so +there's a sprag clutch which prevents + + align:start position:0% +there's a sprag clutch which prevents + + + align:start position:0% +there's a sprag clutch which prevents +the rotor system from trying to drive + + align:start position:0% +the rotor system from trying to drive + + + align:start position:0% +the rotor system from trying to drive +the engine because that would introduce + + align:start position:0% +the engine because that would introduce + + + align:start position:0% +the engine because that would introduce +a lot more drag but the main rotor and + + align:start position:0% +a lot more drag but the main rotor and + + + align:start position:0% +a lot more drag but the main rotor and +the tail rotor are yoked together so you + + align:start position:0% +the tail rotor are yoked together so you + + + align:start position:0% +the tail rotor are yoked together so you +still have tail rotor control great + + align:start position:0% +still have tail rotor control great + + + align:start position:0% +still have tail rotor control great +question yeah you need much I don't know + + align:start position:0% +question yeah you need much I don't know + + + align:start position:0% +question yeah you need much I don't know +I have to think about why it's useful + + align:start position:0% +I have to think about why it's useful + + + align:start position:0% +I have to think about why it's useful +yeah it's not useful for much that's for + + align:start position:0% +yeah it's not useful for much that's for + + + align:start position:0% +yeah it's not useful for much that's for +sure + + align:start position:0% +sure + + + align:start position:0% +sure +one thing is good about it is the + + align:start position:0% +one thing is good about it is the + + + align:start position:0% +one thing is good about it is the +hydraulic pump is also geared into the + + align:start position:0% +hydraulic pump is also geared into the + + + align:start position:0% +hydraulic pump is also geared into the +transmission so you still have hydraulic + + align:start position:0% +transmission so you still have hydraulic + + + align:start position:0% +transmission so you still have hydraulic +boost even if you're off auto rotating + + align:start position:0% +boost even if you're off auto rotating + + + align:start position:0% +boost even if you're off auto rotating +from super high what can you do with a + + align:start position:0% +from super high what can you do with a + + + align:start position:0% +from super high what can you do with a +helicopter if you have a private you can + + align:start position:0% +helicopter if you have a private you can + + + align:start position:0% +helicopter if you have a private you can +visit schools I visited the Winchester + + align:start position:0% +visit schools I visited the Winchester + + + align:start position:0% +visit schools I visited the Winchester +public schools I'm not sure you can give + + align:start position:0% +public schools I'm not sure you can give + + + align:start position:0% +public schools I'm not sure you can give +them all rides if you only have a + + align:start position:0% +them all rides if you only have a + + + align:start position:0% +them all rides if you only have a +private there's some kind of like I said + + align:start position:0% +private there's some kind of like I said + + + align:start position:0% +private there's some kind of like I said +those those charity laws that + + align:start position:0% +those those charity laws that + + + align:start position:0% +those those charity laws that +regulations that we don't really worry + + align:start position:0% +regulations that we don't really worry + + + align:start position:0% +regulations that we don't really worry +about because you know we have + + align:start position:0% +about because you know we have + + + align:start position:0% +about because you know we have +commercial certificate and the letter of + + align:start position:0% +commercial certificate and the letter of + + + align:start position:0% +commercial certificate and the letter of +authority from the Fisto but here's the + + align:start position:0% +authority from the Fisto but here's the + + + align:start position:0% +authority from the Fisto but here's the +how here's one of the East Coast Aero + + align:start position:0% +how here's one of the East Coast Aero + + + align:start position:0% +how here's one of the East Coast Aero +Club helicopters I flew to the public + + align:start position:0% +Club helicopters I flew to the public + + + align:start position:0% +Club helicopters I flew to the public +schools and winchester's I gave all the + + align:start position:0% +schools and winchester's I gave all the + + + align:start position:0% +schools and winchester's I gave all the +kids rides and when we flew over houses + + align:start position:0% +kids rides and when we flew over houses + + + align:start position:0% +kids rides and when we flew over houses +like this I said oh that's just like the + + align:start position:0% +like this I said oh that's just like the + + + align:start position:0% +like this I said oh that's just like the +house where I grew up if you do that + + align:start position:0% +house where I grew up if you do that + + + align:start position:0% +house where I grew up if you do that +with kids from Weston and Lincoln they + + align:start position:0% +with kids from Weston and Lincoln they + + + align:start position:0% +with kids from Weston and Lincoln they +believe you + + align:start position:0% +believe you + + + align:start position:0% +believe you +they don't parse that as an ironic + + align:start position:0% +they don't parse that as an ironic + + + align:start position:0% +they don't parse that as an ironic +statement all right helicopter pilot + + align:start position:0% +statement all right helicopter pilot + + + align:start position:0% +statement all right helicopter pilot +careers just in case any of you guys are + + align:start position:0% +careers just in case any of you guys are + + + align:start position:0% +careers just in case any of you guys are +thinking about leaving the desk world + + align:start position:0% +thinking about leaving the desk world + + + align:start position:0% +thinking about leaving the desk world +people work as a flight instructor fly + + align:start position:0% +people work as a flight instructor fly + + + align:start position:0% +people work as a flight instructor fly +tours in the Grand Canyon or Alaska and + + align:start position:0% +tours in the Grand Canyon or Alaska and + + + align:start position:0% +tours in the Grand Canyon or Alaska and +then they'll either go to offshore oil + + align:start position:0% +then they'll either go to offshore oil + + + align:start position:0% +then they'll either go to offshore oil +or medevac after that usually offshore + + align:start position:0% +or medevac after that usually offshore + + + align:start position:0% +or medevac after that usually offshore +oil used to be easier to get when oil + + align:start position:0% +oil used to be easier to get when oil + + + align:start position:0% +oil used to be easier to get when oil +when the oil prices are low when oil + + align:start position:0% +when the oil prices are low when oil + + + align:start position:0% +when the oil prices are low when oil +catches a cold the helicopter industry + + align:start position:0% +catches a cold the helicopter industry + + + align:start position:0% +catches a cold the helicopter industry +catches the flu they shut down these oil + + align:start position:0% +catches the flu they shut down these oil + + + align:start position:0% +catches the flu they shut down these oil +rigs and there's a lot less need for + + align:start position:0% +rigs and there's a lot less need for + + + align:start position:0% +rigs and there's a lot less need for +helicopter transport medevac has kind of + + align:start position:0% +helicopter transport medevac has kind of + + + align:start position:0% +helicopter transport medevac has kind of +considered the plum job that's my friend + + align:start position:0% +considered the plum job that's my friend + + + align:start position:0% +considered the plum job that's my friend +Marcus he trained at East Coast there + + align:start position:0% +Marcus he trained at East Coast there + + + align:start position:0% +Marcus he trained at East Coast there +I'll come and now + + align:start position:0% +I'll come and now + + + align:start position:0% +I'll come and now +he's hangs he does 12-hour shifts at a + + align:start position:0% +he's hangs he does 12-hour shifts at a + + + align:start position:0% +he's hangs he does 12-hour shifts at a +volunteer fire station and he did he + + align:start position:0% +volunteer fire station and he did he + + + align:start position:0% +volunteer fire station and he did he +gets paid in North Carolina and goes + + align:start position:0% +gets paid in North Carolina and goes + + + align:start position:0% +gets paid in North Carolina and goes +hospital hospital or sometimes picks + + align:start position:0% +hospital hospital or sometimes picks + + + align:start position:0% +hospital hospital or sometimes picks +people up off of highways and stuff so + + align:start position:0% +people up off of highways and stuff so + + + align:start position:0% +people up off of highways and stuff so +what can you do + + align:start position:0% +what can you do + + + align:start position:0% +what can you do +you can fly low and slow both legally + + align:start position:0% +you can fly low and slow both legally + + + align:start position:0% +you can fly low and slow both legally +and safely he saw there was a carve out + + align:start position:0% +and safely he saw there was a carve out + + + align:start position:0% +and safely he saw there was a carve out +for helicopters able to fly lower one + + align:start position:0% +for helicopters able to fly lower one + + + align:start position:0% +for helicopters able to fly lower one +problematic aspect of flying Piper + + align:start position:0% +problematic aspect of flying Piper + + + align:start position:0% +problematic aspect of flying Piper +warriors and Cessnas is that people + + align:start position:0% +warriors and Cessnas is that people + + + align:start position:0% +warriors and Cessnas is that people +their expectations of what an aircraft + + align:start position:0% +their expectations of what an aircraft + + + align:start position:0% +their expectations of what an aircraft +is and what it can do has been set by + + align:start position:0% +is and what it can do has been set by + + + align:start position:0% +is and what it can do has been set by +their airline experience and the first + + align:start position:0% +their airline experience and the first + + + align:start position:0% +their airline experience and the first +time we try to get up and use the + + align:start position:0% +time we try to get up and use the + + + align:start position:0% +time we try to get up and use the +bathroom in your Piper + + align:start position:0% +bathroom in your Piper + + + align:start position:0% +bathroom in your Piper +you'll discover that JetBlue has some + + align:start position:0% +you'll discover that JetBlue has some + + + align:start position:0% +you'll discover that JetBlue has some +advantages in the aircraft department + + align:start position:0% +advantages in the aircraft department + + + align:start position:0% +advantages in the aircraft department +and your passengers will notice this too + + align:start position:0% +and your passengers will notice this too + + + align:start position:0% +and your passengers will notice this too +is this noisy it's not + + align:start position:0% +is this noisy it's not + + + align:start position:0% +is this noisy it's not +climate-controlled there's no bathroom + + align:start position:0% +climate-controlled there's no bathroom + + + align:start position:0% +climate-controlled there's no bathroom +the helicopters are awesome because + + align:start position:0% +the helicopters are awesome because + + + align:start position:0% +the helicopters are awesome because +people usually haven't even been in one + + align:start position:0% +people usually haven't even been in one + + + align:start position:0% +people usually haven't even been in one +so it's a whole different experience + + align:start position:0% +so it's a whole different experience + + + align:start position:0% +so it's a whole different experience +it's a different view you can take them + + align:start position:0% +it's a different view you can take them + + + align:start position:0% +it's a different view you can take them +on a 10-minute ride from Hanscom field + + align:start position:0% +on a 10-minute ride from Hanscom field + + + align:start position:0% +on a 10-minute ride from Hanscom field +and go back you don't have to say oh + + align:start position:0% +and go back you don't have to say oh + + + align:start position:0% +and go back you don't have to say oh +it's gonna have lunch in Martha's + + align:start position:0% +it's gonna have lunch in Martha's + + + align:start position:0% +it's gonna have lunch in Martha's +Vineyard you just take them on a little + + align:start position:0% +Vineyard you just take them on a little + + + align:start position:0% +Vineyard you just take them on a little +tour and they say wow this is awesome so + + align:start position:0% +tour and they say wow this is awesome so + + + align:start position:0% +tour and they say wow this is awesome so +when I actually want to show people what + + align:start position:0% +when I actually want to show people what + + + align:start position:0% +when I actually want to show people what +GA is like and what my world is like I + + align:start position:0% +GA is like and what my world is like I + + + align:start position:0% +GA is like and what my world is like I +usually take them for a helicopter ride + + align:start position:0% +usually take them for a helicopter ride + + + align:start position:0% +usually take them for a helicopter ride +I don't take them for a trip you know + + align:start position:0% +I don't take them for a trip you know + + + align:start position:0% +I don't take them for a trip you know +the serious is for transportation and + + align:start position:0% +the serious is for transportation and + + + align:start position:0% +the serious is for transportation and +the helicopter is really what I think of + + align:start position:0% +the helicopter is really what I think of + + + align:start position:0% +the helicopter is really what I think of +as the kind of aviation dream that + + align:start position:0% +as the kind of aviation dream that + + + align:start position:0% +as the kind of aviation dream that +people had you know in ancient Greece + + align:start position:0% +people had you know in ancient Greece + + + align:start position:0% +people had you know in ancient Greece +like they didn't dream of going to LA + + align:start position:0% +like they didn't dream of going to LA + + + align:start position:0% +like they didn't dream of going to LA +and for six hours they dreamt of you + + align:start position:0% +and for six hours they dreamt of you + + + align:start position:0% +and for six hours they dreamt of you +know soaring like a bird you can land + + align:start position:0% +know soaring like a bird you can land + + + align:start position:0% +know soaring like a bird you can land +off Airport that's where a lot of a + + align:start position:0% +off Airport that's where a lot of a + + + align:start position:0% +off Airport that's where a lot of a +challenge comes from the helicopter you + + align:start position:0% +challenge comes from the helicopter you + + + align:start position:0% +challenge comes from the helicopter you +know people think you're a pilot of + + align:start position:0% +know people think you're a pilot of + + + align:start position:0% +know people think you're a pilot of +heroic skill if you take off and land at + + align:start position:0% +heroic skill if you take off and land at + + + align:start position:0% +heroic skill if you take off and land at +Hanscom that's not very challenging it's + + align:start position:0% +Hanscom that's not very challenging it's + + + align:start position:0% +Hanscom that's not very challenging it's +not really that different and in some + + align:start position:0% +not really that different and in some + + + align:start position:0% +not really that different and in some +ways it's easier than landing taking off + + align:start position:0% +ways it's easier than landing taking off + + + align:start position:0% +ways it's easier than landing taking off +and landing in a piper or a Cessna when + + align:start position:0% +and landing in a piper or a Cessna when + + + align:start position:0% +and landing in a piper or a Cessna when +you're off Airport you have to exercise + + align:start position:0% +you're off Airport you have to exercise + + + align:start position:0% +you're off Airport you have to exercise +a lot of judgment a lot of skill and + + align:start position:0% +a lot of judgment a lot of skill and + + + align:start position:0% +a lot of judgment a lot of skill and +that's part of your training but it's + + align:start position:0% +that's part of your training but it's + + + align:start position:0% +that's part of your training but it's +also where people get in trouble you + + align:start position:0% +also where people get in trouble you + + + align:start position:0% +also where people get in trouble you +know hitting obstacles and stuff if you + + align:start position:0% +know hitting obstacles and stuff if you + + + align:start position:0% +know hitting obstacles and stuff if you +do get all of your airplane skills you + + align:start position:0% +do get all of your airplane skills you + + + align:start position:0% +do get all of your airplane skills you +can transfer them over to helicopters + + align:start position:0% +can transfer them over to helicopters + + + align:start position:0% +can transfer them over to helicopters +very easily + + align:start position:0% +very easily + + + align:start position:0% +very easily +it's thirty hours minimum of additional + + align:start position:0% +it's thirty hours minimum of additional + + + align:start position:0% +it's thirty hours minimum of additional +training to add a helicopter rating 40s + + align:start position:0% +training to add a helicopter rating 40s + + + align:start position:0% +training to add a helicopter rating 40s +probably a good budget number all right + + align:start position:0% +probably a good budget number all right + + + align:start position:0% +probably a good budget number all right +are there are there helicopter questions + + align:start position:0% + + + + align:start position:0% + +that is a great question you know is + + align:start position:0% +that is a great question you know is + + + align:start position:0% +that is a great question you know is +there any regulation about where you can + + align:start position:0% +there any regulation about where you can + + + align:start position:0% +there any regulation about where you can +land your helicopter the answer is you + + align:start position:0% +land your helicopter the answer is you + + + align:start position:0% +land your helicopter the answer is you +know until about five or ten years ago + + align:start position:0% +know until about five or ten years ago + + + align:start position:0% +know until about five or ten years ago +there wasn't any so it was just + + align:start position:0% +there wasn't any so it was just + + + align:start position:0% +there wasn't any so it was just +permission of the property owner and you + + align:start position:0% +permission of the property owner and you + + + align:start position:0% +permission of the property owner and you +know don't do anything careless or + + align:start position:0% +know don't do anything careless or + + + align:start position:0% +know don't do anything careless or +reckless so basically the whole world + + align:start position:0% +reckless so basically the whole world + + + align:start position:0% +reckless so basically the whole world +was open to helicopter pilots there is a + + align:start position:0% +was open to helicopter pilots there is a + + + align:start position:0% +was open to helicopter pilots there is a +little bit of a tweaking of the law + + align:start position:0% +little bit of a tweaking of the law + + + align:start position:0% +little bit of a tweaking of the law +the FAA passed this they add the out of + + align:start position:0% +the FAA passed this they add the out of + + + align:start position:0% +the FAA passed this they add the out of +this regulation that I think was + + align:start position:0% +this regulation that I think was + + + align:start position:0% +this regulation that I think was +intended for airplanes but they forgot + + align:start position:0% +intended for airplanes but they forgot + + + align:start position:0% +intended for airplanes but they forgot +to carve it out so they said if you make + + align:start position:0% +to carve it out so they said if you make + + + align:start position:0% +to carve it out so they said if you make +more than ten takeoffs and landings in + + align:start position:0% +more than ten takeoffs and landings in + + + align:start position:0% +more than ten takeoffs and landings in +the same place in a year and you have to + + align:start position:0% +the same place in a year and you have to + + + align:start position:0% +the same place in a year and you have to +get it approved as an airport with a + + align:start position:0% +get it approved as an airport with a + + + align:start position:0% +get it approved as an airport with a +huge amount of regulation I think goes + + align:start position:0% +huge amount of regulation I think goes + + + align:start position:0% +huge amount of regulation I think goes +intended for you know like mining + + align:start position:0% +intended for you know like mining + + + align:start position:0% +intended for you know like mining +companies that would set up their own + + align:start position:0% +companies that would set up their own + + + align:start position:0% +companies that would set up their own +landing strip it doesn't really make + + align:start position:0% +landing strip it doesn't really make + + + align:start position:0% +landing strip it doesn't really make +sense for helicopters like if you have a + + align:start position:0% +sense for helicopters like if you have a + + + align:start position:0% +sense for helicopters like if you have a +construction site that you want to + + align:start position:0% +construction site that you want to + + + align:start position:0% +construction site that you want to +regularly visit now it's a bit of a + + align:start position:0% +regularly visit now it's a bit of a + + + align:start position:0% +regularly visit now it's a bit of a +hassle because that eleventh landing in + + align:start position:0% +hassle because that eleventh landing in + + + align:start position:0% +hassle because that eleventh landing in +theory you needed to get approval as an + + align:start position:0% +theory you needed to get approval as an + + + align:start position:0% +theory you needed to get approval as an +airport but as a first approximation you + + align:start position:0% +airport but as a first approximation you + + + align:start position:0% +airport but as a first approximation you +can land anywhere that the property + + align:start position:0% +can land anywhere that the property + + + align:start position:0% +can land anywhere that the property +owner is happy to host you oh and towns + + align:start position:0% +owner is happy to host you oh and towns + + + align:start position:0% +owner is happy to host you oh and towns +also like they haven't they they're + + align:start position:0% +also like they haven't they they're + + + align:start position:0% +also like they haven't they they're +really aggressive about harassing people + + align:start position:0% +really aggressive about harassing people + + + align:start position:0% +really aggressive about harassing people +who try to you know have a helipad at + + align:start position:0% +who try to you know have a helipad at + + + align:start position:0% +who try to you know have a helipad at +their house now just cuz they can they + + align:start position:0% +their house now just cuz they can they + + + align:start position:0% +their house now just cuz they can they +they get them under zoning laws even + + align:start position:0% +they get them under zoning laws even + + + align:start position:0% +they get them under zoning laws even +though they're not really supposed to + + align:start position:0% +though they're not really supposed to + + + align:start position:0% +though they're not really supposed to +the FAA you're supposed to have + + align:start position:0% +the FAA you're supposed to have + + + align:start position:0% +the FAA you're supposed to have +exclusive authority to regulate aviation + + align:start position:0% +exclusive authority to regulate aviation + + + align:start position:0% +exclusive authority to regulate aviation +because think about it there's all this + + align:start position:0% +because think about it there's all this + + + align:start position:0% +because think about it there's all this +you know there's so many levels of + + align:start position:0% +you know there's so many levels of + + + align:start position:0% +you know there's so many levels of +government in the u.s. if you let them + + align:start position:0% +government in the u.s. if you let them + + + align:start position:0% +government in the u.s. if you let them +all just forbid activities they would + + align:start position:0% +all just forbid activities they would + + + align:start position:0% +all just forbid activities they would +you know eventually there would be + + align:start position:0% +you know eventually there would be + + + align:start position:0% +you know eventually there would be +nothing that was legal at all because + + align:start position:0% +nothing that was legal at all because + + + align:start position:0% +nothing that was legal at all because +people in you know Concord and Lexington + + align:start position:0% +people in you know Concord and Lexington + + + align:start position:0% +people in you know Concord and Lexington +would say well we don't want your planes + + align:start position:0% +would say well we don't want your planes + + + align:start position:0% +would say well we don't want your planes +flying over our head so we'll just make + + align:start position:0% +flying over our head so we'll just make + + + align:start position:0% +flying over our head so we'll just make +it illegal to fly a Gulfstream in + + align:start position:0% +it illegal to fly a Gulfstream in + + + align:start position:0% +it illegal to fly a Gulfstream in +Concord + + align:start position:0% + + + + align:start position:0% + +you know I I had that in the earlier + + align:start position:0% +you know I I had that in the earlier + + + align:start position:0% +you know I I had that in the earlier +slide on learning to fly the marginal + + align:start position:0% +slide on learning to fly the marginal + + + align:start position:0% +slide on learning to fly the marginal +cost is about double you know so it goes + + align:start position:0% +cost is about double you know so it goes + + + align:start position:0% +cost is about double you know so it goes +from 150 an hour to 225 or 100 an hour + + align:start position:0% +from 150 an hour to 225 or 100 an hour + + + align:start position:0% +from 150 an hour to 225 or 100 an hour +to 200 because so many rotating + + align:start position:0% +to 200 because so many rotating + + + align:start position:0% +to 200 because so many rotating +components get discarded after 2200 + + align:start position:0% +components get discarded after 2200 + + + align:start position:0% +components get discarded after 2200 +hours so the transmissions the blades + + align:start position:0% +hours so the transmissions the blades + + + align:start position:0% +hours so the transmissions the blades +and so forth so it is more expensive per + + align:start position:0% +and so forth so it is more expensive per + + + align:start position:0% +and so forth so it is more expensive per +hour however like I also said the + + align:start position:0% +hour however like I also said the + + + align:start position:0% +hour however like I also said the +flights tend to be a lot shorter so I + + align:start position:0% +flights tend to be a lot shorter so I + + + align:start position:0% +flights tend to be a lot shorter so I +would say as a hobby overall it's about + + align:start position:0% +would say as a hobby overall it's about + + + align:start position:0% +would say as a hobby overall it's about +the same cost because you're not + + align:start position:0% +the same cost because you're not + + + align:start position:0% +the same cost because you're not +dragging people all the way to the + + align:start position:0% +dragging people all the way to the + + + align:start position:0% +dragging people all the way to the +vineyard or Bar Harbor you're just + + align:start position:0% +vineyard or Bar Harbor you're just + + + align:start position:0% +vineyard or Bar Harbor you're just +taking them into Boston and back out + + align:start position:0% +taking them into Boston and back out + + + align:start position:0% +taking them into Boston and back out +which is about you know 20 minutes of 20 + + align:start position:0% +which is about you know 20 minutes of 20 + + + align:start position:0% +which is about you know 20 minutes of 20 +minutes of flight time in 30 minutes of + + align:start position:0% +minutes of flight time in 30 minutes of + + + align:start position:0% +minutes of flight time in 30 minutes of +engine running time whereas you know an + + align:start position:0% +engine running time whereas you know an + + + align:start position:0% +engine running time whereas you know an +intro airplane flight it would be an + + align:start position:0% +intro airplane flight it would be an + + + align:start position:0% +intro airplane flight it would be an +all-day thing you'd probably fly a + + align:start position:0% +all-day thing you'd probably fly a + + + align:start position:0% +all-day thing you'd probably fly a +couple hours two or three hours so you + + align:start position:0% +couple hours two or three hours so you + + + align:start position:0% +couple hours two or three hours so you +actually probably spend more with the + + align:start position:0% +actually probably spend more with the + + + align:start position:0% +actually probably spend more with the +airplane that's a great question + + align:start position:0% +airplane that's a great question + + + align:start position:0% +airplane that's a great question +all right so I guess we should take a + + align:start position:0% +all right so I guess we should take a + + + align:start position:0% +all right so I guess we should take a +10-minute restroom break and after that + + align:start position:0% +10-minute restroom break and after that + + + align:start position:0% +10-minute restroom break and after that +we're gonna hear from lads about the + + align:start position:0% +we're gonna hear from lads about the + + + align:start position:0% +we're gonna hear from lads about the +f-22 + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/Qj1HvrSKLqY.txt b/Qj1HvrSKLqY.txt new file mode 100644 index 0000000000000000000000000000000000000000..eabf7200559a43f25af6bf73134889fe49c40556 --- /dev/null +++ b/Qj1HvrSKLqY.txt @@ -0,0 +1,9331 @@ +align:start position:0% + +okay so we are going to dive in today + + align:start position:0% +okay so we are going to dive in today + + + align:start position:0% +okay so we are going to dive in today +and talk about uh where demand curves + + align:start position:0% +and talk about uh where demand curves + + + align:start position:0% +and talk about uh where demand curves +come from the motivation for the last + + align:start position:0% +come from the motivation for the last + + + align:start position:0% +come from the motivation for the last +couple lectures was that we showed you a + + align:start position:0% +couple lectures was that we showed you a + + + align:start position:0% +couple lectures was that we showed you a +demand curve and a supply curve and I + + align:start position:0% +demand curve and a supply curve and I + + + align:start position:0% +demand curve and a supply curve and I +promised I tell you what the basis for + + align:start position:0% +promised I tell you what the basis for + + + align:start position:0% +promised I tell you what the basis for +those demand Supply curves are the last + + align:start position:0% +those demand Supply curves are the last + + + align:start position:0% +those demand Supply curves are the last +two lectures we started building that + + align:start position:0% +two lectures we started building that + + + align:start position:0% +two lectures we started building that +basis and today we'll show you where + + align:start position:0% +basis and today we'll show you where + + + align:start position:0% +basis and today we'll show you where +demand curves actually come from so + + align:start position:0% +demand curves actually come from so + + + align:start position:0% +demand curves actually come from so +let's actually derive let's start by + + align:start position:0% +let's actually derive let's start by + + + align:start position:0% +let's actually derive let's start by +actually deriving a demand curve okay so + + align:start position:0% + + + + align:start position:0% + +deriving a demand + + align:start position:0% +deriving a demand + + + align:start position:0% +deriving a demand +curve okay so + + align:start position:0% +curve okay so + + + align:start position:0% +curve okay so +um basically theand curve as we said in + + align:start position:0% +um basically theand curve as we said in + + + align:start position:0% +um basically theand curve as we said in +the first lecture is the relationship + + align:start position:0% +the first lecture is the relationship + + + align:start position:0% +the first lecture is the relationship +between from the price charged for a + + align:start position:0% +between from the price charged for a + + + align:start position:0% +between from the price charged for a +good and the consumer's desired quantity + + align:start position:0% +good and the consumer's desired quantity + + + align:start position:0% +good and the consumer's desired quantity +of the good so what we'll do is return + + align:start position:0% +of the good so what we'll do is return + + + align:start position:0% +of the good so what we'll do is return +to the example before and show you where + + align:start position:0% +to the example before and show you where + + + align:start position:0% +to the example before and show you where +that comes from so remember the example + + align:start position:0% +that comes from so remember the example + + + align:start position:0% +that comes from so remember the example +before remember we utility function + + align:start position:0% +before remember we utility function + + + align:start position:0% +before remember we utility function +which was the square root of s * C + + align:start position:0% +which was the square root of s * C + + + align:start position:0% +which was the square root of s * C +slices times cookies okay we had a + + align:start position:0% +slices times cookies okay we had a + + + align:start position:0% +slices times cookies okay we had a +budget constraint which was Y is equal + + align:start position:0% +budget constraint which was Y is equal + + + align:start position:0% +budget constraint which was Y is equal +to the price of slices times the number + + align:start position:0% +to the price of slices times the number + + + align:start position:0% +to the price of slices times the number +of slices plus the price of cookies + + align:start position:0% +of slices plus the price of cookies + + + align:start position:0% +of slices plus the price of cookies +times the number of cookies and we + + align:start position:0% +times the number of cookies and we + + + align:start position:0% +times the number of cookies and we +assume to start that y was 24 the price + + align:start position:0% +assume to start that y was 24 the price + + + align:start position:0% +assume to start that y was 24 the price +of slices was four and and the price of + + align:start position:0% +of slices was four and and the price of + + + align:start position:0% +of slices was four and and the price of +cookies was + + align:start position:0% +cookies was + + + align:start position:0% +cookies was +two okay so how do we derive a demand + + align:start position:0% +two okay so how do we derive a demand + + + align:start position:0% +two okay so how do we derive a demand +curve Step + + align:start position:0% +curve Step + + + align:start position:0% +curve Step +One is we solve for we solve for optimal + + align:start position:0% +One is we solve for we solve for optimal + + + align:start position:0% +One is we solve for we solve for optimal +consumption solve for for SAR C star + + align:start position:0% +consumption solve for for SAR C star + + + align:start position:0% +consumption solve for for SAR C star +stop solve for the the optimal + + align:start position:0% +stop solve for the the optimal + + + align:start position:0% +stop solve for the the optimal +consumption pair how do we do that well + + align:start position:0% +consumption pair how do we do that well + + + align:start position:0% +consumption pair how do we do that well +as we said last time constrained + + align:start position:0% +as we said last time constrained + + + align:start position:0% +as we said last time constrained +optimization are the point where you can + + align:start position:0% +optimization are the point where you can + + + align:start position:0% +optimization are the point where you can +the highest difference curves you can + + align:start position:0% +the highest difference curves you can + + + align:start position:0% +the highest difference curves you can +reach given your budget constraint leads + + align:start position:0% +reach given your budget constraint leads + + + align:start position:0% +reach given your budget constraint leads +you to set + + align:start position:0% +you to set + + + align:start position:0% +you to set +mrss equal to + + align:start position:0% +mrss equal to + + + align:start position:0% +mrss equal to +mrrt that's the tangency condition + + align:start position:0% +mrrt that's the tangency condition + + + align:start position:0% +mrrt that's the tangency condition +that's the point where you're as well + + align:start position:0% +that's the point where you're as well + + + align:start position:0% +that's the point where you're as well +off as possible remember it's marginal + + align:start position:0% +off as possible remember it's marginal + + + align:start position:0% +off as possible remember it's marginal +thinking in economics it's the next unit + + align:start position:0% +thinking in economics it's the next unit + + + align:start position:0% +thinking in economics it's the next unit +you want to consume pizza and cookies + + align:start position:0% +you want to consume pizza and cookies + + + align:start position:0% +you want to consume pizza and cookies +until the next unit makes you as happy + + align:start position:0% +until the next unit makes you as happy + + + align:start position:0% +until the next unit makes you as happy +as the price the market charges how + + align:start position:0% +as the price the market charges how + + + align:start position:0% +as the price the market charges how +happy does it make you well that's your + + align:start position:0% +happy does it make you well that's your + + + align:start position:0% +happy does it make you well that's your +margin rate of substitution that's minus + + align:start position:0% +margin rate of substitution that's minus + + + align:start position:0% +margin rate of substitution that's minus +s over C what is the market charge well + + align:start position:0% +s over C what is the market charge well + + + align:start position:0% +s over C what is the market charge well +that's minus the price ratio which is + + align:start position:0% +that's minus the price ratio which is + + + align:start position:0% +that's minus the price ratio which is +minus a + + align:start position:0% + + + + align:start position:0% + +half okay so basically we derived that + + align:start position:0% +half okay so basically we derived that + + + align:start position:0% +half okay so basically we derived that +last time or uh yes we derived that two + + align:start position:0% +last time or uh yes we derived that two + + + align:start position:0% +last time or uh yes we derived that two +times ago that is the constrained + + align:start position:0% +times ago that is the constrained + + + align:start position:0% +times ago that is the constrained +optimization now we then or last time + + align:start position:0% +optimization now we then or last time + + + align:start position:0% +optimization now we then or last time +now but we go to the next step now which + + align:start position:0% +now but we go to the next step now which + + + align:start position:0% +now but we go to the next step now which +is would say well what does that imply + + align:start position:0% +is would say well what does that imply + + + align:start position:0% +is would say well what does that imply +for optimal slices and cookies well we + + align:start position:0% +for optimal slices and cookies well we + + + align:start position:0% +for optimal slices and cookies well we +just plug that into the budget + + align:start position:0% +just plug that into the budget + + + align:start position:0% +just plug that into the budget +constraint we have we have this equation + + align:start position:0% +constraint we have we have this equation + + + align:start position:0% +constraint we have we have this equation +which is one equation in in uh two + + align:start position:0% +which is one equation in in uh two + + + align:start position:0% +which is one equation in in uh two +unknowns we also this equation which is + + align:start position:0% +unknowns we also this equation which is + + + align:start position:0% +unknowns we also this equation which is +that + + align:start position:0% +that + + + align:start position:0% +that +24 equals 4S + 2 + + align:start position:0% +24 equals 4S + 2 + + + align:start position:0% +24 equals 4S + 2 +C so now we have two equations and two + + align:start position:0% +C so now we have two equations and two + + + align:start position:0% +C so now we have two equations and two +unknowns okay we know how to do that + + align:start position:0% +unknowns okay we know how to do that + + + align:start position:0% +unknowns okay we know how to do that +okay and we solve that we get that c + + align:start position:0% +okay and we solve that we get that c + + + align:start position:0% +okay and we solve that we get that c +star equals 6 and S star equals 3 we + + align:start position:0% +star equals 6 and S star equals 3 we + + + align:start position:0% +star equals 6 and S star equals 3 we +just solve those two equations and two + + align:start position:0% +just solve those two equations and two + + + align:start position:0% +just solve those two equations and two +unknowns and then we get + + align:start position:0% +unknowns and then we get + + + align:start position:0% +unknowns and then we get +C star is six n s star is + + align:start position:0% +C star is six n s star is + + + align:start position:0% +C star is six n s star is +three okay so that is + + align:start position:0% +three okay so that is + + + align:start position:0% +three okay so that is +Illustrated in the top panel of figure + + align:start position:0% +Illustrated in the top panel of figure + + + align:start position:0% +Illustrated in the top panel of figure +one uh in the future let's not make it + + align:start position:0% +one uh in the future let's not make it + + + align:start position:0% +one uh in the future let's not make it +so compressed more I'm I'm okay with + + align:start position:0% +so compressed more I'm I'm okay with + + + align:start position:0% +so compressed more I'm I'm okay with +killing a few more trees to make sure + + align:start position:0% +killing a few more trees to make sure + + + align:start position:0% +killing a few more trees to make sure +our fine students don't have to hurt + + align:start position:0% +our fine students don't have to hurt + + + align:start position:0% +our fine students don't have to hurt +their Vision okay so basically that is + + align:start position:0% +their Vision okay so basically that is + + + align:start position:0% +their Vision okay so basically that is +if you look at in figure 41 at the very + + align:start position:0% +if you look at in figure 41 at the very + + + align:start position:0% +if you look at in figure 41 at the very +top you look at budget constraint one + + align:start position:0% +top you look at budget constraint one + + + align:start position:0% +top you look at budget constraint one +okay that is our original budget + + align:start position:0% +okay that is our original budget + + + align:start position:0% +okay that is our original budget +constraint we just had you and the + + align:start position:0% +constraint we just had you and the + + + align:start position:0% +constraint we just had you and the +tangency the Alum point is at Point a + + align:start position:0% +tangency the Alum point is at Point a + + + align:start position:0% +tangency the Alum point is at Point a +you want six cookies and three slices of + + align:start position:0% +you want six cookies and three slices of + + + align:start position:0% +you want six cookies and three slices of +pizza okay this is reviewing what we did + + align:start position:0% +pizza okay this is reviewing what we did + + + align:start position:0% +pizza okay this is reviewing what we did +before questions about that though + + align:start position:0% +before questions about that though + + + align:start position:0% +before questions about that though +because this is some math you're G have + + align:start position:0% +because this is some math you're G have + + + align:start position:0% +because this is some math you're G have +to do over and over and over again till + + align:start position:0% +to do over and over and over again till + + + align:start position:0% +to do over and over and over again till +you're sick of it questions about + + align:start position:0% +you're sick of it questions about + + + align:start position:0% +you're sick of it questions about +that okay so now let's ask what happens + + align:start position:0% +that okay so now let's ask what happens + + + align:start position:0% +that okay so now let's ask what happens +if the price of cookies + + align:start position:0% +if the price of cookies + + + align:start position:0% +if the price of cookies +changes what happens if the price of + + align:start position:0% +changes what happens if the price of + + + align:start position:0% +changes what happens if the price of +cookies Rises to Rises to three so let's + + align:start position:0% +cookies Rises to Rises to three so let's + + + align:start position:0% +cookies Rises to Rises to three so let's +say the price of + + align:start position:0% +say the price of + + + align:start position:0% +say the price of +cookies goes from two to + + align:start position:0% +cookies goes from two to + + + align:start position:0% +cookies goes from two to +three well the new slope of the budget + + align:start position:0% +three well the new slope of the budget + + + align:start position:0% +three well the new slope of the budget +constraint is now instead of minus one2 + + align:start position:0% +constraint is now instead of minus one2 + + + align:start position:0% +constraint is now instead of minus one2 +it's minus 1/3 so un optimization + + align:start position:0% +it's minus 1/3 so un optimization + + + align:start position:0% +it's minus 1/3 so un optimization +problem is set Min - s over c equal to + + align:start position:0% +problem is set Min - s over c equal to + + + align:start position:0% +problem is set Min - s over c equal to +minus 13 not minus + + align:start position:0% +minus 13 not minus + + + align:start position:0% +minus 13 not minus +one2 your budget constraint is now + + align:start position:0% +one2 your budget constraint is now + + + align:start position:0% +one2 your budget constraint is now +24 = 4S + 3 C + + align:start position:0% +24 = 4S + 3 C + + + align:start position:0% +24 = 4S + 3 C +once you have two equations in two + + align:start position:0% +once you have two equations in two + + + align:start position:0% +once you have two equations in two +unknowns you've solved that and you get + + align:start position:0% +unknowns you've solved that and you get + + + align:start position:0% +unknowns you've solved that and you get +that c star equals 4 SAR equals + + align:start position:0% + + + + align:start position:0% + +3 okay yeah question speak up so + + align:start position:0% +3 okay yeah question speak up so + + + align:start position:0% +3 okay yeah question speak up so +everyone can hear + + align:start position:0% +everyone can hear + + + align:start position:0% +everyone can hear +you oh uh negative s over C I'm sorry + + align:start position:0% +you oh uh negative s over C I'm sorry + + + align:start position:0% +you oh uh negative s over C I'm sorry +what is your + + align:start position:0% + + + + align:start position:0% + +question is it + + align:start position:0% +question is it + + + align:start position:0% +question is it +negative uh did I do that wrong + + align:start position:0% +negative uh did I do that wrong + + + align:start position:0% +negative uh did I do that wrong +yes you're right my bad neg3 over4 I + + align:start position:0% +yes you're right my bad neg3 over4 I + + + align:start position:0% +yes you're right my bad neg3 over4 I +should never do that with look at my + + align:start position:0% +should never do that with look at my + + + align:start position:0% +should never do that with look at my +notes good catch neg3 over4 okay so you + + align:start position:0% +notes good catch neg3 over4 okay so you + + + align:start position:0% +notes good catch neg3 over4 okay so you +solve that and you end up getting the + + align:start position:0% +solve that and you end up getting the + + + align:start position:0% +solve that and you end up getting the +optimum of cookies is four Optimum slice + + align:start position:0% +optimum of cookies is four Optimum slice + + + align:start position:0% +optimum of cookies is four Optimum slice +of pizza is three that is point B on the + + align:start position:0% +of pizza is three that is point B on the + + + align:start position:0% +of pizza is three that is point B on the +top + + align:start position:0% +top + + + align:start position:0% +top +diagram how did we get there well + + align:start position:0% +diagram how did we get there well + + + align:start position:0% +diagram how did we get there well +mathematically I showed you subject to + + align:start position:0% +mathematically I showed you subject to + + + align:start position:0% +mathematically I showed you subject to +one mathematical mistake I showed you + + align:start position:0% +one mathematical mistake I showed you + + + align:start position:0% +one mathematical mistake I showed you +how to get there graphically how do we + + align:start position:0% +how to get there graphically how do we + + + align:start position:0% +how to get there graphically how do we +get there well we draw the new budget + + align:start position:0% +get there well we draw the new budget + + + align:start position:0% +get there well we draw the new budget +constraint + + align:start position:0% +constraint + + + align:start position:0% +constraint +bc2 okay and we find the tangency + + align:start position:0% +bc2 okay and we find the tangency + + + align:start position:0% +bc2 okay and we find the tangency +between the indifference curve and that + + align:start position:0% +between the indifference curve and that + + + align:start position:0% +between the indifference curve and that +new budget constraint bc2 offers a + + align:start position:0% +new budget constraint bc2 offers a + + + align:start position:0% +new budget constraint bc2 offers a +smaller opportunity set as we discussed + + align:start position:0% +smaller opportunity set as we discussed + + + align:start position:0% +smaller opportunity set as we discussed +last time so you'll end up with fewer + + align:start position:0% +last time so you'll end up with fewer + + + align:start position:0% +last time so you'll end up with fewer +Goods you have a smaller opportunity set + + align:start position:0% +Goods you have a smaller opportunity set + + + align:start position:0% +Goods you have a smaller opportunity set +and you do you end up with the same + + align:start position:0% +and you do you end up with the same + + + align:start position:0% +and you do you end up with the same +amount of pizza but with fewer + + align:start position:0% +amount of pizza but with fewer + + + align:start position:0% +amount of pizza but with fewer +cookies likewise what if the price of + + align:start position:0% +cookies likewise what if the price of + + + align:start position:0% +cookies likewise what if the price of +cookies fell to 4/3 what if the price of + + align:start position:0% +cookies fell to 4/3 what if the price of + + + align:start position:0% +cookies fell to 4/3 what if the price of +cookies + + align:start position:0% +cookies + + + align:start position:0% +cookies +went from 2 to + + align:start position:0% + + + + align:start position:0% + +4/3 well once again you could do the + + align:start position:0% +4/3 well once again you could do the + + + align:start position:0% +4/3 well once again you could do the +math and you'll find that basically when + + align:start position:0% +math and you'll find that basically when + + + align:start position:0% +math and you'll find that basically when +you do that you're going to want three + + align:start position:0% +you do that you're going to want three + + + align:start position:0% +you do that you're going to want three +slices and nine + + align:start position:0% +slices and nine + + + align:start position:0% +slices and nine +cookies and graphically you can see that + + align:start position:0% +cookies and graphically you can see that + + + align:start position:0% +cookies and graphically you can see that +that's a outward shift in the budget + + align:start position:0% +that's a outward shift in the budget + + + align:start position:0% +that's a outward shift in the budget +constraint to + + align:start position:0% +constraint to + + + align:start position:0% +constraint to +bc3 that's the rightmost budget + + align:start position:0% +bc3 that's the rightmost budget + + + align:start position:0% +bc3 that's the rightmost budget +constraint your indifference curve is + + align:start position:0% +constraint your indifference curve is + + + align:start position:0% +constraint your indifference curve is +tangent with that budget constraint at + + align:start position:0% +tangent with that budget constraint at + + + align:start position:0% +tangent with that budget constraint at +nine cookies and three slices + + align:start position:0% +nine cookies and three slices + + + align:start position:0% +nine cookies and three slices +pizza so what's happening here we are + + align:start position:0% +pizza so what's happening here we are + + + align:start position:0% +pizza so what's happening here we are +shifting the price of cookies and + + align:start position:0% +shifting the price of cookies and + + + align:start position:0% +shifting the price of cookies and +showing you based on tools you've + + align:start position:0% +showing you based on tools you've + + + align:start position:0% +showing you based on tools you've +learned how that impacts how many + + align:start position:0% +learned how that impacts how many + + + align:start position:0% +learned how that impacts how many +cookies you want how many slices you + + align:start position:0% +cookies you want how many slices you + + + align:start position:0% +cookies you want how many slices you +want in other words we're drawing the + + align:start position:0% +want in other words we're drawing the + + + align:start position:0% +want in other words we're drawing the +demand curve look at the translation + + align:start position:0% +demand curve look at the translation + + + align:start position:0% +demand curve look at the translation +from the top figure to the bottom figure + + align:start position:0% +from the top figure to the bottom figure + + + align:start position:0% +from the top figure to the bottom figure +the bottom figure has on it cookies on + + align:start position:0% +the bottom figure has on it cookies on + + + align:start position:0% +the bottom figure has on it cookies on +the x- axis and the price of cookies on + + align:start position:0% +the x- axis and the price of cookies on + + + align:start position:0% +the x- axis and the price of cookies on +the y- axis well that's a demand curve + + align:start position:0% +the y- axis well that's a demand curve + + + align:start position:0% +the y- axis well that's a demand curve +we've just drawn it I've just shown you + + align:start position:0% +we've just drawn it I've just shown you + + + align:start position:0% +we've just drawn it I've just shown you +for three different prices of cookies + + align:start position:0% +for three different prices of cookies + + + align:start position:0% +for three different prices of cookies +how many different cookies you + + align:start position:0% +how many different cookies you + + + align:start position:0% +how many different cookies you +want so we are we have now derived the + + align:start position:0% +want so we are we have now derived the + + + align:start position:0% +want so we are we have now derived the +domain curve we derived the domain curve + + align:start position:0% +domain curve we derived the domain curve + + + align:start position:0% +domain curve we derived the domain curve +by op by optimizing your utility at + + align:start position:0% +by op by optimizing your utility at + + + align:start position:0% +by op by optimizing your utility at +different prices and finding which + + align:start position:0% +different prices and finding which + + + align:start position:0% +different prices and finding which +quantity you want at each of those + + align:start position:0% +quantity you want at each of those + + + align:start position:0% +quantity you want at each of those +different prices and that's the demain + + align:start position:0% +different prices and that's the demain + + + align:start position:0% +different prices and that's the demain +curve it's the quantity you want at each + + align:start position:0% +curve it's the quantity you want at each + + + align:start position:0% +curve it's the quantity you want at each +price so that's where the demain curve + + align:start position:0% +price so that's where the demain curve + + + align:start position:0% +price so that's where the demain curve +comes + + align:start position:0% +comes + + + align:start position:0% +comes +from okay yeah + + align:start position:0% + + + + align:start position:0% + +number + + align:start position:0% +number + + + align:start position:0% +number +of great point someone noticed and that + + align:start position:0% +of great point someone noticed and that + + + align:start position:0% +of great point someone noticed and that +as we varied the price of cookies the + + align:start position:0% +as we varied the price of cookies the + + + align:start position:0% +as we varied the price of cookies the +number of slice of pie did not change + + align:start position:0% +number of slice of pie did not change + + + align:start position:0% +number of slice of pie did not change +that is not a general law that is a + + align:start position:0% +that is not a general law that is a + + + align:start position:0% +that is not a general law that is a +specific feature of this utility + + align:start position:0% +specific feature of this utility + + + align:start position:0% +specific feature of this utility +function in general when you change one + + align:start position:0% +function in general when you change one + + + align:start position:0% +function in general when you change one +price both Goods will change what's nice + + align:start position:0% +price both Goods will change what's nice + + + align:start position:0% +price both Goods will change what's nice +one reason we use this convenient + + align:start position:0% +one reason we use this convenient + + + align:start position:0% +one reason we use this convenient +utility function is has some nice + + align:start position:0% +utility function is has some nice + + + align:start position:0% +utility function is has some nice +mathematical properties and one is it + + align:start position:0% +mathematical properties and one is it + + + align:start position:0% +mathematical properties and one is it +makes life easy by having the slice of + + align:start position:0% +makes life easy by having the slice of + + + align:start position:0% +makes life easy by having the slice of +pizza stay the same the price so + + align:start position:0% +pizza stay the same the price so + + + align:start position:0% +pizza stay the same the price so +essentially what we're saying here is + + align:start position:0% +essentially what we're saying here is + + + align:start position:0% +essentially what we're saying here is +that we have for pizza we have what we + + align:start position:0% +that we have for pizza we have what we + + + align:start position:0% +that we have for pizza we have what we +call a flat price consumption curve okay + + align:start position:0% +call a flat price consumption curve okay + + + align:start position:0% +call a flat price consumption curve okay +which is BAS a cross price consumption + + align:start position:0% +which is BAS a cross price consumption + + + align:start position:0% +which is BAS a cross price consumption +curve which is basically when the price + + align:start position:0% +curve which is basically when the price + + + align:start position:0% +curve which is basically when the price +of one good changes the demand for the + + align:start position:0% +of one good changes the demand for the + + + align:start position:0% +of one good changes the demand for the +other good doesn't change and that's + + align:start position:0% +other good doesn't change and that's + + + align:start position:0% +other good doesn't change and that's +just a feature of this particular + + align:start position:0% +just a feature of this particular + + + align:start position:0% +just a feature of this particular +utility function but it's not + + align:start position:0% + + + + align:start position:0% + +General + + align:start position:0% +General + + + align:start position:0% +General +okay now in fact you could yeah go + + align:start position:0% + + + + align:start position:0% + +ahead the margin exactly so I I skipped + + align:start position:0% +ahead the margin exactly so I I skipped + + + align:start position:0% +ahead the margin exactly so I I skipped +a step which is defining the mrss I + + align:start position:0% +a step which is defining the mrss I + + + align:start position:0% +a step which is defining the mrss I +defined that last time or two time I + + align:start position:0% +defined that last time or two time I + + + align:start position:0% +defined that last time or two time I +don't remember two times ago I think the + + align:start position:0% +don't remember two times ago I think the + + + align:start position:0% +don't remember two times ago I think the +mrss is remember the the M negative of + + align:start position:0% +mrss is remember the the M negative of + + + align:start position:0% +mrss is remember the the M negative of +the ratio of the Marge utility of + + align:start position:0% +the ratio of the Marge utility of + + + align:start position:0% +the ratio of the Marge utility of +cookies to Mar utility of pizza okay and + + align:start position:0% +cookies to Mar utility of pizza okay and + + + align:start position:0% +cookies to Mar utility of pizza okay and +that's minus that so so what the way we + + align:start position:0% +that's minus that so so what the way we + + + align:start position:0% +that's minus that so so what the way we +got this we did two lectures ago we + + align:start position:0% +got this we did two lectures ago we + + + align:start position:0% +got this we did two lectures ago we +basically uh uh took the derivative of + + align:start position:0% +basically uh uh took the derivative of + + + align:start position:0% +basically uh uh took the derivative of +the utility function first with respect + + align:start position:0% +the utility function first with respect + + + align:start position:0% +the utility function first with respect +to cookies then with respect to Pizza we + + align:start position:0% +to cookies then with respect to Pizza we + + + align:start position:0% +to cookies then with respect to Pizza we +got the two different margin utilities + + align:start position:0% +got the two different margin utilities + + + align:start position:0% +got the two different margin utilities +and then we took the ratio that gives + + align:start position:0% +and then we took the ratio that gives + + + align:start position:0% +and then we took the ratio that gives +the margin rate of substitution all + + align:start position:0% +the margin rate of substitution all + + + align:start position:0% +the margin rate of substitution all +right good question good to clarify + + align:start position:0% +right good question good to clarify + + + align:start position:0% +right good question good to clarify +where that came from so this is building + + align:start position:0% +where that came from so this is building + + + align:start position:0% +where that came from so this is building +on the work we did two lectures + + align:start position:0% +on the work we did two lectures + + + align:start position:0% +on the work we did two lectures +ago other + + align:start position:0% + + + + align:start position:0% + +questions okay so that is where demand + + align:start position:0% +questions okay so that is where demand + + + align:start position:0% +questions okay so that is where demand +curves come from fun exercise at home do + + align:start position:0% +curves come from fun exercise at home do + + + align:start position:0% +curves come from fun exercise at home do +the same exercise changing the price of + + align:start position:0% +the same exercise changing the price of + + + align:start position:0% +the same exercise changing the price of +pizza do the reverse exercise you will + + align:start position:0% +pizza do the reverse exercise you will + + + align:start position:0% +pizza do the reverse exercise you will +find as well there's a flat there's no + + align:start position:0% +find as well there's a flat there's no + + + align:start position:0% +find as well there's a flat there's no +effect the number of cookies but you + + align:start position:0% +effect the number of cookies but you + + + align:start position:0% +effect the number of cookies but you +will find effect on the number of slices + + align:start position:0% +will find effect on the number of slices + + + align:start position:0% +will find effect on the number of slices +of pizza and you can show how that will + + align:start position:0% +of pizza and you can show how that will + + + align:start position:0% +of pizza and you can show how that will +how that'll vary okay now now that we + + align:start position:0% +how that'll vary okay now now that we + + + align:start position:0% +how that'll vary okay now now that we +know what demand curves are I want to + + align:start position:0% +know what demand curves are I want to + + + align:start position:0% +know what demand curves are I want to +talk about what do they look like let's + + align:start position:0% +talk about what do they look like let's + + + align:start position:0% +talk about what do they look like let's +talk about the + + align:start position:0% +talk about the + + + align:start position:0% +talk about the +shape of demand curves what drives what + + align:start position:0% +shape of demand curves what drives what + + + align:start position:0% +shape of demand curves what drives what +they look + + align:start position:0% +they look + + + align:start position:0% +they look +like okay and what drives what demand + + align:start position:0% +like okay and what drives what demand + + + align:start position:0% +like okay and what drives what demand +curves look like is going to be what we + + align:start position:0% +curves look like is going to be what we + + + align:start position:0% +curves look like is going to be what we +call the elasticity of + + align:start position:0% +call the elasticity of + + + align:start position:0% +call the elasticity of +demand okay the elasticity of + + align:start position:0% +demand okay the elasticity of + + + align:start position:0% +demand okay the elasticity of +demand Epsilon is going to be the + + align:start position:0% +demand Epsilon is going to be the + + + align:start position:0% +demand Epsilon is going to be the +percentage change in quantity Delta Q + + align:start position:0% +percentage change in quantity Delta Q + + + align:start position:0% +percentage change in quantity Delta Q +over Q per percentage change in price or + + align:start position:0% +over Q per percentage change in price or + + + align:start position:0% +over Q per percentage change in price or +a continuous time DQ + + align:start position:0% +a continuous time DQ + + + align:start position:0% +a continuous time DQ +DP and basically we're gonna we're going + + align:start position:0% +DP and basically we're gonna we're going + + + align:start position:0% +DP and basically we're gonna we're going +to generally work in discrete space but + + align:start position:0% +to generally work in discrete space but + + + align:start position:0% +to generally work in discrete space but +the math you can do continuously I I + + align:start position:0% +the math you can do continuously I I + + + align:start position:0% +the math you can do continuously I I +write it both ways because you're G to + + align:start position:0% +write it both ways because you're G to + + + align:start position:0% +write it both ways because you're G to +the examples we'll use will sort of do + + align:start position:0% +the examples we'll use will sort of do + + + align:start position:0% +the examples we'll use will sort of do +in discrete space it's a little easier + + align:start position:0% +in discrete space it's a little easier + + + align:start position:0% +in discrete space it's a little easier +to see it but basically it's the + + align:start position:0% +to see it but basically it's the + + + align:start position:0% +to see it but basically it's the +derivative of the quantity with respect + + align:start position:0% +derivative of the quantity with respect + + + align:start position:0% +derivative of the quantity with respect +to the price it's the percentage change + + align:start position:0% +to the price it's the percentage change + + + align:start position:0% +to the price it's the percentage change +in quantity with respect to price okay + + align:start position:0% +in quantity with respect to price okay + + + align:start position:0% +in quantity with respect to price okay +so approximately equals approximately + + align:start position:0% +so approximately equals approximately + + + align:start position:0% +so approximately equals approximately +equals the + + align:start position:0% +equals the + + + align:start position:0% +equals the +derivative okay so basically that is the + + align:start position:0% +derivative okay so basically that is the + + + align:start position:0% +derivative okay so basically that is the +elasticity of demand this tells you how + + align:start position:0% +elasticity of demand this tells you how + + + align:start position:0% +elasticity of demand this tells you how +responsive people's demand is to the + + align:start position:0% +responsive people's demand is to the + + + align:start position:0% +responsive people's demand is to the +price they have to + + align:start position:0% +price they have to + + + align:start position:0% +price they have to +pay once again I find it very useful to + + align:start position:0% +pay once again I find it very useful to + + + align:start position:0% +pay once again I find it very useful to +fix ideas in this class to think about + + align:start position:0% +fix ideas in this class to think about + + + align:start position:0% +fix ideas in this class to think about +extreme cases that never exist in + + align:start position:0% +extreme cases that never exist in + + + align:start position:0% +extreme cases that never exist in +reality but can help you understand the + + align:start position:0% +reality but can help you understand the + + + align:start position:0% +reality but can help you understand the +intuition so let's look at figure + + align:start position:0% +intuition so let's look at figure + + + align:start position:0% +intuition so let's look at figure +42 figure 42 would be a case of + + align:start position:0% +42 figure 42 would be a case of + + + align:start position:0% +42 figure 42 would be a case of +perfectly inelastic demand that that + + align:start position:0% +perfectly inelastic demand that that + + + align:start position:0% +perfectly inelastic demand that that +would be + + align:start position:0% +would be + + + align:start position:0% +would be +Ada equals z that we call perfectly + + align:start position:0% +Ada equals z that we call perfectly + + + align:start position:0% +Ada equals z that we call perfectly +inelastic demand that's a vertical + + align:start position:0% +inelastic demand that's a vertical + + + align:start position:0% +inelastic demand that's a vertical +demand + + align:start position:0% +demand + + + align:start position:0% +demand +curve in this case demand does not + + align:start position:0% +curve in this case demand does not + + + align:start position:0% +curve in this case demand does not +respond to + + align:start position:0% +respond to + + + align:start position:0% +respond to +prices okay can anyone think of a good + + align:start position:0% +prices okay can anyone think of a good + + + align:start position:0% +prices okay can anyone think of a good +that even could come close to a + + align:start position:0% +that even could come close to a + + + align:start position:0% +that even could come close to a +perfectly in AAS demand or feature even + + align:start position:0% +perfectly in AAS demand or feature even + + + align:start position:0% +perfectly in AAS demand or feature even +features of a good yeah like + + align:start position:0% +features of a good yeah like + + + align:start position:0% +features of a good yeah like +what gas gas would be well it's you're + + align:start position:0% +what gas gas would be well it's you're + + + align:start position:0% +what gas gas would be well it's you're +right in the sense + + align:start position:0% +right in the sense + + + align:start position:0% +right in the sense +it's a very interesting example in the + + align:start position:0% +it's a very interesting example in the + + + align:start position:0% +it's a very interesting example in the +sense it's sort of inelastic because + + align:start position:0% +sense it's sort of inelastic because + + + align:start position:0% +sense it's sort of inelastic because +like you got to get to work on the other + + align:start position:0% +like you got to get to work on the other + + + align:start position:0% +like you got to get to work on the other +hand there's a bus there's your bike you + + align:start position:0% +hand there's a bus there's your bike you + + + align:start position:0% +hand there's a bus there's your bike you +could walk you could buy a new car so + + align:start position:0% +could walk you could buy a new car so + + + align:start position:0% +could walk you could buy a new car so +it's not perfectly an elastic but it's + + align:start position:0% +it's not perfectly an elastic but it's + + + align:start position:0% +it's not perfectly an elastic but it's +it's somewhat what else + + align:start position:0% +it's somewhat what else + + + align:start position:0% +it's somewhat what else +yeah water would be something uh but + + align:start position:0% +yeah water would be something uh but + + + align:start position:0% +yeah water would be something uh but +once again not perfectly because like + + align:start position:0% +once again not perfectly because like + + + align:start position:0% +once again not perfectly because like +you can drink Coke you can drink juice + + align:start position:0% +you can drink Coke you can drink juice + + + align:start position:0% +you can drink Coke you can drink juice +you can drink other things you're on the + + align:start position:0% +you can drink other things you're on the + + + align:start position:0% +you can drink other things you're on the +right track yeah insulin is the classic + + align:start position:0% +right track yeah insulin is the classic + + + align:start position:0% +right track yeah insulin is the classic +example we use okay there's no + + align:start position:0% +example we use okay there's no + + + align:start position:0% +example we use okay there's no +substitute when you're having diabetic + + align:start position:0% +substitute when you're having diabetic + + + align:start position:0% +substitute when you're having diabetic +you know when your diabetic trauma for + + align:start position:0% +you know when your diabetic trauma for + + + align:start position:0% +you know when your diabetic trauma for +insulin uh you will not say you know + + align:start position:0% +insulin uh you will not say you know + + + align:start position:0% +insulin uh you will not say you know +it's a buck more I'm just going to die + + align:start position:0% +it's a buck more I'm just going to die + + + align:start position:0% +it's a buck more I'm just going to die +okay uh it is uh we think it's fairly + + align:start position:0% +okay uh it is uh we think it's fairly + + + align:start position:0% +okay uh it is uh we think it's fairly +now it's not perfectly nothing's + + align:start position:0% +now it's not perfectly nothing's + + + align:start position:0% +now it's not perfectly nothing's +perfectly in elastic at some point if + + align:start position:0% +perfectly in elastic at some point if + + + align:start position:0% +perfectly in elastic at some point if +insulin was a million dollars you might + + align:start position:0% +insulin was a million dollars you might + + + align:start position:0% +insulin was a million dollars you might +just not buy it because you can't afford + + align:start position:0% +just not buy it because you can't afford + + + align:start position:0% +just not buy it because you can't afford +it but it's certainly locally + + align:start position:0% +it but it's certainly locally + + + align:start position:0% +it but it's certainly locally +inelastic okay so that be an example of + + align:start position:0% +inelastic okay so that be an example of + + + align:start position:0% +inelastic okay so that be an example of +kind of but once again these are great + + align:start position:0% +kind of but once again these are great + + + align:start position:0% +kind of but once again these are great +examples of things which the examples + + align:start position:0% +examples of things which the examples + + + align:start position:0% +examples of things which the examples +we're given are Goods which should be + + align:start position:0% +we're given are Goods which should be + + + align:start position:0% +we're given are Goods which should be +somewhat inelastic but not perfectly + + align:start position:0% +somewhat inelastic but not perfectly + + + align:start position:0% +somewhat inelastic but not perfectly +okay likewise in figure 43 + + align:start position:0% +okay likewise in figure 43 + + + align:start position:0% +okay likewise in figure 43 +we consider a good with perfectly + + align:start position:0% +we consider a good with perfectly + + + align:start position:0% +we consider a good with perfectly +elastic demand which is Epsilon equals + + align:start position:0% +elastic demand which is Epsilon equals + + + align:start position:0% +elastic demand which is Epsilon equals +negative + + align:start position:0% +negative + + + align:start position:0% +negative +Infinity perfectly elastic demand that + + align:start position:0% +Infinity perfectly elastic demand that + + + align:start position:0% +Infinity perfectly elastic demand that +is any infinite tmal change in price + + align:start position:0% +is any infinite tmal change in price + + + align:start position:0% +is any infinite tmal change in price +causes an infinite change in + + align:start position:0% +causes an infinite change in + + + align:start position:0% +causes an infinite change in +quantity once again doesn't exist in + + align:start position:0% +quantity once again doesn't exist in + + + align:start position:0% +quantity once again doesn't exist in +reality but what types of goods would + + align:start position:0% +reality but what types of goods would + + + align:start position:0% +reality but what types of goods would +have very very very elastic + + align:start position:0% +have very very very elastic + + + align:start position:0% +have very very very elastic +demand + + align:start position:0% +demand + + + align:start position:0% +demand +yeah luxury goods would have elastic + + align:start position:0% +yeah luxury goods would have elastic + + + align:start position:0% +yeah luxury goods would have elastic +demand because basically you know you + + align:start position:0% +demand because basically you know you + + + align:start position:0% +demand because basically you know you +don't really need them them what + + align:start position:0% +don't really need them them what + + + align:start position:0% +don't really need them them what +else + + align:start position:0% +else + + + align:start position:0% +else +yeah yeah so McDonald's versus Burger + + align:start position:0% +yeah yeah so McDonald's versus Burger + + + align:start position:0% +yeah yeah so McDonald's versus Burger +King okay now we may have our + + align:start position:0% +King okay now we may have our + + + align:start position:0% +King okay now we may have our +preferences but the bottom line is + + align:start position:0% +preferences but the bottom line is + + + align:start position:0% +preferences but the bottom line is +McDonald's charged twice as much as + + align:start position:0% +McDonald's charged twice as much as + + + align:start position:0% +McDonald's charged twice as much as +Burger King for a burger everyone just + + align:start position:0% +Burger King for a burger everyone just + + + align:start position:0% +Burger King for a burger everyone just +go to Burger King okay basically it's + + align:start position:0% +go to Burger King okay basically it's + + + align:start position:0% +go to Burger King okay basically it's +there is it's there there's a point at + + align:start position:0% +there is it's there there's a point at + + + align:start position:0% +there is it's there there's a point at +which uh there're so and essentially + + align:start position:0% +which uh there're so and essentially + + + align:start position:0% +which uh there're so and essentially +what is a + + align:start position:0% +what is a + + + align:start position:0% +what is a +question oh no we're we're good examples + + align:start position:0% +question oh no we're we're good examples + + + align:start position:0% +question oh no we're we're good examples +but here's the key + + align:start position:0% +but here's the key + + + align:start position:0% +but here's the key +feature that differentiates elasticity + + align:start position:0% +feature that differentiates elasticity + + + align:start position:0% +feature that differentiates elasticity +it's + + align:start position:0% +it's + + + align:start position:0% +it's +substitutability Goods with no + + align:start position:0% +substitutability Goods with no + + + align:start position:0% +substitutability Goods with no +substitutes are not + + align:start position:0% +substitutes are not + + + align:start position:0% +substitutes are not +elastic Goods with lots of substitutes + + align:start position:0% +elastic Goods with lots of substitutes + + + align:start position:0% +elastic Goods with lots of substitutes +are very elastic that's why I + + align:start position:0% +are very elastic that's why I + + + align:start position:0% +are very elastic that's why I +immediately respond to gas by talking + + align:start position:0% +immediately respond to gas by talking + + + align:start position:0% +immediately respond to gas by talking +about all the that's so embedded in my + + align:start position:0% +about all the that's so embedded in my + + + align:start position:0% +about all the that's so embedded in my +brain that when someone brought off gas + + align:start position:0% +brain that when someone brought off gas + + + align:start position:0% +brain that when someone brought off gas +what did I go to I went to all the + + align:start position:0% +what did I go to I went to all the + + + align:start position:0% +what did I go to I went to all the +substitutes because more substitutes + + align:start position:0% +substitutes because more substitutes + + + align:start position:0% +substitutes because more substitutes +there are the more elastic the good is + + align:start position:0% +there are the more elastic the good is + + + align:start position:0% +there are the more elastic the good is +okay so basically you that's essentially + + align:start position:0% +okay so basically you that's essentially + + + align:start position:0% +okay so basically you that's essentially +how to think about elasticity think + + align:start position:0% +how to think about elasticity think + + + align:start position:0% +how to think about elasticity think +about + + align:start position:0% +about + + + align:start position:0% +about +substitutability okay the degree of + + align:start position:0% +substitutability okay the degree of + + + align:start position:0% +substitutability okay the degree of +substitutability is the degree of + + align:start position:0% +substitutability is the degree of + + + align:start position:0% +substitutability is the degree of +elasticity and obviously everything in + + align:start position:0% +elasticity and obviously everything in + + + align:start position:0% +elasticity and obviously everything in +the world is going to lie between these + + align:start position:0% +the world is going to lie between these + + + align:start position:0% +the world is going to lie between these +two extremes there's nothing in the + + align:start position:0% +two extremes there's nothing in the + + + align:start position:0% +two extremes there's nothing in the +world that's ever purely inelastic and + + align:start position:0% +world that's ever purely inelastic and + + + align:start position:0% +world that's ever purely inelastic and +purely elastic but things are going to + + align:start position:0% +purely elastic but things are going to + + + align:start position:0% +purely elastic but things are going to +lie between these two extremes and the + + align:start position:0% +lie between these two extremes and the + + + align:start position:0% +lie between these two extremes and the +where they lie will be a function of how + + align:start position:0% +where they lie will be a function of how + + + align:start position:0% +where they lie will be a function of how +substitutable they + + align:start position:0% +substitutable they + + + align:start position:0% +substitutable they +are okay questions about + + align:start position:0% +are okay questions about + + + align:start position:0% +are okay questions about +that now let me make a point that we are + + align:start position:0% +that now let me make a point that we are + + + align:start position:0% +that now let me make a point that we are +going to um in this class um uh once + + align:start position:0% +going to um in this class um uh once + + + align:start position:0% +going to um in this class um uh once +again be cheating a little bit about uh + + align:start position:0% +again be cheating a little bit about uh + + + align:start position:0% +again be cheating a little bit about uh +linear versus nonlinear demand curves a + + align:start position:0% +linear versus nonlinear demand curves a + + + align:start position:0% +linear versus nonlinear demand curves a +constant elasticity demand curve would + + align:start position:0% +constant elasticity demand curve would + + + align:start position:0% +constant elasticity demand curve would +have to be + + align:start position:0% +have to be + + + align:start position:0% +have to be +nonlinear you should if you don't see + + align:start position:0% +nonlinear you should if you don't see + + + align:start position:0% +nonlinear you should if you don't see +that right away it's something you + + align:start position:0% +that right away it's something you + + + align:start position:0% +that right away it's something you +should go home and think about a + + align:start position:0% +should go home and think about a + + + align:start position:0% +should go home and think about a +constant elasticity but we're going to + + align:start position:0% +constant elasticity but we're going to + + + align:start position:0% +constant elasticity but we're going to +we're going to talk about curves we're + + align:start position:0% +we're going to talk about curves we're + + + align:start position:0% +we're going to talk about curves we're +going to talk about one elasticity and + + align:start position:0% +going to talk about one elasticity and + + + align:start position:0% +going to talk about one elasticity and +draw linear curves so once again just + + align:start position:0% +draw linear curves so once again just + + + align:start position:0% +draw linear curves so once again just +think is very local approximations so + + align:start position:0% +think is very local approximations so + + + align:start position:0% +think is very local approximations so +it's approximately right okay so don't + + align:start position:0% +it's approximately right okay so don't + + + align:start position:0% +it's approximately right okay so don't +get too thrown off by the nonlinear + + align:start position:0% +get too thrown off by the nonlinear + + + align:start position:0% +get too thrown off by the nonlinear +linear part of this stuff and once it's + + align:start position:0% +linear part of this stuff and once it's + + + align:start position:0% +linear part of this stuff and once it's +unclear + + align:start position:0% +unclear + + + align:start position:0% +unclear +ask + + align:start position:0% + + + + align:start position:0% + +yeah no it's it's it it's the it's the + + align:start position:0% +yeah no it's it's it it's the it's the + + + align:start position:0% +yeah no it's it's it it's the it's the +elasticity it's how much a change + + align:start position:0% +elasticity it's how much a change + + + align:start position:0% +elasticity it's how much a change +incremental change in price changes + + align:start position:0% + + + + align:start position:0% + +quantity okay so now now let's talk + + align:start position:0% +quantity okay so now now let's talk + + + align:start position:0% +quantity okay so now now let's talk +about another topic which is we've + + align:start position:0% +about another topic which is we've + + + align:start position:0% +about another topic which is we've +talked we remember we talked about what + + align:start position:0% +talked we remember we talked about what + + + align:start position:0% +talked we remember we talked about what +moves budget constraints we talked about + + align:start position:0% +moves budget constraints we talked about + + + align:start position:0% +moves budget constraints we talked about +prices changing income changing so let's + + align:start position:0% +prices changing income changing so let's + + + align:start position:0% +prices changing income changing so let's +talk about what happens when to demand + + align:start position:0% +talk about what happens when to demand + + + align:start position:0% +talk about what happens when to demand +curves when income + + align:start position:0% +curves when income + + + align:start position:0% +curves when income +changes income and demand + + align:start position:0% + + + + align:start position:0% + +curves okay so now let's go to figure + + align:start position:0% +curves okay so now let's go to figure + + + align:start position:0% +curves okay so now let's go to figure +44 once again we start at Point + + align:start position:0% +44 once again we start at Point + + + align:start position:0% +44 once again we start at Point +a that is our original setup with the + + align:start position:0% +a that is our original setup with the + + + align:start position:0% +a that is our original setup with the +budget strength 24 equal 4S + 2 C and + + align:start position:0% +budget strength 24 equal 4S + 2 C and + + + align:start position:0% +budget strength 24 equal 4S + 2 C and +the utility function unal square root of + + align:start position:0% +the utility function unal square root of + + + align:start position:0% +the utility function unal square root of +c and that gets a solution at Point + + align:start position:0% +c and that gets a solution at Point + + + align:start position:0% +c and that gets a solution at Point +a okay now imagine that your income + + align:start position:0% +a okay now imagine that your income + + + align:start position:0% +a okay now imagine that your income +rises from $24 to + + align:start position:0% +rises from $24 to + + + align:start position:0% +rises from $24 to +$32 nothing else has changed your + + align:start position:0% +$32 nothing else has changed your + + + align:start position:0% +$32 nothing else has changed your +preference is the same price is the same + + align:start position:0% +preference is the same price is the same + + + align:start position:0% +preference is the same price is the same +but your income has risen from $24 to + + align:start position:0% +but your income has risen from $24 to + + + align:start position:0% +but your income has risen from $24 to +$32 well in that case the + + align:start position:0% +$32 well in that case the + + + align:start position:0% +$32 well in that case the +optimization is now you're still you're + + align:start position:0% +optimization is now you're still you're + + + align:start position:0% +optimization is now you're still you're +you're still setting minus s over C + + align:start position:0% +you're still setting minus s over C + + + align:start position:0% +you're still setting minus s over C +to a price ratio okay you're still + + align:start position:0% +to a price ratio okay you're still + + + align:start position:0% +to a price ratio okay you're still +setting s over C to the price ratio + + align:start position:0% +setting s over C to the price ratio + + + align:start position:0% +setting s over C to the price ratio +minus one2 that hasn't changed because + + align:start position:0% +minus one2 that hasn't changed because + + + align:start position:0% +minus one2 that hasn't changed because +the price ratio hasn't changed and your + + align:start position:0% +the price ratio hasn't changed and your + + + align:start position:0% +the price ratio hasn't changed and your +preferen haven't changed what's changed + + align:start position:0% +preferen haven't changed what's changed + + + align:start position:0% +preferen haven't changed what's changed +is the second equation which your bud + + align:start position:0% +is the second equation which your bud + + + align:start position:0% +is the second equation which your bud +rate is now 32 equals 4S plus 2 + + align:start position:0% +rate is now 32 equals 4S plus 2 + + + align:start position:0% +rate is now 32 equals 4S plus 2 +C so the tangency condition hasn't + + align:start position:0% +C so the tangency condition hasn't + + + align:start position:0% +C so the tangency condition hasn't +changed which change R goes up is the + + align:start position:0% +changed which change R goes up is the + + + align:start position:0% +changed which change R goes up is the +budget constraint and we solve for that + + align:start position:0% +budget constraint and we solve for that + + + align:start position:0% +budget constraint and we solve for that +you'll now see you get that c star + + align:start position:0% +you'll now see you get that c star + + + align:start position:0% +you'll now see you get that c star +equals 8 and SAR equals + + align:start position:0% +equals 8 and SAR equals + + + align:start position:0% +equals 8 and SAR equals +4 so you changed your consumption but + + align:start position:0% +4 so you changed your consumption but + + + align:start position:0% +4 so you changed your consumption but +not because price have changed you're + + align:start position:0% +not because price have changed you're + + + align:start position:0% +not because price have changed you're +richer you want more that is exactly + + align:start position:0% +richer you want more that is exactly + + + align:start position:0% +richer you want more that is exactly +what we see in at point + + align:start position:0% +what we see in at point + + + align:start position:0% +what we see in at point +B point B shows remember when your + + align:start position:0% +B point B shows remember when your + + + align:start position:0% +B point B shows remember when your +income goes up there's a parallel shift + + align:start position:0% +income goes up there's a parallel shift + + + align:start position:0% +income goes up there's a parallel shift +outward in the budget constraint income + + align:start position:0% +outward in the budget constraint income + + + align:start position:0% +outward in the budget constraint income +goes up parallel shift outward in the + + align:start position:0% +goes up parallel shift outward in the + + + align:start position:0% +goes up parallel shift outward in the +budget constraint you still want to find + + align:start position:0% +budget constraint you still want to find + + + align:start position:0% +budget constraint you still want to find +the tangency that tangency is still + + align:start position:0% +the tangency that tangency is still + + + align:start position:0% +the tangency that tangency is still +going to solve this condition because + + align:start position:0% +going to solve this condition because + + + align:start position:0% +going to solve this condition because +prices and preferences have haven't + + align:start position:0% +prices and preferences have haven't + + + align:start position:0% +prices and preferences have haven't +changed it's just going to be a higher + + align:start position:0% +changed it's just going to be a higher + + + align:start position:0% +changed it's just going to be a higher +quantity and that's what happens at + + align:start position:0% +quantity and that's what happens at + + + align:start position:0% +quantity and that's what happens at +point + + align:start position:0% +point + + + align:start position:0% +point +B same tangency at a higher quantity + + align:start position:0% +B same tangency at a higher quantity + + + align:start position:0% +B same tangency at a higher quantity +likewise at Point C we show what happens + + align:start position:0% +likewise at Point C we show what happens + + + align:start position:0% +likewise at Point C we show what happens +if your income Falls to + + align:start position:0% +if your income Falls to + + + align:start position:0% +if your income Falls to +$16 then you want less pizza and fewer + + align:start position:0% +$16 then you want less pizza and fewer + + + align:start position:0% +$16 then you want less pizza and fewer +fewer less pizza and fewer cookies four + + align:start position:0% +fewer less pizza and fewer cookies four + + + align:start position:0% +fewer less pizza and fewer cookies four +cookies and two + + align:start position:0% +cookies and two + + + align:start position:0% +cookies and two +slices what is that lead us to that + + align:start position:0% +slices what is that lead us to that + + + align:start position:0% +slices what is that lead us to that +leads us to a relationship now between + + align:start position:0% +leads us to a relationship now between + + + align:start position:0% +leads us to a relationship now between +your income + + align:start position:0% +your income + + + align:start position:0% +your income +and the quantity demanded and that + + align:start position:0% +and the quantity demanded and that + + + align:start position:0% +and the quantity demanded and that +relationship is shown in the second + + align:start position:0% +relationship is shown in the second + + + align:start position:0% +relationship is shown in the second +panel of figure 44 we call this the + + align:start position:0% +panel of figure 44 we call this the + + + align:start position:0% +panel of figure 44 we call this the +angle + + align:start position:0% + + + + align:start position:0% + +curve the angle curve which is the name + + align:start position:0% +curve the angle curve which is the name + + + align:start position:0% +curve the angle curve which is the name +for the relationship between income and + + align:start position:0% +for the relationship between income and + + + align:start position:0% +for the relationship between income and +quantity demanded and you can draw an + + align:start position:0% +quantity demanded and you can draw an + + + align:start position:0% +quantity demanded and you can draw an +angle curve for S and an angle curve for + + align:start position:0% +angle curve for S and an angle curve for + + + align:start position:0% +angle curve for S and an angle curve for +C here we're drawing the angle curve for + + align:start position:0% +C here we're drawing the angle curve for + + + align:start position:0% +C here we're drawing the angle curve for +C okay and the Ang the angle curve the + + align:start position:0% +C okay and the Ang the angle curve the + + + align:start position:0% +C okay and the Ang the angle curve the +slope of the angle curve is what we call + + align:start position:0% +slope of the angle curve is what we call + + + align:start position:0% +slope of the angle curve is what we call +the in elasticity of demand or + + align:start position:0% +the in elasticity of demand or + + + align:start position:0% +the in elasticity of demand or +gamma which is Delta Q over Q over Delta + + align:start position:0% +gamma which is Delta Q over Q over Delta + + + align:start position:0% +gamma which is Delta Q over Q over Delta +y over y or approximately DQ + + align:start position:0% +y over y or approximately DQ + + + align:start position:0% +y over y or approximately DQ +Dy okay so + + align:start position:0% +Dy okay so + + + align:start position:0% +Dy okay so +basically this is instead of how does + + align:start position:0% +basically this is instead of how does + + + align:start position:0% +basically this is instead of how does +demand change with price which is the + + align:start position:0% +demand change with price which is the + + + align:start position:0% +demand change with price which is the +demand curve this is how does demand + + align:start position:0% +demand curve this is how does demand + + + align:start position:0% +demand curve this is how does demand +change with income or what we call the + + align:start position:0% +change with income or what we call the + + + align:start position:0% +change with income or what we call the +angle curve + + align:start position:0% +angle curve + + + align:start position:0% +angle curve +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +now and we're going to come in a few + + align:start position:0% +now and we're going to come in a few + + + align:start position:0% +now and we're going to come in a few +minutes about why this is important but + + align:start position:0% +minutes about why this is important but + + + align:start position:0% +minutes about why this is important but +let's talk about the properties of + + align:start position:0% +let's talk about the properties of + + + align:start position:0% +let's talk about the properties of +gamma okay gamma is much more + + align:start position:0% +gamma okay gamma is much more + + + align:start position:0% +gamma okay gamma is much more +interesting than Epsilon Epsilon you + + align:start position:0% +interesting than Epsilon Epsilon you + + + align:start position:0% +interesting than Epsilon Epsilon you +know some negative number zero to minus + + align:start position:0% +know some negative number zero to minus + + + align:start position:0% +know some negative number zero to minus +infinity gamma can have a much larger + + align:start position:0% +infinity gamma can have a much larger + + + align:start position:0% +infinity gamma can have a much larger +range in fact gamma is usually greater + + align:start position:0% +range in fact gamma is usually greater + + + align:start position:0% +range in fact gamma is usually greater +than zero in fact when gamma is greater + + align:start position:0% +than zero in fact when gamma is greater + + + align:start position:0% +than zero in fact when gamma is greater +than zero we call them normal + + align:start position:0% +than zero we call them normal + + + align:start position:0% +than zero we call them normal +Goods normal Goods goods are Goods where + + align:start position:0% +Goods normal Goods goods are Goods where + + + align:start position:0% +Goods normal Goods goods are Goods where +gamma is greater than + + align:start position:0% +gamma is greater than + + + align:start position:0% +gamma is greater than +zero but gamma does not have to be + + align:start position:0% +zero but gamma does not have to be + + + align:start position:0% +zero but gamma does not have to be +greater than zero well Epsilon has to be + + align:start position:0% +greater than zero well Epsilon has to be + + + align:start position:0% +greater than zero well Epsilon has to be +less than or equal to zero gamma does + + align:start position:0% +less than or equal to zero gamma does + + + align:start position:0% +less than or equal to zero gamma does +not gamma could actually be less than + + align:start position:0% +not gamma could actually be less than + + + align:start position:0% +not gamma could actually be less than +zero does anyone know how that could + + align:start position:0% +zero does anyone know how that could + + + align:start position:0% +zero does anyone know how that could +happen how could it happen that you get + + align:start position:0% +happen how could it happen that you get + + + align:start position:0% +happen how could it happen that you get +richer and want less of something what's + + align:start position:0% +richer and want less of something what's + + + align:start position:0% +richer and want less of something what's +an example yeah it's what's what's + + align:start position:0% +an example yeah it's what's what's + + + align:start position:0% +an example yeah it's what's what's +called inferior good okay but give an + + align:start position:0% +called inferior good okay but give an + + + align:start position:0% +called inferior good okay but give an +example + + align:start position:0% + + + + align:start position:0% + +right right exactly so as you get richer + + align:start position:0% +right right exactly so as you get richer + + + align:start position:0% +right right exactly so as you get richer +you want to get rid of things that you + + align:start position:0% +you want to get rid of things that you + + + align:start position:0% +you want to get rid of things that you +only eating because they were cheap + + align:start position:0% +only eating because they were cheap + + + align:start position:0% +only eating because they were cheap +what's an example of that yeah Ramen is + + align:start position:0% +what's an example of that yeah Ramen is + + + align:start position:0% +what's an example of that yeah Ramen is +the example of that Ramen is the + + align:start position:0% +the example of that Ramen is the + + + align:start position:0% +the example of that Ramen is the +ultimate inferior good no one wants to + + align:start position:0% +ultimate inferior good no one wants to + + + align:start position:0% +ultimate inferior good no one wants to +eat ramen I realize there's fancy Ramen + + align:start position:0% +eat ramen I realize there's fancy Ramen + + + align:start position:0% +eat ramen I realize there's fancy Ramen +restrant but you know nobody should go + + align:start position:0% +restrant but you know nobody should go + + + align:start position:0% +restrant but you know nobody should go +there okay people want to eat R people + + align:start position:0% +there okay people want to eat R people + + + align:start position:0% +there okay people want to eat R people +eat ramen because it's cheap okay no in + + align:start position:0% +eat ramen because it's cheap okay no in + + + align:start position:0% +eat ramen because it's cheap okay no in +all seriousness it is sort of amazing + + align:start position:0% +all seriousness it is sort of amazing + + + align:start position:0% +all seriousness it is sort of amazing +that Ramen is become sort of a + + align:start position:0% +that Ramen is become sort of a + + + align:start position:0% +that Ramen is become sort of a +restaurant food after all you know it is + + align:start position:0% +restaurant food after all you know it is + + + align:start position:0% +restaurant food after all you know it is +in other countries I realize but most + + align:start position:0% +in other countries I realize but most + + + align:start position:0% +in other countries I realize but most +consumption of ramen is done by she pack + + align:start position:0% +consumption of ramen is done by she pack + + + align:start position:0% +consumption of ramen is done by she pack +it to the supermarket okay as you get + + align:start position:0% +it to the supermarket okay as you get + + + align:start position:0% +it to the supermarket okay as you get +richer you consume less Ramen you might + + align:start position:0% +richer you consume less Ramen you might + + + align:start position:0% +richer you consume less Ramen you might +not consume zero you might still like it + + align:start position:0% +not consume zero you might still like it + + + align:start position:0% +not consume zero you might still like it +but you're not need it five days a week + + align:start position:0% +but you're not need it five days a week + + + align:start position:0% +but you're not need it five days a week +like when you're starving you know + + align:start position:0% +like when you're starving you know + + + align:start position:0% +like when you're starving you know +entrepreneur trying to make your own + + align:start position:0% +entrepreneur trying to make your own + + + align:start position:0% +entrepreneur trying to make your own +business okay so Ram is example of an + + align:start position:0% +business okay so Ram is example of an + + + align:start position:0% +business okay so Ram is example of an +inferior good a good that as you get + + align:start position:0% +inferior good a good that as you get + + + align:start position:0% +inferior good a good that as you get +richer you have less of it because + + align:start position:0% +richer you have less of it because + + + align:start position:0% +richer you have less of it because +basically you're only eating it because + + align:start position:0% +basically you're only eating it because + + + align:start position:0% +basically you're only eating it because +it was + + align:start position:0% +it was + + + align:start position:0% +it was +cheap okay now even within normal Goods + + align:start position:0% +cheap okay now even within normal Goods + + + align:start position:0% +cheap okay now even within normal Goods +we have a distinction which is within + + align:start position:0% +we have a distinction which is within + + + align:start position:0% +we have a distinction which is within +normal Goods we distinguish between two + + align:start position:0% +normal Goods we distinguish between two + + + align:start position:0% +normal Goods we distinguish between two +things which gamma greater than one and + + align:start position:0% +things which gamma greater than one and + + + align:start position:0% +things which gamma greater than one and +Gamma less than + + align:start position:0% +Gamma less than + + + align:start position:0% +Gamma less than +one what do you think we call Goods with + + align:start position:0% +one what do you think we call Goods with + + + align:start position:0% +one what do you think we call Goods with +gamma greater than one versus gamma less + + align:start position:0% +gamma greater than one versus gamma less + + + align:start position:0% +gamma greater than one versus gamma less +than one and this relates to examples + + align:start position:0% +than one and this relates to examples + + + align:start position:0% +than one and this relates to examples +that were given + + align:start position:0% +that were given + + + align:start position:0% +that were given +before yeah or which + + align:start position:0% +before yeah or which + + + align:start position:0% +before yeah or which +one greater than one so basically luxury + + align:start position:0% +one greater than one so basically luxury + + + align:start position:0% +one greater than one so basically luxury +goods are where as your income Rises the + + align:start position:0% +goods are where as your income Rises the + + + align:start position:0% +goods are where as your income Rises the +percent of your income spent on the good + + align:start position:0% +percent of your income spent on the good + + + align:start position:0% +percent of your income spent on the good +goes up let's be very clear as your gun + + align:start position:0% +goes up let's be very clear as your gun + + + align:start position:0% +goes up let's be very clear as your gun +Rises you consume more of everything + + align:start position:0% +Rises you consume more of everything + + + align:start position:0% +Rises you consume more of everything +generally + + align:start position:0% +generally + + + align:start position:0% +generally +but it's how does the budget share + + align:start position:0% +but it's how does the budget share + + + align:start position:0% +but it's how does the budget share +change do you spend more and more of + + align:start position:0% +change do you spend more and more of + + + align:start position:0% +change do you spend more and more of +your budget on that good as you get + + align:start position:0% +your budget on that good as you get + + + align:start position:0% +your budget on that good as you get +richer and that's what we call a luxury + + align:start position:0% +richer and that's what we call a luxury + + + align:start position:0% +richer and that's what we call a luxury +good so a classic luxury good would be + + align:start position:0% +good so a classic luxury good would be + + + align:start position:0% +good so a classic luxury good would be +eating at restaurants when you're + + align:start position:0% +eating at restaurants when you're + + + align:start position:0% +eating at restaurants when you're +poor you have to buy you have to make + + align:start position:0% +poor you have to buy you have to make + + + align:start position:0% +poor you have to buy you have to make +your own dinners because eating + + align:start position:0% +your own dinners because eating + + + align:start position:0% +your own dinners because eating +restaurants too expensive as you get + + align:start position:0% +restaurants too expensive as you get + + + align:start position:0% +restaurants too expensive as you get +richer a larger and larger share of your + + align:start position:0% +richer a larger and larger share of your + + + align:start position:0% +richer a larger and larger share of your +budget will be consumed by eating at + + align:start position:0% +budget will be consumed by eating at + + + align:start position:0% +budget will be consumed by eating at +restaurants okay that's a luxury good + + align:start position:0% +restaurants okay that's a luxury good + + + align:start position:0% +restaurants okay that's a luxury good +what about Gamma less than one what we + + align:start position:0% +what about Gamma less than one what we + + + align:start position:0% +what about Gamma less than one what we +call that + + align:start position:0% + + + + align:start position:0% + +anyone got any ideas gamma less than one + + align:start position:0% +anyone got any ideas gamma less than one + + + align:start position:0% +anyone got any ideas gamma less than one +yeah what + + align:start position:0% +yeah what + + + align:start position:0% +yeah what +then no GI and good is well that we'll + + align:start position:0% +then no GI and good is well that we'll + + + align:start position:0% +then no GI and good is well that we'll +come back to that gamma you're you're + + align:start position:0% +come back to that gamma you're you're + + + align:start position:0% +come back to that gamma you're you're +one step ahead gamma less than one + + align:start position:0% +one step ahead gamma less than one + + + align:start position:0% +one step ahead gamma less than one +simpler than that so if these are + + align:start position:0% +simpler than that so if these are + + + align:start position:0% +simpler than that so if these are +luxuries what are + + align:start position:0% +luxuries what are + + + align:start position:0% +luxuries what are +these + + align:start position:0% +these + + + align:start position:0% +these +Necessities sorry for the small + + align:start position:0% + + + + align:start position:0% + +writing Necessities these are Goods + + align:start position:0% +writing Necessities these are Goods + + + align:start position:0% +writing Necessities these are Goods +where as your income goes up you don't + + align:start position:0% +where as your income goes up you don't + + + align:start position:0% +where as your income goes up you don't +have less of them Ramen is an inferior + + align:start position:0% +have less of them Ramen is an inferior + + + align:start position:0% +have less of them Ramen is an inferior +good you literally have less Ramen but + + align:start position:0% +good you literally have less Ramen but + + + align:start position:0% +good you literally have less Ramen but +this is like eating at home eating at + + align:start position:0% +this is like eating at home eating at + + + align:start position:0% +this is like eating at home eating at +home you don't necessarily you don't eat + + align:start position:0% +home you don't necessarily you don't eat + + + align:start position:0% +home you don't necessarily you don't eat +spend less on eating at home as you get + + align:start position:0% +spend less on eating at home as you get + + + align:start position:0% +spend less on eating at home as you get +richer but you might spend a lower share + + align:start position:0% +richer but you might spend a lower share + + + align:start position:0% +richer but you might spend a lower share +or this could be clothes or this could + + align:start position:0% +or this could be clothes or this could + + + align:start position:0% +or this could be clothes or this could +be + + align:start position:0% +be + + + align:start position:0% +be +rent things where if I get rich you get + + align:start position:0% +rent things where if I get rich you get + + + align:start position:0% +rent things where if I get rich you get +a nicer apartment but if you get really + + align:start position:0% +a nicer apartment but if you get really + + + align:start position:0% +a nicer apartment but if you get really +rich you know when you're poor your + + align:start position:0% +rich you know when you're poor your + + + align:start position:0% +rich you know when you're poor your +apartment's 60% of your income when + + align:start position:0% +apartment's 60% of your income when + + + align:start position:0% +apartment's 60% of your income when +you're rich it's going to fall yeah + + align:start position:0% + + + + align:start position:0% + +more than zero exactly exactly it's less + + align:start position:0% +more than zero exactly exactly it's less + + + align:start position:0% +more than zero exactly exactly it's less +than one but more than zero that's a + + align:start position:0% +than one but more than zero that's a + + + align:start position:0% +than one but more than zero that's a +great Point these are both greater than + + align:start position:0% +great Point these are both greater than + + + align:start position:0% +great Point these are both greater than +one this is less than one but greater + + align:start position:0% +one this is less than one but greater + + + align:start position:0% +one this is less than one but greater +than zero if it's less than zero it's + + align:start position:0% +than zero if it's less than zero it's + + + align:start position:0% +than zero if it's less than zero it's +inferior so that's the interesting + + align:start position:0% +inferior so that's the interesting + + + align:start position:0% +inferior so that's the interesting +distinction between necessity inferior + + align:start position:0% +distinction between necessity inferior + + + align:start position:0% +distinction between necessity inferior +let me explain this very clear inferior + + align:start position:0% +let me explain this very clear inferior + + + align:start position:0% +let me explain this very clear inferior +is it's very unclear I mean inferior is + + align:start position:0% +is it's very unclear I mean inferior is + + + align:start position:0% +is it's very unclear I mean inferior is +as your income goes up you literally + + align:start position:0% +as your income goes up you literally + + + align:start position:0% +as your income goes up you literally +have less of it necessity as your income + + align:start position:0% +have less of it necessity as your income + + + align:start position:0% +have less of it necessity as your income +goes up you have more of it but it goes + + align:start position:0% +goes up you have more of it but it goes + + + align:start position:0% +goes up you have more of it but it goes +but it rises F slower than your income + + align:start position:0% +but it rises F slower than your income + + + align:start position:0% +but it rises F slower than your income +so rent is the perfect example richer + + align:start position:0% +so rent is the perfect example richer + + + align:start position:0% +so rent is the perfect example richer +people have nicer Apartments than poorer + + align:start position:0% +people have nicer Apartments than poorer + + + align:start position:0% +people have nicer Apartments than poorer +people but richer people spend a smaller + + align:start position:0% +people but richer people spend a smaller + + + align:start position:0% +people but richer people spend a smaller +share of their budget on apartments than + + align:start position:0% +share of their budget on apartments than + + + align:start position:0% +share of their budget on apartments than +do poor + + align:start position:0% +do poor + + + align:start position:0% +do poor +people okay it's a necessity richer + + align:start position:0% +people okay it's a necessity richer + + + align:start position:0% +people okay it's a necessity richer +people have nicer watches than poor + + align:start position:0% +people have nicer watches than poor + + + align:start position:0% +people have nicer watches than poor +people and it's a rising share of their + + align:start position:0% +people and it's a rising share of their + + + align:start position:0% +people and it's a rising share of their +budget as they get richer because they + + align:start position:0% +budget as they get richer because they + + + align:start position:0% +budget as they get richer because they +don't have a nice watch when they're + + align:start position:0% +don't have a nice watch when they're + + + align:start position:0% +don't have a nice watch when they're +poor and as they get rich they buy nicer + + align:start position:0% +poor and as they get rich they buy nicer + + + align:start position:0% +poor and as they get rich they buy nicer +and nicer + + align:start position:0% +and nicer + + + align:start position:0% +and nicer +watches okay + + align:start position:0% + + + + align:start position:0% + +yeah we're going to do that in one + + align:start position:0% +yeah we're going to do that in one + + + align:start position:0% +yeah we're going to do that in one +minute other questions + + align:start position:0% +minute other questions + + + align:start position:0% +minute other questions +okay these are The Primitives that allow + + align:start position:0% +okay these are The Primitives that allow + + + align:start position:0% +okay these are The Primitives that allow +us to go on to do um the fun the the + + align:start position:0% +us to go on to do um the fun the the + + + align:start position:0% +us to go on to do um the fun the the +sort of fundamental goal of this lecture + + align:start position:0% +sort of fundamental goal of this lecture + + + align:start position:0% +sort of fundamental goal of this lecture +which is to get into + + align:start position:0% +which is to get into + + + align:start position:0% +which is to get into +behind the mechanics of what happens + + align:start position:0% +behind the mechanics of what happens + + + align:start position:0% +behind the mechanics of what happens +when you change prices did everyone get + + align:start position:0% +when you change prices did everyone get + + + align:start position:0% +when you change prices did everyone get +this can I put this + + align:start position:0% +this can I put this + + + align:start position:0% +this can I put this +up okay what happens what's the + + align:start position:0% +up okay what happens what's the + + + align:start position:0% +up okay what happens what's the +mechanics of what happens when you + + align:start position:0% +mechanics of what happens when you + + + align:start position:0% +mechanics of what happens when you +change + + align:start position:0% +change + + + align:start position:0% +change +prices now you said you say John you + + align:start position:0% +prices now you said you say John you + + + align:start position:0% +prices now you said you say John you +just showed what happens when you change + + align:start position:0% +just showed what happens when you change + + + align:start position:0% +just showed what happens when you change +prices the price goes up people want + + align:start position:0% +prices the price goes up people want + + + align:start position:0% +prices the price goes up people want +less of it the price goes down people + + align:start position:0% +less of it the price goes down people + + + align:start position:0% +less of it the price goes down people +want more of it you derive the demand + + align:start position:0% +want more of it you derive the demand + + + align:start position:0% +want more of it you derive the demand +curve let us go a half hour early and I + + align:start position:0% +curve let us go a half hour early and I + + + align:start position:0% +curve let us go a half hour early and I +say no I will not let you go a half hour + + align:start position:0% +say no I will not let you go a half hour + + + align:start position:0% +say no I will not let you go a half hour +early because there's actually a very + + align:start position:0% +early because there's actually a very + + + align:start position:0% +early because there's actually a very +important underlying mechanics going on + + align:start position:0% +important underlying mechanics going on + + + align:start position:0% +important underlying mechanics going on +when the price changes and this + + align:start position:0% +when the price changes and this + + + align:start position:0% +when the price changes and this +mechanics is largely not so relevant for + + align:start position:0% +mechanics is largely not so relevant for + + + align:start position:0% +mechanics is largely not so relevant for +most Goods we do but for some Goods who + + align:start position:0% +most Goods we do but for some Goods who + + + align:start position:0% +most Goods we do but for some Goods who +delay the semester to be critical and + + align:start position:0% +delay the semester to be critical and + + + align:start position:0% +delay the semester to be critical and +that's why it's important to understand + + align:start position:0% +that's why it's important to understand + + + align:start position:0% +that's why it's important to understand +the mechanics and this is um basically + + align:start position:0% +the mechanics and this is um basically + + + align:start position:0% +the mechanics and this is um basically +the fact that when a price changes when + + align:start position:0% +the fact that when a price changes when + + + align:start position:0% +the fact that when a price changes when +a price changes so this calls mechanics + + align:start position:0% +a price changes so this calls mechanics + + + align:start position:0% +a price changes so this calls mechanics +of a price + + align:start position:0% + + + + align:start position:0% + +change when a price changes two things + + align:start position:0% +change when a price changes two things + + + align:start position:0% +change when a price changes two things +happen simultaneously you may not + + align:start position:0% +happen simultaneously you may not + + + align:start position:0% +happen simultaneously you may not +realize it but actually when a price + + align:start position:0% +realize it but actually when a price + + + align:start position:0% +realize it but actually when a price +changes two things + + align:start position:0% +changes two things + + + align:start position:0% +changes two things +happen the first is what we call the + + align:start position:0% +happen the first is what we call the + + + align:start position:0% +happen the first is what we call the +substitution + + align:start position:0% + + + + align:start position:0% + +effect the substitution effect which is + + align:start position:0% +effect the substitution effect which is + + + align:start position:0% +effect the substitution effect which is +when relative prices change you want to + + align:start position:0% +when relative prices change you want to + + + align:start position:0% +when relative prices change you want to +shift away from the good that's gotten + + align:start position:0% +shift away from the good that's gotten + + + align:start position:0% +shift away from the good that's gotten +relatively expensive towards the good + + align:start position:0% +relatively expensive towards the good + + + align:start position:0% +relatively expensive towards the good +that's gotten less + + align:start position:0% +that's gotten less + + + align:start position:0% +that's gotten less +expensive that's the substitution effect + + align:start position:0% +expensive that's the substitution effect + + + align:start position:0% +expensive that's the substitution effect +you say yeah that makes sense that's a + + align:start position:0% +you say yeah that makes sense that's a + + + align:start position:0% +you say yeah that makes sense that's a +price change but the second one is the + + align:start position:0% +price change but the second one is the + + + align:start position:0% +price change but the second one is the +income + + align:start position:0% +income + + + align:start position:0% +income +effect which is when a price changes + + align:start position:0% +effect which is when a price changes + + + align:start position:0% +effect which is when a price changes +you're also effectively richer or poorer + + align:start position:0% +you're also effectively richer or poorer + + + align:start position:0% +you're also effectively richer or poorer +and that also affects your + + align:start position:0% +and that also affects your + + + align:start position:0% +and that also affects your +demand so when a price changes two + + align:start position:0% +demand so when a price changes two + + + align:start position:0% +demand so when a price changes two +things happen Goods become + + align:start position:0% +things happen Goods become + + + align:start position:0% +things happen Goods become +differentially attractive and you're + + align:start position:0% +differentially attractive and you're + + + align:start position:0% +differentially attractive and you're +richer or poor and both things drive + + align:start position:0% +richer or poor and both things drive + + + align:start position:0% +richer or poor and both things drive +your response to that price change and + + align:start position:0% +your response to that price change and + + + align:start position:0% +your response to that price change and +it turns out understanding the + + align:start position:0% +it turns out understanding the + + + align:start position:0% +it turns out understanding the +difference between them will end up + + align:start position:0% +difference between them will end up + + + align:start position:0% +difference between them will end up +being critical for a number of things + + align:start position:0% +being critical for a number of things + + + align:start position:0% +being critical for a number of things +we'll do this semester and that's why + + align:start position:0% +we'll do this semester and that's why + + + align:start position:0% +we'll do this semester and that's why +I'm bothering telling you so + + align:start position:0% + + + + align:start position:0% + +okay so let to understand this we're + + align:start position:0% +okay so let to understand this we're + + + align:start position:0% +okay so let to understand this we're +going to go through one of the more + + align:start position:0% +going to go through one of the more + + + align:start position:0% +going to go through one of the more +complicated examples of this class so + + align:start position:0% +complicated examples of this class so + + + align:start position:0% +complicated examples of this class so +that's why I'm leaving time with time + + align:start position:0% +that's why I'm leaving time with time + + + align:start position:0% +that's why I'm leaving time with time +for it we're going to talk about + + align:start position:0% +for it we're going to talk about + + + align:start position:0% +for it we're going to talk about +decomposing a price change into an + + align:start position:0% +decomposing a price change into an + + + align:start position:0% +decomposing a price change into an +income and substitution effect and then + + align:start position:0% +income and substitution effect and then + + + align:start position:0% +income and substitution effect and then +I get we're going to do the math of this + + align:start position:0% +I get we're going to do the math of this + + + align:start position:0% +I get we're going to do the math of this +in section or did we yeah we'll do the + + align:start position:0% +in section or did we yeah we'll do the + + + align:start position:0% +in section or did we yeah we'll do the +mathematics of this in section it's hard + + align:start position:0% +mathematics of this in section it's hard + + + align:start position:0% +mathematics of this in section it's hard +enough I'll do the graphics here and the + + align:start position:0% +enough I'll do the graphics here and the + + + align:start position:0% +enough I'll do the graphics here and the +intuition the math will be covered in + + align:start position:0% +intuition the math will be covered in + + + align:start position:0% +intuition the math will be covered in +section okay so now let's go back to our + + align:start position:0% +section okay so now let's go back to our + + + align:start position:0% +section okay so now let's go back to our +classic example we start at Point a + + align:start position:0% +classic example we start at Point a + + + align:start position:0% +classic example we start at Point a +we're on original budget constraint one + + align:start position:0% +we're on original budget constraint one + + + align:start position:0% +we're on original budget constraint one +so this is figure four five look at bc1 + + align:start position:0% +so this is figure four five look at bc1 + + + align:start position:0% +so this is figure four five look at bc1 +that's original budget constraint and + + align:start position:0% +that's original budget constraint and + + + align:start position:0% +that's original budget constraint and +our indifference curve is tangent at + + align:start position:0% +our indifference curve is tangent at + + + align:start position:0% +our indifference curve is tangent at +Point a so as we've said a number of + + align:start position:0% +Point a so as we've said a number of + + + align:start position:0% +Point a so as we've said a number of +times this sem this lecture we choose + + align:start position:0% +times this sem this lecture we choose + + + align:start position:0% +times this sem this lecture we choose +six cookies and three pizzas that's our + + align:start position:0% +six cookies and three pizzas that's our + + + align:start position:0% +six cookies and three pizzas that's our +base + + align:start position:0% +base + + + align:start position:0% +base +case now imagine that the price of + + align:start position:0% +case now imagine that the price of + + + align:start position:0% +case now imagine that the price of +cookies rises from $2 to + + align:start position:0% +cookies rises from $2 to + + + align:start position:0% +cookies rises from $2 to +$3 well we know what happens we solve + + align:start position:0% +$3 well we know what happens we solve + + + align:start position:0% +$3 well we know what happens we solve +for that already earlier this lecture + + align:start position:0% +for that already earlier this lecture + + + align:start position:0% +for that already earlier this lecture +when the price cookies rise from $2 $3 + + align:start position:0% +when the price cookies rise from $2 $3 + + + align:start position:0% +when the price cookies rise from $2 $3 +we know you move from point A to point + + align:start position:0% +we know you move from point A to point + + + align:start position:0% +we know you move from point A to point +C you move from consuming six cookies + + align:start position:0% +C you move from consuming six cookies + + + align:start position:0% +C you move from consuming six cookies +and three slices of pizza of four + + align:start position:0% +and three slices of pizza of four + + + align:start position:0% +and three slices of pizza of four +cookies and three slice of pizza we + + align:start position:0% +cookies and three slice of pizza we + + + align:start position:0% +cookies and three slice of pizza we +already solve for that great you already + + align:start position:0% +already solve for that great you already + + + align:start position:0% +already solve for that great you already +know that why aren't we done + + align:start position:0% +know that why aren't we done + + + align:start position:0% +know that why aren't we done +we are done because that's composed of + + align:start position:0% +we are done because that's composed of + + + align:start position:0% +we are done because that's composed of +two effects a substitution effect and + + align:start position:0% +two effects a substitution effect and + + + align:start position:0% +two effects a substitution effect and +income effect how do we measure these + + align:start position:0% +income effect how do we measure these + + + align:start position:0% +income effect how do we measure these +well the way we do it + + align:start position:0% +well the way we do it + + + align:start position:0% +well the way we do it +graphically is we say the substitution + + align:start position:0% +graphically is we say the substitution + + + align:start position:0% +graphically is we say the substitution +effect is technically + + align:start position:0% +effect is technically + + + align:start position:0% +effect is technically +defined as the change in the quantity + + align:start position:0% +defined as the change in the quantity + + + align:start position:0% +defined as the change in the quantity +purchased holding utility constant so + + align:start position:0% +purchased holding utility constant so + + + align:start position:0% +purchased holding utility constant so +it's Delta + + align:start position:0% +it's Delta + + + align:start position:0% +it's Delta +Q at + + align:start position:0% +Q at + + + align:start position:0% +Q at +ubar holding your utility + + align:start position:0% +ubar holding your utility + + + align:start position:0% +ubar holding your utility +constant how would you change change + + align:start position:0% +constant how would you change change + + + align:start position:0% +constant how would you change change +your mix of + + align:start position:0% +your mix of + + + align:start position:0% +your mix of +goods how do we measure that we measure + + align:start position:0% +goods how do we measure that we measure + + + align:start position:0% +goods how do we measure that we measure +by drawing an imaginary budget + + align:start position:0% +by drawing an imaginary budget + + + align:start position:0% +by drawing an imaginary budget +constraint BC Prime this isn't a real + + align:start position:0% +constraint BC Prime this isn't a real + + + align:start position:0% +constraint BC Prime this isn't a real +budget constraints imaginary and we find + + align:start position:0% +budget constraints imaginary and we find + + + align:start position:0% +budget constraints imaginary and we find +the point and what is BC Prime BC Prime + + align:start position:0% +the point and what is BC Prime BC Prime + + + align:start position:0% +the point and what is BC Prime BC Prime +has two features first of all it is + + align:start position:0% +has two features first of all it is + + + align:start position:0% +has two features first of all it is +parallel to the new budget + + align:start position:0% +parallel to the new budget + + + align:start position:0% +parallel to the new budget +constraint it's parallel to the new it's + + align:start position:0% +constraint it's parallel to the new it's + + + align:start position:0% +constraint it's parallel to the new it's +got the new price ratios the slope of + + align:start position:0% +got the new price ratios the slope of + + + align:start position:0% +got the new price ratios the slope of +the new budget constraint of BC Prime is + + align:start position:0% +the new budget constraint of BC Prime is + + + align:start position:0% +the new budget constraint of BC Prime is +the same as bc2 so minus 3/4 right that + + align:start position:0% +the same as bc2 so minus 3/4 right that + + + align:start position:0% +the same as bc2 so minus 3/4 right that +was the uh the slope was uh yeah minus + + align:start position:0% +was the uh the slope was uh yeah minus + + + align:start position:0% +was the uh the slope was uh yeah minus +3/4 okay so the new budget constraint + + align:start position:0% +3/4 okay so the new budget constraint + + + align:start position:0% +3/4 okay so the new budget constraint +has a slope of minus 3/4s but it is + + align:start position:0% +has a slope of minus 3/4s but it is + + + align:start position:0% +has a slope of minus 3/4s but it is +tangent to the original indifference + + align:start position:0% +tangent to the original indifference + + + align:start position:0% +tangent to the original indifference +curve the one that contains point + + align:start position:0% +curve the one that contains point + + + align:start position:0% +curve the one that contains point +a so once again how do we measure the + + align:start position:0% +a so once again how do we measure the + + + align:start position:0% +a so once again how do we measure the +substitution effect we measure it by + + align:start position:0% +substitution effect we measure it by + + + align:start position:0% +substitution effect we measure it by +drawing a new budget constraint + + align:start position:0% +drawing a new budget constraint + + + align:start position:0% +drawing a new budget constraint +imaginary budget + + align:start position:0% +imaginary budget + + + align:start position:0% +imaginary budget +constraint that is parallel to the new + + align:start position:0% +constraint that is parallel to the new + + + align:start position:0% +constraint that is parallel to the new +budget constraint it it's the new price + + align:start position:0% +budget constraint it it's the new price + + + align:start position:0% +budget constraint it it's the new price +ratio minus 3/4 instead of minus a half + + align:start position:0% +ratio minus 3/4 instead of minus a half + + + align:start position:0% +ratio minus 3/4 instead of minus a half +but tangent to the old indifference + + align:start position:0% +but tangent to the old indifference + + + align:start position:0% +but tangent to the old indifference +curve and think about what that's doing + + align:start position:0% +curve and think about what that's doing + + + align:start position:0% +curve and think about what that's doing +we're showing you the change in qu + + align:start position:0% +we're showing you the change in qu + + + align:start position:0% +we're showing you the change in qu +quantity you get at a constant utility + + align:start position:0% +quantity you get at a constant utility + + + align:start position:0% +quantity you get at a constant utility +how do we keep utility constant we stay + + align:start position:0% +how do we keep utility constant we stay + + + align:start position:0% +how do we keep utility constant we stay +in the same indifference curve so by + + align:start position:0% +in the same indifference curve so by + + + align:start position:0% +in the same indifference curve so by +staying in the same indifference curve + + align:start position:0% +staying in the same indifference curve + + + align:start position:0% +staying in the same indifference curve +we're holding utility constant and we're + + align:start position:0% +we're holding utility constant and we're + + + align:start position:0% +we're holding utility constant and we're +showing you that even with utility + + align:start position:0% +showing you that even with utility + + + align:start position:0% +showing you that even with utility +constant you would want fewer cookies + + align:start position:0% +constant you would want fewer cookies + + + align:start position:0% +constant you would want fewer cookies +why would you want why would you want + + align:start position:0% +why would you want why would you want + + + align:start position:0% +why would you want why would you want +fewer cookies you'd move from six + + align:start position:0% +fewer cookies you'd move from six + + + align:start position:0% +fewer cookies you'd move from six +cookies to 4.89 cookies why because + + align:start position:0% +cookies to 4.89 cookies why because + + + align:start position:0% +cookies to 4.89 cookies why because +cookies have gotten more expensive Rel + + align:start position:0% +cookies have gotten more expensive Rel + + + align:start position:0% +cookies have gotten more expensive Rel +to Pizza + + align:start position:0% +to Pizza + + + align:start position:0% +to Pizza +that's the pure substance doesn't matter + + align:start position:0% +that's the pure substance doesn't matter + + + align:start position:0% +that's the pure substance doesn't matter +you're rich or poor it's just cookies + + align:start position:0% +you're rich or poor it's just cookies + + + align:start position:0% +you're rich or poor it's just cookies +have got more expensive you want fewer + + align:start position:0% +have got more expensive you want fewer + + + align:start position:0% +have got more expensive you want fewer +of + + align:start position:0% +of + + + align:start position:0% +of +them it's easy understand if we go + + align:start position:0% +them it's easy understand if we go + + + align:start position:0% +them it's easy understand if we go +directly to the second + + align:start position:0% +directly to the second + + + align:start position:0% +directly to the second +effect okay if we go directly to the + + align:start position:0% +effect okay if we go directly to the + + + align:start position:0% +effect okay if we go directly to the +second effect okay which is um oh well + + align:start position:0% +second effect okay which is um oh well + + + align:start position:0% +second effect okay which is um oh well +no actually let me do one thing first I + + align:start position:0% +no actually let me do one thing first I + + + align:start position:0% +no actually let me do one thing first I +want to First prove to + + align:start position:0% +want to First prove to + + + align:start position:0% +want to First prove to +you that the substitution effect is + + align:start position:0% +you that the substitution effect is + + + align:start position:0% +you that the substitution effect is +always + + align:start position:0% +always + + + align:start position:0% +always +negative the substitution effect is + + align:start position:0% +negative the substitution effect is + + + align:start position:0% +negative the substitution effect is +always + + align:start position:0% +always + + + align:start position:0% +always +negative okay so to prove that so + + align:start position:0% +negative okay so to prove that so + + + align:start position:0% +negative okay so to prove that so +graphically we can prove that by just + + align:start position:0% +graphically we can prove that by just + + + align:start position:0% +graphically we can prove that by just +noting that if you're on the same + + align:start position:0% +noting that if you're on the same + + + align:start position:0% +noting that if you're on the same +indifference + + align:start position:0% +indifference + + + align:start position:0% +indifference +curve and you're tangent to a steeper + + align:start position:0% +curve and you're tangent to a steeper + + + align:start position:0% +curve and you're tangent to a steeper +budget + + align:start position:0% +budget + + + align:start position:0% +budget +constraint you must be to the left right + + align:start position:0% +constraint you must be to the left right + + + align:start position:0% +constraint you must be to the left right +if I'm the same IND different Square the + + align:start position:0% +if I'm the same IND different Square the + + + align:start position:0% +if I'm the same IND different Square the +bud straight steepen I must be to the + + align:start position:0% +bud straight steepen I must be to the + + + align:start position:0% +bud straight steepen I must be to the +left of the original point so it's got + + align:start position:0% +left of the original point so it's got + + + align:start position:0% +left of the original point so it's got +to be a negative + + align:start position:0% +to be a negative + + + align:start position:0% +to be a negative +effect + + align:start position:0% +effect + + + align:start position:0% +effect +mathematically think of this in Five + + align:start position:0% +mathematically think of this in Five + + + align:start position:0% +mathematically think of this in Five +Steps step one the substitution effect + + align:start position:0% +Steps step one the substitution effect + + + align:start position:0% +Steps step one the substitution effect +puts you at the tangency of the + + align:start position:0% +puts you at the tangency of the + + + align:start position:0% +puts you at the tangency of the +difference curve in + + align:start position:0% +difference curve in + + + align:start position:0% +difference curve in +prices we know at that + + align:start position:0% +prices we know at that + + + align:start position:0% +prices we know at that +tangency that mu C over muu s + + align:start position:0% +tangency that mu C over muu s + + + align:start position:0% +tangency that mu C over muu s +equals PC over PS I just canceled the + + align:start position:0% +equals PC over PS I just canceled the + + + align:start position:0% +equals PC over PS I just canceled the +negatives okay we know those are equal + + align:start position:0% +negatives okay we know those are equal + + + align:start position:0% +negatives okay we know those are equal +at any tangency we know those are equal + + align:start position:0% +at any tangency we know those are equal + + + align:start position:0% +at any tangency we know those are equal +at every + + align:start position:0% +at every + + + align:start position:0% +at every +tangency we know that this has gone up + + align:start position:0% +tangency we know that this has gone up + + + align:start position:0% +tangency we know that this has gone up +price of cookies has gone up Rel to + + align:start position:0% +price of cookies has gone up Rel to + + + align:start position:0% +price of cookies has gone up Rel to +pizza slices right once again jump in if + + align:start position:0% +pizza slices right once again jump in if + + + align:start position:0% +pizza slices right once again jump in if +anything's not + + align:start position:0% +anything's not + + + align:start position:0% +anything's not +clear if that goes up what has to happen + + align:start position:0% +clear if that goes up what has to happen + + + align:start position:0% +clear if that goes up what has to happen +this has to go up they have to be equal + + align:start position:0% +this has to go up they have to be equal + + + align:start position:0% +this has to go up they have to be equal +the right side went up so the left side + + align:start position:0% +the right side went up so the left side + + + align:start position:0% +the right side went up so the left side +has to go up how do you make the + + align:start position:0% +has to go up how do you make the + + + align:start position:0% +has to go up how do you make the +marginal utility ratio go up how do you + + align:start position:0% +marginal utility ratio go up how do you + + + align:start position:0% +marginal utility ratio go up how do you +make it so that the ratio marginal of + + align:start position:0% +make it so that the ratio marginal of + + + align:start position:0% +make it so that the ratio marginal of +cookies the marginality of slices goes + + align:start position:0% +cookies the marginality of slices goes + + + align:start position:0% +cookies the marginality of slices goes +up what do you do how can you + + align:start position:0% +up what do you do how can you + + + align:start position:0% +up what do you do how can you +operationalize that + + align:start position:0% +operationalize that + + + align:start position:0% +operationalize that +well how do you make the numerator + + align:start position:0% +well how do you make the numerator + + + align:start position:0% +well how do you make the numerator +higher how do you make the Marge utility + + align:start position:0% +higher how do you make the Marge utility + + + align:start position:0% +higher how do you make the Marge utility +of cookies + + align:start position:0% +of cookies + + + align:start position:0% +of cookies +bigger + + align:start position:0% +bigger + + + align:start position:0% +bigger +yeah yeah remember Marge utilities are + + align:start position:0% +yeah yeah remember Marge utilities are + + + align:start position:0% +yeah yeah remember Marge utilities are +negative function of quantity I said + + align:start position:0% +negative function of quantity I said + + + align:start position:0% +negative function of quantity I said +they're confusing the fewer cookies you + + align:start position:0% +they're confusing the fewer cookies you + + + align:start position:0% +they're confusing the fewer cookies you +have the more each cookie is + + align:start position:0% +have the more each cookie is + + + align:start position:0% +have the more each cookie is +worth if you have fewer cookies that + + align:start position:0% +worth if you have fewer cookies that + + + align:start position:0% +worth if you have fewer cookies that +means you have to have more slices if + + align:start position:0% +means you have to have more slices if + + + align:start position:0% +means you have to have more slices if +you have more slices what does that do + + align:start position:0% +you have more slices what does that do + + + align:start position:0% +you have more slices what does that do +to the marginality of slices it lowers + + align:start position:0% +to the marginality of slices it lowers + + + align:start position:0% +to the marginality of slices it lowers +it so by shifting from cookies to slices + + align:start position:0% +it so by shifting from cookies to slices + + + align:start position:0% +it so by shifting from cookies to slices +you lower the r you rate I'm sorry you + + align:start position:0% +you lower the r you rate I'm sorry you + + + align:start position:0% +you lower the r you rate I'm sorry you +raise the ratio margin utilities you + + align:start position:0% +raise the ratio margin utilities you + + + align:start position:0% +raise the ratio margin utilities you +raise the numerator and lower the + + align:start position:0% +raise the numerator and lower the + + + align:start position:0% +raise the numerator and lower the +denominator through that + + align:start position:0% +denominator through that + + + align:start position:0% +denominator through that +shift so you therefore say that if + + align:start position:0% +shift so you therefore say that if + + + align:start position:0% +shift so you therefore say that if +you're going to be tangent and you're + + align:start position:0% +you're going to be tangent and you're + + + align:start position:0% +you're going to be tangent and you're +going have a higher price ratio you + + align:start position:0% +going have a higher price ratio you + + + align:start position:0% +going have a higher price ratio you +must have fewer cookies and more slices + + align:start position:0% +must have fewer cookies and more slices + + + align:start position:0% +must have fewer cookies and more slices +by definition and that's the proof that + + align:start position:0% +by definition and that's the proof that + + + align:start position:0% +by definition and that's the proof that +substitution effects are + + align:start position:0% + + + + align:start position:0% + +negative okay questions about that + + align:start position:0% + + + + align:start position:0% + +if the price goes up + + align:start position:0% +if the price goes up + + + align:start position:0% +if the price goes up +Absolutely I'll tell you that in a + + align:start position:0% +Absolutely I'll tell you that in a + + + align:start position:0% +Absolutely I'll tell you that in a +minute but this if the price goes + + align:start position:0% +minute but this if the price goes + + + align:start position:0% +minute but this if the price goes +up + + align:start position:0% + + + + align:start position:0% + +okay other questions it's a good + + align:start position:0% +okay other questions it's a good + + + align:start position:0% +okay other questions it's a good +question good clarification okay now + + align:start position:0% +question good clarification okay now + + + align:start position:0% +question good clarification okay now +let's go to the second effect the income + + align:start position:0% +let's go to the second effect the income + + + align:start position:0% +let's go to the second effect the income +effect the income effect is say is + + align:start position:0% +effect the income effect is say is + + + align:start position:0% +effect the income effect is say is +measuring the change the effect of the + + align:start position:0% +measuring the change the effect of the + + + align:start position:0% +measuring the change the effect of the +the Delta + + align:start position:0% +the Delta + + + align:start position:0% +the Delta +quantity due to income effectively + + align:start position:0% +quantity due to income effectively + + + align:start position:0% +quantity due to income effectively +Rising + + align:start position:0% +Rising + + + align:start position:0% +Rising +what do you mean income Rises your + + align:start position:0% +what do you mean income Rises your + + + align:start position:0% +what do you mean income Rises your +income hasn't changed + + align:start position:0% +income hasn't changed + + + align:start position:0% +income hasn't changed +here why is income effectively risen why + + align:start position:0% +here why is income effectively risen why + + + align:start position:0% +here why is income effectively risen why +are you effectively Rich I'm sorry um + + align:start position:0% +are you effectively Rich I'm sorry um + + + align:start position:0% +are you effectively Rich I'm sorry um +sorry the income is Fallen my bad your + + align:start position:0% +sorry the income is Fallen my bad your + + + align:start position:0% +sorry the income is Fallen my bad your +income's effectively fallen in this case + + align:start position:0% +income's effectively fallen in this case + + + align:start position:0% +income's effectively fallen in this case +why are you effectively + + align:start position:0% +why are you effectively + + + align:start position:0% +why are you effectively +poor now your income hasn't changed why + + align:start position:0% +poor now your income hasn't changed why + + + align:start position:0% +poor now your income hasn't changed why +effectively poor + + align:start position:0% +effectively poor + + + align:start position:0% +effectively poor +yeah yeah your opportunity set has been + + align:start position:0% +yeah yeah your opportunity set has been + + + align:start position:0% +yeah yeah your opportunity set has been +constricted so your income itself hasn't + + align:start position:0% +constricted so your income itself hasn't + + + align:start position:0% +constricted so your income itself hasn't +fallen but your resources have what you + + align:start position:0% +fallen but your resources have what you + + + align:start position:0% +fallen but your resources have what you +can buy with that income has fallen + + align:start position:0% +can buy with that income has fallen + + + align:start position:0% +can buy with that income has fallen +you're effectively + + align:start position:0% +you're effectively + + + align:start position:0% +you're effectively +poor so it's not really that why is + + align:start position:0% +poor so it's not really that why is + + + align:start position:0% +poor so it's not really that why is +Fallen it's sort of why over sort of the + + align:start position:0% +Fallen it's sort of why over sort of the + + + align:start position:0% +Fallen it's sort of why over sort of the +composite price you know the the price + + align:start position:0% +composite price you know the the price + + + align:start position:0% +composite price you know the the price +level has fallen why over the price + + align:start position:0% +level has fallen why over the price + + + align:start position:0% +level has fallen why over the price +levels Fallen the overall price level in + + align:start position:0% +levels Fallen the overall price level in + + + align:start position:0% +levels Fallen the overall price level in +society's increased pizza's the same + + align:start position:0% +society's increased pizza's the same + + + align:start position:0% +society's increased pizza's the same +cookies are up so your effective income + + align:start position:0% +cookies are up so your effective income + + + align:start position:0% +cookies are up so your effective income +is Fallen your real income is + + align:start position:0% +is Fallen your real income is + + + align:start position:0% +is Fallen your real income is +Fallen okay you're effectively poor what + + align:start position:0% +Fallen okay you're effectively poor what + + + align:start position:0% +Fallen okay you're effectively poor what +does that mean if you're effectively + + align:start position:0% +does that mean if you're effectively + + + align:start position:0% +does that mean if you're effectively +poor what's going to happen + + align:start position:0% +poor what's going to happen + + + align:start position:0% +poor what's going to happen +well what does that depend on that + + align:start position:0% +well what does that depend on that + + + align:start position:0% +well what does that depend on that +depends + + align:start position:0% +depends + + + align:start position:0% +depends +on + + align:start position:0% +on + + + align:start position:0% +on +this that's why I bother telling you so + + align:start position:0% +this that's why I bother telling you so + + + align:start position:0% +this that's why I bother telling you so +I'm a big Dr Seuss fan okay basically if + + align:start position:0% +I'm a big Dr Seuss fan okay basically if + + + align:start position:0% +I'm a big Dr Seuss fan okay basically if +it's a normal + + align:start position:0% +it's a normal + + + align:start position:0% +it's a normal +good and the and your income goes down + + align:start position:0% +good and the and your income goes down + + + align:start position:0% +good and the and your income goes down +what will you do you'll have less of it + + align:start position:0% +what will you do you'll have less of it + + + align:start position:0% +what will you do you'll have less of it +but if it's an inferior good and income + + align:start position:0% +but if it's an inferior good and income + + + align:start position:0% +but if it's an inferior good and income +goes down what will you do you'll have + + align:start position:0% +goes down what will you do you'll have + + + align:start position:0% +goes down what will you do you'll have +more of it so while the substitution + + align:start position:0% +more of it so while the substitution + + + align:start position:0% +more of it so while the substitution +effect can be signed the income effect + + align:start position:0% +effect can be signed the income effect + + + align:start position:0% +effect can be signed the income effect +cannot the in effect cannot be signed + + align:start position:0% +cannot the in effect cannot be signed + + + align:start position:0% +cannot the in effect cannot be signed +because it depends on whether it's a + + align:start position:0% +because it depends on whether it's a + + + align:start position:0% +because it depends on whether it's a +normal or inferior + + align:start position:0% +normal or inferior + + + align:start position:0% +normal or inferior +good + + align:start position:0% +good + + + align:start position:0% +good +okay in the case we're showing here in + + align:start position:0% +okay in the case we're showing here in + + + align:start position:0% +okay in the case we're showing here in +figure four five this is a normal good + + align:start position:0% +figure four five this is a normal good + + + align:start position:0% +figure four five this is a normal good +so the income effect works in tandem + + align:start position:0% +so the income effect works in tandem + + + align:start position:0% +so the income effect works in tandem +with the substitution effect the + + align:start position:0% +with the substitution effect the + + + align:start position:0% +with the substitution effect the +substitution effect you want so you want + + align:start position:0% +substitution effect you want so you want + + + align:start position:0% +substitution effect you want so you want +fewer cookies for two reasons let's + + align:start position:0% +fewer cookies for two reasons let's + + + align:start position:0% +fewer cookies for two reasons let's +here's the intuition here's the key + + align:start position:0% +here's the intuition here's the key + + + align:start position:0% +here's the intuition here's the key +intuition you want fewer cookies for two + + align:start position:0% +intuition you want fewer cookies for two + + + align:start position:0% +intuition you want fewer cookies for two +reasons first cookies are a worse deal + + align:start position:0% +reasons first cookies are a worse deal + + + align:start position:0% +reasons first cookies are a worse deal +you have the opportunity cost of cookies + + align:start position:0% +you have the opportunity cost of cookies + + + align:start position:0% +you have the opportunity cost of cookies +has + + align:start position:0% +has + + + align:start position:0% +has +risen second you're effectively poorer + + align:start position:0% +risen second you're effectively poorer + + + align:start position:0% +risen second you're effectively poorer +your opportunity set is constricted and + + align:start position:0% +your opportunity set is constricted and + + + align:start position:0% +your opportunity set is constricted and +cookies are normal good so for those two + + align:start position:0% +cookies are normal good so for those two + + + align:start position:0% +cookies are normal good so for those two +reasons you want fewer + + align:start position:0% +reasons you want fewer + + + align:start position:0% +reasons you want fewer +cookies but what if cookies were an + + align:start position:0% +cookies but what if cookies were an + + + align:start position:0% +cookies but what if cookies were an +inferior good then the graph would look + + align:start position:0% +inferior good then the graph would look + + + align:start position:0% +inferior good then the graph would look +like figure + + align:start position:0% +like figure + + + align:start position:0% +like figure +46 the graph like figure 46 in this case + + align:start position:0% +46 the graph like figure 46 in this case + + + align:start position:0% +46 the graph like figure 46 in this case +the substitution effect would go one way + + align:start position:0% +the substitution effect would go one way + + + align:start position:0% +the substitution effect would go one way +but the income effect would go the other + + align:start position:0% +but the income effect would go the other + + + align:start position:0% +but the income effect would go the other +way and the net would be + + align:start position:0% +way and the net would be + + + align:start position:0% +way and the net would be +unclear now we've drawn figure 46 such + + align:start position:0% +unclear now we've drawn figure 46 such + + + align:start position:0% +unclear now we've drawn figure 46 such +that the demand for cookie still Falls + + align:start position:0% +that the demand for cookie still Falls + + + align:start position:0% +that the demand for cookie still Falls +but you don't have to draw it that + + align:start position:0% +but you don't have to draw it that + + + align:start position:0% +but you don't have to draw it that +way okay so the key thing is the + + align:start position:0% +way okay so the key thing is the + + + align:start position:0% +way okay so the key thing is the +substitution effect has to be the + + align:start position:0% +substitution effect has to be the + + + align:start position:0% +substitution effect has to be the +opposite of the sign of the price change + + align:start position:0% +opposite of the sign of the price change + + + align:start position:0% +opposite of the sign of the price change +negative but let's be clear it's good + + align:start position:0% +negative but let's be clear it's good + + + align:start position:0% +negative but let's be clear it's good +clarification Subs effect has to be the + + align:start position:0% +clarification Subs effect has to be the + + + align:start position:0% +clarification Subs effect has to be the +opposite of the sign of the price change + + align:start position:0% +opposite of the sign of the price change + + + align:start position:0% +opposite of the sign of the price change +the income effect does not think effect + + align:start position:0% +the income effect does not think effect + + + align:start position:0% +the income effect does not think effect +depends on whether it's a normal or + + align:start position:0% +depends on whether it's a normal or + + + align:start position:0% +depends on whether it's a normal or +inferior + + align:start position:0% +inferior + + + align:start position:0% +inferior +good this is pretty confusing so I find + + align:start position:0% +good this is pretty confusing so I find + + + align:start position:0% +good this is pretty confusing so I find +it's useful to um to actually uh think + + align:start position:0% +it's useful to um to actually uh think + + + align:start position:0% +it's useful to um to actually uh think +about well let's let's actually rush + + align:start position:0% +about well let's let's actually rush + + + align:start position:0% +about well let's let's actually rush +through figure 4 six let's what figure + + align:start position:0% +through figure 4 six let's what figure + + + align:start position:0% +through figure 4 six let's what figure +46 is because it's not this I I I rush + + align:start position:0% +46 is because it's not this I I I rush + + + align:start position:0% +46 is because it's not this I I I rush +you figure 46 let's go back figure 46 is + + align:start position:0% +you figure 46 let's go back figure 46 is + + + align:start position:0% +you figure 46 let's go back figure 46 is +no longer pizza and cookies figure 46 is + + align:start position:0% +no longer pizza and cookies figure 46 is + + + align:start position:0% +no longer pizza and cookies figure 46 is +now steak and potatoes okay because + + align:start position:0% +now steak and potatoes okay because + + + align:start position:0% +now steak and potatoes okay because +pizza and cookies are both normal Goods + + align:start position:0% +pizza and cookies are both normal Goods + + + align:start position:0% +pizza and cookies are both normal Goods +potatoes is the classic inferior + + align:start position:0% +potatoes is the classic inferior + + + align:start position:0% +potatoes is the classic inferior +good right poor people especially back + + align:start position:0% +good right poor people especially back + + + align:start position:0% +good right poor people especially back +in the day used to have to eat potatoes + + align:start position:0% +in the day used to have to eat potatoes + + + align:start position:0% +in the day used to have to eat potatoes +because they were cheap to grow and very + + align:start position:0% +because they were cheap to grow and very + + + align:start position:0% +because they were cheap to grow and very +filling and steak was + + align:start position:0% +filling and steak was + + + align:start position:0% +filling and steak was +unaffordable but basically as you get + + align:start position:0% +unaffordable but basically as you get + + + align:start position:0% +unaffordable but basically as you get +richer you want fewer potatoes and more + + align:start position:0% +richer you want fewer potatoes and more + + + align:start position:0% +richer you want fewer potatoes and more +steak okay especially an Agricultural + + align:start position:0% +steak okay especially an Agricultural + + + align:start position:0% +steak okay especially an Agricultural +Society okay so let's say originally + + align:start position:0% +Society okay so let's say originally + + + align:start position:0% +Society okay so let's say originally +people are at + + align:start position:0% +people are at + + + align:start position:0% +people are at +bc1 where the price of steak is $5 the + + align:start position:0% +bc1 where the price of steak is $5 the + + + align:start position:0% +bc1 where the price of steak is $5 the +price of potatoes a + + align:start position:0% +price of potatoes a + + + align:start position:0% +price of potatoes a +dollar the price of steak is $5 the + + align:start position:0% +dollar the price of steak is $5 the + + + align:start position:0% +dollar the price of steak is $5 the +price of potato is a dollar and let's + + align:start position:0% +price of potato is a dollar and let's + + + align:start position:0% +price of potato is a dollar and let's +say their income is $25 so in this + + align:start position:0% +say their income is $25 so in this + + + align:start position:0% +say their income is $25 so in this +example incomes + + align:start position:0% +example incomes + + + align:start position:0% +example incomes +25 the price of a stake + + align:start position:0% +25 the price of a stake + + + align:start position:0% +25 the price of a stake +is five and the price of + + align:start position:0% +is five and the price of + + + align:start position:0% +is five and the price of +potatoes is + + align:start position:0% +potatoes is + + + align:start position:0% +potatoes is +one okay so the budget constraint looks + + align:start position:0% +one okay so the budget constraint looks + + + align:start position:0% +one okay so the budget constraint looks +like + + align:start position:0% +like + + + align:start position:0% +like +bc1 you can have for $25 you can have 25 + + align:start position:0% +bc1 you can have for $25 you can have 25 + + + align:start position:0% +bc1 you can have for $25 you can have 25 +potatoes or five + + align:start position:0% +potatoes or five + + + align:start position:0% +potatoes or five +steaks and let's say your preferences + + align:start position:0% +steaks and let's say your preferences + + + align:start position:0% +steaks and let's say your preferences +are such that you end up at Point a you + + align:start position:0% +are such that you end up at Point a you + + + align:start position:0% +are such that you end up at Point a you +choose to have three and a half steaks + + align:start position:0% +choose to have three and a half steaks + + + align:start position:0% +choose to have three and a half steaks +and seven and a half potatoes okay once + + align:start position:0% +and seven and a half potatoes okay once + + + align:start position:0% +and seven and a half potatoes okay once +again I just got that through the magic + + align:start position:0% +again I just got that through the magic + + + align:start position:0% +again I just got that through the magic +we showed you last time this is + + align:start position:0% +we showed you last time this is + + + align:start position:0% +we showed you last time this is +constrained optimization I'm not writing + + align:start position:0% +constrained optimization I'm not writing + + + align:start position:0% +constrained optimization I'm not writing +down the utility function I'm just going + + align:start position:0% +down the utility function I'm just going + + + align:start position:0% +down the utility function I'm just going +right to the results but you know how to + + align:start position:0% +right to the results but you know how to + + + align:start position:0% +right to the results but you know how to +get there + + align:start position:0% +get there + + + align:start position:0% +get there +now let's say that things change and the + + align:start position:0% +now let's say that things change and the + + + align:start position:0% +now let's say that things change and the +price of potatoes rise to $3 a + + align:start position:0% +price of potatoes rise to $3 a + + + align:start position:0% +price of potatoes rise to $3 a +pound steak is still five bucks a pound + + align:start position:0% +pound steak is still five bucks a pound + + + align:start position:0% +pound steak is still five bucks a pound +potatoes are now $3 a pound now what + + align:start position:0% +potatoes are now $3 a pound now what + + + align:start position:0% +potatoes are now $3 a pound now what +happens is your budget strange shifts + + align:start position:0% +happens is your budget strange shifts + + + align:start position:0% +happens is your budget strange shifts +into + + align:start position:0% + + + + align:start position:0% + +bc2 your budget constraint is pivoted in + + align:start position:0% +bc2 your budget constraint is pivoted in + + + align:start position:0% +bc2 your budget constraint is pivoted in +massively so now you still have five + + align:start position:0% +massively so now you still have five + + + align:start position:0% +massively so now you still have five +Stakes of all you want is stake but you + + align:start position:0% +Stakes of all you want is stake but you + + + align:start position:0% +Stakes of all you want is stake but you +can only have 8.3 potatoes on your $25 + + align:start position:0% +can only have 8.3 potatoes on your $25 + + + align:start position:0% +can only have 8.3 potatoes on your $25 +of income new budget screen is bc2 + + align:start position:0% +of income new budget screen is bc2 + + + align:start position:0% +of income new budget screen is bc2 +what happens well let's look at the + + align:start position:0% +what happens well let's look at the + + + align:start position:0% +what happens well let's look at the +income and substitution effects the + + align:start position:0% +income and substitution effects the + + + align:start position:0% +income and substitution effects the +substitution effect we get by drawing an + + align:start position:0% +substitution effect we get by drawing an + + + align:start position:0% +substitution effect we get by drawing an +imaginary budget constraint BC Prime + + align:start position:0% +imaginary budget constraint BC Prime + + + align:start position:0% +imaginary budget constraint BC Prime +what are the features of BC prime it is + + align:start position:0% +what are the features of BC prime it is + + + align:start position:0% +what are the features of BC prime it is +parallel to the new budget + + align:start position:0% +parallel to the new budget + + + align:start position:0% +parallel to the new budget +constraint but tangent to the old + + align:start position:0% +constraint but tangent to the old + + + align:start position:0% +constraint but tangent to the old +indifference curve and so that puts us + + align:start position:0% +indifference curve and so that puts us + + + align:start position:0% +indifference curve and so that puts us +at point B so substitution effect lowers + + align:start position:0% +at point B so substitution effect lowers + + + align:start position:0% +at point B so substitution effect lowers +our demand for for + + align:start position:0% +our demand for for + + + align:start position:0% +our demand for for +potatoes from 7 and2 to four we knew had + + align:start position:0% +potatoes from 7 and2 to four we knew had + + + align:start position:0% +potatoes from 7 and2 to four we knew had +to lower it subst effect is + + align:start position:0% +to lower it subst effect is + + + align:start position:0% +to lower it subst effect is +unambiguously signed the price went up + + align:start position:0% +unambiguously signed the price went up + + + align:start position:0% +unambiguously signed the price went up +so you got to have few of them that's + + align:start position:0% +so you got to have few of them that's + + + align:start position:0% +so you got to have few of them that's +unambiguous the income effect however + + align:start position:0% +unambiguous the income effect however + + + align:start position:0% +unambiguous the income effect however +goes the other way because potatoes are + + align:start position:0% +goes the other way because potatoes are + + + align:start position:0% +goes the other way because potatoes are +inferior in other words now that you're + + align:start position:0% +inferior in other words now that you're + + + align:start position:0% +inferior in other words now that you're +so poor now potatoes so expensive you + + align:start position:0% +so poor now potatoes so expensive you + + + align:start position:0% +so poor now potatoes so expensive you +don't have money for steak anymore so + + align:start position:0% +don't have money for steak anymore so + + + align:start position:0% +don't have money for steak anymore so +you gotta have more potatoes it's ironic + + align:start position:0% +you gotta have more potatoes it's ironic + + + align:start position:0% +you gotta have more potatoes it's ironic +right but basically potatoes getting + + align:start position:0% +right but basically potatoes getting + + + align:start position:0% +right but basically potatoes getting +expensive has made you poor when you're + + align:start position:0% +expensive has made you poor when you're + + + align:start position:0% +expensive has made you poor when you're +poor you got to have more + + align:start position:0% +poor you got to have more + + + align:start position:0% +poor you got to have more +potatoes okay and so the income effect + + align:start position:0% +potatoes okay and so the income effect + + + align:start position:0% +potatoes okay and so the income effect +goes the other way because potatoes are + + align:start position:0% +goes the other way because potatoes are + + + align:start position:0% +goes the other way because potatoes are +an inferior good effect takes you back + + align:start position:0% +an inferior good effect takes you back + + + align:start position:0% +an inferior good effect takes you back +from wanting four potatoes up to wanting + + align:start position:0% +from wanting four potatoes up to wanting + + + align:start position:0% +from wanting four potatoes up to wanting +five potatoes so the net effect if we + + align:start position:0% +five potatoes so the net effect if we + + + align:start position:0% +five potatoes so the net effect if we +didn't income substitution would we just + + align:start position:0% +didn't income substitution would we just + + + align:start position:0% +didn't income substitution would we just +see well with your demand curve would + + align:start position:0% +see well with your demand curve would + + + align:start position:0% +see well with your demand curve would +just say oh well you know demand curve + + align:start position:0% +just say oh well you know demand curve + + + align:start position:0% +just say oh well you know demand curve +slop down it's you know we get a higher + + align:start position:0% +slop down it's you know we get a higher + + + align:start position:0% +slop down it's you know we get a higher +price leads to fewer potatoes but we + + align:start position:0% +price leads to fewer potatoes but we + + + align:start position:0% +price leads to fewer potatoes but we +miss the fact that the substitution + + align:start position:0% +miss the fact that the substitution + + + align:start position:0% +miss the fact that the substitution +effects are going opposite + + align:start position:0% +effects are going opposite + + + align:start position:0% +effects are going opposite +directions okay questions about that + + align:start position:0% +directions okay questions about that + + + align:start position:0% +directions okay questions about that +example + + align:start position:0% + + + + align:start position:0% + +yeah they're all price going there's the + + align:start position:0% +yeah they're all price going there's the + + + align:start position:0% +yeah they're all price going there's the +price of potatoes going up to three from + + align:start position:0% +price of potatoes going up to three from + + + align:start position:0% +price of potatoes going up to three from +I'm sorry the price of potatoes went + + align:start position:0% +I'm sorry the price of potatoes went + + + align:start position:0% +I'm sorry the price of potatoes went +from one to + + align:start position:0% +from one to + + + align:start position:0% +from one to +three okay Price p went from one to + + align:start position:0% +three okay Price p went from one to + + + align:start position:0% +three okay Price p went from one to +three that led to a substition effect + + align:start position:0% +three that led to a substition effect + + + align:start position:0% +three that led to a substition effect +that we know which way it goes when a + + align:start position:0% +that we know which way it goes when a + + + align:start position:0% +that we know which way it goes when a +price goes up you want less of something + + align:start position:0% +price goes up you want less of something + + + align:start position:0% +price goes up you want less of something +the substitution effect but an income + + align:start position:0% +the substitution effect but an income + + + align:start position:0% +the substitution effect but an income +effect that went the other way now that + + align:start position:0% +effect that went the other way now that + + + align:start position:0% +effect that went the other way now that +leads the natural question can you + + align:start position:0% +leads the natural question can you + + + align:start position:0% +leads the natural question can you +actually get an income effect for an + + align:start position:0% +actually get an income effect for an + + + align:start position:0% +actually get an income effect for an +inferior good that ends up bigger than + + align:start position:0% +inferior good that ends up bigger than + + + align:start position:0% +inferior good that ends up bigger than +the substitution effect that is Could + + align:start position:0% +the substitution effect that is Could + + + align:start position:0% +the substitution effect that is Could +you actually get get demand curves to + + align:start position:0% +you actually get get demand curves to + + + align:start position:0% +you actually get get demand curves to +not slope down think about what would + + align:start position:0% +not slope down think about what would + + + align:start position:0% +not slope down think about what would +happen if the income effect was so big + + align:start position:0% +happen if the income effect was so big + + + align:start position:0% +happen if the income effect was so big +that it pushed you past the original + + align:start position:0% +that it pushed you past the original + + + align:start position:0% +that it pushed you past the original +point it pushed you to the right past + + align:start position:0% +point it pushed you to the right past + + + align:start position:0% +point it pushed you to the right past +the original intersection well that + + align:start position:0% +the original intersection well that + + + align:start position:0% +the original intersection well that +would imply something funky that would + + align:start position:0% +would imply something funky that would + + + align:start position:0% +would imply something funky that would +imply demand curve slope down demand + + align:start position:0% +imply demand curve slope down demand + + + align:start position:0% +imply demand curve slope down demand +curve slope up instead of sloping down + + align:start position:0% +curve slope up instead of sloping down + + + align:start position:0% +curve slope up instead of sloping down +then apply demand curve slope up that + + align:start position:0% +then apply demand curve slope up that + + + align:start position:0% +then apply demand curve slope up that +would say higher prices make you want + + align:start position:0% +would say higher prices make you want + + + align:start position:0% +would say higher prices make you want +more of something which violates what we + + align:start position:0% +more of something which violates what we + + + align:start position:0% +more of something which violates what we +the very first lecture of this class we + + align:start position:0% +the very first lecture of this class we + + + align:start position:0% +the very first lecture of this class we +said domain curves slop + + align:start position:0% +said domain curves slop + + + align:start position:0% +said domain curves slop +down but it's possible theoretically + + align:start position:0% +down but it's possible theoretically + + + align:start position:0% +down but it's possible theoretically +that you can get what's called a gfin + + align:start position:0% + + + + align:start position:0% + +good a gfin good is a good where the + + align:start position:0% +good a gfin good is a good where the + + + align:start position:0% +good a gfin good is a good where the +income effect the good is so + + align:start position:0% +income effect the good is so + + + align:start position:0% +income effect the good is so +inferior that the income effect + + align:start position:0% +inferior that the income effect + + + align:start position:0% +inferior that the income effect +dominates the substitution effect you + + align:start position:0% +dominates the substitution effect you + + + align:start position:0% +dominates the substitution effect you +end up with a wrong signed relationship + + align:start position:0% +end up with a wrong signed relationship + + + align:start position:0% +end up with a wrong signed relationship +between price and demand you actually + + align:start position:0% +between price and demand you actually + + + align:start position:0% +between price and demand you actually +get that a higher price leads to more + + align:start position:0% +get that a higher price leads to more + + + align:start position:0% +get that a higher price leads to more +demand or an upward sloping demand + + align:start position:0% +demand or an upward sloping demand + + + align:start position:0% +demand or an upward sloping demand +curve now can that happen well I like to + + align:start position:0% +curve now can that happen well I like to + + + align:start position:0% +curve now can that happen well I like to +I like the name GF and because it rhymes + + align:start position:0% +I like the name GF and because it rhymes + + + align:start position:0% +I like the name GF and because it rhymes +with Griffin and Griffins are + + align:start position:0% +with Griffin and Griffins are + + + align:start position:0% +with Griffin and Griffins are +imaginary okay GI and goods are also + + align:start position:0% +imaginary okay GI and goods are also + + + align:start position:0% +imaginary okay GI and goods are also +largely imaginary it's a great + + align:start position:0% +largely imaginary it's a great + + + align:start position:0% +largely imaginary it's a great +theoretical concept but they don't + + align:start position:0% +theoretical concept but they don't + + + align:start position:0% +theoretical concept but they don't +really exist + + align:start position:0% +really exist + + + align:start position:0% +really exist +yeah a VIN Goods is a different Vin + + align:start position:0% +yeah a VIN Goods is a different Vin + + + align:start position:0% +yeah a VIN Goods is a different Vin +that's a totally different concept + + align:start position:0% +that's a totally different concept + + + align:start position:0% +that's a totally different concept +that's that's the concept that basically + + align:start position:0% +that's that's the concept that basically + + + align:start position:0% +that's that's the concept that basically +you want more when the price is up + + align:start position:0% +you want more when the price is up + + + align:start position:0% +you want more when the price is up +because you care about your social + + align:start position:0% +because you care about your social + + + align:start position:0% +because you care about your social +standing uh but that's that's sort of a + + align:start position:0% +standing uh but that's that's sort of a + + + align:start position:0% +standing uh but that's that's sort of a +behavioral economics thing we'll come + + align:start position:0% +behavioral economics thing we'll come + + + align:start position:0% +behavioral economics thing we'll come +back to that talk behav it's not a + + align:start position:0% +back to that talk behav it's not a + + + align:start position:0% +back to that talk behav it's not a +standard economics + + align:start position:0% +standard economics + + + align:start position:0% +standard economics +effect so GI and goods really don't + + align:start position:0% +effect so GI and goods really don't + + + align:start position:0% +effect so GI and goods really don't +exist um the classic example people + + align:start position:0% +exist um the classic example people + + + align:start position:0% +exist um the classic example people +often have had was well gee when the + + align:start position:0% +often have had was well gee when the + + + align:start position:0% +often have had was well gee when the +price of + + align:start position:0% +price of + + + align:start position:0% +price of +potatoes um went up uh in Ireland cuz + + align:start position:0% +potatoes um went up uh in Ireland cuz + + + align:start position:0% +potatoes um went up uh in Ireland cuz +the potato blight people ended up + + align:start position:0% +the potato blight people ended up + + + align:start position:0% +the potato blight people ended up +consuming more potatoes so potato + + align:start position:0% +consuming more potatoes so potato + + + align:start position:0% +consuming more potatoes so potato +consumption went up per person in + + align:start position:0% +consumption went up per person in + + + align:start position:0% +consumption went up per person in +Ireland when the price of potatoes went + + align:start position:0% +Ireland when the price of potatoes went + + + align:start position:0% +Ireland when the price of potatoes went +up during the potato blight people said + + align:start position:0% +up during the potato blight people said + + + align:start position:0% +up during the potato blight people said +aha potatoes are a GI and good but + + align:start position:0% +aha potatoes are a GI and good but + + + align:start position:0% +aha potatoes are a GI and good but +here's what they got wrong here's where + + align:start position:0% +here's what they got wrong here's where + + + align:start position:0% +here's what they got wrong here's where +empirical economics is fun they missed + + align:start position:0% +empirical economics is fun they missed + + + align:start position:0% +empirical economics is fun they missed +the fact that what other effect did the + + align:start position:0% +the fact that what other effect did the + + + align:start position:0% +the fact that what other effect did the +potato blight have it chased all the + + align:start position:0% +potato blight have it chased all the + + + align:start position:0% +potato blight have it chased all the +people who could afford it out of + + align:start position:0% +people who could afford it out of + + + align:start position:0% +people who could afford it out of +Ireland the only people who left were + + align:start position:0% +Ireland the only people who left were + + + align:start position:0% +Ireland the only people who left were +super poor so yeah so yeah on average + + align:start position:0% +super poor so yeah so yeah on average + + + align:start position:0% +super poor so yeah so yeah on average +potatoes per person went up but it + + align:start position:0% +potatoes per person went up but it + + + align:start position:0% +potatoes per person went up but it +wasn't that each person consume more + + align:start position:0% +wasn't that each person consume more + + + align:start position:0% +wasn't that each person consume more +it's just people who didn't consume many + + align:start position:0% +it's just people who didn't consume many + + + align:start position:0% +it's just people who didn't consume many +potatoes left all people left were just + + align:start position:0% +potatoes left all people left were just + + + align:start position:0% +potatoes left all people left were just +huge potato consumers so if you look at + + align:start position:0% +huge potato consumers so if you look at + + + align:start position:0% +huge potato consumers so if you look at +the data you see potatoes per capita + + align:start position:0% +the data you see potatoes per capita + + + align:start position:0% +the data you see potatoes per capita +went up it's a given good what you're + + align:start position:0% +went up it's a given good what you're + + + align:start position:0% +went up it's a given good what you're +missing is the Capas are + + align:start position:0% +missing is the Capas are + + + align:start position:0% +missing is the Capas are +different each person eat more potatoes + + align:start position:0% +different each person eat more potatoes + + + align:start position:0% +different each person eat more potatoes +it's just the non-p poat eaters left + + align:start position:0% +it's just the non-p poat eaters left + + + align:start position:0% +it's just the non-p poat eaters left +people left with The Potato Eaters and + + align:start position:0% +people left with The Potato Eaters and + + + align:start position:0% +people left with The Potato Eaters and +that's why empirical economics is fun + + align:start position:0% +that's why empirical economics is fun + + + align:start position:0% +that's why empirical economics is fun +because it can help explain these kind + + align:start position:0% +because it can help explain these kind + + + align:start position:0% +because it can help explain these kind +of anomalies so where does this leave us + + align:start position:0% +of anomalies so where does this leave us + + + align:start position:0% +of anomalies so where does this leave us +let's draw let's draw a chart here to + + align:start position:0% +let's draw let's draw a chart here to + + + align:start position:0% +let's draw let's draw a chart here to +explain this all okay so this let's + + align:start position:0% +explain this all okay so this let's + + + align:start position:0% +explain this all okay so this let's +imagine we're going to have here the + + align:start position:0% +imagine we're going to have here the + + + align:start position:0% +imagine we're going to have here the +price + + align:start position:0% +price + + + align:start position:0% +price +change the price change we're going to + + align:start position:0% +change the price change we're going to + + + align:start position:0% +change the price change we're going to +have the substitution + + align:start position:0% +have the substitution + + + align:start position:0% +have the substitution +effect the income + + align:start position:0% +effect the income + + + align:start position:0% +effect the income +effect and the net + + align:start position:0% +effect and the net + + + align:start position:0% +effect and the net +effect okay and we're going to start + + align:start position:0% +effect okay and we're going to start + + + align:start position:0% +effect okay and we're going to start +with normal + + align:start position:0% +with normal + + + align:start position:0% +with normal +Goods we're start with normal Goods so + + align:start position:0% +Goods we're start with normal Goods so + + + align:start position:0% +Goods we're start with normal Goods so +with normal Goods if the price goes up + + align:start position:0% +with normal Goods if the price goes up + + + align:start position:0% +with normal Goods if the price goes up +like I just showed you + + align:start position:0% +like I just showed you + + + align:start position:0% +like I just showed you +the subs effect must be negative must be + + align:start position:0% +the subs effect must be negative must be + + + align:start position:0% +the subs effect must be negative must be +the opposite of the price + + align:start position:0% +the opposite of the price + + + align:start position:0% +the opposite of the price +change the income + + align:start position:0% +change the income + + + align:start position:0% +change the income +effect if it's a normal good must also + + align:start position:0% +effect if it's a normal good must also + + + align:start position:0% +effect if it's a normal good must also +be + + align:start position:0% +be + + + align:start position:0% +be +negative therefore on net you get a + + align:start position:0% +negative therefore on net you get a + + + align:start position:0% +negative therefore on net you get a +higher price leads to lower + + align:start position:0% +higher price leads to lower + + + align:start position:0% +higher price leads to lower +demand likewise if the price goes down + + align:start position:0% +demand likewise if the price goes down + + + align:start position:0% +demand likewise if the price goes down +this is what this good this good + + align:start position:0% +this is what this good this good + + + align:start position:0% +this is what this good this good +question was highlighting I was just + + align:start position:0% +question was highlighting I was just + + + align:start position:0% +question was highlighting I was just +looking a price going up well in that + + align:start position:0% +looking a price going up well in that + + + align:start position:0% +looking a price going up well in that +case the substitution effect let's think + + align:start position:0% +case the substitution effect let's think + + + align:start position:0% +case the substitution effect let's think +about the + + align:start position:0% +about the + + + align:start position:0% +about the +intuition if the price of cookies went + + align:start position:0% +intuition if the price of cookies went + + + align:start position:0% +intuition if the price of cookies went +down we have just lowered the + + align:start position:0% +down we have just lowered the + + + align:start position:0% +down we have just lowered the +opportunity cost of having + + align:start position:0% +opportunity cost of having + + + align:start position:0% +opportunity cost of having +cookies therefore we're going to want + + align:start position:0% +cookies therefore we're going to want + + + align:start position:0% +cookies therefore we're going to want +more cookies and fewer Pizza through the + + align:start position:0% +more cookies and fewer Pizza through the + + + align:start position:0% +more cookies and fewer Pizza through the +substitution effect so therefore the + + align:start position:0% +substitution effect so therefore the + + + align:start position:0% +substitution effect so therefore the +substitution effect will be positive if + + align:start position:0% +substitution effect will be positive if + + + align:start position:0% +substitution effect will be positive if +the price goes down the income effect + + align:start position:0% +the price goes down the income effect + + + align:start position:0% +the price goes down the income effect +will also be positive why why the income + + align:start position:0% +will also be positive why why the income + + + align:start position:0% +will also be positive why why the income +effect be positive if the price of + + align:start position:0% +effect be positive if the price of + + + align:start position:0% +effect be positive if the price of +cookies goes + + align:start position:0% +cookies goes + + + align:start position:0% +cookies goes +down why the income effect be positive + + align:start position:0% +down why the income effect be positive + + + align:start position:0% +down why the income effect be positive +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +you're effectively richer you can buy + + align:start position:0% +you're effectively richer you can buy + + + align:start position:0% +you're effectively richer you can buy +more cookies with the same money since + + align:start position:0% +more cookies with the same money since + + + align:start position:0% +more cookies with the same money since +you're richer you want more normal Goods + + align:start position:0% +you're richer you want more normal Goods + + + align:start position:0% +you're richer you want more normal Goods +cookies are normal good you want more + + align:start position:0% +cookies are normal good you want more + + + align:start position:0% +cookies are normal good you want more +cookies so this goes + + align:start position:0% +cookies so this goes + + + align:start position:0% +cookies so this goes +up now what's more interesting is what + + align:start position:0% +up now what's more interesting is what + + + align:start position:0% +up now what's more interesting is what +if these goods were inferior what if + + align:start position:0% +if these goods were inferior what if + + + align:start position:0% +if these goods were inferior what if +cookies were + + align:start position:0% +cookies were + + + align:start position:0% +cookies were +inferior so now when the price goes + + align:start position:0% +inferior so now when the price goes + + + align:start position:0% +inferior so now when the price goes +up what happens to substitution effect + + align:start position:0% +up what happens to substitution effect + + + align:start position:0% +up what happens to substitution effect +through Subs effect is demand it goes + + align:start position:0% +through Subs effect is demand it goes + + + align:start position:0% +through Subs effect is demand it goes +down as this gentleman helpfully pointed + + align:start position:0% +down as this gentleman helpfully pointed + + + align:start position:0% +down as this gentleman helpfully pointed +it goes down why because we know the + + align:start position:0% +it goes down why because we know the + + + align:start position:0% +it goes down why because we know the +sign of substitution effects they're + + align:start position:0% +sign of substitution effects they're + + + align:start position:0% +sign of substitution effects they're +always the opposite of the price change + + align:start position:0% +always the opposite of the price change + + + align:start position:0% +always the opposite of the price change +no mystery there price goes up + + align:start position:0% +no mystery there price goes up + + + align:start position:0% +no mystery there price goes up +substitution effects are Subs effect + + align:start position:0% +substitution effects are Subs effect + + + align:start position:0% +substitution effects are Subs effect +drives demand down price goes down + + align:start position:0% +drives demand down price goes down + + + align:start position:0% +drives demand down price goes down +substitution effect um I'm sorry goes up + + align:start position:0% +substitution effect um I'm sorry goes up + + + align:start position:0% +substitution effect um I'm sorry goes up +yeah right PR price goes up Subs effect + + align:start position:0% +yeah right PR price goes up Subs effect + + + align:start position:0% +yeah right PR price goes up Subs effect +drives demand down price goes down + + align:start position:0% +drives demand down price goes down + + + align:start position:0% +drives demand down price goes down +substitute effect drives demand up those + + align:start position:0% +substitute effect drives demand up those + + + align:start position:0% +substitute effect drives demand up those +never change so here if the price goes + + align:start position:0% +never change so here if the price goes + + + align:start position:0% +never change so here if the price goes +down substitute effect will be positive + + align:start position:0% +down substitute effect will be positive + + + align:start position:0% +down substitute effect will be positive +those don't change what changes is the + + align:start position:0% +those don't change what changes is the + + + align:start position:0% +those don't change what changes is the +income effect if it's an inferior good + + align:start position:0% +income effect if it's an inferior good + + + align:start position:0% +income effect if it's an inferior good +if it's an inferior + + align:start position:0% +if it's an inferior + + + align:start position:0% +if it's an inferior +good now when the price goes up okay + + align:start position:0% +good now when the price goes up okay + + + align:start position:0% +good now when the price goes up okay +when the price goes up you want more of + + align:start position:0% +when the price goes up you want more of + + + align:start position:0% +when the price goes up you want more of +it and when the price goes down you want + + align:start position:0% +it and when the price goes down you want + + + align:start position:0% +it and when the price goes down you want +less of it so the net is + + align:start position:0% + + + + align:start position:0% + +unclear okay so once again if goods are + + align:start position:0% +unclear okay so once again if goods are + + + align:start position:0% +unclear okay so once again if goods are +normal then demand curves look like them + + align:start position:0% +normal then demand curves look like them + + + align:start position:0% +normal then demand curves look like them +you know then basically there's no this + + align:start position:0% +you know then basically there's no this + + + align:start position:0% +you know then basically there's no this +this seems if goods are normal it seems + + align:start position:0% +this seems if goods are normal it seems + + + align:start position:0% +this seems if goods are normal it seems +like I just wasted 20 minutes to your + + align:start position:0% +like I just wasted 20 minutes to your + + + align:start position:0% +like I just wasted 20 minutes to your +time right because if goods are normal + + align:start position:0% +time right because if goods are normal + + + align:start position:0% +time right because if goods are normal +it's like well look yeah they build on + + align:start position:0% +it's like well look yeah they build on + + + align:start position:0% +it's like well look yeah they build on +each other but we end up in the same + + align:start position:0% +each other but we end up in the same + + + align:start position:0% +each other but we end up in the same +place in the imaginary B strs imaginary + + align:start position:0% +place in the imaginary B strs imaginary + + + align:start position:0% +place in the imaginary B strs imaginary +anyway so who cares the answer is I'll + + align:start position:0% +anyway so who cares the answer is I'll + + + align:start position:0% +anyway so who cares the answer is I'll +tell you why we care in three or four Le + + align:start position:0% +tell you why we care in three or four Le + + + align:start position:0% +tell you why we care in three or four Le +in about six + + align:start position:0% +in about six + + + align:start position:0% +in about six +lectures because it turns out when you + + align:start position:0% +lectures because it turns out when you + + + align:start position:0% +lectures because it turns out when you +make your decisions about how hard + + align:start position:0% +make your decisions about how hard + + + align:start position:0% +make your decisions about how hard +you're going to work or how much you're + + align:start position:0% +you're going to work or how much you're + + + align:start position:0% +you're going to work or how much you're +going to save income sub effects are + + align:start position:0% +going to save income sub effects are + + + align:start position:0% +going to save income sub effects are +going to start to work against each + + align:start position:0% +going to start to work against each + + + align:start position:0% +going to start to work against each +other this case is only really + + align:start position:0% +other this case is only really + + + align:start position:0% +other this case is only really +interesting if the income affects if + + align:start position:0% +interesting if the income affects if + + + align:start position:0% +interesting if the income affects if +it's an inferior good and then you can + + align:start position:0% +it's an inferior good and then you can + + + align:start position:0% +it's an inferior good and then you can +get some interesting things although + + align:start position:0% +get some interesting things although + + + align:start position:0% +get some interesting things although +practice we don't really have gi and + + align:start position:0% +practice we don't really have gi and + + + align:start position:0% +practice we don't really have gi and +goods but in theory at least you can get + + align:start position:0% +goods but in theory at least you can get + + + align:start position:0% +goods but in theory at least you can get +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +things okay questions about + + align:start position:0% +things okay questions about + + + align:start position:0% +things okay questions about +that okay one other announcement please + + align:start position:0% +that okay one other announcement please + + + align:start position:0% +that okay one other announcement please +don't go um I really love that you guys + + align:start position:0% +don't go um I really love that you guys + + + align:start position:0% +don't go um I really love that you guys +come after lecture and ask me questions + + align:start position:0% +come after lecture and ask me questions + + + align:start position:0% +come after lecture and ask me questions +that's awesome I just do have to say on + + align:start position:0% +that's awesome I just do have to say on + + + align:start position:0% +that's awesome I just do have to say on +Mondays I have to sort of book out of + + align:start position:0% +Mondays I have to sort of book out of + + + align:start position:0% +Mondays I have to sort of book out of +here fairly quickly uh so don't feel + + align:start position:0% +here fairly quickly uh so don't feel + + + align:start position:0% +here fairly quickly uh so don't feel +dissed I do have office hours and if you + + align:start position:0% +dissed I do have office hours and if you + + + align:start position:0% +dissed I do have office hours and if you +can't make the office hours just email + + align:start position:0% +can't make the office hours just email + + + align:start position:0% +can't make the office hours just email +me I have I'm in the office lots of + + align:start position:0% +me I have I'm in the office lots of + + + align:start position:0% +me I have I'm in the office lots of +times just email and we can talk thanks \ No newline at end of file diff --git a/Rs3Ll0KYfcA.txt b/Rs3Ll0KYfcA.txt new file mode 100644 index 0000000000000000000000000000000000000000..5e7959446747dd0096b68bf596a7b72ee5cdba9e --- /dev/null +++ b/Rs3Ll0KYfcA.txt @@ -0,0 +1,14848 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right Steph let's go into Claudia + + align:start position:0% +all right Steph let's go into Claudia + + + align:start position:0% +all right Steph let's go into Claudia +Goldin and Lawrence Katz Katz okay on + + align:start position:0% + + + + align:start position:0% + +the big picture issue which is you have + + align:start position:0% +the big picture issue which is you have + + + align:start position:0% +the big picture issue which is you have +drawn for us in the big picture on some + + align:start position:0% +drawn for us in the big picture on some + + + align:start position:0% +drawn for us in the big picture on some +I intended and the consideration that I + + align:start position:0% +I intended and the consideration that I + + + align:start position:0% +I intended and the consideration that I +had was on the research and development + + align:start position:0% +had was on the research and development + + + align:start position:0% +had was on the research and development +process which is not something that they + + align:start position:0% +process which is not something that they + + + align:start position:0% +process which is not something that they +touched on here which could maybe + + align:start position:0% +touched on here which could maybe + + + align:start position:0% +touched on here which could maybe +provide a short-term fix and I'd love to + + align:start position:0% +provide a short-term fix and I'd love to + + + align:start position:0% +provide a short-term fix and I'd love to +hear your input + + align:start position:0% +hear your input + + + align:start position:0% +hear your input +mm-hmm is there in the research and + + align:start position:0% +mm-hmm is there in the research and + + + align:start position:0% +mm-hmm is there in the research and +development process people who openly + + align:start position:0% +development process people who openly + + + align:start position:0% +development process people who openly +talk about the ways in which their + + align:start position:0% +talk about the ways in which their + + + align:start position:0% +talk about the ways in which their +technology may cause social disruption + + align:start position:0% +technology may cause social disruption + + + align:start position:0% +technology may cause social disruption +and if so can you identify someone you + + align:start position:0% +and if so can you identify someone you + + + align:start position:0% +and if so can you identify someone you +know on a project that you've worked on + + align:start position:0% +know on a project that you've worked on + + + align:start position:0% +know on a project that you've worked on +or affirmed that you know that's + + align:start position:0% +or affirmed that you know that's + + + align:start position:0% +or affirmed that you know that's +concerned about the social or economic + + align:start position:0% +concerned about the social or economic + + + align:start position:0% +concerned about the social or economic +implications of the technologies that + + align:start position:0% +implications of the technologies that + + + align:start position:0% +implications of the technologies that +they are building but they might decide + + align:start position:0% +they are building but they might decide + + + align:start position:0% +they are building but they might decide +like this is my niche this is what I + + align:start position:0% +like this is my niche this is what I + + + align:start position:0% +like this is my niche this is what I +haven't seen before and like these are + + align:start position:0% +haven't seen before and like these are + + + align:start position:0% +haven't seen before and like these are +the reasons why this particular + + align:start position:0% +the reasons why this particular + + + align:start position:0% +the reasons why this particular +technology would like take advantage of + + align:start position:0% +technology would like take advantage of + + + align:start position:0% +technology would like take advantage of +this on see sort of marking and so I + + align:start position:0% +this on see sort of marking and so I + + + align:start position:0% +this on see sort of marking and so I +don't know if that's what you're trying + + align:start position:0% +don't know if that's what you're trying + + + align:start position:0% +don't know if that's what you're trying +to get at with I think it was like okay + + align:start position:0% +to get at with I think it was like okay + + + align:start position:0% +to get at with I think it was like okay +if we do this it would cheat society + + align:start position:0% +if we do this it would cheat society + + + align:start position:0% +if we do this it would cheat society +this way like Bluebird said okay if we + + align:start position:0% +this way like Bluebird said okay if we + + + align:start position:0% +this way like Bluebird said okay if we +do this this no to get rid of all these + + align:start position:0% +do this this no to get rid of all these + + + align:start position:0% +do this this no to get rid of all these +cab drivers and there's gonna be like + + align:start position:0% +cab drivers and there's gonna be like + + + align:start position:0% +cab drivers and there's gonna be like +those assumptions is that you're kind of + + align:start position:0% +those assumptions is that you're kind of + + + align:start position:0% +those assumptions is that you're kind of +like certain yeah okay yeah I think your + + align:start position:0% +like certain yeah okay yeah I think your + + + align:start position:0% +like certain yeah okay yeah I think your +ego was more like oh this is gonna be a + + align:start position:0% +ego was more like oh this is gonna be a + + + align:start position:0% +ego was more like oh this is gonna be a +huge hit it's really gonna change like + + align:start position:0% +huge hit it's really gonna change like + + + align:start position:0% +huge hit it's really gonna change like +Society right yes okay all right so I + + align:start position:0% +Society right yes okay all right so I + + + align:start position:0% +Society right yes okay all right so I +mean I guess into my consideration of + + align:start position:0% +mean I guess into my consideration of + + + align:start position:0% +mean I guess into my consideration of +business and consumer markets and and in + + align:start position:0% +business and consumer markets and and in + + + align:start position:0% +business and consumer markets and and in +some of the research that I'm conducting + + align:start position:0% +some of the research that I'm conducting + + + align:start position:0% +some of the research that I'm conducting +for my favor of autonomous vehicles one + + align:start position:0% +for my favor of autonomous vehicles one + + + align:start position:0% +for my favor of autonomous vehicles one +of the questions that I've been asked + + align:start position:0% +of the questions that I've been asked + + + align:start position:0% +of the questions that I've been asked +and asked by anthropologists to firms + + align:start position:0% +and asked by anthropologists to firms + + + align:start position:0% +and asked by anthropologists to firms +and I think the interviewing or even as + + align:start position:0% +and I think the interviewing or even as + + + align:start position:0% +and I think the interviewing or even as +I'm going over you know literature base + + align:start position:0% +I'm going over you know literature base + + + align:start position:0% +I'm going over you know literature base +and public releases to the press is + + align:start position:0% +and public releases to the press is + + + align:start position:0% +and public releases to the press is +essentially who on the staff is in + + align:start position:0% +essentially who on the staff is in + + + align:start position:0% +essentially who on the staff is in +charge of answering questions or raising + + align:start position:0% +charge of answering questions or raising + + + align:start position:0% +charge of answering questions or raising +considerations about social disruption + + align:start position:0% +considerations about social disruption + + + align:start position:0% +considerations about social disruption +or economic disruption that your + + align:start position:0% +or economic disruption that your + + + align:start position:0% +or economic disruption that your +technology might cause + + align:start position:0% +technology might cause + + + align:start position:0% +technology might cause +and if firm can't answer that when you + + align:start position:0% +and if firm can't answer that when you + + + align:start position:0% +and if firm can't answer that when you +have your answer that they're not that + + align:start position:0% +have your answer that they're not that + + + align:start position:0% +have your answer that they're not that +they don't consider that as a part of + + align:start position:0% +they don't consider that as a part of + + + align:start position:0% +they don't consider that as a part of +their research and development process + + align:start position:0% +their research and development process + + + align:start position:0% +their research and development process +and I think it's possible that some + + align:start position:0% +and I think it's possible that some + + + align:start position:0% +and I think it's possible that some +people would argue that that's beyond + + align:start position:0% +people would argue that that's beyond + + + align:start position:0% +people would argue that that's beyond +the scope of what the firm should be + + align:start position:0% +the scope of what the firm should be + + + align:start position:0% +the scope of what the firm should be +doing right and they should be focusing + + align:start position:0% +doing right and they should be focusing + + + align:start position:0% +doing right and they should be focusing +on the technology they perhaps should + + align:start position:0% +on the technology they perhaps should + + + align:start position:0% +on the technology they perhaps should +not have an episode stuff from you down + + align:start position:0% +not have an episode stuff from you down + + + align:start position:0% +not have an episode stuff from you down +the station meter perhaps they shouldn't + + align:start position:0% +the station meter perhaps they shouldn't + + + align:start position:0% +the station meter perhaps they shouldn't +just have an ethicist that they consult + + align:start position:0% +just have an ethicist that they consult + + + align:start position:0% +just have an ethicist that they consult +with but it should not be someone who's + + align:start position:0% +with but it should not be someone who's + + + align:start position:0% +with but it should not be someone who's +you know sort of formally a part of + + align:start position:0% +you know sort of formally a part of + + + align:start position:0% +you know sort of formally a part of +their staff so I'd love to hear your + + align:start position:0% +their staff so I'd love to hear your + + + align:start position:0% +their staff so I'd love to hear your +perspective on this is perhaps a + + align:start position:0% +perspective on this is perhaps a + + + align:start position:0% +perspective on this is perhaps a +short-term fix as we you know it's sort + + align:start position:0% +short-term fix as we you know it's sort + + + align:start position:0% +short-term fix as we you know it's sort +of promote technological advances + + align:start position:0% +of promote technological advances + + + align:start position:0% +of promote technological advances +should there be someone who's constantly + + align:start position:0% +should there be someone who's constantly + + + align:start position:0% +should there be someone who's constantly +you know raising a flag and saying huh + + align:start position:0% +you know raising a flag and saying huh + + + align:start position:0% +you know raising a flag and saying huh +perhaps this might not be a good idea to + + align:start position:0% +perhaps this might not be a good idea to + + + align:start position:0% +perhaps this might not be a good idea to +deploy in the timeframe that we have set + + align:start position:0% +deploy in the timeframe that we have set + + + align:start position:0% +deploy in the timeframe that we have set +for ourselves so I'm working on the + + align:start position:0% +for ourselves so I'm working on the + + + align:start position:0% +for ourselves so I'm working on the +mobility the teacher project as part of + + align:start position:0% +mobility the teacher project as part of + + + align:start position:0% +mobility the teacher project as part of +my thesis and so a lot of it it's + + align:start position:0% +my thesis and so a lot of it it's + + + align:start position:0% +my thesis and so a lot of it it's +anonymous vehicles and it does seem well + + align:start position:0% +anonymous vehicles and it does seem well + + + align:start position:0% +anonymous vehicles and it does seem well +first of all like with that example + + align:start position:0% +first of all like with that example + + + align:start position:0% +first of all like with that example +specifically none of the companies are + + align:start position:0% +specifically none of the companies are + + + align:start position:0% +specifically none of the companies are +working on it are very secretive about + + align:start position:0% +working on it are very secretive about + + + align:start position:0% +working on it are very secretive about +what they're doing so it's like not very + + align:start position:0% +what they're doing so it's like not very + + + align:start position:0% +what they're doing so it's like not very +clear as to like what's going on within + + align:start position:0% +clear as to like what's going on within + + + align:start position:0% +clear as to like what's going on within +the companies but outside of them at + + align:start position:0% +the companies but outside of them at + + + align:start position:0% +the companies but outside of them at +least with this example there is a lot + + align:start position:0% +least with this example there is a lot + + + align:start position:0% +least with this example there is a lot +of work and awareness about potential + + align:start position:0% +of work and awareness about potential + + + align:start position:0% +of work and awareness about potential +disruptions my questioning whether + + align:start position:0% +disruptions my questioning whether + + + align:start position:0% +disruptions my questioning whether +that's always been the case or kind of + + align:start position:0% +that's always been the case or kind of + + + align:start position:0% +that's always been the case or kind of +the recent disruptions have let spur + + align:start position:0% +the recent disruptions have let spur + + + align:start position:0% +the recent disruptions have let spur +people to think about this more so like + + align:start position:0% +people to think about this more so like + + + align:start position:0% +people to think about this more so like +there's a group at the MIT H lab at our + + align:start position:0% +there's a group at the MIT H lab at our + + + align:start position:0% +there's a group at the MIT H lab at our +Cube talk to them age lab age age AG + + align:start position:0% +Cube talk to them age lab age age AG + + + align:start position:0% +Cube talk to them age lab age age AG +yeah well they do a lot of stuff related + + align:start position:0% +yeah well they do a lot of stuff related + + + align:start position:0% +yeah well they do a lot of stuff related +to like how people are aging but they + + align:start position:0% +to like how people are aging but they + + + align:start position:0% +to like how people are aging but they +also have a big group that's working on + + align:start position:0% +also have a big group that's working on + + + align:start position:0% +also have a big group that's working on +the autonomous vehicles less so on the + + align:start position:0% +the autonomous vehicles less so on the + + + align:start position:0% +the autonomous vehicles less so on the +technology side but how it's like + + align:start position:0% +technology side but how it's like + + + align:start position:0% +technology side but how it's like +affecting people so they have a lot of + + align:start position:0% +affecting people so they have a lot of + + + align:start position:0% +affecting people so they have a lot of +experiments where they're like letting + + align:start position:0% +experiments where they're like letting + + + align:start position:0% +experiments where they're like letting +people drive autonomous cars and like + + align:start position:0% +people drive autonomous cars and like + + + align:start position:0% +people drive autonomous cars and like +recording them with their consent and + + align:start position:0% +recording them with their consent and + + + align:start position:0% +recording them with their consent and +they're trying to get knowledge not like + + align:start position:0% +they're trying to get knowledge not like + + + align:start position:0% +they're trying to get knowledge not like +how people are interacting with these + + align:start position:0% +how people are interacting with these + + + align:start position:0% +how people are interacting with these +technologies like what changes we have + + align:start position:0% +technologies like what changes we have + + + align:start position:0% +technologies like what changes we have +like what negative change to have so + + align:start position:0% +like what negative change to have so + + + align:start position:0% +like what negative change to have so +like they showed us a video of this guy + + align:start position:0% +like they showed us a video of this guy + + + align:start position:0% +like they showed us a video of this guy +who's like looking down at his phone for + + align:start position:0% +who's like looking down at his phone for + + + align:start position:0% +who's like looking down at his phone for +like two minutes while driving like all + + align:start position:0% +like two minutes while driving like all + + + align:start position:0% +like two minutes while driving like all +the Mass Pike we're just terrifying + + align:start position:0% +the Mass Pike we're just terrifying + + + align:start position:0% +the Mass Pike we're just terrifying +and so like as we transition from like a + + align:start position:0% +and so like as we transition from like a + + + align:start position:0% +and so like as we transition from like a +not quite autonomous vehicles like a poi + + align:start position:0% +not quite autonomous vehicles like a poi + + + align:start position:0% +not quite autonomous vehicles like a poi +one like he's like now he expected to + + align:start position:0% +one like he's like now he expected to + + + align:start position:0% +one like he's like now he expected to +see like more accident for the near + + align:start position:0% +see like more accident for the near + + + align:start position:0% +see like more accident for the near +future until we get to the point so I + + align:start position:0% +future until we get to the point so I + + + align:start position:0% +future until we get to the point so I +think people are thinking about like the + + align:start position:0% +think people are thinking about like the + + + align:start position:0% +think people are thinking about like the +how these technologies and their + + align:start position:0% +how these technologies and their + + + align:start position:0% +how these technologies and their +developments + + align:start position:0% +developments + + + align:start position:0% +developments +affect things other than just like how + + align:start position:0% +affect things other than just like how + + + align:start position:0% +affect things other than just like how +we're getting from place to place it's + + align:start position:0% +we're getting from place to place it's + + + align:start position:0% +we're getting from place to place it's +not like such a simple story + + align:start position:0% +not like such a simple story + + + align:start position:0% +not like such a simple story +would you mind elaborating the reason I + + align:start position:0% +would you mind elaborating the reason I + + + align:start position:0% +would you mind elaborating the reason I +bring up this point and why I'm thinking + + align:start position:0% +bring up this point and why I'm thinking + + + align:start position:0% +bring up this point and why I'm thinking +on it so fully is because bill assess + + align:start position:0% +on it so fully is because bill assess + + + align:start position:0% +on it so fully is because bill assess +that a very important component of + + align:start position:0% +that a very important component of + + + align:start position:0% +that a very important component of +driverless vehicles as the impact that + + align:start position:0% +driverless vehicles as the impact that + + + align:start position:0% +driverless vehicles as the impact that +it's going to have on the workforce + + align:start position:0% +it's going to have on the workforce + + + align:start position:0% +it's going to have on the workforce +right on truck drivers and you know live + + align:start position:0% +right on truck drivers and you know live + + + align:start position:0% +right on truck drivers and you know live +delivery laborers um do you think that + + align:start position:0% +delivery laborers um do you think that + + + align:start position:0% +delivery laborers um do you think that +those are considerations that have been + + align:start position:0% +those are considerations that have been + + + align:start position:0% +those are considerations that have been +raised + + align:start position:0% +raised + + + align:start position:0% +raised +you know these will be driverless cars + + align:start position:0% +you know these will be driverless cars + + + align:start position:0% +you know these will be driverless cars +and do you think that there's maybe a + + align:start position:0% +and do you think that there's maybe a + + + align:start position:0% +and do you think that there's maybe a +role for someone to be highlighting that + + align:start position:0% +role for someone to be highlighting that + + + align:start position:0% +role for someone to be highlighting that +as an issue within each innovation team + + align:start position:0% +as an issue within each innovation team + + + align:start position:0% +as an issue within each innovation team +yeah I do like that hasn't been as much + + align:start position:0% +yeah I do like that hasn't been as much + + + align:start position:0% +yeah I do like that hasn't been as much +of a focus in our work like people talk + + align:start position:0% +of a focus in our work like people talk + + + align:start position:0% +of a focus in our work like people talk +about it but no one really talks it up + + align:start position:0% +about it but no one really talks it up + + + align:start position:0% +about it but no one really talks it up +they're like that's gonna be a problem + + align:start position:0% + + + + align:start position:0% + +but I do think that that is especially + + align:start position:0% +but I do think that that is especially + + + align:start position:0% +but I do think that that is especially +after this election people are talking + + align:start position:0% +after this election people are talking + + + align:start position:0% +after this election people are talking +one work about like disruptive + + align:start position:0% +one work about like disruptive + + + align:start position:0% +one work about like disruptive +technologies like I hadn't heard people + + align:start position:0% +technologies like I hadn't heard people + + + align:start position:0% +technologies like I hadn't heard people +talk about it much but then at the same + + align:start position:0% +talk about it much but then at the same + + + align:start position:0% +talk about it much but then at the same +to podcasts today like this really could + + align:start position:0% +to podcasts today like this really could + + + align:start position:0% +to podcasts today like this really could +happen like what happens to all these + + align:start position:0% +happen like what happens to all these + + + align:start position:0% +happen like what happens to all these +like drivers like I never thought about + + align:start position:0% +like drivers like I never thought about + + + align:start position:0% +like drivers like I never thought about +it until I saw Logan so like I think + + align:start position:0% +it until I saw Logan so like I think + + + align:start position:0% +it until I saw Logan so like I think +that's interesting I was like permeating + + align:start position:0% +that's interesting I was like permeating + + + align:start position:0% +that's interesting I was like permeating +this all so I want to hold this + + align:start position:0% +this all so I want to hold this + + + align:start position:0% +this all so I want to hold this +discussion until next week's class which + + align:start position:0% +discussion until next week's class which + + + align:start position:0% +discussion until next week's class which +is about to future work I'm gonna did + + align:start position:0% +is about to future work I'm gonna did + + + align:start position:0% +is about to future work I'm gonna did +exactly like it's about this problem so + + align:start position:0% +exactly like it's about this problem so + + + align:start position:0% +exactly like it's about this problem so +you know we we've gotten it on the table + + align:start position:0% +you know we we've gotten it on the table + + + align:start position:0% +you know we we've gotten it on the table +everybody's gonna have a chance to think + + align:start position:0% +everybody's gonna have a chance to think + + + align:start position:0% +everybody's gonna have a chance to think +about it and you can go back and watch + + align:start position:0% +about it and you can go back and watch + + + align:start position:0% +about it and you can go back and watch +Logan you can recount your favorite + + align:start position:0% +Logan you can recount your favorite + + + align:start position:0% +Logan you can recount your favorite +stories but Steph do bring this up again + + align:start position:0% +stories but Steph do bring this up again + + + align:start position:0% +stories but Steph do bring this up again +when we go after these issues next week + + align:start position:0% +when we go after these issues next week + + + align:start position:0% +when we go after these issues next week +but focus is more now on + + align:start position:0% +but focus is more now on + + + align:start position:0% +but focus is more now on +cats and gold in the bow more if you + + align:start position:0% +cats and gold in the bow more if you + + + align:start position:0% +cats and gold in the bow more if you +would thank you + + align:start position:0% +would thank you + + + align:start position:0% +would thank you +I'm not trying to silence you step I + + align:start position:0% +I'm not trying to silence you step I + + + align:start position:0% +I'm not trying to silence you step I +promise you air time in the next class I + + align:start position:0% + + + + align:start position:0% + +guess whatever you know my critiques of + + align:start position:0% +guess whatever you know my critiques of + + + align:start position:0% +guess whatever you know my critiques of +my social science education and I think + + align:start position:0% +my social science education and I think + + + align:start position:0% +my social science education and I think +this is generally my critique of social + + align:start position:0% +this is generally my critique of social + + + align:start position:0% +this is generally my critique of social +science education generally is that + + align:start position:0% +science education generally is that + + + align:start position:0% +science education generally is that +there are benefits to talking about an + + align:start position:0% +there are benefits to talking about an + + + align:start position:0% +there are benefits to talking about an +issue but there's only so much time sort + + align:start position:0% +issue but there's only so much time sort + + + align:start position:0% +issue but there's only so much time sort +of like public discourse can get you I + + align:start position:0% +of like public discourse can get you I + + + align:start position:0% +of like public discourse can get you I +especially like finding around people + + align:start position:0% +especially like finding around people + + + align:start position:0% +especially like finding around people +setting their academic environment where + + align:start position:0% +setting their academic environment where + + + align:start position:0% +setting their academic environment where +the most of us you know sir I can feel + + align:start position:0% +the most of us you know sir I can feel + + + align:start position:0% +the most of us you know sir I can feel +like for the most part are on the same + + align:start position:0% +like for the most part are on the same + + + align:start position:0% +like for the most part are on the same +side between so I struggle to come up + + align:start position:0% +side between so I struggle to come up + + + align:start position:0% +side between so I struggle to come up +with you know sort of good questions and + + align:start position:0% +with you know sort of good questions and + + + align:start position:0% +with you know sort of good questions and +think about what might actually be + + align:start position:0% +think about what might actually be + + + align:start position:0% +think about what might actually be +meaningful as we're having the + + align:start position:0% +meaningful as we're having the + + + align:start position:0% +meaningful as we're having the +conversation about an issue is large and + + align:start position:0% +conversation about an issue is large and + + + align:start position:0% +conversation about an issue is large and +it's difficult to grapple with is + + align:start position:0% +it's difficult to grapple with is + + + align:start position:0% +it's difficult to grapple with is +inequality especially as a as cats and + + align:start position:0% +inequality especially as a as cats and + + + align:start position:0% +inequality especially as a as cats and +golden purported but I think one of you + + align:start position:0% +golden purported but I think one of you + + + align:start position:0% +golden purported but I think one of you +talked about how relative to bumbles + + align:start position:0% +talked about how relative to bumbles + + + align:start position:0% +talked about how relative to bumbles +analysis if America should shift towards + + align:start position:0% +analysis if America should shift towards + + + align:start position:0% +analysis if America should shift towards +a focus on primarily promoting + + align:start position:0% +a focus on primarily promoting + + + align:start position:0% +a focus on primarily promoting +breakthrough innovations where we can + + align:start position:0% +breakthrough innovations where we can + + + align:start position:0% +breakthrough innovations where we can +still maintain competitive advantages in + + align:start position:0% +still maintain competitive advantages in + + + align:start position:0% +still maintain competitive advantages in +the research and development system + + align:start position:0% +the research and development system + + + align:start position:0% +the research and development system +rather than even concerning ourselves at + + align:start position:0% +rather than even concerning ourselves at + + + align:start position:0% +rather than even concerning ourselves at +all with you know the fixing of the + + align:start position:0% +all with you know the fixing of the + + + align:start position:0% +all with you know the fixing of the +education system or the fixing of the + + align:start position:0% +education system or the fixing of the + + + align:start position:0% +education system or the fixing of the +R&D sort of inside a question that Matt + + align:start position:0% +R&D sort of inside a question that Matt + + + align:start position:0% +R&D sort of inside a question that Matt +had asked earlier in the semester where + + align:start position:0% +had asked earlier in the semester where + + + align:start position:0% +had asked earlier in the semester where +he said it is the impetus on us as a + + align:start position:0% +he said it is the impetus on us as a + + + align:start position:0% +he said it is the impetus on us as a +civil society to educate to educate + + align:start position:0% +civil society to educate to educate + + + align:start position:0% +civil society to educate to educate +everyone is that even advantageous to us + + align:start position:0% +everyone is that even advantageous to us + + + align:start position:0% +everyone is that even advantageous to us +and people even want to be educated and + + align:start position:0% +and people even want to be educated and + + + align:start position:0% +and people even want to be educated and +what are the benefits and you know + + align:start position:0% +what are the benefits and you know + + + align:start position:0% +what are the benefits and you know +putting it making this resource + + align:start position:0% +putting it making this resource + + + align:start position:0% +putting it making this resource +available to all when it seems like + + align:start position:0% +available to all when it seems like + + + align:start position:0% +available to all when it seems like +we're already feeling spectacular yet + + align:start position:0% +we're already feeling spectacular yet + + + align:start position:0% +we're already feeling spectacular yet +this experiment that it's you know who + + align:start position:0% +this experiment that it's you know who + + + align:start position:0% +this experiment that it's you know who + + align:start position:0% + + + align:start position:0% +I think we're family yeah here's old and + + align:start position:0% +I think we're family yeah here's old and + + + align:start position:0% +I think we're family yeah here's old and +that's like Browns will be short or + + align:start position:0% +that's like Browns will be short or + + + align:start position:0% +that's like Browns will be short or +something our stuff out nations right + + align:start position:0% +something our stuff out nations right + + + align:start position:0% +something our stuff out nations right +well not great not that great again it's + + align:start position:0% +well not great not that great again it's + + + align:start position:0% +well not great not that great again it's +like saying oh yeah it's like we really + + align:start position:0% +like saying oh yeah it's like we really + + + align:start position:0% +like saying oh yeah it's like we really +can't change one system to like a whole + + align:start position:0% +can't change one system to like a whole + + + align:start position:0% +can't change one system to like a whole +new one what you do is you have to make + + align:start position:0% +new one what you do is you have to make + + + align:start position:0% +new one what you do is you have to make +Chipotle and then make sure we have pop + + align:start position:0% +Chipotle and then make sure we have pop + + + align:start position:0% +Chipotle and then make sure we have pop +and chain I get to go back the next + + align:start position:0% +and chain I get to go back the next + + + align:start position:0% +and chain I get to go back the next +system I'm gonna use this metaphor to + + align:start position:0% +system I'm gonna use this metaphor to + + + align:start position:0% +system I'm gonna use this metaphor to +make hamburger at the heart of what + + align:start position:0% +make hamburger at the heart of what + + + align:start position:0% +make hamburger at the heart of what +you're saying you know just sort of + + align:start position:0% +you're saying you know just sort of + + + align:start position:0% +you're saying you know just sort of +elucidate where I'm coming from and + + align:start position:0% +elucidate where I'm coming from and + + + align:start position:0% +elucidate where I'm coming from and +asking this question I there's a an + + align:start position:0% +asking this question I there's a an + + + align:start position:0% +asking this question I there's a an +education professor who I grew close to + + align:start position:0% +education professor who I grew close to + + + align:start position:0% +education professor who I grew close to +during my time at Walden who in its + + align:start position:0% +during my time at Walden who in its + + + align:start position:0% +during my time at Walden who in its +first day of his ph.d program his + + align:start position:0% +first day of his ph.d program his + + + align:start position:0% +first day of his ph.d program his +adviser posed to everyone if you had the + + align:start position:0% +adviser posed to everyone if you had the + + + align:start position:0% +adviser posed to everyone if you had the +option would you blow up the education + + align:start position:0% +option would you blow up the education + + + align:start position:0% +option would you blow up the education +system and start again or would you + + align:start position:0% +system and start again or would you + + + align:start position:0% +system and start again or would you +change it incremental and his answer was + + align:start position:0% +change it incremental and his answer was + + + align:start position:0% +change it incremental and his answer was +blown up and start over right but we + + align:start position:0% +blown up and start over right but we + + + align:start position:0% +blown up and start over right but we +don't have that option we don't have the + + align:start position:0% +don't have that option we don't have the + + + align:start position:0% +don't have that option we don't have the +privilege of you know bringing in the + + align:start position:0% +privilege of you know bringing in the + + + align:start position:0% +privilege of you know bringing in the +Chipotle's and then seeing if they work + + align:start position:0% +Chipotle's and then seeing if they work + + + align:start position:0% +Chipotle's and then seeing if they work +and then adopting all the McDonald's to + + align:start position:0% +and then adopting all the McDonald's to + + + align:start position:0% +and then adopting all the McDonald's to +suit that consumer market right like we + + align:start position:0% +suit that consumer market right like we + + + align:start position:0% +suit that consumer market right like we +we very much recognize that students are + + align:start position:0% +we very much recognize that students are + + + align:start position:0% +we very much recognize that students are +humans and the humans have a very + + align:start position:0% +humans and the humans have a very + + + align:start position:0% +humans and the humans have a very +particular I think consideration than do + + align:start position:0% +particular I think consideration than do + + + align:start position:0% +particular I think consideration than do +technologies or other kinds of recent + + align:start position:0% +technologies or other kinds of recent + + + align:start position:0% +technologies or other kinds of recent +development projects so if we are to + + align:start position:0% +development projects so if we are to + + + align:start position:0% +development projects so if we are to +meet the kinds of goals that golden and + + align:start position:0% +meet the kinds of goals that golden and + + + align:start position:0% +meet the kinds of goals that golden and +cats and Bumble and Freeman are + + align:start position:0% +cats and Bumble and Freeman are + + + align:start position:0% +cats and Bumble and Freeman are +advocating for and improving our + + align:start position:0% +advocating for and improving our + + + align:start position:0% +advocating for and improving our +education system right how do we deal + + align:start position:0% +education system right how do we deal + + + align:start position:0% +education system right how do we deal +with the fact that these are human lives + + align:start position:0% +with the fact that these are human lives + + + align:start position:0% +with the fact that these are human lives +with whom we're experimenting + + align:start position:0% + + + + align:start position:0% + +what interesting is like what are we to + + align:start position:0% +what interesting is like what are we to + + + align:start position:0% +what interesting is like what are we to +find is education are we different + + align:start position:0% +find is education are we different + + + align:start position:0% +find is education are we different +education is I want people to know that + + align:start position:0% +education is I want people to know that + + + align:start position:0% +education is I want people to know that +science really well - it's communicated + + align:start position:0% +science really well - it's communicated + + + align:start position:0% +science really well - it's communicated +to take yeah independently in it or we + + align:start position:0% +to take yeah independently in it or we + + + align:start position:0% +to take yeah independently in it or we +find it it's like we're gonna get out of + + align:start position:0% +find it it's like we're gonna get out of + + + align:start position:0% +find it it's like we're gonna get out of +a four-year college right so I think a + + align:start position:0% +a four-year college right so I think a + + + align:start position:0% +a four-year college right so I think a +lot of document is the current + + align:start position:0% +lot of document is the current + + + align:start position:0% +lot of document is the current +infrastructure or the relationship for + + align:start position:0% +infrastructure or the relationship for + + + align:start position:0% +infrastructure or the relationship for +the last hundred years has been colleges + + align:start position:0% +the last hundred years has been colleges + + + align:start position:0% +the last hundred years has been colleges +so many l'éducation is graduating in + + align:start position:0% +so many l'éducation is graduating in + + + align:start position:0% +so many l'éducation is graduating in +college you'll be making is I want to + + align:start position:0% +college you'll be making is I want to + + + align:start position:0% +college you'll be making is I want to +make the best most educated person with + + align:start position:0% +make the best most educated person with + + + align:start position:0% +make the best most educated person with +all my tools right now and being able to + + align:start position:0% +all my tools right now and being able to + + + align:start position:0% +all my tools right now and being able to +port them into society well in terms of + + align:start position:0% +port them into society well in terms of + + + align:start position:0% +port them into society well in terms of +into jobs really well how will we make + + align:start position:0% +into jobs really well how will we make + + + align:start position:0% +into jobs really well how will we make +that ideal system you started making + + align:start position:0% +that ideal system you started making + + + align:start position:0% +that ideal system you started making +that system and it's not gonna change + + align:start position:0% +that system and it's not gonna change + + + align:start position:0% +that system and it's not gonna change +overnight right like you know like you + + align:start position:0% +overnight right like you know like you + + + align:start position:0% +overnight right like you know like you +don't grow up two years old and you know + + align:start position:0% +don't grow up two years old and you know + + + align:start position:0% +don't grow up two years old and you know +next a year I mean but like it's it's + + align:start position:0% +next a year I mean but like it's it's + + + align:start position:0% +next a year I mean but like it's it's +very rare right I think it's you start + + align:start position:0% +very rare right I think it's you start + + + align:start position:0% +very rare right I think it's you start +making the new system and you kind of + + align:start position:0% +making the new system and you kind of + + + align:start position:0% +making the new system and you kind of +start to pour over there's a whole issue + + align:start position:0% +start to pour over there's a whole issue + + + align:start position:0% +start to pour over there's a whole issue +with trying to change a current system + + align:start position:0% +with trying to change a current system + + + align:start position:0% +with trying to change a current system +because they're already playing well + + align:start position:0% +because they're already playing well + + + align:start position:0% +because they're already playing well +this happens with later mature markets + + align:start position:0% +this happens with later mature markets + + + align:start position:0% +this happens with later mature markets +what happens is there's gonna be three + + align:start position:0% +what happens is there's gonna be three + + + align:start position:0% +what happens is there's gonna be three +or four or five players right so we talk + + align:start position:0% +or four or five players right so we talk + + + align:start position:0% +or four or five players right so we talk +about institutions we have Harvard MIT + + align:start position:0% +about institutions we have Harvard MIT + + + align:start position:0% +about institutions we have Harvard MIT +Stanford they're trying to fight against + + align:start position:0% +Stanford they're trying to fight against + + + align:start position:0% +Stanford they're trying to fight against +each other because they don't wanna it's + + align:start position:0% +each other because they don't wanna it's + + + align:start position:0% +each other because they don't wanna it's +hard to be different we have to compete + + align:start position:0% +hard to be different we have to compete + + + align:start position:0% +hard to be different we have to compete +against someone like that and so we have + + align:start position:0% +against someone like that and so we have + + + align:start position:0% +against someone like that and so we have +to play their games the reason an + + align:start position:0% +to play their games the reason an + + + align:start position:0% +to play their games the reason an +innovator can come in is because they + + align:start position:0% +innovator can come in is because they + + + align:start position:0% +innovator can come in is because they +don't have to play that well no I + + align:start position:0% +don't have to play that well no I + + + align:start position:0% +don't have to play that well no I +remember that Chipotle versus Burger + + align:start position:0% +remember that Chipotle versus Burger + + + align:start position:0% +remember that Chipotle versus Burger +King McDonald's was discussed I don't + + align:start position:0% +King McDonald's was discussed I don't + + + align:start position:0% +King McDonald's was discussed I don't +know well you know let me say something + + align:start position:0% +know well you know let me say something + + + align:start position:0% +know well you know let me say something +to which is that we are gonna dig into + + align:start position:0% +to which is that we are gonna dig into + + + align:start position:0% +to which is that we are gonna dig into +the textbook reading on legacy sectors + + align:start position:0% +the textbook reading on legacy sectors + + + align:start position:0% +the textbook reading on legacy sectors +because there's no question but + + align:start position:0% +because there's no question but + + + align:start position:0% +because there's no question but +education and higher education in + + align:start position:0% +education and higher education in + + + align:start position:0% +education and higher education in +particular our legacy systems and the + + align:start position:0% +particular our legacy systems and the + + + align:start position:0% +particular our legacy systems and the +whole issue of how do you bring change + + align:start position:0% +whole issue of how do you bring change + + + align:start position:0% +whole issue of how do you bring change +in the legacy systems is kind of an + + align:start position:0% +in the legacy systems is kind of an + + + align:start position:0% +in the legacy systems is kind of an +underlying theme here so I'm glad we're + + align:start position:0% +underlying theme here so I'm glad we're + + + align:start position:0% +underlying theme here so I'm glad we're +right at the brink I'm trying to figure + + align:start position:0% +right at the brink I'm trying to figure + + + align:start position:0% +right at the brink I'm trying to figure +this out you know I I guess I would you + + align:start position:0% +this out you know I I guess I would you + + + align:start position:0% +this out you know I I guess I would you +know posit that the meaning of Freeman's + + align:start position:0% +know posit that the meaning of Freeman's + + + align:start position:0% +know posit that the meaning of Freeman's +reading for us I think was that there + + align:start position:0% +reading for us I think was that there + + + align:start position:0% +reading for us I think was that there +are real economic consequences to your + + align:start position:0% +are real economic consequences to your + + + align:start position:0% +are real economic consequences to your +leadership in science and engineering + + align:start position:0% +leadership in science and engineering + + + align:start position:0% +leadership in science and engineering +and the science and engineering talent + + align:start position:0% +and the science and engineering talent + + + align:start position:0% +and the science and engineering talent +base and that Katz and gold and take us + + align:start position:0% +base and that Katz and gold and take us + + + align:start position:0% +base and that Katz and gold and take us +to kind of a next step and enable us to + + align:start position:0% +to kind of a next step and enable us to + + + align:start position:0% +to kind of a next step and enable us to +address a larger set of societal + + align:start position:0% +address a larger set of societal + + + align:start position:0% +address a larger set of societal +problems and tie it significantly to the + + align:start position:0% +problems and tie it significantly to the + + + align:start position:0% +problems and tie it significantly to the +education system in other words the + + align:start position:0% +education system in other words the + + + align:start position:0% +education system in other words the +growing problem of the polarization of + + align:start position:0% +growing problem of the polarization of + + + align:start position:0% +growing problem of the polarization of +our society and the growing income + + align:start position:0% +our society and the growing income + + + align:start position:0% +our society and the growing income +inequality in our society that will + + align:start position:0% +inequality in our society that will + + + align:start position:0% +inequality in our society that will +affect the quality of the democracy and + + align:start position:0% +affect the quality of the democracy and + + + align:start position:0% +affect the quality of the democracy and +then probably already is that's very + + align:start position:0% +then probably already is that's very + + + align:start position:0% +then probably already is that's very +much tied to these curves here and how + + align:start position:0% +much tied to these curves here and how + + + align:start position:0% +much tied to these curves here and how +we're moving what portion of the + + align:start position:0% +we're moving what portion of the + + + align:start position:0% +we're moving what portion of the +population we're moving on to that + + align:start position:0% +population we're moving on to that + + + align:start position:0% +population we're moving on to that +upward technology curve and what portion + + align:start position:0% +upward technology curve and what portion + + + align:start position:0% +upward technology curve and what portion +of the population we're leaving behind + + align:start position:0% +of the population we're leaving behind + + + align:start position:0% +of the population we're leaving behind +that's that's the meaning of that + + align:start position:0% +that's that's the meaning of that + + + align:start position:0% +that's that's the meaning of that +crossover point in the in the 1970s and + + align:start position:0% +crossover point in the in the 1970s and + + + align:start position:0% +crossover point in the in the 1970s and +what are the policies that would really + + align:start position:0% +what are the policies that would really + + + align:start position:0% +what are the policies that would really +address trying to get those lines back + + align:start position:0% +address trying to get those lines back + + + align:start position:0% +address trying to get those lines back +into parallel right because that seems + + align:start position:0% +into parallel right because that seems + + + align:start position:0% +into parallel right because that seems +to me a pretty important societal + + align:start position:0% +to me a pretty important societal + + + align:start position:0% +to me a pretty important societal +problem so Freeman identifies a set of + + align:start position:0% +problem so Freeman identifies a set of + + + align:start position:0% +problem so Freeman identifies a set of +economic issues that lead that draw us + + align:start position:0% +economic issues that lead that draw us + + + align:start position:0% +economic issues that lead that draw us +to be concerned with the science and + + align:start position:0% +to be concerned with the science and + + + align:start position:0% +to be concerned with the science and +engineering talent base and Katz and + + align:start position:0% +engineering talent base and Katz and + + + align:start position:0% +engineering talent base and Katz and +golden tell us by the way there are very + + align:start position:0% +golden tell us by the way there are very + + + align:start position:0% +golden tell us by the way there are very +deep societal well-being problems that + + align:start position:0% +deep societal well-being problems that + + + align:start position:0% +deep societal well-being problems that +are tied to the education system is as + + align:start position:0% +are tied to the education system is as + + + align:start position:0% +are tied to the education system is as +well and then you know bowel mole points + + align:start position:0% +well and then you know bowel mole points + + + align:start position:0% +well and then you know bowel mole points +to us and says you know by the way you + + align:start position:0% +to us and says you know by the way you + + + align:start position:0% +to us and says you know by the way you +know these folks are studying the higher + + align:start position:0% +know these folks are studying the higher + + + align:start position:0% +know these folks are studying the higher +education system but that's not the only + + align:start position:0% +education system but that's not the only + + + align:start position:0% +education system but that's not the only +route here we have to understand this + + align:start position:0% +route here we have to understand this + + + align:start position:0% +route here we have to understand this +other dimension if you want to introduce + + align:start position:0% +other dimension if you want to introduce + + + align:start position:0% +other dimension if you want to introduce +innovation and the overall economy + + align:start position:0% +innovation and the overall economy + + + align:start position:0% +innovation and the overall economy +education for incremental advance he's + + align:start position:0% +education for incremental advance he's + + + align:start position:0% +education for incremental advance he's +probably not the only system we ought to + + align:start position:0% +probably not the only system we ought to + + + align:start position:0% +probably not the only system we ought to +be worried about and that's kind of what + + align:start position:0% +be worried about and that's kind of what + + + align:start position:0% +be worried about and that's kind of what +Stef's you know round of questions here + + align:start position:0% +Stef's you know round of questions here + + + align:start position:0% +Stef's you know round of questions here +was driving and I think if I've + + align:start position:0% +was driving and I think if I've + + + align:start position:0% +was driving and I think if I've +interpreted you're right which is what + + align:start position:0% +interpreted you're right which is what + + + align:start position:0% +interpreted you're right which is what +is that more disruptive education system + + align:start position:0% +is that more disruptive education system + + + align:start position:0% +is that more disruptive education system +that we have to contemplate here if we + + align:start position:0% +that we have to contemplate here if we + + + align:start position:0% +that we have to contemplate here if we +want to educate not only for incremental + + align:start position:0% +want to educate not only for incremental + + + align:start position:0% +want to educate not only for incremental +advance but for true innovation as well + + align:start position:0% +advance but for true innovation as well + + + align:start position:0% +advance but for true innovation as well +is that fair + + align:start position:0% +is that fair + + + align:start position:0% +is that fair +sort of yeah why don't you make it why + + align:start position:0% +sort of yeah why don't you make it why + + + align:start position:0% +sort of yeah why don't you make it why +don't you make some you know some key + + align:start position:0% +don't you make some you know some key + + + align:start position:0% +don't you make some you know some key +points in your mind about what these + + align:start position:0% +points in your mind about what these + + + align:start position:0% +points in your mind about what these +pieces mean you just heard my version + + align:start position:0% +pieces mean you just heard my version + + + align:start position:0% +pieces mean you just heard my version +but truffles as you know I favor these + + align:start position:0% +but truffles as you know I favor these + + + align:start position:0% +but truffles as you know I favor these +how many of you have heard of rent + + align:start position:0% +how many of you have heard of rent + + + align:start position:0% +how many of you have heard of rent +pedagogy of the oppressed like Halle + + align:start position:0% +pedagogy of the oppressed like Halle + + + align:start position:0% +pedagogy of the oppressed like Halle +Berry do you know what pedagogy means + + align:start position:0% + + + + align:start position:0% + +I'm gonna well they're a little late for + + align:start position:0% +I'm gonna well they're a little late for + + + align:start position:0% +I'm gonna well they're a little late for +this one is there someone was there + + align:start position:0% +this one is there someone was there + + + align:start position:0% +this one is there someone was there +anyone who had read pedagogy of the + + align:start position:0% +anyone who had read pedagogy of the + + + align:start position:0% +anyone who had read pedagogy of the +oppressed how many of you ever taken a + + align:start position:0% +oppressed how many of you ever taken a + + + align:start position:0% +oppressed how many of you ever taken a +course in our education education policy + + align:start position:0% +course in our education education policy + + + align:start position:0% +course in our education education policy +how many of you have very strict set for + + align:start position:0% +how many of you have very strict set for + + + align:start position:0% +how many of you have very strict set for +this course of exceptionalism or how + + align:start position:0% +this course of exceptionalism or how + + + align:start position:0% +this course of exceptionalism or how +many of you taken her feel like you're + + align:start position:0% +many of you taken her feel like you're + + + align:start position:0% +many of you taken her feel like you're +stakeholders in the national color in a + + align:start position:0% +stakeholders in the national color in a + + + align:start position:0% +stakeholders in the national color in a +conversation about the change in + + align:start position:0% +conversation about the change in + + + align:start position:0% +conversation about the change in +national education policy or in the + + align:start position:0% +national education policy or in the + + + align:start position:0% +national education policy or in the +state education policy okay we found + + align:start position:0% +state education policy okay we found + + + align:start position:0% +state education policy okay we found +something + + align:start position:0% +something + + + align:start position:0% +something +okay who feels like they're sticklers + + align:start position:0% +okay who feels like they're sticklers + + + align:start position:0% +okay who feels like they're sticklers +are in the education policy stable + + align:start position:0% +are in the education policy stable + + + align:start position:0% +are in the education policy stable +they're back to play an active cycle + + align:start position:0% +they're back to play an active cycle + + + align:start position:0% +they're back to play an active cycle +they're like you're willing to show up + + align:start position:0% +they're like you're willing to show up + + + align:start position:0% +they're like you're willing to show up +you know to Congress to go to programs + + align:start position:0% +you know to Congress to go to programs + + + align:start position:0% +you know to Congress to go to programs +to talk to legislators right and so I + + align:start position:0% +to talk to legislators right and so I + + + align:start position:0% +to talk to legislators right and so I +think that I mean that kind of + + align:start position:0% +think that I mean that kind of + + + align:start position:0% +think that I mean that kind of +highlights to me the divide between the + + align:start position:0% +highlights to me the divide between the + + + align:start position:0% +highlights to me the divide between the +kinds of stuff like golden cats formal + + align:start position:0% +kinds of stuff like golden cats formal + + + align:start position:0% +kinds of stuff like golden cats formal +freemen consider are talking about right + + align:start position:0% +freemen consider are talking about right + + + align:start position:0% +freemen consider are talking about right +that it's and this is again hitching + + align:start position:0% +that it's and this is again hitching + + + align:start position:0% +that it's and this is again hitching +sort of my issues with the way in which + + align:start position:0% +sort of my issues with the way in which + + + align:start position:0% +sort of my issues with the way in which +we teach social sciences that so much of + + align:start position:0% +we teach social sciences that so much of + + + align:start position:0% +we teach social sciences that so much of +the Socratic method which is essentially + + align:start position:0% +the Socratic method which is essentially + + + align:start position:0% +the Socratic method which is essentially +you know Bill explaining to us what it + + align:start position:0% +you know Bill explaining to us what it + + + align:start position:0% +you know Bill explaining to us what it +is that we + + align:start position:0% +is that we + + + align:start position:0% +is that we +having that sort of flesh it out in + + align:start position:0% +having that sort of flesh it out in + + + align:start position:0% +having that sort of flesh it out in +debate you know in a lively and in a + + align:start position:0% +debate you know in a lively and in a + + + align:start position:0% +debate you know in a lively and in a +logical way um he is right like it's the + + align:start position:0% +logical way um he is right like it's the + + + align:start position:0% +logical way um he is right like it's the +Socratic method is to get us thinking + + align:start position:0% +Socratic method is to get us thinking + + + align:start position:0% +Socratic method is to get us thinking +about what this means truly an + + align:start position:0% +about what this means truly an + + + align:start position:0% +about what this means truly an +implementation of how to grapple with + + align:start position:0% +implementation of how to grapple with + + + align:start position:0% +implementation of how to grapple with +theory thank you yeah + + align:start position:0% +theory thank you yeah + + + align:start position:0% +theory thank you yeah +as you start bringing that up it might + + align:start position:0% +as you start bringing that up it might + + + align:start position:0% +as you start bringing that up it might +have been maybe instructive for us to + + align:start position:0% +have been maybe instructive for us to + + + align:start position:0% +have been maybe instructive for us to +have a couple of readings by a couple of + + align:start position:0% +have a couple of readings by a couple of + + + align:start position:0% +have a couple of readings by a couple of +states who are grappling with sort of + + align:start position:0% +states who are grappling with sort of + + + align:start position:0% +states who are grappling with sort of +education issues and grappling with some + + align:start position:0% +education issues and grappling with some + + + align:start position:0% +education issues and grappling with some +issues particularly those that are like + + align:start position:0% +issues particularly those that are like + + + align:start position:0% +issues particularly those that are like +I am the lead administrator I'm in + + align:start position:0% +I am the lead administrator I'm in + + + align:start position:0% +I am the lead administrator I'm in +charge of like the education for maybe + + align:start position:0% +charge of like the education for maybe + + + align:start position:0% +charge of like the education for maybe +like the city of Chicago versus looks + + align:start position:0% +like the city of Chicago versus looks + + + align:start position:0% +like the city of Chicago versus looks +like the state of Illinois and like how + + align:start position:0% +like the state of Illinois and like how + + + align:start position:0% +like the state of Illinois and like how +they're actually going about kind of + + align:start position:0% +they're actually going about kind of + + + align:start position:0% +they're actually going about kind of +grappling with these public institutions + + align:start position:0% +grappling with these public institutions + + + align:start position:0% +grappling with these public institutions +trying to changing these things because + + align:start position:0% +trying to changing these things because + + + align:start position:0% +trying to changing these things because +it's really nice to kind of look at the + + align:start position:0% +it's really nice to kind of look at the + + + align:start position:0% +it's really nice to kind of look at the +macroscopic level and be okay we're not + + align:start position:0% +macroscopic level and be okay we're not + + + align:start position:0% +macroscopic level and be okay we're not +graduating enough or low mass you know + + align:start position:0% +graduating enough or low mass you know + + + align:start position:0% +graduating enough or low mass you know +science and engineers but in reality + + align:start position:0% +science and engineers but in reality + + + align:start position:0% +science and engineers but in reality +education as we said because we have it + + align:start position:0% +education as we said because we have it + + + align:start position:0% +education as we said because we have it +sort of like really distributed model in + + align:start position:0% +sort of like really distributed model in + + + align:start position:0% +sort of like really distributed model in +the US and print like Sweden it's like + + align:start position:0% +the US and print like Sweden it's like + + + align:start position:0% +the US and print like Sweden it's like +I'm looking at this not only like + + align:start position:0% +I'm looking at this not only like + + + align:start position:0% +I'm looking at this not only like +community college by community college + + align:start position:0% +community college by community college + + + align:start position:0% +community college by community college +but like state by state and like that's + + align:start position:0% +but like state by state and like that's + + + align:start position:0% +but like state by state and like that's +how folks sort of interact with these + + align:start position:0% +how folks sort of interact with these + + + align:start position:0% +how folks sort of interact with these +education sort issues and I think maybe + + align:start position:0% +education sort issues and I think maybe + + + align:start position:0% +education sort issues and I think maybe +justifying and what I'm trying to get + + align:start position:0% +justifying and what I'm trying to get + + + align:start position:0% +justifying and what I'm trying to get +from her is like you have these active + + align:start position:0% +from her is like you have these active + + + align:start position:0% +from her is like you have these active +stakeholders that are really involved in + + align:start position:0% +stakeholders that are really involved in + + + align:start position:0% +stakeholders that are really involved in +sort of their small pools and like might + + align:start position:0% +sort of their small pools and like might + + + align:start position:0% +sort of their small pools and like might +have a little bit more of an effect + + align:start position:0% +have a little bit more of an effect + + + align:start position:0% +have a little bit more of an effect +there like a lot more ideas on like how + + align:start position:0% +there like a lot more ideas on like how + + + align:start position:0% +there like a lot more ideas on like how +to innovate within their own pools to + + align:start position:0% +to innovate within their own pools to + + + align:start position:0% +to innovate within their own pools to +get to this state where we want like + + align:start position:0% +get to this state where we want like + + + align:start position:0% +get to this state where we want like +sort of breakthrough education in + + align:start position:0% +sort of breakthrough education in + + + align:start position:0% +sort of breakthrough education in +addition to like incremental advances + + align:start position:0% +addition to like incremental advances + + + align:start position:0% +addition to like incremental advances +and so I think my recommendation would + + align:start position:0% +and so I think my recommendation would + + + align:start position:0% +and so I think my recommendation would +be like is there someone maybe in this + + align:start position:0% +be like is there someone maybe in this + + + align:start position:0% +be like is there someone maybe in this +pedagogy across book that could offer an + + align:start position:0% +pedagogy across book that could offer an + + + align:start position:0% +pedagogy across book that could offer an +alternative and are there folks within + + align:start position:0% +alternative and are there folks within + + + align:start position:0% +alternative and are there folks within +like who do education professionally and + + align:start position:0% +like who do education professionally and + + + align:start position:0% +like who do education professionally and +who do educational administration do + + align:start position:0% +who do educational administration do + + + align:start position:0% +who do educational administration do +they have these same thoughts and are + + align:start position:0% +they have these same thoughts and are + + + align:start position:0% +they have these same thoughts and are +they worried about these same things and + + align:start position:0% +they worried about these same things and + + + align:start position:0% +they worried about these same things and +are they trying to like look at these + + align:start position:0% +are they trying to like look at these + + + align:start position:0% +are they trying to like look at these +problems at the same level and there are + + align:start position:0% +problems at the same level and there are + + + align:start position:0% +problems at the same level and there are +their opinions and I think this is a + + align:start position:0% +their opinions and I think this is a + + + align:start position:0% +their opinions and I think this is a +crucial point for me are their opinions + + align:start position:0% +crucial point for me are their opinions + + + align:start position:0% +crucial point for me are their opinions +respective right because a PhD from the + + align:start position:0% +respective right because a PhD from the + + + align:start position:0% +respective right because a PhD from the +you know Stanford Graduate School of + + align:start position:0% +you know Stanford Graduate School of + + + align:start position:0% +you know Stanford Graduate School of +Education or the Harvard Graduate School + + align:start position:0% +Education or the Harvard Graduate School + + + align:start position:0% +Education or the Harvard Graduate School +of Education does not mean the same + + align:start position:0% +of Education does not mean the same + + + align:start position:0% +of Education does not mean the same +things to most people as a PhD and you + + align:start position:0% +things to most people as a PhD and you + + + align:start position:0% +things to most people as a PhD and you +know material science from those + + align:start position:0% +know material science from those + + + align:start position:0% +know material science from those +institutions and that that concerns me + + align:start position:0% +institutions and that that concerns me + + + align:start position:0% +institutions and that that concerns me +right because if it's the individuals + + align:start position:0% +right because if it's the individuals + + + align:start position:0% +right because if it's the individuals +there's + + align:start position:0% +there's + + + align:start position:0% +there's +so I guess it on your current own + + align:start position:0% +so I guess it on your current own + + + align:start position:0% +so I guess it on your current own +education and we have mentioned it + + align:start position:0% +education and we have mentioned it + + + align:start position:0% +education and we have mentioned it +before in this class of those who can do + + align:start position:0% +before in this class of those who can do + + + align:start position:0% +before in this class of those who can do +those who can't teach right and it is + + align:start position:0% +those who can't teach right and it is + + + align:start position:0% +those who can't teach right and it is +that sort of point of disrespect that we + + align:start position:0% +that sort of point of disrespect that we + + + align:start position:0% +that sort of point of disrespect that we +got out at the beginning of class that I + + align:start position:0% +got out at the beginning of class that I + + + align:start position:0% +got out at the beginning of class that I +think merits far more consideration by + + align:start position:0% +think merits far more consideration by + + + align:start position:0% +think merits far more consideration by +this group than do perhaps the contents + + align:start position:0% +this group than do perhaps the contents + + + align:start position:0% +this group than do perhaps the contents +of the economics reading by Romer + + align:start position:0% +of the economics reading by Romer + + + align:start position:0% +of the economics reading by Romer +because if we ourselves are not + + align:start position:0% +because if we ourselves are not + + + align:start position:0% +because if we ourselves are not +convinced that teaching is a worthwhile + + align:start position:0% +convinced that teaching is a worthwhile + + + align:start position:0% +convinced that teaching is a worthwhile +profession and that the education of + + align:start position:0% +profession and that the education of + + + align:start position:0% +profession and that the education of +young people is a worthwhile activity + + align:start position:0% +young people is a worthwhile activity + + + align:start position:0% +young people is a worthwhile activity +then who who can be convinced of that + + align:start position:0% +then who who can be convinced of that + + + align:start position:0% +then who who can be convinced of that +right if we are involved and invested in + + align:start position:0% +right if we are involved and invested in + + + align:start position:0% +right if we are involved and invested in +the promotion of more equitable + + align:start position:0% +the promotion of more equitable + + + align:start position:0% +the promotion of more equitable +education and science and technology + + align:start position:0% +education and science and technology + + + align:start position:0% +education and science and technology +because we know that that's the key to + + align:start position:0% +because we know that that's the key to + + + align:start position:0% +because we know that that's the key to +driving economic growth and also + + align:start position:0% +driving economic growth and also + + + align:start position:0% +driving economic growth and also +prosperity and decreasing inequality + + align:start position:0% +prosperity and decreasing inequality + + + align:start position:0% +prosperity and decreasing inequality +right and so that's why to me when Bill + + align:start position:0% +right and so that's why to me when Bill + + + align:start position:0% +right and so that's why to me when Bill +says you know that golden and cats are + + align:start position:0% +says you know that golden and cats are + + + align:start position:0% +says you know that golden and cats are +talking about where the policies that + + align:start position:0% +talking about where the policies that + + + align:start position:0% +talking about where the policies that +would address us getting back to a more + + align:start position:0% +would address us getting back to a more + + + align:start position:0% +would address us getting back to a more +equitable you know economic system to me + + align:start position:0% +equitable you know economic system to me + + + align:start position:0% +equitable you know economic system to me +it's not about policies it's about + + align:start position:0% +it's not about policies it's about + + + align:start position:0% +it's not about policies it's about +culture right it's about our perceptions + + align:start position:0% +culture right it's about our perceptions + + + align:start position:0% +culture right it's about our perceptions +of other people and what they are doing + + align:start position:0% +of other people and what they are doing + + + align:start position:0% +of other people and what they are doing +with their lives and about our + + align:start position:0% +with their lives and about our + + + align:start position:0% +with their lives and about our +distancing of ourselves as but that's + + align:start position:0% +distancing of ourselves as but that's + + + align:start position:0% +distancing of ourselves as but that's +not my issue that's not my brown right + + align:start position:0% +not my issue that's not my brown right + + + align:start position:0% +not my issue that's not my brown right +so we get to I think it's unfair and a + + align:start position:0% +so we get to I think it's unfair and a + + + align:start position:0% +so we get to I think it's unfair and a +little bit intellectually irresponsible + + align:start position:0% +little bit intellectually irresponsible + + + align:start position:0% +little bit intellectually irresponsible +of us to claim that distance while also + + align:start position:0% +of us to claim that distance while also + + + align:start position:0% +of us to claim that distance while also +protecting it so I would pause it to all + + align:start position:0% +protecting it so I would pause it to all + + + align:start position:0% +protecting it so I would pause it to all +of you that if you you know have time + + align:start position:0% +of you that if you you know have time + + + align:start position:0% +of you that if you you know have time +and the next maybe two or three years to + + align:start position:0% +and the next maybe two or three years to + + + align:start position:0% +and the next maybe two or three years to +pick up this book I'll go do your little + + align:start position:0% +pick up this book I'll go do your little + + + align:start position:0% +pick up this book I'll go do your little +press library which was alone it's about + + align:start position:0% +press library which was alone it's about + + + align:start position:0% +press library which was alone it's about +the education system in Brazil and about + + align:start position:0% +the education system in Brazil and about + + + align:start position:0% +the education system in Brazil and about +the ways in which students have been + + align:start position:0% +the ways in which students have been + + + align:start position:0% +the ways in which students have been +disregarded by the system and conceived + + align:start position:0% +disregarded by the system and conceived + + + align:start position:0% +disregarded by the system and conceived +of as passive recipients of knowledge + + align:start position:0% +of as passive recipients of knowledge + + + align:start position:0% +of as passive recipients of knowledge +rather than as active learners and sort + + align:start position:0% +rather than as active learners and sort + + + align:start position:0% +rather than as active learners and sort +of the the metaphor that he utilizes is + + align:start position:0% +of the the metaphor that he utilizes is + + + align:start position:0% +of the the metaphor that he utilizes is +that they're receptacles right and I + + align:start position:0% +that they're receptacles right and I + + + align:start position:0% +that they're receptacles right and I +mean sort of dumped in knowledge and + + align:start position:0% +mean sort of dumped in knowledge and + + + align:start position:0% +mean sort of dumped in knowledge and +then we expect them to regurgitate it + + align:start position:0% +then we expect them to regurgitate it + + + align:start position:0% +then we expect them to regurgitate it +out and to be able to apply it in the + + align:start position:0% +out and to be able to apply it in the + + + align:start position:0% +out and to be able to apply it in the +field where is his understanding of + + align:start position:0% +field where is his understanding of + + + align:start position:0% +field where is his understanding of +pedagogy which is the study of teaching + + align:start position:0% +pedagogy which is the study of teaching + + + align:start position:0% +pedagogy which is the study of teaching +the study of warning is that individuals + + align:start position:0% +the study of warning is that individuals + + + align:start position:0% +the study of warning is that individuals +have to grapple with something and + + align:start position:0% +have to grapple with something and + + + align:start position:0% +have to grapple with something and +that's in sort of at the heart of what + + align:start position:0% +that's in sort of at the heart of what + + + align:start position:0% +that's in sort of at the heart of what +really we'll be talking about in the + + align:start position:0% +really we'll be talking about in the + + + align:start position:0% +really we'll be talking about in the +mitx reading way + + align:start position:0% +mitx reading way + + + align:start position:0% +mitx reading way +the when they start talking about + + align:start position:0% +the when they start talking about + + + align:start position:0% +the when they start talking about +Seymour Cup hair who was a brilliant + + align:start position:0% +Seymour Cup hair who was a brilliant + + + align:start position:0% +Seymour Cup hair who was a brilliant +professor and researcher at MIT who + + align:start position:0% +professor and researcher at MIT who + + + align:start position:0% +professor and researcher at MIT who +created the Bobo constructionism which + + align:start position:0% +created the Bobo constructionism which + + + align:start position:0% +created the Bobo constructionism which +is the study of the study of something + + align:start position:0% +is the study of the study of something + + + align:start position:0% +is the study of the study of something +by doing that something and that is + + align:start position:0% +by doing that something and that is + + + align:start position:0% +by doing that something and that is +actually being very widely adopted in + + align:start position:0% +actually being very widely adopted in + + + align:start position:0% +actually being very widely adopted in +Southeast Asia in countries like + + align:start position:0% +Southeast Asia in countries like + + + align:start position:0% +Southeast Asia in countries like +Singapore and Thailand who are you know + + align:start position:0% +Singapore and Thailand who are you know + + + align:start position:0% +Singapore and Thailand who are you know +experiencing momentous economic advances + + align:start position:0% +experiencing momentous economic advances + + + align:start position:0% +experiencing momentous economic advances +and the research and development sector + + align:start position:0% +and the research and development sector + + + align:start position:0% +and the research and development sector +so I think very much you know pedagogy + + align:start position:0% +so I think very much you know pedagogy + + + align:start position:0% +so I think very much you know pedagogy +and considerations of the culture of a + + align:start position:0% +and considerations of the culture of a + + + align:start position:0% +and considerations of the culture of a +really relevant when you talk about + + align:start position:0% +really relevant when you talk about + + + align:start position:0% +really relevant when you talk about +education well I think we need to get + + align:start position:0% +education well I think we need to get + + + align:start position:0% +education well I think we need to get +back to dollars here though because if + + align:start position:0% +back to dollars here though because if + + + align:start position:0% +back to dollars here though because if +you are head of household single parent + + align:start position:0% +you are head of household single parent + + + align:start position:0% +you are head of household single parent +or single income family you wouldn't + + align:start position:0% +or single income family you wouldn't + + + align:start position:0% +or single income family you wouldn't +think that you can have a family on a + + align:start position:0% +think that you can have a family on a + + + align:start position:0% +think that you can have a family on a +high k12 teacher's salary + + align:start position:0% +high k12 teacher's salary + + + align:start position:0% +high k12 teacher's salary +you can't and even in here you yes + + align:start position:0% +you can't and even in here you yes + + + align:start position:0% +you can't and even in here you yes +the average came to talk to your salary + + align:start position:0% +the average came to talk to your salary + + + align:start position:0% +the average came to talk to your salary +is higher in say Los Angeles and it is + + align:start position:0% +is higher in say Los Angeles and it is + + + align:start position:0% +is higher in say Los Angeles and it is +in central Illinois or scroll price the + + align:start position:0% +in central Illinois or scroll price the + + + align:start position:0% +in central Illinois or scroll price the +US so they compensate for like living + + align:start position:0% +US so they compensate for like living + + + align:start position:0% +US so they compensate for like living +since it's that you still cannot be + + align:start position:0% +since it's that you still cannot be + + + align:start position:0% +since it's that you still cannot be +single parent had a concave your child + + align:start position:0% +single parent had a concave your child + + + align:start position:0% +single parent had a concave your child +salaries that only come out like you can + + align:start position:0% +salaries that only come out like you can + + + align:start position:0% +salaries that only come out like you can +sure you can think that k12 educational + + align:start position:0% +sure you can think that k12 educational + + + align:start position:0% +sure you can think that k12 educational +needs to be reformed you can be + + align:start position:0% +needs to be reformed you can be + + + align:start position:0% +needs to be reformed you can be +passionate about teaching but if you are + + align:start position:0% +passionate about teaching but if you are + + + align:start position:0% +passionate about teaching but if you are +financially responsible for a family + + align:start position:0% +financially responsible for a family + + + align:start position:0% +financially responsible for a family +unit can't be a teacher in k-12 doesn't + + align:start position:0% +unit can't be a teacher in k-12 doesn't + + + align:start position:0% +unit can't be a teacher in k-12 doesn't +matter how much you care about it so the + + align:start position:0% +matter how much you care about it so the + + + align:start position:0% +matter how much you care about it so the +reading those like I think they need + + align:start position:0% +reading those like I think they need + + + align:start position:0% +reading those like I think they need +like 50 hours to get knowledge so to me + + align:start position:0% +like 50 hours to get knowledge so to me + + + align:start position:0% +like 50 hours to get knowledge so to me +and I'm gonna do I'm gonna push it so we + + align:start position:0% +and I'm gonna do I'm gonna push it so we + + + align:start position:0% +and I'm gonna do I'm gonna push it so we +can get out of here reasonable time + + align:start position:0% +can get out of here reasonable time + + + align:start position:0% +can get out of here reasonable time +level I'm gonna do the last reading from + + align:start position:0% +level I'm gonna do the last reading from + + + align:start position:0% +level I'm gonna do the last reading from +our textbook and then come back to the + + align:start position:0% +our textbook and then come back to the + + + align:start position:0% +our textbook and then come back to the +MITx reading so + + align:start position:0% + + + + align:start position:0% + +I figured I'd put I'd put myself up here + + align:start position:0% +I figured I'd put I'd put myself up here + + + align:start position:0% +I figured I'd put I'd put myself up here +I had to really struggle with this Marty + + align:start position:0% +I had to really struggle with this Marty + + + align:start position:0% +I had to really struggle with this Marty +and I can tell you so look here's what's + + align:start position:0% +and I can tell you so look here's what's + + + align:start position:0% +and I can tell you so look here's what's +here's what's different right so new + + align:start position:0% +here's what's different right so new + + + align:start position:0% +here's what's different right so new +technology innovations are very slow to + + align:start position:0% +technology innovations are very slow to + + + align:start position:0% +technology innovations are very slow to +enter legacy sectors right remember + + align:start position:0% +enter legacy sectors right remember + + + align:start position:0% +enter legacy sectors right remember +discussing energy you know we did we + + align:start position:0% +discussing energy you know we did we + + + align:start position:0% +discussing energy you know we did we +invented fire you know I don't know how + + align:start position:0% +invented fire you know I don't know how + + + align:start position:0% +invented fire you know I don't know how +many millions of years that took then we + + align:start position:0% +many millions of years that took then we + + + align:start position:0% +many millions of years that took then we +you know burned trees we did that for + + align:start position:0% +you know burned trees we did that for + + + align:start position:0% +you know burned trees we did that for +millennia shall we say lightning struck + + align:start position:0% +millennia shall we say lightning struck + + + align:start position:0% +millennia shall we say lightning struck +right and we and we move to coal right + + align:start position:0% +right and we and we move to coal right + + + align:start position:0% +right and we and we move to coal right +move to coal and then you know we moved + + align:start position:0% +move to coal and then you know we moved + + + align:start position:0% +move to coal and then you know we moved +to oil and that's about as far as we've + + align:start position:0% +to oil and that's about as far as we've + + + align:start position:0% +to oil and that's about as far as we've +gotten essentially at since that time + + align:start position:0% + + + + align:start position:0% + +from compared to wood so similarly + + align:start position:0% +from compared to wood so similarly + + + align:start position:0% +from compared to wood so similarly +another legacy sector higher education + + align:start position:0% +another legacy sector higher education + + + align:start position:0% +another legacy sector higher education +you know what was the last really big + + align:start position:0% +you know what was the last really big + + + align:start position:0% +you know what was the last really big +you know reform in education so we went + + align:start position:0% +you know reform in education so we went + + + align:start position:0% +you know reform in education so we went +from like well that was an advanced + + align:start position:0% +from like well that was an advanced + + + align:start position:0% +from like well that was an advanced +there's no question about it but you + + align:start position:0% +there's no question about it but you + + + align:start position:0% +there's no question about it but you +know we had the platonic you know + + align:start position:0% +know we had the platonic you know + + + align:start position:0% +know we had the platonic you know +Academy and then you know momentous + + align:start position:0% +Academy and then you know momentous + + + align:start position:0% +Academy and then you know momentous +breakthrough around 1500 1500 years + + align:start position:0% +breakthrough around 1500 1500 years + + + align:start position:0% +breakthrough around 1500 1500 years +later we came up with the book right + + align:start position:0% +later we came up with the book right + + + align:start position:0% +later we came up with the book right +that was clearly a great break sir + + align:start position:0% +that was clearly a great break sir + + + align:start position:0% +that was clearly a great break sir +that's from a technological advanced + + align:start position:0% +that's from a technological advanced + + + align:start position:0% +that's from a technological advanced +period I mean that's that's about it + + align:start position:0% +period I mean that's that's about it + + + align:start position:0% +period I mean that's that's about it +right until we finally figured it out + + align:start position:0% +right until we finally figured it out + + + align:start position:0% +right until we finally figured it out +how to use this kind of stuff and we're + + align:start position:0% +how to use this kind of stuff and we're + + + align:start position:0% +how to use this kind of stuff and we're +starting to figure out how to bring that + + align:start position:0% +starting to figure out how to bring that + + + align:start position:0% +starting to figure out how to bring that +IT revolution into the classroom so that + + align:start position:0% +IT revolution into the classroom so that + + + align:start position:0% +IT revolution into the classroom so that +presents if the issue is bringing change + + align:start position:0% +presents if the issue is bringing change + + + align:start position:0% +presents if the issue is bringing change +into this system technology obviously + + align:start position:0% +into this system technology obviously + + + align:start position:0% +into this system technology obviously +can be a change driver and that's that's + + align:start position:0% +can be a change driver and that's that's + + + align:start position:0% +can be a change driver and that's that's +an interesting story that's not the only + + align:start position:0% +an interesting story that's not the only + + + align:start position:0% +an interesting story that's not the only +you know change in reform story as you + + align:start position:0% +you know change in reform story as you + + + align:start position:0% +you know change in reform story as you +just pointed out does stuff there's + + align:start position:0% +just pointed out does stuff there's + + + align:start position:0% +just pointed out does stuff there's +other important changes that to be + + align:start position:0% +other important changes that to be + + + align:start position:0% +other important changes that to be +considered but really within the last + + align:start position:0% +considered but really within the last + + + align:start position:0% +considered but really within the last +you know five six years we've actually + + align:start position:0% +you know five six years we've actually + + + align:start position:0% +you know five six years we've actually +seen the entry of + + align:start position:0% +seen the entry of + + + align:start position:0% +seen the entry of +IT type tools into into the classroom + + align:start position:0% +IT type tools into into the classroom + + + align:start position:0% +IT type tools into into the classroom +setting the classroom setting with + + align:start position:0% +setting the classroom setting with + + + align:start position:0% +setting the classroom setting with +potential potential momentous change so + + align:start position:0% +potential potential momentous change so + + + align:start position:0% +potential potential momentous change so +you know there's an open question here + + align:start position:0% +you know there's an open question here + + + align:start position:0% +you know there's an open question here +about whether MOOCs and online education + + align:start position:0% +about whether MOOCs and online education + + + align:start position:0% +about whether MOOCs and online education +are going to be a disruptive innovation + + align:start position:0% +are going to be a disruptive innovation + + + align:start position:0% +are going to be a disruptive innovation +and whether they will disrupt higher + + align:start position:0% +and whether they will disrupt higher + + + align:start position:0% +and whether they will disrupt higher +education and substitute in effect + + align:start position:0% +education and substitute in effect + + + align:start position:0% +education and substitute in effect +create a new model you know is to say + + align:start position:0% +create a new model you know is to say + + + align:start position:0% +create a new model you know is to say +Chipotle replaces McDonald's kind of + + align:start position:0% +Chipotle replaces McDonald's kind of + + + align:start position:0% +Chipotle replaces McDonald's kind of +approach say I told you I'd steal your + + align:start position:0% +approach say I told you I'd steal your + + + align:start position:0% +approach say I told you I'd steal your +in that forum are you and will Higher + + align:start position:0% +in that forum are you and will Higher + + + align:start position:0% +in that forum are you and will Higher +Education respond right will it respond + + align:start position:0% +Education respond right will it respond + + + align:start position:0% +Education respond right will it respond +with a blended model or will attempt to + + align:start position:0% +with a blended model or will attempt to + + + align:start position:0% +with a blended model or will attempt to +keep its existing model so we'll talk + + align:start position:0% +keep its existing model so we'll talk + + + align:start position:0% +keep its existing model so we'll talk +about that for a minute + + align:start position:0% +about that for a minute + + + align:start position:0% +about that for a minute +you know as we've seen universities are + + align:start position:0% +you know as we've seen universities are + + + align:start position:0% +you know as we've seen universities are +pretty deep you know present a deep + + align:start position:0% +pretty deep you know present a deep + + + align:start position:0% +pretty deep you know present a deep +problem for this kind of disruption + + align:start position:0% +problem for this kind of disruption + + + align:start position:0% +problem for this kind of disruption +because they are legacy sectors and they + + align:start position:0% +because they are legacy sectors and they + + + align:start position:0% +because they are legacy sectors and they +you know like all legacy sectors they + + align:start position:0% +you know like all legacy sectors they + + + align:start position:0% +you know like all legacy sectors they +tended to resist disruptive change + + align:start position:0% +tended to resist disruptive change + + + align:start position:0% +tended to resist disruptive change +higher institutions of higher education + + align:start position:0% +higher institutions of higher education + + + align:start position:0% +higher institutions of higher education +conduct almost no research almost no R&D + + align:start position:0% +conduct almost no research almost no R&D + + + align:start position:0% +conduct almost no research almost no R&D +on education itself almost none it's + + align:start position:0% +on education itself almost none it's + + + align:start position:0% +on education itself almost none it's +astonishing services sector generally + + align:start position:0% +astonishing services sector generally + + + align:start position:0% +astonishing services sector generally +are not particularly good at this but + + align:start position:0% +are not particularly good at this but + + + align:start position:0% +are not particularly good at this but +higher education may lead the pack there + + align:start position:0% +higher education may lead the pack there + + + align:start position:0% +higher education may lead the pack there +are very perverse pricing issues in + + align:start position:0% +are very perverse pricing issues in + + + align:start position:0% +are very perverse pricing issues in +higher education as you all are paying + + align:start position:0% +higher education as you all are paying + + + align:start position:0% +higher education as you all are paying +tuition at the moment understand it's a + + align:start position:0% +tuition at the moment understand it's a + + + align:start position:0% +tuition at the moment understand it's a +very decentralized model it's very hard + + align:start position:0% +very decentralized model it's very hard + + + align:start position:0% +very decentralized model it's very hard +to spread change and spread new ideas to + + align:start position:0% +to spread change and spread new ideas to + + + align:start position:0% +to spread change and spread new ideas to +transition new ideas because this is a + + align:start position:0% +transition new ideas because this is a + + + align:start position:0% +transition new ideas because this is a +very decentralized system there's in + + align:start position:0% +very decentralized system there's in + + + align:start position:0% +very decentralized system there's in +legacy sector terms there's a collective + + align:start position:0% +legacy sector terms there's a collective + + + align:start position:0% +legacy sector terms there's a collective +action problem how do you get collective + + align:start position:0% +action problem how do you get collective + + + align:start position:0% +action problem how do you get collective +action it costs literally thousands of + + align:start position:0% +action it costs literally thousands of + + + align:start position:0% +action it costs literally thousands of +institutions and I'm just focused on + + align:start position:0% +institutions and I'm just focused on + + + align:start position:0% +institutions and I'm just focused on +higher education at this point there's a + + align:start position:0% +higher education at this point there's a + + + align:start position:0% +higher education at this point there's a +whole additional story for online in the + + align:start position:0% +whole additional story for online in the + + + align:start position:0% +whole additional story for online in the +k-12 sector what's happened you all are + + align:start position:0% +k-12 sector what's happened you all are + + + align:start position:0% +k-12 sector what's happened you all are +familiar with EDX the entry of a non + + align:start position:0% +familiar with EDX the entry of a non + + + align:start position:0% +familiar with EDX the entry of a non +profit model here and frankly I have to + + align:start position:0% +profit model here and frankly I have to + + + align:start position:0% +profit model here and frankly I have to +give you know to mendes credit to + + align:start position:0% +give you know to mendes credit to + + + align:start position:0% +give you know to mendes credit to +Raphael rife because I never thought + + align:start position:0% +Raphael rife because I never thought + + + align:start position:0% +Raphael rife because I never thought +universities themselves would originate + + align:start position:0% +universities themselves would originate + + + align:start position:0% +universities themselves would originate +you know potentially disruptive changes + + align:start position:0% +you know potentially disruptive changes + + + align:start position:0% +you know potentially disruptive changes +for themselves that kind of violates my + + align:start position:0% +for themselves that kind of violates my + + + align:start position:0% +for themselves that kind of violates my +rule set but you know + + align:start position:0% +rule set but you know + + + align:start position:0% +rule set but you know +fail you know basically personally drove + + align:start position:0% +fail you know basically personally drove + + + align:start position:0% +fail you know basically personally drove +a fair amount of this and you know his + + align:start position:0% +a fair amount of this and you know his + + + align:start position:0% +a fair amount of this and you know his +background you know he was a poor kid + + align:start position:0% +background you know he was a poor kid + + + align:start position:0% +background you know he was a poor kid +growing up in Venezuela and you know + + align:start position:0% +growing up in Venezuela and you know + + + align:start position:0% +growing up in Venezuela and you know +from a family that had not sent children + + align:start position:0% +from a family that had not sent children + + + align:start position:0% +from a family that had not sent children +to college and you know he managed to + + align:start position:0% +to college and you know he managed to + + + align:start position:0% +to college and you know he managed to +get to go to the Technical College in + + align:start position:0% +get to go to the Technical College in + + + align:start position:0% +get to go to the Technical College in +Venezuela was a real breakthrough for + + align:start position:0% +Venezuela was a real breakthrough for + + + align:start position:0% +Venezuela was a real breakthrough for +him and you know ends up at MIT through + + align:start position:0% +him and you know ends up at MIT through + + + align:start position:0% +him and you know ends up at MIT through +a series of miracles and you know + + align:start position:0% +a series of miracles and you know + + + align:start position:0% +a series of miracles and you know +becomes president and you know he thinks + + align:start position:0% +becomes president and you know he thinks + + + align:start position:0% +becomes president and you know he thinks +all the time about that community that + + align:start position:0% +all the time about that community that + + + align:start position:0% +all the time about that community that +he left behind you know I know from + + align:start position:0% +he left behind you know I know from + + + align:start position:0% +he left behind you know I know from +knowing him in conversations with him + + align:start position:0% +knowing him in conversations with him + + + align:start position:0% +knowing him in conversations with him +just how he saw this online education + + align:start position:0% +just how he saw this online education + + + align:start position:0% +just how he saw this online education +model as a remarkable new tool to get + + align:start position:0% +model as a remarkable new tool to get + + + align:start position:0% +model as a remarkable new tool to get +education and educational platforms + + align:start position:0% +education and educational platforms + + + align:start position:0% +education and educational platforms +everywhere I mean it is a remarkable new + + align:start position:0% +everywhere I mean it is a remarkable new + + + align:start position:0% +everywhere I mean it is a remarkable new +entrant possibility in education and he + + align:start position:0% +entrant possibility in education and he + + + align:start position:0% +entrant possibility in education and he +did this frankly he drove the creation + + align:start position:0% +did this frankly he drove the creation + + + align:start position:0% +did this frankly he drove the creation +of EDX and they were corresponding + + align:start position:0% +of EDX and they were corresponding + + + align:start position:0% +of EDX and they were corresponding +examples coming out of Stanford Udacity + + align:start position:0% +examples coming out of Stanford Udacity + + + align:start position:0% +examples coming out of Stanford Udacity +and Coursera it's you know it's in a + + align:start position:0% +and Coursera it's you know it's in a + + + align:start position:0% +and Coursera it's you know it's in a +comparable period but he wanted to do a + + align:start position:0% +comparable period but he wanted to do a + + + align:start position:0% +comparable period but he wanted to do a +non profit model because he thought it + + align:start position:0% +non profit model because he thought it + + + align:start position:0% +non profit model because he thought it +would be better geared to this mission + + align:start position:0% +would be better geared to this mission + + + align:start position:0% +would be better geared to this mission +of significantly improving education + + align:start position:0% +of significantly improving education + + + align:start position:0% +of significantly improving education +everywhere that a new tool set would be + + align:start position:0% +everywhere that a new tool set would be + + + align:start position:0% +everywhere that a new tool set would be +in hand suppose kids like him growing up + + align:start position:0% +in hand suppose kids like him growing up + + + align:start position:0% +in hand suppose kids like him growing up +on Sandlot baseball Lots in Venezuela + + align:start position:0% +on Sandlot baseball Lots in Venezuela + + + align:start position:0% +on Sandlot baseball Lots in Venezuela +you know could have had access to + + align:start position:0% +you know could have had access to + + + align:start position:0% +you know could have had access to +you know MIT courses right what would + + align:start position:0% +you know MIT courses right what would + + + align:start position:0% +you know MIT courses right what would +that be like so you know that that was + + align:start position:0% +that be like so you know that that was + + + align:start position:0% +that be like so you know that that was +his story and that's the story behind + + align:start position:0% +his story and that's the story behind + + + align:start position:0% +his story and that's the story behind +the creation of EDX and you know the + + align:start position:0% +the creation of EDX and you know the + + + align:start position:0% +the creation of EDX and you know the +nonprofit model enables certain kinds of + + align:start position:0% +nonprofit model enables certain kinds of + + + align:start position:0% +nonprofit model enables certain kinds of +things for-profit model enables other + + align:start position:0% +things for-profit model enables other + + + align:start position:0% +things for-profit model enables other +things but one of the interesting + + align:start position:0% +things but one of the interesting + + + align:start position:0% +things but one of the interesting +features of EDX is that it is an + + align:start position:0% +features of EDX is that it is an + + + align:start position:0% +features of EDX is that it is an +open-source model it's an open-source + + align:start position:0% +open-source model it's an open-source + + + align:start position:0% +open-source model it's an open-source +technology platform and people + + align:start position:0% +technology platform and people + + + align:start position:0% +technology platform and people +contribute and constantly build up the + + align:start position:0% +contribute and constantly build up the + + + align:start position:0% +contribute and constantly build up the +quality of the technology behind the + + align:start position:0% +quality of the technology behind the + + + align:start position:0% +quality of the technology behind the +model it's harder to do that in a four + + align:start position:0% +model it's harder to do that in a four + + + align:start position:0% +model it's harder to do that in a four +profit kind of approach it's still + + align:start position:0% +profit kind of approach it's still + + + align:start position:0% +profit kind of approach it's still +finding its way towards a business model + + align:start position:0% +finding its way towards a business model + + + align:start position:0% +finding its way towards a business model +we'll talk about it + + align:start position:0% +we'll talk about it + + + align:start position:0% +we'll talk about it +the other major MOOC providers are + + align:start position:0% +the other major MOOC providers are + + + align:start position:0% +the other major MOOC providers are +listed here you're familiar with them + + align:start position:0% +listed here you're familiar with them + + + align:start position:0% +listed here you're familiar with them +they're on for-profit models you know + + align:start position:0% +they're on for-profit models you know + + + align:start position:0% +they're on for-profit models you know +the political world took a look at these + + align:start position:0% +the political world took a look at these + + + align:start position:0% +the political world took a look at these +MOOCs and had different ideological + + align:start position:0% +MOOCs and had different ideological + + + align:start position:0% +MOOCs and had different ideological +reactions you know on the right to some + + align:start position:0% +reactions you know on the right to some + + + align:start position:0% +reactions you know on the right to some +extent they saw an opportunity of these + + align:start position:0% +extent they saw an opportunity of these + + + align:start position:0% +extent they saw an opportunity of these +free online educational courses as an + + align:start position:0% +free online educational courses as an + + + align:start position:0% +free online educational courses as an +opportunity to get rid of these pesky + + align:start position:0% +opportunity to get rid of these pesky + + + align:start position:0% +opportunity to get rid of these pesky +left-wing universities that are + + align:start position:0% +left-wing universities that are + + + align:start position:0% +left-wing universities that are +constantly training the wrong people on + + align:start position:0% +constantly training the wrong people on + + + align:start position:0% +constantly training the wrong people on +the left it was a it was a sense that oh + + align:start position:0% +the left it was a it was a sense that oh + + + align:start position:0% +the left it was a it was a sense that oh +we can finally get rid of tuition right + + align:start position:0% +we can finally get rid of tuition right + + + align:start position:0% +we can finally get rid of tuition right +have the Bernie Sanders free tuition + + align:start position:0% +have the Bernie Sanders free tuition + + + align:start position:0% +have the Bernie Sanders free tuition +dream because online education doesn't + + align:start position:0% +dream because online education doesn't + + + align:start position:0% +dream because online education doesn't +cost anything and we'll just do that + + align:start position:0% +cost anything and we'll just do that + + + align:start position:0% +cost anything and we'll just do that +right you know obviously there's that's + + align:start position:0% +right you know obviously there's that's + + + align:start position:0% +right you know obviously there's that's +a little bit of magical thinking here on + + align:start position:0% +a little bit of magical thinking here on + + + align:start position:0% +a little bit of magical thinking here on +both sides but states have begun passing + + align:start position:0% +both sides but states have begun passing + + + align:start position:0% +both sides but states have begun passing +laws doing things like requiring $10,000 + + align:start position:0% +laws doing things like requiring $10,000 + + + align:start position:0% +laws doing things like requiring $10,000 +you know bas and you know comparable + + align:start position:0% +you know bas and you know comparable + + + align:start position:0% +you know bas and you know comparable +kinds of issues but the real question + + align:start position:0% +kinds of issues but the real question + + + align:start position:0% +kinds of issues but the real question +what a deep question here is what's + + align:start position:0% +what a deep question here is what's + + + align:start position:0% +what a deep question here is what's +gonna happen to the residential campus + + align:start position:0% +gonna happen to the residential campus + + + align:start position:0% +gonna happen to the residential campus +right is online just going to displace + + align:start position:0% +right is online just going to displace + + + align:start position:0% +right is online just going to displace +this whole thing and if not why not so + + align:start position:0% +this whole thing and if not why not so + + + align:start position:0% +this whole thing and if not why not so +they're online I think as all of you + + align:start position:0% +they're online I think as all of you + + + align:start position:0% +they're online I think as all of you +understand it can do some things really + + align:start position:0% +understand it can do some things really + + + align:start position:0% +understand it can do some things really +well it's a whole new tool set for + + align:start position:0% +well it's a whole new tool set for + + + align:start position:0% +well it's a whole new tool set for +visualization for representation + + align:start position:0% +visualization for representation + + + align:start position:0% +visualization for representation +it offers incredible opportunities for + + align:start position:0% +it offers incredible opportunities for + + + align:start position:0% +it offers incredible opportunities for +reinforcement and assessment that a + + align:start position:0% +reinforcement and assessment that a + + + align:start position:0% +reinforcement and assessment that a +lecturer can't do you can use feedback + + align:start position:0% +lecturer can't do you can use feedback + + + align:start position:0% +lecturer can't do you can use feedback +loops to and repetition to you know do + + align:start position:0% +loops to and repetition to you know do + + + align:start position:0% +loops to and repetition to you know do +continuous assessment which you know + + align:start position:0% +continuous assessment which you know + + + align:start position:0% +continuous assessment which you know +there's no way your standard college and + + align:start position:0% +there's no way your standard college and + + + align:start position:0% +there's no way your standard college and +university lecture class could ever + + align:start position:0% +university lecture class could ever + + + align:start position:0% +university lecture class could ever +replicate those kinds of capabilities + + align:start position:0% +replicate those kinds of capabilities + + + align:start position:0% +replicate those kinds of capabilities +and they're pretty important so online + + align:start position:0% +and they're pretty important so online + + + align:start position:0% +and they're pretty important so online +is going to have some features that are + + align:start position:0% +is going to have some features that are + + + align:start position:0% +is going to have some features that are +better than what you know lectures can + + align:start position:0% +better than what you know lectures can + + + align:start position:0% +better than what you know lectures can +do and then potentially if you move the + + align:start position:0% +do and then potentially if you move the + + + align:start position:0% +do and then potentially if you move the +lecture online then you can free up your + + align:start position:0% +lecture online then you can free up your + + + align:start position:0% +lecture online then you can free up your +classroom for much more interchange and + + align:start position:0% +classroom for much more interchange and + + + align:start position:0% +classroom for much more interchange and +interpersonal + + align:start position:0% +interpersonal + + + align:start position:0% +interpersonal +kinds of communication and more the + + align:start position:0% +kinds of communication and more the + + + align:start position:0% +kinds of communication and more the +learning-by-doing + + align:start position:0% +learning-by-doing + + + align:start position:0% +learning-by-doing +opportunities that that Steph was + + align:start position:0% +opportunities that that Steph was + + + align:start position:0% +opportunities that that Steph was +suggesting so maybe it frees up you know + + align:start position:0% +suggesting so maybe it frees up you know + + + align:start position:0% +suggesting so maybe it frees up you know +what the classroom could become now + + align:start position:0% +what the classroom could become now + + + align:start position:0% +what the classroom could become now +vital educational elements remain face + + align:start position:0% +vital educational elements remain face + + + align:start position:0% +vital educational elements remain face +to face right at least at the moment + + align:start position:0% +to face right at least at the moment + + + align:start position:0% +to face right at least at the moment +online can't replicate these so oral + + align:start position:0% +online can't replicate these so oral + + + align:start position:0% +online can't replicate these so oral +expression oral presentation advocacy + + align:start position:0% +expression oral presentation advocacy + + + align:start position:0% +expression oral presentation advocacy +skills that kind of the way in which you + + align:start position:0% +skills that kind of the way in which you + + + align:start position:0% +skills that kind of the way in which you +have to organize your expertise to be + + align:start position:0% +have to organize your expertise to be + + + align:start position:0% +have to organize your expertise to be +able to speak about a subject area face + + align:start position:0% +able to speak about a subject area face + + + align:start position:0% +able to speak about a subject area face +to face can do this right it's really + + align:start position:0% +to face can do this right it's really + + + align:start position:0% +to face can do this right it's really +hard to do that effectively at this + + align:start position:0% +hard to do that effectively at this + + + align:start position:0% +hard to do that effectively at this +point with the technology online written + + align:start position:0% +point with the technology online written + + + align:start position:0% +point with the technology online written +analysis so far online writing + + align:start position:0% +analysis so far online writing + + + align:start position:0% +analysis so far online writing +evaluation leaves a lot to be desired + + align:start position:0% +evaluation leaves a lot to be desired + + + align:start position:0% +evaluation leaves a lot to be desired +research look in the end you really do + + align:start position:0% +research look in the end you really do + + + align:start position:0% +research look in the end you really do +research on lab benches with colleagues + + align:start position:0% +research on lab benches with colleagues + + + align:start position:0% +research on lab benches with colleagues +right it's still quite face to face and + + align:start position:0% +right it's still quite face to face and + + + align:start position:0% +right it's still quite face to face and +you can replicate some of that through + + align:start position:0% +you can replicate some of that through + + + align:start position:0% +you can replicate some of that through +simulation and modeling but a lot of it + + align:start position:0% +simulation and modeling but a lot of it + + + align:start position:0% +simulation and modeling but a lot of it +you can't so there's a lot that probably + + align:start position:0% +you can't so there's a lot that probably + + + align:start position:0% +you can't so there's a lot that probably +needs to stay on the face to face side + + align:start position:0% +needs to stay on the face to face side + + + align:start position:0% +needs to stay on the face to face side +so these kinds of skills learning + + align:start position:0% +so these kinds of skills learning + + + align:start position:0% +so these kinds of skills learning +requires a lot of human scaffolding for + + align:start position:0% +requires a lot of human scaffolding for + + + align:start position:0% +requires a lot of human scaffolding for +discourse or argumentation mentoring for + + align:start position:0% +discourse or argumentation mentoring for + + + align:start position:0% +discourse or argumentation mentoring for +making the case for research for making + + align:start position:0% +making the case for research for making + + + align:start position:0% +making the case for research for making +the conceptual leap and a lot of what + + align:start position:0% +the conceptual leap and a lot of what + + + align:start position:0% +the conceptual leap and a lot of what +occurs in the classroom the + + align:start position:0% +occurs in the classroom the + + + align:start position:0% +occurs in the classroom the +socialization process of the classroom + + align:start position:0% +socialization process of the classroom + + + align:start position:0% +socialization process of the classroom +drives a lot of learning right there + + align:start position:0% +drives a lot of learning right there + + + align:start position:0% +drives a lot of learning right there +kind of back and forth the kind of + + align:start position:0% +kind of back and forth the kind of + + + align:start position:0% +kind of back and forth the kind of +competition the kind of connections + + align:start position:0% +competition the kind of connections + + + align:start position:0% +competition the kind of connections +between people friendships that build + + align:start position:0% +between people friendships that build + + + align:start position:0% +between people friendships that build +the kind of community feeling if a class + + align:start position:0% +the kind of community feeling if a class + + + align:start position:0% +the kind of community feeling if a class +comes together those are very powerful + + align:start position:0% +comes together those are very powerful + + + align:start position:0% +comes together those are very powerful +learning aids right these are very + + align:start position:0% +learning aids right these are very + + + align:start position:0% +learning aids right these are very +powerful learning tools and obviously + + align:start position:0% +powerful learning tools and obviously + + + align:start position:0% +powerful learning tools and obviously +you can't get that stuff sitting in a + + align:start position:0% +you can't get that stuff sitting in a + + + align:start position:0% +you can't get that stuff sitting in a +basement in front of a blue screen right + + align:start position:0% +basement in front of a blue screen right + + + align:start position:0% +basement in front of a blue screen right +so the real question here is how do you + + align:start position:0% +so the real question here is how do you + + + align:start position:0% +so the real question here is how do you +optimize the two sides how do we let + + align:start position:0% +optimize the two sides how do we let + + + align:start position:0% +optimize the two sides how do we let +online do what it does best + + align:start position:0% +online do what it does best + + + align:start position:0% +online do what it does best +and how do we let the face-to-face peace + + align:start position:0% +and how do we let the face-to-face peace + + + align:start position:0% +and how do we let the face-to-face peace +thrive and do more right that's really + + align:start position:0% +thrive and do more right that's really + + + align:start position:0% +thrive and do more right that's really +the opportunity that we now have is to + + align:start position:0% +the opportunity that we now have is to + + + align:start position:0% +the opportunity that we now have is to +completely restructure education with a + + align:start position:0% +completely restructure education with a + + + align:start position:0% +completely restructure education with a +whole new toolset then in turn will + + align:start position:0% +whole new toolset then in turn will + + + align:start position:0% +whole new toolset then in turn will +enable that face-to-face education to + + align:start position:0% +enable that face-to-face education to + + + align:start position:0% +enable that face-to-face education to +kind of rise to a new level right that's + + align:start position:0% +kind of rise to a new level right that's + + + align:start position:0% +kind of rise to a new level right that's +the dream that's the hope + + align:start position:0% +the dream that's the hope + + + align:start position:0% +the dream that's the hope +that's the reform this potentially + + align:start position:0% +that's the reform this potentially + + + align:start position:0% +that's the reform this potentially +enables so it's a human-machine + + align:start position:0% +enables so it's a human-machine + + + align:start position:0% +enables so it's a human-machine +symbiosis remember it's JCR Licklider + + align:start position:0% +symbiosis remember it's JCR Licklider + + + align:start position:0% +symbiosis remember it's JCR Licklider +let the computer do what it's good at + + align:start position:0% +let the computer do what it's good at + + + align:start position:0% +let the computer do what it's good at +and let people do what they're good at + + align:start position:0% +and let people do what they're good at + + + align:start position:0% +and let people do what they're good at +and you have a symbiosis of the two + + align:start position:0% +and you have a symbiosis of the two + + + align:start position:0% +and you have a symbiosis of the two +that's what we could get in education + + align:start position:0% +that's what we could get in education + + + align:start position:0% +that's what we could get in education +now that's the opportunity space and + + align:start position:0% +now that's the opportunity space and + + + align:start position:0% +now that's the opportunity space and +that's a blended learning model now the + + align:start position:0% +that's a blended learning model now the + + + align:start position:0% +that's a blended learning model now the +technology is gonna change + + align:start position:0% +technology is gonna change + + + align:start position:0% +technology is gonna change +and it's gonna get better at some of + + align:start position:0% +and it's gonna get better at some of + + + align:start position:0% +and it's gonna get better at some of +these things right but that's an ongoing + + align:start position:0% +these things right but that's an ongoing + + + align:start position:0% +these things right but that's an ongoing +and extended process what happens to the + + align:start position:0% +and extended process what happens to the + + + align:start position:0% +and extended process what happens to the +university right for a long time + + align:start position:0% +university right for a long time + + + align:start position:0% +university right for a long time +newspaper journalists for writing + + align:start position:0% +newspaper journalists for writing + + + align:start position:0% +newspaper journalists for writing +articles oh haha what's gonna happen to + + align:start position:0% +articles oh haha what's gonna happen to + + + align:start position:0% +articles oh haha what's gonna happen to +universities is what happened to us is + + align:start position:0% +universities is what happened to us is + + + align:start position:0% +universities is what happened to us is +journalists write all our newspapers + + align:start position:0% +journalists write all our newspapers + + + align:start position:0% +journalists write all our newspapers +went out of business essentially right + + align:start position:0% +went out of business essentially right + + + align:start position:0% +went out of business essentially right +ha ha it's gonna happen to you to see + + align:start position:0% +ha ha it's gonna happen to you to see + + + align:start position:0% +ha ha it's gonna happen to you to see +you know this online revolution it's + + align:start position:0% +you know this online revolution it's + + + align:start position:0% +you know this online revolution it's +going to drive you under right it's + + align:start position:0% +going to drive you under right it's + + + align:start position:0% +going to drive you under right it's +problematic if we do that because + + align:start position:0% +problematic if we do that because + + + align:start position:0% +problematic if we do that because +frankly universities create the course + + align:start position:0% +frankly universities create the course + + + align:start position:0% +frankly universities create the course +content right they are fairly important + + align:start position:0% +content right they are fairly important + + + align:start position:0% +content right they are fairly important +institutions after all on the content + + align:start position:0% +institutions after all on the content + + + align:start position:0% +institutions after all on the content +side there are research engines as well + + align:start position:0% +side there are research engines as well + + + align:start position:0% +side there are research engines as well +as teaching centers right so we kind of + + align:start position:0% +as teaching centers right so we kind of + + + align:start position:0% +as teaching centers right so we kind of +need that research in the American + + align:start position:0% +need that research in the American + + + align:start position:0% +need that research in the American +system and many other countries we blend + + align:start position:0% +system and many other countries we blend + + + align:start position:0% +system and many other countries we blend +the research model and the teaching + + align:start position:0% +the research model and the teaching + + + align:start position:0% +the research model and the teaching +model so there's a lot of learning by + + align:start position:0% +model so there's a lot of learning by + + + align:start position:0% +model so there's a lot of learning by +doing more so in the graduate education + + align:start position:0% +doing more so in the graduate education + + + align:start position:0% +doing more so in the graduate education +phase but there's a lot of learning by + + align:start position:0% +phase but there's a lot of learning by + + + align:start position:0% +phase but there's a lot of learning by +doing in that system so you need these + + align:start position:0% +doing in that system so you need these + + + align:start position:0% +doing in that system so you need these +institutions for that stuff and you know + + align:start position:0% +institutions for that stuff and you know + + + align:start position:0% +institutions for that stuff and you know +if you drive if you use the model to + + align:start position:0% +if you drive if you use the model to + + + align:start position:0% +if you drive if you use the model to +drive the university model under you've + + align:start position:0% +drive the university model under you've + + + align:start position:0% +drive the university model under you've +got these underlying you know really + + align:start position:0% +got these underlying you know really + + + align:start position:0% +got these underlying you know really +deep kind of problems so there's a + + align:start position:0% +deep kind of problems so there's a + + + align:start position:0% +deep kind of problems so there's a +question about whether or not + + align:start position:0% +question about whether or not + + + align:start position:0% +question about whether or not +universities will adapt you know could + + align:start position:0% +universities will adapt you know could + + + align:start position:0% +universities will adapt you know could +and part of that story is bringing + + align:start position:0% +and part of that story is bringing + + + align:start position:0% +and part of that story is bringing +learning science to online education and + + align:start position:0% +learning science to online education and + + + align:start position:0% +learning science to online education and +we're going to get to that in just a + + align:start position:0% +we're going to get to that in just a + + + align:start position:0% +we're going to get to that in just a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +it does the online revolution does + + align:start position:0% +it does the online revolution does + + + align:start position:0% +it does the online revolution does +create incredible opportunities we + + align:start position:0% +create incredible opportunities we + + + align:start position:0% +create incredible opportunities we +talked earlier about the possibility of + + align:start position:0% +talked earlier about the possibility of + + + align:start position:0% +talked earlier about the possibility of +you know worldwide availability of high + + align:start position:0% +you know worldwide availability of high + + + align:start position:0% +you know worldwide availability of high +quality education it's not a blended + + align:start position:0% +quality education it's not a blended + + + align:start position:0% +quality education it's not a blended +model but it's pretty good right it's + + align:start position:0% +model but it's pretty good right it's + + + align:start position:0% +model but it's pretty good right it's +pretty good material you can learn a lot + + align:start position:0% +pretty good material you can learn a lot + + + align:start position:0% +pretty good material you can learn a lot +from it that's a staggering new + + align:start position:0% +from it that's a staggering new + + + align:start position:0% +from it that's a staggering new +opportunity for education worldwide and + + align:start position:0% +opportunity for education worldwide and + + + align:start position:0% +opportunity for education worldwide and +that's precisely why Raphael rife pushed + + align:start position:0% +that's precisely why Raphael rife pushed + + + align:start position:0% +that's precisely why Raphael rife pushed +this effort that was the vision that he + + align:start position:0% +this effort that was the vision that he + + + align:start position:0% +this effort that was the vision that he +saw frankly Martine so what if they did + + align:start position:0% +saw frankly Martine so what if they did + + + align:start position:0% +saw frankly Martine so what if they did +like a little special Institute that + + align:start position:0% +like a little special Institute that + + + align:start position:0% +like a little special Institute that +just focuses exactly what the vision is + + align:start position:0% +just focuses exactly what the vision is + + + align:start position:0% +just focuses exactly what the vision is +because you see our folks a lot on like + + align:start position:0% +because you see our folks a lot on like + + + align:start position:0% +because you see our folks a lot on like +the vision of what ARPANET would be so + + align:start position:0% +the vision of what ARPANET would be so + + + align:start position:0% +the vision of what ARPANET would be so +the vision of like in an ideal education + + align:start position:0% +the vision of like in an ideal education + + + align:start position:0% +the vision of like in an ideal education +world which I know they have an + + align:start position:0% +world which I know they have an + + + align:start position:0% +world which I know they have an +initiative but like I have that DARPA + + align:start position:0% +initiative but like I have that DARPA + + + align:start position:0% +initiative but like I have that DARPA +identity like project managers I mean + + align:start position:0% +identity like project managers I mean + + + align:start position:0% +identity like project managers I mean +it's an interesting idea and there was + + align:start position:0% +it's an interesting idea and there was + + + align:start position:0% +it's an interesting idea and there was +discussion of creating a DARPA within + + align:start position:0% +discussion of creating a DARPA within + + + align:start position:0% +discussion of creating a DARPA within +the Department of Education I have to + + align:start position:0% +the Department of Education I have to + + + align:start position:0% +the Department of Education I have to +say I was skeptical about whether that + + align:start position:0% +say I was skeptical about whether that + + + align:start position:0% +say I was skeptical about whether that +can work because there's no real + + align:start position:0% +can work because there's no real + + + align:start position:0% +can work because there's no real +tradition of R&D in the Department of + + align:start position:0% +tradition of R&D in the Department of + + + align:start position:0% +tradition of R&D in the Department of +Education it's really quite limited and + + align:start position:0% +Education it's really quite limited and + + + align:start position:0% +Education it's really quite limited and +would they understand the model enough + + align:start position:0% +would they understand the model enough + + + align:start position:0% +would they understand the model enough +interestingly today or yesterday + + align:start position:0% +interestingly today or yesterday + + + align:start position:0% +interestingly today or yesterday +DARPA issued a broad area announcement + + align:start position:0% +DARPA issued a broad area announcement + + + align:start position:0% +DARPA issued a broad area announcement +for you guessed it develop a learning + + align:start position:0% +for you guessed it develop a learning + + + align:start position:0% +for you guessed it develop a learning +machine for lifelong education that's + + align:start position:0% +machine for lifelong education that's + + + align:start position:0% +machine for lifelong education that's +the challenge right so DARPA + + align:start position:0% +the challenge right so DARPA + + + align:start position:0% +the challenge right so DARPA +is now in this territory in some very + + align:start position:0% +is now in this territory in some very + + + align:start position:0% +is now in this territory in some very +interesting ways and actually the + + align:start position:0% +interesting ways and actually the + + + align:start position:0% +interesting ways and actually the +military's in this territory the + + align:start position:0% +military's in this territory the + + + align:start position:0% +military's in this territory the +military has done more than any other + + align:start position:0% +military has done more than any other + + + align:start position:0% +military has done more than any other +organization by far to use computer + + align:start position:0% +organization by far to use computer + + + align:start position:0% +organization by far to use computer +gaming as a training tool right and + + align:start position:0% +gaming as a training tool right and + + + align:start position:0% +gaming as a training tool right and +computer gaming is you all I'd + + align:start position:0% +computer gaming is you all I'd + + + align:start position:0% +computer gaming is you all I'd +understand probably a lot better than I + + align:start position:0% +understand probably a lot better than I + + + align:start position:0% +understand probably a lot better than I +do + + align:start position:0% +do + + + align:start position:0% +do +operates on an education kind of model + + align:start position:0% +operates on an education kind of model + + + align:start position:0% +operates on an education kind of model +right it's another word learning that + + align:start position:0% +right it's another word learning that + + + align:start position:0% +right it's another word learning that +game is a very complex process and has + + align:start position:0% +game is a very complex process and has + + + align:start position:0% +game is a very complex process and has +acquired over time and + + align:start position:0% +acquired over time and + + + align:start position:0% +acquired over time and +a good game gets that flow right of + + align:start position:0% +a good game gets that flow right of + + + align:start position:0% +a good game gets that flow right of +helping introduce the new new elements + + align:start position:0% +helping introduce the new new elements + + + align:start position:0% +helping introduce the new new elements +of the game to you and the learning that + + align:start position:0% +of the game to you and the learning that + + + align:start position:0% +of the game to you and the learning that +game requires and manageable steps and + + align:start position:0% +game requires and manageable steps and + + + align:start position:0% +game requires and manageable steps and +then reinforcing that and reiterating or + + align:start position:0% +then reinforcing that and reiterating or + + + align:start position:0% +then reinforcing that and reiterating or +put you back into feedback loops so that + + align:start position:0% +put you back into feedback loops so that + + + align:start position:0% +put you back into feedback loops so that +you get it and then driving you to the + + align:start position:0% +you get it and then driving you to the + + + align:start position:0% +you get it and then driving you to the +next stage of the game that's a very + + align:start position:0% +next stage of the game that's a very + + + align:start position:0% +next stage of the game that's a very +interesting potential educational tool + + align:start position:0% +interesting potential educational tool + + + align:start position:0% +interesting potential educational tool +probably some of the best work in the + + align:start position:0% +probably some of the best work in the + + + align:start position:0% +probably some of the best work in the +country that's being done on that is + + align:start position:0% +country that's being done on that is + + + align:start position:0% +country that's being done on that is +being done by Eric Hoffer here at MIT + + align:start position:0% +being done by Eric Hoffer here at MIT + + + align:start position:0% +being done by Eric Hoffer here at MIT +who's developed a whole new set of + + align:start position:0% +who's developed a whole new set of + + + align:start position:0% +who's developed a whole new set of +Education games for K through 12 I'm + + align:start position:0% +Education games for K through 12 I'm + + + align:start position:0% +Education games for K through 12 I'm +surprised that industry hasn't moved in + + align:start position:0% +surprised that industry hasn't moved in + + + align:start position:0% +surprised that industry hasn't moved in +on the sector I think it's gradually + + align:start position:0% +on the sector I think it's gradually + + + align:start position:0% +on the sector I think it's gradually +starting to happen but that's that's an + + align:start position:0% +starting to happen but that's that's an + + + align:start position:0% +starting to happen but that's that's an +interesting part of this story because + + align:start position:0% +interesting part of this story because + + + align:start position:0% +interesting part of this story because +the only story here is not MOOCs right + + align:start position:0% +the only story here is not MOOCs right + + + align:start position:0% +the only story here is not MOOCs right +MOOCs came about because a whole bunch + + align:start position:0% +MOOCs came about because a whole bunch + + + align:start position:0% +MOOCs came about because a whole bunch +of computer nerds at places like MIT and + + align:start position:0% +of computer nerds at places like MIT and + + + align:start position:0% +of computer nerds at places like MIT and +Stanford saw wait a minute we got we got + + align:start position:0% +Stanford saw wait a minute we got we got + + + align:start position:0% +Stanford saw wait a minute we got we got +broadband around the world we have a + + align:start position:0% +broadband around the world we have a + + + align:start position:0% +broadband around the world we have a +whole new delivery mechanism we've got a + + align:start position:0% +whole new delivery mechanism we've got a + + + align:start position:0% +whole new delivery mechanism we've got a +whole new tool set let's do something + + align:start position:0% +whole new tool set let's do something + + + align:start position:0% +whole new tool set let's do something +right and they rush to fill that void + + align:start position:0% +right and they rush to fill that void + + + align:start position:0% +right and they rush to fill that void +and and you know the edx was created by + + align:start position:0% +and and you know the edx was created by + + + align:start position:0% +and and you know the edx was created by +you know folks out of our computer + + align:start position:0% +you know folks out of our computer + + + align:start position:0% +you know folks out of our computer +science department rushy + + align:start position:0% + + + + align:start position:0% + +we figured out the printing press was a + + align:start position:0% +we figured out the printing press was a + + + align:start position:0% +we figured out the printing press was a +thing and we keep mass printing books + + align:start position:0% +thing and we keep mass printing books + + + align:start position:0% +thing and we keep mass printing books +who was the one who decided how do we + + align:start position:0% +who was the one who decided how do we + + + align:start position:0% +who was the one who decided how do we +change maybe from a Socratic like + + align:start position:0% +change maybe from a Socratic like + + + align:start position:0% +change maybe from a Socratic like +teacher-student apprentice relationship + + align:start position:0% +teacher-student apprentice relationship + + + align:start position:0% +teacher-student apprentice relationship +to like teacher and then large lecture + + align:start position:0% +to like teacher and then large lecture + + + align:start position:0% +to like teacher and then large lecture +hall what were the sort of driving + + align:start position:0% +hall what were the sort of driving + + + align:start position:0% +hall what were the sort of driving +initiatives are like who started with + + align:start position:0% +initiatives are like who started with + + + align:start position:0% +initiatives are like who started with +these kind of large lecture halls and + + align:start position:0% +these kind of large lecture halls and + + + align:start position:0% +these kind of large lecture halls and +kind of these same maybe like blue + + align:start position:0% +kind of these same maybe like blue + + + align:start position:0% +kind of these same maybe like blue +kleiner based like vision for how is + + align:start position:0% +kleiner based like vision for how is + + + align:start position:0% +kleiner based like vision for how is +education gonna look once I have a + + align:start position:0% +education gonna look once I have a + + + align:start position:0% +education gonna look once I have a +textbook and so now how is it you like + + align:start position:0% +textbook and so now how is it you like + + + align:start position:0% +textbook and so now how is it you like +you need sort of the same people just + + align:start position:0% +you need sort of the same people just + + + align:start position:0% +you need sort of the same people just +sort of start taking a look as how's + + align:start position:0% +sort of start taking a look as how's + + + align:start position:0% +sort of start taking a look as how's +education you look in the sort of + + align:start position:0% +education you look in the sort of + + + align:start position:0% +education you look in the sort of +blended learning model and I don't know + + align:start position:0% +blended learning model and I don't know + + + align:start position:0% +blended learning model and I don't know +even if MIT or Stanford all these people + + align:start position:0% +even if MIT or Stanford all these people + + + align:start position:0% +even if MIT or Stanford all these people +have any sort of idea of like what that + + align:start position:0% +have any sort of idea of like what that + + + align:start position:0% +have any sort of idea of like what that +vision for that learning what it all is + + align:start position:0% +vision for that learning what it all is + + + align:start position:0% +vision for that learning what it all is +well I think we're starting to look at + + align:start position:0% +well I think we're starting to look at + + + align:start position:0% +well I think we're starting to look at +it in a pretty serious way here in a + + align:start position:0% +it in a pretty serious way here in a + + + align:start position:0% +it in a pretty serious way here in a +number of other places as well you know + + align:start position:0% +number of other places as well you know + + + align:start position:0% +number of other places as well you know +good intellectual work is ongoing let me + + align:start position:0% +good intellectual work is ongoing let me + + + align:start position:0% +good intellectual work is ongoing let me +close off with a couple of points about + + align:start position:0% +close off with a couple of points about + + + align:start position:0% +close off with a couple of points about +this + + align:start position:0% +this + + + align:start position:0% +this +but let's and let's be sure to hold on + + align:start position:0% +but let's and let's be sure to hold on + + + align:start position:0% +but let's and let's be sure to hold on +to your question guys I think it'll be + + align:start position:0% +to your question guys I think it'll be + + + align:start position:0% +to your question guys I think it'll be +particularly relevant we talk about the + + align:start position:0% +particularly relevant we talk about the + + + align:start position:0% +particularly relevant we talk about the +learning science piece to Rasheed one + + align:start position:0% +learning science piece to Rasheed one + + + align:start position:0% +learning science piece to Rasheed one +thing that we're learning about these + + align:start position:0% +thing that we're learning about these + + + align:start position:0% +thing that we're learning about these +MOOCs is you know how many people want + + align:start position:0% +MOOCs is you know how many people want + + + align:start position:0% +MOOCs is you know how many people want +to go and sit in front of you know blue + + align:start position:0% +to go and sit in front of you know blue + + + align:start position:0% +to go and sit in front of you know blue +screens in their basement and take a + + align:start position:0% +screens in their basement and take a + + + align:start position:0% +screens in their basement and take a +one-off course right I mean you know I + + align:start position:0% +one-off course right I mean you know I + + + align:start position:0% +one-off course right I mean you know I +may be Bill Gates you know I have to + + align:start position:0% +may be Bill Gates you know I have to + + + align:start position:0% +may be Bill Gates you know I have to +confess that I probably came to college + + align:start position:0% +confess that I probably came to college + + + align:start position:0% +confess that I probably came to college +because I wanted the degree right that's + + align:start position:0% +because I wanted the degree right that's + + + align:start position:0% +because I wanted the degree right that's +probably why it took all those courses + + align:start position:0% +probably why it took all those courses + + + align:start position:0% +probably why it took all those courses +right in the end I wanted something that + + align:start position:0% +right in the end I wanted something that + + + align:start position:0% +right in the end I wanted something that +would translate into economic gain for + + align:start position:0% +would translate into economic gain for + + + align:start position:0% +would translate into economic gain for +me that's obviously a profound motivator + + align:start position:0% +me that's obviously a profound motivator + + + align:start position:0% +me that's obviously a profound motivator +so platforms that are organized simply + + align:start position:0% +so platforms that are organized simply + + + align:start position:0% +so platforms that are organized simply +around offering one-off courses without + + align:start position:0% +around offering one-off courses without + + + align:start position:0% +around offering one-off courses without +a coherent framework without a resulting + + align:start position:0% +a coherent framework without a resulting + + + align:start position:0% +a coherent framework without a resulting +credential that's not a very good + + align:start position:0% +credential that's not a very good + + + align:start position:0% +credential that's not a very good +economic model so the MOOC offerors have + + align:start position:0% +economic model so the MOOC offerors have + + + align:start position:0% +economic model so the MOOC offerors have +been very much moving in the direction + + align:start position:0% +been very much moving in the direction + + + align:start position:0% +been very much moving in the direction +of trying to find some kind of + + align:start position:0% +of trying to find some kind of + + + align:start position:0% +of trying to find some kind of +certificate that will certify that + + align:start position:0% +certificate that will certify that + + + align:start position:0% +certificate that will certify that +you've accomplished something so you + + align:start position:0% +you've accomplished something so you + + + align:start position:0% +you've accomplished something so you +know a lot of people will be just + + align:start position:0% +know a lot of people will be just + + + align:start position:0% +know a lot of people will be just +interested in content and I've certainly + + align:start position:0% +interested in content and I've certainly + + + align:start position:0% +interested in content and I've certainly +taken mooc courses just because i was + + align:start position:0% +taken mooc courses just because i was + + + align:start position:0% +taken mooc courses just because i was +intrigued with the content but a lot of + + align:start position:0% +intrigued with the content but a lot of + + + align:start position:0% +intrigued with the content but a lot of +people are going to be motivated by the + + align:start position:0% +people are going to be motivated by the + + + align:start position:0% +people are going to be motivated by the +community that credential and you know + + align:start position:0% +community that credential and you know + + + align:start position:0% +community that credential and you know +MOOCs are moving in the direction of + + align:start position:0% +MOOCs are moving in the direction of + + + align:start position:0% +MOOCs are moving in the direction of +offering credentials for completing + + align:start position:0% +offering credentials for completing + + + align:start position:0% +offering credentials for completing +things + + align:start position:0% +things + + + align:start position:0% +things +I mean Georgia Tech and Udacity have a + + align:start position:0% +I mean Georgia Tech and Udacity have a + + + align:start position:0% +I mean Georgia Tech and Udacity have a +master's degree in computer science now + + align:start position:0% +master's degree in computer science now + + + align:start position:0% +master's degree in computer science now +which is available online at a + + align:start position:0% +which is available online at a + + + align:start position:0% +which is available online at a +remarkably reasonable price farlow one + + align:start position:0% +remarkably reasonable price farlow one + + + align:start position:0% +remarkably reasonable price farlow one +in class you know on on-campus tuition + + align:start position:0% +in class you know on on-campus tuition + + + align:start position:0% +in class you know on on-campus tuition +levels mit is very in a very innovative + + align:start position:0% +levels mit is very in a very innovative + + + align:start position:0% +levels mit is very in a very innovative +way doing these mini masters courses I + + align:start position:0% +way doing these mini masters courses I + + + align:start position:0% +way doing these mini masters courses I +think we've got we did one in an area of + + align:start position:0% +think we've got we did one in an area of + + + align:start position:0% +think we've got we did one in an area of +MIT is famous for which is supply chain + + align:start position:0% +MIT is famous for which is supply chain + + + align:start position:0% +MIT is famous for which is supply chain +management and there's several more to + + align:start position:0% +management and there's several more to + + + align:start position:0% +management and there's several more to +come the D lab has just picked one up + + align:start position:0% +come the D lab has just picked one up + + + align:start position:0% +come the D lab has just picked one up +the development world development + + align:start position:0% +the development world development + + + align:start position:0% +the development world development +community is doing one there's going to + + align:start position:0% +community is doing one there's going to + + + align:start position:0% +community is doing one there's going to +be more at MIT that's a very interesting + + align:start position:0% +be more at MIT that's a very interesting + + + align:start position:0% +be more at MIT that's a very interesting +model + + align:start position:0% +model + + + align:start position:0% +model +you get a quote micro masters + + align:start position:0% +you get a quote micro masters + + + align:start position:0% +you get a quote micro masters +certificate for completing the course + + align:start position:0% +certificate for completing the course + + + align:start position:0% +certificate for completing the course +and you pay you pay because there's got + + align:start position:0% +and you pay you pay because there's got + + + align:start position:0% +and you pay you pay because there's got +to be assessment right and that cost + + align:start position:0% +to be assessment right and that cost + + + align:start position:0% +to be assessment right and that cost +somebody who's got to do that assessment + + align:start position:0% +somebody who's got to do that assessment + + + align:start position:0% +somebody who's got to do that assessment +so that's gonna be a cost so you pay a + + align:start position:0% +so that's gonna be a cost so you pay a + + + align:start position:0% +so that's gonna be a cost so you pay a +modest amount for that assessment and + + align:start position:0% +modest amount for that assessment and + + + align:start position:0% +modest amount for that assessment and +you take a year-long micro masters + + align:start position:0% +you take a year-long micro masters + + + align:start position:0% +you take a year-long micro masters +course and then MIT if you've done + + align:start position:0% +course and then MIT if you've done + + + align:start position:0% +course and then MIT if you've done +really well MIT will accept you for a + + align:start position:0% +really well MIT will accept you for a + + + align:start position:0% +really well MIT will accept you for a +semester on campus right now they can + + align:start position:0% +semester on campus right now they can + + + align:start position:0% +semester on campus right now they can +only offer that to a modest number of + + align:start position:0% +only offer that to a modest number of + + + align:start position:0% +only offer that to a modest number of +the thousands of people that are getting + + align:start position:0% +the thousands of people that are getting + + + align:start position:0% +the thousands of people that are getting +the micro masters degree but interesting + + align:start position:0% +the micro masters degree but interesting + + + align:start position:0% +the micro masters degree but interesting +the other universities now once you + + align:start position:0% +the other universities now once you + + + align:start position:0% +the other universities now once you +complete the MIT micro masters piece + + align:start position:0% +complete the MIT micro masters piece + + + align:start position:0% +complete the MIT micro masters piece +they are enabling you to come on campus + + align:start position:0% +they are enabling you to come on campus + + + align:start position:0% +they are enabling you to come on campus +and complete you know and get a real + + align:start position:0% +and complete you know and get a real + + + align:start position:0% +and complete you know and get a real +masters in the course of an additional + + align:start position:0% +masters in the course of an additional + + + align:start position:0% +masters in the course of an additional +semester of work so that's a very + + align:start position:0% +semester of work so that's a very + + + align:start position:0% +semester of work so that's a very +interesting model that's obviously much + + align:start position:0% +interesting model that's obviously much + + + align:start position:0% +interesting model that's obviously much +more of a blended model you get a lot of + + align:start position:0% +more of a blended model you get a lot of + + + align:start position:0% +more of a blended model you get a lot of +content and information which online is + + align:start position:0% +content and information which online is + + + align:start position:0% +content and information which online is +pretty good at on the online side and + + align:start position:0% +pretty good at on the online side and + + + align:start position:0% +pretty good at on the online side and +then you really come in for an intensive + + align:start position:0% +then you really come in for an intensive + + + align:start position:0% +then you really come in for an intensive +classroom experience which is much more + + align:start position:0% +classroom experience which is much more + + + align:start position:0% +classroom experience which is much more +the way in which they've designed the + + align:start position:0% +the way in which they've designed the + + + align:start position:0% +the way in which they've designed the +micro masters here when you do the real + + align:start position:0% +micro masters here when you do the real + + + align:start position:0% +micro masters here when you do the real +mess is much more learning-by-doing you + + align:start position:0% +mess is much more learning-by-doing you + + + align:start position:0% +mess is much more learning-by-doing you +can take one off courses at MIT so + + align:start position:0% +can take one off courses at MIT so + + + align:start position:0% +can take one off courses at MIT so +there's lots of issues I think right and + + align:start position:0% +there's lots of issues I think right and + + + align:start position:0% +there's lots of issues I think right and +MIT used to have an extension school you + + align:start position:0% +MIT used to have an extension school you + + + align:start position:0% +MIT used to have an extension school you +know in its early day it's called a + + align:start position:0% +know in its early day it's called a + + + align:start position:0% +know in its early day it's called a +Lowell Institute which is essentially an + + align:start position:0% +Lowell Institute which is essentially an + + + align:start position:0% +Lowell Institute which is essentially an +adult educational program it was + + align:start position:0% +adult educational program it was + + + align:start position:0% +adult educational program it was +available for citizens of Boston very + + align:start position:0% +available for citizens of Boston very + + + align:start position:0% +available for citizens of Boston very +innovative and interesting on its old + + align:start position:0% +innovative and interesting on its old + + + align:start position:0% +innovative and interesting on its old +historic campus right across the river + + align:start position:0% +historic campus right across the river + + + align:start position:0% +historic campus right across the river +and back Bay somehow that got lost in + + align:start position:0% +and back Bay somehow that got lost in + + + align:start position:0% +and back Bay somehow that got lost in +the process but in a way MIT is just + + align:start position:0% +the process but in a way MIT is just + + + align:start position:0% +the process but in a way MIT is just +open a whole new school right that's MIT + + align:start position:0% +open a whole new school right that's MIT + + + align:start position:0% +open a whole new school right that's MIT +X and it's a massive worldwide global + + align:start position:0% +X and it's a massive worldwide global + + + align:start position:0% +X and it's a massive worldwide global +extension school so there's a whole new + + align:start position:0% +extension school so there's a whole new + + + align:start position:0% +extension school so there's a whole new +school here we just haven't fully + + align:start position:0% +school here we just haven't fully + + + align:start position:0% +school here we just haven't fully +recognized you yet and look lifelong + + align:start position:0% +recognized you yet and look lifelong + + + align:start position:0% +recognized you yet and look lifelong +learning may be the best application + + align:start position:0% +learning may be the best application + + + align:start position:0% +learning may be the best application +right because in lifelong learning in + + align:start position:0% +right because in lifelong learning in + + + align:start position:0% +right because in lifelong learning in +theory at least you've already learned + + align:start position:0% +theory at least you've already learned + + + align:start position:0% +theory at least you've already learned +those explanatory skills those oral + + align:start position:0% +those explanatory skills those oral + + + align:start position:0% +those explanatory skills those oral +presentation skills you've already + + align:start position:0% +presentation skills you've already + + + align:start position:0% +presentation skills you've already +learned those writing skills right + + align:start position:0% +learned those writing skills right + + + align:start position:0% +learned those writing skills right +you've already got a lot of those + + align:start position:0% +you've already got a lot of those + + + align:start position:0% +you've already got a lot of those +fundamental pieces which are largely a + + align:start position:0% +fundamental pieces which are largely a + + + align:start position:0% +fundamental pieces which are largely a +part of the undergraduate education + + align:start position:0% +part of the undergraduate education + + + align:start position:0% +part of the undergraduate education +scene but also part of the high school + + align:start position:0% +scene but also part of the high school + + + align:start position:0% +scene but also part of the high school +senior Theory you've got some of those + + align:start position:0% +senior Theory you've got some of those + + + align:start position:0% +senior Theory you've got some of those +down and then what you're in for + + align:start position:0% +down and then what you're in for + + + align:start position:0% +down and then what you're in for +after you know doing work in a relevant + + align:start position:0% +after you know doing work in a relevant + + + align:start position:0% +after you know doing work in a relevant +area you're in to enhance your career + + align:start position:0% +area you're in to enhance your career + + + align:start position:0% +area you're in to enhance your career +skill set in a lifelong learning setting + + align:start position:0% +skill set in a lifelong learning setting + + + align:start position:0% +skill set in a lifelong learning setting +the average age of a student at a + + align:start position:0% +the average age of a student at a + + + align:start position:0% +the average age of a student at a +community college is 29 in other words + + align:start position:0% +community college is 29 in other words + + + align:start position:0% +community college is 29 in other words +they're already in the workforce 40% of + + align:start position:0% +they're already in the workforce 40% of + + + align:start position:0% +they're already in the workforce 40% of +what community colleges now offer our + + align:start position:0% +what community colleges now offer our + + + align:start position:0% +what community colleges now offer our +certificates in quasi professional areas + + align:start position:0% +certificates in quasi professional areas + + + align:start position:0% +certificates in quasi professional areas +that in effect certified to employers + + align:start position:0% +that in effect certified to employers + + + align:start position:0% +that in effect certified to employers +that you've got an additional skill set + + align:start position:0% +that you've got an additional skill set + + + align:start position:0% +that you've got an additional skill set +right that's very interesting right that + + align:start position:0% +right that's very interesting right that + + + align:start position:0% +right that's very interesting right that +lifelong learning opportunity to upgrade + + align:start position:0% +lifelong learning opportunity to upgrade + + + align:start position:0% +lifelong learning opportunity to upgrade +your skill set and qualify for you a new + + align:start position:0% +your skill set and qualify for you a new + + + align:start position:0% +your skill set and qualify for you a new +set of you know career areas that's a + + align:start position:0% +set of you know career areas that's a + + + align:start position:0% +set of you know career areas that's a +really important feature that's a really + + align:start position:0% +really important feature that's a really + + + align:start position:0% +really important feature that's a really +important problem for those people who + + align:start position:0% +important problem for those people who + + + align:start position:0% +important problem for those people who +got left behind right through this + + align:start position:0% +got left behind right through this + + + align:start position:0% +got left behind right through this +failure of our higher education system + + align:start position:0% +failure of our higher education system + + + align:start position:0% +failure of our higher education system +to graduate enough people right that's a + + align:start position:0% +to graduate enough people right that's a + + + align:start position:0% +to graduate enough people right that's a +really interesting promising option for + + align:start position:0% +really interesting promising option for + + + align:start position:0% +really interesting promising option for +what one I can help us with and lifelong + + align:start position:0% +what one I can help us with and lifelong + + + align:start position:0% +what one I can help us with and lifelong +learning maybe the best tool we've got + + align:start position:0% +learning maybe the best tool we've got + + + align:start position:0% +learning maybe the best tool we've got +that MOOCs and online education can + + align:start position:0% +that MOOCs and online education can + + + align:start position:0% +that MOOCs and online education can +apply to so those are some you know some + + align:start position:0% +apply to so those are some you know some + + + align:start position:0% +apply to so those are some you know some +features of what online education may + + align:start position:0% +features of what online education may + + + align:start position:0% +features of what online education may +offer us the economic model we're still + + align:start position:0% +offer us the economic model we're still + + + align:start position:0% +offer us the economic model we're still +feeling our way what's the business + + align:start position:0% +feeling our way what's the business + + + align:start position:0% +feeling our way what's the business +model how are these cost centers going + + align:start position:0% +model how are these cost centers going + + + align:start position:0% +model how are these cost centers going +to justify themselves we're not there + + align:start position:0% +to justify themselves we're not there + + + align:start position:0% +to justify themselves we're not there +yet but it looks like the certificate + + align:start position:0% +yet but it looks like the certificate + + + align:start position:0% +yet but it looks like the certificate +kind of micro masters kind of stuff is a + + align:start position:0% +kind of micro masters kind of stuff is a + + + align:start position:0% +kind of micro masters kind of stuff is a +probably good way to do this lifelong + + align:start position:0% +probably good way to do this lifelong + + + align:start position:0% +probably good way to do this lifelong +learning maybe another very good way to + + align:start position:0% +learning maybe another very good way to + + + align:start position:0% +learning maybe another very good way to +do it will universities be willing all + + align:start position:0% +do it will universities be willing all + + + align:start position:0% +do it will universities be willing all +right so we're sort of at a situation + + align:start position:0% +right so we're sort of at a situation + + + align:start position:0% +right so we're sort of at a situation +now where universities offer a bunch of + + align:start position:0% +now where universities offer a bunch of + + + align:start position:0% +now where universities offer a bunch of +MOOCs over on one side purely online and + + align:start position:0% +MOOCs over on one side purely online and + + + align:start position:0% +MOOCs over on one side purely online and +then they're running their same old + + align:start position:0% +then they're running their same old + + + align:start position:0% +then they're running their same old +University + + align:start position:0% +University + + + align:start position:0% +University +right with lecture classes and nothing + + align:start position:0% +right with lecture classes and nothing + + + align:start position:0% +right with lecture classes and nothing +really changes because as we discussed + + align:start position:0% +really changes because as we discussed + + + align:start position:0% +really changes because as we discussed +the blended model is what's key to the + + align:start position:0% +the blended model is what's key to the + + + align:start position:0% +the blended model is what's key to the +reform right because that will drive a + + align:start position:0% +reform right because that will drive a + + + align:start position:0% +reform right because that will drive a +new kind of classroom the kind of + + align:start position:0% +new kind of classroom the kind of + + + align:start position:0% +new kind of classroom the kind of +cultural change you're talking about + + align:start position:0% +cultural change you're talking about + + + align:start position:0% +cultural change you're talking about +Steph right it could be a driver for + + align:start position:0% +Steph right it could be a driver for + + + align:start position:0% +Steph right it could be a driver for +this so unless universities are willing + + align:start position:0% +this so unless universities are willing + + + align:start position:0% +this so unless universities are willing +to really think hard about the blended + + align:start position:0% +to really think hard about the blended + + + align:start position:0% +to really think hard about the blended +model then we won't get the revolution + + align:start position:0% +model then we won't get the revolution + + + align:start position:0% +model then we won't get the revolution +that we really need right it kind of + + align:start position:0% +that we really need right it kind of + + + align:start position:0% +that we really need right it kind of +transformation of what goes on in the + + align:start position:0% +transformation of what goes on in the + + + align:start position:0% +transformation of what goes on in the +classroom and then full utilization is + + align:start position:0% +classroom and then full utilization is + + + align:start position:0% +classroom and then full utilization is +whole new tool set right that gives us + + align:start position:0% +whole new tool set right that gives us + + + align:start position:0% +whole new tool set right that gives us +essentially information and content + + align:start position:0% +essentially information and content + + + align:start position:0% +essentially information and content +access so you know we're still gonna + + align:start position:0% +access so you know we're still gonna + + + align:start position:0% +access so you know we're still gonna +need and the term I think you were + + align:start position:0% +need and the term I think you were + + + align:start position:0% +need and the term I think you were +looking for stuff in your argument and + + align:start position:0% +looking for stuff in your argument and + + + align:start position:0% +looking for stuff in your argument and +it's a term that we use in the legacy + + align:start position:0% +it's a term that we use in the legacy + + + align:start position:0% +it's a term that we use in the legacy +sector analysis who are the change + + align:start position:0% +sector analysis who are the change + + + align:start position:0% +sector analysis who are the change +agents going to be how are we going to + + align:start position:0% +agents going to be how are we going to + + + align:start position:0% +agents going to be how are we going to +drive change here and then that gets us + + align:start position:0% +drive change here and then that gets us + + + align:start position:0% +drive change here and then that gets us +into where next + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +well my team provides huge subsidies to + + align:start position:0% +well my team provides huge subsidies to + + + align:start position:0% +well my team provides huge subsidies to +graduate students and a massive system + + align:start position:0% +graduate students and a massive system + + + align:start position:0% +graduate students and a massive system +and fellowships so they're not paying + + align:start position:0% +and fellowships so they're not paying + + + align:start position:0% +and fellowships so they're not paying +tuition but they in terms of the + + align:start position:0% +tuition but they in terms of the + + + align:start position:0% +tuition but they in terms of the +research side yes research output + + align:start position:0% +research side yes research output + + + align:start position:0% +research side yes research output +graduate students at core but tuition + + align:start position:0% +graduate students at core but tuition + + + align:start position:0% +graduate students at core but tuition +believe me undergraduate so we'll see + + align:start position:0% +believe me undergraduate so we'll see + + + align:start position:0% +believe me undergraduate so we'll see +I'm not yet clear who's gonna drive this + + align:start position:0% +I'm not yet clear who's gonna drive this + + + align:start position:0% +I'm not yet clear who's gonna drive this +revolution a blended learning education + + align:start position:0% +revolution a blended learning education + + + align:start position:0% +revolution a blended learning education +model and you know MIT is now exploring + + align:start position:0% +model and you know MIT is now exploring + + + align:start position:0% +model and you know MIT is now exploring +it I mean there's over 90 online classes + + align:start position:0% +it I mean there's over 90 online classes + + + align:start position:0% +it I mean there's over 90 online classes +and over 90 percent of MIT students you + + align:start position:0% +and over 90 percent of MIT students you + + + align:start position:0% +and over 90 percent of MIT students you +all can tell me this is true according + + align:start position:0% +all can tell me this is true according + + + align:start position:0% +all can tell me this is true according +to my friend Sanjay sarva VP for online + + align:start position:0% +to my friend Sanjay sarva VP for online + + + align:start position:0% +to my friend Sanjay sarva VP for online +learning + + align:start position:0% +learning + + + align:start position:0% +learning +Sanjay says 90 percent of undergraduate + + align:start position:0% +Sanjay says 90 percent of undergraduate + + + align:start position:0% +Sanjay says 90 percent of undergraduate +students now have a blended learning + + align:start position:0% +students now have a blended learning + + + align:start position:0% +students now have a blended learning +experience in their undergraduate + + align:start position:0% +experience in their undergraduate + + + align:start position:0% +experience in their undergraduate +careers is that sound right to you all + + align:start position:0% +careers is that sound right to you all + + + align:start position:0% +careers is that sound right to you all +okay I'm reassured let me try to layout + + align:start position:0% +okay I'm reassured let me try to layout + + + align:start position:0% +okay I'm reassured let me try to layout +and then we'll have you know twenty + + align:start position:0% +and then we'll have you know twenty + + + align:start position:0% +and then we'll have you know twenty +minutes plus for discussion the authors + + align:start position:0% +minutes plus for discussion the authors + + + align:start position:0% +minutes plus for discussion the authors +of this 2016 report on learning science + + align:start position:0% +of this 2016 report on learning science + + + align:start position:0% +of this 2016 report on learning science +were Sanjay Sarma Karen Wilcox of + + align:start position:0% +were Sanjay Sarma Karen Wilcox of + + + align:start position:0% +were Sanjay Sarma Karen Wilcox of +aero-astro Eric Klopfer who I mentioned + + align:start position:0% +aero-astro Eric Klopfer who I mentioned + + + align:start position:0% +aero-astro Eric Klopfer who I mentioned +before Phillip will pella my office in + + align:start position:0% +before Phillip will pella my office in + + + align:start position:0% +before Phillip will pella my office in +Washington + + align:start position:0% + + + + align:start position:0% + +the new online platforms as I said a + + align:start position:0% +the new online platforms as I said a + + + align:start position:0% +the new online platforms as I said a +little little earlier came out of + + align:start position:0% +little little earlier came out of + + + align:start position:0% +little little earlier came out of +computer science departments because + + align:start position:0% +computer science departments because + + + align:start position:0% +computer science departments because +they saw these incredible broadband + + align:start position:0% +they saw these incredible broadband + + + align:start position:0% +they saw these incredible broadband +access opportunities and believe me they + + align:start position:0% +access opportunities and believe me they + + + align:start position:0% +access opportunities and believe me they +were real and then I was in Egypt about + + align:start position:0% +were real and then I was in Egypt about + + + align:start position:0% +were real and then I was in Egypt about +four years ago teaching at the American + + align:start position:0% +four years ago teaching at the American + + + align:start position:0% +four years ago teaching at the American +University of Cairo for about 10 days or + + align:start position:0% +University of Cairo for about 10 days or + + + align:start position:0% +University of Cairo for about 10 days or +participating in programs there and + + align:start position:0% +participating in programs there and + + + align:start position:0% +participating in programs there and +lecturing and you know I realized that + + align:start position:0% +lecturing and you know I realized that + + + align:start position:0% +lecturing and you know I realized that +the availability you know of these + + align:start position:0% +the availability you know of these + + + align:start position:0% +the availability you know of these +things is a complete worldwide + + align:start position:0% +things is a complete worldwide + + + align:start position:0% +things is a complete worldwide +phenomenon and I asked my Egyptian + + align:start position:0% +phenomenon and I asked my Egyptian + + + align:start position:0% +phenomenon and I asked my Egyptian +friends you know how many people in your + + align:start position:0% +friends you know how many people in your + + + align:start position:0% +friends you know how many people in your +country do you think have access to an + + align:start position:0% +country do you think have access to an + + + align:start position:0% +country do you think have access to an +iPhone they thought about it and they + + align:start position:0% +iPhone they thought about it and they + + + align:start position:0% +iPhone they thought about it and they +said well you know between friends and + + align:start position:0% +said well you know between friends and + + + align:start position:0% +said well you know between friends and +neighbors and connections we probably + + align:start position:0% +neighbors and connections we probably + + + align:start position:0% +neighbors and connections we probably +have you know well over 80% of our + + align:start position:0% +have you know well over 80% of our + + + align:start position:0% +have you know well over 80% of our +population with access to iPhones so in + + align:start position:0% +population with access to iPhones so in + + + align:start position:0% +population with access to iPhones so in +other words I mean this is a it's a + + align:start position:0% +other words I mean this is a it's a + + + align:start position:0% +other words I mean this is a it's a +pretty poor developing country that's an + + align:start position:0% +pretty poor developing country that's an + + + align:start position:0% +pretty poor developing country that's an +astonishing access system that's an + + align:start position:0% +astonishing access system that's an + + + align:start position:0% +astonishing access system that's an +amazing access there's a whole new + + align:start position:0% +amazing access there's a whole new + + + align:start position:0% +amazing access there's a whole new +delivery vehicle out there and the + + align:start position:0% +delivery vehicle out there and the + + + align:start position:0% +delivery vehicle out there and the +computer science departments logically + + align:start position:0% +computer science departments logically + + + align:start position:0% +computer science departments logically +saw that first so they realized it was + + align:start position:0% +saw that first so they realized it was + + + align:start position:0% +saw that first so they realized it was +in a tool and they raced to create + + align:start position:0% +in a tool and they raced to create + + + align:start position:0% +in a tool and they raced to create +content to do that largely you know kind + + align:start position:0% +content to do that largely you know kind + + + align:start position:0% +content to do that largely you know kind +of just videoing classrooms right and + + align:start position:0% +of just videoing classrooms right and + + + align:start position:0% +of just videoing classrooms right and +what this group felt was look we better + + align:start position:0% +what this group felt was look we better + + + align:start position:0% +what this group felt was look we better +figure out how to optimize the online + + align:start position:0% +figure out how to optimize the online + + + align:start position:0% +figure out how to optimize the online +education pieces that we're now doing + + align:start position:0% +education pieces that we're now doing + + + align:start position:0% +education pieces that we're now doing +how do we understand what's been + + align:start position:0% +how do we understand what's been + + + align:start position:0% +how do we understand what's been +happening in cognitive science and + + align:start position:0% +happening in cognitive science and + + + align:start position:0% +happening in cognitive science and +learning science which comes out of the + + align:start position:0% +learning science which comes out of the + + + align:start position:0% +learning science which comes out of the +education side and in neuroscience and + + align:start position:0% +education side and in neuroscience and + + + align:start position:0% +education side and in neuroscience and +take advantage of what they've been + + align:start position:0% +take advantage of what they've been + + + align:start position:0% +take advantage of what they've been +learning about learning in the last 15 + + align:start position:0% +learning about learning in the last 15 + + + align:start position:0% +learning about learning in the last 15 +years and try and embed those + + align:start position:0% +years and try and embed those + + + align:start position:0% +years and try and embed those +capabilities for better learning into + + align:start position:0% +capabilities for better learning into + + + align:start position:0% +capabilities for better learning into +our online courses and was you know it + + align:start position:0% +our online courses and was you know it + + + align:start position:0% +our online courses and was you know it +was a great aim because the MOOC + + align:start position:0% +was a great aim because the MOOC + + + align:start position:0% +was a great aim because the MOOC +development community hadn't frankly + + align:start position:0% +development community hadn't frankly + + + align:start position:0% +development community hadn't frankly +seriously you don't organize the way I + + align:start position:0% +seriously you don't organize the way I + + + align:start position:0% +seriously you don't organize the way I +thought about this so this report made a + + align:start position:0% +thought about this so this report made a + + + align:start position:0% +thought about this so this report made a +real contribution + + align:start position:0% +real contribution + + + align:start position:0% +real contribution +and there's now a whole research + + align:start position:0% +and there's now a whole research + + + align:start position:0% +and there's now a whole research +community when I attended you know their + + align:start position:0% +community when I attended you know their + + + align:start position:0% +community when I attended you know their +annual meeting last month at MIT and it + + align:start position:0% +annual meeting last month at MIT and it + + + align:start position:0% +annual meeting last month at MIT and it +was a community from all over the world + + align:start position:0% +was a community from all over the world + + + align:start position:0% +was a community from all over the world +universities from everywhere were + + align:start position:0% +universities from everywhere were + + + align:start position:0% +universities from everywhere were +present it was fascinating so there were + + align:start position:0% +present it was fascinating so there were + + + align:start position:0% +present it was fascinating so there were +four key recommendations integrate + + align:start position:0% +four key recommendations integrate + + + align:start position:0% +four key recommendations integrate +learning science from education with + + align:start position:0% +learning science from education with + + + align:start position:0% +learning science from education with +cognitive science and neuroscience + + align:start position:0% +cognitive science and neuroscience + + + align:start position:0% +cognitive science and neuroscience +these are disciplinary communities that + + align:start position:0% +these are disciplinary communities that + + + align:start position:0% +these are disciplinary communities that +never talk to each other right that are + + align:start position:0% +never talk to each other right that are + + + align:start position:0% +never talk to each other right that are +in no communication they're coming up + + align:start position:0% +in no communication they're coming up + + + align:start position:0% +in no communication they're coming up +with significant territories and there + + align:start position:0% +with significant territories and there + + + align:start position:0% +with significant territories and there +could be a lot of benefit from + + align:start position:0% +could be a lot of benefit from + + + align:start position:0% +could be a lot of benefit from +crossovers so that was one of the points + + align:start position:0% +crossovers so that was one of the points + + + align:start position:0% +crossovers so that was one of the points +optimally structured online courses and + + align:start position:0% +optimally structured online courses and + + + align:start position:0% +optimally structured online courses and +modules can be an important facilitator + + align:start position:0% +modules can be an important facilitator + + + align:start position:0% +modules can be an important facilitator +for higher education emphasis on + + align:start position:0% +for higher education emphasis on + + + align:start position:0% +for higher education emphasis on +optimally structured so they're all + + align:start position:0% +optimally structured so they're all + + + align:start position:0% +optimally structured so they're all +these phenomena and this report looked + + align:start position:0% +these phenomena and this report looked + + + align:start position:0% +these phenomena and this report looked +at a number of the phenomena that effect + + align:start position:0% +at a number of the phenomena that effect + + + align:start position:0% +at a number of the phenomena that effect +learning like mind wandering segmenting + + align:start position:0% +learning like mind wandering segmenting + + + align:start position:0% +learning like mind wandering segmenting +learning into more bite-sized + + align:start position:0% +learning into more bite-sized + + + align:start position:0% +learning into more bite-sized +understandable manageable pieces + + align:start position:0% +understandable manageable pieces + + + align:start position:0% +understandable manageable pieces +retrieval learning in other words what's + + align:start position:0% +retrieval learning in other words what's + + + align:start position:0% +retrieval learning in other words what's +the right mix between study and test + + align:start position:0% +the right mix between study and test + + + align:start position:0% +the right mix between study and test +right the reinforcement mechanism how do + + align:start position:0% +right the reinforcement mechanism how do + + + align:start position:0% +right the reinforcement mechanism how do +you do spaced retrieval in other words + + align:start position:0% +you do spaced retrieval in other words + + + align:start position:0% +you do spaced retrieval in other words +recovery of information over an extended + + align:start position:0% +recovery of information over an extended + + + align:start position:0% +recovery of information over an extended +period of time how do you optimize that + + align:start position:0% +period of time how do you optimize that + + + align:start position:0% +period of time how do you optimize that +what's the role of curiosity can you use + + align:start position:0% +what's the role of curiosity can you use + + + align:start position:0% +what's the role of curiosity can you use +that as a driver in the learning space + + align:start position:0% +that as a driver in the learning space + + + align:start position:0% +that as a driver in the learning space +so they began to look at all of these + + align:start position:0% +so they began to look at all of these + + + align:start position:0% +so they began to look at all of these +phenomena which have actually been + + align:start position:0% +phenomena which have actually been + + + align:start position:0% +phenomena which have actually been +studied a number of these fields and + + align:start position:0% +studied a number of these fields and + + + align:start position:0% +studied a number of these fields and +attempted to incorporate them in I'm not + + align:start position:0% +attempted to incorporate them in I'm not + + + align:start position:0% +attempted to incorporate them in I'm not +going to try to wander through each one + + align:start position:0% +going to try to wander through each one + + + align:start position:0% +going to try to wander through each one +of these elements but you know here's + + align:start position:0% +of these elements but you know here's + + + align:start position:0% +of these elements but you know here's +some of the here's some of the + + align:start position:0% +some of the here's some of the + + + align:start position:0% +some of the here's some of the +literature and the MRI scans you know + + align:start position:0% +literature and the MRI scans you know + + + align:start position:0% +literature and the MRI scans you know +show you mine wandering I mean that's + + align:start position:0% +show you mine wandering I mean that's + + + align:start position:0% +show you mine wandering I mean that's +you know different parts of the brain + + align:start position:0% +you know different parts of the brain + + + align:start position:0% +you know different parts of the brain +are zipping around the different + + align:start position:0% +are zipping around the different + + + align:start position:0% +are zipping around the different +territories and you know it's a + + align:start position:0% +territories and you know it's a + + + align:start position:0% +territories and you know it's a +phenomena that needs to be accounted for + + align:start position:0% +phenomena that needs to be accounted for + + + align:start position:0% +phenomena that needs to be accounted for +it's a it's a very natural phenomena + + align:start position:0% +it's a it's a very natural phenomena + + + align:start position:0% +it's a it's a very natural phenomena +right mind-wandering is you know it's + + align:start position:0% +right mind-wandering is you know it's + + + align:start position:0% +right mind-wandering is you know it's +Darwinian right it's very important for + + align:start position:0% +Darwinian right it's very important for + + + align:start position:0% +Darwinian right it's very important for +our minds to wonder right if we're able + + align:start position:0% +our minds to wonder right if we're able + + + align:start position:0% +our minds to wonder right if we're able +to completely stay on topic + + align:start position:0% +to completely stay on topic + + + align:start position:0% +to completely stay on topic +you know the saber-tooth Tiger 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are all + + align:start position:0% +stuff that's you know these are all + + + align:start position:0% +stuff that's you know these are all +change models these are all potential + + align:start position:0% +change models these are all potential + + + align:start position:0% +change models these are all potential +ways in which change agents can operate + + align:start position:0% +ways in which change agents can operate + + + align:start position:0% +ways in which change agents can operate +but there's a very deep you know + + align:start position:0% +but there's a very deep you know + + + align:start position:0% +but there's a very deep you know +question about how do we do a change + + align:start position:0% +question about how do we do a change + + + align:start position:0% +question about how do we do a change +model within a higher education legacy + + align:start position:0% +model within a higher education legacy + + + align:start position:0% +model within a higher education legacy +sector because it's a very decentralized + + align:start position:0% +sector because it's a very decentralized + + + align:start position:0% +sector because it's a very decentralized +system and mi t--'s learning lessons and + + align:start position:0% +system and mi t--'s learning lessons and + + + align:start position:0% +system and mi t--'s learning lessons and +other universities that are doing this + + align:start position:0% +other universities that are doing this + + + align:start position:0% +other universities that are doing this +or learning lessons but how do we + + align:start position:0% +or learning lessons but how do we + + + align:start position:0% +or learning lessons but how do we +exchange these lessons and get these + + align:start position:0% +exchange these lessons and get these + + + align:start position:0% +exchange these lessons and get these +lessons adopted through the community + + align:start position:0% +lessons adopted through the community + + + align:start position:0% +lessons adopted through the community +that's a tough assignment that's well as + + align:start position:0% +that's a tough assignment that's well as + + + align:start position:0% +that's a tough assignment that's well as +test points about + + align:start position:0% +test points about + + + align:start position:0% +test points about +her implication was how do we get change + + align:start position:0% +her implication was how do we get change + + + align:start position:0% +her implication was how do we get change +agents willing to step up to the plate + + align:start position:0% +agents willing to step up to the plate + + + align:start position:0% +agents willing to step up to the plate +and drive this stuff yes alright we've + + align:start position:0% +and drive this stuff yes alright we've + + + align:start position:0% +and drive this stuff yes alright we've +got twenty minutes for Q&A Lily it's you + + align:start position:0% + + + + align:start position:0% + +whichever one you prefer let's start we + + align:start position:0% +whichever one you prefer let's start we + + + align:start position:0% +whichever one you prefer let's start we +ended with us in my TX online learning + + align:start position:0% +ended with us in my TX online learning + + + align:start position:0% +ended with us in my TX online learning +so let's go to that paper and discuss it + + align:start position:0% +so let's go to that paper and discuss it + + + align:start position:0% +so let's go to that paper and discuss it +okay a couple of people had questions + + align:start position:0% +okay a couple of people had questions + + + align:start position:0% +okay a couple of people had questions +including myself as to what sort of + + align:start position:0% +including myself as to what sort of + + + align:start position:0% +including myself as to what sort of +areas the online or blended learning it + + align:start position:0% +areas the online or blended learning it + + + align:start position:0% +areas the online or blended learning it +could be what subject areas the bread + + align:start position:0% +could be what subject areas the bread + + + align:start position:0% +could be what subject areas the bread +friendly about those practices and if + + align:start position:0% +friendly about those practices and if + + + align:start position:0% +friendly about those practices and if +it's just impossible to really implement + + align:start position:0% +it's just impossible to really implement + + + align:start position:0% +it's just impossible to really implement +this sort of style in some subject areas + + align:start position:0% +this sort of style in some subject areas + + + align:start position:0% +this sort of style in some subject areas +so for example I would not wanted to + + align:start position:0% +so for example I would not wanted to + + + align:start position:0% +so for example I would not wanted to +take this course if it was online course + + align:start position:0% +take this course if it was online course + + + align:start position:0% +take this course if it was online course +I don't have a three hour looking stand + + align:start position:0% +I don't have a three hour looking stand + + + align:start position:0% +I don't have a three hour looking stand +sitting at my computer and I wouldn't + + align:start position:0% +sitting at my computer and I wouldn't + + + align:start position:0% +sitting at my computer and I wouldn't +have you know sure you can start to have + + align:start position:0% +have you know sure you can start to have + + + align:start position:0% +have you know sure you can start to have +a discussion group and everyone Tunes in + + align:start position:0% +a discussion group and everyone Tunes in + + + align:start position:0% +a discussion group and everyone Tunes in +on their own devices and so you could + + align:start position:0% +on their own devices and so you could + + + align:start position:0% +on their own devices and so you could +have this interact pseudo interactive + + align:start position:0% +have this interact pseudo interactive + + + align:start position:0% +have this interact pseudo interactive +discussion but I there's just something + + align:start position:0% +discussion but I there's just something + + + align:start position:0% +discussion but I there's just something +about sitting around a seminar table and + + align:start position:0% +about sitting around a seminar table and + + + align:start position:0% +about sitting around a seminar table and +interacting with other humans for me so + + align:start position:0% +interacting with other humans for me so + + + align:start position:0% +interacting with other humans for me so +I wanted to hear what what what you all + + align:start position:0% +I wanted to hear what what what you all + + + align:start position:0% +I wanted to hear what what what you all +thought about the applicability of the + + align:start position:0% +thought about the applicability of the + + + align:start position:0% +thought about the applicability of the +mydx + + align:start position:0% + + + + align:start position:0% + +feels I've always questioned how either + + align:start position:0% +feels I've always questioned how either + + + align:start position:0% +feels I've always questioned how either +it could be improved or whether it is + + align:start position:0% +it could be improved or whether it is + + + align:start position:0% +it could be improved or whether it is +suitable for a lot of engineering + + align:start position:0% +suitable for a lot of engineering + + + align:start position:0% +suitable for a lot of engineering +classes just from like my experience + + align:start position:0% +classes just from like my experience + + + align:start position:0% +classes just from like my experience +both is like a student and then like as + + align:start position:0% +both is like a student and then like as + + + align:start position:0% +both is like a student and then like as +a TA greeting stuff like it's not like + + align:start position:0% +a TA greeting stuff like it's not like + + + align:start position:0% +a TA greeting stuff like it's not like +so many of the questions they're not + + align:start position:0% +so many of the questions they're not + + + align:start position:0% +so many of the questions they're not +just about like getting the right + + align:start position:0% +just about like getting the right + + + align:start position:0% +just about like getting the right +answered it's not like making sure you + + align:start position:0% +answered it's not like making sure you + + + align:start position:0% +answered it's not like making sure you +understand like how to approach the + + align:start position:0% +understand like how to approach the + + + align:start position:0% +understand like how to approach the +problem like did you just make like one + + align:start position:0% +problem like did you just make like one + + + align:start position:0% +problem like did you just make like one +little mistake along the way and that + + align:start position:0% +little mistake along the way and that + + + align:start position:0% +little mistake along the way and that +gives you the wrong answer like a lot of + + align:start position:0% +gives you the wrong answer like a lot of + + + align:start position:0% +gives you the wrong answer like a lot of +times it's not even numbers involved and + + align:start position:0% +times it's not even numbers involved and + + + align:start position:0% +times it's not even numbers involved and +so I know like what they did subsea + + align:start position:0% +so I know like what they did subsea + + + align:start position:0% +so I know like what they did subsea +chemistry is one of the classes that was + + align:start position:0% +chemistry is one of the classes that was + + + align:start position:0% +chemistry is one of the classes that was +like first really involved with EDX and + + align:start position:0% +like first really involved with EDX and + + + align:start position:0% +like first really involved with EDX and +I know that students would get really + + align:start position:0% +I know that students would get really + + + align:start position:0% +I know that students would get really +frustrated when things are like oh I + + align:start position:0% +frustrated when things are like oh I + + + align:start position:0% +frustrated when things are like oh I +rounded this number wrong and that's why + + align:start position:0% +rounded this number wrong and that's why + + + align:start position:0% +rounded this number wrong and that's why +my answers off or like all these like + + align:start position:0% +my answers off or like all these like + + + align:start position:0% +my answers off or like all these like +little things said EDX just like wasn't + + align:start position:0% +little things said EDX just like wasn't + + + align:start position:0% +little things said EDX just like wasn't +sensitive to pick up on and so I don't + + align:start position:0% +sensitive to pick up on and so I don't + + + align:start position:0% +sensitive to pick up on and so I don't +know if that's a question of the + + align:start position:0% +know if that's a question of the + + + align:start position:0% +know if that's a question of the +technology improving such that like we + + align:start position:0% +technology improving such that like we + + + align:start position:0% +technology improving such that like we +have better like machine learning + + align:start position:0% +have better like machine learning + + + align:start position:0% +have better like machine learning +artificial intelligence to tell what + + align:start position:0% +artificial intelligence to tell what + + + align:start position:0% +artificial intelligence to tell what +students are doing or whether that's + + align:start position:0% +students are doing or whether that's + + + align:start position:0% +students are doing or whether that's +just like a limitation that will be + + align:start position:0% +just like a limitation that will be + + + align:start position:0% +just like a limitation that will be +present whether teachers professors + + align:start position:0% +present whether teachers professors + + + align:start position:0% +present whether teachers professors +still have a role in online your + + align:start position:0% +still have a role in online your + + + align:start position:0% +still have a role in online your +automated education is that one of the + + align:start position:0% +automated education is that one of the + + + align:start position:0% +automated education is that one of the +important features of being physically + + align:start position:0% +important features of being physically + + + align:start position:0% +important features of being physically +in a classroom or interacting the TA + + align:start position:0% +in a classroom or interacting the TA + + + align:start position:0% +in a classroom or interacting the TA +like yourself or the students or the + + align:start position:0% +like yourself or the students or the + + + align:start position:0% +like yourself or the students or the +professor is that their most important + + align:start position:0% +professor is that their most important + + + align:start position:0% +professor is that their most important +even more a valuable skill of theirs as + + align:start position:0% +even more a valuable skill of theirs as + + + align:start position:0% +even more a valuable skill of theirs as +opposed to knowing their material inside + + align:start position:0% +opposed to knowing their material inside + + + align:start position:0% +opposed to knowing their material inside +nowadays knowing the having the teaching + + align:start position:0% +nowadays knowing the having the teaching + + + align:start position:0% +nowadays knowing the having the teaching +ability to identify what your problem is + + align:start position:0% +ability to identify what your problem is + + + align:start position:0% +ability to identify what your problem is +and like understand the students + + align:start position:0% +and like understand the students + + + align:start position:0% +and like understand the students +psychology and understand the learning + + align:start position:0% +psychology and understand the learning + + + align:start position:0% +psychology and understand the learning +process so that they can't just point at + + align:start position:0% +process so that they can't just point at + + + align:start position:0% +process so that they can't just point at +your answer and say this is wrong to do + + align:start position:0% +your answer and say this is wrong to do + + + align:start position:0% +your answer and say this is wrong to do +this but understand why you're wrong and + + align:start position:0% +this but understand why you're wrong and + + + align:start position:0% +this but understand why you're wrong and +where and then then redirect you and + + align:start position:0% +where and then then redirect you and + + + align:start position:0% +where and then then redirect you and +sort of course correct you so that's I + + align:start position:0% +sort of course correct you so that's I + + + align:start position:0% +sort of course correct you so that's I +think that will always be an important + + align:start position:0% +think that will always be an important + + + align:start position:0% +think that will always be an important +element of a truly well-rounded + + align:start position:0% +element of a truly well-rounded + + + align:start position:0% +element of a truly well-rounded +education and you only get that + + align:start position:0% +education and you only get that + + + align:start position:0% +education and you only get that +interacting I do think the technology is + + align:start position:0% +interacting I do think the technology is + + + align:start position:0% +interacting I do think the technology is +a sense now you know the face-to-face + + align:start position:0% +a sense now you know the face-to-face + + + align:start position:0% +a sense now you know the face-to-face +component is a lot of learning + + align:start position:0% +component is a lot of learning + + + align:start position:0% +component is a lot of learning +especially in the class like this + + align:start position:0% +especially in the class like this + + + align:start position:0% +especially in the class like this +right but let's just say 5 10 20 years + + align:start position:0% +right but let's just say 5 10 20 years + + + align:start position:0% +right but let's just say 5 10 20 years +from now we cannot just slop a pair of + + align:start position:0% +from now we cannot just slop a pair of + + + align:start position:0% +from now we cannot just slop a pair of +VR goggles on and we're sitting in + + align:start position:0% +VR goggles on and we're sitting in + + + align:start position:0% +VR goggles on and we're sitting in +simulated room and then bill doesn't + + align:start position:0% +simulated room and then bill doesn't + + + align:start position:0% +simulated room and then bill doesn't +need to fly in for every lecture that + + align:start position:0% +need to fly in for every lecture that + + + align:start position:0% +need to fly in for every lecture that +same experience great idea Kevin yeah I + + align:start position:0% +same experience great idea Kevin yeah I + + + align:start position:0% +same experience great idea Kevin yeah I +think that's allowable but I think as it + + align:start position:0% +think that's allowable but I think as it + + + align:start position:0% +think that's allowable but I think as it +stands now but like we don't even be in + + align:start position:0% +stands now but like we don't even be in + + + align:start position:0% +stands now but like we don't even be in +the same room having I still a role for + + align:start position:0% +the same room having I still a role for + + + align:start position:0% +the same room having I still a role for +human educator right for great students + + align:start position:0% +human educator right for great students + + + align:start position:0% +human educator right for great students +so far I think Chloe and Kevin so far + + align:start position:0% +so far I think Chloe and Kevin so far + + + align:start position:0% +so far I think Chloe and Kevin so far +our ability and much of our + + align:start position:0% +our ability and much of our + + + align:start position:0% +our ability and much of our +communication is not the words that + + align:start position:0% +communication is not the words that + + + align:start position:0% +communication is not the words that +we're mouthing it's the expressions we + + align:start position:0% +we're mouthing it's the expressions we + + + align:start position:0% +we're mouthing it's the expressions we +use it's eye contact it's hand + + align:start position:0% +use it's eye contact it's hand + + + align:start position:0% +use it's eye contact it's hand +expressions there's just a whole range + + align:start position:0% +expressions there's just a whole range + + + align:start position:0% +expressions there's just a whole range +of stuff that accompanies what we're + + align:start position:0% +of stuff that accompanies what we're + + + align:start position:0% +of stuff that accompanies what we're +actually saying that we use as part of + + align:start position:0% +actually saying that we use as part of + + + align:start position:0% +actually saying that we use as part of +our communication systems and so far the + + align:start position:0% +our communication systems and so far the + + + align:start position:0% +our communication systems and so far the +technology has not been precise enough + + align:start position:0% +technology has not been precise enough + + + align:start position:0% +technology has not been precise enough +to enable us to capture that incredible + + align:start position:0% +to enable us to capture that incredible + + + align:start position:0% +to enable us to capture that incredible +depth that face-to-face allows and to + + align:start position:0% +depth that face-to-face allows and to + + + align:start position:0% +depth that face-to-face allows and to +some extent it's frustrating in other + + align:start position:0% +some extent it's frustrating in other + + + align:start position:0% +some extent it's frustrating in other +words because that mix of you know non + + align:start position:0% +words because that mix of you know non + + + align:start position:0% +words because that mix of you know non +spoken communication skills doesn't get + + align:start position:0% +spoken communication skills doesn't get + + + align:start position:0% +spoken communication skills doesn't get +fully picked up people are frustrated by + + align:start position:0% +fully picked up people are frustrated by + + + align:start position:0% +fully picked up people are frustrated by +the experience right this is a notorious + + align:start position:0% +the experience right this is a notorious + + + align:start position:0% +the experience right this is a notorious +problem in conference calls even in + + align:start position:0% +problem in conference calls even in + + + align:start position:0% +problem in conference calls even in +video conference calls right people + + align:start position:0% +video conference calls right people + + + align:start position:0% +video conference calls right people +don't quite see what the other person is + + align:start position:0% +don't quite see what the other person is + + + align:start position:0% +don't quite see what the other person is +driving at are trying to communicate + + align:start position:0% +driving at are trying to communicate + + + align:start position:0% +driving at are trying to communicate +because this raft of other kinds of + + align:start position:0% +because this raft of other kinds of + + + align:start position:0% +because this raft of other kinds of +communication has not picked up now + + align:start position:0% +communication has not picked up now + + + align:start position:0% +communication has not picked up now +that's not to say that this won't get a + + align:start position:0% +that's not to say that this won't get a + + + align:start position:0% +that's not to say that this won't get a +lot better right and we've obviously + + align:start position:0% +lot better right and we've obviously + + + align:start position:0% +lot better right and we've obviously +moved to a whole new level of high + + align:start position:0% +moved to a whole new level of high + + + align:start position:0% +moved to a whole new level of high +definition and a lot of different you + + align:start position:0% +definition and a lot of different you + + + align:start position:0% +definition and a lot of different you +know in a lot of different machineries + + align:start position:0% +know in a lot of different machineries + + + align:start position:0% +know in a lot of different machineries +so it may well get better at the moment + + align:start position:0% +so it may well get better at the moment + + + align:start position:0% +so it may well get better at the moment +it's not good enough yet to substitute + + align:start position:0% +it's not good enough yet to substitute + + + align:start position:0% +it's not good enough yet to substitute +for there + + align:start position:0% +for there + + + align:start position:0% +for there +being next to you seeing how oh it's not + + align:start position:0% +being next to you seeing how oh it's not + + + align:start position:0% +being next to you seeing how oh it's not +how the original is but form follows + + align:start position:0% +how the original is but form follows + + + align:start position:0% +how the original is but form follows +function and because as a different form + + align:start position:0% +function and because as a different form + + + align:start position:0% +function and because as a different form +you have other functions that we + + align:start position:0% +you have other functions that we + + + align:start position:0% +you have other functions that we +wouldn't have here so if it's all in + + align:start position:0% +wouldn't have here so if it's all in + + + align:start position:0% +wouldn't have here so if it's all in +line then like other people can be + + align:start position:0% +line then like other people can be + + + align:start position:0% +line then like other people can be +telling what I'm doing what would they + + align:start position:0% +telling what I'm doing what would they + + + align:start position:0% +telling what I'm doing what would they +got wrong written get recommendations + + align:start position:0% +got wrong written get recommendations + + + align:start position:0% +got wrong written get recommendations +yeah the things like the system hasn't + + align:start position:0% +yeah the things like the system hasn't + + + align:start position:0% +yeah the things like the system hasn't +been perfected as well or like you said + + align:start position:0% +been perfected as well or like you said + + + align:start position:0% +been perfected as well or like you said +you don't want to stay into three out of + + align:start position:0% +you don't want to stay into three out of + + + align:start position:0% +you don't want to stay into three out of +lectures like I usually watch that like + + align:start position:0% +lectures like I usually watch that like + + + align:start position:0% +lectures like I usually watch that like +videos that like three exit they're like + + align:start position:0% +videos that like three exit they're like + + + align:start position:0% +videos that like three exit they're like +education I want to do so there's new + + align:start position:0% +education I want to do so there's new + + + align:start position:0% +education I want to do so there's new +functions you can do or you can like you + + align:start position:0% +functions you can do or you can like you + + + align:start position:0% +functions you can do or you can like you +know another really important aspect + + align:start position:0% +know another really important aspect + + + align:start position:0% +know another really important aspect +that I thought thought of from like an + + align:start position:0% +that I thought thought of from like an + + + align:start position:0% +that I thought thought of from like an +organizational standpoint it's like in + + align:start position:0% +organizational standpoint it's like in + + + align:start position:0% +organizational standpoint it's like in +this class or we're going to talk up + + align:start position:0% +this class or we're going to talk up + + + align:start position:0% +this class or we're going to talk up +form and other people that might be more + + align:start position:0% +form and other people that might be more + + + align:start position:0% +form and other people that might be more +shy might not want to say something so + + align:start position:0% +shy might not want to say something so + + + align:start position:0% +shy might not want to say something so +that's all I can get people that online + + align:start position:0% +that's all I can get people that online + + + align:start position:0% +that's all I can get people that online +you know or talking heads but physically + + align:start position:0% +you know or talking heads but physically + + + align:start position:0% +you know or talking heads but physically +like won't say a word + + align:start position:0% +like won't say a word + + + align:start position:0% +like won't say a word +so that adds new dynamics and depending + + align:start position:0% +so that adds new dynamics and depending + + + align:start position:0% +so that adds new dynamics and depending +on the personalities of other people can + + align:start position:0% +on the personalities of other people can + + + align:start position:0% +on the personalities of other people can +can excel right that's why I try to make + + align:start position:0% +can excel right that's why I try to make + + + align:start position:0% +can excel right that's why I try to make +some of you all of you be discussion + + align:start position:0% +some of you all of you be discussion + + + align:start position:0% +some of you all of you be discussion +leaders a lot the course of this I mean + + align:start position:0% +leaders a lot the course of this I mean + + + align:start position:0% +leaders a lot the course of this I mean +are the issue also is like racism like + + align:start position:0% +are the issue also is like racism like + + + align:start position:0% +are the issue also is like racism like +if you don't know the gender the + + align:start position:0% +if you don't know the gender the + + + align:start position:0% +if you don't know the gender the +background of a person you only judgment + + align:start position:0% +background of a person you only judgment + + + align:start position:0% +background of a person you only judgment +based on the ideas right or the content + + align:start position:0% +based on the ideas right or the content + + + align:start position:0% +based on the ideas right or the content +of their characters you know I was gonna + + align:start position:0% +of their characters you know I was gonna + + + align:start position:0% +of their characters you know I was gonna +blank so that allows other people to + + align:start position:0% +blank so that allows other people to + + + align:start position:0% +blank so that allows other people to +leader like excel yeah I think there's + + align:start position:0% +leader like excel yeah I think there's + + + align:start position:0% +leader like excel yeah I think there's +three sides to every coin so I agree + + align:start position:0% +three sides to every coin so I agree + + + align:start position:0% +three sides to every coin so I agree +that and on the internet could + + align:start position:0% +that and on the internet could + + + align:start position:0% +that and on the internet could +definitely be a future plus that I mean + + align:start position:0% +definitely be a future plus that I mean + + + align:start position:0% +definitely be a future plus that I mean +you have people trolling your class like + + align:start position:0% +you have people trolling your class like + + + align:start position:0% +you have people trolling your class like +the post is like the odds array like + + align:start position:0% +the post is like the odds array like + + + align:start position:0% +the post is like the odds array like +your books can be anonymous what the + + align:start position:0% +your books can be anonymous what the + + + align:start position:0% +your books can be anonymous what the +construct you know who you are + + align:start position:0% +construct you know who you are + + + align:start position:0% +construct you know who you are +and like I think please they're like + + align:start position:0% +and like I think please they're like + + + align:start position:0% +and like I think please they're like +those seek you out and that's very like + + align:start position:0% +those seek you out and that's very like + + + align:start position:0% +those seek you out and that's very like +an 8020 thread opens for I mean I don't + + align:start position:0% +an 8020 thread opens for I mean I don't + + + align:start position:0% +an 8020 thread opens for I mean I don't +think everyone's used to not start oh + + align:start position:0% +think everyone's used to not start oh + + + align:start position:0% +think everyone's used to not start oh +yeah listen to come with a big + + align:start position:0% +yeah listen to come with a big + + + align:start position:0% +yeah listen to come with a big +interested in + + align:start position:0% +interested in + + + align:start position:0% +interested in +Canha even if we got to the point with + + align:start position:0% +Canha even if we got to the point with + + + align:start position:0% +Canha even if we got to the point with +technology evolved you know you've only + + align:start position:0% +technology evolved you know you've only + + + align:start position:0% +technology evolved you know you've only +got the deployments colleges perfect + + align:start position:0% +got the deployments colleges perfect + + + align:start position:0% +got the deployments colleges perfect +they're like we could simulate being in + + align:start position:0% +they're like we could simulate being in + + + align:start position:0% +they're like we could simulate being in +this class together I mean I think + + align:start position:0% +this class together I mean I think + + + align:start position:0% +this class together I mean I think +there's still a lot of value in the fact + + align:start position:0% +there's still a lot of value in the fact + + + align:start position:0% +there's still a lot of value in the fact +that like on my way home I'll passed by + + align:start position:0% +that like on my way home I'll passed by + + + align:start position:0% +that like on my way home I'll passed by +the Becky lounge and I'll talk to + + align:start position:0% +the Becky lounge and I'll talk to + + + align:start position:0% +the Becky lounge and I'll talk to +someone about their next startup like + + align:start position:0% +someone about their next startup like + + + align:start position:0% +someone about their next startup like +yeah I think there's I mean just like + + align:start position:0% +yeah I think there's I mean just like + + + align:start position:0% +yeah I think there's I mean just like +when we talked about + + align:start position:0% +when we talked about + + + align:start position:0% +when we talked about +decentralizing manufacturing there's a + + align:start position:0% +decentralizing manufacturing there's a + + + align:start position:0% +decentralizing manufacturing there's a +lot of know-how and innovation + + align:start position:0% +lot of know-how and innovation + + + align:start position:0% +lot of know-how and innovation +capability embodied and just having + + align:start position:0% +capability embodied and just having + + + align:start position:0% +capability embodied and just having +things together physically blossom with + + align:start position:0% +things together physically blossom with + + + align:start position:0% +things together physically blossom with +the whole blended learning mom I don't + + align:start position:0% +the whole blended learning mom I don't + + + align:start position:0% +the whole blended learning mom I don't +think anyone's really trying to say + + align:start position:0% +think anyone's really trying to say + + + align:start position:0% +think anyone's really trying to say +we're gonna throw away like in a + + align:start position:0% +we're gonna throw away like in a + + + align:start position:0% +we're gonna throw away like in a +basement based interaction like that and + + align:start position:0% +basement based interaction like that and + + + align:start position:0% +basement based interaction like that and +then back to your original point about + + align:start position:0% +then back to your original point about + + + align:start position:0% +then back to your original point about +what this is like learning like online + + align:start position:0% +what this is like learning like online + + + align:start position:0% +what this is like learning like online +learning Park really well or I think + + align:start position:0% +learning Park really well or I think + + + align:start position:0% +learning Park really well or I think +right now my experience has been it + + align:start position:0% +right now my experience has been it + + + align:start position:0% +right now my experience has been it +works pretty well or how he's better for + + align:start position:0% +works pretty well or how he's better for + + + align:start position:0% +works pretty well or how he's better for +quantitative I know classes + + align:start position:0% +quantitative I know classes + + + align:start position:0% +quantitative I know classes +but I've been working over the last + + align:start position:0% +but I've been working over the last + + + align:start position:0% +but I've been working over the last +semester and like setting up an + + align:start position:0% +semester and like setting up an + + + align:start position:0% +semester and like setting up an +undergraduate law class here and one of + + align:start position:0% +undergraduate law class here and one of + + + align:start position:0% +undergraduate law class here and one of +one of the initiatives is putting on a + + align:start position:0% +one of the initiatives is putting on a + + + align:start position:0% +one of the initiatives is putting on a +lot of the content online and what we + + align:start position:0% +lot of the content online and what we + + + align:start position:0% +lot of the content online and what we +found up the move kind of format allows + + align:start position:0% +found up the move kind of format allows + + + align:start position:0% +found up the move kind of format allows +us to do is give maybe some of the + + align:start position:0% +us to do is give maybe some of the + + + align:start position:0% +us to do is give maybe some of the +instructional video and bite-sized + + align:start position:0% +instructional video and bite-sized + + + align:start position:0% +instructional video and bite-sized +pieces + + align:start position:0% +pieces + + + align:start position:0% +pieces +online beforehand and it opens a lot of + + align:start position:0% +online beforehand and it opens a lot of + + + align:start position:0% +online beforehand and it opens a lot of +in-class time to actually do like a case + + align:start position:0% +in-class time to actually do like a case + + + align:start position:0% +in-class time to actually do like a case +discussion and opens up new + + align:start position:0% +discussion and opens up new + + + align:start position:0% +discussion and opens up new +opportunities there okay + + align:start position:0% +opportunities there okay + + + align:start position:0% +opportunities there okay +oh it's just I was actually going to add + + align:start position:0% +oh it's just I was actually going to add + + + align:start position:0% +oh it's just I was actually going to add +tears I just feel in Europe and and STS + + align:start position:0% +tears I just feel in Europe and and STS + + + align:start position:0% +tears I just feel in Europe and and STS +for a year by the professor name goes + + align:start position:0% +for a year by the professor name goes + + + align:start position:0% +for a year by the professor name goes +with Torelli who started off in + + align:start position:0% +with Torelli who started off in + + + align:start position:0% +with Torelli who started off in +mechanical engineering has a pH and also + + align:start position:0% +mechanical engineering has a pH and also + + + align:start position:0% +mechanical engineering has a pH and also +science remote Society think at the same + + align:start position:0% +science remote Society think at the same + + + align:start position:0% +science remote Society think at the same +time when you talk for a long time I + + align:start position:0% +time when you talk for a long time I + + + align:start position:0% +time when you talk for a long time I +think an arrow Astro as well so she's + + align:start position:0% +think an arrow Astro as well so she's + + + align:start position:0% +think an arrow Astro as well so she's +very storied no professional emeritus + + align:start position:0% +very storied no professional emeritus + + + align:start position:0% +very storied no professional emeritus +and since earning a program called + + align:start position:0% +and since earning a program called + + + align:start position:0% +and since earning a program called +liberal studies and engineering and one + + align:start position:0% +liberal studies and engineering and one + + + align:start position:0% +liberal studies and engineering and one +of the challenges that we had + + align:start position:0% +of the challenges that we had + + + align:start position:0% +of the challenges that we had +producing modules for the program is + + align:start position:0% +producing modules for the program is + + + align:start position:0% +producing modules for the program is +that it although it did have the + + align:start position:0% +that it although it did have the + + + align:start position:0% +that it although it did have the +quantitative components that you're + + align:start position:0% +quantitative components that you're + + + align:start position:0% +quantitative components that you're +saying I think are pretty easy to + + align:start position:0% +saying I think are pretty easy to + + + align:start position:0% +saying I think are pretty easy to +communicate there is a lot of nuances + + align:start position:0% +communicate there is a lot of nuances + + + align:start position:0% +communicate there is a lot of nuances +behind the materials that we had + + align:start position:0% +behind the materials that we had + + + align:start position:0% +behind the materials that we had +selected that mean it was complicated + + align:start position:0% +selected that mean it was complicated + + + align:start position:0% +selected that mean it was complicated +for us to convey both the content and to + + align:start position:0% +for us to convey both the content and to + + + align:start position:0% +for us to convey both the content and to +then ask questions about it and I think + + align:start position:0% +then ask questions about it and I think + + + align:start position:0% +then ask questions about it and I think +one of the examples that was stood out + + align:start position:0% +one of the examples that was stood out + + + align:start position:0% +one of the examples that was stood out +to me was when we were doing a module on + + align:start position:0% +to me was when we were doing a module on + + + align:start position:0% +to me was when we were doing a module on +wells and specifically implementing + + align:start position:0% +wells and specifically implementing + + + align:start position:0% +wells and specifically implementing +wells and developing world in the + + align:start position:0% +wells and developing world in the + + + align:start position:0% +wells and developing world in the +community in Tanzania there is a drawing + + align:start position:0% +community in Tanzania there is a drawing + + + align:start position:0% +community in Tanzania there is a drawing +of the well that had been built I think + + align:start position:0% +of the well that had been built I think + + + align:start position:0% +of the well that had been built I think +in the 16th or 17th century that he had + + align:start position:0% +in the 16th or 17th century that he had + + + align:start position:0% +in the 16th or 17th century that he had +scanned and put into the module but it + + align:start position:0% +scanned and put into the module but it + + + align:start position:0% +scanned and put into the module but it +was not the mechanism by which the water + + align:start position:0% +was not the mechanism by which the water + + + align:start position:0% +was not the mechanism by which the water +was pulled up from the ground was not + + align:start position:0% +was pulled up from the ground was not + + + align:start position:0% +was pulled up from the ground was not +very clear and like the piston just was + + align:start position:0% +very clear and like the piston just was + + + align:start position:0% +very clear and like the piston just was +not very well drawn and that prevented a + + align:start position:0% +not very well drawn and that prevented a + + + align:start position:0% +not very well drawn and that prevented a +lot of I guess like I was the one who + + align:start position:0% +lot of I guess like I was the one who + + + align:start position:0% +lot of I guess like I was the one who +was like writing a lot of the material + + align:start position:0% +was like writing a lot of the material + + + align:start position:0% +was like writing a lot of the material +and then it was then sent to me and then + + align:start position:0% +and then it was then sent to me and then + + + align:start position:0% +and then it was then sent to me and then +I had to do it and then I need to give + + align:start position:0% +I had to do it and then I need to give + + + align:start position:0% +I had to do it and then I need to give +him feedback on my process of doing it + + align:start position:0% +him feedback on my process of doing it + + + align:start position:0% +him feedback on my process of doing it +and it prevented a lot of my ability to + + align:start position:0% +and it prevented a lot of my ability to + + + align:start position:0% +and it prevented a lot of my ability to +actually do the problems so I think + + align:start position:0% +actually do the problems so I think + + + align:start position:0% +actually do the problems so I think +that's one of the really interesting + + align:start position:0% +that's one of the really interesting + + + align:start position:0% +that's one of the really interesting +things about MOOCs as well and + + align:start position:0% +things about MOOCs as well and + + + align:start position:0% +things about MOOCs as well and +especially multi disciplinary MOOCs but + + align:start position:0% +especially multi disciplinary MOOCs but + + + align:start position:0% +especially multi disciplinary MOOCs but +there's so many nuances behind the + + align:start position:0% +there's so many nuances behind the + + + align:start position:0% +there's so many nuances behind the +material but even if the content seems + + align:start position:0% +material but even if the content seems + + + align:start position:0% +material but even if the content seems +fairly straightforward and you have no + + align:start position:0% +fairly straightforward and you have no + + + align:start position:0% +fairly straightforward and you have no +way to interact or rather if you don't + + align:start position:0% +way to interact or rather if you don't + + + align:start position:0% +way to interact or rather if you don't +have an immediate way to interact with + + align:start position:0% +have an immediate way to interact with + + + align:start position:0% +have an immediate way to interact with +the instructor it does add an extra + + align:start position:0% +the instructor it does add an extra + + + align:start position:0% +the instructor it does add an extra +layer of complication and your ability + + align:start position:0% +layer of complication and your ability + + + align:start position:0% +layer of complication and your ability +to solve something and I think that + + align:start position:0% +to solve something and I think that + + + align:start position:0% +to solve something and I think that +that's precisely why we benefit from the + + align:start position:0% +that's precisely why we benefit from the + + + align:start position:0% +that's precisely why we benefit from the +blended model because when you can come + + align:start position:0% +blended model because when you can come + + + align:start position:0% +blended model because when you can come +to class and say hey professor you know + + align:start position:0% +to class and say hey professor you know + + + align:start position:0% +to class and say hey professor you know +you uploaded this image in the problem + + align:start position:0% +you uploaded this image in the problem + + + align:start position:0% +you uploaded this image in the problem +side and I have no idea you know how the + + align:start position:0% +side and I have no idea you know how the + + + align:start position:0% +side and I have no idea you know how the +piston actually operates could you + + align:start position:0% +piston actually operates could you + + + align:start position:0% +piston actually operates could you +explain this to me more clearly or could + + align:start position:0% +explain this to me more clearly or could + + + align:start position:0% +explain this to me more clearly or could +you be driving reloaded so part of the + + align:start position:0% +you be driving reloaded so part of the + + + align:start position:0% +you be driving reloaded so part of the +motivation by the way for filming this + + align:start position:0% +motivation by the way for filming this + + + align:start position:0% +motivation by the way for filming this +class is for us to think about whether + + align:start position:0% +class is for us to think about whether + + + align:start position:0% +class is for us to think about whether +or not we take more of the lecture + + align:start position:0% +or not we take more of the lecture + + + align:start position:0% +or not we take more of the lecture +segments online and then have even a + + align:start position:0% +segments online and then have even a + + + align:start position:0% +segments online and then have even a +more of an organized discussion focus + + align:start position:0% +more of an organized discussion focus + + + align:start position:0% +more of an organized discussion focus +you know in the face-to-face classroom + + align:start position:0% +you know in the face-to-face classroom + + + align:start position:0% +you know in the face-to-face classroom +so that's one of the + + align:start position:0% +so that's one of the + + + align:start position:0% +so that's one of the +part of the reason of the filming here + + align:start position:0% +part of the reason of the filming here + + + align:start position:0% +part of the reason of the filming here +is to create an online course but it's + + align:start position:0% +is to create an online course but it's + + + align:start position:0% +is to create an online course but it's +also possible to use this for more of a + + align:start position:0% +also possible to use this for more of a + + + align:start position:0% +also possible to use this for more of a +blended model here so I wanted to come + + align:start position:0% +blended model here so I wanted to come + + + align:start position:0% +blended model here so I wanted to come +bring something out that they'll + + align:start position:0% +bring something out that they'll + + + align:start position:0% +bring something out that they'll +mentioned earlier which I think will + + align:start position:0% +mentioned earlier which I think will + + + align:start position:0% +mentioned earlier which I think will +also transition us into the fun billion + + align:start position:0% +also transition us into the fun billion + + + align:start position:0% +also transition us into the fun billion +and Weiss reading Phil mentioned + + align:start position:0% + + + + align:start position:0% + +graduate programs online so you complete + + align:start position:0% +graduate programs online so you complete + + + align:start position:0% +graduate programs online so you complete +a year-long certificate sort of program + + align:start position:0% +a year-long certificate sort of program + + + align:start position:0% +a year-long certificate sort of program +and then can complete the remainder of + + align:start position:0% +and then can complete the remainder of + + + align:start position:0% +and then can complete the remainder of +your graduate work on-site + + align:start position:0% +your graduate work on-site + + + align:start position:0% +your graduate work on-site +I think that's a really interesting + + align:start position:0% +I think that's a really interesting + + + align:start position:0% +I think that's a really interesting +model an idea so I can see that working + + align:start position:0% +model an idea so I can see that working + + + align:start position:0% +model an idea so I can see that working +well for things like first of all oh + + align:start position:0% +well for things like first of all oh + + + align:start position:0% +well for things like first of all oh +look at this I can see that working + + align:start position:0% +look at this I can see that working + + + align:start position:0% +look at this I can see that working +other things like maybe business + + align:start position:0% +other things like maybe business + + + align:start position:0% +other things like maybe business +engineering computer science etc and + + align:start position:0% +engineering computer science etc and + + + align:start position:0% +engineering computer science etc and +those graduate programs are typically + + align:start position:0% +those graduate programs are typically + + + align:start position:0% +those graduate programs are typically +quite expensive and can be two to three + + align:start position:0% +quite expensive and can be two to three + + + align:start position:0% +quite expensive and can be two to three +years and unlike a lot of TV programs or + + align:start position:0% +years and unlike a lot of TV programs or + + + align:start position:0% +years and unlike a lot of TV programs or +science programs you don't feel it's not + + align:start position:0% +science programs you don't feel it's not + + + align:start position:0% +science programs you don't feel it's not +paid for so we're talking maybe fifty + + align:start position:0% +paid for so we're talking maybe fifty + + + align:start position:0% +paid for so we're talking maybe fifty +thousand dollars a year for two to three + + align:start position:0% +thousand dollars a year for two to three + + + align:start position:0% +thousand dollars a year for two to three +years which brings me to something that + + align:start position:0% +years which brings me to something that + + + align:start position:0% +years which brings me to something that +came up in Phil's reading which is + + align:start position:0% +came up in Phil's reading which is + + + align:start position:0% +came up in Phil's reading which is +student loans and increasing levels of + + align:start position:0% +student loans and increasing levels of + + + align:start position:0% +student loans and increasing levels of +student loans and I was doing a little + + align:start position:0% +student loans and I was doing a little + + + align:start position:0% +student loans and I was doing a little +bit of research does anyone have I have + + align:start position:0% +bit of research does anyone have I have + + + align:start position:0% +bit of research does anyone have I have +any idea what the current outstanding + + align:start position:0% +any idea what the current outstanding + + + align:start position:0% +any idea what the current outstanding +student loan debt is new us trillions + + align:start position:0% +student loan debt is new us trillions + + + align:start position:0% +student loan debt is new us trillions +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +1.5 trillion and they're not + + align:start position:0% +1.5 trillion and they're not + + + align:start position:0% +1.5 trillion and they're not +collateralized and the default rates are + + align:start position:0% +collateralized and the default rates are + + + align:start position:0% +collateralized and the default rates are +increasing so they are yeah last I heard + + align:start position:0% +increasing so they are yeah last I heard + + + align:start position:0% +increasing so they are yeah last I heard +it thought they were down not according + + align:start position:0% +it thought they were down not according + + + align:start position:0% +it thought they were down not according +to this + + align:start position:0% +to this + + + align:start position:0% +to this +2017 statistics correct whatever it was + + align:start position:0% +2017 statistics correct whatever it was + + + align:start position:0% +2017 statistics correct whatever it was +in 2016 + + align:start position:0% + + + + align:start position:0% + +so with that in mind could the could the + + align:start position:0% +so with that in mind could the could the + + + align:start position:0% +so with that in mind could the could the +master's program blended online then a + + align:start position:0% +master's program blended online then a + + + align:start position:0% +master's program blended online then a +concatenated or shortened on-site + + align:start position:0% +concatenated or shortened on-site + + + align:start position:0% +concatenated or shortened on-site +learning via really no improve the + + align:start position:0% +learning via really no improve the + + + align:start position:0% +learning via really no improve the +situation with student loan debt while + + align:start position:0% +situation with student loan debt while + + + align:start position:0% +situation with student loan debt while +still qualifying the person with a + + align:start position:0% +still qualifying the person with a + + + align:start position:0% +still qualifying the person with a +graduate degree I would just be curious + + align:start position:0% +graduate degree I would just be curious + + + align:start position:0% +graduate degree I would just be curious +what's the breakdown is between + + align:start position:0% +what's the breakdown is between + + + align:start position:0% +what's the breakdown is between +different fields I know for like MBAs + + align:start position:0% +different fields I know for like MBAs + + + align:start position:0% +different fields I know for like MBAs +and like law school so much it's like + + align:start position:0% +and like law school so much it's like + + + align:start position:0% +and like law school so much it's like +building your network while you're there + + align:start position:0% +building your network while you're there + + + align:start position:0% +building your network while you're there +so like people are willing to take on + + align:start position:0% +so like people are willing to take on + + + align:start position:0% +so like people are willing to take on +like hundreds of thousands of dollars + + align:start position:0% +like hundreds of thousands of dollars + + + align:start position:0% +like hundreds of thousands of dollars +and whoa it's just like half connections + + align:start position:0% +and whoa it's just like half connections + + + align:start position:0% +and whoa it's just like half connections +like the Harvard community or whatever + + align:start position:0% +like the Harvard community or whatever + + + align:start position:0% +like the Harvard community or whatever +so like if that is only a small section + + align:start position:0% +so like if that is only a small section + + + align:start position:0% +so like if that is only a small section +of like the total loan that are + + align:start position:0% +of like the total loan that are + + + align:start position:0% +of like the total loan that are +outstanding that I think this could be + + align:start position:0% +outstanding that I think this could be + + + align:start position:0% +outstanding that I think this could be +impactful but if that's like outweighing + + align:start position:0% +impactful but if that's like outweighing + + + align:start position:0% +impactful but if that's like outweighing +it I'm not worried about that class + + align:start position:0% +it I'm not worried about that class + + + align:start position:0% +it I'm not worried about that class +we're paying the loans yeah like the + + align:start position:0% +we're paying the loans yeah like the + + + align:start position:0% +we're paying the loans yeah like the +first year out they might like $300,000 + + align:start position:0% +first year out they might like $300,000 + + + align:start position:0% +first year out they might like $300,000 +in loan and while they are paying in + + align:start position:0% +in loan and while they are paying in + + + align:start position:0% +in loan and while they are paying in +fact like I think they would still be + + align:start position:0% +fact like I think they would still be + + + align:start position:0% +fact like I think they would still be +willing to take out three hundred + + align:start position:0% +willing to take out three hundred + + + align:start position:0% +willing to take out three hundred +thousand dollars of loans regardless and + + align:start position:0% +thousand dollars of loans regardless and + + + align:start position:0% +thousand dollars of loans regardless and +their technologies there's the goodness + + align:start position:0% +their technologies there's the goodness + + + align:start position:0% +their technologies there's the goodness +of the programs that are putting out + + align:start position:0% +of the programs that are putting out + + + align:start position:0% +of the programs that are putting out +these quizzes there's a lot of I think + + align:start position:0% +these quizzes there's a lot of I think + + + align:start position:0% +these quizzes there's a lot of I think +predatory right like that + + align:start position:0% +predatory right like that + + + align:start position:0% +predatory right like that +what does it mean it's the one that just + + align:start position:0% +what does it mean it's the one that just + + + align:start position:0% +what does it mean it's the one that just +got shut down it was really bad yeah + + align:start position:0% +got shut down it was really bad yeah + + + align:start position:0% +got shut down it was really bad yeah +exactly an agent and it also presumes + + align:start position:0% +exactly an agent and it also presumes + + + align:start position:0% +exactly an agent and it also presumes +that they're useful like there's is like + + align:start position:0% +that they're useful like there's is like + + + align:start position:0% +that they're useful like there's is like +there's an instrumentality or a utility + + align:start position:0% +there's an instrumentality or a utility + + + align:start position:0% +there's an instrumentality or a utility +but like coefficient that you gain from + + align:start position:0% +but like coefficient that you gain from + + + align:start position:0% +but like coefficient that you gain from +having participated in these courses and + + align:start position:0% +having participated in these courses and + + + align:start position:0% +having participated in these courses and +I don't know if the return on investment + + align:start position:0% +I don't know if the return on investment + + + align:start position:0% +I don't know if the return on investment +is going to be good for someone who + + align:start position:0% +is going to be good for someone who + + + align:start position:0% +is going to be good for someone who +doesn't already have sort of a + + align:start position:0% +doesn't already have sort of a + + + align:start position:0% +doesn't already have sort of a +foundational degree and in something + + align:start position:0% +foundational degree and in something + + + align:start position:0% +foundational degree and in something +like in it assumes that this that the + + align:start position:0% +like in it assumes that this that the + + + align:start position:0% +like in it assumes that this that the +job market is willing to us to accept + + align:start position:0% +job market is willing to us to accept + + + align:start position:0% +job market is willing to us to accept +the people who are graduating with this + + align:start position:0% +the people who are graduating with this + + + align:start position:0% +the people who are graduating with this +knowledge and I don't know if that's + + align:start position:0% +knowledge and I don't know if that's + + + align:start position:0% +knowledge and I don't know if that's +true right now + + align:start position:0% +true right now + + + align:start position:0% +true right now +there's a really good breakdown on + + align:start position:0% +there's a really good breakdown on + + + align:start position:0% +there's a really good breakdown on +four-year universities by the way not + + align:start position:0% +four-year universities by the way not + + + align:start position:0% +four-year universities by the way not +just graduate programs so yeah so Lily + + align:start position:0% +just graduate programs so yeah so Lily + + + align:start position:0% +just graduate programs so yeah so Lily +do you want to make a make a closing set + + align:start position:0% +do you want to make a make a closing set + + + align:start position:0% +do you want to make a make a closing set +of points about these two readings yeah + + align:start position:0% +of points about these two readings yeah + + + align:start position:0% +of points about these two readings yeah +pay off your student loans and don't + + align:start position:0% +pay off your student loans and don't + + + align:start position:0% +pay off your student loans and don't +default on them or else our entire + + align:start position:0% +default on them or else our entire + + + align:start position:0% +default on them or else our entire +economy you know there's a critical + + align:start position:0% +economy you know there's a critical + + + align:start position:0% +economy you know there's a critical +default number just as the housing + + align:start position:0% +default number just as the housing + + + align:start position:0% +default number just as the housing +market at me all right so read all by + + align:start position:0% +market at me all right so read all by + + + align:start position:0% +market at me all right so read all by +Schwartz doesn't thing about pure + + align:start position:0% + + + + align:start position:0% + +example is like there's federally + + align:start position:0% +example is like there's federally + + + align:start position:0% +example is like there's federally +subsidized student loans if you get + + align:start position:0% +subsidized student loans if you get + + + align:start position:0% +subsidized student loans if you get +clever there's like you use your + + align:start position:0% +clever there's like you use your + + + align:start position:0% +clever there's like you use your +favorite subsidized student loans invest + + align:start position:0% +favorite subsidized student loans invest + + + align:start position:0% +favorite subsidized student loans invest +properly and then like float those + + align:start position:0% +properly and then like float those + + + align:start position:0% +properly and then like float those +because those are inherently like safer + + align:start position:0% +because those are inherently like safer + + + align:start position:0% +because those are inherently like safer +so like even if you don't wanna I should + + align:start position:0% +so like even if you don't wanna I should + + + align:start position:0% +so like even if you don't wanna I should +say like there are a lot of options to + + align:start position:0% +say like there are a lot of options to + + + align:start position:0% +say like there are a lot of options to +pay back you student was so Lily bring + + align:start position:0% +pay back you student was so Lily bring + + + align:start position:0% +pay back you student was so Lily bring +us to a couple of key conclusions about + + align:start position:0% +us to a couple of key conclusions about + + + align:start position:0% +us to a couple of key conclusions about +the two readings + + align:start position:0% + + + + align:start position:0% + +I think in general the readings led us + + align:start position:0% +I think in general the readings led us + + + align:start position:0% +I think in general the readings led us +to believe that online learning or at + + align:start position:0% +to believe that online learning or at + + + align:start position:0% +to believe that online learning or at +least limit learning is going to + + align:start position:0% + + + + align:start position:0% + +increase in usage or popularity whether + + align:start position:0% +increase in usage or popularity whether + + + align:start position:0% +increase in usage or popularity whether +the institutions the universities like + + align:start position:0% +the institutions the universities like + + + align:start position:0% +the institutions the universities like +it or not and no that's I think I + + align:start position:0% +it or not and no that's I think I + + + align:start position:0% +it or not and no that's I think I +covered everything else good let me do + + align:start position:0% +covered everything else good let me do + + + align:start position:0% +covered everything else good let me do +just a quick wrap-up Freeman taught us + + align:start position:0% +just a quick wrap-up Freeman taught us + + + align:start position:0% +just a quick wrap-up Freeman taught us +about the talent base and you know how + + align:start position:0% +about the talent base and you know how + + + align:start position:0% +about the talent base and you know how +it's gonna affect the innovation system + + align:start position:0% +it's gonna affect the innovation system + + + align:start position:0% +it's gonna affect the innovation system +and you know made us aware of the fact + + align:start position:0% +and you know made us aware of the fact + + + align:start position:0% +and you know made us aware of the fact +that the S&T talent base is going to be + + align:start position:0% +that the S&T talent base is going to be + + + align:start position:0% +that the S&T talent base is going to be +a pretty key component of us you know + + align:start position:0% +a pretty key component of us you know + + + align:start position:0% +a pretty key component of us you know +overall comparative advantage as other + + align:start position:0% +overall comparative advantage as other + + + align:start position:0% +overall comparative advantage as other +people moved in copy the model roamers + + align:start position:0% +people moved in copy the model roamers + + + align:start position:0% +people moved in copy the model roamers +core point was that government policy is + + align:start position:0% +core point was that government policy is + + + align:start position:0% +core point was that government policy is +focused on really on capital supply and + + align:start position:0% +focused on really on capital supply and + + + align:start position:0% +focused on really on capital supply and +you know and really on the demand side + + align:start position:0% +you know and really on the demand side + + + align:start position:0% +you know and really on the demand side +of the equation right and that the + + align:start position:0% +of the equation right and that the + + + align:start position:0% +of the equation right and that the +talent supply system really was not a + + align:start position:0% +talent supply system really was not a + + + align:start position:0% +talent supply system really was not a +particularly significant federal + + align:start position:0% +particularly significant federal + + + align:start position:0% +particularly significant federal +government focus it probably needs to be + + align:start position:0% +government focus it probably needs to be + + + align:start position:0% +government focus it probably needs to be +because that's a very important factor + + align:start position:0% +because that's a very important factor + + + align:start position:0% +because that's a very important factor +in innovation as we discussed earlier + + align:start position:0% +in innovation as we discussed earlier + + + align:start position:0% +in innovation as we discussed earlier +with his prospector Theory and then he + + align:start position:0% +with his prospector Theory and then he + + + align:start position:0% +with his prospector Theory and then he +drove us to look at higher educational + + align:start position:0% +drove us to look at higher educational + + + align:start position:0% +drove us to look at higher educational +institutions and how they don't get the + + align:start position:0% +institutions and how they don't get the + + + align:start position:0% +institutions and how they don't get the +economic signaling that would lead them + + align:start position:0% +economic signaling that would lead them + + + align:start position:0% +economic signaling that would lead them +to increase the supply and he helped us + + align:start position:0% +to increase the supply and he helped us + + + align:start position:0% +to increase the supply and he helped us +think about what some of the barriers + + align:start position:0% +think about what some of the barriers + + + align:start position:0% +think about what some of the barriers +were and how you could change that + + align:start position:0% +were and how you could change that + + + align:start position:0% +were and how you could change that +economic signaling to change the way in + + align:start position:0% +economic signaling to change the way in + + + align:start position:0% +economic signaling to change the way in +which the higher education system dealt + + align:start position:0% +which the higher education system dealt + + + align:start position:0% +which the higher education system dealt +with a supply cat question Katz and + + align:start position:0% +with a supply cat question Katz and + + + align:start position:0% +with a supply cat question Katz and +golden taught us about the tie between + + align:start position:0% +golden taught us about the tie between + + + align:start position:0% +golden taught us about the tie between +the ever-increasing technology + + align:start position:0% +the ever-increasing technology + + + align:start position:0% +the ever-increasing technology +requirements of the economy since the + + align:start position:0% +requirements of the economy since the + + + align:start position:0% +requirements of the economy since the +Industrial Revolution we've been on a + + align:start position:0% +Industrial Revolution we've been on a + + + align:start position:0% +Industrial Revolution we've been on a +rising curve and it may be accelerating + + align:start position:0% +rising curve and it may be accelerating + + + align:start position:0% +rising curve and it may be accelerating +and then they demonstrated for us how + + align:start position:0% +and then they demonstrated for us how + + + align:start position:0% +and then they demonstrated for us how +important it is to keep the education + + align:start position:0% +important it is to keep the education + + + align:start position:0% +important it is to keep the education +curve the talent base ahead of that + + align:start position:0% +curve the talent base ahead of that + + + align:start position:0% +curve the talent base ahead of that +curve playing off of that curve if you + + align:start position:0% +curve playing off of that curve if you + + + align:start position:0% +curve playing off of that curve if you +let them cross like we did in the 1970s + + align:start position:0% +let them cross like we did in the 1970s + + + align:start position:0% +let them cross like we did in the 1970s +then you start to drive towards pretty + + align:start position:0% +then you start to drive towards pretty + + + align:start position:0% +then you start to drive towards pretty +serious economic inequality problems + + align:start position:0% +serious economic inequality problems + + + align:start position:0% +serious economic inequality problems +because you're leaving a large part of + + align:start position:0% +because you're leaving a large part of + + + align:start position:0% +because you're leaving a large part of +your population behind unable + + align:start position:0% +your population behind unable + + + align:start position:0% +your population behind unable +to get back on that rising parallel and + + align:start position:0% +to get back on that rising parallel and + + + align:start position:0% +to get back on that rising parallel and +stay up with the technology curve and + + align:start position:0% +stay up with the technology curve and + + + align:start position:0% +stay up with the technology curve and +earn the corresponding incomes bammel + + align:start position:0% +earn the corresponding incomes bammel + + + align:start position:0% +earn the corresponding incomes bammel +alerted us to the fact that education + + align:start position:0% +alerted us to the fact that education + + + align:start position:0% +alerted us to the fact that education +for invention and innovation by the way + + align:start position:0% +for invention and innovation by the way + + + align:start position:0% +for invention and innovation by the way +looks different than standard education + + align:start position:0% +looks different than standard education + + + align:start position:0% +looks different than standard education +systems and Science and Technology today + + align:start position:0% +systems and Science and Technology today + + + align:start position:0% +systems and Science and Technology today +which are more geared towards + + align:start position:0% +which are more geared towards + + + align:start position:0% +which are more geared towards +historically towards you know + + align:start position:0% +historically towards you know + + + align:start position:0% +historically towards you know +incremental advances mi t--'s online + + align:start position:0% +incremental advances mi t--'s online + + + align:start position:0% +incremental advances mi t--'s online +education report got us thinking about + + align:start position:0% +education report got us thinking about + + + align:start position:0% +education report got us thinking about +learning science how you could apply + + align:start position:0% +learning science how you could apply + + + align:start position:0% +learning science how you could apply +learning science to really optimize both + + align:start position:0% +learning science to really optimize both + + + align:start position:0% +learning science to really optimize both +the online model and the blended + + align:start position:0% +the online model and the blended + + + align:start position:0% +the online model and the blended +learning model and then the reading from + + align:start position:0% +learning model and then the reading from + + + align:start position:0% +learning model and then the reading from +the textbook you know showed us a set of + + align:start position:0% +the textbook you know showed us a set of + + + align:start position:0% +the textbook you know showed us a set of +the challenges for online education how + + align:start position:0% +the challenges for online education how + + + align:start position:0% +the challenges for online education how +it's a potentially disruptive tool in a + + align:start position:0% +it's a potentially disruptive tool in a + + + align:start position:0% +it's a potentially disruptive tool in a +legacy sector education system and got + + align:start position:0% +legacy sector education system and got + + + align:start position:0% +legacy sector education system and got +us thinking about who are the change + + align:start position:0% +us thinking about who are the change + + + align:start position:0% +us thinking about who are the change +agents that might really drive the + + align:start position:0% +agents that might really drive the + + + align:start position:0% +agents that might really drive the +optimal model which is really probably a + + align:start position:0% +optimal model which is really probably a + + + align:start position:0% +optimal model which is really probably a +blended learning model + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/SU4RVM15Hfw.txt b/SU4RVM15Hfw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f1907ff9db4533c4b062aca5b78c1128c3cc80f4 --- /dev/null +++ b/SU4RVM15Hfw.txt @@ -0,0 +1,34 @@ +KRISHNA RAJAGOPAL: Really, +what opening learning means + +is opening learning +for thousands, + +hundreds of thousands, +millions, tens of millions. + +The impact of OCW in opening +learning for millions + +around the world is multiplied +by the role of educators + +elsewhere. + +When they take +materials from OCW + +and repurpose them and +use them and make them + +part of their own teaching, +for each one educator that + +does that, there's +dozens or hundreds + +more people for whom the +opportunities to learn + +are opened up by what +we've shared through OCW. \ No newline at end of file diff --git a/ShvQYLXCjos.txt b/ShvQYLXCjos.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ad11aebc47cec645c3ab8f6bd6332cf763efcb9 --- /dev/null +++ b/ShvQYLXCjos.txt @@ -0,0 +1,2469 @@ +PROFESSOR: So we are honored +to have Professor Tomohiro + +Tachi here today visiting +from the University of Tokyo. + +We first met in +SIGGRAPH 2006, which + +was in Boston, big +graphics conference, + +when he was a PhD student. + +And Tomohiro has very +quickly become a star + +in the area of +computational origami, + +and it's really exciting to see +in particular his perspective + +coming from an +architecture background + +and how that +influences his work. + +He's going to talk about +lots of exciting things + +in the context of architectural +origami for our grand finale + +lecture. + +So please welcome Tomohiro. + +[APPLAUSE] + +PROFESSOR: Thank +you very much, Eric. + +So I'm Tomohiro Tachi from +the University of Tokyo, + +and I'm going to talk about +architecture origami, which + +is architectural form +design systems based + +in computational origami. + +So first, introduction. + +I have been doing origami as a +hobby, as well as my research. + +Well, it was before my research +started that I began folding. + +These are examples of folding +using a traditional way + +of box pleating or +a 3D curved surface. + +This is pure origami, +and there is also + +applied origami, +which is applying + +origami for +engineering purposes. + +For example, we can +use sheet folding + +for manufacturing a +3D surface or use it + +for increasing the +structure's stiffness. + +These are examples of +a formed 3D surface + +from a sheet of metal. + +We can use a dynamic +property of origami + +for deployable +structure, such as this + +is folding of solar panels +used for spatial structures. + +A good thing about origami is +that unlike the truss structure + +or scissors structure, +you can form basically + +a continuous surface, +and that continuity + +is preserved all the way +of the transformation. + +So this makes +origami potentially + +useful for adaptive +environment, which + +includes context customized +design or personal design + +so that you can make some +kind of origami structures + +that fit customized to your +body or customised to the design + +context. + +And you can, of course, do +fabrication oriented design + +so that you can efficiently +use the material + +to build the 3D +structure that you want. + +What I'm proposing with +the architectural origami, + +it's different from +origami architecture. + +I have been using the word +"origami architecture," which + +might mean the application +of origami to design. + +So this is the direction +of application. + +We start from some kind +of shape or pattern + +and see how it is folded +or see the behavior + +by simulating, or directly +applying in physical world. + +But that can result in +very restricted design + +because origami is +very constrained, + +and that would +just result in just + +a copy of some known +origami pattern to design. + +Or sometimes, there are lots +of origami inspired designs + +that don't use any of the +origami properties that + +might be useful for +engineering purpose. + +So what I am proposing +with the word + +"architectural origami" is +that origami theory for design + +and a design system +that uses that. + +So the idea is in +this direction. + +We want to get some kind +of designed property, + +like how it behaves in +3D or in time, also, + +and we want to extract the +characteristics of origami + +and obtain the solution from +that required condition, + +and also design +contexts that are + +given by the design purpose. + +This is the outline. + +First is Origamizer. + +I'm going to talk about +basically the software I've + +been developing, the systems. + +One is Origamizer. + +Some of you have +attended Eric's class, + +so the theoretic side of +the Origamizer altorithm, + +but I'm going to talk +about the software itself + +and the algorithm that +efficiently works. + +So first, Origamizer. + +This is the software is +available on my web page. + +It's freely available. + +It's about origami design. + +This is my oldest +work as research. + +We had a tree method or +circle river packing method + +developed by Meguro +and Lang, which + +is using stick figure for +representing the model + +and designed by packing +circles and rivers. + +I think Jason has +talked in the class. + +So this is existing +method for origami design, + +and what I wanted +to do is make 3D + +instead of this +kind of 1D figure. + +So this is what we can get +from the circle river packing + +method, and with Origamizer +or Freeform Origami, + +we can get this kind of 3D form. + +You can say that what +you see is what you fold. + +In this case, what you see is +not what you fold, actually. + +So I manually designed +something like that. + +It's a laptop PC. + +Well, I think it's the +most complicated one. + +So for example, you can see +there is an RGB output here + +and USB outputs here, and +this is the touch pad, + +and this is keyboard. + +Good thing about that +is the function key + +is a little bit narrower +than the normal key here. + +Anyway, this is what +I've been working on. + +Well, I think it +was my hobby, but I + +was trying to make some kind of +box pleating to make anything. + +And also, this is more +three dimensional figure. + +The body is represented +basically by blocks of cubes. + +And I did more purely geometric +things with concave vertex. + +This was very important for me. + +It's very easy to make a +convex polyhedron with paper. + +Just wrapping paper +will result in folding. + +But it's very hard to +make concave vertex. + +When I finished this model, I +thought everything is possible, + +so I did a software +to do this for me. + +The program is to realize +arbitrarily given polyhedra + +surface with a developable +surface by folding. + +The geometric constraints +is, of course, + +developability so that it can +be folded from a sheet of paper. + +In this case, we forget +about continuous motion + +from a sheet of paper +to the resulting state. + +We believe that physically +it exists, so it works. + +It can be applied in engineering +sense for fabrication + +by folding and bending. + +We put arbitrary polyhedron +and get the crease pattern, + +and by only folding +this part, you + +get the folded state that's the +same as this arbitrarily given + +polyhedron. + +The idea is to use tuck. + +This is a given polyhedron, and +this grey area is our tucks. + +By folding a tuck, it's hidden. + +It's flat folded and it's hidden +behind a polyhedron's surface, + +like in this movie. + +When it's in developed +state, it forms + +a plane with a +surface polyhedron. + +This is good because we can +make a negative curvature + +vertex, a concave or +negative curvature vertex. + +The basic algorithm is to +start from making the problem + +into laying out the surface +polygons onto a plane. + +By properly aligning, we can get +the edge tucking molecule that + +folds the edge to edge and +vertex tucking molecule which + +folds vertices to vertex, and +we can pack them and tesselate + +the surface with these elements. + +We can parameterize +this configuration, + +and we can solve it by +solving non-linear equation + +and inequality conditions. + +That's the basic idea. + +What we have is +geometric constraints, + +which are represented +by equations. + +So these are the +equations, where + +this one represents the +total sum, sums up 2 pi, + +and this shows that this forms +a closed loop for each vertex. + +We assign these conditions +for each vertex, + +and we solve that by two +step linear mapping, which + +is basically solving this +equation and this equation. + +Good thing about that is +that it becomes linear, + +which means that +you can pre-compute + +and you can go around +the solution space. + +I will show you later +the design system. + +I don't go into details, but +there are several inequality + +conditions, which are +for making crease pattern + +and for making it to fit into 3D +configuration of the polyhedron + +and tuck property, +which is assumed + +place of the tuck that's hidden. + +So this is a system. + +You put the input +here in this window, + +and you have the layout +of the surface polygons, + +and then you get the +crease pattern like that. + +It automatically generates +the crease pattern, + +and here you see it's +edited in real time. + +By the way, this is real time. + +The linear equations +are represented + +by linear equations, so you can +pre-compute the linear matrix + +and then you can calculate the +configuration interactively. + +You can also do some +kind of boundary editing. + +Do you have questions? + +AUDIENCE: Yes. + +Does this maximize the amout +of paper on the outside? + +PROFESSOR: It's about +maximizing the size + +of the model with respect +to the paper size. + +It's not. + +Yes, you can, of +course, implement + +some kind of optimization +onto the program, + +but I keep it more free so that +the software user can search + +within the solution space that +satisfies these origamizing + +conditions. + +So this is a series of +results that are folded. + +This is how to fold +an origami bunny. + +First thing you do is +to get crease pattern + +using Origamizer, +and then fold along + +the given crease +pattern like this. + +Interesting thing +about that is that it's + +changing the +lighting conditions. + +It starts from +natural light and it + +becomes into artificial light. + +It takes about 10 +hours or something. + +And it's done. + +And I have this one. + +[APPLAUSE] + +There are two existing +models, not one, + +so it's very easy to reproduce. + +One thing that I'm +doing with Eric + +is to prove that +anything is possible. + +The software is a little +bit approximation, + +or it doesn't work +in some cases, + +so we are doing really +make it possible. + +This is the part +of the Origamizer, + +so if you have questions +for Origamizer. + +Yes? + +AUDIENCE: So for the +input of the model + +that you can use, does it +take [INAUDIBLE], the format? + +AUDIENCE: It's polygons. + +AUDIENCE: What's the +file format that you + +have to import in in order to-- + +PROFESSOR: Format of 3D input. + +It's basically OBJ file that +this particular software + +accepts, but basically, +it's OK if it's + +a polyhedral surface with +actually any topology + +because you can basically assign +the boundary of paper onto it + +so that it always +becomes a disk. + +Yes? + +AUDIENCE: You mentioned that +earlier on in the process, + +you need to properly lay out +the polygons onto the plane. + +What constitutes proper layout? + +PROFESSOR: Your question +is, what is a proper layout? + +This is basically given +by these conditions. + +In an intuitive way, if +you lay out polygons, + +I want to fold this line onto +this line with, actually, + +a single line, so +you have to keep + +this symmetric +against some line. + +So that gives a constraint. + +This is the basic equations +that you have to solve, + +and there are several +others, such as the boundary + +should be convex because +we don't want to end up + +in some kind of very +complex boundary. + +If it's foldable +form a convex paper, + +then it's foldable +from a square, + +so that's the +convexity of paper. + +No intersection, of +course, between polygons. + +It's a little bit difficult, +but when you place crease lines, + +then it might hit +adjacent crease lines. + +That's pretty bad, so +you have to avoid that. + +Also, you have to fit +to the 3D surface. + +Sometimes a tuck +that's coming inside + +is bad, so you have +to adjust that, + +and in order to do that, +you need a condition. + +AUDIENCE: Did you find +that you were moving around + +where the edges of +the [INAUDIBLE] model, + +or can you just start +anywhere and randomly come up + +with a solution? + +PROFESSOR: It's how to solve? + +AUDIENCE: Yeah. + +Does it get a lot harder +as the polygons increase? + +PROFESSOR: It's not a step by +step approach to laying out + +one piece at a +time, but it's more + +like solving all the equations +all at the same time using + +big vector equation. + +AUDIENCE: Maybe what he means +is, is it numerically well + +conditioned? + +PROFESSOR: No. + +That's why we need +extra work for proving. + +AUDIENCE: That it's +always [INAUDIBLE]. + +PROFESSOR: That's a question. + +Well, it's not always. + +There are sometimes +that produces + +some kind of over constrained +part and free part. + +AUDIENCE: Also, are the tucks +under mechanical tension? + +Does it want to stay tucked +or does it want to come apart? + +PROFESSOR: Physical +property of the tuck. + +AUDIENCE: Yes. + +PROFESSOR: Because +of the crimping + +that's done to each of these +vertices to fit the curvature, + +it stays in this form. + +You don't have any +glues or crimps here. + +This is actually a good +property of this design method. + +Yes? + +AUDIENCE: To +approximate a curve, + +you're breaking it down into +smaller straight edge segments. + +Is that useful or plannable +as to what the lower bound is + +to how granular you make +the curve approximation? + +PROFESSOR: About the +condition for the input. + +In this system, I +don't give any kind + +of numerical upper +boundary for the regularity + +of triangles or something. + +But I think it's good if +we can do for anything, + +so that's why I'm working +with Eric on proving. + +AUDIENCE: Is there a Mac +version of the program? + +PROFESSOR: Mac version? + +No, it's still +Windows version only. + +It's written with cross platform +library, so sometime in future. + +So let's move on to the next +topic and software, which + +is Freeform Origami. + +So the objective +of Freeform Origami + +is that we don't want to +spend too much time to make + +this kind of 3D +form, and also, we + +want some kind of conditions, +not only developability. + +We want some condition +that most origami has. + +This is flat +foldability so that it + +folds flat, and also +transformability or elastic + +properties. + +We want to use these good +properties from origami + +while we want to make some +kind of freeform surface. + +So the approach here is start +from existing origami models + +and then modify that +to a different shape + +while keeping the +origami conditions + +with direct, straightforward +user interface. + +Here, I used triangular mesh for +representing the origami model, + +and we represent +the origami models + +by the vertex +coordinates of the model. + +These variables are constrained +by developability and flat + +foldability This is a very +direct way of implementing + +origami deformation. + +First thing we want to +keep is developability, + +which is that you can fold +from a sheet of paper. + +In engineering sense, +it means that it + +can be manufactured from +a sheet material, which + +is very nice, by folding +and bending only. + +The condition is +globally represented + +that there exists some +isometric mapping to a plane, + +but if the surface is +a topological disk, + +it can be represented by a +local condition of every point. + +So every point on the surface, +the Gauss curvature is zero. + +Actually, we are thinking +of a non-smooth surface, + +but we are thinking of a +piecewise linear surface, which + +allows variation. + +Smooth developer surface is only +allowed to be in these forms, + +but we have lots of +different form variations + +if we allow creases. + +Even in this case, we have +to think about Gauss area, + +and it's very easy +to define Gauss area + +for a C2 version of surface +by multiplying curvatures, + +but for polyhedra case, we +use instead Gauss area, which + +is represented by this, which +is 2 pi minus sum of angles + +around the vertex. + +It's a very simple +way to express + +that it's folded from a plane. + +This sums up to 2 pi. + +This is what you can +use for developability. + +We want to also have flat +foldability for the surface. + +This is applicable for +compactly packaging a surface + +from 3D to 2D and from 2D to 3D. + +It's also represented +by isometric condition, + +like in developability. + +And also, we have a little bit +of layering condition, which + +is actually NP +complete, which is hard, + +but for practical purposes, +we can avoid that. + +The first one is isometry. + +That can be +similarly represented + +by angle condition, which is +called Kawasaki's theorem, so + +that the alternating sum +of each vertex is zero. + +And the layer ordering +is NP complete, + +but we can use, for example, +sufficient condition given + +by Kawasaki or +empirical condition, + +which basically given for +each local adjacent angle, + +so it's very easy to implement. + +And it works, so we forget +about NP complete part. + +And also, we can give +several constraints. + +For example, this +fold doesn't want + +to fold so that it +forms a planar surface, + +or you can fix the point +to a point in 3D space, + +or we can make some +edge to be rigid. + +So we have these coordinates, +and these are the variables + +to represent the configuration, +and be assign developability, + +flat foldability, or +other constraints. + +This forms an +under-determined system, + +which means that it gives you +a multi-dimensional solution + +space. + +Within the solution +space, we move. + +We transform the +surface so that you + +will get the always +valid solution. + +That's the method +we are applying. + +In order to solve +that, we can use + +the Jacobian of the constraints +and calculate it numerically. + +So for each step, it's a given +assumed transformation mold, + +and this gives you a +valid transformation mold + +by using the generalized +inverse or pseudo inverse. + +You can implement +software like this. + +The top is what happens +with Freeform Origami. + +This is a crease +pattern of the paper + +and this is the folded +pattern when it's X-rayed. + +You can see that if +you drag this point up, + +then all the crease pattern +and the flat folded pattern + +changes at the same time. + +This is for comparison. + +This is kind of a simulation. + +In this case, the model cannot +change the crease pattern, + +which makes a less flexible +motion for origami. + +So we want to do some +mesh modification + +because if you change +the crease pattern, then + +it will end up being +degenerate triangles, + +so that we need to do some kind +of edge collapse operation. + +However, in order to do that, +we have several conditions. + +We have to keep +Maekawa's theorem + +if the surface is +flat foldable, and we + +use that for doing +edge collapsing + +and mesh modification. + +You see these patterns +change, and these + +are getting very +degenerate triangles + +that are removed +by this operation. + +This is interesting +because you will end up + +in different patterns. + +This part is similar to diamond +pattern or Yoshimura pattern, + +and this part is kept the +same as Miura-Ori pattern. + +Mesh modification +enables to transform + +to produce more +variations for pattern. + +From now, I will show some +examples of Freeform Origami. + +First one is starting +from Miura-Ori. + +I think it's well known. + +This is actually very old, +you can see from napkin folds. + +For paper models, I think you +can see pictures from Bauhaus. + +Anyway, this is +called Miura-Ori, + +and it gives you +expansive motion, + +and also it can be +compactly packaged + +and it's developable, of course. + +So this is a variation of that, +and this is another example. + +This model is called +Melting Ice Cream. + +The idea is that using a +variation of Miura-Ori, + +it forms a 3D surface that +is irregular and asymmetric, + +while it can be folded flat +so that you can roll it up, + +carry out. + +This is a model. + +This is another example. + +Here, I wanted to start +from regular Miura-Ori + +and then to transform into +a more free form surface. + +You can also generalize +Ron Resch pattern. + +This is one of Ron Resch's +designed triangular + +tessellations. + +Good thing about +this is that it forms + +a kind of composite +surface when its folded. + +So it's composed with +top surface and tucks + +inside, just like this +bunny, but it's more flexible + +and you can fold from +a sheet to the 3D form. + +In order to design this, +we assigned the condition + +that in 3D state, these three +vertices form one vertex. + +That's extra constraints +to enable generalization + +of Ron Resch pattern. + +So for example, you +can get this kind + +of asymmetric polyhedral surface +with this generalized pattern, + +or this form with this pattern. + +Each triangle has +different shapes. + +A little bit of +differentiated shape. + +Or you can just apply to +some regular triangular mesh + +and then get some nice +crumpled paper like that. + +I think this is a good way +for using this software. + +You can design crumpled paper. + +It's very hard to crumple +paper in real life. + +If you feel it's very +difficult, then you + +can use this software +to crumple up paper. + +This is a generalized version +of Yoshimura pattern or diamond + +pattern that you can use for a +kind of shell-like structure. + +This is another pattern +called waterbomb pattern. + +It's supposed to be +playing the puffer fish + +motion by [INAUDIBLE]. + +Anyway, this type of pattern +is called waterbomb pattern. + +I think the oldest known +is by Shuzo Fujimoto. + +It's kind of a flexible pattern. + +Because it's flat +foldable, it can + +be used for +deployable structure, + +and because of the +elastic property + +that the folding gives, you +can use for textured material + +or cloth folding. + +This is an example +of deformation. + +This is the normal +waterbomb pattern. + +This is based on triangles. + +This one forms more planar +surface when it's in 3D, + +and this is some generalization. + +This is the folded form. + +I think it's a little +bit too small to show. + +This is the pattern, +and you fold it + +into a kind of a +butterfly shape, + +and it forms a hyperbolic +paraboloidal shape, + +but it's a subtle shape. + +This is another way to make +a [INAUDIBLE] in paper, + +and this exists. + +This was Freeform Origami. + +Do you have any questions +about Freeform Origami? + +AUDIENCE: Why can't you solve +directly for the final shape + +that you want? + +PROFESSOR: The question +is, why do I not + +search for the 3D shape +instead of gradually changing? + +This is because the +constraints are non-linear, + +and that makes it possible that +the solution doesn't exist. + +If you do it +continuously, then it + +is always true that you +get the right answer. + +This is a demonstration. + +This is good because +basically, you + +can interact with the +geometry of the origami + +to find some new results. + +It's more similar to when you +design with paper, like when + +you interact with real +material, but this + +gives more flexible change +of material than simulation. + +I wanted to make that kind +of interaction possible, + +so this moves like that, and +that changes the pattern. + +That's the reason I +do it in this way, + +solve the equation +by deformation. + +Any questions? + +AUDIENCE: I'm just +curious, how long + +did it take you to develop +both this and the Origamizer? + +PROFESSOR: The time for +developing the software. + +Well, it's always continuing. + +I'm always containing +developing, + +so it's very hard to say. + +I don't know. + +I think basically it starts +to work in half a year, + +and then polish a lot of times. + +AUDIENCE: Did you want +to show the demo one? + +PROFESSOR: No. + +Not yet. + +So then we talk about +the rigid origami. + +Question? + +AUDIENCE: I might not +understand it correctly, + +but in either of these programs, +or is there a program that + +exists that allows the +user to design dynamically + +like this curved crease origami? + +PROFESSOR: So curved crease +origami is quite hard. + +I have tried with this software, +and it works for some cases, + +and it doesn't work +for most of the cases + +because there are too +much degrees of freedom. + +If you simulate curve folding by +very thin quadrilateral strips, + +so that's a future work +so that the software + +can work with curve folding. + +If it's a coarse +approximation, then it works. + +So rigid origami. + +This is the closest part +of computational origami + +to architecture. + +So rigid origami is +plates and hinges model + +for origami like this. + +So each rigid panel is +connected to adjacent panel + +with a rotational +hinge, one axis hinge. + +The panels do not deform, and it +produces a synchronized motion. + +So that's a model +when you want to apply + +origami's dynamic +features to some designs. + +And this is a comparison, and +this illustrates the energy + +that's caused by the +distortion of facets. + +For example, this model +falls to this state, + +but there is no path that gives +you zero energy deformation. + +But this is rigid +foldable, which + +keeps each of the +faces not deforming. + +And it's useful for a +self deployable structure + +or architectural structure +that is very large. + +You can substitute +panels with thick panels. + +I will talk in the last part. + +So like this. + +So rigid origami. + +Here, we want to apply rigid +origami to design purposes. + +In order to do that, we +want to think about first + +to also generalize +rigid foldability + +to different shapes, and also +to generalize into cylinders + +and other topology, like +compound structures. + +Before that, I would like to +show example of rigid folding. + +This is the +simulation of folding. + +AUDIENCE: Could you play +the lower left again? + +PROFESSOR: So this is +a triangulated model + +of a tesselation +designed by Ray Schamp. + +This is a waterbomb +tessellation. + +So first thing we want to +do is to simulate folding + +to understand the geometry, the +kinematics of rigid origami. + +This can be represented. + +First easy representation +is a truss model, + +which you basically use vertex +coordinates as the variables + +and then constrain them +with rigid bars that + +are connected to vertices. + +And this one is +different representation + +that uses folding angle. + +This is a more direct +way, and I have a software + +called Rigid Origami +Simulator which basically + +is based on this constraint +and representation. + +The configuration is +represented by folding angles, + +and then the folding angles +are constrained at each vertex + +by this equation, which +is a three by three matrix + +form, which actually +gives nine equations, + +but only three of +them are independent. + +We have three equations +for each vertex. + +That will give also +under-determined system + +so that you can simulate folding +using also generalized inverse + +so that you can search +within the solution space + +by giving some pieces kind of +a force that's asserted to each + +of the edges, and +then this results + +in the deformation +that is valid. + +In generic case, +because there are + +three constraints +for each vertex + +and one variable for each edge, +we have this degree of freedom. + +First way to design +rigid origami is + +to use this information from +Euler's polyhedral formula, + +we can say that any triangular +mesh-- well, not any. + +It's a generic triangular mesh-- +produces a degree of freedom, + +which is number of edges +on the boundary minus 3. + +So for example, in this +[? hyper ?] triangular model, + +this gives one degree of +freedom because the boundary + +edges are four. + +And we can generalize +it to cases + +where there are holes also. + +With this idea, you can make +hexagonal tripod shell, which + +is using six edged, +hexagonal boundary, + +so that the degree +of freedom is three, + +and then we pin joint three +of the vertices, which + +gives nine constraints. + +Because of the rigid body +degree of freedom, which is six, + +we have nine degrees of +freedom of transformation, + +and then that's our +constraint by nine, + +so it produces static structure. + +By changing the position +of these points, + +you can get the different forms. + +For example, this is the +shape, triangular form. + +The position of these pods +changes the overall shape, + +and it's static when it's +fixed, it's all pin joint. + +This is an example. + +If you change the +position of the leg, + +then you get the +different shapes, + +3D configuration like this. + +This is one way to build +rigid origami structures. + +This is quite obvious result. + +Theoretically, it's more +interesting to think about + +the one that you cannot +imagine the transformation, + +for example, quadrilateral mesh. + +So for quadrilateral +mesh, each vertex + +has also three constraints +so that this itself + +forms a one DOF structure. + +Think about when you form a +mesh with this, like Miura-Ori. + +Basically, if you define +this folding angle, + +then all the folding +angles here are defined. + +If you have another +degree for vertex, + +then everything is +here defined, and you + +want to have another +vertex here that + +is defined by this +folding angle. + +Then you will have a problem +here because this folding angle + +and this folding +angle contradict. + +In general, it contradicts so +that you cannot make an array + +of folding by +quadrilateral mesh. + +However, as you can +see from this figure, + +there exist examples +like Miura-Ori + +that give one degree +of freedom motion. + +This is actually a very +interesting thing happening. + +And also, this is great +because all the constraints + +are redundant. + +You can remove this part, so you +can put a hole in the center, + +but still, it results +in the same motion. + +You can design more +freely with this kind + +of robust, redundant +constraint structure. + +What I want to do is to +generalize this to a freeform. + +We start from Miura-Ori +and also start + +from this pattern, which is +not a developable surface, + +but also gives one +degree of freedom motion + +with redundant constraints in +its quadrilateral mesh design. + +These can be generalized to +rigid, non-symmetric forms. + +Miura-Ori is +something like that, + +and we can extract the +property of rigid folding + +by looking at these vertex. + +If it's a flat +foldable vertex, it's + +a degree four vertex +with flat foldability, + +and this gives a +folding motion where + +the opposite folding +angle are the same + +and these are the +same, and also, + +that the folding angle +here and here are related. + +If you look at the tangent +of half of the angle, + +then it's linearly related. + +This is very useful because if +you find one configuration that + +works, then you will have +continuous folding that works. + +In this way, you can +make sufficient condition + +for making a quadrilateral +mesh rigid foldable. + +This is easy to get because it's +only the finite folding motion. + +So the continuous folding +motion from a sheet + +to the folded +state is guaranteed + +by one 3D configuration that +satisfies these conditions. + +In order to get one +configuration that + +satisfies this configuration, +we can use the Freeform Origami, + +so it's very easy +for us to do that. + +This is an example +of rigid origami + +that's using +redundant constraints. + +It produces one degree +of freedom motion + +and it's very light because +this part and this part + +counterbalance the gravity. + +This is another example. + +Quadrilateral mesh can be +a rigid folding motion. + +You can apply to something +like curve folding. + +It's rigid foldable +curve folding. + +This is kind of +contradictory, but we + +can rationalize curve folding +into quadrilateral mesh. + +Then you can produce one degree +of freedom motion like that. + +Another example with +thickness is here. + +It's interesting that it's +one degree of freedom motion + +so that every motion is +coded in the pattern here. + +Another example is +using Eggbox pattern. + +This actually has +the same property + +as the Miura-Ori vertex or flat +foldable degree for vertex, + +so that you can +use the same idea + +to produce rigid +foldable variations. + +You can actually combine +with origami structure + +if you define this +mountain fold, valley fold, + +and also add complementary +mountain fold + +and complementary valley +fold, defined here. + +If you use that kind of +extension of the origami, + +then you will get +design variations + +that combine origami. + +This part is origami +vertex but this is not. + +This can have positive +Gaussian curvature + +while this part is zero +Gaussian curvature. + +The interesting +point is that you + +can develop the +flat folded state + +or actually, in this case, it's +two flat folded states because + +in this case, it's +not totally developed, + +but complementary +fold lines are folded. + +So that's why I call it +bidirectionally flat foldable + +planar quadrilateral mesh, and +that can be rigidity foldable. + +This is an example. + +This was about a +disk, and we can + +develop into a +cylindrical structure. + +And cylinder is not trivial +because, for example, this + +is known origami +pattern, but this + +doesn't transform +to this pattern + +because this is has a +different number or edges. + +You cannot produce this kind +of motion in rigid folding + +mechanism. + +You can see what's the problem +by looking at this kind of disk + +surface that is +rigidly foldable, + +and it forms a +cylinder at one state + +but it doesn't produce in +a continuous motion that + +fix this loop. + +But there exists. + +So the idea is to mirror reflect +one part of Miura-Ori vertex. + +Actually, you can see from the +origami model by Thoki Yenn. + +It's called Flip Flop. + +It's a very interesting model. + +You can develop more generalized +origami cylinders like these. + +I think this is rigid +foldable cylinders. + +Since it's using +quadrilateral panels, + +it similarly produces one +degree of freedom motion. + +And you can see, for +example, like that. + +This is the motion produced. + +Any part produces +the whole motion. + +And also, you can make some +kind of design variations. + +This is using grasshopper +on rhinoceros. + +This is the given shape, the +section, and from the section, + +you can make a rigid +foldable cylinder and also + +composite structures like this. + +So we can make +composite structures + +like this, so it's great +that it fills the space. + +It tessellates while +preserving the one + +degree of freedom motion. + +This is an implementation +with thick panels. + +Think I have got the +cylindrical tessellation model. + +This is a tessellated model, +which moves like that. + +It's kind of a volume that +flattens into two states, + +and it's good that +it's rigidly foldable + +and it's one degree +of freedom mechanism. + +I want to generalize more. + +This is symmetric. + +There exists one axis that +repeats the unit structure. + +I want to make it more general. + +I like the asymmetry +than symmetry. + +I think you do also. + +But you have to think about +the conditions around a hole, + +and actually, this is +a difficult condition + +to be solved then +the disk version. + +However, you can do that +by fixing the first loop, + +then you know that this +part is rigid foldable, + +so you can continue +deformation from there. + +This is kind of +sufficient condition, + +but useful for designing +something like this. + +It's more free form. + +For example, this +is also one degree + +of freedom rigid +foldable cylinder. + +This is an example folded. + +It folds like that. + +This is also an example. + +This forms a torus +when it's unfolded. + +Or this type of structure. + +So it's also cylindrical. + +And for kind of +architectural image. + +This is a rigid +origami for cylinder. + +And how to implement rigid +origami to real model, + +because in architecture +design or any other designs, + +we want some kind of +finite thickness model. + +There's no ideal origami. + +Well, probably +Origamido can produce. + +Anyway, we want some thick +panels and rotating hinges + +to produce rigid origami. + +This is the typical +way to do that. + +So you put the hinge +on the valley side. + +The main problem of this one +is that each vertex, there + +are several fold lines that +are joining at the vertex, + +but this will no +longer be concurrent. + +But rigid origami mechanism +assumes that the fold lines are + +concurrent, which means +that it includes translation + +constraints and it +increases the number + +of constraints for each vertex. + +So previously, it was +three constraints there, + +but it becomes six constraints +because it includes + +transformation, +which is very bad, + +but there is asymmetric +vertex that allows that. + +So using asymmetry, you can +make something like that. + +Also, there is a way that you +can slide the hinge like that, + +but there is a problem +in the case like this. + +The problem of sliding is in +global accumulation of errors. + +So what I do is instead +of shifting hinge, + +you can trim the volume +of the vertex valley + +side of the model. + +This is actually very easy. + +You assume that this +folds to pi minus delta, + +and you can just +remove this part + +according to this +maximum folding angle. + +And you can define this point +by offsetting the edges, which + +is basically calculating +with a straight skeleton. + +This also can be applied +to constant thickness + +panels, which is more +easy to be manufactured, + +only with three axis +milling machine. + +This is a thick panel, +thick rigid origami + +using this method. + +This is an example using +a constant thickness model + +where no error is +accumulated, like this model, + +a slideable hinge. + +This is implemented by +using grasshopper again. + +Grasshopper is a good tool +to implement something + +that does not require iterative +optimization calculation, + +but it's very good for forward +calculation of geometry. + +That calculates the +pattern, and then you + +can lay out the pattern. + +This is a cloth, and +we put the thick panels + +on both sides of the cloth to +make a rigid foldable structure + +like this. + +In the center, there +is a cloth that + +represents the ideal origami. + +This is what happens. + +I would like to give an +example of rigid origami + +design for architecture. + +So this example is that we +are given existing building + +openings, and we want to connect +these openings temporarily. + +I want that to be compactly +folded to fit to this facade, + +but because this is +quite large like that, + +you cannot make from +a flexible material. + +That will be a problem if +you make it as a structure. + +So in order to solve +that kind of problem, + +we can use freeform origami to +design to fit the condition. + +So these red lines are the +openings of two buildings that + +are actually not parallel, +and the sizes are different. + +But still, you can connect +it on freefrom origami, + +and also, you can keep the +boundary to fit on the ground, + +and then you can get +these form variations + +and you can choose one of them +and calculate the paneling + +patterns. + +This is a rendering +representation, + +but basically, you can +make this kind of structure + +that can connect to buildings. + +Thank you very much. + +[APPLAUSE] + +This was more hand craft thing. + +I did this with +Dukes there, and we + +wanted to test +the metal folding, + +whether curved folding is +useful for manufacturing things. + +I think that's +true, but this model + +required a lot of hammering +and it wasn't so easy. + +I think you can +have a way to make + +it more easily constructed. + +So this is a table +just by folding + +a sheet of metal or chair. + +This one? + +So this one is a +combination of four papers. + +In this case, I did +not restrict to be + +foldable from one +sheet of paper. + +Well, for design, +I do not do that. + +You can only find +it by simulating + +and see the collision. + +Basically, there will +be no local collision + +for this quadrilateral +mesh, but there + +might be some global collisions +where this and this part + +are colliding. + +AUDIENCE: For example, +for Ron Resch pattern. + +PROFESSOR: Ron Resch pattern. + +I only do a local +collision test, + +which is between facets +that are adjacent, + +which still works for +that kind of good model. + +I think I will show +all of the things here. + +Like that. + +PROFESSOR: Any other questions? + +All right. + +Thanks again. + +PROFESSOR: Thank you very much. + +[APPLAUSE] \ No newline at end of file diff --git a/TDYMriH63us.txt b/TDYMriH63us.txt new file mode 100644 index 0000000000000000000000000000000000000000..1e7769a2ab41c04174b46f0f8adf52120ce3b935 --- /dev/null +++ b/TDYMriH63us.txt @@ -0,0 +1,2323 @@ +align:start position:0% + +we have to set up a little better the + + align:start position:0% +we have to set up a little better the + + + align:start position:0% +we have to set up a little better the +geometry of the calculation and for that + + align:start position:0% +geometry of the calculation and for that + + + align:start position:0% +geometry of the calculation and for that +we have to think of various angles we + + align:start position:0% +we have to think of various angles we + + + align:start position:0% +we have to think of various angles we +oriented there the electric field along + + align:start position:0% +oriented there the electric field along + + + align:start position:0% +oriented there the electric field along +the Z direction but that's not going to + + align:start position:0% +the Z direction but that's not going to + + + align:start position:0% +the Z direction but that's not going to +be too convenient for our calculation so + + align:start position:0% +be too convenient for our calculation so + + + align:start position:0% +be too convenient for our calculation so +these calculations are a bit of of an + + align:start position:0% +these calculations are a bit of of an + + + align:start position:0% +these calculations are a bit of of an +art to do them they're not that trivial + + align:start position:0% +art to do them they're not that trivial + + + align:start position:0% +art to do them they're not that trivial +not terribly difficult but I think if + + align:start position:0% +not terribly difficult but I think if + + + align:start position:0% +not terribly difficult but I think if +you appreciate it you will next time you + + align:start position:0% +you appreciate it you will next time you + + + align:start position:0% +you appreciate it you will next time you +ever have to do one of these things it + + align:start position:0% +ever have to do one of these things it + + + align:start position:0% +ever have to do one of these things it +will become clear so first you have to + + align:start position:0% +will become clear so first you have to + + + align:start position:0% +will become clear so first you have to +think physically is there an angle in + + align:start position:0% +think physically is there an angle in + + + align:start position:0% +think physically is there an angle in +this problem is there any no important + + align:start position:0% +this problem is there any no important + + + align:start position:0% +this problem is there any no important +angle happening here it's a question to + + align:start position:0% +angle happening here it's a question to + + + align:start position:0% +angle happening here it's a question to +you I think if you figure out that you + + align:start position:0% +you I think if you figure out that you + + + align:start position:0% +you I think if you figure out that you +have a chance of doing a diagram that + + align:start position:0% +have a chance of doing a diagram that + + + align:start position:0% +have a chance of doing a diagram that +reflects this is there a physical angle + + align:start position:0% +reflects this is there a physical angle + + + align:start position:0% +reflects this is there a physical angle +you think in this process a relevant + + align:start position:0% +you think in this process a relevant + + + align:start position:0% +you think in this process a relevant +angle yes perfect yeah the relevant + + align:start position:0% +angle yes perfect yeah the relevant + + + align:start position:0% +angle yes perfect yeah the relevant +angle is you have a direction already + + align:start position:0% +angle is you have a direction already + + + align:start position:0% +angle is you have a direction already +for the electric field so if the + + align:start position:0% +for the electric field so if the + + + align:start position:0% +for the electric field so if the +electron comes off there's going to be + + align:start position:0% +electron comes off there's going to be + + + align:start position:0% +electron comes off there's going to be +an angle with respect to a territory so + + align:start position:0% +an angle with respect to a territory so + + + align:start position:0% +an angle with respect to a territory so +that's our physical angle in this + + align:start position:0% +that's our physical angle in this + + + align:start position:0% +that's our physical angle in this +question so let's try to draw this in a + + align:start position:0% +question so let's try to draw this in a + + + align:start position:0% +question so let's try to draw this in a +in a way so I will draw it this way and + + align:start position:0% +in a way so I will draw it this way and + + + align:start position:0% +in a way so I will draw it this way and +I brought colored chalk for this now + + align:start position:0% +I brought colored chalk for this now + + + align:start position:0% +I brought colored chalk for this now +I'll put the z-axis here and I'll put + + align:start position:0% +I'll put the z-axis here and I'll put + + + align:start position:0% +I'll put the z-axis here and I'll put +the electron momentum in this direction + + align:start position:0% + + + + align:start position:0% + +kay is the lateral momentum now the + + align:start position:0% +kay is the lateral momentum now the + + + align:start position:0% +kay is the lateral momentum now the +electric field is gonna come at some + + align:start position:0% +electric field is gonna come at some + + + align:start position:0% +electric field is gonna come at some +angle with respect to thee or the + + align:start position:0% +angle with respect to thee or the + + + align:start position:0% +angle with respect to thee or the +electron momentum is at some angle with + + align:start position:0% +electron momentum is at some angle with + + + align:start position:0% +electron momentum is at some angle with +respect to the electric field so that + + align:start position:0% +respect to the electric field so that + + + align:start position:0% +respect to the electric field so that +angle will presumably stay there for the + + align:start position:0% +angle will presumably stay there for the + + + align:start position:0% +angle will presumably stay there for the +rest of the calculation so let's do it + + align:start position:0% +rest of the calculation so let's do it + + + align:start position:0% +rest of the calculation so let's do it +with green so here is my electric field + + align:start position:0% +with green so here is my electric field + + + align:start position:0% +with green so here is my electric field +and it's gonna have an angle theta with + + align:start position:0% +and it's gonna have an angle theta with + + + align:start position:0% +and it's gonna have an angle theta with +respect to the direction of the electric + + align:start position:0% +respect to the direction of the electric + + + align:start position:0% +respect to the direction of the electric +field or a photon incident direction now + + align:start position:0% +field or a photon incident direction now + + + align:start position:0% +field or a photon incident direction now +this is actually more like the + + align:start position:0% +this is actually more like the + + + align:start position:0% +this is actually more like the +polarization of the photo of the the + + align:start position:0% +polarization of the photo of the the + + + align:start position:0% +polarization of the photo of the the +electric field is the direction of the + + align:start position:0% +electric field is the direction of the + + + align:start position:0% +electric field is the direction of the +polarization of the photo so one more + + align:start position:0% +polarization of the photo so one more + + + align:start position:0% +polarization of the photo so one more +vector however the position that we have + + align:start position:0% +vector however the position that we have + + + align:start position:0% +vector however the position that we have +to integrate over because we have the + + align:start position:0% +to integrate over because we have the + + + align:start position:0% +to integrate over because we have the +whole hydrogen atom and the whole of + + align:start position:0% +whole hydrogen atom and the whole of + + + align:start position:0% +whole hydrogen atom and the whole of +space to integrate so X has a position + + align:start position:0% +space to integrate so X has a position + + + align:start position:0% +space to integrate so X has a position +so I'll use another color here + + align:start position:0% +so I'll use another color here + + + align:start position:0% +so I'll use another color here +unfortunately the colors are not that + + align:start position:0% +unfortunately the colors are not that + + + align:start position:0% +unfortunately the colors are not that +different + + align:start position:0% +different + + + align:start position:0% +different +here is our the vector R so now I have + + align:start position:0% +here is our the vector R so now I have + + + align:start position:0% +here is our the vector R so now I have +several angles I have theta for the + + align:start position:0% +several angles I have theta for the + + + align:start position:0% +several angles I have theta for the +electro electric field but now that I've + + align:start position:0% +electro electric field but now that I've + + + align:start position:0% +electro electric field but now that I've +put all these axes I not only have theta + + align:start position:0% +put all these axes I not only have theta + + + align:start position:0% +put all these axes I not only have theta +but I also have Phi for the electrode + + align:start position:0% +but I also have Phi for the electrode + + + align:start position:0% +but I also have Phi for the electrode +for the electric field and for our I + + align:start position:0% +for the electric field and for our I + + + align:start position:0% +for the electric field and for our I +will have fade a prime + + align:start position:0% + + + + align:start position:0% + +and Phi prime so R has a fader Prime and + + align:start position:0% +and Phi prime so R has a fader Prime and + + + align:start position:0% +and Phi prime so R has a fader Prime and +a Phi Prime we usually ask theta and Phi + + align:start position:0% +a Phi Prime we usually ask theta and Phi + + + align:start position:0% +a Phi Prime we usually ask theta and Phi +but the answers at the end of the day + + align:start position:0% +but the answers at the end of the day + + + align:start position:0% +but the answers at the end of the day +are going to depend on theta and if you + + align:start position:0% +are going to depend on theta and if you + + + align:start position:0% +are going to depend on theta and if you +have theta here we want a failure to + + align:start position:0% +have theta here we want a failure to + + + align:start position:0% +have theta here we want a failure to +remain so theta prime and Phi prime are + + align:start position:0% +remain so theta prime and Phi prime are + + + align:start position:0% +remain so theta prime and Phi prime are +going to be our variables of integration + + align:start position:0% +going to be our variables of integration + + + align:start position:0% +going to be our variables of integration +because you integrate over R finally we + + align:start position:0% +because you integrate over R finally we + + + align:start position:0% +because you integrate over R finally we +have one more angle that we have to + + align:start position:0% +have one more angle that we have to + + + align:start position:0% +have one more angle that we have to +define so we have theta phi theta prime + + align:start position:0% +define so we have theta phi theta prime + + + align:start position:0% +define so we have theta phi theta prime +phi prime and the angle that was here + + align:start position:0% + + + + align:start position:0% + +this was the angle between R and the + + align:start position:0% +this was the angle between R and the + + + align:start position:0% +this was the angle between R and the +direction of the electric field and we + + align:start position:0% +direction of the electric field and we + + + align:start position:0% +direction of the electric field and we +call it theta so we have to give it a + + align:start position:0% +call it theta so we have to give it a + + + align:start position:0% +call it theta so we have to give it a +new name here and this angle I'll call + + align:start position:0% +new name here and this angle I'll call + + + align:start position:0% +new name here and this angle I'll call +it gamma here the angle between E and R + + align:start position:0% + + + + align:start position:0% + +ok so we have everything defined here + + align:start position:0% +ok so we have everything defined here + + + align:start position:0% +ok so we have everything defined here +maybe it should list it e has angle + + align:start position:0% +maybe it should list it e has angle + + + align:start position:0% +maybe it should list it e has angle +theta and Phi the direction of e are as + + align:start position:0% +theta and Phi the direction of e are as + + + align:start position:0% +theta and Phi the direction of e are as +angles theta Prime and Phi prime and + + align:start position:0% +angles theta Prime and Phi prime and + + + align:start position:0% +angles theta Prime and Phi prime and +gamma is the and O between E and R and K + + align:start position:0% +gamma is the and O between E and R and K + + + align:start position:0% +gamma is the and O between E and R and K +a long Z hat so this is our situation + + align:start position:0% + + + + align:start position:0% + +so what are we trying to calculate well + + align:start position:0% +so what are we trying to calculate well + + + align:start position:0% +so what are we trying to calculate well +we want to use Fermi's golden rule so we + + align:start position:0% +we want to use Fermi's golden rule so we + + + align:start position:0% +we want to use Fermi's golden rule so we +need to calculate final H prime initial + + align:start position:0% +need to calculate final H prime initial + + + align:start position:0% +need to calculate final H prime initial +that's the matrix element of the + + align:start position:0% +that's the matrix element of the + + + align:start position:0% +that's the matrix element of the +Hamiltonian H prime between the final + + align:start position:0% +Hamiltonian H prime between the final + + + align:start position:0% +Hamiltonian H prime between the final +and initial States so what is this well + + align:start position:0% +and initial States so what is this well + + + align:start position:0% +and initial States so what is this well +these are all wave functions that depend + + align:start position:0% +these are all wave functions that depend + + + align:start position:0% +these are all wave functions that depend +all over space and this is a function of + + align:start position:0% +all over space and this is a function of + + + align:start position:0% +all over space and this is a function of +space or let's do it this is integral D + + align:start position:0% +space or let's do it this is integral D + + + align:start position:0% +space or let's do it this is integral D +cubed X let's put the final state first + + align:start position:0% +cubed X let's put the final state first + + + align:start position:0% +cubed X let's put the final state first +because it shows up there so it's one + + align:start position:0% +because it shows up there so it's one + + + align:start position:0% +because it shows up there so it's one +over L cube e to the minus I K dot R so + + align:start position:0% +over L cube e to the minus I K dot R so + + + align:start position:0% +over L cube e to the minus I K dot R so +here is our final state u final then the + + align:start position:0% +here is our final state u final then the + + + align:start position:0% +here is our final state u final then the +Hamiltonian that's simple + + align:start position:0% +Hamiltonian that's simple + + + align:start position:0% +Hamiltonian that's simple +he not R cosine what cosine gamma J + + align:start position:0% +he not R cosine what cosine gamma J + + + align:start position:0% +he not R cosine what cosine gamma J +right this is what we had there is the + + align:start position:0% +right this is what we had there is the + + + align:start position:0% +right this is what we had there is the +angle between the electric field and our + + align:start position:0% +angle between the electric field and our + + + align:start position:0% +angle between the electric field and our +became was theta to begin but now has + + align:start position:0% +became was theta to begin but now has + + + align:start position:0% +became was theta to begin but now has +become gamma and then the final state so + + align:start position:0% +become gamma and then the final state so + + + align:start position:0% +become gamma and then the final state so +this is our H Prime and then the initial + + align:start position:0% +this is our H Prime and then the initial + + + align:start position:0% +this is our H Prime and then the initial +state is one over PI 0 cube e to the + + align:start position:0% +state is one over PI 0 cube e to the + + + align:start position:0% +state is one over PI 0 cube e to the +minus R over a 0 okay this is our task + + align:start position:0% +minus R over a 0 okay this is our task + + + align:start position:0% +minus R over a 0 okay this is our task +this is a matrix animation here it is an + + align:start position:0% +this is a matrix animation here it is an + + + align:start position:0% +this is a matrix animation here it is an +integral of a plane wave against an + + align:start position:0% +integral of a plane wave against an + + + align:start position:0% +integral of a plane wave against an +electron wave function and an extra R + + align:start position:0% +electron wave function and an extra R + + + align:start position:0% +electron wave function and an extra R +dependence here + + align:start position:0% +dependence here + + + align:start position:0% +dependence here +this could be range from undoable to too + + align:start position:0% +this could be range from undoable to too + + + align:start position:0% +this could be range from undoable to too +difficult + + align:start position:0% +difficult + + + align:start position:0% +difficult +basically unhappiness just a little + + align:start position:0% +basically unhappiness just a little + + + align:start position:0% +basically unhappiness just a little +difficult but but this is an integral + + align:start position:0% +difficult but but this is an integral + + + align:start position:0% +difficult but but this is an integral +that will see what are the challenges on + + align:start position:0% +that will see what are the challenges on + + + align:start position:0% +that will see what are the challenges on +this integral so let's take a few + + align:start position:0% +this integral so let's take a few + + + align:start position:0% +this integral so let's take a few +constants out so e e0 pi 0 that all will + + align:start position:0% +constants out so e e0 pi 0 that all will + + + align:start position:0% +constants out so e e0 pi 0 that all will +go out so this is e 0 over square root + + align:start position:0% +go out so this is e 0 over square root + + + align:start position:0% +go out so this is e 0 over square root +of pi L cube a 0 cube so I took the else + + align:start position:0% +of pi L cube a 0 cube so I took the else + + + align:start position:0% +of pi L cube a 0 cube so I took the else +how the PE and this thing alright let's + + align:start position:0% +how the PE and this thing alright let's + + + align:start position:0% +how the PE and this thing alright let's +write the integral more explicitly this + + align:start position:0% +write the integral more explicitly this + + + align:start position:0% +write the integral more explicitly this +is R squared V R sign the volume element + + align:start position:0% +is R squared V R sign the volume element + + + align:start position:0% +is R squared V R sign the volume element +sine theta V theta D Phi + + align:start position:0% +sine theta V theta D Phi + + + align:start position:0% +sine theta V theta D Phi +but I'm integrating over X which is + + align:start position:0% +but I'm integrating over X which is + + + align:start position:0% +but I'm integrating over X which is +integrating over R and R is Theta Prime + + align:start position:0% +integrating over R and R is Theta Prime + + + align:start position:0% +integrating over R and R is Theta Prime +and Phi prime so these are all this ones + + align:start position:0% +and Phi prime so these are all this ones + + + align:start position:0% +and Phi prime so these are all this ones +I'm integrating over all values of theta + + align:start position:0% +I'm integrating over all values of theta + + + align:start position:0% +I'm integrating over all values of theta +Prime and Phi prime then what do I have + + align:start position:0% +Prime and Phi prime then what do I have + + + align:start position:0% +Prime and Phi prime then what do I have +I have this exponent K dot R well my + + align:start position:0% +I have this exponent K dot R well my + + + align:start position:0% +I have this exponent K dot R well my +diagram should help be K dot R is EC it + + align:start position:0% +diagram should help be K dot R is EC it + + + align:start position:0% +diagram should help be K dot R is EC it +if both the cosine of theta prime so + + align:start position:0% +if both the cosine of theta prime so + + + align:start position:0% +if both the cosine of theta prime so +it's e to the minus I K the magnitude of + + align:start position:0% +it's e to the minus I K the magnitude of + + + align:start position:0% +it's e to the minus I K the magnitude of +K the magnitude of R cosine theta prime + + align:start position:0% +K the magnitude of R cosine theta prime + + + align:start position:0% +K the magnitude of R cosine theta prime +because after all K was allowed the + + align:start position:0% +because after all K was allowed the + + + align:start position:0% +because after all K was allowed the +z-axis R is along the v theta prime + + align:start position:0% +z-axis R is along the v theta prime + + + align:start position:0% +z-axis R is along the v theta prime +direction + + align:start position:0% + + + + align:start position:0% + +okay we're progressing this this that + + align:start position:0% +okay we're progressing this this that + + + align:start position:0% +okay we're progressing this this that +term it's R cosine gamma and the final + + align:start position:0% +term it's R cosine gamma and the final + + + align:start position:0% +term it's R cosine gamma and the final +term is not that difficult e to the + + align:start position:0% +term is not that difficult e to the + + + align:start position:0% +term is not that difficult e to the +minus R over a zero okay that's what we + + align:start position:0% +minus R over a zero okay that's what we + + + align:start position:0% +minus R over a zero okay that's what we +have to do an integral over Phi prime + + align:start position:0% +have to do an integral over Phi prime + + + align:start position:0% +have to do an integral over Phi prime +theta Prime and R this is our challenge + + align:start position:0% +theta Prime and R this is our challenge + + + align:start position:0% +theta Prime and R this is our challenge +and the reason it's a challenge is the + + align:start position:0% +and the reason it's a challenge is the + + + align:start position:0% +and the reason it's a challenge is the +cosine gamma because this gamma is the + + align:start position:0% +cosine gamma because this gamma is the + + + align:start position:0% +cosine gamma because this gamma is the +angle it depends on theta depends on + + align:start position:0% +angle it depends on theta depends on + + + align:start position:0% +angle it depends on theta depends on +theta Prime there was a Phi Phi Prime + + align:start position:0% +theta Prime there was a Phi Phi Prime + + + align:start position:0% +theta Prime there was a Phi Phi Prime +that's the problem + + align:start position:0% +that's the problem + + + align:start position:0% +that's the problem +if we can solve that cosine gamma thing + + align:start position:0% +if we can solve that cosine gamma thing + + + align:start position:0% +if we can solve that cosine gamma thing +we can do this integral and I think even + + align:start position:0% +we can do this integral and I think even + + + align:start position:0% +we can do this integral and I think even +if you were doing it numerically that + + align:start position:0% +if you were doing it numerically that + + + align:start position:0% +if you were doing it numerically that +cosine gamma there is it's a little bit + + align:start position:0% +cosine gamma there is it's a little bit + + + align:start position:0% +cosine gamma there is it's a little bit +of a headache you don't want to do an + + align:start position:0% +of a headache you don't want to do an + + + align:start position:0% +of a headache you don't want to do an +integral that you can really do like + + align:start position:0% +integral that you can really do like + + + align:start position:0% +integral that you can really do like +this numerically so you really want to + + align:start position:0% +this numerically so you really want to + + + align:start position:0% +this numerically so you really want to +do it so what we need is to calculate so + + align:start position:0% +do it so what we need is to calculate so + + + align:start position:0% +do it so what we need is to calculate so +we can begin by saying I'm gonna + + align:start position:0% +we can begin by saying I'm gonna + + + align:start position:0% +we can begin by saying I'm gonna +calculate what cosine gamma is and here + + align:start position:0% +calculate what cosine gamma is and here + + + align:start position:0% +calculate what cosine gamma is and here +is a way you can calculate cosine gamma + + align:start position:0% +is a way you can calculate cosine gamma + + + align:start position:0% +is a way you can calculate cosine gamma +when you have two unit vectors cosine of + + align:start position:0% +when you have two unit vectors cosine of + + + align:start position:0% +when you have two unit vectors cosine of +the angle between two unit vectors is + + align:start position:0% +the angle between two unit vectors is + + + align:start position:0% +the angle between two unit vectors is +just the dot product of those two unit + + align:start position:0% +just the dot product of those two unit + + + align:start position:0% +just the dot product of those two unit +vectors so for gamma we can consider a + + align:start position:0% +vectors so for gamma we can consider a + + + align:start position:0% +vectors so for gamma we can consider a +unit vector along e and a unit vector + + align:start position:0% +unit vector along e and a unit vector + + + align:start position:0% +unit vector along e and a unit vector +along R and take the dot product and + + align:start position:0% +along R and take the dot product and + + + align:start position:0% +along R and take the dot product and +remember for an arbitrary unit vector + + align:start position:0% +remember for an arbitrary unit vector + + + align:start position:0% +remember for an arbitrary unit vector +its sine theta cos Phi sine theta sine + + align:start position:0% +its sine theta cos Phi sine theta sine + + + align:start position:0% +its sine theta cos Phi sine theta sine +Phi cos theta this is the Theta Phi + + align:start position:0% +Phi cos theta this is the Theta Phi + + + align:start position:0% +Phi cos theta this is the Theta Phi +decomposition of an arbitrary unit + + align:start position:0% +decomposition of an arbitrary unit + + + align:start position:0% +decomposition of an arbitrary unit +vector so cosine gamma is the dot + + align:start position:0% +vector so cosine gamma is the dot + + + align:start position:0% +vector so cosine gamma is the dot +product of a vector n along the + + align:start position:0% +product of a vector n along the + + + align:start position:0% +product of a vector n along the +e times a vector n along R and vector n + + align:start position:0% +e times a vector n along R and vector n + + + align:start position:0% +e times a vector n along R and vector n +along E&R are just with theta in one + + align:start position:0% +along E&R are just with theta in one + + + align:start position:0% +along E&R are just with theta in one +case and Phi and theta prime and Phi + + align:start position:0% +case and Phi and theta prime and Phi + + + align:start position:0% +case and Phi and theta prime and Phi +prime so when I make the dot product I + + align:start position:0% +prime so when I make the dot product I + + + align:start position:0% +prime so when I make the dot product I +get sine theta cos Phi sine theta prime + + align:start position:0% +get sine theta cos Phi sine theta prime + + + align:start position:0% +get sine theta cos Phi sine theta prime +cos Phi prime that is the product of the + + align:start position:0% +cos Phi prime that is the product of the + + + align:start position:0% +cos Phi prime that is the product of the +X components plus sine theta sine Phi + + align:start position:0% +X components plus sine theta sine Phi + + + align:start position:0% +X components plus sine theta sine Phi +prime times sine some theta sine Phi + + align:start position:0% +prime times sine some theta sine Phi + + + align:start position:0% +prime times sine some theta sine Phi +sine theta prime sine Phi prime plus cos + + align:start position:0% +sine theta prime sine Phi prime plus cos + + + align:start position:0% +sine theta prime sine Phi prime plus cos +theta cos theta prime okay doesn't look + + align:start position:0% +theta cos theta prime okay doesn't look + + + align:start position:0% +theta cos theta prime okay doesn't look +much easier but at least is explicit but + + align:start position:0% +much easier but at least is explicit but + + + align:start position:0% +much easier but at least is explicit but +it's actually much easier + + align:start position:0% + + + + align:start position:0% + +and why is that because of there's a lot + + align:start position:0% +and why is that because of there's a lot + + + align:start position:0% +and why is that because of there's a lot +of factors in common here in fact sine + + align:start position:0% +of factors in common here in fact sine + + + align:start position:0% +of factors in common here in fact sine +theta and sine theta prime are in both + + align:start position:0% + + + + align:start position:0% + +so what you get here is cosine gamma is + + align:start position:0% +so what you get here is cosine gamma is + + + align:start position:0% +so what you get here is cosine gamma is +equal to sine theta sine theta Prime and + + align:start position:0% +equal to sine theta sine theta Prime and + + + align:start position:0% +equal to sine theta sine theta Prime and +then you have closed Phi plus Phi prime + + align:start position:0% +then you have closed Phi plus Phi prime + + + align:start position:0% +then you have closed Phi plus Phi prime +plus sine Phi sine Phi Prime and that's + + align:start position:0% +plus sine Phi sine Phi Prime and that's + + + align:start position:0% +plus sine Phi sine Phi Prime and that's +cosine of Phi minus Phi prime plus cos + + align:start position:0% +cosine of Phi minus Phi prime plus cos + + + align:start position:0% +cosine of Phi minus Phi prime plus cos +theta cos theta prime okay so that's + + align:start position:0% +theta cos theta prime okay so that's + + + align:start position:0% +theta cos theta prime okay so that's +cosine gamma now suppose you were to put + + align:start position:0% +cosine gamma now suppose you were to put + + + align:start position:0% +cosine gamma now suppose you were to put +this whole thing in here okay it's a big + + align:start position:0% +this whole thing in here okay it's a big + + + align:start position:0% +this whole thing in here okay it's a big +mess but all quantities that we know but + + align:start position:0% +mess but all quantities that we know but + + + align:start position:0% +mess but all quantities that we know but +there's one nice thing though a very + + align:start position:0% +there's one nice thing though a very + + + align:start position:0% +there's one nice thing though a very +nice thing happening think of the + + align:start position:0% +nice thing happening think of the + + + align:start position:0% +nice thing happening think of the +integral over D Phi Prime this does not + + align:start position:0% +integral over D Phi Prime this does not + + + align:start position:0% +integral over D Phi Prime this does not +depend on Phi prime this does not depend + + align:start position:0% +depend on Phi prime this does not depend + + + align:start position:0% +depend on Phi prime this does not depend +on Phi prime but cosine gamma can depend + + align:start position:0% +on Phi prime but cosine gamma can depend + + + align:start position:0% +on Phi prime but cosine gamma can depend +on Phi Prime but it here it has this + + align:start position:0% +on Phi Prime but it here it has this + + + align:start position:0% +on Phi Prime but it here it has this +thing goes in a Phi minus Phi prime so + + align:start position:0% +thing goes in a Phi minus Phi prime so + + + align:start position:0% +thing goes in a Phi minus Phi prime so +when you try to do the integral of this + + align:start position:0% +when you try to do the integral of this + + + align:start position:0% +when you try to do the integral of this +D Phi Prime with this term so this term + + align:start position:0% +D Phi Prime with this term so this term + + + align:start position:0% +D Phi Prime with this term so this term +will give eventually the integral of D + + align:start position:0% +will give eventually the integral of D + + + align:start position:0% +will give eventually the integral of D +Phi prime times cosine of Phi minus Phi + + align:start position:0% +Phi prime times cosine of Phi minus Phi + + + align:start position:0% +Phi prime times cosine of Phi minus Phi +Prime there's a lot of messy things but + + align:start position:0% +Prime there's a lot of messy things but + + + align:start position:0% +Prime there's a lot of messy things but +this integral is zero because you're + + align:start position:0% +this integral is zero because you're + + + align:start position:0% +this integral is zero because you're +averaging over a full turn so happily + + align:start position:0% +averaging over a full turn so happily + + + align:start position:0% +averaging over a full turn so happily +all this term + + align:start position:0% + + + + align:start position:0% + +will not contribute and that's what + + align:start position:0% +will not contribute and that's what + + + align:start position:0% +will not contribute and that's what +makes the integral doable so what do we + + align:start position:0% +makes the integral doable so what do we + + + align:start position:0% +makes the integral doable so what do we +have then our whole matrix element F H + + align:start position:0% +have then our whole matrix element F H + + + align:start position:0% +have then our whole matrix element F H +prime I has become ie naught over square + + align:start position:0% +prime I has become ie naught over square + + + align:start position:0% +prime I has become ie naught over square +root of pi L cube a zero cube and now + + align:start position:0% +root of pi L cube a zero cube and now + + + align:start position:0% +root of pi L cube a zero cube and now +you just have to integrate this is the + + align:start position:0% +you just have to integrate this is the + + + align:start position:0% +you just have to integrate this is the +only term that contributes and when you + + align:start position:0% +only term that contributes and when you + + + align:start position:0% +only term that contributes and when you +put this term for sure you can now do + + align:start position:0% +put this term for sure you can now do + + + align:start position:0% +put this term for sure you can now do +the D Phi prime integral because that + + align:start position:0% +the D Phi prime integral because that + + + align:start position:0% +the D Phi prime integral because that +term is fire-dependent so that integral + + align:start position:0% +term is fire-dependent so that integral + + + align:start position:0% +term is fire-dependent so that integral +gives you just a factor of two pi from + + align:start position:0% +gives you just a factor of two pi from + + + align:start position:0% +gives you just a factor of two pi from +the integral of D Phi and from this + + align:start position:0% +the integral of D Phi and from this + + + align:start position:0% +the integral of D Phi and from this +thing cosine theta is the angle between + + align:start position:0% +thing cosine theta is the angle between + + + align:start position:0% +thing cosine theta is the angle between +the electric field and K so it's a + + align:start position:0% +the electric field and K so it's a + + + align:start position:0% +the electric field and K so it's a +constant for your integral you're + + align:start position:0% +constant for your integral you're + + + align:start position:0% +constant for your integral you're +integrating over theta Prime and Phi + + align:start position:0% +integrating over theta Prime and Phi + + + align:start position:0% +integrating over theta Prime and Phi +prime so cosine theta also goes out and + + align:start position:0% +prime so cosine theta also goes out and + + + align:start position:0% +prime so cosine theta also goes out and +here is the integral that remains our + + align:start position:0% +here is the integral that remains our + + + align:start position:0% +here is the integral that remains our +cube the our it was R squared but there + + align:start position:0% +cube the our it was R squared but there + + + align:start position:0% +cube the our it was R squared but there +was an extra R from the perturbation or + + align:start position:0% +was an extra R from the perturbation or + + + align:start position:0% +was an extra R from the perturbation or +cube D or e to the minus a over R R over + + align:start position:0% +cube D or e to the minus a over R R over + + + align:start position:0% +cube D or e to the minus a over R R over +a zero and this thing you can pass two + + align:start position:0% +a zero and this thing you can pass two + + + align:start position:0% +a zero and this thing you can pass two +cosine variables it's pretty useful so + + align:start position:0% +cosine variables it's pretty useful so + + + align:start position:0% +cosine variables it's pretty useful so +this goes minus 1 to 1 D cos theta prime + + align:start position:0% +this goes minus 1 to 1 D cos theta prime + + + align:start position:0% +this goes minus 1 to 1 D cos theta prime +cos theta prime e to the minus I K R cos + + align:start position:0% +cos theta prime e to the minus I K R cos + + + align:start position:0% +cos theta prime e to the minus I K R cos +theta Prime + + align:start position:0% + + + + align:start position:0% + +this close theta Prime came from here + + align:start position:0% +this close theta Prime came from here + + + align:start position:0% +this close theta Prime came from here +and that's that's it so this is a nice + + align:start position:0% +and that's that's it so this is a nice + + + align:start position:0% +and that's that's it so this is a nice +result + + align:start position:0% +result + + + align:start position:0% +result +it looks still too difficult but we've + + align:start position:0% +it looks still too difficult but we've + + + align:start position:0% +it looks still too difficult but we've +made great progress and in fact we've + + align:start position:0% +made great progress and in fact we've + + + align:start position:0% +made great progress and in fact we've +dealt with a really difficult part of + + align:start position:0% +dealt with a really difficult part of + + + align:start position:0% +dealt with a really difficult part of +this problem which is orienting yourself + + align:start position:0% +this problem which is orienting yourself + + + align:start position:0% +this problem which is orienting yourself +of how you're going to approach the + + align:start position:0% +of how you're going to approach the + + + align:start position:0% +of how you're going to approach the +matrix element so to finish up I'll just + + align:start position:0% +matrix element so to finish up I'll just + + + align:start position:0% +matrix element so to finish up I'll just +give you a little more of the answer + + align:start position:0% +give you a little more of the answer + + + align:start position:0% +give you a little more of the answer +we'll complete the discussion we need + + align:start position:0% +we'll complete the discussion we need + + + align:start position:0% +we'll complete the discussion we need +probably 15 more minutes to finish it up + + align:start position:0% +probably 15 more minutes to finish it up + + + align:start position:0% +probably 15 more minutes to finish it up +so the only thing I'm gonna say now is + + align:start position:0% +so the only thing I'm gonna say now is + + + align:start position:0% +so the only thing I'm gonna say now is +that if you look at the notes every + + align:start position:0% +that if you look at the notes every + + + align:start position:0% +that if you look at the notes every +integral here is easily doable so + + align:start position:0% +integral here is easily doable so + + + align:start position:0% +integral here is easily doable so +basically there's two integrals and the + + align:start position:0% +basically there's two integrals and the + + + align:start position:0% +basically there's two integrals and the +way to do the B's first do they are + + align:start position:0% +way to do the B's first do they are + + + align:start position:0% +way to do the B's first do they are +integral you'll have to have this terms + + align:start position:0% +integral you'll have to have this terms + + + align:start position:0% +integral you'll have to have this terms +and then do the theta integral and they + + align:start position:0% +and then do the theta integral and they + + + align:start position:0% +and then do the theta integral and they +are kind of simple both of them you have + + align:start position:0% +are kind of simple both of them you have + + + align:start position:0% +are kind of simple both of them you have +to keep up a lot of constants but here + + align:start position:0% +to keep up a lot of constants but here + + + align:start position:0% +to keep up a lot of constants but here +is the answer for the matrix element so + + align:start position:0% +is the answer for the matrix element so + + + align:start position:0% +is the answer for the matrix element so +that part of the integral I think you + + align:start position:0% +that part of the integral I think you + + + align:start position:0% +that part of the integral I think you +all can do and though but you have to + + align:start position:0% +all can do and though but you have to + + + align:start position:0% +all can do and though but you have to +take your time I 32 square root of pi e + + align:start position:0% +take your time I 32 square root of pi e + + + align:start position:0% +take your time I 32 square root of pi e +e not a zero I did a lot of work here + + align:start position:0% +e not a zero I did a lot of work here + + + align:start position:0% +e not a zero I did a lot of work here +actually in writing it in a + + align:start position:0% +actually in writing it in a + + + align:start position:0% +actually in writing it in a +comprehensible way because it's pretty + + align:start position:0% +comprehensible way because it's pretty + + + align:start position:0% +comprehensible way because it's pretty +messy l cube a zero cube one over one + + align:start position:0% +messy l cube a zero cube one over one + + + align:start position:0% +messy l cube a zero cube one over one +plus K squared a zero squared cube + + align:start position:0% +plus K squared a zero squared cube + + + align:start position:0% +plus K squared a zero squared cube +cosine theta it's a + + align:start position:0% +cosine theta it's a + + + align:start position:0% +cosine theta it's a +by now it starts to simplify a little + + align:start position:0% + + + + align:start position:0% + +okay that was actually plenty of work to + + align:start position:0% +okay that was actually plenty of work to + + + align:start position:0% +okay that was actually plenty of work to +get it to write it this way I'm pretty + + align:start position:0% +get it to write it this way I'm pretty + + + align:start position:0% +get it to write it this way I'm pretty +feel pretty happy about that writing why + + align:start position:0% +feel pretty happy about that writing why + + + align:start position:0% +feel pretty happy about that writing why +first okay there's this numbers nothing + + align:start position:0% +first okay there's this numbers nothing + + + align:start position:0% +first okay there's this numbers nothing +I can do about it but there's a + + align:start position:0% +I can do about it but there's a + + + align:start position:0% +I can do about it but there's a +multitude of concert I could have + + align:start position:0% +multitude of concert I could have + + + align:start position:0% +multitude of concert I could have +simplified and done all kinds of things + + align:start position:0% +simplified and done all kinds of things + + + align:start position:0% +simplified and done all kinds of things +but it was not worth it first okay a + + align:start position:0% +but it was not worth it first okay a + + + align:start position:0% +but it was not worth it first okay a +knot that's unit free this is unit free + + align:start position:0% +knot that's unit free this is unit free + + + align:start position:0% +knot that's unit free this is unit free +this is unit three K is one over length + + align:start position:0% +this is unit three K is one over length + + + align:start position:0% +this is unit three K is one over length +K a knot to the four is a length cube + + align:start position:0% +K a knot to the four is a length cube + + + align:start position:0% +K a knot to the four is a length cube +and here is a length cube no units here + + align:start position:0% +and here is a length cube no units here + + + align:start position:0% +and here is a length cube no units here +either here nice unit + + align:start position:0% +either here nice unit + + + align:start position:0% +either here nice unit +this is units of energy y electric field + + align:start position:0% +this is units of energy y electric field + + + align:start position:0% +this is units of energy y electric field +times distance is potential times + + align:start position:0% +times distance is potential times + + + align:start position:0% +times distance is potential times +electric electric charges energy so this + + align:start position:0% +electric electric charges energy so this + + + align:start position:0% +electric electric charges energy so this +is how this should be the matrix element + + align:start position:0% +is how this should be the matrix element + + + align:start position:0% +is how this should be the matrix element +of an energy between normalizable states + + align:start position:0% +of an energy between normalizable states + + + align:start position:0% +of an energy between normalizable states +should be an energy and that has become + + align:start position:0% +should be an energy and that has become + + + align:start position:0% +should be an energy and that has become +clear here the next steps that we'll + + align:start position:0% +clear here the next steps that we'll + + + align:start position:0% +clear here the next steps that we'll +have to do which we'll do next time is + + align:start position:0% +have to do which we'll do next time is + + + align:start position:0% +have to do which we'll do next time is +to integrate over states and put in the + + align:start position:0% +to integrate over states and put in the + + + align:start position:0% +to integrate over states and put in the +density of states and and do a little + + align:start position:0% +density of states and and do a little + + + align:start position:0% +density of states and and do a little +simplification but now it's all trivial + + align:start position:0% +simplification but now it's all trivial + + + align:start position:0% +simplification but now it's all trivial +we don't really have to integrate + + align:start position:0% +we don't really have to integrate + + + align:start position:0% +we don't really have to integrate +anymore because Fermi's golden rule did + + align:start position:0% +anymore because Fermi's golden rule did + + + align:start position:0% +anymore because Fermi's golden rule did +the job for us \ No newline at end of file diff --git a/TDo3r5M1LNo.txt b/TDo3r5M1LNo.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4164b4710c9613f77296223a07efd2f6ba5c270 --- /dev/null +++ b/TDo3r5M1LNo.txt @@ -0,0 +1,13563 @@ +align:start position:0% + +all right welcome back to double o six + + align:start position:0% +all right welcome back to double o six + + + align:start position:0% +all right welcome back to double o six +and our dynamic programming quadruple of + + align:start position:0% +and our dynamic programming quadruple of + + + align:start position:0% +and our dynamic programming quadruple of +lectures we are + + align:start position:0% +lectures we are + + + align:start position:0% +lectures we are +over halfway through uh into lecture + + align:start position:0% +over halfway through uh into lecture + + + align:start position:0% +over halfway through uh into lecture +three of four + + align:start position:0% +three of four + + + align:start position:0% +three of four +uh today we're going to follow up on + + align:start position:0% +uh today we're going to follow up on + + + align:start position:0% +uh today we're going to follow up on +this idea + + align:start position:0% +this idea + + + align:start position:0% +this idea +of problem constraints and expansion + + align:start position:0% +of problem constraints and expansion + + + align:start position:0% +of problem constraints and expansion +that was + + align:start position:0% +that was + + + align:start position:0% +that was +mentioned especially towards the end of + + align:start position:0% +mentioned especially towards the end of + + + align:start position:0% +mentioned especially towards the end of +last lecture we saw + + align:start position:0% +last lecture we saw + + + align:start position:0% +last lecture we saw +an example of sub-problem expansion by a + + align:start position:0% +an example of sub-problem expansion by a + + + align:start position:0% +an example of sub-problem expansion by a +factor of two + + align:start position:0% +factor of two + + + align:start position:0% +factor of two +in the two-player game with coins where + + align:start position:0% +in the two-player game with coins where + + + align:start position:0% +in the two-player game with coins where +we wanted to + + align:start position:0% +we wanted to + + + align:start position:0% +we wanted to +have two versions of the game one where + + align:start position:0% +have two versions of the game one where + + + align:start position:0% +have two versions of the game one where +i go first and one where you go first so + + align:start position:0% +i go first and one where you go first so + + + align:start position:0% +i go first and one where you go first so +this was + + align:start position:0% +this was + + + align:start position:0% +this was +expanding the number of sub problems by + + align:start position:0% +expanding the number of sub problems by + + + align:start position:0% +expanding the number of sub problems by +factor of two today we'll see a bunch + + align:start position:0% +factor of two today we'll see a bunch + + + align:start position:0% +factor of two today we'll see a bunch +more examples of this idea + + align:start position:0% +more examples of this idea + + + align:start position:0% +more examples of this idea +including in one setting we've seen + + align:start position:0% +including in one setting we've seen + + + align:start position:0% +including in one setting we've seen +already which is bellman ford which you + + align:start position:0% +already which is bellman ford which you + + + align:start position:0% +already which is bellman ford which you +can think of + + align:start position:0% +can think of + + + align:start position:0% +can think of +as a dynamic program maybe it's a good + + align:start position:0% +as a dynamic program maybe it's a good + + + align:start position:0% +as a dynamic program maybe it's a good +time to mention that bellman + + align:start position:0% +time to mention that bellman + + + align:start position:0% +time to mention that bellman +invented dynamic programming in the 50s + + align:start position:0% +invented dynamic programming in the 50s + + + align:start position:0% +invented dynamic programming in the 50s +same bellman in the bellman ford + + align:start position:0% +same bellman in the bellman ford + + + align:start position:0% +same bellman in the bellman ford +algorithm this was actually independent + + align:start position:0% +algorithm this was actually independent + + + align:start position:0% +algorithm this was actually independent +discovery by both of them + + align:start position:0% +discovery by both of them + + + align:start position:0% +discovery by both of them +and other people so + + align:start position:0% +and other people so + + + align:start position:0% +and other people so +he invented dynamic programming and then + + align:start position:0% +he invented dynamic programming and then + + + align:start position:0% +he invented dynamic programming and then +a few years later he applied it to solve + + align:start position:0% +a few years later he applied it to solve + + + align:start position:0% +a few years later he applied it to solve +the single source shortest paths problem + + align:start position:0% +the single source shortest paths problem + + + align:start position:0% +the single source shortest paths problem +so we saw them in the other order we saw + + align:start position:0% +so we saw them in the other order we saw + + + align:start position:0% +so we saw them in the other order we saw +single source shortest paths first + + align:start position:0% +single source shortest paths first + + + align:start position:0% +single source shortest paths first +because it's a little easier + + align:start position:0% +because it's a little easier + + + align:start position:0% +because it's a little easier +and now we're seeing the general + + align:start position:0% +and now we're seeing the general + + + align:start position:0% +and now we're seeing the general +framework that this fits into + + align:start position:0% +framework that this fits into + + + align:start position:0% +framework that this fits into +and so we'll see how how that works uh + + align:start position:0% +and so we'll see how how that works uh + + + align:start position:0% +and so we'll see how how that works uh +why did bellman call dynamic programming + + align:start position:0% +why did bellman call dynamic programming + + + align:start position:0% +why did bellman call dynamic programming +dynamic programming mostly because it + + align:start position:0% +dynamic programming mostly because it + + + align:start position:0% +dynamic programming mostly because it +sounded cool + + align:start position:0% +sounded cool + + + align:start position:0% +sounded cool +and he was trying to impress uh + + align:start position:0% +and he was trying to impress uh + + + align:start position:0% +and he was trying to impress uh +government agencies giving him grants + + align:start position:0% +government agencies giving him grants + + + align:start position:0% +government agencies giving him grants +i mean how can you argue with something + + align:start position:0% +i mean how can you argue with something + + + align:start position:0% +i mean how can you argue with something +as cool sounding as dynamic programming + + align:start position:0% +as cool sounding as dynamic programming + + + align:start position:0% +as cool sounding as dynamic programming +but there is some logic to it + + align:start position:0% +but there is some logic to it + + + align:start position:0% +but there is some logic to it +programming is a reference to an old + + align:start position:0% +programming is a reference to an old + + + align:start position:0% +programming is a reference to an old +form of this word which means + + align:start position:0% +form of this word which means + + + align:start position:0% +form of this word which means +optimization and generally we're trying + + align:start position:0% +optimization and generally we're trying + + + align:start position:0% +optimization and generally we're trying +to optimize things + + align:start position:0% +to optimize things + + + align:start position:0% +to optimize things +and instead of optimizing according to + + align:start position:0% +and instead of optimizing according to + + + align:start position:0% +and instead of optimizing according to +some static kind of + + align:start position:0% +some static kind of + + + align:start position:0% +some static kind of +approach or program we're doing it + + align:start position:0% +approach or program we're doing it + + + align:start position:0% +approach or program we're doing it +dynamically this is + + align:start position:0% +dynamically this is + + + align:start position:0% +dynamically this is +a reference to the local brute force + + align:start position:0% +a reference to the local brute force + + + align:start position:0% +a reference to the local brute force +we're doing to optimize at each stage + + align:start position:0% +we're doing to optimize at each stage + + + align:start position:0% +we're doing to optimize at each stage +so you can't tell at the top whether + + align:start position:0% +so you can't tell at the top whether + + + align:start position:0% +so you can't tell at the top whether +what you're going to do in the middle + + align:start position:0% +what you're going to do in the middle + + + align:start position:0% +what you're going to do in the middle +and so it's kind of each each + + align:start position:0% +and so it's kind of each each + + + align:start position:0% +and so it's kind of each each +sub-problem is is + + align:start position:0% +sub-problem is is + + + align:start position:0% +sub-problem is is +behaving differently and so in that + + align:start position:0% +behaving differently and so in that + + + align:start position:0% +behaving differently and so in that +sense dynamic + + align:start position:0% +sense dynamic + + + align:start position:0% +sense dynamic +it sounds cool all right then we'll go + + align:start position:0% +it sounds cool all right then we'll go + + + align:start position:0% +it sounds cool all right then we'll go +to all pair shortest paths we'll see a + + align:start position:0% +to all pair shortest paths we'll see a + + + align:start position:0% +to all pair shortest paths we'll see a +new algorithm for that + + align:start position:0% +new algorithm for that + + + align:start position:0% +new algorithm for that +that's not asymptotically any better but + + align:start position:0% +that's not asymptotically any better but + + + align:start position:0% +that's not asymptotically any better but +it's nice and simple and another way to + + align:start position:0% +it's nice and simple and another way to + + + align:start position:0% +it's nice and simple and another way to +a cool way to see uh subproblem + + align:start position:0% +a cool way to see uh subproblem + + + align:start position:0% +a cool way to see uh subproblem +expansion and then we'll look at a + + align:start position:0% +expansion and then we'll look at a + + + align:start position:0% +expansion and then we'll look at a +couple of sort of practical + + align:start position:0% +couple of sort of practical + + + align:start position:0% +couple of sort of practical +problems uh parenthesizing arithmetic + + align:start position:0% +problems uh parenthesizing arithmetic + + + align:start position:0% +problems uh parenthesizing arithmetic +expressions + + align:start position:0% +expressions + + + align:start position:0% +expressions +and a real world problem piano and + + align:start position:0% +and a real world problem piano and + + + align:start position:0% +and a real world problem piano and +guitar fingering so assigning a + + align:start position:0% +guitar fingering so assigning a + + + align:start position:0% +guitar fingering so assigning a +fingering to how to play a piece + + align:start position:0% +fingering to how to play a piece + + + align:start position:0% +fingering to how to play a piece +and we're going to do that with our sort + + align:start position:0% +and we're going to do that with our sort + + + align:start position:0% +and we're going to do that with our sort +bot framework so quick recollection of + + align:start position:0% +bot framework so quick recollection of + + + align:start position:0% +bot framework so quick recollection of +what that is + + align:start position:0% +what that is + + + align:start position:0% +what that is +we define subproblems and we saw how to + + align:start position:0% +we define subproblems and we saw how to + + + align:start position:0% +we define subproblems and we saw how to +do that for sequences we try either + + align:start position:0% +do that for sequences we try either + + + align:start position:0% +do that for sequences we try either +prefixes suffixes or substrings + + align:start position:0% +prefixes suffixes or substrings + + + align:start position:0% +prefixes suffixes or substrings +we prefer prefixes and suffix because + + align:start position:0% +we prefer prefixes and suffix because + + + align:start position:0% +we prefer prefixes and suffix because +there's fewer of them + + align:start position:0% +there's fewer of them + + + align:start position:0% +there's fewer of them +if there's more than one sequence we + + align:start position:0% +if there's more than one sequence we + + + align:start position:0% +if there's more than one sequence we +take the product of those spaces + + align:start position:0% +take the product of those spaces + + + align:start position:0% +take the product of those spaces +um and then the idea we're going to + + align:start position:0% +um and then the idea we're going to + + + align:start position:0% +um and then the idea we're going to +stress today is we can always add + + align:start position:0% +stress today is we can always add + + + align:start position:0% +stress today is we can always add +sub-problems to make the next step + + align:start position:0% +sub-problems to make the next step + + + align:start position:0% +sub-problems to make the next step +easier + + align:start position:0% +easier + + + align:start position:0% +easier +in particular adding constraints to + + align:start position:0% +in particular adding constraints to + + + align:start position:0% +in particular adding constraints to +sub-problems in some sense lets us + + align:start position:0% +sub-problems in some sense lets us + + + align:start position:0% +sub-problems in some sense lets us +remember things about the subproblem + + align:start position:0% +remember things about the subproblem + + + align:start position:0% +remember things about the subproblem +that's calling us + + align:start position:0% +that's calling us + + + align:start position:0% +that's calling us +or about the past is one way to think + + align:start position:0% +or about the past is one way to think + + + align:start position:0% +or about the past is one way to think +about it or in general to remember state + + align:start position:0% +about it or in general to remember state + + + align:start position:0% +about it or in general to remember state +just by adding more sub problems we can + + align:start position:0% +just by adding more sub problems we can + + + align:start position:0% +just by adding more sub problems we can +remember more stuff + + align:start position:0% +remember more stuff + + + align:start position:0% +remember more stuff +not just what things we're working on + + align:start position:0% +not just what things we're working on + + + align:start position:0% +not just what things we're working on +but some context + + align:start position:0% +but some context + + + align:start position:0% +but some context +and that's what we'll see lots of + + align:start position:0% +and that's what we'll see lots of + + + align:start position:0% +and that's what we'll see lots of +examples of today it'll hopefully make + + align:start position:0% +examples of today it'll hopefully make + + + align:start position:0% +examples of today it'll hopefully make +sense by the end of the lecture + + align:start position:0% +sense by the end of the lecture + + + align:start position:0% +sense by the end of the lecture +then we need to relate these sub + + align:start position:0% +then we need to relate these sub + + + align:start position:0% +then we need to relate these sub +problems with a recurrence relation + + align:start position:0% +problems with a recurrence relation + + + align:start position:0% +problems with a recurrence relation +which we usually just call a relation + + align:start position:0% +which we usually just call a relation + + + align:start position:0% +which we usually just call a relation +and the key idea here + + align:start position:0% +and the key idea here + + + align:start position:0% +and the key idea here +is to come up with a question that if + + align:start position:0% +is to come up with a question that if + + + align:start position:0% +is to come up with a question that if +you knew the answer to that question + + align:start position:0% +you knew the answer to that question + + + align:start position:0% +you knew the answer to that question +you could reduce + + align:start position:0% +you could reduce + + + align:start position:0% +you could reduce +the subproblem you're trying to solve to + + align:start position:0% +the subproblem you're trying to solve to + + + align:start position:0% +the subproblem you're trying to solve to +smaller sub-problem solutions + + align:start position:0% +smaller sub-problem solutions + + + align:start position:0% +smaller sub-problem solutions +so this question is sort of the + + align:start position:0% +so this question is sort of the + + + align:start position:0% +so this question is sort of the +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +aspect of some fundamental aspect of a + + align:start position:0% +aspect of some fundamental aspect of a + + + align:start position:0% +aspect of some fundamental aspect of a +solution typically + + align:start position:0% +solution typically + + + align:start position:0% +solution typically +when you're dealing with suffixes you + + align:start position:0% +when you're dealing with suffixes you + + + align:start position:0% +when you're dealing with suffixes you +want to ask some question about the + + align:start position:0% +want to ask some question about the + + + align:start position:0% +want to ask some question about the +first item s of i + + align:start position:0% +first item s of i + + + align:start position:0% +first item s of i +when you're dealing with prefixes you + + align:start position:0% +when you're dealing with prefixes you + + + align:start position:0% +when you're dealing with prefixes you +want to ask a question about some the + + align:start position:0% +want to ask a question about some the + + + align:start position:0% +want to ask a question about some the +near the last + + align:start position:0% +near the last + + + align:start position:0% +near the last +item s of i minus one and for sub + + align:start position:0% +item s of i minus one and for sub + + + align:start position:0% +item s of i minus one and for sub +strings who knows somewhere in the + + align:start position:0% +strings who knows somewhere in the + + + align:start position:0% +strings who knows somewhere in the +middle + + align:start position:0% +middle + + + align:start position:0% +middle +we'll see an example of that today once + + align:start position:0% +we'll see an example of that today once + + + align:start position:0% +we'll see an example of that today once +you have + + align:start position:0% +you have + + + align:start position:0% +you have +this is a reveal late something coming + + align:start position:0% +this is a reveal late something coming + + + align:start position:0% +this is a reveal late something coming +later + + align:start position:0% +later + + + align:start position:0% +later +uh once you have identified such a + + align:start position:0% +uh once you have identified such a + + + align:start position:0% +uh once you have identified such a +question the + + align:start position:0% +question the + + + align:start position:0% +question the +dynamic programming approach is don't be + + align:start position:0% +dynamic programming approach is don't be + + + align:start position:0% +dynamic programming approach is don't be +smart about how to answer that question + + align:start position:0% +smart about how to answer that question + + + align:start position:0% +smart about how to answer that question +just locally brute force try all + + align:start position:0% +just locally brute force try all + + + align:start position:0% +just locally brute force try all +possible answers to the question + + align:start position:0% +possible answers to the question + + + align:start position:0% +possible answers to the question +for each one recurse and + + align:start position:0% +for each one recurse and + + + align:start position:0% +for each one recurse and +take the best solution according to + + align:start position:0% +take the best solution according to + + + align:start position:0% +take the best solution according to +whatever metric you're trying to do + + align:start position:0% +whatever metric you're trying to do + + + align:start position:0% +whatever metric you're trying to do +typically minimization or maximization + + align:start position:0% +typically minimization or maximization + + + align:start position:0% +typically minimization or maximization +another way to think of this local bird + + align:start position:0% +another way to think of this local bird + + + align:start position:0% +another way to think of this local bird +force which i like to think in my head + + align:start position:0% +force which i like to think in my head + + + align:start position:0% +force which i like to think in my head +so maybe + + align:start position:0% +so maybe + + + align:start position:0% +so maybe +some people like this some people don't + + align:start position:0% +some people like this some people don't + + + align:start position:0% +some people like this some people don't +is to think about guessing the answer + + align:start position:0% +is to think about guessing the answer + + + align:start position:0% +is to think about guessing the answer +to the question and so you know maybe + + align:start position:0% +to the question and so you know maybe + + + align:start position:0% +to the question and so you know maybe +the the answer could be zero one or two + + align:start position:0% +the the answer could be zero one or two + + + align:start position:0% +the the answer could be zero one or two +and uh my algorithm will say guess which + + align:start position:0% +and uh my algorithm will say guess which + + + align:start position:0% +and uh my algorithm will say guess which +is the right answer + + align:start position:0% +is the right answer + + + align:start position:0% +is the right answer +and i'll assume that my algorithm + + align:start position:0% +and i'll assume that my algorithm + + + align:start position:0% +and i'll assume that my algorithm +correctly guesses the + + align:start position:0% +correctly guesses the + + + align:start position:0% +correctly guesses the +answer and analyze that + + align:start position:0% +answer and analyze that + + + align:start position:0% +answer and analyze that +so we can think of the program as going + + align:start position:0% +so we can think of the program as going + + + align:start position:0% +so we can think of the program as going +straight through uh you know + + align:start position:0% +straight through uh you know + + + align:start position:0% +straight through uh you know +guessing the answer and then recursing + + align:start position:0% +guessing the answer and then recursing + + + align:start position:0% +guessing the answer and then recursing +and then combining the solutions however + + align:start position:0% +and then combining the solutions however + + + align:start position:0% +and then combining the solutions however +but then at the end of course we can't + + align:start position:0% +but then at the end of course we can't + + + align:start position:0% +but then at the end of course we can't +assume that the guess was correct + + align:start position:0% +assume that the guess was correct + + + align:start position:0% +assume that the guess was correct +in fact we have to loop over all those + + align:start position:0% +in fact we have to loop over all those + + + align:start position:0% +in fact we have to loop over all those +guesses so it's the same thing just + + align:start position:0% +guesses so it's the same thing just + + + align:start position:0% +guesses so it's the same thing just +if you think of it this way there's less + + align:start position:0% +if you think of it this way there's less + + + align:start position:0% +if you think of it this way there's less +looping in your program but when you + + align:start position:0% +looping in your program but when you + + + align:start position:0% +looping in your program but when you +analyze it definitely the loop is really + + align:start position:0% +analyze it definitely the loop is really + + + align:start position:0% +analyze it definitely the loop is really +there you have to pay for all the + + align:start position:0% +there you have to pay for all the + + + align:start position:0% +there you have to pay for all the +possible answers + + align:start position:0% +possible answers + + + align:start position:0% +possible answers +okay uh then we need to make sure this + + align:start position:0% +okay uh then we need to make sure this + + + align:start position:0% +okay uh then we need to make sure this +relation is acyclic + + align:start position:0% +relation is acyclic + + + align:start position:0% +relation is acyclic +get a subproblem dag and i like to + + align:start position:0% +get a subproblem dag and i like to + + + align:start position:0% +get a subproblem dag and i like to +specify an explicit topological order to + + align:start position:0% +specify an explicit topological order to + + + align:start position:0% +specify an explicit topological order to +make that clear + + align:start position:0% +make that clear + + + align:start position:0% +make that clear +we have base cases for the relation we + + align:start position:0% +we have base cases for the relation we + + + align:start position:0% +we have base cases for the relation we +have to solve the original problem in + + align:start position:0% +have to solve the original problem in + + + align:start position:0% +have to solve the original problem in +terms of these sub problems and then we + + align:start position:0% +terms of these sub problems and then we + + + align:start position:0% +terms of these sub problems and then we +analyze the running time + + align:start position:0% +analyze the running time + + + align:start position:0% +analyze the running time +usually as the number of sub-problems + + align:start position:0% +usually as the number of sub-problems + + + align:start position:0% +usually as the number of sub-problems +times the non-recursive work in each + + align:start position:0% +times the non-recursive work in each + + + align:start position:0% +times the non-recursive work in each +in the relation so recursion is free + + align:start position:0% +in the relation so recursion is free + + + align:start position:0% +in the relation so recursion is free +because we're multiplying by the number + + align:start position:0% +because we're multiplying by the number + + + align:start position:0% +because we're multiplying by the number +of subproblems you can also sum over the + + align:start position:0% +of subproblems you can also sum over the + + + align:start position:0% +of subproblems you can also sum over the +sub-problems sometimes that gives you + + align:start position:0% +sub-problems sometimes that gives you + + + align:start position:0% +sub-problems sometimes that gives you +a tighter bound and then of course we + + align:start position:0% +a tighter bound and then of course we + + + align:start position:0% +a tighter bound and then of course we +also have to add on + + align:start position:0% +also have to add on + + + align:start position:0% +also have to add on +the running time we spend in the + + align:start position:0% +the running time we spend in the + + + align:start position:0% +the running time we spend in the +original problem + + align:start position:0% +original problem + + + align:start position:0% +original problem +all right so that was quick recap now + + align:start position:0% +all right so that was quick recap now + + + align:start position:0% +all right so that was quick recap now +one + + align:start position:0% +one + + + align:start position:0% +one +problem we saw in this framework uh two + + align:start position:0% +problem we saw in this framework uh two + + + align:start position:0% +problem we saw in this framework uh two +lectures ago the first lecture was + + align:start position:0% +lectures ago the first lecture was + + + align:start position:0% +lectures ago the first lecture was +single source shortest paths in a dag + + align:start position:0% +single source shortest paths in a dag + + + align:start position:0% +single source shortest paths in a dag +which a lot of dynamic programs actually + + align:start position:0% +which a lot of dynamic programs actually + + + align:start position:0% +which a lot of dynamic programs actually +can be reduced to shorter + + align:start position:0% +can be reduced to shorter + + + align:start position:0% +can be reduced to shorter +single short shortest paths on a dag in + + align:start position:0% +single short shortest paths on a dag in + + + align:start position:0% +single short shortest paths on a dag in +fact the reverse is true + + align:start position:0% +fact the reverse is true + + + align:start position:0% +fact the reverse is true +single source shortest paths and a dag + + align:start position:0% +single source shortest paths and a dag + + + align:start position:0% +single source shortest paths and a dag +can be thought of the dag relaxation + + align:start position:0% +can be thought of the dag relaxation + + + align:start position:0% +can be thought of the dag relaxation +algorithm we saw + + align:start position:0% +algorithm we saw + + + align:start position:0% +algorithm we saw +is essentially a dynamic program where + + align:start position:0% +is essentially a dynamic program where + + + align:start position:0% +is essentially a dynamic program where +the sub problems are delta of sv + + align:start position:0% +the sub problems are delta of sv + + + align:start position:0% +the sub problems are delta of sv +the relation is delta of sv is the min + + align:start position:0% +the relation is delta of sv is the min + + + align:start position:0% +the relation is delta of sv is the min +so what are we thinking about here + + align:start position:0% +so what are we thinking about here + + + align:start position:0% +so what are we thinking about here +we're guessing this is sort of a new + + align:start position:0% +we're guessing this is sort of a new + + + align:start position:0% +we're guessing this is sort of a new +uh phrase i want to add we're guessing + + align:start position:0% +uh phrase i want to add we're guessing + + + align:start position:0% +uh phrase i want to add we're guessing +uh oh actually i wrote it right here + + align:start position:0% +uh oh actually i wrote it right here + + + align:start position:0% +uh oh actually i wrote it right here +the last edge uv on a shortest s to v + + align:start position:0% +the last edge uv on a shortest s to v + + + align:start position:0% +the last edge uv on a shortest s to v +path + + align:start position:0% +path + + + align:start position:0% +path +right so delta of sv the problem we're + + align:start position:0% +right so delta of sv the problem we're + + + align:start position:0% +right so delta of sv the problem we're +trying to solve is uh + + align:start position:0% +trying to solve is uh + + + align:start position:0% +trying to solve is uh +find shortest s to v path and it's + + align:start position:0% +find shortest s to v path and it's + + + align:start position:0% +find shortest s to v path and it's +you know it's some path and we don't + + align:start position:0% +you know it's some path and we don't + + + align:start position:0% +you know it's some path and we don't +know what it looks like + + align:start position:0% +know what it looks like + + + align:start position:0% +know what it looks like +but uh some feature of the solution of + + align:start position:0% +but uh some feature of the solution of + + + align:start position:0% +but uh some feature of the solution of +this path we're trying to find is well + + align:start position:0% +this path we're trying to find is well + + + align:start position:0% +this path we're trying to find is well +what's the last edge + + align:start position:0% +what's the last edge + + + align:start position:0% +what's the last edge +it comes from some vertex u unless the + + align:start position:0% +it comes from some vertex u unless the + + + align:start position:0% +it comes from some vertex u unless the +path is of length 0 + + align:start position:0% +path is of length 0 + + + align:start position:0% +path is of length 0 +and you know s equals v that's a special + + align:start position:0% +and you know s equals v that's a special + + + align:start position:0% +and you know s equals v that's a special +case dealt with in the base case + + align:start position:0% +case dealt with in the base case + + + align:start position:0% +case dealt with in the base case +otherwise there's some vertex u before v + + align:start position:0% +otherwise there's some vertex u before v + + + align:start position:0% +otherwise there's some vertex u before v +we don't know what it is so we're going + + align:start position:0% +we don't know what it is so we're going + + + align:start position:0% +we don't know what it is so we're going +to locally brute force + + align:start position:0% +to locally brute force + + + align:start position:0% +to locally brute force +or guess what the right answer is so + + align:start position:0% +or guess what the right answer is so + + + align:start position:0% +or guess what the right answer is so +look at all incoming edges + + align:start position:0% +look at all incoming edges + + + align:start position:0% +look at all incoming edges +from u to v and for each of them take + + align:start position:0% +from u to v and for each of them take + + + align:start position:0% +from u to v and for each of them take +the recursive shortest path from s to u + + align:start position:0% +the recursive shortest path from s to u + + + align:start position:0% +the recursive shortest path from s to u +plus the weight of the edge okay so this + + align:start position:0% +plus the weight of the edge okay so this + + + align:start position:0% +plus the weight of the edge okay so this +is the guessing or local brute force + + align:start position:0% +is the guessing or local brute force + + + align:start position:0% +is the guessing or local brute force +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +and the reason this works is because g + + align:start position:0% +and the reason this works is because g + + + align:start position:0% +and the reason this works is because g +is acyclic + + align:start position:0% +is acyclic + + + align:start position:0% +is acyclic +and so it has a topological order + + align:start position:0% +and so it has a topological order + + + align:start position:0% +and so it has a topological order +otherwise + + align:start position:0% +otherwise + + + align:start position:0% +otherwise +if graph if the graph has a cycle and + + align:start position:0% +if graph if the graph has a cycle and + + + align:start position:0% +if graph if the graph has a cycle and +that's the case we want to go to next + + align:start position:0% +that's the case we want to go to next + + + align:start position:0% +that's the case we want to go to next +uh this recursive call from delta of sv + + align:start position:0% +uh this recursive call from delta of sv + + + align:start position:0% +uh this recursive call from delta of sv +to delta of su + + align:start position:0% +to delta of su + + + align:start position:0% +to delta of su +will have loops in it and so you'll + + align:start position:0% +will have loops in it and so you'll + + + align:start position:0% +will have loops in it and so you'll +never evaluate this recursion you'll + + align:start position:0% +never evaluate this recursion you'll + + + align:start position:0% +never evaluate this recursion you'll +never finish you'll never memoize + + align:start position:0% +never finish you'll never memoize + + + align:start position:0% +never finish you'll never memoize +you'll be sad it'll take infinite time + + align:start position:0% +you'll be sad it'll take infinite time + + + align:start position:0% +you'll be sad it'll take infinite time +alright so don't use this algorithm + + align:start position:0% +alright so don't use this algorithm + + + align:start position:0% +alright so don't use this algorithm +unless you have a dag for dag it's great + + align:start position:0% +unless you have a dag for dag it's great + + + align:start position:0% +unless you have a dag for dag it's great +it's linear time + + align:start position:0% +it's linear time + + + align:start position:0% +it's linear time +so that was a little review now here is + + align:start position:0% +so that was a little review now here is + + + align:start position:0% +so that was a little review now here is +a single source shortest paths in + + align:start position:0% +a single source shortest paths in + + + align:start position:0% +a single source shortest paths in +general graphs which we know as + + align:start position:0% +general graphs which we know as + + + align:start position:0% +general graphs which we know as +bellman ford but rephrased into the sort + + align:start position:0% +bellman ford but rephrased into the sort + + + align:start position:0% +bellman ford but rephrased into the sort +bot + + align:start position:0% +bot + + + align:start position:0% +bot +framework okay so uh we defined this + + align:start position:0% +framework okay so uh we defined this + + + align:start position:0% +framework okay so uh we defined this +problem in the bellman ford lecture + + align:start position:0% +problem in the bellman ford lecture + + + align:start position:0% +problem in the bellman ford lecture +delta sub k + + align:start position:0% +delta sub k + + + align:start position:0% +delta sub k +of sv remember this was the weight of + + align:start position:0% +of sv remember this was the weight of + + + align:start position:0% +of sv remember this was the weight of +the shortest path from s to v + + align:start position:0% +the shortest path from s to v + + + align:start position:0% +the shortest path from s to v +that is restricted to use at most k + + align:start position:0% +that is restricted to use at most k + + + align:start position:0% +that is restricted to use at most k +edges + + align:start position:0% +edges + + + align:start position:0% +edges +this made the problem feasible we ended + + align:start position:0% +this made the problem feasible we ended + + + align:start position:0% +this made the problem feasible we ended +up taking the product of the graph into + + align:start position:0% +up taking the product of the graph into + + + align:start position:0% +up taking the product of the graph into +many into + + align:start position:0% +many into + + + align:start position:0% +many into +you know all these different subproblems + + align:start position:0% +you know all these different subproblems + + + align:start position:0% +you know all these different subproblems +in fact + + align:start position:0% +in fact + + + align:start position:0% +in fact +but from the perspective of dynamic + + align:start position:0% +but from the perspective of dynamic + + + align:start position:0% +but from the perspective of dynamic +programming we think of this as a + + align:start position:0% +programming we think of this as a + + + align:start position:0% +programming we think of this as a +subproblem constraint + + align:start position:0% +subproblem constraint + + + align:start position:0% +subproblem constraint +what we really want is the shortest suv + + align:start position:0% +what we really want is the shortest suv + + + align:start position:0% +what we really want is the shortest suv +path but that's hard + + align:start position:0% +path but that's hard + + + align:start position:0% +path but that's hard +so we're going to break it up into + + align:start position:0% +so we're going to break it up into + + + align:start position:0% +so we're going to break it up into +smaller pieces for each k + + align:start position:0% +smaller pieces for each k + + + align:start position:0% +smaller pieces for each k +between zero and v we're going to say + + align:start position:0% +between zero and v we're going to say + + + align:start position:0% +between zero and v we're going to say +well let's think about this problem + + align:start position:0% +well let's think about this problem + + + align:start position:0% +well let's think about this problem +restricted to use at most k edges + + align:start position:0% +restricted to use at most k edges + + + align:start position:0% +restricted to use at most k edges +and we and for simple paths you know if + + align:start position:0% +and we and for simple paths you know if + + + align:start position:0% +and we and for simple paths you know if +there are no negative weight cycles we + + align:start position:0% +there are no negative weight cycles we + + + align:start position:0% +there are no negative weight cycles we +only have to go up to v minus one + + align:start position:0% +only have to go up to v minus one + + + align:start position:0% +only have to go up to v minus one +uh we prove that and we know then we're + + align:start position:0% +uh we prove that and we know then we're + + + align:start position:0% +uh we prove that and we know then we're +happy + + align:start position:0% +happy + + + align:start position:0% +happy +but that's that's sort of the last thing + + align:start position:0% +but that's that's sort of the last thing + + + align:start position:0% +but that's that's sort of the last thing +we want to solve so if we look down at + + align:start position:0% +we want to solve so if we look down at + + + align:start position:0% +we want to solve so if we look down at +the original problem we want + + align:start position:0% +the original problem we want + + + align:start position:0% +the original problem we want +it's delta sub v minus 1 of sv + + align:start position:0% +it's delta sub v minus 1 of sv + + + align:start position:0% +it's delta sub v minus 1 of sv +for all v so though if we could solve + + align:start position:0% +for all v so though if we could solve + + + align:start position:0% +for all v so though if we could solve +these sub problems as we saw with bowman + + align:start position:0% +these sub problems as we saw with bowman + + + align:start position:0% +these sub problems as we saw with bowman +ford + + align:start position:0% +ford + + + align:start position:0% +ford +we can solve the original problem unless + + align:start position:0% +we can solve the original problem unless + + + align:start position:0% +we can solve the original problem unless +there are negative weight cycles and we + + align:start position:0% +there are negative weight cycles and we + + + align:start position:0% +there are negative weight cycles and we +use delta sub v + + align:start position:0% +use delta sub v + + + align:start position:0% +use delta sub v +of sv to check whether they're negative + + align:start position:0% +of sv to check whether they're negative + + + align:start position:0% +of sv to check whether they're negative +weight cycles i don't want to repeat + + align:start position:0% +weight cycles i don't want to repeat + + + align:start position:0% +weight cycles i don't want to repeat +that but that's the + + align:start position:0% +that but that's the + + + align:start position:0% +that but that's the +all in the original problem and then we + + align:start position:0% +all in the original problem and then we + + + align:start position:0% +all in the original problem and then we +can take + + align:start position:0% +can take + + + align:start position:0% +can take +this relation that we wrote for + + align:start position:0% +this relation that we wrote for + + + align:start position:0% +this relation that we wrote for +dag shortest paths and just port it over + + align:start position:0% +dag shortest paths and just port it over + + + align:start position:0% +dag shortest paths and just port it over +here + + align:start position:0% +here + + + align:start position:0% +here +so remember this for a general graph + + align:start position:0% +so remember this for a general graph + + + align:start position:0% +so remember this for a general graph +this has cycles so we can't use it + + align:start position:0% +this has cycles so we can't use it + + + align:start position:0% +this has cycles so we can't use it +because we're just referring to + + align:start position:0% +because we're just referring to + + + align:start position:0% +because we're just referring to +arbitrary delta of svs + + align:start position:0% +arbitrary delta of svs + + + align:start position:0% +arbitrary delta of svs +so there's no reason to expect no cycles + + align:start position:0% +so there's no reason to expect no cycles + + + align:start position:0% +so there's no reason to expect no cycles +there + + align:start position:0% +there + + + align:start position:0% +there +in fact the call graph is exactly the + + align:start position:0% +in fact the call graph is exactly the + + + align:start position:0% +in fact the call graph is exactly the +graph g so it has a cycle if only if g + + align:start position:0% +graph g so it has a cycle if only if g + + + align:start position:0% +graph g so it has a cycle if only if g +does + + align:start position:0% +does + + + align:start position:0% +does +but now over here i'm writing exactly + + align:start position:0% +but now over here i'm writing exactly + + + align:start position:0% +but now over here i'm writing exactly +the same formula + + align:start position:0% +the same formula + + + align:start position:0% +the same formula +for this min but i added a sub k here + + align:start position:0% +for this min but i added a sub k here + + + align:start position:0% +for this min but i added a sub k here +and a sub + + align:start position:0% +and a sub + + + align:start position:0% +and a sub +k minus 1 here the observation being if + + align:start position:0% +k minus 1 here the observation being if + + + align:start position:0% +k minus 1 here the observation being if +i've already guessed what the last edge + + align:start position:0% +i've already guessed what the last edge + + + align:start position:0% +i've already guessed what the last edge +uv is for this path + + align:start position:0% +uv is for this path + + + align:start position:0% +uv is for this path +then if this whole thing has length at + + align:start position:0% +then if this whole thing has length at + + + align:start position:0% +then if this whole thing has length at +most + + align:start position:0% +most + + + align:start position:0% +most +k then this piece has length at most + + align:start position:0% +k then this piece has length at most + + + align:start position:0% +k then this piece has length at most +k minus 1. so i only need to + + align:start position:0% +k minus 1. so i only need to + + + align:start position:0% +k minus 1. so i only need to +do solve delta sub k minus 1 of sv + + align:start position:0% +do solve delta sub k minus 1 of sv + + + align:start position:0% +do solve delta sub k minus 1 of sv +here and so that's what i wrote sorry i + + align:start position:0% +here and so that's what i wrote sorry i + + + align:start position:0% +here and so that's what i wrote sorry i +have s u that's what i wrote here + + align:start position:0% +have s u that's what i wrote here + + + align:start position:0% +have s u that's what i wrote here +there's one other thing which is as i + + align:start position:0% +there's one other thing which is as i + + + align:start position:0% +there's one other thing which is as i +mentioned a little while ago + + align:start position:0% +mentioned a little while ago + + + align:start position:0% +mentioned a little while ago +it could be that we use fewer than k + + align:start position:0% +it could be that we use fewer than k + + + align:start position:0% +it could be that we use fewer than k +edges and so + + align:start position:0% +edges and so + + + align:start position:0% +edges and so +let's consider the case where we don't + + align:start position:0% +let's consider the case where we don't + + + align:start position:0% +let's consider the case where we don't +follow a last edge + + align:start position:0% +follow a last edge + + + align:start position:0% +follow a last edge +and we just add to this min the + + align:start position:0% +and we just add to this min the + + + align:start position:0% +and we just add to this min the +uh shortest path using at most k minus + + align:start position:0% +uh shortest path using at most k minus + + + align:start position:0% +uh shortest path using at most k minus +one edges that's one option + + align:start position:0% +one edges that's one option + + + align:start position:0% +one edges that's one option +for having at most k edges if we wrote + + align:start position:0% +for having at most k edges if we wrote + + + align:start position:0% +for having at most k edges if we wrote +equality here + + align:start position:0% +equality here + + + align:start position:0% +equality here +then we would remove that like the last + + align:start position:0% +then we would remove that like the last + + + align:start position:0% +then we would remove that like the last +problem session + + align:start position:0% +problem session + + + align:start position:0% +problem session +okay good + + align:start position:0% +okay good + + + align:start position:0% +okay good +so the key observation here is that this + + align:start position:0% +so the key observation here is that this + + + align:start position:0% +so the key observation here is that this +recurrence + + align:start position:0% +recurrence + + + align:start position:0% +recurrence +does not have cycles just by adding this + + align:start position:0% +does not have cycles just by adding this + + + align:start position:0% +does not have cycles just by adding this +index + + align:start position:0% +index + + + align:start position:0% +index +if we solve these problems in order of + + align:start position:0% +if we solve these problems in order of + + + align:start position:0% +if we solve these problems in order of +increasing k + + align:start position:0% +increasing k + + + align:start position:0% +increasing k +all of the references from delta sub k + + align:start position:0% +all of the references from delta sub k + + + align:start position:0% +all of the references from delta sub k +are in terms of delta sub k minus 1 + + align:start position:0% +are in terms of delta sub k minus 1 + + + align:start position:0% +are in terms of delta sub k minus 1 +and so this is now magically acyclic + + align:start position:0% +and so this is now magically acyclic + + + align:start position:0% +and so this is now magically acyclic +this is why bellman ford worked + + align:start position:0% +this is why bellman ford worked + + + align:start position:0% +this is why bellman ford worked +this but now i think in a very pleasing + + align:start position:0% +this but now i think in a very pleasing + + + align:start position:0% +this but now i think in a very pleasing +way we're taking our graph that cyclic + + align:start position:0% +way we're taking our graph that cyclic + + + align:start position:0% +way we're taking our graph that cyclic +and by spreading it out over various + + align:start position:0% +and by spreading it out over various + + + align:start position:0% +and by spreading it out over various +copies of k and referencing always the + + align:start position:0% +copies of k and referencing always the + + + align:start position:0% +copies of k and referencing always the +smaller one + + align:start position:0% +smaller one + + + align:start position:0% +smaller one +we get an acyclic graph acyclic + + align:start position:0% +we get an acyclic graph acyclic + + + align:start position:0% +we get an acyclic graph acyclic +relations + + align:start position:0% +relations + + + align:start position:0% +relations +we have base cases like normal and then + + align:start position:0% +we have base cases like normal and then + + + align:start position:0% +we have base cases like normal and then +we can analyze the running time + + align:start position:0% +we can analyze the running time + + + align:start position:0% +we can analyze the running time +in the usual way which is uh summing + + align:start position:0% +in the usual way which is uh summing + + + align:start position:0% +in the usual way which is uh summing +so uh what is this uh how much does this + + align:start position:0% +so uh what is this uh how much does this + + + align:start position:0% +so uh what is this uh how much does this +cost we're going to take this the cost + + align:start position:0% +cost we're going to take this the cost + + + align:start position:0% +cost we're going to take this the cost +of computing the relation + + align:start position:0% +of computing the relation + + + align:start position:0% +of computing the relation +which is the number of incoming edges to + + align:start position:0% +which is the number of incoming edges to + + + align:start position:0% +which is the number of incoming edges to +v + + align:start position:0% +v + + + align:start position:0% +v +that's this theta and then + + align:start position:0% +that's this theta and then + + + align:start position:0% +that's this theta and then +some overall sub problems so sum over k + + align:start position:0% +some overall sub problems so sum over k + + + align:start position:0% +some overall sub problems so sum over k +and sum over v + + align:start position:0% +and sum over v + + + align:start position:0% +and sum over v +i wrote it as a sum instead of our + + align:start position:0% +i wrote it as a sum instead of our + + + align:start position:0% +i wrote it as a sum instead of our +product because this thing + + align:start position:0% +product because this thing + + + align:start position:0% +product because this thing +is theta e + + align:start position:0% +is theta e + + + align:start position:0% +is theta e +right the sum of incoming edges over all + + align:start position:0% +right the sum of incoming edges over all + + + align:start position:0% +right the sum of incoming edges over all +vertices is exactly + + align:start position:0% +vertices is exactly + + + align:start position:0% +vertices is exactly +the size of e and then we sum there's no + + align:start position:0% +the size of e and then we sum there's no + + + align:start position:0% +the size of e and then we sum there's no +k in this formula so we just multiply by + + align:start position:0% +k in this formula so we just multiply by + + + align:start position:0% +k in this formula so we just multiply by +v and we get v + + align:start position:0% +v and we get v + + + align:start position:0% +v and we get v +e so our good friend belmont ford recast + + align:start position:0% +e so our good friend belmont ford recast + + + align:start position:0% +e so our good friend belmont ford recast +kind of the opposite way before we were + + align:start position:0% +kind of the opposite way before we were + + + align:start position:0% +kind of the opposite way before we were +using relaxations now we're just writing + + align:start position:0% +using relaxations now we're just writing + + + align:start position:0% +using relaxations now we're just writing +them in explicitly + + align:start position:0% +them in explicitly + + + align:start position:0% +them in explicitly +but essentially the same computation + + align:start position:0% +but essentially the same computation + + + align:start position:0% +but essentially the same computation +just in a different order + + align:start position:0% +just in a different order + + + align:start position:0% +just in a different order +okay cool so those are reviews of + + align:start position:0% +okay cool so those are reviews of + + + align:start position:0% +okay cool so those are reviews of +old algorithms but in this new framework + + align:start position:0% +old algorithms but in this new framework + + + align:start position:0% +old algorithms but in this new framework +show how powerful it is let's look at + + align:start position:0% +show how powerful it is let's look at + + + align:start position:0% +show how powerful it is let's look at +another example which is our friend + + align:start position:0% +another example which is our friend + + + align:start position:0% +another example which is our friend +right here all pairs shortest paths + + align:start position:0% +right here all pairs shortest paths + + + align:start position:0% +right here all pairs shortest paths +okay a few lectures ago we saw johnson's + + align:start position:0% +okay a few lectures ago we saw johnson's + + + align:start position:0% +okay a few lectures ago we saw johnson's +algorithm which solves this + + align:start position:0% +algorithm which solves this + + + align:start position:0% +algorithm which solves this +very well so + + align:start position:0% +very well so + + + align:start position:0% +very well so +one option we could use is just + + align:start position:0% +one option we could use is just + + + align:start position:0% +one option we could use is just +this same set of sub problems but for + + align:start position:0% +this same set of sub problems but for + + + align:start position:0% +this same set of sub problems but for +all u and v + + align:start position:0% +all u and v + + + align:start position:0% +all u and v +right so for u and v and v + + align:start position:0% +right so for u and v and v + + + align:start position:0% +right so for u and v and v +that's what we really care about um and + + align:start position:0% +that's what we really care about um and + + + align:start position:0% +that's what we really care about um and +then we could say + + align:start position:0% +then we could say + + + align:start position:0% +then we could say +k up to v something like that + + align:start position:0% +k up to v something like that + + + align:start position:0% +k up to v something like that +so this would work but it would give the + + align:start position:0% +so this would work but it would give the + + + align:start position:0% +so this would work but it would give the +same running time as + + align:start position:0% +same running time as + + + align:start position:0% +same running time as +running bellman ford v times this is one + + align:start position:0% +running bellman ford v times this is one + + + align:start position:0% +running bellman ford v times this is one +solution we know + + align:start position:0% +solution we know + + + align:start position:0% +solution we know +but not the best solution we know for + + align:start position:0% +but not the best solution we know for + + + align:start position:0% +but not the best solution we know for +how to solve shortest paths + + align:start position:0% +how to solve shortest paths + + + align:start position:0% +how to solve shortest paths +so this would give v squared + + align:start position:0% +so this would give v squared + + + align:start position:0% +so this would give v squared +e which is at most + + align:start position:0% +e which is at most + + + align:start position:0% +e which is at most +v to the fourth for dense graphs it is + + align:start position:0% +v to the fourth for dense graphs it is + + + align:start position:0% +v to the fourth for dense graphs it is +theta v to the fourth + + align:start position:0% +theta v to the fourth + + + align:start position:0% +theta v to the fourth +so this is v times v times e um but + + align:start position:0% +so this is v times v times e um but + + + align:start position:0% +so this is v times v times e um but +worst case is v to the fourth + + align:start position:0% +worst case is v to the fourth + + + align:start position:0% +worst case is v to the fourth +uh what i'd like to show you now is a + + align:start position:0% +uh what i'd like to show you now is a + + + align:start position:0% +uh what i'd like to show you now is a +different way to solve this problem + + align:start position:0% +different way to solve this problem + + + align:start position:0% +different way to solve this problem +almost identical but gives v cubed + + align:start position:0% +almost identical but gives v cubed + + + align:start position:0% +almost identical but gives v cubed +running time + + align:start position:0% +running time + + + align:start position:0% +running time +which for dense graphs is really good so + + align:start position:0% +which for dense graphs is really good so + + + align:start position:0% +which for dense graphs is really good so +we're going to reduce this 4 down to a + + align:start position:0% +we're going to reduce this 4 down to a + + + align:start position:0% +we're going to reduce this 4 down to a +3. + + align:start position:0% +3. + + + align:start position:0% +3. +this is an algorithm called floyd + + align:start position:0% +this is an algorithm called floyd + + + align:start position:0% +this is an algorithm called floyd +warshall + + align:start position:0% +warshall + + + align:start position:0% +warshall +it's definitely not an obvious algorithm + + align:start position:0% +it's definitely not an obvious algorithm + + + align:start position:0% +it's definitely not an obvious algorithm +it's a very cool idea + + align:start position:0% +it's a very cool idea + + + align:start position:0% +it's a very cool idea +and it's a nice example of a different + + align:start position:0% +and it's a nice example of a different + + + align:start position:0% +and it's a nice example of a different +way remember this is sub problem + + align:start position:0% +way remember this is sub problem + + + align:start position:0% +way remember this is sub problem +expansion we took + + align:start position:0% +expansion we took + + + align:start position:0% +expansion we took +the problems we cared about multiplied + + align:start position:0% +the problems we cared about multiplied + + + align:start position:0% +the problems we cared about multiplied +by this choice of k + + align:start position:0% +by this choice of k + + + align:start position:0% +by this choice of k +here we're going to do the same thing + + align:start position:0% +here we're going to do the same thing + + + align:start position:0% +here we're going to do the same thing +but define it differently + + align:start position:0% +but define it differently + + + align:start position:0% +but define it differently +we're going to define those sub problems + + align:start position:0% +we're going to define those sub problems + + + align:start position:0% +we're going to define those sub problems +differently so first i want to number + + align:start position:0% +differently so first i want to number + + + align:start position:0% +differently so first i want to number +the vertices + + align:start position:0% + + + + align:start position:0% + +starting at 1 for convenience so let's + + align:start position:0% +starting at 1 for convenience so let's + + + align:start position:0% +starting at 1 for convenience so let's +see why + + align:start position:0% +see why + + + align:start position:0% +see why +and then we're going to define some sub + + align:start position:0% +and then we're going to define some sub + + + align:start position:0% +and then we're going to define some sub +problems which are + + align:start position:0% + + + + align:start position:0% + +delta i'll call it u v comma k + + align:start position:0% +delta i'll call it u v comma k + + + align:start position:0% +delta i'll call it u v comma k +maybe to avoid conflict i will + + align:start position:0% +maybe to avoid conflict i will + + + align:start position:0% +maybe to avoid conflict i will +write a d here this is just a definition + + align:start position:0% +write a d here this is just a definition + + + align:start position:0% +write a d here this is just a definition +local to this algorithm + + align:start position:0% +local to this algorithm + + + align:start position:0% +local to this algorithm +so i want the weight of + + align:start position:0% +so i want the weight of + + + align:start position:0% +so i want the weight of +shortest s to v path + + align:start position:0% + + + + align:start position:0% + +okay so far just the same as the problem + + align:start position:0% +okay so far just the same as the problem + + + align:start position:0% +okay so far just the same as the problem +we actually want to solve this is + + align:start position:0% +we actually want to solve this is + + + align:start position:0% +we actually want to solve this is +delta of sorry uv + + align:start position:0% + + + + align:start position:0% + +but i'm going to add a constraint which + + align:start position:0% +but i'm going to add a constraint which + + + align:start position:0% +but i'm going to add a constraint which +is + + align:start position:0% + + + + align:start position:0% + +using only vertices + + align:start position:0% + + + + align:start position:0% + +in uv + + align:start position:0% +in uv + + + align:start position:0% +in uv +and 1 2 + + align:start position:0% +and 1 2 + + + align:start position:0% +and 1 2 +up to k so this is the divine + + align:start position:0% +up to k so this is the divine + + + align:start position:0% +up to k so this is the divine +inspiration to define sub problems this + + align:start position:0% +inspiration to define sub problems this + + + align:start position:0% +inspiration to define sub problems this +way + + align:start position:0% +way + + + align:start position:0% +way +it's a different constraint than the one + + align:start position:0% +it's a different constraint than the one + + + align:start position:0% +it's a different constraint than the one +we saw here + + align:start position:0% +we saw here + + + align:start position:0% +we saw here +which was using at most k + + align:start position:0% +which was using at most k + + + align:start position:0% +which was using at most k +edges so in some sense what's slow about + + align:start position:0% +edges so in some sense what's slow about + + + align:start position:0% +edges so in some sense what's slow about +this algorithm + + align:start position:0% +this algorithm + + + align:start position:0% +this algorithm +is that we have to loop over all the + + align:start position:0% +is that we have to loop over all the + + + align:start position:0% +is that we have to loop over all the +incoming vertices + + align:start position:0% +incoming vertices + + + align:start position:0% +incoming vertices +this is expensive you know costs order + + align:start position:0% +this is expensive you know costs order + + + align:start position:0% +this is expensive you know costs order +the degree which ends up with an e term + + align:start position:0% +the degree which ends up with an e term + + + align:start position:0% +the degree which ends up with an e term +we're going to try to convert that e + + align:start position:0% +we're going to try to convert that e + + + align:start position:0% +we're going to try to convert that e +term into a v + + align:start position:0% +term into a v + + + align:start position:0% +term into a v +term by just knowing + + align:start position:0% +term by just knowing + + + align:start position:0% +term by just knowing +which vertex to come from which sounds + + align:start position:0% +which vertex to come from which sounds + + + align:start position:0% +which vertex to come from which sounds +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +but it turns out if you write the sub + + align:start position:0% +but it turns out if you write the sub + + + align:start position:0% +but it turns out if you write the sub +problems this way so + + align:start position:0% +problems this way so + + + align:start position:0% +problems this way so +i'm naming the vertices and say well + + align:start position:0% +i'm naming the vertices and say well + + + align:start position:0% +i'm naming the vertices and say well +let me just find a path that uses uv + + align:start position:0% +let me just find a path that uses uv + + + align:start position:0% +let me just find a path that uses uv +and the vertex labeled one there's only + + align:start position:0% +and the vertex labeled one there's only + + + align:start position:0% +and the vertex labeled one there's only +like two options i could go straight + + align:start position:0% +like two options i could go straight + + + align:start position:0% +like two options i could go straight +from u to v + + align:start position:0% +from u to v + + + align:start position:0% +from u to v +or i could go from u to one to v and + + align:start position:0% +or i could go from u to one to v and + + + align:start position:0% +or i could go from u to one to v and +then how about with one and two and one + + align:start position:0% +then how about with one and two and one + + + align:start position:0% +then how about with one and two and one +and two and three + + align:start position:0% +and two and three + + + align:start position:0% +and two and three +the same vertices okay by + + align:start position:0% +the same vertices okay by + + + align:start position:0% +the same vertices okay by +label instead of by counting them + + align:start position:0% +label instead of by counting them + + + align:start position:0% +label instead of by counting them +slight tweak but it turns out this uh + + align:start position:0% +slight tweak but it turns out this uh + + + align:start position:0% +slight tweak but it turns out this uh +speeds up the algorithm so let me first + + align:start position:0% +speeds up the algorithm so let me first + + + align:start position:0% +speeds up the algorithm so let me first +tell you how many sub problems there are + + align:start position:0% + + + + align:start position:0% + +okay this is uh v cubed sub problems + + align:start position:0% +okay this is uh v cubed sub problems + + + align:start position:0% +okay this is uh v cubed sub problems +two choices for u and v and i have uh + + align:start position:0% +two choices for u and v and i have uh + + + align:start position:0% +two choices for u and v and i have uh +v choices for sorry i have v choices for + + align:start position:0% +v choices for sorry i have v choices for + + + align:start position:0% +v choices for sorry i have v choices for +u v choices for v and v choices for k + + align:start position:0% +u v choices for v and v choices for k + + + align:start position:0% +u v choices for v and v choices for k +roughly v cubed of these + + align:start position:0% +roughly v cubed of these + + + align:start position:0% +roughly v cubed of these +uh but the key thing is that sounds like + + align:start position:0% +uh but the key thing is that sounds like + + + align:start position:0% +uh but the key thing is that sounds like +a lot + + align:start position:0% +a lot + + + align:start position:0% +a lot +but the relation becomes cheaper now + + align:start position:0% +but the relation becomes cheaper now + + + align:start position:0% +but the relation becomes cheaper now +because i can just write delta u + + align:start position:0% +because i can just write delta u + + + align:start position:0% +because i can just write delta u +sorry d of uvk + + align:start position:0% +sorry d of uvk + + + align:start position:0% +sorry d of uvk +is the min of two things + + align:start position:0% +is the min of two things + + + align:start position:0% +is the min of two things +d of u v k minus one + + align:start position:0% +d of u v k minus one + + + align:start position:0% +d of u v k minus one +and d of u + + align:start position:0% +and d of u + + + align:start position:0% +and d of u +k k minus one + + align:start position:0% +k k minus one + + + align:start position:0% +k k minus one +plus d of k + + align:start position:0% +plus d of k + + + align:start position:0% +plus d of k +v k minus one + + align:start position:0% +v k minus one + + + align:start position:0% +v k minus one +okay it's a strange it's a strange + + align:start position:0% +okay it's a strange it's a strange + + + align:start position:0% +okay it's a strange it's a strange +formula because we're using + + align:start position:0% +formula because we're using + + + align:start position:0% +formula because we're using +indices like k for vertices also um + + align:start position:0% +indices like k for vertices also um + + + align:start position:0% +indices like k for vertices also um +as well as u and v for vertices but + + align:start position:0% +as well as u and v for vertices but + + + align:start position:0% +as well as u and v for vertices but +we're also using k + + align:start position:0% +we're also using k + + + align:start position:0% +we're also using k +as a counter but we can do this because + + align:start position:0% +as a counter but we can do this because + + + align:start position:0% +as a counter but we can do this because +our vertices are numbered + + align:start position:0% +our vertices are numbered + + + align:start position:0% +our vertices are numbered +okay so the idea is the following we + + align:start position:0% +okay so the idea is the following we + + + align:start position:0% +okay so the idea is the following we +have vertex u + + align:start position:0% +have vertex u + + + align:start position:0% +have vertex u +we have a vertex v and we've already + + align:start position:0% +we have a vertex v and we've already + + + align:start position:0% +we have a vertex v and we've already +found the shortest path + + align:start position:0% +found the shortest path + + + align:start position:0% +found the shortest path +that uses vertices 1 through k minus 1 + + align:start position:0% +that uses vertices 1 through k minus 1 + + + align:start position:0% +that uses vertices 1 through k minus 1 +that's what this quantity is so it could + + align:start position:0% +that's what this quantity is so it could + + + align:start position:0% +that's what this quantity is so it could +be + + align:start position:0% +be + + + align:start position:0% +be +and now we're thinking we're trying to + + align:start position:0% +and now we're thinking we're trying to + + + align:start position:0% +and now we're thinking we're trying to +add in this vertex k and think about + + align:start position:0% +add in this vertex k and think about + + + align:start position:0% +add in this vertex k and think about +what are all the paths that could go + + align:start position:0% +what are all the paths that could go + + + align:start position:0% +what are all the paths that could go +from u to v using one up to k + + align:start position:0% +from u to v using one up to k + + + align:start position:0% +from u to v using one up to k +well it could be the shortest path from + + align:start position:0% +well it could be the shortest path from + + + align:start position:0% +well it could be the shortest path from +u to v using one up to k doesn't use + + align:start position:0% +u to v using one up to k doesn't use + + + align:start position:0% +u to v using one up to k doesn't use +vertex k + + align:start position:0% +vertex k + + + align:start position:0% +vertex k +that's the first option just use + + align:start position:0% +that's the first option just use + + + align:start position:0% +that's the first option just use +vertices one up to k minus one maybe we + + align:start position:0% +vertices one up to k minus one maybe we + + + align:start position:0% +vertices one up to k minus one maybe we +don't need + + align:start position:0% +don't need + + + align:start position:0% +don't need +to use k or it could be that the path + + align:start position:0% +to use k or it could be that the path + + + align:start position:0% +to use k or it could be that the path +goes through k + + align:start position:0% +goes through k + + + align:start position:0% +goes through k +well it starts at u and it goes to k + + align:start position:0% +well it starts at u and it goes to k + + + align:start position:0% +well it starts at u and it goes to k +and then it goes from k to v okay all + + align:start position:0% +and then it goes from k to v okay all + + + align:start position:0% +and then it goes from k to v okay all +using + + align:start position:0% +using + + + align:start position:0% +using +for simple paths if we assume there are + + align:start position:0% +for simple paths if we assume there are + + + align:start position:0% +for simple paths if we assume there are +no negative weight cycles and you have + + align:start position:0% +no negative weight cycles and you have + + + align:start position:0% +no negative weight cycles and you have +to run down and forward to detect them + + align:start position:0% +to run down and forward to detect them + + + align:start position:0% +to run down and forward to detect them +but assuming no negative weight cycles + + align:start position:0% +but assuming no negative weight cycles + + + align:start position:0% +but assuming no negative weight cycles +the shortest path from u to v through k + + align:start position:0% +the shortest path from u to v through k + + + align:start position:0% +the shortest path from u to v through k +must start by using vertices less than k + + align:start position:0% +must start by using vertices less than k + + + align:start position:0% +must start by using vertices less than k +and then use vertices less than k again + + align:start position:0% +and then use vertices less than k again + + + align:start position:0% +and then use vertices less than k again +and that's what i've written here it's + + align:start position:0% +and that's what i've written here it's + + + align:start position:0% +and that's what i've written here it's +from u to k using k minus 1 + + align:start position:0% +from u to k using k minus 1 + + + align:start position:0% +from u to k using k minus 1 +up to k minus 1 labels and from k to v + + align:start position:0% +up to k minus 1 labels and from k to v + + + align:start position:0% +up to k minus 1 labels and from k to v +using labels up to k minus one okay the + + align:start position:0% +using labels up to k minus one okay the + + + align:start position:0% +using labels up to k minus one okay the +cool thing here + + align:start position:0% +cool thing here + + + align:start position:0% +cool thing here +is the min only has two terms so this + + align:start position:0% +is the min only has two terms so this + + + align:start position:0% +is the min only has two terms so this +takes constant time + + align:start position:0% +takes constant time + + + align:start position:0% +takes constant time +non-recursive work so this is uh + + align:start position:0% +non-recursive work so this is uh + + + align:start position:0% +non-recursive work so this is uh +k is not on the shortest path and this + + align:start position:0% +k is not on the shortest path and this + + + align:start position:0% +k is not on the shortest path and this +is k is on the shortest path + + align:start position:0% + + + + align:start position:0% + +cool so this is constant non-recursive + + align:start position:0% +cool so this is constant non-recursive + + + align:start position:0% +cool so this is constant non-recursive +work + + align:start position:0% + + + + align:start position:0% + +so if we jump ahead to the running time + + align:start position:0% +so if we jump ahead to the running time + + + align:start position:0% +so if we jump ahead to the running time +with this algorithm we get + + align:start position:0% + + + + align:start position:0% + +the number of sub-problems which is v + + align:start position:0% +the number of sub-problems which is v + + + align:start position:0% +the number of sub-problems which is v +cubed times + + align:start position:0% +cubed times + + + align:start position:0% +cubed times +the number the amount of work per + + align:start position:0% +the number the amount of work per + + + align:start position:0% +the number the amount of work per +sub-problem which is constant + + align:start position:0% +sub-problem which is constant + + + align:start position:0% +sub-problem which is constant +so that's just a v cubed algorithm + + align:start position:0% +so that's just a v cubed algorithm + + + align:start position:0% +so that's just a v cubed algorithm +for dense graphs this is really good + + align:start position:0% +for dense graphs this is really good + + + align:start position:0% +for dense graphs this is really good +this is when e is v squared then + + align:start position:0% +this is when e is v squared then + + + align:start position:0% +this is when e is v squared then +this is the same thing as v times e so + + align:start position:0% +this is the same thing as v times e so + + + align:start position:0% +this is the same thing as v times e so +as good as bellman ford + + align:start position:0% +as good as bellman ford + + + align:start position:0% +as good as bellman ford +uh it's not as good as johnson for + + align:start position:0% +uh it's not as good as johnson for + + + align:start position:0% +uh it's not as good as johnson for +sparse graphs + + align:start position:0% +sparse graphs + + + align:start position:0% +sparse graphs +sparse graphs remember or in general + + align:start position:0% +sparse graphs remember or in general + + + align:start position:0% +sparse graphs remember or in general +with with + + align:start position:0% +with with + + + align:start position:0% +with with +johnson we got v squared log n + + align:start position:0% +johnson we got v squared log n + + + align:start position:0% +johnson we got v squared log n +plus v e and this is always spending v + + align:start position:0% +plus v e and this is always spending v + + + align:start position:0% +plus v e and this is always spending v +cubed + + align:start position:0% +cubed + + + align:start position:0% +cubed +but it's cool because it's a very simple + + align:start position:0% +but it's cool because it's a very simple + + + align:start position:0% +but it's cool because it's a very simple +algorithm let's uh + + align:start position:0% +algorithm let's uh + + + align:start position:0% +algorithm let's uh +quickly write the topological order + + align:start position:0% +quickly write the topological order + + + align:start position:0% +quickly write the topological order +this is + + align:start position:0% + + + + align:start position:0% + +all we need is to guarantee that we + + align:start position:0% +all we need is to guarantee that we + + + align:start position:0% +all we need is to guarantee that we +solve problems in increasing k + + align:start position:0% +solve problems in increasing k + + + align:start position:0% +solve problems in increasing k +order because every reference here is to + + align:start position:0% +order because every reference here is to + + + align:start position:0% +order because every reference here is to +a smaller k + + align:start position:0% +a smaller k + + + align:start position:0% +a smaller k +for the third argument um and so for + + align:start position:0% +for the third argument um and so for + + + align:start position:0% +for the third argument um and so for +example you can just write + + align:start position:0% +example you can just write + + + align:start position:0% +example you can just write +a tripoli nested loop k equals zero one + + align:start position:0% +a tripoli nested loop k equals zero one + + + align:start position:0% +a tripoli nested loop k equals zero one +up to v and um + + align:start position:0% +up to v and um + + + align:start position:0% +up to v and um +u and v and v and v + + align:start position:0% +u and v and v and v + + + align:start position:0% +u and v and v and v +so if you wanted to write this algorithm + + align:start position:0% +so if you wanted to write this algorithm + + + align:start position:0% +so if you wanted to write this algorithm +bottom up you just write this triple for + + align:start position:0% +bottom up you just write this triple for + + + align:start position:0% +bottom up you just write this triple for +loop + + align:start position:0% +loop + + + align:start position:0% +loop +and then plug in this recurrence + + align:start position:0% +and then plug in this recurrence + + + align:start position:0% +and then plug in this recurrence +relation here + + align:start position:0% +relation here + + + align:start position:0% +relation here +and think of d as a table as a + + align:start position:0% +and think of d as a table as a + + + align:start position:0% +and think of d as a table as a +set mapping instead of uh as a function + + align:start position:0% +set mapping instead of uh as a function + + + align:start position:0% +set mapping instead of uh as a function +call + + align:start position:0% +call + + + align:start position:0% +call +and boom in four lines you've got your + + align:start position:0% +and boom in four lines you've got your + + + align:start position:0% +and boom in four lines you've got your +algorithm except you also need a base + + align:start position:0% +algorithm except you also need a base + + + align:start position:0% +algorithm except you also need a base +case + + align:start position:0% +case + + + align:start position:0% +case +base case here is + + align:start position:0% + + + + align:start position:0% + +uv0 so i have to define what that means + + align:start position:0% +uv0 so i have to define what that means + + + align:start position:0% +uv0 so i have to define what that means +but + + align:start position:0% +but + + + align:start position:0% +but +when k equals zero the one through k set + + align:start position:0% +when k equals zero the one through k set + + + align:start position:0% +when k equals zero the one through k set +is empty + + align:start position:0% +is empty + + + align:start position:0% +is empty +so all i'm allowed to use are use my + + align:start position:0% +so all i'm allowed to use are use my + + + align:start position:0% +so all i'm allowed to use are use my +vertices u and v + + align:start position:0% +vertices u and v + + + align:start position:0% +vertices u and v +and so there are three cases for this 0 + + align:start position:0% +and so there are three cases for this 0 + + + align:start position:0% +and so there are three cases for this 0 +if u equals v + + align:start position:0% +if u equals v + + + align:start position:0% +if u equals v +it's w of uv if there's an edge + + align:start position:0% +it's w of uv if there's an edge + + + align:start position:0% +it's w of uv if there's an edge +from u to v and it's infinity otherwise + + align:start position:0% + + + + align:start position:0% + +okay but easy base case constant time + + align:start position:0% +okay but easy base case constant time + + + align:start position:0% +okay but easy base case constant time +for each + + align:start position:0% +for each + + + align:start position:0% +for each +and then the original problems we want + + align:start position:0% +and then the original problems we want + + + align:start position:0% +and then the original problems we want +to solve + + align:start position:0% + + + + align:start position:0% + +are delta u v sides of v + + align:start position:0% +are delta u v sides of v + + + align:start position:0% +are delta u v sides of v +because i number the vertices one + + align:start position:0% +because i number the vertices one + + + align:start position:0% +because i number the vertices one +through size of v and if k equals size + + align:start position:0% +through size of v and if k equals size + + + align:start position:0% +through size of v and if k equals size +of v that means i get to use all my + + align:start position:0% +of v that means i get to use all my + + + align:start position:0% +of v that means i get to use all my +vertices so that is + + align:start position:0% +vertices so that is + + + align:start position:0% +vertices so that is +regular shortest paths this is assuming + + align:start position:0% +regular shortest paths this is assuming + + + align:start position:0% +regular shortest paths this is assuming +no negative weight cycles + + align:start position:0% + + + + align:start position:0% + +okay we already know how to do negative + + align:start position:0% +okay we already know how to do negative + + + align:start position:0% +okay we already know how to do negative +weight cycle detection so i'm not going + + align:start position:0% +weight cycle detection so i'm not going + + + align:start position:0% +weight cycle detection so i'm not going +to + + align:start position:0% +to + + + align:start position:0% +to +talk about that again but then this will + + align:start position:0% +talk about that again but then this will + + + align:start position:0% +talk about that again but then this will +be + + align:start position:0% +be + + + align:start position:0% +be +my shortest pathways because uh yeah + + align:start position:0% +my shortest pathways because uh yeah + + + align:start position:0% +my shortest pathways because uh yeah +i implicitly assumed here that my path + + align:start position:0% +i implicitly assumed here that my path + + + align:start position:0% +i implicitly assumed here that my path +was simple because + + align:start position:0% +was simple because + + + align:start position:0% +was simple because +i imagine that i only use k once zero or + + align:start position:0% +i imagine that i only use k once zero or + + + align:start position:0% +i imagine that i only use k once zero or +one time + + align:start position:0% +one time + + + align:start position:0% +one time +and that's true if there are no negative + + align:start position:0% +and that's true if there are no negative + + + align:start position:0% +and that's true if there are no negative +weight cycles + + align:start position:0% +weight cycles + + + align:start position:0% +weight cycles +cool and we already did the time part of + + align:start position:0% +cool and we already did the time part of + + + align:start position:0% +cool and we already did the time part of +sort bot + + align:start position:0% +sort bot + + + align:start position:0% +sort bot +so v cubed algorithm very simple + + align:start position:0% +so v cubed algorithm very simple + + + align:start position:0% +so v cubed algorithm very simple +basically five lines of code and you've + + align:start position:0% +basically five lines of code and you've + + + align:start position:0% +basically five lines of code and you've +got all pair shortest paths + + align:start position:0% +got all pair shortest paths + + + align:start position:0% +got all pair shortest paths +and if your graph is dense this is a + + align:start position:0% +and if your graph is dense this is a + + + align:start position:0% +and if your graph is dense this is a +great running time if your grass + + align:start position:0% +great running time if your grass + + + align:start position:0% +great running time if your grass +graph is not dense you should use + + align:start position:0% +graph is not dense you should use + + + align:start position:0% +graph is not dense you should use +johnson like you will + + align:start position:0% +johnson like you will + + + align:start position:0% +johnson like you will +and or like you have implemented in your + + align:start position:0% +and or like you have implemented in your + + + align:start position:0% +and or like you have implemented in your +problem set + + align:start position:0% +problem set + + + align:start position:0% +problem set +yeah so how was this compared to just + + align:start position:0% +yeah so how was this compared to just + + + align:start position:0% +yeah so how was this compared to just +running dijkstra's outdoor a bunch of + + align:start position:0% +running dijkstra's outdoor a bunch of + + + align:start position:0% +running dijkstra's outdoor a bunch of +times + + align:start position:0% +times + + + align:start position:0% +times +ah what about using dijkstra so let's + + align:start position:0% +ah what about using dijkstra so let's + + + align:start position:0% +ah what about using dijkstra so let's +compute so uh running dijkstra v times + + align:start position:0% +compute so uh running dijkstra v times + + + align:start position:0% +compute so uh running dijkstra v times +is + + align:start position:0% +is + + + align:start position:0% +is +the running time of um + + align:start position:0% + + + + align:start position:0% + +johnson + + align:start position:0% + + + + align:start position:0% + +so running dijkstra a bunch of times is + + align:start position:0% +so running dijkstra a bunch of times is + + + align:start position:0% +so running dijkstra a bunch of times is +great if your graph has + + align:start position:0% +great if your graph has + + + align:start position:0% +great if your graph has +only non-negative edge weights then you + + align:start position:0% +only non-negative edge weights then you + + + align:start position:0% +only non-negative edge weights then you +should just run dijkstra + + align:start position:0% +should just run dijkstra + + + align:start position:0% +should just run dijkstra +you get this running time and for sparse + + align:start position:0% +you get this running time and for sparse + + + align:start position:0% +you get this running time and for sparse +graphs this is superior + + align:start position:0% +graphs this is superior + + + align:start position:0% +graphs this is superior +if you have negative edge weights you + + align:start position:0% +if you have negative edge weights you + + + align:start position:0% +if you have negative edge weights you +should run johnson which is bellman ford + + align:start position:0% +should run johnson which is bellman ford + + + align:start position:0% +should run johnson which is bellman ford +once and then dijkstra + + align:start position:0% +once and then dijkstra + + + align:start position:0% +once and then dijkstra +v times and we're comparing this to + + align:start position:0% +v times and we're comparing this to + + + align:start position:0% +v times and we're comparing this to +the cubed which we just got + + align:start position:0% +the cubed which we just got + + + align:start position:0% +the cubed which we just got +so this i mean how these compare depends + + align:start position:0% +so this i mean how these compare depends + + + align:start position:0% +so this i mean how these compare depends +on how v and e relate + + align:start position:0% +on how v and e relate + + + align:start position:0% +on how v and e relate +so on the one hand maybe uh v + + align:start position:0% +so on the one hand maybe uh v + + + align:start position:0% +so on the one hand maybe uh v +is theta e that's what i would call a + + align:start position:0% +is theta e that's what i would call a + + + align:start position:0% +is theta e that's what i would call a +very sparse graph it's quite common + + align:start position:0% +very sparse graph it's quite common + + + align:start position:0% +very sparse graph it's quite common +then the running time we get here + + align:start position:0% +then the running time we get here + + + align:start position:0% +then the running time we get here +is uh v squared + + align:start position:0% +is uh v squared + + + align:start position:0% +is uh v squared +log v okay roughly v squared + + align:start position:0% +log v okay roughly v squared + + + align:start position:0% +log v okay roughly v squared +on the other hand if we have a very + + align:start position:0% +on the other hand if we have a very + + + align:start position:0% +on the other hand if we have a very +dense graph v is theta + + align:start position:0% +dense graph v is theta + + + align:start position:0% +dense graph v is theta +e squared which for simple graphs the + + align:start position:0% +e squared which for simple graphs the + + + align:start position:0% +e squared which for simple graphs the +most we could hope for + + align:start position:0% +most we could hope for + + + align:start position:0% +most we could hope for +uh then this running time + + align:start position:0% +uh then this running time + + + align:start position:0% +uh then this running time +is v cubed + + align:start position:0% +is v cubed + + + align:start position:0% +is v cubed +okay so if you know the v is near e + + align:start position:0% +okay so if you know the v is near e + + + align:start position:0% +okay so if you know the v is near e +squared then this is giving you + + align:start position:0% +squared then this is giving you + + + align:start position:0% +squared then this is giving you +v cubed anyway from the ve term so why + + align:start position:0% +v cubed anyway from the ve term so why + + + align:start position:0% +v cubed anyway from the ve term so why +not just use + + align:start position:0% +not just use + + + align:start position:0% +not just use +this algorithm and often you know a + + align:start position:0% +this algorithm and often you know a + + + align:start position:0% +this algorithm and often you know a +priori whether your graph is very sparse + + align:start position:0% +priori whether your graph is very sparse + + + align:start position:0% +priori whether your graph is very sparse +or very dense or somewhere in between + + align:start position:0% +or very dense or somewhere in between + + + align:start position:0% +or very dense or somewhere in between +if it's somewhere in between you should + + align:start position:0% +if it's somewhere in between you should + + + align:start position:0% +if it's somewhere in between you should +still use johnson's algorithm because + + align:start position:0% +still use johnson's algorithm because + + + align:start position:0% +still use johnson's algorithm because +you're going to get the benefit from + + align:start position:0% +you're going to get the benefit from + + + align:start position:0% +you're going to get the benefit from +sparsity + + align:start position:0% +sparsity + + + align:start position:0% +sparsity +and only have to pay this ve instead of + + align:start position:0% +and only have to pay this ve instead of + + + align:start position:0% +and only have to pay this ve instead of +the v cubed + + align:start position:0% +the v cubed + + + align:start position:0% +the v cubed +but if you know ahead of time you know + + align:start position:0% +but if you know ahead of time you know + + + align:start position:0% +but if you know ahead of time you know +constant fraction of the edges are there + + align:start position:0% +constant fraction of the edges are there + + + align:start position:0% +constant fraction of the edges are there +then just use uh or you have a small + + align:start position:0% +then just use uh or you have a small + + + align:start position:0% +then just use uh or you have a small +enough graph that you don't care + + align:start position:0% +enough graph that you don't care + + + align:start position:0% +enough graph that you don't care +just run a floyd washall because it's + + align:start position:0% +just run a floyd washall because it's + + + align:start position:0% +just run a floyd washall because it's +simple and fast + + align:start position:0% +simple and fast + + + align:start position:0% +simple and fast +good question any other questions + + align:start position:0% +good question any other questions + + + align:start position:0% +good question any other questions +so this is an example of sub problem + + align:start position:0% +so this is an example of sub problem + + + align:start position:0% +so this is an example of sub problem +expansion a very non-intuitive one where + + align:start position:0% +expansion a very non-intuitive one where + + + align:start position:0% +expansion a very non-intuitive one where +we + + align:start position:0% +we + + + align:start position:0% +we +use some prefix of the vertices but + + align:start position:0% +use some prefix of the vertices but + + + align:start position:0% +use some prefix of the vertices but +notice it's prefixes again right i + + align:start position:0% +notice it's prefixes again right i + + + align:start position:0% +notice it's prefixes again right i +numbered the vertices from 1 up to v + + align:start position:0% +numbered the vertices from 1 up to v + + + align:start position:0% +numbered the vertices from 1 up to v +and i took a prefix of those vertices so + + align:start position:0% +and i took a prefix of those vertices so + + + align:start position:0% +and i took a prefix of those vertices so +i just solved the problem using prefix + + align:start position:0% +i just solved the problem using prefix + + + align:start position:0% +i just solved the problem using prefix +vertices 1 through k so it's actually a + + align:start position:0% +vertices 1 through k so it's actually a + + + align:start position:0% +vertices 1 through k so it's actually a +familiar idea + + align:start position:0% +familiar idea + + + align:start position:0% +familiar idea +if if all you'd seen are all our dynamic + + align:start position:0% +if if all you'd seen are all our dynamic + + + align:start position:0% +if if all you'd seen are all our dynamic +programming examples of prefixes + + align:start position:0% +programming examples of prefixes + + + align:start position:0% +programming examples of prefixes +suffixes + + align:start position:0% +suffixes + + + align:start position:0% +suffixes +substrings actually it's a pretty + + align:start position:0% +substrings actually it's a pretty + + + align:start position:0% +substrings actually it's a pretty +natural way to solve for his paths + + align:start position:0% +natural way to solve for his paths + + + align:start position:0% +natural way to solve for his paths +maybe even more natural than this + + align:start position:0% + + + + align:start position:0% + +anyway all right enough shortest paths + + align:start position:0% +anyway all right enough shortest paths + + + align:start position:0% +anyway all right enough shortest paths +let's solve two more problems that are + + align:start position:0% +let's solve two more problems that are + + + align:start position:0% +let's solve two more problems that are +more in our standard wheelhouse they + + align:start position:0% +more in our standard wheelhouse they + + + align:start position:0% +more in our standard wheelhouse they +will involve sequences of inputs + + align:start position:0% +will involve sequences of inputs + + + align:start position:0% +will involve sequences of inputs +not graphs first one is arithmetic + + align:start position:0% +not graphs first one is arithmetic + + + align:start position:0% +not graphs first one is arithmetic +parenthesization + + align:start position:0% +parenthesization + + + align:start position:0% +parenthesization +so first let me define this problem + + align:start position:0% + + + + align:start position:0% + +okay we are given a + + align:start position:0% +okay we are given a + + + align:start position:0% +okay we are given a +formula with say plus and times let me + + align:start position:0% +formula with say plus and times let me + + + align:start position:0% +formula with say plus and times let me +give you + + align:start position:0% +give you + + + align:start position:0% +give you +an actual example seven + + align:start position:0% +an actual example seven + + + align:start position:0% +an actual example seven +plus four times three + + align:start position:0% +plus four times three + + + align:start position:0% +plus four times three +plus five okay + + align:start position:0% +plus five okay + + + align:start position:0% +plus five okay +now when you read this because you've + + align:start position:0% +now when you read this because you've + + + align:start position:0% +now when you read this because you've +been well trained + + align:start position:0% +been well trained + + + align:start position:0% +been well trained +you think okay i'm going to multiply 4 + + align:start position:0% +you think okay i'm going to multiply 4 + + + align:start position:0% +you think okay i'm going to multiply 4 +and 3 first because that has a higher + + align:start position:0% +and 3 first because that has a higher + + + align:start position:0% +and 3 first because that has a higher +precedence and then i'll add + + align:start position:0% +precedence and then i'll add + + + align:start position:0% +precedence and then i'll add +the results up but uh what i'm going to + + align:start position:0% +the results up but uh what i'm going to + + + align:start position:0% +the results up but uh what i'm going to +let you do is parenthesize this + + align:start position:0% +let you do is parenthesize this + + + align:start position:0% +let you do is parenthesize this +expression however you want + + align:start position:0% +expression however you want + + + align:start position:0% +expression however you want +for example you can add parentheses here + + align:start position:0% +for example you can add parentheses here + + + align:start position:0% +for example you can add parentheses here +and here okay you must make a balanced + + align:start position:0% +and here okay you must make a balanced + + + align:start position:0% +and here okay you must make a balanced +parenthesis expression + + align:start position:0% +parenthesis expression + + + align:start position:0% +parenthesis expression +a valid way to to pair up or not just + + align:start position:0% +a valid way to to pair up or not just + + + align:start position:0% +a valid way to to pair up or not just +para but a valid way to evaluate this + + align:start position:0% +para but a valid way to evaluate this + + + align:start position:0% +para but a valid way to evaluate this +expression any ordering you want + + align:start position:0% +expression any ordering you want + + + align:start position:0% +expression any ordering you want +uh i could be inconsistent i could for + + align:start position:0% +uh i could be inconsistent i could for + + + align:start position:0% +uh i could be inconsistent i could for +example do this sum + + align:start position:0% +example do this sum + + + align:start position:0% +example do this sum +and then do this product and then do + + align:start position:0% +and then do this product and then do + + + align:start position:0% +and then do this product and then do +this sum + + align:start position:0% +this sum + + + align:start position:0% +this sum +okay but some kind of expression tree + + align:start position:0% +okay but some kind of expression tree + + + align:start position:0% +okay but some kind of expression tree +uh over this and each one evaluates to + + align:start position:0% +uh over this and each one evaluates to + + + align:start position:0% +uh over this and each one evaluates to +something so this is + + align:start position:0% +something so this is + + + align:start position:0% +something so this is +11 and this is eight and so this + + align:start position:0% +11 and this is eight and so this + + + align:start position:0% +11 and this is eight and so this +is 88 and my goal is to maximize + + align:start position:0% +is 88 and my goal is to maximize + + + align:start position:0% +is 88 and my goal is to maximize +that computation and i claim that this + + align:start position:0% +that computation and i claim that this + + + align:start position:0% +that computation and i claim that this +is the way to maximize that particular + + align:start position:0% +is the way to maximize that particular + + + align:start position:0% +is the way to maximize that particular +example + + align:start position:0% +example + + + align:start position:0% +example +okay so let me write it in general and + + align:start position:0% +okay so let me write it in general and + + + align:start position:0% +okay so let me write it in general and +get my notation to match + + align:start position:0% +get my notation to match + + + align:start position:0% +get my notation to match +notes so given a formula + + align:start position:0% + + + + align:start position:0% + +a0 star 1 + + align:start position:0% +a0 star 1 + + + align:start position:0% +a0 star 1 +a1 star 2 + + align:start position:0% +a1 star 2 + + + align:start position:0% +a1 star 2 +a2 and so on up to star + + align:start position:0% +a2 and so on up to star + + + align:start position:0% +a2 and so on up to star +n minus 1 a n minus 1 + + align:start position:0% + + + + align:start position:0% + +where each + + align:start position:0% +where each + + + align:start position:0% +where each +a i is an integer as we like in this + + align:start position:0% +a i is an integer as we like in this + + + align:start position:0% +a i is an integer as we like in this +class + + align:start position:0% +class + + + align:start position:0% +class +and each star i is either + + align:start position:0% +and each star i is either + + + align:start position:0% +and each star i is either +plus or times okay so i'm using star as + + align:start position:0% +plus or times okay so i'm using star as + + + align:start position:0% +plus or times okay so i'm using star as +a generic operator it's + + align:start position:0% +a generic operator it's + + + align:start position:0% +a generic operator it's +it has chose star because it is the + + align:start position:0% +it has chose star because it is the + + + align:start position:0% +it has chose star because it is the +superposition of star on time + + align:start position:0% +superposition of star on time + + + align:start position:0% +superposition of star on time +on top of a time symbol so it's + + align:start position:0% +on top of a time symbol so it's + + + align:start position:0% +on top of a time symbol so it's +clear so you're given some formula any + + align:start position:0% +clear so you're given some formula any + + + align:start position:0% +clear so you're given some formula any +mixture of plus + + align:start position:0% +mixture of plus + + + align:start position:0% +mixture of plus +and times that you like involving n + + align:start position:0% +and times that you like involving n + + + align:start position:0% +and times that you like involving n +integers + + align:start position:0% +integers + + + align:start position:0% +integers +and your goal is to place parentheses + + align:start position:0% +and your goal is to place parentheses + + + align:start position:0% +and your goal is to place parentheses +to maximize the result + + align:start position:0% + + + + align:start position:0% + +okay so you can try all the combinations + + align:start position:0% +okay so you can try all the combinations + + + align:start position:0% +okay so you can try all the combinations +here if i + + align:start position:0% +here if i + + + align:start position:0% +here if i +for example take the product of 4 times + + align:start position:0% +for example take the product of 4 times + + + align:start position:0% +for example take the product of 4 times +3 i get 12. + + align:start position:0% +3 i get 12. + + + align:start position:0% +3 i get 12. +for if i do that first i get 12. then if + + align:start position:0% +for if i do that first i get 12. then if + + + align:start position:0% +for if i do that first i get 12. then if +i add 5 and 7 i get + + align:start position:0% +i add 5 and 7 i get + + + align:start position:0% +i add 5 and 7 i get +24 which is less than 88. + + align:start position:0% +24 which is less than 88. + + + align:start position:0% +24 which is less than 88. +and i checked them all and this one is + + align:start position:0% +and i checked them all and this one is + + + align:start position:0% +and i checked them all and this one is +the maximum + + align:start position:0% +the maximum + + + align:start position:0% +the maximum +for that example okay so + + align:start position:0% +for that example okay so + + + align:start position:0% +for that example okay so +interesting problem um sort of it's a + + align:start position:0% +interesting problem um sort of it's a + + + align:start position:0% +interesting problem um sort of it's a +bit of a toy problem but it's motivated + + align:start position:0% +bit of a toy problem but it's motivated + + + align:start position:0% +bit of a toy problem but it's motivated +by lots of + + align:start position:0% +by lots of + + + align:start position:0% +by lots of +actual problems which i won't go into + + align:start position:0% +actual problems which i won't go into + + + align:start position:0% +actual problems which i won't go into +here + + align:start position:0% +here + + + align:start position:0% +here +so to apply this framework + + align:start position:0% +so to apply this framework + + + align:start position:0% +so to apply this framework +you know we need to identify some + + align:start position:0% +you know we need to identify some + + + align:start position:0% +you know we need to identify some +sub-problems this is a + + align:start position:0% +sub-problems this is a + + + align:start position:0% +sub-problems this is a +sequence problem we're given a sequence + + align:start position:0% +sequence problem we're given a sequence + + + align:start position:0% +sequence problem we're given a sequence +of symbols + + align:start position:0% +of symbols + + + align:start position:0% +of symbols +and so natural things to try our + + align:start position:0% +and so natural things to try our + + + align:start position:0% +and so natural things to try our +prefixes suffixes and substrings + + align:start position:0% +prefixes suffixes and substrings + + + align:start position:0% +prefixes suffixes and substrings +i'm going to jump ahead and think about + + align:start position:0% +i'm going to jump ahead and think about + + + align:start position:0% +i'm going to jump ahead and think about +the relation first + + align:start position:0% +the relation first + + + align:start position:0% +the relation first +i want to identify some question about + + align:start position:0% +i want to identify some question about + + + align:start position:0% +i want to identify some question about +the sub-problem + + align:start position:0% +the sub-problem + + + align:start position:0% +the sub-problem +or its solution that would let me reduce + + align:start position:0% +or its solution that would let me reduce + + + align:start position:0% +or its solution that would let me reduce +to smaller sub problems + + align:start position:0% +to smaller sub problems + + + align:start position:0% +to smaller sub problems +this is a little trickier this is very + + align:start position:0% +this is a little trickier this is very + + + align:start position:0% +this is a little trickier this is very +different we're not always doing + + align:start position:0% +different we're not always doing + + + align:start position:0% +different we're not always doing +something on the left or on the right + + align:start position:0% +something on the left or on the right + + + align:start position:0% +something on the left or on the right +or we can't assume there's something + + align:start position:0% +or we can't assume there's something + + + align:start position:0% +or we can't assume there's something +happening on the left because maybe we + + align:start position:0% +happening on the left because maybe we + + + align:start position:0% +happening on the left because maybe we +take a product in the middle first + + align:start position:0% +take a product in the middle first + + + align:start position:0% +take a product in the middle first +if i take a product in the middle first + + align:start position:0% +if i take a product in the middle first + + + align:start position:0% +if i take a product in the middle first +then i have some result here + + align:start position:0% +then i have some result here + + + align:start position:0% +then i have some result here +but i still have three things i have the + + align:start position:0% +but i still have three things i have the + + + align:start position:0% +but i still have three things i have the +thing to the left i have the thing in + + align:start position:0% +thing to the left i have the thing in + + + align:start position:0% +thing to the left i have the thing in +the middle + + align:start position:0% +the middle + + + align:start position:0% +the middle +and i have the thing on the right it + + align:start position:0% +and i have the thing on the right it + + + align:start position:0% +and i have the thing on the right it +turns out to be very messy to think + + align:start position:0% +turns out to be very messy to think + + + align:start position:0% +turns out to be very messy to think +about what the first operation is + + align:start position:0% +about what the first operation is + + + align:start position:0% +about what the first operation is +because we can think of this as a tree + + align:start position:0% +because we can think of this as a tree + + + align:start position:0% +because we can think of this as a tree +um + + align:start position:0% +um + + + align:start position:0% +um +where we take a product here we take a + + align:start position:0% +where we take a product here we take a + + + align:start position:0% +where we take a product here we take a +sum + + align:start position:0% +sum + + + align:start position:0% +sum +of 7 and 4 + + align:start position:0% + + + + align:start position:0% + +and 3 and 5 over here and then take the + + align:start position:0% +and 3 and 5 over here and then take the + + + align:start position:0% +and 3 and 5 over here and then take the +product at the root + + align:start position:0% +product at the root + + + align:start position:0% +product at the root +but i don't know what the tree is right + + align:start position:0% +but i don't know what the tree is right + + + align:start position:0% +but i don't know what the tree is right +i only know these numbers and these + + align:start position:0% +i only know these numbers and these + + + align:start position:0% +i only know these numbers and these +operators but i don't know how to + + align:start position:0% +operators but i don't know how to + + + align:start position:0% +operators but i don't know how to +organize this tree + + align:start position:0% +organize this tree + + + align:start position:0% +organize this tree +and so the idea is if you think of this + + align:start position:0% +and so the idea is if you think of this + + + align:start position:0% +and so the idea is if you think of this +tree what is the one thing that's the + + align:start position:0% +tree what is the one thing that's the + + + align:start position:0% +tree what is the one thing that's the +easiest to identify + + align:start position:0% +easiest to identify + + + align:start position:0% +easiest to identify +it's the root the root corresponds to + + align:start position:0% +it's the root the root corresponds to + + + align:start position:0% +it's the root the root corresponds to +the + + align:start position:0% +the + + + align:start position:0% +the +last operation i do in this computation + + align:start position:0% +last operation i do in this computation + + + align:start position:0% +last operation i do in this computation +the last thing i did was take a product + + align:start position:0% +the last thing i did was take a product + + + align:start position:0% +the last thing i did was take a product +and that's a lot easier because uh if i + + align:start position:0% +and that's a lot easier because uh if i + + + align:start position:0% +and that's a lot easier because uh if i +guess + + align:start position:0% +guess + + + align:start position:0% +guess +who's at the root which operator is at + + align:start position:0% +who's at the root which operator is at + + + align:start position:0% +who's at the root which operator is at +the root that naturally decomposes into + + align:start position:0% +the root that naturally decomposes into + + + align:start position:0% +the root that naturally decomposes into +the left subtree + + align:start position:0% +the left subtree + + + align:start position:0% +the left subtree +and the right subtree and those will + + align:start position:0% +and the right subtree and those will + + + align:start position:0% +and the right subtree and those will +always be + + align:start position:0% +always be + + + align:start position:0% +always be +substrings we kind of know this this + + align:start position:0% +substrings we kind of know this this + + + align:start position:0% +substrings we kind of know this this +node corresponds to everything left of + + align:start position:0% +node corresponds to everything left of + + + align:start position:0% +node corresponds to everything left of +this operator + + align:start position:0% +this operator + + + align:start position:0% +this operator +and this sub substring or this + + align:start position:0% +and this sub substring or this + + + align:start position:0% +and this sub substring or this +subtree corresponds to everything to the + + align:start position:0% +subtree corresponds to everything to the + + + align:start position:0% +subtree corresponds to everything to the +right of the operator + + align:start position:0% +right of the operator + + + align:start position:0% +right of the operator +so this is our idea + + align:start position:0% + + + + align:start position:0% + +is we're going to guess + + align:start position:0% + + + + align:start position:0% + +which operation + + align:start position:0% +which operation + + + align:start position:0% +which operation +star i is evaluated + + align:start position:0% +star i is evaluated + + + align:start position:0% +star i is evaluated +last + + align:start position:0% + + + + align:start position:0% + +or in other words at the root + + align:start position:0% + + + + align:start position:0% + +so this is a question it has uh + + align:start position:0% +so this is a question it has uh + + + align:start position:0% +so this is a question it has uh +n possible answers i guess actually n + + align:start position:0% +n possible answers i guess actually n + + + align:start position:0% +n possible answers i guess actually n +minus one + + align:start position:0% +minus one + + + align:start position:0% +minus one +from operator one to operator n minus + + align:start position:0% +from operator one to operator n minus + + + align:start position:0% +from operator one to operator n minus +one + + align:start position:0% +one + + + align:start position:0% +one +and so uh we'll just brute force all + + align:start position:0% +and so uh we'll just brute force all + + + align:start position:0% +and so uh we'll just brute force all +those choices + + align:start position:0% +those choices + + + align:start position:0% +those choices +okay so i wanted to start here because + + align:start position:0% +okay so i wanted to start here because + + + align:start position:0% +okay so i wanted to start here because +uh to realize that + + align:start position:0% +uh to realize that + + + align:start position:0% +uh to realize that +if i choose some star i in the middle + + align:start position:0% +if i choose some star i in the middle + + + align:start position:0% +if i choose some star i in the middle +which might be the right thing like in + + align:start position:0% +which might be the right thing like in + + + align:start position:0% +which might be the right thing like in +this example + + align:start position:0% +this example + + + align:start position:0% +this example +star i is the the middle one middle + + align:start position:0% +star i is the the middle one middle + + + align:start position:0% +star i is the the middle one middle +operator + + align:start position:0% +operator + + + align:start position:0% +operator +i naturally decompose into everything to + + align:start position:0% +i naturally decompose into everything to + + + align:start position:0% +i naturally decompose into everything to +the left of that operator and everything + + align:start position:0% +the left of that operator and everything + + + align:start position:0% +the left of that operator and everything +to the right of that operator + + align:start position:0% +to the right of that operator + + + align:start position:0% +to the right of that operator +this is a prefix this is a suffix + + align:start position:0% +this is a prefix this is a suffix + + + align:start position:0% +this is a prefix this is a suffix +so you might think oh my sub problems + + align:start position:0% +so you might think oh my sub problems + + + align:start position:0% +so you might think oh my sub problems +are all prefixes and all suffixes but + + align:start position:0% +are all prefixes and all suffixes but + + + align:start position:0% +are all prefixes and all suffixes but +that would be wrong + + align:start position:0% +that would be wrong + + + align:start position:0% +that would be wrong +because if you have a bunch of operators + + align:start position:0% +because if you have a bunch of operators + + + align:start position:0% +because if you have a bunch of operators +and say you choose this one to be last + + align:start position:0% + + + + align:start position:0% + +so i have a prefix here and a suffix + + align:start position:0% +so i have a prefix here and a suffix + + + align:start position:0% +so i have a prefix here and a suffix +here and then there'll be some + + align:start position:0% +here and then there'll be some + + + align:start position:0% +here and then there'll be some +within this suffix i'll choose some + + align:start position:0% +within this suffix i'll choose some + + + align:start position:0% +within this suffix i'll choose some +operator to be the root of that one + + align:start position:0% +operator to be the root of that one + + + align:start position:0% +operator to be the root of that one +and i have a prefix and a suffix of this + + align:start position:0% +and i have a prefix and a suffix of this + + + align:start position:0% +and i have a prefix and a suffix of this +suffix but + + align:start position:0% +suffix but + + + align:start position:0% +suffix but +in particular i will have to evaluate + + align:start position:0% +in particular i will have to evaluate + + + align:start position:0% +in particular i will have to evaluate +this sub-problem which is a prefix of a + + align:start position:0% +this sub-problem which is a prefix of a + + + align:start position:0% +this sub-problem which is a prefix of a +suffix in other words + + align:start position:0% +suffix in other words + + + align:start position:0% +suffix in other words +a substring so never use a mixture of + + align:start position:0% +a substring so never use a mixture of + + + align:start position:0% +a substring so never use a mixture of +prefixes and suffixes + + align:start position:0% +prefixes and suffixes + + + align:start position:0% +prefixes and suffixes +if you need both you probably need all + + align:start position:0% +if you need both you probably need all + + + align:start position:0% +if you need both you probably need all +sub strings + + align:start position:0% +sub strings + + + align:start position:0% +sub strings +so our sub problems + + align:start position:0% +so our sub problems + + + align:start position:0% +so our sub problems +are going to be substrings + + align:start position:0% + + + + align:start position:0% + +okay i'm not going to write the sub + + align:start position:0% +okay i'm not going to write the sub + + + align:start position:0% +okay i'm not going to write the sub +problems quite yet because there's + + align:start position:0% +problems quite yet because there's + + + align:start position:0% +problems quite yet because there's +another idea + + align:start position:0% +another idea + + + align:start position:0% +another idea +we need so what do i need to do with a + + align:start position:0% +we need so what do i need to do with a + + + align:start position:0% +we need so what do i need to do with a +substring + + align:start position:0% +substring + + + align:start position:0% +substring +so i'm going to guess the middle + + align:start position:0% +so i'm going to guess the middle + + + align:start position:0% +so i'm going to guess the middle +operator and then evaluate the left + + align:start position:0% +operator and then evaluate the left + + + align:start position:0% +operator and then evaluate the left +substring evaluate the right substring + + align:start position:0% +substring evaluate the right substring + + + align:start position:0% +substring evaluate the right substring +what am i trying to do with those + + align:start position:0% +what am i trying to do with those + + + align:start position:0% +what am i trying to do with those +substrings i guess i'm trying to solve + + align:start position:0% +substrings i guess i'm trying to solve + + + align:start position:0% +substrings i guess i'm trying to solve +this problem which is + + align:start position:0% +this problem which is + + + align:start position:0% +this problem which is +place parentheses in order to maximize + + align:start position:0% +place parentheses in order to maximize + + + align:start position:0% +place parentheses in order to maximize +the result and then return what the + + align:start position:0% +the result and then return what the + + + align:start position:0% +the result and then return what the +result + + align:start position:0% +result + + + align:start position:0% +result +is okay and i can use parent pointers to + + align:start position:0% +is okay and i can use parent pointers to + + + align:start position:0% +is okay and i can use parent pointers to +reconstruct what the + + align:start position:0% +reconstruct what the + + + align:start position:0% +reconstruct what the +parentheses actually are + + align:start position:0% + + + + align:start position:0% + +so is it enough once i guess what the + + align:start position:0% +so is it enough once i guess what the + + + align:start position:0% +so is it enough once i guess what the +last operator is + + align:start position:0% +last operator is + + + align:start position:0% +last operator is +is it enough to maximize the part to the + + align:start position:0% +is it enough to maximize the part to the + + + align:start position:0% +is it enough to maximize the part to the +right and maximize the part to the left + + align:start position:0% +right and maximize the part to the left + + + align:start position:0% +right and maximize the part to the left +will that always maximize my sum or + + align:start position:0% +will that always maximize my sum or + + + align:start position:0% +will that always maximize my sum or +product according to what this operator + + align:start position:0% +product according to what this operator + + + align:start position:0% +product according to what this operator +is + + align:start position:0% +is + + + align:start position:0% +is +and you think about it for a while yeah + + align:start position:0% +and you think about it for a while yeah + + + align:start position:0% +and you think about it for a while yeah +if i want to maximize a sum + + align:start position:0% +if i want to maximize a sum + + + align:start position:0% +if i want to maximize a sum +i should maximize the two parts and if i + + align:start position:0% +i should maximize the two parts and if i + + + align:start position:0% +i should maximize the two parts and if i +want to maximize a product i should + + align:start position:0% +want to maximize a product i should + + + align:start position:0% +want to maximize a product i should +maximize the two parts that seems right + + align:start position:0% +maximize the two parts that seems right + + + align:start position:0% +maximize the two parts that seems right +except i didn't say that my integers are + + align:start position:0% +except i didn't say that my integers are + + + align:start position:0% +except i didn't say that my integers are +positive + + align:start position:0% +positive + + + align:start position:0% +positive +so it's true if the integers are + + align:start position:0% +so it's true if the integers are + + + align:start position:0% +so it's true if the integers are +positive but to make this problem more + + align:start position:0% +positive but to make this problem more + + + align:start position:0% +positive but to make this problem more +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +we're going to allow the integers to be + + align:start position:0% +we're going to allow the integers to be + + + align:start position:0% +we're going to allow the integers to be +negative + + align:start position:0% +negative + + + align:start position:0% +negative +so for example uh 7 + + align:start position:0% +so for example uh 7 + + + align:start position:0% +so for example uh 7 +plus minus 4 times 3 + + align:start position:0% +plus minus 4 times 3 + + + align:start position:0% +plus minus 4 times 3 +plus minus 5. so i just added a couple + + align:start position:0% +plus minus 5. so i just added a couple + + + align:start position:0% +plus minus 5. so i just added a couple +of minuses + + align:start position:0% +of minuses + + + align:start position:0% +of minuses +to a couple of the numbers here + + align:start position:0% +to a couple of the numbers here + + + align:start position:0% +to a couple of the numbers here +then it's no longer best to pair them + + align:start position:0% +then it's no longer best to pair them + + + align:start position:0% +then it's no longer best to pair them +this way so if i pair them this way + + align:start position:0% +this way so if i pair them this way + + + align:start position:0% +this way so if i pair them this way +like this or if i add parentheses this + + align:start position:0% +like this or if i add parentheses this + + + align:start position:0% +like this or if i add parentheses this +way i get + + align:start position:0% +way i get + + + align:start position:0% +way i get +3 here and i get minus 2 here + + align:start position:0% +3 here and i get minus 2 here + + + align:start position:0% +3 here and i get minus 2 here +so i get product of that as negative 6 + + align:start position:0% +so i get product of that as negative 6 + + + align:start position:0% +so i get product of that as negative 6 +which is probably not the maximum in + + align:start position:0% +which is probably not the maximum in + + + align:start position:0% +which is probably not the maximum in +fact i can do better i believe by + + align:start position:0% + + + + align:start position:0% + +doing the left operator last + + align:start position:0% + + + + align:start position:0% + +so this is a i claim the best + + align:start position:0% +so this is a i claim the best + + + align:start position:0% +so this is a i claim the best +parenthesization if i remembered it + + align:start position:0% +parenthesization if i remembered it + + + align:start position:0% +parenthesization if i remembered it +correctly + + align:start position:0% +correctly + + + align:start position:0% +correctly +so this is minus two times minus four + + align:start position:0% +so this is minus two times minus four + + + align:start position:0% +so this is minus two times minus four +is eight + + align:start position:0% + + + + align:start position:0% + +uh plus seven is fifteen + + align:start position:0% +uh plus seven is fifteen + + + align:start position:0% +uh plus seven is fifteen +okay so i got a positive number + + align:start position:0% +okay so i got a positive number + + + align:start position:0% +okay so i got a positive number +definitely better than the negative + + align:start position:0% +definitely better than the negative + + + align:start position:0% +definitely better than the negative +number i got + + align:start position:0% +number i got + + + align:start position:0% +number i got +and i claim this is the best and the key + + align:start position:0% +and i claim this is the best and the key + + + align:start position:0% +and i claim this is the best and the key +property here is + + align:start position:0% +property here is + + + align:start position:0% +property here is +when we take a product of two negative + + align:start position:0% +when we take a product of two negative + + + align:start position:0% +when we take a product of two negative +numbers we get a positive number so + + align:start position:0% +numbers we get a positive number so + + + align:start position:0% +numbers we get a positive number so +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +you actually want to make things small + + align:start position:0% +you actually want to make things small + + + align:start position:0% +you actually want to make things small +because small + + align:start position:0% +because small + + + align:start position:0% +because small +might mean very negative you take two + + align:start position:0% +might mean very negative you take two + + + align:start position:0% +might mean very negative you take two +very big + + align:start position:0% +very big + + + align:start position:0% +very big +negative numbers very small negative + + align:start position:0% +negative numbers very small negative + + + align:start position:0% +negative numbers very small negative +numbers in other words + + align:start position:0% +numbers in other words + + + align:start position:0% +numbers in other words +you take their product you get a very + + align:start position:0% +you take their product you get a very + + + align:start position:0% +you take their product you get a very +big product positively + + align:start position:0% +big product positively + + + align:start position:0% +big product positively +because the signs cancel okay so this + + align:start position:0% +because the signs cancel okay so this + + + align:start position:0% +because the signs cancel okay so this +seems tricky + + align:start position:0% +seems tricky + + + align:start position:0% +seems tricky +we want to work on substrings but we + + align:start position:0% +we want to work on substrings but we + + + align:start position:0% +we want to work on substrings but we +don't know whether we're trying to + + align:start position:0% +don't know whether we're trying to + + + align:start position:0% +don't know whether we're trying to +maximize or you might think well maybe + + align:start position:0% +maximize or you might think well maybe + + + align:start position:0% +maximize or you might think well maybe +i'm trying to maximize the absolute + + align:start position:0% +i'm trying to maximize the absolute + + + align:start position:0% +i'm trying to maximize the absolute +value + + align:start position:0% +value + + + align:start position:0% +value +but that's not good maybe overall on + + align:start position:0% +but that's not good maybe overall on + + + align:start position:0% +but that's not good maybe overall on +this entire expression i get + + align:start position:0% +this entire expression i get + + + align:start position:0% +this entire expression i get +negative a million and that's not what i + + align:start position:0% +negative a million and that's not what i + + + align:start position:0% +negative a million and that's not what i +wanted i wanted to maximize the sum + + align:start position:0% +wanted i wanted to maximize the sum + + + align:start position:0% +wanted i wanted to maximize the sum +so i need to i still need to solve the + + align:start position:0% +so i need to i still need to solve the + + + align:start position:0% +so i need to i still need to solve the +max + + align:start position:0% +max + + + align:start position:0% +max +uh evaluation that i can get the max + + align:start position:0% +uh evaluation that i can get the max + + + align:start position:0% +uh evaluation that i can get the max +parenthesization + + align:start position:0% +parenthesization + + + align:start position:0% +parenthesization +but i also need to solve the min + + align:start position:0% +but i also need to solve the min + + + align:start position:0% +but i also need to solve the min +parenthesization + + align:start position:0% +parenthesization + + + align:start position:0% +parenthesization +if i can solve max and min i'll know the + + align:start position:0% +if i can solve max and min i'll know the + + + align:start position:0% +if i can solve max and min i'll know the +entire kind of range that i could get + + align:start position:0% +entire kind of range that i could get + + + align:start position:0% +entire kind of range that i could get +and i really only i'll care about men + + align:start position:0% +and i really only i'll care about men + + + align:start position:0% +and i really only i'll care about men +especially when it lets me go negative + + align:start position:0% +especially when it lets me go negative + + + align:start position:0% +especially when it lets me go negative +but let's just solve it in all cases the + + align:start position:0% +but let's just solve it in all cases the + + + align:start position:0% +but let's just solve it in all cases the +min and the max + + align:start position:0% +min and the max + + + align:start position:0% +min and the max +and then just brute force the rest + + align:start position:0% +and then just brute force the rest + + + align:start position:0% +and then just brute force the rest +that's what i'm going to write down + + align:start position:0% +that's what i'm going to write down + + + align:start position:0% +that's what i'm going to write down +so that was some motivation on why we + + align:start position:0% +so that was some motivation on why we + + + align:start position:0% +so that was some motivation on why we +are going to define subproblems this way + + align:start position:0% +are going to define subproblems this way + + + align:start position:0% +are going to define subproblems this way +so i'm going to define x of i comma j + + align:start position:0% +so i'm going to define x of i comma j + + + align:start position:0% +so i'm going to define x of i comma j +comma + + align:start position:0% +comma + + + align:start position:0% +comma +opt to be + + align:start position:0% +opt to be + + + align:start position:0% +opt to be +so opt here is going to be either + + align:start position:0% +so opt here is going to be either + + + align:start position:0% +so opt here is going to be either +min or max and this is my + + align:start position:0% +min or max and this is my + + + align:start position:0% +min or max and this is my +sub problem expansion i really just care + + align:start position:0% +sub problem expansion i really just care + + + align:start position:0% +sub problem expansion i really just care +about max + + align:start position:0% +about max + + + align:start position:0% +about max +at the very end but i'm going to care + + align:start position:0% +at the very end but i'm going to care + + + align:start position:0% +at the very end but i'm going to care +about min along the way + + align:start position:0% +about min along the way + + + align:start position:0% +about min along the way +and i j is going to specify my substring + + align:start position:0% +and i j is going to specify my substring + + + align:start position:0% +and i j is going to specify my substring +so this is going to be the opt value + + align:start position:0% +so this is going to be the opt value + + + align:start position:0% +so this is going to be the opt value +opt stands for optimum here or + + align:start position:0% +opt stands for optimum here or + + + align:start position:0% +opt stands for optimum here or +optimization + + align:start position:0% +optimization + + + align:start position:0% +optimization +uh the upped value i can get for the + + align:start position:0% +uh the upped value i can get for the + + + align:start position:0% +uh the upped value i can get for the +substring + + align:start position:0% +substring + + + align:start position:0% +substring +a i start plus one + + align:start position:0% +a i start plus one + + + align:start position:0% +a i start plus one +a i plus one and so on + + align:start position:0% +a i plus one and so on + + + align:start position:0% +a i plus one and so on +to uh star j minus one + + align:start position:0% +to uh star j minus one + + + align:start position:0% +to uh star j minus one +a j minus one okay + + align:start position:0% +a j minus one okay + + + align:start position:0% +a j minus one okay +being careful to get my indices correct + + align:start position:0% +being careful to get my indices correct + + + align:start position:0% +being careful to get my indices correct +here and + + align:start position:0% +here and + + + align:start position:0% +here and +i want uh 0 less than or equal to i + + align:start position:0% +i want uh 0 less than or equal to i + + + align:start position:0% +i want uh 0 less than or equal to i +less than j less than or equal to n + + align:start position:0% +less than j less than or equal to n + + + align:start position:0% +less than j less than or equal to n +i claim and opt + + align:start position:0% +i claim and opt + + + align:start position:0% +i claim and opt +like this okay so i'm going to get the + + align:start position:0% +like this okay so i'm going to get the + + + align:start position:0% +like this okay so i'm going to get the +mean value and the max value separately + + align:start position:0% +mean value and the max value separately + + + align:start position:0% +mean value and the max value separately +those are two different sub problems + + align:start position:0% +those are two different sub problems + + + align:start position:0% +those are two different sub problems +it's my expansion this is the constraint + + align:start position:0% +it's my expansion this is the constraint + + + align:start position:0% +it's my expansion this is the constraint +i'm adding + + align:start position:0% +i'm adding + + + align:start position:0% +i'm adding +and i'm only focusing on this substring + + align:start position:0% +and i'm only focusing on this substring + + + align:start position:0% +and i'm only focusing on this substring +from i inclusive to j exclusive + + align:start position:0% +from i inclusive to j exclusive + + + align:start position:0% +from i inclusive to j exclusive +okay so i claim those are good sub + + align:start position:0% +okay so i claim those are good sub + + + align:start position:0% +okay so i claim those are good sub +problems + + align:start position:0% +problems + + + align:start position:0% +problems +let's write down a recurrence relation + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so i want to write x of i j + + align:start position:0% +so i want to write x of i j + + + align:start position:0% +so i want to write x of i j +off on the left + + align:start position:0% + + + + align:start position:0% + +and i want to optimize so this will be + + align:start position:0% +and i want to optimize so this will be + + + align:start position:0% +and i want to optimize so this will be +min or max + + align:start position:0% +min or max + + + align:start position:0% +min or max +on a set of choices what is my set of + + align:start position:0% +on a set of choices what is my set of + + + align:start position:0% +on a set of choices what is my set of +choices + + align:start position:0% +choices + + + align:start position:0% +choices +well uh like i said i want to guess what + + align:start position:0% +well uh like i said i want to guess what + + + align:start position:0% +well uh like i said i want to guess what +is the last + + align:start position:0% +is the last + + + align:start position:0% +is the last +operation evaluated i wrote star i here + + align:start position:0% +operation evaluated i wrote star i here + + + align:start position:0% +operation evaluated i wrote star i here +but star i + + align:start position:0% +but star i + + + align:start position:0% +but star i +is already defined so i'm going to use + + align:start position:0% +is already defined so i'm going to use + + + align:start position:0% +is already defined so i'm going to use +star k so i'm going to + + align:start position:0% +star k so i'm going to + + + align:start position:0% +star k so i'm going to +guess what which of my operations + + align:start position:0% +guess what which of my operations + + + align:start position:0% +guess what which of my operations +between + + align:start position:0% +between + + + align:start position:0% +between +i plus 1 and j minus 1 is the last one + + align:start position:0% +i plus 1 and j minus 1 is the last one + + + align:start position:0% +i plus 1 and j minus 1 is the last one +and i evaluate + + align:start position:0% +and i evaluate + + + align:start position:0% +and i evaluate +and that decomposes into everything left + + align:start position:0% +and that decomposes into everything left + + + align:start position:0% +and that decomposes into everything left +of k + + align:start position:0% +of k + + + align:start position:0% +of k +so that would be x of i + + align:start position:0% +so that would be x of i + + + align:start position:0% +so that would be x of i +uh comma k comma something + + align:start position:0% +uh comma k comma something + + + align:start position:0% +uh comma k comma something +and then we will do operator star k + + align:start position:0% +and then we will do operator star k + + + align:start position:0% +and then we will do operator star k +on the part after k which is from k + + align:start position:0% +on the part after k which is from k + + + align:start position:0% +on the part after k which is from k +to j something + + align:start position:0% +to j something + + + align:start position:0% +to j something +okay and i'm choosing between + + align:start position:0% +okay and i'm choosing between + + + align:start position:0% +okay and i'm choosing between +i think it's i less than k less than j + + align:start position:0% +i think it's i less than k less than j + + + align:start position:0% +i think it's i less than k less than j +so k is some operator in between because + + align:start position:0% +so k is some operator in between because + + + align:start position:0% +so k is some operator in between because +i started i plus 1 + + align:start position:0% +i started i plus 1 + + + align:start position:0% +i started i plus 1 +and i end at j minus 1 so those are the + + align:start position:0% +and i end at j minus 1 so those are the + + + align:start position:0% +and i end at j minus 1 so those are the +possible choices for + + align:start position:0% +possible choices for + + + align:start position:0% +possible choices for +k i tried them all that's my local brute + + align:start position:0% +k i tried them all that's my local brute + + + align:start position:0% +k i tried them all that's my local brute +force + + align:start position:0% +force + + + align:start position:0% +force +and then i take what i can get on the + + align:start position:0% +and then i take what i can get on the + + + align:start position:0% +and then i take what i can get on the +left what i can get on the right + + align:start position:0% +left what i can get on the right + + + align:start position:0% +left what i can get on the right +and multiply or add them according to + + align:start position:0% +and multiply or add them according to + + + align:start position:0% +and multiply or add them according to +whether that operator is + + align:start position:0% +whether that operator is + + + align:start position:0% +whether that operator is +plus or times now should i + + align:start position:0% +plus or times now should i + + + align:start position:0% +plus or times now should i +maximize or minimize this one should i + + align:start position:0% +maximize or minimize this one should i + + + align:start position:0% +maximize or minimize this one should i +maximize or minimize this one + + align:start position:0% +maximize or minimize this one + + + align:start position:0% +maximize or minimize this one +i don't know so i'm just gonna do more + + align:start position:0% +i don't know so i'm just gonna do more + + + align:start position:0% +i don't know so i'm just gonna do more +local brute force + + align:start position:0% +local brute force + + + align:start position:0% +local brute force +um i'll say well let's just say opt + + align:start position:0% +um i'll say well let's just say opt + + + align:start position:0% +um i'll say well let's just say opt +prime + + align:start position:0% +prime + + + align:start position:0% +prime +for the left or maybe i'll call it opt l + + align:start position:0% +for the left or maybe i'll call it opt l + + + align:start position:0% +for the left or maybe i'll call it opt l +for left and opt r for the right part + + align:start position:0% +for left and opt r for the right part + + + align:start position:0% +for left and opt r for the right part +and i'll just add this to my for loop + + align:start position:0% +and i'll just add this to my for loop + + + align:start position:0% +and i'll just add this to my for loop +let's just try uh opt l + + align:start position:0% +let's just try uh opt l + + + align:start position:0% +let's just try uh opt l +and opt r just take all possible choices + + align:start position:0% +and opt r just take all possible choices + + + align:start position:0% +and opt r just take all possible choices +among min and max + + align:start position:0% + + + + align:start position:0% + +you know you could think hard and for + + align:start position:0% +you know you could think hard and for + + + align:start position:0% +you know you could think hard and for +addition for example + + align:start position:0% +addition for example + + + align:start position:0% +addition for example +if you're maximizing you should really + + align:start position:0% +if you're maximizing you should really + + + align:start position:0% +if you're maximizing you should really +only need to maximize the two parts and + + align:start position:0% +only need to maximize the two parts and + + + align:start position:0% +only need to maximize the two parts and +if you're minimizing you + + align:start position:0% +if you're minimizing you + + + align:start position:0% +if you're minimizing you +you can prove you only need to minimize + + align:start position:0% +you can prove you only need to minimize + + + align:start position:0% +you can prove you only need to minimize +the two parts + + align:start position:0% +the two parts + + + align:start position:0% +the two parts +but let's for multiplication it's messy + + align:start position:0% +but let's for multiplication it's messy + + + align:start position:0% +but let's for multiplication it's messy +it could be + + align:start position:0% +it could be + + + align:start position:0% +it could be +really any of the options because + + align:start position:0% +really any of the options because + + + align:start position:0% +really any of the options because +sometimes + + align:start position:0% +sometimes + + + align:start position:0% +sometimes +when you minimize you get a negative + + align:start position:0% +when you minimize you get a negative + + + align:start position:0% +when you minimize you get a negative +term sometimes when you + + align:start position:0% +term sometimes when you + + + align:start position:0% +term sometimes when you +sometimes you don't and so you know it + + align:start position:0% +sometimes you don't and so you know it + + + align:start position:0% +sometimes you don't and so you know it +depends what you're trying to do + + align:start position:0% +depends what you're trying to do + + + align:start position:0% +depends what you're trying to do +you have to consider all the signs but + + align:start position:0% +you have to consider all the signs but + + + align:start position:0% +you have to consider all the signs but +we don't need to think hard + + align:start position:0% +we don't need to think hard + + + align:start position:0% +we don't need to think hard +we can just try all options there's only + + align:start position:0% +we can just try all options there's only + + + align:start position:0% +we can just try all options there's only +four choices for opt l and opt r among + + align:start position:0% +four choices for opt l and opt r among + + + align:start position:0% +four choices for opt l and opt r among +min and max you could do mid min min max + + align:start position:0% +min and max you could do mid min min max + + + align:start position:0% +min and max you could do mid min min max +max min and max max + + align:start position:0% +max min and max max + + + align:start position:0% +max min and max max +so try it's just a multiplication by + + align:start position:0% +so try it's just a multiplication by + + + align:start position:0% +so try it's just a multiplication by +four in this for loop + + align:start position:0% +four in this for loop + + + align:start position:0% +four in this for loop +the big cost is actually this one + + align:start position:0% +the big cost is actually this one + + + align:start position:0% +the big cost is actually this one +because there are j + + align:start position:0% +because there are j + + + align:start position:0% +because there are j +minus i choices for k + + align:start position:0% +minus i choices for k + + + align:start position:0% +minus i choices for k +there's a constant number of choices for + + align:start position:0% +there's a constant number of choices for + + + align:start position:0% +there's a constant number of choices for +opt l and opt r + + align:start position:0% +opt l and opt r + + + align:start position:0% +opt l and opt r +and you need to prove that this is + + align:start position:0% +and you need to prove that this is + + + align:start position:0% +and you need to prove that this is +correct i won't do it here + + align:start position:0% +correct i won't do it here + + + align:start position:0% +correct i won't do it here +but the idea is if you're trying to + + align:start position:0% +but the idea is if you're trying to + + + align:start position:0% +but the idea is if you're trying to +minimize or maximize your + + align:start position:0% +minimize or maximize your + + + align:start position:0% +minimize or maximize your +sum or product it's enough to know + + align:start position:0% +sum or product it's enough to know + + + align:start position:0% +sum or product it's enough to know +what ranges these could come in the + + align:start position:0% +what ranges these could come in the + + + align:start position:0% +what ranges these could come in the +optimal choice will always be an extreme + + align:start position:0% +optimal choice will always be an extreme + + + align:start position:0% +optimal choice will always be an extreme +in that range + + align:start position:0% +in that range + + + align:start position:0% +in that range +okay and that's we consider all of them + + align:start position:0% +okay and that's we consider all of them + + + align:start position:0% +okay and that's we consider all of them +here and so we get + + align:start position:0% +here and so we get + + + align:start position:0% +here and so we get +this recurrence now it needs a base case + + align:start position:0% +this recurrence now it needs a base case + + + align:start position:0% +this recurrence now it needs a base case +and we need to check that it's acyclic + + align:start position:0% +and we need to check that it's acyclic + + + align:start position:0% +and we need to check that it's acyclic +but topological order is just increasing + + align:start position:0% +but topological order is just increasing + + + align:start position:0% +but topological order is just increasing +j minus i this is the usual order for + + align:start position:0% +j minus i this is the usual order for + + + align:start position:0% +j minus i this is the usual order for +um for substring problems because this + + align:start position:0% +um for substring problems because this + + + align:start position:0% +um for substring problems because this +is increasing length of the substring + + align:start position:0% +is increasing length of the substring + + + align:start position:0% +is increasing length of the substring +so start with very tiny substrings here + + align:start position:0% +so start with very tiny substrings here + + + align:start position:0% +so start with very tiny substrings here +we'll start with length one substrings + + align:start position:0% +we'll start with length one substrings + + + align:start position:0% +we'll start with length one substrings +we just have an ai there + + align:start position:0% +we just have an ai there + + + align:start position:0% +we just have an ai there +so that's going to be our base case and + + align:start position:0% +so that's going to be our base case and + + + align:start position:0% +so that's going to be our base case and +you grow up to the entire string + + align:start position:0% +you grow up to the entire string + + + align:start position:0% +you grow up to the entire string +and it doesn't matter how we order + + align:start position:0% +and it doesn't matter how we order + + + align:start position:0% +and it doesn't matter how we order +relative to opt as long as we are + + align:start position:0% +relative to opt as long as we are + + + align:start position:0% +relative to opt as long as we are +increasing in j minus i + + align:start position:0% +increasing in j minus i + + + align:start position:0% +increasing in j minus i +because i decay and k to j will always + + align:start position:0% +because i decay and k to j will always + + + align:start position:0% +because i decay and k to j will always +be strictly smaller than i to j and so + + align:start position:0% +be strictly smaller than i to j and so + + + align:start position:0% +be strictly smaller than i to j and so +this will be + + align:start position:0% +this will be + + + align:start position:0% +this will be +acyclic the base case is + + align:start position:0% +acyclic the base case is + + + align:start position:0% +acyclic the base case is +x of i i plus 1 opt + + align:start position:0% +x of i i plus 1 opt + + + align:start position:0% +x of i i plus 1 opt +this is always a i doesn't matter what + + align:start position:0% +this is always a i doesn't matter what + + + align:start position:0% +this is always a i doesn't matter what +opt is because there's nothing there's + + align:start position:0% +opt is because there's nothing there's + + + align:start position:0% +opt is because there's nothing there's +no choice + + align:start position:0% +no choice + + + align:start position:0% +no choice +you just have a single number in that + + align:start position:0% +you just have a single number in that + + + align:start position:0% +you just have a single number in that +substring because we're exclusive on i + + align:start position:0% +substring because we're exclusive on i + + + align:start position:0% +substring because we're exclusive on i +plus 1. + + align:start position:0% +plus 1. + + + align:start position:0% +plus 1. +okay and then the original problem we + + align:start position:0% +okay and then the original problem we + + + align:start position:0% +okay and then the original problem we +want to solve + + align:start position:0% +want to solve + + + align:start position:0% +want to solve +is x of 0 n + + align:start position:0% +is x of 0 n + + + align:start position:0% +is x of 0 n +max could also solve min and see how + + align:start position:0% +max could also solve min and see how + + + align:start position:0% +max could also solve min and see how +small you can get it + + align:start position:0% +small you can get it + + + align:start position:0% +small you can get it +so if you wanted to maximize the + + align:start position:0% +so if you wanted to maximize the + + + align:start position:0% +so if you wanted to maximize the +absolute value you could solve the max + + align:start position:0% +absolute value you could solve the max + + + align:start position:0% +absolute value you could solve the max +problem and the min problem and take the + + align:start position:0% +problem and the min problem and take the + + + align:start position:0% +problem and the min problem and take the +largest + + align:start position:0% +largest + + + align:start position:0% +largest +of those two options and how much time + + align:start position:0% +of those two options and how much time + + + align:start position:0% +of those two options and how much time +does this take + + align:start position:0% +does this take + + + align:start position:0% +does this take +well how many sub problems are there for + + align:start position:0% +well how many sub problems are there for + + + align:start position:0% +well how many sub problems are there for +substring problems we have n squared sub + + align:start position:0% +substring problems we have n squared sub + + + align:start position:0% +substring problems we have n squared sub +problems now we multiplied the number of + + align:start position:0% +problems now we multiplied the number of + + + align:start position:0% +problems now we multiplied the number of +subproblems by 2 + + align:start position:0% +subproblems by 2 + + + align:start position:0% +subproblems by 2 +but that's still n squared okay so we + + align:start position:0% +but that's still n squared okay so we + + + align:start position:0% +but that's still n squared okay so we +have n + + align:start position:0% +have n + + + align:start position:0% +have n +squared sub problems + + align:start position:0% + + + + align:start position:0% + +and how much work per subproblem are we + + align:start position:0% +and how much work per subproblem are we + + + align:start position:0% +and how much work per subproblem are we +doing well + + align:start position:0% +doing well + + + align:start position:0% +doing well +uh as i mentioned we're we're doing j + + align:start position:0% +uh as i mentioned we're we're doing j + + + align:start position:0% +uh as i mentioned we're we're doing j +minus i choices for k + + align:start position:0% +minus i choices for k + + + align:start position:0% +minus i choices for k +constant number of choices for opt l and + + align:start position:0% +constant number of choices for opt l and + + + align:start position:0% +constant number of choices for opt l and +opt r so this is theta j minus i + + align:start position:0% +opt r so this is theta j minus i + + + align:start position:0% +opt r so this is theta j minus i +which if i'll be sloppy that's at most + + align:start position:0% +which if i'll be sloppy that's at most + + + align:start position:0% +which if i'll be sloppy that's at most +big o of n + + align:start position:0% +big o of n + + + align:start position:0% +big o of n +and it turns out to be the right answer + + align:start position:0% +and it turns out to be the right answer + + + align:start position:0% +and it turns out to be the right answer +anyway so + + align:start position:0% +anyway so + + + align:start position:0% +anyway so +uh there's linear amount of + + align:start position:0% +uh there's linear amount of + + + align:start position:0% +uh there's linear amount of +non-recursive work + + align:start position:0% +non-recursive work + + + align:start position:0% +non-recursive work +in fact it's like a triangular number + + align:start position:0% +in fact it's like a triangular number + + + align:start position:0% +in fact it's like a triangular number +but uh that's still theta + + align:start position:0% +but uh that's still theta + + + align:start position:0% +but uh that's still theta +uh n cubed + + align:start position:0% + + + + align:start position:0% + +okay same running time as uh v cubed we + + align:start position:0% +okay same running time as uh v cubed we + + + align:start position:0% +okay same running time as uh v cubed we +just got but + + align:start position:0% +just got but + + + align:start position:0% +just got but +polynomial time and this is pretty + + align:start position:0% +polynomial time and this is pretty + + + align:start position:0% +polynomial time and this is pretty +impressive because we're really brute + + align:start position:0% +impressive because we're really brute + + + align:start position:0% +impressive because we're really brute +forcing all possible parenthesizations + + align:start position:0% +forcing all possible parenthesizations + + + align:start position:0% +forcing all possible parenthesizations +they're about four to the n + + align:start position:0% +they're about four to the n + + + align:start position:0% +they're about four to the n +exponentially many uh parenthesizations + + align:start position:0% +exponentially many uh parenthesizations + + + align:start position:0% +exponentially many uh parenthesizations +of an expression + + align:start position:0% +of an expression + + + align:start position:0% +of an expression +but we're finding the biggest the one + + align:start position:0% +but we're finding the biggest the one + + + align:start position:0% +but we're finding the biggest the one +that evaluates to the largest value and + + align:start position:0% +that evaluates to the largest value and + + + align:start position:0% +that evaluates to the largest value and +the one that + + align:start position:0% +the one that + + + align:start position:0% +the one that +evaluates the smallest value in just n + + align:start position:0% +evaluates the smallest value in just n + + + align:start position:0% +evaluates the smallest value in just n +cubed time polynomial + + align:start position:0% +cubed time polynomial + + + align:start position:0% +cubed time polynomial +and a key here was subproblem expansion + + align:start position:0% +and a key here was subproblem expansion + + + align:start position:0% +and a key here was subproblem expansion +where we in addition to solving the max + + align:start position:0% +where we in addition to solving the max + + + align:start position:0% +where we in addition to solving the max +problem we also solved the min + + align:start position:0% +problem we also solved the min + + + align:start position:0% +problem we also solved the min +problem because sometimes you want to + + align:start position:0% +problem because sometimes you want to + + + align:start position:0% +problem because sometimes you want to +take + + align:start position:0% +take + + + align:start position:0% +take +two very small negative numbers and + + align:start position:0% +two very small negative numbers and + + + align:start position:0% +two very small negative numbers and +product them together to get a larger + + align:start position:0% +product them together to get a larger + + + align:start position:0% +product them together to get a larger +positive number + + align:start position:0% + + + + align:start position:0% + +cool question + + align:start position:0% +cool question + + + align:start position:0% +cool question +would anything go wrong if i added minus + + align:start position:0% +would anything go wrong if i added minus + + + align:start position:0% +would anything go wrong if i added minus +a divide + + align:start position:0% +a divide + + + align:start position:0% +a divide +so what if i had operators minus and + + align:start position:0% +so what if i had operators minus and + + + align:start position:0% +so what if i had operators minus and +divide + + align:start position:0% +divide + + + align:start position:0% +divide +uh it's a good question i'm i'm certain + + align:start position:0% +uh it's a good question i'm i'm certain + + + align:start position:0% +uh it's a good question i'm i'm certain +that + + align:start position:0% +that + + + align:start position:0% +that +minus should work fine if we do min and + + align:start position:0% +minus should work fine if we do min and + + + align:start position:0% +minus should work fine if we do min and +max this will still evaluate the + + align:start position:0% +max this will still evaluate the + + + align:start position:0% +max this will still evaluate the +should still evaluate the largest thing + + align:start position:0% +should still evaluate the largest thing + + + align:start position:0% +should still evaluate the largest thing +for division i need to think about the + + align:start position:0% +for division i need to think about the + + + align:start position:0% +for division i need to think about the +cases + + align:start position:0% +cases + + + align:start position:0% +cases +i would guess it works but what we need + + align:start position:0% +i would guess it works but what we need + + + align:start position:0% +i would guess it works but what we need +to prove + + align:start position:0% +to prove + + + align:start position:0% +to prove +is that the way to maximize or minimize + + align:start position:0% +is that the way to maximize or minimize + + + align:start position:0% +is that the way to maximize or minimize +a division say given two numbers in the + + align:start position:0% +a division say given two numbers in the + + + align:start position:0% +a division say given two numbers in the +left and right uh is + + align:start position:0% +left and right uh is + + + align:start position:0% +left and right uh is +that it either corresponds to maximizing + + align:start position:0% +that it either corresponds to maximizing + + + align:start position:0% +that it either corresponds to maximizing +or minimizing the thing on the left + + align:start position:0% +or minimizing the thing on the left + + + align:start position:0% +or minimizing the thing on the left +and then maximize or minimizing the + + align:start position:0% +and then maximize or minimizing the + + + align:start position:0% +and then maximize or minimizing the +thing on the right so as long as you + + align:start position:0% +thing on the right so as long as you + + + align:start position:0% +thing on the right so as long as you +have this kind of + + align:start position:0% +have this kind of + + + align:start position:0% +have this kind of +it's not exactly monotonicity it's just + + align:start position:0% +it's not exactly monotonicity it's just + + + align:start position:0% +it's not exactly monotonicity it's just +that in order to compute max or min + + align:start position:0% +that in order to compute max or min + + + align:start position:0% +that in order to compute max or min +it suffices to know the maximum + + align:start position:0% +it suffices to know the maximum + + + align:start position:0% +it suffices to know the maximum +of the two parts it's like interval + + align:start position:0% +of the two parts it's like interval + + + align:start position:0% +of the two parts it's like interval +arithmetic you know interval arithmetic + + align:start position:0% +arithmetic you know interval arithmetic + + + align:start position:0% +arithmetic you know interval arithmetic +i want to know what is the what are the + + align:start position:0% +i want to know what is the what are the + + + align:start position:0% +i want to know what is the what are the +extremes i can get on + + align:start position:0% +extremes i can get on + + + align:start position:0% +extremes i can get on +the output of a division if i'm given + + align:start position:0% +the output of a division if i'm given + + + align:start position:0% +the output of a division if i'm given +that a number is in some interval here + + align:start position:0% +that a number is in some interval here + + + align:start position:0% +that a number is in some interval here +and some interval here + + align:start position:0% +and some interval here + + + align:start position:0% +and some interval here +if the answer is always use one of the + + align:start position:0% +if the answer is always use one of the + + + align:start position:0% +if the answer is always use one of the +extreme endpoints here and use one of + + align:start position:0% +extreme endpoints here and use one of + + + align:start position:0% +extreme endpoints here and use one of +the extreme endpoints here then this + + align:start position:0% +the extreme endpoints here then this + + + align:start position:0% +the extreme endpoints here then this +algorithm will work otherwise + + align:start position:0% +algorithm will work otherwise + + + align:start position:0% +algorithm will work otherwise +all bets are off cool + + align:start position:0% +all bets are off cool + + + align:start position:0% +all bets are off cool +so if you negate if you put a minus here + + align:start position:0% +so if you negate if you put a minus here + + + align:start position:0% +so if you negate if you put a minus here +that will work fine because it's just + + align:start position:0% +that will work fine because it's just + + + align:start position:0% +that will work fine because it's just +negating this range and then it's + + align:start position:0% +negating this range and then it's + + + align:start position:0% +negating this range and then it's +just like sum but + + align:start position:0% +just like sum but + + + align:start position:0% +just like sum but +oh divided be careful about zero yeah + + align:start position:0% +oh divided be careful about zero yeah + + + align:start position:0% +oh divided be careful about zero yeah +actually so it doesn't work because + + align:start position:0% +actually so it doesn't work because + + + align:start position:0% +actually so it doesn't work because +we care about how close this can get to + + align:start position:0% +we care about how close this can get to + + + align:start position:0% +we care about how close this can get to +zero for division + + align:start position:0% +zero for division + + + align:start position:0% +zero for division +it might be enough to to consider those + + align:start position:0% +it might be enough to to consider those + + + align:start position:0% +it might be enough to to consider those +it's like instead of minimizing + + align:start position:0% +it's like instead of minimizing + + + align:start position:0% +it's like instead of minimizing +and instead of computing this entire + + align:start position:0% +and instead of computing this entire + + + align:start position:0% +and instead of computing this entire +interval if this interval spans 0 + + align:start position:0% +interval if this interval spans 0 + + + align:start position:0% +interval if this interval spans 0 +maybe i need to know if zero is here + + align:start position:0% +maybe i need to know if zero is here + + + align:start position:0% +maybe i need to know if zero is here +i need to know how close to zero i can + + align:start position:0% +i need to know how close to zero i can + + + align:start position:0% +i need to know how close to zero i can +get on the left side and how close to + + align:start position:0% +get on the left side and how close to + + + align:start position:0% +get on the left side and how close to +zero i can get on the right side still + + align:start position:0% +zero i can get on the right side still + + + align:start position:0% +zero i can get on the right side still +just four quantities i need to know + + align:start position:0% +just four quantities i need to know + + + align:start position:0% +just four quantities i need to know +i would guess for division that's enough + + align:start position:0% +i would guess for division that's enough + + + align:start position:0% +i would guess for division that's enough +yeah nice + + align:start position:0% +yeah nice + + + align:start position:0% +yeah nice +solid little problem so then we'd be + + align:start position:0% +solid little problem so then we'd be + + + align:start position:0% +solid little problem so then we'd be +multiplying the sub problem space + + align:start position:0% +multiplying the sub problem space + + + align:start position:0% +multiplying the sub problem space +instead of by two + + align:start position:0% +instead of by two + + + align:start position:0% +instead of by two +by four hey maybe we should put this on + + align:start position:0% +by four hey maybe we should put this on + + + align:start position:0% +by four hey maybe we should put this on +the final no + + align:start position:0% +the final no + + + align:start position:0% +the final no +now it's in lecture so we can't use it + + align:start position:0% +now it's in lecture so we can't use it + + + align:start position:0% +now it's in lecture so we can't use it +but + + align:start position:0% +but + + + align:start position:0% +but +it's a cool it's a cool set of problems + + align:start position:0% +it's a cool it's a cool set of problems + + + align:start position:0% +it's a cool it's a cool set of problems +right you can do a lot with dynamic + + align:start position:0% +right you can do a lot with dynamic + + + align:start position:0% +right you can do a lot with dynamic +programming + + align:start position:0% +programming + + + align:start position:0% +programming +just uh you don't need to be that clever + + align:start position:0% +just uh you don't need to be that clever + + + align:start position:0% +just uh you don't need to be that clever +just brute force + + align:start position:0% +just brute force + + + align:start position:0% +just brute force +anything that seems hard and when it + + align:start position:0% +anything that seems hard and when it + + + align:start position:0% +anything that seems hard and when it +works it works great + + align:start position:0% + + + + align:start position:0% + +all right and this class is all about + + align:start position:0% +all right and this class is all about + + + align:start position:0% +all right and this class is all about +understanding when it works + + align:start position:0% +understanding when it works + + + align:start position:0% +understanding when it works +and when it doesn't work of course we + + align:start position:0% +and when it doesn't work of course we + + + align:start position:0% +and when it doesn't work of course we +will only give you problems where it + + align:start position:0% +will only give you problems where it + + + align:start position:0% +will only give you problems where it +works + + align:start position:0% + + + + align:start position:0% + +but it's important to understand when it + + align:start position:0% +but it's important to understand when it + + + align:start position:0% +but it's important to understand when it +doesn't work for example + + align:start position:0% +doesn't work for example + + + align:start position:0% +doesn't work for example +dag shortest paths that algorithm on a + + align:start position:0% +dag shortest paths that algorithm on a + + + align:start position:0% +dag shortest paths that algorithm on a +non-dag + + align:start position:0% +non-dag + + + align:start position:0% +non-dag +very bad infinite time okay + + align:start position:0% +very bad infinite time okay + + + align:start position:0% +very bad infinite time okay +our last example is piano fingering + + align:start position:0% + + + + align:start position:0% + +so here we're given + + align:start position:0% +so here we're given + + + align:start position:0% +so here we're given +a sequence of notes + + align:start position:0% + + + + align:start position:0% + +t zero t one t for note + + align:start position:0% +t zero t one t for note + + + align:start position:0% +t zero t one t for note +up to n t n minus one um + + align:start position:0% +up to n t n minus one um + + + align:start position:0% +up to n t n minus one um +these are single notes + + align:start position:0% + + + + align:start position:0% + +and all the single notes all the single + + align:start position:0% +and all the single notes all the single + + + align:start position:0% +and all the single notes all the single +notes + + align:start position:0% +notes + + + align:start position:0% +notes +right and we have fingers on our + + align:start position:0% +right and we have fingers on our + + + align:start position:0% +right and we have fingers on our +hands this is not like two-finger + + align:start position:0% +hands this is not like two-finger + + + align:start position:0% +hands this is not like two-finger +algorithm this is the + + align:start position:0% +algorithm this is the + + + align:start position:0% +algorithm this is the +five-finger algorithm uh + + align:start position:0% +five-finger algorithm uh + + + align:start position:0% +five-finger algorithm uh +so in general i'm going to assume an + + align:start position:0% +so in general i'm going to assume an + + + align:start position:0% +so in general i'm going to assume an +arbitrary + + align:start position:0% +arbitrary + + + align:start position:0% +arbitrary +uh anthropomorphic + + align:start position:0% +uh anthropomorphic + + + align:start position:0% +uh anthropomorphic +object so this is five for humans + + align:start position:0% +object so this is five for humans + + + align:start position:0% +object so this is five for humans +most humans some humans i think the + + align:start position:0% +most humans some humans i think the + + + align:start position:0% +most humans some humans i think the +maximum on each hand + + align:start position:0% +maximum on each hand + + + align:start position:0% +maximum on each hand +is seven could be smaller maybe you've + + align:start position:0% +is seven could be smaller maybe you've + + + align:start position:0% +is seven could be smaller maybe you've +had an accident + + align:start position:0% +had an accident + + + align:start position:0% +had an accident +okay i'll solve it for arbitrary f + + align:start position:0% +okay i'll solve it for arbitrary f + + + align:start position:0% +okay i'll solve it for arbitrary f +and what we'd like to do is assign + + align:start position:0% +and what we'd like to do is assign + + + align:start position:0% +and what we'd like to do is assign +fingers to notes + + align:start position:0% +fingers to notes + + + align:start position:0% +fingers to notes +to tell our pianist which finger to use + + align:start position:0% +to tell our pianist which finger to use + + + align:start position:0% +to tell our pianist which finger to use +for each note + + align:start position:0% +for each note + + + align:start position:0% +for each note +so normally when you're given sheet + + align:start position:0% +so normally when you're given sheet + + + align:start position:0% +so normally when you're given sheet +music it just gives you + + align:start position:0% +music it just gives you + + + align:start position:0% +music it just gives you +a sequence of notes you want to play it + + align:start position:0% +a sequence of notes you want to play it + + + align:start position:0% +a sequence of notes you want to play it +doesn't tell you which finger you want + + align:start position:0% +doesn't tell you which finger you want + + + align:start position:0% +doesn't tell you which finger you want +to play it with + + align:start position:0% +to play it with + + + align:start position:0% +to play it with +unless you have some nice uh training + + align:start position:0% +unless you have some nice uh training + + + align:start position:0% +unless you have some nice uh training +booklets and they have a little number + + align:start position:0% +booklets and they have a little number + + + align:start position:0% +booklets and they have a little number +on top of each and then you number them + + align:start position:0% +on top of each and then you number them + + + align:start position:0% +on top of each and then you number them +one two three four five and + + align:start position:0% +one two three four five and + + + align:start position:0% +one two three four five and +symmetrically one two three four + + align:start position:0% +symmetrically one two three four + + + align:start position:0% +symmetrically one two three four +five and so here's a giant piano + + align:start position:0% +five and so here's a giant piano + + + align:start position:0% +five and so here's a giant piano +for my giant hands um so uh + + align:start position:0% +for my giant hands um so uh + + + align:start position:0% +for my giant hands um so uh +if jason were here he could sing these + + align:start position:0% +if jason were here he could sing these + + + align:start position:0% +if jason were here he could sing these +notes so maybe i play this + + align:start position:0% +notes so maybe i play this + + + align:start position:0% +notes so maybe i play this +with my first finger this with my second + + align:start position:0% +with my first finger this with my second + + + align:start position:0% +with my first finger this with my second +finger let's just say i'm doing a scale + + align:start position:0% +finger let's just say i'm doing a scale + + + align:start position:0% +finger let's just say i'm doing a scale +so i can walk and now i think typical + + align:start position:0% +so i can walk and now i think typical + + + align:start position:0% +so i can walk and now i think typical +way to do a scale is to reach over with + + align:start position:0% +way to do a scale is to reach over with + + + align:start position:0% +way to do a scale is to reach over with +your + + align:start position:0% +your + + + align:start position:0% +your +first finger second finger i guess and + + align:start position:0% +first finger second finger i guess and + + + align:start position:0% +first finger second finger i guess and +then do something like this + + align:start position:0% +then do something like this + + + align:start position:0% +then do something like this +no okay clearly i don't know scales + + align:start position:0% +no okay clearly i don't know scales + + + align:start position:0% +no okay clearly i don't know scales +um or how to play a piano but you know + + align:start position:0% +um or how to play a piano but you know + + + align:start position:0% +um or how to play a piano but you know +there's there's limits here i can + + align:start position:0% +there's there's limits here i can + + + align:start position:0% +there's there's limits here i can +if i'm going from this note and i want + + align:start position:0% +if i'm going from this note and i want + + + align:start position:0% +if i'm going from this note and i want +to go to another note + + align:start position:0% +to go to another note + + + align:start position:0% +to go to another note +uh over here okay maybe i have a decent + + align:start position:0% +uh over here okay maybe i have a decent + + + align:start position:0% +uh over here okay maybe i have a decent +span + + align:start position:0% +span + + + align:start position:0% +span +from first finger to fifth finger but my + + align:start position:0% +from first finger to fifth finger but my + + + align:start position:0% +from first finger to fifth finger but my +span from my first finger to my second + + align:start position:0% +span from my first finger to my second + + + align:start position:0% +span from my first finger to my second +finger is + + align:start position:0% +finger is + + + align:start position:0% +finger is +not as big i can't reach as far so if i + + align:start position:0% +not as big i can't reach as far so if i + + + align:start position:0% +not as big i can't reach as far so if i +want to play this note and then this + + align:start position:0% +want to play this note and then this + + + align:start position:0% +want to play this note and then this +note i'd like to + + align:start position:0% +note i'd like to + + + align:start position:0% +note i'd like to +start here with a very extreme finger on + + align:start position:0% +start here with a very extreme finger on + + + align:start position:0% +start here with a very extreme finger on +the left + + align:start position:0% +the left + + + align:start position:0% +the left +and then go to a very extreme finger on + + align:start position:0% +and then go to a very extreme finger on + + + align:start position:0% +and then go to a very extreme finger on +the right so + + align:start position:0% +the right so + + + align:start position:0% +the right so +i'm going to formalize this problem + + align:start position:0% +i'm going to formalize this problem + + + align:start position:0% +i'm going to formalize this problem +pretty abstractly because i don't want + + align:start position:0% +pretty abstractly because i don't want + + + align:start position:0% +pretty abstractly because i don't want +to get into + + align:start position:0% +to get into + + + align:start position:0% +to get into +music performance i'm going to say that + + align:start position:0% +music performance i'm going to say that + + + align:start position:0% +music performance i'm going to say that +there's a metric + + align:start position:0% +there's a metric + + + align:start position:0% +there's a metric +d for if i'm at note t + + align:start position:0% +d for if i'm at note t + + + align:start position:0% +d for if i'm at note t +with finger f and i want to go to note t + + align:start position:0% +with finger f and i want to go to note t + + + align:start position:0% +with finger f and i want to go to note t +prime with finger f + + align:start position:0% +prime with finger f + + + align:start position:0% +prime with finger f +prime then this function + + align:start position:0% +prime then this function + + + align:start position:0% +prime then this function +d of t f t prime f prime gives me the + + align:start position:0% +d of t f t prime f prime gives me the + + + align:start position:0% +d of t f t prime f prime gives me the +difficulty of doing that + + align:start position:0% + + + + align:start position:0% + +the difficulty of playing + + align:start position:0% +the difficulty of playing + + + align:start position:0% +the difficulty of playing +note t with finger f + + align:start position:0% +note t with finger f + + + align:start position:0% +note t with finger f +and then playing + + align:start position:0% + + + + align:start position:0% + +note t prime with finger f prime + + align:start position:0% +note t prime with finger f prime + + + align:start position:0% +note t prime with finger f prime +it's w is width uh so this is a + + align:start position:0% +it's w is width uh so this is a + + + align:start position:0% +it's w is width uh so this is a +transition difficulty + + align:start position:0% +transition difficulty + + + align:start position:0% +transition difficulty +i'm not going to worry about difficulty + + align:start position:0% +i'm not going to worry about difficulty + + + align:start position:0% +i'm not going to worry about difficulty +of the whole piece other than saying + + align:start position:0% +of the whole piece other than saying + + + align:start position:0% +of the whole piece other than saying +i've got to play this note then i've got + + align:start position:0% +i've got to play this note then i've got + + + align:start position:0% +i've got to play this note then i've got +to play this note and for now just + + align:start position:0% +to play this note and for now just + + + align:start position:0% +to play this note and for now just +single notes + + align:start position:0% +single notes + + + align:start position:0% +single notes +you play a single note with your right + + align:start position:0% +you play a single note with your right + + + align:start position:0% +you play a single note with your right +hand then you play another single note + + align:start position:0% +hand then you play another single note + + + align:start position:0% +hand then you play another single note +with your right hand then another single + + align:start position:0% +with your right hand then another single + + + align:start position:0% +with your right hand then another single +note with your right hand + + align:start position:0% +note with your right hand + + + align:start position:0% +note with your right hand +let's assume no pauses for now no rests + + align:start position:0% +let's assume no pauses for now no rests + + + align:start position:0% +let's assume no pauses for now no rests +and great so we uh + + align:start position:0% +and great so we uh + + + align:start position:0% +and great so we uh +have this difficulty from going from the + + align:start position:0% +have this difficulty from going from the + + + align:start position:0% +have this difficulty from going from the +ith note to the i + + align:start position:0% +ith note to the i + + + align:start position:0% +ith note to the i +plus first note and then our goal is to + + align:start position:0% +plus first note and then our goal is to + + + align:start position:0% +plus first note and then our goal is to +minimize the sum of difficulties + + align:start position:0% +minimize the sum of difficulties + + + align:start position:0% +minimize the sum of difficulties +minimum sum of + + align:start position:0% +minimum sum of + + + align:start position:0% +minimum sum of +d t i f i + + align:start position:0% +d t i f i + + + align:start position:0% +d t i f i +t i plus 1 f i plus 1. + + align:start position:0% +t i plus 1 f i plus 1. + + + align:start position:0% +t i plus 1 f i plus 1. +and these f i's and f i plus 1 + + align:start position:0% +and these f i's and f i plus 1 + + + align:start position:0% +and these f i's and f i plus 1 +is what we want to compute we don't know + + align:start position:0% +is what we want to compute we don't know + + + align:start position:0% +is what we want to compute we don't know +which fingers to use we're only given + + align:start position:0% +which fingers to use we're only given + + + align:start position:0% +which fingers to use we're only given +which notes to play okay so this is + + align:start position:0% +which notes to play okay so this is + + + align:start position:0% +which notes to play okay so this is +actually a natural problem there are + + align:start position:0% +actually a natural problem there are + + + align:start position:0% +actually a natural problem there are +lots of papers about this problem i've + + align:start position:0% +lots of papers about this problem i've + + + align:start position:0% +lots of papers about this problem i've +read a bunch of them + + align:start position:0% +read a bunch of them + + + align:start position:0% +read a bunch of them +obviously not super well about how to + + align:start position:0% +obviously not super well about how to + + + align:start position:0% +obviously not super well about how to +compute how to play scales + + align:start position:0% +compute how to play scales + + + align:start position:0% +compute how to play scales +but um there are notes like are there + + align:start position:0% +but um there are notes like are there + + + align:start position:0% +but um there are notes like are there +there are constraints in this usually + + align:start position:0% +there are constraints in this usually + + + align:start position:0% +there are constraints in this usually +people write this + + align:start position:0% +people write this + + + align:start position:0% +people write this +metric as a sum of different penalty + + align:start position:0% +metric as a sum of different penalty + + + align:start position:0% +metric as a sum of different penalty +terms + + align:start position:0% +terms + + + align:start position:0% +terms +if i want to minimize difficulty + + align:start position:0% +if i want to minimize difficulty + + + align:start position:0% +if i want to minimize difficulty +difficulty is high + + align:start position:0% +difficulty is high + + + align:start position:0% +difficulty is high +if i play a note far on the left + + align:start position:0% +if i play a note far on the left + + + align:start position:0% +if i play a note far on the left +on the left so if i go from a low note + + align:start position:0% +on the left so if i go from a low note + + + align:start position:0% +on the left so if i go from a low note +to a high note + + align:start position:0% +to a high note + + + align:start position:0% +to a high note +that's easier to do if i use a lower + + align:start position:0% +that's easier to do if i use a lower + + + align:start position:0% +that's easier to do if i use a lower +numbered finger and go to a higher + + align:start position:0% +numbered finger and go to a higher + + + align:start position:0% +numbered finger and go to a higher +numbered finger you don't want the + + align:start position:0% +numbered finger you don't want the + + + align:start position:0% +numbered finger you don't want the +you don't want to go like i was doing + + align:start position:0% +you don't want to go like i was doing + + + align:start position:0% +you don't want to go like i was doing +from + + align:start position:0% +from + + + align:start position:0% +from +a high numbered finger to a low numbered + + align:start position:0% +a high numbered finger to a low numbered + + + align:start position:0% +a high numbered finger to a low numbered +finger + + align:start position:0% +finger + + + align:start position:0% +finger +to play a note on the right that's + + align:start position:0% +to play a note on the right that's + + + align:start position:0% +to play a note on the right that's +annoying so i'd like to do an assignment + + align:start position:0% +annoying so i'd like to do an assignment + + + align:start position:0% +annoying so i'd like to do an assignment +if i can that avoids that so i'll just + + align:start position:0% +if i can that avoids that so i'll just + + + align:start position:0% +if i can that avoids that so i'll just +have some penalty of like 100 + + align:start position:0% +have some penalty of like 100 + + + align:start position:0% +have some penalty of like 100 +if that happens and zero if it doesn't + + align:start position:0% +if that happens and zero if it doesn't + + + align:start position:0% +if that happens and zero if it doesn't +happen sum up a bunch of terms like that + + align:start position:0% +happen sum up a bunch of terms like that + + + align:start position:0% +happen sum up a bunch of terms like that +other examples are avoid the fourth and + + align:start position:0% +other examples are avoid the fourth and + + + align:start position:0% +other examples are avoid the fourth and +fifth fingers the weak fingers + + align:start position:0% +fifth fingers the weak fingers + + + align:start position:0% +fifth fingers the weak fingers +or if i'm playing a portion of the song + + align:start position:0% +or if i'm playing a portion of the song + + + align:start position:0% +or if i'm playing a portion of the song +that is + + align:start position:0% +that is + + + align:start position:0% +that is +legato then i don't want to use the same + + align:start position:0% +legato then i don't want to use the same + + + align:start position:0% +legato then i don't want to use the same +finger to play + + align:start position:0% +finger to play + + + align:start position:0% +finger to play +two notes uh right after the other i've + + align:start position:0% +two notes uh right after the other i've + + + align:start position:0% +two notes uh right after the other i've +gotta use two different fingers for that + + align:start position:0% +gotta use two different fingers for that + + + align:start position:0% +gotta use two different fingers for that +so you have a penalty if f i equals f i + + align:start position:0% +so you have a penalty if f i equals f i + + + align:start position:0% +so you have a penalty if f i equals f i +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +and these two notes are not the same uh + + align:start position:0% +and these two notes are not the same uh + + + align:start position:0% +and these two notes are not the same uh +then + + align:start position:0% +then + + + align:start position:0% +then +and we're in legato mode then we add a + + align:start position:0% +and we're in legato mode then we add a + + + align:start position:0% +and we're in legato mode then we add a +penalty term + + align:start position:0% +penalty term + + + align:start position:0% +penalty term +and things like that i would prefer if + + align:start position:0% +and things like that i would prefer if + + + align:start position:0% +and things like that i would prefer if +i'm going from a very low note to a very + + align:start position:0% +i'm going from a very low note to a very + + + align:start position:0% +i'm going from a very low note to a very +high note + + align:start position:0% +high note + + + align:start position:0% +high note +i'd like to use more extreme fingers + + align:start position:0% +i'd like to use more extreme fingers + + + align:start position:0% +i'd like to use more extreme fingers +things like that + + align:start position:0% +things like that + + + align:start position:0% +things like that +okay but we're just going to assume this + + align:start position:0% +okay but we're just going to assume this + + + align:start position:0% +okay but we're just going to assume this +di d function is given to us + + align:start position:0% +di d function is given to us + + + align:start position:0% +di d function is given to us +it's some you know const was + + align:start position:0% +it's some you know const was + + + align:start position:0% +it's some you know const was +some polynomial size if you imagine the + + align:start position:0% +some polynomial size if you imagine the + + + align:start position:0% +some polynomial size if you imagine the +notes on your keyboard + + align:start position:0% +notes on your keyboard + + + align:start position:0% +notes on your keyboard +are n notes or m notes then some + + align:start position:0% +are n notes or m notes then some + + + align:start position:0% +are n notes or m notes then some +polynomial and m + + align:start position:0% +polynomial and m + + + align:start position:0% +polynomial and m +size to this function okay + + align:start position:0% + + + + align:start position:0% + +so how do we solve this problem + + align:start position:0% +so how do we solve this problem + + + align:start position:0% +so how do we solve this problem +i'm running low on time so let me + + align:start position:0% + + + + align:start position:0% + +give you + + align:start position:0% + + + + align:start position:0% + +the idea + + align:start position:0% +the idea + + + align:start position:0% +the idea +and this is going to use sub-problem + + align:start position:0% +and this is going to use sub-problem + + + align:start position:0% +and this is going to use sub-problem +expansion + + align:start position:0% + + + + align:start position:0% + +so the sub-problems are going to be + + align:start position:0% +so the sub-problems are going to be + + + align:start position:0% +so the sub-problems are going to be +x of i comma f this is the minimum + + align:start position:0% +x of i comma f this is the minimum + + + align:start position:0% +x of i comma f this is the minimum +total difficulty + + align:start position:0% + + + + align:start position:0% + +to play a suffix because i like suffixes + + align:start position:0% +to play a suffix because i like suffixes + + + align:start position:0% +to play a suffix because i like suffixes +ti up to tn minus one + + align:start position:0% +ti up to tn minus one + + + align:start position:0% +ti up to tn minus one +uh starting + + align:start position:0% + + + + align:start position:0% + +with finger f + + align:start position:0% + + + + align:start position:0% + +uh on note ti + + align:start position:0% +uh on note ti + + + align:start position:0% +uh on note ti +okay so the obvious sub problems would + + align:start position:0% +okay so the obvious sub problems would + + + align:start position:0% +okay so the obvious sub problems would +be without this + + align:start position:0% +be without this + + + align:start position:0% +be without this +constraint this here is a sub problem + + align:start position:0% +constraint this here is a sub problem + + + align:start position:0% +constraint this here is a sub problem +constraint + + align:start position:0% +constraint + + + align:start position:0% +constraint +and you could try to define the sub + + align:start position:0% +and you could try to define the sub + + + align:start position:0% +and you could try to define the sub +problems just as what's the best way to + + align:start position:0% +problems just as what's the best way to + + + align:start position:0% +problems just as what's the best way to +play a suffix + + align:start position:0% +play a suffix + + + align:start position:0% +play a suffix +but i claim it's important to know which + + align:start position:0% +but i claim it's important to know which + + + align:start position:0% +but i claim it's important to know which +finger we start with so we're going to + + align:start position:0% +finger we start with so we're going to + + + align:start position:0% +finger we start with so we're going to +multiply the number of sub-problems by + + align:start position:0% +multiply the number of sub-problems by + + + align:start position:0% +multiply the number of sub-problems by +capital f which is just five so + + align:start position:0% +capital f which is just five so + + + align:start position:0% +capital f which is just five so +very small sub-problem expansion and + + align:start position:0% +very small sub-problem expansion and + + + align:start position:0% +very small sub-problem expansion and +then we're going to constrain each + + align:start position:0% +then we're going to constrain each + + + align:start position:0% +then we're going to constrain each +sub-problem to say well what if i + + align:start position:0% +sub-problem to say well what if i + + + align:start position:0% +sub-problem to say well what if i +started with my first finger what if i + + align:start position:0% +started with my first finger what if i + + + align:start position:0% +started with my first finger what if i +started with my second finger what if + + align:start position:0% +started with my second finger what if + + + align:start position:0% +started with my second finger what if +up to the fifth finger try them all + + align:start position:0% +up to the fifth finger try them all + + + align:start position:0% +up to the fifth finger try them all +okay then i turns out i can write a + + align:start position:0% +okay then i turns out i can write a + + + align:start position:0% +okay then i turns out i can write a +relation + + align:start position:0% +relation + + + align:start position:0% +relation +which is x of i f + + align:start position:0% +which is x of i f + + + align:start position:0% +which is x of i f +equals the min what should i what should + + align:start position:0% +equals the min what should i what should + + + align:start position:0% +equals the min what should i what should +i min + + align:start position:0% +i min + + + align:start position:0% +i min +over i'll just uh guess + + align:start position:0% +over i'll just uh guess + + + align:start position:0% +over i'll just uh guess +this i'm already told what my first + + align:start position:0% +this i'm already told what my first + + + align:start position:0% +this i'm already told what my first +finger is + + align:start position:0% +finger is + + + align:start position:0% +finger is +to use which finger i should use for ti + + align:start position:0% +to use which finger i should use for ti + + + align:start position:0% +to use which finger i should use for ti +so what's the next thing that matters + + align:start position:0% +so what's the next thing that matters + + + align:start position:0% +so what's the next thing that matters +well i guess what finger to use + + align:start position:0% +well i guess what finger to use + + + align:start position:0% +well i guess what finger to use +for the ti plus one the very next note + + align:start position:0% +for the ti plus one the very next note + + + align:start position:0% +for the ti plus one the very next note +which what is the next finger i use + + align:start position:0% +which what is the next finger i use + + + align:start position:0% +which what is the next finger i use +i will call that f prime and minimize + + align:start position:0% +i will call that f prime and minimize + + + align:start position:0% +i will call that f prime and minimize +over f prime between one and capital f + + align:start position:0% +over f prime between one and capital f + + + align:start position:0% +over f prime between one and capital f +of the remaining suffix + + align:start position:0% +of the remaining suffix + + + align:start position:0% +of the remaining suffix +starting with f prime plus my difficulty + + align:start position:0% +starting with f prime plus my difficulty + + + align:start position:0% +starting with f prime plus my difficulty +function + + align:start position:0% +function + + + align:start position:0% +function +from t i comma f to t i plus 1 + + align:start position:0% +from t i comma f to t i plus 1 + + + align:start position:0% +from t i comma f to t i plus 1 +comma f prime end of bracket + + align:start position:0% +comma f prime end of bracket + + + align:start position:0% +comma f prime end of bracket +okay so there's kind of a lot going here + + align:start position:0% +okay so there's kind of a lot going here + + + align:start position:0% +okay so there's kind of a lot going here +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +lowercase f prime + + align:start position:0% + + + + align:start position:0% + +but actually if you think about what i'd + + align:start position:0% +but actually if you think about what i'd + + + align:start position:0% +but actually if you think about what i'd +like to write the recurrence on + + align:start position:0% +like to write the recurrence on + + + align:start position:0% +like to write the recurrence on +i start with the suffix i i like to + + align:start position:0% +i start with the suffix i i like to + + + align:start position:0% +i start with the suffix i i like to +recurse on the smaller suffix so that's + + align:start position:0% +recurse on the smaller suffix so that's + + + align:start position:0% +recurse on the smaller suffix so that's +x of i plus one + + align:start position:0% +x of i plus one + + + align:start position:0% +x of i plus one +and so here uh if if i know that i'm + + align:start position:0% +and so here uh if if i know that i'm + + + align:start position:0% +and so here uh if if i know that i'm +parametrizing by finger number + + align:start position:0% +parametrizing by finger number + + + align:start position:0% +parametrizing by finger number +for i well then i in order to even call + + align:start position:0% +for i well then i in order to even call + + + align:start position:0% +for i well then i in order to even call +this function i need to know what finger + + align:start position:0% +this function i need to know what finger + + + align:start position:0% +this function i need to know what finger +i'm using for i plus one so once you + + align:start position:0% +i'm using for i plus one so once you + + + align:start position:0% +i'm using for i plus one so once you +decide on these sub problems it's really + + align:start position:0% +decide on these sub problems it's really + + + align:start position:0% +decide on these sub problems it's really +obvious you need to guess + + align:start position:0% +obvious you need to guess + + + align:start position:0% +obvious you need to guess +what is the next finger and then recurse + + align:start position:0% +what is the next finger and then recurse + + + align:start position:0% +what is the next finger and then recurse +on that finger recurs on the remaining + + align:start position:0% +on that finger recurs on the remaining + + + align:start position:0% +on that finger recurs on the remaining +suffix of that finger + + align:start position:0% +suffix of that finger + + + align:start position:0% +suffix of that finger +now why did we need to know what f what + + align:start position:0% +now why did we need to know what f what + + + align:start position:0% +now why did we need to know what f what +these + + align:start position:0% +these + + + align:start position:0% +these +fingers were why not just guess what the + + align:start position:0% +fingers were why not just guess what the + + + align:start position:0% +fingers were why not just guess what the +first finger is + + align:start position:0% +first finger is + + + align:start position:0% +first finger is +uh well it has to do with this + + align:start position:0% +uh well it has to do with this + + + align:start position:0% +uh well it has to do with this +difficulty function for this difficulty + + align:start position:0% +difficulty function for this difficulty + + + align:start position:0% +difficulty function for this difficulty +function i know that i want to measure + + align:start position:0% +function i know that i want to measure + + + align:start position:0% +function i know that i want to measure +the difficulty from t i to t i plus one + + align:start position:0% +the difficulty from t i to t i plus one + + + align:start position:0% +the difficulty from t i to t i plus one +and to do that because this function is + + align:start position:0% +and to do that because this function is + + + align:start position:0% +and to do that because this function is +parametrized by four things i need to + + align:start position:0% +parametrized by four things i need to + + + align:start position:0% +parametrized by four things i need to +know both the finger for ti + + align:start position:0% +know both the finger for ti + + + align:start position:0% +know both the finger for ti +and at the same time the finger for ti + + align:start position:0% +and at the same time the finger for ti + + + align:start position:0% +and at the same time the finger for ti +plus one + + align:start position:0% +plus one + + + align:start position:0% +plus one +if i remove this f i could you know add + + align:start position:0% +if i remove this f i could you know add + + + align:start position:0% +if i remove this f i could you know add +a min over one finger but i can't really + + align:start position:0% +a min over one finger but i can't really + + + align:start position:0% +a min over one finger but i can't really +add a + + align:start position:0% +add a + + + align:start position:0% +add a +min over two fingers so what this does + + align:start position:0% +min over two fingers so what this does + + + align:start position:0% +min over two fingers so what this does +by parameterizing by f here and writing + + align:start position:0% +by parameterizing by f here and writing + + + align:start position:0% +by parameterizing by f here and writing +down the optimal + + align:start position:0% +down the optimal + + + align:start position:0% +down the optimal +for each starting finger f i can + + align:start position:0% +for each starting finger f i can + + + align:start position:0% +for each starting finger f i can +at some sense i'm remembering + + align:start position:0% +at some sense i'm remembering + + + align:start position:0% +at some sense i'm remembering +in this call what finger i started with + + align:start position:0% +in this call what finger i started with + + + align:start position:0% +in this call what finger i started with +because i told it you have to start with + + align:start position:0% +because i told it you have to start with + + + align:start position:0% +because i told it you have to start with +finger f prime and so locally to + + align:start position:0% +finger f prime and so locally to + + + align:start position:0% +finger f prime and so locally to +x i f um + + align:start position:0% +x i f um + + + align:start position:0% +x i f um +i know what finger f prime is being used + + align:start position:0% +i know what finger f prime is being used + + + align:start position:0% +i know what finger f prime is being used +for t i plus pos1 and also + + align:start position:0% +for t i plus pos1 and also + + + align:start position:0% +for t i plus pos1 and also +because of the definition of x i f i + + align:start position:0% +because of the definition of x i f i + + + align:start position:0% +because of the definition of x i f i +know what finger i'm using for ti + + align:start position:0% +know what finger i'm using for ti + + + align:start position:0% +know what finger i'm using for ti +and so i get to know both of these + + align:start position:0% +and so i get to know both of these + + + align:start position:0% +and so i get to know both of these +fingers one comes out of this min + + align:start position:0% +fingers one comes out of this min + + + align:start position:0% +fingers one comes out of this min +and the other is given to me as this + + align:start position:0% +and the other is given to me as this + + + align:start position:0% +and the other is given to me as this +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +and then of course if i can solve these + + align:start position:0% +and then of course if i can solve these + + + align:start position:0% +and then of course if i can solve these +problems i can solve the original + + align:start position:0% +problems i can solve the original + + + align:start position:0% +problems i can solve the original +problem + + align:start position:0% +problem + + + align:start position:0% +problem +by just one more min + + align:start position:0% +by just one more min + + + align:start position:0% +by just one more min +of 1 up 1 up to capital f + + align:start position:0% +of 1 up 1 up to capital f + + + align:start position:0% +of 1 up 1 up to capital f +of x 0 little + + align:start position:0% +of x 0 little + + + align:start position:0% +of x 0 little +f right i don't know which finger to + + align:start position:0% +f right i don't know which finger to + + + align:start position:0% +f right i don't know which finger to +start with but that's just + + align:start position:0% +start with but that's just + + + align:start position:0% +start with but that's just +f choices and so then this recurrence + + align:start position:0% +f choices and so then this recurrence + + + align:start position:0% +f choices and so then this recurrence +gives me + + align:start position:0% +gives me + + + align:start position:0% +gives me +the overall solution in i'll just jump + + align:start position:0% +the overall solution in i'll just jump + + + align:start position:0% +the overall solution in i'll just jump +to the time you need a base case + + align:start position:0% +to the time you need a base case + + + align:start position:0% +to the time you need a base case +and uh topological order but it is + + align:start position:0% +and uh topological order but it is + + + align:start position:0% +and uh topological order but it is +n f squared time there are n + + align:start position:0% +n f squared time there are n + + + align:start position:0% +n f squared time there are n +times f sub problems here and for each + + align:start position:0% +times f sub problems here and for each + + + align:start position:0% +times f sub problems here and for each +one + + align:start position:0% +one + + + align:start position:0% +one +i'm doing an optimization over f choices + + align:start position:0% +i'm doing an optimization over f choices + + + align:start position:0% +i'm doing an optimization over f choices +so i get n times f + + align:start position:0% +so i get n times f + + + align:start position:0% +so i get n times f +squared it's a polynomial and if f is a + + align:start position:0% +squared it's a polynomial and if f is a + + + align:start position:0% +squared it's a polynomial and if f is a +constant this is actually linear + + align:start position:0% +constant this is actually linear + + + align:start position:0% +constant this is actually linear +time very fast dp now what i described + + align:start position:0% +time very fast dp now what i described + + + align:start position:0% +time very fast dp now what i described +here is for + + align:start position:0% +here is for + + + align:start position:0% +here is for +one hand one note at a time but you can + + align:start position:0% +one hand one note at a time but you can + + + align:start position:0% +one hand one note at a time but you can +generalize this to + + align:start position:0% +generalize this to + + + align:start position:0% +generalize this to +two hands each with one note well that's + + align:start position:0% +two hands each with one note well that's + + + align:start position:0% +two hands each with one note well that's +just ten fingers so + + align:start position:0% +just ten fingers so + + + align:start position:0% +just ten fingers so +uh you could solve this separately for + + align:start position:0% +uh you could solve this separately for + + + align:start position:0% +uh you could solve this separately for +the right hand and left hand if you know + + align:start position:0% +the right hand and left hand if you know + + + align:start position:0% +the right hand and left hand if you know +which notes are being played + + align:start position:0% +which notes are being played + + + align:start position:0% +which notes are being played +with left-handed right hand but some + + align:start position:0% +with left-handed right hand but some + + + align:start position:0% +with left-handed right hand but some +pieces that's not obvious + + align:start position:0% +pieces that's not obvious + + + align:start position:0% +pieces that's not obvious +so to make it more interesting what if + + align:start position:0% +so to make it more interesting what if + + + align:start position:0% +so to make it more interesting what if +you have multiple notes + + align:start position:0% +you have multiple notes + + + align:start position:0% +you have multiple notes +at the same time and let's say i think + + align:start position:0% +at the same time and let's say i think + + + align:start position:0% +at the same time and let's say i think +it's reasonable so you can only play + + align:start position:0% +it's reasonable so you can only play + + + align:start position:0% +it's reasonable so you can only play +up to f notes at a time + + align:start position:0% +up to f notes at a time + + + align:start position:0% +up to f notes at a time +one for each finger and so we have an + + align:start position:0% +one for each finger and so we have an + + + align:start position:0% +one for each finger and so we have an +upper bound of the number of notes + + align:start position:0% +upper bound of the number of notes + + + align:start position:0% +upper bound of the number of notes +at a time that we're playing which is + + align:start position:0% +at a time that we're playing which is + + + align:start position:0% +at a time that we're playing which is +good + + align:start position:0% +good + + + align:start position:0% +good +oh i have a drawing of this dp by the + + align:start position:0% +oh i have a drawing of this dp by the + + + align:start position:0% +oh i have a drawing of this dp by the +way + + align:start position:0% +way + + + align:start position:0% +way +as a subproblem dag so + + align:start position:0% +as a subproblem dag so + + + align:start position:0% +as a subproblem dag so +this is the original problem which is we + + align:start position:0% +this is the original problem which is we + + + align:start position:0% +this is the original problem which is we +don't know which finger to + + align:start position:0% +don't know which finger to + + + align:start position:0% +don't know which finger to +start with but then we just have a + + align:start position:0% +start with but then we just have a + + + align:start position:0% +start with but then we just have a +complete bipartite graph here + + align:start position:0% +complete bipartite graph here + + + align:start position:0% +complete bipartite graph here +where we write on each of these edges + + align:start position:0% +where we write on each of these edges + + + align:start position:0% +where we write on each of these edges +what is the difficulty of this + + align:start position:0% +what is the difficulty of this + + + align:start position:0% +what is the difficulty of this +transition + + align:start position:0% +transition + + + align:start position:0% +transition +the y axis here is which finger i'm + + align:start position:0% +the y axis here is which finger i'm + + + align:start position:0% +the y axis here is which finger i'm +using one two three four five + + align:start position:0% +using one two three four five + + + align:start position:0% +using one two three four five +and the x-axis is which suffix i'm + + align:start position:0% +and the x-axis is which suffix i'm + + + align:start position:0% +and the x-axis is which suffix i'm +considering which note + + align:start position:0% +considering which note + + + align:start position:0% +considering which note +do i start on and so you could solve + + align:start position:0% +do i start on and so you could solve + + + align:start position:0% +do i start on and so you could solve +this with shortest paths and a dag + + align:start position:0% +this with shortest paths and a dag + + + align:start position:0% +this with shortest paths and a dag +or you could just solve it directly this + + align:start position:0% +or you could just solve it directly this + + + align:start position:0% +or you could just solve it directly this +dp either top down or bottom up + + align:start position:0% +dp either top down or bottom up + + + align:start position:0% +dp either top down or bottom up +okay jumping ahead + + align:start position:0% +okay jumping ahead + + + align:start position:0% +okay jumping ahead +so if you do multiple notes at a time + + align:start position:0% +so if you do multiple notes at a time + + + align:start position:0% +so if you do multiple notes at a time +instead of this finger choice which just + + align:start position:0% +instead of this finger choice which just + + + align:start position:0% +instead of this finger choice which just +had f choices + + align:start position:0% +had f choices + + + align:start position:0% +had f choices +we have + + align:start position:0% + + + + align:start position:0% + +what do i write here t + + align:start position:0% +what do i write here t + + + align:start position:0% +what do i write here t +to the f uh + + align:start position:0% +to the f uh + + + align:start position:0% +to the f uh +possible states + + align:start position:0% +possible states + + + align:start position:0% +possible states +where t is the maximum number of notes + + align:start position:0% +where t is the maximum number of notes + + + align:start position:0% +where t is the maximum number of notes +that i could play at once + + align:start position:0% + + + + align:start position:0% + +and usually this is at most f one for + + align:start position:0% +and usually this is at most f one for + + + align:start position:0% +and usually this is at most f one for +finger but we could generalize + + align:start position:0% +finger but we could generalize + + + align:start position:0% +finger but we could generalize +and this is you know number of fingers + + align:start position:0% + + + + align:start position:0% + +so i could deal with all 10 fingers of a + + align:start position:0% +so i could deal with all 10 fingers of a + + + align:start position:0% +so i could deal with all 10 fingers of a +typical + + align:start position:0% +typical + + + align:start position:0% +typical +human set of arms hands + + align:start position:0% +human set of arms hands + + + align:start position:0% +human set of arms hands +and say there's at most 10 and so this + + align:start position:0% +and say there's at most 10 and so this + + + align:start position:0% +and say there's at most 10 and so this +is 10 to the 10. it's a + + align:start position:0% +is 10 to the 10. it's a + + + align:start position:0% +is 10 to the 10. it's a +big constant but it's constant uh like a + + align:start position:0% +big constant but it's constant uh like a + + + align:start position:0% +big constant but it's constant uh like a +billion + + align:start position:0% +billion + + + align:start position:0% +billion +billion right 10 billion + + align:start position:0% +billion right 10 billion + + + align:start position:0% +billion right 10 billion +but then is that times n and maybe that + + align:start position:0% +but then is that times n and maybe that + + + align:start position:0% +but then is that times n and maybe that +squared times + + align:start position:0% +squared times + + + align:start position:0% +squared times +n will let me exhaustively enumerate all + + align:start position:0% +n will let me exhaustively enumerate all + + + align:start position:0% +n will let me exhaustively enumerate all +the possible things i could do + + align:start position:0% +the possible things i could do + + + align:start position:0% +the possible things i could do +be doing with all of my hands so you can + + align:start position:0% +be doing with all of my hands so you can + + + align:start position:0% +be doing with all of my hands so you can +apply this not only to + + align:start position:0% +apply this not only to + + + align:start position:0% +apply this not only to +piano fingering but also to guitar + + align:start position:0% +piano fingering but also to guitar + + + align:start position:0% +piano fingering but also to guitar +fingering also to rock band rock band is + + align:start position:0% +fingering also to rock band rock band is + + + align:start position:0% +fingering also to rock band rock band is +an easy case where you just have five + + align:start position:0% +an easy case where you just have five + + + align:start position:0% +an easy case where you just have five +buttons and usually only four fingers + + align:start position:0% +buttons and usually only four fingers + + + align:start position:0% +buttons and usually only four fingers +that you use + + align:start position:0% +that you use + + + align:start position:0% +that you use +and this doesn't really make any sound + + align:start position:0% +and this doesn't really make any sound + + + align:start position:0% +and this doesn't really make any sound +so it's not that exciting + + align:start position:0% +so it's not that exciting + + + align:start position:0% +so it's not that exciting +so the case where f equals four + + align:start position:0% +so the case where f equals four + + + align:start position:0% +so the case where f equals four +is uh you can apply to optimally figure + + align:start position:0% +is uh you can apply to optimally figure + + + align:start position:0% +is uh you can apply to optimally figure +out which + + align:start position:0% +out which + + + align:start position:0% +out which +which finger once you have a difficulty + + align:start position:0% +which finger once you have a difficulty + + + align:start position:0% +which finger once you have a difficulty +function of what transitions are easy + + align:start position:0% +function of what transitions are easy + + + align:start position:0% +function of what transitions are easy +and hard + + align:start position:0% +and hard + + + align:start position:0% +and hard +for rock band then you can optimally + + align:start position:0% +for rock band then you can optimally + + + align:start position:0% +for rock band then you can optimally +figure out your fingering for rock band + + align:start position:0% +figure out your fingering for rock band + + + align:start position:0% +figure out your fingering for rock band +songs + + align:start position:0% +songs + + + align:start position:0% +songs +with a real guitar this is a little bit + + align:start position:0% +with a real guitar this is a little bit + + + align:start position:0% +with a real guitar this is a little bit +harder and + + align:start position:0% +harder and + + + align:start position:0% +harder and +because there are actually multiple ways + + align:start position:0% +because there are actually multiple ways + + + align:start position:0% +because there are actually multiple ways +to play the same note + + align:start position:0% +to play the same note + + + align:start position:0% +to play the same note +for example i can play + + align:start position:0% +for example i can play + + + align:start position:0% +for example i can play +the note of this string like this + + align:start position:0% +the note of this string like this + + + align:start position:0% +the note of this string like this +these should both sound the same my + + align:start position:0% +these should both sound the same my + + + align:start position:0% +these should both sound the same my +guitar were + + align:start position:0% +guitar were + + + align:start position:0% +guitar were +perfectly tuned which is not + + align:start position:0% +perfectly tuned which is not + + + align:start position:0% +perfectly tuned which is not +and that's you know properties of + + align:start position:0% +and that's you know properties of + + + align:start position:0% +and that's you know properties of +strings and the way these things are + + align:start position:0% +strings and the way these things are + + + align:start position:0% +strings and the way these things are +are played so in addition to what finger + + align:start position:0% +are played so in addition to what finger + + + align:start position:0% +are played so in addition to what finger +i use i should also decide which string + + align:start position:0% +i use i should also decide which string + + + align:start position:0% +i use i should also decide which string +to play that note on if all i'm given is + + align:start position:0% +to play that note on if all i'm given is + + + align:start position:0% +to play that note on if all i'm given is +sheet music different notes to play + + align:start position:0% +sheet music different notes to play + + + align:start position:0% +sheet music different notes to play +another thing i could guess is which + + align:start position:0% +another thing i could guess is which + + + align:start position:0% +another thing i could guess is which +string to play that note on + + align:start position:0% +string to play that note on + + + align:start position:0% +string to play that note on +so for example maybe i want to play my + + align:start position:0% +so for example maybe i want to play my + + + align:start position:0% +so for example maybe i want to play my +favorite song + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +the super mario brothers my favorite + + align:start position:0% +the super mario brothers my favorite + + + align:start position:0% +the super mario brothers my favorite +song um + + align:start position:0% +song um + + + align:start position:0% +song um +i can keep going but i actually can't + + align:start position:0% +i can keep going but i actually can't + + + align:start position:0% +i can keep going but i actually can't +keep going it won't be as impressive + + align:start position:0% +keep going it won't be as impressive + + + align:start position:0% +keep going it won't be as impressive +uh i don't actually know how to play + + align:start position:0% +uh i don't actually know how to play + + + align:start position:0% +uh i don't actually know how to play +guitar uh but the + + align:start position:0% +guitar uh but the + + + align:start position:0% +guitar uh but the +there are a lot of choices there right + + align:start position:0% +there are a lot of choices there right + + + align:start position:0% +there are a lot of choices there right +um i started with uh playing this note + + align:start position:0% +um i started with uh playing this note + + + align:start position:0% +um i started with uh playing this note +down on this um down on this string + + align:start position:0% +down on this um down on this string + + + align:start position:0% +down on this um down on this string +that's good i could have also played it + + align:start position:0% +that's good i could have also played it + + + align:start position:0% +that's good i could have also played it +on this string + + align:start position:0% +on this string + + + align:start position:0% +on this string +but that's more work for my finger so i + + align:start position:0% +but that's more work for my finger so i + + + align:start position:0% +but that's more work for my finger so i +have a diff penalty function that says + + align:start position:0% +have a diff penalty function that says + + + align:start position:0% +have a diff penalty function that says +well if i play an open string that's a + + align:start position:0% +well if i play an open string that's a + + + align:start position:0% +well if i play an open string that's a +lot easier + + align:start position:0% +lot easier + + + align:start position:0% +lot easier +and then i had a transition from here + + align:start position:0% +and then i had a transition from here + + + align:start position:0% +and then i had a transition from here +this note + + align:start position:0% +this note + + + align:start position:0% +this note +to this note to this note and if you + + align:start position:0% +to this note to this note and if you + + + align:start position:0% +to this note to this note and if you +focus on my fingering here i chose to + + align:start position:0% +focus on my fingering here i chose to + + + align:start position:0% +focus on my fingering here i chose to +use my + + align:start position:0% +use my + + + align:start position:0% +use my +index finger for the first one because + + align:start position:0% +index finger for the first one because + + + align:start position:0% +index finger for the first one because +that index finger is always the easiest + + align:start position:0% +that index finger is always the easiest + + + align:start position:0% +that index finger is always the easiest +to use + + align:start position:0% +to use + + + align:start position:0% +to use +but also gives me lots of room to move + + align:start position:0% +but also gives me lots of room to move + + + align:start position:0% +but also gives me lots of room to move +my pinky over to here + + align:start position:0% +my pinky over to here + + + align:start position:0% +my pinky over to here +and then i like to use my middle finger + + align:start position:0% +and then i like to use my middle finger + + + align:start position:0% +and then i like to use my middle finger +to come up here + + align:start position:0% +to come up here + + + align:start position:0% +to come up here +you could also use your index finger + + align:start position:0% +you could also use your index finger + + + align:start position:0% +you could also use your index finger +it's just a little bit more of a reach + + align:start position:0% +it's just a little bit more of a reach + + + align:start position:0% +it's just a little bit more of a reach +so you have to define some difficulty + + align:start position:0% +so you have to define some difficulty + + + align:start position:0% +so you have to define some difficulty +function it might depend on how + + align:start position:0% +function it might depend on how + + + align:start position:0% +function it might depend on how +big your fingers are you can do that and + + align:start position:0% +big your fingers are you can do that and + + + align:start position:0% +big your fingers are you can do that and +then optimize using these algorithms + + align:start position:0% +then optimize using these algorithms + + + align:start position:0% +then optimize using these algorithms +what is the best guitar fingering for a + + align:start position:0% +what is the best guitar fingering for a + + + align:start position:0% +what is the best guitar fingering for a +given piece + + align:start position:0% +given piece + + + align:start position:0% +given piece +one note at a time or several notes at a + + align:start position:0% +one note at a time or several notes at a + + + align:start position:0% +one note at a time or several notes at a +time you could even add in parameters + + align:start position:0% +time you could even add in parameters + + + align:start position:0% +time you could even add in parameters +like + + align:start position:0% +like + + + align:start position:0% +like +oh maybe i want to play a bar + + align:start position:0% +oh maybe i want to play a bar + + + align:start position:0% +oh maybe i want to play a bar +that's not a perfect bar but this would + + align:start position:0% +that's not a perfect bar but this would + + + align:start position:0% +that's not a perfect bar but this would +be great for my + + align:start position:0% +be great for my + + + align:start position:0% +be great for my +playing this note down here and this + + align:start position:0% +playing this note down here and this + + + align:start position:0% +playing this note down here and this +note up here + + align:start position:0% +note up here + + + align:start position:0% +note up here +bad example uh so you could do other + + align:start position:0% +bad example uh so you could do other + + + align:start position:0% +bad example uh so you could do other +things with the guitar to make it more + + align:start position:0% +things with the guitar to make it more + + + align:start position:0% +things with the guitar to make it more +interesting + + align:start position:0% +interesting + + + align:start position:0% +interesting +and you know generalize this dynamic + + align:start position:0% +and you know generalize this dynamic + + + align:start position:0% +and you know generalize this dynamic +program suitably + + align:start position:0% +program suitably + + + align:start position:0% +program suitably +but i think this gives you a flavor how + + align:start position:0% +but i think this gives you a flavor how + + + align:start position:0% +but i think this gives you a flavor how +with subproblem expansion i can capture + + align:start position:0% +with subproblem expansion i can capture + + + align:start position:0% +with subproblem expansion i can capture +almost + + align:start position:0% +almost + + + align:start position:0% +almost +any aspect of a problem that i want as + + align:start position:0% +any aspect of a problem that i want as + + + align:start position:0% +any aspect of a problem that i want as +long as the number of states that i + + align:start position:0% +long as the number of states that i + + + align:start position:0% +long as the number of states that i +need to keep track of is small i can + + align:start position:0% +need to keep track of is small i can + + + align:start position:0% +need to keep track of is small i can +just multiply the number of subproblems + + align:start position:0% +just multiply the number of subproblems + + + align:start position:0% +just multiply the number of subproblems +by that state + + align:start position:0% +by that state + + + align:start position:0% +by that state +and i can keep track of any kind of + + align:start position:0% +and i can keep track of any kind of + + + align:start position:0% +and i can keep track of any kind of +transition from one state to another + + align:start position:0% +transition from one state to another + + + align:start position:0% +transition from one state to another +which i could also do with taking the + + align:start position:0% +which i could also do with taking the + + + align:start position:0% +which i could also do with taking the +product of a graph + + align:start position:0% +product of a graph + + + align:start position:0% +product of a graph +but dynamic programming gives you a kind + + align:start position:0% +but dynamic programming gives you a kind + + + align:start position:0% +but dynamic programming gives you a kind +of methodical way to think about this + + align:start position:0% +of methodical way to think about this + + + align:start position:0% +of methodical way to think about this +by figuring out some property in this + + align:start position:0% +by figuring out some property in this + + + align:start position:0% +by figuring out some property in this +case the state of how my + + align:start position:0% +case the state of how my + + + align:start position:0% +case the state of how my +how my fingers are applied to the + + align:start position:0% +how my fingers are applied to the + + + align:start position:0% +how my fingers are applied to the +instrument + + align:start position:0% +instrument + + + align:start position:0% +instrument +and then just sort of brute forcing the + + align:start position:0% +and then just sort of brute forcing the + + + align:start position:0% +and then just sort of brute forcing the +rest a very powerful + + align:start position:0% + + + + align:start position:0% + +framework + + align:start position:0% +framework + + + align:start position:0% +framework +you \ No newline at end of file diff --git a/TbRh71BMJvw.txt b/TbRh71BMJvw.txt new file mode 100644 index 0000000000000000000000000000000000000000..556a1ba2414ad00433c4eb7acb87dc0342b2b259 --- /dev/null +++ b/TbRh71BMJvw.txt @@ -0,0 +1,1139 @@ +align:start position:0% + +let us now revisit the subject of + + align:start position:0% +let us now revisit the subject of + + + align:start position:0% +let us now revisit the subject of +expectations and develop an important + + align:start position:0% +expectations and develop an important + + + align:start position:0% +expectations and develop an important +linearity property for the case we were + + align:start position:0% +linearity property for the case we were + + + align:start position:0% +linearity property for the case we were +dealing with multiple random variables + + align:start position:0% +dealing with multiple random variables + + + align:start position:0% +dealing with multiple random variables +we already have a linearity property if + + align:start position:0% +we already have a linearity property if + + + align:start position:0% +we already have a linearity property if +we have a linear function of a single + + align:start position:0% +we have a linear function of a single + + + align:start position:0% +we have a linear function of a single +random variable then expectations behave + + align:start position:0% +random variable then expectations behave + + + align:start position:0% +random variable then expectations behave +in a linear fashion but now if we have + + align:start position:0% +in a linear fashion but now if we have + + + align:start position:0% +in a linear fashion but now if we have +multiple random variables we have this + + align:start position:0% +multiple random variables we have this + + + align:start position:0% +multiple random variables we have this +additional property the expected value + + align:start position:0% +additional property the expected value + + + align:start position:0% +additional property the expected value +of the sum of two random variables is + + align:start position:0% +of the sum of two random variables is + + + align:start position:0% +of the sum of two random variables is +equal to the sum of their expectations + + align:start position:0% +equal to the sum of their expectations + + + align:start position:0% +equal to the sum of their expectations +let us go through the derivation of this + + align:start position:0% +let us go through the derivation of this + + + align:start position:0% +let us go through the derivation of this +very important fact because it is a nice + + align:start position:0% +very important fact because it is a nice + + + align:start position:0% +very important fact because it is a nice +exercise in applying the expected value + + align:start position:0% +exercise in applying the expected value + + + align:start position:0% +exercise in applying the expected value +rule and also manipulating PMF and joint + + align:start position:0% +rule and also manipulating PMF and joint + + + align:start position:0% +rule and also manipulating PMF and joint +pmfs we're dealing with the expected + + align:start position:0% +pmfs we're dealing with the expected + + + align:start position:0% +pmfs we're dealing with the expected +value of a function of two random + + align:start position:0% +value of a function of two random + + + align:start position:0% +value of a function of two random +variables which function if we write it + + align:start position:0% +variables which function if we write it + + + align:start position:0% +variables which function if we write it +this way we are dealing with the + + align:start position:0% +this way we are dealing with the + + + align:start position:0% +this way we are dealing with the +function G which is just the sum of its + + align:start position:0% +function G which is just the sum of its + + + align:start position:0% +function G which is just the sum of its +two entries so now we can continue with + + align:start position:0% +two entries so now we can continue with + + + align:start position:0% +two entries so now we can continue with +the application of the expected value + + align:start position:0% +the application of the expected value + + + align:start position:0% +the application of the expected value +rule and we obtain the sum over all + + align:start position:0% +rule and we obtain the sum over all + + + align:start position:0% +rule and we obtain the sum over all +possible XY pairs here we need to write + + align:start position:0% +possible XY pairs here we need to write + + + align:start position:0% +possible XY pairs here we need to write +G of XY but in our case the function + + align:start position:0% +G of XY but in our case the function + + + align:start position:0% +G of XY but in our case the function +we're dealing with is just X plus y and + + align:start position:0% +we're dealing with is just X plus y and + + + align:start position:0% +we're dealing with is just X plus y and +then we weigh according to the entries + + align:start position:0% +then we weigh according to the entries + + + align:start position:0% +then we weigh according to the entries +of the joint PMF so this is just an + + align:start position:0% +of the joint PMF so this is just an + + + align:start position:0% +of the joint PMF so this is just an +application of the expected value rule + + align:start position:0% +application of the expected value rule + + + align:start position:0% +application of the expected value rule +to this particular function now let us + + align:start position:0% +to this particular function now let us + + + align:start position:0% +to this particular function now let us +take this sum and break it into two + + align:start position:0% +take this sum and break it into two + + + align:start position:0% +take this sum and break it into two +pieces one involving only the X term and + + align:start position:0% +pieces one involving only the X term and + + + align:start position:0% +pieces one involving only the X term and +another piece involving only the y term + + align:start position:0% + + + + align:start position:0% + +now if we look at this double summation + + align:start position:0% +now if we look at this double summation + + + align:start position:0% +now if we look at this double summation +look at the inner some it's a sum over + + align:start position:0% +look at the inner some it's a sum over + + + align:start position:0% +look at the inner some it's a sum over +wise while we're adding over wise the + + align:start position:0% +wise while we're adding over wise the + + + align:start position:0% +wise while we're adding over wise the +value of X remains fixed so X is a + + align:start position:0% +value of X remains fixed so X is a + + + align:start position:0% +value of X remains fixed so X is a +constant as far as the sum is concerned + + align:start position:0% +constant as far as the sum is concerned + + + align:start position:0% +constant as far as the sum is concerned +so X can be pulled outside this + + align:start position:0% +so X can be pulled outside this + + + align:start position:0% +so X can be pulled outside this +summation + + align:start position:0% + + + + align:start position:0% + +let us just continue with this term the + + align:start position:0% +let us just continue with this term the + + + align:start position:0% +let us just continue with this term the +first one and see that a simplification + + align:start position:0% +first one and see that a simplification + + + align:start position:0% +first one and see that a simplification +happens this quantity here is the sum of + + align:start position:0% +happens this quantity here is the sum of + + + align:start position:0% +happens this quantity here is the sum of +the probabilities of the different Y's + + align:start position:0% +the probabilities of the different Y's + + + align:start position:0% +the probabilities of the different Y's +that can go together with a particular X + + align:start position:0% +that can go together with a particular X + + + align:start position:0% +that can go together with a particular X +so it is just equal to the probability + + align:start position:0% +so it is just equal to the probability + + + align:start position:0% +so it is just equal to the probability +of that particular X it's the marginal + + align:start position:0% +of that particular X it's the marginal + + + align:start position:0% +of that particular X it's the marginal +PMF if we carry out a similar step for + + align:start position:0% +PMF if we carry out a similar step for + + + align:start position:0% +PMF if we carry out a similar step for +the second term we will obtain the sum + + align:start position:0% +the second term we will obtain the sum + + + align:start position:0% +the second term we will obtain the sum +over Y's it's just a symmetrical + + align:start position:0% +over Y's it's just a symmetrical + + + align:start position:0% +over Y's it's just a symmetrical +argument and at this point we recognize + + align:start position:0% +argument and at this point we recognize + + + align:start position:0% +argument and at this point we recognize +that what we have in front of us is just + + align:start position:0% +that what we have in front of us is just + + + align:start position:0% +that what we have in front of us is just +the expected value of X this is the + + align:start position:0% +the expected value of X this is the + + + align:start position:0% +the expected value of X this is the +first term plus the expected value of y + + align:start position:0% +first term plus the expected value of y + + + align:start position:0% +first term plus the expected value of y +so this completes the derivation of this + + align:start position:0% +so this completes the derivation of this + + + align:start position:0% +so this completes the derivation of this +important linearity property of course + + align:start position:0% +important linearity property of course + + + align:start position:0% +important linearity property of course +we proved the linearity property for the + + align:start position:0% +we proved the linearity property for the + + + align:start position:0% +we proved the linearity property for the +case of the sum of two random variables + + align:start position:0% +case of the sum of two random variables + + + align:start position:0% +case of the sum of two random variables +but you can proceed in a similar way or + + align:start position:0% +but you can proceed in a similar way or + + + align:start position:0% +but you can proceed in a similar way or +maybe using the action and one can + + align:start position:0% +maybe using the action and one can + + + align:start position:0% +maybe using the action and one can +easily establish by following the same + + align:start position:0% +easily establish by following the same + + + align:start position:0% +easily establish by following the same +kind of argument that we have a + + align:start position:0% +kind of argument that we have a + + + align:start position:0% +kind of argument that we have a +linearity property when we add any + + align:start position:0% +linearity property when we add any + + + align:start position:0% +linearity property when we add any +finite number of random variables the + + align:start position:0% +finite number of random variables the + + + align:start position:0% +finite number of random variables the +expected value of a sum is the sum of + + align:start position:0% +expected value of a sum is the sum of + + + align:start position:0% +expected value of a sum is the sum of +the expected values just for a little + + align:start position:0% +the expected values just for a little + + + align:start position:0% +the expected values just for a little +bit of practice if for example we're + + align:start position:0% +bit of practice if for example we're + + + align:start position:0% +bit of practice if for example we're +dealing with this expression the + + align:start position:0% +dealing with this expression the + + + align:start position:0% +dealing with this expression the +expected value of that expression would + + align:start position:0% +expected value of that expression would + + + align:start position:0% +expected value of that expression would +be the expected value of 2 X plus the + + align:start position:0% +be the expected value of 2 X plus the + + + align:start position:0% +be the expected value of 2 X plus the +expected value of 3 y minus the expected + + align:start position:0% +expected value of 3 y minus the expected + + + align:start position:0% +expected value of 3 y minus the expected +value of Z and then using the linearity + + align:start position:0% +value of Z and then using the linearity + + + align:start position:0% +value of Z and then using the linearity +property for linear functions of a + + align:start position:0% +property for linear functions of a + + + align:start position:0% +property for linear functions of a +single random variable we can pull the + + align:start position:0% +single random variable we can pull the + + + align:start position:0% +single random variable we can pull the +constants out of the expectations and + + align:start position:0% +constants out of the expectations and + + + align:start position:0% +constants out of the expectations and +this would be twice the expected value + + align:start position:0% +this would be twice the expected value + + + align:start position:0% +this would be twice the expected value +of x plus 3 times the expected value of + + align:start position:0% +of x plus 3 times the expected value of + + + align:start position:0% +of x plus 3 times the expected value of +y minus the expected value of z + + align:start position:0% + + + + align:start position:0% + +what we will do next is to use the + + align:start position:0% +what we will do next is to use the + + + align:start position:0% +what we will do next is to use the +linearity property of expectations to + + align:start position:0% +linearity property of expectations to + + + align:start position:0% +linearity property of expectations to +solve a problem that would otherwise be + + align:start position:0% +solve a problem that would otherwise be + + + align:start position:0% +solve a problem that would otherwise be +quite difficult we will use the + + align:start position:0% +quite difficult we will use the + + + align:start position:0% +quite difficult we will use the +linearity property to find the mean of a + + align:start position:0% +linearity property to find the mean of a + + + align:start position:0% +linearity property to find the mean of a +binomial random variable let X be a + + align:start position:0% +binomial random variable let X be a + + + align:start position:0% +binomial random variable let X be a +binomial random variable with parameters + + align:start position:0% +binomial random variable with parameters + + + align:start position:0% +binomial random variable with parameters +N and P and we can interpret X as the + + align:start position:0% +N and P and we can interpret X as the + + + align:start position:0% +N and P and we can interpret X as the +number of successes in n independent + + align:start position:0% +number of successes in n independent + + + align:start position:0% +number of successes in n independent +trials where each one of the trials has + + align:start position:0% +trials where each one of the trials has + + + align:start position:0% +trials where each one of the trials has +a probability P of resulting in a + + align:start position:0% +a probability P of resulting in a + + + align:start position:0% +a probability P of resulting in a +success well we know the PMF of a + + align:start position:0% +success well we know the PMF of a + + + align:start position:0% +success well we know the PMF of a +binomial and we can use the definition + + align:start position:0% +binomial and we can use the definition + + + align:start position:0% +binomial and we can use the definition +of expectation to obtain this expression + + align:start position:0% +of expectation to obtain this expression + + + align:start position:0% +of expectation to obtain this expression +this is just the PMF of the binomial and + + align:start position:0% +this is just the PMF of the binomial and + + + align:start position:0% +this is just the PMF of the binomial and +therefore what we have here is the usual + + align:start position:0% +therefore what we have here is the usual + + + align:start position:0% +therefore what we have here is the usual +definition of the expected value now if + + align:start position:0% +definition of the expected value now if + + + align:start position:0% +definition of the expected value now if +you look at this sum it appears quite + + align:start position:0% +you look at this sum it appears quite + + + align:start position:0% +you look at this sum it appears quite +formidable and it would be quite hard to + + align:start position:0% +formidable and it would be quite hard to + + + align:start position:0% +formidable and it would be quite hard to +evaluate it instead we're going to use a + + align:start position:0% +evaluate it instead we're going to use a + + + align:start position:0% +evaluate it instead we're going to use a +very useful trick we will employ what we + + align:start position:0% +very useful trick we will employ what we + + + align:start position:0% +very useful trick we will employ what we +have called indicator variables so let + + align:start position:0% +have called indicator variables so let + + + align:start position:0% +have called indicator variables so let +us define a random variable X I which is + + align:start position:0% +us define a random variable X I which is + + + align:start position:0% +us define a random variable X I which is +a 1 if the i trial is a success and 0 + + align:start position:0% +a 1 if the i trial is a success and 0 + + + align:start position:0% +a 1 if the i trial is a success and 0 +otherwise + + align:start position:0% +otherwise + + + align:start position:0% +otherwise +now if we want to count successes what + + align:start position:0% +now if we want to count successes what + + + align:start position:0% +now if we want to count successes what +we want to count is how many of the x + + align:start position:0% +we want to count is how many of the x + + + align:start position:0% +we want to count is how many of the x +i's are equal to 1 + + align:start position:0% +i's are equal to 1 + + + align:start position:0% +i's are equal to 1 +so if we add the x i's this will have a + + align:start position:0% +so if we add the x i's this will have a + + + align:start position:0% +so if we add the x i's this will have a +contribution of 1 from each one of the + + align:start position:0% +contribution of 1 from each one of the + + + align:start position:0% +contribution of 1 from each one of the +successes so when you add them up you + + align:start position:0% +successes so when you add them up you + + + align:start position:0% +successes so when you add them up you +obtain the total number of successes so + + align:start position:0% +obtain the total number of successes so + + + align:start position:0% +obtain the total number of successes so +we have expressed a random variable as a + + align:start position:0% +we have expressed a random variable as a + + + align:start position:0% +we have expressed a random variable as a +sum of much simpler random variables so + + align:start position:0% +sum of much simpler random variables so + + + align:start position:0% +sum of much simpler random variables so +at this point we can now use linearity + + align:start position:0% +at this point we can now use linearity + + + align:start position:0% +at this point we can now use linearity +of expectations to write that the + + align:start position:0% +of expectations to write that the + + + align:start position:0% +of expectations to write that the +expected value of x will be the expected + + align:start position:0% +expected value of x will be the expected + + + align:start position:0% +expected value of x will be the expected +value of x1 plus all the way to the + + align:start position:0% +value of x1 plus all the way to the + + + align:start position:0% +value of x1 plus all the way to the +expected value of x n now what is the + + align:start position:0% +expected value of x n now what is the + + + align:start position:0% +expected value of x n now what is the +expected value of x1 it is a Bernoulli + + align:start position:0% +expected value of x1 it is a Bernoulli + + + align:start position:0% +expected value of x1 it is a Bernoulli +random variable that takes the + + align:start position:0% +random variable that takes the + + + align:start position:0% +random variable that takes the +one with probability P and takes the + + align:start position:0% +one with probability P and takes the + + + align:start position:0% +one with probability P and takes the +value of zero with probability one minus + + align:start position:0% +value of zero with probability one minus + + + align:start position:0% +value of zero with probability one minus +P the expected value of this random + + align:start position:0% +P the expected value of this random + + + align:start position:0% +P the expected value of this random +variable is P and similarly for each one + + align:start position:0% +variable is P and similarly for each one + + + align:start position:0% +variable is P and similarly for each one +of these terms in the summation and so + + align:start position:0% +of these terms in the summation and so + + + align:start position:0% +of these terms in the summation and so +the final end result is equal to n times + + align:start position:0% +the final end result is equal to n times + + + align:start position:0% +the final end result is equal to n times +P this answer of course makes also + + align:start position:0% +P this answer of course makes also + + + align:start position:0% +P this answer of course makes also +intuitive sense if we have P equal to + + align:start position:0% +intuitive sense if we have P equal to + + + align:start position:0% +intuitive sense if we have P equal to +1/2 and we toss a coin hundred times the + + align:start position:0% +1/2 and we toss a coin hundred times the + + + align:start position:0% +1/2 and we toss a coin hundred times the +expected number or the average number of + + align:start position:0% +expected number or the average number of + + + align:start position:0% +expected number or the average number of +heads we expect to see will be one-half + + align:start position:0% +heads we expect to see will be one-half + + + align:start position:0% +heads we expect to see will be one-half +times 100 which is 50 the higher P is + + align:start position:0% +times 100 which is 50 the higher P is + + + align:start position:0% +times 100 which is 50 the higher P is +the more successes we expect to see and + + align:start position:0% +the more successes we expect to see and + + + align:start position:0% +the more successes we expect to see and +of course if we double n we expect to + + align:start position:0% +of course if we double n we expect to + + + align:start position:0% +of course if we double n we expect to +see twice as many successes so this is + + align:start position:0% +see twice as many successes so this is + + + align:start position:0% +see twice as many successes so this is +an illustration of the power of breaking + + align:start position:0% +an illustration of the power of breaking + + + align:start position:0% +an illustration of the power of breaking +up problems into simpler pieces that are + + align:start position:0% +up problems into simpler pieces that are + + + align:start position:0% +up problems into simpler pieces that are +easier to analyze and linearity of + + align:start position:0% +easier to analyze and linearity of + + + align:start position:0% +easier to analyze and linearity of +expectations is one more tool that we + + align:start position:0% +expectations is one more tool that we + + + align:start position:0% +expectations is one more tool that we +have in our hands for breaking up + + align:start position:0% +have in our hands for breaking up + + + align:start position:0% +have in our hands for breaking up +perhaps complicated random variables + + align:start position:0% +perhaps complicated random variables + + + align:start position:0% +perhaps complicated random variables +into simpler ones and then analyzing + + align:start position:0% +into simpler ones and then analyzing + + + align:start position:0% +into simpler ones and then analyzing +them separately \ No newline at end of file diff --git a/TcvY8Nt0ZGA.txt b/TcvY8Nt0ZGA.txt new file mode 100644 index 0000000000000000000000000000000000000000..a0682e03ef2e2d982b5b879aa4b129e7d53c8004 --- /dev/null +++ b/TcvY8Nt0ZGA.txt @@ -0,0 +1,2823 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: We want +to start talking + +about a seemingly +simple but very complex + +system in physics, the +harmonic oscillator. + +So the next part is actually +due to Professor Vladan Vuletic, + +who worked out the +topic very nicely about, + +how precisely can you +measure frequencies? + +And I don't need to +remind you that some + +of the most accurate +measurements in all of physics + +are done by measuring frequency. + +It's actually a kind +of unwritten rule. + +If you want to measure +something precisely, + +make sure that you find a +way that this quantity can + +be measured in a +frequency measurement. + +Because frequencies, +that's what we + +can measure-- with synthesizers, +with clocks, and such. + +So therefore, the question, +how precisely can you + +measure frequency, is a +question which is actually + +relevant for all +precision measurements. + +Well, we know we +have Fourier theorem. + +If you have an oscillator which +oscillates for a time delta t, + +we have the Fourier +theorem which + +says we have a finite width of +the frequency spectrum delta + +omega, or there is the spread +of frequency components involved + +in such a way that delta +omega times delta t + +is large or equal than 1/2. + +The case of 1/2 is realized +for Gaussian wave packets. + +And of course, Fourier theorem +should also-- this Fourier + +limit should remind you of +Heisenberg's uncertainty + +relation. + +Of course, Fourier limit and +Heisenberg uncertainty relation + +are related because what +Heisenberg expressed + +turns out to be simply +the limit due to the wave + +nature of matter. + +OK. + +So I brought the +clicker because I + +want you to think about some +seemingly simple question. + +The first question is whether +the uncertainty delta omega + +times delta t larger than +1/2, does this uncertainty + +hold for purely +classical systems? + +So think about it and +answer in your clicker. + +A is 1 and B-- oh, +I should say that. + +So we now assume we have a +purely classical-- you can even + +think a mechanical, +large mechanical object, + +purely classical +harmonic oscillator. + +You can observe it +for time delta t, + +or it oscillates +for time delta t. + +Can you determine its +frequency better then + +this uncertainty suggests? + +19, 20. + +Just make up your mind. + +As I said, your +responses are not + +recorded, so nothing to risk. + +OK. + +Yes. + +OK, the majority gave +the right answer. + +The situation is that +the answer is yes, + +if you have a good +signal to noise ratio. + +So what happens is, if you-- +we have to bring in the fact + +that we have noise. + +So if you have a wave formed, +there may be noise around it. + +And if you look at the spectrum, +the spectral components + +have a certain width. + +And this width, delta omega, +is given by Fourier's theorem + +by the time delta t you +had for observation. + +But as you see, you can +determine the center + +of this spectral peak with an +accuracy delta omega, which + +may be much better than the +[? width ?] delta omega. + +And the rule of +thumb is that you + +can split a line by your +signal to noise ratio. + +So typically, the +accuracy of a measurement + +is whatever the width +of the spectrum is, + +and then you can split the line +by the signal to noise ratio. + +This is called +splitting the line. + +Factor of hundred is usually +regarded as straightforward. + +But if you want to go +to larger than that, + +it becomes a challenge. + +Because even if you have a very +good signal to noise ratio, + +you really have to make sure +that you know the line shape, + +that you know that it is, +for instance, symmetric, + +and that the line center +of the observed shape + +is really where +the frequency is. + +I will give you some +examples in a few moments. + +But before that, I would like +to continue our discussion + +whether we can measure +the angle of frequency + +to better than the +Heisenberg limit + +in case of a +quantum-mechanical oscillator. + +So the question is, can +you measure the frequency + +of a quantum-mechanical harmonic +oscillator in a time delta t + +to an accuracy which is better +than the limit of Heisenberg's + +uncertainty? + +OK, your vote, please. + +All right. + +OK. + +Why don't we hold +that for a second + +and proceed to the next +question which is the same? + +But now, instead of a +quantum-mechanical harmonic + +oscillator, we take +something we are + +very familiar with-- +an optical laser-- + +and we observe a laser pulse +lasting a duration delta t. + +So same situation, but +instead of observing + +a quantum-mechanical +harmonic oscillator, + +we observe a laser pulse. + +For the laser, can we +measure the frequency + +of the optical radiation better +than this equality tells us? + +OK. + +At least people are consistent +because the first thing + +I wanted to tell you is +that, is the laser actually + +a classical harmonic oscillator +or quantum harmonic oscillator? + +Well, we use a +quantum description + +of light and the laser is +the population of photons + +in the single note of the +electromagnetic field. + +So in that sense, the +laser is fully quantum. + +But in the limit that +the laser is many, + +many photons-- and some of you +know about coherence states. + +If there's a coherent state +with a large photon number, + +the laser is actually +the classical limit + +of an electromagnetic field. + +So maybe that tells +me that the answers + +to questions 2 and question 3 +should probably be the same. + +And I want to say more about it. + +So at least in this class, +you were consistent. + +I have often seen +a big discrepancy + +in the answers between +question 2 and question 3. + +OK, so the answer is yes. + +So both for the laser-- I +first explain the laser to you, + +and then we go back to the +pure quantum system, thing + +has actually certain subtleties. + +But for the laser, +it is obvious, + +at least if I tell you +how I want to measure it, + +because I can take the +laser and create a beat + +note with another +very stable laser. + +And I record this beat +note on a photodiode. + +I can realize by making +this other laser, + +the local oscillator +stronger and stronger, + +I can create a +beat note which is + +larger and larger +and corresponds + +to a macroscopic +electric current which + +can be measured with +very high precision. + +So you can realize an +arbitrarily high signal + +to noise ratio by using a +strong local oscillator. + +And then you can actually +say the photocurrent, which + +comes out of the +photodiode, is actually-- + +you can regard this microscopic +current as purely classical. + +And then of course, the answer +to the first question applies. + +So that takes care of question +3 by mapping it actually + +on question 2. + +But now by saying +that the laser also + +has a quantum-mechanical limit +and I'm not changing anything, + +we realize that probably +the answer to question 2 + +should also be yes. + +So let's, therefore, +ask our self, what + +is the situation when the +Heisenberg uncertainty + +relation applies? + +Well, one is we have +to be really careful. + +It predicts the outcome +of a single measurement + +on a single quantum system. + +Let me write that down. + +Or if the Heisenberg +uncertainty relation + +sets a limit, how well we +prepare a quantum system. + +It's about a single +quantum system, + +and then we perform +a single measurement. + +So in a sense, if +we would say all + +you have is a single photon, +which is a very special quantum + +system. + +You have a single +photon and you measure + +the frequency of the +photon only once. + +Then your will find the limit, +which is the Heisenberg limit. + +You cannot, with a single +measurement on a single photon, + +determine the accuracy of the +frequency better than this. + +And of course, you can +get higher accuracy + +by doing repeated measurements +or by using many photons. + +We talk about it more in 8.422, +but I just want to remind you, + +if you have n +uncorrelated photons. + +In other words, we +perform n measurements + +on n different objects, then +the signal to noise ratio + +is-- just by Poisson +distribution, square root n. + +And therefore, the +resolution for the frequency + +of the photons is better than +the Heisenberg or the Fourier + +limit by 1 over +the square root n. + +Some of you-- and actually, +in Professor Vuletic's group, + +there is research on it that +if you have correlated-- well, + +in his case, correlated atoms. + +But if you had +correlated photons, + +then you can even do better. + +You can reach what is sometimes +called the Heisenberg limit + +where you are better +than the limitation + +given by Fourier's theorem or +by the Heisenberg uncertainty + +relation by a factor of 1/n. + +OK. + +So as far as the question 2 +where the quantum harmonic + +oscillator is +concerned, we would + +say the answer is +yes, if you have + +is single photon at +frequency omega 0, + +which interacts with the +quantum harmonic oscillator + +at frequency omega 0. + +However, the answer +would, even in that case, + +be no if you have +harmonic oscillator levels + +and you take a photon and +by a nonlinear process + +excite the n-th level. + +So you have a single photon now. + +You can resolve the energy +delta E of this level. + +A single photon, +a single quantum + +object, you can +define the energy-- + +that's Heisenberg's +uncertainty relation. + +The energy is determined +to that precision. + +But your frequency omega +of the optical pulse + +is n times omega 0 +using nonlinear process. + +And then you can determine +the frequency of the harmonic + +oscillator, even +for a single quantum + +system and a single +photon with a precision + +which is 1/n times better. + +So you have to be +also careful, but I + +don't want to beat +it to death now, + +to distinguish between the +accuracy at which Heisenberg's + +uncertainty relation +maybe limits + +the measurement of +an energy level. + +And how this is related +to the frequency + +of the harmonic oscillator. + +And by going sort of +immediately to the n-th level, + +you can, of course, measure +the distance between two levels + +more accurately because you +have increased your [INAUDIBLE]. + +Any questions? + +AUDIENCE: Sorry, I just +got a little confused + +about when yes means one +thing and no means one thing. + +So you're saying that you can +beat the uncertainty relation + +in questions 1, 2, and 3 +if you can put it in a way + +where you get good +signal to noise? + +PROFESSOR: OK, I gave you-- +sorry for being complicated, + +but the physics is complicated. + +I try to give it to you +in different layers. + +I first looked at +the classical limit, + +which is pretty clear-cut. + +Then, I used a laser. + +The laser has a +classical limit where + +the answer is the same as +in the classical limit. + +But then we can talk +also in the laser + +in the limit of single photons. + +And then I said, OK, the +single photon interacting + +with a single +quantum system, this + +is really when it is quantum. + +And if you have a two-level +system and you [INAUDIBLE] + +it with a single +photon, then you + +can make a measurement which +is limited by this inequality. + +But then I said +there is a caveat. + +And this is if you bring +in a nonlinear process. + +So if your bring in a nonlinear +process, we can go up n steps. + +We can drive-- we can, +by some nonlinearity, + +drive the harmonic oscillator +from the ground state + +to the n state. + +Then, everything we have +said about a single photon + +and the measurement of +the resonance and such + +applies to this photon. + +But the energy level of +the harmonic oscillator + +has now been measured with +n times higher precision + +because we can divide by n. + +So the answer is yes, yes, then +quantum mechanics we cannot + +make it more accurate +unless we pull some tricks. + +And nonlinear physics +would be a trick. + +So in general, the +situation where you really + +limit it by this inequality +where your precision is limited + +would really only apply to a +single photon, a single quantum + +physics, and linear physics. + +Other questions? + +AUDIENCE: Yes. + +Maybe just the phrasing. + +AUDIENCE: What does delta +t mean for a single photon + +measurement? + +PROFESSOR: Delta t +could be the time + +you allow yourself to +make the measurement. + +You have a +measurement apparatus. + +You switch it on, +you switch it off. + +Eventually, you want to +get out of grad school. + +I mean, you don't want to take +an infinite amount of time + +for the measurements. + +There's always a +window, delta t, + +and there's a fundamental limit. + +The duration of the measurement +limits the precision + +of the measurement. + +OK. + +The next thing I want to +discuss is the analogy, but also + +the differences between +a harmonic oscillator + +and a two-level system. + +So what is a two-level system? + +Well, it's a system +with two levels. + +What is a harmonic oscillator? + +Well, it's a system which +has an infinite number + +of equidistant levels. + +I will tell you tell you +later in this course when + +we talk about the AC +and DC stark effect, + +you talk about the +polarizability and light + +scattering that you can regard +the atom or the electron + +in the atom as a +harmonic oscillator. + +An atom scatters light +exactly in the same way + +as the charge which is connected +to some support structure + +with a spring. + +How an oscillating charge +would scatter light? + +Well, you know of course, the +atom is a two-level system. + +And the sort of model I make +for the electron as a harmonic + +oscillator at a single +resonance frequency, which + +is 100% exact in the limit +of [? low ?] laser power. + +Well, this realize is +a harmonic oscillator. + +So therefore, what I'm +telling you by this example, + +that there are situations +where a two-level system + +and a harmonic +oscillator are the same. + +Or, create the same +[? observance, ?] + +create the same physics. + +Do you have any idea when the +two systems may look the same + +or when the two systems +react exactly in the same way + +to, for instance, +external radiation? + +AUDIENCE: At very +low temperatures? + +PROFESSOR: At very +low temperature? + +Well-- + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes. + +Well, we assume these +are atoms and we always + +start in the common state. + +So let's assume we +have 0 temperature. + +We have an atom. + +And maybe what I'm asking is, +if I excite the atom and I said, + +there may be a situation where +the atom is a two-level system + +but it reacts like a +harmonic oscillator, + +when does it break down? + +AUDIENCE: When the [INAUDIBLE]. + +PROFESSOR: Exactly. + +When we go beyond +the perturbative + +limit when we use a +strong excitation. + +So in other words-- and I +like to give you the answer + +before I give you the full +explanation, which now comes. + +If you start out in +the ground state, + +you can see at 0 temperature, we +have mainly all the population + +there. + +If you start now +driving the system, + +we put-- and I will say a +little bit more about it. + +A little bit into +the excited state. + +But it is the nature of a +harmonic oscillator when + +you put something +into the excited state + +that immediately a little bit +goes into the second excited + +state. + +And this is, of course, +something which you can only do + +in a harmonic oscillator but +you cannot do in a level system. + +So to the extent that +we have weak excitation + +and we can neglect the +excitation in higher levels. + +To that extent, a two-level +system and harmonic oscillator + +are identical. + +Actually, what I'm +saying appears trivial, + +but I really want you +to think about it. + +It's actually a very +profound statement. + +When can you describe a +quantum-mechanical system + +as a harmonic oscillator? + +For weak excitation +when all what matters + +is that you have put a +small fraction of the system + +into the first excited state. + +And you immediately realize that +the feature which distinguishes + +a two-level system from +a harmonic oscillator + +is the phenomenon of, +let's say, saturation. + +You cannot go higher. + +If you do not saturate +a two-level system, + +it behaves like a +harmonic oscillator. + +And therefore, it behaves +completely classical. + +OK, let's work that +out a little bit. + +I'll give you some examples. + +So the phenomenon of a two-level +system is it has saturation. + +The maximum energy you +can put in is one quantum. + +Whereas, a harmonic oscillator +can never be saturated. + +Just think of the harmonic +oscillator potential parabola. + +You can drive the system +as high as you want. + +So you can go in this +classical language + +to arbitrarily large amplitudes. + +So what I just mentioned +where the equivalence holds-- + +I always want you to +have an example in mind-- + +is the Lorentz model for an +atom where you describe the atom + +as an electron connected +with a spring to the nucleus. + +And as we will see +in a few weeks, + +this model gives the +identical answer, + +identical to the +quantum-mechanical treatment + +for probabilities like +the polarizability + +and the index of refraction +for gas of atoms or molecules. + +So if you have a +two-level system, + +we can often think we have +an s, ground state, and then + +p, excited state. + +And if you do a +weak excitation, we + +have sort of a wave +function, which is all, + +lets say, positive +one side-- one sign. + +And then we [INAUDIBLE] +a p orbital, + +which has a note which +is positive and negative. + +And now we have the +positive-negative + +and the positive and the-- +there is the resonance + +frequency between the two. + +And that together results +in an oscillating dipole. + +So the simple model +of superimposing + +an s state and a p state +at a certain frequency + +gives us an oscillating +dipole, which + +is the realization of +a harmonic oscillator. + +But the harmonic +oscillator, it oscillates. + +And this is, of course, +valid for sufficiently small + +excitation. + +So the question we +have already addressed + +in the discussion, +what is small? + +So "small" means population +of higher-excited states + +is negligible. + +So in other words, as long as +the excitation of the first + +excited state is small, then +we can neglect the excitation + +in the second excited state, +which is even smaller. + +So let me kind of bring +out the difference + +between a two-level system +and a harmonic oscillator + +a little bit more by discussing +the situational of cavity QED. + +Let's assume we want 100% +population in the first excited + +state. + +If you have a +harmonic oscillator + +and the system is prepared +in the first excited state, + +this is also called Fock state +with one quantum of excitation. + +And it's a rather special state +where people have worked hard + +to generate it because you +cannot realize it in a harmonic + +oscillator. + +And let me sort of explain +that in the following way. + +If you have a +harmonic oscillator, + +you start and you +would drive it. + +And you try to put 100% +in the n equals 1 state. + +Before you have accumulated +100% in the n equals 1 state, + +you drive it already +to higher states. + +And of course, you +know when you start + +driving a harmonic +oscillator, classical + +or quantum-mechanically, you +create a coherent state, which + +is a superposition +of excited states. + +So we would say an n equals +1 state cannot be excited. + +We usually get a +coherent state, which + +is a superposition of many, +or at least several, states. + +Whereas in a +two-level system, we + +can just do a [INAUDIBLE] pulse. + +And to put all the atoms +in the excited state + +is nothing special. + +Whereas, to have a cavity +filled with photons + +and selectively excite +the n equals 1 state, + +this is special +because it's not easy. + +It's not straightforward. + +So in cavity QED, +you can do it if you + +have anharmonicities +or nonlinearities. + +So let me explain that. + +Well, it's an anharmonicity +or some form of-- so + +if you have a +situation where you + +have your harmonic oscillator, +but the energy levels + +are not equidistance. + +So the difference between this +first and second excited state + +are not the same, then +you can drive the system. + +You can prepare Fock +state in n equals + +1 like in a two-level system. + +And you're out of resonance +to drive it to higher states. + +So here, what you utilize is +a sort of two-level system. + +And that allows you to create +those special state which + +are regarded as +non-classical, very + +special states of the +harmonic oscillator. + +And one way how you +can create it-- well, + +if you have an empty +cavity, each photon + +has the same energy. + +Then you have an equidistant +harmonic oscillator. + +But if you put, for instance-- +you add an atom to the cavity, + +and the radiation is +interacting with the atom, + +then you'll get-- we'll +talk about it later. + +The atom and the photons +interact with the Rabi + +frequency, and then +you get a splitting, + +called the normal +mode splitting. + +And this level splitting +is proportional to the Rabi + +frequency. + +And we'll discuss it +later, but many of you + +know that the Rabi +frequency scales + +with the square root +of the photon number. + +So therefore, you +have a splitting + +which is proportional to +square root 1, square root + +2, square root 3. + +And you have a spectrum +which is no longer + +an equidistant system. + +And then you can create +non-classical states + +of the photon field, +non-classical states + +of a harmonic oscillator. + +So anyway, I thought I +wanted to bring it up + +at the beginning of the +class, because a lot what + +we are discussing +in this class is + +we'll rediscover in +many situations-- + +in atoms, in the +light, in the way how + +light and atoms interact, +harmonic oscillators + +and two-level systems. + +Often, I say they are the same. + +They behave in the same way. + +But I hope this introductory +[? mark ?] tells you, when can + +you think in one +limit and when do you + +have to apply the other limit? + +Any questions about that? + +Yes, Nancy. + +AUDIENCE: So are we saying +here that without changing + +the [INAUDIBLE] of the +harmonic oscillator, + +we cannot use it as a +harmonic oscillator? + +Like [INAUDIBLE]? + +Because when you put an atom +in that [INAUDIBLE] changed, + +it was no more a +harmonic oscillator. + +The levels changed. + +PROFESSOR: Maybe +all I'm saying is + +this is a pure +harmonic oscillator. + +And in a pure +harmonic oscillator, + +I think it's-- I don't +know a proof of it, + +but it seems impossible to +prepare a system in the first + +excited state because every +attempt to put an excitation + +into the system would +carry it higher up. + +You would create a wave packet. + +You would create +a superposition. + +So you have to do some thing. + +You have to break the +degeneracy of the spectrum + +of the harmonic oscillator. + +Of course, what you can do +is you can put in an atom. + +You can use the atom as an +aid to just put in exactly one + +photon into your cavity, and +then you can remove the atom. + +Then you are back to an +ideal harmonic oscillator, + +but you have overcome +the limitation + +of the harmonic oscillator +in preparing certain states. + +Another take-home message you +may take from this discussion + +is harmonic +oscillators-- yes, we + +have quantum +harmonic oscillators. + +But even the quantum +harmonic oscillator + +follows a classical description. + +So the real quantumness-- what +makes quantum optics quantum + +optics and cavity QED a +wonderful example of quantum + +physics is the physics +embedded in a two-level system. + +That we can put one quantum +excitation into something, + +exactly one is as much +quantum as you can get. + +This is realized in +a two-level system + +and this is related to the +phenomenon of saturation. + +You can saturate a +two-level system, + +but you cannot saturate +a harmonic oscillator. + +So with that, let me +make the transition + +to another simple system. + +And we want to spend +some time on it. + +And these are rotating systems. + +So a system which rotates. + +Well, what do you think? + +Will it behave, using +the discussion we just + +had, more like a +classical system + +or more like a +quantum-mechanical system? + +Of course, I gave you a +very special definition. + +What brings out quantum +mechanics in a system? + +The harmonic oscillator +is always linear. + +You can drive it as +hard as you want. + +You drive it hundred +times stronger + +and the reaction is +hundred times more. + +Everything is linear. + +The quantumness of a two-level +system comes from saturation. + +What about a rotating system? + +Something which +can go in a circle. + +AUDIENCE: [INAUDIBLE]. + +So you're not going to have +this degeneracy [INAUDIBLE]. + +PROFESSOR: OK, very good. + +You're immediately applying +what is the spectrum. + +The spectrum is not +equidistant, so it + +should bring in a difference. + +It's sometimes hard to +ask a simple question + +without giving the answer away. + +But what I had in +mind was a gyroscope, + +a gyroscope which is precessing. + +And what I wanted +to sort of lead you + +with the question is, if you +have something which rotates, + +the amplitude is limited. + +A rotating object, let's assume +a magnetic, classical magnetic + +moment. + +It can have a precession +angle which is 180 degrees, + +but that's a maximum. + +In other words, the rotating +system when you excite it + +has a maximum amplitude, +exactly as a two-level system. + +So that's what a rotating +system and a two-level system-- + +actually then, I'm +now specializing + +on more rotating gyroscope. + +If you have a free +rotator, this, of course, + +can rotate with [INAUDIBLE] +angular momentum + +and the excitation spectrum +would not be bound. + +So I think I have to rephrase +the question the next time + +I teach the class. + +I wanted to ask you here about +a special rotating system, which + +is a precessing gyroscope. + +So rotating system. + +If you think about +precessing gyroscope, + +it has a bound on the +amplitude it can be excited. + +So what I want to show you, +today and in the next lecture, + +is the motion of classical +magnetic moments. + +When you think about the motion +of classical magnetic moments, + +think about a compass +needle, a magnetized needle + +which has angular momentum. + +And then, the system is acted +upon with a magnetic field. + +So this is our system. + +And if angular momentum, +magnetic moments, and torque + +come into play, we have the +physics of classical rotation. + +But the excitation +spectrum here is limited + +because you can flip +a compass needle + +and this is a +maximum excitation. + +When the North Pole points in +the opposite direction, that's + +the maximum excitation +you can give it. + +So therefore, it has a limited +amplitude of its excitation, + +unlike a harmonic oscillator. + +And at this point you may +say, but maybe somewhat + +similar or analogous +to a two-level system. + +But the surprising +result is-- at least + +it was surprising when I +first learned about it. + +That it's not just +somewhat analogous + +to a two-level +system, it actually + +captures exactly a +lot of the properties + +of the dynamics of +a two-level system. + +So let me write that down. + +The motion of classical magnetic +moments provides a model. + +It's actually an +exact model which + +captures essentially +all features + +of the quantum mechanical +two-level system. + +I want to show you today and +the next lecture the concepts + +or Rabi frequency, of +generalized of resonant Rabi + +frequency, all of that you +find in the classical motion + +of a magnetic moment. + +Or, for instance, the +physics of rapid [INAUDIBLE] + +following, [INAUDIBLE]. + +A lot of physics +we would usually + +associate with the +quantum system, + +we find it here in a +purely classical system. + +What aspects of the two-level +system will we not find? + +Any ideas? + +Will? + +AUDIENCE: Spontaneous emission? + +PROFESSOR: Spontaneous +emission, definitely. + +Yes. + +But actually, in a +two-level system, + +in a quantum-mechanical +two-level system, which + +we drive with a +single frequency, + +spontaneous emission +is also missing. + +Spontaneous emission, as +we will discuss later, + +only comes into play when we say +the excited state of the system + +interacts with many, +many modes and not just + +the one mode we apply. + +And typically, if you +go to high frequency, + +we have an optical oscillator, +we cannot avoid spontaneous + +emission. + +Whereas, for a +quantum-mechanical spin 1/2 + +interacting with microwaves, +we can completely + +eliminate spontaneous emission. + +So spontaneous +emission, I would say, + +comes into play +at high frequency. + +So that's correct. + +But there is one aspect +even at low frequency, + +one aspect of quantum mechanics +which we cannot capture. + +AUDIENCE: Having different +G in a magnetic field? + +PROFESSOR: Different +G factors, yes. + +That's, as we see, a +more quantitative aspect. + +But there is one very important +feature about quantum mechanics + +you will never get in +a classical system. + +AUDIENCE: Spin? + +PROFESSOR: Spin. + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: OK. + +I think you're skirting around. + +It's a quantum measurement +process and projection. + +If you perform a measurement +on a compass needle, + +it can be at any angle. + +But if you do a measurement +on a quantum system, + +you do a projection. + +After the measurement +projects a system + +in either spin up or spin down. + +So the probabilistic +nature, the projection + +occurring in a +quantum measurement + +is, of course, absent +in a classical system. + +But when you say spin +1/2 and quantum levels, + +this is sort of implied in it. + +If there are only two levels, +there's only up and down + +and not an infinite +number of angles. + +So what we will actually see is +that we find an exact analogy + +between the classic system and +the quantum mechanical system + +when we compare +expectation values. + +But the individual measurement, +the individual quantum + +measurement because it is +projective is different. + +OK, with that +motivation, we are now + +talking about +magnetic resonance. + +And we will later do a fully +quantum mechanical description, + +but to get the concepts and +also understand the analogies + +to a classical system, +we want to understand + +what happens when we have +a classic magnetic moment + +in magnetic fields. + +And that includes static +fields, but then we + +want to excite the system. + +We want to drive the system, +and this is time-varying fields. + +And we will assume that the +fields are spatially uniform. + +So let me just remind you of +the obvious equations of motion + +that also allows me to +introduce the nomenclature. + +The interaction energy between +a classical magnetic moment + +mu and the magnetic +field is mu dot B. + +The force is the gradient +of the interaction energy, + +but it is 0 for uniform fields. + +So therefore, we don't +need to look at the force. + +But the next thing which we then +have to consider is the torque. + +And when we think about the +classical magnetic moment, + +you can think about +a compass needle. + +But magnetic materials +are complicated. + +If I think about the +simplest magnetic moment, + +I think about a loop of +current I and area A. + +And that's sort of the classical +model for magnetic moment. + +So we have a magnetic moment mu. + +And if we now add a magnetic +field, which is at an angle, + +we have a torque. + +But just to make +sure the torque is + +something which is nothing +else than the Lewin's + +force on the electrons. + +But since electron is +forced to go in a circle, + +we don't have to look at the +Lewin's force microscopically. + +We just immediately +jump to the torque. + +And the torque is what describes +the dynamics of the system. + +So we have torque. + +When we have torque, we want +to formulate the problem + +in terms of angular momentum. + +And our equation of motion +is the classical equation + +of motion that the derivative +of angular momentum + +is given by that. + +Now, what makes those equations +immediately solvable-- + +and to find the +very easy limit is + +that the magnetic moment +of the system we assume + +is proportional to +its angular momentum. + +Well, if you have a +mechanical object which + +goes in a-- if you have a +charged object which circles + +around a central potential, +then you, of course, + +find immediately that +if it moves faster, + +it has more angular momentum. + +It has a larger magnetic moment. + +So we use that as the +defining equation for what + +is called the +gyromagnetic ratio. + +Which, of course, is +very closely related + +to G factors, which we +define later on for atoms. + +The gyromagnetic ratio is the +ratio between magnetic moment + +and angular momentum. + +And then, we find that the +derivative of angular momentum + +is given by this equation. + +And this is now +an equation which + +you have seen in +classical mechanics + +and in many situations. + +The solution of that +is a pure precession. + +The motion is pure precession +of the angular momentum + +around the axis of +the magnetic field. + +So in other words, we have the +axis of the magnetic field. + +We have the angular momentum. + +And at a constant +tipping angle, we + +have the tip of the +angular momentum + +precesses around +the magnetic field. + +And the precession happens +with an angular frequency + +which is called the +Larmor frequency. + +The Larmor frequency, the +frequency of precession, + +is proportional to +the magnetic field + +and the gyromagnetic ratio. + +So let me give you an +example for an electron. + +The gyromagnetic ratio is 2 pi +times 2.8 megahertz per Gauss. + +And we've discussed +last class what + +it means when I take out 2 pi. + +Because the Larmor frequency +is an angular frequency. + +And angular frequency +is not measured in Hertz + +because there is a 2 pi factor. + +And I just make it obvious +where the 2 pi factor is hidden. + +Now, this is for the electron. + +But if you have an ensemble +of classical charges, + +an [INAUDIBLE] distribution +of classical charges-- + +well, with the same +charge to mass ratio, + +you find that the gyromagnetic +ratio is 1/2 of that. + +And this here is +the Bohr magneton, + +which we will use quite +often in this course. + +The third example is the proton. + +The proton is heavier, +has a heavier mass. + +About 1,000 times heavier +than the electron. + +And therefore, the +Larmor frequency is not + +megahertz per Gauss, it +is kilohertz per Gauss. + +Any questions? + +These are more definitions +and setting the stage. + +Let me make a note. + +It's one of the +many notes I will + +make in this course +about factors of 2. + +There are factors of 2. + +If you miss it, you +qualitatively miss the physics. + +And let me in that +context by talking + +about precession frequencies +and magnetic moment, + +explain a factor of +2 which is related + +to the G factor of the electron. + +So if you have the electron +which has spin of 1/2, + +in units of the +Bohr magneton, what + +is the magnetic moment +of the electron? + +1/2, 1, or 2? + +What is the magnetic +moment of the electron? + +1/2, 1, or 2? + +AUDIENCE: 2. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I should have a +clicker question on there. + +No. + +It's 1. + +1 Bohr magneton. + +And let me sort of show +the level structure of it. + +This is [INAUDIBLE] energy. + +You have spin up and +you have spin down. + +The difference is 2.8 +megahertz per Gauss. + +And if you ask, what is +the precession frequency + +of an electron in +a magnetic field? + +It's 2.8 megahertz if +the field is 1 Gauss. + +And if you want to +drive the rotation, + +if you want to change the +precession angle-- we'll + +talk about that +in great detail-- + +you better drive the +system at 2.8 megahertz. + +But 2.8 megahertz is the +difference of plus 1.4 + +and minus 1.4. + +And therefore, the energy of +the electron in a magnetic field + +is either plus or minus +1.4 megahertz per Gauss, + +and 1.4 is 1 Bohr magneton. + +The magnetic moment of the +electron is 1 Bohr magneton. + +So precesses at 2.8. + +OK, but let us contrast this +with a classical current + +distribution, which has +1 unit of h bar, which + +means the magnetic moment +is 1 Bohr magneton exactly + +as the electron has. + +Well, quantum +mechanically means it + +has three different +level-- minus 1, + +[INAUDIBLE] 0, and 1 because it +has 1 unit of angular momentum. + +Since the system has +1 Bohr magneton, when + +the system stands +up or stands down, + +the difference between +spin up and spin down + +is 2.8 megahertz per Gauss. + +OK, my question now is, what +is the precession frequency + +of this classical charge +distribution which + +has 1 unit h bar of +angular momentum? + +And I've just shown you +the level structure. + +If you will now create a +wave packet of those three + +levels, which means-- a wave +packet of the three levels + +means you have a spin which +points in one direction. + +What is the precession +frequency of that system? + +Let's have a clicker question. + +So what is the +precession frequency? + +Oops, what happened? + +So let me give +you three choices. + +2.4, 1.4, or 0.0 +megahertz per Gauss. + +So please vote for A, B, or C. + +Yes, it's 1.4. + +So they have the +same magnetic moment. + +Quantum mechanically, you would +see here is a G factor of 2. + +Here's a G factor of 1. + +But the easiest explanation +is it precesses. + +The precession is a beat note +between two energy levels. + +Here, you have the beat note +between those two energy + +levels happens at 1.4 megahertz. + +Therefore, when you +want to drive it + +with an external +radiation, you have + +to drive it at 1.4 megahertz. + +You want to drive +it level by level. + +Whereas, this system has a +beat note between two levels, + +and the difference +is 2.8 megahertz. + +Anyway, whenever you get +confused about factors of 2 + +with magnetic moment +and precessing system, + +just think about those +two simple examples. + +They have all the factors of 2 +hidden in the simplest example + +possible. + +All right. + +We have a rotating system. + +have a system which precesses. + +So we want to learn about +rotations in general. + +And what I want to +show you is that + +under very general +circumstances, + +we can solve the equation, +the dynamics of the system, + +by going into rotating frame. + +You all know about +rotating wave [INAUDIBLE] + +rotating wave approximations +that's in quantum physics. + +I'm simply talking +about a classical system + +and I want to +solve the equations + +for the classical system +by going to rotating frame. + +And I want to show you where +this is exact and where not. + +OK, so this is +actually something + +which we do in undergraduate, +in 8.01-- definitely, in 8.012. + +But let me remind you when we +have a rotating vector which + +rotates with a constant +angular frequency, + +then the time derivative of the +vector is the cross product. + +But now we want +to allow-- so this + +is when the vector is +constant and it just rotates. + +But now, we want to assume +that there is something else. + +There is an arbitrary +time dependence + +of the vector in +the rotating frame. + +So we have a vector +which changes + +according to A dot [INAUDIBLE]. + +But it also rotates. + +And that means-- +and this is exactly + +shown in classical mechanics +that in the inertia frame, + +the time derivative +is the sum of the two. + +It is the change of the +vector in the rotating + +frame plus omega cross A. +So it has this equation. + +Has the simple +two limiting cases + +that if there is no change +in the rotating frame, + +then we retrieve the +kinematics of pure rotation. + +When our rotating +frame is not rotating + +or it rotates at 0 angular +frequency, then of course + +the two time derivatives +are the same. + +But anyway, what I derived for +you is an operator equation + +that the time derivative +in the rotating frame + +is related to the time +derivative in the inertia + +frame in this way. + +And now we want to apply it +to our angular momentum L dot. + +So this is just applying +the operator equation + +to our angular +momentum L. And now + +we want to specialize +that-- we just + +discussed that the +time [INAUDIBLE]. + +I'm just looking +for a sign problem, + +but it's sometimes hard to fix +sign problems at the board. + +The creation of motion +for the angular momentum + +was that it's L cross gamma B. + +Oh, I changed the order. + +There is no sign problem. + +And then, I add this. + +So if we now describe +our precessing, + +classical magnetic moment, +which has the equation of motion + +that L dot is L cross +gamma B, if you describe it + +in a rotating frame, then +the equation of motion + +gets modified as follows. + +Now, what happens is we-- +let me factor out the gamma. + +Gamma L cross B +is the real field. + +So what we observe +is that when we + +go into a rotating +frame-- and this + +is exact-- that the real +magnetic field gets replaced + +by an effective magnetic field. + +Because there is an +extra term added to it, + +which we can call a +fictitious magnetic field. + +So this is just an +exact transformation + +of our equation of +motion for a precessing + +system into the rotating frame. + +And now, of course, we +haven't made any assumptions + +what the rotating frequency is. + +But if you would choose +the rotating frequency + +to be the Larmor frequency +minus gamma times B, + +then our effective +magnetic field vanishes. + +And then we know, because +there is no magnetic field, + +that the angular momentum is +constant in the rotating frame. + +In other words, the +dynamics of the system + +means that L is constant +in a rotating frame. + +And if you want to know what +happens in the original, + +in the [? lab ?] frame, +in the inertial frame, + +we just have to rotate back. + +OK, that's something we +want to take advantage of. + +But we fully apply +it in the next class. + +I have only a few +minutes left today, + +and I want to spend +those few minutes to talk + +about another factor of 2. + +Now, let me ask +you the following. + +If you have an electron +in a magnetic field, well, + +you know that the +electron goes in circles. + +It's the cyclotron +motion of the electron. + +Now, just give me one second. + +I forgot to mention something +for the classical system. + +For a classical +charge distribution, + +the Larmor frequency is +the charge of the particle. + +In case of the electron, it's e. + +Divided by 2m times B. +So the Larmor frequency + +is e over 2m times B. + +So therefore, we +know that when we + +have an [INAUDIBLE] of +positive and negative charges, + +and there is an effective +magnetic moment, + +that this magnetic moment +would precess at the Larmor + +frequency which is given +by this expression. + +So who knows what the frequency +of the cyclotron motion is? + +So when we have a +free electron, what + +is the frequency at +which it revolves? + +At which it goes in circles? + +AUDIENCE: 2 times +the Larmor frequency. + +PROFESSOR: It's two times +the Larmor frequency. + +OK, I just wanted to mention it. + +There's an important factor of +2 which you should know about. + +In previous classes, I +spent 10 or 20 minutes + +to teach you about +a few of them which + +is called Larmor's theorem. + +But I summarized the argument +on the atomic physics wiki + +and I can't say +more here in class + +than I've written on the wiki. + +So please read on our +atomic physics wiki + +about Larmor's theorem. + +Larmor's theorem shows you +that under certain assumptions, + +you can transform away the +effect of a magnetic field + +by going to the +Larmor frequency. + +That looks exactly like +what we have discussed here. + +But what we discussed +here was exact. + +There was no approximation. + +Whereas, the derivation +of Larmor's theorem, + +which talks about +charge distributions-- + +not about magnetic moments, +about charge distributions-- + +has to make certain +approximations. + +So just want to +point your attention + +to that there are two +derivations about Larmor + +frequency. + +One is exact, which +I gave to you. + +There is another one which +is Larmor's theorem, which + +applies to isolated +charges which is not exact. + +But they both conclude +that you can transform away + +the effect of a +magnetic field by going + +to rotating frame at +the Larmor frequency. + +And the fact that Larmor's +theorem is not exact + +is actually illustrated by +this example of a free electron + +where you have a factor of 2. + +And this comes +because the term which + +you neglect when you +derive Larmor's theorem + +is negligible if +the situation is + +that you have electrons +and charges forming + +magnetic moments. + +But if you have a free +electron, the neglected term + +is exactly 1/2 of +the dominant term. + +And that is why the +cyclotron frequency is twice + +about Larmor frequency. + +So never confuse the cyclotron +and the Larmor frequency. + +And the factor of +2 is not related + +to a G factor of the +electron or such. + +It's really the difference +between the physics + +of a free charge and the +physics of a magnetic moment. + +Any questions? + +OK, well, then we are +finished for today. + +A reminder, no class +on Wednesday, but we + +have class on Friday in +the different classroom. \ No newline at end of file diff --git a/UcWsDwg1XwM.txt b/UcWsDwg1XwM.txt new file mode 100644 index 0000000000000000000000000000000000000000..6cc650437c91ae12c8c3b2207769592a758a7918 --- /dev/null +++ b/UcWsDwg1XwM.txt @@ -0,0 +1,1431 @@ +PROFESSOR: Hi, I'm Gilbert +Strang, and this is the very + +first in a series of videos +about highlights of calculus. + +I'm doing these just because +I hope they'll be helpful. + +It seems to me so easy to be +lost in the big calculus + +textbooks and the many, many +problems and in the details. + +But do you see the +big picture? + +Well, I hope this will help. + +For me, calculus is about the + +relation between two functions. + +And one example for those two +functions, one good example, + +is function 1, the distance, +distance traveled, what you + +see on a trip meter in a car. + +And function 2, the one that +goes with distance, is speed, + +how quickly you're going, how +fast you're traveling. + +So that's one pair +of functions. + +Let me give another pair. + +I could get more and more, but +I think if we get these two + +pairs, we can move forward. + +So in this second pair, +height is function 1, + +how high you've climbed. + +If it's a graph, how far the +graph goes above the axis. + +Up, in other words. + +So that's height, and then +the other one tells you + +how fast you climb. + +The height tells how +far you climbed. + +It could be a mountain. + +And then the slope tells you how +quickly you're climbing at + +each point. + +Are you going nearly +straight up? + +Flat? + +Possibly down? + +So distance and speed, height +and slope will serve as good + +examples to start with. + +And let me give you some +letters, some algebra letters + +that you might use. + +Distance, maybe I would +call that f of t. + +So f for how far or for +function, and the idea is that + +t is the input. + +It's the time when you're +asking for the distance. + +The output is the distance. + +Or in the case of height, +maybe y of x would + +be the right one. + +x is how far you go across. + +That's the input. + +And at each x, you have an +output y how far up? + +So f is telling you how far. + +y is telling you the +height of a graph. + +That's function 1, two examples +of function 1. + +Now, what about slope? + +Well, luckily, speed and slope +start with the same letter, so + +I'll often use s for the speed +or the slope for this second-- + +oh, it even stands for +a second function. + +But let me tell you +also the right-- + +the official-- + +letters that make the connection +between function 2 + +and function 1. + +If my function is a function of +time, the distance, how far + +I go, then the speed is-- + +the right letters are df dt. + +Everybody uses those letters. + +So let me say again how +to pronounce: df dt. + +And Leibniz came up with +that notation, and + +he just got it right. + +And what would this one be? + +Well, corresponding to this, it +looks the same, or dy dx. + +Again, I'll just repeat how +to say that: dy dx. + +And that is the slope, and we +have to understand what those + +symbols mean. + +Right now, I'm just writing +them down as symbols. + +May I begin with the most +important and the simplest + +example of all? + +Let me take that case. + +OK, so the key example here, +the one to get completely + +straight is the case +of constant + +speed, constant slope. + +I'll just graph that. + +So here I'm go to graph. + +Shall I make it the speed? + +Yeah, let's say speed. + +So time is going +along that way. + +Speed is up this way. + +And I'm going to say in this +first example that the speed + +is the same. + +We're traveling at the +constant speed + +of let's say 40. + +So it stays at the +height of 40. + +Oh, properly, I should add units +like miles per hour or + +kilometers per hour or meters +per second or whatever. + +For now, I'll just write 40. + +OK, now if we're traveling at a +speed of 40 miles per hour, + +what's the distance? + +Well, let me start with the +trip meter at zero. + +so this is time again, +and now this is + +going to be the distance. + +After one hour, my +distance is 40. + +So if I mark t equal to +1, I've reached 40. + +That's height of 40. + +At t equal to 2, I've +reached 80. + +At t equal to 1/2, half an +hour, I've reached 20. + +Those points lie on a line. + +The graph of distance covered +when you're just traveling at + +a steady rate, constant rate, +constant speed is just a + +straight line. + +And now I can make +the connection. + +I've been speaking here about +distance and speed. + +But now let me think of +this as the height-- + +40 is that height. + +80 is that height-- + +and ask about slope. + +What is slope? + +So let's just remember what's +the connection here. + +What's the slope if that's the +distance if I look at my trip + +meter and I know I'm traveling +along at that constant speed, + +how do I find that speed? + +Well, slope, it's the distance +up, which would be 40 after + +one hour, divided +by the distance + +across, 40/1, or 80/2. + +Doesn't matter, because we're +traveling at constant speed, + +so the slope, which is up, +over, across is 40/1, + +80/2, 20 over 1/2. + +I'll put 80/2 as one +example: 40. + +Oh, let me do it-- + +that's arithmetic. + +Let me do it with algebra. + +We don't need calculus +yet, by the way. + +Calculus is coming +pretty quickly. + +This is the step we can take. + +Because the speed is constant, +we can just divide the + +distance by the time to find-- + +and this slope, let me +right speed also. + +Up, over, across, distance +over time, f/t, + +that gives us s. + +This is s. + +OK, what about-- + +calculus goes both ways. + +We can go both ways here. + +We already have practically. + +Here I went in the direction +from 1 to 2. + +Now, I want to go in +the direction-- + +suppose I know the speed. + +How do I recover the distance? + +If I know my speed is 40 and I +know I started at zero, what's + +my distance? + +Distance or height, +either one. + +So these are like both. + +Now, I'm just going +the other way. + +Well, you see how. + +How do I find f? + +It's s times t, right? + +Your algebra automatically says +if you see a t there, you + +can put it there. + +So it's s times t. + +It's a straight line. + +s times t, s times +x, y equal sx. + +Let me put another-- + +the same idea with +my y, x letters. + +It's that line. + +In other words, if that one +is constant, this one is a + +straight line. + +OK, straightforward, but +very, very fundamental. + +In fact, can I call your +attention to something a + +little more? + +Suppose I measured between +time 2 and time 1. + +So I'm looking between time 2 +and time 1, and I look how far + +I went in that time. + +But what I'm trying is-- + +I'm going to put in another +little symbol because it's + +going to be really +worth knowing. + +It's really the change in f +divided by the change in t. + +I use that letter delta +to indicate + +a difference between-- + +the difference between time 2 +and time 1 was 1, and the + +difference between height +2 and height 1 was 40. + +You see, I'm looking at +this little piece. + +And, of course, the +slope is still 40. + +It's still the slope +of that line. + +Yeah, so that really what I'm +measuring in speed there, I + +don't always have to be starting +at t equals 0, and I + +don't always have to be starting +at f equals 0. + +Oh, let me draw that. + +Suppose I started +at f equals 40. + +My trip meter happened +to start at 40. + +After an hour, I'd +be up to 80. + +After another hour, +I'd be up to 120. + +Do you see that this starting +the trip meter, who cares + +where the trip meter started? + +It's the change in the trip +meter that tells how + +long the trip was. + +Clear. + +OK, so that's that example. + +We come back to it because it's +the basic one where the + +speed is constant. + +And even if now I have to move +to a changing speed, you have + +to let me bring calculus +into these lectures. + +OK, I'm going to draw another +picture, and you + +tell me about the-- + +yeah, let me draw function 1, +another example of function 1. + +So again I have time. + +I have distance. + +I'm going to start at zero, but +I'm not going to keep the + +speed constant. + +I'm going to start out at +a good speed, but I'm + +going to slow down. + +Do you see me slowing +down there? + +I don't mean slowing down +with the chalk. + +I mean slowing down +with slope. + +The slope started out steep. + +By here, by that point, +the slope was zero. + +What was the car doing here? + +The car is certainly moving +forward because the distance + +is increasing. + +Here it's increasing faster. + +Here it's increasing barely. + +In other words, we're putting +on the brakes. + +The car is slowing down. + +We're coming to a red light. + +In fact, there is the red light +right at that time. + +Now, just stay with it to think +what would the speed + +look like for this problem? + +If that's a picture of +the function, just + +let's get some idea. + +I'm not going to have +a formula yet. + +I'm not putting in +all the details. + +Well, actually, I don't plan to +put in all the details of + +calculus of every possible +step we might take. + +It's the important ones I'm +hoping to show you and I'm + +hoping for you to see that +they are important. + +OK, what is important? + +Roughly, what does the +graph looks like? + +Well, the speed-- + +the slope-- + +started out somewhere +up there. + +Yeah, it started out at a good +speed and slowed down. + +And by this point, ha! + +Let's mark that time +here on that graph. + +Do you see what is the +speed at that moment? + +The speed at that +moment is zero. + +The car has stopped. + +The speed is decreasing. + +Let me make it decrease, +decrease, decrease, decrease, + +and at that moment, the speed +is zero right there. + +That's that point. + +See, two different pictures, +two different functions. + +but same information. + +So calculus has the job of given +one of those functions, + +find the other one. + +Given this function, +find that one. + +This way is called-- + +from function one to function +two, that's called + +differential calculus. + +Big, impressive word anyway. + +That's function one to two, +finding the speed. + +Going the other direction is +called integral calculus. + +The step is called integration +when you take the speed over + +that period of time, and you +recover the distance. + +So it's differential calculus +in one direction, integral + +calculus in the other. + +Now, here's a question. + +Let me continue that curve +a little longer. + +I got it to the red light. + +Now imagine that the distance +starts going + +down from that point. + +What's happening? + +The distance is decreasing. + +The car is going backwards. + +It's going in reverse. + +The speed, what's the speed? + +Negative. + +The speed, because distance is +going from higher to lower, + +that counts for negative +speed. + +The speed curve would +be going down here. + +Do you see that that's a not +brilliantly drawn picture, but + +you're seeing the-- + +that's the farthest it went. + +Then the car started backwards, +and the speed curve + +reflected that by going +below zero. + +You see, two different curves, +but same information. + +I'm remembering an old movie. + +I don't know if you saw an +old B movie called Ferris + +Bueller's Day Off. + +Did you see that? + +So the kid had borrowed +his father's-- + +not borrowed, but lifted his +father's good car and drove it + +a lot like so and put +on a lot of mileage. + +The trip meter was way up, and +he knew his father was going + +to notice this. + +So he had the idea to put the +car up on a lift, put it in + +reverse, and go for a +while, and the trip + +meter would go backwards. + +I don't know if trip meters +do go backwards. + +It's kind of tough to watch them +while going in reverse. + +But if whoever made the car +understood calculus, as you + +do, the speedometer-- + +now that I think of it, +speedometers don't have a + +below zero. + +They should have. And trip +meters should go backwards. + +I mean, that movie was just made +for a calculus person. + +Maybe I'm remembering more. + +I think it didn't work +or something. + +And the kid got mad and kicked +the car, and it fell off the + +lift, went through +the glass window. + +Anyway, calculus would +have saved him if + +only the car had been-- + +or the meters in the car had +been made correctly. + +All right, that's one pair. + +That's our first real pair in +which the speed changes. + +OK. + +I thought in this first video, +later, even today, I'll get to + +a case where we have formulas. + +That's what calculus +moves into. + +When f of t is given by some +formula, well, here it's given + +by a formula: s times t. + +A simple formula. + +And then, knowing that, we +know that the speed is s. + +Later, we got more functions. + +But let me take an example, just +because these pairs of + +functions are everywhere. + +What could I take? + +Maybe height of a person. + +Height of a person. + +OK, so this is now another +example, just to get practice + +in the relation between the +height of a person and the + +rate of change of the height. + +So this is the height. + +Maybe I'll call it y. + +Let me write height +of a person. + +And what is this going to be? + +What is function two? + +Well, slope doesn't +seem quite right. + +The point about function two is +it tells how fast function + +one changes. + +It's the rate of change +of the height. + +It's the rate of change. + +So let me call it s, and it'll +be the rate of change. + +Good if I use those words. + +Yeah, so I want to think +just how we grow, a + +typical person growing. + +In fact, as I wrote this on +the board, I thought of + +another pair. + +Can I just say it in words, this +other pair, and then I'll + +come back to this one? + +Here's another pair. + +This could be money in a bank. + +Wealth sounds better. + +Let's call it wealth. + +That's zippier. + +And then what is this one? + +If this is your wealth, +your total + +assets, what's your worth? + +This would be the rate +of change, how + +quickly you're saving. + +s could be for saving. + +Or if you're down here, s +is for spending, right? + +If s is positive, that means +you're wealth is increasing, + +you're saving. + +Negative s means you're +spending, and your wealth goes + +whatever, maybe-- + +I hope-- up. + +Height is mostly up, right? + +So let me come back to +height of a person. + +Now, where-- + +oh, and this is time in years. + +This is t in years, and +this, too, of course. + +Actually, I realize +you started at t + +equals zero: birth. + +You do start at a certain-- + +actually, what do I know? + +You don't say tall. + +You say long. + +But then as soon as you can +stand up, it's tall, + +so let's say tall. + +Shall we guessed 20 inches? + +If that's way off, I apologize +to everybody. + +Let me just say 20, 20 inches. + +OK, at year zero. + +OK, and then presumably +you grow. + +OK, so you grow a little. + +What are we headed for? + +About 60, 70 inches +or something. + +Anyway, you grow. + +Let's say that's 10 years old +and here is 20 years old. + +OK, so you grow. + +Maybe you grow faster +than that. + +Let's say you're a healthy +person here. + +OK, up you grow. + +And then at about maybe age 12 +or 13, there's a growth spurt. + +And maybe the point is, how do +we see that growth spurt on + +the two graphs? + +Differently, but it's the +same growth spurt. + +OK, so here your height +suddenly jumps up. + +Boy, yeah, you catch +up with everybody. + +And then at about 12 or 13 well, +then unfortunately, it + +doesn't do that forever, and +it kind of levels off here. + +It levels off, and actually +you don't + +grow a whole lot more. + +In fact, I think when you get +to about-- oh, I don't know. + +Whatever. + +We won't discuss this point. + +I say when you get too old, +you probably lose some. + +Let's not emphasize that. + +OK, so here is the-- + +now, what's happening +over here? + +Well, it's the slope +of that graph. + +So the slope might be-- + +this is time zero, but you're +growing right away. + +The s graph, the rate +of growth graph, + +doesn't start at zero. + +It starts how fast you're +growing, whatever you're + +growing, whatever +that slope is. + +It's fantastic that when we +draw graphs of things, the + +word "slope" is suddenly +the right word. + +OK, so you're growing, maybe +at a pretty good rate here. + +And let me mark out +10 and 20 years. + +And OK, you're doing well, +you're coming along here, and + +then the growth spurt. + +OK, so then suddenly, your +rate of growth takes off. + +But it doesn't stay +that way, right? + +Your rate of growth levels +off, in fact, + +levels way off, levels-- + +you'll come down to here, and +you probably don't grow a lot. + +Do you see the two? + +This was the growth curve. + +This was the fast growth. + +But then it stopped. + +Up here, it slowed down. + +Here, it dropped. + +And oh, if we allow for this +person who lived too long, + +height actually drops. + +OK, there is an example +in which I don't-- + +also I'm sure people have +devised approximate formulas + +for average growth rates, +but you see, I'm not-- + +it's the idea of the relation +between function one and + +function two that +I'm emphasizing. + +Now, my last example, let me +take one more example, one + +more example for this +first lecture. + +So let me take a case in +which the speed is-- + +so here will be my two-- + +let's use speed. + +Let's use this as distance. + +This is distance again, +and graph two, as + +always, will be speed. + +And I'm going to take +a case in which + +it's given by a formula. + +I'm going to let the speed +be increasing steadily. + +OK, so my speed graph this time +is going to go up at a + +constant rate. + +So this is the speed s. + +This is the time t. + +So this would be s equals-- + +s is proportional to t. + +That's where you get +a straight line. + +s is let's say a times t. + +That a, a physicist, if we were +physicists, would say + +acceleration. + +You're accelerating. + +You're keeping your foot on the +gas, steadily speeding up, + +and so then s is proportional +to t. + +Now, think about the distance. + +What's happening +with distance? + +If this is accelerating, you're + +going faster and faster. + +You're covering more and more +speed, more and more distance, + +more and more quickly. + +If this is slope, the +slope is increasing. + +Look, the graph-- + +let's start the trip +meter at zero. + +So you started with +a speed of zero. + +You were not really increasing +distance until you got + +slightly beyond zero, +and then it + +slightly started to increase. + +But then it increases faster +and faster, right? + +It never gets infinitely fast, +but it keeps going upwards. + +And the calculus question +would be + +can we give a formula-- + +an equation-- + +for the distance? + +Because in this case, I guess +I started with function two, + +and therefore, it's function +one that I want to look at. + +It's always pairs +of functions. + +OK, now, let's think where this +would actually happen. + +If we were leaning over the +Tower of Pisa or whatever, + +like Galileo, and drop +something, or even just drop + +something anywhere, that +would be-- we drop it. + +At the beginning, it has no +speed, but of course, + +instantly it picks up speed. + +The a would have something to +do with the gravitational + +constant for the Earth, +whatever, and then maybe-- + +yeah. + +And what would be +the distance? + +OK, now can I just mention a +small miracle of calculus? + +A small miracle. + +I'm going this direction now +from speed to distance so I'm + +doing integral calculus. + +And we'll get to that later. + +In the first lectures, +we're almost always + +going from one to two. + +But here is a neat fact about +going from two to one, that if + +this is the time t, then, of +course, this height here will + +be a times t. + +And the amazing fact is that +this graph tells you the area + +under this one. + +Graph one-- + +function one-- + +tells you the area under +the graph two. + +And in this example with a nice +constant acceleration, + +steady increase in speed, +we know this. + +This is a triangle. + +It has a base of t. + +It has a height of at. + +And the area of a triangle, of +course, the area, and my point + +is that the area is +function one-- + +amazing; that's just +terrific-- + +will be-- the area of this +triangle here is 1/2 of the + +base times the height. + +That's the area, and calculus +will tell us + +that's function one. + +So this function is 1/2 +of a times t squared. + +So there is a function one, +and here is df dt. + +If I go back to the first +letters that I mentioned, if + +this is my function f, then +this is my function that-- + +and notice what kind +of a curve that is. + +Do you recognize that +with a square? + +That tells me it's a parabola, +a famous and important curve. + +And, of course, it's important +because it + +has such a neat formula. + +OK, so we have found +the function one. + +We've recovered the information +in that lost black + +box, the distance box, the trip +meter, from what we did + +find in black box two, the +speed, the record of speed. + +And notice, I'm using the +speed all the way + +from here to here. + +The speed kind of tells me how +the distance is piled up. + +The distance is kind of a +running total, where the speed + +at that moment is an +instant thing. + +Oh, we have to do that +in future lectures. + +The difference between a +running total of total + +distance covered and a speed +that's telling me at a moment, + +at an instant how distance +is changing. + +The slope at this very point +t, that slope is + +this height, is at. + +OK, so there you have +the first-- + +well, I'll say the second. + +The first pair of calculus +was this one. + +f equals st, and it's +derivative was s. + +Our second pair is f is this, +and will you allow + +me to write df dt? + +If f is 1/2 of at squared, +then df dt is at. + +You'll see this rule again. + +The power two dropped +to a power one. + +But the two multiplied the thing +so it canceled the 1/2 + +and just left the a. + +OK, that's a start on the +highlights of calculus. + +Thanks. + +NARRATOR: This has been +a production of MIT + +OpenCourseWare and +Gilbert Strang. + +Funding for this video was +provided by the Lord + +Foundation. + +To help OCW continue to provide +free and open access + +to MIT courses, please +make a donation at + +ocw.mit.edu/donate. \ No newline at end of file diff --git a/V3plr-Sn-g0.txt b/V3plr-Sn-g0.txt new file mode 100644 index 0000000000000000000000000000000000000000..375364b86f1645ca28a02eb29bf7e245f3cec202 --- /dev/null +++ b/V3plr-Sn-g0.txt @@ -0,0 +1,15163 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a creative common license. 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To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% +Courseware at ocw.mmit.edu. + + + align:start position:0% +Courseware at ocw.mmit.edu. +>> Start with a little bit of recap from uh + + align:start position:0% +>> Start with a little bit of recap from uh + + + align:start position:0% +>> Start with a little bit of recap from uh +actually two Fridays ago. Uh but just a + + align:start position:0% +actually two Fridays ago. Uh but just a + + + align:start position:0% +actually two Fridays ago. Uh but just a +reminder of things to keep in mind while + + align:start position:0% +reminder of things to keep in mind while + + + align:start position:0% +reminder of things to keep in mind while +you guys are testing. You know on on one + + align:start position:0% +you guys are testing. You know on on one + + + align:start position:0% +you guys are testing. You know on on one +hand most of you are as are pretty much + + align:start position:0% +hand most of you are as are pretty much + + + align:start position:0% +hand most of you are as are pretty much +the most expert players in your game at + + align:start position:0% +the most expert players in your game at + + + align:start position:0% +the most expert players in your game at +this point in time as you know compared + + align:start position:0% +this point in time as you know compared + + + align:start position:0% +this point in time as you know compared +to anybody else in the world. You know + + align:start position:0% +to anybody else in the world. You know + + + align:start position:0% +to anybody else in the world. You know +the game better than anybody else and + + align:start position:0% +the game better than anybody else and + + + align:start position:0% +the game better than anybody else and +the kinds of things that um I that that + + align:start position:0% +the kinds of things that um I that that + + + align:start position:0% +the kinds of things that um I that that +means you suck as a tester but that does + + align:start position:0% +means you suck as a tester but that does + + + align:start position:0% +means you suck as a tester but that does +you still have a a role to play as + + align:start position:0% +you still have a a role to play as + + + align:start position:0% +you still have a a role to play as +testers. Um you can be looking for the + + align:start position:0% +testers. Um you can be looking for the + + + align:start position:0% +testers. Um you can be looking for the +degenerate strategies. You can look and + + align:start position:0% +degenerate strategies. You can look and + + + align:start position:0% +degenerate strategies. You can look and +you can be looking for exploits. + + align:start position:0% +you can be looking for exploits. + + + align:start position:0% +you can be looking for exploits. +Sometimes it takes more imagination than + + align:start position:0% +Sometimes it takes more imagination than + + + align:start position:0% +Sometimes it takes more imagination than +a sleep depth MIT student is available + + align:start position:0% +a sleep depth MIT student is available + + + align:start position:0% +a sleep depth MIT student is available +has available to them to be able to see + + align:start position:0% +has available to them to be able to see + + + align:start position:0% +has available to them to be able to see +these exploits. But because you know the + + align:start position:0% +these exploits. But because you know the + + + align:start position:0% +these exploits. But because you know the +systems better than anyone else you're + + align:start position:0% +systems better than anyone else you're + + + align:start position:0% +systems better than anyone else you're +in a good position uh to to spot that I + + align:start position:0% +in a good position uh to to spot that I + + + align:start position:0% +in a good position uh to to spot that I +mean the kinds of things that you're + + align:start position:0% +mean the kinds of things that you're + + + align:start position:0% +mean the kinds of things that you're +looking for are obviously you know + + align:start position:0% +looking for are obviously you know + + + align:start position:0% +looking for are obviously you know +strategies where there like like a + + align:start position:0% +strategies where there like like a + + + align:start position:0% +strategies where there like like a +dominant strategy and I mentioned that + + align:start position:0% +dominant strategy and I mentioned that + + + align:start position:0% +dominant strategy and I mentioned that +uh uh the the last time we we were in + + align:start position:0% +uh uh the the last time we we were in + + + align:start position:0% +uh uh the the last time we we were in +this room. Um but also look for those um + + align:start position:0% +this room. Um but also look for those um + + + align:start position:0% +this room. Um but also look for those um +those strategies where like okay I have + + align:start position:0% +those strategies where like okay I have + + + align:start position:0% +those strategies where like okay I have +to those those decision points where I + + align:start position:0% +to those those decision points where I + + + align:start position:0% +to those those decision points where I +could do decision A or I could do the + + align:start position:0% +could do decision A or I could do the + + + align:start position:0% +could do decision A or I could do the +decision B. But if I if I change my + + align:start position:0% +decision B. But if I if I change my + + + align:start position:0% +decision B. But if I if I change my +strategy and nobody else has changes + + align:start position:0% +strategy and nobody else has changes + + + align:start position:0% +strategy and nobody else has changes +their strategy, I'm just screwed, you + + align:start position:0% +their strategy, I'm just screwed, you + + + align:start position:0% +their strategy, I'm just screwed, you +know, and and and that makes it really + + align:start position:0% +know, and and and that makes it really + + + align:start position:0% +know, and and and that makes it really +really hesitant for someone to to to + + align:start position:0% +really hesitant for someone to to to + + + align:start position:0% +really hesitant for someone to to to +say, "Well, + + align:start position:0% +say, "Well, + + + align:start position:0% +say, "Well, +strategy B could be really interesting. + + align:start position:0% +strategy B could be really interesting. + + + align:start position:0% +strategy B could be really interesting. +you know I could go for this kind of + + align:start position:0% +you know I could go for this kind of + + + align:start position:0% +you know I could go for this kind of +play but on the assumption that the only + + align:start position:0% +play but on the assumption that the only + + + align:start position:0% +play but on the assumption that the only +way how this is going to be beneficial + + align:start position:0% +way how this is going to be beneficial + + + align:start position:0% +way how this is going to be beneficial +is if everybody else also changes their + + align:start position:0% +is if everybody else also changes their + + + align:start position:0% +is if everybody else also changes their +strategy now you have a situation where + + align:start position:0% +strategy now you have a situation where + + + align:start position:0% +strategy now you have a situation where +uh where nobody wants to try that second + + align:start position:0% +uh where nobody wants to try that second + + + align:start position:0% +uh where nobody wants to try that second +option you know that's that's one way to + + align:start position:0% +option you know that's that's one way to + + + align:start position:0% +option you know that's that's one way to +think about parts you know it's like if + + align:start position:0% +think about parts you know it's like if + + + align:start position:0% +think about parts you know it's like if +you change your decision and and the + + align:start position:0% +you change your decision and and the + + + align:start position:0% +you change your decision and and the +only way that you can change your + + align:start position:0% +only way that you can change your + + + align:start position:0% +only way that you can change your +decision is at a cost to yourself you + + align:start position:0% +decision is at a cost to yourself you + + + align:start position:0% +decision is at a cost to yourself you +know and the and the benefits of + + align:start position:0% +know and the and the benefits of + + + align:start position:0% +know and the and the benefits of +changing that decision is going to be + + align:start position:0% +changing that decision is going to be + + + align:start position:0% +changing that decision is going to be +like higher higher than it's going to be + + align:start position:0% +like higher higher than it's going to be + + + align:start position:0% +like higher higher than it's going to be +lower than the risks that you're taking + + align:start position:0% +lower than the risks that you're taking + + + align:start position:0% +lower than the risks that you're taking +on then you know you've got a situation + + align:start position:0% +on then you know you've got a situation + + + align:start position:0% +on then you know you've got a situation +where it's very difficult to break out + + align:start position:0% +where it's very difficult to break out + + + align:start position:0% +where it's very difficult to break out +of one dominant strategy. So I mean if + + align:start position:0% +of one dominant strategy. So I mean if + + + align:start position:0% +of one dominant strategy. So I mean if +you got a situation where there are like + + align:start position:0% +you got a situation where there are like + + + align:start position:0% +you got a situation where there are like +three dominant strategies then none of + + align:start position:0% +three dominant strategies then none of + + + align:start position:0% +three dominant strategies then none of +them are dominant anymore. You know it's + + align:start position:0% +them are dominant anymore. You know it's + + + align:start position:0% +them are dominant anymore. You know it's +like you know that that that's great. + + align:start position:0% +like you know that that that's great. + + + align:start position:0% +like you know that that that's great. +You now have an option uh of different + + align:start position:0% +You now have an option uh of different + + + align:start position:0% +You now have an option uh of different +things that you can choose. Um so that's + + align:start position:0% +things that you can choose. Um so that's + + + align:start position:0% +things that you can choose. Um so that's +just one thing to keep in mind while you + + align:start position:0% +just one thing to keep in mind while you + + + align:start position:0% +just one thing to keep in mind while you +guys are looking at your game. You know, + + align:start position:0% +guys are looking at your game. You know, + + + align:start position:0% +guys are looking at your game. You know, +if you just end up if everyone just ends + + align:start position:0% +if you just end up if everyone just ends + + + align:start position:0% +if you just end up if everyone just ends +up adopting the same strategy and you're + + align:start position:0% +up adopting the same strategy and you're + + + align:start position:0% +up adopting the same strategy and you're +just hoping the chance of your, you + + align:start position:0% +just hoping the chance of your, you + + + align:start position:0% +just hoping the chance of your, you +know, the chance of drawing the right + + align:start position:0% +know, the chance of drawing the right + + + align:start position:0% +know, the chance of drawing the right +cards going to win your game, then you + + align:start position:0% +cards going to win your game, then you + + + align:start position:0% +cards going to win your game, then you +start to think, then you've got a game + + align:start position:0% +start to think, then you've got a game + + + align:start position:0% +start to think, then you've got a game +where the individual players decisions + + align:start position:0% +where the individual players decisions + + + align:start position:0% +where the individual players decisions +aren't quite that influential on the + + align:start position:0% +aren't quite that influential on the + + + align:start position:0% +aren't quite that influential on the +outcome. And uh um I still need to play + + align:start position:0% +outcome. And uh um I still need to play + + + align:start position:0% +outcome. And uh um I still need to play +your games to be able to see what you + + align:start position:0% +your games to be able to see what you + + + align:start position:0% +your games to be able to see what you +guys are going for, but on the most + + align:start position:0% +guys are going for, but on the most + + + align:start position:0% +guys are going for, but on the most +part, it looks like you guys are not + + align:start position:0% +part, it looks like you guys are not + + + align:start position:0% +part, it looks like you guys are not +going for a purely chance based game. + + align:start position:0% +going for a purely chance based game. + + + align:start position:0% +going for a purely chance based game. +you're looking for something where + + align:start position:0% +you're looking for something where + + + align:start position:0% +you're looking for something where +someone's decision actually matters. Um + + align:start position:0% +someone's decision actually matters. Um + + + align:start position:0% +someone's decision actually matters. Um +so so that's so that's that's one one + + align:start position:0% +so so that's so that's that's one one + + + align:start position:0% +so so that's so that's that's one one +reminder um from a game theory point of + + align:start position:0% +reminder um from a game theory point of + + + align:start position:0% +reminder um from a game theory point of +view and um the other one I never really + + align:start position:0% +view and um the other one I never really + + + align:start position:0% +view and um the other one I never really +got time to talk about games as a system + + align:start position:0% +got time to talk about games as a system + + + align:start position:0% +got time to talk about games as a system +of conflict and we don't have a huge + + align:start position:0% +of conflict and we don't have a huge + + + align:start position:0% +of conflict and we don't have a huge +amount of time because uh we have + + align:start position:0% +amount of time because uh we have + + + align:start position:0% +amount of time because uh we have +today's readings to go through um but um + + align:start position:0% +today's readings to go through um but um + + + align:start position:0% +today's readings to go through um but um +the I if you think about games as you + + align:start position:0% +the I if you think about games as you + + + align:start position:0% +the I if you think about games as you +know a games where multiple people are + + align:start position:0% +know a games where multiple people are + + + align:start position:0% +know a games where multiple people are +striving for some sort of goal and + + align:start position:0% +striving for some sort of goal and + + + align:start position:0% +striving for some sort of goal and +they're going to be winners and they're + + align:start position:0% +they're going to be winners and they're + + + align:start position:0% +they're going to be winners and they're +going to be losers and the idea of + + align:start position:0% +going to be losers and the idea of + + + align:start position:0% +going to be losers and the idea of +thinking of games as some kind of + + align:start position:0% +thinking of games as some kind of + + + align:start position:0% +thinking of games as some kind of +conflict makes sense. Um + + align:start position:0% +conflict makes sense. Um + + + align:start position:0% +conflict makes sense. Um +uh and you can think of them as you know + + align:start position:0% +uh and you can think of them as you know + + + align:start position:0% +uh and you can think of them as you know +are games competitive or games + + align:start position:0% +are games competitive or games + + + align:start position:0% +are games competitive or games +cooperative uh folks throw out some + + align:start position:0% +cooperative uh folks throw out some + + + align:start position:0% +cooperative uh folks throw out some +games that are known to be co-op + + align:start position:0% +games that are known to be co-op + + + align:start position:0% +games that are known to be co-op +cooperative + + align:start position:0% +cooperative + + + align:start position:0% +cooperative +>> perfect cooperative + + align:start position:0% +>> perfect cooperative + + + align:start position:0% +>> perfect cooperative +>> there are certain modes in certain + + align:start position:0% +>> there are certain modes in certain + + + align:start position:0% +>> there are certain modes in certain +different games that you know sort of + + align:start position:0% +different games that you know sort of + + + align:start position:0% +different games that you know sort of +flip it from from from compet from + + align:start position:0% +flip it from from from compet from + + + align:start position:0% +flip it from from from compet from +competent to cooperative + + align:start position:0% +competent to cooperative + + + align:start position:0% +competent to cooperative +>> for dead + + align:start position:0% +>> for dead + + + align:start position:0% +>> for dead +>> for dead is is designed for four people + + align:start position:0% +>> for dead is is designed for four people + + + align:start position:0% +>> for dead is is designed for four people +to play all going for the same goal + + align:start position:0% +to play all going for the same goal + + + align:start position:0% +to play all going for the same goal +>> of war of multiplayer. Yeah, + + align:start position:0% +>> of war of multiplayer. Yeah, + + + align:start position:0% +>> of war of multiplayer. Yeah, +>> diplomacy is interesting. Yeah, because + + align:start position:0% +>> diplomacy is interesting. Yeah, because + + + align:start position:0% +>> diplomacy is interesting. Yeah, because +like + + align:start position:0% +like + + + align:start position:0% +like +>> it's kind of a risk of cooperation. + + align:start position:0% + + + + align:start position:0% + +>> Pandemic uh pandemic is you against the + + align:start position:0% +>> Pandemic uh pandemic is you against the + + + align:start position:0% +>> Pandemic uh pandemic is you against the +the the board actually you against the + + align:start position:0% +the the board actually you against the + + + align:start position:0% +the the board actually you against the +game rules. Um and actually that that + + align:start position:0% +game rules. Um and actually that that + + + align:start position:0% +game rules. Um and actually that that +that leads into today's uh lecture a + + align:start position:0% +that leads into today's uh lecture a + + + align:start position:0% +that leads into today's uh lecture a +bit. So hang on to that idea of of + + align:start position:0% +bit. So hang on to that idea of of + + + align:start position:0% +bit. So hang on to that idea of of +pandmic. But um but there is one + + align:start position:0% +pandmic. But um but there is one + + + align:start position:0% +pandmic. But um but there is one +argument that all games are competitive. + + align:start position:0% +argument that all games are competitive. + + + align:start position:0% +argument that all games are competitive. +Even games like Left 4 Dead where you're + + align:start position:0% +Even games like Left 4 Dead where you're + + + align:start position:0% +Even games like Left 4 Dead where you're +playing against a computer or Pandemic + + align:start position:0% +playing against a computer or Pandemic + + + align:start position:0% +playing against a computer or Pandemic +where you're playing against the game + + align:start position:0% +where you're playing against the game + + + align:start position:0% +where you're playing against the game +rules. Um or + + align:start position:0% +rules. Um or + + + align:start position:0% +rules. Um or +>> Shadows or Camelot. + + align:start position:0% +>> Shadows or Camelot. + + + align:start position:0% +>> Shadows or Camelot. +>> Shadows of Camelot. I'm not playing + + align:start position:0% +>> Shadows of Camelot. I'm not playing + + + align:start position:0% +>> Shadows of Camelot. I'm not playing +>> those trader. Yeah, + + align:start position:0% +>> those trader. Yeah, + + + align:start position:0% +>> those trader. Yeah, +>> you're you're mostly playing against the + + align:start position:0% +>> you're you're mostly playing against the + + + align:start position:0% +>> you're you're mostly playing against the +game rules unless there's a trader. + + align:start position:0% +game rules unless there's a trader. + + + align:start position:0% +game rules unless there's a trader. +There's not always one in the game. + + align:start position:0% +There's not always one in the game. + + + align:start position:0% +There's not always one in the game. +>> But but you know that but but the the + + align:start position:0% +>> But but you know that but but the the + + + align:start position:0% +>> But but you know that but but the the +the basic idea is that even in a purely + + align:start position:0% +the basic idea is that even in a purely + + + align:start position:0% +the basic idea is that even in a purely +even a game that's generally assumed to + + align:start position:0% +even a game that's generally assumed to + + + align:start position:0% +even a game that's generally assumed to +be co-op, you're still playing against + + align:start position:0% +be co-op, you're still playing against + + + align:start position:0% +be co-op, you're still playing against +the world. So it's competitive against + + align:start position:0% +the world. So it's competitive against + + + align:start position:0% +the world. So it's competitive against +the world and just just not you're not + + align:start position:0% +the world and just just not you're not + + + align:start position:0% +the world and just just not you're not +comp competing against the other human + + align:start position:0% +comp competing against the other human + + + align:start position:0% +comp competing against the other human +people that that are playing it. If if + + align:start position:0% +people that that are playing it. If if + + + align:start position:0% +people that that are playing it. If if +you're competing against anyone is + + align:start position:0% +you're competing against anyone is + + + align:start position:0% +you're competing against anyone is +probably the deciding you know who set + + align:start position:0% +probably the deciding you know who set + + + align:start position:0% +probably the deciding you know who set +it up to to give you some challenge. So + + align:start position:0% +it up to to give you some challenge. So + + + align:start position:0% +it up to to give you some challenge. So +that's one way to think of all games are + + align:start position:0% +that's one way to think of all games are + + + align:start position:0% +that's one way to think of all games are +competitive. Obviously the games that + + align:start position:0% +competitive. Obviously the games that + + + align:start position:0% +competitive. Obviously the games that +are that people generally think of as + + align:start position:0% +are that people generally think of as + + + align:start position:0% +are that people generally think of as +competitive you know zero sum games like + + align:start position:0% +competitive you know zero sum games like + + + align:start position:0% +competitive you know zero sum games like +you know chess for instance there one + + align:start position:0% +you know chess for instance there one + + + align:start position:0% +you know chess for instance there one +winner there's one loser and there's a + + align:start position:0% +winner there's one loser and there's a + + + align:start position:0% +winner there's one loser and there's a +draw out and nobody wins + + align:start position:0% +draw out and nobody wins + + + align:start position:0% +draw out and nobody wins +uh or uh those those games people + + align:start position:0% +uh or uh those those games people + + + align:start position:0% +uh or uh those those games people +generally think of as competitive but + + align:start position:0% +generally think of as competitive but + + + align:start position:0% +generally think of as competitive but +then that's the other way to think about + + align:start position:0% +then that's the other way to think about + + + align:start position:0% +then that's the other way to think about +cooperation is that all games are also + + align:start position:0% +cooperation is that all games are also + + + align:start position:0% +cooperation is that all games are also +cooperative because if you don't agree + + align:start position:0% +cooperative because if you don't agree + + + align:start position:0% +cooperative because if you don't agree +on the rules if you know if you all + + align:start position:0% +on the rules if you know if you all + + + align:start position:0% +on the rules if you know if you all +decide not to play on the same rules + + align:start position:0% +decide not to play on the same rules + + + align:start position:0% +decide not to play on the same rules +then then you've got uh that you don't + + align:start position:0% +then then you've got uh that you don't + + + align:start position:0% +then then you've got uh that you don't +actually have game + + align:start position:0% +actually have game + + + align:start position:0% +actually have game +anymore. So, you all have to cooperate + + align:start position:0% +anymore. So, you all have to cooperate + + + align:start position:0% +anymore. So, you all have to cooperate +and say we have the same set we all we + + align:start position:0% +and say we have the same set we all we + + + align:start position:0% +and say we have the same set we all we +have the same set of rules and we're + + align:start position:0% +have the same set of rules and we're + + + align:start position:0% +have the same set of rules and we're +going to play according to to to them. + + align:start position:0% +going to play according to to to them. + + + align:start position:0% +going to play according to to to them. +That's not necessarily the same thing as + + align:start position:0% +That's not necessarily the same thing as + + + align:start position:0% +That's not necessarily the same thing as +saying that everyone knows all the + + align:start position:0% +saying that everyone knows all the + + + align:start position:0% +saying that everyone knows all the +rules. Um, you know, there are plenty of + + align:start position:0% +rules. Um, you know, there are plenty of + + + align:start position:0% +rules. Um, you know, there are plenty of +games, especially computer games where, + + align:start position:0% +games, especially computer games where, + + + align:start position:0% +games, especially computer games where, +you know, you're going into the game not + + align:start position:0% +you know, you're going into the game not + + + align:start position:0% +you know, you're going into the game not +knowing all the rules and you're going + + align:start position:0% +knowing all the rules and you're going + + + align:start position:0% +knowing all the rules and you're going +to try to figure out the rules of being + + align:start position:0% +to try to figure out the rules of being + + + align:start position:0% +to try to figure out the rules of being +what the system lets you. Um, role + + align:start position:0% +what the system lets you. Um, role + + + align:start position:0% +what the system lets you. Um, role +playing games where you're just sort of + + align:start position:0% +playing games where you're just sort of + + + align:start position:0% +playing games where you're just sort of +like, you know, I want to do this. I + + align:start position:0% +like, you know, I want to do this. I + + + align:start position:0% +like, you know, I want to do this. I +want to, you know, get drunk now. And + + align:start position:0% +want to, you know, get drunk now. And + + + align:start position:0% +want to, you know, get drunk now. And +how do I do that? And then the GM tells + + align:start position:0% +how do I do that? And then the GM tells + + + align:start position:0% +how do I do that? And then the GM tells +you the rules, you know, role against + + align:start position:0% +you the rules, you know, role against + + + align:start position:0% +you the rules, you know, role against +your your + + align:start position:0% +your your + + + align:start position:0% +your your +>> constitution. + + align:start position:0% +>> constitution. + + + align:start position:0% +>> constitution. +>> Constitution. Is it the constitution? + + align:start position:0% +>> Constitution. Is it the constitution? + + + align:start position:0% +>> Constitution. Is it the constitution? +>> Yeah, probably. But + + align:start position:0% +>> Yeah, probably. But + + + align:start position:0% +>> Yeah, probably. But +>> always good possibly. + + align:start position:0% +>> always good possibly. + + + align:start position:0% +>> always good possibly. +Um then uh uh and then and then and then + + align:start position:0% +Um then uh uh and then and then and then + + + align:start position:0% +Um then uh uh and then and then and then +you you get told the rules and then you + + align:start position:0% +you you get told the rules and then you + + + align:start position:0% +you you get told the rules and then you +you go and do it. Um live action role + + align:start position:0% +you go and do it. Um live action role + + + align:start position:0% +you go and do it. Um live action role +playing. I know there's a bunch of + + align:start position:0% +playing. I know there's a bunch of + + + align:start position:0% +playing. I know there's a bunch of +people here who who play that. You + + align:start position:0% +people here who who play that. You + + + align:start position:0% +people here who who play that. You +usually get a subset of all the rules + + align:start position:0% +usually get a subset of all the rules + + + align:start position:0% +usually get a subset of all the rules +that were written for the game. like you + + align:start position:0% +that were written for the game. like you + + + align:start position:0% +that were written for the game. like you +get the subset that pertains to you and + + align:start position:0% +get the subset that pertains to you and + + + align:start position:0% +get the subset that pertains to you and +you assume that everybody else has the + + align:start position:0% +you assume that everybody else has the + + + align:start position:0% +you assume that everybody else has the +subset that pertains pertains to them + + align:start position:0% +subset that pertains pertains to them + + + align:start position:0% +subset that pertains pertains to them +and that they're playing according to + + align:start position:0% +and that they're playing according to + + + align:start position:0% +and that they're playing according to +it. It's a strong order system and that + + align:start position:0% +it. It's a strong order system and that + + + align:start position:0% +it. It's a strong order system and that +and even in a game especially the kinds + + align:start position:0% +and even in a game especially the kinds + + + align:start position:0% +and even in a game especially the kinds +that have played in in in MIT which are + + align:start position:0% +that have played in in in MIT which are + + + align:start position:0% +that have played in in in MIT which are +fiercely competitive you know it's like + + align:start position:0% +fiercely competitive you know it's like + + + align:start position:0% +fiercely competitive you know it's like +you're literally there assassin games + + align:start position:0% +you're literally there assassin games + + + align:start position:0% +you're literally there assassin games +you literally want to lead someone into + + align:start position:0% +you literally want to lead someone into + + + align:start position:0% +you literally want to lead someone into +a dark alley and shoot them. uh because + + align:start position:0% +a dark alley and shoot them. uh because + + + align:start position:0% +a dark alley and shoot them. uh because +even then you have to assume that + + align:start position:0% +even then you have to assume that + + + align:start position:0% +even then you have to assume that +whatever rules that person you're + + align:start position:0% +whatever rules that person you're + + + align:start position:0% +whatever rules that person you're +leading down a dark alley in order to + + align:start position:0% +leading down a dark alley in order to + + + align:start position:0% +leading down a dark alley in order to +shoot them um whatever rules they got + + align:start position:0% +shoot them um whatever rules they got + + + align:start position:0% +shoot them um whatever rules they got +they're playing by those rules. They're + + align:start position:0% +they're playing by those rules. They're + + + align:start position:0% +they're playing by those rules. They're +not going to say you know it's like if + + align:start position:0% +not going to say you know it's like if + + + align:start position:0% +not going to say you know it's like if +hey if you shoot them man say that + + align:start position:0% +hey if you shoot them man say that + + + align:start position:0% +hey if you shoot them man say that +didn't work. You have to assume that + + align:start position:0% +didn't work. You have to assume that + + + align:start position:0% +didn't work. You have to assume that +actually didn't work because they have + + align:start position:0% +actually didn't work because they have + + + align:start position:0% +actually didn't work because they have +rules that tell them when it works and + + align:start position:0% +rules that tell them when it works and + + + align:start position:0% +rules that tell them when it works and +when it didn't work. Um so so that's so + + align:start position:0% +when it didn't work. Um so so that's so + + + align:start position:0% +when it didn't work. Um so so that's so +it's still cooperated even though it's + + align:start position:0% +it's still cooperated even though it's + + + align:start position:0% +it's still cooperated even though it's +is competitive play and uh uh some + + align:start position:0% +is competitive play and uh uh some + + + align:start position:0% +is competitive play and uh uh some +terminology now um the systemic + + align:start position:0% +terminology now um the systemic + + + align:start position:0% +terminology now um the systemic +cooperation which is you know is what + + align:start position:0% +cooperation which is you know is what + + + align:start position:0% +cooperation which is you know is what +I'm describing is the you are agreeing + + align:start position:0% +I'm describing is the you are agreeing + + + align:start position:0% +I'm describing is the you are agreeing +that the system works and you are + + align:start position:0% +that the system works and you are + + + align:start position:0% +that the system works and you are +agreeing how the system works. These are + + align:start position:0% +agreeing how the system works. These are + + + align:start position:0% +agreeing how the system works. These are +the ways how I'm going to interact with + + align:start position:0% +the ways how I'm going to interact with + + + align:start position:0% +the ways how I'm going to interact with +the system. when you're playing uh + + align:start position:0% +the system. when you're playing uh + + + align:start position:0% +the system. when you're playing uh +Golden Eye or Perfect Dark um on a split + + align:start position:0% +Golden Eye or Perfect Dark um on a split + + + align:start position:0% +Golden Eye or Perfect Dark um on a split +screen or Halo on split screen and you + + align:start position:0% +screen or Halo on split screen and you + + + align:start position:0% +screen or Halo on split screen and you +agree not to look at somebody else's + + align:start position:0% +agree not to look at somebody else's + + + align:start position:0% +agree not to look at somebody else's +screen. Um then you know then that's a + + align:start position:0% +screen. Um then you know then that's a + + + align:start position:0% +screen. Um then you know then that's a +system then that's systematic rule. You + + align:start position:0% +system then that's systematic rule. You + + + align:start position:0% +system then that's systematic rule. You +might also decide no it's on the screen + + align:start position:0% +might also decide no it's on the screen + + + align:start position:0% +might also decide no it's on the screen +I can't avoid seeing it. Therefore we + + align:start position:0% +I can't avoid seeing it. Therefore we + + + align:start position:0% +I can't avoid seeing it. Therefore we +can all look at each other's screen. + + align:start position:0% +can all look at each other's screen. + + + align:start position:0% +can all look at each other's screen. +That also systemic rule + + align:start position:0% +That also systemic rule + + + align:start position:0% +That also systemic rule +>> even though the goals are the same. + + align:start position:0% +>> even though the goals are the same. + + + align:start position:0% +>> even though the goals are the same. +Let's shoot each other. Um and and then + + align:start position:0% +Let's shoot each other. Um and and then + + + align:start position:0% +Let's shoot each other. Um and and then +there's player cooperation which is a + + align:start position:0% +there's player cooperation which is a + + + align:start position:0% +there's player cooperation which is a +little bit more like uh the games like + + align:start position:0% +little bit more like uh the games like + + + align:start position:0% +little bit more like uh the games like +pandemic and death or dead. So yeah, + + align:start position:0% +pandemic and death or dead. So yeah, + + + align:start position:0% +pandemic and death or dead. So yeah, +explicitly trying to help each other + + align:start position:0% +explicitly trying to help each other + + + align:start position:0% +explicitly trying to help each other +attain a shared goal. Um and that I'm + + align:start position:0% +attain a shared goal. Um and that I'm + + + align:start position:0% +attain a shared goal. Um and that I'm +just trying to sort of like + + align:start position:0% +just trying to sort of like + + + align:start position:0% +just trying to sort of like +differentiate the the the two because + + align:start position:0% +differentiate the the the two because + + + align:start position:0% +differentiate the the the two because +it's useful sometimes to sort of try to + + align:start position:0% +it's useful sometimes to sort of try to + + + align:start position:0% +it's useful sometimes to sort of try to +to figure out um the differences. + + align:start position:0% +to figure out um the differences. + + + align:start position:0% +to figure out um the differences. +There's a game um that I don't think who + + align:start position:0% +There's a game um that I don't think who + + + align:start position:0% +There's a game um that I don't think who +I'm making you play called the war on + + align:start position:0% +I'm making you play called the war on + + + align:start position:0% +I'm making you play called the war on +terror uh that we have in the uh in the + + align:start position:0% +terror uh that we have in the uh in the + + + align:start position:0% +terror uh that we have in the uh in the +lab. And one of the things about this + + align:start position:0% +lab. And one of the things about this + + + align:start position:0% +lab. And one of the things about this +game is that this game actually doesn't + + align:start position:0% +game is that this game actually doesn't + + + align:start position:0% +game is that this game actually doesn't +end. Um if you look at the rules, it + + align:start position:0% +end. Um if you look at the rules, it + + + align:start position:0% +end. Um if you look at the rules, it +seems like there are conditions for the + + align:start position:0% +seems like there are conditions for the + + + align:start position:0% +seems like there are conditions for the +game to end, but they're really really + + align:start position:0% +game to end, but they're really really + + + align:start position:0% +game to end, but they're really really +hard to reach. Um and and if you're + + align:start position:0% +hard to reach. Um and and if you're + + + align:start position:0% +hard to reach. Um and and if you're +interested in seeing how the game ends, + + align:start position:0% +interested in seeing how the game ends, + + + align:start position:0% +interested in seeing how the game ends, +you know, I I'll be happy to to pass you + + align:start position:0% +you know, I I'll be happy to to pass you + + + align:start position:0% +you know, I I'll be happy to to pass you +the board and you can try and figure it + + align:start position:0% +the board and you can try and figure it + + + align:start position:0% +the board and you can try and figure it +out or or play it. But of course, that's + + align:start position:0% +out or or play it. But of course, that's + + + align:start position:0% +out or or play it. But of course, that's +the point that they're trying to make, + + align:start position:0% +the point that they're trying to make, + + + align:start position:0% +the point that they're trying to make, +right? It's war and turn. It never + + align:start position:0% +right? It's war and turn. It never + + + align:start position:0% +right? It's war and turn. It never +really ends. You just keep going. Uh it + + align:start position:0% +really ends. You just keep going. Uh it + + + align:start position:0% +really ends. You just keep going. Uh it +perpet perpetuates your the audience + + align:start position:0% +perpet perpetuates your the audience + + + align:start position:0% +perpet perpetuates your the audience +yourself. And it's designed to be a + + align:start position:0% +yourself. And it's designed to be a + + + align:start position:0% +yourself. And it's designed to be a +cooperative uh to be a competitive game. + + align:start position:0% +cooperative uh to be a competitive game. + + + align:start position:0% +cooperative uh to be a competitive game. +Everybody tries to take down all the + + align:start position:0% +Everybody tries to take down all the + + + align:start position:0% +Everybody tries to take down all the +other states, the other nation states by + + align:start position:0% +other states, the other nation states by + + + align:start position:0% +other states, the other nation states by +either sponsoring terrorist activity or + + align:start position:0% +either sponsoring terrorist activity or + + + align:start position:0% +either sponsoring terrorist activity or +trying to put to defend themselves from + + align:start position:0% +trying to put to defend themselves from + + + align:start position:0% +trying to put to defend themselves from +terrorist activity, which means + + align:start position:0% +terrorist activity, which means + + + align:start position:0% +terrorist activity, which means +everybody's responsible for terrorism in + + align:start position:0% +everybody's responsible for terrorism in + + + align:start position:0% +everybody's responsible for terrorism in +the end. in the game. Um, and but but in + + align:start position:0% +the end. in the game. Um, and but but in + + + align:start position:0% +the end. in the game. Um, and but but in +the end, what they're hoping is that at + + align:start position:0% +the end, what they're hoping is that at + + + align:start position:0% +the end, what they're hoping is that at +some point of time, the players are + + align:start position:0% +some point of time, the players are + + + align:start position:0% +some point of time, the players are +going to cooperate because this game is + + align:start position:0% +going to cooperate because this game is + + + align:start position:0% +going to cooperate because this game is +not going to end. That that was the + + align:start position:0% +not going to end. That that was the + + + align:start position:0% +not going to end. That that was the +whole point of of of the game and and + + align:start position:0% +whole point of of of the game and and + + + align:start position:0% +whole point of of of the game and and +the entire group coming to that + + align:start position:0% +the entire group coming to that + + + align:start position:0% +the entire group coming to that +conclusion in a shared way, you know, is + + align:start position:0% +conclusion in a shared way, you know, is + + + align:start position:0% +conclusion in a shared way, you know, is +kind of what the game designers were + + align:start position:0% +kind of what the game designers were + + + align:start position:0% +kind of what the game designers were +trying to go for. Um, it's a funny game. + + align:start position:0% +trying to go for. Um, it's a funny game. + + + align:start position:0% +trying to go for. Um, it's a funny game. +Anybody who play Crunch is the same is + + align:start position:0% +Anybody who play Crunch is the same is + + + align:start position:0% +Anybody who play Crunch is the same is +done by the same folks, but it's uh a + + align:start position:0% +done by the same folks, but it's uh a + + + align:start position:0% +done by the same folks, but it's uh a +little a little bit more on the we have + + align:start position:0% +little a little bit more on the we have + + + align:start position:0% +little a little bit more on the we have +an opinion and we want you to hear it + + align:start position:0% +an opinion and we want you to hear it + + + align:start position:0% +an opinion and we want you to hear it +than you know this is a game that you + + align:start position:0% +than you know this is a game that you + + + align:start position:0% +than you know this is a game that you +actually want to try to play. Um it's + + align:start position:0% +actually want to try to play. Um it's + + + align:start position:0% +actually want to try to play. Um it's +funny it has a butter color with the + + align:start position:0% +funny it has a butter color with the + + + align:start position:0% +funny it has a butter color with the +word evil on it + + align:start position:0% +word evil on it + + + align:start position:0% +word evil on it +and you wear it at a specific time. + + align:start position:0% + + + + align:start position:0% + +So um so so that so that's some opinions + + align:start position:0% +So um so so that so that's some opinions + + + align:start position:0% +So um so so that so that's some opinions +about uh cooperation. That's there + + align:start position:0% +about uh cooperation. That's there + + + align:start position:0% +about uh cooperation. That's there +systemic cooperation where you're + + align:start position:0% +systemic cooperation where you're + + + align:start position:0% +systemic cooperation where you're +agreeing on the rules or you're agreeing + + align:start position:0% +agreeing on the rules or you're agreeing + + + align:start position:0% +agreeing on the rules or you're agreeing +that the system works. Um and there's + + align:start position:0% +that the system works. Um and there's + + + align:start position:0% +that the system works. Um and there's +player cooperation which means players + + align:start position:0% +player cooperation which means players + + + align:start position:0% +player cooperation which means players +are actually agreeing to work towards + + align:start position:0% +are actually agreeing to work towards + + + align:start position:0% +are actually agreeing to work towards +some sort of shadow goal. And there are + + align:start position:0% +some sort of shadow goal. And there are + + + align:start position:0% +some sort of shadow goal. And there are +games where it flips between cooperation + + align:start position:0% +games where it flips between cooperation + + + align:start position:0% +games where it flips between cooperation +and player cooperation player + + align:start position:0% +and player cooperation player + + + align:start position:0% +and player cooperation player +competition. It's like uh web um castle + + align:start position:0% +competition. It's like uh web um castle + + + align:start position:0% +competition. It's like uh web um castle +crashes. Who's played Castle Crashers? + + align:start position:0% +crashes. Who's played Castle Crashers? + + + align:start position:0% +crashes. Who's played Castle Crashers? +>> The game's awesome. It's a great game. + + align:start position:0% +>> The game's awesome. It's a great game. + + + align:start position:0% +>> The game's awesome. It's a great game. +It's Xbox Live arcade game. You run + + align:start position:0% +It's Xbox Live arcade game. You run + + + align:start position:0% +It's Xbox Live arcade game. You run +around. It's a sidescrolling game where + + align:start position:0% +around. It's a sidescrolling game where + + + align:start position:0% +around. It's a sidescrolling game where +you're a little knight with, you know, a + + align:start position:0% +you're a little knight with, you know, a + + + align:start position:0% +you're a little knight with, you know, a +sword. + + align:start position:0% +sword. + + + align:start position:0% +sword. +>> Oh, it's a sword. + + align:start position:0% +>> Oh, it's a sword. + + + align:start position:0% +>> Oh, it's a sword. +>> Well, no, it's it's an axe. Give me a + + align:start position:0% +>> Well, no, it's it's an axe. Give me a + + + align:start position:0% +>> Well, no, it's it's an axe. Give me a +fish. + + align:start position:0% +fish. + + + align:start position:0% +fish. +>> Some sort of legending device. Um, + + align:start position:0% +>> Some sort of legending device. Um, + + + align:start position:0% +>> Some sort of legending device. Um, +>> yeah, fish. + + align:start position:0% +>> yeah, fish. + + + align:start position:0% +>> yeah, fish. +>> A fish is awesome. + + align:start position:0% +>> A fish is awesome. + + + align:start position:0% +>> A fish is awesome. +>> And and and in general, you know, if + + align:start position:0% +>> And and and in general, you know, if + + + align:start position:0% +>> And and and in general, you know, if +you're playing with three other people + + align:start position:0% +you're playing with three other people + + + align:start position:0% +you're playing with three other people +with controllers right next to you on + + align:start position:0% +with controllers right next to you on + + + align:start position:0% +with controllers right next to you on +the couch, you're pretty much going for + + align:start position:0% +the couch, you're pretty much going for + + + align:start position:0% +the couch, you're pretty much going for +the same goal. There are there are you + + align:start position:0% +the same goal. There are there are you + + + align:start position:0% +the same goal. There are there are you +four and there are a whole bunch of + + align:start position:0% +four and there are a whole bunch of + + + align:start position:0% +four and there are a whole bunch of +baddies on screen and you just prime and + + align:start position:0% +baddies on screen and you just prime and + + + align:start position:0% +baddies on screen and you just prime and +kill it all. + + align:start position:0% +kill it all. + + + align:start position:0% +kill it all. +>> But then as soon as you beat the last + + align:start position:0% +>> But then as soon as you beat the last + + + align:start position:0% +>> But then as soon as you beat the last +one, the the game switches from defeat + + align:start position:0% +one, the the game switches from defeat + + + align:start position:0% +one, the the game switches from defeat +all the baddies to save the princess. + + align:start position:0% +all the baddies to save the princess. + + + align:start position:0% +all the baddies to save the princess. +And wait, wait a minute. That's one. + + align:start position:0% +And wait, wait a minute. That's one. + + + align:start position:0% +And wait, wait a minute. That's one. +>> No, no, you've already saved the + + align:start position:0% +>> No, no, you've already saved the + + + align:start position:0% +>> No, no, you've already saved the +princess. It goes from + + align:start position:0% +princess. It goes from + + + align:start position:0% +princess. It goes from +>> to get the princess. + + align:start position:0% +>> to get the princess. + + + align:start position:0% +>> to get the princess. +>> Yeah. Yeah, it's get it becomes get the + + align:start position:0% +>> Yeah. Yeah, it's get it becomes get the + + + align:start position:0% +>> Yeah. Yeah, it's get it becomes get the +princess. There's one princess that has + + align:start position:0% +princess. There's one princess that has + + + align:start position:0% +princess. There's one princess that has +four knights and it becomes a + + align:start position:0% +four knights and it becomes a + + + align:start position:0% +four knights and it becomes a +competitive game. of it's like + + align:start position:0% +competitive game. of it's like + + + align:start position:0% +competitive game. of it's like +everything that you're using against the + + align:start position:0% +everything that you're using against the + + + align:start position:0% +everything that you're using against the +the baddies becomes something that you + + align:start position:0% +the baddies becomes something that you + + + align:start position:0% +the baddies becomes something that you +use on your teammates. Um and and there + + align:start position:0% +use on your teammates. Um and and there + + + align:start position:0% +use on your teammates. Um and and there +are games that flip-flop between that + + align:start position:0% +are games that flip-flop between that + + + align:start position:0% +are games that flip-flop between that +diplomacy is a really fluid game with + + align:start position:0% +diplomacy is a really fluid game with + + + align:start position:0% +diplomacy is a really fluid game with +their friends. It's like you have to + + align:start position:0% +their friends. It's like you have to + + + align:start position:0% +their friends. It's like you have to +assume everybody's competitive in that + + align:start position:0% +assume everybody's competitive in that + + + align:start position:0% +assume everybody's competitive in that +game, but the only way to attain your + + align:start position:0% +game, but the only way to attain your + + + align:start position:0% +game, but the only way to attain your +goals is to cooperate occasionally. Um + + align:start position:0% +goals is to cooperate occasionally. Um + + + align:start position:0% +goals is to cooperate occasionally. Um +and and so and so you all that's player + + align:start position:0% +and and so and so you all that's player + + + align:start position:0% +and and so and so you all that's player +cooperation. No one's disagreeing on + + align:start position:0% +cooperation. No one's disagreeing on + + + align:start position:0% +cooperation. No one's disagreeing on +rules. So that's there systemic + + align:start position:0% +rules. So that's there systemic + + + align:start position:0% +rules. So that's there systemic +cooperation all the way through but then + + align:start position:0% +cooperation all the way through but then + + + align:start position:0% +cooperation all the way through but then +there's clear competition and + + align:start position:0% +there's clear competition and + + + align:start position:0% +there's clear competition and +cooperation back and forth. Um so you + + align:start position:0% +cooperation back and forth. Um so you + + + align:start position:0% +cooperation back and forth. Um so you +know uh so that's cooperation. + + align:start position:0% +know uh so that's cooperation. + + + align:start position:0% +know uh so that's cooperation. +Um finally uh + + align:start position:0% +Um finally uh + + + align:start position:0% +Um finally uh +think think a little bit about level + + align:start position:0% +think think a little bit about level + + + align:start position:0% +think think a little bit about level +playing field or what it means in your + + align:start position:0% +playing field or what it means in your + + + align:start position:0% +playing field or what it means in your +game to have a level playing field. Cuz + + align:start position:0% +game to have a level playing field. Cuz + + + align:start position:0% +game to have a level playing field. Cuz +you know in many of your games + + align:start position:0% +you know in many of your games + + + align:start position:0% +you know in many of your games +especially car games you're going to + + align:start position:0% +especially car games you're going to + + + align:start position:0% +especially car games you're going to +start with some sort of deal. you're + + align:start position:0% +start with some sort of deal. you're + + + align:start position:0% +start with some sort of deal. you're +going to start with some sort of hand or + + align:start position:0% +going to start with some sort of hand or + + + align:start position:0% +going to start with some sort of hand or +maybe a drawing in some sort of + + align:start position:0% +maybe a drawing in some sort of + + + align:start position:0% +maybe a drawing in some sort of +systematic way from a shuffle deck. That + + align:start position:0% +systematic way from a shuffle deck. That + + + align:start position:0% +systematic way from a shuffle deck. That +pretty much means that you know uh + + align:start position:0% +pretty much means that you know uh + + + align:start position:0% +pretty much means that you know uh +you're starting out with something + + align:start position:0% +you're starting out with something + + + align:start position:0% +you're starting out with something +that's effectively random, but then um + + align:start position:0% +that's effectively random, but then um + + + align:start position:0% +that's effectively random, but then um +it could be also influenced by your + + align:start position:0% +it could be also influenced by your + + + align:start position:0% +it could be also influenced by your +knowledge of the game, like skill of the + + align:start position:0% +knowledge of the game, like skill of the + + + align:start position:0% +knowledge of the game, like skill of the +game. Um and uh and you want to see how + + align:start position:0% +game. Um and uh and you want to see how + + + align:start position:0% +game. Um and uh and you want to see how +h at what point h how how do you want to + + align:start position:0% +h at what point h how how do you want to + + + align:start position:0% +h at what point h how how do you want to +balance it between someone's skill + + align:start position:0% +balance it between someone's skill + + + align:start position:0% +balance it between someone's skill +familiarity with the game against pure + + align:start position:0% +familiarity with the game against pure + + + align:start position:0% +familiarity with the game against pure +chance right you know um a level playing + + align:start position:0% +chance right you know um a level playing + + + align:start position:0% +chance right you know um a level playing +field means a lot means a different + + align:start position:0% +field means a lot means a different + + + align:start position:0% +field means a lot means a different +thing to a lot of different people uh + + align:start position:0% +thing to a lot of different people uh + + + align:start position:0% +thing to a lot of different people uh +some people's mean uh for some people it + + align:start position:0% +some people's mean uh for some people it + + + align:start position:0% +some people's mean uh for some people it +may mean no matter what skill level I am + + align:start position:0% +may mean no matter what skill level I am + + + align:start position:0% +may mean no matter what skill level I am +I have a chance at winning so you're + + align:start position:0% +I have a chance at winning so you're + + + align:start position:0% +I have a chance at winning so you're +sort of biasing it towards chance for + + align:start position:0% +sort of biasing it towards chance for + + + align:start position:0% +sort of biasing it towards chance for +some people it means Um a level playing + + align:start position:0% +some people it means Um a level playing + + + align:start position:0% +some people it means Um a level playing +field is no matter what hand I I get + + align:start position:0% +field is no matter what hand I I get + + + align:start position:0% +field is no matter what hand I I get +given there is a valid strategy or the + + align:start position:0% +given there is a valid strategy or the + + + align:start position:0% +given there is a valid strategy or the +goals then get set in a way that allows + + align:start position:0% +goals then get set in a way that allows + + + align:start position:0% +goals then get set in a way that allows +me to attain it. A lot of trick- taking + + align:start position:0% +me to attain it. A lot of trick- taking + + + align:start position:0% +me to attain it. A lot of trick- taking +games especially games with with bidding + + align:start position:0% +games especially games with with bidding + + + align:start position:0% +games especially games with with bidding +actually have auto automatic correcting + + align:start position:0% +actually have auto automatic correcting + + + align:start position:0% +actually have auto automatic correcting +system in in there is like you only bid + + align:start position:0% +system in in there is like you only bid + + + align:start position:0% +system in in there is like you only bid +a game that you think that you can win. + + align:start position:0% +a game that you think that you can win. + + + align:start position:0% +a game that you think that you can win. +Um, and the whole idea is the game is to + + align:start position:0% +Um, and the whole idea is the game is to + + + align:start position:0% +Um, and the whole idea is the game is to +push your opponent to bid on something + + align:start position:0% +push your opponent to bid on something + + + align:start position:0% +push your opponent to bid on something +which they couldn't uh which they + + align:start position:0% +which they couldn't uh which they + + + align:start position:0% +which they couldn't uh which they +couldn't actually get. So, you know, + + align:start position:0% +couldn't actually get. So, you know, + + + align:start position:0% +couldn't actually get. So, you know, +that's that's a double playing field, + + align:start position:0% +that's that's a double playing field, + + + align:start position:0% +that's that's a double playing field, +right? You actually have a crappy hand, + + align:start position:0% +right? You actually have a crappy hand, + + + align:start position:0% +right? You actually have a crappy hand, +but that's not chance so much as + + align:start position:0% +but that's not chance so much as + + + align:start position:0% +but that's not chance so much as +as the as the decisions that you're + + align:start position:0% +as the as the decisions that you're + + + align:start position:0% +as the as the decisions that you're +making. So + + align:start position:0% +making. So + + + align:start position:0% +making. So +um + + align:start position:0% +um + + + align:start position:0% +um +so the + + align:start position:0% +so the + + + align:start position:0% +so the +what I will advocate in this class um if + + align:start position:0% +what I will advocate in this class um if + + + align:start position:0% +what I will advocate in this class um if +there's still time in the testing and + + align:start position:0% +there's still time in the testing and + + + align:start position:0% +there's still time in the testing and +there's of course there's two more + + align:start position:0% +there's of course there's two more + + + align:start position:0% +there's of course there's two more +coming back to this so so so so + + align:start position:0% +coming back to this so so so so + + + align:start position:0% +coming back to this so so so so +is when you're trying to balance it out + + align:start position:0% +is when you're trying to balance it out + + + align:start position:0% +is when you're trying to balance it out +towards whatever your interpretation of + + align:start position:0% +towards whatever your interpretation of + + + align:start position:0% +towards whatever your interpretation of +a level playing field is going to be um + + align:start position:0% +a level playing field is going to be um + + + align:start position:0% +a level playing field is going to be um +try to pick uh decisions that sort of + + align:start position:0% +try to pick uh decisions that sort of + + + align:start position:0% +try to pick uh decisions that sort of +push you in the direction of meaningful + + align:start position:0% +push you in the direction of meaningful + + + align:start position:0% +push you in the direction of meaningful +the decisions things that players can + + align:start position:0% +the decisions things that players can + + + align:start position:0% +the decisions things that players can +make a decision and they can see the + + align:start position:0% +make a decision and they can see the + + + align:start position:0% +make a decision and they can see the +consequences. They can understand how + + align:start position:0% +consequences. They can understand how + + + align:start position:0% +consequences. They can understand how +those consequences play out in the game + + align:start position:0% +those consequences play out in the game + + + align:start position:0% +those consequences play out in the game +um and the outcome and the outcome of + + align:start position:0% +um and the outcome and the outcome of + + + align:start position:0% +um and the outcome and the outcome of +the overall game is going to be going to + + align:start position:0% +the overall game is going to be going to + + + align:start position:0% +the overall game is going to be going to +be a result of that. Um that is again + + align:start position:0% +be a result of that. Um that is again + + + align:start position:0% +be a result of that. Um that is again +not necessarily the only definition. So + + align:start position:0% +not necessarily the only definition. So + + + align:start position:0% +not necessarily the only definition. So +I want to be very very clear what I'm + + align:start position:0% +I want to be very very clear what I'm + + + align:start position:0% +I want to be very very clear what I'm +asking of you here is not necessarily + + align:start position:0% +asking of you here is not necessarily + + + align:start position:0% +asking of you here is not necessarily +the only definition of a well-designed + + align:start position:0% +the only definition of a well-designed + + + align:start position:0% +the only definition of a well-designed +game. Um, you're designing a game to be + + align:start position:0% +game. Um, you're designing a game to be + + + align:start position:0% +game. Um, you're designing a game to be +p played from ages 3 to 90. You know, + + align:start position:0% +p played from ages 3 to 90. You know, + + + align:start position:0% +p played from ages 3 to 90. You know, +you probably want a game where making a + + align:start position:0% +you probably want a game where making a + + + align:start position:0% +you probably want a game where making a +meaningful decision isn't going to bias + + align:start position:0% +meaningful decision isn't going to bias + + + align:start position:0% +meaningful decision isn't going to bias +the game to the point that the really + + align:start position:0% +the game to the point that the really + + + align:start position:0% +the game to the point that the really +experienced people or really smart + + align:start position:0% +experienced people or really smart + + + align:start position:0% +experienced people or really smart +people are going to end up winning this + + align:start position:0% +people are going to end up winning this + + + align:start position:0% +people are going to end up winning this +game because that's just not for the + + align:start position:0% +game because that's just not for the + + + align:start position:0% +game because that's just not for the +three of us. Um now in this part in this + + align:start position:0% +three of us. Um now in this part in this + + + align:start position:0% +three of us. Um now in this part in this +part particular class um try to bias it + + align:start position:0% +part particular class um try to bias it + + + align:start position:0% +part particular class um try to bias it +so that in that competitive sense you + + align:start position:0% +so that in that competitive sense you + + + align:start position:0% +so that in that competitive sense you +want everyone to feel like they have a + + align:start position:0% +want everyone to feel like they have a + + + align:start position:0% +want everyone to feel like they have a +chance of winning but I want you to bias + + align:start position:0% +chance of winning but I want you to bias + + + align:start position:0% +chance of winning but I want you to bias +your game towards the and whe and and + + align:start position:0% +your game towards the and whe and and + + + align:start position:0% +your game towards the and whe and and +whether you win or lose is going to be + + align:start position:0% +whether you win or lose is going to be + + + align:start position:0% +whether you win or lose is going to be +based on the outcome of these decisions. + + align:start position:0% +based on the outcome of these decisions. + + + align:start position:0% +based on the outcome of these decisions. +clearly understanding the outcome of + + align:start position:0% +clearly understanding the outcome of + + + align:start position:0% +clearly understanding the outcome of +position that you made in the game, not + + align:start position:0% +position that you made in the game, not + + + align:start position:0% +position that you made in the game, not +necessarily just what you would what + + align:start position:0% +necessarily just what you would what + + + align:start position:0% +necessarily just what you would what +what you were dealt or what you were + + align:start position:0% +what you were dealt or what you were + + + align:start position:0% +what you were dealt or what you were +shar + + align:start position:0% +shar + + + align:start position:0% +shar +um + + align:start position:0% +um + + + align:start position:0% +um +you can still use those things in a + + align:start position:0% +you can still use those things in a + + + align:start position:0% +you can still use those things in a +game, right? You know, sometimes it's, + + align:start position:0% +game, right? You know, sometimes it's, + + + align:start position:0% +game, right? You know, sometimes it's, +you know, the whole idea of, oh my god, + + align:start position:0% +you know, the whole idea of, oh my god, + + + align:start position:0% +you know, the whole idea of, oh my god, +I hope this red card, I hope this red + + align:start position:0% +I hope this red card, I hope this red + + + align:start position:0% +I hope this red card, I hope this red +card, you know, it's like, oh, but then + + align:start position:0% +card, you know, it's like, oh, but then + + + align:start position:0% +card, you know, it's like, oh, but then +but then you think things like + + align:start position:0% +but then you think things like + + + align:start position:0% +but then you think things like +probability, right? You know, it's like + + align:start position:0% +probability, right? You know, it's like + + + align:start position:0% +probability, right? You know, it's like +how much information are you giving to + + align:start position:0% +how much information are you giving to + + + align:start position:0% +how much information are you giving to +the player about what the probability + + align:start position:0% +the player about what the probability + + + align:start position:0% +the player about what the probability +that that's the right card going to be? + + align:start position:0% +that that's the right card going to be? + + + align:start position:0% +that that's the right card going to be? +Are you letting them look at the deck + + align:start position:0% +Are you letting them look at the deck + + + align:start position:0% +Are you letting them look at the deck +ahead of time? You know, are you giving + + align:start position:0% +ahead of time? You know, are you giving + + + align:start position:0% +ahead of time? You know, are you giving +them information about how many of those + + align:start position:0% +them information about how many of those + + + align:start position:0% +them information about how many of those +cards are in the deck, you know, so that + + align:start position:0% +cards are in the deck, you know, so that + + + align:start position:0% +cards are in the deck, you know, so that +they can actually make guesses on all + + align:start position:0% +they can actually make guesses on all + + + align:start position:0% +they can actually make guesses on all +right, we've played through half this + + align:start position:0% +right, we've played through half this + + + align:start position:0% +right, we've played through half this +deck and we haven't seen any of those + + align:start position:0% +deck and we haven't seen any of those + + + align:start position:0% +deck and we haven't seen any of those +cards yet, that means my the probability + + align:start position:0% +cards yet, that means my the probability + + + align:start position:0% +cards yet, that means my the probability +of that card showing up is now gone up. + + align:start position:0% +of that card showing up is now gone up. + + + align:start position:0% +of that card showing up is now gone up. +And that's now we come to the decision + + align:start position:0% +And that's now we come to the decision + + + align:start position:0% +And that's now we come to the decision +that you get to make. Do I do I draw? Do + + align:start position:0% +that you get to make. Do I do I draw? Do + + + align:start position:0% +that you get to make. Do I do I draw? Do +I you know do I hold that that so uh so + + align:start position:0% +I you know do I hold that that so uh so + + + align:start position:0% +I you know do I hold that that so uh so +try so that's my suggestion for this + + align:start position:0% +try so that's my suggestion for this + + + align:start position:0% +try so that's my suggestion for this +class I would love it to be able to see + + align:start position:0% +class I would love it to be able to see + + + align:start position:0% +class I would love it to be able to see +a little bit to to to see those kinds of + + align:start position:0% +a little bit to to to see those kinds of + + + align:start position:0% +a little bit to to to see those kinds of +uh those kind of things come out come + + align:start position:0% +uh those kind of things come out come + + + align:start position:0% +uh those kind of things come out come +come out this class + + align:start position:0% +come out this class + + + align:start position:0% +come out this class +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so that's uh that's all the things that + + align:start position:0% +so that's uh that's all the things that + + + align:start position:0% +so that's uh that's all the things that +have remaining there so now we can erase + + align:start position:0% +have remaining there so now we can erase + + + align:start position:0% +have remaining there so now we can erase +that after this class + + align:start position:0% +that after this class + + + align:start position:0% +that after this class +all right so uh now on actually Before + + align:start position:0% +all right so uh now on actually Before + + + align:start position:0% +all right so uh now on actually Before +we move on, anyone have any questions + + align:start position:0% +we move on, anyone have any questions + + + align:start position:0% +we move on, anyone have any questions +regarding that? + + align:start position:0% + + + + align:start position:0% + +No. + + align:start position:0% +No. + + + align:start position:0% +No. +Um, one point of administration. Um, who + + align:start position:0% +Um, one point of administration. Um, who + + + align:start position:0% +Um, one point of administration. Um, who +here needs to print on Gambit printers, + + align:start position:0% +here needs to print on Gambit printers, + + + align:start position:0% +here needs to print on Gambit printers, +right? Or who here has access to other + + align:start position:0% +right? Or who here has access to other + + + align:start position:0% +right? Or who here has access to other +printers that you guys are fairly + + align:start position:0% +printers that you guys are fairly + + + align:start position:0% +printers that you guys are fairly +confident about using for your + + align:start position:0% +confident about using for your + + + align:start position:0% +confident about using for your +assignment? + + align:start position:0% +assignment? + + + align:start position:0% +assignment? +>> You need + + align:start position:0% +>> You need + + + align:start position:0% +>> You need +>> No, I mean, would you say that you need + + align:start position:0% +>> No, I mean, would you say that you need + + + align:start position:0% +>> No, I mean, would you say that you need +a printer or you have access? You said + + align:start position:0% +a printer or you have access? You said + + + align:start position:0% +a printer or you have access? You said +both. + + align:start position:0% +both. + + + align:start position:0% +both. +>> All right. So, who needs to use camera + + align:start position:0% +>> All right. So, who needs to use camera + + + align:start position:0% +>> All right. So, who needs to use camera +printers? Uh, who absolutely needs to + + align:start position:0% +printers? Uh, who absolutely needs to + + + align:start position:0% +printers? Uh, who absolutely needs to +use candle printers? Okay, because we + + align:start position:0% +use candle printers? Okay, because we + + + align:start position:0% +use candle printers? Okay, because we +don't we don't actually have like a + + align:start position:0% +don't we don't actually have like a + + + align:start position:0% +don't we don't actually have like a +computer set up for anybody to to log in + + align:start position:0% +computer set up for anybody to to log in + + + align:start position:0% +computer set up for anybody to to log in +and actually all our Europs just started + + align:start position:0% +and actually all our Europs just started + + + align:start position:0% +and actually all our Europs just started +working. So, I would suggest not using + + align:start position:0% +working. So, I would suggest not using + + + align:start position:0% +working. So, I would suggest not using +any of the computers in this lab because + + align:start position:0% +any of the computers in this lab because + + + align:start position:0% +any of the computers in this lab because +lab work on it. Um, okay. So, if you've + + align:start position:0% +lab work on it. Um, okay. So, if you've + + + align:start position:0% +lab work on it. Um, okay. So, if you've +all got access to printers, that's + + align:start position:0% +all got access to printers, that's + + + align:start position:0% +all got access to printers, that's +awesome. Um, I know you sent an email + + align:start position:0% +awesome. Um, I know you sent an email + + + align:start position:0% +awesome. Um, I know you sent an email +about card stock. Uh that that card + + align:start position:0% +about card stock. Uh that that card + + + align:start position:0% +about card stock. Uh that that card +stock's actually out of stock. + + align:start position:0% +stock's actually out of stock. + + + align:start position:0% +stock's actually out of stock. +>> That's ironic. + + align:start position:0% +>> That's ironic. + + + align:start position:0% +>> That's ironic. +>> Yeah. I went to order it and I was like, + + align:start position:0% +>> Yeah. I went to order it and I was like, + + + align:start position:0% +>> Yeah. I went to order it and I was like, +"Oh shit." + + align:start position:0% +"Oh shit." + + + align:start position:0% +"Oh shit." +>> I'm going to take off with a long time, + + align:start position:0% +>> I'm going to take off with a long time, + + + align:start position:0% +>> I'm going to take off with a long time, +but I'm sure there's other card stock. + + align:start position:0% +but I'm sure there's other card stock. + + + align:start position:0% +but I'm sure there's other card stock. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +>> isn't there like a Staples or somewhere? + + align:start position:0% +>> isn't there like a Staples or somewhere? + + + align:start position:0% +>> isn't there like a Staples or somewhere? +>> Tech has Staples. Stock Town has + + align:start position:0% +>> Tech has Staples. Stock Town has + + + align:start position:0% +>> Tech has Staples. Stock Town has +Staples. + + align:start position:0% +Staples. + + + align:start position:0% +Staples. +>> Copy Tech has I went to Copy Tech and + + align:start position:0% +>> Copy Tech has I went to Copy Tech and + + + align:start position:0% +>> Copy Tech has I went to Copy Tech and +they said they can print and cut your + + align:start position:0% +they said they can print and cut your + + + align:start position:0% +they said they can print and cut your +cards for you. + + align:start position:0% +cards for you. + + + align:start position:0% +cards for you. +>> Nice. + + align:start position:0% +>> Nice. + + + align:start position:0% +>> Nice. +>> Yeah. Yeah. They they they they have a + + align:start position:0% +>> Yeah. Yeah. They they they they have a + + + align:start position:0% +>> Yeah. Yeah. They they they they have a +pretty awesome uh card printer. They the + + align:start position:0% +pretty awesome uh card printer. They the + + + align:start position:0% +pretty awesome uh card printer. They the +their cutter is harsh harsh harsh. Um, + + align:start position:0% +their cutter is harsh harsh harsh. Um, + + + align:start position:0% +their cutter is harsh harsh harsh. Um, +>> what does that what does that mean? + + align:start position:0% +>> what does that what does that mean? + + + align:start position:0% +>> what does that what does that mean? +>> Well, first of all, really pointy at the + + align:start position:0% +>> Well, first of all, really pointy at the + + + align:start position:0% +>> Well, first of all, really pointy at the +corners, which is kind of cool if that's + + align:start position:0% +corners, which is kind of cool if that's + + + align:start position:0% +corners, which is kind of cool if that's +what you were going for, but I don't + + align:start position:0% +what you were going for, but I don't + + + align:start position:0% +what you were going for, but I don't +think + + align:start position:0% +think + + + align:start position:0% +think +>> Can they Can they roundy it or do we + + align:start position:0% +>> Can they Can they roundy it or do we + + + align:start position:0% +>> Can they Can they roundy it or do we +have to use + + align:start position:0% +have to use + + + align:start position:0% +have to use +>> I don't + + align:start position:0% +>> I don't + + + align:start position:0% +>> I don't +>> They can't. + + align:start position:0% +>> They can't. + + + align:start position:0% +>> They can't. +>> They They can't. I have a rounder. Uh, I + + align:start position:0% +>> They They can't. I have a rounder. Uh, I + + + align:start position:0% +>> They They can't. I have a rounder. Uh, I +have a corner punch that, you know, you + + align:start position:0% +have a corner punch that, you know, you + + + align:start position:0% +have a corner punch that, you know, you +have to do it four times for each card. + + align:start position:0% +have to do it four times for each card. + + + align:start position:0% +have to do it four times for each card. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +>> we can we'll do it. You can do it. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. just ask me and you can borrow it. + + align:start position:0% +>> Yeah. just ask me and you can borrow it. + + + align:start position:0% +>> Yeah. just ask me and you can borrow it. +You may want to do it on some test cards + + align:start position:0% +You may want to do it on some test cards + + + align:start position:0% +You may want to do it on some test cards +before doing it on all your questions to + + align:start position:0% +before doing it on all your questions to + + + align:start position:0% +before doing it on all your questions to +get a sense of how it works. It works + + align:start position:0% +get a sense of how it works. It works + + + align:start position:0% +get a sense of how it works. It works +better on card stock than it does on + + align:start position:0% +better on card stock than it does on + + + align:start position:0% +better on card stock than it does on +paper. Uh and I wouldn't suggest + + align:start position:0% +paper. Uh and I wouldn't suggest + + + align:start position:0% +paper. Uh and I wouldn't suggest +punching more than one card at a time. + + align:start position:0% +punching more than one card at a time. + + + align:start position:0% +punching more than one card at a time. +The the other thing is um if you're + + align:start position:0% +The the other thing is um if you're + + + align:start position:0% +The the other thing is um if you're +printing it on a um not like copy check + + align:start position:0% +printing it on a um not like copy check + + + align:start position:0% +printing it on a um not like copy check +where they obviously know what kind of + + align:start position:0% +where they obviously know what kind of + + + align:start position:0% +where they obviously know what kind of +paper goes best with their printers. you + + align:start position:0% +paper goes best with their printers. you + + + align:start position:0% +paper goes best with their printers. you +know, if you're printing it on something + + align:start position:0% +know, if you're printing it on something + + + align:start position:0% +know, if you're printing it on something +like a laser jet, uh, if you go to the + + align:start position:0% +like a laser jet, uh, if you go to the + + + align:start position:0% +like a laser jet, uh, if you go to the +paper manufacturers's website, they + + align:start position:0% +paper manufacturers's website, they + + + align:start position:0% +paper manufacturers's website, they +actually, a lot of them actually + + align:start position:0% +actually, a lot of them actually + + + align:start position:0% +actually, a lot of them actually +specifically say laser jet compatible. + + align:start position:0% +specifically say laser jet compatible. + + + align:start position:0% +specifically say laser jet compatible. +Um, and the problem isn't actually the + + align:start position:0% +Um, and the problem isn't actually the + + + align:start position:0% +Um, and the problem isn't actually the +weight of the card. It's not like the + + align:start position:0% +weight of the card. It's not like the + + + align:start position:0% +weight of the card. It's not like the +folding of the paper as it goes through + + align:start position:0% +folding of the paper as it goes through + + + align:start position:0% +folding of the paper as it goes through +the printer. It's whether the toner will + + align:start position:0% +the printer. It's whether the toner will + + + align:start position:0% +the printer. It's whether the toner will +bond to the paper, like does the paper + + align:start position:0% +bond to the paper, like does the paper + + + align:start position:0% +bond to the paper, like does the paper +get hot enough, you know, without + + align:start position:0% +get hot enough, you know, without + + + align:start position:0% +get hot enough, you know, without +catching fire. Um, does the paper get + + align:start position:0% +catching fire. Um, does the paper get + + + align:start position:0% +catching fire. Um, does the paper get +hot enough for the toner to actually + + align:start position:0% +hot enough for the toner to actually + + + align:start position:0% +hot enough for the toner to actually +bond? Um, and a lot of card stocks + + align:start position:0% +bond? Um, and a lot of card stocks + + + align:start position:0% +bond? Um, and a lot of card stocks +actually don't because they're so thick + + align:start position:0% +actually don't because they're so thick + + + align:start position:0% +actually don't because they're so thick +that the heat doesn't transfer well. And + + align:start position:0% +that the heat doesn't transfer well. And + + + align:start position:0% +that the heat doesn't transfer well. And +as a result of that, other prints, it + + align:start position:0% +as a result of that, other prints, it + + + align:start position:0% +as a result of that, other prints, it +looks great when it comes out and it + + align:start position:0% +looks great when it comes out and it + + + align:start position:0% +looks great when it comes out and it +starts flaking. Uh, so that's that's + + align:start position:0% +starts flaking. Uh, so that's that's + + + align:start position:0% +starts flaking. Uh, so that's that's +that's the problem that you can cast + + align:start position:0% +that's the problem that you can cast + + + align:start position:0% +that's the problem that you can cast +off. Sure, some card stocks just jam + + align:start position:0% +off. Sure, some card stocks just jam + + + align:start position:0% +off. Sure, some card stocks just jam +your printer, but majority of modern + + align:start position:0% +your printer, but majority of modern + + + align:start position:0% +your printer, but majority of modern +laser jets actually deal pretty well + + align:start position:0% +laser jets actually deal pretty well + + + align:start position:0% +laser jets actually deal pretty well +with that. It gets worse with it with + + align:start position:0% +with that. It gets worse with it with + + + align:start position:0% +with that. It gets worse with it with +paper. + + align:start position:0% +paper. + + + align:start position:0% +paper. +>> Uh, did you want us to print on card + + align:start position:0% +>> Uh, did you want us to print on card + + + align:start position:0% +>> Uh, did you want us to print on card +stock for Wednesday or was that for when + + align:start position:0% +stock for Wednesday or was that for when + + + align:start position:0% +stock for Wednesday or was that for when +it's due? + + align:start position:0% +it's due? + + + align:start position:0% +it's due? +>> When it's due. + + align:start position:0% +>> When it's due. + + + align:start position:0% +>> When it's due. +>> Okay. So when + + align:start position:0% +>> Okay. So when + + + align:start position:0% +>> Okay. So when +>> and in fact printing card stock for when + + align:start position:0% +>> and in fact printing card stock for when + + + align:start position:0% +>> and in fact printing card stock for when +it's due is not necessary. It is it is + + align:start position:0% +it's due is not necessary. It is it is + + + align:start position:0% +it's due is not necessary. It is it is +much appreciated. + + align:start position:0% +much appreciated. + + + align:start position:0% +much appreciated. +It was a great thing for you to do for + + align:start position:0% +It was a great thing for you to do for + + + align:start position:0% +It was a great thing for you to do for +yourself if you want to make copies for + + align:start position:0% +yourself if you want to make copies for + + + align:start position:0% +yourself if you want to make copies for +your friends or your team uh that you + + align:start position:0% +your friends or your team uh that you + + + align:start position:0% +your friends or your team uh that you +actually want to end up playing. Uh to + + align:start position:0% +actually want to end up playing. Uh to + + + align:start position:0% +actually want to end up playing. Uh to +be perfectly honest, if you say, you + + align:start position:0% +be perfectly honest, if you say, you + + + align:start position:0% +be perfectly honest, if you say, you +know, we our printer wasn't working and + + align:start position:0% +know, we our printer wasn't working and + + + align:start position:0% +know, we our printer wasn't working and +all we could do were these like regular + + align:start position:0% +all we could do were these like regular + + + align:start position:0% +all we could do were these like regular +weight papers, but it's all been cut in + + align:start position:0% +weight papers, but it's all been cut in + + + align:start position:0% +weight papers, but it's all been cut in +the right shape so that I can make so + + align:start position:0% +the right shape so that I can make so + + + align:start position:0% +the right shape so that I can make so +that we can just play the game. That's + + align:start position:0% +that we can just play the game. That's + + + align:start position:0% +that we can just play the game. That's +fine. We can still, you know, we're not + + align:start position:0% +fine. We can still, you know, we're not + + + align:start position:0% +fine. We can still, you know, we're not +going to take the weight of your paper + + align:start position:0% +going to take the weight of your paper + + + align:start position:0% +going to take the weight of your paper +into the cover. + + align:start position:0% +into the cover. + + + align:start position:0% +into the cover. +>> Weigh the deck first. + + align:start position:0% +>> Weigh the deck first. + + + align:start position:0% +>> Weigh the deck first. +>> G per card. It's in size. + + align:start position:0% +>> G per card. It's in size. + + + align:start position:0% +>> G per card. It's in size. +>> All right. If anyone played what was it? + + align:start position:0% +>> All right. If anyone played what was it? + + + align:start position:0% +>> All right. If anyone played what was it? +Modern uh high society books or + + align:start position:0% +Modern uh high society books or + + + align:start position:0% +Modern uh high society books or +something. + + align:start position:0% +something. + + + align:start position:0% +something. +>> Yes, + + align:start position:0% +>> Yes, + + + align:start position:0% +>> Yes, +>> those are awesome. + + align:start position:0% +>> those are awesome. + + + align:start position:0% +>> those are awesome. +>> They were like they were like they were + + align:start position:0% +>> They were like they were like they were + + + align:start position:0% +>> They were like they were like they were +like kids books, you know. + + align:start position:0% + + + + align:start position:0% + +>> All right, cool. Um if anyone does have + + align:start position:0% +>> All right, cool. Um if anyone does have + + + align:start position:0% +>> All right, cool. Um if anyone does have +issues printing, uh before you jump + + align:start position:0% +issues printing, uh before you jump + + + align:start position:0% +issues printing, uh before you jump +straight into the gamma print printer, + + align:start position:0% +straight into the gamma print printer, + + + align:start position:0% +straight into the gamma print printer, +talk talk to Jason or I. Uh you know, + + align:start position:0% +talk talk to Jason or I. Uh you know, + + + align:start position:0% +talk talk to Jason or I. Uh you know, +Jason is usually in a room right next to + + align:start position:0% +Jason is usually in a room right next to + + + align:start position:0% +Jason is usually in a room right next to +TV lounge, my room, which is down the + + align:start position:0% +TV lounge, my room, which is down the + + + align:start position:0% +TV lounge, my room, which is down the +corridor. Uh and we can and we might be + + align:start position:0% +corridor. Uh and we can and we might be + + + align:start position:0% +corridor. Uh and we can and we might be +able to help you with with that. But in + + align:start position:0% +able to help you with with that. But in + + + align:start position:0% +able to help you with with that. But in +general, if you got access to other + + align:start position:0% +general, if you got access to other + + + align:start position:0% +general, if you got access to other +printers, go right for it because going + + align:start position:0% +printers, go right for it because going + + + align:start position:0% +printers, go right for it because going +to run us like + + align:start position:0% +to run us like + + + align:start position:0% +to run us like +again not for Wednesday. For Wednesday, + + align:start position:0% +again not for Wednesday. For Wednesday, + + + align:start position:0% +again not for Wednesday. For Wednesday, +just have something testable so that uh + + align:start position:0% +just have something testable so that uh + + + align:start position:0% +just have something testable so that uh +can uh folks can print but before the + + align:start position:0% +can uh folks can print but before the + + + align:start position:0% +can uh folks can print but before the +date is due try to print something. Uh + + align:start position:0% +date is due try to print something. Uh + + + align:start position:0% +date is due try to print something. Uh +you don't want to leave it till last + + align:start position:0% +you don't want to leave it till last + + + align:start position:0% +you don't want to leave it till last +minute and you don't want to like + + align:start position:0% +minute and you don't want to like + + + align:start position:0% +minute and you don't want to like +suddenly realize that your paper doesn't + + align:start position:0% +suddenly realize that your paper doesn't + + + align:start position:0% +suddenly realize that your paper doesn't +work very well with the printer on the + + align:start position:0% +work very well with the printer on the + + + align:start position:0% +work very well with the printer on the +last minute. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Right. So uh today's reading was Bartle + + align:start position:0% +Right. So uh today's reading was Bartle + + + align:start position:0% +Right. So uh today's reading was Bartle +and uh chapter 11 I think of the uh of + + align:start position:0% +and uh chapter 11 I think of the uh of + + + align:start position:0% +and uh chapter 11 I think of the uh of +breathway as well and um in general + + align:start position:0% +breathway as well and um in general + + + align:start position:0% +breathway as well and um in general +they have both them are asking the same + + align:start position:0% +they have both them are asking the same + + + align:start position:0% +they have both them are asking the same +question which is who are you designing + + align:start position:0% +question which is who are you designing + + + align:start position:0% +question which is who are you designing +your game for um on the assumption that + + align:start position:0% +your game for um on the assumption that + + + align:start position:0% +your game for um on the assumption that +it's not you're not designing the game + + align:start position:0% +it's not you're not designing the game + + + align:start position:0% +it's not you're not designing the game +for yourself and of course realistically + + align:start position:0% +for yourself and of course realistically + + + align:start position:0% +for yourself and of course realistically +if you're going to get a job making + + align:start position:0% +if you're going to get a job making + + + align:start position:0% +if you're going to get a job making +games that's the majority of the games + + align:start position:0% +games that's the majority of the games + + + align:start position:0% +games that's the majority of the games +that you're going to design are not + + align:start position:0% +that you're going to design are not + + + align:start position:0% +that you're going to design are not +games like uh games for something in the + + align:start position:0% +games like uh games for something in the + + + align:start position:0% +games like uh games for something in the +game for some other demographic. Um and + + align:start position:0% +game for some other demographic. Um and + + + align:start position:0% +game for some other demographic. Um and +um the bar paper is a little bit more + + align:start position:0% +um the bar paper is a little bit more + + + align:start position:0% +um the bar paper is a little bit more +influential in sort of uh helping people + + align:start position:0% +influential in sort of uh helping people + + + align:start position:0% +influential in sort of uh helping people +think about uh games because it kind of + + align:start position:0% +think about uh games because it kind of + + + align:start position:0% +think about uh games because it kind of +shifted the question from what's the age + + align:start position:0% +shifted the question from what's the age + + + align:start position:0% +shifted the question from what's the age +group, what's the demographic, you know, + + align:start position:0% +group, what's the demographic, you know, + + + align:start position:0% +group, what's the demographic, you know, +what do people out there who are already + + align:start position:0% +what do people out there who are already + + + align:start position:0% +what do people out there who are already +buying games going to want? Uh and he + + align:start position:0% +buying games going to want? Uh and he + + + align:start position:0% +buying games going to want? Uh and he +kind of flipped that into what sort of + + align:start position:0% +kind of flipped that into what sort of + + + align:start position:0% +kind of flipped that into what sort of +things are people looking for in the + + align:start position:0% +things are people looking for in the + + + align:start position:0% +things are people looking for in the +game. um he doesn't actually take it to + + align:start position:0% +game. um he doesn't actually take it to + + + align:start position:0% +game. um he doesn't actually take it to +the next step which is where well I + + align:start position:0% +the next step which is where well I + + + align:start position:0% +the next step which is where well I +think he wrote that in the 70s or the + + align:start position:0% +think he wrote that in the 70s or the + + + align:start position:0% +think he wrote that in the 70s or the +80s I did anyone remember + + align:start position:0% +80s I did anyone remember + + + align:start position:0% +80s I did anyone remember +>> I think it was like 90 + + align:start position:0% +>> I think it was like 90 + + + align:start position:0% +>> I think it was like 90 +I think + + align:start position:0% +I think + + + align:start position:0% +I think +was 1990s + + align:start position:0% +was 1990s + + + align:start position:0% +was 1990s +>> right + + align:start position:0% +>> right + + + align:start position:0% +>> right +he talks about actually + + align:start position:0% +he talks about actually + + + align:start position:0% +he talks about actually +>> no ever that's right um but uh he but a + + align:start position:0% +>> no ever that's right um but uh he but a + + + align:start position:0% +>> no ever that's right um but uh he but a +lot of the the ideas come from the 70s + + align:start position:0% +lot of the the ideas come from the 70s + + + align:start position:0% +lot of the the ideas come from the 70s +actually because that's when he made the + + align:start position:0% +actually because that's when he made the + + + align:start position:0% +actually because that's when he made the +first mod. Uh Richard B. + + align:start position:0% +first mod. Uh Richard B. + + + align:start position:0% +first mod. Uh Richard B. +>> What exactly is a mud? They never + + align:start position:0% +>> What exactly is a mud? They never + + + align:start position:0% +>> What exactly is a mud? They never +actually described. I just said assumed + + align:start position:0% +actually described. I just said assumed + + + align:start position:0% +actually described. I just said assumed +everyone knew what a mud was. + + align:start position:0% +everyone knew what a mud was. + + + align:start position:0% +everyone knew what a mud was. +>> Mud stands for multi-user engine. Anyone + + align:start position:0% +>> Mud stands for multi-user engine. Anyone + + + align:start position:0% +>> Mud stands for multi-user engine. Anyone +want to describe that? + + align:start position:0% +want to describe that? + + + align:start position:0% +want to describe that? +>> It's like + + align:start position:0% +>> It's like + + + align:start position:0% +>> It's like +like an online text adventure thing + + align:start position:0% +like an online text adventure thing + + + align:start position:0% +like an online text adventure thing +where everyone's kind of like + + align:start position:0% +where everyone's kind of like + + + align:start position:0% +where everyone's kind of like +interacting with the same text base + + align:start position:0% +interacting with the same text base + + + align:start position:0% +interacting with the same text base +dungeon thing. Let's describe is imagine + + align:start position:0% +dungeon thing. Let's describe is imagine + + + align:start position:0% +dungeon thing. Let's describe is imagine +that wow was presented inactic fiction. + + align:start position:0% +that wow was presented inactic fiction. + + + align:start position:0% +that wow was presented inactic fiction. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> So that's I found that kind of annoying + + align:start position:0% +>> So that's I found that kind of annoying + + + align:start position:0% +>> So that's I found that kind of annoying +in the text. He just assumed everyone + + align:start position:0% +in the text. He just assumed everyone + + + align:start position:0% +in the text. He just assumed everyone +knew what mud was but never actually + + align:start position:0% +knew what mud was but never actually + + + align:start position:0% +knew what mud was but never actually +said this is what mud is. + + align:start position:0% +said this is what mud is. + + + align:start position:0% +said this is what mud is. +>> Yeah. Yeah. Because because the the the + + align:start position:0% +>> Yeah. Yeah. Because because the the the + + + align:start position:0% +>> Yeah. Yeah. Because because the the the +folks who are reading their article + + align:start position:0% +folks who are reading their article + + + align:start position:0% +folks who are reading their article +actually I believe he formatted that for + + align:start position:0% +actually I believe he formatted that for + + + align:start position:0% +actually I believe he formatted that for +a forum post for a mud community. So + + align:start position:0% +a forum post for a mud community. So + + + align:start position:0% +a forum post for a mud community. So +that's assumption. + + align:start position:0% +that's assumption. + + + align:start position:0% +that's assumption. +Um but yeah um apologies for that. Um + + align:start position:0% +Um but yeah um apologies for that. Um + + + align:start position:0% +Um but yeah um apologies for that. Um +actually if you're interested he does + + align:start position:0% +actually if you're interested he does + + + align:start position:0% +actually if you're interested he does +define it right at the bottom which is + + align:start position:0% +define it right at the bottom which is + + + align:start position:0% +define it right at the bottom which is +like right at the end of the article. + + align:start position:0% +like right at the end of the article. + + + align:start position:0% +like right at the end of the article. +here she talks about specifically this + + align:start position:0% +here she talks about specifically this + + + align:start position:0% +here she talks about specifically this +is what I I mean by somewhere in the + + align:start position:0% +is what I I mean by somewhere in the + + + align:start position:0% +is what I I mean by somewhere in the +footnote says there's like you know + + align:start position:0% +footnote says there's like you know + + + align:start position:0% +footnote says there's like you know +these text text adventures uh text style + + align:start position:0% +these text text adventures uh text style + + + align:start position:0% +these text text adventures uh text style +online games with multiple people + + align:start position:0% +online games with multiple people + + + align:start position:0% +online games with multiple people +interacting and uh and if you look at + + align:start position:0% +interacting and uh and if you look at + + + align:start position:0% +interacting and uh and if you look at +the rest of the website there's actually + + align:start position:0% +the rest of the website there's actually + + + align:start position:0% +the rest of the website there's actually +a bunch of stuff about how work but for + + align:start position:0% +a bunch of stuff about how work but for + + + align:start position:0% +a bunch of stuff about how work but for +the most part that was that was sort of + + align:start position:0% +the most part that was that was sort of + + + align:start position:0% +the most part that was that was sort of +online multiplayer gaming uh back when + + align:start position:0% +online multiplayer gaming uh back when + + + align:start position:0% +online multiplayer gaming uh back when +he started um he was he's he's credited + + align:start position:0% +he started um he was he's he's credited + + + align:start position:0% +he started um he was he's he's credited +for having built the first the first one + + align:start position:0% +for having built the first the first one + + + align:start position:0% +for having built the first the first one +and frankly + + align:start position:0% +and frankly + + + align:start position:0% +and frankly +not all that different from MMOGs that + + align:start position:0% +not all that different from MMOGs that + + + align:start position:0% +not all that different from MMOGs that +you get today. Uh, you know, the + + align:start position:0% +you get today. Uh, you know, the + + + align:start position:0% +you get today. Uh, you know, the +difference being that they were all + + align:start position:0% +difference being that they were all + + + align:start position:0% +difference being that they were all +text, but you still went out hunting + + align:start position:0% +text, but you still went out hunting + + + align:start position:0% +text, but you still went out hunting +uh uh monsters. They call them mobiles + + align:start position:0% +uh uh monsters. They call them mobiles + + + align:start position:0% +uh uh monsters. They call them mobiles +or mobs. And in fact, actually, there's + + align:start position:0% +or mobs. And in fact, actually, there's + + + align:start position:0% +or mobs. And in fact, actually, there's +still some of the terminology they're + + align:start position:0% +still some of the terminology they're + + + align:start position:0% +still some of the terminology they're +playing around. Um, they drop loot. You + + align:start position:0% +playing around. Um, they drop loot. You + + + align:start position:0% +playing around. Um, they drop loot. You +know, you will pick up this loot and + + align:start position:0% +know, you will pick up this loot and + + + align:start position:0% +know, you will pick up this loot and +show it off. And sometimes some games + + align:start position:0% +show it off. And sometimes some games + + + align:start position:0% +show it off. And sometimes some games +that you sell off the loot, some that + + align:start position:0% +that you sell off the loot, some that + + + align:start position:0% +that you sell off the loot, some that +most games that you exchange loot uh and + + align:start position:0% +most games that you exchange loot uh and + + + align:start position:0% +most games that you exchange loot uh and +then you would use your loot to go and + + align:start position:0% +then you would use your loot to go and + + + align:start position:0% +then you would use your loot to go and +kill other monsters and get better loot. + + align:start position:0% +kill other monsters and get better loot. + + + align:start position:0% +kill other monsters and get better loot. +Uh sometimes you do it with other + + align:start position:0% +Uh sometimes you do it with other + + + align:start position:0% +Uh sometimes you do it with other +people. Sometimes you attack other + + align:start position:0% +people. Sometimes you attack other + + + align:start position:0% +people. Sometimes you attack other +people. Uh sometimes you just hang + + align:start position:0% +people. Uh sometimes you just hang + + + align:start position:0% +people. Uh sometimes you just hang +around and chat and talk about things + + align:start position:0% +around and chat and talk about things + + + align:start position:0% +around and chat and talk about things +that are completely not in game like + + align:start position:0% +that are completely not in game like + + + align:start position:0% +that are completely not in game like +what if I have a bunch of + + align:start position:0% +what if I have a bunch of + + + align:start position:0% +what if I have a bunch of +some awesome Um + + align:start position:0% +some awesome Um + + + align:start position:0% +some awesome Um +and uh sometimes sometimes it will take + + align:start position:0% +and uh sometimes sometimes it will take + + + align:start position:0% +and uh sometimes sometimes it will take +multiple people to take down a to take a + + align:start position:0% +multiple people to take down a to take a + + + align:start position:0% +multiple people to take down a to take a +monster you know and it was just handled + + align:start position:0% +monster you know and it was just handled + + + align:start position:0% +monster you know and it was just handled +that you know how fast can you type kind + + align:start position:0% +that you know how fast can you type kind + + + align:start position:0% +that you know how fast can you type kind +of thing. Um you know attack monster + + align:start position:0% +of thing. Um you know attack monster + + + align:start position:0% +of thing. Um you know attack monster +attack monster attack and I think you + + align:start position:0% +attack monster attack and I think you + + + align:start position:0% +attack monster attack and I think you +can just hit repeat + + align:start position:0% +can just hit repeat + + + align:start position:0% +can just hit repeat +um and uh but uh + + align:start position:0% +um and uh but uh + + + align:start position:0% +um and uh but uh +the behaviors are also not all that + + align:start position:0% +the behaviors are also not all that + + + align:start position:0% +the behaviors are also not all that +different. And um how he describes it is + + align:start position:0% +different. And um how he describes it is + + + align:start position:0% +different. And um how he describes it is +a whole a a game kind will will kind of + + align:start position:0% +a whole a a game kind will will kind of + + + align:start position:0% +a whole a a game kind will will kind of +sight sight itself in a position where + + align:start position:0% +sight sight itself in a position where + + + align:start position:0% +sight sight itself in a position where +it is like ve variably + + align:start position:0% +it is like ve variably + + + align:start position:0% +it is like ve variably +appealing to various kinds of players. + + align:start position:0% +appealing to various kinds of players. + + + align:start position:0% +appealing to various kinds of players. +Uh and that's how he describes it. Where + + align:start position:0% +Uh and that's how he describes it. Where + + + align:start position:0% +Uh and that's how he describes it. Where +game studies has kind of gone to on + + align:start position:0% +game studies has kind of gone to on + + + align:start position:0% +game studies has kind of gone to on +since then is the realization that just + + align:start position:0% +since then is the realization that just + + + align:start position:0% +since then is the realization that just +because you're uh actually some people + + align:start position:0% +because you're uh actually some people + + + align:start position:0% +because you're uh actually some people +throw out the four types that he that he + + align:start position:0% +throw out the four types that he that he + + + align:start position:0% +throw out the four types that he that he +>> explorers + + align:start position:0% + + + + align:start position:0% + +and killers. Yeah. So you know it's like + + align:start position:0% +and killers. Yeah. So you know it's like + + + align:start position:0% +and killers. Yeah. So you know it's like +there are these four types of players + + align:start position:0% +there are these four types of players + + + align:start position:0% +there are these four types of players +and just like just because you're + + align:start position:0% +and just like just because you're + + + align:start position:0% +and just like just because you're +achiever in one game doesn't necessarily + + align:start position:0% +achiever in one game doesn't necessarily + + + align:start position:0% +achiever in one game doesn't necessarily +mean that you're going to be achie + + align:start position:0% +mean that you're going to be achie + + + align:start position:0% +mean that you're going to be achie +nothing. different people play different + + align:start position:0% +nothing. different people play different + + + align:start position:0% +nothing. different people play different +games or possibly even different times + + align:start position:0% +games or possibly even different times + + + align:start position:0% +games or possibly even different times +of the day in the same game for + + align:start position:0% +of the day in the same game for + + + align:start position:0% +of the day in the same game for +different reasons. Uh and uh and that's + + align:start position:0% +different reasons. Uh and uh and that's + + + align:start position:0% +different reasons. Uh and uh and that's +where we go back to earlier concepts + + align:start position:0% +where we go back to earlier concepts + + + align:start position:0% +where we go back to earlier concepts +that we brought up in this class like + + align:start position:0% +that we brought up in this class like + + + align:start position:0% +that we brought up in this class like +the different kind kinds of fun. What + + align:start position:0% +the different kind kinds of fun. What + + + align:start position:0% +the different kind kinds of fun. What +are people trying to get out of their + + align:start position:0% +are people trying to get out of their + + + align:start position:0% +are people trying to get out of their +game, right? Um so but he was you know + + align:start position:0% +game, right? Um so but he was you know + + + align:start position:0% +game, right? Um so but he was you know +um if you're looking at the context of + + align:start position:0% +um if you're looking at the context of + + + align:start position:0% +um if you're looking at the context of +any one mud you know and a little slice + + align:start position:0% +any one mud you know and a little slice + + + align:start position:0% +any one mud you know and a little slice +of what you saw of somebody's + + align:start position:0% +of what you saw of somebody's + + + align:start position:0% +of what you saw of somebody's +personality when they were logged in and + + align:start position:0% +personality when they were logged in and + + + align:start position:0% +personality when they were logged in and +all the things that they were doing and + + align:start position:0% +all the things that they were doing and + + + align:start position:0% +all the things that they were doing and +it and the kinds of things that they + + align:start position:0% +it and the kinds of things that they + + + align:start position:0% +it and the kinds of things that they +tended to keep doing every time you + + align:start position:0% +tended to keep doing every time you + + + align:start position:0% +tended to keep doing every time you +logged in. It was fairly easy to sort of + + align:start position:0% +logged in. It was fairly easy to sort of + + + align:start position:0% +logged in. It was fairly easy to sort of +stereotype them into somewhere along + + align:start position:0% +stereotype them into somewhere along + + + align:start position:0% +stereotype them into somewhere along +those lines. Even he acknowledges that + + align:start position:0% +those lines. Even he acknowledges that + + + align:start position:0% +those lines. Even he acknowledges that +nobody's really all the way on on one of + + align:start position:0% +nobody's really all the way on on one of + + + align:start position:0% +nobody's really all the way on on one of +these lines. grief griefers I I think + + align:start position:0% +these lines. grief griefers I I think + + + align:start position:0% +these lines. grief griefers I I think +are the words that I hear generally use + + align:start position:0% +are the words that I hear generally use + + + align:start position:0% +are the words that I hear generally use +for killers nowadays, but even then + + align:start position:0% +for killers nowadays, but even then + + + align:start position:0% +for killers nowadays, but even then +that's not quite the way that he's using + + align:start position:0% +that's not quite the way that he's using + + + align:start position:0% +that's not quite the way that he's using +it. He's actually using it as somebody + + align:start position:0% +it. He's actually using it as somebody + + + align:start position:0% +it. He's actually using it as somebody +who's generally still playing by the + + align:start position:0% +who's generally still playing by the + + + align:start position:0% +who's generally still playing by the +rules of game, you know, u you know, + + align:start position:0% +rules of game, you know, u you know, + + + align:start position:0% +rules of game, you know, u you know, +they're not they're out there to cause + + align:start position:0% +they're not they're out there to cause + + + align:start position:0% +they're not they're out there to cause +misery to other people, but they're not + + align:start position:0% +misery to other people, but they're not + + + align:start position:0% +misery to other people, but they're not +there to break the game. Um there's + + align:start position:0% +there to break the game. Um there's + + + align:start position:0% +there to break the game. Um there's +there is a class of people of reavers + + align:start position:0% +there is a class of people of reavers + + + align:start position:0% +there is a class of people of reavers +where they're deliberately trying to + + align:start position:0% +where they're deliberately trying to + + + align:start position:0% +where they're deliberately trying to +find ways to exploit the system to just + + align:start position:0% +find ways to exploit the system to just + + + align:start position:0% +find ways to exploit the system to just +make to make the game just kind of + + align:start position:0% +make to make the game just kind of + + + align:start position:0% +make to make the game just kind of +silly. Um but all the other dynamically + + align:start position:0% +silly. Um but all the other dynamically + + + align:start position:0% +silly. Um but all the other dynamically +it draws are very much there. It's like + + align:start position:0% +it draws are very much there. It's like + + + align:start position:0% +it draws are very much there. It's like +you get a whole bunch of socializers + + align:start position:0% +you get a whole bunch of socializers + + + align:start position:0% +you get a whole bunch of socializers +together, people who want to do nothing + + align:start position:0% +together, people who want to do nothing + + + align:start position:0% +together, people who want to do nothing +but chat and have a good time. Uh don't + + align:start position:0% +but chat and have a good time. Uh don't + + + align:start position:0% +but chat and have a good time. Uh don't +really care about game and it's going to + + align:start position:0% +really care about game and it's going to + + + align:start position:0% +really care about game and it's going to +be a whole bunch of people going right + + align:start position:0% +be a whole bunch of people going right + + + align:start position:0% +be a whole bunch of people going right +after them and saying these are great + + align:start position:0% +after them and saying these are great + + + align:start position:0% +after them and saying these are great +people to grief. uh you know because + + align:start position:0% +people to grief. uh you know because + + + align:start position:0% +people to grief. uh you know because +they are enjoying themselves so much. We + + align:start position:0% +they are enjoying themselves so much. We + + + align:start position:0% +they are enjoying themselves so much. We +could end that. + + align:start position:0% +could end that. + + + align:start position:0% +could end that. +Um Second Life, you guessed a lot of + + align:start position:0% +Um Second Life, you guessed a lot of + + + align:start position:0% +Um Second Life, you guessed a lot of +this because Second Life has that whole + + align:start position:0% +this because Second Life has that whole + + + align:start position:0% +this because Second Life has that whole +like uh um you know, you can do anything + + align:start position:0% +like uh um you know, you can do anything + + + align:start position:0% +like uh um you know, you can do anything +you want and socializing is one of the + + align:start position:0% +you want and socializing is one of the + + + align:start position:0% +you want and socializing is one of the +big things. Uh personalizing is one of + + align:start position:0% +big things. Uh personalizing is one of + + + align:start position:0% +big things. Uh personalizing is one of +those big things. But um so so so do + + align:start position:0% +those big things. But um so so so do + + + align:start position:0% +those big things. But um so so so do +keep in mind that you know um that the + + align:start position:0% +keep in mind that you know um that the + + + align:start position:0% +keep in mind that you know um that the +way that he's talking about it sounds + + align:start position:0% +way that he's talking about it sounds + + + align:start position:0% +way that he's talking about it sounds +like all of these different + + align:start position:0% +like all of these different + + + align:start position:0% +like all of these different +personalities are somewhat mutually + + align:start position:0% +personalities are somewhat mutually + + + align:start position:0% +personalities are somewhat mutually +exclusive when really the discussion has + + align:start position:0% +exclusive when really the discussion has + + + align:start position:0% +exclusive when really the discussion has +come has now come on to how do you sort + + align:start position:0% +come has now come on to how do you sort + + + align:start position:0% +come has now come on to how do you sort +of cater to all of these uh different to + + align:start position:0% +of cater to all of these uh different to + + + align:start position:0% +of cater to all of these uh different to +all of these different desires at any + + align:start position:0% +all of these different desires at any + + + align:start position:0% +all of these different desires at any +given time. I may be achiever today, I + + align:start position:0% +given time. I may be achiever today, I + + + align:start position:0% +given time. I may be achiever today, I +may be an explorer tomorrow. And he even + + align:start position:0% +may be an explorer tomorrow. And he even + + + align:start position:0% +may be an explorer tomorrow. And he even +talks about explorers thinking that + + align:start position:0% +talks about explorers thinking that + + + align:start position:0% +talks about explorers thinking that +achievers are beginner explorers, you + + align:start position:0% +achievers are beginner explorers, you + + + align:start position:0% +achievers are beginner explorers, you +know, because it's like once you've + + align:start position:0% +know, because it's like once you've + + + align:start position:0% +know, because it's like once you've +already beaten the game, what else is + + align:start position:0% +already beaten the game, what else is + + + align:start position:0% +already beaten the game, what else is +there left to do but explore what else + + align:start position:0% +there left to do but explore what else + + + align:start position:0% +there left to do but explore what else +the game can do, you know? So, so, so + + align:start position:0% +the game can do, you know? So, so, so + + + align:start position:0% +the game can do, you know? So, so, so +that's so he he himself acknowledges + + align:start position:0% +that's so he he himself acknowledges + + + align:start position:0% +that's so he he himself acknowledges +that there's some personality transfer + + align:start position:0% +that there's some personality transfer + + + align:start position:0% +that there's some personality transfer +that can happen. + + align:start position:0% +that can happen. + + + align:start position:0% +that can happen. +Uh, but it's kind of interesting how he + + align:start position:0% +Uh, but it's kind of interesting how he + + + align:start position:0% +Uh, but it's kind of interesting how he +talks about the feedback loops about of + + align:start position:0% +talks about the feedback loops about of + + + align:start position:0% +talks about the feedback loops about of +people, right? You know, it's like you + + align:start position:0% +people, right? You know, it's like you + + + align:start position:0% +people, right? You know, it's like you +get a whole bunch of um what was it? You + + align:start position:0% +get a whole bunch of um what was it? You + + + align:start position:0% +get a whole bunch of um what was it? You +get a whole bunch of achievers and you + + align:start position:0% +get a whole bunch of achievers and you + + + align:start position:0% +get a whole bunch of achievers and you +get a whole bunch of um + + align:start position:0% +get a whole bunch of um + + + align:start position:0% +get a whole bunch of um +>> socializing + + align:start position:0% + + + + align:start position:0% + +increases. + + align:start position:0% +increases. + + + align:start position:0% +increases. +>> Yeah, increases because the competition + + align:start position:0% +>> Yeah, increases because the competition + + + align:start position:0% +>> Yeah, increases because the competition +is now higher or something like that. + + align:start position:0% +is now higher or something like that. + + + align:start position:0% +is now higher or something like that. +But he also makes this weird assumption + + align:start position:0% +But he also makes this weird assumption + + + align:start position:0% +But he also makes this weird assumption +that there is a finite pool of people + + align:start position:0% +that there is a finite pool of people + + + align:start position:0% +that there is a finite pool of people +who can be playing the game which is + + align:start position:0% +who can be playing the game which is + + + align:start position:0% +who can be playing the game which is +actually true. Even in a, you know, + + align:start position:0% +actually true. Even in a, you know, + + + align:start position:0% +actually true. Even in a, you know, +a 10 to 20 million player game like + + align:start position:0% +a 10 to 20 million player game like + + + align:start position:0% +a 10 to 20 million player game like +World of Warcraft, you know, all those + + align:start position:0% +World of Warcraft, you know, all those + + + align:start position:0% +World of Warcraft, you know, all those +things have to be um like we don't have + + align:start position:0% +things have to be um like we don't have + + + align:start position:0% +things have to be um like we don't have +20 million people logging on to one + + align:start position:0% +20 million people logging on to one + + + align:start position:0% +20 million people logging on to one +server, you know, + + align:start position:0% +server, you know, + + + align:start position:0% +server, you know, +they say I want eight eight heights of + + align:start position:0% +they say I want eight eight heights of + + + align:start position:0% +they say I want eight eight heights of +sheep or something, + + align:start position:0% +sheep or something, + + + align:start position:0% +sheep or something, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> Eight sheep. + + align:start position:0% +>> Eight sheep. + + + align:start position:0% +>> Eight sheep. +>> Exactly. Exactly. And then like once you + + align:start position:0% +>> Exactly. Exactly. And then like once you + + + align:start position:0% +>> Exactly. Exactly. And then like once you +hit level 80, you can start uh doing + + align:start position:0% +hit level 80, you can start uh doing + + + align:start position:0% +hit level 80, you can start uh doing +these raids that are just really big + + align:start position:0% +these raids that are just really big + + + align:start position:0% +these raids that are just really big +down + + align:start position:0% +down + + + align:start position:0% +down +>> for lots of people. Uh like 25. It's + + align:start position:0% +>> for lots of people. Uh like 25. It's + + + align:start position:0% +>> for lots of people. Uh like 25. It's +currently 25 is the highest. They used + + align:start position:0% +currently 25 is the highest. They used + + + align:start position:0% +currently 25 is the highest. They used +to be like 40. Um but yeah, and you just + + align:start position:0% +to be like 40. Um but yeah, and you just + + + align:start position:0% +to be like 40. Um but yeah, and you just +kill bigger monsters and get lots of + + align:start position:0% +kill bigger monsters and get lots of + + + align:start position:0% +kill bigger monsters and get lots of +boot. Um, and then there's PvP, which + + align:start position:0% +boot. Um, and then there's PvP, which + + + align:start position:0% +boot. Um, and then there's PvP, which +you go, the main thing right now is like + + align:start position:0% +you go, the main thing right now is like + + + align:start position:0% +you go, the main thing right now is like +arenas, and you have a team of two or + + align:start position:0% +arenas, and you have a team of two or + + + align:start position:0% +arenas, and you have a team of two or +three or five, and you fight other + + align:start position:0% +three or five, and you fight other + + + align:start position:0% +three or five, and you fight other +players with your gear that you obtain + + align:start position:0% +players with your gear that you obtain + + + align:start position:0% +players with your gear that you obtain +by doing battlegrounds and and lots of + + align:start position:0% +by doing battlegrounds and and lots of + + + align:start position:0% +by doing battlegrounds and and lots of +arena. Uh, yeah, and it's that's + + align:start position:0% +arena. Uh, yeah, and it's that's + + + align:start position:0% +arena. Uh, yeah, and it's that's +basically WoW. + + align:start position:0% +basically WoW. + + + align:start position:0% +basically WoW. +>> They use um I can't remember. Are there + + align:start position:0% +>> They use um I can't remember. Are there + + + align:start position:0% +>> They use um I can't remember. Are there +roleplay servers? + + align:start position:0% +roleplay servers? + + + align:start position:0% +roleplay servers? +>> Yes, there are world roleplay servers. I + + align:start position:0% +>> Yes, there are world roleplay servers. I + + + align:start position:0% +>> Yes, there are world roleplay servers. I +have actually never visited one + + align:start position:0% +have actually never visited one + + + align:start position:0% +have actually never visited one +>> so I can't talk about that. + + align:start position:0% +>> so I can't talk about that. + + + align:start position:0% +>> so I can't talk about that. +>> So it's a lot of dancing. + + align:start position:0% + + + + align:start position:0% + +>> Dance is a you know typing in slash + + align:start position:0% +>> Dance is a you know typing in slash + + + align:start position:0% +>> Dance is a you know typing in slash +dance made your your your character + + align:start position:0% +dance made your your your character + + + align:start position:0% +dance made your your your character +dance and it was one of those things + + align:start position:0% +dance and it was one of those things + + + align:start position:0% +dance and it was one of those things +that really is popular among socialized + + align:start position:0% +that really is popular among socialized + + + align:start position:0% +that really is popular among socialized +type uh players all all over any + + align:start position:0% +type uh players all all over any + + + align:start position:0% +type uh players all all over any +episode. Um but it's not just a I mean + + align:start position:0% +episode. Um but it's not just a I mean + + + align:start position:0% +episode. Um but it's not just a I mean +slash dance means other things now. It + + align:start position:0% +slash dance means other things now. It + + + align:start position:0% +slash dance means other things now. It +it could it could be I'm bored, right? + + align:start position:0% +it could it could be I'm bored, right? + + + align:start position:0% +it could it could be I'm bored, right? +You know, it's like I have nothing to do + + align:start position:0% +You know, it's like I have nothing to do + + + align:start position:0% +You know, it's like I have nothing to do +right now. I have to wait for this + + align:start position:0% +right now. I have to wait for this + + + align:start position:0% +right now. I have to wait for this +stupid thing to respond. I guess + + align:start position:0% +stupid thing to respond. I guess + + + align:start position:0% +stupid thing to respond. I guess +it's it's more fun than just standing + + align:start position:0% +it's it's more fun than just standing + + + align:start position:0% +it's it's more fun than just standing +there. Um + + align:start position:0% +there. Um + + + align:start position:0% +there. Um +but the uh uh there is a group in in WoW + + align:start position:0% +but the uh uh there is a group in in WoW + + + align:start position:0% +but the uh uh there is a group in in WoW +and I I guess I would may maybe not a + + align:start position:0% +and I I guess I would may maybe not a + + + align:start position:0% +and I I guess I would may maybe not a +group there is there there are folks who + + align:start position:0% +group there is there there are folks who + + + align:start position:0% +group there is there there are folks who +play World of Warcraft um and they + + align:start position:0% +play World of Warcraft um and they + + + align:start position:0% +play World of Warcraft um and they +engage in this thing called theory craft + + align:start position:0% +engage in this thing called theory craft + + + align:start position:0% +engage in this thing called theory craft +which is how do we optimize uh the way + + align:start position:0% +which is how do we optimize uh the way + + + align:start position:0% +which is how do we optimize uh the way +how you build a character um and uh to + + align:start position:0% +how you build a character um and uh to + + + align:start position:0% +how you build a character um and uh to +the and the things that you equip a play + + align:start position:0% +the and the things that you equip a play + + + align:start position:0% +the and the things that you equip a play +a character for to be make that + + align:start position:0% +a character for to be make that + + + align:start position:0% +a character for to be make that +character really really good at doing + + align:start position:0% +character really really good at doing + + + align:start position:0% +character really really good at doing +one or two different things. Um, so if + + align:start position:0% +one or two different things. Um, so if + + + align:start position:0% +one or two different things. Um, so if +you're building up, you know, a + + align:start position:0% +you're building up, you know, a + + + align:start position:0% +you're building up, you know, a +character that's designed to heal, you + + align:start position:0% +character that's designed to heal, you + + + align:start position:0% +character that's designed to heal, you +know, what class should they be, what + + align:start position:0% +know, what class should they be, what + + + align:start position:0% +know, what class should they be, what +race should they be, what equipment + + align:start position:0% +race should they be, what equipment + + + align:start position:0% +race should they be, what equipment +should they be getting, you know, + + align:start position:0% +should they be getting, you know, + + + align:start position:0% +should they be getting, you know, +depending on what amount of time you are + + align:start position:0% +depending on what amount of time you are + + + align:start position:0% +depending on what amount of time you are +in in the game. Um, and uh, you know, + + align:start position:0% +in in the game. Um, and uh, you know, + + + align:start position:0% +in in the game. Um, and uh, you know, +they're they're going to try to like + + align:start position:0% +they're they're going to try to like + + + align:start position:0% +they're they're going to try to like +derive as much of math of of the kind + + align:start position:0% +derive as much of math of of the kind + + + align:start position:0% +derive as much of math of of the kind +of, you know, cause and effect in + + align:start position:0% +of, you know, cause and effect in + + + align:start position:0% +of, you know, cause and effect in +anything as we possibly can. Um, there's + + align:start position:0% +anything as we possibly can. Um, there's + + + align:start position:0% +anything as we possibly can. Um, there's +a client called the STS uh, which uh, + + align:start position:0% +a client called the STS uh, which uh, + + + align:start position:0% +a client called the STS uh, which uh, +which which is I can't remember if they + + align:start position:0% +which which is I can't remember if they + + + align:start position:0% +which which is I can't remember if they +actually exclam + + align:start position:0% + + + + align:start position:0% + +>> um it's actually kind of funny uh the + + align:start position:0% +>> um it's actually kind of funny uh the + + + align:start position:0% +>> um it's actually kind of funny uh the +elitist jerks forums had one guy who + + align:start position:0% +elitist jerks forums had one guy who + + + align:start position:0% +elitist jerks forums had one guy who +just happened to write a artic a forum + + align:start position:0% +just happened to write a artic a forum + + + align:start position:0% +just happened to write a artic a forum +post about dressing up in real life like + + align:start position:0% +post about dressing up in real life like + + + align:start position:0% +post about dressing up in real life like +you know like this is how you get like + + align:start position:0% +you know like this is how you get like + + + align:start position:0% +you know like this is how you get like +really nice Taylor clothes and these are + + align:start position:0% +really nice Taylor clothes and these are + + + align:start position:0% +really nice Taylor clothes and these are +things you'll be looking for because he + + align:start position:0% +things you'll be looking for because he + + + align:start position:0% +things you'll be looking for because he +worked at a men so + + align:start position:0% +worked at a men so + + + align:start position:0% +worked at a men so +uh fashion uh space. Um and it turned + + align:start position:0% +uh fashion uh space. Um and it turned + + + align:start position:0% +uh fashion uh space. Um and it turned +out that that community was really + + align:start position:0% +out that that community was really + + + align:start position:0% +out that that community was really +really really interested in learning + + align:start position:0% +really really interested in learning + + + align:start position:0% +really really interested in learning +more about that. Uh you know, which is + + align:start position:0% +more about that. Uh you know, which is + + + align:start position:0% +more about that. Uh you know, which is +actually not that weird, right? It's + + align:start position:0% +actually not that weird, right? It's + + + align:start position:0% +actually not that weird, right? It's +like you care about what armor you get + + align:start position:0% +like you care about what armor you get + + + align:start position:0% +like you care about what armor you get +in the game. If you care about what + + align:start position:0% +in the game. If you care about what + + + align:start position:0% +in the game. If you care about what +clothes you wear in real life, + + align:start position:0% +clothes you wear in real life, + + + align:start position:0% +clothes you wear in real life, +especially if it might have some impact + + align:start position:0% +especially if it might have some impact + + + align:start position:0% +especially if it might have some impact +on your real life, the job that you're + + align:start position:0% +on your real life, the job that you're + + + align:start position:0% +on your real life, the job that you're +looking for. Okay? You know, so um so I + + align:start position:0% +looking for. Okay? You know, so um so I + + + align:start position:0% +looking for. Okay? You know, so um so I +would actually put those more in the + + align:start position:0% +would actually put those more in the + + + align:start position:0% +would actually put those more in the +explorers part of thing, you know. Sure, + + align:start position:0% +explorers part of thing, you know. Sure, + + + align:start position:0% +explorers part of thing, you know. Sure, +they're looking for to optimize. They're + + align:start position:0% +they're looking for to optimize. They're + + + align:start position:0% +they're looking for to optimize. They're +looking to do the best, but they're not + + align:start position:0% +looking to do the best, but they're not + + + align:start position:0% +looking to do the best, but they're not +looking to be necessarily rewarded by + + align:start position:0% +looking to be necessarily rewarded by + + + align:start position:0% +looking to be necessarily rewarded by +the game system. They're using the game + + align:start position:0% +the game system. They're using the game + + + align:start position:0% +the game system. They're using the game +system to test their ideas against, you + + align:start position:0% +system to test their ideas against, you + + + align:start position:0% +system to test their ideas against, you +know, it's like, I'm looking for a + + align:start position:0% +know, it's like, I'm looking for a + + + align:start position:0% +know, it's like, I'm looking for a +better way to to suck up more damage, + + align:start position:0% +better way to to suck up more damage, + + + align:start position:0% +better way to to suck up more damage, +you know, because I'm a tank. I I'm I'm + + align:start position:0% +you know, because I'm a tank. I I'm I'm + + + align:start position:0% +you know, because I'm a tank. I I'm I'm +supposedly absorbing all the damage all + + align:start position:0% +supposedly absorbing all the damage all + + + align:start position:0% +supposedly absorbing all the damage all +all the other call it uh uh all the + + align:start position:0% +all the other call it uh uh all the + + + align:start position:0% +all the other call it uh uh all the +attentions of the of the of the + + align:start position:0% +attentions of the of the of the + + + align:start position:0% +attentions of the of the of the +characters being controlled by the + + align:start position:0% +characters being controlled by the + + + align:start position:0% +characters being controlled by the +computer. while the rest of my folks who + + align:start position:0% +computer. while the rest of my folks who + + + align:start position:0% +computer. while the rest of my folks who +put out a lot of damage, you know, can + + align:start position:0% +put out a lot of damage, you know, can + + + align:start position:0% +put out a lot of damage, you know, can +do their job. Um, but I'm not interested + + align:start position:0% +do their job. Um, but I'm not interested + + + align:start position:0% +do their job. Um, but I'm not interested +in what the system has deemed to be you + + align:start position:0% +in what the system has deemed to be you + + + align:start position:0% +in what the system has deemed to be you +have absolved tons of damage. Good job. + + align:start position:0% +have absolved tons of damage. Good job. + + + align:start position:0% +have absolved tons of damage. Good job. +I don't care what the system says. I + + align:start position:0% +I don't care what the system says. I + + + align:start position:0% +I don't care what the system says. I +care how the system operates so that I + + align:start position:0% +care how the system operates so that I + + + align:start position:0% +care how the system operates so that I +can optimize it through some sort of + + align:start position:0% +can optimize it through some sort of + + + align:start position:0% +can optimize it through some sort of +metric that I figured out and my friends + + align:start position:0% +metric that I figured out and my friends + + + align:start position:0% +metric that I figured out and my friends +have figured out and the community has + + align:start position:0% +have figured out and the community has + + + align:start position:0% +have figured out and the community has +figured out. So, I want to understand + + align:start position:0% +figured out. So, I want to understand + + + align:start position:0% +figured out. So, I want to understand +the system in the end. that's what it + + align:start position:0% +the system in the end. that's what it + + + align:start position:0% +the system in the end. that's what it +comes down to the the metric that + + align:start position:0% +comes down to the the metric that + + + align:start position:0% +comes down to the the metric that +they're using it is how do I optimize + + align:start position:0% +they're using it is how do I optimize + + + align:start position:0% +they're using it is how do I optimize +but for the most part uh people who + + align:start position:0% +but for the most part uh people who + + + align:start position:0% +but for the most part uh people who +engage in that kind of theory craft you + + align:start position:0% +engage in that kind of theory craft you + + + align:start position:0% +engage in that kind of theory craft you +know it's like oh no this this armor + + align:start position:0% +know it's like oh no this this armor + + + align:start position:0% +know it's like oh no this this armor +combined with those pants uh you know I + + align:start position:0% +combined with those pants uh you know I + + + align:start position:0% +combined with those pants uh you know I +now find proof or something uh you know + + align:start position:0% +now find proof or something uh you know + + + align:start position:0% +now find proof or something uh you know +those are those are well in the area of + + align:start position:0% +those are those are well in the area of + + + align:start position:0% +those are those are well in the area of +explor + + align:start position:0% +explor + + + align:start position:0% +explor +behavior seems very much let's find the + + align:start position:0% +behavior seems very much let's find the + + + align:start position:0% +behavior seems very much let's find the +best solution whereas achievers are very + + align:start position:0% +best solution whereas achievers are very + + + align:start position:0% +best solution whereas achievers are very +much folks like you know how do I get to + + align:start position:0% +much folks like you know how do I get to + + + align:start position:0% +much folks like you know how do I get to +level you know it's like um how do I get + + align:start position:0% +level you know it's like um how do I get + + + align:start position:0% +level you know it's like um how do I get +the coolest + + align:start position:0% +the coolest + + + align:start position:0% +the coolest +in World of Warcraft right hands. Um, + + align:start position:0% +in World of Warcraft right hands. Um, + + + align:start position:0% +in World of Warcraft right hands. Um, +you know, and every once in a while + + align:start position:0% +you know, and every once in a while + + + align:start position:0% +you know, and every once in a while +Blizzard, the company that makes it will + + align:start position:0% +Blizzard, the company that makes it will + + + align:start position:0% +Blizzard, the company that makes it will +release some of your stuff and the + + align:start position:0% +release some of your stuff and the + + + align:start position:0% +release some of your stuff and the +achievers are like, I got to get that. + + align:start position:0% +achievers are like, I got to get that. + + + align:start position:0% +achievers are like, I got to get that. +You know, it's like uh because the + + align:start position:0% +You know, it's like uh because the + + + align:start position:0% +You know, it's like uh because the +stakes are usually high and it takes a + + align:start position:0% +stakes are usually high and it takes a + + + align:start position:0% +stakes are usually high and it takes a +lot of effort and a lot of money to be + + align:start position:0% +lot of effort and a lot of money to be + + + align:start position:0% +lot of effort and a lot of money to be +able to get one of those things, but and + + align:start position:0% +able to get one of those things, but and + + + align:start position:0% +able to get one of those things, but and +to be able to get it gives you some + + align:start position:0% +to be able to get it gives you some + + + align:start position:0% +to be able to get it gives you some +recognizable status. You'll see someone + + align:start position:0% +recognizable status. You'll see someone + + + align:start position:0% +recognizable status. You'll see someone +with the limited edition some kind of uh + + align:start position:0% +with the limited edition some kind of uh + + + align:start position:0% +with the limited edition some kind of uh +amount and you only and you know that + + align:start position:0% +amount and you only and you know that + + + align:start position:0% +amount and you only and you know that +the only that they could have done that + + align:start position:0% +the only that they could have done that + + + align:start position:0% +the only that they could have done that +is to spend a heck of a lot of time in + + align:start position:0% +is to spend a heck of a lot of time in + + + align:start position:0% +is to spend a heck of a lot of time in +this game and play the game really well. + + align:start position:0% +this game and play the game really well. + + + align:start position:0% +this game and play the game really well. +You know, that's that's the kind of + + align:start position:0% +You know, that's that's the kind of + + + align:start position:0% +You know, that's that's the kind of +recognition they're looking for. So, + + align:start position:0% +recognition they're looking for. So, + + + align:start position:0% +recognition they're looking for. So, +that's kind of the difference between + + align:start position:0% +that's kind of the difference between + + + align:start position:0% +that's kind of the difference between +achievements and sports. + + align:start position:0% +achievements and sports. + + + align:start position:0% +achievements and sports. +Um so I actually want to try one little + + align:start position:0% +Um so I actually want to try one little + + + align:start position:0% +Um so I actually want to try one little +activity which is I got that I got the + + align:start position:0% +activity which is I got that I got the + + + align:start position:0% +activity which is I got that I got the +chart that um uh + + align:start position:0% +chart that um uh + + + align:start position:0% +chart that um uh +uh lays out the whole player versus you + + align:start position:0% +uh lays out the whole player versus you + + + align:start position:0% +uh lays out the whole player versus you +know player interacting and acting + + align:start position:0% +know player interacting and acting + + + align:start position:0% +know player interacting and acting +player and and the world um and he uses + + align:start position:0% +player and and the world um and he uses + + + align:start position:0% +player and and the world um and he uses +this to describe where your game could + + align:start position:0% +this to describe where your game could + + + align:start position:0% +this to describe where your game could +be at any given time. you know, if + + align:start position:0% +be at any given time. you know, if + + + align:start position:0% +be at any given time. you know, if +you're acting on players, then you know, + + align:start position:0% +you're acting on players, then you know, + + + align:start position:0% +you're acting on players, then you know, +you're the kind of person uh then then + + align:start position:0% +you're the kind of person uh then then + + + align:start position:0% +you're the kind of person uh then then +your game is kind of biased towards + + align:start position:0% +your game is kind of biased towards + + + align:start position:0% +your game is kind of biased towards +killers. Uh if you are in if you're more + + align:start position:0% +killers. Uh if you are in if you're more + + + align:start position:0% +killers. Uh if you are in if you're more +if you're designing your game to be more + + align:start position:0% +if you're designing your game to be more + + + align:start position:0% +if you're designing your game to be more +about interacting with other players, + + align:start position:0% +about interacting with other players, + + + align:start position:0% +about interacting with other players, +then you're sort of biasing it towards + + align:start position:0% +then you're sort of biasing it towards + + + align:start position:0% +then you're sort of biasing it towards +the socializers. Interacting with the + + align:start position:0% +the socializers. Interacting with the + + + align:start position:0% +the socializers. Interacting with the +world is more the achievers, you know. + + align:start position:0% +world is more the achievers, you know. + + + align:start position:0% +world is more the achievers, you know. +Oh, sorry. No, acting on on the world is + + align:start position:0% +Oh, sorry. No, acting on on the world is + + + align:start position:0% +Oh, sorry. No, acting on on the world is +more the achievers, you know. And given + + align:start position:0% +more the achievers, you know. And given + + + align:start position:0% +more the achievers, you know. And given +these quests, I've beaten all the quests + + align:start position:0% +these quests, I've beaten all the quests + + + align:start position:0% +these quests, I've beaten all the quests +and like 100 per + + align:start position:0% +and like 100 per + + + align:start position:0% +and like 100 per +the the quest told me that's + + align:start position:0% +the the quest told me that's + + + align:start position:0% +the the quest told me that's +achievements. And uh interacting with + + align:start position:0% +achievements. And uh interacting with + + + align:start position:0% +achievements. And uh interacting with +the world is more of the explorance. + + align:start position:0% +the world is more of the explorance. + + + align:start position:0% +the world is more of the explorance. +It's like you know um what else can I do + + align:start position:0% +It's like you know um what else can I do + + + align:start position:0% +It's like you know um what else can I do +with this world? You know, there are + + align:start position:0% +with this world? You know, there are + + + align:start position:0% +with this world? You know, there are +these goals that are set. That's great, + + align:start position:0% +these goals that are set. That's great, + + + align:start position:0% +these goals that are set. That's great, +but other than this world that I can do + + align:start position:0% +but other than this world that I can do + + + align:start position:0% +but other than this world that I can do +good stuff. I found the distinction + + align:start position:0% +good stuff. I found the distinction + + + align:start position:0% +good stuff. I found the distinction +between acting and interacting + + align:start position:0% +between acting and interacting + + + align:start position:0% +between acting and interacting +incredibly + + align:start position:0% +incredibly + + + align:start position:0% +incredibly +hard to get at. Like I didn't really + + align:start position:0% +hard to get at. Like I didn't really + + + align:start position:0% +hard to get at. Like I didn't really +understand what he was trying to say. It + + align:start position:0% +understand what he was trying to say. It + + + align:start position:0% +understand what he was trying to say. It +was it was easier. I think he he came + + align:start position:0% +was it was easier. I think he he came + + + align:start position:0% +was it was easier. I think he he came +across those two terms because they + + align:start position:0% +across those two terms because they + + + align:start position:0% +across those two terms because they +sounded cute. Uh you know acting + + align:start position:0% +sounded cute. Uh you know acting + + + align:start position:0% +sounded cute. Uh you know acting +interacting is like + + align:start position:0% +interacting is like + + + align:start position:0% +interacting is like +>> I mean how do you interact without + + align:start position:0% +>> I mean how do you interact without + + + align:start position:0% +>> I mean how do you interact without +acting? + + align:start position:0% +acting? + + + align:start position:0% +acting? +>> Well what does what does that mean? + + align:start position:0% +>> Well what does what does that mean? + + + align:start position:0% +>> Well what does what does that mean? +>> Yeah it's um + + align:start position:0% +>> Yeah it's um + + + align:start position:0% +>> Yeah it's um +>> and like the the really classic example + + align:start position:0% +>> and like the the really classic example + + + align:start position:0% +>> and like the the really classic example +they use like that acting on a player is + + align:start position:0% +they use like that acting on a player is + + + align:start position:0% +they use like that acting on a player is +like a killer + + align:start position:0% +like a killer + + + align:start position:0% +like a killer +>> trying to attack another player but like + + align:start position:0% +>> trying to attack another player but like + + + align:start position:0% +>> trying to attack another player but like +the other player fights back. There's an + + align:start position:0% +the other player fights back. There's an + + + align:start position:0% +the other player fights back. There's an +interaction there. Right. + + align:start position:0% +interaction there. Right. + + + align:start position:0% +interaction there. Right. +>> Sure. But the thing about it, + + align:start position:0% +>> Sure. But the thing about it, + + + align:start position:0% +>> Sure. But the thing about it, +>> what's he trying to say? + + align:start position:0% +>> what's he trying to say? + + + align:start position:0% +>> what's he trying to say? +>> Ah, so what so I believe what he means + + align:start position:0% +>> Ah, so what so I believe what he means + + + align:start position:0% +>> Ah, so what so I believe what he means +by that is that the killer is actually + + align:start position:0% +by that is that the killer is actually + + + align:start position:0% +by that is that the killer is actually +less interested in what the the player + + align:start position:0% +less interested in what the the player + + + align:start position:0% +less interested in what the the player +does back to them. I mean, in some + + align:start position:0% +does back to them. I mean, in some + + + align:start position:0% +does back to them. I mean, in some +sense, they are interacting because + + align:start position:0% +sense, they are interacting because + + + align:start position:0% +sense, they are interacting because +they're trying to see what sort of + + align:start position:0% +they're trying to see what sort of + + + align:start position:0% +they're trying to see what sort of +response they get, right? And it's like, + + align:start position:0% +response they get, right? And it's like, + + + align:start position:0% +response they get, right? And it's like, +I'm going to do something to this + + align:start position:0% +I'm going to do something to this + + + align:start position:0% +I'm going to do something to this +player. This player is either going to + + align:start position:0% +player. This player is either going to + + + align:start position:0% +player. This player is either going to +die or fight back or whine uh about the + + align:start position:0% +die or fight back or whine uh about the + + + align:start position:0% +die or fight back or whine uh about the +fact that I'm hating them so much. Um, + + align:start position:0% +fact that I'm hating them so much. Um, + + + align:start position:0% +fact that I'm hating them so much. Um, +but they're not looking for the + + align:start position:0% +but they're not looking for the + + + align:start position:0% +but they're not looking for the +competitive fit. They're they're not + + align:start position:0% +competitive fit. They're they're not + + + align:start position:0% +competitive fit. They're they're not +really interested in you and now that + + align:start position:0% +really interested in you and now that + + + align:start position:0% +really interested in you and now that +person going to turn around and attack + + align:start position:0% +person going to turn around and attack + + + align:start position:0% +person going to turn around and attack +me. + + align:start position:0% +me. + + + align:start position:0% +me. +>> I know. But the whole point is supposed + + align:start position:0% +>> I know. But the whole point is supposed + + + align:start position:0% +>> I know. But the whole point is supposed +to be that the killers are griefers. So + + align:start position:0% +to be that the killers are griefers. So + + + align:start position:0% +to be that the killers are griefers. So +they really care about how people + + align:start position:0% +they really care about how people + + + align:start position:0% +they really care about how people +respond to them. Like he he says later + + align:start position:0% +respond to them. Like he he says later + + + align:start position:0% +respond to them. Like he he says later +on that like one of the most annoying + + align:start position:0% +on that like one of the most annoying + + + align:start position:0% +on that like one of the most annoying +things you can do to a griefer is just + + align:start position:0% +things you can do to a griefer is just + + + align:start position:0% +things you can do to a griefer is just +ignore them, not rise to the debate, + + align:start position:0% +ignore them, not rise to the debate, + + + align:start position:0% +ignore them, not rise to the debate, +right? So interacting + + align:start position:0% +right? So interacting + + + align:start position:0% +right? So interacting +>> seems to be the crucial thing. So again, + + align:start position:0% +>> seems to be the crucial thing. So again, + + + align:start position:0% +>> seems to be the crucial thing. So again, +I feel like he's + + align:start position:0% +I feel like he's + + + align:start position:0% +I feel like he's +>> well, okay. So yeah, I I admit that the + + align:start position:0% +>> well, okay. So yeah, I I admit that the + + + align:start position:0% +>> well, okay. So yeah, I I admit that the +terms are, but uh well, I guess if I can + + align:start position:0% +terms are, but uh well, I guess if I can + + + align:start position:0% +terms are, but uh well, I guess if I can +jump how I kind of perceive it as like + + align:start position:0% +jump how I kind of perceive it as like + + + align:start position:0% +jump how I kind of perceive it as like +does the person care about how the other + + align:start position:0% +does the person care about how the other + + + align:start position:0% +does the person care about how the other +thing works in a sense, you know what I + + align:start position:0% +thing works in a sense, you know what I + + + align:start position:0% +thing works in a sense, you know what I +mean? So it's like it is it is the case + + align:start position:0% +mean? So it's like it is it is the case + + + align:start position:0% +mean? So it's like it is it is the case +that a griefer wants to get a certain + + align:start position:0% +that a griefer wants to get a certain + + + align:start position:0% +that a griefer wants to get a certain +reaction, but like beyond that, it + + align:start position:0% +reaction, but like beyond that, it + + + align:start position:0% +reaction, but like beyond that, it +doesn't matter, right? So in the same + + align:start position:0% +doesn't matter, right? So in the same + + + align:start position:0% +doesn't matter, right? So in the same +case with the game system, right? like I + + align:start position:0% +case with the game system, right? like I + + + align:start position:0% +case with the game system, right? like I +want it to do this thing. I want it to + + align:start position:0% +want it to do this thing. I want it to + + + align:start position:0% +want it to do this thing. I want it to +give me points, but why it did that or + + align:start position:0% +give me points, but why it did that or + + + align:start position:0% +give me points, but why it did that or +how the mechanic works is kind of + + align:start position:0% +how the mechanic works is kind of + + + align:start position:0% +how the mechanic works is kind of +irrelevant. I don't know. I mean, that's + + align:start position:0% +irrelevant. I don't know. I mean, that's + + + align:start position:0% +irrelevant. I don't know. I mean, that's +kind of how I understood it. + + align:start position:0% +kind of how I understood it. + + + align:start position:0% +kind of how I understood it. +>> Well, well, in particular, like with the + + align:start position:0% +>> Well, well, in particular, like with the + + + align:start position:0% +>> Well, well, in particular, like with the +the interacting + + align:start position:0% +the interacting + + + align:start position:0% +the interacting +when when somebody is like trying to + + align:start position:0% +when when somebody is like trying to + + + align:start position:0% +when when somebody is like trying to +player kill or something, it the the + + align:start position:0% +player kill or something, it the the + + + align:start position:0% +player kill or something, it the the +reaction is not necessarily the reaction + + align:start position:0% +reaction is not necessarily the reaction + + + align:start position:0% +reaction is not necessarily the reaction +they're looking for is to like piss + + align:start position:0% +they're looking for is to like piss + + + align:start position:0% +they're looking for is to like piss +somebody off, right? Um, and that + + align:start position:0% +somebody off, right? Um, and that + + + align:start position:0% +somebody off, right? Um, and that +reaction is not necessarily part of the + + align:start position:0% +reaction is not necessarily part of the + + + align:start position:0% +reaction is not necessarily part of the +game. + + align:start position:0% +game. + + + align:start position:0% +game. +So like the the the the it it is acting + + align:start position:0% +So like the the the the it it is acting + + + align:start position:0% +So like the the the the it it is acting +on them because you are taking like what + + align:start position:0% +on them because you are taking like what + + + align:start position:0% +on them because you are taking like what +the game allows you to do and using this + + align:start position:0% +the game allows you to do and using this + + + align:start position:0% +the game allows you to do and using this +against a person but you don't care + + align:start position:0% +against a person but you don't care + + + align:start position:0% +against a person but you don't care +about what they use in the game against + + align:start position:0% +about what they use in the game against + + + align:start position:0% +about what they use in the game against +you. You you more care about this like + + align:start position:0% +you. You you more care about this like + + + align:start position:0% +you. You you more care about this like +abstract idea. + + align:start position:0% +abstract idea. + + + align:start position:0% +abstract idea. +>> So I think the the interaction is not + + align:start position:0% +>> So I think the the interaction is not + + + align:start position:0% +>> So I think the the interaction is not +actually part of the game. So acting is + + align:start position:0% +actually part of the game. So acting is + + + align:start position:0% +actually part of the game. So acting is +specifically to do with game mechanics + + align:start position:0% +specifically to do with game mechanics + + + align:start position:0% +specifically to do with game mechanics +whereas interacting is to do with + + align:start position:0% +whereas interacting is to do with + + + align:start position:0% +whereas interacting is to do with +something which is so maybe acting is + + align:start position:0% +something which is so maybe acting is + + + align:start position:0% +something which is so maybe acting is +like something mechanical whereas + + align:start position:0% +like something mechanical whereas + + + align:start position:0% +like something mechanical whereas +interacting is something dynamics + + align:start position:0% +interacting is something dynamics + + + align:start position:0% +interacting is something dynamics +related or like well I I see it as like + + align:start position:0% +related or like well I I see it as like + + + align:start position:0% +related or like well I I see it as like +acting is + + align:start position:0% +acting is + + + align:start position:0% +acting is +um sort of like a a single direction + + align:start position:0% +um sort of like a a single direction + + + align:start position:0% +um sort of like a a single direction +with mechanics. So, for example, the + + align:start position:0% +with mechanics. So, for example, the + + + align:start position:0% +with mechanics. So, for example, the +mechanic there is is being able to like + + align:start position:0% +mechanic there is is being able to like + + + align:start position:0% +mechanic there is is being able to like +hit somebody in the head with your + + align:start position:0% +hit somebody in the head with your + + + align:start position:0% +hit somebody in the head with your +sword, right? + + align:start position:0% +sword, right? + + + align:start position:0% +sword, right? +>> Um whereas interacting would be the case + + align:start position:0% +>> Um whereas interacting would be the case + + + align:start position:0% +>> Um whereas interacting would be the case +where you're hitting each other on each + + align:start position:0% +where you're hitting each other on each + + + align:start position:0% +where you're hitting each other on each +other's heads with your sword, which is + + align:start position:0% +other's heads with your sword, which is + + + align:start position:0% +other's heads with your sword, which is +an entirely different thing and is more + + align:start position:0% +an entirely different thing and is more + + + align:start position:0% +an entirely different thing and is more +of like a competitive thing rather than + + align:start position:0% +of like a competitive thing rather than + + + align:start position:0% +of like a competitive thing rather than +the I just want to make you angry. + + align:start position:0% +the I just want to make you angry. + + + align:start position:0% +the I just want to make you angry. +>> Well, and I think the unidirectional + + align:start position:0% +>> Well, and I think the unidirectional + + + align:start position:0% +>> Well, and I think the unidirectional +perspective makes sense. Um you could + + align:start position:0% +perspective makes sense. Um you could + + + align:start position:0% +perspective makes sense. Um you could +think of it as going with the hitting on + + align:start position:0% +think of it as going with the hitting on + + + align:start position:0% +think of it as going with the hitting on +the head example, right? If I'm acting, + + align:start position:0% +the head example, right? If I'm acting, + + + align:start position:0% +the head example, right? If I'm acting, +then I care that information is flowing + + align:start position:0% +then I care that information is flowing + + + align:start position:0% +then I care that information is flowing +one way. I am dealing damage to you. If + + align:start position:0% +one way. I am dealing damage to you. If + + + align:start position:0% +one way. I am dealing damage to you. If +I'm interacting, I'm curious as to like + + align:start position:0% +I'm interacting, I'm curious as to like + + + align:start position:0% +I'm interacting, I'm curious as to like +how that is computed and what that means + + align:start position:0% +how that is computed and what that means + + + align:start position:0% +how that is computed and what that means +for me in return. + + align:start position:0% +for me in return. + + + align:start position:0% +for me in return. +>> Does that make sense? So like if I'm + + align:start position:0% +>> Does that make sense? So like if I'm + + + align:start position:0% +>> Does that make sense? So like if I'm +>> really bad terminology + + align:start position:0% +>> really bad terminology + + + align:start position:0% +>> really bad terminology +a bunch of other examples of things that + + align:start position:0% +a bunch of other examples of things that + + + align:start position:0% +a bunch of other examples of things that +you do to like maximize interacting + + align:start position:0% +you do to like maximize interacting + + + align:start position:0% +you do to like maximize interacting +versus acting and like the interacting + + align:start position:0% +versus acting and like the interacting + + + align:start position:0% +versus acting and like the interacting +examples are things like make make + + align:start position:0% +examples are things like make make + + + align:start position:0% +examples are things like make make +simple puzzles and then the acting ones + + align:start position:0% +simple puzzles and then the acting ones + + + align:start position:0% +simple puzzles and then the acting ones +are like make hard puzzles and like + + align:start position:0% +are like make hard puzzles and like + + + align:start position:0% +are like make hard puzzles and like +>> wait what what + + align:start position:0% +>> wait what what + + + align:start position:0% +>> wait what what +so so in the context of a mud a puzzle + + align:start position:0% +so so in the context of a mud a puzzle + + + align:start position:0% +so so in the context of a mud a puzzle +is often like a door right you know it's + + align:start position:0% +is often like a door right you know it's + + + align:start position:0% +is often like a door right you know it's +like you've got to solve this puzzle be + + align:start position:0% +like you've got to solve this puzzle be + + + align:start position:0% +like you've got to solve this puzzle be +able to get into a new area because + + align:start position:0% +able to get into a new area because + + + align:start position:0% +able to get into a new area because +that's really the only thing that like + + align:start position:0% +that's really the only thing that like + + + align:start position:0% +that's really the only thing that like +sometimes you get new loot. Um, and the + + align:start position:0% +sometimes you get new loot. Um, and the + + + align:start position:0% +sometimes you get new loot. Um, and the +idea behind that is if you're sort of if + + align:start position:0% +idea behind that is if you're sort of if + + + align:start position:0% +idea behind that is if you're sort of if +you're sort of either privileging it to + + align:start position:0% +you're sort of either privileging it to + + + align:start position:0% +you're sort of either privileging it to +getting people to uh talk with each + + align:start position:0% +getting people to uh talk with each + + + align:start position:0% +getting people to uh talk with each +other more and socialize with each other + + align:start position:0% +other more and socialize with each other + + + align:start position:0% +other more and socialize with each other +more or you're privileging it to getting + + align:start position:0% +more or you're privileging it to getting + + + align:start position:0% +more or you're privileging it to getting +people to look at the world more, see + + align:start position:0% +people to look at the world more, see + + + align:start position:0% +people to look at the world more, see +more of the world and and and and + + align:start position:0% +more of the world and and and and + + + align:start position:0% +more of the world and and and and +understand how how it works. Then in a + + align:start position:0% +understand how how it works. Then in a + + + align:start position:0% +understand how how it works. Then in a +sense you don't want to put too many + + align:start position:0% +sense you don't want to put too many + + + align:start position:0% +sense you don't want to put too many +barriers between you know the people + + align:start position:0% +barriers between you know the people + + + align:start position:0% +barriers between you know the people +who've been playing for a long time and + + align:start position:0% +who've been playing for a long time and + + + align:start position:0% +who've been playing for a long time and +people who just started playing the + + align:start position:0% +people who just started playing the + + + align:start position:0% +people who just started playing the +people who uh uh uh you know who are in + + align:start position:0% +people who uh uh uh you know who are in + + + align:start position:0% +people who uh uh uh you know who are in +one area of the world and people who are + + align:start position:0% +one area of the world and people who are + + + align:start position:0% +one area of the world and people who are +in another area of the world you kind of + + align:start position:0% +in another area of the world you kind of + + + align:start position:0% +in another area of the world you kind of +want quick flow. So in muds that's that + + align:start position:0% +want quick flow. So in muds that's that + + + align:start position:0% +want quick flow. So in muds that's that +that's one thing where the the + + align:start position:0% +that's one thing where the the + + + align:start position:0% +that's one thing where the the +definition of puzzle is very specific. + + align:start position:0% +definition of puzzle is very specific. + + + align:start position:0% +definition of puzzle is very specific. +It's like but I have to move this set of + + align:start position:0% +It's like but I have to move this set of + + + align:start position:0% +It's like but I have to move this set of +levers. This is another another point + + align:start position:0% +levers. This is another another point + + + align:start position:0% +levers. This is another another point +that I found was really strange because + + align:start position:0% +that I found was really strange because + + + align:start position:0% +that I found was really strange because +I would expect an explorer who is a + + align:start position:0% +I would expect an explorer who is a + + + align:start position:0% +I would expect an explorer who is a +supposed to be a world interacting + + align:start position:0% +supposed to be a world interacting + + + align:start position:0% +supposed to be a world interacting +person + + align:start position:0% +person + + + align:start position:0% +person +>> to really enjoy deep puzzles which + + align:start position:0% +>> to really enjoy deep puzzles which + + + align:start position:0% +>> to really enjoy deep puzzles which +reward them for knowing a lot about the + + align:start position:0% +reward them for knowing a lot about the + + + align:start position:0% +reward them for knowing a lot about the +world. + + align:start position:0% +world. + + + align:start position:0% +world. +>> Ah but the problem with puzzles in Merks + + align:start position:0% +>> Ah but the problem with puzzles in Merks + + + align:start position:0% +>> Ah but the problem with puzzles in Merks +is that they're usual they're usually + + align:start position:0% +is that they're usual they're usually + + + align:start position:0% +is that they're usual they're usually +single solution. + + align:start position:0% +single solution. + + + align:start position:0% +single solution. +>> That's the so there's less pleasure to + + align:start position:0% +>> That's the so there's less pleasure to + + + align:start position:0% +>> That's the so there's less pleasure to +be uh to be found in a very difficult + + align:start position:0% +be uh to be found in a very difficult + + + align:start position:0% +be uh to be found in a very difficult +puzzle because all that told you was you + + align:start position:0% +puzzle because all that told you was you + + + align:start position:0% +puzzle because all that told you was you +just solved this one thing. There is + + align:start position:0% +just solved this one thing. There is + + + align:start position:0% +just solved this one thing. There is +still puzzle that there is still some + + align:start position:0% +still puzzle that there is still some + + + align:start position:0% +still puzzle that there is still some +pleasure there. The interest that most + + align:start position:0% +pleasure there. The interest that most + + + align:start position:0% +pleasure there. The interest that most +that that explorers are way more + + align:start position:0% +that that explorers are way more + + + align:start position:0% +that that explorers are way more +compelled by kind of like that uh like + + align:start position:0% +compelled by kind of like that uh like + + + align:start position:0% +compelled by kind of like that uh like +the dynamics right is like understanding + + align:start position:0% +the dynamics right is like understanding + + + align:start position:0% +the dynamics right is like understanding +the interaction of how of mechanics + + align:start position:0% +the interaction of how of mechanics + + + align:start position:0% +the interaction of how of mechanics +especially if they behave in a way that + + align:start position:0% +especially if they behave in a way that + + + align:start position:0% +especially if they behave in a way that +might not have been originally designed + + align:start position:0% +might not have been originally designed + + + align:start position:0% +might not have been originally designed +that way you know it's like that's what + + align:start position:0% +that way you know it's like that's what + + + align:start position:0% +that way you know it's like that's what +they're looking for. They're not looking + + align:start position:0% +they're looking for. They're not looking + + + align:start position:0% +they're looking for. They're not looking +for what is the solution that was + + align:start position:0% +for what is the solution that was + + + align:start position:0% +for what is the solution that was +designed in the game. They're looking + + align:start position:0% +designed in the game. They're looking + + + align:start position:0% +designed in the game. They're looking +for how do I get this game to do + + align:start position:0% +for how do I get this game to do + + + align:start position:0% +for how do I get this game to do +something that it might not have been + + align:start position:0% +something that it might not have been + + + align:start position:0% +something that it might not have been +designed to do originally but will be + + align:start position:0% +designed to do originally but will be + + + align:start position:0% +designed to do originally but will be +cool once they figure it out. Um so so + + align:start position:0% +cool once they figure it out. Um so so + + + align:start position:0% +cool once they figure it out. Um so so +that I mean that that unfortunately + + align:start position:0% +that I mean that that unfortunately + + + align:start position:0% +that I mean that that unfortunately +you're absolutely right that one but + + align:start position:0% +you're absolutely right that one but + + + align:start position:0% +you're absolutely right that one but +that one suffers from the very specific + + align:start position:0% +that one suffers from the very specific + + + align:start position:0% +that one suffers from the very specific +terminology of what a puzzle is and as + + align:start position:0% +terminology of what a puzzle is and as + + + align:start position:0% +terminology of what a puzzle is and as +opposed to the sort of more general + + align:start position:0% +opposed to the sort of more general + + + align:start position:0% +opposed to the sort of more general +definition of what a puzzle is. Um, the + + align:start position:0% +definition of what a puzzle is. Um, the + + + align:start position:0% +definition of what a puzzle is. Um, the +reason why why at least for achievers, + + align:start position:0% +reason why why at least for achievers, + + + align:start position:0% +reason why why at least for achievers, +hard puzzles are very important because + + align:start position:0% +hard puzzles are very important because + + + align:start position:0% +hard puzzles are very important because +there's because if you make a puzzle + + align:start position:0% +there's because if you make a puzzle + + + align:start position:0% +there's because if you make a puzzle +that most people aren't going to be able + + align:start position:0% +that most people aren't going to be able + + + align:start position:0% +that most people aren't going to be able +to get, being able to get that puzzle + + align:start position:0% +to get, being able to get that puzzle + + + align:start position:0% +to get, being able to get that puzzle +gives you some bad status. Usually some + + align:start position:0% +gives you some bad status. Usually some + + + align:start position:0% +gives you some bad status. Usually some +sort of visible reward even. It's like + + align:start position:0% +sort of visible reward even. It's like + + + align:start position:0% +sort of visible reward even. It's like +you're now in a location that nobody + + align:start position:0% +you're now in a location that nobody + + + align:start position:0% +you're now in a location that nobody +else can get to or you're now you now + + align:start position:0% +else can get to or you're now you now + + + align:start position:0% +else can get to or you're now you now +have have a piece of equipment that that + + align:start position:0% +have have a piece of equipment that that + + + align:start position:0% +have have a piece of equipment that that +that no one else has. Whereas explorers, + + align:start position:0% +that no one else has. Whereas explorers, + + + align:start position:0% +that no one else has. Whereas explorers, +you know, they will probably have a + + align:start position:0% +you know, they will probably have a + + + align:start position:0% +you know, they will probably have a +advantage in solving difficult puzzles, + + align:start position:0% +advantage in solving difficult puzzles, + + + align:start position:0% +advantage in solving difficult puzzles, +but they're not necessarily the sort of + + align:start position:0% +but they're not necessarily the sort of + + + align:start position:0% +but they're not necessarily the sort of +thing that makes them want to interact + + align:start position:0% +thing that makes them want to interact + + + align:start position:0% +thing that makes them want to interact +well. You know, they lots of mechanics + + align:start position:0% +well. You know, they lots of mechanics + + + align:start position:0% +well. You know, they lots of mechanics +that sort of interact with each other in + + align:start position:0% +that sort of interact with each other in + + + align:start position:0% +that sort of interact with each other in +really really interesting ways, more + + align:start position:0% +really really interesting ways, more + + + align:start position:0% +really really interesting ways, more +likely to be interested to explore. + + align:start position:0% + + + + align:start position:0% + +Um, but you're right, acting and + + align:start position:0% +Um, but you're right, acting and + + + align:start position:0% +Um, but you're right, acting and +interacting crappy crappy terminology. + + align:start position:0% +interacting crappy crappy terminology. + + + align:start position:0% +interacting crappy crappy terminology. +Like + + align:start position:0% +Like + + + align:start position:0% +Like +>> I mean you're talking about how reefers + + align:start position:0% +>> I mean you're talking about how reefers + + + align:start position:0% +>> I mean you're talking about how reefers +are more like actors where they just + + align:start position:0% +are more like actors where they just + + + align:start position:0% +are more like actors where they just +they try to get people to interact with + + align:start position:0% +they try to get people to interact with + + + align:start position:0% +they try to get people to interact with +them or try to get people to get annoyed + + align:start position:0% +them or try to get people to get annoyed + + + align:start position:0% +them or try to get people to get annoyed +them. I've definitely seen actually it + + align:start position:0% +them. I've definitely seen actually it + + + align:start position:0% +them. I've definitely seen actually it +was last year we took game design but + + align:start position:0% +was last year we took game design but + + + align:start position:0% +was last year we took game design but +not not game inter uh 300 where we + + align:start position:0% +not not game inter uh 300 where we + + + align:start position:0% +not not game inter uh 300 where we +watched a video of briefers in uh Team + + align:start position:0% +watched a video of briefers in uh Team + + + align:start position:0% +watched a video of briefers in uh Team +Fortress 2 where there's a + + align:start position:0% +Fortress 2 where there's a + + + align:start position:0% +Fortress 2 where there's a +>> like there's a certain door that if they + + align:start position:0% +>> like there's a certain door that if they + + + align:start position:0% +>> like there's a certain door that if they +stand in a certain spot that it won't + + align:start position:0% +stand in a certain spot that it won't + + + align:start position:0% +stand in a certain spot that it won't +open. So this person started making + + align:start position:0% +open. So this person started making + + + align:start position:0% +open. So this person started making +everyone interact like, "Okay, we're + + align:start position:0% +everyone interact like, "Okay, we're + + + align:start position:0% +everyone interact like, "Okay, we're +going to play a game show. Do you want + + align:start position:0% +going to play a game show. Do you want + + + align:start position:0% +going to play a game show. Do you want +to leave? You have to answer correctly." + + align:start position:0% +to leave? You have to answer correctly." + + + align:start position:0% +to leave? You have to answer correctly." +>> Yeah. What is the capital of + + align:start position:0% +>> Yeah. What is the capital of + + + align:start position:0% +>> Yeah. What is the capital of +>> See, like that that I see that as more + + align:start position:0% +>> See, like that that I see that as more + + + align:start position:0% +>> See, like that that I see that as more +of like an explorer thing. Like you you + + align:start position:0% +of like an explorer thing. Like you you + + + align:start position:0% +of like an explorer thing. Like you you +found some some weird combination of the + + align:start position:0% +found some some weird combination of the + + + align:start position:0% +found some some weird combination of the +interaction and the mechanics that + + align:start position:0% +interaction and the mechanics that + + + align:start position:0% +interaction and the mechanics that +allows you to do something new, + + align:start position:0% +allows you to do something new, + + + align:start position:0% +allows you to do something new, +>> which is turn Team Fortress 2 into a + + align:start position:0% +>> which is turn Team Fortress 2 into a + + + align:start position:0% +>> which is turn Team Fortress 2 into a +game show. + + align:start position:0% +game show. + + + align:start position:0% +game show. +>> It was pretty funny. + + align:start position:0% +>> It was pretty funny. + + + align:start position:0% +>> It was pretty funny. +>> Can't fight. + + align:start position:0% +>> Can't fight. + + + align:start position:0% +>> Can't fight. +>> Grief Explorer is a combination of + + align:start position:0% +>> Grief Explorer is a combination of + + + align:start position:0% +>> Grief Explorer is a combination of +bubble types, right? if you're going to + + align:start position:0% +bubble types, right? if you're going to + + + align:start position:0% +bubble types, right? if you're going to +be a successful breeder. + + align:start position:0% + + + + align:start position:0% + +>> I mean, and and that's absolutely true, + + align:start position:0% +>> I mean, and and that's absolutely true, + + + align:start position:0% +>> I mean, and and that's absolutely true, +right? In all in order to be to if your + + align:start position:0% +right? In all in order to be to if your + + + align:start position:0% +right? In all in order to be to if your +personality is oriented one way, you may + + align:start position:0% +personality is oriented one way, you may + + + align:start position:0% +personality is oriented one way, you may +have to engage in some other behaviors + + align:start position:0% +have to engage in some other behaviors + + + align:start position:0% +have to engage in some other behaviors +in order to be able to + + align:start position:0% +in order to be able to + + + align:start position:0% +in order to be able to +in order to be able to maximize that + + align:start position:0% +in order to be able to maximize that + + + align:start position:0% +in order to be able to maximize that +that core behavior that you're looking + + align:start position:0% +that core behavior that you're looking + + + align:start position:0% +that core behavior that you're looking +for. So yeah, you know, people who are + + align:start position:0% +for. So yeah, you know, people who are + + + align:start position:0% +for. So yeah, you know, people who are +looking at exploits uh at at at try + + align:start position:0% +looking at exploits uh at at at try + + + align:start position:0% +looking at exploits uh at at at try +trying to understand how the world works + + align:start position:0% +trying to understand how the world works + + + align:start position:0% +trying to understand how the world works +so they can cause maximum damage and + + align:start position:0% +so they can cause maximum damage and + + + align:start position:0% +so they can cause maximum damage and +maximum grief to other people, you know, + + align:start position:0% +maximum grief to other people, you know, + + + align:start position:0% +maximum grief to other people, you know, +uh it's that's definitely one good way + + align:start position:0% +uh it's that's definitely one good way + + + align:start position:0% +uh it's that's definitely one good way +of doing it. But what I find is that as + + align:start position:0% +of doing it. But what I find is that as + + + align:start position:0% +of doing it. But what I find is that as +soon as they find it, they're not + + align:start position:0% +soon as they find it, they're not + + + align:start position:0% +soon as they find it, they're not +interested in finding more ways until + + align:start position:0% +interested in finding more ways until + + + align:start position:0% +interested in finding more ways until +that first way gets boring, you know, + + align:start position:0% +that first way gets boring, you know, + + + align:start position:0% +that first way gets boring, you know, +or or or gets fixed. + + align:start position:0% +or or or gets fixed. + + + align:start position:0% +or or or gets fixed. +So, Team Fortress, I know there's a lot + + align:start position:0% +So, Team Fortress, I know there's a lot + + + align:start position:0% +So, Team Fortress, I know there's a lot +of like teleporting you directly in + + align:start position:0% +of like teleporting you directly in + + + align:start position:0% +of like teleporting you directly in +front of turret and stuff like that. + + align:start position:0% +front of turret and stuff like that. + + + align:start position:0% +front of turret and stuff like that. +Teleporting your own teammates in front + + align:start position:0% +Teleporting your own teammates in front + + + align:start position:0% +Teleporting your own teammates in front +of turret. It's like + + align:start position:0% +of turret. It's like + + + align:start position:0% +of turret. It's like +that. + + align:start position:0% +that. + + + align:start position:0% +that. +>> I don't understand. + + align:start position:0% +>> I don't understand. + + + align:start position:0% +>> I don't understand. +>> You don't understand. What? + + align:start position:0% +>> You don't understand. What? + + + align:start position:0% +>> You don't understand. What? +>> It's grief. + + align:start position:0% +>> It's grief. + + + align:start position:0% +>> It's grief. +>> No, it's not actually fun. + + align:start position:0% +>> No, it's not actually fun. + + + align:start position:0% +>> No, it's not actually fun. +>> It's like I'm going to mess with you + + align:start position:0% +>> It's like I'm going to mess with you + + + align:start position:0% +>> It's like I'm going to mess with you +just for the hell of it. Um, I remember + + align:start position:0% +just for the hell of it. Um, I remember + + + align:start position:0% +just for the hell of it. Um, I remember +in Sims Online, an effective way to + + align:start position:0% +in Sims Online, an effective way to + + + align:start position:0% +in Sims Online, an effective way to +greet would be to organize a band of + + align:start position:0% +greet would be to organize a band of + + + align:start position:0% +greet would be to organize a band of +people and arrive in a property since + + align:start position:0% +people and arrive in a property since + + + align:start position:0% +people and arrive in a property since +there was a population limit. + + align:start position:0% +there was a population limit. + + + align:start position:0% +there was a population limit. +>> Mhm. + + align:start position:0% +>> Mhm. + + + align:start position:0% +>> Mhm. +>> Like 12 people or something on any given + + align:start position:0% +>> Like 12 people or something on any given + + + align:start position:0% +>> Like 12 people or something on any given +lot. If that lot was a business that + + align:start position:0% +lot. If that lot was a business that + + + align:start position:0% +lot. If that lot was a business that +required a lot of people to come through + + align:start position:0% +required a lot of people to come through + + + align:start position:0% +required a lot of people to come through +and then you just had 12 of your people + + align:start position:0% +and then you just had 12 of your people + + + align:start position:0% +and then you just had 12 of your people +show up and then like mill around and + + align:start position:0% +show up and then like mill around and + + + align:start position:0% +show up and then like mill around and +sell out profanities, you could tie the + + align:start position:0% +sell out profanities, you could tie the + + + align:start position:0% +sell out profanities, you could tie the +place and lock it up. No one else could + + align:start position:0% +place and lock it up. No one else could + + + align:start position:0% +place and lock it up. No one else could +go there, visit it, sometimes including + + align:start position:0% +go there, visit it, sometimes including + + + align:start position:0% +go there, visit it, sometimes including +other owners and stuff like that. It was + + align:start position:0% +other owners and stuff like that. It was + + + align:start position:0% +other owners and stuff like that. It was +very frustrating. + + align:start position:0% +very frustrating. + + + align:start position:0% +very frustrating. +>> Um, in fact, some of that behavior they + + align:start position:0% +>> Um, in fact, some of that behavior they + + + align:start position:0% +>> Um, in fact, some of that behavior they +got towards organized crime level + + align:start position:0% +got towards organized crime level + + + align:start position:0% +got towards organized crime level +actually. I mean, I would call it real + + align:start position:0% +actually. I mean, I would call it real + + + align:start position:0% +actually. I mean, I would call it real +crime. It was virtual. But um there + + align:start position:0% +crime. It was virtual. But um there + + + align:start position:0% +crime. It was virtual. But um there +there are actually good number of + + align:start position:0% +there are actually good number of + + + align:start position:0% +there are actually good number of +articles about the Sims online mafia + + align:start position:0% +articles about the Sims online mafia + + + align:start position:0% +articles about the Sims online mafia +because um that game had so much so much + + align:start position:0% +because um that game had so much so much + + + align:start position:0% +because um that game had so much so much +built in for actually for socializers um + + align:start position:0% +built in for actually for socializers um + + + align:start position:0% +built in for actually for socializers um +to be able to communicate, express + + align:start position:0% +to be able to communicate, express + + + align:start position:0% +to be able to communicate, express +yourself. I mean, if you played the + + align:start position:0% +yourself. I mean, if you played the + + + align:start position:0% +yourself. I mean, if you played the +original Sims, there's the whole range + + align:start position:0% +original Sims, there's the whole range + + + align:start position:0% +original Sims, there's the whole range +of different expressive things that you + + align:start position:0% +of different expressive things that you + + + align:start position:0% +of different expressive things that you +can do to sort of communicate how you're + + align:start position:0% +can do to sort of communicate how you're + + + align:start position:0% +can do to sort of communicate how you're +feeling and and uh and and to be able + + align:start position:0% +feeling and and uh and and to be able + + + align:start position:0% +feeling and and uh and and to be able +chatting with people. And um someone I + + align:start position:0% +chatting with people. And um someone I + + + align:start position:0% +chatting with people. And um someone I +think it might have been Max itself + + align:start position:0% +think it might have been Max itself + + + align:start position:0% +think it might have been Max itself +actually like charted out the web the + + align:start position:0% +actually like charted out the web the + + + align:start position:0% +actually like charted out the web the +web of influence of all the players and + + align:start position:0% +web of influence of all the players and + + + align:start position:0% +web of influence of all the players and +there was like one alpha player, you + + align:start position:0% +there was like one alpha player, you + + + align:start position:0% +there was like one alpha player, you +know, that was kind of in charge of + + align:start position:0% +know, that was kind of in charge of + + + align:start position:0% +know, that was kind of in charge of +everything. Uh and if and if she decided + + align:start position:0% +everything. Uh and if and if she decided + + + align:start position:0% +everything. Uh and if and if she decided +that nobody was going that that you know + + align:start position:0% +that nobody was going that that you know + + + align:start position:0% +that nobody was going that that you know +that this person was someone that she + + align:start position:0% +that this person was someone that she + + + align:start position:0% +that this person was someone that she +didn't want uh spending too much time + + align:start position:0% +didn't want uh spending too much time + + + align:start position:0% +didn't want uh spending too much time +with online because somehow pissed her + + align:start position:0% +with online because somehow pissed her + + + align:start position:0% +with online because somehow pissed her +off or or you know pissed one of her + + align:start position:0% +off or or you know pissed one of her + + + align:start position:0% +off or or you know pissed one of her +friends off or something and then she + + align:start position:0% +friends off or something and then she + + + align:start position:0% +friends off or something and then she +organized it like that very very + + align:start position:0% +organized it like that very very + + + align:start position:0% +organized it like that very very +effectively. Um it was called the second + + align:start position:0% +effectively. Um it was called the second + + + align:start position:0% +effectively. Um it was called the second +market. Uh and you get that in in you + + align:start position:0% +market. Uh and you get that in in you + + + align:start position:0% +market. Uh and you get that in in you +you'll get that similar behavior in + + align:start position:0% +you'll get that similar behavior in + + + align:start position:0% +you'll get that similar behavior in +second a lot. Um, but and it's kind of + + align:start position:0% +second a lot. Um, but and it's kind of + + + align:start position:0% +second a lot. Um, but and it's kind of +interesting to see how different worlds + + align:start position:0% +interesting to see how different worlds + + + align:start position:0% +interesting to see how different worlds +respond to that. Eve online, I think, is + + align:start position:0% +respond to that. Eve online, I think, is + + + align:start position:0% +respond to that. Eve online, I think, is +the world which is well actually one one + + align:start position:0% +the world which is well actually one one + + + align:start position:0% +the world which is well actually one one +thing I'd like to do is I like to throw + + align:start position:0% +thing I'd like to do is I like to throw + + + align:start position:0% +thing I'd like to do is I like to throw +different games up on that chart. Um, so + + align:start position:0% +different games up on that chart. Um, so + + + align:start position:0% +different games up on that chart. Um, so +um I am looking mostly at multiplayer + + align:start position:0% +um I am looking mostly at multiplayer + + + align:start position:0% +um I am looking mostly at multiplayer +games, specifically + + align:start position:0% +games, specifically + + + align:start position:0% +games, specifically +pre preferably online multiplayer games. + + align:start position:0% +pre preferably online multiplayer games. + + + align:start position:0% +pre preferably online multiplayer games. +Um, but and I don't know all all the + + align:start position:0% +Um, but and I don't know all all the + + + align:start position:0% +Um, but and I don't know all all the +games that are out there. So, I'd like + + align:start position:0% +games that are out there. So, I'd like + + + align:start position:0% +games that are out there. So, I'd like +people to like sort of call out games + + align:start position:0% +people to like sort of call out games + + + align:start position:0% +people to like sort of call out games +and tell me roughly where it should be + + align:start position:0% +and tell me roughly where it should be + + + align:start position:0% +and tell me roughly where it should be +put up. If you disagree, then by all + + align:start position:0% +put up. If you disagree, then by all + + + align:start position:0% +put up. If you disagree, then by all +means, put up your hand and suggest that + + align:start position:0% +means, put up your hand and suggest that + + + align:start position:0% +means, put up your hand and suggest that +it should be moved. + + align:start position:0% +it should be moved. + + + align:start position:0% +it should be moved. +>> Uh, Minecraft should go definitely + + align:start position:0% +>> Uh, Minecraft should go definitely + + + align:start position:0% +>> Uh, Minecraft should go definitely +towards like world interacting like + + align:start position:0% +towards like world interacting like + + + align:start position:0% +towards like world interacting like +explorer bit. + + align:start position:0% +explorer bit. + + + align:start position:0% +explorer bit. +>> You're far far. + + align:start position:0% +>> You're far far. + + + align:start position:0% +>> You're far far. +>> So, what is Minecraft? I've heard of it. + + align:start position:0% +>> So, what is Minecraft? I've heard of it. + + + align:start position:0% +>> So, what is Minecraft? I've heard of it. +I just don't know what exactly. + + align:start position:0% +I just don't know what exactly. + + + align:start position:0% +I just don't know what exactly. +>> Basically, go around mining things and + + align:start position:0% +>> Basically, go around mining things and + + + align:start position:0% +>> Basically, go around mining things and +creating objects and you can create like + + align:start position:0% +creating objects and you can create like + + + align:start position:0% +creating objects and you can create like +your own worlds. So it's kind of like I + + align:start position:0% +your own worlds. So it's kind of like I + + + align:start position:0% +your own worlds. So it's kind of like I +guess + + align:start position:0% +guess + + + align:start position:0% +guess +>> Eve is definitely a world interacting as + + align:start position:0% +>> Eve is definitely a world interacting as + + + align:start position:0% +>> Eve is definitely a world interacting as +well. + + align:start position:0% +well. + + + align:start position:0% +well. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> So about that same as Eve. + + align:start position:0% +>> So about that same as Eve. + + + align:start position:0% +>> So about that same as Eve. +>> Uh I would say Eve is also player + + align:start position:0% +>> Uh I would say Eve is also player + + + align:start position:0% +>> Uh I would say Eve is also player +interacting. + + align:start position:0% +interacting. + + + align:start position:0% +interacting. +>> Yeah. I mean I guess then I see it's in + + align:start position:0% +>> Yeah. I mean I guess then I see it's in + + + align:start position:0% +>> Yeah. I mean I guess then I see it's in +the middle then like you have to form + + align:start position:0% +the middle then like you have to form + + + align:start position:0% +the middle then like you have to form +corporations of bunches of people in + + align:start position:0% +corporations of bunches of people in + + + align:start position:0% +corporations of bunches of people in +order to do anything. + + align:start position:0% +order to do anything. + + + align:start position:0% +order to do anything. +>> That's true. You have to you have to be + + align:start position:0% +>> That's true. You have to you have to be + + + align:start position:0% +>> That's true. You have to you have to be +really good at social skills actually. + + align:start position:0% +really good at social skills actually. + + + align:start position:0% +really good at social skills actually. +Is that one of the games that's like + + align:start position:0% +Is that one of the games that's like + + + align:start position:0% +Is that one of the games that's like +most ruthless? + + align:start position:0% + + + + align:start position:0% + +>> Yeah, I interact with people and the + + align:start position:0% +>> Yeah, I interact with people and the + + + align:start position:0% +>> Yeah, I interact with people and the +world a lot. + + align:start position:0% +world a lot. + + + align:start position:0% +world a lot. +>> Like I think it's more strongly player + + align:start position:0% +>> Like I think it's more strongly player + + + align:start position:0% +>> Like I think it's more strongly player +interacting and world interacting than + + align:start position:0% +interacting and world interacting than + + + align:start position:0% +interacting and world interacting than +most games. + + align:start position:0% +most games. + + + align:start position:0% +most games. +>> You cannot you cannot ignore this in any + + align:start position:0% +>> You cannot you cannot ignore this in any + + + align:start position:0% +>> You cannot you cannot ignore this in any +particular + + align:start position:0% +particular + + + align:start position:0% +particular +>> but there's also like a huge amount of + + align:start position:0% +>> but there's also like a huge amount of + + + align:start position:0% +>> but there's also like a huge amount of +achievement and player versus player + + align:start position:0% +achievement and player versus player + + + align:start position:0% +achievement and player versus player +conflict and this kind of stuff, right? + + align:start position:0% +conflict and this kind of stuff, right? + + + align:start position:0% +conflict and this kind of stuff, right? +So clearly surely it shouldn't be that + + align:start position:0% +So clearly surely it shouldn't be that + + + align:start position:0% +So clearly surely it shouldn't be that +far down the interacting scale. + + align:start position:0% +far down the interacting scale. + + + align:start position:0% +far down the interacting scale. +I mean consider for instance Second Life + + align:start position:0% +I mean consider for instance Second Life + + + align:start position:0% +I mean consider for instance Second Life +instead which would be like way further + + align:start position:0% +instead which would be like way further + + + align:start position:0% +instead which would be like way further +down the interacting + + align:start position:0% +down the interacting + + + align:start position:0% +down the interacting +end of the spectrum online surely + + align:start position:0% + + + + align:start position:0% + +>> assuming that + + align:start position:0% +>> assuming that + + + align:start position:0% +>> assuming that +>> I'm not sure like PvP is the opposite. + + align:start position:0% +>> I'm not sure like PvP is the opposite. + + + align:start position:0% +>> I'm not sure like PvP is the opposite. +>> Yeah. No, I mean it's not + + align:start position:0% +>> Yeah. No, I mean it's not + + + align:start position:0% +>> Yeah. No, I mean it's not +>> I think it's definitely player + + align:start position:0% +>> I think it's definitely player + + + align:start position:0% +>> I think it's definitely player +interaction more than player action. + + align:start position:0% +interaction more than player action. + + + align:start position:0% +interaction more than player action. +>> Yeah, I believe something like having + + align:start position:0% +>> Yeah, I believe something like having + + + align:start position:0% +>> Yeah, I believe something like having +PvP tournaments I think would be + + align:start position:0% +PvP tournaments I think would be + + + align:start position:0% +PvP tournaments I think would be +definitely a lot of interaction. Yeah, I + + align:start position:0% +definitely a lot of interaction. Yeah, I + + + align:start position:0% +definitely a lot of interaction. Yeah, I +think that's that's like the distinction + + align:start position:0% +think that's that's like the distinction + + + align:start position:0% +think that's that's like the distinction +between griefing and like people + + align:start position:0% +between griefing and like people + + + align:start position:0% +between griefing and like people +fighting each other. + + align:start position:0% +fighting each other. + + + align:start position:0% +fighting each other. +>> Griefing can be interacting too. Like + + align:start position:0% +>> Griefing can be interacting too. Like + + + align:start position:0% +>> Griefing can be interacting too. Like +how he put it. I what I got from his + + align:start position:0% +how he put it. I what I got from his + + + align:start position:0% +how he put it. I what I got from his +article is that acting was like I go and + + align:start position:0% +article is that acting was like I go and + + + align:start position:0% +article is that acting was like I go and +kill someone and ha I killed them and + + align:start position:0% +kill someone and ha I killed them and + + + align:start position:0% +kill someone and ha I killed them and +that's it. Or I go through the world + + align:start position:0% +that's it. Or I go through the world + + + align:start position:0% +that's it. Or I go through the world +like I killed monster, I killed monster + + align:start position:0% +like I killed monster, I killed monster + + + align:start position:0% +like I killed monster, I killed monster +and you just have a goal and you want to + + align:start position:0% +and you just have a goal and you want to + + + align:start position:0% +and you just have a goal and you want to +get the goal instead of emerging from + + align:start position:0% +get the goal instead of emerging from + + + align:start position:0% +get the goal instead of emerging from +your goal. Um so I don't know. I + + align:start position:0% +your goal. Um so I don't know. I + + + align:start position:0% +your goal. Um so I don't know. I +definitely think there griefing can be + + align:start position:0% +definitely think there griefing can be + + + align:start position:0% +definitely think there griefing can be +hugely interactive. Like there could be + + align:start position:0% +hugely interactive. Like there could be + + + align:start position:0% +hugely interactive. Like there could be +a whole bunch of like if you in Eve if + + align:start position:0% +a whole bunch of like if you in Eve if + + + align:start position:0% +a whole bunch of like if you in Eve if +you infiltrate someone's company + + align:start position:0% +you infiltrate someone's company + + + align:start position:0% +you infiltrate someone's company +>> and you like steal$10. + + align:start position:0% +>> and you like steal$10. + + + align:start position:0% +>> and you like steal$10. +>> Exactly. Like that's hugely interactive + + align:start position:0% +>> Exactly. Like that's hugely interactive + + + align:start position:0% +>> Exactly. Like that's hugely interactive +griefing. + + align:start position:0% +griefing. + + + align:start position:0% +griefing. +>> But the briefing consider Team Fortress, + + align:start position:0% +>> But the briefing consider Team Fortress, + + + align:start position:0% +>> But the briefing consider Team Fortress, +right? Is Team Fortress player + + align:start position:0% +right? Is Team Fortress player + + + align:start position:0% +right? Is Team Fortress player +interacting because that means it's a + + align:start position:0% +interacting because that means it's a + + + align:start position:0% +interacting because that means it's a +socializer game. + + align:start position:0% +socializer game. + + + align:start position:0% +socializer game. +>> I I I personally do not think Team + + align:start position:0% +>> I I I personally do not think Team + + + align:start position:0% +>> I I I personally do not think Team +Fortress calls them a player + + align:start position:0% +Fortress calls them a player + + + align:start position:0% +Fortress calls them a player +interacting. Yes, but but um Left for + + align:start position:0% +interacting. Yes, but but um Left for + + + align:start position:0% +interacting. Yes, but but um Left for +Dead is + + align:start position:0% +Dead is + + + align:start position:0% +Dead is +>> uh + + align:start position:0% +>> uh + + + align:start position:0% +>> uh +>> definitely interaction. + + align:start position:0% +>> definitely interaction. + + + align:start position:0% +>> definitely interaction. +>> I would say probably more well it + + align:start position:0% +>> I would say probably more well it + + + align:start position:0% +>> I would say probably more well it +depends on what way you're doing. + + align:start position:0% +depends on what way you're doing. + + + align:start position:0% +depends on what way you're doing. +>> Horrible. + + align:start position:0% +>> Horrible. + + + align:start position:0% +>> Horrible. +>> So + + align:start position:0% +>> So + + + align:start position:0% +>> So +>> with Left for Dead, you can play you're + + align:start position:0% +>> with Left for Dead, you can play you're + + + align:start position:0% +>> with Left for Dead, you can play you're +interacting but then you're also like + + align:start position:0% +interacting but then you're also like + + + align:start position:0% +interacting but then you're also like +online you can go against other players + + align:start position:0% +online you can go against other players + + + align:start position:0% +online you can go against other players +who are actually the zombies against + + align:start position:0% +who are actually the zombies against + + + align:start position:0% +who are actually the zombies against +you. + + align:start position:0% +you. + + + align:start position:0% +you. +>> Right. So So let's talk about the basic + + align:start position:0% +>> Right. So So let's talk about the basic + + + align:start position:0% +>> Right. So So let's talk about the basic +mode where you don't have that. + + align:start position:0% +mode where you don't have that. + + + align:start position:0% +mode where you don't have that. +>> Yeah, that's about those modes + + align:start position:0% +>> Yeah, that's about those modes + + + align:start position:0% +>> Yeah, that's about those modes +separately. + + align:start position:0% +separately. + + + align:start position:0% +separately. +>> Yeah. Right. So the basic most common + + align:start position:0% +>> Yeah. Right. So the basic most common + + + align:start position:0% +>> Yeah. Right. So the basic most common +mode it's going to be four players + + align:start position:0% +mode it's going to be four players + + + align:start position:0% +mode it's going to be four players +playing cooperative cooperatively + + align:start position:0% +playing cooperative cooperatively + + + align:start position:0% +playing cooperative cooperatively +against the game world. + + align:start position:0% +against the game world. + + + align:start position:0% +against the game world. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +>> that's just interacting world + + align:start position:0% +>> that's just interacting world + + + align:start position:0% +>> that's just interacting world +>> and + + align:start position:0% +>> and + + + align:start position:0% +>> and +there is + + align:start position:0% +there is + + + align:start position:0% +there is +a lot of interaction that goes on uh + + align:start position:0% +a lot of interaction that goes on uh + + + align:start position:0% +a lot of interaction that goes on uh +between players because you cannot + + align:start position:0% +between players because you cannot + + + align:start position:0% +between players because you cannot +basically survive unless you get keep + + align:start position:0% +basically survive unless you get keep + + + align:start position:0% +basically survive unless you get keep +each other's backs. So, I would say + + align:start position:0% +each other's backs. So, I would say + + + align:start position:0% +each other's backs. So, I would say +>> and there's and there's built-in Well, + + align:start position:0% +>> and there's and there's built-in Well, + + + align:start position:0% +>> and there's and there's built-in Well, +one second. And there's built-in + + align:start position:0% +one second. And there's built-in + + + align:start position:0% +one second. And there's built-in +functions to help other people. So, + + align:start position:0% +functions to help other people. So, + + + align:start position:0% +functions to help other people. So, +someone might get knocked off the ledge + + align:start position:0% +someone might get knocked off the ledge + + + align:start position:0% +someone might get knocked off the ledge +and be holding on. You have to pull it + + align:start position:0% +and be holding on. You have to pull it + + + align:start position:0% +and be holding on. You have to pull it +back up. Um, at the same time, + + align:start position:0% +back up. Um, at the same time, + + + align:start position:0% +back up. Um, at the same time, +>> at the same time, there's also an + + align:start position:0% +>> at the same time, there's also an + + + align:start position:0% +>> at the same time, there's also an +intelligent engine that sort of plans + + align:start position:0% +intelligent engine that sort of plans + + + align:start position:0% +intelligent engine that sort of plans +that level for you and places zombies + + align:start position:0% +that level for you and places zombies + + + align:start position:0% +that level for you and places zombies +strategically to maintain you in a state + + align:start position:0% +strategically to maintain you in a state + + + align:start position:0% +strategically to maintain you in a state +of nervousness. Um, and so it's + + align:start position:0% +of nervousness. Um, and so it's + + + align:start position:0% +of nervousness. Um, and so it's +different every single time you play. + + align:start position:0% +different every single time you play. + + + align:start position:0% +different every single time you play. +Uh, so those kind of balance out and + + align:start position:0% +Uh, so those kind of balance out and + + + align:start position:0% +Uh, so those kind of balance out and +probably place it somewhere in the + + align:start position:0% +probably place it somewhere in the + + + align:start position:0% +probably place it somewhere in the +middle. maybe a little bit more player + + align:start position:0% +middle. maybe a little bit more player + + + align:start position:0% +middle. maybe a little bit more player +bias than world bias because you really + + align:start position:0% +bias than world bias because you really + + + align:start position:0% +bias than world bias because you really +have to stick together. + + align:start position:0% +have to stick together. + + + align:start position:0% +have to stick together. +>> So, so it's weird because it almost like + + align:start position:0% +>> So, so it's weird because it almost like + + + align:start position:0% +>> So, so it's weird because it almost like +you want to have like a plane. + + align:start position:0% +you want to have like a plane. + + + align:start position:0% +you want to have like a plane. +>> It's in like Yeah. + + align:start position:0% +>> It's in like Yeah. + + + align:start position:0% +>> It's in like Yeah. +>> I think it' be Yeah. I think the big + + align:start position:0% +>> I think it' be Yeah. I think the big + + + align:start position:0% +>> I think it' be Yeah. I think the big +problem with this sort of graph is that + + align:start position:0% +problem with this sort of graph is that + + + align:start position:0% +problem with this sort of graph is that +you can't really necessarily separate + + align:start position:0% +you can't really necessarily separate + + + align:start position:0% +you can't really necessarily separate +games into one of these quadrants. + + align:start position:0% +games into one of these quadrants. + + + align:start position:0% +games into one of these quadrants. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +>> games + + align:start position:0% +>> games + + + align:start position:0% +>> games +world and that is actually more + + align:start position:0% +world and that is actually more + + + align:start position:0% +world and that is actually more +interaction. It might be a little more + + align:start position:0% +interaction. It might be a little more + + + align:start position:0% +interaction. It might be a little more +useful to actually draw like areas + + align:start position:0% +useful to actually draw like areas + + + align:start position:0% +useful to actually draw like areas +within the graph to sort of like + + align:start position:0% +within the graph to sort of like + + + align:start position:0% +within the graph to sort of like +represent a game. I guess draw an area + + align:start position:0% +represent a game. I guess draw an area + + + align:start position:0% +represent a game. I guess draw an area +that encompasses like all the pieces the + + align:start position:0% +that encompasses like all the pieces the + + + align:start position:0% +that encompasses like all the pieces the +game sort of + + align:start position:0% +game sort of + + + align:start position:0% +game sort of +can be complicated with games that have + + align:start position:0% +can be complicated with games that have + + + align:start position:0% +can be complicated with games that have +very distinct modes, you know, like Halo + + align:start position:0% +very distinct modes, you know, like Halo + + + align:start position:0% +very distinct modes, you know, like Halo +co-op and Halo multiplayer and Halo + + align:start position:0% +co-op and Halo multiplayer and Halo + + + align:start position:0% +co-op and Halo multiplayer and Halo +Slayer very different. + + align:start position:0% +Slayer very different. + + + align:start position:0% +Slayer very different. +>> Uh but yeah, + + align:start position:0% +>> Uh but yeah, + + + align:start position:0% +>> Uh but yeah, +that will probably be a good refinement + + align:start position:0% +that will probably be a good refinement + + + align:start position:0% +that will probably be a good refinement +is just like create some sort of like + + align:start position:0% +is just like create some sort of like + + + align:start position:0% +is just like create some sort of like +scatter charts all over again + + align:start position:0% +scatter charts all over again + + + align:start position:0% +scatter charts all over again +>> because I could definitely see there + + align:start position:0% +>> because I could definitely see there + + + align:start position:0% +>> because I could definitely see there +being a game where there's a lot of + + align:start position:0% +being a game where there's a lot of + + + align:start position:0% +being a game where there's a lot of +acting on the world and interacting with + + align:start position:0% +acting on the world and interacting with + + + align:start position:0% +acting on the world and interacting with +players and if you're just separating + + align:start position:0% +players and if you're just separating + + + align:start position:0% +players and if you're just separating +you know these into distinct points that + + align:start position:0% +you know these into distinct points that + + + align:start position:0% +you know these into distinct points that +isn't possible with this graph + + align:start position:0% +isn't possible with this graph + + + align:start position:0% +isn't possible with this graph +>> right so that's another problem problem + + align:start position:0% +>> right so that's another problem problem + + + align:start position:0% +>> right so that's another problem problem +is the assumption that + + align:start position:0% +is the assumption that + + + align:start position:0% +is the assumption that +acting and interacting are like like + + align:start position:0% +acting and interacting are like like + + + align:start position:0% +acting and interacting are like like +mutually opposite at least for these two + + align:start position:0% +mutually opposite at least for these two + + + align:start position:0% +mutually opposite at least for these two +axes it almost seems like you know do + + align:start position:0% +axes it almost seems like you know do + + + align:start position:0% +axes it almost seems like you know do +people generally accept + + align:start position:0% +people generally accept + + + align:start position:0% +people generally accept +No, that one less than that interacting. + + align:start position:0% +No, that one less than that interacting. + + + align:start position:0% +No, that one less than that interacting. +>> If you just warp space and then you can + + align:start position:0% +>> If you just warp space and then you can + + + align:start position:0% +>> If you just warp space and then you can +have like different quadrants + + align:start position:0% +have like different quadrants + + + align:start position:0% +have like different quadrants +overlapping + + align:start position:0% + + + + align:start position:0% + +>> I think different values for like player + + align:start position:0% +>> I think different values for like player + + + align:start position:0% +>> I think different values for like player +world interacting and acting. They + + align:start position:0% +world interacting and acting. They + + + align:start position:0% +world interacting and acting. They +shouldn't necessarily be connected. + + align:start position:0% +shouldn't necessarily be connected. + + + align:start position:0% +shouldn't necessarily be connected. +>> I think Eve definitely world is very + + align:start position:0% +>> I think Eve definitely world is very + + + align:start position:0% +>> I think Eve definitely world is very +high and player is very high. World is + + align:start position:0% +high and player is very high. World is + + + align:start position:0% +high and player is very high. World is +very high. Player is very high. But as + + align:start position:0% +very high. Player is very high. But as + + + align:start position:0% +very high. Player is very high. But as +player is interacting and the world is + + align:start position:0% +player is interacting and the world is + + + align:start position:0% +player is interacting and the world is +active world, + + align:start position:0% +active world, + + + align:start position:0% +active world, +>> I mean because I mean you don't I mean + + align:start position:0% +>> I mean because I mean you don't I mean + + + align:start position:0% +>> I mean because I mean you don't I mean +you're exploring the world spatially a + + align:start position:0% +you're exploring the world spatially a + + + align:start position:0% +you're exploring the world spatially a +lot. Are you exploring the systems of + + align:start position:0% +lot. Are you exploring the systems of + + + align:start position:0% +lot. Are you exploring the systems of +the world or not or you really exploring + + align:start position:0% +the world or not or you really exploring + + + align:start position:0% +the world or not or you really exploring +the system by people? + + align:start position:0% +the system by people? + + + align:start position:0% +the system by people? +>> That's true. + + align:start position:0% +>> That's true. + + + align:start position:0% +>> That's true. +I mean the nice thing about um what you + + align:start position:0% +I mean the nice thing about um what you + + + align:start position:0% +I mean the nice thing about um what you +know things like uh EO 9 uh for folks + + align:start position:0% +know things like uh EO 9 uh for folks + + + align:start position:0% +know things like uh EO 9 uh for folks +who don't know EVA line is a space + + align:start position:0% +who don't know EVA line is a space + + + align:start position:0% +who don't know EVA line is a space +exploration game basically where uh + + align:start position:0% +exploration game basically where uh + + + align:start position:0% +exploration game basically where uh +where you start off as a captain correct + + align:start position:0% +where you start off as a captain correct + + + align:start position:0% +where you start off as a captain correct +me if I'm wrong or people + + align:start position:0% +me if I'm wrong or people + + + align:start position:0% +me if I'm wrong or people +>> pretty much a super sandbox game. + + align:start position:0% +>> pretty much a super sandbox game. + + + align:start position:0% +>> pretty much a super sandbox game. +>> Yeah. Well um but for the most part + + align:start position:0% +>> Yeah. Well um but for the most part + + + align:start position:0% +>> Yeah. Well um but for the most part +you're traveling in space that's that + + align:start position:0% +you're traveling in space that's that + + + align:start position:0% +you're traveling in space that's that +that you get out of your ship and like + + align:start position:0% +that you get out of your ship and like + + + align:start position:0% +that you get out of your ship and like +walk on foot. + + align:start position:0% +walk on foot. + + + align:start position:0% +walk on foot. +>> Have they added that? cuz I know they + + align:start position:0% +>> Have they added that? cuz I know they + + + align:start position:0% +>> Have they added that? cuz I know they +wanted to add an expansion where you + + align:start position:0% +wanted to add an expansion where you + + + align:start position:0% +wanted to add an expansion where you +could actually walk on planets. Last + + align:start position:0% +could actually walk on planets. Last + + + align:start position:0% +could actually walk on planets. Last +time I heard they hadn't. + + align:start position:0% +time I heard they hadn't. + + + align:start position:0% +time I heard they hadn't. +>> Last time I heard they had dust 66 or + + align:start position:0% +>> Last time I heard they had dust 66 or + + + align:start position:0% +>> Last time I heard they had dust 66 or +something like that. + + align:start position:0% +something like that. + + + align:start position:0% +something like that. +>> Yeah, which is a separate game. + + align:start position:0% +>> Yeah, which is a separate game. + + + align:start position:0% +>> Yeah, which is a separate game. +>> It's a separate game. So So no, you're + + align:start position:0% +>> It's a separate game. So So no, you're + + + align:start position:0% +>> It's a separate game. So So no, you're +traveling through space. You're not like + + align:start position:0% +traveling through space. You're not like + + + align:start position:0% +traveling through space. You're not like +landing anything. Uh but you're but the + + align:start position:0% +landing anything. Uh but you're but the + + + align:start position:0% +landing anything. Uh but you're but the +whole idea is that it's all built around + + align:start position:0% +whole idea is that it's all built around + + + align:start position:0% +whole idea is that it's all built around +this economy where you know you can do + + align:start position:0% +this economy where you know you can do + + + align:start position:0% +this economy where you know you can do +things like mining. Of course you and + + align:start position:0% +things like mining. Of course you and + + + align:start position:0% +things like mining. Of course you and +can cash. But the real power in in in in + + align:start position:0% +can cash. But the real power in in in in + + + align:start position:0% +can cash. But the real power in in in in +the game comes when players start to + + align:start position:0% +the game comes when players start to + + + align:start position:0% +the game comes when players start to +ally with each other. Form form armadas, + + align:start position:0% +ally with each other. Form form armadas, + + + align:start position:0% +ally with each other. Form form armadas, +form trade trade groups, you know, form + + align:start position:0% +form trade trade groups, you know, form + + + align:start position:0% +form trade trade groups, you know, form +areas that you can patrol and control uh + + align:start position:0% +areas that you can patrol and control uh + + + align:start position:0% +areas that you can patrol and control uh +uh and you know, areas where if you + + align:start position:0% +uh and you know, areas where if you + + + align:start position:0% +uh and you know, areas where if you +don't agree if you don't get along with + + align:start position:0% +don't agree if you don't get along with + + + align:start position:0% +don't agree if you don't get along with +the the people who are in control of the + + align:start position:0% +the the people who are in control of the + + + align:start position:0% +the the people who are in control of the +space, you will die once you fly there. + + align:start position:0% +space, you will die once you fly there. + + + align:start position:0% +space, you will die once you fly there. +And the only the only thing that's + + align:start position:0% +And the only the only thing that's + + + align:start position:0% +And the only the only thing that's +really making that happen are other + + align:start position:0% +really making that happen are other + + + align:start position:0% +really making that happen are other +players deciding that this social + + align:start position:0% +players deciding that this social + + + align:start position:0% +players deciding that this social +contract is is + + align:start position:0% +contract is is + + + align:start position:0% +contract is is +so it's pretty damn amazing. What uh + + align:start position:0% +so it's pretty damn amazing. What uh + + + align:start position:0% +so it's pretty damn amazing. What uh +some folks were talking about earlier + + align:start position:0% +some folks were talking about earlier + + + align:start position:0% +some folks were talking about earlier +was there was a big story about how um + + align:start position:0% +was there was a big story about how um + + + align:start position:0% +was there was a big story about how um +basically one person got into very very + + align:start position:0% +basically one person got into very very + + + align:start position:0% +basically one person got into very very +powerful position in one of these plants + + align:start position:0% +powerful position in one of these plants + + + align:start position:0% +powerful position in one of these plants +and decided to be back taking the + + align:start position:0% +and decided to be back taking the + + + align:start position:0% +and decided to be back taking the +majority of one uh of one plant's + + align:start position:0% +majority of one uh of one plant's + + + align:start position:0% +majority of one uh of one plant's +financial resources with that person. + + align:start position:0% +financial resources with that person. + + + align:start position:0% +financial resources with that person. +And remember, this is a this is a fairly + + align:start position:0% +And remember, this is a this is a fairly + + + align:start position:0% +And remember, this is a this is a fairly +modern people online game. All in game + + align:start position:0% +modern people online game. All in game + + + align:start position:0% +modern people online game. All in game +assets cannot be traded for real money. + + align:start position:0% +assets cannot be traded for real money. + + + align:start position:0% +assets cannot be traded for real money. +>> It's it's illegal. So that + + align:start position:0% +>> It's it's illegal. So that + + + align:start position:0% +>> It's it's illegal. So that +>> illegal like in game so you can get your + + align:start position:0% +>> illegal like in game so you can get your + + + align:start position:0% +>> illegal like in game so you can get your +account banned. + + align:start position:0% +account banned. + + + align:start position:0% +account banned. +>> But so what I so what happened was if I + + align:start position:0% +>> But so what I so what happened was if I + + + align:start position:0% +>> But so what I so what happened was if I +talking about the one that you're + + align:start position:0% +talking about the one that you're + + + align:start position:0% +talking about the one that you're +talking about, someone got to a really + + align:start position:0% +talking about, someone got to a really + + + align:start position:0% +talking about, someone got to a really +power place in like this banking clan + + align:start position:0% +power place in like this banking clan + + + align:start position:0% +power place in like this banking clan +and then took all of their assets and + + align:start position:0% +and then took all of their assets and + + + align:start position:0% +and then took all of their assets and +traded for real money. So got $10,000 by + + align:start position:0% +traded for real money. So got $10,000 by + + + align:start position:0% +traded for real money. So got $10,000 by +trading by selling it on + + align:start position:0% +trading by selling it on + + + align:start position:0% +trading by selling it on +One, + + align:start position:0% +One, + + + align:start position:0% +One, +>> one was a guy who infiltrated heck of a + + align:start position:0% +>> one was a guy who infiltrated heck of a + + + align:start position:0% +>> one was a guy who infiltrated heck of a +bunch of money. One was like a parent + + align:start position:0% +bunch of money. One was like a parent + + + align:start position:0% +bunch of money. One was like a parent +who was going through financial trouble + + align:start position:0% +who was going through financial trouble + + + align:start position:0% +who was going through financial trouble +and held like a fifth of the assets of + + align:start position:0% +and held like a fifth of the assets of + + + align:start position:0% +and held like a fifth of the assets of +some of like the major bank and cashed + + align:start position:0% +some of like the major bank and cashed + + + align:start position:0% +some of like the major bank and cashed +it in for like $6,000 to help pay off + + align:start position:0% +it in for like $6,000 to help pay off + + + align:start position:0% +it in for like $6,000 to help pay off +part of his house and like his kids + + align:start position:0% +part of his house and like his kids + + + align:start position:0% +part of his house and like his kids +medical bills and then posted a poly and + + align:start position:0% +medical bills and then posted a poly and + + + align:start position:0% +medical bills and then posted a poly and +quit the game. + + align:start position:0% +quit the game. + + + align:start position:0% +quit the game. +>> I thought you got banned from the game. + + align:start position:0% +>> I thought you got banned from the game. + + + align:start position:0% +>> I thought you got banned from the game. +>> He was banned from the game, but he he + + align:start position:0% +>> He was banned from the game, but he he + + + align:start position:0% +>> He was banned from the game, but he he +also quit the game. + + align:start position:0% +also quit the game. + + + align:start position:0% +also quit the game. +because there's no coffee. + + align:start position:0% +because there's no coffee. + + + align:start position:0% +because there's no coffee. +>> Yeah. He was like, "I'm sorry everybody, + + align:start position:0% +>> Yeah. He was like, "I'm sorry everybody, + + + align:start position:0% +>> Yeah. He was like, "I'm sorry everybody, +but uh this guy." + + align:start position:0% +but uh this guy." + + + align:start position:0% +but uh this guy." +>> I mean, the the amazing one was the guy + + align:start position:0% +>> I mean, the the amazing one was the guy + + + align:start position:0% +>> I mean, the the amazing one was the guy +who actually infiltrated the company and + + align:start position:0% +who actually infiltrated the company and + + + align:start position:0% +who actually infiltrated the company and +just like took it down as like a year + + align:start position:0% +just like took it down as like a year + + + align:start position:0% +just like took it down as like a year +years longer. + + align:start position:0% +years longer. + + + align:start position:0% +years longer. +>> He was their friend and all that. + + align:start position:0% +>> He was their friend and all that. + + + align:start position:0% +>> He was their friend and all that. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +Trying to get in and then managed to + + align:start position:0% +Trying to get in and then managed to + + + align:start position:0% +Trying to get in and then managed to +take down this gigantic in-game + + align:start position:0% +take down this gigantic in-game + + + align:start position:0% +take down this gigantic in-game +corporation. + + align:start position:0% +corporation. + + + align:start position:0% +corporation. +>> How many How many players are you + + align:start position:0% +>> How many How many players are you + + + align:start position:0% +>> How many How many players are you +online? Active players. + + align:start position:0% +online? Active players. + + + align:start position:0% +online? Active players. +>> No, I feel like active players are It + + align:start position:0% +>> No, I feel like active players are It + + + align:start position:0% +>> No, I feel like active players are It +sounds a lot moment. + + align:start position:0% +sounds a lot moment. + + + align:start position:0% +sounds a lot moment. +>> Yeah. No, I mean + + align:start position:0% +>> Yeah. No, I mean + + + align:start position:0% +>> Yeah. No, I mean +active we have active accounts. + + align:start position:0% +active we have active accounts. + + + align:start position:0% +active we have active accounts. +>> Are they are do they have like new + + align:start position:0% +>> Are they are do they have like new + + + align:start position:0% +>> Are they are do they have like new +players arriving regularly? + + align:start position:0% +players arriving regularly? + + + align:start position:0% +players arriving regularly? +>> They're the kind of game that's they've + + align:start position:0% +>> They're the kind of game that's they've + + + align:start position:0% +>> They're the kind of game that's they've +been like + + align:start position:0% +been like + + + align:start position:0% +been like +>> it's like a ridiculous learning curve. + + align:start position:0% +>> it's like a ridiculous learning curve. + + + align:start position:0% +>> it's like a ridiculous learning curve. +>> Yeah. It's like four months or + + align:start position:0% +>> Yeah. It's like four months or + + + align:start position:0% +>> Yeah. It's like four months or +something. It's insane. But it's uh but + + align:start position:0% +something. It's insane. But it's uh but + + + align:start position:0% +something. It's insane. But it's uh but +but the interesting thing about the + + align:start position:0% +but the interesting thing about the + + + align:start position:0% +but the interesting thing about the +particular case where someone + + align:start position:0% +particular case where someone + + + align:start position:0% +particular case where someone +infiltrated, took all their money and uh + + align:start position:0% +infiltrated, took all their money and uh + + + align:start position:0% +infiltrated, took all their money and uh +uh and and basically decimated uh this + + align:start position:0% +uh and and basically decimated uh this + + + align:start position:0% +uh and and basically decimated uh this +plan deliberately was that that person + + align:start position:0% +plan deliberately was that that person + + + align:start position:0% +plan deliberately was that that person +didn't actually give a compound for it. + + align:start position:0% +didn't actually give a compound for it. + + + align:start position:0% +didn't actually give a compound for it. +I believe it was like + + align:start position:0% +I believe it was like + + + align:start position:0% +I believe it was like +>> he was totally sell the most recent one + + align:start position:0% +>> he was totally sell the most recent one + + + align:start position:0% +>> he was totally sell the most recent one +I read about theoretically had the tens + + align:start position:0% +I read about theoretically had the tens + + + align:start position:0% +I read about theoretically had the tens +of thousands of US dollars of assets in + + align:start position:0% +of thousands of US dollars of assets in + + + align:start position:0% +of thousands of US dollars of assets in +the game and did not cash in any of it + + align:start position:0% +the game and did not cash in any of it + + + align:start position:0% +the game and did not cash in any of it +for real money because there is no + + align:start position:0% +for real money because there is no + + + align:start position:0% +for real money because there is no +authorized mechanism. And the article I + + align:start position:0% +authorized mechanism. And the article I + + + align:start position:0% +authorized mechanism. And the article I +read basically an end note was no one + + align:start position:0% +read basically an end note was no one + + + align:start position:0% +read basically an end note was no one +knows what you can do with it. He's + + align:start position:0% +knows what you can do with it. He's + + + align:start position:0% +knows what you can do with it. He's +technically rich but it's not there's no + + align:start position:0% +technically rich but it's not there's no + + + align:start position:0% +technically rich but it's not there's no +good legal mechanism of illegal gain + + align:start position:0% +good legal mechanism of illegal gain + + + align:start position:0% +good legal mechanism of illegal gain +allowed. I don't think he got banned at + + align:start position:0% +allowed. I don't think he got banned at + + + align:start position:0% +allowed. I don't think he got banned at +all because it's part of the game. is + + align:start position:0% +all because it's part of the game. is + + + align:start position:0% +all because it's part of the game. is +it's considered part of and and once and + + align:start position:0% +it's considered part of and and once and + + + align:start position:0% +it's considered part of and and once and +at least for the definition of Eve uh + + align:start position:0% +at least for the definition of Eve uh + + + align:start position:0% +at least for the definition of Eve uh +stories like that tends to have helped + + align:start position:0% +stories like that tends to have helped + + + align:start position:0% +stories like that tends to have helped +its reputation or anything as this is + + align:start position:0% +its reputation or anything as this is + + + align:start position:0% +its reputation or anything as this is +the this is this is the wild west in + + align:start position:0% +the this is this is the wild west in + + + align:start position:0% +the this is this is the wild west in +space you know and we're trying to + + align:start position:0% +space you know and we're trying to + + + align:start position:0% +space you know and we're trying to +encourage this kind of creative play + + align:start position:0% +encourage this kind of creative play + + + align:start position:0% +encourage this kind of creative play +>> and you know uh other than the real + + align:start position:0% +>> and you know uh other than the real + + + align:start position:0% +>> and you know uh other than the real +money transaction part where you get + + align:start position:0% +money transaction part where you get + + + align:start position:0% +money transaction part where you get +your content all that's part of the game + + align:start position:0% +your content all that's part of the game + + + align:start position:0% +your content all that's part of the game +so I'm not entirely sure it became + + align:start position:0% +so I'm not entirely sure it became + + + align:start position:0% +so I'm not entirely sure it became +really confident at griefing you know it + + align:start position:0% +really confident at griefing you know it + + + align:start position:0% +really confident at griefing you know it +was an incredibly smart practical + + align:start position:0% +was an incredibly smart practical + + + align:start position:0% +was an incredibly smart practical +>> see I I would not call that griefing + + align:start position:0% +>> see I I would not call that griefing + + + align:start position:0% +>> see I I would not call that griefing +Like it was not I mean it may have been + + align:start position:0% +Like it was not I mean it may have been + + + align:start position:0% +Like it was not I mean it may have been +done to like annoy the people who are + + align:start position:0% +done to like annoy the people who are + + + align:start position:0% +done to like annoy the people who are +running the company that he took down + + align:start position:0% +running the company that he took down + + + align:start position:0% +running the company that he took down +but like I see it as exploration like I + + align:start position:0% +but like I see it as exploration like I + + + align:start position:0% +but like I see it as exploration like I +am going to try and exploration and + + align:start position:0% +am going to try and exploration and + + + align:start position:0% +am going to try and exploration and +player interaction you know like + + align:start position:0% +player interaction you know like + + + align:start position:0% +player interaction you know like +>> I would say achieving because I mean + + align:start position:0% +>> I would say achieving because I mean + + + align:start position:0% +>> I would say achieving because I mean +a major corporation all by myself. Yeah, + + align:start position:0% +a major corporation all by myself. Yeah, + + + align:start position:0% +a major corporation all by myself. Yeah, +it might actually be + + align:start position:0% +it might actually be + + + align:start position:0% +it might actually be +do you put that in your resume like + + align:start position:0% +do you put that in your resume like + + + align:start position:0% +do you put that in your resume like +single-handedly? + + align:start position:0% +single-handedly? + + + align:start position:0% +single-handedly? +>> I think if you're + + align:start position:0% +>> I think if you're + + + align:start position:0% +>> I think if you're +>> we could get hired by a lawyer + + align:start position:0% +>> we could get hired by a lawyer + + + align:start position:0% +>> we could get hired by a lawyer +>> and you don't mind + + align:start position:0% +>> and you don't mind + + + align:start position:0% +>> and you don't mind +this company. + + align:start position:0% +this company. + + + align:start position:0% +this company. +>> So, okay. So, what I would actually like + + align:start position:0% +>> So, okay. So, what I would actually like + + + align:start position:0% +>> So, okay. So, what I would actually like +to end this um this with we've got about + + align:start position:0% +to end this um this with we've got about + + + align:start position:0% +to end this um this with we've got about +15 minutes um the special time I would + + align:start position:0% +15 minutes um the special time I would + + + align:start position:0% +15 minutes um the special time I would +say how how many here we have 1 2 3 4 5 + + align:start position:0% +say how how many here we have 1 2 3 4 5 + + + align:start position:0% +say how how many here we have 1 2 3 4 5 +6 7 8 9 10 11 12 13 14 15 16 positive. + + align:start position:0% +6 7 8 9 10 11 12 13 14 15 16 positive. + + + align:start position:0% +6 7 8 9 10 11 12 13 14 15 16 positive. +Awesome. So, groups of four and uh what + + align:start position:0% +Awesome. So, groups of four and uh what + + + align:start position:0% +Awesome. So, groups of four and uh what +I'd like folks to do, am I doing this + + align:start position:0% +I'd like folks to do, am I doing this + + + align:start position:0% +I'd like folks to do, am I doing this +right? + + align:start position:0% +right? + + + align:start position:0% +right? +>> Yeah. Okay. And and um I'd like folks to + + align:start position:0% +>> Yeah. Okay. And and um I'd like folks to + + + align:start position:0% +>> Yeah. Okay. And and um I'd like folks to +come up with other axis. um you know not + + align:start position:0% +come up with other axis. um you know not + + + align:start position:0% +come up with other axis. um you know not +necessarily anything having to do with + + align:start position:0% +necessarily anything having to do with + + + align:start position:0% +necessarily anything having to do with +with with models. Just give me two + + align:start position:0% +with with models. Just give me two + + + align:start position:0% +with with models. Just give me two +things that you kind of feel are + + align:start position:0% +things that you kind of feel are + + + align:start position:0% +things that you kind of feel are +diametrically opposed but you know in + + align:start position:0% +diametrically opposed but you know in + + + align:start position:0% +diametrically opposed but you know in +describing a game or any series of games + + align:start position:0% +describing a game or any series of games + + + align:start position:0% +describing a game or any series of games +you could sort of like place games along + + align:start position:0% +you could sort of like place games along + + + align:start position:0% +you could sort of like place games along +some axis. Um, if you have time, we can + + align:start position:0% +some axis. Um, if you have time, we can + + + align:start position:0% +some axis. Um, if you have time, we can +talk about another two different terms, + + align:start position:0% +talk about another two different terms, + + + align:start position:0% +talk about another two different terms, +but you know, something to help describe + + align:start position:0% +but you know, something to help describe + + + align:start position:0% +but you know, something to help describe +to people, you know, okay, this game is + + align:start position:0% +to people, you know, okay, this game is + + + align:start position:0% +to people, you know, okay, this game is +kind of on the far extreme of one, this + + align:start position:0% +kind of on the far extreme of one, this + + + align:start position:0% +kind of on the far extreme of one, this +game is on the far extreme of the other. + + align:start position:0% +game is on the far extreme of the other. + + + align:start position:0% +game is on the far extreme of the other. +Um, the goal here is to come up with + + align:start position:0% +Um, the goal here is to come up with + + + align:start position:0% +Um, the goal here is to come up with +terms that are that will help you sort + + align:start position:0% +terms that are that will help you sort + + + align:start position:0% +terms that are that will help you sort +of identify what this who this game + + align:start position:0% +of identify what this who this game + + + align:start position:0% +of identify what this who this game +might be targeted towards, you know, + + align:start position:0% +might be targeted towards, you know, + + + align:start position:0% +might be targeted towards, you know, +what kind of player this game might be + + align:start position:0% +what kind of player this game might be + + + align:start position:0% +what kind of player this game might be +targeted. not necessarily using bottles + + align:start position:0% +targeted. not necessarily using bottles + + + align:start position:0% +targeted. not necessarily using bottles +terminology at all, you know, but borrow + + align:start position:0% +terminology at all, you know, but borrow + + + align:start position:0% +terminology at all, you know, but borrow +terminology as we have said is kind of + + align:start position:0% +terminology as we have said is kind of + + + align:start position:0% +terminology as we have said is kind of +weak. Uh so let's so let's throw out + + align:start position:0% +weak. Uh so let's so let's throw out + + + align:start position:0% +weak. Uh so let's so let's throw out +some some some other words, some other + + align:start position:0% +some some some other words, some other + + + align:start position:0% +some some some other words, some other +things. Use things that you use to + + align:start position:0% +things. Use things that you use to + + + align:start position:0% +things. Use things that you use to +describe games already, but you know if + + align:start position:0% +describe games already, but you know if + + + align:start position:0% +describe games already, but you know if +that fails because you haven't really + + align:start position:0% +that fails because you haven't really + + + align:start position:0% +that fails because you haven't really +thought about it that way. Come up with + + align:start position:0% +thought about it that way. Come up with + + + align:start position:0% +thought about it that way. Come up with +some new words, you know, + + align:start position:0% +some new words, you know, + + + align:start position:0% +some new words, you know, +>> real English words. + + align:start position:0% + + + + align:start position:0% + +Random versus strategy. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Oh, + + align:start position:0% +Oh, + + + align:start position:0% +Oh, +>> original versus copy. + + align:start position:0% + + + + align:start position:0% + +>> Really? That's why it resonates, right? + + align:start position:0% +>> Really? That's why it resonates, right? + + + align:start position:0% +>> Really? That's why it resonates, right? +It makes it fairly sort of easy to sort + + align:start position:0% +It makes it fairly sort of easy to sort + + + align:start position:0% +It makes it fairly sort of easy to sort +of like discuss this, you know. I mean, + + align:start position:0% +of like discuss this, you know. I mean, + + + align:start position:0% +of like discuss this, you know. I mean, +I'd rather use the word trans, but + + align:start position:0% +I'd rather use the word trans, but + + + align:start position:0% +I'd rather use the word trans, but +randomly, you know, get the point across + + align:start position:0% +randomly, you know, get the point across + + + align:start position:0% +randomly, you know, get the point across +pretty clearly. + + align:start position:0% +pretty clearly. + + + align:start position:0% +pretty clearly. +>> Strategy or random versus deterministic, + + align:start position:0% +>> Strategy or random versus deterministic, + + + align:start position:0% +>> Strategy or random versus deterministic, +>> right? So I think that should be random + + align:start position:0% +>> right? So I think that should be random + + + align:start position:0% +>> right? So I think that should be random +deterministic and or reactive and + + align:start position:0% +deterministic and or reactive and + + + align:start position:0% +deterministic and or reactive and +deliberative. + + align:start position:0% +deliberative. + + + align:start position:0% +deliberative. +>> I like that. + + align:start position:0% +>> I like that. + + + align:start position:0% +>> I like that. +>> That's fancy. + + align:start position:0% +>> That's fancy. + + + align:start position:0% +>> That's fancy. +>> We use good words. + + align:start position:0% + + + + align:start position:0% + +>> Wait. So reactive and deliberative. + + align:start position:0% +>> Wait. So reactive and deliberative. + + + align:start position:0% +>> Wait. So reactive and deliberative. +and deliberate + + align:start position:0% +and deliberate + + + align:start position:0% +and deliberate +>> or random + + align:start position:0% + + + + align:start position:0% + +>> because you can definitely still have + + align:start position:0% +>> because you can definitely still have + + + align:start position:0% +>> because you can definitely still have +randomness and have strategy, + + align:start position:0% +randomness and have strategy, + + + align:start position:0% +randomness and have strategy, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> But random deterministic. + + align:start position:0% +>> But random deterministic. + + + align:start position:0% +>> But random deterministic. +>> Yeah, then it'll be somewhere on the + + align:start position:0% +>> Yeah, then it'll be somewhere on the + + + align:start position:0% +>> Yeah, then it'll be somewhere on the +axis, right? + + align:start position:0% +axis, right? + + + align:start position:0% +axis, right? +>> So, + + align:start position:0% +>> So, + + + align:start position:0% +>> So, +>> well, I mean, the problem is you can + + align:start position:0% +>> well, I mean, the problem is you can + + + align:start position:0% +>> well, I mean, the problem is you can +have like incredible amounts of + + align:start position:0% +have like incredible amounts of + + + align:start position:0% +have like incredible amounts of +randomness, but if you're can just like + + align:start position:0% +randomness, but if you're can just like + + + align:start position:0% +randomness, but if you're can just like +figure out the probabilities, you can + + align:start position:0% +figure out the probabilities, you can + + + align:start position:0% +figure out the probabilities, you can +still have like an optimal strategy, + + align:start position:0% +still have like an optimal strategy, + + + align:start position:0% +still have like an optimal strategy, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +>> But then that's rander. Deterministic is + + align:start position:0% +>> But then that's rander. Deterministic is + + + align:start position:0% +>> But then that's rander. Deterministic is +because you can't have a system that's + + align:start position:0% +because you can't have a system that's + + + align:start position:0% +because you can't have a system that's +so complex yet deterministic that + + align:start position:0% +so complex yet deterministic that + + + align:start position:0% +so complex yet deterministic that +there's no way you can predict what's + + align:start position:0% +there's no way you can predict what's + + + align:start position:0% +there's no way you can predict what's +going to happen next. + + align:start position:0% +going to happen next. + + + align:start position:0% +going to happen next. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Robot + + align:start position:0% + + + + align:start position:0% + +is theoretically possible. But uh but + + align:start position:0% +is theoretically possible. But uh but + + + align:start position:0% +is theoretically possible. But uh but +yeah, this is this is + + align:start position:0% + + + + align:start position:0% + +>> player versus system agency. player + + align:start position:0% +>> player versus system agency. player + + + align:start position:0% +>> player versus system agency. player +versus Oh, so system player is a system + + align:start position:0% +versus Oh, so system player is a system + + + align:start position:0% +versus Oh, so system player is a system +and agency is kind of your it's + + align:start position:0% +and agency is kind of your it's + + + align:start position:0% +and agency is kind of your it's +distributed. + + align:start position:0% +distributed. + + + align:start position:0% +distributed. +>> It's a name of your of your tactics, + + align:start position:0% +>> It's a name of your of your tactics, + + + align:start position:0% +>> It's a name of your of your tactics, +right? + + align:start position:0% +right? + + + align:start position:0% +right? +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> You also had low learning curve versus + + align:start position:0% +>> You also had low learning curve versus + + + align:start position:0% +>> You also had low learning curve versus +high learning curve. + + align:start position:0% +high learning curve. + + + align:start position:0% +high learning curve. +>> Definitely not into that. + + align:start position:0% + + + + align:start position:0% + +>> Fast versus slow. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% + + + + align:start position:0% + +>> so another learning another uh axis we + + align:start position:0% +>> so another learning another uh axis we + + + align:start position:0% +>> so another learning another uh axis we +had was um I guess if you call it + + align:start position:0% +had was um I guess if you call it + + + align:start position:0% +had was um I guess if you call it +the like freedom and like the + + align:start position:0% +the like freedom and like the + + + align:start position:0% +the like freedom and like the +predetermined like paths in the game, + + align:start position:0% +predetermined like paths in the game, + + + align:start position:0% +predetermined like paths in the game, +>> huh? + + align:start position:0% +>> huh? + + + align:start position:0% +>> huh? +>> Constraint. + + align:start position:0% +>> Constraint. + + + align:start position:0% +>> Constraint. +>> Yeah. Well, + + align:start position:0% +>> Yeah. Well, + + + align:start position:0% +>> Yeah. Well, +>> freedom versus constraint. Yeah, I can't + + align:start position:0% +>> freedom versus constraint. Yeah, I can't + + + align:start position:0% +>> freedom versus constraint. Yeah, I can't +remember the terms. Was it like glutus + + align:start position:0% +remember the terms. Was it like glutus + + + align:start position:0% +remember the terms. Was it like glutus +and py or something like that? + + align:start position:0% +and py or something like that? + + + align:start position:0% +and py or something like that? +>> Well, okay. So, one word that I use that + + align:start position:0% +>> Well, okay. So, one word that I use that + + + align:start position:0% +>> Well, okay. So, one word that I use that +I hear often to some describe games on + + align:start position:0% +I hear often to some describe games on + + + align:start position:0% +I hear often to some describe games on +rails. + + align:start position:0% +rails. + + + align:start position:0% +rails. +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> Um I mean + + align:start position:0% +>> Um I mean + + + align:start position:0% +>> Um I mean +13 hours of Final Fantasy + + align:start position:0% + + + + align:start position:0% + +unreal. You get to do one thing, you get + + align:start position:0% +unreal. You get to do one thing, you get + + + align:start position:0% +unreal. You get to do one thing, you get +to push the X button for 60 hours. + + align:start position:0% + + + + align:start position:0% + +I would say a subset of what you're + + align:start position:0% +I would say a subset of what you're + + + align:start position:0% +I would say a subset of what you're +talking about, but it's a very broad + + align:start position:0% +talking about, but it's a very broad + + + align:start position:0% +talking about, but it's a very broad +one. It's one that people generally + + align:start position:0% +one. It's one that people generally + + + align:start position:0% +one. It's one that people generally +understand as embodying this sort of + + align:start position:0% +understand as embodying this sort of + + + align:start position:0% +understand as embodying this sort of +like freedom like you you get to dig + + align:start position:0% +like freedom like you you get to dig + + + align:start position:0% +like freedom like you you get to dig +around basically, right? You know, you + + align:start position:0% +around basically, right? You know, you + + + align:start position:0% +around basically, right? You know, you +get to play Grand Theft Auto totally not + + align:start position:0% +get to play Grand Theft Auto totally not + + + align:start position:0% +get to play Grand Theft Auto totally not +following the story line and you know As + + align:start position:0% +following the story line and you know As + + + align:start position:0% +following the story line and you know As +time goes on, it becomes a little bit + + align:start position:0% +time goes on, it becomes a little bit + + + align:start position:0% +time goes on, it becomes a little bit +less of that. You can you get to do less + + align:start position:0% +less of that. You can you get to do less + + + align:start position:0% +less of that. You can you get to do less +crazy things. But the whole idea is that + + align:start position:0% +crazy things. But the whole idea is that + + + align:start position:0% +crazy things. But the whole idea is that +that world has ramps everywhere so that + + align:start position:0% +that world has ramps everywhere so that + + + align:start position:0% +that world has ramps everywhere so that +you can drive cars and vehicles and + + align:start position:0% +you can drive cars and vehicles and + + + align:start position:0% +you can drive cars and vehicles and +anything. + + align:start position:0% +anything. + + + align:start position:0% +anything. +>> Okay. Anything else? + + align:start position:0% +>> Okay. Anything else? + + + align:start position:0% +>> Okay. Anything else? +>> Uh there's like realism versus + + align:start position:0% +>> Uh there's like realism versus + + + align:start position:0% +>> Uh there's like realism versus +abstraction. + + align:start position:0% +abstraction. + + + align:start position:0% +abstraction. +>> What something? So, so like the the + + align:start position:0% +>> What something? So, so like the the + + + align:start position:0% +>> What something? So, so like the the +difference between you know like Eve + + align:start position:0% +difference between you know like Eve + + + align:start position:0% +difference between you know like Eve +Online for example which is supposed to + + align:start position:0% +Online for example which is supposed to + + + align:start position:0% +Online for example which is supposed to +be very realistic simulating something + + align:start position:0% +be very realistic simulating something + + + align:start position:0% +be very realistic simulating something +whereas poker for example is just cards + + align:start position:0% +whereas poker for example is just cards + + + align:start position:0% +whereas poker for example is just cards +and numbers + + align:start position:0% +and numbers + + + align:start position:0% +and numbers +>> something on the on the freedom sand box + + align:start position:0% +>> something on the on the freedom sand box + + + align:start position:0% +>> something on the on the freedom sand box +versus preturn on rails there's a very + + align:start position:0% +versus preturn on rails there's a very + + + align:start position:0% +versus preturn on rails there's a very +interesting thing in uh at least I've + + align:start position:0% +interesting thing in uh at least I've + + + align:start position:0% +interesting thing in uh at least I've +seen it done in Balders game too there's + + align:start position:0% +seen it done in Balders game too there's + + + align:start position:0% +seen it done in Balders game too there's +a pre-triven point in the game where you + + align:start position:0% +a pre-triven point in the game where you + + + align:start position:0% +a pre-triven point in the game where you +are told you need x amount of money to + + align:start position:0% +are told you need x amount of money to + + + align:start position:0% +are told you need x amount of money to +be able to pay for the ship out of here + + align:start position:0% +be able to pay for the ship out of here + + + align:start position:0% +be able to pay for the ship out of here +and you're placed in a sort of sandbox + + align:start position:0% +and you're placed in a sort of sandbox + + + align:start position:0% +and you're placed in a sort of sandbox +environment and you are given + + align:start position:0% +environment and you are given + + + align:start position:0% +environment and you are given +It is not you're not told that you can + + align:start position:0% +It is not you're not told that you can + + + align:start position:0% +It is not you're not told that you can +have whatever ways you can think of to + + align:start position:0% +have whatever ways you can think of to + + + align:start position:0% +have whatever ways you can think of to +make that amount of money whichever + + align:start position:0% +make that amount of money whichever + + + align:start position:0% +make that amount of money whichever +amount of money you can leave that part + + align:start position:0% +amount of money you can leave that part + + + align:start position:0% +amount of money you can leave that part +of the game. + + align:start position:0% +of the game. + + + align:start position:0% +of the game. +>> So it's a predetermined sandbox section. + + align:start position:0% +>> So it's a predetermined sandbox section. + + + align:start position:0% +>> So it's a predetermined sandbox section. +>> No I mean yeah I mean if it's a you know + + align:start position:0% +>> No I mean yeah I mean if it's a you know + + + align:start position:0% +>> No I mean yeah I mean if it's a you know +a lot of adventure games a lot of role + + align:start position:0% +a lot of adventure games a lot of role + + + align:start position:0% +a lot of adventure games a lot of role +playing games are largely predetermined + + align:start position:0% +playing games are largely predetermined + + + align:start position:0% +playing games are largely predetermined +with areas of of freedom. Even in a game + + align:start position:0% +with areas of of freedom. Even in a game + + + align:start position:0% +with areas of of freedom. Even in a game +like Final Fantasy maybe not 13 but in + + align:start position:0% +like Final Fantasy maybe not 13 but in + + + align:start position:0% +like Final Fantasy maybe not 13 but in +in in other games in the in the series + + align:start position:0% +in in other games in the in the series + + + align:start position:0% +in in other games in the in the series +the story is largely predetermined but + + align:start position:0% +the story is largely predetermined but + + + align:start position:0% +the story is largely predetermined but +what you do in combat is very very + + align:start position:0% +what you do in combat is very very + + + align:start position:0% +what you do in combat is very very +fluid. uh you know and and that's kind + + align:start position:0% +fluid. uh you know and and that's kind + + + align:start position:0% +fluid. uh you know and and that's kind +of like the the dichotomy that those + + align:start position:0% +of like the the dichotomy that those + + + align:start position:0% +of like the the dichotomy that those +that square + + align:start position:0% +that square + + + align:start position:0% +that square +and in the past kind of decided that + + align:start position:0% +and in the past kind of decided that + + + align:start position:0% +and in the past kind of decided that +that was okay. This helps us cater to + + align:start position:0% +that was okay. This helps us cater to + + + align:start position:0% +that was okay. This helps us cater to +people who want some flexibility in how + + align:start position:0% +people who want some flexibility in how + + + align:start position:0% +people who want some flexibility in how +they're going to play by making the + + align:start position:0% +they're going to play by making the + + + align:start position:0% +they're going to play by making the +combat system fluid enough that they can + + align:start position:0% +combat system fluid enough that they can + + + align:start position:0% +combat system fluid enough that they can +do play they want as but also lets us + + align:start position:0% +do play they want as but also lets us + + + align:start position:0% +do play they want as but also lets us +cater to the people who really want that + + align:start position:0% +cater to the people who really want that + + + align:start position:0% +cater to the people who really want that +that long overarching epic narrative you + + align:start position:0% +that long overarching epic narrative you + + + align:start position:0% +that long overarching epic narrative you +know and we can only we can only create + + align:start position:0% +know and we can only we can only create + + + align:start position:0% +know and we can only we can only create +one we can branch into different because + + align:start position:0% +one we can branch into different because + + + align:start position:0% +one we can branch into different because +so that's + + align:start position:0% +so that's + + + align:start position:0% +so that's +>> there others + + align:start position:0% +>> there others + + + align:start position:0% +>> there others +I mean might be a + + align:start position:0% +I mean might be a + + + align:start position:0% +I mean might be a +figure + + align:start position:0% + + + + align:start position:0% + +there's only one way to do it whereas + + align:start position:0% +there's only one way to do it whereas + + + align:start position:0% +there's only one way to do it whereas +sol + + align:start position:0% + + + + align:start position:0% + +you you could have multiple solutions + + align:start position:0% +you you could have multiple solutions + + + align:start position:0% +you you could have multiple solutions +and + + align:start position:0% +and + + + align:start position:0% +and +>> you know solution + + align:start position:0% + + + + align:start position:0% + +that tells you + + align:start position:0% +that tells you + + + align:start position:0% +that tells you +the game is catered to it Can I tell you + + align:start position:0% +the game is catered to it Can I tell you + + + align:start position:0% +the game is catered to it Can I tell you +something about the constraints on the + + align:start position:0% +something about the constraints on the + + + align:start position:0% +something about the constraints on the +budget of the + + align:start position:0% +budget of the + + + align:start position:0% +budget of the +>> No, I would I mean I prefer games that + + align:start position:0% +>> No, I would I mean I prefer games that + + + align:start position:0% +>> No, I would I mean I prefer games that +are much more + + align:start position:0% + + + + align:start position:0% + +>> right because the the interesting thing + + align:start position:0% +>> right because the the interesting thing + + + align:start position:0% +>> right because the the interesting thing +about multiple solutions to single + + align:start position:0% +about multiple solutions to single + + + align:start position:0% +about multiple solutions to single +solutions and multiple solutions + + align:start position:0% +solutions and multiple solutions + + + align:start position:0% +solutions and multiple solutions +um it could be all design like I I could + + align:start position:0% +um it could be all design like I I could + + + align:start position:0% +um it could be all design like I I could +design in a game in fact if you play DSX + + align:start position:0% +design in a game in fact if you play DSX + + + align:start position:0% +design in a game in fact if you play DSX +uh or any of the sequels uh they + + align:start position:0% +uh or any of the sequels uh they + + + align:start position:0% +uh or any of the sequels uh they +specifically stated that they made this + + align:start position:0% +specifically stated that they made this + + + align:start position:0% +specifically stated that they made this +game with multiple solutions in mind and + + align:start position:0% +game with multiple solutions in mind and + + + align:start position:0% +game with multiple solutions in mind and +for DSX 2 they designed it so that um + + align:start position:0% +for DSX 2 they designed it so that um + + + align:start position:0% +for DSX 2 they designed it so that um +they thought this puzzle needs kind of + + align:start position:0% +they thought this puzzle needs kind of + + + align:start position:0% +they thought this puzzle needs kind of +three solutions and they actually will + + align:start position:0% +three solutions and they actually will + + + align:start position:0% +three solutions and they actually will +design the environment for it. So while + + align:start position:0% +design the environment for it. So while + + + align:start position:0% +design the environment for it. So while +the game kind of like touted it as you + + align:start position:0% +the game kind of like touted it as you + + + align:start position:0% +the game kind of like touted it as you +know you get to play with the system you + + align:start position:0% +know you get to play with the system you + + + align:start position:0% +know you get to play with the system you +get to you know figure out how all these + + align:start position:0% +get to you know figure out how all these + + + align:start position:0% +get to you know figure out how all these +things combine and come up with + + align:start position:0% +things combine and come up with + + + align:start position:0% +things combine and come up with +solutions at your own really that they + + align:start position:0% +solutions at your own really that they + + + align:start position:0% +solutions at your own really that they +tried to like design it so that you have + + align:start position:0% +tried to like design it so that you have + + + align:start position:0% +tried to like design it so that you have +three very clear options but they wanted + + align:start position:0% +three very clear options but they wanted + + + align:start position:0% +three very clear options but they wanted +people to realize that they had options + + align:start position:0% +people to realize that they had options + + + align:start position:0% +people to realize that they had options +and so you can have multiple solutions + + align:start position:0% +and so you can have multiple solutions + + + align:start position:0% +and so you can have multiple solutions +whereas like freedom sandboxing kind of + + align:start position:0% +whereas like freedom sandboxing kind of + + + align:start position:0% +whereas like freedom sandboxing kind of +implies not necessarily design like you + + align:start position:0% +implies not necessarily design like you + + + align:start position:0% +implies not necessarily design like you +know you got lot lots of little things + + align:start position:0% +know you got lot lots of little things + + + align:start position:0% +know you got lot lots of little things +that you can do and lots of different + + align:start position:0% +that you can do and lots of different + + + align:start position:0% +that you can do and lots of different +spaces that you can explor + + align:start position:0% +spaces that you can explor + + + align:start position:0% +spaces that you can explor +But u it's not like um you've got one + + align:start position:0% +But u it's not like um you've got one + + + align:start position:0% +But u it's not like um you've got one +obstacle and three different ways to + + align:start position:0% +obstacle and three different ways to + + + align:start position:0% +obstacle and three different ways to +solve it. You've got all kinds of + + align:start position:0% +solve it. You've got all kinds of + + + align:start position:0% +solve it. You've got all kinds of +different things that you could be + + align:start position:0% +different things that you could be + + + align:start position:0% +different things that you could be +doing. You could be like choosing not. + + align:start position:0% +doing. You could be like choosing not. + + + align:start position:0% +doing. You could be like choosing not. +So these are different axis. I just want + + align:start position:0% +So these are different axis. I just want + + + align:start position:0% +So these are different axis. I just want +to point out that these are different + + align:start position:0% +to point out that these are different + + + align:start position:0% +to point out that these are different +ways to different things. + + align:start position:0% + + + + align:start position:0% + +>> Um you can have in terms of rule + + align:start position:0% +>> Um you can have in terms of rule + + + align:start position:0% +>> Um you can have in terms of rule +changing games whether it's dynamic + + align:start position:0% +changing games whether it's dynamic + + + align:start position:0% +changing games whether it's dynamic +rules or static rules. + + align:start position:0% +rules or static rules. + + + align:start position:0% +rules or static rules. +>> Okay. So so + + align:start position:0% +>> Okay. So so + + + align:start position:0% +>> Okay. So so +uh I'll put dynamic static and + + align:start position:0% + + + + align:start position:0% + +Are the rules going to change in the + + align:start position:0% +Are the rules going to change in the + + + align:start position:0% +Are the rules going to change in the +game? Yeah, that's there are some games + + align:start position:0% +game? Yeah, that's there are some games + + + align:start position:0% +game? Yeah, that's there are some games +over here. The whole point is change + + align:start position:0% + + + + align:start position:0% + +versus + + align:start position:0% +versus + + + align:start position:0% +versus +>> the rules. + + align:start position:0% +>> the rules. + + + align:start position:0% +>> the rules. +>> We had this before and then PvP version. + + align:start position:0% + + + + align:start position:0% + +time scale of decisions. + + align:start position:0% +time scale of decisions. + + + align:start position:0% +time scale of decisions. +>> So short model. + + align:start position:0% +>> So short model. + + + align:start position:0% +>> So short model. +>> Yeah. Like Twitch games versus games + + align:start position:0% +>> Yeah. Like Twitch games versus games + + + align:start position:0% +>> Yeah. Like Twitch games versus games +>> contemplate decisions. + + align:start position:0% +>> contemplate decisions. + + + align:start position:0% +>> contemplate decisions. +>> Sort of like contemplative and reactive. + + align:start position:0% +>> Sort of like contemplative and reactive. + + + align:start position:0% +>> Sort of like contemplative and reactive. +>> How is that compared to reactive? Is + + align:start position:0% +>> How is that compared to reactive? Is + + + align:start position:0% +>> How is that compared to reactive? Is +that are you guys going for basically + + align:start position:0% +that are you guys going for basically + + + align:start position:0% +that are you guys going for basically +the same thing? Like reactive means + + align:start position:0% +the same thing? Like reactive means + + + align:start position:0% +the same thing? Like reactive means +things are coming at you and you have to + + align:start position:0% +things are coming at you and you have to + + + align:start position:0% +things are coming at you and you have to +respond really really quickly. Maybe not + + align:start position:0% +respond really really quickly. Maybe not + + + align:start position:0% +respond really really quickly. Maybe not +even about it. And deliberate is like + + align:start position:0% +even about it. And deliberate is like + + + align:start position:0% +even about it. And deliberate is like +like a turnbased game. + + align:start position:0% +like a turnbased game. + + + align:start position:0% +like a turnbased game. +as much time as you want to think about + + align:start position:0% +as much time as you want to think about + + + align:start position:0% +as much time as you want to think about +how long you want to make a decision. + + align:start position:0% +how long you want to make a decision. + + + align:start position:0% +how long you want to make a decision. +Doesn't necessarily mean that, you know, + + align:start position:0% +Doesn't necessarily mean that, you know, + + + align:start position:0% +Doesn't necessarily mean that, you know, +you can have a turnbased game that's + + align:start position:0% +you can have a turnbased game that's + + + align:start position:0% +you can have a turnbased game that's +very fastpaced, you know, uh because the + + align:start position:0% +very fastpaced, you know, uh because the + + + align:start position:0% +very fastpaced, you know, uh because the +the weight of any given decision is not + + align:start position:0% +the weight of any given decision is not + + + align:start position:0% +the weight of any given decision is not +going to be so huge. So pace, you know, + + align:start position:0% +going to be so huge. So pace, you know, + + + align:start position:0% +going to be so huge. So pace, you know, +I'm I'm just going to put pace up here + + align:start position:0% +I'm I'm just going to put pace up here + + + align:start position:0% +I'm I'm just going to put pace up here +because + + align:start position:0% +because + + + align:start position:0% +because +you know, slow and fast, + + align:start position:0% + + + + align:start position:0% + +you know, as one way of describing the + + align:start position:0% +you know, as one way of describing the + + + align:start position:0% +you know, as one way of describing the +game, uh uh reactive versus libertous + + align:start position:0% +game, uh uh reactive versus libertous + + + align:start position:0% +game, uh uh reactive versus libertous +a related way of starting game. I bet + + align:start position:0% +a related way of starting game. I bet + + + align:start position:0% +a related way of starting game. I bet +you could take like two of these and put + + align:start position:0% +you could take like two of these and put + + + align:start position:0% +you could take like two of these and put +them on axis and then you can + + align:start position:0% +them on axis and then you can + + + align:start position:0% +them on axis and then you can +but you know I guess every once in a + + align:start position:0% +but you know I guess every once in a + + + align:start position:0% +but you know I guess every once in a +while you find that game that you like + + align:start position:0% +while you find that game that you like + + + align:start position:0% +while you find that game that you like +both here and here at the same time + + align:start position:0% +both here and here at the same time + + + align:start position:0% +both here and here at the same time +which is fine. It's just not a way to + + align:start position:0% +which is fine. It's just not a way to + + + align:start position:0% +which is fine. It's just not a way to +talk about these things. + + align:start position:0% +talk about these things. + + + align:start position:0% +talk about these things. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +these are really really useful terms uh + + align:start position:0% +these are really really useful terms uh + + + align:start position:0% +these are really really useful terms uh +better than + + align:start position:0% + + + + align:start position:0% + +is more + + align:start position:0% +is more + + + align:start position:0% +is more +>> a little bit more boxing. + + align:start position:0% +>> a little bit more boxing. + + + align:start position:0% +>> a little bit more boxing. +It's a little bit more restrictive than + + align:start position:0% +It's a little bit more restrictive than + + + align:start position:0% +It's a little bit more restrictive than +freedom + + align:start position:0% +freedom + + + align:start position:0% +freedom +is more like values that box on rails + + align:start position:0% +is more like values that box on rails + + + align:start position:0% +is more like values that box on rails +are more like back of the box. you know + + align:start position:0% +are more like back of the box. you know + + + align:start position:0% +are more like back of the box. you know +the future + + align:start position:0% +the future + + + align:start position:0% +the future +really + + align:start position:0% +really + + + align:start position:0% +really +you wouldn't \ No newline at end of file diff --git a/VSSF1LCnE20.txt b/VSSF1LCnE20.txt new file mode 100644 index 0000000000000000000000000000000000000000..38d5ae7313fba5c58b3b989fbb352561fc23d5d9 --- /dev/null +++ b/VSSF1LCnE20.txt @@ -0,0 +1,18264 @@ +align:start position:0% + +also i forgot to mention this point the + + align:start position:0% +also i forgot to mention this point the + + + align:start position:0% +also i forgot to mention this point the +output + + align:start position:0% +output + + + align:start position:0% +output +of microarray studies is foreign to + + align:start position:0% +of microarray studies is foreign to + + + align:start position:0% +of microarray studies is foreign to +basic biology researchers they're used + + align:start position:0% +basic biology researchers they're used + + + align:start position:0% +basic biology researchers they're used +to looking at + + align:start position:0% +to looking at + + + align:start position:0% +to looking at +three or four or five or 20 numbers and + + align:start position:0% +three or four or five or 20 numbers and + + + align:start position:0% +three or four or five or 20 numbers and +performing uh some an easy analysis in + + align:start position:0% +performing uh some an easy analysis in + + + align:start position:0% +performing uh some an easy analysis in +an excel spreadsheet + + align:start position:0% +an excel spreadsheet + + + align:start position:0% +an excel spreadsheet +but the point or doing a blast of one + + align:start position:0% +but the point or doing a blast of one + + + align:start position:0% +but the point or doing a blast of one +gene at a time but the data from these + + align:start position:0% +gene at a time but the data from these + + + align:start position:0% +gene at a time but the data from these +microarrays does not easily load into + + align:start position:0% +microarrays does not easily load into + + + align:start position:0% +microarrays does not easily load into +standard tools the analysis is + + align:start position:0% +standard tools the analysis is + + + align:start position:0% +standard tools the analysis is +non-standard excel does not cut it excel + + align:start position:0% +non-standard excel does not cut it excel + + + align:start position:0% +non-standard excel does not cut it excel +can barely load some of these data sets + + align:start position:0% +can barely load some of these data sets + + + align:start position:0% +can barely load some of these data sets +and so all this + + align:start position:0% +and so all this + + + align:start position:0% +and so all this +is uh actually representing an + + align:start position:0% +is uh actually representing an + + + align:start position:0% +is uh actually representing an +interesting term so this is the other + + align:start position:0% +interesting term so this is the other + + + align:start position:0% +interesting term so this is the other +point of view which is now that the + + align:start position:0% +point of view which is now that the + + + align:start position:0% +point of view which is now that the +standard biologist uh the tools are no + + align:start position:0% +standard biologist uh the tools are no + + + align:start position:0% +standard biologist uh the tools are no +longer fitting nicely onto the desktop + + align:start position:0% +longer fitting nicely onto the desktop + + + align:start position:0% +longer fitting nicely onto the desktop +productivity suite that they previously + + align:start position:0% +productivity suite that they previously + + + align:start position:0% +productivity suite that they previously +had and this is in some way a full + + align:start position:0% +had and this is in some way a full + + + align:start position:0% +had and this is in some way a full +circle it used to be of course that + + align:start position:0% +circle it used to be of course that + + + align:start position:0% +circle it used to be of course that +computers were run by the high priests + + align:start position:0% +computers were run by the high priests + + + align:start position:0% +computers were run by the high priests +in the computer center and not only were + + align:start position:0% +in the computer center and not only were + + + align:start position:0% +in the computer center and not only were +they um do they know about how to boot + + align:start position:0% +they um do they know about how to boot + + + align:start position:0% +they um do they know about how to boot +up the computer and to make the computer + + align:start position:0% +up the computer and to make the computer + + + align:start position:0% +up the computer and to make the computer +do whatever it did but they were also + + align:start position:0% +do whatever it did but they were also + + + align:start position:0% +do whatever it did but they were also +pretty steeped in the math and in uh the + + align:start position:0% +pretty steeped in the math and in uh the + + + align:start position:0% +pretty steeped in the math and in uh the +in the computational sciences so that + + align:start position:0% +in the computational sciences so that + + + align:start position:0% +in the computational sciences so that +they could actually interpret the + + align:start position:0% +they could actually interpret the + + + align:start position:0% +they could actually interpret the +results of a of the study with the + + align:start position:0% +results of a of the study with the + + + align:start position:0% +results of a of the study with the +advent of the personal computer and uh + + align:start position:0% +advent of the personal computer and uh + + + align:start position:0% +advent of the personal computer and uh +incredibly useful tools like like excel + + align:start position:0% +incredibly useful tools like like excel + + + align:start position:0% +incredibly useful tools like like excel +there was a lot that was now + + align:start position:0% +there was a lot that was now + + + align:start position:0% +there was a lot that was now +democratized and brought back to the um + + align:start position:0% +democratized and brought back to the um + + + align:start position:0% +democratized and brought back to the um +to the desk of the individual biology + + align:start position:0% +to the desk of the individual biology + + + align:start position:0% +to the desk of the individual biology +researcher but then when we scale back + + align:start position:0% +researcher but then when we scale back + + + align:start position:0% +researcher but then when we scale back +up to large data sets that are not + + align:start position:0% +up to large data sets that are not + + + align:start position:0% +up to large data sets that are not +trivially analyzable with current uh + + align:start position:0% +trivially analyzable with current uh + + + align:start position:0% +trivially analyzable with current uh +desktop tools + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the biologist education is is then the + + align:start position:0% +the biologist education is is then the + + + align:start position:0% +the biologist education is is then the +biologist computational education is + + align:start position:0% +biologist computational education is + + + align:start position:0% +biologist computational education is +lacking the uh biologists desktop tools + + align:start position:0% +lacking the uh biologists desktop tools + + + align:start position:0% +lacking the uh biologists desktop tools +are lacking and again + + align:start position:0% +are lacking and again + + + align:start position:0% +are lacking and again +they are um + + align:start position:0% +they are um + + + align:start position:0% +they are um +not in the loop + + align:start position:0% +not in the loop + + + align:start position:0% +not in the loop +and let me tell you this and i'll get to + + align:start position:0% +and let me tell you this and i'll get to + + + align:start position:0% +and let me tell you this and i'll get to +more interesting details in a second but + + align:start position:0% +more interesting details in a second but + + + align:start position:0% +more interesting details in a second but +something that you have to understand + + align:start position:0% +something that you have to understand + + + align:start position:0% +something that you have to understand +this is creating a lot of resentment + + align:start position:0% +this is creating a lot of resentment + + + align:start position:0% +this is creating a lot of resentment +in among standard biologists around this + + align:start position:0% +in among standard biologists around this + + + align:start position:0% +in among standard biologists around this +whole genomic revolution because not + + align:start position:0% +whole genomic revolution because not + + + align:start position:0% +whole genomic revolution because not +only i mean what you'll hear mostly is + + align:start position:0% +only i mean what you'll hear mostly is + + + align:start position:0% +only i mean what you'll hear mostly is +voicing of + + align:start position:0% +voicing of + + + align:start position:0% +voicing of +um + + align:start position:0% +um + + + align:start position:0% +um +skepticism about the methodologies but + + align:start position:0% +skepticism about the methodologies but + + + align:start position:0% +skepticism about the methodologies but +what's really going on is that they're + + align:start position:0% +what's really going on is that they're + + + align:start position:0% +what's really going on is that they're +justifiably feeling quite threatened for + + align:start position:0% +justifiably feeling quite threatened for + + + align:start position:0% +justifiably feeling quite threatened for +a big part of what they've been doing + + align:start position:0% +a big part of what they've been doing + + + align:start position:0% +a big part of what they've been doing +previously because they're just going to + + align:start position:0% +previously because they're just going to + + + align:start position:0% +previously because they're just going to +be disinterme disintermediated by the + + align:start position:0% +be disinterme disintermediated by the + + + align:start position:0% +be disinterme disintermediated by the +commoditization + + align:start position:0% +commoditization + + + align:start position:0% +commoditization +and the um quantification and the + + align:start position:0% +and the um quantification and the + + + align:start position:0% +and the um quantification and the +competition expertise that is required + + align:start position:0% +competition expertise that is required + + + align:start position:0% +competition expertise that is required +so what what are the characteristics of + + align:start position:0% +so what what are the characteristics of + + + align:start position:0% +so what what are the characteristics of +a microarray how do you + + align:start position:0% +a microarray how do you + + + align:start position:0% +a microarray how do you +recognize a microarray when when you are + + align:start position:0% +recognize a microarray when when you are + + + align:start position:0% +recognize a microarray when when you are +being uh + + align:start position:0% +being uh + + + align:start position:0% +being uh +marketed one + + align:start position:0% +marketed one + + + align:start position:0% +marketed one +the first is that it should have a small + + align:start position:0% +the first is that it should have a small + + + align:start position:0% +the first is that it should have a small +form factor so part one private small + + align:start position:0% +form factor so part one private small + + + align:start position:0% +form factor so part one private small +capable of measuring a significant + + align:start position:0% +capable of measuring a significant + + + align:start position:0% +capable of measuring a significant +fraction of some ohm + + align:start position:0% +fraction of some ohm + + + align:start position:0% +fraction of some ohm +the the genome + + align:start position:0% +the the genome + + + align:start position:0% +the the genome +the transcriptome or the proteome + + align:start position:0% +the transcriptome or the proteome + + + align:start position:0% +the transcriptome or the proteome +so i think + + align:start position:0% +so i think + + + align:start position:0% +so i think +small form factor is an obvious one but + + align:start position:0% +small form factor is an obvious one but + + + align:start position:0% +small form factor is an obvious one but +it also needs to measure a large part of + + align:start position:0% +it also needs to measure a large part of + + + align:start position:0% +it also needs to measure a large part of +the total output of the system otherwise + + align:start position:0% +the total output of the system otherwise + + + align:start position:0% +the total output of the system otherwise +it's not a microarray in the sense that + + align:start position:0% +it's not a microarray in the sense that + + + align:start position:0% +it's not a microarray in the sense that +we commonly understand it + + align:start position:0% +we commonly understand it + + + align:start position:0% +we commonly understand it +there has to be minimal labor and data + + align:start position:0% +there has to be minimal labor and data + + + align:start position:0% +there has to be minimal labor and data +acquisition so that it's an industrial + + align:start position:0% +acquisition so that it's an industrial + + + align:start position:0% +acquisition so that it's an industrial +process and not a labor intensive + + align:start position:0% +process and not a labor intensive + + + align:start position:0% +process and not a labor intensive +process + + align:start position:0% + + + + align:start position:0% + +you need to have an automated data path + + align:start position:0% +you need to have an automated data path + + + align:start position:0% +you need to have an automated data path +to a digital electronic format + + align:start position:0% + + + + align:start position:0% + +and there has to be sustainable high + + align:start position:0% +and there has to be sustainable high + + + align:start position:0% +and there has to be sustainable high +throughput processing + + align:start position:0% + + + + align:start position:0% + +and that begs the question then is this + + align:start position:0% +and that begs the question then is this + + + align:start position:0% +and that begs the question then is this +a microarray well this is a very nice + + align:start position:0% +a microarray well this is a very nice + + + align:start position:0% +a microarray well this is a very nice +piece of technology from xiomix + + align:start position:0% +piece of technology from xiomix + + + align:start position:0% +piece of technology from xiomix +which um has on these pillars these + + align:start position:0% +which um has on these pillars these + + + align:start position:0% +which um has on these pillars these +antibodies that allows you to measure in + + align:start position:0% +antibodies that allows you to measure in + + + align:start position:0% +antibodies that allows you to measure in +a very consistent systematic uh fashion + + align:start position:0% +a very consistent systematic uh fashion + + + align:start position:0% +a very consistent systematic uh fashion +uh 200 protein measurements are + + align:start position:0% +uh 200 protein measurements are + + + align:start position:0% +uh 200 protein measurements are +typically + + align:start position:0% +typically + + + align:start position:0% +typically +30 proteins measured in sextiplet and + + align:start position:0% +30 proteins measured in sextiplet and + + + align:start position:0% +30 proteins measured in sextiplet and +sex tuple + + align:start position:0% +sex tuple + + + align:start position:0% +sex tuple +for redundancy + + align:start position:0% +for redundancy + + + align:start position:0% +for redundancy +so + + align:start position:0% +so + + + align:start position:0% +so +it's kind of a microarray it's small + + align:start position:0% +it's kind of a microarray it's small + + + align:start position:0% +it's kind of a microarray it's small +it's an array + + align:start position:0% +it's an array + + + align:start position:0% +it's an array +but as typically used it's measuring + + align:start position:0% +but as typically used it's measuring + + + align:start position:0% +but as typically used it's measuring +between 30 + + align:start position:0% +between 30 + + + align:start position:0% +between 30 +and + + align:start position:0% +and + + + align:start position:0% +and +200 proteins and therefore i would argue + + align:start position:0% +200 proteins and therefore i would argue + + + align:start position:0% +200 proteins and therefore i would argue +it's not a microarray + + align:start position:0% +it's not a microarray + + + align:start position:0% +it's not a microarray +and you know basically they're trying to + + align:start position:0% +and you know basically they're trying to + + + align:start position:0% +and you know basically they're trying to +sell their venture capitalists that this + + align:start position:0% +sell their venture capitalists that this + + + align:start position:0% +sell their venture capitalists that this +is going to be as revolutionary + + align:start position:0% +is going to be as revolutionary + + + align:start position:0% +is going to be as revolutionary +revolutionary as the standard fmetrix + + align:start position:0% +revolutionary as the standard fmetrix + + + align:start position:0% +revolutionary as the standard fmetrix +mic uh rna expression microwaves i've + + align:start position:0% +mic uh rna expression microwaves i've + + + align:start position:0% +mic uh rna expression microwaves i've +told you about but it doesn't scale it + + align:start position:0% +told you about but it doesn't scale it + + + align:start position:0% +told you about but it doesn't scale it +doesn't give you the comprehensiveness + + align:start position:0% +doesn't give you the comprehensiveness + + + align:start position:0% +doesn't give you the comprehensiveness +and therefore you know in advance that + + align:start position:0% +and therefore you know in advance that + + + align:start position:0% +and therefore you know in advance that +this is only + + align:start position:0% +this is only + + + align:start position:0% +this is only +a + + align:start position:0% +a + + + align:start position:0% +a +somewhat more efficient version of the + + align:start position:0% +somewhat more efficient version of the + + + align:start position:0% +somewhat more efficient version of the +elisa test the antibody based test + + align:start position:0% +elisa test the antibody based test + + + align:start position:0% +elisa test the antibody based test +it's not leveraged + + align:start position:0% +it's not leveraged + + + align:start position:0% +it's not leveraged +similarly when you're looking at two two + + align:start position:0% +similarly when you're looking at two two + + + align:start position:0% +similarly when you're looking at two two +dimensional gels + + align:start position:0% +dimensional gels + + + align:start position:0% +dimensional gels +there you are capturing a large percent + + align:start position:0% +there you are capturing a large percent + + + align:start position:0% +there you are capturing a large percent +of the proteome but it's neither small + + align:start position:0% +of the proteome but it's neither small + + + align:start position:0% +of the proteome but it's neither small +nor is there an automatic data path to + + align:start position:0% +nor is there an automatic data path to + + + align:start position:0% +nor is there an automatic data path to +analysis because you basically have to + + align:start position:0% +analysis because you basically have to + + + align:start position:0% +analysis because you basically have to +pick out these different blots and um + + align:start position:0% +pick out these different blots and um + + + align:start position:0% +pick out these different blots and um +and apply some intelligence about which + + align:start position:0% +and apply some intelligence about which + + + align:start position:0% +and apply some intelligence about which +ones you pick and then feed them into + + align:start position:0% +ones you pick and then feed them into + + + align:start position:0% +ones you pick and then feed them into +the mass spec and then do the + + align:start position:0% +the mass spec and then do the + + + align:start position:0% +the mass spec and then do the +decompolation it's it's actually not a + + align:start position:0% +decompolation it's it's actually not a + + + align:start position:0% +decompolation it's it's actually not a +high throughput data path and + + align:start position:0% +high throughput data path and + + + align:start position:0% +high throughput data path and +i you know when i when you speak as i + + align:start position:0% +i you know when i when you speak as i + + + align:start position:0% +i you know when i when you speak as i +have to those who are really in the know + + align:start position:0% +have to those who are really in the know + + + align:start position:0% +have to those who are really in the know +about this + + align:start position:0% +about this + + + align:start position:0% +about this +area + + align:start position:0% +area + + + align:start position:0% +area +and they don't have uh an immediate + + align:start position:0% +and they don't have uh an immediate + + + align:start position:0% +and they don't have uh an immediate +sales pitch to the venture capitalists + + align:start position:0% +sales pitch to the venture capitalists + + + align:start position:0% +sales pitch to the venture capitalists +on the horizon they'll acknowledge to + + align:start position:0% +on the horizon they'll acknowledge to + + + align:start position:0% +on the horizon they'll acknowledge to +you + + align:start position:0% +you + + + align:start position:0% +you +that this is not ready for prime time + + align:start position:0% +that this is not ready for prime time + + + align:start position:0% +that this is not ready for prime time +and + + align:start position:0% +and + + + align:start position:0% +and +which explains why i had so much + + align:start position:0% +which explains why i had so much + + + align:start position:0% +which explains why i had so much +cognitive dissonance in the late 1990s + + align:start position:0% +cognitive dissonance in the late 1990s + + + align:start position:0% +cognitive dissonance in the late 1990s +where everybody's saying + + align:start position:0% +where everybody's saying + + + align:start position:0% +where everybody's saying +forget this genomics you know proteomics + + align:start position:0% +forget this genomics you know proteomics + + + align:start position:0% +forget this genomics you know proteomics +is it and i'm saying that's great i'd + + align:start position:0% +is it and i'm saying that's great i'd + + + align:start position:0% +is it and i'm saying that's great i'd +love to go to proteomics but i don't see + + align:start position:0% +love to go to proteomics but i don't see + + + align:start position:0% +love to go to proteomics but i don't see +these cheap high throughput + + align:start position:0% +these cheap high throughput + + + align:start position:0% +these cheap high throughput +comprehensive electronically data + + align:start position:0% +comprehensive electronically data + + + align:start position:0% +comprehensive electronically data +acquired + + align:start position:0% +acquired + + + align:start position:0% +acquired +sources available today that's the goal + + align:start position:0% +sources available today that's the goal + + + align:start position:0% +sources available today that's the goal +i believe we'll reach it but i think + + align:start position:0% +i believe we'll reach it but i think + + + align:start position:0% +i believe we'll reach it but i think +we're actually a full five years at + + align:start position:0% +we're actually a full five years at + + + align:start position:0% +we're actually a full five years at +least away from + + align:start position:0% +least away from + + + align:start position:0% +least away from +a high-throughput version of this + + align:start position:0% + + + + align:start position:0% + +and what do we actually use these + + align:start position:0% +and what do we actually use these + + + align:start position:0% +and what do we actually use these +micrates to look for but we rarely + + align:start position:0% +micrates to look for but we rarely + + + align:start position:0% +micrates to look for but we rarely +uh use it to find a single gene + + align:start position:0% +uh use it to find a single gene + + + align:start position:0% +uh use it to find a single gene +responsible uh + + align:start position:0% +responsible uh + + + align:start position:0% +responsible uh +for a process we but we frequently use + + align:start position:0% +for a process we but we frequently use + + + align:start position:0% +for a process we but we frequently use +it to find a pathway we frequently uh + + align:start position:0% +it to find a pathway we frequently uh + + + align:start position:0% +it to find a pathway we frequently uh +use it to find a set of genes working in + + align:start position:0% +use it to find a set of genes working in + + + align:start position:0% +use it to find a set of genes working in +a coordinated fashion the assumption + + align:start position:0% +a coordinated fashion the assumption + + + align:start position:0% +a coordinated fashion the assumption +being that there's structure at the + + align:start position:0% +being that there's structure at the + + + align:start position:0% +being that there's structure at the +biological scale + + align:start position:0% +biological scale + + + align:start position:0% +biological scale +and + + align:start position:0% +and + + + align:start position:0% +and +what do i mean by that that genes behave + + align:start position:0% +what do i mean by that that genes behave + + + align:start position:0% +what do i mean by that that genes behave +in coordinated fashion and so the + + align:start position:0% +in coordinated fashion and so the + + + align:start position:0% +in coordinated fashion and so the +questions that immediately are asked is + + align:start position:0% +questions that immediately are asked is + + + align:start position:0% +questions that immediately are asked is +why should this assumption hold + + align:start position:0% +why should this assumption hold + + + align:start position:0% +why should this assumption hold +and what evidence do we have that it + + align:start position:0% +and what evidence do we have that it + + + align:start position:0% +and what evidence do we have that it +does + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so why does clustering work in + + align:start position:0% +so why does clustering work in + + + align:start position:0% +so why does clustering work in +functional genomics + + align:start position:0% + + + + align:start position:0% + +well what do we see in the night sky + + align:start position:0% +well what do we see in the night sky + + + align:start position:0% +well what do we see in the night sky +when we look up + + align:start position:0% +when we look up + + + align:start position:0% +when we look up +we see a fairly apparently uniform + + align:start position:0% +we see a fairly apparently uniform + + + align:start position:0% +we see a fairly apparently uniform +uh star field + + align:start position:0% +uh star field + + + align:start position:0% +uh star field +but when we look with the right + + align:start position:0% +but when we look with the right + + + align:start position:0% +but when we look with the right +instruments we see clusters of stars + + align:start position:0% +instruments we see clusters of stars + + + align:start position:0% +instruments we see clusters of stars +from which we have been able to + + align:start position:0% +from which we have been able to + + + align:start position:0% +from which we have been able to +apply our + + align:start position:0% +apply our + + + align:start position:0% +apply our +classical and then uh icelandic + + align:start position:0% +classical and then uh icelandic + + + align:start position:0% +classical and then uh icelandic +mechanics to figure out what are the + + align:start position:0% +mechanics to figure out what are the + + + align:start position:0% +mechanics to figure out what are the +forces that uh hold these um + + align:start position:0% +forces that uh hold these um + + + align:start position:0% +forces that uh hold these um +clusters together and make them behave + + align:start position:0% +clusters together and make them behave + + + align:start position:0% +clusters together and make them behave +the way we see them behaving + + align:start position:0% +the way we see them behaving + + + align:start position:0% +the way we see them behaving +similarly when the gene + + align:start position:0% +similarly when the gene + + + align:start position:0% +similarly when the gene +um + + align:start position:0% +um + + + align:start position:0% +um +the genome project + + align:start position:0% +the genome project + + + align:start position:0% +the genome project +uh + + align:start position:0% +uh + + + align:start position:0% +uh +essentially came to a conclusion this in + + align:start position:0% +essentially came to a conclusion this in + + + align:start position:0% +essentially came to a conclusion this in +this year what we had was the gene + + align:start position:0% +this year what we had was the gene + + + align:start position:0% +this year what we had was the gene +universe we had the list of genes that + + align:start position:0% +universe we had the list of genes that + + + align:start position:0% +universe we had the list of genes that +form part of this universe + + align:start position:0% +form part of this universe + + + align:start position:0% +form part of this universe +and here for instance is a a bunch of + + align:start position:0% +and here for instance is a a bunch of + + + align:start position:0% +and here for instance is a a bunch of +such genes + + align:start position:0% +such genes + + + align:start position:0% +such genes +however this really doesn't tell us + + align:start position:0% +however this really doesn't tell us + + + align:start position:0% +however this really doesn't tell us +anything about how these genes + + align:start position:0% +anything about how these genes + + + align:start position:0% +anything about how these genes +interrelate and although there's a bunch + + align:start position:0% +interrelate and although there's a bunch + + + align:start position:0% +interrelate and although there's a bunch +of hoopla made about the human genome + + align:start position:0% +of hoopla made about the human genome + + + align:start position:0% +of hoopla made about the human genome +project + + align:start position:0% +project + + + align:start position:0% +project +it doesn't come it doesn't start become + + align:start position:0% +it doesn't come it doesn't start become + + + align:start position:0% +it doesn't come it doesn't start become +really interesting until you can do + + align:start position:0% +really interesting until you can do + + + align:start position:0% +really interesting until you can do +something like this a figure that i + + align:start position:0% +something like this a figure that i + + + align:start position:0% +something like this a figure that i +borrowed from the kyoto encyclopedia of + + align:start position:0% +borrowed from the kyoto encyclopedia of + + + align:start position:0% +borrowed from the kyoto encyclopedia of +genes and genomes keg + + align:start position:0% +genes and genomes keg + + + align:start position:0% +genes and genomes keg +which is a pathway representation + + align:start position:0% +which is a pathway representation + + + align:start position:0% +which is a pathway representation +understanding it how just as how the + + align:start position:0% +understanding it how just as how the + + + align:start position:0% +understanding it how just as how the +stars are interrelated in a galaxy how + + align:start position:0% +stars are interrelated in a galaxy how + + + align:start position:0% +stars are interrelated in a galaxy how +the genes interrelate in pathways so + + align:start position:0% +the genes interrelate in pathways so + + + align:start position:0% +the genes interrelate in pathways so +first of all + + align:start position:0% +first of all + + + align:start position:0% +first of all +why should that why why do i say the + + align:start position:0% +why should that why why do i say the + + + align:start position:0% +why should that why why do i say the +structure + + align:start position:0% +structure + + + align:start position:0% +structure +in the in the transcriptome it's because + + align:start position:0% +in the in the transcriptome it's because + + + align:start position:0% +in the in the transcriptome it's because +in fact in order to get things done like + + align:start position:0% +in fact in order to get things done like + + + align:start position:0% +in fact in order to get things done like +in this case make sure that cell kills + + align:start position:0% +in this case make sure that cell kills + + + align:start position:0% +in this case make sure that cell kills +itself there has to be coordinated + + align:start position:0% +itself there has to be coordinated + + + align:start position:0% +itself there has to be coordinated +expression of genes + + align:start position:0% +expression of genes + + + align:start position:0% +expression of genes +as we explained to you previously there + + align:start position:0% +as we explained to you previously there + + + align:start position:0% +as we explained to you previously there +are many reasons why gene expression and + + align:start position:0% +are many reasons why gene expression and + + + align:start position:0% +are many reasons why gene expression and +protein expression may not be correlated + + align:start position:0% +protein expression may not be correlated + + + align:start position:0% +protein expression may not be correlated +but if there was no coordination at all + + align:start position:0% +but if there was no coordination at all + + + align:start position:0% +but if there was no coordination at all +of gene + + align:start position:0% +of gene + + + align:start position:0% +of gene +expression + + align:start position:0% +expression + + + align:start position:0% +expression +two things would be true + + align:start position:0% +two things would be true + + + align:start position:0% +two things would be true +one + + align:start position:0% +one + + + align:start position:0% +one +the genes would be behaving randomly + + align:start position:0% +the genes would be behaving randomly + + + align:start position:0% +the genes would be behaving randomly +together + + align:start position:0% +together + + + align:start position:0% +together +in other words it would not be working + + align:start position:0% +in other words it would not be working + + + align:start position:0% +in other words it would not be working +together to make a process which seems + + align:start position:0% +together to make a process which seems + + + align:start position:0% +together to make a process which seems +unlikely and then clustering would never + + align:start position:0% +unlikely and then clustering would never + + + align:start position:0% +unlikely and then clustering would never +work + + align:start position:0% +work + + + align:start position:0% +work +because + + align:start position:0% +because + + + align:start position:0% +because +there would be no coordinated action of + + align:start position:0% +there would be no coordinated action of + + + align:start position:0% +there would be no coordinated action of +genes and the reason this coordinate + + align:start position:0% +genes and the reason this coordinate + + + align:start position:0% +genes and the reason this coordinate +action is in order to get the job done + + align:start position:0% +action is in order to get the job done + + + align:start position:0% +action is in order to get the job done +these + + align:start position:0% +these + + + align:start position:0% +these +out of principles of parcel money that + + align:start position:0% +out of principles of parcel money that + + + align:start position:0% +out of principles of parcel money that +is you don't have a gene product unless + + align:start position:0% +is you don't have a gene product unless + + + align:start position:0% +is you don't have a gene product unless +you need it + + align:start position:0% +you need it + + + align:start position:0% +you need it +these things are only generated when in + + align:start position:0% +these things are only generated when in + + + align:start position:0% +these things are only generated when in +fact you need them for this + + align:start position:0% +fact you need them for this + + + align:start position:0% +fact you need them for this +process in this case cell death + + align:start position:0% +process in this case cell death + + + align:start position:0% +process in this case cell death +and that allows people to + + align:start position:0% +and that allows people to + + + align:start position:0% +and that allows people to +do + + align:start position:0% +do + + + align:start position:0% +do +these clustering analysis and there'll + + align:start position:0% +these clustering analysis and there'll + + + align:start position:0% +these clustering analysis and there'll +be another lecture on clustering and i + + align:start position:0% +be another lecture on clustering and i + + + align:start position:0% +be another lecture on clustering and i +just want to give you a taste of what + + align:start position:0% +just want to give you a taste of what + + + align:start position:0% +just want to give you a taste of what +what i mean by clustering so here's the + + align:start position:0% +what i mean by clustering so here's the + + + align:start position:0% +what i mean by clustering so here's the +world's smallest microarray you have + + align:start position:0% +world's smallest microarray you have + + + align:start position:0% +world's smallest microarray you have +three experiments on which and on this + + align:start position:0% +three experiments on which and on this + + + align:start position:0% +three experiments on which and on this +little small + + align:start position:0% +little small + + + align:start position:0% +little small +microarray you're only measuring a gene + + align:start position:0% +microarray you're only measuring a gene + + + align:start position:0% +microarray you're only measuring a gene +three times + + align:start position:0% +three times + + + align:start position:0% +three times +and across these three experiments you + + align:start position:0% +and across these three experiments you + + + align:start position:0% +and across these three experiments you +therefore have + + align:start position:0% +therefore have + + + align:start position:0% +therefore have +three measurements of each gene + + align:start position:0% +three measurements of each gene + + + align:start position:0% +three measurements of each gene +and the most standard type of clustering + + align:start position:0% +and the most standard type of clustering + + + align:start position:0% +and the most standard type of clustering +is the so-called phylogenetic type tree + + align:start position:0% +is the so-called phylogenetic type tree + + + align:start position:0% +is the so-called phylogenetic type tree +or the dendrogram where you calculate + + align:start position:0% +or the dendrogram where you calculate + + + align:start position:0% +or the dendrogram where you calculate +all the correlation coefficients between + + align:start position:0% +all the correlation coefficients between + + + align:start position:0% +all the correlation coefficients between +every uh column in this case every set + + align:start position:0% +every uh column in this case every set + + + align:start position:0% +every uh column in this case every set +of genes and the correlation + + align:start position:0% +of genes and the correlation + + + align:start position:0% +of genes and the correlation +coefficients are shown as here + + align:start position:0% +coefficients are shown as here + + + align:start position:0% +coefficients are shown as here +you then figure out which genes are the + + align:start position:0% +you then figure out which genes are the + + + align:start position:0% +you then figure out which genes are the +closest together based on their + + align:start position:0% +closest together based on their + + + align:start position:0% +closest together based on their +correlation metric which in this case + + align:start position:0% +correlation metric which in this case + + + align:start position:0% +correlation metric which in this case +is 0.88 and you bring them together and + + align:start position:0% +is 0.88 and you bring them together and + + + align:start position:0% +is 0.88 and you bring them together and +then you you can summarize in a variety + + align:start position:0% +then you you can summarize in a variety + + + align:start position:0% +then you you can summarize in a variety +of ways that pair let's say by their + + align:start position:0% +of ways that pair let's say by their + + + align:start position:0% +of ways that pair let's say by their +by their + + align:start position:0% +by their + + + align:start position:0% +by their +median + + align:start position:0% +median + + + align:start position:0% +median +and + + align:start position:0% +and + + + align:start position:0% +and +from there + + align:start position:0% +from there + + + align:start position:0% +from there +you add on the next closest uh genes so + + align:start position:0% +you add on the next closest uh genes so + + + align:start position:0% +you add on the next closest uh genes so +very specifically g1 and gene two get + + align:start position:0% +very specifically g1 and gene two get + + + align:start position:0% +very specifically g1 and gene two get +put together because they're the closest + + align:start position:0% +put together because they're the closest + + + align:start position:0% +put together because they're the closest +and then the next closest to the + + align:start position:0% +and then the next closest to the + + + align:start position:0% +and then the next closest to the +joint uh um + + align:start position:0% +joint uh um + + + align:start position:0% +joint uh um +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +branch there is gene three and + + align:start position:0% +branch there is gene three and + + + align:start position:0% +branch there is gene three and +recursively this gets built up until you + + align:start position:0% +recursively this gets built up until you + + + align:start position:0% +recursively this gets built up until you +have + + align:start position:0% +have + + + align:start position:0% +have +one of these classical large dendrograms + + align:start position:0% +one of these classical large dendrograms + + + align:start position:0% +one of these classical large dendrograms +where again + + align:start position:0% +where again + + + align:start position:0% +where again +each row + + align:start position:0% +each row + + + align:start position:0% +each row +is a gene + + align:start position:0% +is a gene + + + align:start position:0% +is a gene +the columns are different experiments or + + align:start position:0% +the columns are different experiments or + + + align:start position:0% +the columns are different experiments or +samples in this case a time course but + + align:start position:0% +samples in this case a time course but + + + align:start position:0% +samples in this case a time course but +there are different distinct samples and + + align:start position:0% +there are different distinct samples and + + + align:start position:0% +there are different distinct samples and +what you see here is that every row + + align:start position:0% +what you see here is that every row + + + align:start position:0% +what you see here is that every row +that's close to one another is close to + + align:start position:0% +that's close to one another is close to + + + align:start position:0% +that's close to one another is close to +one another because they have a higher + + align:start position:0% +one another because they have a higher + + + align:start position:0% +one another because they have a higher +uh correlation between these two ones + + align:start position:0% +uh correlation between these two ones + + + align:start position:0% +uh correlation between these two ones +that are close to each other than + + align:start position:0% +that are close to each other than + + + align:start position:0% +that are close to each other than +between um two rows are far apart now + + align:start position:0% +between um two rows are far apart now + + + align:start position:0% +between um two rows are far apart now +there's something i'm i'm lighting up + + align:start position:0% +there's something i'm i'm lighting up + + + align:start position:0% +there's something i'm i'm lighting up +some complexity for instance you can + + align:start position:0% +some complexity for instance you can + + + align:start position:0% +some complexity for instance you can +toggle around the whole uh branch so + + align:start position:0% +toggle around the whole uh branch so + + + align:start position:0% +toggle around the whole uh branch so +that + + align:start position:0% +that + + + align:start position:0% +that +you might actually have some blocks some + + align:start position:0% +you might actually have some blocks some + + + align:start position:0% +you might actually have some blocks some +um rows which might not be together in + + align:start position:0% +um rows which might not be together in + + + align:start position:0% +um rows which might not be together in +some um rearrangements of this tree + + align:start position:0% +some um rearrangements of this tree + + + align:start position:0% +some um rearrangements of this tree +nonetheless by and large within the + + align:start position:0% +nonetheless by and large within the + + + align:start position:0% +nonetheless by and large within the +sub-branch you'll find typically that + + align:start position:0% +sub-branch you'll find typically that + + + align:start position:0% +sub-branch you'll find typically that +genes with a similar expression pattern + + align:start position:0% +genes with a similar expression pattern + + + align:start position:0% +genes with a similar expression pattern +are + + align:start position:0% +are + + + align:start position:0% +are +are put together because of the highest + + align:start position:0% +are put together because of the highest + + + align:start position:0% +are put together because of the highest +correlation coefficient and the + + align:start position:0% +correlation coefficient and the + + + align:start position:0% +correlation coefficient and the +diagrammatic version of it is as follows + + align:start position:0% +diagrammatic version of it is as follows + + + align:start position:0% +diagrammatic version of it is as follows +higher expression levels is red + + align:start position:0% +higher expression levels is red + + + align:start position:0% +higher expression levels is red +lower expression levels is green and you + + align:start position:0% +lower expression levels is green and you + + + align:start position:0% +lower expression levels is green and you +see that the red and the green bunches + + align:start position:0% +see that the red and the green bunches + + + align:start position:0% +see that the red and the green bunches +together because in fact + + align:start position:0% +together because in fact + + + align:start position:0% +together because in fact +each of those genes in each row + + align:start position:0% +each of those genes in each row + + + align:start position:0% +each of those genes in each row +are clustered together by their + + align:start position:0% +are clustered together by their + + + align:start position:0% +are clustered together by their +expression pattern that's all there is + + align:start position:0% +expression pattern that's all there is + + + align:start position:0% +expression pattern that's all there is +to it and then when you look + + align:start position:0% +to it and then when you look + + + align:start position:0% +to it and then when you look +what these bunches actually represent + + align:start position:0% +what these bunches actually represent + + + align:start position:0% +what these bunches actually represent +and what people do is essentially they + + align:start position:0% +and what people do is essentially they + + + align:start position:0% +and what people do is essentially they +draw lines + + align:start position:0% +draw lines + + + align:start position:0% +draw lines +uh and unfortunately it's not much more + + align:start position:0% +uh and unfortunately it's not much more + + + align:start position:0% +uh and unfortunately it's not much more +fancy than that at least in the + + align:start position:0% +fancy than that at least in the + + + align:start position:0% +fancy than that at least in the +publications that occur from 2019 + + align:start position:0% +publications that occur from 2019 + + + align:start position:0% +publications that occur from 2019 +to 2003 and draw lines next to these um + + align:start position:0% +to 2003 and draw lines next to these um + + + align:start position:0% +to 2003 and draw lines next to these um +groups you can actually find for some of + + align:start position:0% +groups you can actually find for some of + + + align:start position:0% +groups you can actually find for some of +them + + align:start position:0% +them + + + align:start position:0% +them +some functions such as cell cycle + + align:start position:0% +some functions such as cell cycle + + + align:start position:0% +some functions such as cell cycle +or coagulation + + align:start position:0% +or coagulation + + + align:start position:0% +or coagulation +or um + + align:start position:0% +or um + + + align:start position:0% +or um +or apoptosis you'll find + + align:start position:0% +or apoptosis you'll find + + + align:start position:0% +or apoptosis you'll find +different groups of genes clustered in + + align:start position:0% +different groups of genes clustered in + + + align:start position:0% +different groups of genes clustered in +that fashion that correspond to those + + align:start position:0% +that fashion that correspond to those + + + align:start position:0% +that fashion that correspond to those +different processes note however that + + align:start position:0% +different processes note however that + + + align:start position:0% +different processes note however that +for whatever reason lines were not drawn + + align:start position:0% +for whatever reason lines were not drawn + + + align:start position:0% +for whatever reason lines were not drawn +against these other + + align:start position:0% +against these other + + + align:start position:0% +against these other +blocks of genes + + align:start position:0% +blocks of genes + + + align:start position:0% +blocks of genes +and + + align:start position:0% +and + + + align:start position:0% +and +i'll argue in another lecture that why + + align:start position:0% +i'll argue in another lecture that why + + + align:start position:0% +i'll argue in another lecture that why +that's a mistake and furthermore i'll + + align:start position:0% +that's a mistake and furthermore i'll + + + align:start position:0% +that's a mistake and furthermore i'll +argue in another lecture why + + align:start position:0% +argue in another lecture why + + + align:start position:0% +argue in another lecture why +this act of drawing lines like these + + align:start position:0% +this act of drawing lines like these + + + align:start position:0% +this act of drawing lines like these +blocks although it's ground in the basic + + align:start position:0% +blocks although it's ground in the basic + + + align:start position:0% +blocks although it's ground in the basic +truth that these genes more or less work + + align:start position:0% +truth that these genes more or less work + + + align:start position:0% +truth that these genes more or less work +together + + align:start position:0% +together + + + align:start position:0% +together +where you draw the boundary of that line + + align:start position:0% +where you draw the boundary of that line + + + align:start position:0% +where you draw the boundary of that line +is an act of uh creative imagination and + + align:start position:0% +is an act of uh creative imagination and + + + align:start position:0% +is an act of uh creative imagination and +does not stand up well to uh statistical + + align:start position:0% +does not stand up well to uh statistical + + + align:start position:0% +does not stand up well to uh statistical +analysis in other words based on the + + align:start position:0% +analysis in other words based on the + + + align:start position:0% +analysis in other words based on the +knowledge of a particular biologist you + + align:start position:0% +knowledge of a particular biologist you + + + align:start position:0% +knowledge of a particular biologist you +might decide to change the boundaries of + + align:start position:0% +might decide to change the boundaries of + + + align:start position:0% +might decide to change the boundaries of +that of that + + align:start position:0% +that of that + + + align:start position:0% +that of that +box and there's + + align:start position:0% +box and there's + + + align:start position:0% +box and there's +well better well-grounded information + + align:start position:0% +well better well-grounded information + + + align:start position:0% +well better well-grounded information +theoretic methods which allows you to + + align:start position:0% +theoretic methods which allows you to + + + align:start position:0% +theoretic methods which allows you to +draw those + + align:start position:0% +draw those + + + align:start position:0% +draw those +functionally related groups more soundly + + align:start position:0% +functionally related groups more soundly + + + align:start position:0% +functionally related groups more soundly +and this is just a close-up of that + + align:start position:0% +and this is just a close-up of that + + + align:start position:0% +and this is just a close-up of that +so the point here is that + + align:start position:0% +so the point here is that + + + align:start position:0% +so the point here is that +if you're not looking for a global + + align:start position:0% +if you're not looking for a global + + + align:start position:0% +if you're not looking for a global +pattern as i just showed you if you're + + align:start position:0% +pattern as i just showed you if you're + + + align:start position:0% +pattern as i just showed you if you're +not trying to see + + align:start position:0% +not trying to see + + + align:start position:0% +not trying to see +how things are working + + align:start position:0% +how things are working + + + align:start position:0% +how things are working +across + + align:start position:0% +across + + + align:start position:0% +across +a process like coagulation or apoptosis + + align:start position:0% +a process like coagulation or apoptosis + + + align:start position:0% +a process like coagulation or apoptosis +and if you're not looking for guilt by + + align:start position:0% +and if you're not looking for guilt by + + + align:start position:0% +and if you're not looking for guilt by +association by which i mean + + align:start position:0% + + + + align:start position:0% + +let's say you know + + align:start position:0% +let's say you know + + + align:start position:0% +let's say you know +the function of all these genes and all + + align:start position:0% +the function of all these genes and all + + + align:start position:0% +the function of all these genes and all +these genes but not these + + align:start position:0% +these genes but not these + + + align:start position:0% +these genes but not these +genes here in the in the middle by guilt + + align:start position:0% +genes here in the in the middle by guilt + + + align:start position:0% +genes here in the in the middle by guilt +associated by association says + + align:start position:0% +associated by association says + + + align:start position:0% +associated by association says +essentially that if you know the + + align:start position:0% +essentially that if you know the + + + align:start position:0% +essentially that if you know the +function of these genes and know the + + align:start position:0% +function of these genes and know the + + + align:start position:0% +function of these genes and know the +function of g these genes because these + + align:start position:0% +function of g these genes because these + + + align:start position:0% +function of g these genes because these +are + + align:start position:0% +are + + + align:start position:0% +are +co-regulated in the same fashion you can + + align:start position:0% +co-regulated in the same fashion you can + + + align:start position:0% +co-regulated in the same fashion you can +impute something about that process and + + align:start position:0% +impute something about that process and + + + align:start position:0% +impute something about that process and +that + + align:start position:0% +that + + + align:start position:0% +that +heuristic course as it may be has been + + align:start position:0% +heuristic course as it may be has been + + + align:start position:0% +heuristic course as it may be has been +actually exploited very successfully by + + align:start position:0% +actually exploited very successfully by + + + align:start position:0% +actually exploited very successfully by +uh + + align:start position:0% +uh + + + align:start position:0% +uh +many investigators but if so if you're + + align:start position:0% +many investigators but if so if you're + + + align:start position:0% +many investigators but if so if you're +not using uh guilt by association + + align:start position:0% +not using uh guilt by association + + + align:start position:0% +not using uh guilt by association +or and if you're not looking for global + + align:start position:0% +or and if you're not looking for global + + + align:start position:0% +or and if you're not looking for global +patterns then microwave technology may + + align:start position:0% +patterns then microwave technology may + + + align:start position:0% +patterns then microwave technology may +be inappropriate and misleading and it + + align:start position:0% +be inappropriate and misleading and it + + + align:start position:0% +be inappropriate and misleading and it +may be inappropriate and misleading + + align:start position:0% +may be inappropriate and misleading + + + align:start position:0% +may be inappropriate and misleading +because the micro rays themselves are + + align:start position:0% +because the micro rays themselves are + + + align:start position:0% +because the micro rays themselves are +much more noisy than people understand + + align:start position:0% +much more noisy than people understand + + + align:start position:0% +much more noisy than people understand +and therefore if you're just looking + + align:start position:0% +and therefore if you're just looking + + + align:start position:0% +and therefore if you're just looking +specifically if you're trying to answer + + align:start position:0% +specifically if you're trying to answer + + + align:start position:0% +specifically if you're trying to answer +the question do these three genes get + + align:start position:0% +the question do these three genes get + + + align:start position:0% +the question do these three genes get +expressed differentially then you're + + align:start position:0% +expressed differentially then you're + + + align:start position:0% +expressed differentially then you're +probably using the wrong technology for + + align:start position:0% +probably using the wrong technology for + + + align:start position:0% +probably using the wrong technology for +the wrong costs and with much + + align:start position:0% +the wrong costs and with much + + + align:start position:0% +the wrong costs and with much +greater danger + + align:start position:0% +greater danger + + + align:start position:0% +greater danger +of being misled so and why is that a + + align:start position:0% +of being misled so and why is that a + + + align:start position:0% +of being misled so and why is that a +problem + + align:start position:0% +problem + + + align:start position:0% +problem +well let me give you a decision + + align:start position:0% +well let me give you a decision + + + align:start position:0% +well let me give you a decision +theoretic view + + align:start position:0% +theoretic view + + + align:start position:0% +theoretic view +of + + align:start position:0% +of + + + align:start position:0% +of +microarray analysis + + align:start position:0% +microarray analysis + + + align:start position:0% +microarray analysis +as + + align:start position:0% +as + + + align:start position:0% +as +we showed all i think think about it + + align:start position:0% +we showed all i think think about it + + + align:start position:0% +we showed all i think think about it +so the most basic microwave experiment + + align:start position:0% +so the most basic microwave experiment + + + align:start position:0% +so the most basic microwave experiment +asked the following question across a + + align:start position:0% +asked the following question across a + + + align:start position:0% +asked the following question across a +set of experiments + + align:start position:0% +set of experiments + + + align:start position:0% +set of experiments +is a gene up + + align:start position:0% +is a gene up + + + align:start position:0% +is a gene up +or down + + align:start position:0% +or down + + + align:start position:0% +or down +regulated or more specifically of the + + align:start position:0% +regulated or more specifically of the + + + align:start position:0% +regulated or more specifically of the +thousands of genes that we're measuring + + align:start position:0% +thousands of genes that we're measuring + + + align:start position:0% +thousands of genes that we're measuring +which are up or down regulated + + align:start position:0% +which are up or down regulated + + + align:start position:0% +which are up or down regulated +and for some you'll you'll use some + + align:start position:0% +and for some you'll you'll use some + + + align:start position:0% +and for some you'll you'll use some +statistic and you find it it is indeed + + align:start position:0% +statistic and you find it it is indeed + + + align:start position:0% +statistic and you find it it is indeed +upregulated and for others it is not + + align:start position:0% +upregulated and for others it is not + + + align:start position:0% +upregulated and for others it is not +upper regulated if the gene is said to + + align:start position:0% +upper regulated if the gene is said to + + + align:start position:0% +upper regulated if the gene is said to +be up regulated is the gene relevant to + + align:start position:0% +be up regulated is the gene relevant to + + + align:start position:0% +be up regulated is the gene relevant to +the process being studied let's say + + align:start position:0% +the process being studied let's say + + + align:start position:0% +the process being studied let's say +cancer yes in that case it's a true + + align:start position:0% +cancer yes in that case it's a true + + + align:start position:0% +cancer yes in that case it's a true +positive + + align:start position:0% +positive + + + align:start position:0% +positive +it's perhaps a real target for cancer + + align:start position:0% +it's perhaps a real target for cancer + + + align:start position:0% +it's perhaps a real target for cancer +treatment so therefore + + align:start position:0% +treatment so therefore + + + align:start position:0% +treatment so therefore +big reward because either your drug + + align:start position:0% +big reward because either your drug + + + align:start position:0% +big reward because either your drug +company or your researcher publishing + + align:start position:0% +company or your researcher publishing + + + align:start position:0% +company or your researcher publishing +your finding if the gene is not relevant + + align:start position:0% +your finding if the gene is not relevant + + + align:start position:0% +your finding if the gene is not relevant +to the process being studied it's a + + align:start position:0% +to the process being studied it's a + + + align:start position:0% +to the process being studied it's a +false positive therefore you've wasted + + align:start position:0% +false positive therefore you've wasted + + + align:start position:0% +false positive therefore you've wasted +your money + + align:start position:0% +your money + + + align:start position:0% +your money +if the gene is not significantly up or + + align:start position:0% +if the gene is not significantly up or + + + align:start position:0% +if the gene is not significantly up or +down regulated in other words it doesn't + + align:start position:0% +down regulated in other words it doesn't + + + align:start position:0% +down regulated in other words it doesn't +look interesting by this experiment if + + align:start position:0% +look interesting by this experiment if + + + align:start position:0% +look interesting by this experiment if +the gene is relevant to the process + + align:start position:0% +the gene is relevant to the process + + + align:start position:0% +the gene is relevant to the process +being studied then you've missed it it's + + align:start position:0% +being studied then you've missed it it's + + + align:start position:0% +being studied then you've missed it it's +a false negative so then again you've + + align:start position:0% +a false negative so then again you've + + + align:start position:0% +a false negative so then again you've +lost an opportunity + + align:start position:0% +lost an opportunity + + + align:start position:0% +lost an opportunity +however if the gene is not significantly + + align:start position:0% +however if the gene is not significantly + + + align:start position:0% +however if the gene is not significantly +up or down regulated and it's not + + align:start position:0% +up or down regulated and it's not + + + align:start position:0% +up or down regulated and it's not +relevant to the process being studied + + align:start position:0% +relevant to the process being studied + + + align:start position:0% +relevant to the process being studied +then it's a true negative so there's + + align:start position:0% +then it's a true negative so there's + + + align:start position:0% +then it's a true negative so there's +that's great you're not wasting time and + + align:start position:0% +that's great you're not wasting time and + + + align:start position:0% +that's great you're not wasting time and +here's the problem so you have 10 000 + + align:start position:0% +here's the problem so you have 10 000 + + + align:start position:0% +here's the problem so you have 10 000 +genes + + align:start position:0% +genes + + + align:start position:0% +genes +let's say or 20 000 genes that you're + + align:start position:0% +let's say or 20 000 genes that you're + + + align:start position:0% +let's say or 20 000 genes that you're +measuring a microwave experiment + + align:start position:0% +measuring a microwave experiment + + + align:start position:0% +measuring a microwave experiment +and the biologist + + align:start position:0% +and the biologist + + + align:start position:0% +and the biologist +and the um + + align:start position:0% +and the um + + + align:start position:0% +and the um +the biologist + + align:start position:0% +the biologist + + + align:start position:0% +the biologist +and the uh big pharma can't bear the + + align:start position:0% +and the uh big pharma can't bear the + + + align:start position:0% +and the uh big pharma can't bear the +thought + + align:start position:0% +thought + + + align:start position:0% +thought +that they're gonna miss + + align:start position:0% +that they're gonna miss + + + align:start position:0% +that they're gonna miss +the blockbuster false negative + + align:start position:0% +the blockbuster false negative + + + align:start position:0% +the blockbuster false negative +um + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +consequently + + align:start position:0% +consequently + + + align:start position:0% +consequently +what they do is they change the + + align:start position:0% +what they do is they change the + + + align:start position:0% +what they do is they change the +threshold for declaring something to be + + align:start position:0% +threshold for declaring something to be + + + align:start position:0% +threshold for declaring something to be +a um up or down regulated so that more + + align:start position:0% +a um up or down regulated so that more + + + align:start position:0% +a um up or down regulated so that more +and more + + align:start position:0% + + + + align:start position:0% + +genes are considered to be + + align:start position:0% +genes are considered to be + + + align:start position:0% +genes are considered to be +um up or down regulated but the problem + + align:start position:0% +um up or down regulated but the problem + + + align:start position:0% +um up or down regulated but the problem +is that not only does this increase your + + align:start position:0% +is that not only does this increase your + + + align:start position:0% +is that not only does this increase your +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +the number of true positives you find + + align:start position:0% +the number of true positives you find + + + align:start position:0% +the number of true positives you find +but also hugely increases your number of + + align:start position:0% +but also hugely increases your number of + + + align:start position:0% +but also hugely increases your number of +false positives and the problem again + + align:start position:0% +false positives and the problem again + + + align:start position:0% +false positives and the problem again +this gets back to the biologists don't + + align:start position:0% +this gets back to the biologists don't + + + align:start position:0% +this gets back to the biologists don't +understand the difference between a + + align:start position:0% +understand the difference between a + + + align:start position:0% +understand the difference between a +northern blot on a gene they understand + + align:start position:0% +northern blot on a gene they understand + + + align:start position:0% +northern blot on a gene they understand +and then their microarray on ten + + align:start position:0% +and then their microarray on ten + + + align:start position:0% +and then their microarray on ten +thousand genes that they know nothing + + align:start position:0% +thousand genes that they know nothing + + + align:start position:0% +thousand genes that they know nothing +about + + align:start position:0% +about + + + align:start position:0% +about +because + + align:start position:0% +because + + + align:start position:0% +because +they can be given literally thousands of + + align:start position:0% +they can be given literally thousands of + + + align:start position:0% +they can be given literally thousands of +false positive and the typical + + align:start position:0% +false positive and the typical + + + align:start position:0% +false positive and the typical +interaction you'll have with the basic + + align:start position:0% +interaction you'll have with the basic + + + align:start position:0% +interaction you'll have with the basic +biologists will say when you do this + + align:start position:0% +biologists will say when you do this + + + align:start position:0% +biologists will say when you do this +kind of analysis this kind of analysis + + align:start position:0% +kind of analysis this kind of analysis + + + align:start position:0% +kind of analysis this kind of analysis +for them to say + + align:start position:0% +for them to say + + + align:start position:0% +for them to say +oh zach um i see that you said + + align:start position:0% +oh zach um i see that you said + + + align:start position:0% +oh zach um i see that you said +statistically significantly only um + + align:start position:0% +statistically significantly only um + + + align:start position:0% +statistically significantly only um +we could only place bets about 10 genes + + align:start position:0% +we could only place bets about 10 genes + + + align:start position:0% +we could only place bets about 10 genes +but i see it down the list + + align:start position:0% +but i see it down the list + + + align:start position:0% +but i see it down the list +that you've said not to be significantly + + align:start position:0% +that you've said not to be significantly + + + align:start position:0% +that you've said not to be significantly +differentially expressed a gene that i + + align:start position:0% +differentially expressed a gene that i + + + align:start position:0% +differentially expressed a gene that i +know from my own + + align:start position:0% +know from my own + + + align:start position:0% +know from my own +research is in fact differentially + + align:start position:0% +research is in fact differentially + + + align:start position:0% +research is in fact differentially +expressed but it just doesn't have a + + align:start position:0% +expressed but it just doesn't have a + + + align:start position:0% +expressed but it just doesn't have a +p-value that reaches a level of + + align:start position:0% +p-value that reaches a level of + + + align:start position:0% +p-value that reaches a level of +significance so therefore couldn't we + + align:start position:0% +significance so therefore couldn't we + + + align:start position:0% +significance so therefore couldn't we +actually just push the whole special + + align:start position:0% +actually just push the whole special + + + align:start position:0% +actually just push the whole special +down to at least + + align:start position:0% +down to at least + + + align:start position:0% +down to at least +the same threshold as the gene that i + + align:start position:0% +the same threshold as the gene that i + + + align:start position:0% +the same threshold as the gene that i +already know something about and the + + align:start position:0% +already know something about and the + + + align:start position:0% +already know something about and the +answer is unfortunately if you do that + + align:start position:0% +answer is unfortunately if you do that + + + align:start position:0% +answer is unfortunately if you do that +then you're + + align:start position:0% +then you're + + + align:start position:0% +then you're +it'll so happen also there's nothing to + + align:start position:0% +it'll so happen also there's nothing to + + + align:start position:0% +it'll so happen also there's nothing to +say that these other genes that have now + + align:start position:0% +say that these other genes that have now + + + align:start position:0% +say that these other genes that have now +included lists are anything at all like + + align:start position:0% +included lists are anything at all like + + + align:start position:0% +included lists are anything at all like +this gene that you happen to know a lot + + align:start position:0% +this gene that you happen to know a lot + + + align:start position:0% +this gene that you happen to know a lot +about so you're using prior knowledge + + align:start position:0% +about so you're using prior knowledge + + + align:start position:0% +about so you're using prior knowledge +it's not you're not using the microwave + + align:start position:0% +it's not you're not using the microwave + + + align:start position:0% +it's not you're not using the microwave +you're using prior knowledge to say + + align:start position:0% +you're using prior knowledge to say + + + align:start position:0% +you're using prior knowledge to say +something about it and therefore you get + + align:start position:0% +something about it and therefore you get + + + align:start position:0% +something about it and therefore you get +a lot of false positives and the problem + + align:start position:0% +a lot of false positives and the problem + + + align:start position:0% +a lot of false positives and the problem +is each one of the false positive is one + + align:start position:0% +is each one of the false positive is one + + + align:start position:0% +is each one of the false positive is one +postdoc going off to do + + align:start position:0% +postdoc going off to do + + + align:start position:0% +postdoc going off to do +a validation study and turns out with + + align:start position:0% +a validation study and turns out with + + + align:start position:0% +a validation study and turns out with +tens of thousands of jeans you can + + align:start position:0% +tens of thousands of jeans you can + + + align:start position:0% +tens of thousands of jeans you can +launch a lot of post docs so even the + + align:start position:0% +launch a lot of post docs so even the + + + align:start position:0% +launch a lot of post docs so even the +farm-up industry with these big deep + + align:start position:0% +farm-up industry with these big deep + + + align:start position:0% +farm-up industry with these big deep +pockets actually got exhausted by this + + align:start position:0% +pockets actually got exhausted by this + + + align:start position:0% +pockets actually got exhausted by this +and actually quite turned off by a lot + + align:start position:0% +and actually quite turned off by a lot + + + align:start position:0% +and actually quite turned off by a lot +of these technologies because a lot of + + align:start position:0% +of these technologies because a lot of + + + align:start position:0% +of these technologies because a lot of +um the genes that they thought they were + + align:start position:0% +um the genes that they thought they were + + + align:start position:0% +um the genes that they thought they were +going to look after these top genes + + align:start position:0% +going to look after these top genes + + + align:start position:0% +going to look after these top genes +which look kind of interesting you + + align:start position:0% +which look kind of interesting you + + + align:start position:0% +which look kind of interesting you +always make a story and create a story + + align:start position:0% +always make a story and create a story + + + align:start position:0% +always make a story and create a story +about why this gene may be involved in + + align:start position:0% +about why this gene may be involved in + + + align:start position:0% +about why this gene may be involved in +your favorite disease process turned out + + align:start position:0% +your favorite disease process turned out + + + align:start position:0% +your favorite disease process turned out +not to be the case so by not + + align:start position:0% +not to be the case so by not + + + align:start position:0% +not to be the case so by not +understanding this decision um theoretic + + align:start position:0% +understanding this decision um theoretic + + + align:start position:0% +understanding this decision um theoretic +uh + + align:start position:0% +uh + + + align:start position:0% +uh +view a lot of money was wasted and a lot + + align:start position:0% +view a lot of money was wasted and a lot + + + align:start position:0% +view a lot of money was wasted and a lot +of disappointment was made in this + + align:start position:0% +of disappointment was made in this + + + align:start position:0% +of disappointment was made in this +technology which is one of the reasons i + + align:start position:0% +technology which is one of the reasons i + + + align:start position:0% +technology which is one of the reasons i +wrote in the first sentence of the first + + align:start position:0% +wrote in the first sentence of the first + + + align:start position:0% +wrote in the first sentence of the first +chapter of my book my creator integrated + + align:start position:0% +chapter of my book my creator integrated + + + align:start position:0% +chapter of my book my creator integrated +genomics the uh functional genomic + + align:start position:0% +genomics the uh functional genomic + + + align:start position:0% +genomics the uh functional genomic +meltdown is imminent and i wrote i first + + align:start position:0% +meltdown is imminent and i wrote i first + + + align:start position:0% +meltdown is imminent and i wrote i first +wrote that in 2000 and everything that + + align:start position:0% +wrote that in 2000 and everything that + + + align:start position:0% +wrote that in 2000 and everything that +i've + + align:start position:0% +i've + + + align:start position:0% +i've +everything that's happened since shows + + align:start position:0% +everything that's happened since shows + + + align:start position:0% +everything that's happened since shows +is true that although there's more + + align:start position:0% +is true that although there's more + + + align:start position:0% +is true that although there's more +interesting science being developed the + + align:start position:0% +interesting science being developed the + + + align:start position:0% +interesting science being developed the +fact is a lot of the companies that were + + align:start position:0% +fact is a lot of the companies that were + + + align:start position:0% +fact is a lot of the companies that were +built around this and some of the + + align:start position:0% +built around this and some of the + + + align:start position:0% +built around this and some of the +bioinformatics companies that are built + + align:start position:0% +bioinformatics companies that are built + + + align:start position:0% +bioinformatics companies that are built +around this are just going down the + + align:start position:0% +around this are just going down the + + + align:start position:0% +around this are just going down the +tubes + + align:start position:0% +tubes + + + align:start position:0% +tubes +so let's just remind ourselves about + + align:start position:0% +so let's just remind ourselves about + + + align:start position:0% +so let's just remind ourselves about +um by the way i'm very optimistic about + + align:start position:0% +um by the way i'm very optimistic about + + + align:start position:0% +um by the way i'm very optimistic about +optimistic about the whole field but i'm + + align:start position:0% +optimistic about the whole field but i'm + + + align:start position:0% +optimistic about the whole field but i'm +optimistic about the whole field when + + align:start position:0% +optimistic about the whole field when + + + align:start position:0% +optimistic about the whole field when +we're careful in our use of the um + + align:start position:0% +we're careful in our use of the um + + + align:start position:0% +we're careful in our use of the um +technology both in understands the + + align:start position:0% +technology both in understands the + + + align:start position:0% +technology both in understands the +actual engineering part of the + + align:start position:0% +actual engineering part of the + + + align:start position:0% +actual engineering part of the +technology and understanding the + + align:start position:0% +technology and understanding the + + + align:start position:0% +technology and understanding the +quantitative analysis so i know that + + align:start position:0% +quantitative analysis so i know that + + + align:start position:0% +quantitative analysis so i know that +we've gone through this with you uh + + align:start position:0% +we've gone through this with you uh + + + align:start position:0% +we've gone through this with you uh +several times but i want to revisit + + align:start position:0% +several times but i want to revisit + + + align:start position:0% +several times but i want to revisit +actually + + align:start position:0% +actually + + + align:start position:0% +actually +is everybody + + align:start position:0% +is everybody + + + align:start position:0% +is everybody +is everybody comfortable + + align:start position:0% + + + + align:start position:0% + +in the way basic microarrays work do i + + align:start position:0% +in the way basic microarrays work do i + + + align:start position:0% +in the way basic microarrays work do i +have to revisit it + + align:start position:0% +have to revisit it + + + align:start position:0% +have to revisit it +you want me i do not have to revisit it + + align:start position:0% +you want me i do not have to revisit it + + + align:start position:0% +you want me i do not have to revisit it +thank you all right + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +now we can just remind ourselves about + + align:start position:0% +now we can just remind ourselves about + + + align:start position:0% +now we can just remind ourselves about +the the difference between the two + + align:start position:0% +the the difference between the two + + + align:start position:0% +the the difference between the two +platforms + + align:start position:0% +platforms + + + align:start position:0% +platforms +um + + align:start position:0% +um + + + align:start position:0% +um +alphametrics as you know um does not + + align:start position:0% +alphametrics as you know um does not + + + align:start position:0% +alphametrics as you know um does not +represent on each spot on the microarray + + align:start position:0% +represent on each spot on the microarray + + + align:start position:0% +represent on each spot on the microarray +the entire uh gene it just represents a + + align:start position:0% +the entire uh gene it just represents a + + + align:start position:0% +the entire uh gene it just represents a +few oligonu nucleotides that they have + + align:start position:0% +few oligonu nucleotides that they have + + + align:start position:0% +few oligonu nucleotides that they have +chosen to be representative of part of + + align:start position:0% +chosen to be representative of part of + + + align:start position:0% +chosen to be representative of part of +the gene more on the + + align:start position:0% +the gene more on the + + + align:start position:0% +the gene more on the +three prime end of the gene + + align:start position:0% +three prime end of the gene + + + align:start position:0% +three prime end of the gene +and what they will calculate as we'll + + align:start position:0% +and what they will calculate as we'll + + + align:start position:0% +and what they will calculate as we'll +get to is some measure of the + + align:start position:0% +get to is some measure of the + + + align:start position:0% +get to is some measure of the +hybridization of these + + align:start position:0% +hybridization of these + + + align:start position:0% +hybridization of these +perfectly matched probes to this gene + + align:start position:0% +perfectly matched probes to this gene + + + align:start position:0% +perfectly matched probes to this gene +versus a probe + + align:start position:0% +versus a probe + + + align:start position:0% +versus a probe +which is exactly the same to this one + + align:start position:0% +which is exactly the same to this one + + + align:start position:0% +which is exactly the same to this one +but has a central base which is a + + align:start position:0% +but has a central base which is a + + + align:start position:0% +but has a central base which is a +perfect which is a mismatch to the uh + + align:start position:0% +perfect which is a mismatch to the uh + + + align:start position:0% +perfect which is a mismatch to the uh +designated area in that gene + + align:start position:0% +designated area in that gene + + + align:start position:0% +designated area in that gene +so there the measure of um + + align:start position:0% +so there the measure of um + + + align:start position:0% +so there the measure of um +the measure of the gene is essentially + + align:start position:0% +the measure of the gene is essentially + + + align:start position:0% +the measure of the gene is essentially +the difference between the perfect + + align:start position:0% +the difference between the perfect + + + align:start position:0% +the difference between the perfect +matches and the mismatches in aggregate + + align:start position:0% +matches and the mismatches in aggregate + + + align:start position:0% +matches and the mismatches in aggregate +across the entire probe set whereas + + align:start position:0% +across the entire probe set whereas + + + align:start position:0% +across the entire probe set whereas +in the pat brown + + align:start position:0% +in the pat brown + + + align:start position:0% +in the pat brown +inspired um + + align:start position:0% +inspired um + + + align:start position:0% +inspired um +do-it-yourself spotted industry what + + align:start position:0% +do-it-yourself spotted industry what + + + align:start position:0% +do-it-yourself spotted industry what +you're doing is + + align:start position:0% +you're doing is + + + align:start position:0% +you're doing is +you're um + + align:start position:0% + + + + align:start position:0% + +you're spotting these uh probes right + + align:start position:0% +you're spotting these uh probes right + + + align:start position:0% +you're spotting these uh probes right +onto the uh glass slide and then you're + + align:start position:0% +onto the uh glass slide and then you're + + + align:start position:0% +onto the uh glass slide and then you're +gonna have a competitive uh + + align:start position:0% +gonna have a competitive uh + + + align:start position:0% +gonna have a competitive uh +hybridization between a a reference set + + align:start position:0% +hybridization between a a reference set + + + align:start position:0% +hybridization between a a reference set +of um + + align:start position:0% + + + + align:start position:0% + +uh cdnas and the test set of cdnas + + align:start position:0% +uh cdnas and the test set of cdnas + + + align:start position:0% +uh cdnas and the test set of cdnas +and that has some implications which + + align:start position:0% +and that has some implications which + + + align:start position:0% +and that has some implications which +we'll get to shortly + + align:start position:0% +we'll get to shortly + + + align:start position:0% +we'll get to shortly +so we'll make a point because i'm going + + align:start position:0% +so we'll make a point because i'm going + + + align:start position:0% +so we'll make a point because i'm going +to ask you a question later that the + + align:start position:0% +to ask you a question later that the + + + align:start position:0% +to ask you a question later that the +spotted arrays have to end up on the + + align:start position:0% +spotted arrays have to end up on the + + + align:start position:0% +spotted arrays have to end up on the +slide through some physical process such + + align:start position:0% +slide through some physical process such + + + align:start position:0% +slide through some physical process such +as a printing head + + align:start position:0% + + + + align:start position:0% + +whereas in the lithographic + + align:start position:0% +whereas in the lithographic + + + align:start position:0% +whereas in the lithographic +techniques built by alphametrics what + + align:start position:0% +techniques built by alphametrics what + + + align:start position:0% +techniques built by alphametrics what +you do is you + + align:start position:0% +you do is you + + + align:start position:0% +you do is you +after you create the first layer which + + align:start position:0% +after you create the first layer which + + + align:start position:0% +after you create the first layer which +is bonded to the + + align:start position:0% +is bonded to the + + + align:start position:0% +is bonded to the +the glass or silicon substrate you're + + align:start position:0% +the glass or silicon substrate you're + + + align:start position:0% +the glass or silicon substrate you're +going to chemically add + + align:start position:0% +going to chemically add + + + align:start position:0% +going to chemically add +let's say a nucleotide g masking off the + + align:start position:0% +let's say a nucleotide g masking off the + + + align:start position:0% +let's say a nucleotide g masking off the +rest of the um array where you don't um + + align:start position:0% +rest of the um array where you don't um + + + align:start position:0% +rest of the um array where you don't um +want to add that g nucleotide and then + + align:start position:0% +want to add that g nucleotide and then + + + align:start position:0% +want to add that g nucleotide and then +you map let's say you want to add an a + + align:start position:0% +you map let's say you want to add an a + + + align:start position:0% +you map let's say you want to add an a +the next step you mask up a mask off + + align:start position:0% +the next step you mask up a mask off + + + align:start position:0% +the next step you mask up a mask off +everywhere that you don't want to have + + align:start position:0% +everywhere that you don't want to have + + + align:start position:0% +everywhere that you don't want to have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the a added and so on + + align:start position:0% +the a added and so on + + + align:start position:0% +the a added and so on +so clear so far now the problem of + + align:start position:0% +so clear so far now the problem of + + + align:start position:0% +so clear so far now the problem of +course is that + + align:start position:0% +course is that + + + align:start position:0% +course is that +to do this for a 25 mirror requires in + + align:start position:0% +to do this for a 25 mirror requires in + + + align:start position:0% +to do this for a 25 mirror requires in +other words a argument nucleotide is 25 + + align:start position:0% +other words a argument nucleotide is 25 + + + align:start position:0% +other words a argument nucleotide is 25 +long is on the order of 100 + + align:start position:0% +long is on the order of 100 + + + align:start position:0% +long is on the order of 100 +masking procedures anybody any anybody + + align:start position:0% +masking procedures anybody any anybody + + + align:start position:0% +masking procedures anybody any anybody +have any idea how many masking + + align:start position:0% +have any idea how many masking + + + align:start position:0% +have any idea how many masking +procedures you do for a pentium 4 + + align:start position:0% + + + + align:start position:0% + +on the order of 20 to 30. + + align:start position:0% +on the order of 20 to 30. + + + align:start position:0% +on the order of 20 to 30. +so they're having to do four times as + + align:start position:0% +so they're having to do four times as + + + align:start position:0% +so they're having to do four times as +much + + align:start position:0% +much + + + align:start position:0% +much +photo with the + + align:start position:0% +photo with the + + + align:start position:0% +photo with the +lithography + + align:start position:0% +lithography + + + align:start position:0% +lithography +as for pending four so that's going to + + align:start position:0% +as for pending four so that's going to + + + align:start position:0% +as for pending four so that's going to +limit + + align:start position:0% +limit + + + align:start position:0% +limit +their + + align:start position:0% +their + + + align:start position:0% +their +their costs at some level and + + align:start position:0% +their costs at some level and + + + align:start position:0% +their costs at some level and +furthermore um let me just say it right + + align:start position:0% +furthermore um let me just say it right + + + align:start position:0% +furthermore um let me just say it right +here turns out that 25 mirrors are not + + align:start position:0% +here turns out that 25 mirrors are not + + + align:start position:0% +here turns out that 25 mirrors are not +the ideal length for hybridization the + + align:start position:0% +the ideal length for hybridization the + + + align:start position:0% +the ideal length for hybridization the +longer if you get to a longer length + + align:start position:0% +longer if you get to a longer length + + + align:start position:0% +longer if you get to a longer length +let's say a 60 more 70 mer you get much + + align:start position:0% +let's say a 60 more 70 mer you get much + + + align:start position:0% +let's say a 60 more 70 mer you get much +more sensitivity and much more + + align:start position:0% +more sensitivity and much more + + + align:start position:0% +more sensitivity and much more +specificity + + align:start position:0% +specificity + + + align:start position:0% +specificity +but they can't economically do it + + align:start position:0% +but they can't economically do it + + + align:start position:0% +but they can't economically do it +because of the limits of + + align:start position:0% +because of the limits of + + + align:start position:0% +because of the limits of +photolithography but the advantage of + + align:start position:0% +photolithography but the advantage of + + + align:start position:0% +photolithography but the advantage of +lithography is that you can get + + align:start position:0% +lithography is that you can get + + + align:start position:0% +lithography is that you can get +extremely + + align:start position:0% +extremely + + + align:start position:0% +extremely +compact and high resolution + + align:start position:0% +compact and high resolution + + + align:start position:0% +compact and high resolution +so you can put a lot of genes on one + + align:start position:0% +so you can put a lot of genes on one + + + align:start position:0% +so you can put a lot of genes on one +chip like the entire transcriptome + + align:start position:0% +chip like the entire transcriptome + + + align:start position:0% +chip like the entire transcriptome +so this is just a summary + + align:start position:0% +so this is just a summary + + + align:start position:0% +so this is just a summary +of uh + + align:start position:0% +of uh + + + align:start position:0% +of uh +of what i just + + align:start position:0% +of what i just + + + align:start position:0% +of what i just +said here + + align:start position:0% + + + + align:start position:0% + +it's also + + align:start position:0% +it's also + + + align:start position:0% +it's also +you know we like to think of these uh in + + align:start position:0% +you know we like to think of these uh in + + + align:start position:0% +you know we like to think of these uh in +some sort of computational abstraction + + align:start position:0% +some sort of computational abstraction + + + align:start position:0% +some sort of computational abstraction +but it's important also to realize that + + align:start position:0% +but it's important also to realize that + + + align:start position:0% +but it's important also to realize that +these are real molecules that uh during + + align:start position:0% +these are real molecules that uh during + + + align:start position:0% +these are real molecules that uh during +the hybridization reaction are tethered + + align:start position:0% +the hybridization reaction are tethered + + + align:start position:0% +the hybridization reaction are tethered +to the substrate and therefore their + + align:start position:0% +to the substrate and therefore their + + + align:start position:0% +to the substrate and therefore their +secondary and tertiary structure may in + + align:start position:0% +secondary and tertiary structure may in + + + align:start position:0% +secondary and tertiary structure may in +fact influence + + align:start position:0% +fact influence + + + align:start position:0% +fact influence +how + + align:start position:0% +how + + + align:start position:0% +how +they're able to hybridize with the + + align:start position:0% +they're able to hybridize with the + + + align:start position:0% +they're able to hybridize with the +molecules from the sample and it turns + + align:start position:0% +molecules from the sample and it turns + + + align:start position:0% +molecules from the sample and it turns +out that + + align:start position:0% +out that + + + align:start position:0% +out that +certain uh types certain types of + + align:start position:0% + + + + align:start position:0% + +dna probes just don't work well as well + + align:start position:0% +dna probes just don't work well as well + + + align:start position:0% +dna probes just don't work well as well +as you'd expect computationally because + + align:start position:0% +as you'd expect computationally because + + + align:start position:0% +as you'd expect computationally because +of these effects and if you look at + + align:start position:0% +of these effects and if you look at + + + align:start position:0% +of these effects and if you look at +alphametrics + + align:start position:0% +alphametrics + + + align:start position:0% +alphametrics +probe sets there's some probes that + + align:start position:0% +probe sets there's some probes that + + + align:start position:0% +probe sets there's some probes that +never work + + align:start position:0% +never work + + + align:start position:0% +never work +and despite the fact that they're well + + align:start position:0% +and despite the fact that they're well + + + align:start position:0% +and despite the fact that they're well +designed from the point of view of + + align:start position:0% +designed from the point of view of + + + align:start position:0% +designed from the point of view of +finding a + + align:start position:0% +finding a + + + align:start position:0% +finding a +matching hybridization sequence but it's + + align:start position:0% +matching hybridization sequence but it's + + + align:start position:0% +matching hybridization sequence but it's +because of these kind of effects + + align:start position:0% +because of these kind of effects + + + align:start position:0% +because of these kind of effects +and note also that they're not all of + + align:start position:0% +and note also that they're not all of + + + align:start position:0% +and note also that they're not all of +the same length the efficiency of the + + align:start position:0% +the same length the efficiency of the + + + align:start position:0% +the same length the efficiency of the +masking reaction is not 100 by any means + + align:start position:0% +masking reaction is not 100 by any means + + + align:start position:0% +masking reaction is not 100 by any means +and what you will find in each one of + + align:start position:0% +and what you will find in each one of + + + align:start position:0% +and what you will find in each one of +those uh probes + + align:start position:0% +those uh probes + + + align:start position:0% +those uh probes +is in fact millions of dna molecules + + align:start position:0% +is in fact millions of dna molecules + + + align:start position:0% +is in fact millions of dna molecules +which have a distribution which + + align:start position:0% +which have a distribution which + + + align:start position:0% +which have a distribution which +hopefully is close to the desired uh 25 + + align:start position:0% +hopefully is close to the desired uh 25 + + + align:start position:0% +hopefully is close to the desired uh 25 +member but in fact often is considerably + + align:start position:0% +member but in fact often is considerably + + + align:start position:0% +member but in fact often is considerably +lower + + align:start position:0% +lower + + + align:start position:0% +lower +and + + align:start position:0% +and + + + align:start position:0% +and +unfortunately there's no way for the end + + align:start position:0% +unfortunately there's no way for the end + + + align:start position:0% +unfortunately there's no way for the end +user to be able to ascertain just how + + align:start position:0% +user to be able to ascertain just how + + + align:start position:0% +user to be able to ascertain just how +good the job they've done + + align:start position:0% + + + + align:start position:0% + +hey that's right + + align:start position:0% +hey that's right + + + align:start position:0% +hey that's right +so + + align:start position:0% +so + + + align:start position:0% +so +so given that fact if we can already see + + align:start position:0% +so given that fact if we can already see + + + align:start position:0% +so given that fact if we can already see +that + + align:start position:0% +that + + + align:start position:0% +that +um even though we can achieve a higher + + align:start position:0% +um even though we can achieve a higher + + + align:start position:0% +um even though we can achieve a higher +density with these alpha metrics um + + align:start position:0% +density with these alpha metrics um + + + align:start position:0% +density with these alpha metrics um +microarrays there is still a lot of + + align:start position:0% +microarrays there is still a lot of + + + align:start position:0% +microarrays there is still a lot of +variation that we can expect from + + align:start position:0% +variation that we can expect from + + + align:start position:0% +variation that we can expect from +different + + align:start position:0% +different + + + align:start position:0% +different +probes within a probe set + + align:start position:0% +probes within a probe set + + + align:start position:0% +probes within a probe set +which is why for example you might not + + align:start position:0% +which is why for example you might not + + + align:start position:0% +which is why for example you might not +see that in + + align:start position:0% +see that in + + + align:start position:0% +see that in +a single probe set that the perfect + + align:start position:0% +a single probe set that the perfect + + + align:start position:0% +a single probe set that the perfect +matches have it all the same intensity + + align:start position:0% +matches have it all the same intensity + + + align:start position:0% +matches have it all the same intensity +you can see for instance if there's 11 + + align:start position:0% +you can see for instance if there's 11 + + + align:start position:0% +you can see for instance if there's 11 +uh perk match probes five of them will + + align:start position:0% +uh perk match probes five of them will + + + align:start position:0% +uh perk match probes five of them will +be really lit up + + align:start position:0% +be really lit up + + + align:start position:0% +be really lit up +and + + align:start position:0% +and + + + align:start position:0% +and +six will be quite dark + + align:start position:0% +six will be quite dark + + + align:start position:0% +six will be quite dark +and there's many other reasons + + align:start position:0% +and there's many other reasons + + + align:start position:0% +and there's many other reasons +why that might be the case + + align:start position:0% +why that might be the case + + + align:start position:0% +why that might be the case +and i just want to um make the following + + align:start position:0% +and i just want to um make the following + + + align:start position:0% +and i just want to um make the following +point as i said + + align:start position:0% +point as i said + + + align:start position:0% +point as i said +when you're looking for instance in a + + align:start position:0% +when you're looking for instance in a + + + align:start position:0% +when you're looking for instance in a +sporolation + + align:start position:0% +sporolation + + + align:start position:0% +sporolation +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +in + + align:start position:0% +in + + + align:start position:0% +in +yeast what we're looking at is a let's + + align:start position:0% +yeast what we're looking at is a let's + + + align:start position:0% +yeast what we're looking at is a let's +say a test sample versus + + align:start position:0% +say a test sample versus + + + align:start position:0% +say a test sample versus +a + + align:start position:0% + + + + align:start position:0% + +a reference uh sample + + align:start position:0% +a reference uh sample + + + align:start position:0% +a reference uh sample +and we are looking for their competitive + + align:start position:0% +and we are looking for their competitive + + + align:start position:0% +and we are looking for their competitive +hybridization to the + + align:start position:0% +hybridization to the + + + align:start position:0% +hybridization to the +target now + + align:start position:0% +target now + + + align:start position:0% +target now +a couple of problems immediately arise + + align:start position:0% +a couple of problems immediately arise + + + align:start position:0% +a couple of problems immediately arise +uh + + align:start position:0% +uh + + + align:start position:0% +uh +such as unfortunately it turns out for + + align:start position:0% +such as unfortunately it turns out for + + + align:start position:0% +such as unfortunately it turns out for +reasons that have yet to be made clear + + align:start position:0% +reasons that have yet to be made clear + + + align:start position:0% +reasons that have yet to be made clear +to me + + align:start position:0% +to me + + + align:start position:0% +to me +uh in fact if anybody in this room has + + align:start position:0% +uh in fact if anybody in this room has + + + align:start position:0% +uh in fact if anybody in this room has +any insight i'd be very curious that + + align:start position:0% +any insight i'd be very curious that + + + align:start position:0% +any insight i'd be very curious that +which one which one gets the c c3 versus + + align:start position:0% +which one which one gets the c c3 versus + + + align:start position:0% +which one which one gets the c c3 versus +c5 die actually makes difference so if + + align:start position:0% +c5 die actually makes difference so if + + + align:start position:0% +c5 die actually makes difference so if +you switch around the dies you'll get + + align:start position:0% +you switch around the dies you'll get + + + align:start position:0% +you switch around the dies you'll get +different ratios so something + + align:start position:0% +different ratios so something + + + align:start position:0% +different ratios so something +hysterically about the attachment of the + + align:start position:0% +hysterically about the attachment of the + + + align:start position:0% +hysterically about the attachment of the +different dye that causes a difference + + align:start position:0% +different dye that causes a difference + + + align:start position:0% +different dye that causes a difference +in the + + align:start position:0% +in the + + + align:start position:0% +in the +competition reaction and so people who + + align:start position:0% +competition reaction and so people who + + + align:start position:0% +competition reaction and so people who +are practitioners of this and who are um + + align:start position:0% +are practitioners of this and who are um + + + align:start position:0% +are practitioners of this and who are um +uh fastidious about it in fact perform + + align:start position:0% +uh fastidious about it in fact perform + + + align:start position:0% +uh fastidious about it in fact perform +both uh both labels uh ford and both the + + align:start position:0% +both uh both labels uh ford and both the + + + align:start position:0% +both uh both labels uh ford and both the +site three site five and sci-fi site + + align:start position:0% +site three site five and sci-fi site + + + align:start position:0% +site three site five and sci-fi site +three uh label to actually better + + align:start position:0% +three uh label to actually better + + + align:start position:0% +three uh label to actually better +understand the limits of that technology + + align:start position:0% +understand the limits of that technology + + + align:start position:0% +understand the limits of that technology +it's not clear to me why that's + + align:start position:0% +it's not clear to me why that's + + + align:start position:0% +it's not clear to me why that's +happening the other point to note is if + + align:start position:0% +happening the other point to note is if + + + align:start position:0% +happening the other point to note is if +you wanna compare + + align:start position:0% +you wanna compare + + + align:start position:0% +you wanna compare +um + + align:start position:0% +um + + + align:start position:0% +um +across different microarray experiments + + align:start position:0% +across different microarray experiments + + + align:start position:0% +across different microarray experiments +you probably want to have the same + + align:start position:0% +you probably want to have the same + + + align:start position:0% +you probably want to have the same +reference sample + + align:start position:0% +reference sample + + + align:start position:0% +reference sample +and that sounds like a trivial thing to + + align:start position:0% +and that sounds like a trivial thing to + + + align:start position:0% +and that sounds like a trivial thing to +say because you want you'd like to see + + align:start position:0% +say because you want you'd like to see + + + align:start position:0% +say because you want you'd like to see +for instance let's say this uh condition + + align:start position:0% +for instance let's say this uh condition + + + align:start position:0% +for instance let's say this uh condition +the test condition it's a bunch of + + align:start position:0% +the test condition it's a bunch of + + + align:start position:0% +the test condition it's a bunch of +different cancers and you want to + + align:start position:0% +different cancers and you want to + + + align:start position:0% +different cancers and you want to +compare it against a + + align:start position:0% +compare it against a + + + align:start position:0% +compare it against a +reference + + align:start position:0% +reference + + + align:start position:0% +reference +rna which might be in + + align:start position:0% +rna which might be in + + + align:start position:0% +rna which might be in +stanford what they do is they pool + + align:start position:0% +stanford what they do is they pool + + + align:start position:0% +stanford what they do is they pool +together all their different + + align:start position:0% +together all their different + + + align:start position:0% +together all their different +lymph node tissue types + + align:start position:0% +lymph node tissue types + + + align:start position:0% +lymph node tissue types +problem of course is if you deplete your + + align:start position:0% +problem of course is if you deplete your + + + align:start position:0% +problem of course is if you deplete your +uh + + align:start position:0% +uh + + + align:start position:0% +uh +your supply + + align:start position:0% +your supply + + + align:start position:0% +your supply +or um if you if you deplete your supply + + align:start position:0% +or um if you if you deplete your supply + + + align:start position:0% +or um if you if you deplete your supply +you're gonna get a different set of + + align:start position:0% +you're gonna get a different set of + + + align:start position:0% +you're gonna get a different set of +ratios with the new supply and + + align:start position:0% +ratios with the new supply and + + + align:start position:0% +ratios with the new supply and +um because you have different abundance + + align:start position:0% +um because you have different abundance + + + align:start position:0% +um because you have different abundance +of rnas in the reference uh + + align:start position:0% +of rnas in the reference uh + + + align:start position:0% +of rnas in the reference uh +sample you're going to get different uh + + align:start position:0% +sample you're going to get different uh + + + align:start position:0% +sample you're going to get different uh +ratios + + align:start position:0% +ratios + + + align:start position:0% +ratios +and so you see drift in the ratios + + align:start position:0% +and so you see drift in the ratios + + + align:start position:0% +and so you see drift in the ratios +across experiments uh over time with + + align:start position:0% +across experiments uh over time with + + + align:start position:0% +across experiments uh over time with +with this + + align:start position:0% +with this + + + align:start position:0% +with this +with this kind of setup and it's highly + + align:start position:0% +with this kind of setup and it's highly + + + align:start position:0% +with this kind of setup and it's highly +problematic the general the mass general + + align:start position:0% +problematic the general the mass general + + + align:start position:0% +problematic the general the mass general +they're actually developing they've + + align:start position:0% +they're actually developing they've + + + align:start position:0% +they're actually developing they've +developed a synthetic soup of + + align:start position:0% +developed a synthetic soup of + + + align:start position:0% +developed a synthetic soup of +uh spiked in rna controls i think 256 + + align:start position:0% +uh spiked in rna controls i think 256 + + + align:start position:0% +uh spiked in rna controls i think 256 +different rna controls + + align:start position:0% +different rna controls + + + align:start position:0% +different rna controls +and that will give you a standard + + align:start position:0% +and that will give you a standard + + + align:start position:0% +and that will give you a standard +reference pool but unfortunately it's + + align:start position:0% +reference pool but unfortunately it's + + + align:start position:0% +reference pool but unfortunately it's +not quite the same as having the full uh + + align:start position:0% +not quite the same as having the full uh + + + align:start position:0% +not quite the same as having the full uh +eukaryotic + + align:start position:0% +eukaryotic + + + align:start position:0% +eukaryotic +reference pool so the ratios you might + + align:start position:0% +reference pool so the ratios you might + + + align:start position:0% +reference pool so the ratios you might +get from that artificial pool might be + + align:start position:0% +get from that artificial pool might be + + + align:start position:0% +get from that artificial pool might be +quite a bit different + + align:start position:0% +quite a bit different + + + align:start position:0% +quite a bit different +from uh what you get in other + + align:start position:0% +from uh what you get in other + + + align:start position:0% +from uh what you get in other +experiments so just want to make it + + align:start position:0% +experiments so just want to make it + + + align:start position:0% +experiments so just want to make it +clear to you that that is not + + align:start position:0% +clear to you that that is not + + + align:start position:0% +clear to you that that is not +a done deal + + align:start position:0% +a done deal + + + align:start position:0% +a done deal +so how does affimetrics uh how do you + + align:start position:0% +so how does affimetrics uh how do you + + + align:start position:0% +so how does affimetrics uh how do you +use actually afrometrics to determine um + + align:start position:0% +use actually afrometrics to determine um + + + align:start position:0% +use actually afrometrics to determine um +the intensity of gene expression i just + + align:start position:0% +the intensity of gene expression i just + + + align:start position:0% +the intensity of gene expression i just +said that for the spotted arrays all + + align:start position:0% +said that for the spotted arrays all + + + align:start position:0% +said that for the spotted arrays all +you're doing is actually reporting a + + align:start position:0% +you're doing is actually reporting a + + + align:start position:0% +you're doing is actually reporting a +ratio + + align:start position:0% +ratio + + + align:start position:0% +ratio +and a ratio that typically has a normal + + align:start position:0% +and a ratio that typically has a normal + + + align:start position:0% +and a ratio that typically has a normal +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +what you're doing in f metrics is a + + align:start position:0% +what you're doing in f metrics is a + + + align:start position:0% +what you're doing in f metrics is a +multi-step process first of all you're + + align:start position:0% +multi-step process first of all you're + + + align:start position:0% +multi-step process first of all you're +going to take the average of the lowest + + align:start position:0% +going to take the average of the lowest + + + align:start position:0% +going to take the average of the lowest +uh two percent of the cell intensities + + align:start position:0% +uh two percent of the cell intensities + + + align:start position:0% +uh two percent of the cell intensities +in the sector + + align:start position:0% +in the sector + + + align:start position:0% +in the sector +this is the background of each sector + + align:start position:0% +this is the background of each sector + + + align:start position:0% +this is the background of each sector +and then you subtract the background + + align:start position:0% +and then you subtract the background + + + align:start position:0% +and then you subtract the background +from the average intensities of all + + align:start position:0% +from the average intensities of all + + + align:start position:0% +from the average intensities of all +cells in this sector + + align:start position:0% +cells in this sector + + + align:start position:0% +cells in this sector +and you calculate a background noise + + align:start position:0% +and you calculate a background noise + + + align:start position:0% +and you calculate a background noise +which is essentially a + + align:start position:0% +which is essentially a + + + align:start position:0% +which is essentially a +measure of + + align:start position:0% +measure of + + + align:start position:0% +measure of +variance of the pixels and the scaling + + align:start position:0% +variance of the pixels and the scaling + + + align:start position:0% +variance of the pixels and the scaling +factor and normalization factors which + + align:start position:0% +factor and normalization factors which + + + align:start position:0% +factor and normalization factors which +are settings and comply to f metrics + + align:start position:0% +are settings and comply to f metrics + + + align:start position:0% +are settings and comply to f metrics +and this is actually somewhat out of + + align:start position:0% +and this is actually somewhat out of + + + align:start position:0% +and this is actually somewhat out of +date but um + + align:start position:0% +date but um + + + align:start position:0% +date but um +i'll give you updates shortly so + + align:start position:0% +i'll give you updates shortly so + + + align:start position:0% +i'll give you updates shortly so +what is reported for instance most often + + align:start position:0% +what is reported for instance most often + + + align:start position:0% +what is reported for instance most often +as the um + + align:start position:0% + + + + align:start position:0% + +intensity of gene expression is the + + align:start position:0% +intensity of gene expression is the + + + align:start position:0% +intensity of gene expression is the +average difference which essentially + + align:start position:0% +average difference which essentially + + + align:start position:0% +average difference which essentially +is um the difference between the perk + + align:start position:0% +is um the difference between the perk + + + align:start position:0% +is um the difference between the perk +matches and the mismatches across + + align:start position:0% +matches and the mismatches across + + + align:start position:0% +matches and the mismatches across +the entire uh + + align:start position:0% +the entire uh + + + align:start position:0% +the entire uh +probe set so a per pair first of all is + + align:start position:0% +probe set so a per pair first of all is + + + align:start position:0% +probe set so a per pair first of all is +said to be positive if the difference + + align:start position:0% +said to be positive if the difference + + + align:start position:0% +said to be positive if the difference +between the perfect match and the + + align:start position:0% +between the perfect match and the + + + align:start position:0% +between the perfect match and the +mismatch is greater than um + + align:start position:0% +mismatch is greater than um + + + align:start position:0% +mismatch is greater than um +the + + align:start position:0% +the + + + align:start position:0% +the +amount of the noise that is computed + + align:start position:0% +amount of the noise that is computed + + + align:start position:0% +amount of the noise that is computed +based on the background and a probe pair + + align:start position:0% +based on the background and a probe pair + + + align:start position:0% +based on the background and a probe pair +is negative + + align:start position:0% +is negative + + + align:start position:0% +is negative +if the mismatch is greater than the + + align:start position:0% +if the mismatch is greater than the + + + align:start position:0% +if the mismatch is greater than the +perfect match by the same amount + + align:start position:0% +perfect match by the same amount + + + align:start position:0% +perfect match by the same amount +so therefore not all pro pairs will be + + align:start position:0% +so therefore not all pro pairs will be + + + align:start position:0% +so therefore not all pro pairs will be +scored as positive negative and + + align:start position:0% +scored as positive negative and + + + align:start position:0% +scored as positive negative and +then what you have is you calculate a + + align:start position:0% +then what you have is you calculate a + + + align:start position:0% +then what you have is you calculate a +trimmed mean + + align:start position:0% +trimmed mean + + + align:start position:0% +trimmed mean +across the uh + + align:start position:0% +across the uh + + + align:start position:0% +across the uh +the positive or negative um + + align:start position:0% +the positive or negative um + + + align:start position:0% +the positive or negative um +probes that you're not by the way to be + + align:start position:0% +probes that you're not by the way to be + + + align:start position:0% +probes that you're not by the way to be +a highly fluky + + align:start position:0% +a highly fluky + + + align:start position:0% +a highly fluky +um + + align:start position:0% +um + + + align:start position:0% +um +non-robust + + align:start position:0% +non-robust + + + align:start position:0% +non-robust +measure of intensity + + align:start position:0% +measure of intensity + + + align:start position:0% +measure of intensity +and um + + align:start position:0% +and um + + + align:start position:0% +and um +and that was ensconced in an algorithm + + align:start position:0% +and that was ensconced in an algorithm + + + align:start position:0% +and that was ensconced in an algorithm +called + + align:start position:0% +called + + + align:start position:0% +called +mass microarray analysis sweep 4.0 so + + align:start position:0% +mass microarray analysis sweep 4.0 so + + + align:start position:0% +mass microarray analysis sweep 4.0 so +that when you read papers and see mass + + align:start position:0% +that when you read papers and see mass + + + align:start position:0% +that when you read papers and see mass +4.0 + + align:start position:0% +4.0 + + + align:start position:0% +4.0 +that's the method that they're using to + + align:start position:0% +that's the method that they're using to + + + align:start position:0% +that's the method that they're using to +interpret the data and the problem is it + + align:start position:0% +interpret the data and the problem is it + + + align:start position:0% +interpret the data and the problem is it +was it was both uh oversensitive to + + align:start position:0% +was it was both uh oversensitive to + + + align:start position:0% +was it was both uh oversensitive to +outliers because they're using the term + + align:start position:0% +outliers because they're using the term + + + align:start position:0% +outliers because they're using the term +mean and it was uh also + + align:start position:0% + + + + align:start position:0% + +relatively incentive sensitive to + + align:start position:0% +relatively incentive sensitive to + + + align:start position:0% +relatively incentive sensitive to +central moment so instead in mass + + align:start position:0% +central moment so instead in mass + + + align:start position:0% +central moment so instead in mass +5.0 and i will in mass 5.0 they are + + align:start position:0% +5.0 and i will in mass 5.0 they are + + + align:start position:0% +5.0 and i will in mass 5.0 they are +using the chooky by weight + + align:start position:0% +using the chooky by weight + + + align:start position:0% +using the chooky by weight +statistic which is a much more robust uh + + align:start position:0% +statistic which is a much more robust uh + + + align:start position:0% +statistic which is a much more robust uh +statistic of + + align:start position:0% +statistic of + + + align:start position:0% +statistic of +outliers and i will upload a paper uh + + align:start position:0% +outliers and i will upload a paper uh + + + align:start position:0% +outliers and i will upload a paper uh +today to the my courses website which + + align:start position:0% +today to the my courses website which + + + align:start position:0% +today to the my courses website which +will allow you to read the analysis uh + + align:start position:0% +will allow you to read the analysis uh + + + align:start position:0% +will allow you to read the analysis uh +of how they approach this + + align:start position:0% +of how they approach this + + + align:start position:0% +of how they approach this +and this was actually done by + + align:start position:0% +and this was actually done by + + + align:start position:0% +and this was actually done by +alphametrics and is now part of their + + align:start position:0% +alphametrics and is now part of their + + + align:start position:0% +alphametrics and is now part of their +standard uh interpretation software uh + + align:start position:0% +standard uh interpretation software uh + + + align:start position:0% +standard uh interpretation software uh +mass 5.0 + + align:start position:0% + + + + align:start position:0% + +another competing uh microarray or + + align:start position:0% +another competing uh microarray or + + + align:start position:0% +another competing uh microarray or +genius or high throughput gene + + align:start position:0% +genius or high throughput gene + + + align:start position:0% +genius or high throughput gene +expression technology is a serial + + align:start position:0% +expression technology is a serial + + + align:start position:0% +expression technology is a serial +analysis of gene expression did the tool + + align:start position:0% +analysis of gene expression did the tool + + + align:start position:0% +analysis of gene expression did the tool +tell you about this at all + + align:start position:0% +tell you about this at all + + + align:start position:0% +tell you about this at all +he did all right so suffice it to say + + align:start position:0% +he did all right so suffice it to say + + + align:start position:0% +he did all right so suffice it to say +that it looks digital and that what + + align:start position:0% +that it looks digital and that what + + + align:start position:0% +that it looks digital and that what +you're doing is literally counting the + + align:start position:0% +you're doing is literally counting the + + + align:start position:0% +you're doing is literally counting the +number of tags with a particular + + align:start position:0% +number of tags with a particular + + + align:start position:0% +number of tags with a particular +sequence but turns out this has noise as + + align:start position:0% +sequence but turns out this has noise as + + + align:start position:0% +sequence but turns out this has noise as +well for a number of reasons one our + + align:start position:0% +well for a number of reasons one our + + + align:start position:0% +well for a number of reasons one our +sequencing technology is not 100 + + align:start position:0% +sequencing technology is not 100 + + + align:start position:0% +sequencing technology is not 100 +it has error um and also uh sometimes + + align:start position:0% +it has error um and also uh sometimes + + + align:start position:0% +it has error um and also uh sometimes +the tags are not perfectly chosen either + + align:start position:0% +the tags are not perfectly chosen either + + + align:start position:0% +the tags are not perfectly chosen either +so it's it it actually + + align:start position:0% +so it's it it actually + + + align:start position:0% +so it's it it actually +in the right clicks you mean in the + + align:start position:0% +in the right clicks you mean in the + + + align:start position:0% +in the right clicks you mean in the +right hands with the right set of genes + + align:start position:0% +right hands with the right set of genes + + + align:start position:0% +right hands with the right set of genes +it does a nice job but in actual + + align:start position:0% +it does a nice job but in actual + + + align:start position:0% +it does a nice job but in actual +practice i've seen it to be fairly noisy + + align:start position:0% +practice i've seen it to be fairly noisy + + + align:start position:0% +practice i've seen it to be fairly noisy +and certainly not + + align:start position:0% +and certainly not + + + align:start position:0% +and certainly not +cost competitive with um + + align:start position:0% +cost competitive with um + + + align:start position:0% +cost competitive with um +the + + align:start position:0% +the + + + align:start position:0% +the +standard microwave technology + + align:start position:0% +standard microwave technology + + + align:start position:0% +standard microwave technology +quite interesting is this um very nice + + align:start position:0% +quite interesting is this um very nice + + + align:start position:0% +quite interesting is this um very nice +technology out of illumina + + align:start position:0% +technology out of illumina + + + align:start position:0% +technology out of illumina +so they're using this for genotyping but + + align:start position:0% +so they're using this for genotyping but + + + align:start position:0% +so they're using this for genotyping but +they're thinking about using it for um + + align:start position:0% +they're thinking about using it for um + + + align:start position:0% +they're thinking about using it for um +the expression microarrays and it's as + + align:start position:0% +the expression microarrays and it's as + + + align:start position:0% +the expression microarrays and it's as +follows you actually have a fiber optic + + align:start position:0% +follows you actually have a fiber optic + + + align:start position:0% +follows you actually have a fiber optic +bundle + + align:start position:0% +bundle + + + align:start position:0% +bundle +and the um + + align:start position:0% +and the um + + + align:start position:0% +and the um +the tip of the fiber optic bundle is um + + align:start position:0% + + + + align:start position:0% + +sculpted so that it fits in nicely these + + align:start position:0% +sculpted so that it fits in nicely these + + + align:start position:0% +sculpted so that it fits in nicely these +it has a groove that that fits another + + align:start position:0% +it has a groove that that fits another + + + align:start position:0% +it has a groove that that fits another +with um it has yeah it has a groove + + align:start position:0% +with um it has yeah it has a groove + + + align:start position:0% +with um it has yeah it has a groove +which fits a bump nicely on these + + align:start position:0% +which fits a bump nicely on these + + + align:start position:0% +which fits a bump nicely on these +optically coated uh beads + + align:start position:0% +optically coated uh beads + + + align:start position:0% +optically coated uh beads +so that we can do the following we can + + align:start position:0% +so that we can do the following we can + + + align:start position:0% +so that we can do the following we can +attach + + align:start position:0% +attach + + + align:start position:0% +attach +to these optical each of these objects + + align:start position:0% +to these optical each of these objects + + + align:start position:0% +to these optical each of these objects +each of the different optical optically + + align:start position:0% +each of the different optical optically + + + align:start position:0% +each of the different optical optically +coated beads a different + + align:start position:0% +coated beads a different + + + align:start position:0% +coated beads a different +piece of dna + + align:start position:0% +piece of dna + + + align:start position:0% +piece of dna +so we could literally have millions of + + align:start position:0% +so we could literally have millions of + + + align:start position:0% +so we could literally have millions of +different + + align:start position:0% +different + + + align:start position:0% +different +optically coated beads + + align:start position:0% +optically coated beads + + + align:start position:0% +optically coated beads +each with their different + + align:start position:0% +each with their different + + + align:start position:0% +each with their different +dnas and then they will settle into the + + align:start position:0% +dnas and then they will settle into the + + + align:start position:0% +dnas and then they will settle into the +groove on the end of the sculpted + + align:start position:0% +groove on the end of the sculpted + + + align:start position:0% +groove on the end of the sculpted +fiber optic cable + + align:start position:0% +fiber optic cable + + + align:start position:0% +fiber optic cable +and then you can perform a hybridization + + align:start position:0% +and then you can perform a hybridization + + + align:start position:0% +and then you can perform a hybridization +reaction with a sample + + align:start position:0% +reaction with a sample + + + align:start position:0% +reaction with a sample +and then by + + align:start position:0% +and then by + + + align:start position:0% +and then by +by sending down a + + align:start position:0% +by sending down a + + + align:start position:0% +by sending down a +laser down that fiber optic cable you + + align:start position:0% +laser down that fiber optic cable you + + + align:start position:0% +laser down that fiber optic cable you +can actually determine which of these + + align:start position:0% +can actually determine which of these + + + align:start position:0% +can actually determine which of these +beads has a hybridized uh + + align:start position:0% +beads has a hybridized uh + + + align:start position:0% +beads has a hybridized uh +piece of dna versus which does not + + align:start position:0% +piece of dna versus which does not + + + align:start position:0% +piece of dna versus which does not +and this allows you to do it in a very + + align:start position:0% +and this allows you to do it in a very + + + align:start position:0% +and this allows you to do it in a very +high fashion millions of different + + align:start position:0% +high fashion millions of different + + + align:start position:0% +high fashion millions of different +um hybrid hybridization reactions it's + + align:start position:0% +um hybrid hybridization reactions it's + + + align:start position:0% +um hybrid hybridization reactions it's +currently being used for doing millions + + align:start position:0% +currently being used for doing millions + + + align:start position:0% +currently being used for doing millions +of different genotypes so it's it's + + align:start position:0% +of different genotypes so it's it's + + + align:start position:0% +of different genotypes so it's it's +recognizing a whole bunch of different + + align:start position:0% +recognizing a whole bunch of different + + + align:start position:0% +recognizing a whole bunch of different +genotypes with different pieces of dna + + align:start position:0% +genotypes with different pieces of dna + + + align:start position:0% +genotypes with different pieces of dna +corresponding to different genotypes but + + align:start position:0% +corresponding to different genotypes but + + + align:start position:0% +corresponding to different genotypes but +also it's been it can be used to do + + align:start position:0% +also it's been it can be used to do + + + align:start position:0% +also it's been it can be used to do +expression microarrays + + align:start position:0% +expression microarrays + + + align:start position:0% +expression microarrays +and it's a and there are some groups + + align:start position:0% +and it's a and there are some groups + + + align:start position:0% +and it's a and there are some groups +around the country that are not going to + + align:start position:0% +around the country that are not going to + + + align:start position:0% +around the country that are not going to +use it being infused and for those of + + align:start position:0% +use it being infused and for those of + + + align:start position:0% +use it being infused and for those of +you who are in the enterprise program + + align:start position:0% +you who are in the enterprise program + + + align:start position:0% +you who are in the enterprise program +looking at how illumina was funded and + + align:start position:0% +looking at how illumina was funded and + + + align:start position:0% +looking at how illumina was funded and +how they got together with scientists + + align:start position:0% +how they got together with scientists + + + align:start position:0% +how they got together with scientists +to avoid uh being sued by ethametrics is + + align:start position:0% +to avoid uh being sued by ethametrics is + + + align:start position:0% +to avoid uh being sued by ethametrics is +actually a great uh case history which i + + align:start position:0% +actually a great uh case history which i + + + align:start position:0% +actually a great uh case history which i +don't have time for but the point is + + align:start position:0% +don't have time for but the point is + + + align:start position:0% +don't have time for but the point is +that fmetrix has a very broad patent + + align:start position:0% +that fmetrix has a very broad patent + + + align:start position:0% +that fmetrix has a very broad patent +around the measurement of + + align:start position:0% +around the measurement of + + + align:start position:0% +around the measurement of +expression in two dimensions and in a + + align:start position:0% +expression in two dimensions and in a + + + align:start position:0% +expression in two dimensions and in a +two-dimensional form factor um + + align:start position:0% +two-dimensional form factor um + + + align:start position:0% +two-dimensional form factor um +essentially with any way that you put + + align:start position:0% +essentially with any way that you put + + + align:start position:0% +essentially with any way that you put +place these uh dna spots down and this + + align:start position:0% +place these uh dna spots down and this + + + align:start position:0% +place these uh dna spots down and this +gets away from that patent in a very + + align:start position:0% +gets away from that patent in a very + + + align:start position:0% +gets away from that patent in a very +creative way + + align:start position:0% +creative way + + + align:start position:0% +creative way +um and + + align:start position:0% +um and + + + align:start position:0% +um and +also in the economical way + + align:start position:0% +also in the economical way + + + align:start position:0% +also in the economical way +sure it's the uh the main benefit here + + align:start position:0% +sure it's the uh the main benefit here + + + align:start position:0% +sure it's the uh the main benefit here +you don't have to tag the + + align:start position:0% +you don't have to tag the + + + align:start position:0% +you don't have to tag the +dna + + align:start position:0% + + + + align:start position:0% + +there's a couple of factors first of all + + align:start position:0% +there's a couple of factors first of all + + + align:start position:0% +there's a couple of factors first of all +you're not limited + + align:start position:0% +you're not limited + + + align:start position:0% +you're not limited +um + + align:start position:0% +um + + + align:start position:0% +um +having this form factor uh of this big + + align:start position:0% +having this form factor uh of this big + + + align:start position:0% +having this form factor uh of this big +where you're going to do this + + align:start position:0% +where you're going to do this + + + align:start position:0% +where you're going to do this +photolithographic even so with a + + align:start position:0% +photolithographic even so with a + + + align:start position:0% +photolithographic even so with a +photolithic lithograph process uh + + align:start position:0% +photolithic lithograph process uh + + + align:start position:0% +photolithic lithograph process uh +because of the registration of scanning + + align:start position:0% +because of the registration of scanning + + + align:start position:0% +because of the registration of scanning +uh the registration of the graph + + align:start position:0% +uh the registration of the graph + + + align:start position:0% +uh the registration of the graph +lithography there's very um there's + + align:start position:0% +lithography there's very um there's + + + align:start position:0% +lithography there's very um there's +limits to how much um how many different + + align:start position:0% +limits to how much um how many different + + + align:start position:0% +limits to how much um how many different +probes you can have on one chip whereas + + align:start position:0% +probes you can have on one chip whereas + + + align:start position:0% +probes you can have on one chip whereas +here because each + + align:start position:0% +here because each + + + align:start position:0% +here because each +bead + + align:start position:0% +bead + + + align:start position:0% +bead +is its own can have its own unique + + align:start position:0% +is its own can have its own unique + + + align:start position:0% +is its own can have its own unique +id so you know which which one it is and + + align:start position:0% +id so you know which which one it is and + + + align:start position:0% +id so you know which which one it is and +can have its own um + + align:start position:0% +can have its own um + + + align:start position:0% +can have its own um +piece of dna it's going to settle + + align:start position:0% +piece of dna it's going to settle + + + align:start position:0% +piece of dna it's going to settle +assemble and this is you know a very + + align:start position:0% +assemble and this is you know a very + + + align:start position:0% +assemble and this is you know a very +microscopic view of this you can have + + align:start position:0% +microscopic view of this you can have + + + align:start position:0% +microscopic view of this you can have +many more different because it's + + align:start position:0% +many more different because it's + + + align:start position:0% +many more different because it's +essentially self-assembling if you swirl + + align:start position:0% +essentially self-assembling if you swirl + + + align:start position:0% +essentially self-assembling if you swirl +around the fiber optic cable and the + + align:start position:0% +around the fiber optic cable and the + + + align:start position:0% +around the fiber optic cable and the +super beads and basically all + + align:start position:0% +super beads and basically all + + + align:start position:0% +super beads and basically all +self-assemble onto this tip of that + + align:start position:0% +self-assemble onto this tip of that + + + align:start position:0% +self-assemble onto this tip of that +cable you get many many more different + + align:start position:0% +cable you get many many more different + + + align:start position:0% +cable you get many many more different +types + + align:start position:0% +types + + + align:start position:0% +types +of + + align:start position:0% +of + + + align:start position:0% +of +beads and therefore of probes + + align:start position:0% +beads and therefore of probes + + + align:start position:0% +beads and therefore of probes +in one sample + + align:start position:0% +in one sample + + + align:start position:0% +in one sample +and the process of labeling the beads + + align:start position:0% +and the process of labeling the beads + + + align:start position:0% +and the process of labeling the beads +and attaching + + align:start position:0% +and attaching + + + align:start position:0% +and attaching +the + + align:start position:0% +the + + + align:start position:0% +the +the probe is actually much cheaper than + + align:start position:0% +the probe is actually much cheaper than + + + align:start position:0% +the probe is actually much cheaper than +the atherometrics technique so it's + + align:start position:0% +the atherometrics technique so it's + + + align:start position:0% +the atherometrics technique so it's +higher density more economical and it + + align:start position:0% +higher density more economical and it + + + align:start position:0% +higher density more economical and it +gets away from the patent + + align:start position:0% + + + + align:start position:0% + +another technology is ancient technology + + align:start position:0% +another technology is ancient technology + + + align:start position:0% +another technology is ancient technology +the same people who brought you + + align:start position:0% +the same people who brought you + + + align:start position:0% +the same people who brought you +high resolution family photos said if + + align:start position:0% +high resolution family photos said if + + + align:start position:0% +high resolution family photos said if +we're able to put down pico leaders in + + align:start position:0% +we're able to put down pico leaders in + + + align:start position:0% +we're able to put down pico leaders in +the precisely the right spot so that + + align:start position:0% +the precisely the right spot so that + + + align:start position:0% +the precisely the right spot so that +your kid looks the way your kid looks + + align:start position:0% +your kid looks the way your kid looks + + + align:start position:0% +your kid looks the way your kid looks +perhaps we can use the same technology + + align:start position:0% +perhaps we can use the same technology + + + align:start position:0% +perhaps we can use the same technology +to spot + + align:start position:0% +to spot + + + align:start position:0% +to spot +a piece of uh dna + + align:start position:0% +a piece of uh dna + + + align:start position:0% +a piece of uh dna +onto + + align:start position:0% +onto + + + align:start position:0% +onto +a flat surface and in fact + + align:start position:0% +a flat surface and in fact + + + align:start position:0% +a flat surface and in fact +they use a + + align:start position:0% +they use a + + + align:start position:0% +they use a +so a spinoff of hewlett packard before + + align:start position:0% +so a spinoff of hewlett packard before + + + align:start position:0% +so a spinoff of hewlett packard before +it split off into agilent so + + align:start position:0% +it split off into agilent so + + + align:start position:0% +it split off into agilent so +spin up the spin-off of heel packer + + align:start position:0% +spin up the spin-off of heel packer + + + align:start position:0% +spin up the spin-off of heel packer +printers + + align:start position:0% +printers + + + align:start position:0% +printers +actually develop a system where they + + align:start position:0% +actually develop a system where they + + + align:start position:0% +actually develop a system where they +actually have four colors catg + + align:start position:0% +actually have four colors catg + + + align:start position:0% +actually have four colors catg +and they spit the four colors onto uh + + align:start position:0% +and they spit the four colors onto uh + + + align:start position:0% +and they spit the four colors onto uh +the glass slide and they do successive + + align:start position:0% +the glass slide and they do successive + + + align:start position:0% +the glass slide and they do successive +in cyto uh synthesis of of algomers up + + align:start position:0% +in cyto uh synthesis of of algomers up + + + align:start position:0% +in cyto uh synthesis of of algomers up +to 50 to 60 long and because + + align:start position:0% +to 50 to 60 long and because + + + align:start position:0% +to 50 to 60 long and because +uh your pictures of your baby have to + + align:start position:0% +uh your pictures of your baby have to + + + align:start position:0% +uh your pictures of your baby have to +look good + + align:start position:0% +look good + + + align:start position:0% +look good +and have much more high tolerances than + + align:start position:0% +and have much more high tolerances than + + + align:start position:0% +and have much more high tolerances than +anybody cares about in + + align:start position:0% + + + + align:start position:0% + +pat brown's group let's say these are + + align:start position:0% +pat brown's group let's say these are + + + align:start position:0% +pat brown's group let's say these are +very good looking + + align:start position:0% +very good looking + + + align:start position:0% +very good looking +spots with very nice consistent shapes + + align:start position:0% +spots with very nice consistent shapes + + + align:start position:0% +spots with very nice consistent shapes +and + + align:start position:0% +and + + + align:start position:0% +and +it's also very cheap so + + align:start position:0% +it's also very cheap so + + + align:start position:0% +it's also very cheap so +this is what the kind of shapes that you + + align:start position:0% +this is what the kind of shapes that you + + + align:start position:0% +this is what the kind of shapes that you +get with the + + align:start position:0% +get with the + + + align:start position:0% +get with the +mechanical pins which is the normal way + + align:start position:0% +mechanical pins which is the normal way + + + align:start position:0% +mechanical pins which is the normal way +spot and these are much more consistent + + align:start position:0% +spot and these are much more consistent + + + align:start position:0% +spot and these are much more consistent +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +precise + + align:start position:0% +precise + + + align:start position:0% +precise +spots that you get with the inkjet + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +there's many other uses for microwaves + + align:start position:0% +there's many other uses for microwaves + + + align:start position:0% +there's many other uses for microwaves +if you recall at the beginning of + + align:start position:0% +if you recall at the beginning of + + + align:start position:0% +if you recall at the beginning of +lecture or i didn't describe a + + align:start position:0% +lecture or i didn't describe a + + + align:start position:0% +lecture or i didn't describe a +microarray as being about expression i + + align:start position:0% +microarray as being about expression i + + + align:start position:0% +microarray as being about expression i +said it had to be + + align:start position:0% +said it had to be + + + align:start position:0% +said it had to be +able to have a form a small form factor + + align:start position:0% +able to have a form a small form factor + + + align:start position:0% +able to have a form a small form factor +it had to be able to interrogate for a + + align:start position:0% +it had to be able to interrogate for a + + + align:start position:0% +it had to be able to interrogate for a +large amount of the ohm that you were + + align:start position:0% +large amount of the ohm that you were + + + align:start position:0% +large amount of the ohm that you were +measuring and had to have a direct data + + align:start position:0% +measuring and had to have a direct data + + + align:start position:0% +measuring and had to have a direct data +path + + align:start position:0% +path + + + align:start position:0% +path +to an electronic format and so on + + align:start position:0% +to an electronic format and so on + + + align:start position:0% +to an electronic format and so on +so + + align:start position:0% +so + + + align:start position:0% +so +can we use the same kind of microarrays + + align:start position:0% +can we use the same kind of microarrays + + + align:start position:0% +can we use the same kind of microarrays +to study for instance + + align:start position:0% + + + + align:start position:0% + +gene expression control so zinc finger + + align:start position:0% +gene expression control so zinc finger + + + align:start position:0% +gene expression control so zinc finger +uh proteins are what are proteins that + + align:start position:0% +uh proteins are what are proteins that + + + align:start position:0% +uh proteins are what are proteins that +actually uh + + align:start position:0% +actually uh + + + align:start position:0% +actually uh +bind to dna + + align:start position:0% +bind to dna + + + align:start position:0% +bind to dna +as you see here so this is a finger + + align:start position:0% +as you see here so this is a finger + + + align:start position:0% +as you see here so this is a finger +around the dna molecule + + align:start position:0% +around the dna molecule + + + align:start position:0% +around the dna molecule +and there's different parts of this that + + align:start position:0% +and there's different parts of this that + + + align:start position:0% +and there's different parts of this that +do the recognition and binding to a + + align:start position:0% +do the recognition and binding to a + + + align:start position:0% +do the recognition and binding to a +consensus site on the dna + + align:start position:0% +consensus site on the dna + + + align:start position:0% +consensus site on the dna +and so for + + align:start position:0% +and so for + + + align:start position:0% +and so for +understanding that understanding that it + + align:start position:0% +understanding that understanding that it + + + align:start position:0% +understanding that understanding that it +was a consensus sequence with a limited + + align:start position:0% +was a consensus sequence with a limited + + + align:start position:0% +was a consensus sequence with a limited +repertoire of possible values + + align:start position:0% +repertoire of possible values + + + align:start position:0% +repertoire of possible values +you could actually create + + align:start position:0% + + + + align:start position:0% + +a ong nucleotide that had all the + + align:start position:0% +a ong nucleotide that had all the + + + align:start position:0% +a ong nucleotide that had all the +possible permutations for this + + align:start position:0% +possible permutations for this + + + align:start position:0% +possible permutations for this +recognition site + + align:start position:0% +recognition site + + + align:start position:0% +recognition site +and + + align:start position:0% +and + + + align:start position:0% +and +this will and then you then ligate + + align:start position:0% +this will and then you then ligate + + + align:start position:0% +this will and then you then ligate +that + + align:start position:0% +that + + + align:start position:0% +that +oligonucleotide to a surface like the + + align:start position:0% +oligonucleotide to a surface like the + + + align:start position:0% +oligonucleotide to a surface like the +microarray + + align:start position:0% +microarray + + + align:start position:0% +microarray +and this is actual uh results + + align:start position:0% +and this is actual uh results + + + align:start position:0% +and this is actual uh results +that you obtain + + align:start position:0% +that you obtain + + + align:start position:0% +that you obtain +when + + align:start position:0% +when + + + align:start position:0% +when +you take different + + align:start position:0% +you take different + + + align:start position:0% +you take different +transcription factor mutants + + align:start position:0% +transcription factor mutants + + + align:start position:0% +transcription factor mutants +and you see that they bind on different + + align:start position:0% +and you see that they bind on different + + + align:start position:0% +and you see that they bind on different +spots + + align:start position:0% +spots + + + align:start position:0% +spots +on the microarray + + align:start position:0% +on the microarray + + + align:start position:0% +on the microarray +based on + + align:start position:0% +based on + + + align:start position:0% +based on +their affinity with a different + + align:start position:0% +their affinity with a different + + + align:start position:0% +their affinity with a different +concession sequence and since you know + + align:start position:0% +concession sequence and since you know + + + align:start position:0% +concession sequence and since you know +which spot corresponds to which + + align:start position:0% +which spot corresponds to which + + + align:start position:0% +which spot corresponds to which +consensus sequence you can quickly + + align:start position:0% +consensus sequence you can quickly + + + align:start position:0% +consensus sequence you can quickly +develop a notion of what are the + + align:start position:0% +develop a notion of what are the + + + align:start position:0% +develop a notion of what are the +consensus sequences what is shared and + + align:start position:0% +consensus sequences what is shared and + + + align:start position:0% +consensus sequences what is shared and +what is not shared among these uh + + align:start position:0% +what is not shared among these uh + + + align:start position:0% +what is not shared among these uh +mutants and therefore what is important + + align:start position:0% +mutants and therefore what is important + + + align:start position:0% +mutants and therefore what is important +for the binary binding activity as shown + + align:start position:0% +for the binary binding activity as shown + + + align:start position:0% +for the binary binding activity as shown +by this um + + align:start position:0% +by this um + + + align:start position:0% +by this um +uh cartoon that represents the + + align:start position:0% +uh cartoon that represents the + + + align:start position:0% +uh cartoon that represents the +the conservation of the picker binding + + align:start position:0% +the conservation of the picker binding + + + align:start position:0% +the conservation of the picker binding +consensus sequence and now so a lot of + + align:start position:0% +consensus sequence and now so a lot of + + + align:start position:0% +consensus sequence and now so a lot of +this work actually was pioneered by + + align:start position:0% +this work actually was pioneered by + + + align:start position:0% +this work actually was pioneered by +uh one of our faculty members in hst + + align:start position:0% +uh one of our faculty members in hst + + + align:start position:0% +uh one of our faculty members in hst +martha bullock + + align:start position:0% +martha bullock + + + align:start position:0% +martha bullock +and it's now been scaled up so you can + + align:start position:0% +and it's now been scaled up so you can + + + align:start position:0% +and it's now been scaled up so you can +actually buy a lot of microarrays that + + align:start position:0% +actually buy a lot of microarrays that + + + align:start position:0% +actually buy a lot of microarrays that +allow you to do + + align:start position:0% +allow you to do + + + align:start position:0% +allow you to do +much larger + + align:start position:0% + + + + align:start position:0% + +scale assessments of thousands of + + align:start position:0% +scale assessments of thousands of + + + align:start position:0% +scale assessments of thousands of +different + + align:start position:0% +different + + + align:start position:0% +different +binding sites + + align:start position:0% + + + + align:start position:0% + +these are the uh protein microarrays + + align:start position:0% +these are the uh protein microarrays + + + align:start position:0% +these are the uh protein microarrays +that i discussed with you previously and + + align:start position:0% +that i discussed with you previously and + + + align:start position:0% +that i discussed with you previously and +you can have a variety of different uh + + align:start position:0% +you can have a variety of different uh + + + align:start position:0% +you can have a variety of different uh +baits + + align:start position:0% +baits + + + align:start position:0% +baits +a small molecule present on the + + align:start position:0% +a small molecule present on the + + + align:start position:0% +a small molecule present on the +microarray an antibody + + align:start position:0% +microarray an antibody + + + align:start position:0% +microarray an antibody +present on the microarray or a different + + align:start position:0% +present on the microarray or a different + + + align:start position:0% +present on the microarray or a different +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +protein base + + align:start position:0% +protein base + + + align:start position:0% +protein base +and or you can even use uh + + align:start position:0% +and or you can even use uh + + + align:start position:0% +and or you can even use uh +phages phages of bait the problem with + + align:start position:0% +phages phages of bait the problem with + + + align:start position:0% +phages phages of bait the problem with +all of these is that as i said we don't + + align:start position:0% +all of these is that as i said we don't + + + align:start position:0% +all of these is that as i said we don't +have yet + + align:start position:0% +have yet + + + align:start position:0% +have yet +uh for this particularly for the + + align:start position:0% +uh for this particularly for the + + + align:start position:0% +uh for this particularly for the +proteins high throughput methods of uh + + align:start position:0% +proteins high throughput methods of uh + + + align:start position:0% +proteins high throughput methods of uh +doing this so for instance + + align:start position:0% +doing this so for instance + + + align:start position:0% +doing this so for instance +selecting and laying down the antibodies + + align:start position:0% +selecting and laying down the antibodies + + + align:start position:0% +selecting and laying down the antibodies +for the entire proteome is just not + + align:start position:0% +for the entire proteome is just not + + + align:start position:0% +for the entire proteome is just not +within our + + align:start position:0% +within our + + + align:start position:0% +within our +um + + align:start position:0% +um + + + align:start position:0% +um +vision we just don't know how to get + + align:start position:0% +vision we just don't know how to get + + + align:start position:0% +vision we just don't know how to get +there currently + + align:start position:0% +there currently + + + align:start position:0% +there currently +in a reproducible fashion we can do it + + align:start position:0% +in a reproducible fashion we can do it + + + align:start position:0% +in a reproducible fashion we can do it +for maybe hundreds of different proteins + + align:start position:0% +for maybe hundreds of different proteins + + + align:start position:0% +for maybe hundreds of different proteins +and these are the kinds of results that + + align:start position:0% +and these are the kinds of results that + + + align:start position:0% +and these are the kinds of results that +you get that you do in fact get these + + align:start position:0% +you get that you do in fact get these + + + align:start position:0% +you get that you do in fact get these +good-looking graphs where you can show + + align:start position:0% +good-looking graphs where you can show + + + align:start position:0% +good-looking graphs where you can show +that you can reliably identify the + + align:start position:0% +that you can reliably identify the + + + align:start position:0% +that you can reliably identify the +differential expression of different + + align:start position:0% +differential expression of different + + + align:start position:0% +differential expression of different +proteins but again these are form very + + align:start position:0% +proteins but again these are form very + + + align:start position:0% +proteins but again these are form very +small numbers + + align:start position:0% +small numbers + + + align:start position:0% +small numbers +of + + align:start position:0% +of + + + align:start position:0% +of +genes + + align:start position:0% + + + + align:start position:0% + +whoops + + align:start position:0% + + + + align:start position:0% + +others have tried + + align:start position:0% +others have tried + + + align:start position:0% +others have tried +the notion of a universal microarray + + align:start position:0% +the notion of a universal microarray + + + align:start position:0% +the notion of a universal microarray +where + + align:start position:0% +where + + + align:start position:0% +where +what you're doing is + + align:start position:0% +what you're doing is + + + align:start position:0% +what you're doing is +you rather than + + align:start position:0% +you rather than + + + align:start position:0% +you rather than +having to re-engineer the microarray all + + align:start position:0% +having to re-engineer the microarray all + + + align:start position:0% +having to re-engineer the microarray all +the time you're going to create a + + align:start position:0% +the time you're going to create a + + + align:start position:0% +the time you're going to create a +generic microarray and then you're going + + align:start position:0% +generic microarray and then you're going + + + align:start position:0% +generic microarray and then you're going +to create + + align:start position:0% +to create + + + align:start position:0% +to create +a + + align:start position:0% +a + + + align:start position:0% +a +some custom technology to link that + + align:start position:0% +some custom technology to link that + + + align:start position:0% +some custom technology to link that +generic microarray to the system that + + align:start position:0% +generic microarray to the system that + + + align:start position:0% +generic microarray to the system that +you're interested in so this + + align:start position:0% +you're interested in so this + + + align:start position:0% +you're interested in so this +universal microarray has these zip codes + + align:start position:0% +universal microarray has these zip codes + + + align:start position:0% +universal microarray has these zip codes +which basically basically are + + align:start position:0% +which basically basically are + + + align:start position:0% +which basically basically are +standardized sequences + + align:start position:0% +standardized sequences + + + align:start position:0% +standardized sequences +that + + align:start position:0% +that + + + align:start position:0% +that +recognize a bit of dna with a + + align:start position:0% +recognize a bit of dna with a + + + align:start position:0% +recognize a bit of dna with a +complementary sequence which you then + + align:start position:0% +complementary sequence which you then + + + align:start position:0% +complementary sequence which you then +add chemically to + + align:start position:0% +add chemically to + + + align:start position:0% +add chemically to +the sequence that you want to + + align:start position:0% +the sequence that you want to + + + align:start position:0% +the sequence that you want to +interrogate interrogate for and such + + align:start position:0% +interrogate interrogate for and such + + + align:start position:0% +interrogate interrogate for and such +universal arrays + + align:start position:0% +universal arrays + + + align:start position:0% +universal arrays +don't require re-engineering of the um + + align:start position:0% +don't require re-engineering of the um + + + align:start position:0% +don't require re-engineering of the um +zip code part of the + + align:start position:0% +zip code part of the + + + align:start position:0% +zip code part of the +of the uh probe but only the the part of + + align:start position:0% +of the uh probe but only the the part of + + + align:start position:0% +of the uh probe but only the the part of +the probe that you want to interrogate + + align:start position:0% +the probe that you want to interrogate + + + align:start position:0% +the probe that you want to interrogate +for + + align:start position:0% +for + + + align:start position:0% +for +and it works actually reasonably well as + + align:start position:0% +and it works actually reasonably well as + + + align:start position:0% +and it works actually reasonably well as +shown in these experiments i want to + + align:start position:0% +shown in these experiments i want to + + + align:start position:0% +shown in these experiments i want to +point out that + + align:start position:0% +point out that + + + align:start position:0% +point out that +a lot of these technologies became + + align:start position:0% +a lot of these technologies became + + + align:start position:0% +a lot of these technologies became +popular when like when uh aftermetric + + align:start position:0% +popular when like when uh aftermetric + + + align:start position:0% +popular when like when uh aftermetric +microarrays were + + align:start position:0% +microarrays were + + + align:start position:0% +microarrays were +more poorly performing and much more + + align:start position:0% +more poorly performing and much more + + + align:start position:0% +more poorly performing and much more +expensive four years ago and that metric + + align:start position:0% +expensive four years ago and that metric + + + align:start position:0% +expensive four years ago and that metric +microarray at harvard cost with their + + align:start position:0% +microarray at harvard cost with their + + + align:start position:0% +microarray at harvard cost with their +academic discount discount cost about + + align:start position:0% +academic discount discount cost about + + + align:start position:0% +academic discount discount cost about +two thousand dollars now costs about two + + align:start position:0% +two thousand dollars now costs about two + + + align:start position:0% +two thousand dollars now costs about two +hundred dollars for + + align:start position:0% + + + + align:start position:0% + +eight times as many genes + + align:start position:0% +eight times as many genes + + + align:start position:0% +eight times as many genes +so the price factor has gone uh price + + align:start position:0% +so the price factor has gone uh price + + + align:start position:0% +so the price factor has gone uh price +factor has gone way down + + align:start position:0% +factor has gone way down + + + align:start position:0% +factor has gone way down +these other technologies are just going + + align:start position:0% +these other technologies are just going + + + align:start position:0% +these other technologies are just going +to go away it's um sort of a microsoft + + align:start position:0% +to go away it's um sort of a microsoft + + + align:start position:0% +to go away it's um sort of a microsoft +effect the technology is good enough + + align:start position:0% +effect the technology is good enough + + + align:start position:0% +effect the technology is good enough +and cheap enough that there's very + + align:start position:0% +and cheap enough that there's very + + + align:start position:0% +and cheap enough that there's very +little incentive to invest a lot of your + + align:start position:0% +little incentive to invest a lot of your + + + align:start position:0% +little incentive to invest a lot of your +own time to + + align:start position:0% +own time to + + + align:start position:0% +own time to +make these little technologies better + + align:start position:0% +make these little technologies better + + + align:start position:0% +make these little technologies better +plus as i said there's uh patent control + + align:start position:0% +plus as i said there's uh patent control + + + align:start position:0% +plus as i said there's uh patent control +uh by alpha metrics uh which makes it uh + + align:start position:0% +uh by alpha metrics uh which makes it uh + + + align:start position:0% +uh by alpha metrics uh which makes it uh +harder to create a business out of there + + align:start position:0% + + + + align:start position:0% + +the short answer is yes and then i'm + + align:start position:0% +the short answer is yes and then i'm + + + align:start position:0% +the short answer is yes and then i'm +going to show you uh quite literally how + + align:start position:0% +going to show you uh quite literally how + + + align:start position:0% +going to show you uh quite literally how +just how bad + + align:start position:0% +just how bad + + + align:start position:0% +just how bad +uh that + + align:start position:0% +uh that + + + align:start position:0% +uh that +intergenerational differences + + align:start position:0% +intergenerational differences + + + align:start position:0% +intergenerational differences +you'll you'll have heard a lot about + + align:start position:0% +you'll you'll have heard a lot about + + + align:start position:0% +you'll you'll have heard a lot about +tissue microarrays what a tissue micro + + align:start position:0% +tissue microarrays what a tissue micro + + + align:start position:0% +tissue microarrays what a tissue micro +rays they're essentially these + + align:start position:0% +rays they're essentially these + + + align:start position:0% +rays they're essentially these +collections + + align:start position:0% +collections + + + align:start position:0% +collections +of uh hopefully homogeneous uh samples + + align:start position:0% +of uh hopefully homogeneous uh samples + + + align:start position:0% +of uh hopefully homogeneous uh samples +so for instance you could take a tumor + + align:start position:0% +so for instance you could take a tumor + + + align:start position:0% +so for instance you could take a tumor +and could slice it and dice it into + + align:start position:0% +and could slice it and dice it into + + + align:start position:0% +and could slice it and dice it into +these small salon slices that you lay + + align:start position:0% +these small salon slices that you lay + + + align:start position:0% +these small salon slices that you lay +down on the microwave and then you can + + align:start position:0% +down on the microwave and then you can + + + align:start position:0% +down on the microwave and then you can +stain it for a variety of things and + + align:start position:0% +stain it for a variety of things and + + + align:start position:0% +stain it for a variety of things and +then you can + + align:start position:0% +then you can + + + align:start position:0% +then you can +look under the microscope and if you're + + align:start position:0% +look under the microscope and if you're + + + align:start position:0% +look under the microscope and if you're +clever get an image recognition program + + align:start position:0% +clever get an image recognition program + + + align:start position:0% +clever get an image recognition program +to detect a particular color for a + + align:start position:0% +to detect a particular color for a + + + align:start position:0% +to detect a particular color for a +particular stain + + align:start position:0% +particular stain + + + align:start position:0% +particular stain +uh to see + + align:start position:0% +uh to see + + + align:start position:0% +uh to see +how much of a process is present based + + align:start position:0% +how much of a process is present based + + + align:start position:0% +how much of a process is present based +on the stating characteristics of that + + align:start position:0% +on the stating characteristics of that + + + align:start position:0% +on the stating characteristics of that +uh tissue or the morphological change in + + align:start position:0% +uh tissue or the morphological change in + + + align:start position:0% +uh tissue or the morphological change in +that tissue it's not yet a high + + align:start position:0% +that tissue it's not yet a high + + + align:start position:0% +that tissue it's not yet a high +throughput technique and it sort of + + align:start position:0% +throughput technique and it sort of + + + align:start position:0% +throughput technique and it sort of +fails the microarray definition that i + + align:start position:0% +fails the microarray definition that i + + + align:start position:0% +fails the microarray definition that i +discussed previously but i think that as + + align:start position:0% +discussed previously but i think that as + + + align:start position:0% +discussed previously but i think that as +we get better in the image analysis part + + align:start position:0% +we get better in the image analysis part + + + align:start position:0% +we get better in the image analysis part +of it it might it does have a shot as + + align:start position:0% +of it it might it does have a shot as + + + align:start position:0% +of it it might it does have a shot as +becoming much more of + + align:start position:0% +becoming much more of + + + align:start position:0% +becoming much more of +a commodity microarray + + align:start position:0% + + + + align:start position:0% + +how could they ever do something like + + align:start position:0% +how could they ever do something like + + + align:start position:0% +how could they ever do something like +this though given the fact that + + align:start position:0% +this though given the fact that + + + align:start position:0% +this though given the fact that +mechanical environments themselves + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% + + + + align:start position:0% + +well the answer is the following um + + align:start position:0% +well the answer is the following um + + + align:start position:0% +well the answer is the following um +the question that you you just raised is + + align:start position:0% +the question that you you just raised is + + + align:start position:0% +the question that you you just raised is +almost always true in genomics it can + + align:start position:0% +almost always true in genomics it can + + + align:start position:0% +almost always true in genomics it can +it's a general more general question + + align:start position:0% +it's a general more general question + + + align:start position:0% +it's a general more general question +three complex systems how can we just do + + align:start position:0% +three complex systems how can we just do + + + align:start position:0% +three complex systems how can we just do +this and the answer is low-hanging fruit + + align:start position:0% +this and the answer is low-hanging fruit + + + align:start position:0% +this and the answer is low-hanging fruit +in other words there are some strong + + align:start position:0% +in other words there are some strong + + + align:start position:0% +in other words there are some strong +effects + + align:start position:0% +effects + + + align:start position:0% +effects +in other words if there is a lymphocytic + + align:start position:0% +in other words if there is a lymphocytic + + + align:start position:0% +in other words if there is a lymphocytic +infiltrate into a tissue you'll have a + + align:start position:0% +infiltrate into a tissue you'll have a + + + align:start position:0% +infiltrate into a tissue you'll have a +lot of immunoglobulins + + align:start position:0% +lot of immunoglobulins + + + align:start position:0% +lot of immunoglobulins +present as opposed to not so if you + + align:start position:0% +present as opposed to not so if you + + + align:start position:0% +present as opposed to not so if you +stain for for immunoglobulins you'll see + + align:start position:0% +stain for for immunoglobulins you'll see + + + align:start position:0% +stain for for immunoglobulins you'll see +it'll light up + + align:start position:0% +it'll light up + + + align:start position:0% +it'll light up +if you're looking for + + align:start position:0% +if you're looking for + + + align:start position:0% +if you're looking for +genes that if you're doing insight to + + align:start position:0% +genes that if you're doing insight to + + + align:start position:0% +genes that if you're doing insight to +hybridization for for um an apathetic + + align:start position:0% +hybridization for for um an apathetic + + + align:start position:0% +hybridization for for um an apathetic +gene + + align:start position:0% +gene + + + align:start position:0% +gene +those + + align:start position:0% +those + + + align:start position:0% +those +uh samples that have more apoptosis in + + align:start position:0% +uh samples that have more apoptosis in + + + align:start position:0% +uh samples that have more apoptosis in +them will light up more + + align:start position:0% +them will light up more + + + align:start position:0% +them will light up more +now the way you handle them + + align:start position:0% +now the way you handle them + + + align:start position:0% +now the way you handle them +is without a doubt going to influence it + + align:start position:0% +is without a doubt going to influence it + + + align:start position:0% +is without a doubt going to influence it +which part of the tumor this piece of + + align:start position:0% +which part of the tumor this piece of + + + align:start position:0% +which part of the tumor this piece of +salami was originally uh sliced out + + align:start position:0% +salami was originally uh sliced out + + + align:start position:0% +salami was originally uh sliced out +of + + align:start position:0% +of + + + align:start position:0% +of +will also have an effect + + align:start position:0% +will also have an effect + + + align:start position:0% +will also have an effect +but + + align:start position:0% +but + + + align:start position:0% +but +if that was less of whatever what i was + + align:start position:0% +if that was less of whatever what i was + + + align:start position:0% +if that was less of whatever what i was +getting at you know + + align:start position:0% + + + + align:start position:0% + +i see i see where you come from these + + align:start position:0% +i see i see where you come from these + + + align:start position:0% +i see i see where you come from these +are not + + align:start position:0% +are not + + + align:start position:0% +are not +this is not cell culture + + align:start position:0% +this is not cell culture + + + align:start position:0% +this is not cell culture +this is a hunk of tissue that was taken + + align:start position:0% +this is a hunk of tissue that was taken + + + align:start position:0% +this is a hunk of tissue that was taken +taken out of the patient + + align:start position:0% +taken out of the patient + + + align:start position:0% +taken out of the patient +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +either through freezing or through some + + align:start position:0% +either through freezing or through some + + + align:start position:0% +either through freezing or through some +other process + + align:start position:0% +other process + + + align:start position:0% +other process +and laid and laid down onto that slide + + align:start position:0% +and laid and laid down onto that slide + + + align:start position:0% +and laid and laid down onto that slide +it's not the tissue culture experiment + + align:start position:0% + + + + align:start position:0% + +that's a very good question + + align:start position:0% + + + + align:start position:0% + +and that speaks to the next + + align:start position:0% +and that speaks to the next + + + align:start position:0% +and that speaks to the next +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +generation of microwaves which i'm not + + align:start position:0% +generation of microwaves which i'm not + + + align:start position:0% +generation of microwaves which i'm not +willing to speak about which is when you + + align:start position:0% +willing to speak about which is when you + + + align:start position:0% +willing to speak about which is when you +have a conflict layer + + align:start position:0% +have a conflict layer + + + align:start position:0% +have a conflict layer +of living cells as opposed to this fixed + + align:start position:0% +of living cells as opposed to this fixed + + + align:start position:0% +of living cells as opposed to this fixed +tissue that you're going to stain + + align:start position:0% +tissue that you're going to stain + + + align:start position:0% +tissue that you're going to stain +you can then there's that's another type + + align:start position:0% +you can then there's that's another type + + + align:start position:0% +you can then there's that's another type +of microwave can then actually for + + align:start position:0% +of microwave can then actually for + + + align:start position:0% +of microwave can then actually for +instance target drugs + + align:start position:0% +instance target drugs + + + align:start position:0% +instance target drugs +and different drugs at different points + + align:start position:0% +and different drugs at different points + + + align:start position:0% +and different drugs at different points +in this microarray and see how these + + align:start position:0% +in this microarray and see how these + + + align:start position:0% +in this microarray and see how these +cells react + + align:start position:0% +cells react + + + align:start position:0% +cells react +but god knows + + align:start position:0% +but god knows + + + align:start position:0% +but god knows +what that means + + align:start position:0% +what that means + + + align:start position:0% +what that means +in this in a set of five blasts but + + align:start position:0% +in this in a set of five blasts but + + + align:start position:0% +in this in a set of five blasts but +spread as a monolayer + + align:start position:0% +spread as a monolayer + + + align:start position:0% +spread as a monolayer +um + + align:start position:0% +um + + + align:start position:0% +um +i think it's a big open + + align:start position:0% + + + + align:start position:0% + +picture subject they tried to make any + + align:start position:0% +picture subject they tried to make any + + + align:start position:0% +picture subject they tried to make any +conclusions about something like that by + + align:start position:0% +conclusions about something like that by + + + align:start position:0% +conclusions about something like that by +entering individual cells in their + + align:start position:0% +entering individual cells in their + + + align:start position:0% +entering individual cells in their +player + + align:start position:0% +player + + + align:start position:0% +player +well i'm glad you're laughing because + + align:start position:0% +well i'm glad you're laughing because + + + align:start position:0% +well i'm glad you're laughing because +i'm glad you're laughing because um i've + + align:start position:0% +i'm glad you're laughing because um i've + + + align:start position:0% +i'm glad you're laughing because um i've +been crying about the way these much + + align:start position:0% +been crying about the way these much + + + align:start position:0% +been crying about the way these much +more boring microarrays have been used + + align:start position:0% +more boring microarrays have been used + + + align:start position:0% +more boring microarrays have been used +in the past and i'm going to give you + + align:start position:0% +in the past and i'm going to give you + + + align:start position:0% +in the past and i'm going to give you +the bad news shortly + + align:start position:0% +the bad news shortly + + + align:start position:0% +the bad news shortly +but i just want to tell you that people + + align:start position:0% +but i just want to tell you that people + + + align:start position:0% +but i just want to tell you that people +are publishing in first-class journals + + align:start position:0% +are publishing in first-class journals + + + align:start position:0% +are publishing in first-class journals +the kind of thing i'm just + + align:start position:0% +the kind of thing i'm just + + + align:start position:0% +the kind of thing i'm just +describing now and some of the + + align:start position:0% +describing now and some of the + + + align:start position:0% +describing now and some of the +luminaries in our field and so what you + + align:start position:0% +luminaries in our field and so what you + + + align:start position:0% +luminaries in our field and so what you +have to understand guys there's a lot of + + align:start position:0% +have to understand guys there's a lot of + + + align:start position:0% +have to understand guys there's a lot of +bugosity in the field of genomics and + + align:start position:0% +bugosity in the field of genomics and + + + align:start position:0% +bugosity in the field of genomics and +part of what this course aims to do is + + align:start position:0% +part of what this course aims to do is + + + align:start position:0% +part of what this course aims to do is +for you to um + + align:start position:0% +for you to um + + + align:start position:0% +for you to um +learn the limitations when joel for + + align:start position:0% +learn the limitations when joel for + + + align:start position:0% +learn the limitations when joel for +instance talks about snips you'll learn + + align:start position:0% +instance talks about snips you'll learn + + + align:start position:0% +instance talks about snips you'll learn +that half of all step studies are just + + align:start position:0% +that half of all step studies are just + + + align:start position:0% +that half of all step studies are just +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +and uh what i'm about to tell you is at + + align:start position:0% +and uh what i'm about to tell you is at + + + align:start position:0% +and uh what i'm about to tell you is at +least half of all microwave studies are + + align:start position:0% +least half of all microwave studies are + + + align:start position:0% +least half of all microwave studies are +wrong but big companies are being formed + + align:start position:0% +wrong but big companies are being formed + + + align:start position:0% +wrong but big companies are being formed +around this monolayer targeting with uh + + align:start position:0% +around this monolayer targeting with uh + + + align:start position:0% +around this monolayer targeting with uh +drugs uh kind of stuff pod so this is an + + align:start position:0% +drugs uh kind of stuff pod so this is an + + + align:start position:0% +drugs uh kind of stuff pod so this is an +opportunity for you to um + + align:start position:0% +opportunity for you to um + + + align:start position:0% +opportunity for you to um +make a big name for you yourself in the + + align:start position:0% +make a big name for you yourself in the + + + align:start position:0% +make a big name for you yourself in the +future + + align:start position:0% +future + + + align:start position:0% +future +in fact so here comes the debunking + + align:start position:0% +in fact so here comes the debunking + + + align:start position:0% +in fact so here comes the debunking +so + + align:start position:0% +so + + + align:start position:0% +so +plenty of elders are the following + + align:start position:0% +plenty of elders are the following + + + align:start position:0% +plenty of elders are the following +following + + align:start position:0% +following + + + align:start position:0% +following +indeed what is there that does not + + align:start position:0% +indeed what is there that does not + + + align:start position:0% +indeed what is there that does not +appear fabulous when it comes to our + + align:start position:0% +appear fabulous when it comes to our + + + align:start position:0% +appear fabulous when it comes to our +knowledge for the first time how many + + align:start position:0% +knowledge for the first time how many + + + align:start position:0% +knowledge for the first time how many +things too are looked upon as quite + + align:start position:0% +things too are looked upon as quite + + + align:start position:0% +things too are looked upon as quite +impossible until they have been actually + + align:start position:0% +impossible until they have been actually + + + align:start position:0% +impossible until they have been actually +affected so it's a very optimistic + + align:start position:0% +affected so it's a very optimistic + + + align:start position:0% +affected so it's a very optimistic +statement about you know the future of + + align:start position:0% +statement about you know the future of + + + align:start position:0% +statement about you know the future of +science like technology and engineering + + align:start position:0% +science like technology and engineering + + + align:start position:0% +science like technology and engineering +that they know that they will come + + align:start position:0% +that they know that they will come + + + align:start position:0% +that they know that they will come +and this is plymouth elder who wrote + + align:start position:0% +and this is plymouth elder who wrote + + + align:start position:0% +and this is plymouth elder who wrote +this big tomb called uh natural history + + align:start position:0% +this big tomb called uh natural history + + + align:start position:0% +this big tomb called uh natural history +which was very well regarded uh he's a + + align:start position:0% +which was very well regarded uh he's a + + + align:start position:0% +which was very well regarded uh he's a +roman st a roman uh patriarch um and + + align:start position:0% +roman st a roman uh patriarch um and + + + align:start position:0% +roman st a roman uh patriarch um and +note when he died uh 79 a.d and that + + align:start position:0% +note when he died uh 79 a.d and that + + + align:start position:0% +note when he died uh 79 a.d and that +there's significance to that date of + + align:start position:0% +there's significance to that date of + + + align:start position:0% +there's significance to that date of +death because what he was was in fact + + align:start position:0% +death because what he was was in fact + + + align:start position:0% +death because what he was was in fact +not a true um experimentalist uh + + align:start position:0% +not a true um experimentalist uh + + + align:start position:0% +not a true um experimentalist uh +scientist using the scientific method as + + align:start position:0% +scientist using the scientific method as + + + align:start position:0% +scientist using the scientific method as +we currently understand it he was more + + align:start position:0% +we currently understand it he was more + + + align:start position:0% +we currently understand it he was more +of a description a description a + + align:start position:0% +of a description a description a + + + align:start position:0% +of a description a description a +description based person describing what + + align:start position:0% +description based person describing what + + + align:start position:0% +description based person describing what +he sees in incredible detail annotating + + align:start position:0% +he sees in incredible detail annotating + + + align:start position:0% +he sees in incredible detail annotating +meticulously taxonomizing it but not + + align:start position:0% +meticulously taxonomizing it but not + + + align:start position:0% +meticulously taxonomizing it but not +really + + align:start position:0% +really + + + align:start position:0% +really +putting forward any hypotheses about how + + align:start position:0% +putting forward any hypotheses about how + + + align:start position:0% +putting forward any hypotheses about how +things work + + align:start position:0% +things work + + + align:start position:0% +things work +and and because he did not understand + + align:start position:0% +and and because he did not understand + + + align:start position:0% +and and because he did not understand +the mechanisms of things + + align:start position:0% +the mechanisms of things + + + align:start position:0% +the mechanisms of things +when he went to visit do his last + + align:start position:0% +when he went to visit do his last + + + align:start position:0% +when he went to visit do his last +scientific investigation which was look + + align:start position:0% +scientific investigation which was look + + + align:start position:0% +scientific investigation which was look +at a a local volcano which happened to + + align:start position:0% +at a a local volcano which happened to + + + align:start position:0% +at a a local volcano which happened to +be called vesuvius when he went to the + + align:start position:0% +be called vesuvius when he went to the + + + align:start position:0% +be called vesuvius when he went to the +boat to visit vesuvius + + align:start position:0% +boat to visit vesuvius + + + align:start position:0% +boat to visit vesuvius +um + + align:start position:0% +um + + + align:start position:0% +um +he misunderstood its basic nature so in + + align:start position:0% +he misunderstood its basic nature so in + + + align:start position:0% +he misunderstood its basic nature so in +fact he died + + align:start position:0% +fact he died + + + align:start position:0% +fact he died +um as his son was trying to drag him + + align:start position:0% +um as his son was trying to drag him + + + align:start position:0% +um as his son was trying to drag him +from the island uh probably from + + align:start position:0% +from the island uh probably from + + + align:start position:0% +from the island uh probably from +asphyxia from the vapors from this + + align:start position:0% +asphyxia from the vapors from this + + + align:start position:0% +asphyxia from the vapors from this +volcano + + align:start position:0% +volcano + + + align:start position:0% +volcano +and consequently + + align:start position:0% +and consequently + + + align:start position:0% +and consequently +um i asked the question are we in danger + + align:start position:0% +um i asked the question are we in danger + + + align:start position:0% +um i asked the question are we in danger +of an imminent genomic plinium eruption + + align:start position:0% +of an imminent genomic plinium eruption + + + align:start position:0% +of an imminent genomic plinium eruption +now plinian eruption is actually a term + + align:start position:0% +now plinian eruption is actually a term + + + align:start position:0% +now plinian eruption is actually a term +of the trade used by geologists to + + align:start position:0% +of the trade used by geologists to + + + align:start position:0% +of the trade used by geologists to +describe a + + align:start position:0% +describe a + + + align:start position:0% +describe a +massive explosion that results in a lot + + align:start position:0% +massive explosion that results in a lot + + + align:start position:0% +massive explosion that results in a lot +of hot air and ash going up into the + + align:start position:0% +of hot air and ash going up into the + + + align:start position:0% +of hot air and ash going up into the +stratosphere + + align:start position:0% +stratosphere + + + align:start position:0% +stratosphere +and i think we can argue that we're in + + align:start position:0% +and i think we can argue that we're in + + + align:start position:0% +and i think we can argue that we're in +similar danger because of over promising + + align:start position:0% +similar danger because of over promising + + + align:start position:0% +similar danger because of over promising +the slowness to acknowledge the + + align:start position:0% +the slowness to acknowledge the + + + align:start position:0% +the slowness to acknowledge the +limitations of our measurement + + align:start position:0% +limitations of our measurement + + + align:start position:0% +limitations of our measurement +techniques + + align:start position:0% +techniques + + + align:start position:0% +techniques +the challenge of linking genomic data to + + align:start position:0% +the challenge of linking genomic data to + + + align:start position:0% +the challenge of linking genomic data to +biological and clinical significance and + + align:start position:0% +biological and clinical significance and + + + align:start position:0% +biological and clinical significance and +the lack of formal hypothesis testing + + align:start position:0% +the lack of formal hypothesis testing + + + align:start position:0% +the lack of formal hypothesis testing +and + + align:start position:0% +and + + + align:start position:0% +and +the lack of sufficient + + align:start position:0% +the lack of sufficient + + + align:start position:0% +the lack of sufficient +uh multidisciplinary expertise + + align:start position:0% +uh multidisciplinary expertise + + + align:start position:0% +uh multidisciplinary expertise +for all these reasons the fact that todd + + align:start position:0% +for all these reasons the fact that todd + + + align:start position:0% +for all these reasons the fact that todd +might roll his eyes at this tissue + + align:start position:0% +might roll his eyes at this tissue + + + align:start position:0% +might roll his eyes at this tissue +culture experiment doesn't mean that + + align:start position:0% +culture experiment doesn't mean that + + + align:start position:0% +culture experiment doesn't mean that +probably all vcs will think it's great + + align:start position:0% +probably all vcs will think it's great + + + align:start position:0% +probably all vcs will think it's great +because they won't have that + + align:start position:0% +because they won't have that + + + align:start position:0% +because they won't have that +multidisciplinary expertise + + align:start position:0% +multidisciplinary expertise + + + align:start position:0% +multidisciplinary expertise +and so our functional genomics is over + + align:start position:0% +and so our functional genomics is over + + + align:start position:0% +and so our functional genomics is over +promising + + align:start position:0% +promising + + + align:start position:0% +promising +absolutely yes + + align:start position:0% +absolutely yes + + + align:start position:0% +absolutely yes +so let's go through it let's go back to + + align:start position:0% +so let's go through it let's go back to + + + align:start position:0% +so let's go through it let's go back to +our world's smallest microarray + + align:start position:0% +our world's smallest microarray + + + align:start position:0% +our world's smallest microarray +three genes measured before and after an + + align:start position:0% +three genes measured before and after an + + + align:start position:0% +three genes measured before and after an +intervention and in fact the content of + + align:start position:0% +intervention and in fact the content of + + + align:start position:0% +intervention and in fact the content of +nature genetics science + + align:start position:0% +nature genetics science + + + align:start position:0% +nature genetics science +um journal articles about microarrays in + + align:start position:0% +um journal articles about microarrays in + + + align:start position:0% +um journal articles about microarrays in +the first four years of functional + + align:start position:0% +the first four years of functional + + + align:start position:0% +the first four years of functional +genomics of + + align:start position:0% +genomics of + + + align:start position:0% +genomics of +lots of publications functional genomics + + align:start position:0% +lots of publications functional genomics + + + align:start position:0% +lots of publications functional genomics +which i think of as 1999 to 2003 so + + align:start position:0% +which i think of as 1999 to 2003 so + + + align:start position:0% +which i think of as 1999 to 2003 so +plenty of papers which did the following + + align:start position:0% +plenty of papers which did the following + + + align:start position:0% +plenty of papers which did the following +sophisticated calculation you take each + + align:start position:0% +sophisticated calculation you take each + + + align:start position:0% +sophisticated calculation you take each +gene before an answer after intervention + + align:start position:0% +gene before an answer after intervention + + + align:start position:0% +gene before an answer after intervention +take the ratio and you report the ratios + + align:start position:0% +take the ratio and you report the ratios + + + align:start position:0% +take the ratio and you report the ratios +and you sort them from high to low so + + align:start position:0% +and you sort them from high to low so + + + align:start position:0% +and you sort them from high to low so +that in fact gene two which is two point + + align:start position:0% +that in fact gene two which is two point + + + align:start position:0% +that in fact gene two which is two point +one over point three it gives you a + + align:start position:0% +one over point three it gives you a + + + align:start position:0% +one over point three it gives you a +ratio of seven therefore it's the most + + align:start position:0% +ratio of seven therefore it's the most + + + align:start position:0% +ratio of seven therefore it's the most +upregulated gene that is lists like that + + align:start position:0% +upregulated gene that is lists like that + + + align:start position:0% +upregulated gene that is lists like that +that you'd get so for instance and i + + align:start position:0% +that you'd get so for instance and i + + + align:start position:0% +that you'd get so for instance and i +feel feel bad for this poor guy because + + align:start position:0% +feel feel bad for this poor guy because + + + align:start position:0% +feel feel bad for this poor guy because +i always cite his his article but + + align:start position:0% +i always cite his his article but + + + align:start position:0% +i always cite his his article but +because i just don't want to change my + + align:start position:0% +because i just don't want to change my + + + align:start position:0% +because i just don't want to change my +slides but this is a good point so this + + align:start position:0% +slides but this is a good point so this + + + align:start position:0% +slides but this is a good point so this +group + + align:start position:0% +group + + + align:start position:0% +group +out of yale did the following + + align:start position:0% +out of yale did the following + + + align:start position:0% +out of yale did the following +interesting experiment which you should + + align:start position:0% +interesting experiment which you should + + + align:start position:0% +interesting experiment which you should +think about as you have your next meal + + align:start position:0% +think about as you have your next meal + + + align:start position:0% +think about as you have your next meal +rats who are starved live twice as long + + align:start position:0% +rats who are starved live twice as long + + + align:start position:0% +rats who are starved live twice as long +as uh unstarved brats and so what they + + align:start position:0% +as uh unstarved brats and so what they + + + align:start position:0% +as uh unstarved brats and so what they +did is they uh starved uh + + align:start position:0% +did is they uh starved uh + + + align:start position:0% +did is they uh starved uh +these rats uh and compared them to + + align:start position:0% +these rats uh and compared them to + + + align:start position:0% +these rats uh and compared them to +non-starved rats and looked at the + + align:start position:0% +non-starved rats and looked at the + + + align:start position:0% +non-starved rats and looked at the +expression profile of + + align:start position:0% +expression profile of + + + align:start position:0% +expression profile of +the + + align:start position:0% +the + + + align:start position:0% +the +muscle tissue + + align:start position:0% +muscle tissue + + + align:start position:0% +muscle tissue +and what they saw using the naphometrics + + align:start position:0% +and what they saw using the naphometrics + + + align:start position:0% +and what they saw using the naphometrics +technology was pretty interesting that + + align:start position:0% +technology was pretty interesting that + + + align:start position:0% +technology was pretty interesting that +there were a bunch of genes that are + + align:start position:0% +there were a bunch of genes that are + + + align:start position:0% +there were a bunch of genes that are +involved in mopping up free radicals + + align:start position:0% +involved in mopping up free radicals + + + align:start position:0% +involved in mopping up free radicals +these bad things that screw up the + + align:start position:0% +these bad things that screw up the + + + align:start position:0% +these bad things that screw up the +structure of your proteins and dna + + align:start position:0% +structure of your proteins and dna + + + align:start position:0% +structure of your proteins and dna +a bunch of genes that are involved in + + align:start position:0% +a bunch of genes that are involved in + + + align:start position:0% +a bunch of genes that are involved in +mopping up free radicals and and + + align:start position:0% +mopping up free radicals and and + + + align:start position:0% +mopping up free radicals and and +combating oxidative the oxidative stress + + align:start position:0% +combating oxidative the oxidative stress + + + align:start position:0% +combating oxidative the oxidative stress +were down regulated in these + + align:start position:0% +were down regulated in these + + + align:start position:0% +were down regulated in these +starved mice i want to point out that + + align:start position:0% +starved mice i want to point out that + + + align:start position:0% +starved mice i want to point out that +they had for instance down by 1.5 fold + + align:start position:0% +they had for instance down by 1.5 fold + + + align:start position:0% +they had for instance down by 1.5 fold +down by 1.6 fold remember those numbers + + align:start position:0% +down by 1.6 fold remember those numbers + + + align:start position:0% +down by 1.6 fold remember those numbers +well i won't be cute about it the fact + + align:start position:0% +well i won't be cute about it the fact + + + align:start position:0% +well i won't be cute about it the fact +is + + align:start position:0% +is + + + align:start position:0% +is +those full changes are especially when + + align:start position:0% +those full changes are especially when + + + align:start position:0% +those full changes are especially when +they had a limited number of the + + align:start position:0% +they had a limited number of the + + + align:start position:0% +they had a limited number of the +replicas like three replicas are just + + align:start position:0% +replicas like three replicas are just + + + align:start position:0% +replicas like three replicas are just +not + + align:start position:0% +not + + + align:start position:0% +not +sustainable + + align:start position:0% +sustainable + + + align:start position:0% +sustainable +in any kind of analysis + + align:start position:0% +in any kind of analysis + + + align:start position:0% +in any kind of analysis +even today + + align:start position:0% +even today + + + align:start position:0% +even today +unless you do a lot more replicates and + + align:start position:0% +unless you do a lot more replicates and + + + align:start position:0% +unless you do a lot more replicates and +use much better platforms so for here + + align:start position:0% +use much better platforms so for here + + + align:start position:0% +use much better platforms so for here +for example is a study + + align:start position:0% +for example is a study + + + align:start position:0% +for example is a study +that we did + + align:start position:0% +that we did + + + align:start position:0% +that we did +using a + + align:start position:0% +using a + + + align:start position:0% +using a +insight chip insight used to make a + + align:start position:0% +insight chip insight used to make a + + + align:start position:0% +insight chip insight used to make a +spotted microarray they're one of the + + align:start position:0% +spotted microarray they're one of the + + + align:start position:0% +spotted microarray they're one of the +technologies that went away with a + + align:start position:0% +technologies that went away with a + + + align:start position:0% +technologies that went away with a +genomic + + align:start position:0% +genomic + + + align:start position:0% +genomic +implosion or meltdown and what you see + + align:start position:0% +implosion or meltdown and what you see + + + align:start position:0% +implosion or meltdown and what you see +here i've taken the microarray and i've + + align:start position:0% +here i've taken the microarray and i've + + + align:start position:0% +here i've taken the microarray and i've +strung out into a line into a vector the + + align:start position:0% +strung out into a line into a vector the + + + align:start position:0% +strung out into a line into a vector the +8 000 genes + + align:start position:0% +8 000 genes + + + align:start position:0% +8 000 genes +and i'm showing you + + align:start position:0% +and i'm showing you + + + align:start position:0% +and i'm showing you +the + + align:start position:0% +the + + + align:start position:0% +the +ratio + + align:start position:0% +ratio + + + align:start position:0% +ratio +of these genes + + align:start position:0% +of these genes + + + align:start position:0% +of these genes +across two conditions in this case + + align:start position:0% +across two conditions in this case + + + align:start position:0% +across two conditions in this case +cardiac muscle of a mouse before and + + align:start position:0% +cardiac muscle of a mouse before and + + + align:start position:0% +cardiac muscle of a mouse before and +after cocaine + + align:start position:0% +after cocaine + + + align:start position:0% +after cocaine +and what you see is that most of genes + + align:start position:0% +and what you see is that most of genes + + + align:start position:0% +and what you see is that most of genes +have a ratio of one + + align:start position:0% +have a ratio of one + + + align:start position:0% +have a ratio of one +and some a little bit above and a little + + align:start position:0% +and some a little bit above and a little + + + align:start position:0% +and some a little bit above and a little +bit below + + align:start position:0% + + + + align:start position:0% + +what to make of it you know where do we + + align:start position:0% +what to make of it you know where do we + + + align:start position:0% +what to make of it you know where do we +draw the line what is uh what is up + + align:start position:0% +draw the line what is uh what is up + + + align:start position:0% +draw the line what is uh what is up +regulated is this uh + + align:start position:0% +regulated is this uh + + + align:start position:0% +regulated is this uh +this 1.4 fold up regulated and above is + + align:start position:0% +this 1.4 fold up regulated and above is + + + align:start position:0% +this 1.4 fold up regulated and above is +that the significance level + + align:start position:0% +that the significance level + + + align:start position:0% +that the significance level +well i did the following thing i + + align:start position:0% +well i did the following thing i + + + align:start position:0% +well i did the following thing i +applied a fourier transform + + align:start position:0% +applied a fourier transform + + + align:start position:0% +applied a fourier transform +to this data + + align:start position:0% +to this data + + + align:start position:0% +to this data +where + + align:start position:0% +where + + + align:start position:0% +where +the + + align:start position:0% +the + + + align:start position:0% +the +the dimensional cross across which i was + + align:start position:0% +the dimensional cross across which i was + + + align:start position:0% +the dimensional cross across which i was +doing the fourier transform was that of + + align:start position:0% +doing the fourier transform was that of + + + align:start position:0% +doing the fourier transform was that of +the linear position + + align:start position:0% +the linear position + + + align:start position:0% +the linear position +on the microarray + + align:start position:0% +on the microarray + + + align:start position:0% +on the microarray +and as you know the fourier transform + + align:start position:0% +and as you know the fourier transform + + + align:start position:0% +and as you know the fourier transform +identifies + + align:start position:0% +identifies + + + align:start position:0% +identifies +elements which have periodicity + + align:start position:0% +elements which have periodicity + + + align:start position:0% +elements which have periodicity +and what i found was the following + + align:start position:0% +and what i found was the following + + + align:start position:0% +and what i found was the following +periodicity a periodicity of four + + align:start position:0% +periodicity a periodicity of four + + + align:start position:0% +periodicity a periodicity of four +pinocity of nine and some other + + align:start position:0% +pinocity of nine and some other + + + align:start position:0% +pinocity of nine and some other +periodicities but here huge period to + + align:start position:0% +periodicities but here huge period to + + + align:start position:0% +periodicities but here huge period to +see it four anybody have any idea why uh + + align:start position:0% +see it four anybody have any idea why uh + + + align:start position:0% +see it four anybody have any idea why uh +there was this periodicity of four in + + align:start position:0% +there was this periodicity of four in + + + align:start position:0% +there was this periodicity of four in +the data remember this is regardless of + + align:start position:0% +the data remember this is regardless of + + + align:start position:0% +the data remember this is regardless of +which gene it was + + align:start position:0% +which gene it was + + + align:start position:0% +which gene it was +across this chip there's a periodicity + + align:start position:0% +across this chip there's a periodicity + + + align:start position:0% +across this chip there's a periodicity +of four + + align:start position:0% + + + + align:start position:0% + +chip what + + align:start position:0% + + + + align:start position:0% + +approved ship what about it + + align:start position:0% + + + + align:start position:0% + +you're getting closer + + align:start position:0% + + + + align:start position:0% + +you got it + + align:start position:0% +you got it + + + align:start position:0% +you got it +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +what the inside chip looks like and the + + align:start position:0% +what the inside chip looks like and the + + + align:start position:0% +what the inside chip looks like and the +reason it looks like that because they + + align:start position:0% +reason it looks like that because they + + + align:start position:0% +reason it looks like that because they +used four pins + + align:start position:0% +used four pins + + + align:start position:0% +used four pins +each pin + + align:start position:0% +each pin + + + align:start position:0% +each pin +took care of different quadrant and so + + align:start position:0% +took care of different quadrant and so + + + align:start position:0% +took care of different quadrant and so +there's even slightly different physical + + align:start position:0% +there's even slightly different physical + + + align:start position:0% +there's even slightly different physical +chemical properties of each pin + + align:start position:0% +chemical properties of each pin + + + align:start position:0% +chemical properties of each pin +in the engineering pin you would get + + align:start position:0% +in the engineering pin you would get + + + align:start position:0% +in the engineering pin you would get +a slight systematic change in the amount + + align:start position:0% +a slight systematic change in the amount + + + align:start position:0% +a slight systematic change in the amount +of probe laid down consequently and it + + align:start position:0% +of probe laid down consequently and it + + + align:start position:0% +of probe laid down consequently and it +turned out that you got the chip much + + align:start position:0% +turned out that you got the chip much + + + align:start position:0% +turned out that you got the chip much +more than 1.5 fold changes in exp in the + + align:start position:0% +more than 1.5 fold changes in exp in the + + + align:start position:0% +more than 1.5 fold changes in exp in the +readout just based on which quadrant you + + align:start position:0% +readout just based on which quadrant you + + + align:start position:0% +readout just based on which quadrant you +were in + + align:start position:0% +were in + + + align:start position:0% +were in +and now just based on the physicality + + align:start position:0% +and now just based on the physicality + + + align:start position:0% +and now just based on the physicality +now ethometrics in the past has not been + + align:start position:0% +now ethometrics in the past has not been + + + align:start position:0% +now ethometrics in the past has not been +uh guilt-free in this matter for + + align:start position:0% +uh guilt-free in this matter for + + + align:start position:0% +uh guilt-free in this matter for +instance depending which way the + + align:start position:0% +instance depending which way the + + + align:start position:0% +instance depending which way the +hybridization solution was washed on you + + align:start position:0% +hybridization solution was washed on you + + + align:start position:0% +hybridization solution was washed on you +can see different you can see intensity + + align:start position:0% +can see different you can see intensity + + + align:start position:0% +can see different you can see intensity +effects going this way or that way + + align:start position:0% +effects going this way or that way + + + align:start position:0% +effects going this way or that way +and if there's a thermal gradient in the + + align:start position:0% +and if there's a thermal gradient in the + + + align:start position:0% +and if there's a thermal gradient in the +hybridization chamber + + align:start position:0% +hybridization chamber + + + align:start position:0% +hybridization chamber +you could also see + + align:start position:0% +you could also see + + + align:start position:0% +you could also see +different intensities that were + + align:start position:0% +different intensities that were + + + align:start position:0% +different intensities that were +chip geometry dependent and independent + + align:start position:0% +chip geometry dependent and independent + + + align:start position:0% +chip geometry dependent and independent +of the gene yes + + align:start position:0% + + + + align:start position:0% + +because of course i knew those four pins + + align:start position:0% +because of course i knew those four pins + + + align:start position:0% +because of course i knew those four pins +i said i wonder if there's anything + + align:start position:0% +i said i wonder if there's anything + + + align:start position:0% +i said i wonder if there's anything +different about the pins + + align:start position:0% +different about the pins + + + align:start position:0% +different about the pins +by the way the second and the second um + + align:start position:0% +by the way the second and the second um + + + align:start position:0% +by the way the second and the second um +and now i by the way and i almost do + + align:start position:0% +and now i by the way and i almost do + + + align:start position:0% +and now i by the way and i almost do +that routinely as a as + + align:start position:0% +that routinely as a as + + + align:start position:0% +that routinely as a as +any series i do as a sanity check or + + align:start position:0% +any series i do as a sanity check or + + + align:start position:0% +any series i do as a sanity check or +just run for a transform to see there's + + align:start position:0% +just run for a transform to see there's + + + align:start position:0% +just run for a transform to see there's +regularity the other periodicity was due + + align:start position:0% +regularity the other periodicity was due + + + align:start position:0% +regularity the other periodicity was due +to how often they uh replace the + + align:start position:0% +to how often they uh replace the + + + align:start position:0% +to how often they uh replace the +printhead + + align:start position:0% +printhead + + + align:start position:0% +printhead +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +but of course the manufacturer would + + align:start position:0% +but of course the manufacturer would + + + align:start position:0% +but of course the manufacturer would +never tell you this + + align:start position:0% +never tell you this + + + align:start position:0% +never tell you this +let's make things a little bit more + + align:start position:0% +let's make things a little bit more + + + align:start position:0% +let's make things a little bit more +interesting so this is an experiment + + align:start position:0% +interesting so this is an experiment + + + align:start position:0% +interesting so this is an experiment +that a tool did with uh morris white at + + align:start position:0% +that a tool did with uh morris white at + + + align:start position:0% +that a tool did with uh morris white at +the joslin + + align:start position:0% +the joslin + + + align:start position:0% +the joslin +during using a now obsolete set of chips + + align:start position:0% +during using a now obsolete set of chips + + + align:start position:0% +during using a now obsolete set of chips +they had four patients + + align:start position:0% +they had four patients + + + align:start position:0% +they had four patients +with + + align:start position:0% +with + + + align:start position:0% +with +glucose intolerance so it's not quite + + align:start position:0% +glucose intolerance so it's not quite + + + align:start position:0% +glucose intolerance so it's not quite +diabetes + + align:start position:0% +diabetes + + + align:start position:0% +diabetes +but it's + + align:start position:0% +but it's + + + align:start position:0% +but it's +the inability to bring down your blood + + align:start position:0% +the inability to bring down your blood + + + align:start position:0% +the inability to bring down your blood +sugar rapidly enough after you give them + + align:start position:0% +sugar rapidly enough after you give them + + + align:start position:0% +sugar rapidly enough after you give them +a challenge of glucose and using a + + align:start position:0% +a challenge of glucose and using a + + + align:start position:0% +a challenge of glucose and using a +selection a collection of three chips + + align:start position:0% +selection a collection of three chips + + + align:start position:0% +selection a collection of three chips +you measured 35 000 genes so we did it + + align:start position:0% +you measured 35 000 genes so we did it + + + align:start position:0% +you measured 35 000 genes so we did it +on patient one patient two + + align:start position:0% +on patient one patient two + + + align:start position:0% +on patient one patient two +patient three and patient four + + align:start position:0% +patient three and patient four + + + align:start position:0% +patient three and patient four +and we repeated the same experiment with + + align:start position:0% +and we repeated the same experiment with + + + align:start position:0% +and we repeated the same experiment with +the same extracts + + align:start position:0% +the same extracts + + + align:start position:0% +the same extracts +of rna from the patient's uh muscles + + align:start position:0% +of rna from the patient's uh muscles + + + align:start position:0% +of rna from the patient's uh muscles +these are from the patient's muscles so + + align:start position:0% +these are from the patient's muscles so + + + align:start position:0% +these are from the patient's muscles so +let me ask you the following question + + align:start position:0% +let me ask you the following question + + + align:start position:0% +let me ask you the following question +for gene five on this microarray what + + align:start position:0% +for gene five on this microarray what + + + align:start position:0% +for gene five on this microarray what +should the ratio between + + align:start position:0% +should the ratio between + + + align:start position:0% +should the ratio between +be between gene five here and gene five + + align:start position:0% +be between gene five here and gene five + + + align:start position:0% +be between gene five here and gene five +here + + align:start position:0% + + + + align:start position:0% + +did someone say one thank you the answer + + align:start position:0% +did someone say one thank you the answer + + + align:start position:0% +did someone say one thank you the answer +is one + + align:start position:0% +is one + + + align:start position:0% +is one +what should the ratio between be between + + align:start position:0% +what should the ratio between be between + + + align:start position:0% +what should the ratio between be between +gene five here and gene five here + + align:start position:0% + + + + align:start position:0% + +who knows + + align:start position:0% +who knows + + + align:start position:0% +who knows +it shouldn't be one the answer is who + + align:start position:0% +it shouldn't be one the answer is who + + + align:start position:0% +it shouldn't be one the answer is who +knows because it depends on the + + align:start position:0% +knows because it depends on the + + + align:start position:0% +knows because it depends on the +individual right they're different + + align:start position:0% +individual right they're different + + + align:start position:0% +individual right they're different +they're different individuals good + + align:start position:0% +they're different individuals good + + + align:start position:0% +they're different individuals good +so now that we understand that + + align:start position:0% +so now that we understand that + + + align:start position:0% +so now that we understand that +let's repeat + + align:start position:0% +let's repeat + + + align:start position:0% +let's repeat +the intra patient variation + + align:start position:0% +the intra patient variation + + + align:start position:0% +the intra patient variation +should be the fold should be one the + + align:start position:0% +should be the fold should be one the + + + align:start position:0% +should be the fold should be one the +inter patient variation we don't know + + align:start position:0% +inter patient variation we don't know + + + align:start position:0% +inter patient variation we don't know +but let's say this ratio for the sake of + + align:start position:0% +but let's say this ratio for the sake of + + + align:start position:0% +but let's say this ratio for the sake of +argument between gene five and patient + + align:start position:0% +argument between gene five and patient + + + align:start position:0% +argument between gene five and patient +one patient two is a ratio of five okay + + align:start position:0% +one patient two is a ratio of five okay + + + align:start position:0% +one patient two is a ratio of five okay +what should this ratio be between of + + align:start position:0% +what should this ratio be between of + + + align:start position:0% +what should this ratio be between of +gene five from patient one + + align:start position:0% +gene five from patient one + + + align:start position:0% +gene five from patient one +close to five as well so what should the + + align:start position:0% +close to five as well so what should the + + + align:start position:0% +close to five as well so what should the +ratio of the ratios be + + align:start position:0% +ratio of the ratios be + + + align:start position:0% +ratio of the ratios be +one thank you + + align:start position:0% +one thank you + + + align:start position:0% +one thank you +so + + align:start position:0% +so + + + align:start position:0% +so +to repeat the intro patient variation + + align:start position:0% +to repeat the intro patient variation + + + align:start position:0% +to repeat the intro patient variation +ratio should be one + + align:start position:0% +ratio should be one + + + align:start position:0% +ratio should be one +the ratio of the ratios of the inter + + align:start position:0% +the ratio of the ratios of the inter + + + align:start position:0% +the ratio of the ratios of the inter +patient variation should be one yes the + + align:start position:0% +patient variation should be one yes the + + + align:start position:0% +patient variation should be one yes the +measurements actually were pretty close + + align:start position:0% +measurements actually were pretty close + + + align:start position:0% +measurements actually were pretty close +in time and all that it was actually the + + align:start position:0% +in time and all that it was actually the + + + align:start position:0% +in time and all that it was actually the +same rna sample that we took and we + + align:start position:0% +same rna sample that we took and we + + + align:start position:0% +same rna sample that we took and we +hybridized it all at the same time + + align:start position:0% + + + + align:start position:0% + +but all good questions to ask + + align:start position:0% +but all good questions to ask + + + align:start position:0% +but all good questions to ask +in fact never reported typically in the + + align:start position:0% +in fact never reported typically in the + + + align:start position:0% +in fact never reported typically in the +journal article + + align:start position:0% + + + + align:start position:0% + +in fact now that begs + + align:start position:0% +in fact now that begs + + + align:start position:0% +in fact now that begs +i have to give you an anecdote you'll + + align:start position:0% +i have to give you an anecdote you'll + + + align:start position:0% +i have to give you an anecdote you'll +learn about clustering uh in the lecture + + align:start position:0% +learn about clustering uh in the lecture + + + align:start position:0% +learn about clustering uh in the lecture +later by um + + align:start position:0% +later by um + + + align:start position:0% +later by um +steve greenberg but um todd golub did + + align:start position:0% +steve greenberg but um todd golub did + + + align:start position:0% +steve greenberg but um todd golub did +one of the first studies of the + + align:start position:0% +one of the first studies of the + + + align:start position:0% +one of the first studies of the +differences that you can find in + + align:start position:0% +differences that you can find in + + + align:start position:0% +differences that you can find in +two physiological conditions or + + align:start position:0% +two physiological conditions or + + + align:start position:0% +two physiological conditions or +pathological conditions based on + + align:start position:0% +pathological conditions based on + + + align:start position:0% +pathological conditions based on +expression and he looked at + + align:start position:0% +expression and he looked at + + + align:start position:0% +expression and he looked at +acute myelogenous leukemia versus + + align:start position:0% +acute myelogenous leukemia versus + + + align:start position:0% +acute myelogenous leukemia versus +lymphobatic leukemia aml this is all and + + align:start position:0% +lymphobatic leukemia aml this is all and + + + align:start position:0% +lymphobatic leukemia aml this is all and +sure enough using a supervised learning + + align:start position:0% +sure enough using a supervised learning + + + align:start position:0% +sure enough using a supervised learning +algorithm that you'll learn about + + align:start position:0% +algorithm that you'll learn about + + + align:start position:0% +algorithm that you'll learn about +you could do it without a problem + + align:start position:0% +you could do it without a problem + + + align:start position:0% +you could do it without a problem +however when i uh here also the tesla + + align:start position:0% +however when i uh here also the tesla + + + align:start position:0% +however when i uh here also the tesla +and training set when i put all the data + + align:start position:0% +and training set when i put all the data + + + align:start position:0% +and training set when i put all the data +together i found out i could actually + + align:start position:0% +together i found out i could actually + + + align:start position:0% +together i found out i could actually +distinguish another group + + align:start position:0% +distinguish another group + + + align:start position:0% +distinguish another group +not aml versus alab but the test set + + align:start position:0% +not aml versus alab but the test set + + + align:start position:0% +not aml versus alab but the test set +versus the training set + + align:start position:0% +versus the training set + + + align:start position:0% +versus the training set +i said to myself what the heck is this + + align:start position:0% +i said to myself what the heck is this + + + align:start position:0% +i said to myself what the heck is this +and i just want to talk back to todd + + align:start position:0% +and i just want to talk back to todd + + + align:start position:0% +and i just want to talk back to todd +because after all todd's one my former + + align:start position:0% +because after all todd's one my former + + + align:start position:0% +because after all todd's one my former +intern so i have no problem getting uh + + align:start position:0% +intern so i have no problem getting uh + + + align:start position:0% +intern so i have no problem getting uh +calling him up i said what gibbs he says + + align:start position:0% +calling him up i said what gibbs he says + + + align:start position:0% +calling him up i said what gibbs he says +they were hybridized on different days + + align:start position:0% +they were hybridized on different days + + + align:start position:0% +they were hybridized on different days +and that wasn't published in the + + align:start position:0% +and that wasn't published in the + + + align:start position:0% +and that wasn't published in the +literature but + + align:start position:0% +literature but + + + align:start position:0% +literature but +just by doing a different day same + + align:start position:0% +just by doing a different day same + + + align:start position:0% +just by doing a different day same +technician but different days a slightly + + align:start position:0% +technician but different days a slightly + + + align:start position:0% +technician but different days a slightly +different hybridization reaction and + + align:start position:0% +different hybridization reaction and + + + align:start position:0% +different hybridization reaction and +that could be picked up just by looking + + align:start position:0% +that could be picked up just by looking + + + align:start position:0% +that could be picked up just by looking +at the data anyway so we'll remember + + align:start position:0% +at the data anyway so we'll remember + + + align:start position:0% +at the data anyway so we'll remember +where we were here the intra patient + + align:start position:0% +where we were here the intra patient + + + align:start position:0% +where we were here the intra patient +ratio one the ratio of the inter patient + + align:start position:0% +ratio one the ratio of the inter patient + + + align:start position:0% +ratio one the ratio of the inter patient +ratios one what in fact happens + + align:start position:0% +ratios one what in fact happens + + + align:start position:0% +ratios one what in fact happens +well this is actually kind of crummy by + + align:start position:0% +well this is actually kind of crummy by + + + align:start position:0% +well this is actually kind of crummy by +2004 standards but it was not bad when + + align:start position:0% +2004 standards but it was not bad when + + + align:start position:0% +2004 standards but it was not bad when +we did it here's one chip the other chip + + align:start position:0% +we did it here's one chip the other chip + + + align:start position:0% +we did it here's one chip the other chip +one chip the other chip one chip the + + align:start position:0% +one chip the other chip one chip the + + + align:start position:0% +one chip the other chip one chip the +other chip for the four patients and you + + align:start position:0% +other chip for the four patients and you + + + align:start position:0% +other chip for the four patients and you +see here what looks like a one-to-one + + align:start position:0% +see here what looks like a one-to-one + + + align:start position:0% +see here what looks like a one-to-one +line but it's kind of muddy and the rate + + align:start position:0% +line but it's kind of muddy and the rate + + + align:start position:0% +line but it's kind of muddy and the rate +the coex coefficients were 0.76 to 0.84 + + align:start position:0% +the coex coefficients were 0.76 to 0.84 + + + align:start position:0% +the coex coefficients were 0.76 to 0.84 +currently i would anybody who does + + align:start position:0% +currently i would anybody who does + + + align:start position:0% +currently i would anybody who does +more poorly than a correlation + + align:start position:0% +more poorly than a correlation + + + align:start position:0% +more poorly than a correlation +coefficient of + + align:start position:0% +coefficient of + + + align:start position:0% +coefficient of +0.97 i question how good their + + align:start position:0% +0.97 i question how good their + + + align:start position:0% +0.97 i question how good their +hybridization laboratory + + align:start position:0% +hybridization laboratory + + + align:start position:0% +hybridization laboratory +is nonetheless that's what we have but + + align:start position:0% +is nonetheless that's what we have but + + + align:start position:0% +is nonetheless that's what we have but +you still can believe it's a good + + align:start position:0% +you still can believe it's a good + + + align:start position:0% +you still can believe it's a good +one-to-one um + + align:start position:0% +one-to-one um + + + align:start position:0% +one-to-one um +ratio however + + align:start position:0% + + + + align:start position:0% + +what was the + + align:start position:0% +what was the + + + align:start position:0% +what was the +ratio of the ratios now here's the ratio + + align:start position:0% +ratio of the ratios now here's the ratio + + + align:start position:0% +ratio of the ratios now here's the ratio +of the ratios in one case + + align:start position:0% +of the ratios in one case + + + align:start position:0% +of the ratios in one case +versus the other case and you don't have + + align:start position:0% +versus the other case and you don't have + + + align:start position:0% +versus the other case and you don't have +to be a statistician to realize that + + align:start position:0% +to be a statistician to realize that + + + align:start position:0% +to be a statistician to realize that +there's no signal here these are blobs + + align:start position:0% +there's no signal here these are blobs + + + align:start position:0% +there's no signal here these are blobs +now what does a blob mean + + align:start position:0% +now what does a blob mean + + + align:start position:0% +now what does a blob mean +it means + + align:start position:0% +it means + + + align:start position:0% +it means +that with one set of chips this gene was + + align:start position:0% +that with one set of chips this gene was + + + align:start position:0% +that with one set of chips this gene was +10 times higher because of the log scale + + align:start position:0% +10 times higher because of the log scale + + + align:start position:0% +10 times higher because of the log scale +in patient one than patient three with + + align:start position:0% +in patient one than patient three with + + + align:start position:0% +in patient one than patient three with +the other set of chips this gene was ten + + align:start position:0% +the other set of chips this gene was ten + + + align:start position:0% +the other set of chips this gene was ten +times lower in patient one than patient + + align:start position:0% +times lower in patient one than patient + + + align:start position:0% +times lower in patient one than patient +three so this + + align:start position:0% +three so this + + + align:start position:0% +three so this +this is particularly heinous we have + + align:start position:0% +this is particularly heinous we have + + + align:start position:0% +this is particularly heinous we have +not only the wrong magnitude with the + + align:start position:0% +not only the wrong magnitude with the + + + align:start position:0% +not only the wrong magnitude with the +wrong direction of regulation + + align:start position:0% +wrong direction of regulation + + + align:start position:0% +wrong direction of regulation +and you can by inspection you know this + + align:start position:0% +and you can by inspection you know this + + + align:start position:0% +and you can by inspection you know this +is happening a lot so right away you + + align:start position:0% +is happening a lot so right away you + + + align:start position:0% +is happening a lot so right away you +should be asking yourself the question + + align:start position:0% +should be asking yourself the question + + + align:start position:0% +should be asking yourself the question +how can this be i mean after all zack's + + align:start position:0% +how can this be i mean after all zack's + + + align:start position:0% +how can this be i mean after all zack's +telling me about all how these + + align:start position:0% +telling me about all how these + + + align:start position:0% +telling me about all how these +microwaves are wonderful how can this be + + align:start position:0% +microwaves are wonderful how can this be + + + align:start position:0% +microwaves are wonderful how can this be +that this is so bad after all in the end + + align:start position:0% +that this is so bad after all in the end + + + align:start position:0% +that this is so bad after all in the end +there is some some signal here and why + + align:start position:0% +there is some some signal here and why + + + align:start position:0% +there is some some signal here and why +is it so bad any any idea why it is so + + align:start position:0% +is it so bad any any idea why it is so + + + align:start position:0% +is it so bad any any idea why it is so +bad + + align:start position:0% + + + + align:start position:0% + +anybody have any ideas why these results + + align:start position:0% +anybody have any ideas why these results + + + align:start position:0% +anybody have any ideas why these results +are so bad + + align:start position:0% +are so bad + + + align:start position:0% +are so bad +we didn't + + align:start position:0% +we didn't + + + align:start position:0% +we didn't +we were not particularly worse than + + align:start position:0% +we were not particularly worse than + + + align:start position:0% +we were not particularly worse than +anybody else at that time + + align:start position:0% + + + + align:start position:0% + +but we weren't doing that on different + + align:start position:0% +but we weren't doing that on different + + + align:start position:0% +but we weren't doing that on different +days there was some other kind of + + align:start position:0% +days there was some other kind of + + + align:start position:0% +days there was some other kind of +variation + + align:start position:0% +variation + + + align:start position:0% +variation +so let me ask a lead go ahead + + align:start position:0% + + + + align:start position:0% + +but which kind of measurements are the + + align:start position:0% +but which kind of measurements are the + + + align:start position:0% +but which kind of measurements are the +most sensitive to that kind of + + align:start position:0% +most sensitive to that kind of + + + align:start position:0% +most sensitive to that kind of +compounding + + align:start position:0% +compounding + + + align:start position:0% +compounding +what kind of measurements + + align:start position:0% + + + + align:start position:0% + +what kind of + + align:start position:0% +what kind of + + + align:start position:0% +what kind of +when you have what in the denominator + + align:start position:0% +when you have what in the denominator + + + align:start position:0% +when you have what in the denominator +makes a ratio change the most + + align:start position:0% +makes a ratio change the most + + + align:start position:0% +makes a ratio change the most +small numbers right + + align:start position:0% +small numbers right + + + align:start position:0% +small numbers right +so + + align:start position:0% + + + + align:start position:0% + +when you have a gene expression which + + align:start position:0% +when you have a gene expression which + + + align:start position:0% +when you have a gene expression which +goes from point six to point three + + align:start position:0% +goes from point six to point three + + + align:start position:0% +goes from point six to point three +that's a two-fold difference when you + + align:start position:0% +that's a two-fold difference when you + + + align:start position:0% +that's a two-fold difference when you +have it goes from six hundred to three + + align:start position:0% +have it goes from six hundred to three + + + align:start position:0% +have it goes from six hundred to three +hundred that's a two-fold difference + + align:start position:0% +hundred that's a two-fold difference + + + align:start position:0% +hundred that's a two-fold difference +you add a little bit of noise + + align:start position:0% +you add a little bit of noise + + + align:start position:0% +you add a little bit of noise +this one flips on the left and that + + align:start position:0% +this one flips on the left and that + + + align:start position:0% +this one flips on the left and that +one's pretty stable on the right + + align:start position:0% +one's pretty stable on the right + + + align:start position:0% +one's pretty stable on the right +well guess what two-thirds of + + align:start position:0% +well guess what two-thirds of + + + align:start position:0% +well guess what two-thirds of +transcriptome expressed at very very low + + align:start position:0% +transcriptome expressed at very very low + + + align:start position:0% +transcriptome expressed at very very low +levels has you have one or two copies of + + align:start position:0% +levels has you have one or two copies of + + + align:start position:0% +levels has you have one or two copies of +rna + + align:start position:0% +rna + + + align:start position:0% +rna +one-third or less of transcriptome you + + align:start position:0% +one-third or less of transcriptome you + + + align:start position:0% +one-third or less of transcriptome you +have hundreds of copies of rna millions + + align:start position:0% +have hundreds of copies of rna millions + + + align:start position:0% +have hundreds of copies of rna millions +of copies of rna of that gene those are + + align:start position:0% +of copies of rna of that gene those are + + + align:start position:0% +of copies of rna of that gene those are +easily picked up by these microarrays + + align:start position:0% +easily picked up by these microarrays + + + align:start position:0% +easily picked up by these microarrays +but they're very noisy when you get down + + align:start position:0% +but they're very noisy when you get down + + + align:start position:0% +but they're very noisy when you get down +to these very low levels because of + + align:start position:0% +to these very low levels because of + + + align:start position:0% +to these very low levels because of +exactly that problem + + align:start position:0% +exactly that problem + + + align:start position:0% +exactly that problem +and so if you don't have a method that + + align:start position:0% +and so if you don't have a method that + + + align:start position:0% +and so if you don't have a method that +looks at a very variance + + align:start position:0% +looks at a very variance + + + align:start position:0% +looks at a very variance +and that does not take into account + + align:start position:0% +and that does not take into account + + + align:start position:0% +and that does not take into account +expression intensity your host + + align:start position:0% +expression intensity your host + + + align:start position:0% +expression intensity your host +and that's why just putting a uh + + align:start position:0% +and that's why just putting a uh + + + align:start position:0% +and that's why just putting a uh +a fold cut off + + align:start position:0% +a fold cut off + + + align:start position:0% +a fold cut off +that says i'm going to look at + + align:start position:0% +that says i'm going to look at + + + align:start position:0% +that says i'm going to look at +everything that's twofold or greater you + + align:start position:0% +everything that's twofold or greater you + + + align:start position:0% +everything that's twofold or greater you +know that you're gonna find a bunch of + + align:start position:0% +know that you're gonna find a bunch of + + + align:start position:0% +know that you're gonna find a bunch of +things that two-fold or greater at lower + + align:start position:0% +things that two-fold or greater at lower + + + align:start position:0% +things that two-fold or greater at lower +expression levels but they're just wrong + + align:start position:0% +expression levels but they're just wrong + + + align:start position:0% +expression levels but they're just wrong +and + + align:start position:0% +and + + + align:start position:0% +and +thank goodness in 2004 you can't get a + + align:start position:0% +thank goodness in 2004 you can't get a + + + align:start position:0% +thank goodness in 2004 you can't get a +journal article now published unless you + + align:start position:0% +journal article now published unless you + + + align:start position:0% +journal article now published unless you +do a variance analysis but that was not + + align:start position:0% +do a variance analysis but that was not + + + align:start position:0% +do a variance analysis but that was not +true + + align:start position:0% +true + + + align:start position:0% +true +in 1999 to 2002 at the very least + + align:start position:0% + + + + align:start position:0% + +even more worrying + + align:start position:0% +even more worrying + + + align:start position:0% +even more worrying +so as bioinformaticians were spoiled by + + align:start position:0% +so as bioinformaticians were spoiled by + + + align:start position:0% +so as bioinformaticians were spoiled by +the following fact + + align:start position:0% + + + + align:start position:0% + +is it really quarter to two + + align:start position:0% +is it really quarter to two + + + align:start position:0% +is it really quarter to two +and i have until when + + align:start position:0% + + + + align:start position:0% + +ugh all right + + align:start position:0% +ugh all right + + + align:start position:0% +ugh all right +okay uh time flies when you're having + + align:start position:0% +okay uh time flies when you're having + + + align:start position:0% +okay uh time flies when you're having +fun um + + align:start position:0% +fun um + + + align:start position:0% +fun um +we were spoiled in bioinformatics by + + align:start position:0% +we were spoiled in bioinformatics by + + + align:start position:0% +we were spoiled in bioinformatics by +having this international resource + + align:start position:0% +having this international resource + + + align:start position:0% +having this international resource +called genbank where we put all our + + align:start position:0% +called genbank where we put all our + + + align:start position:0% +called genbank where we put all our +gene sequences into an international + + align:start position:0% +gene sequences into an international + + + align:start position:0% +gene sequences into an international +resource and allowed researchers to + + align:start position:0% +resource and allowed researchers to + + + align:start position:0% +resource and allowed researchers to +compare different things across + + align:start position:0% +compare different things across + + + align:start position:0% +compare different things across +different systems and we thought we + + align:start position:0% +different systems and we thought we + + + align:start position:0% +different systems and we thought we +could do the same thing for microarrays + + align:start position:0% +could do the same thing for microarrays + + + align:start position:0% +could do the same thing for microarrays +so for the 60 cancer cell lines that the + + align:start position:0% +so for the 60 cancer cell lines that the + + + align:start position:0% +so for the 60 cancer cell lines that the +national cancer institute + + align:start position:0% +national cancer institute + + + align:start position:0% +national cancer institute +collects to test + + align:start position:0% +collects to test + + + align:start position:0% +collects to test +the thousands of drugs that they obtain + + align:start position:0% +the thousands of drugs that they obtain + + + align:start position:0% +the thousands of drugs that they obtain +from pharmaceutical industries from the + + align:start position:0% +from pharmaceutical industries from the + + + align:start position:0% +from pharmaceutical industries from the +rainforest from china and so on to test + + align:start position:0% +rainforest from china and so on to test + + + align:start position:0% +rainforest from china and so on to test +for chemotherapeutic efficacy + + align:start position:0% +for chemotherapeutic efficacy + + + align:start position:0% +for chemotherapeutic efficacy +we + + align:start position:0% +we + + + align:start position:0% +we +they have these 60 cancer cell lines + + align:start position:0% +they have these 60 cancer cell lines + + + align:start position:0% +they have these 60 cancer cell lines +that they've been keeping around for + + align:start position:0% +that they've been keeping around for + + + align:start position:0% +that they've been keeping around for +years + + align:start position:0% +years + + + align:start position:0% +years +and so todd's group at the white head + + align:start position:0% +and so todd's group at the white head + + + align:start position:0% +and so todd's group at the white head +did state-of-the-art hybridization with + + align:start position:0% +did state-of-the-art hybridization with + + + align:start position:0% +did state-of-the-art hybridization with +metrics and pat brown's group the best + + align:start position:0% +metrics and pat brown's group the best + + + align:start position:0% +metrics and pat brown's group the best +practitioners of spotted rays did the + + align:start position:0% +practitioners of spotted rays did the + + + align:start position:0% +practitioners of spotted rays did the +same analysis uh with spotted arrays and + + align:start position:0% +same analysis uh with spotted arrays and + + + align:start position:0% +same analysis uh with spotted arrays and +shown here is something that you don't + + align:start position:0% +shown here is something that you don't + + + align:start position:0% +shown here is something that you don't +have to be a statistician to understand + + align:start position:0% +have to be a statistician to understand + + + align:start position:0% +have to be a statistician to understand +the correlation of the genes that were + + align:start position:0% +the correlation of the genes that were + + + align:start position:0% +the correlation of the genes that were +in common across both platforms + + align:start position:0% +in common across both platforms + + + align:start position:0% +in common across both platforms +and the correlation was terrible + + align:start position:0% +and the correlation was terrible + + + align:start position:0% +and the correlation was terrible +there was almost no correlation that + + align:start position:0% +there was almost no correlation that + + + align:start position:0% +there was almost no correlation that +meant that you could not compare the + + align:start position:0% +meant that you could not compare the + + + align:start position:0% +meant that you could not compare the +results from one platform to the other + + align:start position:0% +results from one platform to the other + + + align:start position:0% +results from one platform to the other +and when i first published this + + align:start position:0% +and when i first published this + + + align:start position:0% +and when i first published this +experiment this result a couple years + + align:start position:0% +experiment this result a couple years + + + align:start position:0% +experiment this result a couple years +ago + + align:start position:0% +ago + + + align:start position:0% +ago +it was actually a result of a course + + align:start position:0% +it was actually a result of a course + + + align:start position:0% +it was actually a result of a course +like this one of the students did as a + + align:start position:0% +like this one of the students did as a + + + align:start position:0% +like this one of the students did as a +final project i told him why didn't you + + align:start position:0% +final project i told him why didn't you + + + align:start position:0% +final project i told him why didn't you +compare these two platforms and i was + + align:start position:0% +compare these two platforms and i was + + + align:start position:0% +compare these two platforms and i was +convinced that he was wrong and i looked + + align:start position:0% +convinced that he was wrong and i looked + + + align:start position:0% +convinced that he was wrong and i looked +at him he wasn't but i thought there + + align:start position:0% +at him he wasn't but i thought there + + + align:start position:0% +at him he wasn't but i thought there +might be some fluke since then there's + + align:start position:0% +might be some fluke since then there's + + + align:start position:0% +might be some fluke since then there's +been about four or five papers doing + + align:start position:0% +been about four or five papers doing + + + align:start position:0% +been about four or five papers doing +this again and it's getting better + + align:start position:0% +this again and it's getting better + + + align:start position:0% +this again and it's getting better +but it's still pretty bad correlation + + align:start position:0% +but it's still pretty bad correlation + + + align:start position:0% +but it's still pretty bad correlation +now is up to about 0.6 + + align:start position:0% +now is up to about 0.6 + + + align:start position:0% +now is up to about 0.6 +across the different platforms + + align:start position:0% +across the different platforms + + + align:start position:0% +across the different platforms +that's a real problem + + align:start position:0% +that's a real problem + + + align:start position:0% +that's a real problem +obviously + + align:start position:0% +obviously + + + align:start position:0% +obviously +here's one of the many reasons + + align:start position:0% +here's one of the many reasons + + + align:start position:0% +here's one of the many reasons +subsequently that we've discovered for + + align:start position:0% +subsequently that we've discovered for + + + align:start position:0% +subsequently that we've discovered for +this problem + + align:start position:0% +this problem + + + align:start position:0% +this problem +shown in + + align:start position:0% +shown in + + + align:start position:0% +shown in +um + + align:start position:0% +um + + + align:start position:0% +um +orange + + align:start position:0% +orange + + + align:start position:0% +orange +is the refseq the reference sequence + + align:start position:0% +is the refseq the reference sequence + + + align:start position:0% +is the refseq the reference sequence +that the national center for + + align:start position:0% +that the national center for + + + align:start position:0% +that the national center for +biotechnology information maintains a + + align:start position:0% +biotechnology information maintains a + + + align:start position:0% +biotechnology information maintains a +curated resource of what is the + + align:start position:0% +curated resource of what is the + + + align:start position:0% +curated resource of what is the +definitive definitive mrna sequence of + + align:start position:0% +definitive definitive mrna sequence of + + + align:start position:0% +definitive definitive mrna sequence of +that gene + + align:start position:0% + + + + align:start position:0% + +shown in black are the athametric probes + + align:start position:0% +shown in black are the athametric probes + + + align:start position:0% +shown in black are the athametric probes +which part of the genome they + + align:start position:0% +which part of the genome they + + + align:start position:0% +which part of the genome they +interrogate well watch it + + align:start position:0% +interrogate well watch it + + + align:start position:0% +interrogate well watch it +these seems to be falling off the edge + + align:start position:0% +these seems to be falling off the edge + + + align:start position:0% +these seems to be falling off the edge +so if you have for instance a cdna that + + align:start position:0% +so if you have for instance a cdna that + + + align:start position:0% +so if you have for instance a cdna that +interrogates + + align:start position:0% +interrogates + + + align:start position:0% +interrogates +this part + + align:start position:0% +this part + + + align:start position:0% +this part +and an atometrics that is off the refseq + + align:start position:0% +and an atometrics that is off the refseq + + + align:start position:0% +and an atometrics that is off the refseq +it may have in fact a very poor + + align:start position:0% +it may have in fact a very poor + + + align:start position:0% +it may have in fact a very poor +a reproducibility and we've subsequently + + align:start position:0% +a reproducibility and we've subsequently + + + align:start position:0% +a reproducibility and we've subsequently +done a study that we've actually looked + + align:start position:0% +done a study that we've actually looked + + + align:start position:0% +done a study that we've actually looked +at the position by the way alphametrics + + align:start position:0% +at the position by the way alphametrics + + + align:start position:0% +at the position by the way alphametrics +previously had considered the exact + + align:start position:0% +previously had considered the exact + + + align:start position:0% +previously had considered the exact +sequences of these probes as proprietary + + align:start position:0% +sequences of these probes as proprietary + + + align:start position:0% +sequences of these probes as proprietary +so it's only the last year + + align:start position:0% +so it's only the last year + + + align:start position:0% +so it's only the last year +that they've revealed what those algo + + align:start position:0% +that they've revealed what those algo + + + align:start position:0% +that they've revealed what those algo +nucleotide sequences are so that we can + + align:start position:0% +nucleotide sequences are so that we can + + + align:start position:0% +nucleotide sequences are so that we can +actually + + align:start position:0% +actually + + + align:start position:0% +actually +position them on the + + align:start position:0% +position them on the + + + align:start position:0% +position them on the +gene to know where in fact they're + + align:start position:0% +gene to know where in fact they're + + + align:start position:0% +gene to know where in fact they're +interrogating the gene and it's + + align:start position:0% +interrogating the gene and it's + + + align:start position:0% +interrogating the gene and it's +constantly when we eliminated those + + align:start position:0% +constantly when we eliminated those + + + align:start position:0% +constantly when we eliminated those +ethymetrics probes which fell off the + + align:start position:0% +ethymetrics probes which fell off the + + + align:start position:0% +ethymetrics probes which fell off the +gene we had much better correlation + + align:start position:0% +gene we had much better correlation + + + align:start position:0% +gene we had much better correlation +across platforms previously there's + + align:start position:0% +across platforms previously there's + + + align:start position:0% +across platforms previously there's +other reasons but that's i think a major + + align:start position:0% +other reasons but that's i think a major + + + align:start position:0% +other reasons but that's i think a major +reason yeah + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% +no + + + align:start position:0% +no +so + + align:start position:0% +so + + + align:start position:0% +so +here is a study that was done by one of + + align:start position:0% +here is a study that was done by one of + + + align:start position:0% +here is a study that was done by one of +our fellows of metrics going from h + + align:start position:0% +our fellows of metrics going from h + + + align:start position:0% +our fellows of metrics going from h +eugene fl which is one generation to hu + + align:start position:0% +eugene fl which is one generation to hu + + + align:start position:0% +eugene fl which is one generation to hu +gene so to u-95a + + align:start position:0% +gene so to u-95a + + + align:start position:0% +gene so to u-95a +same + + align:start position:0% +same + + + align:start position:0% +same +so this is looking at human rna + + align:start position:0% +so this is looking at human rna + + + align:start position:0% +so this is looking at human rna +for the same genes + + align:start position:0% +for the same genes + + + align:start position:0% +for the same genes +we took the same rna from the same + + align:start position:0% +we took the same rna from the same + + + align:start position:0% +we took the same rna from the same +muscle and hybridized hybridized on the + + align:start position:0% +muscle and hybridized hybridized on the + + + align:start position:0% +muscle and hybridized hybridized on the +same day + + align:start position:0% +same day + + + align:start position:0% +same day +look at qualitative correlation + + align:start position:0% +look at qualitative correlation + + + align:start position:0% +look at qualitative correlation +coefficients we got 0.7 and 0.59 + + align:start position:0% +coefficients we got 0.7 and 0.59 + + + align:start position:0% +coefficients we got 0.7 and 0.59 +why do you think that is + + align:start position:0% + + + + align:start position:0% + +the answer is they picked different + + align:start position:0% +the answer is they picked different + + + align:start position:0% +the answer is they picked different +probe sets as i learned more about the + + align:start position:0% +probe sets as i learned more about the + + + align:start position:0% +probe sets as i learned more about the +human genome you could be more and more + + align:start position:0% +human genome you could be more and more + + + align:start position:0% +human genome you could be more and more +accurate about which + + align:start position:0% +accurate about which + + + align:start position:0% +accurate about which +although nucleotides uniquely represent + + align:start position:0% +although nucleotides uniquely represent + + + align:start position:0% +although nucleotides uniquely represent +that gene as opposed to matching another + + align:start position:0% +that gene as opposed to matching another + + + align:start position:0% +that gene as opposed to matching another +gene + + align:start position:0% +gene + + + align:start position:0% +gene +and so what we found is + + align:start position:0% +and so what we found is + + + align:start position:0% +and so what we found is +the the more the pro the larger number + + align:start position:0% +the the more the pro the larger number + + + align:start position:0% +the the more the pro the larger number +of probe pairs shared between the + + align:start position:0% +of probe pairs shared between the + + + align:start position:0% +of probe pairs shared between the +generations of mathematics microarrays + + align:start position:0% +generations of mathematics microarrays + + + align:start position:0% +generations of mathematics microarrays +the better the correlation + + align:start position:0% +the better the correlation + + + align:start position:0% +the better the correlation +between + + align:start position:0% +between + + + align:start position:0% +between +those microarrays + + align:start position:0% +those microarrays + + + align:start position:0% +those microarrays +but to answer your question + + align:start position:0% +but to answer your question + + + align:start position:0% +but to answer your question +that means that if it was done on the + + align:start position:0% +that means that if it was done on the + + + align:start position:0% +that means that if it was done on the +previous generation of microarrays even + + align:start position:0% +previous generation of microarrays even + + + align:start position:0% +previous generation of microarrays even +within asymmetrics family + + align:start position:0% +within asymmetrics family + + + align:start position:0% +within asymmetrics family +reproducibility is not good + + align:start position:0% +reproducibility is not good + + + align:start position:0% +reproducibility is not good +at least for those genes that don't meet + + align:start position:0% +at least for those genes that don't meet + + + align:start position:0% +at least for those genes that don't meet +those criteria + + align:start position:0% +those criteria + + + align:start position:0% +those criteria +which is a huge uh waste because + + align:start position:0% +which is a huge uh waste because + + + align:start position:0% +which is a huge uh waste because +remember unlike um remember what i told + + align:start position:0% +remember unlike um remember what i told + + + align:start position:0% +remember unlike um remember what i told +you we can do dna sequencing on on blood + + align:start position:0% +you we can do dna sequencing on on blood + + + align:start position:0% +you we can do dna sequencing on on blood +but expression analysis has to be done + + align:start position:0% +but expression analysis has to be done + + + align:start position:0% +but expression analysis has to be done +on the tissue that you care about so + + align:start position:0% +on the tissue that you care about so + + + align:start position:0% +on the tissue that you care about so +someone used up some precious brain + + align:start position:0% +someone used up some precious brain + + + align:start position:0% +someone used up some precious brain +specimens to do that they're gone + + align:start position:0% +specimens to do that they're gone + + + align:start position:0% +specimens to do that they're gone +and it'll take them several years to + + align:start position:0% +and it'll take them several years to + + + align:start position:0% +and it'll take them several years to +recreate them + + align:start position:0% +recreate them + + + align:start position:0% +recreate them +when i actually first presented this at + + align:start position:0% +when i actually first presented this at + + + align:start position:0% +when i actually first presented this at +nih actually heard a groan ripple + + align:start position:0% +nih actually heard a groan ripple + + + align:start position:0% +nih actually heard a groan ripple +through the whole audience uh because + + align:start position:0% +through the whole audience uh because + + + align:start position:0% +through the whole audience uh because +they had actually just blithely gone + + align:start position:0% +they had actually just blithely gone + + + align:start position:0% +they had actually just blithely gone +from german one generation to the other + + align:start position:0% +from german one generation to the other + + + align:start position:0% +from german one generation to the other +and assumed that they would just be able + + align:start position:0% +and assumed that they would just be able + + + align:start position:0% +and assumed that they would just be able +to analyze everything together + + align:start position:0% +to analyze everything together + + + align:start position:0% +to analyze everything together +and that was millions of dollars not the + + align:start position:0% +and that was millions of dollars not the + + + align:start position:0% +and that was millions of dollars not the +tube + + align:start position:0% +tube + + + align:start position:0% +tube +please + + align:start position:0% +please + + + align:start position:0% +please +so + + align:start position:0% +so + + + align:start position:0% +so +you assume that all the old stuff is + + align:start position:0% +you assume that all the old stuff is + + + align:start position:0% +you assume that all the old stuff is +jump no + + align:start position:0% +jump no + + + align:start position:0% +jump no +but you what you do is you try to figure + + align:start position:0% +but you what you do is you try to figure + + + align:start position:0% +but you what you do is you try to figure +out which which stuff is reproducible + + align:start position:0% +out which which stuff is reproducible + + + align:start position:0% +out which which stuff is reproducible +and you're careful about it + + align:start position:0% +and you're careful about it + + + align:start position:0% +and you're careful about it +and it's actually quite doable + + align:start position:0% +and it's actually quite doable + + + align:start position:0% +and it's actually quite doable +and we do it but doing naively actually + + align:start position:0% +and we do it but doing naively actually + + + align:start position:0% +and we do it but doing naively actually +can't do it wholesale the way they + + align:start position:0% +can't do it wholesale the way they + + + align:start position:0% +can't do it wholesale the way they +thought they were going to do it yes + + align:start position:0% + + + + align:start position:0% + +if you have a tissue + + align:start position:0% +if you have a tissue + + + align:start position:0% +if you have a tissue +plus it's not it's even at 200 a shot + + align:start position:0% +plus it's not it's even at 200 a shot + + + align:start position:0% +plus it's not it's even at 200 a shot +from the chip plus um labor costs maybe + + align:start position:0% +from the chip plus um labor costs maybe + + + align:start position:0% +from the chip plus um labor costs maybe + + align:start position:0% + + + align:start position:0% +a shot so 500 is you know 500 times 100 + + align:start position:0% +a shot so 500 is you know 500 times 100 + + + align:start position:0% +a shot so 500 is you know 500 times 100 +patients so it's looking like real money + + align:start position:0% +patients so it's looking like real money + + + align:start position:0% +patients so it's looking like real money +and + + align:start position:0% +and + + + align:start position:0% +and +but i think the real problem there is um + + align:start position:0% +but i think the real problem there is um + + + align:start position:0% +but i think the real problem there is um +limited uh tissue resources turns out to + + align:start position:0% +limited uh tissue resources turns out to + + + align:start position:0% +limited uh tissue resources turns out to +be a real issue + + align:start position:0% +be a real issue + + + align:start position:0% +be a real issue +uh for those of you who ever tried to do + + align:start position:0% +uh for those of you who ever tried to do + + + align:start position:0% +uh for those of you who ever tried to do +one of these experiments getting the + + align:start position:0% +one of these experiments getting the + + + align:start position:0% +one of these experiments getting the +right tissue the right annotation out of + + align:start position:0% +right tissue the right annotation out of + + + align:start position:0% +right tissue the right annotation out of +the medical system is very hard + + align:start position:0% +the medical system is very hard + + + align:start position:0% +the medical system is very hard +in fact that's why i really like the + + align:start position:0% +in fact that's why i really like the + + + align:start position:0% +in fact that's why i really like the +memp program because it + + align:start position:0% +memp program because it + + + align:start position:0% +memp program because it +makes the engineers go and deal with + + align:start position:0% +makes the engineers go and deal with + + + align:start position:0% +makes the engineers go and deal with +doctors so they understand what kind of + + align:start position:0% +doctors so they understand what kind of + + + align:start position:0% +doctors so they understand what kind of +social pressures or efficacious getting + + align:start position:0% +social pressures or efficacious getting + + + align:start position:0% +social pressures or efficacious getting +the right kind of biomaterials out of + + align:start position:0% +the right kind of biomaterials out of + + + align:start position:0% +the right kind of biomaterials out of +the medical system so it sounds like a + + align:start position:0% +the medical system so it sounds like a + + + align:start position:0% +the medical system so it sounds like a +trivial issue but it's not + + align:start position:0% +trivial issue but it's not + + + align:start position:0% +trivial issue but it's not +so let me show you the following graph + + align:start position:0% +so let me show you the following graph + + + align:start position:0% +so let me show you the following graph +shown here + + align:start position:0% +shown here + + + align:start position:0% +shown here +on the x-axis + + align:start position:0% +on the x-axis + + + align:start position:0% +on the x-axis +is the amount of spiked in + + align:start position:0% +is the amount of spiked in + + + align:start position:0% +is the amount of spiked in +probe so this is a problem known + + align:start position:0% +probe so this is a problem known + + + align:start position:0% +probe so this is a problem known +quantity and here's the readout from + + align:start position:0% +quantity and here's the readout from + + + align:start position:0% +quantity and here's the readout from +asymmetrics on intensity + + align:start position:0% +asymmetrics on intensity + + + align:start position:0% +asymmetrics on intensity +shown in + + align:start position:0% +shown in + + + align:start position:0% +shown in +red + + align:start position:0% +red + + + align:start position:0% +red +are the perfect match probes and you see + + align:start position:0% +are the perfect match probes and you see + + + align:start position:0% +are the perfect match probes and you see +as you add more and more + + align:start position:0% +as you add more and more + + + align:start position:0% +as you add more and more +probe it increases just as you'd hope + + align:start position:0% +probe it increases just as you'd hope + + + align:start position:0% +probe it increases just as you'd hope +the signal increases but what you see + + align:start position:0% +the signal increases but what you see + + + align:start position:0% +the signal increases but what you see +here is that it saturates at the high + + align:start position:0% +here is that it saturates at the high + + + align:start position:0% +here is that it saturates at the high +levels right + + align:start position:0% +levels right + + + align:start position:0% +levels right +as you'd expect it to + + align:start position:0% +as you'd expect it to + + + align:start position:0% +as you'd expect it to +now pretty interesting is that the + + align:start position:0% +now pretty interesting is that the + + + align:start position:0% +now pretty interesting is that the +mismatch probes these are probes that + + align:start position:0% +mismatch probes these are probes that + + + align:start position:0% +mismatch probes these are probes that +were designed not to hybridize with the + + align:start position:0% +were designed not to hybridize with the + + + align:start position:0% +were designed not to hybridize with the +target sequence + + align:start position:0% +target sequence + + + align:start position:0% +target sequence +they too in fact rise + + align:start position:0% +they too in fact rise + + + align:start position:0% +they too in fact rise +also they lag but they rise as well with + + align:start position:0% +also they lag but they rise as well with + + + align:start position:0% +also they lag but they rise as well with +the amount of spiked in control + + align:start position:0% +the amount of spiked in control + + + align:start position:0% +the amount of spiked in control +and in fact they don't quite saturate + + align:start position:0% +and in fact they don't quite saturate + + + align:start position:0% +and in fact they don't quite saturate +what does that mean it means that the + + align:start position:0% +what does that mean it means that the + + + align:start position:0% +what does that mean it means that the +average difference + + align:start position:0% +average difference + + + align:start position:0% +average difference +actually starts dropping down because + + align:start position:0% +actually starts dropping down because + + + align:start position:0% +actually starts dropping down because +even though the perfect match is + + align:start position:0% +even though the perfect match is + + + align:start position:0% +even though the perfect match is +saturating the the the thing that you're + + align:start position:0% +saturating the the the thing that you're + + + align:start position:0% +saturating the the the thing that you're +subtracting out the mismatch keeps on + + align:start position:0% +subtracting out the mismatch keeps on + + + align:start position:0% +subtracting out the mismatch keeps on +rising so the higher levels you actually + + align:start position:0% +rising so the higher levels you actually + + + align:start position:0% +rising so the higher levels you actually +get a dropping signal + + align:start position:0% +get a dropping signal + + + align:start position:0% +get a dropping signal +that's lousy and so and that's what they + + align:start position:0% +that's lousy and so and that's what they + + + align:start position:0% +that's lousy and so and that's what they +uh + + align:start position:0% +uh + + + align:start position:0% +uh +clear solution background here with the + + align:start position:0% +clear solution background here with the + + + align:start position:0% +clear solution background here with the +eukaryotic background for the spiking it + + align:start position:0% +eukaryotic background for the spiking it + + + align:start position:0% +eukaryotic background for the spiking it +gets even noisier you get less + + align:start position:0% +gets even noisier you get less + + + align:start position:0% +gets even noisier you get less +sensitivity and even more market effect + + align:start position:0% +sensitivity and even more market effect + + + align:start position:0% +sensitivity and even more market effect +the all of these things are true and yet + + align:start position:0% +the all of these things are true and yet + + + align:start position:0% +the all of these things are true and yet +you can actually do very very good + + align:start position:0% +you can actually do very very good + + + align:start position:0% +you can actually do very very good +science with microarrays and actually + + align:start position:0% +science with microarrays and actually + + + align:start position:0% +science with microarrays and actually +discover lots of biology but just have + + align:start position:0% +discover lots of biology but just have + + + align:start position:0% +discover lots of biology but just have +to be aware of these limitations + + align:start position:0% + + + + align:start position:0% + +let's get back to the dangers of + + align:start position:0% +let's get back to the dangers of + + + align:start position:0% +let's get back to the dangers of +dimensionality + + align:start position:0% + + + + align:start position:0% + +remember how i said in the very first + + align:start position:0% +remember how i said in the very first + + + align:start position:0% +remember how i said in the very first +lecture i gave my somewhat lame metaphor + + align:start position:0% +lecture i gave my somewhat lame metaphor + + + align:start position:0% +lecture i gave my somewhat lame metaphor +about if every base was a bead on a + + align:start position:0% +about if every base was a bead on a + + + align:start position:0% +about if every base was a bead on a +necklace and every uh + + align:start position:0% +necklace and every uh + + + align:start position:0% +necklace and every uh +necklace was worn and the necklace was + + align:start position:0% +necklace was worn and the necklace was + + + align:start position:0% +necklace was worn and the necklace was +worn by everybody in chase stadium to + + align:start position:0% +worn by everybody in chase stadium to + + + align:start position:0% +worn by everybody in chase stadium to +take on the order of a thousand shea + + align:start position:0% +take on the order of a thousand shea + + + align:start position:0% +take on the order of a thousand shea +stadiums to have + + align:start position:0% +stadiums to have + + + align:start position:0% +stadiums to have +a + + align:start position:0% +a + + + align:start position:0% +a +as many beads as we have bases in a + + align:start position:0% +as many beads as we have bases in a + + + align:start position:0% +as many beads as we have bases in a +single human genome i'll try to impress + + align:start position:0% +single human genome i'll try to impress + + + align:start position:0% +single human genome i'll try to impress +you with even though we'd like to think + + align:start position:0% +you with even though we'd like to think + + + align:start position:0% +you with even though we'd like to think +that gigabytes are + + align:start position:0% +that gigabytes are + + + align:start position:0% +that gigabytes are +are tractable it's still a pretty big + + align:start position:0% +are tractable it's still a pretty big + + + align:start position:0% +are tractable it's still a pretty big +amount so let me revisit that question + + align:start position:0% +amount so let me revisit that question + + + align:start position:0% +amount so let me revisit that question +given a thousand stadia full of people + + align:start position:0% +given a thousand stadia full of people + + + align:start position:0% +given a thousand stadia full of people +with necklaces with beads of ten colors + + align:start position:0% +with necklaces with beads of ten colors + + + align:start position:0% +with necklaces with beads of ten colors +and let's say that one and one thousand + + align:start position:0% +and let's say that one and one thousand + + + align:start position:0% +and let's say that one and one thousand +necklace beads are different every uh + + align:start position:0% +necklace beads are different every uh + + + align:start position:0% +necklace beads are different every uh +baseball season and you notice that the + + align:start position:0% +baseball season and you notice that the + + + align:start position:0% +baseball season and you notice that the +third seat on the fifth row of old games + + align:start position:0% +third seat on the fifth row of old games + + + align:start position:0% +third seat on the fifth row of old games +has a yellow bead in the middle of the + + align:start position:0% +has a yellow bead in the middle of the + + + align:start position:0% +has a yellow bead in the middle of the +necklace every year in the season opener + + align:start position:0% +necklace every year in the season opener + + + align:start position:0% +necklace every year in the season opener +at the largest new york stadium + + align:start position:0% +at the largest new york stadium + + + align:start position:0% +at the largest new york stadium +in the last 26 wins in the last 102 + + align:start position:0% +in the last 26 wins in the last 102 + + + align:start position:0% +in the last 26 wins in the last 102 +years the new york yankees have won the + + align:start position:0% +years the new york yankees have won the + + + align:start position:0% +years the new york yankees have won the +world world series in fact let me see + + align:start position:0% +world world series in fact let me see + + + align:start position:0% +world world series in fact let me see +that + + align:start position:0% +that + + + align:start position:0% +that +every time in the last 102 years that + + align:start position:0% +every time in the last 102 years that + + + align:start position:0% +every time in the last 102 years that +you the very old sports fan + + align:start position:0% +you the very old sports fan + + + align:start position:0% +you the very old sports fan +have seen that this + + align:start position:0% +have seen that this + + + align:start position:0% +have seen that this +uh equally old person is wearing a + + align:start position:0% +uh equally old person is wearing a + + + align:start position:0% +uh equally old person is wearing a +yellow bead in the same spot in the + + align:start position:0% +yellow bead in the same spot in the + + + align:start position:0% +yellow bead in the same spot in the +necklace + + align:start position:0% +necklace + + + align:start position:0% +necklace +each one of those 102 uh + + align:start position:0% +each one of those 102 uh + + + align:start position:0% +each one of those 102 uh +world series the yankees have won + + align:start position:0% +world series the yankees have won + + + align:start position:0% +world series the yankees have won +okay i'm just asserting that as a fact + + align:start position:0% +okay i'm just asserting that as a fact + + + align:start position:0% +okay i'm just asserting that as a fact +how good a bet is it that the b + + align:start position:0% +how good a bet is it that the b + + + align:start position:0% +how good a bet is it that the b +uh will be also yellow on that position + + align:start position:0% +uh will be also yellow on that position + + + align:start position:0% +uh will be also yellow on that position +next time the yankees are in the world + + align:start position:0% +next time the yankees are in the world + + + align:start position:0% +next time the yankees are in the world +series + + align:start position:0% +series + + + align:start position:0% +series +do any of you want to put money their + + align:start position:0% +do any of you want to put money their + + + align:start position:0% +do any of you want to put money their +own money on that though + + align:start position:0% + + + + align:start position:0% + +anybody give me a dollar for that bet + + align:start position:0% +anybody give me a dollar for that bet + + + align:start position:0% +anybody give me a dollar for that bet +with a million in exchange + + align:start position:0% + + + + align:start position:0% + +the billions of exchange + + align:start position:0% +the billions of exchange + + + align:start position:0% +the billions of exchange +the answer is no of course because + + align:start position:0% +the answer is no of course because + + + align:start position:0% +the answer is no of course because +it's all too easy + + align:start position:0% +it's all too easy + + + align:start position:0% +it's all too easy +after the fact to look through all the + + align:start position:0% +after the fact to look through all the + + + align:start position:0% +after the fact to look through all the +games + + align:start position:0% +games + + + align:start position:0% +games +and through all the + + align:start position:0% +and through all the + + + align:start position:0% +and through all the +millions of combinations of necklaces + + align:start position:0% +millions of combinations of necklaces + + + align:start position:0% +millions of combinations of necklaces +find one necklace + + align:start position:0% +find one necklace + + + align:start position:0% +find one necklace +that was hardly highly correlated with a + + align:start position:0% +that was hardly highly correlated with a + + + align:start position:0% +that was hardly highly correlated with a +particular outcome whether it be the + + align:start position:0% +particular outcome whether it be the + + + align:start position:0% +particular outcome whether it be the +yankee + + align:start position:0% +yankee + + + align:start position:0% +yankee +yankee or yankees winning the world + + align:start position:0% +yankee or yankees winning the world + + + align:start position:0% +yankee or yankees winning the world +series + + align:start position:0% +series + + + align:start position:0% +series +or the color of + + align:start position:0% +or the color of + + + align:start position:0% +or the color of +the coke bottle tops that day + + align:start position:0% +the coke bottle tops that day + + + align:start position:0% +the coke bottle tops that day +the point is if you have enough + + align:start position:0% +the point is if you have enough + + + align:start position:0% +the point is if you have enough +opportunities + + align:start position:0% +opportunities + + + align:start position:0% +opportunities +to test something you're only going to + + align:start position:0% +to test something you're only going to + + + align:start position:0% +to test something you're only going to +find it + + align:start position:0% +find it + + + align:start position:0% +find it +which brings us to the following point + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +if you have that much in the way of + + align:start position:0% +if you have that much in the way of + + + align:start position:0% +if you have that much in the way of +genes + + align:start position:0% +genes + + + align:start position:0% +genes +and only hundreds of patients + + align:start position:0% +and only hundreds of patients + + + align:start position:0% +and only hundreds of patients +it's going to be all too easy + + align:start position:0% +it's going to be all too easy + + + align:start position:0% +it's going to be all too easy +to find the correlation between the + + align:start position:0% +to find the correlation between the + + + align:start position:0% +to find the correlation between the +values of those set of genes + + align:start position:0% +values of those set of genes + + + align:start position:0% +values of those set of genes +and the outcome that you care about + + align:start position:0% +and the outcome that you care about + + + align:start position:0% +and the outcome that you care about +let's say + + align:start position:0% +let's say + + + align:start position:0% +let's say +um + + align:start position:0% + + + + align:start position:0% + +mortality + + align:start position:0% + + + + align:start position:0% + +please do + + align:start position:0% + + + + align:start position:0% + +that would be a good final project just + + align:start position:0% +that would be a good final project just + + + align:start position:0% +that would be a good final project just +to calculate that probability well i i i + + align:start position:0% +to calculate that probability well i i i + + + align:start position:0% +to calculate that probability well i i i +get what you're saying it you know but + + align:start position:0% +get what you're saying it you know but + + + align:start position:0% +get what you're saying it you know but +it and it would accept if wholeheartedly + + align:start position:0% +it and it would accept if wholeheartedly + + + align:start position:0% +it and it would accept if wholeheartedly +without any reservations if you were + + align:start position:0% +without any reservations if you were + + + align:start position:0% +without any reservations if you were +talking about just sort of but maybe + + align:start position:0% +talking about just sort of but maybe + + + align:start position:0% +talking about just sort of but maybe +maybe i could listen carefully + + align:start position:0% +maybe i could listen carefully + + + align:start position:0% +maybe i could listen carefully +but uh just about + + align:start position:0% +but uh just about + + + align:start position:0% +but uh just about +any necklace in the audience or whatever + + align:start position:0% +any necklace in the audience or whatever + + + align:start position:0% +any necklace in the audience or whatever +but but as you begin to i mean the + + align:start position:0% +but but as you begin to i mean the + + + align:start position:0% +but but as you begin to i mean the +example that you gave was + + align:start position:0% +example that you gave was + + + align:start position:0% +example that you gave was +you know you started to get more and + + align:start position:0% +you know you started to get more and + + + align:start position:0% +you know you started to get more and +more and more and more specific and + + align:start position:0% +more and more and more specific and + + + align:start position:0% +more and more and more specific and +if i remember correctly the more + + align:start position:0% +if i remember correctly the more + + + align:start position:0% +if i remember correctly the more +specifications that you put on a + + align:start position:0% +specifications that you put on a + + + align:start position:0% +specifications that you put on a +probability then you know it's bigger + + align:start position:0% +probability then you know it's bigger + + + align:start position:0% +probability then you know it's bigger +the harder it is + + align:start position:0% +the harder it is + + + align:start position:0% +the harder it is +right + + align:start position:0% +right + + + align:start position:0% +right +and so then you begin to get into + + align:start position:0% +and so then you begin to get into + + + align:start position:0% +and so then you begin to get into +correlations that actually + + align:start position:0% +correlations that actually + + + align:start position:0% +correlations that actually +are probabilistically significant except + + align:start position:0% +are probabilistically significant except + + + align:start position:0% +are probabilistically significant except +that you're absolutely right everything + + align:start position:0% +that you're absolutely right everything + + + align:start position:0% +that you're absolutely right everything +you said is true but you missed the + + align:start position:0% +you said is true but you missed the + + + align:start position:0% +you said is true but you missed the +wrong fact which is i have the + + align:start position:0% +wrong fact which is i have the + + + align:start position:0% +wrong fact which is i have the +opportunity now to look at all the + + align:start position:0% +opportunity now to look at all the + + + align:start position:0% +opportunity now to look at all the +people in all these thousands of stadia + + align:start position:0% +people in all these thousands of stadia + + + align:start position:0% +people in all these thousands of stadia +stadia and all i had to do was find + + align:start position:0% +stadia and all i had to do was find + + + align:start position:0% +stadia and all i had to do was find +one bead + + align:start position:0% +one bead + + + align:start position:0% +one bead +on one necklace + + align:start position:0% +on one necklace + + + align:start position:0% +on one necklace +that was that would predict the game i + + align:start position:0% +that was that would predict the game i + + + align:start position:0% +that was that would predict the game i +had millions of opportunities to to find + + align:start position:0% +had millions of opportunities to to find + + + align:start position:0% +had millions of opportunities to to find +that + + align:start position:0% +that + + + align:start position:0% +that +but no but you see that's very good time + + align:start position:0% +but no but you see that's very good time + + + align:start position:0% +but no but you see that's very good time +because you just went through that same + + align:start position:0% +because you just went through that same + + + align:start position:0% +because you just went through that same +error that all the functional genomics + + align:start position:0% +error that all the functional genomics + + + align:start position:0% +error that all the functional genomics +makes + + align:start position:0% +makes + + + align:start position:0% +makes +because after the fact i can always find + + align:start position:0% +because after the fact i can always find + + + align:start position:0% +because after the fact i can always find +with a thousand of genes some genomes up + + align:start position:0% +with a thousand of genes some genomes up + + + align:start position:0% +with a thousand of genes some genomes up +or down + + align:start position:0% +or down + + + align:start position:0% +or down +by dumb luck across the phenotype that i + + align:start position:0% +by dumb luck across the phenotype that i + + + align:start position:0% +by dumb luck across the phenotype that i +care about cancer versus + + align:start position:0% +care about cancer versus + + + align:start position:0% +care about cancer versus +bad cancer versus good cancer + + align:start position:0% +bad cancer versus good cancer + + + align:start position:0% +bad cancer versus good cancer +and that's an important intuition to + + align:start position:0% +and that's an important intuition to + + + align:start position:0% +and that's an important intuition to +have and that's i'm glad you asked the + + align:start position:0% +have and that's i'm glad you asked the + + + align:start position:0% +have and that's i'm glad you asked the +question because that's exactly it's + + align:start position:0% +question because that's exactly it's + + + align:start position:0% +question because that's exactly it's +your + + align:start position:0% +your + + + align:start position:0% +your +if indeed i had been able to + + align:start position:0% +if indeed i had been able to + + + align:start position:0% +if indeed i had been able to +um if i had a hypothesis i kept updating + + align:start position:0% +um if i had a hypothesis i kept updating + + + align:start position:0% +um if i had a hypothesis i kept updating +and every time i got stronger stronger + + align:start position:0% +and every time i got stronger stronger + + + align:start position:0% +and every time i got stronger stronger +than boy was i a genius by finding that + + align:start position:0% +than boy was i a genius by finding that + + + align:start position:0% +than boy was i a genius by finding that +yellow bead but if if after the fact + + align:start position:0% +yellow bead but if if after the fact + + + align:start position:0% +yellow bead but if if after the fact +after having done all the experiments of + + align:start position:0% +after having done all the experiments of + + + align:start position:0% +after having done all the experiments of +the 102 world series i look and search + + align:start position:0% +the 102 world series i look and search + + + align:start position:0% +the 102 world series i look and search +all the all the uh attendance to find + + align:start position:0% +all the all the uh attendance to find + + + align:start position:0% +all the all the uh attendance to find +which beat it correlates you know i'm + + align:start position:0% +which beat it correlates you know i'm + + + align:start position:0% +which beat it correlates you know i'm +gonna find it it's certain that i'm + + align:start position:0% +gonna find it it's certain that i'm + + + align:start position:0% +gonna find it it's certain that i'm +going to find such a bead but what's the + + align:start position:0% +going to find such a bead but what's the + + + align:start position:0% +going to find such a bead but what's the +likelihood that that beat is going to be + + align:start position:0% +likelihood that that beat is going to be + + + align:start position:0% +likelihood that that beat is going to be +useful for the next world series zero + + align:start position:0% +useful for the next world series zero + + + align:start position:0% +useful for the next world series zero +or something + + align:start position:0% +or something + + + align:start position:0% +or something +well you you can hypothesize the correct + + align:start position:0% +well you you can hypothesize the correct + + + align:start position:0% +well you you can hypothesize the correct +the correct approach for scientists and + + align:start position:0% +the correct approach for scientists and + + + align:start position:0% +the correct approach for scientists and +just keep impeding + + align:start position:0% +just keep impeding + + + align:start position:0% +just keep impeding +would be to hypothesize that you + + align:start position:0% +would be to hypothesize that you + + + align:start position:0% +would be to hypothesize that you +wouldn't say it is but you'd say + + align:start position:0% +wouldn't say it is but you'd say + + + align:start position:0% +wouldn't say it is but you'd say +if + + align:start position:0% +if + + + align:start position:0% +if +you know if this is truly an omni that + + align:start position:0% +you know if this is truly an omni that + + + align:start position:0% +you know if this is truly an omni that +actually exists then we should see it + + align:start position:0% +actually exists then we should see it + + + align:start position:0% +actually exists then we should see it +and then if you saw it you would be able + + align:start position:0% +and then if you saw it you would be able + + + align:start position:0% +and then if you saw it you would be able +to make a stronger statement about it + + align:start position:0% +to make a stronger statement about it + + + align:start position:0% +to make a stronger statement about it +right that is correct + + align:start position:0% +right that is correct + + + align:start position:0% +right that is correct +but that's not what happens so + + align:start position:0% + + + + align:start position:0% + +so remember this this uh this is my + + align:start position:0% +so remember this this uh this is my + + + align:start position:0% +so remember this this uh this is my +poster child for you that i gave you of + + align:start position:0% +poster child for you that i gave you of + + + align:start position:0% +poster child for you that i gave you of +large muscle lymphoma + + align:start position:0% +large muscle lymphoma + + + align:start position:0% +large muscle lymphoma +and this is i like i like this paper a + + align:start position:0% +and this is i like i like this paper a + + + align:start position:0% +and this is i like i like this paper a +lot it's groundbreaking and it says the + + align:start position:0% +lot it's groundbreaking and it says the + + + align:start position:0% +lot it's groundbreaking and it says the +list of genes that this distinguished + + align:start position:0% +list of genes that this distinguished + + + align:start position:0% +list of genes that this distinguished +being low and high clinical risk + + align:start position:0% +being low and high clinical risk + + + align:start position:0% +being low and high clinical risk +remember this one this paper all right + + align:start position:0% +remember this one this paper all right + + + align:start position:0% +remember this one this paper all right +this appeared i think in + + align:start position:0% + + + + align:start position:0% + +nature 2002 + + align:start position:0% +nature 2002 + + + align:start position:0% +nature 2002 +same disease + + align:start position:0% +same disease + + + align:start position:0% +same disease +different microarray platform + + align:start position:0% +different microarray platform + + + align:start position:0% +different microarray platform +is out of todd's group + + align:start position:0% +is out of todd's group + + + align:start position:0% +is out of todd's group +and they too find a high and low + + align:start position:0% +and they too find a high and low + + + align:start position:0% +and they too find a high and low +risk + + align:start position:0% +risk + + + align:start position:0% +risk +uh cohort that predicted by a set of + + align:start position:0% +uh cohort that predicted by a set of + + + align:start position:0% +uh cohort that predicted by a set of +genes + + align:start position:0% +genes + + + align:start position:0% +genes +i have a process point which is how the + + align:start position:0% +i have a process point which is how the + + + align:start position:0% +i have a process point which is how the +hell you produce would use essentially + + align:start position:0% +hell you produce would use essentially + + + align:start position:0% +hell you produce would use essentially +the same technique + + align:start position:0% +the same technique + + + align:start position:0% +the same technique +on the same disease and get into another + + align:start position:0% +on the same disease and get into another + + + align:start position:0% +on the same disease and get into another +first class journal this was i think + + align:start position:0% +first class journal this was i think + + + align:start position:0% +first class journal this was i think +uh + + align:start position:0% +uh + + + align:start position:0% +uh +nature + + align:start position:0% +nature + + + align:start position:0% +nature +medicine + + align:start position:0% +medicine + + + align:start position:0% +medicine +or was it new in the journal can't + + align:start position:0% +or was it new in the journal can't + + + align:start position:0% +or was it new in the journal can't +remember which new journal i think human + + align:start position:0% +remember which new journal i think human + + + align:start position:0% +remember which new journal i think human +journal + + align:start position:0% +journal + + + align:start position:0% +journal +yeah no no no that was nature medicine + + align:start position:0% +yeah no no no that was nature medicine + + + align:start position:0% +yeah no no no that was nature medicine +then you get a third paper + + align:start position:0% +then you get a third paper + + + align:start position:0% +then you get a third paper +and now i fully don't understand how + + align:start position:0% +and now i fully don't understand how + + + align:start position:0% +and now i fully don't understand how +this can happen same disease + + align:start position:0% + + + + align:start position:0% + +same question also using microarrays and + + align:start position:0% +same question also using microarrays and + + + align:start position:0% +same question also using microarrays and +they too find a high and low risk group + + align:start position:0% + + + + align:start position:0% + +what was the overlap in the set of genes + + align:start position:0% +what was the overlap in the set of genes + + + align:start position:0% +what was the overlap in the set of genes +that predicted um outcome of these + + align:start position:0% + + + + align:start position:0% + +on the order of + + align:start position:0% +on the order of + + + align:start position:0% +on the order of +20 to 30 + + align:start position:0% +20 to 30 + + + align:start position:0% +20 to 30 +depending on how you sliced it + + align:start position:0% +depending on how you sliced it + + + align:start position:0% +depending on how you sliced it +which is getting pretty close + + align:start position:0% +which is getting pretty close + + + align:start position:0% +which is getting pretty close +to chance now i think there's some + + align:start position:0% +to chance now i think there's some + + + align:start position:0% +to chance now i think there's some +signal there there clearly some signal + + align:start position:0% +signal there there clearly some signal + + + align:start position:0% +signal there there clearly some signal +there but i don't know if the how much + + align:start position:0% +there but i don't know if the how much + + + align:start position:0% +there but i don't know if the how much +of this yellow bead phenomenon we have + + align:start position:0% +of this yellow bead phenomenon we have + + + align:start position:0% +of this yellow bead phenomenon we have +which you know is basically the multiple + + align:start position:0% +which you know is basically the multiple + + + align:start position:0% +which you know is basically the multiple +hypothesis testing problem revisited in + + align:start position:0% +hypothesis testing problem revisited in + + + align:start position:0% +hypothesis testing problem revisited in +a very very ambitious way + + align:start position:0% +a very very ambitious way + + + align:start position:0% +a very very ambitious way +and the problem is + + align:start position:0% +and the problem is + + + align:start position:0% +and the problem is +this is more than an active problem i'm + + align:start position:0% +this is more than an active problem i'm + + + align:start position:0% +this is more than an active problem i'm +just irked of course that the same thing + + align:start position:0% +just irked of course that the same thing + + + align:start position:0% +just irked of course that the same thing +got published three times in first class + + align:start position:0% +got published three times in first class + + + align:start position:0% +got published three times in first class +journals the real problem is that + + align:start position:0% +journals the real problem is that + + + align:start position:0% +journals the real problem is that +patients are being stratified today in + + align:start position:0% +patients are being stratified today in + + + align:start position:0% +patients are being stratified today in +oncology protocols based on expression + + align:start position:0% +oncology protocols based on expression + + + align:start position:0% +oncology protocols based on expression +profiles so you know that if they're not + + align:start position:0% +profiles so you know that if they're not + + + align:start position:0% +profiles so you know that if they're not +taking this multiple hypothesis testing + + align:start position:0% +taking this multiple hypothesis testing + + + align:start position:0% +taking this multiple hypothesis testing +really to heart + + align:start position:0% +really to heart + + + align:start position:0% +really to heart +patients are being + + align:start position:0% +patients are being + + + align:start position:0% +patients are being +stratified the wrong way + + align:start position:0% +stratified the wrong way + + + align:start position:0% +stratified the wrong way +uh + + align:start position:0% +uh + + + align:start position:0% +uh +based on a subset of genes + + align:start position:0% +based on a subset of genes + + + align:start position:0% +based on a subset of genes +and remember i told you that you could + + align:start position:0% +and remember i told you that you could + + + align:start position:0% +and remember i told you that you could +get together as groups of two for a + + align:start position:0% +get together as groups of two for a + + + align:start position:0% +get together as groups of two for a +final product i would strongly urge at + + align:start position:0% +final product i would strongly urge at + + + align:start position:0% +final product i would strongly urge at +least one group to think about looking + + align:start position:0% +least one group to think about looking + + + align:start position:0% +least one group to think about looking +at something like this + + align:start position:0% +at something like this + + + align:start position:0% +at something like this +perhaps this very study because no one i + + align:start position:0% +perhaps this very study because no one i + + + align:start position:0% +perhaps this very study because no one i +to my knowledge yet has actually + + align:start position:0% +to my knowledge yet has actually + + + align:start position:0% +to my knowledge yet has actually +published this and uh you know shown + + align:start position:0% +published this and uh you know shown + + + align:start position:0% +published this and uh you know shown +that emperor is not at least wearing + + align:start position:0% +that emperor is not at least wearing + + + align:start position:0% +that emperor is not at least wearing +enough clothes + + align:start position:0% +enough clothes + + + align:start position:0% +enough clothes +what was overlap and what was the + + align:start position:0% +what was overlap and what was the + + + align:start position:0% +what was overlap and what was the +characteristic of the genes that + + align:start position:0% +characteristic of the genes that + + + align:start position:0% +characteristic of the genes that +overlapped and across those and could + + align:start position:0% +overlapped and across those and could + + + align:start position:0% +overlapped and across those and could +you in fact come up with a robust uh + + align:start position:0% +you in fact come up with a robust uh + + + align:start position:0% +you in fact come up with a robust uh +more robust uh set of predictors based + + align:start position:0% +more robust uh set of predictors based + + + align:start position:0% +more robust uh set of predictors based +on + + align:start position:0% +on + + + align:start position:0% +on +those three studies but that's highly + + align:start position:0% +those three studies but that's highly + + + align:start position:0% +those three studies but that's highly +problematic and i think most of the + + align:start position:0% +problematic and i think most of the + + + align:start position:0% +problematic and i think most of the +fault is in this overfitting problem + + align:start position:0% + + + + align:start position:0% + +so why are these studies inconsistent + + align:start position:0% +so why are these studies inconsistent + + + align:start position:0% +so why are these studies inconsistent +well also there are different + + align:start position:0% +well also there are different + + + align:start position:0% +well also there are different +populations not all humans are the same + + align:start position:0% +populations not all humans are the same + + + align:start position:0% +populations not all humans are the same +and this brings me to another point + + align:start position:0% +and this brings me to another point + + + align:start position:0% +and this brings me to another point +which is why all of a sudden is it okay + + align:start position:0% +which is why all of a sudden is it okay + + + align:start position:0% +which is why all of a sudden is it okay +to do 100 patients and do a clinical + + align:start position:0% +to do 100 patients and do a clinical + + + align:start position:0% +to do 100 patients and do a clinical +study whereas for everything else that + + align:start position:0% +study whereas for everything else that + + + align:start position:0% +study whereas for everything else that +we've ever did with much fewer variables + + align:start position:0% +we've ever did with much fewer variables + + + align:start position:0% +we've ever did with much fewer variables +we have to get thousands of patients the + + align:start position:0% +we have to get thousands of patients the + + + align:start position:0% +we have to get thousands of patients the +answer of course is because we have + + align:start position:0% +answer of course is because we have + + + align:start position:0% +answer of course is because we have +limited resources and so on but i think + + align:start position:0% +limited resources and so on but i think + + + align:start position:0% +limited resources and so on but i think +it's that somewhat delusional to think + + align:start position:0% +it's that somewhat delusional to think + + + align:start position:0% +it's that somewhat delusional to think +that we could get + + align:start position:0% +that we could get + + + align:start position:0% +that we could get +uh + + align:start position:0% +uh + + + align:start position:0% +uh +as good + + align:start position:0% +as good + + + align:start position:0% +as good +predictors with all hundreds of patients + + align:start position:0% +predictors with all hundreds of patients + + + align:start position:0% +predictors with all hundreds of patients +as we could get with thousands now it's + + align:start position:0% +as we could get with thousands now it's + + + align:start position:0% +as we could get with thousands now it's +true that we can characterize two groups + + align:start position:0% +true that we can characterize two groups + + + align:start position:0% +true that we can characterize two groups +because we have all these thousands of + + align:start position:0% +because we have all these thousands of + + + align:start position:0% +because we have all these thousands of +genes to measure and we can measure + + align:start position:0% +genes to measure and we can measure + + + align:start position:0% +genes to measure and we can measure +broad patterns in fact botstein who's + + align:start position:0% +broad patterns in fact botstein who's + + + align:start position:0% +broad patterns in fact botstein who's +one of the uh + + align:start position:0% +one of the uh + + + align:start position:0% +one of the uh +leaders in this area never pretends that + + align:start position:0% +leaders in this area never pretends that + + + align:start position:0% +leaders in this area never pretends that +any single gene is a reliable + + align:start position:0% +any single gene is a reliable + + + align:start position:0% +any single gene is a reliable +measurement it's he says it's just + + align:start position:0% +measurement it's he says it's just + + + align:start position:0% +measurement it's he says it's just +giving you an overall impression of the + + align:start position:0% +giving you an overall impression of the + + + align:start position:0% +giving you an overall impression of the +biology the pattern that's going on but + + align:start position:0% +biology the pattern that's going on but + + + align:start position:0% +biology the pattern that's going on but +when you start then taking a set of + + align:start position:0% +when you start then taking a set of + + + align:start position:0% +when you start then taking a set of +specific genes and then hanging + + align:start position:0% +specific genes and then hanging + + + align:start position:0% +specific genes and then hanging +someone's prognosis on that then you + + align:start position:0% +someone's prognosis on that then you + + + align:start position:0% +someone's prognosis on that then you +know you're you're perhaps getting close + + align:start position:0% +know you're you're perhaps getting close + + + align:start position:0% +know you're you're perhaps getting close +to a line where you have to be a lot + + align:start position:0% +to a line where you have to be a lot + + + align:start position:0% +to a line where you have to be a lot +more methodologically strict understand + + align:start position:0% +more methodologically strict understand + + + align:start position:0% +more methodologically strict understand +what is what is the + + align:start position:0% +what is what is the + + + align:start position:0% +what is what is the +what are the power and significance of + + align:start position:0% +what are the power and significance of + + + align:start position:0% +what are the power and significance of +your studies + + align:start position:0% +your studies + + + align:start position:0% +your studies +again some of them are using different + + align:start position:0% +again some of them are using different + + + align:start position:0% +again some of them are using different +measurement platforms there's + + align:start position:0% +measurement platforms there's + + + align:start position:0% +measurement platforms there's +overfitting and some use of indirect + + align:start position:0% +overfitting and some use of indirect + + + align:start position:0% +overfitting and some use of indirect +measures + + align:start position:0% +measures + + + align:start position:0% +measures +so that's exactly where i wanted to end + + align:start position:0% +so that's exactly where i wanted to end + + + align:start position:0% +so that's exactly where i wanted to end +up today + + align:start position:0% + + + + align:start position:0% + +i want to give you a heads up that soon + + align:start position:0% +i want to give you a heads up that soon + + + align:start position:0% +i want to give you a heads up that soon +you're going to be getting your first + + align:start position:0% +you're going to be getting your first + + + align:start position:0% +you're going to be getting your first +problem set it's going to be a very + + align:start position:0% +problem set it's going to be a very + + + align:start position:0% +problem set it's going to be a very +simple one which is it's gonna be a + + align:start position:0% +simple one which is it's gonna be a + + + align:start position:0% +simple one which is it's gonna be a +treasure hunt through all the um through + + align:start position:0% +treasure hunt through all the um through + + + align:start position:0% +treasure hunt through all the um through +all the um national uh databases to + + align:start position:0% +all the um national uh databases to + + + align:start position:0% +all the um national uh databases to +allow you to just make sure you touch + + align:start position:0% +allow you to just make sure you touch + + + align:start position:0% +allow you to just make sure you touch +all the databases and so that you can + + align:start position:0% +all the databases and so that you can + + + align:start position:0% +all the databases and so that you can +be a modern biological resource + + align:start position:0% +be a modern biological resource + + + align:start position:0% +be a modern biological resource +researcher and find out what you need to + + align:start position:0% +researcher and find out what you need to + + + align:start position:0% +researcher and find out what you need to +find out about the different biological + + align:start position:0% +find out about the different biological + + + align:start position:0% +find out about the different biological +uh + + align:start position:0% +uh + + + align:start position:0% +uh +databases + + align:start position:0% +databases + + + align:start position:0% +databases +uh later the other problems that's going + + align:start position:0% +uh later the other problems that's going + + + align:start position:0% +uh later the other problems that's going +to be one around clustering and + + align:start position:0% +to be one around clustering and + + + align:start position:0% +to be one around clustering and +classification just make sure you can do + + align:start position:0% +classification just make sure you can do + + + align:start position:0% +classification just make sure you can do +it uh correctly but i'd like you to + + align:start position:0% +it uh correctly but i'd like you to + + + align:start position:0% +it uh correctly but i'd like you to +start thinking about your your final + + align:start position:0% +start thinking about your your final + + + align:start position:0% +start thinking about your your final +projects and it's now uh mid february + + align:start position:0% +projects and it's now uh mid february + + + align:start position:0% +projects and it's now uh mid february +again i really would like you to have um + + align:start position:0% +again i really would like you to have um + + + align:start position:0% +again i really would like you to have um +settle down your final project no later + + align:start position:0% +settle down your final project no later + + + align:start position:0% +settle down your final project no later +by then mid + + align:start position:0% +by then mid + + + align:start position:0% +by then mid +um + + align:start position:0% +um + + + align:start position:0% +um +march so therefore if uh you're having + + align:start position:0% +march so therefore if uh you're having + + + align:start position:0% +march so therefore if uh you're having +any doubts that you have that you're + + align:start position:0% +any doubts that you have that you're + + + align:start position:0% +any doubts that you have that you're +honing in on a project please talk to me + + align:start position:0% +honing in on a project please talk to me + + + align:start position:0% +honing in on a project please talk to me +earlier than later + + align:start position:0% +earlier than later + + + align:start position:0% +earlier than later +and there's nothing wrong in fact it's + + align:start position:0% +and there's nothing wrong in fact it's + + + align:start position:0% +and there's nothing wrong in fact it's +just opposites it's great if you can + + align:start position:0% +just opposites it's great if you can + + + align:start position:0% +just opposites it's great if you can +think of a problem that you would + + align:start position:0% +think of a problem that you would + + + align:start position:0% +think of a problem that you would +actually like to put the research on + + align:start position:0% +actually like to put the research on + + + align:start position:0% +actually like to put the research on +there's nothing more motivated than that + + align:start position:0% +there's nothing more motivated than that + + + align:start position:0% +there's nothing more motivated than that +to + + align:start position:0% +to + + + align:start position:0% +to +address \ No newline at end of file diff --git a/VrMHA3yX_QI.txt b/VrMHA3yX_QI.txt new file mode 100644 index 0000000000000000000000000000000000000000..52585f9acccde9eae18c7f7f7053e7727520add1 --- /dev/null +++ b/VrMHA3yX_QI.txt @@ -0,0 +1,8483 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +well what we're going to do today is + + align:start position:0% +well what we're going to do today is + + + align:start position:0% +well what we're going to do today is +climb a pretty big mountain because + + align:start position:0% +climb a pretty big mountain because + + + align:start position:0% +climb a pretty big mountain because +we're going to go from a neuron net with + + align:start position:0% +we're going to go from a neuron net with + + + align:start position:0% +we're going to go from a neuron net with +two + + align:start position:0% +two + + + align:start position:0% +two +parameters to discussing the kind of + + align:start position:0% +parameters to discussing the kind of + + + align:start position:0% +parameters to discussing the kind of +neural Nets in which people end up + + align:start position:0% +neural Nets in which people end up + + + align:start position:0% +neural Nets in which people end up +dealing with + + align:start position:0% +dealing with + + + align:start position:0% +dealing with +60 60 million + + align:start position:0% +60 60 million + + + align:start position:0% +60 60 million +parameters so it's going to be a pretty + + align:start position:0% +parameters so it's going to be a pretty + + + align:start position:0% +parameters so it's going to be a pretty +big + + align:start position:0% +big + + + align:start position:0% +big +jump but along the way our couple things + + align:start position:0% +jump but along the way our couple things + + + align:start position:0% +jump but along the way our couple things +I wanted to uh underscore from our + + align:start position:0% +I wanted to uh underscore from our + + + align:start position:0% +I wanted to uh underscore from our +previous + + align:start position:0% +previous + + + align:start position:0% +previous +discussion last time I I tried to + + align:start position:0% +discussion last time I I tried to + + + align:start position:0% +discussion last time I I tried to +develop some intuition for the kinds of + + align:start position:0% +develop some intuition for the kinds of + + + align:start position:0% +develop some intuition for the kinds of +formulas that you use to actually do the + + align:start position:0% +formulas that you use to actually do the + + + align:start position:0% +formulas that you use to actually do the +calculations in a small neural net about + + align:start position:0% +calculations in a small neural net about + + + align:start position:0% +calculations in a small neural net about +how the weights are going to change and + + align:start position:0% +how the weights are going to change and + + + align:start position:0% +how the weights are going to change and +the main thing I tried to emphasize is + + align:start position:0% +the main thing I tried to emphasize is + + + align:start position:0% +the main thing I tried to emphasize is +that when you have a a neural net like + + align:start position:0% +that when you have a a neural net like + + + align:start position:0% +that when you have a a neural net like +this one + + align:start position:0% + + + + align:start position:0% + +everything is sort of + + align:start position:0% +everything is sort of + + + align:start position:0% +everything is sort of +divided uh in each + + align:start position:0% +divided uh in each + + + align:start position:0% +divided uh in each +column you can't have the Performance + + align:start position:0% +column you can't have the Performance + + + align:start position:0% +column you can't have the Performance +Based on this output affect some weight + + align:start position:0% +Based on this output affect some weight + + + align:start position:0% +Based on this output affect some weight +change back here without going through + + align:start position:0% +change back here without going through + + + align:start position:0% +change back here without going through +this finite number of output variables + + align:start position:0% +this finite number of output variables + + + align:start position:0% +this finite number of output variables +the + + align:start position:0% +the + + + align:start position:0% +the +y1s by the way there's no Y2 and y4 this + + align:start position:0% +y1s by the way there's no Y2 and y4 this + + + align:start position:0% +y1s by the way there's no Y2 and y4 this +is there's no Y2 and Y3 the dealing with + + align:start position:0% +is there's no Y2 and Y3 the dealing with + + + align:start position:0% +is there's no Y2 and Y3 the dealing with +this is a really a notational nightmare + + align:start position:0% +this is a really a notational nightmare + + + align:start position:0% +this is a really a notational nightmare +and I spent a little time a lot of time + + align:start position:0% +and I spent a little time a lot of time + + + align:start position:0% +and I spent a little time a lot of time +yesterday trying to clean it up a little + + align:start position:0% +yesterday trying to clean it up a little + + + align:start position:0% +yesterday trying to clean it up a little +bit but basically what I'm trying to say + + align:start position:0% +bit but basically what I'm trying to say + + + align:start position:0% +bit but basically what I'm trying to say +has nothing to do with the notation I've + + align:start position:0% +has nothing to do with the notation I've + + + align:start position:0% +has nothing to do with the notation I've +used but rather with the fact that + + align:start position:0% +used but rather with the fact that + + + align:start position:0% +used but rather with the fact that +there's a limited number of ways in + + align:start position:0% +there's a limited number of ways in + + + align:start position:0% +there's a limited number of ways in +which that can influence this even + + align:start position:0% +which that can influence this even + + + align:start position:0% +which that can influence this even +though the number of paths through this + + align:start position:0% +though the number of paths through this + + + align:start position:0% +though the number of paths through this +network can be growing + + align:start position:0% +network can be growing + + + align:start position:0% +network can be growing +exponential so those equations + + align:start position:0% +exponential so those equations + + + align:start position:0% +exponential so those equations +underneath are equations that are derive + + align:start position:0% +underneath are equations that are derive + + + align:start position:0% +underneath are equations that are derive +from trying to figure out how the output + + align:start position:0% +from trying to figure out how the output + + + align:start position:0% +from trying to figure out how the output +performance + + align:start position:0% +performance + + + align:start position:0% +performance +depends on some of these weights back + + align:start position:0% +depends on some of these weights back + + + align:start position:0% +depends on some of these weights back +here and what I've calculated is I've + + align:start position:0% +here and what I've calculated is I've + + + align:start position:0% +here and what I've calculated is I've +calculated the dependence of the + + align:start position:0% +calculated the dependence of the + + + align:start position:0% +calculated the dependence of the +performance on W1 going that way and I + + align:start position:0% +performance on W1 going that way and I + + + align:start position:0% +performance on W1 going that way and I +and I've also calculated the dependence + + align:start position:0% +and I've also calculated the dependence + + + align:start position:0% +and I've also calculated the dependence +on + + align:start position:0% +on + + + align:start position:0% +on +performance of performance on W1 going + + align:start position:0% +performance of performance on W1 going + + + align:start position:0% +performance of performance on W1 going +W1 going that way so that's one of the + + align:start position:0% +W1 going that way so that's one of the + + + align:start position:0% +W1 going that way so that's one of the +equations I've got down there and + + align:start position:0% +equations I've got down there and + + + align:start position:0% +equations I've got down there and +another one deals with W3 and it + + align:start position:0% +another one deals with W3 and it + + + align:start position:0% +another one deals with W3 and it +involves going + + align:start position:0% + + + + align:start position:0% + +both this + + align:start position:0% +both this + + + align:start position:0% +both this +way and this way and all I've done in in + + align:start position:0% +way and this way and all I've done in in + + + align:start position:0% +way and this way and all I've done in in +both cases in all four cases is just + + align:start position:0% +both cases in all four cases is just + + + align:start position:0% +both cases in all four cases is just +take the partial derivative of + + align:start position:0% +take the partial derivative of + + + align:start position:0% +take the partial derivative of +performance with respect to those + + align:start position:0% +performance with respect to those + + + align:start position:0% +performance with respect to those +weights and use the chain rule to expand + + align:start position:0% +weights and use the chain rule to expand + + + align:start position:0% +weights and use the chain rule to expand +it and when I do + + align:start position:0% + + + + align:start position:0% + +that this is the stuff I get and that's + + align:start position:0% +that this is the stuff I get and that's + + + align:start position:0% +that this is the stuff I get and that's +just a whole bunch of partial + + align:start position:0% +just a whole bunch of partial + + + align:start position:0% +just a whole bunch of partial +derivatives but if you look at it and + + align:start position:0% +derivatives but if you look at it and + + + align:start position:0% +derivatives but if you look at it and +let it sing a little bit to you what you + + align:start position:0% +let it sing a little bit to you what you + + + align:start position:0% +let it sing a little bit to you what you +see is that there's a lot of redundancy + + align:start position:0% +see is that there's a lot of redundancy + + + align:start position:0% +see is that there's a lot of redundancy +in the + + align:start position:0% +in the + + + align:start position:0% +in the +computation so for + + align:start position:0% +computation so for + + + align:start position:0% +computation so for +example this guy here partial of + + align:start position:0% +example this guy here partial of + + + align:start position:0% +example this guy here partial of +performance with spec + + align:start position:0% +performance with spec + + + align:start position:0% +performance with spec +W1 depends on both Paths of + + align:start position:0% +W1 depends on both Paths of + + + align:start position:0% +W1 depends on both Paths of +course but look at the first elements + + align:start position:0% +course but look at the first elements + + + align:start position:0% +course but look at the first elements +here these guys right + + align:start position:0% +here these guys right + + + align:start position:0% +here these guys right +here and look at the first elements in + + align:start position:0% +here and look at the first elements in + + + align:start position:0% +here and look at the first elements in +the expression for calculating the + + align:start position:0% +the expression for calculating the + + + align:start position:0% +the expression for calculating the +partial derivative of performance + + align:start position:0% +partial derivative of performance + + + align:start position:0% +partial derivative of performance +respective + + align:start position:0% +respective + + + align:start position:0% +respective +W3 these guys + + align:start position:0% + + + + align:start position:0% + +they're the + + align:start position:0% +they're the + + + align:start position:0% +they're the +same and not only that if you look + + align:start position:0% +same and not only that if you look + + + align:start position:0% +same and not only that if you look +inside these + + align:start position:0% +inside these + + + align:start position:0% +inside these +expressions and look at this particular + + align:start position:0% +expressions and look at this particular + + + align:start position:0% +expressions and look at this particular +piece + + align:start position:0% +piece + + + align:start position:0% +piece +here you see that that is an expression + + align:start position:0% +here you see that that is an expression + + + align:start position:0% +here you see that that is an expression +that was needed in order to calculate + + align:start position:0% +that was needed in order to calculate + + + align:start position:0% +that was needed in order to calculate +one of the downstream weights changes + + align:start position:0% +one of the downstream weights changes + + + align:start position:0% +one of the downstream weights changes +one of the downstream + + align:start position:0% +one of the downstream + + + align:start position:0% +one of the downstream +weights but it happens to be the same + + align:start position:0% +weights but it happens to be the same + + + align:start position:0% +weights but it happens to be the same +thing as you see over here + + align:start position:0% +thing as you see over here + + + align:start position:0% +thing as you see over here +here and likewise this + + align:start position:0% +here and likewise this + + + align:start position:0% +here and likewise this +piece is the + + align:start position:0% +piece is the + + + align:start position:0% +piece is the +same is the same + + align:start position:0% +same is the same + + + align:start position:0% +same is the same +thing you see over + + align:start position:0% + + + + align:start position:0% + +here so each time you move further and + + align:start position:0% +here so each time you move further and + + + align:start position:0% +here so each time you move further and +further back from the outputs toward the + + align:start position:0% +further back from the outputs toward the + + + align:start position:0% +further back from the outputs toward the +inputs you're reusing a lot of + + align:start position:0% +inputs you're reusing a lot of + + + align:start position:0% +inputs you're reusing a lot of +computation that you've already + + align:start position:0% +computation that you've already + + + align:start position:0% +computation that you've already +done so I've trying to find find a way + + align:start position:0% +done so I've trying to find find a way + + + align:start position:0% +done so I've trying to find find a way +to sloganizer + + align:start position:0% + + + + align:start position:0% + +what's done is done and cannot be no no + + align:start position:0% +what's done is done and cannot be no no + + + align:start position:0% +what's done is done and cannot be no no +no that's not quite right is it it's um + + align:start position:0% +no that's not quite right is it it's um + + + align:start position:0% +no that's not quite right is it it's um +what's computed is computed and need not + + align:start position:0% +what's computed is computed and need not + + + align:start position:0% +what's computed is computed and need not +be + + align:start position:0% +be + + + align:start position:0% +be +recomputed okay so that's what's going + + align:start position:0% +recomputed okay so that's what's going + + + align:start position:0% +recomputed okay so that's what's going +on here and that's why this is a + + align:start position:0% +on here and that's why this is a + + + align:start position:0% +on here and that's why this is a +calculation that's linear in the + + align:start position:0% +calculation that's linear in the + + + align:start position:0% +calculation that's linear in the +depth the depth of the neural net not + + align:start position:0% +depth the depth of the neural net not + + + align:start position:0% +depth the depth of the neural net not +exponential there's another thing I + + align:start position:0% +exponential there's another thing I + + + align:start position:0% +exponential there's another thing I +wanted to point out in connection with + + align:start position:0% +wanted to point out in connection with + + + align:start position:0% +wanted to point out in connection with +uh these neural + + align:start position:0% +uh these neural + + + align:start position:0% +uh these neural +Nets and that has to do with what + + align:start position:0% +Nets and that has to do with what + + + align:start position:0% +Nets and that has to do with what +happens when we look at a single + + align:start position:0% +happens when we look at a single + + + align:start position:0% +happens when we look at a single +neuron and note that what we've got is + + align:start position:0% +neuron and note that what we've got is + + + align:start position:0% +neuron and note that what we've got is +we've got a bunch of Weights which are + + align:start position:0% +we've got a bunch of Weights which are + + + align:start position:0% +we've got a bunch of Weights which are +multiplied times a bunch of inputs like + + align:start position:0% + + + + align:start position:0% + +so and then those are all summed up in a + + align:start position:0% +so and then those are all summed up in a + + + align:start position:0% +so and then those are all summed up in a +summing + + align:start position:0% +summing + + + align:start position:0% +summing +box before they enter some kind of + + align:start position:0% +box before they enter some kind of + + + align:start position:0% +box before they enter some kind of +nonlinearity in our case a sigmoid + + align:start position:0% +nonlinearity in our case a sigmoid + + + align:start position:0% +nonlinearity in our case a sigmoid +function + + align:start position:0% +function + + + align:start position:0% +function +but if I ask you to write down the + + align:start position:0% +but if I ask you to write down the + + + align:start position:0% +but if I ask you to write down the +expression for the value we've got there + + align:start position:0% +expression for the value we've got there + + + align:start position:0% +expression for the value we've got there +what is it well it's just the + + align:start position:0% +what is it well it's just the + + + align:start position:0% +what is it well it's just the +sum of the W's times the + + align:start position:0% + + + + align:start position:0% + +X's what's + + align:start position:0% + + + + align:start position:0% + +that that's a DOT + + align:start position:0% +that that's a DOT + + + align:start position:0% +that that's a DOT +product remember a few lectures ago I + + align:start position:0% +product remember a few lectures ago I + + + align:start position:0% +product remember a few lectures ago I +said that some of us believe that the + + align:start position:0% +said that some of us believe that the + + + align:start position:0% +said that some of us believe that the +dot product is a fundamental calculation + + align:start position:0% +dot product is a fundamental calculation + + + align:start position:0% +dot product is a fundamental calculation +that takes place in our heads + + align:start position:0% +that takes place in our heads + + + align:start position:0% +that takes place in our heads +so this is why we think + + align:start position:0% +so this is why we think + + + align:start position:0% +so this is why we think +so if neural Nets are doing anything + + align:start position:0% +so if neural Nets are doing anything + + + align:start position:0% +so if neural Nets are doing anything +like this then there's a DOT product + + align:start position:0% +like this then there's a DOT product + + + align:start position:0% +like this then there's a DOT product +between some weights and some input + + align:start position:0% +between some weights and some input + + + align:start position:0% +between some weights and some input +values now it's a funny kind of dot + + align:start position:0% +values now it's a funny kind of dot + + + align:start position:0% +values now it's a funny kind of dot +product + + align:start position:0% +product + + + align:start position:0% +product +because in the models that we've been + + align:start position:0% +because in the models that we've been + + + align:start position:0% +because in the models that we've been +using these input variables are all or + + align:start position:0% +using these input variables are all or + + + align:start position:0% +using these input variables are all or +none or zero or one but that's okay I + + align:start position:0% +none or zero or one but that's okay I + + + align:start position:0% +none or zero or one but that's okay I +have an in good authority that there are + + align:start position:0% +have an in good authority that there are + + + align:start position:0% +have an in good authority that there are +neurons in our head for which the values + + align:start position:0% +neurons in our head for which the values + + + align:start position:0% +neurons in our head for which the values +that are produced are not exactly all or + + align:start position:0% +that are produced are not exactly all or + + + align:start position:0% +that are produced are not exactly all or +none but rather have a kind of + + align:start position:0% +none but rather have a kind of + + + align:start position:0% +none but rather have a kind of +proportionality to them so you get a + + align:start position:0% +proportionality to them so you get a + + + align:start position:0% +proportionality to them so you get a +real dot product type of operation out + + align:start position:0% +real dot product type of operation out + + + align:start position:0% +real dot product type of operation out +of + + align:start position:0% +of + + + align:start position:0% +of +that so that's by way of a couple of + + align:start position:0% +that so that's by way of a couple of + + + align:start position:0% +that so that's by way of a couple of +asides that I wanted to underscore + + align:start position:0% +asides that I wanted to underscore + + + align:start position:0% +asides that I wanted to underscore +before we get into the um Center of + + align:start position:0% +before we get into the um Center of + + + align:start position:0% +before we get into the um Center of +today's discussion which will be to uh + + align:start position:0% +today's discussion which will be to uh + + + align:start position:0% +today's discussion which will be to uh +talk about these so-called deep + + align:start position:0% +talk about these so-called deep + + + align:start position:0% +talk about these so-called deep +Nets now let's see what's a deep net + + align:start position:0% +Nets now let's see what's a deep net + + + align:start position:0% +Nets now let's see what's a deep net +do + + align:start position:0% +do + + + align:start position:0% +do +well from last time you know that a deep + + align:start position:0% +well from last time you know that a deep + + + align:start position:0% +well from last time you know that a deep +net does that sort of + + align:start position:0% +net does that sort of + + + align:start position:0% +net does that sort of +thing and it's interesting to look at + + align:start position:0% +thing and it's interesting to look at + + + align:start position:0% +thing and it's interesting to look at +some of the uh some of the offerings + + align:start position:0% +some of the uh some of the offerings + + + align:start position:0% +some of the uh some of the offerings +here by the way how how good was this uh + + align:start position:0% +here by the way how how good was this uh + + + align:start position:0% +here by the way how how good was this uh +performance in 2012 well it turned out + + align:start position:0% +performance in 2012 well it turned out + + + align:start position:0% +performance in 2012 well it turned out +that + + align:start position:0% +that + + + align:start position:0% +that +the fraction of the time that the + + align:start position:0% +the fraction of the time that the + + + align:start position:0% +the fraction of the time that the +system had the right answer in its top + + align:start position:0% +system had the right answer in its top + + + align:start position:0% +system had the right answer in its top +five choices was about + + align:start position:0% +five choices was about + + + align:start position:0% +five choices was about +15% and the fraction of the time that it + + align:start position:0% +15% and the fraction of the time that it + + + align:start position:0% +15% and the fraction of the time that it +got exactly the right answer as its top + + align:start position:0% +got exactly the right answer as its top + + + align:start position:0% +got exactly the right answer as its top +pick was about 37% uh error 15% error if + + align:start position:0% +pick was about 37% uh error 15% error if + + + align:start position:0% +pick was about 37% uh error 15% error if +you count it as an error if + + align:start position:0% +you count it as an error if + + + align:start position:0% +you count it as an error if +it's what am I saying you got it right + + align:start position:0% +it's what am I saying you got it right + + + align:start position:0% +it's what am I saying you got it right +if you got it in the top five and the + + align:start position:0% +if you got it in the top five and the + + + align:start position:0% +if you got it in the top five and the +error rate on that calculation about 15% + + align:start position:0% +error rate on that calculation about 15% + + + align:start position:0% +error rate on that calculation about 15% +if you say you only get it right if you + + align:start position:0% +if you say you only get it right if you + + + align:start position:0% +if you say you only get it right if you +got it if it was your Top Choice then + + align:start position:0% +got it if it was your Top Choice then + + + align:start position:0% +got it if it was your Top Choice then +the error rate was about + + align:start position:0% +the error rate was about + + + align:start position:0% +the error rate was about +37% so pretty good uh especially since + + align:start position:0% +37% so pretty good uh especially since + + + align:start position:0% +37% so pretty good uh especially since +some of these things are highly + + align:start position:0% +some of these things are highly + + + align:start position:0% +some of these things are highly +ambiguous even to + + align:start position:0% +ambiguous even to + + + align:start position:0% +ambiguous even to +us and what kind of a system did that + + align:start position:0% +us and what kind of a system did that + + + align:start position:0% +us and what kind of a system did that +well it wasn't um it wasn't uh one that + + align:start position:0% +well it wasn't um it wasn't uh one that + + + align:start position:0% +well it wasn't um it wasn't uh one that +looked exactly like that although that + + align:start position:0% +looked exactly like that although that + + + align:start position:0% +looked exactly like that although that +is the essence of it the system actually + + align:start position:0% +is the essence of it the system actually + + + align:start position:0% +is the essence of it the system actually +looked like that there's quite a lot of + + align:start position:0% +looked like that there's quite a lot of + + + align:start position:0% +looked like that there's quite a lot of +stuff in there and what I'm going to + + align:start position:0% +stuff in there and what I'm going to + + + align:start position:0% +stuff in there and what I'm going to +talk about is not exactly this system + + align:start position:0% +talk about is not exactly this system + + + align:start position:0% +talk about is not exactly this system +but I'm going to talk about the stuff of + + align:start position:0% +but I'm going to talk about the stuff of + + + align:start position:0% +but I'm going to talk about the stuff of +which such such systems are made because + + align:start position:0% +which such such systems are made because + + + align:start position:0% +which such such systems are made because +there's nothing particularly special + + align:start position:0% +there's nothing particularly special + + + align:start position:0% +there's nothing particularly special +about this it just happens to be a + + align:start position:0% +about this it just happens to be a + + + align:start position:0% +about this it just happens to be a +particular assembly of components that + + align:start position:0% +particular assembly of components that + + + align:start position:0% +particular assembly of components that +tend to reappear when everyone when + + align:start position:0% +tend to reappear when everyone when + + + align:start position:0% +tend to reappear when everyone when +anyone does this sort of neural net + + align:start position:0% +anyone does this sort of neural net + + + align:start position:0% +anyone does this sort of neural net +stuff so let me explain that uh This Way + + align:start position:0% +stuff so let me explain that uh This Way + + + align:start position:0% +stuff so let me explain that uh This Way +first thing we I need to talk about is + + align:start position:0% +first thing we I need to talk about is + + + align:start position:0% +first thing we I need to talk about is +the concept of + + align:start position:0% +the concept of + + + align:start position:0% +the concept of +um well I don't like the term it's + + align:start position:0% +um well I don't like the term it's + + + align:start position:0% +um well I don't like the term it's +called convolution I don't like the term + + align:start position:0% +called convolution I don't like the term + + + align:start position:0% +called convolution I don't like the term +because you know in in the second best + + align:start position:0% +because you know in in the second best + + + align:start position:0% +because you know in in the second best +course at The Institute signals and + + align:start position:0% +course at The Institute signals and + + + align:start position:0% +course at The Institute signals and +systems you learn about impulse + + align:start position:0% +systems you learn about impulse + + + align:start position:0% +systems you learn about impulse +responses and convolution integrals and + + align:start position:0% +responses and convolution integrals and + + + align:start position:0% +responses and convolution integrals and +stuff like that and this hints at that + + align:start position:0% +stuff like that and this hints at that + + + align:start position:0% +stuff like that and this hints at that +but it's not the same thing because + + align:start position:0% +but it's not the same thing because + + + align:start position:0% +but it's not the same thing because +there's no there's no memory involved in + + align:start position:0% +there's no there's no memory involved in + + + align:start position:0% +there's no there's no memory involved in +in what's going on as these signals are + + align:start position:0% +in what's going on as these signals are + + + align:start position:0% +in what's going on as these signals are +processed but they call it convolutional + + align:start position:0% +processed but they call it convolutional + + + align:start position:0% +processed but they call it convolutional +don't that's anyway so here you are + + align:start position:0% +don't that's anyway so here you are + + + align:start position:0% +don't that's anyway so here you are +you've got some kind of + + align:start position:0% +you've got some kind of + + + align:start position:0% +you've got some kind of +image and even with lots of uh computing + + align:start position:0% +image and even with lots of uh computing + + + align:start position:0% +image and even with lots of uh computing +power uh and gpus and all that sort of + + align:start position:0% +power uh and gpus and all that sort of + + + align:start position:0% +power uh and gpus and all that sort of +stuff we're not talking about images + + align:start position:0% +stuff we're not talking about images + + + align:start position:0% +stuff we're not talking about images +with you know 4,000 4 million pixels + + align:start position:0% +with you know 4,000 4 million pixels + + + align:start position:0% +with you know 4,000 4 million pixels +we're talking about images that might be + + align:start position:0% +we're talking about images that might be + + + align:start position:0% +we're talking about images that might be +256 on a + + align:start position:0% + + + + align:start position:0% + +side as I say we're not talking about + + align:start position:0% +side as I say we're not talking about + + + align:start position:0% +side as I say we're not talking about +images that are a thousand by a thousand + + align:start position:0% +images that are a thousand by a thousand + + + align:start position:0% +images that are a thousand by a thousand +or 4,000 by 4,000 or anything like that + + align:start position:0% +or 4,000 by 4,000 or anything like that + + + align:start position:0% +or 4,000 by 4,000 or anything like that +they tend to be a uh kind of compressed + + align:start position:0% +they tend to be a uh kind of compressed + + + align:start position:0% +they tend to be a uh kind of compressed +into a 256 by 256 image and now what we + + align:start position:0% +into a 256 by 256 image and now what we + + + align:start position:0% +into a 256 by 256 image and now what we +do is we um run over + + align:start position:0% +do is we um run over + + + align:start position:0% +do is we um run over +this with a + + align:start position:0% +this with a + + + align:start position:0% +this with a +neuron that is looking only at a 10x10 + + align:start position:0% +neuron that is looking only at a 10x10 + + + align:start position:0% +neuron that is looking only at a 10x10 +square like + + align:start position:0% + + + + align:start position:0% + +so and that produces an output and next + + align:start position:0% +so and that produces an output and next + + + align:start position:0% +so and that produces an output and next +we run over that uh again having shifted + + align:start position:0% +we run over that uh again having shifted + + + align:start position:0% +we run over that uh again having shifted +this Neuron a little bit + + align:start position:0% +this Neuron a little bit + + + align:start position:0% +this Neuron a little bit +like + + align:start position:0% +like + + + align:start position:0% +like +so and then the next thing we do is we + + align:start position:0% +so and then the next thing we do is we + + + align:start position:0% +so and then the next thing we do is we +shift it + + align:start position:0% +shift it + + + align:start position:0% +shift it +again so we get that output right there + + align:start position:0% +again so we get that output right there + + + align:start position:0% +again so we get that output right there +so each of + + align:start position:0% +so each of + + + align:start position:0% +so each of +those deployments of a neuron produces + + align:start position:0% +those deployments of a neuron produces + + + align:start position:0% +those deployments of a neuron produces +an output and that output is associated + + align:start position:0% +an output and that output is associated + + + align:start position:0% +an output and that output is associated +with a particular place in the image + + align:start position:0% +with a particular place in the image + + + align:start position:0% +with a particular place in the image +this is a process uh that is called + + align:start position:0% + + + + align:start position:0% + +convolution as a term of Art + + align:start position:0% +convolution as a term of Art + + + align:start position:0% +convolution as a term of Art +this + + align:start position:0% +this + + + align:start position:0% +this +guy this convolution operation results + + align:start position:0% +guy this convolution operation results + + + align:start position:0% +guy this convolution operation results +in a bunch of points over + + align:start position:0% + + + + align:start position:0% + +here and the next thing that we + + align:start position:0% +here and the next thing that we + + + align:start position:0% +here and the next thing that we +do with those points is we look in local + + align:start position:0% +do with those points is we look in local + + + align:start position:0% +do with those points is we look in local +neighborhoods and see what the maximum + + align:start position:0% +neighborhoods and see what the maximum + + + align:start position:0% +neighborhoods and see what the maximum +value is and then we take that maximum + + align:start position:0% +value is and then we take that maximum + + + align:start position:0% +value is and then we take that maximum +value and we construct yet another + + align:start position:0% +value and we construct yet another + + + align:start position:0% +value and we construct yet another +mapping of the image over here using + + align:start position:0% +mapping of the image over here using + + + align:start position:0% +mapping of the image over here using +that maximum value then we slide that + + align:start position:0% +that maximum value then we slide that + + + align:start position:0% +that maximum value then we slide that +all over like so and we produce another + + align:start position:0% +all over like so and we produce another + + + align:start position:0% +all over like so and we produce another +value and then we slide that value then + + align:start position:0% +value and then we slide that value then + + + align:start position:0% +value and then we slide that value then +we slide that over one more time with a + + align:start position:0% +we slide that over one more time with a + + + align:start position:0% +we slide that over one more time with a +different color and now we got get + + align:start position:0% +different color and now we got get + + + align:start position:0% +different color and now we got get +another value so this process is called + + align:start position:0% + + + + align:start position:0% + +pooling and because we're taking the + + align:start position:0% +pooling and because we're taking the + + + align:start position:0% +pooling and because we're taking the +maximum this particular kind of pooling + + align:start position:0% +maximum this particular kind of pooling + + + align:start position:0% +maximum this particular kind of pooling +is called Max pooling + + align:start position:0% +is called Max pooling + + + align:start position:0% +is called Max pooling +so now let's see what's next um this is + + align:start position:0% +so now let's see what's next um this is + + + align:start position:0% +so now let's see what's next um this is +taking a particular neuron and running + + align:start position:0% +taking a particular neuron and running + + + align:start position:0% +taking a particular neuron and running +it across the image but maybe there are + + align:start position:0% +it across the image but maybe there are + + + align:start position:0% +it across the image but maybe there are +lots of we call that a kernel uh again + + align:start position:0% +lots of we call that a kernel uh again + + + align:start position:0% +lots of we call that a kernel uh again +uh sucking some terminology out of + + align:start position:0% +uh sucking some terminology out of + + + align:start position:0% +uh sucking some terminology out of +signals and systems but now what we're + + align:start position:0% +signals and systems but now what we're + + + align:start position:0% +signals and systems but now what we're +going to do is we're going to say we're + + align:start position:0% +going to do is we're going to say we're + + + align:start position:0% +going to do is we're going to say we're +going we we can use a whole bunch of + + align:start position:0% +going we we can use a whole bunch of + + + align:start position:0% +going we we can use a whole bunch of +kernels so the thing that I produced + + align:start position:0% +kernels so the thing that I produced + + + align:start position:0% +kernels so the thing that I produced +with one kernel can now be + + align:start position:0% +with one kernel can now be + + + align:start position:0% +with one kernel can now be +repeated many times like so in fact a + + align:start position:0% +repeated many times like so in fact a + + + align:start position:0% +repeated many times like so in fact a +typical number is 100 + + align:start position:0% +typical number is 100 + + + align:start position:0% +typical number is 100 +times so now what we've got is we've got + + align:start position:0% +times so now what we've got is we've got + + + align:start position:0% +times so now what we've got is we've got +a 256x 256 image we've gone over it with + + align:start position:0% +a 256x 256 image we've gone over it with + + + align:start position:0% +a 256x 256 image we've gone over it with +a + + align:start position:0% +a + + + align:start position:0% +a +10x10 kernel we've taken the maximum + + align:start position:0% +10x10 kernel we've taken the maximum + + + align:start position:0% +10x10 kernel we've taken the maximum +value of values that are in the vicinity + + align:start position:0% +value of values that are in the vicinity + + + align:start position:0% +value of values that are in the vicinity +of each other and then we've repeated + + align:start position:0% +of each other and then we've repeated + + + align:start position:0% +of each other and then we've repeated +that 96 100 + + align:start position:0% +that 96 100 + + + align:start position:0% +that 96 100 +times so now we can take that and we can + + align:start position:0% +times so now we can take that and we can + + + align:start position:0% +times so now we can take that and we can +feed all those results into some kind of + + align:start position:0% +feed all those results into some kind of + + + align:start position:0% +feed all those results into some kind of +neural net and then we can do perhaps a + + align:start position:0% +neural net and then we can do perhaps a + + + align:start position:0% +neural net and then we can do perhaps a +fully connected job on the final layers + + align:start position:0% +fully connected job on the final layers + + + align:start position:0% +fully connected job on the final layers +of this and then the in the ultimate + + align:start position:0% +of this and then the in the ultimate + + + align:start position:0% +of this and then the in the ultimate +output we get some sort of + + align:start position:0% +output we get some sort of + + + align:start position:0% +output we get some sort of +indication of How likely it is that the + + align:start position:0% +indication of How likely it is that the + + + align:start position:0% +indication of How likely it is that the +thing that's being seen is say a + + align:start position:0% + + + + align:start position:0% + +might so that's roughly how these things + + align:start position:0% +might so that's roughly how these things + + + align:start position:0% +might so that's roughly how these things +work so what have we talked about so far + + align:start position:0% +work so what have we talked about so far + + + align:start position:0% +work so what have we talked about so far +we've talked about pooling and we've + + align:start position:0% +we've talked about pooling and we've + + + align:start position:0% +we've talked about pooling and we've +talked about convolution and now we can + + align:start position:0% +talked about convolution and now we can + + + align:start position:0% +talked about convolution and now we can +talk about some of the good + + align:start position:0% +talk about some of the good + + + align:start position:0% +talk about some of the good +stuff but before I I get into that this + + align:start position:0% +stuff but before I I get into that this + + + align:start position:0% +stuff but before I I get into that this +is this is what we can do now and and + + align:start position:0% +is this is what we can do now and and + + + align:start position:0% +is this is what we can do now and and +and you can compare this with what was + + align:start position:0% +and you can compare this with what was + + + align:start position:0% +and you can compare this with what was +done in the old + + align:start position:0% + + + + align:start position:0% + +days it was done in the old days before + + align:start position:0% +days it was done in the old days before + + + align:start position:0% +days it was done in the old days before +massive amounts of computing became + + align:start position:0% +massive amounts of computing became + + + align:start position:0% +massive amounts of computing became +available uh is a kind of neural + + align:start position:0% + + + + align:start position:0% + +net activity that's a little easier to + + align:start position:0% +net activity that's a little easier to + + + align:start position:0% +net activity that's a little easier to +see you might in the old days only + + align:start position:0% +see you might in the old days only + + + align:start position:0% +see you might in the old days only +have enough computing power to deal with + + align:start position:0% +have enough computing power to deal with + + + align:start position:0% +have enough computing power to deal with +a small grid of picture elements or + + align:start position:0% +a small grid of picture elements or + + + align:start position:0% +a small grid of picture elements or +so-called pixels and then each of these + + align:start position:0% +so-called pixels and then each of these + + + align:start position:0% +so-called pixels and then each of these +might be a value that is fed as an input + + align:start position:0% +might be a value that is fed as an input + + + align:start position:0% +might be a value that is fed as an input +into some kind of neuron and so you + + align:start position:0% +into some kind of neuron and so you + + + align:start position:0% +into some kind of neuron and so you +might have a column of + + align:start position:0% +might have a column of + + + align:start position:0% +might have a column of +neurons that are looking at these pixels + + align:start position:0% +neurons that are looking at these pixels + + + align:start position:0% +neurons that are looking at these pixels +in in in your in your in your image and + + align:start position:0% +in in in your in your in your image and + + + align:start position:0% +in in in your in your in your image and +then there might be a small number of + + align:start position:0% +then there might be a small number of + + + align:start position:0% +then there might be a small number of +columns that follow from that and + + align:start position:0% +columns that follow from that and + + + align:start position:0% +columns that follow from that and +finally something that say this neuron + + align:start position:0% +finally something that say this neuron + + + align:start position:0% +finally something that say this neuron +is looking for things that are a number + + align:start position:0% +is looking for things that are a number + + + align:start position:0% +is looking for things that are a number +one that is to say something that looks + + align:start position:0% +one that is to say something that looks + + + align:start position:0% +one that is to say something that looks +like a number + + align:start position:0% +like a number + + + align:start position:0% +like a number +one in the image so this stuff up here + + align:start position:0% +one in the image so this stuff up here + + + align:start position:0% +one in the image so this stuff up here +is a con is what you can do when you + + align:start position:0% +is a con is what you can do when you + + + align:start position:0% +is a con is what you can do when you +have a massive amount of computation + + align:start position:0% +have a massive amount of computation + + + align:start position:0% +have a massive amount of computation +rela to the kind of thing you used to + + align:start position:0% +rela to the kind of thing you used to + + + align:start position:0% +rela to the kind of thing you used to +see in the old + + align:start position:0% + + + + align:start position:0% + +days so what's + + align:start position:0% +days so what's + + + align:start position:0% +days so what's +different well what's different is + + align:start position:0% +different well what's different is + + + align:start position:0% +different well what's different is +instead of a few hundred parameters + + align:start position:0% +instead of a few hundred parameters + + + align:start position:0% +instead of a few hundred parameters +we've got a lot more instead of 10 + + align:start position:0% +we've got a lot more instead of 10 + + + align:start position:0% +we've got a lot more instead of 10 +digits we have a thousand + + align:start position:0% +digits we have a thousand + + + align:start position:0% +digits we have a thousand +classes instead of a few hundred samples + + align:start position:0% +classes instead of a few hundred samples + + + align:start position:0% +classes instead of a few hundred samples +we have + + align:start position:0% +we have + + + align:start position:0% +we have +maybe a thousand examples of each class + + align:start position:0% +maybe a thousand examples of each class + + + align:start position:0% +maybe a thousand examples of each class +so that makes a million + + align:start position:0% +so that makes a million + + + align:start position:0% +so that makes a million +samples and we got 60 million parameters + + align:start position:0% +samples and we got 60 million parameters + + + align:start position:0% +samples and we got 60 million parameters +to play + + align:start position:0% +to play + + + align:start position:0% +to play +with and the surprising thing is that + + align:start position:0% +with and the surprising thing is that + + + align:start position:0% +with and the surprising thing is that +the net result is we've got a function + + align:start position:0% +the net result is we've got a function + + + align:start position:0% +the net result is we've got a function +approximator that astonishes everybody + + align:start position:0% +approximator that astonishes everybody + + + align:start position:0% +approximator that astonishes everybody +and no one quite knows why it works + + align:start position:0% +and no one quite knows why it works + + + align:start position:0% +and no one quite knows why it works +except that when you throw an immense + + align:start position:0% +except that when you throw an immense + + + align:start position:0% +except that when you throw an immense +amount of + + align:start position:0% +amount of + + + align:start position:0% +amount of +computation uh into this kind of + + align:start position:0% +computation uh into this kind of + + + align:start position:0% +computation uh into this kind of +arrangement it's possible to get a + + align:start position:0% +arrangement it's possible to get a + + + align:start position:0% +arrangement it's possible to get a +performance that no one expected would + + align:start position:0% +performance that no one expected would + + + align:start position:0% +performance that no one expected would +be + + align:start position:0% +be + + + align:start position:0% +be +possible so that's sort of the bottom + + align:start position:0% +possible so that's sort of the bottom + + + align:start position:0% +possible so that's sort of the bottom +line but now uh there are a couple of + + align:start position:0% +line but now uh there are a couple of + + + align:start position:0% +line but now uh there are a couple of +ideas beyond that that I think are + + align:start position:0% +ideas beyond that that I think are + + + align:start position:0% +ideas beyond that that I think are +especially interesting and I I want to + + align:start position:0% +especially interesting and I I want to + + + align:start position:0% +especially interesting and I I want to +talk about those first idea that's + + align:start position:0% +talk about those first idea that's + + + align:start position:0% +talk about those first idea that's +especially interesting is the idea of + + align:start position:0% +especially interesting is the idea of + + + align:start position:0% +especially interesting is the idea of +Auto + + align:start position:0% +Auto + + + align:start position:0% +Auto +coding and here's how the idea of Auto + + align:start position:0% +coding and here's how the idea of Auto + + + align:start position:0% +coding and here's how the idea of Auto +coding + + align:start position:0% + + + + align:start position:0% + +works I'm going to run out of board + + align:start position:0% +works I'm going to run out of board + + + align:start position:0% +works I'm going to run out of board +space so I think I'll do it right + + align:start position:0% +space so I think I'll do it right + + + align:start position:0% +space so I think I'll do it right +here you have some input + + align:start position:0% + + + + align:start position:0% + +values they go into a layer of neurons + + align:start position:0% +values they go into a layer of neurons + + + align:start position:0% +values they go into a layer of neurons +the input layer + + align:start position:0% +the input layer + + + align:start position:0% +the input layer +then there is a so-called hidden layer + + align:start position:0% +then there is a so-called hidden layer + + + align:start position:0% +then there is a so-called hidden layer +that's much + + align:start position:0% + + + + align:start position:0% + +smaller so maybe there are in an example + + align:start position:0% +smaller so maybe there are in an example + + + align:start position:0% +smaller so maybe there are in an example +there'll be 10 neurons here and just a + + align:start position:0% +there'll be 10 neurons here and just a + + + align:start position:0% +there'll be 10 neurons here and just a +couple here and then these expand to an + + align:start position:0% +couple here and then these expand to an + + + align:start position:0% +couple here and then these expand to an +output layer like + + align:start position:0% +output layer like + + + align:start position:0% +output layer like +so now we can take the output layer Z1 + + align:start position:0% +so now we can take the output layer Z1 + + + align:start position:0% +so now we can take the output layer Z1 +through + + align:start position:0% +through + + + align:start position:0% +through +ZN and compare it with the with desired + + align:start position:0% +ZN and compare it with the with desired + + + align:start position:0% +ZN and compare it with the with desired +values D1 through DN + + align:start position:0% + + + + align:start position:0% + +you following me so far now the trick is + + align:start position:0% +you following me so far now the trick is + + + align:start position:0% +you following me so far now the trick is +to say well what are the desired + + align:start position:0% +to say well what are the desired + + + align:start position:0% +to say well what are the desired +values let's let the desired + + align:start position:0% +values let's let the desired + + + align:start position:0% +values let's let the desired +values be the input + + align:start position:0% + + + + align:start position:0% + +values so what we're going to do is + + align:start position:0% +values so what we're going to do is + + + align:start position:0% +values so what we're going to do is +we're going to train this net up so the + + align:start position:0% +we're going to train this net up so the + + + align:start position:0% +we're going to train this net up so the +output's the same as the + + align:start position:0% +output's the same as the + + + align:start position:0% +output's the same as the +input what's good of that but we're + + align:start position:0% +input what's good of that but we're + + + align:start position:0% +input what's good of that but we're +going to force it down through this neck + + align:start position:0% +going to force it down through this neck + + + align:start position:0% +going to force it down through this neck +down piece of network + + align:start position:0% +down piece of network + + + align:start position:0% +down piece of network +so if this network is going to + + align:start position:0% +so if this network is going to + + + align:start position:0% +so if this network is going to +succeed in taking all the possibilities + + align:start position:0% +succeed in taking all the possibilities + + + align:start position:0% +succeed in taking all the possibilities +here and cramming them into + + align:start position:0% +here and cramming them into + + + align:start position:0% +here and cramming them into +this smaller inner layer this so-called + + align:start position:0% +this smaller inner layer this so-called + + + align:start position:0% +this smaller inner layer this so-called +hidden layer such that they it can + + align:start position:0% +hidden layer such that they it can + + + align:start position:0% +hidden layer such that they it can +reproduce the input at the output it + + align:start position:0% +reproduce the input at the output it + + + align:start position:0% +reproduce the input at the output it +must be doing some kind of + + align:start position:0% +must be doing some kind of + + + align:start position:0% +must be doing some kind of +generalization of the kinds of things it + + align:start position:0% +generalization of the kinds of things it + + + align:start position:0% +generalization of the kinds of things it +sees on its + + align:start position:0% +sees on its + + + align:start position:0% +sees on its +input and that's a very clever idea and + + align:start position:0% +input and that's a very clever idea and + + + align:start position:0% +input and that's a very clever idea and +it's seen in various forms in a large + + align:start position:0% +it's seen in various forms in a large + + + align:start position:0% +it's seen in various forms in a large +fraction of the papers that appear on + + align:start position:0% +fraction of the papers that appear on + + + align:start position:0% +fraction of the papers that appear on +deep neural + + align:start position:0% +deep neural + + + align:start position:0% +deep neural +Nets but now I want to talk about an + + align:start position:0% +Nets but now I want to talk about an + + + align:start position:0% +Nets but now I want to talk about an +example so I can show you a + + align:start position:0% +example so I can show you a + + + align:start position:0% +example so I can show you a +demonstration okay so um we don't have + + align:start position:0% +demonstration okay so um we don't have + + + align:start position:0% +demonstration okay so um we don't have +gpus and we don't have three days to do + + align:start position:0% +gpus and we don't have three days to do + + + align:start position:0% +gpus and we don't have three days to do +this so I'm going to make it uh make up + + align:start position:0% +this so I'm going to make it uh make up + + + align:start position:0% +this so I'm going to make it uh make up +a very simple + + align:start position:0% +a very simple + + + align:start position:0% +a very simple +example that's reminiscent of what goes + + align:start position:0% +example that's reminiscent of what goes + + + align:start position:0% +example that's reminiscent of what goes +on here but but uh involves hardly any + + align:start position:0% +on here but but uh involves hardly any + + + align:start position:0% +on here but but uh involves hardly any +computation what I'm going to imagine is + + align:start position:0% +computation what I'm going to imagine is + + + align:start position:0% +computation what I'm going to imagine is +we're trying to recognize + + align:start position:0% +we're trying to recognize + + + align:start position:0% +we're trying to recognize +animals from + + align:start position:0% +animals from + + + align:start position:0% +animals from +how tall they + + align:start position:0% +how tall they + + + align:start position:0% +how tall they +are uh from the Shadows that they cast + + align:start position:0% +are uh from the Shadows that they cast + + + align:start position:0% +are uh from the Shadows that they cast +so we're going to recognize three + + align:start position:0% +so we're going to recognize three + + + align:start position:0% +so we're going to recognize three +animals a + + align:start position:0% + + + + align:start position:0% + +cheetah um a + + align:start position:0% +cheetah um a + + + align:start position:0% +cheetah um a +zebra and and a + + align:start position:0% +zebra and and a + + + align:start position:0% +zebra and and a +giraffe and they they will each cast a + + align:start position:0% +giraffe and they they will each cast a + + + align:start position:0% +giraffe and they they will each cast a +shadow on a + + align:start position:0% +shadow on a + + + align:start position:0% +shadow on a +Blackboard like me no uh no vampire + + align:start position:0% +Blackboard like me no uh no vampire + + + align:start position:0% +Blackboard like me no uh no vampire +involved here and what we're going to do + + align:start position:0% +involved here and what we're going to do + + + align:start position:0% +involved here and what we're going to do +is we're going to use the the + + align:start position:0% +is we're going to use the the + + + align:start position:0% +is we're going to use the the +shadow as a input to a neural net all + + align:start position:0% +shadow as a input to a neural net all + + + align:start position:0% +shadow as a input to a neural net all +right so let's see how that would + + align:start position:0% + + + + align:start position:0% + +work so there is + + align:start position:0% +work so there is + + + align:start position:0% +work so there is +um our + + align:start position:0% +um our + + + align:start position:0% +um our +Network and if I just clicked into one + + align:start position:0% +Network and if I just clicked into one + + + align:start position:0% +Network and if I just clicked into one +of these test samples that's the U + + align:start position:0% +of these test samples that's the U + + + align:start position:0% +of these test samples that's the U +height of the shadow that a cheetah cast + + align:start position:0% +height of the shadow that a cheetah cast + + + align:start position:0% +height of the shadow that a cheetah cast +on a + + align:start position:0% +on a + + + align:start position:0% +on a +wall and uh there are 10 input neurons + + align:start position:0% +wall and uh there are 10 input neurons + + + align:start position:0% +wall and uh there are 10 input neurons +corresponding to each level of the + + align:start position:0% +corresponding to each level of the + + + align:start position:0% +corresponding to each level of the +Shadow uh they're rammed through three + + align:start position:0% +Shadow uh they're rammed through three + + + align:start position:0% +Shadow uh they're rammed through three +inner layer neurons and from that it + + align:start position:0% +inner layer neurons and from that it + + + align:start position:0% +inner layer neurons and from that it +spreads out and becomes the outer layer + + align:start position:0% +spreads out and becomes the outer layer + + + align:start position:0% +spreads out and becomes the outer layer +values and we're going to compare those + + align:start position:0% +values and we're going to compare those + + + align:start position:0% +values and we're going to compare those +outer layer values to the desired values + + align:start position:0% +outer layer values to the desired values + + + align:start position:0% +outer layer values to the desired values +but the desired values are the same as + + align:start position:0% +but the desired values are the same as + + + align:start position:0% +but the desired values are the same as +the input values so this column is a + + align:start position:0% +the input values so this column is a + + + align:start position:0% +the input values so this column is a +column of input values on the far right + + align:start position:0% +column of input values on the far right + + + align:start position:0% +column of input values on the far right +we have our column of desired values and + + align:start position:0% +we have our column of desired values and + + + align:start position:0% +we have our column of desired values and +we haven't trained this dret yet all + + align:start position:0% +we haven't trained this dret yet all + + + align:start position:0% +we haven't trained this dret yet all +we've got is random values in there so + + align:start position:0% +we've got is random values in there so + + + align:start position:0% +we've got is random values in there so +if we run the test samples + + align:start position:0% +if we run the test samples + + + align:start position:0% +if we run the test samples +through we get that and that yeah + + align:start position:0% +through we get that and that yeah + + + align:start position:0% +through we get that and that yeah +cheetahs are short zebras are medium + + align:start position:0% +cheetahs are short zebras are medium + + + align:start position:0% +cheetahs are short zebras are medium +height and giraffes are tall but our + + align:start position:0% +height and giraffes are tall but our + + + align:start position:0% +height and giraffes are tall but our +output is + + align:start position:0% +output is + + + align:start position:0% +output is +just pretty much 0 five for all of them + + align:start position:0% +just pretty much 0 five for all of them + + + align:start position:0% +just pretty much 0 five for all of them +for all of those Shadow Heights all + + align:start position:0% +for all of those Shadow Heights all + + + align:start position:0% +for all of those Shadow Heights all +right no training so + + align:start position:0% +right no training so + + + align:start position:0% +right no training so +far so let's run this thing we're just + + align:start position:0% +far so let's run this thing we're just + + + align:start position:0% +far so let's run this thing we're just +using simple back prop just like just + + align:start position:0% +using simple back prop just like just + + + align:start position:0% +using simple back prop just like just +like on our world's simplest neur + + align:start position:0% +like on our world's simplest neur + + + align:start position:0% +like on our world's simplest neur +net and it's interesting to see + + align:start position:0% + + + + align:start position:0% + +that what happens is we you see all + + align:start position:0% +that what happens is we you see all + + + align:start position:0% +that what happens is we you see all +those values changing now I need to + + align:start position:0% +those values changing now I need to + + + align:start position:0% +those values changing now I need to +mention that when you when you see a + + align:start position:0% +mention that when you when you see a + + + align:start position:0% +mention that when you when you see a +green connection that means it's a + + align:start position:0% +green connection that means it's a + + + align:start position:0% +green connection that means it's a +positive weight and and the green and + + align:start position:0% +positive weight and and the green and + + + align:start position:0% +positive weight and and the green and +the density of the green indicates how + + align:start position:0% +the density of the green indicates how + + + align:start position:0% +the density of the green indicates how +how positive it is and the red ones are + + align:start position:0% +how positive it is and the red ones are + + + align:start position:0% +how positive it is and the red ones are +negative weights and the intensity of + + align:start position:0% +negative weights and the intensity of + + + align:start position:0% +negative weights and the intensity of +the red indicates how red it is so here + + align:start position:0% +the red indicates how red it is so here + + + align:start position:0% +the red indicates how red it is so here +you can see that we we still have from + + align:start position:0% +you can see that we we still have from + + + align:start position:0% +you can see that we we still have from +from our random inputs a variety of red + + align:start position:0% +from our random inputs a variety of red + + + align:start position:0% +from our random inputs a variety of red +and green values we haven't really done + + align:start position:0% +and green values we haven't really done + + + align:start position:0% +and green values we haven't really done +much training so everything uh correctly + + align:start position:0% +much training so everything uh correctly + + + align:start position:0% +much training so everything uh correctly +looks pretty much + + align:start position:0% +looks pretty much + + + align:start position:0% +looks pretty much +random so let's run this + + align:start position:0% +random so let's run this + + + align:start position:0% +random so let's run this +thing and after only a + + align:start position:0% +thing and after only a + + + align:start position:0% +thing and after only a +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +iterations uh going through these uh + + align:start position:0% +iterations uh going through these uh + + + align:start position:0% +iterations uh going through these uh +examples and trying to make the output + + align:start position:0% +examples and trying to make the output + + + align:start position:0% +examples and trying to make the output +the same as the input we reached a point + + align:start position:0% +the same as the input we reached a point + + + align:start position:0% +the same as the input we reached a point +where the airor rate has dropped in fact + + align:start position:0% +where the airor rate has dropped in fact + + + align:start position:0% +where the airor rate has dropped in fact +it's dropped so much it's interesting to + + align:start position:0% +it's dropped so much it's interesting to + + + align:start position:0% +it's dropped so much it's interesting to +relook at the test cases so here's a + + align:start position:0% +relook at the test cases so here's a + + + align:start position:0% +relook at the test cases so here's a +test case where we have a cheetah + + align:start position:0% +test case where we have a cheetah + + + align:start position:0% +test case where we have a cheetah +and now the output value is in fact very + + align:start position:0% +and now the output value is in fact very + + + align:start position:0% +and now the output value is in fact very +close to the desired value in all in all + + align:start position:0% +close to the desired value in all in all + + + align:start position:0% +close to the desired value in all in all +the output in all the output neurons so + + align:start position:0% +the output in all the output neurons so + + + align:start position:0% +the output in all the output neurons so +if we look at another + + align:start position:0% +if we look at another + + + align:start position:0% +if we look at another +one once again there's a correspondence + + align:start position:0% +one once again there's a correspondence + + + align:start position:0% +one once again there's a correspondence +in the right two + + align:start position:0% +in the right two + + + align:start position:0% +in the right two +columns and if we look at the final one + + align:start position:0% +columns and if we look at the final one + + + align:start position:0% +columns and if we look at the final one +yeah there's a correspondence in the + + align:start position:0% +yeah there's a correspondence in the + + + align:start position:0% +yeah there's a correspondence in the +right two + + align:start position:0% + + + + align:start position:0% + +columns now when you back up from this + + align:start position:0% +columns now when you back up from this + + + align:start position:0% +columns now when you back up from this +and say well what's going on + + align:start position:0% +and say well what's going on + + + align:start position:0% +and say well what's going on +here it turns out that you're not + + align:start position:0% +here it turns out that you're not + + + align:start position:0% +here it turns out that you're not +training this + + align:start position:0% +training this + + + align:start position:0% +training this +thing to classify animals you're + + align:start position:0% +thing to classify animals you're + + + align:start position:0% +thing to classify animals you're +training it to understand the nature of + + align:start position:0% +training it to understand the nature of + + + align:start position:0% +training it to understand the nature of +the things that it sees in the + + align:start position:0% +the things that it sees in the + + + align:start position:0% +the things that it sees in the +environment because all it sees is the + + align:start position:0% +environment because all it sees is the + + + align:start position:0% +environment because all it sees is the +height of a shadow it doesn't know + + align:start position:0% +height of a shadow it doesn't know + + + align:start position:0% +height of a shadow it doesn't know +anything about the classifications + + align:start position:0% +anything about the classifications + + + align:start position:0% +anything about the classifications +you're going to try to get out of that + + align:start position:0% +you're going to try to get out of that + + + align:start position:0% +you're going to try to get out of that +all it sees is that there are there's a + + align:start position:0% +all it sees is that there are there's a + + + align:start position:0% +all it sees is that there are there's a +kind of consistency in the kind of data + + align:start position:0% +kind of consistency in the kind of data + + + align:start position:0% +kind of consistency in the kind of data +that it sees on the input + + align:start position:0% +that it sees on the input + + + align:start position:0% +that it sees on the input +values right now you might say okay oh + + align:start position:0% +values right now you might say okay oh + + + align:start position:0% +values right now you might say okay oh +that's cool because what must be + + align:start position:0% +that's cool because what must be + + + align:start position:0% +that's cool because what must be +happening is that that hidden layer + + align:start position:0% +happening is that that hidden layer + + + align:start position:0% +happening is that that hidden layer +because everything is forced through + + align:start position:0% +because everything is forced through + + + align:start position:0% +because everything is forced through +that narrow pipe must be doing some kind + + align:start position:0% +that narrow pipe must be doing some kind + + + align:start position:0% +that narrow pipe must be doing some kind +of + + align:start position:0% +of + + + align:start position:0% +of +generalization so it ought to be the + + align:start position:0% +generalization so it ought to be the + + + align:start position:0% +generalization so it ought to be the +case that if we click on each of those + + align:start position:0% +case that if we click on each of those + + + align:start position:0% +case that if we click on each of those +neurons we ought to see it specialized + + align:start position:0% +neurons we ought to see it specialized + + + align:start position:0% +neurons we ought to see it specialized +to a particular height because that's + + align:start position:0% +to a particular height because that's + + + align:start position:0% +to a particular height because that's +what sorts of stuff that's the sort of + + align:start position:0% +what sorts of stuff that's the sort of + + + align:start position:0% +what sorts of stuff that's the sort of +stuff that's presented on the + + align:start position:0% +stuff that's presented on the + + + align:start position:0% +stuff that's presented on the +input well let's go see what is what in + + align:start position:0% +input well let's go see what is what in + + + align:start position:0% +input well let's go see what is what in +fact is the maximum stimulation to be + + align:start position:0% +fact is the maximum stimulation to be + + + align:start position:0% +fact is the maximum stimulation to be +seen on the neurons in that hidden + + align:start position:0% +seen on the neurons in that hidden + + + align:start position:0% +seen on the neurons in that hidden +layer so if I when I click on these guys + + align:start position:0% +layer so if I when I click on these guys + + + align:start position:0% +layer so if I when I click on these guys +what we're going to see is the input + + align:start position:0% +what we're going to see is the input + + + align:start position:0% +what we're going to see is the input +values that maximally stimulate that + + align:start position:0% +values that maximally stimulate that + + + align:start position:0% +values that maximally stimulate that +neuron and by the way I have no idea how + + align:start position:0% +neuron and by the way I have no idea how + + + align:start position:0% +neuron and by the way I have no idea how +this is going to turn out because this + + align:start position:0% +this is going to turn out because this + + + align:start position:0% +this is going to turn out because this +is all you know the initialization is + + align:start position:0% +is all you know the initialization is + + + align:start position:0% +is all you know the initialization is +all + + align:start position:0% +all + + + align:start position:0% +all +random well that's good that one looks + + align:start position:0% +random well that's good that one looks + + + align:start position:0% +random well that's good that one looks +like it's generalized the notion of + + align:start position:0% +like it's generalized the notion of + + + align:start position:0% +like it's generalized the notion of +short + + align:start position:0% +short + + + align:start position:0% +short +ug that doesn't look like medium in fact + + align:start position:0% +ug that doesn't look like medium in fact + + + align:start position:0% +ug that doesn't look like medium in fact +um the maximum stimulation doesn't + + align:start position:0% +um the maximum stimulation doesn't + + + align:start position:0% +um the maximum stimulation doesn't +involve any stimulation from that lower + + align:start position:0% +involve any stimulation from that lower + + + align:start position:0% +involve any stimulation from that lower +neuron here look at this + + align:start position:0% +neuron here look at this + + + align:start position:0% +neuron here look at this +one that doesn't look like tall so we + + align:start position:0% +one that doesn't look like tall so we + + + align:start position:0% +one that doesn't look like tall so we +got one that looks like short and two + + align:start position:0% +got one that looks like short and two + + + align:start position:0% +got one that looks like short and two +look just look completely + + align:start position:0% + + + + align:start position:0% + +random so in fact maybe we better back + + align:start position:0% +random so in fact maybe we better back + + + align:start position:0% +random so in fact maybe we better back +off the idea that what's going on in + + align:start position:0% +off the idea that what's going on in + + + align:start position:0% +off the idea that what's going on in +that hidden layer is generalization and + + align:start position:0% +that hidden layer is generalization and + + + align:start position:0% +that hidden layer is generalization and +say um that what's going on in there is + + align:start position:0% +say um that what's going on in there is + + + align:start position:0% +say um that what's going on in there is +maybe the encoding of the + + align:start position:0% +maybe the encoding of the + + + align:start position:0% +maybe the encoding of the +generalization it doesn't look like a + + align:start position:0% +generalization it doesn't look like a + + + align:start position:0% +generalization it doesn't look like a +encoding we can see but there is an + + align:start position:0% +encoding we can see but there is an + + + align:start position:0% +encoding we can see but there is an +encoding there is a generalization + + align:start position:0% +encoding there is a generalization + + + align:start position:0% +encoding there is a generalization +that's let me start that over we don't + + align:start position:0% +that's let me start that over we don't + + + align:start position:0% +that's let me start that over we don't +see the + + align:start position:0% +see the + + + align:start position:0% +see the +generalization in the stimulating values + + align:start position:0% +generalization in the stimulating values + + + align:start position:0% +generalization in the stimulating values +what we have instead is we have some + + align:start position:0% +what we have instead is we have some + + + align:start position:0% +what we have instead is we have some +kind of encoded + + align:start position:0% +kind of encoded + + + align:start position:0% +kind of encoded +generalization and because we've got + + align:start position:0% +generalization and because we've got + + + align:start position:0% +generalization and because we've got +this stuff encoded it's what makes these + + align:start position:0% +this stuff encoded it's what makes these + + + align:start position:0% +this stuff encoded it's what makes these +neuron Nets so extraordinarily difficult + + align:start position:0% +neuron Nets so extraordinarily difficult + + + align:start position:0% +neuron Nets so extraordinarily difficult +to understand we don't just don't + + align:start position:0% +to understand we don't just don't + + + align:start position:0% +to understand we don't just don't +understand what they're doing we don't + + align:start position:0% +understand what they're doing we don't + + + align:start position:0% +understand what they're doing we don't +understand why they can recognize a + + align:start position:0% +understand why they can recognize a + + + align:start position:0% +understand why they can recognize a +cheetah we don't understand why it can + + align:start position:0% +cheetah we don't understand why it can + + + align:start position:0% +cheetah we don't understand why it can +recognize a school bus in some cases but + + align:start position:0% +recognize a school bus in some cases but + + + align:start position:0% +recognize a school bus in some cases but +not in others because we don't really + + align:start position:0% +not in others because we don't really + + + align:start position:0% +not in others because we don't really +understand + + align:start position:0% +understand + + + align:start position:0% +understand +and what these neurons are responding to + + align:start position:0% +and what these neurons are responding to + + + align:start position:0% +and what these neurons are responding to +well that's not quite true uh there's + + align:start position:0% +well that's not quite true uh there's + + + align:start position:0% +well that's not quite true uh there's +been a a lot of work recently on trying + + align:start position:0% +been a a lot of work recently on trying + + + align:start position:0% +been a a lot of work recently on trying +to to sort that out but it's still a a + + align:start position:0% +to to sort that out but it's still a a + + + align:start position:0% +to to sort that out but it's still a a +lot of me mystery in this world but in + + align:start position:0% +lot of me mystery in this world but in + + + align:start position:0% +lot of me mystery in this world but in +any event that's the that's the auto + + align:start position:0% +any event that's the that's the auto + + + align:start position:0% +any event that's the that's the auto +coding idea it comes in various guyses + + align:start position:0% +coding idea it comes in various guyses + + + align:start position:0% +coding idea it comes in various guyses +sometimes people talk about bolts + + align:start position:0% +sometimes people talk about bolts + + + align:start position:0% +sometimes people talk about bolts +machines and things of that sort but + + align:start position:0% +machines and things of that sort but + + + align:start position:0% +machines and things of that sort but +it's basically all the same sort of idea + + align:start position:0% +it's basically all the same sort of idea + + + align:start position:0% +it's basically all the same sort of idea +and so you can do this layer by layer + + align:start position:0% +and so you can do this layer by layer + + + align:start position:0% +and so you can do this layer by layer +once you've trained the input layer then + + align:start position:0% +once you've trained the input layer then + + + align:start position:0% +once you've trained the input layer then +you can use that layer to train the next + + align:start position:0% +you can use that layer to train the next + + + align:start position:0% +you can use that layer to train the next +layer and then that can train the next + + align:start position:0% +layer and then that can train the next + + + align:start position:0% +layer and then that can train the next +layer after that and it's only at the + + align:start position:0% +layer after that and it's only at the + + + align:start position:0% +layer after that and it's only at the +very very end that you say to yourself + + align:start position:0% +very very end that you say to yourself + + + align:start position:0% +very very end that you say to yourself +well now I've accumulated a lot of + + align:start position:0% +well now I've accumulated a lot of + + + align:start position:0% +well now I've accumulated a lot of +knowledge about the environment and what + + align:start position:0% +knowledge about the environment and what + + + align:start position:0% +knowledge about the environment and what +can be seen in the environment maybe + + align:start position:0% +can be seen in the environment maybe + + + align:start position:0% +can be seen in the environment maybe +it's time to get around to using some + + align:start position:0% +it's time to get around to using some + + + align:start position:0% +it's time to get around to using some +some samples of particular classes and + + align:start position:0% +some samples of particular classes and + + + align:start position:0% +some samples of particular classes and +train on train on + + align:start position:0% +train on train on + + + align:start position:0% +train on train on +classes so that's the story on autoc + + align:start position:0% + + + + align:start position:0% + +coding now the next thing to talk + + align:start position:0% +coding now the next thing to talk + + + align:start position:0% +coding now the next thing to talk +about is that final layer + + align:start position:0% + + + + align:start position:0% + +so let's see what the final ER might + + align:start position:0% +so let's see what the final ER might + + + align:start position:0% +so let's see what the final ER might +look + + align:start position:0% +look + + + align:start position:0% +look +like let's see it uh it uh might look + + align:start position:0% +like let's see it uh it uh might look + + + align:start position:0% +like let's see it uh it uh might look +like this there's a + + align:start position:0% +like this there's a + + + align:start position:0% +like this there's a +summer there's a minus one up here now + + align:start position:0% +summer there's a minus one up here now + + + align:start position:0% +summer there's a minus one up here now +let's see there's a minus one up here + + align:start position:0% +let's see there's a minus one up here + + + align:start position:0% +let's see there's a minus one up here +back there's a minus one up there + + align:start position:0% +back there's a minus one up there + + + align:start position:0% +back there's a minus one up there +there's a multiplier here and there's a + + align:start position:0% +there's a multiplier here and there's a + + + align:start position:0% +there's a multiplier here and there's a +threshold value there + + align:start position:0% +threshold value there + + + align:start position:0% +threshold value there +now likewise there's some other input + + align:start position:0% +now likewise there's some other input + + + align:start position:0% +now likewise there's some other input +values here let me call This One X and + + align:start position:0% +values here let me call This One X and + + + align:start position:0% +values here let me call This One X and +it gets multiplied by some + + align:start position:0% +it gets multiplied by some + + + align:start position:0% +it gets multiplied by some +weight and then that goes into the + + align:start position:0% +weight and then that goes into the + + + align:start position:0% +weight and then that goes into the +summer as well and that in turn goes + + align:start position:0% +summer as well and that in turn goes + + + align:start position:0% +summer as well and that in turn goes +into a summing into a + + align:start position:0% +into a summing into a + + + align:start position:0% +into a summing into a +sigmoid that looks like + + align:start position:0% +sigmoid that looks like + + + align:start position:0% +sigmoid that looks like +so and finally you get an output which + + align:start position:0% +so and finally you get an output which + + + align:start position:0% +so and finally you get an output which +will call + + align:start position:0% +will call + + + align:start position:0% +will call +Z so it's clear that if you uh just + + align:start position:0% +Z so it's clear that if you uh just + + + align:start position:0% +Z so it's clear that if you uh just +write out the value of Z as it depends + + align:start position:0% +write out the value of Z as it depends + + + align:start position:0% +write out the value of Z as it depends +on those + + align:start position:0% +on those + + + align:start position:0% +on those +inputs Now using the formula that we uh + + align:start position:0% +inputs Now using the formula that we uh + + + align:start position:0% +inputs Now using the formula that we uh +worked with last time then what you see + + align:start position:0% +worked with last time then what you see + + + align:start position:0% +worked with last time then what you see +is that + + align:start position:0% +is that + + + align:start position:0% +is that +Z is equal + + align:start position:0% + + + + align:start position:0% + +to + + align:start position:0% +to + + + align:start position:0% +to +1 over 1 + e to the + + align:start position:0% +1 over 1 + e to the + + + align:start position:0% +1 over 1 + e to the +minus + + align:start position:0% +minus + + + align:start position:0% +minus +W * + + align:start position:0% +W * + + + align:start position:0% +W * +x minus t + + align:start position:0% +x minus t + + + align:start position:0% +x minus t +uh plus T I guess + + align:start position:0% + + + + align:start position:0% + +right so that's a sigmoid function that + + align:start position:0% +right so that's a sigmoid function that + + + align:start position:0% +right so that's a sigmoid function that +um depends on the value of that weight + + align:start position:0% +um depends on the value of that weight + + + align:start position:0% +um depends on the value of that weight +and on the value of that + + align:start position:0% +and on the value of that + + + align:start position:0% +and on the value of that +threshold so let's look at how + + align:start position:0% +threshold so let's look at how + + + align:start position:0% +threshold so let's look at how +that those values might change + + align:start position:0% +that those values might change + + + align:start position:0% +that those values might change +things + + align:start position:0% +things + + + align:start position:0% +things +so here we have an ordinary + + align:start position:0% + + + + align:start position:0% + +sigo and what happens if we shift it + + align:start position:0% +sigo and what happens if we shift it + + + align:start position:0% +sigo and what happens if we shift it +with a with the threshold value if we + + align:start position:0% +with a with the threshold value if we + + + align:start position:0% +with a with the threshold value if we +change that threshold + + align:start position:0% +change that threshold + + + align:start position:0% +change that threshold +value then it's going to shift the place + + align:start position:0% +value then it's going to shift the place + + + align:start position:0% +value then it's going to shift the place +where + + align:start position:0% + + + + align:start position:0% + +that sigmoid comes + + align:start position:0% + + + + align:start position:0% + +down so a change in t could cause this + + align:start position:0% +down so a change in t could cause this + + + align:start position:0% +down so a change in t could cause this +thing to shift over that + + align:start position:0% +thing to shift over that + + + align:start position:0% +thing to shift over that +way and if we change the value of w that + + align:start position:0% +way and if we change the value of w that + + + align:start position:0% +way and if we change the value of w that +could change how steep this guy is + + align:start position:0% + + + + align:start position:0% + +so we might think that the + + align:start position:0% +so we might think that the + + + align:start position:0% +so we might think that the +performance since it depends on W and + + align:start position:0% +performance since it depends on W and + + + align:start position:0% +performance since it depends on W and +T should be adjusted in such a + + align:start position:0% +T should be adjusted in such a + + + align:start position:0% +T should be adjusted in such a +way as + + align:start position:0% +way as + + + align:start position:0% +way as +to make the classification do the right + + align:start position:0% +to make the classification do the right + + + align:start position:0% +to make the classification do the right +thing but what what's the right thing + + align:start position:0% +thing but what what's the right thing + + + align:start position:0% +thing but what what's the right thing +well that depends on the samples that + + align:start position:0% +well that depends on the samples that + + + align:start position:0% +well that depends on the samples that +we've + + align:start position:0% + + + + align:start position:0% + +seen suppose for + + align:start position:0% +seen suppose for + + + align:start position:0% +seen suppose for +example that this is our Sigma + + align:start position:0% + + + + align:start position:0% + +function and we see some uh examples of + + align:start position:0% +function and we see some uh examples of + + + align:start position:0% +function and we see some uh examples of +a + + align:start position:0% +a + + + align:start position:0% +a +class some positive examples of a class + + align:start position:0% +class some positive examples of a class + + + align:start position:0% +class some positive examples of a class +that have values that lie at that point + + align:start position:0% +that have values that lie at that point + + + align:start position:0% +that have values that lie at that point +and that point at that + + align:start position:0% +and that point at that + + + align:start position:0% +and that point at that +point and we have + + align:start position:0% +point and we have + + + align:start position:0% +point and we have +some values that correspond + + align:start position:0% +some values that correspond + + + align:start position:0% +some values that correspond +to situations where the class is not one + + align:start position:0% +to situations where the class is not one + + + align:start position:0% +to situations where the class is not one +of the things that are associated with + + align:start position:0% +of the things that are associated with + + + align:start position:0% +of the things that are associated with +this neuron and in that case what we see + + align:start position:0% +this neuron and in that case what we see + + + align:start position:0% +this neuron and in that case what we see +is examples that are over in this + + align:start position:0% +is examples that are over in this + + + align:start position:0% +is examples that are over in this +vicinity + + align:start position:0% + + + + align:start position:0% + +here so the probability that we would + + align:start position:0% +here so the probability that we would + + + align:start position:0% +here so the probability that we would +see this particular guy in this world is + + align:start position:0% +see this particular guy in this world is + + + align:start position:0% +see this particular guy in this world is +associated with the value on the sigma + + align:start position:0% +associated with the value on the sigma + + + align:start position:0% +associated with the value on the sigma +white curve so you can think of this as + + align:start position:0% +white curve so you can think of this as + + + align:start position:0% +white curve so you can think of this as +the probability of that positive example + + align:start position:0% +the probability of that positive example + + + align:start position:0% +the probability of that positive example +and this is the probability of that + + align:start position:0% +and this is the probability of that + + + align:start position:0% +and this is the probability of that +positive example and this is the + + align:start position:0% +positive example and this is the + + + align:start position:0% +positive example and this is the +probability of that positive example + + align:start position:0% +probability of that positive example + + + align:start position:0% +probability of that positive example +what's the probability of this negative + + align:start position:0% +what's the probability of this negative + + + align:start position:0% +what's the probability of this negative +example well it's one + + align:start position:0% +example well it's one + + + align:start position:0% +example well it's one +minus the value on that curve and this + + align:start position:0% +minus the value on that curve and this + + + align:start position:0% +minus the value on that curve and this +one's one minus the value on that + + align:start position:0% +one's one minus the value on that + + + align:start position:0% +one's one minus the value on that +curve so we could go through the + + align:start position:0% +curve so we could go through the + + + align:start position:0% +curve so we could go through the +calculations and what we would determine + + align:start position:0% +calculations and what we would determine + + + align:start position:0% +calculations and what we would determine +is that to maximize the probability of + + align:start position:0% +is that to maximize the probability of + + + align:start position:0% +is that to maximize the probability of +seeing this data this this particular + + align:start position:0% +seeing this data this this particular + + + align:start position:0% +seeing this data this this particular +stuff in a set of experiments to + + align:start position:0% +stuff in a set of experiments to + + + align:start position:0% +stuff in a set of experiments to +maximize that probability we would have + + align:start position:0% +maximize that probability we would have + + + align:start position:0% +maximize that probability we would have +to adjust T and W so as to get this + + align:start position:0% +to adjust T and W so as to get this + + + align:start position:0% +to adjust T and W so as to get this +curve doing the optimal thing and it's + + align:start position:0% +curve doing the optimal thing and it's + + + align:start position:0% +curve doing the optimal thing and it's +nothing mysterious about it it's just + + align:start position:0% +nothing mysterious about it it's just + + + align:start position:0% +nothing mysterious about it it's just +more partial derivatives and that sort + + align:start position:0% +more partial derivatives and that sort + + + align:start position:0% +more partial derivatives and that sort +of thing but the bottom line is that the + + align:start position:0% +of thing but the bottom line is that the + + + align:start position:0% +of thing but the bottom line is that the +probability of seeing this + + align:start position:0% + + + + align:start position:0% + +data is dependent on the shape of this + + align:start position:0% +data is dependent on the shape of this + + + align:start position:0% +data is dependent on the shape of this +curve and shape of this curve is + + align:start position:0% +curve and shape of this curve is + + + align:start position:0% +curve and shape of this curve is +dependent on those parameters and if we + + align:start position:0% +dependent on those parameters and if we + + + align:start position:0% +dependent on those parameters and if we +want to maximize the probability that + + align:start position:0% +want to maximize the probability that + + + align:start position:0% +want to maximize the probability that +we've seen this data then we have to + + align:start position:0% +we've seen this data then we have to + + + align:start position:0% +we've seen this data then we have to +adjust those parameters + + align:start position:0% +adjust those parameters + + + align:start position:0% +adjust those parameters +accordingly let's have a let's have a + + align:start position:0% +accordingly let's have a let's have a + + + align:start position:0% +accordingly let's have a let's have a +look at a demonstration + + align:start position:0% + + + + align:start position:0% + +okay so there's an ordinary sigid + + align:start position:0% +okay so there's an ordinary sigid + + + align:start position:0% +okay so there's an ordinary sigid +curve here are a couple positive + + align:start position:0% +curve here are a couple positive + + + align:start position:0% +curve here are a couple positive +examples here's + + align:start position:0% +examples here's + + + align:start position:0% +examples here's +a negative + + align:start position:0% + + + + align:start position:0% + +example let's put in some more positive + + align:start position:0% +example let's put in some more positive + + + align:start position:0% +example let's put in some more positive +examples over here + + align:start position:0% +examples over here + + + align:start position:0% +examples over here +and now let's run a a good + + align:start position:0% +and now let's run a a good + + + align:start position:0% +and now let's run a a good +old gradient Ascent algorithm on + + align:start position:0% +old gradient Ascent algorithm on + + + align:start position:0% +old gradient Ascent algorithm on +that and this is what + + align:start position:0% +that and this is what + + + align:start position:0% +that and this is what +happens you see how the probability as + + align:start position:0% +happens you see how the probability as + + + align:start position:0% +happens you see how the probability as +we adjust the shape of the curve the + + align:start position:0% +we adjust the shape of the curve the + + + align:start position:0% +we adjust the shape of the curve the +probability of seeing those examples of + + align:start position:0% +probability of seeing those examples of + + + align:start position:0% +probability of seeing those examples of +the class goes up and the probability of + + align:start position:0% +the class goes up and the probability of + + + align:start position:0% +the class goes up and the probability of +seeing the non-example goes + + align:start position:0% +seeing the non-example goes + + + align:start position:0% +seeing the non-example goes +down so what if we put some more uh + + align:start position:0% +down so what if we put some more uh + + + align:start position:0% +down so what if we put some more uh +examples in uh if we put a negative + + align:start position:0% +examples in uh if we put a negative + + + align:start position:0% +examples in uh if we put a negative +example there not much is going to + + align:start position:0% +example there not much is going to + + + align:start position:0% +example there not much is going to +happen What would happen if we put a + + align:start position:0% +happen What would happen if we put a + + + align:start position:0% +happen What would happen if we put a +positive example right + + align:start position:0% +positive example right + + + align:start position:0% +positive example right +there then we're going to start seeing + + align:start position:0% +there then we're going to start seeing + + + align:start position:0% +there then we're going to start seeing +some dramatic shifts in the shape of the + + align:start position:0% + + + + align:start position:0% + +curve so that's probably a noise point + + align:start position:0% +curve so that's probably a noise point + + + align:start position:0% +curve so that's probably a noise point +but we can put some more negative + + align:start position:0% +but we can put some more negative + + + align:start position:0% +but we can put some more negative +examples in + + align:start position:0% +examples in + + + align:start position:0% +examples in +there and see how that adjusts the Curve + + align:start position:0% + + + + align:start position:0% + +all right so that's what we're doing + + align:start position:0% +all right so that's what we're doing + + + align:start position:0% +all right so that's what we're doing +we're viewing this output value as + + align:start position:0% +we're viewing this output value as + + + align:start position:0% +we're viewing this output value as +something that's related to the + + align:start position:0% +something that's related to the + + + align:start position:0% +something that's related to the +probability of seeing a + + align:start position:0% +probability of seeing a + + + align:start position:0% +probability of seeing a +class and we're adjusting the parameters + + align:start position:0% +class and we're adjusting the parameters + + + align:start position:0% +class and we're adjusting the parameters +on that output layer so as to maximize + + align:start position:0% +on that output layer so as to maximize + + + align:start position:0% +on that output layer so as to maximize +the probability of the sample data that + + align:start position:0% +the probability of the sample data that + + + align:start position:0% +the probability of the sample data that +we've got in + + align:start position:0% +we've got in + + + align:start position:0% +we've got in +hand + + align:start position:0% +hand + + + align:start position:0% +hand +right now there's one more + + align:start position:0% +right now there's one more + + + align:start position:0% +right now there's one more +thing you can see what we've got here is + + align:start position:0% +thing you can see what we've got here is + + + align:start position:0% +thing you can see what we've got here is +we've got the basic idea of back + + align:start position:0% +we've got the basic idea of back + + + align:start position:0% +we've got the basic idea of back +propagation which has layers and layers + + align:start position:0% +propagation which has layers and layers + + + align:start position:0% +propagation which has layers and layers +of ADD + + align:start position:0% +of ADD + + + align:start position:0% +of ADD +um let me be flattering and call them + + align:start position:0% +um let me be flattering and call them + + + align:start position:0% +um let me be flattering and call them +ideas layered on top so here's the next + + align:start position:0% +ideas layered on top so here's the next + + + align:start position:0% +ideas layered on top so here's the next +here's the next idea that's layered on + + align:start position:0% +here's the next idea that's layered on + + + align:start position:0% +here's the next idea that's layered on +top so + + align:start position:0% +top so + + + align:start position:0% +top so +um we've got an output value + + align:start position:0% +um we've got an output value + + + align:start position:0% +um we've got an output value +here and it's a function after all and + + align:start position:0% +here and it's a function after all and + + + align:start position:0% +here and it's a function after all and +it's a it's it's got a value and we're + + align:start position:0% +it's a it's it's got a value and we're + + + align:start position:0% +it's a it's it's got a value and we're +going to have a uh if we have a th + + align:start position:0% +going to have a uh if we have a th + + + align:start position:0% +going to have a uh if we have a th +classes we're going to have a th output + + align:start position:0% +classes we're going to have a th output + + + align:start position:0% +classes we're going to have a th output +neurons and each is going to be + + align:start position:0% +neurons and each is going to be + + + align:start position:0% +neurons and each is going to be +producing some kind kind of value and we + + align:start position:0% +producing some kind kind of value and we + + + align:start position:0% +producing some kind kind of value and we +can think of that value as a + + align:start position:0% +can think of that value as a + + + align:start position:0% +can think of that value as a +probability but what it really but I + + align:start position:0% +probability but what it really but I + + + align:start position:0% +probability but what it really but I +don't want to write a probability yet I + + align:start position:0% +don't want to write a probability yet I + + + align:start position:0% +don't want to write a probability yet I +just want to say that what we've got for + + align:start position:0% +just want to say that what we've got for + + + align:start position:0% +just want to say that what we've got for +this output neuron is a function of + + align:start position:0% +this output neuron is a function of + + + align:start position:0% +this output neuron is a function of +class one and then there'll another be + + align:start position:0% +class one and then there'll another be + + + align:start position:0% +class one and then there'll another be +another output neuron which is a + + align:start position:0% +another output neuron which is a + + + align:start position:0% +another output neuron which is a +function of class two and these values + + align:start position:0% +function of class two and these values + + + align:start position:0% +function of class two and these values +will be presumably higher this will be + + align:start position:0% +will be presumably higher this will be + + + align:start position:0% +will be presumably higher this will be +higher if we are in fact looking at + + align:start position:0% +higher if we are in fact looking at + + + align:start position:0% +higher if we are in fact looking at +class one and this one down here will be + + align:start position:0% +class one and this one down here will be + + + align:start position:0% +class one and this one down here will be +in fact higher if we're looking at class + + align:start position:0% + + + + align:start position:0% + +in so what we like to do is we' like to + + align:start position:0% +in so what we like to do is we' like to + + + align:start position:0% +in so what we like to do is we' like to +uh not just pick one of these uh outputs + + align:start position:0% +uh not just pick one of these uh outputs + + + align:start position:0% +uh not just pick one of these uh outputs +and say well you're the you're the + + align:start position:0% +and say well you're the you're the + + + align:start position:0% +and say well you're the you're the +you've got the highest value so you win + + align:start position:0% +you've got the highest value so you win + + + align:start position:0% +you've got the highest value so you win +what we want to do instead is we want to + + align:start position:0% +what we want to do instead is we want to + + + align:start position:0% +what we want to do instead is we want to +give some we want to associate some kind + + align:start position:0% +give some we want to associate some kind + + + align:start position:0% +give some we want to associate some kind +of probability with each of the + + align:start position:0% +of probability with each of the + + + align:start position:0% +of probability with each of the +classes because after all we want to do + + align:start position:0% +classes because after all we want to do + + + align:start position:0% +classes because after all we want to do +things like find the most probable + + align:start position:0% +things like find the most probable + + + align:start position:0% +things like find the most probable +five so what we do is we say all right + + align:start position:0% +five so what we do is we say all right + + + align:start position:0% +five so what we do is we say all right +so the actual probability + + align:start position:0% +so the actual probability + + + align:start position:0% +so the actual probability +of class + + align:start position:0% +of class + + + align:start position:0% +of class +one is equal to the output of that + + align:start position:0% +one is equal to the output of that + + + align:start position:0% +one is equal to the output of that +sigmoid + + align:start position:0% + + + + align:start position:0% + +function divided by the sum over all + + align:start position:0% + + + + align:start position:0% + +functions so that takes all of that + + align:start position:0% +functions so that takes all of that + + + align:start position:0% +functions so that takes all of that +entire output vector and converts each + + align:start position:0% +entire output vector and converts each + + + align:start position:0% +entire output vector and converts each +output value into + + align:start position:0% +output value into + + + align:start position:0% +output value into +probability so when we use that sigo + + align:start position:0% +probability so when we use that sigo + + + align:start position:0% +probability so when we use that sigo +function we did it with a view toward + + align:start position:0% +function we did it with a view toward + + + align:start position:0% +function we did it with a view toward +thinking about that as a probability in + + align:start position:0% +thinking about that as a probability in + + + align:start position:0% +thinking about that as a probability in +fact we we assumed it was a probability + + align:start position:0% +fact we we assumed it was a probability + + + align:start position:0% +fact we we assumed it was a probability +when we uh made this argument but in the + + align:start position:0% +when we uh made this argument but in the + + + align:start position:0% +when we uh made this argument but in the +end there there's there's such an + + align:start position:0% +end there there's there's such an + + + align:start position:0% +end there there's there's such an +there's an output for each of those + + align:start position:0% +there's an output for each of those + + + align:start position:0% +there's an output for each of those +classes and so what we get is in the end + + align:start position:0% +classes and so what we get is in the end + + + align:start position:0% +classes and so what we get is in the end +not exactly a probability until we + + align:start position:0% +not exactly a probability until we + + + align:start position:0% +not exactly a probability until we +divide by a normalizing + + align:start position:0% +divide by a normalizing + + + align:start position:0% +divide by a normalizing +factor so this by the way is + + align:start position:0% +factor so this by the way is + + + align:start position:0% +factor so this by the way is +called this by the way is called uh not + + align:start position:0% +called this by the way is called uh not + + + align:start position:0% +called this by the way is called uh not +on my list of things but it soon will + + align:start position:0% + + + + align:start position:0% + +be since we're not talking about taking + + align:start position:0% +be since we're not talking about taking + + + align:start position:0% +be since we're not talking about taking +the maximum and identify ing + + align:start position:0% +the maximum and identify ing + + + align:start position:0% +the maximum and identify ing +the and using that to classify the + + align:start position:0% +the and using that to classify the + + + align:start position:0% +the and using that to classify the +picture what we're going to do is we're + + align:start position:0% +picture what we're going to do is we're + + + align:start position:0% +picture what we're going to do is we're +going to say uh we're going to use + + align:start position:0% +going to say uh we're going to use + + + align:start position:0% +going to say uh we're going to use +what's called + + align:start position:0% + + + + align:start position:0% + +softmax so we're going to give a a range + + align:start position:0% +softmax so we're going to give a a range + + + align:start position:0% +softmax so we're going to give a a range +of classifications and we're going to + + align:start position:0% +of classifications and we're going to + + + align:start position:0% +of classifications and we're going to +associate a probability with each and + + align:start position:0% +associate a probability with each and + + + align:start position:0% +associate a probability with each and +that's what that's what you saw in in in + + align:start position:0% +that's what that's what you saw in in in + + + align:start position:0% +that's what that's what you saw in in in +in all of those samples you saw yes this + + align:start position:0% +in all of those samples you saw yes this + + + align:start position:0% +in all of those samples you saw yes this +is a container ship but maybe it's also + + align:start position:0% +is a container ship but maybe it's also + + + align:start position:0% +is a container ship but maybe it's also +this or that or third or fourth or fifth + + align:start position:0% +this or that or third or fourth or fifth + + + align:start position:0% +this or that or third or fourth or fifth +thing so that is + + align:start position:0% + + + + align:start position:0% + +a pretty good summary of the kinds of + + align:start position:0% +a pretty good summary of the kinds of + + + align:start position:0% +a pretty good summary of the kinds of +things that are involved but now we've + + align:start position:0% +things that are involved but now we've + + + align:start position:0% +things that are involved but now we've +got one more step because what we can do + + align:start position:0% +got one more step because what we can do + + + align:start position:0% +got one more step because what we can do +now is we can take this output layer + + align:start position:0% +now is we can take this output layer + + + align:start position:0% +now is we can take this output layer +idea the softmax idea and we can put it + + align:start position:0% +idea the softmax idea and we can put it + + + align:start position:0% +idea the softmax idea and we can put it +together with the auto coding + + align:start position:0% + + + + align:start position:0% + +idea so we've trained this uh middle + + align:start position:0% +idea so we've trained this uh middle + + + align:start position:0% +idea so we've trained this uh middle +layer up and now we're going to detach + + align:start position:0% +layer up and now we're going to detach + + + align:start position:0% +layer up and now we're going to detach +it from the output layer but retain + + align:start position:0% +it from the output layer but retain + + + align:start position:0% +it from the output layer but retain +those weights that connect the input to + + align:start position:0% +those weights that connect the input to + + + align:start position:0% +those weights that connect the input to +the hidden layer and when we do that + + align:start position:0% +the hidden layer and when we do that + + + align:start position:0% +the hidden layer and when we do that +what we're going to see is something + + align:start position:0% +what we're going to see is something + + + align:start position:0% +what we're going to see is something +that looks like + + align:start position:0% +that looks like + + + align:start position:0% +that looks like +this and now we've got a trained first + + align:start position:0% +this and now we've got a trained first + + + align:start position:0% +this and now we've got a trained first +layer but an untrained output layer + + align:start position:0% +layer but an untrained output layer + + + align:start position:0% +layer but an untrained output layer +we're going to freeze the input layer + + align:start position:0% +we're going to freeze the input layer + + + align:start position:0% +we're going to freeze the input layer +and train the output layer using that + + align:start position:0% +and train the output layer using that + + + align:start position:0% +and train the output layer using that +that that that so-called that sigmoid + + align:start position:0% +that that that so-called that sigmoid + + + align:start position:0% +that that that so-called that sigmoid +curve let's see what happens when we do + + align:start position:0% +curve let's see what happens when we do + + + align:start position:0% +curve let's see what happens when we do +that oh by the way let's let's run our + + align:start position:0% +that oh by the way let's let's run our + + + align:start position:0% +that oh by the way let's let's run our +test samples + + align:start position:0% +test samples + + + align:start position:0% +test samples +through you can see it's not doing + + align:start position:0% +through you can see it's not doing + + + align:start position:0% +through you can see it's not doing +anything the output is half for each of + + align:start position:0% +anything the output is half for each of + + + align:start position:0% +anything the output is half for each of +the + + align:start position:0% +the + + + align:start position:0% +the +categories even though we we got a train + + align:start position:0% +categories even though we we got a train + + + align:start position:0% +categories even though we we got a train +middle layer so we have to train the + + align:start position:0% +middle layer so we have to train the + + + align:start position:0% +middle layer so we have to train the +outer layer let's see how long it takes + + align:start position:0% +outer layer let's see how long it takes + + + align:start position:0% +outer layer let's see how long it takes +whoa that was pretty + + align:start position:0% +whoa that was pretty + + + align:start position:0% +whoa that was pretty +fast now there's a extraordinarily good + + align:start position:0% +fast now there's a extraordinarily good + + + align:start position:0% +fast now there's a extraordinarily good +match between the outputs and the + + align:start position:0% +match between the outputs and the + + + align:start position:0% +match between the outputs and the +desired outputs so that's a combination + + align:start position:0% +desired outputs so that's a combination + + + align:start position:0% +desired outputs so that's a combination +of the auto coding idea and the softmax + + align:start position:0% + + + + align:start position:0% + +idea they get one more + + align:start position:0% +idea they get one more + + + align:start position:0% +idea they get one more +idea that's worthy + + align:start position:0% +idea that's worthy + + + align:start position:0% +idea that's worthy +mention and that's the idea of dropout + + align:start position:0% + + + + align:start position:0% + +the the plague of any neural net is that + + align:start position:0% +the the plague of any neural net is that + + + align:start position:0% +the the plague of any neural net is that +it gets stuck in some kind of local + + align:start position:0% +it gets stuck in some kind of local + + + align:start position:0% +it gets stuck in some kind of local +maximum so it was discovered that these + + align:start position:0% +maximum so it was discovered that these + + + align:start position:0% +maximum so it was discovered that these +things train better if on every + + align:start position:0% +things train better if on every + + + align:start position:0% +things train better if on every +iteration you you + + align:start position:0% +iteration you you + + + align:start position:0% +iteration you you +um flip a coin for each + + align:start position:0% +um flip a coin for each + + + align:start position:0% +um flip a coin for each +neuron and if the coin ends up tails you + + align:start position:0% +neuron and if the coin ends up tails you + + + align:start position:0% +neuron and if the coin ends up tails you +assume it's just died and has no + + align:start position:0% +assume it's just died and has no + + + align:start position:0% +assume it's just died and has no +influence on the output it's called + + align:start position:0% +influence on the output it's called + + + align:start position:0% +influence on the output it's called +dropping out those + + align:start position:0% +dropping out those + + + align:start position:0% +dropping out those +neurons and then on the Next Generation + + align:start position:0% +neurons and then on the Next Generation + + + align:start position:0% +neurons and then on the Next Generation +you drop out a different + + align:start position:0% +you drop out a different + + + align:start position:0% +you drop out a different +set so what this seems to do is it seems + + align:start position:0% +set so what this seems to do is it seems + + + align:start position:0% +set so what this seems to do is it seems +to get this thing from prevent this + + align:start position:0% +to get this thing from prevent this + + + align:start position:0% +to get this thing from prevent this +thing from going + + align:start position:0% +thing from going + + + align:start position:0% +thing from going +into a frozen local maximum + + align:start position:0% + + + + align:start position:0% + +state so that's deep Nets uh they should + + align:start position:0% +state so that's deep Nets uh they should + + + align:start position:0% +state so that's deep Nets uh they should +be called by the way wide + + align:start position:0% +be called by the way wide + + + align:start position:0% +be called by the way wide +Nets because they tend to be enormously + + align:start position:0% +Nets because they tend to be enormously + + + align:start position:0% +Nets because they tend to be enormously +wide but rarely more than 10 + + align:start position:0% +wide but rarely more than 10 + + + align:start position:0% +wide but rarely more than 10 +layers 10 layers 10 columns uh + + align:start position:0% +layers 10 layers 10 columns uh + + + align:start position:0% +layers 10 layers 10 columns uh +deep now let's see where' it go from + + align:start position:0% +deep now let's see where' it go from + + + align:start position:0% +deep now let's see where' it go from +here um maybe what we should do is talk + + align:start position:0% +here um maybe what we should do is talk + + + align:start position:0% +here um maybe what we should do is talk +about the + + align:start position:0% +about the + + + align:start position:0% +about the +awesome uh curiosity in the current + + align:start position:0% +awesome uh curiosity in the current + + + align:start position:0% +awesome uh curiosity in the current +state-ofthe-art + + align:start position:0% +state-ofthe-art + + + align:start position:0% +state-ofthe-art +and that is + + align:start position:0% +and that is + + + align:start position:0% +and that is +that all of this sophistication with uh + + align:start position:0% +that all of this sophistication with uh + + + align:start position:0% +that all of this sophistication with uh +output layers that are probabilities and + + align:start position:0% +output layers that are probabilities and + + + align:start position:0% +output layers that are probabilities and +uh training using autoc coding or bolman + + align:start position:0% +uh training using autoc coding or bolman + + + align:start position:0% +uh training using autoc coding or bolman +machines + + align:start position:0% +machines + + + align:start position:0% +machines +um it doesn't seem to help much relative + + align:start position:0% +um it doesn't seem to help much relative + + + align:start position:0% +um it doesn't seem to help much relative +to plain + + align:start position:0% +to plain + + + align:start position:0% +to plain +old back + + align:start position:0% +old back + + + align:start position:0% +old back +propagation so back propagation with a + + align:start position:0% +propagation so back propagation with a + + + align:start position:0% +propagation so back propagation with a +convolutional net seems to be do just + + align:start position:0% +convolutional net seems to be do just + + + align:start position:0% +convolutional net seems to be do just +about as good as + + align:start position:0% +about as good as + + + align:start position:0% +about as good as +anything and while while we're on the + + align:start position:0% +anything and while while we're on the + + + align:start position:0% +anything and while while we're on the +subject of a a ordinary deep net I'd + + align:start position:0% +subject of a a ordinary deep net I'd + + + align:start position:0% +subject of a a ordinary deep net I'd +like to examine a situation here where + + align:start position:0% +like to examine a situation here where + + + align:start position:0% +like to examine a situation here where +we have a deep + + align:start position:0% +we have a deep + + + align:start position:0% +we have a deep +net well it's not really it's not very + + align:start position:0% +net well it's not really it's not very + + + align:start position:0% +net well it's not really it's not very +it's a classroom deep net + + align:start position:0% + + + + align:start position:0% + +and we'll put five layers in + + align:start position:0% +and we'll put five layers in + + + align:start position:0% +and we'll put five layers in +there and its job is still to do the + + align:start position:0% +there and its job is still to do the + + + align:start position:0% +there and its job is still to do the +same thing it's a classify an animal as + + align:start position:0% +same thing it's a classify an animal as + + + align:start position:0% +same thing it's a classify an animal as +a cheetah a zebra or a giraffe based on + + align:start position:0% +a cheetah a zebra or a giraffe based on + + + align:start position:0% +a cheetah a zebra or a giraffe based on +the height of the Shadow it + + align:start position:0% +the height of the Shadow it + + + align:start position:0% +the height of the Shadow it +casts and as before if it's green that + + align:start position:0% +casts and as before if it's green that + + + align:start position:0% +casts and as before if it's green that +means positive if it's red that means + + align:start position:0% +means positive if it's red that means + + + align:start position:0% +means positive if it's red that means +negative and right at the moment we have + + align:start position:0% +negative and right at the moment we have + + + align:start position:0% +negative and right at the moment we have +no + + align:start position:0% +no + + + align:start position:0% +no +training so if we run our test samples + + align:start position:0% +training so if we run our test samples + + + align:start position:0% +training so if we run our test samples +through the output is always a half no + + align:start position:0% +through the output is always a half no + + + align:start position:0% +through the output is always a half no +matter what the animal + + align:start position:0% +matter what the animal + + + align:start position:0% +matter what the animal +is all right so what we're going to do + + align:start position:0% +is all right so what we're going to do + + + align:start position:0% +is all right so what we're going to do +is just going to use ordinary back + + align:start position:0% +is just going to use ordinary back + + + align:start position:0% +is just going to use ordinary back +propop on + + align:start position:0% +propop on + + + align:start position:0% +propop on +this same thing as + + align:start position:0% +this same thing as + + + align:start position:0% +this same thing as +in that uh sample that's underneath the + + align:start position:0% +in that uh sample that's underneath the + + + align:start position:0% +in that uh sample that's underneath the +Blackboard only now we've got a lot more + + align:start position:0% +Blackboard only now we've got a lot more + + + align:start position:0% +Blackboard only now we've got a lot more +parameters we've got five columns and + + align:start position:0% +parameters we've got five columns and + + + align:start position:0% +parameters we've got five columns and +each one of them has nine or 10 neurons + + align:start position:0% +each one of them has nine or 10 neurons + + + align:start position:0% +each one of them has nine or 10 neurons +in it so let's let's let this one + + align:start position:0% + + + + align:start position:0% + +run now look at that stuff on right it's + + align:start position:0% +run now look at that stuff on right it's + + + align:start position:0% +run now look at that stuff on right it's +all turned red at first I thought this + + align:start position:0% +all turned red at first I thought this + + + align:start position:0% +all turned red at first I thought this +was a bug in my + + align:start position:0% +was a bug in my + + + align:start position:0% +was a bug in my +program but you know it makes absolute + + align:start position:0% +program but you know it makes absolute + + + align:start position:0% +program but you know it makes absolute +sense if you don't know what the actual + + align:start position:0% +sense if you don't know what the actual + + + align:start position:0% +sense if you don't know what the actual +animal is going to be and there are a + + align:start position:0% +animal is going to be and there are a + + + align:start position:0% +animal is going to be and there are a +whole bunch of possibilities you better + + align:start position:0% +whole bunch of possibilities you better + + + align:start position:0% +whole bunch of possibilities you better +just say no for everybody it's like when + + align:start position:0% +just say no for everybody it's like when + + + align:start position:0% +just say no for everybody it's like when +a biologist says we don't know that's + + align:start position:0% +a biologist says we don't know that's + + + align:start position:0% +a biologist says we don't know that's +the most probable + + align:start position:0% +the most probable + + + align:start position:0% +the most probable +answer well but eventually after about + + align:start position:0% +answer well but eventually after about + + + align:start position:0% +answer well but eventually after about +160,000 iterations it seems to have got + + align:start position:0% +160,000 iterations it seems to have got + + + align:start position:0% +160,000 iterations it seems to have got +it let's run the test samples through + + align:start position:0% + + + + align:start position:0% + +yeah it's doing great let's do it again + + align:start position:0% +yeah it's doing great let's do it again + + + align:start position:0% +yeah it's doing great let's do it again +just to see if this is a + + align:start position:0% + + + + align:start position:0% + +fluke all red on the right + + align:start position:0% + + + + align:start position:0% + +side finally you start seeing some + + align:start position:0% +side finally you start seeing some + + + align:start position:0% +side finally you start seeing some +changes go in the in the in the final + + align:start position:0% +changes go in the in the in the final + + + align:start position:0% +changes go in the in the in the final +layers there and if you look at the air + + align:start position:0% +layers there and if you look at the air + + + align:start position:0% +layers there and if you look at the air +rate uh down at the bottom you see that + + align:start position:0% +rate uh down at the bottom you see that + + + align:start position:0% +rate uh down at the bottom you see that +it kind of kind of falls off a cliff so + + align:start position:0% +it kind of kind of falls off a cliff so + + + align:start position:0% +it kind of kind of falls off a cliff so +nothing happens for a real long time and + + align:start position:0% +nothing happens for a real long time and + + + align:start position:0% +nothing happens for a real long time and +then it falls off the + + align:start position:0% + + + + align:start position:0% + +cliff now what would happen uh if uh + + align:start position:0% +cliff now what would happen uh if uh + + + align:start position:0% +cliff now what would happen uh if uh +this uh neural net were not quite so + + align:start position:0% +this uh neural net were not quite so + + + align:start position:0% +this uh neural net were not quite so +wide good question but before we get to + + align:start position:0% +wide good question but before we get to + + + align:start position:0% +wide good question but before we get to +that question what I'm going to do is + + align:start position:0% +that question what I'm going to do is + + + align:start position:0% +that question what I'm going to do is +I'm going to do a a funny kind of + + align:start position:0% +I'm going to do a a funny kind of + + + align:start position:0% +I'm going to do a a funny kind of +variation on the theme of Dropout what + + align:start position:0% +variation on the theme of Dropout what + + + align:start position:0% +variation on the theme of Dropout what +I'm going to do is I'm going to kill off + + align:start position:0% +I'm going to do is I'm going to kill off + + + align:start position:0% +I'm going to do is I'm going to kill off +one neuron in each column + + align:start position:0% +one neuron in each column + + + align:start position:0% +one neuron in each column +and then see what if if I can retrain + + align:start position:0% +and then see what if if I can retrain + + + align:start position:0% +and then see what if if I can retrain +the network to do the right + + align:start position:0% +the network to do the right + + + align:start position:0% +the network to do the right +thing so I'm going to reassign those to + + align:start position:0% +thing so I'm going to reassign those to + + + align:start position:0% +thing so I'm going to reassign those to +some other purpose so now there's one + + align:start position:0% +some other purpose so now there's one + + + align:start position:0% +some other purpose so now there's one +fewer neuron in the network if we rerun + + align:start position:0% +fewer neuron in the network if we rerun + + + align:start position:0% +fewer neuron in the network if we rerun +that we see that it trains itself up + + align:start position:0% +that we see that it trains itself up + + + align:start position:0% +that we see that it trains itself up +very fast so we seem to be still close + + align:start position:0% +very fast so we seem to be still close + + + align:start position:0% +very fast so we seem to be still close +enough to a solution we can do + + align:start position:0% +enough to a solution we can do + + + align:start position:0% +enough to a solution we can do +without uh one uh you know one of the + + align:start position:0% +without uh one uh you know one of the + + + align:start position:0% +without uh one uh you know one of the +neurons in each column let's do it + + align:start position:0% +neurons in each column let's do it + + + align:start position:0% +neurons in each column let's do it +again yeah it goes up a little bit but + + align:start position:0% +again yeah it goes up a little bit but + + + align:start position:0% +again yeah it goes up a little bit but +quickly Falls falls down to a + + align:start position:0% +quickly Falls falls down to a + + + align:start position:0% +quickly Falls falls down to a +solution try + + align:start position:0% +solution try + + + align:start position:0% +solution try +again quickly falls down to a + + align:start position:0% +again quickly falls down to a + + + align:start position:0% +again quickly falls down to a +solution oh my God how much is this am I + + align:start position:0% +solution oh my God how much is this am I + + + align:start position:0% +solution oh my God how much is this am I +going to do each time I knock something + + align:start position:0% +going to do each time I knock something + + + align:start position:0% +going to do each time I knock something +out and retrain it finds a solution very + + align:start position:0% +out and retrain it finds a solution very + + + align:start position:0% +out and retrain it finds a solution very +fast + + align:start position:0% + + + + align:start position:0% + +whoa I got all the way down to two + + align:start position:0% +whoa I got all the way down to two + + + align:start position:0% +whoa I got all the way down to two +neurons in each column and it still has + + align:start position:0% +neurons in each column and it still has + + + align:start position:0% +neurons in each column and it still has +a + + align:start position:0% +a + + + align:start position:0% +a +solution it's interesting don't you + + align:start position:0% +solution it's interesting don't you + + + align:start position:0% +solution it's interesting don't you +think uh but let's uh repeat the + + align:start position:0% +think uh but let's uh repeat the + + + align:start position:0% +think uh but let's uh repeat the +experiment but this time we're going to + + align:start position:0% +experiment but this time we're going to + + + align:start position:0% +experiment but this time we're going to +do it a little differently we're going + + align:start position:0% +do it a little differently we're going + + + align:start position:0% +do it a little differently we're going +to take our five layers and we're going + + align:start position:0% +to take our five layers and we're going + + + align:start position:0% +to take our five layers and we're going +to before we do any training I'm going + + align:start position:0% +to before we do any training I'm going + + + align:start position:0% +to before we do any training I'm going +to knock + + align:start position:0% + + + + align:start position:0% + +out all but two neurons in each column + + align:start position:0% +out all but two neurons in each column + + + align:start position:0% +out all but two neurons in each column +now I know that with two ands in each + + align:start position:0% +now I know that with two ands in each + + + align:start position:0% +now I know that with two ands in each +column I've got it a solution I just + + align:start position:0% +column I've got it a solution I just + + + align:start position:0% +column I've got it a solution I just +showed it I just showed one let's run it + + align:start position:0% +showed it I just showed one let's run it + + + align:start position:0% +showed it I just showed one let's run it +with uh this + + align:start position:0% + + + + align:start position:0% + +way it looks like increasingly bad + + align:start position:0% +way it looks like increasingly bad + + + align:start position:0% +way it looks like increasingly bad +news what's happened is that this sucker + + align:start position:0% +news what's happened is that this sucker + + + align:start position:0% +news what's happened is that this sucker +has got itself into a local maximum + + align:start position:0% +has got itself into a local maximum + + + align:start position:0% +has got itself into a local maximum +so now you can see + + align:start position:0% +so now you can see + + + align:start position:0% +so now you can see +why there's been a breakthrough in in + + align:start position:0% +why there's been a breakthrough in in + + + align:start position:0% +why there's been a breakthrough in in +this neural net learning stuff and it's + + align:start position:0% +this neural net learning stuff and it's + + + align:start position:0% +this neural net learning stuff and it's +because when you widen the net you turn + + align:start position:0% +because when you widen the net you turn + + + align:start position:0% +because when you widen the net you turn +local Maxima into saddle + + align:start position:0% +local Maxima into saddle + + + align:start position:0% +local Maxima into saddle +points so now it's got a way of crawling + + align:start position:0% +points so now it's got a way of crawling + + + align:start position:0% +points so now it's got a way of crawling +its way through this vast space without + + align:start position:0% +its way through this vast space without + + + align:start position:0% +its way through this vast space without +getting stuck on a local maximum as + + align:start position:0% +getting stuck on a local maximum as + + + align:start position:0% +getting stuck on a local maximum as +suggested by + + align:start position:0% +suggested by + + + align:start position:0% +suggested by +this all right so those are some uh I + + align:start position:0% +this all right so those are some uh I + + + align:start position:0% +this all right so those are some uh I +think interesting uh + + align:start position:0% +think interesting uh + + + align:start position:0% +think interesting uh +things to look at um by way of uh these + + align:start position:0% +things to look at um by way of uh these + + + align:start position:0% +things to look at um by way of uh these +demonstrations but now I'd like to go + + align:start position:0% +demonstrations but now I'd like to go + + + align:start position:0% +demonstrations but now I'd like to go +back to my slide set and show you some + + align:start position:0% +back to my slide set and show you some + + + align:start position:0% +back to my slide set and show you some +examples that will address the question + + align:start position:0% +examples that will address the question + + + align:start position:0% +examples that will address the question +of whether these things are seeing like + + align:start position:0% +of whether these things are seeing like + + + align:start position:0% +of whether these things are seeing like +we + + align:start position:0% + + + + align:start position:0% + +see so you can try these examples online + + align:start position:0% +see so you can try these examples online + + + align:start position:0% +see so you can try these examples online +there are a variety of websites that + + align:start position:0% +there are a variety of websites that + + + align:start position:0% +there are a variety of websites that +allow you to put in your own picture + + align:start position:0% +allow you to put in your own picture + + + align:start position:0% +allow you to put in your own picture +and there uh is a cottage industry of + + align:start position:0% +and there uh is a cottage industry of + + + align:start position:0% +and there uh is a cottage industry of +producing uh papers in journals uh that + + align:start position:0% +producing uh papers in journals uh that + + + align:start position:0% +producing uh papers in journals uh that +fool neuron Nets so in this case a very + + align:start position:0% +fool neuron Nets so in this case a very + + + align:start position:0% +fool neuron Nets so in this case a very +small number of pixels have been changed + + align:start position:0% +small number of pixels have been changed + + + align:start position:0% +small number of pixels have been changed +you don't see the difference but it's + + align:start position:0% +you don't see the difference but it's + + + align:start position:0% +you don't see the difference but it's +enough to take it take this particular + + align:start position:0% +enough to take it take this particular + + + align:start position:0% +enough to take it take this particular +neural net from a high confidence that + + align:start position:0% +neural net from a high confidence that + + + align:start position:0% +neural net from a high confidence that +it's looking at a school bus to to to + + align:start position:0% +it's looking at a school bus to to to + + + align:start position:0% +it's looking at a school bus to to to +thinking that it's not a not a school + + align:start position:0% +thinking that it's not a not a school + + + align:start position:0% +thinking that it's not a not a school +bus those are some things that think are + + align:start position:0% +bus those are some things that think are + + + align:start position:0% +bus those are some things that think are +a school + + align:start position:0% + + + + align:start position:0% + +bus so to appears to be the case that + + align:start position:0% +bus so to appears to be the case that + + + align:start position:0% +bus so to appears to be the case that +what is triggering this school bus + + align:start position:0% +what is triggering this school bus + + + align:start position:0% +what is triggering this school bus +result is that it's seeing enough local + + align:start position:0% +result is that it's seeing enough local + + + align:start position:0% +result is that it's seeing enough local +evidence that this is not one of the + + align:start position:0% +evidence that this is not one of the + + + align:start position:0% +evidence that this is not one of the +other 999 + + align:start position:0% +other 999 + + + align:start position:0% +other 999 +classes and and enough positive evidence + + align:start position:0% +classes and and enough positive evidence + + + align:start position:0% +classes and and enough positive evidence +from the from these these local looks to + + align:start position:0% +from the from these these local looks to + + + align:start position:0% +from the from these these local looks to +conclude that it's a school + + align:start position:0% + + + + align:start position:0% + +bus so do you see any of those things I + + align:start position:0% + + + + align:start position:0% + +don't here you can say okay well look at + + align:start position:0% +don't here you can say okay well look at + + + align:start position:0% +don't here you can say okay well look at +that base one yeah that looks like it's + + align:start position:0% +that base one yeah that looks like it's + + + align:start position:0% +that base one yeah that looks like it's +got a little bit of baseball texture in + + align:start position:0% +got a little bit of baseball texture in + + + align:start position:0% +got a little bit of baseball texture in +it so maybe what it's doing is looking + + align:start position:0% +it so maybe what it's doing is looking + + + align:start position:0% +it so maybe what it's doing is looking +at + + align:start position:0% + + + + align:start position:0% + +texture uh these are some uh examples + + align:start position:0% +texture uh these are some uh examples + + + align:start position:0% +texture uh these are some uh examples +from a a recent and very famous uh paper + + align:start position:0% +from a a recent and very famous uh paper + + + align:start position:0% +from a a recent and very famous uh paper +by Google uh which uses essentially the + + align:start position:0% +by Google uh which uses essentially the + + + align:start position:0% +by Google uh which uses essentially the +same ideas to put captions on uh + + align:start position:0% +same ideas to put captions on uh + + + align:start position:0% +same ideas to put captions on uh +pictures so the thing that this by the + + align:start position:0% +pictures so the thing that this by the + + + align:start position:0% +pictures so the thing that this by the +way is what has stimulated all this + + align:start position:0% +way is what has stimulated all this + + + align:start position:0% +way is what has stimulated all this +enormous concern about artificial + + align:start position:0% +enormous concern about artificial + + + align:start position:0% +enormous concern about artificial +intelligence because naive viewer looks + + align:start position:0% +intelligence because naive viewer looks + + + align:start position:0% +intelligence because naive viewer looks +at that picture and says oh my God this + + align:start position:0% +at that picture and says oh my God this + + + align:start position:0% +at that picture and says oh my God this +thing knows what it's like to play or be + + align:start position:0% +thing knows what it's like to play or be + + + align:start position:0% +thing knows what it's like to play or be +young or move or what a frisbee is and + + align:start position:0% +young or move or what a frisbee is and + + + align:start position:0% +young or move or what a frisbee is and +of course it knows none of that it just + + align:start position:0% +of course it knows none of that it just + + + align:start position:0% +of course it knows none of that it just +knows how to label this + + align:start position:0% +knows how to label this + + + align:start position:0% +knows how to label this +picture and to the credit of the people + + align:start position:0% +picture and to the credit of the people + + + align:start position:0% +picture and to the credit of the people +wrote this paper they show examples that + + align:start position:0% +wrote this paper they show examples that + + + align:start position:0% +wrote this paper they show examples that +don't do so + + align:start position:0% +don't do so + + + align:start position:0% +don't do so +well so yeah it's a cat but it's not + + align:start position:0% +well so yeah it's a cat but it's not + + + align:start position:0% +well so yeah it's a cat but it's not +lying's a little girl but she's not + + align:start position:0% +lying's a little girl but she's not + + + align:start position:0% +lying's a little girl but she's not +blowing + + align:start position:0% +blowing + + + align:start position:0% +blowing +bubbles what about this one + + align:start position:0% + + + + align:start position:0% + +so we've been doing our own work in my + + align:start position:0% +so we've been doing our own work in my + + + align:start position:0% +so we've been doing our own work in my +laboratory on uh on some of this and and + + align:start position:0% +laboratory on uh on some of this and and + + + align:start position:0% +laboratory on uh on some of this and and +and and the way the following set of + + align:start position:0% +and and the way the following set of + + + align:start position:0% +and and the way the following set of +pictures was produced was this you you + + align:start position:0% +pictures was produced was this you you + + + align:start position:0% +pictures was produced was this you you +take an image and you separate into a + + align:start position:0% +take an image and you separate into a + + + align:start position:0% +take an image and you separate into a +bunch of slices representing each + + align:start position:0% +bunch of slices representing each + + + align:start position:0% +bunch of slices representing each +representing a particular frequency band + + align:start position:0% +representing a particular frequency band + + + align:start position:0% +representing a particular frequency band +and then you go into one of those uh + + align:start position:0% +and then you go into one of those uh + + + align:start position:0% +and then you go into one of those uh +frequency bands and you knock out a + + align:start position:0% +frequency bands and you knock out a + + + align:start position:0% +frequency bands and you knock out a +rectangle from the picture and then you + + align:start position:0% +rectangle from the picture and then you + + + align:start position:0% +rectangle from the picture and then you +reassemble the + + align:start position:0% +reassemble the + + + align:start position:0% +reassemble the +thing and if you hadn't knocked that + + align:start position:0% +thing and if you hadn't knocked that + + + align:start position:0% +thing and if you hadn't knocked that +piece out when you reassemble it it + + align:start position:0% +piece out when you reassemble it it + + + align:start position:0% +piece out when you reassemble it it +would look exactly like it did when you + + align:start position:0% +would look exactly like it did when you + + + align:start position:0% +would look exactly like it did when you +started so what we're doing is we knock + + align:start position:0% +started so what we're doing is we knock + + + align:start position:0% +started so what we're doing is we knock +out as much as we can and still retain + + align:start position:0% +out as much as we can and still retain + + + align:start position:0% +out as much as we can and still retain +the neural Net's impression that it's + + align:start position:0% +the neural Net's impression that it's + + + align:start position:0% +the neural Net's impression that it's +the thing that it started out thinking + + align:start position:0% +the thing that it started out thinking + + + align:start position:0% +the thing that it started out thinking +it was so what do you think this + + align:start position:0% + + + + align:start position:0% + +is It's identified by a neural net as a + + align:start position:0% +is It's identified by a neural net as a + + + align:start position:0% +is It's identified by a neural net as a +railroad car because this is the image + + align:start position:0% +railroad car because this is the image + + + align:start position:0% +railroad car because this is the image +that it started + + align:start position:0% +that it started + + + align:start position:0% +that it started +with how about this one that's easy + + align:start position:0% +with how about this one that's easy + + + align:start position:0% +with how about this one that's easy +right that's a guitar we weren't able to + + align:start position:0% +right that's a guitar we weren't able to + + + align:start position:0% +right that's a guitar we weren't able to +mutilate that one very much and still + + align:start position:0% +mutilate that one very much and still + + + align:start position:0% +mutilate that one very much and still +retain the guitar of + + align:start position:0% +retain the guitar of + + + align:start position:0% +retain the guitar of +it how about this + + align:start position:0% +it how about this + + + align:start position:0% +it how about this +one what's that what a lamp any other + + align:start position:0% +one what's that what a lamp any other + + + align:start position:0% +one what's that what a lamp any other +ideas Ken what do you think it + + align:start position:0% +ideas Ken what do you think it + + + align:start position:0% +ideas Ken what do you think it +is see he's an expert on the + + align:start position:0% +is see he's an expert on the + + + align:start position:0% +is see he's an expert on the +subject who was identified as a + + align:start position:0% +subject who was identified as a + + + align:start position:0% +subject who was identified as a +barbell what's + + align:start position:0% +barbell what's + + + align:start position:0% +barbell what's +that what cello you didn't see the + + align:start position:0% +that what cello you didn't see the + + + align:start position:0% +that what cello you didn't see the +little girl or the instructor how about + + align:start position:0% +little girl or the instructor how about + + + align:start position:0% +little girl or the instructor how about +this + + align:start position:0% +this + + + align:start position:0% +this +one + + align:start position:0% + + + + align:start position:0% + +what it's a + + align:start position:0% +what it's a + + + align:start position:0% +what it's a +grasshopper what's this wow you're + + align:start position:0% +grasshopper what's this wow you're + + + align:start position:0% +grasshopper what's this wow you're +good it's actually not a two-headed + + align:start position:0% +good it's actually not a two-headed + + + align:start position:0% +good it's actually not a two-headed +wolf so two wolves are close + + align:start position:0% + + + + align:start position:0% + +together it's a bird right + + align:start position:0% +together it's a bird right + + + align:start position:0% +together it's a bird right +good for you it's a + + align:start position:0% + + + + align:start position:0% + +rabbit about + + align:start position:0% + + + + align:start position:0% + +that Russian wolf + + align:start position:0% + + + + align:start position:0% + +found if you've been to Venice you + + align:start position:0% +found if you've been to Venice you + + + align:start position:0% +found if you've been to Venice you +recognize + + align:start position:0% + + + + align:start position:0% + +this so bottom line is that these things + + align:start position:0% +this so bottom line is that these things + + + align:start position:0% +this so bottom line is that these things +are an engineering Marvel and do great + + align:start position:0% +are an engineering Marvel and do great + + + align:start position:0% +are an engineering Marvel and do great +things but they don't see like we see \ No newline at end of file diff --git a/W_rm0DcTeqo.txt b/W_rm0DcTeqo.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4954cb0d7c209bb3f3cc1758d2b7755303778a2 --- /dev/null +++ b/W_rm0DcTeqo.txt @@ -0,0 +1,771 @@ +align:start position:0% + +I came to Caltech during my first year + + align:start position:0% +I came to Caltech during my first year + + + align:start position:0% +I came to Caltech during my first year +in my Graduate Studies and I saw people + + align:start position:0% +in my Graduate Studies and I saw people + + + align:start position:0% +in my Graduate Studies and I saw people +looking at diversity at the Single Cell + + align:start position:0% +looking at diversity at the Single Cell + + + align:start position:0% +looking at diversity at the Single Cell +level and they were using bacteria at + + align:start position:0% +level and they were using bacteria at + + + align:start position:0% +level and they were using bacteria at +the time and they had toothpicks and + + align:start position:0% +the time and they had toothpicks and + + + align:start position:0% +the time and they had toothpicks and +they were picking tens of thousands of + + align:start position:0% +they were picking tens of thousands of + + + align:start position:0% +they were picking tens of thousands of +colonies off these plates with + + align:start position:0% +colonies off these plates with + + + align:start position:0% +colonies off these plates with +toothpicks and putting them into Wells + + align:start position:0% +toothpicks and putting them into Wells + + + align:start position:0% +toothpicks and putting them into Wells +and this is how they were physically + + align:start position:0% +and this is how they were physically + + + align:start position:0% +and this is how they were physically +isolating individual bacteria to look at + + align:start position:0% +isolating individual bacteria to look at + + + align:start position:0% +isolating individual bacteria to look at +different anomatic expression levels say + + align:start position:0% +different anomatic expression levels say + + + align:start position:0% +different anomatic expression levels say +I looked at that you know and I was + + align:start position:0% +I looked at that you know and I was + + + align:start position:0% +I looked at that you know and I was +going there's got to be a better way to + + align:start position:0% +going there's got to be a better way to + + + align:start position:0% +going there's got to be a better way to +do this so I came across a Steven Quakes + + align:start position:0% +do this so I came across a Steven Quakes + + + align:start position:0% +do this so I came across a Steven Quakes +Lab at Tech and they were doing + + align:start position:0% +Lab at Tech and they were doing + + + align:start position:0% +Lab at Tech and they were doing +microlitic devices very simple ones at + + align:start position:0% +microlitic devices very simple ones at + + + align:start position:0% +microlitic devices very simple ones at +the time they were doing um uh T + + align:start position:0% +the time they were doing um uh T + + + align:start position:0% +the time they were doing um uh T +channels and they' etched them into um a + + align:start position:0% +channels and they' etched them into um a + + + align:start position:0% +channels and they' etched them into um a +silicon surface or a glass surface and + + align:start position:0% +silicon surface or a glass surface and + + + align:start position:0% +silicon surface or a glass surface and +they were using them for sizing + + align:start position:0% +they were using them for sizing + + + align:start position:0% +they were using them for sizing +DNA so I guess that was probably the + + align:start position:0% +DNA so I guess that was probably the + + + align:start position:0% +DNA so I guess that was probably the +turning point where I said well maybe I + + align:start position:0% +turning point where I said well maybe I + + + align:start position:0% +turning point where I said well maybe I +can take these small systems where + + align:start position:0% +can take these small systems where + + + align:start position:0% +can take these small systems where +you're moving small pieces of fluid + + align:start position:0% +you're moving small pieces of fluid + + + align:start position:0% +you're moving small pieces of fluid +around and use them to manipulate single + + align:start position:0% +around and use them to manipulate single + + + align:start position:0% +around and use them to manipulate single +cells or single proteins so this is what + + align:start position:0% +cells or single proteins so this is what + + + align:start position:0% +cells or single proteins so this is what +the lab was gradually grown to on + + align:start position:0% +the lab was gradually grown to on + + + align:start position:0% +the lab was gradually grown to on +building very large complex chips with + + align:start position:0% +building very large complex chips with + + + align:start position:0% +building very large complex chips with +thousands of Chambers in which each one + + align:start position:0% +thousands of Chambers in which each one + + + align:start position:0% +thousands of Chambers in which each one +can hold a single cell but the process + + align:start position:0% +can hold a single cell but the process + + + align:start position:0% +can hold a single cell but the process +along the way was was nonintuitive so + + align:start position:0% +along the way was was nonintuitive so + + + align:start position:0% +along the way was was nonintuitive so +there was a lot of stops and starts + + align:start position:0% +there was a lot of stops and starts + + + align:start position:0% +there was a lot of stops and starts +along the + + align:start position:0% +along the + + + align:start position:0% +along the +way we make these small elastomeric + + align:start position:0% +way we make these small elastomeric + + + align:start position:0% +way we make these small elastomeric +microfic chips in the lab and the way we + + align:start position:0% +microfic chips in the lab and the way we + + + align:start position:0% +microfic chips in the lab and the way we +go about doing this is actually a bit + + align:start position:0% +go about doing this is actually a bit + + + align:start position:0% +go about doing this is actually a bit +like making a cake you make the chips in + + align:start position:0% +like making a cake you make the chips in + + + align:start position:0% +like making a cake you make the chips in +layers so typically for a two- layer + + align:start position:0% +layers so typically for a two- layer + + + align:start position:0% +layers so typically for a two- layer +device we have molds on Silicon Wafers + + align:start position:0% +device we have molds on Silicon Wafers + + + align:start position:0% +device we have molds on Silicon Wafers +patterned with micr panels it's very + + align:start position:0% +patterned with micr panels it's very + + + align:start position:0% +patterned with micr panels it's very +similar to the process used to pattern + + align:start position:0% +similar to the process used to pattern + + + align:start position:0% +similar to the process used to pattern +electronic circuits these patterns + + align:start position:0% +electronic circuits these patterns + + + align:start position:0% +electronic circuits these patterns +essentially are the active conduits for + + align:start position:0% +essentially are the active conduits for + + + align:start position:0% +essentially are the active conduits for +flowing liquid through the chips and + + align:start position:0% +flowing liquid through the chips and + + + align:start position:0% +flowing liquid through the chips and +during the assembly you align these + + align:start position:0% +during the assembly you align these + + + align:start position:0% +during the assembly you align these +channels on top of each other and in + + align:start position:0% +channels on top of each other and in + + + align:start position:0% +channels on top of each other and in +between the channels there's a thin + + align:start position:0% +between the channels there's a thin + + + align:start position:0% +between the channels there's a thin +layer of + + align:start position:0% +layer of + + + align:start position:0% +layer of +silicone and where the channels cross + + align:start position:0% +silicone and where the channels cross + + + align:start position:0% +silicone and where the channels cross +over each other these areas become + + align:start position:0% +over each other these areas become + + + align:start position:0% +over each other these areas become +valves so just like electronic switches + + align:start position:0% +valves so just like electronic switches + + + align:start position:0% +valves so just like electronic switches +these little thin layers of rubber are + + align:start position:0% +these little thin layers of rubber are + + + align:start position:0% +these little thin layers of rubber are +mechanical switches for gating fluid and + + align:start position:0% +mechanical switches for gating fluid and + + + align:start position:0% +mechanical switches for gating fluid and +moving things around in order to + + align:start position:0% +moving things around in order to + + + align:start position:0% +moving things around in order to +communicate with the chip what we do is + + align:start position:0% +communicate with the chip what we do is + + + align:start position:0% +communicate with the chip what we do is +we actually use pneumatic pressure and + + align:start position:0% +we actually use pneumatic pressure and + + + align:start position:0% +we actually use pneumatic pressure and +we actually hook these up through a very + + align:start position:0% +we actually hook these up through a very + + + align:start position:0% +we actually hook these up through a very +small tubing out of the top of the Chip + + align:start position:0% +small tubing out of the top of the Chip + + + align:start position:0% +small tubing out of the top of the Chip +And The gating of the air inside these + + align:start position:0% +And The gating of the air inside these + + + align:start position:0% +And The gating of the air inside these +devices is clicking open and shut these + + align:start position:0% +devices is clicking open and shut these + + + align:start position:0% +devices is clicking open and shut these +valves inside the devices those are + + align:start position:0% +valves inside the devices those are + + + align:start position:0% +valves inside the devices those are +actively controlled by the solenoid + + align:start position:0% +actively controlled by the solenoid + + + align:start position:0% +actively controlled by the solenoid +valves which are run by a lab view + + align:start position:0% +valves which are run by a lab view + + + align:start position:0% +valves which are run by a lab view +computer program + + align:start position:0% + + + + align:start position:0% + +from a biological perspective I think + + align:start position:0% +from a biological perspective I think + + + align:start position:0% +from a biological perspective I think +that the central goal of the chips is + + align:start position:0% +that the central goal of the chips is + + + align:start position:0% +that the central goal of the chips is +really to explore the diversity in + + align:start position:0% +really to explore the diversity in + + + align:start position:0% +really to explore the diversity in +biological and chemical systems so in + + align:start position:0% +biological and chemical systems so in + + + align:start position:0% +biological and chemical systems so in +some sense you're saying I've got a + + align:start position:0% +some sense you're saying I've got a + + + align:start position:0% +some sense you're saying I've got a +million different cells and I know + + align:start position:0% +million different cells and I know + + + align:start position:0% +million different cells and I know +they're doing something slightly + + align:start position:0% +they're doing something slightly + + + align:start position:0% +they're doing something slightly +different so how do we look at the + + align:start position:0% +different so how do we look at the + + + align:start position:0% +different so how do we look at the +cells + + align:start position:0% +cells + + + align:start position:0% +cells +individually so how do we take each cell + + align:start position:0% +individually so how do we take each cell + + + align:start position:0% +individually so how do we take each cell +put it in its own small environment and + + align:start position:0% +put it in its own small environment and + + + align:start position:0% +put it in its own small environment and +take a snapshot of it of what it's doing + + align:start position:0% +take a snapshot of it of what it's doing + + + align:start position:0% +take a snapshot of it of what it's doing +on its day-to-day life or in an + + align:start position:0% +on its day-to-day life or in an + + + align:start position:0% +on its day-to-day life or in an +artificial surrounding one of the + + align:start position:0% +artificial surrounding one of the + + + align:start position:0% +artificial surrounding one of the +applications for the chip is for food + + align:start position:0% +applications for the chip is for food + + + align:start position:0% +applications for the chip is for food +born illnesses and the way you can + + align:start position:0% +born illnesses and the way you can + + + align:start position:0% +born illnesses and the way you can +conceive of actually looking at foodborn + + align:start position:0% +conceive of actually looking at foodborn + + + align:start position:0% +conceive of actually looking at foodborn +illnesses is to take a drop of say the + + align:start position:0% +illnesses is to take a drop of say the + + + align:start position:0% +illnesses is to take a drop of say the +contaminated suspected food and load + + align:start position:0% +contaminated suspected food and load + + + align:start position:0% +contaminated suspected food and load +this thing in the chip and look for + + align:start position:0% +this thing in the chip and look for + + + align:start position:0% +this thing in the chip and look for +bacteria or viruses that you suspect of + + align:start position:0% +bacteria or viruses that you suspect of + + + align:start position:0% +bacteria or viruses that you suspect of +causing this type of a infection I think + + align:start position:0% +causing this type of a infection I think + + + align:start position:0% +causing this type of a infection I think +realistically we can have these things + + align:start position:0% +realistically we can have these things + + + align:start position:0% +realistically we can have these things +ready in 5 years and that the + + align:start position:0% +ready in 5 years and that the + + + align:start position:0% +ready in 5 years and that the +infrastructure from the chips has been + + align:start position:0% +infrastructure from the chips has been + + + align:start position:0% +infrastructure from the chips has been +welld developed and is being defined by + + align:start position:0% +welld developed and is being defined by + + + align:start position:0% +welld developed and is being defined by +several Laboratories across the country + + align:start position:0% +several Laboratories across the country + + + align:start position:0% +several Laboratories across the country +every today so we're certainly learning + + align:start position:0% +every today so we're certainly learning + + + align:start position:0% +every today so we're certainly learning +a lot on how to manipulate + + align:start position:0% +a lot on how to manipulate + + + align:start position:0% +a lot on how to manipulate +fluids and also there is a big interest + + align:start position:0% +fluids and also there is a big interest + + + align:start position:0% +fluids and also there is a big interest +from the mems community on making + + align:start position:0% +from the mems community on making + + + align:start position:0% +from the mems community on making +integrated sensors and detectors for + + align:start position:0% +integrated sensors and detectors for + + + align:start position:0% +integrated sensors and detectors for +these type of chips \ No newline at end of file diff --git a/Wcy-zCt8llk.txt b/Wcy-zCt8llk.txt new file mode 100644 index 0000000000000000000000000000000000000000..fac8137cff16485895837b36cdf93de6fb6cd4d6 --- /dev/null +++ b/Wcy-zCt8llk.txt @@ -0,0 +1,15543 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu started by + + align:start position:0% +ocw.mit.edu started by + + + align:start position:0% +ocw.mit.edu started by +um reminding you what we did uh uh in n + + align:start position:0% +um reminding you what we did uh uh in n + + + align:start position:0% +um reminding you what we did uh uh in n +neure and particular um there was a + + align:start position:0% +neure and particular um there was a + + + align:start position:0% +neure and particular um there was a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +um + + align:start position:0% +um + + + align:start position:0% +um +um uh confusion seems like U maybe some + + align:start position:0% +um uh confusion seems like U maybe some + + + align:start position:0% +um uh confusion seems like U maybe some +part that went too fast so so I will + + align:start position:0% +part that went too fast so so I will + + + align:start position:0% +part that went too fast so so I will +um try to um yeah + + align:start position:0% + + + + align:start position:0% + +um so again we start Say by choosing + + align:start position:0% + + + + align:start position:0% + +the worksheet matric to be the + + align:start position:0% + + + + align:start position:0% + +minkovski then then the W she action + + align:start position:0% +minkovski then then the W she action + + + align:start position:0% +minkovski then then the W she action +just + + align:start position:0% +just + + + align:start position:0% +just +reduce to that of a a bunch of fre scale + + align:start position:0% + + + + align:start position:0% + +field just reduce to a bunch of free + + align:start position:0% +field just reduce to a bunch of free + + + align:start position:0% +field just reduce to a bunch of free +scal + + align:start position:0% +scal + + + align:start position:0% +scal +fields and those free scal field is a + + align:start position:0% +fields and those free scal field is a + + + align:start position:0% +fields and those free scal field is a +bit unusual because in particular this a + + align:start position:0% +bit unusual because in particular this a + + + align:start position:0% +bit unusual because in particular this a +zero + + align:start position:0% +zero + + + align:start position:0% +zero +component which will have a wrong sign + + align:start position:0% +component which will have a wrong sign + + + align:start position:0% +component which will have a wrong sign +kinetic term okay but of course this is + + align:start position:0% +kinetic term okay but of course this is + + + align:start position:0% +kinetic term okay but of course this is +not our full story you still have to imp + + align:start position:0% +not our full story you still have to imp + + + align:start position:0% +not our full story you still have to imp +impose the so called the um voral + + align:start position:0% +impose the so called the um voral + + + align:start position:0% +impose the so called the um voral +constraint uh corresponding to that the + + align:start position:0% +constraint uh corresponding to that the + + + align:start position:0% +constraint uh corresponding to that the +strance of this series should be zero so + + align:start position:0% +strance of this series should be zero so + + + align:start position:0% +strance of this series should be zero so +which is the + + align:start position:0% +which is the + + + align:start position:0% +which is the +consequence of the equation motion for + + align:start position:0% +consequence of the equation motion for + + + align:start position:0% +consequence of the equation motion for +gamma and you can but never this you can + + align:start position:0% +gamma and you can but never this you can + + + align:start position:0% +gamma and you can but never this you can +write down the most General solution to + + align:start position:0% +write down the most General solution to + + + align:start position:0% +write down the most General solution to +this + + align:start position:0% +this + + + align:start position:0% +this +problem so let me write it here so the + + align:start position:0% +problem so let me write it here so the + + + align:start position:0% +problem so let me write it here so the +most general of of close + + align:start position:0% + + + + align:start position:0% + +string so the most General solution can + + align:start position:0% +string so the most General solution can + + + align:start position:0% +string so the most General solution can +be written as X + + align:start position:0% +be written as X + + + align:start position:0% +be written as X +mu + + align:start position:0% +mu + + + align:start position:0% +mu +plus P me + + align:start position:0% + + + + align:start position:0% + +so so I've now written the um what I + + align:start position:0% +so so I've now written the um what I + + + align:start position:0% +so so I've now written the um what I +quote previous by XL and XR I have + + align:start position:0% +quote previous by XL and XR I have + + + align:start position:0% +quote previous by XL and XR I have +written them exe in terms of the fre + + align:start position:0% +written them exe in terms of the fre + + + align:start position:0% +written them exe in terms of the fre +modes okay and I have written them + + align:start position:0% +modes okay and I have written them + + + align:start position:0% +modes okay and I have written them +expressly in terms of free modes and uh + + align:start position:0% +expressly in terms of free modes and uh + + + align:start position:0% +expressly in terms of free modes and uh +uh they in this form so in compare with + + align:start position:0% +uh they in this form so in compare with + + + align:start position:0% +uh they in this form so in compare with +what we discussed before previous here + + align:start position:0% +what we discussed before previous here + + + align:start position:0% +what we discussed before previous here +because P mu V mu then we discussed last + + align:start position:0% +because P mu V mu then we discussed last + + + align:start position:0% +because P mu V mu then we discussed last +time that this V mu should be considered + + align:start position:0% +time that this V mu should be considered + + + align:start position:0% +time that this V mu should be considered +as relates to the center of mass + + align:start position:0% +as relates to the center of mass + + + align:start position:0% +as relates to the center of mass +momentum of the whole string and uh for + + align:start position:0% +momentum of the whole string and uh for + + + align:start position:0% +momentum of the whole string and uh for +example for the Clos Str that's the + + align:start position:0% + + + + align:start position:0% + +relation okay so s for the open string + + align:start position:0% + + + + align:start position:0% + +similarly for the open string if you use + + align:start position:0% +similarly for the open string if you use + + + align:start position:0% +similarly for the open string if you use +the Lum boundary + + align:start position:0% +the Lum boundary + + + align:start position:0% +the Lum boundary +condition you use the Luman boundary + + align:start position:0% +condition you use the Luman boundary + + + align:start position:0% +condition you use the Luman boundary +condition then you find + + align:start position:0% +condition then you find + + + align:start position:0% +condition then you find +the again I will substitute the explicit + + align:start position:0% +the again I will substitute the explicit + + + align:start position:0% +the again I will substitute the explicit +expression for + + align:start position:0% +expression for + + + align:start position:0% +expression for +the for the XL and + + align:start position:0% +the for the XL and + + + align:start position:0% +the for the XL and +XR so now become two alpha Prime P mu to + + align:start position:0% +XR so now become two alpha Prime P mu to + + + align:start position:0% +XR so now become two alpha Prime P mu to +so again this is our previous V so this + + align:start position:0% +so again this is our previous V so this + + + align:start position:0% +so again this is our previous V so this +two is related to like the open string + + align:start position:0% +two is related to like the open string + + + align:start position:0% +two is related to like the open string +on Sigma only go from 0 to Pi rather + + align:start position:0% +on Sigma only go from 0 to Pi rather + + + align:start position:0% +on Sigma only go from 0 to Pi rather +than 2 + + align:start position:0% +than 2 + + + align:start position:0% +than 2 +pi and then you can write the the + + align:start position:0% +pi and then you can write the the + + + align:start position:0% +pi and then you can write the the +oscillator yeah this x a XR in terms of + + align:start position:0% +oscillator yeah this x a XR in terms of + + + align:start position:0% +oscillator yeah this x a XR in terms of +the + + align:start position:0% +the + + + align:start position:0% +the +explicit uh fre + + align:start position:0% +explicit uh fre + + + align:start position:0% +explicit uh fre +transform so here you only have one set + + align:start position:0% +transform so here you only have one set + + + align:start position:0% +transform so here you only have one set +of + + align:start position:0% + + + + align:start position:0% + +modes Sigma okay and the course n Sigma + + align:start position:0% +modes Sigma okay and the course n Sigma + + + align:start position:0% +modes Sigma okay and the course n Sigma +just come from we have XL plus XR and XL + + align:start position:0% +just come from we have XL plus XR and XL + + + align:start position:0% +just come from we have XL plus XR and XL +which is equal to XR and uh yeah when + + align:start position:0% +which is equal to XR and uh yeah when + + + align:start position:0% +which is equal to XR and uh yeah when +these two become the same when these two + + align:start position:0% +these two become the same when these two + + + align:start position:0% +these two become the same when these two +become the same then these two combine + + align:start position:0% +become the same then these two combine + + + align:start position:0% +become the same then these two combine +because the sigma have opposite sign + + align:start position:0% +because the sigma have opposite sign + + + align:start position:0% +because the sigma have opposite sign +that combine to cosine Sigma okay yeah + + align:start position:0% +that combine to cosine Sigma okay yeah + + + align:start position:0% +that combine to cosine Sigma okay yeah +cosine M + + align:start position:0% + + + + align:start position:0% + +Sigma + + align:start position:0% +Sigma + + + align:start position:0% +Sigma +yeah so this is the most General + + align:start position:0% +yeah so this is the most General + + + align:start position:0% +yeah so this is the most General +classical + + align:start position:0% +classical + + + align:start position:0% +classical +solution and in the light conage + + align:start position:0% + + + + align:start position:0% + +you con + + align:start position:0% + + + + align:start position:0% + +cage this + + align:start position:0% +cage this + + + align:start position:0% +cage this +X+ can be set into + + align:start position:0% +X+ can be set into + + + align:start position:0% +X+ can be set into +zero and also everything related to + + align:start position:0% +zero and also everything related to + + + align:start position:0% +zero and also everything related to +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +plus Alpha TAA + + align:start position:0% +plus Alpha TAA + + + align:start position:0% +plus Alpha TAA +plus all the oscillation modes also set + + align:start position:0% +plus all the oscillation modes also set + + + align:start position:0% +plus all the oscillation modes also set +to be zero related to the plus set to + + align:start position:0% +to be zero related to the plus set to + + + align:start position:0% +to be zero related to the plus set to +zero so there's only T term left in the + + align:start position:0% +zero so there's only T term left in the + + + align:start position:0% +zero so there's only T term left in the +L + + align:start position:0% + + + + align:start position:0% + +conage and this voral constraint they be + + align:start position:0% + + + + align:start position:0% + +and the Boral constraint they + + align:start position:0% +and the Boral constraint they + + + align:start position:0% +and the Boral constraint they +become i x + + align:start position:0% + + + + align:start position:0% + +minus so this V pass is the same as that + + align:start position:0% +minus so this V pass is the same as that + + + align:start position:0% +minus so this V pass is the same as that +uh uh related to the p+ that way + + align:start position:0% + + + + align:start position:0% + +only single V + + align:start position:0% + + + + align:start position:0% + +plus okay so in those equations the I + + align:start position:0% +plus okay so in those equations the I + + + align:start position:0% +plus okay so in those equations the I +should be considered as a sum okay you + + align:start position:0% +should be considered as a sum okay you + + + align:start position:0% +should be considered as a sum okay you +sum over all directions all transverse + + align:start position:0% + + + + align:start position:0% + +directions so from the raor con Str you + + align:start position:0% +directions so from the raor con Str you + + + align:start position:0% +directions so from the raor con Str you +can deduce x + + align:start position:0% + + + + align:start position:0% + +minus you can deduce X x minus yeah + + align:start position:0% +minus you can deduce X x minus yeah + + + align:start position:0% +minus you can deduce X x minus yeah +again let me just write here our + + align:start position:0% +again let me just write here our + + + align:start position:0% +again let me just write here our +convention is always X + + align:start position:0% +convention is always X + + + align:start position:0% +convention is always X +mu is equal to + + align:start position:0% +mu is equal to + + + align:start position:0% +mu is equal to +X+ + + align:start position:0% +X+ + + + align:start position:0% +X+ +xus then x + + align:start position:0% +xus then x + + + align:start position:0% +xus then x +i and I goes from 2 to D minus 1 and X + + align:start position:0% +i and I goes from 2 to D minus 1 and X + + + align:start position:0% +i and I goes from 2 to D minus 1 and X ++us is say 1 / < + + align:start position:0% ++us is say 1 / < + + + align:start position:0% ++us is say 1 / < +tk2 + + align:start position:0% +tk2 + + + align:start position:0% +tk2 +x0 plusus X1 okay + + align:start position:0% + + + + align:start position:0% + +so from here you can deduce the x + + align:start position:0% +so from here you can deduce the x + + + align:start position:0% +so from here you can deduce the x +minus and also it means that independent + + align:start position:0% + + + + align:start position:0% + +variables so this will determine the the + + align:start position:0% +variables so this will determine the the + + + align:start position:0% +variables so this will determine the the +x minus up to a constant because this + + align:start position:0% +x minus up to a constant because this + + + align:start position:0% +x minus up to a constant because this +determines the tower and sigma + + align:start position:0% +determines the tower and sigma + + + align:start position:0% +determines the tower and sigma +derivative up to constant so the + + align:start position:0% +derivative up to constant so the + + + align:start position:0% +derivative up to constant so the +independent + + align:start position:0% + + + + align:start position:0% + +variables are XR + + align:start position:0% +variables are XR + + + align:start position:0% +variables are XR +I and then also this P p+ or + + align:start position:0% +I and then also this P p+ or + + + align:start position:0% +I and then also this P p+ or +v+ which appears in the plus and then + + align:start position:0% +v+ which appears in the plus and then + + + align:start position:0% +v+ which appears in the plus and then +the x minus the zero modes for the for + + align:start position:0% +the x minus the zero modes for the for + + + align:start position:0% +the x minus the zero modes for the for +the x minus which is not determined by + + align:start position:0% +the x minus which is not determined by + + + align:start position:0% +the x minus which is not determined by +those things and uh and this two this is + + align:start position:0% +those things and uh and this two this is + + + align:start position:0% +those things and uh and this two this is +just a constant and again these two are + + align:start position:0% +just a constant and again these two are + + + align:start position:0% +just a constant and again these two are +constant this are are two dimensional + + align:start position:0% +constant this are are two dimensional + + + align:start position:0% +constant this are are two dimensional +Fields okay + + align:start position:0% + + + + align:start position:0% + +any questions so + + align:start position:0% + + + + align:start position:0% + +far + + align:start position:0% + + + + align:start position:0% + +good so so as we emphasize that the zero + + align:start position:0% +good so so as we emphasize that the zero + + + align:start position:0% +good so so as we emphasize that the zero +mode part of this equation are + + align:start position:0% +mode part of this equation are + + + align:start position:0% +mode part of this equation are +particularly important so Zero part yeah + + align:start position:0% +particularly important so Zero part yeah + + + align:start position:0% +particularly important so Zero part yeah +let me call this equation + + align:start position:0% + + + + align:start position:0% + +one this equation two + + align:start position:0% +one this equation two + + + align:start position:0% +one this equation two +so the Zero part of those equations are + + align:start position:0% +so the Zero part of those equations are + + + align:start position:0% +so the Zero part of those equations are +particularly + + align:start position:0% + + + + align:start position:0% + +important and uh for + + align:start position:0% +important and uh for + + + align:start position:0% +important and uh for +example say from equation one so the + + align:start position:0% +example say from equation one so the + + + align:start position:0% +example say from equation one so the +zero mode part for the first equation so + + align:start position:0% +zero mode part for the first equation so + + + align:start position:0% +zero mode part for the first equation so +let's do the for the uh uh say let's do + + align:start position:0% +let's do the for the uh uh say let's do + + + align:start position:0% +let's do the for the uh uh say let's do +for close stre then the zero mode part + + align:start position:0% +for close stre then the zero mode part + + + align:start position:0% +for close stre then the zero mode part +just just Alpha Prime P minus okay if + + align:start position:0% +just just Alpha Prime P minus okay if + + + align:start position:0% +just just Alpha Prime P minus okay if +you take derivative over to so you just + + align:start position:0% +you take derivative over to so you just + + + align:start position:0% +you take derivative over to so you just +get the alpha Prim P minus and the right + + align:start position:0% +get the alpha Prim P minus and the right + + + align:start position:0% +get the alpha Prim P minus and the right +hand + + align:start position:0% +hand + + + align:start position:0% +hand +side so right hand side let let me also + + align:start position:0% +side so right hand side let let me also + + + align:start position:0% +side so right hand side let let me also +rewrite the v+ in terms of alpha Prime + + align:start position:0% +rewrite the v+ in terms of alpha Prime + + + align:start position:0% +rewrite the v+ in terms of alpha Prime +so this is to Alpha Prime + + align:start position:0% + + + + align:start position:0% + +p+ and the zero mode means that you you + + align:start position:0% +p+ and the zero mode means that you you + + + align:start position:0% +p+ and the zero mode means that you you +integrate + + align:start position:0% + + + + align:start position:0% + +over you integrate over the string + + align:start position:0% + + + + align:start position:0% + +okay so this is the first + + align:start position:0% +okay so this is the first + + + align:start position:0% +okay so this is the first +equation and so the zero mode equation + + align:start position:0% +equation and so the zero mode equation + + + align:start position:0% +equation and so the zero mode equation +become like + + align:start position:0% + + + + align:start position:0% + +that so now let me just uh uh uh make a + + align:start position:0% +that so now let me just uh uh uh make a + + + align:start position:0% +that so now let me just uh uh uh make a +brief comment which I I uh + + align:start position:0% +brief comment which I I uh + + + align:start position:0% +brief comment which I I uh +um uh uh at the beginning I forgot to + + align:start position:0% +um uh uh at the beginning I forgot to + + + align:start position:0% +um uh uh at the beginning I forgot to +mention last time which uh uh the cause + + align:start position:0% +mention last time which uh uh the cause + + + align:start position:0% +mention last time which uh uh the cause +some confusion later is that if you look + + align:start position:0% +some confusion later is that if you look + + + align:start position:0% +some confusion later is that if you look +at this + + align:start position:0% + + + + align:start position:0% + +expression + + align:start position:0% +expression + + + align:start position:0% +expression +okay this is actually + + align:start position:0% +okay this is actually + + + align:start position:0% +okay this is actually +precisely so if you look at that two + + align:start position:0% +precisely so if you look at that two + + + align:start position:0% +precisely so if you look at that two +dimensional field Theory this is + + align:start position:0% +dimensional field Theory this is + + + align:start position:0% +dimensional field Theory this is +actually precisely the + + align:start position:0% +actually precisely the + + + align:start position:0% +actually precisely the +harmonin the classical harmonin for that + + align:start position:0% +harmonin the classical harmonin for that + + + align:start position:0% +harmonin the classical harmonin for that +field Theory okay for the XI part okay + + align:start position:0% +field Theory okay for the XI part okay + + + align:start position:0% +field Theory okay for the XI part okay +this is just a free scaler field the and + + align:start position:0% +this is just a free scaler field the and + + + align:start position:0% +this is just a free scaler field the and +so so I yeah so in particular even write + + align:start position:0% +so so I yeah so in particular even write + + + align:start position:0% +so so I yeah so in particular even write +that more precise let's take out this + + align:start position:0% +that more precise let's take out this + + + align:start position:0% +that more precise let's take out this +p+ and then this become two 4 Pi Alpha + + align:start position:0% +p+ and then this become two 4 Pi Alpha + + + align:start position:0% +p+ and then this become two 4 Pi Alpha +Prime and then this just become exactly + + align:start position:0% +Prime and then this just become exactly + + + align:start position:0% +Prime and then this just become exactly +the honin of that series corresponding + + align:start position:0% +the honin of that series corresponding + + + align:start position:0% +the honin of that series corresponding +to for the XI okay so for + + align:start position:0% + + + + align:start position:0% + +hxi is the + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +hiton for + + align:start position:0% +hiton for + + + align:start position:0% +hiton for +two dimensional Quantum + + align:start position:0% +two dimensional Quantum + + + align:start position:0% +two dimensional Quantum +Fields Quantum field the of x + + align:start position:0% + + + + align:start position:0% + +i for the transverse directions + + align:start position:0% + + + + align:start position:0% + +okay so you can also write this + + align:start position:0% +okay so you can also write this + + + align:start position:0% +okay so you can also write this +explicity in terms of those + + align:start position:0% +explicity in terms of those + + + align:start position:0% +explicity in terms of those +modes in terms of those + + align:start position:0% +modes in terms of those + + + align:start position:0% +modes in terms of those +modes then for + + align:start position:0% +modes then for + + + align:start position:0% +modes then for +example you write P minus yeah if you + + align:start position:0% +example you write P minus yeah if you + + + align:start position:0% +example you write P minus yeah if you +can + + align:start position:0% +can + + + align:start position:0% +can +modes then become P minus equal to 2 + + align:start position:0% + + + + align:start position:0% + +p+ p i + + align:start position:0% +p+ p i + + + align:start position:0% +p+ p i +s plus 1/ Alpha Prime so if you just + + align:start position:0% +s plus 1/ Alpha Prime so if you just + + + align:start position:0% +s plus 1/ Alpha Prime so if you just +substitute those expansion into here + + align:start position:0% +substitute those expansion into here + + + align:start position:0% +substitute those expansion into here +then you can also write it explicit in + + align:start position:0% +then you can also write it explicit in + + + align:start position:0% +then you can also write it explicit in +terms of + + align:start position:0% + + + + align:start position:0% + +modes and then + + align:start position:0% + + + + align:start position:0% + +okay and uh then you can combine so this + + align:start position:0% +okay and uh then you can combine so this + + + align:start position:0% +okay and uh then you can combine so this +is p minus then you can multiply this to + + align:start position:0% +is p minus then you can multiply this to + + + align:start position:0% +is p minus then you can multiply this to +the other side combine all the P + + align:start position:0% +the other side combine all the P + + + align:start position:0% +the other side combine all the P +together you can write + + align:start position:0% +together you can write + + + align:start position:0% +together you can write +it as + + align:start position:0% +it as + + + align:start position:0% +it as +m² which is defined to be P mu P mu + + align:start position:0% +m² which is defined to be P mu P mu + + + align:start position:0% +m² which is defined to be P mu P mu +minus P mu P + + align:start position:0% +minus P mu P + + + align:start position:0% +minus P mu P +mu which is then 2 p+ p minus minus p i + + align:start position:0% +mu which is then 2 p+ p minus minus p i + + + align:start position:0% +mu which is then 2 p+ p minus minus p i +s and then this then become equal + + align:start position:0% +s and then this then become equal + + + align:start position:0% +s and then this then become equal +to one + + align:start position:0% +to one + + + align:start position:0% +to one +alpha 1 Alpha and 1 Alpha Prime sum M = + + align:start position:0% +alpha 1 Alpha and 1 Alpha Prime sum M = + + + align:start position:0% +alpha 1 Alpha and 1 Alpha Prime sum M = +to + + align:start position:0% +to + + + align:start position:0% +to +zero Alpha minus m i Alpha Mi I plus + + align:start position:0% +zero Alpha minus m i Alpha Mi I plus + + + align:start position:0% +zero Alpha minus m i Alpha Mi I plus +Alpha tus Mi I of M + + align:start position:0% + + + + align:start position:0% + +okay then you see that the this + + align:start position:0% +okay then you see that the this + + + align:start position:0% +okay then you see that the this +constraint for for p Prime for p minus + + align:start position:0% +constraint for for p Prime for p minus + + + align:start position:0% +constraint for for p Prime for p minus +now can be written can be Rewritten in + + align:start position:0% +now can be written can be Rewritten in + + + align:start position:0% +now can be written can be Rewritten in +terms of the + + align:start position:0% + + + + align:start position:0% + +relation of the mass of the whole string + + align:start position:0% +relation of the mass of the whole string + + + align:start position:0% +relation of the mass of the whole string +in terms of its oscillation modes + + align:start position:0% +in terms of its oscillation modes + + + align:start position:0% +in terms of its oscillation modes +okay in terms of it oscillation mode + + align:start position:0% +okay in terms of it oscillation mode + + + align:start position:0% +okay in terms of it oscillation mode +modes and similarly for the open stren + + align:start position:0% +modes and similarly for the open stren + + + align:start position:0% +modes and similarly for the open stren +so this is for the closed stren for the + + align:start position:0% +so this is for the closed stren for the + + + align:start position:0% +so this is for the closed stren for the +open the exact the same thing applies + + align:start position:0% +open the exact the same thing applies + + + align:start position:0% +open the exact the same thing applies +just you only have now one set of + + align:start position:0% + + + + align:start position:0% + +mode and the + + align:start position:0% + + + + align:start position:0% + +um so remember in those expressions uh + + align:start position:0% +um so remember in those expressions uh + + + align:start position:0% +um so remember in those expressions uh +um I is always sum of I is always + + align:start position:0% +um I is always sum of I is always + + + align:start position:0% +um I is always sum of I is always +assumed + + align:start position:0% + + + + align:start position:0% + +and whenever I wrote m equal to z m not + + align:start position:0% +and whenever I wrote m equal to z m not + + + align:start position:0% +and whenever I wrote m equal to z m not +equal to zero means you always Su from + + align:start position:0% +equal to zero means you always Su from + + + align:start position:0% +equal to zero means you always Su from +minus infinity to plus infinity and + + align:start position:0% +minus infinity to plus infinity and + + + align:start position:0% +minus infinity to plus infinity and +except for m equal to zero okay uh + + align:start position:0% + + + + align:start position:0% + +yeah yes any + + align:start position:0% + + + + align:start position:0% + +questions so this is the consequence of + + align:start position:0% +questions so this is the consequence of + + + align:start position:0% +questions so this is the consequence of +the zero modes for + + align:start position:0% +the zero modes for + + + align:start position:0% +the zero modes for +one and the consequence of for the zero + + align:start position:0% +one and the consequence of for the zero + + + align:start position:0% +one and the consequence of for the zero +modes for two + + align:start position:0% +modes for two + + + align:start position:0% +modes for two +Q again you can just integrate of all + + align:start position:0% +Q again you can just integrate of all + + + align:start position:0% +Q again you can just integrate of all +stram uh all direction of the + + align:start position:0% +stram uh all direction of the + + + align:start position:0% +stram uh all direction of the +stream then then the left hand side just + + align:start position:0% +stream then then the left hand side just + + + align:start position:0% +stream then then the left hand side just +get + + align:start position:0% + + + + align:start position:0% + +zero because the x minus is a periodic + + align:start position:0% +zero because the x minus is a periodic + + + align:start position:0% +zero because the x minus is a periodic +function so this is a total derivative + + align:start position:0% +function so this is a total derivative + + + align:start position:0% +function so this is a total derivative +and so this give you exactly zero and + + align:start position:0% +and so this give you exactly zero and + + + align:start position:0% +and so this give you exactly zero and +then this then put the constraint + + align:start position:0% + + + + align:start position:0% + +on the right hand + + align:start position:0% +on the right hand + + + align:start position:0% +on the right hand +[Applause] + + align:start position:0% + + + + align:start position:0% + +side uh uh on this expression which can + + align:start position:0% +side uh uh on this expression which can + + + align:start position:0% +side uh uh on this expression which can +be written + + align:start position:0% +be written + + + align:start position:0% +be written +explicitly so you can also then plug + + align:start position:0% +explicitly so you can also then plug + + + align:start position:0% +explicitly so you can also then plug +into the explicit mode and then they + + align:start position:0% +into the explicit mode and then they + + + align:start position:0% +into the explicit mode and then they +become some M notal to + + align:start position:0% +become some M notal to + + + align:start position:0% +become some M notal to +zero Alpha minus Mi i al Mi I equal to + + align:start position:0% + + + + align:start position:0% + +okay so so this is sometimes called a + + align:start position:0% +okay so so this is sometimes called a + + + align:start position:0% +okay so so this is sometimes called a +level matching condition so this tells + + align:start position:0% +level matching condition so this tells + + + align:start position:0% +level matching condition so this tells +you that the oscillation from the left + + align:start position:0% +you that the oscillation from the left + + + align:start position:0% +you that the oscillation from the left +moving part this is for the closed + + align:start position:0% +moving part this is for the closed + + + align:start position:0% +moving part this is for the closed +string for the open string this equation + + align:start position:0% +string for the open string this equation + + + align:start position:0% +string for the open string this equation +just does not give you anything for the + + align:start position:0% +just does not give you anything for the + + + align:start position:0% +just does not give you anything for the +Clos string this give you a long trival + + align:start position:0% +Clos string this give you a long trival + + + align:start position:0% +Clos string this give you a long trival +constraint oh I got a wind + + align:start position:0% +constraint oh I got a wind + + + align:start position:0% +constraint oh I got a wind +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +so so for coing this just tells you that + + align:start position:0% +so so for coing this just tells you that + + + align:start position:0% +so so for coing this just tells you that +the left moving part and Right Moving + + align:start position:0% +the left moving part and Right Moving + + + align:start position:0% +the left moving part and Right Moving +part have to be balanced and uh and this + + align:start position:0% +part have to be balanced and uh and this + + + align:start position:0% +part have to be balanced and uh and this +is related to that string is + + align:start position:0% +is related to that string is + + + align:start position:0% +is related to that string is +periodic along the string is periodic so + + align:start position:0% +periodic along the string is periodic so + + + align:start position:0% +periodic along the string is periodic so +there's no special point on the string + + align:start position:0% +there's no special point on the string + + + align:start position:0% +there's no special point on the string +and then then there's no special then + + align:start position:0% +and then then there's no special then + + + align:start position:0% +and then then there's no special then +you can actually not distinguish between + + align:start position:0% +you can actually not distinguish between + + + align:start position:0% +you can actually not distinguish between +the left moving and the Right Moving + + align:start position:0% +the left moving and the Right Moving + + + align:start position:0% +the left moving and the Right Moving +part + + align:start position:0% + + + + align:start position:0% + +okay good so this is the + + align:start position:0% +okay good so this is the + + + align:start position:0% +okay good so this is the +the whole classical story so the classic + + align:start position:0% +the whole classical story so the classic + + + align:start position:0% +the whole classical story so the classic +uh uh uh uh this is in some sense the + + align:start position:0% +uh uh uh uh this is in some sense the + + + align:start position:0% +uh uh uh uh this is in some sense the +complete classical story + + align:start position:0% +complete classical story + + + align:start position:0% +complete classical story +okay and then so Quantum mechanically we + + align:start position:0% +okay and then so Quantum mechanically we + + + align:start position:0% +okay and then so Quantum mechanically we +just need to quantize those + + align:start position:0% +just need to quantize those + + + align:start position:0% +just need to quantize those +guys quantize those guys and those are + + align:start position:0% +guys quantize those guys and those are + + + align:start position:0% +guys quantize those guys and those are +just ordinary Quantum mechanic de + + align:start position:0% +just ordinary Quantum mechanic de + + + align:start position:0% +just ordinary Quantum mechanic de +Freedom we don't need to worry about and + + align:start position:0% +Freedom we don't need to worry about and + + + align:start position:0% +Freedom we don't need to worry about and +and this just become um a quantization + + align:start position:0% +and this just become um a quantization + + + align:start position:0% +and this just become um a quantization +of a free scaler field + + align:start position:0% +of a free scaler field + + + align:start position:0% +of a free scaler field +Theory okay + + align:start position:0% +Theory okay + + + align:start position:0% +Theory okay +uh when you say free SC so all these + + align:start position:0% +uh when you say free SC so all these + + + align:start position:0% +uh when you say free SC so all these +modes are massive or is there any + + align:start position:0% +modes are massive or is there any + + + align:start position:0% +modes are massive or is there any +condition they can be massless no no no + + align:start position:0% +condition they can be massless no no no + + + align:start position:0% +condition they can be massless no no no +this is a m field + + align:start position:0% + + + + align:start position:0% + +Theory we Conta in this Theory right + + align:start position:0% +Theory we Conta in this Theory right + + + align:start position:0% +Theory we Conta in this Theory right +yeah so this is Master scale of fil + + align:start position:0% +yeah so this is Master scale of fil + + + align:start position:0% +yeah so this is Master scale of fil +Series in two Dimension but the that + + align:start position:0% +Series in two Dimension but the that + + + align:start position:0% +Series in two Dimension but the that +mass is no this mass is the mass of the + + align:start position:0% +mass is no this mass is the mass of the + + + align:start position:0% +mass is no this mass is the mass of the +string okay no this is the mass of the + + align:start position:0% +string okay no this is the mass of the + + + align:start position:0% +string okay no this is the mass of the +center + + align:start position:0% +center + + + align:start position:0% +center +of this is the total mass of the string + + align:start position:0% +of this is the total mass of the string + + + align:start position:0% +of this is the total mass of the string +yeah not the uh uh when I say the Mist + + align:start position:0% +yeah not the uh uh when I say the Mist + + + align:start position:0% +yeah not the uh uh when I say the Mist +this is a m scal field the in the W heat + + align:start position:0% +this is a m scal field the in the W heat + + + align:start position:0% +this is a m scal field the in the W heat +This Is A Spacetime description so we + + align:start position:0% +This Is A Spacetime description so we + + + align:start position:0% +This Is A Spacetime description so we +should separate it's important to + + align:start position:0% +should separate it's important to + + + align:start position:0% +should separate it's important to +separate two things things things happen + + align:start position:0% +separate two things things things happen + + + align:start position:0% +separate two things things things happen +on the world sheet and things happen in + + align:start position:0% +on the world sheet and things happen in + + + align:start position:0% +on the world sheet and things happen in +space time and uh so this is the mass of + + align:start position:0% +space time and uh so this is the mass of + + + align:start position:0% +space time and uh so this is the mass of +the string viewed as object moving in + + align:start position:0% +the string viewed as object moving in + + + align:start position:0% +the string viewed as object moving in +the space time and when I say quantizing + + align:start position:0% +the space time and when I say quantizing + + + align:start position:0% +the space time and when I say quantizing +a mass scal of field theory is to think + + align:start position:0% +a mass scal of field theory is to think + + + align:start position:0% +a mass scal of field theory is to think +of of those the mo so X I describe the + + align:start position:0% +of of those the mo so X I describe the + + + align:start position:0% +of of those the mo so X I describe the +motion of the string think of them as a + + align:start position:0% +motion of the string think of them as a + + + align:start position:0% +motion of the string think of them as a +field the on the both sheet and that's a + + align:start position:0% +field the on the both sheet and that's a + + + align:start position:0% +field the on the both sheet and that's a +m is failed Theory okay + + align:start position:0% +m is failed Theory okay + + + align:start position:0% +m is failed Theory okay +right + + align:start position:0% +right + + + align:start position:0% +right +yes + + align:start position:0% + + + + align:start position:0% + +moment uh + + align:start position:0% +moment uh + + + align:start position:0% +moment uh +um it's the is the conserve the loss of + + align:start position:0% +um it's the is the conserve the loss of + + + align:start position:0% +um it's the is the conserve the loss of +charge for the string corresponding to + + align:start position:0% +charge for the string corresponding to + + + align:start position:0% +charge for the string corresponding to +the + + align:start position:0% +the + + + align:start position:0% +the +translation is the conserved the loss of + + align:start position:0% +translation is the conserved the loss of + + + align:start position:0% +translation is the conserved the loss of +charge corresponding to the the + + align:start position:0% +charge corresponding to the the + + + align:start position:0% +charge corresponding to the the +translation yeah so so that's what we + + align:start position:0% +translation yeah so so that's what we + + + align:start position:0% +translation yeah so so that's what we +derived last time so we show that this V + + align:start position:0% +derived last time so we show that this V + + + align:start position:0% +derived last time so we show that this V +what would be original right V here are + + align:start position:0% +what would be original right V here are + + + align:start position:0% +what would be original right V here are +related to the to the center of mass + + align:start position:0% +related to the to the center of mass + + + align:start position:0% +related to the to the center of mass +momentum in this particular + + align:start position:0% +momentum in this particular + + + align:start position:0% +momentum in this particular +way + + align:start position:0% + + + + align:start position:0% + +yes sorry which + + align:start position:0% + + + + align:start position:0% + +one yeah + + align:start position:0% +one yeah + + + align:start position:0% +one yeah +or just a remark no this is a remark and + + align:start position:0% +or just a remark no this is a remark and + + + align:start position:0% +or just a remark no this is a remark and +this will make more + + align:start position:0% +this will make more + + + align:start position:0% +this will make more +latal uh for us this is not essentially + + align:start position:0% +latal uh for us this is not essentially + + + align:start position:0% +latal uh for us this is not essentially +for us this is not the essential remark + + align:start position:0% +for us this is not the essential remark + + + align:start position:0% +for us this is not the essential remark +but it will be more + + align:start position:0% +but it will be more + + + align:start position:0% +but it will be more +natural when I when I um when we work + + align:start position:0% +natural when I when I um when we work + + + align:start position:0% +natural when I when I um when we work +out the Zero Point + + align:start position:0% +out the Zero Point + + + align:start position:0% +out the Zero Point +Energy and uh when we work out Z Point + + align:start position:0% +Energy and uh when we work out Z Point + + + align:start position:0% +Energy and uh when we work out Z Point +Energy then that's a more natural uh + + align:start position:0% +Energy then that's a more natural uh + + + align:start position:0% +Energy then that's a more natural uh +thing to consider because that can will + + align:start position:0% +thing to consider because that can will + + + align:start position:0% +thing to consider because that can will +actually give you a a way of the + + align:start position:0% +actually give you a a way of the + + + align:start position:0% +actually give you a a way of the +Computing Zer Point + + align:start position:0% +Computing Zer Point + + + align:start position:0% +Computing Zer Point +Energy yeah + + align:start position:0% + + + + align:start position:0% + +yes you PL this + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +yeah you're supposed to have + + align:start position:0% +yeah you're supposed to have + + + align:start position:0% +yeah you're supposed to have +M number + + align:start position:0% +M number + + + align:start position:0% +M number +of sorry what I saying so here if you + + align:start position:0% +of sorry what I saying so here if you + + + align:start position:0% +of sorry what I saying so here if you +plug in this here you in the end you got + + align:start position:0% +plug in this here you in the end you got + + + align:start position:0% +plug in this here you in the end you got +- M * but if you directly use this and + + align:start position:0% +- M * but if you directly use this and + + + align:start position:0% +- M * but if you directly use this and +well this + + align:start position:0% +well this + + + align:start position:0% +well this +oh this is trival to see we can see it + + align:start position:0% +oh this is trival to see we can see it + + + align:start position:0% +oh this is trival to see we can see it +immediately + + align:start position:0% +immediately + + + align:start position:0% +immediately +here first if you take the derivative + + align:start position:0% +here first if you take the derivative + + + align:start position:0% +here first if you take the derivative +you just get pi and then you just get + + align:start position:0% +you just get pi and then you just get + + + align:start position:0% +you just get pi and then you just get +that + + align:start position:0% +that + + + align:start position:0% +that +term and when you take derivative here + + align:start position:0% +term and when you take derivative here + + + align:start position:0% +term and when you take derivative here +then you cancel the M yes and then in + + align:start position:0% +then you cancel the M yes and then in + + + align:start position:0% +then you cancel the M yes and then in +order to get zero mode then M and M + + align:start position:0% +order to get zero mode then M and M + + + align:start position:0% +order to get zero mode then M and M +minus M have to cancel so the only + + align:start position:0% +minus M have to cancel so the only + + + align:start position:0% +minus M have to cancel so the only +structure uh can happen is this one then + + align:start position:0% +structure uh can happen is this one then + + + align:start position:0% +structure uh can happen is this one then +the only thing left remaining is to + + align:start position:0% +the only thing left remaining is to + + + align:start position:0% +the only thing left remaining is to +check the coefficient here is one and + + align:start position:0% +check the coefficient here is one and + + + align:start position:0% +check the coefficient here is one and +and that's we have to do the calculation + + align:start position:0% +and that's we have to do the calculation + + + align:start position:0% +and that's we have to do the calculation +and uh and the rest you don't need to do + + align:start position:0% +and uh and the rest you don't need to do + + + align:start position:0% +and uh and the rest you don't need to do +the calculation yeah the only thing to + + align:start position:0% +the calculation yeah the only thing to + + + align:start position:0% +the calculation yeah the only thing to +do the calculation is for this + + align:start position:0% +do the calculation is for this + + + align:start position:0% +do the calculation is for this +one + + align:start position:0% +one + + + align:start position:0% +one +yeah yeah so uh just kind of to overview + + align:start position:0% +yeah yeah so uh just kind of to overview + + + align:start position:0% +yeah yeah so uh just kind of to overview +so all we're doing is um three fields in + + align:start position:0% +so all we're doing is um three fields in + + + align:start position:0% +so all we're doing is um three fields in +a two dimensional World sheet with a Def + + align:start position:0% +a two dimensional World sheet with a Def + + + align:start position:0% +a two dimensional World sheet with a Def +morphism and variance as a gauge + + align:start position:0% +morphism and variance as a gauge + + + align:start position:0% +morphism and variance as a gauge +Symmetry and that gauge symmetry gives + + align:start position:0% +Symmetry and that gauge symmetry gives + + + align:start position:0% +Symmetry and that gauge symmetry gives +us some complicated constraints which we + + align:start position:0% +us some complicated constraints which we + + + align:start position:0% +us some complicated constraints which we +then get rid of solve that constraint + + align:start position:0% +then get rid of solve that constraint + + + align:start position:0% +then get rid of solve that constraint +yeah yeah that's all there is yeah yeah + + align:start position:0% +yeah yeah that's all there is yeah yeah + + + align:start position:0% +yeah yeah that's all there is yeah yeah +that's right so as I said before solving + + align:start position:0% +that's right so as I said before solving + + + align:start position:0% +that's right so as I said before solving +the constraint help you two + + align:start position:0% +the constraint help you two + + + align:start position:0% +the constraint help you two +things first you solve this constraint + + align:start position:0% +things first you solve this constraint + + + align:start position:0% +things first you solve this constraint +and the second you get rid of this X+ + + align:start position:0% +and the second you get rid of this X+ + + + align:start position:0% +and the second you get rid of this X+ +and x minus and because X Plus because + + align:start position:0% +and x minus and because X Plus because + + + align:start position:0% +and x minus and because X Plus because +those are the dangerous field Theory and + + align:start position:0% +those are the dangerous field Theory and + + + align:start position:0% +those are the dangerous field Theory and +now we get rid of and and what remaining + + align:start position:0% +now we get rid of and and what remaining + + + align:start position:0% +now we get rid of and and what remaining +XI are are are good well behav they're + + align:start position:0% +XI are are are good well behav they're + + + align:start position:0% +XI are are are good well behav they're +good boys they they the the good well + + align:start position:0% +good boys they they the the good well + + + align:start position:0% +good boys they they the the good well +behaved field Series + + align:start position:0% + + + + align:start position:0% + +yeah any other + + align:start position:0% +yeah any other + + + align:start position:0% +yeah any other +questions one so is it known how to do + + align:start position:0% +questions one so is it known how to do + + + align:start position:0% +questions one so is it known how to do +basically stream Theory well is it known + + align:start position:0% +basically stream Theory well is it known + + + align:start position:0% +basically stream Theory well is it known +how to do this to deal with the the poly + + align:start position:0% +how to do this to deal with the the poly + + + align:start position:0% +how to do this to deal with the the poly +action not in the light conage oh sure + + align:start position:0% +action not in the light conage oh sure + + + align:start position:0% +action not in the light conage oh sure +okay yeah but that take much longer time + + align:start position:0% +okay yeah but that take much longer time + + + align:start position:0% +okay yeah but that take much longer time +okay got it even in the light con + + align:start position:0% +okay got it even in the light con + + + align:start position:0% +okay got it even in the light con +Gage I'm still trying + + align:start position:0% +Gage I'm still trying + + + align:start position:0% +Gage I'm still trying +to telling the story + + align:start position:0% +to telling the story + + + align:start position:0% +to telling the story +telling a long story short okay and so + + align:start position:0% +telling a long story short okay and so + + + align:start position:0% +telling a long story short okay and so +I'm trying to give you the essence and + + align:start position:0% +I'm trying to give you the essence and + + + align:start position:0% +I'm trying to give you the essence and +uh but make sure but I'm trying to tell + + align:start position:0% +uh but make sure but I'm trying to tell + + + align:start position:0% +uh but make sure but I'm trying to tell +you the essence but at the same time I + + align:start position:0% +you the essence but at the same time I + + + align:start position:0% +you the essence but at the same time I +want you to understand so make sure you + + align:start position:0% +want you to understand so make sure you + + + align:start position:0% +want you to understand so make sure you +answer the you ask whatever it's not + + align:start position:0% +answer the you ask whatever it's not + + + align:start position:0% +answer the you ask whatever it's not +clear + + align:start position:0% +clear + + + align:start position:0% +clear +but for example in the next semester + + align:start position:0% +but for example in the next semester + + + align:start position:0% +but for example in the next semester +undergraduate stren for + + align:start position:0% +undergraduate stren for + + + align:start position:0% +undergraduate stren for +undergraduate you will reach this + + align:start position:0% +undergraduate you will reach this + + + align:start position:0% +undergraduate you will reach this +point essentially + + align:start position:0% +point essentially + + + align:start position:0% +point essentially +after maybe 15 + + align:start position:0% +after maybe 15 + + + align:start position:0% +after maybe 15 +lectures and uh and we reached here + + align:start position:0% +lectures and uh and we reached here + + + align:start position:0% +lectures and uh and we reached here +maybe only two or three lectures and uh + + align:start position:0% +maybe only two or three lectures and uh + + + align:start position:0% +maybe only two or three lectures and uh +and so uh uh as I trying to just give + + align:start position:0% +and so uh uh as I trying to just give + + + align:start position:0% +and so uh uh as I trying to just give +you the essence and uh and try to uh not + + align:start position:0% +you the essence and uh and try to uh not + + + align:start position:0% +you the essence and uh and try to uh not +to give you too many technical details + + align:start position:0% +to give you too many technical details + + + align:start position:0% +to give you too many technical details +say cross checks ET and there many cross + + align:start position:0% +say cross checks ET and there many cross + + + align:start position:0% +say cross checks ET and there many cross +check you can do ET yeah I'm not doing + + align:start position:0% +check you can do ET yeah I'm not doing + + + align:start position:0% +check you can do ET yeah I'm not doing +those things just give you the essence + + align:start position:0% +those things just give you the essence + + + align:start position:0% +those things just give you the essence +got it + + align:start position:0% +got it + + + align:start position:0% +got it +right any other + + align:start position:0% + + + + align:start position:0% + +questions good + + align:start position:0% +questions good + + + align:start position:0% +questions good +okay so so now we can so this is the + + align:start position:0% +okay so so now we can so this is the + + + align:start position:0% +okay so so now we can so this is the +review of the classical story so now + + align:start position:0% +review of the classical story so now + + + align:start position:0% +review of the classical story so now +let's do the quantum + + align:start position:0% + + + + align:start position:0% + +story again this is a just quick review + + align:start position:0% +story again this is a just quick review + + + align:start position:0% +story again this is a just quick review +of what we did last + + align:start position:0% +of what we did last + + + align:start position:0% +of what we did last +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +time so Quantum + + align:start position:0% + + + + align:start position:0% + +mechanically this just become a uh all + + align:start position:0% +mechanically this just become a uh all + + + align:start position:0% +mechanically this just become a uh all +those become + + align:start position:0% +those become + + + align:start position:0% +those become +operators all those become operators and + + align:start position:0% +operators all those become operators and + + + align:start position:0% +operators all those become operators and +also become + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +operators + + align:start position:0% +operators + + + align:start position:0% +operators +okay so this commutator as we said last + + align:start position:0% +okay so this commutator as we said last + + + align:start position:0% +okay so this commutator as we said last +time impli that one/ square root of Mi + + align:start position:0% +time impli that one/ square root of Mi + + + align:start position:0% +time impli that one/ square root of Mi +should be considered as a standard U + + align:start position:0% +should be considered as a standard U + + + align:start position:0% +should be considered as a standard U +allation + + align:start position:0% +allation + + + align:start position:0% +allation +operators for M greater than + + align:start position:0% +operators for M greater than + + + align:start position:0% +operators for M greater than +zero and + + align:start position:0% +zero and + + + align:start position:0% +zero and +uh the mode with negative M should be + + align:start position:0% +uh the mode with negative M should be + + + align:start position:0% +uh the mode with negative M should be +considered as the creation + + align:start position:0% +considered as the creation + + + align:start position:0% +considered as the creation +operators okay creation operators and + + align:start position:0% +operators okay creation operators and + + + align:start position:0% +operators okay creation operators and +then this is like the + + align:start position:0% +then this is like the + + + align:start position:0% +then this is like the +standard uh quantization of fil Theory + + align:start position:0% +standard uh quantization of fil Theory + + + align:start position:0% +standard uh quantization of fil Theory +you reduce to infinite number of + + align:start position:0% +you reduce to infinite number of + + + align:start position:0% +you reduce to infinite number of +harmonic oscillators and in particular + + align:start position:0% +harmonic oscillators and in particular + + + align:start position:0% +harmonic oscillators and in particular +this + + align:start position:0% + + + + align:start position:0% + +product just reduced to M + + align:start position:0% +product just reduced to M + + + align:start position:0% +product just reduced to M +times this A M I dager am m i just + + align:start position:0% +times this A M I dager am m i just + + + align:start position:0% +times this A M I dager am m i just +become m m Mi + + align:start position:0% +become m m Mi + + + align:start position:0% +become m m Mi +I okay so M Mi I is the oscillation + + align:start position:0% +I okay so M Mi I is the oscillation + + + align:start position:0% +I okay so M Mi I is the oscillation +oscillator number occupation number say + + align:start position:0% +oscillator number occupation number say + + + align:start position:0% +oscillator number occupation number say +for each harmonic oscillator + + align:start position:0% +for each harmonic oscillator + + + align:start position:0% +for each harmonic oscillator +and then then the typical + + align:start position:0% + + + + align:start position:0% + +State then the typical + + align:start position:0% + + + + align:start position:0% + +state of the system just obtained by + + align:start position:0% +state of the system just obtained by + + + align:start position:0% +state of the system just obtained by +acting not s on the vacuum for example + + align:start position:0% +acting not s on the vacuum for example + + + align:start position:0% +acting not s on the vacuum for example +for the open string we only have one set + + align:start position:0% +for the open string we only have one set + + + align:start position:0% +for the open string we only have one set +of mode so then we have this form M1 + + align:start position:0% +of mode so then we have this form M1 + + + align:start position:0% +of mode so then we have this form M1 +M1 Alpha minus M2 I I 2 and two on the + + align:start position:0% +M1 Alpha minus M2 I I 2 and two on the + + + align:start position:0% +M1 Alpha minus M2 I I 2 and two on the +vacuum and the + + align:start position:0% +vacuum and the + + + align:start position:0% +vacuum and the +vacuum also have a quantum number P + + align:start position:0% +vacuum also have a quantum number P + + + align:start position:0% +vacuum also have a quantum number P +mu because the because uh uh uh because + + align:start position:0% +mu because the because uh uh uh because + + + align:start position:0% +mu because the because uh uh uh because +those p p both p+ and Pi here are + + align:start position:0% +those p p both p+ and Pi here are + + + align:start position:0% +those p p both p+ and Pi here are +quantum + + align:start position:0% +quantum + + + align:start position:0% +quantum +operators and so so we take the vacuum + + align:start position:0% +operators and so so we take the vacuum + + + align:start position:0% +operators and so so we take the vacuum +to be acting state of them and they + + align:start position:0% +to be acting state of them and they + + + align:start position:0% +to be acting state of them and they +independent of those Alphas so so this + + align:start position:0% +independent of those Alphas so so this + + + align:start position:0% +independent of those Alphas so so this +vacuum is the only vacuum for the + + align:start position:0% +vacuum is the only vacuum for the + + + align:start position:0% +vacuum is the only vacuum for the +oscillators and but they are still + + align:start position:0% +oscillators and but they are still + + + align:start position:0% +oscillators and but they are still +labeled by a space time momentum okay so + + align:start position:0% +labeled by a space time momentum okay so + + + align:start position:0% +labeled by a space time momentum okay so +labeled by the SpaceTime momentum of the + + align:start position:0% +labeled by the SpaceTime momentum of the + + + align:start position:0% +labeled by the SpaceTime momentum of the +string so this is for the open + + align:start position:0% + + + + align:start position:0% + +string for the open + + align:start position:0% +string for the open + + + align:start position:0% +string for the open +string and for the closed + + align:start position:0% + + + + align:start position:0% + +string for the close + + align:start position:0% +string for the close + + + align:start position:0% +string for the close +stren + + align:start position:0% +stren + + + align:start position:0% +stren +similarly you just have two set of modes + + align:start position:0% +similarly you just have two set of modes + + + align:start position:0% +similarly you just have two set of modes +minus i1 and one Al + + align:start position:0% +minus i1 and one Al + + + align:start position:0% +minus i1 and one Al +M2 I2 + + align:start position:0% + + + + align:start position:0% + +and2 and then also you have the other + + align:start position:0% +and2 and then also you have the other + + + align:start position:0% +and2 and then also you have the other +say let me call it K1 J1 + + align:start position:0% +say let me call it K1 J1 + + + align:start position:0% +say let me call it K1 J1 +L1 Alpha minus + + align:start position:0% +L1 Alpha minus + + + align:start position:0% +L1 Alpha minus +K2 J2 L2 + + align:start position:0% +K2 J2 L2 + + + align:start position:0% +K2 J2 L2 +Etc on the vacuum so this is a typical + + align:start position:0% +Etc on the vacuum so this is a typical + + + align:start position:0% +Etc on the vacuum so this is a typical +State for the close string + + align:start position:0% + + + + align:start position:0% + +but the allowed State should still + + align:start position:0% +but the allowed State should still + + + align:start position:0% +but the allowed State should still +satisfy this + + align:start position:0% +satisfy this + + + align:start position:0% +satisfy this +constraint okay should still satisfy + + align:start position:0% +constraint okay should still satisfy + + + align:start position:0% +constraint okay should still satisfy +this + + align:start position:0% +this + + + align:start position:0% +this +constraint so this constraint can be + + align:start position:0% +constraint so this constraint can be + + + align:start position:0% +constraint so this constraint can be +written + + align:start position:0% +written + + + align:start position:0% +written +as with the with the following + + align:start position:0% +as with the with the following + + + align:start position:0% +as with the with the following +constraint is that oscillated number on + + align:start position:0% +constraint is that oscillated number on + + + align:start position:0% +constraint is that oscillated number on +the left hand side for the left moving + + align:start position:0% +the left hand side for the left moving + + + align:start position:0% +the left hand side for the left moving +modes or + + align:start position:0% +modes or + + + align:start position:0% +modes or +TAA and uh and oscillator L for the + + align:start position:0% +TAA and uh and oscillator L for the + + + align:start position:0% +TAA and uh and oscillator L for the +Right Moving modes they have to be the + + align:start position:0% +Right Moving modes they have to be the + + + align:start position:0% +Right Moving modes they have to be the +same so so so so let me rewrite this + + align:start position:0% +same so so so so let me rewrite this + + + align:start position:0% +same so so so so let me rewrite this +equation in terms of oscillated numbers + + align:start position:0% +equation in terms of oscillated numbers + + + align:start position:0% +equation in terms of oscillated numbers +so this means I some so let me now + + align:start position:0% +so this means I some so let me now + + + align:start position:0% +so this means I some so let me now +writing from M to Infinity so M and + + align:start position:0% + + + + align:start position:0% + +I okay so this just form that equation + + align:start position:0% +I okay so this just form that equation + + + align:start position:0% +I okay so this just form that equation +okay so this is sometimes called yeah so + + align:start position:0% +okay so this is sometimes called yeah so + + + align:start position:0% +okay so this is sometimes called yeah so +this is called the level matching + + align:start position:0% + + + + align:start position:0% + +condition so for close string you cannot + + align:start position:0% +condition so for close string you cannot + + + align:start position:0% +condition so for close string you cannot +just act + + align:start position:0% +just act + + + align:start position:0% +just act +arbitr Alpha and Alpha + + align:start position:0% + + + + align:start position:0% + +TAA the number of + + align:start position:0% +TAA the number of + + + align:start position:0% +TAA the number of +modes the total thing you act from the + + align:start position:0% +modes the total thing you act from the + + + align:start position:0% +modes the total thing you act from the +left hand side from the uh Alpha and + + align:start position:0% +left hand side from the uh Alpha and + + + align:start position:0% +left hand side from the uh Alpha and +those from the TAA they have to be + + align:start position:0% +those from the TAA they have to be + + + align:start position:0% +those from the TAA they have to be +balanced by this + + align:start position:0% +balanced by this + + + align:start position:0% +balanced by this +equation okay which is a consequence + + align:start position:0% +equation okay which is a consequence + + + align:start position:0% +equation okay which is a consequence +that there's no spal point on the + + align:start position:0% + + + + align:start position:0% + +scen okay + + align:start position:0% + + + + align:start position:0% + +so so now we can also rewrite those + + align:start position:0% +so so now we can also rewrite those + + + align:start position:0% +so so now we can also rewrite those +equations at the quantum + + align:start position:0% +equations at the quantum + + + align:start position:0% +equations at the quantum +level okay so those equation at the + + align:start position:0% +level okay so those equation at the + + + align:start position:0% +level okay so those equation at the +quantum level those equation just tells + + align:start position:0% +quantum level those equation just tells + + + align:start position:0% +quantum level those equation just tells +you that for those + + align:start position:0% +you that for those + + + align:start position:0% +you that for those +States for those States the P mu are not + + align:start position:0% +States for those States the P mu are not + + + align:start position:0% +States for those States the P mu are not +arbitrary P mu are not arbitrary P mu + + align:start position:0% +arbitrary P mu are not arbitrary P mu + + + align:start position:0% +arbitrary P mu are not arbitrary P mu +must satisfy this kind of + + align:start position:0% +must satisfy this kind of + + + align:start position:0% +must satisfy this kind of +constraint you me must satisfy this kind + + align:start position:0% +constraint you me must satisfy this kind + + + align:start position:0% +constraint you me must satisfy this kind +of constraint and uh uh that can in turn + + align:start position:0% +of constraint and uh uh that can in turn + + + align:start position:0% +of constraint and uh uh that can in turn +be interpreted as the determine the mass + + align:start position:0% +be interpreted as the determine the mass + + + align:start position:0% +be interpreted as the determine the mass +of the + + align:start position:0% +of the + + + align:start position:0% +of the +string okay determine the mass of the + + align:start position:0% +string okay determine the mass of the + + + align:start position:0% +string okay determine the mass of the +string so so the MTH of the string then + + align:start position:0% +string so so the MTH of the string then + + + align:start position:0% +string so so the MTH of the string then +for the + + align:start position:0% +for the + + + align:start position:0% +for the +open mass of string can be written one + + align:start position:0% +open mass of string can be written one + + + align:start position:0% +open mass of string can be written one +over alha Prime Su over I Su over y + + align:start position:0% +over alha Prime Su over I Su over y + + + align:start position:0% +over alha Prime Su over I Su over y +infinity and M Mi I then plus some 0 + + align:start position:0% +infinity and M Mi I then plus some 0 + + + align:start position:0% +infinity and M Mi I then plus some 0 +point + + align:start position:0% +point + + + align:start position:0% +point +energy so so this is just the frequency + + align:start position:0% +energy so so this is just the frequency + + + align:start position:0% +energy so so this is just the frequency +of each + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +mode so this is just a frequency of the + + align:start position:0% +mode so this is just a frequency of the + + + align:start position:0% +mode so this is just a frequency of the +each + + align:start position:0% +each + + + align:start position:0% +each +mode uh a frequency of each mode and + + align:start position:0% +mode uh a frequency of each mode and + + + align:start position:0% +mode uh a frequency of each mode and +this is the occupation number so this is + + align:start position:0% +this is the occupation number so this is + + + align:start position:0% +this is the occupation number so this is +the standard harmonic oscillator uh uh + + align:start position:0% +the standard harmonic oscillator uh uh + + + align:start position:0% +the standard harmonic oscillator uh uh +result and uh um then Quantum level of + + align:start position:0% +result and uh um then Quantum level of + + + align:start position:0% +result and uh um then Quantum level of +course there's ordering issue because + + align:start position:0% +course there's ordering issue because + + + align:start position:0% +course there's ordering issue because +the + + align:start position:0% +the + + + align:start position:0% +the +the alpha M and M don't commute so + + align:start position:0% +the alpha M and M don't commute so + + + align:start position:0% +the alpha M and M don't commute so +because one is creation one isation + + align:start position:0% +because one is creation one isation + + + align:start position:0% +because one is creation one isation +operator so the ordering here matters so + + align:start position:0% +operator so the ordering here matters so + + + align:start position:0% +operator so the ordering here matters so +the ordering here + + align:start position:0% + + + + align:start position:0% + +matters so in + + align:start position:0% +matters so in + + + align:start position:0% +matters so in +principle + + align:start position:0% +principle + + + align:start position:0% +principle +um + + align:start position:0% +um + + + align:start position:0% +um +um yeah uh matter similarly you can + + align:start position:0% +um yeah uh matter similarly you can + + + align:start position:0% +um yeah uh matter similarly you can +write + + align:start position:0% +write + + + align:start position:0% +write +it so that will create uh uh uh give + + align:start position:0% +it so that will create uh uh uh give + + + align:start position:0% +it so that will create uh uh uh give +rise to this uh uh uh this uh uh Zero + + align:start position:0% +rise to this uh uh uh this uh uh Zero + + + align:start position:0% +rise to this uh uh uh this uh uh Zero +Point Energy or ordering uh L so + + align:start position:0% +Point Energy or ordering uh L so + + + align:start position:0% +Point Energy or ordering uh L so +similarly for the for the Clos + + align:start position:0% +similarly for the for the Clos + + + align:start position:0% +similarly for the for the Clos +stream then you just have + + align:start position:0% +stream then you just have + + + align:start position:0% +stream then you just have +a two sets of + + align:start position:0% +a two sets of + + + align:start position:0% +a two sets of +modes + + align:start position:0% + + + + align:start position:0% + +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +okay a + + align:start position:0% + + + + align:start position:0% + +z so a + + align:start position:0% + + + + align:start position:0% + +zero can be so he so this is the place + + align:start position:0% +zero can be so he so this is the place + + + align:start position:0% +zero can be so he so this is the place +this remark is + + align:start position:0% +this remark is + + + align:start position:0% +this remark is +useful because the because the uh this + + align:start position:0% +useful because the because the uh this + + + align:start position:0% +useful because the because the uh this +just come + + align:start position:0% +just come + + + align:start position:0% +just come +from this just come from essentially + + align:start position:0% +from this just come from essentially + + + align:start position:0% +from this just come from essentially +this part just come from essentially + + align:start position:0% +this part just come from essentially + + + align:start position:0% +this part just come from essentially +it's just the + + align:start position:0% +it's just the + + + align:start position:0% +it's just the +honin of the XI and just XI viewed as a + + align:start position:0% +honin of the XI and just XI viewed as a + + + align:start position:0% +honin of the XI and just XI viewed as a +field Ser on the W sheet and the field + + align:start position:0% +field Ser on the W sheet and the field + + + align:start position:0% +field Ser on the W sheet and the field +Ser of XI essentially is a bunch of + + align:start position:0% +Ser of XI essentially is a bunch of + + + align:start position:0% +Ser of XI essentially is a bunch of +harmonical oscillators and for each + + align:start position:0% +harmonical oscillators and for each + + + align:start position:0% +harmonical oscillators and for each +harmonical oscillator we do know what is + + align:start position:0% +harmonical oscillator we do know what is + + + align:start position:0% +harmonical oscillator we do know what is +the ordinary number + + align:start position:0% +the ordinary number + + + align:start position:0% +the ordinary number +is just one2 the 0 point energy just + + align:start position:0% +is just one2 the 0 point energy just + + + align:start position:0% +is just one2 the 0 point energy just +one2 and then you just add all of them + + align:start position:0% +one2 and then you just add all of them + + + align:start position:0% +one2 and then you just add all of them +together okay just add all them together + + align:start position:0% +together okay just add all them together + + + align:start position:0% +together okay just add all them together +so so for example for the open string so + + align:start position:0% +so so for example for the open string so + + + align:start position:0% +so so for example for the open string so +this just become Alpha D minus 2 so D + + align:start position:0% +this just become Alpha D minus 2 so D + + + align:start position:0% +this just become Alpha D minus 2 so D +minus 2 because D minus 2 direct + + align:start position:0% +minus 2 because D minus 2 direct + + + align:start position:0% +minus 2 because D minus 2 direct +directions and then you sum m equal to + + align:start position:0% +directions and then you sum m equal to + + + align:start position:0% +directions and then you sum m equal to +Infinity 12 + + align:start position:0% +Infinity 12 + + + align:start position:0% +Infinity 12 +Omega okay half Omega and and Omega is + + align:start position:0% +Omega okay half Omega and and Omega is + + + align:start position:0% +Omega okay half Omega and and Omega is +M then I told you this beautiful trick + + align:start position:0% +M then I told you this beautiful trick + + + align:start position:0% +M then I told you this beautiful trick +last time that this should be equal to D + + align:start position:0% +last time that this should be equal to D + + + align:start position:0% +last time that this should be equal to D +minus 2 / 22 IDE by 24 one of alpha + + align:start position:0% +minus 2 / 22 IDE by 24 one of alpha + + + align:start position:0% +minus 2 / 22 IDE by 24 one of alpha +Prime because this guy go sum m y to + + align:start position:0% +Prime because this guy go sum m y to + + + align:start position:0% +Prime because this guy go sum m y to +Infinity M give you minus one + + align:start position:0% +Infinity M give you minus one + + + align:start position:0% +Infinity M give you minus one +12 okay so this is for the + + align:start position:0% +12 okay so this is for the + + + align:start position:0% +12 okay so this is for the +open so similarly for the closed string + + align:start position:0% +open so similarly for the closed string + + + align:start position:0% +open so similarly for the closed string +you can do the similar thing just differ + + align:start position:0% +you can do the similar thing just differ + + + align:start position:0% +you can do the similar thing just differ +by some two ET so this give you D minus + + align:start position:0% +by some two ET so this give you D minus + + + align:start position:0% +by some two ET so this give you D minus + + align:start position:0% + + + align:start position:0% +24 4 / Alpha Prime + + align:start position:0% +24 4 / Alpha Prime + + + align:start position:0% +24 4 / Alpha Prime +closed + + align:start position:0% + + + + align:start position:0% + +okay so this vacuum + + align:start position:0% + + + + align:start position:0% + +energy so so this can also be + + align:start position:0% +energy so so this can also be + + + align:start position:0% +energy so so this can also be +interpreted as a vacuum energy on the + + align:start position:0% +interpreted as a vacuum energy on the + + + align:start position:0% +interpreted as a vacuum energy on the +circle vacuum energy of this Quantum F + + align:start position:0% +circle vacuum energy of this Quantum F + + + align:start position:0% +circle vacuum energy of this Quantum F +on the circle and in Quantum field + + align:start position:0% +on the circle and in Quantum field + + + align:start position:0% +on the circle and in Quantum field +Series this is sometimes called the + + align:start position:0% +Series this is sometimes called the + + + align:start position:0% +Series this is sometimes called the +cosmal energy and uh and you can check + + align:start position:0% +cosmal energy and uh and you can check + + + align:start position:0% +cosmal energy and uh and you can check +yourself that those answers are agree + + align:start position:0% +yourself that those answers are agree + + + align:start position:0% +yourself that those answers are agree +with the standard the uh expression for + + align:start position:0% +with the standard the uh expression for + + + align:start position:0% +with the standard the uh expression for +the custom energy on the circle um yeah + + align:start position:0% +the custom energy on the circle um yeah + + + align:start position:0% +the custom energy on the circle um yeah +if you choose your unit property because + + align:start position:0% +if you choose your unit property because + + + align:start position:0% +if you choose your unit property because +we have chosen the uh the size to be 2 + + align:start position:0% +we have chosen the uh the size to be 2 + + + align:start position:0% +we have chosen the uh the size to be 2 +pi + + align:start position:0% + + + + align:start position:0% + +okay good so this + + align:start position:0% +okay good so this + + + align:start position:0% +okay good so this +summarize what we + + align:start position:0% +summarize what we + + + align:start position:0% +summarize what we +did uh uh summarize what the uh we did + + align:start position:0% +did uh uh summarize what the uh we did + + + align:start position:0% +did uh uh summarize what the uh we did +so far uh um + + align:start position:0% +so far uh um + + + align:start position:0% +so far uh um +any questions on + + align:start position:0% + + + + align:start position:0% + +this good no more questions every + + align:start position:0% +this good no more questions every + + + align:start position:0% +this good no more questions every +everything is Crystal + + align:start position:0% +everything is Crystal + + + align:start position:0% +everything is Crystal +Clear then I should have immediately + + align:start position:0% +Clear then I should have immediately + + + align:start position:0% +Clear then I should have immediately +have a + + align:start position:0% + + + + align:start position:0% + +crit yes so so the 26 Dimensions comes + + align:start position:0% +crit yes so so the 26 Dimensions comes + + + align:start position:0% +crit yes so so the 26 Dimensions comes +from making this zero yeah uh um no + + align:start position:0% +from making this zero yeah uh um no + + + align:start position:0% +from making this zero yeah uh um no +no if you put the 26 here this is not + + align:start position:0% +no if you put the 26 here this is not + + + align:start position:0% +no if you put the 26 here this is not +zero I'm sorry making this + + align:start position:0% +zero I'm sorry making this + + + align:start position:0% +zero I'm sorry making this +sorry I apolog not zero so I would just + + align:start position:0% +sorry I apolog not zero so I would just + + + align:start position:0% +sorry I apolog not zero so I would just +observe so the 26 Dimensions be comes + + align:start position:0% +observe so the 26 Dimensions be comes + + + align:start position:0% +observe so the 26 Dimensions be comes +from the fact that somehow 26 - 2 over + + align:start position:0% +from the fact that somehow 26 - 2 over + + + align:start position:0% +from the fact that somehow 26 - 2 over +24 is one it's like a piece of + + align:start position:0% +24 is one it's like a piece of + + + align:start position:0% +24 is one it's like a piece of +numerology but it's like yeah yeah okay + + align:start position:0% +numerology but it's like yeah yeah okay + + + align:start position:0% +numerology but it's like yeah yeah okay +yeah that's a very good + + align:start position:0% +yeah that's a very good + + + align:start position:0% +yeah that's a very good +observation uh uh uh that's exactly the + + align:start position:0% +observation uh uh uh that's exactly the + + + align:start position:0% +observation uh uh uh that's exactly the +reason I write in this + + align:start position:0% +reason I write in this + + + align:start position:0% +reason I write in this +way right so so let me just make a + + align:start position:0% +way right so so let me just make a + + + align:start position:0% +way right so so let me just make a +comment yeah maybe I make a comment + + align:start position:0% +comment yeah maybe I make a comment + + + align:start position:0% +comment yeah maybe I make a comment +later uh + + align:start position:0% +later uh + + + align:start position:0% +later uh +um anyway so so from here from this two + + align:start position:0% + + + + align:start position:0% + +expression from this expression and this + + align:start position:0% + + + + align:start position:0% + +expression you see this picture which I + + align:start position:0% +expression you see this picture which I + + + align:start position:0% +expression you see this picture which I +said at the + + align:start position:0% + + + + align:start position:0% + +beginning so each of these + + align:start position:0% +beginning so each of these + + + align:start position:0% +beginning so each of these +describe a state of a + + align:start position:0% +describe a state of a + + + align:start position:0% +describe a state of a +string and the the state of a string + + align:start position:0% +string and the the state of a string + + + align:start position:0% +string and the the state of a string +the state of such a stram they they + + align:start position:0% +the state of such a stram they they + + + align:start position:0% +the state of such a stram they they +oscillates in this particular + + align:start position:0% +oscillates in this particular + + + align:start position:0% +oscillates in this particular +way say they + + align:start position:0% +way say they + + + align:start position:0% +way say they +have say they have this U uh those + + align:start position:0% +have say they have this U uh those + + + align:start position:0% +have say they have this U uh those +oscillation modes and then they Moves In + + align:start position:0% +oscillation modes and then they Moves In + + + align:start position:0% +oscillation modes and then they Moves In +Space time with such a center of mass + + align:start position:0% +Space time with such a center of mass + + + align:start position:0% +Space time with such a center of mass +momentum okay with such Sy of mass + + align:start position:0% +momentum okay with such Sy of mass + + + align:start position:0% +momentum okay with such Sy of mass +momentum so such + + align:start position:0% +momentum so such + + + align:start position:0% +momentum so such +object + + align:start position:0% +object + + + align:start position:0% +object +is you look at it from a far it just + + align:start position:0% +is you look at it from a far it just + + + align:start position:0% +is you look at it from a far it just +like a particle okay it just like a + + align:start position:0% +like a particle okay it just like a + + + align:start position:0% +like a particle okay it just like a +particle so so we have we have + + align:start position:0% +particle so so we have we have + + + align:start position:0% +particle so so we have we have +established it so now let's look at the + + align:start position:0% +established it so now let's look at the + + + align:start position:0% +established it so now let's look at the +uh + + align:start position:0% + + + + align:start position:0% + +Spectrum so each of a string of a so + + align:start position:0% +Spectrum so each of a string of a so + + + align:start position:0% +Spectrum so each of a string of a so +each state of a + + align:start position:0% + + + + align:start position:0% + +string can be consider the map to a + + align:start position:0% +string can be consider the map to a + + + align:start position:0% +string can be consider the map to a +space plan time particle + + align:start position:0% + + + + align:start position:0% + +okay so let's now work + + align:start position:0% +okay so let's now work + + + align:start position:0% +okay so let's now work +out and uh and the and the mass of the + + align:start position:0% +out and uh and the and the mass of the + + + align:start position:0% +out and uh and the and the mass of the +particle can be worked out by those + + align:start position:0% +particle can be worked out by those + + + align:start position:0% +particle can be worked out by those +formulas okay so let's now just work out + + align:start position:0% +formulas okay so let's now just work out + + + align:start position:0% +formulas okay so let's now just work out +what are the nest particles because we + + align:start position:0% +what are the nest particles because we + + + align:start position:0% +what are the nest particles because we +are interested in the n's particles + + align:start position:0% +are interested in the n's particles + + + align:start position:0% +are interested in the n's particles +typically + + align:start position:0% +typically + + + align:start position:0% +typically +okay so so now let's start from the + + align:start position:0% +okay so so now let's start from the + + + align:start position:0% +okay so so now let's start from the +beginning now so now let's start with + + align:start position:0% +beginning now so now let's start with + + + align:start position:0% +beginning now so now let's start with +open string + + align:start position:0% + + + + align:start position:0% + +so so the so the lowest mode of course + + align:start position:0% +so so the so the lowest mode of course + + + align:start position:0% +so so the so the lowest mode of course +is just the + + align:start position:0% + + + + align:start position:0% + +vacuum P + + align:start position:0% +vacuum P + + + align:start position:0% +vacuum P +mu okay there's no + + align:start position:0% +mu okay there's no + + + align:start position:0% +mu okay there's no +oscillators so for such a mode NM I just + + align:start position:0% +oscillators so for such a mode NM I just + + + align:start position:0% +oscillators so for such a mode NM I just +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero for all M and + + align:start position:0% +zero for all M and + + + align:start position:0% +zero for all M and +I + + align:start position:0% + + + + align:start position:0% + +okay and uh so this is should be just A + + align:start position:0% +okay and uh so this is should be just A + + + align:start position:0% +okay and uh so this is should be just A +Spacetime scalar so this should describe + + align:start position:0% +Spacetime scalar so this should describe + + + align:start position:0% +Spacetime scalar so this should describe +a space space time scaler because + + align:start position:0% +a space space time scaler because + + + align:start position:0% +a space space time scaler because +there's no uh there's no other Quantum + + align:start position:0% +there's no uh there's no other Quantum + + + align:start position:0% +there's no uh there's no other Quantum +Lumber other than the momentum so it + + align:start position:0% +Lumber other than the momentum so it + + + align:start position:0% +Lumber other than the momentum so it +should be A Spacetime + + align:start position:0% +should be A Spacetime + + + align:start position:0% +should be A Spacetime +scalar so should be should should + + align:start position:0% +scalar so should be should should + + + align:start position:0% +scalar so should be should should +describe a scaler + + align:start position:0% +describe a scaler + + + align:start position:0% +describe a scaler +particle describe scal particle and the + + align:start position:0% +particle describe scal particle and the + + + align:start position:0% +particle describe scal particle and the +mass of the particle we can just read + + align:start position:0% +mass of the particle we can just read + + + align:start position:0% +mass of the particle we can just read +from + + align:start position:0% + + + + align:start position:0% + +here and uh so the M + + align:start position:0% +here and uh so the M + + + align:start position:0% +here and uh so the M +Square equal to minus so this is for the + + align:start position:0% +Square equal to minus so this is for the + + + align:start position:0% +Square equal to minus so this is for the +open string so we use this formula + + align:start position:0% +open string so we use this formula + + + align:start position:0% +open string so we use this formula +because that's the only thing because + + align:start position:0% +because that's the only thing because + + + align:start position:0% +because that's the only thing because +this here is zero so the only thing come + + align:start position:0% +this here is zero so the only thing come + + + align:start position:0% +this here is zero so the only thing come +from a zero term so so you just given by + + align:start position:0% +from a zero term so so you just given by + + + align:start position:0% +from a zero term so so you just given by +minus D- 24 or tus 2 by 24 1/ Alpha + + align:start position:0% +minus D- 24 or tus 2 by 24 1/ Alpha + + + align:start position:0% +minus D- 24 or tus 2 by 24 1/ Alpha +Prime + + align:start position:0% + + + + align:start position:0% + +okay so one immediate thing you notice + + align:start position:0% +okay so one immediate thing you notice + + + align:start position:0% +okay so one immediate thing you notice +you say this guy is smaller than + + align:start position:0% +you say this guy is smaller than + + + align:start position:0% +you say this guy is smaller than +zero for D greater than two say for any + + align:start position:0% +zero for D greater than two say for any + + + align:start position:0% +zero for D greater than two say for any +space time dimension greater than two + + align:start position:0% +space time dimension greater than two + + + align:start position:0% +space time dimension greater than two +you actually find the mass square netive + + align:start position:0% +you actually find the mass square netive + + + align:start position:0% +you actually find the mass square netive +mass + + align:start position:0% +mass + + + align:start position:0% +mass +square so people actually give a fancy + + align:start position:0% +square so people actually give a fancy + + + align:start position:0% +square so people actually give a fancy +name for for such kind of particle they + + align:start position:0% +name for for such kind of particle they + + + align:start position:0% +name for for such kind of particle they +call + + align:start position:0% +call + + + align:start position:0% +call +tum and in the 60s actually people + + align:start position:0% +tum and in the 60s actually people + + + align:start position:0% +tum and in the 60s actually people +designed the experiment to look for such + + align:start position:0% +designed the experiment to look for such + + + align:start position:0% +designed the experiment to look for such +particles uh particles of lative mass + + align:start position:0% +particles uh particles of lative mass + + + align:start position:0% +particles uh particles of lative mass +netive mass + + align:start position:0% +netive mass + + + align:start position:0% +netive mass +square um + + align:start position:0% +square um + + + align:start position:0% +square um +anyway um so uh so these are the + + align:start position:0% +anyway um so uh so these are the + + + align:start position:0% +anyway um so uh so these are the +weird uh + + align:start position:0% +weird uh + + + align:start position:0% +weird uh +yeah we not go into + + align:start position:0% + + + + align:start position:0% + +here let me just say for the + + align:start position:0% + + + + align:start position:0% + +following wait in the in the the if you + + align:start position:0% +following wait in the in the the if you + + + align:start position:0% +following wait in the in the the if you +see excitations with negative mass + + align:start position:0% +see excitations with negative mass + + + align:start position:0% +see excitations with negative mass +square typically tells you that the + + align:start position:0% +square typically tells you that the + + + align:start position:0% +square typically tells you that the +system have instability that you are not + + align:start position:0% +system have instability that you are not + + + align:start position:0% +system have instability that you are not +in the lowest energy State okay you're + + align:start position:0% +in the lowest energy State okay you're + + + align:start position:0% +in the lowest energy State okay you're +not in the low state so so what this + + align:start position:0% +not in the low state so so what this + + + align:start position:0% +not in the low state so so what this +tells + + align:start position:0% +tells + + + align:start position:0% +tells +you is that this open this open stream + + align:start position:0% +you is that this open this open stream + + + align:start position:0% +you is that this open this open stream +propagate in the flat movy space time + + align:start position:0% +propagate in the flat movy space time + + + align:start position:0% +propagate in the flat movy space time +may not be the lowest configuration of + + align:start position:0% +may not be the lowest configuration of + + + align:start position:0% +may not be the lowest configuration of +the + + align:start position:0% +the + + + align:start position:0% +the +stream but that is okay uh uh if you're + + align:start position:0% +stream but that is okay uh uh if you're + + + align:start position:0% +stream but that is okay uh uh if you're +not in the lowest configuration uh does + + align:start position:0% +not in the lowest configuration uh does + + + align:start position:0% +not in the lowest configuration uh does +not uh uh uh it's not a big deal and uh + + align:start position:0% +not uh uh uh it's not a big deal and uh + + + align:start position:0% +not uh uh uh it's not a big deal and uh +it just means you have not found the + + align:start position:0% +it just means you have not found the + + + align:start position:0% +it just means you have not found the +correct ground state does not mean the + + align:start position:0% +correct ground state does not mean the + + + align:start position:0% +correct ground state does not mean the +Ser is inconsistent okay and uh and so + + align:start position:0% +Ser is inconsistent okay and uh and so + + + align:start position:0% +Ser is inconsistent okay and uh and so +so so even though this is + + align:start position:0% +so so even though this is + + + align:start position:0% +so so even though this is +unpleasant but this thing is tolerable + + align:start position:0% +unpleasant but this thing is tolerable + + + align:start position:0% +unpleasant but this thing is tolerable +okay this thing is + + align:start position:0% + + + + align:start position:0% + +tolerable any problem with + + align:start position:0% +tolerable any problem with + + + align:start position:0% +tolerable any problem with +this but you already set all n equals to + + align:start position:0% +this but you already set all n equals to + + + align:start position:0% +this but you already set all n equals to +zero so that is the ground state no this + + align:start position:0% +zero so that is the ground state no this + + + align:start position:0% +zero so that is the ground state no this +is a ground state on the W + + align:start position:0% +is a ground state on the W + + + align:start position:0% +is a ground state on the W +sheet but on the in the space time this + + align:start position:0% +sheet but on the in the space time this + + + align:start position:0% +sheet but on the in the space time this +corresponding to a particle this + + align:start position:0% +corresponding to a particle this + + + align:start position:0% +corresponding to a particle this +corresponding to excitation in the space + + align:start position:0% +corresponding to excitation in the space + + + align:start position:0% +corresponding to excitation in the space +time and so this corresponding to + + align:start position:0% +time and so this corresponding to + + + align:start position:0% +time and so this corresponding to +excitation in the space time is the + + align:start position:0% +excitation in the space time is the + + + align:start position:0% +excitation in the space time is the +active mass square and typically if you + + align:start position:0% +active mass square and typically if you + + + align:start position:0% +active mass square and typically if you +have something with a netive mass square + + align:start position:0% +have something with a netive mass square + + + align:start position:0% +have something with a netive mass square +let me just say one more words here then + + align:start position:0% +let me just say one more words here then + + + align:start position:0% +let me just say one more words here then +that means you're sitting on the top of + + align:start position:0% +that means you're sitting on the top of + + + align:start position:0% +that means you're sitting on the top of +a hill and that's where you have a + + align:start position:0% +a hill and that's where you have a + + + align:start position:0% +a hill and that's where you have a +elective mass square and so means you + + align:start position:0% +elective mass square and so means you + + + align:start position:0% +elective mass square and so means you +are in the some kind of unstable state + + align:start position:0% +are in the some kind of unstable state + + + align:start position:0% +are in the some kind of unstable state +but uh but of course you are allowed to + + align:start position:0% +but uh but of course you are allowed to + + + align:start position:0% +but uh but of course you are allowed to +sit on the top of a hill yeah it's not a + + align:start position:0% +sit on the top of a hill yeah it's not a + + + align:start position:0% +sit on the top of a hill yeah it's not a +big deal why why is unstable like more + + align:start position:0% +big deal why why is unstable like more + + + align:start position:0% +big deal why why is unstable like more +expandation on the top of the hill is it + + align:start position:0% +expandation on the top of the hill is it + + + align:start position:0% +expandation on the top of the hill is it +stable why why means on the top of here + + align:start position:0% +stable why why means on the top of here + + + align:start position:0% +stable why why means on the top of here +ah if you write if you write a scaler + + align:start position:0% +ah if you write if you write a scaler + + + align:start position:0% +ah if you write if you write a scaler +field + + align:start position:0% +field + + + align:start position:0% +field +Theory yeah so so this corresponding to + + align:start position:0% +Theory yeah so so this corresponding to + + + align:start position:0% +Theory yeah so so this corresponding to +a scaler field in space time now okay so + + align:start position:0% +a scaler field in space time now okay so + + + align:start position:0% +a scaler field in space time now okay so +now if I write a scaler field theory in + + align:start position:0% +now if I write a scaler field theory in + + + align:start position:0% +now if I write a scaler field theory in +space + + align:start position:0% +space + + + align:start position:0% +space +time say let me call five we s to mass + + align:start position:0% +time say let me call five we s to mass + + + align:start position:0% +time say let me call five we s to mass +square so that means the potential for + + align:start position:0% +square so that means the potential for + + + align:start position:0% +square so that means the potential for +for this mass square is like this okay + + align:start position:0% +for this mass square is like this okay + + + align:start position:0% +for this mass square is like this okay +then that means that the five want + + align:start position:0% +then that means that the five want + + + align:start position:0% +then that means that the five want +increase + + align:start position:0% +increase + + + align:start position:0% +increase +yeah is that the same thing as a example + + align:start position:0% +yeah is that the same thing as a example + + + align:start position:0% +yeah is that the same thing as a example +for spontaneous yeah that's right + + align:start position:0% +for spontaneous yeah that's right + + + align:start position:0% +for spontaneous yeah that's right +similar for but except here we don't + + align:start position:0% +similar for but except here we don't + + + align:start position:0% +similar for but except here we don't +know what is the bottom yeah we just + + align:start position:0% +know what is the bottom yeah we just + + + align:start position:0% +know what is the bottom yeah we just +sitting at the + + align:start position:0% + + + + align:start position:0% + +top anyway so later we will find a way + + align:start position:0% +top anyway so later we will find a way + + + align:start position:0% +top anyway so later we will find a way +to get rid of this so it's okay so you + + align:start position:0% +to get rid of this so it's okay so you + + + align:start position:0% +to get rid of this so it's okay so you +don't need to worry about this + + align:start position:0% +don't need to worry about this + + + align:start position:0% +don't need to worry about this +here so the second mode the second no is + + align:start position:0% +here so the second mode the second no is + + + align:start position:0% +here so the second mode the second no is +mode you just you add Alpha minus + + align:start position:0% +mode you just you add Alpha minus + + + align:start position:0% +mode you just you add Alpha minus +one on the on this worksheet ground + + align:start position:0% +one on the on this worksheet ground + + + align:start position:0% +one on the on this worksheet ground +state okay so now this thing is + + align:start position:0% +state okay so now this thing is + + + align:start position:0% +state okay so now this thing is +interesting first this index + + align:start position:0% +interesting first this index + + + align:start position:0% +interesting first this index +I this index I and this index I is A + + align:start position:0% +I this index I and this index I is A + + + align:start position:0% +I this index I and this index I is A +Spacetime + + align:start position:0% +Spacetime + + + align:start position:0% +Spacetime +index okay it's A Spacetime index and so + + align:start position:0% +index okay it's A Spacetime index and so + + + align:start position:0% +index okay it's A Spacetime index and so +this actually means this transform + + align:start position:0% + + + + align:start position:0% + +means this state X transform as a + + align:start position:0% + + + + align:start position:0% + +vector + + align:start position:0% +vector + + + align:start position:0% +vector +under s o minus + + align:start position:0% +under s o minus + + + align:start position:0% +under s o minus +2 the rotation of the XI directions and + + align:start position:0% +2 the rotation of the XI directions and + + + align:start position:0% +2 the rotation of the XI directions and +remember in the Lal Gage Len symm is + + align:start position:0% +remember in the Lal Gage Len symm is + + + align:start position:0% +remember in the Lal Gage Len symm is +broken and this is the only symmet which + + align:start position:0% +broken and this is the only symmet which + + + align:start position:0% +broken and this is the only symmet which +is Manifest and so that suggest this + + align:start position:0% +is Manifest and so that suggest this + + + align:start position:0% +is Manifest and so that suggest this +state should be should be A Spacetime + + align:start position:0% +state should be should be A Spacetime + + + align:start position:0% +state should be should be A Spacetime +Vector okay should be A Spacetime Vector + + align:start position:0% +Vector okay should be A Spacetime Vector + + + align:start position:0% +Vector okay should be A Spacetime Vector +so so so uh so should be A Spacetime + + align:start position:0% + + + + align:start position:0% + +Vector so now let's work out this + + align:start position:0% + + + + align:start position:0% + +Mass so now m equal to + + align:start position:0% +Mass so now m equal to + + + align:start position:0% +Mass so now m equal to +one so m equal to + + align:start position:0% +one so m equal to + + + align:start position:0% +one so m equal to +one and so you just have one + + align:start position:0% +one and so you just have one + + + align:start position:0% +one and so you just have one +here and uh so so uh then you just put + + align:start position:0% +here and uh so so uh then you just put + + + align:start position:0% +here and uh so so uh then you just put +the one here so this is the alpha prime + + align:start position:0% +the one here so this is the alpha prime + + + align:start position:0% +the one here so this is the alpha prime +one + + align:start position:0% +one + + + align:start position:0% +one +minus D minus 2ide by + + align:start position:0% +minus D minus 2ide by + + + align:start position:0% +minus D minus 2ide by +24 so this is 26 minus t/ Alpha Prime + + align:start position:0% +24 so this is 26 minus t/ Alpha Prime + + + align:start position:0% +24 so this is 26 minus t/ Alpha Prime +okay so now you see the + + align:start position:0% +okay so now you see the + + + align:start position:0% +okay so now you see the +26 or divid by 24 Alpha + + align:start position:0% + + + + align:start position:0% + +Prime so now you see this magic number + + align:start position:0% + + + + align:start position:0% + +26 okay but now + + align:start position:0% + + + + align:start position:0% + +how so + + align:start position:0% + + + + align:start position:0% + +now we emphasized before in the lightco + + align:start position:0% +now we emphasized before in the lightco + + + align:start position:0% +now we emphasized before in the lightco +gauge even though only this s so D minus + + align:start position:0% +gauge even though only this s so D minus + + + align:start position:0% +gauge even though only this s so D minus +2 is Manifest because you break lowen + + align:start position:0% +2 is Manifest because you break lowen + + + align:start position:0% +2 is Manifest because you break lowen +SYM the gauge break lowen + + align:start position:0% +SYM the gauge break lowen + + + align:start position:0% +SYM the gauge break lowen +symmetry but your theory is still + + align:start position:0% +symmetry but your theory is still + + + align:start position:0% +symmetry but your theory is still +secretly Len + + align:start position:0% +secretly Len + + + align:start position:0% +secretly Len +symmetric should still be lent invariant + + align:start position:0% +symmetric should still be lent invariant + + + align:start position:0% +symmetric should still be lent invariant +because the string is propagated in + + align:start position:0% +because the string is propagated in + + + align:start position:0% +because the string is propagated in +the flat movy space time that means all + + align:start position:0% +the flat movy space time that means all + + + align:start position:0% +the flat movy space time that means all +your particle spectrum they must fall + + align:start position:0% +your particle spectrum they must fall + + + align:start position:0% +your particle spectrum they must fall +into representations of the full laen + + align:start position:0% +into representations of the full laen + + + align:start position:0% +into representations of the full laen +group okay the must fall into the + + align:start position:0% +group okay the must fall into the + + + align:start position:0% +group okay the must fall into the +representations of the full laen group + + align:start position:0% +representations of the full laen group + + + align:start position:0% +representations of the full laen group +even though the Len image is not + + align:start position:0% +even though the Len image is not + + + align:start position:0% +even though the Len image is not +manifest here + + align:start position:0% +manifest here + + + align:start position:0% +manifest here +okay and now + + align:start position:0% +okay and now + + + align:start position:0% +okay and now +let us recall a important + + align:start position:0% + + + + align:start position:0% + +fact a Loreno + + align:start position:0% +fact a Loreno + + + align:start position:0% +fact a Loreno +Vector a + + align:start position:0% +Vector a + + + align:start position:0% +Vector a +vector a vector + + align:start position:0% +vector a vector + + + align:start position:0% +vector a vector +field yeah just a vector + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +particle in d minkovski space time + + align:start position:0% + + + + align:start position:0% + +D dimensional movy space + + align:start position:0% +D dimensional movy space + + + align:start position:0% +D dimensional movy space +time if this particle is + + align:start position:0% +time if this particle is + + + align:start position:0% +time if this particle is +massive then have D minus one + + align:start position:0% + + + + align:start position:0% + +independent components say independent + + align:start position:0% +independent components say independent + + + align:start position:0% +independent components say independent +modes and if it's + + align:start position:0% + + + + align:start position:0% + +massless then I have D minus 2 + + align:start position:0% +massless then I have D minus 2 + + + align:start position:0% +massless then I have D minus 2 +independent modes okay so so the + + align:start position:0% +independent modes okay so so the + + + align:start position:0% +independent modes okay so so the +situation we are familiar with is the D + + align:start position:0% +situation we are familiar with is the D + + + align:start position:0% +situation we are familiar with is the D +equal to four four dimensional space + + align:start position:0% +equal to four four dimensional space + + + align:start position:0% +equal to four four dimensional space +time so in four dimensional space + + align:start position:0% +time so in four dimensional space + + + align:start position:0% +time so in four dimensional space +time a mess Vector is a photon Photon + + align:start position:0% +time a mess Vector is a photon Photon + + + align:start position:0% +time a mess Vector is a photon Photon +have two polarizations have two + + align:start position:0% +have two polarizations have two + + + align:start position:0% +have two polarizations have two +independent modes and uh but if but you + + align:start position:0% +independent modes and uh but if but you + + + align:start position:0% +independent modes and uh but if but you +have a v but if you have a massive + + align:start position:0% +have a v but if you have a massive + + + align:start position:0% +have a v but if you have a massive +Vector then you actually have three + + align:start position:0% +Vector then you actually have three + + + align:start position:0% +Vector then you actually have three +polarization rather than + + align:start position:0% +polarization rather than + + + align:start position:0% +polarization rather than +two + + align:start position:0% +two + + + align:start position:0% +two +okay but now we see a + + align:start position:0% +okay but now we see a + + + align:start position:0% +okay but now we see a +problem here we see a vector + + align:start position:0% +problem here we see a vector + + + align:start position:0% +problem here we see a vector +but this Vector only have D minus 2 + + align:start position:0% +but this Vector only have D minus 2 + + + align:start position:0% +but this Vector only have D minus 2 +components okay here because I because + + align:start position:0% +components okay here because I because + + + align:start position:0% +components okay here because I because +these are the only independent + + align:start position:0% +these are the only independent + + + align:start position:0% +these are the only independent +modes + + align:start position:0% +modes + + + align:start position:0% +modes +here we have a + + align:start position:0% + + + + align:start position:0% + +vector which + + align:start position:0% +vector which + + + align:start position:0% +vector which +has + + align:start position:0% +has + + + align:start position:0% +has +only D minus + + align:start position:0% +only D minus + + + align:start position:0% +only D minus +2 component + + align:start position:0% + + + + align:start position:0% + +independent components + + align:start position:0% + + + + align:start position:0% + +okay so if you compare with this list + + align:start position:0% +okay so if you compare with this list + + + align:start position:0% +okay so if you compare with this list +because there's nothing else because + + align:start position:0% +because there's nothing else because + + + align:start position:0% +because there's nothing else because +these are the only independent modes + + align:start position:0% +these are the only independent modes + + + align:start position:0% +these are the only independent modes +here okay in the light Cong there's + + align:start position:0% +here okay in the light Cong there's + + + align:start position:0% +here okay in the light Cong there's +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +else so by compare with our Lage of the + + align:start position:0% +else so by compare with our Lage of the + + + align:start position:0% +else so by compare with our Lage of the +L symmetry we conclude the only way this + + align:start position:0% +L symmetry we conclude the only way this + + + align:start position:0% +L symmetry we conclude the only way this +particle can be mathematically + + align:start position:0% +particle can be mathematically + + + align:start position:0% +particle can be mathematically +consistent + + align:start position:0% +consistent + + + align:start position:0% +consistent +is said it has to be a massless particle + + align:start position:0% +is said it has to be a massless particle + + + align:start position:0% +is said it has to be a massless particle +so that means M Square have to be + + align:start position:0% +so that means M Square have to be + + + align:start position:0% +so that means M Square have to be +zero okay so so m² has to be zero means + + align:start position:0% +zero okay so so m² has to be zero means + + + align:start position:0% +zero okay so so m² has to be zero means +that D must be equal to + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay and uh we actually find a mass this + + align:start position:0% +okay and uh we actually find a mass this + + + align:start position:0% +okay and uh we actually find a mass this +particle so we actually find the + + align:start position:0% +particle so we actually find the + + + align:start position:0% +particle so we actually find the +photon so we actually find the photon + + align:start position:0% +photon so we actually find the photon + + + align:start position:0% +photon so we actually find the photon +okay in the string excitations + + align:start position:0% + + + + align:start position:0% + +yeah one second let me just finish this + + align:start position:0% +yeah one second let me just finish this + + + align:start position:0% +yeah one second let me just finish this +for D Lal to + + align:start position:0% + + + + align:start position:0% + +26 the rent image is + + align:start position:0% + + + + align:start position:0% + +lost rent symm is + + align:start position:0% +lost rent symm is + + + align:start position:0% +lost rent symm is +not it's because that means this + + align:start position:0% +not it's because that means this + + + align:start position:0% +not it's because that means this +particle when M square is not zero no + + align:start position:0% +particle when M square is not zero no + + + align:start position:0% +particle when M square is not zero no +matter what + + align:start position:0% +matter what + + + align:start position:0% +matter what +these states cannot fall into + + align:start position:0% +these states cannot fall into + + + align:start position:0% +these states cannot fall into +representation of a lawence s a lawence + + align:start position:0% +representation of a lawence s a lawence + + + align:start position:0% +representation of a lawence s a lawence +group and uh so means that Len symmetry + + align:start position:0% +group and uh so means that Len symmetry + + + align:start position:0% +group and uh so means that Len symmetry +is not + + align:start position:0% +is not + + + align:start position:0% +is not +maintained even the lent symmetry is a + + align:start position:0% +maintained even the lent symmetry is a + + + align:start position:0% +maintained even the lent symmetry is a +symmetry of the classical action but + + align:start position:0% +symmetry of the classical action but + + + align:start position:0% +symmetry of the classical action but +it's not maintained at Quantum + + align:start position:0% +it's not maintained at Quantum + + + align:start position:0% +it's not maintained at Quantum +level somehow in the quantization + + align:start position:0% +level somehow in the quantization + + + align:start position:0% +level somehow in the quantization +procedure a symmetry which is mainly + + align:start position:0% +procedure a symmetry which is mainly + + + align:start position:0% +procedure a symmetry which is mainly +which is in your classical + + align:start position:0% +which is in your classical + + + align:start position:0% +which is in your classical +Theory is lost + + align:start position:0% + + + + align:start position:0% + +okay and this tells + + align:start position:0% +okay and this tells + + + align:start position:0% +okay and this tells +you that the quantization is not + + align:start position:0% + + + + align:start position:0% + +consistent okay it's Inc consistent + + align:start position:0% +consistent okay it's Inc consistent + + + align:start position:0% +consistent okay it's Inc consistent +because because it + + align:start position:0% +because because it + + + align:start position:0% +because because it +means whatever it is if you have + + align:start position:0% +means whatever it is if you have + + + align:start position:0% +means whatever it is if you have +something propagated in minkovski space + + align:start position:0% +something propagated in minkovski space + + + align:start position:0% +something propagated in minkovski space +time + + align:start position:0% + + + + align:start position:0% + +it has to for into representations of + + align:start position:0% +it has to for into representations of + + + align:start position:0% +it has to for into representations of +the lent + + align:start position:0% +the lent + + + align:start position:0% +the lent +group that means + + align:start position:0% +group that means + + + align:start position:0% +group that means +that yeah this just cannot be the right + + align:start position:0% +that yeah this just cannot be the right + + + align:start position:0% +that yeah this just cannot be the right +uh you have to go back to redo your + + align:start position:0% +uh you have to go back to redo your + + + align:start position:0% +uh you have to go back to redo your +thing uh this is not propagating in the + + align:start position:0% +thing uh this is not propagating in the + + + align:start position:0% +thing uh this is not propagating in the +movi space time + + align:start position:0% +movi space time + + + align:start position:0% +movi space time +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +alternatively yeah so this is the uh a + + align:start position:0% +alternatively yeah so this is the uh a + + + align:start position:0% +alternatively yeah so this is the uh a +conclusion that D must be equal to 26 + + align:start position:0% +conclusion that D must be equal to 26 + + + align:start position:0% +conclusion that D must be equal to 26 +okay so you can reach the same + + align:start position:0% +okay so you can reach the same + + + align:start position:0% +okay so you can reach the same +conclusion fun the following + + align:start position:0% +conclusion fun the following + + + align:start position:0% +conclusion fun the following +way so so right now um so the way we did + + align:start position:0% +way so so right now um so the way we did + + + align:start position:0% +way so so right now um so the way we did +this is said we we FG this a zero yeah + + align:start position:0% +this is said we we FG this a zero yeah + + + align:start position:0% +this is said we we FG this a zero yeah +we did not fge it but uh but we did + + align:start position:0% +we did not fge it but uh but we did + + + align:start position:0% +we did not fge it but uh but we did +something uh do a infinite sum and find + + align:start position:0% +something uh do a infinite sum and find + + + align:start position:0% +something uh do a infinite sum and find +the finite answer yeah we have to do a + + align:start position:0% +the finite answer yeah we have to do a + + + align:start position:0% +the finite answer yeah we have to do a +infinite sum of positive numbers and + + align:start position:0% +infinite sum of positive numbers and + + + align:start position:0% +infinite sum of positive numbers and +then find the netive number and uh and + + align:start position:0% +then find the netive number and uh and + + + align:start position:0% +then find the netive number and uh and +then and then we find somehow there's + + align:start position:0% +then and then we find somehow there's + + + align:start position:0% +then and then we find somehow there's +something Demus two and D minus one + + align:start position:0% +something Demus two and D minus one + + + align:start position:0% +something Demus two and D minus one +somehow missing one somehow + + align:start position:0% + + + + align:start position:0% + +anyway anyway but this is actually a + + align:start position:0% +anyway anyway but this is actually a + + + align:start position:0% +anyway anyway but this is actually a +deep story it's not say just missing one + + align:start position:0% +deep story it's not say just missing one + + + align:start position:0% +deep story it's not say just missing one +or something like + + align:start position:0% +or something like + + + align:start position:0% +or something like +that so you can reach the same + + align:start position:0% +that so you can reach the same + + + align:start position:0% +that so you can reach the same +conclusion by doing the following say + + align:start position:0% +conclusion by doing the following say + + + align:start position:0% +conclusion by doing the following say +you put here a + + align:start position:0% +you put here a + + + align:start position:0% +you put here a +zero as undetermined + + align:start position:0% +zero as undetermined + + + align:start position:0% +zero as undetermined +coefficient and it it turns out the same + + align:start position:0% +coefficient and it it turns out the same + + + align:start position:0% +coefficient and it it turns out the same +a zero yeah so so you can check so here + + align:start position:0% +a zero yeah so so you can check so here + + + align:start position:0% +a zero yeah so so you can check so here +it tells you that Len image is + + align:start position:0% +it tells you that Len image is + + + align:start position:0% +it tells you that Len image is +lost so you can double check this + + align:start position:0% +lost so you can double check this + + + align:start position:0% +lost so you can double check this +conclusion as follows so remember said + + align:start position:0% +conclusion as follows so remember said + + + align:start position:0% +conclusion as follows so remember said +that that classical action is in warant + + align:start position:0% +that that classical action is in warant + + + align:start position:0% +that that classical action is in warant +on the Len Symmetry and then this + + align:start position:0% +on the Len Symmetry and then this + + + align:start position:0% +on the Len Symmetry and then this +conserve the loss of charge + + align:start position:0% +conserve the loss of charge + + + align:start position:0% +conserve the loss of charge +corresponding to the laen Lauren + + align:start position:0% +corresponding to the laen Lauren + + + align:start position:0% +corresponding to the laen Lauren +transformation and those those charges + + align:start position:0% +transformation and those those charges + + + align:start position:0% +transformation and those those charges +that become generators of Lauren + + align:start position:0% +that become generators of Lauren + + + align:start position:0% +that become generators of Lauren +symmetry at Quantum level just in + + align:start position:0% +symmetry at Quantum level just in + + + align:start position:0% +symmetry at Quantum level just in +Quantum field + + align:start position:0% +Quantum field + + + align:start position:0% +Quantum field +the and uh then by consistency + + align:start position:0% +the and uh then by consistency + + + align:start position:0% +the and uh then by consistency +those + + align:start position:0% +those + + + align:start position:0% +those +Loren conserve the Lorent + + align:start position:0% +Loren conserve the Lorent + + + align:start position:0% +Loren conserve the Lorent +charges as a Quantum operator they must + + align:start position:0% +charges as a Quantum operator they must + + + align:start position:0% +charges as a Quantum operator they must +satisfy Loren + + align:start position:0% +satisfy Loren + + + align:start position:0% +satisfy Loren +algebra okay then you can check with a + + align:start position:0% +algebra okay then you can check with a + + + align:start position:0% +algebra okay then you can check with a +general D and with General a + + align:start position:0% + + + + align:start position:0% + +zero and that the rent algebra is only + + align:start position:0% +zero and that the rent algebra is only + + + align:start position:0% +zero and that the rent algebra is only +satisfied in the D 26 Dimension and with + + align:start position:0% +satisfied in the D 26 Dimension and with + + + align:start position:0% +satisfied in the D 26 Dimension and with +a zero given by these formulas Okay so + + align:start position:0% +a zero given by these formulas Okay so + + + align:start position:0% +a zero given by these formulas Okay so +that will be a rigorous way to derive it + + align:start position:0% +that will be a rigorous way to derive it + + + align:start position:0% +that will be a rigorous way to derive it +okay rigorous way to derive it but we + + align:start position:0% +okay rigorous way to derive it but we + + + align:start position:0% +okay rigorous way to derive it but we +are not doing it here because that will + + align:start position:0% +are not doing it here because that will + + + align:start position:0% +are not doing it here because that will +take a will take liit + + align:start position:0% + + + + align:start position:0% + +time does that also involve the + + align:start position:0% +time does that also involve the + + + align:start position:0% +time does that also involve the +commutator of this mode H this that + + align:start position:0% +commutator of this mode H this that + + + align:start position:0% +commutator of this mode H this that +dation also involve the Comm of this + + align:start position:0% +dation also involve the Comm of this + + + align:start position:0% +dation also involve the Comm of this +Alpha mode yeah yes then you you also + + align:start position:0% +Alpha mode yeah yes then you you also + + + align:start position:0% +Alpha mode yeah yes then you you also +need to look at the + + align:start position:0% +need to look at the + + + align:start position:0% +need to look at the +sorry + + align:start position:0% + + + + align:start position:0% + +also no no no no no no you just uh + + align:start position:0% +also no no no no no no you just uh + + + align:start position:0% +also no no no no no no you just uh +assume some general a z here you + + align:start position:0% +assume some general a z here you + + + align:start position:0% +assume some general a z here you +determine this by by requiring that the + + align:start position:0% +determine this by by requiring that the + + + align:start position:0% +determine this by by requiring that the +the algebra is satisfied + + align:start position:0% +the algebra is satisfied + + + align:start position:0% +the algebra is satisfied +yeah alra also in term of this mod yeah + + align:start position:0% +yeah alra also in term of this mod yeah + + + align:start position:0% +yeah alra also in term of this mod yeah +yeah in terms of alpha that's right then + + align:start position:0% +yeah in terms of alpha that's right then + + + align:start position:0% +yeah in terms of alpha that's right then +in + + align:start position:0% +in + + + align:start position:0% +in +Computing oh those commutators are + + align:start position:0% +Computing oh those commutators are + + + align:start position:0% +Computing oh those commutators are +fine those commutator just from standard + + align:start position:0% + + + + align:start position:0% + +ation sorry which one over + + align:start position:0% +ation sorry which one over + + + align:start position:0% +ation sorry which one over +24 no no for forget about one over 24 + + align:start position:0% +24 no no for forget about one over 24 + + + align:start position:0% +24 no no for forget about one over 24 +there's no one over 24 there's no one + + align:start position:0% +there's no one over 24 there's no one + + + align:start position:0% +there's no one over 24 there's no one +over + + align:start position:0% +over + + + align:start position:0% +over +24 uh you + + align:start position:0% +24 uh you + + + align:start position:0% +24 uh you +just write a Z here as undetermined + + align:start position:0% +just write a Z here as undetermined + + + align:start position:0% +just write a Z here as undetermined +constant and check it by consistency + + align:start position:0% +constant and check it by consistency + + + align:start position:0% +constant and check it by consistency +determined by + + align:start position:0% + + + + align:start position:0% + +consistency yeah no yes + + align:start position:0% +consistency yeah no yes + + + align:start position:0% +consistency yeah no yes +this whole construction with our VI we + + align:start position:0% +this whole construction with our VI we + + + align:start position:0% +this whole construction with our VI we +have to work Dimensions anyway so why do + + align:start position:0% +have to work Dimensions anyway so why do + + + align:start position:0% +have to work Dimensions anyway so why do +we so much about invari sorry I mean we + + align:start position:0% +we so much about invari sorry I mean we + + + align:start position:0% +we so much about invari sorry I mean we +have to workus four dimensions anyway + + align:start position:0% +have to workus four dimensions anyway + + + align:start position:0% +have to workus four dimensions anyway +yeah so then shouldn't we then just to + + align:start position:0% +yeah so then shouldn't we then just to + + + align:start position:0% +yeah so then shouldn't we then just to +begin with like space is just not + + align:start position:0% +begin with like space is just not + + + align:start position:0% +begin with like space is just not +correct right yeah uh uh uh uh so so you + + align:start position:0% +correct right yeah uh uh uh uh so so you + + + align:start position:0% +correct right yeah uh uh uh uh so so you +will find actually U this conclusion + + align:start position:0% +will find actually U this conclusion + + + align:start position:0% +will find actually U this conclusion +does not depend on the details + + align:start position:0% +does not depend on the details + + + align:start position:0% +does not depend on the details +uh uh it does not depend on details and + + align:start position:0% +uh uh it does not depend on details and + + + align:start position:0% +uh uh it does not depend on details and +this yeah so um so you can generalize + + align:start position:0% +this yeah so um so you can generalize + + + align:start position:0% +this yeah so um so you can generalize +this uh to to more General case say + + align:start position:0% +this uh to to more General case say + + + align:start position:0% +this uh to to more General case say +curve space time EXC and the curve space + + align:start position:0% +curve space time EXC and the curve space + + + align:start position:0% +curve space time EXC and the curve space +time is C which you might uh uh then you + + align:start position:0% +time is C which you might uh uh then you + + + align:start position:0% +time is C which you might uh uh then you +find the same conclusion will will + + align:start position:0% +find the same conclusion will will + + + align:start position:0% +find the same conclusion will will +happen yeah the same conclusion will + + align:start position:0% +happen yeah the same conclusion will + + + align:start position:0% +happen yeah the same conclusion will +happen and uh and then you reduce to + + align:start position:0% +happen and uh and then you reduce to + + + align:start position:0% +happen and uh and then you reduce to +four dimensions then you will find the + + align:start position:0% +four dimensions then you will find the + + + align:start position:0% +four dimensions then you will find the +four dimension a massive Vector which + + align:start position:0% +four dimension a massive Vector which + + + align:start position:0% +four dimension a massive Vector which +only have two polarizations + + align:start position:0% +only have two polarizations + + + align:start position:0% +only have two polarizations +yeah yes maybe Rel to this question uh + + align:start position:0% +yeah yes maybe Rel to this question uh + + + align:start position:0% +yeah yes maybe Rel to this question uh +we have no evidence that symmetry holds + + align:start position:0% +we have no evidence that symmetry holds + + + align:start position:0% +we have no evidence that symmetry holds +in the compac dimensions so why do we + + align:start position:0% +in the compac dimensions so why do we + + + align:start position:0% +in the compac dimensions so why do we +want to keep it there yeah you say it + + align:start position:0% +want to keep it there yeah you say it + + + align:start position:0% +want to keep it there yeah you say it +doesn't matter uh uh this is only a + + align:start position:0% +doesn't matter uh uh this is only a + + + align:start position:0% +doesn't matter uh uh this is only a +question as far as you have some + + align:start position:0% +question as far as you have some + + + align:start position:0% +question as far as you have some +uncompact directions okay as far as we + + align:start position:0% +uncompact directions okay as far as we + + + align:start position:0% +uncompact directions okay as far as we +have some Len directions and this will + + align:start position:0% +have some Len directions and this will + + + align:start position:0% +have some Len directions and this will +apply okay yeah yes can I going back a + + align:start position:0% +apply okay yeah yes can I going back a + + + align:start position:0% +apply okay yeah yes can I going back a +little bit to the Aon thing how do we + + align:start position:0% +little bit to the Aon thing how do we + + + align:start position:0% +little bit to the Aon thing how do we +know for a fact that the string tension + + align:start position:0% +know for a fact that the string tension + + + align:start position:0% +know for a fact that the string tension +is positive because example I think in + + align:start position:0% +is positive because example I think in + + + align:start position:0% +is positive because example I think in +like qcd strings isn't string tension + + align:start position:0% +like qcd strings isn't string tension + + + align:start position:0% +like qcd strings isn't string tension +negative uh not really how do you define + + align:start position:0% +negative uh not really how do you define + + + align:start position:0% +negative uh not really how do you define +elective string tension a negative + + align:start position:0% +elective string tension a negative + + + align:start position:0% +elective string tension a negative +tension I don't know I just read that in + + align:start position:0% +tension I don't know I just read that in + + + align:start position:0% +tension I don't know I just read that in +qcg strings they have negative string + + align:start position:0% +qcg strings they have negative string + + + align:start position:0% +qcg strings they have negative string +tension no no I think here so Alpha + + align:start position:0% +tension no no I think here so Alpha + + + align:start position:0% +tension no no I think here so Alpha +Prime just really Alpha Prime is a scale + + align:start position:0% +Prime just really Alpha Prime is a scale + + + align:start position:0% +Prime just really Alpha Prime is a scale +it's a physical + + align:start position:0% +it's a physical + + + align:start position:0% +it's a physical +scale deter yeah tension it's a it's a + + align:start position:0% +scale deter yeah tension it's a it's a + + + align:start position:0% +scale deter yeah tension it's a it's a +yeah uh it's it's defined to be positive + + align:start position:0% +yeah uh it's it's defined to be positive + + + align:start position:0% +yeah uh it's it's defined to be positive +just by definition it's POS positive + + align:start position:0% + + + + align:start position:0% + +yeah other + + align:start position:0% +yeah other + + + align:start position:0% +yeah other +questions okay so + + align:start position:0% +questions okay so + + + align:start position:0% +questions okay so +um so let me just say a little bit more + + align:start position:0% + + + + align:start position:0% + +regarding so now we have found attacking + + align:start position:0% +regarding so now we have found attacking + + + align:start position:0% +regarding so now we have found attacking +and the massless vector and also we have + + align:start position:0% +and the massless vector and also we have + + + align:start position:0% +and the massless vector and also we have +fix the space time Dimension to 26 okay + + align:start position:0% +fix the space time Dimension to 26 okay + + + align:start position:0% +fix the space time Dimension to 26 okay +we have fixed space time to + + align:start position:0% +we have fixed space time to + + + align:start position:0% +we have fixed space time to +26 so so + + align:start position:0% +26 so so + + + align:start position:0% +26 so so +now so if you fix now fix t equal to + + align:start position:0% +now so if you fix now fix t equal to + + + align:start position:0% +now so if you fix now fix t equal to +26 then the higher excitations are all + + align:start position:0% + + + + align:start position:0% + +massive okay so for the for the photon + + align:start position:0% +massive okay so for the for the photon + + + align:start position:0% +massive okay so for the for the photon +essentially is this guy so this guy is + + align:start position:0% +essentially is this guy so this guy is + + + align:start position:0% +essentially is this guy so this guy is +negative this guy cancel this guy so + + align:start position:0% +negative this guy cancel this guy so + + + align:start position:0% +negative this guy cancel this guy so +when you go the + + align:start position:0% +when you go the + + + align:start position:0% +when you go the +higher high exitation then this guy will + + align:start position:0% +higher high exitation then this guy will + + + align:start position:0% +higher high exitation then this guy will +dominate and the M Square will be all + + align:start position:0% +dominate and the M Square will be all + + + align:start position:0% +dominate and the M Square will be all +positive and the scale is controlled by + + align:start position:0% +positive and the scale is controlled by + + + align:start position:0% +positive and the scale is controlled by +this one over Alpha Prime okay so so we + + align:start position:0% +this one over Alpha Prime okay so so we + + + align:start position:0% +this one over Alpha Prime okay so so we +be all massive with + + align:start position:0% + + + + align:start position:0% + +spacing given + + align:start position:0% +spacing given + + + align:start position:0% +spacing given +by say uh uh uh one over Alpha Prime so + + align:start position:0% +by say uh uh uh one over Alpha Prime so + + + align:start position:0% +by say uh uh uh one over Alpha Prime so +so with a spacing M Square given by one + + align:start position:0% +so with a spacing M Square given by one + + + align:start position:0% +so with a spacing M Square given by one +over Alpha + + align:start position:0% +over Alpha + + + align:start position:0% +over Alpha +Prime for example the next level would + + align:start position:0% + + + + align:start position:0% + +be so Alpha minus one alpha minus one + + align:start position:0% +be so Alpha minus one alpha minus one + + + align:start position:0% +be so Alpha minus one alpha minus one +some I some J or Alpha minus 2 + + align:start position:0% +some I some J or Alpha minus 2 + + + align:start position:0% +some I some J or Alpha minus 2 +I acting on z p okay so those things + + align:start position:0% +I acting on z p okay so those things + + + align:start position:0% +I acting on z p okay so those things +acting on yeah to avoid confusion let me + + align:start position:0% +acting on yeah to avoid confusion let me + + + align:start position:0% +acting on yeah to avoid confusion let me +write it more clearly so this acum the p + + align:start position:0% +write it more clearly so this acum the p + + + align:start position:0% +write it more clearly so this acum the p +and alha minus 2 i on0 + + align:start position:0% +and alha minus 2 i on0 + + + align:start position:0% +and alha minus 2 i on0 +p + + align:start position:0% +p + + + align:start position:0% +p +okay so this would be like a tensor + + align:start position:0% +okay so this would be like a tensor + + + align:start position:0% +okay so this would be like a tensor +because this have two index and this + + align:start position:0% +because this have two index and this + + + align:start position:0% +because this have two index and this +again like a + + align:start position:0% +again like a + + + align:start position:0% +again like a +vector again like a vector so so so + + align:start position:0% +vector again like a vector so so so + + + align:start position:0% +vector again like a vector so so so +those will be the mass square one over + + align:start position:0% +those will be the mass square one over + + + align:start position:0% +those will be the mass square one over +Alpha + + align:start position:0% +Alpha + + + align:start position:0% +Alpha +Prime Alp Prime and you can + + align:start position:0% +Prime Alp Prime and you can + + + align:start position:0% +Prime Alp Prime and you can +check actually they actually fall into + + align:start position:0% +check actually they actually fall into + + + align:start position:0% +check actually they actually fall into +the uh they fall nicely into + + align:start position:0% +the uh they fall nicely into + + + align:start position:0% +the uh they fall nicely into +representations of the Lance group okay + + align:start position:0% +representations of the Lance group okay + + + align:start position:0% +representations of the Lance group okay +for licing to ration the r + + align:start position:0% +for licing to ration the r + + + align:start position:0% +for licing to ration the r +gr yes uh where is the one with only one + + align:start position:0% +gr yes uh where is the one with only one + + + align:start position:0% +gr yes uh where is the one with only one +index getting its + + align:start position:0% +index getting its + + + align:start position:0% +index getting its +extra uh uh sorry say it again so the + + align:start position:0% +extra uh uh sorry say it again so the + + + align:start position:0% +extra uh uh sorry say it again so the +one with one index since it's massive it + + align:start position:0% +one with one index since it's massive it + + + align:start position:0% +one with one index since it's massive it +supposed to have D minus1 de right they + + align:start position:0% +supposed to have D minus1 de right they + + + align:start position:0% +supposed to have D minus1 de right they +have a + + align:start position:0% +have a + + + align:start position:0% +have a +um D oh yeah what's happening uh that's + + align:start position:0% +um D oh yeah what's happening uh that's + + + align:start position:0% +um D oh yeah what's happening uh that's +a very good question um so so what's + + align:start position:0% +a very good question um so so what's + + + align:start position:0% +a very good question um so so what's +happening is that this should give rise + + align:start position:0% +happening is that this should give rise + + + align:start position:0% +happening is that this should give rise +to a tensor rep it should give a tensor + + align:start position:0% +to a tensor rep it should give a tensor + + + align:start position:0% +to a tensor rep it should give a tensor +representation but this is not enough + + align:start position:0% +representation but this is not enough + + + align:start position:0% +representation but this is not enough +and this act together to form a tensor + + align:start position:0% +and this act together to form a tensor + + + align:start position:0% +and this act together to form a tensor +representation yeah because this because + + align:start position:0% +representation yeah because this because + + + align:start position:0% +representation yeah because this because +I only going from one to from two to D + + align:start position:0% +I only going from one to from two to D + + + align:start position:0% +I only going from one to from two to D +minus one so you need add them + + align:start position:0% + + + + align:start position:0% + +together + + align:start position:0% +together + + + align:start position:0% +together +good so so just to summarize story for + + align:start position:0% +good so so just to summarize story for + + + align:start position:0% +good so so just to summarize story for +the open stream we find the Tagan we + + align:start position:0% +the open stream we find the Tagan we + + + align:start position:0% +the open stream we find the Tagan we +find The M Vector which is should be + + align:start position:0% +find The M Vector which is should be + + + align:start position:0% +find The M Vector which is should be +inter can be interpreted maybe as a + + align:start position:0% +inter can be interpreted maybe as a + + + align:start position:0% +inter can be interpreted maybe as a +photon and then you find lot of massive + + align:start position:0% +photon and then you find lot of massive + + + align:start position:0% +photon and then you find lot of massive +particles infinite number + + align:start position:0% +particles infinite number + + + align:start position:0% +particles infinite number +of massive + + align:start position:0% +of massive + + + align:start position:0% +of massive +particles okay so + + align:start position:0% +particles okay so + + + align:start position:0% +particles okay so +any other questions or do you want to + + align:start position:0% +any other questions or do you want to + + + align:start position:0% +any other questions or do you want to +have a + + align:start position:0% + + + + align:start position:0% + +break we are a little bit out of time + + align:start position:0% +break we are a little bit out of time + + + align:start position:0% +break we are a little bit out of time +yeah maybe let me give you a three + + align:start position:0% +yeah maybe let me give you a three + + + align:start position:0% +yeah maybe let me give you a three +minutes + + align:start position:0% + + + + align:start position:0% + +break yeah yeah yeah yeah yeah let's + + align:start position:0% +break yeah yeah yeah yeah yeah let's + + + align:start position:0% +break yeah yeah yeah yeah yeah let's +have a break + + align:start position:0% +have a break + + + align:start position:0% +have a break +now so again the lowest state is just z + + align:start position:0% +now so again the lowest state is just z + + + align:start position:0% +now so again the lowest state is just z +p and then again all the nend is + + align:start position:0% + + + + align:start position:0% + +zero all the N are zero so I just read + + align:start position:0% +zero all the N are zero so I just read + + + align:start position:0% +zero all the N are zero so I just read +from the answer from + + align:start position:0% + + + + align:start position:0% + +here then m s for the Clos string just + + align:start position:0% +here then m s for the Clos string just + + + align:start position:0% +here then m s for the Clos string just +equal to a z for the Clos string so so + + align:start position:0% +equal to a z for the Clos string so so + + + align:start position:0% +equal to a z for the Clos string so so +here is + + align:start position:0% +here is + + + align:start position:0% +here is +now + + align:start position:0% +now + + + align:start position:0% +now +m² minus r + + align:start position:0% +m² minus r + + + align:start position:0% +m² minus r +4/ by Alpha + + align:start position:0% +4/ by Alpha + + + align:start position:0% +4/ by Alpha +Prime D minus 2ide + + align:start position:0% +Prime D minus 2ide + + + align:start position:0% +Prime D minus 2ide +24 so again this is + + align:start position:0% +24 so again this is + + + align:start position:0% +24 so again this is +tonic for D greater than + + align:start position:0% +tonic for D greater than + + + align:start position:0% +tonic for D greater than +two okay tonic for D greater than two + + align:start position:0% +two okay tonic for D greater than two + + + align:start position:0% +two okay tonic for D greater than two +and this is a + + align:start position:0% +and this is a + + + align:start position:0% +and this is a +scalar and this is + + align:start position:0% +scalar and this is + + + align:start position:0% +scalar and this is +scalar because there's no other quantum + + align:start position:0% + + + + align:start position:0% + +number okay + + align:start position:0% +number okay + + + align:start position:0% +number okay +yeah so now we are familiar with the T + + align:start position:0% +yeah so now we are familiar with the T + + + align:start position:0% +yeah so now we are familiar with the T +so we don't need to worry about + + align:start position:0% +so we don't need to worry about + + + align:start position:0% +so we don't need to worry about +it so let's look at the + + align:start position:0% + + + + align:start position:0% + +next so next + + align:start position:0% +next so next + + + align:start position:0% +next so next +naively you may say let's do this + + align:start position:0% +naively you may say let's do this + + + align:start position:0% +naively you may say let's do this +one as open string + + align:start position:0% + + + + align:start position:0% + +case but this is not + + align:start position:0% + + + + align:start position:0% + +allowed okay this is not + + align:start position:0% +allowed okay this is not + + + align:start position:0% +allowed okay this is not +allowed why + + align:start position:0% +allowed why + + + align:start position:0% +allowed why +that's right it does not satisfy this + + align:start position:0% +that's right it does not satisfy this + + + align:start position:0% +that's right it does not satisfy this +condition because this one you only have + + align:start position:0% +condition because this one you only have + + + align:start position:0% +condition because this one you only have +the left moving excitations but does not + + align:start position:0% +the left moving excitations but does not + + + align:start position:0% +the left moving excitations but does not +have the right moving excitations you + + align:start position:0% +have the right moving excitations you + + + align:start position:0% +have the right moving excitations you +are not + + align:start position:0% +are not + + + align:start position:0% +are not +balanced so so you also need to add so + + align:start position:0% +balanced so so you also need to add so + + + align:start position:0% +balanced so so you also need to add so +the so the next one will be this + + align:start position:0% + + + + align:start position:0% + +guy + + align:start position:0% + + + + align:start position:0% + +okay so now oh here I have a j + + align:start position:0% + + + + align:start position:0% + +now I have a + + align:start position:0% +now I have a + + + align:start position:0% +now I have a +j so this will have + + align:start position:0% + + + + align:start position:0% + +m² 26 minus D / 20 Alpha 4 Alpha + + align:start position:0% +m² 26 minus D / 20 Alpha 4 Alpha + + + align:start position:0% +m² 26 minus D / 20 Alpha 4 Alpha +Prime 6 Alpha + + align:start position:0% + + + + align:start position:0% + +Prime so now you can again now look + + align:start position:0% + + + + align:start position:0% + +for what the r + + align:start position:0% +for what the r + + + align:start position:0% +for what the r +what representations of the rent group + + align:start position:0% +what representations of the rent group + + + align:start position:0% +what representations of the rent group +will give you + + align:start position:0% +will give you + + + align:start position:0% +will give you +this again you find + + align:start position:0% +this again you find + + + align:start position:0% +this again you find +none unless you are in the D equal to + + align:start position:0% +none unless you are in the D equal to + + + align:start position:0% +none unless you are in the D equal to +26 okay the same story + + align:start position:0% + + + + align:start position:0% + +happens the same story happens + + align:start position:0% +happens the same story happens + + + align:start position:0% +happens the same story happens +again only for D equal to + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +four into representations + + align:start position:0% + + + + align:start position:0% + +of lence + + align:start position:0% + + + + align:start position:0% + +group at + + align:start position:0% + + + + align:start position:0% + +which the m² again is mass this m² is + + align:start position:0% +which the m² again is mass this m² is + + + align:start position:0% +which the m² again is mass this m² is +mass + + align:start position:0% + + + + align:start position:0% + +this so you turns out actually + + align:start position:0% +this so you turns out actually + + + align:start position:0% +this so you turns out actually +this does not transform under + + align:start position:0% +this does not transform under + + + align:start position:0% +this does not transform under +irreducible representation of Laurence + + align:start position:0% +irreducible representation of Laurence + + + align:start position:0% +irreducible representation of Laurence +group it's + + align:start position:0% +group it's + + + align:start position:0% +group it's +actually it's actually a reducible so it + + align:start position:0% +actually it's actually a reducible so it + + + align:start position:0% +actually it's actually a reducible so it +can be separated into several + + align:start position:0% +can be separated into several + + + align:start position:0% +can be separated into several +subsets so so this can be further + + align:start position:0% +subsets so so this can be further + + + align:start position:0% +subsets so so this can be further +decomposed to + + align:start position:0% + + + + align:start position:0% + +so you can take some all the I and J + + align:start position:0% +so you can take some all the I and J + + + align:start position:0% +so you can take some all the I and J +together take the same + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +okay yeah some I so take the take this + + align:start position:0% +okay yeah some I so take the take this + + + align:start position:0% +okay yeah some I so take the take this +guy I have take this two the index be + + align:start position:0% +guy I have take this two the index be + + + align:start position:0% +guy I have take this two the index be +the same and the sum of all the + + align:start position:0% +the same and the sum of all the + + + align:start position:0% +the same and the sum of all the +directions + + align:start position:0% +directions + + + align:start position:0% +directions +so this does not + + align:start position:0% +so this does not + + + align:start position:0% +so this does not +transform under the rotation of ice so + + align:start position:0% +transform under the rotation of ice so + + + align:start position:0% +transform under the rotation of ice so +this is a + + align:start position:0% + + + + align:start position:0% + +scaler this is is a mass + + align:start position:0% + + + + align:start position:0% + +scaler okay and you can + + align:start position:0% +scaler okay and you can + + + align:start position:0% +scaler okay and you can +also have the + + align:start position:0% + + + + align:start position:0% + +situation so all the state at are lineus + + align:start position:0% +situation so all the state at are lineus + + + align:start position:0% +situation so all the state at are lineus +position of those States so they D minus + + align:start position:0% +position of those States so they D minus + + + align:start position:0% +position of those States so they D minus +2 so they D minus 2 * D minus 2 of + + align:start position:0% +2 so they D minus 2 * D minus 2 of + + + align:start position:0% +2 so they D minus 2 * D minus 2 of +them okay D- 2 * D- 2 of them so this + + align:start position:0% +them okay D- 2 * D- 2 of them so this + + + align:start position:0% +them okay D- 2 * D- 2 of them so this +tus 2 say the one of them can be can be + + align:start position:0% +tus 2 say the one of them can be can be + + + align:start position:0% +tus 2 say the one of them can be can be +de composed into a scalar and I can also + + align:start position:0% +de composed into a scalar and I can also + + + align:start position:0% +de composed into a scalar and I can also +take the linear for position of + + align:start position:0% + + + + align:start position:0% + +them with a symmetric Trace + + align:start position:0% + + + + align:start position:0% + +L and the trace l so the trace part is + + align:start position:0% +L and the trace l so the trace part is + + + align:start position:0% +L and the trace l so the trace part is +essentially this + + align:start position:0% +essentially this + + + align:start position:0% +essentially this +scaler and we I can also take a trace + + align:start position:0% +scaler and we I can also take a trace + + + align:start position:0% +scaler and we I can also take a trace +list part Trace list + + align:start position:0% +list part Trace list + + + align:start position:0% +list part Trace list +EIG okay because the the trace part is + + align:start position:0% +EIG okay because the the trace part is + + + align:start position:0% +EIG okay because the the trace part is +already covered by this one I don't want + + align:start position:0% +already covered by this one I don't want + + + align:start position:0% +already covered by this one I don't want +to + + align:start position:0% +to + + + align:start position:0% +to +repeat and this is precisely the + + align:start position:0% +repeat and this is precisely the + + + align:start position:0% +repeat and this is precisely the +generalization what we normally call the + + align:start position:0% +generalization what we normally call the + + + align:start position:0% +generalization what we normally call the +spin + + align:start position:0% + + + + align:start position:0% + +tentation uh to General + + align:start position:0% +tentation uh to General + + + align:start position:0% +tentation uh to General +Dimension + + align:start position:0% +Dimension + + + align:start position:0% +Dimension +okay so we have found a mass spin two + + align:start position:0% +okay so we have found a mass spin two + + + align:start position:0% +okay so we have found a mass spin two +particle so this is a mass spin two + + align:start position:0% +particle so this is a mass spin two + + + align:start position:0% +particle so this is a mass spin two +particle + + align:start position:0% + + + + align:start position:0% + +and then you can also of course take + + align:start position:0% +and then you can also of course take + + + align:start position:0% +and then you can also of course take +it to be + + align:start position:0% + + + + align:start position:0% + +antisymmetric so that's the only + + align:start position:0% +antisymmetric so that's the only + + + align:start position:0% +antisymmetric so that's the only +possibility + + align:start position:0% + + + + align:start position:0% + +now BJ anti symmetric in i + + align:start position:0% + + + + align:start position:0% + +j okay so this is sometime so this is + + align:start position:0% +j okay so this is sometime so this is + + + align:start position:0% +j okay so this is sometime so this is +called antisymmetric so this will give + + align:start position:0% +called antisymmetric so this will give + + + align:start position:0% +called antisymmetric so this will give +rise to antisymmetric + + align:start position:0% +rise to antisymmetric + + + align:start position:0% +rise to antisymmetric +tensor in space + + align:start position:0% + + + + align:start position:0% + +time so this is object with two + + align:start position:0% +time so this is object with two + + + align:start position:0% +time so this is object with two +index and the uh and the two index anti + + align:start position:0% +index and the uh and the two index anti + + + align:start position:0% +index and the uh and the two index anti +symmetric okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +similarly the high + + align:start position:0% +similarly the high + + + align:start position:0% +similarly the high +modes are all + + align:start position:0% + + + + align:start position:0% + +massive for example at the next + + align:start position:0% +massive for example at the next + + + align:start position:0% +massive for example at the next +level next Mass + + align:start position:0% +level next Mass + + + align:start position:0% +level next Mass +level m² is equal to 4/ Alpha Prime + + align:start position:0% + + + + align:start position:0% + +so any questions on + + align:start position:0% +so any questions on + + + align:start position:0% +so any questions on +this this an symmetric tensor what is + + align:start position:0% +this this an symmetric tensor what is + + + align:start position:0% +this this an symmetric tensor what is +that it's + + align:start position:0% + + + + align:start position:0% + +like an symmetric tensor but what's the + + align:start position:0% +like an symmetric tensor but what's the + + + align:start position:0% +like an symmetric tensor but what's the +spin H what's the spin um yeah nor uh in + + align:start position:0% +spin H what's the spin um yeah nor uh in + + + align:start position:0% +spin H what's the spin um yeah nor uh in +the four dimension would be something + + align:start position:0% +the four dimension would be something + + + align:start position:0% +the four dimension would be something +what we normally call 1 comma 1 one + + align:start position:0% +what we normally call 1 comma 1 one + + + align:start position:0% +what we normally call 1 comma 1 one +representation of the lence + + align:start position:0% +representation of the lence + + + align:start position:0% +representation of the lence +group + + align:start position:0% +group + + + align:start position:0% +group +yeah yeah it's not it's not 02 it's yeah + + align:start position:0% +yeah yeah it's not it's not 02 it's yeah + + + align:start position:0% +yeah yeah it's not it's not 02 it's yeah +it's it's what we normally call one + + align:start position:0% +it's it's what we normally call one + + + align:start position:0% +it's it's what we normally call one +comma one + + align:start position:0% +comma one + + + align:start position:0% +comma one +yeah yes + + align:start position:0% +yeah yes + + + align:start position:0% +yeah yes +form no no this is just arbitrary uh + + align:start position:0% +form no no this is just arbitrary uh + + + align:start position:0% +form no no this is just arbitrary uh +yeah so this is your so this is your H + + align:start position:0% +yeah so this is your so this is your H + + + align:start position:0% +yeah so this is your so this is your H +so this is your state space at this + + align:start position:0% +so this is your state space at this + + + align:start position:0% +so this is your state space at this +level right and so so the general state + + align:start position:0% +level right and so so the general state + + + align:start position:0% +level right and so so the general state +will be linear with position of them and + + align:start position:0% +will be linear with position of them and + + + align:start position:0% +will be linear with position of them and +those States they transform + + align:start position:0% +those States they transform + + + align:start position:0% +those States they transform +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +separated under lent symmetry so we + + align:start position:0% +separated under lent symmetry so we + + + align:start position:0% +separated under lent symmetry so we +separate them and so for example + + align:start position:0% +separate them and so for example + + + align:start position:0% +separate them and so for example +symmetric things they transform + + align:start position:0% +symmetric things they transform + + + align:start position:0% +symmetric things they transform +separated on the L transformation on the + + align:start position:0% +separated on the L transformation on the + + + align:start position:0% +separated on the L transformation on the +this guys yeah so so they should + + align:start position:0% +this guys yeah so so they should + + + align:start position:0% +this guys yeah so so they should +corresponding to different SpaceTime + + align:start position:0% +corresponding to different SpaceTime + + + align:start position:0% +corresponding to different SpaceTime +Fields so each of those each of those + + align:start position:0% +Fields so each of those each of those + + + align:start position:0% +Fields so each of those each of those +things should correspond + + align:start position:0% +things should correspond + + + align:start position:0% +things should correspond +into to A Spacetime field + + align:start position:0% + + + + align:start position:0% + +okay okay so now let me just summarize + + align:start position:0% +okay okay so now let me just summarize + + + align:start position:0% +okay okay so now let me just summarize +what we have + + align:start position:0% + + + + align:start position:0% + +found so we have found so let's + + align:start position:0% +found so we have found so let's + + + align:start position:0% +found so we have found so let's +collect the Mist excitations we found + + align:start position:0% +collect the Mist excitations we found + + + align:start position:0% +collect the Mist excitations we found +because as we will see the mass + + align:start position:0% +because as we will see the mass + + + align:start position:0% +because as we will see the mass +excitation is the most important one + + align:start position:0% +excitation is the most important one + + + align:start position:0% +excitation is the most important one +yeah let me also + + align:start position:0% +yeah let me also + + + align:start position:0% +yeah let me also +mention yeah let me just + + align:start position:0% + + + + align:start position:0% + +emphasize in physics it's always M this + + align:start position:0% +emphasize in physics it's always M this + + + align:start position:0% +emphasize in physics it's always M this +particle give you something + + align:start position:0% +particle give you something + + + align:start position:0% +particle give you something +interesting okay for example here even + + align:start position:0% +interesting okay for example here even + + + align:start position:0% +interesting okay for example here even +for D L equal to + + align:start position:0% +for D L equal to + + + align:start position:0% +for D L equal to +26 those massive particles as I said + + align:start position:0% +26 those massive particles as I said + + + align:start position:0% +26 those massive particles as I said +maybe I did not emphasize even for D not + + align:start position:0% +maybe I did not emphasize even for D not + + + align:start position:0% +maybe I did not emphasize even for D not +equal to 26 this massive particles that + + align:start position:0% +equal to 26 this massive particles that + + + align:start position:0% +equal to 26 this massive particles that +do form into representations of the r + + align:start position:0% +do form into representations of the r + + + align:start position:0% +do form into representations of the r +symmetry for any Dimension only for + + align:start position:0% +symmetry for any Dimension only for + + + align:start position:0% +symmetry for any Dimension only for +those massless particles okay something + + align:start position:0% +those massless particles okay something + + + align:start position:0% +those massless particles okay something +it's + + align:start position:0% +it's + + + align:start position:0% +it's +funny and so of course we also know the + + align:start position:0% +funny and so of course we also know the + + + align:start position:0% +funny and so of course we also know the +n Medical they they give r long range + + align:start position:0% +n Medical they they give r long range + + + align:start position:0% +n Medical they they give r long range +interaction ex so now let's say let's + + align:start position:0% +interaction ex so now let's say let's + + + align:start position:0% +interaction ex so now let's say let's +collect the mless + + align:start position:0% + + + + align:start position:0% + +particles M + + align:start position:0% + + + + align:start position:0% + +expectations so I we write them in terms + + align:start position:0% +expectations so I we write them in terms + + + align:start position:0% +expectations so I we write them in terms +of the SpaceTime + + align:start position:0% +of the SpaceTime + + + align:start position:0% +of the SpaceTime +Fields so for the open + + align:start position:0% + + + + align:start position:0% + +string essentially we find a m this + + align:start position:0% +string essentially we find a m this + + + align:start position:0% +string essentially we find a m this +Vector field + + align:start position:0% +Vector field + + + align:start position:0% +Vector field +okay so this is our Photon so at the + + align:start position:0% +okay so this is our Photon so at the + + + align:start position:0% +okay so this is our Photon so at the +moment I put as a code Photon because we + + align:start position:0% +moment I put as a code Photon because we + + + align:start position:0% +moment I put as a code Photon because we +we only find the mass this particle we + + align:start position:0% +we only find the mass this particle we + + + align:start position:0% +we only find the mass this particle we +we don't know whether this is our our + + align:start position:0% +we don't know whether this is our our + + + align:start position:0% +we don't know whether this is our our +own beloved Photon + + align:start position:0% +own beloved Photon + + + align:start position:0% +own beloved Photon +yet and for the close + + align:start position:0% +yet and for the close + + + align:start position:0% +yet and for the close +string then we find the symmetric + + align:start position:0% +string then we find the symmetric + + + align:start position:0% +string then we find the symmetric +tensor M so this is what we normally + + align:start position:0% +tensor M so this is what we normally + + + align:start position:0% +tensor M so this is what we normally +call the + + align:start position:0% + + + + align:start position:0% + +graviton so again code it we find the + + align:start position:0% +graviton so again code it we find the + + + align:start position:0% +graviton so again code it we find the +mass is spin two particle which if you + + align:start position:0% +mass is spin two particle which if you + + + align:start position:0% +mass is spin two particle which if you +write in terms of field will + + align:start position:0% +write in terms of field will + + + align:start position:0% +write in terms of field will +be like grav symmetric tensor or B mu mu + + align:start position:0% +be like grav symmetric tensor or B mu mu + + + align:start position:0% +be like grav symmetric tensor or B mu mu +which is anti symmetric + + align:start position:0% +which is anti symmetric + + + align:start position:0% +which is anti symmetric +tensor and now this mu mu this all run + + align:start position:0% +tensor and now this mu mu this all run + + + align:start position:0% +tensor and now this mu mu this all run +in all SpaceTime Dimensions okay and + + align:start position:0% +in all SpaceTime Dimensions okay and + + + align:start position:0% +in all SpaceTime Dimensions okay and +then we have a five then you have a + + align:start position:0% +then we have a five then you have a + + + align:start position:0% +then we have a five then you have a +scaler Fields so this is just called + + align:start position:0% +scaler Fields so this is just called + + + align:start position:0% +scaler Fields so this is just called +antisymmetric tensor and this F is + + align:start position:0% +antisymmetric tensor and this F is + + + align:start position:0% +antisymmetric tensor and this F is +called + + align:start position:0% +called + + + align:start position:0% +called +D it's not F which is that scal of field + + align:start position:0% +D it's not F which is that scal of field + + + align:start position:0% +D it's not F which is that scal of field +is often called the + + align:start position:0% + + + + align:start position:0% + +Delon so so + + align:start position:0% +Delon so so + + + align:start position:0% +Delon so so +far even we qu them Photon call this one + + align:start position:0% +far even we qu them Photon call this one + + + align:start position:0% +far even we qu them Photon call this one +Photon and the H mu they are + + align:start position:0% +Photon and the H mu they are + + + align:start position:0% +Photon and the H mu they are +not the qu them Photon and graviton is + + align:start position:0% +not the qu them Photon and graviton is + + + align:start position:0% +not the qu them Photon and graviton is +actually a little bit cheating because + + align:start position:0% +actually a little bit cheating because + + + align:start position:0% +actually a little bit cheating because +we don't know whether they really + + align:start position:0% +we don't know whether they really + + + align:start position:0% +we don't know whether they really +behaves like a photon or like a graviton + + align:start position:0% +behaves like a photon or like a graviton + + + align:start position:0% +behaves like a photon or like a graviton +okay we just find a mass this been one + + align:start position:0% +okay we just find a mass this been one + + + align:start position:0% +okay we just find a mass this been one +particle and the mass is been two + + align:start position:0% +particle and the mass is been two + + + align:start position:0% +particle and the mass is been two +particle but actually there is something + + align:start position:0% +particle but actually there is something + + + align:start position:0% +particle but actually there is something +very + + align:start position:0% +very + + + align:start position:0% +very +general one can say just from General + + align:start position:0% + + + + align:start position:0% + +principle just from General principle + + align:start position:0% +principle just from General principle + + + align:start position:0% +principle just from General principle +one can show based on the r Co variance + + align:start position:0% +one can show based on the r Co variance + + + align:start position:0% +one can show based on the r Co variance +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +nor coar and the say and + + align:start position:0% +nor coar and the say and + + + align:start position:0% +nor coar and the say and +absence of non physical States EXA say + + align:start position:0% + + + + align:start position:0% + +unitarity Etc just based on those + + align:start position:0% +unitarity Etc just based on those + + + align:start position:0% +unitarity Etc just based on those +General principle one can + + align:start position:0% +General principle one can + + + align:start position:0% +General principle one can +argue that at the low Energies + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +knowes the Dynamics of + + align:start position:0% + + + + align:start position:0% + +any dynamics of any m phot m this Vector + + align:start position:0% + + + + align:start position:0% + +field should be + + align:start position:0% + + + + align:start position:0% + +Max + + align:start position:0% + + + + align:start position:0% + +well and uh for the graviton uh for the + + align:start position:0% +well and uh for the graviton uh for the + + + align:start position:0% +well and uh for the graviton uh for the +M spin two + + align:start position:0% +M spin two + + + align:start position:0% +M spin two +particle must be inant gravity + + align:start position:0% + + + + align:start position:0% + +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +why if you say tomorrow suppose you + + align:start position:0% +why if you say tomorrow suppose you + + + align:start position:0% +why if you say tomorrow suppose you +invent a theory + + align:start position:0% +invent a theory + + + align:start position:0% +invent a theory +yourself and suppose that's a quantum + + align:start position:0% +yourself and suppose that's a quantum + + + align:start position:0% +yourself and suppose that's a quantum +theory + + align:start position:0% + + + + align:start position:0% + +and that the just happens you have a + + align:start position:0% +and that the just happens you have a + + + align:start position:0% +and that the just happens you have a +massive spin two + + align:start position:0% +massive spin two + + + align:start position:0% +massive spin two +particle then you don't have to do + + align:start position:0% +particle then you don't have to do + + + align:start position:0% +particle then you don't have to do +calculations then you say if my Ser is + + align:start position:0% +calculations then you say if my Ser is + + + align:start position:0% +calculations then you say if my Ser is +consistent this spin two particle must + + align:start position:0% +consistent this spin two particle must + + + align:start position:0% +consistent this spin two particle must +behave like a gravit + + align:start position:0% +behave like a gravit + + + align:start position:0% +behave like a gravit +okay you're saying there's no other + + align:start position:0% +okay you're saying there's no other + + + align:start position:0% +okay you're saying there's no other +varant you can write such yeah + + align:start position:0% +varant you can write such yeah + + + align:start position:0% +varant you can write such yeah +essentially just you can show the low + + align:start position:0% +essentially just you can show the low + + + align:start position:0% +essentially just you can show the low +energies it's always just based on gaug + + align:start position:0% +energies it's always just based on gaug + + + align:start position:0% +energies it's always just based on gaug +symmetry EXA the only thing you can have + + align:start position:0% +symmetry EXA the only thing you can have + + + align:start position:0% +symmetry EXA the only thing you can have +is those things yeah is Ein and + + align:start position:0% +is those things yeah is Ein and + + + align:start position:0% +is those things yeah is Ein and +gravity + + align:start position:0% +gravity + + + align:start position:0% +gravity +good and this can be actually checked + + align:start position:0% +good and this can be actually checked + + + align:start position:0% +good and this can be actually checked +explicitly so now let me erase those + + align:start position:0% +explicitly so now let me erase those + + + align:start position:0% +explicitly so now let me erase those +things + + align:start position:0% +things + + + align:start position:0% +things +now leave + + align:start position:0% + + + + align:start position:0% + +them so this can actually be checked + + align:start position:0% +them so this can actually be checked + + + align:start position:0% +them so this can actually be checked +explicitly so in string Ser you can not + + align:start position:0% +explicitly so in string Ser you can not + + + align:start position:0% +explicitly so in string Ser you can not +only not not only can you find the + + align:start position:0% +only not not only can you find the + + + align:start position:0% +only not not only can you find the +Spectrum you can also compute the + + align:start position:0% +Spectrum you can also compute the + + + align:start position:0% +Spectrum you can also compute the +scattering amplitude among those + + align:start position:0% +scattering amplitude among those + + + align:start position:0% +scattering amplitude among those +particles okay so as I outline before + + align:start position:0% +particles okay so as I outline before + + + align:start position:0% +particles okay so as I outline before +essentially perform past integrals with + + align:start position:0% +essentially perform past integrals with + + + align:start position:0% +essentially perform past integrals with +some initial string States going to some + + align:start position:0% +some initial string States going to some + + + align:start position:0% +some initial string States going to some +final string States ET okay so of course + + align:start position:0% +final string States ET okay so of course + + + align:start position:0% +final string States ET okay so of course +this will be too far for us so we will + + align:start position:0% +this will be too far for us so we will + + + align:start position:0% +this will be too far for us so we will +not go into that let me just tell you + + align:start position:0% +not go into that let me just tell you + + + align:start position:0% +not go into that let me just tell you +the + + align:start position:0% + + + + align:start position:0% + +answer so you can confirm this + + align:start position:0% +answer so you can confirm this + + + align:start position:0% +answer so you can confirm this +so this + + align:start position:0% +so this + + + align:start position:0% +so this +expectation this + + align:start position:0% + + + + align:start position:0% + +confirmed is + + align:start position:0% +confirmed is + + + align:start position:0% +confirmed is +confirmed by + + align:start position:0% + + + + align:start position:0% + +explicit String + + align:start position:0% + + + + align:start position:0% + +Theory calculation + + align:start position:0% + + + + align:start position:0% + +of + + align:start position:0% + + + + align:start position:0% + +scattering of these particles + + align:start position:0% + + + + align:start position:0% + +okay for example let's + + align:start position:0% +okay for example let's + + + align:start position:0% +okay for example let's +consider so we have this spin Mass spin + + align:start position:0% +consider so we have this spin Mass spin + + + align:start position:0% +consider so we have this spin Mass spin +two particle H which I called H so let's + + align:start position:0% +two particle H which I called H so let's + + + align:start position:0% +two particle H which I called H so let's +consider you start with initial state + + align:start position:0% +consider you start with initial state + + + align:start position:0% +consider you start with initial state +with 2 H then the scatter to get this on + + align:start position:0% +with 2 H then the scatter to get this on + + + align:start position:0% +with 2 H then the scatter to get this on +two final say which again H so this is a + + align:start position:0% +two final say which again H so this is a + + + align:start position:0% +two final say which again H so this is a +say graviton graviton scattering start + + align:start position:0% +say graviton graviton scattering start + + + align:start position:0% +say graviton graviton scattering start +with two graviton scatter + + align:start position:0% +with two graviton scatter + + + align:start position:0% +with two graviton scatter +them so in s Theory it will be say say + + align:start position:0% +them so in s Theory it will be say say + + + align:start position:0% +them so in s Theory it will be say say +at the lowest order we will have a + + align:start position:0% +at the lowest order we will have a + + + align:start position:0% +at the lowest order we will have a +diagram like + + align:start position:0% +diagram like + + + align:start position:0% +diagram like +this so niest lowest + + align:start position:0% + + + + align:start position:0% + +order I'm not drawing very well + + align:start position:0% + + + + align:start position:0% + +anyway uh hope this is + + align:start position:0% + + + + align:start position:0% + +clear so you start with two initial + + align:start position:0% +clear so you start with two initial + + + align:start position:0% +clear so you start with two initial +string States you scatter into some + + align:start position:0% +string States you scatter into some + + + align:start position:0% +string States you scatter into some +final State okay so this is a no string + + align:start position:0% +final State okay so this is a no string + + + align:start position:0% +final State okay so this is a no string +series skying diagram you can principle + + align:start position:0% +series skying diagram you can principle + + + align:start position:0% +series skying diagram you can principle +compute this using path integral which + + align:start position:0% +compute this using path integral which + + + align:start position:0% +compute this using path integral which +are outed earlier uh of course we will + + align:start position:0% +are outed earlier uh of course we will + + + align:start position:0% +are outed earlier uh of course we will +not compute this part in and uh so you + + align:start position:0% +not compute this part in and uh so you + + + align:start position:0% +not compute this part in and uh so you +see there two vertex here one is + + align:start position:0% +see there two vertex here one is + + + align:start position:0% +see there two vertex here one is +proportional to string you have two + + align:start position:0% +proportional to string you have two + + + align:start position:0% +proportional to string you have two +string mer into + + align:start position:0% +string mer into + + + align:start position:0% +string mer into +one + + align:start position:0% +one + + + align:start position:0% +one +string and then you have a string then + + align:start position:0% +string and then you have a string then + + + align:start position:0% +string and then you have a string then +split into two so there are two two uh + + align:start position:0% +split into two so there are two two uh + + + align:start position:0% +split into two so there are two two uh +uh uh remember each of T thing + + align:start position:0% +uh uh remember each of T thing + + + align:start position:0% +uh uh remember each of T thing +corresponding to a g string okay + + align:start position:0% + + + + align:start position:0% + +so this would be the process in string + + align:start position:0% +so this would be the process in string + + + align:start position:0% +so this would be the process in string +Series so this would be the process in + + align:start position:0% +Series so this would be the process in + + + align:start position:0% +Series so this would be the process in +string Ser so now if you go to + + align:start position:0% + + + + align:start position:0% + +leres say l enes means if you consider + + align:start position:0% +leres say l enes means if you consider + + + align:start position:0% +leres say l enes means if you consider +the energy of the initial and final + + align:start position:0% +the energy of the initial and final + + + align:start position:0% +the energy of the initial and final +particles to be much much smaller than + + align:start position:0% +particles to be much much smaller than + + + align:start position:0% +particles to be much much smaller than +one of alpha Prime so remember one of + + align:start position:0% +one of alpha Prime so remember one of + + + align:start position:0% +one of alpha Prime so remember one of +alpha Prime is the scale which go from + + align:start position:0% +alpha Prime is the scale which go from + + + align:start position:0% +alpha Prime is the scale which go from +masses to massive + + align:start position:0% +masses to massive + + + align:start position:0% +masses to massive +particles so if we consider very low + + align:start position:0% +particles so if we consider very low + + + align:start position:0% +particles so if we consider very low +energy process which e is much much + + align:start position:0% +energy process which e is much much + + + align:start position:0% +energy process which e is much much +smaller than one of alha prime then the + + align:start position:0% +smaller than one of alha prime then the + + + align:start position:0% +smaller than one of alha prime then the +contribution of the mass so in some + + align:start position:0% +contribution of the mass so in some + + + align:start position:0% +contribution of the mass so in some +sense in the + + align:start position:0% +sense in the + + + align:start position:0% +sense in the +string in this intermediate channel when + + align:start position:0% +string in this intermediate channel when + + + align:start position:0% +string in this intermediate channel when +you go to from two initial state to two + + align:start position:0% +you go to from two initial state to two + + + align:start position:0% +you go to from two initial state to two +final State this intermediate channel + + align:start position:0% +final State this intermediate channel + + + align:start position:0% +final State this intermediate channel +the infinite number of string states can + + align:start position:0% +the infinite number of string states can + + + align:start position:0% +the infinite number of string states can +can can participate in this intermediate + + align:start position:0% +can can participate in this intermediate + + + align:start position:0% +can can participate in this intermediate +process but in the process but if energy + + align:start position:0% +process but in the process but if energy + + + align:start position:0% +process but in the process but if energy +sufficiently know then from your common + + align:start position:0% +sufficiently know then from your common + + + align:start position:0% +sufficiently know then from your common +sense or you can do calculation and then + + align:start position:0% +sense or you can do calculation and then + + + align:start position:0% +sense or you can do calculation and then +the contribution of the massive State + + align:start position:0% +the contribution of the massive State + + + align:start position:0% +the contribution of the massive State +become actually not important so + + align:start position:0% +become actually not important so + + + align:start position:0% +become actually not important so +essentially uh what is important is + + align:start position:0% +essentially uh what is important is + + + align:start position:0% +essentially uh what is important is +those Mass particles propagating between + + align:start position:0% +those Mass particles propagating between + + + align:start position:0% +those Mass particles propagating between +them and then you can show that actually + + align:start position:0% +them and then you can show that actually + + + align:start position:0% +them and then you can show that actually +just precisely + + align:start position:0% +just precisely + + + align:start position:0% +just precisely +reduce to the Einstein + + align:start position:0% +reduce to the Einstein + + + align:start position:0% +reduce to the Einstein +gravity precisely reduce to Einstein + + align:start position:0% +gravity precisely reduce to Einstein + + + align:start position:0% +gravity precisely reduce to Einstein +gravity so more + + align:start position:0% +gravity so more + + + align:start position:0% +gravity so more +explicitly so so so yeah so so when you + + align:start position:0% +explicitly so so so yeah so so when you + + + align:start position:0% +explicitly so so so yeah so so when you +go to leries then only Mass modes + + align:start position:0% +go to leries then only Mass modes + + + align:start position:0% +go to leries then only Mass modes +M mode + + align:start position:0% + + + + align:start position:0% + +exchange + + align:start position:0% + + + + align:start position:0% + +Dominate comate and then you find that + + align:start position:0% +Dominate comate and then you find that + + + align:start position:0% +Dominate comate and then you find that +the answer is precisely agree in the low + + align:start position:0% +the answer is precisely agree in the low + + + align:start position:0% +the answer is precisely agree in the low +energy + + align:start position:0% +energy + + + align:start position:0% +energy +limit + + align:start position:0% +limit + + + align:start position:0% +limit +agree + + align:start position:0% +agree + + + align:start position:0% +agree +with + + align:start position:0% +with + + + align:start position:0% +with +that from einon Gravity + + align:start position:0% +that from einon Gravity + + + align:start position:0% +that from einon Gravity +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +of course you not only + + align:start position:0% +of course you not only + + + align:start position:0% +of course you not only +have graviton you also have this p and + + align:start position:0% +have graviton you also have this p and + + + align:start position:0% +have graviton you also have this p and +five they also Mass this modes so so + + align:start position:0% +five they also Mass this modes so so + + + align:start position:0% +five they also Mass this modes so so +this is a slight gener slight generation + + align:start position:0% +this is a slight gener slight generation + + + align:start position:0% +this is a slight gener slight generation +of an gravity a gen is adding some + + align:start position:0% +of an gravity a gen is adding some + + + align:start position:0% +of an gravity a gen is adding some +gravity CLE + + align:start position:0% +gravity CLE + + + align:start position:0% +gravity CLE +to such b and the five + + align:start position:0% + + + + align:start position:0% + +okay so in fact + + align:start position:0% +okay so in fact + + + align:start position:0% +okay so in fact +you can write down a soal Lowery + + align:start position:0% +you can write down a soal Lowery + + + align:start position:0% +you can write down a soal Lowery +effective + + align:start position:0% +effective + + + align:start position:0% +effective +action so soal Lowery effective action + + align:start position:0% +action so soal Lowery effective action + + + align:start position:0% +action so soal Lowery effective action +so let me call l e + + align:start position:0% + + + + align:start position:0% + +here something like + + align:start position:0% + + + + align:start position:0% + +this so five is this five + + align:start position:0% +this so five is this five + + + align:start position:0% +this so five is this five +here and R is the standard reach Scala + + align:start position:0% +here and R is the standard reach Scala + + + align:start position:0% +here and R is the standard reach Scala +for + + align:start position:0% +for + + + align:start position:0% +for +the Einstein + + align:start position:0% + + + + align:start position:0% + +gravity okay H is the three index tensor + + align:start position:0% +gravity okay H is the three index tensor + + + align:start position:0% +gravity okay H is the three index tensor +formed out of + + align:start position:0% + + + + align:start position:0% + +B okay so so H Square just a kinetic + + align:start position:0% +B okay so so H Square just a kinetic + + + align:start position:0% +B okay so so H Square just a kinetic +term for B + + align:start position:0% +term for B + + + align:start position:0% +term for B +so you can show so more precisely you + + align:start position:0% +so you can show so more precisely you + + + align:start position:0% +so you can show so more precisely you +can + + align:start position:0% +can + + + align:start position:0% +can +show that the scattering amplitude you + + align:start position:0% +show that the scattering amplitude you + + + align:start position:0% +show that the scattering amplitude you +obtained from the stren Ser then you + + align:start position:0% +obtained from the stren Ser then you + + + align:start position:0% +obtained from the stren Ser then you +take a low energy + + align:start position:0% +take a low energy + + + align:start position:0% +take a low energy +limit that + + align:start position:0% +limit that + + + align:start position:0% +limit that +answer precisely the + + align:start position:0% +answer precisely the + + + align:start position:0% +answer precisely the +same as the scattering amplitude you + + align:start position:0% +same as the scattering amplitude you + + + align:start position:0% +same as the scattering amplitude you +calculated from this Theory say expanded + + align:start position:0% +calculated from this Theory say expanded + + + align:start position:0% +calculated from this Theory say expanded +around minkovski space time okay so this + + align:start position:0% +around minkovski space time okay so this + + + align:start position:0% +around minkovski space time okay so this +is Einstein gravity coup to some scal + + align:start position:0% +is Einstein gravity coup to some scal + + + align:start position:0% +is Einstein gravity coup to some scal +field okay + + align:start position:0% +field okay + + + align:start position:0% +field okay +and + + align:start position:0% + + + + align:start position:0% + +so yes so what about higher Loops or + + align:start position:0% +so yes so what about higher Loops or + + + align:start position:0% +so yes so what about higher Loops or +higher + + align:start position:0% + + + + align:start position:0% + +energies of course then will not be the + + align:start position:0% +energies of course then will not be the + + + align:start position:0% +energies of course then will not be the +same this is no energies + + align:start position:0% +same this is no energies + + + align:start position:0% +same this is no energies +okay so so let me make one more Rec + + align:start position:0% + + + + align:start position:0% + +Mark make one more remark in Einstein + + align:start position:0% +Mark make one more remark in Einstein + + + align:start position:0% +Mark make one more remark in Einstein +gravity + + align:start position:0% + + + + align:start position:0% + +so like this so inant gravity cou to the + + align:start position:0% +so like this so inant gravity cou to the + + + align:start position:0% +so like this so inant gravity cou to the +metal field so when I say einan gravity + + align:start position:0% +metal field so when I say einan gravity + + + align:start position:0% +metal field so when I say einan gravity +always imply einan gravity plus some + + align:start position:0% +always imply einan gravity plus some + + + align:start position:0% +always imply einan gravity plus some +other Metal Field which you can add so + + align:start position:0% +other Metal Field which you can add so + + + align:start position:0% +other Metal Field which you can add so +in an gravity such a scattering + + align:start position:0% +in an gravity such a scattering + + + align:start position:0% +in an gravity such a scattering +process said no + + align:start position:0% +process said no + + + align:start position:0% +process said no +order we all know is proportional to G + + align:start position:0% +order we all know is proportional to G + + + align:start position:0% +order we all know is proportional to G +Newton okay so this this is the the same + + align:start position:0% +Newton okay so this this is the the same + + + align:start position:0% +Newton okay so this this is the the same +G Newton which Newton + + align:start position:0% +G Newton which Newton + + + align:start position:0% +G Newton which Newton +observed and such a yeah let me call + + align:start position:0% +observed and such a yeah let me call + + + align:start position:0% +observed and such a yeah let me call +this say scattering for this is a + + align:start position:0% +this say scattering for this is a + + + align:start position:0% +this say scattering for this is a +A4 and then then the scattering uh for + + align:start position:0% +A4 and then then the scattering uh for + + + align:start position:0% +A4 and then then the scattering uh for +the for the anant gravity is propor to + + align:start position:0% +the for the anant gravity is propor to + + + align:start position:0% +the for the anant gravity is propor to +to G Newton so this is one graviton + + align:start position:0% +to G Newton so this is one graviton + + + align:start position:0% +to G Newton so this is one graviton +exchange okay it's proportional to + + align:start position:0% +exchange okay it's proportional to + + + align:start position:0% +exchange okay it's proportional to +Newton constant this is attractive force + + align:start position:0% +Newton constant this is attractive force + + + align:start position:0% +Newton constant this is attractive force +between two + + align:start position:0% +between two + + + align:start position:0% +between two +objects and uh but you if you look at + + align:start position:0% +objects and uh but you if you look at + + + align:start position:0% +objects and uh but you if you look at +this string + + align:start position:0% +this string + + + align:start position:0% +this string +diagram then this string diagram is + + align:start position:0% +diagram then this string diagram is + + + align:start position:0% +diagram then this string diagram is +proportional to GS squ so we + + align:start position:0% +proportional to GS squ so we + + + align:start position:0% +proportional to GS squ so we +conclude that the relation between the + + align:start position:0% +conclude that the relation between the + + + align:start position:0% +conclude that the relation between the +Newton constant and the string coupling + + align:start position:0% +Newton constant and the string coupling + + + align:start position:0% +Newton constant and the string coupling +must be g g Newton proportional to GS + + align:start position:0% +must be g g Newton proportional to GS + + + align:start position:0% +must be g g Newton proportional to GS +squ up to some say dimensional numbers + + align:start position:0% +squ up to some say dimensional numbers + + + align:start position:0% +squ up to some say dimensional numbers +or some numerical + + align:start position:0% + + + + align:start position:0% + +factors okay so this is a very important + + align:start position:0% +factors okay so this is a very important + + + align:start position:0% +factors okay so this is a very important +relation you should always keep in + + align:start position:0% + + + + align:start position:0% + +mind so now here is an important + + align:start position:0% +mind so now here is an important + + + align:start position:0% +mind so now here is an important +point is p just + + align:start position:0% +point is p just + + + align:start position:0% +point is p just +asked what happens at the roof levels so + + align:start position:0% +asked what happens at the roof levels so + + + align:start position:0% +asked what happens at the roof levels so +so you can compare the Tre level process + + align:start position:0% +so you can compare the Tre level process + + + align:start position:0% +so you can compare the Tre level process +ex you find they agree very well you say + + align:start position:0% +ex you find they agree very well you say + + + align:start position:0% +ex you find they agree very well you say +what happens at roof + + align:start position:0% +what happens at roof + + + align:start position:0% +what happens at roof +levels so now let me call this equation + + align:start position:0% + + + + align:start position:0% + +one so at Loop level + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +one is notoriously + + align:start position:0% +one is notoriously + + + align:start position:0% +one is notoriously +Divergent say if you calculate some + + align:start position:0% +Divergent say if you calculate some + + + align:start position:0% +Divergent say if you calculate some +scatter amplitude to the loop level then + + align:start position:0% +scatter amplitude to the loop level then + + + align:start position:0% +scatter amplitude to the loop level then +find the the the r + + align:start position:0% +find the the the r + + + align:start position:0% +find the the the r +Divergent in particular more and more + + align:start position:0% +Divergent in particular more and more + + + align:start position:0% +Divergent in particular more and more +Divergent when you go to more and more + + align:start position:0% +Divergent when you go to more and more + + + align:start position:0% +Divergent when you go to more and more +higher + + align:start position:0% +higher + + + align:start position:0% +higher +Loops + + align:start position:0% +Loops + + + align:start position:0% +Loops +okay more + + align:start position:0% + + + + align:start position:0% + +Divergent at the higher orders in pation + + align:start position:0% +Divergent at the higher orders in pation + + + align:start position:0% +Divergent at the higher orders in pation +the we say at the higher loops + + align:start position:0% + + + + align:start position:0% + +so that's what we normally mean say a + + align:start position:0% +so that's what we normally mean say a + + + align:start position:0% +so that's what we normally mean say a +series non + + align:start position:0% + + + + align:start position:0% + +realizable so this tells + + align:start position:0% +realizable so this tells + + + align:start position:0% +realizable so this tells +you so if you take this gravity Series + + align:start position:0% +you so if you take this gravity Series + + + align:start position:0% +you so if you take this gravity Series +so this is just essentially Ouran + + align:start position:0% +so this is just essentially Ouran + + + align:start position:0% +so this is just essentially Ouran +gravity compared to some Fields if you + + align:start position:0% +gravity compared to some Fields if you + + + align:start position:0% +gravity compared to some Fields if you +take the einan + + align:start position:0% +take the einan + + + align:start position:0% +take the einan +gravity it's expand around flat + + align:start position:0% +gravity it's expand around flat + + + align:start position:0% +gravity it's expand around flat +space quantize that been two + + align:start position:0% +space quantize that been two + + + align:start position:0% +space quantize that been two +excitations then that will fail because + + align:start position:0% +excitations then that will fail because + + + align:start position:0% +excitations then that will fail because +at certain point you don't know what you + + align:start position:0% +at certain point you don't know what you + + + align:start position:0% +at certain point you don't know what you +are doing because you get all + + align:start position:0% +are doing because you get all + + + align:start position:0% +are doing because you get all +divergencies which you cannot + + align:start position:0% +divergencies which you cannot + + + align:start position:0% +divergencies which you cannot +renormalize okay you can + + align:start position:0% +renormalize okay you can + + + align:start position:0% +renormalize okay you can +normalize so what this of course this + + align:start position:0% +normalize so what this of course this + + + align:start position:0% +normalize so what this of course this +does what this tells + + align:start position:0% +does what this tells + + + align:start position:0% +does what this tells +you is that this equation itself likely + + align:start position:0% +you is that this equation itself likely + + + align:start position:0% +you is that this equation itself likely +does not describe the right UV physics + + align:start position:0% +does not describe the right UV physics + + + align:start position:0% +does not describe the right UV physics +so that's why you see all these + + align:start position:0% +so that's why you see all these + + + align:start position:0% +so that's why you see all these +divergencies because you maybe ignore + + align:start position:0% +divergencies because you maybe ignore + + + align:start position:0% +divergencies because you maybe ignore +some more important + + align:start position:0% +some more important + + + align:start position:0% +some more important +physics which you cannot + + align:start position:0% + + + + align:start position:0% + +renormalize but now you can go to this + + align:start position:0% +renormalize but now you can go to this + + + align:start position:0% +renormalize but now you can go to this +so this is supposed to only agree with + + align:start position:0% +so this is supposed to only agree with + + + align:start position:0% +so this is supposed to only agree with +the stren series at lges which the + + align:start position:0% +the stren series at lges which the + + + align:start position:0% +the stren series at lges which the +massive mode + + align:start position:0% +massive mode + + + align:start position:0% +massive mode +is are not important but in scen the + + align:start position:0% +is are not important but in scen the + + + align:start position:0% +is are not important but in scen the +there this infinite number of massive + + align:start position:0% +there this infinite number of massive + + + align:start position:0% +there this infinite number of massive +mode EX + + align:start position:0% +mode EX + + + align:start position:0% +mode EX +so you find in string + + align:start position:0% + + + + align:start position:0% + +theory if you do similar Loop + + align:start position:0% +theory if you do similar Loop + + + align:start position:0% +theory if you do similar Loop +calculation in string + + align:start position:0% +calculation in string + + + align:start position:0% +calculation in string +theory the screen Loop + + align:start position:0% + + + + align:start position:0% + +diagrams magically are all U be + + align:start position:0% + + + + align:start position:0% + +fight okay or you ref find it so there's + + align:start position:0% +fight okay or you ref find it so there's + + + align:start position:0% +fight okay or you ref find it so there's +no such divergencies + + align:start position:0% +no such divergencies + + + align:start position:0% +no such divergencies +there's no such divergencies + + align:start position:0% +there's no such divergencies + + + align:start position:0% +there's no such divergencies +so so this is the first hint + + align:start position:0% +so so this is the first hint + + + align:start position:0% +so so this is the first hint +so this was the first h of s the as a + + align:start position:0% +so this was the first h of s the as a + + + align:start position:0% +so this was the first h of s the as a +consistent theory of + + align:start position:0% +consistent theory of + + + align:start position:0% +consistent theory of +gravity and uh uh because at least at + + align:start position:0% +gravity and uh uh because at least at + + + align:start position:0% +gravity and uh uh because at least at +the perative + + align:start position:0% + + + + align:start position:0% + +level at perative level you can really + + align:start position:0% +level at perative level you can really + + + align:start position:0% +level at perative level you can really +quantize a masses in two particles and + + align:start position:0% +quantize a masses in two particles and + + + align:start position:0% +quantize a masses in two particles and +uh to calculate their physics in the + + align:start position:0% +uh to calculate their physics in the + + + align:start position:0% +uh to calculate their physics in the +self-consistent + + align:start position:0% +self-consistent + + + align:start position:0% +self-consistent +way + + align:start position:0% +way + + + align:start position:0% +way +okay any questions on + + align:start position:0% +okay any questions on + + + align:start position:0% +okay any questions on +this yes in that calculation you have to + + align:start position:0% +this yes in that calculation you have to + + + align:start position:0% +this yes in that calculation you have to +use all the yeah yeah yeah that's are + + align:start position:0% +use all the yeah yeah yeah that's are + + + align:start position:0% +use all the yeah yeah yeah that's are +crucial so that's why this kind of thing + + align:start position:0% +crucial so that's why this kind of thing + + + align:start position:0% +crucial so that's why this kind of thing +is not good enough because that does not + + align:start position:0% +is not good enough because that does not + + + align:start position:0% +is not good enough because that does not +have enough degree Freedom so in you + + align:start position:0% +have enough degree Freedom so in you + + + align:start position:0% +have enough degree Freedom so in you +have all this additional degree Freedom + + align:start position:0% +have all this additional degree Freedom + + + align:start position:0% +have all this additional degree Freedom +that make your UV structure completely + + align:start position:0% +that make your UV structure completely + + + align:start position:0% +that make your UV structure completely +different yes you take that action cut + + align:start position:0% +different yes you take that action cut + + + align:start position:0% +different yes you take that action cut +it from + + align:start position:0% +it from + + + align:start position:0% +it from +above would it approximately + + align:start position:0% +above would it approximately + + + align:start position:0% +above would it approximately +ex no it's a yeah so so this will + + align:start position:0% +ex no it's a yeah so so this will + + + align:start position:0% +ex no it's a yeah so so this will +work as what normally works as a ler + + align:start position:0% +work as what normally works as a ler + + + align:start position:0% +work as what normally works as a ler +effective + + align:start position:0% +effective + + + align:start position:0% +effective +Theory L work as if L when you when you + + align:start position:0% +Theory L work as if L when you when you + + + align:start position:0% +Theory L work as if L when you when you +when you consistently integrate out the + + align:start position:0% +when you consistently integrate out the + + + align:start position:0% +when you consistently integrate out the +massive mode and uh yeah so uh so so + + align:start position:0% +massive mode and uh yeah so uh so so + + + align:start position:0% +massive mode and uh yeah so uh so so +even at Loop level this can capture + + align:start position:0% +even at Loop level this can capture + + + align:start position:0% +even at Loop level this can capture +indeed at no energies even at noop this + + align:start position:0% +indeed at no energies even at noop this + + + align:start position:0% +indeed at no energies even at noop this +can capture uh uh some of the stren + + align:start position:0% +can capture uh uh some of the stren + + + align:start position:0% +can capture uh uh some of the stren +series um results but but you have to re + + align:start position:0% +series um results but but you have to re + + + align:start position:0% +series um results but but you have to re +normalize properly ex + + align:start position:0% +normalize properly ex + + + align:start position:0% +normalize properly ex +yeah yes so does this imply that for + + align:start position:0% +yeah yes so does this imply that for + + + align:start position:0% +yeah yes so does this imply that for +like large objects not things on on + + align:start position:0% +like large objects not things on on + + + align:start position:0% +like large objects not things on on +these very small scales that we should + + align:start position:0% +these very small scales that we should + + + align:start position:0% +these very small scales that we should +reproduce Einstein the Einstein field + + align:start position:0% +reproduce Einstein the Einstein field + + + align:start position:0% +reproduce Einstein the Einstein field +equations yeah is that okay this is + + align:start position:0% +equations yeah is that okay this is + + + align:start position:0% +equations yeah is that okay this is +sufficient to show that yeah that's what + + align:start position:0% +sufficient to show that yeah that's what + + + align:start position:0% +sufficient to show that yeah that's what +it tells you okay yeah yeah for example + + align:start position:0% +it tells you okay yeah yeah for example + + + align:start position:0% +it tells you okay yeah yeah for example +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um if you measure the the gravity + + align:start position:0% +um if you measure the the gravity + + + align:start position:0% +um if you measure the the gravity +between you and me you want to see the + + align:start position:0% +between you and me you want to see the + + + align:start position:0% +between you and me you want to see the +difference right okay yeah actually you + + align:start position:0% +difference right okay yeah actually you + + + align:start position:0% +difference right okay yeah actually you +will see a + + align:start position:0% +will see a + + + align:start position:0% +will see a +difference uh so this series is a little + + align:start position:0% +difference uh so this series is a little + + + align:start position:0% +difference uh so this series is a little +bit different because of this massive + + align:start position:0% +bit different because of this massive + + + align:start position:0% +bit different because of this massive +scaler field I see so so so when you so + + align:start position:0% +scaler field I see so so so when you so + + + align:start position:0% +scaler field I see so so so when you so +so in ordinary gravity uh uh the + + align:start position:0% +so in ordinary gravity uh uh the + + + align:start position:0% +so in ordinary gravity uh uh the +attractive force between you and me just + + align:start position:0% +attractive force between you and me just + + + align:start position:0% +attractive force between you and me just +come from graviton right but in this + + align:start position:0% +come from graviton right but in this + + + align:start position:0% +come from graviton right but in this +series because this Scala is massless + + align:start position:0% +series because this Scala is massless + + + align:start position:0% +series because this Scala is massless +and uh and actually have additional + + align:start position:0% +and uh and actually have additional + + + align:start position:0% +and uh and actually have additional +attractive force and so this the is + + align:start position:0% +attractive force and so this the is + + + align:start position:0% +attractive force and so this the is +actually not the same + + align:start position:0% +actually not the same + + + align:start position:0% +actually not the same +uh so this Theory even though it's + + align:start position:0% +uh so this Theory even though it's + + + align:start position:0% +uh so this Theory even though it's +trival gen very simple generation of Ein + + align:start position:0% +trival gen very simple generation of Ein + + + align:start position:0% +trival gen very simple generation of Ein +and gravity but actually give you a + + align:start position:0% +and gravity but actually give you a + + + align:start position:0% +and gravity but actually give you a +different Gravity Force so so that's why + + align:start position:0% +different Gravity Force so so that's why + + + align:start position:0% +different Gravity Force so so that's why +if the screen C is going to describe the + + align:start position:0% +if the screen C is going to describe the + + + align:start position:0% +if the screen C is going to describe the +real life somehow this scal of field has + + align:start position:0% +real life somehow this scal of field has + + + align:start position:0% +real life somehow this scal of field has +become massive some other mechanism has + + align:start position:0% +become massive some other mechanism has + + + align:start position:0% +become massive some other mechanism has +to make the scal of field massive I see + + align:start position:0% +to make the scal of field massive I see + + + align:start position:0% +to make the scal of field massive I see +yeah yeah of course we also don't + + align:start position:0% +yeah yeah of course we also don't + + + align:start position:0% +yeah yeah of course we also don't +observe B mu mu and this also have to + + align:start position:0% +observe B mu mu and this also have to + + + align:start position:0% +observe B mu mu and this also have to +become + + align:start position:0% +become + + + align:start position:0% +become +massive + + align:start position:0% +massive + + + align:start position:0% +massive +see and and will we really uh find out + + align:start position:0% +see and and will we really uh find out + + + align:start position:0% +see and and will we really uh find out +that's mechanism to make the message + + align:start position:0% +that's mechanism to make the message + + + align:start position:0% +that's mechanism to make the message +yeah uh um so this is uh uh yeah so this + + align:start position:0% +yeah uh um so this is uh uh yeah so this + + + align:start position:0% +yeah uh um so this is uh uh yeah so this +is the one of the very important + + align:start position:0% +is the one of the very important + + + align:start position:0% +is the one of the very important +question since early days of in people + + align:start position:0% +question since early days of in people + + + align:start position:0% +question since early days of in people +have been try to look for all kind of + + align:start position:0% +have been try to look for all kind of + + + align:start position:0% +have been try to look for all kind of +mechanism to do it Etc yeah so so there + + align:start position:0% +mechanism to do it Etc yeah so so there + + + align:start position:0% +mechanism to do it Etc yeah so so there +there is an agreed upon way of doing + + align:start position:0% +there is an agreed upon way of doing + + + align:start position:0% +there is an agreed upon way of doing +this or is it still okay uh it depends + + align:start position:0% +this or is it still okay uh it depends + + + align:start position:0% +this or is it still okay uh it depends +yeah this goes to Al Point yeah uh uh + + align:start position:0% +yeah this goes to Al Point yeah uh uh + + + align:start position:0% +yeah this goes to Al Point yeah uh uh +yeah uh weight from Alex point + + align:start position:0% +yeah uh weight from Alex point + + + align:start position:0% +yeah uh weight from Alex point +yes ask how do we know this effective + + align:start position:0% +yes ask how do we know this effective + + + align:start position:0% +yes ask how do we know this effective +Theory couples to other fields as + + align:start position:0% + + + + align:start position:0% + +Einstein um so what do you mean uh you + + align:start position:0% +Einstein um so what do you mean uh you + + + align:start position:0% +Einstein um so what do you mean uh you +can add + + align:start position:0% +can add + + + align:start position:0% +can add +um uh the comping between them this and + + align:start position:0% +um uh the comping between them this and + + + align:start position:0% +um uh the comping between them this and +gravity through the yeah here right this + + align:start position:0% +gravity through the yeah here right this + + + align:start position:0% +gravity through the yeah here right this +one here of course you should use cing + + align:start position:0% +one here of course you should use cing + + + align:start position:0% +one here of course you should use cing +derivative yeah yeah here I did not yeah + + align:start position:0% +derivative yeah yeah here I did not yeah + + + align:start position:0% +derivative yeah yeah here I did not yeah +I'm not very careful in defining this + + align:start position:0% +I'm not very careful in defining this + + + align:start position:0% +I'm not very careful in defining this +but here you use S and der ex + + align:start position:0% +but here you use S and der ex + + + align:start position:0% +but here you use S and der ex +yeah what about what about coupling to + + align:start position:0% +yeah what about what about coupling to + + + align:start position:0% +yeah what about what about coupling to +the open strs or to photons or to you + + align:start position:0% +the open strs or to photons or to you + + + align:start position:0% +the open strs or to photons or to you +know matter will be the same + + align:start position:0% + + + + align:start position:0% + +thing as what you would expect that I'm + + align:start position:0% +thing as what you would expect that I'm + + + align:start position:0% +thing as what you would expect that I'm +just + + align:start position:0% + + + + align:start position:0% + +saying just gener it just governed by + + align:start position:0% +saying just gener it just governed by + + + align:start position:0% +saying just gener it just governed by +General Corian just general quarian have + + align:start position:0% +General Corian just general quarian have + + + align:start position:0% +General Corian just general quarian have +to arise ateres okay so the general + + align:start position:0% +to arise ateres okay so the general + + + align:start position:0% +to arise ateres okay so the general +principle is effective for uh including + + align:start position:0% +principle is effective for uh including + + + align:start position:0% +principle is effective for uh including +matter as well yeah yeah then you can + + align:start position:0% +matter as well yeah yeah then you can + + + align:start position:0% +matter as well yeah yeah then you can +check they can check at it's string + + align:start position:0% +check they can check at it's string + + + align:start position:0% +check they can check at it's string +anything you can check is consistent + + align:start position:0% +anything you can check is consistent + + + align:start position:0% +anything you can check is consistent +with that + + align:start position:0% + + + + align:start position:0% + +principle good so now it's a lot of + + align:start position:0% +principle good so now it's a lot of + + + align:start position:0% +principle good so now it's a lot of +point so so let me just make a side + + align:start position:0% +point so so let me just make a side + + + align:start position:0% +point so so let me just make a side +remark on the physical consequence of + + align:start position:0% +remark on the physical consequence of + + + align:start position:0% +remark on the physical consequence of +this Scala field so we see that this + + align:start position:0% +this Scala field so we see that this + + + align:start position:0% +this Scala field so we see that this +Scala field is important because the uh + + align:start position:0% +Scala field is important because the uh + + + align:start position:0% +Scala field is important because the uh +because it actually Comm mediates say + + align:start position:0% +because it actually Comm mediates say + + + align:start position:0% +because it actually Comm mediates say +ractive force uh but actually there's + + align:start position:0% +ractive force uh but actually there's + + + align:start position:0% +ractive force uh but actually there's +another very important role this uh uh + + align:start position:0% +another very important role this uh uh + + + align:start position:0% +another very important role this uh uh +uh uh this scal Fields + + align:start position:0% + + + + align:start position:0% + +does is that if you look at this know + + align:start position:0% +does is that if you look at this know + + + align:start position:0% +does is that if you look at this know +effective + + align:start position:0% +effective + + + align:start position:0% +effective +action so let me now write this uh G + + align:start position:0% + + + + align:start position:0% + +Newton as one / g string + + align:start position:0% +Newton as one / g string + + + align:start position:0% +Newton as one / g string +Square then this have the structure + + align:start position:0% +Square then this have the structure + + + align:start position:0% +Square then this have the structure +proportional to one which is Str Square + + align:start position:0% +proportional to one which is Str Square + + + align:start position:0% +proportional to one which is Str Square +times exponential minus + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay so now this very important + + align:start position:0% +okay so now this very important + + + align:start position:0% +okay so now this very important +thing so now you + + align:start position:0% +thing so now you + + + align:start position:0% +thing so now you +see if + + align:start position:0% +see if + + + align:start position:0% +see if +five behave + + align:start position:0% +five behave + + + align:start position:0% +five behave +longly and if you and this is actually + + align:start position:0% +longly and if you and this is actually + + + align:start position:0% +longly and if you and this is actually +multiply this guy this actually + + align:start position:0% +multiply this guy this actually + + + align:start position:0% +multiply this guy this actually +effectively yeah because this is + + align:start position:0% +effectively yeah because this is + + + align:start position:0% +effectively yeah because this is +multiplied by the uh by the Einstein + + align:start position:0% +multiplied by the uh by the Einstein + + + align:start position:0% +multiplied by the uh by the Einstein +scaler + + align:start position:0% + + + + align:start position:0% + +so this effectively modifies your Newton + + align:start position:0% +so this effectively modifies your Newton + + + align:start position:0% +so this effectively modifies your Newton +constant okay so effectively modify + + align:start position:0% +constant okay so effectively modify + + + align:start position:0% +constant okay so effectively modify +newon constant so + + align:start position:0% +newon constant so + + + align:start position:0% +newon constant so +in in fact you can actually interpret + + align:start position:0% +in in fact you can actually interpret + + + align:start position:0% +in in fact you can actually interpret +this + + align:start position:0% +this + + + align:start position:0% +this +GS as the expectation value of this + + align:start position:0% +GS as the expectation value of this + + + align:start position:0% +GS as the expectation value of this +F + + align:start position:0% +F + + + align:start position:0% +F +okay as the expectation value of this + + align:start position:0% +okay as the expectation value of this + + + align:start position:0% +okay as the expectation value of this +F yeah because if you can change F and + + align:start position:0% +F yeah because if you can change F and + + + align:start position:0% +F yeah because if you can change F and +then change active GS and the GS can be + + align:start position:0% +then change active GS and the GS can be + + + align:start position:0% +then change active GS and the GS can be +interpreted as expectation value of + + align:start position:0% +interpreted as expectation value of + + + align:start position:0% +interpreted as expectation value of +five so so so this is + + align:start position:0% +five so so so this is + + + align:start position:0% +five so so so this is +something very important and very + + align:start position:0% +something very important and very + + + align:start position:0% +something very important and very +deep because remember GS is essentially + + align:start position:0% +deep because remember GS is essentially + + + align:start position:0% +deep because remember GS is essentially +the + + align:start position:0% +the + + + align:start position:0% +the +only the only parameter in string the + + align:start position:0% +only the only parameter in string the + + + align:start position:0% +only the only parameter in string the +the only Dimension is parameter in + + align:start position:0% +the only Dimension is parameter in + + + align:start position:0% +the only Dimension is parameter in +string the which characterize the + + align:start position:0% +string the which characterize the + + + align:start position:0% +string the which characterize the +strength of the + + align:start position:0% + + + + align:start position:0% + +string and now we see this constant is + + align:start position:0% +string and now we see this constant is + + + align:start position:0% +string and now we see this constant is +not + + align:start position:0% +not + + + align:start position:0% +not +arbitrary it's actually determined by + + align:start position:0% +arbitrary it's actually determined by + + + align:start position:0% +arbitrary it's actually determined by +some Dynamic + + align:start position:0% +some Dynamic + + + align:start position:0% +some Dynamic +field okay so that actually means that + + align:start position:0% +field okay so that actually means that + + + align:start position:0% +field okay so that actually means that +string C there's no free parameter + + align:start position:0% +string C there's no free parameter + + + align:start position:0% +string C there's no free parameter +there's no free Dimension is parameter + + align:start position:0% +there's no free Dimension is parameter + + + align:start position:0% +there's no free Dimension is parameter +everything in some sense determined by + + align:start position:0% +everything in some sense determined by + + + align:start position:0% +everything in some sense determined by +Dynamics so so this is a very remarkable + + align:start position:0% +Dynamics so so this is a very remarkable + + + align:start position:0% +Dynamics so so this is a very remarkable +feature so this make people think in the + + align:start position:0% +feature so this make people think in the + + + align:start position:0% +feature so this make people think in the +early days of + + align:start position:0% +early days of + + + align:start position:0% +early days of +strory that you actually may be able to + + align:start position:0% +strory that you actually may be able to + + + align:start position:0% +strory that you actually may be able to +derive + + align:start position:0% +derive + + + align:start position:0% +derive +the mass of the + + align:start position:0% +the mass of the + + + align:start position:0% +the mass of the +electron because there's no free + + align:start position:0% +electron because there's no free + + + align:start position:0% +electron because there's no free +parameter in stre series so you should + + align:start position:0% +parameter in stre series so you should + + + align:start position:0% +parameter in stre series so you should +be able to derive everything from first + + align:start position:0% +be able to derive everything from first + + + align:start position:0% +be able to derive everything from first +principle yeah anyway + + align:start position:0% +principle yeah anyway + + + align:start position:0% +principle yeah anyway +yeah but this + + align:start position:0% +yeah but this + + + align:start position:0% +yeah but this +also create a problem for the issue I + + align:start position:0% +also create a problem for the issue I + + + align:start position:0% +also create a problem for the issue I +just + + align:start position:0% +just + + + align:start position:0% +just +mentioned again this is a side remark uh + + align:start position:0% +mentioned again this is a side remark uh + + + align:start position:0% +mentioned again this is a side remark uh +but this a fun + + align:start position:0% + + + + align:start position:0% + +remark so + + align:start position:0% + + + + align:start position:0% + +so the top so Str we mentioned before is + + align:start position:0% +so the top so Str we mentioned before is + + + align:start position:0% +so the top so Str we mentioned before is +a summation of + + align:start position:0% +a summation of + + + align:start position:0% +a summation of +topology and the topology is weighted by + + align:start position:0% +topology and the topology is weighted by + + + align:start position:0% +topology and the topology is weighted by +this g string so if this string is small + + align:start position:0% +this g string so if this string is small + + + align:start position:0% +this g string so if this string is small +then you only need to look at the lowest + + align:start position:0% +then you only need to look at the lowest + + + align:start position:0% +then you only need to look at the lowest +topology because the higher topology are + + align:start position:0% +topology because the higher topology are + + + align:start position:0% +topology because the higher topology are +supprised by higher power of g string + + align:start position:0% +supprised by higher power of g string + + + align:start position:0% +supprised by higher power of g string +okay in particular if g string become + + align:start position:0% +okay in particular if g string become + + + align:start position:0% +okay in particular if g string become +order one then to + + align:start position:0% +order one then to + + + align:start position:0% +order one then to +calculate such a + + align:start position:0% +calculate such a + + + align:start position:0% +calculate such a +scattering then you need to sum of all + + align:start position:0% +scattering then you need to sum of all + + + align:start position:0% +scattering then you need to sum of all +possible topologies and then that will + + align:start position:0% +possible topologies and then that will + + + align:start position:0% +possible topologies and then that will +be unmanageable problem which we don't + + align:start position:0% +be unmanageable problem which we don't + + + align:start position:0% +be unmanageable problem which we don't +know how to do and so so so so so we + + align:start position:0% +know how to do and so so so so so we + + + align:start position:0% +know how to do and so so so so so we +want this gen to be very + + align:start position:0% +want this gen to be very + + + align:start position:0% +want this gen to be very +small so that actually uh we can + + align:start position:0% +small so that actually uh we can + + + align:start position:0% +small so that actually uh we can +actually uh control this + + align:start position:0% +actually uh control this + + + align:start position:0% +actually uh control this +Theory okay but now we have a + + align:start position:0% +Theory okay but now we have a + + + align:start position:0% +Theory okay but now we have a +difficulty but we also said we want this + + align:start position:0% +difficulty but we also said we want this + + + align:start position:0% +difficulty but we also said we want this +Scala field to be to develop a + + align:start position:0% +Scala field to be to develop a + + + align:start position:0% +Scala field to be to develop a +mass we want to the Scala field to + + align:start position:0% +mass we want to the Scala field to + + + align:start position:0% +mass we want to the Scala field to +develop for mass and it's actually not + + align:start position:0% +develop for mass and it's actually not + + + align:start position:0% +develop for mass and it's actually not +easy to arrange the scaler field to + + align:start position:0% +easy to arrange the scaler field to + + + align:start position:0% +easy to arrange the scaler field to +develop a mass and the same time to make + + align:start position:0% +develop a mass and the same time to make + + + align:start position:0% +develop a mass and the same time to make +this expectation to be very small okay + + align:start position:0% +this expectation to be very small okay + + + align:start position:0% +this expectation to be very small okay +and uh and actually that turns out to be + + align:start position:0% +and uh and actually that turns out to be + + + align:start position:0% +and uh and actually that turns out to be +a non-trivial problem yeah yeah so it's + + align:start position:0% +a non-trivial problem yeah yeah so it's + + + align:start position:0% +a non-trivial problem yeah yeah so it's +actually not that + + align:start position:0% + + + + align:start position:0% + +easy okay so so my last + + align:start position:0% +easy okay so so my last + + + align:start position:0% +easy okay so so my last +comment I'm still + + align:start position:0% + + + + align:start position:0% + +very so so earlier we said the + + align:start position:0% +very so so earlier we said the + + + align:start position:0% +very so so earlier we said the +Tang so so the for the so so what we + + align:start position:0% +Tang so so the for the so so what we + + + align:start position:0% +Tang so so the for the so so what we +describ so far this is called the + + align:start position:0% +describ so far this is called the + + + align:start position:0% +describ so far this is called the +bosonic stream because we only have bons + + align:start position:0% +bosonic stream because we only have bons + + + align:start position:0% +bosonic stream because we only have bons +we only have bons it's called bosonic + + align:start position:0% +we only have bons it's called bosonic + + + align:start position:0% +we only have bons it's called bosonic +Stream So this bonic string can be + + align:start position:0% +Stream So this bonic string can be + + + align:start position:0% +Stream So this bonic string can be +generalized to so what's called super + + align:start position:0% +generalized to so what's called super + + + align:start position:0% +generalized to so what's called super +String + + align:start position:0% + + + + align:start position:0% + +Theory called super + + align:start position:0% +Theory called super + + + align:start position:0% +Theory called super +string so what super string does is the + + align:start position:0% +string so what super string does is the + + + align:start position:0% +string so what super string does is the +following after you fix this + + align:start position:0% + + + + align:start position:0% + +cage so after you fixing this cage + + align:start position:0% +cage so after you fixing this cage + + + align:start position:0% +cage so after you fixing this cage +again the super string can be written as + + align:start position:0% +again the super string can be written as + + + align:start position:0% +again the super string can be written as +some Karan W sheet Theory with some + + align:start position:0% +some Karan W sheet Theory with some + + + align:start position:0% +some Karan W sheet Theory with some +intrinsic matric and in the super string + + align:start position:0% +intrinsic matric and in the super string + + + align:start position:0% +intrinsic matric and in the super string +after you fix the cage the work sheet + + align:start position:0% +after you fix the cage the work sheet + + + align:start position:0% +after you fix the cage the work sheet +metric to be + + align:start position:0% +metric to be + + + align:start position:0% +metric to be +minkovski then the super string action + + align:start position:0% +minkovski then the super string action + + + align:start position:0% +minkovski then the super string action +can be written as the + + align:start position:0% + + + + align:start position:0% + +following you just essentially have the + + align:start position:0% +following you just essentially have the + + + align:start position:0% +following you just essentially have the +previously fre + + align:start position:0% + + + + align:start position:0% + +scaler + + align:start position:0% +scaler + + + align:start position:0% +scaler +action but then you add some Fons + + align:start position:0% + + + + align:start position:0% + +there are some formulas okay you just + + align:start position:0% +there are some formulas okay you just + + + align:start position:0% +there are some formulas okay you just +add some + + align:start position:0% +add some + + + align:start position:0% +add some +Fons so the reason you could add such so + + align:start position:0% +Fons so the reason you could add such so + + + align:start position:0% +Fons so the reason you could add such so +this is just some two dimensional Fons + + align:start position:0% +this is just some two dimensional Fons + + + align:start position:0% +this is just some two dimensional Fons +living on the world + + align:start position:0% + + + + align:start position:0% + +sheet some 2D yes so this a two + + align:start position:0% +sheet some 2D yes so this a two + + + align:start position:0% +sheet some 2D yes so this a two +dimensional spinner field living on the + + align:start position:0% +dimensional spinner field living on the + + + align:start position:0% +dimensional spinner field living on the +world sheet so the reason you can add + + align:start position:0% +world sheet so the reason you can add + + + align:start position:0% +world sheet so the reason you can add +such a thing because those things don't + + align:start position:0% +such a thing because those things don't + + + align:start position:0% +such a thing because those things don't +have obvious geometric interpretation so + + align:start position:0% +have obvious geometric interpretation so + + + align:start position:0% +have obvious geometric interpretation so +you can consider them as describe some + + align:start position:0% +you can consider them as describe some + + + align:start position:0% +you can consider them as describe some +internal degre freedom of the scen and + + align:start position:0% +internal degre freedom of the scen and + + + align:start position:0% +internal degre freedom of the scen and +so this guy provide this space time uh + + align:start position:0% +so this guy provide this space time uh + + + align:start position:0% +so this guy provide this space time uh +interpretation of moving in the space + + align:start position:0% +interpretation of moving in the space + + + align:start position:0% +interpretation of moving in the space +time and those are just some + + align:start position:0% +time and those are just some + + + align:start position:0% +time and those are just some +additional internal D fre on the work + + align:start position:0% +additional internal D fre on the work + + + align:start position:0% +additional internal D fre on the work +sheet it turns out by adding this fion + + align:start position:0% +sheet it turns out by adding this fion + + + align:start position:0% +sheet it turns out by adding this fion +actually things change a lot actually do + + align:start position:0% +actually things change a lot actually do + + + align:start position:0% +actually things change a lot actually do +not change very much uh itend since does + + align:start position:0% +not change very much uh itend since does + + + align:start position:0% +not change very much uh itend since does +not change very much because this is a + + align:start position:0% +not change very much because this is a + + + align:start position:0% +not change very much because this is a +free Fon series it's also very easy to + + align:start position:0% +free Fon series it's also very easy to + + + align:start position:0% +free Fon series it's also very easy to +quantize and and everything we did + + align:start position:0% +quantize and and everything we did + + + align:start position:0% +quantize and and everything we did +before just carry + + align:start position:0% +before just carry + + + align:start position:0% +before just carry +over except you need to add those Fon + + align:start position:0% +over except you need to add those Fon + + + align:start position:0% +over except you need to add those Fon +you need to also quantize those three + + align:start position:0% + + + + align:start position:0% + +Fons tend out when you do that there are + + align:start position:0% +Fons tend out when you do that there are + + + align:start position:0% +Fons tend out when you do that there are +actually + + align:start position:0% +actually + + + align:start position:0% +actually +two + + align:start position:0% +two + + + align:start position:0% +two +different quantization + + align:start position:0% + + + + align:start position:0% + +scheme quation procedure quation + + align:start position:0% +scheme quation procedure quation + + + align:start position:0% +scheme quation procedure quation +process two different quations + + align:start position:0% +process two different quations + + + align:start position:0% +process two different quations +exist so when you add this + + align:start position:0% +exist so when you add this + + + align:start position:0% +exist so when you add this +formans with no tum so you actually can + + align:start position:0% +formans with no tum so you actually can + + + align:start position:0% +formans with no tum so you actually can +get rid of tan by including this + + align:start position:0% +get rid of tan by including this + + + align:start position:0% +get rid of tan by including this +formans okay so then the lowest mode is + + align:start position:0% +formans okay so then the lowest mode is + + + align:start position:0% +formans okay so then the lowest mode is +the lowest mode is just the your Mist + + align:start position:0% +the lowest mode is just the your Mist + + + align:start position:0% +the lowest mode is just the your Mist +mode + + align:start position:0% +mode + + + align:start position:0% +mode +okay and the reason that you can have + + align:start position:0% +okay and the reason that you can have + + + align:start position:0% +okay and the reason that you can have +more than one + + align:start position:0% +more than one + + + align:start position:0% +more than one +quantization is that we have have fans + + align:start position:0% +quantization is that we have have fans + + + align:start position:0% +quantization is that we have have fans +and this is fan defined on the circle so + + align:start position:0% +and this is fan defined on the circle so + + + align:start position:0% +and this is fan defined on the circle so +fan on the circle you can Define to be + + align:start position:0% +fan on the circle you can Define to be + + + align:start position:0% +fan on the circle you can Define to be +periodic or antiperiodic so now you have + + align:start position:0% +periodic or antiperiodic so now you have + + + align:start position:0% +periodic or antiperiodic so now you have +some choices and depend on whether you + + align:start position:0% +some choices and depend on whether you + + + align:start position:0% +some choices and depend on whether you +choose for to be periodic anti periodic + + align:start position:0% +choose for to be periodic anti periodic + + + align:start position:0% +choose for to be periodic anti periodic +ET and then the story become different + + align:start position:0% +ET and then the story become different + + + align:start position:0% +ET and then the story become different +okay and uh I will not go into there but + + align:start position:0% +okay and uh I will not go into there but + + + align:start position:0% +okay and uh I will not go into there but +in principle just with enough + + align:start position:0% +in principle just with enough + + + align:start position:0% +in principle just with enough +time in principle noww you can do it + + align:start position:0% +time in principle noww you can do it + + + align:start position:0% +time in principle noww you can do it +yourself because the just Quant free + + align:start position:0% +yourself because the just Quant free + + + align:start position:0% +yourself because the just Quant free +field Theory actually you still cannot + + align:start position:0% +field Theory actually you still cannot + + + align:start position:0% +field Theory actually you still cannot +do it yourself um yeah there's still a + + align:start position:0% +do it yourself um yeah there's still a + + + align:start position:0% +do it yourself um yeah there's still a +little bit more stty than that but but + + align:start position:0% +little bit more stty than that but but + + + align:start position:0% +little bit more stty than that but but +the principle is very + + align:start position:0% +the principle is very + + + align:start position:0% +the principle is very +similar so so in this case you get rid + + align:start position:0% +similar so so in this case you get rid + + + align:start position:0% +similar so so in this case you get rid +of + + align:start position:0% +of + + + align:start position:0% +of +Tang so this two pro this two procedure + + align:start position:0% +Tang so this two pro this two procedure + + + align:start position:0% +Tang so this two pro this two procedure +course called type 2 a and type 2 b + + align:start position:0% +course called type 2 a and type 2 b + + + align:start position:0% +course called type 2 a and type 2 b +string so they give you two type of + + align:start position:0% +string so they give you two type of + + + align:start position:0% +string so they give you two type of +string series one is called type 2 a and + + align:start position:0% +string series one is called type 2 a and + + + align:start position:0% +string series one is called type 2 a and +one is called type to B so also another + + align:start position:0% +one is called type to B so also another + + + align:start position:0% +one is called type to B so also another +important difference instead of D equal + + align:start position:0% +important difference instead of D equal + + + align:start position:0% +important difference instead of D equal +to 26 now only requires D equal to 10 + + align:start position:0% +to 26 now only requires D equal to 10 + + + align:start position:0% +to 26 now only requires D equal to 10 +okay + + align:start position:0% + + + + align:start position:0% + +10 so now let me just write down the + + align:start position:0% +10 so now let me just write down the + + + align:start position:0% +10 so now let me just write down the +massive + + align:start position:0% +massive + + + align:start position:0% +massive +Spectrum so now because you have Fons + + align:start position:0% +Spectrum so now because you have Fons + + + align:start position:0% +Spectrum so now because you have Fons +now you actually the this SpaceTime + + align:start position:0% +now you actually the this SpaceTime + + + align:start position:0% +now you actually the this SpaceTime +particle can also have Fons previously + + align:start position:0% +particle can also have Fons previously + + + align:start position:0% +particle can also have Fons previously +it's all aonic particles Now by adding + + align:start position:0% +it's all aonic particles Now by adding + + + align:start position:0% +it's all aonic particles Now by adding +this work sheet formans turns out this + + align:start position:0% +this work sheet formans turns out this + + + align:start position:0% +this work sheet formans turns out this +can also generate the space time foran + + align:start position:0% +can also generate the space time foran + + + align:start position:0% +can also generate the space time foran +can generate space time for meons and uh + + align:start position:0% +can generate space time for meons and uh + + + align:start position:0% +can generate space time for meons and uh +so so so now the Mass + + align:start position:0% + + + + align:start position:0% + +Spectrum so now these are lowest + + align:start position:0% +Spectrum so now these are lowest + + + align:start position:0% +Spectrum so now these are lowest +particles there's no tack + + align:start position:0% +particles there's no tack + + + align:start position:0% +particles there's no tack +here so these are all now become all 10 + + align:start position:0% +here so these are all now become all 10 + + + align:start position:0% +here so these are all now become all 10 +dimensional Fields so for type 2 a again + + align:start position:0% +dimensional Fields so for type 2 a again + + + align:start position:0% +dimensional Fields so for type 2 a again +you have + + align:start position:0% +you have + + + align:start position:0% +you have +this graviton you have this P mu then + + align:start position:0% +this graviton you have this P mu then + + + align:start position:0% +this graviton you have this P mu then +you have this Theon + + align:start position:0% +you have this Theon + + + align:start position:0% +you have this Theon +and then you have a lot of vector field + + align:start position:0% +and then you have a lot of vector field + + + align:start position:0% +and then you have a lot of vector field +come from the Clos string so this is for + + align:start position:0% +come from the Clos string so this is for + + + align:start position:0% +come from the Clos string so this is for +the Clos + + align:start position:0% + + + + align:start position:0% + +string now you actually have a gauge + + align:start position:0% +string now you actually have a gauge + + + align:start position:0% +string now you actually have a gauge +field also in the close string you want + + align:start position:0% +field also in the close string you want + + + align:start position:0% +field also in the close string you want +gauge field and a three form tensor + + align:start position:0% +gauge field and a three form tensor + + + align:start position:0% +gauge field and a three form tensor +field so you have three indexes uh fully + + align:start position:0% +field so you have three indexes uh fully + + + align:start position:0% +field so you have three indexes uh fully +antisymmetric is the gaue field just + + align:start position:0% +antisymmetric is the gaue field just + + + align:start position:0% +antisymmetric is the gaue field just +coming from the premium by + + align:start position:0% +coming from the premium by + + + align:start position:0% +coming from the premium by +linear uh yeah yeah yeah right that's + + align:start position:0% +linear uh yeah yeah yeah right that's + + + align:start position:0% +linear uh yeah yeah yeah right that's +right they are related actually uh + + align:start position:0% +right they are related actually uh + + + align:start position:0% +right they are related actually uh +related to fium B lineus + + align:start position:0% +related to fium B lineus + + + align:start position:0% +related to fium B lineus +yeah so those thing are exactly the same + + align:start position:0% +yeah so those thing are exactly the same + + + align:start position:0% +yeah so those thing are exactly the same +as + + align:start position:0% +as + + + align:start position:0% +as +before and then you get some additional + + align:start position:0% +before and then you get some additional + + + align:start position:0% +before and then you get some additional +field so this are normally called the + + align:start position:0% +field so this are normally called the + + + align:start position:0% +field so this are normally called the +remone remone + + align:start position:0% +remone remone + + + align:start position:0% +remone remone +field + + align:start position:0% +field + + + align:start position:0% +field +okay uh called REM remone + + align:start position:0% +okay uh called REM remone + + + align:start position:0% +okay uh called REM remone +field and then you can also and then + + align:start position:0% +field and then you can also and then + + + align:start position:0% +field and then you can also and then +plus Fons so we not write down the for + + align:start position:0% +plus Fons so we not write down the for + + + align:start position:0% +plus Fons so we not write down the for +meons it turn out this series is + + align:start position:0% +meons it turn out this series is + + + align:start position:0% +meons it turn out this series is +actually super symmetric so each of + + align:start position:0% +actually super symmetric so each of + + + align:start position:0% +actually super symmetric so each of +those fields they have some super fic + + align:start position:0% +those fields they have some super fic + + + align:start position:0% +those fields they have some super fic +patter so it's actually a super + + align:start position:0% +patter so it's actually a super + + + align:start position:0% +patter so it's actually a super +symmetric Theory so then you also have + + align:start position:0% +symmetric Theory so then you also have + + + align:start position:0% +symmetric Theory so then you also have +type 2 + + align:start position:0% +type 2 + + + align:start position:0% +type 2 +B and again the bosonic thing you have H + + align:start position:0% +B and again the bosonic thing you have H + + + align:start position:0% +B and again the bosonic thing you have H +mu mu B mu mu + + align:start position:0% +mu mu B mu mu + + + align:start position:0% +mu mu B mu mu +five and then you have a a lot of scale + + align:start position:0% +five and then you have a a lot of scale + + + align:start position:0% +five and then you have a a lot of scale +of field + + align:start position:0% +of field + + + align:start position:0% +of field +Kai then another anti symmetric + + align:start position:0% +Kai then another anti symmetric + + + align:start position:0% +Kai then another anti symmetric +tensor C mu mu2 and then a for form + + align:start position:0% + + + + align:start position:0% + +field okay so this is again is soal REM + + align:start position:0% +field okay so this is again is soal REM + + + align:start position:0% +field okay so this is again is soal REM +REM then plusform + + align:start position:0% + + + + align:start position:0% + +meals + + align:start position:0% + + + + align:start position:0% + +okay and the low energy the of them + + align:start position:0% +okay and the low energy the of them + + + align:start position:0% +okay and the low energy the of them +become So-Cal type 2 a and type 2 b + + align:start position:0% +become So-Cal type 2 a and type 2 b + + + align:start position:0% +become So-Cal type 2 a and type 2 b +super gravity so these are super + + align:start position:0% +super gravity so these are super + + + align:start position:0% +super gravity so these are super +symmetric series and and then the + + align:start position:0% +symmetric series and and then the + + + align:start position:0% +symmetric series and and then the +corresponding to generation of gravity + + align:start position:0% +corresponding to generation of gravity + + + align:start position:0% +corresponding to generation of gravity +called the super gravity so we we do not + + align:start position:0% +called the super gravity so we we do not + + + align:start position:0% +called the super gravity so we we do not +need to go into there um + + align:start position:0% + + + + align:start position:0% + +yes so if you were going to do string + + align:start position:0% +yes so if you were going to do string + + + align:start position:0% +yes so if you were going to do string +theory for example or like a + + align:start position:0% +theory for example or like a + + + align:start position:0% +theory for example or like a +generalization on membranes as you had + + align:start position:0% +generalization on membranes as you had + + + align:start position:0% +generalization on membranes as you had +mentioned before if you were doing this + + align:start position:0% +mentioned before if you were doing this + + + align:start position:0% +mentioned before if you were doing this +on two manifolds would you also have to + + align:start position:0% +on two manifolds would you also have to + + + align:start position:0% +on two manifolds would you also have to +include anyon + + align:start position:0% +include anyon + + + align:start position:0% +include anyon +contributions you may oh boy okay I + + align:start position:0% +contributions you may oh boy okay I + + + align:start position:0% +contributions you may oh boy okay I +don't know yeah nobody have succeeded in + + align:start position:0% +don't know yeah nobody have succeeded in + + + align:start position:0% +don't know yeah nobody have succeeded in +doing this yeah yeah you + + align:start position:0% + + + + align:start position:0% + +may okay it's uh + + align:start position:0% +may okay it's uh + + + align:start position:0% +may okay it's uh +um actually um + + align:start position:0% +um actually um + + + align:start position:0% +um actually um +um today I have to be particularly snow + + align:start position:0% +um today I have to be particularly snow + + + align:start position:0% +um today I have to be particularly snow +because the I have the much more grand + + align:start position:0% +because the I have the much more grand + + + align:start position:0% +because the I have the much more grand +plan for + + align:start position:0% +plan for + + + align:start position:0% +plan for +today um that also means that there's + + align:start position:0% +today um that also means that there's + + + align:start position:0% +today um that also means that there's +definitely you can only do the first two + + align:start position:0% +definitely you can only do the first two + + + align:start position:0% +definitely you can only do the first two +problem in your + + align:start position:0% +problem in your + + + align:start position:0% +problem in your +pet but only there's only four problem + + align:start position:0% +pet but only there's only four problem + + + align:start position:0% +pet but only there's only four problem +your pet but you can only do the first + + align:start position:0% +your pet but you can only do the first + + + align:start position:0% +your pet but you can only do the first +two so you want to submit the first + + align:start position:0% +two so you want to submit the first + + + align:start position:0% +two so you want to submit the first +two or you want to wait until next week + + align:start position:0% +two or you want to wait until next week + + + align:start position:0% +two or you want to wait until next week +to do it all together + + align:start position:0% + + + + align:start position:0% + +but if we if we do all together next + + align:start position:0% +but if we if we do all together next + + + align:start position:0% +but if we if we do all together next +week so po about the + + align:start position:0% +week so po about the + + + align:start position:0% +week so po about the +next yeah one week later + + align:start position:0% +next yeah one week later + + + align:start position:0% +next yeah one week later +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +H okay yeah yeah then let's maybe then + + align:start position:0% +H okay yeah yeah then let's maybe then + + + align:start position:0% +H okay yeah yeah then let's maybe then +let's just defer to one week next Friday + + align:start position:0% +let's just defer to one week next Friday + + + align:start position:0% +let's just defer to one week next Friday +yeah next Friday yeah next + + align:start position:0% +yeah next Friday yeah next + + + align:start position:0% +yeah next Friday yeah next +Friday + + align:start position:0% +Friday + + + align:start position:0% +Friday +um yeah then the next time so + + align:start position:0% +um yeah then the next time so + + + align:start position:0% +um yeah then the next time so +this in some conclude our basic + + align:start position:0% +this in some conclude our basic + + + align:start position:0% +this in some conclude our basic +discussion of the stream the all the + + align:start position:0% +discussion of the stream the all the + + + align:start position:0% +discussion of the stream the all the +essentially have seen the most of the + + align:start position:0% +essentially have seen the most of the + + + align:start position:0% +essentially have seen the most of the +Magics of stream Theory and uh uh even + + align:start position:0% +Magics of stream Theory and uh uh even + + + align:start position:0% +Magics of stream Theory and uh uh even +though it's very fast and + + align:start position:0% +though it's very fast and + + + align:start position:0% +though it's very fast and +uh uh so next time we will talk about de + + align:start position:0% +uh uh so next time we will talk about de + + + align:start position:0% +uh uh so next time we will talk about de +brains and which is + + align:start position:0% +brains and which is + + + align:start position:0% +brains and which is +a a lot of piece of magic from stream + + align:start position:0% +a a lot of piece of magic from stream + + + align:start position:0% +a a lot of piece of magic from stream +Ser yeah \ No newline at end of file diff --git a/XGyUFPCwlPI.txt b/XGyUFPCwlPI.txt new file mode 100644 index 0000000000000000000000000000000000000000..99f41c96d1b60c4e0dcdc35f01767356f066feb6 --- /dev/null +++ b/XGyUFPCwlPI.txt @@ -0,0 +1,8643 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +I'm just gonna go very quickly through + + align:start position:0% +I'm just gonna go very quickly through + + + align:start position:0% +I'm just gonna go very quickly through +the World Economic Forum I basically I + + align:start position:0% +the World Economic Forum I basically I + + + align:start position:0% +the World Economic Forum I basically I +only wanted you to all to glance at this + + align:start position:0% +only wanted you to all to glance at this + + + align:start position:0% +only wanted you to all to glance at this +and get an idea of it because what it's + + align:start position:0% +and get an idea of it because what it's + + + align:start position:0% +and get an idea of it because what it's +in here for is to show that you know + + align:start position:0% +in here for is to show that you know + + + align:start position:0% +in here for is to show that you know +we're not the only ones trying to think + + align:start position:0% +we're not the only ones trying to think + + + align:start position:0% +we're not the only ones trying to think +about innovation factors right they are + + align:start position:0% +about innovation factors right they are + + + align:start position:0% +about innovation factors right they are +trying to figure out what these factors + + align:start position:0% +trying to figure out what these factors + + + align:start position:0% +trying to figure out what these factors +are as they assess different national + + align:start position:0% +are as they assess different national + + + align:start position:0% +are as they assess different national +economies they have a whole compel + + align:start position:0% +economies they have a whole compel + + + align:start position:0% +economies they have a whole compel +competitiveness rating system which they + + align:start position:0% +competitiveness rating system which they + + + align:start position:0% +competitiveness rating system which they +get out every other year so in 2015 2016 + + align:start position:0% +get out every other year so in 2015 2016 + + + align:start position:0% +get out every other year so in 2015 2016 +as you saw Switzerland was number one + + align:start position:0% +as you saw Switzerland was number one + + + align:start position:0% +as you saw Switzerland was number one +Singapore number two in the US was + + align:start position:0% +Singapore number two in the US was + + + align:start position:0% +Singapore number two in the US was +number three in their rating and then + + align:start position:0% +number three in their rating and then + + + align:start position:0% +number three in their rating and then +they have a whole series of elements + + align:start position:0% +they have a whole series of elements + + + align:start position:0% +they have a whole series of elements +that they consider in their global + + align:start position:0% +that they consider in their global + + + align:start position:0% +that they consider in their global +competitiveness analysis so they look at + + align:start position:0% +competitiveness analysis so they look at + + + align:start position:0% +competitiveness analysis so they look at +what they call factor driven economies + + align:start position:0% +what they call factor driven economies + + + align:start position:0% +what they call factor driven economies +and the pillars there are institutions + + align:start position:0% +and the pillars there are institutions + + + align:start position:0% +and the pillars there are institutions +and infrastructure and macroeconomic + + align:start position:0% +and infrastructure and macroeconomic + + + align:start position:0% +and infrastructure and macroeconomic +environment and you know in in actually + + align:start position:0% +environment and you know in in actually + + + align:start position:0% +environment and you know in in actually +early stage education as a pillar and + + align:start position:0% +early stage education as a pillar and + + + align:start position:0% +early stage education as a pillar and +health and then efficiency driven + + align:start position:0% +health and then efficiency driven + + + align:start position:0% +health and then efficiency driven +economies they call them that's higher + + align:start position:0% +economies they call them that's higher + + + align:start position:0% +economies they call them that's higher +education that's market efficiency for + + align:start position:0% +education that's market efficiency for + + + align:start position:0% +education that's market efficiency for +goods that's labor market efficiency + + align:start position:0% +goods that's labor market efficiency + + + align:start position:0% +goods that's labor market efficiency +that's financial market developments + + align:start position:0% +that's financial market developments + + + align:start position:0% +that's financial market developments +technology readiness and so forth and + + align:start position:0% +technology readiness and so forth and + + + align:start position:0% +technology readiness and so forth and +then innovation driven economies + + align:start position:0% +then innovation driven economies + + + align:start position:0% +then innovation driven economies +business sophistication and innovation + + align:start position:0% +business sophistication and innovation + + + align:start position:0% +business sophistication and innovation +capability so they have a very different + + align:start position:0% +capability so they have a very different + + + align:start position:0% +capability so they have a very different +mix here I just wanted to throw in kind + + align:start position:0% +mix here I just wanted to throw in kind + + + align:start position:0% +mix here I just wanted to throw in kind +of a comparative way of other people + + align:start position:0% +of a comparative way of other people + + + align:start position:0% +of a comparative way of other people +looking at the problems that we're + + align:start position:0% +looking at the problems that we're + + + align:start position:0% +looking at the problems that we're +talking about and the kind of pillars + + align:start position:0% +talking about and the kind of pillars + + + align:start position:0% +talking about and the kind of pillars +that they come about and how they sort + + align:start position:0% +that they come about and how they sort + + + align:start position:0% +that they come about and how they sort +different kind of world economies and + + align:start position:0% +different kind of world economies and + + + align:start position:0% +different kind of world economies and +organize them but a lot of these factors + + align:start position:0% +organize them but a lot of these factors + + + align:start position:0% +organize them but a lot of these factors +we've just been we've just been talking + + align:start position:0% +we've just been we've just been talking + + + align:start position:0% +we've just been we've just been talking +about kind of the core I think of what + + align:start position:0% +about kind of the core I think of what + + + align:start position:0% +about kind of the core I think of what +to take what the takeaway is from from + + align:start position:0% +to take what the takeaway is from from + + + align:start position:0% +to take what the takeaway is from from +this study and let me get you also had + + align:start position:0% +this study and let me get you also had + + + align:start position:0% +this study and let me get you also had +Rycroft Lilly as well right so why don't + + align:start position:0% +Rycroft Lilly as well right so why don't + + + align:start position:0% +Rycroft Lilly as well right so why don't +I get Rycroft out on the table - that's + + align:start position:0% +I get Rycroft out on the table - that's + + + align:start position:0% +I get Rycroft out on the table - that's +Bob Rycroft and and cash they did this + + align:start position:0% +Bob Rycroft and and cash they did this + + + align:start position:0% +Bob Rycroft and and cash they did this +piece back in 1999 and I'm leading into + + align:start position:0% +piece back in 1999 and I'm leading into + + + align:start position:0% +piece back in 1999 and I'm leading into +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +how do you look at some of these more + + align:start position:0% +how do you look at some of these more + + + align:start position:0% +how do you look at some of these more +indirect innovation factors right + + align:start position:0% +indirect innovation factors right + + + align:start position:0% +indirect innovation factors right +because they + + align:start position:0% +because they + + + align:start position:0% +because they +they remain important and we're just + + align:start position:0% +they remain important and we're just + + + align:start position:0% +they remain important and we're just +gonna pick three right and you know + + align:start position:0% +gonna pick three right and you know + + + align:start position:0% +gonna pick three right and you know +they're looking at a kind of an element + + align:start position:0% +they're looking at a kind of an element + + + align:start position:0% +they're looking at a kind of an element +of innovation organization which i think + + align:start position:0% +of innovation organization which i think + + + align:start position:0% +of innovation organization which i think +is a core factor but they're talking + + align:start position:0% +is a core factor but they're talking + + + align:start position:0% +is a core factor but they're talking +about kind of a sub piece of it this + + align:start position:0% +about kind of a sub piece of it this + + + align:start position:0% +about kind of a sub piece of it this +kind of networking theory of innovation + + align:start position:0% +kind of networking theory of innovation + + + align:start position:0% +kind of networking theory of innovation +organization I think it's it's an + + align:start position:0% +organization I think it's it's an + + + align:start position:0% +organization I think it's it's an +intriguing piece they argue that we are + + align:start position:0% +intriguing piece they argue that we are + + + align:start position:0% +intriguing piece they argue that we are +now at a stage in the world economy that + + align:start position:0% +now at a stage in the world economy that + + + align:start position:0% +now at a stage in the world economy that +complex technologies drive the economy + + align:start position:0% +complex technologies drive the economy + + + align:start position:0% +complex technologies drive the economy +so with complex technologies the lone + + align:start position:0% +so with complex technologies the lone + + + align:start position:0% +so with complex technologies the lone +inventor and the garage working solo + + align:start position:0% +inventor and the garage working solo + + + align:start position:0% +inventor and the garage working solo +that's a myth that doesn't work anymore + + align:start position:0% +that's a myth that doesn't work anymore + + + align:start position:0% +that's a myth that doesn't work anymore +right because the context that lead to + + align:start position:0% +right because the context that lead to + + + align:start position:0% +right because the context that lead to +innovation are just too complex they + + align:start position:0% +innovation are just too complex they + + + align:start position:0% +innovation are just too complex they +argue so that means that the traditional + + align:start position:0% +argue so that means that the traditional + + + align:start position:0% +argue so that means that the traditional +focus of us technology policy on R&D at + + align:start position:0% +focus of us technology policy on R&D at + + + align:start position:0% +focus of us technology policy on R&D at +particular institutions and in open + + align:start position:0% +particular institutions and in open + + + align:start position:0% +particular institutions and in open +markets that's that's not only right + + align:start position:0% +markets that's that's not only right + + + align:start position:0% +markets that's that's not only right +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +they argue so they say that a much more + + align:start position:0% +they argue so they say that a much more + + + align:start position:0% +they argue so they say that a much more +self-conscious networked learning + + align:start position:0% +self-conscious networked learning + + + align:start position:0% +self-conscious networked learning +environment is actually key and what + + align:start position:0% +environment is actually key and what + + + align:start position:0% +environment is actually key and what +does that mean well complex technologies + + align:start position:0% +does that mean well complex technologies + + + align:start position:0% +does that mean well complex technologies +we know dominate world exports 82% of + + align:start position:0% +we know dominate world exports 82% of + + + align:start position:0% +we know dominate world exports 82% of +1995 compared to you know 43 percent in + + align:start position:0% +1995 compared to you know 43 percent in + + + align:start position:0% +1995 compared to you know 43 percent in +1970 the rise in complex products means + + align:start position:0% +1970 the rise in complex products means + + + align:start position:0% +1970 the rise in complex products means +a rise in complex organizational models + + align:start position:0% +a rise in complex organizational models + + + align:start position:0% +a rise in complex organizational models +that goes with it the number of + + align:start position:0% +that goes with it the number of + + + align:start position:0% +that goes with it the number of +corporate alliances corporate in + + align:start position:0% +corporate alliances corporate in + + + align:start position:0% +corporate alliances corporate in +relationships the connectedness of the + + align:start position:0% +relationships the connectedness of the + + + align:start position:0% +relationships the connectedness of the +actors becomes all that much more + + align:start position:0% +actors becomes all that much more + + + align:start position:0% +actors becomes all that much more +critical when the dominant products are + + align:start position:0% +critical when the dominant products are + + + align:start position:0% +critical when the dominant products are +complex technology-based so as product + + align:start position:0% +complex technology-based so as product + + + align:start position:0% +complex technology-based so as product +complexity grows the need for innovative + + align:start position:0% +complexity grows the need for innovative + + + align:start position:0% +complexity grows the need for innovative +networks grows and technological process + + align:start position:0% +networks grows and technological process + + + align:start position:0% +networks grows and technological process +progress in this phase really requires + + align:start position:0% +progress in this phase really requires + + + align:start position:0% +progress in this phase really requires +that network learning integrating and + + align:start position:0% +that network learning integrating and + + + align:start position:0% +that network learning integrating and +applying a whole wide variety of new + + align:start position:0% +applying a whole wide variety of new + + + align:start position:0% +applying a whole wide variety of new +science and technology knowledge and + + align:start position:0% +science and technology knowledge and + + + align:start position:0% +science and technology knowledge and +know-how that now becomes key gee-whiz + + align:start position:0% +know-how that now becomes key gee-whiz + + + align:start position:0% +know-how that now becomes key gee-whiz +you know we're not organized around that + + align:start position:0% +you know we're not organized around that + + + align:start position:0% +you know we're not organized around that +there + + align:start position:0% +there + + + align:start position:0% +there +these guys are right we've got an + + align:start position:0% +these guys are right we've got an + + + align:start position:0% +these guys are right we've got an +innovation system that's organized I'm + + align:start position:0% +innovation system that's organized I'm + + + align:start position:0% +innovation system that's organized I'm +on our much earlier idea of how + + align:start position:0% +on our much earlier idea of how + + + align:start position:0% +on our much earlier idea of how +technologies evolve it doesn't + + align:start position:0% +technologies evolve it doesn't + + + align:start position:0% +technologies evolve it doesn't +necessarily reflect the reality of the + + align:start position:0% +necessarily reflect the reality of the + + + align:start position:0% +necessarily reflect the reality of the +complexity and the fact that the + + align:start position:0% +complexity and the fact that the + + + align:start position:0% +complexity and the fact that the +complexity dries much more complex + + align:start position:0% +complexity dries much more complex + + + align:start position:0% +complexity dries much more complex +organizational system which includes + + align:start position:0% +organizational system which includes + + + align:start position:0% +organizational system which includes +networking they argue so they they cite + + align:start position:0% +networking they argue so they they cite + + + align:start position:0% +networking they argue so they they cite +George Brown who is a great former + + align:start position:0% +George Brown who is a great former + + + align:start position:0% +George Brown who is a great former +chairman of the House Science Committee + + align:start position:0% +chairman of the House Science Committee + + + align:start position:0% +chairman of the House Science Committee +on the point that neglects of the + + align:start position:0% +on the point that neglects of the + + + align:start position:0% +on the point that neglects of the +processes of knowledge and their + + align:start position:0% +processes of knowledge and their + + + align:start position:0% +processes of knowledge and their +diffusion and application needs to be a + + align:start position:0% +diffusion and application needs to be a + + + align:start position:0% +diffusion and application needs to be a +core concern of the innovation system + + align:start position:0% +core concern of the innovation system + + + align:start position:0% +core concern of the innovation system +and Brown is talking about particularly + + align:start position:0% +and Brown is talking about particularly + + + align:start position:0% +and Brown is talking about particularly +at the governmental level the + + align:start position:0% +at the governmental level the + + + align:start position:0% +at the governmental level the +governmental kind of role here there's + + align:start position:0% +governmental kind of role here there's + + + align:start position:0% +governmental kind of role here there's +new kinds of learning that need to take + + align:start position:0% +new kinds of learning that need to take + + + align:start position:0% +new kinds of learning that need to take +place and need to be organized around if + + align:start position:0% +place and need to be organized around if + + + align:start position:0% +place and need to be organized around if +you're going to have this kind of + + align:start position:0% +you're going to have this kind of + + + align:start position:0% +you're going to have this kind of +learning network system so a shared + + align:start position:0% +learning network system so a shared + + + align:start position:0% +learning network system so a shared +network learning which cuts across a + + align:start position:0% +network learning which cuts across a + + + align:start position:0% +network learning which cuts across a +series of institutions institutional + + align:start position:0% +series of institutions institutional + + + align:start position:0% +series of institutions institutional +engineering that brings in other parts + + align:start position:0% +engineering that brings in other parts + + + align:start position:0% +engineering that brings in other parts +of the systems like the regulatory side + + align:start position:0% +of the systems like the regulatory side + + + align:start position:0% +of the systems like the regulatory side +into the network there's got to be a + + align:start position:0% +into the network there's got to be a + + + align:start position:0% +into the network there's got to be a +whole evaluation and what they call Co + + align:start position:0% +whole evaluation and what they call Co + + + align:start position:0% +whole evaluation and what they call Co +evaluation between complex organizations + + align:start position:0% +evaluation between complex organizations + + + align:start position:0% +evaluation between complex organizations +and the technologies that they're + + align:start position:0% +and the technologies that they're + + + align:start position:0% +and the technologies that they're +developing so learning by doing learning + + align:start position:0% +developing so learning by doing learning + + + align:start position:0% +developing so learning by doing learning +by using learning from scientific and + + align:start position:0% +by using learning from scientific and + + + align:start position:0% +by using learning from scientific and +technology advances learning from + + align:start position:0% +technology advances learning from + + + align:start position:0% +technology advances learning from +spillover is learning from interaction + + align:start position:0% +spillover is learning from interaction + + + align:start position:0% +spillover is learning from interaction +they argue that these are whole new + + align:start position:0% +they argue that these are whole new + + + align:start position:0% +they argue that these are whole new +features of learning they need to occur + + align:start position:0% +features of learning they need to occur + + + align:start position:0% +features of learning they need to occur +that honestly accounted for our current + + align:start position:0% +that honestly accounted for our current + + + align:start position:0% +that honestly accounted for our current +learning systems so they need to be + + align:start position:0% +learning systems so they need to be + + + align:start position:0% +learning systems so they need to be +changed to really accommodate the kind + + align:start position:0% +changed to really accommodate the kind + + + align:start position:0% +changed to really accommodate the kind +of new realities of the way in which + + align:start position:0% +of new realities of the way in which + + + align:start position:0% +of new realities of the way in which +innovation is going to have to get + + align:start position:0% +innovation is going to have to get + + + align:start position:0% +innovation is going to have to get +organized + + align:start position:0% +organized + + + align:start position:0% +organized +so that's their that's their proposition + + align:start position:0% +so that's their that's their proposition + + + align:start position:0% +so that's their that's their proposition +I thought it was just kind of a fun read + + align:start position:0% +I thought it was just kind of a fun read + + + align:start position:0% +I thought it was just kind of a fun read +it tells us a little more about the + + align:start position:0% +it tells us a little more about the + + + align:start position:0% +it tells us a little more about the +determinism piece that we were talking + + align:start position:0% +determinism piece that we were talking + + + align:start position:0% +determinism piece that we were talking +about earlier complex technologies + + align:start position:0% +about earlier complex technologies + + + align:start position:0% +about earlier complex technologies +demand new organizational models and if + + align:start position:0% +demand new organizational models and if + + + align:start position:0% +demand new organizational models and if +Nelson is right innovation organization + + align:start position:0% +Nelson is right innovation organization + + + align:start position:0% +Nelson is right innovation organization +really amounts to a core direct + + align:start position:0% +really amounts to a core direct + + + align:start position:0% +really amounts to a core direct +innovation factor then you know stuff + + align:start position:0% +innovation factor then you know stuff + + + align:start position:0% +innovation factor then you know stuff +like what Rycroft and cash are proposing + + align:start position:0% +like what Rycroft and cash are proposing + + + align:start position:0% +like what Rycroft and cash are proposing +you know become significant + + align:start position:0% +you know become significant + + + align:start position:0% +you know become significant +Lily it's all yours that was yeah I'm + + align:start position:0% +Lily it's all yours that was yeah I'm + + + align:start position:0% +Lily it's all yours that was yeah I'm +gonna I'm gonna go high-speed for the + + align:start position:0% +gonna I'm gonna go high-speed for the + + + align:start position:0% +gonna I'm gonna go high-speed for the +rest of the class and actually in the + + align:start position:0% +rest of the class and actually in the + + + align:start position:0% +rest of the class and actually in the +United States we're experiencing the + + align:start position:0% +United States we're experiencing the + + + align:start position:0% +United States we're experiencing the +lowest unemployment rate since 2008 + + align:start position:0% +lowest unemployment rate since 2008 + + + align:start position:0% +lowest unemployment rate since 2008 +however little economies are projected + + align:start position:0% +however little economies are projected + + + align:start position:0% +however little economies are projected +slower and so that sort of brought me to + + align:start position:0% +slower and so that sort of brought me to + + + align:start position:0% +slower and so that sort of brought me to +a question there was a question for you + + align:start position:0% +a question there was a question for you + + + align:start position:0% +a question there was a question for you +as well which is why is it not enough or + + align:start position:0% +as well which is why is it not enough or + + + align:start position:0% +as well which is why is it not enough or +is it enough for growth rates to be + + align:start position:0% +is it enough for growth rates to be + + + align:start position:0% +is it enough for growth rates to be +positive and slow and steady + + align:start position:0% +positive and slow and steady + + + align:start position:0% +positive and slow and steady +so what's what is the magic thing that + + align:start position:0% +so what's what is the magic thing that + + + align:start position:0% +so what's what is the magic thing that +happens between a corporative about + + align:start position:0% +happens between a corporative about + + + align:start position:0% +happens between a corporative about +where we yeah run to and about three + + align:start position:0% +where we yeah run to and about three + + + align:start position:0% +where we yeah run to and about three +percent which seems to be more about an + + align:start position:0% +percent which seems to be more about an + + + align:start position:0% +percent which seems to be more about an +optimistic atmosphere and do we need to + + align:start position:0% +optimistic atmosphere and do we need to + + + align:start position:0% +optimistic atmosphere and do we need to +maybe host for the next 50 years post + + align:start position:0% +maybe host for the next 50 years post + + + align:start position:0% +maybe host for the next 50 years post +2008 crisis little building the economy + + align:start position:0% +2008 crisis little building the economy + + + align:start position:0% +2008 crisis little building the economy +struggling do we need to readjust + + align:start position:0% +struggling do we need to readjust + + + align:start position:0% +struggling do we need to readjust +ourselves to adapt we should be trying + + align:start position:0% +ourselves to adapt we should be trying + + + align:start position:0% +ourselves to adapt we should be trying +to push further and try to keep our + + align:start position:0% +to push further and try to keep our + + + align:start position:0% +to push further and try to keep our +growth when I was reading and I was I + + align:start position:0% +growth when I was reading and I was I + + + align:start position:0% +growth when I was reading and I was I +felt like well maybe that extremely high + + align:start position:0% +felt like well maybe that extremely high + + + align:start position:0% +felt like well maybe that extremely high +growth rate so at least from what I see + + align:start position:0% +growth rate so at least from what I see + + + align:start position:0% +growth rate so at least from what I see +maybe we should just + + align:start position:0% + + + + align:start position:0% + +so I kind of stay on that so let me take + + align:start position:0% +so I kind of stay on that so let me take + + + align:start position:0% +so I kind of stay on that so let me take +that on for a minute because if + + align:start position:0% +that on for a minute because if + + + align:start position:0% +that on for a minute because if +technological and related innovation is + + align:start position:0% +technological and related innovation is + + + align:start position:0% +technological and related innovation is +the dominant cause it affect your growth + + align:start position:0% +the dominant cause it affect your growth + + + align:start position:0% +the dominant cause it affect your growth +and your societal well-being depends + + align:start position:0% +and your societal well-being depends + + + align:start position:0% +and your societal well-being depends +upon your ability to have that growth + + align:start position:0% +upon your ability to have that growth + + + align:start position:0% +upon your ability to have that growth +and to spread that well bring across the + + align:start position:0% +and to spread that well bring across the + + + align:start position:0% +and to spread that well bring across the +society then if we're stuck at a one at + + align:start position:0% +society then if we're stuck at a one at + + + align:start position:0% +society then if we're stuck at a one at +a 1.8 two percent growth rate isn't that + + align:start position:0% +a 1.8 two percent growth rate isn't that + + + align:start position:0% +a 1.8 two percent growth rate isn't that +gonna be an enduring disruptive problem + + align:start position:0% +gonna be an enduring disruptive problem + + + align:start position:0% +gonna be an enduring disruptive problem +in the society are we gonna be a lot + + align:start position:0% +in the society are we gonna be a lot + + + align:start position:0% +in the society are we gonna be a lot +better off if we could push that up to + + align:start position:0% +better off if we could push that up to + + + align:start position:0% +better off if we could push that up to +three well if we've got a deep problem + + align:start position:0% +three well if we've got a deep problem + + + align:start position:0% +three well if we've got a deep problem +of economic income inequality at this + + align:start position:0% +of economic income inequality at this + + + align:start position:0% +of economic income inequality at this +point an economic growth rate helps a + + align:start position:0% +point an economic growth rate helps a + + + align:start position:0% +point an economic growth rate helps a +lot in dealing with that it's much more + + align:start position:0% +lot in dealing with that it's much more + + + align:start position:0% +lot in dealing with that it's much more +problematic to deal with that with a low + + align:start position:0% +problematic to deal with that with a low + + + align:start position:0% +problematic to deal with that with a low +growth rate for example so this kind of + + align:start position:0% +growth rate for example so this kind of + + + align:start position:0% +growth rate for example so this kind of +barbell effect that we've got in the + + align:start position:0% +barbell effect that we've got in the + + + align:start position:0% +barbell effect that we've got in the +Society of a growing up the middle class + + align:start position:0% +Society of a growing up the middle class + + + align:start position:0% +Society of a growing up the middle class +and then a thinning middle and a growing + + align:start position:0% +and then a thinning middle and a growing + + + align:start position:0% +and then a thinning middle and a growing +lower end services lower paid services + + align:start position:0% +lower end services lower paid services + + + align:start position:0% +lower end services lower paid services +sector which the middle is being pushed + + align:start position:0% +sector which the middle is being pushed + + + align:start position:0% +sector which the middle is being pushed +into it's a lot harder to fix that + + align:start position:0% +into it's a lot harder to fix that + + + align:start position:0% +into it's a lot harder to fix that +unless you've got a stronger growth rate + + align:start position:0% +unless you've got a stronger growth rate + + + align:start position:0% +unless you've got a stronger growth rate +I'd argue I understand your point how + + align:start position:0% +I'd argue I understand your point how + + + align:start position:0% +I'd argue I understand your point how +much stuff do we really need right you + + align:start position:0% +much stuff do we really need right you + + + align:start position:0% +much stuff do we really need right you +know how many things do we actually have + + align:start position:0% +know how many things do we actually have + + + align:start position:0% +know how many things do we actually have +to have right is there a whole new way + + align:start position:0% +to have right is there a whole new way + + + align:start position:0% +to have right is there a whole new way +of kind of organizing the society so + + align:start position:0% +of kind of organizing the society so + + + align:start position:0% +of kind of organizing the society so +you're making an interesting underlying + + align:start position:0% +you're making an interesting underlying + + + align:start position:0% +you're making an interesting underlying +point I think max + + align:start position:0% + + + + align:start position:0% + +um competitive Pisa we're supposed to be + + align:start position:0% +um competitive Pisa we're supposed to be + + + align:start position:0% +um competitive Pisa we're supposed to be +beating or you know other countries see + + align:start position:0% +beating or you know other countries see + + + align:start position:0% +beating or you know other countries see +ourselves leaders we're not the ones to + + align:start position:0% +ourselves leaders we're not the ones to + + + align:start position:0% +ourselves leaders we're not the ones to +do the discovery around in Turkey or + + align:start position:0% +do the discovery around in Turkey or + + + align:start position:0% +do the discovery around in Turkey or +whatever and the gains are substantial a + + align:start position:0% +whatever and the gains are substantial a + + + align:start position:0% +whatever and the gains are substantial a +first mover advantage is substantial but + + align:start position:0% +first mover advantage is substantial but + + + align:start position:0% +first mover advantage is substantial but +I guess I would say but it's a good + + align:start position:0% +I guess I would say but it's a good + + + align:start position:0% +I guess I would say but it's a good +question of like how much do you really + + align:start position:0% +question of like how much do you really + + + align:start position:0% +question of like how much do you really +need to consume perhaps it's not + + align:start position:0% +need to consume perhaps it's not + + + align:start position:0% +need to consume perhaps it's not +necessarily the 1.8 percent that's the + + align:start position:0% +necessarily the 1.8 percent that's the + + + align:start position:0% +necessarily the 1.8 percent that's the +problem it's the one-two punch of sort + + align:start position:0% +problem it's the one-two punch of sort + + + align:start position:0% +problem it's the one-two punch of sort +of the dot-com our our technological + + align:start position:0% +of the dot-com our our technological + + + align:start position:0% +of the dot-com our our technological +wave or bubble bursting and we ran + + align:start position:0% +wave or bubble bursting and we ran + + + align:start position:0% +wave or bubble bursting and we ran +immediately after that having also + + align:start position:0% +immediately after that having also + + + align:start position:0% +immediately after that having also +Francis that's compounded each other but + + align:start position:0% +Francis that's compounded each other but + + + align:start position:0% +Francis that's compounded each other but +one of your points from brought up + + align:start position:0% +one of your points from brought up + + + align:start position:0% +one of your points from brought up +another question if someone made and + + align:start position:0% +another question if someone made and + + + align:start position:0% +another question if someone made and +that is what do do we have we identify + + align:start position:0% +that is what do do we have we identify + + + align:start position:0% +that is what do do we have we identify +either + + align:start position:0% +either + + + align:start position:0% +either +within the United States or + + align:start position:0% +within the United States or + + + align:start position:0% +within the United States or +internationally what would be our next + + align:start position:0% +internationally what would be our next + + + align:start position:0% +internationally what would be our next +innovative wave and is it the same for + + align:start position:0% +innovative wave and is it the same for + + + align:start position:0% +innovative wave and is it the same for +the United States as as it is for the + + align:start position:0% +the United States as as it is for the + + + align:start position:0% +the United States as as it is for the +rest of the world or how we unite + + align:start position:0% +rest of the world or how we unite + + + align:start position:0% +rest of the world or how we unite +identified it early + + align:start position:0% + + + + align:start position:0% + +that's what I do + + align:start position:0% +that's what I do + + + align:start position:0% +that's what I do +the human genome project was over 10 + + align:start position:0% +the human genome project was over 10 + + + align:start position:0% +the human genome project was over 10 +years of cost but there's a lot like + + align:start position:0% + + + + align:start position:0% + +yeah you know something like for example + + align:start position:0% +yeah you know something like for example + + + align:start position:0% +yeah you know something like for example +the light bulb actually figured out the + + align:start position:0% +the light bulb actually figured out the + + + align:start position:0% +the light bulb actually figured out the +left + + align:start position:0% +left + + + align:start position:0% +left +it's a beautiful label but then on top + + align:start position:0% +it's a beautiful label but then on top + + + align:start position:0% +it's a beautiful label but then on top +of that there was only infrastructure + + align:start position:0% +of that there was only infrastructure + + + align:start position:0% +of that there was only infrastructure +and moving over a key that technology + + align:start position:0% +and moving over a key that technology + + + align:start position:0% +and moving over a key that technology +that really stole over so Lily why don't + + align:start position:0% +that really stole over so Lily why don't + + + align:start position:0% +that really stole over so Lily why don't +we go to rock Crofton cash I just want + + align:start position:0% +we go to rock Crofton cash I just want + + + align:start position:0% +we go to rock Crofton cash I just want +attention so one was how do you start + + align:start position:0% +attention so one was how do you start + + + align:start position:0% +attention so one was how do you start +the proper balance or can identify + + align:start position:0% +the proper balance or can identify + + + align:start position:0% +the proper balance or can identify +proper balance between encouraging + + align:start position:0% +proper balance between encouraging + + + align:start position:0% +proper balance between encouraging +competitive are indeed inside a single + + align:start position:0% +competitive are indeed inside a single + + + align:start position:0% +competitive are indeed inside a single +industry or field ending or encouraging + + align:start position:0% +industry or field ending or encouraging + + + align:start position:0% +industry or field ending or encouraging +this collective learning that for a + + align:start position:0% +this collective learning that for a + + + align:start position:0% +this collective learning that for a +carbon capture is so important and I + + align:start position:0% +carbon capture is so important and I + + + align:start position:0% +carbon capture is so important and I +also had so my question is is it + + align:start position:0% +also had so my question is is it + + + align:start position:0% +also had so my question is is it +possible to foster networking and shared + + align:start position:0% +possible to foster networking and shared + + + align:start position:0% +possible to foster networking and shared +learning while protecting the profits + + align:start position:0% +learning while protecting the profits + + + align:start position:0% +learning while protecting the profits +and patents + + align:start position:0% + + + + align:start position:0% + +so you don't see that biotech like IP + + align:start position:0% +so you don't see that biotech like IP + + + align:start position:0% +so you don't see that biotech like IP +battle over the Chris Berg nine + + align:start position:0% +battle over the Chris Berg nine + + + align:start position:0% +battle over the Chris Berg nine +technology that's huge because there's + + align:start position:0% +technology that's huge because there's + + + align:start position:0% +technology that's huge because there's +so many different companies like five or + + align:start position:0% +so many different companies like five or + + + align:start position:0% +so many different companies like five or +six being spawned out of these core + + align:start position:0% +six being spawned out of these core + + + align:start position:0% +six being spawned out of these core +ideas and these like IP technology is + + align:start position:0% +ideas and these like IP technology is + + + align:start position:0% +ideas and these like IP technology is +that their licensing from essentially + + align:start position:0% +that their licensing from essentially + + + align:start position:0% +that their licensing from essentially +two different entities and like whether + + align:start position:0% +two different entities and like whether + + + align:start position:0% +two different entities and like whether +whoever gets those price they have to + + align:start position:0% +whoever gets those price they have to + + + align:start position:0% +whoever gets those price they have to +pay me to so I think it makes sense like + + align:start position:0% +pay me to so I think it makes sense like + + + align:start position:0% +pay me to so I think it makes sense like +yeah for the how to share knowledge on a + + align:start position:0% +yeah for the how to share knowledge on a + + + align:start position:0% +yeah for the how to share knowledge on a +more mature level but for you know early + + align:start position:0% +more mature level but for you know early + + + align:start position:0% +more mature level but for you know early +technology the early companies it's hard + + align:start position:0% +technology the early companies it's hard + + + align:start position:0% +technology the early companies it's hard +to say because you know you're still + + align:start position:0% +to say because you know you're still + + + align:start position:0% +to say because you know you're still +trying to protect your market share + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +I'm Germany another just to add a point + + align:start position:0% +I'm Germany another just to add a point + + + align:start position:0% +I'm Germany another just to add a point +to this IP point that you all have been + + align:start position:0% +to this IP point that you all have been + + + align:start position:0% +to this IP point that you all have been +raising so in our panoply of direct and + + align:start position:0% +raising so in our panoply of direct and + + + align:start position:0% +raising so in our panoply of direct and +indirect innovation factors this whole + + align:start position:0% +indirect innovation factors this whole + + + align:start position:0% +indirect innovation factors this whole +world of intellectual property rights is + + align:start position:0% +world of intellectual property rights is + + + align:start position:0% +world of intellectual property rights is +indirect but we can all see how + + align:start position:0% +indirect but we can all see how + + + align:start position:0% +indirect but we can all see how +potentially significant it could be in + + align:start position:0% +potentially significant it could be in + + + align:start position:0% +potentially significant it could be in +other words it's not going to + + align:start position:0% +other words it's not going to + + + align:start position:0% +other words it's not going to +fundamentally affect your ability to + + align:start position:0% +fundamentally affect your ability to + + + align:start position:0% +fundamentally affect your ability to +undertake the innovation itself but it + + align:start position:0% +undertake the innovation itself but it + + + align:start position:0% +undertake the innovation itself but it +sure may affect your ability to realize + + align:start position:0% +sure may affect your ability to realize + + + align:start position:0% +sure may affect your ability to realize +gains off of it + + align:start position:0% + + + + align:start position:0% + +Oh guys a quick question about the + + align:start position:0% +Oh guys a quick question about the + + + align:start position:0% +Oh guys a quick question about the +dimensions of the advantage of a first + + align:start position:0% +dimensions of the advantage of a first + + + align:start position:0% +dimensions of the advantage of a first +and so in the Nelson you say that the + + align:start position:0% +and so in the Nelson you say that the + + + align:start position:0% +and so in the Nelson you say that the +first person necessarily yeah and I just + + align:start position:0% +first person necessarily yeah and I just + + + align:start position:0% +first person necessarily yeah and I just +me and do it in really something like + + align:start position:0% +me and do it in really something like + + + align:start position:0% +me and do it in really something like +energy where maybe the first person and + + align:start position:0% +energy where maybe the first person and + + + align:start position:0% +energy where maybe the first person and +you're setting up a bunch of urea plant + + align:start position:0% +you're setting up a bunch of urea plant + + + align:start position:0% +you're setting up a bunch of urea plant +and get stuck with outdated I man I + + align:start position:0% +and get stuck with outdated I man I + + + align:start position:0% +and get stuck with outdated I man I +agree with you I think the distinction + + align:start position:0% +agree with you I think the distinction + + + align:start position:0% +agree with you I think the distinction +here and I probably should have been + + align:start position:0% +here and I probably should have been + + + align:start position:0% +here and I probably should have been +more explicit but the first mover + + align:start position:0% +more explicit but the first mover + + + align:start position:0% +more explicit but the first mover +advantage in launching an innovation + + align:start position:0% +advantage in launching an innovation + + + align:start position:0% +advantage in launching an innovation +wave in other words a national or + + align:start position:0% +wave in other words a national or + + + align:start position:0% +wave in other words a national or +regional advantage for the benefit imme + + align:start position:0% +regional advantage for the benefit imme + + + align:start position:0% +regional advantage for the benefit imme +I think it's very real I think you know + + align:start position:0% +I think it's very real I think you know + + + align:start position:0% +I think it's very real I think you know +the point you made that the first mover + + align:start position:0% +the point you made that the first mover + + + align:start position:0% +the point you made that the first mover +advantage for a particular firm may be + + align:start position:0% +advantage for a particular firm may be + + + align:start position:0% +advantage for a particular firm may be +much more questionable others may see + + align:start position:0% +much more questionable others may see + + + align:start position:0% +much more questionable others may see +what they're doing and be able to make + + align:start position:0% +what they're doing and be able to make + + + align:start position:0% +what they're doing and be able to make +improvements and bring those out more + + align:start position:0% +improvements and bring those out more + + + align:start position:0% +improvements and bring those out more +rapidly than the initial firm it's kind + + align:start position:0% +rapidly than the initial firm it's kind + + + align:start position:0% +rapidly than the initial firm it's kind +of locked in to its initial approach and + + align:start position:0% +of locked in to its initial approach and + + + align:start position:0% +of locked in to its initial approach and +we see we see in many cases with new + + align:start position:0% +we see we see in many cases with new + + + align:start position:0% +we see we see in many cases with new +inventions that bring on innovation + + align:start position:0% +inventions that bring on innovation + + + align:start position:0% +inventions that bring on innovation +advances we can certainly see firms that + + align:start position:0% +advances we can certainly see firms that + + + align:start position:0% +advances we can certainly see firms that +have a first mover advantage we can also + + align:start position:0% +have a first mover advantage we can also + + + align:start position:0% +have a first mover advantage we can also +see second movers that are able to + + align:start position:0% +see second movers that are able to + + + align:start position:0% +see second movers that are able to +capture that so I think it's a more + + align:start position:0% +capture that so I think it's a more + + + align:start position:0% +capture that so I think it's a more +complex question at the company level + + align:start position:0% +complex question at the company level + + + align:start position:0% +complex question at the company level +but I think it's clearer at the regional + + align:start position:0% +but I think it's clearer at the regional + + + align:start position:0% +but I think it's clearer at the regional +economy national economy kind of level + + align:start position:0% +economy national economy kind of level + + + align:start position:0% +economy national economy kind of level +so I would argue that the US by building + + align:start position:0% +so I would argue that the US by building + + + align:start position:0% +so I would argue that the US by building +strong innovation capacity and its + + align:start position:0% +strong innovation capacity and its + + + align:start position:0% +strong innovation capacity and its +ability to lead most of the innovation + + align:start position:0% +ability to lead most of the innovation + + + align:start position:0% +ability to lead most of the innovation +waves of the second half of the 20th + + align:start position:0% +waves of the second half of the 20th + + + align:start position:0% +waves of the second half of the 20th +century that was a huge advantage that + + align:start position:0% +century that was a huge advantage that + + + align:start position:0% +century that was a huge advantage that +was a huge gain so no sooner did the + + align:start position:0% +was a huge gain so no sooner did the + + + align:start position:0% +was a huge gain so no sooner did the +u.s. miss the quality manufacturing wave + + align:start position:0% +u.s. miss the quality manufacturing wave + + + align:start position:0% +u.s. miss the quality manufacturing wave +to Japan seventies and eighties but it + + align:start position:0% +to Japan seventies and eighties but it + + + align:start position:0% +to Japan seventies and eighties but it +came right back with the IT innovation + + align:start position:0% +came right back with the IT innovation + + + align:start position:0% +came right back with the IT innovation +wave in the 90s which Japan missed so + + align:start position:0% +wave in the 90s which Japan missed so + + + align:start position:0% +wave in the 90s which Japan missed so +when you put your economy at the edge of + + align:start position:0% +when you put your economy at the edge of + + + align:start position:0% +when you put your economy at the edge of +the frontier right leadership of the + + align:start position:0% +the frontier right leadership of the + + + align:start position:0% +the frontier right leadership of the +frontier capturing those innovation ways + + align:start position:0% +frontier capturing those innovation ways + + + align:start position:0% +frontier capturing those innovation ways +becomes pretty important + + align:start position:0% + + + + align:start position:0% + +but I digress Lily why don't you give us + + align:start position:0% +but I digress Lily why don't you give us + + + align:start position:0% +but I digress Lily why don't you give us +a closing thought why don't you give us + + align:start position:0% +a closing thought why don't you give us + + + align:start position:0% +a closing thought why don't you give us +a closing thought on Rycroft in cash it + + align:start position:0% +a closing thought on Rycroft in cash it + + + align:start position:0% +a closing thought on Rycroft in cash it +was all this learning-by-doing was a + + align:start position:0% +was all this learning-by-doing was a + + + align:start position:0% +was all this learning-by-doing was a +little too squishy yeah right you need a + + align:start position:0% +little too squishy yeah right you need a + + + align:start position:0% +little too squishy yeah right you need a +more exact portrait got it okay well I + + align:start position:0% +more exact portrait got it okay well I + + + align:start position:0% +more exact portrait got it okay well I +think that's a valid critique all right + + align:start position:0% +think that's a valid critique all right + + + align:start position:0% +think that's a valid critique all right +so I'm gonna race through the next + + align:start position:0% +so I'm gonna race through the next + + + align:start position:0% +so I'm gonna race through the next +couple which Martina I think you've got + + align:start position:0% + + + + align:start position:0% + +this is Egil's mills burg and i'm not + + align:start position:0% +this is Egil's mills burg and i'm not + + + align:start position:0% +this is Egil's mills burg and i'm not +gonna spend a lot of time on it but + + align:start position:0% +gonna spend a lot of time on it but + + + align:start position:0% +gonna spend a lot of time on it but +again it's one of these indirect factors + + align:start position:0% +again it's one of these indirect factors + + + align:start position:0% +again it's one of these indirect factors +that turns out to you know have some + + align:start position:0% +that turns out to you know have some + + + align:start position:0% +that turns out to you know have some +significance here his point is the old + + align:start position:0% +significance here his point is the old + + + align:start position:0% +significance here his point is the old +economy was a world of tangible assets + + align:start position:0% +economy was a world of tangible assets + + + align:start position:0% +economy was a world of tangible assets +what counted were your plant your + + align:start position:0% +what counted were your plant your + + + align:start position:0% +what counted were your plant your +equipment your land your physical + + align:start position:0% +equipment your land your physical + + + align:start position:0% +equipment your land your physical +resources your product inventory your + + align:start position:0% +resources your product inventory your + + + align:start position:0% +resources your product inventory your +infrastructure support system physical + + align:start position:0% +infrastructure support system physical + + + align:start position:0% +infrastructure support system physical +stuff in the 21st century of a new + + align:start position:0% +stuff in the 21st century of a new + + + align:start position:0% +stuff in the 21st century of a new +economy intellectual and intangible + + align:start position:0% +economy intellectual and intangible + + + align:start position:0% +economy intellectual and intangible +assets those are key right so we have a + + align:start position:0% +assets those are key right so we have a + + + align:start position:0% +assets those are key right so we have a +wonderful 19th century accounting system + + align:start position:0% +wonderful 19th century accounting system + + + align:start position:0% +wonderful 19th century accounting system +it's really it's wonderful + + align:start position:0% +it's really it's wonderful + + + align:start position:0% +it's really it's wonderful +it can really value the old economy it + + align:start position:0% +it can really value the old economy it + + + align:start position:0% +it can really value the old economy it +really can value the new economy right + + align:start position:0% +really can value the new economy right + + + align:start position:0% +really can value the new economy right +and we we've been discussing this whole + + align:start position:0% +and we we've been discussing this whole + + + align:start position:0% +and we we've been discussing this whole +problem with the ability to get capital + + align:start position:0% +problem with the ability to get capital + + + align:start position:0% +problem with the ability to get capital +on the advances if you've got an + + align:start position:0% +on the advances if you've got an + + + align:start position:0% +on the advances if you've got an +accounting system that can't value true + + align:start position:0% +accounting system that can't value true + + + align:start position:0% +accounting system that can't value true +value in the new economy then of course + + align:start position:0% +value in the new economy then of course + + + align:start position:0% +value in the new economy then of course +you're gonna have a serious problem + + align:start position:0% +you're gonna have a serious problem + + + align:start position:0% +you're gonna have a serious problem +getting capital funding available right + + align:start position:0% +getting capital funding available right + + + align:start position:0% +getting capital funding available right +so here's an indirect thing you know the + + align:start position:0% +so here's an indirect thing you know the + + + align:start position:0% +so here's an indirect thing you know the +accounting system that turns out to have + + align:start position:0% +accounting system that turns out to have + + + align:start position:0% +accounting system that turns out to have +a fairly significant effect so the + + align:start position:0% +a fairly significant effect so the + + + align:start position:0% +a fairly significant effect so the +inability to measure intangible + + align:start position:0% +inability to measure intangible + + + align:start position:0% +inability to measure intangible +undermines the willingness of firms to + + align:start position:0% +undermines the willingness of firms to + + + align:start position:0% +undermines the willingness of firms to +invest in innovation because they can't + + align:start position:0% +invest in innovation because they can't + + + align:start position:0% +invest in innovation because they can't +really score it and get gains from it + + align:start position:0% +really score it and get gains from it + + + align:start position:0% +really score it and get gains from it +and it limits the investment flow into + + align:start position:0% +and it limits the investment flow into + + + align:start position:0% +and it limits the investment flow into +innovation as a result so any argues + + align:start position:0% +innovation as a result so any argues + + + align:start position:0% +innovation as a result so any argues +paints a picture of how this intangible + + align:start position:0% +paints a picture of how this intangible + + + align:start position:0% +paints a picture of how this intangible +process you know came about and arguing + + align:start position:0% +process you know came about and arguing + + + align:start position:0% +process you know came about and arguing +that by the late 90s there was a looking + + align:start position:0% +that by the late 90s there was a looking + + + align:start position:0% +that by the late 90s there was a looking +at the US economy overall that was about + + align:start position:0% +at the US economy overall that was about + + + align:start position:0% +at the US economy overall that was about +one point one trillion invest in + + align:start position:0% +one point one trillion invest in + + + align:start position:0% +one point one trillion invest in +intangible assets in the manufacturing + + align:start position:0% +intangible assets in the manufacturing + + + align:start position:0% +intangible assets in the manufacturing +sector in that same sector there was a + + align:start position:0% +sector in that same sector there was a + + + align:start position:0% +sector in that same sector there was a +trillion dollars in combined in R&D + + align:start position:0% +trillion dollars in combined in R&D + + + align:start position:0% +trillion dollars in combined in R&D +business processes and software more + + align:start position:0% +business processes and software more + + + align:start position:0% +business processes and software more +much more in tangible and intangible + + align:start position:0% +much more in tangible and intangible + + + align:start position:0% +much more in tangible and intangible +capital he argues became eighty-two + + align:start position:0% +capital he argues became eighty-two + + + align:start position:0% +capital he argues became eighty-two +percent of US firms market value just an + + align:start position:0% +percent of US firms market value just an + + + align:start position:0% +percent of US firms market value just an +overwhelming portion of their market + + align:start position:0% +overwhelming portion of their market + + + align:start position:0% +overwhelming portion of their market +value so we need new metrics for how + + align:start position:0% +value so we need new metrics for how + + + align:start position:0% +value so we need new metrics for how +firms invest in these qualitative + + align:start position:0% +firms invest in these qualitative + + + align:start position:0% +firms invest in these qualitative +innovation factors so that we can drive + + align:start position:0% +innovation factors so that we can drive + + + align:start position:0% +innovation factors so that we can drive +investment in efficient way into the + + align:start position:0% +investment in efficient way into the + + + align:start position:0% +investment in efficient way into the +right places and we just don't have them + + align:start position:0% +right places and we just don't have them + + + align:start position:0% +right places and we just don't have them +we only measure a couple of things we + + align:start position:0% +we only measure a couple of things we + + + align:start position:0% +we only measure a couple of things we +measure total company R&D investment + + align:start position:0% +measure total company R&D investment + + + align:start position:0% +measure total company R&D investment +that gets reported on you know quarterly + + align:start position:0% +that gets reported on you know quarterly + + + align:start position:0% +that gets reported on you know quarterly +reports and we get company patent + + align:start position:0% +reports and we get company patent + + + align:start position:0% +reports and we get company patent +filings that gets revealed as well but + + align:start position:0% +filings that gets revealed as well but + + + align:start position:0% +filings that gets revealed as well but +then all this other stuff and maybe + + align:start position:0% +then all this other stuff and maybe + + + align:start position:0% +then all this other stuff and maybe +these aren't the right factors maybe + + align:start position:0% +these aren't the right factors maybe + + + align:start position:0% +these aren't the right factors maybe +some number completely wrong but there's + + align:start position:0% +some number completely wrong but there's + + + align:start position:0% +some number completely wrong but there's +a whole set of other potential measures + + align:start position:0% +a whole set of other potential measures + + + align:start position:0% +a whole set of other potential measures +we don't even ask for right or even + + align:start position:0% +we don't even ask for right or even + + + align:start position:0% +we don't even ask for right or even +think about how they could be best + + align:start position:0% +think about how they could be best + + + align:start position:0% +think about how they could be best +organized so that's Eagles you know core + + align:start position:0% +organized so that's Eagles you know core + + + align:start position:0% +organized so that's Eagles you know core +idea here you know that's why you need + + align:start position:0% +idea here you know that's why you need + + + align:start position:0% +idea here you know that's why you need +to get some of these indirect innovation + + align:start position:0% +to get some of these indirect innovation + + + align:start position:0% +to get some of these indirect innovation +factors right along with the direct ones + + align:start position:0% +factors right along with the direct ones + + + align:start position:0% +factors right along with the direct ones +another example this was you know Judy + + align:start position:0% +another example this was you know Judy + + + align:start position:0% +another example this was you know Judy +Anne's Gupta's early book on venture + + align:start position:0% +Anne's Gupta's early book on venture + + + align:start position:0% +Anne's Gupta's early book on venture +capital right kind of an early history + + align:start position:0% +capital right kind of an early history + + + align:start position:0% +capital right kind of an early history +of venture capital came out in 2000 + + align:start position:0% +of venture capital came out in 2000 + + + align:start position:0% +of venture capital came out in 2000 +venture capital by 1999 had grown from + + align:start position:0% +venture capital by 1999 had grown from + + + align:start position:0% +venture capital by 1999 had grown from +three by going from three billion at the + + align:start position:0% +three by going from three billion at the + + + align:start position:0% +three by going from three billion at the +beginning of the decade to thirty + + align:start position:0% +beginning of the decade to thirty + + + align:start position:0% +beginning of the decade to thirty +billion now venture capital in 2015 was + + align:start position:0% +billion now venture capital in 2015 was + + + align:start position:0% +billion now venture capital in 2015 was +sixty billion + + align:start position:0% +sixty billion + + + align:start position:0% +sixty billion +okay so venture capital was built on the + + align:start position:0% +okay so venture capital was built on the + + + align:start position:0% +okay so venture capital was built on the +idea that introducing new technologies + + align:start position:0% +idea that introducing new technologies + + + align:start position:0% +idea that introducing new technologies +to live + + align:start position:0% +to live + + + align:start position:0% +to live +is much higher investor returns remember + + align:start position:0% +is much higher investor returns remember + + + align:start position:0% +is much higher investor returns remember +that chart that one of you cleverly + + align:start position:0% +that chart that one of you cleverly + + + align:start position:0% +that chart that one of you cleverly +asked me how many years it covered was + + align:start position:0% +asked me how many years it covered was + + + align:start position:0% +asked me how many years it covered was +that that was Martine you know this is + + align:start position:0% +that that was Martine you know this is + + + align:start position:0% +that that was Martine you know this is +he's saying the same thing in other + + align:start position:0% +he's saying the same thing in other + + + align:start position:0% +he's saying the same thing in other +words if you can capture the gains of + + align:start position:0% +words if you can capture the gains of + + + align:start position:0% +words if you can capture the gains of +radical investment they can be really + + align:start position:0% +radical investment they can be really + + + align:start position:0% +radical investment they can be really +big and that's what the venture capital + + align:start position:0% +big and that's what the venture capital + + + align:start position:0% +big and that's what the venture capital +sector is organized around and he notes + + align:start position:0% +sector is organized around and he notes + + + align:start position:0% +sector is organized around and he notes +this interesting history right so we're + + align:start position:0% +this interesting history right so we're + + + align:start position:0% +this interesting history right so we're +in one of the capitals of venture + + align:start position:0% +in one of the capitals of venture + + + align:start position:0% +in one of the capitals of venture +capital we're in the place that rigea + + align:start position:0% +capital we're in the place that rigea + + + align:start position:0% +capital we're in the place that rigea +nated it the east coast model originally + + align:start position:0% +nated it the east coast model originally + + + align:start position:0% +nated it the east coast model originally +was much more focused on what we would + + align:start position:0% +was much more focused on what we would + + + align:start position:0% +was much more focused on what we would +call today financial engineer you know + + align:start position:0% +call today financial engineer you know + + + align:start position:0% +call today financial engineer you know +tax benefits short-term returns that + + align:start position:0% +tax benefits short-term returns that + + + align:start position:0% +tax benefits short-term returns that +conceptual framework kind of dominated + + align:start position:0% +conceptual framework kind of dominated + + + align:start position:0% +conceptual framework kind of dominated +the early boston venture capital model + + align:start position:0% +the early boston venture capital model + + + align:start position:0% +the early boston venture capital model +the west coast developed a very + + align:start position:0% +the west coast developed a very + + + align:start position:0% +the west coast developed a very +different model around science and + + align:start position:0% +different model around science and + + + align:start position:0% +different model around science and +technology driven growth in places like + + align:start position:0% +technology driven growth in places like + + + align:start position:0% +technology driven growth in places like +Sandia Road in Silicon Valley it's still + + align:start position:0% +Sandia Road in Silicon Valley it's still + + + align:start position:0% +Sandia Road in Silicon Valley it's still +its capital so now those distinctions + + align:start position:0% +its capital so now those distinctions + + + align:start position:0% +its capital so now those distinctions +are pretty much disappeared both sides + + align:start position:0% +are pretty much disappeared both sides + + + align:start position:0% +are pretty much disappeared both sides +are on the same game and you include + + align:start position:0% +are on the same game and you include + + + align:start position:0% +are on the same game and you include +within the term of venture capital some + + align:start position:0% +within the term of venture capital some + + + align:start position:0% +within the term of venture capital some +people include a much broader + + align:start position:0% +people include a much broader + + + align:start position:0% +people include a much broader +phraseology including angel investors + + align:start position:0% +phraseology including angel investors + + + align:start position:0% +phraseology including angel investors +corporate and corporate venture firms + + align:start position:0% +corporate and corporate venture firms + + + align:start position:0% +corporate and corporate venture firms +foundation venture firms sometimes + + align:start position:0% +foundation venture firms sometimes + + + align:start position:0% +foundation venture firms sometimes +University endowment funds that go to + + align:start position:0% +University endowment funds that go to + + + align:start position:0% +University endowment funds that go to +them to a venture kind of purpose so + + align:start position:0% +them to a venture kind of purpose so + + + align:start position:0% +them to a venture kind of purpose so +it's a bigger landscape than it was you + + align:start position:0% +it's a bigger landscape than it was you + + + align:start position:0% +it's a bigger landscape than it was you +know at the early stages but the + + align:start position:0% +know at the early stages but the + + + align:start position:0% +know at the early stages but the +eastcoast model which did things like + + align:start position:0% +eastcoast model which did things like + + + align:start position:0% +eastcoast model which did things like +late stage buyouts turnarounds roll ups + + align:start position:0% +late stage buyouts turnarounds roll ups + + + align:start position:0% +late stage buyouts turnarounds roll ups +consolidations in addition to + + align:start position:0% +consolidations in addition to + + + align:start position:0% +consolidations in addition to +early-stage venture that's now prevalent + + align:start position:0% +early-stage venture that's now prevalent + + + align:start position:0% +early-stage venture that's now prevalent +frankly in both the East Coast and West + + align:start position:0% +frankly in both the East Coast and West + + + align:start position:0% +frankly in both the East Coast and West +Coast models so the two sides have kind + + align:start position:0% +Coast models so the two sides have kind + + + align:start position:0% +Coast models so the two sides have kind +of merged the originator of the venture + + align:start position:0% +of merged the originator of the venture + + + align:start position:0% +of merged the originator of the venture +capital idea was General George Daurio + + align:start position:0% +capital idea was General George Daurio + + + align:start position:0% +capital idea was General George Daurio +who was war ii general helped in the + + align:start position:0% +who was war ii general helped in the + + + align:start position:0% +who was war ii general helped in the +organization of industry in europe + + align:start position:0% +organization of industry in europe + + + align:start position:0% +organization of industry in europe +during what we're - and following it so + + align:start position:0% +during what we're - and following it so + + + align:start position:0% +during what we're - and following it so +a remarkable figure he taught at the + + align:start position:0% +a remarkable figure he taught at the + + + align:start position:0% +a remarkable figure he taught at the +Harvard Business School but he's the one + + align:start position:0% +Harvard Business School but he's the one + + + align:start position:0% +Harvard Business School but he's the one +who kind of saw this potential gain from + + align:start position:0% +who kind of saw this potential gain from + + + align:start position:0% +who kind of saw this potential gain from +innovation based growth and the West + + align:start position:0% +innovation based growth and the West + + + align:start position:0% +innovation based growth and the West +Coast model really was kind of a + + align:start position:0% +Coast model really was kind of a + + + align:start position:0% +Coast model really was kind of a +maverick model it was very high risk + + align:start position:0% +maverick model it was very high risk + + + align:start position:0% +maverick model it was very high risk +investment + + align:start position:0% +investment + + + align:start position:0% +investment +based on quite unproven technologies and + + align:start position:0% +based on quite unproven technologies and + + + align:start position:0% +based on quite unproven technologies and +that turned out to be the right model + + align:start position:0% +that turned out to be the right model + + + align:start position:0% +that turned out to be the right model +right the problem is we're not frankly + + align:start position:0% +right the problem is we're not frankly + + + align:start position:0% +right the problem is we're not frankly +doing enough of that in enough areas + + align:start position:0% +doing enough of that in enough areas + + + align:start position:0% +doing enough of that in enough areas +we'll get to that in another point of + + align:start position:0% +we'll get to that in another point of + + + align:start position:0% +we'll get to that in another point of +class so that's the venture capital + + align:start position:0% +class so that's the venture capital + + + align:start position:0% +class so that's the venture capital +story and let me just close and then + + align:start position:0% +story and let me just close and then + + + align:start position:0% +story and let me just close and then +we'll have some dialogue that Martine + + align:start position:0% +we'll have some dialogue that Martine + + + align:start position:0% +we'll have some dialogue that Martine +will lead this is Charles Schultz who + + align:start position:0% +will lead this is Charles Schultz who + + + align:start position:0% +will lead this is Charles Schultz who +was you know quite a famous economist he + + align:start position:0% +was you know quite a famous economist he + + + align:start position:0% +was you know quite a famous economist he +was budget director for Lyndon Johnson + + align:start position:0% +was budget director for Lyndon Johnson + + + align:start position:0% +was budget director for Lyndon Johnson +and he for Jimmy Carter who's head of + + align:start position:0% +and he for Jimmy Carter who's head of + + + align:start position:0% +and he for Jimmy Carter who's head of +the Council of Economic Advisers very + + align:start position:0% +the Council of Economic Advisers very + + + align:start position:0% +the Council of Economic Advisers very +highly thought of economist Minnesota + + align:start position:0% +highly thought of economist Minnesota + + + align:start position:0% +highly thought of economist Minnesota +deep historical role in governmental + + align:start position:0% +deep historical role in governmental + + + align:start position:0% +deep historical role in governmental +policy making he's taking a look at the + + align:start position:0% +policy making he's taking a look at the + + + align:start position:0% +policy making he's taking a look at the +debate which will actually get into in + + align:start position:0% +debate which will actually get into in + + + align:start position:0% +debate which will actually get into in +our next class about what's going on + + align:start position:0% +our next class about what's going on + + + align:start position:0% +our next class about what's going on +with Japan's economy of the 70s and 80s + + align:start position:0% +with Japan's economy of the 70s and 80s + + + align:start position:0% +with Japan's economy of the 70s and 80s +where they're bringing on this new + + align:start position:0% +where they're bringing on this new + + + align:start position:0% +where they're bringing on this new +innovation wave of quality manufacturing + + align:start position:0% +innovation wave of quality manufacturing + + + align:start position:0% +innovation wave of quality manufacturing +and the u.s. is trying to figure out how + + align:start position:0% +and the u.s. is trying to figure out how + + + align:start position:0% +and the u.s. is trying to figure out how +to respond right and he's talking about + + align:start position:0% +to respond right and he's talking about + + + align:start position:0% +to respond right and he's talking about +the political debate much as we were + + align:start position:0% +the political debate much as we were + + + align:start position:0% +the political debate much as we were +talking about the political debate + + align:start position:0% +talking about the political debate + + + align:start position:0% +talking about the political debate +that's going on now + + align:start position:0% +that's going on now + + + align:start position:0% +that's going on now +he was talking about the current + + align:start position:0% +he was talking about the current + + + align:start position:0% +he was talking about the current +political bait of that time right when + + align:start position:0% +political bait of that time right when + + + align:start position:0% +political bait of that time right when +he writes this in 1983 and there was a + + align:start position:0% +he writes this in 1983 and there was a + + + align:start position:0% +he writes this in 1983 and there was a +big debate over u.s. competitiveness + + align:start position:0% +big debate over u.s. competitiveness + + + align:start position:0% +big debate over u.s. competitiveness +there was a deep concern that the u.s. + + align:start position:0% +there was a deep concern that the u.s. + + + align:start position:0% +there was a deep concern that the u.s. +was guess what D industrializing sound + + align:start position:0% +was guess what D industrializing sound + + + align:start position:0% +was guess what D industrializing sound +familiar that essential US heavy + + align:start position:0% +familiar that essential US heavy + + + align:start position:0% +familiar that essential US heavy +industry was in decline and the 80s + + align:start position:0% +industry was in decline and the 80s + + + align:start position:0% +industry was in decline and the 80s +concern was that the US may have been at + + align:start position:0% +concern was that the US may have been at + + + align:start position:0% +concern was that the US may have been at +the cutting edge of technology advanced + + align:start position:0% +the cutting edge of technology advanced + + + align:start position:0% +the cutting edge of technology advanced +but it was not implementing those + + align:start position:0% +but it was not implementing those + + + align:start position:0% +but it was not implementing those +technology advances whereas by + + align:start position:0% +technology advances whereas by + + + align:start position:0% +technology advances whereas by +comparison the US perception of the time + + align:start position:0% +comparison the US perception of the time + + + align:start position:0% +comparison the US perception of the time +was that they had a very activist + + align:start position:0% +was that they had a very activist + + + align:start position:0% +was that they had a very activist +governmental kind of role an + + align:start position:0% +governmental kind of role an + + + align:start position:0% +governmental kind of role an +interventionist government a kind of + + align:start position:0% +interventionist government a kind of + + + align:start position:0% +interventionist government a kind of +role that's identifying technological + + align:start position:0% +role that's identifying technological + + + align:start position:0% +role that's identifying technological +winners and moving those right into + + align:start position:0% +winners and moving those right into + + + align:start position:0% +winners and moving those right into +implementation so in a way Martine it's + + align:start position:0% +implementation so in a way Martine it's + + + align:start position:0% +implementation so in a way Martine it's +like that the point you were raising + + align:start position:0% +like that the point you were raising + + + align:start position:0% +like that the point you were raising +earlier don't just do sculptures do + + align:start position:0% +earlier don't just do sculptures do + + + align:start position:0% +earlier don't just do sculptures do +buildings Japan was deep into the + + align:start position:0% +buildings Japan was deep into the + + + align:start position:0% +buildings Japan was deep into the +building phase the US was still at the + + align:start position:0% +building phase the US was still at the + + + align:start position:0% +building phase the US was still at the +sculpture phase so and it's its + + align:start position:0% +sculpture phase so and it's its + + + align:start position:0% +sculpture phase so and it's its +principle arm for doing this was meaty + + align:start position:0% +principle arm for doing this was meaty + + + align:start position:0% +principle arm for doing this was meaty +and which is now called MIT + + align:start position:0% +and which is now called MIT + + + align:start position:0% +and which is now called MIT +but still very prevalent but much less + + align:start position:0% +but still very prevalent but much less + + + align:start position:0% +but still very prevalent but much less +interventionist now than it was back or + + align:start position:0% +interventionist now than it was back or + + + align:start position:0% +interventionist now than it was back or +considerably less interventionist now + + align:start position:0% +considerably less interventionist now + + + align:start position:0% +considerably less interventionist now +than it was back in the 70s and 80s + + align:start position:0% +than it was back in the 70s and 80s + + + align:start position:0% +than it was back in the 70s and 80s +what proposals are the parties coming up + + align:start position:0% +what proposals are the parties coming up + + + align:start position:0% +what proposals are the parties coming up +with on how to deal with us well here's + + align:start position:0% +with on how to deal with us well here's + + + align:start position:0% +with on how to deal with us well here's +what the Democrats were up to they + + align:start position:0% +what the Democrats were up to they + + + align:start position:0% +what the Democrats were up to they +decided there shall be an Industrial + + align:start position:0% +decided there shall be an Industrial + + + align:start position:0% +decided there shall be an Industrial +Development Bank it would just like in + + align:start position:0% +Development Bank it would just like in + + + align:start position:0% +Development Bank it would just like in +Japan pick winners and heaven forbid it + + align:start position:0% +Japan pick winners and heaven forbid it + + + align:start position:0% +Japan pick winners and heaven forbid it +would protect losers right so no one + + align:start position:0% +would protect losers right so no one + + + align:start position:0% +would protect losers right so no one +would have to lose jobs will be + + align:start position:0% +would have to lose jobs will be + + + align:start position:0% +would have to lose jobs will be +protected and so forth and yet they + + align:start position:0% +protected and so forth and yet they + + + align:start position:0% +protected and so forth and yet they +would also select you know winning new + + align:start position:0% +would also select you know winning new + + + align:start position:0% +would also select you know winning new +areas to get investment and it would + + align:start position:0% +areas to get investment and it would + + + align:start position:0% +areas to get investment and it would +work to rehab failing major industries + + align:start position:0% +work to rehab failing major industries + + + align:start position:0% +work to rehab failing major industries +upgrade them protect their workforces + + align:start position:0% +upgrade them protect their workforces + + + align:start position:0% +upgrade them protect their workforces +but also attempt on working on a new + + align:start position:0% +but also attempt on working on a new + + + align:start position:0% +but also attempt on working on a new +labor agreement between management and + + align:start position:0% +labor agreement between management and + + + align:start position:0% +labor agreement between management and +labor to get labor cost cuts that would + + align:start position:0% +labor to get labor cost cuts that would + + + align:start position:0% +labor to get labor cost cuts that would +help fund the restoration of these + + align:start position:0% +help fund the restoration of these + + + align:start position:0% +help fund the restoration of these +sectors that was the Democrats idea + + align:start position:0% +sectors that was the Democrats idea + + + align:start position:0% +sectors that was the Democrats idea +right the Republican idea was to you + + align:start position:0% +right the Republican idea was to you + + + align:start position:0% +right the Republican idea was to you +guessed it support reductions in + + align:start position:0% +guessed it support reductions in + + + align:start position:0% +guessed it support reductions in +marginal tax rates right Schultz is very + + align:start position:0% +marginal tax rates right Schultz is very + + + align:start position:0% +marginal tax rates right Schultz is very +concerned about this idea his concern is + + align:start position:0% +concerned about this idea his concern is + + + align:start position:0% +concerned about this idea his concern is +that the US government is not able to + + align:start position:0% +that the US government is not able to + + + align:start position:0% +that the US government is not able to +select a winning industrial structure + + align:start position:0% +select a winning industrial structure + + + align:start position:0% +select a winning industrial structure +this is just not a good job for + + align:start position:0% +this is just not a good job for + + + align:start position:0% +this is just not a good job for +government to be doing it will not be + + align:start position:0% +government to be doing it will not be + + + align:start position:0% +government to be doing it will not be +good at this the regional politics the + + align:start position:0% +good at this the regional politics the + + + align:start position:0% +good at this the regional politics the +state politics are just so powerful that + + align:start position:0% +state politics are just so powerful that + + + align:start position:0% +state politics are just so powerful that +it's going to unglue the government's + + align:start position:0% +it's going to unglue the government's + + + align:start position:0% +it's going to unglue the government's +ability to kind of pick a winning + + align:start position:0% +ability to kind of pick a winning + + + align:start position:0% +ability to kind of pick a winning +technology sector and ride with it it's + + align:start position:0% +technology sector and ride with it it's + + + align:start position:0% +technology sector and ride with it it's +gonna have to be dispersed everybody's + + align:start position:0% +gonna have to be dispersed everybody's + + + align:start position:0% +gonna have to be dispersed everybody's +gonna have to have gains jobs are gonna + + align:start position:0% +gonna have to have gains jobs are gonna + + + align:start position:0% +gonna have to have gains jobs are gonna +have to be located all over the place + + align:start position:0% +have to be located all over the place + + + align:start position:0% +have to be located all over the place +just not something that's going to be + + align:start position:0% +just not something that's going to be + + + align:start position:0% +just not something that's going to be +supported well that the political system + + align:start position:0% +supported well that the political system + + + align:start position:0% +supported well that the political system +really cannot efficiently choose between + + align:start position:0% +really cannot efficiently choose between + + + align:start position:0% +really cannot efficiently choose between +individual firms and particular regions + + align:start position:0% +individual firms and particular regions + + + align:start position:0% +individual firms and particular regions +for getting support at this stage of the + + align:start position:0% +for getting support at this stage of the + + + align:start position:0% +for getting support at this stage of the +industrial process so find a support Rd + + align:start position:0% +industrial process so find a support Rd + + + align:start position:0% +industrial process so find a support Rd +but when it comes closer much further + + align:start position:0% +but when it comes closer much further + + + align:start position:0% +but when it comes closer much further +down the pipeline and you're actually + + align:start position:0% +down the pipeline and you're actually + + + align:start position:0% +down the pipeline and you're actually +picking industrial winners that's a + + align:start position:0% +picking industrial winners that's a + + + align:start position:0% +picking industrial winners that's a +really tricky political + + align:start position:0% +really tricky political + + + align:start position:0% +really tricky political +he warns us about so a lot of this class + + align:start position:0% +he warns us about so a lot of this class + + + align:start position:0% +he warns us about so a lot of this class +is you all were driving us towards today + + align:start position:0% +is you all were driving us towards today + + + align:start position:0% +is you all were driving us towards today +is going to be what is the governmental + + align:start position:0% +is going to be what is the governmental + + + align:start position:0% +is going to be what is the governmental +role right so Schultz stands as a + + align:start position:0% +role right so Schultz stands as a + + + align:start position:0% +role right so Schultz stands as a +warning about the political + + align:start position:0% +warning about the political + + + align:start position:0% +warning about the political +imperfections of government the + + align:start position:0% +imperfections of government the + + + align:start position:0% +imperfections of government the +political difficulties of government in + + align:start position:0% +political difficulties of government in + + + align:start position:0% +political difficulties of government in +undertaking an interventionist role so + + align:start position:0% +undertaking an interventionist role so + + + align:start position:0% +undertaking an interventionist role so +it's I think that's probably a pretty + + align:start position:0% +it's I think that's probably a pretty + + + align:start position:0% +it's I think that's probably a pretty +good son we all skipped the rest of + + align:start position:0% +good son we all skipped the rest of + + + align:start position:0% +good son we all skipped the rest of +Schultz but that's that's really his + + align:start position:0% +Schultz but that's that's really his + + + align:start position:0% +Schultz but that's that's really his +core idea is to tell us a cautionary + + align:start position:0% +core idea is to tell us a cautionary + + + align:start position:0% +core idea is to tell us a cautionary +tale about what the government of role + + align:start position:0% +tale about what the government of role + + + align:start position:0% +tale about what the government of role +is gonna be that the sheer massive + + align:start position:0% +is gonna be that the sheer massive + + + align:start position:0% +is gonna be that the sheer massive +weight of politics is not going to + + align:start position:0% +weight of politics is not going to + + + align:start position:0% +weight of politics is not going to +necessarily drive optimal technology + + align:start position:0% +necessarily drive optimal technology + + + align:start position:0% +necessarily drive optimal technology +decision making now Martine let me turn + + align:start position:0% +decision making now Martine let me turn + + + align:start position:0% +decision making now Martine let me turn +it over to you and let's go through + + align:start position:0% +it over to you and let's go through + + + align:start position:0% +it over to you and let's go through +these three + + align:start position:0% +these three + + + align:start position:0% +these three +so first Eagles and then maybe do a + + align:start position:0% +so first Eagles and then maybe do a + + + align:start position:0% +so first Eagles and then maybe do a +couple of questions on that and say some + + align:start position:0% +couple of questions on that and say some + + + align:start position:0% +couple of questions on that and say some +points and then let's do gupti on the + + align:start position:0% +points and then let's do gupti on the + + + align:start position:0% +points and then let's do gupti on the +venture capital structure yeah let's + + align:start position:0% +venture capital structure yeah let's + + + align:start position:0% +venture capital structure yeah let's +let's have an overview and you know and + + align:start position:0% +let's have an overview and you know and + + + align:start position:0% +let's have an overview and you know and +we'll start with Mills Berg's and then + + align:start position:0% +we'll start with Mills Berg's and then + + + align:start position:0% +we'll start with Mills Berg's and then +go into a couple of questions most + + align:start position:0% +go into a couple of questions most + + + align:start position:0% +go into a couple of questions most +likely will determine the long term + + align:start position:0% +likely will determine the long term + + + align:start position:0% +likely will determine the long term +company most likely the company so these + + align:start position:0% +company most likely the company so these + + + align:start position:0% +company most likely the company so these +long term innovations on these things + + align:start position:0% +long term innovations on these things + + + align:start position:0% +long term innovations on these things +that are hard to measure and so couple + + align:start position:0% +that are hard to measure and so couple + + + align:start position:0% +that are hard to measure and so couple +questions + + align:start position:0% +questions + + + align:start position:0% +questions +that were left up order what innovation + + align:start position:0% +that were left up order what innovation + + + align:start position:0% +that were left up order what innovation +trends in sectors represent the most + + align:start position:0% +trends in sectors represent the most + + + align:start position:0% +trends in sectors represent the most +promising growth areas for DC next what + + align:start position:0% +promising growth areas for DC next what + + + align:start position:0% +promising growth areas for DC next what +can intensify the shift to long-term + + align:start position:0% +can intensify the shift to long-term + + + align:start position:0% +can intensify the shift to long-term +intrinsic value for short-term + + align:start position:0% +intrinsic value for short-term + + + align:start position:0% +intrinsic value for short-term +objectives + + align:start position:0% + + + + align:start position:0% + +is anybody also like if anybody has any + + align:start position:0% + + + + align:start position:0% + +think about particularly the old + + align:start position:0% +think about particularly the old + + + align:start position:0% +think about particularly the old +accounting system which is kind of I + + align:start position:0% +accounting system which is kind of I + + + align:start position:0% +accounting system which is kind of I +think I've been easy I guess it wasn't + + align:start position:0% + + + + align:start position:0% + +doing it but I think particularly I + + align:start position:0% + + + + align:start position:0% + +don't know Management Studies or kind of + + align:start position:0% +don't know Management Studies or kind of + + + align:start position:0% +don't know Management Studies or kind of +behavioral things that we can take a + + align:start position:0% +behavioral things that we can take a + + + align:start position:0% +behavioral things that we can take a +look at how these intentional seem like + + align:start position:0% +look at how these intentional seem like + + + align:start position:0% +look at how these intentional seem like +something like you know when you see it + + align:start position:0% + + + + align:start position:0% + +and so I don't know if there have been + + align:start position:0% +and so I don't know if there have been + + + align:start position:0% +and so I don't know if there have been +any efforts sustained or even accepted + + align:start position:0% +any efforts sustained or even accepted + + + align:start position:0% +any efforts sustained or even accepted +argued over to like start valuing these + + align:start position:0% +argued over to like start valuing these + + + align:start position:0% +argued over to like start valuing these +intangible things so rushing a very + + align:start position:0% +intangible things so rushing a very + + + align:start position:0% +intangible things so rushing a very +interesting point and there's been a + + align:start position:0% +interesting point and there's been a + + + align:start position:0% +interesting point and there's been a +significant amount of work in Britain + + align:start position:0% +significant amount of work in Britain + + + align:start position:0% +significant amount of work in Britain +actually to try and figure out + + align:start position:0% +actually to try and figure out + + + align:start position:0% +actually to try and figure out +measurement systems for these + + align:start position:0% +measurement systems for these + + + align:start position:0% +measurement systems for these +intangibles these kind of know-how based + + align:start position:0% +intangibles these kind of know-how based + + + align:start position:0% +intangibles these kind of know-how based +assets and then following from that work + + align:start position:0% +assets and then following from that work + + + align:start position:0% +assets and then following from that work +and the EU on trying to measure these + + align:start position:0% +and the EU on trying to measure these + + + align:start position:0% +and the EU on trying to measure these +interestingly we really haven't done + + align:start position:0% +interestingly we really haven't done + + + align:start position:0% +interestingly we really haven't done +much in the US on this as crucial as it + + align:start position:0% +much in the US on this as crucial as it + + + align:start position:0% +much in the US on this as crucial as it +is I think it's really important to have + + align:start position:0% +is I think it's really important to have + + + align:start position:0% +is I think it's really important to have +some sort of standardized way to measure + + align:start position:0% +some sort of standardized way to measure + + + align:start position:0% +some sort of standardized way to measure +this because otherwise it all comes down + + align:start position:0% +this because otherwise it all comes down + + + align:start position:0% +this because otherwise it all comes down +to like trust between companies and + + align:start position:0% +to like trust between companies and + + + align:start position:0% +to like trust between companies and +inventors and investors and companies + + align:start position:0% +inventors and investors and companies + + + align:start position:0% +inventors and investors and companies +will always have an incentive to oversee + + align:start position:0% +will always have an incentive to oversee + + + align:start position:0% +will always have an incentive to oversee +what their intangible assets are and + + align:start position:0% +what their intangible assets are and + + + align:start position:0% +what their intangible assets are and +in order to prove what whether they're + + align:start position:0% +in order to prove what whether they're + + + align:start position:0% +in order to prove what whether they're +being honest or not so there needs some + + align:start position:0% +being honest or not so there needs some + + + align:start position:0% +being honest or not so there needs some +sort of standardization process other + + align:start position:0% +sort of standardization process other + + + align:start position:0% +sort of standardization process other +and my clearly investing standpoint + + align:start position:0% +and my clearly investing standpoint + + + align:start position:0% +and my clearly investing standpoint +isn't the fact that like value valuing + + align:start position:0% +isn't the fact that like value valuing + + + align:start position:0% +isn't the fact that like value valuing +like intangibles and things like IP main + + align:start position:0% +like intangibles and things like IP main + + + align:start position:0% +like intangibles and things like IP main +reason why there could be like hidden + + align:start position:0% +reason why there could be like hidden + + + align:start position:0% +reason why there could be like hidden +values or kind of this pricing based on + + align:start position:0% +values or kind of this pricing based on + + + align:start position:0% +values or kind of this pricing based on +because not everyone has a good idea of + + align:start position:0% +because not everyone has a good idea of + + + align:start position:0% +because not everyone has a good idea of +these things that's how they can find + + align:start position:0% +these things that's how they can find + + + align:start position:0% +these things that's how they can find +it's sort of an edge based off like + + align:start position:0% +it's sort of an edge based off like + + + align:start position:0% +it's sort of an edge based off like +other companies that might not have to + + align:start position:0% +other companies that might not have to + + + align:start position:0% +other companies that might not have to +sink inside I feel like that might be + + align:start position:0% +sink inside I feel like that might be + + + align:start position:0% +sink inside I feel like that might be +one of the reasons why there hasn't been + + align:start position:0% +one of the reasons why there hasn't been + + + align:start position:0% +one of the reasons why there hasn't been +a push to kind of I don't know + + align:start position:0% +a push to kind of I don't know + + + align:start position:0% +a push to kind of I don't know +standardize how do you want to find + + align:start position:0% +standardize how do you want to find + + + align:start position:0% +standardize how do you want to find +those not only because especially like I + + align:start position:0% +those not only because especially like I + + + align:start position:0% +those not only because especially like I +think he brought up like customer + + align:start position:0% +think he brought up like customer + + + align:start position:0% +think he brought up like customer +satisfaction I do like really hard to be + + align:start position:0% +satisfaction I do like really hard to be + + + align:start position:0% +satisfaction I do like really hard to be +around a way to come up with a metric to + + align:start position:0% +around a way to come up with a metric to + + + align:start position:0% +around a way to come up with a metric to +say I feel like it'd be difficult but + + align:start position:0% +say I feel like it'd be difficult but + + + align:start position:0% +say I feel like it'd be difficult but +interesting that's also curious whether + + align:start position:0% +interesting that's also curious whether + + + align:start position:0% +interesting that's also curious whether +he's talking about a system that's + + align:start position:0% +he's talking about a system that's + + + align:start position:0% +he's talking about a system that's +applicable to companies of different + + align:start position:0% +applicable to companies of different + + + align:start position:0% +applicable to companies of different +industries they're just companies within + + align:start position:0% +industries they're just companies within + + + align:start position:0% +industries they're just companies within +like the same industry like are you + + align:start position:0% +like the same industry like are you + + + align:start position:0% +like the same industry like are you +looking at Dropbox and box or are you + + align:start position:0% +looking at Dropbox and box or are you + + + align:start position:0% +looking at Dropbox and box or are you +looking at like Dropbox and Facebook + + align:start position:0% +looking at like Dropbox and Facebook + + + align:start position:0% +looking at like Dropbox and Facebook +like should you can you actually prepare + + align:start position:0% +like should you can you actually prepare + + + align:start position:0% +like should you can you actually prepare +like a cross that was even like the same + + align:start position:0% +like a cross that was even like the same + + + align:start position:0% +like a cross that was even like the same +industry but across like applications + + align:start position:0% +industry but across like applications + + + align:start position:0% +industry but across like applications +then interesting question to that is why + + align:start position:0% +then interesting question to that is why + + + align:start position:0% +then interesting question to that is why +are we treating intellectual property + + align:start position:0% +are we treating intellectual property + + + align:start position:0% +are we treating intellectual property +for different industries the same and so + + align:start position:0% +for different industries the same and so + + + align:start position:0% +for different industries the same and so +why is it is really high tea + + align:start position:0% +why is it is really high tea + + + align:start position:0% +why is it is really high tea +like for a Facebook was very quick to + + align:start position:0% +like for a Facebook was very quick to + + + align:start position:0% +like for a Facebook was very quick to +capture value relatively to other + + align:start position:0% +capture value relatively to other + + + align:start position:0% +capture value relatively to other +industries versus like energy where they + + align:start position:0% +industries versus like energy where they + + + align:start position:0% +industries versus like energy where they +might take you years and years and then + + align:start position:0% +might take you years and years and then + + + align:start position:0% +might take you years and years and then +even to execute twenty years is a short + + align:start position:0% +even to execute twenty years is a short + + + align:start position:0% +even to execute twenty years is a short +timeframe because it might take you ten + + align:start position:0% +timeframe because it might take you ten + + + align:start position:0% +timeframe because it might take you ten +years so at times you kind of get + + align:start position:0% +years so at times you kind of get + + + align:start position:0% +years so at times you kind of get +started that's + + align:start position:0% + + + + align:start position:0% + +so maybe really biotech + + align:start position:0% + + + + align:start position:0% + +why aren't there longer intellectual + + align:start position:0% +why aren't there longer intellectual + + + align:start position:0% +why aren't there longer intellectual +property cycles for those districts + + align:start position:0% + + + + align:start position:0% + +so I mean in 20 years these general + + align:start position:0% +so I mean in 20 years these general + + + align:start position:0% +so I mean in 20 years these general +general remark but there is a pharmacy + + align:start position:0% +general remark but there is a pharmacy + + + align:start position:0% +general remark but there is a pharmacy +to go there Pam laws that will extend + + align:start position:0% +to go there Pam laws that will extend + + + align:start position:0% +to go there Pam laws that will extend +the life have either had to compensate + + align:start position:0% + + + + align:start position:0% + +when we talk about when we do a class on + + align:start position:0% +when we talk about when we do a class on + + + align:start position:0% +when we talk about when we do a class on +the life science health science kind of + + align:start position:0% +the life science health science kind of + + + align:start position:0% +the life science health science kind of +case study will get a lot will get + + align:start position:0% +case study will get a lot will get + + + align:start position:0% +case study will get a lot will get +deeply into this whole question about + + align:start position:0% +deeply into this whole question about + + + align:start position:0% +deeply into this whole question about +patent term and could you start to very + + align:start position:0% +patent term and could you start to very + + + align:start position:0% +patent term and could you start to very +patent term and to encourage small + + align:start position:0% +patent term and to encourage small + + + align:start position:0% +patent term and to encourage small +market drugs third world disease drugs + + align:start position:0% +market drugs third world disease drugs + + + align:start position:0% +market drugs third world disease drugs +which wouldn't ordinarily come about + + align:start position:0% +which wouldn't ordinarily come about + + + align:start position:0% +which wouldn't ordinarily come about +through the system where you're right + + align:start position:0% +through the system where you're right + + + align:start position:0% +through the system where you're right +martine we've got to capture a billion + + align:start position:0% +martine we've got to capture a billion + + + align:start position:0% +martine we've got to capture a billion +eight just in upfront in order to bring + + align:start position:0% +eight just in upfront in order to bring + + + align:start position:0% +eight just in upfront in order to bring +a drug to market + + align:start position:0% + + + + align:start position:0% + +sure and he had all these brilliant + + align:start position:0% +sure and he had all these brilliant + + + align:start position:0% +sure and he had all these brilliant +people who are the best in the nation + + align:start position:0% +people who are the best in the nation + + + align:start position:0% +people who are the best in the nation +and the old case work for him but he's a + + align:start position:0% +and the old case work for him but he's a + + + align:start position:0% +and the old case work for him but he's a +bad boss that all these great minds are + + align:start position:0% +bad boss that all these great minds are + + + align:start position:0% +bad boss that all these great minds are +under stress working for him so they + + align:start position:0% +under stress working for him so they + + + align:start position:0% +under stress working for him so they +there's called the traders eight be + + align:start position:0% +there's called the traders eight be + + + align:start position:0% +there's called the traders eight be +chose to leave him and goes and start + + align:start position:0% +chose to leave him and goes and start + + + align:start position:0% +chose to leave him and goes and start +their own company will be needed they + + align:start position:0% +their own company will be needed they + + + align:start position:0% +their own company will be needed they +wrote a letter to the sky called arthur + + align:start position:0% +wrote a letter to the sky called arthur + + + align:start position:0% +wrote a letter to the sky called arthur +la roque who's a Wall Street financier + + align:start position:0% +la roque who's a Wall Street financier + + + align:start position:0% +la roque who's a Wall Street financier +and they asked him that if he could get + + align:start position:0% +and they asked him that if he could get + + + align:start position:0% +and they asked him that if he could get +some thought to create their own company + + align:start position:0% +some thought to create their own company + + + align:start position:0% +some thought to create their own company +and they have this strong IP and the + + align:start position:0% +and they have this strong IP and the + + + align:start position:0% +and they have this strong IP and the +strong knowledge that the industry and + + align:start position:0% +strong knowledge that the industry and + + + align:start position:0% +strong knowledge that the industry and +the original without of those would get + + align:start position:0% +the original without of those would get + + + align:start position:0% +the original without of those would get +into a venture capital it really didn't + + align:start position:0% +into a venture capital it really didn't + + + align:start position:0% +into a venture capital it really didn't +speed up until the ninety + + align:start position:0% +speed up until the ninety + + + align:start position:0% +speed up until the ninety +revolution because originally venture + + align:start position:0% +revolution because originally venture + + + align:start position:0% +revolution because originally venture +capital was very much a longhorn cattle + + align:start position:0% +capital was very much a longhorn cattle + + + align:start position:0% +capital was very much a longhorn cattle +what happened is that you would invest + + align:start position:0% +what happened is that you would invest + + + align:start position:0% +what happened is that you would invest +money and we expected it to they really + + align:start position:0% +money and we expected it to they really + + + align:start position:0% +money and we expected it to they really +get a core capability they are able to + + align:start position:0% +get a core capability they are able to + + + align:start position:0% +get a core capability they are able to +reap profits for a long period of time + + align:start position:0% +reap profits for a long period of time + + + align:start position:0% +reap profits for a long period of time +will that change when the it can be a + + align:start position:0% +will that change when the it can be a + + + align:start position:0% +will that change when the it can be a +fast way of making a return and so + + align:start position:0% +fast way of making a return and so + + + align:start position:0% +fast way of making a return and so +adventure telephone become a lot like + + align:start position:0% +adventure telephone become a lot like + + + align:start position:0% +adventure telephone become a lot like +hedge funds took a lot more racing so + + align:start position:0% +hedge funds took a lot more racing so + + + align:start position:0% +hedge funds took a lot more racing so +pretty much the way a VC firm runs is + + align:start position:0% +pretty much the way a VC firm runs is + + + align:start position:0% +pretty much the way a VC firm runs is +they'll mate they they land around ten + + align:start position:0% +they'll mate they they land around ten + + + align:start position:0% +they'll mate they they land around ten +years the way they work is that they + + align:start position:0% +years the way they work is that they + + + align:start position:0% +years the way they work is that they +they focus on outliers and winning with + + align:start position:0% +they focus on outliers and winning with + + + align:start position:0% +they focus on outliers and winning with +outliers so pretty much each of us about + + align:start position:0% +outliers so pretty much each of us about + + + align:start position:0% +outliers so pretty much each of us about +I mean like whoa I'm just so they'll + + align:start position:0% +I mean like whoa I'm just so they'll + + + align:start position:0% +I mean like whoa I'm just so they'll +give us each legacy round but they only + + align:start position:0% +give us each legacy round but they only + + + align:start position:0% +give us each legacy round but they only +expect to have us to really become with + + align:start position:0% +expect to have us to really become with + + + align:start position:0% +expect to have us to really become with +a face book and they know that every + + align:start position:0% +a face book and they know that every + + + align:start position:0% +a face book and they know that every +single year there's probably only like + + align:start position:0% +single year there's probably only like + + + align:start position:0% +single year there's probably only like +ten combinations and they focus on these + + align:start position:0% +ten combinations and they focus on these + + + align:start position:0% +ten combinations and they focus on these +multiple hi patty Richards if you make + + align:start position:0% +multiple hi patty Richards if you make + + + align:start position:0% +multiple hi patty Richards if you make +less than 15 extra original investment + + align:start position:0% +less than 15 extra original investment + + + align:start position:0% +less than 15 extra original investment +as a senior conservative advocacy and + + align:start position:0% +as a senior conservative advocacy and + + + align:start position:0% +as a senior conservative advocacy and +there's still only like a couple decent + + align:start position:0% +there's still only like a couple decent + + + align:start position:0% +there's still only like a couple decent +ones and what they focus on one thing + + align:start position:0% +ones and what they focus on one thing + + + align:start position:0% +ones and what they focus on one thing +looks I'm doing now actually focus on + + align:start position:0% +looks I'm doing now actually focus on + + + align:start position:0% +looks I'm doing now actually focus on +helping you build out a team in that + + align:start position:0% +helping you build out a team in that + + + align:start position:0% +helping you build out a team in that +paper they actually talked about we look + + align:start position:0% +paper they actually talked about we look + + + align:start position:0% +paper they actually talked about we look +a lot of the technology but also the + + align:start position:0% +a lot of the technology but also the + + + align:start position:0% +a lot of the technology but also the +person because pretty much we're gonna + + align:start position:0% +person because pretty much we're gonna + + + align:start position:0% +person because pretty much we're gonna +help you grow this company like it's + + align:start position:0% +help you grow this company like it's + + + align:start position:0% +help you grow this company like it's +like yeah it's it's gonna be changing + + align:start position:0% +like yeah it's it's gonna be changing + + + align:start position:0% +like yeah it's it's gonna be changing +rapidly you have to change of the person + + align:start position:0% +rapidly you have to change of the person + + + align:start position:0% +rapidly you have to change of the person +during each phase of it and so this is a + + align:start position:0% +during each phase of it and so this is a + + + align:start position:0% +during each phase of it and so this is a +form of capital is become very popular + + align:start position:0% +form of capital is become very popular + + + align:start position:0% +form of capital is become very popular +if you look into the I think you have + + align:start position:0% +if you look into the I think you have + + + align:start position:0% +if you look into the I think you have +some of the numbers there for how much + + align:start position:0% +some of the numbers there for how much + + + align:start position:0% +some of the numbers there for how much +how much was raised in twenty fifteen + + align:start position:0% +how much was raised in twenty fifteen + + + align:start position:0% +how much was raised in twenty fifteen +sixty billion so there is kind of like a + + align:start position:0% +sixty billion so there is kind of like a + + + align:start position:0% +sixty billion so there is kind of like a +capital bubble and it's really illogical + + align:start position:0% +capital bubble and it's really illogical + + + align:start position:0% +capital bubble and it's really illogical +because you there's only ten truly + + align:start position:0% +because you there's only ten truly + + + align:start position:0% +because you there's only ten truly +invested at the same time though because + + align:start position:0% +invested at the same time though because + + + align:start position:0% +invested at the same time though because +it's a really great business or that way + + align:start position:0% +it's a really great business or that way + + + align:start position:0% +it's a really great business or that way +a lot of people putting in money + + align:start position:0% + + + + align:start position:0% + +and so couple questions from that era + + align:start position:0% +and so couple questions from that era + + + align:start position:0% +and so couple questions from that era +what innovation threatens that careers + + align:start position:0% +what innovation threatens that careers + + + align:start position:0% +what innovation threatens that careers +represent the most promising growth + + align:start position:0% +represent the most promising growth + + + align:start position:0% +represent the most promising growth +areas for years + + align:start position:0% + + + + align:start position:0% + +yeah I do Lily so you said that in the + + align:start position:0% +yeah I do Lily so you said that in the + + + align:start position:0% +yeah I do Lily so you said that in the +first round or like the younger couple + + align:start position:0% +first round or like the younger couple + + + align:start position:0% +first round or like the younger couple +years ago was more the expectation was + + align:start position:0% +years ago was more the expectation was + + + align:start position:0% +years ago was more the expectation was +or longer returns now we've been spoiled + + align:start position:0% +or longer returns now we've been spoiled + + + align:start position:0% +or longer returns now we've been spoiled +with the tech revolution and people want + + align:start position:0% +with the tech revolution and people want + + + align:start position:0% +with the tech revolution and people want +returns two years right here + + align:start position:0% +returns two years right here + + + align:start position:0% +returns two years right here +more or less like if you're a really + + align:start position:0% +more or less like if you're a really + + + align:start position:0% +more or less like if you're a really +great company you're gonna exit and can + + align:start position:0% +great company you're gonna exit and can + + + align:start position:0% +great company you're gonna exit and can +we see the head made you can they have + + align:start position:0% +we see the head made you can they have + + + align:start position:0% +we see the head made you can they have +funds that mix long term and short term + + align:start position:0% +funds that mix long term and short term + + + align:start position:0% +funds that mix long term and short term +is that what they're gonna have to do + + align:start position:0% +is that what they're gonna have to do + + + align:start position:0% +is that what they're gonna have to do +because you I see short term and this + + align:start position:0% +because you I see short term and this + + + align:start position:0% +because you I see short term and this +huge influx if we have excess capital + + align:start position:0% +huge influx if we have excess capital + + + align:start position:0% +huge influx if we have excess capital +now if you say they're leave X number of + + align:start position:0% +now if you say they're leave X number of + + + align:start position:0% +now if you say they're leave X number of +companies that really did it big in the + + align:start position:0% +companies that really did it big in the + + + align:start position:0% +companies that really did it big in the +short term we have excess capital all + + align:start position:0% +short term we have excess capital all + + + align:start position:0% +short term we have excess capital all +this as compared to previous years so do + + align:start position:0% +this as compared to previous years so do + + + align:start position:0% +this as compared to previous years so do +you think that pcs are going to have to + + align:start position:0% +you think that pcs are going to have to + + + align:start position:0% +you think that pcs are going to have to +start paying more attention to long term + + align:start position:0% +start paying more attention to long term + + + align:start position:0% +start paying more attention to long term +returns and is that a more sustainable + + align:start position:0% +returns and is that a more sustainable + + + align:start position:0% +returns and is that a more sustainable +business model for them so what's + + align:start position:0% +business model for them so what's + + + align:start position:0% +business model for them so what's +happened is it's not so much like beef + + align:start position:0% +happened is it's not so much like beef + + + align:start position:0% +happened is it's not so much like beef +seasoned terms of nature because they + + align:start position:0% +seasoned terms of nature because they + + + align:start position:0% +seasoned terms of nature because they +the way ABC phone works is that no money + + align:start position:0% +the way ABC phone works is that no money + + + align:start position:0% +the way ABC phone works is that no money +and they need to increase that capital + + align:start position:0% +and they need to increase that capital + + + align:start position:0% +and they need to increase that capital +so a lot of times they can't say oh well + + align:start position:0% +so a lot of times they can't say oh well + + + align:start position:0% +so a lot of times they can't say oh well +we're gonna much better it's gonna be + + align:start position:0% +we're gonna much better it's gonna be + + + align:start position:0% +we're gonna much better it's gonna be +net profitable but not in terms of money + + align:start position:0% +net profitable but not in terms of money + + + align:start position:0% +net profitable but not in terms of money +oh good for society that doesn't usually + + align:start position:0% +oh good for society that doesn't usually + + + align:start position:0% +oh good for society that doesn't usually +happen what ends up happening recently + + align:start position:0% +happen what ends up happening recently + + + align:start position:0% +happen what ends up happening recently +there's been a fund that's like that + + align:start position:0% +there's been a fund that's like that + + + align:start position:0% +there's been a fund that's like that +that was invested where the investor + + align:start position:0% +that was invested where the investor + + + align:start position:0% +that was invested where the investor +like Jack mahabhava energy and also they + + align:start position:0% +like Jack mahabhava energy and also they + + + align:start position:0% +like Jack mahabhava energy and also they +focus on having like it's pretty much + + align:start position:0% +focus on having like it's pretty much + + + align:start position:0% +focus on having like it's pretty much +like the reason I bring that up is + + align:start position:0% +like the reason I bring that up is + + + align:start position:0% +like the reason I bring that up is +because it looks like they're trying to + + align:start position:0% +because it looks like they're trying to + + + align:start position:0% +because it looks like they're trying to +make huge returns of the capital what + + align:start position:0% +make huge returns of the capital what + + + align:start position:0% +make huge returns of the capital what +they're doing is these people that is a + + align:start position:0% +they're doing is these people that is a + + + align:start position:0% +they're doing is these people that is a +mix of philanthropy and + + align:start position:0% +mix of philanthropy and + + + align:start position:0% +mix of philanthropy and +patience yeah yeah so related to that + + align:start position:0% +patience yeah yeah so related to that + + + align:start position:0% +patience yeah yeah so related to that +like therapy see friends that will only + + align:start position:0% +like therapy see friends that will only + + + align:start position:0% +like therapy see friends that will only +be liked by series a financier to be + + align:start position:0% +be liked by series a financier to be + + + align:start position:0% +be liked by series a financier to be +financing or mezzanine funds and their + + align:start position:0% +financing or mezzanine funds and their + + + align:start position:0% +financing or mezzanine funds and their +firms up what do we think since that I'm + + align:start position:0% +firms up what do we think since that I'm + + + align:start position:0% +firms up what do we think since that I'm +so at different stages and companies but + + align:start position:0% +so at different stages and companies but + + + align:start position:0% +so at different stages and companies but +then we do run into the upper limit + + align:start position:0% +then we do run into the upper limit + + + align:start position:0% +then we do run into the upper limit +where you have group like the engine + + align:start position:0% + + + + align:start position:0% + +number of funds especially in Silicon + + align:start position:0% +number of funds especially in Silicon + + + align:start position:0% +number of funds especially in Silicon +Valley that life just like so easy see + + align:start position:0% +Valley that life just like so easy see + + + align:start position:0% +Valley that life just like so easy see +now but are also like long/short equity + + align:start position:0% +now but are also like long/short equity + + + align:start position:0% +now but are also like long/short equity +funds like they're willing to weed out + + align:start position:0% +funds like they're willing to weed out + + + align:start position:0% +funds like they're willing to weed out +but also like in the short term thing + + align:start position:0% +but also like in the short term thing + + + align:start position:0% +but also like in the short term thing +around we're getting some returns that + + align:start position:0% +around we're getting some returns that + + + align:start position:0% +around we're getting some returns that +way so I think that might be a response + + align:start position:0% +way so I think that might be a response + + + align:start position:0% +way so I think that might be a response +to how like to address that problem with + + align:start position:0% +to how like to address that problem with + + + align:start position:0% +to how like to address that problem with +what to do + + align:start position:0% + + + + align:start position:0% + +it also just really early to tell + + align:start position:0% +it also just really early to tell + + + align:start position:0% +it also just really early to tell +because I guess the idea of these in + + align:start position:0% +because I guess the idea of these in + + + align:start position:0% +because I guess the idea of these in +there to go was like what so I guess + + align:start position:0% +there to go was like what so I guess + + + align:start position:0% +there to go was like what so I guess +we're probably not so I'm not according + + align:start position:0% +we're probably not so I'm not according + + + align:start position:0% +we're probably not so I'm not according +but like is it kind of hard to see out + + align:start position:0% +but like is it kind of hard to see out + + + align:start position:0% +but like is it kind of hard to see out +you know these phones are now just + + align:start position:0% +you know these phones are now just + + + align:start position:0% +you know these phones are now just +starting to pop up like past 15 like + + align:start position:0% +starting to pop up like past 15 like + + + align:start position:0% +starting to pop up like past 15 like +towards of 20 years and are we you know + + align:start position:0% +towards of 20 years and are we you know + + + align:start position:0% +towards of 20 years and are we you know +is it a little bit early for us to say + + align:start position:0% +is it a little bit early for us to say + + + align:start position:0% +is it a little bit early for us to say +maybe these might have more success or + + align:start position:0% +maybe these might have more success or + + + align:start position:0% +maybe these might have more success or +what success yeah yeah just to put a few + + align:start position:0% +what success yeah yeah just to put a few + + + align:start position:0% +what success yeah yeah just to put a few +numbers on the table so venture capital + + align:start position:0% +numbers on the table so venture capital + + + align:start position:0% +numbers on the table so venture capital +funding in 2015 was sixty billion + + align:start position:0% +funding in 2015 was sixty billion + + + align:start position:0% +funding in 2015 was sixty billion +venture capital funding before the Great + + align:start position:0% +venture capital funding before the Great + + + align:start position:0% +venture capital funding before the Great +Recession was about sixty billion as + + align:start position:0% +Recession was about sixty billion as + + + align:start position:0% +Recession was about sixty billion as +well so we're sort of back to that + + align:start position:0% +well so we're sort of back to that + + + align:start position:0% +well so we're sort of back to that +number but when you think about I mean + + align:start position:0% +number but when you think about I mean + + + align:start position:0% +number but when you think about I mean +after all right if growth is driven by + + align:start position:0% +after all right if growth is driven by + + + align:start position:0% +after all right if growth is driven by +technological and related innovation and + + align:start position:0% +technological and related innovation and + + + align:start position:0% +technological and related innovation and +you've got 19 I got a 19 trillion dollar + + align:start position:0% +you've got 19 I got a 19 trillion dollar + + + align:start position:0% +you've got 19 I got a 19 trillion dollar +economy say nationwide right it's sixty + + align:start position:0% +economy say nationwide right it's sixty + + + align:start position:0% +economy say nationwide right it's sixty +sixty billion dollars is nothing right + + align:start position:0% +sixty billion dollars is nothing right + + + align:start position:0% +sixty billion dollars is nothing right +that's not a lot of money to be banking + + align:start position:0% +that's not a lot of money to be banking + + + align:start position:0% +that's not a lot of money to be banking +on what our future growth is gonna be so + + align:start position:0% +on what our future growth is gonna be so + + + align:start position:0% +on what our future growth is gonna be so +you know I the issue I think Martine + + align:start position:0% +you know I the issue I think Martine + + + align:start position:0% +you know I the issue I think Martine +shrewdly raised was you know we're not + + align:start position:0% +shrewdly raised was you know we're not + + + align:start position:0% +shrewdly raised was you know we're not +on an innovation wave at the moment + + align:start position:0% +on an innovation wave at the moment + + + align:start position:0% +on an innovation wave at the moment +we're on the kind of scale up part of + + align:start position:0% +we're on the kind of scale up part of + + + align:start position:0% +we're on the kind of scale up part of +the IT wave it's not the 1990s anymore + + align:start position:0% +the IT wave it's not the 1990s anymore + + + align:start position:0% +the IT wave it's not the 1990s anymore +VC's really work amazingly when they're + + align:start position:0% +VC's really work amazingly when they're + + + align:start position:0% +VC's really work amazingly when they're +right on the cusp of an innovation wave + + align:start position:0% +right on the cusp of an innovation wave + + + align:start position:0% +right on the cusp of an innovation wave +and playing for that very rapid scale-up + + align:start position:0% +and playing for that very rapid scale-up + + + align:start position:0% +and playing for that very rapid scale-up +and growth so art rocks investments in + + align:start position:0% +and growth so art rocks investments in + + + align:start position:0% +and growth so art rocks investments in +Intel which really you're absolutely + + align:start position:0% +Intel which really you're absolutely + + + align:start position:0% +Intel which really you're absolutely +right martine did drive the creation of + + align:start position:0% +right martine did drive the creation of + + + align:start position:0% +right martine did drive the creation of +the west coast model you know that was + + align:start position:0% +the west coast model you know that was + + + align:start position:0% +the west coast model you know that was +just at the cusp of the IT wave and the + + align:start position:0% +just at the cusp of the IT wave and the + + + align:start position:0% +just at the cusp of the IT wave and the +vc firms really wrote it and we're not + + align:start position:0% +vc firms really wrote it and we're not + + + align:start position:0% +vc firms really wrote it and we're not +at on one of those ways at the moment so + + align:start position:0% +at on one of those ways at the moment so + + + align:start position:0% +at on one of those ways at the moment so +the VC model has gotten much more + + align:start position:0% +the VC model has gotten much more + + + align:start position:0% +the VC model has gotten much more +complicated because the number of firms + + align:start position:0% +complicated because the number of firms + + + align:start position:0% +complicated because the number of firms +they were actually going to carry the + + align:start position:0% +they were actually going to carry the + + + align:start position:0% +they were actually going to carry the +kind of rewards that + + align:start position:0% +kind of rewards that + + + align:start position:0% +kind of rewards that +typically in a scale up part of the raft + + align:start position:0% +typically in a scale up part of the raft + + + align:start position:0% +typically in a scale up part of the raft +fast scale a part of innovation wave is + + align:start position:0% +fast scale a part of innovation wave is + + + align:start position:0% +fast scale a part of innovation wave is +just slower things are slower we're + + align:start position:0% +just slower things are slower we're + + + align:start position:0% +just slower things are slower we're +waiting for the waves right and you know + + align:start position:0% +waiting for the waves right and you know + + + align:start position:0% +waiting for the waves right and you know +like surfers and it's I think the old + + align:start position:0% +like surfers and it's I think the old + + + align:start position:0% +like surfers and it's I think the old +model the Maverick model will come right + + align:start position:0% +model the Maverick model will come right + + + align:start position:0% +model the Maverick model will come right +back if we get onto one of these waves + + align:start position:0% +back if we get onto one of these waves + + + align:start position:0% +back if we get onto one of these waves +but you know as we've discussed these + + align:start position:0% +but you know as we've discussed these + + + align:start position:0% +but you know as we've discussed these +are typically 40 year long propositions + + align:start position:0% +are typically 40 year long propositions + + + align:start position:0% +are typically 40 year long propositions +and you can be in a long trough before a + + align:start position:0% +and you can be in a long trough before a + + + align:start position:0% +and you can be in a long trough before a +wave takes off so that's really the + + align:start position:0% +wave takes off so that's really the + + + align:start position:0% +wave takes off so that's really the +that's the fundamental question into + + align:start position:0% +that's the fundamental question into + + + align:start position:0% +that's the fundamental question into +this industry on the other hand maybe + + align:start position:0% +this industry on the other hand maybe + + + align:start position:0% +this industry on the other hand maybe +there's another way of looking at it + + align:start position:0% +there's another way of looking at it + + + align:start position:0% +there's another way of looking at it +right maybe the other way of looking at + + align:start position:0% +right maybe the other way of looking at + + + align:start position:0% +right maybe the other way of looking at +it is could use spur waves more rapidly + + align:start position:0% +it is could use spur waves more rapidly + + + align:start position:0% +it is could use spur waves more rapidly +and is the short term return model of + + align:start position:0% +and is the short term return model of + + + align:start position:0% +and is the short term return model of +venture capital a real barrier in our + + align:start position:0% +venture capital a real barrier in our + + + align:start position:0% +venture capital a real barrier in our +ability to stand up longer stronger more + + align:start position:0% +ability to stand up longer stronger more + + + align:start position:0% +ability to stand up longer stronger more +enduring innovation ways sooner right so + + align:start position:0% +enduring innovation ways sooner right so + + + align:start position:0% +enduring innovation ways sooner right so +there's a couple of ways of looking at + + align:start position:0% +there's a couple of ways of looking at + + + align:start position:0% +there's a couple of ways of looking at +this that you know that I think are + + align:start position:0% +this that you know that I think are + + + align:start position:0% +this that you know that I think are +intriguing and we're gonna we're gonna + + align:start position:0% +intriguing and we're gonna we're gonna + + + align:start position:0% +intriguing and we're gonna we're gonna +take a dive into venture capital later + + align:start position:0% +take a dive into venture capital later + + + align:start position:0% +take a dive into venture capital later +in the class kind of looking a little + + align:start position:0% +in the class kind of looking a little + + + align:start position:0% +in the class kind of looking a little +more detail to it as you suggested Matt + + align:start position:0% +more detail to it as you suggested Matt + + + align:start position:0% +more detail to it as you suggested Matt +about the engine it's one of my favorite + + align:start position:0% +about the engine it's one of my favorite + + + align:start position:0% +about the engine it's one of my favorite +quotes Martine I was going to use it to + + align:start position:0% + + + + align:start position:0% + +enough water we're not focusing on + + align:start position:0% +enough water we're not focusing on + + + align:start position:0% +enough water we're not focusing on +resources and resource and we'll end up + + align:start position:0% +resources and resource and we'll end up + + + align:start position:0% +resources and resource and we'll end up +happening is we have IT ways but now we + + align:start position:0% +happening is we have IT ways but now we + + + align:start position:0% +happening is we have IT ways but now we +are you doing more business right and so + + align:start position:0% +are you doing more business right and so + + + align:start position:0% +are you doing more business right and so +his point of view is more that we we + + align:start position:0% +his point of view is more that we we + + + align:start position:0% +his point of view is more that we we +have better things in some sense but + + align:start position:0% + + + + align:start position:0% + +it's just really big times and that + + align:start position:0% +it's just really big times and that + + + align:start position:0% +it's just really big times and that +might actually be a huge opportunity + + align:start position:0% +might actually be a huge opportunity + + + align:start position:0% +might actually be a huge opportunity +because if you know 50 90 billion + + align:start position:0% +because if you know 50 90 billion + + + align:start position:0% +because if you know 50 90 billion +dollars of the capital or focusing on + + align:start position:0% +dollars of the capital or focusing on + + + align:start position:0% +dollars of the capital or focusing on +these can your impact and you're one of + + align:start position:0% +these can your impact and you're one of + + + align:start position:0% +these can your impact and you're one of +the investors is okay always 10 more + + align:start position:0% +the investors is okay always 10 more + + + align:start position:0% +the investors is okay always 10 more +years + + align:start position:0% + + + + align:start position:0% + +the big thing to is we're talking about + + align:start position:0% +the big thing to is we're talking about + + + align:start position:0% +the big thing to is we're talking about +entrepreneurs how the first the the + + align:start position:0% +entrepreneurs how the first the the + + + align:start position:0% +entrepreneurs how the first the the +first inventor usually didn't capture + + align:start position:0% +first inventor usually didn't capture + + + align:start position:0% +first inventor usually didn't capture +that value this is actually an + + align:start position:0% +that value this is actually an + + + align:start position:0% +that value this is actually an +opportunity for maybe the first inventor + + align:start position:0% +opportunity for maybe the first inventor + + + align:start position:0% +opportunity for maybe the first inventor +to capture on a value and then people + + align:start position:0% +to capture on a value and then people + + + align:start position:0% +to capture on a value and then people +focus on that being punning the first + + align:start position:0% +focus on that being punning the first + + + align:start position:0% +focus on that being punning the first +way the major again the drawback of that + + align:start position:0% +way the major again the drawback of that + + + align:start position:0% +way the major again the drawback of that +too is that say somebody this room + + align:start position:0% + + + + align:start position:0% + +somebody could see the technology braids + + align:start position:0% +somebody could see the technology braids + + + align:start position:0% +somebody could see the technology braids +1 million three million dollars scale + + align:start position:0% +1 million three million dollars scale + + + align:start position:0% +1 million three million dollars scale +there's something valuable is a person + + align:start position:0% +there's something valuable is a person + + + align:start position:0% +there's something valuable is a person +venice versus facebook was the may be + + align:start position:0% +venice versus facebook was the may be + + + align:start position:0% +venice versus facebook was the may be +that that divide between the first hyper + + align:start position:0% +that that divide between the first hyper + + + align:start position:0% +that that divide between the first hyper +rapid effects right so you're driving us + + align:start position:0% +rapid effects right so you're driving us + + + align:start position:0% +rapid effects right so you're driving us +I think to important point Martine about + + align:start position:0% +I think to important point Martine about + + + align:start position:0% +I think to important point Martine about +the venture capital sector as its + + align:start position:0% +the venture capital sector as its + + + align:start position:0% +the venture capital sector as its +organized now right it's really + + align:start position:0% +organized now right it's really + + + align:start position:0% +organized now right it's really +organized for this right that's what it + + align:start position:0% +organized for this right that's what it + + + align:start position:0% +organized for this right that's what it +wants right + + align:start position:0% +wants right + + + align:start position:0% +wants right +it doesn't know what to do with this + + align:start position:0% +it doesn't know what to do with this + + + align:start position:0% +it doesn't know what to do with this +right and it's desperately trying to + + align:start position:0% +right and it's desperately trying to + + + align:start position:0% +right and it's desperately trying to +make this look like this right that's + + align:start position:0% +make this look like this right that's + + + align:start position:0% +make this look like this right that's +kind of where we are there's a problem + + align:start position:0% +kind of where we are there's a problem + + + align:start position:0% +kind of where we are there's a problem +with his model right it's not + + align:start position:0% +with his model right it's not + + + align:start position:0% +with his model right it's not +it's not there and so just as we + + align:start position:0% +it's not there and so just as we + + + align:start position:0% +it's not there and so just as we +critique the Merrill Lynch piece for you + + align:start position:0% +critique the Merrill Lynch piece for you + + + align:start position:0% +critique the Merrill Lynch piece for you +know the gap here in a longer-term + + align:start position:0% +know the gap here in a longer-term + + + align:start position:0% +know the gap here in a longer-term +patient capital it turns out that the VC + + align:start position:0% +patient capital it turns out that the VC + + + align:start position:0% +patient capital it turns out that the VC +model isn't really helping us where we + + align:start position:0% +model isn't really helping us where we + + + align:start position:0% +model isn't really helping us where we +really need a lot of help which is more + + align:start position:0% +really need a lot of help which is more + + + align:start position:0% +really need a lot of help which is more +in this kind of territory right yeah so + + align:start position:0% +in this kind of territory right yeah so + + + align:start position:0% +in this kind of territory right yeah so +I'm Martha was pushing us and Martine + + align:start position:0% +I'm Martha was pushing us and Martine + + + align:start position:0% +I'm Martha was pushing us and Martine +you mentioned it as well this whole + + align:start position:0% +you mentioned it as well this whole + + + align:start position:0% +you mentioned it as well this whole +gates is organized this new group that + + align:start position:0% +gates is organized this new group that + + + align:start position:0% +gates is organized this new group that +wants to deal with exactly this problem + + align:start position:0% +wants to deal with exactly this problem + + + align:start position:0% +wants to deal with exactly this problem +they want to start dealing with some of + + align:start position:0% +they want to start dealing with some of + + + align:start position:0% +they want to start dealing with some of +this stuff not just trying to focus on + + align:start position:0% +this stuff not just trying to focus on + + + align:start position:0% +this stuff not just trying to focus on +this right in order to get an energy + + align:start position:0% +this right in order to get an energy + + + align:start position:0% +this right in order to get an energy +innovation wave going so that may be big + + align:start position:0% +innovation wave going so that may be big + + + align:start position:0% +innovation wave going so that may be big +enough to be a different model I don't + + align:start position:0% +enough to be a different model I don't + + + align:start position:0% +enough to be a different model I don't +know it's not 60 billion and it's a long + + align:start position:0% +know it's not 60 billion and it's a long + + + align:start position:0% +know it's not 60 billion and it's a long +way away from it but he is shaking down + + align:start position:0% +way away from it but he is shaking down + + + align:start position:0% +way away from it but he is shaking down +people with a lot of money yeah it's + + align:start position:0% +people with a lot of money yeah it's + + + align:start position:0% +people with a lot of money yeah it's +fine + + align:start position:0% +fine + + + align:start position:0% +fine +as long as all we want is software and + + align:start position:0% +as long as all we want is software and + + + align:start position:0% +as long as all we want is software and +biotech it's great right it's great it's + + align:start position:0% +biotech it's great right it's great it's + + + align:start position:0% +biotech it's great right it's great it's +fabulous and some services sectors media + + align:start position:0% +fabulous and some services sectors media + + + align:start position:0% +fabulous and some services sectors media +and entertainment are good too right but + + align:start position:0% +and entertainment are good too right but + + + align:start position:0% +and entertainment are good too right but +if the society wants some other stuff + + align:start position:0% +if the society wants some other stuff + + + align:start position:0% +if the society wants some other stuff +right then we got a serious problem on + + align:start position:0% + + + + align:start position:0% + +the energy solution for the world right + + align:start position:0% +the energy solution for the world right + + + align:start position:0% +the energy solution for the world right +because energy is a huge loser in the + + align:start position:0% +because energy is a huge loser in the + + + align:start position:0% +because energy is a huge loser in the +current venture capital mark yeah + + align:start position:0% + + + + align:start position:0% + +they're more like institutions now like + + align:start position:0% +they're more like institutions now like + + + align:start position:0% +they're more like institutions now like +there's only really pod that matter like + + align:start position:0% + + + + align:start position:0% + +so yeah they're comically MIT and + + align:start position:0% +so yeah they're comically MIT and + + + align:start position:0% +so yeah they're comically MIT and +Harvard subway there's really like if + + align:start position:0% +Harvard subway there's really like if + + + align:start position:0% +Harvard subway there's really like if +you're at all so if you're getting + + align:start position:0% +you're at all so if you're getting + + + align:start position:0% +you're at all so if you're getting +investment you want from one of the top + + align:start position:0% +investment you want from one of the top + + + align:start position:0% +investment you want from one of the top +ones because you have to get multiple + + align:start position:0% +ones because you have to get multiple + + + align:start position:0% +ones because you have to get multiple +rounds of funding so if you get the + + align:start position:0% +rounds of funding so if you get the + + + align:start position:0% +rounds of funding so if you get the +first round an investor it's gonna get + + align:start position:0% +first round an investor it's gonna get + + + align:start position:0% +first round an investor it's gonna get +so much in the future but another thing + + align:start position:0% +so much in the future but another thing + + + align:start position:0% +so much in the future but another thing +too is that Silicon Valley which is the + + align:start position:0% +too is that Silicon Valley which is the + + + align:start position:0% +too is that Silicon Valley which is the +cool thing is like they've come up with + + align:start position:0% +cool thing is like they've come up with + + + align:start position:0% +cool thing is like they've come up with +all these ideas of how to like stretch + + align:start position:0% +all these ideas of how to like stretch + + + align:start position:0% +all these ideas of how to like stretch +routine to make innovation and how they + + align:start position:0% +routine to make innovation and how they + + + align:start position:0% +routine to make innovation and how they +focus a lot on disruptive business + + align:start position:0% +focus a lot on disruptive business + + + align:start position:0% +focus a lot on disruptive business +models so it might be interesting is if + + align:start position:0% +models so it might be interesting is if + + + align:start position:0% +models so it might be interesting is if +somebody right now we can say that there + + align:start position:0% +somebody right now we can say that there + + + align:start position:0% +somebody right now we can say that there +are a lot like the early telegraph line + + align:start position:0% + + + + align:start position:0% + +I think talk like fusion startups right + + align:start position:0% +I think talk like fusion startups right + + + align:start position:0% +I think talk like fusion startups right +now well you probably know even why + + align:start position:0% +now well you probably know even why + + + align:start position:0% +now well you probably know even why +comment there is only two years down all + + align:start position:0% +comment there is only two years down all + + + align:start position:0% +comment there is only two years down all +right so I'm gonna push us to do a few + + align:start position:0% +right so I'm gonna push us to do a few + + + align:start position:0% +right so I'm gonna push us to do a few +why don't you give us a few comments on + + align:start position:0% +why don't you give us a few comments on + + + align:start position:0% +why don't you give us a few comments on +Schultz and we'll close out the session + + align:start position:0% + + + + align:start position:0% + +when they're not really there inherently + + align:start position:0% +when they're not really there inherently + + + align:start position:0% +when they're not really there inherently +that's not their nature they've done + + align:start position:0% +that's not their nature they've done + + + align:start position:0% +that's not their nature they've done +better what opening point is that + + align:start position:0% +better what opening point is that + + + align:start position:0% +better what opening point is that +economies have done better when the + + align:start position:0% +economies have done better when the + + + align:start position:0% +economies have done better when the +government needs a supportive role I + + align:start position:0% +government needs a supportive role I + + + align:start position:0% +government needs a supportive role I +mean he does talk about a lot about + + align:start position:0% +mean he does talk about a lot about + + + align:start position:0% +mean he does talk about a lot about +Japan + + align:start position:0% +Japan + + + align:start position:0% +Japan +I think another factor to consider for + + align:start position:0% +I think another factor to consider for + + + align:start position:0% +I think another factor to consider for +Japan and also South Korea because I + + align:start position:0% +Japan and also South Korea because I + + + align:start position:0% +Japan and also South Korea because I +don't think + + align:start position:0% +don't think + + + align:start position:0% +don't think +that is that their population periods + + align:start position:0% +that is that their population periods + + + align:start position:0% +that is that their population periods +were in a certain way usually and that's + + align:start position:0% +were in a certain way usually and that's + + + align:start position:0% +were in a certain way usually and that's +why they kind of die off very quickly so + + align:start position:0% +why they kind of die off very quickly so + + + align:start position:0% +why they kind of die off very quickly so +that might be but so yeah is it this + + align:start position:0% +that might be but so yeah is it this + + + align:start position:0% +that might be but so yeah is it this +idea do we create the supportive + + align:start position:0% +idea do we create the supportive + + + align:start position:0% +idea do we create the supportive +environment or do we focus on industries + + align:start position:0% +environment or do we focus on industries + + + align:start position:0% +environment or do we focus on industries +I think it also might have been Ferguson + + align:start position:0% +I think it also might have been Ferguson + + + align:start position:0% +I think it also might have been Ferguson +in the last book in the last week's + + align:start position:0% +in the last book in the last week's + + + align:start position:0% +in the last book in the last week's +class about specific cities that focus + + align:start position:0% +class about specific cities that focus + + + align:start position:0% +class about specific cities that focus +is very interesting especially + + align:start position:0% +is very interesting especially + + + align:start position:0% +is very interesting especially +contrasting with this funny thinking + + align:start position:0% +contrasting with this funny thinking + + + align:start position:0% +contrasting with this funny thinking +wondering would he be writing I didn't + + align:start position:0% +wondering would he be writing I didn't + + + align:start position:0% +wondering would he be writing I didn't +look up any of his papers because he and + + align:start position:0% +look up any of his papers because he and + + + align:start position:0% +look up any of his papers because he and +I can think oh my gosh Schultz is the + + align:start position:0% +I can think oh my gosh Schultz is the + + + align:start position:0% +I can think oh my gosh Schultz is the +reason we have the president we have + + align:start position:0% +reason we have the president we have + + + align:start position:0% +reason we have the president we have +today telling everyone we're not the + + align:start position:0% +today telling everyone we're not the + + + align:start position:0% +today telling everyone we're not the +industrializing don't worry we're not + + align:start position:0% +industrializing don't worry we're not + + + align:start position:0% +industrializing don't worry we're not +the industrializing but we really + + align:start position:0% +the industrializing but we really + + + align:start position:0% +the industrializing but we really +weren't we and so all knowledge comes + + align:start position:0% +weren't we and so all knowledge comes + + + align:start position:0% +weren't we and so all knowledge comes +from freakanomics + + align:start position:0% +from freakanomics + + + align:start position:0% +from freakanomics +so we're not the industrializing or even + + align:start position:0% +so we're not the industrializing or even + + + align:start position:0% +so we're not the industrializing or even +if we are don't worry because the jobs + + align:start position:0% +if we are don't worry because the jobs + + + align:start position:0% +if we are don't worry because the jobs +are gonna be replaced by the technology + + align:start position:0% +are gonna be replaced by the technology + + + align:start position:0% +are gonna be replaced by the technology +that we're developing and so don't worry + + align:start position:0% +that we're developing and so don't worry + + + align:start position:0% +that we're developing and so don't worry +don't worry and we really let a lot of + + align:start position:0% +don't worry and we really let a lot of + + + align:start position:0% +don't worry and we really let a lot of +the industry here get away from us into + + align:start position:0% +the industry here get away from us into + + + align:start position:0% +the industry here get away from us into +other countries you know you raise a + + align:start position:0% +other countries you know you raise a + + + align:start position:0% +other countries you know you raise a +very interesting point Lily Schultz is + + align:start position:0% +very interesting point Lily Schultz is + + + align:start position:0% +very interesting point Lily Schultz is +writing in 1983 solo doesn't get the + + align:start position:0% +writing in 1983 solo doesn't get the + + + align:start position:0% +writing in 1983 solo doesn't get the +Nobel Prize until 1987 so growth + + align:start position:0% +Nobel Prize until 1987 so growth + + + align:start position:0% +Nobel Prize until 1987 so growth +economics doesn't we were talking in + + align:start position:0% +economics doesn't we were talking in + + + align:start position:0% +economics doesn't we were talking in +Beth and I were talking a bit a bit + + align:start position:0% +Beth and I were talking a bit a bit + + + align:start position:0% +Beth and I were talking a bit a bit +about this before class but growth + + align:start position:0% +about this before class but growth + + + align:start position:0% +about this before class but growth +economics doesn't really lock in until + + align:start position:0% +economics doesn't really lock in until + + + align:start position:0% +economics doesn't really lock in until +you know really we + + align:start position:0% +you know really we + + + align:start position:0% +you know really we +start to see what's happening in the + + align:start position:0% +start to see what's happening in the + + + align:start position:0% +start to see what's happening in the +1990s that's when it's you can't ignore + + align:start position:0% +1990s that's when it's you can't ignore + + + align:start position:0% +1990s that's when it's you can't ignore +growth theory right you see it right in + + align:start position:0% +growth theory right you see it right in + + + align:start position:0% +growth theory right you see it right in +front of you so Schultz is out of in a + + align:start position:0% +front of you so Schultz is out of in a + + + align:start position:0% +front of you so Schultz is out of in a +ways out of classical economics he keeps + + align:start position:0% +ways out of classical economics he keeps + + + align:start position:0% +ways out of classical economics he keeps +pointing us to Japan success story being + + align:start position:0% +pointing us to Japan success story being + + + align:start position:0% +pointing us to Japan success story being +the national savings rate right so low + + align:start position:0% +the national savings rate right so low + + + align:start position:0% +the national savings rate right so low +says you know it's useful but that's not + + align:start position:0% +says you know it's useful but that's not + + + align:start position:0% +says you know it's useful but that's not +the driver right it's this technological + + align:start position:0% +the driver right it's this technological + + + align:start position:0% +the driver right it's this technological +related innovation so in a way you can + + align:start position:0% +related innovation so in a way you can + + + align:start position:0% +related innovation so in a way you can +see Schultz just as you suggest as a + + align:start position:0% +see Schultz just as you suggest as a + + + align:start position:0% +see Schultz just as you suggest as a +dialog within different stages of + + align:start position:0% +dialog within different stages of + + + align:start position:0% +dialog within different stages of +economics thinking right and Schultz in + + align:start position:0% +economics thinking right and Schultz in + + + align:start position:0% +economics thinking right and Schultz in +what in many ways is certainly in the + + align:start position:0% +what in many ways is certainly in the + + + align:start position:0% +what in many ways is certainly in the +neoclassical and early in a way earlier + + align:start position:0% +neoclassical and early in a way earlier + + + align:start position:0% +neoclassical and early in a way earlier +classical economics thinking about + + align:start position:0% +classical economics thinking about + + + align:start position:0% +classical economics thinking about +growth before new growth theory develops + + align:start position:0% +growth before new growth theory develops + + + align:start position:0% +growth before new growth theory develops +from people like solo and and and Romer + + align:start position:0% +from people like solo and and and Romer + + + align:start position:0% +from people like solo and and and Romer +so that's part of what he's saying here + + align:start position:0% +so that's part of what he's saying here + + + align:start position:0% +so that's part of what he's saying here +but I do think that his point about the + + align:start position:0% +but I do think that his point about the + + + align:start position:0% +but I do think that his point about the +difficulty of the political system to + + align:start position:0% +difficulty of the political system to + + + align:start position:0% +difficulty of the political system to +operate in a sophisticated technology + + align:start position:0% +operate in a sophisticated technology + + + align:start position:0% +operate in a sophisticated technology +realm I think that's very real right so + + align:start position:0% +realm I think that's very real right so + + + align:start position:0% +realm I think that's very real right so +every time we kind of and you know I'm + + align:start position:0% +every time we kind of and you know I'm + + + align:start position:0% +every time we kind of and you know I'm +guilty of this periodically every time + + align:start position:0% +guilty of this periodically every time + + + align:start position:0% +guilty of this periodically every time +we want to expand the governmental role + + align:start position:0% +we want to expand the governmental role + + + align:start position:0% +we want to expand the governmental role +and push it further down the pipeline + + align:start position:0% +and push it further down the pipeline + + + align:start position:0% +and push it further down the pipeline +Schultz always stands as a warning for + + align:start position:0% +Schultz always stands as a warning for + + + align:start position:0% +Schultz always stands as a warning for +me about the complexity of how the + + align:start position:0% +me about the complexity of how the + + + align:start position:0% +me about the complexity of how the +political process is going to wrestle + + align:start position:0% +political process is going to wrestle + + + align:start position:0% +political process is going to wrestle +with this and the system that the reward + + align:start position:0% +with this and the system that the reward + + + align:start position:0% +with this and the system that the reward +system in the political system is not + + align:start position:0% +system in the political system is not + + + align:start position:0% +system in the political system is not +the same reward system that technology + + align:start position:0% +the same reward system that technology + + + align:start position:0% +the same reward system that technology +stand up necessarily needs + + align:start position:0% + + + + align:start position:0% + +so Martina closing thought for us on + + align:start position:0% +so Martina closing thought for us on + + + align:start position:0% +so Martina closing thought for us on +Schultz good summary all right I want to + + align:start position:0% +Schultz good summary all right I want to + + + align:start position:0% +Schultz good summary all right I want to +thank our three discussion leaders for + + align:start position:0% +thank our three discussion leaders for + + + align:start position:0% +thank our three discussion leaders for +getting us off to such a good start good + + align:start position:0% +getting us off to such a good start good + + + align:start position:0% +getting us off to such a good start good +work team who set a model for us at a + + align:start position:0% +work team who set a model for us at a + + + align:start position:0% +work team who set a model for us at a +threshold I think now our classes + + align:start position:0% +threshold I think now our classes + + + align:start position:0% +threshold I think now our classes +participation is pretty well settle I + + align:start position:0% +participation is pretty well settle I + + + align:start position:0% +participation is pretty well settle I +think we've got a great size I think + + align:start position:0% +think we've got a great size I think + + + align:start position:0% +think we've got a great size I think +there's gonna be I can just tell from + + align:start position:0% +there's gonna be I can just tell from + + + align:start position:0% +there's gonna be I can just tell from +the discussion today it's gonna be + + align:start position:0% +the discussion today it's gonna be + + + align:start position:0% +the discussion today it's gonna be +terrific you guys are gonna be great and + + align:start position:0% +terrific you guys are gonna be great and + + + align:start position:0% +terrific you guys are gonna be great and +I think we had to have a lot of fun so + + align:start position:0% +I think we had to have a lot of fun so + + + align:start position:0% +I think we had to have a lot of fun so +um I had a good time last week but I'm + + align:start position:0% +um I had a good time last week but I'm + + + align:start position:0% +um I had a good time last week but I'm +really reassured about where this is + + align:start position:0% +really reassured about where this is + + + align:start position:0% +really reassured about where this is +going so thank you all for participating + + align:start position:0% +going so thank you all for participating + + + align:start position:0% +going so thank you all for participating +so I'll see you on the 28th and I will + + align:start position:0% +so I'll see you on the 28th and I will + + + align:start position:0% +so I'll see you on the 28th and I will +put out a longer term list of discussion + + align:start position:0% +put out a longer term list of discussion + + + align:start position:0% +put out a longer term list of discussion +leaders in the interim \ No newline at end of file diff --git a/XfWkgDLc4xA.txt b/XfWkgDLc4xA.txt new file mode 100644 index 0000000000000000000000000000000000000000..717399af8fc243193aeb32b907a0f598af44462d --- /dev/null +++ b/XfWkgDLc4xA.txt @@ -0,0 +1,10871 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu if you look at syllabus uh I + + align:start position:0% +ocw.mit.edu if you look at syllabus uh I + + + align:start position:0% +ocw.mit.edu if you look at syllabus uh I +have my office hour Monday 5 to 6 and I + + align:start position:0% +have my office hour Monday 5 to 6 and I + + + align:start position:0% +have my office hour Monday 5 to 6 and I +would like to I know many of you but + + align:start position:0% +would like to I know many of you but + + + align:start position:0% +would like to I know many of you but +also I many of you I do not know uh if + + align:start position:0% +also I many of you I do not know uh if + + + align:start position:0% +also I many of you I do not know uh if +we have not met before uh I would like + + align:start position:0% +we have not met before uh I would like + + + align:start position:0% +we have not met before uh I would like +to ask you come to my office hour and + + align:start position:0% +to ask you come to my office hour and + + + align:start position:0% +to ask you come to my office hour and +let's uh chat a little bit and see + + align:start position:0% +let's uh chat a little bit and see + + + align:start position:0% +let's uh chat a little bit and see +what's your + + align:start position:0% +what's your + + + align:start position:0% +what's your +interest um that way I can better uh + + align:start position:0% +interest um that way I can better uh + + + align:start position:0% +interest um that way I can better uh +prepare + + align:start position:0% +prepare + + + align:start position:0% +prepare +myself I also uh read through your uh + + align:start position:0% +myself I also uh read through your uh + + + align:start position:0% +myself I also uh read through your uh +feedback in the first class uh as I + + align:start position:0% +feedback in the first class uh as I + + + align:start position:0% +feedback in the first class uh as I +expected the interest VAR broadly and + + align:start position:0% +expected the interest VAR broadly and + + + align:start position:0% +expected the interest VAR broadly and +all also uh the background vares broadly + + align:start position:0% +all also uh the background vares broadly + + + align:start position:0% +all also uh the background vares broadly +uh uh that's always the later uh I + + align:start position:0% +uh uh that's always the later uh I + + + align:start position:0% +uh uh that's always the later uh I +encounter in the past we don't have a a + + align:start position:0% +encounter in the past we don't have a a + + + align:start position:0% +encounter in the past we don't have a a +good solution for that so I ask if you + + align:start position:0% +good solution for that so I ask if you + + + align:start position:0% +good solution for that so I ask if you +have learned this stuff be patient uh if + + align:start position:0% +have learned this stuff be patient uh if + + + align:start position:0% +have learned this stuff be patient uh if +you haven't uh will'll come over there + + align:start position:0% +you haven't uh will'll come over there + + + align:start position:0% +you haven't uh will'll come over there +uh get get there and uh many of you also + + align:start position:0% +uh get get there and uh many of you also + + + align:start position:0% +uh get get there and uh many of you also +are very much interested in + + align:start position:0% +are very much interested in + + + align:start position:0% +are very much interested in +liquid so I want to uh tell you that + + align:start position:0% +liquid so I want to uh tell you that + + + align:start position:0% +liquid so I want to uh tell you that +liquid is very difficult okay and uh uh + + align:start position:0% +liquid is very difficult okay and uh uh + + + align:start position:0% +liquid is very difficult okay and uh uh +when I uh wrote the book I put + + align:start position:0% +when I uh wrote the book I put + + + align:start position:0% +when I uh wrote the book I put +everything on a parallel paths I can + + align:start position:0% +everything on a parallel paths I can + + + align:start position:0% +everything on a parallel paths I can +deal with um solid Crystal solid + + align:start position:0% +deal with um solid Crystal solid + + + align:start position:0% +deal with um solid Crystal solid +crystalline solid and gas photons + + align:start position:0% +crystalline solid and gas photons + + + align:start position:0% +crystalline solid and gas photons +electrons but when it came to liquid uh + + align:start position:0% +electrons but when it came to liquid uh + + + align:start position:0% +electrons but when it came to liquid uh +it become a lot more complicated so if + + align:start position:0% +it become a lot more complicated so if + + + align:start position:0% +it become a lot more complicated so if +you look at the book there was a + + align:start position:0% +you look at the book there was a + + + align:start position:0% +you look at the book there was a +specific chapter on liquid and that you + + align:start position:0% +specific chapter on liquid and that you + + + align:start position:0% +specific chapter on liquid and that you +have to be more patient and wait uh + + align:start position:0% +have to be more patient and wait uh + + + align:start position:0% +have to be more patient and wait uh +until almost the end uh of this uh uh + + align:start position:0% +until almost the end uh of this uh uh + + + align:start position:0% +until almost the end uh of this uh uh +class uh okay with that uh uh uh + + align:start position:0% +class uh okay with that uh uh uh + + + align:start position:0% +class uh okay with that uh uh uh +remember I would like to see you uh if + + align:start position:0% +remember I would like to see you uh if + + + align:start position:0% +remember I would like to see you uh if +we haven't talked before come to my + + align:start position:0% +we haven't talked before come to my + + + align:start position:0% +we haven't talked before come to my +office hour and let's know each other + + align:start position:0% +office hour and let's know each other + + + align:start position:0% +office hour and let's know each other +better uh if you uh think about what we + + align:start position:0% +better uh if you uh think about what we + + + align:start position:0% +better uh if you uh think about what we +talked in the last + + align:start position:0% +talked in the last + + + align:start position:0% +talked in the last +lecture last + + align:start position:0% + + + + align:start position:0% + +time + + align:start position:0% +time + + + align:start position:0% +time +we reviewed the classical + + align:start position:0% +we reviewed the classical + + + align:start position:0% +we reviewed the classical +law this uh for heat for momentum right + + align:start position:0% +law this uh for heat for momentum right + + + align:start position:0% +law this uh for heat for momentum right +uh heat conduction heat conversion + + align:start position:0% +uh heat conduction heat conversion + + + align:start position:0% +uh heat conduction heat conversion +thermal + + align:start position:0% +thermal + + + align:start position:0% +thermal +radiation in terms of momentum for + + align:start position:0% +radiation in terms of momentum for + + + align:start position:0% +radiation in terms of momentum for +example uh the living share + + align:start position:0% +example uh the living share + + + align:start position:0% +example uh the living share +stressn and uh we uh also oh SL Mass + + align:start position:0% +stressn and uh we uh also oh SL Mass + + + align:start position:0% +stressn and uh we uh also oh SL Mass +diffusion fix law so those are the + + align:start position:0% +diffusion fix law so those are the + + + align:start position:0% +diffusion fix law so those are the +constitute relations for the transport + + align:start position:0% +constitute relations for the transport + + + align:start position:0% +constitute relations for the transport +processes + + align:start position:0% +processes + + + align:start position:0% +processes +is so we did classical + + align:start position:0% + + + + align:start position:0% + +laws and uh uh I also we went into more + + align:start position:0% +laws and uh uh I also we went into more + + + align:start position:0% +laws and uh uh I also we went into more +microscopic picture behind this + + align:start position:0% +microscopic picture behind this + + + align:start position:0% +microscopic picture behind this +classical laws and we say at the end uh + + align:start position:0% +classical laws and we say at the end uh + + + align:start position:0% +classical laws and we say at the end uh +in terms of carriers for energy momentum + + align:start position:0% +in terms of carriers for energy momentum + + + align:start position:0% +in terms of carriers for energy momentum +charge uh uh say we only have uh + + align:start position:0% +charge uh uh say we only have uh + + + align:start position:0% +charge uh uh say we only have uh +essentially four types major types + + align:start position:0% +essentially four types major types + + + align:start position:0% +essentially four types major types +molecules uh electrons photons and latis + + align:start position:0% +molecules uh electrons photons and latis + + + align:start position:0% +molecules uh electrons photons and latis +vibration I brought up the name Fons + + align:start position:0% +vibration I brought up the name Fons + + + align:start position:0% +vibration I brought up the name Fons +right so we went to uh some microscopic + + align:start position:0% +right so we went to uh some microscopic + + + align:start position:0% +right so we went to uh some microscopic +description + + align:start position:0% + + + + align:start position:0% + +for those transport + + align:start position:0% + + + + align:start position:0% + +processes + + align:start position:0% +processes + + + align:start position:0% +processes +and uh uh what I simplify all this + + align:start position:0% +and uh uh what I simplify all this + + + align:start position:0% +and uh uh what I simplify all this +problem is a gas picture I have + + align:start position:0% +problem is a gas picture I have + + + align:start position:0% +problem is a gas picture I have +molecular gas in a box I have electron + + align:start position:0% +molecular gas in a box I have electron + + + align:start position:0% +molecular gas in a box I have electron +gas in a box and the Fon gas in a box so + + align:start position:0% +gas in a box and the Fon gas in a box so + + + align:start position:0% +gas in a box and the Fon gas in a box so +uh that's why we can do a parallel + + align:start position:0% +uh that's why we can do a parallel + + + align:start position:0% +uh that's why we can do a parallel +treatment for all those energy + + align:start position:0% +treatment for all those energy + + + align:start position:0% +treatment for all those energy +carriers and uh what I'm going to do in + + align:start position:0% +carriers and uh what I'm going to do in + + + align:start position:0% +carriers and uh what I'm going to do in +today's + + align:start position:0% +today's + + + align:start position:0% +today's +lecture is trying to give a first crack + + align:start position:0% +lecture is trying to give a first crack + + + align:start position:0% +lecture is trying to give a first crack +on the questions that we're going to + + align:start position:0% +on the questions that we're going to + + + align:start position:0% +on the questions that we're going to +answer through the whole + + align:start position:0% +answer through the whole + + + align:start position:0% +answer through the whole +semester and uh uh those + + align:start position:0% +semester and uh uh those + + + align:start position:0% +semester and uh uh those +questions what are the question I want + + align:start position:0% +questions what are the question I want + + + align:start position:0% +questions what are the question I want +to ask I want to ask now if I look at + + align:start position:0% +to ask I want to ask now if I look at + + + align:start position:0% +to ask I want to ask now if I look at +this micro scop + + align:start position:0% + + + + align:start position:0% + +picture I want to take first one + + align:start position:0% +picture I want to take first one + + + align:start position:0% +picture I want to take first one +individual + + align:start position:0% +individual + + + align:start position:0% +individual +carrier and ask + + align:start position:0% +carrier and ask + + + align:start position:0% +carrier and ask +what's its energy I can also ask what's + + align:start position:0% +what's its energy I can also ask what's + + + align:start position:0% +what's its energy I can also ask what's +momentum charge but let me just pick the + + align:start position:0% +momentum charge but let me just pick the + + + align:start position:0% +momentum charge but let me just pick the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +first and then I'm going to look at a + + align:start position:0% +first and then I'm going to look at a + + + align:start position:0% +first and then I'm going to look at a +cluster a box of those uh carriers + + align:start position:0% +cluster a box of those uh carriers + + + align:start position:0% +cluster a box of those uh carriers +molecules at certain + + align:start position:0% +molecules at certain + + + align:start position:0% +molecules at certain +temperature I ask how + + align:start position:0% +temperature I ask how + + + align:start position:0% +temperature I ask how +many of those uh carriers have certain + + align:start position:0% +many of those uh carriers have certain + + + align:start position:0% +many of those uh carriers have certain +energy and how far how far they travel + + align:start position:0% +energy and how far how far they travel + + + align:start position:0% +energy and how far how far they travel +so first question is how + + align:start position:0% + + + + align:start position:0% + +much okay here you can see how much + + align:start position:0% +much okay here you can see how much + + + align:start position:0% +much okay here you can see how much +energy but there one + + align:start position:0% + + + + align:start position:0% + +carrier right and then I'm going to + + align:start position:0% +carrier right and then I'm going to + + + align:start position:0% +carrier right and then I'm going to +ask how many of + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +uh how fast they + + align:start position:0% + + + + align:start position:0% + +travel and how far they + + align:start position:0% + + + + align:start position:0% + +travel and how they + + align:start position:0% + + + + align:start position:0% + +interact + + align:start position:0% + + + + align:start position:0% + +okay and with that we can start I give + + align:start position:0% +okay and with that we can start I give + + + align:start position:0% +okay and with that we can start I give +you a simple derivation of the diffusion + + align:start position:0% +you a simple derivation of the diffusion + + + align:start position:0% +you a simple derivation of the diffusion +laws uh last time we showed ohms law for + + align:start position:0% +laws uh last time we showed ohms law for + + + align:start position:0% +laws uh last time we showed ohms law for +example uh this time I will show you uh + + align:start position:0% +example uh this time I will show you uh + + + align:start position:0% +example uh this time I will show you uh +the uh FAL heat conduction law and with + + align:start position:0% +the uh FAL heat conduction law and with + + + align:start position:0% +the uh FAL heat conduction law and with +that you can go back and do other laws + + align:start position:0% +that you can go back and do other laws + + + align:start position:0% +that you can go back and do other laws +the fixed law and new and share stress + + align:start position:0% +the fixed law and new and share stress + + + align:start position:0% +the fixed law and new and share stress +law this can all be similar + + align:start position:0% +law this can all be similar + + + align:start position:0% +law this can all be similar +done so uh let's look at per energy of + + align:start position:0% +done so uh let's look at per energy of + + + align:start position:0% +done so uh let's look at per energy of +per carrier right so we + + align:start position:0% +per carrier right so we + + + align:start position:0% +per carrier right so we +can say how + + align:start position:0% + + + + align:start position:0% + +much look at the one carrier so I have a + + align:start position:0% +much look at the one carrier so I have a + + + align:start position:0% +much look at the one carrier so I have a +box + + align:start position:0% +box + + + align:start position:0% +box +of gas molecules let say I have + + align:start position:0% + + + + align:start position:0% + +hydrogen and this is a d + + align:start position:0% + + + + align:start position:0% + +Atomic molecule right so we have two + + align:start position:0% +Atomic molecule right so we have two + + + align:start position:0% +Atomic molecule right so we have two +hydrogen + + align:start position:0% +hydrogen + + + align:start position:0% +hydrogen +atoms and we have one hydrogen another + + align:start position:0% +atoms and we have one hydrogen another + + + align:start position:0% +atoms and we have one hydrogen another +hydrogen atom they are bound + + align:start position:0% +hydrogen atom they are bound + + + align:start position:0% +hydrogen atom they are bound +together and then when I look at the + + align:start position:0% +together and then when I look at the + + + align:start position:0% +together and then when I look at the +energy of this + + align:start position:0% +energy of this + + + align:start position:0% +energy of this +molecule I look at the possible modes + + align:start position:0% +molecule I look at the possible modes + + + align:start position:0% +molecule I look at the possible modes +possible ways of storing energy by the + + align:start position:0% +possible ways of storing energy by the + + + align:start position:0% +possible ways of storing energy by the +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +what are the forms of + + align:start position:0% + + + + align:start position:0% + +energy I'm sorry potential ener okay so + + align:start position:0% +energy I'm sorry potential ener okay so + + + align:start position:0% +energy I'm sorry potential ener okay so +we have kinetic + + align:start position:0% +we have kinetic + + + align:start position:0% +we have kinetic +energy that's a + + align:start position:0% + + + + align:start position:0% + +translation so this hydrogen molecule is + + align:start position:0% +translation so this hydrogen molecule is + + + align:start position:0% +translation so this hydrogen molecule is +moving around right and in that case I + + align:start position:0% +moving around right and in that case I + + + align:start position:0% +moving around right and in that case I +look at the mass Center I can say okay I + + align:start position:0% +look at the mass Center I can say okay I + + + align:start position:0% +look at the mass Center I can say okay I +don't care about this two individual + + align:start position:0% +don't care about this two individual + + + align:start position:0% +don't care about this two individual +atoms + + align:start position:0% +atoms + + + align:start position:0% +atoms +they they are just a cluster and they + + align:start position:0% +they they are just a cluster and they + + + align:start position:0% +they they are just a cluster and they +move at certain + + align:start position:0% +move at certain + + + align:start position:0% +move at certain +velocity and the kinetic energy E equals + + align:start position:0% +velocity and the kinetic energy E equals + + + align:start position:0% +velocity and the kinetic energy E equals +12 m² right so last time I made a + + align:start position:0% +12 m² right so last time I made a + + + align:start position:0% +12 m² right so last time I made a +statement if you understand energy + + align:start position:0% +statement if you understand energy + + + align:start position:0% +statement if you understand energy +momentum and entropy and now we looking + + align:start position:0% +momentum and entropy and now we looking + + + align:start position:0% +momentum and entropy and now we looking +go into the molecular picture and look + + align:start position:0% +go into the molecular picture and look + + + align:start position:0% +go into the molecular picture and look +at those energy so this is a translation + + align:start position:0% +at those energy so this is a translation + + + align:start position:0% +at those energy so this is a translation +kinetic + + align:start position:0% +kinetic + + + align:start position:0% +kinetic +energy what other Energies + + align:start position:0% +energy what other Energies + + + align:start position:0% +energy what other Energies +R Vibra rotation vibration okay and uh's + + align:start position:0% +R Vibra rotation vibration okay and uh's + + + align:start position:0% +R Vibra rotation vibration okay and uh's +let's look at the vibration so this two + + align:start position:0% +let's look at the vibration so this two + + + align:start position:0% +let's look at the vibration so this two +molecules are bound by Spring we in fact + + align:start position:0% +molecules are bound by Spring we in fact + + + align:start position:0% +molecules are bound by Spring we in fact +talked about uh the uh uh the inter + + align:start position:0% +talked about uh the uh uh the inter + + + align:start position:0% +talked about uh the uh uh the inter +Atomic force in the last lecture right + + align:start position:0% +Atomic force in the last lecture right + + + align:start position:0% +Atomic force in the last lecture right +the minimum point is the equilibrium so + + align:start position:0% +the minimum point is the equilibrium so + + + align:start position:0% +the minimum point is the equilibrium so +we can approximate as a a Sprint and + + align:start position:0% +we can approximate as a a Sprint and + + + align:start position:0% +we can approximate as a a Sprint and +this is a relative + + align:start position:0% +this is a relative + + + align:start position:0% +this is a relative +vibration within this two + + align:start position:0% +vibration within this two + + + align:start position:0% +vibration within this two +atoms that's another way to store the + + align:start position:0% +atoms that's another way to store the + + + align:start position:0% +atoms that's another way to store the +energy right so the + + align:start position:0% + + + + align:start position:0% + +vibration and in fact you can simplify + + align:start position:0% +vibration and in fact you can simplify + + + align:start position:0% +vibration and in fact you can simplify +this because this now is the two atom + + align:start position:0% +this because this now is the two atom + + + align:start position:0% +this because this now is the two atom +motion but if you simplify it relative + + align:start position:0% +motion but if you simplify it relative + + + align:start position:0% +motion but if you simplify it relative +with the center of the mass and you can + + align:start position:0% +with the center of the mass and you can + + + align:start position:0% +with the center of the mass and you can +essentially do a effective Mass sprin + + align:start position:0% +essentially do a effective Mass sprin + + + align:start position:0% +essentially do a effective Mass sprin +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so this is a classical Mass spring + + align:start position:0% +so this is a classical Mass spring + + + align:start position:0% +so this is a classical Mass spring +problem and you know for this classical + + align:start position:0% +problem and you know for this classical + + + align:start position:0% +problem and you know for this classical +sprad Mass what's the + + align:start position:0% +sprad Mass what's the + + + align:start position:0% +sprad Mass what's the +energy + + align:start position:0% +energy + + + align:start position:0% +energy +energy let's say you have the + + align:start position:0% +energy let's say you have the + + + align:start position:0% +energy let's say you have the +displacement is x k x² okay half K x² + + align:start position:0% +displacement is x k x² okay half K x² + + + align:start position:0% +displacement is x k x² okay half K x² +that's the + + align:start position:0% + + + + align:start position:0% + +potential there's another part + + align:start position:0% +potential there's another part + + + align:start position:0% +potential there's another part +right translation also MV s this is the + + align:start position:0% +right translation also MV s this is the + + + align:start position:0% +right translation also MV s this is the +way not the center of mass moving it's a + + align:start position:0% +way not the center of mass moving it's a + + + align:start position:0% +way not the center of mass moving it's a +relative vibration so the mass is + + align:start position:0% +relative vibration so the mass is + + + align:start position:0% +relative vibration so the mass is +relative to the center the + + align:start position:0% +relative to the center the + + + align:start position:0% +relative to the center the +potential this is the potential energy + + align:start position:0% +potential this is the potential energy + + + align:start position:0% +potential this is the potential energy +KX s + + align:start position:0% + + + + align:start position:0% + +right uh yeah I'm not considering + + align:start position:0% +right uh yeah I'm not considering + + + align:start position:0% +right uh yeah I'm not considering +gravity you can add gravitation yeah + + align:start position:0% +gravity you can add gravitation yeah + + + align:start position:0% +gravity you can add gravitation yeah +that's a that's a that that's + + align:start position:0% +that's a that's a that that's + + + align:start position:0% +that's a that's a that that's +possible okay so we have uh + + align:start position:0% +possible okay so we have uh + + + align:start position:0% +possible okay so we have uh +vibration and you also mention + + align:start position:0% +vibration and you also mention + + + align:start position:0% +vibration and you also mention +rotation so we have also + + align:start position:0% + + + + align:start position:0% + +rotation and rotation is now I can take + + align:start position:0% +rotation and rotation is now I can take + + + align:start position:0% +rotation and rotation is now I can take +a simple picture I fix this Sprint + + align:start position:0% +a simple picture I fix this Sprint + + + align:start position:0% +a simple picture I fix this Sprint +right and now I have a rod with two + + align:start position:0% +right and now I have a rod with two + + + align:start position:0% +right and now I have a rod with two +balls attached to it and they will + + align:start position:0% +balls attached to it and they will + + + align:start position:0% +balls attached to it and they will +rotate and the energy of rotational + + align:start position:0% +rotate and the energy of rotational + + + align:start position:0% +rotate and the energy of rotational +energy is 12 I Omega + + align:start position:0% +energy is 12 I Omega + + + align:start position:0% +energy is 12 I Omega +squ + + align:start position:0% + + + + align:start position:0% + +right I is the moment of + + align:start position:0% +right I is the moment of + + + align:start position:0% +right I is the moment of +inertia and Omega square is Omega is the + + align:start position:0% +inertia and Omega square is Omega is the + + + align:start position:0% +inertia and Omega square is Omega is the +angular momentum the angular of + + align:start position:0% +angular momentum the angular of + + + align:start position:0% +angular momentum the angular of +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +right so so we + + align:start position:0% +right so so we + + + align:start position:0% +right so so we +have translation vibration rotation + + align:start position:0% +have translation vibration rotation + + + align:start position:0% +have translation vibration rotation +anything + + align:start position:0% + + + + align:start position:0% + +else anything + + align:start position:0% + + + + align:start position:0% + +else don't forget a + + align:start position:0% +else don't forget a + + + align:start position:0% +else don't forget a +charge + + align:start position:0% +charge + + + align:start position:0% +charge +right so if I look at individual + + align:start position:0% +right so if I look at individual + + + align:start position:0% +right so if I look at individual +hydrogen + + align:start position:0% +hydrogen + + + align:start position:0% +hydrogen +atom and it + + align:start position:0% +atom and it + + + align:start position:0% +atom and it +has + + align:start position:0% +has + + + align:start position:0% +has +nucle and has + + align:start position:0% +nucle and has + + + align:start position:0% +nucle and has +electrons + + align:start position:0% +electrons + + + align:start position:0% +electrons +Mo + + align:start position:0% +Mo + + + align:start position:0% +Mo +WR okay so we also have + + align:start position:0% + + + + align:start position:0% + +electronic and the + + align:start position:0% +electronic and the + + + align:start position:0% +electronic and the +electronic uh energy I can rather either + + align:start position:0% +electronic uh energy I can rather either + + + align:start position:0% +electronic uh energy I can rather either +use e symbol or potential the + + align:start position:0% +use e symbol or potential the + + + align:start position:0% +use e symbol or potential the +interaction of two charge let's say here + + align:start position:0% +interaction of two charge let's say here + + + align:start position:0% +interaction of two charge let's say here +is q1 here is a + + align:start position:0% +is q1 here is a + + + align:start position:0% +is q1 here is a +Q2 then the colum potential right the + + align:start position:0% +Q2 then the colum potential right the + + + align:start position:0% +Q2 then the colum potential right the +colum interaction two + + align:start position:0% +colum interaction two + + + align:start position:0% +colum interaction two +charges anyone remember + + align:start position:0% + + + + align:start position:0% + +that q1 Q2 4 Pi Epsilon R Epsilon is di + + align:start position:0% +that q1 Q2 4 Pi Epsilon R Epsilon is di + + + align:start position:0% +that q1 Q2 4 Pi Epsilon R Epsilon is di +electric + + align:start position:0% +electric + + + align:start position:0% +electric +constant right R is the separation + + align:start position:0% +constant right R is the separation + + + align:start position:0% +constant right R is the separation +between the + + align:start position:0% +between the + + + align:start position:0% +between the +two okay so those are the form of + + align:start position:0% +two okay so those are the form of + + + align:start position:0% +two okay so those are the form of +energy this molecule stores with it so + + align:start position:0% +energy this molecule stores with it so + + + align:start position:0% +energy this molecule stores with it so +when we think about internal energy of a + + align:start position:0% +when we think about internal energy of a + + + align:start position:0% +when we think about internal energy of a +gas they are stored in those forms + + align:start position:0% +gas they are stored in those forms + + + align:start position:0% +gas they are stored in those forms +translation vibration rotation + + align:start position:0% + + + + align:start position:0% + +electronic + + align:start position:0% +electronic + + + align:start position:0% +electronic +okay and so that's the case of uh a + + align:start position:0% +okay and so that's the case of uh a + + + align:start position:0% +okay and so that's the case of uh a +molecule and if we go to + + align:start position:0% + + + + align:start position:0% + +solid which is a lot more complex we'll + + align:start position:0% +solid which is a lot more complex we'll + + + align:start position:0% +solid which is a lot more complex we'll +talk more later but see last time we + + align:start position:0% +talk more later but see last time we + + + align:start position:0% +talk more later but see last time we +gave a simple picture of collected atom + + align:start position:0% +gave a simple picture of collected atom + + + align:start position:0% +gave a simple picture of collected atom +by Sprint so it has a + + align:start position:0% + + + + align:start position:0% + +vibration + + align:start position:0% +vibration + + + align:start position:0% +vibration +right and also each atom has + + align:start position:0% +right and also each atom has + + + align:start position:0% +right and also each atom has +electrons and nuc so it has the + + align:start position:0% + + + + align:start position:0% + +electronic and uh in fact uh for solid + + align:start position:0% +electronic and uh in fact uh for solid + + + align:start position:0% +electronic and uh in fact uh for solid +it doesn't have this rotation right the + + align:start position:0% +it doesn't have this rotation right the + + + align:start position:0% +it doesn't have this rotation right the +atoms don't rotate it's fixed there so + + align:start position:0% +atoms don't rotate it's fixed there so + + + align:start position:0% +atoms don't rotate it's fixed there so +that's in that sense that's better right + + align:start position:0% +that's in that sense that's better right + + + align:start position:0% +that's in that sense that's better right +when I deal with a liquid I have more + + align:start position:0% +when I deal with a liquid I have more + + + align:start position:0% +when I deal with a liquid I have more +trouble because all this other + + align:start position:0% + + + + align:start position:0% + +possibilities okay so uh let's leave + + align:start position:0% +possibilities okay so uh let's leave + + + align:start position:0% +possibilities okay so uh let's leave +this to + + align:start position:0% +this to + + + align:start position:0% +this to +later and uh what I want to say is those + + align:start position:0% +later and uh what I want to say is those + + + align:start position:0% +later and uh what I want to say is those +are all the classical form + + align:start position:0% +are all the classical form + + + align:start position:0% +are all the classical form +classical + + align:start position:0% +classical + + + align:start position:0% +classical +Expressions right and what we're going + + align:start position:0% +Expressions right and what we're going + + + align:start position:0% +Expressions right and what we're going +to move on next is to give the quantized + + align:start position:0% +to move on next is to give the quantized + + + align:start position:0% +to move on next is to give the quantized +form in quantum + + align:start position:0% +form in quantum + + + align:start position:0% +form in quantum +mechanics right what are the micro the + + align:start position:0% +mechanics right what are the micro the + + + align:start position:0% +mechanics right what are the micro the +energy of the translation vibration + + align:start position:0% +energy of the translation vibration + + + align:start position:0% +energy of the translation vibration +rotation and + + align:start position:0% +rotation and + + + align:start position:0% +rotation and +electronic and there we see the + + align:start position:0% +electronic and there we see the + + + align:start position:0% +electronic and there we see the +quantization of energy levels and that's + + align:start position:0% +quantization of energy levels and that's + + + align:start position:0% +quantization of energy levels and that's +very important + + align:start position:0% + + + + align:start position:0% + +okay now this is a uh individual um + + align:start position:0% +okay now this is a uh individual um + + + align:start position:0% +okay now this is a uh individual um +energy how + + align:start position:0% +energy how + + + align:start position:0% +energy how +much what we look next + + align:start position:0% + + + + align:start position:0% + +is how many of + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% +them + + + align:start position:0% +them +okay and I have a + + align:start position:0% +okay and I have a + + + align:start position:0% +okay and I have a +box of Mo + + align:start position:0% +box of Mo + + + align:start position:0% +box of Mo +here and of course I can say well per + + align:start position:0% +here and of course I can say well per + + + align:start position:0% +here and of course I can say well per +unit volume this is the + + align:start position:0% +unit volume this is the + + + align:start position:0% +unit volume this is the +L of + + align:start position:0% + + + + align:start position:0% + +molecules per unit + + align:start position:0% + + + + align:start position:0% + +volume right that's the L of molec per + + align:start position:0% +volume right that's the L of molec per + + + align:start position:0% +volume right that's the L of molec per +unit + + align:start position:0% +unit + + + align:start position:0% +unit +volume but each molecule could have one + + align:start position:0% +volume but each molecule could have one + + + align:start position:0% +volume but each molecule could have one +MV squ that way in my current picture is + + align:start position:0% +MV squ that way in my current picture is + + + align:start position:0% +MV squ that way in my current picture is +not defined + + align:start position:0% +not defined + + + align:start position:0% +not defined +velocity right it could be anywhere from + + align:start position:0% +velocity right it could be anywhere from + + + align:start position:0% +velocity right it could be anywhere from +negative infinite velocity Vector + + align:start position:0% +negative infinite velocity Vector + + + align:start position:0% +negative infinite velocity Vector +negative infinite to positive infinite + + align:start position:0% +negative infinite to positive infinite + + + align:start position:0% +negative infinite to positive infinite +so the question is if I give you a box + + align:start position:0% +so the question is if I give you a box + + + align:start position:0% +so the question is if I give you a box +of gas at certain temperature T now I'm + + align:start position:0% +of gas at certain temperature T now I'm + + + align:start position:0% +of gas at certain temperature T now I'm +bring the Thal + + align:start position:0% +bring the Thal + + + align:start position:0% +bring the Thal +part how much energy what's the + + align:start position:0% +part how much energy what's the + + + align:start position:0% +part how much energy what's the +probability of the molecule had has + + align:start position:0% +probability of the molecule had has + + + align:start position:0% +probability of the molecule had has +certain value of energy + + align:start position:0% +certain value of energy + + + align:start position:0% +certain value of energy +e right because the Lum of molecules is + + align:start position:0% +e right because the Lum of molecules is + + + align:start position:0% +e right because the Lum of molecules is +very + + align:start position:0% +very + + + align:start position:0% +very +large I have to bring in this + + align:start position:0% +large I have to bring in this + + + align:start position:0% +large I have to bring in this +statistical + + align:start position:0% +statistical + + + align:start position:0% +statistical +picture okay so at temperature + + align:start position:0% + + + + align:start position:0% + +T temperature + + align:start position:0% + + + + align:start position:0% + +t + + align:start position:0% + + + + align:start position:0% + +is let's look at the translation only so + + align:start position:0% +is let's look at the translation only so + + + align:start position:0% +is let's look at the translation only so +I can simplify my picture even uh um + + align:start position:0% +I can simplify my picture even uh um + + + align:start position:0% +I can simplify my picture even uh um +more simplified I don't consider + + align:start position:0% +more simplified I don't consider + + + align:start position:0% +more simplified I don't consider +hydrogen atom I consider helium + + align:start position:0% +hydrogen atom I consider helium + + + align:start position:0% +hydrogen atom I consider helium +atom right monatomic gas translation + + align:start position:0% +atom right monatomic gas translation + + + align:start position:0% +atom right monatomic gas translation +energy only of course there electronic + + align:start position:0% +energy only of course there electronic + + + align:start position:0% +energy only of course there electronic +part so at temperature T how much is is + + align:start position:0% +part so at temperature T how much is is + + + align:start position:0% +part so at temperature T how much is is +say what's the + + align:start position:0% +say what's the + + + align:start position:0% +say what's the +probability of a molecule has actually + + align:start position:0% +probability of a molecule has actually + + + align:start position:0% +probability of a molecule has actually +certain value of + + align:start position:0% + + + + align:start position:0% + +energy right what's the + + align:start position:0% + + + + align:start position:0% + +answer yeah so that's the this is going + + align:start position:0% +answer yeah so that's the this is going + + + align:start position:0% +answer yeah so that's the this is going +to the + + align:start position:0% +to the + + + align:start position:0% +to the +statistical uh thermal physics + + align:start position:0% +statistical uh thermal physics + + + align:start position:0% +statistical uh thermal physics +statistical + + align:start position:0% +statistical + + + align:start position:0% +statistical +physics and the distribution is given by + + align:start position:0% +physics and the distribution is given by + + + align:start position:0% +physics and the distribution is given by +the + + align:start position:0% +the + + + align:start position:0% +the +famous Borman + + align:start position:0% + + + + align:start position:0% + +factor I try to use all captors + + align:start position:0% + + + + align:start position:0% + +now so BS my Factor tells you the + + align:start position:0% +now so BS my Factor tells you the + + + align:start position:0% +now so BS my Factor tells you the +probability of finding um a molecule or + + align:start position:0% +probability of finding um a molecule or + + + align:start position:0% +probability of finding um a molecule or +atom has certain energy e at + + align:start position:0% +atom has certain energy e at + + + align:start position:0% +atom has certain energy e at +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +T + + align:start position:0% +T + + + align:start position:0% +T +is a normalization this is probability + + align:start position:0% +is a normalization this is probability + + + align:start position:0% +is a normalization this is probability +right so it's a has a normalization + + align:start position:0% +right so it's a has a normalization + + + align:start position:0% +right so it's a has a normalization +constant minus + + align:start position:0% +constant minus + + + align:start position:0% +constant minus +E over + + align:start position:0% +E over + + + align:start position:0% +E over +KBT and this KB is the bman constant we + + align:start position:0% +KBT and this KB is the bman constant we + + + align:start position:0% +KBT and this KB is the bman constant we +mentioned last time KB is + + align:start position:0% +mentioned last time KB is + + + align:start position:0% +mentioned last time KB is +1.38 10 to Theus 23 J per + + align:start position:0% + + + + align:start position:0% + +K right so that's the bman factor and uh + + align:start position:0% +K right so that's the bman factor and uh + + + align:start position:0% +K right so that's the bman factor and uh +some of you taking statistical physics + + align:start position:0% +some of you taking statistical physics + + + align:start position:0% +some of you taking statistical physics +and that's easy if you haven't taken it + + align:start position:0% +and that's easy if you haven't taken it + + + align:start position:0% +and that's easy if you haven't taken it +you learned a relance law + + align:start position:0% +you learned a relance law + + + align:start position:0% +you learned a relance law +anytime people look at that the + + align:start position:0% +anytime people look at that the + + + align:start position:0% +anytime people look at that the +temperature dependent they always like + + align:start position:0% +temperature dependent they always like + + + align:start position:0% +temperature dependent they always like +to put the exponential Factor that's + + align:start position:0% +to put the exponential Factor that's + + + align:start position:0% +to put the exponential Factor that's +because BS m is behind it + + align:start position:0% +because BS m is behind it + + + align:start position:0% +because BS m is behind it +okay and then we'll come back to this + + align:start position:0% +okay and then we'll come back to this + + + align:start position:0% +okay and then we'll come back to this +later + + align:start position:0% +later + + + align:start position:0% +later +on so I'm going to build on this + + align:start position:0% +on so I'm going to build on this + + + align:start position:0% +on so I'm going to build on this +exponential factor and to determine + + align:start position:0% +exponential factor and to determine + + + align:start position:0% +exponential factor and to determine +what's the average energy per molecule + + align:start position:0% +what's the average energy per molecule + + + align:start position:0% +what's the average energy per molecule +translation energy per + + align:start position:0% +translation energy per + + + align:start position:0% +translation energy per +molecule and how I do it first I need to + + align:start position:0% +molecule and how I do it first I need to + + + align:start position:0% +molecule and how I do it first I need to +find this normalization factor + + align:start position:0% +find this normalization factor + + + align:start position:0% +find this normalization factor +a and I determine this probability so + + align:start position:0% +a and I determine this probability so + + + align:start position:0% +a and I determine this probability so +let's exam the translational energy m v + + align:start position:0% +let's exam the translational energy m v + + + align:start position:0% +let's exam the translational energy m v +s so V is really has this Vector right + + align:start position:0% +s so V is really has this Vector right + + + align:start position:0% +s so V is really has this Vector right +VX v y v z so I write VX s + v y 2 + VZ + + align:start position:0% + + + + align:start position:0% + +squ + + align:start position:0% +squ + + + align:start position:0% +squ +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +now I take advantage of the definition + + align:start position:0% +now I take advantage of the definition + + + align:start position:0% +now I take advantage of the definition +for this F + + align:start position:0% +for this F + + + align:start position:0% +for this F +probability is is I find the molecule + + align:start position:0% +probability is is I find the molecule + + + align:start position:0% +probability is is I find the molecule +having velocity from minus infinite to + + align:start position:0% +having velocity from minus infinite to + + + align:start position:0% +having velocity from minus infinite to +plus infinite must normaliz to one right + + align:start position:0% +plus infinite must normaliz to one right + + + align:start position:0% +plus infinite must normaliz to one right +that's all the range you can have so + + align:start position:0% +that's all the range you can have so + + + align:start position:0% +that's all the range you can have so +from the + + align:start position:0% +from the + + + align:start position:0% +from the +normalization from minus infinite to + + align:start position:0% +normalization from minus infinite to + + + align:start position:0% +normalization from minus infinite to +plus infinite for VX v y VZ right I'm + + align:start position:0% +plus infinite for VX v y VZ right I'm + + + align:start position:0% +plus infinite for VX v y VZ right I'm +doing it first I'll do it in C + + align:start position:0% +doing it first I'll do it in C + + + align:start position:0% +doing it first I'll do it in C +coordinate then I'll transfer to a + + align:start position:0% +coordinate then I'll transfer to a + + + align:start position:0% +coordinate then I'll transfer to a +spherical coordinate so let's look at + + align:start position:0% +spherical coordinate so let's look at + + + align:start position:0% +spherical coordinate so let's look at +first coordinate from minus infinite to + + align:start position:0% +first coordinate from minus infinite to + + + align:start position:0% +first coordinate from minus infinite to +plus infinite + + align:start position:0% +plus infinite + + + align:start position:0% +plus infinite +dvx minus infinite to plus infinite + + align:start position:0% +dvx minus infinite to plus infinite + + + align:start position:0% +dvx minus infinite to plus infinite +dvy + + align:start position:0% + + + + align:start position:0% + +and one warning is that you will often + + align:start position:0% +and one warning is that you will often + + + align:start position:0% +and one warning is that you will often +encounter many of those integral forms + + align:start position:0% +encounter many of those integral forms + + + align:start position:0% +encounter many of those integral forms +because we when we look at the + + align:start position:0% +because we when we look at the + + + align:start position:0% +because we when we look at the +probability we have to + + align:start position:0% +probability we have to + + + align:start position:0% +probability we have to +integrate uh from from all the possible + + align:start position:0% +integrate uh from from all the possible + + + align:start position:0% +integrate uh from from all the possible +States so VX V + + align:start position:0% +States so VX V + + + align:start position:0% +States so VX V +VZ and uh F so I put a bman factor so + + align:start position:0% +VZ and uh F so I put a bman factor so + + + align:start position:0% +VZ and uh F so I put a bman factor so +this is a integrant is uh uh I'm going + + align:start position:0% +this is a integrant is uh uh I'm going + + + align:start position:0% +this is a integrant is uh uh I'm going +to be lazy I'm not writing that + + align:start position:0% +to be lazy I'm not writing that + + + align:start position:0% +to be lazy I'm not writing that +exponential e so you put in there this + + align:start position:0% +exponential e so you put in there this + + + align:start position:0% +exponential e so you put in there this +should equal to + + align:start position:0% +should equal to + + + align:start position:0% +should equal to +one + + align:start position:0% +one + + + align:start position:0% +one +right you look at it if you plug in your + + align:start position:0% +right you look at it if you plug in your + + + align:start position:0% +right you look at it if you plug in your +e in VX Square v y Square VZ square and + + align:start position:0% +e in VX Square v y Square VZ square and + + + align:start position:0% +e in VX Square v y Square VZ square and +you can Factor it out and you can do + + align:start position:0% +you can Factor it out and you can do + + + align:start position:0% +you can Factor it out and you can do +your integration for dvx individually + + align:start position:0% +your integration for dvx individually + + + align:start position:0% +your integration for dvx individually +dvy individually DV Z + + align:start position:0% +dvy individually DV Z + + + align:start position:0% +dvy individually DV Z +individually and with that you only have + + align:start position:0% +individually and with that you only have + + + align:start position:0% +individually and with that you only have +a constant a you do not + + align:start position:0% +a constant a you do not + + + align:start position:0% +a constant a you do not +know and you determine that constant + + align:start position:0% +know and you determine that constant + + + align:start position:0% +know and you determine that constant +a right so I'm not going through the + + align:start position:0% +a right so I'm not going through the + + + align:start position:0% +a right so I'm not going through the +integral and you can either check the + + align:start position:0% +integral and you can either check the + + + align:start position:0% +integral and you can either check the +integration table or there's a nice + + align:start position:0% +integration table or there's a nice + + + align:start position:0% +integration table or there's a nice +mathematic trick + + align:start position:0% +mathematic trick + + + align:start position:0% +mathematic trick +if you like to play you can find that + + align:start position:0% +if you like to play you can find that + + + align:start position:0% +if you like to play you can find that +Integra + + align:start position:0% +Integra + + + align:start position:0% +Integra +integration value so here what I have is + + align:start position:0% +integration value so here what I have is + + + align:start position:0% +integration value so here what I have is +2 pi KB T three halves three halves is + + align:start position:0% +2 pi KB T three halves three halves is + + + align:start position:0% +2 pi KB T three halves three halves is +because each of this contribute + + align:start position:0% + + + + align:start position:0% + +one2 + + align:start position:0% +one2 + + + align:start position:0% +one2 +okay so now I have if I plug in this a + + align:start position:0% +okay so now I have if I plug in this a + + + align:start position:0% +okay so now I have if I plug in this a +into the f I get + + align:start position:0% +into the f I get + + + align:start position:0% +into the f I get +F in terms of VX v y v z the + + align:start position:0% +F in terms of VX v y v z the + + + align:start position:0% +F in terms of VX v y v z the +distribution at temperature T is m 2 pi + + align:start position:0% +distribution at temperature T is m 2 pi + + + align:start position:0% +distribution at temperature T is m 2 pi +KBT 3 hals + + align:start position:0% +KBT 3 hals + + + align:start position:0% +KBT 3 hals +exponential I want to write the whole + + align:start position:0% +exponential I want to write the whole + + + align:start position:0% +exponential I want to write the whole +thing so this is a VX S Plus v y 2 plus + + align:start position:0% +thing so this is a VX S Plus v y 2 plus + + + align:start position:0% +thing so this is a VX S Plus v y 2 plus +VZ + + align:start position:0% +VZ + + + align:start position:0% +VZ +squide by 2 KBT + + align:start position:0% +squide by 2 KBT + + + align:start position:0% +squide by 2 KBT +and this is a Maxwell + + align:start position:0% + + + + align:start position:0% + +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +Maxwell velocity + + align:start position:0% + + + + align:start position:0% + +distribution + + align:start position:0% +distribution + + + align:start position:0% +distribution +distribution + + align:start position:0% + + + + align:start position:0% + +okay so it looks uh uh uh pretty uh + + align:start position:0% +okay so it looks uh uh uh pretty uh + + + align:start position:0% +okay so it looks uh uh uh pretty uh +tedious but essentially it's 1 half it's + + align:start position:0% +tedious but essentially it's 1 half it's + + + align:start position:0% +tedious but essentially it's 1 half it's +it's an energy + + align:start position:0% +it's an energy + + + align:start position:0% +it's an energy +expression2 M + + align:start position:0% +expression2 M + + + align:start position:0% +expression2 M +Square + + align:start position:0% +Square + + + align:start position:0% +Square +Maxwell what you heard about + + align:start position:0% +Maxwell what you heard about + + + align:start position:0% +Maxwell what you heard about +Maxwell what other things you heard + + align:start position:0% +Maxwell what other things you heard + + + align:start position:0% +Maxwell what other things you heard +about + + align:start position:0% + + + + align:start position:0% + +Maxwell Max Square equation right you + + align:start position:0% +Maxwell Max Square equation right you + + + align:start position:0% +Maxwell Max Square equation right you +probably heard that rather than this + + align:start position:0% +probably heard that rather than this + + + align:start position:0% +probably heard that rather than this +let's say uh in fact you look at all + + align:start position:0% +let's say uh in fact you look at all + + + align:start position:0% +let's say uh in fact you look at all +those very famous people in the + + align:start position:0% +those very famous people in the + + + align:start position:0% +those very famous people in the +say + + align:start position:0% +say + + + align:start position:0% +say +1800 1900 they've done many things right + + align:start position:0% +1800 1900 they've done many things right + + + align:start position:0% +1800 1900 they've done many things right +newon not just the newon mechanics law + + align:start position:0% +newon not just the newon mechanics law + + + align:start position:0% +newon not just the newon mechanics law +new Optics + + align:start position:0% +new Optics + + + align:start position:0% +new Optics +also you can do all + + align:start position:0% +also you can do all + + + align:start position:0% +also you can do all +that okay here is velocity I'm using VX + + align:start position:0% +that okay here is velocity I'm using VX + + + align:start position:0% +that okay here is velocity I'm using VX +v y + + align:start position:0% +v y + + + align:start position:0% +v y +VZ right I could make my life much + + align:start position:0% +VZ right I could make my life much + + + align:start position:0% +VZ right I could make my life much +easier if I use very often when I do + + align:start position:0% +easier if I use very often when I do + + + align:start position:0% +easier if I use very often when I do +this integration I change the coordinate + + align:start position:0% +this integration I change the coordinate + + + align:start position:0% +this integration I change the coordinate +rather than dvx dvy dvz I do a spherical + + align:start position:0% +rather than dvx dvy dvz I do a spherical + + + align:start position:0% +rather than dvx dvy dvz I do a spherical +coordinate because it's + + align:start position:0% +coordinate because it's + + + align:start position:0% +coordinate because it's +symmetric okay so if I change my + + align:start position:0% +symmetric okay so if I change my + + + align:start position:0% +symmetric okay so if I change my +coordinate to from a + + align:start position:0% +coordinate to from a + + + align:start position:0% +coordinate to from a +dvx DV y DV Z into a spherical + + align:start position:0% +dvx DV y DV Z into a spherical + + + align:start position:0% +dvx DV y DV Z into a spherical +coordinate due to symmetry is 4 Pi v² d + + align:start position:0% +coordinate due to symmetry is 4 Pi v² d + + + align:start position:0% +coordinate due to symmetry is 4 Pi v² d +v right V now is the r the + + align:start position:0% +v right V now is the r the + + + align:start position:0% +v right V now is the r the +radius and so the range of way is from + + align:start position:0% +radius and so the range of way is from + + + align:start position:0% +radius and so the range of way is from +zero to positive infinite is not from + + align:start position:0% +zero to positive infinite is not from + + + align:start position:0% +zero to positive infinite is not from +negative infinite to infinite right when + + align:start position:0% +negative infinite to infinite right when + + + align:start position:0% +negative infinite to infinite right when +you do if you think about from DX Dy DZ + + align:start position:0% +you do if you think about from DX Dy DZ + + + align:start position:0% +you do if you think about from DX Dy DZ +into R + + align:start position:0% +into R + + + align:start position:0% +into R +coordinate okay so because of that and + + align:start position:0% +coordinate okay so because of that and + + + align:start position:0% +coordinate okay so because of that and +my in my normalization when I do + + align:start position:0% +my in my normalization when I do + + + align:start position:0% +my in my normalization when I do +normalization if I use spherical + + align:start position:0% +normalization if I use spherical + + + align:start position:0% +normalization if I use spherical +coordinate is 0 to + + align:start position:0% +coordinate is 0 to + + + align:start position:0% +coordinate is 0 to +infinite and fway now I do not use VX v + + align:start position:0% +infinite and fway now I do not use VX v + + + align:start position:0% +infinite and fway now I do not use VX v +y v z I use f way and D way + + align:start position:0% +y v z I use f way and D way + + + align:start position:0% +y v z I use f way and D way +equals + + align:start position:0% +equals + + + align:start position:0% +equals +1 that's another way to do it okay and + + align:start position:0% +1 that's another way to do it okay and + + + align:start position:0% +1 that's another way to do it okay and +in this + + align:start position:0% +in this + + + align:start position:0% +in this +case your + + align:start position:0% +case your + + + align:start position:0% +case your +FV equals 4 Pi + + align:start position:0% +FV equals 4 Pi + + + align:start position:0% +FV equals 4 Pi +v² m 2 pi + + align:start position:0% +v² m 2 pi + + + align:start position:0% +v² m 2 pi +KBT + + align:start position:0% +KBT + + + align:start position:0% +KBT + + align:start position:0% + + + align:start position:0% +exponential minus M v² over 2 + + align:start position:0% +exponential minus M v² over 2 + + + align:start position:0% +exponential minus M v² over 2 +KBT it's simple rewriting the caran into + + align:start position:0% +KBT it's simple rewriting the caran into + + + align:start position:0% +KBT it's simple rewriting the caran into +spherical but the point I want to make + + align:start position:0% +spherical but the point I want to make + + + align:start position:0% +spherical but the point I want to make +is if you use + + align:start position:0% +is if you use + + + align:start position:0% +is if you use +way you uh uh you you do not do uh say + + align:start position:0% +way you uh uh you you do not do uh say + + + align:start position:0% +way you uh uh you you do not do uh say +because 4 Pi V square is already + + align:start position:0% +because 4 Pi V square is already + + + align:start position:0% +because 4 Pi V square is already +included here so you can't substitute + + align:start position:0% +included here so you can't substitute + + + align:start position:0% +included here so you can't substitute +this back into here and just do your VX + + align:start position:0% +this back into here and just do your VX + + + align:start position:0% +this back into here and just do your VX +V with again let's be consistent on + + align:start position:0% +V with again let's be consistent on + + + align:start position:0% +V with again let's be consistent on +which coordinate system you will be + + align:start position:0% +which coordinate system you will be + + + align:start position:0% +which coordinate system you will be +using okay so what does this tells me + + align:start position:0% +using okay so what does this tells me + + + align:start position:0% +using okay so what does this tells me +this math right I'm jumping into a + + align:start position:0% +this math right I'm jumping into a + + + align:start position:0% +this math right I'm jumping into a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +MTH because f is a probability + + align:start position:0% +MTH because f is a probability + + + align:start position:0% +MTH because f is a probability +right so now with that probability I can + + align:start position:0% +right so now with that probability I can + + + align:start position:0% +right so now with that probability I can +calculate the average I can calculate + + align:start position:0% +calculate the average I can calculate + + + align:start position:0% +calculate the average I can calculate +what's the average energy per + + align:start position:0% +what's the average energy per + + + align:start position:0% +what's the average energy per +molecule what's the average uh um any + + align:start position:0% +molecule what's the average uh um any + + + align:start position:0% +molecule what's the average uh um any +other numbers that you will be in + + align:start position:0% +other numbers that you will be in + + + align:start position:0% +other numbers that you will be in +interesting so if I calculate the + + align:start position:0% +interesting so if I calculate the + + + align:start position:0% +interesting so if I calculate the +average + + align:start position:0% +average + + + align:start position:0% +average +e per mcle the translation right so my + + align:start position:0% +e per mcle the translation right so my + + + align:start position:0% +e per mcle the translation right so my +average will be now depending on which + + align:start position:0% +average will be now depending on which + + + align:start position:0% +average will be now depending on which +system I I you choose you can do CTI or + + align:start position:0% +system I I you choose you can do CTI or + + + align:start position:0% +system I I you choose you can do CTI or +you can + + align:start position:0% +you can + + + align:start position:0% +you can +do the + + align:start position:0% +do the + + + align:start position:0% +do the +spherical now I'm going to write simply + + align:start position:0% +spherical now I'm going to write simply + + + align:start position:0% +spherical now I'm going to write simply +as a spherical so zero to infinite and + + align:start position:0% +as a spherical so zero to infinite and + + + align:start position:0% +as a spherical so zero to infinite and +the energy + + align:start position:0% +the energy + + + align:start position:0% +the energy +is 12 + + align:start position:0% +is 12 + + + align:start position:0% +is 12 +m² that's the average quantity the + + align:start position:0% +m² that's the average quantity the + + + align:start position:0% +m² that's the average quantity the +quantity I want to find what's the + + align:start position:0% +quantity I want to find what's the + + + align:start position:0% +quantity I want to find what's the +average given + + align:start position:0% +average given + + + align:start position:0% +average given +my f + + align:start position:0% +my f + + + align:start position:0% +my f +distribution right so I times f v i + + align:start position:0% +distribution right so I times f v i + + + align:start position:0% +distribution right so I times f v i +integrate over + + align:start position:0% + + + + align:start position:0% + +way now you can do your + + align:start position:0% +way now you can do your + + + align:start position:0% +way now you can do your +math to find that + + align:start position:0% +math to find that + + + align:start position:0% +math to find that +integral okay that's why I'm warning you + + align:start position:0% +integral okay that's why I'm warning you + + + align:start position:0% +integral okay that's why I'm warning you +you don't want to if you use a way you + + align:start position:0% +you don't want to if you use a way you + + + align:start position:0% +you don't want to if you use a way you +want be consistently all + + align:start position:0% +want be consistently all + + + align:start position:0% +want be consistently all +way you don't do VX v y v z if you do VX + + align:start position:0% +way you don't do VX v y v z if you do VX + + + align:start position:0% +way you don't do VX v y v z if you do VX +V VZ you start from here you do your + + align:start position:0% +V VZ you start from here you do your + + + align:start position:0% +V VZ you start from here you do your +ction at the beginning that f is + + align:start position:0% +ction at the beginning that f is + + + align:start position:0% +ction at the beginning that f is +different from what I write + + align:start position:0% +different from what I write + + + align:start position:0% +different from what I write +here it's the same thing but just be + + align:start position:0% +here it's the same thing but just be + + + align:start position:0% +here it's the same thing but just be +consistency + + align:start position:0% +consistency + + + align:start position:0% +consistency +so again I say you can go do that + + align:start position:0% +so again I say you can go do that + + + align:start position:0% +so again I say you can go do that +homework and what you have here is a + + align:start position:0% +homework and what you have here is a + + + align:start position:0% +homework and what you have here is a +one3 KBT all the m m give you a very + + align:start position:0% +one3 KBT all the m m give you a very + + + align:start position:0% +one3 KBT all the m m give you a very +beautiful very simple + + align:start position:0% + + + + align:start position:0% + +result so + + align:start position:0% +result so + + + align:start position:0% +result so +KBT is a + + align:start position:0% +KBT is a + + + align:start position:0% +KBT is a +quantity you will see often if you go to + + align:start position:0% +quantity you will see often if you go to + + + align:start position:0% +quantity you will see often if you go to +microscopic word that's the thermal + + align:start position:0% +microscopic word that's the thermal + + + align:start position:0% +microscopic word that's the thermal +energy average thermal energy + + align:start position:0% +energy average thermal energy + + + align:start position:0% +energy average thermal energy +translation energy of the + + align:start position:0% +translation energy of the + + + align:start position:0% +translation energy of the +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +okay yes + + align:start position:0% + + + + align:start position:0% + +divide if you divide by this that's one + + align:start position:0% +divide if you divide by this that's one + + + align:start position:0% +divide if you divide by this that's one +okay right so that's I already that's + + align:start position:0% +okay right so that's I already that's + + + align:start position:0% +okay right so that's I already that's +why my normalization + + align:start position:0% +why my normalization + + + align:start position:0% +why my normalization +Factor right we're doing the + + align:start position:0% +Factor right we're doing the + + + align:start position:0% +Factor right we're doing the +normalization + + align:start position:0% +normalization + + + align:start position:0% +normalization +factor okay so with this I can go to say + + align:start position:0% +factor okay so with this I can go to say + + + align:start position:0% +factor okay so with this I can go to say +what's the average velocity I say how + + align:start position:0% +what's the average velocity I say how + + + align:start position:0% +what's the average velocity I say how +right how much here is how much average + + align:start position:0% +right how much here is how much average + + + align:start position:0% +right how much here is how much average +energy pericle let's see based on this + + align:start position:0% +energy pericle let's see based on this + + + align:start position:0% +energy pericle let's see based on this +because of this + + align:start position:0% +because of this + + + align:start position:0% +because of this +translation 12 M Square so what's the + + align:start position:0% +translation 12 M Square so what's the + + + align:start position:0% +translation 12 M Square so what's the +average + + align:start position:0% +average + + + align:start position:0% +average +speed of the molecule so we can go to + + align:start position:0% +speed of the molecule so we can go to + + + align:start position:0% +speed of the molecule so we can go to +calculate + + align:start position:0% + + + + align:start position:0% + +it right uh so I have average 12 m + + align:start position:0% +it right uh so I have average 12 m + + + align:start position:0% +it right uh so I have average 12 m +w² equal 23 KBT + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +V Square I take a square root of that so + + align:start position:0% +V Square I take a square root of that so + + + align:start position:0% +V Square I take a square root of that so +I can tell the magnitude is uh um here I + + align:start position:0% +I can tell the magnitude is uh um here I + + + align:start position:0% +I can tell the magnitude is uh um here I +have three + + align:start position:0% +have three + + + align:start position:0% +have three +KBT over + + align:start position:0% + + + + align:start position:0% + +M okay what's the order magnitud let's + + align:start position:0% +M okay what's the order magnitud let's + + + align:start position:0% +M okay what's the order magnitud let's +put in numbers I always like to put in + + align:start position:0% +put in numbers I always like to put in + + + align:start position:0% +put in numbers I always like to put in +numbers I take a + + align:start position:0% + + + + align:start position:0% + +helium + + align:start position:0% +helium + + + align:start position:0% +helium +gas and helium I can count how many + + align:start position:0% +gas and helium I can count how many + + + align:start position:0% +gas and helium I can count how many +what's the mass right helium has uh two + + align:start position:0% +what's the mass right helium has uh two + + + align:start position:0% +what's the mass right helium has uh two +neutrons two + + align:start position:0% +neutrons two + + + align:start position:0% +neutrons two +protons two electron masses to light + + align:start position:0% +protons two electron masses to light + + + align:start position:0% +protons two electron masses to light +electron masses are 2000 one one or 2 + + align:start position:0% +electron masses are 2000 one one or 2 + + + align:start position:0% +electron masses are 2000 one one or 2 +th000 of the mass of proton I forget + + align:start position:0% +th000 of the mass of proton I forget + + + align:start position:0% +th000 of the mass of proton I forget +about the electron Mass right so is + + align:start position:0% +about the electron Mass right so is + + + align:start position:0% +about the electron Mass right so is +four * proton Mass proton Mass 1 6 7 10 + + align:start position:0% +four * proton Mass proton Mass 1 6 7 10 + + + align:start position:0% +four * proton Mass proton Mass 1 6 7 10 +the mass 31 + + align:start position:0% +the mass 31 + + + align:start position:0% +the mass 31 +kilo again I only + + align:start position:0% +kilo again I only + + + align:start position:0% +kilo again I only +remember SI unit not 31 I'm sorry uh + + align:start position:0% +remember SI unit not 31 I'm sorry uh + + + align:start position:0% +remember SI unit not 31 I'm sorry uh +that's 31 is the electron + + align:start position:0% + + + + align:start position:0% + +27 okay so if I plug in this Mass KBT is + + align:start position:0% +27 okay so if I plug in this Mass KBT is + + + align:start position:0% +27 okay so if I plug in this Mass KBT is +1.38 10 the 23 temperature 300 + + align:start position:0% +1.38 10 the 23 temperature 300 + + + align:start position:0% +1.38 10 the 23 temperature 300 +kin right so what I'll get is a average + + align:start position:0% +kin right so what I'll get is a average + + + align:start position:0% +kin right so what I'll get is a average +veloc uh + + align:start position:0% +veloc uh + + + align:start position:0% +veloc uh +speed this one is 1.36 10 the 3r + + align:start position:0% +speed this one is 1.36 10 the 3r + + + align:start position:0% +speed this one is 1.36 10 the 3r +m/s it's about thousand m/ + + align:start position:0% +m/s it's about thousand m/ + + + align:start position:0% +m/s it's about thousand m/ +second yes velocity uh you could go to + + align:start position:0% +second yes velocity uh you could go to + + + align:start position:0% +second yes velocity uh you could go to +calculate right uh you can you you can + + align:start position:0% +calculate right uh you can you you can + + + align:start position:0% +calculate right uh you can you you can +calculate the uh it's also KBT it's way + + align:start position:0% +calculate the uh it's also KBT it's way + + + align:start position:0% +calculate the uh it's also KBT it's way +Mass + + align:start position:0% +Mass + + + align:start position:0% +Mass +V + + align:start position:0% +V + + + align:start position:0% +V +Square do that you'll get also KBT + + align:start position:0% +Square do that you'll get also KBT + + + align:start position:0% +Square do that you'll get also KBT +that's the + + align:start position:0% +that's the + + + align:start position:0% +that's the +variance okay so this is a helium now if + + align:start position:0% +variance okay so this is a helium now if + + + align:start position:0% +variance okay so this is a helium now if +you put a a air air average + + align:start position:0% +you put a a air air average + + + align:start position:0% +you put a a air air average +mass + + align:start position:0% +mass + + + align:start position:0% +mass +27 right so you put in 27 you get about + + align:start position:0% +27 right so you put in 27 you get about + + + align:start position:0% +27 right so you put in 27 you get about +500 m/ + + align:start position:0% +500 m/ + + + align:start position:0% +500 m/ +second those molecules are moving pretty + + align:start position:0% +second those molecules are moving pretty + + + align:start position:0% +second those molecules are moving pretty +fast and the last lecture we discussed + + align:start position:0% +fast and the last lecture we discussed + + + align:start position:0% +fast and the last lecture we discussed +the momentum the + + align:start position:0% +the momentum the + + + align:start position:0% +the momentum the +pressure right we're filling one + + align:start position:0% +pressure right we're filling one + + + align:start position:0% +pressure right we're filling one +atmospher pressure and that's the + + align:start position:0% +atmospher pressure and that's the + + + align:start position:0% +atmospher pressure and that's the +momentum from this fast moving + + align:start position:0% + + + + align:start position:0% + +molecules + + align:start position:0% +molecules + + + align:start position:0% +molecules +right so uh one more common and this a + + align:start position:0% +right so uh one more common and this a + + + align:start position:0% +right so uh one more common and this a +three half + + align:start position:0% +three half + + + align:start position:0% +three half +KBT there is a very + + align:start position:0% +KBT there is a very + + + align:start position:0% +KBT there is a very +fundamental theorem behind this and that + + align:start position:0% +fundamental theorem behind this and that + + + align:start position:0% +fundamental theorem behind this and that +is if the distribution oyss the bman + + align:start position:0% + + + + align:start position:0% + +distribution and at a high + + align:start position:0% +distribution and at a high + + + align:start position:0% +distribution and at a high +temperature so by doing that high + + align:start position:0% +temperature so by doing that high + + + align:start position:0% +temperature so by doing that high +temperature I can do the integration + + align:start position:0% +temperature I can do the integration + + + align:start position:0% +temperature I can do the integration +later on when we introduce Quantum you + + align:start position:0% +later on when we introduce Quantum you + + + align:start position:0% +later on when we introduce Quantum you +can't do the integration anymore + + align:start position:0% +can't do the integration anymore + + + align:start position:0% +can't do the integration anymore +okay so at high temperature the energy + + align:start position:0% +okay so at high temperature the energy + + + align:start position:0% +okay so at high temperature the energy +very close so I can do + + align:start position:0% +very close so I can do + + + align:start position:0% +very close so I can do +integration and if the energy form for + + align:start position:0% +integration and if the energy form for + + + align:start position:0% +integration and if the energy form for +each energy form if it's a + + align:start position:0% +each energy form if it's a + + + align:start position:0% +each energy form if it's a +quadratic so what that do I mean so if + + align:start position:0% +quadratic so what that do I mean so if + + + align:start position:0% +quadratic so what that do I mean so if +you look at the kinetic + + align:start position:0% +you look at the kinetic + + + align:start position:0% +you look at the kinetic +energy this is 12 mvx squ right so each + + align:start position:0% +energy this is 12 mvx squ right so each + + + align:start position:0% +energy this is 12 mvx squ right so each +quadratic form if you go to do the + + align:start position:0% +quadratic form if you go to do the + + + align:start position:0% +quadratic form if you go to do the +average energy you find that average + + align:start position:0% +average energy you find that average + + + align:start position:0% +average energy you find that average +energy is 1 12 + + align:start position:0% +energy is 1 12 + + + align:start position:0% +energy is 1 12 +KT okay so 1 12 KT 1 12 KT 1 K KT that's + + align:start position:0% +KT okay so 1 12 KT 1 12 KT 1 K KT that's + + + align:start position:0% +KT okay so 1 12 KT 1 12 KT 1 K KT that's +32 KT and that's called the equip + + align:start position:0% +32 KT and that's called the equip + + + align:start position:0% +32 KT and that's called the equip +partition + + align:start position:0% + + + + align:start position:0% + +theorem okay + + align:start position:0% +theorem okay + + + align:start position:0% +theorem okay +uh I gave that's example of the uh + + align:start position:0% +uh I gave that's example of the uh + + + align:start position:0% +uh I gave that's example of the uh +translational + + align:start position:0% +translational + + + align:start position:0% +translational +energy and if you go to + + align:start position:0% +energy and if you go to + + + align:start position:0% +energy and if you go to +vibration you see + + align:start position:0% +vibration you see + + + align:start position:0% +vibration you see +here right it's a quadratic + + align:start position:0% +here right it's a quadratic + + + align:start position:0% +here right it's a quadratic +Term 12 KX Square the velocity 12 MV squ + + align:start position:0% +Term 12 KX Square the velocity 12 MV squ + + + align:start position:0% +Term 12 KX Square the velocity 12 MV squ +so at a very high temperature this is 1 + + align:start position:0% +so at a very high temperature this is 1 + + + align:start position:0% +so at a very high temperature this is 1 +12 KT average speaking this is 1 12 KT + + align:start position:0% + + + + align:start position:0% + +and the + + align:start position:0% +and the + + + align:start position:0% +and the +rotation 12 I Omega + + align:start position:0% +rotation 12 I Omega + + + align:start position:0% +rotation 12 I Omega +Square again it's quadratic right at the + + align:start position:0% +Square again it's quadratic right at the + + + align:start position:0% +Square again it's quadratic right at the +high + + align:start position:0% +high + + + align:start position:0% +high +temperature that's 1 12 KT and in fact + + align:start position:0% +temperature that's 1 12 KT and in fact + + + align:start position:0% +temperature that's 1 12 KT and in fact +the rotation that high temperature is + + align:start position:0% +the rotation that high temperature is + + + align:start position:0% +the rotation that high temperature is +only 80 kin or so for molecules the + + align:start position:0% +only 80 kin or so for molecules the + + + align:start position:0% +only 80 kin or so for molecules the +vibration need go to few thousand + + align:start position:0% +vibration need go to few thousand + + + align:start position:0% +vibration need go to few thousand +degree okay so that's why you learned + + align:start position:0% +degree okay so that's why you learned + + + align:start position:0% +degree okay so that's why you learned +the ideal gas law before + + align:start position:0% +the ideal gas law before + + + align:start position:0% +the ideal gas law before +right cway for different monatomic ideal + + align:start position:0% +right cway for different monatomic ideal + + + align:start position:0% +right cway for different monatomic ideal +gas diatomic ideal gas they have + + align:start position:0% +gas diatomic ideal gas they have + + + align:start position:0% +gas diatomic ideal gas they have +different CV + + align:start position:0% +different CV + + + align:start position:0% +different CV +values that's because diatomic gas you + + align:start position:0% +values that's because diatomic gas you + + + align:start position:0% +values that's because diatomic gas you +have the rotational modes coming in and + + align:start position:0% +have the rotational modes coming in and + + + align:start position:0% +have the rotational modes coming in and +monotonic only the + + align:start position:0% +monotonic only the + + + align:start position:0% +monotonic only the +translation that's the equal partion + + align:start position:0% +translation that's the equal partion + + + align:start position:0% +translation that's the equal partion +theorem well we'll go to discuss that + + align:start position:0% +theorem well we'll go to discuss that + + + align:start position:0% +theorem well we'll go to discuss that +more later on but here with that we get + + align:start position:0% +more later on but here with that we get + + + align:start position:0% +more later on but here with that we get +a fill in how fast and how much energy + + align:start position:0% +a fill in how fast and how much energy + + + align:start position:0% +a fill in how fast and how much energy +they + + align:start position:0% +they + + + align:start position:0% +they +have right next what we want to answer + + align:start position:0% +have right next what we want to answer + + + align:start position:0% +have right next what we want to answer +is how far they + + align:start position:0% + + + + align:start position:0% + +travel okay so we + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% + + + + align:start position:0% + +how far they travel by how far I mean + + align:start position:0% +how far they travel by how far I mean + + + align:start position:0% +how far they travel by how far I mean +think about the air molecules in this + + align:start position:0% +think about the air molecules in this + + + align:start position:0% +think about the air molecules in this +room right we + + align:start position:0% +room right we + + + align:start position:0% +room right we +have huge L always I give Lum is 10 to + + align:start position:0% +have huge L always I give Lum is 10 to + + + align:start position:0% +have huge L always I give Lum is 10 to +23r one more right huge Lum of + + align:start position:0% +23r one more right huge Lum of + + + align:start position:0% +23r one more right huge Lum of +molecules and they will collide with + + align:start position:0% +molecules and they will collide with + + + align:start position:0% +molecules and they will collide with +each other right so normally they carry + + align:start position:0% +each other right so normally they carry + + + align:start position:0% +each other right so normally they carry +their + + align:start position:0% +their + + + align:start position:0% +their +energy and then the next time they + + align:start position:0% +energy and then the next time they + + + align:start position:0% +energy and then the next time they +collide with other molecule so I want to + + align:start position:0% +collide with other molecule so I want to + + + align:start position:0% +collide with other molecule so I want to +give a very quick + + align:start position:0% +give a very quick + + + align:start position:0% +give a very quick +estimation what's the distance between + + align:start position:0% +estimation what's the distance between + + + align:start position:0% +estimation what's the distance between +those + + align:start position:0% +those + + + align:start position:0% +those +Collision how far they + + align:start position:0% +Collision how far they + + + align:start position:0% +Collision how far they +travel and uh so to do that let's say in + + align:start position:0% +travel and uh so to do that let's say in + + + align:start position:0% +travel and uh so to do that let's say in +this case I have to think about the + + align:start position:0% +this case I have to think about the + + + align:start position:0% +this case I have to think about the +molecule no longer a point right I have + + align:start position:0% +molecule no longer a point right I have + + + align:start position:0% +molecule no longer a point right I have +to think about the final size of the + + align:start position:0% +to think about the final size of the + + + align:start position:0% +to think about the final size of the +molecule the final size if you think + + align:start position:0% +molecule the final size if you think + + + align:start position:0% +molecule the final size if you think +what determin the size it could be the + + align:start position:0% +what determin the size it could be the + + + align:start position:0% +what determin the size it could be the +electric field potential right you have + + align:start position:0% +electric field potential right you have + + + align:start position:0% +electric field potential right you have +a nucle and there say electric field + + align:start position:0% +a nucle and there say electric field + + + align:start position:0% +a nucle and there say electric field +spell out and then when the two molec + + align:start position:0% +spell out and then when the two molec + + + align:start position:0% +spell out and then when the two molec +collide with with each other and that's + + align:start position:0% +collide with with each other and that's + + + align:start position:0% +collide with with each other and that's +when the fields start to + + align:start position:0% +when the fields start to + + + align:start position:0% +when the fields start to +interact + + align:start position:0% +interact + + + align:start position:0% +interact +okay and so I give a let's say a + + align:start position:0% +okay and so I give a let's say a + + + align:start position:0% +okay and so I give a let's say a +diameter of a molecule as d + + align:start position:0% + + + + align:start position:0% + +okay this diameter could be + + align:start position:0% +okay this diameter could be + + + align:start position:0% +okay this diameter could be +typically a few + + align:start position:0% +typically a few + + + align:start position:0% +typically a few +Armstrongs one Armstrong two + + align:start position:0% +Armstrongs one Armstrong two + + + align:start position:0% +Armstrongs one Armstrong two +Armstrong + + align:start position:0% +Armstrong + + + align:start position:0% +Armstrong +okay and uh now if I think about this + + align:start position:0% +okay and uh now if I think about this + + + align:start position:0% +okay and uh now if I think about this +molecule final size is moving and the + + align:start position:0% +molecule final size is moving and the + + + align:start position:0% +molecule final size is moving and the +Collision + + align:start position:0% +Collision + + + align:start position:0% +Collision +happens when there is another molecule + + align:start position:0% +happens when there is another molecule + + + align:start position:0% +happens when there is another molecule +within distance of + + align:start position:0% +within distance of + + + align:start position:0% +within distance of +d right so this is a + + align:start position:0% + + + + align:start position:0% + +2d + + align:start position:0% +2d + + + align:start position:0% +2d +okay and the way I can think about the + + align:start position:0% +okay and the way I can think about the + + + align:start position:0% +okay and the way I can think about the +do a very quick estimation is let's say + + align:start position:0% +do a very quick estimation is let's say + + + align:start position:0% +do a very quick estimation is let's say +I have a molecule and they uh over a + + align:start position:0% +I have a molecule and they uh over a + + + align:start position:0% +I have a molecule and they uh over a +trajector say uh uh a tube of diameter + + align:start position:0% +trajector say uh uh a tube of diameter + + + align:start position:0% +trajector say uh uh a tube of diameter +2D it travel certain + + align:start position:0% +2D it travel certain + + + align:start position:0% +2D it travel certain +distance so this tube is diameter + + align:start position:0% +distance so this tube is diameter + + + align:start position:0% +distance so this tube is diameter +2D right and travel certain distance + + align:start position:0% +2D right and travel certain distance + + + align:start position:0% +2D right and travel certain distance +let's say here this distance is + + align:start position:0% +let's say here this distance is + + + align:start position:0% +let's say here this distance is +L and then what's the volume so that two + + align:start position:0% +L and then what's the volume so that two + + + align:start position:0% +L and then what's the volume so that two +is + + align:start position:0% +is + + + align:start position:0% +is +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +the area times distance right so the + + align:start position:0% +the area times distance right so the + + + align:start position:0% +the area times distance right so the +volume is um + + align:start position:0% +volume is um + + + align:start position:0% +volume is um +okay 4 + + align:start position:0% +okay 4 + + + align:start position:0% +okay 4 +Pi uh 2D + + align:start position:0% +Pi uh 2D + + + align:start position:0% +Pi uh 2D +square + + align:start position:0% +square + + + align:start position:0% +square +right this is the + + align:start position:0% +right this is the + + + align:start position:0% +right this is the +area times the + + align:start position:0% +area times the + + + align:start position:0% +area times the +length gives me the + + align:start position:0% +length gives me the + + + align:start position:0% +length gives me the +volume that this molecule this tube + + align:start position:0% +volume that this molecule this tube + + + align:start position:0% +volume that this molecule this tube +sweeps + + align:start position:0% +sweeps + + + align:start position:0% +sweeps +right now how I decide the average + + align:start position:0% +right now how I decide the average + + + align:start position:0% +right now how I decide the average +distance between one + + align:start position:0% +distance between one + + + align:start position:0% +distance between one +Collision One Collision + + align:start position:0% +Collision One Collision + + + align:start position:0% +Collision One Collision +right now is when the lambra density per + + align:start position:0% +right now is when the lambra density per + + + align:start position:0% +right now is when the lambra density per +unit volume this is the lambra of + + align:start position:0% +unit volume this is the lambra of + + + align:start position:0% +unit volume this is the lambra of +molecule per unit volume times volume + + align:start position:0% +molecule per unit volume times volume + + + align:start position:0% +molecule per unit volume times volume +when that equals one that's one + + align:start position:0% +when that equals one that's one + + + align:start position:0% +when that equals one that's one +Collis do you + + align:start position:0% +Collis do you + + + align:start position:0% +Collis do you +agree so when the average L of say the + + align:start position:0% +agree so when the average L of say the + + + align:start position:0% +agree so when the average L of say the +per unit volume what's the L of molecule + + align:start position:0% +per unit volume what's the L of molecule + + + align:start position:0% +per unit volume what's the L of molecule +times over this tube of + + align:start position:0% +times over this tube of + + + align:start position:0% +times over this tube of +2D the length L when this equals + + align:start position:0% +2D the length L when this equals + + + align:start position:0% +2D the length L when this equals +one that's one C + + align:start position:0% +one that's one C + + + align:start position:0% +one that's one C +this molecule will have with other + + align:start position:0% +this molecule will have with other + + + align:start position:0% +this molecule will have with other +molecules and under this one condition + + align:start position:0% +molecules and under this one condition + + + align:start position:0% +molecules and under this one condition +that + + align:start position:0% +that + + + align:start position:0% +that +L is really what I call the mean free + + align:start position:0% +L is really what I call the mean free + + + align:start position:0% +L is really what I call the mean free +path the average distance between + + align:start position:0% + + + + align:start position:0% + +Collision equals here you can say is uh + + align:start position:0% +Collision equals here you can say is uh + + + align:start position:0% +Collision equals here you can say is uh +Pi d s Over N uh times + + align:start position:0% +Pi d s Over N uh times + + + align:start position:0% +Pi d s Over N uh times +n right this is the mean free + + align:start position:0% +n right this is the mean free + + + align:start position:0% +n right this is the mean free +pass that the molecule travels between + + align:start position:0% + + + + align:start position:0% + +Collision + + align:start position:0% + + + + align:start position:0% + +okay and if you do a better job this one + + align:start position:0% +okay and if you do a better job this one + + + align:start position:0% +okay and if you do a better job this one +is assuming the other molecu do not move + + align:start position:0% +is assuming the other molecu do not move + + + align:start position:0% +is assuming the other molecu do not move +right just a stationary distribute there + + align:start position:0% +right just a stationary distribute there + + + align:start position:0% +right just a stationary distribute there +and if you do all the more detail it + + align:start position:0% +and if you do all the more detail it + + + align:start position:0% +and if you do all the more detail it +turns out this expression is still + + align:start position:0% +turns out this expression is still + + + align:start position:0% +turns out this expression is still +pretty good so the mean free + + align:start position:0% +pretty good so the mean free + + + align:start position:0% +pretty good so the mean free +pass + + align:start position:0% + + + + align:start position:0% + +mean free + + align:start position:0% + + + + align:start position:0% + +pass is more accurate is put a square + + align:start position:0% +pass is more accurate is put a square + + + align:start position:0% +pass is more accurate is put a square +root of two here is pi d s * + + align:start position:0% + + + + align:start position:0% + +n okay now with that we can go to guess + + align:start position:0% +n okay now with that we can go to guess + + + align:start position:0% +n okay now with that we can go to guess +estimate uh the uh mean free path of the + + align:start position:0% +estimate uh the uh mean free path of the + + + align:start position:0% +estimate uh the uh mean free path of the +air + + align:start position:0% +air + + + align:start position:0% +air +molecules or typical gas so if it's a + + align:start position:0% +molecules or typical gas so if it's a + + + align:start position:0% +molecules or typical gas so if it's a +gas ideal + + align:start position:0% + + + + align:start position:0% + +gas if the ideal gas and we know + + align:start position:0% +gas if the ideal gas and we know + + + align:start position:0% +gas if the ideal gas and we know +pressure we derived last time in fact is + + align:start position:0% +pressure we derived last time in fact is + + + align:start position:0% +pressure we derived last time in fact is +n this + + align:start position:0% + + + + align:start position:0% + +KBT right n is the L of Po per unit + + align:start position:0% +KBT right n is the L of Po per unit + + + align:start position:0% +KBT right n is the L of Po per unit +volume not the more fraction right so + + align:start position:0% +volume not the more fraction right so + + + align:start position:0% +volume not the more fraction right so +this is L poly per unit volume so I + + align:start position:0% +this is L poly per unit volume so I + + + align:start position:0% +this is L poly per unit volume so I +replace this n and uh in this case what + + align:start position:0% +replace this n and uh in this case what + + + align:start position:0% +replace this n and uh in this case what +I get that the mean free pass is + + align:start position:0% +I get that the mean free pass is + + + align:start position:0% +I get that the mean free pass is +KBT square root two Pi d s + + align:start position:0% + + + + align:start position:0% + +pressure okay so let's put in L and say + + align:start position:0% +pressure okay so let's put in L and say + + + align:start position:0% +pressure okay so let's put in L and say +what's the mean free + + align:start position:0% +what's the mean free + + + align:start position:0% +what's the mean free +pass in a t condition + + align:start position:0% +pass in a t condition + + + align:start position:0% +pass in a t condition +gamma is + + align:start position:0% +gamma is + + + align:start position:0% +gamma is +KBT is uh KB is + + align:start position:0% +KBT is uh KB is + + + align:start position:0% +KBT is uh KB is +1.38 10^ Theus + + align:start position:0% +1.38 10^ Theus + + + align:start position:0% +1.38 10^ Theus + + align:start position:0% + + + align:start position:0% +jar K * + + align:start position:0% +jar K * + + + align:start position:0% +jar K * + + align:start position:0% + + + align:start position:0% +cin and uh square root of 2 pi d d let + + align:start position:0% +cin and uh square root of 2 pi d d let + + + align:start position:0% +cin and uh square root of 2 pi d d let +me take a 2.5 unstr + + align:start position:0% +me take a 2.5 unstr + + + align:start position:0% +me take a 2.5 unstr +strong this by now means mean to be + + align:start position:0% +strong this by now means mean to be + + + align:start position:0% +strong this by now means mean to be +accurate meter + + align:start position:0% + + + + align:start position:0% + +squar okay + + align:start position:0% +squar okay + + + align:start position:0% +squar okay +pressure one atmosphere so 1 10 the + + align:start position:0% +pressure one atmosphere so 1 10 the + + + align:start position:0% +pressure one atmosphere so 1 10 the +5ifth + + align:start position:0% + + + + align:start position:0% + +right Newton per meter + + align:start position:0% +right Newton per meter + + + align:start position:0% +right Newton per meter +squar and you go to putting all the L so + + align:start position:0% +squar and you go to putting all the L so + + + align:start position:0% +squar and you go to putting all the L so +this is month 23rd this is minus + + align:start position:0% +this is month 23rd this is minus + + + align:start position:0% +this is month 23rd this is minus +20 right and uh uh here so that means + + align:start position:0% +20 right and uh uh here so that means + + + align:start position:0% +20 right and uh uh here so that means +20us 20us 3 and here is 10 5th so minus + + align:start position:0% +20us 20us 3 and here is 10 5th so minus + + + align:start position:0% +20us 20us 3 and here is 10 5th so minus +8 and uh uh this 300 you go to check + + align:start position:0% +8 and uh uh this 300 you go to check + + + align:start position:0% +8 and uh uh this 300 you go to check +your numbers I give you a value I + + align:start position:0% + + + + align:start position:0% + +have uh this one I get + + align:start position:0% +have uh this one I get + + + align:start position:0% +have uh this one I get +.14 + + align:start position:0% +.14 + + + align:start position:0% +.14 +so14 Micron so 10 Theus + + align:start position:0% +so14 Micron so 10 Theus + + + align:start position:0% +so14 Micron so 10 Theus + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% +lomer that's about the average distance + + align:start position:0% +lomer that's about the average distance + + + align:start position:0% +lomer that's about the average distance +the air molecules travel in this + + align:start position:0% + + + + align:start position:0% + +room okay and if you recall before I + + align:start position:0% +room okay and if you recall before I + + + align:start position:0% +room okay and if you recall before I +said a dis + + align:start position:0% +said a dis + + + align:start position:0% +said a dis +drive and the dis in magnetic disc is a + + align:start position:0% +drive and the dis in magnetic disc is a + + + align:start position:0% +drive and the dis in magnetic disc is a +few nanometer now the separation and + + align:start position:0% +few nanometer now the separation and + + + align:start position:0% +few nanometer now the separation and +they're still using FR mechanics to + + align:start position:0% +they're still using FR mechanics to + + + align:start position:0% +they're still using FR mechanics to +design that slider so that they do not + + align:start position:0% +design that slider so that they do not + + + align:start position:0% +design that slider so that they do not +collide with this and you come to a reg + + align:start position:0% +collide with this and you come to a reg + + + align:start position:0% +collide with this and you come to a reg +where the air molecule do not collide + + align:start position:0% +where the air molecule do not collide + + + align:start position:0% +where the air molecule do not collide +with each other they'll collide with + + align:start position:0% +with each other they'll collide with + + + align:start position:0% +with each other they'll collide with +boundary more + + align:start position:0% +boundary more + + + align:start position:0% +boundary more +often right so this is the Aver mean + + align:start position:0% +often right so this is the Aver mean + + + align:start position:0% +often right so this is the Aver mean +free + + align:start position:0% +free + + + align:start position:0% +free +pa now you can say in the case of ideal + + align:start position:0% +pa now you can say in the case of ideal + + + align:start position:0% +pa now you can say in the case of ideal +gas that pressure is in the + + align:start position:0% +gas that pressure is in the + + + align:start position:0% +gas that pressure is in the +denominator how many of you do vacuum + + align:start position:0% +denominator how many of you do vacuum + + + align:start position:0% +denominator how many of you do vacuum +related have vacuum + + align:start position:0% +related have vacuum + + + align:start position:0% +related have vacuum +experience right so vacuum typical + + align:start position:0% +experience right so vacuum typical + + + align:start position:0% +experience right so vacuum typical +vacuum let's say 10 to- 6 + + align:start position:0% +vacuum let's say 10 to- 6 + + + align:start position:0% +vacuum let's say 10 to- 6 +to right you can use + + align:start position:0% +to right you can use + + + align:start position:0% +to right you can use +uh uh typical diffusion pump to easily + + align:start position:0% +uh uh typical diffusion pump to easily + + + align:start position:0% +uh uh typical diffusion pump to easily +drive to 10us 6 T so what's the molecule + + align:start position:0% +drive to 10us 6 T so what's the molecule + + + align:start position:0% +drive to 10us 6 T so what's the molecule +mean free pass when it's 10us 6 + + align:start position:0% + + + + align:start position:0% + +to uh I put in there 10 to- 6 to is 10^ + + align:start position:0% +to uh I put in there 10 to- 6 to is 10^ + + + align:start position:0% +to uh I put in there 10 to- 6 to is 10^ +the- 6 remember uh here is 10 to the 5th + + align:start position:0% +the- 6 remember uh here is 10 to the 5th + + + align:start position:0% +the- 6 remember uh here is 10 to the 5th +but the one to is 7 760 right uh one + + align:start position:0% +but the one to is 7 760 right uh one + + + align:start position:0% +but the one to is 7 760 right uh one +atmosphere is + + align:start position:0% +atmosphere is + + + align:start position:0% +atmosphere is +7602 so this is the pressure you put in + + align:start position:0% +7602 so this is the pressure you put in + + + align:start position:0% +7602 so this is the pressure you put in +there and you get 100 + + align:start position:0% +there and you get 100 + + + align:start position:0% +there and you get 100 +m okay so in vacuum pump vacuum system + + align:start position:0% +m okay so in vacuum pump vacuum system + + + align:start position:0% +m okay so in vacuum pump vacuum system +the molecule do not collide with each + + align:start position:0% +the molecule do not collide with each + + + align:start position:0% +the molecule do not collide with each +other you use a + + align:start position:0% +other you use a + + + align:start position:0% +other you use a +evaporator you heat it up you hit the + + align:start position:0% +evaporator you heat it up you hit the + + + align:start position:0% +evaporator you heat it up you hit the +atom the atom go out go + + align:start position:0% +atom the atom go out go + + + align:start position:0% +atom the atom go out go +straight to your target so it's + + align:start position:0% +straight to your target so it's + + + align:start position:0% +straight to your target so it's +completely a a ballistic trajectory you + + align:start position:0% +completely a a ballistic trajectory you + + + align:start position:0% +completely a a ballistic trajectory you +don't do the heat conduction diffusion + + align:start position:0% +don't do the heat conduction diffusion + + + align:start position:0% +don't do the heat conduction diffusion +Theory anymore you don't you you you + + align:start position:0% +Theory anymore you don't you you you + + + align:start position:0% +Theory anymore you don't you you you +have to trace the + + align:start position:0% +have to trace the + + + align:start position:0% +have to trace the +trajectory + + align:start position:0% +trajectory + + + align:start position:0% +trajectory +right okay so this is a uh how far we + + align:start position:0% +right okay so this is a uh how far we + + + align:start position:0% +right okay so this is a uh how far we +have some + + align:start position:0% +have some + + + align:start position:0% +have some +idea and uh next + + align:start position:0% +idea and uh next + + + align:start position:0% +idea and uh next +let's briefly discuss how they interact + + align:start position:0% +let's briefly discuss how they interact + + + align:start position:0% +let's briefly discuss how they interact +with each + + align:start position:0% +with each + + + align:start position:0% +with each +other + + align:start position:0% + + + + align:start position:0% + +how do they + + align:start position:0% + + + + align:start position:0% + +interact + + align:start position:0% +interact + + + align:start position:0% +interact +okay and I mentioned when the two + + align:start position:0% +okay and I mentioned when the two + + + align:start position:0% +okay and I mentioned when the two +molecules right uh collide with each + + align:start position:0% +molecules right uh collide with each + + + align:start position:0% +molecules right uh collide with each +other it's + + align:start position:0% +other it's + + + align:start position:0% +other it's +really the electric field extend certain + + align:start position:0% +really the electric field extend certain + + + align:start position:0% +really the electric field extend certain +space and when uh the two molecule gets + + align:start position:0% +space and when uh the two molecule gets + + + align:start position:0% +space and when uh the two molecule gets +Clos the electric field Collide say + + align:start position:0% +Clos the electric field Collide say + + + align:start position:0% +Clos the electric field Collide say +repel each other so they go different + + align:start position:0% +repel each other so they go different + + + align:start position:0% +repel each other so they go different +trajectory right so you + + align:start position:0% +trajectory right so you + + + align:start position:0% +trajectory right so you +have simple you can think about that two + + align:start position:0% +have simple you can think about that two + + + align:start position:0% +have simple you can think about that two +B + + align:start position:0% +B + + + align:start position:0% +B +Collis and if you want to do the + + align:start position:0% +Collis and if you want to do the + + + align:start position:0% +Collis and if you want to do the +trajectory and uh uh the uh you what you + + align:start position:0% +trajectory and uh uh the uh you what you + + + align:start position:0% +trajectory and uh uh the uh you what you +do is during the Collision you have + + align:start position:0% +do is during the Collision you have + + + align:start position:0% +do is during the Collision you have +energy conservation you have momentum + + align:start position:0% +energy conservation you have momentum + + + align:start position:0% +energy conservation you have momentum +conservation right so in that case this + + align:start position:0% +conservation right so in that case this + + + align:start position:0% +conservation right so in that case this +is really the microscopical word the + + align:start position:0% +is really the microscopical word the + + + align:start position:0% +is really the microscopical word the +basic conservation laws the conservation + + align:start position:0% +basic conservation laws the conservation + + + align:start position:0% +basic conservation laws the conservation +principle you apply so you have + + align:start position:0% + + + + align:start position:0% + +energy and momentum conservation + + align:start position:0% + + + + align:start position:0% + +and uh if the Collision is among the air + + align:start position:0% +and uh if the Collision is among the air + + + align:start position:0% +and uh if the Collision is among the air +molecules uh it's + + align:start position:0% +molecules uh it's + + + align:start position:0% +molecules uh it's +uh typical it's a limited the how fast + + align:start position:0% +uh typical it's a limited the how fast + + + align:start position:0% +uh typical it's a limited the how fast +the how far the molecu travel so it's a + + align:start position:0% +the how far the molecu travel so it's a + + + align:start position:0% +the how far the molecu travel so it's a +internal you can think that more as the + + align:start position:0% +internal you can think that more as the + + + align:start position:0% +internal you can think that more as the +internal stuff intern interal + + align:start position:0% +internal stuff intern interal + + + align:start position:0% +internal stuff intern interal +loss but when you think about the the + + align:start position:0% +loss but when you think about the the + + + align:start position:0% +loss but when you think about the the +energy conversion what does really + + align:start position:0% +energy conversion what does really + + + align:start position:0% +energy conversion what does really +energy conversion + + align:start position:0% + + + + align:start position:0% + +mean energy conversion is one type of + + align:start position:0% +mean energy conversion is one type of + + + align:start position:0% +mean energy conversion is one type of +energy going to the other type right so + + align:start position:0% +energy going to the other type right so + + + align:start position:0% +energy going to the other type right so +when gas molecule drive a + + align:start position:0% +when gas molecule drive a + + + align:start position:0% +when gas molecule drive a +turbine is this kinetic + + align:start position:0% +turbine is this kinetic + + + align:start position:0% +turbine is this kinetic +energy becomes the average mode + + align:start position:0% +energy becomes the average mode + + + align:start position:0% +energy becomes the average mode +of the + + align:start position:0% + + + + align:start position:0% + +blade now another type is think about + + align:start position:0% +blade now another type is think about + + + align:start position:0% +blade now another type is think about +the photo voltic + + align:start position:0% +the photo voltic + + + align:start position:0% +the photo voltic +Cel what's the energy conversion of + + align:start position:0% +Cel what's the energy conversion of + + + align:start position:0% +Cel what's the energy conversion of +course what you want is that Photon + + align:start position:0% +course what you want is that Photon + + + align:start position:0% +course what you want is that Photon +eventually come out to get electricity + + align:start position:0% +eventually come out to get electricity + + + align:start position:0% +eventually come out to get electricity +right but what you get in the + + align:start position:0% +right but what you get in the + + + align:start position:0% +right but what you get in the +microscopic level is a electron is sit + + align:start position:0% +microscopic level is a electron is sit + + + align:start position:0% +microscopic level is a electron is sit +over + + align:start position:0% +over + + + align:start position:0% +over +here a photon comes in and lift the + + align:start position:0% +here a photon comes in and lift the + + + align:start position:0% +here a photon comes in and lift the +electron to + + align:start position:0% +electron to + + + align:start position:0% +electron to +here you have the first step of your + + align:start position:0% +here you have the first step of your + + + align:start position:0% +here you have the first step of your +energy conversion + + align:start position:0% +energy conversion + + + align:start position:0% +energy conversion +already + + align:start position:0% +already + + + align:start position:0% +already +right of course that's not your pH yet + + align:start position:0% +right of course that's not your pH yet + + + align:start position:0% +right of course that's not your pH yet +and the light from the lamp is absorbed + + align:start position:0% +and the light from the lamp is absorbed + + + align:start position:0% +and the light from the lamp is absorbed +by all the stuff around us eventually + + align:start position:0% +by all the stuff around us eventually + + + align:start position:0% +by all the stuff around us eventually +that's the energy conversion except at + + align:start position:0% +that's the energy conversion except at + + + align:start position:0% +that's the energy conversion except at +the end we can't capture + + align:start position:0% +the end we can't capture + + + align:start position:0% +the end we can't capture +it + + align:start position:0% +it + + + align:start position:0% +it +right and uh uh so you have different + + align:start position:0% +right and uh uh so you have different + + + align:start position:0% +right and uh uh so you have different +losses in the process that you have to + + align:start position:0% +losses in the process that you have to + + + align:start position:0% +losses in the process that you have to +take care if you want to finally extract + + align:start position:0% +take care if you want to finally extract + + + align:start position:0% +take care if you want to finally extract +things that's + + align:start position:0% +things that's + + + align:start position:0% +things that's +useful okay so this kind of interaction + + align:start position:0% +useful okay so this kind of interaction + + + align:start position:0% +useful okay so this kind of interaction +is dealing with the Collision dealing + + align:start position:0% +is dealing with the Collision dealing + + + align:start position:0% +is dealing with the Collision dealing +with the interaction this is arguably + + align:start position:0% +with the interaction this is arguably + + + align:start position:0% +with the interaction this is arguably +the most complicated step in the + + align:start position:0% +the most complicated step in the + + + align:start position:0% +the most complicated step in the +transport + + align:start position:0% +transport + + + align:start position:0% +transport +okay now with that uh let's go to what I + + align:start position:0% +okay now with that uh let's go to what I + + + align:start position:0% +okay now with that uh let's go to what I +want to give you is is A Simple kinetica + + align:start position:0% +want to give you is is A Simple kinetica + + + align:start position:0% +want to give you is is A Simple kinetica +Theory uh of + + align:start position:0% + + + + align:start position:0% + +Transport so I know there are see uh how + + align:start position:0% +Transport so I know there are see uh how + + + align:start position:0% +Transport so I know there are see uh how +many how long air molecule travel and + + align:start position:0% +many how long air molecule travel and + + + align:start position:0% +many how long air molecule travel and +then what I'm I know their velocity what + + align:start position:0% +then what I'm I know their velocity what + + + align:start position:0% +then what I'm I know their velocity what +I'm going to do + + align:start position:0% +I'm going to do + + + align:start position:0% +I'm going to do +next is to show how we can do a simple + + align:start position:0% +next is to show how we can do a simple + + + align:start position:0% +next is to show how we can do a simple +derivation for the foral law of heat + + align:start position:0% +derivation for the foral law of heat + + + align:start position:0% +derivation for the foral law of heat +conduction and as said you can do the + + align:start position:0% +conduction and as said you can do the + + + align:start position:0% +conduction and as said you can do the +same derivation using the same strategy + + align:start position:0% +same derivation using the same strategy + + + align:start position:0% +same derivation using the same strategy +for Mass diffusion for momentum say uh + + align:start position:0% +for Mass diffusion for momentum say uh + + + align:start position:0% +for Mass diffusion for momentum say uh +transfer and uh uh uh ENT in fact you + + align:start position:0% +transfer and uh uh uh ENT in fact you + + + align:start position:0% +transfer and uh uh uh ENT in fact you +have homework on this + + align:start position:0% +have homework on this + + + align:start position:0% +have homework on this +so I'm + + align:start position:0% +so I'm + + + align:start position:0% +so I'm +considering induction only no no average + + align:start position:0% +considering induction only no no average + + + align:start position:0% +considering induction only no no average +motion right I have the uh gas molecules + + align:start position:0% +motion right I have the uh gas molecules + + + align:start position:0% +motion right I have the uh gas molecules +and any gas in fact it applies to + + align:start position:0% +and any gas in fact it applies to + + + align:start position:0% +and any gas in fact it applies to +electron apply to Fon as long as I have + + align:start position:0% +electron apply to Fon as long as I have + + + align:start position:0% +electron apply to Fon as long as I have +this gas + + align:start position:0% +this gas + + + align:start position:0% +this gas +picture right and I have a temperature + + align:start position:0% +picture right and I have a temperature + + + align:start position:0% +picture right and I have a temperature +gradient in the X Direction so this is a + + align:start position:0% +gradient in the X Direction so this is a + + + align:start position:0% +gradient in the X Direction so this is a +he flow in the X + + align:start position:0% + + + + align:start position:0% + +direction right temperature gradient + + align:start position:0% +direction right temperature gradient + + + align:start position:0% +direction right temperature gradient +that + + align:start position:0% +that + + + align:start position:0% +that +and I want to derive the fal + + align:start position:0% +and I want to derive the fal + + + align:start position:0% +and I want to derive the fal +law and the microscopically if I can + + align:start position:0% +law and the microscopically if I can + + + align:start position:0% +law and the microscopically if I can +count basically I'm counting so when I + + align:start position:0% +count basically I'm counting so when I + + + align:start position:0% +count basically I'm counting so when I +look at the + + align:start position:0% +look at the + + + align:start position:0% +look at the +flux right across certain + + align:start position:0% +flux right across certain + + + align:start position:0% +flux right across certain +cross-section so here I'm going to say + + align:start position:0% +cross-section so here I'm going to say + + + align:start position:0% +cross-section so here I'm going to say +this is the cross-section I'm looking at + + align:start position:0% +this is the cross-section I'm looking at + + + align:start position:0% +this is the cross-section I'm looking at +here is the + + align:start position:0% +here is the + + + align:start position:0% +here is the +X on the left I have molecules on on the + + align:start position:0% +X on the left I have molecules on on the + + + align:start position:0% +X on the left I have molecules on on the +right I have + + align:start position:0% +right I have + + + align:start position:0% +right I have +molecules right and the molecules are + + align:start position:0% +molecules right and the molecules are + + + align:start position:0% +molecules right and the molecules are +doing random + + align:start position:0% +doing random + + + align:start position:0% +doing random +motion and on the left there are slight + + align:start position:0% +motion and on the left there are slight + + + align:start position:0% +motion and on the left there are slight +higher temperature on the right slight + + align:start position:0% +higher temperature on the right slight + + + align:start position:0% +higher temperature on the right slight +lower + + align:start position:0% +lower + + + align:start position:0% +lower +temperature now some of this molecule + + align:start position:0% +temperature now some of this molecule + + + align:start position:0% +temperature now some of this molecule +will go across this imaginary interface + + align:start position:0% +will go across this imaginary interface + + + align:start position:0% +will go across this imaginary interface +I + + align:start position:0% +I + + + align:start position:0% +I +draw without Collision so I count that + + align:start position:0% +draw without Collision so I count that + + + align:start position:0% +draw without Collision so I count that +this molecule that can go through the + + align:start position:0% +this molecule that can go through the + + + align:start position:0% +this molecule that can go through the +interface face so from left to right Ms + + align:start position:0% +interface face so from left to right Ms + + + align:start position:0% +interface face so from left to right Ms +from right to left that's my left + + align:start position:0% +from right to left that's my left + + + align:start position:0% +from right to left that's my left +flux okay so I'm doing my energy + + align:start position:0% +flux okay so I'm doing my energy + + + align:start position:0% +flux okay so I'm doing my energy +balance and uh so what I count I say + + align:start position:0% +balance and uh so what I count I say + + + align:start position:0% +balance and uh so what I count I say +left I have here within how how I say I + + align:start position:0% +left I have here within how how I say I + + + align:start position:0% +left I have here within how how I say I +say what's the range this is a the VX * + + align:start position:0% +say what's the range this is a the VX * + + + align:start position:0% +say what's the range this is a the VX * +t t is the time between Collis okay + + align:start position:0% +t t is the time between Collis okay + + + align:start position:0% +t t is the time between Collis okay +that's something I forgot to mention to + + align:start position:0% +that's something I forgot to mention to + + + align:start position:0% +that's something I forgot to mention to +because I have mean free pass so I have + + align:start position:0% +because I have mean free pass so I have + + + align:start position:0% +because I have mean free pass so I have +the mean free pass divide by velocity + + align:start position:0% +the mean free pass divide by velocity + + + align:start position:0% +the mean free pass divide by velocity +that gives or speed gives me the average + + align:start position:0% +that gives or speed gives me the average + + + align:start position:0% +that gives or speed gives me the average +time between Collision + + align:start position:0% +time between Collision + + + align:start position:0% +time between Collision +right so I say VX because this is + + align:start position:0% +right so I say VX because this is + + + align:start position:0% +right so I say VX because this is +velocity in the X component in X + + align:start position:0% +velocity in the X component in X + + + align:start position:0% +velocity in the X component in X +direction we x * + + align:start position:0% +direction we x * + + + align:start position:0% +direction we x * +to as long as those molecules is with + + align:start position:0% +to as long as those molecules is with + + + align:start position:0% +to as long as those molecules is with +this range they can go across this + + align:start position:0% +this range they can go across this + + + align:start position:0% +this range they can go across this +imaginary interface here right + + align:start position:0% +imaginary interface here right + + + align:start position:0% +imaginary interface here right +and of course only half of them have + + align:start position:0% +and of course only half of them have + + + align:start position:0% +and of course only half of them have +that chance half goes this way half go + + align:start position:0% +that chance half goes this way half go + + + align:start position:0% +that chance half goes this way half go +the other way I'm doing the random right + + align:start position:0% +the other way I'm doing the random right + + + align:start position:0% +the other way I'm doing the random right +right Browning motion so I have my + + align:start position:0% +right Browning motion so I have my + + + align:start position:0% +right Browning motion so I have my +Q + + align:start position:0% +Q + + + align:start position:0% +Q +is + + align:start position:0% +is + + + align:start position:0% +is +uh2 this is the average Lum per unit per + + align:start position:0% +uh2 this is the average Lum per unit per + + + align:start position:0% +uh2 this is the average Lum per unit per +unit + + align:start position:0% +unit + + + align:start position:0% +unit +volume and times VX this is the speed so + + align:start position:0% +volume and times VX this is the speed so + + + align:start position:0% +volume and times VX this is the speed so +if you look at this this gives me + + align:start position:0% +if you look at this this gives me + + + align:start position:0% +if you look at this this gives me +here is per unit volume here is meter + + align:start position:0% +here is per unit volume here is meter + + + align:start position:0% +here is per unit volume here is meter +per second so that gives me per meter + + align:start position:0% +per second so that gives me per meter + + + align:start position:0% +per second so that gives me per meter +Square per + + align:start position:0% +Square per + + + align:start position:0% +Square per +second that's the + + align:start position:0% +second that's the + + + align:start position:0% +second that's the +flux right the + + align:start position:0% +flux right the + + + align:start position:0% +flux right the +flux of the particles per meter Square + + align:start position:0% +flux of the particles per meter Square + + + align:start position:0% +flux of the particles per meter Square +per + + align:start position:0% +per + + + align:start position:0% +per +second and times each particle carry + + align:start position:0% +second and times each particle carry + + + align:start position:0% +second and times each particle carry +this + + align:start position:0% +this + + + align:start position:0% +this +energy so you can replace that energy by + + align:start position:0% +energy so you can replace that energy by + + + align:start position:0% +energy so you can replace that energy by +charge that's a diffusion of + + align:start position:0% +charge that's a diffusion of + + + align:start position:0% +charge that's a diffusion of +charge right if you do one that's a + + align:start position:0% +charge right if you do one that's a + + + align:start position:0% +charge right if you do one that's a +diffus usion or if you if you times the + + align:start position:0% +diffus usion or if you if you times the + + + align:start position:0% +diffus usion or if you if you times the +mass of particle that's the diffusion of + + align:start position:0% +mass of particle that's the diffusion of + + + align:start position:0% +mass of particle that's the diffusion of +mass in terms of the + + align:start position:0% +mass in terms of the + + + align:start position:0% +mass in terms of the +weight right so here is xus VX * + + align:start position:0% +weight right so here is xus VX * + + + align:start position:0% +weight right so here is xus VX * +T that's on the left going to right and + + align:start position:0% +T that's on the left going to right and + + + align:start position:0% +T that's on the left going to right and +then minus from the right going to left + + align:start position:0% +then minus from the right going to left + + + align:start position:0% +then minus from the right going to left +so there are also half of this this is + + align:start position:0% +so there are also half of this this is + + + align:start position:0% +so there are also half of this this is +also VX over to that's the chance going + + align:start position:0% +also VX over to that's the chance going + + + align:start position:0% +also VX over to that's the chance going +from left to the right so that's the + + align:start position:0% +from left to the right so that's the + + + align:start position:0% +from left to the right so that's the +difference of the two gives + + align:start position:0% +difference of the two gives + + + align:start position:0% +difference of the two gives +me you see here the it's VX plus + + align:start position:0% + + + + align:start position:0% + +top + + align:start position:0% +top + + + align:start position:0% +top +right so that's my heat flux if you + + align:start position:0% +right so that's my heat flux if you + + + align:start position:0% +right so that's my heat flux if you +check this is a 1/ m square or cubic + + align:start position:0% +check this is a 1/ m square or cubic + + + align:start position:0% +check this is a 1/ m square or cubic +here is meter per second here is jar so + + align:start position:0% +here is meter per second here is jar so + + + align:start position:0% +here is meter per second here is jar so +I will get a watt per met + + align:start position:0% +I will get a watt per met + + + align:start position:0% +I will get a watt per met +Square okay and of course what I'm going + + align:start position:0% +Square okay and of course what I'm going + + + align:start position:0% +Square okay and of course what I'm going +to do next uh here is a VX X components + + align:start position:0% +to do next uh here is a VX X components + + + align:start position:0% +to do next uh here is a VX X components +what I'm going to do next is to write it + + align:start position:0% +what I'm going to do next is to write it + + + align:start position:0% +what I'm going to do next is to write it +into differential form this is a very + + align:start position:0% +into differential form this is a very + + + align:start position:0% +into differential form this is a very +short right as long as I'm dealing with + + align:start position:0% +short right as long as I'm dealing with + + + align:start position:0% +short right as long as I'm dealing with +microscopic I can write this 100 nomer + + align:start position:0% +microscopic I can write this 100 nomer + + + align:start position:0% +microscopic I can write this 100 nomer +range into differential + + align:start position:0% +range into differential + + + align:start position:0% +range into differential +form so I do my + + align:start position:0% +form so I do my + + + align:start position:0% +form so I do my +differential + + align:start position:0% + + + + align:start position:0% + +what I have is a q equals because this + + align:start position:0% +what I have is a q equals because this + + + align:start position:0% +what I have is a q equals because this +is a positive is minus so I have minus + + align:start position:0% +is a positive is minus so I have minus + + + align:start position:0% +is a positive is minus so I have minus +in the front 12 d n VX t uh e that's + + align:start position:0% +in the front 12 d n VX t uh e that's + + + align:start position:0% +in the front 12 d n VX t uh e that's +what's + + align:start position:0% +what's + + + align:start position:0% +what's +inside and + + align:start position:0% +inside and + + + align:start position:0% +inside and +DX and + + align:start position:0% +DX and + + + align:start position:0% +DX and +the the X difference is VX T Mass VX T + + align:start position:0% +the the X difference is VX T Mass VX T + + + align:start position:0% +the the X difference is VX T Mass VX T +so I have 2 VX + + align:start position:0% + + + + align:start position:0% + +T + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so now I'm doing a little scaping I'm + + align:start position:0% +so now I'm doing a little scaping I'm + + + align:start position:0% +so now I'm doing a little scaping I'm +going to put the VX pull VX + + align:start position:0% +going to put the VX pull VX + + + align:start position:0% +going to put the VX pull VX +out I neglect all those temperature + + align:start position:0% +out I neglect all those temperature + + + align:start position:0% +out I neglect all those temperature +dependence of + + align:start position:0% +dependence of + + + align:start position:0% +dependence of +velocity and this is actually could you + + align:start position:0% +velocity and this is actually could you + + + align:start position:0% +velocity and this is actually could you +can have C mass and heat transfer but + + align:start position:0% +can have C mass and heat transfer but + + + align:start position:0% +can have C mass and heat transfer but +I'm scaping making the sense easier so + + align:start position:0% +I'm scaping making the sense easier so + + + align:start position:0% +I'm scaping making the sense easier so +what I have here is one2 canel I have uh + + align:start position:0% +what I have here is one2 canel I have uh + + + align:start position:0% +what I have here is one2 canel I have uh +VX s + + align:start position:0% +VX s + + + align:start position:0% +VX s +to and d n * e is + + align:start position:0% +to and d n * e is + + + align:start position:0% +to and d n * e is +U and + + align:start position:0% + + + + align:start position:0% + +DX right U is energy per unit + + align:start position:0% +DX right U is energy per unit + + + align:start position:0% +DX right U is energy per unit +volume + + align:start position:0% +volume + + + align:start position:0% +volume +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +VX square is 13 of V + + align:start position:0% +VX square is 13 of V + + + align:start position:0% +VX square is 13 of V +Square I'm doing + + align:start position:0% +Square I'm doing + + + align:start position:0% +Square I'm doing +right so what I have here oh the + + align:start position:0% +right so what I have here oh the + + + align:start position:0% +right so what I have here oh the +negative sign so I have 1/3 + + align:start position:0% +negative sign so I have 1/3 + + + align:start position:0% +negative sign so I have 1/3 +v² T and + + align:start position:0% +v² T and + + + align:start position:0% +v² T and +D DT I'm using CH rule DT + + align:start position:0% +D DT I'm using CH rule DT + + + align:start position:0% +D DT I'm using CH rule DT +DX what's is Du + + align:start position:0% +DX what's is Du + + + align:start position:0% +DX what's is Du +DT that's the heat yeah specific heat + + align:start position:0% +DT that's the heat yeah specific heat + + + align:start position:0% +DT that's the heat yeah specific heat +per unit volume right so this one is say + + align:start position:0% +per unit volume right so this one is say + + + align:start position:0% +per unit volume right so this one is say +is the specific here is jar meter cubic + + align:start position:0% +is the specific here is jar meter cubic + + + align:start position:0% +is the specific here is jar meter cubic +K typically we do specific per unit + + align:start position:0% +K typically we do specific per unit + + + align:start position:0% +K typically we do specific per unit +density per unit Mass but it's fine so + + align:start position:0% +density per unit Mass but it's fine so + + + align:start position:0% +density per unit Mass but it's fine so +what I have here is a k foral + + align:start position:0% +what I have here is a k foral + + + align:start position:0% +what I have here is a k foral +dtdx and I also + + align:start position:0% +dtdx and I also + + + align:start position:0% +dtdx and I also +obtain expression for k is + + align:start position:0% +obtain expression for k is + + + align:start position:0% +obtain expression for k is + + align:start position:0% + + + align:start position:0% +say V T + + align:start position:0% +say V T + + + align:start position:0% +say V T +square right uh no c v s t c v² t and + + align:start position:0% +square right uh no c v s t c v² t and + + + align:start position:0% +square right uh no c v s t c v² t and +which is 13 C GMA uh way CV gamma so + + align:start position:0% +which is 13 C GMA uh way CV gamma so + + + align:start position:0% +which is 13 C GMA uh way CV gamma so +this is + + align:start position:0% + + + + align:start position:0% + +the fal law and also the expression for + + align:start position:0% +the fal law and also the expression for + + + align:start position:0% +the fal law and also the expression for +the thermal + + align:start position:0% +the thermal + + + align:start position:0% +the thermal +conductivity right + + align:start position:0% + + + + align:start position:0% + +okay and if you look at thermal + + align:start position:0% +okay and if you look at thermal + + + align:start position:0% +okay and if you look at thermal +connectivity it's proportional to the + + align:start position:0% +connectivity it's proportional to the + + + align:start position:0% +connectivity it's proportional to the +mean free + + align:start position:0% +mean free + + + align:start position:0% +mean free +pass proportional + + align:start position:0% +pass proportional + + + align:start position:0% +pass proportional +velocity proportional specific heat if + + align:start position:0% +velocity proportional specific heat if + + + align:start position:0% +velocity proportional specific heat if +you check for + + align:start position:0% +you check for + + + align:start position:0% +you check for +gas what which gas has highest thermal + + align:start position:0% + + + + align:start position:0% + +conductivity + + align:start position:0% +conductivity + + + align:start position:0% +conductivity +hel so the velocity is higher + + align:start position:0% + + + + align:start position:0% + +okay and so we have with that I have the + + align:start position:0% +okay and so we have with that I have the + + + align:start position:0% +okay and so we have with that I have the +uh uh simple derivation and later on + + align:start position:0% +uh uh simple derivation and later on + + + align:start position:0% +uh uh simple derivation and later on +we're going to give you more complicated + + align:start position:0% +we're going to give you more complicated + + + align:start position:0% +we're going to give you more complicated +derivation Bas on BS man equation but + + align:start position:0% +derivation Bas on BS man equation but + + + align:start position:0% +derivation Bas on BS man equation but +this is a hand waving one and it's + + align:start position:0% +this is a hand waving one and it's + + + align:start position:0% +this is a hand waving one and it's +pretty good at the end if you use bman + + align:start position:0% +pretty good at the end if you use bman + + + align:start position:0% +pretty good at the end if you use bman +you'll still get K = 1/3 CV + + align:start position:0% + + + + align:start position:0% + +gamma + + align:start position:0% +gamma + + + align:start position:0% +gamma +okay any questions here or + + align:start position:0% + + + + align:start position:0% + +doubt if + + align:start position:0% +doubt if + + + align:start position:0% +doubt if +not let's make a few + + align:start position:0% +not let's make a few + + + align:start position:0% +not let's make a few +comment so those of course I already to + + align:start position:0% +comment so those of course I already to + + + align:start position:0% +comment so those of course I already to +learned the + + align:start position:0% +learned the + + + align:start position:0% +learned the +classical diffusion Theory right and you + + align:start position:0% +classical diffusion Theory right and you + + + align:start position:0% +classical diffusion Theory right and you +can see + + align:start position:0% +can see + + + align:start position:0% +can see +immediately if I do uh take the example + + align:start position:0% +immediately if I do uh take the example + + + align:start position:0% +immediately if I do uh take the example +of the uh this + + align:start position:0% +of the uh this + + + align:start position:0% +of the uh this +drive my space is much smaller than this + + align:start position:0% +drive my space is much smaller than this + + + align:start position:0% +drive my space is much smaller than this +mean free pass I cannot do the + + align:start position:0% +mean free pass I cannot do the + + + align:start position:0% +mean free pass I cannot do the +derivative + + align:start position:0% + + + + align:start position:0% + +anymore right so I have to go to look at + + align:start position:0% +anymore right so I have to go to look at + + + align:start position:0% +anymore right so I have to go to look at +more complicated so this is where the + + align:start position:0% +more complicated so this is where the + + + align:start position:0% +more complicated so this is where the +Nano start to + + align:start position:0% +Nano start to + + + align:start position:0% +Nano start to +deviate so what what we're looking when + + align:start position:0% +deviate so what what we're looking when + + + align:start position:0% +deviate so what what we're looking when +we're looking to the what's the + + align:start position:0% +we're looking to the what's the + + + align:start position:0% +we're looking to the what's the +fundamental difference + + align:start position:0% +fundamental difference + + + align:start position:0% +fundamental difference +right + + align:start position:0% + + + + align:start position:0% + +so I + + align:start position:0% + + + + align:start position:0% + +have and uh what's really the microl Lal + + align:start position:0% +have and uh what's really the microl Lal + + + align:start position:0% +have and uh what's really the microl Lal +fundamental + + align:start position:0% + + + + align:start position:0% + +difference and there are several + + align:start position:0% +difference and there are several + + + align:start position:0% +difference and there are several +regimes one + + align:start position:0% +regimes one + + + align:start position:0% +regimes one +is I always have a device + + align:start position:0% +is I always have a device + + + align:start position:0% +is I always have a device +characteristical lens for example in the + + align:start position:0% +characteristical lens for example in the + + + align:start position:0% +characteristical lens for example in the +slider the the dis Drive is the + + align:start position:0% +slider the the dis Drive is the + + + align:start position:0% +slider the the dis Drive is the +separation between slider and disk right + + align:start position:0% +separation between slider and disk right + + + align:start position:0% +separation between slider and disk right +so I have one is a charistic length the + + align:start position:0% +so I have one is a charistic length the + + + align:start position:0% +so I have one is a charistic length the +mean free path if the mean free path + + align:start position:0% +mean free path if the mean free path + + + align:start position:0% +mean free path if the mean free path +becomes larger or + + align:start position:0% +becomes larger or + + + align:start position:0% +becomes larger or +comparable to uh separation let's say d + + align:start position:0% +comparable to uh separation let's say d + + + align:start position:0% +comparable to uh separation let's say d +a characteristical + + align:start position:0% +a characteristical + + + align:start position:0% +a characteristical +length of the transport + + align:start position:0% +length of the transport + + + align:start position:0% +length of the transport +problem right and in that case the + + align:start position:0% +problem right and in that case the + + + align:start position:0% +problem right and in that case the +diffusion Theory will no longer be valid + + align:start position:0% +diffusion Theory will no longer be valid + + + align:start position:0% +diffusion Theory will no longer be valid +and the air molecule will collide with + + align:start position:0% +and the air molecule will collide with + + + align:start position:0% +and the air molecule will collide with +the + + align:start position:0% +the + + + align:start position:0% +the +boundary and as long as a Quantum + + align:start position:0% +boundary and as long as a Quantum + + + align:start position:0% +boundary and as long as a Quantum +effects is not + + align:start position:0% +effects is not + + + align:start position:0% +effects is not +important then you run into a classical + + align:start position:0% +important then you run into a classical + + + align:start position:0% +important then you run into a classical +size effect regime so classical size + + align:start position:0% + + + + align:start position:0% + +effect + + align:start position:0% + + + + align:start position:0% + +so this is a one case + + align:start position:0% +so this is a one case + + + align:start position:0% +so this is a one case +right but you can ask how do you know + + align:start position:0% +right but you can ask how do you know + + + align:start position:0% +right but you can ask how do you know +your Quantum size effect is not + + align:start position:0% +your Quantum size effect is not + + + align:start position:0% +your Quantum size effect is not +important right so let's take a look now + + align:start position:0% +important right so let's take a look now + + + align:start position:0% +important right so let's take a look now +we going to move a little bit into + + align:start position:0% +we going to move a little bit into + + + align:start position:0% +we going to move a little bit into +Quantum and + + align:start position:0% + + + + align:start position:0% + +uh so the Le case + + align:start position:0% +uh so the Le case + + + align:start position:0% +uh so the Le case +is a Quantum size + + align:start position:0% + + + + align:start position:0% + +effect and in + + align:start position:0% +effect and in + + + align:start position:0% +effect and in +fact sometimes I don't like to call it a + + align:start position:0% +fact sometimes I don't like to call it a + + + align:start position:0% +fact sometimes I don't like to call it a +Quantum size effect I like to call it + + align:start position:0% +Quantum size effect I like to call it + + + align:start position:0% +Quantum size effect I like to call it +wave + + align:start position:0% +wave + + + align:start position:0% +wave +effect right and this is a case when you + + align:start position:0% +effect right and this is a case when you + + + align:start position:0% +effect right and this is a case when you +have to think about the wavelength as + + align:start position:0% +have to think about the wavelength as + + + align:start position:0% +have to think about the wavelength as +another characteristic Things N + + align:start position:0% +another characteristic Things N + + + align:start position:0% +another characteristic Things N +scale and uh uh I would I prefer to call + + align:start position:0% +scale and uh uh I would I prefer to call + + + align:start position:0% +scale and uh uh I would I prefer to call +this wave + + align:start position:0% + + + + align:start position:0% + +effects I'm not I'm sure that people + + align:start position:0% +effects I'm not I'm sure that people + + + align:start position:0% +effects I'm not I'm sure that people +don't always agree with + + align:start position:0% +don't always agree with + + + align:start position:0% +don't always agree with +me but say uh here let's take a look + + align:start position:0% +me but say uh here let's take a look + + + align:start position:0% +me but say uh here let's take a look +plus with the quantum with the uh w + + align:start position:0% +plus with the quantum with the uh w + + + align:start position:0% +plus with the quantum with the uh w +uh What uh uh take a basic picture here + + align:start position:0% +uh What uh uh take a basic picture here + + + align:start position:0% +uh What uh uh take a basic picture here +uh we know we're going to get into more + + align:start position:0% +uh we know we're going to get into more + + + align:start position:0% +uh we know we're going to get into more +in the next + + align:start position:0% +in the next + + + align:start position:0% +in the next +lecture that uh see anything from + + align:start position:0% +lecture that uh see anything from + + + align:start position:0% +lecture that uh see anything from +Quantum per picture is both wave and the + + align:start position:0% +Quantum per picture is both wave and the + + + align:start position:0% +Quantum per picture is both wave and the +particle right so wave has a wave + + align:start position:0% +particle right so wave has a wave + + + align:start position:0% +particle right so wave has a wave +length and so we have a wave + + align:start position:0% +length and so we have a wave + + + align:start position:0% +length and so we have a wave +length this is my + + align:start position:0% +length this is my + + + align:start position:0% +length this is my +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +right and uh in the quantum picture + + align:start position:0% +right and uh in the quantum picture + + + align:start position:0% +right and uh in the quantum picture +again say we're going more in the leure + + align:start position:0% +again say we're going more in the leure + + + align:start position:0% +again say we're going more in the leure +lecture the + + align:start position:0% +lecture the + + + align:start position:0% +lecture the +wavelength and the momentum is related + + align:start position:0% +wavelength and the momentum is related + + + align:start position:0% +wavelength and the momentum is related +through the pl constant H right H is a + + align:start position:0% +through the pl constant H right H is a + + + align:start position:0% +through the pl constant H right H is a +PL constant 6.6 10 Theus 34 jar uh jar + + align:start position:0% +PL constant 6.6 10 Theus 34 jar uh jar + + + align:start position:0% +PL constant 6.6 10 Theus 34 jar uh jar +second okay + + align:start position:0% + + + + align:start position:0% + +so now when the waves waves effect is + + align:start position:0% +so now when the waves waves effect is + + + align:start position:0% +so now when the waves waves effect is +important I'm going to give a very + + align:start position:0% +important I'm going to give a very + + + align:start position:0% +important I'm going to give a very +simple argument example in fact I say + + align:start position:0% +simple argument example in fact I say + + + align:start position:0% +simple argument example in fact I say +you will say that a significant + + align:start position:0% +you will say that a significant + + + align:start position:0% +you will say that a significant +difference even though we in my most + + align:start position:0% +difference even though we in my most + + + align:start position:0% +difference even though we in my most +most of my research is fall into + + align:start position:0% +most of my research is fall into + + + align:start position:0% +most of my research is fall into +classical size effect regim but I've + + align:start position:0% +classical size effect regim but I've + + + align:start position:0% +classical size effect regim but I've +been always thinking it's much better if + + align:start position:0% +been always thinking it's much better if + + + align:start position:0% +been always thinking it's much better if +you start with W picture to understand + + align:start position:0% +you start with W picture to understand + + + align:start position:0% +you start with W picture to understand +uh how the wave we go from wave to the + + align:start position:0% +uh how the wave we go from wave to the + + + align:start position:0% +uh how the wave we go from wave to the +particle why that's because when you go + + align:start position:0% +particle why that's because when you go + + + align:start position:0% +particle why that's because when you go +nrow there is always the + + align:start position:0% +nrow there is always the + + + align:start position:0% +nrow there is always the +interface a interface idea interface is + + align:start position:0% +interface a interface idea interface is + + + align:start position:0% +interface a interface idea interface is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +thickness zero thickness is compared + + align:start position:0% +thickness zero thickness is compared + + + align:start position:0% +thickness zero thickness is compared +anything is too thin too small right so + + align:start position:0% +anything is too thin too small right so + + + align:start position:0% +anything is too thin too small right so +there the wave effect always one can + + align:start position:0% +there the wave effect always one can + + + align:start position:0% +there the wave effect always one can +start with think about the wave + + align:start position:0% +start with think about the wave + + + align:start position:0% +start with think about the wave +reflection at the + + align:start position:0% +reflection at the + + + align:start position:0% +reflection at the +interface + + align:start position:0% +interface + + + align:start position:0% +interface +so uh even though + + align:start position:0% +so uh even though + + + align:start position:0% +so uh even though +um most of you probably don't deal with + + align:start position:0% +um most of you probably don't deal with + + + align:start position:0% +um most of you probably don't deal with +waves very often I want to emphasize we + + align:start position:0% +waves very often I want to emphasize we + + + align:start position:0% +waves very often I want to emphasize we +spend a lot of time talk about the + + align:start position:0% +spend a lot of time talk about the + + + align:start position:0% +spend a lot of time talk about the +waves uh so let me make a simple + + align:start position:0% +waves uh so let me make a simple + + + align:start position:0% +waves uh so let me make a simple +argument of standing we I have a film or + + align:start position:0% +argument of standing we I have a film or + + + align:start position:0% +argument of standing we I have a film or +uh in the first lecture I say if you go + + align:start position:0% +uh in the first lecture I say if you go + + + align:start position:0% +uh in the first lecture I say if you go +to Professor M when this website you'll + + align:start position:0% +to Professor M when this website you'll + + + align:start position:0% +to Professor M when this website you'll +see he make beautiful dots right Nano + + align:start position:0% +see he make beautiful dots right Nano + + + align:start position:0% +see he make beautiful dots right Nano +siiz + + align:start position:0% +siiz + + + align:start position:0% +siiz +dots and uh uh so I simplify that as a + + align:start position:0% +dots and uh uh so I simplify that as a + + + align:start position:0% +dots and uh uh so I simplify that as a +film I make a two Dimension vers + + align:start position:0% +film I make a two Dimension vers + + + align:start position:0% +film I make a two Dimension vers +freestanding film I got the electron + + align:start position:0% +freestanding film I got the electron + + + align:start position:0% +freestanding film I got the electron +wave + + align:start position:0% +wave + + + align:start position:0% +wave +inside right I have charge inside or I + + align:start position:0% +inside right I have charge inside or I + + + align:start position:0% +inside right I have charge inside or I +have atom you can sing it either + + align:start position:0% +have atom you can sing it either + + + align:start position:0% +have atom you can sing it either +way so this is a wave + + align:start position:0% +way so this is a wave + + + align:start position:0% +way so this is a wave +inside and there's a boundary cannot + + align:start position:0% +inside and there's a boundary cannot + + + align:start position:0% +inside and there's a boundary cannot +come + + align:start position:0% +come + + + align:start position:0% +come +out right so what do you have there + + align:start position:0% + + + + align:start position:0% + +so confined the boundary simplest + + align:start position:0% +so confined the boundary simplest + + + align:start position:0% +so confined the boundary simplest +picture is clamped right you see okay my + + align:start position:0% +picture is clamped right you see okay my + + + align:start position:0% +picture is clamped right you see okay my +wave you I thought I depends I wasn't + + align:start position:0% +wave you I thought I depends I wasn't + + + align:start position:0% +wave you I thought I depends I wasn't +sure I'm coming to this stage so I + + align:start position:0% +sure I'm coming to this stage so I + + + align:start position:0% +sure I'm coming to this stage so I +didn't bring the violin I have okay + + align:start position:0% +didn't bring the violin I have okay + + + align:start position:0% +didn't bring the violin I have okay +standing wave it's a standing wave right + + align:start position:0% +standing wave it's a standing wave right + + + align:start position:0% +standing wave it's a standing wave right +so let's start with standing wave + + align:start position:0% +so let's start with standing wave + + + align:start position:0% +so let's start with standing wave +picture and I have a final + + align:start position:0% +picture and I have a final + + + align:start position:0% +picture and I have a final +thickness + + align:start position:0% +thickness + + + align:start position:0% +thickness +okay let me say my simplest picture is + + align:start position:0% +okay let me say my simplest picture is + + + align:start position:0% +okay let me say my simplest picture is +standing W with at the boundary is zero + + align:start position:0% +standing W with at the boundary is zero + + + align:start position:0% +standing W with at the boundary is zero +vibration I clamp this two + + align:start position:0% +vibration I clamp this two + + + align:start position:0% +vibration I clamp this two +boundaries right so then my wave form + + align:start position:0% +boundaries right so then my wave form + + + align:start position:0% +boundaries right so then my wave form +this is + + align:start position:0% +this is + + + align:start position:0% +this is +a the standing W the simplest one mode + + align:start position:0% +a the standing W the simplest one mode + + + align:start position:0% +a the standing W the simplest one mode +of standing W and the next + + align:start position:0% + + + + align:start position:0% + +mode right so I have those different + + align:start position:0% +mode right so I have those different + + + align:start position:0% +mode right so I have those different +modes of standing wave + + align:start position:0% +modes of standing wave + + + align:start position:0% +modes of standing wave +inside and I can use the Expression I + + align:start position:0% +inside and I can use the Expression I + + + align:start position:0% +inside and I can use the Expression I +gave and this requirement to give you + + align:start position:0% +gave and this requirement to give you + + + align:start position:0% +gave and this requirement to give you +basic quantization + + align:start position:0% +basic quantization + + + align:start position:0% +basic quantization +result so how we do + + align:start position:0% +result so how we do + + + align:start position:0% +result so how we do +it Lambda / two right that's the basic + + align:start position:0% +it Lambda / two right that's the basic + + + align:start position:0% +it Lambda / two right that's the basic +length and here is 2 * Lambda over two + + align:start position:0% +length and here is 2 * Lambda over two + + + align:start position:0% +length and here is 2 * Lambda over two +uh say so it's just + + align:start position:0% +uh say so it's just + + + align:start position:0% +uh say so it's just +Lambda and times + + align:start position:0% +Lambda and times + + + align:start position:0% +Lambda and times +n this n is uh integer no longer the + + align:start position:0% +n this n is uh integer no longer the + + + align:start position:0% +n this n is uh integer no longer the +number density + + align:start position:0% +number density + + + align:start position:0% +number density +anymore right so Lambda or 2 * n should + + align:start position:0% +anymore right so Lambda or 2 * n should + + + align:start position:0% +anymore right so Lambda or 2 * n should +equal + + align:start position:0% + + + + align:start position:0% + +to the thickness D or + + align:start position:0% +to the thickness D or + + + align:start position:0% +to the thickness D or +diameter right order mag so this is + + align:start position:0% +diameter right order mag so this is + + + align:start position:0% +diameter right order mag so this is +D and this gives me Lambda equal 2D / n + + align:start position:0% + + + + align:start position:0% + +right and that will give me + + align:start position:0% +right and that will give me + + + align:start position:0% +right and that will give me +momentum equal H over + + align:start position:0% +momentum equal H over + + + align:start position:0% +momentum equal H over +Lambda and that's a uh 2 n + + align:start position:0% +Lambda and that's a uh 2 n + + + align:start position:0% +Lambda and that's a uh 2 n +d h wait wait wait sorry so 2 NH over no + + align:start position:0% +d h wait wait wait sorry so 2 NH over no + + + align:start position:0% +d h wait wait wait sorry so 2 NH over no +NH over + + align:start position:0% +NH over + + + align:start position:0% +NH over +2D + + align:start position:0% +2D + + + align:start position:0% +2D +right that's momentum + + align:start position:0% + + + + align:start position:0% + +okay I now I say I come to kinetic + + align:start position:0% +okay I now I say I come to kinetic + + + align:start position:0% +okay I now I say I come to kinetic +energy this is a I'm jumping here I say + + align:start position:0% +energy this is a I'm jumping here I say + + + align:start position:0% +energy this is a I'm jumping here I say +okay this wave also has a momentum and + + align:start position:0% +okay this wave also has a momentum and + + + align:start position:0% +okay this wave also has a momentum and +has a kinetic + + align:start position:0% +has a kinetic + + + align:start position:0% +has a kinetic +energy and this is a quantized momentum + + align:start position:0% +energy and this is a quantized momentum + + + align:start position:0% +energy and this is a quantized momentum +because that n must be integer n = 1 + + align:start position:0% +because that n must be integer n = 1 + + + align:start position:0% +because that n must be integer n = 1 +2 right so now the + + align:start position:0% +2 right so now the + + + align:start position:0% +2 right so now the +energy n + + align:start position:0% +energy n + + + align:start position:0% +energy n +is if I do the classic is MV + + align:start position:0% +is if I do the classic is MV + + + align:start position:0% +is if I do the classic is MV +s and I write it into a momentum Square + + align:start position:0% +s and I write it into a momentum Square + + + align:start position:0% +s and I write it into a momentum Square +2 m because momentum is MV I put the + + align:start position:0% +2 m because momentum is MV I put the + + + align:start position:0% +2 m because momentum is MV I put the +momentum in so I will get 8 m d s and n² + + align:start position:0% +momentum in so I will get 8 m d s and n² + + + align:start position:0% +momentum in so I will get 8 m d s and n² +* + + align:start position:0% +* + + + align:start position:0% +* +h² so now suddenly the energy of this + + align:start position:0% +h² so now suddenly the energy of this + + + align:start position:0% +h² so now suddenly the energy of this +particle is + + align:start position:0% +particle is + + + align:start position:0% +particle is +discontinuous because of the wave + + align:start position:0% +discontinuous because of the wave + + + align:start position:0% +discontinuous because of the wave +requirement + + align:start position:0% +requirement + + + align:start position:0% +requirement +right so I need to ask is this + + align:start position:0% +right so I need to ask is this + + + align:start position:0% +right so I need to ask is this +important so that clearly depends on + + align:start position:0% +important so that clearly depends on + + + align:start position:0% +important so that clearly depends on +what's the m and what's the N right if + + align:start position:0% +what's the m and what's the N right if + + + align:start position:0% +what's the m and what's the N right if +the m and uh say what's m and what's D + + align:start position:0% +the m and uh say what's m and what's D + + + align:start position:0% +the m and uh say what's m and what's D +if m and d are large the energy + + align:start position:0% +if m and d are large the energy + + + align:start position:0% +if m and d are large the energy +separation is very + + align:start position:0% +separation is very + + + align:start position:0% +separation is very +small if they are + + align:start position:0% +small if they are + + + align:start position:0% +small if they are +small this becomes very + + align:start position:0% +small this becomes very + + + align:start position:0% +small this becomes very +important how important it + + align:start position:0% +important how important it + + + align:start position:0% +important how important it +is so we need to have again order + + align:start position:0% +is so we need to have again order + + + align:start position:0% +is so we need to have again order +magnitude even though I always give you + + align:start position:0% +magnitude even though I always give you + + + align:start position:0% +magnitude even though I always give you +very L very small + + align:start position:0% +very L very small + + + align:start position:0% +very L very small +lambers but I want you to be proficient + + align:start position:0% +lambers but I want you to be proficient + + + align:start position:0% +lambers but I want you to be proficient +in those lambers you can choose whatever + + align:start position:0% +in those lambers you can choose whatever + + + align:start position:0% +in those lambers you can choose whatever +unit uh you use so let me first give + + align:start position:0% +unit uh you use so let me first give + + + align:start position:0% +unit uh you use so let me first give +order magnitud of KBT right we + + align:start position:0% +order magnitud of KBT right we + + + align:start position:0% +order magnitud of KBT right we +said everything is equal partition and 1 + + align:start position:0% +said everything is equal partition and 1 + + + align:start position:0% +said everything is equal partition and 1 +half KBT so KBT is good L to remember + + align:start position:0% +half KBT so KBT is good L to remember + + + align:start position:0% +half KBT so KBT is good L to remember +how large is + + align:start position:0% + + + + align:start position:0% + +KBT KBT is + + align:start position:0% +KBT KBT is + + + align:start position:0% +KBT KBT is +1.38 10 the minus 23rd jar C and times + + align:start position:0% +1.38 10 the minus 23rd jar C and times + + + align:start position:0% +1.38 10 the minus 23rd jar C and times + + align:start position:0% + + + align:start position:0% +kin and this gives + + align:start position:0% + + + + align:start position:0% + +me + + align:start position:0% + + + + align:start position:0% + +let me do that by + + align:start position:0% +let me do that by + + + align:start position:0% +let me do that by +hard okay is + + align:start position:0% + + + + align:start position:0% + +uh uh + + align:start position:0% + + + + align:start position:0% + +4 16 10 to the 21 + + align:start position:0% +4 16 10 to the 21 + + + align:start position:0% +4 16 10 to the 21 +JW you see I don't remember this + + align:start position:0% +JW you see I don't remember this + + + align:start position:0% +JW you see I don't remember this +number the problem the reason is here I + + align:start position:0% +number the problem the reason is here I + + + align:start position:0% +number the problem the reason is here I +make a jump most time I like to remember + + align:start position:0% +make a jump most time I like to remember + + + align:start position:0% +make a jump most time I like to remember +in electron + + align:start position:0% +in electron + + + align:start position:0% +in electron +volts + + align:start position:0% +volts + + + align:start position:0% +volts +okay one electron volt is one electron + + align:start position:0% +okay one electron volt is one electron + + + align:start position:0% +okay one electron volt is one electron +actually under one volt what's energy so + + align:start position:0% +actually under one volt what's energy so + + + align:start position:0% +actually under one volt what's energy so +one electron what's the charge of + + align:start position:0% + + + + align:start position:0% + +electron 19 + + align:start position:0% +electron 19 + + + align:start position:0% +electron 19 +colum Time 1 + + align:start position:0% +colum Time 1 + + + align:start position:0% +colum Time 1 +volt so this is 1.6 10 to the m 19 jar + + align:start position:0% +volt so this is 1.6 10 to the m 19 jar + + + align:start position:0% +volt so this is 1.6 10 to the m 19 jar +and if you convert this KBT into jar + + align:start position:0% +and if you convert this KBT into jar + + + align:start position:0% +and if you convert this KBT into jar +this is 26 Mill electron + + align:start position:0% +this is 26 Mill electron + + + align:start position:0% +this is 26 Mill electron +volt that's what I + + align:start position:0% +volt that's what I + + + align:start position:0% +volt that's what I +remember oh thank + + align:start position:0% +remember oh thank + + + align:start position:0% +remember oh thank +you yeah I used to be able to do braing + + align:start position:0% +you yeah I used to be able to do braing + + + align:start position:0% +you yeah I used to be able to do braing +calculations 26 M electron + + align:start position:0% +calculations 26 M electron + + + align:start position:0% +calculations 26 M electron +volts that's a room + + align:start position:0% +volts that's a room + + + align:start position:0% +volts that's a room +temperature okay so while I do that + + align:start position:0% +temperature okay so while I do that + + + align:start position:0% +temperature okay so while I do that +let's go to look at + + align:start position:0% +let's go to look at + + + align:start position:0% +let's go to look at +the right I'm going to put the + + align:start position:0% +the right I'm going to put the + + + align:start position:0% +the right I'm going to put the +electron into a film let's say the uh + + align:start position:0% +electron into a film let's say the uh + + + align:start position:0% +electron into a film let's say the uh +film is uh 100 unstr + + align:start position:0% +film is uh 100 unstr + + + align:start position:0% +film is uh 100 unstr +strong 10 + + align:start position:0% +strong 10 + + + align:start position:0% +strong 10 +NMM okay so one + + align:start position:0% +NMM okay so one + + + align:start position:0% +NMM okay so one +electron uh let's be consistent + + align:start position:0% + + + + align:start position:0% + +electron + + align:start position:0% +electron + + + align:start position:0% +electron +in 10 NM + + align:start position:0% + + + + align:start position:0% + +film what's the mass of + + align:start position:0% + + + + align:start position:0% + +electron 9.1 10 to Theus + + align:start position:0% +electron 9.1 10 to Theus + + + align:start position:0% +electron 9.1 10 to Theus + + align:start position:0% + + + + align:start position:0% + +kilogram okay so you plug in the + + align:start position:0% +kilogram okay so you plug in the + + + align:start position:0% +kilogram okay so you plug in the +L here is a 9.1 10 the- + + align:start position:0% +L here is a 9.1 10 the- + + + align:start position:0% +L here is a 9.1 10 the- + + align:start position:0% + + + align:start position:0% +kilogram + + align:start position:0% +kilogram + + + align:start position:0% +kilogram +here is 10us uh because 100 10 NM is 10 + + align:start position:0% +here is 10us uh because 100 10 NM is 10 + + + align:start position:0% +here is 10us uh because 100 10 NM is 10 +Theus 8 m + + align:start position:0% +Theus 8 m + + + align:start position:0% +Theus 8 m +squar right H is a 6.6 10 the- + + align:start position:0% +squar right H is a 6.6 10 the- + + + align:start position:0% +squar right H is a 6.6 10 the- +34 jar + + align:start position:0% +34 jar + + + align:start position:0% +34 jar +second okay so you do that I have Lum + + align:start position:0% +second okay so you do that I have Lum + + + align:start position:0% +second okay so you do that I have Lum +here + + align:start position:0% + + + + align:start position:0% + +I have then n for electron is uh + + align:start position:0% + + + + align:start position:0% + +6 uh 6 10 the minus 21 n² in terms of + + align:start position:0% +6 uh 6 10 the minus 21 n² in terms of + + + align:start position:0% +6 uh 6 10 the minus 21 n² in terms of +Jar or in terms of electron volt is 37 + + align:start position:0% +Jar or in terms of electron volt is 37 + + + align:start position:0% +Jar or in terms of electron volt is 37 +10 Theus 2 n² electron + + align:start position:0% + + + + align:start position:0% + +okay so I said KBT is 26 milron W so if + + align:start position:0% +okay so I said KBT is 26 milron W so if + + + align:start position:0% +okay so I said KBT is 26 milron W so if +you look at the electron in this 10 NM + + align:start position:0% +you look at the electron in this 10 NM + + + align:start position:0% +you look at the electron in this 10 NM +film the separation between energy Nal + + align:start position:0% +film the separation between energy Nal + + + align:start position:0% +film the separation between energy Nal +1al 2 that's a difference is three times + + align:start position:0% +1al 2 that's a difference is three times + + + align:start position:0% +1al 2 that's a difference is three times +those + + align:start position:0% +those + + + align:start position:0% +those +L that becomes comparable to + + align:start position:0% +L that becomes comparable to + + + align:start position:0% +L that becomes comparable to +KBT right so this shows the quantum fat + + align:start position:0% +KBT right so this shows the quantum fat + + + align:start position:0% +KBT right so this shows the quantum fat +become + + align:start position:0% +become + + + align:start position:0% +become +important and uh but if it's a a air + + align:start position:0% +important and uh but if it's a a air + + + align:start position:0% +important and uh but if it's a a air +molecule in this + + align:start position:0% +molecule in this + + + align:start position:0% +molecule in this +space that M now goes 20 so remember the + + align:start position:0% +space that M now goes 20 so remember the + + + align:start position:0% +space that M now goes 20 so remember the +proton mass is 2,000 times + + align:start position:0% +proton mass is 2,000 times + + + align:start position:0% +proton mass is 2,000 times +larger + + align:start position:0% +larger + + + align:start position:0% +larger +right so this energy separation becomes + + align:start position:0% +right so this energy separation becomes + + + align:start position:0% +right so this energy separation becomes +very + + align:start position:0% +very + + + align:start position:0% +very +small if it's a air molecule so for air + + align:start position:0% +small if it's a air molecule so for air + + + align:start position:0% +small if it's a air molecule so for air +molec I don't need to worry about + + align:start position:0% +molec I don't need to worry about + + + align:start position:0% +molec I don't need to worry about +Quantum size effect but for electron I + + align:start position:0% +Quantum size effect but for electron I + + + align:start position:0% +Quantum size effect but for electron I +need to start + + align:start position:0% +need to start + + + align:start position:0% +need to start +worry right so this is a uh where when + + align:start position:0% +worry right so this is a uh where when + + + align:start position:0% +worry right so this is a uh where when +we go to Nano we could encounter both + + align:start position:0% +we go to Nano we could encounter both + + + align:start position:0% +we go to Nano we could encounter both +Quantum and classic size + + align:start position:0% +Quantum and classic size + + + align:start position:0% +Quantum and classic size +effect and also as I said at the + + align:start position:0% +effect and also as I said at the + + + align:start position:0% +effect and also as I said at the +interface if it's ideal interface + + align:start position:0% +interface if it's ideal interface + + + align:start position:0% +interface if it's ideal interface +thickness Zero The Wave picture always + + align:start position:0% +thickness Zero The Wave picture always + + + align:start position:0% +thickness Zero The Wave picture always +becomes very very + + align:start position:0% +becomes very very + + + align:start position:0% +becomes very very +important + + align:start position:0% +important + + + align:start position:0% +important +right and uh final commment so we have + + align:start position:0% +right and uh final commment so we have + + + align:start position:0% +right and uh final commment so we have +Quantum size effect classical size + + align:start position:0% +Quantum size effect classical size + + + align:start position:0% +Quantum size effect classical size +effect the final commment is time right + + align:start position:0% +effect the final commment is time right + + + align:start position:0% +effect the final commment is time right +I shoot the + + align:start position:0% +I shoot the + + + align:start position:0% +I shoot the +laser a very fast laser microc + + align:start position:0% +laser a very fast laser microc + + + align:start position:0% +laser a very fast laser microc +laser you say can use the foral law to + + align:start position:0% +laser you say can use the foral law to + + + align:start position:0% +laser you say can use the foral law to +describe the + + align:start position:0% +describe the + + + align:start position:0% +describe the +transort and when is that becoming + + align:start position:0% +transort and when is that becoming + + + align:start position:0% +transort and when is that becoming +important + + align:start position:0% +important + + + align:start position:0% +important +right this is where this tow the time + + align:start position:0% +right this is where this tow the time + + + align:start position:0% +right this is where this tow the time +becomes important and you need to look + + align:start position:0% +becomes important and you need to look + + + align:start position:0% +becomes important and you need to look +at your transable process how does that + + align:start position:0% +at your transable process how does that + + + align:start position:0% +at your transable process how does that +compare to this + + align:start position:0% +compare to this + + + align:start position:0% +compare to this +time so mean free part for air molecule + + align:start position:0% +time so mean free part for air molecule + + + align:start position:0% +time so mean free part for air molecule + + align:start position:0% + + + align:start position:0% +NM + + align:start position:0% +NM + + + align:start position:0% +NM +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +500 right so that's about 10 Theus + + align:start position:0% +500 right so that's about 10 Theus + + + align:start position:0% +500 right so that's about 10 Theus +8 second so if you do micro second don't + + align:start position:0% +8 second so if you do micro second don't + + + align:start position:0% +8 second so if you do micro second don't +worry about it if you do pick second or + + align:start position:0% +worry about it if you do pick second or + + + align:start position:0% +worry about it if you do pick second or +n second you start to worry about + + align:start position:0% +n second you start to worry about + + + align:start position:0% +n second you start to worry about +it right so you have time scale you have + + align:start position:0% +it right so you have time scale you have + + + align:start position:0% +it right so you have time scale you have +length scale and this is where you need + + align:start position:0% +length scale and this is where you need + + + align:start position:0% +length scale and this is where you need +to be able to tell you safe in one + + align:start position:0% +to be able to tell you safe in one + + + align:start position:0% +to be able to tell you safe in one +regime you need to go say you have to + + align:start position:0% +regime you need to go say you have to + + + align:start position:0% +regime you need to go say you have to +think about the what kind of size effect + + align:start position:0% +think about the what kind of size effect + + + align:start position:0% +think about the what kind of size effect +what what kind of + + align:start position:0% +what what kind of + + + align:start position:0% +what what kind of +effects any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay if not uh remember I would like to + + align:start position:0% +okay if not uh remember I would like to + + + align:start position:0% +okay if not uh remember I would like to +see you uh in my office hour and prefer + + align:start position:0% +see you uh in my office hour and prefer + + + align:start position:0% +see you uh in my office hour and prefer +preferably the first few + + align:start position:0% +preferably the first few + + + align:start position:0% +preferably the first few +weeks \ No newline at end of file diff --git a/Y5oTQvNt47I.txt b/Y5oTQvNt47I.txt new file mode 100644 index 0000000000000000000000000000000000000000..1ca1154e0b89edc4373f5f82c1ebf3f83298455b --- /dev/null +++ b/Y5oTQvNt47I.txt @@ -0,0 +1,2259 @@ +align:start position:0% + +so far so good we've really calculated + + align:start position:0% +so far so good we've really calculated + + + align:start position:0% +so far so good we've really calculated +it we could stop here but there is a + + align:start position:0% +it we could stop here but there is a + + + align:start position:0% +it we could stop here but there is a +nice interpretation of of this Darwin + + align:start position:0% +nice interpretation of of this Darwin + + + align:start position:0% +nice interpretation of of this Darwin +term that gives you intuition as to what + + align:start position:0% +term that gives you intuition as to what + + + align:start position:0% +term that gives you intuition as to what +it's what's really happening see when + + align:start position:0% +it's what's really happening see when + + + align:start position:0% +it's what's really happening see when +you look at this terms over all these + + align:start position:0% +you look at this terms over all these + + + align:start position:0% +you look at this terms over all these +interactions with this class you say + + align:start position:0% +interactions with this class you say + + + align:start position:0% +interactions with this class you say +well the kinetic energy was not + + align:start position:0% +well the kinetic energy was not + + + align:start position:0% +well the kinetic energy was not +relativistic that gives rise to this + + align:start position:0% +relativistic that gives rise to this + + + align:start position:0% +relativistic that gives rise to this +term there is a story for the spin orbit + + align:start position:0% +term there is a story for the spin orbit + + + align:start position:0% +term there is a story for the spin orbit +as well we think of the proton creates + + align:start position:0% +as well we think of the proton creates + + + align:start position:0% +as well we think of the proton creates +an electric field you the electron are + + align:start position:0% +an electric field you the electron are + + + align:start position:0% +an electric field you the electron are +moving around as you move inside the + + align:start position:0% +moving around as you move inside the + + + align:start position:0% +moving around as you move inside the +static electric field you see a magnetic + + align:start position:0% +static electric field you see a magnetic + + + align:start position:0% +static electric field you see a magnetic +field the magnetic field interacts with + + align:start position:0% +field the magnetic field interacts with + + + align:start position:0% +field the magnetic field interacts with +your dipole moment of the electron + + align:start position:0% +your dipole moment of the electron + + + align:start position:0% +your dipole moment of the electron +that's the story here so what's the + + align:start position:0% +that's the story here so what's the + + + align:start position:0% +that's the story here so what's the +story for this term where where does it + + align:start position:0% +story for this term where where does it + + + align:start position:0% +story for this term where where does it +come from what is the physics behind it + + align:start position:0% +come from what is the physics behind it + + + align:start position:0% +come from what is the physics behind it +that's what I want to discuss now so the + + align:start position:0% +that's what I want to discuss now so the + + + align:start position:0% +that's what I want to discuss now so the +physics interpretation of the Darwin + + align:start position:0% +physics interpretation of the Darwin + + + align:start position:0% +physics interpretation of the Darwin +term is that + + align:start position:0% + + + + align:start position:0% + +the electron behaves as not as if it + + align:start position:0% +the electron behaves as not as if it + + + align:start position:0% +the electron behaves as not as if it +would be a point particle but as if it + + align:start position:0% +would be a point particle but as if it + + + align:start position:0% +would be a point particle but as if it +would be kind of a little ball where the + + align:start position:0% +would be kind of a little ball where the + + + align:start position:0% +would be kind of a little ball where the +charge is spread out with we know that + + align:start position:0% +charge is spread out with we know that + + + align:start position:0% +charge is spread out with we know that +any model of the electrode any + + align:start position:0% +any model of the electrode any + + + align:start position:0% +any model of the electrode any +mechanical model of the electron where + + align:start position:0% +mechanical model of the electron where + + + align:start position:0% +mechanical model of the electron where +you think of it as a ball the spinning + + align:start position:0% +you think of it as a ball the spinning + + + align:start position:0% +you think of it as a ball the spinning +doesn't work for the spin but somehow + + align:start position:0% +doesn't work for the spin but somehow + + + align:start position:0% +doesn't work for the spin but somehow +here we can see that this extra + + align:start position:0% +here we can see that this extra + + + align:start position:0% +here we can see that this extra +correction to the energy is the + + align:start position:0% +correction to the energy is the + + + align:start position:0% +correction to the energy is the +correction that would appear if somehow + + align:start position:0% +correction that would appear if somehow + + + align:start position:0% +correction that would appear if somehow +the electron instead of feeling the + + align:start position:0% +the electron instead of feeling the + + + align:start position:0% +the electron instead of feeling the +potential of the nucleus at one point as + + align:start position:0% +potential of the nucleus at one point as + + + align:start position:0% +potential of the nucleus at one point as +if it would be a point Paris as if it + + align:start position:0% +if it would be a point Paris as if it + + + align:start position:0% +if it would be a point Paris as if it +would be spread so let me make a drawing + + align:start position:0% +would be spread so let me make a drawing + + + align:start position:0% +would be spread so let me make a drawing +here here is the proton and it creates a + + align:start position:0% +here here is the proton and it creates a + + + align:start position:0% +here here is the proton and it creates a +potential and we would put an electron + + align:start position:0% +potential and we would put an electron + + + align:start position:0% +potential and we would put an electron +at a point R there is the electron but + + align:start position:0% +at a point R there is the electron but + + + align:start position:0% +at a point R there is the electron but +now we're gonna think that this electron + + align:start position:0% +now we're gonna think that this electron + + + align:start position:0% +now we're gonna think that this electron +is really a cloud like this and the + + align:start position:0% +is really a cloud like this and the + + + align:start position:0% +is really a cloud like this and the +charge is distributed over there and now + + align:start position:0% +charge is distributed over there and now + + + align:start position:0% +charge is distributed over there and now +I'm going to try to estimate what + + align:start position:0% +I'm going to try to estimate what + + + align:start position:0% +I'm going to try to estimate what +happens to the potential energy if it's + + align:start position:0% +happens to the potential energy if it's + + + align:start position:0% +happens to the potential energy if it's +really behaving like that so for that + + align:start position:0% +really behaving like that so for that + + + align:start position:0% +really behaving like that so for that +I'm gonna make another coordinate system + + align:start position:0% +I'm gonna make another coordinate system + + + align:start position:0% +I'm gonna make another coordinate system +sort of starting here I'm gonna call the + + align:start position:0% +sort of starting here I'm gonna call the + + + align:start position:0% +sort of starting here I'm gonna call the +vector that goes to an arbitrary point + + align:start position:0% +vector that goes to an arbitrary point + + + align:start position:0% +vector that goes to an arbitrary point +here vector u so from the origin or + + align:start position:0% +here vector u so from the origin or + + + align:start position:0% +here vector u so from the origin or +center of this charge distribution we'll + + align:start position:0% +center of this charge distribution we'll + + + align:start position:0% +center of this charge distribution we'll +put a vector U and then I have this + + align:start position:0% +put a vector U and then I have this + + + align:start position:0% +put a vector U and then I have this +vector over here which is R + u and + + align:start position:0% +vector over here which is R + u and + + + align:start position:0% +vector over here which is R + u and +these new points to a little bit of + + align:start position:0% +these new points to a little bit of + + + align:start position:0% +these new points to a little bit of +charge a little cubed here for example + + align:start position:0% + + + + align:start position:0% + +so this is our setup now the potential + + align:start position:0% +so this is our setup now the potential + + + align:start position:0% +so this is our setup now the potential +YouTube view to the proton-proton to + + align:start position:0% +YouTube view to the proton-proton to + + + align:start position:0% +YouTube view to the proton-proton to +have a potential V of R which is equal + + align:start position:0% +have a potential V of R which is equal + + + align:start position:0% +have a potential V of R which is equal +to minus the charge of the electron + + align:start position:0% +to minus the charge of the electron + + + align:start position:0% +to minus the charge of the electron +times the scalar potential Phi of R is + + align:start position:0% +times the scalar potential Phi of R is + + + align:start position:0% +times the scalar potential Phi of R is +minus e times E over R which is our + + align:start position:0% +minus e times E over R which is our + + + align:start position:0% +minus e times E over R which is our +familiar minus y squared over R so the + + align:start position:0% +familiar minus y squared over R so the + + + align:start position:0% +familiar minus y squared over R so the +potential energy this is potential + + align:start position:0% +potential energy this is potential + + + align:start position:0% +potential energy this is potential +energy if you had a point particle for a + + align:start position:0% +energy if you had a point particle for a + + + align:start position:0% +energy if you had a point particle for a +point particle + + align:start position:0% + + + + align:start position:0% + +you have that the protoid create and + + align:start position:0% +you have that the protoid create and + + + align:start position:0% +you have that the protoid create and +potential at a distance are you + + align:start position:0% +potential at a distance are you + + + align:start position:0% +potential at a distance are you +multiplied by the charge and you get the + + align:start position:0% +multiplied by the charge and you get the + + + align:start position:0% +multiplied by the charge and you get the +potential energy so how do we do it + + align:start position:0% +potential energy so how do we do it + + + align:start position:0% +potential energy so how do we do it +a little more generally I'm gonna hold + + align:start position:0% +a little more generally I'm gonna hold + + + align:start position:0% +a little more generally I'm gonna hold +this V tilde of are the potential energy + + align:start position:0% +this V tilde of are the potential energy + + + align:start position:0% +this V tilde of are the potential energy +the true potential energy potential + + align:start position:0% +the true potential energy potential + + + align:start position:0% +the true potential energy potential +energy energy when the center of the + + align:start position:0% +energy energy when the center of the + + + align:start position:0% +energy energy when the center of the +electron is at our electron at R so what + + align:start position:0% +electron is at our electron at R so what + + + align:start position:0% +electron is at our electron at R so what +is the true potential energy when the + + align:start position:0% +is the true potential energy when the + + + align:start position:0% +is the true potential energy when the +center of the electron is at R well I + + align:start position:0% +center of the electron is at R well I + + + align:start position:0% +center of the electron is at R well I +would have to do an integral over the + + align:start position:0% +would have to do an integral over the + + + align:start position:0% +would have to do an integral over the +electron of the little amount of charges + + align:start position:0% +electron of the little amount of charges + + + align:start position:0% +electron of the little amount of charges +times the potential at those points for + + align:start position:0% + + + + align:start position:0% + +every piece of charge I must multiply + + align:start position:0% +every piece of charge I must multiply + + + align:start position:0% +every piece of charge I must multiply +the charge times the potential generated + + align:start position:0% +the charge times the potential generated + + + align:start position:0% +the charge times the potential generated +by the proton and that would give me the + + align:start position:0% +by the proton and that would give me the + + + align:start position:0% +by the proton and that would give me the +total energy of this electron in this + + align:start position:0% +total energy of this electron in this + + + align:start position:0% +total energy of this electron in this +potential V of R so let me use a + + align:start position:0% +potential V of R so let me use a + + + align:start position:0% +potential V of R so let me use a +terminology here I will describe the + + align:start position:0% +terminology here I will describe the + + + align:start position:0% +terminology here I will describe the +charge density density Rho of you the + + align:start position:0% +charge density density Rho of you the + + + align:start position:0% +charge density density Rho of you the +density of charge at a position given by + + align:start position:0% +density of charge at a position given by + + + align:start position:0% +density of charge at a position given by +au vector I'll write it as minus e times + + align:start position:0% +au vector I'll write it as minus e times + + + align:start position:0% +au vector I'll write it as minus e times +Rho 0 of + + align:start position:0% +Rho 0 of + + + align:start position:0% +Rho 0 of +a little bit of notation I apologize but + + align:start position:0% +a little bit of notation I apologize but + + + align:start position:0% +a little bit of notation I apologize but +it's necessary to do things cleanly the + + align:start position:0% +it's necessary to do things cleanly the + + + align:start position:0% +it's necessary to do things cleanly the +charge density of the electron electron + + align:start position:0% +charge density of the electron electron + + + align:start position:0% +charge density of the electron electron +is given by Rho of U minus zero zero and + + align:start position:0% +is given by Rho of U minus zero zero and + + + align:start position:0% +is given by Rho of U minus zero zero and +then it should be true that the integral + + align:start position:0% +then it should be true that the integral + + + align:start position:0% +then it should be true that the integral +over the electron of the cube u Rho zero + + align:start position:0% +over the electron of the cube u Rho zero + + + align:start position:0% +over the electron of the cube u Rho zero +of U is equal to one + + align:start position:0% +of U is equal to one + + + align:start position:0% +of U is equal to one +look at that integral why should it be + + align:start position:0% +look at that integral why should it be + + + align:start position:0% +look at that integral why should it be +equal to one it should be equal to one + + align:start position:0% +equal to one it should be equal to one + + + align:start position:0% +equal to one it should be equal to one +because then the integral of the charge + + align:start position:0% +because then the integral of the charge + + + align:start position:0% +because then the integral of the charge +density the integral of this over all of + + align:start position:0% +density the integral of this over all of + + + align:start position:0% +density the integral of this over all of +space would be minus e times one and + + align:start position:0% +space would be minus e times one and + + + align:start position:0% +space would be minus e times one and +that's exactly what you expect so Rho + + align:start position:0% +that's exactly what you expect so Rho + + + align:start position:0% +that's exactly what you expect so Rho +zero is a unit free well 1 over length + + align:start position:0% +zero is a unit free well 1 over length + + + align:start position:0% +zero is a unit free well 1 over length +cube is a charge free quantity the + + align:start position:0% +cube is a charge free quantity the + + + align:start position:0% +cube is a charge free quantity the +charge is carried by this constant over + + align:start position:0% +charge is carried by this constant over + + + align:start position:0% +charge is carried by this constant over +here so what happens in with this V of R + + align:start position:0% +here so what happens in with this V of R + + + align:start position:0% +here so what happens in with this V of R +this V of R is the charge little charge + + align:start position:0% +this V of R is the charge little charge + + + align:start position:0% +this V of R is the charge little charge +q is the cube u times Rho of u times v @ + + align:start position:0% +q is the cube u times Rho of u times v @ + + + align:start position:0% +q is the cube u times Rho of u times v @ +r plus you look the charge is this at + + align:start position:0% +r plus you look the charge is this at + + + align:start position:0% +r plus you look the charge is this at +some little element and then the + + align:start position:0% +some little element and then the + + + align:start position:0% +some little element and then the +potential there is the potential at R + + align:start position:0% +potential there is the potential at R + + + align:start position:0% +potential there is the potential at R +Plus u so one more step VFR if you take + + align:start position:0% +Plus u so one more step VFR if you take + + + align:start position:0% +Plus u so one more step VFR if you take +from Rho this extra - e - e times Phi of + + align:start position:0% +from Rho this extra - e - e times Phi of + + + align:start position:0% +from Rho this extra - e - e times Phi of +R is what we call the potential energy + + align:start position:0% +R is what we call the potential energy + + + align:start position:0% +R is what we call the potential energy +due to + + align:start position:0% +due to + + + align:start position:0% +due to +are so take the minus e out and append + + align:start position:0% +are so take the minus e out and append + + + align:start position:0% +are so take the minus e out and append +it to the capital phi here so that we + + align:start position:0% +it to the capital phi here so that we + + + align:start position:0% +it to the capital phi here so that we +have integral d cube u Rho 0 of u v of r + + align:start position:0% +have integral d cube u Rho 0 of u v of r + + + align:start position:0% +have integral d cube u Rho 0 of u v of r ++ u ok + + align:start position:0% ++ u ok + + + align:start position:0% ++ u ok +this was our dog it gives you the new + + align:start position:0% +this was our dog it gives you the new + + + align:start position:0% +this was our dog it gives you the new +energy the true potential energy of this + + align:start position:0% +energy the true potential energy of this + + + align:start position:0% +energy the true potential energy of this +electron but when the center is at R as + + align:start position:0% +electron but when the center is at R as + + + align:start position:0% +electron but when the center is at R as +the smearing of the potential energy of + + align:start position:0% +the smearing of the potential energy of + + + align:start position:0% +the smearing of the potential energy of +a point particle smeared over the + + align:start position:0% +a point particle smeared over the + + + align:start position:0% +a point particle smeared over the +electron so this is a formula that + + align:start position:0% +electron so this is a formula that + + + align:start position:0% +electron so this is a formula that +represents our intuition and moreover it + + align:start position:0% +represents our intuition and moreover it + + + align:start position:0% +represents our intuition and moreover it +has the Rho 0 here that tells you the + + align:start position:0% +has the Rho 0 here that tells you the + + + align:start position:0% +has the Rho 0 here that tells you the +weight that you should apply at any + + align:start position:0% +weight that you should apply at any + + + align:start position:0% +weight that you should apply at any +point because this Rho 0 is proportional + + align:start position:0% +point because this Rho 0 is proportional + + + align:start position:0% +point because this Rho 0 is proportional +to the charge very good we have a + + align:start position:0% +to the charge very good we have a + + + align:start position:0% +to the charge very good we have a +formula but you know I was supposed to + + align:start position:0% +formula but you know I was supposed to + + + align:start position:0% +formula but you know I was supposed to +explain that term and we have not + + align:start position:0% +explain that term and we have not + + + align:start position:0% +explain that term and we have not +explained it yet but now it's time to + + align:start position:0% +explained it yet but now it's time to + + + align:start position:0% +explained it yet but now it's time to +explain it we're going to try to do a + + align:start position:0% +explain it we're going to try to do a + + + align:start position:0% +explain it we're going to try to do a +computation that helps us do that the + + align:start position:0% +computation that helps us do that the + + + align:start position:0% +computation that helps us do that the +idea is that we would expand the + + align:start position:0% +idea is that we would expand the + + + align:start position:0% +idea is that we would expand the +potential around our the point R and + + align:start position:0% +potential around our the point R and + + + align:start position:0% +potential around our the point R and +threebees as a small deviation because + + align:start position:0% +threebees as a small deviation because + + + align:start position:0% +threebees as a small deviation because +after all we expect this little ball + + align:start position:0% +after all we expect this little ball + + + align:start position:0% +after all we expect this little ball +that I drew big here for the purposes of + + align:start position:0% +that I drew big here for the purposes of + + + align:start position:0% +that I drew big here for the purposes of +illustration to be rather small so let's + + align:start position:0% +illustration to be rather small so let's + + + align:start position:0% +illustration to be rather small so let's +write V of R + u us V of R in Taylor + + align:start position:0% +write V of R + u us V of R in Taylor + + + align:start position:0% +write V of R + u us V of R in Taylor +series but the next term is the + + align:start position:0% +series but the next term is the + + + align:start position:0% +series but the next term is the +derivative of V with respect to position + + align:start position:0% +derivative of V with respect to position + + + align:start position:0% +derivative of V with respect to position +evaluated at R multiplied by the + + align:start position:0% +evaluated at R multiplied by the + + + align:start position:0% +evaluated at R multiplied by the +deviation that you moved so + + align:start position:0% +deviation that you moved so + + + align:start position:0% +deviation that you moved so +some over i bv the ex i evaluated at R + + align:start position:0% +some over i bv the ex i evaluated at R + + + align:start position:0% +some over i bv the ex i evaluated at R +times you I this is the component of + + align:start position:0% +times you I this is the component of + + + align:start position:0% +times you I this is the component of +this vector you that's the first term in + + align:start position:0% +this vector you that's the first term in + + + align:start position:0% +this vector you that's the first term in +the Taylor series and we need one more + + align:start position:0% +the Taylor series and we need one more + + + align:start position:0% +the Taylor series and we need one more +plus 1/2 sum over i and j ii v DX i the + + align:start position:0% +plus 1/2 sum over i and j ii v DX i the + + + align:start position:0% +plus 1/2 sum over i and j ii v DX i the +xj evaluated at our UI UJ and then we + + align:start position:0% +xj evaluated at our UI UJ and then we + + + align:start position:0% +xj evaluated at our UI UJ and then we +have to integrate here we substitute in + + align:start position:0% +have to integrate here we substitute in + + + align:start position:0% +have to integrate here we substitute in +here and integrate so v tilde of are + + align:start position:0% +here and integrate so v tilde of are + + + align:start position:0% +here and integrate so v tilde of are +let's see what it is + + align:start position:0% +let's see what it is + + + align:start position:0% +let's see what it is +well i can put this whole thing let me + + align:start position:0% +well i can put this whole thing let me + + + align:start position:0% +well i can put this whole thing let me +we don't want to write so much so let's + + align:start position:0% +we don't want to write so much so let's + + + align:start position:0% +we don't want to write so much so let's +try to do it a little quick we're + + align:start position:0% +try to do it a little quick we're + + + align:start position:0% +try to do it a little quick we're +integrating over you and here let's + + align:start position:0% +integrating over you and here let's + + + align:start position:0% +integrating over you and here let's +think of the first term here when you + + align:start position:0% +think of the first term here when you + + + align:start position:0% +think of the first term here when you +plug in the first term this function of + + align:start position:0% +plug in the first term this function of + + + align:start position:0% +plug in the first term this function of +r has nothing to do with you so it goes + + align:start position:0% +r has nothing to do with you so it goes + + + align:start position:0% +r has nothing to do with you so it goes +out and you get v of r times the + + align:start position:0% +out and you get v of r times the + + + align:start position:0% +out and you get v of r times the +integral D cube u Rho 0 of you for the + + align:start position:0% +integral D cube u Rho 0 of you for the + + + align:start position:0% +integral D cube u Rho 0 of you for the +next term in here these derivatives are + + align:start position:0% +next term in here these derivatives are + + + align:start position:0% +next term in here these derivatives are +evaluated at R have nothing to do with + + align:start position:0% +evaluated at R have nothing to do with + + + align:start position:0% +evaluated at R have nothing to do with +you they go out so plus sum over i DV DX + + align:start position:0% +you they go out so plus sum over i DV DX + + + align:start position:0% +you they go out so plus sum over i DV DX +i of our integral D cube u Rho 0 of you + + align:start position:0% +i of our integral D cube u Rho 0 of you + + + align:start position:0% +i of our integral D cube u Rho 0 of you +you our last herbs + + align:start position:0% +you our last herbs + + + align:start position:0% +you our last herbs +these derivatives go out there evaluated + + align:start position:0% +these derivatives go out there evaluated + + + align:start position:0% +these derivatives go out there evaluated +at R they have nothing to do with you so + + align:start position:0% +at R they have nothing to do with you so + + + align:start position:0% +at R they have nothing to do with you so +plus 1/2 sum over I + + align:start position:0% +plus 1/2 sum over I + + + align:start position:0% +plus 1/2 sum over I +J ii v the X I the XJ evaluated as our + + align:start position:0% +J ii v the X I the XJ evaluated as our + + + align:start position:0% +J ii v the X I the XJ evaluated as our +integral D cubed u bro of you you I you + + align:start position:0% +integral D cubed u bro of you you I you + + + align:start position:0% +integral D cubed u bro of you you I you +J okay all these terms are happily we + + align:start position:0% +J okay all these terms are happily we + + + align:start position:0% +J okay all these terms are happily we +can interpret much of what we have here + + align:start position:0% +can interpret much of what we have here + + + align:start position:0% +can interpret much of what we have here +so what is this first integral V of R + + align:start position:0% + + + + align:start position:0% + +equals this integral is our + + align:start position:0% +equals this integral is our + + + align:start position:0% +equals this integral is our +normalization integral over here that's + + align:start position:0% +normalization integral over here that's + + + align:start position:0% +normalization integral over here that's +equal to 1 so this is very nice that's + + align:start position:0% +equal to 1 so this is very nice that's + + + align:start position:0% +equal to 1 so this is very nice that's +what you would expect that to first + + align:start position:0% +what you would expect that to first + + + align:start position:0% +what you would expect that to first +approximation the total energy of the + + align:start position:0% +approximation the total energy of the + + + align:start position:0% +approximation the total energy of the +letter when it is at R is a fee as if it + + align:start position:0% +letter when it is at R is a fee as if it + + + align:start position:0% +letter when it is at R is a fee as if it +would be a point particle at R now let's + + align:start position:0% +would be a point particle at R now let's + + + align:start position:0% +would be a point particle at R now let's +look at the next terms now we will + + align:start position:0% +look at the next terms now we will + + + align:start position:0% +look at the next terms now we will +assume assume that the distribution of + + align:start position:0% +assume assume that the distribution of + + + align:start position:0% +assume assume that the distribution of +charge is fairly symmetric so that means + + align:start position:0% +charge is fairly symmetric so that means + + + align:start position:0% +charge is fairly symmetric so that means +that role of U vector is actually a + + align:start position:0% +that role of U vector is actually a + + + align:start position:0% +that role of U vector is actually a +function role 0 of U where u is the + + align:start position:0% +function role 0 of U where u is the + + + align:start position:0% +function role 0 of U where u is the +length of the new vector so it just + + align:start position:0% +length of the new vector so it just + + + align:start position:0% +length of the new vector so it just +depends on the distance from the point + + align:start position:0% +depends on the distance from the point + + + align:start position:0% +depends on the distance from the point +that you're looking that's a charge + + align:start position:0% +that you're looking that's a charge + + + align:start position:0% +that you're looking that's a charge +why would it be more complicated if that + + align:start position:0% +why would it be more complicated if that + + + align:start position:0% +why would it be more complicated if that +is the case if this is very curly + + align:start position:0% +is the case if this is very curly + + + align:start position:0% +is the case if this is very curly +symmetric you can already see that this + + align:start position:0% +symmetric you can already see that this + + + align:start position:0% +symmetric you can already see that this +integrals would vanish because you're + + align:start position:0% +integrals would vanish because you're + + + align:start position:0% +integrals would vanish because you're +integrating the spherically symmetric + + align:start position:0% +integrating the spherically symmetric + + + align:start position:0% +integrating the spherically symmetric +quantity times a power of a coordinate + + align:start position:0% +quantity times a power of a coordinate + + + align:start position:0% +quantity times a power of a coordinate +that's something you did in the homework + + align:start position:0% +that's something you did in the homework + + + align:start position:0% +that's something you did in the homework +as well for this stark effect you + + align:start position:0% +as well for this stark effect you + + + align:start position:0% +as well for this stark effect you +realize that integrals of strata + + align:start position:0% +realize that integrals of strata + + + align:start position:0% +realize that integrals of strata +symmetric functions and powers of XY and + + align:start position:0% +symmetric functions and powers of XY and + + + align:start position:0% +symmetric functions and powers of XY and +Z will they get killed and unless those + + align:start position:0% +Z will they get killed and unless those + + + align:start position:0% +Z will they get killed and unless those +are even powers so this is an odd power + + align:start position:0% +are even powers so this is an odd power + + + align:start position:0% +are even powers so this is an odd power +and that's zero so this term is gone and + + align:start position:0% + + + + align:start position:0% + +this integral it's interesting as well + + align:start position:0% +this integral it's interesting as well + + + align:start position:0% +this integral it's interesting as well +when you have a spherically symmetric + + align:start position:0% +when you have a spherically symmetric + + + align:start position:0% +when you have a spherically symmetric +quantity and you have I and J different + + align:start position:0% +quantity and you have I and J different + + + align:start position:0% +quantity and you have I and J different +the integral would be zero it's like + + align:start position:0% +the integral would be zero it's like + + + align:start position:0% +the integral would be zero it's like +having a power of X and a power of Y in + + align:start position:0% +having a power of X and a power of Y in + + + align:start position:0% +having a power of X and a power of Y in +your homework so if that integral would + + align:start position:0% +your homework so if that integral would + + + align:start position:0% +your homework so if that integral would +be zero it would only be non 0 if i is + + align:start position:0% +be zero it would only be non 0 if i is + + + align:start position:0% +be zero it would only be non 0 if i is +equal to j the first component for + + align:start position:0% +equal to j the first component for + + + align:start position:0% +equal to j the first component for +example 1 u 1 u 1 but that integral + + align:start position:0% +example 1 u 1 u 1 but that integral + + + align:start position:0% +example 1 u 1 u 1 but that integral +would be the same as u 2 u 2 or u 3 u 3 + + align:start position:0% +would be the same as u 2 u 2 or u 3 u 3 + + + align:start position:0% +would be the same as u 2 u 2 or u 3 u 3 +so in fact each of these integrals is + + align:start position:0% +so in fact each of these integrals is + + + align:start position:0% +so in fact each of these integrals is +proportional to Delta IJ but equal to + + align:start position:0% +proportional to Delta IJ but equal to + + + align:start position:0% +proportional to Delta IJ but equal to +one-third of the integral of the cube u + + align:start position:0% +one-third of the integral of the cube u + + + align:start position:0% +one-third of the integral of the cube u +Rho of you output the Delta IJ here + + align:start position:0% +Rho of you output the Delta IJ here + + + align:start position:0% +Rho of you output the Delta IJ here +times u squared u squared is u 1 square + + align:start position:0% +times u squared u squared is u 1 square + + + align:start position:0% +times u squared u squared is u 1 square +plus u 2 square plus u 3 squared each + + align:start position:0% +plus u 2 square plus u 3 squared each + + + align:start position:0% +plus u 2 square plus u 3 squared each +one gives the same integral therefore + + align:start position:0% +one gives the same integral therefore + + + align:start position:0% +one gives the same integral therefore +the result has a 1/3 in front so what do + + align:start position:0% +the result has a 1/3 in front so what do + + + align:start position:0% +the result has a 1/3 in front so what do +we get plus 1/6 and here we get a big + + align:start position:0% +we get plus 1/6 and here we get a big + + + align:start position:0% +we get plus 1/6 and here we get a big +smile + + align:start position:0% +smile + + + align:start position:0% +smile +why because Delta IJ with this thing is + + align:start position:0% +why because Delta IJ with this thing is + + + align:start position:0% +why because Delta IJ with this thing is +the laplacian of V evaluated at R have + + align:start position:0% +the laplacian of V evaluated at R have + + + align:start position:0% +the laplacian of V evaluated at R have +the same derivative sound so what do we + + align:start position:0% +the same derivative sound so what do we + + + align:start position:0% +the same derivative sound so what do we +get here 1/6 of the laplacian of V + + align:start position:0% +get here 1/6 of the laplacian of V + + + align:start position:0% +get here 1/6 of the laplacian of V +evaluated at R times the integral the + + align:start position:0% +evaluated at R times the integral the + + + align:start position:0% +evaluated at R times the integral the +cube u Rho 0 of you + + align:start position:0% +cube u Rho 0 of you + + + align:start position:0% +cube u Rho 0 of you +squirt very nice already starting to + + align:start position:0% +squirt very nice already starting to + + + align:start position:0% +squirt very nice already starting to +look like what we wanted laplacian can + + align:start position:0% +look like what we wanted laplacian can + + + align:start position:0% +look like what we wanted laplacian can +we do a little better yes we can it's + + align:start position:0% +we do a little better yes we can it's + + + align:start position:0% +we do a little better yes we can it's +possible let's assume the charge + + align:start position:0% +possible let's assume the charge + + + align:start position:0% +possible let's assume the charge +particle has a size so let's assume the + + align:start position:0% +particle has a size so let's assume the + + + align:start position:0% +particle has a size so let's assume the +electron trunk is a ball of radius the + + align:start position:0% +electron trunk is a ball of radius the + + + align:start position:0% +electron trunk is a ball of radius the +Compton wavelength which is h-bar over M + + align:start position:0% +Compton wavelength which is h-bar over M + + + align:start position:0% +Compton wavelength which is h-bar over M +C so that means Rho 0 of U is nonzero + + align:start position:0% +C so that means Rho 0 of U is nonzero + + + align:start position:0% +C so that means Rho 0 of U is nonzero +when u is less than this lambda and it's + + align:start position:0% +when u is less than this lambda and it's + + + align:start position:0% +when u is less than this lambda and it's +0 when u is greater than this lambda + + align:start position:0% +0 when u is greater than this lambda + + + align:start position:0% +0 when u is greater than this lambda +that's a ball some density up to there + + align:start position:0% +that's a ball some density up to there + + + align:start position:0% +that's a ball some density up to there +and this must integrate to 1 so it's 1 + + align:start position:0% +and this must integrate to 1 so it's 1 + + + align:start position:0% +and this must integrate to 1 so it's 1 +over the volume of that ball 4 PI lambda + + align:start position:0% +over the volume of that ball 4 PI lambda + + + align:start position:0% +over the volume of that ball 4 PI lambda +cube over 3 + + align:start position:0% + + + + align:start position:0% + +do this integral this integral gives you + + align:start position:0% +do this integral this integral gives you + + + align:start position:0% +do this integral this integral gives you +actually three-fifths of lambda squared + + align:start position:0% +actually three-fifths of lambda squared + + + align:start position:0% +actually three-fifths of lambda squared +with that function so the end result is + + align:start position:0% +with that function so the end result is + + + align:start position:0% +with that function so the end result is +that V tilde of R is equal to V of R + + align:start position:0% + + + + align:start position:0% + +plus three-fifths of this thing times + + align:start position:0% +plus three-fifths of this thing times + + + align:start position:0% +plus three-fifths of this thing times +that is one-tenth h squared M Squared C + + align:start position:0% +that is one-tenth h squared M Squared C + + + align:start position:0% +that is one-tenth h squared M Squared C +squared laplacian of V the new + + align:start position:0% +squared laplacian of V the new + + + align:start position:0% +squared laplacian of V the new +correction to the potential in this + + align:start position:0% +correction to the potential in this + + + align:start position:0% +correction to the potential in this +model came out to this one-tenth that's + + align:start position:0% +model came out to this one-tenth that's + + + align:start position:0% +model came out to this one-tenth that's +pretty close I must say there's an 1/8 + + align:start position:0% +pretty close I must say there's an 1/8 + + + align:start position:0% +pretty close I must say there's an 1/8 +there we assume the electron is a ball + + align:start position:0% +there we assume the electron is a ball + + + align:start position:0% +there we assume the electron is a ball +of size the Compton wavelength of + + align:start position:0% +of size the Compton wavelength of + + + align:start position:0% +of size the Compton wavelength of +electron it's a very rough assumption so + + align:start position:0% +electron it's a very rough assumption so + + + align:start position:0% +electron it's a very rough assumption so +even to see the number not coming off by + + align:start position:0% +even to see the number not coming off by + + + align:start position:0% +even to see the number not coming off by +a factor of a hundred is quite nice so + + align:start position:0% +a factor of a hundred is quite nice so + + + align:start position:0% +a factor of a hundred is quite nice so +that's the interpretation the + + align:start position:0% +that's the interpretation the + + + align:start position:0% +that's the interpretation the +nonlocality the spread out of the + + align:start position:0% +nonlocality the spread out of the + + + align:start position:0% +nonlocality the spread out of the +electron into a little ball of its + + align:start position:0% +electron into a little ball of its + + + align:start position:0% +electron into a little ball of its +Compton size is it's quite significant + + align:start position:0% +Compton size is it's quite significant + + + align:start position:0% +Compton size is it's quite significant +this the Compton wavelength of the + + align:start position:0% +this the Compton wavelength of the + + + align:start position:0% +this the Compton wavelength of the +electron is fundamental in quantum field + + align:start position:0% +electron is fundamental in quantum field + + + align:start position:0% +electron is fundamental in quantum field +theory the Compton wavelength of an + + align:start position:0% +theory the Compton wavelength of an + + + align:start position:0% +theory the Compton wavelength of an +electron is the size of a photon whose + + align:start position:0% +electron is the size of a photon whose + + + align:start position:0% +electron is the size of a photon whose +energy is equal to the rest mass of the + + align:start position:0% +energy is equal to the rest mass of the + + + align:start position:0% +energy is equal to the rest mass of the +electron so if you have a photon of the + + align:start position:0% +electron so if you have a photon of the + + + align:start position:0% +electron so if you have a photon of the +size equal of a wavelength equal the + + align:start position:0% +size equal of a wavelength equal the + + + align:start position:0% +size equal of a wavelength equal the +Compton length of the electron that + + align:start position:0% +Compton length of the electron that + + + align:start position:0% +Compton length of the electron that +photon pucks enough energy to create + + align:start position:0% +photon pucks enough energy to create + + + align:start position:0% +photon pucks enough energy to create +electron positron pairs that's why in + + align:start position:0% +electron positron pairs that's why in + + + align:start position:0% +electron positron pairs that's why in +quantum field theory you care about this + + align:start position:0% +quantum field theory you care about this + + + align:start position:0% +quantum field theory you care about this +and the quantum field theory is really + + align:start position:0% +and the quantum field theory is really + + + align:start position:0% +and the quantum field theory is really +the way you do relativistic quantum + + align:start position:0% +the way you do relativistic quantum + + + align:start position:0% +the way you do relativistic quantum +mechanics so it's not + + align:start position:0% +mechanics so it's not + + + align:start position:0% +mechanics so it's not +pricing that in in relativistic analysis + + align:start position:0% +pricing that in in relativistic analysis + + + align:start position:0% +pricing that in in relativistic analysis +such as that of the Dirac equation we + + align:start position:0% +such as that of the Dirac equation we + + + align:start position:0% +such as that of the Dirac equation we +find a role for the Compton wavelength + + align:start position:0% +find a role for the Compton wavelength + + + align:start position:0% +find a role for the Compton wavelength +of the electron and a correction + + align:start position:0% +of the electron and a correction + + + align:start position:0% +of the electron and a correction +associated with it \ No newline at end of file diff --git a/YQ7HEE8-OfA.txt b/YQ7HEE8-OfA.txt new file mode 100644 index 0000000000000000000000000000000000000000..6114ef34bcc4d1d8158016bf7e38f057129353f1 --- /dev/null +++ b/YQ7HEE8-OfA.txt @@ -0,0 +1,1930 @@ +This is a brief, +so, the equation, + +and we got the characteristic +equation from the last time. + +The general topic for today is +going to be oscillations, + +which are extremely important +in the applications and in + +everyday life. +But, the oscillations, + +we know, are associated with a +complex root. + +So, they correspond to complex +roots of the characteristic + +equation. +r squared plus br plus k equals + +zero. +I'd like to begin. + +Most of the lecture will be +about discussing the relations + +between these numbers, +these constants, + +and the various properties that +the solutions, + +oscillatory solutions, +have. + +But, before that, +I'd like to begin by clearing + +up a couple of questions almost +everybody has at some point or + +other when they study the case +of complex roots. + +Complex roots are the case +which produce oscillations in + +the solutions. +That's the relation, + +and that's why I'm talking +about this for the first few + +minutes. +Now, what is the problem? + +The complex roots, +of course, there will be two + +roots, and they occur at the +complex conjugates of each + +other. +So, they will be of the form a + +plus or minus bi. +Last time, I showed you, + +I took the root r equals a plus +bi, + +which leads to the solution. +The corresponding solution is a + +complex solution which is e to +the at, (a plus i b)t. + +And, what we did was the + +problem was to get real +solutions out of that. + +We needed two real solutions, +and the way I got them was by + +separating this into its real +part and its imaginary part. + +And, I proved a little theorem +for you that said both of those + +give solutions. +So, the real part was e to the + +a t times cosine b t, +and the imaginary + +part was e to the at sine b t. + +And, those were the two +solutions. + +So, here was y1. +And, the point was those, + +out of the complex solutions, +we got real solutions. + +We have to have real solutions +because we live in the real + +world. +The equation is real. + +Its coefficients are real. +They represent real quantities. + +That's the way the solutions, +therefore, have to be. + +So, these, the point is, +these are now real solutions, + +these two guys, +y1 and y2. + +Now, the first question almost +everybody has, + +and I was pleased to see at the +end of the lecture, + +a few people came up and asked +me, yeah, well, + +you took a plus bi, +but there was another root, + +a minus bi. +You didn't use that one. + +That would give two more +solutions, right? + +Of course, they didn't say +that. + +They were too smart. +They just said, + +what about that other root? +Well, what about it? + +The reason I don't have to talk +about the other root is because + +although it does give to +solutions, it doesn't give two + +new ones. +Maybe I can indicate that most + +clearly here even though you +won't be able to take notes by + +just using colored chalk. +Suppose, instead of plus bi, + +I used a minus bi. + +What would have changed? +Well, this would now become + +minus here. +Would this change? + +No, because e to the minus ibt +is the cosine of + +minus b, but that's the same as +the cosine of b. + +How about here? +This would become the sine of + +minus bt. +But that's simply the negative + +of the sine of bt. +So, the only change would have + +been to put a minus sign there. +Now, I don't care if I get y2 + +or negative y2 because what am I +going to do with it? + +When I get it, +I'm going to write y, + +the general solution, +as c1 y1 plus c2 y2. + +So, if I get negative y2, +that just changes that + +arbitrary constant from c2 to +minus c2, which is just as + +arbitrary a constant. +So, in other words, + +there's no reason to use the +other root because it doesn't + +give anything new. +Now, there the story could + +stop. +And, I would like it to stop, + +frankly, but I don't dare +because there's a second + +question. +And, I'm visiting recitations + +not this semester, +but in previous semesters. + +In 18.03, so many recitations +do this. + +I have to partly inoculate you +against it, and partly tell you + +that some of the engineering +courses do do it, + +and therefore you probably +should learn it also. + +So, there is another way of +proceeding, which is what you + +might have thought. +Hey, look, we got two complex + +roots. +That gives us two solutions, + +which are different. +Neither one is a constant + +multiple of the other. +So, the other approach is, + +use, as a general solution, +y equals, now, + +I'm going to put a capital C +here. + +You will see why in just a +second, times e to the (a plus b + +i) times t. + +And then, I will use the other +solution: C2 times e to the (a + +minus b i) t. + +These are two independent +solutions. + +And therefore, +can't I get the general + +solution in that form? +Now, in a sense, + +you can. +The whole problem is the + +following, of course, +that I'm only interested in + +real solutions. +This is a complex function. + +This is another complex +function. + +It's got an i in it, +in other words, + +when I write it out as u plus +iv. + +If I expect to be able to get a +real solution out of that, + +that means I have to make, +allow these coefficients to be + +complex numbers, +and not real numbers. + +So, in other words, +what I'm saying is that an + +expression like this, +where the a plus bi and a minus + +bi are complex roots of that +characteristic equation, + +is formally a very general, +complex solution to the + +equation. +And therefore, + +the problem becomes, +how, from this expression, + +do I get the real solutions? +So, the problem is, + +I accept these as the complex +solutions. + +My problem is, +to find among all these guys + +where C1 and C2 are allowed to +be complex, the problem is, + +which of the green solutions +are real? + +Now, there are many ways of +getting the answer. + +There is a super hack way. +The super hack way is to say, + +well, this one is C1 plus i d1. + +This is C2 plus i d2. + +And, I'll write all this out in +terms of what it is, + +you know, cosine plus i sine, +and don't forget the e to the + +at. +And, I will write it all out, + +and it will take an entire +board. + +And then, I will just see what +the condition is. + +I'll write its real part, +and its imaginary part. + +And then, I will say the +imaginary part has got to be + +zero. +And, then I will see what it's + +like. +That works fine. + +It just takes too much space. +And also, it doesn't teach you + +a few things that I think you +should know. + +So, I'm going to give another. +So, let's say we can answer + +this two ways: +by hack, in other words, + +multiply everything out. +Multiply all out, + +make the imaginary part equal +zero. + +Now, here's a better way, +in my opinion. + +What I'm trying to do is, +this is some complex function, + +u plus iv. +How do I know when a complex + +function is real? +I want this to be real. + +Well, the hack method +corresponds to, + +say, v must be equal to zero. +It's real if v is zero. + +So, expand it out, +and see why v is zero. + +There's a slightly more subtle +method, which is to change i to + +minus i. +And, what? + +And, see if it stays the same +because if I change i to minus i + +and it turns out, +the expression doesn't change, + +then it must have been real, +if the expression doesn't + +change when I change I to minus +I. + +Well, sure. +But you will see it works. + +Now, that's what I'm going to +apply to this. + +If I want this to be real, +I phrase the question, + +I rephrase the question for the +green solution as change, + +so I'm going to change i to +minus i in the green thing, + +and that's going to give me +what conditions, + +and that will give conditions +on the C's. + +Well, let's do it. +In fact, it's easier done than + +talked about. +Let's change, + +take the green solution, +and change. + +Well, I better recopy it, +C1. + +So, these are complex numbers. +That's why I wrote them as + +capital letters because little +letters you tend to interpret as + +real numbers. +So, C1 e to the (a plus b i)t, + +I'll recopy it quickly, +plus C2 e to the (a minus b i). + +Okay, we're going to change i +to negative i. + +Now, here's a complex number. +What happens to it when you + +change i to negative i? +You change it into its-- Class? + +What do we change it to? +Its complex conjugate. + +And, the notation for complex +conjugate is you put a bar over + +it. +So, in other words, + +when I do that, +the C1 changes to C1 bar, + +complex conjugate, +the complex conjugate of C1. + +What happens to this guy? +This guy changes to e to the (a + +minus b i) t. +This changes to the complex + +conjugate of C2 now, +times e to the (a plus b i) t. + +Well, I want these two to be + +the same. +I want the two expressions the + +same. +Why do I want them the same? + +Because, if there's no change, +that will mean that it's real. + +Now, when is that going to +happen? + +That happens if, +well, here is this, + +that. +If C2 should be equal to C1 + +bar, that's only one condition. +There's another condition. + +C2 bar should equal C1. +So, I get two conditions, + +but there's really only one +condition there because if this + +is true, that's true too. +I simply put bars over both + +things, and two bars cancel each +other out. + +If you take the complex +conjugate and do it again, + +you get back where you started. +Change i to minus i, + +and then i to minus i again. +Well, never mind. + +Anyway, these are the same. +This equation doesn't say + +anything that the first one +didn't say already. + +So, this one is redundant. +And, our conclusion is that the + +real solutions to the equation +are, in their entirety, + +I now don't need both C2 and +C1. + +One of them will do, +and since I'm going to write it + +out as a complex number, +I will write it out in terms of + +its coefficient. +So, it's C1. + +Let's just simply write it. +C plus i times d, + +that's the coefficient. +That's what I called C1 before. + +And, that's times e to the (a +plus b i) t. + +There's no reason why I put bi +here and id there, + +in case you're wondering, +sheer caprice. + +And what's the other term? +Now, the other term is + +completely determined. +Its coefficient must be C minus + +i d times e to the +(a minus b i) t. + +In other words, +this thing is perfectly + +general. +Any complex number times that + +first root you use, +exponentiated, + +and the second term can be +described as the complex + +conjugate of the first. +The coefficient is the complex + +conjugate, and this part is the +complex conjugate of that. + +Now, it's in this form, +many engineers write the + +solution this way, +and physicists, + +too, so, scientists and +engineers we will include. + +Write the solution this way. +Write the real solutions this + +way in that complex form. +Well, why do they do something + +so perverse? +You will have to ask them. + +But, in fact, +when we studied Fourier series, + +we will probably have to do +something, have to do that at + +one point. +If you work a lot with complex + +numbers, it turns out to be, +in some ways, + +a more convenient +representation than the one I've + +given you in terms of sines and +cosines. + +Well, from this, +how would I get, + +suppose I insisted, +well, if someone gave it to me + +in that form, +I don't see how I would convert + +it back into sines and cosines. +And, I'd like to show you how + +to do that efficiently, +too, because, + +again, it's one of the +fundamental techniques that I + +think you should know. +And, I didn't get a chance to + +say it when we studied complex +numbers that first lecture. + +It's in the notes, +but it doesn't prove anything + +since I don't think it made you +use it in an example. + +So, the problem is, +now, by way of finishing this + +up, too, to change this to the +old form, I mean the form + +involving sines and cosines. +Now, again, there are two ways + +of doing it. +The hack way is you write it + +all out. +Well, e to the (a plus b i)t + +turns into e to the a t times + +cosine this plus i sine that. +And, the other term does, + +too. +And then you've got stuff out + +front. +And, the thing stretches over + +two boards. +But you group all the terms + +together. +You finally get it. + +By the way, when you do it, +you'll find that the imaginary + +part disappears completely. +It has to because that's the + +way we chose the coefficients. +So, here's the hack method. + +Write it all out: +blah, blah, blah, + +blah, blah, blah, +blah, and nicer. + +Nicer, and teach you something +you're supposed to know. + +Write it this way. +First of all, + +you notice that both terms have +an e to the a t + +factor. +Let's get rid of that right + +away. +I'm pulling it out front + +because that's automatically +real, and therefore, + +isn't going to affect the rest +of the answer at all. + +So, let's pull out that, +and what's left? + +Well, what's left, +you see, involves just the two + +parameters, C and d, +so I'm going to have a C term. + +And, I'm going to have a d +term. + +What multiplies the arbitrary +constant, C? + +Answer: after I remove the e to +the a t, + +what multiplies it is, +e to the b i t plus e to the -- + +e to the b i t. +Let's write it i b t. + +And, the other term is plus e +to the negative i b t. + +See how I got that, + +pulled it out? +And, how about the d? + +What goes with d? +d goes with, + +well, first of all, +there's an I in front that i + +better not forget. +And then, the rest of it is i. + +So, it's i d times, +it's e to the b i t, + +e to the i b t minus, +now, e to the minus i b t. + +So, that's the way the solution + +looks. +It doesn't look a lot better, + +but now you must use the magic +formulas, which, + +I want you to know as well as +you know Euler's formula, + +even better than you know +Euler's formula. + +They're a consequence of +Euler's formula. + +They're Euler's formula read +backwards. + +Euler's formula says you've got +a complex exponential here. + +Here's how to write it in terms +of sines and cosines. + +The backwards thing says you've +got a sine or a cosine. + +Here is the way to write it in +terms of complex exponentials. + +And, remember, +the way to do it is, + +cosine a is equal to e to the i +a t, i a, plus e to the negative + +i a divided by two. + +And, sine of a is almost the +same thing, except you use a + +minus sign. +And, what everybody forgets, + +you have to divide by i. +So, this is a backwards version + +of Euler's formula. +The two of them taken together + +are equivalent to Euler's +formula. + +If I took cosine a, +multiply this through by i, + +and added them up, +on the right-hand side I'd get + +exactly e to the ia. +I'd get Euler's formula, + +in other words. +All right, so, + +what does this come out to be, +finally? + +This particular sum of +exponentials, + +you should always recognize as +real. + +You know it's real because when +you change i to minus i, + +the two terms switch. +And therefore, + +the expression doesn't change. +What is it? + +This part is twice the cosine +of bt. + +What's this part? +This part is 2 i times the sine + +of bt. +And so, what does the whole + +thing come to be? +It is e to the a t times 2C + +cosine bt plus i times, +did I lose possibly a, + +no it's okay, +minus i times i is minus, + +so, minus 2d times the sine of +bt. + +Shall I write that out? + +So, in other words, +it's e to the a t times 2C + +cosine b t minus 2d times the +sine of b t, + +which is, since 2C and negative + +2d are just arbitrary constants, +just as arbitrary as the + +constants of C and d themselves +are. + +This is our old form of writing +the real solution. + +Here's the way using science +and cosines, and there's the way + +that uses complex numbers and +complex functions throughout. + +Notice they both have two +arbitrary constants in them, + +C and d, two arbitrary +constants. + +That, you expect. +But that has two arbitrary + +constants in it, +too, just the real and + +imaginary parts of that complex +coefficient, C plus i d. + +Well, that took half the + +period, and it was a long, +I don't consider it a + +digression because learning +those ways of dealing with + +complex numbers of complex +functions is a fairly important + +goal in this course, +actually. + +But let's get back now to +studying what the oscillations + +actually look like. + +Okay, well, I'd like to save a +little time, but very quickly, + +you don't have to reproduce +this sketch. + +I remember very well from +Friday to Monday, + +but I can't expect you to for a +variety of reasons. + +I mean, I have to think about +this stuff all weekend. + +And you, God forbid. +So, here's the picture, + +and I won't explain anymore +what's in it, + +except there's the mass. +Here is the spring constant, + +the spring with its constant +here. + +Here's the dashpot with its +constant. + +The equation is from Newton's +law: m x double, + +so this will be x, +and here's, let's say, + +the equilibrium point is over +here. + +It looks like m x double prime; +we derived this last time, + +plus c x prime plus k x equals +zero. + +And now, if I put that in +standard form, + +it's going to look like x +double prime plus c over m x + +prime plus k over m times x +equals zero. + +And, finally, + +the standard form in which your +book writes it, + +which is good, +it's a standard form in general + +that is used in the science and +engineering courses. + +One writes this as, +just to be perverse, + +I'm going to change x back to +y, okay, mostly just to be + +eclectic, to get you used to +every conceivable notation. + +So, I'm going to write this to +change x to y. + +So, that's going to become y +double prime. + +And now, this is given a new +name, p, except to get rid of + +lots of twos, +which would really screw up the + +formulas, make it 2p. +You will see why in a minute. + +So, there's 2p times y prime, +and this thing we + +are going to call omega nought +squared. + +Now, that's okay. +It's a positive number. + +Any positive number is the +square of some other positive + +number. +Take a square root. + +You will see why, +it makes the formulas much + +pretty to call it that. +And, it makes also a lot of + +things much easier to remember. +So, all I'm doing is changing + +the names of the constants that +way in order to get better + +formulas, easier to remember +formulas at the end. + +Now, we are interested in the +case where there is + +oscillations. +In other words, + +I only care about the case in +which this has complex roots, + +because if it has just real +roots, that's the over-damped + +case. +I don't get any oscillations. + +By far, oscillations are by far +the more important of the cases, + +I mean, just because, +I don't know, + +I could go on for five minutes +listing things that oscillate, + +oscillations, +you know, like this. + +So they can oscillate by going +to sleep, and waking up, + +and going to sleep, +and waking up. + +They could oscillate. +So, that means we're going to + +get complex roots. +The characteristic equation is + +going to be r squared plus 2p. +So, p is a constant, + +now, right? +Often, p I use in this position + +to indicate a function of t. +But here, p is a constant. + +So, r squared plus 2p times r +plus omega nought squared is + +equal to zero. + +Now, what are its roots? +Well, you see right away the + +first advantage in putting in +the two there. + +When I use the quadratic +formula, it's negative 2p over + +two. +Remember that two in the + +denominator. +So, that's simply negative p. + +And, how about the rest? +Plus or minus the square root + +of, now do it in your head. +4p squared minus 4 omega nought + +squared. +So, there's a four in both of + +those terms. +When I pull it outside becomes + +two. +And, the two in the denominator + +is lurking, waiting to +annihilate it. + +So, that two disappears +entirely, and it will we are + +left with is, +simply, p squared minus omega + +nought squared. + +Now, whenever people write +quadratic equations, + +and arbitrarily put a two in +there, it's because they were + +going to want to solve the +quadratic equation using the + +quadratic formula, +and they don't want all those + +twos and fours to be cluttering +up the formula. + +That's what we are doing here. +Okay, now, the first case is + +where p is equal to zero. +This is going to explain + +immediately why I wrote that +omega nought squared, + +as you probably already know +from physics. + +If p is equal to zero, +the mass isn't zero. + +Otherwise, nothing good would +be happening here. + +It must be that the damping is +zero. + +So, p is equal to zero +corresponds to undamped. + +There is no dashpot. +The oscillations are undamped. + +And, the equation, +then, becomes the solutions, + +then, are, well, +the equation becomes the + +equation of simple harmonic +motion, which, + +I think you already are used to +writing in this form. + +And, the reason you're writing +in this form because you know + +when you do that, +this becomes the circular + +frequency of the oscillations. +The solutions are pure + +oscillations, +and omega nought is + +the circular frequency. +So, right away from the + +equation itself, +if you write it in this form, + +you can read off what the +frequency of the solutions is + +going to be, the circular +frequency of the solutions. + +Now, the solutions themselves, +of course, look like, + +the general solutions look like +y equal, in this particular + +case, the p part is zero. +This is zero. + +It's simply, +so, in this case, + +r is equal to omega nought i +times omega naught plus or + +minus, but as before we don't +bother with the minus sign since + +one of those roots is good +enough. + +And then, the solutions are +simply c1 cosine omega nought t + +plus c2 sine omega nought t. + +That's if you write it out in + +the sign, and if you write it +using the trigonometric + +identity, then the other way of +writing it is a times the cosine + +of omega nought t. + +But now you will have to put it +a phase lag. + +So, you have those two forms of +writing it. + +And, I assume you remember +writing the little triangle, + +which converts one into the +other. + +Okay, so this justifies calling +this omega nought squared + +rather than k over m. + +And now, the question is what +does the damp case look like? + +It requires a somewhat closer +analysis, and it requires a + +certain amount of thinking. +So, let's begin with an epsilon + +bit of thinking. +So, here's my question. + +So, in the damped case, +I want to be sure that I'm + +getting oscillations. +When do I get oscillations if, + +well, we get oscillations if +those roots are really complex, + +and not masquerading. +Now, when are the roots going + +to be really complex? +This has to be, + +the inside has to be negative. +p squared minus omega squared + +must be negative. + +p squared minus omega nought +squared must be less than zero + +so that we are taking a square +root of negative number, + +and we are getting a real +complex roots, + +really complex roots. +In other words, + +now, this says, +remember these numbers are all + +positive, p and omega nought are +positive. + +So, the condition is that p +should be + +less than omega nought. +In other words, + +the damping should be less than +the circular frequency, + +except p is not the damping. +It's half the damping, + +and it's not really the damping +either because it involved the + +m, too. +You'd better just call it p. + +Naturally, I could write the +condition out in terms of c, + +m, and k. +So, your book does that, + +but I'm not going to. +It gives it in terms of c, + +m, and k, which somebody might +want to know. + +But, you know, +we don't have to do everything + +here. +Okay, so let's assume that this + +is true. +What is the solution look like? + +Well, we already experimented +with that last time. + +Remember, there was some +guiding thing which was an + +exponential. +And then, down here, + +we wrote the negative. +So, this was an exponential. + +In fact, it was the +exponential, e to the negative + +pt. +And, in between that, + +the curve tried to do its +thing. + +So, the solution looks sort of +like this. + +It oscillated, +but it had to use that + +exponential function as its +guidelines, as its amplitude, + +in other words. +Now, this is a truly terrible + +picture. +It's so terrible, + +it's unusable. +Okay, this picture never + +happened. +Unfortunately, + +this is not my forte along with +a lot of other things. + +All right, let's try it better. +Here's our better picture. + +Okay, there's the exponential. +At this point, + +I'm supposed to have a lecture +demonstration. + +It's supposed to go up on the +thing, so you can all see it. + +But then, you wouldn't be able +to copy it. + +So, at least we are on even +terms now. + +Okay, how does the actual curve +look? + +Well, I'm just trying to be +fair. + +That's all. +Okay, after a while, + +the point is, +just so we have something to + +aim at, let's say, +okay, here we are going to go, + +we're going to get down through +there. + +Okay then, this is our better +curve. + +Okay, so I am a solution, +a particular solution + +satisfying this initial +condition. + +I started here, +and that was my initial + +velocity. +The slope of that thing gave me + +the initial velocity. +Now, the interesting question + +is, the first, +in some ways, + +the most interesting question, +though there will be others, + +too, is what is this spacing? +Well, that's a period. + +And now, it's half a period. +I clearly ought to think of + +this as the whole period. +So, let's call that, + +I'm going to call this pi over, +so this spacing here, + +from there to there, +I will call that pi divided by + +omega one because this, +from here to here, + +should be, I hope, +twice that, two pi over omega + +one. +Now, my question is, + +so this, for a solution, +it's, in fact, + +is going to cross the axis +regularly in that way. + +My question is, +how does this period, + +so this is going to be its half +period. + +I will put period in quotation +marks because this isn't really + +a periodic function because it's +decreasing all the time in + +amplitude. +But, it's trying to be + +periodic. +At lease it's doing something + +periodically. +It's crossing the axis + +periodically. +So, this is the half period. + +Two pi over omega one +would be its full + +period. +What I want to know is, + +how does that half period, +or how does-- omega one is + +called its pseudo-frequency. +This should really be called + +its pseudo-period. +Everything is pseudo. + +Everything is fake here. +Like, the amoeba has its fake + +foot and stuff like that. +Okay, so this is its + +pseudo-period, +pseudo-frequency, + +pseudo-circular frequency, +but that's hopeless. + +I guess it should be circular +pseudo-frequency, + +or I don't know how you say +that. + +I don't think pseudo is a word +all by itself, + +not even in 18.03, +circular. + +Okay, here's my question. +If the damping goes up, + +this is the damping term. +If the damping goes up, + +what happens to the +pseudo-frequency? + +The frequency is how often the +curve, this is high-frequency, + +and this is low-frequency, +okay? + +So, my question is, +which way does the frequency + +go? +If the damping goes up, + +does the frequency go up or +down? + +Down. +I mean, I'm just asking you to + +answer intuitively on the basis +of your intuition about how this + +thing explains, +how this thing goes, + +and now let's get the formula. +What, in fact, + +is omega one? +What is omega one? + +The answer is when I solve the +equation, so, + +r is now, so in other words, +if omega one is, + +sorry, if I have p, +if p is no longer zero as it + +was in the undamped case, +what is the root, + +now? +Okay, well, the root is minus p + +plus or minus the square root of +p squared, -- + +-- now I'm going to write it +this way, minus, + +to indicate that it's really a +negative number, + +omega squared minus p squared. + +Now, I'm going to call this, +because you see when I change + +this to sines and cosines, +the square root of this number + +is what's going to become that +new frequency. + +I'm going to call that minus p +plus or minus the square root of + +minus omega one squared. +That's going to be the new + +frequency. +And therefore, + +the root is going to change so +that the corresponding solution + +is going to look, +how? + +Well, it's going to be e to the +negative pt times, + +let's write it out first in +terms of sines and cosines, + +times the cosine of, +well, the square root of omega + +one squared is omega one. + +But, there's an i out front +because of the negative sign in + +front of that. +So, it's going to be the cosine + +of omega one t +plus c2 times the sine of omega + +one t. +Or, if you prefer to write it + +out in the other form, +it's e to the minus p t times + +some amplitude, +which depends on c1 and c2, + +times the cosine of omega one t +minus the phase lag. + +Now, when I do that, + +you see omega one is +this pseudo-frequency. + +In other words, +this number omega one is the + +same one that I identified here. +And, why is that? + +Well, because, +what are two successive times? + +Suppose it crosses, +suppose the solution crosses + +the x-axis, sorry, +y-- the t-axis. + +For the first time, +at the point t1, + +what's the next time it crosses +t2? + +Let's jump to the two times +across it. + +So, I want this to be a whole +period, not a half period. + +What's t2? +Well, I say that t2 is nothing + +but 2 pi divided by omega one. + +And, you can see that because +when I plug in, + +if it's zero, +if I have a point where it's + +zero, so, omega one t minus phi, + +when will it be zero for the +first time? + +Well, that will be when the +cosine has to be zero. + +So, it will be some multiple +of, it will be, + +say, pi over two. +Then, the next time this + +happens will be, +if that happens at t1, + +then the next time it happens +will be at t1 plus 2 pi divided + +by omega one. + +That will also be pi over two +plus how much? + +Plus 2 pi, which is the next +time the cosine gets around and + +is doing its thing, +becoming zero as it goes down, + +not as it's coming up again. +In other words, + +this is what you should add to +the first time to get this + +second time that the cosine +becomes zero coming in the + +direction from top to the +bottom. + +So, this is, +in fact, the frequency with + +which it's crossing the axis. +Now, notice, + +I'm running out of boards. +What a disaster! + +In that expression, +take a look at it. + +I want to know what depends on +what. + +So, p, in that, +we got constants. + +We got p. +We got phi. + +We got A. +What else we got? + +Omega one. +What do these things depend + +upon? +You've got to keep it firmly in + +mind. +This depends only on the ODE. + +It's basically the damping. +It depends on c and m. + +Essentially, it's c over 2m + +actually. +How about phi? + +Well, phi, what else depends +only on the ODE? + +Omega one depends +only on the ODE. + +What's the formula for omega +one? + +Omega one squared. + +Where do we have it? +Omega one squared, + +I never wrote the formula for +you. + +So, we have omega nought +squared minus p squared equals + +omega one squared. + +What's the relation between +them? + +That's the Pythagorean theorem. +If this is omega nought, + +then this omega one, +this is p. + +They make a little, +right triangle in other words. + +The omega one depends on the +spring. + +So, it's equal to, +well, it's equal to that thing. + +So, it depends on the damping. +It depends upon the damping, + +and it depends on the spring +constant. + +How about the phi and the A? +What do they depend on? + +They depend upon the initial +conditions. + +So, the mass of constants, +they have different functions. + +What's making this complicated +is that our answer needs four + +parameters to describe it. +This tells you how fast it's + +coming down. +This tells you the phase lag. + +This amplitude modifies, +it tells you whether the + +exponential curve starts going, +is like that or goes like this. + +And, finally, +the omega one is this + +pseudo-frequency, +which tells you how it's + +bobbing up and down. \ No newline at end of file diff --git a/YQwDoQYAoK0.txt b/YQwDoQYAoK0.txt new file mode 100644 index 0000000000000000000000000000000000000000..5c6154074565356d61be490a9db791385b9ac5a0 --- /dev/null +++ b/YQwDoQYAoK0.txt @@ -0,0 +1,12019 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu hello uh today we're going + + align:start position:0% +ocw.mit.edu hello uh today we're going + + + align:start position:0% +ocw.mit.edu hello uh today we're going +to talk about uh the safety analysis + + align:start position:0% +to talk about uh the safety analysis + + + align:start position:0% +to talk about uh the safety analysis +report and we're going to do an example + + align:start position:0% +report and we're going to do an example + + + align:start position:0% +report and we're going to do an example +on the loss of coolant accident + + align:start position:0% +on the loss of coolant accident + + + align:start position:0% +on the loss of coolant accident +what I'm going to go over is what is in + + align:start position:0% +what I'm going to go over is what is in + + + align:start position:0% +what I'm going to go over is what is in +fact the contents of a safety analysis + + align:start position:0% +fact the contents of a safety analysis + + + align:start position:0% +fact the contents of a safety analysis +report most of you know it is the + + align:start position:0% +report most of you know it is the + + + align:start position:0% +report most of you know it is the +document that is filed with the nuclear + + align:start position:0% +document that is filed with the nuclear + + + align:start position:0% +document that is filed with the nuclear +Regulatory Commission that provides a + + align:start position:0% +Regulatory Commission that provides a + + + align:start position:0% +Regulatory Commission that provides a +technical basis for the site the design + + align:start position:0% +technical basis for the site the design + + + align:start position:0% +technical basis for the site the design +of the plant the subsequent safety + + align:start position:0% +of the plant the subsequent safety + + + align:start position:0% +of the plant the subsequent safety +analysis that's done to show that it + + align:start position:0% +analysis that's done to show that it + + + align:start position:0% +analysis that's done to show that it +meets all regulatory criteria one of the + + align:start position:0% +meets all regulatory criteria one of the + + + align:start position:0% +meets all regulatory criteria one of the +key and important chapters is this + + align:start position:0% +key and important chapters is this + + + align:start position:0% +key and important chapters is this +chapter 15 in the safety analysis report + + align:start position:0% +chapter 15 in the safety analysis report + + + align:start position:0% +chapter 15 in the safety analysis report +that goes over all the transients and + + align:start position:0% +that goes over all the transients and + + + align:start position:0% +that goes over all the transients and +accidents that Happ have to be analyzed + + align:start position:0% +accidents that Happ have to be analyzed + + + align:start position:0% +accidents that Happ have to be analyzed +as part of your design basis and I'm + + align:start position:0% +as part of your design basis and I'm + + + align:start position:0% +as part of your design basis and I'm +going to go through one particular + + align:start position:0% +going to go through one particular + + + align:start position:0% +going to go through one particular +example which is a loss of coolon + + align:start position:0% +example which is a loss of coolon + + + align:start position:0% +example which is a loss of coolon +accident so you can get a feel for uh + + align:start position:0% +accident so you can get a feel for uh + + + align:start position:0% +accident so you can get a feel for uh +what types of work are in fact done to + + align:start position:0% +what types of work are in fact done to + + + align:start position:0% +what types of work are in fact done to +be able to demonstrate compliance to the + + align:start position:0% +be able to demonstrate compliance to the + + + align:start position:0% +be able to demonstrate compliance to the +regulations and we'll review some of + + align:start position:0% +regulations and we'll review some of + + + align:start position:0% +regulations and we'll review some of +those regulations as + + align:start position:0% +those regulations as + + + align:start position:0% +those regulations as +well so why are we worried about nuclear + + align:start position:0% +well so why are we worried about nuclear + + + align:start position:0% +well so why are we worried about nuclear +power plants in the sense of um public + + align:start position:0% +power plants in the sense of um public + + + align:start position:0% +power plants in the sense of um public +health and safety well we're worried + + align:start position:0% +health and safety well we're worried + + + align:start position:0% +health and safety well we're worried +about it because during the during the + + align:start position:0% +about it because during the during the + + + align:start position:0% +about it because during the during the +operation of a nuclear reactor and we + + align:start position:0% +operation of a nuclear reactor and we + + + align:start position:0% +operation of a nuclear reactor and we +now know what fision products are is we + + align:start position:0% +now know what fision products are is we + + + align:start position:0% +now know what fision products are is we +produce certain Isotopes iodine + + align:start position:0% +produce certain Isotopes iodine + + + align:start position:0% +produce certain Isotopes iodine +strontium rium and rium and cesium and + + align:start position:0% +strontium rium and rium and cesium and + + + align:start position:0% +strontium rium and rium and cesium and +what we end up producing here with these + + align:start position:0% +what we end up producing here with these + + + align:start position:0% +what we end up producing here with these +Isotopes are various materials that are + + align:start position:0% +Isotopes are various materials that are + + + align:start position:0% +Isotopes are various materials that are +either gaseous or volatile or highly + + align:start position:0% +either gaseous or volatile or highly + + + align:start position:0% +either gaseous or volatile or highly +volatile that might if an accident + + align:start position:0% +volatile that might if an accident + + + align:start position:0% +volatile that might if an accident +occurs in the reactor uh become released + + align:start position:0% +occurs in the reactor uh become released + + + align:start position:0% +occurs in the reactor uh become released +and cre a certain health hazard to the + + align:start position:0% +and cre a certain health hazard to the + + + align:start position:0% +and cre a certain health hazard to the +public and you can see iodine has an + + align:start position:0% +public and you can see iodine has an + + + align:start position:0% +public and you can see iodine has an +external whole body iodine does cause + + align:start position:0% +external whole body iodine does cause + + + align:start position:0% +external whole body iodine does cause +thyroid cancer and it is highly toxic + + align:start position:0% +thyroid cancer and it is highly toxic + + + align:start position:0% +thyroid cancer and it is highly toxic +strontium as you I'm sure well remember + + align:start position:0% +strontium as you I'm sure well remember + + + align:start position:0% +strontium as you I'm sure well remember +it goes into your bones and your lungs + + align:start position:0% +it goes into your bones and your lungs + + + align:start position:0% +it goes into your bones and your lungs +uh ruthenium I think is the proper + + align:start position:0% +uh ruthenium I think is the proper + + + align:start position:0% +uh ruthenium I think is the proper +pronunciation it goes to your kidneys + + align:start position:0% +pronunciation it goes to your kidneys + + + align:start position:0% +pronunciation it goes to your kidneys +and cesium is an internal Hazard to the + + align:start position:0% +and cesium is an internal Hazard to the + + + align:start position:0% +and cesium is an internal Hazard to the +whole body so we're going to try to do + + align:start position:0% +whole body so we're going to try to do + + + align:start position:0% +whole body so we're going to try to do +an aent analysis to show how we can + + align:start position:0% +an aent analysis to show how we can + + + align:start position:0% +an aent analysis to show how we can +confine these materials these fion + + align:start position:0% +confine these materials these fion + + + align:start position:0% +confine these materials these fion +products if you will that have varying + + align:start position:0% +products if you will that have varying + + + align:start position:0% +products if you will that have varying +Half Lives to keep them from getting out + + align:start position:0% +Half Lives to keep them from getting out + + + align:start position:0% +Half Lives to keep them from getting out +into the environment or if they get out + + align:start position:0% +into the environment or if they get out + + + align:start position:0% +into the environment or if they get out +they they're only released in very small + + align:start position:0% +they they're only released in very small + + + align:start position:0% +they they're only released in very small +quantities the other thing that we worry + + align:start position:0% +quantities the other thing that we worry + + + align:start position:0% +quantities the other thing that we worry +about in nuclear power plants is once + + align:start position:0% +about in nuclear power plants is once + + + align:start position:0% +about in nuclear power plants is once +you shut down a reactor as we already + + align:start position:0% +you shut down a reactor as we already + + + align:start position:0% +you shut down a reactor as we already +know the power doesn't immediately go to + + align:start position:0% +know the power doesn't immediately go to + + + align:start position:0% +know the power doesn't immediately go to +zero because of the Decay power of the + + align:start position:0% +zero because of the Decay power of the + + + align:start position:0% +zero because of the Decay power of the +reactor we have a certain amount of time + + align:start position:0% +reactor we have a certain amount of time + + + align:start position:0% +reactor we have a certain amount of time +and this is in uh seconds here + + align:start position:0% +and this is in uh seconds here + + + align:start position:0% +and this is in uh seconds here +that the reactor is still producing heat + + align:start position:0% +that the reactor is still producing heat + + + align:start position:0% +that the reactor is still producing heat +from the standpoint of the Decay + + align:start position:0% +from the standpoint of the Decay + + + align:start position:0% +from the standpoint of the Decay +products and you can see within like say + + align:start position:0% +products and you can see within like say + + + align:start position:0% +products and you can see within like say +one hour We're producing roughly 07 or + + align:start position:0% +one hour We're producing roughly 07 or + + + align:start position:0% +one hour We're producing roughly 07 or +8% of the total heat that that the + + align:start position:0% +8% of the total heat that that the + + + align:start position:0% +8% of the total heat that that the +reactor has has been able to capable of + + align:start position:0% +reactor has has been able to capable of + + + align:start position:0% +reactor has has been able to capable of +generating and that is a substantial + + align:start position:0% +generating and that is a substantial + + + align:start position:0% +generating and that is a substantial +amount of heat when you're talking about + + align:start position:0% +amount of heat when you're talking about + + + align:start position:0% +amount of heat when you're talking about +say a 3,000 megawatt thermal reactor and + + align:start position:0% +say a 3,000 megawatt thermal reactor and + + + align:start position:0% +say a 3,000 megawatt thermal reactor and +we're talking about here it shows a weak + + align:start position:0% +we're talking about here it shows a weak + + + align:start position:0% +we're talking about here it shows a weak +you can see it's uh uh about 1 100 a + + align:start position:0% +you can see it's uh uh about 1 100 a + + + align:start position:0% +you can see it's uh uh about 1 100 a +little bit lower and then in a year it's + + align:start position:0% +little bit lower and then in a year it's + + + align:start position:0% +little bit lower and then in a year it's +really quite low but this is the time + + align:start position:0% +really quite low but this is the time + + + align:start position:0% +really quite low but this is the time +period of concern for us because the + + align:start position:0% +period of concern for us because the + + + align:start position:0% +period of concern for us because the +reactor even if it's shut down still + + align:start position:0% +reactor even if it's shut down still + + + align:start position:0% +reactor even if it's shut down still +needs to be cooled and that's the whole + + align:start position:0% +needs to be cooled and that's the whole + + + align:start position:0% +needs to be cooled and that's the whole +purpose of all these Safety Systems + + align:start position:0% +purpose of all these Safety Systems + + + align:start position:0% +purpose of all these Safety Systems +there is no question that that we can + + align:start position:0% +there is no question that that we can + + + align:start position:0% +there is no question that that we can +shut down these reactors but we cannot + + align:start position:0% +shut down these reactors but we cannot + + + align:start position:0% +shut down these reactors but we cannot +shut down the dek process because that's + + align:start position:0% +shut down the dek process because that's + + + align:start position:0% +shut down the dek process because that's +a natural process of radioactive + + align:start position:0% +a natural process of radioactive + + + align:start position:0% +a natural process of radioactive +DC we have certain things that we worry + + align:start position:0% +DC we have certain things that we worry + + + align:start position:0% +DC we have certain things that we worry +about in reactor and we call those + + align:start position:0% +about in reactor and we call those + + + align:start position:0% +about in reactor and we call those +critical safety functions which need to + + align:start position:0% +critical safety functions which need to + + + align:start position:0% +critical safety functions which need to +be in general + + align:start position:0% +be in general + + + align:start position:0% +be in general +maintained and the critical safety + + align:start position:0% +maintained and the critical safety + + + align:start position:0% +maintained and the critical safety +functions as listed here and people + + align:start position:0% +functions as listed here and people + + + align:start position:0% +functions as listed here and people +might have somewhat different + + align:start position:0% +might have somewhat different + + + align:start position:0% +might have somewhat different +definitions but we want to keep the + + align:start position:0% +definitions but we want to keep the + + + align:start position:0% +definitions but we want to keep the +fision products within the fuel as one + + align:start position:0% +fision products within the fuel as one + + + align:start position:0% +fision products within the fuel as one +safety function and part of that means + + align:start position:0% +safety function and part of that means + + + align:start position:0% +safety function and part of that means +we need to control the reactor power and + + align:start position:0% +we need to control the reactor power and + + + align:start position:0% +we need to control the reactor power and +we need to be able to shut down the + + align:start position:0% +we need to be able to shut down the + + + align:start position:0% +we need to be able to shut down the +reactor reliably in other words if you + + align:start position:0% +reactor reliably in other words if you + + + align:start position:0% +reactor reliably in other words if you +can't shut down the reactor there's no + + align:start position:0% +can't shut down the reactor there's no + + + align:start position:0% +can't shut down the reactor there's no +real means by which you cannot + + align:start position:0% +real means by which you cannot + + + align:start position:0% +real means by which you cannot +ultimately avoid an accident should + + align:start position:0% +ultimately avoid an accident should + + + align:start position:0% +ultimately avoid an accident should +something break we also need to cool the + + align:start position:0% +something break we also need to cool the + + + align:start position:0% +something break we also need to cool the +reactor and and the spend fuel in the + + align:start position:0% +reactor and and the spend fuel in the + + + align:start position:0% +reactor and and the spend fuel in the +spend fuel pool but that basically means + + align:start position:0% +spend fuel pool but that basically means + + + align:start position:0% +spend fuel pool but that basically means +we want to maintain the cooling + + align:start position:0% +we want to maintain the cooling + + + align:start position:0% +we want to maintain the cooling +inventory which is means water in the + + align:start position:0% +inventory which is means water in the + + + align:start position:0% +inventory which is means water in the +primary system we want to maintain flow + + align:start position:0% +primary system we want to maintain flow + + + align:start position:0% +primary system we want to maintain flow +which means circulation of water and we + + align:start position:0% +which means circulation of water and we + + + align:start position:0% +which means circulation of water and we +want to maintain the capability to + + align:start position:0% +want to maintain the capability to + + + align:start position:0% +want to maintain the capability to +remove heat from the reactor in terms of + + align:start position:0% +remove heat from the reactor in terms of + + + align:start position:0% +remove heat from the reactor in terms of +an ultimate heat sink whether that be a + + align:start position:0% +an ultimate heat sink whether that be a + + + align:start position:0% +an ultimate heat sink whether that be a +a steam or some heat exchanger that is + + align:start position:0% +a steam or some heat exchanger that is + + + align:start position:0% +a steam or some heat exchanger that is +ultimately tied to some external + + align:start position:0% +ultimately tied to some external + + + align:start position:0% +ultimately tied to some external +Source obviously we want to keep the + + align:start position:0% +Source obviously we want to keep the + + + align:start position:0% +Source obviously we want to keep the +radioactive material out of our + + align:start position:0% +radioactive material out of our + + + align:start position:0% +radioactive material out of our +environment or our biosphere which + + align:start position:0% +environment or our biosphere which + + + align:start position:0% +environment or our biosphere which +basically gets into the maintenance of + + align:start position:0% +basically gets into the maintenance of + + + align:start position:0% +basically gets into the maintenance of +containment integrity and in order to do + + align:start position:0% +containment integrity and in order to do + + + align:start position:0% +containment integrity and in order to do +that we need to make sure that we don't + + align:start position:0% +that we need to make sure that we don't + + + align:start position:0% +that we need to make sure that we don't +over pressurize the containment we don't + + align:start position:0% +over pressurize the containment we don't + + + align:start position:0% +over pressurize the containment we don't +overheat the containment which might + + align:start position:0% +overheat the containment which might + + + align:start position:0% +overheat the containment which might +cause it to fracture or in fact over + + align:start position:0% +cause it to fracture or in fact over + + + align:start position:0% +cause it to fracture or in fact over +pressurize and we we don't want to have + + align:start position:0% +pressurize and we we don't want to have + + + align:start position:0% +pressurize and we we don't want to have +the plant designed such that even though + + align:start position:0% +the plant designed such that even though + + + align:start position:0% +the plant designed such that even though +the containment may be robust and sound + + align:start position:0% +the containment may be robust and sound + + + align:start position:0% +the containment may be robust and sound +there's a mechanism by which the + + align:start position:0% +there's a mechanism by which the + + + align:start position:0% +there's a mechanism by which the +radioactive materials can in fact pass + + align:start position:0% +radioactive materials can in fact pass + + + align:start position:0% +radioactive materials can in fact pass +through the containment inadvertently + + align:start position:0% +through the containment inadvertently + + + align:start position:0% +through the containment inadvertently +right to the outside this is called + + align:start position:0% +right to the outside this is called + + + align:start position:0% +right to the outside this is called +containment + + align:start position:0% +containment + + + align:start position:0% +containment +bypass and the other thing that happens + + align:start position:0% +bypass and the other thing that happens + + + align:start position:0% +bypass and the other thing that happens +in terms of keeping material out of the + + align:start position:0% +in terms of keeping material out of the + + + align:start position:0% +in terms of keeping material out of the +biosphere is we want to make sure that + + align:start position:0% +biosphere is we want to make sure that + + + align:start position:0% +biosphere is we want to make sure that +whatever material is released from the + + align:start position:0% +whatever material is released from the + + + align:start position:0% +whatever material is released from the +core is sort of captured in in the + + align:start position:0% +core is sort of captured in in the + + + align:start position:0% +core is sort of captured in in the +containment itself so we're looking at + + align:start position:0% +containment itself so we're looking at + + + align:start position:0% +containment itself so we're looking at +what kinds of chemicals might be put + + align:start position:0% +what kinds of chemicals might be put + + + align:start position:0% +what kinds of chemicals might be put +into the water that might be ultimately + + align:start position:0% +into the water that might be ultimately + + + align:start position:0% +into the water that might be ultimately +used to quench the the steam that might + + align:start position:0% +used to quench the the steam that might + + + align:start position:0% +used to quench the the steam that might +be formed as a result of a main coolant + + align:start position:0% +be formed as a result of a main coolant + + + align:start position:0% +be formed as a result of a main coolant +pipe break where we could scrub the uh + + align:start position:0% +pipe break where we could scrub the uh + + + align:start position:0% +pipe break where we could scrub the uh +scrub the steam such that there's + + align:start position:0% +scrub the steam such that there's + + + align:start position:0% +scrub the steam such that there's +chemical capture and hopefully + + align:start position:0% +chemical capture and hopefully + + + align:start position:0% +chemical capture and hopefully +deposition within the building rather + + align:start position:0% +deposition within the building rather + + + align:start position:0% +deposition within the building rather +than be released outside into the + + align:start position:0% +than be released outside into the + + + align:start position:0% +than be released outside into the +environment as a gas so the last basic + + align:start position:0% +environment as a gas so the last basic + + + align:start position:0% +environment as a gas so the last basic +function is making sure that our + + align:start position:0% +function is making sure that our + + + align:start position:0% +function is making sure that our +Personnel are protected from the + + align:start position:0% +Personnel are protected from the + + + align:start position:0% +Personnel are protected from the +radiation either during a normal + + align:start position:0% +radiation either during a normal + + + align:start position:0% +radiation either during a normal +operation or during accidents so if you + + align:start position:0% +operation or during accidents so if you + + + align:start position:0% +operation or during accidents so if you +look at some of these major critical + + align:start position:0% +look at some of these major critical + + + align:start position:0% +look at some of these major critical +safy functions if if you can design a + + align:start position:0% +safy functions if if you can design a + + + align:start position:0% +safy functions if if you can design a +safety system that can address these + + align:start position:0% +safety system that can address these + + + align:start position:0% +safety system that can address these +questions you have been successful in + + align:start position:0% +questions you have been successful in + + + align:start position:0% +questions you have been successful in +terms of meeting not only the criteria + + align:start position:0% +terms of meeting not only the criteria + + + align:start position:0% +terms of meeting not only the criteria +but preventing uh essentially + + align:start position:0% +but preventing uh essentially + + + align:start position:0% +but preventing uh essentially +uncontrolled release of radiation from + + align:start position:0% +uncontrolled release of radiation from + + + align:start position:0% +uncontrolled release of radiation from +the reactor plan now this is a graphic + + align:start position:0% +the reactor plan now this is a graphic + + + align:start position:0% +the reactor plan now this is a graphic +that that's symbol symbolizes some of + + align:start position:0% +that that's symbol symbolizes some of + + + align:start position:0% +that that's symbol symbolizes some of +our emergency safety functions and if we + + align:start position:0% +our emergency safety functions and if we + + + align:start position:0% +our emergency safety functions and if we +start with the Reactor Core one of the + + align:start position:0% +start with the Reactor Core one of the + + + align:start position:0% +start with the Reactor Core one of the +things obviously that can happen is we + + align:start position:0% +things obviously that can happen is we + + + align:start position:0% +things obviously that can happen is we +could have some kind of a break into + + align:start position:0% +could have some kind of a break into + + + align:start position:0% +could have some kind of a break into +from the reactor primary system system + + align:start position:0% +from the reactor primary system system + + + align:start position:0% +from the reactor primary system system +where water is escaped into the + + align:start position:0% +where water is escaped into the + + + align:start position:0% +where water is escaped into the +containment we can control reactivity by + + align:start position:0% +containment we can control reactivity by + + + align:start position:0% +containment we can control reactivity by +shutting the reactor down quite quickly + + align:start position:0% +shutting the reactor down quite quickly + + + align:start position:0% +shutting the reactor down quite quickly +using either control rods or perhaps + + align:start position:0% +using either control rods or perhaps + + + align:start position:0% +using either control rods or perhaps +some soluble Boron that will shut the + + align:start position:0% +some soluble Boron that will shut the + + + align:start position:0% +some soluble Boron that will shut the +reactor down and that's one of the + + align:start position:0% +reactor down and that's one of the + + + align:start position:0% +reactor down and that's one of the +critical safety functions but once + + align:start position:0% +critical safety functions but once + + + align:start position:0% +critical safety functions but once +we inject this hot water into the + + align:start position:0% +we inject this hot water into the + + + align:start position:0% +we inject this hot water into the +containment we want to take and use some + + align:start position:0% +containment we want to take and use some + + + align:start position:0% +containment we want to take and use some +filters some sprays that would remove + + align:start position:0% +filters some sprays that would remove + + + align:start position:0% +filters some sprays that would remove +some of this reactivity radio activity + + align:start position:0% +some of this reactivity radio activity + + + align:start position:0% +some of this reactivity radio activity +from the containment atmosphere such + + align:start position:0% +from the containment atmosphere such + + + align:start position:0% +from the containment atmosphere such +that if there is a vent the material is + + align:start position:0% +that if there is a vent the material is + + + align:start position:0% +that if there is a vent the material is +more or less plated out or condensed on + + align:start position:0% +more or less plated out or condensed on + + + align:start position:0% +more or less plated out or condensed on +the walls in the containment or or on + + align:start position:0% +the walls in the containment or or on + + + align:start position:0% +the walls in the containment or or on +the piping of of the reactor building or + + align:start position:0% +the piping of of the reactor building or + + + align:start position:0% +the piping of of the reactor building or +systems now obviously there's a + + align:start position:0% +systems now obviously there's a + + + align:start position:0% +systems now obviously there's a +tremendous amount of heat released into + + align:start position:0% +tremendous amount of heat released into + + + align:start position:0% +tremendous amount of heat released into +this containment we need to find a + + align:start position:0% +this containment we need to find a + + + align:start position:0% +this containment we need to find a +mechanism to keep the heat uh from + + align:start position:0% +mechanism to keep the heat uh from + + + align:start position:0% +mechanism to keep the heat uh from +building up in here that might over + + align:start position:0% +building up in here that might over + + + align:start position:0% +building up in here that might over +pressurize the containment and we would + + align:start position:0% +pressurize the containment and we would + + + align:start position:0% +pressurize the containment and we would +have some sort of a heat exchanger that + + align:start position:0% +have some sort of a heat exchanger that + + + align:start position:0% +have some sort of a heat exchanger that +will go into the contain to remove the + + align:start position:0% +will go into the contain to remove the + + + align:start position:0% +will go into the contain to remove the +heat that might be generated that would + + align:start position:0% +heat that might be generated that would + + + align:start position:0% +heat that might be generated that would +certainly be generated either from Decay + + align:start position:0% +certainly be generated either from Decay + + + align:start position:0% +certainly be generated either from Decay +heat or for the energy stored in the + + align:start position:0% +heat or for the energy stored in the + + + align:start position:0% +heat or for the energy stored in the +reactor uh cooling system now this + + align:start position:0% +reactor uh cooling system now this + + + align:start position:0% +reactor uh cooling system now this +containment obviously must be robust and + + align:start position:0% +containment obviously must be robust and + + + align:start position:0% +containment obviously must be robust and +must be designed such that whatever + + align:start position:0% +must be designed such that whatever + + + align:start position:0% +must be designed such that whatever +internal pressure is released from the + + align:start position:0% +internal pressure is released from the + + + align:start position:0% +internal pressure is released from the +primary system it can be managed in in + + align:start position:0% +primary system it can be managed in in + + + align:start position:0% +primary system it can be managed in in +the uh and by the containment which is + + align:start position:0% +the uh and by the containment which is + + + align:start position:0% +the uh and by the containment which is +it must be sufficiently sized to handle + + align:start position:0% +it must be sufficiently sized to handle + + + align:start position:0% +it must be sufficiently sized to handle +all the blow down Lo which is the + + align:start position:0% +all the blow down Lo which is the + + + align:start position:0% +all the blow down Lo which is the +pressure loads that might be released + + align:start position:0% +pressure loads that might be released + + + align:start position:0% +pressure loads that might be released +from from the accident situation and the + + align:start position:0% +from from the accident situation and the + + + align:start position:0% +from from the accident situation and the +purpose here is to prevent radioactive + + align:start position:0% +purpose here is to prevent radioactive + + + align:start position:0% +purpose here is to prevent radioactive +dispersal of this uh whatever + + align:start position:0% +dispersal of this uh whatever + + + align:start position:0% +dispersal of this uh whatever +radioactivity is released into the + + align:start position:0% +radioactivity is released into the + + + align:start position:0% +radioactivity is released into the +environment so we have several functions + + align:start position:0% +environment so we have several functions + + + align:start position:0% +environment so we have several functions +here we have removal of of contaminants + + align:start position:0% +here we have removal of of contaminants + + + align:start position:0% +here we have removal of of contaminants +from the air in the containment we have + + align:start position:0% +from the air in the containment we have + + + align:start position:0% +from the air in the containment we have +Neutron absorbers that go in to shut the + + align:start position:0% +Neutron absorbers that go in to shut the + + + align:start position:0% +Neutron absorbers that go in to shut the +reactor down and we also have a heat + + align:start position:0% +reactor down and we also have a heat + + + align:start position:0% +reactor down and we also have a heat +exchanger by which we can remove the + + align:start position:0% +exchanger by which we can remove the + + + align:start position:0% +exchanger by which we can remove the +heat uh from the uh from the containment + + align:start position:0% +heat uh from the uh from the containment + + + align:start position:0% +heat uh from the uh from the containment +and the one other very important + + align:start position:0% +and the one other very important + + + align:start position:0% +and the one other very important +function is to manage the Decay heat and + + align:start position:0% +function is to manage the Decay heat and + + + align:start position:0% +function is to manage the Decay heat and +that's core cooling which is emergency + + align:start position:0% +that's core cooling which is emergency + + + align:start position:0% +that's core cooling which is emergency +core cooling water that once this thing + + align:start position:0% +core cooling water that once this thing + + + align:start position:0% +core cooling water that once this thing +breaks or is vented the water is needed + + align:start position:0% +breaks or is vented the water is needed + + + align:start position:0% +breaks or is vented the water is needed +to be inserted into the reactor core to + + align:start position:0% +to be inserted into the reactor core to + + + align:start position:0% +to be inserted into the reactor core to +continuously cool The Vessel even though + + align:start position:0% +continuously cool The Vessel even though + + + align:start position:0% +continuously cool The Vessel even though +there's a break this water has to be + + align:start position:0% +there's a break this water has to be + + + align:start position:0% +there's a break this water has to be +recirculated such that that core is if + + align:start position:0% +recirculated such that that core is if + + + align:start position:0% +recirculated such that that core is if +not always covered substantially covered + + align:start position:0% +not always covered substantially covered + + + align:start position:0% +not always covered substantially covered +to prevent fuel damage or fuel failure + + align:start position:0% +to prevent fuel damage or fuel failure + + + align:start position:0% +to prevent fuel damage or fuel failure +what what I'm going to go over now is + + align:start position:0% +what what I'm going to go over now is + + + align:start position:0% +what what I'm going to go over now is +what um each one of these systems so + + align:start position:0% +what um each one of these systems so + + + align:start position:0% +what um each one of these systems so +that we can build it up to this graphic + + align:start position:0% +that we can build it up to this graphic + + + align:start position:0% +that we can build it up to this graphic +that I just showed you which integrated + + align:start position:0% +that I just showed you which integrated + + + align:start position:0% +that I just showed you which integrated +them all now the first system that I + + align:start position:0% +them all now the first system that I + + + align:start position:0% +them all now the first system that I +want to talk about is the emergency core + + align:start position:0% +want to talk about is the emergency core + + + align:start position:0% +want to talk about is the emergency core +cooling system which is emergency + + align:start position:0% +cooling system which is emergency + + + align:start position:0% +cooling system which is emergency +cooling injection and we start with the + + align:start position:0% +cooling injection and we start with the + + + align:start position:0% +cooling injection and we start with the +refueling water storage tank which + + align:start position:0% +refueling water storage tank which + + + align:start position:0% +refueling water storage tank which +contains borated water obviously used to + + align:start position:0% +contains borated water obviously used to + + + align:start position:0% +contains borated water obviously used to +shut down the reactor as well and that + + align:start position:0% +shut down the reactor as well and that + + + align:start position:0% +shut down the reactor as well and that +is pumped upon an event that would lose + + align:start position:0% +is pumped upon an event that would lose + + + align:start position:0% +is pumped upon an event that would lose +cool cooling from the primary system + + align:start position:0% +cool cooling from the primary system + + + align:start position:0% +cool cooling from the primary system +namely the pressure drops at a certain + + align:start position:0% +namely the pressure drops at a certain + + + align:start position:0% +namely the pressure drops at a certain +level this system is used to pump water + + align:start position:0% +level this system is used to pump water + + + align:start position:0% +level this system is used to pump water +into the core low pressure safety + + align:start position:0% +into the core low pressure safety + + + align:start position:0% +into the core low pressure safety +injection and high pressure safety + + align:start position:0% +injection and high pressure safety + + + align:start position:0% +injection and high pressure safety +injection and we also have what is + + align:start position:0% +injection and we also have what is + + + align:start position:0% +injection and we also have what is +called an accumulator now this + + align:start position:0% +called an accumulator now this + + + align:start position:0% +called an accumulator now this +accumulator is automatically actuated + + align:start position:0% +accumulator is automatically actuated + + + align:start position:0% +accumulator is automatically actuated +because it is essentially a pressurized + + align:start position:0% +because it is essentially a pressurized + + + align:start position:0% +because it is essentially a pressurized +tank of water that when the pressure is + + align:start position:0% +tank of water that when the pressure is + + + align:start position:0% +tank of water that when the pressure is +reduced to a certain level automatically + + align:start position:0% +reduced to a certain level automatically + + + align:start position:0% +reduced to a certain level automatically +injects water into the core now this is + + align:start position:0% +injects water into the core now this is + + + align:start position:0% +injects water into the core now this is +before or any of these pumping systems + + align:start position:0% +before or any of these pumping systems + + + align:start position:0% +before or any of these pumping systems +will be + + align:start position:0% +will be + + + align:start position:0% +will be +actuated because it takes a certain + + align:start position:0% +actuated because it takes a certain + + + align:start position:0% +actuated because it takes a certain +amount of time for the pumps to start + + align:start position:0% +amount of time for the pumps to start + + + align:start position:0% +amount of time for the pumps to start +the power be Supply but these pumps are + + align:start position:0% +the power be Supply but these pumps are + + + align:start position:0% +the power be Supply but these pumps are +as as I mentioned low pressure and high + + align:start position:0% +as as I mentioned low pressure and high + + + align:start position:0% +as as I mentioned low pressure and high +pressure high pressure is used for + + align:start position:0% +pressure high pressure is used for + + + align:start position:0% +pressure high pressure is used for +relatively small brakes low pressure is + + align:start position:0% +relatively small brakes low pressure is + + + align:start position:0% +relatively small brakes low pressure is +used for relatively large brakes but + + align:start position:0% +used for relatively large brakes but + + + align:start position:0% +used for relatively large brakes but +both can be used to flood the core in + + align:start position:0% +both can be used to flood the core in + + + align:start position:0% +both can be used to flood the core in +the event of a major pipe Brak and the + + align:start position:0% +the event of a major pipe Brak and the + + + align:start position:0% +the event of a major pipe Brak and the +accumulator is a passive system that + + align:start position:0% +accumulator is a passive system that + + + align:start position:0% +accumulator is a passive system that +just operates automatically based on a + + align:start position:0% +just operates automatically based on a + + + align:start position:0% +just operates automatically based on a +loss of pressure significant loss of + + align:start position:0% +loss of pressure significant loss of + + + align:start position:0% +loss of pressure significant loss of +pressure in the primary + + align:start position:0% +pressure in the primary + + + align:start position:0% +pressure in the primary +system now we have the recirculation + + align:start position:0% +system now we have the recirculation + + + align:start position:0% +system now we have the recirculation +system obviously water is being removed + + align:start position:0% +system obviously water is being removed + + + align:start position:0% +system obviously water is being removed +from the primary system flooding into + + align:start position:0% +from the primary system flooding into + + + align:start position:0% +from the primary system flooding into +the containment and entering into the + + align:start position:0% +the containment and entering into the + + + align:start position:0% +the containment and entering into the +containment sump which is in the + + align:start position:0% +containment sump which is in the + + + align:start position:0% +containment sump which is in the +basement where all the water essentially + + align:start position:0% +basement where all the water essentially + + + align:start position:0% +basement where all the water essentially +ends up now if we just kept adding water + + align:start position:0% +ends up now if we just kept adding water + + + align:start position:0% +ends up now if we just kept adding water +the reactor would fill up and obviously + + align:start position:0% +the reactor would fill up and obviously + + + align:start position:0% +the reactor would fill up and obviously +not not necessarily cooled I mean the + + align:start position:0% +not not necessarily cooled I mean the + + + align:start position:0% +not not necessarily cooled I mean the +containment would be filled up so what + + align:start position:0% +containment would be filled up so what + + + align:start position:0% +containment would be filled up so what +we do is to keep water in the core + + align:start position:0% +we do is to keep water in the core + + + align:start position:0% +we do is to keep water in the core +itself not just in the containment we + + align:start position:0% +itself not just in the containment we + + + align:start position:0% +itself not just in the containment we +pump water from this sump through a uh + + align:start position:0% +pump water from this sump through a uh + + + align:start position:0% +pump water from this sump through a uh +recirculation system both on a high and + + align:start position:0% +recirculation system both on a high and + + + align:start position:0% +recirculation system both on a high and +low pressure that would inject the water + + align:start position:0% +low pressure that would inject the water + + + align:start position:0% +low pressure that would inject the water +back into the core so we have a + + align:start position:0% +back into the core so we have a + + + align:start position:0% +back into the core so we have a +recirculation of the + + align:start position:0% +recirculation of the + + + align:start position:0% +recirculation of the +containment water Sy the containment the + + align:start position:0% +containment water Sy the containment the + + + align:start position:0% +containment water Sy the containment the +water in the containment that would + + align:start position:0% +water in the containment that would + + + align:start position:0% +water in the containment that would +allow for continuous core cooling now + + align:start position:0% +allow for continuous core cooling now + + + align:start position:0% +allow for continuous core cooling now +it's a high pressure and a low pressure + + align:start position:0% +it's a high pressure and a low pressure + + + align:start position:0% +it's a high pressure and a low pressure +pressure system but this assures that + + align:start position:0% +pressure system but this assures that + + + align:start position:0% +pressure system but this assures that +even though the water is continuously + + align:start position:0% +even though the water is continuously + + + align:start position:0% +even though the water is continuously +coming out of the reactor it is able to + + align:start position:0% +coming out of the reactor it is able to + + + align:start position:0% +coming out of the reactor it is able to +be recirculated and placed back into the + + align:start position:0% + + + + align:start position:0% + +core the next system that's very + + align:start position:0% +core the next system that's very + + + align:start position:0% +core the next system that's very +important that we've already discussed + + align:start position:0% +important that we've already discussed + + + align:start position:0% +important that we've already discussed +in general is what we called a post + + align:start position:0% +in general is what we called a post + + + align:start position:0% +in general is what we called a post +accident radioactivity removal system + + align:start position:0% +accident radioactivity removal system + + + align:start position:0% +accident radioactivity removal system +and this is essentially a containment + + align:start position:0% +and this is essentially a containment + + + align:start position:0% +and this is essentially a containment +spray system that is in the top of the + + align:start position:0% +spray system that is in the top of the + + + align:start position:0% +spray system that is in the top of the +containment that is used to not only can + + align:start position:0% +containment that is used to not only can + + + align:start position:0% +containment that is used to not only can +quench the steam water mixture that is + + align:start position:0% +quench the steam water mixture that is + + + align:start position:0% +quench the steam water mixture that is +released + + align:start position:0% +released + + + align:start position:0% +released +from the brake in the pipe which you as + + align:start position:0% +from the brake in the pipe which you as + + + align:start position:0% +from the brake in the pipe which you as +you can imagine High Press water of + + align:start position:0% +you can imagine High Press water of + + + align:start position:0% +you can imagine High Press water of +2,000 lb per square in flashing in the + + align:start position:0% +2,000 lb per square in flashing in the + + + align:start position:0% +2,000 lb per square in flashing in the +steam creating a very very hot + + align:start position:0% +steam creating a very very hot + + + align:start position:0% +steam creating a very very hot +environment and a pressurized + + align:start position:0% +environment and a pressurized + + + align:start position:0% +environment and a pressurized +environment so we need to do is to + + align:start position:0% +environment so we need to do is to + + + align:start position:0% +environment so we need to do is to +condense the steam by spraying it with + + align:start position:0% +condense the steam by spraying it with + + + align:start position:0% +condense the steam by spraying it with +water and inserting in this case sodium + + align:start position:0% +water and inserting in this case sodium + + + align:start position:0% +water and inserting in this case sodium +hydroxide into this water into this + + align:start position:0% +hydroxide into this water into this + + + align:start position:0% +hydroxide into this water into this +water such that when it's sprayed it + + align:start position:0% +water such that when it's sprayed it + + + align:start position:0% +water such that when it's sprayed it +assists in the capture and the chemical + + align:start position:0% +assists in the capture and the chemical + + + align:start position:0% +assists in the capture and the chemical +uh retardation of the Vision products + + align:start position:0% +uh retardation of the Vision products + + + align:start position:0% +uh retardation of the Vision products +such that they more easily played out or + + align:start position:0% +such that they more easily played out or + + + align:start position:0% +such that they more easily played out or +are in fact captured chemically in a + + align:start position:0% +are in fact captured chemically in a + + + align:start position:0% +are in fact captured chemically in a +nonvolatile form so we also have in this + + align:start position:0% +nonvolatile form so we also have in this + + + align:start position:0% +nonvolatile form so we also have in this +system a capability to recirculate from + + align:start position:0% +system a capability to recirculate from + + + align:start position:0% +system a capability to recirculate from +the Sun this water and it goes back into + + align:start position:0% +the Sun this water and it goes back into + + + align:start position:0% +the Sun this water and it goes back into +the containment sprays provide + + align:start position:0% +the containment sprays provide + + + align:start position:0% +the containment sprays provide +continuous recirculation so we have a + + align:start position:0% +continuous recirculation so we have a + + + align:start position:0% +continuous recirculation so we have a +recirculation from the sump into the + + align:start position:0% +recirculation from the sump into the + + + align:start position:0% +recirculation from the sump into the +core and recirculation from the sump + + align:start position:0% +core and recirculation from the sump + + + align:start position:0% +core and recirculation from the sump +into the containment spray purpose of + + align:start position:0% +into the containment spray purpose of + + + align:start position:0% +into the containment spray purpose of +this is is to reduce pressure in the + + align:start position:0% +this is is to reduce pressure in the + + + align:start position:0% +this is is to reduce pressure in the +containment and to essentially + + align:start position:0% +containment and to essentially + + + align:start position:0% +containment and to essentially +immobilize some of the fishing + + align:start position:0% +immobilize some of the fishing + + + align:start position:0% +immobilize some of the fishing +products now having said all that we + + align:start position:0% +products now having said all that we + + + align:start position:0% +products now having said all that we +need a mechanism to remove heat from the + + align:start position:0% +need a mechanism to remove heat from the + + + align:start position:0% +need a mechanism to remove heat from the +container remember this is still + + align:start position:0% +container remember this is still + + + align:start position:0% +container remember this is still +producing a tremendous amount of heat + + align:start position:0% +producing a tremendous amount of heat + + + align:start position:0% +producing a tremendous amount of heat +assuming we can still keep it cool from + + align:start position:0% +assuming we can still keep it cool from + + + align:start position:0% +assuming we can still keep it cool from +the emergency cooling injection and we + + align:start position:0% +the emergency cooling injection and we + + + align:start position:0% +the emergency cooling injection and we +also have a lot of heat of vaporization + + align:start position:0% +also have a lot of heat of vaporization + + + align:start position:0% +also have a lot of heat of vaporization +that needs to be removed otherwise + + align:start position:0% +that needs to be removed otherwise + + + align:start position:0% +that needs to be removed otherwise +gradually the system will begin to + + align:start position:0% +gradually the system will begin to + + + align:start position:0% +gradually the system will begin to +overheat so we have a system whereby we + + align:start position:0% +overheat so we have a system whereby we + + + align:start position:0% +overheat so we have a system whereby we +have a containment heat exchanger that + + align:start position:0% +have a containment heat exchanger that + + + align:start position:0% +have a containment heat exchanger that +is used + + align:start position:0% +is used + + + align:start position:0% +is used +to essentially cool the water that's + + align:start position:0% +to essentially cool the water that's + + + align:start position:0% +to essentially cool the water that's +being recirculated not only to the + + align:start position:0% +being recirculated not only to the + + + align:start position:0% +being recirculated not only to the +sprays but also into the recirculation + + align:start position:0% +sprays but also into the recirculation + + + align:start position:0% +sprays but also into the recirculation +system of the of the core so we have + + align:start position:0% +system of the of the core so we have + + + align:start position:0% +system of the of the core so we have +water going through the heat exchanges + + align:start position:0% +water going through the heat exchanges + + + align:start position:0% +water going through the heat exchanges +that are in containment that will that + + align:start position:0% +that are in containment that will that + + + align:start position:0% +that are in containment that will that +will ultimately cool the the water + + align:start position:0% +will ultimately cool the the water + + + align:start position:0% +will ultimately cool the the water +that's being recirculated so that we can + + align:start position:0% +that's being recirculated so that we can + + + align:start position:0% +that's being recirculated so that we can +eventually cool down this system system + + align:start position:0% +eventually cool down this system system + + + align:start position:0% +eventually cool down this system system +without having it over + + align:start position:0% + + + + align:start position:0% + +pressurized now so if you put all this + + align:start position:0% +pressurized now so if you put all this + + + align:start position:0% +pressurized now so if you put all this +together for pressurized water reactor + + align:start position:0% +together for pressurized water reactor + + + align:start position:0% +together for pressurized water reactor +again and I'll review all the systems we + + align:start position:0% +again and I'll review all the systems we + + + align:start position:0% +again and I'll review all the systems we +have the core and the reactor control + + align:start position:0% +have the core and the reactor control + + + align:start position:0% +have the core and the reactor control +rods being the first mechanism that is + + align:start position:0% +rods being the first mechanism that is + + + align:start position:0% +rods being the first mechanism that is +used to shut down the Plant and we have + + align:start position:0% +used to shut down the Plant and we have + + + align:start position:0% +used to shut down the Plant and we have +our steam generator as you know and and + + align:start position:0% +our steam generator as you know and and + + + align:start position:0% +our steam generator as you know and and +the feed for the from the turbine goes + + align:start position:0% +the feed for the from the turbine goes + + + align:start position:0% +the feed for the from the turbine goes +in and the steam comes out here is our + + align:start position:0% +in and the steam comes out here is our + + + align:start position:0% +in and the steam comes out here is our +accumulator which is has a nitrogen over + + align:start position:0% +accumulator which is has a nitrogen over + + + align:start position:0% +accumulator which is has a nitrogen over +pressure which upon loss of pressure in + + align:start position:0% +pressure which upon loss of pressure in + + + align:start position:0% +pressure which upon loss of pressure in +the core would automatically insert + + align:start position:0% +the core would automatically insert + + + align:start position:0% +the core would automatically insert +coolant into the core should there be a + + align:start position:0% +coolant into the core should there be a + + + align:start position:0% +coolant into the core should there be a +break we also now have a high pressure + + align:start position:0% +break we also now have a high pressure + + + align:start position:0% +break we also now have a high pressure +safety injection system that will inject + + align:start position:0% +safety injection system that will inject + + + align:start position:0% +safety injection system that will inject +water into the core from the refueling + + align:start position:0% +water into the core from the refueling + + + align:start position:0% +water into the core from the refueling +water storage tank and we have if you + + align:start position:0% +water storage tank and we have if you + + + align:start position:0% +water storage tank and we have if you +will a low pressure injection system + + align:start position:0% +will a low pressure injection system + + + align:start position:0% +will a low pressure injection system +that will also provide water into the + + align:start position:0% +that will also provide water into the + + + align:start position:0% +that will also provide water into the +core for low pressure and we have Boron + + align:start position:0% +core for low pressure and we have Boron + + + align:start position:0% +core for low pressure and we have Boron +that's capable of being in inserted as + + align:start position:0% +that's capable of being in inserted as + + + align:start position:0% +that's capable of being in inserted as +well as needed and we have the system + + align:start position:0% +well as needed and we have the system + + + align:start position:0% +well as needed and we have the system +again from the same common water source + + align:start position:0% +again from the same common water source + + + align:start position:0% +again from the same common water source +that will spray water into the + + align:start position:0% +that will spray water into the + + + align:start position:0% +that will spray water into the +containment to Quench and cool down the + + align:start position:0% +containment to Quench and cool down the + + + align:start position:0% +containment to Quench and cool down the +containment with the capability to + + align:start position:0% +containment with the capability to + + + align:start position:0% +containment with the capability to +recirculate back into either the high or + + align:start position:0% +recirculate back into either the high or + + + align:start position:0% +recirculate back into either the high or +low pressure system so that in in + + align:start position:0% +low pressure system so that in in + + + align:start position:0% +low pressure system so that in in +essence is the emergency core cooling + + align:start position:0% +essence is the emergency core cooling + + + align:start position:0% +essence is the emergency core cooling +system for a pressurized water reactor + + align:start position:0% +system for a pressurized water reactor + + + align:start position:0% +system for a pressurized water reactor +boiling water reactors are somewhat + + align:start position:0% +boiling water reactors are somewhat + + + align:start position:0% +boiling water reactors are somewhat +different and we'll discuss in Greater + + align:start position:0% +different and we'll discuss in Greater + + + align:start position:0% +different and we'll discuss in Greater +detail how these systems work but let me + + align:start position:0% +detail how these systems work but let me + + + align:start position:0% +detail how these systems work but let me +just contrast them for you we have again + + align:start position:0% +just contrast them for you we have again + + + align:start position:0% +just contrast them for you we have again +the core and as you recall in a Boiling + + align:start position:0% +the core and as you recall in a Boiling + + + align:start position:0% +the core and as you recall in a Boiling +Water Reactor the main feed water goes + + align:start position:0% +Water Reactor the main feed water goes + + + align:start position:0% +Water Reactor the main feed water goes +into the reactor and comes out as Sten + + align:start position:0% +into the reactor and comes out as Sten + + + align:start position:0% +into the reactor and comes out as Sten +goes right to the turban in The Boiling + + align:start position:0% +goes right to the turban in The Boiling + + + align:start position:0% +goes right to the turban in The Boiling +Water Reactor we also have a uh + + align:start position:0% +Water Reactor we also have a uh + + + align:start position:0% +Water Reactor we also have a uh +containment spray system + + align:start position:0% +containment spray system + + + align:start position:0% +containment spray system +which is also recirculating water but if + + align:start position:0% +which is also recirculating water but if + + + align:start position:0% +which is also recirculating water but if +you have a breake in the pipe in the + + align:start position:0% +you have a breake in the pipe in the + + + align:start position:0% +you have a breake in the pipe in the +vessel what boiling water reactors have + + align:start position:0% +vessel what boiling water reactors have + + + align:start position:0% +vessel what boiling water reactors have +is this containment this is their + + align:start position:0% +is this containment this is their + + + align:start position:0% +is this containment this is their +containment and the idea is if the pipe + + align:start position:0% +containment and the idea is if the pipe + + + align:start position:0% +containment and the idea is if the pipe +is broken the spray from the uh + + align:start position:0% +is broken the spray from the uh + + + align:start position:0% +is broken the spray from the uh +pressurized water which is now at about + + align:start position:0% +pressurized water which is now at about + + + align:start position:0% +pressurized water which is now at about +1,000 pounds of a square goes into this + + align:start position:0% +1,000 pounds of a square goes into this + + + align:start position:0% +1,000 pounds of a square goes into this +containment Dome and is blown into this + + align:start position:0% +containment Dome and is blown into this + + + align:start position:0% +containment Dome and is blown into this +Taurus this this area here is a almost a + + align:start position:0% +Taurus this this area here is a almost a + + + align:start position:0% +Taurus this this area here is a almost a +donut shaped type device which contains + + align:start position:0% +donut shaped type device which contains + + + align:start position:0% +donut shaped type device which contains +water and once the the pipe break occurs + + align:start position:0% +water and once the the pipe break occurs + + + align:start position:0% +water and once the the pipe break occurs +the water steam mixture blows down into + + align:start position:0% +the water steam mixture blows down into + + + align:start position:0% +the water steam mixture blows down into +this water and essentially quenches + + align:start position:0% +this water and essentially quenches + + + align:start position:0% +this water and essentially quenches +itself in the Taurus water which + + align:start position:0% +itself in the Taurus water which + + + align:start position:0% +itself in the Taurus water which +provides the pressure relief that + + align:start position:0% +provides the pressure relief that + + + align:start position:0% +provides the pressure relief that +containment sprays pretty much did in + + align:start position:0% +containment sprays pretty much did in + + + align:start position:0% +containment sprays pretty much did in +the PW rks now the water from here from + + align:start position:0% +the PW rks now the water from here from + + + align:start position:0% +the PW rks now the water from here from +these to from this Taurus is can also be + + align:start position:0% +these to from this Taurus is can also be + + + align:start position:0% +these to from this Taurus is can also be +recirculated directly into the core + + align:start position:0% +recirculated directly into the core + + + align:start position:0% +recirculated directly into the core +above the core which originally was a + + align:start position:0% +above the core which originally was a + + + align:start position:0% +above the core which originally was a +very big Advantage for bwrs when the + + align:start position:0% +very big Advantage for bwrs when the + + + align:start position:0% +very big Advantage for bwrs when the +emergency core cooling system issues + + align:start position:0% +emergency core cooling system issues + + + align:start position:0% +emergency core cooling system issues +were raised back in the early 70s so we + + align:start position:0% +were raised back in the early 70s so we + + + align:start position:0% +were raised back in the early 70s so we +take water from the Taurus and insert it + + align:start position:0% +take water from the Taurus and insert it + + + align:start position:0% +take water from the Taurus and insert it +back over the core we also have a water + + align:start position:0% +back over the core we also have a water + + + align:start position:0% +back over the core we also have a water +injection system that would allow one + + align:start position:0% +injection system that would allow one + + + align:start position:0% +injection system that would allow one +to to make up water early in the + + align:start position:0% +to to make up water early in the + + + align:start position:0% +to to make up water early in the +transient and we also have a residual + + align:start position:0% +transient and we also have a residual + + + align:start position:0% +transient and we also have a residual +heat removal system that also takes the + + align:start position:0% +heat removal system that also takes the + + + align:start position:0% +heat removal system that also takes the +heat from the Taurus and transfers that + + align:start position:0% +heat from the Taurus and transfers that + + + align:start position:0% +heat from the Taurus and transfers that +heat to an external Source providing + + align:start position:0% +heat to an external Source providing + + + align:start position:0% +heat to an external Source providing +cooler water to continue to recirculate + + align:start position:0% +cooler water to continue to recirculate + + + align:start position:0% +cooler water to continue to recirculate +the sprays so the big difference between + + align:start position:0% +the sprays so the big difference between + + + align:start position:0% +the sprays so the big difference between +a pwr and a + + align:start position:0% +a pwr and a + + + align:start position:0% +a pwr and a +bwr is that a bwr has a builtin + + align:start position:0% +bwr is that a bwr has a builtin + + + align:start position:0% +bwr is that a bwr has a builtin +suppression pool for the steam that may + + align:start position:0% +suppression pool for the steam that may + + + align:start position:0% +suppression pool for the steam that may +be released it has direct containment + + align:start position:0% +be released it has direct containment + + + align:start position:0% +be released it has direct containment +core spray I should say from this uh + + align:start position:0% +core spray I should say from this uh + + + align:start position:0% +core spray I should say from this uh +from the suppression pool and has the + + align:start position:0% +from the suppression pool and has the + + + align:start position:0% +from the suppression pool and has the +ability to recirculate water and cool it + + align:start position:0% +ability to recirculate water and cool it + + + align:start position:0% +ability to recirculate water and cool it +uh from and cool the tame it if you will + + align:start position:0% +uh from and cool the tame it if you will + + + align:start position:0% +uh from and cool the tame it if you will +from the uh suppression pool as well and + + align:start position:0% +from the uh suppression pool as well and + + + align:start position:0% +from the uh suppression pool as well and +you you do have a highpressure cool + + align:start position:0% +you you do have a highpressure cool + + + align:start position:0% +you you do have a highpressure cool +injection system that could also be + + align:start position:0% +injection system that could also be + + + align:start position:0% +injection system that could also be +called in to address uh brakes that + + align:start position:0% +called in to address uh brakes that + + + align:start position:0% +called in to address uh brakes that +perhaps are not as as large as a ve Loca + + align:start position:0% +perhaps are not as as large as a ve Loca + + + align:start position:0% +perhaps are not as as large as a ve Loca +the uh the advantage and and and the + + align:start position:0% +the uh the advantage and and and the + + + align:start position:0% +the uh the advantage and and and the +difference also between a pwr and a + + align:start position:0% +difference also between a pwr and a + + + align:start position:0% +difference also between a pwr and a +bwr is that in a bwr as we'll see in + + align:start position:0% +bwr is that in a bwr as we'll see in + + + align:start position:0% +bwr is that in a bwr as we'll see in +future lectures there is an automatic + + align:start position:0% +future lectures there is an automatic + + + align:start position:0% +future lectures there is an automatic +depressurization system and this system + + align:start position:0% +depressurization system and this system + + + align:start position:0% +depressurization system and this system +basically reduces the pressure of the of + + align:start position:0% +basically reduces the pressure of the of + + + align:start position:0% +basically reduces the pressure of the of +the core to a relatively low pressure + + align:start position:0% +the core to a relatively low pressure + + + align:start position:0% +the core to a relatively low pressure +allowing for the use of low pressure uh + + align:start position:0% +allowing for the use of low pressure uh + + + align:start position:0% +allowing for the use of low pressure uh +coolant injection systems as opposed to + + align:start position:0% +coolant injection systems as opposed to + + + align:start position:0% +coolant injection systems as opposed to +Reg lying on the high press injection + + align:start position:0% +Reg lying on the high press injection + + + align:start position:0% +Reg lying on the high press injection +systems so an automatic depressurization + + align:start position:0% +systems so an automatic depressurization + + + align:start position:0% +systems so an automatic depressurization +system makes recirculation of water much + + align:start position:0% +system makes recirculation of water much + + + align:start position:0% +system makes recirculation of water much +easier depending upon the type of of + + align:start position:0% +easier depending upon the type of of + + + align:start position:0% +easier depending upon the type of of +accident that you + + align:start position:0% +accident that you + + + align:start position:0% +accident that you +have now let me uh go over now what the + + align:start position:0% +have now let me uh go over now what the + + + align:start position:0% +have now let me uh go over now what the +sighting criteria are for nuclear power + + align:start position:0% +sighting criteria are for nuclear power + + + align:start position:0% +sighting criteria are for nuclear power +plants recall one of the key issues is + + align:start position:0% +plants recall one of the key issues is + + + align:start position:0% +plants recall one of the key issues is +nuclear plants have to meet certain + + align:start position:0% +nuclear plants have to meet certain + + + align:start position:0% +nuclear plants have to meet certain +standards as a result of of their design + + align:start position:0% +standards as a result of of their design + + + align:start position:0% +standards as a result of of their design +which forces the design to to look a + + align:start position:0% +which forces the design to to look a + + + align:start position:0% +which forces the design to to look a +certain way and and it clearly the + + align:start position:0% +certain way and and it clearly the + + + align:start position:0% +certain way and and it clearly the +reactor design will depend on how these + + align:start position:0% +reactor design will depend on how these + + + align:start position:0% +reactor design will depend on how these +criteria these sighing criteria are met + + align:start position:0% +criteria these sighing criteria are met + + + align:start position:0% +criteria these sighing criteria are met +and because we're we're concerned about + + align:start position:0% +and because we're we're concerned about + + + align:start position:0% +and because we're we're concerned about +the people we have certain defined + + align:start position:0% +the people we have certain defined + + + align:start position:0% +the people we have certain defined +certain areas like an exclusion area a + + align:start position:0% +certain areas like an exclusion area a + + + align:start position:0% +certain areas like an exclusion area a +low population Zone and a population + + align:start position:0% +low population Zone and a population + + + align:start position:0% +low population Zone and a population +Center distance so that the sighting is + + align:start position:0% +Center distance so that the sighting is + + + align:start position:0% +Center distance so that the sighting is +such that if there is an accident as few + + align:start position:0% +such that if there is an accident as few + + + align:start position:0% +such that if there is an accident as few +people as possible would be affected and + + align:start position:0% +people as possible would be affected and + + + align:start position:0% +people as possible would be affected and +in the analysis of these design basis + + align:start position:0% +in the analysis of these design basis + + + align:start position:0% +in the analysis of these design basis +accidents we assume a bounding fision + + align:start position:0% +accidents we assume a bounding fision + + + align:start position:0% +accidents we assume a bounding fision +product release which is the highest + + align:start position:0% +product release which is the highest + + + align:start position:0% +product release which is the highest +that we we we can expect and the + + align:start position:0% +that we we we can expect and the + + + align:start position:0% +that we we we can expect and the +exclusion area is defined such that if + + align:start position:0% +exclusion area is defined such that if + + + align:start position:0% +exclusion area is defined such that if +somebody who sits on this exclusion area + + align:start position:0% +somebody who sits on this exclusion area + + + align:start position:0% +somebody who sits on this exclusion area +boundary which typically is the the + + align:start position:0% +boundary which typically is the the + + + align:start position:0% +boundary which typically is the the +property line of the plant for 2 hours + + align:start position:0% +property line of the plant for 2 hours + + + align:start position:0% +property line of the plant for 2 hours +immediately after this accident your + + align:start position:0% +immediately after this accident your + + + align:start position:0% +immediately after this accident your +total dose total whole body dose would + + align:start position:0% +total dose total whole body dose would + + + align:start position:0% +total dose total whole body dose would +not be higher than 25 rim + + align:start position:0% +not be higher than 25 rim + + + align:start position:0% +not be higher than 25 rim +or 25,000 Mig and no higher than 300 G + + align:start position:0% +or 25,000 Mig and no higher than 300 G + + + align:start position:0% +or 25,000 Mig and no higher than 300 G +to the th and that's again due to the I + + align:start position:0% +to the th and that's again due to the I + + + align:start position:0% +to the th and that's again due to the I +the low population zone is defined such + + align:start position:0% +the low population zone is defined such + + + align:start position:0% +the low population zone is defined such +that if a person is at this boundary + + align:start position:0% +that if a person is at this boundary + + + align:start position:0% +that if a person is at this boundary +area boundary Zone that person if for + + align:start position:0% +area boundary Zone that person if for + + + align:start position:0% +area boundary Zone that person if for +the entire duration of the release which + + align:start position:0% +the entire duration of the release which + + + align:start position:0% +the entire duration of the release which +could be hours perhaps days would not + + align:start position:0% +could be hours perhaps days would not + + + align:start position:0% +could be hours perhaps days would not +exceed 25 R + + align:start position:0% +exceed 25 R + + + align:start position:0% +exceed 25 R +dose and then there ought to be a + + align:start position:0% +dose and then there ought to be a + + + align:start position:0% +dose and then there ought to be a +population Center or a population Center + + align:start position:0% +population Center or a population Center + + + align:start position:0% +population Center or a population Center +which you know you don't want to put + + align:start position:0% +which you know you don't want to put + + + align:start position:0% +which you know you don't want to put +this next to New York City for example + + align:start position:0% +this next to New York City for example + + + align:start position:0% +this next to New York City for example +even though you meet the first two + + align:start position:0% +even though you meet the first two + + + align:start position:0% +even though you meet the first two +criteria so they have a criteria of 1.33 + + align:start position:0% +criteria so they have a criteria of 1.33 + + + align:start position:0% +criteria so they have a criteria of 1.33 +times the distance to the outer boundary + + align:start position:0% +times the distance to the outer boundary + + + align:start position:0% +times the distance to the outer boundary +of the center from the reactor so it is + + align:start position:0% +of the center from the reactor so it is + + + align:start position:0% +of the center from the reactor so it is +within this envelope which the NRC has + + align:start position:0% +within this envelope which the NRC has + + + align:start position:0% +within this envelope which the NRC has +judged to be acceptable in terms of an + + align:start position:0% +judged to be acceptable in terms of an + + + align:start position:0% +judged to be acceptable in terms of an +accidental dose that you design your + + align:start position:0% +accidental dose that you design your + + + align:start position:0% +accidental dose that you design your +plan and and the most restrictive of + + align:start position:0% +plan and and the most restrictive of + + + align:start position:0% +plan and and the most restrictive of +course is is 25 Grand at the site + + align:start position:0% +course is is 25 Grand at the site + + + align:start position:0% +course is is 25 Grand at the site +boundary all of this depends on certain + + align:start position:0% +boundary all of this depends on certain + + + align:start position:0% +boundary all of this depends on certain +assumptions of + + align:start position:0% +assumptions of + + + align:start position:0% +assumptions of +meteorology and the geology and the + + align:start position:0% +meteorology and the geology and the + + + align:start position:0% +meteorology and the geology and the +hydrology of the area what's the + + align:start position:0% +hydrology of the area what's the + + + align:start position:0% +hydrology of the area what's the +Contours of the land around this + + align:start position:0% +Contours of the land around this + + + align:start position:0% +Contours of the land around this +particular power + + align:start position:0% +particular power + + + align:start position:0% +particular power +plant now the NRC has issued General + + align:start position:0% +plant now the NRC has issued General + + + align:start position:0% +plant now the NRC has issued General +design criteria to help + + align:start position:0% +design criteria to help + + + align:start position:0% +design criteria to help +designers uh address what they believe + + align:start position:0% +designers uh address what they believe + + + align:start position:0% +designers uh address what they believe +what the NRC believes are key safety and + + align:start position:0% +what the NRC believes are key safety and + + + align:start position:0% +what the NRC believes are key safety and +general design issues and and IT + + align:start position:0% +general design issues and and IT + + + align:start position:0% +general design issues and and IT +addresses the design fabrication + + align:start position:0% +addresses the design fabrication + + + align:start position:0% +addresses the design fabrication +construction testing and performance + + align:start position:0% +construction testing and performance + + + align:start position:0% +construction testing and performance +requires requirements of systems + + align:start position:0% +requires requirements of systems + + + align:start position:0% +requires requirements of systems +structures and components that are + + align:start position:0% +structures and components that are + + + align:start position:0% +structures and components that are +important to safety and can and so that + + align:start position:0% +important to safety and can and so that + + + align:start position:0% +important to safety and can and so that +the facility has reasonable Assurance + + align:start position:0% +the facility has reasonable Assurance + + + align:start position:0% +the facility has reasonable Assurance +these are key words reasonable Assurance + + align:start position:0% +these are key words reasonable Assurance + + + align:start position:0% +these are key words reasonable Assurance +not perfect zero risk reasonable + + align:start position:0% +not perfect zero risk reasonable + + + align:start position:0% +not perfect zero risk reasonable +assurance that the facility can be + + align:start position:0% +assurance that the facility can be + + + align:start position:0% +assurance that the facility can be +operated without undue risk public + + align:start position:0% +operated without undue risk public + + + align:start position:0% +operated without undue risk public +health and safety so the NRC in + + align:start position:0% +health and safety so the NRC in + + + align:start position:0% +health and safety so the NRC in +establishing these General design + + align:start position:0% +establishing these General design + + + align:start position:0% +establishing these General design +criteria which are found at 10c far part + + align:start position:0% +criteria which are found at 10c far part + + + align:start position:0% +criteria which are found at 10c far part +50 appendix a it sets certain categories + + align:start position:0% +50 appendix a it sets certain categories + + + align:start position:0% +50 appendix a it sets certain categories +of requirements General requirements for + + align:start position:0% +of requirements General requirements for + + + align:start position:0% +of requirements General requirements for +the facility how you're going to be + + align:start position:0% +the facility how you're going to be + + + align:start position:0% +the facility how you're going to be +protected by these multiple Vision + + align:start position:0% +protected by these multiple Vision + + + align:start position:0% +protected by these multiple Vision +product barriers which are the defenses + + align:start position:0% +product barriers which are the defenses + + + align:start position:0% +product barriers which are the defenses +that you that are needed as physical + + align:start position:0% +that you that are needed as physical + + + align:start position:0% +that you that are needed as physical +barriers what kinds of reactor + + align:start position:0% +barriers what kinds of reactor + + + align:start position:0% +barriers what kinds of reactor +Protection Systems would require be + + align:start position:0% +Protection Systems would require be + + + align:start position:0% +Protection Systems would require be +required or reactor shutdown systems + + align:start position:0% +required or reactor shutdown systems + + + align:start position:0% +required or reactor shutdown systems +what do you expect for heat removal + + align:start position:0% +what do you expect for heat removal + + + align:start position:0% +what do you expect for heat removal +systems what do you expect for in the + + align:start position:0% +systems what do you expect for in the + + + align:start position:0% +systems what do you expect for in the +design for a containment and how do you + + align:start position:0% +design for a containment and how do you + + + align:start position:0% +design for a containment and how do you +control Fuel and reactivities in terms + + align:start position:0% +control Fuel and reactivities in terms + + + align:start position:0% +control Fuel and reactivities in terms +of what kind of design limits would you + + align:start position:0% +of what kind of design limits would you + + + align:start position:0% +of what kind of design limits would you +need to impose in your in your facility + + align:start position:0% +need to impose in your in your facility + + + align:start position:0% +need to impose in your in your facility +to make sure that you have a design that + + align:start position:0% +to make sure that you have a design that + + + align:start position:0% +to make sure that you have a design that +can be uh operated without under risk to + + align:start position:0% +can be uh operated without under risk to + + + align:start position:0% +can be uh operated without under risk to +public health and safety one of the key + + align:start position:0% +public health and safety one of the key + + + align:start position:0% +public health and safety one of the key +features in this design criteria is what + + align:start position:0% +features in this design criteria is what + + + align:start position:0% +features in this design criteria is what +people call the single failure crit + + align:start position:0% +people call the single failure crit + + + align:start position:0% +people call the single failure crit +criteria and that essentially says even + + align:start position:0% +criteria and that essentially says even + + + align:start position:0% +criteria and that essentially says even +though you've designed all these Safety + + align:start position:0% +though you've designed all these Safety + + + align:start position:0% +though you've designed all these Safety +Systems you need to + + align:start position:0% +Systems you need to + + + align:start position:0% +Systems you need to +assume that you have a single failure of + + align:start position:0% +assume that you have a single failure of + + + align:start position:0% +assume that you have a single failure of +one of those Key + + align:start position:0% +one of those Key + + + align:start position:0% +one of those Key +Systems in the assumed in the analysis + + align:start position:0% +Systems in the assumed in the analysis + + + align:start position:0% +Systems in the assumed in the analysis +and and to demonstrate that you still + + align:start position:0% +and and to demonstrate that you still + + + align:start position:0% +and and to demonstrate that you still +meet the criteria even though you had a + + align:start position:0% +meet the criteria even though you had a + + + align:start position:0% +meet the criteria even though you had a +single failure of the most important + + align:start position:0% +single failure of the most important + + + align:start position:0% +single failure of the most important +active component or passive component if + + align:start position:0% +active component or passive component if + + + align:start position:0% +active component or passive component if +it doesn't act if it doesn't properly + + align:start position:0% +it doesn't act if it doesn't properly + + + align:start position:0% +it doesn't act if it doesn't properly +function or a single failure of a + + align:start position:0% +function or a single failure of a + + + align:start position:0% +function or a single failure of a +passive component assuming all the + + align:start position:0% +passive component assuming all the + + + align:start position:0% +passive component assuming all the +passive all Active Components work to + + align:start position:0% +passive all Active Components work to + + + align:start position:0% +passive all Active Components work to +make sure that you you you able to lose + + align:start position:0% +make sure that you you you able to lose + + + align:start position:0% +make sure that you you you able to lose +the capability of that component and + + align:start position:0% +the capability of that component and + + + align:start position:0% +the capability of that component and +still meet your safety + + align:start position:0% +still meet your safety + + + align:start position:0% +still meet your safety +goal the intended course of this is to + + align:start position:0% +goal the intended course of this is to + + + align:start position:0% +goal the intended course of this is to +be able to achieve High + + align:start position:0% +be able to achieve High + + + align:start position:0% +be able to achieve High +reliability uh of of uh meaning the + + align:start position:0% +reliability uh of of uh meaning the + + + align:start position:0% +reliability uh of of uh meaning the +function again we're talking function + + align:start position:0% +function again we're talking function + + + align:start position:0% +function again we're talking function +without necessarily having to quantify + + align:start position:0% +without necessarily having to quantify + + + align:start position:0% +without necessarily having to quantify +it as you would perhaps in p + + align:start position:0% +it as you would perhaps in p + + + align:start position:0% +it as you would perhaps in p +because Pras do not assume single + + align:start position:0% +because Pras do not assume single + + + align:start position:0% +because Pras do not assume single +failure but assume everything can + + align:start position:0% +failure but assume everything can + + + align:start position:0% +failure but assume everything can +possibly fail with a certain + + align:start position:0% +possibly fail with a certain + + + align:start position:0% +possibly fail with a certain +likelihood so what you're trying to do + + align:start position:0% +likelihood so what you're trying to do + + + align:start position:0% +likelihood so what you're trying to do +is ultimately find the single worst + + align:start position:0% +is ultimately find the single worst + + + align:start position:0% +is ultimately find the single worst +failure that that that that the plant + + align:start position:0% +failure that that that that the plant + + + align:start position:0% +failure that that that that the plant +would hopefully be able to manage and + + align:start position:0% +would hopefully be able to manage and + + + align:start position:0% +would hopefully be able to manage and +this would enable you to understand + + align:start position:0% +this would enable you to understand + + + align:start position:0% +this would enable you to understand +system vulnerabilities in other words if + + align:start position:0% +system vulnerabilities in other words if + + + align:start position:0% +system vulnerabilities in other words if +this failure would create a much worse + + align:start position:0% +this failure would create a much worse + + + align:start position:0% +this failure would create a much worse +situation than you're willing to + + align:start position:0% +situation than you're willing to + + + align:start position:0% +situation than you're willing to +tolerate even though you may meet the + + align:start position:0% +tolerate even though you may meet the + + + align:start position:0% +tolerate even though you may meet the +criteria you would like to try to + + align:start position:0% +criteria you would like to try to + + + align:start position:0% +criteria you would like to try to +mitigate that by improving the + + align:start position:0% +mitigate that by improving the + + + align:start position:0% +mitigate that by improving the +performance of the design plan to avoid + + align:start position:0% +performance of the design plan to avoid + + + align:start position:0% +performance of the design plan to avoid +those particular + + align:start position:0% +those particular + + + align:start position:0% +those particular +consequences there are other General + + align:start position:0% +consequences there are other General + + + align:start position:0% +consequences there are other General +design criteria and I'm only going to + + align:start position:0% +design criteria and I'm only going to + + + align:start position:0% +design criteria and I'm only going to +feature just a few General design + + align:start position:0% +feature just a few General design + + + align:start position:0% +feature just a few General design +criteria number 10 talks about the + + align:start position:0% +criteria number 10 talks about the + + + align:start position:0% +criteria number 10 talks about the +reactor design and and here it talks + + align:start position:0% +reactor design and and here it talks + + + align:start position:0% +reactor design and and here it talks +about the core and Associated coolant + + align:start position:0% +about the core and Associated coolant + + + align:start position:0% +about the core and Associated coolant +and control system with appropriate + + align:start position:0% +and control system with appropriate + + + align:start position:0% +and control system with appropriate +margin interesting word to ensure that + + align:start position:0% +margin interesting word to ensure that + + + align:start position:0% +margin interesting word to ensure that +the acceptable fuel design limits will + + align:start position:0% +the acceptable fuel design limits will + + + align:start position:0% +the acceptable fuel design limits will +not be exceeded now under any conditions + + align:start position:0% +not be exceeded now under any conditions + + + align:start position:0% +not be exceeded now under any conditions +of normal and anticipated operational + + align:start position:0% +of normal and anticipated operational + + + align:start position:0% +of normal and anticipated operational +occurrences what it means is there are + + align:start position:0% +occurrences what it means is there are + + + align:start position:0% +occurrences what it means is there are +things that you that might occur during + + align:start position:0% +things that you that might occur during + + + align:start position:0% +things that you that might occur during +the operation of this plan we need to + + align:start position:0% +the operation of this plan we need to + + + align:start position:0% +the operation of this plan we need to +show in the reactor design that the that + + align:start position:0% +show in the reactor design that the that + + + align:start position:0% +show in the reactor design that the that +the plant can manage and manage these + + align:start position:0% +the plant can manage and manage these + + + align:start position:0% +the plant can manage and manage these +events such that these fuel design + + align:start position:0% +events such that these fuel design + + + align:start position:0% +events such that these fuel design +limits are not exceeding and then this + + align:start position:0% +limits are not exceeding and then this + + + align:start position:0% +limits are not exceeding and then this +other one Criterion 11 which is also an + + align:start position:0% +other one Criterion 11 which is also an + + + align:start position:0% +other one Criterion 11 which is also an +interesting one it says reactor inherent + + align:start position:0% +interesting one it says reactor inherent + + + align:start position:0% +interesting one it says reactor inherent +protection and basically it says that if + + align:start position:0% +protection and basically it says that if + + + align:start position:0% +protection and basically it says that if +you have a core design you want to be + + align:start position:0% +you have a core design you want to be + + + align:start position:0% +you have a core design you want to be +able that the inherent nuclear feedback + + align:start position:0% +able that the inherent nuclear feedback + + + align:start position:0% +able that the inherent nuclear feedback +characteristics can deal with and + + align:start position:0% +characteristics can deal with and + + + align:start position:0% +characteristics can deal with and +compensate for prompt reactivity + + align:start position:0% +compensate for prompt reactivity + + + align:start position:0% +compensate for prompt reactivity +excursions what that basically means is + + align:start position:0% +excursions what that basically means is + + + align:start position:0% +excursions what that basically means is +do not run the plant with positive power + + align:start position:0% +do not run the plant with positive power + + + align:start position:0% +do not run the plant with positive power +coefficients or to the extent that you + + align:start position:0% +coefficients or to the extent that you + + + align:start position:0% +coefficients or to the extent that you +can avoid them positive feedback + + align:start position:0% +can avoid them positive feedback + + + align:start position:0% +can avoid them positive feedback +coefficients which we've already + + align:start position:0% +coefficients which we've already + + + align:start position:0% +coefficients which we've already +discussed so this is a general design + + align:start position:0% +discussed so this is a general design + + + align:start position:0% +discussed so this is a general design +criteria that is very very important + + align:start position:0% +criteria that is very very important + + + align:start position:0% +criteria that is very very important +because it attempts to compensate for + + align:start position:0% +because it attempts to compensate for + + + align:start position:0% +because it attempts to compensate for +the failure of active systems we have + + align:start position:0% +the failure of active systems we have + + + align:start position:0% +the failure of active systems we have +inherent core design features that limit + + align:start position:0% +inherent core design features that limit + + + align:start position:0% +inherent core design features that limit +the effect of increases in + + align:start position:0% +the effect of increases in + + + align:start position:0% +the effect of increases in +reactivity General design criteria 35 + + align:start position:0% +reactivity General design criteria 35 + + + align:start position:0% +reactivity General design criteria 35 +which is perhaps most famous which says + + align:start position:0% +which is perhaps most famous which says + + + align:start position:0% +which is perhaps most famous which says +the emergency core cooling system must + + align:start position:0% +the emergency core cooling system must + + + align:start position:0% +the emergency core cooling system must +be designed to withstand a double-ended + + align:start position:0% +be designed to withstand a double-ended + + + align:start position:0% +be designed to withstand a double-ended +Guillotine break + + align:start position:0% +Guillotine break + + + align:start position:0% +Guillotine break +Loca and concurrent with in addition two + + align:start position:0% +Loca and concurrent with in addition two + + + align:start position:0% +Loca and concurrent with in addition two +a loss of offsite power and a single + + align:start position:0% +a loss of offsite power and a single + + + align:start position:0% +a loss of offsite power and a single +failure of the most of an active eccs + + align:start position:0% +failure of the most of an active eccs + + + align:start position:0% +failure of the most of an active eccs +component in the worst possible place so + + align:start position:0% +component in the worst possible place so + + + align:start position:0% +component in the worst possible place so +what have we done here and I'm going to + + align:start position:0% +what have we done here and I'm going to + + + align:start position:0% +what have we done here and I'm going to +go to the board for a second and show + + align:start position:0% +go to the board for a second and show + + + align:start position:0% +go to the board for a second and show +you if you if I can what that basically + + align:start position:0% +you if you if I can what that basically + + + align:start position:0% +you if you if I can what that basically +means so we're talking + + align:start position:0% +means so we're talking + + + align:start position:0% +means so we're talking +about a + + align:start position:0% +about a + + + align:start position:0% +about a +reactor that has a + + align:start position:0% +reactor that has a + + + align:start position:0% +reactor that has a +break in the primary cooling system and + + align:start position:0% +break in the primary cooling system and + + + align:start position:0% +break in the primary cooling system and +what is a double-ended gutin break we'll + + align:start position:0% +what is a double-ended gutin break we'll + + + align:start position:0% +what is a double-ended gutin break we'll +get we'll get to an example of that + + align:start position:0% +get we'll get to an example of that + + + align:start position:0% +get we'll get to an example of that +later but basically if you look at a + + align:start position:0% +later but basically if you look at a + + + align:start position:0% +later but basically if you look at a +pipe you're going to assume and this + + align:start position:0% +pipe you're going to assume and this + + + align:start position:0% +pipe you're going to assume and this +pipe could be 24 to 36 in you're going + + align:start position:0% +pipe could be 24 to 36 in you're going + + + align:start position:0% +pipe could be 24 to 36 in you're going +to assume in this + + align:start position:0% +to assume in this + + + align:start position:0% +to assume in this +analysis that this + + align:start position:0% + + + + align:start position:0% + +pipe essentially breaks in two where the + + align:start position:0% +pipe essentially breaks in two where the + + + align:start position:0% +pipe essentially breaks in two where the +water can flow out of both ends + + align:start position:0% +water can flow out of both ends + + + align:start position:0% +water can flow out of both ends +uncontrollably + + align:start position:0% +uncontrollably + + + align:start position:0% +uncontrollably +that's called a double-ended Guillotine + + align:start position:0% +that's called a double-ended Guillotine + + + align:start position:0% +that's called a double-ended Guillotine +break so in addition to that + + align:start position:0% +break so in addition to that + + + align:start position:0% +break so in addition to that +double-ended Guillotine break which is + + align:start position:0% +double-ended Guillotine break which is + + + align:start position:0% +double-ended Guillotine break which is +highly improbable because most of the + + align:start position:0% +highly improbable because most of the + + + align:start position:0% +highly improbable because most of the +time if pipes break they leak or they + + align:start position:0% +time if pipes break they leak or they + + + align:start position:0% +time if pipes break they leak or they +have breaks which are just more or less + + align:start position:0% +have breaks which are just more or less + + + align:start position:0% +have breaks which are just more or less +tears something like this is very very + + align:start position:0% +tears something like this is very very + + + align:start position:0% +tears something like this is very very +incredible but if you're supposed to + + align:start position:0% +incredible but if you're supposed to + + + align:start position:0% +incredible but if you're supposed to +postulate that that occurs followed by a + + align:start position:0% +postulate that that occurs followed by a + + + align:start position:0% +postulate that that occurs followed by a +loss of power which means you don't have + + align:start position:0% +loss of power which means you don't have + + + align:start position:0% +loss of power which means you don't have +power to your to your emergency cooling + + align:start position:0% +power to your to your emergency cooling + + + align:start position:0% +power to your to your emergency cooling +pump so you need to provide emergency + + align:start position:0% +pump so you need to provide emergency + + + align:start position:0% +pump so you need to provide emergency +diesel generators which brings its own + + align:start position:0% +diesel generators which brings its own + + + align:start position:0% +diesel generators which brings its own +issues and you have to have also if you + + align:start position:0% +issues and you have to have also if you + + + align:start position:0% +issues and you have to have also if you +have of emergency core cooling system + + align:start position:0% +have of emergency core cooling system + + + align:start position:0% +have of emergency core cooling system +you have to be able to compensate for uh + + align:start position:0% +you have to be able to compensate for uh + + + align:start position:0% +you have to be able to compensate for uh +the worst failure of any component in + + align:start position:0% +the worst failure of any component in + + + align:start position:0% +the worst failure of any component in +that eccs system so it's a fairly tough + + align:start position:0% +that eccs system so it's a fairly tough + + + align:start position:0% +that eccs system so it's a fairly tough +Challenge and the original thinking was + + align:start position:0% +Challenge and the original thinking was + + + align:start position:0% +Challenge and the original thinking was +that this pretty much covered and + + align:start position:0% +that this pretty much covered and + + + align:start position:0% +that this pretty much covered and +bounded the worst case scenario and if + + align:start position:0% +bounded the worst case scenario and if + + + align:start position:0% +bounded the worst case scenario and if +you met this criteria your re reor is + + align:start position:0% +you met this criteria your re reor is + + + align:start position:0% +you met this criteria your re reor is +probably going to end up being safe and + + align:start position:0% +probably going to end up being safe and + + + align:start position:0% +probably going to end up being safe and +that's how in the in the early days + + align:start position:0% +that's how in the in the early days + + + align:start position:0% +that's how in the in the early days +before the the onset of probalistic + + align:start position:0% +before the the onset of probalistic + + + align:start position:0% +before the the onset of probalistic +riskk assessment this was judged to be + + align:start position:0% +riskk assessment this was judged to be + + + align:start position:0% +riskk assessment this was judged to be +the overarching safety + + align:start position:0% +the overarching safety + + + align:start position:0% +the overarching safety +criteria in addition to this criteria + + align:start position:0% +criteria in addition to this criteria + + + align:start position:0% +criteria in addition to this criteria +they they have concept of defense and + + align:start position:0% +they they have concept of defense and + + + align:start position:0% +they they have concept of defense and +it's and it's a safety philosophy that + + align:start position:0% +it's and it's a safety philosophy that + + + align:start position:0% +it's and it's a safety philosophy that +the regulatory agency still has in place + + align:start position:0% +the regulatory agency still has in place + + + align:start position:0% +the regulatory agency still has in place +as a means even though you can do all + + align:start position:0% +as a means even though you can do all + + + align:start position:0% +as a means even though you can do all +the Pras you want they still want to see + + align:start position:0% +the Pras you want they still want to see + + + align:start position:0% +the Pras you want they still want to see +what they they would call successive + + align:start position:0% +what they they would call successive + + + align:start position:0% +what they they would call successive +compensatory measures to prevent + + align:start position:0% +compensatory measures to prevent + + + align:start position:0% +compensatory measures to prevent +accidents prevention and or mitigate + + align:start position:0% +accidents prevention and or mitigate + + + align:start position:0% +accidents prevention and or mitigate +damage if a malfunction accident or + + align:start position:0% +damage if a malfunction accident or + + + align:start position:0% +damage if a malfunction accident or +naturally caused event occurs so they + + align:start position:0% +naturally caused event occurs so they + + + align:start position:0% +naturally caused event occurs so they +want to be sure that there are multiple + + align:start position:0% +want to be sure that there are multiple + + + align:start position:0% +want to be sure that there are multiple +layers of defense that don't necessarily + + align:start position:0% +layers of defense that don't necessarily + + + align:start position:0% +layers of defense that don't necessarily +mean that they are barriers physical + + align:start position:0% +mean that they are barriers physical + + + align:start position:0% +mean that they are barriers physical +barriers they just mean there there are + + align:start position:0% +barriers they just mean there there are + + + align:start position:0% +barriers they just mean there there are +levels upon levels to make sure that the + + align:start position:0% +levels upon levels to make sure that the + + + align:start position:0% +levels upon levels to make sure that the +public health and safety is protected + + align:start position:0% +public health and safety is protected + + + align:start position:0% +public health and safety is protected +now this is chart here gives you an + + align:start position:0% +now this is chart here gives you an + + + align:start position:0% +now this is chart here gives you an +example of the type of multi-layer + + align:start position:0% +example of the type of multi-layer + + + align:start position:0% +example of the type of multi-layer +protection and and I'm going to go + + align:start position:0% +protection and and I'm going to go + + + align:start position:0% +protection and and I'm going to go +through these relatively quickly and and + + align:start position:0% +through these relatively quickly and and + + + align:start position:0% +through these relatively quickly and and +the number one refers to the accident + + align:start position:0% +the number one refers to the accident + + + align:start position:0% +the number one refers to the accident +type or actually defers number of + + align:start position:0% +type or actually defers number of + + + align:start position:0% +type or actually defers number of +barriers I'm sorry the first is the + + align:start position:0% +barriers I'm sorry the first is the + + + align:start position:0% +barriers I'm sorry the first is the +ceramic pellet where you're expecting + + align:start position:0% +ceramic pellet where you're expecting + + + align:start position:0% +ceramic pellet where you're expecting +only a small fraction of the material to + + align:start position:0% +only a small fraction of the material to + + + align:start position:0% +only a small fraction of the material to +be released obviously the cladding in + + align:start position:0% +be released obviously the cladding in + + + align:start position:0% +be released obviously the cladding in +which the fuel is placed is a physical + + align:start position:0% +which the fuel is placed is a physical + + + align:start position:0% +which the fuel is placed is a physical +barrier where you're supposed to not + + align:start position:0% +barrier where you're supposed to not + + + align:start position:0% +barrier where you're supposed to not +have uh in other words you can't have + + align:start position:0% +have uh in other words you can't have + + + align:start position:0% +have uh in other words you can't have +more than 05% of the of the tubes + + align:start position:0% +more than 05% of the of the tubes + + + align:start position:0% +more than 05% of the of the tubes +developed leaks to which fision products + + align:start position:0% +developed leaks to which fision products + + + align:start position:0% +developed leaks to which fision products +can escape then you have the reactor + + align:start position:0% +can escape then you have the reactor + + + align:start position:0% +can escape then you have the reactor +vessel and piping which is the primary + + align:start position:0% +vessel and piping which is the primary + + + align:start position:0% +vessel and piping which is the primary +Bounder which has a 8 to 10 in thick + + align:start position:0% +Bounder which has a 8 to 10 in thick + + + align:start position:0% +Bounder which has a 8 to 10 in thick +reactor vessel and 3 to 4 in thick + + align:start position:0% +reactor vessel and 3 to 4 in thick + + + align:start position:0% +reactor vessel and 3 to 4 in thick +piping steel piping containing the + + align:start position:0% +piping steel piping containing the + + + align:start position:0% +piping steel piping containing the +cooling water then you of course you + + align:start position:0% +cooling water then you of course you + + + align:start position:0% +cooling water then you of course you +have the containment which we already + + align:start position:0% +have the containment which we already + + + align:start position:0% +have the containment which we already +talked about then we have the exclusion + + align:start position:0% +talked about then we have the exclusion + + + align:start position:0% +talked about then we have the exclusion +area then we have the low population + + align:start position:0% +area then we have the low population + + + align:start position:0% +area then we have the low population +Zone and then the population distance so + + align:start position:0% +Zone and then the population distance so + + + align:start position:0% +Zone and then the population distance so +in NRC World these are the multiple + + align:start position:0% +in NRC World these are the multiple + + + align:start position:0% +in NRC World these are the multiple +barriers to public exposure and public + + align:start position:0% +barriers to public exposure and public + + + align:start position:0% +barriers to public exposure and public +risk if the mitigation system doesn't + + align:start position:0% +risk if the mitigation system doesn't + + + align:start position:0% +risk if the mitigation system doesn't +work which is the safety systems and the + + align:start position:0% +work which is the safety systems and the + + + align:start position:0% +work which is the safety systems and the +containment you then have the uh + + align:start position:0% +containment you then have the uh + + + align:start position:0% +containment you then have the uh +availability of distance and emergency + + align:start position:0% +availability of distance and emergency + + + align:start position:0% +availability of distance and emergency +response evacuation plan as needed to + + align:start position:0% +response evacuation plan as needed to + + + align:start position:0% +response evacuation plan as needed to +protect the public health and + + align:start position:0% +protect the public health and + + + align:start position:0% +protect the public health and +safety excuse me now the strategy of the + + align:start position:0% +safety excuse me now the strategy of the + + + align:start position:0% +safety excuse me now the strategy of the +NRC in terms of defense and depth is + + align:start position:0% +NRC in terms of defense and depth is + + + align:start position:0% +NRC in terms of defense and depth is +obviously first of all design of PL such + + align:start position:0% +obviously first of all design of PL such + + + align:start position:0% +obviously first of all design of PL such +accidents are + + align:start position:0% +accidents are + + + align:start position:0% +accidents are +prevented if an accident occurs you want + + align:start position:0% +prevented if an accident occurs you want + + + align:start position:0% +prevented if an accident occurs you want +to be able + + align:start position:0% +to be able + + + align:start position:0% +to be able +to by postulating an accident have + + align:start position:0% +to by postulating an accident have + + + align:start position:0% +to by postulating an accident have +Safety Systems in place to deal with + + align:start position:0% +Safety Systems in place to deal with + + + align:start position:0% +Safety Systems in place to deal with +that + + align:start position:0% +that + + + align:start position:0% +that +accident if you postulate that uh a + + align:start position:0% +accident if you postulate that uh a + + + align:start position:0% +accident if you postulate that uh a +release from when the reative cooling + + align:start position:0% +release from when the reative cooling + + + align:start position:0% +release from when the reative cooling +system occurs you want to have a + + align:start position:0% +system occurs you want to have a + + + align:start position:0% +system occurs you want to have a +containment that cont contains the + + align:start position:0% +containment that cont contains the + + + align:start position:0% +containment that cont contains the +release once it's released in + + align:start position:0% +release once it's released in + + + align:start position:0% +release once it's released in +containment you want to have in place an + + align:start position:0% +containment you want to have in place an + + + align:start position:0% +containment you want to have in place an +accident management plan to to assure + + align:start position:0% +accident management plan to to assure + + + align:start position:0% +accident management plan to to assure +that within the plant you can mitigate + + align:start position:0% +that within the plant you can mitigate + + + align:start position:0% +that within the plant you can mitigate +the consequences in other words cool the + + align:start position:0% +the consequences in other words cool the + + + align:start position:0% +the consequences in other words cool the +core down prevent the release of radio + + align:start position:0% +core down prevent the release of radio + + + align:start position:0% +core down prevent the release of radio +radi radioactivity either directly or + + align:start position:0% +radi radioactivity either directly or + + + align:start position:0% +radi radioactivity either directly or +indirectly having failed that you're + + align:start position:0% +indirectly having failed that you're + + + align:start position:0% +indirectly having failed that you're +going to postulate containment leakage + + align:start position:0% +going to postulate containment leakage + + + align:start position:0% +going to postulate containment leakage +and you then must develop and Implement + + align:start position:0% +and you then must develop and Implement + + + align:start position:0% +and you then must develop and Implement +site local site plans and emergency + + align:start position:0% +site local site plans and emergency + + + align:start position:0% +site local site plans and emergency +plans to evacuate up to a 10 mile radius + + align:start position:0% +plans to evacuate up to a 10 mile radius + + + align:start position:0% +plans to evacuate up to a 10 mile radius +from the plant and actually physically + + align:start position:0% +from the plant and actually physically + + + align:start position:0% +from the plant and actually physically +move people you also have what is called + + align:start position:0% +move people you also have what is called + + + align:start position:0% +move people you also have what is called +a 50 m ingestion pathway where within 50 + + align:start position:0% +a 50 m ingestion pathway where within 50 + + + align:start position:0% +a 50 m ingestion pathway where within 50 +miles of the plant based on an accident + + align:start position:0% +miles of the plant based on an accident + + + align:start position:0% +miles of the plant based on an accident +scenario you might be having + + align:start position:0% +scenario you might be having + + + align:start position:0% +scenario you might be having +contamination of the ground water iodine + + align:start position:0% +contamination of the ground water iodine + + + align:start position:0% +contamination of the ground water iodine +strontium and you need a plan to deal + + align:start position:0% +strontium and you need a plan to deal + + + align:start position:0% +strontium and you need a plan to deal +with that as well and within this + + align:start position:0% +with that as well and within this + + + align:start position:0% +with that as well and within this +strategy the nuclear Regulatory + + align:start position:0% +strategy the nuclear Regulatory + + + align:start position:0% +strategy the nuclear Regulatory +Commission says we have protected the + + align:start position:0% +Commission says we have protected the + + + align:start position:0% +Commission says we have protected the +public health and safety not only from + + align:start position:0% +public health and safety not only from + + + align:start position:0% +public health and safety not only from +normal due to due to due to accidents + + align:start position:0% +normal due to due to due to accidents + + + align:start position:0% +normal due to due to due to accidents +routine accidents but also in case there + + align:start position:0% +routine accidents but also in case there + + + align:start position:0% +routine accidents but also in case there +are severe accidents that require + + align:start position:0% +are severe accidents that require + + + align:start position:0% +are severe accidents that require +evacuation now + + align:start position:0% +evacuation now + + + align:start position:0% +evacuation now +the this information is essentially + + align:start position:0% +the this information is essentially + + + align:start position:0% +the this information is essentially +summarized as I mentioned earlier in a + + align:start position:0% +summarized as I mentioned earlier in a + + + align:start position:0% +summarized as I mentioned earlier in a +safety analysis report and and there are + + align:start position:0% +safety analysis report and and there are + + + align:start position:0% +safety analysis report and and there are +17 basic + + align:start position:0% +17 basic + + + align:start position:0% +17 basic +chapters it describes completely the + + align:start position:0% +chapters it describes completely the + + + align:start position:0% +chapters it describes completely the +facility and its safety basis it starts + + align:start position:0% +facility and its safety basis it starts + + + align:start position:0% +facility and its safety basis it starts +with a general description of the plant + + align:start position:0% +with a general description of the plant + + + align:start position:0% +with a general description of the plant +a general description of the site upon + + align:start position:0% +a general description of the site upon + + + align:start position:0% +a general description of the site upon +which the plant is is put it talks about + + align:start position:0% +which the plant is is put it talks about + + + align:start position:0% +which the plant is is put it talks about +the design of structures components + + align:start position:0% +the design of structures components + + + align:start position:0% +the design of structures components +equipment and systems it goes into quite + + align:start position:0% +equipment and systems it goes into quite + + + align:start position:0% +equipment and systems it goes into quite +a lot of detail about the reactor and + + align:start position:0% +a lot of detail about the reactor and + + + align:start position:0% +a lot of detail about the reactor and +the cooling systems and how the systems + + align:start position:0% +the cooling systems and how the systems + + + align:start position:0% +the cooling systems and how the systems +are Inc connected talks about engineered + + align:start position:0% +are Inc connected talks about engineered + + + align:start position:0% +are Inc connected talks about engineered +safety features these are the features + + align:start position:0% +safety features these are the features + + + align:start position:0% +safety features these are the features +that we would call emergency uh + + align:start position:0% +that we would call emergency uh + + + align:start position:0% +that we would call emergency uh +emergency core cooling + + align:start position:0% +emergency core cooling + + + align:start position:0% +emergency core cooling +systems and then we talk about how the + + align:start position:0% +systems and then we talk about how the + + + align:start position:0% +systems and then we talk about how the +plant is monitored and control we talk + + align:start position:0% +plant is monitored and control we talk + + + align:start position:0% +plant is monitored and control we talk +about the generation of electricity and + + align:start position:0% +about the generation of electricity and + + + align:start position:0% +about the generation of electricity and +all the auxiliary systems that are + + align:start position:0% +all the auxiliary systems that are + + + align:start position:0% +all the auxiliary systems that are +needed to either uh clean up the plant + + align:start position:0% +needed to either uh clean up the plant + + + align:start position:0% +needed to either uh clean up the plant +in terms of cleaning up the water + + align:start position:0% +in terms of cleaning up the water + + + align:start position:0% +in terms of cleaning up the water +providing uh more efficient operation + + align:start position:0% +providing uh more efficient operation + + + align:start position:0% +providing uh more efficient operation +through feed water heaters and so forth + + align:start position:0% +through feed water heaters and so forth + + + align:start position:0% +through feed water heaters and so forth +so all the systems are necessary for + + align:start position:0% +so all the systems are necessary for + + + align:start position:0% +so all the systems are necessary for +normal Power Plant then we talk about + + align:start position:0% +normal Power Plant then we talk about + + + align:start position:0% +normal Power Plant then we talk about +the Steam and power conversion system + + align:start position:0% +the Steam and power conversion system + + + align:start position:0% +the Steam and power conversion system +how would you how you going to manage + + align:start position:0% +how would you how you going to manage + + + align:start position:0% +how would you how you going to manage +the lowlevel waste what kind of + + align:start position:0% +the lowlevel waste what kind of + + + align:start position:0% +the lowlevel waste what kind of +radiation protection program you'll put + + align:start position:0% +radiation protection program you'll put + + + align:start position:0% +radiation protection program you'll put +into place how you going to run the + + align:start position:0% +into place how you going to run the + + + align:start position:0% +into place how you going to run the +plant in the sense how is the or plant + + align:start position:0% +plant in the sense how is the or plant + + + align:start position:0% +plant in the sense how is the or plant +organized what kind of initial startup + + align:start position:0% +organized what kind of initial startup + + + align:start position:0% +organized what kind of initial startup +test you going to propose to run the + + align:start position:0% +test you going to propose to run the + + + align:start position:0% +test you going to propose to run the +accident analysis I mentioned in chapter + + align:start position:0% +accident analysis I mentioned in chapter + + + align:start position:0% +accident analysis I mentioned in chapter +15 goes over what we call the design + + align:start position:0% +15 goes over what we call the design + + + align:start position:0% +15 goes over what we call the design +basis accidents and you're going to need + + align:start position:0% +basis accidents and you're going to need + + + align:start position:0% +basis accidents and you're going to need +to demonstrate that you meet the + + align:start position:0% +to demonstrate that you meet the + + + align:start position:0% +to demonstrate that you meet the +criteria that the NRC has set forth in + + align:start position:0% +criteria that the NRC has set forth in + + + align:start position:0% +criteria that the NRC has set forth in +the general design criteria and chapter + + align:start position:0% +the general design criteria and chapter + + + align:start position:0% +the general design criteria and chapter +16 is a very important chapter because + + align:start position:0% +16 is a very important chapter because + + + align:start position:0% +16 is a very important chapter because +it identifies what is called the + + align:start position:0% +it identifies what is called the + + + align:start position:0% +it identifies what is called the +technical specifications what these + + align:start position:0% +technical specifications what these + + + align:start position:0% +technical specifications what these +are are based on all this analysis and + + align:start position:0% +are are based on all this analysis and + + + align:start position:0% +are are based on all this analysis and +based on all of these systems particular + + align:start position:0% +based on all of these systems particular + + + align:start position:0% +based on all of these systems particular +particularly the safety analysis what + + align:start position:0% +particularly the safety analysis what + + + align:start position:0% +particularly the safety analysis what +are the operational limits that you are + + align:start position:0% +are the operational limits that you are + + + align:start position:0% +are the operational limits that you are +are to operate within what is the safety + + align:start position:0% +are to operate within what is the safety + + + align:start position:0% +are to operate within what is the safety +parameter what is the power levels What + + align:start position:0% +parameter what is the power levels What + + + align:start position:0% +parameter what is the power levels What +are the conditions for operation if you + + align:start position:0% +are the conditions for operation if you + + + align:start position:0% +are the conditions for operation if you +have a system out of service or not + + align:start position:0% +have a system out of service or not + + + align:start position:0% +have a system out of service or not +what kinds of uh inspections and + + align:start position:0% +what kinds of uh inspections and + + + align:start position:0% +what kinds of uh inspections and +surveillances you're required to perform + + align:start position:0% +surveillances you're required to perform + + + align:start position:0% +surveillances you're required to perform +this is essentially the ultimate rule + + align:start position:0% +this is essentially the ultimate rule + + + align:start position:0% +this is essentially the ultimate rule +book for operations based on all of this + + align:start position:0% +book for operations based on all of this + + + align:start position:0% +book for operations based on all of this +analysis and system design in chapter 17 + + align:start position:0% +analysis and system design in chapter 17 + + + align:start position:0% +analysis and system design in chapter 17 +is a chapter that describe describes + + align:start position:0% +is a chapter that describe describes + + + align:start position:0% +is a chapter that describe describes +your quality assurance program which is + + align:start position:0% +your quality assurance program which is + + + align:start position:0% +your quality assurance program which is +intended to assure that you are + + align:start position:0% +intended to assure that you are + + + align:start position:0% +intended to assure that you are +operating the plant within the + + align:start position:0% +operating the plant within the + + + align:start position:0% +operating the plant within the +guidelines specified and within the + + align:start position:0% +guidelines specified and within the + + + align:start position:0% +guidelines specified and within the +design of the plant + + align:start position:0% +design of the plant + + + align:start position:0% +design of the plant +just called the design + + align:start position:0% +just called the design + + + align:start position:0% +just called the design +basis now design basis accidents now + + align:start position:0% +basis now design basis accidents now + + + align:start position:0% +basis now design basis accidents now +these are postulated accidents that the + + align:start position:0% +these are postulated accidents that the + + + align:start position:0% +these are postulated accidents that the +facility is designed and built to + + align:start position:0% +facility is designed and built to + + + align:start position:0% +facility is designed and built to +withstand without exceeding these off + + align:start position:0% +withstand without exceeding these off + + + align:start position:0% +withstand without exceeding these off +offsite exposure guidelines that's 10 + + align:start position:0% +offsite exposure guidelines that's 10 + + + align:start position:0% +offsite exposure guidelines that's 10 +CFR part 100 so again each design basis + + align:start position:0% +CFR part 100 so again each design basis + + + align:start position:0% +CFR part 100 so again each design basis +accident has one single failure of a + + align:start position:0% +accident has one single failure of a + + + align:start position:0% +accident has one single failure of a +component which basically is like which + + align:start position:0% +component which basically is like which + + + align:start position:0% +component which basically is like which +is the single failure criteria and + + align:start position:0% +is the single failure criteria and + + + align:start position:0% +is the single failure criteria and +failures Beyond those are not required + + align:start position:0% +failures Beyond those are not required + + + align:start position:0% +failures Beyond those are not required +in a p as I mentioned earlier you can + + align:start position:0% +in a p as I mentioned earlier you can + + + align:start position:0% +in a p as I mentioned earlier you can +assume anything fails with a certain + + align:start position:0% +assume anything fails with a certain + + + align:start position:0% +assume anything fails with a certain +probability so you are establishing a + + align:start position:0% +probability so you are establishing a + + + align:start position:0% +probability so you are establishing a +set of design basis accidents and you + + align:start position:0% +set of design basis accidents and you + + + align:start position:0% +set of design basis accidents and you +need to show postulated and you need to + + align:start position:0% +need to show postulated and you need to + + + align:start position:0% +need to show postulated and you need to +show the facility can can meet those um + + align:start position:0% +show the facility can can meet those um + + + align:start position:0% +show the facility can can meet those um +can meet those criteria so here are the + + align:start position:0% +can meet those criteria so here are the + + + align:start position:0% +can meet those criteria so here are the +types of accidents that are are looked + + align:start position:0% +types of accidents that are are looked + + + align:start position:0% +types of accidents that are are looked +at and these are the class numers numers + + align:start position:0% +at and these are the class numers numers + + + align:start position:0% +at and these are the class numers numers +those goes from class one to class 9 + + align:start position:0% +those goes from class one to class 9 + + + align:start position:0% +those goes from class one to class 9 +class number one trivial accidents are + + align:start position:0% +class number one trivial accidents are + + + align:start position:0% +class number one trivial accidents are +considered as part of the design small + + align:start position:0% +considered as part of the design small + + + align:start position:0% +considered as part of the design small +spills leaks inside containment you + + align:start position:0% +spills leaks inside containment you + + + align:start position:0% +spills leaks inside containment you +might have class two some small leaks + + align:start position:0% +might have class two some small leaks + + + align:start position:0% +might have class two some small leaks +outside of + + align:start position:0% +outside of + + + align:start position:0% +outside of +containment and that could be pipe + + align:start position:0% +containment and that could be pipe + + + align:start position:0% +containment and that could be pipe +brakes uh maybe in a secondary system + + align:start position:0% +brakes uh maybe in a secondary system + + + align:start position:0% +brakes uh maybe in a secondary system +maybe a steam generator tube tube leak + + align:start position:0% +maybe a steam generator tube tube leak + + + align:start position:0% +maybe a steam generator tube tube leak +and so forth then you have class three + + align:start position:0% +and so forth then you have class three + + + align:start position:0% +and so forth then you have class three +which is a rad system failure where you + + align:start position:0% +which is a rad system failure where you + + + align:start position:0% +which is a rad system failure where you +might have an equipment failure in the + + align:start position:0% +might have an equipment failure in the + + + align:start position:0% +might have an equipment failure in the +rad was area where you might release + + align:start position:0% +rad was area where you might release + + + align:start position:0% +rad was area where you might release +some radioactivity remember all this is + + align:start position:0% +some radioactivity remember all this is + + + align:start position:0% +some radioactivity remember all this is +associated with releases or potential + + align:start position:0% +associated with releases or potential + + + align:start position:0% +associated with releases or potential +releases events that release + + align:start position:0% +releases events that release + + + align:start position:0% +releases events that release +radioactivity which is class four into + + align:start position:0% +radioactivity which is class four into + + + align:start position:0% +radioactivity which is class four into +the primary system which may means there + + align:start position:0% +the primary system which may means there + + + align:start position:0% +the primary system which may means there +might be a fuel failure you have a fuel + + align:start position:0% +might be a fuel failure you have a fuel + + + align:start position:0% +might be a fuel failure you have a fuel +defect or some kind of a transient that + + align:start position:0% +defect or some kind of a transient that + + + align:start position:0% +defect or some kind of a transient that +causes some sort of a failure So you + + align:start position:0% +causes some sort of a failure So you + + + align:start position:0% +causes some sort of a failure So you +you're you're releasing radioactivity + + align:start position:0% +you're you're releasing radioactivity + + + align:start position:0% +you're you're releasing radioactivity +into the primary system and events that + + align:start position:0% +into the primary system and events that + + + align:start position:0% +into the primary system and events that +release radioactivity in the secondary + + align:start position:0% +release radioactivity in the secondary + + + align:start position:0% +release radioactivity in the secondary +system which means if you have a primary + + align:start position:0% +system which means if you have a primary + + + align:start position:0% +system which means if you have a primary +system uh + + align:start position:0% +system uh + + + align:start position:0% +system uh +release that might get into the + + align:start position:0% +release that might get into the + + + align:start position:0% +release that might get into the +secondary and typically these occur with + + align:start position:0% +secondary and typically these occur with + + + align:start position:0% +secondary and typically these occur with +steam generary + + align:start position:0% +steam generary + + + align:start position:0% +steam generary +tubings now you might have refueling + + align:start position:0% +tubings now you might have refueling + + + align:start position:0% +tubings now you might have refueling +accidents outside the containment which + + align:start position:0% +accidents outside the containment which + + + align:start position:0% +accidents outside the containment which +is basically in the in the refueling uh + + align:start position:0% +is basically in the in the refueling uh + + + align:start position:0% +is basically in the in the refueling uh +spin fuel storage pool where you drop + + align:start position:0% +spin fuel storage pool where you drop + + + align:start position:0% +spin fuel storage pool where you drop +one or something falls into the pool if + + align:start position:0% +one or something falls into the pool if + + + align:start position:0% +one or something falls into the pool if +you will then you have accidents to + + align:start position:0% +you will then you have accidents to + + + align:start position:0% +you will then you have accidents to +spend fuel outside of containment this + + align:start position:0% +spend fuel outside of containment this + + + align:start position:0% +spend fuel outside of containment this +is inside and this is outside and you do + + align:start position:0% +is inside and this is outside and you do + + + align:start position:0% +is inside and this is outside and you do +the same things outside of contain and + + align:start position:0% +the same things outside of contain and + + + align:start position:0% +the same things outside of contain and +obviously it's much more serious because + + align:start position:0% +obviously it's much more serious because + + + align:start position:0% +obviously it's much more serious because +the these are not typically uh Shield + + align:start position:0% +the these are not typically uh Shield + + + align:start position:0% +the these are not typically uh Shield +typically contained but may be in + + align:start position:0% +typically contained but may be in + + + align:start position:0% +typically contained but may be in +casts then you have accident initiated + + align:start position:0% +casts then you have accident initiated + + + align:start position:0% +casts then you have accident initiated +events considered in design basis in the + + align:start position:0% +events considered in design basis in the + + + align:start position:0% +events considered in design basis in the +safety analysis report these are most of + + align:start position:0% +safety analysis report these are most of + + + align:start position:0% +safety analysis report these are most of +the ones that are now we're going to + + align:start position:0% +the ones that are now we're going to + + + align:start position:0% +the ones that are now we're going to +talk about in chapter 15 reative + + align:start position:0% +talk about in chapter 15 reative + + + align:start position:0% +talk about in chapter 15 reative +transients rupture of the primary piping + + align:start position:0% +transients rupture of the primary piping + + + align:start position:0% +transients rupture of the primary piping +uh steamline brakes loss of flows and so + + align:start position:0% +uh steamline brakes loss of flows and so + + + align:start position:0% +uh steamline brakes loss of flows and so +forth and then you have class nine which + + align:start position:0% +forth and then you have class nine which + + + align:start position:0% +forth and then you have class nine which +are hypothetical accidents more severe + + align:start position:0% +are hypothetical accidents more severe + + + align:start position:0% +are hypothetical accidents more severe +than Class 8 these are severe accidents + + align:start position:0% +than Class 8 these are severe accidents + + + align:start position:0% +than Class 8 these are severe accidents +which are not necessarily part of the + + align:start position:0% +which are not necessarily part of the + + + align:start position:0% +which are not necessarily part of the +design basis but are looked at which is + + align:start position:0% +design basis but are looked at which is + + + align:start position:0% +design basis but are looked at which is +successive failures and multiple + + align:start position:0% +successive failures and multiple + + + align:start position:0% +successive failures and multiple +barriers that normally are functional so + + align:start position:0% +barriers that normally are functional so + + + align:start position:0% +barriers that normally are functional so +beyond well class 9 you do look at in + + align:start position:0% +beyond well class 9 you do look at in + + + align:start position:0% +beyond well class 9 you do look at in +the analysis but beyond class n are + + align:start position:0% +the analysis but beyond class n are + + + align:start position:0% +the analysis but beyond class n are +severe accidents I should correct myself + + align:start position:0% +severe accidents I should correct myself + + + align:start position:0% +severe accidents I should correct myself +so you do look at hypothetical accidents + + align:start position:0% +so you do look at hypothetical accidents + + + align:start position:0% +so you do look at hypothetical accidents +of failure but they are uh judged to be + + align:start position:0% +of failure but they are uh judged to be + + + align:start position:0% +of failure but they are uh judged to be +very unlikely and then beyond class nine + + align:start position:0% +very unlikely and then beyond class nine + + + align:start position:0% +very unlikely and then beyond class nine +are the severe accidents that are not + + align:start position:0% +are the severe accidents that are not + + + align:start position:0% +are the severe accidents that are not +part of the design + + align:start position:0% +part of the design + + + align:start position:0% +part of the design +cases so this chart and the subsequent + + align:start position:0% +cases so this chart and the subsequent + + + align:start position:0% +cases so this chart and the subsequent +charts will give you examples of the + + align:start position:0% +charts will give you examples of the + + + align:start position:0% +charts will give you examples of the +types of accidents or transients that + + align:start position:0% +types of accidents or transients that + + + align:start position:0% +types of accidents or transients that +need to be considered as part of the + + align:start position:0% +need to be considered as part of the + + + align:start position:0% +need to be considered as part of the +design basis accidents so first is + + align:start position:0% +design basis accidents so first is + + + align:start position:0% +design basis accidents so first is +increase in heat removal by the + + align:start position:0% +increase in heat removal by the + + + align:start position:0% +increase in heat removal by the +secondary system what this basically + + align:start position:0% +secondary system what this basically + + + align:start position:0% +secondary system what this basically +does is cool down the core and and for + + align:start position:0% +does is cool down the core and and for + + + align:start position:0% +does is cool down the core and and for +most reactants that have a negative + + align:start position:0% +most reactants that have a negative + + + align:start position:0% +most reactants that have a negative +moderat temperature coefficient that's + + align:start position:0% +moderat temperature coefficient that's + + + align:start position:0% +moderat temperature coefficient that's +an increase in reactivity so you can see + + align:start position:0% +an increase in reactivity so you can see + + + align:start position:0% +an increase in reactivity so you can see +feed water malfunctions that result in + + align:start position:0% +feed water malfunctions that result in + + + align:start position:0% +feed water malfunctions that result in +decrease in feed water temperature + + align:start position:0% +decrease in feed water temperature + + + align:start position:0% +decrease in feed water temperature +increase in flow uh pressure increasing + + align:start position:0% +increase in flow uh pressure increasing + + + align:start position:0% +increase in flow uh pressure increasing +flow then you have a decrease in heat + + align:start position:0% +flow then you have a decrease in heat + + + align:start position:0% +flow then you have a decrease in heat +removal which is where you're not able + + align:start position:0% +removal which is where you're not able + + + align:start position:0% +removal which is where you're not able +to remove as much heat from the from the + + align:start position:0% +to remove as much heat from the from the + + + align:start position:0% +to remove as much heat from the from the +from the from the secondary system and + + align:start position:0% +from the from the secondary system and + + + align:start position:0% +from the from the secondary system and +by the secondary system so these kinds + + align:start position:0% +by the secondary system so these kinds + + + align:start position:0% +by the secondary system so these kinds +of things happen such as turbine trips + + align:start position:0% +of things happen such as turbine trips + + + align:start position:0% +of things happen such as turbine trips +you loose load loss of condenser vacuum + + align:start position:0% +you loose load loss of condenser vacuum + + + align:start position:0% +you loose load loss of condenser vacuum +every one of these basically is used and + + align:start position:0% +every one of these basically is used and + + + align:start position:0% +every one of these basically is used and +analyzed to see if there's any damage to + + align:start position:0% +analyzed to see if there's any damage to + + + align:start position:0% +analyzed to see if there's any damage to +the core then you have a decrease in + + align:start position:0% +the core then you have a decrease in + + + align:start position:0% +the core then you have a decrease in +reactor cooling system flow rate where + + align:start position:0% +reactor cooling system flow rate where + + + align:start position:0% +reactor cooling system flow rate where +you might have a failure in a main + + align:start position:0% +you might have a failure in a main + + + align:start position:0% +you might have a failure in a main +cooling pump or a cooling pump seizure + + align:start position:0% +cooling pump or a cooling pump seizure + + + align:start position:0% +cooling pump or a cooling pump seizure +or pump shaft breake uh so what this is + + align:start position:0% +or pump shaft breake uh so what this is + + + align:start position:0% +or pump shaft breake uh so what this is +a list of are what Engineers can imagine + + align:start position:0% +a list of are what Engineers can imagine + + + align:start position:0% +a list of are what Engineers can imagine +as possible things that might break in + + align:start position:0% +as possible things that might break in + + + align:start position:0% +as possible things that might break in +the reactor and you have to analyze + + align:start position:0% +the reactor and you have to analyze + + + align:start position:0% +the reactor and you have to analyze +every one of these to show that the + + align:start position:0% +every one of these to show that the + + + align:start position:0% +every one of these to show that the +reactor and the core do not exceed + + align:start position:0% +reactor and the core do not exceed + + + align:start position:0% +reactor and the core do not exceed +certain fuel temperature limits or + + align:start position:0% +certain fuel temperature limits or + + + align:start position:0% +certain fuel temperature limits or +certain Source terms going on in terms + + align:start position:0% +certain Source terms going on in terms + + + align:start position:0% +certain Source terms going on in terms +of reactivity and power distribution an + + align:start position:0% +of reactivity and power distribution an + + + align:start position:0% +of reactivity and power distribution an +anomalies you can have an uncontrolled + + align:start position:0% +anomalies you can have an uncontrolled + + + align:start position:0% +anomalies you can have an uncontrolled +Rod withdrawal you could have Rod + + align:start position:0% +Rod withdrawal you could have Rod + + + align:start position:0% +Rod withdrawal you could have Rod +misoperation you could have essentially + + align:start position:0% +misoperation you could have essentially + + + align:start position:0% +misoperation you could have essentially +failures of certain flow controllers + + align:start position:0% +failures of certain flow controllers + + + align:start position:0% +failures of certain flow controllers +that will increase or decrease + + align:start position:0% +that will increase or decrease + + + align:start position:0% +that will increase or decrease +reactivity you might eject a rod from a + + align:start position:0% +reactivity you might eject a rod from a + + + align:start position:0% +reactivity you might eject a rod from a +pwr or drop a rod in bwr recall that bwr + + align:start position:0% +pwr or drop a rod in bwr recall that bwr + + + align:start position:0% +pwr or drop a rod in bwr recall that bwr +is the rods come in from the bottom and + + align:start position:0% +is the rods come in from the bottom and + + + align:start position:0% +is the rods come in from the bottom and +uh the PW or the rod drop in from the + + align:start position:0% +uh the PW or the rod drop in from the + + + align:start position:0% +uh the PW or the rod drop in from the +top so you have you have to address + + align:start position:0% +top so you have you have to address + + + align:start position:0% +top so you have you have to address +every one of these particular trans + + align:start position:0% +every one of these particular trans + + + align:start position:0% +every one of these particular trans +hands to be sure that the reactor is + + align:start position:0% +hands to be sure that the reactor is + + + align:start position:0% +hands to be sure that the reactor is +capable of managing then you have a + + align:start position:0% +capable of managing then you have a + + + align:start position:0% +capable of managing then you have a +decreas in reactor coolant inventory + + align:start position:0% +decreas in reactor coolant inventory + + + align:start position:0% +decreas in reactor coolant inventory +this one is the familiar one inadvertent + + align:start position:0% +this one is the familiar one inadvertent + + + align:start position:0% +this one is the familiar one inadvertent +opening of a pressurizer relief safety + + align:start position:0% +opening of a pressurizer relief safety + + + align:start position:0% +opening of a pressurizer relief safety +or relief valve in a pwr or a regulating + + align:start position:0% +or relief valve in a pwr or a regulating + + + align:start position:0% +or relief valve in a pwr or a regulating +or safety valve in a BW one this is + + align:start position:0% +or safety valve in a BW one this is + + + align:start position:0% +or safety valve in a BW one this is +essentially TMI you need to design the + + align:start position:0% +essentially TMI you need to design the + + + align:start position:0% +essentially TMI you need to design the +plant to that you can hand handle an + + align:start position:0% +plant to that you can hand handle an + + + align:start position:0% +plant to that you can hand handle an +inadvertent opening of the pressurizer + + align:start position:0% +inadvertent opening of the pressurizer + + + align:start position:0% +inadvertent opening of the pressurizer +relief + + align:start position:0% +relief + + + align:start position:0% +relief +Val you can break a steam generator tube + + align:start position:0% +Val you can break a steam generator tube + + + align:start position:0% +Val you can break a steam generator tube +you can break an instrument line and you + + align:start position:0% +you can break an instrument line and you + + + align:start position:0% +you can break an instrument line and you +can have all kinds of system spectrum of + + align:start position:0% +can have all kinds of system spectrum of + + + align:start position:0% +can have all kinds of system spectrum of +pipe Brakes in a BW or inside a + + align:start position:0% +pipe Brakes in a BW or inside a + + + align:start position:0% +pipe Brakes in a BW or inside a +container so what we're talking about + + align:start position:0% +container so what we're talking about + + + align:start position:0% +container so what we're talking about +here is a spectrum and again for loss of + + align:start position:0% +here is a spectrum and again for loss of + + + align:start position:0% +here is a spectrum and again for loss of +coolant accidents a spectrum of prible + + align:start position:0% +coolant accidents a spectrum of prible + + + align:start position:0% +coolant accidents a spectrum of prible +break size from very small to this + + align:start position:0% +break size from very small to this + + + align:start position:0% +break size from very small to this +double-ended Guillotine brake and you + + align:start position:0% +double-ended Guillotine brake and you + + + align:start position:0% +double-ended Guillotine brake and you +need to show that it's okay can manage + + align:start position:0% +need to show that it's okay can manage + + + align:start position:0% +need to show that it's okay can manage +with the Safety Systems you've installed + + align:start position:0% +with the Safety Systems you've installed + + + align:start position:0% +with the Safety Systems you've installed +with the single F + + align:start position:0% +with the single F + + + align:start position:0% +with the single F +criteria continuing and you have all + + align:start position:0% +criteria continuing and you have all + + + align:start position:0% +criteria continuing and you have all +kinds of releases from subsystems or + + align:start position:0% +kinds of releases from subsystems or + + + align:start position:0% +kinds of releases from subsystems or +components typically in the rad waste + + align:start position:0% +components typically in the rad waste + + + align:start position:0% +components typically in the rad waste +area where you might be able to drop a + + align:start position:0% +area where you might be able to drop a + + + align:start position:0% +area where you might be able to drop a +fuel assembly and damage a fuel + + align:start position:0% +fuel assembly and damage a fuel + + + align:start position:0% +fuel assembly and damage a fuel +something so all of this has to be + + align:start position:0% +something so all of this has to be + + + align:start position:0% +something so all of this has to be +analyzed and in so doing what you've + + align:start position:0% +analyzed and in so doing what you've + + + align:start position:0% +analyzed and in so doing what you've +created is is essentially a + + align:start position:0% +created is is essentially a + + + align:start position:0% +created is is essentially a +uh a complete as best you can + + align:start position:0% +uh a complete as best you can + + + align:start position:0% +uh a complete as best you can +understanding of of how systems can fail + + align:start position:0% +understanding of of how systems can fail + + + align:start position:0% +understanding of of how systems can fail +and what the consequences of those + + align:start position:0% +and what the consequences of those + + + align:start position:0% +and what the consequences of those +failures might be to the core now the + + align:start position:0% +failures might be to the core now the + + + align:start position:0% +failures might be to the core now the +emergency core cooling system there was + + align:start position:0% +emergency core cooling system there was + + + align:start position:0% +emergency core cooling system there was +a rule published in January + + align:start position:0% +a rule published in January + + + align:start position:0% +a rule published in January +1974 under 10 + + align:start position:0% +1974 under 10 + + + align:start position:0% +1974 under 10 +5046 and I recommend you you look at all + + align:start position:0% +5046 and I recommend you you look at all + + + align:start position:0% +5046 and I recommend you you look at all +of these rules and see what the + + align:start position:0% +of these rules and see what the + + + align:start position:0% +of these rules and see what the +requirements are this is just a summary + + align:start position:0% +requirements are this is just a summary + + + align:start position:0% +requirements are this is just a summary +of of the key requirements of that rule + + align:start position:0% +of of the key requirements of that rule + + + align:start position:0% +of of the key requirements of that rule +this rule is now undergoing changes to + + align:start position:0% +this rule is now undergoing changes to + + + align:start position:0% +this rule is now undergoing changes to +make it more risk informed + + align:start position:0% +make it more risk informed + + + align:start position:0% +make it more risk informed +performance-based but the foundations of + + align:start position:0% +performance-based but the foundations of + + + align:start position:0% +performance-based but the foundations of +it are are pretty much the same so you + + align:start position:0% +it are are pretty much the same so you + + + align:start position:0% +it are are pretty much the same so you +have to under this rule postulate + + align:start position:0% +have to under this rule postulate + + + align:start position:0% +have to under this rule postulate +several loss of coolant accidents of + + align:start position:0% +several loss of coolant accidents of + + + align:start position:0% +several loss of coolant accidents of +different sizes and locations doesn't + + align:start position:0% +different sizes and locations doesn't + + + align:start position:0% +different sizes and locations doesn't +have to be on only the cold leg or the + + align:start position:0% +have to be on only the cold leg or the + + + align:start position:0% +have to be on only the cold leg or the +hot leg and typically you look for the + + align:start position:0% +hot leg and typically you look for the + + + align:start position:0% +hot leg and typically you look for the +worst location that you have found the + + align:start position:0% +worst location that you have found the + + + align:start position:0% +worst location that you have found the +most severe loss of coolant accident + + align:start position:0% +most severe loss of coolant accident + + + align:start position:0% +most severe loss of coolant accident +size and location then you have to + + align:start position:0% +size and location then you have to + + + align:start position:0% +size and location then you have to +postulate as we mentioned loss of + + align:start position:0% +postulate as we mentioned loss of + + + align:start position:0% +postulate as we mentioned loss of +offsite or onsite power and the most + + align:start position:0% +offsite or onsite power and the most + + + align:start position:0% +offsite or onsite power and the most +damaged single failure in the eccs + + align:start position:0% +damaged single failure in the eccs + + + align:start position:0% +damaged single failure in the eccs +system + + align:start position:0% +system + + + align:start position:0% +system +now in order to be successful in terms + + align:start position:0% +now in order to be successful in terms + + + align:start position:0% +now in order to be successful in terms +of showing your plant is properly + + align:start position:0% +of showing your plant is properly + + + align:start position:0% +of showing your plant is properly +designed you need to prove that the peak + + align:start position:0% +designed you need to prove that the peak + + + align:start position:0% +designed you need to prove that the peak +planning temperature cannot exceed 2200 + + align:start position:0% +planning temperature cannot exceed 2200 + + + align:start position:0% +planning temperature cannot exceed 2200 +de + + align:start position:0% +de + + + align:start position:0% +de +F that the oxidation of the clading + + align:start position:0% +F that the oxidation of the clading + + + align:start position:0% +F that the oxidation of the clading +cannot be more than 177% of its + + align:start position:0% +cannot be more than 177% of its + + + align:start position:0% +cannot be more than 177% of its +thickness and that the hydrogen + + align:start position:0% +thickness and that the hydrogen + + + align:start position:0% +thickness and that the hydrogen +generation from that steam cladding + + align:start position:0% +generation from that steam cladding + + + align:start position:0% +generation from that steam cladding +interaction cannot exceed 1% of its + + align:start position:0% +interaction cannot exceed 1% of its + + + align:start position:0% +interaction cannot exceed 1% of its +potential the core must continue to be + + align:start position:0% +potential the core must continue to be + + + align:start position:0% +potential the core must continue to be +coolable you need to show that and you + + align:start position:0% +coolable you need to show that and you + + + align:start position:0% +coolable you need to show that and you +need to show the long term cooling must + + align:start position:0% +need to show the long term cooling must + + + align:start position:0% +need to show the long term cooling must +be provided even after the reactor is + + align:start position:0% +be provided even after the reactor is + + + align:start position:0% +be provided even after the reactor is +stabilized so under these conditions you + + align:start position:0% +stabilized so under these conditions you + + + align:start position:0% +stabilized so under these conditions you +meet must meet these acceptance + + align:start position:0% + + + + align:start position:0% + +criteria now this + + align:start position:0% + + + + align:start position:0% + +chart so if you look at this + + align:start position:0% +chart so if you look at this + + + align:start position:0% +chart so if you look at this +double-ended Guillotine break which is + + align:start position:0% +double-ended Guillotine break which is + + + align:start position:0% +double-ended Guillotine break which is +the largest uh chart the largest break + + align:start position:0% +the largest uh chart the largest break + + + align:start position:0% +the largest uh chart the largest break +you can see now this is in a two + + align:start position:0% +you can see now this is in a two + + + align:start position:0% +you can see now this is in a two +Loop uh + + align:start position:0% +Loop uh + + + align:start position:0% +Loop uh +pwr you have the core and you have the + + align:start position:0% +pwr you have the core and you have the + + + align:start position:0% +pwr you have the core and you have the +steam + + align:start position:0% +steam + + + align:start position:0% +steam +generator and you have a cold leg intact + + align:start position:0% +generator and you have a cold leg intact + + + align:start position:0% +generator and you have a cold leg intact +and they assume a guillotine breake of + + align:start position:0% +and they assume a guillotine breake of + + + align:start position:0% +and they assume a guillotine breake of +one of these it looks like a hot leg and + + align:start position:0% +one of these it looks like a hot leg and + + + align:start position:0% +one of these it looks like a hot leg and +you can see various injection + + align:start position:0% +you can see various injection + + + align:start position:0% +you can see various injection +pads uh no this is a c leg as well is + + align:start position:0% +pads uh no this is a c leg as well is + + + align:start position:0% +pads uh no this is a c leg as well is +this hot + + align:start position:0% +this hot + + + align:start position:0% +this hot +Co this looks like the Hot Leg Hot Leg + + align:start position:0% +Co this looks like the Hot Leg Hot Leg + + + align:start position:0% +Co this looks like the Hot Leg Hot Leg +you see you have in points of coolant + + align:start position:0% +you see you have in points of coolant + + + align:start position:0% +you see you have in points of coolant +into the cold and or the Hot + + align:start position:0% +into the cold and or the Hot + + + align:start position:0% +into the cold and or the Hot +Legs now the double-ended gillotin break + + align:start position:0% +Legs now the double-ended gillotin break + + + align:start position:0% +Legs now the double-ended gillotin break +occurs + + align:start position:0% +occurs + + + align:start position:0% +occurs +here and what we're trying to do now + + align:start position:0% +here and what we're trying to do now + + + align:start position:0% +here and what we're trying to do now +this is this is also a c I apologize + + align:start position:0% +this is this is also a c I apologize + + + align:start position:0% +this is this is also a c I apologize +what happens in this case is the water + + align:start position:0% +what happens in this case is the water + + + align:start position:0% +what happens in this case is the water +coming out of the vessel floods out of + + align:start position:0% +coming out of the vessel floods out of + + + align:start position:0% +coming out of the vessel floods out of +here and the emergency cor cooling + + align:start position:0% +here and the emergency cor cooling + + + align:start position:0% +here and the emergency cor cooling +system obviously assumes this injection + + align:start position:0% +system obviously assumes this injection + + + align:start position:0% +system obviously assumes this injection +here but essentially no water gets + + align:start position:0% +here but essentially no water gets + + + align:start position:0% +here but essentially no water gets +injected through this Loop so you have + + align:start position:0% +injected through this Loop so you have + + + align:start position:0% +injected through this Loop so you have +essentially a a thre Loop injection + + align:start position:0% +essentially a a thre Loop injection + + + align:start position:0% +essentially a a thre Loop injection +system and this system is in fact + + align:start position:0% +system and this system is in fact + + + align:start position:0% +system and this system is in fact +analyed in in in event tree space now an + + align:start position:0% +analyed in in in event tree space now an + + + align:start position:0% +analyed in in in event tree space now an +event tree is + + align:start position:0% +event tree is + + + align:start position:0% +event tree is +obviously uh a high level look at what + + align:start position:0% +obviously uh a high level look at what + + + align:start position:0% +obviously uh a high level look at what +things you need to function to be able + + align:start position:0% +things you need to function to be able + + + align:start position:0% +things you need to function to be able +to + + align:start position:0% +to + + + align:start position:0% +to +successfully uh manage this particular + + align:start position:0% +successfully uh manage this particular + + + align:start position:0% +successfully uh manage this particular +accident and we'll talk about this in a + + align:start position:0% +accident and we'll talk about this in a + + + align:start position:0% +accident and we'll talk about this in a +subsequent lecture but the assumption is + + align:start position:0% +subsequent lecture but the assumption is + + + align:start position:0% +subsequent lecture but the assumption is +you have an initiating event which + + align:start position:0% +you have an initiating event which + + + align:start position:0% +you have an initiating event which +happens to be a pip + + align:start position:0% +happens to be a pip + + + align:start position:0% +happens to be a pip +you also need to have electric power and + + align:start position:0% +you also need to have electric power and + + + align:start position:0% +you also need to have electric power and +and if you have electric power now this + + align:start position:0% +and if you have electric power now this + + + align:start position:0% +and if you have electric power now this +could be either on site or offsite now + + align:start position:0% +could be either on site or offsite now + + + align:start position:0% +could be either on site or offsite now +in the case that of a large locco you + + align:start position:0% +in the case that of a large locco you + + + align:start position:0% +in the case that of a large locco you +assume offsite power is lost and you + + align:start position:0% +assume offsite power is lost and you + + + align:start position:0% +assume offsite power is lost and you +then must rely on your emergency diesels + + align:start position:0% +then must rely on your emergency diesels + + + align:start position:0% +then must rely on your emergency diesels +to provide emergency power for your eccs + + align:start position:0% +to provide emergency power for your eccs + + + align:start position:0% +to provide emergency power for your eccs +systems so they can be turned on to pump + + align:start position:0% +systems so they can be turned on to pump + + + align:start position:0% +systems so they can be turned on to pump +water then you have to say all right + + align:start position:0% +water then you have to say all right + + + align:start position:0% +water then you have to say all right +does my eccs system function in other + + align:start position:0% +does my eccs system function in other + + + align:start position:0% +does my eccs system function in other +words providing Co does my fision + + align:start position:0% +words providing Co does my fision + + + align:start position:0% +words providing Co does my fision +product removal system function and is + + align:start position:0% +product removal system function and is + + + align:start position:0% +product removal system function and is +my containment Integrity being + + align:start position:0% +my containment Integrity being + + + align:start position:0% +my containment Integrity being +maintained now in P world you can have + + align:start position:0% +maintained now in P world you can have + + + align:start position:0% +maintained now in P world you can have +certain probabilities of success and + + align:start position:0% +certain probabilities of success and + + + align:start position:0% +certain probabilities of success and +failure for each of these particular + + align:start position:0% +failure for each of these particular + + + align:start position:0% +failure for each of these particular +steps and when you multiply them out you + + align:start position:0% +steps and when you multiply them out you + + + align:start position:0% +steps and when you multiply them out you +will have some sense of likelihood of + + align:start position:0% +will have some sense of likelihood of + + + align:start position:0% +will have some sense of likelihood of +the event occurring now in this case the + + align:start position:0% +the event occurring now in this case the + + + align:start position:0% +the event occurring now in this case the +expectation is that you'll have success + + align:start position:0% +expectation is that you'll have success + + + align:start position:0% +expectation is that you'll have success +in all of the these paths if you assume + + align:start position:0% +in all of the these paths if you assume + + + align:start position:0% +in all of the these paths if you assume +a single failure which can be managed + + align:start position:0% +a single failure which can be managed + + + align:start position:0% +a single failure which can be managed +here single failure can be managed here + + align:start position:0% +here single failure can be managed here + + + align:start position:0% +here single failure can be managed here +other you have no power single fail + + align:start position:0% +other you have no power single fail + + + align:start position:0% +other you have no power single fail +managed here and so you're looking at + + align:start position:0% +managed here and so you're looking at + + + align:start position:0% +managed here and so you're looking at +pretty much this path in a p you're + + align:start position:0% +pretty much this path in a p you're + + + align:start position:0% +pretty much this path in a p you're +looking at all the paths and all the + + align:start position:0% +looking at all the paths and all the + + + align:start position:0% +looking at all the paths and all the +consequences of these paths to see what + + align:start position:0% +consequences of these paths to see what + + + align:start position:0% +consequences of these paths to see what +happens but in a deterministic analysis + + align:start position:0% +happens but in a deterministic analysis + + + align:start position:0% +happens but in a deterministic analysis +which is what the NRC currently requires + + align:start position:0% +which is what the NRC currently requires + + + align:start position:0% +which is what the NRC currently requires +you need only look at the single failure + + align:start position:0% +you need only look at the single failure + + + align:start position:0% +you need only look at the single failure +of of uh a most important component in + + align:start position:0% +of of uh a most important component in + + + align:start position:0% +of of uh a most important component in +the coral cooling system and loss of + + align:start position:0% +the coral cooling system and loss of + + + align:start position:0% +the coral cooling system and loss of +power and you assume that the emergency + + align:start position:0% +power and you assume that the emergency + + + align:start position:0% +power and you assume that the emergency +diesels turn + + align:start position:0% +diesels turn + + + align:start position:0% +diesels turn +on one of the key factors in this + + align:start position:0% +on one of the key factors in this + + + align:start position:0% +on one of the key factors in this +scenario is determining how the react + + align:start position:0% +scenario is determining how the react + + + align:start position:0% +scenario is determining how the react +reactor will be shut down because you + + align:start position:0% +reactor will be shut down because you + + + align:start position:0% +reactor will be shut down because you +must shut down the reactor uh because + + align:start position:0% +must shut down the reactor uh because + + + align:start position:0% +must shut down the reactor uh because +without that you will be creating a huge + + align:start position:0% +without that you will be creating a huge + + + align:start position:0% +without that you will be creating a huge +amount of heat that even the current EC + + align:start position:0% +amount of heat that even the current EC + + + align:start position:0% +amount of heat that even the current EC +eccs systems are not capable of REM move + + align:start position:0% +eccs systems are not capable of REM move + + + align:start position:0% +eccs systems are not capable of REM move +so this is a chart from I think from a + + align:start position:0% +so this is a chart from I think from a + + + align:start position:0% +so this is a chart from I think from a +combustion engineering reative + + align:start position:0% +combustion engineering reative + + + align:start position:0% +combustion engineering reative +protective system uh set points now + + align:start position:0% +protective system uh set points now + + + align:start position:0% +protective system uh set points now +obviously you can shut down the reactor + + align:start position:0% +obviously you can shut down the reactor + + + align:start position:0% +obviously you can shut down the reactor +on high power L which typically with + + align:start position:0% +on high power L which typically with + + + align:start position:0% +on high power L which typically with +four cooling pumps operating it's set at + + align:start position:0% +four cooling pumps operating it's set at + + + align:start position:0% +four cooling pumps operating it's set at +106% rated power you can shut down the + + align:start position:0% +106% rated power you can shut down the + + + align:start position:0% +106% rated power you can shut down the +reactor on low low reactor coolant flow + + align:start position:0% +reactor on low low reactor coolant flow + + + align:start position:0% +reactor on low low reactor coolant flow +which is 95% power and that addresses + + align:start position:0% +which is 95% power and that addresses + + + align:start position:0% +which is 95% power and that addresses +one of the transients that we walking so + + align:start position:0% +one of the transients that we walking so + + + align:start position:0% +one of the transients that we walking so +what we have is we have all these design + + align:start position:0% +what we have is we have all these design + + + align:start position:0% +what we have is we have all these design +basis accidents and transients and then + + align:start position:0% +basis accidents and transients and then + + + align:start position:0% +basis accidents and transients and then +we say well how do we control reactivity + + align:start position:0% +we say well how do we control reactivity + + + align:start position:0% +we say well how do we control reactivity +and how do we get the plant to shut down + + align:start position:0% +and how do we get the plant to shut down + + + align:start position:0% +and how do we get the plant to shut down +so that we can deal with it and these + + align:start position:0% +so that we can deal with it and these + + + align:start position:0% +so that we can deal with it and these +are the trips the reactor shutdown + + align:start position:0% +are the trips the reactor shutdown + + + align:start position:0% +are the trips the reactor shutdown +systems that are available high pressure + + align:start position:0% +systems that are available high pressure + + + align:start position:0% +systems that are available high pressure +Riser pressure that means you're not + + align:start position:0% +Riser pressure that means you're not + + + align:start position:0% +Riser pressure that means you're not +getting enough cooling so you have a + + align:start position:0% +getting enough cooling so you have a + + + align:start position:0% +getting enough cooling so you have a +trip of 2400 PSI versus uh 2200 PSI you + + align:start position:0% +trip of 2400 PSI versus uh 2200 PSI you + + + align:start position:0% +trip of 2400 PSI versus uh 2200 PSI you +have a thermal margin low pressure trip + + align:start position:0% +have a thermal margin low pressure trip + + + align:start position:0% +have a thermal margin low pressure trip +which basically measures the amount or + + align:start position:0% +which basically measures the amount or + + + align:start position:0% +which basically measures the amount or +the efficiency of heat removal from the + + align:start position:0% +the efficiency of heat removal from the + + + align:start position:0% +the efficiency of heat removal from the +core + + align:start position:0% +core + + + align:start position:0% +core +then you have a low steam generator + + align:start position:0% +then you have a low steam generator + + + align:start position:0% +then you have a low steam generator +water lad which means you probably have + + align:start position:0% +water lad which means you probably have + + + align:start position:0% +water lad which means you probably have +a leak somewhere uh and and the question + + align:start position:0% +a leak somewhere uh and and the question + + + align:start position:0% +a leak somewhere uh and and the question +is is it on on the primary side or on + + align:start position:0% +is is it on on the primary side or on + + + align:start position:0% +is is it on on the primary side or on +the secondary side but this one would be + + align:start position:0% +the secondary side but this one would be + + + align:start position:0% +the secondary side but this one would be +more or less on the on the primary side + + align:start position:0% +more or less on the on the primary side + + + align:start position:0% +more or less on the on the primary side +you're losing water from the steam could + + align:start position:0% +you're losing water from the steam could + + + align:start position:0% +you're losing water from the steam could +be coming out of the tube or the whole + + align:start position:0% +be coming out of the tube or the whole + + + align:start position:0% +be coming out of the tube or the whole +level in the reactor could be going down + + align:start position:0% +level in the reactor could be going down + + + align:start position:0% +level in the reactor could be going down +low steam generator pressure also is a + + align:start position:0% +low steam generator pressure also is a + + + align:start position:0% +low steam generator pressure also is a +problem because that + + align:start position:0% +problem because that + + + align:start position:0% +problem because that +means you're not getting sufficient + + align:start position:0% +means you're not getting sufficient + + + align:start position:0% +means you're not getting sufficient +Cooling and you're probably getting + + align:start position:0% +Cooling and you're probably getting + + + align:start position:0% +Cooling and you're probably getting +boiling in the core because remember + + align:start position:0% +boiling in the core because remember + + + align:start position:0% +boiling in the core because remember +these reactors designed to operate 22 + + align:start position:0% +these reactors designed to operate 22 + + + align:start position:0% +these reactors designed to operate 22 +lbs and then you have high containment + + align:start position:0% +lbs and then you have high containment + + + align:start position:0% +lbs and then you have high containment +pressure which is obviously now you've + + align:start position:0% +pressure which is obviously now you've + + + align:start position:0% +pressure which is obviously now you've +got a release into containment if any of + + align:start position:0% +got a release into containment if any of + + + align:start position:0% +got a release into containment if any of +none of these trips have worked you + + align:start position:0% +none of these trips have worked you + + + align:start position:0% +none of these trips have worked you +might trip on high containment pressure + + align:start position:0% +might trip on high containment pressure + + + align:start position:0% +might trip on high containment pressure +which is only 4 PSI G and that will shut + + align:start position:0% +which is only 4 PSI G and that will shut + + + align:start position:0% +which is only 4 PSI G and that will shut +you down so you have all these trips to + + align:start position:0% +you down so you have all these trips to + + + align:start position:0% +you down so you have all these trips to +put in place that would allow you to + + align:start position:0% +put in place that would allow you to + + + align:start position:0% +put in place that would allow you to +shut the reactor down which is the most + + align:start position:0% +shut the reactor down which is the most + + + align:start position:0% +shut the reactor down which is the most +important thing in in managing a + + align:start position:0% +important thing in in managing a + + + align:start position:0% +important thing in in managing a +significant accident now this chart + + align:start position:0% +significant accident now this chart + + + align:start position:0% +significant accident now this chart +shows the vertical sequence of some of + + align:start position:0% +shows the vertical sequence of some of + + + align:start position:0% +shows the vertical sequence of some of +these + + align:start position:0% +these + + + align:start position:0% +these +alarms on this is largely on pressure a + + align:start position:0% +alarms on this is largely on pressure a + + + align:start position:0% +alarms on this is largely on pressure a +pressure control program at 2500 lb is + + align:start position:0% +pressure control program at 2500 lb is + + + align:start position:0% +pressure control program at 2500 lb is +safety relief valve open this you have a + + align:start position:0% +safety relief valve open this you have a + + + align:start position:0% +safety relief valve open this you have a +high press reactor trip at 2400 lb which + + align:start position:0% +high press reactor trip at 2400 lb which + + + align:start position:0% +high press reactor trip at 2400 lb which +basically has both pilot operated relief + + align:start position:0% +basically has both pilot operated relief + + + align:start position:0% +basically has both pilot operated relief +valve open then you have plus the the + + align:start position:0% +valve open then you have plus the the + + + align:start position:0% +valve open then you have plus the the +safety valve well the safety valve up + + align:start position:0% +safety valve well the safety valve up + + + align:start position:0% +safety valve well the safety valve up +here then you have the spray valves full + + align:start position:0% +here then you have the spray valves full + + + align:start position:0% +here then you have the spray valves full +open above 2300 now these spray valves + + align:start position:0% +open above 2300 now these spray valves + + + align:start position:0% +open above 2300 now these spray valves +are in the pressurizer to quench the uh + + align:start position:0% +are in the pressurizer to quench the uh + + + align:start position:0% +are in the pressurizer to quench the uh +the the the pressure in the in in the + + align:start position:0% +the the the pressure in the in in the + + + align:start position:0% +the the the pressure in the in in the +primary system by by reducing + + align:start position:0% +primary system by by reducing + + + align:start position:0% +primary system by by reducing +pressurizer by reducing pressure in the + + align:start position:0% +pressurizer by reducing pressure in the + + + align:start position:0% +pressurizer by reducing pressure in the +pressurizer then you have all kinds of + + align:start position:0% +pressurizer then you have all kinds of + + + align:start position:0% +pressurizer then you have all kinds of +control set points and if the pressure + + align:start position:0% +control set points and if the pressure + + + align:start position:0% +control set points and if the pressure +goes too low you can you can in fact put + + align:start position:0% +goes too low you can you can in fact put + + + align:start position:0% +goes too low you can you can in fact put +heaters back on to get the pressure + + align:start position:0% +heaters back on to get the pressure + + + align:start position:0% +heaters back on to get the pressure +above 2200 you have a low pressure alarm + + align:start position:0% +above 2200 you have a low pressure alarm + + + align:start position:0% +above 2200 you have a low pressure alarm +and then you have a thermal low pressure + + align:start position:0% +and then you have a thermal low pressure + + + align:start position:0% +and then you have a thermal low pressure +trip which basically means the pressure + + align:start position:0% +trip which basically means the pressure + + + align:start position:0% +trip which basically means the pressure +is not high enough to remove the heat + + align:start position:0% +is not high enough to remove the heat + + + align:start position:0% +is not high enough to remove the heat +efficiently or effectively and then you + + align:start position:0% +efficiently or effectively and then you + + + align:start position:0% +efficiently or effectively and then you +have certain low pressure trip because + + align:start position:0% +have certain low pressure trip because + + + align:start position:0% +have certain low pressure trip because +if you're down to 1700 lb you're + + align:start position:0% +if you're down to 1700 lb you're + + + align:start position:0% +if you're down to 1700 lb you're +probably ending up boiling so and then + + align:start position:0% +probably ending up boiling so and then + + + align:start position:0% +probably ending up boiling so and then +of course down very very low 1600 lb you + + align:start position:0% +of course down very very low 1600 lb you + + + align:start position:0% +of course down very very low 1600 lb you +have a low low pressure alarm and safety + + align:start position:0% +have a low low pressure alarm and safety + + + align:start position:0% +have a low low pressure alarm and safety +injection signal so when you're down to + + align:start position:0% +injection signal so when you're down to + + + align:start position:0% +injection signal so when you're down to +1600 lb the the pressure control program + + align:start position:0% +1600 lb the the pressure control program + + + align:start position:0% +1600 lb the the pressure control program +knows the core is now at a point + + align:start position:0% +knows the core is now at a point + + + align:start position:0% +knows the core is now at a point +where we're not getting any water to the + + align:start position:0% +where we're not getting any water to the + + + align:start position:0% +where we're not getting any water to the +core pressure is going down there must + + align:start position:0% +core pressure is going down there must + + + align:start position:0% +core pressure is going down there must +be a large leak and we want to start + + align:start position:0% +be a large leak and we want to start + + + align:start position:0% +be a large leak and we want to start +injecting cool automatically and that + + align:start position:0% +injecting cool automatically and that + + + align:start position:0% +injecting cool automatically and that +turns on CCS system high pressure and + + align:start position:0% +turns on CCS system high pressure and + + + align:start position:0% +turns on CCS system high pressure and +then if the pressure goes down low + + align:start position:0% +then if the pressure goes down low + + + align:start position:0% +then if the pressure goes down low +enough low + + align:start position:0% +enough low + + + align:start position:0% +enough low +pressure what I'm going to go through + + align:start position:0% +pressure what I'm going to go through + + + align:start position:0% +pressure what I'm going to go through +right now is a typical loss of cool and + + align:start position:0% +right now is a typical loss of cool and + + + align:start position:0% +right now is a typical loss of cool and +accident analysis results now this comes + + align:start position:0% +accident analysis results now this comes + + + align:start position:0% +accident analysis results now this comes +from a u + + align:start position:0% +from a u + + + align:start position:0% +from a u +pwr I believe it's New England power + + align:start position:0% +pwr I believe it's New England power + + + align:start position:0% +pwr I believe it's New England power +project that was supposed to be built in + + align:start position:0% +project that was supposed to be built in + + + align:start position:0% +project that was supposed to be built in +Charlestown never was but it's symbolic + + align:start position:0% +Charlestown never was but it's symbolic + + + align:start position:0% +Charlestown never was but it's symbolic +of say a Westinghouse sebr nuclear power + + align:start position:0% +of say a Westinghouse sebr nuclear power + + + align:start position:0% +of say a Westinghouse sebr nuclear power +plant so this is for a large break logo + + align:start position:0% +plant so this is for a large break logo + + + align:start position:0% +plant so this is for a large break logo +and this is double-ended Guillotine + + align:start position:0% +and this is double-ended Guillotine + + + align:start position:0% +and this is double-ended Guillotine +break + + align:start position:0% +break + + + align:start position:0% +break +6.48 double Guillotine break this is in + + align:start position:0% +6.48 double Guillotine break this is in + + + align:start position:0% +6.48 double Guillotine break this is in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +size and we're talking about now times + + align:start position:0% +size and we're talking about now times + + + align:start position:0% +size and we're talking about now times +of events and how fast they occur for + + align:start position:0% +of events and how fast they occur for + + + align:start position:0% +of events and how fast they occur for +example you get the break at Time Zero + + align:start position:0% +example you get the break at Time Zero + + + align:start position:0% +example you get the break at Time Zero +in 1 second you will get a trip of the + + align:start position:0% +in 1 second you will get a trip of the + + + align:start position:0% +in 1 second you will get a trip of the +reactor you'll get a safety injection + + align:start position:0% +reactor you'll get a safety injection + + + align:start position:0% +reactor you'll get a safety injection +signal probably before then uh from the + + align:start position:0% +signal probably before then uh from the + + + align:start position:0% +signal probably before then uh from the +containment pressure signal but the + + align:start position:0% +containment pressure signal but the + + + align:start position:0% +containment pressure signal but the +reactor will trip almost about the same + + align:start position:0% +reactor will trip almost about the same + + + align:start position:0% +reactor will trip almost about the same +time because you've now had a large + + align:start position:0% +time because you've now had a large + + + align:start position:0% +time because you've now had a large +break quickly the pressure in the + + align:start position:0% +break quickly the pressure in the + + + align:start position:0% +break quickly the pressure in the +containment Rises and you'll get the + + align:start position:0% +containment Rises and you'll get the + + + align:start position:0% +containment Rises and you'll get the +trip signal the accumulator will inject + + align:start position:0% +trip signal the accumulator will inject + + + align:start position:0% +trip signal the accumulator will inject +within 12 seconds pressure will be down + + align:start position:0% +within 12 seconds pressure will be down + + + align:start position:0% +within 12 seconds pressure will be down +low enough the blowdown which means the + + align:start position:0% +low enough the blowdown which means the + + + align:start position:0% +low enough the blowdown which means the +end of the period whereby all of the + + align:start position:0% +end of the period whereby all of the + + + align:start position:0% +end of the period whereby all of the +water in the core is essentially out of + + align:start position:0% +water in the core is essentially out of + + + align:start position:0% +water in the core is essentially out of +the core will take place after 26 + + align:start position:0% +the core will take place after 26 + + + align:start position:0% +the core will take place after 26 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +the bottom of core recovery the bottom + + align:start position:0% +the bottom of core recovery the bottom + + + align:start position:0% +the bottom of core recovery the bottom +of core recovery which means water will + + align:start position:0% +of core recovery which means water will + + + align:start position:0% +of core recovery which means water will +get back to the bottom of the core in + + align:start position:0% +get back to the bottom of the core in + + + align:start position:0% +get back to the bottom of the core in +about 40 seconds the core is not + + align:start position:0% +about 40 seconds the core is not + + + align:start position:0% +about 40 seconds the core is not +uncovered the accumulator is empty in 55 + + align:start position:0% +uncovered the accumulator is empty in 55 + + + align:start position:0% +uncovered the accumulator is empty in 55 +seconds the pump start injecting in in + + align:start position:0% +seconds the pump start injecting in in + + + align:start position:0% +seconds the pump start injecting in in +26 seconds and the bypass basically is + + align:start position:0% +26 seconds and the bypass basically is + + + align:start position:0% +26 seconds and the bypass basically is +you're + + align:start position:0% +you're + + + align:start position:0% +you're +essentially + + align:start position:0% +essentially + + + align:start position:0% +essentially +um not having uh coolant come out well + + align:start position:0% +um not having uh coolant come out well + + + align:start position:0% +um not having uh coolant come out well +you still have coolant come out of the + + align:start position:0% +you still have coolant come out of the + + + align:start position:0% +you still have coolant come out of the +hole out of the hole but the bypass + + align:start position:0% +hole out of the hole but the bypass + + + align:start position:0% +hole out of the hole but the bypass +basically is in in the in the core + + align:start position:0% +basically is in in the in the core + + + align:start position:0% +basically is in in the in the core +you'll have certain bypass paths but you + + align:start position:0% +you'll have certain bypass paths but you + + + align:start position:0% +you'll have certain bypass paths but you +will be essentially beginning to inject + + align:start position:0% +will be essentially beginning to inject + + + align:start position:0% +will be essentially beginning to inject +coolant in 26 seconds after you have + + align:start position:0% +coolant in 26 seconds after you have + + + align:start position:0% +coolant in 26 seconds after you have +this major pipe + + align:start position:0% +this major pipe + + + align:start position:0% +this major pipe +rate now one of the things you also need + + align:start position:0% +rate now one of the things you also need + + + align:start position:0% +rate now one of the things you also need +to look at is the containment you + + align:start position:0% +to look at is the containment you + + + align:start position:0% +to look at is the containment you +calculate the nree volume in the + + align:start position:0% +calculate the nree volume in the + + + align:start position:0% +calculate the nree volume in the +containment you look at the initial + + align:start position:0% +containment you look at the initial + + + align:start position:0% +containment you look at the initial +pressure temperature reactor water + + align:start position:0% +pressure temperature reactor water + + + align:start position:0% +pressure temperature reactor water +storage tank pressure Rea react to + + align:start position:0% +storage tank pressure Rea react to + + + align:start position:0% +storage tank pressure Rea react to +fueling refueling water storage tank + + align:start position:0% +fueling refueling water storage tank + + + align:start position:0% +fueling refueling water storage tank +temperature which is a source of your + + align:start position:0% +temperature which is a source of your + + + align:start position:0% +temperature which is a source of your +cooling water for the core what your + + align:start position:0% +cooling water for the core what your + + + align:start position:0% +cooling water for the core what your +outside temperature is and humidity + + align:start position:0% +outside temperature is and humidity + + + align:start position:0% +outside temperature is and humidity +number of spray pumps operating and so + + align:start position:0% +number of spray pumps operating and so + + + align:start position:0% +number of spray pumps operating and so +forth in in the U in the containment it + + align:start position:0% +forth in in the U in the containment it + + + align:start position:0% +forth in in the U in the containment it +also has what we call structural heat + + align:start position:0% +also has what we call structural heat + + + align:start position:0% +also has what we call structural heat +sinks they try to calculate the mass of + + align:start position:0% +sinks they try to calculate the mass of + + + align:start position:0% +sinks they try to calculate the mass of +material in the containment that can + + align:start position:0% +material in the containment that can + + + align:start position:0% +material in the containment that can +absorb this heat such that you can + + align:start position:0% +absorb this heat such that you can + + + align:start position:0% +absorb this heat such that you can +properly size the amount of heat removal + + align:start position:0% +properly size the amount of heat removal + + + align:start position:0% +properly size the amount of heat removal +and the sizing of your containment + + align:start position:0% +and the sizing of your containment + + + align:start position:0% +and the sizing of your containment +sprays now these these are the results + + align:start position:0% +sprays now these these are the results + + + align:start position:0% +sprays now these these are the results +that this particular + + align:start position:0% +that this particular + + + align:start position:0% +that this particular +transient uh created the peak clad + + align:start position:0% +transient uh created the peak clad + + + align:start position:0% +transient uh created the peak clad +temperature was 2148 degrees F very very + + align:start position:0% +temperature was 2148 degrees F very very + + + align:start position:0% +temperature was 2148 degrees F very very +close to the uh limit of 2200 lb the + + align:start position:0% +close to the uh limit of 2200 lb the + + + align:start position:0% +close to the uh limit of 2200 lb the +peak glad location above the bottom this + + align:start position:0% +peak glad location above the bottom this + + + align:start position:0% +peak glad location above the bottom this +zirconium hydrogen reaction rate where + + align:start position:0% +zirconium hydrogen reaction rate where + + + align:start position:0% +zirconium hydrogen reaction rate where +it occurred obviously about the same + + align:start position:0% +it occurred obviously about the same + + + align:start position:0% +it occurred obviously about the same +place the percentage + + align:start position:0% +place the percentage + + + align:start position:0% +place the percentage +reaction the hot rod burst time in + + align:start position:0% +reaction the hot rod burst time in + + + align:start position:0% +reaction the hot rod burst time in +second clearly there was some fuel + + align:start position:0% +second clearly there was some fuel + + + align:start position:0% +second clearly there was some fuel +failure here which isn't which is not uh + + align:start position:0% +failure here which isn't which is not uh + + + align:start position:0% +failure here which isn't which is not uh +you know you can have fuel failure and + + align:start position:0% +you know you can have fuel failure and + + + align:start position:0% +you know you can have fuel failure and +you do have fuel failure and it occurred + + align:start position:0% +you do have fuel failure and it occurred + + + align:start position:0% +you do have fuel failure and it occurred +in 21 seconds and and obviously at that + + align:start position:0% +in 21 seconds and and obviously at that + + + align:start position:0% +in 21 seconds and and obviously at that +location so the calculations basically + + align:start position:0% +location so the calculations basically + + + align:start position:0% +location so the calculations basically +started at these levels 3,400 megaw + + align:start position:0% +started at these levels 3,400 megaw + + + align:start position:0% +started at these levels 3,400 megaw +thermal linear heat rate roughly of 12 + + align:start position:0% +thermal linear heat rate roughly of 12 + + + align:start position:0% +thermal linear heat rate roughly of 12 +peaking factor for the core we've gone + + align:start position:0% +peaking factor for the core we've gone + + + align:start position:0% +peaking factor for the core we've gone +over that the 3D Peak was 2 three and + + align:start position:0% +over that the 3D Peak was 2 three and + + + align:start position:0% +over that the 3D Peak was 2 three and +here's the volume of the + + align:start position:0% +here's the volume of the + + + align:start position:0% +here's the volume of the +accumulator so what this analysis + + align:start position:0% +accumulator so what this analysis + + + align:start position:0% +accumulator so what this analysis +basically shows they they just barely + + align:start position:0% +basically shows they they just barely + + + align:start position:0% +basically shows they they just barely +made the limit for varying pipe brake + + align:start position:0% +made the limit for varying pipe brake + + + align:start position:0% +made the limit for varying pipe brake +sizes and pipe brake location but you + + align:start position:0% +sizes and pipe brake location but you + + + align:start position:0% +sizes and pipe brake location but you +can see the difference between a + + align:start position:0% +can see the difference between a + + + align:start position:0% +can see the difference between a +double-ended Guillotine break and a 60% + + align:start position:0% +double-ended Guillotine break and a 60% + + + align:start position:0% +double-ended Guillotine break and a 60% +Guillotine break was a very small + + align:start position:0% +Guillotine break was a very small + + + align:start position:0% +Guillotine break was a very small +temperature which should have given + + align:start position:0% +temperature which should have given + + + align:start position:0% +temperature which should have given +people an indication that perhaps + + align:start position:0% +people an indication that perhaps + + + align:start position:0% +people an indication that perhaps +smaller brakes aren't necessarily as + + align:start position:0% +smaller brakes aren't necessarily as + + + align:start position:0% +smaller brakes aren't necessarily as +benign as people thought + + align:start position:0% +benign as people thought + + + align:start position:0% +benign as people thought +now this is a couple of charts of the uh + + align:start position:0% +now this is a couple of charts of the uh + + + align:start position:0% +now this is a couple of charts of the uh +Power profile and other key parameters + + align:start position:0% +Power profile and other key parameters + + + align:start position:0% +Power profile and other key parameters +during this event clearly as you can see + + align:start position:0% +during this event clearly as you can see + + + align:start position:0% +during this event clearly as you can see +when you shut the reactor down the power + + align:start position:0% +when you shut the reactor down the power + + + align:start position:0% +when you shut the reactor down the power +goes down to more or less it's asmic to + + align:start position:0% +goes down to more or less it's asmic to + + + align:start position:0% +goes down to more or less it's asmic to +K value in a very very short time + + align:start position:0% +K value in a very very short time + + + align:start position:0% +K value in a very very short time +seconds couple of seconds one second but + + align:start position:0% +seconds couple of seconds one second but + + + align:start position:0% +seconds couple of seconds one second but +it stays at roughly the 7% so power + + align:start position:0% +it stays at roughly the 7% so power + + + align:start position:0% +it stays at roughly the 7% so power +which is right here is the problem we + + align:start position:0% +which is right here is the problem we + + + align:start position:0% +which is right here is the problem we +need to remove this he + + align:start position:0% +need to remove this he + + + align:start position:0% +need to remove this he +the if you look at the flow from the + + align:start position:0% +the if you look at the flow from the + + + align:start position:0% +the if you look at the flow from the +brake you can see it goes up pretty fast + + align:start position:0% +brake you can see it goes up pretty fast + + + align:start position:0% +brake you can see it goes up pretty fast +and then gradually within a few seconds + + align:start position:0% +and then gradually within a few seconds + + + align:start position:0% +and then gradually within a few seconds +it goes down to zero probably 25 seconds + + align:start position:0% +it goes down to zero probably 25 seconds + + + align:start position:0% +it goes down to zero probably 25 seconds +it's done all the water is out of the + + align:start position:0% +it's done all the water is out of the + + + align:start position:0% +it's done all the water is out of the +core of course + + align:start position:0% +core of course + + + align:start position:0% +core of course +essential if you look at the pressure in + + align:start position:0% +essential if you look at the pressure in + + + align:start position:0% +essential if you look at the pressure in +the coolant system you can see it + + align:start position:0% +the coolant system you can see it + + + align:start position:0% +the coolant system you can see it +started somewhat below 2,000 lb when the + + align:start position:0% +started somewhat below 2,000 lb when the + + + align:start position:0% +started somewhat below 2,000 lb when the +break occurred and gradually came down + + align:start position:0% +break occurred and gradually came down + + + align:start position:0% +break occurred and gradually came down +to say a few atmospheric pressure pounds + + align:start position:0% +to say a few atmospheric pressure pounds + + + align:start position:0% +to say a few atmospheric pressure pounds +in roughly 25 seconds a very rapid High + + align:start position:0% +in roughly 25 seconds a very rapid High + + + align:start position:0% +in roughly 25 seconds a very rapid High +energetic blowdown what this chart shows + + align:start position:0% +energetic blowdown what this chart shows + + + align:start position:0% +energetic blowdown what this chart shows +the water level in the + + align:start position:0% +the water level in the + + + align:start position:0% +the water level in the +core where within um let's just say 30 + + align:start position:0% +core where within um let's just say 30 + + + align:start position:0% +core where within um let's just say 30 +seconds it's empty or very very low and + + align:start position:0% +seconds it's empty or very very low and + + + align:start position:0% +seconds it's empty or very very low and +gradually it begins to fill up in the + + align:start position:0% +gradually it begins to fill up in the + + + align:start position:0% +gradually it begins to fill up in the +core but this is the area of + + align:start position:0% +core but this is the area of + + + align:start position:0% +core but this is the area of +vulnerability because remember core + + align:start position:0% +vulnerability because remember core + + + align:start position:0% +vulnerability because remember core +height is roughly 12 12 ft so the core + + align:start position:0% +height is roughly 12 12 ft so the core + + + align:start position:0% +height is roughly 12 12 ft so the core +is covered for a period of time and + + align:start position:0% +is covered for a period of time and + + + align:start position:0% +is covered for a period of time and +gradually begins to Reflow and during + + align:start position:0% +gradually begins to Reflow and during + + + align:start position:0% +gradually begins to Reflow and during +this period you'll obviously be getting + + align:start position:0% +this period you'll obviously be getting + + + align:start position:0% +this period you'll obviously be getting +some fuel + + align:start position:0% +some fuel + + + align:start position:0% +some fuel +failures this is the peak clad + + align:start position:0% +failures this is the peak clad + + + align:start position:0% +failures this is the peak clad +temperature at various locations as a + + align:start position:0% +temperature at various locations as a + + + align:start position:0% +temperature at various locations as a +function of time you can see initially + + align:start position:0% +function of time you can see initially + + + align:start position:0% +function of time you can see initially +with the accumulator function it brings + + align:start position:0% +with the accumulator function it brings + + + align:start position:0% +with the accumulator function it brings +the temperature down once it's done the + + align:start position:0% +the temperature down once it's done the + + + align:start position:0% +the temperature down once it's done the +temperature continues to rise since the + + align:start position:0% +temperature continues to rise since the + + + align:start position:0% +temperature continues to rise since the +core is uncovered at 7 and 1 12 ft and + + align:start position:0% +core is uncovered at 7 and 1 12 ft and + + + align:start position:0% +core is uncovered at 7 and 1 12 ft and +approaches this limit value which + + align:start position:0% +approaches this limit value which + + + align:start position:0% +approaches this limit value which +ultimately when water gets up and begins + + align:start position:0% +ultimately when water gets up and begins + + + align:start position:0% +ultimately when water gets up and begins +to refill pulls down the uh the fuel in + + align:start position:0% +to refill pulls down the uh the fuel in + + + align:start position:0% +to refill pulls down the uh the fuel in +that particular area you'll also see at + + align:start position:0% +that particular area you'll also see at + + + align:start position:0% +that particular area you'll also see at +a different location the the peak clad + + align:start position:0% +a different location the the peak clad + + + align:start position:0% +a different location the the peak clad +temperature goes up pretty high now why + + align:start position:0% +temperature goes up pretty high now why + + + align:start position:0% +temperature goes up pretty high now why +this occurs you get a double Peak I'm + + align:start position:0% +this occurs you get a double Peak I'm + + + align:start position:0% +this occurs you get a double Peak I'm +not exactly sure but if you go back and + + align:start position:0% +not exactly sure but if you go back and + + + align:start position:0% +not exactly sure but if you go back and +look at the analysis you'll be able to + + align:start position:0% +look at the analysis you'll be able to + + + align:start position:0% +look at the analysis you'll be able to +see that at this location you might have + + align:start position:0% +see that at this location you might have + + + align:start position:0% +see that at this location you might have +had uh some other kind of core + + align:start position:0% +had uh some other kind of core + + + align:start position:0% +had uh some other kind of core +uncovering that lower + + align:start position:0% +uncovering that lower + + + align:start position:0% +uncovering that lower +core uh this is a containment pressure + + align:start position:0% +core uh this is a containment pressure + + + align:start position:0% +core uh this is a containment pressure +spike you can see very quickly the + + align:start position:0% +spike you can see very quickly the + + + align:start position:0% +spike you can see very quickly the +reactor Tri on containment pressure and + + align:start position:0% +reactor Tri on containment pressure and + + + align:start position:0% +reactor Tri on containment pressure and +it kept going up going up until the + + align:start position:0% +it kept going up going up until the + + + align:start position:0% +it kept going up going up until the +containment sprays got on then gradually + + align:start position:0% +containment sprays got on then gradually + + + align:start position:0% +containment sprays got on then gradually +the containment pressure went down you + + align:start position:0% +the containment pressure went down you + + + align:start position:0% +the containment pressure went down you +can see in this double end Guillotine + + align:start position:0% +can see in this double end Guillotine + + + align:start position:0% +can see in this double end Guillotine +break pressure was around 20 22 to 25 + + align:start position:0% +break pressure was around 20 22 to 25 + + + align:start position:0% +break pressure was around 20 22 to 25 +psi this chart is a is a is a very + + align:start position:0% +psi this chart is a is a is a very + + + align:start position:0% +psi this chart is a is a is a very +complete chart of of what's going on in + + align:start position:0% +complete chart of of what's going on in + + + align:start position:0% +complete chart of of what's going on in +the core as a function of time and + + align:start position:0% +the core as a function of time and + + + align:start position:0% +the core as a function of time and +seconds this is in seconds so let's + + align:start position:0% +seconds this is in seconds so let's + + + align:start position:0% +seconds this is in seconds so let's +let's kind of pick a uh a number here + + align:start position:0% +let's kind of pick a uh a number here + + + align:start position:0% +let's kind of pick a uh a number here +let's identify the top of the core and + + align:start position:0% +let's identify the top of the core and + + + align:start position:0% +let's identify the top of the core and +the bottom of the core and if this is + + align:start position:0% +the bottom of the core and if this is + + + align:start position:0% +the bottom of the core and if this is +the pressure line essentially the + + align:start position:0% +the pressure line essentially the + + + align:start position:0% +the pressure line essentially the +blowdown is done within I guess probably + + align:start position:0% +blowdown is done within I guess probably + + + align:start position:0% +blowdown is done within I guess probably +25 seconds the earlier chart show and + + align:start position:0% +25 seconds the earlier chart show and + + + align:start position:0% +25 seconds the earlier chart show and +this is the essentially the liquid + + align:start position:0% +this is the essentially the liquid + + + align:start position:0% +this is the essentially the liquid +volume in the core so you're essentially + + align:start position:0% +volume in the core so you're essentially + + + align:start position:0% +volume in the core so you're essentially +uncovered from roughly seven or 8 + + align:start position:0% +uncovered from roughly seven or 8 + + + align:start position:0% +uncovered from roughly seven or 8 +seconds and you begin to cover the core + + align:start position:0% +seconds and you begin to cover the core + + + align:start position:0% +seconds and you begin to cover the core +in about 18 seconds and you cover the + + align:start position:0% +in about 18 seconds and you cover the + + + align:start position:0% +in about 18 seconds and you cover the +core in about 30 seconds so the core has + + align:start position:0% +core in about 30 seconds so the core has + + + align:start position:0% +core in about 30 seconds so the core has +been uncovered for relative + + align:start position:0% +been uncovered for relative + + + align:start position:0% +been uncovered for relative +say 20 or so seconds and during this + + align:start position:0% +say 20 or so seconds and during this + + + align:start position:0% +say 20 or so seconds and during this +time whatever fuel failure occurs will + + align:start position:0% +time whatever fuel failure occurs will + + + align:start position:0% +time whatever fuel failure occurs will +be occurring but once it's filled it + + align:start position:0% +be occurring but once it's filled it + + + align:start position:0% +be occurring but once it's filled it +pretty much + + align:start position:0% +pretty much + + + align:start position:0% +pretty much +stabilizes now this is + + align:start position:0% +stabilizes now this is + + + align:start position:0% +stabilizes now this is +again another chart of the peak + + align:start position:0% +again another chart of the peak + + + align:start position:0% +again another chart of the peak +temperature and the peak CL temperature + + align:start position:0% +temperature and the peak CL temperature + + + align:start position:0% +temperature and the peak CL temperature +which shows a number of small Peaks now + + align:start position:0% +which shows a number of small Peaks now + + + align:start position:0% +which shows a number of small Peaks now +this is probably + + align:start position:0% +this is probably + + + align:start position:0% +this is probably +accumulator uh not exactly sure why this + + align:start position:0% +accumulator uh not exactly sure why this + + + align:start position:0% +accumulator uh not exactly sure why this +goes up and goes down but there must + + align:start position:0% +goes up and goes down but there must + + + align:start position:0% +goes up and goes down but there must +have been some other water injection + + align:start position:0% +have been some other water injection + + + align:start position:0% +have been some other water injection +here and then it sort of Peaks and then + + align:start position:0% +here and then it sort of Peaks and then + + + align:start position:0% +here and then it sort of Peaks and then +stabiliz probably + + align:start position:0% +stabiliz probably + + + align:start position:0% +stabiliz probably +Transit + + align:start position:0% +Transit + + + align:start position:0% +Transit +um but again we're talking seconds + + align:start position:0% +um but again we're talking seconds + + + align:start position:0% +um but again we're talking seconds +things go really really fast in in light + + align:start position:0% +things go really really fast in in light + + + align:start position:0% +things go really really fast in in light +water + + align:start position:0% +water + + + align:start position:0% +water +reactors now what these next few charts + + align:start position:0% +reactors now what these next few charts + + + align:start position:0% +reactors now what these next few charts +basically are are available to you I put + + align:start position:0% +basically are are available to you I put + + + align:start position:0% +basically are are available to you I put +them on on the on the on the on the + + align:start position:0% +them on on the on the on the on the + + + align:start position:0% +them on on the on the on the on the +handout sheet is a + + align:start position:0% +handout sheet is a + + + align:start position:0% +handout sheet is a +description of what occurs and this is + + align:start position:0% +description of what occurs and this is + + + align:start position:0% +description of what occurs and this is +in the + + align:start position:0% +in the + + + align:start position:0% +in the +fsar what occurs and what is the verbal + + align:start position:0% +fsar what occurs and what is the verbal + + + align:start position:0% +fsar what occurs and what is the verbal +description of what happens in this + + align:start position:0% +description of what happens in this + + + align:start position:0% +description of what happens in this +trans + + align:start position:0% +trans + + + align:start position:0% +trans +and I'm just going to put them in the in + + align:start position:0% +and I'm just going to put them in the in + + + align:start position:0% +and I'm just going to put them in the in +the handout so you'll get a sense and + + align:start position:0% +the handout so you'll get a sense and + + + align:start position:0% +the handout so you'll get a sense and +read it through once you go back and + + align:start position:0% +read it through once you go back and + + + align:start position:0% +read it through once you go back and +look at some of these charts you can + + align:start position:0% +look at some of these charts you can + + + align:start position:0% +look at some of these charts you can +then begin to understand the depth of + + align:start position:0% +then begin to understand the depth of + + + align:start position:0% +then begin to understand the depth of +the analysis and the results that that + + align:start position:0% +the analysis and the results that that + + + align:start position:0% +the analysis and the results that that +come from that particular analysis + + align:start position:0% +come from that particular analysis + + + align:start position:0% +come from that particular analysis +there's an awful lot of work that goes + + align:start position:0% +there's an awful lot of work that goes + + + align:start position:0% +there's an awful lot of work that goes +into this very sophisticated + + align:start position:0% +into this very sophisticated + + + align:start position:0% +into this very sophisticated +thermohydraulic modeling core modeling + + align:start position:0% +thermohydraulic modeling core modeling + + + align:start position:0% +thermohydraulic modeling core modeling +therm hydraulic modeling of the reactor + + align:start position:0% +therm hydraulic modeling of the reactor + + + align:start position:0% +therm hydraulic modeling of the reactor +the containment system all the energy + + align:start position:0% +the containment system all the energy + + + align:start position:0% +the containment system all the energy +absorbing systems are available in the + + align:start position:0% +absorbing systems are available in the + + + align:start position:0% +absorbing systems are available in the +containment so you have uh I think at + + align:start position:0% +containment so you have uh I think at + + + align:start position:0% +containment so you have uh I think at +least one record of what are the key + + align:start position:0% +least one record of what are the key + + + align:start position:0% +least one record of what are the key +parameters and what might one think + + align:start position:0% +parameters and what might one think + + + align:start position:0% +parameters and what might one think +about when + + align:start position:0% +about when + + + align:start position:0% +about when +one analyzes this event and you can see + + align:start position:0% +one analyzes this event and you can see + + + align:start position:0% +one analyzes this event and you can see +the conclusions of the thermal analysis + + align:start position:0% +the conclusions of the thermal analysis + + + align:start position:0% +the conclusions of the thermal analysis +they they basically say they meet the + + align:start position:0% +they they basically say they meet the + + + align:start position:0% +they they basically say they meet the +acceptance criteria P flag temperature + + align:start position:0% +acceptance criteria P flag temperature + + + align:start position:0% +acceptance criteria P flag temperature +does not exceed that and they show that + + align:start position:0% +does not exceed that and they show that + + + align:start position:0% +does not exceed that and they show that +the four criteria that I mentioned are + + align:start position:0% +the four criteria that I mentioned are + + + align:start position:0% +the four criteria that I mentioned are +able to be met therefore they have + + align:start position:0% +able to be met therefore they have + + + align:start position:0% +able to be met therefore they have +addressed the general design criteria as + + align:start position:0% +addressed the general design criteria as + + + align:start position:0% +addressed the general design criteria as +it relates to L law of + + align:start position:0% +it relates to L law of + + + align:start position:0% +it relates to L law of +call now I've gone over this relatively + + align:start position:0% +call now I've gone over this relatively + + + align:start position:0% +call now I've gone over this relatively +fast uh the homework is going to be + + align:start position:0% +fast uh the homework is going to be + + + align:start position:0% +fast uh the homework is going to be +reading chapter 14 and Neath these are + + align:start position:0% +reading chapter 14 and Neath these are + + + align:start position:0% +reading chapter 14 and Neath these are +the problems in 14 chapter 14 9 11 12 21 + + align:start position:0% +the problems in 14 chapter 14 9 11 12 21 + + + align:start position:0% +the problems in 14 chapter 14 9 11 12 21 +and + + align:start position:0% +and + + + align:start position:0% +and +23 what I want you to get out of this + + align:start position:0% +23 what I want you to get out of this + + + align:start position:0% +23 what I want you to get out of this +lecture basically is is a couple of of + + align:start position:0% +lecture basically is is a couple of of + + + align:start position:0% +lecture basically is is a couple of of +key points Decay heat is really + + align:start position:0% +key points Decay heat is really + + + align:start position:0% +key points Decay heat is really +important the safety of the plant is not + + align:start position:0% +important the safety of the plant is not + + + align:start position:0% +important the safety of the plant is not +assured as soon as it shuts down the + + align:start position:0% +assured as soon as it shuts down the + + + align:start position:0% +assured as soon as it shuts down the +fact that you need emergency core + + align:start position:0% +fact that you need emergency core + + + align:start position:0% +fact that you need emergency core +cooling systems to manage only the Decay + + align:start position:0% +cooling systems to manage only the Decay + + + align:start position:0% +cooling systems to manage only the Decay +heat and that's most people don't + + align:start position:0% +heat and that's most people don't + + + align:start position:0% +heat and that's most people don't +realize that but that's where the + + align:start position:0% +realize that but that's where the + + + align:start position:0% +realize that but that's where the +problems are the emergency core cooling + + align:start position:0% +problems are the emergency core cooling + + + align:start position:0% +problems are the emergency core cooling +systems are robustly + + align:start position:0% +systems are robustly + + + align:start position:0% +systems are robustly +designed uh we didn't get into the + + align:start position:0% +designed uh we didn't get into the + + + align:start position:0% +designed uh we didn't get into the +redundancy and how many trains of + + align:start position:0% +redundancy and how many trains of + + + align:start position:0% +redundancy and how many trains of +emergency core cooling system are there + + align:start position:0% +emergency core cooling system are there + + + align:start position:0% +emergency core cooling system are there +could be two three some plants have four + + align:start position:0% +could be two three some plants have four + + + align:start position:0% +could be two three some plants have four +trains which means four independent + + align:start position:0% +trains which means four independent + + + align:start position:0% +trains which means four independent +systems to provide cooling water to the + + align:start position:0% +systems to provide cooling water to the + + + align:start position:0% +systems to provide cooling water to the +uh core and then understanding that it's + + align:start position:0% +uh core and then understanding that it's + + + align:start position:0% +uh core and then understanding that it's +not just keeping the core cooled but + + align:start position:0% +not just keeping the core cooled but + + + align:start position:0% +not just keeping the core cooled but +it's keeping the containment cooled that + + align:start position:0% +it's keeping the containment cooled that + + + align:start position:0% +it's keeping the containment cooled that +is really important because you really + + align:start position:0% +is really important because you really + + + align:start position:0% +is really important because you really +want to keep that containment intact so + + align:start position:0% +want to keep that containment intact so + + + align:start position:0% +want to keep that containment intact so +that there's no release even though + + align:start position:0% +that there's no release even though + + + align:start position:0% +that there's no release even though +there might be a mess inside that's + + align:start position:0% +there might be a mess inside that's + + + align:start position:0% +there might be a mess inside that's +Three Mile Island show it was all + + align:start position:0% +Three Mile Island show it was all + + + align:start position:0% +Three Mile Island show it was all +essentially contained and in order to do + + align:start position:0% +essentially contained and in order to do + + + align:start position:0% +essentially contained and in order to do +that you got to keep adding heat you had + + align:start position:0% +that you got to keep adding heat you had + + + align:start position:0% +that you got to keep adding heat you had +to keep you got to keep removing heat + + align:start position:0% +to keep you got to keep removing heat + + + align:start position:0% +to keep you got to keep removing heat +from the containment continuing to flow + + align:start position:0% +from the containment continuing to flow + + + align:start position:0% +from the containment continuing to flow +cooling over the core for a long period + + align:start position:0% +cooling over the core for a long period + + + align:start position:0% +cooling over the core for a long period +of time until the core ultimately cools + + align:start position:0% +of time until the core ultimately cools + + + align:start position:0% +of time until the core ultimately cools +down uh the the other message is the + + align:start position:0% +down uh the the other message is the + + + align:start position:0% +down uh the the other message is the +analysis to justifi these so-called + + align:start position:0% +analysis to justifi these so-called + + + align:start position:0% +analysis to justifi these so-called +design basis accidents is exhaustive the + + align:start position:0% +design basis accidents is exhaustive the + + + align:start position:0% +design basis accidents is exhaustive the +transients that have been identified uh + + align:start position:0% +transients that have been identified uh + + + align:start position:0% +transients that have been identified uh +in in the FSS in chapter 15 all need + + align:start position:0% +in in the FSS in chapter 15 all need + + + align:start position:0% +in in the FSS in chapter 15 all need +special analysis and special + + align:start position:0% +special analysis and special + + + align:start position:0% +special analysis and special +understanding and modeling to be able to + + align:start position:0% +understanding and modeling to be able to + + + align:start position:0% +understanding and modeling to be able to +understand what happens if this occurs + + align:start position:0% +understand what happens if this occurs + + + align:start position:0% +understand what happens if this occurs +and then that occurs the single failure + + align:start position:0% +and then that occurs the single failure + + + align:start position:0% +and then that occurs the single failure +criter IA is a very important criteria + + align:start position:0% +criter IA is a very important criteria + + + align:start position:0% +criter IA is a very important criteria +for deterministic analysis but there are + + align:start position:0% +for deterministic analysis but there are + + + align:start position:0% +for deterministic analysis but there are +many people in in the risk assessment + + align:start position:0% +many people in in the risk assessment + + + align:start position:0% +many people in in the risk assessment +community that argue that in doing a p + + align:start position:0% +community that argue that in doing a p + + + align:start position:0% +community that argue that in doing a p +you don't have to assume single failure + + align:start position:0% +you don't have to assume single failure + + + align:start position:0% +you don't have to assume single failure +which is still a very debatable + + align:start position:0% +which is still a very debatable + + + align:start position:0% +which is still a very debatable +debatable question because in pasas it + + align:start position:0% +debatable question because in pasas it + + + align:start position:0% +debatable question because in pasas it +provides you with a lot of additional + + align:start position:0% +provides you with a lot of additional + + + align:start position:0% +provides you with a lot of additional +information and assumes that everything + + align:start position:0% +information and assumes that everything + + + align:start position:0% +information and assumes that everything +can fail but you're also taking credit + + align:start position:0% +can fail but you're also taking credit + + + align:start position:0% +can fail but you're also taking credit +for systems that are not necessarily + + align:start position:0% +for systems that are not necessarily + + + align:start position:0% +for systems that are not necessarily +safety related systems or safety grade + + align:start position:0% +safety related systems or safety grade + + + align:start position:0% +safety related systems or safety grade +systems so hopefully these are the key + + align:start position:0% +systems so hopefully these are the key + + + align:start position:0% +systems so hopefully these are the key +mess messages that you get out of this + + align:start position:0% +mess messages that you get out of this + + + align:start position:0% +mess messages that you get out of this +lecture and uh the homework you + + align:start position:0% +lecture and uh the homework you + + + align:start position:0% +lecture and uh the homework you +hopefully uh elicit um perhaps more + + align:start position:0% +hopefully uh elicit um perhaps more + + + align:start position:0% +hopefully uh elicit um perhaps more +questions what I would highly recommend + + align:start position:0% +questions what I would highly recommend + + + align:start position:0% +questions what I would highly recommend +is you go and look at a final safety + + align:start position:0% +is you go and look at a final safety + + + align:start position:0% +is you go and look at a final safety +analysis report I know the NRC in recent + + align:start position:0% +analysis report I know the NRC in recent + + + align:start position:0% +analysis report I know the NRC in recent +times has pulled a lot of those off the + + align:start position:0% +times has pulled a lot of those off the + + + align:start position:0% +times has pulled a lot of those off the +internet but you might have in your + + align:start position:0% +internet but you might have in your + + + align:start position:0% +internet but you might have in your +local library perhaps in a nuclear + + align:start position:0% +local library perhaps in a nuclear + + + align:start position:0% +local library perhaps in a nuclear +engineering Library copies of old + + align:start position:0% +engineering Library copies of old + + + align:start position:0% +engineering Library copies of old +FSS uh we have have several at uh at the + + align:start position:0% +FSS uh we have have several at uh at the + + + align:start position:0% +FSS uh we have have several at uh at the +MIT nuclear engineering Library where + + align:start position:0% +MIT nuclear engineering Library where + + + align:start position:0% +MIT nuclear engineering Library where +you can kind of see the depth of the + + align:start position:0% +you can kind of see the depth of the + + + align:start position:0% +you can kind of see the depth of the +analysis the codes that they're used + + align:start position:0% +analysis the codes that they're used + + + align:start position:0% +analysis the codes that they're used +because it's it is it is difficult to to + + align:start position:0% +because it's it is it is difficult to to + + + align:start position:0% +because it's it is it is difficult to to +demonstrate uh the safety of these + + align:start position:0% +demonstrate uh the safety of these + + + align:start position:0% +demonstrate uh the safety of these +plants uh and we need very highly train + + align:start position:0% +plants uh and we need very highly train + + + align:start position:0% +plants uh and we need very highly train +people to do that okay if there + + align:start position:0% +people to do that okay if there + + + align:start position:0% +people to do that okay if there +hopefully you'll have some questions for + + align:start position:0% +hopefully you'll have some questions for + + + align:start position:0% +hopefully you'll have some questions for +your professor and um we look to see you + + align:start position:0% +your professor and um we look to see you + + + align:start position:0% +your professor and um we look to see you +next time thank you \ No newline at end of file diff --git a/YVHM8dSkimo.txt b/YVHM8dSkimo.txt new file mode 100644 index 0000000000000000000000000000000000000000..f17d5ad70dd5bb561d9b254ae2adc2d8864ea1f8 --- /dev/null +++ b/YVHM8dSkimo.txt @@ -0,0 +1,16211 @@ +align:start position:0% + +all right okay so let's start with we're + + align:start position:0% +all right okay so let's start with we're + + + align:start position:0% +all right okay so let's start with we're +talking about music today which is fun + + align:start position:0% +talking about music today which is fun + + + align:start position:0% +talking about music today which is fun +and awesome but first let me give you a + + align:start position:0% +and awesome but first let me give you a + + + align:start position:0% +and awesome but first let me give you a +brief whirlwind + + align:start position:0% +brief whirlwind + + + align:start position:0% +brief whirlwind +reminder of what we did last time we + + align:start position:0% +reminder of what we did last time we + + + align:start position:0% +reminder of what we did last time we +talked about hearing in general and + + align:start position:0% +talked about hearing in general and + + + align:start position:0% +talked about hearing in general and +speech in particular + + align:start position:0% +speech in particular + + + align:start position:0% +speech in particular +and we started as usual with + + align:start position:0% +and we started as usual with + + + align:start position:0% +and we started as usual with +computational theory thinking about what + + align:start position:0% +computational theory thinking about what + + + align:start position:0% +computational theory thinking about what +is the problem of audition + + align:start position:0% +is the problem of audition + + + align:start position:0% +is the problem of audition +and what is sound that's the first step + + align:start position:0% +and what is sound that's the first step + + + align:start position:0% +and what is sound that's the first step +of that sound is pressure waves + + align:start position:0% +of that sound is pressure waves + + + align:start position:0% +of that sound is pressure waves +traveling through the air + + align:start position:0% +traveling through the air + + + align:start position:0% +traveling through the air +and the cool thing about hearing is that + + align:start position:0% +and the cool thing about hearing is that + + + align:start position:0% +and the cool thing about hearing is that +we extract lots of information from this + + align:start position:0% +we extract lots of information from this + + + align:start position:0% +we extract lots of information from this +very very simple signal of pressure + + align:start position:0% +very very simple signal of pressure + + + align:start position:0% +very very simple signal of pressure +waves arriving at the ear we use it to + + align:start position:0% +waves arriving at the ear we use it to + + + align:start position:0% +waves arriving at the ear we use it to +recognize sounds to + + align:start position:0% +recognize sounds to + + + align:start position:0% +recognize sounds to +localize sounds to figure out what + + align:start position:0% +localize sounds to figure out what + + + align:start position:0% +localize sounds to figure out what +things are made of and to understand + + align:start position:0% +things are made of and to understand + + + align:start position:0% +things are made of and to understand +events around us and all kinds of things + + align:start position:0% +events around us and all kinds of things + + + align:start position:0% +events around us and all kinds of things +and these problems are a major + + align:start position:0% +and these problems are a major + + + align:start position:0% +and these problems are a major +computational challenge + + align:start position:0% +computational challenge + + + align:start position:0% +computational challenge +and in particular they are ill-posed + + align:start position:0% +and in particular they are ill-posed + + + align:start position:0% +and in particular they are ill-posed +that means that + + align:start position:0% +that means that + + + align:start position:0% +that means that +the available information doesn't give + + align:start position:0% +the available information doesn't give + + + align:start position:0% +the available information doesn't give +you a unique solution if you consider + + align:start position:0% +you a unique solution if you consider + + + align:start position:0% +you a unique solution if you consider +the computational problem narrowly and + + align:start position:0% +the computational problem narrowly and + + + align:start position:0% +the computational problem narrowly and +that's true for separating sound sources + + align:start position:0% +that's true for separating sound sources + + + align:start position:0% +that's true for separating sound sources +so if you have two sound sources at once + + align:start position:0% +so if you have two sound sources at once + + + align:start position:0% +so if you have two sound sources at once +to say two people speaking or a person + + align:start position:0% +to say two people speaking or a person + + + align:start position:0% +to say two people speaking or a person +speaking and a lot of background noise + + align:start position:0% +speaking and a lot of background noise + + + align:start position:0% +speaking and a lot of background noise +that's known as the cocktail party + + align:start position:0% +that's known as the cocktail party + + + align:start position:0% +that's known as the cocktail party +problem those sounds add on top of each + + align:start position:0% +problem those sounds add on top of each + + + align:start position:0% +problem those sounds add on top of each +other and there's no way to pull them + + align:start position:0% +other and there's no way to pull them + + + align:start position:0% +other and there's no way to pull them +apart without bringing in other + + align:start position:0% +apart without bringing in other + + + align:start position:0% +apart without bringing in other +information knowledge about the world or + + align:start position:0% +information knowledge about the world or + + + align:start position:0% +information knowledge about the world or +knowledge about the nature of voices or + + align:start position:0% +knowledge about the nature of voices or + + + align:start position:0% +knowledge about the nature of voices or +speaking or who's speaking or you need + + align:start position:0% +speaking or who's speaking or you need + + + align:start position:0% +speaking or who's speaking or you need +something else or else it's imposed that + + align:start position:0% +something else or else it's imposed that + + + align:start position:0% +something else or else it's imposed that +is not solvable just from the basic + + align:start position:0% +is not solvable just from the basic + + + align:start position:0% +is not solvable just from the basic +input + + align:start position:0% +input + + + align:start position:0% +input +another case of an old post problem in + + align:start position:0% +another case of an old post problem in + + + align:start position:0% +another case of an old post problem in +audition is the case of reverb so the + + align:start position:0% +audition is the case of reverb so the + + + align:start position:0% +audition is the case of reverb so the +sound that i'm making right now that's + + align:start position:0% +sound that i'm making right now that's + + + align:start position:0% +sound that i'm making right now that's +coming out my mouth is bouncing off the + + align:start position:0% +coming out my mouth is bouncing off the + + + align:start position:0% +coming out my mouth is bouncing off the +walls and is arriving at your ears over + + align:start position:0% +walls and is arriving at your ears over + + + align:start position:0% +walls and is arriving at your ears over +each little piece of sound that i make + + align:start position:0% +each little piece of sound that i make + + + align:start position:0% +each little piece of sound that i make +is arriving at different latencies after + + align:start position:0% +is arriving at different latencies after + + + align:start position:0% +is arriving at different latencies after +i say it as it travels different paths + + align:start position:0% +i say it as it travels different paths + + + align:start position:0% +i say it as it travels different paths +bouncing around the room and there's not + + align:start position:0% +bouncing around the room and there's not + + + align:start position:0% +bouncing around the room and there's not +too much reverb in here so it's not + + align:start position:0% +too much reverb in here so it's not + + + align:start position:0% +too much reverb in here so it's not +uh it's not that noticeable but if we + + align:start position:0% +uh it's not that noticeable but if we + + + align:start position:0% +uh it's not that noticeable but if we +did this in a cathedral you'd hear all + + align:start position:0% +did this in a cathedral you'd hear all + + + align:start position:0% +did this in a cathedral you'd hear all +these um echoes + + align:start position:0% +these um echoes + + + align:start position:0% +these um echoes +okay and so that makes another ill post + + align:start position:0% +okay and so that makes another ill post + + + align:start position:0% +okay and so that makes another ill post +problem because all of those different + + align:start position:0% +problem because all of those different + + + align:start position:0% +problem because all of those different +sounds are added on top of themselves + + align:start position:0% +sounds are added on top of themselves + + + align:start position:0% +sounds are added on top of themselves +diminished in volume over time and you + + align:start position:0% +diminished in volume over time and you + + + align:start position:0% +diminished in volume over time and you +get the sum of all of those and you have + + align:start position:0% +get the sum of all of those and you have + + + align:start position:0% +get the sum of all of those and you have +to pull it apart and figure out what + + align:start position:0% +to pull it apart and figure out what + + + align:start position:0% +to pull it apart and figure out what +that sound is + + align:start position:0% +that sound is + + + align:start position:0% +that sound is +so both problems are solved by using + + align:start position:0% +so both problems are solved by using + + + align:start position:0% +so both problems are solved by using +knowledge of the real world in the case + + align:start position:0% +knowledge of the real world in the case + + + align:start position:0% +knowledge of the real world in the case +of reverb it's actual implicit knowledge + + align:start position:0% +of reverb it's actual implicit knowledge + + + align:start position:0% +of reverb it's actual implicit knowledge +that you all have that you didn't know + + align:start position:0% +that you all have that you didn't know + + + align:start position:0% +that you all have that you didn't know +you have about the physics of reverb + + align:start position:0% +you have about the physics of reverb + + + align:start position:0% +you have about the physics of reverb +because if we play you sounds with the + + align:start position:0% +because if we play you sounds with the + + + align:start position:0% +because if we play you sounds with the +wrong physics of reverb you won't be + + align:start position:0% +wrong physics of reverb you won't be + + + align:start position:0% +wrong physics of reverb you won't be +able to deal with reverb and that says + + align:start position:0% +able to deal with reverb and that says + + + align:start position:0% +able to deal with reverb and that says +it's implicit knowledge in your head + + align:start position:0% +it's implicit knowledge in your head + + + align:start position:0% +it's implicit knowledge in your head +which is pretty cool that you use to + + align:start position:0% +which is pretty cool that you use to + + + align:start position:0% +which is pretty cool that you use to +constrain the opposed problem + + align:start position:0% +constrain the opposed problem + + + align:start position:0% +constrain the opposed problem +we talked about speech phonemes are + + align:start position:0% +we talked about speech phonemes are + + + align:start position:0% +we talked about speech phonemes are +sounds that distinguish two different + + align:start position:0% +sounds that distinguish two different + + + align:start position:0% +sounds that distinguish two different +words in a language like make and bake + + align:start position:0% +words in a language like make and bake + + + align:start position:0% +words in a language like make and bake +those are two different sounds that make + + align:start position:0% +those are two different sounds that make + + + align:start position:0% +those are two different sounds that make +the difference between two words each + + align:start position:0% +the difference between two words each + + + align:start position:0% +the difference between two words each +speech sound is um each possible speech + + align:start position:0% +speech sound is um each possible speech + + + align:start position:0% +speech sound is um each possible speech +sound is not a phoneme in every language + + align:start position:0% +sound is not a phoneme in every language + + + align:start position:0% +sound is not a phoneme in every language +of the world + + align:start position:0% +of the world + + + align:start position:0% +of the world +languages have some subset of the space + + align:start position:0% +languages have some subset of the space + + + align:start position:0% +languages have some subset of the space +of possible phonemes that distinguish + + align:start position:0% +of possible phonemes that distinguish + + + align:start position:0% +of possible phonemes that distinguish +words in their in their language + + align:start position:0% +words in their in their language + + + align:start position:0% +words in their in their language +phonemes include vowels that have these + + align:start position:0% +phonemes include vowels that have these + + + align:start position:0% +phonemes include vowels that have these +stacked harmonics of um in the in the + + align:start position:0% +stacked harmonics of um in the in the + + + align:start position:0% +stacked harmonics of um in the in the +spectrogram and consonants which are the + + align:start position:0% +spectrogram and consonants which are the + + + align:start position:0% +spectrogram and consonants which are the +quick transitions in the vertical + + align:start position:0% +quick transitions in the vertical + + + align:start position:0% +quick transitions in the vertical +stripes in the spectrogram leading into + + align:start position:0% +stripes in the spectrogram leading into + + + align:start position:0% +stripes in the spectrogram leading into +the harmonic stacks of vowels + + align:start position:0% +the harmonic stacks of vowels + + + align:start position:0% +the harmonic stacks of vowels +we talked about the problem of talker + + align:start position:0% +we talked about the problem of talker + + + align:start position:0% +we talked about the problem of talker +variability that a given phoneme or word + + align:start position:0% +variability that a given phoneme or word + + + align:start position:0% +variability that a given phoneme or word +sounds very different looks very + + align:start position:0% +sounds very different looks very + + + align:start position:0% +sounds very different looks very +different in the spectrogram if spoken + + align:start position:0% +different in the spectrogram if spoken + + + align:start position:0% +different in the spectrogram if spoken +by two different people + + align:start position:0% +by two different people + + + align:start position:0% +by two different people +and conversely the same person speaking + + align:start position:0% +and conversely the same person speaking + + + align:start position:0% +and conversely the same person speaking +two different words looks very different + + align:start position:0% +two different words looks very different + + + align:start position:0% +two different words looks very different +in the spectrogram and so that means + + align:start position:0% +in the spectrogram and so that means + + + align:start position:0% +in the spectrogram and so that means +that the identity of the speaker and the + + align:start position:0% +that the identity of the speaker and the + + + align:start position:0% +that the identity of the speaker and the +identity of the word being said are kind + + align:start position:0% +identity of the word being said are kind + + + align:start position:0% +identity of the word being said are kind +of all mushed up together and that means + + align:start position:0% +of all mushed up together and that means + + + align:start position:0% +of all mushed up together and that means +that if you want to recognize the voice + + align:start position:0% +that if you want to recognize the voice + + + align:start position:0% +that if you want to recognize the voice +independent of what's being said + + align:start position:0% +independent of what's being said + + + align:start position:0% +independent of what's being said +or recognize the word independent of + + align:start position:0% +or recognize the word independent of + + + align:start position:0% +or recognize the word independent of +who's saying it you have a big + + align:start position:0% +who's saying it you have a big + + + align:start position:0% +who's saying it you have a big +computational challenge a classic + + align:start position:0% +computational challenge a classic + + + align:start position:0% +computational challenge a classic +invariance problem yeah ben + + align:start position:0% +invariance problem yeah ben + + + align:start position:0% +invariance problem yeah ben +i don't mean to hold this up i just want + + align:start position:0% +i don't mean to hold this up i just want + + + align:start position:0% +i don't mean to hold this up i just want +to be sure that i'm understanding this + + align:start position:0% +to be sure that i'm understanding this + + + align:start position:0% +to be sure that i'm understanding this +consonants are + + align:start position:0% +consonants are + + + align:start position:0% +consonants are +the difference between consonants and + + align:start position:0% +the difference between consonants and + + + align:start position:0% +the difference between consonants and +vowels + + align:start position:0% +vowels + + + align:start position:0% +vowels +like are valves just harmonic like + + align:start position:0% +like are valves just harmonic like + + + align:start position:0% +like are valves just harmonic like +connective elements between like + + align:start position:0% +connective elements between like + + + align:start position:0% +connective elements between like +consonants and our consonants + + align:start position:0% +consonants and our consonants + + + align:start position:0% +consonants and our consonants +like percussive or are they actual + + align:start position:0% +like percussive or are they actual + + + align:start position:0% +like percussive or are they actual +like i i just didn't understand that + + align:start position:0% +like i i just didn't understand that + + + align:start position:0% +like i i just didn't understand that +yeah so in in the spectrogram + + align:start position:0% +yeah so in in the spectrogram + + + align:start position:0% +yeah so in in the spectrogram +those those i don't i didn't put that on + + align:start position:0% +those those i don't i didn't put that on + + + align:start position:0% +those those i don't i didn't put that on +the slide here but those horizontal red + + align:start position:0% +the slide here but those horizontal red + + + align:start position:0% +the slide here but those horizontal red +stripes in the slides that i showed you + + align:start position:0% +stripes in the slides that i showed you + + + align:start position:0% +stripes in the slides that i showed you +last time those in the spectrogram those + + align:start position:0% +last time those in the spectrogram those + + + align:start position:0% +last time those in the spectrogram those +are bands of energy at different + + align:start position:0% +are bands of energy at different + + + align:start position:0% +are bands of energy at different +frequencies that are sustained over a + + align:start position:0% +frequencies that are sustained over a + + + align:start position:0% +frequencies that are sustained over a +chunk of time and those are typical of + + align:start position:0% +chunk of time and those are typical of + + + align:start position:0% +chunk of time and those are typical of +vowels + + align:start position:0% +vowels + + + align:start position:0% +vowels +right or singing or music also um and + + align:start position:0% +right or singing or music also um and + + + align:start position:0% +right or singing or music also um and +those harmonic sounds that have pitch + + align:start position:0% +those harmonic sounds that have pitch + + + align:start position:0% +those harmonic sounds that have pitch +and so vowels have those kind of + + align:start position:0% +and so vowels have those kind of + + + align:start position:0% +and so vowels have those kind of +sustained chunks that look like this in + + align:start position:0% +sustained chunks that look like this in + + + align:start position:0% +sustained chunks that look like this in +the spectrogram and then they're these + + align:start position:0% +the spectrogram and then they're these + + + align:start position:0% +the spectrogram and then they're these +weird vertical stripes and transitions + + align:start position:0% +weird vertical stripes and transitions + + + align:start position:0% +weird vertical stripes and transitions +in and out of the vowels that are the + + align:start position:0% +in and out of the vowels that are the + + + align:start position:0% +in and out of the vowels that are the +consonants + + align:start position:0% + + + + align:start position:0% + +just + + align:start position:0% +just + + + align:start position:0% +just +the air is just flowing through and + + align:start position:0% +the air is just flowing through and + + + align:start position:0% +the air is just flowing through and +you're filtering it somehow by + + align:start position:0% +you're filtering it somehow by + + + align:start position:0% +you're filtering it somehow by +positioning your vocal tract certainly + + align:start position:0% +positioning your vocal tract certainly + + + align:start position:0% +positioning your vocal tract certainly +and constantly starting to close off + + align:start position:0% +and constantly starting to close off + + + align:start position:0% +and constantly starting to close off +that air or or restrict it at some point + + align:start position:0% +that air or or restrict it at some point + + + align:start position:0% +that air or or restrict it at some point +um so like + + align:start position:0% +um so like + + + align:start position:0% +um so like +s's and s you're not pushing all the way + + align:start position:0% +s's and s you're not pushing all the way + + + align:start position:0% +s's and s you're not pushing all the way +off but you're really constricting the + + align:start position:0% +off but you're really constricting the + + + align:start position:0% +off but you're really constricting the +vocal tract and a lot of other constants + + align:start position:0% +vocal tract and a lot of other constants + + + align:start position:0% +vocal tract and a lot of other constants +you're actually fully closing + + align:start position:0% + + + + align:start position:0% + +okay and then we talked a bit about the + + align:start position:0% +okay and then we talked a bit about the + + + align:start position:0% +okay and then we talked a bit about the +brain basis and i pointed out that the + + align:start position:0% +brain basis and i pointed out that the + + + align:start position:0% +brain basis and i pointed out that the +neuroanatomy of sound processing the + + align:start position:0% +neuroanatomy of sound processing the + + + align:start position:0% +neuroanatomy of sound processing the +subcortical neuroanatomy is much more + + align:start position:0% +subcortical neuroanatomy is much more + + + align:start position:0% +subcortical neuroanatomy is much more +complicated than the subcortical + + align:start position:0% +complicated than the subcortical + + + align:start position:0% +complicated than the subcortical +neuroanatomy of + + align:start position:0% +neuroanatomy of + + + align:start position:0% +neuroanatomy of +vision envision you have one stop in the + + align:start position:0% +vision envision you have one stop in the + + + align:start position:0% +vision envision you have one stop in the +lgn and then you go up to cortex coming + + align:start position:0% +lgn and then you go up to cortex coming + + + align:start position:0% +lgn and then you go up to cortex coming +up from the retina in audition you have + + align:start position:0% +up from the retina in audition you have + + + align:start position:0% +up from the retina in audition you have +many stops between the cochlea where you + + align:start position:0% +many stops between the cochlea where you + + + align:start position:0% +many stops between the cochlea where you +pick up sounds + + align:start position:0% +pick up sounds + + + align:start position:0% +pick up sounds +in in the inner ear + + align:start position:0% +in in the inner ear + + + align:start position:0% +in in the inner ear +and auditory cortex um some of those + + align:start position:0% +and auditory cortex um some of those + + + align:start position:0% +and auditory cortex um some of those +stops are shown up here and we didn't + + align:start position:0% +stops are shown up here and we didn't + + + align:start position:0% +stops are shown up here and we didn't +discuss them + + align:start position:0% +discuss them + + + align:start position:0% +discuss them +um so then we talked about primary + + align:start position:0% +um so then we talked about primary + + + align:start position:0% +um so then we talked about primary +auditory cortex that's on the top of the + + align:start position:0% +auditory cortex that's on the top of the + + + align:start position:0% +auditory cortex that's on the top of the +temporal lobes like right in there + + align:start position:0% +temporal lobes like right in there + + + align:start position:0% +temporal lobes like right in there +medially you went in + + align:start position:0% +medially you went in + + + align:start position:0% +medially you went in +um and it has this tonatopic property + + align:start position:0% +um and it has this tonatopic property + + + align:start position:0% +um and it has this tonatopic property +and that is a map of frequency space + + align:start position:0% +and that is a map of frequency space + + + align:start position:0% +and that is a map of frequency space +with this kind of systematic high low + + align:start position:0% +with this kind of systematic high low + + + align:start position:0% +with this kind of systematic high low +high mapping of frequency space + + align:start position:0% +high mapping of frequency space + + + align:start position:0% +high mapping of frequency space +that you can see here high low high like + + align:start position:0% +that you can see here high low high like + + + align:start position:0% +that you can see here high low high like +that this is the top of the temporal + + align:start position:0% +that this is the top of the temporal + + + align:start position:0% +that this is the top of the temporal +lobe right there + + align:start position:0% +lobe right there + + + align:start position:0% +lobe right there +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um and i pointed out that in animals and + + align:start position:0% +um and i pointed out that in animals and + + + align:start position:0% +um and i pointed out that in animals and +in + + align:start position:0% +in + + + align:start position:0% +in +one recent mri study the response + + align:start position:0% +one recent mri study the response + + + align:start position:0% +one recent mri study the response +properties of primary auditory cortex + + align:start position:0% +properties of primary auditory cortex + + + align:start position:0% +properties of primary auditory cortex +are well modeled by these fairly simple + + align:start position:0% +are well modeled by these fairly simple + + + align:start position:0% +are well modeled by these fairly simple +linear filters known as spectrotemporal + + align:start position:0% +linear filters known as spectrotemporal + + + align:start position:0% +linear filters known as spectrotemporal +receptive fields or stiffs shown here + + align:start position:0% +receptive fields or stiffs shown here + + + align:start position:0% +receptive fields or stiffs shown here +okay so this they're kind of simple + + align:start position:0% +okay so this they're kind of simple + + + align:start position:0% +okay so this they're kind of simple +acoustic properties of a given band of + + align:start position:0% +acoustic properties of a given band of + + + align:start position:0% +acoustic properties of a given band of +frequencies rising or falling at + + align:start position:0% +frequencies rising or falling at + + + align:start position:0% +frequencies rising or falling at +different rates + + align:start position:0% +different rates + + + align:start position:0% +different rates +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so today + + align:start position:0% +okay so today + + + align:start position:0% +okay so today +we're going to talk about music + + align:start position:0% +we're going to talk about music + + + align:start position:0% +we're going to talk about music +and this is also an important moment in + + align:start position:0% +and this is also an important moment in + + + align:start position:0% +and this is also an important moment in +the course because up to now we've been + + align:start position:0% +the course because up to now we've been + + + align:start position:0% +the course because up to now we've been +talking about functions that are mostly + + align:start position:0% +talking about functions that are mostly + + + align:start position:0% +talking about functions that are mostly +shared with animals speech is kind of on + + align:start position:0% +shared with animals speech is kind of on + + + align:start position:0% +shared with animals speech is kind of on +the cusp i was going to make this + + align:start position:0% +the cusp i was going to make this + + + align:start position:0% +the cusp i was going to make this +point before speech and that it's + + align:start position:0% +point before speech and that it's + + + align:start position:0% +point before speech and that it's +actually muddy because lots of animals + + align:start position:0% +actually muddy because lots of animals + + + align:start position:0% +actually muddy because lots of animals +are really good at speech perception you + + align:start position:0% +are really good at speech perception you + + + align:start position:0% +are really good at speech perception you +know chinchillas can distinguish ba from + + align:start position:0% +know chinchillas can distinguish ba from + + + align:start position:0% +know chinchillas can distinguish ba from +paw go figure anyway um so that they can + + align:start position:0% +paw go figure anyway um so that they can + + + align:start position:0% +paw go figure anyway um so that they can +perceive speech but obviously they don't + + align:start position:0% +perceive speech but obviously they don't + + + align:start position:0% +perceive speech but obviously they don't +use it in the same way but music is most + + align:start position:0% +use it in the same way but music is most + + + align:start position:0% +use it in the same way but music is most +definitely uniquely human + + align:start position:0% +definitely uniquely human + + + align:start position:0% +definitely uniquely human +and so most of the things we'll be + + align:start position:0% +and so most of the things we'll be + + + align:start position:0% +and so most of the things we'll be +talking about from here on out are + + align:start position:0% +talking about from here on out are + + + align:start position:0% +talking about from here on out are +things about the human brain in + + align:start position:0% +things about the human brain in + + + align:start position:0% +things about the human brain in +particular + + align:start position:0% +particular + + + align:start position:0% +particular +and i think these are the coolest things + + align:start position:0% +and i think these are the coolest things + + + align:start position:0% +and i think these are the coolest things +in human cognitive neuroscience because + + align:start position:0% +in human cognitive neuroscience because + + + align:start position:0% +in human cognitive neuroscience because +they tell us something about who we are + + align:start position:0% +they tell us something about who we are + + + align:start position:0% +they tell us something about who we are +as human beings + + align:start position:0% +as human beings + + + align:start position:0% +as human beings +but they're also the hardest ones to + + align:start position:0% +but they're also the hardest ones to + + + align:start position:0% +but they're also the hardest ones to +study + + align:start position:0% +study + + + align:start position:0% +study +why is that + + align:start position:0% + + + + align:start position:0% + +no animal models + + align:start position:0% +no animal models + + + align:start position:0% +no animal models +right and i'm always lamenting about the + + align:start position:0% +right and i'm always lamenting about the + + + align:start position:0% +right and i'm always lamenting about the +shortcomings of each of the methods in + + align:start position:0% +shortcomings of each of the methods in + + + align:start position:0% +shortcomings of each of the methods in +human cognitive neuroscience and we have + + align:start position:0% +human cognitive neuroscience and we have + + + align:start position:0% +human cognitive neuroscience and we have +lots of them and they complement each + + align:start position:0% +lots of them and they complement each + + + align:start position:0% +lots of them and they complement each +other but there's a whole host of things + + align:start position:0% +other but there's a whole host of things + + + align:start position:0% +other but there's a whole host of things +that none of those methods are good for + + align:start position:0% +that none of those methods are good for + + + align:start position:0% +that none of those methods are good for +and so now we're really out on thin ice + + align:start position:0% +and so now we're really out on thin ice + + + align:start position:0% +and so now we're really out on thin ice +trying to understand these things uh + + align:start position:0% +trying to understand these things uh + + + align:start position:0% +trying to understand these things uh +with a weaker set of methods where we + + align:start position:0% +with a weaker set of methods where we + + + align:start position:0% +with a weaker set of methods where we +can't go back and validate them with + + align:start position:0% +can't go back and validate them with + + + align:start position:0% +can't go back and validate them with +animal models and that's just life + + align:start position:0% +animal models and that's just life + + + align:start position:0% +animal models and that's just life +that's what we do + + align:start position:0% +that's what we do + + + align:start position:0% +that's what we do +okay so now let's back up for a second + + align:start position:0% +okay so now let's back up for a second + + + align:start position:0% +okay so now let's back up for a second +and consider why am i allocating a whole + + align:start position:0% +and consider why am i allocating a whole + + + align:start position:0% +and consider why am i allocating a whole +lecture for such a fluffy frivolous + + align:start position:0% +lecture for such a fluffy frivolous + + + align:start position:0% +lecture for such a fluffy frivolous +topic as music + + align:start position:0% +topic as music + + + align:start position:0% +topic as music +and i would say + + align:start position:0% +and i would say + + + align:start position:0% +and i would say +that's because it's not fluffy it's + + align:start position:0% +that's because it's not fluffy it's + + + align:start position:0% +that's because it's not fluffy it's +actually fundamental + + align:start position:0% +actually fundamental + + + align:start position:0% +actually fundamental +and it's fundamental in the sense that + + align:start position:0% +and it's fundamental in the sense that + + + align:start position:0% +and it's fundamental in the sense that +music is both uniquely human no other + + align:start position:0% +music is both uniquely human no other + + + align:start position:0% +music is both uniquely human no other +animal has anything remotely like human + + align:start position:0% +animal has anything remotely like human + + + align:start position:0% +animal has anything remotely like human +music and it's also universally human + + align:start position:0% +music and it's also universally human + + + align:start position:0% +music and it's also universally human +that is every human culture that's been + + align:start position:0% +that is every human culture that's been + + + align:start position:0% +that is every human culture that's been +studied has some kind of music so music + + align:start position:0% +studied has some kind of music so music + + + align:start position:0% +studied has some kind of music so music +is really an essential part of what it + + align:start position:0% +is really an essential part of what it + + + align:start position:0% +is really an essential part of what it +means to be a human being it's really at + + align:start position:0% +means to be a human being it's really at + + + align:start position:0% +means to be a human being it's really at +the core of humanity and that alone + + align:start position:0% +the core of humanity and that alone + + + align:start position:0% +the core of humanity and that alone +makes it interesting + + align:start position:0% +makes it interesting + + + align:start position:0% +makes it interesting +but further question + + align:start position:0% +but further question + + + align:start position:0% +but further question +birdsong doesn't count no birdsong + + align:start position:0% +birdsong doesn't count no birdsong + + + align:start position:0% +birdsong doesn't count no birdsong +doesn't count in all kinds of ways + + align:start position:0% +doesn't count in all kinds of ways + + + align:start position:0% +doesn't count in all kinds of ways +um uh one it doesn't have anywhere near + + align:start position:0% +um uh one it doesn't have anywhere near + + + align:start position:0% +um uh one it doesn't have anywhere near +the flexibility and variability there's + + align:start position:0% +the flexibility and variability there's + + + align:start position:0% +the flexibility and variability there's +like narrow domains in which you know + + align:start position:0% +like narrow domains in which you know + + + align:start position:0% +like narrow domains in which you know +each each um + + align:start position:0% +each each um + + + align:start position:0% +each each um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +zebra finch male zebra finch makes a + + align:start position:0% +zebra finch male zebra finch makes a + + + align:start position:0% +zebra finch male zebra finch makes a +slightly different version of the call + + align:start position:0% +slightly different version of the call + + + align:start position:0% +slightly different version of the call +but within an extremely narrow range + + align:start position:0% +but within an extremely narrow range + + + align:start position:0% +but within an extremely narrow range +uh there's actually a brain imaging + + align:start position:0% +uh there's actually a brain imaging + + + align:start position:0% +uh there's actually a brain imaging +study that looks in a brain imaging in + + align:start position:0% +study that looks in a brain imaging in + + + align:start position:0% +study that looks in a brain imaging in +birds + + align:start position:0% +birds + + + align:start position:0% +birds +songbirds + + align:start position:0% +songbirds + + + align:start position:0% +songbirds +and asks do they have reward um + + align:start position:0% +and asks do they have reward um + + + align:start position:0% +and asks do they have reward um +reward uh brain region responses to + + align:start position:0% +reward uh brain region responses to + + + align:start position:0% +reward uh brain region responses to +music + + align:start position:0% +music + + + align:start position:0% +music +um and the answer is yes in some cases + + align:start position:0% +um and the answer is yes in some cases + + + align:start position:0% +um and the answer is yes in some cases +like like do they enjoy it right is that + + align:start position:0% +like like do they enjoy it right is that + + + align:start position:0% +like like do they enjoy it right is that +part of that you know the answer is yes + + align:start position:0% +part of that you know the answer is yes + + + align:start position:0% +part of that you know the answer is yes +but only when the significance of the + + align:start position:0% +but only when the significance of the + + + align:start position:0% +but only when the significance of the +bird song is something that's relevant + + align:start position:0% +bird song is something that's relevant + + + align:start position:0% +bird song is something that's relevant +to them like there's a potential mate + + align:start position:0% +to them like there's a potential mate + + + align:start position:0% +to them like there's a potential mate +right here then they like it + + align:start position:0% +right here then they like it + + + align:start position:0% +right here then they like it +but they don't like it just for the + + align:start position:0% +but they don't like it just for the + + + align:start position:0% +but they don't like it just for the +sound and that makes it very different + + align:start position:0% +sound and that makes it very different + + + align:start position:0% +sound and that makes it very different +from humans and there are other + + align:start position:0% +from humans and there are other + + + align:start position:0% +from humans and there are other +differences as well + + align:start position:0% +differences as well + + + align:start position:0% +differences as well +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so it's further really important to us + + align:start position:0% +so it's further really important to us + + + align:start position:0% +so it's further really important to us +humans in a whole bunch of ways one we + + align:start position:0% +humans in a whole bunch of ways one we + + + align:start position:0% +humans in a whole bunch of ways one we +have been doing it for a very long time + + align:start position:0% +have been doing it for a very long time + + + align:start position:0% +have been doing it for a very long time +um and so for example the archaeological + + align:start position:0% +um and so for example the archaeological + + + align:start position:0% +um and so for example the archaeological +record shows these 40 000 year old bone + + align:start position:0% +record shows these 40 000 year old bone + + + align:start position:0% +record shows these 40 000 year old bone +flutes + + align:start position:0% +flutes + + + align:start position:0% +flutes +that you can see from the structure of + + align:start position:0% +that you can see from the structure of + + + align:start position:0% +that you can see from the structure of +the fruit of flute make + + align:start position:0% +the fruit of flute make + + + align:start position:0% +the fruit of flute make +particular sets of + + align:start position:0% +particular sets of + + + align:start position:0% +particular sets of +of possible pitches + + align:start position:0% +of possible pitches + + + align:start position:0% +of possible pitches +and further most people have thought + + align:start position:0% +and further most people have thought + + + align:start position:0% +and further most people have thought +about this have argued that singing + + align:start position:0% +about this have argued that singing + + + align:start position:0% +about this have argued that singing +probably goes back much farther than the + + align:start position:0% +probably goes back much farther than the + + + align:start position:0% +probably goes back much farther than the +bone flutes after all you don't have to + + align:start position:0% +bone flutes after all you don't have to + + + align:start position:0% +bone flutes after all you don't have to +make anything to do it you can just sing + + align:start position:0% +make anything to do it you can just sing + + + align:start position:0% +make anything to do it you can just sing +right + + align:start position:0% +right + + + align:start position:0% +right +some have even speculated that singing + + align:start position:0% +some have even speculated that singing + + + align:start position:0% +some have even speculated that singing +evolved before language okay it's just + + align:start position:0% +evolved before language okay it's just + + + align:start position:0% +evolved before language okay it's just +speculation but that's possible in any + + align:start position:0% +speculation but that's possible in any + + + align:start position:0% +speculation but that's possible in any +case it goes way back evolutionarily + + align:start position:0% +case it goes way back evolutionarily + + + align:start position:0% +case it goes way back evolutionarily +it also arises early in development so + + align:start position:0% +it also arises early in development so + + + align:start position:0% +it also arises early in development so +very young infants are extremely + + align:start position:0% +very young infants are extremely + + + align:start position:0% +very young infants are extremely +interested in music + + align:start position:0% +interested in music + + + align:start position:0% +interested in music +they're sensitive to beat and melody + + align:start position:0% +they're sensitive to beat and melody + + + align:start position:0% +they're sensitive to beat and melody +independent of pitch we'll talk more + + align:start position:0% +independent of pitch we'll talk more + + + align:start position:0% +independent of pitch we'll talk more +about that a little bit + + align:start position:0% +about that a little bit + + + align:start position:0% +about that a little bit +and finally if you're not impressed with + + align:start position:0% +and finally if you're not impressed with + + + align:start position:0% +and finally if you're not impressed with +any of those arguments people spend a + + align:start position:0% +any of those arguments people spend a + + + align:start position:0% +any of those arguments people spend a +lot of money on music and if that's your + + align:start position:0% +lot of money on music and if that's your + + + align:start position:0% +lot of money on music and if that's your +index of importance it's really + + align:start position:0% +index of importance it's really + + + align:start position:0% +index of importance it's really +important + + align:start position:0% +important + + + align:start position:0% +important +last year 43 billion in sales okay + + align:start position:0% +last year 43 billion in sales okay + + + align:start position:0% +last year 43 billion in sales okay +so i'd say it's not a frivolous topic + + align:start position:0% +so i'd say it's not a frivolous topic + + + align:start position:0% +so i'd say it's not a frivolous topic +it's a fundamental topic it's near the + + align:start position:0% +it's a fundamental topic it's near the + + + align:start position:0% +it's a fundamental topic it's near the +core of what it means to be a human + + align:start position:0% +core of what it means to be a human + + + align:start position:0% +core of what it means to be a human +being + + align:start position:0% +being + + + align:start position:0% +being +and all of this raises a really obvious + + align:start position:0% +and all of this raises a really obvious + + + align:start position:0% +and all of this raises a really obvious +question + + align:start position:0% +question + + + align:start position:0% +question +why do we create and like music in the + + align:start position:0% +why do we create and like music in the + + + align:start position:0% +why do we create and like music in the +first place what is it for + + align:start position:0% +first place what is it for + + + align:start position:0% +first place what is it for +right + + align:start position:0% +right + + + align:start position:0% +right +and this is a puzzle that + + align:start position:0% +and this is a puzzle that + + + align:start position:0% +and this is a puzzle that +people have thought about for + + align:start position:0% +people have thought about for + + + align:start position:0% +people have thought about for +at least centuries probably millennia + + align:start position:0% +at least centuries probably millennia + + + align:start position:0% +at least centuries probably millennia +and this includes all kinds of major + + align:start position:0% +and this includes all kinds of major + + + align:start position:0% +and this includes all kinds of major +thinkers like darwin + + align:start position:0% +thinkers like darwin + + + align:start position:0% +thinkers like darwin +who said + + align:start position:0% +who said + + + align:start position:0% +who said +as neither the enjoyment nor the + + align:start position:0% +as neither the enjoyment nor the + + + align:start position:0% +as neither the enjoyment nor the +capacity of producing musical notes are + + align:start position:0% +capacity of producing musical notes are + + + align:start position:0% +capacity of producing musical notes are +faculties of the least direct use to man + + align:start position:0% +faculties of the least direct use to man + + + align:start position:0% +faculties of the least direct use to man +in reference to his ordinary habits of + + align:start position:0% +in reference to his ordinary habits of + + + align:start position:0% +in reference to his ordinary habits of +life they must be ranked among the most + + align:start position:0% +life they must be ranked among the most + + + align:start position:0% +life they must be ranked among the most +mysterious with which he is endowed okay + + align:start position:0% +mysterious with which he is endowed okay + + + align:start position:0% +mysterious with which he is endowed okay +so + + align:start position:0% +so + + + align:start position:0% +so +darwin is sort of implicitly assuming + + align:start position:0% +darwin is sort of implicitly assuming + + + align:start position:0% +darwin is sort of implicitly assuming +here that music is an evolved capacity + + align:start position:0% +here that music is an evolved capacity + + + align:start position:0% +here that music is an evolved capacity +right it's not something that we just + + align:start position:0% +right it's not something that we just + + + align:start position:0% +right it's not something that we just +learn and that cultures invent if they + + align:start position:0% +learn and that cultures invent if they + + + align:start position:0% +learn and that cultures invent if they +feel like it or don't feel like it + + align:start position:0% +feel like it or don't feel like it + + + align:start position:0% +feel like it or don't feel like it +but it's actually evolved + + align:start position:0% +but it's actually evolved + + + align:start position:0% +but it's actually evolved +and shaped by natural selection and that + + align:start position:0% +and shaped by natural selection and that + + + align:start position:0% +and shaped by natural selection and that +means there must be some function that + + align:start position:0% +means there must be some function that + + + align:start position:0% +means there must be some function that +natural selection was acting on that was + + align:start position:0% +natural selection was acting on that was + + + align:start position:0% +natural selection was acting on that was +relevant to survival okay + + align:start position:0% +relevant to survival okay + + + align:start position:0% +relevant to survival okay +so + + align:start position:0% +so + + + align:start position:0% +so +um people have speculated about what + + align:start position:0% +um people have speculated about what + + + align:start position:0% +um people have speculated about what +that function might be + + align:start position:0% +that function might be + + + align:start position:0% +that function might be +those who think that music is an evolved + + align:start position:0% +those who think that music is an evolved + + + align:start position:0% +those who think that music is an evolved +function including darwin he speculated + + align:start position:0% +function including darwin he speculated + + + align:start position:0% +function including darwin he speculated +that it's for sexual selection + + align:start position:0% +that it's for sexual selection + + + align:start position:0% +that it's for sexual selection +and his writing is so beautiful i won't + + align:start position:0% +and his writing is so beautiful i won't + + + align:start position:0% +and his writing is so beautiful i won't +paraphrase it he says + + align:start position:0% +paraphrase it he says + + + align:start position:0% +paraphrase it he says +it appears probable that the progenitors + + align:start position:0% +it appears probable that the progenitors + + + align:start position:0% +it appears probable that the progenitors +of man either the males or females or + + align:start position:0% +of man either the males or females or + + + align:start position:0% +of man either the males or females or +both sexes before acquiring the power of + + align:start position:0% +both sexes before acquiring the power of + + + align:start position:0% +both sexes before acquiring the power of +expressing their mutual love in + + align:start position:0% +expressing their mutual love in + + + align:start position:0% +expressing their mutual love in +articulate language + + align:start position:0% +articulate language + + + align:start position:0% +articulate language +endeavored to charm each other with + + align:start position:0% +endeavored to charm each other with + + + align:start position:0% +endeavored to charm each other with +musical notes and rhythm + + align:start position:0% +musical notes and rhythm + + + align:start position:0% +musical notes and rhythm +okay so that's darwin speculation just a + + align:start position:0% +okay so that's darwin speculation just a + + + align:start position:0% +okay so that's darwin speculation just a +speculation but a lovely one + + align:start position:0% +speculation but a lovely one + + + align:start position:0% +speculation but a lovely one +also note that he threw away this + + align:start position:0% +also note that he threw away this + + + align:start position:0% +also note that he threw away this +radical idea in here before acquiring + + align:start position:0% +radical idea in here before acquiring + + + align:start position:0% +radical idea in here before acquiring +the power to express their mutual love + + align:start position:0% +the power to express their mutual love + + + align:start position:0% +the power to express their mutual love +in articulate language so he's think + + align:start position:0% +in articulate language so he's think + + + align:start position:0% +in articulate language so he's think +he's speculating that that um music came + + align:start position:0% +he's speculating that that um music came + + + align:start position:0% +he's speculating that that um music came +before language again all speculation + + align:start position:0% +before language again all speculation + + + align:start position:0% +before language again all speculation +but interesting speculation + + align:start position:0% +but interesting speculation + + + align:start position:0% +but interesting speculation +more recently + + align:start position:0% +more recently + + + align:start position:0% +more recently +up the street + + align:start position:0% +up the street + + + align:start position:0% +up the street +there's a bunch of people who've been + + align:start position:0% +there's a bunch of people who've been + + + align:start position:0% +there's a bunch of people who've been +thinking about this a lot + + align:start position:0% +thinking about this a lot + + + align:start position:0% +thinking about this a lot +uh and sam mayor at harvard has been + + align:start position:0% +uh and sam mayor at harvard has been + + + align:start position:0% +uh and sam mayor at harvard has been +arguing that the function of music and + + align:start position:0% +arguing that the function of music and + + + align:start position:0% +arguing that the function of music and +song in particular which he thinks is + + align:start position:0% +song in particular which he thinks is + + + align:start position:0% +song in particular which he thinks is +really the the fundamental basic kind of + + align:start position:0% +really the the fundamental basic kind of + + + align:start position:0% +really the the fundamental basic kind of +native form of of music um has an + + align:start position:0% +native form of of music um has an + + + align:start position:0% +native form of of music um has an +evolutionary role in managing parent + + align:start position:0% +evolutionary role in managing parent + + + align:start position:0% +evolutionary role in managing parent +offspring conflict and that's something + + align:start position:0% +offspring conflict and that's something + + + align:start position:0% +offspring conflict and that's something +that many evolutionary theorists have + + align:start position:0% +that many evolutionary theorists have + + + align:start position:0% +that many evolutionary theorists have +written about the genetic interests of a + + align:start position:0% +written about the genetic interests of a + + + align:start position:0% +written about the genetic interests of a +parent and an offspring are highly + + align:start position:0% +parent and an offspring are highly + + + align:start position:0% +parent and an offspring are highly +overlapping but not completely + + align:start position:0% +overlapping but not completely + + + align:start position:0% +overlapping but not completely +overlapping the parent has other + + align:start position:0% +overlapping the parent has other + + + align:start position:0% +overlapping the parent has other +offspring to take care of besides this + + align:start position:0% +offspring to take care of besides this + + + align:start position:0% +offspring to take care of besides this +one right here that one right there + + align:start position:0% +one right here that one right there + + + align:start position:0% +one right here that one right there +wants 100 of the parents effort therein + + align:start position:0% +wants 100 of the parents effort therein + + + align:start position:0% +wants 100 of the parents effort therein +lies the conflict + + align:start position:0% +lies the conflict + + + align:start position:0% +lies the conflict +um and so + + align:start position:0% +um and so + + + align:start position:0% +um and so +mayors proposed that + + align:start position:0% +mayors proposed that + + + align:start position:0% +mayors proposed that +that infant directed song + + align:start position:0% +that infant directed song + + + align:start position:0% +that infant directed song +arose in this kind of arms race between + + align:start position:0% +arose in this kind of arms race between + + + align:start position:0% +arose in this kind of arms race between +the somewhat competing interests of the + + align:start position:0% +the somewhat competing interests of the + + + align:start position:0% +the somewhat competing interests of the +parent and the offspring and it kind of + + align:start position:0% +parent and the offspring and it kind of + + + align:start position:0% +parent and the offspring and it kind of +manages this need the infant has to know + + align:start position:0% +manages this need the infant has to know + + + align:start position:0% +manages this need the infant has to know +the parent is there + + align:start position:0% +the parent is there + + + align:start position:0% +the parent is there +with the fact that the parent has other + + align:start position:0% +with the fact that the parent has other + + + align:start position:0% +with the fact that the parent has other +needs i guess idea they can sing while + + align:start position:0% +needs i guess idea they can sing while + + + align:start position:0% +needs i guess idea they can sing while +attending to other + + align:start position:0% +attending to other + + + align:start position:0% +attending to other +other + + align:start position:0% +other + + + align:start position:0% +other +offspring + + align:start position:0% +offspring + + + align:start position:0% +offspring +and on and on so there's other kinds of + + align:start position:0% +and on and on so there's other kinds of + + + align:start position:0% +and on and on so there's other kinds of +speculations like this but importantly + + align:start position:0% +speculations like this but importantly + + + align:start position:0% +speculations like this but importantly +this is not the only kind of view + + align:start position:0% +this is not the only kind of view + + + align:start position:0% +this is not the only kind of view +it's not necessarily the case that music + + align:start position:0% +it's not necessarily the case that music + + + align:start position:0% +it's not necessarily the case that music +is an evolved capacity so others have + + align:start position:0% +is an evolved capacity so others have + + + align:start position:0% +is an evolved capacity so others have +argued that it's not + + align:start position:0% +argued that it's not + + + align:start position:0% +argued that it's not +so steve pinker + + align:start position:0% +so steve pinker + + + align:start position:0% +so steve pinker +also up the street has argued that music + + align:start position:0% +also up the street has argued that music + + + align:start position:0% +also up the street has argued that music +is auditory cheesecake + + align:start position:0% +is auditory cheesecake + + + align:start position:0% +is auditory cheesecake +an exquisite confection crafted to + + align:start position:0% +an exquisite confection crafted to + + + align:start position:0% +an exquisite confection crafted to +tickle the sensitive spots of at least + + align:start position:0% +tickle the sensitive spots of at least + + + align:start position:0% +tickle the sensitive spots of at least +six of our mental faculties + + align:start position:0% +six of our mental faculties + + + align:start position:0% +six of our mental faculties +if advantage from our species the rest + + align:start position:0% +if advantage from our species the rest + + + align:start position:0% +if advantage from our species the rest +of our lifestyle would be virtually + + align:start position:0% +of our lifestyle would be virtually + + + align:start position:0% +of our lifestyle would be virtually +unchanged + + align:start position:0% +unchanged + + + align:start position:0% +unchanged +i think that might say a little more + + align:start position:0% +i think that might say a little more + + + align:start position:0% +i think that might say a little more +about steve pinker than it does about + + align:start position:0% +about steve pinker than it does about + + + align:start position:0% +about steve pinker than it does about +music + + align:start position:0% +music + + + align:start position:0% +music +nonetheless it's a possible view okay + + align:start position:0% +nonetheless it's a possible view okay + + + align:start position:0% +nonetheless it's a possible view okay +um what he's saying is that music is not + + align:start position:0% +um what he's saying is that music is not + + + align:start position:0% +um what he's saying is that music is not +an evolutionary adaptation at all + + align:start position:0% +an evolutionary adaptation at all + + + align:start position:0% +an evolutionary adaptation at all +but an alternate use of neural machinery + + align:start position:0% +but an alternate use of neural machinery + + + align:start position:0% +but an alternate use of neural machinery +that evolved for some other function and + + align:start position:0% +that evolved for some other function and + + + align:start position:0% +that evolved for some other function and +then once you have this neural machinery + + align:start position:0% +then once you have this neural machinery + + + align:start position:0% +then once you have this neural machinery +what the hell you can invent cultural + + align:start position:0% +what the hell you can invent cultural + + + align:start position:0% +what the hell you can invent cultural +forms and use it to do other things like + + align:start position:0% +forms and use it to do other things like + + + align:start position:0% +forms and use it to do other things like +music okay + + align:start position:0% +music okay + + + align:start position:0% +music okay +and the most obvious kind of + + align:start position:0% +and the most obvious kind of + + + align:start position:0% +and the most obvious kind of +neural machinery that you might co-opt + + align:start position:0% +neural machinery that you might co-opt + + + align:start position:0% +neural machinery that you might co-opt +for that function would be neural + + align:start position:0% +for that function would be neural + + + align:start position:0% +for that function would be neural +machinery for speech or neural machinery + + align:start position:0% +machinery for speech or neural machinery + + + align:start position:0% +machinery for speech or neural machinery +for language + + align:start position:0% +for language + + + align:start position:0% +for language +okay which as i argued briefly last time + + align:start position:0% +okay which as i argued briefly last time + + + align:start position:0% +okay which as i argued briefly last time +are not the same thing one is the + + align:start position:0% +are not the same thing one is the + + + align:start position:0% +are not the same thing one is the +auditory perception of speech sounds and + + align:start position:0% +auditory perception of speech sounds and + + + align:start position:0% +auditory perception of speech sounds and +the other is the understanding of + + align:start position:0% +the other is the understanding of + + + align:start position:0% +the other is the understanding of +linguistic meaning + + align:start position:0% +linguistic meaning + + + align:start position:0% +linguistic meaning +okay so the nice thing about this is + + align:start position:0% +okay so the nice thing about this is + + + align:start position:0% +okay so the nice thing about this is +finally after all this entertaining but + + align:start position:0% +finally after all this entertaining but + + + align:start position:0% +finally after all this entertaining but +like you know kind of speculative stuff + + align:start position:0% +like you know kind of speculative stuff + + + align:start position:0% +like you know kind of speculative stuff +we have an empirical question + + align:start position:0% +we have an empirical question + + + align:start position:0% +we have an empirical question +this is something we can ask empirically + + align:start position:0% +this is something we can ask empirically + + + align:start position:0% +this is something we can ask empirically +does music actually use the same + + align:start position:0% +does music actually use the same + + + align:start position:0% +does music actually use the same +machinery + + align:start position:0% +machinery + + + align:start position:0% +machinery +as speech or language or does it not + + align:start position:0% +as speech or language or does it not + + + align:start position:0% +as speech or language or does it not +okay some of the rest of these + + align:start position:0% +okay some of the rest of these + + + align:start position:0% +okay some of the rest of these +speculations are very hard to test so + + align:start position:0% +speculations are very hard to test so + + + align:start position:0% +speculations are very hard to test so +stay tuned we'll get back to that + + align:start position:0% +stay tuned we'll get back to that + + + align:start position:0% +stay tuned we'll get back to that +shortly + + align:start position:0% +shortly + + + align:start position:0% +shortly +but first um let's let's step back and + + align:start position:0% +but first um let's let's step back and + + + align:start position:0% +but first um let's let's step back and +think okay if music is an evolved + + align:start position:0% +think okay if music is an evolved + + + align:start position:0% +think okay if music is an evolved +capacity + + align:start position:0% +capacity + + + align:start position:0% +capacity +it should be + + align:start position:0% +it should be + + + align:start position:0% +it should be +innate in some sense at least + + align:start position:0% +innate in some sense at least + + + align:start position:0% +innate in some sense at least +genetically specified right because + + align:start position:0% +genetically specified right because + + + align:start position:0% +genetically specified right because +that's what evolution does is that + + align:start position:0% +that's what evolution does is that + + + align:start position:0% +that's what evolution does is that +it you know natural selection acts on + + align:start position:0% +it you know natural selection acts on + + + align:start position:0% +it you know natural selection acts on +the um on the genome to uh to produce + + align:start position:0% +the um on the genome to uh to produce + + + align:start position:0% +the um on the genome to uh to produce +things that are genetically specified + + align:start position:0% +things that are genetically specified + + + align:start position:0% +things that are genetically specified +and it should be present in all human + + align:start position:0% +and it should be present in all human + + + align:start position:0% +and it should be present in all human +societies right since the branching out + + align:start position:0% +societies right since the branching out + + + align:start position:0% +societies right since the branching out +of human societies is very recent in + + align:start position:0% +of human societies is very recent in + + + align:start position:0% +of human societies is very recent in +human evolution so is it + + align:start position:0% +human evolution so is it + + + align:start position:0% +human evolution so is it +well + + align:start position:0% +well + + + align:start position:0% +well +his music is an innate + + align:start position:0% +his music is an innate + + + align:start position:0% +his music is an innate +um + + align:start position:0% +um + + + align:start position:0% +um +so let's suppose suppose we found + + align:start position:0% +so let's suppose suppose we found + + + align:start position:0% +so let's suppose suppose we found +specialized machinery in the brain in + + align:start position:0% +specialized machinery in the brain in + + + align:start position:0% +specialized machinery in the brain in +adults + + align:start position:0% +adults + + + align:start position:0% +adults +for music and we showed really + + align:start position:0% +for music and we showed really + + + align:start position:0% +for music and we showed really +definitively it's really really really + + align:start position:0% +definitively it's really really really + + + align:start position:0% +definitively it's really really really +specialized for music + + align:start position:0% +specialized for music + + + align:start position:0% +specialized for music +would that prove innateness + + align:start position:0% +would that prove innateness + + + align:start position:0% +would that prove innateness +no why not + + align:start position:0% + + + + align:start position:0% + +bingo thank you very good + + align:start position:0% +bingo thank you very good + + + align:start position:0% +bingo thank you very good +yup + + align:start position:0% +yup + + + align:start position:0% +yup +exactly so this is something that many + + align:start position:0% +exactly so this is something that many + + + align:start position:0% +exactly so this is something that many +many people are confused about including + + align:start position:0% +many people are confused about including + + + align:start position:0% +many people are confused about including +colleagues of mine most of the popular + + align:start position:0% +colleagues of mine most of the popular + + + align:start position:0% +colleagues of mine most of the popular +scientific press + + align:start position:0% +scientific press + + + align:start position:0% +scientific press +just because there's a specialized bit + + align:start position:0% +just because there's a specialized bit + + + align:start position:0% +just because there's a specialized bit +of brain that does x doesn't mean x is + + align:start position:0% +of brain that does x doesn't mean x is + + + align:start position:0% +of brain that does x doesn't mean x is +an eight it could be learned and the + + align:start position:0% +an eight it could be learned and the + + + align:start position:0% +an eight it could be learned and the +clearest example of that is the visual + + align:start position:0% +clearest example of that is the visual + + + align:start position:0% +clearest example of that is the visual +word form area everybody get that + + align:start position:0% +word form area everybody get that + + + align:start position:0% +word form area everybody get that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so we've got to try something else + + align:start position:0% +okay so we've got to try something else + + + align:start position:0% +okay so we've got to try something else +what if we find sensitivity to music in + + align:start position:0% +what if we find sensitivity to music in + + + align:start position:0% +what if we find sensitivity to music in +some very music particular way + + align:start position:0% +some very music particular way + + + align:start position:0% +some very music particular way +in newborns + + align:start position:0% +in newborns + + + align:start position:0% +in newborns +okay now that will get closer + + align:start position:0% +okay now that will get closer + + + align:start position:0% +okay now that will get closer +but here's the problem + + align:start position:0% +but here's the problem + + + align:start position:0% +but here's the problem +fetuses can hear pretty well in the womb + + align:start position:0% +fetuses can hear pretty well in the womb + + + align:start position:0% +fetuses can hear pretty well in the womb +and if the mom is singing or even if + + align:start position:0% +and if the mom is singing or even if + + + align:start position:0% +and if the mom is singing or even if +there's music in the ambient room some + + align:start position:0% +there's music in the ambient room some + + + align:start position:0% +there's music in the ambient room some +of that sound gets into the womb + + align:start position:0% +of that sound gets into the womb + + + align:start position:0% +of that sound gets into the womb +so that means + + align:start position:0% +so that means + + + align:start position:0% +so that means +that even if you show sensitivity to + + align:start position:0% +that even if you show sensitivity to + + + align:start position:0% +that even if you show sensitivity to +music even in some very particular way + + align:start position:0% +music even in some very particular way + + + align:start position:0% +music even in some very particular way +in a newborn + + align:start position:0% +in a newborn + + + align:start position:0% +in a newborn +it's not a really tight argument that it + + align:start position:0% +it's not a really tight argument that it + + + align:start position:0% +it's not a really tight argument that it +wasn't impart learned okay + + align:start position:0% +wasn't impart learned okay + + + align:start position:0% +wasn't impart learned okay +so this is a real challenge + + align:start position:0% +so this is a real challenge + + + align:start position:0% +so this is a real challenge +it may just be impossible to answer i'm + + align:start position:0% +it may just be impossible to answer i'm + + + align:start position:0% +it may just be impossible to answer i'm +not sure i don't know how i don't know + + align:start position:0% +not sure i don't know how i don't know + + + align:start position:0% +not sure i don't know how i don't know +what method could actually answer this + + align:start position:0% +what method could actually answer this + + + align:start position:0% +what method could actually answer this +but at the very least it's really + + align:start position:0% +but at the very least it's really + + + align:start position:0% +but at the very least it's really +difficult and nobody's nailed it + + align:start position:0% +difficult and nobody's nailed it + + + align:start position:0% +difficult and nobody's nailed it +so we can backtrack and ask the + + align:start position:0% +so we can backtrack and ask the + + + align:start position:0% +so we can backtrack and ask the +related not quite as definitive question + + align:start position:0% +related not quite as definitive question + + + align:start position:0% +related not quite as definitive question +but okay how early developing is it so + + align:start position:0% +but okay how early developing is it so + + + align:start position:0% +but okay how early developing is it so +often developmental psychologists kind + + align:start position:0% +often developmental psychologists kind + + + align:start position:0% +often developmental psychologists kind +of take this hedge it's like we can't + + align:start position:0% +of take this hedge it's like we can't + + + align:start position:0% +of take this hedge it's like we can't +exactly establish definitive innateness + + align:start position:0% +exactly establish definitive innateness + + + align:start position:0% +exactly establish definitive innateness +but if things are really there very + + align:start position:0% +but if things are really there very + + + align:start position:0% +but if things are really there very +early and develop very fast that's a + + align:start position:0% +early and develop very fast that's a + + + align:start position:0% +early and develop very fast that's a +suggestion that at least the system is + + align:start position:0% +suggestion that at least the system is + + + align:start position:0% +suggestion that at least the system is +designed to pick it up quickly so even + + align:start position:0% +designed to pick it up quickly so even + + + align:start position:0% +designed to pick it up quickly so even +if there's a role for experience there's + + align:start position:0% +if there's a role for experience there's + + + align:start position:0% +if there's a role for experience there's +some things that are picked up really + + align:start position:0% +some things that are picked up really + + + align:start position:0% +some things that are picked up really +fast and some things that aren't + + align:start position:0% +fast and some things that aren't + + + align:start position:0% +fast and some things that aren't +and so how quickly is it picked up + + align:start position:0% +and so how quickly is it picked up + + + align:start position:0% +and so how quickly is it picked up +so turns out there's a bunch of studies + + align:start position:0% +so turns out there's a bunch of studies + + + align:start position:0% +so turns out there's a bunch of studies +that have looked at this + + align:start position:0% +that have looked at this + + + align:start position:0% +that have looked at this +and young infants are in fact highly + + align:start position:0% +and young infants are in fact highly + + + align:start position:0% +and young infants are in fact highly +attuned to music + + align:start position:0% +attuned to music + + + align:start position:0% +attuned to music +they're sensitive to pitch + + align:start position:0% +they're sensitive to pitch + + + align:start position:0% +they're sensitive to pitch +and to rhythm + + align:start position:0% +and to rhythm + + + align:start position:0% +and to rhythm +and in one charming study they took two + + align:start position:0% +and in one charming study they took two + + + align:start position:0% +and in one charming study they took two +to three day old infants who were + + align:start position:0% +to three day old infants who were + + + align:start position:0% +to three day old infants who were +sleeping + + align:start position:0% +sleeping + + + align:start position:0% +sleeping +put eeg electrodes on them + + align:start position:0% +put eeg electrodes on them + + + align:start position:0% +put eeg electrodes on them +and played them + + align:start position:0% +and played them + + + align:start position:0% +and played them +um they wanted to test beat induction + + align:start position:0% +um they wanted to test beat induction + + + align:start position:0% +um they wanted to test beat induction +which is you know when you hear a + + align:start position:0% +which is you know when you hear a + + + align:start position:0% +which is you know when you hear a +rhythmic beat you get entrained to the + + align:start position:0% +rhythmic beat you get entrained to the + + + align:start position:0% +rhythmic beat you get entrained to the +beat and you know when the next beat is + + align:start position:0% +beat and you know when the next beat is + + + align:start position:0% +beat and you know when the next beat is +right and that's true even if it's not + + align:start position:0% +right and that's true even if it's not + + + align:start position:0% +right and that's true even if it's not +just a single pulse so they played these + + align:start position:0% +just a single pulse so they played these + + + align:start position:0% +just a single pulse so they played these +infants sounds like this + + align:start position:0% + + + + align:start position:0% + +oh but the audio's not on + + align:start position:0% + + + + align:start position:0% + +now it's going to blast everyone + + align:start position:0% + + + + align:start position:0% + +all right hang on + + align:start position:0% +all right hang on + + + align:start position:0% +all right hang on +oh it is playing turn up more okay + + align:start position:0% + + + + align:start position:0% + +i didn't want to deafen people + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +it's not but that's supposed to work + + align:start position:0% +it's not but that's supposed to work + + + align:start position:0% +it's not but that's supposed to work +right + + align:start position:0% +right + + + align:start position:0% +right +it has worked before + + align:start position:0% + + + + align:start position:0% + +let's just check your system settings + + align:start position:0% +let's just check your system settings + + + align:start position:0% +let's just check your system settings +really quickly + + align:start position:0% + + + + align:start position:0% + +because i can hear you from my system + + align:start position:0% +because i can hear you from my system + + + align:start position:0% +because i can hear you from my system +yeah it's weird okay + + align:start position:0% + + + + align:start position:0% + +wait if i can hear you from my system + + align:start position:0% +wait if i can hear you from my system + + + align:start position:0% +wait if i can hear you from my system +you are then it is going out yeah + + align:start position:0% +you are then it is going out yeah + + + align:start position:0% +you are then it is going out yeah +um oh somebody + + align:start position:0% +um oh somebody + + + align:start position:0% +um oh somebody +okay ah + + align:start position:0% +okay ah + + + align:start position:0% +okay ah +okay try it one more time okay here we + + align:start position:0% +okay try it one more time okay here we + + + align:start position:0% +okay try it one more time okay here we +go + + align:start position:0% + + + + align:start position:0% + +did you hear that glitch let me do it + + align:start position:0% +did you hear that glitch let me do it + + + align:start position:0% +did you hear that glitch let me do it +again + + align:start position:0% +again + + + align:start position:0% +again +let's take it back here + + align:start position:0% + + + + align:start position:0% + +everybody hear the hiccup in the in the + + align:start position:0% +everybody hear the hiccup in the in the + + + align:start position:0% +everybody hear the hiccup in the in the +beat + + align:start position:0% +beat + + + align:start position:0% +beat +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's what these guys tested they + + align:start position:0% +so that's what these guys tested they + + + align:start position:0% +so that's what these guys tested they +played rhythms like that + + align:start position:0% +played rhythms like that + + + align:start position:0% +played rhythms like that +to two to three day old infants + + align:start position:0% +to two to three day old infants + + + align:start position:0% +to two to three day old infants +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% + + + + align:start position:0% + +oh now it's working okay great okay + + align:start position:0% +oh now it's working okay great okay + + + align:start position:0% +oh now it's working okay great okay +anyway so here's what they find with + + align:start position:0% +anyway so here's what they find with + + + align:start position:0% +anyway so here's what they find with +their erps + + align:start position:0% +their erps + + + align:start position:0% +their erps +this is um the onset of that little + + align:start position:0% +this is um the onset of that little + + + align:start position:0% +this is um the onset of that little +hiccup + + align:start position:0% +hiccup + + + align:start position:0% +hiccup +the time when that beat was supposed to + + align:start position:0% +the time when that beat was supposed to + + + align:start position:0% +the time when that beat was supposed to +happen and didn't the missing beat right + + align:start position:0% +happen and didn't the missing beat right + + + align:start position:0% +happen and didn't the missing beat right +there and this is an erp response + + align:start position:0% +there and this is an erp response + + + align:start position:0% +there and this is an erp response +happening about 200 milliseconds later + + align:start position:0% +happening about 200 milliseconds later + + + align:start position:0% +happening about 200 milliseconds later +for that kind of missing but expected + + align:start position:0% +for that kind of missing but expected + + + align:start position:0% +for that kind of missing but expected +beat + + align:start position:0% +beat + + + align:start position:0% +beat +um and and um let's see this is a + + align:start position:0% +um and and um let's see this is a + + + align:start position:0% +um and and um let's see this is a +standard where the beat keeps going now + + align:start position:0% +standard where the beat keeps going now + + + align:start position:0% +standard where the beat keeps going now +you might say well of course they're + + align:start position:0% +you might say well of course they're + + + align:start position:0% +you might say well of course they're +different one has a beat there and one + + align:start position:0% +different one has a beat there and one + + + align:start position:0% +different one has a beat there and one +doesn't they're acoustically different + + align:start position:0% +doesn't they're acoustically different + + + align:start position:0% +doesn't they're acoustically different +so they have a control condition which + + align:start position:0% +so they have a control condition which + + + align:start position:0% +so they have a control condition which +has a beat but a different preceding uh + + align:start position:0% +has a beat but a different preceding uh + + + align:start position:0% +has a beat but a different preceding uh +context so where that beat is is not um + + align:start position:0% +context so where that beat is is not um + + + align:start position:0% +context so where that beat is is not um +i'm sorry where it has a missing beat + + align:start position:0% +i'm sorry where it has a missing beat + + + align:start position:0% +i'm sorry where it has a missing beat +but that's expected by the previous + + align:start position:0% +but that's expected by the previous + + + align:start position:0% +but that's expected by the previous +context okay so that's just evidence + + align:start position:0% +context okay so that's just evidence + + + align:start position:0% +context okay so that's just evidence +that um even young infants have some + + align:start position:0% +that um even young infants have some + + + align:start position:0% +that um even young infants have some +sense of + + align:start position:0% +sense of + + + align:start position:0% +sense of +of beat + + align:start position:0% +of beat + + + align:start position:0% +of beat +so moving a little later by five to six + + align:start position:0% +so moving a little later by five to six + + + align:start position:0% +so moving a little later by five to six +months + + align:start position:0% +months + + + align:start position:0% +months +infants can recognize a familiar melody + + align:start position:0% +infants can recognize a familiar melody + + + align:start position:0% +infants can recognize a familiar melody +even if it's shifted in pitch from the + + align:start position:0% +even if it's shifted in pitch from the + + + align:start position:0% +even if it's shifted in pitch from the +version that they learned okay and + + align:start position:0% +version that they learned okay and + + + align:start position:0% +version that they learned okay and +that's really cool because that means + + align:start position:0% +that's really cool because that means + + + align:start position:0% +that's really cool because that means +they use relative to pitch not absolute + + align:start position:0% +they use relative to pitch not absolute + + + align:start position:0% +they use relative to pitch not absolute +pitch and that's something that you know + + align:start position:0% +pitch and that's something that you know + + + align:start position:0% +pitch and that's something that you know +adults do in music we're very good at + + align:start position:0% +adults do in music we're very good at + + + align:start position:0% +adults do in music we're very good at +that but no animal can do that you can + + align:start position:0% +that but no animal can do that you can + + + align:start position:0% +that but no animal can do that you can +train animals to do various things like + + align:start position:0% +train animals to do various things like + + + align:start position:0% +train animals to do various things like +recognize a particular pair of sounds or + + align:start position:0% +recognize a particular pair of sounds or + + + align:start position:0% +recognize a particular pair of sounds or +even a few sounds a few pitches but if + + align:start position:0% +even a few sounds a few pitches but if + + + align:start position:0% +even a few sounds a few pitches but if +you transpose it they don't recognize + + align:start position:0% +you transpose it they don't recognize + + + align:start position:0% +you transpose it they don't recognize +that yeah + + align:start position:0% + + + + align:start position:0% + +yes hang on to that thought it takes + + align:start position:0% +yes hang on to that thought it takes + + + align:start position:0% +yes hang on to that thought it takes +more work to show that it's music per se + + align:start position:0% +more work to show that it's music per se + + + align:start position:0% +more work to show that it's music per se +rather than just rhythm and pitch we'd + + align:start position:0% +rather than just rhythm and pitch we'd + + + align:start position:0% +rather than just rhythm and pitch we'd +have to say what we meant by rhythm if + + align:start position:0% +have to say what we meant by rhythm if + + + align:start position:0% +have to say what we meant by rhythm if +we load a lot enough into the idea of + + align:start position:0% +we load a lot enough into the idea of + + + align:start position:0% +we load a lot enough into the idea of +rhythm then it's like most of music + + align:start position:0% +rhythm then it's like most of music + + + align:start position:0% +rhythm then it's like most of music +right there but you know we might say + + align:start position:0% +right there but you know we might say + + + align:start position:0% +right there but you know we might say +just even beat how about that right + + align:start position:0% +just even beat how about that right + + + align:start position:0% +just even beat how about that right +and actually already this study already + + align:start position:0% +and actually already this study already + + + align:start position:0% +and actually already this study already +is not just an even beat because it has + + align:start position:0% +is not just an even beat because it has + + + align:start position:0% +is not just an even beat because it has +more context than that that that is for + + align:start position:0% +more context than that that that is for + + + align:start position:0% +more context than that that that is for +example the the beats + + align:start position:0% +example the the beats + + + align:start position:0% +example the the beats +uh in this erp infant study + + align:start position:0% +uh in this erp infant study + + + align:start position:0% +uh in this erp infant study +were not um emphasized louder the + + align:start position:0% +were not um emphasized louder the + + + align:start position:0% +were not um emphasized louder the +infants have to be able to pick out what + + align:start position:0% +infants have to be able to pick out what + + + align:start position:0% +infants have to be able to pick out what +the beat is from that complex sound it's + + align:start position:0% +the beat is from that complex sound it's + + + align:start position:0% +the beat is from that complex sound it's +not it's not automatically there in the + + align:start position:0% +not it's not automatically there in the + + + align:start position:0% +not it's not automatically there in the +acoustic signal as the louder + + align:start position:0% +acoustic signal as the louder + + + align:start position:0% +acoustic signal as the louder +onset sound okay + + align:start position:0% +onset sound okay + + + align:start position:0% +onset sound okay +okay + + align:start position:0% + + + + align:start position:0% + +five month old infants if you play them + + align:start position:0% +five month old infants if you play them + + + align:start position:0% +five month old infants if you play them +a melody for one or two weeks so they + + align:start position:0% +a melody for one or two weeks so they + + + align:start position:0% +a melody for one or two weeks so they +get really familiar with it and learn it + + align:start position:0% +get really familiar with it and learn it + + + align:start position:0% +get really familiar with it and learn it +and then you don't play it again and you + + align:start position:0% +and then you don't play it again and you + + + align:start position:0% +and then you don't play it again and you +come back eight months later they + + align:start position:0% +come back eight months later they + + + align:start position:0% +come back eight months later they +remember it + + align:start position:0% +remember it + + + align:start position:0% +remember it +okay so music is really salient to + + align:start position:0% +okay so music is really salient to + + + align:start position:0% +okay so music is really salient to +infants + + align:start position:0% +infants + + + align:start position:0% +infants +on the other hand newborn infants + + align:start position:0% +on the other hand newborn infants + + + align:start position:0% +on the other hand newborn infants +appreciation of music is not uh um + + align:start position:0% + + + + align:start position:0% + +what is that not doing there + + align:start position:0% +what is that not doing there + + + align:start position:0% +what is that not doing there +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +that's right um so they don't prefer um + + align:start position:0% +that's right um so they don't prefer um + + + align:start position:0% +that's right um so they don't prefer um +consonants over dissonance + + align:start position:0% +consonants over dissonance + + + align:start position:0% +consonants over dissonance +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% +and um + + + align:start position:0% +and um +they're insensitive to key + + align:start position:0% +they're insensitive to key + + + align:start position:0% +they're insensitive to key +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so um and and and they um + + align:start position:0% +so um and and and they um + + + align:start position:0% +so um and and and they um +they detect + + align:start position:0% +they detect + + + align:start position:0% +they detect +timing changes in rhythms + + align:start position:0% +timing changes in rhythms + + + align:start position:0% +timing changes in rhythms +um whether they are timing changes that + + align:start position:0% +um whether they are timing changes that + + + align:start position:0% +um whether they are timing changes that +are typical in the kind of music they've + + align:start position:0% +are typical in the kind of music they've + + + align:start position:0% +are typical in the kind of music they've +heard + + align:start position:0% +heard + + + align:start position:0% +heard +or typical and a more foreign kind of + + align:start position:0% +or typical and a more foreign kind of + + + align:start position:0% +or typical and a more foreign kind of +music okay + + align:start position:0% +music okay + + + align:start position:0% +music okay +and so + + align:start position:0% +and so + + + align:start position:0% +and so +a really nice study that shows this + + align:start position:0% +a really nice study that shows this + + + align:start position:0% +a really nice study that shows this +is that in western music it's really + + align:start position:0% +is that in western music it's really + + + align:start position:0% +is that in western music it's really +common to have the most most western + + align:start position:0% +common to have the most most western + + + align:start position:0% +common to have the most most western +music has isochronous beat so you can + + align:start position:0% +music has isochronous beat so you can + + + align:start position:0% +music has isochronous beat so you can +see that over here here's an isochronous + + align:start position:0% +see that over here here's an isochronous + + + align:start position:0% +see that over here here's an isochronous +beat those are even temporal intervals + + align:start position:0% +beat those are even temporal intervals + + + align:start position:0% +beat those are even temporal intervals +and there's a whole note here and then + + align:start position:0% +and there's a whole note here and then + + + align:start position:0% +and there's a whole note here and then +half notes and they're all uh multiples + + align:start position:0% +half notes and they're all uh multiples + + + align:start position:0% +half notes and they're all uh multiples +of each other just holes and halves + + align:start position:0% +of each other just holes and halves + + + align:start position:0% +of each other just holes and halves +with the beat happening every four + + align:start position:0% + + + + align:start position:0% + +notes okay + + align:start position:0% +notes okay + + + align:start position:0% +notes okay +um non-isochronous beat has this funny + + align:start position:0% +um non-isochronous beat has this funny + + + align:start position:0% +um non-isochronous beat has this funny +business where there's a whole note then + + align:start position:0% +business where there's a whole note then + + + align:start position:0% +business where there's a whole note then +and a half note making up just um + + align:start position:0% +and a half note making up just um + + + align:start position:0% +and a half note making up just um +uh three + + align:start position:0% +uh three + + + align:start position:0% +uh three +what do you call those things they're + + align:start position:0% +what do you call those things they're + + + align:start position:0% +what do you call those things they're +not beats what are they called + + align:start position:0% +not beats what are they called + + + align:start position:0% +not beats what are they called +sorry three notes i guess but it's not + + align:start position:0% +sorry three notes i guess but it's not + + + align:start position:0% +sorry three notes i guess but it's not +even notes because it's whatever i don't + + align:start position:0% +even notes because it's whatever i don't + + + align:start position:0% +even notes because it's whatever i don't +know what the terminology is but anyway + + align:start position:0% +know what the terminology is but anyway + + + align:start position:0% +know what the terminology is but anyway +this sound here followed by four + + align:start position:0% +this sound here followed by four + + + align:start position:0% +this sound here followed by four +okay this is non-isochronous rhythm + + align:start position:0% +okay this is non-isochronous rhythm + + + align:start position:0% +okay this is non-isochronous rhythm +those are really common + + align:start position:0% +those are really common + + + align:start position:0% +those are really common +in uh balkan music um where they are + + align:start position:0% +in uh balkan music um where they are + + + align:start position:0% +in uh balkan music um where they are +they do all kinds of crazy things like + + align:start position:0% +they do all kinds of crazy things like + + + align:start position:0% +they do all kinds of crazy things like +you know 8 22 or something like that i + + align:start position:0% +you know 8 22 or something like that i + + + align:start position:0% +you know 8 22 or something like that i +mean like really really crazy musical + + align:start position:0% +mean like really really crazy musical + + + align:start position:0% +mean like really really crazy musical +meters they're awesome i love them uh + + align:start position:0% +meters they're awesome i love them uh + + + align:start position:0% +meters they're awesome i love them uh +but they're very other like you know if + + align:start position:0% +but they're very other like you know if + + + align:start position:0% +but they're very other like you know if +you + + align:start position:0% +you + + + align:start position:0% +you +grew up in a you know western society + + align:start position:0% +grew up in a you know western society + + + align:start position:0% +grew up in a you know western society +when you first hear balkan rhythms or + + align:start position:0% +when you first hear balkan rhythms or + + + align:start position:0% +when you first hear balkan rhythms or +it's very hard to copy them + + align:start position:0% +it's very hard to copy them + + + align:start position:0% +it's very hard to copy them +but + + align:start position:0% +but + + + align:start position:0% +but +six-month-old infants get rhythms + + align:start position:0% +six-month-old infants get rhythms + + + align:start position:0% +six-month-old infants get rhythms +equally well if there's isochronous or + + align:start position:0% +equally well if there's isochronous or + + + align:start position:0% +equally well if there's isochronous or +non-isochronous + + align:start position:0% +non-isochronous + + + align:start position:0% +non-isochronous +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um by 12 months they can only get + + align:start position:0% +um by 12 months they can only get + + + align:start position:0% +um by 12 months they can only get +automatically like immediately perceive + + align:start position:0% +automatically like immediately perceive + + + align:start position:0% +automatically like immediately perceive +and appreciate um rhythms uh that are + + align:start position:0% +and appreciate um rhythms uh that are + + + align:start position:0% +and appreciate um rhythms uh that are +familiar from their cultural exposure + + align:start position:0% +familiar from their cultural exposure + + + align:start position:0% +familiar from their cultural exposure +that is isochronous if they're from a + + align:start position:0% +that is isochronous if they're from a + + + align:start position:0% +that is isochronous if they're from a +western society or + + align:start position:0% +western society or + + + align:start position:0% +western society or +a non-isochronous if they're from a + + align:start position:0% +a non-isochronous if they're from a + + + align:start position:0% +a non-isochronous if they're from a +balkan country + + align:start position:0% + + + + align:start position:0% + +uh well so there's a whole bunch of + + align:start position:0% +uh well so there's a whole bunch of + + + align:start position:0% +uh well so there's a whole bunch of +studies i'm just summarizing here that + + align:start position:0% +studies i'm just summarizing here that + + + align:start position:0% +studies i'm just summarizing here that +is they're sensitive to violations right + + align:start position:0% +is they're sensitive to violations right + + + align:start position:0% +is they're sensitive to violations right +by all kinds of measures of you know + + align:start position:0% +by all kinds of measures of you know + + + align:start position:0% +by all kinds of measures of you know +little whatever behavioral thing you can + + align:start position:0% +little whatever behavioral thing you can + + + align:start position:0% +little whatever behavioral thing you can +get out of a five-month-old whether it's + + align:start position:0% +get out of a five-month-old whether it's + + + align:start position:0% +get out of a five-month-old whether it's +how much they're kicking their legs or + + align:start position:0% +how much they're kicking their legs or + + + align:start position:0% +how much they're kicking their legs or +how much often it's obvious how hard + + align:start position:0% +how much often it's obvious how hard + + + align:start position:0% +how much often it's obvious how hard +they're sucking on a pacifier is another + + align:start position:0% +they're sucking on a pacifier is another + + + align:start position:0% +they're sucking on a pacifier is another +measure so you just see can they detect + + align:start position:0% +measure so you just see can they detect + + + align:start position:0% +measure so you just see can they detect +changes in a stimulus or violations by + + align:start position:0% +changes in a stimulus or violations by + + + align:start position:0% +changes in a stimulus or violations by +any of those measures or you could do it + + align:start position:0% +any of those measures or you could do it + + + align:start position:0% +any of those measures or you could do it +with the earpiece okay + + align:start position:0% +with the earpiece okay + + + align:start position:0% +with the earpiece okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so brief exposure + + align:start position:0% +so brief exposure + + + align:start position:0% +so brief exposure +to a previously unfamiliar rhythm is + + align:start position:0% +to a previously unfamiliar rhythm is + + + align:start position:0% +to a previously unfamiliar rhythm is +enough for a 12 month old + + align:start position:0% +enough for a 12 month old + + + align:start position:0% +enough for a 12 month old +to uh to appreciate the relevant + + align:start position:0% +to uh to appreciate the relevant + + + align:start position:0% +to uh to appreciate the relevant +distinctions in that rhythm + + align:start position:0% +distinctions in that rhythm + + + align:start position:0% +distinctions in that rhythm +but not for adults + + align:start position:0% +but not for adults + + + align:start position:0% +but not for adults +okay so if you haven't heard + + align:start position:0% +okay so if you haven't heard + + + align:start position:0% +okay so if you haven't heard +non-isochronous balkan rhythms + + align:start position:0% +non-isochronous balkan rhythms + + + align:start position:0% +non-isochronous balkan rhythms +until now + + align:start position:0% +until now + + + align:start position:0% +until now +and you try dancing to them good luck to + + align:start position:0% +and you try dancing to them good luck to + + + align:start position:0% +and you try dancing to them good luck to +you + + align:start position:0% +you + + + align:start position:0% +you +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you can probably get it eventually but + + align:start position:0% +you can probably get it eventually but + + + align:start position:0% +you can probably get it eventually but +it will take you a long time + + align:start position:0% +it will take you a long time + + + align:start position:0% +it will take you a long time +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so does this sound familiar + + align:start position:0% + + + + align:start position:0% + +perceptual narrowing right so we keep + + align:start position:0% +perceptual narrowing right so we keep + + + align:start position:0% +perceptual narrowing right so we keep +encountering this we encountered this + + align:start position:0% +encountering this we encountered this + + + align:start position:0% +encountering this we encountered this +with face recognition + + align:start position:0% +with face recognition + + + align:start position:0% +with face recognition +um with um same versus other + + align:start position:0% +um with um same versus other + + + align:start position:0% +um with um same versus other +races same versus other species you see + + align:start position:0% +races same versus other species you see + + + align:start position:0% +races same versus other species you see +it in face recognition + + align:start position:0% +it in face recognition + + + align:start position:0% +it in face recognition +we encountered it with phoneme + + align:start position:0% +we encountered it with phoneme + + + align:start position:0% +we encountered it with phoneme +perception the phonemes remember infants + + align:start position:0% +perception the phonemes remember infants + + + align:start position:0% +perception the phonemes remember infants +newborn infants can distinguish all the + + align:start position:0% +newborn infants can distinguish all the + + + align:start position:0% +newborn infants can distinguish all the +phonemes of the world's languages even + + align:start position:0% +phonemes of the world's languages even + + + align:start position:0% +phonemes of the world's languages even +those exotic cliques that i played last + + align:start position:0% +those exotic cliques that i played last + + + align:start position:0% +those exotic cliques that i played last +time from southern african languages + + align:start position:0% +time from southern african languages + + + align:start position:0% +time from southern african languages +and you guys can't distinguish all those + + align:start position:0% +and you guys can't distinguish all those + + + align:start position:0% +and you guys can't distinguish all those +clicks + + align:start position:0% +clicks + + + align:start position:0% +clicks +now so that's perceptual narrowing and + + align:start position:0% +now so that's perceptual narrowing and + + + align:start position:0% +now so that's perceptual narrowing and +it makes sense of course because the + + align:start position:0% +it makes sense of course because the + + + align:start position:0% +it makes sense of course because the +reason we have perceptual narrowing is + + align:start position:0% +reason we have perceptual narrowing is + + + align:start position:0% +reason we have perceptual narrowing is +you don't you want to have invariance + + align:start position:0% +you don't you want to have invariance + + + align:start position:0% +you don't you want to have invariance +you want to appreciate the sameness of + + align:start position:0% +you want to appreciate the sameness of + + + align:start position:0% +you want to appreciate the sameness of +things across transformations and if + + align:start position:0% +things across transformations and if + + + align:start position:0% +things across transformations and if +your uh speech culture or your music + + align:start position:0% +your uh speech culture or your music + + + align:start position:0% +your uh speech culture or your music +culture is telling you these two things + + align:start position:0% +culture is telling you these two things + + + align:start position:0% +culture is telling you these two things +this variation doesn't count you want to + + align:start position:0% +this variation doesn't count you want to + + + align:start position:0% +this variation doesn't count you want to +throw away that difference and treat + + align:start position:0% +throw away that difference and treat + + + align:start position:0% +throw away that difference and treat +them as the same and then once you do + + align:start position:0% +them as the same and then once you do + + + align:start position:0% +them as the same and then once you do +that you can't make that discrimination + + align:start position:0% +that you can't make that discrimination + + + align:start position:0% +that you can't make that discrimination +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +right + + align:start position:0% +right + + + align:start position:0% +right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so on this question we started with is + + align:start position:0% +so on this question we started with is + + + align:start position:0% +so on this question we started with is +music in evolve capacity if so it should + + align:start position:0% +music in evolve capacity if so it should + + + align:start position:0% +music in evolve capacity if so it should +be innate and we haven't really answered + + align:start position:0% +be innate and we haven't really answered + + + align:start position:0% +be innate and we haven't really answered +that question maybe but as i said it's + + align:start position:0% +that question maybe but as i said it's + + + align:start position:0% +that question maybe but as i said it's +really hard + + align:start position:0% +really hard + + + align:start position:0% +really hard +and maybe ultimately unanswerable but + + align:start position:0% +and maybe ultimately unanswerable but + + + align:start position:0% +and maybe ultimately unanswerable but +certainly it's early developing + + align:start position:0% +certainly it's early developing + + + align:start position:0% +certainly it's early developing +what about this other question is it + + align:start position:0% +what about this other question is it + + + align:start position:0% +what about this other question is it +present in all human societies + + align:start position:0% +present in all human societies + + + align:start position:0% +present in all human societies +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh well i said before briefly that it is + + align:start position:0% +uh well i said before briefly that it is + + + align:start position:0% +uh well i said before briefly that it is +oh yeah sorry we have to back up and say + + align:start position:0% +oh yeah sorry we have to back up and say + + + align:start position:0% +oh yeah sorry we have to back up and say +okay what to answer this question we + + align:start position:0% +okay what to answer this question we + + + align:start position:0% +okay what to answer this question we +have to say what is music okay + + align:start position:0% +have to say what is music okay + + + align:start position:0% +have to say what is music okay +to answer whether it's present in all + + align:start position:0% +to answer whether it's present in all + + + align:start position:0% +to answer whether it's present in all +societies and this has been a real + + align:start position:0% +societies and this has been a real + + + align:start position:0% +societies and this has been a real +problem right because uh music is + + align:start position:0% +problem right because uh music is + + + align:start position:0% +problem right because uh music is +notoriously hard to define + + align:start position:0% +notoriously hard to define + + + align:start position:0% +notoriously hard to define +and many people have made a point of + + align:start position:0% +and many people have made a point of + + + align:start position:0% +and many people have made a point of +stretching the definition of music + + align:start position:0% +stretching the definition of music + + + align:start position:0% +stretching the definition of music +including the ridiculous and hilarious + + align:start position:0% +including the ridiculous and hilarious + + + align:start position:0% +including the ridiculous and hilarious +john + + align:start position:0% +john + + + align:start position:0% +john +cage + + align:start position:0% + + + + align:start position:0% + +okay so this is his 1960 tv + + align:start position:0% + + + + align:start position:0% + +a tape appearance machine which will + + align:start position:0% +a tape appearance machine which will + + + align:start position:0% +a tape appearance machine which will +provide much of the resets the machine + + align:start position:0% +provide much of the resets the machine + + + align:start position:0% +provide much of the resets the machine +so we can know where it is which will + + align:start position:0% +so we can know where it is which will + + + align:start position:0% +so we can know where it is which will +provide much of the background uh also + + align:start position:0% +provide much of the background uh also + + + align:start position:0% +provide much of the background uh also +he works with a stopwatch the reason he + + align:start position:0% +he works with a stopwatch the reason he + + + align:start position:0% +he works with a stopwatch the reason he +does this is because these sounds are in + + align:start position:0% +does this is because these sounds are in + + + align:start position:0% +does this is because these sounds are in +no sense accidental in their in their + + align:start position:0% +no sense accidental in their in their + + + align:start position:0% +no sense accidental in their in their +secrets they each must fall + + align:start position:0% +secrets they each must fall + + + align:start position:0% +secrets they each must fall +mathematically at a precise part so he + + align:start position:0% +mathematically at a precise part so he + + + align:start position:0% +mathematically at a precise part so he +watches him watch as he works he takes + + align:start position:0% +watches him watch as he works he takes + + + align:start position:0% +watches him watch as he works he takes +it seriously i think it's interesting if + + align:start position:0% +it seriously i think it's interesting if + + + align:start position:0% +it seriously i think it's interesting if +you are amused you may laugh uh if you + + align:start position:0% +you are amused you may laugh uh if you + + + align:start position:0% +you are amused you may laugh uh if you +like it you may buy the recording + + align:start position:0% +like it you may buy the recording + + + align:start position:0% +like it you may buy the recording +john cage and + + align:start position:0% +john cage and + + + align:start position:0% +john cage and +walmart + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +anyway it goes on like that + + align:start position:0% +anyway it goes on like that + + + align:start position:0% +anyway it goes on like that +i guess it was a little edgier in 1959 + + align:start position:0% +i guess it was a little edgier in 1959 + + + align:start position:0% +i guess it was a little edgier in 1959 +than it is now + + align:start position:0% +than it is now + + + align:start position:0% +than it is now +um but he's making a point + + align:start position:0% +um but he's making a point + + + align:start position:0% +um but he's making a point +he's making a point of what the hell is + + align:start position:0% +he's making a point of what the hell is + + + align:start position:0% +he's making a point of what the hell is +music + + align:start position:0% +music + + + align:start position:0% +music +right + + align:start position:0% +right + + + align:start position:0% +right +and he's saying i can call this music if + + align:start position:0% +and he's saying i can call this music if + + + align:start position:0% +and he's saying i can call this music if +i want + + align:start position:0% +i want + + + align:start position:0% +i want +and everybody's enjoying it + + align:start position:0% +and everybody's enjoying it + + + align:start position:0% +and everybody's enjoying it +anyway + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you can watch the youtube video if + + align:start position:0% +so you can watch the youtube video if + + + align:start position:0% +so you can watch the youtube video if +you want it's quite entertaining + + align:start position:0% +you want it's quite entertaining + + + align:start position:0% +you want it's quite entertaining +um + + align:start position:0% +um + + + align:start position:0% +um +despite this kind of nihilistic view + + align:start position:0% +despite this kind of nihilistic view + + + align:start position:0% +despite this kind of nihilistic view +that anything could count as music there + + align:start position:0% +that anything could count as music there + + + align:start position:0% +that anything could count as music there +are some things we can say + + align:start position:0% +are some things we can say + + + align:start position:0% +are some things we can say +first thing i'd say is if you want to + + align:start position:0% +first thing i'd say is if you want to + + + align:start position:0% +first thing i'd say is if you want to +study music + + align:start position:0% +study music + + + align:start position:0% +study music +you know one of your first things you + + align:start position:0% +you know one of your first things you + + + align:start position:0% +you know one of your first things you +run into is oh what's going to count you + + align:start position:0% +run into is oh what's going to count you + + + align:start position:0% +run into is oh what's going to count you +run into this problem here but actually + + align:start position:0% +run into this problem here but actually + + + align:start position:0% +run into this problem here but actually +i think that doesn't need to be so + + align:start position:0% +i think that doesn't need to be so + + + align:start position:0% +i think that doesn't need to be so +paralyzing as it feels at first you can + + align:start position:0% +paralyzing as it feels at first you can + + + align:start position:0% +paralyzing as it feels at first you can +just take the most canonical forms where + + align:start position:0% +just take the most canonical forms where + + + align:start position:0% +just take the most canonical forms where +all of your subjects will agree that + + align:start position:0% +all of your subjects will agree that + + + align:start position:0% +all of your subjects will agree that +this is music and this isn't and then + + align:start position:0% +this is music and this isn't and then + + + align:start position:0% +this is music and this isn't and then +someday you can study the edge cases + + align:start position:0% +someday you can study the edge cases + + + align:start position:0% +someday you can study the edge cases +later but you don't need to agonize + + align:start position:0% +later but you don't need to agonize + + + align:start position:0% +later but you don't need to agonize +about them in order to get off the + + align:start position:0% +about them in order to get off the + + + align:start position:0% +about them in order to get off the +ground and study it + + align:start position:0% +ground and study it + + + align:start position:0% +ground and study it +further we can ask what is music + + align:start position:0% +further we can ask what is music + + + align:start position:0% +further we can ask what is music +cross-culturally + + align:start position:0% +cross-culturally + + + align:start position:0% +cross-culturally +right i keep forgetting my next point + + align:start position:0% +right i keep forgetting my next point + + + align:start position:0% +right i keep forgetting my next point +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and let me make another point is that + + align:start position:0% +and let me make another point is that + + + align:start position:0% +and let me make another point is that +music is not just about a set of + + align:start position:0% +music is not just about a set of + + + align:start position:0% +music is not just about a set of +acoustic properties + + align:start position:0% +acoustic properties + + + align:start position:0% +acoustic properties +you may think of music as just an + + align:start position:0% +you may think of music as just an + + + align:start position:0% +you may think of music as just an +auditory thing a solitary experience + + align:start position:0% +auditory thing a solitary experience + + + align:start position:0% +auditory thing a solitary experience +because a lot of the time it's like that + + align:start position:0% +because a lot of the time it's like that + + + align:start position:0% +because a lot of the time it's like that +but remember that that's a very recent + + align:start position:0% +but remember that that's a very recent + + + align:start position:0% +but remember that that's a very recent +recent cultural invention + + align:start position:0% +recent cultural invention + + + align:start position:0% +recent cultural invention +right and throughout most of human + + align:start position:0% +right and throughout most of human + + + align:start position:0% +right and throughout most of human +evolution + + align:start position:0% +evolution + + + align:start position:0% +evolution +music has been a fundamentally social + + align:start position:0% +music has been a fundamentally social + + + align:start position:0% +music has been a fundamentally social +phenomenon + + align:start position:0% +phenomenon + + + align:start position:0% +phenomenon +more like this + + align:start position:0% +more like this + + + align:start position:0% +more like this +you know experienced in groups of people + + align:start position:0% +you know experienced in groups of people + + + align:start position:0% +you know experienced in groups of people +as a kind of deeply social + + align:start position:0% +as a kind of deeply social + + + align:start position:0% +as a kind of deeply social +communicative interactive kind of + + align:start position:0% +communicative interactive kind of + + + align:start position:0% +communicative interactive kind of +enterprise or even if not in a large + + align:start position:0% +enterprise or even if not in a large + + + align:start position:0% +enterprise or even if not in a large +group music is very social in this sense + + align:start position:0% +group music is very social in this sense + + + align:start position:0% +group music is very social in this sense +here there's a whole bunch of cool + + align:start position:0% +here there's a whole bunch of cool + + + align:start position:0% +here there's a whole bunch of cool +studies about the role of song + + align:start position:0% +studies about the role of song + + + align:start position:0% +studies about the role of song +in infants and how infants use song to + + align:start position:0% +in infants and how infants use song to + + + align:start position:0% +in infants and how infants use song to +glean information about their social + + align:start position:0% +glean information about their social + + + align:start position:0% +glean information about their social +environment + + align:start position:0% +environment + + + align:start position:0% +environment +and the point is just music is extremely + + align:start position:0% +and the point is just music is extremely + + + align:start position:0% +and the point is just music is extremely +social it's not just defined by its + + align:start position:0% +social it's not just defined by its + + + align:start position:0% +social it's not just defined by its +acoustic properties + + align:start position:0% +acoustic properties + + + align:start position:0% +acoustic properties +okay but in addition + + align:start position:0% +okay but in addition + + + align:start position:0% +okay but in addition +uh we can ask okay let's look across + + align:start position:0% +uh we can ask okay let's look across + + + align:start position:0% +uh we can ask okay let's look across +the um cultures of the world and ask + + align:start position:0% +the um cultures of the world and ask + + + align:start position:0% +the um cultures of the world and ask +are there universals of music is there + + align:start position:0% +are there universals of music is there + + + align:start position:0% +are there universals of music is there +anything in common + + align:start position:0% +anything in common + + + align:start position:0% +anything in common +across all the different kinds of music + + align:start position:0% +across all the different kinds of music + + + align:start position:0% +across all the different kinds of music +that people + + align:start position:0% +that people + + + align:start position:0% +that people +experience in different cultures for + + align:start position:0% +experience in different cultures for + + + align:start position:0% +experience in different cultures for +example are there always discrete + + align:start position:0% +example are there always discrete + + + align:start position:0% +example are there always discrete +pitches or always isochronous beats i + + align:start position:0% +pitches or always isochronous beats i + + + align:start position:0% +pitches or always isochronous beats i +already showed you there aren't always + + align:start position:0% +already showed you there aren't always + + + align:start position:0% +already showed you there aren't always +acronis beads and this is nice because + + align:start position:0% +acronis beads and this is nice because + + + align:start position:0% +acronis beads and this is nice because +it's an empirical question + + align:start position:0% +it's an empirical question + + + align:start position:0% +it's an empirical question +there's a really cool paper from a few + + align:start position:0% +there's a really cool paper from a few + + + align:start position:0% +there's a really cool paper from a few +years ago where they took recordings of + + align:start position:0% +years ago where they took recordings of + + + align:start position:0% +years ago where they took recordings of +music from all over the world all those + + align:start position:0% +music from all over the world all those + + + align:start position:0% +music from all over the world all those +colored dots + + align:start position:0% +colored dots + + + align:start position:0% +colored dots +and they asked + + align:start position:0% +and they asked + + + align:start position:0% +and they asked +what are the properties that are present + + align:start position:0% +what are the properties that are present + + + align:start position:0% +what are the properties that are present +in + + align:start position:0% +in + + + align:start position:0% +in +in + + align:start position:0% +in + + + align:start position:0% +in +most of those musics and how prevalent + + align:start position:0% +most of those musics and how prevalent + + + align:start position:0% +most of those musics and how prevalent +are they and what they found is there's + + align:start position:0% +are they and what they found is there's + + + align:start position:0% +are they and what they found is there's +no single property of music that's + + align:start position:0% +no single property of music that's + + + align:start position:0% +no single property of music that's +present in all of those cultures but + + align:start position:0% +present in all of those cultures but + + + align:start position:0% +present in all of those cultures but +there's many that are present in most + + align:start position:0% +there's many that are present in most + + + align:start position:0% +there's many that are present in most +and there are a lot of regularities + + align:start position:0% +and there are a lot of regularities + + + align:start position:0% +and there are a lot of regularities +so this is a huge table from their um + + align:start position:0% +so this is a huge table from their um + + + align:start position:0% +so this is a huge table from their um +paper where they list many different + + align:start position:0% +paper where they list many different + + + align:start position:0% +paper where they list many different +possible + + align:start position:0% +possible + + + align:start position:0% +possible +universals and what you see is the + + align:start position:0% +universals and what you see is the + + + align:start position:0% +universals and what you see is the +relevant column is this one here and the + + align:start position:0% +relevant column is this one here and the + + + align:start position:0% +relevant column is this one here and the +white is the percent of those 304 + + align:start position:0% +white is the percent of those 304 + + + align:start position:0% +white is the percent of those 304 +cultures that they looked at that have + + align:start position:0% +cultures that they looked at that have + + + align:start position:0% +cultures that they looked at that have +that property in their music okay so + + align:start position:0% +that property in their music okay so + + + align:start position:0% +that property in their music okay so +these top ones are very prevalent just + + align:start position:0% +these top ones are very prevalent just + + + align:start position:0% +these top ones are very prevalent just +not quite universal because there's a + + align:start position:0% +not quite universal because there's a + + + align:start position:0% +not quite universal because there's a +couple of cases that don't happen + + align:start position:0% +couple of cases that don't happen + + + align:start position:0% +couple of cases that don't happen +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um so one of the most common ones is + + align:start position:0% +um so one of the most common ones is + + + align:start position:0% +um so one of the most common ones is +idea that melodies are made up made from + + align:start position:0% +idea that melodies are made up made from + + + align:start position:0% +idea that melodies are made up made from +a limited set of discrete pitches seven + + align:start position:0% +a limited set of discrete pitches seven + + + align:start position:0% +a limited set of discrete pitches seven +or fewer + + align:start position:0% +or fewer + + + align:start position:0% +or fewer +and that those pitches are arranged in + + align:start position:0% +and that those pitches are arranged in + + + align:start position:0% +and that those pitches are arranged in +some kind of scale + + align:start position:0% +some kind of scale + + + align:start position:0% +some kind of scale +with unequal intervals between the notes + + align:start position:0% +with unequal intervals between the notes + + + align:start position:0% +with unequal intervals between the notes +okay so that's as close to a universal + + align:start position:0% +okay so that's as close to a universal + + + align:start position:0% +okay so that's as close to a universal +of music as you can get although you can + + align:start position:0% +of music as you can get although you can + + + align:start position:0% +of music as you can get although you can +see from that little teeny black snip + + align:start position:0% +see from that little teeny black snip + + + align:start position:0% +see from that little teeny black snip +that it's not quite perfectly universal + + align:start position:0% +that it's not quite perfectly universal + + + align:start position:0% +that it's not quite perfectly universal +uh and the second thing is that most + + align:start position:0% +uh and the second thing is that most + + + align:start position:0% +uh and the second thing is that most +music + + align:start position:0% +music + + + align:start position:0% +music +has some kind of regular pulse right + + align:start position:0% +has some kind of regular pulse right + + + align:start position:0% +has some kind of regular pulse right +either an isochronous beat or even the + + align:start position:0% +either an isochronous beat or even the + + + align:start position:0% +either an isochronous beat or even the +non-isochronous ones + + align:start position:0% +non-isochronous ones + + + align:start position:0% +non-isochronous ones +have different subdivisions with + + align:start position:0% +have different subdivisions with + + + align:start position:0% +have different subdivisions with +different numbers of beats so that + + align:start position:0% +different numbers of beats so that + + + align:start position:0% +different numbers of beats so that +there's a systematic rhythmic pattern + + align:start position:0% +there's a systematic rhythmic pattern + + + align:start position:0% +there's a systematic rhythmic pattern +okay so there's + + align:start position:0% +okay so there's + + + align:start position:0% +okay so there's +something kind of like melody and + + align:start position:0% +something kind of like melody and + + + align:start position:0% +something kind of like melody and +something kind of like rhythm in almost + + align:start position:0% +something kind of like rhythm in almost + + + align:start position:0% +something kind of like rhythm in almost +all the world's musics + + align:start position:0% +all the world's musics + + + align:start position:0% +all the world's musics +they did find some pretty weird ones + + align:start position:0% +they did find some pretty weird ones + + + align:start position:0% +they did find some pretty weird ones +one i can't resist playing for you this + + align:start position:0% +one i can't resist playing for you this + + + align:start position:0% +one i can't resist playing for you this +is from papua new guinea + + align:start position:0% +is from papua new guinea + + + align:start position:0% +is from papua new guinea +so as they say the closest thing to an + + align:start position:0% +so as they say the closest thing to an + + + align:start position:0% +so as they say the closest thing to an +absolute universal was song containing + + align:start position:0% +absolute universal was song containing + + + align:start position:0% +absolute universal was song containing +discreet pitches or regular rhythmic + + align:start position:0% +discreet pitches or regular rhythmic + + + align:start position:0% +discreet pitches or regular rhythmic +patterns or both + + align:start position:0% +patterns or both + + + align:start position:0% +patterns or both +which implied to almost the entire + + align:start position:0% +which implied to almost the entire + + + align:start position:0% +which implied to almost the entire +sample however music examples from papua + + align:start position:0% +sample however music examples from papua + + + align:start position:0% +sample however music examples from papua +new guinea + + align:start position:0% +new guinea + + + align:start position:0% +new guinea +contain combinations of + + align:start position:0% +contain combinations of + + + align:start position:0% +contain combinations of +friction blocks swung slats ribbon reeds + + align:start position:0% +friction blocks swung slats ribbon reeds + + + align:start position:0% +friction blocks swung slats ribbon reeds +and moaning voices i don't know what + + align:start position:0% +and moaning voices i don't know what + + + align:start position:0% +and moaning voices i don't know what +those things are either but i'll play + + align:start position:0% +those things are either but i'll play + + + align:start position:0% +those things are either but i'll play +them for you in a second + + align:start position:0% +them for you in a second + + + align:start position:0% +them for you in a second +uh that contained neither discrete + + align:start position:0% +uh that contained neither discrete + + + align:start position:0% +uh that contained neither discrete +pitches + + align:start position:0% +pitches + + + align:start position:0% +pitches +nor an isochronous beat okay here we go + + align:start position:0% +nor an isochronous beat okay here we go + + + align:start position:0% +nor an isochronous beat okay here we go +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay pretty wild huh + + align:start position:0% +okay pretty wild huh + + + align:start position:0% +okay pretty wild huh +okay so uh maybe wilder arguably than + + align:start position:0% +okay so uh maybe wilder arguably than + + + align:start position:0% +okay so uh maybe wilder arguably than +john cage but anyway so there are some + + align:start position:0% +john cage but anyway so there are some + + + align:start position:0% +john cage but anyway so there are some +like pretty um pretty um remote edges to + + align:start position:0% +like pretty um pretty um remote edges to + + + align:start position:0% +like pretty um pretty um remote edges to +the concept of of music + + align:start position:0% +the concept of of music + + + align:start position:0% +the concept of of music +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um i mentioned before uh the case of + + align:start position:0% +um i mentioned before uh the case of + + + align:start position:0% +um i mentioned before uh the case of +consonants and dissonance and that + + align:start position:0% +consonants and dissonance and that + + + align:start position:0% +consonants and dissonance and that +infants don't prefer one over the other + + align:start position:0% +infants don't prefer one over the other + + + align:start position:0% +infants don't prefer one over the other +um in fact this this uh links to a + + align:start position:0% +um in fact this this uh links to a + + + align:start position:0% +um in fact this this uh links to a +really cool recent study from josh + + align:start position:0% +really cool recent study from josh + + + align:start position:0% +really cool recent study from josh +mcdermott's lab and so the question he + + align:start position:0% +mcdermott's lab and so the question he + + + align:start position:0% +mcdermott's lab and so the question he +asked is why do we like consonant sounds + + align:start position:0% +asked is why do we like consonant sounds + + + align:start position:0% +asked is why do we like consonant sounds +like this + + align:start position:0% +like this + + + align:start position:0% +like this +whoops i'm gonna play + + align:start position:0% +whoops i'm gonna play + + + align:start position:0% +whoops i'm gonna play +here we go + + align:start position:0% +here we go + + + align:start position:0% +here we go +kind of nice right + + align:start position:0% +kind of nice right + + + align:start position:0% +kind of nice right +but we're not so + + align:start position:0% +but we're not so + + + align:start position:0% +but we're not so +hot about this + + align:start position:0% +hot about this + + + align:start position:0% +hot about this +right everybody get that intuition okay + + align:start position:0% +right everybody get that intuition okay + + + align:start position:0% +right everybody get that intuition okay +so what's up with that + + align:start position:0% +so what's up with that + + + align:start position:0% +so what's up with that +um so many people have hypothesized for + + align:start position:0% +um so many people have hypothesized for + + + align:start position:0% +um so many people have hypothesized for +a long time that that difference is + + align:start position:0% +a long time that that difference is + + + align:start position:0% +a long time that that difference is +based in biology or there even it's like + + align:start position:0% +based in biology or there even it's like + + + align:start position:0% +based in biology or there even it's like +a physical uh analog of it beats and + + align:start position:0% +a physical uh analog of it beats and + + + align:start position:0% +a physical uh analog of it beats and +stuff like that + + align:start position:0% +stuff like that + + + align:start position:0% +stuff like that +but actually uh it's a it's an empirical + + align:start position:0% +but actually uh it's a it's an empirical + + + align:start position:0% +but actually uh it's a it's an empirical +question and so one way to ask that + + align:start position:0% +question and so one way to ask that + + + align:start position:0% +question and so one way to ask that +question is to + + align:start position:0% +question is to + + + align:start position:0% +question is to +go to a culture that's had minimal + + align:start position:0% +go to a culture that's had minimal + + + align:start position:0% +go to a culture that's had minimal +exposure to western music all of which + + align:start position:0% +exposure to western music all of which + + + align:start position:0% +exposure to western music all of which +really prefers consonants over + + align:start position:0% +really prefers consonants over + + + align:start position:0% +really prefers consonants over +dissonance yes kylie + + align:start position:0% + + + + align:start position:0% + +oh yeah yeah i'm sorry totally different + + align:start position:0% +oh yeah yeah i'm sorry totally different + + + align:start position:0% +oh yeah yeah i'm sorry totally different +word consonants + + align:start position:0% +word consonants + + + align:start position:0% +word consonants +c-e has no relationship to consonant + + align:start position:0% +c-e has no relationship to consonant + + + align:start position:0% +c-e has no relationship to consonant +consonants + + align:start position:0% +consonants + + + align:start position:0% +consonants +as distinguished from vowels okay a + + align:start position:0% +as distinguished from vowels okay a + + + align:start position:0% +as distinguished from vowels okay a +consonant and a vowel those are two + + align:start position:0% +consonant and a vowel those are two + + + align:start position:0% +consonant and a vowel those are two +different kinds of phonemes + + align:start position:0% +different kinds of phonemes + + + align:start position:0% +different kinds of phonemes +here consonants is that difference + + align:start position:0% +here consonants is that difference + + + align:start position:0% +here consonants is that difference +between those two sounds i just played + + align:start position:0% +between those two sounds i just played + + + align:start position:0% +between those two sounds i just played +right and it has to do with the um the + + align:start position:0% +right and it has to do with the um the + + + align:start position:0% +right and it has to do with the um the +precise intervals of those + + align:start position:0% +precise intervals of those + + + align:start position:0% +precise intervals of those +of those harmonics in the harmonic stack + + align:start position:0% +of those harmonics in the harmonic stack + + + align:start position:0% +of those harmonics in the harmonic stack +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +okay so what mcdermott and his + + align:start position:0% +okay so what mcdermott and his + + + align:start position:0% +okay so what mcdermott and his +co-workers did + + align:start position:0% +co-workers did + + + align:start position:0% +co-workers did +is go to go to a bolivian culture + + align:start position:0% +is go to go to a bolivian culture + + + align:start position:0% +is go to go to a bolivian culture +in the rain forest in a very remote + + align:start position:0% +in the rain forest in a very remote + + + align:start position:0% +in the rain forest in a very remote +location + + align:start position:0% +location + + + align:start position:0% +location +to test these people here the chimane + + align:start position:0% +to test these people here the chimane + + + align:start position:0% +to test these people here the chimane +and the chimane black televisions and + + align:start position:0% +and the chimane black televisions and + + + align:start position:0% +and the chimane black televisions and +have very little access to + + align:start position:0% +have very little access to + + + align:start position:0% +have very little access to +recorded music and radio + + align:start position:0% +recorded music and radio + + + align:start position:0% +recorded music and radio +their village doesn't have electricity + + align:start position:0% +their village doesn't have electricity + + + align:start position:0% +their village doesn't have electricity +or tap water you can't get there by road + + align:start position:0% +or tap water you can't get there by road + + + align:start position:0% +or tap water you can't get there by road +and you have to get there by canoe + + align:start position:0% +and you have to get there by canoe + + + align:start position:0% +and you have to get there by canoe +so that's what mcdermott and his team + + align:start position:0% +so that's what mcdermott and his team + + + align:start position:0% +so that's what mcdermott and his team +did they went down there to visit the + + align:start position:0% +did they went down there to visit the + + + align:start position:0% +did they went down there to visit the +chimane + + align:start position:0% +chimane + + + align:start position:0% +chimane +and + + align:start position:0% +and + + + align:start position:0% +and +and what they found they played them + + align:start position:0% +and what they found they played them + + + align:start position:0% +and what they found they played them +consonant sounds and dissonant sounds + + align:start position:0% +consonant sounds and dissonant sounds + + + align:start position:0% +consonant sounds and dissonant sounds +and with a translator and spent a lot of + + align:start position:0% +and with a translator and spent a lot of + + + align:start position:0% +and with a translator and spent a lot of +time making sure that they really + + align:start position:0% +time making sure that they really + + + align:start position:0% +time making sure that they really +understood the difference between + + align:start position:0% +understood the difference between + + + align:start position:0% +understood the difference between +liking and not liking and they tested + + align:start position:0% +liking and not liking and they tested + + + align:start position:0% +liking and not liking and they tested +their understanding of what it means to + + align:start position:0% +their understanding of what it means to + + + align:start position:0% +their understanding of what it means to +like something or not like it and all + + align:start position:0% +like something or not like it and all + + + align:start position:0% +like something or not like it and all +kinds of other ways and the upshot is + + align:start position:0% +kinds of other ways and the upshot is + + + align:start position:0% +kinds of other ways and the upshot is +the chimani do not have a present a + + align:start position:0% +the chimani do not have a present a + + + align:start position:0% +the chimani do not have a present a +preference for consonants over + + align:start position:0% +preference for consonants over + + + align:start position:0% +preference for consonants over +dissonance + + align:start position:0% +dissonance + + + align:start position:0% +dissonance +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so it's not a cultural universal + + align:start position:0% +so it's not a cultural universal + + + align:start position:0% +so it's not a cultural universal +and that's consistent with the idea that + + align:start position:0% +and that's consistent with the idea that + + + align:start position:0% +and that's consistent with the idea that +it's not a preference in infants either + + align:start position:0% +it's not a preference in infants either + + + align:start position:0% +it's not a preference in infants either +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so this is something specific to + + align:start position:0% +okay so this is something specific to + + + align:start position:0% +okay so this is something specific to +western music + + align:start position:0% +western music + + + align:start position:0% +western music +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's kind of introduction to what + + align:start position:0% +so that's kind of introduction to what + + + align:start position:0% +so that's kind of introduction to what +you know some stuff about what music is + + align:start position:0% +you know some stuff about what music is + + + align:start position:0% +you know some stuff about what music is +and what its variability is and the fact + + align:start position:0% +and what its variability is and the fact + + + align:start position:0% +and what its variability is and the fact +that it's + + align:start position:0% +that it's + + + align:start position:0% +that it's +its presence is universal and there are + + align:start position:0% +its presence is universal and there are + + + align:start position:0% +its presence is universal and there are +many very common properties across the + + align:start position:0% +many very common properties across the + + + align:start position:0% +many very common properties across the +world's musics and it develops early + + align:start position:0% +world's musics and it develops early + + + align:start position:0% +world's musics and it develops early +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so let's ask is music a separate + + align:start position:0% +uh so let's ask is music a separate + + + align:start position:0% +uh so let's ask is music a separate +capacity in the mind and brain all right + + align:start position:0% +capacity in the mind and brain all right + + + align:start position:0% +capacity in the mind and brain all right +so let's start with the classic way this + + align:start position:0% +so let's start with the classic way this + + + align:start position:0% +so let's start with the classic way this +has been asked for many decades and + + align:start position:0% +has been asked for many decades and + + + align:start position:0% +has been asked for many decades and +that's to study patients with brain + + align:start position:0% +that's to study patients with brain + + + align:start position:0% +that's to study patients with brain +damage + + align:start position:0% +damage + + + align:start position:0% +damage +and it turns out there is such a thing + + align:start position:0% +and it turns out there is such a thing + + + align:start position:0% +and it turns out there is such a thing +as amusia the loss of music ability + + align:start position:0% +as amusia the loss of music ability + + + align:start position:0% +as amusia the loss of music ability +after brain damage okay + + align:start position:0% +after brain damage okay + + + align:start position:0% +after brain damage okay +um or um yeah and so there are both + + align:start position:0% +um or um yeah and so there are both + + + align:start position:0% +um or um yeah and so there are both +sides of this there are people who have + + align:start position:0% +sides of this there are people who have + + + align:start position:0% +sides of this there are people who have +impaired ability to recognize melodies + + align:start position:0% +impaired ability to recognize melodies + + + align:start position:0% +impaired ability to recognize melodies +without impaired speech perception and + + align:start position:0% +without impaired speech perception and + + + align:start position:0% +without impaired speech perception and +there's the opposite people who have + + align:start position:0% +there's the opposite people who have + + + align:start position:0% +there's the opposite people who have +impaired speech recognition without + + align:start position:0% +impaired speech recognition without + + + align:start position:0% +impaired speech recognition without +impaired melody recognition + + align:start position:0% +impaired melody recognition + + + align:start position:0% +impaired melody recognition +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that is of course a double + + align:start position:0% +so that is of course a double + + + align:start position:0% +so that is of course a double +dissociation sort of it's a little mucky + + align:start position:0% +dissociation sort of it's a little mucky + + + align:start position:0% +dissociation sort of it's a little mucky +in there i'm just if you state the words + + align:start position:0% +in there i'm just if you state the words + + + align:start position:0% +in there i'm just if you state the words +simply like that if you look in detail + + align:start position:0% +simply like that if you look in detail + + + align:start position:0% +simply like that if you look in detail +there's some muck as there often is + + align:start position:0% +there's some muck as there often is + + + align:start position:0% +there's some muck as there often is +so let's look in a little more detail at + + align:start position:0% +so let's look in a little more detail at + + + align:start position:0% +so let's look in a little more detail at +these two cases the most interesting + + align:start position:0% +these two cases the most interesting + + + align:start position:0% +these two cases the most interesting +ones who + + align:start position:0% +ones who + + + align:start position:0% +ones who +who seem to have + + align:start position:0% +who seem to have + + + align:start position:0% +who seem to have +problems with auditory tunes but not + + align:start position:0% +problems with auditory tunes but not + + + align:start position:0% +problems with auditory tunes but not +with words or other familiar sounds + + align:start position:0% +with words or other familiar sounds + + + align:start position:0% +with words or other familiar sounds +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so here is a horizontal slice this is an + + align:start position:0% +so here is a horizontal slice this is an + + + align:start position:0% +so here is a horizontal slice this is an +old study so it's a cat scan showing you + + align:start position:0% +old study so it's a cat scan showing you + + + align:start position:0% +old study so it's a cat scan showing you +something's up with the anterior + + align:start position:0% +something's up with the anterior + + + align:start position:0% +something's up with the anterior +temporal lobes in this patient + + align:start position:0% +temporal lobes in this patient + + + align:start position:0% +temporal lobes in this patient +and this was true of these two + + align:start position:0% +and this was true of these two + + + align:start position:0% +and this was true of these two +classic patients cn and gl both of them + + align:start position:0% +classic patients cn and gl both of them + + + align:start position:0% +classic patients cn and gl both of them +were very bad at recognizing melodies + + align:start position:0% +were very bad at recognizing melodies + + + align:start position:0% +were very bad at recognizing melodies +okay even highly familiar melodies you + + align:start position:0% +okay even highly familiar melodies you + + + align:start position:0% +okay even highly familiar melodies you +know happy birthday and stuff like that + + align:start position:0% +know happy birthday and stuff like that + + + align:start position:0% +know happy birthday and stuff like that +they don't recognize + + align:start position:0% +they don't recognize + + + align:start position:0% +they don't recognize +um they mostly have intact rhythm + + align:start position:0% +um they mostly have intact rhythm + + + align:start position:0% +um they mostly have intact rhythm +perception and this is a this is a core + + align:start position:0% +perception and this is a this is a core + + + align:start position:0% +perception and this is a this is a core +question we'll come back to it's a + + align:start position:0% +question we'll come back to it's a + + + align:start position:0% +question we'll come back to it's a +complicated non-resolved situation but + + align:start position:0% +complicated non-resolved situation but + + + align:start position:0% +complicated non-resolved situation but +these guys had intact rhythm perception + + align:start position:0% +these guys had intact rhythm perception + + + align:start position:0% +these guys had intact rhythm perception +and relatively intact language and + + align:start position:0% +and relatively intact language and + + + align:start position:0% +and relatively intact language and +speech perception + + align:start position:0% +speech perception + + + align:start position:0% +speech perception +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +however + + align:start position:0% +however + + + align:start position:0% +however +upon further testing it becomes clear + + align:start position:0% +upon further testing it becomes clear + + + align:start position:0% +upon further testing it becomes clear +that these guys have a more general + + align:start position:0% +that these guys have a more general + + + align:start position:0% +that these guys have a more general +problem with pitch perception + + align:start position:0% +problem with pitch perception + + + align:start position:0% +problem with pitch perception +okay + + align:start position:0% +okay + + + align:start position:0% +okay +even if it's not + + align:start position:0% +even if it's not + + + align:start position:0% +even if it's not +in the context of music okay so this is + + align:start position:0% +in the context of music okay so this is + + + align:start position:0% +in the context of music okay so this is +a question that i asked all of you guys + + align:start position:0% +a question that i asked all of you guys + + + align:start position:0% +a question that i asked all of you guys +to think about for in the opposite + + align:start position:0% +to think about for in the opposite + + + align:start position:0% +to think about for in the opposite +direction in your assignment um for + + align:start position:0% +direction in your assignment um for + + + align:start position:0% +direction in your assignment um for +sunday night right when i asked you + + align:start position:0% +sunday night right when i asked you + + + align:start position:0% +sunday night right when i asked you +whether those um + + align:start position:0% +whether those um + + + align:start position:0% +whether those um +electrodes in in the brains of epilepsy + + align:start position:0% +electrodes in in the brains of epilepsy + + + align:start position:0% +electrodes in in the brains of epilepsy +patients that are sensitive to music too + + align:start position:0% +patients that are sensitive to music too + + + align:start position:0% +patients that are sensitive to music too +sorry to speech porosity to the + + align:start position:0% +sorry to speech porosity to the + + + align:start position:0% +sorry to speech porosity to the +intonation contour in speech i asked you + + align:start position:0% +intonation contour in speech i asked you + + + align:start position:0% +intonation contour in speech i asked you +whether you whether you thought they + + align:start position:0% +whether you whether you thought they + + + align:start position:0% +whether you whether you thought they +would also be sensitive to the + + align:start position:0% +would also be sensitive to the + + + align:start position:0% +would also be sensitive to the +intonation contour in melodies and most + + align:start position:0% +intonation contour in melodies and most + + + align:start position:0% +intonation contour in melodies and most +of you said yes it's pitch pitch contour + + align:start position:0% +of you said yes it's pitch pitch contour + + + align:start position:0% +of you said yes it's pitch pitch contour +must be + + align:start position:0% +must be + + + align:start position:0% +must be +well it's a perfectly reasonable + + align:start position:0% +well it's a perfectly reasonable + + + align:start position:0% +well it's a perfectly reasonable +speculation but not necessarily maybe we + + align:start position:0% +speculation but not necessarily maybe we + + + align:start position:0% +speculation but not necessarily maybe we +have special pitch contour processing + + align:start position:0% +have special pitch contour processing + + + align:start position:0% +have special pitch contour processing +for speech and different pitch contour + + align:start position:0% +for speech and different pitch contour + + + align:start position:0% +for speech and different pitch contour +processing for music right it's possible + + align:start position:0% +processing for music right it's possible + + + align:start position:0% +processing for music right it's possible +it's an empirical question was there a + + align:start position:0% +it's an empirical question was there a + + + align:start position:0% +it's an empirical question was there a +question back there a second ago okay + + align:start position:0% +question back there a second ago okay + + + align:start position:0% +question back there a second ago okay +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +maybe this is about uh pitch for both + + align:start position:0% +maybe this is about uh pitch for both + + + align:start position:0% +maybe this is about uh pitch for both +speech and music uh not music per se + + align:start position:0% +speech and music uh not music per se + + + align:start position:0% +speech and music uh not music per se +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um and so there are there are more + + align:start position:0% +um and so there are there are more + + + align:start position:0% +um and so there are there are more +detailed studies of patients with + + align:start position:0% +detailed studies of patients with + + + align:start position:0% +detailed studies of patients with +congenital amnesia and just like the + + align:start position:0% +congenital amnesia and just like the + + + align:start position:0% +congenital amnesia and just like the +case with + + align:start position:0% +case with + + + align:start position:0% +case with +acquired prosopagnosia versus congenital + + align:start position:0% +acquired prosopagnosia versus congenital + + + align:start position:0% +acquired prosopagnosia versus congenital +prosopagnosia whether you get it from + + align:start position:0% +prosopagnosia whether you get it from + + + align:start position:0% +prosopagnosia whether you get it from +brain damage as an adult or whether + + align:start position:0% +brain damage as an adult or whether + + + align:start position:0% +brain damage as an adult or whether +you've just always had it your whole + + align:start position:0% +you've just always had it your whole + + + align:start position:0% +you've just always had it your whole +life and nobody knows exactly why and + + align:start position:0% +life and nobody knows exactly why and + + + align:start position:0% +life and nobody knows exactly why and +there's no evidence of any brain damage + + align:start position:0% +there's no evidence of any brain damage + + + align:start position:0% +there's no evidence of any brain damage +the same thing happens with a congenital + + align:start position:0% +the same thing happens with a congenital + + + align:start position:0% +the same thing happens with a congenital +amnesia + + align:start position:0% +amnesia + + + align:start position:0% +amnesia +so something like four percent of the + + align:start position:0% +so something like four percent of the + + + align:start position:0% +so something like four percent of the +population + + align:start position:0% +population + + + align:start position:0% +population +is you know they might say they're tone + + align:start position:0% +is you know they might say they're tone + + + align:start position:0% +is you know they might say they're tone +deaf but just to tell you what that + + align:start position:0% +deaf but just to tell you what that + + + align:start position:0% +deaf but just to tell you what that +means it can be really quite extreme + + align:start position:0% +means it can be really quite extreme + + + align:start position:0% +means it can be really quite extreme +they can just completely fail to + + align:start position:0% +they can just completely fail to + + + align:start position:0% +they can just completely fail to +recognize familiar melodies that anyone + + align:start position:0% +recognize familiar melodies that anyone + + + align:start position:0% +recognize familiar melodies that anyone +else could recognize okay + + align:start position:0% +else could recognize okay + + + align:start position:0% +else could recognize okay +they may be unable to detect really + + align:start position:0% +they may be unable to detect really + + + align:start position:0% +they may be unable to detect really +obvious wrong notes in a canonical + + align:start position:0% +obvious wrong notes in a canonical + + + align:start position:0% +obvious wrong notes in a canonical +melody + + align:start position:0% +melody + + + align:start position:0% +melody +they're just really bad at all of this + + align:start position:0% +they're just really bad at all of this + + + align:start position:0% +they're just really bad at all of this +and further they don't have whopping + + align:start position:0% +and further they don't have whopping + + + align:start position:0% +and further they don't have whopping +obvious problems with speech perception + + align:start position:0% +obvious problems with speech perception + + + align:start position:0% +obvious problems with speech perception +so at first + + align:start position:0% +so at first + + + align:start position:0% +so at first +was thought that speech perception was + + align:start position:0% +was thought that speech perception was + + + align:start position:0% +was thought that speech perception was +fine + + align:start position:0% +fine + + + align:start position:0% +fine +but if you look closer it looks like + + align:start position:0% +but if you look closer it looks like + + + align:start position:0% +but if you look closer it looks like +actually there is even outside of music + + align:start position:0% +actually there is even outside of music + + + align:start position:0% +actually there is even outside of music +there is a finer grained deficit in a + + align:start position:0% +there is a finer grained deficit in a + + + align:start position:0% +there is a finer grained deficit in a +pitch contour + + align:start position:0% +pitch contour + + + align:start position:0% +pitch contour +perception that shows up um even in + + align:start position:0% +perception that shows up um even in + + + align:start position:0% +perception that shows up um even in +speech okay it's what i mentioned before + + align:start position:0% +speech okay it's what i mentioned before + + + align:start position:0% +speech okay it's what i mentioned before +so we can ask this in the of sort of the + + align:start position:0% +so we can ask this in the of sort of the + + + align:start position:0% +so we can ask this in the of sort of the +reverse case of the ones you considered + + align:start position:0% +reverse case of the ones you considered + + + align:start position:0% +reverse case of the ones you considered +now we have people who have this problem + + align:start position:0% +now we have people who have this problem + + + align:start position:0% +now we have people who have this problem +with pitch contour perception in music + + align:start position:0% +with pitch contour perception in music + + + align:start position:0% +with pitch contour perception in music +are they going to have a problem also + + align:start position:0% +are they going to have a problem also + + + align:start position:0% +are they going to have a problem also +with pitch contour perception in speech + + align:start position:0% +with pitch contour perception in speech + + + align:start position:0% +with pitch contour perception in speech +okay so that's what this + + align:start position:0% +okay so that's what this + + + align:start position:0% +okay so that's what this +study looked at + + align:start position:0% +study looked at + + + align:start position:0% +study looked at +so they played sounds like this and you + + align:start position:0% +so they played sounds like this and you + + + align:start position:0% +so they played sounds like this and you +have to listen carefully there will be + + align:start position:0% +have to listen carefully there will be + + + align:start position:0% +have to listen carefully there will be +sentences spoken + + align:start position:0% +sentences spoken + + + align:start position:0% +sentences spoken +and you have to see if they're identical + + align:start position:0% +and you have to see if they're identical + + + align:start position:0% +and you have to see if they're identical +or different so listen carefully + + align:start position:0% +or different so listen carefully + + + align:start position:0% +or different so listen carefully +she looks like anne + + align:start position:0% +she looks like anne + + + align:start position:0% +she looks like anne +she looks like anne + + align:start position:0% +she looks like anne + + + align:start position:0% +she looks like anne +many people thought that was different + + align:start position:0% +many people thought that was different + + + align:start position:0% +many people thought that was different +good you got it okay so one is a + + align:start position:0% +good you got it okay so one is a + + + align:start position:0% +good you got it okay so one is a +statement and one is a it's not quite + + align:start position:0% +statement and one is a it's not quite + + + align:start position:0% +statement and one is a it's not quite +it's sort of a question + + align:start position:0% +it's sort of a question + + + align:start position:0% +it's sort of a question +it's in a sort of british accent it's a + + align:start position:0% +it's in a sort of british accent it's a + + + align:start position:0% +it's in a sort of british accent it's a +little harder to detect but different + + align:start position:0% +little harder to detect but different + + + align:start position:0% +little harder to detect but different +intonation contour okay so that's what + + align:start position:0% +intonation contour okay so that's what + + + align:start position:0% +intonation contour okay so that's what +the um that's what the tang at all paper + + align:start position:0% +the um that's what the tang at all paper + + + align:start position:0% +the um that's what the tang at all paper +was talking about is that distinction + + align:start position:0% +was talking about is that distinction + + + align:start position:0% +was talking about is that distinction +right okay so we can then ask that + + align:start position:0% +right okay so we can then ask that + + + align:start position:0% +right okay so we can then ask that +subtle distinction are people with + + align:start position:0% +subtle distinction are people with + + + align:start position:0% +subtle distinction are people with +congenital amusia impaired at that right + + align:start position:0% +congenital amusia impaired at that right + + + align:start position:0% +congenital amusia impaired at that right +so if it's specific to music they + + align:start position:0% +so if it's specific to music they + + + align:start position:0% +so if it's specific to music they +shouldn't be but if it's any intonation + + align:start position:0% +shouldn't be but if it's any intonation + + + align:start position:0% +shouldn't be but if it's any intonation +contour they should be + + align:start position:0% +contour they should be + + + align:start position:0% +contour they should be +oh yeah i'll play the other ones okay so + + align:start position:0% +oh yeah i'll play the other ones okay so + + + align:start position:0% +oh yeah i'll play the other ones okay so +well okay + + align:start position:0% +well okay + + + align:start position:0% +well okay +so they are in fact impaired this is + + align:start position:0% +so they are in fact impaired this is + + + align:start position:0% +so they are in fact impaired this is +accuracy here the controls are way up + + align:start position:0% +accuracy here the controls are way up + + + align:start position:0% +accuracy here the controls are way up +there the a musics are down there + + align:start position:0% +there the a musics are down there + + + align:start position:0% +there the a musics are down there +so they are impaired at this kind of + + align:start position:0% +so they are impaired at this kind of + + + align:start position:0% +so they are impaired at this kind of +pitch contour perception thing even in + + align:start position:0% +pitch contour perception thing even in + + + align:start position:0% +pitch contour perception thing even in +the context of music + + align:start position:0% +the context of music + + + align:start position:0% +the context of music +okay i'm sorry i said that wrong even in + + align:start position:0% +okay i'm sorry i said that wrong even in + + + align:start position:0% +okay i'm sorry i said that wrong even in +the context of speech + + align:start position:0% +the context of speech + + + align:start position:0% +the context of speech +okay so it's not just about music + + align:start position:0% +okay so it's not just about music + + + align:start position:0% +okay so it's not just about music +okay and in the controls they have + + align:start position:0% +okay and in the controls they have + + + align:start position:0% +okay and in the controls they have +sounds like this which they + + align:start position:0% +sounds like this which they + + + align:start position:0% +sounds like this which they +which are just + + align:start position:0% +which are just + + + align:start position:0% +which are just +just tones + + align:start position:0% + + + + align:start position:0% + +okay got that it's the same kind of + + align:start position:0% +okay got that it's the same kind of + + + align:start position:0% +okay got that it's the same kind of +thing but not speech and you see a + + align:start position:0% +thing but not speech and you see a + + + align:start position:0% +thing but not speech and you see a +similar + + align:start position:0% +similar + + + align:start position:0% +similar +deficit in the a musics compared to the + + align:start position:0% +deficit in the a musics compared to the + + + align:start position:0% +deficit in the a musics compared to the +controls + + align:start position:0% +controls + + + align:start position:0% +controls +and then they have a nonsense speech + + align:start position:0% +and then they have a nonsense speech + + + align:start position:0% +and then they have a nonsense speech +version + + align:start position:0% + + + + align:start position:0% + +same deal the music the a musics are + + align:start position:0% +same deal the music the a musics are + + + align:start position:0% +same deal the music the a musics are +impaired + + align:start position:0% +impaired + + + align:start position:0% +impaired +compared to the controls + + align:start position:0% +compared to the controls + + + align:start position:0% +compared to the controls +so that shows that the deficit for these + + align:start position:0% +so that shows that the deficit for these + + + align:start position:0% +so that shows that the deficit for these +guys is not specific to music per se but + + align:start position:0% +guys is not specific to music per se but + + + align:start position:0% +guys is not specific to music per se but +it seems to be a + + align:start position:0% +it seems to be a + + + align:start position:0% +it seems to be a +pitch um contour problem in general that + + align:start position:0% +pitch um contour problem in general that + + + align:start position:0% +pitch um contour problem in general that +extends to speech + + align:start position:0% + + + + align:start position:0% + +we'll get there + + align:start position:0% +we'll get there + + + align:start position:0% +we'll get there +sort of it would have been nice if the + + align:start position:0% +sort of it would have been nice if the + + + align:start position:0% +sort of it would have been nice if the +tang at all paper had included some + + align:start position:0% +tang at all paper had included some + + + align:start position:0% +tang at all paper had included some +musical contour stuff they didn't but + + align:start position:0% +musical contour stuff they didn't but + + + align:start position:0% +musical contour stuff they didn't but +i'll show you some of our data shortly + + align:start position:0% +i'll show you some of our data shortly + + + align:start position:0% +i'll show you some of our data shortly +that gets close to this + + align:start position:0% +that gets close to this + + + align:start position:0% +that gets close to this +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so all of that suggests that this amuseo + + align:start position:0% +so all of that suggests that this amuseo + + + align:start position:0% +so all of that suggests that this amuseo +is really more about pitch than speech + + align:start position:0% +is really more about pitch than speech + + + align:start position:0% +is really more about pitch than speech +i'm sorry what's the matter with me it's + + align:start position:0% +i'm sorry what's the matter with me it's + + + align:start position:0% +i'm sorry what's the matter with me it's +really more about pitch than music + + align:start position:0% +really more about pitch than music + + + align:start position:0% +really more about pitch than music +right + + align:start position:0% +right + + + align:start position:0% +right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but + + align:start position:0% +but + + + align:start position:0% +but +the reading that i signed today for + + align:start position:0% +the reading that i signed today for + + + align:start position:0% +the reading that i signed today for +today + + align:start position:0% +today + + + align:start position:0% +today +is a very new + + align:start position:0% +is a very new + + + align:start position:0% +is a very new +uh twist in this evolving story right so + + align:start position:0% +uh twist in this evolving story right so + + + align:start position:0% +uh twist in this evolving story right so +this used to be a nice clean lecture + + align:start position:0% +this used to be a nice clean lecture + + + align:start position:0% +this used to be a nice clean lecture +with a simple conclusion and now all of + + align:start position:0% +with a simple conclusion and now all of + + + align:start position:0% +with a simple conclusion and now all of +a sudden i ran across that paper it's + + align:start position:0% +a sudden i ran across that paper it's + + + align:start position:0% +a sudden i ran across that paper it's +like wow okay + + align:start position:0% +like wow okay + + + align:start position:0% +like wow okay +that might not be quite the case + + align:start position:0% +that might not be quite the case + + + align:start position:0% +that might not be quite the case +so what do what did you guys get from + + align:start position:0% +so what do what did you guys get from + + + align:start position:0% +so what do what did you guys get from +the reading in what way does that kind + + align:start position:0% +the reading in what way does that kind + + + align:start position:0% +the reading in what way does that kind +of slightly complicate the story here + + align:start position:0% +of slightly complicate the story here + + + align:start position:0% +of slightly complicate the story here +yeah quietly + + align:start position:0% + + + + align:start position:0% + +yeah what they found is that a lot of a + + align:start position:0% +yeah what they found is that a lot of a + + + align:start position:0% +yeah what they found is that a lot of a +musics not all of them + + align:start position:0% +musics not all of them + + + align:start position:0% +musics not all of them +also have problems with rhythm + + align:start position:0% +also have problems with rhythm + + + align:start position:0% +also have problems with rhythm +and that isn't consistent with the idea + + align:start position:0% +and that isn't consistent with the idea + + + align:start position:0% +and that isn't consistent with the idea +that a musia is just about pitch + + align:start position:0% +that a musia is just about pitch + + + align:start position:0% +that a musia is just about pitch +whether in speech speech or + + align:start position:0% +whether in speech speech or + + + align:start position:0% +whether in speech speech or +music + + align:start position:0% +music + + + align:start position:0% +music +right + + align:start position:0% +right + + + align:start position:0% +right +and that says okay many a musics also + + align:start position:0% +and that says okay many a musics also + + + align:start position:0% +and that says okay many a musics also +have problems with rhythm + + align:start position:0% +have problems with rhythm + + + align:start position:0% +have problems with rhythm +okay + + align:start position:0% + + + + align:start position:0% + +um so there's a standard battery that + + align:start position:0% +um so there's a standard battery that + + + align:start position:0% +um so there's a standard battery that +people use that asks + + align:start position:0% +people use that asks + + + align:start position:0% +people use that asks +dana help me what does the standard + + align:start position:0% +dana help me what does the standard + + + align:start position:0% +dana help me what does the standard +battery ask people + + align:start position:0% + + + + align:start position:0% + +kinds of things that people without + + align:start position:0% +kinds of things that people without + + + align:start position:0% +kinds of things that people without +musical training answer fine although + + align:start position:0% +musical training answer fine although + + + align:start position:0% +musical training answer fine although +there's quite a range i'm at the way + + align:start position:0% +there's quite a range i'm at the way + + + align:start position:0% +there's quite a range i'm at the way +bottom end of dana's scale when she + + align:start position:0% +bottom end of dana's scale when she + + + align:start position:0% +bottom end of dana's scale when she +gives these + + align:start position:0% +gives these + + + align:start position:0% +gives these +reasons + + align:start position:0% + + + + align:start position:0% + +just that there's prior evidence on and + + align:start position:0% +just that there's prior evidence on and + + + align:start position:0% +just that there's prior evidence on and +the stuff i showed you and a whole bunch + + align:start position:0% +the stuff i showed you and a whole bunch + + + align:start position:0% +the stuff i showed you and a whole bunch +of other studies seem to suggest that + + align:start position:0% +of other studies seem to suggest that + + + align:start position:0% +of other studies seem to suggest that +amusia both in acquired brain damage and + + align:start position:0% +amusia both in acquired brain damage and + + + align:start position:0% +amusia both in acquired brain damage and +congenital amusia seem to be really when + + align:start position:0% +congenital amusia seem to be really when + + + align:start position:0% +congenital amusia seem to be really when +you drill down more of a problem with + + align:start position:0% +you drill down more of a problem with + + + align:start position:0% +you drill down more of a problem with +pitch per se even pitch in speech + + align:start position:0% +pitch per se even pitch in speech + + + align:start position:0% +pitch per se even pitch in speech +and so then it seems like if it's about + + align:start position:0% +and so then it seems like if it's about + + + align:start position:0% +and so then it seems like if it's about +pitch + + align:start position:0% +pitch + + + align:start position:0% +pitch +why would it also go along with rhythm + + align:start position:0% +why would it also go along with rhythm + + + align:start position:0% +why would it also go along with rhythm +right + + align:start position:0% +right + + + align:start position:0% +right +and so when it goes along with rhythm + + align:start position:0% +and so when it goes along with rhythm + + + align:start position:0% +and so when it goes along with rhythm +that sounds starts to sound more like + + align:start position:0% +that sounds starts to sound more like + + + align:start position:0% +that sounds starts to sound more like +this is something about music right it's + + align:start position:0% +this is something about music right it's + + + align:start position:0% +this is something about music right it's +not you know it gums up the story yeah + + align:start position:0% +not you know it gums up the story yeah + + + align:start position:0% +not you know it gums up the story yeah +talia right + + align:start position:0% + + + + align:start position:0% + +when it comes to like natural speech + + align:start position:0% +when it comes to like natural speech + + + align:start position:0% +when it comes to like natural speech +when you have like some kind of + + align:start position:0% +when you have like some kind of + + + align:start position:0% +when you have like some kind of +incarnation like + + align:start position:0% +incarnation like + + + align:start position:0% +incarnation like +you know pitch differences when you + + align:start position:0% +you know pitch differences when you + + + align:start position:0% +you know pitch differences when you +emphasize like especially in terms of + + align:start position:0% +emphasize like especially in terms of + + + align:start position:0% +emphasize like especially in terms of +like a question + + align:start position:0% +like a question + + + align:start position:0% +like a question +aren't there also some kind of like + + align:start position:0% +aren't there also some kind of like + + + align:start position:0% +aren't there also some kind of like +rhythmic differences yeah + + align:start position:0% +rhythmic differences yeah + + + align:start position:0% +rhythmic differences yeah +so how do you like kind of separate + + align:start position:0% +so how do you like kind of separate + + + align:start position:0% +so how do you like kind of separate +you just have to do a lot of work to try + + align:start position:0% +you just have to do a lot of work to try + + + align:start position:0% +you just have to do a lot of work to try +to separate those out right and so the + + align:start position:0% +to separate those out right and so the + + + align:start position:0% +to separate those out right and so the +paper i signed to you guys did some of + + align:start position:0% +paper i signed to you guys did some of + + + align:start position:0% +paper i signed to you guys did some of +that work and there's still room to + + align:start position:0% +that work and there's still room to + + + align:start position:0% +that work and there's still room to +quibble but they they did you know there + + align:start position:0% +quibble but they they did you know there + + + align:start position:0% +quibble but they they did you know there +was experiment two and they tried to + + align:start position:0% +was experiment two and they tried to + + + align:start position:0% +was experiment two and they tried to +deal with exactly that kind of thing of + + align:start position:0% +deal with exactly that kind of thing of + + + align:start position:0% +deal with exactly that kind of thing of +saying okay let's try to make sure that + + align:start position:0% +saying okay let's try to make sure that + + + align:start position:0% +saying okay let's try to make sure that +um + + align:start position:0% +um + + + align:start position:0% +um +that well actually the controls that + + align:start position:0% +that well actually the controls that + + + align:start position:0% +that well actually the controls that +they were doing slightly different they + + align:start position:0% +they were doing slightly different they + + + align:start position:0% +they were doing slightly different they +were trying to make sure that the + + align:start position:0% +were trying to make sure that the + + + align:start position:0% +were trying to make sure that the +um + + align:start position:0% +um + + + align:start position:0% +um +the beat tasks didn't require pitch + + align:start position:0% +the beat tasks didn't require pitch + + + align:start position:0% +the beat tasks didn't require pitch +right so it's very it's very very tricky + + align:start position:0% +right so it's very it's very very tricky + + + align:start position:0% +right so it's very it's very very tricky +to pull these things apart which is yeah + + align:start position:0% +to pull these things apart which is yeah + + + align:start position:0% +to pull these things apart which is yeah +so like the beat tasks like make sense + + align:start position:0% +so like the beat tasks like make sense + + + align:start position:0% +so like the beat tasks like make sense +but i'm just like in the first one like + + align:start position:0% +but i'm just like in the first one like + + + align:start position:0% +but i'm just like in the first one like +even from the paper that was like a sign + + align:start position:0% +even from the paper that was like a sign + + + align:start position:0% +even from the paper that was like a sign +on sunday + + align:start position:0% +on sunday + + + align:start position:0% +on sunday +like i don't know so you're saying that + + align:start position:0% +like i don't know so you're saying that + + + align:start position:0% +like i don't know so you're saying that +it's totally possible to kind of + + align:start position:0% +it's totally possible to kind of + + + align:start position:0% +it's totally possible to kind of +separate algorithmic differences from + + align:start position:0% +separate algorithmic differences from + + + align:start position:0% +separate algorithmic differences from +like when you're just changing + + align:start position:0% +like when you're just changing + + + align:start position:0% +like when you're just changing +it's really really difficult it's really + + align:start position:0% +it's really really difficult it's really + + + align:start position:0% +it's really really difficult it's really +difficult dana's trying to do + + align:start position:0% +difficult dana's trying to do + + + align:start position:0% +difficult dana's trying to do +experiments that do this right now and + + align:start position:0% +experiments that do this right now and + + + align:start position:0% +experiments that do this right now and +she's invented some delightful and crazy + + align:start position:0% +she's invented some delightful and crazy + + + align:start position:0% +she's invented some delightful and crazy +stimuli that try to have one and not the + + align:start position:0% +stimuli that try to have one and not the + + + align:start position:0% +stimuli that try to have one and not the +other it's very tricky + + align:start position:0% +other it's very tricky + + + align:start position:0% +other it's very tricky +right you can have + + align:start position:0% +right you can have + + + align:start position:0% +right you can have +rhythm without pitch change that you can + + align:start position:0% +rhythm without pitch change that you can + + + align:start position:0% +rhythm without pitch change that you can +totally do right + + align:start position:0% +totally do right + + + align:start position:0% +totally do right +it's really hard or impossible to have a + + align:start position:0% +it's really hard or impossible to have a + + + align:start position:0% +it's really hard or impossible to have a +melodic contour without some beat or + + align:start position:0% +melodic contour without some beat or + + + align:start position:0% +melodic contour without some beat or +other + + align:start position:0% +other + + + align:start position:0% +other +we have some crazy stimuli that sort of + + align:start position:0% +we have some crazy stimuli that sort of + + + align:start position:0% +we have some crazy stimuli that sort of +do that but they're pretty crazy right + + align:start position:0% +do that but they're pretty crazy right + + + align:start position:0% +do that but they're pretty crazy right +so anyway these are very tricky things + + align:start position:0% +so anyway these are very tricky things + + + align:start position:0% +so anyway these are very tricky things +to pull apart um and and this is all + + align:start position:0% +to pull apart um and and this is all + + + align:start position:0% +to pull apart um and and this is all +right right at the cutting edge these + + align:start position:0% +right right at the cutting edge these + + + align:start position:0% +right right at the cutting edge these +things have not been + + align:start position:0% +things have not been + + + align:start position:0% +things have not been +cleanly separated okay i'm running out + + align:start position:0% +cleanly separated okay i'm running out + + + align:start position:0% +cleanly separated okay i'm running out +of time so + + align:start position:0% +of time so + + + align:start position:0% +of time so +do you have a quick question + + align:start position:0% +do you have a quick question + + + align:start position:0% +do you have a quick question +okay sorry about that + + align:start position:0% +okay sorry about that + + + align:start position:0% +okay sorry about that +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so conclusions for the patient + + align:start position:0% +so conclusions for the patient + + + align:start position:0% +so conclusions for the patient +literature there's suggestive evidence + + align:start position:0% +literature there's suggestive evidence + + + align:start position:0% +literature there's suggestive evidence +for specialization for music + + align:start position:0% +for specialization for music + + + align:start position:0% +for specialization for music +but no really clear dissociations + + align:start position:0% +but no really clear dissociations + + + align:start position:0% +but no really clear dissociations +music deficits are frequently but not + + align:start position:0% +music deficits are frequently but not + + + align:start position:0% +music deficits are frequently but not +always associated with just more general + + align:start position:0% +always associated with just more general + + + align:start position:0% +always associated with just more general +pitch deficits + + align:start position:0% +pitch deficits + + + align:start position:0% +pitch deficits +um and all of this is complicated + + align:start position:0% +um and all of this is complicated + + + align:start position:0% +um and all of this is complicated +because there's lots of possible + + align:start position:0% +because there's lots of possible + + + align:start position:0% +because there's lots of possible +components of music right + + align:start position:0% +components of music right + + + align:start position:0% +components of music right +you know when there's pitch deficits is + + align:start position:0% +you know when there's pitch deficits is + + + align:start position:0% +you know when there's pitch deficits is +it is it pitch or relative pitch + + align:start position:0% +it is it pitch or relative pitch + + + align:start position:0% +it is it pitch or relative pitch +interval key melody meter all these + + align:start position:0% +interval key melody meter all these + + + align:start position:0% +interval key melody meter all these +things are different facets of music + + align:start position:0% +things are different facets of music + + + align:start position:0% +things are different facets of music +uh and so it's really not resolved + + align:start position:0% +uh and so it's really not resolved + + + align:start position:0% +uh and so it's really not resolved +exactly what's going on here right it's + + align:start position:0% +exactly what's going on here right it's + + + align:start position:0% +exactly what's going on here right it's +kind of encouraging that there's a space + + align:start position:0% +kind of encouraging that there's a space + + + align:start position:0% +kind of encouraging that there's a space +in there but not resolved + + align:start position:0% +in there but not resolved + + + align:start position:0% +in there but not resolved +okay so let's go on to functional mri + + align:start position:0% +okay so let's go on to functional mri + + + align:start position:0% +okay so let's go on to functional mri +and we're going to run out of time so + + align:start position:0% +and we're going to run out of time so + + + align:start position:0% +and we're going to run out of time so +let me just take a moment to figure out + + align:start position:0% +let me just take a moment to figure out + + + align:start position:0% +let me just take a moment to figure out +how i'm going to do this + + align:start position:0% +how i'm going to do this + + + align:start position:0% +how i'm going to do this +um + + align:start position:0% +um + + + align:start position:0% +um +what the hell am i going to do here + + align:start position:0% +what the hell am i going to do here + + + align:start position:0% +what the hell am i going to do here +okay well i + + align:start position:0% +okay well i + + + align:start position:0% +okay well i +hate to well okay + + align:start position:0% + + + + align:start position:0% + +okay you guys are gonna tell me at 1205. + + align:start position:0% +okay you guys are gonna tell me at 1205. + + + align:start position:0% +okay you guys are gonna tell me at 1205. +yeah okay i'll see maybe we can get off + + align:start position:0% +yeah okay i'll see maybe we can get off + + + align:start position:0% +yeah okay i'll see maybe we can get off +of this okay so here's a really charming + + align:start position:0% +of this okay so here's a really charming + + + align:start position:0% +of this okay so here's a really charming +study from a few years ago + + align:start position:0% +study from a few years ago + + + align:start position:0% +study from a few years ago +that tried to ask whether there are + + align:start position:0% +that tried to ask whether there are + + + align:start position:0% +that tried to ask whether there are +systematic brain regions that are + + align:start position:0% +systematic brain regions that are + + + align:start position:0% +systematic brain regions that are +engaged in processing music and they + + align:start position:0% +engaged in processing music and they + + + align:start position:0% +engaged in processing music and they +used a really fun + + align:start position:0% +used a really fun + + + align:start position:0% +used a really fun +um perceptual illusion okay that you're + + align:start position:0% +um perceptual illusion okay that you're + + + align:start position:0% +um perceptual illusion okay that you're +going to hear i'm going to play a speech + + align:start position:0% +going to hear i'm going to play a speech + + + align:start position:0% +going to hear i'm going to play a speech +clip + + align:start position:0% +clip + + + align:start position:0% +clip +and it's just going to part of it's + + align:start position:0% +and it's just going to part of it's + + + align:start position:0% +and it's just going to part of it's +going to be repeated many times and just + + align:start position:0% +going to be repeated many times and just + + + align:start position:0% +going to be repeated many times and just +listen to it and and think about what it + + align:start position:0% +listen to it and and think about what it + + + align:start position:0% +listen to it and and think about what it +sounds like + + align:start position:0% + + + + align:start position:0% + +to own and eat one + + align:start position:0% +to own and eat one + + + align:start position:0% +to own and eat one +there was a cold drizzle of rain the + + align:start position:0% +there was a cold drizzle of rain the + + + align:start position:0% +there was a cold drizzle of rain the +atmosphere was + + align:start position:0% +atmosphere was + + + align:start position:0% +atmosphere was +murky there was a cold drizzle there was + + align:start position:0% +murky there was a cold drizzle there was + + + align:start position:0% +murky there was a cold drizzle there was +a cold drizzle + + align:start position:0% +a cold drizzle + + + align:start position:0% +a cold drizzle +there was a cold drizzle + + align:start position:0% +there was a cold drizzle + + + align:start position:0% +there was a cold drizzle +there was a cold drizzle + + align:start position:0% +there was a cold drizzle + + + align:start position:0% +there was a cold drizzle +there was a cold drizzle + + align:start position:0% +there was a cold drizzle + + + align:start position:0% +there was a cold drizzle +there was a cold drizzle + + align:start position:0% +there was a cold drizzle + + + align:start position:0% +there was a cold drizzle +what happened + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +what happened + + align:start position:0% + + + + align:start position:0% + +you started to hear a melody + + align:start position:0% +you started to hear a melody + + + align:start position:0% +you started to hear a melody +and you didn't hear the melody the first + + align:start position:0% +and you didn't hear the melody the first + + + align:start position:0% +and you didn't hear the melody the first +time he said it was just normal speech + + align:start position:0% +time he said it was just normal speech + + + align:start position:0% +time he said it was just normal speech +right speech has this kind of intonation + + align:start position:0% +right speech has this kind of intonation + + + align:start position:0% +right speech has this kind of intonation +contour and he's speaking with an + + align:start position:0% +contour and he's speaking with an + + + align:start position:0% +contour and he's speaking with an +intonation contour but then somehow when + + align:start position:0% +intonation contour but then somehow when + + + align:start position:0% +intonation contour but then somehow when +you keep hearing it it turns into a + + align:start position:0% +you keep hearing it it turns into a + + + align:start position:0% +you keep hearing it it turns into a +melody + + align:start position:0% +melody + + + align:start position:0% +melody +okay so it turns out that doesn't work + + align:start position:0% +okay so it turns out that doesn't work + + + align:start position:0% +okay so it turns out that doesn't work +for all speech clips in fact it's really + + align:start position:0% +for all speech clips in fact it's really + + + align:start position:0% +for all speech clips in fact it's really +hard to find speech clips for for which + + align:start position:0% +hard to find speech clips for for which + + + align:start position:0% +hard to find speech clips for for which +it works but there are some + + align:start position:0% +it works but there are some + + + align:start position:0% +it works but there are some +but you know everyone has that + + align:start position:0% +but you know everyone has that + + + align:start position:0% +but you know everyone has that +experience or most people do and that + + align:start position:0% +experience or most people do and that + + + align:start position:0% +experience or most people do and that +gives us a really nice lever because we + + align:start position:0% +gives us a really nice lever because we + + + align:start position:0% +gives us a really nice lever because we +can take that same acoustic sound when + + align:start position:0% +can take that same acoustic sound when + + + align:start position:0% +can take that same acoustic sound when +you hear it as speech and when you hear + + align:start position:0% +you hear it as speech and when you hear + + + align:start position:0% +you hear it as speech and when you hear +it as melody and we can ask are there + + align:start position:0% +it as melody and we can ask are there + + + align:start position:0% +it as melody and we can ask are there +brain regions that respond + + align:start position:0% +brain regions that respond + + + align:start position:0% +brain regions that respond +differentially it's sort of analogous to + + align:start position:0% +differentially it's sort of analogous to + + + align:start position:0% +differentially it's sort of analogous to +upright versus inverted faces although + + align:start position:0% +upright versus inverted faces although + + + align:start position:0% +upright versus inverted faces although +it's even better it's the exact same + + align:start position:0% +it's even better it's the exact same + + + align:start position:0% +it's even better it's the exact same +sound clip that's construed one way at + + align:start position:0% +sound clip that's construed one way at + + + align:start position:0% +sound clip that's construed one way at +first and another way afterwards + + align:start position:0% +first and another way afterwards + + + align:start position:0% +first and another way afterwards +okay everybody get that + + align:start position:0% +okay everybody get that + + + align:start position:0% +okay everybody get that +um + + align:start position:0% +um + + + align:start position:0% +um +okay so that's what these guys did they + + align:start position:0% +okay so that's what these guys did they + + + align:start position:0% +okay so that's what these guys did they +used a standard block design they just + + align:start position:0% +used a standard block design they just + + + align:start position:0% +used a standard block design they just +listened to those + + align:start position:0% +listened to those + + + align:start position:0% +listened to those +sounds and they just looked in the brain + + align:start position:0% +sounds and they just looked in the brain + + + align:start position:0% +sounds and they just looked in the brain +to see what bits respond more + + align:start position:0% +to see what bits respond more + + + align:start position:0% +to see what bits respond more +after the sound starts getting perceived + + align:start position:0% +after the sound starts getting perceived + + + align:start position:0% +after the sound starts getting perceived +as music than before when it was being + + align:start position:0% +as music than before when it was being + + + align:start position:0% +as music than before when it was being +heard as speech and they got a bunch of + + align:start position:0% +heard as speech and they got a bunch of + + + align:start position:0% +heard as speech and they got a bunch of +blobs in the brain it's a bit of a mess + + align:start position:0% +blobs in the brain it's a bit of a mess + + + align:start position:0% +blobs in the brain it's a bit of a mess +but they got some stuff + + align:start position:0% +but they got some stuff + + + align:start position:0% +but they got some stuff +um + + align:start position:0% +um + + + align:start position:0% +um +and um and so that's sort of fun + + align:start position:0% +and um and so that's sort of fun + + + align:start position:0% +and um and so that's sort of fun +um but it's also kind of ambiguous we + + align:start position:0% +um but it's also kind of ambiguous we + + + align:start position:0% +um but it's also kind of ambiguous we +still don't know if this is about + + align:start position:0% +still don't know if this is about + + + align:start position:0% +still don't know if this is about +some kind of pitch processing which is + + align:start position:0% +some kind of pitch processing which is + + + align:start position:0% +some kind of pitch processing which is +becomes more salient + + align:start position:0% +becomes more salient + + + align:start position:0% +becomes more salient +you hear it as abstract pitch or whether + + align:start position:0% +you hear it as abstract pitch or whether + + + align:start position:0% +you hear it as abstract pitch or whether +it's really about melodic contour or + + align:start position:0% +it's really about melodic contour or + + + align:start position:0% +it's really about melodic contour or +what so that's a cool study but i think + + align:start position:0% +what so that's a cool study but i think + + + align:start position:0% +what so that's a cool study but i think +it doesn't really nail what's going on + + align:start position:0% +it doesn't really nail what's going on + + + align:start position:0% +it doesn't really nail what's going on +so another angle at this is to ask + + align:start position:0% +so another angle at this is to ask + + + align:start position:0% +so another angle at this is to ask +whether music recruits neural machinery + + align:start position:0% +whether music recruits neural machinery + + + align:start position:0% +whether music recruits neural machinery +for language okay so let me + + align:start position:0% +for language okay so let me + + + align:start position:0% +for language okay so let me +say why this has been such a pervasive + + align:start position:0% +say why this has been such a pervasive + + + align:start position:0% +say why this has been such a pervasive +question in the field so there's a lot + + align:start position:0% +question in the field so there's a lot + + + align:start position:0% +question in the field so there's a lot +of people who've pointed out for you + + align:start position:0% +of people who've pointed out for you + + + align:start position:0% +of people who've pointed out for you +know 30 years or probably more there are + + align:start position:0% +know 30 years or probably more there are + + + align:start position:0% +know 30 years or probably more there are +many kind of deep commonalities between + + align:start position:0% +many kind of deep commonalities between + + + align:start position:0% +many kind of deep commonalities between +language and music so they're both + + align:start position:0% +language and music so they're both + + + align:start position:0% +language and music so they're both +distinctively or uniquely human they're + + align:start position:0% +distinctively or uniquely human they're + + + align:start position:0% +distinctively or uniquely human they're +natively auditory right that is we can + + align:start position:0% +natively auditory right that is we can + + + align:start position:0% +natively auditory right that is we can +read language but that's very recent + + align:start position:0% +read language but that's very recent + + + align:start position:0% +read language but that's very recent +really language is all about hearing + + align:start position:0% +really language is all about hearing + + + align:start position:0% +really language is all about hearing +evolutionarily + + align:start position:0% +evolutionarily + + + align:start position:0% +evolutionarily +they unfold over time + + align:start position:0% +they unfold over time + + + align:start position:0% +they unfold over time +and they have complex hierarchical + + align:start position:0% +and they have complex hierarchical + + + align:start position:0% +and they have complex hierarchical +structure + + align:start position:0% +structure + + + align:start position:0% +structure +okay so you can parse a sentence in + + align:start position:0% +okay so you can parse a sentence in + + + align:start position:0% +okay so you can parse a sentence in +various ways and there are all kinds of + + align:start position:0% +various ways and there are all kinds of + + + align:start position:0% +various ways and there are all kinds of +people who've come up with ways to have + + align:start position:0% +people who've come up with ways to have + + + align:start position:0% +people who've come up with ways to have +hierarchical parsings of pieces of music + + align:start position:0% +hierarchical parsings of pieces of music + + + align:start position:0% +hierarchical parsings of pieces of music +as well + + align:start position:0% +as well + + + align:start position:0% +as well +so there's kind of a lot of deep + + align:start position:0% +so there's kind of a lot of deep + + + align:start position:0% +so there's kind of a lot of deep +connections between language and music + + align:start position:0% +connections between language and music + + + align:start position:0% +connections between language and music +and so many people have hypothesized + + align:start position:0% +and so many people have hypothesized + + + align:start position:0% +and so many people have hypothesized +that they use common brain machinery + + align:start position:0% +that they use common brain machinery + + + align:start position:0% +that they use common brain machinery +okay and they're in fact many reports + + align:start position:0% +okay and they're in fact many reports + + + align:start position:0% +okay and they're in fact many reports +um from neuroimaging that argue that in + + align:start position:0% +um from neuroimaging that argue that in + + + align:start position:0% +um from neuroimaging that argue that in +fact they do use common machinery like + + align:start position:0% +fact they do use common machinery like + + + align:start position:0% +fact they do use common machinery like +we found overlapping activation in broke + + align:start position:0% +we found overlapping activation in broke + + + align:start position:0% +we found overlapping activation in broke +areas broca's area for people listening + + align:start position:0% +areas broca's area for people listening + + + align:start position:0% +areas broca's area for people listening +to + + align:start position:0% +to + + + align:start position:0% +to +music and speech + + align:start position:0% +music and speech + + + align:start position:0% +music and speech +okay + + align:start position:0% +okay + + + align:start position:0% +okay +however + + align:start position:0% +however + + + align:start position:0% +however +those studies are all group analyses now + + align:start position:0% +those studies are all group analyses now + + + align:start position:0% +those studies are all group analyses now +if i forget if i've gone on my tirade in + + align:start position:0% +if i forget if i've gone on my tirade in + + + align:start position:0% +if i forget if i've gone on my tirade in +here about group analyses have i done + + align:start position:0% +here about group analyses have i done + + + align:start position:0% +here about group analyses have i done +the group analysis tirade in here you'll + + align:start position:0% +the group analysis tirade in here you'll + + + align:start position:0% +the group analysis tirade in here you'll +get more of it later i'll do a brief + + align:start position:0% +get more of it later i'll do a brief + + + align:start position:0% +get more of it later i'll do a brief +version now and you'll get more later + + align:start position:0% +version now and you'll get more later + + + align:start position:0% +version now and you'll get more later +here's a problem group analysis is you + + align:start position:0% +here's a problem group analysis is you + + + align:start position:0% +here's a problem group analysis is you +take you scan 12 subjects you align + + align:start position:0% +take you scan 12 subjects you align + + + align:start position:0% +take you scan 12 subjects you align +their brains as best you can + + align:start position:0% +their brains as best you can + + + align:start position:0% +their brains as best you can +and you do an analysis that goes across + + align:start position:0% +and you do an analysis that goes across + + + align:start position:0% +and you do an analysis that goes across +them okay + + align:start position:0% +them okay + + + align:start position:0% +them okay +and you find some blob say + + align:start position:0% +and you find some blob say + + + align:start position:0% +and you find some blob say +here yeah be there uh for listening to + + align:start position:0% +here yeah be there uh for listening to + + + align:start position:0% +here yeah be there uh for listening to +sentences versus listening to non-word + + align:start position:0% +sentences versus listening to non-word + + + align:start position:0% +sentences versus listening to non-word +strings okay that's a standard finding + + align:start position:0% +strings okay that's a standard finding + + + align:start position:0% +strings okay that's a standard finding +then you do it again for listening to + + align:start position:0% +then you do it again for listening to + + + align:start position:0% +then you do it again for listening to +melodies versus listening to scrambled + + align:start position:0% +melodies versus listening to scrambled + + + align:start position:0% +melodies versus listening to scrambled +melodies + + align:start position:0% +melodies + + + align:start position:0% +melodies +and you find the blob overlaps + + align:start position:0% +and you find the blob overlaps + + + align:start position:0% +and you find the blob overlaps +and you say hey common neural machinery + + align:start position:0% +and you say hey common neural machinery + + + align:start position:0% +and you say hey common neural machinery +for sentence understanding and for music + + align:start position:0% +for sentence understanding and for music + + + align:start position:0% +for sentence understanding and for music +perception + + align:start position:0% +perception + + + align:start position:0% +perception +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now that's that's an interesting + + align:start position:0% +now that's that's an interesting + + + align:start position:0% +now that's that's an interesting +question to ask it's close to the right + + align:start position:0% +question to ask it's close to the right + + + align:start position:0% +question to ask it's close to the right +way to do it but there's a fundamental + + align:start position:0% +way to do it but there's a fundamental + + + align:start position:0% +way to do it but there's a fundamental +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and that is you can find an overlap in a + + align:start position:0% +and that is you can find an overlap in a + + + align:start position:0% +and that is you can find an overlap in a +group analysis even if no single subject + + align:start position:0% +group analysis even if no single subject + + + align:start position:0% +group analysis even if no single subject +shows that overlap at all + + align:start position:0% +shows that overlap at all + + + align:start position:0% +shows that overlap at all +why because those regions vary in their + + align:start position:0% +why because those regions vary in their + + + align:start position:0% +why because those regions vary in their +exact location and if you mush across a + + align:start position:0% +exact location and if you mush across a + + + align:start position:0% +exact location and if you mush across a +whole bunch of individuals you're + + align:start position:0% +whole bunch of individuals you're + + + align:start position:0% +whole bunch of individuals you're +essentially blurring your activation + + align:start position:0% +essentially blurring your activation + + + align:start position:0% +essentially blurring your activation +pattern + + align:start position:0% +pattern + + + align:start position:0% +pattern +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so all of the prior studies + + align:start position:0% +and so all of the prior studies + + + align:start position:0% +and so all of the prior studies +until a few years ago had been group + + align:start position:0% +until a few years ago had been group + + + align:start position:0% +until a few years ago had been group +analyses and they found overlap and who + + align:start position:0% +analyses and they found overlap and who + + + align:start position:0% +analyses and they found overlap and who +the hell knows if there was actually + + align:start position:0% +the hell knows if there was actually + + + align:start position:0% +the hell knows if there was actually +overlapping activation within individual + + align:start position:0% +overlapping activation within individual + + + align:start position:0% +overlapping activation within individual +subjects which there would have to be if + + align:start position:0% +subjects which there would have to be if + + + align:start position:0% +subjects which there would have to be if +it's common machinery or if they're just + + align:start position:0% +it's common machinery or if they're just + + + align:start position:0% +it's common machinery or if they're just +nearby and you muck them up with a group + + align:start position:0% +nearby and you muck them up with a group + + + align:start position:0% +nearby and you muck them up with a group +analysis and they look like they're on + + align:start position:0% +analysis and they look like they're on + + + align:start position:0% +analysis and they look like they're on +top of each other + + align:start position:0% +top of each other + + + align:start position:0% +top of each other +okay if you didn't quite get that we'll + + align:start position:0% +okay if you didn't quite get that we'll + + + align:start position:0% +okay if you didn't quite get that we'll +be coming back to that point for now all + + align:start position:0% +be coming back to that point for now all + + + align:start position:0% +be coming back to that point for now all +you need to know is many people ask this + + align:start position:0% +you need to know is many people ask this + + + align:start position:0% +you need to know is many people ask this +question and the methods were close but + + align:start position:0% +question and the methods were close but + + + align:start position:0% +question and the methods were close but +problematic + + align:start position:0% +problematic + + + align:start position:0% +problematic +um but luckily however at federenko did + + align:start position:0% +um but luckily however at federenko did + + + align:start position:0% +um but luckily however at federenko did +this experiment right a few years ago + + align:start position:0% +this experiment right a few years ago + + + align:start position:0% +this experiment right a few years ago +so here's ev and here's what she did + + align:start position:0% +so here's ev and here's what she did + + + align:start position:0% +so here's ev and here's what she did +she funky functionally identified + + align:start position:0% +she funky functionally identified + + + align:start position:0% +she funky functionally identified +language regions in each subject + + align:start position:0% +language regions in each subject + + + align:start position:0% +language regions in each subject +individually okay we'll talk more about + + align:start position:0% +individually okay we'll talk more about + + + align:start position:0% +individually okay we'll talk more about +exactly how you do that you listen to + + align:start position:0% +exactly how you do that you listen to + + + align:start position:0% +exactly how you do that you listen to +sentences versus non-word strings you + + align:start position:0% +sentences versus non-word strings you + + + align:start position:0% +sentences versus non-word strings you +find a systematic set of brain regions + + align:start position:0% +find a systematic set of brain regions + + + align:start position:0% +find a systematic set of brain regions +that you can identify in each individual + + align:start position:0% +that you can identify in each individual + + + align:start position:0% +that you can identify in each individual +that look like this here is in three + + align:start position:0% +that look like this here is in three + + + align:start position:0% +that look like this here is in three +subjects those red bits are the bits + + align:start position:0% +subjects those red bits are the bits + + + align:start position:0% +subjects those red bits are the bits +that respond more when you + + align:start position:0% +that respond more when you + + + align:start position:0% +that respond more when you +listen to a sentence versus listen to + + align:start position:0% +listen to a sentence versus listen to + + + align:start position:0% +listen to a sentence versus listen to +non-word strings or read sentences + + align:start position:0% +non-word strings or read sentences + + + align:start position:0% +non-word strings or read sentences +versus non-word strings + + align:start position:0% +versus non-word strings + + + align:start position:0% +versus non-word strings +then what she could do is she said now + + align:start position:0% +then what she could do is she said now + + + align:start position:0% +then what she could do is she said now +that i found those exact regions each + + align:start position:0% +that i found those exact regions each + + + align:start position:0% +that i found those exact regions each +subject i can ask of those exact regions + + align:start position:0% +subject i can ask of those exact regions + + + align:start position:0% +subject i can ask of those exact regions +how do they respond to music versus + + align:start position:0% +how do they respond to music versus + + + align:start position:0% +how do they respond to music versus +scrambled music okay so she played stuff + + align:start position:0% +scrambled music okay so she played stuff + + + align:start position:0% +scrambled music okay so she played stuff +like this + + align:start position:0% + + + + align:start position:0% + +okay so nice canonical you know nothing + + align:start position:0% +okay so nice canonical you know nothing + + + align:start position:0% +okay so nice canonical you know nothing +crazy weird we're not going with the new + + align:start position:0% +crazy weird we're not going with the new + + + align:start position:0% +crazy weird we're not going with the new +guinea in music and asking edgy + + align:start position:0% +guinea in music and asking edgy + + + align:start position:0% +guinea in music and asking edgy +questions we're just saying something + + align:start position:0% +questions we're just saying something + + + align:start position:0% +questions we're just saying something +everybody agrees that's music versus you + + align:start position:0% +everybody agrees that's music versus you + + + align:start position:0% +everybody agrees that's music versus you +scramble it and it sounds like this + + align:start position:0% + + + + align:start position:0% + +okay it's actually the same notes yeah i + + align:start position:0% +okay it's actually the same notes yeah i + + + align:start position:0% +okay it's actually the same notes yeah i +know i know a lot of people that go + + align:start position:0% +know i know a lot of people that go + + + align:start position:0% +know i know a lot of people that go +that's cool that's really edgy yeah it + + align:start position:0% +that's cool that's really edgy yeah it + + + align:start position:0% +that's cool that's really edgy yeah it +is but you know to most people it's it's + + align:start position:0% +is but you know to most people it's it's + + + align:start position:0% +is but you know to most people it's it's +not canonical music okay + + align:start position:0% +not canonical music okay + + + align:start position:0% +not canonical music okay +okay and so what i've found is that none + + align:start position:0% +okay and so what i've found is that none + + + align:start position:0% +okay and so what i've found is that none +of those language regions responded more + + align:start position:0% +of those language regions responded more + + + align:start position:0% +of those language regions responded more +to the intact than scrambled music + + align:start position:0% +to the intact than scrambled music + + + align:start position:0% +to the intact than scrambled music +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so language regions are not interested + + align:start position:0% +so language regions are not interested + + + align:start position:0% +so language regions are not interested +in music and we'll talk more about that + + align:start position:0% +in music and we'll talk more about that + + + align:start position:0% +in music and we'll talk more about that +next week or the week after + + align:start position:0% +next week or the week after + + + align:start position:0% +next week or the week after +then she did the opposite she identified + + align:start position:0% +then she did the opposite she identified + + + align:start position:0% +then she did the opposite she identified +brain regions + + align:start position:0% +brain regions + + + align:start position:0% +brain regions +here in a group analysis just to show + + align:start position:0% +here in a group analysis just to show + + + align:start position:0% +here in a group analysis just to show +you where they are anterior in the + + align:start position:0% +you where they are anterior in the + + + align:start position:0% +you where they are anterior in the +temporal lobes that respond more to + + align:start position:0% +temporal lobes that respond more to + + + align:start position:0% +temporal lobes that respond more to +intact than scrambled music okay she + + align:start position:0% +intact than scrambled music okay she + + + align:start position:0% +intact than scrambled music okay she +identified those in each subject and + + align:start position:0% +identified those in each subject and + + + align:start position:0% +identified those in each subject and +measured the response of those regions + + align:start position:0% +measured the response of those regions + + + align:start position:0% +measured the response of those regions +to language + + align:start position:0% +to language + + + align:start position:0% +to language +sentences and non-word strings + + align:start position:0% +sentences and non-word strings + + + align:start position:0% +sentences and non-word strings +and each of those regions + + align:start position:0% +and each of those regions + + + align:start position:0% +and each of those regions +respond exactly the same to sentences + + align:start position:0% +respond exactly the same to sentences + + + align:start position:0% +respond exactly the same to sentences +and non-word strings + + align:start position:0% +and non-word strings + + + align:start position:0% +and non-word strings +so basically + + align:start position:0% +so basically + + + align:start position:0% +so basically +the + + align:start position:0% +the + + + align:start position:0% +the +language regions are not interested in + + align:start position:0% +language regions are not interested in + + + align:start position:0% +language regions are not interested in +music and the music regions are not + + align:start position:0% +music and the music regions are not + + + align:start position:0% +music and the music regions are not +interested in language and therein we + + align:start position:0% +interested in language and therein we + + + align:start position:0% +interested in language and therein we +have a + + align:start position:0% + + + + align:start position:0% + +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so + + align:start position:0% +um so + + + align:start position:0% +um so +um music is not using machinery for + + align:start position:0% +um music is not using machinery for + + + align:start position:0% +um music is not using machinery for +language okay that was one of the + + align:start position:0% +language okay that was one of the + + + align:start position:0% +language okay that was one of the +hypotheses we started with no it's not + + align:start position:0% +hypotheses we started with no it's not + + + align:start position:0% +hypotheses we started with no it's not +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so that's true at least for high-level + + align:start position:0% +so that's true at least for high-level + + + align:start position:0% +so that's true at least for high-level +language processing that computes the + + align:start position:0% +language processing that computes the + + + align:start position:0% +language processing that computes the +meaning of a sentence + + align:start position:0% +meaning of a sentence + + + align:start position:0% +meaning of a sentence +um but what about speech perception + + align:start position:0% +um but what about speech perception + + + align:start position:0% +um but what about speech perception +remember last time i made this + + align:start position:0% +remember last time i made this + + + align:start position:0% +remember last time i made this +distinction between the sounds like ba + + align:start position:0% +distinction between the sounds like ba + + + align:start position:0% +distinction between the sounds like ba +and pa + + align:start position:0% +and pa + + + align:start position:0% +and pa +um which have a whole set of + + align:start position:0% +um which have a whole set of + + + align:start position:0% +um which have a whole set of +computational challenges just under you + + align:start position:0% +computational challenges just under you + + + align:start position:0% +computational challenges just under you +know just perceiving those sounds which + + align:start position:0% +know just perceiving those sounds which + + + align:start position:0% +know just perceiving those sounds which +is quite different than knowing the + + align:start position:0% +is quite different than knowing the + + + align:start position:0% +is quite different than knowing the +meaning of a sentence okay + + align:start position:0% +meaning of a sentence okay + + + align:start position:0% +meaning of a sentence okay +so what about speech perception or in + + align:start position:0% +so what about speech perception or in + + + align:start position:0% +so what about speech perception or in +fact any other aspect of hearing + + align:start position:0% +fact any other aspect of hearing + + + align:start position:0% +fact any other aspect of hearing +okay so what i'm going to try to do + + align:start position:0% +okay so what i'm going to try to do + + + align:start position:0% +okay so what i'm going to try to do +is briefly tell you about one of our + + align:start position:0% +is briefly tell you about one of our + + + align:start position:0% +is briefly tell you about one of our +experiments i'm sorry i try not to turn + + align:start position:0% +experiments i'm sorry i try not to turn + + + align:start position:0% +experiments i'm sorry i try not to turn +this whole course into stuff we've done + + align:start position:0% +this whole course into stuff we've done + + + align:start position:0% +this whole course into stuff we've done +in my lab but it's one of my favorite + + align:start position:0% +in my lab but it's one of my favorite + + + align:start position:0% +in my lab but it's one of my favorite +ever and it's kind of a cool different + + align:start position:0% +ever and it's kind of a cool different + + + align:start position:0% +ever and it's kind of a cool different +um + + align:start position:0% +um + + + align:start position:0% +um +way to go at this question from the + + align:start position:0% +way to go at this question from the + + + align:start position:0% +way to go at this question from the +other mri experiments we've talked about + + align:start position:0% +other mri experiments we've talked about + + + align:start position:0% +other mri experiments we've talked about +before + + align:start position:0% +before + + + align:start position:0% +before +so the background is okay let's step + + align:start position:0% +so the background is okay let's step + + + align:start position:0% +so the background is okay let's step +back what's the overall organization + + align:start position:0% +back what's the overall organization + + + align:start position:0% +back what's the overall organization +organization of auditory cortex and when + + align:start position:0% +organization of auditory cortex and when + + + align:start position:0% +organization of auditory cortex and when +we did this experiment five or six years + + align:start position:0% +we did this experiment five or six years + + + align:start position:0% +we did this experiment five or six years +ago not a whole lot was known basically + + align:start position:0% +ago not a whole lot was known basically + + + align:start position:0% +ago not a whole lot was known basically +everybody agrees whoops my i put the + + align:start position:0% +everybody agrees whoops my i put the + + + align:start position:0% +everybody agrees whoops my i put the +wrong slide in here everybody agrees + + align:start position:0% +wrong slide in here everybody agrees + + + align:start position:0% +wrong slide in here everybody agrees +that primary auditory cortex is right + + align:start position:0% +that primary auditory cortex is right + + + align:start position:0% +that primary auditory cortex is right +there with that high low high frequency + + align:start position:0% +there with that high low high frequency + + + align:start position:0% +there with that high low high frequency +thing we talked about from there but + + align:start position:0% +thing we talked about from there but + + + align:start position:0% +thing we talked about from there but +from there on out and you know in the + + align:start position:0% +from there on out and you know in the + + + align:start position:0% +from there on out and you know in the +last couple years + + align:start position:0% +last couple years + + + align:start position:0% +last couple years +there's an agreement about speech + + align:start position:0% +there's an agreement about speech + + + align:start position:0% +there's an agreement about speech +selective cortex that i showed you + + align:start position:0% +selective cortex that i showed you + + + align:start position:0% +selective cortex that i showed you +briefly last time and other people have + + align:start position:0% +briefly last time and other people have + + + align:start position:0% +briefly last time and other people have +seen that + + align:start position:0% +seen that + + + align:start position:0% +seen that +but there's kind of no lots of + + align:start position:0% +but there's kind of no lots of + + + align:start position:0% +but there's kind of no lots of +hypotheses and no agreement with + + align:start position:0% +hypotheses and no agreement with + + + align:start position:0% +hypotheses and no agreement with +anything else and and no real evidence + + align:start position:0% +anything else and and no real evidence + + + align:start position:0% +anything else and and no real evidence +for really music selective cortex okay + + align:start position:0% +for really music selective cortex okay + + + align:start position:0% +for really music selective cortex okay +so but there's a problem with all the + + align:start position:0% +so but there's a problem with all the + + + align:start position:0% +so but there's a problem with all the +prior work where you sit around and make + + align:start position:0% +prior work where you sit around and make + + + align:start position:0% +prior work where you sit around and make +a hypothesis and say oh let's see + + align:start position:0% +a hypothesis and say oh let's see + + + align:start position:0% +a hypothesis and say oh let's see +are we going to get a higher response to + + align:start position:0% +are we going to get a higher response to + + + align:start position:0% +are we going to get a higher response to +say intact versus scrambled music + + align:start position:0% +say intact versus scrambled music + + + align:start position:0% +say intact versus scrambled music +or you know faces versus objects or + + align:start position:0% +or you know faces versus objects or + + + align:start position:0% +or you know faces versus objects or +whatever right + + align:start position:0% +whatever right + + + align:start position:0% +whatever right +all of those are scientists making up + + align:start position:0% +all of those are scientists making up + + + align:start position:0% +all of those are scientists making up +hypotheses and then testing them + + align:start position:0% +hypotheses and then testing them + + + align:start position:0% +hypotheses and then testing them +and there's nothing wrong with that + + align:start position:0% +and there's nothing wrong with that + + + align:start position:0% +and there's nothing wrong with that +that's what scientists are supposed to + + align:start position:0% +that's what scientists are supposed to + + + align:start position:0% +that's what scientists are supposed to +do invent hypotheses and then make good + + align:start position:0% +do invent hypotheses and then make good + + + align:start position:0% +do invent hypotheses and then make good +designs and go test them + + align:start position:0% +designs and go test them + + + align:start position:0% +designs and go test them +but the problem with that is + + align:start position:0% +but the problem with that is + + + align:start position:0% +but the problem with that is +we can only discover things that we can + + align:start position:0% +we can only discover things that we can + + + align:start position:0% +we can only discover things that we can +think to test + + align:start position:0% +think to test + + + align:start position:0% +think to test +what if deep facts about mind and brain + + align:start position:0% +what if deep facts about mind and brain + + + align:start position:0% +what if deep facts about mind and brain +are things that nobody would think up in + + align:start position:0% +are things that nobody would think up in + + + align:start position:0% +are things that nobody would think up in +the first place + + align:start position:0% +the first place + + + align:start position:0% +the first place +and so that's where we can get real + + align:start position:0% +and so that's where we can get real + + + align:start position:0% +and so that's where we can get real +power from what are known as data-driven + + align:start position:0% +power from what are known as data-driven + + + align:start position:0% +power from what are known as data-driven +studies + + align:start position:0% +studies + + + align:start position:0% +studies +where you collect a boatload of data and + + align:start position:0% +where you collect a boatload of data and + + + align:start position:0% +where you collect a boatload of data and +then use some fancy math and say tell me + + align:start position:0% +then use some fancy math and say tell me + + + align:start position:0% +then use some fancy math and say tell me +what the structure is in this data not + + align:start position:0% +what the structure is in this data not + + + align:start position:0% +what the structure is in this data not +is this hypothesis that i love true in + + align:start position:0% +is this hypothesis that i love true in + + + align:start position:0% +is this hypothesis that i love true in +these data + + align:start position:0% +these data + + + align:start position:0% +these data +and i'll do anything to pull it out if i + + align:start position:0% +and i'll do anything to pull it out if i + + + align:start position:0% +and i'll do anything to pull it out if i +can see it in there find evidence for it + + align:start position:0% +can see it in there find evidence for it + + + align:start position:0% +can see it in there find evidence for it +in there but yeah exactly but if we + + align:start position:0% +in there but yeah exactly but if we + + + align:start position:0% +in there but yeah exactly but if we +collect a whole bunch of data and do + + align:start position:0% +collect a whole bunch of data and do + + + align:start position:0% +collect a whole bunch of data and do +some math and see what the structure is + + align:start position:0% +some math and see what the structure is + + + align:start position:0% +some math and see what the structure is +what do we see + + align:start position:0% +what do we see + + + align:start position:0% +what do we see +okay so that's what we did in this study + + align:start position:0% +okay so that's what we did in this study + + + align:start position:0% +okay so that's what we did in this study +i'm going to speed up to try to give you + + align:start position:0% +i'm going to speed up to try to give you + + + align:start position:0% +i'm going to speed up to try to give you +the the gist here okay so we as sam + + align:start position:0% +the the gist here okay so we as sam + + + align:start position:0% +the the gist here okay so we as sam +norman hagner here and josh mcdermott + + align:start position:0% +norman hagner here and josh mcdermott + + + align:start position:0% +norman hagner here and josh mcdermott +and so we scanned people while they were + + align:start position:0% +and so we scanned people while they were + + + align:start position:0% +and so we scanned people while they were +hearing stuff like this + + align:start position:0% +hearing stuff like this + + + align:start position:0% +hearing stuff like this +we first collected + + align:start position:0% +we first collected + + + align:start position:0% +we first collected +the 165 categories of sounds that people + + align:start position:0% +the 165 categories of sounds that people + + + align:start position:0% +the 165 categories of sounds that people +hear most commonly this is classic + + align:start position:0% +hear most commonly this is classic + + + align:start position:0% +hear most commonly this is classic +cocktail party effect you guys are doing + + align:start position:0% +cocktail party effect you guys are doing + + + align:start position:0% +cocktail party effect you guys are doing +you have to separate me speaking from + + align:start position:0% +you have to separate me speaking from + + + align:start position:0% +you have to separate me speaking from +all this crazy weird changing background + + align:start position:0% +all this crazy weird changing background + + + align:start position:0% +all this crazy weird changing background +um + + align:start position:0% +um + + + align:start position:0% +um +and so anyway we scan people listening + + align:start position:0% +and so anyway we scan people listening + + + align:start position:0% +and so anyway we scan people listening +to these sounds which broadly sample + + align:start position:0% +to these sounds which broadly sample + + + align:start position:0% +to these sounds which broadly sample +auditory experience right and so we + + align:start position:0% +auditory experience right and so we + + + align:start position:0% +auditory experience right and so we +collected sounds people hear most often + + align:start position:0% +collected sounds people hear most often + + + align:start position:0% +collected sounds people hear most often +and that they can recognize from a two + + align:start position:0% +and that they can recognize from a two + + + align:start position:0% +and that they can recognize from a two +second clip okay enough already + + align:start position:0% +second clip okay enough already + + + align:start position:0% +second clip okay enough already +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +just to wake everyone up okay + + align:start position:0% +just to wake everyone up okay + + + align:start position:0% +just to wake everyone up okay +so we scan them listening to those 165 + + align:start position:0% +so we scan them listening to those 165 + + + align:start position:0% +so we scan them listening to those 165 +sounds broad sample of auditory + + align:start position:0% +sounds broad sample of auditory + + + align:start position:0% +sounds broad sample of auditory +experience + + align:start position:0% +experience + + + align:start position:0% +experience +then from each voxel in the brain + + align:start position:0% +then from each voxel in the brain + + + align:start position:0% +then from each voxel in the brain +we measure the exact magnitude of + + align:start position:0% +we measure the exact magnitude of + + + align:start position:0% +we measure the exact magnitude of +response of that voxel to each of the + + align:start position:0% +response of that voxel to each of the + + + align:start position:0% +response of that voxel to each of the +165 sounds and we get a vector like this + + align:start position:0% +165 sounds and we get a vector like this + + + align:start position:0% +165 sounds and we get a vector like this +everybody with me that's one voxel right + + align:start position:0% +everybody with me that's one voxel right + + + align:start position:0% +everybody with me that's one voxel right +there another voxel another oxel okay + + align:start position:0% +there another voxel another oxel okay + + + align:start position:0% +there another voxel another oxel okay +we do this in all of kind of greater + + align:start position:0% +we do this in all of kind of greater + + + align:start position:0% +we do this in all of kind of greater +suburban auditory cortex that is not + + align:start position:0% +suburban auditory cortex that is not + + + align:start position:0% +suburban auditory cortex that is not +just primary cortex but all the stuff + + align:start position:0% +just primary cortex but all the stuff + + + align:start position:0% +just primary cortex but all the stuff +around it that might even remotely you + + align:start position:0% +around it that might even remotely you + + + align:start position:0% +around it that might even remotely you +know that responds in any systematic way + + align:start position:0% +know that responds in any systematic way + + + align:start position:0% +know that responds in any systematic way +to auditory stimulated grab the whole + + align:start position:0% +to auditory stimulated grab the whole + + + align:start position:0% +to auditory stimulated grab the whole +damn thing okay + + align:start position:0% +damn thing okay + + + align:start position:0% +damn thing okay +so you do that in ten subjects + + align:start position:0% +so you do that in ten subjects + + + align:start position:0% +so you do that in ten subjects +you have a big matrix like this a + + align:start position:0% +you have a big matrix like this a + + + align:start position:0% +you have a big matrix like this a +thousand voxels in each subject eleven + + align:start position:0% +thousand voxels in each subject eleven + + + align:start position:0% +thousand voxels in each subject eleven +thousand voxels across the top 165 + + align:start position:0% +thousand voxels across the top 165 + + + align:start position:0% +thousand voxels across the top 165 +sounds that's our data + + align:start position:0% +sounds that's our data + + + align:start position:0% +sounds that's our data +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so each column + + align:start position:0% +so each column + + + align:start position:0% +so each column +um is the response + + align:start position:0% +um is the response + + + align:start position:0% +um is the response +of one voxel in one person's brain to + + align:start position:0% +of one voxel in one person's brain to + + + align:start position:0% +of one voxel in one person's brain to +each of the 165 sounds everybody got it + + align:start position:0% +each of the 165 sounds everybody got it + + + align:start position:0% +each of the 165 sounds everybody got it +okay now we have this lovely matrix + + align:start position:0% +okay now we have this lovely matrix + + + align:start position:0% +okay now we have this lovely matrix +which is basically all the data we care + + align:start position:0% +which is basically all the data we care + + + align:start position:0% +which is basically all the data we care +about from this whole experiment then we + + align:start position:0% +about from this whole experiment then we + + + align:start position:0% +about from this whole experiment then we +throw away all the labels + + align:start position:0% +throw away all the labels + + + align:start position:0% +throw away all the labels +poof it's just a matrix + + align:start position:0% +poof it's just a matrix + + + align:start position:0% +poof it's just a matrix +and then we do some math which + + align:start position:0% +and then we do some math which + + + align:start position:0% +and then we do some math which +essentially says + + align:start position:0% +essentially says + + + align:start position:0% +essentially says +let's boil down the structure in this + + align:start position:0% +let's boil down the structure in this + + + align:start position:0% +let's boil down the structure in this +matrix and discover its fundamental + + align:start position:0% +matrix and discover its fundamental + + + align:start position:0% +matrix and discover its fundamental +components + + align:start position:0% +components + + + align:start position:0% +components +that math happens to be a variant of + + align:start position:0% +that math happens to be a variant of + + + align:start position:0% +that math happens to be a variant of +independent component analysis that + + align:start position:0% +independent component analysis that + + + align:start position:0% +independent component analysis that +means anything to you if it doesn't + + align:start position:0% +means anything to you if it doesn't + + + align:start position:0% +means anything to you if it doesn't +don't worry about it the gist is we're + + align:start position:0% +don't worry about it the gist is we're + + + align:start position:0% +don't worry about it the gist is we're +doing math to say what's the structure + + align:start position:0% +doing math to say what's the structure + + + align:start position:0% +doing math to say what's the structure +in here and we're doing it without any + + align:start position:0% +in here and we're doing it without any + + + align:start position:0% +in here and we're doing it without any +labels so this analysis doesn't even + + align:start position:0% +labels so this analysis doesn't even + + + align:start position:0% +labels so this analysis doesn't even +know where the voxels are or which of + + align:start position:0% +know where the voxels are or which of + + + align:start position:0% +know where the voxels are or which of +your 10 subjects that voxel came from it + + align:start position:0% +your 10 subjects that voxel came from it + + + align:start position:0% +your 10 subjects that voxel came from it +doesn't know which sound is which and so + + align:start position:0% +doesn't know which sound is which and so + + + align:start position:0% +doesn't know which sound is which and so +it's very hypothesis neutral it's a way + + align:start position:0% +it's very hypothesis neutral it's a way + + + align:start position:0% +it's very hypothesis neutral it's a way +to say show me structure + + align:start position:0% +to say show me structure + + + align:start position:0% +to say show me structure +with almost no kind of prior biases just + + align:start position:0% +with almost no kind of prior biases just + + + align:start position:0% +with almost no kind of prior biases just +show me the structure okay so everybody + + align:start position:0% +show me the structure okay so everybody + + + align:start position:0% +show me the structure okay so everybody +get how that's kind of a totally + + align:start position:0% +get how that's kind of a totally + + + align:start position:0% +get how that's kind of a totally +different and kind of thing to do from + + align:start position:0% +different and kind of thing to do from + + + align:start position:0% +different and kind of thing to do from +everything we've talked about so far + + align:start position:0% +everything we've talked about so far + + + align:start position:0% +everything we've talked about so far +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's what we did i'm going to skip + + align:start position:0% +so that's what we did i'm going to skip + + + align:start position:0% +so that's what we did i'm going to skip +the math and the modeling assumptions + + align:start position:0% +the math and the modeling assumptions + + + align:start position:0% +the math and the modeling assumptions +not really that complicated but we're + + align:start position:0% +not really that complicated but we're + + + align:start position:0% +not really that complicated but we're +going to run out of time + + align:start position:0% +going to run out of time + + + align:start position:0% +going to run out of time +so very hypothesis neutral and what we + + align:start position:0% +so very hypothesis neutral and what we + + + align:start position:0% +so very hypothesis neutral and what we +find is + + align:start position:0% +find is + + + align:start position:0% +find is +six components + + align:start position:0% +six components + + + align:start position:0% +six components +account for most of the replicable + + align:start position:0% +account for most of the replicable + + + align:start position:0% +account for most of the replicable +variants in that whole matrix okay i'll + + align:start position:0% +variants in that whole matrix okay i'll + + + align:start position:0% +variants in that whole matrix okay i'll +tell you what a component is in a second + + align:start position:0% +tell you what a component is in a second + + + align:start position:0% +tell you what a component is in a second +do you have a question + + align:start position:0% + + + + align:start position:0% + +it doesn't with pca you assume + + align:start position:0% +it doesn't with pca you assume + + + align:start position:0% +it doesn't with pca you assume +orthogonal axes with ica you don't + + align:start position:0% +orthogonal axes with ica you don't + + + align:start position:0% +orthogonal axes with ica you don't +assume orthogonal and axes and so it's + + align:start position:0% +assume orthogonal and axes and so it's + + + align:start position:0% +assume orthogonal and axes and so it's +very very similar to pca + + align:start position:0% +very very similar to pca + + + align:start position:0% +very very similar to pca +and it starts out as pca and then it + + align:start position:0% +and it starts out as pca and then it + + + align:start position:0% +and it starts out as pca and then it +does some more rigmarole yeah it's the + + align:start position:0% +does some more rigmarole yeah it's the + + + align:start position:0% +does some more rigmarole yeah it's the +same idea + + align:start position:0% +same idea + + + align:start position:0% +same idea +like basically tell me the main + + align:start position:0% +like basically tell me the main + + + align:start position:0% +like basically tell me the main +dimensions of variation + + align:start position:0% + + + + align:start position:0% + +uh yes they are sparse and that is one + + align:start position:0% +uh yes they are sparse and that is one + + + align:start position:0% +uh yes they are sparse and that is one +of the assumptions you use it's actually + + align:start position:0% +of the assumptions you use it's actually + + + align:start position:0% +of the assumptions you use it's actually +there there isn't only one one way to + + align:start position:0% +there there isn't only one one way to + + + align:start position:0% +there there isn't only one one way to +factorize a matrix it's an imposed + + align:start position:0% +factorize a matrix it's an imposed + + + align:start position:0% +factorize a matrix it's an imposed +problem so you need to make some + + align:start position:0% +problem so you need to make some + + + align:start position:0% +problem so you need to make some +assumptions but you can and that's one + + align:start position:0% +assumptions but you can and that's one + + + align:start position:0% +assumptions but you can and that's one +of the ones we made but you can test + + align:start position:0% +of the ones we made but you can test + + + align:start position:0% +of the ones we made but you can test +them okay + + align:start position:0% +them okay + + + align:start position:0% +them okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what we find is six components + + align:start position:0% +so what we find is six components + + + align:start position:0% +so what we find is six components +account for most of the data + + align:start position:0% +account for most of the data + + + align:start position:0% +account for most of the data +and + + align:start position:0% +and + + + align:start position:0% +and +four of those + + align:start position:0% +four of those + + + align:start position:0% +four of those +reflected acoustic properties of the + + align:start position:0% +reflected acoustic properties of the + + + align:start position:0% +reflected acoustic properties of the +stimuli okay + + align:start position:0% +stimuli okay + + + align:start position:0% +stimuli okay +one + + align:start position:0% +one + + + align:start position:0% +one +was high for all the sounds with lots of + + align:start position:0% +was high for all the sounds with lots of + + + align:start position:0% +was high for all the sounds with lots of +low frequencies another was high for all + + align:start position:0% +low frequencies another was high for all + + + align:start position:0% +low frequencies another was high for all +the sounds with high frequencies what is + + align:start position:0% +the sounds with high frequencies what is + + + align:start position:0% +the sounds with high frequencies what is +that + + align:start position:0% + + + + align:start position:0% + +sorry speak up + + align:start position:0% + + + + align:start position:0% + +they're sensitive to frequency but where + + align:start position:0% +they're sensitive to frequency but where + + + align:start position:0% +they're sensitive to frequency but where +is that in the brain that you've already + + align:start position:0% +is that in the brain that you've already + + + align:start position:0% +is that in the brain that you've already +heard about + + align:start position:0% +heard about + + + align:start position:0% +heard about +primary auditory cortex as a tonatopic + + align:start position:0% +primary auditory cortex as a tonatopic + + + align:start position:0% +primary auditory cortex as a tonatopic +map so this is awesome because if you go + + align:start position:0% +map so this is awesome because if you go + + + align:start position:0% +map so this is awesome because if you go +invent some crazy math and you apply it + + align:start position:0% +invent some crazy math and you apply it + + + align:start position:0% +invent some crazy math and you apply it +to your data and you discover something + + align:start position:0% +to your data and you discover something + + + align:start position:0% +to your data and you discover something +you know to be true that's very + + align:start position:0% +you know to be true that's very + + + align:start position:0% +you know to be true that's very +reassuring right the math isn't just + + align:start position:0% +reassuring right the math isn't just + + + align:start position:0% +reassuring right the math isn't just +inventing crazy stuff it's discovering + + align:start position:0% +inventing crazy stuff it's discovering + + + align:start position:0% +inventing crazy stuff it's discovering +stuff we already know to be true + + align:start position:0% +stuff we already know to be true + + + align:start position:0% +stuff we already know to be true +that's known in more biological parts of + + align:start position:0% +that's known in more biological parts of + + + align:start position:0% +that's known in more biological parts of +the field as a positive control invent a + + align:start position:0% +the field as a positive control invent a + + + align:start position:0% +the field as a positive control invent a +new method make sure it can discover the + + align:start position:0% +new method make sure it can discover the + + + align:start position:0% +new method make sure it can discover the +stuff you know to be true okay so check + + align:start position:0% +stuff you know to be true okay so check + + + align:start position:0% +stuff you know to be true okay so check +check okay + + align:start position:0% +check okay + + + align:start position:0% +check okay +um all right + + align:start position:0% +um all right + + + align:start position:0% +um all right +but then it discovered some other stuff + + align:start position:0% +but then it discovered some other stuff + + + align:start position:0% +but then it discovered some other stuff +and i'm just going to tell you about two + + align:start position:0% +and i'm just going to tell you about two + + + align:start position:0% +and i'm just going to tell you about two +of them + + align:start position:0% +of them + + + align:start position:0% +of them +so here's one so i was just loose about + + align:start position:0% +so here's one so i was just loose about + + + align:start position:0% +so here's one so i was just loose about +what a component is a component is + + align:start position:0% +what a component is a component is + + + align:start position:0% +what a component is a component is +a magnitude of response for each of the + + align:start position:0% +a magnitude of response for each of the + + + align:start position:0% +a magnitude of response for each of the +165 sounds + + align:start position:0% +165 sounds + + + align:start position:0% +165 sounds +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and a separate distribution in the brain + + align:start position:0% +and a separate distribution in the brain + + + align:start position:0% +and a separate distribution in the brain +which i'll show you in a moment in a + + align:start position:0% +which i'll show you in a moment in a + + + align:start position:0% +which i'll show you in a moment in a +moment so here's one of those components + + align:start position:0% +moment so here's one of those components + + + align:start position:0% +moment so here's one of those components +and if we we've taken the 165 sounds and + + align:start position:0% +and if we we've taken the 165 sounds and + + + align:start position:0% +and if we we've taken the 165 sounds and +added basic category labels on them we + + align:start position:0% +added basic category labels on them we + + + align:start position:0% +added basic category labels on them we +put them on mechanical turk and people + + align:start position:0% +put them on mechanical turk and people + + + align:start position:0% +put them on mechanical turk and people +told us which category they belong to + + align:start position:0% +told us which category they belong to + + + align:start position:0% +told us which category they belong to +so that enables us to look at this kind + + align:start position:0% +so that enables us to look at this kind + + + align:start position:0% +so that enables us to look at this kind +of mysterious thing and average within a + + align:start position:0% +of mysterious thing and average within a + + + align:start position:0% +of mysterious thing and average within a +category + + align:start position:0% +category + + + align:start position:0% +category +so this is this component + + align:start position:0% +so this is this component + + + align:start position:0% +so this is this component +and if you look at it you see + + align:start position:0% +and if you look at it you see + + + align:start position:0% +and if you look at it you see +that it's really high + + align:start position:0% +that it's really high + + + align:start position:0% +that it's really high +for + + align:start position:0% +for + + + align:start position:0% +for +english speech and foreign speech that + + align:start position:0% +english speech and foreign speech that + + + align:start position:0% +english speech and foreign speech that +our subjects don't understand + + align:start position:0% +our subjects don't understand + + + align:start position:0% +our subjects don't understand +and then oh what's that intermediate + + align:start position:0% +and then oh what's that intermediate + + + align:start position:0% +and then oh what's that intermediate +thing + + align:start position:0% +thing + + + align:start position:0% +thing +oh that's music with vocals + + align:start position:0% +oh that's music with vocals + + + align:start position:0% +oh that's music with vocals +it has a kind of speech + + align:start position:0% +it has a kind of speech + + + align:start position:0% +it has a kind of speech +okay so and way down here that's + + align:start position:0% +okay so and way down here that's + + + align:start position:0% +okay so and way down here that's +non-speech vocalizations stuff like + + align:start position:0% +non-speech vocalizations stuff like + + + align:start position:0% +non-speech vocalizations stuff like +laughing and crying and sighing so + + align:start position:0% +laughing and crying and sighing so + + + align:start position:0% +laughing and crying and sighing so +there's a voice but no speech content + + align:start position:0% +there's a voice but no speech content + + + align:start position:0% +there's a voice but no speech content +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's a speech component + + align:start position:0% +so that's a speech component + + + align:start position:0% +so that's a speech component +and what's and as i mentioned this had + + align:start position:0% +and what's and as i mentioned this had + + + align:start position:0% +and what's and as i mentioned this had +been seen before in the last few years + + align:start position:0% +been seen before in the last few years + + + align:start position:0% +been seen before in the last few years +so it wasn't completely new but what's + + align:start position:0% +so it wasn't completely new but what's + + + align:start position:0% +so it wasn't completely new but what's +cool about this is this just emerged + + align:start position:0% +cool about this is this just emerged + + + align:start position:0% +cool about this is this just emerged +spontaneously from this very broad + + align:start position:0% +spontaneously from this very broad + + + align:start position:0% +spontaneously from this very broad +screen we didn't go and say hey can we + + align:start position:0% +screen we didn't go and say hey can we + + + align:start position:0% +screen we didn't go and say hey can we +find a speech selective region of cortex + + align:start position:0% +find a speech selective region of cortex + + + align:start position:0% +find a speech selective region of cortex +if we try really hard oh yeah we + + align:start position:0% +if we try really hard oh yeah we + + + align:start position:0% +if we try really hard oh yeah we +validate our path this is like let's + + align:start position:0% +validate our path this is like let's + + + align:start position:0% +validate our path this is like let's +sample auditory experience and wow there + + align:start position:0% +sample auditory experience and wow there + + + align:start position:0% +sample auditory experience and wow there +it is yeah + + align:start position:0% + + + + align:start position:0% + +we put them on turk and had people say + + align:start position:0% +we put them on turk and had people say + + + align:start position:0% +we put them on turk and had people say +what category they fit into yeah + + align:start position:0% + + + + align:start position:0% + +absolutely absolutely this is a first + + align:start position:0% +absolutely absolutely this is a first + + + align:start position:0% +absolutely absolutely this is a first +pass and one hopes to go deeper and + + align:start position:0% +pass and one hopes to go deeper and + + + align:start position:0% +pass and one hopes to go deeper and +deeper like if we could separate + + align:start position:0% +deeper like if we could separate + + + align:start position:0% +deeper like if we could separate +um you know + + align:start position:0% +um you know + + + align:start position:0% +um you know +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh oh different aspects of speech + + align:start position:0% +uh oh different aspects of speech + + + align:start position:0% +uh oh different aspects of speech +consonants and vowels fricatives + + align:start position:0% +consonants and vowels fricatives + + + align:start position:0% +consonants and vowels fricatives +whatever there could be much more to be + + align:start position:0% +whatever there could be much more to be + + + align:start position:0% +whatever there could be much more to be +done yeah i get asked + + align:start position:0% +done yeah i get asked + + + align:start position:0% +done yeah i get asked +oh boy okay + + align:start position:0% +oh boy okay + + + align:start position:0% +oh boy okay +uh okay and when do i have to give them + + align:start position:0% +uh okay and when do i have to give them + + + align:start position:0% +uh okay and when do i have to give them +the quiz + + align:start position:0% +the quiz + + + align:start position:0% +the quiz +it's shortish they don't need a full 10 + + align:start position:0% +it's shortish they don't need a full 10 + + + align:start position:0% +it's shortish they don't need a full 10 +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +is what is it seven questions + + align:start position:0% +is what is it seven questions + + + align:start position:0% +is what is it seven questions +eight eight minutes + + align:start position:0% +eight eight minutes + + + align:start position:0% +eight eight minutes +okay + + align:start position:0% +okay + + + align:start position:0% +okay +make me stop definitively at 12 18. okay + + align:start position:0% +make me stop definitively at 12 18. okay + + + align:start position:0% +make me stop definitively at 12 18. okay +so that's cool + + align:start position:0% +so that's cool + + + align:start position:0% +so that's cool +um + + align:start position:0% +um + + + align:start position:0% +um +um it's not exactly new but it's a + + align:start position:0% +um it's not exactly new but it's a + + + align:start position:0% +um it's not exactly new but it's a +really nice way to rediscover things + + align:start position:0% +really nice way to rediscover things + + + align:start position:0% +really nice way to rediscover things +that we uh thought to be true okay + + align:start position:0% +that we uh thought to be true okay + + + align:start position:0% +that we uh thought to be true okay +um all right + + align:start position:0% +um all right + + + align:start position:0% +um all right +then there's component six + + align:start position:0% +then there's component six + + + align:start position:0% +then there's component six +that popped out + + align:start position:0% +that popped out + + + align:start position:0% +that popped out +okay what is component six well if we + + align:start position:0% +okay what is component six well if we + + + align:start position:0% +okay what is component six well if we +average within a category + + align:start position:0% +average within a category + + + align:start position:0% +average within a category +instrumental music and music with vocals + + align:start position:0% +instrumental music and music with vocals + + + align:start position:0% +instrumental music and music with vocals +and everything else is really low + + align:start position:0% +and everything else is really low + + + align:start position:0% +and everything else is really low +we didn't go looking for this + + align:start position:0% +we didn't go looking for this + + + align:start position:0% +we didn't go looking for this +boom music selectivity + + align:start position:0% + + + + align:start position:0% + +that's pretty amazing never really been + + align:start position:0% +that's pretty amazing never really been + + + align:start position:0% +that's pretty amazing never really been +seen before + + align:start position:0% +seen before + + + align:start position:0% +seen before +okay people have looked and they've made + + align:start position:0% +okay people have looked and they've made + + + align:start position:0% +okay people have looked and they've made +some kind of sort of smoke and mirrors + + align:start position:0% +some kind of sort of smoke and mirrors + + + align:start position:0% +some kind of sort of smoke and mirrors +like not really like this is the first + + align:start position:0% +like not really like this is the first + + + align:start position:0% +like not really like this is the first +time it was seen and it just popped out + + align:start position:0% +time it was seen and it just popped out + + + align:start position:0% +time it was seen and it just popped out +of the data and that says that it's not + + align:start position:0% +of the data and that says that it's not + + + align:start position:0% +of the data and that says that it's not +just something you can find if you try + + align:start position:0% +just something you can find if you try + + + align:start position:0% +just something you can find if you try +really hard and go fishing for it it's + + align:start position:0% +really hard and go fishing for it it's + + + align:start position:0% +really hard and go fishing for it it's +actually a significant part of the + + align:start position:0% +actually a significant part of the + + + align:start position:0% +actually a significant part of the +variance in this whole response i'm + + align:start position:0% +variance in this whole response i'm + + + align:start position:0% +variance in this whole response i'm +going to skip everything except + + align:start position:0% +going to skip everything except + + + align:start position:0% +going to skip everything except +clarification questions now because i'm + + align:start position:0% + + + + align:start position:0% + +sort of it's complicated sorry that's a + + align:start position:0% +sort of it's complicated sorry that's a + + + align:start position:0% +sort of it's complicated sorry that's a +lot it's a long answer okay so this + + align:start position:0% +lot it's a long answer okay so this + + + align:start position:0% +lot it's a long answer okay so this +really looks like it's music okay and so + + align:start position:0% +really looks like it's music okay and so + + + align:start position:0% +really looks like it's music okay and so +now + + align:start position:0% +now + + + align:start position:0% +now +um i was vague about what a component is + + align:start position:0% +um i was vague about what a component is + + + align:start position:0% +um i was vague about what a component is +but it's both that response profile and + + align:start position:0% +but it's both that response profile and + + + align:start position:0% +but it's both that response profile and +it's a set of weights in the brain so if + + align:start position:0% +it's a set of weights in the brain so if + + + align:start position:0% +it's a set of weights in the brain so if +you project this one back in the brain + + align:start position:0% +you project this one back in the brain + + + align:start position:0% +you project this one back in the brain +you get this band of speech selective + + align:start position:0% +you get this band of speech selective + + + align:start position:0% +you get this band of speech selective +cortex right below primary auditory + + align:start position:0% +cortex right below primary auditory + + + align:start position:0% +cortex right below primary auditory +cortex like that + + align:start position:0% +cortex like that + + + align:start position:0% +cortex like that +and if you project the music stuff back + + align:start position:0% +and if you project the music stuff back + + + align:start position:0% +and if you project the music stuff back +in the brain + + align:start position:0% +in the brain + + + align:start position:0% +in the brain +you get a patch as sort of an answer to + + align:start position:0% +you get a patch as sort of an answer to + + + align:start position:0% +you get a patch as sort of an answer to +your question you get a patch up in + + align:start position:0% +your question you get a patch up in + + + align:start position:0% +your question you get a patch up in +front of primary auditory cortex and a + + align:start position:0% +front of primary auditory cortex and a + + + align:start position:0% +front of primary auditory cortex and a +patch behind + + align:start position:0% +patch behind + + + align:start position:0% +patch behind +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +and um okay so here we have a double + + align:start position:0% +and um okay so here we have a double + + + align:start position:0% +and um okay so here we have a double +dissociation of speech selectivity and + + align:start position:0% +dissociation of speech selectivity and + + + align:start position:0% +dissociation of speech selectivity and +music selectivity in the brain + + align:start position:0% +music selectivity in the brain + + + align:start position:0% +music selectivity in the brain +okay so music doesn't just use + + align:start position:0% +okay so music doesn't just use + + + align:start position:0% +okay so music doesn't just use +mechanisms for speech as many people + + align:start position:0% +mechanisms for speech as many people + + + align:start position:0% +mechanisms for speech as many people +have proposed it's not true right + + align:start position:0% +have proposed it's not true right + + + align:start position:0% +have proposed it's not true right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +when you see dramatic data like this a + + align:start position:0% +when you see dramatic data like this a + + + align:start position:0% +when you see dramatic data like this a +natural reaction is to say like really + + align:start position:0% +natural reaction is to say like really + + + align:start position:0% +natural reaction is to say like really +get out come on like music specificity + + align:start position:0% +get out come on like music specificity + + + align:start position:0% +get out come on like music specificity +like what + + align:start position:0% +like what + + + align:start position:0% +like what +okay so very briefly dana has just + + align:start position:0% +okay so very briefly dana has just + + + align:start position:0% +okay so very briefly dana has just +replicated this in a new sample of + + align:start position:0% +replicated this in a new sample of + + + align:start position:0% +replicated this in a new sample of +subjects it does not matter if those + + align:start position:0% +subjects it does not matter if those + + + align:start position:0% +subjects it does not matter if those +subjects have have musical training like + + align:start position:0% +subjects have have musical training like + + + align:start position:0% +subjects have have musical training like +students from berkeley school who spend + + align:start position:0% +students from berkeley school who spend + + + align:start position:0% +students from berkeley school who spend +like six hours a day practicing + + align:start position:0% +like six hours a day practicing + + + align:start position:0% +like six hours a day practicing +versus people who have essentially zero + + align:start position:0% +versus people who have essentially zero + + + align:start position:0% +versus people who have essentially zero +music lessons ever in their life + + align:start position:0% +music lessons ever in their life + + + align:start position:0% +music lessons ever in their life +you get those components in both groups + + align:start position:0% +you get those components in both groups + + + align:start position:0% +you get those components in both groups +maybe slightly stronger in the trained + + align:start position:0% +maybe slightly stronger in the trained + + + align:start position:0% +maybe slightly stronger in the trained +musicians we're not quite sure yet but + + align:start position:0% +musicians we're not quite sure yet but + + + align:start position:0% +musicians we're not quite sure yet but +in any case it is totally present in + + align:start position:0% +in any case it is totally present in + + + align:start position:0% +in any case it is totally present in +people with zero musical training that + + align:start position:0% +people with zero musical training that + + + align:start position:0% +people with zero musical training that +doesn't mean it's innate because people + + align:start position:0% +doesn't mean it's innate because people + + + align:start position:0% +doesn't mean it's innate because people +without musical training have musical + + align:start position:0% +without musical training have musical + + + align:start position:0% +without musical training have musical +experience but no explicit training okay + + align:start position:0% +experience but no explicit training okay + + + align:start position:0% +experience but no explicit training okay +skip all of this + + align:start position:0% +skip all of this + + + align:start position:0% +skip all of this +here is her replication boom boom it's + + align:start position:0% +here is her replication boom boom it's + + + align:start position:0% +here is her replication boom boom it's +there with and without training + + align:start position:0% +there with and without training + + + align:start position:0% +there with and without training +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um i'm going to skip all this you can + + align:start position:0% +um i'm going to skip all this you can + + + align:start position:0% +um i'm going to skip all this you can +read it on the slides if i lost you in + + align:start position:0% +read it on the slides if i lost you in + + + align:start position:0% +read it on the slides if i lost you in +here because i want to show you + + align:start position:0% +here because i want to show you + + + align:start position:0% +here because i want to show you +something else okay that music + + align:start position:0% +something else okay that music + + + align:start position:0% +something else okay that music +selectivity + + align:start position:0% +selectivity + + + align:start position:0% +selectivity +was not evident + + align:start position:0% +was not evident + + + align:start position:0% +was not evident +if you just do a direct contrast in the + + align:start position:0% +if you just do a direct contrast in the + + + align:start position:0% +if you just do a direct contrast in the +same data take all the music conditions + + align:start position:0% +same data take all the music conditions + + + align:start position:0% +same data take all the music conditions +all the non-music conditions you get + + align:start position:0% +all the non-music conditions you get + + + align:start position:0% +all the non-music conditions you get +kind of a blurry mess it's not strong + + align:start position:0% +kind of a blurry mess it's not strong + + + align:start position:0% +kind of a blurry mess it's not strong +you have to do the math to siphon it out + + align:start position:0% +you have to do the math to siphon it out + + + align:start position:0% +you have to do the math to siphon it out +and that's okay + + align:start position:0% +and that's okay + + + align:start position:0% +and that's okay +but i like to see things in the raw data + + align:start position:0% +but i like to see things in the raw data + + + align:start position:0% +but i like to see things in the raw data +and so probably what that means is the + + align:start position:0% +and so probably what that means is the + + + align:start position:0% +and so probably what that means is the +music is overlapping with other things + + align:start position:0% +music is overlapping with other things + + + align:start position:0% +music is overlapping with other things +in the brain and so the direct contrast + + align:start position:0% +in the brain and so the direct contrast + + + align:start position:0% +in the brain and so the direct contrast +doesn't work well the math can pull them + + align:start position:0% +doesn't work well the math can pull them + + + align:start position:0% +doesn't work well the math can pull them +apart but wouldn't it be nice to see + + align:start position:0% +apart but wouldn't it be nice to see + + + align:start position:0% +apart but wouldn't it be nice to see +them separately and so we've been doing + + align:start position:0% +them separately and so we've been doing + + + align:start position:0% +them separately and so we've been doing +intracranial recordings from patients + + align:start position:0% +intracranial recordings from patients + + + align:start position:0% +intracranial recordings from patients +with electrodes in their brain and i'll + + align:start position:0% +with electrodes in their brain and i'll + + + align:start position:0% +with electrodes in their brain and i'll +just show you a few + + align:start position:0% +just show you a few + + + align:start position:0% +just show you a few +very cool responses okay so this is a + + align:start position:0% +very cool responses okay so this is a + + + align:start position:0% +very cool responses okay so this is a +single electrode in a single patient + + align:start position:0% +single electrode in a single patient + + + align:start position:0% +single electrode in a single patient +these are the 165 sounds same ones this + + align:start position:0% +these are the 165 sounds same ones this + + + align:start position:0% +these are the 165 sounds same ones this +is the time course and this is a speech + + align:start position:0% +is the time course and this is a speech + + + align:start position:0% +is the time course and this is a speech +selective electrode it responds to + + align:start position:0% +selective electrode it responds to + + + align:start position:0% +selective electrode it responds to +native and foreign music those are the + + align:start position:0% +native and foreign music those are the + + + align:start position:0% +native and foreign music those are the +two green ones + + align:start position:0% +two green ones + + + align:start position:0% +two green ones +uh sorry native and foreign speech and + + align:start position:0% +uh sorry native and foreign speech and + + + align:start position:0% +uh sorry native and foreign speech and +it responds to music with vocals in pink + + align:start position:0% +it responds to music with vocals in pink + + + align:start position:0% +it responds to music with vocals in pink +everybody see how that's a speech + + align:start position:0% +everybody see how that's a speech + + + align:start position:0% +everybody see how that's a speech +selective electrode okay so there's + + align:start position:0% +selective electrode okay so there's + + + align:start position:0% +selective electrode okay so there's +loads of those but we also found these + + align:start position:0% +loads of those but we also found these + + + align:start position:0% +loads of those but we also found these +here is a single electrode look at these + + align:start position:0% +here is a single electrode look at these + + + align:start position:0% +here is a single electrode look at these +are um each + + align:start position:0% +are um each + + + align:start position:0% +are um each +row is a single stimulus here's a + + align:start position:0% +row is a single stimulus here's a + + + align:start position:0% +row is a single stimulus here's a +histogram of responses to all the music + + align:start position:0% +histogram of responses to all the music + + + align:start position:0% +histogram of responses to all the music +with vocals music without vocals + + align:start position:0% +with vocals music without vocals + + + align:start position:0% +with vocals music without vocals +much stronger than to anything else you + + align:start position:0% +much stronger than to anything else you + + + align:start position:0% +much stronger than to anything else you +might be saying well what about those + + align:start position:0% +might be saying well what about those + + + align:start position:0% +might be saying well what about those +things let's look at what those things + + align:start position:0% +things let's look at what those things + + + align:start position:0% +things let's look at what those things +are oh + + align:start position:0% +are oh + + + align:start position:0% +are oh +even the violations aren't really + + align:start position:0% +even the violations aren't really + + + align:start position:0% +even the violations aren't really +violations whistling humming computer + + align:start position:0% +violations whistling humming computer + + + align:start position:0% +violations whistling humming computer +jingle ringtone those are sort of musicy + + align:start position:0% +jingle ringtone those are sort of musicy + + + align:start position:0% +jingle ringtone those are sort of musicy +right + + align:start position:0% +right + + + align:start position:0% +right +so that is an extremely music selective + + align:start position:0% +so that is an extremely music selective + + + align:start position:0% +so that is an extremely music selective +individual electrode in a single + + align:start position:0% +individual electrode in a single + + + align:start position:0% +individual electrode in a single +subject's brain + + align:start position:0% +subject's brain + + + align:start position:0% +subject's brain +no fancy math that might have invented + + align:start position:0% +no fancy math that might have invented + + + align:start position:0% +no fancy math that might have invented +it somehow it's just there right in the + + align:start position:0% +it somehow it's just there right in the + + + align:start position:0% +it somehow it's just there right in the +raw data okay + + align:start position:0% +raw data okay + + + align:start position:0% +raw data okay +further and here's the time course you + + align:start position:0% +further and here's the time course you + + + align:start position:0% +further and here's the time course you +can see the time course of music with + + align:start position:0% +can see the time course of music with + + + align:start position:0% +can see the time course of music with +instruments music with vocals everything + + align:start position:0% +instruments music with vocals everything + + + align:start position:0% +instruments music with vocals everything +else + + align:start position:0% +else + + + align:start position:0% +else +really selective + + align:start position:0% +really selective + + + align:start position:0% +really selective +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is the strongest evidence yet + + align:start position:0% +so this is the strongest evidence yet + + + align:start position:0% +so this is the strongest evidence yet +for music specificity in the human brain + + align:start position:0% +for music specificity in the human brain + + + align:start position:0% +for music specificity in the human brain +but there's one more cool thing that + + align:start position:0% +but there's one more cool thing that + + + align:start position:0% +but there's one more cool thing that +came out of this + + align:start position:0% +came out of this + + + align:start position:0% +came out of this +analysis + + align:start position:0% +analysis + + + align:start position:0% +analysis +and that is we found some electrodes + + align:start position:0% +and that is we found some electrodes + + + align:start position:0% +and that is we found some electrodes +that are not just selected for music but + + align:start position:0% +that are not just selected for music but + + + align:start position:0% +that are not just selected for music but +selective for vocal music selective for + + align:start position:0% +selective for vocal music selective for + + + align:start position:0% +selective for vocal music selective for +song + + align:start position:0% +song + + + align:start position:0% +song +and that's really amazing because as i + + align:start position:0% +and that's really amazing because as i + + + align:start position:0% +and that's really amazing because as i +started off at the beginning many people + + align:start position:0% +started off at the beginning many people + + + align:start position:0% +started off at the beginning many people +have said that song is a kind of native + + align:start position:0% +have said that song is a kind of native + + + align:start position:0% +have said that song is a kind of native +form of music the first one to evolve + + align:start position:0% +form of music the first one to evolve + + + align:start position:0% +form of music the first one to evolve +and all that kind of stuff + + align:start position:0% +and all that kind of stuff + + + align:start position:0% +and all that kind of stuff +and so we did all the controls it's not + + align:start position:0% +and so we did all the controls it's not + + + align:start position:0% +and so we did all the controls it's not +the low-level stuff + + align:start position:0% +the low-level stuff + + + align:start position:0% +the low-level stuff +and + + align:start position:0% +and + + + align:start position:0% +and +there's lots of open questions + + align:start position:0% +there's lots of open questions + + + align:start position:0% +there's lots of open questions +we started with this puzzle + + align:start position:0% +we started with this puzzle + + + align:start position:0% +we started with this puzzle +of of how did uh how did music evolve if + + align:start position:0% +of of how did uh how did music evolve if + + + align:start position:0% +of of how did uh how did music evolve if +indeed it did evolve and we made a + + align:start position:0% +indeed it did evolve and we made a + + + align:start position:0% +indeed it did evolve and we made a +little bit of progress + + align:start position:0% +little bit of progress + + + align:start position:0% +little bit of progress +it's not it doesn't share + + align:start position:0% +it's not it doesn't share + + + align:start position:0% +it's not it doesn't share +machinery with speech and language + + align:start position:0% + + + + align:start position:0% + +if it's auditory cheesecake as pinker + + align:start position:0% +if it's auditory cheesecake as pinker + + + align:start position:0% +if it's auditory cheesecake as pinker +said + + align:start position:0% +said + + + align:start position:0% +said +it's auditory cheesecake that not only + + align:start position:0% +it's auditory cheesecake that not only + + + align:start position:0% +it's auditory cheesecake that not only +uses machinery that evolve for something + + align:start position:0% +uses machinery that evolve for something + + + align:start position:0% +uses machinery that evolve for something +else but changes it throughout + + align:start position:0% +else but changes it throughout + + + align:start position:0% +else but changes it throughout +development and makes it very selective + + align:start position:0% +development and makes it very selective + + + align:start position:0% +development and makes it very selective +okay + + align:start position:0% +okay + + + align:start position:0% +okay +these guys speculated that song is + + align:start position:0% +these guys speculated that song is + + + align:start position:0% +these guys speculated that song is +special maybe it is + + align:start position:0% +special maybe it is + + + align:start position:0% +special maybe it is +and sexual selection who knows we have + + align:start position:0% +and sexual selection who knows we have + + + align:start position:0% +and sexual selection who knows we have +no data + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/YcuKaphreT0.txt b/YcuKaphreT0.txt new file mode 100644 index 0000000000000000000000000000000000000000..fb424aaca2499197a4c1091c7d0d954ad80042cb --- /dev/null +++ b/YcuKaphreT0.txt @@ -0,0 +1,235 @@ +align:start position:0% + +so at the beginning of each semester I + + align:start position:0% +so at the beginning of each semester I + + + align:start position:0% +so at the beginning of each semester I +asked the students what have you heard + + align:start position:0% +asked the students what have you heard + + + align:start position:0% +asked the students what have you heard +about Junior lab and what I find is that + + align:start position:0% +about Junior lab and what I find is that + + + align:start position:0% +about Junior lab and what I find is that +some of them have been worried about + + align:start position:0% +some of them have been worried about + + + align:start position:0% +some of them have been worried about +having to take the class since they + + align:start position:0% +having to take the class since they + + + align:start position:0% +having to take the class since they +joined MIT as freshmen even before they + + align:start position:0% +joined MIT as freshmen even before they + + + align:start position:0% +joined MIT as freshmen even before they +declared their majors and + + align:start position:0% +declared their majors and + + + align:start position:0% +declared their majors and +characterization that I've heard + + align:start position:0% +characterization that I've heard + + + align:start position:0% +characterization that I've heard +multiple times as a junior lab as a + + align:start position:0% +multiple times as a junior lab as a + + + align:start position:0% +multiple times as a junior lab as a +black hole that swallows up all + + align:start position:0% +black hole that swallows up all + + + align:start position:0% +black hole that swallows up all +available time and this reputation was + + align:start position:0% +available time and this reputation was + + + align:start position:0% +available time and this reputation was +not I would say completely undeserved it + + align:start position:0% +not I would say completely undeserved it + + + align:start position:0% +not I would say completely undeserved it +is a very challenging class and it is a + + align:start position:0% +is a very challenging class and it is a + + + align:start position:0% +is a very challenging class and it is a +very time intensive and you really have + + align:start position:0% +very time intensive and you really have + + + align:start position:0% +very time intensive and you really have +to be very judicious in how you invest + + align:start position:0% +to be very judicious in how you invest + + + align:start position:0% +to be very judicious in how you invest +your effort on the other hand many of + + align:start position:0% +your effort on the other hand many of + + + align:start position:0% +your effort on the other hand many of +the elements that we have introduced in + + align:start position:0% +the elements that we have introduced in + + + align:start position:0% +the elements that we have introduced in +the last few years like the flipping the + + align:start position:0% +the last few years like the flipping the + + + align:start position:0% +the last few years like the flipping the +classroom like rearranging a lot of the + + align:start position:0% +classroom like rearranging a lot of the + + + align:start position:0% +classroom like rearranging a lot of the +curriculum really were meant to address + + align:start position:0% +curriculum really were meant to address + + + align:start position:0% +curriculum really were meant to address +this this worry and to really preserve + + align:start position:0% +this this worry and to really preserve + + + align:start position:0% +this this worry and to really preserve +and maybe even purify the essence of the + + align:start position:0% +and maybe even purify the essence of the + + + align:start position:0% +and maybe even purify the essence of the +class while removing some of the + + align:start position:0% +class while removing some of the + + + align:start position:0% +class while removing some of the +elements that really cost a lot of + + align:start position:0% +elements that really cost a lot of + + + align:start position:0% +elements that really cost a lot of +student stress and I think the best way + + align:start position:0% +student stress and I think the best way + + + align:start position:0% +student stress and I think the best way +to see what we've done is to really come + + align:start position:0% +to see what we've done is to really come + + + align:start position:0% +to see what we've done is to really come +and try for try for yourself and I think + + align:start position:0% +and try for try for yourself and I think + + + align:start position:0% +and try for try for yourself and I think +join many students who found that in the + + align:start position:0% +join many students who found that in the + + + align:start position:0% +join many students who found that in the +end time consuming but extremely + + align:start position:0% +end time consuming but extremely + + + align:start position:0% +end time consuming but extremely +rewarding experience \ No newline at end of file diff --git a/YfbXB_MSkSY.txt b/YfbXB_MSkSY.txt new file mode 100644 index 0000000000000000000000000000000000000000..f87087ced1d3dd6c0ffb369fb6d2871b4d8661fb --- /dev/null +++ b/YfbXB_MSkSY.txt @@ -0,0 +1,4106 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: We do +have a little bit + +of finishing to do because +we didn't quite finish + +the dynamics of homogeneous +expansion last time. + +So we'll begin by finishing that +after a brief review of where + +we were last time. + +And then we'll move on to +discuss non-euclidean spaces, + +which I hope will be still +the bulk of today's lecture. + +OK. + +In that case, let's get going. + +Again, as I said, +I want to begin + +by just reviewing +some of the things we + +talked about last time. + +And you should consider +this a good opportunity + +to ask questions if you discover +there are things that you're + +not really sure you understood +as well as you'd like. + +We were talking about the +evolution of a closed universe. + +And to summarize that +calculation we first + +re-shuffled the +first order Friedmann + +equation, the equation for a +dot over a quantity squared, + +by bringing all the d t's to +one side and all the d a's + +on the other side after doing +a little bit of rescaling. + +And we got this equation. + +Which we then said +we can integrate. + +And the integral from +time will go from time 0 + +to some arbitrary final time +that we called t tilde sub f, + +where the "tilde" indicates +that we multiplied by c. + +And the sub f means it's the +final time of our calculation. + +And on the other side +we have to integrate + +with corresponding +limits of integration. + +Corresponding to t equals +0 is a equals zero. + +So the lower limit +of integration is 0. + +And the final limit +of integration + +is just the value of a tilde +at the final time, whatever + +that is. + +Then we discovered +that we could actually + +do the integral on the right +if we made a substitution. + +And in the lecture last time +we did it in two stages. + +But the combined +substitution is just + +to replace a tilde +by cosine theta, + +according to this formula, if +we combine the two substitutions + +that we made last time. + +And if we do that we could +integrate the right hand side. + +And the integral +then gives us t tilde + +f is equal to the +integral of that, + +which is just this expression. + +And the expression below that +is just the substitution itself. + +How to relate a tilde to theta, +according to substitution + +which gave us that formula. + +So these two formulas +together allow + +us to determine t tilde +sub f, and a tilde + +sub f in terms of +theta and alpha. + +And once we had that we +realized we no longer needed + +to keep those sub f's +because that was really + +just a way of keeping +track of our notation + +during the calculation. + +It holds for any theta sub f. + +So it holds for any theta. + +So then we just rewrote those +same formulas without the sub + +f's. + +And here we wrote it +removing the tildes, + +replacing them by +their definitions. + +And this was the final answer. + +This describes the evolution +of a closed universe expressed + +in this parametric form. + +That is, we were not +able to explicitly write + +a as a function of t, which +is what would have liked + +to determine how the expansion +varied as a function of time. + +But instead we introduced +the auxiliary variable theta, + +often called the +development angle. + +And in terms of theta we +can express both t and a, + +and thereby indirectly have +an unambiguous relationship + +between a and t. + +Any questions about that? + +OK. + +Then we noticed that +those were, in fact, + +the equations of a cycloid. + +And I won't go through +the argument again, + +but the key point is +that the evolution + +of our closed universe scale +factor, as a function of time, + +is described by +what would happen + +if you had a disk rolling +on the horizontal axis + +with a point marked on the +disk which was initially + +straight down, and then as +the disk rolls that point + +traces out a cycloid. + +And that is exactly the +evolution of a closed universe. + +It starts at size zero, +goes to a maximum size, + +and then contracts again in +a completely symmetric way. + +The contraction phase +is the mirror image + +of the expansion phase. + +And then we went on to calculate +the age of a closed universe. + +And that was really more +of an exercise in algebra + +than anything else. + +The age is really given by +this formula to start with. + +This expresses the age, t, +in terms of alpha and theta. + +And the only problem with +that is that nobody really + +knows what alpha and theta mean. + +It's much more useful to have an +expression for the age in terms + +of things that astronomers +directly measure. + +And one needs two things +to replace alpha and theta. + +And the kinds of things +astronomers directly measure + +are things like the +Hubble parameter + +and the mass density, where they +often express the mass density + +in terms of omega where omega +is the mass density divided + +by the critical density. + +And that's what I chose +to do in the formulas + +that we went on to derive. + +So our goal is simply to +take that formula for t + +and figure out how to express +the alpha and the theta that + +appear in it so that we +can get an expression + +in terms of h and omega. + +And to do that, we'll +go one step at a time. + +We started by just writing +down the Friedmann equation. + +And the Friedmann +equation has an a in it. + +And everything +else in it is rho, + +which can be expressed in terms +of omega without any trouble, + +and h itself. + +So everything else in +it consists of variables + +that we're accepting to be +part of our final answer. + +So we could solve the Friedmann +equations for a or a tilde + +and that will allow +us to eliminate + +any a tilde's from +our expressions. + +Next, alpha was +originally defined + +in terms of this formula which +only involves rho and a tilde. + +We now know what +to do with a tilde. + +We could substitute +that formula. + +And rho, we always +knew what to do with. + +We could express that +in terms of omega. + +So we can instantly +solve that equation + +and get an equation for alpha +in terms of the quantities + +that we want to appear +in our final answer. + +And there's still one +more thing we need. + +We need an expression for theta. + +And theta we can get by +looking at the other of those + +two parametric +equations, the one that's + +not the "t equals" equation, but +rather the "a equals" equation. + +And in this equation we know +everything except theta itself. + +So we could substitute for a +over root k from up here- that. + +And on the right +hand side we can + +place alpha by that +expression and then the 1 + +minus cosine theta stays. + +And now we could solve +this equation for theta. + +I might just mention that, +in lecture last time I + +actually mis-copied +this equation. + +I forgot the factor of +omega in the numerator. + +So if any of you +were taking notes + +you can go back and +correct your notes. + +But it's correct in +the printed notes. + +And now it's +correct on a screen. + +So this you could either +solve for cosine theta-- + +initially what I did was +to solve for cosine theta. + +But then it turned +out to be more + +useful to know +what sine theta is, + +because sine theta appears +in that parametric expression + +for the age. + +So if you know cosine +theta you can, of course, + +get sine theta because +sine theta is just + +the square root of 1 minus +cosine squared theta. + +And that's what we did. + +And that's how we got +a square root here. + +And since square roots +can have either sign, + +there's a plus or +minus there which + +depends on where you are in +the evolution of our universe. + +The right hand side +here is always positive + +because we define that +square root symbol + +to mean the positive +square root, + +where the plus or minus, in +the end, tells you the sine. + +And sine theta itself-- +we know what theta does. + +It goes from 0 to 2 pi. + +So sine theta +starts out positive + +and after theta crosses +pi, sine theta is + +negative for the second +half of the evolution. + +Meaning, sine theta is negative +for the contracting phase + +and positive for +the expanding phase. + +We then put all that together +into the formula for CT, + +which is alpha theta +minus sine theta. + +The alpha becomes this factor. + +And the theta minus sine +theta becomes the arc sine + +of this expression, minus +or plus that expression, + +where this is just sine +theta from that formula. + +And it's minus sine theta, which +is why the plus minus becomes + +minus or plus. + +The signs get a little tricky, +but it's, in principle, + +straightforward. + +It all just follows +from this formula. + +And if you know +the sine of theta + +you have all your +problems solved. + +So we put all that +together into a table. + +This is just a copy +of the same formula + +that we had on the +previous slide. + +Theta is what appears in +this right hand column. + +It's indicated as the sine +inverse of some expression. + +It refers to that +expression-- an abbreviation. + +So we know what theta does. + +Theta just goes from 0 +to 2 pi in quadrants. + +At least, it pays to divide +it up into quadrants. + +Sine theta is always +positive for the first half + +and negative for +the second half. + +And that means that we have the +plus sign, or the upper sign, + +for the first half of +the motion and the minus + +sign for the second +half of the motion. + +Omega we could just +calculate in terms of theta. + +No problem about filling +in the omega column. + +And we know that we're +expanding for the first half + +and contracting for +the second half, + +so that really +completes the table. + +And the important thing +when you're actually + +using this formula is +to decide what theta is. + +And once you have that, +the sine of that-- + +the inverse sine +of that-- well, no. + +Excuse me. + +Theta itself appears there, +and the sine of theta + +appears there. + +And theta itself you +have to figure out + +which is the relevant +value in terms + +of where you are +in the evolution. + +The point is that sine +theta itself goes-- + +does not uniquely +determine what theta is. + +OK. + +That, I think, +completes our discussion + +of the evolution of +closed universes. + +I think it completes everything +that we did last time. + +So are there any questions? + +OK. + +Good. + +To finish our discussion +of the evolution + +of matter-dominated +universes, we + +go on to discuss open universes. + +And open universes are +really the same algebra + +as closed universes. + +They just differ +by the sine of k. + +Because one doesn't like to +deal with negative numbers, + +I defined kappa to +be equal to minus k, + +so that for our +open universes kappa + +was positive while +k was negative. + +Then I used a different +substitution for a tilde. + +Instead of a tilde +being a divided + +by the square root of +k, which in this case + +would be the square root of a +negative number-- which, one + +doesn't like to deal +with imaginary numbers + +if one doesn't have any need to. + +So instead, for +the open universe + +I'm defining a tilde to +be a divided by the square + +root of kappa, so that +a tilde is again real. + +Then I'm going to skip +all the algebra here. + +There's a little bit more of +it shown in the printed lecture + +notes. + +But there are no +new concepts here. + +Everything is really +the same, conceptually, + +as it was for the +closed universe. + +One difference is +that this time, + +instead of getting +trigonometric functions, + +we find that we get +hypergeometric functions. + +Hyper-- yeah. + +Hyper trigonometric functions, +I think, is the right word. + +That is, sinhs and coshs +instead of sines and cosines. + +The formulas are very similar. + +These are the formulas we get +for the open universe case, + +compared to those formulas +for the closed universe case. + +We get a change in +the order of-- instead + +of theta minus sine theta, we +get sinh theta minus theta. + +But that's what you +have to get if it's + +going to turn out +to be positive. + +Sine theta is always +less than theta. + +So this is a positive quantity. + +Sinh theta is always +greater than theta, + +so this is a positive quantity. + +And same for the second lines. + +Cosh theta minus 1 +is always positive, + +and one minus cosine +theta is always positive. + +So you really know which +order to write them in just + +by knowing that you +want to write down + +something that's positive. + +So these formulas describe the +evolution of the open universe + +exactly the same way as those +formulas describe the evolution + +of a closed, +matter-dominated universe. + +So any questions? + +OK. + +Next step, just repeating what +we did for the closed universe, + +we can derive a formula for +the age of an open universe. + +And again, it's +really just a matter + +of substituting into +the formula we already + +have to be able to re-express it +in terms of useful quantities. + +Which, again, I choose to +be the Hubble expansion + +rate and omega. + +And here I've put together all +three formulas for the age. + +The flat universe, +the first one we + +did, where t is just h +inverse if we bring it + +to the other side, times 2/3. + +And the open universe on the +top, and the closed universe + +on the bottom. + +Now one of the, perhaps +surprising, things + +that one finds here is that +all three of these expressions + +look fairly different +from each other. + +And you might think +that that would + +give some kind of a jagged, +discontinuous curve. + +But you can go ahead and +plot it, which I did. + +And there's the plot. + +It's one nice, smooth curve. + +And we won't go into this +in detail, but many of you + +have had courses in complex +functions, functions + +of a complex variable. + +If you know about functions +of a complex variable + +you can tell that these are, +in fact, all the same function. + +That is, if omega is, +say, bigger than 1, + +this formula can be +evaluated straightforwardly. + +It involves only things +like square roots + +of positive numbers. + +But you could also try +evaluating this formula + +for omega bigger than 1. + +And then you have square roots +of negative numbers appearing. + +But square roots +of negative numbers + +are OK if you know +about complex numbers. + +They're just purely imaginary. + +And then you get trigonometric +functions, and even + +inverse trigonometric functions, +or inverse hyperbolic trig + +functions of +imaginary arguments. + +But all those are well-defined. + +And if you work through +what the definitions are, + +the top line really is +identical to the bottom line. + +Those really are +the same function. + +And that's why one expects +that, when you plot them + +they will join together +smoothly, as they clearly do. + +The point in the middle +here is the first age + +that we derived for +the flat universe + +where omega is equal to 1 +and h t is just equal to 2/3. + +That is, t is equal +to 2/3 h inverse + +for a flat universe, +which is the middle dot. + +And the closed universes +are on the right + +and open universes +are on the left. + +OK. + +Any questions about +these age calculations? + +Yes? + +AUDIENCE: I noticed that, +for the open solution, + +there's a case where you +get some imaginary numbers? + +PROFESSOR: If you +use these formulas + +you don't get any +imaginary numbers. + +But if you tried to use, +say, the bottom formula + +for a value of +omega less than 1 it + +would give you +imaginary numbers. + +And it would, in +fact, if you trace + +through what those +imaginary numbers do, + +it would give you the +formula on the top. + +So it's all consistent. + +It's most straightforward +to use the formula + +on the top for omega less +than 1 and the formula + +on the bottom for +omega greater than 1. + +And then one never +confronts imaginary numbers. + +AUDIENCE: OK. + +PROFESSOR: Any other questions? + +OK. + +Where are we going next? + +Finally, just actually +one last graph + +on the evolution of +matter-dominated universes, + +which is the final +form of a of t + +for a matter-dominated universe. + +If you re-scale things +by dividing a over root + +k by alpha, and c t over +alpha-- if you look back + +at our equations-- +let me go back + +to where the equations were. + +We're really just +graphing these equations. + +If I divide this +equation by alpha, + +I just get a pure +function of theta + +with dimensionless variables. + +And similarly here, if I +divide a over root k by alpha + +I just get 1 minus cosine +theta, which is a pure number. + +So that's what +I've chosen to do. + +And the dimensionality works the +same for the open case as well. + +So it allows you to +draw a plot which + +is just independent +of parameters. + +All the parameters are +absorbed into the way + +the axes are defined, +which are both + +defined as +dimensionless numbers. + +And in that case +the closed universe + +survives for a duration of 2 pi. + +The axis here, at least, has +the same duration as theta. + +It's not actually theta, because +t is not linear in theta. + +But this point +does change by 2 pi + +as theta goes from 0 to 2 pi. + +And one can see here, the +three possible curves. + +A closed universe which +starts and then falls back, + +a flat universe which +goes off to the right + +and has actually a constant +slope as you go out here, + +and an open universe which +behaves slightly differently. + +Actually, I think +I was wrong when + +I said the flat universe +has a constant slope. + +But the open and the flat case +are similar to each other. + +They both go off to infinity, +but in different ways. + +And all three of them merge +as you go backwards in time. + +That's not something that +might have been obvious + +before we wrote +down the equations. + +But in very early +times all universes + +look like they're +flat universes, + +if you go to early enough times. + +And that actually is +an important point + +which we'll talk +about later in terms + +of what's called the flatness +problem of cosmology. + +That basically is the +consequences of that fact. + +Yes? + +AUDIENCE: Why +didn't you just say + +all of them looks like +open universes [INAUDIBLE]? + +PROFESSOR: [LAUGHS] + +AUDIENCE: I mean, what's +special about flat universes? + +PROFESSOR: Well, +actually, there is + +something special about flat. + +Which is that, if we plotted +omega as the function of time + +all of them approach omega +equals 1 as time goes to 0. + +So there is a very +definite meaning + +of saying that they're +all approaching flat, + +rather than they're all +approaching open or closed. + +Good question, though. + +Because from this +graph you really + +can't tell anything +special about the flat. + +Any other questions? + +Yes? + +AUDIENCE: So does this mean +that the open and flat solutions + +will extend indefinitely? + +PROFESSOR: Yeah. + +The open and flat solutions +extend indefinitely in time. + +That's right, they do. + +And one can see that from +the formulas or the graph. + +Yes? + +AUDIENCE: So for plotting +omega as a function of time, + +I'm a little bit +confused as to how + +it changes as-- for example, +an open universe expands, + +or a closed universe-- +because it seemed + +like, from our calculations, +that when the universe was + +expanding, omega was increasing? + +Is that-- at least +for a closed universe? + +PROFESSOR: That is +true for a closed + +universe during the +expanding phase. + +For a closed universe +during the expanding phase, + +omega does increase. + +It starts out as 1 +and then it rises + +to infinity when the universe +reaches its maximum size + +and is about to turn +around and go back. + +Because it doesn't mean +the mass density increases. + +That's maybe what's +confusing you. + +The actual mass density always +decreases as it expands, + +but the critical density +decreases even faster. + +So the ratio, omega, actually +rises for a closed universe + +as it expands. + +For an open universe +it's the reverse. + +For an open universe +omega starts + +out being 1 at +early times, as it + +does for any +matter-dominated universe. + +And as the universe +expands, omega + +gets smaller and smaller +for an open universe. + +And it follows-- I don't +have them on slides here, + +but we do have in +the notes formulas + +that we derived, that we did +on the blackboard, that give us + +omega as a function of theta. + +And those formulas, you +can just look at them + +and see how omega behaves +as the universe evolves. + +Because as the universe +evolves, theta just increases. + +And those formulas +do trivially show + +what I said about +how omega evolves. + +Any other questions? + +Yes? + +AUDIENCE: Why a over alpha root +k, but for a flat universe k + +is 0? + +PROFESSOR: That's right. + +I didn't really say that, +but for the flat universe + +there's an arbitrary +normalization + +that one chooses in +drawing this graph. + +And it was really an +arbitrary choice for me + +to draw the flat case +to join on smoothly + +with the open and closed cases. + +I could have put any constant +in front of t to the 2/3. + +And you're right, then +they would not necessarily + +mesh unless I chose that +constant in the right way. + +Yes? + +AUDIENCE: Based on that, is +there a particular reason + +you decided to chose [INAUDIBLE] +a flat universe looks + +like this? + +Is there a particular +thing you're + +trying to show in +choosing [INAUDIBLE]? + +PROFESSOR: OK. + +The question is, is +there a particular reason + +why I chose the +normalization that I chose? + +If I did not choose +it, it would only + +differ by an overall factor. + +So it would still +look-- the flat line + +by itself would look +indistinguishable, really. + +It would just be +higher or lower. + +So the only question is how +it meshes with the others. + +And since the flat +case really is + +the borderline between +the other two cases, + +and since this constant +that appears in front of t + +to the 2/3 has no +physical meaning whatever, + +it seems the +sensible thing to do + +is to plot it so that +it looks like the limit + +of an open or closed universe. + +Because physically it is the +same as the limit of an open + +or a closed universe +coming from either side. + +Any other questions? + +Those are good questions. + +OK. + +In that case, we are +finished with the evolution + +of matter-dominated +universes, and ready to start + +talking about +non-euclidean spaces. + +So what we'll be doing next +is kind of a mini introduction + +to general relativity, which +how non-euclidean spaces + +enter physics. + +Now, needless to say, +general relativity + +is an entire course +separate from this course. + +And of course that even +has more prerequisites + +that this course +has, so we're not + +going to duplicate +what would be taught + +in the general relativity class. + +But it turns out +that the discussion + +of general relativity does, +in fact, divide pretty + +cleanly into two major issues. + +And we will be dealing with +one of those issues but not + +the other. + +In particular, what we +will be doing in this class + +is learning how the formulas +of general relativity + +is used to describe +curved spaces. + +And we will learn how particles +move in curved spaces. + +So we'll be able to +analyze trajectories + +in any curbed space +if somebody tells you + +what the curved space +itself looks like. + +What we will not be +doing is we won't even + +attempt to describe how general +relativity predicts that matter + +should cause space to curve. + +That would be left +entirely for the GR course + +that you may or may not take. + +But it will not +be discussed here. + +There's only one +point where we will + +need a result of that sort. + +We'll want to know how the +matter in our Friedman Roberson + +Walker universe +affects the curvature. + +And there I would just +give you the result. + +I'll try to make +it sound plausible. + +But I won't make +any pretense being + +able to drive that result. + +That is, we will not be able +to drive how much space curves + +as a consequence of the +matter that's in it. + +But we will write +down the answer + +so you at least know +what the answer is + +for a homogeneous +isotropic universe. + +So here's a picturesque +slide about curve space. + +Four years ago, I +think it was, a postdoc + +here named Mustafa Amin +gave this lecture for me + +because I was out of town. + +And he had much more colorful +transparencies than I ever do. + +So I'll be using some of +his transparencies here. + +And this is one of +his opening slides. + +So this is what we want to +talk about-- curved space + +as illustrated in +that nifty picture. + +So I want to begin with a kind +of an historical introduction. + +To be honest, I'm pretty +much following the logic + +of the first chapter of Steve +Weinberg's General Relativity + +book. + +Non-Euclidean geometry +of course starts + +by thinking about +Euclidean geometry and then + +how one might be +move away from it. + +And historically, there's +kind of a clear cut + +path, which was followed. + +Euclid based his geometry, as +described in Euclid's elements, + +in terms of five postulates. + +The first of which is that +a straight line segment + +can be drawn joining +any two points. + +Sounds clear enough. + +Second, any straight +line segment + +can be extended indefinitely +in a straight line. + +Also sounds obvious, which is +what Euclid was banking on. + +Third, given a +straight line segment, + +a circle can be drawn having +the segment as a radius and one + +endpoint as the center. + +That also-- you can imagine +yourself doing that-- + +seems straightforward enough. + +But then we come to +the fifth postulate, + +which still sounds +pretty obvious. + +But it's certainly much more +complicated than the others. + +The fifth postulate says that +if a straight line falling + +on two straight lines makes the +interior angle on the same side + +are less than two right angles, +the two straight lines-- + +if produced +indefinitely-- meet on + +that-- I think +this is mis-typed. + +Mustafa typed it. + +I guess he's typed +this one, too. + +This one shows the picture. + +Yeah, this should be +on that side in which + +the angles are less +than two right angles. + +So let me just explain it, +independent of the text. + +The question is, +what happens if you + +have one line-- the line that's +shown more or less vertical + +here-- and two lines +that cross it such + +that the interior angles-- +here shown as a and b-- + +are on one side less than pi. + +Less than two right angles is +the way you could describe it. + +Then, as you can see +from the picture, + +these lines will +meet on this side + +and will not meet on that side. + +And that's what +the postulate says + +that under those circumstances +where two lines cross a given + +line such that the +sum of the two angles + +adds up to less +than pi on one side + +that the lines will +be on that side + +and will not be +on the other side. + +Yes? + +AUDIENCE: What +was his motivation + +for making this the +fifth postulate? + +It seems kind of arbitrary. + +PROFESSOR: OK, the question is +what was Euclid's motivation + +for making this the +fifth postulate? + +Well, I have to admit I +haven't had many conversations + +with Euclid so I'm +not sure I know + +the answer to that question. + +But it was what was needed to +basically complete geometry + +as we know it. + +So much of what you've +learned in geometry + +would not be there if there +was not something equivalent + +to this postulate. + +But actually what I'm going +to be talking about next + +is there has been +discovered there + +are a number of substitutes +for this fifth postulate. + +Mathematicians studied +for a long time + +whether or not this +postulate could + +be derived from the others +since it seems so much more + +complicated than the others. + +And there was a strong +desire during thousands + +of years really-- at +least over 1,000 years-- + +among mathematicians to try +to prove the fifth postulate + +from the first four postulates. + +And nobody ever +succeeded in doing that. + +And we now are pretty clear that +it's not possible to do that. + +That the postulate +is independent + +of the other postulates. + +It was discovered along +the way that there + +are a number of equivalent +statements to fifth postulate. + +And you could equally well have +chosen any one of these four + +statements that are +illustrated in these pictures. + +And I'll give you +words one by one + +for what these alternative +versions of the fifth postulate + +would be. + +A, up here, illustrated there, +says that if a straight line + +intersects one of two parallels, +meaning two parallel lines-- + +so this is the one +line intersecting + +two parallel lines. + +If it intersects one of them +as the heavy part of the line + +shows, then the theorem says +that if you continue that line + +it will always +intersect the other. + +And certainly obvious from +the picture, that's the way + +it works. + +But that's equivalent +to the fifth postulate + +and not provable from the +other four postulates. + +A second statement-- +b is the one + +that's illustrated there-- +is the one that I remember + +learning when I was in +high school, I think, + +which says that if you have one +line and another line parallel + +to it-- or rather, I'm sorry +another point off the line + +that there's one and only +one line through that point + +parallel to the original line. + +So that is yet another statement +of this famous fifth postulate. + +Number c is less obvious. + +But it turns out +that once you go away + +from Euclidean geometry, +your space always + +has a built in scale. + +So things are not scalable. + +One example I might mention at +this point of occurred space + +is, say, the +surface of a sphere. + +And the service of a +sphere has some fixed size. + +So if you have a +figure of one size, + +and you wanted, on the +surface of this sphere, + +to make a figure 5 times bigger, +it might not fit on the sphere + +anymore. + +So you can't always +make a figure bigger + +on the surface of the sphere. + +In fact, you could +never make a figure + +bigger without +bending in some way + +on the surface of the sphere. + +So that gives rise to +this third statement + +of the fifth postulate, which +is that, given any figure, + +there exists a figure +similar to it of any size. + +And by similar it means +that for polygons they're + +similar if the corresponding +angles are equal to each other + +as they're supposed to +be on those two images. + +And the corresponding sides +are proportional to each other. + +So a similar figure +is just a blow up-- + +a rescaling-- of +the original figure. + +And you can only do it if +the fifth postulate holds. + +You can do it on a flat space +but not on a curved space. + +And I think that is a +less obvious version + +of the fifth postulate. + +And finally, the +fifth postulate is + +linked to the +behavior of triangles. + +We all learned in +Euclidean geometry + +that the sum of the three angles +of a triangle is 180 degrees. + +That is a crucial theorem +of Euclidean geometry that + +depends directly on the fifth +postulate and is, in fact, + +equivalent to the +fifth postulate. + +So you could assume it and +forget the fifth postulate + +and still prove everything. + +So the fact that-- +actually, I'm sorry. + +It is equivalent to +the fifth postulate. + +But you don't need +to assume that it's + +true for every triangle to +prove the fifth postulate. + +It turns out that sufficient +and mathematicians always + +look for the minimum +axiom to be able to prove + +what they want to prove. + +The minimum version of +the axiom for triangles + +is to simply assume that +there's just one triangle who's + +angles add up 180 degrees. + +And if there exist just one +triangle whose angles add up + +to 180 degrees, then +the fifth postulate + +has to hold-- turns out-- +which is not so obvious, again. + +So these are all +different, equivalent ways + +of staying in the +fifth postulate. + +But it's pretty clear +now that it's not + +possible to prove the fifth +postulate from the first four. + +Any questions about that? + +OK, so a little +bit of history now. + +The first person, apparently, +to seriously explore + +the possibility that the +fifth postulate might be wrong + +was a Jesuit priest named +Giovanni Geralamo Saccheri. + +I'm sure other +people can pronounce + +it much better than I can. + +And in 1733, which is +the same year he died, + +he published a study of +what geometry would be like + +if the fifth postulate +did not hold. + +And he titled it- this +is a lot title, which + +I don't know how to +pronounce really, + +but in English it's +apparently translated + +as Euclid Freed of Every Flaw, +treating the fifth postulate + +as kind of a flaw in Euclid's +axiomization of geometry. + +Saccheri was, in fact, convinced +that the fifth postulate + +was true. + +He didn't really want to +consider the possibility + +that it was false. + +But he was nonetheless +exploring the possibility + +that it was false +because he understood + +the concept of a proof +by contradiction. + +He was looking for +a contradiction + +to be able to prove that +mathematics would not + +be consistent if you assume +the fifth postulate was false. + +And therefore, the +fifth postulate + +would be proven to be true. + +So he was exploring +what would happen + +if the fifth +postulate was false, + +looking all the time to +find some inconsistency, + +and was not able to find any. + +So he considered all +of this a failure. + +But he published it anyway. + +And that's the +publication front page. + +The next person to enter +the stage-- or actually + +three people +together, but I only + +have a nice +transparency on Gauss. + +Gauss, Bolyai, and +Lobachevsky went on + +to seriously explore the +possibility of geometry + +without the fifth +postulate, actually assuming + +that the fifth +postulate is false, + +developing what we call GBL, +Gauss-Bolyai-Lobachevsky + +geometry. + +Gauss was a German +mathematician. + +These were the years he lived. + +He, in fact, was born the +son of a poor, working class + +parents, which I found +a little surprising. + +We kind of think of scholars +in those early years + +as being gentleman who +were part of the nobility. + +But Gauss was not +but, nonetheless, + +went on to be one of the +most important mathematicians + +of his age. + +One of the other things +that surprised me + +and to be honest I just learned +all this from Wikipedia. + +I'm no real expert +on the history. + +But they gave a list +of Gauss' students. + +And they included that Richard +Dedekind, Bernhard Riemann, + +Peter Gustav Lejeune Dirichlet, +which is the name I remember, + +Kirchhoff, and Mobius. + +So quite a list of +famous mathematicians. + +So I have to admit, when +I read that, I was just + +about to send off an email +to all of my former students + +saying, look, what's +happening here? + +You're not competing +at all. [LAUGHING] + +But I decided not to do that. + +It would be impolite. + +And who knows? + +Maybe 100 years +from now my students + +will be as famous as these guys. + +You never know. + +We can plan, I hope. + +OK, so the other guys involved +in this and they were all + +working independently were +Bolyai who was, I think, + +a Prussian military man, +actually, and Lobachevsky + +who was also a professional +mathematician working + +in the university. + +The three of them independently +developed a geometry + +in which the fifth postulate +was assumed to be false. + +There are two ways +it could be false. + +In version with the triangles, +for example, a triangle + +could have more than or +less than 180 degrees. + +Since there were assuming that +the fifth postulate was false, + +it meant they had to be assuming +that every version that we just + +talked about of +the fifth postulate + +is false because they are +all equivalent to each other + +and these people realize that. + +So in particular in the +Gauss-Bolyai-Lobachevsky + +geometry, there are +infinitely many lines parallel + +to a given line. + +And no figures of +different size are similar. + +And the sum of the +angles of a triangle + +are always less than +180 degrees or pi, + +depending on whether you're +a radian person or a degree + +person. + +Now I should mention here +that the surface of the sphere + +is, in fact, a +perfectly good example + +of the non-Euclidean geometry. + +But for some reason it +was not taken seriously + +by mathematicians until +long after these guys + +were doing their work. + +And part of the reason, I guess, +is that the surfaces three + +evaluates not just +one of Euclid's axioms + +but two if we go back +to Euclid's axioms. + +The second of Euclid's axioms +said that any straight line + +segment can be +extended indefinitely + +in a straight line. + +And the surface of the +sphere and the analog + +of the straight line +is a great circle. + +And if you extend +the great circle, + +it comes back on itself. + +So the surface of the sphere +violates the fifth postulate. + +But it also violates +the second postulate. + +But still perfectly +consistent geometry, + +and it is a +non-Euclidean geometry. + +And on the surface +of this sphere, + +these statements +all kind of reverse. + +Instead of having infinitely +many lines parallel to a given + +line, you have no lines that +are parallel to a given line. + +Remember, lines are great +circles and lines are parallel + +if they never meet. + +But any two great circles meet. + +So there are no lines +parallel to a given line + +in the geometry of the +surface of the sphere. + +It's, again, true that no +figures of different size + +are similar. + +That has to be true +for any any geometry + +where the fifth +postulate was false. + +The last one, +again, has a choice. + +And it's the opposite +choice for a sphere + +as for the +Gauss-Bolyai-Lobachevsky + +geometry. + +In the Gauss-Bolyai-Lobachevsky +Bolyai- geometry, + +the sum of the angles is +always less than 180 degrees. + +If you picture a +triangle and a sphere, + +you can imagine that the +edges look like they bulge. + +And the sum of the +angles on the surface + +of the sphere of a +triangle are always + +greater than 180 degrees. + +The easiest way to +convince yourself + +that that's true in at +least one important case + +is to imagine a triangle. + +Here's a sphere. + +Everybody see the sphere? + +There's the North Pole. + +There's an equator. + +Imagine a triangle +where one vertex + +is at the North Pole and the +liver disease or on the equator + +and the triangle +looks like this. + +And these are both 90 +degree angles down here. + +So you already have 180 degrees. + +And any angle you +have on top just + +adds to the 180 +degrees putting you + +above the Euclidean +value of 180 degrees. + +So for a sphere it's +always the opposite + +of this greater +than 180 degrees. + +OK, continuing with Gauss, +Bolyai and Lobachevsky, + +their work was based on +exploring the axioms of Euclid, + +assuming the reverse +of the fifth postulate + +in any one of its forms. + +And they proved +theorems and wrote, + +sort of, their own versions +of Euclid's elements. + +But that still left +open the question + +whether or not all of this +was really consistent. + +That is, from the +thinking of Saccheri + +that we already talked about, +there's always the chance + +that you might find the +contradiction even if you + +haven't found a +contradiction yet. + +And Gauss, Bolyai +and Lobachevsky + +didn't really have any +way of answering that. + +They didn't really +have any way of knowing + +whether if they +continued further + +they might find +some contradiction. + +So what they did certainly +extracted the properties + +of this non-Euclidean geometry. + +But it did not really prove +that the non-Euclidean geometry + +was consistent. + +That happened slightly +later in an argument + +by Felix Klein, who was the +same Klein as the Klein bottle, + +by the way. + +And that was his +famous paper on this + +was published in 1870 somewhat +later than the early work + +that we're talking about. + +And what he did is he gave an +actual construction of the GBL + +geometry. + +And by construction +I mean in terms + +of coordinates using coordinate +geometry ideas, which + +were originally +developed by Descartes. + +That's why we call them +Cartesian coordinate systems. + +So what he gave as a description +of the Gauss-Bolyai-Lobachevsky + +geometry was a space +that consisted of a disk + +with coordinates x and y just +as Descartes would have done. + +He restricts himself to +the inside of the disk. + +So he restricts +himself to x squared + +plus y squared less than 1. + +And what he gave was a +function of two points + +in this disk where the +function represents + +the distance between +those two points. + +He decided that +distances don't have + +to be Euclidean +distances if we're + +trying to explore +non-Euclidean geometry. + +So he invented his +own distance function. + +And it's pretty +complicated looking. + +The function he came up with was +that the cosh of the distance + +between points 1 and 2 divided +by sum number a-- and a + +could be any number-- is +equal to 1 minus x1 times x2-- + +these are the two +x-coordinates for points 1 + +and 2-- minus y1 y2 over +the square root of 1 minus + +x1 squared minus y1 squared. + +Sorry, it's the product of two +square roots in the denominator + +here. + +And the second square +root is the same thing + +for the two coordinates 1 minus +x2 squared minus y2 squared. + +So this formula is certainly +not obvious to anybody. + +But Klein figured out +that this actually + +does-- the geometry +described by these formulas-- + +reproduce completely +the postulates + +of the Gauss-Bolyai-Lobachevsky +geometry, + +including the failure of +Euclid's fifth postulate. + +And since this boils +down to just algebra, + +if algebra is +consistent, it proves + +that the +Gauss-Bolyai-Lobachevsky + +geometry is consistent. + +Now, as I understand it, nobody +can prove that any of this + +actually is consistent. + +People prove +relative consistency. + +So in the assumption that +algebra is consistent, + +theorems about the real +numbers are consistent. + +Felix Klein was +able to prove that + +the Gauss-Bolyai-Lobachevsky +geometry is consistent. + +And this was really +the beginning + +of coordinate geometry. + +I'm sure all of you +are rather familiar + +with coordinate geometry. + +It's a standard topic +now in math courses + +and even in high school. + +And this is really +where it began. + +Euclid had no idea +that it was any value + +in trying to represent geometric +quantities as equations. + +Euclid did everything +in terms of theorems. + +But this opened up +a whole new door + +for how to discuss geometry. + +So the geometry is a slide that +just shows the same formula. + +And I guess this is supposed +to be an image of the disk. + +One thing I should +point out, which + +I forgot to point out, which is +that although this disk looks + +finite, it really is an infinite +space that's being described. + +And one can see that +by looking carefully + +at the distance functions. + +As either one of +these two points-- + +point 1 or point 2-- +approaches the boundary + +x square plus y square +equals 1, this square + +root denominator blows up. + +So the distance between a +point and another point that's + +approaching the boundary +goes to infinity + +as that point +approaches the boundary. + +So boundary's actually +infinitely far away + +even though in +coordinates they are still + +x squared plus y +squared equals 1. + +So this introduces +another important concept, + +which we'll be using in +general relativity, which + +is the coordinates don't +represent distances. + +Distances could +be very different + +from the way the +coordinates look. + +So that boundary, +even though it looks + +like it's right there +on the blackboard, + +is actually very far away +from the other points. + +OK, so after Klein, +the important new idea + +that Klein introduced +was, first of all, + +the explicit construction +but also the general idea + +that you can describe geometry +not by giving postulates + +but instead by actually +doing a construction where + +you've given names to the +points in terms of coordinates + +and you describe what +happens geometrically + +in terms of some distance +function which describes + +the distance between +two arbitrary points. + +And Gauss went on to make +two other very important + +observations about +geometry, which + +has become essential to +our current understanding + +of non-Euclidean geometry. + +So let me mention two other +ideas that Gauss introduced. + +The first one was +the distinction + +between what he called +inner and outer properties + +of a curved surface. + +His curved spaces were +all two dimensional, + +so they were surfaces. + +So this is most easily +described for say + +a surface of a sphere +where we can all + +visualize what +we're talking about. + +The surface of a sphere we +visualize in three Euclidean + +dimensions and we +think of its properties + +as being determined by that +three dimensional space. + +And the geometry of that +three dimensional space. + +And of course the +three dimensional space + +is Euclidean that we're +embedding our sphere into. + +But the non-Euclidean +aspects are all + +seen in the geometry of the +two dimensional surface. + +Figures drawn on the surface +as if the rest of the three + +dimensional space did not exist. + +And that is this key idea of +inner versus outer properties. + +The outer properties +of the sphere + +are properties that relate +to the three dimensional + +space in which the +sphere is embedded. + +But what Gauss realized +is that there's + +a perfectly well defined +mathematics contained entirely + +in the two dimensional space +of the surface of the sphere. + +You could discuss it +without making any reference + +to the three dimensional space +around it if you wanted to, + +it's just a little +more complicated to be + +able to do that. + +But we will in fact be doing +it explicitly very shortly. + +And all it amounts to +from our point of view + +is assigning coordinates to +the points on the surface + +of the sphere and the distance +function for those coordinates. + +And then one has +a full description + +of this two dimensional +space consisting + +of the surface of the sphere +which no longer needs make + +any reference to +the third dimension + +that you imagined the +sphere embedded in. + +So the study of the properties +of that two dimensional space + +is the study of the inner +properties of the space. + +And if you care about +how it's embedded, + +that's called the +outer properties. + +And Gauss made it clear in +the way he described things + +that from his point of view, the +real thing that mathematicians + +should be doing is studying +the inner properties. + +The outer properties are +not that interesting. + +So that's one key idea +that Gauss introduced. + +And the second is the idea +of what we now call a metric. + +And there are really +two pieces to this. + +The first of which +is that instead + +of giving macroscopic distances, +which is what Klein did, + +he told you how to write down +a formula for the distance + +between any two +points, Gauss realized + +that things could +become more interesting + +if instead of trying to +immediately write down + +a function for the distance +between two arbitrary points, + +you can find your attention +to very nearby points. + +And consider the +distance between two + +far away points +as just the length + +of a line that joins them +where every little segment + +in the line is a short distance +which is governed by the rules + +that you've made up +for short distances. + +So if you understand +short distances, + +long distances are +obtained just by adding. + +That's the basic idea. + +So only short +distances are needed. + +And then there's +another important idea + +which is that the short +distances themselves + +for an interesting +class of spaces + +should not be some arbitrary +function of the coordinates + +of the two points but should in +fact be a quadratic function. + +And in two dimensions, +a quadratic function + +mean something like +this, where gxx is just + +any function of x and y, x +and y are the two coordinates + +of the space. + +gxy is also just any +function of x and u. + +gyy is any function and gxx +multiplies the x squared, + +xy multiplies the x times dy and +g sub yy multiplies dy squared. + +And there's no terms portion +for dx by itself or dy by itself + +or dz by itself. + +And there's no +terms proportional + +to the cubes of those +quantities, it's all quadratic. + +That's the assumption. + +Now what underlies +that assumption is not + +that all spaces have +to have this property. + +This does narrow one down to +a particular class of spaces. + +But one way of +characterizing that class + +is that what Gauss understood +is that that class, the class + +of spaces described +by a metric like this, + +are precisely the class of +spaces which are locally + +Euclidean, meaning that even +though the surface is curved, + +any tiny little patch of it +looks flat and can be covered + +by Euclidean coordinates, +redefining coordinates + +in that one little patch only +where the metric in the one + +little patch would just be +the Euclidean metric given + +by the Pythagorean theorem +of Euclidean geometry, + +dx prime squared +plus dy squared, + +which would be the distance +function for a flat space + +and ordinary +Cartesian coordinates. + +And it turns out +that saying that this + +is true in every +microscopic region + +is equivalent to saying that +the metric over the entire space + +can be written as +a quadratic form, + +meaning one that looks +exactly like that. + +And spaces that +have this property + +are now usually called +Riemannian spaces, + +even though it was Gauss +who first identified them. + +And all the spaces that +we deal with in physics, + +in particular the spaces we +deal with general relativity, + +will be Riemannian spaces. + +Or sometimes they're called +pseudo Riemannian spaces + +because time is treated a little +bit differently in physics. + +And the word +"Riemannian" was really + +built on spatial geometry. + +But the word +"pseudo" only changes + +the fact that this becomes the +Lorenz metric, if you know what + +that means, instead of +the Euclidean metric. + +But the same idea +holds, which is + +that the spaces that +we're interested in + +are spaces which locally +look exactly like flat space. + +And that implies that globally, +you can always write down + +a metric function which is +quadratic, as Gauss said + +So the metric should be +a quadratic function that + +specifies the distance only +between infinitesimally + +separated points, not +finitely separated points + +and should have the +form of ds squared + +is equal to some +function of x and y times + +dx squared plus a different +function of x and y times dx + +times dy plus a different +function of x and y times dy + +squared. + +So I'm just writing the same +form that was on the side. + +This is a very +important formula. + +Incidentally, the +two that appears here + +is only because when we write +this in a different notation, + +this term will occur +twice, once as dx times dy, + +and once as dy times dx. + +And the two times it occurs +are equal to each other, + +so here they're just collected +together with a factor of two + +in front. + +Yes. + +STUDENT: Just to make sure, +those three different functions + +you wrote, those +subscripts aren't + +supposed to mean partial +derivatives, right? + +PROFESSOR: No, that's right. + +The subscripts and +this expression + +only mean that this +multiplies dx squared, + +so it has subscripts xx. + +And this multiplies dx times +dy, so it has subscripts xy. + +That's what the subscripts +mean and nothing more. + +So the subscripts +only mean that they're + +the things that appear +in that equation. + +Yes. + +STUDENT: It seems like +the metric is giving us + +distance in terms of an +infintesimal displacement, + +but then a locally Euclidean +space is already tangent + +infintesimally, so how are +we relating the local metric + +with the global metric? + +PROFESSOR: OK, the +question is how + +do we relate the local +metric which I say + +is Euclidean to +the global metric? + +And the answer I +think for now I will + +stick to just giving kind +of a pictorial answer based + +on the picture here. + +That is once you know the +distances between any two + +points in a tiny +little patch here, + +it's then always possible +to construct coordinates, + +here called x prime +and y prime, such + +that the distance between +any two points as calculated + +from the original metric, +which is the one here, + +is exactly the same +as the distance you + +get using this metric. + +And the claim is +that you can always + +define coordinates x prime and +y prime which make that true. + +That claim is not +absolutely obvious. + +But it's something you can +probably visualize if you just + +imagine that every little tiny +piece of this curved surface + +looks like it was just +a flat surface and then + +a flat surface you know +that you can write down + +a Cartesian coordinate system, +which will have the Euclidean + +metric. + +But it's only an +intuitive statement, + +proving it is actually harder. + +Yes. + +STUDENT: [INAUDIBLE] +bottom formula [INAUDIBLE] + +with positive curvature if we +analogize to second derivative. + +PROFESSOR: I'm sorry, +say that again. + +STUDENT: If we +analogize gxx, gyy, + +in the bottom formula there, +[INAUDIBLE] positive curvature + +[INAUDIBLE] second derivative-- + +PROFESSOR: Yeah OK. + +So you're asking does +this mean that we + +have two states of +positive curvature? + +STUDENT: Bottom right. + +PROFESSOR: Bottom +right, oh this. + +These are Mustafa's slides. + +I forgot to say that. + +You can tell from the style, +these are not my slides, + +these are Mustafa's slides. + +And I don't know what +he meant by this. + +You're right, this +does-- well you + +do want the metric +to be positive + +definite, which is not the +same as saying the curvature + +is positive. + +And I think this might +just be the condition + +that the metric is +positive definite, + +that this expression +will always be positive. + +Yeah. + +I'll bet that's what it +is, I don't know for sure. + +I'll bet that's what +that condition is about. + +And you do want that, +the metric had better + +be positive definite +for spatial geometries. + +In fact, in general relativity, +where it's a space time metric, + +it will not be +positive definite. + +For reasons that we'll +talk about later. + +But for geometry, the metric +should be positive definite. + +All distances +should be positive. + +OK. + +So that ends my slides. + +So now I'll continue +on the blackboard. + +OK next I wanted to say +a few general comments + +about general relativity. + +General relativity was of +course invented by the Einstein + +in 1916. + +It's a theory that he was +working on for about 10 years + +after he invented the theory +of special relativity. + +To understand what's +going on there, + +you want to recognize +that special relativity is + +a theory of mechanics +and electrodynamics + +which was designed to be +consistent with the principle + +that the speed of +light is always + +the same speed of light +independent of the speed + +of the source of light or +the speed of the observer + +of the light. + +And it's of course +not easy to do that, + +because you think that if you +move relative to something + +else that's moving, that you +would see its velocity change. + +So in order to make a theory +that where the speed of light + +was an absolute +invariant, Einstein + +had introduced a +number of things. + +And we talked about +those at the beginning + +of the course, the three +primary effects built + +in to special relativity. + +Time dilation, +length contraction, + +and new rules +about simultaneity, + +and how things that look +simultaneous to one observer + +will not look simultaneous +to other observers in a very + +definite, well defined way. + +So by inventing +these rules, Einstein + +was able to devise +a system which + +was consistent with the +idea that the speed of light + +always looked the +same to all observers. + +And at similar times, the +Michelson Morley experiment + +seemed to show that that +was in fact the case + +and ultimately there's a +tremendous amount of evidence + +verifying that what the +hypothesis that Einstein was + +pursuing is the right one +for the way nature behaves. + +The speed of light is invariant. + +But what was lacking in +Einstein's formulation + +of special relativity +was any version + +of a consistent +theory of gravity. + +Gravity had a well defined +description known since Newton. + +But Newton's description +was a description + +of a force at a distance. + +And that is intrinsically +inconsistent with a theory + +like special relativity, +which holds that simultaneity + +is itself relative. + +In Newtonian physics, +the force of gravity + +is equal to Newton's +constant times + +the product of the +two masses that + +are interacting with +each other divided + +by the square of the distance +and then times some union + +vector pointing along the line +that joins the two particles. + +But for that formula to +make any sense at all, + +you have to know where +the two particles are + +at the same instant of time. + +And this r is the distance +between the locations + +of the two particles at +some instant of time. + +And this r hat is +a unit vector that + +points along the line joining +those two particles where + +you've pinned down where +those particles are + +at one instant of time. + +But we know from +the very beginning + +that in special relativity the +notion of two things happening + +at distant points at one +instant of time is ambiguous. + +Different observers will +see different notions + +of what it means for +two events to happen + +at the same time +across this distance. + +And that means there's +no way to make sense out + +of Newton's Law of +gravity in the context + +of special relativity. + +You can't modify +it by just changing + +the way the force +depends on distance. + +You really have to +change the variables + +that it depends on +from the beginning. + +Yes. + +STUDENT: Is that equivalent to +saying the other particle can't + +know how much mass +of one is [INAUDIBLE] + +limit of the information +of the speed of light? + +PROFESSOR: Is that equivalent to +saying that one particle can't + +know what the mass +of the other particle + +is because of limitation. + +Yeah it's the distance, +it's not the mass. + +Because the mass is +preserved in time. + +So one particle +could've measured + +the mass of the other +particle at an earlier time + +and it would be +reasonable to infer, + +given the laws of +physics, that we + +know that would stay the same. + +But one particle +has no way of where + +the other particle +is at the same time. + +And not only does the particle +not have any way of knowing, + +but even an external +observer can't know. + +Because different +external observers + +will have different +definitions of what + +it means to be at the same time. + +So there really is no +way that this could work. + +Now I should mention +that it is still + +possible to have action +at a distance theories + +which are consistent +with special relativity. + +And in fact, Maxwell's equations +can be reformulated that way. + +The easiest way to +make things consistent + +with special relativity is +to describe interactions + +in terms of fields. + +And that is really what +Einstein did originally + +in special relativity. + +He was thinking +about light, he was + +thinking about +Maxwell's equations + +and he was thinking very +explicitly about Maxwell's + +equations. + +And in the Maxwell description +of electromagnetism, + +particles at a +distance don't directly + +interact with each other. + +But rather, each +particle interacts + +with the fields around it and +that is a local interaction. + +A particle interacts +directly only + +with the fields +at the same point. + +But then those fields +obey wave equations + +that can propagate information. + +And the fact that +you have an electron + +here can create a +field which then + +exerts a force on +an electron there. + +And the force on +the electron here + +depends only on the +electric fields here + +or the magnetic fields as well. + +The particle is moving, but +everything is completely local + +and the description +of electromagnetism as + +given in the form of +Maxwell's equations. + +And Maxwell's equations are +completely relativistically + +invariant. + +And that was part of +Einstein's-- it was really + +the key part of Einstein's +motivation in constructing + +the theory of special relativity +in the first place to make + +Maxwell's equations invariant. + +That they held in every frame. + +It is still possible +though and worth + +recognizing that it's possible +to reformulate electromagnetism + +as an action at a +distance theory. + +And it is in fact +described that way + +in volume one of +the Feynman lectures + +for those of you who've looked +at the Feynman lectures. + +In order to make +that work, you have + +to complicate things in +a pretty significant way. + +So I'm going to draw here +just a space time diagram. + +X and CT, CT going up that +way, x going that way. + +So in this diagram +the speed of light + +would be a 45 degree line. + +And let's suppose we have +two particles traveling + +in this space. + +A particle that I will +call a and a particle + +that I will call b. + +Being very original +with these names. + +If we wanted to know +the force on particle a + +at a certain time t indicated +by this dotted line, + +I guess I'll label t to make +it as clear as possible. + +Feynman gives us a formula +where we can determine it + +solely in terms of the +motion of particle B + +without talking +about fields at all. + +But the formula does not depend +on where b is at the same time. + +And it could not +if this is going + +to be a relativistic +description. + +But instead, the way this action +and the distance formulation + +works is when imagine drawing +a 45 degree line backwards, + +meaning a line that +light could travel on, + +and one sees where +that intersects + +the trajectory of particle +B. And that time is t prime. + +And the word that's used for +that symbol is retarded time. + +It's an earlier time. + +It's exactly that time which has +the property that if particle + +b emitted a light +beam at that time, + +it would be arriving at +particle a at just the time + +t that we're interested +in the time when we're + +trying to calculate the +force on particle a. + +And what Feynman gives you in +volume one if you look at it + +is a very complicated +formula that + +determines the +force on particle a + +in terms of not only the +position of this particle + +at time t prime but also +its velocity and even + +its acceleration. + +But if you do know the +position, the velocity, + +and the acceleration +of this particle, + +and of course the +velocity of particle a, + +you can determine +the force on a. + +Not obvious, but it's true. + +But that's certainly +not the easiest way + +to formulate electromagnetism. + +And that's not the way +most of us have learned, + +unless you've +learned by starting + +by reading volume +one of Feynman. + +But most of us learn +Maxwell's equations + +as differential equations. + +Where information is propagated +by the field from one + +point to another. + +In the case of +general relativity, + +one has the same problem. + +How can you describe +something which-- + +and the only approximate +you initially + +know is an action +and the distance, + +how can you describe +it in a way that's + +consistent with relativity? + +And the idea that simultaneity +is not a well defined concept. + +So that was the +problem was Einstein + +was wrestling with +for 10 years, how + +to build a theory +of gravity that + +would be consistent with +the basic principles + +of special relativity. + +And the result of those +10 years of cogitating + +is the theory that we +call general relativity. + +And it's essentially +a theory which + +describes gravity +as a field theory + +similar to Maxwell's +field theory + +where all interactions +are local. + +Nothing interacts at a +distance, but particles interact + +with fields at the +same point, the fields + +can propagate information +by obeying wave equations, + +and the fields then +at a distant point + +can exert forces +on other particles. + +But in the case of general +relativity, what Einstein + +concluded was that the +fields that were relevant, + +the fields that +described gravity, + +were in fact the metric +of space and time. + +So general relativity +is the field theory + +of the metric of space and time. + +And gravity is described +solely as a distortion + +of space and time. + +And that's what general +relativity is about + +and that's what we will +be learning more about. + +Now as I said earlier, now +I can say it perhaps more + +explicitly, what we +will be learning about + +is how to describe the +curvature of space time + +as general relativity +describes it. + +We will learn how that +curvature affects things + +like the motions of particles. + +But we will not in +this course learn + +how the presence of +particles and masses + +affects the curvature +of space time. + +That you'll have to take it in +a relativity course to learn. + +OK, I think that's where +we'll be stopping today. + +Just doesn't pay to start a new +topic with a minute and a half + +left. + +But let me just ask if +there are any questions. + +OK, well class +over, I will see you + +folks in a week, because +there's no class next Tuesday. \ No newline at end of file diff --git a/ZCap6yLxNYA.txt b/ZCap6yLxNYA.txt new file mode 100644 index 0000000000000000000000000000000000000000..932beca94bfff6e965f49f94b5de367e24d19838 --- /dev/null +++ b/ZCap6yLxNYA.txt @@ -0,0 +1,7019 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +today is + + align:start position:0% +today is + + + align:start position:0% +today is +the last lecture of + + align:start position:0% +the last lecture of + + + align:start position:0% +the last lecture of +technical content of the semester + + align:start position:0% +technical content of the semester + + + align:start position:0% +technical content of the semester +so that's kind of exciting and it's the + + align:start position:0% +so that's kind of exciting and it's the + + + align:start position:0% +so that's kind of exciting and it's the +last time we're going to use this little + + align:start position:0% +last time we're going to use this little + + + align:start position:0% +last time we're going to use this little +piece of graph paper + + align:start position:0% +piece of graph paper + + + align:start position:0% +piece of graph paper +which is not particularly exciting but + + align:start position:0% +which is not particularly exciting but + + + align:start position:0% +which is not particularly exciting but +anyway next week we're going to change + + align:start position:0% +anyway next week we're going to change + + + align:start position:0% +anyway next week we're going to change +gears a little bit and do our second + + align:start position:0% +gears a little bit and do our second + + + align:start position:0% +gears a little bit and do our second +social and personal hour on Monday and + + align:start position:0% +social and personal hour on Monday and + + + align:start position:0% +social and personal hour on Monday and +I'll send around reading for that + + align:start position:0% +I'll send around reading for that + + + align:start position:0% +I'll send around reading for that +shortly and on Wednesday we're going to + + align:start position:0% +shortly and on Wednesday we're going to + + + align:start position:0% +shortly and on Wednesday we're going to +do a Zoom game show + + align:start position:0% +do a Zoom game show + + + align:start position:0% +do a Zoom game show +so I hope we have a good attendance for + + align:start position:0% +so I hope we have a good attendance for + + + align:start position:0% +so I hope we have a good attendance for +that because we're going to try to make + + align:start position:0% +that because we're going to try to make + + + align:start position:0% +that because we're going to try to make +it as fun as we can over Zoom uh it + + align:start position:0% +it as fun as we can over Zoom uh it + + + align:start position:0% +it as fun as we can over Zoom uh it +won't be as much fun as in person but + + align:start position:0% +won't be as much fun as in person but + + + align:start position:0% +won't be as much fun as in person but +still anyway that's next week today + + align:start position:0% +still anyway that's next week today + + + align:start position:0% +still anyway that's next week today +we're going to work an example which + + align:start position:0% +we're going to work an example which + + + align:start position:0% +we're going to work an example which +pulls together some Concepts which we've + + align:start position:0% +pulls together some Concepts which we've + + + align:start position:0% +pulls together some Concepts which we've +been uh using the last couple lectures + + align:start position:0% + + + + align:start position:0% + +so this is what we're going to work on + + align:start position:0% +so this is what we're going to work on + + + align:start position:0% +so this is what we're going to work on +today + + align:start position:0% +today + + + align:start position:0% +today +reacting systems + + align:start position:0% + + + + align:start position:0% + +that have gases + + align:start position:0% +that have gases + + + align:start position:0% +that have gases +and + + align:start position:0% +and + + + align:start position:0% +and +condensed phases + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so you know we spent a couple lectures + + align:start position:0% +so you know we spent a couple lectures + + + align:start position:0% +so you know we spent a couple lectures +in the middle of the term on reacting + + align:start position:0% +in the middle of the term on reacting + + + align:start position:0% +in the middle of the term on reacting +systems with just gases and then in the + + align:start position:0% +systems with just gases and then in the + + + align:start position:0% +systems with just gases and then in the +last couple actually we've talked about + + align:start position:0% +last couple actually we've talked about + + + align:start position:0% +last couple actually we've talked about +oxidation + + align:start position:0% +oxidation + + + align:start position:0% +oxidation +which are reacting systems with oxygen + + align:start position:0% +which are reacting systems with oxygen + + + align:start position:0% +which are reacting systems with oxygen +gas and + + align:start position:0% +gas and + + + align:start position:0% +gas and +condensed phases so there's metals and + + align:start position:0% +condensed phases so there's metals and + + + align:start position:0% +condensed phases so there's metals and +oxides so we're going to just generalize + + align:start position:0% +oxides so we're going to just generalize + + + align:start position:0% +oxides so we're going to just generalize +that a little bit + + align:start position:0% +that a little bit + + + align:start position:0% +that a little bit +uh I shouldn't say generalized because + + align:start position:0% +uh I shouldn't say generalized because + + + align:start position:0% +uh I shouldn't say generalized because +we're going to work a specific example + + align:start position:0% +we're going to work a specific example + + + align:start position:0% +we're going to work a specific example +we're going to move away from oxides and + + align:start position:0% +we're going to move away from oxides and + + + align:start position:0% +we're going to move away from oxides and +do an example problem which I really + + align:start position:0% +do an example problem which I really + + + align:start position:0% +do an example problem which I really +think ties together a lot of Concepts + + align:start position:0% +think ties together a lot of Concepts + + + align:start position:0% +think ties together a lot of Concepts +and it's a silicon carbide problem and + + align:start position:0% +and it's a silicon carbide problem and + + + align:start position:0% +and it's a silicon carbide problem and +before I move in here this is not + + align:start position:0% +before I move in here this is not + + + align:start position:0% +before I move in here this is not +everything we're going to do today is + + align:start position:0% +everything we're going to do today is + + + align:start position:0% +everything we're going to do today is +not necessarily particularly the silicon + + align:start position:0% +not necessarily particularly the silicon + + + align:start position:0% +not necessarily particularly the silicon +carbide + + align:start position:0% +carbide + + + align:start position:0% +carbide +um + + align:start position:0% +um + + + align:start position:0% +um +it's particularly the silicon carbide in + + align:start position:0% +it's particularly the silicon carbide in + + + align:start position:0% +it's particularly the silicon carbide in +the details of course but the approach + + align:start position:0% +the details of course but the approach + + + align:start position:0% +the details of course but the approach +is general for a lot of materials + + align:start position:0% + + + + align:start position:0% + +so what I'm going to do is show you + + align:start position:0% +so what I'm going to do is show you + + + align:start position:0% +so what I'm going to do is show you +the phase diagram of silicon carbide and + + align:start position:0% +the phase diagram of silicon carbide and + + + align:start position:0% +the phase diagram of silicon carbide and +briefly talk about why anyone would care + + align:start position:0% +briefly talk about why anyone would care + + + align:start position:0% +briefly talk about why anyone would care +about silicon carbide and then we'll + + align:start position:0% +about silicon carbide and then we'll + + + align:start position:0% +about silicon carbide and then we'll +start working on the problem so let's + + align:start position:0% +start working on the problem so let's + + + align:start position:0% +start working on the problem so let's +see here we go + + align:start position:0% +see here we go + + + align:start position:0% +see here we go +the formation of silicon carbide + + align:start position:0% + + + + align:start position:0% + +okay before I label the solid phases uh + + align:start position:0% +okay before I label the solid phases uh + + + align:start position:0% +okay before I label the solid phases uh +how many somebody how many solid phases + + align:start position:0% +how many somebody how many solid phases + + + align:start position:0% +how many somebody how many solid phases +are there in this diagram + + align:start position:0% + + + + align:start position:0% + +you should be able to read a diagram + + align:start position:0% +you should be able to read a diagram + + + align:start position:0% +you should be able to read a diagram +like this by now + + align:start position:0% +like this by now + + + align:start position:0% +like this by now +three + + align:start position:0% +three + + + align:start position:0% +three +three solid phases silicon is a line + + align:start position:0% +three solid phases silicon is a line + + + align:start position:0% +three solid phases silicon is a line +compound here which is + + align:start position:0% +compound here which is + + + align:start position:0% +compound here which is +you know I've sort of giving you a hint + + align:start position:0% +you know I've sort of giving you a hint + + + align:start position:0% +you know I've sort of giving you a hint +silicon carbide + + align:start position:0% +silicon carbide + + + align:start position:0% +silicon carbide +so silicon silicon carbide and and + + align:start position:0% +so silicon silicon carbide and and + + + align:start position:0% +so silicon silicon carbide and and +carbon right so three solid phases thank + + align:start position:0% +carbon right so three solid phases thank + + + align:start position:0% +carbon right so three solid phases thank +you and one liquid phase + + align:start position:0% +you and one liquid phase + + + align:start position:0% +you and one liquid phase +and all right so here's a parrotectic + + align:start position:0% +and all right so here's a parrotectic + + + align:start position:0% +and all right so here's a parrotectic +reaction right this is a parrotective + + align:start position:0% +reaction right this is a parrotective + + + align:start position:0% +reaction right this is a parrotective +reaction is it t shaped it's a liquid + + align:start position:0% +reaction is it t shaped it's a liquid + + + align:start position:0% +reaction is it t shaped it's a liquid +silicon carbon containing melt and + + align:start position:0% +silicon carbon containing melt and + + + align:start position:0% +silicon carbon containing melt and +graphite + + align:start position:0% +graphite + + + align:start position:0% +graphite +reacting to form silicon carbide so + + align:start position:0% +reacting to form silicon carbide so + + + align:start position:0% +reacting to form silicon carbide so +silicon carbide forms out of a out of a + + align:start position:0% +silicon carbide forms out of a out of a + + + align:start position:0% +silicon carbide forms out of a out of a +parrotectic + + align:start position:0% +parrotectic + + + align:start position:0% +parrotectic +silicon of course melt at 1414c Carbon + + align:start position:0% +silicon of course melt at 1414c Carbon + + + align:start position:0% +silicon of course melt at 1414c Carbon +um doesn't melt actually it sublimes + + align:start position:0% +um doesn't melt actually it sublimes + + + align:start position:0% +um doesn't melt actually it sublimes +and uh it's way off the scales four + + align:start position:0% +and uh it's way off the scales four + + + align:start position:0% +and uh it's way off the scales four +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +degrees or something like that + + align:start position:0% +degrees or something like that + + + align:start position:0% +degrees or something like that +and silicon carbide decomposes it + + align:start position:0% +and silicon carbide decomposes it + + + align:start position:0% +and silicon carbide decomposes it +doesn't melt it decomposes it's very + + align:start position:0% +doesn't melt it decomposes it's very + + + align:start position:0% +doesn't melt it decomposes it's very +high temperature so + + align:start position:0% +high temperature so + + + align:start position:0% +high temperature so +you can see the silicon carbide here is + + align:start position:0% +you can see the silicon carbide here is + + + align:start position:0% +you can see the silicon carbide here is +a refractory + + align:start position:0% +a refractory + + + align:start position:0% +a refractory +material it's a refractory ceramic + + align:start position:0% +material it's a refractory ceramic + + + align:start position:0% +material it's a refractory ceramic +material + + align:start position:0% +material + + + align:start position:0% +material +um so it's a very hard it's corundum + + align:start position:0% +um so it's a very hard it's corundum + + + align:start position:0% +um so it's a very hard it's corundum +that's the mineral + + align:start position:0% +that's the mineral + + + align:start position:0% +that's the mineral +it's also known as Moissanite + + align:start position:0% +it's also known as Moissanite + + + align:start position:0% +it's also known as Moissanite +so it is a wide band Gap + + align:start position:0% +so it is a wide band Gap + + + align:start position:0% +so it is a wide band Gap +semiconductor and an abrasive and I + + align:start position:0% +semiconductor and an abrasive and I + + + align:start position:0% +semiconductor and an abrasive and I +learned a couple things about it I knew + + align:start position:0% +learned a couple things about it I knew + + + align:start position:0% +learned a couple things about it I knew +it's an abrasive a lot of times if you + + align:start position:0% +it's an abrasive a lot of times if you + + + align:start position:0% +it's an abrasive a lot of times if you +go and buy grinding wheels and such or + + align:start position:0% +go and buy grinding wheels and such or + + + align:start position:0% +go and buy grinding wheels and such or +high performance + + align:start position:0% +high performance + + + align:start position:0% +high performance +mechanical abrasives or Ultra hard + + align:start position:0% +mechanical abrasives or Ultra hard + + + align:start position:0% +mechanical abrasives or Ultra hard +components used for brake pads and + + align:start position:0% +components used for brake pads and + + + align:start position:0% +components used for brake pads and +things like that it'll be uh silicon + + align:start position:0% +things like that it'll be uh silicon + + + align:start position:0% +things like that it'll be uh silicon +carbide containing + + align:start position:0% +carbide containing + + + align:start position:0% +carbide containing +um that I knew Southern carbide is a + + align:start position:0% +um that I knew Southern carbide is a + + + align:start position:0% +um that I knew Southern carbide is a +wide band Gap semiconductor and it may + + align:start position:0% +wide band Gap semiconductor and it may + + + align:start position:0% +wide band Gap semiconductor and it may +be the future of Power Electronics + + align:start position:0% +be the future of Power Electronics + + + align:start position:0% +be the future of Power Electronics +so that it's important uh in my area of + + align:start position:0% +so that it's important uh in my area of + + + align:start position:0% +so that it's important uh in my area of +expertise for that reason + + align:start position:0% +expertise for that reason + + + align:start position:0% +expertise for that reason +I also learned today that it was uh the + + align:start position:0% +I also learned today that it was uh the + + + align:start position:0% +I also learned today that it was uh the +first ever LED + + align:start position:0% +first ever LED + + + align:start position:0% +first ever LED +was made with silicon carbide it's about + + align:start position:0% +was made with silicon carbide it's about + + + align:start position:0% +was made with silicon carbide it's about +a hundred and ten years ago and it was + + align:start position:0% +a hundred and ten years ago and it was + + + align:start position:0% +a hundred and ten years ago and it was +noticed uh that silicon carbide can be + + align:start position:0% +noticed uh that silicon carbide can be + + + align:start position:0% +noticed uh that silicon carbide can be +made into an LED + + align:start position:0% +made into an LED + + + align:start position:0% +made into an LED +of course it's not it's not the LED wide + + align:start position:0% +of course it's not it's not the LED wide + + + align:start position:0% +of course it's not it's not the LED wide +band gut material of choice does anyone + + align:start position:0% +band gut material of choice does anyone + + + align:start position:0% +band gut material of choice does anyone +know what why bandgap semiconductor uh + + align:start position:0% +know what why bandgap semiconductor uh + + + align:start position:0% +know what why bandgap semiconductor uh +is providing most of the light quite + + align:start position:0% +is providing most of the light quite + + + align:start position:0% +is providing most of the light quite +possibly in the room you're sitting + + align:start position:0% +possibly in the room you're sitting + + + align:start position:0% +possibly in the room you're sitting +right now + + align:start position:0% +right now + + + align:start position:0% +right now +nobody knows it's a Nobel Prize a couple + + align:start position:0% +nobody knows it's a Nobel Prize a couple + + + align:start position:0% +nobody knows it's a Nobel Prize a couple +years ago gallium nitrite so another + + align:start position:0% +years ago gallium nitrite so another + + + align:start position:0% +years ago gallium nitrite so another +wide band Gap Compound Semiconductor not + + align:start position:0% +wide band Gap Compound Semiconductor not + + + align:start position:0% +wide band Gap Compound Semiconductor not +a refractory material it falls apart + + align:start position:0% +a refractory material it falls apart + + + align:start position:0% +a refractory material it falls apart +more easily in silicon carbide but + + align:start position:0% +more easily in silicon carbide but + + + align:start position:0% +more easily in silicon carbide but +anyway there's lots of exciting reasons + + align:start position:0% +anyway there's lots of exciting reasons + + + align:start position:0% +anyway there's lots of exciting reasons +to know uh about you should know about + + align:start position:0% +to know uh about you should know about + + + align:start position:0% +to know uh about you should know about +silicon carbide and uh I think you + + align:start position:0% +silicon carbide and uh I think you + + + align:start position:0% +silicon carbide and uh I think you +should care about it too because it's + + align:start position:0% +should care about it too because it's + + + align:start position:0% +should care about it too because it's +important for a number of uh reasons and + + align:start position:0% +important for a number of uh reasons and + + + align:start position:0% +important for a number of uh reasons and +it's got an interesting history + + align:start position:0% + + + + align:start position:0% + +enough about that let's talk about a + + align:start position:0% +enough about that let's talk about a + + + align:start position:0% +enough about that let's talk about a +problem + + align:start position:0% + + + + align:start position:0% + +so I'm going to give you a problem it's + + align:start position:0% +so I'm going to give you a problem it's + + + align:start position:0% +so I'm going to give you a problem it's +just like a word problem you might find + + align:start position:0% +just like a word problem you might find + + + align:start position:0% +just like a word problem you might find +on a test or something like that place + + align:start position:0% +on a test or something like that place + + + align:start position:0% +on a test or something like that place +pieces + + align:start position:0% + + + + align:start position:0% + +of silicon carbide + + align:start position:0% +of silicon carbide + + + align:start position:0% +of silicon carbide +and + + align:start position:0% +and + + + align:start position:0% +and +carbon and for now I'll label that + + align:start position:0% +carbon and for now I'll label that + + + align:start position:0% +carbon and for now I'll label that +graphite but let me just keep in mind + + align:start position:0% +graphite but let me just keep in mind + + + align:start position:0% +graphite but let me just keep in mind +it's carbon + + align:start position:0% +it's carbon + + + align:start position:0% +it's carbon +right into a + + align:start position:0% + + + + align:start position:0% + +vacuum oven + + align:start position:0% +vacuum oven + + + align:start position:0% +vacuum oven +vacuum oven is an oven that can operate + + align:start position:0% +vacuum oven is an oven that can operate + + + align:start position:0% +vacuum oven is an oven that can operate +under vacuum they're all over campus + + align:start position:0% +under vacuum they're all over campus + + + align:start position:0% +under vacuum they're all over campus +if you don't know already and now I'm + + align:start position:0% +if you don't know already and now I'm + + + align:start position:0% +if you don't know already and now I'm +going to do it I'm going to put them in + + align:start position:0% +going to do it I'm going to put them in + + + align:start position:0% +going to do it I'm going to put them in +the oven and I'm going to pull vacuum + + align:start position:0% +the oven and I'm going to pull vacuum + + + align:start position:0% +the oven and I'm going to pull vacuum +that means Evacuate the oven + + align:start position:0% + + + + align:start position:0% + +and we're going to pull this vacuum to + + align:start position:0% +and we're going to pull this vacuum to + + + align:start position:0% +and we're going to pull this vacuum to +approximately zero pascals + + align:start position:0% +approximately zero pascals + + + align:start position:0% +approximately zero pascals +so you know there's no absolute vacuum + + align:start position:0% +so you know there's no absolute vacuum + + + align:start position:0% +so you know there's no absolute vacuum +but on this scale your your gauge is + + align:start position:0% +but on this scale your your gauge is + + + align:start position:0% +but on this scale your your gauge is +being zero + + align:start position:0% + + + + align:start position:0% + +we're going to seal it + + align:start position:0% +we're going to seal it + + + align:start position:0% +we're going to seal it +pull vacuum seal + + align:start position:0% +pull vacuum seal + + + align:start position:0% +pull vacuum seal +and then heat + + align:start position:0% + + + + align:start position:0% + +to 1700 C + + align:start position:0% +to 1700 C + + + align:start position:0% +to 1700 C +okay You observe + + align:start position:0% + + + + align:start position:0% + +You observe two things + + align:start position:0% + + + + align:start position:0% + +silicon carbide + + align:start position:0% +silicon carbide + + + align:start position:0% +silicon carbide +and carbon are both still present + + align:start position:0% + + + + align:start position:0% + +you also observe + + align:start position:0% +you also observe + + + align:start position:0% +you also observe +that the pressure + + align:start position:0% + + + + align:start position:0% + +is 4.0 + + align:start position:0% +is 4.0 + + + align:start position:0% +is 4.0 +pascals + + align:start position:0% +pascals + + + align:start position:0% +pascals +so let me draw this + + align:start position:0% + + + + align:start position:0% + +kind of a visualization here of the + + align:start position:0% +kind of a visualization here of the + + + align:start position:0% +kind of a visualization here of the +experiment and what You observe is a + + align:start position:0% +experiment and what You observe is a + + + align:start position:0% +experiment and what You observe is a +vacuum oven it's got a nice + + align:start position:0% +vacuum oven it's got a nice + + + align:start position:0% +vacuum oven it's got a nice +insulated walls nice vacuum seal + + align:start position:0% +insulated walls nice vacuum seal + + + align:start position:0% +insulated walls nice vacuum seal +a lot of money for vacuum furnace that + + align:start position:0% +a lot of money for vacuum furnace that + + + align:start position:0% +a lot of money for vacuum furnace that +can go to 1700 C but there's a number of + + align:start position:0% +can go to 1700 C but there's a number of + + + align:start position:0% +can go to 1700 C but there's a number of +them on campus + + align:start position:0% +them on campus + + + align:start position:0% +them on campus +and okay so here's silicon carbide it's + + align:start position:0% +and okay so here's silicon carbide it's + + + align:start position:0% +and okay so here's silicon carbide it's +a chunk of silicon carbide sitting there + + align:start position:0% +a chunk of silicon carbide sitting there + + + align:start position:0% +a chunk of silicon carbide sitting there +in the vacuum furnace + + align:start position:0% +in the vacuum furnace + + + align:start position:0% +in the vacuum furnace +and a chunk of graphite should be + + align:start position:0% + + + + align:start position:0% + +gray right why not graphite a chunk of + + align:start position:0% +gray right why not graphite a chunk of + + + align:start position:0% +gray right why not graphite a chunk of +graphite + + align:start position:0% +graphite + + + align:start position:0% +graphite +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and you've got some gauges on there + + align:start position:0% +and you've got some gauges on there + + + align:start position:0% +and you've got some gauges on there +often gauges and block diagrams are + + align:start position:0% +often gauges and block diagrams are + + + align:start position:0% +often gauges and block diagrams are +indicated like that so you've got a + + align:start position:0% +indicated like that so you've got a + + + align:start position:0% +indicated like that so you've got a +gauge uh saying that pressure equals 4.0 + + align:start position:0% +gauge uh saying that pressure equals 4.0 + + + align:start position:0% +gauge uh saying that pressure equals 4.0 +Pascal + + align:start position:0% +Pascal + + + align:start position:0% +Pascal +and you've got another gauge reading the + + align:start position:0% +and you've got another gauge reading the + + + align:start position:0% +and you've got another gauge reading the +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +equals 1700 degrees C + + align:start position:0% +equals 1700 degrees C + + + align:start position:0% +equals 1700 degrees C +all right + + align:start position:0% +all right + + + align:start position:0% +all right +this is the problem statement are there + + align:start position:0% +this is the problem statement are there + + + align:start position:0% +this is the problem statement are there +any questions about the problem + + align:start position:0% +any questions about the problem + + + align:start position:0% +any questions about the problem +statement + + align:start position:0% +statement + + + align:start position:0% +statement +I haven't asked a question yet this is a + + align:start position:0% +I haven't asked a question yet this is a + + + align:start position:0% +I haven't asked a question yet this is a +setup + + align:start position:0% +setup + + + align:start position:0% +setup +would somebody Express this observation + + align:start position:0% +would somebody Express this observation + + + align:start position:0% +would somebody Express this observation +in thermodynamics language for me + + align:start position:0% +in thermodynamics language for me + + + align:start position:0% +in thermodynamics language for me +what does this observation mean + + align:start position:0% + + + + align:start position:0% + +there are multiple phases + + align:start position:0% +there are multiple phases + + + align:start position:0% +there are multiple phases +right and the phases are + + align:start position:0% + + + + align:start position:0% + +silicon carbide and carbon oh wait I'm + + align:start position:0% +silicon carbide and carbon oh wait I'm + + + align:start position:0% +silicon carbide and carbon oh wait I'm +sorry that's not yes that's right the + + align:start position:0% +sorry that's not yes that's right the + + + align:start position:0% +sorry that's not yes that's right the +phases are in + + align:start position:0% + + + + align:start position:0% + +someone's just whispered equilibrium + + align:start position:0% +someone's just whispered equilibrium + + + align:start position:0% +someone's just whispered equilibrium +equilibrium right the phases are in + + align:start position:0% +equilibrium right the phases are in + + + align:start position:0% +equilibrium right the phases are in +equilibrium you you heat it up and You + + align:start position:0% +equilibrium you you heat it up and You + + + align:start position:0% +equilibrium you you heat it up and You +observe that they're present this is + + align:start position:0% +observe that they're present this is + + + align:start position:0% +observe that they're present this is +this is a class in equilibrium + + align:start position:0% +this is a class in equilibrium + + + align:start position:0% +this is a class in equilibrium +thermodynamics all right you can infer + + align:start position:0% +thermodynamics all right you can infer + + + align:start position:0% +thermodynamics all right you can infer +from Context that these things are both + + align:start position:0% +from Context that these things are both + + + align:start position:0% +from Context that these things are both +present so they are coexisting and + + align:start position:0% +present so they are coexisting and + + + align:start position:0% +present so they are coexisting and +equilibrium right multiple condensed + + align:start position:0% +equilibrium right multiple condensed + + + align:start position:0% +equilibrium right multiple condensed +phases coexisting and equilibrium what's + + align:start position:0% +phases coexisting and equilibrium what's + + + align:start position:0% +phases coexisting and equilibrium what's +the third phase that's present you can't + + align:start position:0% +the third phase that's present you can't + + + align:start position:0% +the third phase that's present you can't +see it + + align:start position:0% + + + + align:start position:0% + +this is important you need to be able to + + align:start position:0% +this is important you need to be able to + + + align:start position:0% +this is important you need to be able to +interpret these observations in + + align:start position:0% +interpret these observations in + + + align:start position:0% +interpret these observations in +thermodynamics language right and if + + align:start position:0% +thermodynamics language right and if + + + align:start position:0% +thermodynamics language right and if +you're going to solve thermodynamics + + align:start position:0% +you're going to solve thermodynamics + + + align:start position:0% +you're going to solve thermodynamics +problems so we've got two two condensed + + align:start position:0% +problems so we've got two two condensed + + + align:start position:0% +problems so we've got two two condensed +phases in equilibrium there's a third + + align:start position:0% +phases in equilibrium there's a third + + + align:start position:0% +phases in equilibrium there's a third +phase + + align:start position:0% +phase + + + align:start position:0% +phase +uh would somebody tell me what is the + + align:start position:0% +uh would somebody tell me what is the + + + align:start position:0% +uh would somebody tell me what is the +third phase + + align:start position:0% + + + + align:start position:0% + +gas spins yes right there's gas there's + + align:start position:0% +gas spins yes right there's gas there's + + + align:start position:0% +gas spins yes right there's gas there's +a gas phase there you can't see it with + + align:start position:0% +a gas phase there you can't see it with + + + align:start position:0% +a gas phase there you can't see it with +your eyes but it's there your pressure + + align:start position:0% +your eyes but it's there your pressure + + + align:start position:0% +your eyes but it's there your pressure +gauge tells you it's there right there's + + align:start position:0% +gauge tells you it's there right there's + + + align:start position:0% +gauge tells you it's there right there's +some pressure there's some gas pressure + + align:start position:0% +some pressure there's some gas pressure + + + align:start position:0% +some pressure there's some gas pressure +good thank you all right + + align:start position:0% + + + + align:start position:0% + +um here's a question + + align:start position:0% +um here's a question + + + align:start position:0% +um here's a question +question + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% + + + + align:start position:0% + +is the Gibbs + + align:start position:0% + + + + align:start position:0% + +free energy + + align:start position:0% + + + + align:start position:0% + +of formation + + align:start position:0% + + + + align:start position:0% + +of silicon carbide + + align:start position:0% +of silicon carbide + + + align:start position:0% +of silicon carbide +at 1700 degrees C + + align:start position:0% + + + + align:start position:0% + +that is silicon and it's solid phase + + align:start position:0% +that is silicon and it's solid phase + + + align:start position:0% +that is silicon and it's solid phase +plus carbon and its graphite phase + + align:start position:0% +plus carbon and its graphite phase + + + align:start position:0% +plus carbon and its graphite phase +going to silicon carbide + + align:start position:0% +going to silicon carbide + + + align:start position:0% +going to silicon carbide +and I'm asking for Delta formation + + align:start position:0% + + + + align:start position:0% + +and I'm going to give you some reference + + align:start position:0% +and I'm going to give you some reference + + + align:start position:0% +and I'm going to give you some reference +data you need a little bit more + + align:start position:0% +data you need a little bit more + + + align:start position:0% +data you need a little bit more +information to answer that question + + align:start position:0% +information to answer that question + + + align:start position:0% +information to answer that question +reference data + + align:start position:0% + + + + align:start position:0% + +you have you know or you measure + + align:start position:0% +you have you know or you measure + + + align:start position:0% +you have you know or you measure +that the saturation Vapor pressures + + align:start position:0% + + + + align:start position:0% + +at + + align:start position:0% +at + + + align:start position:0% +at +1700 degrees C are this is the data you + + align:start position:0% +1700 degrees C are this is the data you + + + align:start position:0% +1700 degrees C are this is the data you +have + + align:start position:0% +have + + + align:start position:0% +have +P silicon saturation + + align:start position:0% + + + + align:start position:0% + +1700 degrees C equals 4.4 + + align:start position:0% +1700 degrees C equals 4.4 + + + align:start position:0% +1700 degrees C equals 4.4 +pascals + + align:start position:0% +pascals + + + align:start position:0% +pascals +and P + + align:start position:0% +and P + + + align:start position:0% +and P +carbon saturation + + align:start position:0% +carbon saturation + + + align:start position:0% +carbon saturation +at 1700 degrees C what do you think it + + align:start position:0% +at 1700 degrees C what do you think it + + + align:start position:0% +at 1700 degrees C what do you think it +is is it larger than silicon or is it + + align:start position:0% +is is it larger than silicon or is it + + + align:start position:0% +is is it larger than silicon or is it +smaller than silicon the saturation + + align:start position:0% +smaller than silicon the saturation + + + align:start position:0% +smaller than silicon the saturation +vapor pressure of carbon uh + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +what are the saturation Vapor pressures + + align:start position:0% +what are the saturation Vapor pressures + + + align:start position:0% +what are the saturation Vapor pressures +of these refractor materials are they + + align:start position:0% +of these refractor materials are they + + + align:start position:0% +of these refractor materials are they +higher + + align:start position:0% +higher + + + align:start position:0% +higher +than that of silicon are they lower than + + align:start position:0% +than that of silicon are they lower than + + + align:start position:0% +than that of silicon are they lower than +that of silicon + + align:start position:0% + + + + align:start position:0% + +think about what you know about bonding + + align:start position:0% +think about what you know about bonding + + + align:start position:0% +think about what you know about bonding +think about what you know about + + align:start position:0% +think about what you know about + + + align:start position:0% +think about what you know about +refractory materials + + align:start position:0% +refractory materials + + + align:start position:0% +refractory materials +ask yourselves + + align:start position:0% +ask yourselves + + + align:start position:0% +ask yourselves +what's more volatile + + align:start position:0% + + + + align:start position:0% + +so with the saturation vapor pressure of + + align:start position:0% +so with the saturation vapor pressure of + + + align:start position:0% +so with the saturation vapor pressure of +carbon be zero then + + align:start position:0% + + + + align:start position:0% + +the saturation vapor pressure of nothing + + align:start position:0% +the saturation vapor pressure of nothing + + + align:start position:0% +the saturation vapor pressure of nothing +there's no component or compound for + + align:start position:0% +there's no component or compound for + + + align:start position:0% +there's no component or compound for +which the saturation vapor pressure is + + align:start position:0% +which the saturation vapor pressure is + + + align:start position:0% +which the saturation vapor pressure is +zero right think back to the urinary + + align:start position:0% +zero right think back to the urinary + + + align:start position:0% +zero right think back to the urinary +phase diagrams it's always final + + align:start position:0% +phase diagrams it's always final + + + align:start position:0% +phase diagrams it's always final +it's something right it exists but how + + align:start position:0% +it's something right it exists but how + + + align:start position:0% +it's something right it exists but how +does it compare to that of silicon + + align:start position:0% + + + + align:start position:0% + +it would be much smaller much smaller + + align:start position:0% +it would be much smaller much smaller + + + align:start position:0% +it would be much smaller much smaller +right exactly + + align:start position:0% +right exactly + + + align:start position:0% +right exactly +much much less than P sat + + align:start position:0% +much much less than P sat + + + align:start position:0% +much much less than P sat +of silicon that's right because these + + align:start position:0% +of silicon that's right because these + + + align:start position:0% +of silicon that's right because these +are and this is this should be something + + align:start position:0% +are and this is this should be something + + + align:start position:0% +are and this is this should be something +that you just sort of intuitively + + align:start position:0% +that you just sort of intuitively + + + align:start position:0% +that you just sort of intuitively +understand which is that + + align:start position:0% +understand which is that + + + align:start position:0% +understand which is that +more strongly bounded bound compounds + + align:start position:0% +more strongly bounded bound compounds + + + align:start position:0% +more strongly bounded bound compounds +refractory compounds + + align:start position:0% +refractory compounds + + + align:start position:0% +refractory compounds +are less volatile + + align:start position:0% +are less volatile + + + align:start position:0% +are less volatile +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +have lower Vapor pressures they also + + align:start position:0% +have lower Vapor pressures they also + + + align:start position:0% +have lower Vapor pressures they also +have lower melting points right + + align:start position:0% +have lower melting points right + + + align:start position:0% +have lower melting points right +you know that you know Carbon uh is um + + align:start position:0% +you know that you know Carbon uh is um + + + align:start position:0% +you know that you know Carbon uh is um +very strongly covalently bonded to + + align:start position:0% +very strongly covalently bonded to + + + align:start position:0% +very strongly covalently bonded to +itself + + align:start position:0% +itself + + + align:start position:0% +itself +silicon is strongly but less so + + align:start position:0% +silicon is strongly but less so + + + align:start position:0% +silicon is strongly but less so +covalently bonded through itself + + align:start position:0% +covalently bonded through itself + + + align:start position:0% +covalently bonded through itself +germanium is even more volatile it falls + + align:start position:0% +germanium is even more volatile it falls + + + align:start position:0% +germanium is even more volatile it falls +apart more easily and by the time you + + align:start position:0% +apart more easily and by the time you + + + align:start position:0% +apart more easily and by the time you +get to tin and lead you have really high + + align:start position:0% +get to tin and lead you have really high + + + align:start position:0% +get to tin and lead you have really high +vapor pressure low melting point + + align:start position:0% +vapor pressure low melting point + + + align:start position:0% +vapor pressure low melting point +materials so right there's some + + align:start position:0% +materials so right there's some + + + align:start position:0% +materials so right there's some +periodic table knowledge there all right + + align:start position:0% +periodic table knowledge there all right + + + align:start position:0% +periodic table knowledge there all right +um both of these uh + + align:start position:0% +um both of these uh + + + align:start position:0% +um both of these uh +are about below 10 to the minus 5 pescal + + align:start position:0% + + + + align:start position:0% + +so you have these two materials that + + align:start position:0% +so you have these two materials that + + + align:start position:0% +so you have these two materials that +have very very low saturation vapor + + align:start position:0% +have very very low saturation vapor + + + align:start position:0% +have very very low saturation vapor +pressure and one that has a reasonable + + align:start position:0% +pressure and one that has a reasonable + + + align:start position:0% +pressure and one that has a reasonable +saturation vapor pressure that's the + + align:start position:0% +saturation vapor pressure that's the + + + align:start position:0% +saturation vapor pressure that's the +reference data okay here's the problem + + align:start position:0% +reference data okay here's the problem + + + align:start position:0% +reference data okay here's the problem +statement what is the Gibbs free energy + + align:start position:0% +statement what is the Gibbs free energy + + + align:start position:0% +statement what is the Gibbs free energy +formation of silicon carbide + + align:start position:0% + + + + align:start position:0% + +so what I'm going to do is I'm going to + + align:start position:0% +so what I'm going to do is I'm going to + + + align:start position:0% +so what I'm going to do is I'm going to +start by + + align:start position:0% +start by + + + align:start position:0% +start by +um + + align:start position:0% +um + + + align:start position:0% +um +I'm not going to start by asking how do + + align:start position:0% +I'm not going to start by asking how do + + + align:start position:0% +I'm not going to start by asking how do +you solve this problem I'm going to + + align:start position:0% +you solve this problem I'm going to + + + align:start position:0% +you solve this problem I'm going to +start just by writing down an expression + + align:start position:0% +start just by writing down an expression + + + align:start position:0% +start just by writing down an expression +for the thing we want to solve for just + + align:start position:0% +for the thing we want to solve for just + + + align:start position:0% +for the thing we want to solve for just +manipulating terms + + align:start position:0% +manipulating terms + + + align:start position:0% +manipulating terms +trying to think out loud here + + align:start position:0% +trying to think out loud here + + + align:start position:0% +trying to think out loud here +on the page so let's see + + align:start position:0% +on the page so let's see + + + align:start position:0% +on the page so let's see +Delta formation + + align:start position:0% +Delta formation + + + align:start position:0% +Delta formation +of silicon carbide + + align:start position:0% +of silicon carbide + + + align:start position:0% +of silicon carbide +well just by definition I know what that + + align:start position:0% +well just by definition I know what that + + + align:start position:0% +well just by definition I know what that +is it's a Gibbs free energy of silicon + + align:start position:0% +is it's a Gibbs free energy of silicon + + + align:start position:0% +is it's a Gibbs free energy of silicon +carbide minus the Gibbs free energy of + + align:start position:0% +carbide minus the Gibbs free energy of + + + align:start position:0% +carbide minus the Gibbs free energy of +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +in its reference State and it's pure + + align:start position:0% +in its reference State and it's pure + + + align:start position:0% +in its reference State and it's pure +State minus it gives free energy of + + align:start position:0% +State minus it gives free energy of + + + align:start position:0% +State minus it gives free energy of +carbon in its reference State because + + align:start position:0% +carbon in its reference State because + + + align:start position:0% +carbon in its reference State because +it's um and the Stoichiometry is really + + align:start position:0% +it's um and the Stoichiometry is really + + + align:start position:0% +it's um and the Stoichiometry is really +easy right one mole of silicon and one + + align:start position:0% +easy right one mole of silicon and one + + + align:start position:0% +easy right one mole of silicon and one +mole of carbon + + align:start position:0% +mole of carbon + + + align:start position:0% +mole of carbon +forms one mole of silicon carbide so you + + align:start position:0% +forms one mole of silicon carbide so you + + + align:start position:0% +forms one mole of silicon carbide so you +know this expression is very very easy + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +well + + align:start position:0% +well + + + align:start position:0% +well +four one mole + + align:start position:0% + + + + align:start position:0% + +of silicon carbide + + align:start position:0% +of silicon carbide + + + align:start position:0% +of silicon carbide +G + + align:start position:0% + + + + align:start position:0% + +sub carbide equals + + align:start position:0% + + + + align:start position:0% + +all right this is just partial molar + + align:start position:0% +all right this is just partial molar + + + align:start position:0% +all right this is just partial molar +properties + + align:start position:0% +properties + + + align:start position:0% +properties +so this we know + + align:start position:0% +so this we know + + + align:start position:0% +so this we know +and it's just the chemical potential of + + align:start position:0% +and it's just the chemical potential of + + + align:start position:0% +and it's just the chemical potential of +silicon plus the chemical potential of + + align:start position:0% +silicon plus the chemical potential of + + + align:start position:0% +silicon plus the chemical potential of +carbon right as we know in silicon + + align:start position:0% +carbon right as we know in silicon + + + align:start position:0% +carbon right as we know in silicon +carbide in silicon carbide so it's just + + align:start position:0% +carbide in silicon carbide so it's just + + + align:start position:0% +carbide in silicon carbide so it's just +partial molar properties which stuff we + + align:start position:0% +partial molar properties which stuff we + + + align:start position:0% +partial molar properties which stuff we +all we know + + align:start position:0% +all we know + + + align:start position:0% +all we know +um + + align:start position:0% +um + + + align:start position:0% +um +and + + align:start position:0% +and + + + align:start position:0% +and +I'm just going to plug this in and what + + align:start position:0% +I'm just going to plug this in and what + + + align:start position:0% +I'm just going to plug this in and what +we get + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +the free energy of formation of silicon + + align:start position:0% +the free energy of formation of silicon + + + align:start position:0% +the free energy of formation of silicon +carbide expressed in terms of the + + align:start position:0% +carbide expressed in terms of the + + + align:start position:0% +carbide expressed in terms of the +chemical potentials so it's a chemical + + align:start position:0% +chemical potentials so it's a chemical + + + align:start position:0% +chemical potentials so it's a chemical +potential of silicon + + align:start position:0% +potential of silicon + + + align:start position:0% +potential of silicon +and silicon carbide + + align:start position:0% +and silicon carbide + + + align:start position:0% +and silicon carbide +plus the chemical potential of carbon + + align:start position:0% +plus the chemical potential of carbon + + + align:start position:0% +plus the chemical potential of carbon +in silicon carbide minus the chemical + + align:start position:0% +in silicon carbide minus the chemical + + + align:start position:0% +in silicon carbide minus the chemical +potential of silicon + + align:start position:0% +potential of silicon + + + align:start position:0% +potential of silicon +and its reference state + + align:start position:0% +and its reference state + + + align:start position:0% +and its reference state +minus the chemical potential of carbon + + align:start position:0% +minus the chemical potential of carbon + + + align:start position:0% +minus the chemical potential of carbon +it's reference date + + align:start position:0% +it's reference date + + + align:start position:0% +it's reference date +I'm going to do one more thing I'm just + + align:start position:0% +I'm going to do one more thing I'm just + + + align:start position:0% +I'm going to do one more thing I'm just +going to rearrange + + align:start position:0% +going to rearrange + + + align:start position:0% +going to rearrange +I'm going to see it's silken in silicon + + align:start position:0% +I'm going to see it's silken in silicon + + + align:start position:0% +I'm going to see it's silken in silicon +carbide + + align:start position:0% +carbide + + + align:start position:0% +carbide +minus silicon in its reference state + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +chemical potential of carbon + + align:start position:0% +chemical potential of carbon + + + align:start position:0% +chemical potential of carbon +in silicon carbide minus chemical + + align:start position:0% +in silicon carbide minus chemical + + + align:start position:0% +in silicon carbide minus chemical +potential of carbon and it's reference + + align:start position:0% +potential of carbon and it's reference + + + align:start position:0% +potential of carbon and it's reference +States + + align:start position:0% +States + + + align:start position:0% +States +so I have the free energy formation + + align:start position:0% +so I have the free energy formation + + + align:start position:0% +so I have the free energy formation +expressed in terms of differences in + + align:start position:0% +expressed in terms of differences in + + + align:start position:0% +expressed in terms of differences in +chemical potential + + align:start position:0% + + + + align:start position:0% + +and you can see how this is similar to + + align:start position:0% +and you can see how this is similar to + + + align:start position:0% +and you can see how this is similar to +solution modeling right I have I have + + align:start position:0% +solution modeling right I have I have + + + align:start position:0% +solution modeling right I have I have +Delta Muse this is a Delta Mu this is a + + align:start position:0% +Delta Muse this is a Delta Mu this is a + + + align:start position:0% +Delta Muse this is a Delta Mu this is a +Delta Mu + + align:start position:0% +Delta Mu + + + align:start position:0% +Delta Mu +it's just a the Stoichiometry is fixed + + align:start position:0% +it's just a the Stoichiometry is fixed + + + align:start position:0% +it's just a the Stoichiometry is fixed +and so we don't have to worry about + + align:start position:0% +and so we don't have to worry about + + + align:start position:0% +and so we don't have to worry about +composition variables anymore we just + + align:start position:0% +composition variables anymore we just + + + align:start position:0% +composition variables anymore we just +have one of these and one of these + + align:start position:0% +have one of these and one of these + + + align:start position:0% +have one of these and one of these +all right and I'm gonna I'm gonna tackle + + align:start position:0% +all right and I'm gonna I'm gonna tackle + + + align:start position:0% +all right and I'm gonna I'm gonna tackle +these one at a time so I'm going to + + align:start position:0% +these one at a time so I'm going to + + + align:start position:0% +these one at a time so I'm going to +tackle this one first so I'll just label + + align:start position:0% +tackle this one first so I'll just label + + + align:start position:0% +tackle this one first so I'll just label +it one and I'm going to tackle this one + + align:start position:0% +it one and I'm going to tackle this one + + + align:start position:0% +it one and I'm going to tackle this one +second I'm going to label it two so if + + align:start position:0% +second I'm going to label it two so if + + + align:start position:0% +second I'm going to label it two so if +we can if we can find equations for + + align:start position:0% +we can if we can find equations for + + + align:start position:0% +we can if we can find equations for +these quantities right then then we then + + align:start position:0% +these quantities right then then we then + + + align:start position:0% +these quantities right then then we then +we we know our answer so + + align:start position:0% +we we know our answer so + + + align:start position:0% +we we know our answer so +um so I'm going to take these one at a + + align:start position:0% +um so I'm going to take these one at a + + + align:start position:0% +um so I'm going to take these one at a +time + + align:start position:0% +time + + + align:start position:0% +time +and then I'm going to start asking uh + + align:start position:0% +and then I'm going to start asking uh + + + align:start position:0% +and then I'm going to start asking uh +asking you book some questions so um + + align:start position:0% +asking you book some questions so um + + + align:start position:0% +asking you book some questions so um +look alert + + align:start position:0% + + + + align:start position:0% + +let's take one further + + align:start position:0% +let's take one further + + + align:start position:0% +let's take one further +one + + align:start position:0% + + + + align:start position:0% + +how here what I want to do sorry + + align:start position:0% + + + + align:start position:0% + +one of the things I want to do with this + + align:start position:0% +one of the things I want to do with this + + + align:start position:0% +one of the things I want to do with this +working an example thing is I wanna + + align:start position:0% +working an example thing is I wanna + + + align:start position:0% +working an example thing is I wanna +flip back and forth between equations + + align:start position:0% +flip back and forth between equations + + + align:start position:0% +flip back and forth between equations +and word problems word problems and + + align:start position:0% +and word problems word problems and + + + align:start position:0% +and word problems word problems and +equations like this + + align:start position:0% +equations like this + + + align:start position:0% +equations like this +you have to be nimble and you have to + + align:start position:0% +you have to be nimble and you have to + + + align:start position:0% +you have to be nimble and you have to +know the material well enough to do that + + align:start position:0% +know the material well enough to do that + + + align:start position:0% +know the material well enough to do that +you know by now that's an important + + align:start position:0% +you know by now that's an important + + + align:start position:0% +you know by now that's an important +skill so how does + + align:start position:0% +skill so how does + + + align:start position:0% +skill so how does +the chemical potential + + align:start position:0% + + + + align:start position:0% + +of carbon + + align:start position:0% +of carbon + + + align:start position:0% +of carbon +differ + + align:start position:0% + + + + align:start position:0% + +from its pure + + align:start position:0% +from its pure + + + align:start position:0% +from its pure +reference state + + align:start position:0% + + + + align:start position:0% + +right this sentence + + align:start position:0% +right this sentence + + + align:start position:0% +right this sentence +is this expression right this expression + + align:start position:0% +is this expression right this expression + + + align:start position:0% +is this expression right this expression +is the difference in chemical potential + + align:start position:0% +is the difference in chemical potential + + + align:start position:0% +is the difference in chemical potential +for carbon in between this compound and + + align:start position:0% +for carbon in between this compound and + + + align:start position:0% +for carbon in between this compound and +its reference State that's what that + + align:start position:0% +its reference State that's what that + + + align:start position:0% +its reference State that's what that +expresses right that's also what this + + align:start position:0% +expresses right that's also what this + + + align:start position:0% +expresses right that's also what this +expresses right how does a chemical + + align:start position:0% +expresses right how does a chemical + + + align:start position:0% +expresses right how does a chemical +potential of carbon differ from its peer + + align:start position:0% +potential of carbon differ from its peer + + + align:start position:0% +potential of carbon differ from its peer +reference state + + align:start position:0% +reference state + + + align:start position:0% +reference state +so I'll ask you somebody please + + align:start position:0% +so I'll ask you somebody please + + + align:start position:0% +so I'll ask you somebody please +volunteer and answer how does the + + align:start position:0% +volunteer and answer how does the + + + align:start position:0% +volunteer and answer how does the +chemical potential of carbon differ from + + align:start position:0% +chemical potential of carbon differ from + + + align:start position:0% +chemical potential of carbon differ from +its pure reference state + + align:start position:0% +its pure reference state + + + align:start position:0% +its pure reference state +and while you're thinking about that I + + align:start position:0% +and while you're thinking about that I + + + align:start position:0% +and while you're thinking about that I +will just return to + + align:start position:0% +will just return to + + + align:start position:0% +will just return to +my observation + + align:start position:0% + + + + align:start position:0% + +um so I guess it's kind of like the + + align:start position:0% +um so I guess it's kind of like the + + + align:start position:0% +um so I guess it's kind of like the +piece that right where they're in + + align:start position:0% +piece that right where they're in + + + align:start position:0% +piece that right where they're in +equilibrium it's an equilibrium with a + + align:start position:0% +equilibrium it's an equilibrium with a + + + align:start position:0% +equilibrium it's an equilibrium with a +pure phase + + align:start position:0% +pure phase + + + align:start position:0% +pure phase +okay good and so + + align:start position:0% + + + + align:start position:0% + +your answer is + + align:start position:0% +your answer is + + + align:start position:0% +your answer is +oh um it should be the same right + + align:start position:0% +oh um it should be the same right + + + align:start position:0% +oh um it should be the same right +right + + align:start position:0% + + + + align:start position:0% + +um yeah okay it doesn't + + align:start position:0% + + + + align:start position:0% + +it doesn't it doesn't differ + + align:start position:0% +it doesn't it doesn't differ + + + align:start position:0% +it doesn't it doesn't differ +why + + align:start position:0% +why + + + align:start position:0% +why +pure carbon is in equilibrium + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% + + + + align:start position:0% + +silicon carbide that's an observation + + align:start position:0% +silicon carbide that's an observation + + + align:start position:0% +silicon carbide that's an observation +what that means is that chemical + + align:start position:0% +what that means is that chemical + + + align:start position:0% +what that means is that chemical +potential of carbon + + align:start position:0% +potential of carbon + + + align:start position:0% +potential of carbon +in silicon carbide is the same as the + + align:start position:0% +in silicon carbide is the same as the + + + align:start position:0% +in silicon carbide is the same as the +chemical potential of carbon in that + + align:start position:0% +chemical potential of carbon in that + + + align:start position:0% +chemical potential of carbon in that +graphite phase which is sitting there + + align:start position:0% +graphite phase which is sitting there + + + align:start position:0% +graphite phase which is sitting there +which is by definition the chemical + + align:start position:0% +which is by definition the chemical + + + align:start position:0% +which is by definition the chemical +potential of carbon in its reference + + align:start position:0% +potential of carbon in its reference + + + align:start position:0% +potential of carbon in its reference +state + + align:start position:0% +state + + + align:start position:0% +state +good + + align:start position:0% +good + + + align:start position:0% +good +and let me remind you why that is + + align:start position:0% +and let me remind you why that is + + + align:start position:0% +and let me remind you why that is +because this is you know the type of + + align:start position:0% +because this is you know the type of + + + align:start position:0% +because this is you know the type of +thing we've been doing all semester is + + align:start position:0% +thing we've been doing all semester is + + + align:start position:0% +thing we've been doing all semester is +thinking about the conditions for + + align:start position:0% +thinking about the conditions for + + + align:start position:0% +thinking about the conditions for +equilibrium + + align:start position:0% + + + + align:start position:0% + +the criteria for equilibrium if you're + + align:start position:0% +the criteria for equilibrium if you're + + + align:start position:0% +the criteria for equilibrium if you're +like here's graphite + + align:start position:0% +like here's graphite + + + align:start position:0% +like here's graphite +they're so carbide well + + align:start position:0% +they're so carbide well + + + align:start position:0% +they're so carbide well +there's a gas phase too right + + align:start position:0% +there's a gas phase too right + + + align:start position:0% +there's a gas phase too right +the carbon atoms are exchanging + + align:start position:0% +the carbon atoms are exchanging + + + align:start position:0% +the carbon atoms are exchanging +I'm going to draw some carbon atoms in + + align:start position:0% +I'm going to draw some carbon atoms in + + + align:start position:0% +I'm going to draw some carbon atoms in +the gas + + align:start position:0% + + + + align:start position:0% + +the carbon atoms + + align:start position:0% +the carbon atoms + + + align:start position:0% +the carbon atoms +are exchanging + + align:start position:0% + + + + align:start position:0% + +freely right + + align:start position:0% +freely right + + + align:start position:0% +freely right +that's an unconstrained internal process + + align:start position:0% + + + + align:start position:0% + +they're exchanging freely between + + align:start position:0% + + + + align:start position:0% + +silicon carbide and carbon + + align:start position:0% +silicon carbide and carbon + + + align:start position:0% +silicon carbide and carbon +well graphite via Vapor phase + + align:start position:0% + + + + align:start position:0% + +via the vapor phase + + align:start position:0% + + + + align:start position:0% + +when we had conservation of mass + + align:start position:0% +when we had conservation of mass + + + align:start position:0% +when we had conservation of mass +with mass exchange between two phases + + align:start position:0% +with mass exchange between two phases + + + align:start position:0% +with mass exchange between two phases +that led to the condition for chemical + + align:start position:0% +that led to the condition for chemical + + + align:start position:0% +that led to the condition for chemical +equilibrium right chemical equilibrium + + align:start position:0% + + + + align:start position:0% + +all right that was about the middle of + + align:start position:0% +all right that was about the middle of + + + align:start position:0% +all right that was about the middle of +the term that we arrived at that so + + align:start position:0% +the term that we arrived at that so + + + align:start position:0% +the term that we arrived at that so +chemical equilibrium right that's that's + + align:start position:0% +chemical equilibrium right that's that's + + + align:start position:0% +chemical equilibrium right that's that's +what I wrote down here okay + + align:start position:0% +what I wrote down here okay + + + align:start position:0% +what I wrote down here okay +so uh that's great that means that um + + align:start position:0% +so uh that's great that means that um + + + align:start position:0% +so uh that's great that means that um +what is this term equal to what is the + + align:start position:0% +what is this term equal to what is the + + + align:start position:0% +what is this term equal to what is the +determine the expression in the + + align:start position:0% +determine the expression in the + + + align:start position:0% +determine the expression in the +parentheses equal to + + align:start position:0% + + + + align:start position:0% + +zero zero right exactly there's no + + align:start position:0% +zero zero right exactly there's no + + + align:start position:0% +zero zero right exactly there's no +difference in chemical potential + + align:start position:0% +difference in chemical potential + + + align:start position:0% +difference in chemical potential +for carbon + + align:start position:0% +for carbon + + + align:start position:0% +for carbon +between the compound + + align:start position:0% +between the compound + + + align:start position:0% +between the compound +and the pure state right thank you Ian + + align:start position:0% +and the pure state right thank you Ian + + + align:start position:0% +and the pure state right thank you Ian +okay great so half the term half the + + align:start position:0% +okay great so half the term half the + + + align:start position:0% +okay great so half the term half the +right hand side of the equation is put + + align:start position:0% +right hand side of the equation is put + + + align:start position:0% +right hand side of the equation is put +to bed let's let's put the other half + + align:start position:0% +to bed let's let's put the other half + + + align:start position:0% +to bed let's let's put the other half +for the right hand side Tibet let's take + + align:start position:0% +for the right hand side Tibet let's take + + + align:start position:0% +for the right hand side Tibet let's take +care of part two + + align:start position:0% +care of part two + + + align:start position:0% +care of part two +which is + + align:start position:0% +which is + + + align:start position:0% +which is +um right expressing in words uh part two + + align:start position:0% +um right expressing in words uh part two + + + align:start position:0% +um right expressing in words uh part two +is uh + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% + + + + align:start position:0% + +the difference in chemical potential for + + align:start position:0% +the difference in chemical potential for + + + align:start position:0% +the difference in chemical potential for +silicon between the compound and a cure + + align:start position:0% +silicon between the compound and a cure + + + align:start position:0% +silicon between the compound and a cure +state + + align:start position:0% +state + + + align:start position:0% +state +so I'll write that out in words how does + + align:start position:0% +so I'll write that out in words how does + + + align:start position:0% +so I'll write that out in words how does +the chemical potential + + align:start position:0% + + + + align:start position:0% + +of silicon + + align:start position:0% + + + + align:start position:0% + +differ + + align:start position:0% +differ + + + align:start position:0% +differ +from + + align:start position:0% +from + + + align:start position:0% +from +its pure + + align:start position:0% +its pure + + + align:start position:0% +its pure +referenced + + align:start position:0% + + + + align:start position:0% + +okay so that's that's what that okay + + align:start position:0% +okay so that's that's what that okay + + + align:start position:0% +okay so that's that's what that okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um this is a little harder + + align:start position:0% + + + + align:start position:0% + +but I'll walk you through this uh are + + align:start position:0% +but I'll walk you through this uh are + + + align:start position:0% +but I'll walk you through this uh are +there any um + + align:start position:0% +there any um + + + align:start position:0% +there any um +initial thoughts on how to go at this + + align:start position:0% +initial thoughts on how to go at this + + + align:start position:0% +initial thoughts on how to go at this +they don't want to take a Gamble + + align:start position:0% + + + + align:start position:0% + +let me give you a hint + + align:start position:0% +let me give you a hint + + + align:start position:0% +let me give you a hint +okay if + + align:start position:0% +okay if + + + align:start position:0% +okay if +if solid silicon + + align:start position:0% +if solid silicon + + + align:start position:0% +if solid silicon +or I should say liquid because we're + + align:start position:0% +or I should say liquid because we're + + + align:start position:0% +or I should say liquid because we're +above the melting point + + align:start position:0% +above the melting point + + + align:start position:0% +above the melting point +um condensed + + align:start position:0% + + + + align:start position:0% + +I said solid in the lecture now so + + align:start position:0% +I said solid in the lecture now so + + + align:start position:0% +I said solid in the lecture now so +that's a typo if condensed silicon were + + align:start position:0% +that's a typo if condensed silicon were + + + align:start position:0% +that's a typo if condensed silicon were +present + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +the partial pressure + + align:start position:0% + + + + align:start position:0% + +P silicon + + align:start position:0% +P silicon + + + align:start position:0% +P silicon +would be equal to + + align:start position:0% + + + + align:start position:0% + +what would the partial pressure of + + align:start position:0% +what would the partial pressure of + + + align:start position:0% +what would the partial pressure of +silicon be equal to + + align:start position:0% +silicon be equal to + + + align:start position:0% +silicon be equal to +if + + align:start position:0% +if + + + align:start position:0% +if +condensed silicon were present + + align:start position:0% +condensed silicon were present + + + align:start position:0% +condensed silicon were present +if condensed silicon can be present what + + align:start position:0% +if condensed silicon can be present what + + + align:start position:0% +if condensed silicon can be present what +would the partial pressure of silicon + + align:start position:0% +would the partial pressure of silicon + + + align:start position:0% +would the partial pressure of silicon +equal to + + align:start position:0% + + + + align:start position:0% + +the saturation volume right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's a hypothetical because there's + + align:start position:0% +so that's a hypothetical because there's + + + align:start position:0% +so that's a hypothetical because there's +no condensed silicon there but it's the + + align:start position:0% +no condensed silicon there but it's the + + + align:start position:0% +no condensed silicon there but it's the +starting point if condos Okay so + + align:start position:0% +starting point if condos Okay so + + + align:start position:0% +starting point if condos Okay so +therefore + + align:start position:0% + + + + align:start position:0% + +chemical potential of silicon + + align:start position:0% + + + + align:start position:0% + +minus chemical potential of silicon + + align:start position:0% +minus chemical potential of silicon + + + align:start position:0% +minus chemical potential of silicon +and its reference State equals + + align:start position:0% + + + + align:start position:0% + +this is a bit of a + + align:start position:0% +this is a bit of a + + + align:start position:0% +this is a bit of a +kind of an aha thing you have to you + + align:start position:0% +kind of an aha thing you have to you + + + align:start position:0% +kind of an aha thing you have to you +have to see the connection here between + + align:start position:0% +have to see the connection here between + + + align:start position:0% +have to see the connection here between +different different parts of the of the + + align:start position:0% +different different parts of the of the + + + align:start position:0% +different different parts of the of the +semester + + align:start position:0% +semester + + + align:start position:0% +semester +the chemical potential of silicon in + + align:start position:0% +the chemical potential of silicon in + + + align:start position:0% +the chemical potential of silicon in +this system relative to what it would be + + align:start position:0% +this system relative to what it would be + + + align:start position:0% +this system relative to what it would be +if condensed silicon were present if + + align:start position:0% +if condensed silicon were present if + + + align:start position:0% +if condensed silicon were present if +condensed silicon were present the + + align:start position:0% +condensed silicon were present the + + + align:start position:0% +condensed silicon were present the +chemical potential would be equal to its + + align:start position:0% +chemical potential would be equal to its + + + align:start position:0% +chemical potential would be equal to its +reference State chemical potential + + align:start position:0% +reference State chemical potential + + + align:start position:0% +reference State chemical potential +also if condensed silicon were present + + align:start position:0% +also if condensed silicon were present + + + align:start position:0% +also if condensed silicon were present +the pressure would be equal to the + + align:start position:0% +the pressure would be equal to the + + + align:start position:0% +the pressure would be equal to the +saturation pressure + + align:start position:0% +saturation pressure + + + align:start position:0% +saturation pressure +foreign + + align:start position:0% + + + + align:start position:0% + +therefore the chemical potential + + align:start position:0% +therefore the chemical potential + + + align:start position:0% +therefore the chemical potential +difference of silicon relative to the + + align:start position:0% +difference of silicon relative to the + + + align:start position:0% +difference of silicon relative to the +reference state is RT log P silicon + + align:start position:0% +reference state is RT log P silicon + + + align:start position:0% +reference state is RT log P silicon +over P silicon set + + align:start position:0% + + + + align:start position:0% + +why is this this is recognizing + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +in silicon carbide + + align:start position:0% + + + + align:start position:0% + +is in equilibrium + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% +with + + + align:start position:0% +with +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +in the gas phase + + align:start position:0% + + + + align:start position:0% + +right here's another there are you have + + align:start position:0% +right here's another there are you have + + + align:start position:0% +right here's another there are you have +to imagine this silicon carbide + + align:start position:0% + + + + align:start position:0% + +and there's silicon vapor + + align:start position:0% + + + + align:start position:0% + +you can't see it but it's there + + align:start position:0% +you can't see it but it's there + + + align:start position:0% +you can't see it but it's there +and you know that the Silicon vapor is + + align:start position:0% +and you know that the Silicon vapor is + + + align:start position:0% +and you know that the Silicon vapor is +in equilibrium with the Silicon the + + align:start position:0% +in equilibrium with the Silicon the + + + align:start position:0% +in equilibrium with the Silicon the +silicon carbide those components are in + + align:start position:0% +silicon carbide those components are in + + + align:start position:0% +silicon carbide those components are in +equilibrium because they can freely + + align:start position:0% +equilibrium because they can freely + + + align:start position:0% +equilibrium because they can freely +Exchange + + align:start position:0% +Exchange + + + align:start position:0% +Exchange +so they're in chemical equilibrium so + + align:start position:0% +so they're in chemical equilibrium so + + + align:start position:0% +so they're in chemical equilibrium so +whatever the chemical potential of this + + align:start position:0% +whatever the chemical potential of this + + + align:start position:0% +whatever the chemical potential of this +Vapor phase is it's the same as the + + align:start position:0% +Vapor phase is it's the same as the + + + align:start position:0% +Vapor phase is it's the same as the +chemical potential of silicon in this + + align:start position:0% +chemical potential of silicon in this + + + align:start position:0% +chemical potential of silicon in this +compound + + align:start position:0% +compound + + + align:start position:0% +compound +and you know how to calculate the + + align:start position:0% +and you know how to calculate the + + + align:start position:0% +and you know how to calculate the +chemical potential of a vapor phase it's + + align:start position:0% +chemical potential of a vapor phase it's + + + align:start position:0% +chemical potential of a vapor phase it's +RG log partial pressure over the + + align:start position:0% +RG log partial pressure over the + + + align:start position:0% +RG log partial pressure over the +reference partial pressure + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that was cool if we're not we're done + + align:start position:0% +that was cool if we're not we're done + + + align:start position:0% +that was cool if we're not we're done +yet + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +is + + align:start position:0% +is + + + align:start position:0% +is +partial pressure of silicon + + align:start position:0% + + + + align:start position:0% + +I'll remind you the total pressure now + + align:start position:0% + + + + align:start position:0% + +equals 4.0 pascals the total pressure + + align:start position:0% +equals 4.0 pascals the total pressure + + + align:start position:0% +equals 4.0 pascals the total pressure +equals four pascals right + + align:start position:0% + + + + align:start position:0% + +gas + + align:start position:0% +gas + + + align:start position:0% +gas +phase + + align:start position:0% +phase + + + align:start position:0% +phase +what are the gas phase components + + align:start position:0% + + + + align:start position:0% + +what sort of molecules am I finding in + + align:start position:0% +what sort of molecules am I finding in + + + align:start position:0% +what sort of molecules am I finding in +the gas phase + + align:start position:0% +the gas phase + + + align:start position:0% +the gas phase +foreign + + align:start position:0% + + + + align:start position:0% + +thanks for that what else + + align:start position:0% + + + + align:start position:0% + +probably nitrogen oxygen if it's like + + align:start position:0% +probably nitrogen oxygen if it's like + + + align:start position:0% +probably nitrogen oxygen if it's like +from the General Air no because we + + align:start position:0% +from the General Air no because we + + + align:start position:0% +from the General Air no because we +pulled back in before we did this that + + align:start position:0% +pulled back in before we did this that + + + align:start position:0% +pulled back in before we did this that +was that was a key thing so we there's + + align:start position:0% +was that was a key thing so we there's + + + align:start position:0% +was that was a key thing so we there's +nothing in there except what we put in + + align:start position:0% +nothing in there except what we put in + + + align:start position:0% +nothing in there except what we put in +there which was silicon and silicon it's + + align:start position:0% +there which was silicon and silicon it's + + + align:start position:0% +there which was silicon and silicon it's +carbon and silicon carbide so what other + + align:start position:0% +carbon and silicon carbide so what other + + + align:start position:0% +carbon and silicon carbide so what other +components are in the uh gas in general + + align:start position:0% +components are in the uh gas in general + + + align:start position:0% +components are in the uh gas in general +what else could be there + + align:start position:0% + + + + align:start position:0% + +drugs + + align:start position:0% +drugs + + + align:start position:0% +drugs +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +carbon yeah this carbon and we could + + align:start position:0% +carbon yeah this carbon and we could + + + align:start position:0% +carbon yeah this carbon and we could +allow that there's maybe some cell + + align:start position:0% +allow that there's maybe some cell + + + align:start position:0% +allow that there's maybe some cell +carbine molecules + + align:start position:0% + + + + align:start position:0% + +turns out doesn't matter whether the + + align:start position:0% +turns out doesn't matter whether the + + + align:start position:0% +turns out doesn't matter whether the +Silicon carbon molecules right we know + + align:start position:0% +Silicon carbon molecules right we know + + + align:start position:0% +Silicon carbon molecules right we know +that carbon and silicon carbide are + + align:start position:0% +that carbon and silicon carbide are + + + align:start position:0% +that carbon and silicon carbide are +saturated right we know they're + + align:start position:0% +saturated right we know they're + + + align:start position:0% +saturated right we know they're +saturated + + align:start position:0% +saturated + + + align:start position:0% +saturated +that's just by observation right because + + align:start position:0% +that's just by observation right because + + + align:start position:0% +that's just by observation right because +the pure components are there so their + + align:start position:0% +the pure components are there so their + + + align:start position:0% +the pure components are there so their +Vapor pressures are saturated + + align:start position:0% +Vapor pressures are saturated + + + align:start position:0% +Vapor pressures are saturated +they're saturated + + align:start position:0% +they're saturated + + + align:start position:0% +they're saturated +but + + align:start position:0% +but + + + align:start position:0% +but +their saturation Vapor pressures + + align:start position:0% + + + + align:start position:0% + +are they're negligible + + align:start position:0% + + + + align:start position:0% + +because they're refractory materials we + + align:start position:0% +because they're refractory materials we + + + align:start position:0% +because they're refractory materials we +talked about that 20 minutes ago okay + + align:start position:0% +talked about that 20 minutes ago okay + + + align:start position:0% +talked about that 20 minutes ago okay +so what does that mean somebody a quick + + align:start position:0% +so what does that mean somebody a quick + + + align:start position:0% +so what does that mean somebody a quick +question if that's all right + + align:start position:0% +question if that's all right + + + align:start position:0% +question if that's all right +um + + align:start position:0% +um + + + align:start position:0% +um +earlier I think we talked about how the + + align:start position:0% +earlier I think we talked about how the + + + align:start position:0% +earlier I think we talked about how the +carbon wouldn't vaporize nearly as much + + align:start position:0% +carbon wouldn't vaporize nearly as much + + + align:start position:0% +carbon wouldn't vaporize nearly as much +as the silicone so would it make sense + + align:start position:0% +as the silicone so would it make sense + + + align:start position:0% +as the silicone so would it make sense +to ignore it in future calculations or + + align:start position:0% +to ignore it in future calculations or + + + align:start position:0% +to ignore it in future calculations or +do we still need to take it into account + + align:start position:0% +do we still need to take it into account + + + align:start position:0% +do we still need to take it into account +even though it's + + align:start position:0% +even though it's + + + align:start position:0% +even though it's +less likely to vaporize so Sarah you're + + align:start position:0% +less likely to vaporize so Sarah you're + + + align:start position:0% +less likely to vaporize so Sarah you're +you're your question is exactly my + + align:start position:0% +you're your question is exactly my + + + align:start position:0% +you're your question is exactly my +question + + align:start position:0% +question + + + align:start position:0% +question +which is this so the + + align:start position:0% +which is this so the + + + align:start position:0% +which is this so the +what is the Silicon partial pressure and + + align:start position:0% +what is the Silicon partial pressure and + + + align:start position:0% +what is the Silicon partial pressure and +if it's not clear right now why your + + align:start position:0% +if it's not clear right now why your + + + align:start position:0% +if it's not clear right now why your +question is my question I'll make that + + align:start position:0% +question is my question I'll make that + + + align:start position:0% +question is my question I'll make that +clear but somebody please what knowing + + align:start position:0% +clear but somebody please what knowing + + + align:start position:0% +clear but somebody please what knowing +here's your observations and some facts + + align:start position:0% +here's your observations and some facts + + + align:start position:0% +here's your observations and some facts +and things that you know would somebody + + align:start position:0% +and things that you know would somebody + + + align:start position:0% +and things that you know would somebody +make uh + + align:start position:0% +make uh + + + align:start position:0% +make uh +I guess + + align:start position:0% +I guess + + + align:start position:0% +I guess +for the Silicon partial pressure + + align:start position:0% + + + + align:start position:0% + +it's equal to the total pressure thank + + align:start position:0% +it's equal to the total pressure thank + + + align:start position:0% +it's equal to the total pressure thank +you yes that's exactly right the Silicon + + align:start position:0% +you yes that's exactly right the Silicon + + + align:start position:0% +you yes that's exactly right the Silicon +partial pressure is basically the same + + align:start position:0% +partial pressure is basically the same + + + align:start position:0% +partial pressure is basically the same +as the total pressure + + align:start position:0% +as the total pressure + + + align:start position:0% +as the total pressure +in other words the vapor + + align:start position:0% +in other words the vapor + + + align:start position:0% +in other words the vapor +is essentially + + align:start position:0% + + + + align:start position:0% + +pure silicon + + align:start position:0% + + + + align:start position:0% + +that's the second kind of big + + align:start position:0% +that's the second kind of big + + + align:start position:0% +that's the second kind of big +intellectual connection which you need + + align:start position:0% +intellectual connection which you need + + + align:start position:0% +intellectual connection which you need +to make to solve this problem the first + + align:start position:0% +to make to solve this problem the first + + + align:start position:0% +to make to solve this problem the first +was + + align:start position:0% +was + + + align:start position:0% +was +the change in chemical potential for for + + align:start position:0% +the change in chemical potential for for + + + align:start position:0% +the change in chemical potential for for +gases when they're rarified the second + + align:start position:0% +gases when they're rarified the second + + + align:start position:0% +gases when they're rarified the second +is well it's sort of a more pragmatic + + align:start position:0% +is well it's sort of a more pragmatic + + + align:start position:0% +is well it's sort of a more pragmatic +thing right you have all these things in + + align:start position:0% +thing right you have all these things in + + + align:start position:0% +thing right you have all these things in +the gas phase but I know that the + + align:start position:0% +the gas phase but I know that the + + + align:start position:0% +the gas phase but I know that the +pressure of carbon and sodium carbide is + + align:start position:0% +pressure of carbon and sodium carbide is + + + align:start position:0% +pressure of carbon and sodium carbide is +really small unmeasurable on my gauge + + align:start position:0% +really small unmeasurable on my gauge + + + align:start position:0% +really small unmeasurable on my gauge +right definitely not making a + + align:start position:0% +right definitely not making a + + + align:start position:0% +right definitely not making a +contribution to that 4.0 pascals maybe + + align:start position:0% +contribution to that 4.0 pascals maybe + + + align:start position:0% +contribution to that 4.0 pascals maybe +at the six decimal point or something + + align:start position:0% +at the six decimal point or something + + + align:start position:0% +at the six decimal point or something +but who cares right it's 4.0 Pascal so + + align:start position:0% +but who cares right it's 4.0 Pascal so + + + align:start position:0% +but who cares right it's 4.0 Pascal so +my gauge only has two digits of + + align:start position:0% +my gauge only has two digits of + + + align:start position:0% +my gauge only has two digits of +precision anyway + + align:start position:0% +precision anyway + + + align:start position:0% +precision anyway +so I can infer that that pressure is + + align:start position:0% +so I can infer that that pressure is + + + align:start position:0% +so I can infer that that pressure is +totally silicon + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +so now I plug + + align:start position:0% +so now I plug + + + align:start position:0% +so now I plug +and I chug the chemical potential of + + align:start position:0% +and I chug the chemical potential of + + + align:start position:0% +and I chug the chemical potential of +silicon in this system + + align:start position:0% +silicon in this system + + + align:start position:0% +silicon in this system +minus the chemical potential of silicon + + align:start position:0% +minus the chemical potential of silicon + + + align:start position:0% +minus the chemical potential of silicon +for condensed pure silicon which is RT + + align:start position:0% +for condensed pure silicon which is RT + + + align:start position:0% +for condensed pure silicon which is RT +log + + align:start position:0% +log + + + align:start position:0% +log +P silicon + + align:start position:0% +P silicon + + + align:start position:0% +P silicon +P silicon sap + + align:start position:0% + + + + align:start position:0% + +is just + + align:start position:0% +is just + + + align:start position:0% +is just +r t log + + align:start position:0% +r t log + + + align:start position:0% +r t log +4.0 over 4.4 + + align:start position:0% + + + + align:start position:0% + +so I'm putting it all together + + align:start position:0% + + + + align:start position:0% + +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +Delta formation G of silicon carbide + + align:start position:0% +Delta formation G of silicon carbide + + + align:start position:0% +Delta formation G of silicon carbide +it's two terms chemical potential of + + align:start position:0% +it's two terms chemical potential of + + + align:start position:0% +it's two terms chemical potential of +silicon minus chemical potential of + + align:start position:0% +silicon minus chemical potential of + + + align:start position:0% +silicon minus chemical potential of +silicon and its reference state + + align:start position:0% +silicon and its reference state + + + align:start position:0% +silicon and its reference state +and the chemical potential of carbon + + align:start position:0% +and the chemical potential of carbon + + + align:start position:0% +and the chemical potential of carbon +minus chemical potential of carbon and + + align:start position:0% +minus chemical potential of carbon and + + + align:start position:0% +minus chemical potential of carbon and +its reference state + + align:start position:0% +its reference state + + + align:start position:0% +its reference state +and + + align:start position:0% +and + + + align:start position:0% +and +that zero + + align:start position:0% +that zero + + + align:start position:0% +that zero +and this is r t log 4.0 over 4.4 + + align:start position:0% +and this is r t log 4.0 over 4.4 + + + align:start position:0% +and this is r t log 4.0 over 4.4 +which happens to equal to minus 1563 + + align:start position:0% +which happens to equal to minus 1563 + + + align:start position:0% +which happens to equal to minus 1563 +pictures per month + + align:start position:0% +pictures per month + + + align:start position:0% +pictures per month +that's the answer + + align:start position:0% +that's the answer + + + align:start position:0% +that's the answer +so I I intentionally left a good amount + + align:start position:0% +so I I intentionally left a good amount + + + align:start position:0% +so I I intentionally left a good amount +of time to talk about this problem but I + + align:start position:0% +of time to talk about this problem but I + + + align:start position:0% +of time to talk about this problem but I +want to start with sort of a a um + + align:start position:0% + + + + align:start position:0% + +sort of a strategy for solving those + + align:start position:0% +sort of a strategy for solving those + + + align:start position:0% +sort of a strategy for solving those +types of problems and to solving all + + align:start position:0% +types of problems and to solving all + + + align:start position:0% +types of problems and to solving all +thermal problems actually + + align:start position:0% + + + + align:start position:0% + +the key + + align:start position:0% +the key + + + align:start position:0% +the key +to solving such problems + + align:start position:0% + + + + align:start position:0% + +this is sort of the intellectual key is + + align:start position:0% +this is sort of the intellectual key is + + + align:start position:0% +this is sort of the intellectual key is +to ask + + align:start position:0% +to ask + + + align:start position:0% +to ask +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +who + + align:start position:0% +who + + + align:start position:0% +who +is in + + align:start position:0% +is in + + + align:start position:0% +is in +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +with + + align:start position:0% + + + + align:start position:0% + +boom + + align:start position:0% + + + + align:start position:0% + +this is the key + + align:start position:0% +this is the key + + + align:start position:0% +this is the key +to getting good at these problems + + align:start position:0% +to getting good at these problems + + + align:start position:0% +to getting good at these problems +what do I mean by that + + align:start position:0% +what do I mean by that + + + align:start position:0% +what do I mean by that +we have vapor + + align:start position:0% +we have vapor + + + align:start position:0% +we have vapor +we have Vapor Carbon + + align:start position:0% +we have Vapor Carbon + + + align:start position:0% +we have Vapor Carbon +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +silicon carbide + + align:start position:0% +silicon carbide + + + align:start position:0% +silicon carbide +we have condensed silicon carbide + + align:start position:0% +we have condensed silicon carbide + + + align:start position:0% +we have condensed silicon carbide +we have condensed graphite + + align:start position:0% +we have condensed graphite + + + align:start position:0% +we have condensed graphite +and the components + + align:start position:0% + + + + align:start position:0% + +are freely exchanging + + align:start position:0% + + + + align:start position:0% + +right so this here we have these + + align:start position:0% +right so this here we have these + + + align:start position:0% +right so this here we have these +components freely exchanging right + + align:start position:0% +components freely exchanging right + + + align:start position:0% +components freely exchanging right +exchanging Mass + + align:start position:0% + + + + align:start position:0% + +back to the basics right back when we + + align:start position:0% +back to the basics right back when we + + + align:start position:0% +back to the basics right back when we +developed + + align:start position:0% +developed + + + align:start position:0% +developed +chemical equilibrium chemical + + align:start position:0% +chemical equilibrium chemical + + + align:start position:0% +chemical equilibrium chemical +equilibrium + + align:start position:0% + + + + align:start position:0% + +as opposed to + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +vapor + + align:start position:0% +vapor + + + align:start position:0% +vapor +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +imagine + + align:start position:0% +imagine + + + align:start position:0% +imagine +silicon carbide you know silicon carbon + + align:start position:0% +silicon carbide you know silicon carbon + + + align:start position:0% +silicon carbide you know silicon carbon +silicon carbide + + align:start position:0% +silicon carbide + + + align:start position:0% +silicon carbide +okay + + align:start position:0% + + + + align:start position:0% + +those are in equilibrium + + align:start position:0% +those are in equilibrium + + + align:start position:0% +those are in equilibrium +but what about + + align:start position:0% +but what about + + + align:start position:0% +but what about +solid silicon + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +not an equilibrium + + align:start position:0% +not an equilibrium + + + align:start position:0% +not an equilibrium +not an equilibrium + + align:start position:0% +not an equilibrium + + + align:start position:0% +not an equilibrium +[Music] + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% + + + + align:start position:0% + +in equilibrium + + align:start position:0% + + + + align:start position:0% + +with + + align:start position:0% + + + + align:start position:0% + +condensed silicon + + align:start position:0% + + + + align:start position:0% + +what does that mean + + align:start position:0% +what does that mean + + + align:start position:0% +what does that mean +it means that the vapor pressure + + align:start position:0% + + + + align:start position:0% + +is below + + align:start position:0% + + + + align:start position:0% + +saturation + + align:start position:0% + + + + align:start position:0% + +because when I saturate the vapor + + align:start position:0% +because when I saturate the vapor + + + align:start position:0% +because when I saturate the vapor +pressure of a thing that thing starts + + align:start position:0% +pressure of a thing that thing starts + + + align:start position:0% +pressure of a thing that thing starts +condensing right starts condensing out + + align:start position:0% +condensing right starts condensing out + + + align:start position:0% +condensing right starts condensing out +of the air it starts raining silicon + + align:start position:0% +of the air it starts raining silicon + + + align:start position:0% +of the air it starts raining silicon +right if the vapor pressure reaches the + + align:start position:0% +right if the vapor pressure reaches the + + + align:start position:0% +right if the vapor pressure reaches the +saturation vapor pressure of silicon it + + align:start position:0% +saturation vapor pressure of silicon it + + + align:start position:0% +saturation vapor pressure of silicon it +would start raining silicon in that + + align:start position:0% +would start raining silicon in that + + + align:start position:0% +would start raining silicon in that +system + + align:start position:0% +system + + + align:start position:0% +system +that didn't happen + + align:start position:0% +that didn't happen + + + align:start position:0% +that didn't happen +so the vapor pressure is below + + align:start position:0% + + + + align:start position:0% + +okay so that was a lot of stuff + + align:start position:0% +okay so that was a lot of stuff + + + align:start position:0% +okay so that was a lot of stuff +um all wrapped up into one problem + + align:start position:0% +um all wrapped up into one problem + + + align:start position:0% +um all wrapped up into one problem +it's good that I have 10 minutes to to + + align:start position:0% +it's good that I have 10 minutes to to + + + align:start position:0% +it's good that I have 10 minutes to to +talk about it so I'm happy to take + + align:start position:0% +talk about it so I'm happy to take + + + align:start position:0% +talk about it so I'm happy to take +questions about this or anything else + + align:start position:0% +questions about this or anything else + + + align:start position:0% +questions about this or anything else +um I will mention uh one last thing on + + align:start position:0% +um I will mention uh one last thing on + + + align:start position:0% +um I will mention uh one last thing on +course scheduling Wednesdays office + + align:start position:0% +course scheduling Wednesdays office + + + align:start position:0% +course scheduling Wednesdays office +hours I'm planning to do a really + + align:start position:0% +hours I'm planning to do a really + + + align:start position:0% +hours I'm planning to do a really +informal + + align:start position:0% +informal + + + align:start position:0% +informal +kind of semester in review + + align:start position:0% + + + + align:start position:0% + +so um + + align:start position:0% +so um + + + align:start position:0% +so um +hopefully that'll be useful but back to + + align:start position:0% +hopefully that'll be useful but back to + + + align:start position:0% +hopefully that'll be useful but back to +this problem + + align:start position:0% + + + + align:start position:0% + +questions confusion + + align:start position:0% +questions confusion + + + align:start position:0% +questions confusion +I have a question about something very + + align:start position:0% +I have a question about something very + + + align:start position:0% +I have a question about something very +early on so how is it that we knew that + + align:start position:0% +early on so how is it that we knew that + + + align:start position:0% +early on so how is it that we knew that +the vapor pressure of carbon was a lot + + align:start position:0% +the vapor pressure of carbon was a lot + + + align:start position:0% +the vapor pressure of carbon was a lot +less than silicon was that reading from + + align:start position:0% +less than silicon was that reading from + + + align:start position:0% +less than silicon was that reading from +the graph or no no so that was not so + + align:start position:0% +the graph or no no so that was not so + + + align:start position:0% +the graph or no no so that was not so +there's two things first of all um I + + align:start position:0% +there's two things first of all um I + + + align:start position:0% +there's two things first of all um I +just I gave you reference data so that + + align:start position:0% +just I gave you reference data so that + + + align:start position:0% +just I gave you reference data so that +was like data given with the problem + + align:start position:0% +was like data given with the problem + + + align:start position:0% +was like data given with the problem +so one way is that it was just in the + + align:start position:0% +so one way is that it was just in the + + + align:start position:0% +so one way is that it was just in the +problem statement right so you say you + + align:start position:0% +problem statement right so you say you + + + align:start position:0% +problem statement right so you say you +know it's fine but you know it is worth + + align:start position:0% +know it's fine but you know it is worth + + + align:start position:0% +know it's fine but you know it is worth +asking yourself would you have been able + + align:start position:0% +asking yourself would you have been able + + + align:start position:0% +asking yourself would you have been able +to infer that if + + align:start position:0% +to infer that if + + + align:start position:0% +to infer that if +if that hadn't been given in the problem + + align:start position:0% +if that hadn't been given in the problem + + + align:start position:0% +if that hadn't been given in the problem +and + + align:start position:0% + + + + align:start position:0% + +yeah you might guess that you might know + + align:start position:0% +yeah you might guess that you might know + + + align:start position:0% +yeah you might guess that you might know +the silicon carbide and graphite of + + align:start position:0% +the silicon carbide and graphite of + + + align:start position:0% +the silicon carbide and graphite of +refractory materials right you might + + align:start position:0% +refractory materials right you might + + + align:start position:0% +refractory materials right you might +know that they're very + + align:start position:0% +know that they're very + + + align:start position:0% +know that they're very +tightly bound molecular solids + + align:start position:0% +tightly bound molecular solids + + + align:start position:0% +tightly bound molecular solids +with a huge cohesion energy + + align:start position:0% +with a huge cohesion energy + + + align:start position:0% +with a huge cohesion energy +it's very hard to break them up + + align:start position:0% + + + + align:start position:0% + +and the phase diagram here tells you + + align:start position:0% +and the phase diagram here tells you + + + align:start position:0% +and the phase diagram here tells you +that silicon is a lot more volatile than + + align:start position:0% +that silicon is a lot more volatile than + + + align:start position:0% +that silicon is a lot more volatile than +either sodium carbide or carbon it's got + + align:start position:0% +either sodium carbide or carbon it's got + + + align:start position:0% +either sodium carbide or carbon it's got +a much lower melting point + + align:start position:0% +a much lower melting point + + + align:start position:0% +a much lower melting point +right + + align:start position:0% +right + + + align:start position:0% +right +so you might just guess and I wouldn't + + align:start position:0% +so you might just guess and I wouldn't + + + align:start position:0% +so you might just guess and I wouldn't +ask you to do that but + + align:start position:0% +ask you to do that but + + + align:start position:0% +ask you to do that but +um you know you might be able to infer + + align:start position:0% +um you know you might be able to infer + + + align:start position:0% +um you know you might be able to infer +that the saturation vapor pressure of + + align:start position:0% +that the saturation vapor pressure of + + + align:start position:0% +that the saturation vapor pressure of +sodium carbide and carbon is is very low + + align:start position:0% +sodium carbide and carbon is is very low + + + align:start position:0% +sodium carbide and carbon is is very low +and if you remember the saturation vapor + + align:start position:0% +and if you remember the saturation vapor + + + align:start position:0% +and if you remember the saturation vapor +pressure + + align:start position:0% + + + + align:start position:0% + +it's proportional to e to the minus + + align:start position:0% +it's proportional to e to the minus + + + align:start position:0% +it's proportional to e to the minus +Delta h + + align:start position:0% +Delta h + + + align:start position:0% +Delta h +of formation + + align:start position:0% + + + + align:start position:0% + +you remember that from from unitary + + align:start position:0% +you remember that from from unitary + + + align:start position:0% +you remember that from from unitary +phase diagram so a material that has a + + align:start position:0% +phase diagram so a material that has a + + + align:start position:0% +phase diagram so a material that has a +very large energy formation has a very + + align:start position:0% +very large energy formation has a very + + + align:start position:0% +very large energy formation has a very +small saturation of vapor pressure so + + align:start position:0% +small saturation of vapor pressure so + + + align:start position:0% +small saturation of vapor pressure so +maybe you know that that sodium carbide + + align:start position:0% +maybe you know that that sodium carbide + + + align:start position:0% +maybe you know that that sodium carbide +and carbon are very happily bonded + + align:start position:0% +and carbon are very happily bonded + + + align:start position:0% +and carbon are very happily bonded +solids + + align:start position:0% +solids + + + align:start position:0% +solids +again I wouldn't ask you to necessarily + + align:start position:0% +again I wouldn't ask you to necessarily + + + align:start position:0% +again I wouldn't ask you to necessarily +come up with that in the context of a + + align:start position:0% +come up with that in the context of a + + + align:start position:0% +come up with that in the context of a +big problem like this but it could be + + align:start position:0% +big problem like this but it could be + + + align:start position:0% +big problem like this but it could be +done + + align:start position:0% +done + + + align:start position:0% +done +it would be it would be an educated + + align:start position:0% +it would be it would be an educated + + + align:start position:0% +it would be it would be an educated +guess + + align:start position:0% +guess + + + align:start position:0% +guess +does it help + + align:start position:0% +does it help + + + align:start position:0% +does it help +yeah that helps a lot thanks yeah I mean + + align:start position:0% +yeah that helps a lot thanks yeah I mean + + + align:start position:0% +yeah that helps a lot thanks yeah I mean +you know the volatile compounds are + + align:start position:0% +you know the volatile compounds are + + + align:start position:0% +you know the volatile compounds are +compounds that you can smell right so + + align:start position:0% +compounds that you can smell right so + + + align:start position:0% +compounds that you can smell right so +you can't smell silicon you can't I mean + + align:start position:0% +you can't smell silicon you can't I mean + + + align:start position:0% +you can't smell silicon you can't I mean +maybe a dog can but doggy dog noses are + + align:start position:0% +maybe a dog can but doggy dog noses are + + + align:start position:0% +maybe a dog can but doggy dog noses are +amazing but you can't smell soap you + + align:start position:0% +amazing but you can't smell soap you + + + align:start position:0% +amazing but you can't smell soap you +can't smell these things and and the the + + align:start position:0% +can't smell these things and and the the + + + align:start position:0% +can't smell these things and and the the +amount that you could smell something + + align:start position:0% +amount that you could smell something + + + align:start position:0% +amount that you could smell something +corresponds to its volatility right you + + align:start position:0% +corresponds to its volatility right you + + + align:start position:0% +corresponds to its volatility right you +know this when you're dealing with + + align:start position:0% +know this when you're dealing with + + + align:start position:0% +know this when you're dealing with +solvents and paint solvents and stuff + + align:start position:0% +solvents and paint solvents and stuff + + + align:start position:0% +solvents and paint solvents and stuff +very volatile compounds a very smelly + + align:start position:0% +very volatile compounds a very smelly + + + align:start position:0% +very volatile compounds a very smelly +compounds because they have a large + + align:start position:0% +compounds because they have a large + + + align:start position:0% +compounds because they have a large +vapor pressure + + align:start position:0% +vapor pressure + + + align:start position:0% +vapor pressure +just in the air so you know things like + + align:start position:0% +just in the air so you know things like + + + align:start position:0% +just in the air so you know things like +that + + align:start position:0% + + + + align:start position:0% + +can dogs smell silicon that is the + + align:start position:0% +can dogs smell silicon that is the + + + align:start position:0% +can dogs smell silicon that is the +question that everyone is dying to us + + align:start position:0% +question that everyone is dying to us + + + align:start position:0% +question that everyone is dying to us +all right what else what else + + align:start position:0% +all right what else what else + + + align:start position:0% +all right what else what else +no other questions well maybe that was + + align:start position:0% +no other questions well maybe that was + + + align:start position:0% +no other questions well maybe that was +maybe that was clear + + align:start position:0% +maybe that was clear + + + align:start position:0% +maybe that was clear +all right + + align:start position:0% +all right + + + align:start position:0% +all right +if they know the questions we can get + + align:start position:0% +if they know the questions we can get + + + align:start position:0% +if they know the questions we can get +out six minutes early + + align:start position:0% +out six minutes early + + + align:start position:0% +out six minutes early +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +I will see everyone on Monday and again + + align:start position:0% +I will see everyone on Monday and again + + + align:start position:0% +I will see everyone on Monday and again +uh homework due Sunday at 8 pm \ No newline at end of file diff --git a/ZYMWsmertQk.txt b/ZYMWsmertQk.txt new file mode 100644 index 0000000000000000000000000000000000000000..27464f5ced1c82dbc23c36f3d921eb1d25d68433 --- /dev/null +++ b/ZYMWsmertQk.txt @@ -0,0 +1,12075 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay uh so the um Tome exam + + align:start position:0% +ocw.mit.edu okay uh so the um Tome exam + + + align:start position:0% +ocw.mit.edu okay uh so the um Tome exam +uh it should be released by the end of + + align:start position:0% +uh it should be released by the end of + + + align:start position:0% +uh it should be released by the end of +this lecture + + align:start position:0% +this lecture + + + align:start position:0% +this lecture +and uh I hope we will be fine problems I + + align:start position:0% +and uh I hope we will be fine problems I + + + align:start position:0% +and uh I hope we will be fine problems I +spend the weekend trying to make up the + + align:start position:0% +spend the weekend trying to make up the + + + align:start position:0% +spend the weekend trying to make up the +problem in addition writing five letters + + align:start position:0% +problem in addition writing five letters + + + align:start position:0% +problem in addition writing five letters +and write a + + align:start position:0% +and write a + + + align:start position:0% +and write a +report uh but see uh um so making + + align:start position:0% +report uh but see uh um so making + + + align:start position:0% +report uh but see uh um so making +problem is always uh difficult but also + + align:start position:0% +problem is always uh difficult but also + + + align:start position:0% +problem is always uh difficult but also +interesting so I was talking to Jonathon + + align:start position:0% +interesting so I was talking to Jonathon + + + align:start position:0% +interesting so I was talking to Jonathon +hopefully he'll write a paper based on + + align:start position:0% +hopefully he'll write a paper based on + + + align:start position:0% +hopefully he'll write a paper based on +his problems + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um now coming back to uh what we're + + align:start position:0% +um now coming back to uh what we're + + + align:start position:0% +um now coming back to uh what we're +talking uh in the last + + align:start position:0% +talking uh in the last + + + align:start position:0% +talking uh in the last +lecture uh we were discussing really the + + align:start position:0% +lecture uh we were discussing really the + + + align:start position:0% +lecture uh we were discussing really the +now uh chapter eight the title is the + + align:start position:0% +now uh chapter eight the title is the + + + align:start position:0% +now uh chapter eight the title is the +carp transport energy + + align:start position:0% +carp transport energy + + + align:start position:0% +carp transport energy +conversion and uh uh my view here is uh + + align:start position:0% +conversion and uh uh my view here is uh + + + align:start position:0% +conversion and uh uh my view here is uh +uh when we think about the energy + + align:start position:0% +uh when we think about the energy + + + align:start position:0% +uh when we think about the energy +conversion it's microscopically + + align:start position:0% +conversion it's microscopically + + + align:start position:0% +conversion it's microscopically +it's one form of the energy carrier + + align:start position:0% +it's one form of the energy carrier + + + align:start position:0% +it's one form of the energy carrier +transform the energy into the other form + + align:start position:0% +transform the energy into the other form + + + align:start position:0% +transform the energy into the other form +and uh uh and that trans that the + + align:start position:0% +and uh uh and that trans that the + + + align:start position:0% +and uh uh and that trans that the +coupling process uh is the what we when + + align:start position:0% +coupling process uh is the what we when + + + align:start position:0% +coupling process uh is the what we when +we use bman equation is reflected in the + + align:start position:0% +we use bman equation is reflected in the + + + align:start position:0% +we use bman equation is reflected in the +scattering term and in this scattering + + align:start position:0% +scattering term and in this scattering + + + align:start position:0% +scattering term and in this scattering +term we have a scattering rate uh which + + align:start position:0% +term we have a scattering rate uh which + + + align:start position:0% +term we have a scattering rate uh which +approximately in the perturbation limit + + align:start position:0% +approximately in the perturbation limit + + + align:start position:0% +approximately in the perturbation limit +uh we can use the firmy Golden Rule to + + align:start position:0% +uh we can use the firmy Golden Rule to + + + align:start position:0% +uh we can use the firmy Golden Rule to +calculate that scattering rate so we + + align:start position:0% +calculate that scattering rate so we + + + align:start position:0% +calculate that scattering rate so we +took a electron Fon cing as example we + + align:start position:0% +took a electron Fon cing as example we + + + align:start position:0% +took a electron Fon cing as example we +say okay if I have the Fong lce vibrate + + align:start position:0% +say okay if I have the Fong lce vibrate + + + align:start position:0% +say okay if I have the Fong lce vibrate +and change the separation between the + + align:start position:0% +and change the separation between the + + + align:start position:0% +and change the separation between the +atoms and that's effectly changing the + + align:start position:0% +atoms and that's effectly changing the + + + align:start position:0% +atoms and that's effectly changing the +periodicity of that the electron + + align:start position:0% +periodicity of that the electron + + + align:start position:0% +periodicity of that the electron +experience and that's the deformation + + align:start position:0% +experience and that's the deformation + + + align:start position:0% +experience and that's the deformation +potential and with that deformation + + align:start position:0% +potential and with that deformation + + + align:start position:0% +potential and with that deformation +potential we actually uh went through + + align:start position:0% +potential we actually uh went through + + + align:start position:0% +potential we actually uh went through +the uh derivation redund the froming + + align:start position:0% +the uh derivation redund the froming + + + align:start position:0% +the uh derivation redund the froming +Golden Rule and say what's that scatter + + align:start position:0% +Golden Rule and say what's that scatter + + + align:start position:0% +Golden Rule and say what's that scatter +Matrix look like and from that that we + + align:start position:0% +Matrix look like and from that that we + + + align:start position:0% +Matrix look like and from that that we +say that actually gives L fir Golden + + align:start position:0% +say that actually gives L fir Golden + + + align:start position:0% +say that actually gives L fir Golden +Rule and in the manipulation of scatter + + align:start position:0% +Rule and in the manipulation of scatter + + + align:start position:0% +Rule and in the manipulation of scatter +Matrix naturally give you the energy and + + align:start position:0% +Matrix naturally give you the energy and + + + align:start position:0% +Matrix naturally give you the energy and +the momentum + + align:start position:0% +the momentum + + + align:start position:0% +the momentum +conservation and then we move down to + + align:start position:0% +conservation and then we move down to + + + align:start position:0% +conservation and then we move down to +say okay if I plug in the scattering + + align:start position:0% +say okay if I plug in the scattering + + + align:start position:0% +say okay if I plug in the scattering +rate which is typically coupling two + + align:start position:0% +rate which is typically coupling two + + + align:start position:0% +rate which is typically coupling two +different particles into the scattering + + align:start position:0% +different particles into the scattering + + + align:start position:0% +different particles into the scattering +term which has to include include all + + align:start position:0% +term which has to include include all + + + align:start position:0% +term which has to include include all +the possible collisions all the possible + + align:start position:0% +the possible collisions all the possible + + + align:start position:0% +the possible collisions all the possible +scatter and uh of course we know this + + align:start position:0% +scatter and uh of course we know this + + + align:start position:0% +scatter and uh of course we know this +scatter term is very + + align:start position:0% +scatter term is very + + + align:start position:0% +scatter term is very +complicated but at the end of last + + align:start position:0% +complicated but at the end of last + + + align:start position:0% +complicated but at the end of last +lecture I said uh uh this is a uh uh + + align:start position:0% +lecture I said uh uh this is a uh uh + + + align:start position:0% +lecture I said uh uh this is a uh uh +very often presented in books in say uh + + align:start position:0% +very often presented in books in say uh + + + align:start position:0% +very often presented in books in say uh +s physics or electrical electronics if + + align:start position:0% +s physics or electrical electronics if + + + align:start position:0% +s physics or electrical electronics if +you split this F into a first zero order + + align:start position:0% +you split this F into a first zero order + + + align:start position:0% +you split this F into a first zero order +which a even term and the OD term and + + align:start position:0% +which a even term and the OD term and + + + align:start position:0% +which a even term and the OD term and +using that because any function can + + align:start position:0% +using that because any function can + + + align:start position:0% +using that because any function can +always have a even and OD term right + + align:start position:0% +always have a even and OD term right + + + align:start position:0% +always have a even and OD term right +summation uh any function split into a + + align:start position:0% +summation uh any function split into a + + + align:start position:0% +summation uh any function split into a +even out term summation and then plug in + + align:start position:0% +even out term summation and then plug in + + + align:start position:0% +even out term summation and then plug in +back into the scattering + + align:start position:0% +back into the scattering + + + align:start position:0% +back into the scattering +integral you find out that this uh uh + + align:start position:0% +integral you find out that this uh uh + + + align:start position:0% +integral you find out that this uh uh +split led to actually in the case of + + align:start position:0% +split led to actually in the case of + + + align:start position:0% +split led to actually in the case of +example with discussing electron Fon uh + + align:start position:0% +example with discussing electron Fon uh + + + align:start position:0% +example with discussing electron Fon uh +led to two terms uh in the scatter and + + align:start position:0% +led to two terms uh in the scatter and + + + align:start position:0% +led to two terms uh in the scatter and +one of the + + align:start position:0% +one of the + + + align:start position:0% +one of the +term is + + align:start position:0% +term is + + + align:start position:0% +term is +approximately you can use the relaxation + + align:start position:0% +approximately you can use the relaxation + + + align:start position:0% +approximately you can use the relaxation +approximation and turns out the physic + + align:start position:0% +approximation and turns out the physic + + + align:start position:0% +approximation and turns out the physic +physically this term is elastic + + align:start position:0% +physically this term is elastic + + + align:start position:0% +physically this term is elastic +scattering it's a process where there's + + align:start position:0% +scattering it's a process where there's + + + align:start position:0% +scattering it's a process where there's +no uh uh say uh uh for example when + + align:start position:0% +no uh uh say uh uh for example when + + + align:start position:0% +no uh uh say uh uh for example when +electron Fon scatter there's no energy + + align:start position:0% +electron Fon scatter there's no energy + + + align:start position:0% +electron Fon scatter there's no energy +change just a Direction + + align:start position:0% +change just a Direction + + + align:start position:0% +change just a Direction +Change okay or the the other term is the + + align:start position:0% +Change okay or the the other term is the + + + align:start position:0% +Change okay or the the other term is the +inas scatter and turns out the in + + align:start position:0% +inas scatter and turns out the in + + + align:start position:0% +inas scatter and turns out the in +scattering term you cannot rigorous + + align:start position:0% +scattering term you cannot rigorous + + + align:start position:0% +scattering term you cannot rigorous +speaking you cannot use relaxation time + + align:start position:0% +speaking you cannot use relaxation time + + + align:start position:0% +speaking you cannot use relaxation time +approximation so um just don't be + + align:start position:0% +approximation so um just don't be + + + align:start position:0% +approximation so um just don't be +surprised if you write a paper you use + + align:start position:0% +surprised if you write a paper you use + + + align:start position:0% +surprised if you write a paper you use +BS man equation and the end say uh uh + + align:start position:0% +BS man equation and the end say uh uh + + + align:start position:0% +BS man equation and the end say uh uh +people relaxation time say I thought + + align:start position:0% +people relaxation time say I thought + + + align:start position:0% +people relaxation time say I thought +that's not valid in fact we had that + + align:start position:0% +that's not valid in fact we had that + + + align:start position:0% +that's not valid in fact we had that +that experience that's say a reviewer + + align:start position:0% +that experience that's say a reviewer + + + align:start position:0% +that experience that's say a reviewer +say the ver equation is not valid uh for + + align:start position:0% +say the ver equation is not valid uh for + + + align:start position:0% +say the ver equation is not valid uh for +in in your scattering process so this is + + align:start position:0% +in in your scattering process so this is + + + align:start position:0% +in in your scattering process so this is +the where came + + align:start position:0% +the where came + + + align:start position:0% +the where came +from okay and uh uh the uh uh so uh the + + align:start position:0% +from okay and uh uh the uh uh so uh the + + + align:start position:0% +from okay and uh uh the uh uh so uh the +point that I'm going to make next is + + align:start position:0% +point that I'm going to make next is + + + align:start position:0% +point that I'm going to make next is +there are different process you can + + align:start position:0% +there are different process you can + + + align:start position:0% +there are different process you can +write similar Expressions St what along + + align:start position:0% +write similar Expressions St what along + + + align:start position:0% +write similar Expressions St what along +the same approach from a golden rule you + + align:start position:0% +the same approach from a golden rule you + + + align:start position:0% +the same approach from a golden rule you +can calculate the scatter Matrix that's + + align:start position:0% +can calculate the scatter Matrix that's + + + align:start position:0% +can calculate the scatter Matrix that's +the interaction that's the um uh say uh + + align:start position:0% +the interaction that's the um uh say uh + + + align:start position:0% +the interaction that's the um uh say uh +for example + + align:start position:0% + + + + align:start position:0% + +if we have + + align:start position:0% +if we have + + + align:start position:0% +if we have +semiconductor and KN comes in and that + + align:start position:0% +semiconductor and KN comes in and that + + + align:start position:0% +semiconductor and KN comes in and that +can interact the excite the electron LIF + + align:start position:0% +can interact the excite the electron LIF + + + align:start position:0% +can interact the excite the electron LIF +the electron from valence band to the + + align:start position:0% +the electron from valence band to the + + + align:start position:0% +the electron from valence band to the +conduction band and uh uh we have H new + + align:start position:0% +conduction band and uh uh we have H new + + + align:start position:0% +conduction band and uh uh we have H new +here and that process uh you can + + align:start position:0% +here and that process uh you can + + + align:start position:0% +here and that process uh you can +describe using firing Golden Rule that's + + align:start position:0% +describe using firing Golden Rule that's + + + align:start position:0% +describe using firing Golden Rule that's +the absorption SC uh process so you can + + align:start position:0% +the absorption SC uh process so you can + + + align:start position:0% +the absorption SC uh process so you can +calculate the absorption fundamentally + + align:start position:0% +calculate the absorption fundamentally + + + align:start position:0% +calculate the absorption fundamentally +you can calculate the absorption + + align:start position:0% +you can calculate the absorption + + + align:start position:0% +you can calculate the absorption +coefficient of material using this + + align:start position:0% +coefficient of material using this + + + align:start position:0% +coefficient of material using this +approach and uh um now once I have the + + align:start position:0% +approach and uh um now once I have the + + + align:start position:0% +approach and uh um now once I have the +uh uh electron lift create a hole and + + align:start position:0% +uh uh electron lift create a hole and + + + align:start position:0% +uh uh electron lift create a hole and +the electron hole in the valance band + + align:start position:0% +the electron hole in the valance band + + + align:start position:0% +the electron hole in the valance band +and electron in the conduction B and if + + align:start position:0% +and electron in the conduction B and if + + + align:start position:0% +and electron in the conduction B and if +you look at can get it right yeah I want + + align:start position:0% +you look at can get it right yeah I want + + + align:start position:0% +you look at can get it right yeah I want +the solar cell I want to make a solar + + align:start position:0% +the solar cell I want to make a solar + + + align:start position:0% +the solar cell I want to make a solar +cell and the energy of the electron hole + + align:start position:0% +cell and the energy of the electron hole + + + align:start position:0% +cell and the energy of the electron hole +are here and of course you want take + + align:start position:0% +are here and of course you want take + + + align:start position:0% +are here and of course you want take +this energy out to the + + align:start position:0% +this energy out to the + + + align:start position:0% +this energy out to the +electrod then it's a competition + + align:start position:0% +electrod then it's a competition + + + align:start position:0% +electrod then it's a competition +reprocess because if I think about here + + align:start position:0% +reprocess because if I think about here + + + align:start position:0% +reprocess because if I think about here +right I have electron and I have a hole + + align:start position:0% +right I have electron and I have a hole + + + align:start position:0% +right I have electron and I have a hole +it turns out there are different + + align:start position:0% +it turns out there are different + + + align:start position:0% +it turns out there are different +possibilities and of course in the solar + + align:start position:0% +possibilities and of course in the solar + + + align:start position:0% +possibilities and of course in the solar +cell what happens you create a gradient + + align:start position:0% +cell what happens you create a gradient + + + align:start position:0% +cell what happens you create a gradient +of this charge carrier and they will + + align:start position:0% +of this charge carrier and they will + + + align:start position:0% +of this charge carrier and they will +diffuse towards the electrode but that + + align:start position:0% +diffuse towards the electrode but that + + + align:start position:0% +diffuse towards the electrode but that +takes time right any say it takes time + + align:start position:0% +takes time right any say it takes time + + + align:start position:0% +takes time right any say it takes time +to for this diffusion to happen and in + + align:start position:0% +to for this diffusion to happen and in + + + align:start position:0% +to for this diffusion to happen and in +the process the excess energy of the + + align:start position:0% +the process the excess energy of the + + + align:start position:0% +the process the excess energy of the +electron because the electron fullon + + align:start position:0% +electron because the electron fullon + + + align:start position:0% +electron because the electron fullon +scattering that's the one that we + + align:start position:0% +scattering that's the one that we + + + align:start position:0% +scattering that's the one that we +treated you can go to for example PL in + + align:start position:0% +treated you can go to for example PL in + + + align:start position:0% +treated you can go to for example PL in +typical Lumbers and the electron Fon + + align:start position:0% +typical Lumbers and the electron Fon + + + align:start position:0% +typical Lumbers and the electron Fon +scattering is very fast so it's hard to + + align:start position:0% +scattering is very fast so it's hard to + + + align:start position:0% +scattering is very fast so it's hard to +actually get the energy out directly and + + align:start position:0% +actually get the energy out directly and + + + align:start position:0% +actually get the energy out directly and +they will relax to the bottom and this + + align:start position:0% +they will relax to the bottom and this + + + align:start position:0% +they will relax to the bottom and this +is a if you can extract this electron + + align:start position:0% +is a if you can extract this electron + + + align:start position:0% +is a if you can extract this electron +energy before they relax to the bottom + + align:start position:0% +energy before they relax to the bottom + + + align:start position:0% +energy before they relax to the bottom +there's some idea people tried in the + + align:start position:0% +there's some idea people tried in the + + + align:start position:0% +there's some idea people tried in the +past lot of people reading this is hot + + align:start position:0% +past lot of people reading this is hot + + + align:start position:0% +past lot of people reading this is hot +electron right the electron still hot + + align:start position:0% +electron right the electron still hot + + + align:start position:0% +electron right the electron still hot +and uh if you can extract them those are + + align:start position:0% +and uh if you can extract them those are + + + align:start position:0% +and uh if you can extract them those are +hot electron cells people reading in the + + align:start position:0% +hot electron cells people reading in the + + + align:start position:0% +hot electron cells people reading in the +70s nobody has really realize + + align:start position:0% +70s nobody has really realize + + + align:start position:0% +70s nobody has really realize +conceptually is possible nobody has + + align:start position:0% +conceptually is possible nobody has + + + align:start position:0% +conceptually is possible nobody has +really realized and the benefit the S + + align:start position:0% +really realized and the benefit the S + + + align:start position:0% +really realized and the benefit the S +cell so similarly the holes will relax + + align:start position:0% +cell so similarly the holes will relax + + + align:start position:0% +cell so similarly the holes will relax +right and once they got here + + align:start position:0% +right and once they got here + + + align:start position:0% +right and once they got here +then you have the possibility so + + align:start position:0% +then you have the possibility so + + + align:start position:0% +then you have the possibility so +electron and hole will recombine and + + align:start position:0% +electron and hole will recombine and + + + align:start position:0% +electron and hole will recombine and +give off the energy uh and you can have + + align:start position:0% +give off the energy uh and you can have + + + align:start position:0% +give off the energy uh and you can have +two recombination process one is emit H + + align:start position:0% +two recombination process one is emit H + + + align:start position:0% +two recombination process one is emit H +new this is + + align:start position:0% + + + + align:start position:0% + +radiative so R to + + align:start position:0% +radiative so R to + + + align:start position:0% +radiative so R to +recombination right and the other + + align:start position:0% +recombination right and the other + + + align:start position:0% +recombination right and the other +possibility is actually give + + align:start position:0% +possibility is actually give + + + align:start position:0% +possibility is actually give +us a lot of Fons + + align:start position:0% +us a lot of Fons + + + align:start position:0% +us a lot of Fons +right again this is H Omega I just say + + align:start position:0% +right again this is H Omega I just say + + + align:start position:0% +right again this is H Omega I just say +it's still H new but the Fon vibrational + + align:start position:0% +it's still H new but the Fon vibrational + + + align:start position:0% +it's still H new but the Fon vibrational +energy is much smaller right so the bank + + align:start position:0% +energy is much smaller right so the bank + + + align:start position:0% +energy is much smaller right so the bank +Gap energies is usually larger so this + + align:start position:0% +Gap energies is usually larger so this + + + align:start position:0% +Gap energies is usually larger so this +typically will involve + + align:start position:0% +typically will involve + + + align:start position:0% +typically will involve +multi right mod foron processes so uh + + align:start position:0% +multi right mod foron processes so uh + + + align:start position:0% +multi right mod foron processes so uh +this is a long R here + + align:start position:0% + + + + align:start position:0% + +okay so you have red L red recombination + + align:start position:0% +okay so you have red L red recombination + + + align:start position:0% +okay so you have red L red recombination +and of course if you say you want to + + align:start position:0% +and of course if you say you want to + + + align:start position:0% +and of course if you say you want to +make a laser for example you want the + + align:start position:0% +make a laser for example you want the + + + align:start position:0% +make a laser for example you want the +redtive rec combination you don't want + + align:start position:0% +redtive rec combination you don't want + + + align:start position:0% +redtive rec combination you don't want +to lose this you want to extract the + + align:start position:0% +to lose this you want to extract the + + + align:start position:0% +to lose this you want to extract the +energy as photons right it turns out + + align:start position:0% +energy as photons right it turns out + + + align:start position:0% +energy as photons right it turns out +that even you want to make a solar cell + + align:start position:0% +that even you want to make a solar cell + + + align:start position:0% +that even you want to make a solar cell +as we will talk today you want this R + + align:start position:0% +as we will talk today you want this R + + + align:start position:0% +as we will talk today you want this R +recombination other than non R + + align:start position:0% +recombination other than non R + + + align:start position:0% +recombination other than non R +recombination and uh but this even this + + align:start position:0% +recombination and uh but this even this + + + align:start position:0% +recombination and uh but this even this +is not all representative of all the + + align:start position:0% +is not all representative of all the + + + align:start position:0% +is not all representative of all the +possibilities one other possibility is + + align:start position:0% +possibilities one other possibility is + + + align:start position:0% +possibilities one other possibility is +that now I have a electron here I have + + align:start position:0% +that now I have a electron here I have + + + align:start position:0% +that now I have a electron here I have +hole here and they interact of course + + align:start position:0% +hole here and they interact of course + + + align:start position:0% +hole here and they interact of course +they release their + + align:start position:0% +they release their + + + align:start position:0% +they release their +energy and uh in this process they don't + + align:start position:0% +energy and uh in this process they don't + + + align:start position:0% +energy and uh in this process they don't +release to Photon they don't release to + + align:start position:0% +release to Photon they don't release to + + + align:start position:0% +release to Photon they don't release to +Fon they give their energy to Le labor + + align:start position:0% +Fon they give their energy to Le labor + + + align:start position:0% +Fon they give their energy to Le labor +electron and so what they happen is this + + align:start position:0% +electron and so what they happen is this + + + align:start position:0% +electron and so what they happen is this +energy is K the electron here uh to a + + align:start position:0% +energy is K the electron here uh to a + + + align:start position:0% +energy is K the electron here uh to a +higher energy + + align:start position:0% +higher energy + + + align:start position:0% +higher energy +State okay and again you know you don't + + align:start position:0% +State okay and again you know you don't + + + align:start position:0% +State okay and again you know you don't +like this one because once the energy + + align:start position:0% +like this one because once the energy + + + align:start position:0% +like this one because once the energy +this electron gets to higher energy + + align:start position:0% +this electron gets to higher energy + + + align:start position:0% +this electron gets to higher energy +State you will relax quickly back so + + align:start position:0% +State you will relax quickly back so + + + align:start position:0% +State you will relax quickly back so +that excess energy is lost again to the + + align:start position:0% +that excess energy is lost again to the + + + align:start position:0% +that excess energy is lost again to the +Fon because of this process right unless + + align:start position:0% +Fon because of this process right unless + + + align:start position:0% +Fon because of this process right unless +you can like I said extract the hot + + align:start position:0% +you can like I said extract the hot + + + align:start position:0% +you can like I said extract the hot +electron out and this is the OG process + + align:start position:0% + + + + align:start position:0% + +o + + align:start position:0% + + + + align:start position:0% + +combination + + align:start position:0% +combination + + + align:start position:0% +combination +okay so there are uh all those processes + + align:start position:0% +okay so there are uh all those processes + + + align:start position:0% +okay so there are uh all those processes +in theory you can go to describe using + + align:start position:0% +in theory you can go to describe using + + + align:start position:0% +in theory you can go to describe using +the quantum mechanical scattering Matrix + + align:start position:0% +the quantum mechanical scattering Matrix + + + align:start position:0% +the quantum mechanical scattering Matrix +method and write it down and and the uh + + align:start position:0% +method and write it down and and the uh + + + align:start position:0% +method and write it down and and the uh +say uh calculate this scattering + + align:start position:0% +say uh calculate this scattering + + + align:start position:0% +say uh calculate this scattering +rate so if I uh write the BS equation uh + + align:start position:0% +rate so if I uh write the BS equation uh + + + align:start position:0% +rate so if I uh write the BS equation uh +say so this scatter term is a lot more + + align:start position:0% +say so this scatter term is a lot more + + + align:start position:0% +say so this scatter term is a lot more +complex right so before we just use the + + align:start position:0% +complex right so before we just use the + + + align:start position:0% +complex right so before we just use the +um uh say relaxation time approximation + + align:start position:0% +um uh say relaxation time approximation + + + align:start position:0% +um uh say relaxation time approximation +and now you can say I have really for + + align:start position:0% +and now you can say I have really for + + + align:start position:0% +and now you can say I have really for +example I can have uh scatter really + + align:start position:0% +example I can have uh scatter really + + + align:start position:0% +example I can have uh scatter really +electron Fon right this could be + + align:start position:0% +electron Fon right this could be + + + align:start position:0% +electron Fon right this could be +electron Fon scatter I could also have + + align:start position:0% +electron Fon scatter I could also have + + + align:start position:0% +electron Fon scatter I could also have +uh say generation + + align:start position:0% +uh say generation + + + align:start position:0% +uh say generation +right if I have Photon comes in that + + align:start position:0% +right if I have Photon comes in that + + + align:start position:0% +right if I have Photon comes in that +will generate electron hold pairish + + align:start position:0% +will generate electron hold pairish + + + align:start position:0% +will generate electron hold pairish +depends on what carrier you car car say + + align:start position:0% +depends on what carrier you car car say + + + align:start position:0% +depends on what carrier you car car say +considering and uh uh then I have + + align:start position:0% +considering and uh uh then I have + + + align:start position:0% +considering and uh uh then I have +recombination R Rec or long R here all + + align:start position:0% +recombination R Rec or long R here all + + + align:start position:0% +recombination R Rec or long R here all +those are + + align:start position:0% +those are + + + align:start position:0% +those are +possible and this is on the right hand + + align:start position:0% +possible and this is on the right hand + + + align:start position:0% +possible and this is on the right hand +side of the B equation right on the left + + align:start position:0% +side of the B equation right on the left + + + align:start position:0% +side of the B equation right on the left +hand + + align:start position:0% +hand + + + align:start position:0% +hand +side is the transport + + align:start position:0% +side is the transport + + + align:start position:0% +side is the transport +is the + + align:start position:0% +is the + + + align:start position:0% +is the +diffusion and the moving under electric + + align:start position:0% +diffusion and the moving under electric + + + align:start position:0% +diffusion and the moving under electric +field right so at the end I have a + + align:start position:0% +field right so at the end I have a + + + align:start position:0% +field right so at the end I have a +coupling of the energy conversion you + + align:start position:0% +coupling of the energy conversion you + + + align:start position:0% +coupling of the energy conversion you +can think that's the right hand side + + align:start position:0% +can think that's the right hand side + + + align:start position:0% +can think that's the right hand side +right hand side bman equation and uh the + + align:start position:0% +right hand side bman equation and uh the + + + align:start position:0% +right hand side bman equation and uh the +transport is on the left hand side of + + align:start position:0% +transport is on the left hand side of + + + align:start position:0% +transport is on the left hand side of +the equation and there is the competion + + align:start position:0% +the equation and there is the competion + + + align:start position:0% +the equation and there is the competion +uh if you want to extract the useful + + align:start position:0% +uh if you want to extract the useful + + + align:start position:0% +uh if you want to extract the useful +energy out to the + + align:start position:0% +energy out to the + + + align:start position:0% +energy out to the +electrod so uh uh + + align:start position:0% +electrod so uh uh + + + align:start position:0% +electrod so uh uh +just in terms of + + align:start position:0% +just in terms of + + + align:start position:0% +just in terms of +terminology a little bit Sid track uh + + align:start position:0% +terminology a little bit Sid track uh + + + align:start position:0% +terminology a little bit Sid track uh +one terminology if you do uh solar cells + + align:start position:0% +one terminology if you do uh solar cells + + + align:start position:0% +one terminology if you do uh solar cells +you do lasers uh one terminology that's + + align:start position:0% +you do lasers uh one terminology that's + + + align:start position:0% +you do lasers uh one terminology that's +used often is called Quantum efficiency + + align:start position:0% +used often is called Quantum efficiency + + + align:start position:0% +used often is called Quantum efficiency +so what does Quantum efficiency mean so + + align:start position:0% +so what does Quantum efficiency mean so + + + align:start position:0% +so what does Quantum efficiency mean so +just a as + + align:start position:0% + + + + align:start position:0% + +definition and this are all engineering + + align:start position:0% +definition and this are all engineering + + + align:start position:0% +definition and this are all engineering +language at the end because uh + + align:start position:0% +language at the end because uh + + + align:start position:0% +language at the end because uh +to do this calculation you can see + + align:start position:0% +to do this calculation you can see + + + align:start position:0% +to do this calculation you can see +already it's very much very involved + + align:start position:0% +already it's very much very involved + + + align:start position:0% +already it's very much very involved +right so uh uh see the quantum + + align:start position:0% +right so uh uh see the quantum + + + align:start position:0% +right so uh uh see the quantum +efficiency is depends on what I'm making + + align:start position:0% +efficiency is depends on what I'm making + + + align:start position:0% +efficiency is depends on what I'm making +whether I'm making a laser or solar + + align:start position:0% +whether I'm making a laser or solar + + + align:start position:0% +whether I'm making a laser or solar +cell right so if I'm making for example + + align:start position:0% +cell right so if I'm making for example + + + align:start position:0% +cell right so if I'm making for example +uh laser what I want if I make a + + align:start position:0% +uh laser what I want if I make a + + + align:start position:0% +uh laser what I want if I make a +laser for example I want photons right + + align:start position:0% +laser for example I want photons right + + + align:start position:0% +laser for example I want photons right +and uh I inject a current which means I + + align:start position:0% +and uh I inject a current which means I + + + align:start position:0% +and uh I inject a current which means I +inject the electron ho + + align:start position:0% +inject the electron ho + + + align:start position:0% +inject the electron ho +pairs right and one pair of electron + + align:start position:0% +pairs right and one pair of electron + + + align:start position:0% +pairs right and one pair of electron +hole I inject into device in theory + + align:start position:0% +hole I inject into device in theory + + + align:start position:0% +hole I inject into device in theory +perfectly what do you want you want to + + align:start position:0% +perfectly what do you want you want to + + + align:start position:0% +perfectly what do you want you want to +get a one Photon out right so this is + + align:start position:0% +get a one Photon out right so this is + + + align:start position:0% +get a one Photon out right so this is +the Quantum efficiency is uh the Lum of + + align:start position:0% +the Quantum efficiency is uh the Lum of + + + align:start position:0% +the Quantum efficiency is uh the Lum of +photon you get versus Lum of electron + + align:start position:0% +photon you get versus Lum of electron + + + align:start position:0% +photon you get versus Lum of electron +hole you + + align:start position:0% + + + + align:start position:0% + +inject + + align:start position:0% +inject + + + align:start position:0% +inject +right and this is a + + align:start position:0% +right and this is a + + + align:start position:0% +right and this is a +laser or uh say LED now if you use solar + + align:start position:0% +laser or uh say LED now if you use solar + + + align:start position:0% +laser or uh say LED now if you use solar +cell it's a + + align:start position:0% +cell it's a + + + align:start position:0% +cell it's a +reverse right you have one Photon comes + + align:start position:0% +reverse right you have one Photon comes + + + align:start position:0% +reverse right you have one Photon comes +in you want to extract one pair of + + align:start position:0% +in you want to extract one pair of + + + align:start position:0% +in you want to extract one pair of +electron + + align:start position:0% +electron + + + align:start position:0% +electron +holes and uh + + align:start position:0% +holes and uh + + + align:start position:0% +holes and uh +so uh one electron hole pi + + align:start position:0% +so uh one electron hole pi + + + align:start position:0% +so uh one electron hole pi +and one + + align:start position:0% + + + + align:start position:0% + +Photon so this is a solar cell + + align:start position:0% + + + + align:start position:0% + +right and this is quantum + + align:start position:0% +right and this is quantum + + + align:start position:0% +right and this is quantum +efficiency then you read the literature + + align:start position:0% +efficiency then you read the literature + + + align:start position:0% +efficiency then you read the literature +sometime people say what's the external + + align:start position:0% +sometime people say what's the external + + + align:start position:0% +sometime people say what's the external +Quantum efficiency what's the internal + + align:start position:0% +Quantum efficiency what's the internal + + + align:start position:0% +Quantum efficiency what's the internal +Quantum + + align:start position:0% +Quantum + + + align:start position:0% +Quantum +efficiency right so you have + + align:start position:0% +efficiency right so you have + + + align:start position:0% +efficiency right so you have +external you have internal Quantum + + align:start position:0% +external you have internal Quantum + + + align:start position:0% +external you have internal Quantum +efficiency and what talking about is say + + align:start position:0% +efficiency and what talking about is say + + + align:start position:0% +efficiency and what talking about is say +for example uh you make a device make a + + align:start position:0% +for example uh you make a device make a + + + align:start position:0% +for example uh you make a device make a +solar cell you have electrode right what + + align:start position:0% +solar cell you have electrode right what + + + align:start position:0% +solar cell you have electrode right what +can actually be going to the electrode + + align:start position:0% +can actually be going to the electrode + + + align:start position:0% +can actually be going to the electrode +that's externally but how many electron + + align:start position:0% +that's externally but how many electron + + + align:start position:0% +that's externally but how many electron +whole pairs stady state that you have + + align:start position:0% +whole pairs stady state that you have + + + align:start position:0% +whole pairs stady state that you have +inside right the device that's an + + align:start position:0% +inside right the device that's an + + + align:start position:0% +inside right the device that's an +internal so you have a difference + + align:start position:0% +internal so you have a difference + + + align:start position:0% +internal so you have a difference +between internal and external quum + + align:start position:0% +between internal and external quum + + + align:start position:0% +between internal and external quum +efficiency + + align:start position:0% +efficiency + + + align:start position:0% +efficiency +and people use this to + + align:start position:0% +and people use this to + + + align:start position:0% +and people use this to +characterize uh uh how effective because + + align:start position:0% +characterize uh uh how effective because + + + align:start position:0% +characterize uh uh how effective because +say normally we think one pair of uh uh + + align:start position:0% +say normally we think one pair of uh uh + + + align:start position:0% +say normally we think one pair of uh uh +say uh electron hole will generally one + + align:start position:0% +say uh electron hole will generally one + + + align:start position:0% +say uh electron hole will generally one +pair Photon or + + align:start position:0% +pair Photon or + + + align:start position:0% +pair Photon or +Versa however recently if you read + + align:start position:0% +Versa however recently if you read + + + align:start position:0% +Versa however recently if you read +literature there are some people saying + + align:start position:0% +literature there are some people saying + + + align:start position:0% +literature there are some people saying +I have Quantum efficiency larger than + + align:start position:0% +I have Quantum efficiency larger than + + + align:start position:0% +I have Quantum efficiency larger than +one what does that mean right + + align:start position:0% +one what does that mean right + + + align:start position:0% +one what does that mean right +so this is when you think about that you + + align:start position:0% +so this is when you think about that you + + + align:start position:0% +so this is when you think about that you +want to make uh let's + + align:start position:0% +want to make uh let's + + + align:start position:0% +want to make uh let's +suppose I have Bank + + align:start position:0% +suppose I have Bank + + + align:start position:0% +suppose I have Bank +Gap + + align:start position:0% +Gap + + + align:start position:0% +Gap +here right and I + + align:start position:0% +here right and I + + + align:start position:0% +here right and I +have very high energy Photon comes + + align:start position:0% +have very high energy Photon comes + + + align:start position:0% +have very high energy Photon comes +in okay and very high energy Photon so + + align:start position:0% +in okay and very high energy Photon so + + + align:start position:0% +in okay and very high energy Photon so +this is a electron this is a hole and + + align:start position:0% +this is a electron this is a hole and + + + align:start position:0% +this is a electron this is a hole and +generate say high energy electron and a + + align:start position:0% +generate say high energy electron and a + + + align:start position:0% +generate say high energy electron and a +hole in the band and if you're lucky + + align:start position:0% +hole in the band and if you're lucky + + + align:start position:0% +hole in the band and if you're lucky +right this are all the different rate + + align:start position:0% +right this are all the different rate + + + align:start position:0% +right this are all the different rate +process this + + align:start position:0% +process this + + + align:start position:0% +process this +electron when relaxed down it does not + + align:start position:0% +electron when relaxed down it does not + + + align:start position:0% +electron when relaxed down it does not +interact with the + + align:start position:0% +interact with the + + + align:start position:0% +interact with the +Fon it will actually give the access say + + align:start position:0% +Fon it will actually give the access say + + + align:start position:0% +Fon it will actually give the access say +uh energy to lift another electron out + + align:start position:0% +uh energy to lift another electron out + + + align:start position:0% +uh energy to lift another electron out +of the valance + + align:start position:0% +of the valance + + + align:start position:0% +of the valance +band to the conduction + + align:start position:0% +band to the conduction + + + align:start position:0% +band to the conduction +band right of course that means this en + + align:start position:0% +band right of course that means this en + + + align:start position:0% +band right of course that means this en +electron energy has to be larger then + + align:start position:0% +electron energy has to be larger then + + + align:start position:0% +electron energy has to be larger then +the bank Gap otherwise that's + + align:start position:0% +the bank Gap otherwise that's + + + align:start position:0% +the bank Gap otherwise that's +impossible right and that's multicarrier + + align:start position:0% +impossible right and that's multicarrier + + + align:start position:0% +impossible right and that's multicarrier +multiple so one for in this case + + align:start position:0% +multiple so one for in this case + + + align:start position:0% +multiple so one for in this case +effectively one Photon comes in it + + align:start position:0% +effectively one Photon comes in it + + + align:start position:0% +effectively one Photon comes in it +generate more than one electron hold + + align:start position:0% +generate more than one electron hold + + + align:start position:0% +generate more than one electron hold +pairish and uh uh in of course you would + + align:start position:0% +pairish and uh uh in of course you would + + + align:start position:0% +pairish and uh uh in of course you would +love to have that when you try to make a + + align:start position:0% +love to have that when you try to make a + + + align:start position:0% +love to have that when you try to make a +solar cell because that's the uh um + + align:start position:0% +solar cell because that's the uh um + + + align:start position:0% +solar cell because that's the uh um +people to call this multi aiton + + align:start position:0% +people to call this multi aiton + + + align:start position:0% +people to call this multi aiton +generation okay and here you can say you + + align:start position:0% +generation okay and here you can say you + + + align:start position:0% +generation okay and here you can say you +have to compete against the different + + align:start position:0% +have to compete against the different + + + align:start position:0% +have to compete against the different +rate right otherwise they if they fall + + align:start position:0% +rate right otherwise they if they fall + + + align:start position:0% +rate right otherwise they if they fall +on suck the energy + + align:start position:0% +on suck the energy + + + align:start position:0% +on suck the energy +away and you can't have that multi-acid + + align:start position:0% +away and you can't have that multi-acid + + + align:start position:0% +away and you can't have that multi-acid +whether that happens there are lot of + + align:start position:0% +whether that happens there are lot of + + + align:start position:0% +whether that happens there are lot of +fight in the scientific Community + + align:start position:0% +fight in the scientific Community + + + align:start position:0% +fight in the scientific Community +because some people claim they have seen + + align:start position:0% +because some people claim they have seen + + + align:start position:0% +because some people claim they have seen +very high multi exiton Generations or + + align:start position:0% +very high multi exiton Generations or + + + align:start position:0% +very high multi exiton Generations or +other people I just run Professor m b + + align:start position:0% +other people I just run Professor m b + + + align:start position:0% +other people I just run Professor m b +and he was involved in this debate on + + align:start position:0% +and he was involved in this debate on + + + align:start position:0% +and he was involved in this debate on +whether the multi exiton generation is + + align:start position:0% +whether the multi exiton generation is + + + align:start position:0% +whether the multi exiton generation is +indeed happening or not + + align:start position:0% + + + + align:start position:0% + +okay so uh that's uh say just the some + + align:start position:0% +okay so uh that's uh say just the some + + + align:start position:0% +okay so uh that's uh say just the some +side track track in terms of definitions + + align:start position:0% +side track track in terms of definitions + + + align:start position:0% +side track track in terms of definitions +but say coming back to the BSM + + align:start position:0% +but say coming back to the BSM + + + align:start position:0% +but say coming back to the BSM +equation right now say uh we said that + + align:start position:0% +equation right now say uh we said that + + + align:start position:0% +equation right now say uh we said that +on the right hand side you can have + + align:start position:0% +on the right hand side you can have + + + align:start position:0% +on the right hand side you can have +multiple terms on the left hand side is + + align:start position:0% +multiple terms on the left hand side is + + + align:start position:0% +multiple terms on the left hand side is +a standard uh say diffusion drift or see + + align:start position:0% +a standard uh say diffusion drift or see + + + align:start position:0% +a standard uh say diffusion drift or see +in the case of no size effect and when + + align:start position:0% +in the case of no size effect and when + + + align:start position:0% +in the case of no size effect and when +there size effect I have to do pass + + align:start position:0% +there size effect I have to do pass + + + align:start position:0% +there size effect I have to do pass +integral as we solve this B equation + + align:start position:0% +integral as we solve this B equation + + + align:start position:0% +integral as we solve this B equation +right so what I'm going to introduce are + + align:start position:0% +right so what I'm going to introduce are + + + align:start position:0% +right so what I'm going to introduce are +different + + align:start position:0% +different + + + align:start position:0% +different +forms and uh if I talk about electron + + align:start position:0% +forms and uh if I talk about electron + + + align:start position:0% +forms and uh if I talk about electron +right so for example when you have a + + align:start position:0% +right so for example when you have a + + + align:start position:0% +right so for example when you have a +metal and you have laser comes in very + + align:start position:0% +metal and you have laser comes in very + + + align:start position:0% +metal and you have laser comes in very +fast + + align:start position:0% +fast + + + align:start position:0% +fast +laser and uh what happens the laser + + align:start position:0% +laser and uh what happens the laser + + + align:start position:0% +laser and uh what happens the laser +energy is in the case of photon comes + + align:start position:0% +energy is in the case of photon comes + + + align:start position:0% +energy is in the case of photon comes +into metal is used to lift energy of the + + align:start position:0% +into metal is used to lift energy of the + + + align:start position:0% +into metal is used to lift energy of the +electron it's the electron absorption + + align:start position:0% +electron it's the electron absorption + + + align:start position:0% +electron it's the electron absorption +right so that's the first step of the + + align:start position:0% +right so that's the first step of the + + + align:start position:0% +right so that's the first step of the +interaction and uh once the energy of + + align:start position:0% +interaction and uh once the energy of + + + align:start position:0% +interaction and uh once the energy of +the electron lifted to very high + + align:start position:0% +the electron lifted to very high + + + align:start position:0% +the electron lifted to very high +temperature you can see this is really + + align:start position:0% +temperature you can see this is really + + + align:start position:0% +temperature you can see this is really +even electron itself is a long + + align:start position:0% +even electron itself is a long + + + align:start position:0% +even electron itself is a long +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +processess right because the laser + + align:start position:0% +processess right because the laser + + + align:start position:0% +processess right because the laser +frequency is fixed and if I think about + + align:start position:0% +frequency is fixed and if I think about + + + align:start position:0% +frequency is fixed and if I think about +uh typical + + align:start position:0% +uh typical + + + align:start position:0% +uh typical +electronic right uh energy level this is + + align:start position:0% +electronic right uh energy level this is + + + align:start position:0% +electronic right uh energy level this is +a firment level this is a + + align:start position:0% +a firment level this is a + + + align:start position:0% +a firment level this is a +band and electron can be lifted to very + + align:start position:0% +band and electron can be lifted to very + + + align:start position:0% +band and electron can be lifted to very +high + + align:start position:0% +high + + + align:start position:0% +high +energy and but say uh it's not even in + + align:start position:0% +energy and but say uh it's not even in + + + align:start position:0% +energy and but say uh it's not even in +equiv with + + align:start position:0% +equiv with + + + align:start position:0% +equiv with +cell however electron electron + + align:start position:0% +cell however electron electron + + + align:start position:0% +cell however electron electron +interaction itself is very fast because + + align:start position:0% +interaction itself is very fast because + + + align:start position:0% +interaction itself is very fast because +that's a coolum interaction it's a force + + align:start position:0% +that's a coolum interaction it's a force + + + align:start position:0% +that's a coolum interaction it's a force +right it's a speed of + + align:start position:0% +right it's a speed of + + + align:start position:0% +right it's a speed of +light and uh electric field so uh say + + align:start position:0% +light and uh electric field so uh say + + + align:start position:0% +light and uh electric field so uh say +electron themselves critically get + + align:start position:0% +electron themselves critically get + + + align:start position:0% +electron themselves critically get +calized with each other so effectively + + align:start position:0% +calized with each other so effectively + + + align:start position:0% +calized with each other so effectively +you can say electron has a effective + + align:start position:0% +you can say electron has a effective + + + align:start position:0% +you can say electron has a effective +temperature that's + + align:start position:0% +temperature that's + + + align:start position:0% +temperature that's +approximation right and in fact in + + align:start position:0% +approximation right and in fact in + + + align:start position:0% +approximation right and in fact in +literature there are debate whether + + align:start position:0% +literature there are debate whether + + + align:start position:0% +literature there are debate whether +electron how fast it is to get a uniform + + align:start position:0% +electron how fast it is to get a uniform + + + align:start position:0% +electron how fast it is to get a uniform +temperature between + + align:start position:0% +temperature between + + + align:start position:0% +temperature between +electrons let's suppose if you use that + + align:start position:0% +electrons let's suppose if you use that + + + align:start position:0% +electrons let's suppose if you use that +electron temperature right so you have + + align:start position:0% +electron temperature right so you have + + + align:start position:0% +electron temperature right so you have +electron temperature and they are not + + align:start position:0% +electron temperature and they are not + + + align:start position:0% +electron temperature and they are not +the same as the Fon temperature and + + align:start position:0% +the same as the Fon temperature and + + + align:start position:0% +the same as the Fon temperature and +that's where we + + align:start position:0% +that's where we + + + align:start position:0% +that's where we +have right electron fong in + + align:start position:0% +have right electron fong in + + + align:start position:0% +have right electron fong in +interaction and at the same time the + + align:start position:0% +interaction and at the same time the + + + align:start position:0% +interaction and at the same time the +transfer right so if you go to start + + align:start position:0% +transfer right so if you go to start + + + align:start position:0% +transfer right so if you go to start +from the boards my equation write in + + align:start position:0% +from the boards my equation write in + + + align:start position:0% +from the boards my equation write in +these two terms and then you manipulate + + align:start position:0% +these two terms and then you manipulate + + + align:start position:0% +these two terms and then you manipulate +the + + align:start position:0% +the + + + align:start position:0% +the +equation and this is a similar when you + + align:start position:0% +equation and this is a similar when you + + + align:start position:0% +equation and this is a similar when you +read chapter six and when we uh I I + + align:start position:0% +read chapter six and when we uh I I + + + align:start position:0% +read chapter six and when we uh I I +didn't go through you could do the I + + align:start position:0% +didn't go through you could do the I + + + align:start position:0% +didn't go through you could do the I +said you can derive conservation + + align:start position:0% +said you can derive conservation + + + align:start position:0% +said you can derive conservation +equations right so you can go through + + align:start position:0% +equations right so you can go through + + + align:start position:0% +equations right so you can go through +that process and what you happen What + + align:start position:0% +that process and what you happen What + + + align:start position:0% +that process and what you happen What +You Get is some equations like uh uh you + + align:start position:0% +You Get is some equations like uh uh you + + + align:start position:0% +You Get is some equations like uh uh you +can write the electron temperature this + + align:start position:0% +can write the electron temperature this + + + align:start position:0% +can write the electron temperature this +is a model that you can derive from bman + + align:start position:0% +is a model that you can derive from bman + + + align:start position:0% +is a model that you can derive from bman +equation with a lot of assumptions okay + + align:start position:0% +equation with a lot of assumptions okay + + + align:start position:0% +equation with a lot of assumptions okay +again so and what uh say here I have the + + align:start position:0% +again so and what uh say here I have the + + + align:start position:0% +again so and what uh say here I have the +standard diffusion + + align:start position:0% +standard diffusion + + + align:start position:0% +standard diffusion +equation right this is the fal law for + + align:start position:0% +equation right this is the fal law for + + + align:start position:0% +equation right this is the fal law for +electron + + align:start position:0% +electron + + + align:start position:0% +electron +diffusion and uh uh and then say I have + + align:start position:0% +diffusion and uh uh and then say I have + + + align:start position:0% +diffusion and uh uh and then say I have +now the electron + + align:start position:0% +now the electron + + + align:start position:0% +now the electron +cou to Fon tus TP and that's electron + + align:start position:0% +cou to Fon tus TP and that's electron + + + align:start position:0% +cou to Fon tus TP and that's electron +Fon coupling so it's like + + align:start position:0% +Fon coupling so it's like + + + align:start position:0% +Fon coupling so it's like +a say a convection right say electron + + align:start position:0% +a say a convection right say electron + + + align:start position:0% +a say a convection right say electron +Fon temperature difference times that G + + align:start position:0% +Fon temperature difference times that G + + + align:start position:0% +Fon temperature difference times that G +is like effective heat transfer + + align:start position:0% +is like effective heat transfer + + + align:start position:0% +is like effective heat transfer +coefficient between electron + + align:start position:0% +coefficient between electron + + + align:start position:0% +coefficient between electron +Fons and uh similarly you can write the + + align:start position:0% +Fons and uh similarly you can write the + + + align:start position:0% +Fons and uh similarly you can write the +equation TP and + + align:start position:0% +equation TP and + + + align:start position:0% +equation TP and +dtp DT equals Delta and KP + + align:start position:0% +dtp DT equals Delta and KP + + + align:start position:0% +dtp DT equals Delta and KP +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +TP M plus + + align:start position:0% +TP M plus + + + align:start position:0% +TP M plus +g t TP so Y is losing energy the other + + align:start position:0% +g t TP so Y is losing energy the other + + + align:start position:0% +g t TP so Y is losing energy the other +system is gaining energy the Fon is + + align:start position:0% +system is gaining energy the Fon is + + + align:start position:0% +system is gaining energy the Fon is +gaining energy so you have two different + + align:start position:0% +gaining energy so you have two different + + + align:start position:0% +gaining energy so you have two different +temperature and this is called uh say um + + align:start position:0% +temperature and this is called uh say um + + + align:start position:0% +temperature and this is called uh say um +two temperature model right so you have + + align:start position:0% +two temperature model right so you have + + + align:start position:0% +two temperature model right so you have +electron is either its own equilibrium + + align:start position:0% +electron is either its own equilibrium + + + align:start position:0% +electron is either its own equilibrium +local equili and Fon is are the + + align:start position:0% +local equili and Fon is are the + + + align:start position:0% +local equili and Fon is are the +different and uh uh in fact not of this + + align:start position:0% +different and uh uh in fact not of this + + + align:start position:0% +different and uh uh in fact not of this +for example pump and pro experiment you + + align:start position:0% +for example pump and pro experiment you + + + align:start position:0% +for example pump and pro experiment you +can clearly say a typical signal when + + align:start position:0% +can clearly say a typical signal when + + + align:start position:0% +can clearly say a typical signal when +you do a pump Pro basically you have + + align:start position:0% +you do a pump Pro basically you have + + + align:start position:0% +you do a pump Pro basically you have +laser very fast laser comes in and the + + align:start position:0% +laser very fast laser comes in and the + + + align:start position:0% +laser very fast laser comes in and the +reflectance is a measure of the electron + + align:start position:0% +reflectance is a measure of the electron + + + align:start position:0% +reflectance is a measure of the electron +temperature and in those kind of signal + + align:start position:0% +temperature and in those kind of signal + + + align:start position:0% +temperature and in those kind of signal +you say okay your first the type pulse + + align:start position:0% +you say okay your first the type pulse + + + align:start position:0% +you say okay your first the type pulse +comes in and the temperature change and + + align:start position:0% +comes in and the temperature change and + + + align:start position:0% +comes in and the temperature change and +in this region that's the hot electron + + align:start position:0% +in this region that's the hot electron + + + align:start position:0% +in this region that's the hot electron +region and you can clearly see that in + + align:start position:0% +region and you can clearly see that in + + + align:start position:0% +region and you can clearly see that in +the experiment + + align:start position:0% + + + + align:start position:0% + +okay uh so uh uh and for for this region + + align:start position:0% +okay uh so uh uh and for for this region + + + align:start position:0% +okay uh so uh uh and for for this region +in fact using this model is reasonable + + align:start position:0% +in fact using this model is reasonable + + + align:start position:0% +in fact using this model is reasonable +you can solve the uh two temperature + + align:start position:0% +you can solve the uh two temperature + + + align:start position:0% +you can solve the uh two temperature +model and describe the uh electron phon + + align:start position:0% +model and describe the uh electron phon + + + align:start position:0% +model and describe the uh electron phon +temperature but this is a case of + + align:start position:0% +temperature but this is a case of + + + align:start position:0% +temperature but this is a case of +metal what if I have a + + align:start position:0% +metal what if I have a + + + align:start position:0% +metal what if I have a +semiconductor right so uh uh okay one + + align:start position:0% +semiconductor right so uh uh okay one + + + align:start position:0% +semiconductor right so uh uh okay one +more common for this in fact uh because + + align:start position:0% +more common for this in fact uh because + + + align:start position:0% +more common for this in fact uh because +I like to think about BSM equation no I + + align:start position:0% +I like to think about BSM equation no I + + + align:start position:0% +I like to think about BSM equation no I +have not found anybody solving BSM + + align:start position:0% +have not found anybody solving BSM + + + align:start position:0% +have not found anybody solving BSM +equation for electrons that's one and + + align:start position:0% +equation for electrons that's one and + + + align:start position:0% +equation for electrons that's one and +second I have not found say uh this + + align:start position:0% +second I have not found say uh this + + + align:start position:0% +second I have not found say uh this +equation neglect Thermal electric + + align:start position:0% +equation neglect Thermal electric + + + align:start position:0% +equation neglect Thermal electric +transport right if you look at it here + + align:start position:0% +transport right if you look at it here + + + align:start position:0% +transport right if you look at it here +is the specific heat so internal energy + + align:start position:0% +is the specific heat so internal energy + + + align:start position:0% +is the specific heat so internal energy +and this is a heat conduction and then + + align:start position:0% +and this is a heat conduction and then + + + align:start position:0% +and this is a heat conduction and then +when we do charge we know there is a + + align:start position:0% +when we do charge we know there is a + + + align:start position:0% +when we do charge we know there is a +Thermo Electric term right uh the pelty + + align:start position:0% +Thermo Electric term right uh the pelty + + + align:start position:0% +Thermo Electric term right uh the pelty +term that carries heat So in theory you + + align:start position:0% +term that carries heat So in theory you + + + align:start position:0% +term that carries heat So in theory you +should be writing a modified + + align:start position:0% +should be writing a modified + + + align:start position:0% +should be writing a modified +equation and uh uh uh and say even for + + align:start position:0% +equation and uh uh uh and say even for + + + align:start position:0% +equation and uh uh uh and say even for +the diffusion term there should be + + align:start position:0% +the diffusion term there should be + + + align:start position:0% +the diffusion term there should be +modified term uh this is a diffusion + + align:start position:0% +modified term uh this is a diffusion + + + align:start position:0% +modified term uh this is a diffusion +both are the diffusion right and then + + align:start position:0% +both are the diffusion right and then + + + align:start position:0% +both are the diffusion right and then +you say + + align:start position:0% +you say + + + align:start position:0% +you say +ballistic that's a lot more complicated + + align:start position:0% +ballistic that's a lot more complicated + + + align:start position:0% +ballistic that's a lot more complicated +so you say even those kind of problems + + align:start position:0% +so you say even those kind of problems + + + align:start position:0% +so you say even those kind of problems +uh it's not fully answer now if you go + + align:start position:0% +uh it's not fully answer now if you go + + + align:start position:0% +uh it's not fully answer now if you go +to look at the the next I say you have + + align:start position:0% +to look at the the next I say you have + + + align:start position:0% +to look at the the next I say you have +to know what do you deal with you if I + + align:start position:0% +to know what do you deal with you if I + + + align:start position:0% +to know what do you deal with you if I +give you a piece of metal to do the + + align:start position:0% +give you a piece of metal to do the + + + align:start position:0% +give you a piece of metal to do the +experiment versus I give you a piece of + + align:start position:0% +experiment versus I give you a piece of + + + align:start position:0% +experiment versus I give you a piece of +semiconductor to do the experiment right + + align:start position:0% +semiconductor to do the experiment right + + + align:start position:0% +semiconductor to do the experiment right +so if I have a piece of semiconductor + + align:start position:0% +so if I have a piece of semiconductor + + + align:start position:0% +so if I have a piece of semiconductor +what + + align:start position:0% +what + + + align:start position:0% +what +happens right and uh uh here I have like + + align:start position:0% +happens right and uh uh here I have like + + + align:start position:0% +happens right and uh uh here I have like +comes + + align:start position:0% +comes + + + align:start position:0% +comes +in and uh um semiconductor is more + + align:start position:0% +in and uh um semiconductor is more + + + align:start position:0% +in and uh um semiconductor is more +complicated because uh when my light is + + align:start position:0% +complicated because uh when my light is + + + align:start position:0% +complicated because uh when my light is +above the band Gap + + align:start position:0% +above the band Gap + + + align:start position:0% +above the band Gap +right this is a this is a uh uh electron + + align:start position:0% +right this is a this is a uh uh electron + + + align:start position:0% +right this is a this is a uh uh electron +the + + align:start position:0% +the + + + align:start position:0% +the +hole right so my you can say the first + + align:start position:0% +hole right so my you can say the first + + + align:start position:0% +hole right so my you can say the first +step is I will heat + + align:start position:0% +step is I will heat + + + align:start position:0% +step is I will heat +up generate electron hold Pairs and + + align:start position:0% +up generate electron hold Pairs and + + + align:start position:0% +up generate electron hold Pairs and +electron hold pair quickly cool down so + + align:start position:0% +electron hold pair quickly cool down so + + + align:start position:0% +electron hold pair quickly cool down so +to the + + align:start position:0% +to the + + + align:start position:0% +to the +bottom of the condu balance band and + + align:start position:0% +bottom of the condu balance band and + + + align:start position:0% +bottom of the condu balance band and +then they will recombine that process + + align:start position:0% +then they will recombine that process + + + align:start position:0% +then they will recombine that process +could be much smaller this cooling down + + align:start position:0% +could be much smaller this cooling down + + + align:start position:0% +could be much smaller this cooling down +is is a peak of second recombination in + + align:start position:0% +is is a peak of second recombination in + + + align:start position:0% +is is a peak of second recombination in +different Semiconductor in gum asite + + align:start position:0% +different Semiconductor in gum asite + + + align:start position:0% +different Semiconductor in gum asite +which direct Gap is the + + align:start position:0% +which direct Gap is the + + + align:start position:0% +which direct Gap is the +farest could be + + align:start position:0% +farest could be + + + align:start position:0% +farest could be +lanc so that's already two or three + + align:start position:0% +lanc so that's already two or three + + + align:start position:0% +lanc so that's already two or three +order magnitude + + align:start position:0% +order magnitude + + + align:start position:0% +order magnitude +difference and if you deal with a very + + align:start position:0% +difference and if you deal with a very + + + align:start position:0% +difference and if you deal with a very +good + + align:start position:0% +good + + + align:start position:0% +good +silicon with a say um because silicon is + + align:start position:0% +silicon with a say um because silicon is + + + align:start position:0% +silicon with a say um because silicon is +an indirect Gap right you need four LS + + align:start position:0% +an indirect Gap right you need four LS + + + align:start position:0% +an indirect Gap right you need four LS +to have that process happening so it's + + align:start position:0% +to have that process happening so it's + + + align:start position:0% +to have that process happening so it's +much slower so the recompilation in good + + align:start position:0% +much slower so the recompilation in good + + + align:start position:0% +much slower so the recompilation in good +silicon could be as long as a + + align:start position:0% +silicon could be as long as a + + + align:start position:0% +silicon could be as long as a +second okay very long process so what + + align:start position:0% +second okay very long process so what + + + align:start position:0% +second okay very long process so what +happens now you say okay I will have + + align:start position:0% +happens now you say okay I will have + + + align:start position:0% +happens now you say okay I will have +exponential decay absorption + + align:start position:0% +exponential decay absorption + + + align:start position:0% +exponential decay absorption +coefficient right that's what the + + align:start position:0% +coefficient right that's what the + + + align:start position:0% +coefficient right that's what the +profile of electron hold generation + + align:start position:0% +profile of electron hold generation + + + align:start position:0% +profile of electron hold generation +that's what the + + align:start position:0% +that's what the + + + align:start position:0% +that's what the +absorption but uh if you like you say + + align:start position:0% +absorption but uh if you like you say + + + align:start position:0% +absorption but uh if you like you say +okay if I don't know this this + + align:start position:0% +okay if I don't know this this + + + align:start position:0% +okay if I don't know this this +absorption when I do a heat transfer I + + align:start position:0% +absorption when I do a heat transfer I + + + align:start position:0% +absorption when I do a heat transfer I +would use that as my heat + + align:start position:0% +would use that as my heat + + + align:start position:0% +would use that as my heat +Source right + + align:start position:0% +Source right + + + align:start position:0% +Source right +say I say this is my heat Source + + align:start position:0% +say I say this is my heat Source + + + align:start position:0% +say I say this is my heat Source +distribution which is actually not true + + align:start position:0% +distribution which is actually not true + + + align:start position:0% +distribution which is actually not true +if you think about what's the physics + + align:start position:0% +if you think about what's the physics + + + align:start position:0% +if you think about what's the physics +involved what this absorption just say + + align:start position:0% +involved what this absorption just say + + + align:start position:0% +involved what this absorption just say +I'm generating that electron hole pair + + align:start position:0% +I'm generating that electron hole pair + + + align:start position:0% +I'm generating that electron hole pair +distribution and now electron pair has a + + align:start position:0% +distribution and now electron pair has a + + + align:start position:0% +distribution and now electron pair has a +say the excess + + align:start position:0% +say the excess + + + align:start position:0% +say the excess +energy this part of + + align:start position:0% +energy this part of + + + align:start position:0% +energy this part of +energy right because it happens very + + align:start position:0% +energy right because it happens very + + + align:start position:0% +energy right because it happens very +fast P second so I can say Okay + + align:start position:0% +fast P second so I can say Okay + + + align:start position:0% +fast P second so I can say Okay +immediately this part of energy the + + align:start position:0% +immediately this part of energy the + + + align:start position:0% +immediately this part of energy the +profile is very similar so I can say + + align:start position:0% +profile is very similar so I can say + + + align:start position:0% +profile is very similar so I can say +those part of energies generated at this + + align:start position:0% +those part of energies generated at this + + + align:start position:0% +those part of energies generated at this +exponential de and similarly on the + + align:start position:0% +exponential de and similarly on the + + + align:start position:0% +exponential de and similarly on the +whole side you have this + + align:start position:0% +whole side you have this + + + align:start position:0% +whole side you have this +right but then there is also the other + + align:start position:0% +right but then there is also the other + + + align:start position:0% +right but then there is also the other +path across the + + align:start position:0% +path across the + + + align:start position:0% +path across the +Gap it's not released because there's a + + align:start position:0% +Gap it's not released because there's a + + + align:start position:0% +Gap it's not released because there's a +the it takes time for that recombination + + align:start position:0% +the it takes time for that recombination + + + align:start position:0% +the it takes time for that recombination +and also I have to be careful that + + align:start position:0% +and also I have to be careful that + + + align:start position:0% +and also I have to be careful that +recombination whether it's radiative or + + align:start position:0% +recombination whether it's radiative or + + + align:start position:0% +recombination whether it's radiative or +it's non- radiative + + align:start position:0% +it's non- radiative + + + align:start position:0% +it's non- radiative +right it's R it's long R generate Fons + + align:start position:0% +right it's R it's long R generate Fons + + + align:start position:0% +right it's R it's long R generate Fons +if it's redtive generate another + + align:start position:0% +if it's redtive generate another + + + align:start position:0% +if it's redtive generate another +Photon that propagate again is get + + align:start position:0% +Photon that propagate again is get + + + align:start position:0% +Photon that propagate again is get +reabsorbed again in the material right + + align:start position:0% +reabsorbed again in the material right + + + align:start position:0% +reabsorbed again in the material right +you see + + align:start position:0% +you see + + + align:start position:0% +you see +there okay so uh for so for this part + + align:start position:0% +there okay so uh for so for this part + + + align:start position:0% +there okay so uh for so for this part +that's easy because essentially you can + + align:start position:0% +that's easy because essentially you can + + + align:start position:0% +that's easy because essentially you can +use the time right the uh what we can + + align:start position:0% +use the time right the uh what we can + + + align:start position:0% +use the time right the uh what we can +write is if I have + + align:start position:0% +write is if I have + + + align:start position:0% +write is if I have +uh diffusion right I'm concerned because + + align:start position:0% +uh diffusion right I'm concerned because + + + align:start position:0% +uh diffusion right I'm concerned because +I generate a + + align:start position:0% +I generate a + + + align:start position:0% +I generate a +gradient of electron hold Pairs and they + + align:start position:0% +gradient of electron hold Pairs and they + + + align:start position:0% +gradient of electron hold Pairs and they +were diffus into the material and the uh + + align:start position:0% +were diffus into the material and the uh + + + align:start position:0% +were diffus into the material and the uh +you can write the diffusion equation and + + align:start position:0% +you can write the diffusion equation and + + + align:start position:0% +you can write the diffusion equation and +I let me just do a steady state again + + align:start position:0% +I let me just do a steady state again + + + align:start position:0% +I let me just do a steady state again +you can make depends on your experiment + + align:start position:0% +you can make depends on your experiment + + + align:start position:0% +you can make depends on your experiment +depends on what you're doing so I'm + + align:start position:0% +depends on what you're doing so I'm + + + align:start position:0% +depends on what you're doing so I'm +going to write the diffusion equation + + align:start position:0% +going to write the diffusion equation + + + align:start position:0% +going to write the diffusion equation +diffusivity of this electron hole the + + align:start position:0% +diffusivity of this electron hole the + + + align:start position:0% +diffusivity of this electron hole the +concentration + + align:start position:0% + + + + align:start position:0% + +gradient right let's suppose this is the + + align:start position:0% + + + + align:start position:0% + +X okay and for this + + align:start position:0% +X okay and for this + + + align:start position:0% +X okay and for this +recompilation term here and very often + + align:start position:0% +recompilation term here and very often + + + align:start position:0% +recompilation term here and very often +this can be written as a relaxation time + + align:start position:0% +this can be written as a relaxation time + + + align:start position:0% +this can be written as a relaxation time +term in the bardman equation and this is + + align:start position:0% +term in the bardman equation and this is + + + align:start position:0% +term in the bardman equation and this is +recombination + + align:start position:0% +recombination + + + align:start position:0% +recombination +time the read of + + align:start position:0% +time the read of + + + align:start position:0% +time the read of +recombination okay and you can say you + + align:start position:0% +recombination okay and you can say you + + + align:start position:0% +recombination okay and you can say you +include both redtive or non redtive you + + align:start position:0% +include both redtive or non redtive you + + + align:start position:0% +include both redtive or non redtive you +can distinguish them if you want but I'm + + align:start position:0% +can distinguish them if you want but I'm + + + align:start position:0% +can distinguish them if you want but I'm +just going to just say I'm going to + + align:start position:0% +just going to just say I'm going to + + + align:start position:0% +just going to just say I'm going to +write this as n + + align:start position:0% +write this as n + + + align:start position:0% +write this as n +n0 power equal + + align:start position:0% +n0 power equal + + + align:start position:0% +n0 power equal +Z so what happens is the carrier + + align:start position:0% +Z so what happens is the carrier + + + align:start position:0% +Z so what happens is the carrier +carriers + + align:start position:0% +carriers + + + align:start position:0% +carriers +generated will diffuse and they Rec + + align:start position:0% +generated will diffuse and they Rec + + + align:start position:0% +generated will diffuse and they Rec +combine right it's happening at the same + + align:start position:0% +combine right it's happening at the same + + + align:start position:0% +combine right it's happening at the same +time and uh if this recombination is non + + align:start position:0% +time and uh if this recombination is non + + + align:start position:0% +time and uh if this recombination is non +read here you will gener a trail of heat + + align:start position:0% +read here you will gener a trail of heat + + + align:start position:0% +read here you will gener a trail of heat +Source that's different from the + + align:start position:0% +Source that's different from the + + + align:start position:0% +Source that's different from the +exponential absorption + + align:start position:0% +exponential absorption + + + align:start position:0% +exponential absorption +profile right and uh so uh uh see this + + align:start position:0% +profile right and uh so uh uh see this + + + align:start position:0% +profile right and uh so uh uh see this +diffusion so the diffusion lens right + + align:start position:0% +diffusion so the diffusion lens right + + + align:start position:0% +diffusion so the diffusion lens right +how fast this is spread out then you can + + align:start position:0% +how fast this is spread out then you can + + + align:start position:0% +how fast this is spread out then you can +see this is a standard diffusion + + align:start position:0% +see this is a standard diffusion + + + align:start position:0% +see this is a standard diffusion +equation is the diffusivity times time + + align:start position:0% + + + + align:start position:0% + +okay and the diffusivity if I take a + + align:start position:0% +okay and the diffusivity if I take a + + + align:start position:0% +okay and the diffusivity if I take a +silicon as example and this diffusivity + + align:start position:0% +silicon as example and this diffusivity + + + align:start position:0% +silicon as example and this diffusivity +of + + align:start position:0% +of + + + align:start position:0% +of +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +silicon diffusivity you see I only + + align:start position:0% +silicon diffusivity you see I only + + + align:start position:0% +silicon diffusivity you see I only +remember it could be full full auto + + align:start position:0% +remember it could be full full auto + + + align:start position:0% +remember it could be full full auto +magnit higher than thermal diffusivity + + align:start position:0% +magnit higher than thermal diffusivity + + + align:start position:0% +magnit higher than thermal diffusivity +so that's what in my mind and now theral + + align:start position:0% +so that's what in my mind and now theral + + + align:start position:0% +so that's what in my mind and now theral +diffusivity 10 to Theus + + align:start position:0% +diffusivity 10 to Theus + + + align:start position:0% +diffusivity 10 to Theus +4 right uh cm square now Meer Square so + + align:start position:0% +4 right uh cm square now Meer Square so + + + align:start position:0% +4 right uh cm square now Meer Square so +wait so uh the theral diffusivity of + + align:start position:0% +wait so uh the theral diffusivity of + + + align:start position:0% +wait so uh the theral diffusivity of +silicon is of the 10 Theus 4 M Square + + align:start position:0% +silicon is of the 10 Theus 4 M Square + + + align:start position:0% +silicon is of the 10 Theus 4 M Square +per second so diffusivity for electrons + + align:start position:0% +per second so diffusivity for electrons + + + align:start position:0% +per second so diffusivity for electrons +is of the 1 M Square per + + align:start position:0% +is of the 1 M Square per + + + align:start position:0% +is of the 1 M Square per +second okay four magnitude higher and + + align:start position:0% +second okay four magnitude higher and + + + align:start position:0% +second okay four magnitude higher and +relaxation say recombination time right + + align:start position:0% +relaxation say recombination time right + + + align:start position:0% +relaxation say recombination time right +if I do millisecond or second + + align:start position:0% +if I do millisecond or second + + + align:start position:0% +if I do millisecond or second +microc depends on the Purity very + + align:start position:0% +microc depends on the Purity very + + + align:start position:0% +microc depends on the Purity very +sensitive depends on the purity of the + + align:start position:0% +sensitive depends on the purity of the + + + align:start position:0% +sensitive depends on the purity of the +materials right so I have people doing + + align:start position:0% +materials right so I have people doing + + + align:start position:0% +materials right so I have people doing +solar cell I ask her what's the + + align:start position:0% +solar cell I ask her what's the + + + align:start position:0% +solar cell I ask her what's the +recompilation time of your + + align:start position:0% +recompilation time of your + + + align:start position:0% +recompilation time of your +cicon + + align:start position:0% +cicon + + + align:start position:0% +cicon +mul 100 micr okay 100 microc 10 Theus 4 + + align:start position:0% +mul 100 micr okay 100 microc 10 Theus 4 + + + align:start position:0% +mul 100 micr okay 100 microc 10 Theus 4 +second right if I do + + align:start position:0% +second right if I do + + + align:start position:0% +second right if I do +that the square root of D * T you you + + align:start position:0% +that the square root of D * T you you + + + align:start position:0% +that the square root of D * T you you +can go to see how large is + + align:start position:0% +can go to see how large is + + + align:start position:0% +can go to see how large is +diffusion of the charge + + align:start position:0% +diffusion of the charge + + + align:start position:0% +diffusion of the charge +right so you have the point I want to + + align:start position:0% +right so you have the point I want to + + + align:start position:0% +right so you have the point I want to +make is you have to know what you doing + + align:start position:0% +make is you have to know what you doing + + + align:start position:0% +make is you have to know what you doing +in this kind + + align:start position:0% +in this kind + + + align:start position:0% +in this kind +of each process what's the detail charge + + align:start position:0% +of each process what's the detail charge + + + align:start position:0% +of each process what's the detail charge +carrier transport process to even find + + align:start position:0% +carrier transport process to even find + + + align:start position:0% +carrier transport process to even find +out the where for example in your C at + + align:start position:0% +out the where for example in your C at + + + align:start position:0% +out the where for example in your C at +the end heat transfer I always care heat + + align:start position:0% +the end heat transfer I always care heat + + + align:start position:0% +the end heat transfer I always care heat +transfer you have to say where is the + + align:start position:0% +transfer you have to say where is the + + + align:start position:0% +transfer you have to say where is the +heat generated + + align:start position:0% + + + + align:start position:0% + +okay so uh that's what I mean by + + align:start position:0% +okay so uh that's what I mean by + + + align:start position:0% +okay so uh that's what I mean by +coupled charge uh couple the say + + align:start position:0% +coupled charge uh couple the say + + + align:start position:0% +coupled charge uh couple the say +conversion and say energy conversion + + align:start position:0% +conversion and say energy conversion + + + align:start position:0% +conversion and say energy conversion +that's the right hand side and the left + + align:start position:0% +that's the right hand side and the left + + + align:start position:0% +that's the right hand side and the left +hand side is a + + align:start position:0% +hand side is a + + + align:start position:0% +hand side is a +transform and let's look at one specific + + align:start position:0% +transform and let's look at one specific + + + align:start position:0% +transform and let's look at one specific +example and we're not going to uh say uh + + align:start position:0% +example and we're not going to uh say uh + + + align:start position:0% +example and we're not going to uh say uh +this example is all you uh uh you care + + align:start position:0% +this example is all you uh uh you care + + + align:start position:0% +this example is all you uh uh you care +about let's look at solar + + align:start position:0% +about let's look at solar + + + align:start position:0% +about let's look at solar +cell + + align:start position:0% + + + + align:start position:0% + +okay but to do solar cell I first do p + + align:start position:0% +okay but to do solar cell I first do p + + + align:start position:0% +okay but to do solar cell I first do p +in Junction you have to understand that + + align:start position:0% +in Junction you have to understand that + + + align:start position:0% +in Junction you have to understand that +what is p in Junction + + align:start position:0% + + + + align:start position:0% + +right and uh uh I've uh mentioned many + + align:start position:0% +right and uh uh I've uh mentioned many + + + align:start position:0% +right and uh uh I've uh mentioned many +times ON Semiconductor in this course + + align:start position:0% +times ON Semiconductor in this course + + + align:start position:0% +times ON Semiconductor in this course +and not very systematic I understand but + + align:start position:0% +and not very systematic I understand but + + + align:start position:0% +and not very systematic I understand but +see uh the uh basic uh picture we have + + align:start position:0% +see uh the uh basic uh picture we have + + + align:start position:0% +see uh the uh basic uh picture we have +so far is I of course here I'm drawing + + align:start position:0% +so far is I of course here I'm drawing + + + align:start position:0% +so far is I of course here I'm drawing +the band structure right but see this at + + align:start position:0% +the band structure right but see this at + + + align:start position:0% +the band structure right but see this at +the end what matters is because uh it's + + align:start position:0% +the end what matters is because uh it's + + + align:start position:0% +the end what matters is because uh it's +really near the bottom of conduction B + + align:start position:0% +really near the bottom of conduction B + + + align:start position:0% +really near the bottom of conduction B +on top of the bance B right because the + + align:start position:0% +on top of the bance B right because the + + + align:start position:0% +on top of the bance B right because the +carrier quickly relax to that region so + + align:start position:0% +carrier quickly relax to that region so + + + align:start position:0% +carrier quickly relax to that region so +typically when we draw the actually just + + align:start position:0% +typically when we draw the actually just + + + align:start position:0% +typically when we draw the actually just +draw Flat you can draw a point but the + + align:start position:0% +draw Flat you can draw a point but the + + + align:start position:0% +draw Flat you can draw a point but the +flat just this is my bottom conduction B + + align:start position:0% +flat just this is my bottom conduction B + + + align:start position:0% +flat just this is my bottom conduction B +and this is the top of the valance ban + + align:start position:0% +and this is the top of the valance ban + + + align:start position:0% +and this is the top of the valance ban +right and P Junction so when I have n + + align:start position:0% +right and P Junction so when I have n + + + align:start position:0% +right and P Junction so when I have n +type + + align:start position:0% + + + + align:start position:0% + +material my chemical + + align:start position:0% +material my chemical + + + align:start position:0% +material my chemical +potential is here right because if you + + align:start position:0% +potential is here right because if you + + + align:start position:0% +potential is here right because if you +think + + align:start position:0% +think + + + align:start position:0% +think +about uh from a direct distribution the + + align:start position:0% +about uh from a direct distribution the + + + align:start position:0% +about uh from a direct distribution the +E minus + + align:start position:0% +E minus + + + align:start position:0% +E minus +mu right e m mu so this separation is + + align:start position:0% +mu right e m mu so this separation is + + + align:start position:0% +mu right e m mu so this separation is +much more than this e Min mu so I have + + align:start position:0% +much more than this e Min mu so I have + + + align:start position:0% +much more than this e Min mu so I have +more + + align:start position:0% +more + + + align:start position:0% +more +electrons what I draw is a lot of + + align:start position:0% +electrons what I draw is a lot of + + + align:start position:0% +electrons what I draw is a lot of +electron in the conduction band that's + + align:start position:0% +electron in the conduction band that's + + + align:start position:0% +electron in the conduction band that's +end type + + align:start position:0% +end type + + + align:start position:0% +end type +material and then I'm drawing the same + + align:start position:0% +material and then I'm drawing the same + + + align:start position:0% +material and then I'm drawing the same +bank Gap because I'm using the same bank + + align:start position:0% +bank Gap because I'm using the same bank + + + align:start position:0% +bank Gap because I'm using the same bank +Gap material you can use a different + + align:start position:0% +Gap material you can use a different + + + align:start position:0% +Gap material you can use a different +band Gap that's a hydro Junction but + + align:start position:0% +band Gap that's a hydro Junction but + + + align:start position:0% +band Gap that's a hydro Junction but +here so I have this is the n + + align:start position:0% +here so I have this is the n + + + align:start position:0% +here so I have this is the n +type this is a p type right they + + align:start position:0% +type this is a p type right they + + + align:start position:0% +type this is a p type right they +are standard + + align:start position:0% +are standard + + + align:start position:0% +are standard +long not + + align:start position:0% +long not + + + align:start position:0% +long not +collecting now you connect them you put + + align:start position:0% +collecting now you connect them you put + + + align:start position:0% +collecting now you connect them you put +them + + align:start position:0% +them + + + align:start position:0% +them +together say the MU the chemical + + align:start position:0% +together say the MU the chemical + + + align:start position:0% +together say the MU the chemical +potential is the driving force for Mass + + align:start position:0% +potential is the driving force for Mass + + + align:start position:0% +potential is the driving force for Mass +diffusion or charge flow right chemical + + align:start position:0% +diffusion or charge flow right chemical + + + align:start position:0% +diffusion or charge flow right chemical +potential is driving force for diffusion + + align:start position:0% +potential is driving force for diffusion + + + align:start position:0% +potential is driving force for diffusion +when you whenever you have have + + align:start position:0% +when you whenever you have have + + + align:start position:0% +when you whenever you have have +temperature let say uh imbalance in the + + align:start position:0% +temperature let say uh imbalance in the + + + align:start position:0% +temperature let say uh imbalance in the +chemical potential there is a paral flow + + align:start position:0% +chemical potential there is a paral flow + + + align:start position:0% +chemical potential there is a paral flow +so when I collect them together + + align:start position:0% +so when I collect them together + + + align:start position:0% +so when I collect them together +eventually what will + + align:start position:0% +eventually what will + + + align:start position:0% +eventually what will +happen is this is still my B back Gap + + align:start position:0% +happen is this is still my B back Gap + + + align:start position:0% +happen is this is still my B back Gap +right BN Gap and uh this is my mu so I'm + + align:start position:0% +right BN Gap and uh this is my mu so I'm + + + align:start position:0% +right BN Gap and uh this is my mu so I'm +going to + + align:start position:0% +going to + + + align:start position:0% +going to +draw uh mu L here and uh uh on this side + + align:start position:0% +draw uh mu L here and uh uh on this side + + + align:start position:0% +draw uh mu L here and uh uh on this side +is going to + + align:start position:0% + + + + align:start position:0% + +be my P type on this side is my end type + + align:start position:0% +be my P type on this side is my end type + + + align:start position:0% +be my P type on this side is my end type +so Al line the chemical potential first + + align:start position:0% +so Al line the chemical potential first + + + align:start position:0% +so Al line the chemical potential first +and then you connect it the conduction + + align:start position:0% +and then you connect it the conduction + + + align:start position:0% +and then you connect it the conduction +band together balance band together + + align:start position:0% +band together balance band together + + + align:start position:0% +band together balance band together +right and uh I say approximate way to + + align:start position:0% +right and uh I say approximate way to + + + align:start position:0% +right and uh I say approximate way to +connect is Parabola you can solve the + + align:start position:0% +connect is Parabola you can solve the + + + align:start position:0% +connect is Parabola you can solve the +person equation to find out the exact + + align:start position:0% +person equation to find out the exact + + + align:start position:0% +person equation to find out the exact +profile and that's what the say a + + align:start position:0% +profile and that's what the say a + + + align:start position:0% +profile and that's what the say a +typical profile look + + align:start position:0% +typical profile look + + + align:start position:0% +typical profile look +like okay that's your P Junction at the + + align:start position:0% +like okay that's your P Junction at the + + + align:start position:0% +like okay that's your P Junction at the +equilibrium right so and here we have oh + + align:start position:0% +equilibrium right so and here we have oh + + + align:start position:0% +equilibrium right so and here we have oh +I draw two large but that's fine so what + + align:start position:0% +I draw two large but that's fine so what + + + align:start position:0% +I draw two large but that's fine so what +I have here is the difference between + + align:start position:0% +I have here is the difference between + + + align:start position:0% +I have here is the difference between +the + + align:start position:0% +the + + + align:start position:0% +the +conduction bands on the flat region far + + align:start position:0% +conduction bands on the flat region far + + + align:start position:0% +conduction bands on the flat region far +away from the interface this is a uh say + + align:start position:0% +away from the interface this is a uh say + + + align:start position:0% +away from the interface this is a uh say +EV building + + align:start position:0% +EV building + + + align:start position:0% +EV building +potential so that depends on you can + + align:start position:0% +potential so that depends on you can + + + align:start position:0% +potential so that depends on you can +say you can actually do that exercise + + align:start position:0% +say you can actually do that exercise + + + align:start position:0% +say you can actually do that exercise +quickly because uh away in this region + + align:start position:0% +quickly because uh away in this region + + + align:start position:0% +quickly because uh away in this region +you still have your bman statistic or + + align:start position:0% +you still have your bman statistic or + + + align:start position:0% +you still have your bman statistic or +firm direct statistics and on this side + + align:start position:0% +firm direct statistics and on this side + + + align:start position:0% +firm direct statistics and on this side +so you once you align you can find out + + align:start position:0% +so you once you align you can find out + + + align:start position:0% +so you once you align you can find out +what has to be the conduction band Edge + + align:start position:0% +what has to be the conduction band Edge + + + align:start position:0% +what has to be the conduction band Edge +offset that depends on the doping of the + + align:start position:0% +offset that depends on the doping of the + + + align:start position:0% +offset that depends on the doping of the +two + + align:start position:0% +two + + + align:start position:0% +two +material okay + + align:start position:0% +material okay + + + align:start position:0% +material okay +okay and uh uh What uh what physically + + align:start position:0% +okay and uh uh What uh what physically + + + align:start position:0% +okay and uh uh What uh what physically +happening so this n type I have lot of + + align:start position:0% +happening so this n type I have lot of + + + align:start position:0% +happening so this n type I have lot of +uh so for the end type right I can draw + + align:start position:0% +uh so for the end type right I can draw + + + align:start position:0% +uh so for the end type right I can draw +this one I collect the two material this + + align:start position:0% +this one I collect the two material this + + + align:start position:0% +this one I collect the two material this +is the + + align:start position:0% +is the + + + align:start position:0% +is the +interface of the two material in the end + + align:start position:0% +interface of the two material in the end + + + align:start position:0% +interface of the two material in the end +type for example it's a phosphor right + + align:start position:0% +type for example it's a phosphor right + + + align:start position:0% +type for example it's a phosphor right +in Silicon is phosphor and it has five + + align:start position:0% +in Silicon is phosphor and it has five + + + align:start position:0% +in Silicon is phosphor and it has five +five electron this free electron that's + + align:start position:0% +five electron this free electron that's + + + align:start position:0% +five electron this free electron that's +get free is moving to the other side + + align:start position:0% +get free is moving to the other side + + + align:start position:0% +get free is moving to the other side +right so this is n region electron is + + align:start position:0% +right so this is n region electron is + + + align:start position:0% +right so this is n region electron is +lost going to the other side and What's + + align:start position:0% +lost going to the other side and What's + + + align:start position:0% +lost going to the other side and What's +Left Behind is the phosphor atom right + + align:start position:0% +Left Behind is the phosphor atom right + + + align:start position:0% +Left Behind is the phosphor atom right +the phosphor atom now doesn't have uh + + align:start position:0% +the phosphor atom now doesn't have uh + + + align:start position:0% +the phosphor atom now doesn't have uh +electron to balance it anymore so it's a + + align:start position:0% +electron to balance it anymore so it's a + + + align:start position:0% +electron to balance it anymore so it's a +it's a say actually positive + + align:start position:0% +it's a say actually positive + + + align:start position:0% +it's a say actually positive +phosphor atom + + align:start position:0% +phosphor atom + + + align:start position:0% +phosphor atom +region this are not m right those are + + align:start position:0% +region this are not m right those are + + + align:start position:0% +region this are not m right those are +just atom sit on the + + align:start position:0% +just atom sit on the + + + align:start position:0% +just atom sit on the +lce okay and similarly on the P type + + align:start position:0% + + + + align:start position:0% + +side right it's Boron doped and Boron + + align:start position:0% +side right it's Boron doped and Boron + + + align:start position:0% +side right it's Boron doped and Boron +get that + + align:start position:0% +get that + + + align:start position:0% +get that +electron and so Boron becomes negatively + + align:start position:0% +electron and so Boron becomes negatively + + + align:start position:0% +electron and so Boron becomes negatively +charged right so you have negative + + align:start position:0% + + + + align:start position:0% + +charge right this are this space disch + + align:start position:0% +charge right this are this space disch + + + align:start position:0% +charge right this are this space disch +charge region there's no mobile charge + + align:start position:0% +charge region there's no mobile charge + + + align:start position:0% +charge region there's no mobile charge +it's atoms positive charge atom negative + + align:start position:0% +it's atoms positive charge atom negative + + + align:start position:0% +it's atoms positive charge atom negative +charge atom away from the junction you + + align:start position:0% +charge atom away from the junction you + + + align:start position:0% +charge atom away from the junction you +have a Lal region where there is equal + + align:start position:0% +have a Lal region where there is equal + + + align:start position:0% +have a Lal region where there is equal +number of + + align:start position:0% +number of + + + align:start position:0% +number of +electrons and let say the ions but in + + align:start position:0% +electrons and let say the ions but in + + + align:start position:0% +electrons and let say the ions but in +this + + align:start position:0% +this + + + align:start position:0% +this +region it's not + + align:start position:0% +region it's not + + + align:start position:0% +region it's not +neutral right so this is the space + + align:start position:0% +neutral right so this is the space + + + align:start position:0% +neutral right so this is the space +charge region + + align:start position:0% + + + + align:start position:0% + +okay and uh uh this so so again the the + + align:start position:0% +okay and uh uh this so so again the the + + + align:start position:0% +okay and uh uh this so so again the the +weight of this depends on the dopen + + align:start position:0% +weight of this depends on the dopen + + + align:start position:0% +weight of this depends on the dopen +concentration and if you have less dopen + + align:start position:0% +concentration and if you have less dopen + + + align:start position:0% +concentration and if you have less dopen +the space charge region is wider you + + align:start position:0% +the space charge region is wider you + + + align:start position:0% +the space charge region is wider you +have more dopen the space charging + + align:start position:0% +have more dopen the space charging + + + align:start position:0% +have more dopen the space charging +region is lateral and typical + + align:start position:0% +region is lateral and typical + + + align:start position:0% +region is lateral and typical +semiconductor with dopin is a few + + align:start position:0% +semiconductor with dopin is a few + + + align:start position:0% +semiconductor with dopin is a few +microns in this space charge region + + align:start position:0% + + + + align:start position:0% + +okay and uh uh so now that's the uh uh + + align:start position:0% +okay and uh uh so now that's the uh uh + + + align:start position:0% +okay and uh uh so now that's the uh uh +steady state + + align:start position:0% +steady state + + + align:start position:0% +steady state +right and say a DI say a pin Junction is + + align:start position:0% +right and say a DI say a pin Junction is + + + align:start position:0% +right and say a DI say a pin Junction is +a dial we know that say it's a uh on + + align:start position:0% +a dial we know that say it's a uh on + + + align:start position:0% +a dial we know that say it's a uh on +isotropic right and uh if I do a say a + + align:start position:0% +isotropic right and uh if I do a say a + + + align:start position:0% +isotropic right and uh if I do a say a +forward bias what do I + + align:start position:0% + + + + align:start position:0% + +mean forward B + + align:start position:0% +mean forward B + + + align:start position:0% +mean forward B +I apply a voltage right and the voltage + + align:start position:0% +I apply a voltage right and the voltage + + + align:start position:0% +I apply a voltage right and the voltage +will change the electrochemical + + align:start position:0% +will change the electrochemical + + + align:start position:0% +will change the electrochemical +potential so on this two sides I have a + + align:start position:0% +potential so on this two sides I have a + + + align:start position:0% +potential so on this two sides I have a +difference now on electrochemical + + align:start position:0% +difference now on electrochemical + + + align:start position:0% +difference now on electrochemical +potential now if I want to have a + + align:start position:0% +potential now if I want to have a + + + align:start position:0% +potential now if I want to have a +forward + + align:start position:0% +forward + + + align:start position:0% +forward +bias should this going up or going + + align:start position:0% + + + + align:start position:0% + +down huh okay going up right so a + + align:start position:0% +down huh okay going up right so a + + + align:start position:0% +down huh okay going up right so a +forward bias means okay now I have + + align:start position:0% +forward bias means okay now I have + + + align:start position:0% +forward bias means okay now I have +chemical potential on the P + + align:start position:0% +chemical potential on the P + + + align:start position:0% +chemical potential on the P +side and uh electrochemical + + align:start position:0% + + + + align:start position:0% + +potential okay that's + + align:start position:0% +potential okay that's + + + align:start position:0% +potential okay that's +inside + + align:start position:0% +inside + + + align:start position:0% +inside +and + + align:start position:0% + + + + align:start position:0% + +here you'll become flatter + + align:start position:0% + + + + align:start position:0% + +that's a p Junction under forward + + align:start position:0% +that's a p Junction under forward + + + align:start position:0% +that's a p Junction under forward +bias + + align:start position:0% +bias + + + align:start position:0% +bias +right you have to be able to + + align:start position:0% +right you have to be able to + + + align:start position:0% +right you have to be able to +draw this is the n region this is a p + + align:start position:0% +draw this is the n region this is a p + + + align:start position:0% +draw this is the n region this is a p +region and this is a uh you collect so + + align:start position:0% +region and this is a uh you collect so + + + align:start position:0% +region and this is a uh you collect so +so if you think about your collector a + + align:start position:0% +so if you think about your collector a + + + align:start position:0% +so if you think about your collector a +pin Junction you with a + + align:start position:0% +pin Junction you with a + + + align:start position:0% +pin Junction you with a +battery right is this side you connect + + align:start position:0% +battery right is this side you connect + + + align:start position:0% +battery right is this side you connect +negative side or positive side + + align:start position:0% +negative side or positive side + + + align:start position:0% +negative side or positive side +negative side because when you draw + + align:start position:0% +negative side because when you draw + + + align:start position:0% +negative side because when you draw +because I'm reasing this potential is + + align:start position:0% +because I'm reasing this potential is + + + align:start position:0% +because I'm reasing this potential is +I'm reason the negative becoming more + + align:start position:0% +I'm reason the negative becoming more + + + align:start position:0% +I'm reason the negative becoming more +higher there so this is the uh if you + + align:start position:0% + + + + align:start position:0% + +collect this is positive right I + + align:start position:0% +collect this is positive right I + + + align:start position:0% +collect this is positive right I +forgot right that's what you + + align:start position:0% +forgot right that's what you + + + align:start position:0% +forgot right that's what you +come okay so uh now I have uh the uh the + + align:start position:0% +come okay so uh now I have uh the uh the + + + align:start position:0% +come okay so uh now I have uh the uh the +I Le Le at the electrod that's what it + + align:start position:0% +I Le Le at the electrod that's what it + + + align:start position:0% +I Le Le at the electrod that's what it +look + + align:start position:0% +look + + + align:start position:0% +look +like right the question is how these two + + align:start position:0% +like right the question is how these two + + + align:start position:0% +like right the question is how these two +are going to connect to each + + align:start position:0% +are going to connect to each + + + align:start position:0% +are going to connect to each +other right so in the bulk of the P + + align:start position:0% +other right so in the bulk of the P + + + align:start position:0% +other right so in the bulk of the P +Junction away from the space charge + + align:start position:0% +Junction away from the space charge + + + align:start position:0% +Junction away from the space charge +region it's pretty much electron itself + + align:start position:0% +region it's pretty much electron itself + + + align:start position:0% +region it's pretty much electron itself +is at equilibrium so it's still very so + + align:start position:0% +is at equilibrium so it's still very so + + + align:start position:0% +is at equilibrium so it's still very so +it's a diffusion very small + + align:start position:0% +it's a diffusion very small + + + align:start position:0% +it's a diffusion very small +deviation uh from what we have in this + + align:start position:0% +deviation uh from what we have in this + + + align:start position:0% +deviation uh from what we have in this +picture + + align:start position:0% +picture + + + align:start position:0% +picture +here + + align:start position:0% +here + + + align:start position:0% +here +okay but once you get to the space + + align:start position:0% +okay but once you get to the space + + + align:start position:0% +okay but once you get to the space +charge + + align:start position:0% +charge + + + align:start position:0% +charge +region this equilibrium is + + align:start position:0% +region this equilibrium is + + + align:start position:0% +region this equilibrium is +broken there's not holes to low enough + + align:start position:0% +broken there's not holes to low enough + + + align:start position:0% +broken there's not holes to low enough +holes or electron to still keep the + + align:start position:0% +holes or electron to still keep the + + + align:start position:0% +holes or electron to still keep the +electron hole pretty much at equiv with + + align:start position:0% +electron hole pretty much at equiv with + + + align:start position:0% +electron hole pretty much at equiv with +each other so electron and the hole + + align:start position:0% +each other so electron and the hole + + + align:start position:0% +each other so electron and the hole +actually now each have equivalently a + + align:start position:0% +actually now each have equivalently a + + + align:start position:0% +actually now each have equivalently a +separate chemical potential + + align:start position:0% +separate chemical potential + + + align:start position:0% +separate chemical potential +this is a Quai firing level or say + + align:start position:0% +this is a Quai firing level or say + + + align:start position:0% +this is a Quai firing level or say +electrochemical potential so the way to + + align:start position:0% +electrochemical potential so the way to + + + align:start position:0% +electrochemical potential so the way to +draw this and this is + + align:start position:0% +draw this and this is + + + align:start position:0% +draw this and this is +where you have to say the the invention + + align:start position:0% +where you have to say the the invention + + + align:start position:0% +where you have to say the the invention +of P injunction right I don't know + + align:start position:0% +of P injunction right I don't know + + + align:start position:0% +of P injunction right I don't know +whether I told this story before it was + + align:start position:0% +whether I told this story before it was + + + align:start position:0% +whether I told this story before it was +a uh was a + + align:start position:0% +a uh was a + + + align:start position:0% +a uh was a +shakay it was a b in was a + + align:start position:0% +shakay it was a b in was a + + + align:start position:0% +shakay it was a b in was a +braen okay it was the body + + align:start position:0% +braen okay it was the body + + + align:start position:0% +braen okay it was the body +so shley was I if I recall correctly + + align:start position:0% +so shley was I if I recall correctly + + + align:start position:0% +so shley was I if I recall correctly +this shley was the + + align:start position:0% +this shley was the + + + align:start position:0% +this shley was the +manager and uh uh Bin and Bren did the + + align:start position:0% +manager and uh uh Bin and Bren did the + + + align:start position:0% +manager and uh uh Bin and Bren did the +physical lab invention of the P + + align:start position:0% +physical lab invention of the P + + + align:start position:0% +physical lab invention of the P +injunction okay and shock know this is + + align:start position:0% +injunction okay and shock know this is + + + align:start position:0% +injunction okay and shock know this is +very + + align:start position:0% +very + + + align:start position:0% +very +important and he will be left out for + + align:start position:0% +important and he will be left out for + + + align:start position:0% +important and he will be left out for +the lowber + + align:start position:0% +the lowber + + + align:start position:0% +the lowber +price he worked out the theory for + + align:start position:0% +price he worked out the theory for + + + align:start position:0% +price he worked out the theory for +this okay walk around to activate + + align:start position:0% + + + + align:start position:0% + +so uh so uh shle got lowy price for + + align:start position:0% +so uh so uh shle got lowy price for + + + align:start position:0% +so uh so uh shle got lowy price for +twice right shle got lowy price twice + + align:start position:0% +twice right shle got lowy price twice + + + align:start position:0% +twice right shle got lowy price twice +the order so this is + + align:start position:0% +the order so this is + + + align:start position:0% +the order so this is +semiconductor and he got the loby price + + align:start position:0% +semiconductor and he got the loby price + + + align:start position:0% +semiconductor and he got the loby price +for BCS + + align:start position:0% +for BCS + + + align:start position:0% +for BCS +Theory what is that super that's a super + + align:start position:0% +Theory what is that super that's a super + + + align:start position:0% +Theory what is that super that's a super +conductivity uh say uh is + + align:start position:0% +conductivity uh say uh is + + + align:start position:0% +conductivity uh say uh is +a uh uh is Bin shlay and uh uh + + align:start position:0% + + + + align:start position:0% + +Sher Cooper BCS where is BC oh Bing wait + + align:start position:0% +Sher Cooper BCS where is BC oh Bing wait + + + align:start position:0% +Sher Cooper BCS where is BC oh Bing wait +where oh Bing got yeah Bing got low + + align:start position:0% +where oh Bing got yeah Bing got low + + + align:start position:0% +where oh Bing got yeah Bing got low +price twice so okay no so shly got + + align:start position:0% +price twice so okay no so shly got + + + align:start position:0% +price twice so okay no so shly got +once okay uh but anyway so so there was + + align:start position:0% +once okay uh but anyway so so there was + + + align:start position:0% +once okay uh but anyway so so there was +an interesting recount of the invention + + align:start position:0% +an interesting recount of the invention + + + align:start position:0% +an interesting recount of the invention +of the uh diod in the bap + + align:start position:0% +of the uh diod in the bap + + + align:start position:0% +of the uh diod in the bap +so maybe I mixed up the people but + + align:start position:0% +so maybe I mixed up the people but + + + align:start position:0% +so maybe I mixed up the people but +anyway uh uh so my student got a good PR + + align:start position:0% +anyway uh uh so my student got a good PR + + + align:start position:0% +anyway uh uh so my student got a good PR +good good project good result I got to + + align:start position:0% +good good project good result I got to + + + align:start position:0% +good good project good result I got to +get a lab and get my fingers + + align:start position:0% + + + + align:start position:0% + +there uh uh okay where where we are so + + align:start position:0% +there uh uh okay where where we are so + + + align:start position:0% +there uh uh okay where where we are so +here is what happens you have to think + + align:start position:0% +here is what happens you have to think + + + align:start position:0% +here is what happens you have to think +about this is actually very very + + align:start position:0% +about this is actually very very + + + align:start position:0% +about this is actually very very +delicate picture electron is the + + align:start position:0% +delicate picture electron is the + + + align:start position:0% +delicate picture electron is the +conductor in the end type + + align:start position:0% +conductor in the end type + + + align:start position:0% +conductor in the end type +how that transition going into a p type + + align:start position:0% +how that transition going into a p type + + + align:start position:0% +how that transition going into a p type +going to + + align:start position:0% +going to + + + align:start position:0% +going to +holes right holes are the conductor in + + align:start position:0% +holes right holes are the conductor in + + + align:start position:0% +holes right holes are the conductor in +the P + + align:start position:0% +the P + + + align:start position:0% +the P +type it's not an + + align:start position:0% +type it's not an + + + align:start position:0% +type it's not an +easy + + align:start position:0% +easy + + + align:start position:0% +easy +picture and the theory that was s + + align:start position:0% +picture and the theory that was s + + + align:start position:0% +picture and the theory that was s +out and you can go to solve the in fact + + align:start position:0% +out and you can go to solve the in fact + + + align:start position:0% +out and you can go to solve the in fact +that's + + align:start position:0% +that's + + + align:start position:0% +that's +the equation we have here is a carrier + + align:start position:0% +the equation we have here is a carrier + + + align:start position:0% +the equation we have here is a carrier +diffusion + + align:start position:0% +diffusion + + + align:start position:0% +diffusion +equation and uh so what happens is in + + align:start position:0% +equation and uh so what happens is in + + + align:start position:0% +equation and uh so what happens is in +the space charge + + align:start position:0% +the space charge + + + align:start position:0% +the space charge +region they uh say this say I pretty + + align:start position:0% +region they uh say this say I pretty + + + align:start position:0% +region they uh say this say I pretty +much draw Flat because the resistance in + + align:start position:0% +much draw Flat because the resistance in + + + align:start position:0% +much draw Flat because the resistance in +each region is pretty small so + + align:start position:0% +each region is pretty small so + + + align:start position:0% +each region is pretty small so +resistance will determine this coite + + align:start position:0% +resistance will determine this coite + + + align:start position:0% +resistance will determine this coite +Firma level if you think about ohms know + + align:start position:0% +Firma level if you think about ohms know + + + align:start position:0% +Firma level if you think about ohms know +that's a voltage drop if the resistance + + align:start position:0% +that's a voltage drop if the resistance + + + align:start position:0% +that's a voltage drop if the resistance +small it's pretty flat okay so once it + + align:start position:0% +small it's pretty flat okay so once it + + + align:start position:0% +small it's pretty flat okay so once it +get over so this is the junction there + + align:start position:0% +get over so this is the junction there + + + align:start position:0% +get over so this is the junction there +get over to the P side and in fact uh + + align:start position:0% +get over to the P side and in fact uh + + + align:start position:0% +get over to the P side and in fact uh +get out of the space charge + + align:start position:0% +get out of the space charge + + + align:start position:0% +get out of the space charge +region okay and then see this is still + + align:start position:0% +region okay and then see this is still + + + align:start position:0% +region okay and then see this is still +electron here right electron come over + + align:start position:0% +electron here right electron come over + + + align:start position:0% +electron here right electron come over +here and uh uh um but see really what + + align:start position:0% +here and uh uh um but see really what + + + align:start position:0% +here and uh uh um but see really what +happens is the mality carrier which is + + align:start position:0% +happens is the mality carrier which is + + + align:start position:0% +happens is the mality carrier which is +electron in this + + align:start position:0% +electron in this + + + align:start position:0% +electron in this +region right because in this region the + + align:start position:0% +region right because in this region the + + + align:start position:0% +region right because in this region the +major majority electron the hole is + + align:start position:0% +major majority electron the hole is + + + align:start position:0% +major majority electron the hole is +minority in this region is a ho is + + align:start position:0% +minority in this region is a ho is + + + align:start position:0% +minority in this region is a ho is +majority and electron mality so once it + + align:start position:0% +majority and electron mality so once it + + + align:start position:0% +majority and electron mality so once it +comes to this other side it becomes a + + align:start position:0% +comes to this other side it becomes a + + + align:start position:0% +comes to this other side it becomes a +mality and the mality carrier the + + align:start position:0% +mality and the mality carrier the + + + align:start position:0% +mality and the mality carrier the +electron recombine with the + + align:start position:0% +electron recombine with the + + + align:start position:0% +electron recombine with the +hole okay and that's a recombination + + align:start position:0% +hole okay and that's a recombination + + + align:start position:0% +hole okay and that's a recombination +process and so the whole Supply is draw + + align:start position:0% +process and so the whole Supply is draw + + + align:start position:0% +process and so the whole Supply is draw +to this region by because Rec combine + + align:start position:0% +to this region by because Rec combine + + + align:start position:0% +to this region by because Rec combine +with the mity electron so the electron + + align:start position:0% +with the mity electron so the electron + + + align:start position:0% +with the mity electron so the electron +eventually approach equ qua equilibrium + + align:start position:0% +eventually approach equ qua equilibrium + + + align:start position:0% +eventually approach equ qua equilibrium +electron the bulk region so this this + + align:start position:0% +electron the bulk region so this this + + + align:start position:0% +electron the bulk region so this this +recompilation region so you have a long + + align:start position:0% +recompilation region so you have a long + + + align:start position:0% +recompilation region so you have a long +equilibrium in the space charge and then + + align:start position:0% +equilibrium in the space charge and then + + + align:start position:0% +equilibrium in the space charge and then +it's a recombination the drives the qu + + align:start position:0% +it's a recombination the drives the qu + + + align:start position:0% +it's a recombination the drives the qu +formula will approaching each other on + + align:start position:0% +formula will approaching each other on + + + align:start position:0% +formula will approaching each other on +the both + + align:start position:0% +the both + + + align:start position:0% +the both +sides + + align:start position:0% +sides + + + align:start position:0% +sides +okay and with that so the theory was + + align:start position:0% +okay and with that so the theory was + + + align:start position:0% +okay and with that so the theory was +worked out so you can write the dial the + + align:start position:0% +worked out so you can write the dial the + + + align:start position:0% +worked out so you can write the dial the +equation and uh uh let me write down the + + align:start position:0% +equation and uh uh let me write down the + + + align:start position:0% +equation and uh uh let me write down the +the + + align:start position:0% +the + + + align:start position:0% +the +equation I'm not deriving this given in + + align:start position:0% +equation I'm not deriving this given in + + + align:start position:0% +equation I'm not deriving this given in +the book so uh J equals the Dow equation + + align:start position:0% +the book so uh J equals the Dow equation + + + align:start position:0% +the book so uh J equals the Dow equation +JS exponential + + align:start position:0% +JS exponential + + + align:start position:0% +JS exponential +e KBT minus + + align:start position:0% +e KBT minus + + + align:start position:0% +e KBT minus +one okay and the voltage here the this + + align:start position:0% +one okay and the voltage here the this + + + align:start position:0% +one okay and the voltage here the this +voltage difference when between + + align:start position:0% +voltage difference when between + + + align:start position:0% +voltage difference when between +the electrochemical potential on the two + + align:start position:0% +the electrochemical potential on the two + + + align:start position:0% +the electrochemical potential on the two +sides that's the applied external appli + + align:start position:0% +sides that's the applied external appli + + + align:start position:0% +sides that's the applied external appli +voltage + + align:start position:0% + + + + align:start position:0% + +okay and this + + align:start position:0% +okay and this + + + align:start position:0% +okay and this +JS is called saturation current also do + + align:start position:0% +JS is called saturation current also do + + + align:start position:0% +JS is called saturation current also do +current right say it can be written as e + + align:start position:0% +current right say it can be written as e + + + align:start position:0% +current right say it can be written as e +uh for this uh very long + + align:start position:0% +uh for this uh very long + + + align:start position:0% +uh for this uh very long +Junction uh see uh See this is the uh + + align:start position:0% +Junction uh see uh See this is the uh + + + align:start position:0% +Junction uh see uh See this is the uh +conduction band uh the uh um when you + + align:start position:0% +conduction band uh the uh um when you + + + align:start position:0% +conduction band uh the uh um when you +write the uh charge distribution that's + + align:start position:0% +write the uh charge distribution that's + + + align:start position:0% +write the uh charge distribution that's +the uh charge in the conduction B and uh + + align:start position:0% +the uh charge in the conduction B and uh + + + align:start position:0% +the uh charge in the conduction B and uh +here and the valance band and this is + + align:start position:0% +here and the valance band and this is + + + align:start position:0% +here and the valance band and this is +the + + align:start position:0% +the + + + align:start position:0% +the +acceptor and uh the s doent in the + + align:start position:0% +acceptor and uh the s doent in the + + + align:start position:0% +acceptor and uh the s doent in the +acceptor is in the P type region and the + + align:start position:0% +acceptor is in the P type region and the + + + align:start position:0% +acceptor is in the P type region and the +holes the recombination time of Hol + + align:start position:0% +holes the recombination time of Hol + + + align:start position:0% +holes the recombination time of Hol +diffusivity uh a is D so that's a + + align:start position:0% +diffusivity uh a is D so that's a + + + align:start position:0% +diffusivity uh a is D so that's a +diffusivity and this is the + + align:start position:0% +diffusivity and this is the + + + align:start position:0% +diffusivity and this is the +donor and the diffusivity of the + + align:start position:0% +donor and the diffusivity of the + + + align:start position:0% +donor and the diffusivity of the +electron and the recombination time of + + align:start position:0% +electron and the recombination time of + + + align:start position:0% +electron and the recombination time of +the electron times + + align:start position:0% +the electron times + + + align:start position:0% +the electron times +exponential the bank Gap is a + + align:start position:0% +exponential the bank Gap is a + + + align:start position:0% +exponential the bank Gap is a +EG + + align:start position:0% + + + + align:start position:0% + +KBT so this is the saturation current + + align:start position:0% + + + + align:start position:0% + +or sometimes it's also called Dark + + align:start position:0% +or sometimes it's also called Dark + + + align:start position:0% +or sometimes it's also called Dark +current depends on whether you deal with + + align:start position:0% +current depends on whether you deal with + + + align:start position:0% +current depends on whether you deal with +solar cell or you deal with a + + align:start position:0% +solar cell or you deal with a + + + align:start position:0% +solar cell or you deal with a +diode okay so if you look at the uh this + + align:start position:0% +diode okay so if you look at the uh this + + + align:start position:0% +diode okay so if you look at the uh this +here is the exponential function right + + align:start position:0% +here is the exponential function right + + + align:start position:0% +here is the exponential function right +when we raise the voltage basically + + align:start position:0% +when we raise the voltage basically + + + align:start position:0% +when we raise the voltage basically +that's because the carrier + + align:start position:0% +that's because the carrier + + + align:start position:0% +that's because the carrier +concentration is exponential that's the + + align:start position:0% +concentration is exponential that's the + + + align:start position:0% +concentration is exponential that's the +FID uh distribution or bman distribution + + align:start position:0% +FID uh distribution or bman distribution + + + align:start position:0% +FID uh distribution or bman distribution +right the car concentration depends + + align:start position:0% +right the car concentration depends + + + align:start position:0% +right the car concentration depends +exponentially on the uh energy + + align:start position:0% +exponentially on the uh energy + + + align:start position:0% +exponentially on the uh energy +levels and uh here uh the saturation + + align:start position:0% +levels and uh here uh the saturation + + + align:start position:0% +levels and uh here uh the saturation +current has a exponential dependence + + align:start position:0% +current has a exponential dependence + + + align:start position:0% +current has a exponential dependence +Bank Gap + + align:start position:0% +Bank Gap + + + align:start position:0% +Bank Gap +diffusivity + + align:start position:0% +diffusivity + + + align:start position:0% +diffusivity +faster uh is larger reculation + + align:start position:0% +faster uh is larger reculation + + + align:start position:0% +faster uh is larger reculation +time right is on the + + align:start position:0% + + + + align:start position:0% + +denominator okay + + align:start position:0% +denominator okay + + + align:start position:0% +denominator okay +so if you that's a every electrical + + align:start position:0% +so if you that's a every electrical + + + align:start position:0% +so if you that's a every electrical +engineer Nots + + align:start position:0% + + + + align:start position:0% + +that and in fact see this is a you can + + align:start position:0% +that and in fact see this is a you can + + + align:start position:0% +that and in fact see this is a you can +see the two terms one is the electron + + align:start position:0% +see the two terms one is the electron + + + align:start position:0% +see the two terms one is the electron +the other is a hole and of course in + + align:start position:0% +the other is a hole and of course in + + + align:start position:0% +the other is a hole and of course in +actual device the current is + + align:start position:0% +actual device the current is + + + align:start position:0% +actual device the current is +continuous right and uh uh so if you + + align:start position:0% +continuous right and uh uh so if you + + + align:start position:0% +continuous right and uh uh so if you +draw this is a continuous current this + + align:start position:0% +draw this is a continuous current this + + + align:start position:0% +draw this is a continuous current this +is a j that go through the device and + + align:start position:0% +is a j that go through the device and + + + align:start position:0% +is a j that go through the device and +this is the interface and it turns out + + align:start position:0% +this is the interface and it turns out + + + align:start position:0% +this is the interface and it turns out +that the electron current + + align:start position:0% +that the electron current + + + align:start position:0% +that the electron current +is roughly this is a j the space charge + + align:start position:0% +is roughly this is a j the space charge + + + align:start position:0% +is roughly this is a j the space charge +region and this is + + align:start position:0% +region and this is + + + align:start position:0% +region and this is +recombination so in this region this is + + align:start position:0% +recombination so in this region this is + + + align:start position:0% +recombination so in this region this is +the n region this is p + + align:start position:0% +the n region this is p + + + align:start position:0% +the n region this is p +region right in this region the electron + + align:start position:0% +region right in this region the electron + + + align:start position:0% +region right in this region the electron +or Supply because say the recombination + + align:start position:0% +or Supply because say the recombination + + + align:start position:0% +or Supply because say the recombination +for holes so this is a + + align:start position:0% +for holes so this is a + + + align:start position:0% +for holes so this is a +j + + align:start position:0% +j + + + align:start position:0% +j +electron and uh you can also have a + + align:start position:0% +electron and uh you can also have a + + + align:start position:0% +electron and uh you can also have a +similar complimentary + + align:start position:0% +similar complimentary + + + align:start position:0% +similar complimentary +for for + + align:start position:0% + + + + align:start position:0% + +holes for hole this is the whole + + align:start position:0% +holes for hole this is the whole + + + align:start position:0% +holes for hole this is the whole +current so this is zero here the two add + + align:start position:0% +current so this is zero here the two add + + + align:start position:0% +current so this is zero here the two add +together uh it's + + align:start position:0% +together uh it's + + + align:start position:0% +together uh it's +not not very well + + align:start position:0% +not not very well + + + align:start position:0% +not not very well +D so the two add together + + align:start position:0% + + + + align:start position:0% + +should give you the total constant J + + align:start position:0% +should give you the total constant J + + + align:start position:0% +should give you the total constant J +this is the whole right so in the + + align:start position:0% +this is the whole right so in the + + + align:start position:0% +this is the whole right so in the +electron uh n type region electron is + + align:start position:0% +electron uh n type region electron is + + + align:start position:0% +electron uh n type region electron is +the majority here space charge it's just + + align:start position:0% +the majority here space charge it's just + + + align:start position:0% +the majority here space charge it's just +zip through and then Rec combine with + + align:start position:0% +zip through and then Rec combine with + + + align:start position:0% +zip through and then Rec combine with +minority carrier Rec combine with + + align:start position:0% +minority carrier Rec combine with + + + align:start position:0% +minority carrier Rec combine with +majority + + align:start position:0% +majority + + + align:start position:0% +majority +holes so semiconductor the P Junction + + align:start position:0% +holes so semiconductor the P Junction + + + align:start position:0% +holes so semiconductor the P Junction +this is why people call it's a m carrier + + align:start position:0% +this is why people call it's a m carrier + + + align:start position:0% +this is why people call it's a m carrier +device it's very sensitive to + + align:start position:0% +device it's very sensitive to + + + align:start position:0% +device it's very sensitive to +recombination so what it means because + + align:start position:0% +recombination so what it means because + + + align:start position:0% +recombination so what it means because +it's a mality carrier it's very + + align:start position:0% +it's a mality carrier it's very + + + align:start position:0% +it's a mality carrier it's very +sensitive recombination you want the + + align:start position:0% +sensitive recombination you want the + + + align:start position:0% +sensitive recombination you want the +pure very pure + + align:start position:0% +pure very pure + + + align:start position:0% +pure very pure +semiconductors okay and uh if you recall + + align:start position:0% +semiconductors okay and uh if you recall + + + align:start position:0% +semiconductors okay and uh if you recall +uh previously I common in thermal + + align:start position:0% +uh previously I common in thermal + + + align:start position:0% +uh previously I common in thermal +electrics theral electric don't have + + align:start position:0% +electrics theral electric don't have + + + align:start position:0% +electrics theral electric don't have +this minority carrier it's a majority + + align:start position:0% +this minority carrier it's a majority + + + align:start position:0% +this minority carrier it's a majority +carrier based device so it's less + + align:start position:0% +carrier based device so it's less + + + align:start position:0% +carrier based device so it's less +sensitive to recombination and that's + + align:start position:0% +sensitive to recombination and that's + + + align:start position:0% +sensitive to recombination and that's +why let say we can use a some very low + + align:start position:0% +why let say we can use a some very low + + + align:start position:0% +why let say we can use a some very low +Tech like a b lot of defect still works + + align:start position:0% +Tech like a b lot of defect still works + + + align:start position:0% +Tech like a b lot of defect still works +although the efficiency is not as high + + align:start position:0% +although the efficiency is not as high + + + align:start position:0% +although the efficiency is not as high +but say the pin Junction solar cells you + + align:start position:0% +but say the pin Junction solar cells you + + + align:start position:0% +but say the pin Junction solar cells you +want very pure material let's say + + align:start position:0% +want very pure material let's say + + + align:start position:0% +want very pure material let's say +because + + align:start position:0% +because + + + align:start position:0% +because +recom so this is a again standard drawn + + align:start position:0% +recom so this is a again standard drawn + + + align:start position:0% +recom so this is a again standard drawn +in + + align:start position:0% +in + + + align:start position:0% +in +books but the Le I'm going to tell you + + align:start position:0% +books but the Le I'm going to tell you + + + align:start position:0% +books but the Le I'm going to tell you +something that the most electric + + align:start position:0% +something that the most electric + + + align:start position:0% +something that the most electric +engineer doesn't + + align:start position:0% +engineer doesn't + + + align:start position:0% +engineer doesn't +know and and this is a is a p Junction a + + align:start position:0% +know and and this is a is a p Junction a + + + align:start position:0% +know and and this is a is a p Junction a +cooling or + + align:start position:0% + + + + align:start position:0% + +heating + + align:start position:0% +heating + + + align:start position:0% +heating +huh depends on what bias bias + + align:start position:0% +huh depends on what bias bias + + + align:start position:0% +huh depends on what bias bias +uh maybe yeah it depends on bias yes but + + align:start position:0% +uh maybe yeah it depends on bias yes but + + + align:start position:0% +uh maybe yeah it depends on bias yes but +say um four + + align:start position:0% +say um four + + + align:start position:0% +say um four +B + + align:start position:0% +B + + + align:start position:0% +B +okay of course you all know that the + + align:start position:0% +okay of course you all know that the + + + align:start position:0% +okay of course you all know that the +semiconductor chips have a very severe + + align:start position:0% +semiconductor chips have a very severe + + + align:start position:0% +semiconductor chips have a very severe +heating problem right so the answer l + + align:start position:0% +heating problem right so the answer l + + + align:start position:0% +heating problem right so the answer l +should be + + align:start position:0% +should be + + + align:start position:0% +should be +heated but that's actually not the case + + align:start position:0% +heated but that's actually not the case + + + align:start position:0% +heated but that's actually not the case +right so if you look at when I have a + + align:start position:0% +right so if you look at when I have a + + + align:start position:0% +right so if you look at when I have a +fourward bias and the electron go so + + align:start position:0% +fourward bias and the electron go so + + + align:start position:0% +fourward bias and the electron go so +recall before I said that the C + + align:start position:0% +recall before I said that the C + + + align:start position:0% +recall before I said that the C +coefficient is the average energy of the + + align:start position:0% +coefficient is the average energy of the + + + align:start position:0% +coefficient is the average energy of the +charge relative to chemical + + align:start position:0% +charge relative to chemical + + + align:start position:0% +charge relative to chemical +potential right so in this region the + + align:start position:0% +potential right so in this region the + + + align:start position:0% +potential right so in this region the +electron CB back + + align:start position:0% +electron CB back + + + align:start position:0% +electron CB back +smaller and it comes to this region is + + align:start position:0% +smaller and it comes to this region is + + + align:start position:0% +smaller and it comes to this region is +larger so for electron is actually + + align:start position:0% +larger so for electron is actually + + + align:start position:0% +larger so for electron is actually +pulling heat away from the junction and + + align:start position:0% +pulling heat away from the junction and + + + align:start position:0% +pulling heat away from the junction and +same is for the + + align:start position:0% + + + + align:start position:0% + +holes and then where is heat + + align:start position:0% +holes and then where is heat + + + align:start position:0% +holes and then where is heat +generated the generation so in the space + + align:start position:0% +generated the generation so in the space + + + align:start position:0% +generated the generation so in the space +charge region is actually Cooling and + + align:start position:0% +charge region is actually Cooling and + + + align:start position:0% +charge region is actually Cooling and +the generation is this + + align:start position:0% +the generation is this + + + align:start position:0% +the generation is this +recombination when they recombine + + align:start position:0% +recombination when they recombine + + + align:start position:0% +recombination when they recombine +they release that + + align:start position:0% +they release that + + + align:start position:0% +they release that +heat so if you draw + + align:start position:0% + + + + align:start position:0% + +specially and what happens this is space + + align:start position:0% +specially and what happens this is space + + + align:start position:0% +specially and what happens this is space +charge and uh it's + + align:start position:0% +charge and uh it's + + + align:start position:0% +charge and uh it's +actually uh something like this this is + + align:start position:0% +actually uh something like this this is + + + align:start position:0% +actually uh something like this this is +the this is a q + + align:start position:0% + + + + align:start position:0% + +generated let's say heat + + align:start position:0% +generated let's say heat + + + align:start position:0% +generated let's say heat +generation so Cooling in the center + + align:start position:0% +generation so Cooling in the center + + + align:start position:0% +generation so Cooling in the center +but of course that's only few Micron + + align:start position:0% +but of course that's only few Micron + + + align:start position:0% +but of course that's only few Micron +right and and there are more heat + + align:start position:0% +right and and there are more heat + + + align:start position:0% +right and and there are more heat +generate dump immediate to that and this + + align:start position:0% +generate dump immediate to that and this + + + align:start position:0% +generate dump immediate to that and this +heat reverse back quickly so it's l Co + + align:start position:0% +heat reverse back quickly so it's l Co + + + align:start position:0% +heat reverse back quickly so it's l Co +say heating but say what happens + + align:start position:0% +say heating but say what happens + + + align:start position:0% +say heating but say what happens +physically is actually Cooling in the + + align:start position:0% + + + + align:start position:0% + +junction okay and whether you can take + + align:start position:0% +junction okay and whether you can take + + + align:start position:0% +junction okay and whether you can take +advantage of that and there are in fact + + align:start position:0% +advantage of that and there are in fact + + + align:start position:0% +advantage of that and there are in fact +some papers uh trying to take advantage + + align:start position:0% +some papers uh trying to take advantage + + + align:start position:0% +some papers uh trying to take advantage +you can design how you design internal + + align:start position:0% +you can design how you design internal + + + align:start position:0% +you can design how you design internal +cool device and say lasers or uh + + align:start position:0% +cool device and say lasers or uh + + + align:start position:0% +cool device and say lasers or uh +dials okay so this is pin Junction right + + align:start position:0% +dials okay so this is pin Junction right + + + align:start position:0% +dials okay so this is pin Junction right +now what solar cell + + align:start position:0% +now what solar cell + + + align:start position:0% +now what solar cell +does so solar cell the basic equation is + + align:start position:0% +does so solar cell the basic equation is + + + align:start position:0% +does so solar cell the basic equation is +based on this just add one additional + + align:start position:0% +based on this just add one additional + + + align:start position:0% +based on this just add one additional +term what happens + + align:start position:0% +term what happens + + + align:start position:0% +term what happens +is now let's look at the solar cell + + align:start position:0% + + + + align:start position:0% + +right and uh I have for example I make a + + align:start position:0% +right and uh I have for example I make a + + + align:start position:0% +right and uh I have for example I make a +pin Junction by the way pin Junction is + + align:start position:0% +pin Junction by the way pin Junction is + + + align:start position:0% +pin Junction by the way pin Junction is +not absolutely accessary for solar cell + + align:start position:0% +not absolutely accessary for solar cell + + + align:start position:0% +not absolutely accessary for solar cell +it's most of the diffusion charge + + align:start position:0% +it's most of the diffusion charge + + + align:start position:0% +it's most of the diffusion charge +diffusion okay uh not some sort of cell + + align:start position:0% +diffusion okay uh not some sort of cell + + + align:start position:0% +diffusion okay uh not some sort of cell +like grass cell there's no pin Junction + + align:start position:0% +like grass cell there's no pin Junction + + + align:start position:0% +like grass cell there's no pin Junction +inside okay so what happens is this is + + align:start position:0% +inside okay so what happens is this is + + + align:start position:0% +inside okay so what happens is this is +my pin Junction right I put it under the + + align:start position:0% +my pin Junction right I put it under the + + + align:start position:0% +my pin Junction right I put it under the +sun + + align:start position:0% + + + + align:start position:0% + +and uh the light will come and uh get + + align:start position:0% +and uh the light will come and uh get + + + align:start position:0% +and uh the light will come and uh get +absorbed so the way I make a pin + + align:start position:0% +absorbed so the way I make a pin + + + align:start position:0% +absorbed so the way I make a pin +Junction is for example this is a uh say + + align:start position:0% +Junction is for example this is a uh say + + + align:start position:0% +Junction is for example this is a uh say +a ptype substrate and N type dopin I put + + align:start position:0% +a ptype substrate and N type dopin I put + + + align:start position:0% +a ptype substrate and N type dopin I put +a diffusion put it in contact with + + align:start position:0% +a diffusion put it in contact with + + + align:start position:0% +a diffusion put it in contact with +phosphor and the phosphor diffuse or I + + align:start position:0% +phosphor and the phosphor diffuse or I + + + align:start position:0% +phosphor and the phosphor diffuse or I +implant phosphor into the top layer and + + align:start position:0% +implant phosphor into the top layer and + + + align:start position:0% +implant phosphor into the top layer and +then make a injunction right so uh now + + align:start position:0% +then make a injunction right so uh now + + + align:start position:0% +then make a injunction right so uh now +the light strikes the surface and uh uh + + align:start position:0% +the light strikes the surface and uh uh + + + align:start position:0% +the light strikes the surface and uh uh +the energy was large larger than the + + align:start position:0% +the energy was large larger than the + + + align:start position:0% +the energy was large larger than the +bank Gap will lift the electron from + + align:start position:0% +bank Gap will lift the electron from + + + align:start position:0% +bank Gap will lift the electron from +here to here of course it can go from + + align:start position:0% +here to here of course it can go from + + + align:start position:0% +here to here of course it can go from +here to here right but for Simplicity + + align:start position:0% +here to here right but for Simplicity + + + align:start position:0% +here to here right but for Simplicity +let me focus on the space charge + + align:start position:0% +let me focus on the space charge + + + align:start position:0% +let me focus on the space charge +region so now I have space charge I go + + align:start position:0% +region so now I have space charge I go + + + align:start position:0% +region so now I have space charge I go +in from + + align:start position:0% +in from + + + align:start position:0% +in from +here I lift say here that's the Light + + align:start position:0% +here I lift say here that's the Light + + + align:start position:0% +here I lift say here that's the Light +Strike or higher energy if the bank the + + align:start position:0% +Strike or higher energy if the bank the + + + align:start position:0% +Strike or higher energy if the bank the +energy of the uh photon is larger than + + align:start position:0% +energy of the uh photon is larger than + + + align:start position:0% +energy of the uh photon is larger than +Bang + + align:start position:0% +Bang + + + align:start position:0% +Bang +now I got the access electron where they + + align:start position:0% +now I got the access electron where they + + + align:start position:0% +now I got the access electron where they +go they go here or they go + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% + + + + align:start position:0% + +huh well they go to lower energy + + align:start position:0% +huh well they go to lower energy + + + align:start position:0% +huh well they go to lower energy +first they tend to go to lower energy + + align:start position:0% +first they tend to go to lower energy + + + align:start position:0% +first they tend to go to lower energy +right so they'll go here + + align:start position:0% +right so they'll go here + + + align:start position:0% +right so they'll go here +first and when there are lot more excess + + align:start position:0% +first and when there are lot more excess + + + align:start position:0% +first and when there are lot more excess +electron + + align:start position:0% +electron + + + align:start position:0% +electron +and xess hole the hole goes here + + align:start position:0% +and xess hole the hole goes here + + + align:start position:0% +and xess hole the hole goes here +right so effectively you will raise the + + align:start position:0% +right so effectively you will raise the + + + align:start position:0% +right so effectively you will raise the +chemical potential here you will say so + + align:start position:0% +chemical potential here you will say so + + + align:start position:0% +chemical potential here you will say so +now I have a sort of a pin Junction in + + align:start position:0% +now I have a sort of a pin Junction in + + + align:start position:0% +now I have a sort of a pin Junction in +forward condition byas so what I have is + + align:start position:0% +forward condition byas so what I have is + + + align:start position:0% +forward condition byas so what I have is +really combination of two + + align:start position:0% +really combination of two + + + align:start position:0% +really combination of two +process + + align:start position:0% +process + + + align:start position:0% +process +right I do have the situation I just + + align:start position:0% +right I do have the situation I just + + + align:start position:0% +right I do have the situation I just +draw but say my charge comes from + + align:start position:0% + + + + align:start position:0% + +so I have say one is Generation the + + align:start position:0% +so I have say one is Generation the + + + align:start position:0% +so I have say one is Generation the +other is because this generate they + + align:start position:0% +other is because this generate they + + + align:start position:0% +other is because this generate they +create the forward voltage actually + + align:start position:0% +create the forward voltage actually + + + align:start position:0% +create the forward voltage actually +drive me the charge + + align:start position:0% +drive me the charge + + + align:start position:0% +drive me the charge +back right so that forward voltage + + align:start position:0% +back right so that forward voltage + + + align:start position:0% +back right so that forward voltage +driving + + align:start position:0% +driving + + + align:start position:0% +driving +back is this equation and generation I + + align:start position:0% +back is this equation and generation I + + + align:start position:0% +back is this equation and generation I +just Source a negative term so my P + + align:start position:0% +just Source a negative term so my P + + + align:start position:0% +just Source a negative term so my P +Junction + + align:start position:0% +Junction + + + align:start position:0% +Junction +equation for under illumination + + align:start position:0% + + + + align:start position:0% + +becomes J equals JS exponential + + align:start position:0% +becomes J equals JS exponential + + + align:start position:0% +becomes J equals JS exponential +e + + align:start position:0% +e + + + align:start position:0% +e +KBT Min 1 minus J of the + + align:start position:0% +KBT Min 1 minus J of the + + + align:start position:0% +KBT Min 1 minus J of the +generation this is the pair of electron + + align:start position:0% +generation this is the pair of electron + + + align:start position:0% +generation this is the pair of electron +holes + + align:start position:0% +holes + + + align:start position:0% +holes +I say photons you first you think of + + align:start position:0% +I say photons you first you think of + + + align:start position:0% +I say photons you first you think of +photons absorbed and each Photon + + align:start position:0% +photons absorbed and each Photon + + + align:start position:0% +photons absorbed and each Photon +generate one pair of electron + + align:start position:0% +generate one pair of electron + + + align:start position:0% +generate one pair of electron +hole right and say uh and that electron + + align:start position:0% +hole right and say uh and that electron + + + align:start position:0% +hole right and say uh and that electron +hole should ideally I actually I want to + + align:start position:0% +hole should ideally I actually I want to + + + align:start position:0% +hole should ideally I actually I want to +extract them out to this electrode but + + align:start position:0% +extract them out to this electrode but + + + align:start position:0% +extract them out to this electrode but +once I have voltage generated it will + + align:start position:0% +once I have voltage generated it will + + + align:start position:0% +once I have voltage generated it will +reverse back some so I have the + + align:start position:0% +reverse back some so I have the + + + align:start position:0% +reverse back some so I have the +imbalance between the two that's the + + align:start position:0% +imbalance between the two that's the + + + align:start position:0% +imbalance between the two that's the +lead current is what I want to extract + + align:start position:0% +lead current is what I want to extract + + + align:start position:0% +lead current is what I want to extract +in fact in fact if you look at this + + align:start position:0% +in fact in fact if you look at this + + + align:start position:0% +in fact in fact if you look at this +forward your current should be going + + align:start position:0% +forward your current should be going + + + align:start position:0% +forward your current should be going +this way right that's a noral + + align:start position:0% +this way right that's a noral + + + align:start position:0% +this way right that's a noral +diod if you want to make electricity you + + align:start position:0% +diod if you want to make electricity you + + + align:start position:0% +diod if you want to make electricity you +better get the negative term out of this + + align:start position:0% +better get the negative term out of this + + + align:start position:0% +better get the negative term out of this +that means this direction is not balance + + align:start position:0% +that means this direction is not balance + + + align:start position:0% +that means this direction is not balance +this reverse I take out from + + align:start position:0% +this reverse I take out from + + + align:start position:0% +this reverse I take out from +electrode right so that's the say uh uh + + align:start position:0% +electrode right so that's the say uh uh + + + align:start position:0% +electrode right so that's the say uh uh +uh equation here and uh uh if you draw + + align:start position:0% +uh equation here and uh uh if you draw + + + align:start position:0% +uh equation here and uh uh if you draw +this + + align:start position:0% + + + + align:start position:0% + +characteristics right and uh this is a + + align:start position:0% +characteristics right and uh this is a + + + align:start position:0% +characteristics right and uh this is a +diode of L say under say a Lal + + align:start position:0% +diode of L say under say a Lal + + + align:start position:0% +diode of L say under say a Lal +diode okay and this will be the one that + + align:start position:0% +diode okay and this will be the one that + + + align:start position:0% +diode okay and this will be the one that +you want out + + align:start position:0% +you want out + + + align:start position:0% +you want out +of you want out + + align:start position:0% +of you want out + + + align:start position:0% +of you want out +of say um uh solar cell this is the + + align:start position:0% +of say um uh solar cell this is the + + + align:start position:0% +of say um uh solar cell this is the +current this is the voltage + + align:start position:0% +current this is the voltage + + + align:start position:0% +current this is the voltage +exponentially increase and uh it's in + + align:start position:0% +exponentially increase and uh it's in + + + align:start position:0% +exponentially increase and uh it's in +only in this region negative + + align:start position:0% +only in this region negative + + + align:start position:0% +only in this region negative +current I'm extracting useful + + align:start position:0% +current I'm extracting useful + + + align:start position:0% +current I'm extracting useful +work right so this is say you look at + + align:start position:0% +work right so this is say you look at + + + align:start position:0% +work right so this is say you look at +the uh IV curve of a solar cell you are + + align:start position:0% +the uh IV curve of a solar cell you are + + + align:start position:0% +the uh IV curve of a solar cell you are +you should look at this region how large + + align:start position:0% +you should look at this region how large + + + align:start position:0% +you should look at this region how large +it is so this is the uh at the zero + + align:start position:0% +it is so this is the uh at the zero + + + align:start position:0% +it is so this is the uh at the zero +voltage I have JG and let say either + + align:start position:0% +voltage I have JG and let say either + + + align:start position:0% +voltage I have JG and let say either +zero current I have v o That's open + + align:start position:0% +zero current I have v o That's open + + + align:start position:0% +zero current I have v o That's open +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +voltage right short + + align:start position:0% +voltage right short + + + align:start position:0% +voltage right short +circuit + + align:start position:0% + + + + align:start position:0% + +current and uh of course the + + align:start position:0% +current and uh of course the + + + align:start position:0% +current and uh of course the +power is J * way and you have maximize + + align:start position:0% +power is J * way and you have maximize + + + align:start position:0% +power is J * way and you have maximize +it right so you have to do your DW DV + + align:start position:0% +it right so you have to do your DW DV + + + align:start position:0% +it right so you have to do your DW DV +equals z there you get a v maximum G + + align:start position:0% +equals z there you get a v maximum G + + + align:start position:0% +equals z there you get a v maximum G +maximum + + align:start position:0% +maximum + + + align:start position:0% +maximum +and you look at this it's really the + + align:start position:0% +and you look at this it's really the + + + align:start position:0% +and you look at this it's really the +small square inside so if my maximum is + + align:start position:0% +small square inside so if my maximum is + + + align:start position:0% +small square inside so if my maximum is +here that's the that's the that's the + + align:start position:0% +here that's the that's the that's the + + + align:start position:0% +here that's the that's the that's the +power I'm actually + + align:start position:0% +power I'm actually + + + align:start position:0% +power I'm actually +getting right you ideally you say I want + + align:start position:0% +getting right you ideally you say I want + + + align:start position:0% +getting right you ideally you say I want +this voltage I want this + + align:start position:0% +this voltage I want this + + + align:start position:0% +this voltage I want this +current but actually unless this is a + + align:start position:0% +current but actually unless this is a + + + align:start position:0% +current but actually unless this is a +square you don't get it so people try to + + align:start position:0% +square you don't get it so people try to + + + align:start position:0% +square you don't get it so people try to +get as close to this Square as possible + + align:start position:0% +get as close to this Square as possible + + + align:start position:0% +get as close to this Square as possible +and the quantity they Define that is the + + align:start position:0% +and the quantity they Define that is the + + + align:start position:0% +and the quantity they Define that is the +FI + + align:start position:0% + + + + align:start position:0% + +Factor + + align:start position:0% + + + + align:start position:0% + +okay and f + + align:start position:0% +okay and f + + + align:start position:0% +okay and f +equals J M VM that's a maximum and J uh + + align:start position:0% +equals J M VM that's a maximum and J uh + + + align:start position:0% +equals J M VM that's a maximum and J uh +G + + align:start position:0% +G + + + align:start position:0% +G +V so that's the larger Square outside + + align:start position:0% +V so that's the larger Square outside + + + align:start position:0% +V so that's the larger Square outside +what do you dream to have versus the + + align:start position:0% +what do you dream to have versus the + + + align:start position:0% +what do you dream to have versus the +aure you can + + align:start position:0% +aure you can + + + align:start position:0% +aure you can +extract + + align:start position:0% +extract + + + align:start position:0% +extract +right and then most so you look at this + + align:start position:0% +right and then most so you look at this + + + align:start position:0% +right and then most so you look at this +curve sometimes people make a sale they + + align:start position:0% +curve sometimes people make a sale they + + + align:start position:0% +curve sometimes people make a sale they +look like + + align:start position:0% + + + + align:start position:0% + +this if you with the expert eye you can + + align:start position:0% +this if you with the expert eye you can + + + align:start position:0% +this if you with the expert eye you can +tell what you should + + align:start position:0% + + + + align:start position:0% + +do internal resistance electric + + align:start position:0% +do internal resistance electric + + + align:start position:0% +do internal resistance electric +resistance too large so you have this IV + + align:start position:0% +resistance too large so you have this IV + + + align:start position:0% +resistance too large so you have this IV +in resistance that resistance come from + + align:start position:0% +in resistance that resistance come from + + + align:start position:0% +in resistance that resistance come from +so you have different mechanism that can + + align:start position:0% +so you have different mechanism that can + + + align:start position:0% +so you have different mechanism that can +have say different sort of uh say loss + + align:start position:0% +have say different sort of uh say loss + + + align:start position:0% +have say different sort of uh say loss +in the C and your game is trying to + + align:start position:0% +in the C and your game is trying to + + + align:start position:0% +in the C and your game is trying to +extract as much power as + + align:start position:0% +extract as much power as + + + align:start position:0% +extract as much power as +possible + + align:start position:0% +possible + + + align:start position:0% +possible +right then the question is what's the + + align:start position:0% +right then the question is what's the + + + align:start position:0% +right then the question is what's the +maximum what's the best I can do + + align:start position:0% +maximum what's the best I can do + + + align:start position:0% +maximum what's the best I can do +right first say JG I can say JG is the L + + align:start position:0% +right first say JG I can say JG is the L + + + align:start position:0% +right first say JG I can say JG is the L +of electron whole pair I can say this is + + align:start position:0% +of electron whole pair I can say this is + + + align:start position:0% +of electron whole pair I can say this is +JG is let's say + + align:start position:0% +JG is let's say + + + align:start position:0% +JG is let's say +electron and from the sand to the Earth + + align:start position:0% +electron and from the sand to the Earth + + + align:start position:0% +electron and from the sand to the Earth +that's a vew factor right and this + + align:start position:0% +that's a vew factor right and this + + + align:start position:0% +that's a vew factor right and this +conversion of phot photon you thinking + + align:start position:0% +conversion of phot photon you thinking + + + align:start position:0% +conversion of phot photon you thinking +about the photon from this sign dilute + + align:start position:0% +about the photon from this sign dilute + + + align:start position:0% +about the photon from this sign dilute +as you go larger radius it's water + + align:start position:0% +as you go larger radius it's water + + + align:start position:0% +as you go larger radius it's water +fraction of the uh say uh uh say Photon + + align:start position:0% +fraction of the uh say uh uh say Photon + + + align:start position:0% +fraction of the uh say uh uh say Photon +emitted fall into the Earth and then say + + align:start position:0% +emitted fall into the Earth and then say + + + align:start position:0% +emitted fall into the Earth and then say +the absorption so let's say I do a uh + + align:start position:0% +the absorption so let's say I do a uh + + + align:start position:0% +the absorption so let's say I do a uh +say 1 R uh Omega the reflection that's + + align:start position:0% +say 1 R uh Omega the reflection that's + + + align:start position:0% +say 1 R uh Omega the reflection that's +assuming everything getting the photon + + align:start position:0% +assuming everything getting the photon + + + align:start position:0% +assuming everything getting the photon +the front surface is absorbed of course + + align:start position:0% +the front surface is absorbed of course + + + align:start position:0% +the front surface is absorbed of course +it could have transmission so you really + + align:start position:0% +it could have transmission so you really + + + align:start position:0% +it could have transmission so you really +need to maximize that absorption so this + + align:start position:0% +need to maximize that absorption so this + + + align:start position:0% +need to maximize that absorption so this +is this one you can also write as a + + align:start position:0% +is this one you can also write as a + + + align:start position:0% +is this one you can also write as a +Omega absorption right and and then if + + align:start position:0% +Omega absorption right and and then if + + + align:start position:0% +Omega absorption right and and then if +this is the solar + + align:start position:0% +this is the solar + + + align:start position:0% +this is the solar +Spectrum sand which is the sand + + align:start position:0% +Spectrum sand which is the sand + + + align:start position:0% +Spectrum sand which is the sand +temperature as a function of Omega and + + align:start position:0% +temperature as a function of Omega and + + + align:start position:0% +temperature as a function of Omega and +that's the intensity I divide by H bar + + align:start position:0% +that's the intensity I divide by H bar + + + align:start position:0% +that's the intensity I divide by H bar +Omega that's a lumber + + align:start position:0% +Omega that's a lumber + + + align:start position:0% +Omega that's a lumber +flux right because that's energy + + align:start position:0% +flux right because that's energy + + + align:start position:0% +flux right because that's energy +intensity I just want to count how many + + align:start position:0% +intensity I just want to count how many + + + align:start position:0% +intensity I just want to count how many +Photon because the excess energy I can't + + align:start position:0% +Photon because the excess energy I can't + + + align:start position:0% +Photon because the excess energy I can't +capture unless a mega half Cale + + align:start position:0% +capture unless a mega half Cale + + + align:start position:0% +capture unless a mega half Cale +there and this is D Omega so this gives + + align:start position:0% +there and this is D Omega so this gives + + + align:start position:0% +there and this is D Omega so this gives +me how how many electron hold pairs are + + align:start position:0% +me how how many electron hold pairs are + + + align:start position:0% +me how how many electron hold pairs are +generated in the + + align:start position:0% +generated in the + + + align:start position:0% +generated in the +cell so that gives me uh you can always + + align:start position:0% +cell so that gives me uh you can always + + + align:start position:0% +cell so that gives me uh you can always +Maxim let's suppose this is one that's + + align:start position:0% +Maxim let's suppose this is one that's + + + align:start position:0% +Maxim let's suppose this is one that's +maximum L you can do right absor all + + align:start position:0% +maximum L you can do right absor all + + + align:start position:0% +maximum L you can do right absor all +Photon Genera and of course you have to + + align:start position:0% +Photon Genera and of course you have to + + + align:start position:0% +Photon Genera and of course you have to +count only the photons with wavelengths + + align:start position:0% +count only the photons with wavelengths + + + align:start position:0% +count only the photons with wavelengths +larger than the bank Gap right if this + + align:start position:0% +larger than the bank Gap right if this + + + align:start position:0% +larger than the bank Gap right if this +is band Gap divide by H bar that's the + + align:start position:0% +is band Gap divide by H bar that's the + + + align:start position:0% +is band Gap divide by H bar that's the +corresponding frequency to the G band + + align:start position:0% +corresponding frequency to the G band + + + align:start position:0% +corresponding frequency to the G band +Gap about + + align:start position:0% + + + + align:start position:0% + +semiconductor so this term you can + + align:start position:0% +semiconductor so this term you can + + + align:start position:0% +semiconductor so this term you can +easily + + align:start position:0% +easily + + + align:start position:0% +easily +calculate and part of research is + + align:start position:0% +calculate and part of research is + + + align:start position:0% +calculate and part of research is +actually on how I can maximize this + + align:start position:0% +actually on how I can maximize this + + + align:start position:0% +actually on how I can maximize this +absorption or minimize the material + + align:start position:0% +absorption or minimize the material + + + align:start position:0% +absorption or minimize the material +usage that's relate to your + + align:start position:0% + + + + align:start position:0% + +cost the key is how I can if I want to + + align:start position:0% +cost the key is how I can if I want to + + + align:start position:0% +cost the key is how I can if I want to +answer this question what's my maximum + + align:start position:0% +answer this question what's my maximum + + + align:start position:0% +answer this question what's my maximum +the question is what's here + + align:start position:0% +the question is what's here + + + align:start position:0% +the question is what's here +what's the minimum + + align:start position:0% +what's the minimum + + + align:start position:0% +what's the minimum +here it turns out that you want this JS + + align:start position:0% +here it turns out that you want this JS + + + align:start position:0% +here it turns out that you want this JS +to be small you go to do your math so + + align:start position:0% +to be small you go to do your math so + + + align:start position:0% +to be small you go to do your math so +what's the + + align:start position:0% +what's the + + + align:start position:0% +what's the +minimum and this is where again + + align:start position:0% +minimum and this is where again + + + align:start position:0% +minimum and this is where again +shockly okay and uh uh see he developed + + align:start position:0% +shockly okay and uh uh see he developed + + + align:start position:0% +shockly okay and uh uh see he developed +this say shly and + + align:start position:0% +this say shly and + + + align:start position:0% +this say shly and +quiser + + align:start position:0% + + + + align:start position:0% + +limit he say even if here what we have + + align:start position:0% +limit he say even if here what we have + + + align:start position:0% +limit he say even if here what we have +is + + align:start position:0% +is + + + align:start position:0% +is +really say diffusion + + align:start position:0% +really say diffusion + + + align:start position:0% +really say diffusion +recombination right if you make a very + + align:start position:0% +recombination right if you make a very + + + align:start position:0% +recombination right if you make a very +perfect conductor no say diffusion is + + align:start position:0% +perfect conductor no say diffusion is + + + align:start position:0% +perfect conductor no say diffusion is +very large and recombination no defects + + align:start position:0% +very large and recombination no defects + + + align:start position:0% +very large and recombination no defects +inside no long redtive + + align:start position:0% +inside no long redtive + + + align:start position:0% +inside no long redtive +recombination but you still have to have + + align:start position:0% +recombination but you still have to have + + + align:start position:0% +recombination but you still have to have +the photon comes in you have to have you + + align:start position:0% +the photon comes in you have to have you + + + align:start position:0% +the photon comes in you have to have you +can't just accumulator so there got to + + align:start position:0% +can't just accumulator so there got to + + + align:start position:0% +can't just accumulator so there got to +be the the the this Lum back bance there + + align:start position:0% +be the the the this Lum back bance there + + + align:start position:0% +be the the the this Lum back bance there +so it say the radi of the + + align:start position:0% +so it say the radi of the + + + align:start position:0% +so it say the radi of the +recombination actually gets you + + align:start position:0% +recombination actually gets you + + + align:start position:0% +recombination actually gets you +maximum okay + + align:start position:0% +maximum okay + + + align:start position:0% +maximum okay +so once you have so what shockly say + + align:start position:0% +so once you have so what shockly say + + + align:start position:0% +so once you have so what shockly say +okay now you create a open circuit right + + align:start position:0% +okay now you create a open circuit right + + + align:start position:0% +okay now you create a open circuit right +let's suppose I'm not connecting myself + + align:start position:0% +let's suppose I'm not connecting myself + + + align:start position:0% +let's suppose I'm not connecting myself +I have imbalance between electron + + align:start position:0% +I have imbalance between electron + + + align:start position:0% +I have imbalance between electron +hole that's a EV there's no voltage drop + + align:start position:0% +hole that's a EV there's no voltage drop + + + align:start position:0% +hole that's a EV there's no voltage drop +there's no internal + + align:start position:0% +there's no internal + + + align:start position:0% +there's no internal +resistance so e is my balance in the qu + + align:start position:0% +resistance so e is my balance in the qu + + + align:start position:0% +resistance so e is my balance in the qu +fir level so electron hold L at + + align:start position:0% +fir level so electron hold L at + + + align:start position:0% +fir level so electron hold L at +equili and the photon emission so this + + align:start position:0% +equili and the photon emission so this + + + align:start position:0% +equili and the photon emission so this +is I said before normally we say Photon + + align:start position:0% +is I said before normally we say Photon + + + align:start position:0% +is I said before normally we say Photon +chemical potential + + align:start position:0% +chemical potential + + + align:start position:0% +chemical potential +zero and what chocolate written + + align:start position:0% + + + + align:start position:0% + +down + + align:start position:0% +down + + + align:start position:0% +down +is if you you have this dyamic + + align:start position:0% +is if you you have this dyamic + + + align:start position:0% +is if you you have this dyamic +equilibrium right Photon comes in radi + + align:start position:0% +equilibrium right Photon comes in radi + + + align:start position:0% +equilibrium right Photon comes in radi +recombination and the photon + + align:start position:0% +recombination and the photon + + + align:start position:0% +recombination and the photon +immedate is e h say is H Omega Min e + + align:start position:0% +immedate is e h say is H Omega Min e + + + align:start position:0% +immedate is e h say is H Omega Min e +over + + align:start position:0% +over + + + align:start position:0% +over +KBT uh say let's say here I have uh Mass + + align:start position:0% +KBT uh say let's say here I have uh Mass + + + align:start position:0% +KBT uh say let's say here I have uh Mass +one this a photon right so normally if + + align:start position:0% +one this a photon right so normally if + + + align:start position:0% +one this a photon right so normally if +there's no + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% +that's + + + align:start position:0% +that's +the uh say B Einstein distribution for + + align:start position:0% +the uh say B Einstein distribution for + + + align:start position:0% +the uh say B Einstein distribution for +Photon + + align:start position:0% +Photon + + + align:start position:0% +Photon +right but shly added this + + align:start position:0% +right but shly added this + + + align:start position:0% +right but shly added this +EV so Photon now + + align:start position:0% +EV so Photon now + + + align:start position:0% +EV so Photon now +emitted as a chemical + + align:start position:0% +emitted as a chemical + + + align:start position:0% +emitted as a chemical +potential right you go to read shly qu + + align:start position:0% +potential right you go to read shly qu + + + align:start position:0% +potential right you go to read shly qu +see this is a shockly + + align:start position:0% + + + + align:start position:0% + +quiser uh shockly + + align:start position:0% +quiser uh shockly + + + align:start position:0% +quiser uh shockly +I hope I'm writing everything right shly + + align:start position:0% +I hope I'm writing everything right shly + + + align:start position:0% +I hope I'm writing everything right shly +quiser + + align:start position:0% +quiser + + + align:start position:0% +quiser +uh + + align:start position:0% +uh + + + align:start position:0% +uh +okay this one you have to check the name + + align:start position:0% +okay this one you have to check the name + + + align:start position:0% +okay this one you have to check the name +maybe I'm spelling wrong uh this is sh + + align:start position:0% +maybe I'm spelling wrong uh this is sh + + + align:start position:0% +maybe I'm spelling wrong uh this is sh +quer + + align:start position:0% +quer + + + align:start position:0% +quer +limit and the shockly quiser paper you + + align:start position:0% +limit and the shockly quiser paper you + + + align:start position:0% +limit and the shockly quiser paper you +go to read + + align:start position:0% +go to read + + + align:start position:0% +go to read +it uh it's very difficult they did a b + + align:start position:0% +it uh it's very difficult they did a b + + + align:start position:0% +it uh it's very difficult they did a b +detail balance argument I don't think I + + align:start position:0% +detail balance argument I don't think I + + + align:start position:0% +detail balance argument I don't think I +read full through that paper then I I + + align:start position:0% +read full through that paper then I I + + + align:start position:0% +read full through that paper then I I +read many papers and this is where + + align:start position:0% +read many papers and this is where + + + align:start position:0% +read many papers and this is where +really uh for many years I was always + + align:start position:0% +really uh for many years I was always + + + align:start position:0% +really uh for many years I was always +asking student in the class show me a + + align:start position:0% +asking student in the class show me a + + + align:start position:0% +asking student in the class show me a +better way to derive it + + align:start position:0% +better way to derive it + + + align:start position:0% +better way to derive it +okay and uh uh there's another paper so + + align:start position:0% +okay and uh uh there's another paper so + + + align:start position:0% +okay and uh uh there's another paper so +by + + align:start position:0% + + + + align:start position:0% + +Henry and this is a cited in the book + + align:start position:0% +Henry and this is a cited in the book + + + align:start position:0% +Henry and this is a cited in the book +you can read that JP there's another + + align:start position:0% +you can read that JP there's another + + + align:start position:0% +you can read that JP there's another +paper by Ross + + align:start position:0% +paper by Ross + + + align:start position:0% +paper by Ross +uh uh I forgot where was was it in + + align:start position:0% +uh uh I forgot where was was it in + + + align:start position:0% +uh uh I forgot where was was it in +chemistry journals so the say then there + + align:start position:0% +chemistry journals so the say then there + + + align:start position:0% +chemistry journals so the say then there +was a um I think they there's a paper by + + align:start position:0% + + + + align:start position:0% + +wer Peter wolle um uh those are some of + + align:start position:0% +wer Peter wolle um uh those are some of + + + align:start position:0% +wer Peter wolle um uh those are some of +the good papers and try to read and + + align:start position:0% +the good papers and try to read and + + + align:start position:0% +the good papers and try to read and +really see how you can derive + + align:start position:0% +really see how you can derive + + + align:start position:0% +really see how you can derive +this okay and uh so I spent it actually + + align:start position:0% +this okay and uh so I spent it actually + + + align:start position:0% +this okay and uh so I spent it actually +quite a long time + + align:start position:0% +quite a long time + + + align:start position:0% +quite a long time +and now I think uh I'm roughly I can + + align:start position:0% +and now I think uh I'm roughly I can + + + align:start position:0% +and now I think uh I'm roughly I can +give explanation I'm still trying to + + align:start position:0% +give explanation I'm still trying to + + + align:start position:0% +give explanation I'm still trying to +look at my notes to my notebook and uh I + + align:start position:0% +look at my notes to my notebook and uh I + + + align:start position:0% +look at my notes to my notebook and uh I +didn't quite to figure out what I did uh + + align:start position:0% +didn't quite to figure out what I did uh + + + align:start position:0% +didn't quite to figure out what I did uh +so I'll give you this half this story + + align:start position:0% +so I'll give you this half this story + + + align:start position:0% +so I'll give you this half this story +you can go back to make up the + + align:start position:0% +you can go back to make up the + + + align:start position:0% +you can go back to make up the +rest okay so it turns out this one you + + align:start position:0% +rest okay so it turns out this one you + + + align:start position:0% +rest okay so it turns out this one you +have to my view is you have to this is + + align:start position:0% +have to my view is you have to this is + + + align:start position:0% +have to my view is you have to this is +also uh in war Force paper you have to + + align:start position:0% +also uh in war Force paper you have to + + + align:start position:0% +also uh in war Force paper you have to +look at the electron you have to look at + + align:start position:0% +look at the electron you have to look at + + + align:start position:0% +look at the electron you have to look at +photon + + align:start position:0% +photon + + + align:start position:0% +photon +as a + + align:start position:0% +as a + + + align:start position:0% +as a +combine right because this electron we + + align:start position:0% +combine right because this electron we + + + align:start position:0% +combine right because this electron we +combine with whole and generate + + align:start position:0% +combine with whole and generate + + + align:start position:0% +combine with whole and generate +Photon so uh you can write the first the + + align:start position:0% +Photon so uh you can write the first the + + + align:start position:0% +Photon so uh you can write the first the +the say thermodynamic laws let's say the + + align:start position:0% +the say thermodynamic laws let's say the + + + align:start position:0% +the say thermodynamic laws let's say the +electron + + align:start position:0% +electron + + + align:start position:0% +electron +energy right and the energy equals DQ DQ + + align:start position:0% +energy right and the energy equals DQ DQ + + + align:start position:0% +energy right and the energy equals DQ DQ +is a t d uh SE + + align:start position:0% +is a t d uh SE + + + align:start position:0% +is a t d uh SE +entropy right + + align:start position:0% +entropy right + + + align:start position:0% +entropy right +and mass p d + + align:start position:0% +and mass p d + + + align:start position:0% +and mass p d +v and plus mu e + + align:start position:0% +v and plus mu e + + + align:start position:0% +v and plus mu e +DN + + align:start position:0% + + + + align:start position:0% + +e right so this is + + align:start position:0% +e right so this is + + + align:start position:0% +e right so this is +the first second law together for + + align:start position:0% +the first second law together for + + + align:start position:0% +the first second law together for +electrons I'm going to also + + align:start position:0% +electrons I'm going to also + + + align:start position:0% +electrons I'm going to also +write the + + align:start position:0% +write the + + + align:start position:0% +write the +holes + + align:start position:0% +holes + + + align:start position:0% +holes +tdso must p D way plus + + align:start position:0% +tdso must p D way plus + + + align:start position:0% +tdso must p D way plus +mu uh + + align:start position:0% +mu uh + + + align:start position:0% +mu uh +whole DN + + align:start position:0% +whole DN + + + align:start position:0% +whole DN +ho + + align:start position:0% +ho + + + align:start position:0% +ho +right so in a recompilation + + align:start position:0% +right so in a recompilation + + + align:start position:0% +right so in a recompilation +process I have my electron L reduced by + + align:start position:0% +process I have my electron L reduced by + + + align:start position:0% +process I have my electron L reduced by +one whole L reduced by + + align:start position:0% +one whole L reduced by + + + align:start position:0% +one whole L reduced by +one right and say uh so I sum up so PV I + + align:start position:0% +one right and say uh so I sum up so PV I + + + align:start position:0% +one right and say uh so I sum up so PV I +don't know how to deal with PV in + + align:start position:0% +don't know how to deal with PV in + + + align:start position:0% +don't know how to deal with PV in +semiconductor + + align:start position:0% +semiconductor + + + align:start position:0% +semiconductor +so I dropped it uh I'm still reading + + align:start position:0% +so I dropped it uh I'm still reading + + + align:start position:0% +so I dropped it uh I'm still reading +books so I dropped this okay and the + + align:start position:0% +books so I dropped this okay and the + + + align:start position:0% +books so I dropped this okay and the +book to read is uh lown lifes I was + + align:start position:0% +book to read is uh lown lifes I was + + + align:start position:0% +book to read is uh lown lifes I was +reading last + + align:start position:0% + + + + align:start position:0% + +slide like I said always for in to + + align:start position:0% +slide like I said always for in to + + + align:start position:0% +slide like I said always for in to +sleep + + align:start position:0% + + + + align:start position:0% + +okay now you do that you get a + + align:start position:0% +okay now you do that you get a + + + align:start position:0% +okay now you do that you get a +d + + align:start position:0% +d + + + align:start position:0% +d +e plus D are I should do + + align:start position:0% + + + + align:start position:0% + +whole so t d SE e plus s ho and I said I + + align:start position:0% +whole so t d SE e plus s ho and I said I + + + align:start position:0% +whole so t d SE e plus s ho and I said I +dropped that so uh uh so this is a minus + + align:start position:0% +dropped that so uh uh so this is a minus + + + align:start position:0% +dropped that so uh uh so this is a minus +because when my electron and the whole + + align:start position:0% +because when my electron and the whole + + + align:start position:0% +because when my electron and the whole +Rec combine DN is negative one right so + + align:start position:0% +Rec combine DN is negative one right so + + + align:start position:0% +Rec combine DN is negative one right so +I have so I have mass mu e+ mu H and + + align:start position:0% +I have so I have mass mu e+ mu H and + + + align:start position:0% +I have so I have mass mu e+ mu H and +this is the energy + + align:start position:0% +this is the energy + + + align:start position:0% +this is the energy +EV you have to so here you have to look + + align:start position:0% +EV you have to so here you have to look + + + align:start position:0% +EV you have to so here you have to look +at electron energy increas in this way + + align:start position:0% +at electron energy increas in this way + + + align:start position:0% +at electron energy increas in this way +whole energy increasing that way and you + + align:start position:0% +whole energy increasing that way and you + + + align:start position:0% +whole energy increasing that way and you +have to write the details but uh just + + align:start position:0% +have to write the details but uh just + + + align:start position:0% +have to write the details but uh just +put in fact I was debating whether it's + + align:start position:0% +put in fact I was debating whether it's + + + align:start position:0% +put in fact I was debating whether it's +a negative e or positive e so my son has + + align:start position:0% +a negative e or positive e so my son has + + + align:start position:0% +a negative e or positive e so my son has +a problem + + align:start position:0% +a problem + + + align:start position:0% +a problem +maybe okay like that's why I say I now I + + align:start position:0% +maybe okay like that's why I say I now I + + + align:start position:0% +maybe okay like that's why I say I now I +derived this before but uh just trying + + align:start position:0% +derived this before but uh just trying + + + align:start position:0% +derived this before but uh just trying +to look at my notes and here + + align:start position:0% +to look at my notes and here + + + align:start position:0% +to look at my notes and here +whole + + align:start position:0% +whole + + + align:start position:0% +whole +energy right the system they decrease + + align:start position:0% +energy right the system they decrease + + + align:start position:0% +energy right the system they decrease +energy by H Omega because they re + + align:start position:0% +energy by H Omega because they re + + + align:start position:0% +energy by H Omega because they re +combine so I have uh same probably again + + align:start position:0% +combine so I have uh same probably again + + + align:start position:0% +combine so I have uh same probably again +you have to look at this you have to so + + align:start position:0% +you have to look at this you have to so + + + align:start position:0% +you have to look at this you have to so +this is applying your + + align:start position:0% +this is applying your + + + align:start position:0% +this is applying your +thermodynamics your second law your + + align:start position:0% +thermodynamics your second law your + + + align:start position:0% +thermodynamics your second law your +first law you need to take your system + + align:start position:0% +first law you need to take your system + + + align:start position:0% +first law you need to take your system +and you need to say the sign whether + + align:start position:0% +and you need to say the sign whether + + + align:start position:0% +and you need to say the sign whether +it's increasing or decreasing + + align:start position:0% +it's increasing or decreasing + + + align:start position:0% +it's increasing or decreasing +right then the question + + align:start position:0% +right then the question + + + align:start position:0% +right then the question +is this + + align:start position:0% + + + + align:start position:0% + +right so here is if you take + + align:start position:0% +right so here is if you take + + + align:start position:0% +right so here is if you take +this and uh you go to look at + + align:start position:0% +this and uh you go to look at + + + align:start position:0% +this and uh you go to look at +the electron Fon interaction does it + + align:start position:0% +the electron Fon interaction does it + + + align:start position:0% +the electron Fon interaction does it +generate if you emit a photon that's a + + align:start position:0% +generate if you emit a photon that's a + + + align:start position:0% +generate if you emit a photon that's a +general + + align:start position:0% +general + + + align:start position:0% +general +entropy this is + + align:start position:0% +entropy this is + + + align:start position:0% +entropy this is +where okay I say I can if I if I emit a + + align:start position:0% +where okay I say I can if I if I emit a + + + align:start position:0% +where okay I say I can if I if I emit a +photon I have no introp generation + + align:start position:0% + + + + align:start position:0% + +if I do other stuff so what I want + + align:start position:0% +if I do other stuff so what I want + + + align:start position:0% +if I do other stuff so what I want +basically I'm arguing why this is a you + + align:start position:0% +basically I'm arguing why this is a you + + + align:start position:0% +basically I'm arguing why this is a you +read it's not WR anywhere okay I'm just + + align:start position:0% +read it's not WR anywhere okay I'm just + + + align:start position:0% +read it's not WR anywhere okay I'm just +making this argument why this is the + + align:start position:0% +making this argument why this is the + + + align:start position:0% +making this argument why this is the +most efficient R recombination right and + + align:start position:0% +most efficient R recombination right and + + + align:start position:0% +most efficient R recombination right and +it's a process doesn't generate entropy + + align:start position:0% +it's a process doesn't generate entropy + + + align:start position:0% +it's a process doesn't generate entropy +so what I'm going to have is this is the + + align:start position:0% +so what I'm going to have is this is the + + + align:start position:0% +so what I'm going to have is this is the +entropy decrease because the electron + + align:start position:0% +entropy decrease because the electron + + + align:start position:0% +entropy decrease because the electron +hold loss so I say I will say this is + + align:start position:0% +hold loss so I say I will say this is + + + align:start position:0% +hold loss so I say I will say this is +equal the photon + + align:start position:0% +equal the photon + + + align:start position:0% +equal the photon +entropy that's carried away right if you + + align:start position:0% +entropy that's carried away right if you + + + align:start position:0% +entropy that's carried away right if you +make a Col + + align:start position:0% +make a Col + + + align:start position:0% +make a Col +engine you don't want entropy + + align:start position:0% +engine you don't want entropy + + + align:start position:0% +engine you don't want entropy +generation so this is the entropy of the + + align:start position:0% +generation so this is the entropy of the + + + align:start position:0% +generation so this is the entropy of the +foldon carried + + align:start position:0% +foldon carried + + + align:start position:0% +foldon carried +away and the next step is you have to + + align:start position:0% +away and the next step is you have to + + + align:start position:0% +away and the next step is you have to +write what's the entropy what because I + + align:start position:0% +write what's the entropy what because I + + + align:start position:0% +write what's the entropy what because I +need a distribution what's the entropy + + align:start position:0% +need a distribution what's the entropy + + + align:start position:0% +need a distribution what's the entropy +and distribution function relation right + + align:start position:0% +and distribution function relation right + + + align:start position:0% +and distribution function relation right +and I wasn't assume a prior there's the + + align:start position:0% +and I wasn't assume a prior there's the + + + align:start position:0% +and I wasn't assume a prior there's the +equilibrium so I went + + align:start position:0% +equilibrium so I went + + + align:start position:0% +equilibrium so I went +to say because I know this expression + + align:start position:0% +to say because I know this expression + + + align:start position:0% +to say because I know this expression +but actually I wasn't quite sure whether + + align:start position:0% +but actually I wasn't quite sure whether + + + align:start position:0% +but actually I wasn't quite sure whether +it's valid for equilibrium or non + + align:start position:0% +it's valid for equilibrium or non + + + align:start position:0% +it's valid for equilibrium or non +equinum but then I say n book Clearly + + align:start position:0% +equinum but then I say n book Clearly + + + align:start position:0% +equinum but then I say n book Clearly +say this is General so this is what we + + align:start position:0% +say this is General so this is what we + + + align:start position:0% +say this is General so this is what we +have so for a phon system or bosan right + + align:start position:0% +have so for a phon system or bosan right + + + align:start position:0% +have so for a phon system or bosan right +the + + align:start position:0% +the + + + align:start position:0% +the +entropy of + + align:start position:0% +entropy of + + + align:start position:0% +entropy of +ban is 1 + f log + + align:start position:0% +ban is 1 + f log + + + align:start position:0% +ban is 1 + f log +1 + + + align:start position:0% +1 + + + + align:start position:0% +1 + +F and M F log F so if you use this + + align:start position:0% +F and M F log F so if you use this + + + align:start position:0% +F and M F log F so if you use this +relation if I say one so you take a + + align:start position:0% +relation if I say one so you take a + + + align:start position:0% +relation if I say one so you take a +derivative one mode this is sum up all + + align:start position:0% +derivative one mode this is sum up all + + + align:start position:0% +derivative one mode this is sum up all +modes right so I'm only taking a + + align:start position:0% +modes right so I'm only taking a + + + align:start position:0% +modes right so I'm only taking a +derivative I have one more DF D and you + + align:start position:0% +derivative I have one more DF D and you + + + align:start position:0% +derivative I have one more DF D and you +solve this + + align:start position:0% +solve this + + + align:start position:0% +solve this +equation you'll get the shock + + align:start position:0% +equation you'll get the shock + + + align:start position:0% +equation you'll get the shock +requer + + align:start position:0% +requer + + + align:start position:0% +requer +that + + align:start position:0% +that + + + align:start position:0% +that +expression okay so this is the one that + + align:start position:0% +expression okay so this is the one that + + + align:start position:0% +expression okay so this is the one that +I finally feel comfortable to tell + + align:start position:0% +I finally feel comfortable to tell + + + align:start position:0% +I finally feel comfortable to tell +because in the past I always ask a + + align:start position:0% +because in the past I always ask a + + + align:start position:0% +because in the past I always ask a +student to show me because I read all + + align:start position:0% +student to show me because I read all + + + align:start position:0% +student to show me because I read all +this paper I don't feel + + align:start position:0% +this paper I don't feel + + + align:start position:0% +this paper I don't feel +comfortable but uh maybe you can go to + + align:start position:0% +comfortable but uh maybe you can go to + + + align:start position:0% +comfortable but uh maybe you can go to +make up those detail and convince + + align:start position:0% +make up those detail and convince + + + align:start position:0% +make up those detail and convince +yourself it's a so I'm still debating + + align:start position:0% +yourself it's a so I'm still debating + + + align:start position:0% +yourself it's a so I'm still debating +I'm trying to uh in fact this morning + + align:start position:0% +I'm trying to uh in fact this morning + + + align:start position:0% +I'm trying to uh in fact this morning +this week I have program review on the + + align:start position:0% +this week I have program review on the + + + align:start position:0% +this week I have program review on the +solar PV program project I have with doe + + align:start position:0% +solar PV program project I have with doe + + + align:start position:0% +solar PV program project I have with doe +and one of the question I've been asking + + align:start position:0% +and one of the question I've been asking + + + align:start position:0% +and one of the question I've been asking +and I've been working through this few + + align:start position:0% +and I've been working through this few + + + align:start position:0% +and I've been working through this few +months myself is trying to say what's + + align:start position:0% +months myself is trying to say what's + + + align:start position:0% +months myself is trying to say what's +the entropy generation process in the + + align:start position:0% +the entropy generation process in the + + + align:start position:0% +the entropy generation process in the +solar cell right because with that you + + align:start position:0% +solar cell right because with that you + + + align:start position:0% +solar cell right because with that you +will get the + + align:start position:0% +will get the + + + align:start position:0% +will get the +maximum with shock requer radi + + align:start position:0% +maximum with shock requer radi + + + align:start position:0% +maximum with shock requer radi +recombination and in fact you don't even + + align:start position:0% +recombination and in fact you don't even + + + align:start position:0% +recombination and in fact you don't even +need this equation you don't even need + + align:start position:0% +need this equation you don't even need + + + align:start position:0% +need this equation you don't even need +this equation you just say shock requis + + align:start position:0% +this equation you just say shock requis + + + align:start position:0% +this equation you just say shock requis +give me the voltage that balance the uh + + align:start position:0% +give me the voltage that balance the uh + + + align:start position:0% +give me the voltage that balance the uh +the income com in the lead difference it + + align:start position:0% +the income com in the lead difference it + + + align:start position:0% +the income com in the lead difference it +gives me the current I can extract and + + align:start position:0% +gives me the current I can extract and + + + align:start position:0% +gives me the current I can extract and +you find the maximum power and this is + + align:start position:0% +you find the maximum power and this is + + + align:start position:0% +you find the maximum power and this is +say if you do all the maths you'll find + + align:start position:0% +say if you do all the maths you'll find + + + align:start position:0% +say if you do all the maths you'll find +out that at the end this this typical + + align:start position:0% +out that at the end this this typical + + + align:start position:0% +out that at the end this this typical +curve of uh here the maximum efficiency + + align:start position:0% +curve of uh here the maximum efficiency + + + align:start position:0% +curve of uh here the maximum efficiency +for one single Junction band solar cell + + align:start position:0% +for one single Junction band solar cell + + + align:start position:0% +for one single Junction band solar cell +and this happen this is the bank gap of + + align:start position:0% +and this happen this is the bank gap of + + + align:start position:0% +and this happen this is the bank gap of +semiconductor and this is about + + align:start position:0% +semiconductor and this is about + + + align:start position:0% +semiconductor and this is about +1.4 and the maximum here depends on + + align:start position:0% +1.4 and the maximum here depends on + + + align:start position:0% +1.4 and the maximum here depends on +which spectrum of the solar radiation + + align:start position:0% +which spectrum of the solar radiation + + + align:start position:0% +which spectrum of the solar radiation +you use those lbers change sh requ first + + align:start position:0% +you use those lbers change sh requ first + + + align:start position:0% +you use those lbers change sh requ first +assume it's a black body right and then + + align:start position:0% +assume it's a black body right and then + + + align:start position:0% +assume it's a black body right and then +say later on people take the real solar + + align:start position:0% +say later on people take the real solar + + + align:start position:0% +say later on people take the real solar +spectrum and red the calculation so + + align:start position:0% +spectrum and red the calculation so + + + align:start position:0% +spectrum and red the calculation so +those L is around + + align:start position:0% +those L is around + + + align:start position:0% +those L is around +30% + + align:start position:0% +30% + + + align:start position:0% +30% +efficient that's called Shock requis + + align:start position:0% +efficient that's called Shock requis + + + align:start position:0% +efficient that's called Shock requis +name + + align:start position:0% + + + + align:start position:0% + +okay any + + align:start position:0% +okay any + + + align:start position:0% +okay any +questions so I told you Half Baked + + align:start position:0% +questions so I told you Half Baked + + + align:start position:0% +questions so I told you Half Baked +work I was trying to find from my + + align:start position:0% +work I was trying to find from my + + + align:start position:0% +work I was trying to find from my +notes + + align:start position:0% + + + + align:start position:0% + +okay you should be able to say + + align:start position:0% +okay you should be able to say + + + align:start position:0% +okay you should be able to say +the exam problem now \ No newline at end of file diff --git a/ZyDktXm6v-s.txt b/ZyDktXm6v-s.txt new file mode 100644 index 0000000000000000000000000000000000000000..2452bef7104244cd0e3ac73be011c3a1696d62dc --- /dev/null +++ b/ZyDktXm6v-s.txt @@ -0,0 +1,11488 @@ +align:start position:0% + +okay so let's get started um I'm going + + align:start position:0% +okay so let's get started um I'm going + + + align:start position:0% +okay so let's get started um I'm going +to start with a few + + align:start position:0% +to start with a few + + + align:start position:0% +to start with a few +definitions so a sample space is a + + align:start position:0% +definitions so a sample space is a + + + align:start position:0% +definitions so a sample space is a +collection of all possible outcomes of + + align:start position:0% +collection of all possible outcomes of + + + align:start position:0% +collection of all possible outcomes of +an + + align:start position:0% +an + + + align:start position:0% +an +experiment and it + + align:start position:0% +experiment and it + + + align:start position:0% +experiment and it +uh will denote that uh with capital + + align:start position:0% +uh will denote that uh with capital + + + align:start position:0% +uh will denote that uh with capital +letters a b c things like that uh is any + + align:start position:0% +letters a b c things like that uh is any + + + align:start position:0% +letters a b c things like that uh is any +collection of outcomes including + + align:start position:0% +collection of outcomes including + + + align:start position:0% +collection of outcomes including +individual outcomes the entire sample + + align:start position:0% +individual outcomes the entire sample + + + align:start position:0% +individual outcomes the entire sample +space the null set Etc okay so we have + + align:start position:0% +space the null set Etc okay so we have + + + align:start position:0% +space the null set Etc okay so we have +some kind of an experiment and I'll do + + align:start position:0% +some kind of an experiment and I'll do + + + align:start position:0% +some kind of an experiment and I'll do +some examples uh in a few minutes to add + + align:start position:0% +some examples uh in a few minutes to add + + + align:start position:0% +some examples uh in a few minutes to add +some concrete concreteness to this but + + align:start position:0% +some concrete concreteness to this but + + + align:start position:0% +some concrete concreteness to this but +we have some experiment and um an event + + align:start position:0% +we have some experiment and um an event + + + align:start position:0% +we have some experiment and um an event +is a collection of outcomes of that + + align:start position:0% +is a collection of outcomes of that + + + align:start position:0% +is a collection of outcomes of that +experiment yep um so uh if the outcome + + align:start position:0% +experiment yep um so uh if the outcome + + + align:start position:0% +experiment yep um so uh if the outcome +uh of the experiment is a member of an + + align:start position:0% +uh of the experiment is a member of an + + + align:start position:0% +uh of the experiment is a member of an +event then we say that the event is said + + align:start position:0% +event then we say that the event is said + + + align:start position:0% +event then we say that the event is said +to or we say the event has occurred + + align:start position:0% +to or we say the event has occurred + + + align:start position:0% +to or we say the event has occurred +okay uh and event a is contained in + + align:start position:0% +okay uh and event a is contained in + + + align:start position:0% +okay uh and event a is contained in +event B um if every outcome in B also + + align:start position:0% +event B um if every outcome in B also + + + align:start position:0% +event B um if every outcome in B also +belongs in a okay so here we're just + + align:start position:0% +belongs in a okay so here we're just + + + align:start position:0% +belongs in a okay so here we're just +establishing uh you know sort of a bunch + + align:start position:0% +establishing uh you know sort of a bunch + + + align:start position:0% +establishing uh you know sort of a bunch +of terminology and + + align:start position:0% +of terminology and + + + align:start position:0% +of terminology and +definitions + + align:start position:0% +definitions + + + align:start position:0% +definitions +and um as you have probably gathered + + align:start position:0% +and um as you have probably gathered + + + align:start position:0% +and um as you have probably gathered +these things that I'm defining are sets + + align:start position:0% +these things that I'm defining are sets + + + align:start position:0% +these things that I'm defining are sets +okay and so we're going to use uh many + + align:start position:0% +okay and so we're going to use uh many + + + align:start position:0% +okay and so we're going to use uh many +of the same definitions and results from + + align:start position:0% +of the same definitions and results from + + + align:start position:0% +of the same definitions and results from +set theory in probability Theory because + + align:start position:0% +set theory in probability Theory because + + + align:start position:0% +set theory in probability Theory because +uh you know we're sort of setting + + align:start position:0% +uh you know we're sort of setting + + + align:start position:0% +uh you know we're sort of setting +everything out or you know sort of uh + + align:start position:0% +everything out or you know sort of uh + + + align:start position:0% +everything out or you know sort of uh +the the the foundation that we're using + + align:start position:0% +the the the foundation that we're using + + + align:start position:0% +the the the foundation that we're using +is is the the mathematical Foundation is + + align:start position:0% +is is the the mathematical Foundation is + + + align:start position:0% +is is the the mathematical Foundation is +the one from set theory okay so all the + + align:start position:0% +the one from set theory okay so all the + + + align:start position:0% +the one from set theory okay so all the +results from set theory are going to + + align:start position:0% +results from set theory are going to + + + align:start position:0% +results from set theory are going to +apply the associative commutative + + align:start position:0% +apply the associative commutative + + + align:start position:0% +apply the associative commutative +distributive properties that + + align:start position:0% +distributive properties that + + + align:start position:0% +distributive properties that +Etc and here I'm just going to post some + + align:start position:0% +Etc and here I'm just going to post some + + + align:start position:0% +Etc and here I'm just going to post some +uh useful results okay uh without uh + + align:start position:0% +uh useful results okay uh without uh + + + align:start position:0% +uh useful results okay uh without uh +without um much discussion of them um if + + align:start position:0% +without um much discussion of them um if + + + align:start position:0% +without um much discussion of them um if +you've done some set theory or some + + align:start position:0% +you've done some set theory or some + + + align:start position:0% +you've done some set theory or some +probability Theory these things should + + align:start position:0% +probability Theory these things should + + + align:start position:0% +probability Theory these things should +be uh pretty familiar to you uh if uh a + + align:start position:0% +be uh pretty familiar to you uh if uh a + + + align:start position:0% +be uh pretty familiar to you uh if uh a +if an event a is contained in another + + align:start position:0% +if an event a is contained in another + + + align:start position:0% +if an event a is contained in another +event B then the union of those two + + align:start position:0% +event B then the union of those two + + + align:start position:0% +event B then the union of those two +events is equal to um event B okay if uh + + align:start position:0% +events is equal to um event B okay if uh + + + align:start position:0% +events is equal to um event B okay if uh +a oh I should say should point out a + + align:start position:0% +a oh I should say should point out a + + + align:start position:0% +a oh I should say should point out a +couple of uh notes about notation okay + + align:start position:0% +couple of uh notes about notation okay + + + align:start position:0% +couple of uh notes about notation okay +so uh the the uh sort of um uh sign that + + align:start position:0% +so uh the the uh sort of um uh sign that + + + align:start position:0% +so uh the the uh sort of um uh sign that +looks kind of like a c uh is how we + + align:start position:0% +looks kind of like a c uh is how we + + + align:start position:0% +looks kind of like a c uh is how we +indicate contained in + + align:start position:0% +indicate contained in + + + align:start position:0% +indicate contained in +okay and this is uh that piece of + + align:start position:0% +okay and this is uh that piece of + + + align:start position:0% +okay and this is uh that piece of +notation is straight from set + + align:start position:0% + + + + align:start position:0% + +theory and this capital u kind of thing + + align:start position:0% +theory and this capital u kind of thing + + + align:start position:0% +theory and this capital u kind of thing +is how we indicate Union and again that + + align:start position:0% +is how we indicate Union and again that + + + align:start position:0% +is how we indicate Union and again that +not ation is straight from set + + align:start position:0% +not ation is straight from set + + + align:start position:0% +not ation is straight from set +theory + + align:start position:0% +theory + + + align:start position:0% +theory +okay uh the second uh useful result if a + + align:start position:0% +okay uh the second uh useful result if a + + + align:start position:0% +okay uh the second uh useful result if a +is contained in B and B is contained in + + align:start position:0% +is contained in B and B is contained in + + + align:start position:0% +is contained in B and B is contained in +a uh then a the events A and B are equal + + align:start position:0% +a uh then a the events A and B are equal + + + align:start position:0% +a uh then a the events A and B are equal +okay and if a is contained in B then a + + align:start position:0% +okay and if a is contained in B then a + + + align:start position:0% +okay and if a is contained in B then a +is equal to a now here is actually one + + align:start position:0% +is equal to a now here is actually one + + + align:start position:0% +is equal to a now here is actually one +place where the notation between set + + align:start position:0% +place where the notation between set + + + align:start position:0% +place where the notation between set +theory and probability Theory de uh sort + + align:start position:0% +theory and probability Theory de uh sort + + + align:start position:0% +theory and probability Theory de uh sort +of deviates a little + + align:start position:0% +of deviates a little + + + align:start position:0% +of deviates a little +bit let's see oh actually let me skip + + align:start position:0% +bit let's see oh actually let me skip + + + align:start position:0% +bit let's see oh actually let me skip +ahead okay in set theory typically we + + align:start position:0% +ahead okay in set theory typically we + + + align:start position:0% +ahead okay in set theory typically we +indicate the intersection between two + + align:start position:0% +indicate the intersection between two + + + align:start position:0% +indicate the intersection between two +sets uh with a symbol that looks like + + align:start position:0% +sets uh with a symbol that looks like + + + align:start position:0% +sets uh with a symbol that looks like +this and in probability we usually just + + align:start position:0% +this and in probability we usually just + + + align:start position:0% +this and in probability we usually just +leave that out okay so instead of + + align:start position:0% +leave that out okay so instead of + + + align:start position:0% +leave that out okay so instead of +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about or writing the intersection of a + + align:start position:0% +about or writing the intersection of a + + + align:start position:0% +about or writing the intersection of a +like this we usually just write write + + align:start position:0% +like this we usually just write write + + + align:start position:0% +like this we usually just write write +the intersection of + + align:start position:0% +the intersection of + + + align:start position:0% +the intersection of +a this way okay and I'll follow that + + align:start position:0% +a this way okay and I'll follow that + + + align:start position:0% +a this way okay and I'll follow that +convention most of the time just leave + + align:start position:0% +convention most of the time just leave + + + align:start position:0% +convention most of the time just leave +out the intersection + + align:start position:0% +out the intersection + + + align:start position:0% +out the intersection +symbol okay um and let's see I'll go + + align:start position:0% +symbol okay um and let's see I'll go + + + align:start position:0% +symbol okay um and let's see I'll go +back for a + + align:start position:0% +back for a + + + align:start position:0% +back for a +second and then finally uh the the union + + align:start position:0% +second and then finally uh the the union + + + align:start position:0% +second and then finally uh the the union +between a and a complement uh is equal + + align:start position:0% +between a and a complement uh is equal + + + align:start position:0% +between a and a complement uh is equal +to the sample space okay so again these + + align:start position:0% +to the sample space okay so again these + + + align:start position:0% +to the sample space okay so again these +are mostly definitions taken straight + + align:start position:0% +are mostly definitions taken straight + + + align:start position:0% +are mostly definitions taken straight +from set theory you can check uh + + align:start position:0% +from set theory you can check uh + + + align:start position:0% +from set theory you can check uh +standard uh set theory um references if + + align:start position:0% +standard uh set theory um references if + + + align:start position:0% +standard uh set theory um references if +you need a little uh refresher um but uh + + align:start position:0% +you need a little uh refresher um but uh + + + align:start position:0% +you need a little uh refresher um but uh +the you know for the most part these are + + align:start position:0% +the you know for the most part these are + + + align:start position:0% +the you know for the most part these are +just uh we're going to rely on sort of + + align:start position:0% +just uh we're going to rely on sort of + + + align:start position:0% +just uh we're going to rely on sort of +the apparatus of set theory + + align:start position:0% +the apparatus of set theory + + + align:start position:0% +the apparatus of set theory +initially + + align:start position:0% +initially + + + align:start position:0% +initially +okay okay two other important + + align:start position:0% +okay okay two other important + + + align:start position:0% +okay okay two other important +definitions + + align:start position:0% +definitions + + + align:start position:0% +definitions +um that uh where sort of probability + + align:start position:0% +um that uh where sort of probability + + + align:start position:0% +um that uh where sort of probability +Theory uses slightly different + + align:start position:0% +Theory uses slightly different + + + align:start position:0% +Theory uses slightly different +terminology than set theory is um uh the + + align:start position:0% +terminology than set theory is um uh the + + + align:start position:0% +terminology than set theory is um uh the +the following two so we say that A and B + + align:start position:0% +the following two so we say that A and B + + + align:start position:0% +the following two so we say that A and B +are mutually exclusive if they have no + + align:start position:0% +are mutually exclusive if they have no + + + align:start position:0% +are mutually exclusive if they have no +outcomes in common so we have two events + + align:start position:0% +outcomes in common so we have two events + + + align:start position:0% +outcomes in common so we have two events +and if they don't share any outcomes so + + align:start position:0% +and if they don't share any outcomes so + + + align:start position:0% +and if they don't share any outcomes so +we say they're mutually exclusive we + + align:start position:0% +we say they're mutually exclusive we + + + align:start position:0% +we say they're mutually exclusive we +also sometimes say they're disjoint and + + align:start position:0% +also sometimes say they're disjoint and + + + align:start position:0% +also sometimes say they're disjoint and +in set theory we'll typically uh talk + + align:start position:0% +in set theory we'll typically uh talk + + + align:start position:0% +in set theory we'll typically uh talk +about them being disjoint in probability + + align:start position:0% +about them being disjoint in probability + + + align:start position:0% +about them being disjoint in probability +Theory uh you use the term Mutual + + align:start position:0% +Theory uh you use the term Mutual + + + align:start position:0% +Theory uh you use the term Mutual +exclusive more commonly okay uh A and B + + align:start position:0% +exclusive more commonly okay uh A and B + + + align:start position:0% +exclusive more commonly okay uh A and B +events A and B are exhaustive if their + + align:start position:0% +events A and B are exhaustive if their + + + align:start position:0% +events A and B are exhaustive if their +Union is equal to the entire sample + + align:start position:0% +Union is equal to the entire sample + + + align:start position:0% +Union is equal to the entire sample +space okay and again in set theory uh + + align:start position:0% +space okay and again in set theory uh + + + align:start position:0% +space okay and again in set theory uh +we'll typically use the term + + align:start position:0% +we'll typically use the term + + + align:start position:0% +we'll typically use the term +complimentary instead of exhaustive uh + + align:start position:0% +complimentary instead of exhaustive uh + + + align:start position:0% +complimentary instead of exhaustive uh +and in probability Theory we'll usually + + align:start position:0% +and in probability Theory we'll usually + + + align:start position:0% +and in probability Theory we'll usually +use exhausted okay they mean the same + + align:start position:0% +use exhausted okay they mean the same + + + align:start position:0% +use exhausted okay they mean the same +thing so uh often times we'll talk about + + align:start position:0% +thing so uh often times we'll talk about + + + align:start position:0% +thing so uh often times we'll talk about +and we'll talk about later today um + + align:start position:0% +and we'll talk about later today um + + + align:start position:0% +and we'll talk about later today um +groups of events that are mutually + + align:start position:0% +groups of events that are mutually + + + align:start position:0% +groups of events that are mutually +exclusive and exhaustive and um that uh + + align:start position:0% +exclusive and exhaustive and um that uh + + + align:start position:0% +exclusive and exhaustive and um that uh +that just means that their Union is + + align:start position:0% +that just means that their Union is + + + align:start position:0% +that just means that their Union is +equal to the the um uh sample space but + + align:start position:0% +equal to the the um uh sample space but + + + align:start position:0% +equal to the the um uh sample space but +they have no events in common okay and + + align:start position:0% +they have no events in common okay and + + + align:start position:0% +they have no events in common okay and +another term for that is a partition + + align:start position:0% +another term for that is a partition + + + align:start position:0% +another term for that is a partition +they form a partition of the sample + + align:start position:0% + + + + align:start position:0% + +space okay so now that we have a few of + + align:start position:0% +space okay so now that we have a few of + + + align:start position:0% +space okay so now that we have a few of +those definitions and some of the + + align:start position:0% +those definitions and some of the + + + align:start position:0% +those definitions and some of the +terminology and notation under our belt + + align:start position:0% +terminology and notation under our belt + + + align:start position:0% +terminology and notation under our belt +uh let me Define probability okay okay + + align:start position:0% +uh let me Define probability okay okay + + + align:start position:0% +uh let me Define probability okay okay +so we can take we're we're going to take + + align:start position:0% +so we can take we're we're going to take + + + align:start position:0% +so we can take we're we're going to take +every event a and assign it a number P + + align:start position:0% +every event a and assign it a number P + + + align:start position:0% +every event a and assign it a number P +of a okay and so this is basically a + + align:start position:0% +of a okay and so this is basically a + + + align:start position:0% +of a okay and so this is basically a +function that goes from the sample space + + align:start position:0% +function that goes from the sample space + + + align:start position:0% +function that goes from the sample space +to the real line and what we're we're + + align:start position:0% +to the real line and what we're we're + + + align:start position:0% +to the real line and what we're we're +going to require a few things of this + + align:start position:0% +going to require a few things of this + + + align:start position:0% +going to require a few things of this +function P OFA first of all we're going + + align:start position:0% +function P OFA first of all we're going + + + align:start position:0% +function P OFA first of all we're going +to require that it's uh greater than or + + align:start position:0% +to require that it's uh greater than or + + + align:start position:0% +to require that it's uh greater than or +equal to zero for all events in the + + align:start position:0% +equal to zero for all events in the + + + align:start position:0% +equal to zero for all events in the +sample + + align:start position:0% +sample + + + align:start position:0% +sample +space okay the second second thing that + + align:start position:0% +space okay the second second thing that + + + align:start position:0% +space okay the second second thing that +we're going to require is that the + + align:start position:0% +we're going to require is that the + + + align:start position:0% +we're going to require is that the +function P of uh the sample space the + + align:start position:0% +function P of uh the sample space the + + + align:start position:0% +function P of uh the sample space the +entire sample space is equal to + + align:start position:0% +entire sample space is equal to + + + align:start position:0% +entire sample space is equal to +one and the third thing we're going to + + align:start position:0% +one and the third thing we're going to + + + align:start position:0% +one and the third thing we're going to +require is for any sequence of disjoint + + align:start position:0% +require is for any sequence of disjoint + + + align:start position:0% +require is for any sequence of disjoint +sets I'm going to call those A1 A2 dot + + align:start position:0% +sets I'm going to call those A1 A2 dot + + + align:start position:0% +sets I'm going to call those A1 A2 dot +dot dot okay so it could be a finite + + align:start position:0% +dot dot okay so it could be a finite + + + align:start position:0% +dot dot okay so it could be a finite +sequence it could be an infinite + + align:start position:0% +sequence it could be an infinite + + + align:start position:0% +sequence it could be an infinite +sequence but for any sequence of + + align:start position:0% +sequence but for any sequence of + + + align:start position:0% +sequence but for any sequence of +disjoint sets the probability of the + + align:start position:0% +disjoint sets the probability of the + + + align:start position:0% +disjoint sets the probability of the +Union of that sequence is equal to the + + align:start position:0% +Union of that sequence is equal to the + + + align:start position:0% +Union of that sequence is equal to the +sum of the probabilities of those events + + align:start position:0% +sum of the probabilities of those events + + + align:start position:0% +sum of the probabilities of those events +okay is this um notation familiar to + + align:start position:0% +okay is this um notation familiar to + + + align:start position:0% +okay is this um notation familiar to +most of you this sort of uh uh Union and + + align:start position:0% +most of you this sort of uh uh Union and + + + align:start position:0% +most of you this sort of uh uh Union and +summation + + align:start position:0% +summation + + + align:start position:0% +summation +notation okay so it's important to point + + align:start position:0% +notation okay so it's important to point + + + align:start position:0% +notation okay so it's important to point +out that this thing this function P this + + align:start position:0% +out that this thing this function P this + + + align:start position:0% +out that this thing this function P this +probability isn't necessarily sort of a + + align:start position:0% +probability isn't necessarily sort of a + + + align:start position:0% +probability isn't necessarily sort of a +unique object we're just saying we have + + align:start position:0% +unique object we're just saying we have + + + align:start position:0% +unique object we're just saying we have +a sample space and if we have some + + align:start position:0% +a sample space and if we have some + + + align:start position:0% +a sample space and if we have some +function that satisfies these three + + align:start position:0% +function that satisfies these three + + + align:start position:0% +function that satisfies these three +properties then that um then we're going + + align:start position:0% +properties then that um then we're going + + + align:start position:0% +properties then that um then we're going +to call it a probability + + align:start position:0% +to call it a probability + + + align:start position:0% +to call it a probability +okay and uh it's just simply uh you know + + align:start position:0% +okay and uh it's just simply uh you know + + + align:start position:0% +okay and uh it's just simply uh you know +any any function defined on a sample + + align:start position:0% +any any function defined on a sample + + + align:start position:0% +any any function defined on a sample +space that satisfies these three + + align:start position:0% + + + + align:start position:0% + +properties just a little um comment + + align:start position:0% +properties just a little um comment + + + align:start position:0% +properties just a little um comment +about uh + + align:start position:0% +about uh + + + align:start position:0% +about uh +terminology so the uh different + + align:start position:0% +terminology so the uh different + + + align:start position:0% +terminology so the uh different +textbooks sort of use different terms + + align:start position:0% +textbooks sort of use different terms + + + align:start position:0% +textbooks sort of use different terms +for this object here so sometimes you'll + + align:start position:0% +for this object here so sometimes you'll + + + align:start position:0% +for this object here so sometimes you'll +see a defi called a probability + + align:start position:0% +see a defi called a probability + + + align:start position:0% +see a defi called a probability +distribution or probability function um + + align:start position:0% +distribution or probability function um + + + align:start position:0% +distribution or probability function um +there isn't I'm trying to use kind of + + align:start position:0% +there isn't I'm trying to use kind of + + + align:start position:0% +there isn't I'm trying to use kind of +the most standard terminology that I can + + align:start position:0% +the most standard terminology that I can + + + align:start position:0% +the most standard terminology that I can +find but there is no uh standard + + align:start position:0% +find but there is no uh standard + + + align:start position:0% +find but there is no uh standard +terminology for all of probability + + align:start position:0% +terminology for all of probability + + + align:start position:0% +terminology for all of probability +Theory so just keep that in mind that um + + align:start position:0% +Theory so just keep that in mind that um + + + align:start position:0% +Theory so just keep that in mind that um +you know sometimes the terms are + + align:start position:0% +you know sometimes the terms are + + + align:start position:0% +you know sometimes the terms are +actually uh you know a little amb + + align:start position:0% +actually uh you know a little amb + + + align:start position:0% +actually uh you know a little amb +ambiguous and feel free to ask if you + + align:start position:0% +ambiguous and feel free to ask if you + + + align:start position:0% +ambiguous and feel free to ask if you +ever have any questions about exactly + + align:start position:0% +ever have any questions about exactly + + + align:start position:0% +ever have any questions about exactly +what I'm referring + + align:start position:0% + + + + align:start position:0% + +to Okay so we've got this thing now we + + align:start position:0% +to Okay so we've got this thing now we + + + align:start position:0% +to Okay so we've got this thing now we +call it a probability and you can prove + + align:start position:0% +call it a probability and you can prove + + + align:start position:0% +call it a probability and you can prove +a lot of useful things about + + align:start position:0% +a lot of useful things about + + + align:start position:0% +a lot of useful things about +probabilities using set theory okay so + + align:start position:0% +probabilities using set theory okay so + + + align:start position:0% +probabilities using set theory okay so +if we were doing a course entirely in + + align:start position:0% +if we were doing a course entirely in + + + align:start position:0% +if we were doing a course entirely in +probability we'd probably spend the rest + + align:start position:0% +probability we'd probably spend the rest + + + align:start position:0% +probability we'd probably spend the rest +of the lecture just using the uh sort of + + align:start position:0% +of the lecture just using the uh sort of + + + align:start position:0% +of the lecture just using the uh sort of +mechanics of set theory and proving lots + + align:start position:0% +mechanics of set theory and proving lots + + + align:start position:0% +mechanics of set theory and proving lots +of things about probabilities uh we + + align:start position:0% +of things about probabilities uh we + + + align:start position:0% +of things about probabilities uh we +don't have that luxury here we want to + + align:start position:0% +don't have that luxury here we want to + + + align:start position:0% +don't have that luxury here we want to +get to sort of everything that uh you + + align:start position:0% +get to sort of everything that uh you + + + align:start position:0% +get to sort of everything that uh you +know we're excited about in data + + align:start position:0% +know we're excited about in data + + + align:start position:0% +know we're excited about in data +analysis in the rest of the class and so + + align:start position:0% +analysis in the rest of the class and so + + + align:start position:0% +analysis in the rest of the class and so +what I'm going to do is just list a lot + + align:start position:0% +what I'm going to do is just list a lot + + + align:start position:0% +what I'm going to do is just list a lot +of the um the the sort of useful facts + + align:start position:0% +of the um the the sort of useful facts + + + align:start position:0% +of the um the the sort of useful facts +and useful results about probabilities + + align:start position:0% +and useful results about probabilities + + + align:start position:0% +and useful results about probabilities +that we could prove okay and I'll I'll + + align:start position:0% +that we could prove okay and I'll I'll + + + align:start position:0% +that we could prove okay and I'll I'll +mention a couple of them quickly um + + align:start position:0% +mention a couple of them quickly um + + + align:start position:0% +mention a couple of them quickly um +first of all and we'll uh we'll actually + + align:start position:0% +first of all and we'll uh we'll actually + + + align:start position:0% +first of all and we'll uh we'll actually +use this an example uh either today or + + align:start position:0% +use this an example uh either today or + + + align:start position:0% +use this an example uh either today or +next probably today uh the probability + + align:start position:0% +next probably today uh the probability + + + align:start position:0% +next probably today uh the probability +of a complement so the event that + + align:start position:0% +of a complement so the event that + + + align:start position:0% +of a complement so the event that +contains all of the outcomes that are + + align:start position:0% +contains all of the outcomes that are + + + align:start position:0% +contains all of the outcomes that are +not in event a the probability of a + + align:start position:0% +not in event a the probability of a + + + align:start position:0% +not in event a the probability of a +complement is just equal to one minus + + align:start position:0% +complement is just equal to one minus + + + align:start position:0% +complement is just equal to one minus +the probability of a okay so why is that + + align:start position:0% +the probability of a okay so why is that + + + align:start position:0% +the probability of a okay so why is that +useful well it's useful in particular + + align:start position:0% +useful well it's useful in particular + + + align:start position:0% +useful well it's useful in particular +because sometimes uh the probability of + + align:start position:0% +because sometimes uh the probability of + + + align:start position:0% +because sometimes uh the probability of +a complement uh could be difficult to + + align:start position:0% +a complement uh could be difficult to + + + align:start position:0% +a complement uh could be difficult to +compute and the probability of a could + + align:start position:0% +compute and the probability of a could + + + align:start position:0% +compute and the probability of a could +be very easy to compute and so if you + + align:start position:0% +be very easy to compute and so if you + + + align:start position:0% +be very easy to compute and so if you +want to get at the uh probability of a + + align:start position:0% +want to get at the uh probability of a + + + align:start position:0% +want to get at the uh probability of a +complement this might you know this + + align:start position:0% +complement this might you know this + + + align:start position:0% +complement this might you know this +result could be the easiest way for you + + align:start position:0% +result could be the easiest way for you + + + align:start position:0% +result could be the easiest way for you +to do it okay uh the probability of the + + align:start position:0% +to do it okay uh the probability of the + + + align:start position:0% +to do it okay uh the probability of the +empty set is equal to + + align:start position:0% +empty set is equal to + + + align:start position:0% +empty set is equal to +zero uh if a is contained in B then the + + align:start position:0% +zero uh if a is contained in B then the + + + align:start position:0% +zero uh if a is contained in B then the +probability of a is less than or equal + + align:start position:0% +probability of a is less than or equal + + + align:start position:0% +probability of a is less than or equal +to the probability of + + align:start position:0% +to the probability of + + + align:start position:0% +to the probability of +B uh we can also prove that uh for any + + align:start position:0% +B uh we can also prove that uh for any + + + align:start position:0% +B uh we can also prove that uh for any +events uh the probability of uh that + + align:start position:0% +events uh the probability of uh that + + + align:start position:0% +events uh the probability of uh that +event is between zero and one + + align:start position:0% +event is between zero and one + + + align:start position:0% +event is between zero and one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +probability of a union B is just equal + + align:start position:0% +probability of a union B is just equal + + + align:start position:0% +probability of a union B is just equal +to the sum of the probabilities of those + + align:start position:0% +to the sum of the probabilities of those + + + align:start position:0% +to the sum of the probabilities of those +two events minus uh the probability of + + align:start position:0% +two events minus uh the probability of + + + align:start position:0% +two events minus uh the probability of +their + + align:start position:0% + + + + align:start position:0% + +intersection and finally the probability + + align:start position:0% +intersection and finally the probability + + + align:start position:0% +intersection and finally the probability +of a uh time B complement is equal to + + align:start position:0% +of a uh time B complement is equal to + + + align:start position:0% +of a uh time B complement is equal to +the probability of a minus the + + align:start position:0% +the probability of a minus the + + + align:start position:0% +the probability of a minus the +probability of the + + align:start position:0% +probability of the + + + align:start position:0% +probability of the +intersection okay so just keep in mind + + align:start position:0% +intersection okay so just keep in mind + + + align:start position:0% +intersection okay so just keep in mind +we'll refer back to a number of these + + align:start position:0% +we'll refer back to a number of these + + + align:start position:0% +we'll refer back to a number of these +results uh in the examples that we're + + align:start position:0% +results uh in the examples that we're + + + align:start position:0% +results uh in the examples that we're +doing coming up um so keep those in the + + align:start position:0% +doing coming up um so keep those in the + + + align:start position:0% +doing coming up um so keep those in the +back of your + + align:start position:0% + + + + align:start position:0% + +mind okay so now I'd like to introduce a + + align:start position:0% +mind okay so now I'd like to introduce a + + + align:start position:0% +mind okay so now I'd like to introduce a +an important special + + align:start position:0% +an important special + + + align:start position:0% +an important special +case Okay suppose that we have a sample + + align:start position:0% +case Okay suppose that we have a sample + + + align:start position:0% +case Okay suppose that we have a sample +space and suppose that that sample space + + align:start position:0% +space and suppose that that sample space + + + align:start position:0% +space and suppose that that sample space +is finite so there's a finite number of + + align:start position:0% +is finite so there's a finite number of + + + align:start position:0% +is finite so there's a finite number of +outcomes um in this sample + + align:start position:0% +outcomes um in this sample + + + align:start position:0% +outcomes um in this sample +space let's define a function n uh that + + align:start position:0% +space let's define a function n uh that + + + align:start position:0% +space let's define a function n uh that +that gives the number of elements in a + + align:start position:0% +that gives the number of elements in a + + + align:start position:0% +that gives the number of elements in a +set okay and then Define a probability + + align:start position:0% +set okay and then Define a probability + + + align:start position:0% +set okay and then Define a probability +well we haven't checked to make sure + + align:start position:0% +well we haven't checked to make sure + + + align:start position:0% +well we haven't checked to make sure +it's a probability but Define a function + + align:start position:0% +it's a probability but Define a function + + + align:start position:0% +it's a probability but Define a function +P of a which is just equal to n of a + + align:start position:0% +P of a which is just equal to n of a + + + align:start position:0% +P of a which is just equal to n of a +Over N of f okay so what is this we're + + align:start position:0% +Over N of f okay so what is this we're + + + align:start position:0% +Over N of f okay so what is this we're +defining a function we're saying uh + + align:start position:0% +defining a function we're saying uh + + + align:start position:0% +defining a function we're saying uh +we're we're just going to we're defining + + align:start position:0% +we're we're just going to we're defining + + + align:start position:0% +we're we're just going to we're defining +something that we we hope is going to be + + align:start position:0% +something that we we hope is going to be + + + align:start position:0% +something that we we hope is going to be +a probability we're going to say all we + + align:start position:0% +a probability we're going to say all we + + + align:start position:0% +a probability we're going to say all we +do is we count the number of outcomes in + + align:start position:0% +do is we count the number of outcomes in + + + align:start position:0% +do is we count the number of outcomes in +event and divide by the number of + + align:start position:0% +event and divide by the number of + + + align:start position:0% +event and divide by the number of +outcomes in the sample space and that + + align:start position:0% +outcomes in the sample space and that + + + align:start position:0% +outcomes in the sample space and that +gives us our probability okay all we're + + align:start position:0% +gives us our probability okay all we're + + + align:start position:0% +gives us our probability okay all we're +doing is counting this is called this + + align:start position:0% +doing is counting this is called this + + + align:start position:0% +doing is counting this is called this +has a name it's called a simple sample + + align:start position:0% +has a name it's called a simple sample + + + align:start position:0% +has a name it's called a simple sample +space and we can check in fact that it + + align:start position:0% +space and we can check in fact that it + + + align:start position:0% +space and we can check in fact that it +is a + + align:start position:0% +is a + + + align:start position:0% +is a +probability so how do we check that it's + + align:start position:0% +probability so how do we check that it's + + + align:start position:0% +probability so how do we check that it's +a + + align:start position:0% + + + + align:start position:0% + +probability well I told you before if we + + align:start position:0% +probability well I told you before if we + + + align:start position:0% +probability well I told you before if we +have a function and it satisfies those + + align:start position:0% +have a function and it satisfies those + + + align:start position:0% +have a function and it satisfies those +three aums it's a probability right so + + align:start position:0% +three aums it's a probability right so + + + align:start position:0% +three aums it's a probability right so +all we have to do is check to make sure + + align:start position:0% +all we have to do is check to make sure + + + align:start position:0% +all we have to do is check to make sure +this particular function P of a + + align:start position:0% +this particular function P of a + + + align:start position:0% +this particular function P of a +satisfies uh the three axioms so I did + + align:start position:0% +satisfies uh the three axioms so I did + + + align:start position:0% +satisfies uh the three axioms so I did +it right here okay first of all it's + + align:start position:0% +it right here okay first of all it's + + + align:start position:0% +it right here okay first of all it's +always going to be non- negative because + + align:start position:0% +always going to be non- negative because + + + align:start position:0% +always going to be non- negative because +it's a count so we're fine with axum one + + align:start position:0% +it's a count so we're fine with axum one + + + align:start position:0% +it's a count so we're fine with axum one +axiim 2 probability of the whole sample + + align:start position:0% +axiim 2 probability of the whole sample + + + align:start position:0% +axiim 2 probability of the whole sample +space is going to equal to one that's + + align:start position:0% +space is going to equal to one that's + + + align:start position:0% +space is going to equal to one that's +essentially by definition right because + + align:start position:0% +essentially by definition right because + + + align:start position:0% +essentially by definition right because +we're just counting uh you know we've + + align:start position:0% +we're just counting uh you know we've + + + align:start position:0% +we're just counting uh you know we've +defined P of a as n of a Over N of + + align:start position:0% +defined P of a as n of a Over N of + + + align:start position:0% +defined P of a as n of a Over N of +s right so just P of s is equal to n of + + align:start position:0% +s right so just P of s is equal to n of + + + align:start position:0% +s right so just P of s is equal to n of +s Over N of s so we're fine with axium 2 + + align:start position:0% +s Over N of s so we're fine with axium 2 + + + align:start position:0% +s Over N of s so we're fine with axium 2 +and axium 3 the probability of the Union + + align:start position:0% +and axium 3 the probability of the Union + + + align:start position:0% +and axium 3 the probability of the Union +between A and B is just equal to the + + align:start position:0% +between A and B is just equal to the + + + align:start position:0% +between A and B is just equal to the +number of uh elements in the union of A + + align:start position:0% +number of uh elements in the union of A + + + align:start position:0% +number of uh elements in the union of A +and B um and uh they're since they're um + + align:start position:0% +and B um and uh they're since they're um + + + align:start position:0% +and B um and uh they're since they're um +they're mutually exclusive that means + + align:start position:0% +they're mutually exclusive that means + + + align:start position:0% +they're mutually exclusive that means +that it's just equal to the number of + + align:start position:0% +that it's just equal to the number of + + + align:start position:0% +that it's just equal to the number of +elements uh in a plus the number of + + align:start position:0% +elements uh in a plus the number of + + + align:start position:0% +elements uh in a plus the number of +elements in B + + align:start position:0% +elements in B + + + align:start position:0% +elements in B +okay and then that's just equal to by + + align:start position:0% +okay and then that's just equal to by + + + align:start position:0% +okay and then that's just equal to by +definition probability of a plus b or + + align:start position:0% +definition probability of a plus b or + + + align:start position:0% +definition probability of a plus b or +probability of a plus probability of + + align:start position:0% +probability of a plus probability of + + + align:start position:0% +probability of a plus probability of +B okay questions + + align:start position:0% + + + + align:start position:0% + +about is this okay okay so you can just + + align:start position:0% +about is this okay okay so you can just + + + align:start position:0% +about is this okay okay so you can just +go back and look at the axioms with this + + align:start position:0% +go back and look at the axioms with this + + + align:start position:0% +go back and look at the axioms with this +particular function and double check to + + align:start position:0% +particular function and double check to + + + align:start position:0% +particular function and double check to +convince yourself that it satisfies all + + align:start position:0% +convince yourself that it satisfies all + + + align:start position:0% +convince yourself that it satisfies all +the + + align:start position:0% +the + + + align:start position:0% +the +axioms okay so + + align:start position:0% +axioms okay so + + + align:start position:0% +axioms okay so +um the the why do we have this special + + align:start position:0% +um the the why do we have this special + + + align:start position:0% +um the the why do we have this special +case and why do we consider it well it's + + align:start position:0% +case and why do we consider it well it's + + + align:start position:0% +case and why do we consider it well it's +a really powerful notion if you think + + align:start position:0% +a really powerful notion if you think + + + align:start position:0% +a really powerful notion if you think +about it you can if you can put take an + + align:start position:0% +about it you can if you can put take an + + + align:start position:0% +about it you can if you can put take an +experiment that you're interested in and + + align:start position:0% +experiment that you're interested in and + + + align:start position:0% +experiment that you're interested in and +put it into this framework of a simple + + align:start position:0% +put it into this framework of a simple + + + align:start position:0% +put it into this framework of a simple +sample space in other words create uh + + align:start position:0% +sample space in other words create uh + + + align:start position:0% +sample space in other words create uh +you know sort of Define the experiment + + align:start position:0% +you know sort of Define the experiment + + + align:start position:0% +you know sort of Define the experiment +or or sort of um yeah basically put it + + align:start position:0% +or or sort of um yeah basically put it + + + align:start position:0% +or or sort of um yeah basically put it +into the framework where each outcome is + + align:start position:0% +into the framework where each outcome is + + + align:start position:0% +into the framework where each outcome is +equally likely okay that's what the + + align:start position:0% +equally likely okay that's what the + + + align:start position:0% +equally likely okay that's what the +simple sample space implies all we need + + align:start position:0% +simple sample space implies all we need + + + align:start position:0% +simple sample space implies all we need +to do is Count uh to compute + + align:start position:0% +to do is Count uh to compute + + + align:start position:0% +to do is Count uh to compute +probabilities of events okay so + + align:start position:0% +probabilities of events okay so + + + align:start position:0% +probabilities of events okay so +basically if we're interested in the + + align:start position:0% +basically if we're interested in the + + + align:start position:0% +basically if we're interested in the +probability of a particular event and we + + align:start position:0% +probability of a particular event and we + + + align:start position:0% +probability of a particular event and we +can describe the experiment as you know + + align:start position:0% +can describe the experiment as you know + + + align:start position:0% +can describe the experiment as you know +in the framework of a sample space all + + align:start position:0% +in the framework of a sample space all + + + align:start position:0% +in the framework of a sample space all +we have to do is count and we can + + align:start position:0% +we have to do is count and we can + + + align:start position:0% +we have to do is count and we can +compute the probability is that clear C + + align:start position:0% +compute the probability is that clear C + + + align:start position:0% +compute the probability is that clear C +okay so let me do a very simple example + + align:start position:0% +okay so let me do a very simple example + + + align:start position:0% +okay so let me do a very simple example +first um let's suppose I roll two Fair + + align:start position:0% +first um let's suppose I roll two Fair + + + align:start position:0% +first um let's suppose I roll two Fair +dice okay and I want to compute the + + align:start position:0% +dice okay and I want to compute the + + + align:start position:0% +dice okay and I want to compute the +probability that the sum on the faces of + + align:start position:0% +probability that the sum on the faces of + + + align:start position:0% +probability that the sum on the faces of +the two dice uh come up four when I roll + + align:start position:0% +the two dice uh come up four when I roll + + + align:start position:0% +the two dice uh come up four when I roll +them well if I can put this in the + + align:start position:0% +them well if I can put this in the + + + align:start position:0% +them well if I can put this in the +framework of the simple sample space so + + align:start position:0% +framework of the simple sample space so + + + align:start position:0% +framework of the simple sample space so +in other words have every outcome be + + align:start position:0% +in other words have every outcome be + + + align:start position:0% +in other words have every outcome be +equally likely okay uh then all I have + + align:start position:0% +equally likely okay uh then all I have + + + align:start position:0% +equally likely okay uh then all I have +to do is count all I have to do is count + + align:start position:0% +to do is count all I have to do is count + + + align:start position:0% +to do is count all I have to do is count +all the possible outcomes and count all + + align:start position:0% +all the possible outcomes and count all + + + align:start position:0% +all the possible outcomes and count all +the outcomes that satisfy my particular + + align:start position:0% +the outcomes that satisfy my particular + + + align:start position:0% +the outcomes that satisfy my particular +event and I'm done I've computed my + + align:start position:0% +event and I'm done I've computed my + + + align:start position:0% +event and I'm done I've computed my +probability so that's exactly what I do + + align:start position:0% +probability so that's exactly what I do + + + align:start position:0% +probability so that's exactly what I do +here so what are all of the what are all + + align:start position:0% +here so what are all of the what are all + + + align:start position:0% +here so what are all of the what are all +the possible outcomes of this experiment + + align:start position:0% +the possible outcomes of this experiment + + + align:start position:0% +the possible outcomes of this experiment +well if I have two dice and they're Fair + + align:start position:0% +well if I have two dice and they're Fair + + + align:start position:0% +well if I have two dice and they're Fair +dice that means each uh each face is + + align:start position:0% +dice that means each uh each face is + + + align:start position:0% +dice that means each uh each face is +equally likely to come up and so then + + align:start position:0% +equally likely to come up and so then + + + align:start position:0% +equally likely to come up and so then +each one of these pairs that I've uh + + align:start position:0% +each one of these pairs that I've uh + + + align:start position:0% +each one of these pairs that I've uh +indicated is an equally likely outcome + + align:start position:0% +indicated is an equally likely outcome + + + align:start position:0% +indicated is an equally likely outcome +of this experiment so I could get one on + + align:start position:0% +of this experiment so I could get one on + + + align:start position:0% +of this experiment so I could get one on +the first die and one in the second die + + align:start position:0% +the first die and one in the second die + + + align:start position:0% +the first die and one in the second die +I could get one in the first die and two + + align:start position:0% +I could get one in the first die and two + + + align:start position:0% +I could get one in the first die and two +in the second die Etc okay so if I count + + align:start position:0% +in the second die Etc okay so if I count + + + align:start position:0% +in the second die Etc okay so if I count +up all of those I get + + align:start position:0% +up all of those I get + + + align:start position:0% +up all of those I get +36 and uh the event that I'm interested + + align:start position:0% +36 and uh the event that I'm interested + + + align:start position:0% +36 and uh the event that I'm interested +in is that the sum on the two dice is + + align:start position:0% +in is that the sum on the two dice is + + + align:start position:0% +in is that the sum on the two dice is +equal to three + + align:start position:0% +equal to three + + + align:start position:0% +equal to three +oops oh no no that's right is equal to + + align:start position:0% +oops oh no no that's right is equal to + + + align:start position:0% +oops oh no no that's right is equal to +four sorry is equal to four and how many + + align:start position:0% +four sorry is equal to four and how many + + + align:start position:0% +four sorry is equal to four and how many +different outcomes give me that the sum + + align:start position:0% +different outcomes give me that the sum + + + align:start position:0% +different outcomes give me that the sum +of the two dice is equal to four there + + align:start position:0% +of the two dice is equal to four there + + + align:start position:0% +of the two dice is equal to four there +are three different outcomes exactly so + + align:start position:0% +are three different outcomes exactly so + + + align:start position:0% +are three different outcomes exactly so +one on the first die three on the second + + align:start position:0% +one on the first die three on the second + + + align:start position:0% +one on the first die three on the second +die two on both of them or three in one + + align:start position:0% +die two on both of them or three in one + + + align:start position:0% +die two on both of them or three in one +okay and so then to compute this + + align:start position:0% +okay and so then to compute this + + + align:start position:0% +okay and so then to compute this +probability that's all I did is I + + align:start position:0% +probability that's all I did is I + + + align:start position:0% +probability that's all I did is I +counted the number of uh outcomes in the + + align:start position:0% +counted the number of uh outcomes in the + + + align:start position:0% +counted the number of uh outcomes in the +sample space I counted the number of + + align:start position:0% +sample space I counted the number of + + + align:start position:0% +sample space I counted the number of +outcomes in the event and I + + align:start position:0% +outcomes in the event and I + + + align:start position:0% +outcomes in the event and I +divided okay so that's what makes simple + + align:start position:0% +divided okay so that's what makes simple + + + align:start position:0% +divided okay so that's what makes simple +sample spaces such a powerful notion and + + align:start position:0% +sample spaces such a powerful notion and + + + align:start position:0% +sample spaces such a powerful notion and +a lot of times when we when we want to + + align:start position:0% +a lot of times when we when we want to + + + align:start position:0% +a lot of times when we when we want to +calculate probabilities we can put the + + align:start position:0% +calculate probabilities we can put the + + + align:start position:0% +calculate probabilities we can put the +the sort of experiment into this kind of + + align:start position:0% +the sort of experiment into this kind of + + + align:start position:0% +the sort of experiment into this kind of +framework it makes our lives + + align:start position:0% +framework it makes our lives + + + align:start position:0% +framework it makes our lives +easier okay one more example slightly uh + + align:start position:0% +easier okay one more example slightly uh + + + align:start position:0% +easier okay one more example slightly uh +less uh simple I guess so let's say the + + align:start position:0% +less uh simple I guess so let's say the + + + align:start position:0% +less uh simple I guess so let's say the +state of Massachusetts issues uh license + + align:start position:0% +state of Massachusetts issues uh license + + + align:start position:0% +state of Massachusetts issues uh license +plates with six different characters on + + align:start position:0% +plates with six different characters on + + + align:start position:0% +plates with six different characters on +them and for each character you can use + + align:start position:0% +them and for each character you can use + + + align:start position:0% +them and for each character you can use +one of 26 letters or or one of 10 digits + + align:start position:0% +one of 26 letters or or one of 10 digits + + + align:start position:0% +one of 26 letters or or one of 10 digits +and they're just chosen randomly on the + + align:start position:0% +and they're just chosen randomly on the + + + align:start position:0% +and they're just chosen randomly on the +license plate okay so my question is + + align:start position:0% +license plate okay so my question is + + + align:start position:0% +license plate okay so my question is +what's the probability that I'll receive + + align:start position:0% +what's the probability that I'll receive + + + align:start position:0% +what's the probability that I'll receive +an all digigit license + + align:start position:0% +an all digigit license + + + align:start position:0% +an all digigit license +plate well we have 36 possibilities for + + align:start position:0% +plate well we have 36 possibilities for + + + align:start position:0% +plate well we have 36 possibilities for +the first character 36 possibilities for + + align:start position:0% +the first character 36 possibilities for + + + align:start position:0% +the first character 36 possibilities for +the second character and so forth okay + + align:start position:0% +the second character and so forth okay + + + align:start position:0% +the second character and so forth okay +so just + + align:start position:0% +so just + + + align:start position:0% +so just +intuitively um you you know like I mean + + align:start position:0% +intuitively um you you know like I mean + + + align:start position:0% +intuitively um you you know like I mean +if you were to sort of start enumerating + + align:start position:0% +if you were to sort of start enumerating + + + align:start position:0% +if you were to sort of start enumerating +all of the different possibilities you'd + + align:start position:0% +all of the different possibilities you'd + + + align:start position:0% +all of the different possibilities you'd +figure out pretty quickly you don't have + + align:start position:0% +figure out pretty quickly you don't have + + + align:start position:0% +figure out pretty quickly you don't have +to actually count all of these + + align:start position:0% +to actually count all of these + + + align:start position:0% +to actually count all of these +possibilities you don't have to write + + align:start position:0% +possibilities you don't have to write + + + align:start position:0% +possibilities you don't have to write +all of them down you just have to + + align:start position:0% +all of them down you just have to + + + align:start position:0% +all of them down you just have to +realize that uh there are 36 + + align:start position:0% +realize that uh there are 36 + + + align:start position:0% +realize that uh there are 36 +possibilities for the first character 36 + + align:start position:0% +possibilities for the first character 36 + + + align:start position:0% +possibilities for the first character 36 +for the second and so forth so the total + + align:start position:0% +for the second and so forth so the total + + + align:start position:0% +for the second and so forth so the total +number of possibilities is 36 to the + + align:start position:0% +number of possibilities is 36 to the + + + align:start position:0% +number of possibilities is 36 to the +6th + + align:start position:0% +6th + + + align:start position:0% +6th +okay and it turns out uh that's if I uh + + align:start position:0% +okay and it turns out uh that's if I uh + + + align:start position:0% +okay and it turns out uh that's if I uh +if my calculator if I typed it into my + + align:start position:0% +if my calculator if I typed it into my + + + align:start position:0% +if my calculator if I typed it into my +calculator correctly that's 2176 billion + + align:start position:0% +calculator correctly that's 2176 billion + + + align:start position:0% +calculator correctly that's 2176 billion +okay so we have a lot of possible + + align:start position:0% +okay so we have a lot of possible + + + align:start position:0% +okay so we have a lot of possible +license plate numbers so what's the + + align:start position:0% +license plate numbers so what's the + + + align:start position:0% +license plate numbers so what's the +probability that I'm going to receive a + + align:start position:0% +probability that I'm going to receive a + + + align:start position:0% +probability that I'm going to receive a +license plate with all digits just by + + align:start position:0% +license plate with all digits just by + + + align:start position:0% +license plate with all digits just by +chance well there's only 10 + + align:start position:0% +chance well there's only 10 + + + align:start position:0% +chance well there's only 10 +possibilities for the first um you know + + align:start position:0% +possibilities for the first um you know + + + align:start position:0% +possibilities for the first um you know +for the first character in that license + + align:start position:0% +for the first character in that license + + + align:start position:0% +for the first character in that license +plate 10 for the second and so forth and + + align:start position:0% +plate 10 for the second and so forth and + + + align:start position:0% +plate 10 for the second and so forth and +so that gives me 10 to the 6th uh + + align:start position:0% +so that gives me 10 to the 6th uh + + + align:start position:0% +so that gives me 10 to the 6th uh +possibilities for my all digigit license + + align:start position:0% +possibilities for my all digigit license + + + align:start position:0% +possibilities for my all digigit license +plate or a million okay and so then if + + align:start position:0% +plate or a million okay and so then if + + + align:start position:0% +plate or a million okay and so then if +we do if we uh uh divide do the division + + align:start position:0% +we do if we uh uh divide do the division + + + align:start position:0% +we do if we uh uh divide do the division +we get the probability of a is equal to + + align:start position:0% + + + + align:start position:0% + +.005 okay + + align:start position:0% +.005 okay + + + align:start position:0% +.005 okay +questions is this clear does this make + + align:start position:0% +questions is this clear does this make + + + align:start position:0% +questions is this clear does this make +sense so far good okay so this example + + align:start position:0% +sense so far good okay so this example + + + align:start position:0% +sense so far good okay so this example +and we'll sort of come back to this um + + align:start position:0% +and we'll sort of come back to this um + + + align:start position:0% +and we'll sort of come back to this um +you know this this will arise again + + align:start position:0% +you know this this will arise again + + + align:start position:0% +you know this this will arise again +throughout the semester but this is an + + align:start position:0% +throughout the semester but this is an + + + align:start position:0% +throughout the semester but this is an +example of uh sampling with replacement + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what happens however if Massachusetts uh + + align:start position:0% +what happens however if Massachusetts uh + + + align:start position:0% +what happens however if Massachusetts uh +in their making the license plate + + align:start position:0% +in their making the license plate + + + align:start position:0% +in their making the license plate +decided they didn't want to reuse a + + align:start position:0% +decided they didn't want to reuse a + + + align:start position:0% +decided they didn't want to reuse a +letter or a digit okay now in this + + align:start position:0% +letter or a digit okay now in this + + + align:start position:0% +letter or a digit okay now in this +sample space um there are 36 + + align:start position:0% +sample space um there are 36 + + + align:start position:0% +sample space um there are 36 +possibilities for the first character + + align:start position:0% +possibilities for the first character + + + align:start position:0% +possibilities for the first character +but they're not going to reuse whatever + + align:start position:0% +but they're not going to reuse whatever + + + align:start position:0% +but they're not going to reuse whatever +they use in the first character so + + align:start position:0% +they use in the first character so + + + align:start position:0% +they use in the first character so +there's only 35 for the second character + + align:start position:0% +there's only 35 for the second character + + + align:start position:0% +there's only 35 for the second character +they're not going to reuse uh what + + align:start position:0% +they're not going to reuse uh what + + + align:start position:0% +they're not going to reuse uh what +they're uh using for the second + + align:start position:0% +they're uh using for the second + + + align:start position:0% +they're uh using for the second +character and so forth so it's only 34 + + align:start position:0% +character and so forth so it's only 34 + + + align:start position:0% +character and so forth so it's only 34 +for the third + + align:start position:0% +for the third + + + align:start position:0% +for the third +character and um then we can multiply + + align:start position:0% +character and um then we can multiply + + + align:start position:0% +character and um then we can multiply +those uh the sort of number of + + align:start position:0% +those uh the sort of number of + + + align:start position:0% +those uh the sort of number of +possibilities for each one of the + + align:start position:0% +possibilities for each one of the + + + align:start position:0% +possibilities for each one of the +characters and we come up with something + + align:start position:0% +characters and we come up with something + + + align:start position:0% +characters and we come up with something +well we come up with 36 * 35 * 34 so + + align:start position:0% +well we come up with 36 * 35 * 34 so + + + align:start position:0% +well we come up with 36 * 35 * 34 so +forth and we can write this in a + + align:start position:0% +forth and we can write this in a + + + align:start position:0% +forth and we can write this in a +somewhat more compact way as uh 36 with + + align:start position:0% +somewhat more compact way as uh 36 with + + + align:start position:0% +somewhat more compact way as uh 36 with +an exclamation point after it that's + + align:start position:0% +an exclamation point after it that's + + + align:start position:0% +an exclamation point after it that's +called factorial divided by 30 factorial + + align:start position:0% +called factorial divided by 30 factorial + + + align:start position:0% +called factorial divided by 30 factorial +okay okay so we can uh write um the + + align:start position:0% +okay okay so we can uh write um the + + + align:start position:0% +okay okay so we can uh write um the +number of uh of possible license plates + + align:start position:0% +number of uh of possible license plates + + + align:start position:0% +number of uh of possible license plates +here as 36 factorial over 30 factorial + + align:start position:0% +here as 36 factorial over 30 factorial + + + align:start position:0% +here as 36 factorial over 30 factorial +okay and then in um in in counting the + + align:start position:0% +okay and then in um in in counting the + + + align:start position:0% +okay and then in um in in counting the +number of possibilities in the event uh + + align:start position:0% +number of possibilities in the event uh + + + align:start position:0% +number of possibilities in the event uh +there are 10 possibilities for the first + + align:start position:0% +there are 10 possibilities for the first + + + align:start position:0% +there are 10 possibilities for the first +character uh nine left for the second + + align:start position:0% +character uh nine left for the second + + + align:start position:0% +character uh nine left for the second +and so forth okay and so then I can + + align:start position:0% +and so forth okay and so then I can + + + align:start position:0% +and so forth okay and so then I can +express the number of uh + + align:start position:0% +express the number of uh + + + align:start position:0% +express the number of uh +possibilities um in the the event as 10 + + align:start position:0% +possibilities um in the the event as 10 + + + align:start position:0% +possibilities um in the the event as 10 +factorial over four + + align:start position:0% +factorial over four + + + align:start position:0% +factorial over four +factorial okay and so the probability + + align:start position:0% +factorial okay and so the probability + + + align:start position:0% +factorial okay and so the probability +here is + + align:start position:0% +here is + + + align:start position:0% +here is +0.00001 when I do the + + align:start position:0% +0.00001 when I do the + + + align:start position:0% +0.00001 when I do the +division and this is an example of + + align:start position:0% +division and this is an example of + + + align:start position:0% +division and this is an example of +sampling without replacement and again + + align:start position:0% +sampling without replacement and again + + + align:start position:0% +sampling without replacement and again +this is something that we'll see um sort + + align:start position:0% +this is something that we'll see um sort + + + align:start position:0% +this is something that we'll see um sort +of later on in the semester as + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +okay questions before I go on + + align:start position:0% +okay questions before I go on + + + align:start position:0% +okay questions before I go on +nope oh I guess I just mentioned that so + + align:start position:0% +nope oh I guess I just mentioned that so + + + align:start position:0% +nope oh I guess I just mentioned that so +this is just a note about the the + + align:start position:0% +this is just a note about the the + + + align:start position:0% +this is just a note about the the +factorial + + align:start position:0% + + + + align:start position:0% + +notation okay so to compute + + align:start position:0% +notation okay so to compute + + + align:start position:0% +notation okay so to compute +probabilities in these examples that I + + align:start position:0% +probabilities in these examples that I + + + align:start position:0% +probabilities in these examples that I +just gave you all I did was count okay + + align:start position:0% +just gave you all I did was count okay + + + align:start position:0% +just gave you all I did was count okay +um the counting was a little fancy + + align:start position:0% +um the counting was a little fancy + + + align:start position:0% +um the counting was a little fancy +sometimes but it was just counting okay + + align:start position:0% +sometimes but it was just counting okay + + + align:start position:0% +sometimes but it was just counting okay +so let me actually be a little bit more + + align:start position:0% +so let me actually be a little bit more + + + align:start position:0% +so let me actually be a little bit more +concrete um a little bit more organized + + align:start position:0% +concrete um a little bit more organized + + + align:start position:0% +concrete um a little bit more organized +about the counting rules that I used + + align:start position:0% +about the counting rules that I used + + + align:start position:0% +about the counting rules that I used +okay um and uh another um another term + + align:start position:0% +okay um and uh another um another term + + + align:start position:0% +okay um and uh another um another term +to describe these counting rules is + + align:start position:0% +to describe these counting rules is + + + align:start position:0% +to describe these counting rules is +combinatorics okay so the first uh + + align:start position:0% +combinatorics okay so the first uh + + + align:start position:0% +combinatorics okay so the first uh +counting rule uh that I used in in one + + align:start position:0% +counting rule uh that I used in in one + + + align:start position:0% +counting rule uh that I used in in one +of the examples or actually all the + + align:start position:0% +of the examples or actually all the + + + align:start position:0% +of the examples or actually all the +examples uh if an experiment has two + + align:start position:0% +examples uh if an experiment has two + + + align:start position:0% +examples uh if an experiment has two +parts the first one has M possibilities + + align:start position:0% +parts the first one has M possibilities + + + align:start position:0% +parts the first one has M possibilities +and the second one has n possibilities + + align:start position:0% +and the second one has n possibilities + + + align:start position:0% +and the second one has n possibilities +uh then the experiment has uh M * n + + align:start position:0% +uh then the experiment has uh M * n + + + align:start position:0% +uh then the experiment has uh M * n +possible outcomes + + align:start position:0% +possible outcomes + + + align:start position:0% +possible outcomes +okay so this is so something we're just + + align:start position:0% +okay so this is so something we're just + + + align:start position:0% +okay so this is so something we're just +being complete by including it here but + + align:start position:0% +being complete by including it here but + + + align:start position:0% +being complete by including it here but +this is something you would do + + align:start position:0% +this is something you would do + + + align:start position:0% +this is something you would do +intuitively anyhow + + align:start position:0% + + + + align:start position:0% + +okay uh two other counting rules uh an + + align:start position:0% +okay uh two other counting rules uh an + + + align:start position:0% +okay uh two other counting rules uh an +ordered arrangement of objects is called + + align:start position:0% +ordered arrangement of objects is called + + + align:start position:0% +ordered arrangement of objects is called +a permutation okay the number of + + align:start position:0% +a permutation okay the number of + + + align:start position:0% +a permutation okay the number of +different permutations of n object is n + + align:start position:0% +different permutations of n object is n + + + align:start position:0% +different permutations of n object is n +factorial so I use this counting rule on + + align:start position:0% +factorial so I use this counting rule on + + + align:start position:0% +factorial so I use this counting rule on +the second license plate + + align:start position:0% +the second license plate + + + align:start position:0% +the second license plate +example okay and um the more generally + + align:start position:0% +example okay and um the more generally + + + align:start position:0% +example okay and um the more generally +the number of different permutations of + + align:start position:0% +the number of different permutations of + + + align:start position:0% +the number of different permutations of +n little n objects taken uh from Big N + + align:start position:0% +n little n objects taken uh from Big N + + + align:start position:0% +n little n objects taken uh from Big N +objects is a big n factorial over big n + + align:start position:0% +objects is a big n factorial over big n + + + align:start position:0% +objects is a big n factorial over big n +minus little n factorial okay so this is + + align:start position:0% +minus little n factorial okay so this is + + + align:start position:0% +minus little n factorial okay so this is +exactly the counting rule that I used in + + align:start position:0% +exactly the counting rule that I used in + + + align:start position:0% +exactly the counting rule that I used in +the license plate + + align:start position:0% +the license plate + + + align:start position:0% +the license plate +example and then sometimes we want to + + align:start position:0% +example and then sometimes we want to + + + align:start position:0% +example and then sometimes we want to +count um we want to count outcomes in a + + align:start position:0% +count um we want to count outcomes in a + + + align:start position:0% +count um we want to count outcomes in a +sample space but we don't want to count + + align:start position:0% +sample space but we don't want to count + + + align:start position:0% +sample space but we don't want to count +so in the license plate example order + + align:start position:0% +so in the license plate example order + + + align:start position:0% +so in the license plate example order +was important so a license plate that + + align:start position:0% +was important so a license plate that + + + align:start position:0% +was important so a license plate that +was abc123 is different from a license + + align:start position:0% +was abc123 is different from a license + + + align:start position:0% +was abc123 is different from a license +plate that's + + align:start position:0% +plate that's + + + align:start position:0% +plate that's +BCA F you know uh 231 or something okay + + align:start position:0% +BCA F you know uh 231 or something okay + + + align:start position:0% +BCA F you know uh 231 or something okay +and so um there there are going to be + + align:start position:0% +and so um there there are going to be + + + align:start position:0% +and so um there there are going to be +problems though where order doesn't + + align:start position:0% +problems though where order doesn't + + + align:start position:0% +problems though where order doesn't +matter and we don't want to count uh + + align:start position:0% +matter and we don't want to count uh + + + align:start position:0% +matter and we don't want to count uh +different orderings as different + + align:start position:0% +different orderings as different + + + align:start position:0% +different orderings as different +outcomes and so then we have a third + + align:start position:0% +outcomes and so then we have a third + + + align:start position:0% +outcomes and so then we have a third +counting rule uh which is called the + + align:start position:0% +counting rule uh which is called the + + + align:start position:0% +counting rule uh which is called the +Comin the the counting rule of + + align:start position:0% +Comin the the counting rule of + + + align:start position:0% +Comin the the counting rule of +combinations okay an unordered + + align:start position:0% +combinations okay an unordered + + + align:start position:0% +combinations okay an unordered +Arrangements of object an unordered + + align:start position:0% +Arrangements of object an unordered + + + align:start position:0% +Arrangements of object an unordered +arrangement of objects is called a + + align:start position:0% +arrangement of objects is called a + + + align:start position:0% +arrangement of objects is called a +combination and the number of different + + align:start position:0% +combination and the number of different + + + align:start position:0% +combination and the number of different +combinations of little n objects taken + + align:start position:0% +combinations of little n objects taken + + + align:start position:0% +combinations of little n objects taken +from Big N objects is just the same as + + align:start position:0% +from Big N objects is just the same as + + + align:start position:0% +from Big N objects is just the same as +the number of permutations but we also + + align:start position:0% +the number of permutations but we also + + + align:start position:0% +the number of permutations but we also +divide by little n and that I think of + + align:start position:0% +divide by little n and that I think of + + + align:start position:0% +divide by little n and that I think of +that in some sense as taking out you + + align:start position:0% +that in some sense as taking out you + + + align:start position:0% +that in some sense as taking out you +know sort of making sure we're not + + align:start position:0% +know sort of making sure we're not + + + align:start position:0% +know sort of making sure we're not +double counting uh all of the different + + align:start position:0% +double counting uh all of the different + + + align:start position:0% +double counting uh all of the different +orderings so you're taking out the the + + align:start position:0% +orderings so you're taking out the the + + + align:start position:0% +orderings so you're taking out the the +orderings by dividing by little n + + align:start position:0% +orderings by dividing by little n + + + align:start position:0% +orderings by dividing by little n +factorial + + align:start position:0% +factorial + + + align:start position:0% +factorial +okay uh we typically denote this uh + + align:start position:0% +okay uh we typically denote this uh + + + align:start position:0% +okay uh we typically denote this uh +using um notation like this and we call + + align:start position:0% +using um notation like this and we call + + + align:start position:0% +using um notation like this and we call +it the terminology we use is Big N + + align:start position:0% +it the terminology we use is Big N + + + align:start position:0% +it the terminology we use is Big N +choose little + + align:start position:0% + + + + align:start position:0% + +n + + align:start position:0% +n + + + align:start position:0% +n +okay + + align:start position:0% + + + + align:start position:0% + +okay let's go through a few more + + align:start position:0% +okay let's go through a few more + + + align:start position:0% +okay let's go through a few more +examples okay let's suppose all the + + align:start position:0% +examples okay let's suppose all the + + + align:start position:0% +examples okay let's suppose all the +candidates for the Republican + + align:start position:0% +candidates for the Republican + + + align:start position:0% +candidates for the Republican +Presidential nomination uh gather on + + align:start position:0% +Presidential nomination uh gather on + + + align:start position:0% +Presidential nomination uh gather on +stage for an event um how many + + align:start position:0% +stage for an event um how many + + + align:start position:0% +stage for an event um how many +handshakes are exchanged if all of them + + align:start position:0% +handshakes are exchanged if all of them + + + align:start position:0% +handshakes are exchanged if all of them +are exchanging handshakes with all of + + align:start position:0% +are exchanging handshakes with all of + + + align:start position:0% +are exchanging handshakes with all of +the others by the + + align:start position:0% +the others by the + + + align:start position:0% +the others by the +way who knew apparently he got 12 vot I + + align:start position:0% +way who knew apparently he got 12 vot I + + + align:start position:0% +way who knew apparently he got 12 vot I +checked it on Wikipedia he got 12 votes + + align:start position:0% +checked it on Wikipedia he got 12 votes + + + align:start position:0% +checked it on Wikipedia he got 12 votes +in Iowa did anyone know Jim Gilmore was + + align:start position:0% +in Iowa did anyone know Jim Gilmore was + + + align:start position:0% +in Iowa did anyone know Jim Gilmore was +still in the race no you did okay I had + + align:start position:0% +still in the race no you did okay I had + + + align:start position:0% +still in the race no you did okay I had +no idea anyhow I checked it on Wikipedia + + align:start position:0% +no idea anyhow I checked it on Wikipedia + + + align:start position:0% +no idea anyhow I checked it on Wikipedia +12 votes in Iowa I think he's still in + + align:start position:0% +12 votes in Iowa I think he's still in + + + align:start position:0% +12 votes in Iowa I think he's still in +there okay so let's suppose all nine of + + align:start position:0% +there okay so let's suppose all nine of + + + align:start position:0% +there okay so let's suppose all nine of +these um uh men uh um gentlemen and and + + align:start position:0% +these um uh men uh um gentlemen and and + + + align:start position:0% +these um uh men uh um gentlemen and and +one woman or eight gentlemen one woman + + align:start position:0% +one woman or eight gentlemen one woman + + + align:start position:0% +one woman or eight gentlemen one woman +gather on stage and they're all uh uh + + align:start position:0% +gather on stage and they're all uh uh + + + align:start position:0% +gather on stage and they're all uh uh +exchanging handshakes how many + + align:start position:0% +exchanging handshakes how many + + + align:start position:0% +exchanging handshakes how many +handshakes are + + align:start position:0% +handshakes are + + + align:start position:0% +handshakes are +exchanged + + align:start position:0% + + + + align:start position:0% + +so this isn't a probability problem this + + align:start position:0% +so this isn't a probability problem this + + + align:start position:0% +so this isn't a probability problem this +is just using sort of the counting + + align:start position:0% + + + + align:start position:0% + +rules any guesses + + align:start position:0% +rules any guesses + + + align:start position:0% +rules any guesses +yep nine shoes two okay so do you want + + align:start position:0% +yep nine shoes two okay so do you want + + + align:start position:0% +yep nine shoes two okay so do you want +to explain uh would would you like to + + align:start position:0% +to explain uh would would you like to + + + align:start position:0% +to explain uh would would you like to +take a shot at explaining why that would + + align:start position:0% +take a shot at explaining why that would + + + align:start position:0% +take a shot at explaining why that would +be sure so there's nine candidates and + + align:start position:0% +be sure so there's nine candidates and + + + align:start position:0% +be sure so there's nine candidates and +we want to find the number of way to any + + align:start position:0% +we want to find the number of way to any + + + align:start position:0% +we want to find the number of way to any +two of them so therefore we want to use + + align:start position:0% +two of them so therefore we want to use + + + align:start position:0% +two of them so therefore we want to use +n Cho + + align:start position:0% +n Cho + + + align:start position:0% +n Cho +two that's right that's right so a + + align:start position:0% +two that's right that's right so a + + + align:start position:0% +two that's right that's right so a +handshake involves two of the nine + + align:start position:0% +handshake involves two of the nine + + + align:start position:0% +handshake involves two of the nine +candidates and order doesn't matter + + align:start position:0% +candidates and order doesn't matter + + + align:start position:0% +candidates and order doesn't matter +because Jim Gilmore shaking Carly + + align:start position:0% +because Jim Gilmore shaking Carly + + + align:start position:0% +because Jim Gilmore shaking Carly +fiorina's hand is exactly the same as + + align:start position:0% +fiorina's hand is exactly the same as + + + align:start position:0% +fiorina's hand is exactly the same as +Carly fiorina shaking Jim Gilmore's hand + + align:start position:0% +Carly fiorina shaking Jim Gilmore's hand + + + align:start position:0% +Carly fiorina shaking Jim Gilmore's hand +okay and so we don't want to use a + + align:start position:0% +okay and so we don't want to use a + + + align:start position:0% +okay and so we don't want to use a +permutation counting rule we want to use + + align:start position:0% +permutation counting rule we want to use + + + align:start position:0% +permutation counting rule we want to use +the combination counting rule so you're + + align:start position:0% +the combination counting rule so you're + + + align:start position:0% +the combination counting rule so you're +exactly right + + align:start position:0% + + + + align:start position:0% + +okay okay another + + align:start position:0% +okay okay another + + + align:start position:0% +okay okay another +example so we've got this new building + + align:start position:0% +example so we've got this new building + + + align:start position:0% +example so we've got this new building +you guys should come visit it if you + + align:start position:0% +you guys should come visit it if you + + + align:start position:0% +you guys should come visit it if you +have if you haven't already um so the + + align:start position:0% +have if you haven't already um so the + + + align:start position:0% +have if you haven't already um so the +economics department just moved back + + align:start position:0% +economics department just moved back + + + align:start position:0% +economics department just moved back +into uh a renovated e52 it is + + align:start position:0% + + + + align:start position:0% + +spectacular and uh all of the faculty we + + align:start position:0% +spectacular and uh all of the faculty we + + + align:start position:0% +spectacular and uh all of the faculty we +have all these beautiful newly renovated + + align:start position:0% +have all these beautiful newly renovated + + + align:start position:0% +have all these beautiful newly renovated +faculty offices and all the faculty got + + align:start position:0% +faculty offices and all the faculty got + + + align:start position:0% +faculty offices and all the faculty got +assigned to um one of the offices okay + + align:start position:0% +assigned to um one of the offices okay + + + align:start position:0% +assigned to um one of the offices okay +so I think we have 40 maybe we have 41 + + align:start position:0% +so I think we have 40 maybe we have 41 + + + align:start position:0% +so I think we have 40 maybe we have 41 +faculty offices I'm not sure let's say + + align:start position:0% +faculty offices I'm not sure let's say + + + align:start position:0% +faculty offices I'm not sure let's say +we have 40 faculty offices in the + + align:start position:0% +we have 40 faculty offices in the + + + align:start position:0% +we have 40 faculty offices in the +renovated + + align:start position:0% +renovated + + + align:start position:0% +renovated +e52 now for the purposes of this problem + + align:start position:0% +e52 now for the purposes of this problem + + + align:start position:0% +e52 now for the purposes of this problem +let's assume that they're in a + + align:start position:0% +let's assume that they're in a + + + align:start position:0% +let's assume that they're in a +continuous line they're actually not + + align:start position:0% +continuous line they're actually not + + + align:start position:0% +continuous line they're actually not +they're on two different floors let's + + align:start position:0% +they're on two different floors let's + + + align:start position:0% +they're on two different floors let's +let's assume they're in continuous + + align:start position:0% +let's assume they're in continuous + + + align:start position:0% +let's assume they're in continuous +line and if 40 faculty members are + + align:start position:0% +line and if 40 faculty members are + + + align:start position:0% +line and if 40 faculty members are +placed randomly in the offices what is + + align:start position:0% +placed randomly in the offices what is + + + align:start position:0% +placed randomly in the offices what is +the probability that Esther and I are + + align:start position:0% +the probability that Esther and I are + + + align:start position:0% +the probability that Esther and I are +next to each other in the new uh + + align:start position:0% +next to each other in the new uh + + + align:start position:0% +next to each other in the new uh +e52 by the way this is actually where we + + align:start position:0% +e52 by the way this is actually where we + + + align:start position:0% +e52 by the way this is actually where we +are that's this is Esther up here on the + + align:start position:0% +are that's this is Esther up here on the + + + align:start position:0% +are that's this is Esther up here on the +upper left and I'm over there on + + align:start position:0% +upper left and I'm over there on + + + align:start position:0% +upper left and I'm over there on +the but what's the probability that + + align:start position:0% +the but what's the probability that + + + align:start position:0% +the but what's the probability that +Esther and I are next to each other does + + align:start position:0% +Esther and I are next to each other does + + + align:start position:0% +Esther and I are next to each other does +anyone want to take a stab at + + align:start position:0% + + + + align:start position:0% + +this so let's maybe we should go step by + + align:start position:0% +this so let's maybe we should go step by + + + align:start position:0% +this so let's maybe we should go step by +step how many different ways are there + + align:start position:0% +step how many different ways are there + + + align:start position:0% +step how many different ways are there +to put 40 faculty members into 40 + + align:start position:0% + + + + align:start position:0% + +offices I think I heard it 40 factorial + + align:start position:0% +offices I think I heard it 40 factorial + + + align:start position:0% +offices I think I heard it 40 factorial +right + + align:start position:0% +right + + + align:start position:0% +right +okay and how many uh different ways are + + align:start position:0% +okay and how many uh different ways are + + + align:start position:0% +okay and how many uh different ways are +there to do that where Esther and I are + + align:start position:0% +there to do that where Esther and I are + + + align:start position:0% +there to do that where Esther and I are +sitting next to each + + align:start position:0% + + + + align:start position:0% + +other I hear little murmurings but I'm + + align:start position:0% +other I hear little murmurings but I'm + + + align:start position:0% +other I hear little murmurings but I'm +not sure I'm not sure if I heard the + + align:start position:0% +not sure I'm not sure if I heard the + + + align:start position:0% +not sure I'm not sure if I heard the +right oh + + align:start position:0% + + + + align:start position:0% + +okay um so the the way that I I think + + align:start position:0% +okay um so the the way that I I think + + + align:start position:0% +okay um so the the way that I I think +about this problem is that I think about + + align:start position:0% +about this problem is that I think about + + + align:start position:0% +about this problem is that I think about +oh + + align:start position:0% +oh + + + align:start position:0% +oh +yes sorry 39 factorial times two is that + + align:start position:0% +yes sorry 39 factorial times two is that + + + align:start position:0% +yes sorry 39 factorial times two is that +what you said yeah would you like to try + + align:start position:0% +what you said yeah would you like to try + + + align:start position:0% +what you said yeah would you like to try +to explain it if you speak no okay okay + + align:start position:0% +to explain it if you speak no okay okay + + + align:start position:0% +to explain it if you speak no okay okay +I'll I'll I'll explain it then so so the + + align:start position:0% +I'll I'll I'll explain it then so so the + + + align:start position:0% +I'll I'll I'll explain it then so so the +way I think about this is that uh + + align:start position:0% +way I think about this is that uh + + + align:start position:0% +way I think about this is that uh +someone ties Esther and I together okay + + align:start position:0% +someone ties Esther and I together okay + + + align:start position:0% +someone ties Esther and I together okay +and now we're one unit we have to come + + align:start position:0% +and now we're one unit we have to come + + + align:start position:0% +and now we're one unit we have to come +together right and so now there's only + + align:start position:0% +together right and so now there's only + + + align:start position:0% +together right and so now there's only +39 factorial ways to do the arrangement + + align:start position:0% +39 factorial ways to do the arrangement + + + align:start position:0% +39 factorial ways to do the arrangement +since the two of us are tied together oh + + align:start position:0% +since the two of us are tied together oh + + + align:start position:0% +since the two of us are tied together oh +but there's one extra uh thing we have + + align:start position:0% +but there's one extra uh thing we have + + + align:start position:0% +but there's one extra uh thing we have +to consider which is that she could be + + align:start position:0% +to consider which is that she could be + + + align:start position:0% +to consider which is that she could be +tied to my left or she could be tied to + + align:start position:0% +tied to my left or she could be tied to + + + align:start position:0% +tied to my left or she could be tied to +my right so then we have to multiply by + + align:start position:0% +my right so then we have to multiply by + + + align:start position:0% +my right so then we have to multiply by +two + + align:start position:0% +two + + + align:start position:0% +two +okay so there we have + + align:start position:0% + + + + align:start position:0% + +it okay a yes for your previous example + + align:start position:0% +it okay a yes for your previous example + + + align:start position:0% +it okay a yes for your previous example +does that like the left tie to your left + + align:start position:0% +does that like the left tie to your left + + + align:start position:0% +does that like the left tie to your left +versus tied to your right does that + + align:start position:0% +versus tied to your right does that + + + align:start position:0% +versus tied to your right does that +account for like if one of you has like + + align:start position:0% +account for like if one of you has like + + + align:start position:0% +account for like if one of you has like +the corner + + align:start position:0% +the corner + + + align:start position:0% +the corner +so I'm assuming that the offices are in + + align:start position:0% +so I'm assuming that the offices are in + + + align:start position:0% +so I'm assuming that the offices are in +one one continuous + + align:start position:0% +one one continuous + + + align:start position:0% +one one continuous +line just to make the make the uh + + align:start position:0% +line just to make the make the uh + + + align:start position:0% +line just to make the make the uh +question simpler does that answer your + + align:start position:0% +question simpler does that answer your + + + align:start position:0% +question simpler does that answer your +question + + align:start position:0% + + + + align:start position:0% + +okay okay another example maybe this + + align:start position:0% +okay okay another example maybe this + + + align:start position:0% +okay okay another example maybe this +will um make you hungry because it's + + align:start position:0% +will um make you hungry because it's + + + align:start position:0% +will um make you hungry because it's +right before + + align:start position:0% +right before + + + align:start position:0% +right before +lunchtime um area four has anyone been + + align:start position:0% +lunchtime um area four has anyone been + + + align:start position:0% +lunchtime um area four has anyone been +to area 4 you guys know area four yeah + + align:start position:0% +to area 4 you guys know area four yeah + + + align:start position:0% +to area 4 you guys know area four yeah +okay so I went onto their website as I + + align:start position:0% +okay so I went onto their website as I + + + align:start position:0% +okay so I went onto their website as I +was writing my lecture notes I was + + align:start position:0% +was writing my lecture notes I was + + + align:start position:0% +was writing my lecture notes I was +getting hungry so I went onto area 4's + + align:start position:0% +getting hungry so I went onto area 4's + + + align:start position:0% +getting hungry so I went onto area 4's +website to see what toppings they offer + + align:start position:0% +website to see what toppings they offer + + + align:start position:0% +website to see what toppings they offer +on their pizzas so turns out they have + + align:start position:0% +on their pizzas so turns out they have + + + align:start position:0% +on their pizzas so turns out they have +six vegetarian pizza toppings + + align:start position:0% +six vegetarian pizza toppings + + + align:start position:0% +six vegetarian pizza toppings +caramelized onions pickled banana + + align:start position:0% +caramelized onions pickled banana + + + align:start position:0% +caramelized onions pickled banana +peppers mushrooms green olives + + align:start position:0% +peppers mushrooms green olives + + + align:start position:0% +peppers mushrooms green olives +arugula and eggs I think that's it okay + + align:start position:0% +arugula and eggs I think that's it okay + + + align:start position:0% +arugula and eggs I think that's it okay +and then they have five nonvegetarian + + align:start position:0% +and then they have five nonvegetarian + + + align:start position:0% +and then they have five nonvegetarian +toppings soap raada sausage bacon + + align:start position:0% +toppings soap raada sausage bacon + + + align:start position:0% +toppings soap raada sausage bacon +chicken and anchovies + + align:start position:0% +chicken and anchovies + + + align:start position:0% +chicken and anchovies +okay so let's suppose I um want uh fate + + align:start position:0% +okay so let's suppose I um want uh fate + + + align:start position:0% +okay so let's suppose I um want uh fate +to decide what pizza I order instead of + + align:start position:0% +to decide what pizza I order instead of + + + align:start position:0% +to decide what pizza I order instead of +just choosing my toppings so I write + + align:start position:0% +just choosing my toppings so I write + + + align:start position:0% +just choosing my toppings so I write +each topping on a piece of paper and I + + align:start position:0% +each topping on a piece of paper and I + + + align:start position:0% +each topping on a piece of paper and I +put them in a hat and I randomly choose + + align:start position:0% +put them in a hat and I randomly choose + + + align:start position:0% +put them in a hat and I randomly choose +out two toppings from two pieces of + + align:start position:0% +out two toppings from two pieces of + + + align:start position:0% +out two toppings from two pieces of +paper what's the probability that I end + + align:start position:0% +paper what's the probability that I end + + + align:start position:0% +paper what's the probability that I end +up with a pizza that has one vegetarian + + align:start position:0% +up with a pizza that has one vegetarian + + + align:start position:0% +up with a pizza that has one vegetarian +and one non-vegetarian + + align:start position:0% +and one non-vegetarian + + + align:start position:0% +and one non-vegetarian +topping + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +sorry uh oh you're uh so I I think + + align:start position:0% +sorry uh oh you're uh so I I think + + + align:start position:0% +sorry uh oh you're uh so I I think +you're on the right track but let me uh + + align:start position:0% +you're on the right track but let me uh + + + align:start position:0% +you're on the right track but let me uh +let me put up the explanation so the the + + align:start position:0% +let me put up the explanation so the the + + + align:start position:0% +let me put up the explanation so the the +the idea is first of + + align:start position:0% +the idea is first of + + + align:start position:0% +the idea is first of +all we have to count the number of + + align:start position:0% +all we have to count the number of + + + align:start position:0% +all we have to count the number of +different U possibilities in the sample + + align:start position:0% +different U possibilities in the sample + + + align:start position:0% +different U possibilities in the sample +space and that's just going to be + + align:start position:0% +space and that's just going to be + + + align:start position:0% +space and that's just going to be +um uh sorry that's going to be 11 shoes + + align:start position:0% +um uh sorry that's going to be 11 shoes + + + align:start position:0% +um uh sorry that's going to be 11 shoes +too okay and then the the number of uh + + align:start position:0% +too okay and then the the number of uh + + + align:start position:0% +too okay and then the the number of uh +possibilities of um one vegetarian and + + align:start position:0% +possibilities of um one vegetarian and + + + align:start position:0% +possibilities of um one vegetarian and +one one non-vegetarian topping we have + + align:start position:0% +one one non-vegetarian topping we have + + + align:start position:0% +one one non-vegetarian topping we have +six non-vegetarian possibilities and + + align:start position:0% +six non-vegetarian possibilities and + + + align:start position:0% +six non-vegetarian possibilities and +five ve sorry I have it the wrong way + + align:start position:0% +five ve sorry I have it the wrong way + + + align:start position:0% +five ve sorry I have it the wrong way +around I think six vegetarian and five + + align:start position:0% +around I think six vegetarian and five + + + align:start position:0% +around I think six vegetarian and five +non-vegetarian so we have 30 + + align:start position:0% +non-vegetarian so we have 30 + + + align:start position:0% +non-vegetarian so we have 30 +possibilities and I think this is what + + align:start position:0% +possibilities and I think this is what + + + align:start position:0% +possibilities and I think this is what +you were getting at 30 possibil ities + + align:start position:0% +you were getting at 30 possibil ities + + + align:start position:0% +you were getting at 30 possibil ities +for um the a pizza with one vegetarian + + align:start position:0% +for um the a pizza with one vegetarian + + + align:start position:0% +for um the a pizza with one vegetarian +and one nonvegetarian topping and so + + align:start position:0% +and one nonvegetarian topping and so + + + align:start position:0% +and one nonvegetarian topping and so +then we just divide uh the number of um + + align:start position:0% +then we just divide uh the number of um + + + align:start position:0% +then we just divide uh the number of um +outcomes in that event by the total + + align:start position:0% +outcomes in that event by the total + + + align:start position:0% +outcomes in that event by the total +number of outcomes okay the total number + + align:start position:0% +number of outcomes okay the total number + + + align:start position:0% +number of outcomes okay the total number +of possibilities so we end up with uh 30 + + align:start position:0% +of possibilities so we end up with uh 30 + + + align:start position:0% +of possibilities so we end up with uh 30 +over + + align:start position:0% +over + + + align:start position:0% +over +66 EAS think about it as you have + + align:start position:0% +66 EAS think about it as you have + + + align:start position:0% +66 EAS think about it as you have +everything + + align:start position:0% +everything + + + align:start position:0% +everything +you so you have five and 6 five right so + + align:start position:0% +you so you have five and 6 five right so + + + align:start position:0% +you so you have five and 6 five right so +you have a total of 11 right yes so it's + + align:start position:0% +you have a total of 11 right yes so it's + + + align:start position:0% +you have a total of 11 right yes so it's +6 over 11 and so that's my first topic + + align:start position:0% +6 over 11 and so that's my first topic + + + align:start position:0% +6 over 11 and so that's my first topic +taken out and then I have another + + align:start position:0% +taken out and then I have another + + + align:start position:0% +taken out and then I have another +probability which is 6 over 10 which is + + align:start position:0% +probability which is 6 over 10 which is + + + align:start position:0% +probability which is 6 over 10 which is +the remaining 10 because I already have + + align:start position:0% +the remaining 10 because I already have + + + align:start position:0% +the remaining 10 because I already have +extract so you're absolutely right that + + align:start position:0% +extract so you're absolutely right that + + + align:start position:0% +extract so you're absolutely right that +that is an alternative way that you can + + align:start position:0% +that is an alternative way that you can + + + align:start position:0% +that is an alternative way that you can +think about as opposed to to this way + + align:start position:0% +think about as opposed to to this way + + + align:start position:0% +think about as opposed to to this way +and you get exactly the same answer okay + + align:start position:0% +and you get exactly the same answer okay + + + align:start position:0% +and you get exactly the same answer okay +so you're absolutely right about that um + + align:start position:0% +so you're absolutely right about that um + + + align:start position:0% +so you're absolutely right about that um +the + + align:start position:0% +the + + + align:start position:0% +the +um I think a lot of times when we see + + align:start position:0% +um I think a lot of times when we see + + + align:start position:0% +um I think a lot of times when we see +probability problems there are different + + align:start position:0% +probability problems there are different + + + align:start position:0% +probability problems there are different +ways to approach them that give you the + + align:start position:0% +ways to approach them that give you the + + + align:start position:0% +ways to approach them that give you the +same answer and the reason why I + + align:start position:0% +same answer and the reason why I + + + align:start position:0% +same answer and the reason why I +actually thought about giving the two + + align:start position:0% +actually thought about giving the two + + + align:start position:0% +actually thought about giving the two +alternative ways to solve this problem + + align:start position:0% +alternative ways to solve this problem + + + align:start position:0% +alternative ways to solve this problem +but we don't have quite all of the the + + align:start position:0% +but we don't have quite all of the the + + + align:start position:0% +but we don't have quite all of the the +sort of um Machinery to solve it the the + + align:start position:0% +sort of um Machinery to solve it the the + + + align:start position:0% +sort of um Machinery to solve it the the +way that you suggest but you're + + align:start position:0% +way that you suggest but you're + + + align:start position:0% +way that you suggest but you're +absolutely right yeah so there's there's + + align:start position:0% +absolutely right yeah so there's there's + + + align:start position:0% +absolutely right yeah so there's there's +another way that you can think about + + align:start position:0% +another way that you can think about + + + align:start position:0% +another way that you can think about +this problem in a slightly more General + + align:start position:0% +this problem in a slightly more General + + + align:start position:0% +this problem in a slightly more General +uh + + align:start position:0% +uh + + + align:start position:0% +uh +fashion + + align:start position:0% +fashion + + + align:start position:0% +fashion +okay so uh let's suppose instead of just + + align:start position:0% +okay so uh let's suppose instead of just + + + align:start position:0% +okay so uh let's suppose instead of just +choosing two toppings I was choosing end + + align:start position:0% +choosing two toppings I was choosing end + + + align:start position:0% +choosing two toppings I was choosing end +toppings okay and I asked what the + + align:start position:0% +toppings okay and I asked what the + + + align:start position:0% +toppings okay and I asked what the +probability that my pizza had N1 + + align:start position:0% +probability that my pizza had N1 + + + align:start position:0% +probability that my pizza had N1 +vegetarian toppings and N2 nonvegetarian + + align:start position:0% +vegetarian toppings and N2 nonvegetarian + + + align:start position:0% +vegetarian toppings and N2 nonvegetarian +toppings was + + align:start position:0% +toppings was + + + align:start position:0% +toppings was +okay so this is basically just a + + align:start position:0% +okay so this is basically just a + + + align:start position:0% +okay so this is basically just a +generalization of the problem that I + + align:start position:0% +generalization of the problem that I + + + align:start position:0% +generalization of the problem that I +just did instead of having one + + align:start position:0% +just did instead of having one + + + align:start position:0% +just did instead of having one +vegetarian one + + align:start position:0% +vegetarian one + + + align:start position:0% +vegetarian one +nonvegetarian uh we're having N1 and N2 + + align:start position:0% +nonvegetarian uh we're having N1 and N2 + + + align:start position:0% +nonvegetarian uh we're having N1 and N2 +okay um and note that there would be six + + align:start position:0% +okay um and note that there would be six + + + align:start position:0% +okay um and note that there would be six +choose and one um possibilities for the + + align:start position:0% +choose and one um possibilities for the + + + align:start position:0% +choose and one um possibilities for the +vegetarian topping and there would be + + align:start position:0% +vegetarian topping and there would be + + + align:start position:0% +vegetarian topping and there would be +five choose n two possibilities for the + + align:start position:0% +five choose n two possibilities for the + + + align:start position:0% +five choose n two possibilities for the +non-vegetarian topping so we multiply + + align:start position:0% +non-vegetarian topping so we multiply + + + align:start position:0% +non-vegetarian topping so we multiply +those two together in the + + align:start position:0% +those two together in the + + + align:start position:0% +those two together in the +numerator uh to um count the the number + + align:start position:0% +numerator uh to um count the the number + + + align:start position:0% +numerator uh to um count the the number +of outcomes in the experiment that + + align:start position:0% +of outcomes in the experiment that + + + align:start position:0% +of outcomes in the experiment that +satisfy um our event and then the uh + + align:start position:0% +satisfy um our event and then the uh + + + align:start position:0% +satisfy um our event and then the uh +denominator is just 11 choose in for the + + align:start position:0% +denominator is just 11 choose in for the + + + align:start position:0% +denominator is just 11 choose in for the +total number you know end toppings that + + align:start position:0% +total number you know end toppings that + + + align:start position:0% +total number you know end toppings that +were putting on the pizza + + align:start position:0% + + + + align:start position:0% + +okay and I want to note that uh this + + align:start position:0% +okay and I want to note that uh this + + + align:start position:0% +okay and I want to note that uh this +we're going to refer back to this + + align:start position:0% +we're going to refer back to this + + + align:start position:0% +we're going to refer back to this +example as the basis for a special + + align:start position:0% +example as the basis for a special + + + align:start position:0% +example as the basis for a special +distribution the hypergeometric + + align:start position:0% +distribution the hypergeometric + + + align:start position:0% +distribution the hypergeometric +distribution + + align:start position:0% + + + + align:start position:0% + +okay okay so going forward um it's going + + align:start position:0% +okay okay so going forward um it's going + + + align:start position:0% +okay okay so going forward um it's going +to be important for us to be able to + + align:start position:0% +to be important for us to be able to + + + align:start position:0% +to be important for us to be able to +talk about the relationship between + + align:start position:0% +talk about the relationship between + + + align:start position:0% +talk about the relationship between +these probabilistic events or also known + + align:start position:0% +these probabilistic events or also known + + + align:start position:0% +these probabilistic events or also known +as stochastic events okay and the most + + align:start position:0% +as stochastic events okay and the most + + + align:start position:0% +as stochastic events okay and the most +fundamental of the + + align:start position:0% +fundamental of the + + + align:start position:0% +fundamental of the +relationships that we're going to be + + align:start position:0% +relationships that we're going to be + + + align:start position:0% +relationships that we're going to be +concerned with is uh something called + + align:start position:0% +concerned with is uh something called + + + align:start position:0% +concerned with is uh something called +Independence okay so let me first give + + align:start position:0% +Independence okay so let me first give + + + align:start position:0% +Independence okay so let me first give +you the definition of uh of Independence + + align:start position:0% +you the definition of uh of Independence + + + align:start position:0% +you the definition of uh of Independence +in probability events A and B are + + align:start position:0% +in probability events A and B are + + + align:start position:0% +in probability events A and B are +independent if the probability of the + + align:start position:0% +independent if the probability of the + + + align:start position:0% +independent if the probability of the +their intersection is equal to the + + align:start position:0% +their intersection is equal to the + + + align:start position:0% +their intersection is equal to the +product of their + + align:start position:0% +product of their + + + align:start position:0% +product of their +probabilities so I I never find this + + align:start position:0% +probabilities so I I never find this + + + align:start position:0% +probabilities so I I never find this +definition very intuitive I mean I feel + + align:start position:0% +definition very intuitive I mean I feel + + + align:start position:0% +definition very intuitive I mean I feel +like probably a lot of you have sort of + + align:start position:0% +like probably a lot of you have sort of + + + align:start position:0% +like probably a lot of you have sort of +a uh an intuitive sense of what + + align:start position:0% +a uh an intuitive sense of what + + + align:start position:0% +a uh an intuitive sense of what +Independence means in probability uh but + + align:start position:0% +Independence means in probability uh but + + + align:start position:0% +Independence means in probability uh but +um this is not a very intuitive + + align:start position:0% +um this is not a very intuitive + + + align:start position:0% +um this is not a very intuitive +definition okay or at least in my + + align:start position:0% +definition okay or at least in my + + + align:start position:0% +definition okay or at least in my +opinion it's not um there is there is + + align:start position:0% +opinion it's not um there is there is + + + align:start position:0% +opinion it's not um there is there is +though uh you know I should sort of give + + align:start position:0% +though uh you know I should sort of give + + + align:start position:0% +though uh you know I should sort of give +a word of warning though that sometimes + + align:start position:0% +a word of warning though that sometimes + + + align:start position:0% +a word of warning though that sometimes +our intuition about uh what independent + + align:start position:0% +our intuition about uh what independent + + + align:start position:0% +our intuition about uh what independent +is could lead us astray so let me give + + align:start position:0% +is could lead us astray so let me give + + + align:start position:0% +is could lead us astray so let me give +you an example to illustrate + + align:start position:0% +you an example to illustrate + + + align:start position:0% +you an example to illustrate +that okay suppose I toss one + + align:start position:0% +that okay suppose I toss one + + + align:start position:0% +that okay suppose I toss one +tie now consider two different + + align:start position:0% +tie now consider two different + + + align:start position:0% +tie now consider two different +events a is the event that I roll a + + align:start position:0% +events a is the event that I roll a + + + align:start position:0% +events a is the event that I roll a +number less than five and B is the event + + align:start position:0% +number less than five and B is the event + + + align:start position:0% +number less than five and B is the event +that I roll an even number okay are + + align:start position:0% +that I roll an even number okay are + + + align:start position:0% +that I roll an even number okay are +these events + + align:start position:0% +these events + + + align:start position:0% +these events +independent well your intuition + + align:start position:0% +independent well your intuition + + + align:start position:0% +independent well your intuition +might make you first think well how + + align:start position:0% +might make you first think well how + + + align:start position:0% +might make you first think well how +could they be they were rely on a single + + align:start position:0% +could they be they were rely on a single + + + align:start position:0% +could they be they were rely on a single +role of a single die so how could these + + align:start position:0% +role of a single die so how could these + + + align:start position:0% +role of a single die so how could these +two uh events actually be independent + + align:start position:0% +two uh events actually be independent + + + align:start position:0% +two uh events actually be independent +but in fact they are if we use the + + align:start position:0% +but in fact they are if we use the + + + align:start position:0% +but in fact they are if we use the +definition if we check using the + + align:start position:0% +definition if we check using the + + + align:start position:0% +definition if we check using the +definition of independence um we find + + align:start position:0% +definition of independence um we find + + + align:start position:0% +definition of independence um we find +that you know we write down the + + align:start position:0% +that you know we write down the + + + align:start position:0% +that you know we write down the +probability of the first event is equal + + align:start position:0% +probability of the first event is equal + + + align:start position:0% +probability of the first event is equal +to 2/3 the probability of the second + + align:start position:0% +to 2/3 the probability of the second + + + align:start position:0% +to 2/3 the probability of the second +event is equal to 1/2 and the + + align:start position:0% +event is equal to 1/2 and the + + + align:start position:0% +event is equal to 1/2 and the +probability of their + + align:start position:0% +probability of their + + + align:start position:0% +probability of their +intersection um that the intersection + + align:start position:0% +intersection um that the intersection + + + align:start position:0% +intersection um that the intersection +being an even number less than five + + align:start position:0% +being an even number less than five + + + align:start position:0% +being an even number less than five +rolling even number less than five the + + align:start position:0% +rolling even number less than five the + + + align:start position:0% +rolling even number less than five the +probability of that is equal to 1/3 and + + align:start position:0% +probability of that is equal to 1/3 and + + + align:start position:0% +probability of that is equal to 1/3 and +that is the product of the two uh + + align:start position:0% +that is the product of the two uh + + + align:start position:0% +that is the product of the two uh +probabilities of the individual events + + align:start position:0% +probabilities of the individual events + + + align:start position:0% +probabilities of the individual events +so they are it does in fact satisfy the + + align:start position:0% +so they are it does in fact satisfy the + + + align:start position:0% +so they are it does in fact satisfy the +definition of + + align:start position:0% +definition of + + + align:start position:0% +definition of +independence um and I think that this uh + + align:start position:0% +independence um and I think that this uh + + + align:start position:0% +independence um and I think that this uh +example sort of illustrates the way in + + align:start position:0% +example sort of illustrates the way in + + + align:start position:0% +example sort of illustrates the way in +which we we need to be careful about our + + align:start position:0% +which we we need to be careful about our + + + align:start position:0% +which we we need to be careful about our +intuition and in fact refine our + + align:start position:0% +intuition and in fact refine our + + + align:start position:0% +intuition and in fact refine our +intuition based on this so the really + + align:start position:0% +intuition based on this so the really + + + align:start position:0% +intuition based on this so the really +the proper intuition about independent + + align:start position:0% +the proper intuition about independent + + + align:start position:0% +the proper intuition about independent +events is that if I know that one + + align:start position:0% +events is that if I know that one + + + align:start position:0% +events is that if I know that one +occurred it doesn't tell me anything + + align:start position:0% +occurred it doesn't tell me anything + + + align:start position:0% +occurred it doesn't tell me anything +about the probability that the other + + align:start position:0% +about the probability that the other + + + align:start position:0% +about the probability that the other +occurred okay yes so this is basically + + align:start position:0% +occurred okay yes so this is basically + + + align:start position:0% +occurred okay yes so this is basically +an issue of confusing independence with + + align:start position:0% +an issue of confusing independence with + + + align:start position:0% +an issue of confusing independence with +mutuality right uh yes well so you're + + align:start position:0% +mutuality right uh yes well so you're + + + align:start position:0% +mutuality right uh yes well so you're +right that Independence and mutual + + align:start position:0% +right that Independence and mutual + + + align:start position:0% +right that Independence and mutual +exclusivity are not the same um and it + + align:start position:0% +exclusivity are not the same um and it + + + align:start position:0% +exclusivity are not the same um and it +could be that that's the way your + + align:start position:0% +could be that that's the way your + + + align:start position:0% +could be that that's the way your +intuition was going so so yes in that + + align:start position:0% +intuition was going so so yes in that + + + align:start position:0% +intuition was going so so yes in that +sense you're absolutely right um and so + + align:start position:0% +sense you're absolutely right um and so + + + align:start position:0% +sense you're absolutely right um and so +yeah yeah it's important to to draw that + + align:start position:0% +yeah yeah it's important to to draw that + + + align:start position:0% +yeah yeah it's important to to draw that +distinction okay another sort of useful + + align:start position:0% +distinction okay another sort of useful + + + align:start position:0% +distinction okay another sort of useful +thing that we can prove about + + align:start position:0% +thing that we can prove about + + + align:start position:0% +thing that we can prove about +independence is that if we have two + + align:start position:0% +independence is that if we have two + + + align:start position:0% +independence is that if we have two +independent events um then uh A and B + + align:start position:0% +independent events um then uh A and B + + + align:start position:0% +independent events um then uh A and B +then A and B complement are also + + align:start position:0% +then A and B complement are also + + + align:start position:0% +then A and B complement are also +independent okay and uh I've I've listed + + align:start position:0% +independent okay and uh I've I've listed + + + align:start position:0% +independent okay and uh I've I've listed +the proof there in case you want to + + align:start position:0% +the proof there in case you want to + + + align:start position:0% +the proof there in case you want to +convince yourself that that's + + align:start position:0% +convince yourself that that's + + + align:start position:0% +convince yourself that that's +true and furthermore if we have more + + align:start position:0% +true and furthermore if we have more + + + align:start position:0% +true and furthermore if we have more +than two events + + align:start position:0% +than two events + + + align:start position:0% +than two events +um we Define the sort of uh definition + + align:start position:0% +um we Define the sort of uh definition + + + align:start position:0% +um we Define the sort of uh definition +that we use for Independence kind of + + align:start position:0% +that we use for Independence kind of + + + align:start position:0% +that we use for Independence kind of +generalizes in the way you think it + + align:start position:0% +generalizes in the way you think it + + + align:start position:0% +generalizes in the way you think it +would okay so the events are independent + + align:start position:0% +would okay so the events are independent + + + align:start position:0% +would okay so the events are independent +if the probability of their intersection + + align:start position:0% +if the probability of their intersection + + + align:start position:0% +if the probability of their intersection +is equal to the product of their + + align:start position:0% +is equal to the product of their + + + align:start position:0% +is equal to the product of their +probabilities for uh more than two + + align:start position:0% +probabilities for uh more than two + + + align:start position:0% +probabilities for uh more than two +events + + align:start position:0% + + + + align:start position:0% + +okay okay who's + + align:start position:0% +okay okay who's + + + align:start position:0% +okay okay who's +this okay does anyone want to give the + + align:start position:0% +this okay does anyone want to give the + + + align:start position:0% +this okay does anyone want to give the +class a sort of a two two sentence + + align:start position:0% +class a sort of a two two sentence + + + align:start position:0% +class a sort of a two two sentence +skinny on who Steph Curry is for for + + align:start position:0% +skinny on who Steph Curry is for for + + + align:start position:0% +skinny on who Steph Curry is for for +those people who are not NBA fans y oh + + align:start position:0% +those people who are not NBA fans y oh + + + align:start position:0% +those people who are not NBA fans y oh +the best shooter in NBA history the best + + align:start position:0% +the best shooter in NBA history the best + + + align:start position:0% +the best shooter in NBA history the best +shooter in that was that was a less than + + align:start position:0% +shooter in that was that was a less than + + + align:start position:0% +shooter in that was that was a less than +one sentence description the best + + align:start position:0% +one sentence description the best + + + align:start position:0% +one sentence description the best +shooter in NBA and in particular + + align:start position:0% +shooter in NBA and in particular + + + align:start position:0% +shooter in NBA and in particular +three-point shooter right so I mean okay + + align:start position:0% +three-point shooter right so I mean okay + + + align:start position:0% +three-point shooter right so I mean okay +fine fine so anyhow he's having this + + align:start position:0% +fine fine so anyhow he's having this + + + align:start position:0% +fine fine so anyhow he's having this +absolutely phenomenal season and not I + + align:start position:0% +absolutely phenomenal season and not I + + + align:start position:0% +absolutely phenomenal season and not I +mean not only are sort of NBA fans like + + align:start position:0% +mean not only are sort of NBA fans like + + + align:start position:0% +mean not only are sort of NBA fans like +really excited about it but like sort of + + align:start position:0% +really excited about it but like sort of + + + align:start position:0% +really excited about it but like sort of +data Geeks are really excited about it + + align:start position:0% +data Geeks are really excited about it + + + align:start position:0% +data Geeks are really excited about it +too and we'll actually see some uh some + + align:start position:0% +too and we'll actually see some uh some + + + align:start position:0% +too and we'll actually see some uh some +data of Steph uh on Steph Curry's uh + + align:start position:0% +data of Steph uh on Steph Curry's uh + + + align:start position:0% +data of Steph uh on Steph Curry's uh +shooting uh pretty soon in a in a couple + + align:start position:0% +shooting uh pretty soon in a in a couple + + + align:start position:0% +shooting uh pretty soon in a in a couple +of uh lectures and we'll get to play + + align:start position:0% +of uh lectures and we'll get to play + + + align:start position:0% +of uh lectures and we'll get to play +around with it uh but let me just do an + + align:start position:0% +around with it uh but let me just do an + + + align:start position:0% +around with it uh but let me just do an +example um uh sort of uh um I don't know + + align:start position:0% +example um uh sort of uh um I don't know + + + align:start position:0% +example um uh sort of uh um I don't know +inspired by Steph Curry's performance + + align:start position:0% +inspired by Steph Curry's performance + + + align:start position:0% +inspired by Steph Curry's performance +first okay so his I looked up his threo + + align:start position:0% +first okay so his I looked up his threo + + + align:start position:0% +first okay so his I looked up his threo +field goal percentage so for oh I should + + align:start position:0% +field goal percentage so for oh I should + + + align:start position:0% +field goal percentage so for oh I should +maybe I should take a step back if you + + align:start position:0% +maybe I should take a step back if you + + + align:start position:0% +maybe I should take a step back if you +really don't know anything about + + align:start position:0% +really don't know anything about + + + align:start position:0% +really don't know anything about +basketball a three-point shot is one + + align:start position:0% +basketball a three-point shot is one + + + align:start position:0% +basketball a three-point shot is one +taken from um what's how many feet away + + align:start position:0% +taken from um what's how many feet away + + + align:start position:0% +taken from um what's how many feet away +from the basket is 23 23 feet or more + + align:start position:0% +from the basket is 23 23 feet or more + + + align:start position:0% +from the basket is 23 23 feet or more +away from the uh from the the basket + + align:start position:0% +away from the uh from the the basket + + + align:start position:0% +away from the uh from the the basket +okay and these are uh depending on the + + align:start position:0% +okay and these are uh depending on the + + + align:start position:0% +okay and these are uh depending on the +shooter can be pretty low percentage + + align:start position:0% +shooter can be pretty low percentage + + + align:start position:0% +shooter can be pretty low percentage +shots for Steph Curry they're not low + + align:start position:0% +shots for Steph Curry they're not low + + + align:start position:0% +shots for Steph Curry they're not low +percentage shots he makes 44% of them + + align:start position:0% +percentage shots he makes 44% of them + + + align:start position:0% +percentage shots he makes 44% of them +okay for the purposes of this problem + + align:start position:0% +okay for the purposes of this problem + + + align:start position:0% +okay for the purposes of this problem +let's assume that every three-point shot + + align:start position:0% +let's assume that every three-point shot + + + align:start position:0% +let's assume that every three-point shot +he attempts he has the same probability + + align:start position:0% +he attempts he has the same probability + + + align:start position:0% +he attempts he has the same probability +of making it realistically that's not + + align:start position:0% +of making it realistically that's not + + + align:start position:0% +of making it realistically that's not +true but let's assume that for now and + + align:start position:0% +true but let's assume that for now and + + + align:start position:0% +true but let's assume that for now and +let's also assume that all of these + + align:start position:0% +let's also assume that all of these + + + align:start position:0% +let's also assume that all of these +shots are + + align:start position:0% +shots are + + + align:start position:0% +shots are +independent okay so we're ruling out + + align:start position:0% +independent okay so we're ruling out + + + align:start position:0% +independent okay so we're ruling out +things like him being in a slump or him + + align:start position:0% +things like him being in a slump or him + + + align:start position:0% +things like him being in a slump or him +having a hot hand or something like that + + align:start position:0% +having a hot hand or something like that + + + align:start position:0% +having a hot hand or something like that +okay so for the purposes of this problem + + align:start position:0% +okay so for the purposes of this problem + + + align:start position:0% +okay so for the purposes of this problem +we have a guy he makes three-point shots + + align:start position:0% +we have a guy he makes three-point shots + + + align:start position:0% +we have a guy he makes three-point shots +44% of the time he he uh takes them and + + align:start position:0% +44% of the time he he uh takes them and + + + align:start position:0% +44% of the time he he uh takes them and +uh they're independent there's + + align:start position:0% +uh they're independent there's + + + align:start position:0% +uh they're independent there's +Independence cross + + align:start position:0% +Independence cross + + + align:start position:0% +Independence cross +shots what's the probability ility that + + align:start position:0% +shots what's the probability ility that + + + align:start position:0% +shots what's the probability ility that +he misses the next three shots that he + + align:start position:0% +he misses the next three shots that he + + + align:start position:0% +he misses the next three shots that he +takes and then makes the three after + + align:start position:0% +takes and then makes the three after + + + align:start position:0% +takes and then makes the three after +that question would it be 56 cubed time + + align:start position:0% +that question would it be 56 cubed time + + + align:start position:0% +that question would it be 56 cubed time +44 Cub exactly 56 cubed time 44 + + align:start position:0% +44 Cub exactly 56 cubed time 44 + + + align:start position:0% +44 Cub exactly 56 cubed time 44 +cubed and how did we get to that well we + + align:start position:0% +cubed and how did we get to that well we + + + align:start position:0% +cubed and how did we get to that well we +just take these are independent events + + align:start position:0% +just take these are independent events + + + align:start position:0% +just take these are independent events +so to get the probability of the + + align:start position:0% +so to get the probability of the + + + align:start position:0% +so to get the probability of the +intersection between the event that he + + align:start position:0% +intersection between the event that he + + + align:start position:0% +intersection between the event that he +misses misses misses then makes makes + + align:start position:0% +misses misses misses then makes makes + + + align:start position:0% +misses misses misses then makes makes +makes we just take the sum of the + + align:start position:0% +makes we just take the sum of the + + + align:start position:0% +makes we just take the sum of the +probabilities of each of those events + + align:start position:0% +probabilities of each of those events + + + align:start position:0% +probabilities of each of those events +okay so the probability of miss miss + + align:start position:0% +okay so the probability of miss miss + + + align:start position:0% +okay so the probability of miss miss +miss uh times or yeah the prob the the + + align:start position:0% +miss uh times or yeah the prob the the + + + align:start position:0% +miss uh times or yeah the prob the the +the product of all those probabilities + + align:start position:0% +the product of all those probabilities + + + align:start position:0% +the product of all those probabilities +is equal to 056 cubed * 044 cubed okay + + align:start position:0% +is equal to 056 cubed * 044 cubed okay + + + align:start position:0% +is equal to 056 cubed * 044 cubed okay +or + + align:start position:0% +or + + + align:start position:0% +or +015 now keep in mind that the order that + + align:start position:0% +015 now keep in mind that the order that + + + align:start position:0% +015 now keep in mind that the order that +I that I had in this particular problem + + align:start position:0% +I that I had in this particular problem + + + align:start position:0% +I that I had in this particular problem +doesn't matter I could have asked you + + align:start position:0% +doesn't matter I could have asked you + + + align:start position:0% +doesn't matter I could have asked you +what's the probability of any particular + + align:start position:0% +what's the probability of any particular + + + align:start position:0% +what's the probability of any particular +sequence of three misses and three shots + + align:start position:0% +sequence of three misses and three shots + + + align:start position:0% +sequence of three misses and three shots +made right and you your answer would + + align:start position:0% +made right and you your answer would + + + align:start position:0% +made right and you your answer would +have been exactly the + + align:start position:0% + + + + align:start position:0% + +same so what is the probability that he + + align:start position:0% +same so what is the probability that he + + + align:start position:0% +same so what is the probability that he +misses three and makes three of the next + + align:start position:0% +misses three and makes three of the next + + + align:start position:0% +misses three and makes three of the next +six shots he + + align:start position:0% +six shots he + + + align:start position:0% +six shots he +takes so how do we think about this so + + align:start position:0% +takes so how do we think about this so + + + align:start position:0% +takes so how do we think about this so +now I'm not asking about the probability + + align:start position:0% +now I'm not asking about the probability + + + align:start position:0% +now I'm not asking about the probability +of any particular sequence of three + + align:start position:0% +of any particular sequence of three + + + align:start position:0% +of any particular sequence of three +misses and three uh three completed + + align:start position:0% +misses and three uh three completed + + + align:start position:0% +misses and three uh three completed +shots but just that there are three + + align:start position:0% +shots but just that there are three + + + align:start position:0% +shots but just that there are three +misses and three completed shots have + + align:start position:0% +misses and three completed shots have + + + align:start position:0% +misses and three completed shots have +combinations + + align:start position:0% +combinations + + + align:start position:0% +combinations +those exactly so we know that we know + + align:start position:0% +those exactly so we know that we know + + + align:start position:0% +those exactly so we know that we know +the probability of each particular + + align:start position:0% +the probability of each particular + + + align:start position:0% +the probability of each particular +sequence and so now what we have to do + + align:start position:0% +sequence and so now what we have to do + + + align:start position:0% +sequence and so now what we have to do +is we have to add we have to count up + + align:start position:0% +is we have to add we have to count up + + + align:start position:0% +is we have to add we have to count up +the number of such sequences there are + + align:start position:0% +the number of such sequences there are + + + align:start position:0% +the number of such sequences there are +how do we what's the what's the number + + align:start position:0% +how do we what's the what's the number + + + align:start position:0% +how do we what's the what's the number +of such sequences that there + + align:start position:0% +of such sequences that there + + + align:start position:0% +of such sequences that there +are six choose three exactly + + align:start position:0% +are six choose three exactly + + + align:start position:0% +are six choose three exactly +so there we go why why are there six + + align:start position:0% +so there we go why why are there six + + + align:start position:0% +so there we go why why are there six +choose three sequences of misses and + + align:start position:0% +choose three sequences of misses and + + + align:start position:0% +choose three sequences of misses and +makes in the next six shots he + + align:start position:0% + + + + align:start position:0% + +takes does anyone want to yep well six + + align:start position:0% +takes does anyone want to yep well six + + + align:start position:0% +takes does anyone want to yep well six +shots to take and we want to take those + + align:start position:0% +shots to take and we want to take those + + + align:start position:0% +shots to take and we want to take those +six and choose three in which he will + + align:start position:0% +six and choose three in which he will + + + align:start position:0% +six and choose three in which he will +say Bas that's right okay okay and so if + + align:start position:0% +say Bas that's right okay okay and so if + + + align:start position:0% +say Bas that's right okay okay and so if +we multiply six choose three by the + + align:start position:0% +we multiply six choose three by the + + + align:start position:0% +we multiply six choose three by the +probability of any one such sequence we + + align:start position:0% +probability of any one such sequence we + + + align:start position:0% +probability of any one such sequence we +get a 30 so that's the probability of + + align:start position:0% +get a 30 so that's the probability of + + + align:start position:0% +get a 30 so that's the probability of +any sequence or sorry of that's the + + align:start position:0% +any sequence or sorry of that's the + + + align:start position:0% +any sequence or sorry of that's the +probability he makes the next he makes + + align:start position:0% +probability he makes the next he makes + + + align:start position:0% +probability he makes the next he makes +three of the next six shots he takes y + + align:start position:0% +three of the next six shots he takes y + + + align:start position:0% +three of the next six shots he takes y +if there were more than two options or + + align:start position:0% +if there were more than two options or + + + align:start position:0% +if there were more than two options or +two outcomes that framework for right it + + align:start position:0% +two outcomes that framework for right it + + + align:start position:0% +two outcomes that framework for right it +gets more complicated yes that's + + align:start position:0% + + + + align:start position:0% + +right okay final question what is the + + align:start position:0% +right okay final question what is the + + + align:start position:0% +right okay final question what is the +probability that he makes at least one + + align:start position:0% +probability that he makes at least one + + + align:start position:0% +probability that he makes at least one +shot in the next six that he takes + + align:start position:0% + + + + align:start position:0% + +probability yes one minus the + + align:start position:0% +probability yes one minus the + + + align:start position:0% +probability yes one minus the +probability that he misses all of them + + align:start position:0% +probability that he misses all of them + + + align:start position:0% +probability that he misses all of them +so + + align:start position:0% +so + + + align:start position:0% +so +um as I said earlier in the lecture um + + align:start position:0% +um as I said earlier in the lecture um + + + align:start position:0% +um as I said earlier in the lecture um +you we could calculate this probability + + align:start position:0% +you we could calculate this probability + + + align:start position:0% +you we could calculate this probability +by calculating the probability he makes + + align:start position:0% +by calculating the probability he makes + + + align:start position:0% +by calculating the probability he makes +one shot calculating the probability he + + align:start position:0% +one shot calculating the probability he + + + align:start position:0% +one shot calculating the probability he +makes two shots calculating the + + align:start position:0% +makes two shots calculating the + + + align:start position:0% +makes two shots calculating the +probability he makes three shots and + + align:start position:0% +probability he makes three shots and + + + align:start position:0% +probability he makes three shots and +adding those all together that's a + + align:start position:0% +adding those all together that's a + + + align:start position:0% +adding those all together that's a +perfectly fine way to do it there's an + + align:start position:0% +perfectly fine way to do it there's an + + + align:start position:0% +perfectly fine way to do it there's an +easier way and that's using the the one + + align:start position:0% +easier way and that's using the the one + + + align:start position:0% +easier way and that's using the the one +of the uh sort of facts about + + align:start position:0% +of the uh sort of facts about + + + align:start position:0% +of the uh sort of facts about +probability that I had up earlier and + + align:start position:0% +probability that I had up earlier and + + + align:start position:0% +probability that I had up earlier and +all we have to do is calculate the + + align:start position:0% +all we have to do is calculate the + + + align:start position:0% +all we have to do is calculate the +probability he misses all six of them + + align:start position:0% +probability he misses all six of them + + + align:start position:0% +probability he misses all six of them +which is 0.56 raised to the 6 and + + align:start position:0% +which is 0.56 raised to the 6 and + + + align:start position:0% +which is 0.56 raised to the 6 and +subtract that from one and we get the + + align:start position:0% +subtract that from one and we get the + + + align:start position:0% +subtract that from one and we get the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +okay yes question quick question so + + align:start position:0% +okay yes question quick question so + + + align:start position:0% +okay yes question quick question so +wouldn't like for example let's say he + + align:start position:0% +wouldn't like for example let's say he + + + align:start position:0% +wouldn't like for example let's say he +starts on his six shot U kind of like + + align:start position:0% +starts on his six shot U kind of like + + + align:start position:0% +starts on his six shot U kind of like +dir and he misses the first one would + + align:start position:0% +dir and he misses the first one would + + + align:start position:0% +dir and he misses the first one would +that change his ratings upon like How + + align:start position:0% +that change his ratings upon like How + + + align:start position:0% +that change his ratings upon like How +likely he is to make a three-pointer on + + align:start position:0% +likely he is to make a three-pointer on + + + align:start position:0% +likely he is to make a three-pointer on +Bo well we're sort of I if I understand + + align:start position:0% +Bo well we're sort of I if I understand + + + align:start position:0% +Bo well we're sort of I if I understand +your question correctly we're sort of + + align:start position:0% +your question correctly we're sort of + + + align:start position:0% +your question correctly we're sort of +ruling that out in this question so what + + align:start position:0% +ruling that out in this question so what + + + align:start position:0% +ruling that out in this question so what +I said is that we're going to assume + + align:start position:0% +I said is that we're going to assume + + + align:start position:0% +I said is that we're going to assume +that the probability for any particular + + align:start position:0% +that the probability for any particular + + + align:start position:0% +that the probability for any particular +shot is + + align:start position:0% +shot is + + + align:start position:0% +shot is +044 okay but in you have to upate real + + align:start position:0% +044 okay but in you have to upate real + + + align:start position:0% +044 okay but in you have to upate real +time right well and in particular in + + align:start position:0% +time right well and in particular in + + + align:start position:0% +time right well and in particular in +real life he's going to take higher and + + align:start position:0% +real life he's going to take higher and + + + align:start position:0% +real life he's going to take higher and +lower percentage three-point shots and + + align:start position:0% +lower percentage three-point shots and + + + align:start position:0% +lower percentage three-point shots and +you know if the if the the shot clock is + + align:start position:0% +you know if the if the the shot clock is + + + align:start position:0% +you know if the if the the shot clock is +about to expire he's uh you know likely + + align:start position:0% +about to expire he's uh you know likely + + + align:start position:0% +about to expire he's uh you know likely +to take a lower percentage shot just + + align:start position:0% +to take a lower percentage shot just + + + align:start position:0% +to take a lower percentage shot just +because that's the last chance he's + + align:start position:0% +because that's the last chance he's + + + align:start position:0% +because that's the last chance he's +going to get and so forth so yeah we're + + align:start position:0% +going to get and so forth so yeah we're + + + align:start position:0% +going to get and so forth so yeah we're +kind of abstracting away from that in + + align:start position:0% +kind of abstracting away from that in + + + align:start position:0% +kind of abstracting away from that in +this particular problem but yeah you're + + align:start position:0% +this particular problem but yeah you're + + + align:start position:0% +this particular problem but yeah you're +right + + align:start position:0% +right + + + align:start position:0% +right +okay okay now uh this example is one we + + align:start position:0% +okay okay now uh this example is one we + + + align:start position:0% +okay okay now uh this example is one we +will refer back to uh later on in the + + align:start position:0% +will refer back to uh later on in the + + + align:start position:0% +will refer back to uh later on in the +semester as the basis for a special + + align:start position:0% +semester as the basis for a special + + + align:start position:0% +semester as the basis for a special +distribution the binomial + + align:start position:0% + + + + align:start position:0% + +distribution okay so now on to + + align:start position:0% +distribution okay so now on to + + + align:start position:0% +distribution okay so now on to +uh conditional probability so recall + + align:start position:0% +uh conditional probability so recall + + + align:start position:0% +uh conditional probability so recall +that uh just a minute ago when we were + + align:start position:0% +that uh just a minute ago when we were + + + align:start position:0% +that uh just a minute ago when we were +talking about independence uh knowing + + align:start position:0% +talking about independence uh knowing + + + align:start position:0% +talking about independence uh knowing +that two events are independent means + + align:start position:0% +that two events are independent means + + + align:start position:0% +that two events are independent means +that the occurrence or non-occurrence of + + align:start position:0% +that the occurrence or non-occurrence of + + + align:start position:0% +that the occurrence or non-occurrence of +one event doesn't tell you anything + + align:start position:0% +one event doesn't tell you anything + + + align:start position:0% +one event doesn't tell you anything +about the other okay + + align:start position:0% +about the other okay + + + align:start position:0% +about the other okay +so if you know if I know that a uh + + align:start position:0% +so if you know if I know that a uh + + + align:start position:0% +so if you know if I know that a uh +occurred and a and b are independent + + align:start position:0% +occurred and a and b are independent + + + align:start position:0% +occurred and a and b are independent +then the probability that b is going to + + align:start position:0% +then the probability that b is going to + + + align:start position:0% +then the probability that b is going to +occur or did occur uh doesn't change + + align:start position:0% +occur or did occur uh doesn't change + + + align:start position:0% +occur or did occur uh doesn't change +okay but what if we have two events + + align:start position:0% +okay but what if we have two events + + + align:start position:0% +okay but what if we have two events +where the occurrence of one event + + align:start position:0% +where the occurrence of one event + + + align:start position:0% +where the occurrence of one event +actually tells us something relevant + + align:start position:0% +actually tells us something relevant + + + align:start position:0% +actually tells us something relevant +about the probability of another event + + align:start position:0% +about the probability of another event + + + align:start position:0% +about the probability of another event +okay how can we alter the probability of + + align:start position:0% +okay how can we alter the probability of + + + align:start position:0% +okay how can we alter the probability of +the second event appropriately how can + + align:start position:0% +the second event appropriately how can + + + align:start position:0% +the second event appropriately how can +we in some sense update what uh using + + align:start position:0% +we in some sense update what uh using + + + align:start position:0% +we in some sense update what uh using +the information uh from the first event + + align:start position:0% +the information uh from the first event + + + align:start position:0% +the information uh from the first event +how can we sort of update the + + align:start position:0% +how can we sort of update the + + + align:start position:0% +how can we sort of update the +probability of the second event well we + + align:start position:0% +probability of the second event well we + + + align:start position:0% +probability of the second event well we +use this uh doing by using something + + align:start position:0% +use this uh doing by using something + + + align:start position:0% +use this uh doing by using something +called conditional probability so the + + align:start position:0% +called conditional probability so the + + + align:start position:0% +called conditional probability so the +probability of a I on B which we denote + + align:start position:0% +probability of a I on B which we denote + + + align:start position:0% +probability of a I on B which we denote +this way probability of a with a + + align:start position:0% +this way probability of a with a + + + align:start position:0% +this way probability of a with a +vertical line B is just the probability + + align:start position:0% +vertical line B is just the probability + + + align:start position:0% +vertical line B is just the probability +of the intersection of A and B divided + + align:start position:0% +of the intersection of A and B divided + + + align:start position:0% +of the intersection of A and B divided +by the probability of B okay now this + + align:start position:0% +by the probability of B okay now this + + + align:start position:0% +by the probability of B okay now this +definition only holds if the probability + + align:start position:0% +definition only holds if the probability + + + align:start position:0% +definition only holds if the probability +of B is greater than zero we can't + + align:start position:0% +of B is greater than zero we can't + + + align:start position:0% +of B is greater than zero we can't +condition on an event that has zero + + align:start position:0% +condition on an event that has zero + + + align:start position:0% +condition on an event that has zero +probability so doesn't we don't even + + align:start position:0% +probability so doesn't we don't even + + + align:start position:0% +probability so doesn't we don't even +Define it if uh the probability of B is + + align:start position:0% +Define it if uh the probability of B is + + + align:start position:0% +Define it if uh the probability of B is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero Okay so what I let me see if I yeah + + align:start position:0% +zero Okay so what I let me see if I yeah + + + align:start position:0% +zero Okay so what I let me see if I yeah +so the way I think about conditional + + align:start position:0% +so the way I think about conditional + + + align:start position:0% +so the way I think about conditional +probability and I I hope this is helpful + + align:start position:0% +probability and I I hope this is helpful + + + align:start position:0% +probability and I I hope this is helpful +is I think about the numerator of uh the + + align:start position:0% +is I think about the numerator of uh the + + + align:start position:0% +is I think about the numerator of uh the +uh the conditional probability as + + align:start position:0% +uh the conditional probability as + + + align:start position:0% +uh the conditional probability as +essentially redefining both the event or + + align:start position:0% +essentially redefining both the event or + + + align:start position:0% +essentially redefining both the event or +sorry redefining the event as only the + + align:start position:0% +sorry redefining the event as only the + + + align:start position:0% +sorry redefining the event as only the +part of the event that's now relevant + + align:start position:0% +part of the event that's now relevant + + + align:start position:0% +part of the event that's now relevant +given that we know B occurred and then I + + align:start position:0% +given that we know B occurred and then I + + + align:start position:0% +given that we know B occurred and then I +think about the the denominator as + + align:start position:0% +think about the the denominator as + + + align:start position:0% +think about the the denominator as +redefining the sample space uh as only + + align:start position:0% +redefining the sample space uh as only + + + align:start position:0% +redefining the sample space uh as only +considering the part of the sample space + + align:start position:0% +considering the part of the sample space + + + align:start position:0% +considering the part of the sample space +that's now relevant given that we know + + align:start position:0% +that's now relevant given that we know + + + align:start position:0% +that's now relevant given that we know +be aurtain so it might actually be + + align:start position:0% +be aurtain so it might actually be + + + align:start position:0% +be aurtain so it might actually be +useful for me to + + align:start position:0% +useful for me to + + + align:start position:0% +useful for me to +draw a VIN diagram to illustrate + + align:start position:0% + + + + align:start position:0% + +this okay so let's say we have a sample + + align:start position:0% +this okay so let's say we have a sample + + + align:start position:0% +this okay so let's say we have a sample +space s we have an event a and another + + align:start position:0% +space s we have an event a and another + + + align:start position:0% +space s we have an event a and another +event B + + align:start position:0% +event B + + + align:start position:0% +event B +and we know that b occurred okay so + + align:start position:0% +and we know that b occurred okay so + + + align:start position:0% +and we know that b occurred okay so +basically we're going to be conditioning + + align:start position:0% +basically we're going to be conditioning + + + align:start position:0% +basically we're going to be conditioning +on B then the only part of a that's + + align:start position:0% +on B then the only part of a that's + + + align:start position:0% +on B then the only part of a that's +relevant is this + + align:start position:0% + + + + align:start position:0% + +part right the intersection actually I + + align:start position:0% +part right the intersection actually I + + + align:start position:0% +part right the intersection actually I +could have drawn that colored that in + + align:start position:0% +could have drawn that colored that in + + + align:start position:0% +could have drawn that colored that in +better okay that's the only part of a + + align:start position:0% +better okay that's the only part of a + + + align:start position:0% +better okay that's the only part of a +that's relevant the only part of the + + align:start position:0% +that's relevant the only part of the + + + align:start position:0% +that's relevant the only part of the +sample space that's relevant we know + + align:start position:0% +sample space that's relevant we know + + + align:start position:0% +sample space that's relevant we know +that b + + align:start position:0% +that b + + + align:start position:0% +that b +occurred the only part of the sample + + align:start position:0% +occurred the only part of the sample + + + align:start position:0% +occurred the only part of the sample +space that's relevant is this + + align:start position:0% + + + + align:start position:0% + +okay so essentially the conditional uh + + align:start position:0% +okay so essentially the conditional uh + + + align:start position:0% +okay so essentially the conditional uh +probability formula is basically + + align:start position:0% +probability formula is basically + + + align:start position:0% +probability formula is basically +redefining both the numerator and the + + align:start position:0% +redefining both the numerator and the + + + align:start position:0% +redefining both the numerator and the +denominator + + align:start position:0% +denominator + + + align:start position:0% +denominator +okay based on this new information we + + align:start position:0% + + + + align:start position:0% + +have so as you might suspect there is a + + align:start position:0% +have so as you might suspect there is a + + + align:start position:0% +have so as you might suspect there is a +relationship between uh Independence and + + align:start position:0% +relationship between uh Independence and + + + align:start position:0% +relationship between uh Independence and +conditional + + align:start position:0% +conditional + + + align:start position:0% +conditional +probability so suppose we have two + + align:start position:0% +probability so suppose we have two + + + align:start position:0% +probability so suppose we have two +events a and B and they're + + align:start position:0% +events a and B and they're + + + align:start position:0% +events a and B and they're +independent and uh we have to assume + + align:start position:0% +independent and uh we have to assume + + + align:start position:0% +independent and uh we have to assume +that the probability of B is greater + + align:start position:0% +that the probability of B is greater + + + align:start position:0% +that the probability of B is greater +than zero so we can talk about + + align:start position:0% +than zero so we can talk about + + + align:start position:0% +than zero so we can talk about +conditional probability okay then the + + align:start position:0% +conditional probability okay then the + + + align:start position:0% +conditional probability okay then the +probability of a conditional on + + align:start position:0% +probability of a conditional on + + + align:start position:0% +probability of a conditional on +B is just equal to um by definition the + + align:start position:0% +B is just equal to um by definition the + + + align:start position:0% +B is just equal to um by definition the +probability of the the intersection + + align:start position:0% +probability of the the intersection + + + align:start position:0% +probability of the the intersection +divided by the probability of B but + + align:start position:0% +divided by the probability of B but + + + align:start position:0% +divided by the probability of B but +since they're independent that's equal + + align:start position:0% +since they're independent that's equal + + + align:start position:0% +since they're independent that's equal +to the the probability of the + + align:start position:0% +to the the probability of the + + + align:start position:0% +to the the probability of the +intersection is equal to the product of + + align:start position:0% +intersection is equal to the product of + + + align:start position:0% +intersection is equal to the product of +the probabilities so it's probability of + + align:start position:0% +the probabilities so it's probability of + + + align:start position:0% +the probabilities so it's probability of +a times probability of B over + + align:start position:0% +a times probability of B over + + + align:start position:0% +a times probability of B over +probability of B the probabilities of B + + align:start position:0% +probability of B the probabilities of B + + + align:start position:0% +probability of B the probabilities of B +cancel and we get probability of a okay + + align:start position:0% +cancel and we get probability of a okay + + + align:start position:0% +cancel and we get probability of a okay +so this is exactly what we would have + + align:start position:0% +so this is exactly what we would have + + + align:start position:0% +so this is exactly what we would have +expected happening given our refined + + align:start position:0% +expected happening given our refined + + + align:start position:0% +expected happening given our refined +intuition about what Independence means + + align:start position:0% +intuition about what Independence means + + + align:start position:0% +intuition about what Independence means +Independence means B occurs it doesn't + + align:start position:0% +Independence means B occurs it doesn't + + + align:start position:0% +Independence means B occurs it doesn't +tell us anything about uh the + + align:start position:0% +tell us anything about uh the + + + align:start position:0% +tell us anything about uh the +probability of a and here we have the + + align:start position:0% +probability of a and here we have the + + + align:start position:0% +probability of a and here we have the +probability if a and b are independent + + align:start position:0% +probability if a and b are independent + + + align:start position:0% +probability if a and b are independent +the probability of a conditional on B is + + align:start position:0% +the probability of a conditional on B is + + + align:start position:0% +the probability of a conditional on B is +equal to the probability of a + + align:start position:0% +equal to the probability of a + + + align:start position:0% +equal to the probability of a +okay and note that this uh implication + + align:start position:0% +okay and note that this uh implication + + + align:start position:0% +okay and note that this uh implication +goes both ways if + + align:start position:0% +goes both ways if + + + align:start position:0% +goes both ways if +probability of a uh conditional on B is + + align:start position:0% +probability of a uh conditional on B is + + + align:start position:0% +probability of a uh conditional on B is +equal to probability of a then that also + + align:start position:0% +equal to probability of a then that also + + + align:start position:0% +equal to probability of a then that also +implies Independence + + align:start position:0% + + + + align:start position:0% + +okay okay so I I go back to the the um + + align:start position:0% +okay okay so I I go back to the the um + + + align:start position:0% +okay okay so I I go back to the the um +to the American political system once + + align:start position:0% +to the American political system once + + + align:start position:0% +to the American political system once +again for a you + + align:start position:0% +again for a you + + + align:start position:0% +again for a you +know another example it's such fertile + + align:start position:0% +know another example it's such fertile + + + align:start position:0% +know another example it's such fertile +ground these days um so uh one sort of + + align:start position:0% +ground these days um so uh one sort of + + + align:start position:0% +ground these days um so uh one sort of +interesting part you know sort of uh as + + align:start position:0% +interesting part you know sort of uh as + + + align:start position:0% +interesting part you know sort of uh as +as an observer of the American political + + align:start position:0% +as an observer of the American political + + + align:start position:0% +as an observer of the American political +an observer and a participant in the + + align:start position:0% +an observer and a participant in the + + + align:start position:0% +an observer and a participant in the +American political system I was think + + align:start position:0% +American political system I was think + + + align:start position:0% +American political system I was think +it's very interesting um that there's + + align:start position:0% +it's very interesting um that there's + + + align:start position:0% +it's very interesting um that there's +this you know sort of tension between um + + align:start position:0% +this you know sort of tension between um + + + align:start position:0% +this you know sort of tension between um +the the primaries and the general + + align:start position:0% +the the primaries and the general + + + align:start position:0% +the the primaries and the general +election you know that there's a you + + align:start position:0% +election you know that there's a you + + + align:start position:0% +election you know that there's a you +it's interesting to watch how the + + align:start position:0% +it's interesting to watch how the + + + align:start position:0% +it's interesting to watch how the +candidates are always trying to position + + align:start position:0% +candidates are always trying to position + + + align:start position:0% +candidates are always trying to position +themselves to appeal to the party + + align:start position:0% +themselves to appeal to the party + + + align:start position:0% +themselves to appeal to the party +faithful in the um in the primaries but + + align:start position:0% +faithful in the um in the primaries but + + + align:start position:0% +faithful in the um in the primaries but +then you know when it comes to the + + align:start position:0% +then you know when it comes to the + + + align:start position:0% +then you know when it comes to the +general election they have to somehow + + align:start position:0% +general election they have to somehow + + + align:start position:0% +general election they have to somehow +convince the electorate um that you know + + align:start position:0% +convince the electorate um that you know + + + align:start position:0% +convince the electorate um that you know +they're sort of more Centrist or + + align:start position:0% +they're sort of more Centrist or + + + align:start position:0% +they're sort of more Centrist or +something like that and so there's this + + align:start position:0% +something like that and so there's this + + + align:start position:0% +something like that and so there's this +sort of interesting tension uh that's + + align:start position:0% +sort of interesting tension uh that's + + + align:start position:0% +sort of interesting tension uh that's +always I think uh fun to watch or + + align:start position:0% +always I think uh fun to watch or + + + align:start position:0% +always I think uh fun to watch or +interesting to watch at least Okay so uh + + align:start position:0% +interesting to watch at least Okay so uh + + + align:start position:0% +interesting to watch at least Okay so uh +let me um use that tension to sort of uh + + align:start position:0% +let me um use that tension to sort of uh + + + align:start position:0% +let me um use that tension to sort of uh +uh uh inspire a an example on + + align:start position:0% +uh uh inspire a an example on + + + align:start position:0% +uh uh inspire a an example on +conditional probability okay so let's + + align:start position:0% +conditional probability okay so let's + + + align:start position:0% +conditional probability okay so let's +suppose that we have uh four candidates + + align:start position:0% +suppose that we have uh four candidates + + + align:start position:0% +suppose that we have uh four candidates +with the following probabilities of + + align:start position:0% +with the following probabilities of + + + align:start position:0% +with the following probabilities of +winning the nomination so we have the + + align:start position:0% +winning the nomination so we have the + + + align:start position:0% +winning the nomination so we have the +probability of event A1 which is that uh + + align:start position:0% +probability of event A1 which is that uh + + + align:start position:0% +probability of event A1 which is that uh +Donald Trump wins the nomination is + + align:start position:0% +Donald Trump wins the nomination is + + + align:start position:0% +Donald Trump wins the nomination is +04 um the probability of event A2 which + + align:start position:0% +04 um the probability of event A2 which + + + align:start position:0% +04 um the probability of event A2 which +is uh a cruise winning is 3 and so forth + + align:start position:0% + + + + align:start position:0% + +okay and then let's suppose that + + align:start position:0% +okay and then let's suppose that + + + align:start position:0% +okay and then let's suppose that +conditional on winning the nomination + + align:start position:0% +conditional on winning the nomination + + + align:start position:0% +conditional on winning the nomination +these candidates have the following + + align:start position:0% +these candidates have the following + + + align:start position:0% +these candidates have the following +probabilities of winning the general + + align:start position:0% +probabilities of winning the general + + + align:start position:0% +probabilities of winning the general +election so Donald Trump might have the + + align:start position:0% +election so Donald Trump might have the + + + align:start position:0% +election so Donald Trump might have the +highest probability of winning the + + align:start position:0% +highest probability of winning the + + + align:start position:0% +highest probability of winning the +Republican nomination but he doesn't + + align:start position:0% +Republican nomination but he doesn't + + + align:start position:0% +Republican nomination but he doesn't +have a particularly high probability of + + align:start position:0% +have a particularly high probability of + + + align:start position:0% +have a particularly high probability of +winning the general election conditional + + align:start position:0% +winning the general election conditional + + + align:start position:0% +winning the general election conditional +on winning uh the the nomination okay + + align:start position:0% +on winning uh the the nomination okay + + + align:start position:0% +on winning uh the the nomination okay +and uh maybe perhaps by the way I've + + align:start position:0% +and uh maybe perhaps by the way I've + + + align:start position:0% +and uh maybe perhaps by the way I've +made up these numbers I didn't get these + + align:start position:0% +made up these numbers I didn't get these + + + align:start position:0% +made up these numbers I didn't get these +numbers anywhere but um I don't know + + align:start position:0% +numbers anywhere but um I don't know + + + align:start position:0% +numbers anywhere but um I don't know +they seem at least somewhat plausible to + + align:start position:0% +they seem at least somewhat plausible to + + + align:start position:0% +they seem at least somewhat plausible to +me um and perhaps Marco Rubio among this + + align:start position:0% +me um and perhaps Marco Rubio among this + + + align:start position:0% +me um and perhaps Marco Rubio among this +group has the highest probability of + + align:start position:0% +group has the highest probability of + + + align:start position:0% +group has the highest probability of +winning the general election conditional + + align:start position:0% +winning the general election conditional + + + align:start position:0% +winning the general election conditional +on winning the Republican nomination + + align:start position:0% +on winning the Republican nomination + + + align:start position:0% +on winning the Republican nomination +okay so I gave him A6 by the way I get + + align:start position:0% +okay so I gave him A6 by the way I get + + + align:start position:0% +okay so I gave him A6 by the way I get +this number of are interested in from + + align:start position:0% +this number of are interested in from + + + align:start position:0% +this number of are interested in from +theing Market yes in fact Esther is + + align:start position:0% +theing Market yes in fact Esther is + + + align:start position:0% +theing Market yes in fact Esther is +absolutely right I could have gone I + + align:start position:0% +absolutely right I could have gone I + + + align:start position:0% +absolutely right I could have gone I +could have gone to the sort of political + + align:start position:0% +could have gone to the sort of political + + + align:start position:0% +could have gone to the sort of political +betting markets and and a and gotten + + align:start position:0% +betting markets and and a and gotten + + + align:start position:0% +betting markets and and a and gotten +actual number so yeah that is + + align:start position:0% + + + + align:start position:0% + +correct okay so this is sort of what I + + align:start position:0% +correct okay so this is sort of what I + + + align:start position:0% +correct okay so this is sort of what I +was talking about uh the tension is + + align:start position:0% +was talking about uh the tension is + + + align:start position:0% +was talking about uh the tension is +embodying the fact that the candidates + + align:start position:0% +embodying the fact that the candidates + + + align:start position:0% +embodying the fact that the candidates +with the higher probability of winning + + align:start position:0% +with the higher probability of winning + + + align:start position:0% +with the higher probability of winning +the nomination might not have the higher + + align:start position:0% +the nomination might not have the higher + + + align:start position:0% +the nomination might not have the higher +probability of winning the general + + align:start position:0% +probability of winning the general + + + align:start position:0% +probability of winning the general +election okay so how can we compute the + + align:start position:0% +election okay so how can we compute the + + + align:start position:0% +election okay so how can we compute the +probability of Republican win in the + + align:start position:0% +probability of Republican win in the + + + align:start position:0% +probability of Republican win in the +general election so we've got all this + + align:start position:0% +general election so we've got all this + + + align:start position:0% +general election so we've got all this +information and from this information we + + align:start position:0% +information and from this information we + + + align:start position:0% +information and from this information we +should be able to compute the + + align:start position:0% +should be able to compute the + + + align:start position:0% +should be able to compute the +probability of a republican win in the + + align:start position:0% +probability of a republican win in the + + + align:start position:0% +probability of a republican win in the +general election and in order to do that + + align:start position:0% +general election and in order to do that + + + align:start position:0% +general election and in order to do that +I'm going to do a little side + + align:start position:0% +I'm going to do a little side + + + align:start position:0% +I'm going to do a little side +calculation okay + + align:start position:0% +calculation okay + + + align:start position:0% +calculation okay +so uh let me first start by saying the + + align:start position:0% +so uh let me first start by saying the + + + align:start position:0% +so uh let me first start by saying the +probability of a republican win is just + + align:start position:0% +probability of a republican win is just + + + align:start position:0% +probability of a republican win is just +equal to the probability of the + + align:start position:0% +equal to the probability of the + + + align:start position:0% +equal to the probability of the +intersection between a a republican win + + align:start position:0% +intersection between a a republican win + + + align:start position:0% +intersection between a a republican win +and the sample space okay that's kind of + + align:start position:0% +and the sample space okay that's kind of + + + align:start position:0% +and the sample space okay that's kind of +a almost a a a topology but it's it's + + align:start position:0% +a almost a a a topology but it's it's + + + align:start position:0% +a almost a a a topology but it's it's +going to be helpful for me in the in the + + align:start position:0% +going to be helpful for me in the in the + + + align:start position:0% +going to be helpful for me in the in the +uh calculation + + align:start position:0% +uh calculation + + + align:start position:0% +uh calculation +okay and then I can write the sample + + align:start position:0% +okay and then I can write the sample + + + align:start position:0% +okay and then I can write the sample +space as the union between these four + + align:start position:0% +space as the union between these four + + + align:start position:0% +space as the union between these four +events A1 through A4 and why is that + + align:start position:0% +events A1 through A4 and why is that + + + align:start position:0% +events A1 through A4 and why is that +because A1 through A4 are mutually + + align:start position:0% +because A1 through A4 are mutually + + + align:start position:0% +because A1 through A4 are mutually +exclusive and exhaustive events and + + align:start position:0% +exclusive and exhaustive events and + + + align:start position:0% +exclusive and exhaustive events and +therefore form a a partition okay so if + + align:start position:0% +therefore form a a partition okay so if + + + align:start position:0% +therefore form a a partition okay so if +we the union of all of them is equal to + + align:start position:0% +we the union of all of them is equal to + + + align:start position:0% +we the union of all of them is equal to +the sample space + + align:start position:0% +the sample space + + + align:start position:0% +the sample space +okay so then I write this as the + + align:start position:0% +okay so then I write this as the + + + align:start position:0% +okay so then I write this as the +probability of w + + align:start position:0% +probability of w + + + align:start position:0% +probability of w +um uh intersected with uh A1 Union A2 so + + align:start position:0% +um uh intersected with uh A1 Union A2 so + + + align:start position:0% +um uh intersected with uh A1 Union A2 so +forth okay then um I can I can write + + align:start position:0% +forth okay then um I can I can write + + + align:start position:0% +forth okay then um I can I can write +this I can distribute this the W out uh + + align:start position:0% +this I can distribute this the W out uh + + + align:start position:0% +this I can distribute this the W out uh +and write it as the probability of w + + align:start position:0% +and write it as the probability of w + + + align:start position:0% +and write it as the probability of w +intersected with A1 Union W intersected + + align:start position:0% +intersected with A1 Union W intersected + + + align:start position:0% +intersected with A1 Union W intersected +with A2 so forth okay and since the a1s + + align:start position:0% +with A2 so forth okay and since the a1s + + + align:start position:0% +with A2 so forth okay and since the a1s +are mutually exclusive the intersection + + align:start position:0% +are mutually exclusive the intersection + + + align:start position:0% +are mutually exclusive the intersection +of the a1s with anything is going to be + + align:start position:0% +of the a1s with anything is going to be + + + align:start position:0% +of the a1s with anything is going to be +those that's going to be a mutual + + align:start position:0% +those that's going to be a mutual + + + align:start position:0% +those that's going to be a mutual +exclusive set so I can write this as the + + align:start position:0% +exclusive set so I can write this as the + + + align:start position:0% +exclusive set so I can write this as the +sum of the + + align:start position:0% + + + + align:start position:0% + +probabilities and then using the + + align:start position:0% +probabilities and then using the + + + align:start position:0% +probabilities and then using the +definition of conditional + + align:start position:0% +definition of conditional + + + align:start position:0% +definition of conditional +probability I can write each of these as + + align:start position:0% +probability I can write each of these as + + + align:start position:0% +probability I can write each of these as +the probability of Republicans winning + + align:start position:0% +the probability of Republicans winning + + + align:start position:0% +the probability of Republicans winning +conditional on A1 times the probability + + align:start position:0% +conditional on A1 times the probability + + + align:start position:0% +conditional on A1 times the probability +of + + align:start position:0% +of + + + align:start position:0% +of +A1 and the the the sorry this first term + + align:start position:0% +A1 and the the the sorry this first term + + + align:start position:0% +A1 and the the the sorry this first term +I can write this way just uh using the + + align:start position:0% +I can write this way just uh using the + + + align:start position:0% +I can write this way just uh using the +definition of conditional probability + + align:start position:0% +definition of conditional probability + + + align:start position:0% +definition of conditional probability +right and I can do that with all four + + align:start position:0% +right and I can do that with all four + + + align:start position:0% +right and I can do that with all four +terms and so I get this very nice + + align:start position:0% +terms and so I get this very nice + + + align:start position:0% +terms and so I get this very nice +formula and we know I gave you all of + + align:start position:0% +formula and we know I gave you all of + + + align:start position:0% +formula and we know I gave you all of +these I gave you the set of four of + + align:start position:0% +these I gave you the set of four of + + + align:start position:0% +these I gave you the set of four of +these and I gave you the set of four of + + align:start position:0% +these and I gave you the set of four of + + + align:start position:0% +these and I gave you the set of four of +those so all we have to do is plug in to + + align:start position:0% +those so all we have to do is plug in to + + + align:start position:0% +those so all we have to do is plug in to +get the probability of a republican win + + align:start position:0% +get the probability of a republican win + + + align:start position:0% +get the probability of a republican win +in the general + + align:start position:0% +in the general + + + align:start position:0% +in the general +election + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so I'm actually uh I don't know if + + align:start position:0% +okay so I'm actually uh I don't know if + + + align:start position:0% +okay so I'm actually uh I don't know if +this is good news or bad news I'm + + align:start position:0% +this is good news or bad news I'm + + + align:start position:0% +this is good news or bad news I'm +actually going uh faster than I thought + + align:start position:0% +actually going uh faster than I thought + + + align:start position:0% +actually going uh faster than I thought +I would and I did not think I would get + + align:start position:0% +I would and I did not think I would get + + + align:start position:0% +I would and I did not think I would get +to uh uh base theorem today but uh let's + + align:start position:0% +to uh uh base theorem today but uh let's + + + align:start position:0% +to uh uh base theorem today but uh let's +go ahead and go with + + align:start position:0% +go ahead and go with + + + align:start position:0% +go ahead and go with +it um okay so we have seen oh by the way + + align:start position:0% +it um okay so we have seen oh by the way + + + align:start position:0% +it um okay so we have seen oh by the way +this is the Reverend Thomas baz who is a + + align:start position:0% +this is the Reverend Thomas baz who is a + + + align:start position:0% +this is the Reverend Thomas baz who is a +presbyterian minister in England or + + align:start position:0% +presbyterian minister in England or + + + align:start position:0% +presbyterian minister in England or +Scotland I'm not sure sure anyhow uh he + + align:start position:0% +Scotland I'm not sure sure anyhow uh he + + + align:start position:0% +Scotland I'm not sure sure anyhow uh he +did he did sort of a probability as a + + align:start position:0% +did he did sort of a probability as a + + + align:start position:0% +did he did sort of a probability as a +hobby and he uh came up with uh this in + + align:start position:0% +hobby and he uh came up with uh this in + + + align:start position:0% +hobby and he uh came up with uh this in +enormously useful result called Bas + + align:start position:0% +enormously useful result called Bas + + + align:start position:0% +enormously useful result called Bas +theorem uh which we will see uh + + align:start position:0% +theorem uh which we will see uh + + + align:start position:0% +theorem uh which we will see uh +throughout the semester and uh on on + + align:start position:0% +throughout the semester and uh on on + + + align:start position:0% +throughout the semester and uh on on +which an entire branch of um statistical + + align:start position:0% +which an entire branch of um statistical + + + align:start position:0% +which an entire branch of um statistical +analysis is based so uh probably most of + + align:start position:0% +analysis is based so uh probably most of + + + align:start position:0% +analysis is based so uh probably most of +you have heard about beian analysis and + + align:start position:0% +you have heard about beian analysis and + + + align:start position:0% +you have heard about beian analysis and +this is all the the entire branch of uh + + align:start position:0% +this is all the the entire branch of uh + + + align:start position:0% +this is all the the entire branch of uh +basian analysis is based on uh B theorem + + align:start position:0% +basian analysis is based on uh B theorem + + + align:start position:0% +basian analysis is based on uh B theorem +and sort of the ideas of uh Reverend + + align:start position:0% +and sort of the ideas of uh Reverend + + + align:start position:0% +and sort of the ideas of uh Reverend +Thomas + + align:start position:0% + + + + align:start position:0% + +Bas Okay so we've seen that the + + align:start position:0% +Bas Okay so we've seen that the + + + align:start position:0% +Bas Okay so we've seen that the +probability of the intersection of A and + + align:start position:0% +probability of the intersection of A and + + + align:start position:0% +probability of the intersection of A and +B is equal to the probability of B + + align:start position:0% +B is equal to the probability of B + + + align:start position:0% +B is equal to the probability of B +conditional on a times the probability + + align:start position:0% +conditional on a times the probability + + + align:start position:0% +conditional on a times the probability +of a okay that's just the sort of + + align:start position:0% +of a okay that's just the sort of + + + align:start position:0% +of a okay that's just the sort of +definition of uh conditional probability + + align:start position:0% +definition of uh conditional probability + + + align:start position:0% +definition of uh conditional probability +uh alternatively we could also write + + align:start position:0% +uh alternatively we could also write + + + align:start position:0% +uh alternatively we could also write +that as a probability of a conditional + + align:start position:0% +that as a probability of a conditional + + + align:start position:0% +that as a probability of a conditional +and B times the probability of B okay + + align:start position:0% +and B times the probability of B okay + + + align:start position:0% +and B times the probability of B okay +again just the definition of conditional + + align:start position:0% +again just the definition of conditional + + + align:start position:0% +again just the definition of conditional +probability and this is provided both uh + + align:start position:0% +probability and this is provided both uh + + + align:start position:0% +probability and this is provided both uh +A and B have Pro positive + + align:start position:0% +A and B have Pro positive + + + align:start position:0% +A and B have Pro positive +probabilities okay so putting those two + + align:start position:0% +probabilities okay so putting those two + + + align:start position:0% +probabilities okay so putting those two +together we can write the probability of + + align:start position:0% +together we can write the probability of + + + align:start position:0% +together we can write the probability of +a conditional on B as being equal to the + + align:start position:0% +a conditional on B as being equal to the + + + align:start position:0% +a conditional on B as being equal to the +probability of B conditional on a times + + align:start position:0% +probability of B conditional on a times + + + align:start position:0% +probability of B conditional on a times +the probability of a a divided by the + + align:start position:0% +the probability of a a divided by the + + + align:start position:0% +the probability of a a divided by the +probability of B + + align:start position:0% +probability of B + + + align:start position:0% +probability of B +okay we also saw we saw a slightly more + + align:start position:0% +okay we also saw we saw a slightly more + + + align:start position:0% +okay we also saw we saw a slightly more +complicated version of this two slides + + align:start position:0% +complicated version of this two slides + + + align:start position:0% +complicated version of this two slides +ago but we also saw that we can write + + align:start position:0% +ago but we also saw that we can write + + + align:start position:0% +ago but we also saw that we can write +the probability of b as the probability + + align:start position:0% +the probability of b as the probability + + + align:start position:0% +the probability of b as the probability +of B conditional on a times the + + align:start position:0% +of B conditional on a times the + + + align:start position:0% +of B conditional on a times the +probability of a plus the probability of + + align:start position:0% +probability of a plus the probability of + + + align:start position:0% +probability of a plus the probability of +B conditional on a complement times the + + align:start position:0% +B conditional on a complement times the + + + align:start position:0% +B conditional on a complement times the +probability of a complement okay so let + + align:start position:0% +probability of a complement okay so let + + + align:start position:0% +probability of a complement okay so let +me just go back and make sure you + + align:start position:0% +me just go back and make sure you + + + align:start position:0% +me just go back and make sure you +understand where that came from so that + + align:start position:0% +understand where that came from so that + + + align:start position:0% +understand where that came from so that +is just simply a a simpler version of + + align:start position:0% +is just simply a a simpler version of + + + align:start position:0% +is just simply a a simpler version of +this okay with only uh two events A and + + align:start position:0% +this okay with only uh two events A and + + + align:start position:0% +this okay with only uh two events A and +B inste or sorry a and a complement + + align:start position:0% +B inste or sorry a and a complement + + + align:start position:0% +B inste or sorry a and a complement +instead of A1 through + + align:start position:0% +instead of A1 through + + + align:start position:0% +instead of A1 through +A4 + + align:start position:0% + + + + align:start position:0% + +okay okay so we put these two facts + + align:start position:0% +okay okay so we put these two facts + + + align:start position:0% +okay okay so we put these two facts +together and we get a base theorem okay + + align:start position:0% +together and we get a base theorem okay + + + align:start position:0% +together and we get a base theorem okay +so the probability of a conditional on B + + align:start position:0% +so the probability of a conditional on B + + + align:start position:0% +so the probability of a conditional on B +is equal to the probability of B + + align:start position:0% +is equal to the probability of B + + + align:start position:0% +is equal to the probability of B +conditional on a times the probability + + align:start position:0% +conditional on a times the probability + + + align:start position:0% +conditional on a times the probability +of a uh divided by um that same term + + align:start position:0% +of a uh divided by um that same term + + + align:start position:0% +of a uh divided by um that same term +plus the probability of B conditional on + + align:start position:0% +plus the probability of B conditional on + + + align:start position:0% +plus the probability of B conditional on +a complement times the probability of a + + align:start position:0% +a complement times the probability of a + + + align:start position:0% +a complement times the probability of a +complement okay so uh we could do this + + align:start position:0% +complement okay so uh we could do this + + + align:start position:0% +complement okay so uh we could do this +because a and a complement form a + + align:start position:0% +because a and a complement form a + + + align:start position:0% +because a and a complement form a +partition of s you can do this with any + + align:start position:0% +partition of s you can do this with any + + + align:start position:0% +partition of s you can do this with any +partition of s so basically you can have + + align:start position:0% +partition of s so basically you can have + + + align:start position:0% +partition of s so basically you can have +you can write down Bas theorem uh a more + + align:start position:0% +you can write down Bas theorem uh a more + + + align:start position:0% +you can write down Bas theorem uh a more +complicated version of B phas theorem as + + align:start position:0% +complicated version of B phas theorem as + + + align:start position:0% +complicated version of B phas theorem as +long as uh the the the thing that's + + align:start position:0% +long as uh the the the thing that's + + + align:start position:0% +long as uh the the the thing that's +playing the role of a and a complement + + align:start position:0% +playing the role of a and a complement + + + align:start position:0% +playing the role of a and a complement +is a partition of s okay so we could + + align:start position:0% +is a partition of s okay so we could + + + align:start position:0% +is a partition of s okay so we could +have more than just uh you know sort of + + align:start position:0% +have more than just uh you know sort of + + + align:start position:0% +have more than just uh you know sort of +two terms in the denominator is that + + align:start position:0% +two terms in the denominator is that + + + align:start position:0% +two terms in the denominator is that +clear + + align:start position:0% + + + + align:start position:0% + +okay okay so let me um Let Me Now go to + + align:start position:0% +okay okay so let me um Let Me Now go to + + + align:start position:0% +okay okay so let me um Let Me Now go to +an example using base theorem so why is + + align:start position:0% +an example using base theorem so why is + + + align:start position:0% +an example using base theorem so why is +it that b theum is such a powerful idea + + align:start position:0% +it that b theum is such a powerful idea + + + align:start position:0% +it that b theum is such a powerful idea +why is it that you know that that sort + + align:start position:0% +why is it that you know that that sort + + + align:start position:0% +why is it that you know that that sort +of this algebraic manipulation of you + + align:start position:0% +of this algebraic manipulation of you + + + align:start position:0% +of this algebraic manipulation of you +know sort of conditional probabilities + + align:start position:0% +know sort of conditional probabilities + + + align:start position:0% +know sort of conditional probabilities +has ended up being uh so important such + + align:start position:0% +has ended up being uh so important such + + + align:start position:0% +has ended up being uh so important such +an important part of uh probability well + + align:start position:0% +an important part of uh probability well + + + align:start position:0% +an important part of uh probability well +uh I think this example will at least + + align:start position:0% +uh I think this example will at least + + + align:start position:0% +uh I think this example will at least +give you some notion of how powerful Bas + + align:start position:0% +give you some notion of how powerful Bas + + + align:start position:0% +give you some notion of how powerful Bas +theem can be okay so let's suppose a + + align:start position:0% +theem can be okay so let's suppose a + + + align:start position:0% +theem can be okay so let's suppose a +pregnant woman lives in an area where + + align:start position:0% +pregnant woman lives in an area where + + + align:start position:0% +pregnant woman lives in an area where +the zika virus is fairly rare so one and + + align:start position:0% +the zika virus is fairly rare so one and + + + align:start position:0% +the zika virus is fairly rare so one and +a thousand people uh have it in the area + + align:start position:0% +a thousand people uh have it in the area + + + align:start position:0% +a thousand people uh have it in the area +where she lives okay but still she's + + align:start position:0% +where she lives okay but still she's + + + align:start position:0% +where she lives okay but still she's +concerned so she gets tested um there's + + align:start position:0% +concerned so she gets tested um there's + + + align:start position:0% +concerned so she gets tested um there's +a good test for the zika virus suppose + + align:start position:0% +a good test for the zika virus suppose + + + align:start position:0% +a good test for the zika virus suppose +um but it's not a perfect test and it + + align:start position:0% +um but it's not a perfect test and it + + + align:start position:0% +um but it's not a perfect test and it +gives a positive reading with + + align:start position:0% +gives a positive reading with + + + align:start position:0% +gives a positive reading with +probability 99 if the person has the + + align:start position:0% +probability 99 if the person has the + + + align:start position:0% +probability 99 if the person has the +virus okay and a positive reading with + + align:start position:0% +virus okay and a positive reading with + + + align:start position:0% +virus okay and a positive reading with +probability 05 if the person does not + + align:start position:0% +probability 05 if the person does not + + + align:start position:0% +probability 05 if the person does not +have the virus Okay so we've got in sort + + align:start position:0% +have the virus Okay so we've got in sort + + + align:start position:0% +have the virus Okay so we've got in sort +of uh you know sort of the the world of + + align:start position:0% +of uh you know sort of the the world of + + + align:start position:0% +of uh you know sort of the the world of +medical testing that would be considered + + align:start position:0% +medical testing that would be considered + + + align:start position:0% +medical testing that would be considered +a pretty reliable test right there's + + align:start position:0% +a pretty reliable test right there's + + + align:start position:0% +a pretty reliable test right there's +some false positives some false + + align:start position:0% +some false positives some false + + + align:start position:0% +some false positives some false +negatives but the you know rate of false + + align:start position:0% +negatives but the you know rate of false + + + align:start position:0% +negatives but the you know rate of false +negatives is 1% the rate of false + + align:start position:0% +negatives is 1% the rate of false + + + align:start position:0% +negatives is 1% the rate of false +positives is 5% so it's a pretty + + align:start position:0% +positives is 5% so it's a pretty + + + align:start position:0% +positives is 5% so it's a pretty +reliable test okay so she goes in and + + align:start position:0% +reliable test okay so she goes in and + + + align:start position:0% +reliable test okay so she goes in and +has the test and her reading is + + align:start position:0% +has the test and her reading is + + + align:start position:0% +has the test and her reading is +positive How concerned should she be + + align:start position:0% +positive How concerned should she be + + + align:start position:0% +positive How concerned should she be +now okay so you have your you think you + + align:start position:0% +now okay so you have your you think you + + + align:start position:0% +now okay so you have your you think you +might have a virus you you take a test + + align:start position:0% +might have a virus you you take a test + + + align:start position:0% +might have a virus you you take a test +that's really quite reliable and it + + align:start position:0% +that's really quite reliable and it + + + align:start position:0% +that's really quite reliable and it +comes out positive so what do you + + align:start position:0% +comes out positive so what do you + + + align:start position:0% +comes out positive so what do you +imagine the probability that she + + align:start position:0% +imagine the probability that she + + + align:start position:0% +imagine the probability that she +actually has the viruses does anyone + + align:start position:0% +actually has the viruses does anyone + + + align:start position:0% +actually has the viruses does anyone +want to take a + + align:start position:0% + + + + align:start position:0% + +guess should be that part because I + + align:start position:0% +guess should be that part because I + + + align:start position:0% +guess should be that part because I +think the objective probability of her + + align:start position:0% +think the objective probability of her + + + align:start position:0% +think the objective probability of her +is very very low yeah so so the answer + + align:start position:0% +is very very low yeah so so the answer + + + align:start position:0% +is very very low yeah so so the answer +was she shouldn't be that worried I'm + + align:start position:0% +was she shouldn't be that worried I'm + + + align:start position:0% +was she shouldn't be that worried I'm +sure you can't do the calculation in + + align:start position:0% +sure you can't do the calculation in + + + align:start position:0% +sure you can't do the calculation in +your head but in fact even updating on + + align:start position:0% +your head but in fact even updating on + + + align:start position:0% +your head but in fact even updating on +the information in the test the prob + + align:start position:0% +the information in the test the prob + + + align:start position:0% +the information in the test the prob +ility that she has the virus is pretty + + align:start position:0% +ility that she has the virus is pretty + + + align:start position:0% +ility that she has the virus is pretty +low U because the initial uh probability + + align:start position:0% +low U because the initial uh probability + + + align:start position:0% +low U because the initial uh probability +was only one in a th and the test is not + + align:start position:0% +was only one in a th and the test is not + + + align:start position:0% +was only one in a th and the test is not +perfect so let me go through the + + align:start position:0% +perfect so let me go through the + + + align:start position:0% +perfect so let me go through the +specifics okay so we can use base + + align:start position:0% +specifics okay so we can use base + + + align:start position:0% +specifics okay so we can use base +theorem to calculate the probability + + align:start position:0% +theorem to calculate the probability + + + align:start position:0% +theorem to calculate the probability +that she actually has a virus + + align:start position:0% +that she actually has a virus + + + align:start position:0% +that she actually has a virus +conditional on her positive test the + + align:start position:0% +conditional on her positive test the + + + align:start position:0% +conditional on her positive test the +probability we'll call this the prior + + align:start position:0% +probability we'll call this the prior + + + align:start position:0% +probability we'll call this the prior +probability or the unconditional + + align:start position:0% +probability or the unconditional + + + align:start position:0% +probability or the unconditional +probability of her having the zika virus + + align:start position:0% +probability of her having the zika virus + + + align:start position:0% +probability of her having the zika virus +is 0.1 okay that's because she lives in + + align:start position:0% +is 0.1 okay that's because she lives in + + + align:start position:0% +is 0.1 okay that's because she lives in +an area where not that many people have + + align:start position:0% + + + + align:start position:0% + +it that means also that we can write + + align:start position:0% +it that means also that we can write + + + align:start position:0% +it that means also that we can write +down the probability of the complement + + align:start position:0% +down the probability of the complement + + + align:start position:0% +down the probability of the complement +of uh Z as + + align:start position:0% +of uh Z as + + + align:start position:0% +of uh Z as +0.99 the probability of getting a + + align:start position:0% +0.99 the probability of getting a + + + align:start position:0% +0.99 the probability of getting a +positive test result conditional on + + align:start position:0% +positive test result conditional on + + + align:start position:0% +positive test result conditional on +having the zika virus is 0.99 okay so + + align:start position:0% +having the zika virus is 0.99 okay so + + + align:start position:0% +having the zika virus is 0.99 okay so +that's the there's only 1% of false + + align:start position:0% +that's the there's only 1% of false + + + align:start position:0% +that's the there's only 1% of false +negatives the on the test + + align:start position:0% +negatives the on the test + + + align:start position:0% +negatives the on the test +and the probability of getting a + + align:start position:0% +and the probability of getting a + + + align:start position:0% +and the probability of getting a +positive if you don't have the Eco virus + + align:start position:0% +positive if you don't have the Eco virus + + + align:start position:0% +positive if you don't have the Eco virus +is + + align:start position:0% +is + + + align:start position:0% +is + + align:start position:0% + + + align:start position:0% +okay so we plug all of these into base + + align:start position:0% +okay so we plug all of these into base + + + align:start position:0% +okay so we plug all of these into base +theorem and we get that the probability + + align:start position:0% +theorem and we get that the probability + + + align:start position:0% +theorem and we get that the probability +that she has the virus is uh still less + + align:start position:0% +that she has the virus is uh still less + + + align:start position:0% +that she has the virus is uh still less +than + + align:start position:0% +than + + + align:start position:0% +than +2% + + align:start position:0% +2% + + + align:start position:0% +2% +okay and basically the you know I think + + align:start position:0% +okay and basically the you know I think + + + align:start position:0% +okay and basically the you know I think +some people probably find this res + + align:start position:0% +some people probably find this res + + + align:start position:0% +some people probably find this res +result surprising um and uh maybe I can + + align:start position:0% +result surprising um and uh maybe I can + + + align:start position:0% +result surprising um and uh maybe I can +give you some intuition to sort of you + + align:start position:0% +give you some intuition to sort of you + + + align:start position:0% +give you some intuition to sort of you +know help you understand how how this + + align:start position:0% +know help you understand how how this + + + align:start position:0% +know help you understand how how this +can be so the unconditional or prior + + align:start position:0% +can be so the unconditional or prior + + + align:start position:0% +can be so the unconditional or prior +probability of having the virus was + + align:start position:0% +probability of having the virus was + + + align:start position:0% +probability of having the virus was +quite low one in a thousand we updated + + align:start position:0% +quite low one in a thousand we updated + + + align:start position:0% +quite low one in a thousand we updated +the probability based on the results of + + align:start position:0% +the probability based on the results of + + + align:start position:0% +the probability based on the results of +this test but the test uh was imperfect + + align:start position:0% +this test but the test uh was imperfect + + + align:start position:0% +this test but the test uh was imperfect +so if you think about think about two + + align:start position:0% +so if you think about think about two + + + align:start position:0% +so if you think about think about two +counterfactuals one is that um the test + + align:start position:0% +counterfactuals one is that um the test + + + align:start position:0% +counterfactuals one is that um the test +was perfect no wait how do I want to say + + align:start position:0% +was perfect no wait how do I want to say + + + align:start position:0% +was perfect no wait how do I want to say +this uh yeah the test was perfect um the + + align:start position:0% +this uh yeah the test was perfect um the + + + align:start position:0% +this uh yeah the test was perfect um the +probability of her testing positive + + align:start position:0% +probability of her testing positive + + + align:start position:0% +probability of her testing positive +would be 1 in a thousand um and the + + align:start position:0% +would be 1 in a thousand um and the + + + align:start position:0% +would be 1 in a thousand um and the +other counterfactuals if uh the test was + + align:start position:0% +other counterfactuals if uh the test was + + + align:start position:0% +other counterfactuals if uh the test was +as stated but there was no zika virus + + align:start position:0% +as stated but there was no zika virus + + + align:start position:0% +as stated but there was no zika virus +the probability of her testing positive + + align:start position:0% +the probability of her testing positive + + + align:start position:0% +the probability of her testing positive +would be 50 out of a thousand okay and + + align:start position:0% +would be 50 out of a thousand okay and + + + align:start position:0% +would be 50 out of a thousand okay and +so the the um basically we're ta we're + + align:start position:0% +so the the um basically we're ta we're + + + align:start position:0% +so the the um basically we're ta we're +updating based on valuable but not not + + align:start position:0% +updating based on valuable but not not + + + align:start position:0% +updating based on valuable but not not +perfect information and uh the + + align:start position:0% +perfect information and uh the + + + align:start position:0% +perfect information and uh the +probability doesn't get updated that + + align:start position:0% +probability doesn't get updated that + + + align:start position:0% +probability doesn't get updated that +much as a result + + align:start position:0% +much as a result + + + align:start position:0% +much as a result +okay + + align:start position:0% + + + + align:start position:0% + +yep more than one set depending on each + + align:start position:0% +yep more than one set depending on each + + + align:start position:0% +yep more than one set depending on each +other example so here you + + align:start position:0% +other example so here you + + + align:start position:0% +other example so here you +have condition of conditional of the + + align:start position:0% +have condition of conditional of the + + + align:start position:0% +have condition of conditional of the +test being what do you have another + + align:start position:0% +test being what do you have another + + + align:start position:0% +test being what do you have another +condition yes yes yes so I think what + + align:start position:0% +condition yes yes yes so I think what + + + align:start position:0% +condition yes yes yes so I think what +you're asking is that you have several + + align:start position:0% +you're asking is that you have several + + + align:start position:0% +you're asking is that you have several +pieces of information not just the test + + align:start position:0% +pieces of information not just the test + + + align:start position:0% +pieces of information not just the test +you have whether she has symptoms for + + align:start position:0% +you have whether she has symptoms for + + + align:start position:0% +you have whether she has symptoms for +instance exactly or you have yeah yeah + + align:start position:0% +instance exactly or you have yeah yeah + + + align:start position:0% +instance exactly or you have yeah yeah +exactly so so you you may have a whole + + align:start position:0% +exactly so so you you may have a whole + + + align:start position:0% +exactly so so you you may have a whole +series of different pieces of of + + align:start position:0% +series of different pieces of of + + + align:start position:0% +series of different pieces of of +information and if we can write + + align:start position:0% +information and if we can write + + + align:start position:0% +information and if we can write +down if we can write down the + + align:start position:0% +down if we can write down the + + + align:start position:0% +down if we can write down the +probabilities that she has the zika + + align:start position:0% +probabilities that she has the zika + + + align:start position:0% +probabilities that she has the zika +virus conditional on sorry if we can + + align:start position:0% +virus conditional on sorry if we can + + + align:start position:0% +virus conditional on sorry if we can +write down the probabilities of her + + align:start position:0% +write down the probabilities of her + + + align:start position:0% +write down the probabilities of her +having a Fe fever conditional and having + + align:start position:0% +having a Fe fever conditional and having + + + align:start position:0% +having a Fe fever conditional and having +zika virus probability of her having a + + align:start position:0% +zika virus probability of her having a + + + align:start position:0% +zika virus probability of her having a +fever conditional and her not having the + + align:start position:0% +fever conditional and her not having the + + + align:start position:0% +fever conditional and her not having the +zika virus then we can also update the + + align:start position:0% +zika virus then we can also update the + + + align:start position:0% +zika virus then we can also update the +probabilities uh based on that + + align:start position:0% +probabilities uh based on that + + + align:start position:0% +probabilities uh based on that +information and there are basically two + + align:start position:0% +information and there are basically two + + + align:start position:0% +information and there are basically two +ways we can do it we can do it + + align:start position:0% +ways we can do it we can do it + + + align:start position:0% +ways we can do it we can do it +sequentially or we can uh we could sort + + align:start position:0% +sequentially or we can uh we could sort + + + align:start position:0% +sequentially or we can uh we could sort +of write down a formula that lets us + + align:start position:0% +of write down a formula that lets us + + + align:start position:0% +of write down a formula that lets us +update based on all that information + + align:start position:0% +update based on all that information + + + align:start position:0% +update based on all that information +simultaneously and we'll get the same + + align:start position:0% +simultaneously and we'll get the same + + + align:start position:0% +simultaneously and we'll get the same +answers so + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +okay I think now would be a good place + + align:start position:0% +okay I think now would be a good place + + + align:start position:0% +okay I think now would be a good place +to stop even though we're a few minutes + + align:start position:0% +to stop even though we're a few minutes + + + align:start position:0% +to stop even though we're a few minutes +early the next topic we're going to + + align:start position:0% +early the next topic we're going to + + + align:start position:0% +early the next topic we're going to +cover is random variables and uh we will + + align:start position:0% +cover is random variables and uh we will + + + align:start position:0% +cover is random variables and uh we will +uh do that um on + + align:start position:0% + + + + align:start position:0% + +Wednesday and \ No newline at end of file diff --git a/_hYaOtW4XY4.txt b/_hYaOtW4XY4.txt new file mode 100644 index 0000000000000000000000000000000000000000..5130be4cb7e70d50622c33e1909343a6e415439e --- /dev/null +++ b/_hYaOtW4XY4.txt @@ -0,0 +1,7899 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +coreware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so this is the first uh + + align:start position:0% +ocw.mit.edu okay so this is the first uh + + + align:start position:0% +ocw.mit.edu okay so this is the first uh +true review session in 18085 the the + + align:start position:0% +true review session in 18085 the the + + + align:start position:0% +true review session in 18085 the the +last Wednesday the first + + align:start position:0% +last Wednesday the first + + + align:start position:0% +last Wednesday the first +Wednesday afternoon Was A Brief Review + + align:start position:0% +Wednesday afternoon Was A Brief Review + + + align:start position:0% +Wednesday afternoon Was A Brief Review +of uh topics in linear algebra but now + + align:start position:0% +of uh topics in linear algebra but now + + + align:start position:0% +of uh topics in linear algebra but now +we're into the course we've done four + + align:start position:0% +we're into the course we've done four + + + align:start position:0% +we're into the course we've done four +lectures uh on the first four sections + + align:start position:0% +lectures uh on the first four sections + + + align:start position:0% +lectures uh on the first four sections +of the textbook and one homework problem + + align:start position:0% +of the textbook and one homework problem + + + align:start position:0% +of the textbook and one homework problem +in and back and a second homework + + align:start position:0% +in and back and a second homework + + + align:start position:0% +in and back and a second homework +Set uh for next Monday so I'm ready for + + align:start position:0% +Set uh for next Monday so I'm ready for + + + align:start position:0% +Set uh for next Monday so I'm ready for +any questions including questions that + + align:start position:0% +any questions including questions that + + + align:start position:0% +any questions including questions that +are on the homework if necessary + + align:start position:0% +are on the homework if necessary + + + align:start position:0% +are on the homework if necessary +but anything at all or + + align:start position:0% +but anything at all or + + + align:start position:0% +but anything at all or +uh maybe I'll just ask whether the pace + + align:start position:0% +uh maybe I'll just ask whether the pace + + + align:start position:0% +uh maybe I'll just ask whether the pace +so this is really informal is the pace + + align:start position:0% +so this is really informal is the pace + + + align:start position:0% +so this is really informal is the pace +of the course now today's lecture had a + + align:start position:0% +of the course now today's lecture had a + + + align:start position:0% +of the course now today's lecture had a +lot in it as I realized when I saw that + + align:start position:0% +lot in it as I realized when I saw that + + + align:start position:0% +lot in it as I realized when I saw that +the board was still full of + + align:start position:0% +the board was still full of + + + align:start position:0% +the board was still full of +18085 uh and there was a little more + + align:start position:0% +18085 uh and there was a little more + + + align:start position:0% +18085 uh and there was a little more +still to do because we didn't finish the + + align:start position:0% +still to do because we didn't finish the + + + align:start position:0% +still to do because we didn't finish the +Matrix part but + + align:start position:0% +Matrix part but + + + align:start position:0% +Matrix part but +uh are you okay with the with the sort + + align:start position:0% +uh are you okay with the with the sort + + + align:start position:0% +uh are you okay with the with the sort +of speed of the course that's so that'll + + align:start position:0% +of speed of the course that's so that'll + + + align:start position:0% +of speed of the course that's so that'll +be one question and then what about + + align:start position:0% +be one question and then what about + + + align:start position:0% +be one question and then what about +specifics + + align:start position:0% +specifics + + + align:start position:0% +specifics +uh somebody start off if if you will + + align:start position:0% +uh somebody start off if if you will + + + align:start position:0% +uh somebody start off if if you will +anybody yeah thanks well I actually had + + align:start position:0% +anybody yeah thanks well I actually had + + + align:start position:0% +anybody yeah thanks well I actually had +a question about the lecture earlier + + align:start position:0% +a question about the lecture earlier + + + align:start position:0% +a question about the lecture earlier +today okay go ahead I was just going to + + align:start position:0% +today okay go ahead I was just going to + + + align:start position:0% +today okay go ahead I was just going to +look it up in the text but that's all + + align:start position:0% +look it up in the text but that's all + + + align:start position:0% +look it up in the text but that's all +right um had a chance to but okay so I'm + + align:start position:0% +right um had a chance to but okay so I'm + + + align:start position:0% +right um had a chance to but okay so I'm +not really sure how you take the initial + + align:start position:0% +not really sure how you take the initial + + + align:start position:0% +not really sure how you take the initial +conditions and apply them to the ramp + + align:start position:0% +conditions and apply them to the ramp + + + align:start position:0% +conditions and apply them to the ramp +function to actually get a + + align:start position:0% +function to actually get a + + + align:start position:0% +function to actually get a +uh yeah so the question what was so + + align:start position:0% +uh yeah so the question what was so + + + align:start position:0% +uh yeah so the question what was so +that's what luckily happens to be still + + align:start position:0% +that's what luckily happens to be still + + + align:start position:0% +that's what luckily happens to be still +here on the board right we we've got + + align:start position:0% +here on the board right we we've got + + + align:start position:0% +here on the board right we we've got +these boundary I would call them + + align:start position:0% +these boundary I would call them + + + align:start position:0% +these boundary I would call them +boundary conditions so so this is + + align:start position:0% +boundary conditions so so this is + + + align:start position:0% +boundary conditions so so this is +definitely we're in a part of math + + align:start position:0% +definitely we're in a part of math + + + align:start position:0% +definitely we're in a part of math +that's about boundary value problems + + align:start position:0% +that's about boundary value problems + + + align:start position:0% +that's about boundary value problems +more than time isn't in the picture yeah + + align:start position:0% +more than time isn't in the picture yeah + + + align:start position:0% +more than time isn't in the picture yeah +I mean later time will get into the + + align:start position:0% +I mean later time will get into the + + + align:start position:0% +I mean later time will get into the +picture uh so uh with this particular + + align:start position:0% +picture uh so uh with this particular + + + align:start position:0% +picture uh so uh with this particular +example + + align:start position:0% +example + + + align:start position:0% +example +uh the general solution is a is a + + align:start position:0% +uh the general solution is a is a + + + align:start position:0% +uh the general solution is a is a +standard + + align:start position:0% +standard + + + align:start position:0% +standard +ramp at the point a where where things + + align:start position:0% +ramp at the point a where where things + + + align:start position:0% +ramp at the point a where where things +are happening plus the C plus DX the + + align:start position:0% +are happening plus the C plus DX the + + + align:start position:0% +are happening plus the C plus DX the +usual so it's that's a particular + + align:start position:0% +usual so it's that's a particular + + + align:start position:0% +usual so it's that's a particular +solution that particular solution has + + align:start position:0% +solution that particular solution has + + + align:start position:0% +solution that particular solution has +the right Behavior at the at the impulse + + align:start position:0% +the right Behavior at the at the impulse + + + align:start position:0% +the right Behavior at the at the impulse +it has by the right Behavior I mean that + + align:start position:0% +it has by the right Behavior I mean that + + + align:start position:0% +it has by the right Behavior I mean that +the second derivative of the ramp is a + + align:start position:0% +the second derivative of the ramp is a + + + align:start position:0% +the second derivative of the ramp is a +Delta and when I make put the ramp at a + + align:start position:0% +Delta and when I make put the ramp at a + + + align:start position:0% +Delta and when I make put the ramp at a +then the Delta will show up at a and + + align:start position:0% +then the Delta will show up at a and + + + align:start position:0% +then the Delta will show up at a and +when I put on that minus sign it'll mean + + align:start position:0% +when I put on that minus sign it'll mean + + + align:start position:0% +when I put on that minus sign it'll mean +that the second derivative is + + align:start position:0% +that the second derivative is + + + align:start position:0% +that the second derivative is +minus the Delta so the slope will step + + align:start position:0% +minus the Delta so the slope will step + + + align:start position:0% +minus the Delta so the slope will step +down so that's a particular solution but + + align:start position:0% +down so that's a particular solution but + + + align:start position:0% +down so that's a particular solution but +that by itself what boundary conditions + + align:start position:0% +that by itself what boundary conditions + + + align:start position:0% +that by itself what boundary conditions +what would what does that equal at zero + + align:start position:0% +what would what does that equal at zero + + + align:start position:0% +what would what does that equal at zero +and what does that equal at + + align:start position:0% +and what does that equal at + + + align:start position:0% +and what does that equal at +one uh if you remember the ramp so let + + align:start position:0% +one uh if you remember the ramp so let + + + align:start position:0% +one uh if you remember the ramp so let +me just draw that ramp again so the ramp + + align:start position:0% +me just draw that ramp again so the ramp + + + align:start position:0% +me just draw that ramp again so the ramp +was really based on centered at the + + align:start position:0% +was really based on centered at the + + + align:start position:0% +was really based on centered at the +point + + align:start position:0% +point + + + align:start position:0% +point +a and I'll put it with the minus sign so + + align:start position:0% +a and I'll put it with the minus sign so + + + align:start position:0% +a and I'll put it with the minus sign so +it came along there and down there and + + align:start position:0% +it came along there and down there and + + + align:start position:0% +it came along there and down there and +now suppose this is one end of the of + + align:start position:0% +now suppose this is one end of the of + + + align:start position:0% +now suppose this is one end of the of +our interval and that's the other + + align:start position:0% +our interval and that's the other + + + align:start position:0% +our interval and that's the other +end okay so is that ramp the answer to + + align:start position:0% +end okay so is that ramp the answer to + + + align:start position:0% +end okay so is that ramp the answer to +our problem no + + align:start position:0% +our problem no + + + align:start position:0% +our problem no +it well it happens to satisfy + + align:start position:0% +it well it happens to satisfy + + + align:start position:0% +it well it happens to satisfy +this boundary condition happens to start + + align:start position:0% +this boundary condition happens to start + + + align:start position:0% +this boundary condition happens to start +out at zero but it doesn't end up at + + align:start position:0% +out at zero but it doesn't end up at + + + align:start position:0% +out at zero but it doesn't end up at +zero so just like every particular + + align:start position:0% +zero so just like every particular + + + align:start position:0% +zero so just like every particular +solution uh it it's it's we need a + + align:start position:0% +solution uh it it's it's we need a + + + align:start position:0% +solution uh it it's it's we need a +little more we have to + + align:start position:0% +little more we have to + + + align:start position:0% +little more we have to +include more solutions because that was + + align:start position:0% +include more solutions because that was + + + align:start position:0% +include more solutions because that was +only one all those are equally good + + align:start position:0% +only one all those are equally good + + + align:start position:0% +only one all those are equally good +Solutions if I add C plus DX the second + + align:start position:0% +Solutions if I add C plus DX the second + + + align:start position:0% +Solutions if I add C plus DX the second +derivative of that is zero so it doesn't + + align:start position:0% +derivative of that is zero so it doesn't + + + align:start position:0% +derivative of that is zero so it doesn't +spoil anything at all on the contrary it + + align:start position:0% +spoil anything at all on the contrary it + + + align:start position:0% +spoil anything at all on the contrary it +adds more solutions I mean the great the + + align:start position:0% +adds more solutions I mean the great the + + + align:start position:0% +adds more solutions I mean the great the +great thing we're using here is that our + + align:start position:0% +great thing we're using here is that our + + + align:start position:0% +great thing we're using here is that our +equations are linear + + align:start position:0% +equations are linear + + + align:start position:0% +equations are linear +and when and when Zero's on the right + + align:start position:0% +and when and when Zero's on the right + + + align:start position:0% +and when and when Zero's on the right +hand side notice there's no arbitrary + + align:start position:0% +hand side notice there's no arbitrary + + + align:start position:0% +hand side notice there's no arbitrary +const I'm not putting an arbitrary + + align:start position:0% +const I'm not putting an arbitrary + + + align:start position:0% +const I'm not putting an arbitrary +constant on the particular solution is + + align:start position:0% +constant on the particular solution is + + + align:start position:0% +constant on the particular solution is +one particular solution plus a a a a + + align:start position:0% +one particular solution plus a a a a + + + align:start position:0% +one particular solution plus a a a a +Subspace if I use that language a a lot + + align:start position:0% +Subspace if I use that language a a lot + + + align:start position:0% +Subspace if I use that language a a lot +of solutions to the all the solutions to + + align:start position:0% +of solutions to the all the solutions to + + + align:start position:0% +of solutions to the all the solutions to +the problem with zero on the right hand + + align:start position:0% +the problem with zero on the right hand + + + align:start position:0% +the problem with zero on the right hand +side and these are the these are the + + align:start position:0% +side and these are the these are the + + + align:start position:0% +side and these are the these are the +solutions these are the null space guys + + align:start position:0% +solutions these are the null space guys + + + align:start position:0% +solutions these are the null space guys +the ones that that have zero on the + + align:start position:0% +the ones that that have zero on the + + + align:start position:0% +the ones that that have zero on the +right hand side okay now we need those + + align:start position:0% +right hand side okay now we need those + + + align:start position:0% +right hand side okay now we need those +and the effect of those will be to to + + align:start position:0% +and the effect of those will be to to + + + align:start position:0% +and the effect of those will be to to +move that ramp and what effectively what + + align:start position:0% +move that ramp and what effectively what + + + align:start position:0% +move that ramp and what effectively what +are they going to do they're going to + + align:start position:0% +are they going to do they're going to + + + align:start position:0% +are they going to do they're going to +swing that ramp around it'll stay a ramp + + align:start position:0% +swing that ramp around it'll stay a ramp + + + align:start position:0% +swing that ramp around it'll stay a ramp +but instead of being level here it'll go + + align:start position:0% +but instead of being level here it'll go + + + align:start position:0% +but instead of being level here it'll go +up and instead of uh going down there + + align:start position:0% +up and instead of uh going down there + + + align:start position:0% +up and instead of uh going down there +it'll go down there it'll be the same + + align:start position:0% +it'll go down there it'll be the same + + + align:start position:0% +it'll go down there it'll be the same +ramp with still that slope dropped by + + align:start position:0% +ramp with still that slope dropped by + + + align:start position:0% +ramp with still that slope dropped by +one + + align:start position:0% +one + + + align:start position:0% +one +slope went down by minus1 and that's not + + align:start position:0% +slope went down by minus1 and that's not + + + align:start position:0% +slope went down by minus1 and that's not +going to change here the slope will + + align:start position:0% +going to change here the slope will + + + align:start position:0% +going to change here the slope will +still here go down by minus1 but but now + + align:start position:0% +still here go down by minus1 but but now + + + align:start position:0% +still here go down by minus1 but but now +I've just adjusted it so that it goes + + align:start position:0% +I've just adjusted it so that it goes + + + align:start position:0% +I've just adjusted it so that it goes +through the it satisfies the boundary + + align:start position:0% +through the it satisfies the boundary + + + align:start position:0% +through the it satisfies the boundary +conditions and in the second problem + + align:start position:0% +conditions and in the second problem + + + align:start position:0% +conditions and in the second problem +with the free end uh again here's my + + align:start position:0% +with the free end uh again here's my + + + align:start position:0% +with the free end uh again here's my +ramp but now I'm going to adjust it and + + align:start position:0% +ramp but now I'm going to adjust it and + + + align:start position:0% +ramp but now I'm going to adjust it and +what happened it just needed adjustment + + align:start position:0% +what happened it just needed adjustment + + + align:start position:0% +what happened it just needed adjustment +upwards because the this this was the + + align:start position:0% +upwards because the this this was the + + + align:start position:0% +upwards because the this this was the +zero this was the U equals z fixed guy + + align:start position:0% +zero this was the U equals z fixed guy + + + align:start position:0% +zero this was the U equals z fixed guy +and now if I'm doing U Prime equals + + align:start position:0% +and now if I'm doing U Prime equals + + + align:start position:0% +and now if I'm doing U Prime equals +zero the free guy I can lift the whole + + align:start position:0% +zero the free guy I can lift the whole + + + align:start position:0% +zero the free guy I can lift the whole +thing up so you see I just lifted it up + + align:start position:0% +thing up so you see I just lifted it up + + + align:start position:0% +thing up so you see I just lifted it up +to the point where it came out right + + align:start position:0% +to the point where it came out right + + + align:start position:0% +to the point where it came out right +there so in this case I just needed a c + + align:start position:0% +there so in this case I just needed a c + + + align:start position:0% +there so in this case I just needed a c +and in this case I just needed a DX and + + align:start position:0% +and in this case I just needed a DX and + + + align:start position:0% +and in this case I just needed a DX and +in other cases I might have needed both + + align:start position:0% +in other cases I might have needed both + + + align:start position:0% +in other cases I might have needed both +a little bit of c and a little of DX + + align:start position:0% +a little bit of c and a little of DX + + + align:start position:0% +a little bit of c and a little of DX +anyway that's that's the the what was + + align:start position:0% +anyway that's that's the the what was + + + align:start position:0% +anyway that's that's the the what was +maybe that's sort of repeating what what + + align:start position:0% +maybe that's sort of repeating what what + + + align:start position:0% +maybe that's sort of repeating what what +we did did uh today a little bit uh but + + align:start position:0% +we did did uh today a little bit uh but + + + align:start position:0% +we did did uh today a little bit uh but +mechanically it's just we've got a + + align:start position:0% +mechanically it's just we've got a + + + align:start position:0% +mechanically it's just we've got a +particular solution and and we've we've + + align:start position:0% +particular solution and and we've we've + + + align:start position:0% +particular solution and and we've we've +got the complete solution and then we + + align:start position:0% +got the complete solution and then we + + + align:start position:0% +got the complete solution and then we +just have to choose c and d and we've + + align:start position:0% +just have to choose c and d and we've + + + align:start position:0% +just have to choose c and d and we've +got two conditions to do it with the two + + align:start position:0% +got two conditions to do it with the two + + + align:start position:0% +got two conditions to do it with the two +boundary conditions could have other + + align:start position:0% +boundary conditions could have other + + + align:start position:0% +boundary conditions could have other +boundary conditions now what about here + + align:start position:0% +boundary conditions now what about here + + + align:start position:0% +boundary conditions now what about here +here's a yeah I guess what will often + + align:start position:0% +here's a yeah I guess what will often + + + align:start position:0% +here's a yeah I guess what will often +happen in these review sessions is I get + + align:start position:0% +happen in these review sessions is I get + + + align:start position:0% +happen in these review sessions is I get +on a roll and I just keep carry on with + + align:start position:0% +on a roll and I just keep carry on with + + + align:start position:0% +on a roll and I just keep carry on with +it you know you start me with a question + + align:start position:0% +it you know you start me with a question + + + align:start position:0% +it you know you start me with a question +and I can't stop right so uh I'll go a + + align:start position:0% +and I can't stop right so uh I'll go a + + + align:start position:0% +and I can't stop right so uh I'll go a +little longer but then I will will stop + + align:start position:0% +little longer but then I will will stop + + + align:start position:0% +little longer but then I will will stop +ready for the next one what about so we + + align:start position:0% +ready for the next one what about so we + + + align:start position:0% +ready for the next one what about so we +haven't discussed the the free free U of + + align:start position:0% +haven't discussed the the free free U of + + + align:start position:0% +haven't discussed the the free free U of +zero U Prime sorry free is U Prime + + align:start position:0% +zero U Prime sorry free is U Prime + + + align:start position:0% +zero U Prime sorry free is U Prime +that's free at the left and free at the + + align:start position:0% + + + + align:start position:0% + +right okay what's up with + + align:start position:0% +right okay what's up with + + + align:start position:0% +right okay what's up with +that what's the what's going to be + + align:start position:0% +that what's the what's going to be + + + align:start position:0% +that what's the what's going to be +what's the solution to that again I'm + + align:start position:0% +what's the solution to that again I'm + + + align:start position:0% +what's the solution to that again I'm +looking for minus U Prime equal an + + align:start position:0% +looking for minus U Prime equal an + + + align:start position:0% +looking for minus U Prime equal an +Impulse okay with those two boundary + + align:start position:0% +Impulse okay with those two boundary + + + align:start position:0% +Impulse okay with those two boundary +conditions free free and do you know + + align:start position:0% +conditions free free and do you know + + + align:start position:0% +conditions free free and do you know +what's going to happen no solution no + + align:start position:0% +what's going to happen no solution no + + + align:start position:0% +what's going to happen no solution no +solution now it'd be interesting to see + + align:start position:0% +solution now it'd be interesting to see + + + align:start position:0% +solution now it'd be interesting to see +why + + align:start position:0% +why + + + align:start position:0% +why +not why no + + align:start position:0% +not why no + + + align:start position:0% +not why no +solution well one way to do it is try + + align:start position:0% +solution well one way to do it is try + + + align:start position:0% +solution well one way to do it is try +there other right hand sides could have + + align:start position:0% +there other right hand sides could have + + + align:start position:0% +there other right hand sides could have +a + + align:start position:0% +a + + + align:start position:0% +a +solution so it's not that it's not just + + align:start position:0% +solution so it's not that it's not just + + + align:start position:0% +solution so it's not that it's not just +that this is the something the matter + + align:start position:0% +that this is the something the matter + + + align:start position:0% +that this is the something the matter +here specifically that right hand side + + align:start position:0% +here specifically that right hand side + + + align:start position:0% +here specifically that right hand side +and most right hand sides will fail and + + align:start position:0% +and most right hand sides will fail and + + + align:start position:0% +and most right hand sides will fail and +but let's just see it with this one why + + align:start position:0% +but let's just see it with this one why + + + align:start position:0% +but let's just see it with this one why +does that fail well uh well you can see + + align:start position:0% +does that fail well uh well you can see + + + align:start position:0% +does that fail well uh well you can see +I can't + + align:start position:0% +I can't + + + align:start position:0% +I can't +yeah the slope here is zero and the + + align:start position:0% +yeah the slope here is zero and the + + + align:start position:0% +yeah the slope here is zero and the +slope here is minus one if I adjust + + align:start position:0% +slope here is minus one if I adjust + + + align:start position:0% +slope here is minus one if I adjust +those I I can't get this is asking me to + + align:start position:0% +those I I can't get this is asking me to + + + align:start position:0% +those I I can't get this is asking me to +get slope zero at both ends can't do + + align:start position:0% +get slope zero at both ends can't do + + + align:start position:0% +get slope zero at both ends can't do +that right I can't yeah it's just not + + align:start position:0% +that right I can't yeah it's just not + + + align:start position:0% +that right I can't yeah it's just not +possible for me to to no this this will + + align:start position:0% +possible for me to to no this this will + + + align:start position:0% +possible for me to to no this this will +add a straight line but it's the same + + align:start position:0% +add a straight line but it's the same + + + align:start position:0% +add a straight line but it's the same +straight I I can't get a ramp that comes + + align:start position:0% +straight I I can't get a ramp that comes + + + align:start position:0% +straight I I can't get a ramp that comes +flat at both ends because + + align:start position:0% +flat at both ends because + + + align:start position:0% +flat at both ends because +there once I say what it's doing at the + + align:start position:0% +there once I say what it's doing at the + + + align:start position:0% +there once I say what it's doing at the +ends I've got it and and you see what + + align:start position:0% +ends I've got it and and you see what + + + align:start position:0% +ends I've got it and and you see what +what I mean that that to get I'm looking + + align:start position:0% +what I mean that that to get I'm looking + + + align:start position:0% +what I mean that that to get I'm looking +for one that starts + + align:start position:0% +for one that starts + + + align:start position:0% +for one that starts +flat and ends flat and you know that's + + align:start position:0% +flat and ends flat and you know that's + + + align:start position:0% +flat and ends flat and you know that's +that's uh not in my that's not in my + + align:start position:0% +that's uh not in my that's not in my + + + align:start position:0% +that's uh not in my that's not in my +family of solutions that that problem + + align:start position:0% +family of solutions that that problem + + + align:start position:0% +family of solutions that that problem +just doesn't have a solution and I so + + align:start position:0% +just doesn't have a solution and I so + + + align:start position:0% +just doesn't have a solution and I so +that's one way to do it is look at the + + align:start position:0% +that's one way to do it is look at the + + + align:start position:0% +that's one way to do it is look at the +solutions and realize you can't satisfy + + align:start position:0% +solutions and realize you can't satisfy + + + align:start position:0% +solutions and realize you can't satisfy +both boundary conditions another way + + align:start position:0% +both boundary conditions another way + + + align:start position:0% +both boundary conditions another way +might be this um yeah this is a bit this + + align:start position:0% +might be this um yeah this is a bit this + + + align:start position:0% +might be this um yeah this is a bit this +is a little + + align:start position:0% +is a little + + + align:start position:0% +is a little +bit deeper way and it leads to something + + align:start position:0% +bit deeper way and it leads to something + + + align:start position:0% +bit deeper way and it leads to something +better suppose I take the integ so this + + align:start position:0% +better suppose I take the integ so this + + + align:start position:0% +better suppose I take the integ so this +is an equation that's supposed to hold + + align:start position:0% +is an equation that's supposed to hold + + + align:start position:0% +is an equation that's supposed to hold +let me integrate both sides from zero to + + align:start position:0% +let me integrate both sides from zero to + + + align:start position:0% +let me integrate both sides from zero to +one so there there's the idea I'm + + align:start position:0% +one so there there's the idea I'm + + + align:start position:0% +one so there there's the idea I'm +putting in now to to go a little further + + align:start position:0% +putting in now to to go a little further + + + align:start position:0% +putting in now to to go a little further +to discover when this has a solution or + + align:start position:0% +to discover when this has a solution or + + + align:start position:0% +to discover when this has a solution or +let me take more generally minus U Prime + + align:start position:0% +let me take more generally minus U Prime + + + align:start position:0% +let me take more generally minus U Prime +some f + + align:start position:0% +some f + + + align:start position:0% +some f +ofx so some other some other load not + + align:start position:0% +ofx so some other some other load not + + + align:start position:0% +ofx so some other some other load not +necessarily a point load not necessarily + + align:start position:0% +necessarily a point load not necessarily + + + align:start position:0% +necessarily a point load not necessarily +a uniform load but maybe some other load + + align:start position:0% +a uniform load but maybe some other load + + + align:start position:0% +a uniform load but maybe some other load +and now I'm my boundary conditions I'm + + align:start position:0% +and now I'm my boundary conditions I'm + + + align:start position:0% +and now I'm my boundary conditions I'm +trying to do free + + align:start position:0% +trying to do free + + + align:start position:0% +trying to do free +free and + + align:start position:0% +free and + + + align:start position:0% +free and +usually no solution but let's just see + + align:start position:0% +usually no solution but let's just see + + + align:start position:0% +usually no solution but let's just see +why and and when there might be a + + align:start position:0% +why and and when there might be a + + + align:start position:0% +why and and when there might be a +solution key the key idea is + + align:start position:0% + + + + align:start position:0% + +integrate from from from 0 to + + align:start position:0% +integrate from from from 0 to + + + align:start position:0% +integrate from from from 0 to +1 okay what do I get on the right hand + + align:start position:0% +1 okay what do I get on the right hand + + + align:start position:0% +1 okay what do I get on the right hand +side well I get the integral of + + align:start position:0% +side well I get the integral of + + + align:start position:0% +side well I get the integral of +f whatever it is and I would call that + + align:start position:0% +f whatever it is and I would call that + + + align:start position:0% +f whatever it is and I would call that +the total + + align:start position:0% + + + + align:start position:0% + +load fair enough the total load of uh if + + align:start position:0% +load fair enough the total load of uh if + + + align:start position:0% +load fair enough the total load of uh if +it was a Delta function the total load + + align:start position:0% +it was a Delta function the total load + + + align:start position:0% +it was a Delta function the total load +would be one and it would be all in one + + align:start position:0% +would be one and it would be all in one + + + align:start position:0% +would be one and it would be all in one +spot if it was uniformly over the whole + + align:start position:0% +spot if it was uniformly over the whole + + + align:start position:0% +spot if it was uniformly over the whole +interval uh well guess that would also + + align:start position:0% +interval uh well guess that would also + + + align:start position:0% +interval uh well guess that would also +integrate to one so the total load would + + align:start position:0% +integrate to one so the total load would + + + align:start position:0% +integrate to one so the total load would +be one spread out but could be could be + + align:start position:0% +be one spread out but could be could be + + + align:start position:0% +be one spread out but could be could be +a mixture of the two could be a few + + align:start position:0% +a mixture of the two could be a few + + + align:start position:0% +a mixture of the two could be a few +Delta functions whatever what happens + + align:start position:0% +Delta functions whatever what happens + + + align:start position:0% +Delta functions whatever what happens +when I integrate the left side from 0o + + align:start position:0% +when I integrate the left side from 0o + + + align:start position:0% +when I integrate the left side from 0o +to + + align:start position:0% +to + + + align:start position:0% +to +one can you can you do that one the + + align:start position:0% +one can you can you do that one the + + + align:start position:0% +one can you can you do that one the +integral from 0 to one there's Dopey + + align:start position:0% +integral from 0 to one there's Dopey + + + align:start position:0% +integral from 0 to one there's Dopey +minus sign U Prime + + align:start position:0% +minus sign U Prime + + + align:start position:0% +minus sign U Prime +DX what what does that what do I get why + + align:start position:0% +DX what what does that what do I get why + + + align:start position:0% +DX what what does that what do I get why +why do I say that's a good + + align:start position:0% +why do I say that's a good + + + align:start position:0% +why do I say that's a good +idea if I integrate the second + + align:start position:0% +idea if I integrate the second + + + align:start position:0% +idea if I integrate the second +derivative I get the first derivative + + align:start position:0% +derivative I get the first derivative + + + align:start position:0% +derivative I get the first derivative +the integral the second derivative will + + align:start position:0% +the integral the second derivative will + + + align:start position:0% +the integral the second derivative will +be the first derivative with the + + align:start position:0% +be the first derivative with the + + + align:start position:0% +be the first derivative with the +minus so it's minus the first derivative + + align:start position:0% +minus so it's minus the first derivative + + + align:start position:0% +minus so it's minus the first derivative +and what do I do + + align:start position:0% +and what do I do + + + align:start position:0% +and what do I do +now I plug in the end points right + + align:start position:0% +now I plug in the end points right + + + align:start position:0% +now I plug in the end points right +integrate I'm integrating 0 to one so I + + align:start position:0% +integrate I'm integrating 0 to one so I + + + align:start position:0% +integrate I'm integrating 0 to one so I +I found the integral I put Z to one in + + align:start position:0% +I found the integral I put Z to one in + + + align:start position:0% +I found the integral I put Z to one in +there so I get so what is that that's + + align:start position:0% +there so I get so what is that that's + + + align:start position:0% +there so I get so what is that that's +minus the derivative at + + align:start position:0% +minus the derivative at + + + align:start position:0% +minus the derivative at +1 plus the derivative at + + align:start position:0% + + + + align:start position:0% + +zero okay and now what's that that's + + align:start position:0% +zero okay and now what's that that's + + + align:start position:0% +zero okay and now what's that that's +Zero by my boundary conditions that's + + align:start position:0% +Zero by my boundary conditions that's + + + align:start position:0% +Zero by my boundary conditions that's +zero so what did I just what have I + + align:start position:0% +zero so what did I just what have I + + + align:start position:0% +zero so what did I just what have I +found I've found that if these are the + + align:start position:0% +found I've found that if these are the + + + align:start position:0% +found I've found that if these are the +boundary conditions then when I + + align:start position:0% +boundary conditions then when I + + + align:start position:0% +boundary conditions then when I +integrate the left side it's going to + + align:start position:0% +integrate the left side it's going to + + + align:start position:0% +integrate the left side it's going to +give me zero so when what load s could + + align:start position:0% +give me zero so when what load s could + + + align:start position:0% +give me zero so when what load s could +be okay what loads could give what loads + + align:start position:0% +be okay what loads could give what loads + + + align:start position:0% +be okay what loads could give what loads +F ofx could + + align:start position:0% +F ofx could + + + align:start position:0% +F ofx could +be could allow me to solve this uh + + align:start position:0% + + + + align:start position:0% + +equation the the condition will be I + + align:start position:0% +equation the the condition will be I + + + align:start position:0% +equation the the condition will be I +need what do I need for the total load + + align:start position:0% +need what do I need for the total load + + + align:start position:0% +need what do I need for the total load +to be able to solve this + + align:start position:0% +to be able to solve this + + + align:start position:0% +to be able to solve this +equation the integral of the left side + + align:start position:0% +equation the integral of the left side + + + align:start position:0% +equation the integral of the left side +was + + align:start position:0% +was + + + align:start position:0% +was +zero so the integral of the right side + + align:start position:0% +zero so the integral of the right side + + + align:start position:0% +zero so the integral of the right side +had better be zero okay so that's the + + align:start position:0% +had better be zero okay so that's the + + + align:start position:0% +had better be zero okay so that's the +condition for if I if I have these + + align:start position:0% +condition for if I if I have these + + + align:start position:0% +condition for if I if I have these +boundary conditions then my problem is + + align:start position:0% +boundary conditions then my problem is + + + align:start position:0% +boundary conditions then my problem is +singular usually no solution it's like + + align:start position:0% +singular usually no solution it's like + + + align:start position:0% +singular usually no solution it's like +having a singular matrix it's like + + align:start position:0% +having a singular matrix it's like + + + align:start position:0% +having a singular matrix it's like +having this particular singular Matrix + + align:start position:0% +having this particular singular Matrix + + + align:start position:0% +having this particular singular Matrix +of course as you whoops not that one let + + align:start position:0% +of course as you whoops not that one let + + + align:start position:0% +of course as you whoops not that one let +me get the plus sign in the right + + align:start position:0% +me get the plus sign in the right + + + align:start position:0% +me get the plus sign in the right +position yeah sorry that's a plus Min - + + align:start position:0% +position yeah sorry that's a plus Min - + + + align:start position:0% +position yeah sorry that's a plus Min - +one - one 2 - one minus one one right + + align:start position:0% +one - one 2 - one minus one one right + + + align:start position:0% +one - one 2 - one minus one one right +that's the that's this is the + + align:start position:0% +that's the that's this is the + + + align:start position:0% +that's the that's this is the +discrete version with a with a uh zero + + align:start position:0% +discrete version with a with a uh zero + + + align:start position:0% +discrete version with a with a uh zero +slope at both ends + + align:start position:0% +slope at both ends + + + align:start position:0% +slope at both ends +like it's our T Matrix no it's what + + align:start position:0% +like it's our T Matrix no it's what + + + align:start position:0% +like it's our T Matrix no it's what +Matrix is it b b it's our B Matrix both + + align:start position:0% +Matrix is it b b it's our B Matrix both + + + align:start position:0% +Matrix is it b b it's our B Matrix both +ends okay so let me I'll just come back + + align:start position:0% +ends okay so let me I'll just come back + + + align:start position:0% +ends okay so let me I'll just come back +here and then I'll do the discret one so + + align:start position:0% +here and then I'll do the discret one so + + + align:start position:0% +here and then I'll do the discret one so +what so tell me a a load that we could + + align:start position:0% +what so tell me a a load that we could + + + align:start position:0% +what so tell me a a load that we could +handle a load we could handle + + align:start position:0% +handle a load we could handle + + + align:start position:0% +handle a load we could handle +so the integral has to be zero so + + align:start position:0% +so the integral has to be zero so + + + align:start position:0% +so the integral has to be zero so +suppose my load has + + align:start position:0% +suppose my load has + + + align:start position:0% +suppose my load has +a has a Delta function at + + align:start position:0% +a has a Delta function at + + + align:start position:0% +a has a Delta function at +a well that integral is one so can you + + align:start position:0% +a well that integral is one so can you + + + align:start position:0% +a well that integral is one so can you +fix that to a change that load or do + + align:start position:0% +fix that to a change that load or do + + + align:start position:0% +fix that to a change that load or do +something maybe put on another load to + + align:start position:0% +something maybe put on another load to + + + align:start position:0% +something maybe put on another load to +get a total load of + + align:start position:0% +get a total load of + + + align:start position:0% +get a total load of +zero wh what shall I + + align:start position:0% +zero wh what shall I + + + align:start position:0% +zero wh what shall I +do add another + + align:start position:0% +do add another + + + align:start position:0% +do add another +guy with the minus sign in other + + align:start position:0% +guy with the minus sign in other + + + align:start position:0% +guy with the minus sign in other +words yeah maybe this a Delta function + + align:start position:0% +words yeah maybe this a Delta function + + + align:start position:0% +words yeah maybe this a Delta function +at some other point B well that would do + + align:start position:0% +at some other point B well that would do + + + align:start position:0% +at some other point B well that would do +it right I believe we could solve that + + align:start position:0% +it right I believe we could solve that + + + align:start position:0% +it right I believe we could solve that +problem even with + + align:start position:0% + + + + align:start position:0% + +these bad boundary condition we could + + align:start position:0% +these bad boundary condition we could + + + align:start position:0% +these bad boundary condition we could +solve that problem because the total + + align:start position:0% +solve that problem because the total + + + align:start position:0% +solve that problem because the total +load would be one from that minus one + + align:start position:0% +load would be one from that minus one + + + align:start position:0% +load would be one from that minus one +from that the total load would be zero + + align:start position:0% +from that the total load would be zero + + + align:start position:0% +from that the total load would be zero +you could in other words our What would + + align:start position:0% +you could in other words our What would + + + align:start position:0% +you could in other words our What would +our solution look like it it has to + + align:start position:0% +our solution look like it it has to + + + align:start position:0% +our solution look like it it has to +start with zero slope so would Buzz + + align:start position:0% +start with zero slope so would Buzz + + + align:start position:0% +start with zero slope so would Buzz +along to a and then after B and and what + + align:start position:0% +along to a and then after B and and what + + + align:start position:0% +along to a and then after B and and what +does it have to do here yeah what if I + + align:start position:0% +does it have to do here yeah what if I + + + align:start position:0% +does it have to do here yeah what if I +graph the solution to this guy from zero + + align:start position:0% +graph the solution to this guy from zero + + + align:start position:0% +graph the solution to this guy from zero +to one it it's uh starts with it's free + + align:start position:0% +to one it it's uh starts with it's free + + + align:start position:0% +to one it it's uh starts with it's free +so nothing's happening until I get to a + + align:start position:0% +so nothing's happening until I get to a + + + align:start position:0% +so nothing's happening until I get to a +then what has to happen it's got to uh + + align:start position:0% +then what has to happen it's got to uh + + + align:start position:0% +then what has to happen it's got to uh +let's see if I'm graphing you it it'll + + align:start position:0% +let's see if I'm graphing you it it'll + + + align:start position:0% +let's see if I'm graphing you it it'll +be a ramp right it'll be a ramp yeah + + align:start position:0% +be a ramp right it'll be a ramp yeah + + + align:start position:0% +be a ramp right it'll be a ramp yeah +because I'm two derivative so and it has + + align:start position:0% +because I'm two derivative so and it has + + + align:start position:0% +because I'm two derivative so and it has +to ramp down by one so it'll ramp + + align:start position:0% +to ramp down by one so it'll ramp + + + align:start position:0% +to ramp down by one so it'll ramp +whatever it does d d d I don't know + + align:start position:0% +whatever it does d d d I don't know + + + align:start position:0% +whatever it does d d d I don't know +where it + + align:start position:0% + + + + align:start position:0% + +stops where does it wait a minute I you + + align:start position:0% +stops where does it wait a minute I you + + + align:start position:0% +stops where does it wait a minute I you +know I haven't practiced + + align:start position:0% +know I haven't practiced + + + align:start position:0% +know I haven't practiced +this so I start from the other + + align:start position:0% +this so I start from the other + + + align:start position:0% +this so I start from the other +end the other end is flat the other end + + align:start position:0% +end the other end is flat the other end + + + align:start position:0% +end the other end is flat the other end +is + + align:start position:0% +is + + + align:start position:0% +is +flat + + align:start position:0% + + + + align:start position:0% + +what's + + align:start position:0% +what's + + + align:start position:0% +what's +up that's they got a m meat + + align:start position:0% +up that's they got a m meat + + + align:start position:0% +up that's they got a m meat +here oh the other end is flat but not at + + align:start position:0% +here oh the other end is flat but not at + + + align:start position:0% +here oh the other end is flat but not at +zero dumb stupid right okay yes the + + align:start position:0% +zero dumb stupid right okay yes the + + + align:start position:0% +zero dumb stupid right okay yes the +other end is flat right and it's oh yeah + + align:start position:0% +other end is flat right and it's oh yeah + + + align:start position:0% +other end is flat right and it's oh yeah +look oh wonderful you see it's slope + + align:start position:0% +look oh wonderful you see it's slope + + + align:start position:0% +look oh wonderful you see it's slope +that slope dropped by one and the slope + + align:start position:0% +that slope dropped by one and the slope + + + align:start position:0% +that slope dropped by one and the slope +there increased by one back to zero + + align:start position:0% +there increased by one back to zero + + + align:start position:0% +there increased by one back to zero +slope was Zero it dropped to minus one + + align:start position:0% +slope was Zero it dropped to minus one + + + align:start position:0% +slope was Zero it dropped to minus one +to to because of that load it now it + + align:start position:0% +to to because of that load it now it + + + align:start position:0% +to to because of that load it now it +increased back to zero because of this + + align:start position:0% +increased back to zero because of this + + + align:start position:0% +increased back to zero because of this +load with the minus sign and there's the + + align:start position:0% +load with the minus sign and there's the + + + align:start position:0% +load with the minus sign and there's the +solution yeah so that's a solvable + + align:start position:0% +solution yeah so that's a solvable + + + align:start position:0% +solution yeah so that's a solvable +problem well you say Okay that was a + + align:start position:0% +problem well you say Okay that was a + + + align:start position:0% +problem well you say Okay that was a +little surprising to get an answer for a + + align:start position:0% +little surprising to get an answer for a + + + align:start position:0% +little surprising to get an answer for a +singular problem and no it can happen uh + + align:start position:0% +singular problem and no it can happen uh + + + align:start position:0% +singular problem and no it can happen uh +if we have an total load zero it it will + + align:start position:0% +if we have an total load zero it it will + + + align:start position:0% +if we have an total load zero it it will +happen but there is still a butt that's + + align:start position:0% +happen but there is still a butt that's + + + align:start position:0% +happen but there is still a butt that's +not the only answer tell me uh that that + + align:start position:0% +not the only answer tell me uh that that + + + align:start position:0% +not the only answer tell me uh that that +picture is a solution but not the only + + align:start position:0% +picture is a solution but not the only + + + align:start position:0% +picture is a solution but not the only +one so my point is going to be that when + + align:start position:0% +one so my point is going to be that when + + + align:start position:0% +one so my point is going to be that when +the problem is singular if there's an + + align:start position:0% +the problem is singular if there's an + + + align:start position:0% +the problem is singular if there's an +answer you say great but then something + + align:start position:0% +answer you say great but then something + + + align:start position:0% +answer you say great but then something +has to go wrong and that what goes wrong + + align:start position:0% +has to go wrong and that what goes wrong + + + align:start position:0% +has to go wrong and that what goes wrong +is too many answers so tell me some more + + align:start position:0% +is too many answers so tell me some more + + + align:start position:0% +is too many answers so tell me some more +what other graphs would + + align:start position:0% +what other graphs would + + + align:start position:0% +what other graphs would +be would give would draw solutions to + + align:start position:0% +be would give would draw solutions to + + + align:start position:0% +be would give would draw solutions to +this + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% +problem + + + align:start position:0% +problem +I could shift I could lift the whole + + align:start position:0% +I could shift I could lift the whole + + + align:start position:0% +I could shift I could lift the whole +thing I mean yeah here I've got a A plus + + align:start position:0% +thing I mean yeah here I've got a A plus + + + align:start position:0% +thing I mean yeah here I've got a A plus +C that I haven't used I could just do + + align:start position:0% +C that I haven't used I could just do + + + align:start position:0% +C that I haven't used I could just do +the whole thing higher up any of these + + align:start position:0% +the whole thing higher up any of these + + + align:start position:0% +the whole thing higher up any of these +these would all work yeah yeah all so + + align:start position:0% +these would all work yeah yeah all so + + + align:start position:0% +these would all work yeah yeah all so +I've + + align:start position:0% +I've + + + align:start position:0% +I've +got you know it's like temperature I + + align:start position:0% +got you know it's like temperature I + + + align:start position:0% +got you know it's like temperature I +don't have an absolute temperature here + + align:start position:0% +don't have an absolute temperature here + + + align:start position:0% +don't have an absolute temperature here +uh the all all I've got is I I would + + align:start position:0% +uh the all all I've got is I I would + + + align:start position:0% +uh the all all I've got is I I would +have to you know it's not determined + + align:start position:0% +have to you know it's not determined + + + align:start position:0% +have to you know it's not determined +because there's a plus c that the plus C + + align:start position:0% +because there's a plus c that the plus C + + + align:start position:0% +because there's a plus c that the plus C +satisfied these the plus C satisfied + + align:start position:0% +satisfied these the plus C satisfied + + + align:start position:0% +satisfied these the plus C satisfied +everything that a plus c a constant has + + align:start position:0% +everything that a plus c a constant has + + + align:start position:0% +everything that a plus c a constant has +zero slope it has zero slope its second + + align:start position:0% +zero slope it has zero slope its second + + + align:start position:0% +zero slope it has zero slope its second +derivative is zero so it's like unseen + + align:start position:0% +derivative is zero so it's like unseen + + + align:start position:0% +derivative is zero so it's like unseen +by this equation yeah yeah and and + + align:start position:0% +by this equation yeah yeah and and + + + align:start position:0% +by this equation yeah yeah and and +similarly can I just make the analogy as + + align:start position:0% +similarly can I just make the analogy as + + + align:start position:0% +similarly can I just make the analogy as +I always like to do with discrete stuff + + align:start position:0% +I always like to do with discrete stuff + + + align:start position:0% +I always like to do with discrete stuff +so suppose I tell me a right hand side + + align:start position:0% +so suppose I tell me a right hand side + + + align:start position:0% +so suppose I tell me a right hand side +that we think would + + align:start position:0% +that we think would + + + align:start position:0% +that we think would +probably yeah is this going to be the + + align:start position:0% +probably yeah is this going to be the + + + align:start position:0% +probably yeah is this going to be the +same story for this guy yes if I add + + align:start position:0% +same story for this guy yes if I add + + + align:start position:0% +same story for this guy yes if I add +those that's like where I integrated + + align:start position:0% +those that's like where I integrated + + + align:start position:0% +those that's like where I integrated +there here I would add and I get 0 0 0 + + align:start position:0% +there here I would add and I get 0 0 0 + + + align:start position:0% +there here I would add and I get 0 0 0 +so this has to add to zero if there's a + + align:start position:0% +so this has to add to zero if there's a + + + align:start position:0% +so this has to add to zero if there's a +solution so let me put for example 0 1 + + align:start position:0% +solution so let me put for example 0 1 + + + align:start position:0% +solution so let me put for example 0 1 +minus one that would be kind of like our + + align:start position:0% +minus one that would be kind of like our + + + align:start position:0% +minus one that would be kind of like our +our Delta function in One Direction and + + align:start position:0% +our Delta function in One Direction and + + + align:start position:0% +our Delta function in One Direction and +our Delta function in the other I + + align:start position:0% +our Delta function in the other I + + + align:start position:0% +our Delta function in the other I +believe I can solve that problem so I'm + + align:start position:0% +believe I can solve that problem so I'm + + + align:start position:0% +believe I can solve that problem so I'm +just carrying because I always want you + + align:start position:0% +just carrying because I always want you + + + align:start position:0% +just carrying because I always want you +to see the discret one as well as the + + align:start position:0% +to see the discret one as well as the + + + align:start position:0% +to see the discret one as well as the +continuous continuous involveed this + + align:start position:0% +continuous continuous involveed this + + + align:start position:0% +continuous continuous involveed this +integration the finite one just involves + + align:start position:0% +integration the finite one just involves + + + align:start position:0% +integration the finite one just involves +adding that all the left side adds to + + align:start position:0% +adding that all the left side adds to + + + align:start position:0% +adding that all the left side adds to +zero so the right hand side better add + + align:start position:0% +zero so the right hand side better add + + + align:start position:0% +zero so the right hand side better add +to zero that right hand side does tell + + align:start position:0% +to zero that right hand side does tell + + + align:start position:0% +to zero that right hand side does tell +me a solution well let me start out with + + align:start position:0% +me a solution well let me start out with + + + align:start position:0% +me a solution well let me start out with +a seven there what's the next next uh + + align:start position:0% +a seven there what's the next next uh + + + align:start position:0% +a seven there what's the next next uh +what's the next guy going to + + align:start position:0% +what's the next guy going to + + + align:start position:0% +what's the next guy going to +be uh let see I want seven whatever I + + align:start position:0% +be uh let see I want seven whatever I + + + align:start position:0% +be uh let see I want seven whatever I +put there it go I better have a seven + + align:start position:0% +put there it go I better have a seven + + + align:start position:0% +put there it go I better have a seven +there right s seven good Min - 7 + 14 oh + + align:start position:0% +there right s seven good Min - 7 + 14 oh + + + align:start position:0% +there right s seven good Min - 7 + 14 oh +jeez I didn't know this was going to + + align:start position:0% +jeez I didn't know this was going to + + + align:start position:0% +jeez I didn't know this was going to +happen uh what no no I want to get the + + align:start position:0% +happen uh what no no I want to get the + + + align:start position:0% +happen uh what no no I want to get the +answer one yeah what what was what + + align:start position:0% +answer one yeah what what was what + + + align:start position:0% +answer one yeah what what was what +number goes there six is it six okay + + align:start position:0% +number goes there six is it six okay + + + align:start position:0% +number goes there six is it six okay +it's six yeah good - 7 14 minus 6 is + + align:start position:0% +it's six yeah good - 7 14 minus 6 is + + + align:start position:0% +it's six yeah good - 7 14 minus 6 is +that and now my claim is that we'll come + + align:start position:0% +that and now my claim is that we'll come + + + align:start position:0% +that and now my claim is that we'll come +out right on the third equation so far + + align:start position:0% +out right on the third equation so far + + + align:start position:0% +out right on the third equation so far +I've just matched the first two now this + + align:start position:0% +I've just matched the first two now this + + + align:start position:0% +I've just matched the first two now this +one gives - 7 + 6 that's - one good so + + align:start position:0% +one gives - 7 + 6 that's - one good so + + + align:start position:0% +one gives - 7 + 6 that's - one good so +there is a + + align:start position:0% +there is a + + + align:start position:0% +there is a +solution and I'll leave this problem + + align:start position:0% +solution and I'll leave this problem + + + align:start position:0% +solution and I'll leave this problem +alone if you tell me the rest other + + align:start position:0% +alone if you tell me the rest other + + + align:start position:0% +alone if you tell me the rest other +solutions that that 776 was a solution + + align:start position:0% +solutions that that 776 was a solution + + + align:start position:0% +solutions that that 776 was a solution +to us singular problem with a right hand + + align:start position:0% +to us singular problem with a right hand + + + align:start position:0% +to us singular problem with a right hand +side that had total load zero so it was + + align:start position:0% +side that had total load zero so it was + + + align:start position:0% +side that had total load zero so it was +okay but now that's a solution but there + + align:start position:0% +okay but now that's a solution but there + + + align:start position:0% +okay but now that's a solution but there +are more tell me another + + align:start position:0% + + + + align:start position:0% + +one I I can shift it right I could make + + align:start position:0% +one I I can shift it right I could make + + + align:start position:0% +one I I can shift it right I could make +it 17 17 16 I could add 10 to + + align:start position:0% +it 17 17 16 I could add 10 to + + + align:start position:0% +it 17 17 16 I could add 10 to +everything right that's the plus C that + + align:start position:0% +everything right that's the plus C that + + + align:start position:0% +everything right that's the plus C that +I could do over there now that can't + + align:start position:0% +I could do over there now that can't + + + align:start position:0% +I could do over there now that can't +change because 17 - 17 is is still zero + + align:start position:0% +change because 17 - 17 is is still zero + + + align:start position:0% +change because 17 - 17 is is still zero +everything 7 -7 + 16 will still be + + align:start position:0% +everything 7 -7 + 16 will still be + + + align:start position:0% +everything 7 -7 + 16 will still be +minus1 all good yeah okay so that's + + align:start position:0% +minus1 all good yeah okay so that's + + + align:start position:0% +minus1 all good yeah okay so that's +actually it just like helps our + + align:start position:0% +actually it just like helps our + + + align:start position:0% +actually it just like helps our +intuition and and physically my + + align:start position:0% +intuition and and physically my + + + align:start position:0% +intuition and and physically my +intuition is this that I've got this + + align:start position:0% + + + + align:start position:0% + +bar and nothing's holding it so if I put + + align:start position:0% +bar and nothing's holding it so if I put + + + align:start position:0% +bar and nothing's holding it so if I put +a weight on it + + align:start position:0% +a weight on it + + + align:start position:0% +a weight on it +it'll nothing to hold it uh it'll just + + align:start position:0% +it'll nothing to hold it uh it'll just + + + align:start position:0% +it'll nothing to hold it uh it'll just +rigid motional take it out of sight no + + align:start position:0% +rigid motional take it out of sight no + + + align:start position:0% +rigid motional take it out of sight no +good but if I put another equal weight + + align:start position:0% +good but if I put another equal weight + + + align:start position:0% +good but if I put another equal weight +on it no it's not a weight what do I + + align:start position:0% +on it no it's not a weight what do I + + + align:start position:0% +on it no it's not a weight what do I +call it if I lift it at that + + align:start position:0% +call it if I lift it at that + + + align:start position:0% +call it if I lift it at that +point that's the other Delta function + + align:start position:0% +point that's the other Delta function + + + align:start position:0% +point that's the other Delta function +that's going the other way then it will + + align:start position:0% +that's going the other way then it will + + + align:start position:0% +that's going the other way then it will +sit there but it could it would still be + + align:start position:0% +sit there but it could it would still be + + + align:start position:0% +sit there but it could it would still be +an equilibrium if I just moved it up to + + align:start position:0% +an equilibrium if I just moved it up to + + + align:start position:0% +an equilibrium if I just moved it up to +there or moved it as I like I don't know + + align:start position:0% +there or moved it as I like I don't know + + + align:start position:0% +there or moved it as I like I don't know +if that that is kind of a dumb uh + + align:start position:0% +if that that is kind of a dumb uh + + + align:start position:0% +if that that is kind of a dumb uh +picture but it + + align:start position:0% +picture but it + + + align:start position:0% +picture but it +saying the what we've said from math + + align:start position:0% +saying the what we've said from math + + + align:start position:0% +saying the what we've said from math +well you see where your question LED + + align:start position:0% +well you see where your question LED + + + align:start position:0% +well you see where your question LED +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +thanks over on this plot that you drew + + align:start position:0% +thanks over on this plot that you drew + + + align:start position:0% +thanks over on this plot that you drew +do we have to have equal area above and + + align:start position:0% +do we have to have equal area above and + + + align:start position:0% +do we have to have equal area above and +below the zero point like since we're + + align:start position:0% +below the zero point like since we're + + + align:start position:0% +below the zero point like since we're +integrating it it has to equal zero uh + + align:start position:0% +integrating it it has to equal zero uh + + + align:start position:0% +integrating it it has to equal zero uh +no the integral it was the it was it was + + align:start position:0% +no the integral it was the it was it was + + + align:start position:0% +no the integral it was the it was it was +yeah watch what we integrated we + + align:start position:0% +yeah watch what we integrated we + + + align:start position:0% +yeah watch what we integrated we +integrated u double + + align:start position:0% +integrated u double + + + align:start position:0% +integrated u double +Prime that so that's not the area yeah + + align:start position:0% +Prime that so that's not the area yeah + + + align:start position:0% +Prime that so that's not the area yeah +yeah we integrated uble Prime and got + + align:start position:0% +yeah we integrated uble Prime and got + + + align:start position:0% +yeah we integrated uble Prime and got +its integral was U Prime so that just + + align:start position:0% +its integral was U Prime so that just + + + align:start position:0% +its integral was U Prime so that just +told us that a difference in slopes at + + align:start position:0% +told us that a difference in slopes at + + + align:start position:0% +told us that a difference in slopes at +the end yeah yeah good good yeah because + + align:start position:0% +the end yeah yeah good good yeah because + + + align:start position:0% +the end yeah yeah good good yeah because +we our intuition automatically is if + + align:start position:0% +we our intuition automatically is if + + + align:start position:0% +we our intuition automatically is if +we're integrating something we're + + align:start position:0% +we're integrating something we're + + + align:start position:0% +we're integrating something we're +finding an area but here I'm if it was U + + align:start position:0% +finding an area but here I'm if it was U + + + align:start position:0% +finding an area but here I'm if it was U +then I'd be finding the area under U but + + align:start position:0% +then I'd be finding the area under U but + + + align:start position:0% +then I'd be finding the area under U but +this is where we integrated the second + + align:start position:0% +this is where we integrated the second + + + align:start position:0% +this is where we integrated the second +derivative right good yes oh anything + + align:start position:0% +derivative right good yes oh anything + + + align:start position:0% +derivative right good yes oh anything +now let's change the subject yes please + + align:start position:0% +now let's change the subject yes please + + + align:start position:0% +now let's change the subject yes please +you explain why the those two + + align:start position:0% + + + + align:start position:0% + +um oh yes I guess so I'll try uh yeah + + align:start position:0% +um oh yes I guess so I'll try uh yeah + + + align:start position:0% +um oh yes I guess so I'll try uh yeah +um right and uh + + align:start position:0% +um right and uh + + + align:start position:0% +um right and uh +so let's see so my equ my discrete + + align:start position:0% +so let's see so my equ my discrete + + + align:start position:0% +so let's see so my equ my discrete +equation was like minus + + align:start position:0% +equation was like minus + + + align:start position:0% +equation was like minus +U yeah so so let's back up to the + + align:start position:0% +U yeah so so let's back up to the + + + align:start position:0% +U yeah so so let's back up to the +beginning we we're using we're we've got + + align:start position:0% +beginning we we're using we're we've got + + + align:start position:0% +beginning we we're using we're we've got +this minus sign and we're using a second + + align:start position:0% +this minus sign and we're using a second + + + align:start position:0% +this minus sign and we're using a second +difference so second differences have + + align:start position:0% +difference so second differences have + + + align:start position:0% +difference so second differences have +coefficients 1 - 2 and + + align:start position:0% +coefficients 1 - 2 and + + + align:start position:0% +coefficients 1 - 2 and +1 okay now I'm reversing the signs + + align:start position:0% +1 okay now I'm reversing the signs + + + align:start position:0% +1 okay now I'm reversing the signs +because of my minus so I have minus uh U + + align:start position:0% +because of my minus so I have minus uh U + + + align:start position:0% +because of my minus so I have minus uh U +at some point to let's take that as the + + align:start position:0% +at some point to let's take that as the + + + align:start position:0% +at some point to let's take that as the +point to the left two U's at the C what + + align:start position:0% +point to the left two U's at the C what + + + align:start position:0% +point to the left two U's at the C what +I'll think of as the center point minus + + align:start position:0% +I'll think of as the center point minus + + + align:start position:0% +I'll think of as the center point minus +U + + align:start position:0% +U + + + align:start position:0% +U +ius1 is the load at that Center Point + + align:start position:0% +ius1 is the load at that Center Point + + + align:start position:0% +ius1 is the load at that Center Point +that that Center Point is I * Delta + + align:start position:0% +that that Center Point is I * Delta + + + align:start position:0% +that that Center Point is I * Delta +X that that's what that's where that + + align:start position:0% +X that that's what that's where that + + + align:start position:0% +X that that's what that's where that +that's where I would be looking so that + + align:start position:0% +that's where I would be looking so that + + + align:start position:0% +that's where I would be looking so that +now I'm using + + align:start position:0% +now I'm using + + + align:start position:0% +now I'm using +subscript it's a it's a little bit of + + align:start position:0% +subscript it's a it's a little bit of + + + align:start position:0% +subscript it's a it's a little bit of +practice then to take + + align:start position:0% +practice then to take + + + align:start position:0% +practice then to take +subscripts take this way of writing the + + align:start position:0% +subscripts take this way of writing the + + + align:start position:0% +subscripts take this way of writing the +equation and convert it to a matrix way + + align:start position:0% +equation and convert it to a matrix way + + + align:start position:0% +equation and convert it to a matrix way +I it's it's usually clearer once you see + + align:start position:0% +I it's it's usually clearer once you see + + + align:start position:0% +I it's it's usually clearer once you see +it as a matrix okay now this is this is + + align:start position:0% +it as a matrix okay now this is this is + + + align:start position:0% +it as a matrix okay now this is this is +happening at all the points at at I + + align:start position:0% +happening at all the points at at I + + + align:start position:0% +happening at all the points at at I +equal I + + align:start position:0% +equal I + + + align:start position:0% +equal I +equal at at I equal one let's say I have + + align:start position:0% +equal at at I equal one let's say I have + + + align:start position:0% +equal at at I equal one let's say I have +minus u0 + 2 U1 minus U2 + + align:start position:0% +minus u0 + 2 U1 minus U2 + + + align:start position:0% +minus u0 + 2 U1 minus U2 +is uh F at is the match agrees with the + + align:start position:0% +is uh F at is the match agrees with the + + + align:start position:0% +is uh F at is the match agrees with the +load + + align:start position:0% +load + + + align:start position:0% +load +at the first mesh Point that's the + + align:start position:0% +at the first mesh Point that's the + + + align:start position:0% +at the first mesh Point that's the +center the point H Delta X okay okay and + + align:start position:0% +center the point H Delta X okay okay and + + + align:start position:0% +center the point H Delta X okay okay and +then if I want to back up further I + + align:start position:0% +then if I want to back up further I + + + align:start position:0% +then if I want to back up further I +would have minus U minus one but that + + align:start position:0% +would have minus U minus one but that + + + align:start position:0% +would have minus U minus one but that +doesn't really exist plus 2 U 0us + + align:start position:0% +doesn't really exist plus 2 U 0us + + + align:start position:0% +doesn't really exist plus 2 U 0us +U1 would be the should match the load at + + align:start position:0% +U1 would be the should match the load at + + + align:start position:0% +U1 would be the should match the load at +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so and so on forward but now I want + + align:start position:0% +okay so and so on forward but now I want + + + align:start position:0% +okay so and so on forward but now I want +to put in the boundary condition that's + + align:start position:0% +to put in the boundary condition that's + + + align:start position:0% +to put in the boundary condition that's +what you want me to do right put in this + + align:start position:0% +what you want me to do right put in this + + + align:start position:0% +what you want me to do right put in this +boundary condition so what am I going to + + align:start position:0% +boundary condition so what am I going to + + + align:start position:0% +boundary condition so what am I going to +take as boundary + + align:start position:0% + + + + align:start position:0% + +condition my I it should it has to be + + align:start position:0% +condition my I it should it has to be + + + align:start position:0% +condition my I it should it has to be +some approximation to U Prime of 0 + + align:start position:0% +some approximation to U Prime of 0 + + + align:start position:0% +some approximation to U Prime of 0 +equals + + align:start position:0% +equals + + + align:start position:0% +equals +0 maybe I'm never going to get to minus + + align:start position:0% +0 maybe I'm never going to get to minus + + + align:start position:0% +0 maybe I'm never going to get to minus +one maybe I don't need minus one + + align:start position:0% +one maybe I don't need minus one + + + align:start position:0% +one maybe I don't need minus one +yeah we yeah yeah we we previously + + align:start position:0% +yeah we yeah yeah we we previously + + + align:start position:0% +yeah we yeah yeah we we previously +learned that if you do the forward + + align:start position:0% +learned that if you do the forward + + + align:start position:0% +learned that if you do the forward +difference for the derivative and + + align:start position:0% +difference for the derivative and + + + align:start position:0% +difference for the derivative and +there's inherent error that's right was + + align:start position:0% +there's inherent error that's right was + + + align:start position:0% +there's inherent error that's right was +the yeah exactly so but in these + + align:start position:0% +the yeah exactly so but in these + + + align:start position:0% +the yeah exactly so but in these +examples it appears that's what we chose + + align:start position:0% +examples it appears that's what we chose + + + align:start position:0% +examples it appears that's what we chose +to do we did that's what we knew about + + align:start position:0% +to do we did that's what we knew about + + + align:start position:0% +to do we did that's what we knew about +said before we knew about four were + + align:start position:0% +said before we knew about four were + + + align:start position:0% +said before we knew about four were +different so I I chose to do + + align:start position:0% +different so I I chose to do + + + align:start position:0% +different so I I chose to do +it + + align:start position:0% +it + + + align:start position:0% +it +um but then I'd think better of it yeah + + align:start position:0% +um but then I'd think better of it yeah + + + align:start position:0% +um but then I'd think better of it yeah +I I chose to do it because it made the + + align:start position:0% +I I chose to do it because it made the + + + align:start position:0% +I I chose to do it because it made the +point that we that at that boundary we + + align:start position:0% +point that we that at that boundary we + + + align:start position:0% +point that we that at that boundary we +were introducing a a higher order error + + align:start position:0% +were introducing a a higher order error + + + align:start position:0% +were introducing a a higher order error +first order error that U that that's + + align:start position:0% +first order error that U that that's + + + align:start position:0% +first order error that U that that's +going to wreck things I mean it's going + + align:start position:0% +going to wreck things I mean it's going + + + align:start position:0% +going to wreck things I mean it's going +to spoil the this is second order + + align:start position:0% +to spoil the this is second order + + + align:start position:0% +to spoil the this is second order +accuracy and but let me do that fir that + + align:start position:0% +accuracy and but let me do that fir that + + + align:start position:0% +accuracy and but let me do that fir that +first order so what shall I take I'm + + align:start position:0% +first order so what shall I take I'm + + + align:start position:0% +first order so what shall I take I'm +going to approximate that by you shall I + + align:start position:0% +going to approximate that by you shall I + + + align:start position:0% +going to approximate that by you shall I +take this one as I did in + + align:start position:0% + + + + align:start position:0% + +class okay + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yes oh plus one thanks plus one right + + align:start position:0% +yes oh plus one thanks plus one right + + + align:start position:0% +yes oh plus one thanks plus one right +thanks thank you + + align:start position:0% +thanks thank you + + + align:start position:0% +thanks thank you +good Okie + + align:start position:0% +good Okie + + + align:start position:0% +good Okie +doie all right so yeah this is how we + + align:start position:0% +doie all right so yeah this is how we + + + align:start position:0% +doie all right so yeah this is how we +got to that equation by I if I now bring + + align:start position:0% +got to that equation by I if I now bring + + + align:start position:0% +got to that equation by I if I now bring +in this boundary condition I guess I + + align:start position:0% +in this boundary condition I guess I + + + align:start position:0% +in this boundary condition I guess I +don't have to let me let me take your + + align:start position:0% +don't have to let me let me take your + + + align:start position:0% +don't have to let me let me take your +eye off of that guy for the moment I + + align:start position:0% +eye off of that guy for the moment I + + + align:start position:0% +eye off of that guy for the moment I +think + + align:start position:0% +think + + + align:start position:0% +think +uh we're getting beautiful music here is + + align:start position:0% +uh we're getting beautiful music here is + + + align:start position:0% +uh we're getting beautiful music here is +it coming out of this box or no what + + align:start position:0% +it coming out of this box or no what + + + align:start position:0% +it coming out of this box or no what +anyway okay + + align:start position:0% +anyway okay + + + align:start position:0% +anyway okay +uh okay so I'm going to use this + + align:start position:0% +uh okay so I'm going to use this + + + align:start position:0% +uh okay so I'm going to use this +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +condition to say well okay if U1 is u0 + + align:start position:0% +condition to say well okay if U1 is u0 + + + align:start position:0% +condition to say well okay if U1 is u0 +I'm going to replace this u0 by U1 yeah + + align:start position:0% +I'm going to replace this u0 by U1 yeah + + + align:start position:0% +I'm going to replace this u0 by U1 yeah +yeah that's what I that that's this is + + align:start position:0% +yeah that's what I that that's this is + + + align:start position:0% +yeah that's what I that that's this is +the dire way I replace that u0 by U1 in + + align:start position:0% +the dire way I replace that u0 by U1 in + + + align:start position:0% +the dire way I replace that u0 by U1 in +that in that first equation and then + + align:start position:0% +that in that first equation and then + + + align:start position:0% +that in that first equation and then +what I have is minus U1 and two U1 so + + align:start position:0% +what I have is minus U1 and two U1 so + + + align:start position:0% +what I have is minus U1 and two U1 so +that's the one and I have the minus U2 + + align:start position:0% +that's the one and I have the minus U2 + + + align:start position:0% +that's the one and I have the minus U2 +so so do you see that that + + align:start position:0% +so so do you see that that + + + align:start position:0% +so so do you see that that +equation when I put those together into + + align:start position:0% +equation when I put those together into + + + align:start position:0% +equation when I put those together into +a one is is going + + align:start position:0% +a one is is going + + + align:start position:0% +a one is is going +to uh if this is + + align:start position:0% +to uh if this is + + + align:start position:0% +to uh if this is +U1 this is U2 this is u3 onwards that + + align:start position:0% +U1 this is U2 this is u3 onwards that + + + align:start position:0% +U1 this is U2 this is u3 onwards that +first first equation is U1 minus + + align:start position:0% +first first equation is U1 minus + + + align:start position:0% +first first equation is U1 minus +U2 and that's what I've got that's this + + align:start position:0% +U2 and that's what I've got that's this + + + align:start position:0% +U2 and that's what I've got that's this +this is U1 minus U2 yeah yeah yeah so I + + align:start position:0% +this is U1 minus U2 yeah yeah yeah so I + + + align:start position:0% +this is U1 minus U2 yeah yeah yeah so I +did it I got to that Matrix The Matrix + + align:start position:0% +did it I got to that Matrix The Matrix + + + align:start position:0% +did it I got to that Matrix The Matrix +is actually quite an important Matrix + + align:start position:0% +is actually quite an important Matrix + + + align:start position:0% +is actually quite an important Matrix +but from the point of view of accuracy + + align:start position:0% +but from the point of view of accuracy + + + align:start position:0% +but from the point of view of accuracy +in solving this differential equation + + align:start position:0% +in solving this differential equation + + + align:start position:0% +in solving this differential equation +it's not the greatest it's it's a lost + + align:start position:0% +it's not the greatest it's it's a lost + + + align:start position:0% +it's not the greatest it's it's a lost +accuracy at that point but + + align:start position:0% +accuracy at that point but + + + align:start position:0% +accuracy at that point but +the the way to recover it turned out to + + align:start position:0% +the the way to recover it turned out to + + + align:start position:0% +the the way to recover it turned out to +be just a small adjustment at the + + align:start position:0% +be just a small adjustment at the + + + align:start position:0% +be just a small adjustment at the +boundary so not not a problem thanks + + align:start position:0% +boundary so not not a problem thanks + + + align:start position:0% +boundary so not not a problem thanks +that's good yes thanks what would it + + align:start position:0% +that's good yes thanks what would it + + + align:start position:0% +that's good yes thanks what would it +mean physically is sorry what what would + + align:start position:0% +mean physically is sorry what what would + + + align:start position:0% +mean physically is sorry what what would +it mean physically the boundary + + align:start position:0% +it mean physically the boundary + + + align:start position:0% +it mean physically the boundary +conditions were both at the same + + align:start position:0% +conditions were both at the same + + + align:start position:0% +conditions were both at the same +point when the boundary sorry two + + align:start position:0% +point when the boundary sorry two + + + align:start position:0% +point when the boundary sorry two +boundary conditions at the same point + + align:start position:0% +boundary conditions at the same point + + + align:start position:0% +boundary conditions at the same point +who that's a good question Okay so so + + align:start position:0% +who that's a good question Okay so so + + + align:start position:0% +who that's a good question Okay so so +when would we have two so you're instead + + align:start position:0% +when would we have two so you're instead + + + align:start position:0% +when would we have two so you're instead +of a boundary condition at zero and a + + align:start position:0% +of a boundary condition at zero and a + + + align:start position:0% +of a boundary condition at zero and a +boundary condition at one you're putting + + align:start position:0% +boundary condition at one you're putting + + + align:start position:0% +boundary condition at one you're putting +them is that what you mean put both + + align:start position:0% +them is that what you mean put both + + + align:start position:0% +them is that what you mean put both +boundary conditions at the end okay so + + align:start position:0% +boundary conditions at the end okay so + + + align:start position:0% +boundary conditions at the end okay so +that would be I would that would happen + + align:start position:0% +that would be I would that would happen + + + align:start position:0% +that would be I would that would happen +I I would think that would be more it + + align:start position:0% +I I would think that would be more it + + + align:start position:0% +I I would think that would be more it +would be very typical in uh let me see + + align:start position:0% +would be very typical in uh let me see + + + align:start position:0% +would be very typical in uh let me see +if there's some space here yeah that + + align:start position:0% +if there's some space here yeah that + + + align:start position:0% +if there's some space here yeah that +would be very typical and we will do + + align:start position:0% +would be very typical and we will do + + + align:start position:0% +would be very typical and we will do +it uh um can I change X to T because + + align:start position:0% +it uh um can I change X to T because + + + align:start position:0% +it uh um can I change X to T because +that's what if I if I if I have + + align:start position:0% +that's what if I if I if I have + + + align:start position:0% +that's what if I if I if I have +some this this yeah how how what does + + align:start position:0% +some this this yeah how how what does + + + align:start position:0% +some this this yeah how how what does +this problem look like and U of0 equals + + align:start position:0% +this problem look like and U of0 equals + + + align:start position:0% +this problem look like and U of0 equals +let's say zero and U Prime of zero both + + align:start position:0% +let's say zero and U Prime of zero both + + + align:start position:0% +let's say zero and U Prime of zero both +at the same at the start equals H zero + + align:start position:0% +at the same at the start equals H zero + + + align:start position:0% +at the same at the start equals H zero +or + + align:start position:0% +or + + + align:start position:0% +or +whatever so what kind of a problem is + + align:start position:0% +whatever so what kind of a problem is + + + align:start position:0% +whatever so what kind of a problem is +that that's now these are I would say + + align:start position:0% +that that's now these are I would say + + + align:start position:0% +that that's now these are I would say +initial values initial values instead of + + align:start position:0% +initial values initial values instead of + + + align:start position:0% +initial values initial values instead of +boundary values I now have initial + + align:start position:0% +boundary values I now have initial + + + align:start position:0% +boundary values I now have initial +values and can I solve it + + align:start position:0% +values and can I solve it + + + align:start position:0% +values and can I solve it +yes uh so I'm starting at time Z this is + + align:start position:0% +yes uh so I'm starting at time Z this is + + + align:start position:0% +yes uh so I'm starting at time Z this is +T equals 0 I'm starting at I'm starting + + align:start position:0% +T equals 0 I'm starting at I'm starting + + + align:start position:0% +T equals 0 I'm starting at I'm starting +at + + align:start position:0% +at + + + align:start position:0% +at +rest nothing no no velocity actually no + + align:start position:0% +rest nothing no no velocity actually no + + + align:start position:0% +rest nothing no no velocity actually no +displacement and just going forward in + + align:start position:0% +displacement and just going forward in + + + align:start position:0% +displacement and just going forward in +time so uh uh I could solve that + + align:start position:0% +time so uh uh I could solve that + + + align:start position:0% +time so uh uh I could solve that +differential equation I'd be interested + + align:start position:0% +differential equation I'd be interested + + + align:start position:0% +differential equation I'd be interested +in the corresponding difference equation + + align:start position:0% +in the corresponding difference equation + + + align:start position:0% +in the corresponding difference equation +uh + + align:start position:0% +uh + + + align:start position:0% +uh +all all fine it's a it's a different + + align:start position:0% +all all fine it's a it's a different + + + align:start position:0% +all all fine it's a it's a different +category of problem this is an initial + + align:start position:0% +category of problem this is an initial + + + align:start position:0% +category of problem this is an initial +value + + align:start position:0% +value + + + align:start position:0% +value +problem like a wave like uh well uh yeah + + align:start position:0% +problem like a wave like uh well uh yeah + + + align:start position:0% +problem like a wave like uh well uh yeah +so I mean it's like tracking some + + align:start position:0% +so I mean it's like tracking some + + + align:start position:0% +so I mean it's like tracking some +uh Mass that's uh uh some + + align:start position:0% +uh Mass that's uh uh some + + + align:start position:0% +uh Mass that's uh uh some +satellite uh that so that's what you're + + align:start position:0% +satellite uh that so that's what you're + + + align:start position:0% +satellite uh that so that's what you're +doing in tracking a + + align:start position:0% +doing in tracking a + + + align:start position:0% +doing in tracking a +satellite or or or a planet or something + + align:start position:0% +satellite or or or a planet or something + + + align:start position:0% +satellite or or or a planet or something +the the uh + + align:start position:0% +the the uh + + + align:start position:0% +the the uh +yeah tracking a planet or a satellite + + align:start position:0% +yeah tracking a planet or a satellite + + + align:start position:0% +yeah tracking a planet or a satellite +you're you're solving equations like + + align:start position:0% +you're you're solving equations like + + + align:start position:0% +you're you're solving equations like +this forward in time you you know the + + align:start position:0% +this forward in time you you know the + + + align:start position:0% +this forward in time you you know the +initial position and you know the forces + + align:start position:0% +initial position and you know the forces + + + align:start position:0% +initial position and you know the forces +acting on it probably gravity and and + + align:start position:0% +acting on it probably gravity and and + + + align:start position:0% +acting on it probably gravity and and +you go forward in time + + align:start position:0% + + + + align:start position:0% + +yes what would the Matrix be huh good + + align:start position:0% +yes what would the Matrix be huh good + + + align:start position:0% +yes what would the Matrix be huh good +question what would the Matrix look + + align:start position:0% +question what would the Matrix look + + + align:start position:0% +question what would the Matrix look +like so this + + align:start position:0% +like so this + + + align:start position:0% +like so this +is okay so an electrical engineer would + + align:start position:0% +is okay so an electrical engineer would + + + align:start position:0% +is okay so an electrical engineer would +call a problem like this and the kind of + + align:start position:0% +call a problem like this and the kind of + + + align:start position:0% +call a problem like this and the kind of +Matrix that I'm going to write down I + + align:start position:0% +Matrix that I'm going to write down I + + + align:start position:0% +Matrix that I'm going to write down I +think would be called causal I that word + + align:start position:0% +think would be called causal I that word + + + align:start position:0% +think would be called causal I that word +just popped into my head so let me + + align:start position:0% +just popped into my head so let me + + + align:start position:0% +just popped into my head so let me +mention it + + align:start position:0% +mention it + + + align:start position:0% +mention it +you know part of Science and Engineering + + align:start position:0% +you know part of Science and Engineering + + + align:start position:0% +you know part of Science and Engineering +a big part of it is learning language + + align:start position:0% +a big part of it is learning language + + + align:start position:0% +a big part of it is learning language +learning words and and you have to learn + + align:start position:0% +learning words and and you have to learn + + + align:start position:0% +learning words and and you have to learn +uh sort of the math + + align:start position:0% +uh sort of the math + + + align:start position:0% +uh sort of the math +language and the engineering language + + align:start position:0% +language and the engineering language + + + align:start position:0% +language and the engineering language +for + + align:start position:0% +for + + + align:start position:0% +for +whatever you're focusing on but it's + + align:start position:0% +whatever you're focusing on but it's + + + align:start position:0% +whatever you're focusing on but it's +good also to know a few other languages + + align:start position:0% +good also to know a few other languages + + + align:start position:0% +good also to know a few other languages +and uh electrical engineering languages + + align:start position:0% +and uh electrical engineering languages + + + align:start position:0% +and uh electrical engineering languages +of filters and and causal and other + + align:start position:0% +of filters and and causal and other + + + align:start position:0% +of filters and and causal and other +things that we'll see uh are important + + align:start position:0% +things that we'll see uh are important + + + align:start position:0% +things that we'll see uh are important +what would the Matrix look + + align:start position:0% +what would the Matrix look + + + align:start position:0% +what would the Matrix look +like here's what I think it would + + align:start position:0% +like here's what I think it would + + + align:start position:0% +like here's what I think it would +be I I I've made this a A plus there + + align:start position:0% +be I I I've made this a A plus there + + + align:start position:0% +be I I I've made this a A plus there +just so I'll have to remember that I + + align:start position:0% +just so I'll have to remember that I + + + align:start position:0% +just so I'll have to remember that I +think so I'm looking at U not U1 no well + + align:start position:0% +think so I'm looking at U not U1 no well + + + align:start position:0% +think so I'm looking at U not U1 no well +you not I actually know so let me start + + align:start position:0% +you not I actually know so let me start + + + align:start position:0% +you not I actually know so let me start +with U1 U2 + + align:start position:0% +with U1 U2 + + + align:start position:0% +with U1 U2 +u3 + + align:start position:0% +u3 + + + align:start position:0% +u3 +u4 what would a typical equal some right + + align:start position:0% +u4 what would a typical equal some right + + + align:start position:0% +u4 what would a typical equal some right +side fub1 F2 F3 F4 what do you think + + align:start position:0% +side fub1 F2 F3 F4 what do you think + + + align:start position:0% +side fub1 F2 F3 F4 what do you think +what kind of a matrix am I going to + + align:start position:0% +what kind of a matrix am I going to + + + align:start position:0% +what kind of a matrix am I going to +get before I put it in + + align:start position:0% +get before I put it in + + + align:start position:0% +get before I put it in +there this is a good question what's the + + align:start position:0% +there this is a good question what's the + + + align:start position:0% +there this is a good question what's the +shape of this matrix it's going to + + align:start position:0% +shape of this matrix it's going to + + + align:start position:0% +shape of this matrix it's going to +be + + align:start position:0% +be + + + align:start position:0% +be +triangular instead of being symmetric + + align:start position:0% +triangular instead of being symmetric + + + align:start position:0% +triangular instead of being symmetric +it's going to be triangular I'm going to + + align:start position:0% +it's going to be triangular I'm going to + + + align:start position:0% +it's going to be triangular I'm going to +find let's see a typical value would be + + align:start position:0% +find let's see a typical value would be + + + align:start position:0% +find let's see a typical value would be +say + + align:start position:0% + + + + align:start position:0% + +u3 I because I've used a plus sign oops + + align:start position:0% +u3 I because I've used a plus sign oops + + + align:start position:0% +u3 I because I've used a plus sign oops +I can't make myself do it right uh 1 - 2 + + align:start position:0% +I can't make myself do it right uh 1 - 2 + + + align:start position:0% +I can't make myself do it right uh 1 - 2 +1 that would say + + align:start position:0% +1 that would say + + + align:start position:0% +1 that would say +u3 - 2 u2s plus + + align:start position:0% + + + + align:start position:0% + +U1 would be the new Force this is the + + align:start position:0% +U1 would be the new Force this is the + + + align:start position:0% +U1 would be the new Force this is the +kind of thing we're going to get one one + + align:start position:0% +kind of thing we're going to get one one + + + align:start position:0% +kind of thing we're going to get one one +maybe one something I don't know what + + align:start position:0% +maybe one something I don't know what + + + align:start position:0% +maybe one something I don't know what +this this is up in the Bound in the + + align:start position:0% +this this is up in the Bound in the + + + align:start position:0% +this this is up in the Bound in the +initial values but from now on they'll + + align:start position:0% +initial values but from now on they'll + + + align:start position:0% +initial values but from now on they'll +be it'll be below the diagonal minus + + align:start position:0% +be it'll be below the diagonal minus + + + align:start position:0% +be it'll be below the diagonal minus +it'll be 1 - + + align:start position:0% +it'll be 1 - + + + align:start position:0% +it'll be 1 - +2 one do you + + align:start position:0% +2 one do you + + + align:start position:0% +2 one do you +see we're + + align:start position:0% +see we're + + + align:start position:0% +see we're +marching that's we're we're marching + + align:start position:0% + + + + align:start position:0% + +forward we we start by knowing the + + align:start position:0% +forward we we start by knowing the + + + align:start position:0% +forward we we start by knowing the +and then the equation tells us the next + + align:start position:0% +and then the equation tells us the next + + + align:start position:0% +and then the equation tells us the next +one then the equation tells us the next + + align:start position:0% +one then the equation tells us the next + + + align:start position:0% +one then the equation tells us the next +one that's what initial value problems + + align:start position:0% +one that's what initial value problems + + + align:start position:0% +one that's what initial value problems +do you're told how you begin and you + + align:start position:0% +do you're told how you begin and you + + + align:start position:0% +do you're told how you begin and you +take step you take a step take a step + + align:start position:0% +take step you take a step take a step + + + align:start position:0% +take step you take a step take a step +every time and that that the new value + + align:start position:0% +every time and that that the new value + + + align:start position:0% +every time and that that the new value +just needs to know the older + + align:start position:0% +just needs to know the older + + + align:start position:0% +just needs to know the older +values you see the big difference + + align:start position:0% +values you see the big difference + + + align:start position:0% +values you see the big difference +between that and our problems here our + + align:start position:0% +between that and our problems here our + + + align:start position:0% +between that and our problems here our +problem is looking left and right + + align:start position:0% +problem is looking left and right + + + align:start position:0% +problem is looking left and right +looking back and forward back for one + + align:start position:0% +looking back and forward back for one + + + align:start position:0% +looking back and forward back for one +condition forward for another we start + + align:start position:0% +condition forward for another we start + + + align:start position:0% +condition forward for another we start +with one but we're it's more of + + align:start position:0% +with one but we're it's more of + + + align:start position:0% +with one but we're it's more of +a it's like a hitting problem we we we + + align:start position:0% +a it's like a hitting problem we we we + + + align:start position:0% +a it's like a hitting problem we we we +start for marching forward in our + + align:start position:0% +start for marching forward in our + + + align:start position:0% +start for marching forward in our +problems but we have to hit the other + + align:start position:0% +problems but we have to hit the other + + + align:start position:0% +problems but we have to hit the other +end correctly we don't know the slope we + + align:start position:0% +end correctly we don't know the slope we + + + align:start position:0% +end correctly we don't know the slope we +don't know the starting slope we we know + + align:start position:0% +don't know the starting slope we we know + + + align:start position:0% +don't know the starting slope we we know +what we want to hit + + align:start position:0% +what we want to hit + + + align:start position:0% +what we want to hit +whereas uh + + align:start position:0% +whereas uh + + + align:start position:0% +whereas uh +these problems we're told how we start + + align:start position:0% +these problems we're told how we start + + + align:start position:0% +these problems we're told how we start +and we just follow it in time yeah so + + align:start position:0% +and we just follow it in time yeah so + + + align:start position:0% +and we just follow it in time yeah so +that that's the difference here and + + align:start position:0% +that that's the difference here and + + + align:start position:0% +that that's the difference here and +uh uh yeah sure two questions about that + + align:start position:0% +uh uh yeah sure two questions about that + + + align:start position:0% +uh uh yeah sure two questions about that +okay CHR you wrote that you have U zero + + align:start position:0% +okay CHR you wrote that you have U zero + + + align:start position:0% +okay CHR you wrote that you have U zero +but we also have U1 if we use a forward + + align:start position:0% +but we also have U1 if we use a forward + + + align:start position:0% +but we also have U1 if we use a forward +difference U1 will be zero that's true + + align:start position:0% +difference U1 will be zero that's true + + + align:start position:0% +difference U1 will be zero that's true +so then that would be part of the so + + align:start position:0% +so then that would be part of the so + + + align:start position:0% +so then that would be part of the so +this will not be this will be known yeah + + align:start position:0% +this will not be this will be known yeah + + + align:start position:0% +this will not be this will be known yeah +that'll be known yeah U1 will also be + + align:start position:0% +that'll be known yeah U1 will also be + + + align:start position:0% +that'll be known yeah U1 will also be +known yeah and and really I should maybe + + align:start position:0% +known yeah and and really I should maybe + + + align:start position:0% +known yeah and and really I should maybe +I should have got let me let me put even + + align:start position:0% +I should have got let me let me put even + + + align:start position:0% +I should have got let me let me put even +the other known one okay so we we know + + align:start position:0% +the other known one okay so we we know + + + align:start position:0% +the other known one okay so we we know +this we know this so th those are sort + + align:start position:0% +this we know this so th those are sort + + + align:start position:0% +this we know this so th those are sort +of not in our yeah I that shouldn't be + + align:start position:0% +of not in our yeah I that shouldn't be + + + align:start position:0% +of not in our yeah I that shouldn't be +in our problem some somehow and my + + align:start position:0% +in our problem some somehow and my + + + align:start position:0% +in our problem some somehow and my +question the final question is the last + + align:start position:0% +question the final question is the last + + + align:start position:0% +question the final question is the last +row would also indicate a boundary + + align:start position:0% +row would also indicate a boundary + + + align:start position:0% +row would also indicate a boundary +condition is this no no I think what + + align:start position:0% +condition is this no no I think what + + + align:start position:0% +condition is this no no I think what +would we get at the end no I don't I you + + align:start position:0% +would we get at the end no I don't I you + + + align:start position:0% +would we get at the end no I don't I you +get the one you're always looking back + + align:start position:0% +get the one you're always looking back + + + align:start position:0% +get the one you're always looking back +that's the point lower triangular + + align:start position:0% +that's the point lower triangular + + + align:start position:0% +that's the point lower triangular +matrices are always looking they only + + align:start position:0% +matrices are always looking they only + + + align:start position:0% +matrices are always looking they only +Look Backwards for earlier values and + + align:start position:0% +Look Backwards for earlier values and + + + align:start position:0% +Look Backwards for earlier values and +then they give you the current value so + + align:start position:0% +then they give you the current value so + + + align:start position:0% +then they give you the current value so +that's why lower triangular matrices are + + align:start position:0% +that's why lower triangular matrices are + + + align:start position:0% +that's why lower triangular matrices are +so easy to invert no problem if it's + + align:start position:0% +so easy to invert no problem if it's + + + align:start position:0% +so easy to invert no problem if it's +lower triangular you just like March + + align:start position:0% +lower triangular you just like March + + + align:start position:0% +lower triangular you just like March +forward and if it's upper triangular + + align:start position:0% +forward and if it's upper triangular + + + align:start position:0% +forward and if it's upper triangular +which way do you + + align:start position:0% +which way do you + + + align:start position:0% +which way do you +March so if you get have an upper + + align:start position:0% +March so if you get have an upper + + + align:start position:0% +March so if you get have an upper +triangular problem suppose I gave you + + align:start position:0% +triangular problem suppose I gave you + + + align:start position:0% +triangular problem suppose I gave you +the problem uh + + align:start position:0% +the problem uh + + + align:start position:0% +the problem uh +let me make it upper triangular so x + y + + align:start position:0% +let me make it upper triangular so x + y + + + align:start position:0% +let me make it upper triangular so x + y ++ z = + + align:start position:0% ++ z = + + + align:start position:0% ++ z = +7 uh 2 y + 3 Z = 12 and Z = + + align:start position:0% +7 uh 2 y + 3 Z = 12 and Z = + + + align:start position:0% +7 uh 2 y + 3 Z = 12 and Z = +17 what so that's upper + + align:start position:0% +17 what so that's upper + + + align:start position:0% +17 what so that's upper +triangular where do we start in solving + + align:start position:0% +triangular where do we start in solving + + + align:start position:0% +triangular where do we start in solving +that one from the bottom from the from + + align:start position:0% +that one from the bottom from the from + + + align:start position:0% +that one from the bottom from the from +the right hand end the bottom and we + + align:start position:0% +the right hand end the bottom and we + + + align:start position:0% +the right hand end the bottom and we +March backwards in + + align:start position:0% +March backwards in + + + align:start position:0% +March backwards in +time and what I was saying about AAL L * + + align:start position:0% +time and what I was saying about AAL L * + + + align:start position:0% +time and what I was saying about AAL L * +U yeah here's this is worth seeing what + + align:start position:0% +U yeah here's this is worth seeing what + + + align:start position:0% +U yeah here's this is worth seeing what +I was saying about AAL L * U it was you + + align:start position:0% +I was saying about AAL L * U it was you + + + align:start position:0% +I was saying about AAL L * U it was you +remember + + align:start position:0% +remember + + + align:start position:0% +remember +that those those letters what that was + + align:start position:0% +that those those letters what that was + + + align:start position:0% +that those those letters what that was +saying was that this this Matrix that's + + align:start position:0% +saying was that this this Matrix that's + + + align:start position:0% +saying was that this this Matrix that's +looking both ways can be written as a + + align:start position:0% +looking both ways can be written as a + + + align:start position:0% +looking both ways can be written as a +product of a matrix L that looks only + + align:start position:0% +product of a matrix L that looks only + + + align:start position:0% +product of a matrix L that looks only +looks behind for old values and and you + + align:start position:0% +looks behind for old values and and you + + + align:start position:0% +looks behind for old values and and you +can go forward with it that and the + + align:start position:0% +can go forward with it that and the + + + align:start position:0% +can go forward with it that and the +Matrix U like this one this upper + + align:start position:0% +Matrix U like this one this upper + + + align:start position:0% +Matrix U like this one this upper +triangular 11 one1 Zer below the + + align:start position:0% +triangular 11 one1 Zer below the + + + align:start position:0% +triangular 11 one1 Zer below the +diagonal that you go backward with that + + align:start position:0% +diagonal that you go backward with that + + + align:start position:0% +diagonal that you go backward with that +that's somehow that's appealing it's + + align:start position:0% +that's somehow that's appealing it's + + + align:start position:0% +that's somehow that's appealing it's +like aesthetic to to break up uh a + + align:start position:0% +like aesthetic to to break up uh a + + + align:start position:0% +like aesthetic to to break up uh a +two-way problem into a problem that + + align:start position:0% +two-way problem into a problem that + + + align:start position:0% +two-way problem into a problem that +marches one way and then the other yeah + + align:start position:0% +marches one way and then the other yeah + + + align:start position:0% +marches one way and then the other yeah +and that's uh and of course that's what + + align:start position:0% +and that's uh and of course that's what + + + align:start position:0% +and that's uh and of course that's what +elimination what aims for is this + + align:start position:0% +elimination what aims for is this + + + align:start position:0% +elimination what aims for is this +problem that it can solve by the words + + align:start position:0% +problem that it can solve by the words + + + align:start position:0% +problem that it can solve by the words +would be back substitution when you've + + align:start position:0% +would be back substitution when you've + + + align:start position:0% +would be back substitution when you've +started with your original problem got + + align:start position:0% +started with your original problem got + + + align:start position:0% +started with your original problem got +to this one then you just have a back + + align:start position:0% +to this one then you just have a back + + + align:start position:0% +to this one then you just have a back +substitution you go backwards right oh + + align:start position:0% +substitution you go backwards right oh + + + align:start position:0% +substitution you go backwards right oh +so much I mean I'll mention the calman + + align:start position:0% +so much I mean I'll mention the calman + + + align:start position:0% +so much I mean I'll mention the calman +filter that's a similar process of uh + + align:start position:0% +filter that's a similar process of uh + + + align:start position:0% +filter that's a similar process of uh +going forward that's called prediction + + align:start position:0% +going forward that's called prediction + + + align:start position:0% +going forward that's called prediction +going backward that's called smoothing + + align:start position:0% +going backward that's called smoothing + + + align:start position:0% +going backward that's called smoothing +and so calman had the great idea that he + + align:start position:0% +and so calman had the great idea that he + + + align:start position:0% +and so calman had the great idea that he +could break these uh these uh problems + + align:start position:0% +could break these uh these uh problems + + + align:start position:0% +could break these uh these uh problems +that were fundamental in space uh + + align:start position:0% +that were fundamental in space uh + + + align:start position:0% +that were fundamental in space uh +computations into um into uh for + + align:start position:0% +computations into um into uh for + + + align:start position:0% +computations into um into uh for +prediction and uh + + align:start position:0% +prediction and uh + + + align:start position:0% +prediction and uh +smoothing okay once again we've got off + + align:start position:0% +smoothing okay once again we've got off + + + align:start position:0% +smoothing okay once again we've got off +yes um so you today you introduced the + + align:start position:0% +yes um so you today you introduced the + + + align:start position:0% +yes um so you today you introduced the +uh the be there was a very good Vis + + align:start position:0% +uh the be there was a very good Vis + + + align:start position:0% +uh the be there was a very good Vis +visual oh the be okay yeah right so help + + align:start position:0% +visual oh the be okay yeah right so help + + + align:start position:0% +visual oh the be okay yeah right so help +me visualize what this was all about let + + align:start position:0% +me visualize what this was all about let + + + align:start position:0% +me visualize what this was all about let +me help you even more before before the + + align:start position:0% +me help you even more before before the + + + align:start position:0% +me help you even more before before the +question I should it's better to draw + + align:start position:0% +question I should it's better to draw + + + align:start position:0% +question I should it's better to draw +the + + align:start position:0% +the + + + align:start position:0% +the +beam this + + align:start position:0% +beam this + + + align:start position:0% +beam this +way I like that the beam better this way + + align:start position:0% +way I like that the beam better this way + + + align:start position:0% +way I like that the beam better this way +because the point of the beam problem is + + align:start position:0% +because the point of the beam problem is + + + align:start position:0% +because the point of the beam problem is +loads are acting and and we'll see this + + align:start position:0% +loads are acting and and we'll see this + + + align:start position:0% +loads are acting and and we'll see this +of course later loads are + + align:start position:0% +of course later loads are + + + align:start position:0% +of course later loads are +acting perpendicular to the direction of + + align:start position:0% +acting perpendicular to the direction of + + + align:start position:0% +acting perpendicular to the direction of +the beam that's that's why the beam + + align:start position:0% +the beam that's that's why the beam + + + align:start position:0% +the beam that's that's why the beam +bends so it'll bend a little + + align:start position:0% +bends so it'll bend a little + + + align:start position:0% +bends so it'll bend a little +right and that that is what leads us + + align:start position:0% +right and that that is what leads us + + + align:start position:0% +right and that that is what leads us +it's bending moments and other stuff I + + align:start position:0% +it's bending moments and other stuff I + + + align:start position:0% +it's bending moments and other stuff I +if you haven't met beams well it it'll + + align:start position:0% +if you haven't met beams well it it'll + + + align:start position:0% +if you haven't met beams well it it'll +be great to just have a very half a + + align:start position:0% +be great to just have a very half a + + + align:start position:0% +be great to just have a very half a +lecture about or maybe a lecture about + + align:start position:0% +lecture about or maybe a lecture about + + + align:start position:0% +lecture about or maybe a lecture about +beams uh that gives a fourth order + + align:start position:0% +beams uh that gives a fourth order + + + align:start position:0% +beams uh that gives a fourth order +equation uh that I'll write down again + + align:start position:0% +equation uh that I'll write down again + + + align:start position:0% +equation uh that I'll write down again +fourth derivative equal the load yeah + + align:start position:0% +fourth derivative equal the load yeah + + + align:start position:0% +fourth derivative equal the load yeah +now ready so so this is kind the + + align:start position:0% +now ready so so this is kind the + + + align:start position:0% +now ready so so this is kind the +question I'm understanding why you + + align:start position:0% +question I'm understanding why you + + + align:start position:0% +question I'm understanding why you +always put the negative signs up there + + align:start position:0% +always put the negative signs up there + + + align:start position:0% +always put the negative signs up there +yes um is this like some sort of a you + + align:start position:0% +yes um is this like some sort of a you + + + align:start position:0% +yes um is this like some sort of a you +draw a free body diagram kind of come + + align:start position:0% +draw a free body diagram kind of come + + + align:start position:0% +draw a free body diagram kind of come +out with a negative sign + + align:start position:0% +out with a negative sign + + + align:start position:0% +out with a negative sign +somewhere yeah now here I don't have the + + align:start position:0% +somewhere yeah now here I don't have the + + + align:start position:0% +somewhere yeah now here I don't have the +negative sign because I've got once I've + + align:start position:0% +negative sign because I've got once I've + + + align:start position:0% +negative sign because I've got once I've +got second derivatives twice so the + + align:start position:0% +got second derivatives twice so the + + + align:start position:0% +got second derivatives twice so the +second derivative is in some way + + align:start position:0% +second derivative is in some way + + + align:start position:0% +second derivative is in some way +negative let me I'll complete that + + align:start position:0% +negative let me I'll complete that + + + align:start position:0% +negative let me I'll complete that +sentence in a second somehow the second + + align:start position:0% +sentence in a second somehow the second + + + align:start position:0% +sentence in a second somehow the second +derivative which is the guy that has the + + align:start position:0% +derivative which is the guy that has the + + + align:start position:0% +derivative which is the guy that has the +1 - 2 1 somehow that's a negative thing + + align:start position:0% +1 - 2 1 somehow that's a negative thing + + + align:start position:0% +1 - 2 1 somehow that's a negative thing +but fourth derivative is second + + align:start position:0% +but fourth derivative is second + + + align:start position:0% +but fourth derivative is second +derivative of the second derivative yeah + + align:start position:0% +derivative of the second derivative yeah + + + align:start position:0% +derivative of the second derivative yeah +do you want to tell me what the numbers + + align:start position:0% +do you want to tell me what the numbers + + + align:start position:0% +do you want to tell me what the numbers +would be as long as we're wildly looking + + align:start position:0% +would be as long as we're wildly looking + + + align:start position:0% +would be as long as we're wildly looking +forward to fourth derivative just it it + + align:start position:0% +forward to fourth derivative just it it + + + align:start position:0% +forward to fourth derivative just it it +helps do you want to guess what will a + + align:start position:0% +helps do you want to guess what will a + + + align:start position:0% +helps do you want to guess what will a +typical row of the Matrix + + align:start position:0% +typical row of the Matrix + + + align:start position:0% +typical row of the Matrix +be in + + align:start position:0% +be in + + + align:start position:0% +be in +a for finite when I go to finite + + align:start position:0% +a for finite when I go to finite + + + align:start position:0% +a for finite when I go to finite +differences fourth differences any any + + align:start position:0% +differences fourth differences any any + + + align:start position:0% +differences fourth differences any any +probably have never seen a fourth + + align:start position:0% +probably have never seen a fourth + + + align:start position:0% +probably have never seen a fourth +difference you may not have seen second + + align:start position:0% +difference you may not have seen second + + + align:start position:0% +difference you may not have seen second +differences before that's that was a big + + align:start position:0% +differences before that's that was a big + + + align:start position:0% +differences before that's that was a big +deal then to introduce second + + align:start position:0% +deal then to introduce second + + + align:start position:0% +deal then to introduce second +differences those one minus 2 1es that + + align:start position:0% +differences those one minus 2 1es that + + + align:start position:0% +differences those one minus 2 1es that +was second + + align:start position:0% +was second + + + align:start position:0% +was second +differences fourth 1441 yeah 14641 with + + align:start position:0% +differences fourth 1441 yeah 14641 with + + + align:start position:0% +differences fourth 1441 yeah 14641 with +minus signs 1 - 4 6 -4 and + + align:start position:0% +minus signs 1 - 4 6 -4 and + + + align:start position:0% +minus signs 1 - 4 6 -4 and +one in some way I would get that by + + align:start position:0% +one in some way I would get that by + + + align:start position:0% +one in some way I would get that by +squaring this + + align:start position:0% +squaring this + + + align:start position:0% +squaring this +guy yeah and uh uh so that would be a + + align:start position:0% +guy yeah and uh uh so that would be a + + + align:start position:0% +guy yeah and uh uh so that would be a +fourth + + align:start position:0% +fourth + + + align:start position:0% +fourth +difference and + + align:start position:0% +difference and + + + align:start position:0% +difference and +uh yep and we would get uh it we'd have + + align:start position:0% +uh yep and we would get uh it we'd have + + + align:start position:0% +uh yep and we would get uh it we'd have +oh what's the deal with boundary + + align:start position:0% +oh what's the deal with boundary + + + align:start position:0% +oh what's the deal with boundary +conditions what what are you figuring on + + align:start position:0% +conditions what what are you figuring on + + + align:start position:0% +conditions what what are you figuring on +on beams beam problems uh for a fourth + + align:start position:0% +on beams beam problems uh for a fourth + + + align:start position:0% +on beams beam problems uh for a fourth +order equation and a matrix that's + + align:start position:0% +order equation and a matrix that's + + + align:start position:0% +order equation and a matrix that's +stretching out further what what's going + + align:start position:0% +stretching out further what what's going + + + align:start position:0% +stretching out further what what's going +to happen at the leftand + + align:start position:0% +to happen at the leftand + + + align:start position:0% +to happen at the leftand +boundary I I guess my qu specific + + align:start position:0% +boundary I I guess my qu specific + + + align:start position:0% +boundary I I guess my qu specific +question is how many boundary conditions + + align:start position:0% +question is how many boundary conditions + + + align:start position:0% +question is how many boundary conditions +do I now need four and the typical is + + align:start position:0% +do I now need four and the typical is + + + align:start position:0% +do I now need four and the typical is +two at each end that's the balanced way + + align:start position:0% +two at each end that's the balanced way + + + align:start position:0% +two at each end that's the balanced way +that's the way that would make this + + align:start position:0% +that's the way that would make this + + + align:start position:0% +that's the way that would make this +Matrix sort of symmetric so I have a + + align:start position:0% +Matrix sort of symmetric so I have a + + + align:start position:0% +Matrix sort of symmetric so I have a +maybe at this end I say it's it's uh + + align:start position:0% +maybe at this end I say it's it's uh + + + align:start position:0% +maybe at this end I say it's it's uh +it's held at zero + + align:start position:0% +it's held at zero + + + align:start position:0% +it's held at zero +and uh maybe it's just sitting on a on a + + align:start position:0% +and uh maybe it's just sitting on a on a + + + align:start position:0% +and uh maybe it's just sitting on a on a +log there right that I would that + + align:start position:0% +log there right that I would that + + + align:start position:0% +log there right that I would that +boundary condition I would call Simply + + align:start position:0% +boundary condition I would call Simply + + + align:start position:0% +boundary condition I would call Simply +supported that boundary condition says + + align:start position:0% +supported that boundary condition says + + + align:start position:0% +supported that boundary condition says +that U of 0 is zero because it's sitting + + align:start position:0% +that U of 0 is zero because it's sitting + + + align:start position:0% +that U of 0 is zero because it's sitting +there and but the slope could doesn't + + align:start position:0% +there and but the slope could doesn't + + + align:start position:0% +there and but the slope could doesn't +have to be zero what does have to be + + align:start position:0% +have to be zero what does have to be + + + align:start position:0% +have to be zero what does have to be +zero there it's the yeah sort of the + + align:start position:0% +zero there it's the yeah sort of the + + + align:start position:0% +zero there it's the yeah sort of the +bending moment there's no nobody's here + + align:start position:0% +bending moment there's no nobody's here + + + align:start position:0% +bending moment there's no nobody's here +twisting it right + + align:start position:0% +twisting it right + + + align:start position:0% +twisting it right +so so the other condition in that + + align:start position:0% +so so the other condition in that + + + align:start position:0% +so so the other condition in that +picture would be second derivative + + align:start position:0% +picture would be second derivative + + + align:start position:0% +picture would be second derivative +equals + + align:start position:0% + + + + align:start position:0% + +zero maybe my point is that now you see + + align:start position:0% +zero maybe my point is that now you see + + + align:start position:0% +zero maybe my point is that now you see +this what I said before that the getting + + align:start position:0% +this what I said before that the getting + + + align:start position:0% +this what I said before that the getting +the boundary conditions into the problem + + align:start position:0% +the boundary conditions into the problem + + + align:start position:0% +the boundary conditions into the problem +is often the hardest part because I have + + align:start position:0% +is often the hardest part because I have + + + align:start position:0% +is often the hardest part because I have +to replace U of 0 equals z that + + align:start position:0% +to replace U of 0 equals z that + + + align:start position:0% +to replace U of 0 equals z that +shouldn't be too hard to do but I have + + align:start position:0% +shouldn't be too hard to do but I have + + + align:start position:0% +shouldn't be too hard to do but I have +to use this other condition somehow it's + + align:start position:0% +to use this other condition somehow it's + + + align:start position:0% +to use this other condition somehow it's +going to screw up the 1 - 4 6 -41 and + + align:start position:0% +going to screw up the 1 - 4 6 -41 and + + + align:start position:0% +going to screw up the 1 - 4 6 -41 and +the I'll have two + + align:start position:0% +the I'll have two + + + align:start position:0% +the I'll have two +rows I'll have two boundary rows at the + + align:start position:0% +rows I'll have two boundary rows at the + + + align:start position:0% +rows I'll have two boundary rows at the +top two boundary rows at the + + align:start position:0% +top two boundary rows at the + + + align:start position:0% +top two boundary rows at the +bottom I I don't want to get go further + + align:start position:0% +bottom I I don't want to get go further + + + align:start position:0% +bottom I I don't want to get go further +today but I think maybe just mentioning + + align:start position:0% +today but I think maybe just mentioning + + + align:start position:0% +today but I think maybe just mentioning +this gives you the picture of uh you + + align:start position:0% +this gives you the picture of uh you + + + align:start position:0% +this gives you the picture of uh you +know sort of the how things fit together + + align:start position:0% +know sort of the how things fit together + + + align:start position:0% +know sort of the how things fit together +we we would still have these some nice + + align:start position:0% +we we would still have these some nice + + + align:start position:0% +we we would still have these some nice +constant diagonals in the middle but now + + align:start position:0% +constant diagonals in the middle but now + + + align:start position:0% +constant diagonals in the middle but now +we'll have two boundary rows at each end + + align:start position:0% +we'll have two boundary rows at each end + + + align:start position:0% +we'll have two boundary rows at each end +yeah yeah so that's something to come + + align:start position:0% +yeah yeah so that's something to come + + + align:start position:0% +yeah yeah so that's something to come +right that'll fit yes now back to + + align:start position:0% +right that'll fit yes now back to + + + align:start position:0% +right that'll fit yes now back to +reality which + + align:start position:0% +reality which + + + align:start position:0% +reality which +is any questions yeah thanks you're + + align:start position:0% +is any questions yeah thanks you're + + + align:start position:0% +is any questions yeah thanks you're +saying for the lower di for lower + + align:start position:0% +saying for the lower di for lower + + + align:start position:0% +saying for the lower di for lower +triangular lower triangular guy yeah you + + align:start position:0% +triangular lower triangular guy yeah you + + + align:start position:0% +triangular lower triangular guy yeah you +march forward to invert it what do you + + align:start position:0% +march forward to invert it what do you + + + align:start position:0% +march forward to invert it what do you +mean by that what do I mean by marching + + align:start position:0% +mean by that what do I mean by marching + + + align:start position:0% +mean by that what do I mean by marching +forward okay uh yeah so let's see what + + align:start position:0% +forward okay uh yeah so let's see what + + + align:start position:0% +forward okay uh yeah so let's see what +would + + align:start position:0% +would + + + align:start position:0% +would +I let me let me I'll replace + + align:start position:0% +I let me let me I'll replace + + + align:start position:0% +I let me let me I'll replace +this yeah let's see it better I would + + align:start position:0% +this yeah let's see it better I would + + + align:start position:0% +this yeah let's see it better I would +replace this by maybe U let me I'll use + + align:start position:0% +replace this by maybe U let me I'll use + + + align:start position:0% +replace this by maybe U let me I'll use +a different letter n + 1 at u n + 1 - 2 + + align:start position:0% +a different letter n + 1 at u n + 1 - 2 + + + align:start position:0% +a different letter n + 1 at u n + 1 - 2 +U n's + U + + align:start position:0% +U n's + U + + + align:start position:0% +U n's + U +nus1 is some is some uh right hand side + + align:start position:0% +nus1 is some is some uh right hand side + + + align:start position:0% +nus1 is some is some uh right hand side +if there's a force acting on my thing so + + align:start position:0% +if there's a force acting on my thing so + + + align:start position:0% +if there's a force acting on my thing so +FN maybe my by marching forward I just + + align:start position:0% +FN maybe my by marching forward I just + + + align:start position:0% +FN maybe my by marching forward I just +mean that this + + align:start position:0% +mean that this + + + align:start position:0% +mean that this +equation that I can go in order U I can + + align:start position:0% +equation that I can go in order U I can + + + align:start position:0% +equation that I can go in order U I can +start with u0 and U1 they come from the + + align:start position:0% +start with u0 and U1 they come from the + + + align:start position:0% +start with u0 and U1 they come from the +boundary + + align:start position:0% +boundary + + + align:start position:0% +boundary +conditions then this equation will tell + + align:start position:0% +conditions then this equation will tell + + + align:start position:0% +conditions then this equation will tell +me + + align:start position:0% +me + + + align:start position:0% +me +U2 I use the equation with n is one this + + align:start position:0% +U2 I use the equation with n is one this + + + align:start position:0% +U2 I use the equation with n is one this +says U2 + + align:start position:0% +says U2 + + + align:start position:0% +says U2 +some u1s some U f1s all that I know in + + align:start position:0% +some u1s some U f1s all that I know in + + + align:start position:0% +some u1s some U f1s all that I know in +other words once my once I get started + + align:start position:0% +other words once my once I get started + + + align:start position:0% +other words once my once I get started +I'm on a + + align:start position:0% +I'm on a + + + align:start position:0% +I'm on a +roll if I have two boundary conditions + + align:start position:0% +roll if I have two boundary conditions + + + align:start position:0% +roll if I have two boundary conditions +to get me started then the equation + + align:start position:0% +to get me started then the equation + + + align:start position:0% +to get me started then the equation +tells me U2 and then the next time u3 - + + align:start position:0% +tells me U2 and then the next time u3 - + + + align:start position:0% +tells me U2 and then the next time u3 - +2 U2 + U1 I can find you three so I can + + align:start position:0% +2 U2 + U1 I can find you three so I can + + + align:start position:0% +2 U2 + U1 I can find you three so I can +get those I can go + + align:start position:0% +get those I can go + + + align:start position:0% +get those I can go +forever if you give me enough to start + + align:start position:0% +forever if you give me enough to start + + + align:start position:0% +forever if you give me enough to start +on two things to start + + align:start position:0% +on two things to start + + + align:start position:0% +on two things to start +then I I March forward whereas in in our + + align:start position:0% +then I I March forward whereas in in our + + + align:start position:0% +then I I March forward whereas in in our +problems we've only got one thing to + + align:start position:0% +problems we've only got one thing to + + + align:start position:0% +problems we've only got one thing to +start on and we've got one goal to hit + + align:start position:0% +start on and we've got one goal to hit + + + align:start position:0% +start on and we've got one goal to hit +and that's why we have to solve the + + align:start position:0% +and that's why we have to solve the + + + align:start position:0% +and that's why we have to solve the +whole system together this is this is we + + align:start position:0% +whole system together this is this is we + + + align:start position:0% +whole system together this is this is we +can solve it uh step by step by this is + + align:start position:0% +can solve it uh step by step by this is + + + align:start position:0% +can solve it uh step by step by this is +way faster of + + align:start position:0% +way faster of + + + align:start position:0% +way faster of +course uh to be able to just go forward + + align:start position:0% +course uh to be able to just go forward + + + align:start position:0% +course uh to be able to just go forward +in time yeah + + align:start position:0% +in time yeah + + + align:start position:0% +in time yeah +so yeah I'll mention that the topic of + + align:start position:0% +so yeah I'll mention that the topic of + + + align:start position:0% +so yeah I'll mention that the topic of +initial value problems and finite + + align:start position:0% +initial value problems and finite + + + align:start position:0% +initial value problems and finite +differences for them that uh we can't + + align:start position:0% +differences for them that uh we can't + + + align:start position:0% +differences for them that uh we can't +get to that so we're we're seeing a + + align:start position:0% +get to that so we're we're seeing a + + + align:start position:0% +get to that so we're we're seeing a +little bit here but the it's done + + align:start position:0% +little bit here but the it's done + + + align:start position:0% +little bit here but the it's done +properly in 18086 in the in the second + + align:start position:0% +properly in 18086 in the in the second + + + align:start position:0% +properly in 18086 in the in the second +semester uh is the initial value problem + + align:start position:0% +semester uh is the initial value problem + + + align:start position:0% +semester uh is the initial value problem +start part and that that has its own + + align:start position:0% +start part and that that has its own + + + align:start position:0% +start part and that that has its own +interesting questions yeah yeah okay so + + align:start position:0% +interesting questions yeah yeah okay so + + + align:start position:0% +interesting questions yeah yeah okay so +somehow we've talked about + + align:start position:0% +somehow we've talked about + + + align:start position:0% +somehow we've talked about +U fourth order equations initial value + + align:start position:0% +U fourth order equations initial value + + + align:start position:0% +U fourth order equations initial value +uh + + align:start position:0% +uh + + + align:start position:0% +uh +problems + + align:start position:0% +problems + + + align:start position:0% +problems +uh but no homework problems uh so I'm + + align:start position:0% +uh but no homework problems uh so I'm + + + align:start position:0% +uh but no homework problems uh so I'm +ready for or even related but that's + + align:start position:0% +ready for or even related but that's + + + align:start position:0% +ready for or even related but that's +fine with me any maybe so + + align:start position:0% +fine with me any maybe so + + + align:start position:0% +fine with me any maybe so +that is there a is there a question yeah + + align:start position:0% +that is there a is there a question yeah + + + align:start position:0% +that is there a is there a question yeah +thanks or it doesn't have to be a + + align:start position:0% +thanks or it doesn't have to be a + + + align:start position:0% +thanks or it doesn't have to be a +homework question + + align:start position:0% +homework question + + + align:start position:0% +homework question +another question form of the + + align:start position:0% +another question form of the + + + align:start position:0% +another question form of the +homework Bas can I do everything in and + + align:start position:0% +homework Bas can I do everything in and + + + align:start position:0% +homework Bas can I do everything in and +write down the answers oh good + + align:start position:0% + + + + align:start position:0% + +question you mean I should just send the + + align:start position:0% +question you mean I should just send the + + + align:start position:0% +question you mean I should just send the +homework out to NC where mat lab is do + + align:start position:0% +homework out to NC where mat lab is do + + + align:start position:0% +homework out to NC where mat lab is do +you know that mat lab is just 15 miles + + align:start position:0% +you know that mat lab is just 15 miles + + + align:start position:0% +you know that mat lab is just 15 miles +away I almost get there drive I live + + align:start position:0% +away I almost get there drive I live + + + align:start position:0% +away I almost get there drive I live +two-thirds of the way there uh yeah so I + + align:start position:0% +two-thirds of the way there uh yeah so I + + + align:start position:0% +two-thirds of the way there uh yeah so I +could just we could just send the whole + + align:start position:0% +could just we could just send the whole + + + align:start position:0% +could just we could just send the whole +thing out there and get it back it would + + align:start position:0% +thing out there and get it back it would + + + align:start position:0% +thing out there and get it back it would +that would save a lot of work not + + align:start position:0% +that would save a lot of work not + + + align:start position:0% +that would save a lot of work not +only uh yeah I + + align:start position:0% +only uh yeah I + + + align:start position:0% +only uh yeah I +suppose yeah I I suppose I'm okay why + + align:start position:0% +suppose yeah I I suppose I'm okay why + + + align:start position:0% +suppose yeah I I suppose I'm okay why +why should I say no anything Matt lab + + align:start position:0% +why should I say no anything Matt lab + + + align:start position:0% +why should I say no anything Matt lab +can do and you can make it do I'm okay + + align:start position:0% +can do and you can make it do I'm okay + + + align:start position:0% +can do and you can make it do I'm okay +with that I yeah I don't see that you + + align:start position:0% +with that I yeah I don't see that you + + + align:start position:0% +with that I yeah I don't see that you +have to do things by hand if you've got + + align:start position:0% +have to do things by hand if you've got + + + align:start position:0% +have to do things by hand if you've got +a better way yeah yeah that's okay and + + align:start position:0% +a better way yeah yeah that's okay and + + + align:start position:0% +a better way yeah yeah that's okay and +and then probably the answer gets + + align:start position:0% +and then probably the answer gets + + + align:start position:0% +and then probably the answer gets +printed and you can graph it yeah so so + + align:start position:0% +printed and you can graph it yeah so so + + + align:start position:0% +printed and you can graph it yeah so so +that's fine uh so I mean somehow a + + align:start position:0% +that's fine uh so I mean somehow a + + + align:start position:0% +that's fine uh so I mean somehow a +course like this has got two parts to it + + align:start position:0% +course like this has got two parts to it + + + align:start position:0% +course like this has got two parts to it +or applied math has two parts to it the + + align:start position:0% +or applied math has two parts to it the + + + align:start position:0% +or applied math has two parts to it the +the modeling part set up the equation + + align:start position:0% +the modeling part set up the equation + + + align:start position:0% +the modeling part set up the equation +think what is it you're supposed to do + + align:start position:0% +think what is it you're supposed to do + + + align:start position:0% +think what is it you're supposed to do +and then step two is do it numer the + + align:start position:0% +and then step two is do it numer the + + + align:start position:0% +and then step two is do it numer the +numerical part the Computing part and + + align:start position:0% +numerical part the Computing part and + + + align:start position:0% +numerical part the Computing part and +that's where mat lab python Fortran + + align:start position:0% +that's where mat lab python Fortran + + + align:start position:0% +that's where mat lab python Fortran +whatever is going to do a lot of the + + align:start position:0% +whatever is going to do a lot of the + + + align:start position:0% +whatever is going to do a lot of the +heavy lifting yeah yeah yeah was there + + align:start position:0% +heavy lifting yeah yeah yeah was there + + + align:start position:0% +heavy lifting yeah yeah yeah was there +another question yeah so that home first + + align:start position:0% +another question yeah so that home first + + + align:start position:0% +another question yeah so that home first +homework was certainly uh + + align:start position:0% +homework was certainly uh + + + align:start position:0% +homework was certainly uh +uh very general intentionally because + + align:start position:0% +uh very general intentionally because + + + align:start position:0% +uh very general intentionally because +I'm hoping you will read the book you + + align:start position:0% +I'm hoping you will read the book you + + + align:start position:0% +I'm hoping you will read the book you +know the lecture I'll I'll you'll know + + align:start position:0% +know the lecture I'll I'll you'll know + + + align:start position:0% +know the lecture I'll I'll you'll know +where you'll be able to match the + + align:start position:0% +where you'll be able to match the + + + align:start position:0% +where you'll be able to match the +lectures with the book even later on + + align:start position:0% +lectures with the book even later on + + + align:start position:0% +lectures with the book even later on +when when they separate a little or + + align:start position:0% +when when they separate a little or + + + align:start position:0% +when when they separate a little or +separate more uh you'll see what we're + + align:start position:0% +separate more uh you'll see what we're + + + align:start position:0% +separate more uh you'll see what we're +doing in those + + align:start position:0% +doing in those + + + align:start position:0% +doing in those +the the homework problems you should + + align:start position:0% +the the homework problems you should + + + align:start position:0% +the the homework problems you should +look at some of the others just to see + + align:start position:0% +look at some of the others just to see + + + align:start position:0% +look at some of the others just to see +could do I know how to do that + + align:start position:0% +could do I know how to do that + + + align:start position:0% +could do I know how to do that +right okay let's stop here for this + + align:start position:0% +right okay let's stop here for this + + + align:start position:0% +right okay let's stop here for this +first review I'm sure we'll have more + + align:start position:0% +first review I'm sure we'll have more + + + align:start position:0% +first review I'm sure we'll have more +questions will build up for for the + + align:start position:0% +questions will build up for for the + + + align:start position:0% +questions will build up for for the +second week \ No newline at end of file diff --git a/aJXfyfQs2Mc.txt b/aJXfyfQs2Mc.txt new file mode 100644 index 0000000000000000000000000000000000000000..58c34a52d5ec49eee383d8efc194353139b4f120 --- /dev/null +++ b/aJXfyfQs2Mc.txt @@ -0,0 +1,1155 @@ +align:start position:0% + +we will now consider an example that + + align:start position:0% +we will now consider an example that + + + align:start position:0% +we will now consider an example that +illustrates the difference between the + + align:start position:0% +illustrates the difference between the + + + align:start position:0% +illustrates the difference between the +notion of independence of a collection + + align:start position:0% +notion of independence of a collection + + + align:start position:0% +notion of independence of a collection +of events and the notion of pairwise + + align:start position:0% +of events and the notion of pairwise + + + align:start position:0% +of events and the notion of pairwise +independence within that collection the + + align:start position:0% +independence within that collection the + + + align:start position:0% +independence within that collection the +model is simple we have a fair coin + + align:start position:0% +model is simple we have a fair coin + + + align:start position:0% +model is simple we have a fair coin +which we flip twice so at each flip + + align:start position:0% +which we flip twice so at each flip + + + align:start position:0% +which we flip twice so at each flip +there is probability 1/2 of obtaining + + align:start position:0% +there is probability 1/2 of obtaining + + + align:start position:0% +there is probability 1/2 of obtaining +hands furthermore we assume that the two + + align:start position:0% +hands furthermore we assume that the two + + + align:start position:0% +hands furthermore we assume that the two +flips are independent of each other + + align:start position:0% +flips are independent of each other + + + align:start position:0% +flips are independent of each other +let h1 be the event that the first coin + + align:start position:0% +let h1 be the event that the first coin + + + align:start position:0% +let h1 be the event that the first coin +toss resulted in heads which corresponds + + align:start position:0% +toss resulted in heads which corresponds + + + align:start position:0% +toss resulted in heads which corresponds +to this event in this diagram let H to + + align:start position:0% +to this event in this diagram let H to + + + align:start position:0% +to this event in this diagram let H to +be the event that the second toss + + align:start position:0% +be the event that the second toss + + + align:start position:0% +be the event that the second toss +resulted in heads which is this event in + + align:start position:0% +resulted in heads which is this event in + + + align:start position:0% +resulted in heads which is this event in +the diagram the two ways that we can + + align:start position:0% +the diagram the two ways that we can + + + align:start position:0% +the diagram the two ways that we can +have the second toss being hands now + + align:start position:0% +have the second toss being hands now + + + align:start position:0% +have the second toss being hands now +we're assuming that the tosses are + + align:start position:0% +we're assuming that the tosses are + + + align:start position:0% +we're assuming that the tosses are +independent so the event heads head has + + align:start position:0% +independent so the event heads head has + + + align:start position:0% +independent so the event heads head has +a probability which is equal to the + + align:start position:0% +a probability which is equal to the + + + align:start position:0% +a probability which is equal to the +probability that the first toss resulted + + align:start position:0% +probability that the first toss resulted + + + align:start position:0% +probability that the first toss resulted +in heads that's one-half times the + + align:start position:0% +in heads that's one-half times the + + + align:start position:0% +in heads that's one-half times the +probability that the second toss + + align:start position:0% +probability that the second toss + + + align:start position:0% +probability that the second toss +resulted in heads which is one-half so + + align:start position:0% +resulted in heads which is one-half so + + + align:start position:0% +resulted in heads which is one-half so +the product is 1/4 we have probability + + align:start position:0% +the product is 1/4 we have probability + + + align:start position:0% +the product is 1/4 we have probability +1/4 for this outcome now the total + + align:start position:0% +1/4 for this outcome now the total + + + align:start position:0% +1/4 for this outcome now the total +probability of event h1 is one-half + + align:start position:0% +probability of event h1 is one-half + + + align:start position:0% +probability of event h1 is one-half +which means that the probability of what + + align:start position:0% +which means that the probability of what + + + align:start position:0% +which means that the probability of what +remains should be 1/4 so that the sum of + + align:start position:0% +remains should be 1/4 so that the sum of + + + align:start position:0% +remains should be 1/4 so that the sum of +these two numbers is one-half by the + + align:start position:0% +these two numbers is one-half by the + + + align:start position:0% +these two numbers is one-half by the +same argument the probability of this + + align:start position:0% +same argument the probability of this + + + align:start position:0% +same argument the probability of this +outcome tails heads should be 1/4 we + + align:start position:0% +outcome tails heads should be 1/4 we + + + align:start position:0% +outcome tails heads should be 1/4 we +have a total of 3/4 so what's left is + + align:start position:0% +have a total of 3/4 so what's left is + + + align:start position:0% +have a total of 3/4 so what's left is +1/4 and that's going to be the + + align:start position:0% +1/4 and that's going to be the + + + align:start position:0% +1/4 and that's going to be the +probability of the outcome tails tails + + align:start position:0% +probability of the outcome tails tails + + + align:start position:0% +probability of the outcome tails tails +let us now introduce a new event namely + + align:start position:0% +let us now introduce a new event namely + + + align:start position:0% +let us now introduce a new event namely +the event that the two tosses had the + + align:start position:0% +the event that the two tosses had the + + + align:start position:0% +the event that the two tosses had the +same result so this is the event that we + + align:start position:0% +same result so this is the event that we + + + align:start position:0% +same result so this is the event that we +obtain either heads heads or tails tails + + align:start position:0% + + + + align:start position:0% + +schematically event C corresponds to + + align:start position:0% +schematically event C corresponds to + + + align:start position:0% +schematically event C corresponds to +this blue region in the diagram is event + + align:start position:0% +this blue region in the diagram is event + + + align:start position:0% +this blue region in the diagram is event +C independent from the events h1 and h2 + + align:start position:0% +C independent from the events h1 and h2 + + + align:start position:0% +C independent from the events h1 and h2 +let us first look for pairwise + + align:start position:0% +let us first look for pairwise + + + align:start position:0% +let us first look for pairwise +independence let's look at the + + align:start position:0% +independence let's look at the + + + align:start position:0% +independence let's look at the +probability that H 1 occurs and C occurs + + align:start position:0% +probability that H 1 occurs and C occurs + + + align:start position:0% +probability that H 1 occurs and C occurs +as well so the first toss resulted in + + align:start position:0% +as well so the first toss resulted in + + + align:start position:0% +as well so the first toss resulted in +heads and the two tosses had the same + + align:start position:0% +heads and the two tosses had the same + + + align:start position:0% +heads and the two tosses had the same +result so this is the same as the + + align:start position:0% +result so this is the same as the + + + align:start position:0% +result so this is the same as the +probability of obtaining heads followed + + align:start position:0% +probability of obtaining heads followed + + + align:start position:0% +probability of obtaining heads followed +by heads and this corresponds to just + + align:start position:0% +by heads and this corresponds to just + + + align:start position:0% +by heads and this corresponds to just +this outcome that has probability 1/4 + + align:start position:0% + + + + align:start position:0% + +how about the product of the + + align:start position:0% +how about the product of the + + + align:start position:0% +how about the product of the +probabilities of h1 and of C is it the + + align:start position:0% +probabilities of h1 and of C is it the + + + align:start position:0% +probabilities of h1 and of C is it the +same well the probability of H 1 is 1/2 + + align:start position:0% +same well the probability of H 1 is 1/2 + + + align:start position:0% +same well the probability of H 1 is 1/2 +and the probability of C what is it + + align:start position:0% +and the probability of C what is it + + + align:start position:0% +and the probability of C what is it +event C consists of two outcomes each + + align:start position:0% +event C consists of two outcomes each + + + align:start position:0% +event C consists of two outcomes each +one of these outcomes has probability + + align:start position:0% +one of these outcomes has probability + + + align:start position:0% +one of these outcomes has probability +1/4 so the total is again 1/2 and + + align:start position:0% +1/4 so the total is again 1/2 and + + + align:start position:0% +1/4 so the total is again 1/2 and +therefore the product of these + + align:start position:0% +therefore the product of these + + + align:start position:0% +therefore the product of these +probabilities is 1/4 so we notice that + + align:start position:0% +probabilities is 1/4 so we notice that + + + align:start position:0% +probabilities is 1/4 so we notice that +the probability of the two events + + align:start position:0% +the probability of the two events + + + align:start position:0% +the probability of the two events +happening is the same as the product of + + align:start position:0% +happening is the same as the product of + + + align:start position:0% +happening is the same as the product of +their individual probabilities and + + align:start position:0% +their individual probabilities and + + + align:start position:0% +their individual probabilities and +therefore h1 and C are independent + + align:start position:0% +therefore h1 and C are independent + + + align:start position:0% +therefore h1 and C are independent +events by the same argument h2 and C are + + align:start position:0% +events by the same argument h2 and C are + + + align:start position:0% +events by the same argument h2 and C are +going to be independent it's a + + align:start position:0% +going to be independent it's a + + + align:start position:0% +going to be independent it's a +symmetrical situation h1 and h2 are also + + align:start position:0% +symmetrical situation h1 and h2 are also + + + align:start position:0% +symmetrical situation h1 and h2 are also +independent from each other so we have + + align:start position:0% +independent from each other so we have + + + align:start position:0% +independent from each other so we have +all the conditions for pairwise + + align:start position:0% +all the conditions for pairwise + + + align:start position:0% +all the conditions for pairwise +independence let us now check whether we + + align:start position:0% +independence let us now check whether we + + + align:start position:0% +independence let us now check whether we +have independence to check for + + align:start position:0% +have independence to check for + + + align:start position:0% +have independence to check for +independence we need to also look into + + align:start position:0% +independence we need to also look into + + + align:start position:0% +independence we need to also look into +the probability of all three events + + align:start position:0% +the probability of all three events + + + align:start position:0% +the probability of all three events +happening and see whether it is equal to + + align:start position:0% +happening and see whether it is equal to + + + align:start position:0% +happening and see whether it is equal to +the product of the individual + + align:start position:0% +the product of the individual + + + align:start position:0% +the product of the individual +probabilities so the probability of all + + align:start position:0% +probabilities so the probability of all + + + align:start position:0% +probabilities so the probability of all +three events happening this is the + + align:start position:0% +three events happening this is the + + + align:start position:0% +three events happening this is the +probability that + + align:start position:0% +probability that + + + align:start position:0% +probability that +Schwann occurs and h2 occurs and c + + align:start position:0% +Schwann occurs and h2 occurs and c + + + align:start position:0% +Schwann occurs and h2 occurs and c +occurs what is this event heads in the + + align:start position:0% +occurs what is this event heads in the + + + align:start position:0% +occurs what is this event heads in the +first toss heads in the second toss and + + align:start position:0% +first toss heads in the second toss and + + + align:start position:0% +first toss heads in the second toss and +the two tosses are the same this happens + + align:start position:0% +the two tosses are the same this happens + + + align:start position:0% +the two tosses are the same this happens +if and only if the outcome is heads + + align:start position:0% +if and only if the outcome is heads + + + align:start position:0% +if and only if the outcome is heads +followed by heads and this has + + align:start position:0% +followed by heads and this has + + + align:start position:0% +followed by heads and this has +probability 1/4 on the other hand if we + + align:start position:0% +probability 1/4 on the other hand if we + + + align:start position:0% +probability 1/4 on the other hand if we +calculate the probability of H 1 times + + align:start position:0% +calculate the probability of H 1 times + + + align:start position:0% +calculate the probability of H 1 times +the probability of H 2 times the + + align:start position:0% +the probability of H 2 times the + + + align:start position:0% +the probability of H 2 times the +probability of C we get 1/2 times 1/2 + + align:start position:0% +probability of C we get 1/2 times 1/2 + + + align:start position:0% +probability of C we get 1/2 times 1/2 +times 1/2 which is 1/8 these two numbers + + align:start position:0% +times 1/2 which is 1/8 these two numbers + + + align:start position:0% +times 1/2 which is 1/8 these two numbers +are different and therefore one of the + + align:start position:0% +are different and therefore one of the + + + align:start position:0% +are different and therefore one of the +conditions that we have for Independence + + align:start position:0% +conditions that we have for Independence + + + align:start position:0% +conditions that we have for Independence +is violated so in this example H 1 H 2 + + align:start position:0% +is violated so in this example H 1 H 2 + + + align:start position:0% +is violated so in this example H 1 H 2 +and C are pairwise independent but they + + align:start position:0% +and C are pairwise independent but they + + + align:start position:0% +and C are pairwise independent but they +are not independent in the sense of an + + align:start position:0% +are not independent in the sense of an + + + align:start position:0% +are not independent in the sense of an +independent collection of events how are + + align:start position:0% +independent collection of events how are + + + align:start position:0% +independent collection of events how are +we to understand this intuitively if I + + align:start position:0% +we to understand this intuitively if I + + + align:start position:0% +we to understand this intuitively if I +tell you that event H 1 occurred and I + + align:start position:0% +tell you that event H 1 occurred and I + + + align:start position:0% +tell you that event H 1 occurred and I +ask you for the conditional probability + + align:start position:0% +ask you for the conditional probability + + + align:start position:0% +ask you for the conditional probability +of C given that H 1 what is this this is + + align:start position:0% +of C given that H 1 what is this this is + + + align:start position:0% +of C given that H 1 what is this this is +the probability that we obtain given + + align:start position:0% +the probability that we obtain given + + + align:start position:0% +the probability that we obtain given +that the first event is heads the first + + align:start position:0% +that the first event is heads the first + + + align:start position:0% +that the first event is heads the first +result is heads the only way that you + + align:start position:0% +result is heads the only way that you + + + align:start position:0% +result is heads the only way that you +can have the two tosses having the same + + align:start position:0% +can have the two tosses having the same + + + align:start position:0% +can have the two tosses having the same +result is going to be if the second toss + + align:start position:0% +result is going to be if the second toss + + + align:start position:0% +result is going to be if the second toss +also results in heads and since H 2 and + + align:start position:0% +also results in heads and since H 2 and + + + align:start position:0% +also results in heads and since H 2 and +H 1 are independent this is just the + + align:start position:0% +H 1 are independent this is just the + + + align:start position:0% +H 1 are independent this is just the +probability that we have heads in the + + align:start position:0% +probability that we have heads in the + + + align:start position:0% +probability that we have heads in the +second toss and this number is 1/2 and + + align:start position:0% +second toss and this number is 1/2 and + + + align:start position:0% +second toss and this number is 1/2 and +1/2 is also the same as the probability + + align:start position:0% +1/2 is also the same as the probability + + + align:start position:0% +1/2 is also the same as the probability +of C that's another way of understanding + + align:start position:0% +of C that's another way of understanding + + + align:start position:0% +of C that's another way of understanding +the independence of H 1 and C given that + + align:start position:0% +the independence of H 1 and C given that + + + align:start position:0% +the independence of H 1 and C given that +the first toss resulted in heads this + + align:start position:0% +the first toss resulted in heads this + + + align:start position:0% +the first toss resulted in heads this +does not help you in any way + + align:start position:0% +does not help you in any way + + + align:start position:0% +does not help you in any way +in guessing whether the two tosses will + + align:start position:0% +in guessing whether the two tosses will + + + align:start position:0% +in guessing whether the two tosses will +have the same result or not the first + + align:start position:0% +have the same result or not the first + + + align:start position:0% +have the same result or not the first +one had was heads but the second one + + align:start position:0% +one had was heads but the second one + + + align:start position:0% +one had was heads but the second one +could be either heads or tails with + + align:start position:0% +could be either heads or tails with + + + align:start position:0% +could be either heads or tails with +equal probability so event h1 does not + + align:start position:0% +equal probability so event h1 does not + + + align:start position:0% +equal probability so event h1 does not +carry any useful information about the + + align:start position:0% +carry any useful information about the + + + align:start position:0% +carry any useful information about the +occurrence or non-occurrence of event c + + align:start position:0% +occurrence or non-occurrence of event c + + + align:start position:0% +occurrence or non-occurrence of event c +on the other hand if I were to tell you + + align:start position:0% +on the other hand if I were to tell you + + + align:start position:0% +on the other hand if I were to tell you +that both events h1 and h2 happened what + + align:start position:0% +that both events h1 and h2 happened what + + + align:start position:0% +that both events h1 and h2 happened what +would the conditional probability of C + + align:start position:0% +would the conditional probability of C + + + align:start position:0% +would the conditional probability of C +be if both h1 and h2 occur then the + + align:start position:0% +be if both h1 and h2 occur then the + + + align:start position:0% +be if both h1 and h2 occur then the +results of the two coin tosses were + + align:start position:0% +results of the two coin tosses were + + + align:start position:0% +results of the two coin tosses were +identical so you know that C also + + align:start position:0% +identical so you know that C also + + + align:start position:0% +identical so you know that C also +occurred so this probability is equal to + + align:start position:0% +occurred so this probability is equal to + + + align:start position:0% +occurred so this probability is equal to +1 and this number 1 is different than + + align:start position:0% +1 and this number 1 is different than + + + align:start position:0% +1 and this number 1 is different than +from the unconditional probability of C + + align:start position:0% +from the unconditional probability of C + + + align:start position:0% +from the unconditional probability of C +which is 1/2 so we have here a situation + + align:start position:0% +which is 1/2 so we have here a situation + + + align:start position:0% +which is 1/2 so we have here a situation +where knowledge of h1 having occurred + + align:start position:0% +where knowledge of h1 having occurred + + + align:start position:0% +where knowledge of h1 having occurred +does not help you in making a better + + align:start position:0% +does not help you in making a better + + + align:start position:0% +does not help you in making a better +guess on whether C is going to occur h1 + + align:start position:0% +guess on whether C is going to occur h1 + + + align:start position:0% +guess on whether C is going to occur h1 +by itself does not carry any useful + + align:start position:0% +by itself does not carry any useful + + + align:start position:0% +by itself does not carry any useful +information but the two events together + + align:start position:0% +information but the two events together + + + align:start position:0% +information but the two events together +h1 and and h2 do carry useful + + align:start position:0% +h1 and and h2 do carry useful + + + align:start position:0% +h1 and and h2 do carry useful +information about C once you know that + + align:start position:0% +information about C once you know that + + + align:start position:0% +information about C once you know that +h1 and h2 occurred then C is certain to + + align:start position:0% +h1 and h2 occurred then C is certain to + + + align:start position:0% +h1 and h2 occurred then C is certain to +occur so your original probability for C + + align:start position:0% +occur so your original probability for C + + + align:start position:0% +occur so your original probability for C +which was 1/2 now get revised to a value + + align:start position:0% +which was 1/2 now get revised to a value + + + align:start position:0% +which was 1/2 now get revised to a value +of 1 so h1 and h2 carry information + + align:start position:0% +of 1 so h1 and h2 carry information + + + align:start position:0% +of 1 so h1 and h2 carry information +relevant to C and therefore C is not + + align:start position:0% +relevant to C and therefore C is not + + + align:start position:0% +relevant to C and therefore C is not +independent from these two events + + align:start position:0% +independent from these two events + + + align:start position:0% +independent from these two events +collectively and we say that events h1 + + align:start position:0% +collectively and we say that events h1 + + + align:start position:0% +collectively and we say that events h1 +h2 and C are not independent \ No newline at end of file diff --git a/ayw-96xs-ag.txt b/ayw-96xs-ag.txt new file mode 100644 index 0000000000000000000000000000000000000000..35e4b5016b085158fa636104bccef700d0bc1730 --- /dev/null +++ b/ayw-96xs-ag.txt @@ -0,0 +1,11811 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu um I've handed out a guide + + align:start position:0% +ocw.mit.edu um I've handed out a guide + + + align:start position:0% +ocw.mit.edu um I've handed out a guide +to what we're going to cover today now I + + align:start position:0% +to what we're going to cover today now I + + + align:start position:0% +to what we're going to cover today now I +don't know how much how familiar you are + + align:start position:0% +don't know how much how familiar you are + + + align:start position:0% +don't know how much how familiar you are +with the + + align:start position:0% +with the + + + align:start position:0% +with the +material + + align:start position:0% +material + + + align:start position:0% +material +uh does anybody for + + align:start position:0% +uh does anybody for + + + align:start position:0% +uh does anybody for +instance have any familiarity with what + + align:start position:0% +instance have any familiarity with what + + + align:start position:0% +instance have any familiarity with what +is called space + + align:start position:0% +is called space + + + align:start position:0% +is called space +syntax how much + + align:start position:0% +syntax how much + + + align:start position:0% +syntax how much +familiarity um I saw a presentation that + + align:start position:0% +familiarity um I saw a presentation that + + + align:start position:0% +familiarity um I saw a presentation that +U someone who was working in England on + + align:start position:0% +U someone who was working in England on + + + align:start position:0% +U someone who was working in England on +Space syc to the national capital + + align:start position:0% +Space syc to the national capital + + + align:start position:0% +Space syc to the national capital +parking Planning Commission DC + + align:start position:0% +parking Planning Commission DC + + + align:start position:0% +parking Planning Commission DC +and pretty + + align:start position:0% +and pretty + + + align:start position:0% +and pretty +interesting when was this recently or + + align:start position:0% +interesting when was this recently or + + + align:start position:0% +interesting when was this recently or +yeah + + align:start position:0% + + + + align:start position:0% + +2011 do you know the book spaces a + + align:start position:0% +2011 do you know the book spaces a + + + align:start position:0% +2011 do you know the book spaces a +machine no is that is that what the + + align:start position:0% +machine no is that is that what the + + + align:start position:0% +machine no is that is that what the +reading was from no this is a voluminous + + align:start position:0% +reading was from no this is a voluminous + + + align:start position:0% +reading was from no this is a voluminous +document it costs a lot of money to + + align:start position:0% + + + + align:start position:0% + +buy + + align:start position:0% + + + + align:start position:0% + +uh it really is + + align:start position:0% +uh it really is + + + align:start position:0% +uh it really is +more of an expansion + + align:start position:0% +more of an expansion + + + align:start position:0% +more of an expansion +of the space syntax methodology and the + + align:start position:0% +of the space syntax methodology and the + + + align:start position:0% +of the space syntax methodology and the +idea than we have time for in this + + align:start position:0% +idea than we have time for in this + + + align:start position:0% +idea than we have time for in this +class uh that's why I ask if anybody is + + align:start position:0% +class uh that's why I ask if anybody is + + + align:start position:0% +class uh that's why I ask if anybody is +familiar with it + + align:start position:0% + + + + align:start position:0% + +um okay this is the last class in the + + align:start position:0% +um okay this is the last class in the + + + align:start position:0% +um okay this is the last class in the +first + + align:start position:0% +first + + + align:start position:0% +first +section + + align:start position:0% +section + + + align:start position:0% +section +um and uh we con concentrated again very + + align:start position:0% +um and uh we con concentrated again very + + + align:start position:0% +um and uh we con concentrated again very +very + + align:start position:0% +very + + + align:start position:0% +very +briefly as we + + align:start position:0% +briefly as we + + + align:start position:0% +briefly as we +did on + + align:start position:0% + + + + align:start position:0% + +Tuesday with theories + + align:start position:0% +Tuesday with theories + + + align:start position:0% +Tuesday with theories +which seem + + align:start position:0% +which seem + + + align:start position:0% +which seem +to be determined by the logic from + + align:start position:0% +to be determined by the logic from + + + align:start position:0% +to be determined by the logic from +social + + align:start position:0% +social + + + align:start position:0% +social +science + + align:start position:0% + + + + align:start position:0% + +um there are micro theories within each + + align:start position:0% +um there are micro theories within each + + + align:start position:0% +um there are micro theories within each +of + + align:start position:0% +of + + + align:start position:0% +of +these Lots of rules of thumb lots of + + align:start position:0% +these Lots of rules of thumb lots of + + + align:start position:0% +these Lots of rules of thumb lots of +understanding which is not externalized + + align:start position:0% +understanding which is not externalized + + + align:start position:0% +understanding which is not externalized +theoretically for + + align:start position:0% +theoretically for + + + align:start position:0% +theoretically for +instance one of my favorites + + align:start position:0% + + + + align:start position:0% + +is Fifth Avenue in + + align:start position:0% +is Fifth Avenue in + + + align:start position:0% +is Fifth Avenue in +Park + + align:start position:0% + + + + align:start position:0% + +Avenue a section through a building on + + align:start position:0% +Avenue a section through a building on + + + align:start position:0% +Avenue a section through a building on +Fifth Avenue + + align:start position:0% + + + + align:start position:0% + +I six building on Park Avenue + + align:start position:0% + + + + align:start position:0% + +on fth + + align:start position:0% +on fth + + + align:start position:0% +on fth +Avenue the ground is + + align:start position:0% + + + + align:start position:0% + +significant + + align:start position:0% +significant + + + align:start position:0% +significant +everything that is built is connected to + + align:start position:0% +everything that is built is connected to + + + align:start position:0% +everything that is built is connected to +the ground by mechanical systems + + align:start position:0% +the ground by mechanical systems + + + align:start position:0% +the ground by mechanical systems +generally an escalator for five or six + + align:start position:0% +generally an escalator for five or six + + + align:start position:0% +generally an escalator for five or six +floors the basement is important because + + align:start position:0% +floors the basement is important because + + + align:start position:0% +floors the basement is important because +it's linked only one floor from link to + + align:start position:0% +it's linked only one floor from link to + + + align:start position:0% +it's linked only one floor from link to +a surface only one floor from the + + align:start position:0% + + + + align:start position:0% + +ground two buildings on Park Avenue + + align:start position:0% +ground two buildings on Park Avenue + + + align:start position:0% +ground two buildings on Park Avenue +which you know lever brothers and + + align:start position:0% +which you know lever brothers and + + + align:start position:0% +which you know lever brothers and +Seagram's + + align:start position:0% +Seagram's + + + align:start position:0% +Seagram's +building Diva + + align:start position:0% + + + + align:start position:0% + +Brothers gives up the ground for + + align:start position:0% +Brothers gives up the ground for + + + align:start position:0% +Brothers gives up the ground for +nothing the ground is worthless + + align:start position:0% + + + + align:start position:0% + +Seagram's + + align:start position:0% + + + + align:start position:0% + +building extends a + + align:start position:0% +building extends a + + + align:start position:0% +building extends a +Plaza in return for which it gets more + + align:start position:0% +Plaza in return for which it gets more + + + align:start position:0% +Plaza in return for which it gets more +bu to build + + align:start position:0% + + + + align:start position:0% + +taller the role of the + + align:start position:0% +taller the role of the + + + align:start position:0% +taller the role of the +ground in these two cases are the + + align:start position:0% +ground in these two cases are the + + + align:start position:0% +ground in these two cases are the +subject of an + + align:start position:0% +subject of an + + + align:start position:0% +subject of an +economic theory which is just the ru of + + align:start position:0% +economic theory which is just the ru of + + + align:start position:0% +economic theory which is just the ru of +Thum it's observed + + align:start position:0% +Thum it's observed + + + align:start position:0% +Thum it's observed +I don't have a rule + + align:start position:0% +I don't have a rule + + + align:start position:0% +I don't have a rule +of it's much like uh well other rules of + + align:start position:0% +of it's much like uh well other rules of + + + align:start position:0% +of it's much like uh well other rules of +thumb in our business in + + align:start position:0% + + + + align:start position:0% + +fact it's a curious in a discipline such + + align:start position:0% +fact it's a curious in a discipline such + + + align:start position:0% +fact it's a curious in a discipline such +as architecture there are very few + + align:start position:0% +as architecture there are very few + + + align:start position:0% +as architecture there are very few +theoretical texts there used to be + + align:start position:0% +theoretical texts there used to be + + + align:start position:0% +theoretical texts there used to be +theoretical + + align:start position:0% + + + + align:start position:0% + +texts how do you learn architecture have + + align:start position:0% +texts how do you learn architecture have + + + align:start position:0% +texts how do you learn architecture have +you got a textbook + + align:start position:0% + + + + align:start position:0% + +you can't learn science without a + + align:start position:0% +you can't learn science without a + + + align:start position:0% +you can't learn science without a +textbook textbook is the agreed upon + + align:start position:0% +textbook textbook is the agreed upon + + + align:start position:0% +textbook textbook is the agreed upon +synthesized material which you need to + + align:start position:0% + + + + align:start position:0% + +know I make this preface because some of + + align:start position:0% +know I make this preface because some of + + + align:start position:0% +know I make this preface because some of +the theoretical propositions we will + + align:start position:0% +the theoretical propositions we will + + + align:start position:0% +the theoretical propositions we will +look at today suffer from the same + + align:start position:0% +look at today suffer from the same + + + align:start position:0% +look at today suffer from the same +difficulty + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +they unlike + + align:start position:0% +they unlike + + + align:start position:0% +they unlike +the theories which we looked at on + + align:start position:0% +the theories which we looked at on + + + align:start position:0% +the theories which we looked at on +Tuesday where space was either + + align:start position:0% +Tuesday where space was either + + + align:start position:0% +Tuesday where space was either +neutral or costly or friction producing + + align:start position:0% +neutral or costly or friction producing + + + align:start position:0% +neutral or costly or friction producing +or measure for recording a distribution + + align:start position:0% +or measure for recording a distribution + + + align:start position:0% +or measure for recording a distribution +of some + + align:start position:0% +of some + + + align:start position:0% +of some +process most of what we feel to be true + + align:start position:0% +process most of what we feel to be true + + + align:start position:0% +process most of what we feel to be true +and experience with the city is + + align:start position:0% + + + + align:start position:0% + +lost none of the social science theories + + align:start position:0% +lost none of the social science theories + + + align:start position:0% +lost none of the social science theories +with the exception perhaps of the first + + align:start position:0% +with the exception perhaps of the first + + + align:start position:0% +with the exception perhaps of the first +one which we + + align:start position:0% +one which we + + + align:start position:0% +one which we +discussed has any connection to valuing + + align:start position:0% +discussed has any connection to valuing + + + align:start position:0% +discussed has any connection to valuing +the built environment as something in + + align:start position:0% +the built environment as something in + + + align:start position:0% +the built environment as something in +itself Kevin Lynch is the first of the + + align:start position:0% +itself Kevin Lynch is the first of the + + + align:start position:0% +itself Kevin Lynch is the first of the +protagonists of a theory which deals + + align:start position:0% +protagonists of a theory which deals + + + align:start position:0% +protagonists of a theory which deals +with the quality of the built + + align:start position:0% +with the quality of the built + + + align:start position:0% +with the quality of the built +environment + + align:start position:0% +environment + + + align:start position:0% +environment +on + + align:start position:0% +on + + + align:start position:0% +on +mass not a single building but a system + + align:start position:0% +mass not a single building but a system + + + align:start position:0% +mass not a single building but a system +of + + align:start position:0% + + + + align:start position:0% + +buildings Lynch + + align:start position:0% +buildings Lynch + + + align:start position:0% +buildings Lynch +starts his + + align:start position:0% +starts his + + + align:start position:0% +starts his +work there's an archive of Lynch's work + + align:start position:0% +work there's an archive of Lynch's work + + + align:start position:0% +work there's an archive of Lynch's work +at MIT just down the + + align:start position:0% +at MIT just down the + + + align:start position:0% +at MIT just down the +corridor if you have time one day and + + align:start position:0% +corridor if you have time one day and + + + align:start position:0% +corridor if you have time one day and +you have nothing else to look at his + + align:start position:0% +you have nothing else to look at his + + + align:start position:0% +you have nothing else to look at his +Notebook on his first visit to Italy + + align:start position:0% +Notebook on his first visit to Italy + + + align:start position:0% +Notebook on his first visit to Italy +when he was a young Professor here at + + align:start position:0% +when he was a young Professor here at + + + align:start position:0% +when he was a young Professor here at +MIT he does a detailed drawing of the + + align:start position:0% +MIT he does a detailed drawing of the + + + align:start position:0% +MIT he does a detailed drawing of the +path system linking the major squares + + align:start position:0% +path system linking the major squares + + + align:start position:0% +path system linking the major squares +and Pia the Pia and + + align:start position:0% +and Pia the Pia and + + + align:start position:0% +and Pia the Pia and +churches beautifully + + align:start position:0% +churches beautifully + + + align:start position:0% +churches beautifully +drawn at the end of his four days of + + align:start position:0% +drawn at the end of his four days of + + + align:start position:0% +drawn at the end of his four days of +four or five days in + + align:start position:0% +four or five days in + + + align:start position:0% +four or five days in +Florence he writes a note why did I not + + align:start position:0% +Florence he writes a note why did I not + + + align:start position:0% +Florence he writes a note why did I not +ask the people what they do on Saturday + + align:start position:0% +ask the people what they do on Saturday + + + align:start position:0% +ask the people what they do on Saturday +nights what about the activity in this + + align:start position:0% +nights what about the activity in this + + + align:start position:0% +nights what about the activity in this +town why don't I take that into account + + align:start position:0% +town why don't I take that into account + + + align:start position:0% +town why don't I take that into account +then he leaves + + align:start position:0% +then he leaves + + + align:start position:0% +then he leaves +Florence his preoccupation + + align:start position:0% +Florence his preoccupation + + + align:start position:0% +Florence his preoccupation +with trying to + + align:start position:0% +with trying to + + + align:start position:0% +with trying to +understand the spatial pattern of + + align:start position:0% +understand the spatial pattern of + + + align:start position:0% +understand the spatial pattern of +cities through aring + + align:start position:0% +cities through aring + + + align:start position:0% +cities through aring +people his evidence in his first book + + align:start position:0% +people his evidence in his first book + + + align:start position:0% +people his evidence in his first book +the image of the city what is the image + + align:start position:0% +the image of the city what is the image + + + align:start position:0% +the image of the city what is the image +of the city con the image of the city is + + align:start position:0% +of the city con the image of the city is + + + align:start position:0% +of the city con the image of the city is +made up of three items what are the + + align:start position:0% +made up of three items what are the + + + align:start position:0% +made up of three items what are the +three you've read the book I + + align:start position:0% +three you've read the book I + + + align:start position:0% +three you've read the book I +presume what are the + + align:start position:0% +presume what are the + + + align:start position:0% +presume what are the +three there's a experiment where they + + align:start position:0% +three there's a experiment where they + + + align:start position:0% +three there's a experiment where they +ask people on the street yes and I + + align:start position:0% +ask people on the street yes and I + + + align:start position:0% +ask people on the street yes and I +didn't ask you for what how the study + + align:start position:0% +didn't ask you for what how the study + + + align:start position:0% +didn't ask you for what how the study +was done I asked you what are the three + + align:start position:0% +was done I asked you what are the three + + + align:start position:0% +was done I asked you what are the three +component the three abstract components + + align:start position:0% +component the three abstract components + + + align:start position:0% +component the three abstract components +of I'll tell you identity structure and + + align:start position:0% +of I'll tell you identity structure and + + + align:start position:0% +of I'll tell you identity structure and +meaning that equals + + align:start position:0% +meaning that equals + + + align:start position:0% +meaning that equals +image and you find this out by cognitive + + align:start position:0% +image and you find this out by cognitive + + + align:start position:0% +image and you find this out by cognitive +mapping by asking people how they find + + align:start position:0% +mapping by asking people how they find + + + align:start position:0% +mapping by asking people how they find +their way around cities Los Angeles New + + align:start position:0% +their way around cities Los Angeles New + + + align:start position:0% +their way around cities Los Angeles New +York Boston and so + + align:start position:0% + + + + align:start position:0% + +on what Lynch could not do in that study + + align:start position:0% +on what Lynch could not do in that study + + + align:start position:0% +on what Lynch could not do in that study +was deal with + + align:start position:0% + + + + align:start position:0% + +meaning it's significant that + + align:start position:0% +meaning it's significant that + + + align:start position:0% +meaning it's significant that +the the power that the image of the city + + align:start position:0% +the the power that the image of the city + + + align:start position:0% +the the power that the image of the city +book had escapes the one component which + + align:start position:0% +book had escapes the one component which + + + align:start position:0% +book had escapes the one component which +bedevils us in our evaluation of much of + + align:start position:0% +bedevils us in our evaluation of much of + + + align:start position:0% +bedevils us in our evaluation of much of +the built environment and that's + + align:start position:0% + + + + align:start position:0% + +meaning he Kevin apologized twice in + + align:start position:0% +meaning he Kevin apologized twice in + + + align:start position:0% +meaning he Kevin apologized twice in +different Publications for his inability + + align:start position:0% +different Publications for his inability + + + align:start position:0% +different Publications for his inability +to deal with meaning + + align:start position:0% + + + + align:start position:0% + +I say that as a beginning + + align:start position:0% +I say that as a beginning + + + align:start position:0% +I say that as a beginning +to + + align:start position:0% +to + + + align:start position:0% +to +his uh discussion of his + + align:start position:0% + + + + align:start position:0% + +work when in this + + align:start position:0% +work when in this + + + align:start position:0% +work when in this +class we asked people when he was + + align:start position:0% +class we asked people when he was + + + align:start position:0% +class we asked people when he was +teaching here with + + align:start position:0% +teaching here with + + + align:start position:0% +teaching here with +me uh what they remembered of the + + align:start position:0% +me uh what they remembered of the + + + align:start position:0% +me uh what they remembered of the +book uh they would say + + align:start position:0% +book uh they would say + + + align:start position:0% +book uh they would say +landmarks uh zzz a set of alphabetical + + align:start position:0% +landmarks uh zzz a set of alphabetical + + + align:start position:0% +landmarks uh zzz a set of alphabetical +it items and lynce says that's not what + + align:start position:0% +it items and lynce says that's not what + + + align:start position:0% +it items and lynce says that's not what +I wrote the book for I wrote the book to + + align:start position:0% +I wrote the book for I wrote the book to + + + align:start position:0% +I wrote the book for I wrote the book to +make it clear that if you want to know + + align:start position:0% +make it clear that if you want to know + + + align:start position:0% +make it clear that if you want to know +something about a city you have to ask + + align:start position:0% +something about a city you have to ask + + + align:start position:0% +something about a city you have to ask +the people who live in + + align:start position:0% +the people who live in + + + align:start position:0% +the people who live in +it not take + + align:start position:0% +it not take + + + align:start position:0% +it not take +formulaic + + align:start position:0% + + + + align:start position:0% + +generalizations of course he was being a + + align:start position:0% +generalizations of course he was being a + + + align:start position:0% +generalizations of course he was being a +bit harsh on + + align:start position:0% +bit harsh on + + + align:start position:0% +bit harsh on +himself + + align:start position:0% + + + + align:start position:0% + +but his last book I must say one of the + + align:start position:0% +but his last book I must say one of the + + + align:start position:0% +but his last book I must say one of the +things about all the theorists I'll be + + align:start position:0% +things about all the theorists I'll be + + + align:start position:0% +things about all the theorists I'll be +discussing today is that they've + + align:start position:0% +discussing today is that they've + + + align:start position:0% +discussing today is that they've +published the + + align:start position:0% +published the + + + align:start position:0% +published the +ideas they're not + + align:start position:0% +ideas they're not + + + align:start position:0% +ideas they're not +hermeneutic they're not hermetic they're + + align:start position:0% +hermeneutic they're not hermetic they're + + + align:start position:0% +hermeneutic they're not hermetic they're +not sealed off from + + align:start position:0% + + + + align:start position:0% + +examination in + + align:start position:0% +examination in + + + align:start position:0% +examination in +architecture so much of knowledge is + + align:start position:0% +architecture so much of knowledge is + + + align:start position:0% +architecture so much of knowledge is +internalized + + align:start position:0% + + + + align:start position:0% + +your sensibility to patterns is built up + + align:start position:0% +your sensibility to patterns is built up + + + align:start position:0% +your sensibility to patterns is built up +through much of the practice of + + align:start position:0% + + + + align:start position:0% + +priesthood Lynch and he the others today + + align:start position:0% +priesthood Lynch and he the others today + + + align:start position:0% +priesthood Lynch and he the others today +by the way the others today will be in + + align:start position:0% +by the way the others today will be in + + + align:start position:0% +by the way the others today will be in +order Kevin Lynch Christopher Alexander + + align:start position:0% +order Kevin Lynch Christopher Alexander + + + align:start position:0% +order Kevin Lynch Christopher Alexander +John harrack + + align:start position:0% +John harrack + + + align:start position:0% +John harrack +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +space syntax and the last will look at + + align:start position:0% +space syntax and the last will look at + + + align:start position:0% +space syntax and the last will look at +the work of + + align:start position:0% +the work of + + + align:start position:0% +the work of +the British land use and buil form group + + align:start position:0% +the British land use and buil form group + + + align:start position:0% +the British land use and buil form group +in Cambridge England Lal March s Lal + + align:start position:0% +in Cambridge England Lal March s Lal + + + align:start position:0% +in Cambridge England Lal March s Lal +March I know he was nighted sorry just + + align:start position:0% +March I know he was nighted sorry just + + + align:start position:0% +March I know he was nighted sorry just +Lal + + align:start position:0% +Lal + + + align:start position:0% +Lal +March + + align:start position:0% + + + + align:start position:0% + +uh for + + align:start position:0% +uh for + + + align:start position:0% +uh for +Lynch the problem remains that + + align:start position:0% + + + + align:start position:0% + +let me see if I can find a + + align:start position:0% + + + + align:start position:0% + +phrase no there's there isn't one phrase + + align:start position:0% +phrase no there's there isn't one phrase + + + align:start position:0% +phrase no there's there isn't one phrase +that I can find which sums up he search + + align:start position:0% +that I can find which sums up he search + + + align:start position:0% +that I can find which sums up he search +what I'll do with him + + align:start position:0% +what I'll do with him + + + align:start position:0% +what I'll do with him +is go + + align:start position:0% +is go + + + align:start position:0% +is go +through the performance of Dimension + + align:start position:0% +through the performance of Dimension + + + align:start position:0% +through the performance of Dimension +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +which is the last one which + + align:start position:0% +which is the last one which + + + align:start position:0% +which is the last one which +is he per built up in this + + align:start position:0% +is he per built up in this + + + align:start position:0% +is he per built up in this +class and which is published in the book + + align:start position:0% +class and which is published in the book + + + align:start position:0% +class and which is published in the book +which was called theory of good City + + align:start position:0% +which was called theory of good City + + + align:start position:0% +which was called theory of good City +form and then appeared later as good + + align:start position:0% +form and then appeared later as good + + + align:start position:0% +form and then appeared later as good +City + + align:start position:0% +City + + + align:start position:0% +City +form um and use that as uh and then I + + align:start position:0% +form um and use that as uh and then I + + + align:start position:0% +form um and use that as uh and then I +will compare that with his + + align:start position:0% +will compare that with his + + + align:start position:0% +will compare that with his +writings on a utopian speculation that + + align:start position:0% +writings on a utopian speculation that + + + align:start position:0% +writings on a utopian speculation that +he made just to give some embodiment to + + align:start position:0% +he made just to give some embodiment to + + + align:start position:0% +he made just to give some embodiment to +his + + align:start position:0% + + + + align:start position:0% + +ideas some + + align:start position:0% + + + + align:start position:0% + +generalizations unlike Christopher + + align:start position:0% +generalizations unlike Christopher + + + align:start position:0% +generalizations unlike Christopher +Alexander and John oen ly's work is not + + align:start position:0% +Alexander and John oen ly's work is not + + + align:start position:0% +Alexander and John oen ly's work is not +a critique of contemporary urbanism + + align:start position:0% + + + + align:start position:0% + +his + + align:start position:0% +his + + + align:start position:0% +his +philosophy he in relation to present day + + align:start position:0% +philosophy he in relation to present day + + + align:start position:0% +philosophy he in relation to present day +City and + + align:start position:0% + + + + align:start position:0% + +time he's completely interested in the + + align:start position:0% +time he's completely interested in the + + + align:start position:0% +time he's completely interested in the +complexity and difficulty have + + align:start position:0% +complexity and difficulty have + + + align:start position:0% +complexity and difficulty have +understanding of the form of a + + align:start position:0% +understanding of the form of a + + + align:start position:0% +understanding of the form of a +city he believes there are ranges of + + align:start position:0% +city he believes there are ranges of + + + align:start position:0% +city he believes there are ranges of +understanding + + align:start position:0% +understanding + + + align:start position:0% +understanding +not + + align:start position:0% +not + + + align:start position:0% +not +standards his theory performance + + align:start position:0% +standards his theory performance + + + align:start position:0% +standards his theory performance +Dimension set up + + align:start position:0% +Dimension set up + + + align:start position:0% +Dimension set up +ranges within which different cultures + + align:start position:0% +ranges within which different cultures + + + align:start position:0% +ranges within which different cultures +could construct their own + + align:start position:0% +could construct their own + + + align:start position:0% +could construct their own +standards and which the dimensions could + + align:start position:0% +standards and which the dimensions could + + + align:start position:0% +standards and which the dimensions could +be compared one to another and then + + align:start position:0% +be compared one to another and then + + + align:start position:0% +be compared one to another and then +balanced against + + align:start position:0% +balanced against + + + align:start position:0% +balanced against +two meta criteria + + align:start position:0% +two meta criteria + + + align:start position:0% +two meta criteria +Justice and + + align:start position:0% + + + + align:start position:0% + +application + + align:start position:0% +application + + + align:start position:0% +application +Lynch a human Lynch is humanism + + align:start position:0% +Lynch a human Lynch is humanism + + + align:start position:0% +Lynch a human Lynch is humanism +comes from his appreciation of one of + + align:start position:0% +comes from his appreciation of one of + + + align:start position:0% +comes from his appreciation of one of +the major dimensions of human of the + + align:start position:0% +the major dimensions of human of the + + + align:start position:0% +the major dimensions of human of the +human system and that's its capacity to + + align:start position:0% + + + + align:start position:0% + +learn and + + align:start position:0% + + + + align:start position:0% + +therefore he I ideal Utopia is a + + align:start position:0% +therefore he I ideal Utopia is a + + + align:start position:0% +therefore he I ideal Utopia is a +manifestation of of human being's AB + + align:start position:0% +manifestation of of human being's AB + + + align:start position:0% +manifestation of of human being's AB +ability to change culture and + + align:start position:0% +ability to change culture and + + + align:start position:0% +ability to change culture and +aspirations rather than the + + align:start position:0% +aspirations rather than the + + + align:start position:0% +aspirations rather than the +manifestation of some iron + + align:start position:0% +manifestation of some iron + + + align:start position:0% +manifestation of some iron +law there is no drawing in his + + align:start position:0% +law there is no drawing in his + + + align:start position:0% +law there is no drawing in his +Utopia it's partly because of + + align:start position:0% + + + + align:start position:0% + +his decision that + + align:start position:0% +his decision that + + + align:start position:0% +his decision that +architecture doesn't help much in + + align:start position:0% +architecture doesn't help much in + + + align:start position:0% +architecture doesn't help much in +understanding Urban + + align:start position:0% +understanding Urban + + + align:start position:0% +understanding Urban +form I recall a + + align:start position:0% + + + + align:start position:0% + +disagreement I had in this class with + + align:start position:0% +disagreement I had in this class with + + + align:start position:0% +disagreement I had in this class with +him when I introduced Alder Rossi's book + + align:start position:0% +him when I introduced Alder Rossi's book + + + align:start position:0% +him when I introduced Alder Rossi's book +which was new at the + + align:start position:0% +which was new at the + + + align:start position:0% +which was new at the +time and uh Lynch was very + + align:start position:0% +time and uh Lynch was very + + + align:start position:0% +time and uh Lynch was very +angry and uh writes + + align:start position:0% +angry and uh writes + + + align:start position:0% +angry and uh writes +about the denouncement of Alo rosi I + + align:start position:0% +about the denouncement of Alo rosi I + + + align:start position:0% +about the denouncement of Alo rosi I +tried to argue that there was some very + + align:start position:0% +tried to argue that there was some very + + + align:start position:0% +tried to argue that there was some very +Merit in rossy's + + align:start position:0% +Merit in rossy's + + + align:start position:0% +Merit in rossy's +speculation as an architect and + + align:start position:0% +speculation as an architect and + + + align:start position:0% +speculation as an architect and +so + + align:start position:0% +so + + + align:start position:0% +so +on I don't understand why + + align:start position:0% +on I don't understand why + + + align:start position:0% +on I don't understand why +Lynch disparaged architecture as such he + + align:start position:0% +Lynch disparaged architecture as such he + + + align:start position:0% +Lynch disparaged architecture as such he +didn't disparage architecture as a + + align:start position:0% +didn't disparage architecture as a + + + align:start position:0% +didn't disparage architecture as a +discipline he disparaged the method in + + align:start position:0% +discipline he disparaged the method in + + + align:start position:0% +discipline he disparaged the method in +which Architects took upon themselves + + align:start position:0% +which Architects took upon themselves + + + align:start position:0% +which Architects took upon themselves +the right to invent ideas spatial ideas + + align:start position:0% +the right to invent ideas spatial ideas + + + align:start position:0% +the right to invent ideas spatial ideas +on their + + align:start position:0% +on their + + + align:start position:0% +on their +own again without + + align:start position:0% +own again without + + + align:start position:0% +own again without +consultation it + + align:start position:0% +consultation it + + + align:start position:0% +consultation it +is Lynch was so AUST at the idea of a an + + align:start position:0% +is Lynch was so AUST at the idea of a an + + + align:start position:0% +is Lynch was so AUST at the idea of a an +Imperial rulership of + + align:start position:0% + + + + align:start position:0% + +knowledge and he hesitated every time to + + align:start position:0% +knowledge and he hesitated every time to + + + align:start position:0% +knowledge and he hesitated every time to +embrace something unless it had + + align:start position:0% +embrace something unless it had + + + align:start position:0% +embrace something unless it had +been acknowledged by Human + + align:start position:0% + + + + align:start position:0% + +Experience many of these people whose + + align:start position:0% +Experience many of these people whose + + + align:start position:0% +Experience many of these people whose +theories I'm talking about today + + align:start position:0% +theories I'm talking about today + + + align:start position:0% +theories I'm talking about today +are very much rooted in + + align:start position:0% +are very much rooted in + + + align:start position:0% +are very much rooted in +observing existing patterns and building + + align:start position:0% +observing existing patterns and building + + + align:start position:0% +observing existing patterns and building +on + + align:start position:0% +on + + + align:start position:0% +on +them they differ in respect to the way + + align:start position:0% +them they differ in respect to the way + + + align:start position:0% +them they differ in respect to the way +in which they observe these patterns + + align:start position:0% +in which they observe these patterns + + + align:start position:0% +in which they observe these patterns +what they make of them I will show you + + align:start position:0% +what they make of them I will show you + + + align:start position:0% +what they make of them I will show you +that in Christopher Alexander's pattern + + align:start position:0% +that in Christopher Alexander's pattern + + + align:start position:0% +that in Christopher Alexander's pattern +language he makes absolute + + align:start position:0% +language he makes absolute + + + align:start position:0% +language he makes absolute +decision dis + + align:start position:0% +decision dis + + + align:start position:0% +decision dis +derivations from is observation of human + + align:start position:0% +derivations from is observation of human + + + align:start position:0% +derivations from is observation of human +behavior JN AB Bren never makes a + + align:start position:0% +behavior JN AB Bren never makes a + + + align:start position:0% +behavior JN AB Bren never makes a +categorical good or + + align:start position:0% +categorical good or + + + align:start position:0% +categorical good or +bad John AB Bren believes that all the + + align:start position:0% +bad John AB Bren believes that all the + + + align:start position:0% +bad John AB Bren believes that all the +Agreements are good because they are + + align:start position:0% +Agreements are good because they are + + + align:start position:0% +Agreements are good because they are +saturated with information from culture + + align:start position:0% +saturated with information from culture + + + align:start position:0% +saturated with information from culture +and so + + align:start position:0% +and so + + + align:start position:0% +and so +on + + align:start position:0% + + + + align:start position:0% + +Lynch wishes to build a + + align:start position:0% +Lynch wishes to build a + + + align:start position:0% +Lynch wishes to build a +model for the world as if + + align:start position:0% +model for the world as if + + + align:start position:0% +model for the world as if +urbanism was at the beginning of its + + align:start position:0% + + + + align:start position:0% + +trajectory he believes that in the model + + align:start position:0% +trajectory he believes that in the model + + + align:start position:0% +trajectory he believes that in the model +of + + align:start position:0% +of + + + align:start position:0% +of +science that science started from + + align:start position:0% +science that science started from + + + align:start position:0% +science that science started from +nowhere it kept on repeating experiments + + align:start position:0% +nowhere it kept on repeating experiments + + + align:start position:0% +nowhere it kept on repeating experiments +developing new and new identity new and + + align:start position:0% +developing new and new identity new and + + + align:start position:0% +developing new and new identity new and +new + + align:start position:0% +new + + + align:start position:0% +new +ideology and uh reaching a point where + + align:start position:0% +ideology and uh reaching a point where + + + align:start position:0% +ideology and uh reaching a point where +it was much more + + align:start position:0% +it was much more + + + align:start position:0% +it was much more +sophisticated than where it + + align:start position:0% +sophisticated than where it + + + align:start position:0% +sophisticated than where it +began so he starts off by setting out + + align:start position:0% +began so he starts off by setting out + + + align:start position:0% +began so he starts off by setting out +the dimensions that you had to take this + + align:start position:0% +the dimensions that you had to take this + + + align:start position:0% +the dimensions that you had to take this +is + + align:start position:0% +is + + + align:start position:0% +is +Kepler looking at this trying to derive + + align:start position:0% +Kepler looking at this trying to derive + + + align:start position:0% +Kepler looking at this trying to derive +a theory of the the + + align:start position:0% +a theory of the the + + + align:start position:0% +a theory of the the +Earth's + + align:start position:0% +Earth's + + + align:start position:0% +Earth's +movement Lynch is trying to set forth + + align:start position:0% +movement Lynch is trying to set forth + + + align:start position:0% +movement Lynch is trying to set forth +what are the things that you have to + + align:start position:0% +what are the things that you have to + + + align:start position:0% +what are the things that you have to +take into account and measure + + align:start position:0% +take into account and measure + + + align:start position:0% +take into account and measure +in order to have a comprehensive view of + + align:start position:0% +in order to have a comprehensive view of + + + align:start position:0% +in order to have a comprehensive view of +a City Independent of which place in the + + align:start position:0% +a City Independent of which place in the + + + align:start position:0% +a City Independent of which place in the +world it is independent of which + + align:start position:0% +world it is independent of which + + + align:start position:0% +world it is independent of which +culture he experiments with + + align:start position:0% + + + + align:start position:0% + +these and uh as a set of + + align:start position:0% + + + + align:start position:0% + +ideas + + align:start position:0% +ideas + + + align:start position:0% +ideas +which he writes about which set up which + + align:start position:0% +which he writes about which set up which + + + align:start position:0% +which he writes about which set up which +the pre PR the + + align:start position:0% +the pre PR the + + + align:start position:0% +the pre PR the +prologue + + align:start position:0% +prologue + + + align:start position:0% +prologue +to these + + align:start position:0% +to these + + + align:start position:0% +to these +ideas I gave you in the handout today + + align:start position:0% +ideas I gave you in the handout today + + + align:start position:0% +ideas I gave you in the handout today +one of the sub ideas it was the notion + + align:start position:0% +one of the sub ideas it was the notion + + + align:start position:0% +one of the sub ideas it was the notion +of + + align:start position:0% +of + + + align:start position:0% +of +adaptability again adaptability would + + align:start position:0% +adaptability again adaptability would + + + align:start position:0% +adaptability again adaptability would +interest Lynch because it is the + + align:start position:0% +interest Lynch because it is the + + + align:start position:0% +interest Lynch because it is the +capacity of the human being to change + + align:start position:0% +capacity of the human being to change + + + align:start position:0% +capacity of the human being to change +patterns after + + align:start position:0% +patterns after + + + align:start position:0% +patterns after +learning adaptability in in our class + + align:start position:0% +learning adaptability in in our class + + + align:start position:0% +learning adaptability in in our class +discussion was a separate item it became + + align:start position:0% +discussion was a separate item it became + + + align:start position:0% +discussion was a separate item it became +in the book a subset of the item + + align:start position:0% +in the book a subset of the item + + + align:start position:0% +in the book a subset of the item +fit I gave you this + + align:start position:0% +fit I gave you this + + + align:start position:0% +fit I gave you this +piece on + + align:start position:0% +piece on + + + align:start position:0% +piece on +adaptability as an example of how he + + align:start position:0% +adaptability as an example of how he + + + align:start position:0% +adaptability as an example of how he +would ask you to develop it he + + align:start position:0% +would ask you to develop it he + + + align:start position:0% +would ask you to develop it he +sub let me find an example of what I + + align:start position:0% +sub let me find an example of what I + + + align:start position:0% +sub let me find an example of what I +gave to you + + align:start position:0% + + + + align:start position:0% + +today he tries to break down + + align:start position:0% +today he tries to break down + + + align:start position:0% +today he tries to break down +adaptability into + + align:start position:0% + + + + align:start position:0% + +subcategories manipulability which is + + align:start position:0% +subcategories manipulability which is + + + align:start position:0% +subcategories manipulability which is +different from reversibility + + align:start position:0% +different from reversibility + + + align:start position:0% +different from reversibility +what is resilience what is + + align:start position:0% +what is resilience what is + + + align:start position:0% +what is resilience what is +innovativeness I + + align:start position:0% + + + + align:start position:0% + +then add in your thing I've given you + + align:start position:0% +then add in your thing I've given you + + + align:start position:0% +then add in your thing I've given you +some handwritten response from + + align:start position:0% +some handwritten response from + + + align:start position:0% +some handwritten response from +Lynch not + + align:start position:0% +Lynch not + + + align:start position:0% +Lynch not +because it's that you should read it but + + align:start position:0% +because it's that you should read it but + + + align:start position:0% +because it's that you should read it but +here is an idea he writes this peace on + + align:start position:0% +here is an idea he writes this peace on + + + align:start position:0% +here is an idea he writes this peace on +adaptability circulates it + + align:start position:0% +adaptability circulates it + + + align:start position:0% +adaptability circulates it +somebody an economist sends back + + align:start position:0% +somebody an economist sends back + + + align:start position:0% +somebody an economist sends back +a a review of his + + align:start position:0% +a a review of his + + + align:start position:0% +a a review of his +ideas and then he replies to The + + align:start position:0% +ideas and then he replies to The + + + align:start position:0% +ideas and then he replies to The +Economist this is a handwritten reply to + + align:start position:0% +Economist this is a handwritten reply to + + + align:start position:0% +Economist this is a handwritten reply to +a + + align:start position:0% +a + + + align:start position:0% +a +colleague his imagination is that if we + + align:start position:0% +colleague his imagination is that if we + + + align:start position:0% +colleague his imagination is that if we +each all the students of urbanism took + + align:start position:0% +each all the students of urbanism took + + + align:start position:0% +each all the students of urbanism took +on the task of + + align:start position:0% +on the task of + + + align:start position:0% +on the task of +identifying in specific terms what these + + align:start position:0% +identifying in specific terms what these + + + align:start position:0% +identifying in specific terms what these +cies were + + align:start position:0% +cies were + + + align:start position:0% +cies were +inability we would have a basis for a + + align:start position:0% +inability we would have a basis for a + + + align:start position:0% +inability we would have a basis for a +specific culture settling an item of + + align:start position:0% +specific culture settling an item of + + + align:start position:0% +specific culture settling an item of +reversibility in specific + + align:start position:0% +reversibility in specific + + + align:start position:0% +reversibility in specific +terms um standards would imply that all + + align:start position:0% +terms um standards would imply that all + + + align:start position:0% +terms um standards would imply that all +of them are equal for all cultures of + + align:start position:0% +of them are equal for all cultures of + + + align:start position:0% +of them are equal for all cultures of +course that's not true you could have + + align:start position:0% +course that's not true you could have + + + align:start position:0% +course that's not true you could have +varying standards but for Lynch the idea + + align:start position:0% +varying standards but for Lynch the idea + + + align:start position:0% +varying standards but for Lynch the idea +was that we were in such a rough + + align:start position:0% +was that we were in such a rough + + + align:start position:0% +was that we were in such a rough +State + + align:start position:0% +State + + + align:start position:0% +State +theoretically that you had to set out uh + + align:start position:0% +theoretically that you had to set out uh + + + align:start position:0% +theoretically that you had to set out uh +these items more + + align:start position:0% + + + + align:start position:0% + +systematically he didn't get very far he + + align:start position:0% +systematically he didn't get very far he + + + align:start position:0% +systematically he didn't get very far he +died to + + align:start position:0% +died to + + + align:start position:0% +died to +Young and uh if he were here today he'd + + align:start position:0% +Young and uh if he were here today he'd + + + align:start position:0% +Young and uh if he were here today he'd +add more than I'm able to explain on his + + align:start position:0% +add more than I'm able to explain on his + + + align:start position:0% +add more than I'm able to explain on his +behalf + + align:start position:0% +behalf + + + align:start position:0% +behalf +of + + align:start position:0% +of + + + align:start position:0% +of +um in his collected works there's a + + align:start position:0% +um in his collected works there's a + + + align:start position:0% +um in his collected works there's a +chapter called a place + + align:start position:0% +chapter called a place + + + align:start position:0% +chapter called a place +Utopia now it's interesting that this + + align:start position:0% +Utopia now it's interesting that this + + + align:start position:0% +Utopia now it's interesting that this +place Utopia which is the speculation + + align:start position:0% +place Utopia which is the speculation + + + align:start position:0% +place Utopia which is the speculation +about what an ideal Urban world would + + align:start position:0% +about what an ideal Urban world would + + + align:start position:0% +about what an ideal Urban world would +look like there's no + + align:start position:0% + + + + align:start position:0% + +drawing in the image of the city he uses + + align:start position:0% +drawing in the image of the city he uses + + + align:start position:0% +drawing in the image of the city he uses +little drawings on the side of the text + + align:start position:0% +little drawings on the side of the text + + + align:start position:0% +little drawings on the side of the text +to add information + + align:start position:0% +to add information + + + align:start position:0% +to add information +visually here there is no + + align:start position:0% + + + + align:start position:0% + +drawing I'll just pick out a couple of + + align:start position:0% +drawing I'll just pick out a couple of + + + align:start position:0% +drawing I'll just pick out a couple of +items from the place Utopia has anybody + + align:start position:0% +items from the place Utopia has anybody + + + align:start position:0% +items from the place Utopia has anybody +read a place + + align:start position:0% +read a place + + + align:start position:0% +read a place +Utopia we're not wasting my time then or + + align:start position:0% +Utopia we're not wasting my time then or + + + align:start position:0% +Utopia we're not wasting my time then or +your time + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +propose he says to + + align:start position:0% +propose he says to + + + align:start position:0% +propose he says to +leave I attempt something more modest + + align:start position:0% +leave I attempt something more modest + + + align:start position:0% +leave I attempt something more modest +here without losing track of + + align:start position:0% +here without losing track of + + + align:start position:0% +here without losing track of +society I propose to leave it + + align:start position:0% +society I propose to leave it + + + align:start position:0% +society I propose to leave it +unaccounted for except where it Springs + + align:start position:0% +unaccounted for except where it Springs + + + align:start position:0% +unaccounted for except where it Springs +from from some feature of + + align:start position:0% +from from some feature of + + + align:start position:0% +from from some feature of +place everything about what I'm going to + + align:start position:0% +place everything about what I'm going to + + + align:start position:0% +place everything about what I'm going to +say is he says + + align:start position:0% +say is he says + + + align:start position:0% +say is he says +relates is about how people rate to + + align:start position:0% +relates is about how people rate to + + + align:start position:0% +relates is about how people rate to +their + + align:start position:0% +their + + + align:start position:0% +their +surroundings rather than out of a + + align:start position:0% +surroundings rather than out of a + + + align:start position:0% +surroundings rather than out of a +self-absorbed technical fantasy or + + align:start position:0% +self-absorbed technical fantasy or + + + align:start position:0% +self-absorbed technical fantasy or +mechanical consequence of social + + align:start position:0% +mechanical consequence of social + + + align:start position:0% +mechanical consequence of social +prescription on the other in other words + + align:start position:0% +prescription on the other in other words + + + align:start position:0% +prescription on the other in other words +what he's saying is that there are items + + align:start position:0% +what he's saying is that there are items + + + align:start position:0% +what he's saying is that there are items +which we can learn from Simply the way + + align:start position:0% +which we can learn from Simply the way + + + align:start position:0% +which we can learn from Simply the way +space is used and + + align:start position:0% + + + + align:start position:0% + +manipulated imagine an urban country + + align:start position:0% +manipulated imagine an urban country + + + align:start position:0% +manipulated imagine an urban country +side a highly varied but humanized + + align:start position:0% +side a highly varied but humanized + + + align:start position:0% +side a highly varied but humanized +landscape it is neither Urban or rural + + align:start position:0% +landscape it is neither Urban or rural + + + align:start position:0% +landscape it is neither Urban or rural +in the old sense since houses workplaces + + align:start position:0% +in the old sense since houses workplaces + + + align:start position:0% +in the old sense since houses workplaces +and are set among trees farms and + + align:start position:0% +and are set among trees farms and + + + align:start position:0% +and are set among trees farms and +streams within this extensive + + align:start position:0% +streams within this extensive + + + align:start position:0% +streams within this extensive +Countryside there's a network of small + + align:start position:0% +Countryside there's a network of small + + + align:start position:0% +Countryside there's a network of small +intensive Urban centers the countryside + + align:start position:0% +intensive Urban centers the countryside + + + align:start position:0% +intensive Urban centers the countryside +is as functionally intricate and + + align:start position:0% +is as functionally intricate and + + + align:start position:0% +is as functionally intricate and +interdependent as any contemporary + + align:start position:0% + + + + align:start position:0% + +City the land the space + + align:start position:0% + + + + align:start position:0% + +is not allocated to + + align:start position:0% + + + + align:start position:0% + +owners the use of land is brief in the + + align:start position:0% +owners the use of land is brief in the + + + align:start position:0% +owners the use of land is brief in the +history of + + align:start position:0% +history of + + + align:start position:0% +history of +cities so the much like we've picked up + + align:start position:0% +cities so the much like we've picked up + + + align:start position:0% +cities so the much like we've picked up +from other + + align:start position:0% +from other + + + align:start position:0% +from other +sources it is better for the land to be + + align:start position:0% +sources it is better for the land to be + + + align:start position:0% +sources it is better for the land to be +in the hand of a trust he calls them a + + align:start position:0% +in the hand of a trust he calls them a + + + align:start position:0% +in the hand of a trust he calls them a +regional Regional land and + + align:start position:0% + + + + align:start position:0% + +trust these trust Grant leases for the + + align:start position:0% +trust these trust Grant leases for the + + + align:start position:0% +trust these trust Grant leases for the +present enjoyment of + + align:start position:0% + + + + align:start position:0% + +space everyone is trained to read a + + align:start position:0% +space everyone is trained to read a + + + align:start position:0% +space everyone is trained to read a +place just as everyone is read trained + + align:start position:0% +place just as everyone is read trained + + + align:start position:0% +place just as everyone is read trained +to read a good book there are slow + + align:start position:0% +to read a good book there are slow + + + align:start position:0% +to read a good book there are slow +places and fast + + align:start position:0% + + + + align:start position:0% + +places I can go through this in some + + align:start position:0% +places I can go through this in some + + + align:start position:0% +places I can go through this in some +detail but you can read it + + align:start position:0% +detail but you can read it + + + align:start position:0% +detail but you can read it +yourself what is significant about it is + + align:start position:0% +yourself what is significant about it is + + + align:start position:0% +yourself what is significant about it is +that there's a he doesn't start off with + + align:start position:0% +that there's a he doesn't start off with + + + align:start position:0% +that there's a he doesn't start off with +a definition that a city is anything + + align:start position:0% +a definition that a city is anything + + + align:start position:0% +a definition that a city is anything +that cannot be replicated through a + + align:start position:0% +that cannot be replicated through a + + + align:start position:0% +that cannot be replicated through a +mixture of landscape and + + align:start position:0% +mixture of landscape and + + + align:start position:0% +mixture of landscape and +building he doesn't depict the building + + align:start position:0% +building he doesn't depict the building + + + align:start position:0% +building he doesn't depict the building +he says in a trained Society people will + + align:start position:0% +he says in a trained Society people will + + + align:start position:0% +he says in a trained Society people will +pick good buildings + + align:start position:0% +pick good buildings + + + align:start position:0% +pick good buildings +they will make them from good + + align:start position:0% +they will make them from good + + + align:start position:0% +they will make them from good +materials his emphasis is on depicting + + align:start position:0% +materials his emphasis is on depicting + + + align:start position:0% +materials his emphasis is on depicting +those spaces and buildings or + + align:start position:0% +those spaces and buildings or + + + align:start position:0% +those spaces and buildings or +infrastructure of a city which derive + + align:start position:0% +infrastructure of a city which derive + + + align:start position:0% +infrastructure of a city which derive +from the goodness of + + align:start position:0% +from the goodness of + + + align:start position:0% +from the goodness of +people + + align:start position:0% + + + + align:start position:0% + +now people are not + + align:start position:0% +now people are not + + + align:start position:0% +now people are not +good they're good and bad sometimes they + + align:start position:0% +good they're good and bad sometimes they + + + align:start position:0% +good they're good and bad sometimes they +both we are all good and bad in our life + + align:start position:0% +both we are all good and bad in our life + + + align:start position:0% +both we are all good and bad in our life +there's an element in many of these + + align:start position:0% +there's an element in many of these + + + align:start position:0% +there's an element in many of these +theorists in depicting a society without + + align:start position:0% +theorists in depicting a society without + + + align:start position:0% +theorists in depicting a society without +political + + align:start position:0% +political + + + align:start position:0% +political +friction without individual competition + + align:start position:0% +friction without individual competition + + + align:start position:0% +friction without individual competition +Jon AB bren's + + align:start position:0% +Jon AB bren's + + + align:start position:0% +Jon AB bren's +agreements he says good agreements will + + align:start position:0% +agreements he says good agreements will + + + align:start position:0% +agreements he says good agreements will +be made independent of whether you're + + align:start position:0% +be made independent of whether you're + + + align:start position:0% +be made independent of whether you're +Marxist or capitalist you will have to + + align:start position:0% +Marxist or capitalist you will have to + + + align:start position:0% +Marxist or capitalist you will have to +come to some agreement about where you + + align:start position:0% +come to some agreement about where you + + + align:start position:0% +come to some agreement about where you +enter a building whether they parking + + align:start position:0% +enter a building whether they parking + + + align:start position:0% +enter a building whether they parking +underground or how how many buildings + + align:start position:0% +underground or how how many buildings + + + align:start position:0% +underground or how how many buildings +floors of building they are above + + align:start position:0% + + + + align:start position:0% + +ground C Alexander also bypasses the + + align:start position:0% +ground C Alexander also bypasses the + + + align:start position:0% +ground C Alexander also bypasses the +political impact on his work he makes + + align:start position:0% +political impact on his work he makes + + + align:start position:0% +political impact on his work he makes +patterns he makes decisions about + + align:start position:0% +patterns he makes decisions about + + + align:start position:0% +patterns he makes decisions about +patterns which are not subject to + + align:start position:0% +patterns which are not subject to + + + align:start position:0% +patterns which are not subject to +intercourse for producing + + align:start position:0% +intercourse for producing + + + align:start position:0% +intercourse for producing +agreements these pattern are decided + + align:start position:0% +agreements these pattern are decided + + + align:start position:0% +agreements these pattern are decided +upon through his + + align:start position:0% +upon through his + + + align:start position:0% +upon through his +examination of the nature of + + align:start position:0% + + + + align:start position:0% + +order Alexander has an interesting + + align:start position:0% +order Alexander has an interesting + + + align:start position:0% +order Alexander has an interesting +trajectory in his + + align:start position:0% + + + + align:start position:0% + +work his first book notes on the + + align:start position:0% +work his first book notes on the + + + align:start position:0% +work his first book notes on the +synthesis of I don't know if any of you + + align:start position:0% +synthesis of I don't know if any of you + + + align:start position:0% +synthesis of I don't know if any of you +paid particular attention to Alexander's + + align:start position:0% +paid particular attention to Alexander's + + + align:start position:0% +paid particular attention to Alexander's +work has anybody been an + + align:start position:0% +work has anybody been an + + + align:start position:0% +work has anybody been an +Alexander student + + align:start position:0% + + + + align:start position:0% + +no CH + + align:start position:0% + + + + align:start position:0% + +Alexander when I first ran into him was + + align:start position:0% +Alexander when I first ran into him was + + + align:start position:0% +Alexander when I first ran into him was +at + + align:start position:0% +at + + + align:start position:0% +at +Harvard and he had written notes on the + + align:start position:0% +Harvard and he had written notes on the + + + align:start position:0% +Harvard and he had written notes on the +synthesis of + + align:start position:0% +synthesis of + + + align:start position:0% +synthesis of +form which was an admiration and an + + align:start position:0% +form which was an admiration and an + + + align:start position:0% +form which was an admiration and an +attempt to understand how a culture such + + align:start 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align:start position:0% +enormous +variation and the maintenance of + + align:start position:0% + + + + align:start position:0% + +quality + + align:start position:0% + + + + align:start position:0% + +he look to + + align:start position:0% +he look to + + + align:start position:0% +he look to +computation to enable us to perhaps do + + align:start position:0% +computation to enable us to perhaps do + + + align:start position:0% +computation to enable us to perhaps do +the same kind of thing that's maintain + + align:start position:0% +the same kind of thing that's maintain + + + align:start position:0% +the same kind of thing that's maintain +quality although + + align:start position:0% +quality although + + + align:start position:0% +quality although +explicitly unclear about how we were + + align:start position:0% +explicitly unclear about how we were + + + align:start position:0% +explicitly unclear about how we were +doing + + align:start position:0% +doing + + + align:start position:0% +doing +it + + align:start position:0% + + + + align:start position:0% + +um he's moved through a number of phases + + align:start position:0% +um he's moved through a number of phases + + + align:start position:0% +um he's moved through a number of phases +in his + + align:start position:0% +in his + + + align:start position:0% +in his +work no soon + + align:start position:0% + + + + align:start position:0% + +he been interested in + + align:start position:0% + + + + align:start position:0% + +optimization then he wrote a piece + + align:start position:0% +optimization then he wrote a piece + + + align:start position:0% +optimization then he wrote a piece +about how to maximize + + align:start position:0% +about how to maximize + + + align:start position:0% +about how to maximize +communication a silly piece in which he + + align:start position:0% +communication a silly piece in which he + + + align:start position:0% +communication a silly piece in which he +argues that in the zoning of suburban + + align:start position:0% +argues that in the zoning of suburban + + + align:start position:0% +argues that in the zoning of suburban +housing + + align:start position:0% +housing + + + align:start position:0% +housing +the the the living room should be + + align:start position:0% +the the the living room should be + + + align:start position:0% +the the the living room should be +exposed to the street and curtains would + + align:start position:0% +exposed to the street and curtains would + + + align:start position:0% +exposed to the street and curtains would +not would be unnecessary that people + + align:start position:0% +not would be unnecessary that people + + + align:start position:0% +not would be unnecessary that people +would enjoy partaking in the experience + + align:start position:0% +would enjoy partaking in the experience + + + align:start position:0% +would enjoy partaking in the experience +of being a community a + + align:start position:0% +of being a community a + + + align:start position:0% +of being a community a +remark which might well apply to New + + align:start position:0% +remark which might well apply to New + + + align:start position:0% +remark which might well apply to New +York City but not to an American + + align:start position:0% +York City but not to an American + + + align:start position:0% +York City but not to an American +suburb he then published a significant + + align:start position:0% +suburb he then published a significant + + + align:start position:0% +suburb he then published a significant +paper called + + align:start position:0% + + + + align:start position:0% + +this the structure of a city was not a + + align:start position:0% +this the structure of a city was not a + + + align:start position:0% +this the structure of a city was not a +tree it was more complicated than a tree + + align:start position:0% +tree it was more complicated than a tree + + + align:start position:0% +tree it was more complicated than a tree +didn't have a central trunk with all + + align:start position:0% +didn't have a central trunk with all + + + align:start position:0% +didn't have a central trunk with all +branches regularly sprouting from the + + align:start position:0% +branches regularly sprouting from the + + + align:start position:0% +branches regularly sprouting from the +trunk that geometrically he couldn't + + align:start position:0% +trunk that geometrically he couldn't + + + align:start position:0% +trunk that geometrically he couldn't +expl explained what it was but he knew + + align:start position:0% +expl explained what it was but he knew + + + align:start position:0% +expl explained what it was but he knew +it wasn't a + + align:start position:0% +it wasn't a + + + align:start position:0% +it wasn't a +tree and + + align:start position:0% +tree and + + + align:start position:0% +tree and +then party I think because of his living + + align:start position:0% +then party I think because of his living + + + align:start position:0% +then party I think because of his living +on the west + + align:start position:0% +on the west + + + align:start position:0% +on the west +coast where + + align:start position:0% +coast where + + + align:start position:0% +coast where +perhaps the counterculture has spread + + align:start position:0% +perhaps the counterculture has spread + + + align:start position:0% +perhaps the counterculture has spread +more ideas in American thought + + align:start position:0% +more ideas in American thought + + + align:start position:0% +more ideas in American thought +than than anywhere else in the + + align:start position:0% +than than anywhere else in the + + + align:start position:0% +than than anywhere else in the +world he started arguing that there was + + align:start position:0% +world he started arguing that there was + + + align:start position:0% +world he started arguing that there was +a micro unit called a spatial and which + + align:start position:0% +a micro unit called a spatial and which + + + align:start position:0% +a micro unit called a spatial and which +had spatial and social characteristics + + align:start position:0% +had spatial and social characteristics + + + align:start position:0% +had spatial and social characteristics +what he calls patterns they are + + align:start position:0% +what he calls patterns they are + + + align:start position:0% +what he calls patterns they are +each each micro unit has a pattern they + + align:start position:0% +each each micro unit has a pattern they + + + align:start position:0% +each each micro unit has a pattern they +are good patterns and they are bad + + align:start position:0% + + + + align:start position:0% + +patterns a city is a field of spatial + + align:start position:0% +patterns a city is a field of spatial + + + align:start position:0% +patterns a city is a field of spatial +and social + + align:start position:0% +and social + + + align:start position:0% +and social +relations they are good living patterns + + align:start position:0% +relations they are good living patterns + + + align:start position:0% +relations they are good living patterns +bad dead + + align:start position:0% + + + + align:start position:0% + +ones we do not need Grand planning or + + align:start position:0% +ones we do not need Grand planning or + + + align:start position:0% +ones we do not need Grand planning or +design for the whole town it's in if + + align:start position:0% +design for the whole town it's in if + + + align:start position:0% +design for the whole town it's in if +each thing is made in a context which + + align:start position:0% +each thing is made in a context which + + + align:start position:0% +each thing is made in a context which +the other understands the town emerges + + align:start position:0% +the other understands the town emerges + + + align:start position:0% +the other understands the town emerges +by itself and is continually repaired + + align:start position:0% + + + + align:start position:0% + +he believes that Society has it's a + + align:start position:0% +he believes that Society has it's a + + + align:start position:0% +he believes that Society has it's a +romantic + + align:start position:0% +romantic + + + align:start position:0% +romantic +notion has a history of patterns which + + align:start position:0% +notion has a history of patterns which + + + align:start position:0% +notion has a history of patterns which +are good patterns they're good patterns + + align:start position:0% +are good patterns they're good patterns + + + align:start position:0% +are good patterns they're good patterns +because they lived in they + + align:start position:0% +because they lived in they + + + align:start position:0% +because they lived in they +understood like patri GES he tries you + + align:start position:0% +understood like patri GES he tries you + + + align:start position:0% +understood like patri GES he tries you +Pat remember patri GES is the play + + align:start position:0% + + + + align:start position:0% + +diagram which emotional + + align:start position:0% + + + + align:start position:0% + +objective + + align:start position:0% +objective + + + align:start position:0% +objective +experienced items all can fold into each + + align:start position:0% +experienced items all can fold into each + + + align:start position:0% +experienced items all can fold into each +other here Alexander is very much again + + align:start position:0% +other here Alexander is very much again + + + align:start position:0% +other here Alexander is very much again +trying + + align:start position:0% +trying + + + align:start position:0% +trying +to link feeling and + + align:start position:0% +to link feeling and + + + align:start position:0% +to link feeling and +thought a pattern is one + + align:start position:0% +thought a pattern is one + + + align:start position:0% +thought a pattern is one +which a good pattern is one which is + + align:start position:0% +which a good pattern is one which is + + + align:start position:0% +which a good pattern is one which is +objectively correct but he also so felt + + align:start position:0% +objectively correct but he also so felt + + + align:start position:0% +objectively correct but he also so felt +by you to be + + align:start position:0% + + + + align:start position:0% + +correct a good example is in a piece in + + align:start position:0% +correct a good example is in a piece in + + + align:start position:0% +correct a good example is in a piece in +which he tries to explain to a young + + align:start position:0% +which he tries to explain to a young + + + align:start position:0% +which he tries to explain to a young +architecture student at + + align:start position:0% +architecture student at + + + align:start position:0% +architecture student at +Berkeley what he's all + + align:start position:0% +Berkeley what he's all + + + align:start position:0% +Berkeley what he's all +about he says look at this table they're + + align:start position:0% +about he says look at this table they're + + + align:start position:0% +about he says look at this table they're +sitting + + align:start position:0% +sitting + + + align:start position:0% +sitting +in in a cafe look at this table it's + + align:start position:0% +in in a cafe look at this table it's + + + align:start position:0% +in in a cafe look at this table it's +made of + + align:start position:0% +made of + + + align:start position:0% +made of +wood there difference between making the + + align:start position:0% +wood there difference between making the + + + align:start position:0% +wood there difference between making the +edge of finishing the edge of the wood + + align:start position:0% +edge of finishing the edge of the wood + + + align:start position:0% +edge of finishing the edge of the wood +with sandpaper making the minimal + + align:start position:0% +with sandpaper making the minimal + + + align:start position:0% +with sandpaper making the minimal +transition from one surface to another + + align:start position:0% +transition from one surface to another + + + align:start position:0% +transition from one surface to another +versus the machine like one which our + + align:start position:0% +versus the machine like one which our + + + align:start position:0% +versus the machine like one which our +table is which is just rounded it off in + + align:start position:0% +table is which is just rounded it off in + + + align:start position:0% +table is which is just rounded it off in +a very blunt crude + + align:start position:0% +a very blunt crude + + + align:start position:0% +a very blunt crude +way he says which he ask the student + + align:start position:0% +way he says which he ask the student + + + align:start position:0% +way he says which he ask the student +which of these two is a representation + + align:start position:0% +which of these two is a representation + + + align:start position:0% +which of these two is a representation +of your good self student doesn't + + align:start position:0% +of your good self student doesn't + + + align:start position:0% +of your good self student doesn't +understand what he's talking about why + + align:start position:0% +understand what he's talking about why + + + align:start position:0% +understand what he's talking about why +should uh the edge of a + + align:start position:0% +should uh the edge of a + + + align:start position:0% +should uh the edge of a +table represent your psychological + + align:start position:0% +table represent your psychological + + + align:start position:0% +table represent your psychological +ho I + + align:start position:0% +ho I + + + align:start position:0% +ho I +quote but what if I ask you to tell me + + align:start position:0% +quote but what if I ask you to tell me + + + align:start position:0% +quote but what if I ask you to tell me +which of these two tables you're more + + align:start position:0% +which of these two tables you're more + + + align:start position:0% +which of these two tables you're more +willing to take as a picture of your own + + align:start position:0% +willing to take as a picture of your own + + + align:start position:0% +willing to take as a picture of your own +self which of the two would you consider + + align:start position:0% +self which of the two would you consider + + + align:start position:0% +self which of the two would you consider +a better candidate to picture of your + + align:start position:0% +a better candidate to picture of your + + + align:start position:0% +a better candidate to picture of your +own + + align:start position:0% +own + + + align:start position:0% +own +soul and so on + + align:start position:0% + + + + align:start position:0% + +everything the trouble is that it's + + align:start position:0% +everything the trouble is that it's + + + align:start position:0% +everything the trouble is that it's +difficult to write such + + align:start position:0% +difficult to write such + + + align:start position:0% +difficult to write such +patterns we don't have + + align:start position:0% +patterns we don't have + + + align:start position:0% +patterns we don't have +the tools yet we may one day have + + align:start position:0% +the tools yet we may one day have + + + align:start position:0% +the tools yet we may one day have +them to do that these patterns which are + + align:start position:0% +them to do that these patterns which are + + + align:start position:0% +them to do that these patterns which are +printed in the book the patent language + + align:start position:0% +printed in the book the patent language + + + align:start position:0% +printed in the book the patent language +on biblical + + align:start position:0% +on biblical + + + align:start position:0% +on biblical +paper he almost just + + align:start position:0% +paper he almost just + + + align:start position:0% +paper he almost just +uh a giveaway of a kind + + align:start position:0% + + + + align:start position:0% + +of for + + align:start position:0% +of for + + + align:start position:0% +of for +instance Paton on page + + align:start position:0% +instance Paton on page + + + align:start position:0% +instance Paton on page +115 there's abundant evidence to show + + align:start position:0% +115 there's abundant evidence to show + + + align:start position:0% +115 there's abundant evidence to show +that high buildings make people + + align:start position:0% + + + + align:start position:0% + +crazy now objectively this is not + + align:start position:0% + + + + align:start position:0% + +true there may be reasons why tall + + align:start position:0% +true there may be reasons why tall + + + align:start position:0% +true there may be reasons why tall +buildings are + + align:start position:0% + + + + align:start position:0% + +harmful but as an abstract pattern or as + + align:start position:0% +harmful but as an abstract pattern or as + + + align:start position:0% +harmful but as an abstract pattern or as +a theoretical pattern derived from + + align:start position:0% +a theoretical pattern derived from + + + align:start position:0% +a theoretical pattern derived from +observation it's not + + align:start position:0% +observation it's not + + + align:start position:0% +observation it's not +true I can quote you from Herbert Gans a + + align:start position:0% +true I can quote you from Herbert Gans a + + + align:start position:0% +true I can quote you from Herbert Gans a +well-known Urban sociologist who once + + align:start position:0% +well-known Urban sociologist who once + + + align:start position:0% +well-known Urban sociologist who once +taught you at + + align:start position:0% +taught you at + + + align:start position:0% +taught you at +MIT I quote thus whether housing is high + + align:start position:0% +MIT I quote thus whether housing is high + + + align:start position:0% +MIT I quote thus whether housing is high +or lowrise do not does not by itself + + align:start position:0% +or lowrise do not does not by itself + + + align:start position:0% +or lowrise do not does not by itself +make much + + align:start position:0% +make much + + + align:start position:0% +make much +difference the luxury apartment house + + align:start position:0% +difference the luxury apartment house + + + align:start position:0% +difference the luxury apartment house +has been built in New York + + align:start position:0% +has been built in New York + + + align:start position:0% +has been built in New York +city so + + align:start position:0% +city so + + + align:start position:0% +city so +and for over well over a century now no + + align:start position:0% +and for over well over a century now no + + + align:start position:0% +and for over well over a century now no +one has yet discovered that the + + align:start position:0% +one has yet discovered that the + + + align:start position:0% +one has yet discovered that the +buildings jammed on Park and fifth + + align:start position:0% +buildings jammed on Park and fifth + + + align:start position:0% +buildings jammed on Park and fifth +Avenues and so forth generate + + align:start position:0% +Avenues and so forth generate + + + align:start position:0% +Avenues and so forth generate +pathology conversely when poor people + + align:start position:0% +pathology conversely when poor people + + + align:start position:0% +pathology conversely when poor people +live in even the best design lowrise + + align:start position:0% +live in even the best design lowrise + + + align:start position:0% +live in even the best design lowrise +projects they still do not escape the + + align:start position:0% +projects they still do not escape the + + + align:start position:0% +projects they still do not escape the +problems of poverty + + align:start position:0% + + + + align:start position:0% + +G is + + align:start position:0% +G is + + + align:start position:0% +G is +correct why does Alexander make such a + + align:start position:0% +correct why does Alexander make such a + + + align:start position:0% +correct why does Alexander make such a +statement he's too intelligent to know + + align:start position:0% +statement he's too intelligent to know + + + align:start position:0% +statement he's too intelligent to know +that his statement is + + align:start position:0% +that his statement is + + + align:start position:0% +that his statement is +incorrect I don't + + align:start position:0% +incorrect I don't + + + align:start position:0% +incorrect I don't +know I don't + + align:start position:0% +know I don't + + + align:start position:0% +know I don't +know there's a kind of a + + align:start position:0% +know there's a kind of a + + + align:start position:0% +know there's a kind of a +insistence + + align:start position:0% +insistence + + + align:start position:0% +insistence +that + + align:start position:0% +that + + + align:start position:0% +that +either you in + + align:start position:0% +either you in + + + align:start position:0% +either you in +when I learned + + align:start position:0% +when I learned + + + align:start position:0% +when I learned +debating I was taught that sometimes + + align:start position:0% +debating I was taught that sometimes + + + align:start position:0% +debating I was taught that sometimes +it's good idea to throw out a statement + + align:start position:0% +it's good idea to throw out a statement + + + align:start position:0% +it's good idea to throw out a statement +an assumption a hypothesis just to make + + align:start position:0% +an assumption a hypothesis just to make + + + align:start position:0% +an assumption a hypothesis just to make +the argument more + + align:start position:0% + + + + align:start position:0% + +interesting and if your opponent didn't + + align:start position:0% +interesting and if your opponent didn't + + + align:start position:0% +interesting and if your opponent didn't +catch up on the weakness of your + + align:start position:0% +catch up on the weakness of your + + + align:start position:0% +catch up on the weakness of your +argument you would + + align:start position:0% +argument you would + + + align:start position:0% +argument you would +win I don't think Alexander is into + + align:start position:0% +win I don't think Alexander is into + + + align:start position:0% +win I don't think Alexander is into +debating games but it's often puzzled me + + align:start position:0% +debating games but it's often puzzled me + + + align:start position:0% +debating games but it's often puzzled me +why he took the trouble to assemble + + align:start position:0% +why he took the trouble to assemble + + + align:start position:0% +why he took the trouble to assemble +often very good ideas very downto Earth + + align:start position:0% +often very good ideas very downto Earth + + + align:start position:0% +often very good ideas very downto Earth +ideas he for instance says single + + align:start position:0% +ideas he for instance says single + + + align:start position:0% +ideas he for instance says single +designers don't really produce + + align:start position:0% +designers don't really produce + + + align:start position:0% +designers don't really produce +comprehensive + + align:start position:0% +comprehensive + + + align:start position:0% +comprehensive +results he says I work in the College of + + align:start position:0% +results he says I work in the College of + + + align:start position:0% +results he says I work in the College of +environmental design at Berkeley which + + align:start position:0% +environmental design at Berkeley which + + + align:start position:0% +environmental design at Berkeley which +was designed by a team of the best + + align:start position:0% +was designed by a team of the best + + + align:start position:0% +was designed by a team of the best +highly trained architects in our College + + align:start position:0% + + + + align:start position:0% + +I can't put plants on the sill in my + + align:start position:0% +I can't put plants on the sill in my + + + align:start position:0% +I can't put plants on the sill in my +window because nobody ever thought about + + align:start position:0% +window because nobody ever thought about + + + align:start position:0% +window because nobody ever thought about +what the V position of the window would + + align:start position:0% +what the V position of the window would + + + align:start position:0% +what the V position of the window would +be in the wall in the section of the + + align:start position:0% +be in the wall in the section of the + + + align:start position:0% +be in the wall in the section of the +wall they pushed the window to the + + align:start position:0% +wall they pushed the window to the + + + align:start position:0% +wall they pushed the window to the +inside to allow a maximum use on the + + align:start position:0% +inside to allow a maximum use on the + + + align:start position:0% +inside to allow a maximum use on the +outside where there's no need for any + + align:start position:0% +outside where there's no need for any + + + align:start position:0% +outside where there's no need for any +use why does intelligent people make + + align:start position:0% +use why does intelligent people make + + + align:start position:0% +use why does intelligent people make +such stupid assumptions + + align:start position:0% +such stupid assumptions + + + align:start position:0% +such stupid assumptions +they never consulted + + align:start position:0% +they never consulted + + + align:start position:0% +they never consulted +us well if an architect were redesigning + + align:start position:0% +us well if an architect were redesigning + + + align:start position:0% +us well if an architect were redesigning +MIT School of Architecture and asked me + + align:start position:0% +MIT School of Architecture and asked me + + + align:start position:0% +MIT School of Architecture and asked me +about my office I don't know if I would + + align:start position:0% +about my office I don't know if I would + + + align:start position:0% +about my office I don't know if I would +remember to specify that the window + + align:start position:0% +remember to specify that the window + + + align:start position:0% +remember to specify that the window +needs to be on the outside of the wall + + align:start position:0% +needs to be on the outside of the wall + + + align:start position:0% +needs to be on the outside of the wall +to allow me the space on the inside for + + align:start position:0% +to allow me the space on the inside for + + + align:start position:0% +to allow me the space on the inside for +my plants or for + + align:start position:0% + + + + align:start position:0% + +whatever so his observation is that + + align:start position:0% +whatever so his observation is that + + + align:start position:0% +whatever so his observation is that +somehow the system isn't working modern + + align:start position:0% +somehow the system isn't working modern + + + align:start position:0% +somehow the system isn't working modern +urbanism is a + + align:start position:0% +urbanism is a + + + align:start position:0% +urbanism is a +mess so he proposes a number of rules I + + align:start position:0% +mess so he proposes a number of rules I + + + align:start position:0% +mess so he proposes a number of rules I +won't go through the rules you can see + + align:start position:0% +won't go through the rules you can see + + + align:start position:0% +won't go through the rules you can see +them in uh his later + + align:start position:0% +them in uh his later + + + align:start position:0% +them in uh his later +book a new theory of Urban + + align:start position:0% +book a new theory of Urban + + + align:start position:0% +book a new theory of Urban +Design There are rules about growing a + + align:start position:0% +Design There are rules about growing a + + + align:start position:0% +Design There are rules about growing a +hole about peace meal + + align:start position:0% +hole about peace meal + + + align:start position:0% +hole about peace meal +unpredictable coherence full of feeling + + align:start position:0% +unpredictable coherence full of feeling + + + align:start position:0% +unpredictable coherence full of feeling +no single artist the many people + + align:start position:0% +no single artist the many people + + + align:start position:0% +no single artist the many people +involved the whole idea + + align:start position:0% +involved the whole idea + + + align:start position:0% +involved the whole idea +of a thing having to have + + align:start position:0% + + + + align:start position:0% + +feeling these seven + + align:start position:0% + + + + align:start position:0% + +rules let me find the one about + + align:start position:0% + + + + align:start position:0% + +number rule number three + + align:start position:0% +number rule number three + + + align:start position:0% +number rule number three +visions every project must first be + + align:start position:0% +visions every project must first be + + + align:start position:0% +visions every project must first be +experienced and then expressed as a + + align:start position:0% +experienced and then expressed as a + + + align:start position:0% +experienced and then expressed as a +vision which can be seen in the Inner + + align:start position:0% +vision which can be seen in the Inner + + + align:start position:0% +vision which can be seen in the Inner +Eye I don't know where my inner eye is + + align:start position:0% +Eye I don't know where my inner eye is + + + align:start position:0% +Eye I don't know where my inner eye is +and how to use it it must have this + + align:start position:0% +and how to use it it must have this + + + align:start position:0% +and how to use it it must have this +quality so strongly that can also be + + align:start position:0% +quality so strongly that can also be + + + align:start position:0% +quality so strongly that can also be +communicated to + + align:start position:0% +communicated to + + + align:start position:0% +communicated to +others and and felt by others as a + + align:start position:0% + + + + align:start position:0% + +vision at least Alexander is attempting + + align:start position:0% +vision at least Alexander is attempting + + + align:start position:0% +vision at least Alexander is attempting +to be explicit + + align:start position:0% +to be explicit + + + align:start position:0% +to be explicit +about his + + align:start position:0% +about his + + + align:start position:0% +about his +ideas explicitness is an advantage in + + align:start position:0% +ideas explicitness is an advantage in + + + align:start position:0% +ideas explicitness is an advantage in +debate and explicitness even if you make + + align:start position:0% +debate and explicitness even if you make + + + align:start position:0% +debate and explicitness even if you make +mistakes is better than + + align:start position:0% + + + + align:start position:0% + +dull + + align:start position:0% + + + + align:start position:0% + +hermeticism and all of these people are + + align:start position:0% +hermeticism and all of these people are + + + align:start position:0% +hermeticism and all of these people are +generating + + align:start position:0% +generating + + + align:start position:0% +generating +explicitness as an one of the aspects of + + align:start position:0% +explicitness as an one of the aspects of + + + align:start position:0% +explicitness as an one of the aspects of +their + + align:start position:0% + + + + align:start position:0% + +work in the handout I gave to you + + align:start position:0% + + + + align:start position:0% + +the ex there's a piece from the new + + align:start position:0% +the ex there's a piece from the new + + + align:start position:0% +the ex there's a piece from the new +theory of Urban + + align:start position:0% +theory of Urban + + + align:start position:0% +theory of Urban +Design + + align:start position:0% + + + + align:start position:0% + +This on the left is a piece of Rome a + + align:start position:0% +This on the left is a piece of Rome a + + + align:start position:0% +This on the left is a piece of Rome a +plan of Rome around the pantheon + + align:start position:0% +plan of Rome around the pantheon + + + align:start position:0% +plan of Rome around the pantheon +medieval + + align:start position:0% +medieval + + + align:start position:0% +medieval +real as opposed to an American + + align:start position:0% +real as opposed to an American + + + align:start position:0% +real as opposed to an American +suburb what are the + + align:start position:0% +suburb what are the + + + align:start position:0% +suburb what are the +characteristics of the world depicted on + + align:start position:0% +characteristics of the world depicted on + + + align:start position:0% +characteristics of the world depicted on +the left a good world according to + + align:start position:0% + + + + align:start position:0% + +Alexander the whole is made up of Parts + + align:start position:0% +Alexander the whole is made up of Parts + + + align:start position:0% +Alexander the whole is made up of Parts +which + + align:start position:0% +which + + + align:start position:0% +which +are unique but belong to families of + + align:start position:0% +are unique but belong to families of + + + align:start position:0% +are unique but belong to families of +shape there are + + align:start position:0% +shape there are + + + align:start position:0% +shape there are +churches which all have open space in + + align:start position:0% +churches which all have open space in + + + align:start position:0% +churches which all have open space in +front of them the pantheon and so + + align:start position:0% +front of them the pantheon and so + + + align:start position:0% +front of them the pantheon and so +on S Ignus San + + align:start position:0% +on S Ignus San + + + align:start position:0% +on S Ignus San +jizu they are patterns of + + align:start position:0% +jizu they are patterns of + + + align:start position:0% +jizu they are patterns of +housing which + + align:start position:0% +housing which + + + align:start position:0% +housing which +repeat there are decisions which + + align:start position:0% +repeat there are decisions which + + + align:start position:0% +repeat there are decisions which +have are made through peace meal Edition + + align:start position:0% +have are made through peace meal Edition + + + align:start position:0% +have are made through peace meal Edition +all through rampant industrial + + align:start position:0% +all through rampant industrial + + + align:start position:0% +all through rampant industrial +production + + align:start position:0% + + + + align:start position:0% + +there's a family of belongingness of all + + align:start position:0% +there's a family of belongingness of all + + + align:start position:0% +there's a family of belongingness of all +the + + align:start position:0% + + + + align:start position:0% + +parts in a + + align:start position:0% +parts in a + + + align:start position:0% +parts in a +sense although I don't know who had the + + align:start position:0% +sense although I don't know who had the + + + align:start position:0% +sense although I don't know who had the +vision which produced this plan I don't + + align:start position:0% +vision which produced this plan I don't + + + align:start position:0% +vision which produced this plan I don't +think there was one person one Pope who + + align:start position:0% +think there was one person one Pope who + + + align:start position:0% +think there was one person one Pope who +said our own would be this + + align:start position:0% +said our own would be this + + + align:start position:0% +said our own would be this +way but there were patterns + + align:start position:0% +way but there were patterns + + + align:start position:0% +way but there were patterns +presumably which + + align:start position:0% + + + + align:start position:0% + +people learned + + align:start position:0% +people learned + + + align:start position:0% +people learned +from other + + align:start position:0% +from other + + + align:start position:0% +from other +patterns and decided to reproduce them + + align:start position:0% +patterns and decided to reproduce them + + + align:start position:0% +patterns and decided to reproduce them +in a peac me way so building up from + + align:start position:0% +in a peac me way so building up from + + + align:start position:0% +in a peac me way so building up from +experience building up from categories + + align:start position:0% +experience building up from categories + + + align:start position:0% +experience building up from categories +of knowledge which had already been + + align:start position:0% +of knowledge which had already been + + + align:start position:0% +of knowledge which had already been +tested as opposed to this machine likee + + align:start position:0% +tested as opposed to this machine likee + + + align:start position:0% +tested as opposed to this machine likee +production + + align:start position:0% + + + + align:start position:0% + +Alexander is tough + + align:start position:0% +Alexander is tough + + + align:start position:0% +Alexander is tough +medicine he can be come across as + + align:start position:0% + + + + align:start position:0% + +a arrogant + + align:start position:0% + + + + align:start position:0% + +fool he's recently produced four + + align:start position:0% +fool he's recently produced four + + + align:start position:0% +fool he's recently produced four +volumes called the nature of + + align:start position:0% +volumes called the nature of + + + align:start position:0% +volumes called the nature of +order he's even more + + align:start position:0% + + + + align:start position:0% + +explicit in the nature of order I have + + align:start position:0% +explicit in the nature of order I have + + + align:start position:0% +explicit in the nature of order I have +tried to construct a coherent picture of + + align:start position:0% +tried to construct a coherent picture of + + + align:start position:0% +tried to construct a coherent picture of +life on Earth which makes sense of these + + align:start position:0% +life on Earth which makes sense of these + + + align:start position:0% +life on Earth which makes sense of these +matters gives us something to live for + + align:start position:0% +matters gives us something to live for + + + align:start position:0% +matters gives us something to live for +and worth living + + align:start position:0% +and worth living + + + align:start position:0% +and worth living +for yes like GES I have tried at the + + align:start position:0% +for yes like GES I have tried at the + + + align:start position:0% +for yes like GES I have tried at the +same time to deal with the emotional + + align:start position:0% +same time to deal with the emotional + + + align:start position:0% +same time to deal with the emotional +world and the objective Ordinary World + + align:start position:0% +world and the objective Ordinary World + + + align:start position:0% +world and the objective Ordinary World +around us + + align:start position:0% + + + + align:start position:0% + +what is extraordinary + + align:start position:0% +what is extraordinary + + + align:start position:0% +what is extraordinary +is he writes about the patent + + align:start position:0% + + + + align:start position:0% + +Language by about + + align:start position:0% +Language by about + + + align:start position:0% +Language by about +1975 these investigations which I + + align:start position:0% +1975 these investigations which I + + + align:start position:0% +1975 these investigations which I +undertook with five colleagues gave us + + align:start position:0% +undertook with five colleagues gave us + + + align:start position:0% +undertook with five colleagues gave us +gold we discovered about 250 invariant + + align:start position:0% +gold we discovered about 250 invariant + + + align:start position:0% +gold we discovered about 250 invariant +spatial patterns each one was associated + + align:start position:0% +spatial patterns each one was associated + + + align:start position:0% +spatial patterns each one was associated +with the stability of the human + + align:start position:0% +with the stability of the human + + + align:start position:0% +with the stability of the human +environmental system they were published + + align:start position:0% +environmental system they were published + + + align:start position:0% +environmental system they were published +in a patent language they have become a + + align:start position:0% +in a patent language they have become a + + + align:start position:0% +in a patent language they have become a +standard part of what he's known and + + align:start position:0% +standard part of what he's known and + + + align:start position:0% +standard part of what he's known and +used by + + align:start position:0% + + + + align:start position:0% + +Architects + + align:start position:0% +Architects + + + align:start position:0% +Architects +what what's this all + + align:start position:0% +what what's this all + + + align:start position:0% +what what's this all +about it's not + + align:start position:0% +about it's not + + + align:start position:0% +about it's not +true so why does a man say something + + align:start position:0% +true so why does a man say something + + + align:start position:0% +true so why does a man say something +which is not + + align:start position:0% +which is not + + + align:start position:0% +which is not +true + + align:start position:0% + + + + align:start position:0% + +there it can only be + + align:start position:0% +there it can only be + + + align:start position:0% +there it can only be +provocative and perhaps like John + + align:start position:0% +provocative and perhaps like John + + + align:start position:0% +provocative and perhaps like John +mackenro shouting at an Umpire in a + + align:start position:0% +mackenro shouting at an Umpire in a + + + align:start position:0% +mackenro shouting at an Umpire in a +tennis + + align:start position:0% +tennis + + + align:start position:0% +tennis +game had a reason for provoking + + align:start position:0% +game had a reason for provoking + + + align:start position:0% +game had a reason for provoking +response dealing with satisfaction of + + align:start position:0% +response dealing with satisfaction of + + + align:start position:0% +response dealing with satisfaction of +his inner grief + + align:start position:0% +his inner grief + + + align:start position:0% +his inner grief +publicly um I can only without doing a + + align:start position:0% +publicly um I can only without doing a + + + align:start position:0% +publicly um I can only without doing a +psychoanalysis of this be surprised by + + align:start position:0% +psychoanalysis of this be surprised by + + + align:start position:0% +psychoanalysis of this be surprised by +it the fact is that Architects seldom + + align:start position:0% +it the fact is that Architects seldom + + + align:start position:0% +it the fact is that Architects seldom +read seldom + + align:start position:0% +read seldom + + + align:start position:0% +read seldom +read a book like patent language and + + align:start position:0% +read a book like patent language and + + + align:start position:0% +read a book like patent language and +they're not in the habit + + align:start position:0% +they're not in 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align:start position:0% + +word the idea of how much life is in + + align:start position:0% +word the idea of how much life is in + + + align:start position:0% +word the idea of how much life is in +things is objective in the sense of + + align:start position:0% +things is objective in the sense of + + + align:start position:0% +things is objective in the sense of +observation this quality of life seems + + align:start position:0% +observation this quality of life seems + + + align:start position:0% +observation this quality of life seems +to be correlated with a repeated + + align:start position:0% +to be correlated with a repeated + + + align:start position:0% +to be correlated with a repeated +appearance of 15 getic properties + + align:start position:0% + + + + align:start position:0% + +the appearance of living structure in + + align:start position:0% +the appearance of living structure in + + + align:start position:0% +the appearance of living structure in +things is also 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align:start position:0% +can be reduced to 15 repeated patterns + + + align:start position:0% +can be reduced to 15 repeated patterns +they probably cental centr + + align:start position:0% +they probably cental centr + + + align:start position:0% +they probably cental centr +focused I don't know what they are he + + align:start position:0% +focused I don't know what they are he + + + align:start position:0% +focused I don't know what they are he +says they are true in art in urbanism in + + align:start position:0% +says they are true in art in urbanism in + + + align:start position:0% +says they are true in art in urbanism in +everything that speaks of Life what is + + align:start position:0% +everything that speaks of Life what is + + + align:start position:0% +everything that speaks of Life what is +it that speaks of + + align:start position:0% +it that speaks of + + + align:start position:0% +it that speaks of +life I understand that walking down a + + align:start position:0% +life 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can + + + align:start position:0% +week uh would not evoke that we can +spend a couple of hours + + align:start position:0% +spend a couple of hours + + + align:start position:0% +spend a couple of hours +was starting to write down what would + + align:start position:0% +was starting to write down what would + + + align:start position:0% +was starting to write down what would +you cause you to experience something as + + align:start position:0% +you cause you to experience something as + + + align:start position:0% +you cause you to experience something as +being alive and something which + + align:start position:0% + + + + align:start position:0% + +wasn't I don't know what to say about + + align:start position:0% +wasn't I don't know what to say about + + + align:start position:0% +wasn't I don't know what to say about +the body of work of + + align:start position:0% +the body of work of + + + align:start position:0% +the body of work of +Alexander um it's going to be a Pity + + align:start position:0% +Alexander um it's going to be a Pity + + + align:start position:0% +Alexander um it's going to be a Pity +that he has spent so much energy and + + align:start position:0% +that he has spent so much energy and + + + align:start position:0% +that he has spent so much energy and +will be so + + align:start position:0% + + + + align:start position:0% + +will have such a little ex observable + + align:start position:0% +will have such a little ex observable + + + align:start position:0% +will have such a little ex observable +impact on the way we make buildings and + + align:start position:0% +impact on the way we make buildings and + + + align:start position:0% +impact on the way we make buildings and +make + + align:start position:0% + + + + align:start position:0% + +cities do you are good test + + align:start position:0% +cities do you are good test + + + align:start position:0% +cities do you are good test +group have you been influenced by + + align:start position:0% +group have you been influenced by + + + align:start position:0% +group have you been influenced by +Chris's + + align:start position:0% + + + + align:start position:0% + +work a little + + align:start position:0% +work a little + + + align:start position:0% +work a little +bit a little bit Yeah I am I would say + + align:start position:0% +bit a little bit Yeah I am I would say + + + align:start position:0% +bit a little bit Yeah I am I would say +the same + + align:start position:0% + + + + align:start position:0% + +thing John AB Bren was head of the + + align:start position:0% +thing John AB Bren was head of the + + + align:start position:0% +thing John AB Bren was head of the +Department of architecture year at + + align:start position:0% +Department of architecture year at + + + align:start position:0% +Department of architecture year at +M + + align:start position:0% +M + + + align:start position:0% +M +for a number of + + align:start position:0% +for a number of + + 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position:0% +of these projects to understand +what but you can see in the diagrams + + align:start position:0% +what but you can see in the diagrams + + + align:start position:0% +what but you can see in the diagrams +there are there are Tendencies to + + align:start position:0% +there are there are Tendencies to + + + align:start position:0% +there are there are Tendencies to +reproduce the + + align:start position:0% +reproduce the + + + align:start position:0% +reproduce the +length of + + align:start position:0% +length of + + + align:start position:0% +length of +facades and so + + align:start position:0% +facades and so + + + align:start position:0% +facades and so +on what he argues is that here are a set + + align:start position:0% +on what he argues is that here are a set + + + align:start position:0% +on what he argues is that here are a set +of different + + align:start position:0% +of different + + + align:start position:0% +of different +interpretations of a similar set of 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+ align:start position:0% +a student reproducing extending the the + + + align:start position:0% +a student reproducing extending the the +physical structure of a small town in + + align:start position:0% +physical structure of a small town in + + + align:start position:0% +physical structure of a small town in +ladak in Northern + + align:start position:0% + + + + align:start position:0% + +India he does these exercises with + + align:start position:0% +India he does these exercises with + + + align:start position:0% +India he does these exercises with +students in which you start off with a a + + align:start position:0% +students in which you start off with a a + + + align:start position:0% +students in which you start off with a a +basic + + align:start position:0% + + + + align:start position:0% + +theme the theme is what the culture is + + align:start position:0% +theme the theme is what the culture is + + + align:start position:0% +theme the theme is what the culture is +already + + align:start position:0% + + + + align:start position:0% + +reproducing you understand the + + align:start position:0% +reproducing you understand the + + + align:start position:0% +reproducing you understand the +variations that are possible on that + + align:start position:0% +variations that are possible on that + + + align:start position:0% +variations that are possible on that +theme what agreements have to be made to + + align:start position:0% +theme what agreements have to be made to + + + align:start position:0% +theme what agreements have to be made to +extend the the the items in different + + align:start position:0% +extend the the the items in different + + + align:start position:0% +extend the the the items in different +ways what becomes private what becomes + + align:start position:0% +ways what becomes private what becomes + + + align:start position:0% +ways what becomes private what becomes +public what is negotiated and so on and + + align:start position:0% +public what is negotiated and so on and + + + align:start position:0% +public what is negotiated and so on and +it sets up a pattern which can grow over + + align:start position:0% +it sets up a pattern which can grow over + + + align:start position:0% +it sets up a pattern which can grow over +time with new agreements made for the + + align:start position:0% +time with new agreements made for the + + + align:start position:0% +time with new agreements made for the +use of roofs as the density grows and so + + align:start position:0% +use of roofs as the density grows and so + + + align:start position:0% +use of roofs as the density grows and so +on + + align:start position:0% + + + + align:start position:0% + +there two problems with Hab Brans work + + align:start position:0% +there two problems with Hab Brans work + + + align:start position:0% +there two problems with Hab Brans work +one again it is essentially + + align:start position:0% +one again it is essentially + + + align:start position:0% +one again it is essentially +apolitical I don't mean politics in + + align:start position:0% +apolitical I don't mean politics in + + + align:start position:0% +apolitical I don't mean politics in +the Democratic party versus Republican + + align:start position:0% +the Democratic party versus Republican + + + align:start position:0% +the Democratic party versus Republican +party sense I meant in the + + align:start position:0% +party sense I meant in the + + + align:start position:0% +party sense I meant in the +notion + + align:start position:0% +notion + + + align:start position:0% +notion +that all agreements turn out to be turn + + align:start position:0% +that all agreements turn out to be turn + + + align:start position:0% +that all agreements turn out to be turn +out to be + + align:start position:0% +out to be + + + align:start position:0% +out to be +responsible outcomes + + align:start position:0% +responsible outcomes + + + align:start position:0% +responsible outcomes +I don't know what Aben is using a + + align:start position:0% +I don't know what Aben is using a + + + align:start position:0% +I don't know what Aben is using a +methodology which distinguishes the + + align:start position:0% +methodology which distinguishes the + + + align:start position:0% +methodology which distinguishes the +existing form of Amsterdam from the new + + align:start position:0% +existing form of Amsterdam from the new + + + align:start position:0% +existing form of Amsterdam from the new +extension of Amsterdam by modern + + align:start position:0% +extension of Amsterdam by modern + + + align:start position:0% +extension of Amsterdam by modern +Architects abrain is claims that it's + + align:start position:0% +Architects abrain is claims that it's + + + align:start position:0% +Architects abrain is claims that it's +the modern Architects whove lost all of + + align:start position:0% +the modern Architects whove lost all of + + + align:start position:0% +the modern Architects whove lost all of +the understanding of what Agreements + + align:start position:0% +the understanding of what Agreements + + + align:start position:0% +the understanding of what Agreements +are he doesn't specify what bad + + align:start position:0% +are he doesn't specify what bad + + + align:start position:0% +are he doesn't specify what bad +Agreements are + + align:start position:0% + + + + align:start position:0% + +Aran doesn't do this on Long + + align:start position:0% +Aran doesn't do this on Long + + + align:start position:0% +Aran doesn't do this on Long +Island where there may be waste + + align:start position:0% +Island where there may be waste + + + align:start position:0% +Island where there may be waste +space buildings in the middle of sites + + align:start position:0% +space buildings in the middle of sites + + + align:start position:0% +space buildings in the middle of sites +with a open space around them these are + + align:start position:0% +with a open space around them these are + + + align:start position:0% +with a open space around them these are +all dense built together + + align:start position:0% +all dense built together + + + align:start position:0% +all dense built together +systems much like the original plans of + + align:start position:0% +systems much like the original plans of + + + align:start position:0% +systems much like the original plans of +our and the expansion of the early + + align:start position:0% +our and the expansion of the early + + + align:start position:0% +our and the expansion of the early +expansions of the city of Amsterdam + + align:start position:0% + + + + align:start position:0% + +so I don't know + + align:start position:0% +so I don't know + + + align:start position:0% +so I don't know +what I can't + + align:start position:0% +what I can't + + + align:start position:0% +what I can't +explain the + + align:start position:0% +explain the + + + align:start position:0% +explain the +strategy the strategy is that again like + + align:start position:0% +strategy the strategy is that again like + + + align:start position:0% +strategy the strategy is that again like +Alexander you you learn from what + + align:start position:0% +Alexander you you learn from what + + + align:start position:0% +Alexander you you learn from what +exists you use your Discerning capacity + + align:start position:0% +exists you use your Discerning capacity + + + align:start position:0% +exists you use your Discerning capacity +to build on what exists + + align:start position:0% + + + + align:start position:0% + +you don't in Alexander's case when he + + align:start position:0% +you don't in Alexander's case when he + + + align:start position:0% +you don't in Alexander's case when he +did the Oregon + + align:start position:0% +did the Oregon + + + align:start position:0% +did the Oregon +experiment he said we will not build + + align:start position:0% +experiment he said we will not build + + + align:start position:0% +experiment he said we will not build +individual large buildings all by + + align:start position:0% +individual large buildings all by + + + align:start position:0% +individual large buildings all by +themselves for every in the program for + + align:start position:0% +themselves for every in the program for + + + align:start position:0% +themselves for every in the program for +every large building of + + align:start position:0% + + + + align:start position:0% + +classrooms you need 10% of shops you + + align:start position:0% +classrooms you need 10% of shops you + + + align:start position:0% +classrooms you need 10% of shops you +need 5% of open space you need + + align:start position:0% +need 5% of open space you need + + + align:start position:0% +need 5% of open space you need +20% of housing + + align:start position:0% +20% of housing + + + align:start position:0% +20% of housing +all of these patterns are + + align:start position:0% +all of these patterns are + + + align:start position:0% +all of these patterns are +are breaking down programs which are + + align:start position:0% +are breaking down programs which are + + + align:start position:0% +are breaking down programs which are +large and + + align:start position:0% +large and + + + align:start position:0% +large and +mononuclear into complex patterns and + + align:start position:0% +mononuclear into complex patterns and + + + align:start position:0% +mononuclear into complex patterns and +repeated in small I in small parts in + + align:start position:0% +repeated in small I in small parts in + + + align:start position:0% +repeated in small I in small parts in +small spatial ENT + + align:start position:0% + + + + align:start position:0% + +entities these people of JN AB Bren has + + align:start position:0% +entities these people of JN AB Bren has + + + align:start position:0% +entities these people of JN AB Bren has +gone quite far + + align:start position:0% +gone quite far + + + align:start position:0% +gone quite far +in developing Technologies for + + align:start position:0% +in developing Technologies for + + + align:start position:0% +in developing Technologies for +user situations + + align:start position:0% +user situations + + + align:start position:0% +user situations +in support + + align:start position:0% +in support + + + align:start position:0% +in support +systems + + align:start position:0% + + + + align:start position:0% + +but both Alexander and ab bren's Notions + + align:start position:0% +but both Alexander and ab bren's Notions + + + align:start position:0% +but both Alexander and ab bren's Notions +are intellectually very + + align:start position:0% +are intellectually very + + + align:start position:0% +are intellectually very +responsible they are + + align:start position:0% + + + + align:start position:0% + +conservative I don't know what you do + + align:start position:0% +conservative I don't know what you do + + + align:start position:0% +conservative I don't know what you do +when you build a new + + align:start position:0% +when you build a new + + + align:start position:0% +when you build a new +town and you don't have any + + align:start position:0% +town and you don't have any + + + align:start position:0% +town and you don't have any +infrastructure to ex to build a + + align:start position:0% +infrastructure to ex to build a + + + align:start position:0% +infrastructure to ex to build a +contrapuntal system + + align:start position:0% +contrapuntal system + + + align:start position:0% +contrapuntal system +around um but I'm sure that that can be + + align:start position:0% +around um but I'm sure that that can be + + + align:start position:0% +around um but I'm sure that that can be +resolved by assuming a assuming a set of + + align:start position:0% +resolved by assuming a assuming a set of + + + align:start position:0% +resolved by assuming a assuming a set of +agreements early on based on some + + align:start position:0% +agreements early on based on some + + + align:start position:0% +agreements early on based on some +ingredients from the broader culture of + + align:start position:0% +ingredients from the broader culture of + + + align:start position:0% +ingredients from the broader culture of +the place and so on + + align:start position:0% + + + + align:start position:0% + +we've got a few minutes to touch + + align:start position:0% +we've got a few minutes to touch + + + align:start position:0% +we've got a few minutes to touch +on a different set of + + align:start position:0% +on a different set of + + + align:start position:0% +on a different set of +stories + + align:start position:0% + + + + align:start position:0% + +um B hilia and Julian Hansen wrote a + + align:start position:0% +um B hilia and Julian Hansen wrote a + + + align:start position:0% +um B hilia and Julian Hansen wrote a +book of the social logic of + + align:start position:0% + + + + align:start position:0% + +space in + + align:start position:0% +space in + + + align:start position:0% +space in +which they argued + + align:start position:0% +which they argued + + + align:start position:0% +which they argued +essentially that + + align:start position:0% + + + + align:start position:0% + +the spatial + + align:start position:0% + + + + align:start position:0% + +pattern which surrounds + + align:start position:0% + + + + align:start position:0% + +us affects + + align:start position:0% +us affects + + + align:start position:0% +us affects +us they argued a lot against the notion + + align:start position:0% +us they argued a lot against the notion + + + align:start position:0% +us they argued a lot against the notion +of architectural + + align:start position:0% +of architectural + + + align:start position:0% +of architectural +determinism which argues that + + align:start position:0% +determinism which argues that + + + align:start position:0% +determinism which argues that +architecture determines Our + + align:start position:0% +architecture determines Our + + + align:start position:0% +architecture determines Our +Lives they showed + + align:start position:0% +Lives they showed + + + align:start position:0% +Lives they showed +that the under certain conditions does + + align:start position:0% +that the under certain conditions does + + + align:start position:0% +that the under certain conditions does +the spatial pattern really have + + align:start position:0% +the spatial pattern really have + + + align:start position:0% +the spatial pattern really have +effects the space inent syntax is a word + + align:start position:0% +effects the space inent syntax is a word + + + align:start position:0% +effects the space inent syntax is a word +from Linguistics it uh refers to the + + align:start position:0% +from Linguistics it uh refers to the + + + align:start position:0% +from Linguistics it uh refers to the +proper order of words in a + + align:start position:0% +proper order of words in a + + + align:start position:0% +proper order of words in a +sentence in order for it to make + + align:start position:0% +sentence in order for it to make + + + align:start position:0% +sentence in order for it to make +sense in some languages the verb + + align:start position:0% +sense in some languages the verb + + + align:start position:0% +sense in some languages the verb +precedes the noun I eat a + + align:start position:0% +precedes the noun I eat a + + + align:start position:0% +precedes the noun I eat a +fish in other languages I the fish + + align:start position:0% + + + + align:start position:0% + +eat eat has a + + align:start position:0% +eat eat has a + + + align:start position:0% +eat eat has a +syntax which makes + + align:start position:0% +syntax which makes + + + align:start position:0% +syntax which makes +sense and linguists can probably explain + + align:start position:0% +sense and linguists can probably explain + + + align:start position:0% +sense and linguists can probably explain +the reasons why one system works in the + + align:start position:0% +the reasons why one system works in the + + + align:start position:0% +the reasons why one system works in the +other works and the other doesn't + + align:start position:0% + + + + align:start position:0% + +work the work that has been known as + + align:start position:0% +work the work that has been known as + + + align:start position:0% +work the work that has been known as +space sentex really is more recent + + align:start position:0% +space sentex really is more recent + + + align:start position:0% +space sentex really is more recent +it's the work which is published in this + + align:start position:0% +it's the work which is published in this + + + align:start position:0% +it's the work which is published in this +book space the + + align:start position:0% +book space the + + + align:start position:0% +book space the +machine which is a an extensive document + + align:start position:0% +machine which is a an extensive document + + + align:start position:0% +machine which is a an extensive document +and if any of you are interested in this + + align:start position:0% +and if any of you are interested in this + + + align:start position:0% +and if any of you are interested in this +idea you should probably try to read + + align:start position:0% +idea you should probably try to read + + + align:start position:0% +idea you should probably try to read +parts of + + align:start position:0% +parts of + + + align:start position:0% +parts of +it + + align:start position:0% +it + + + align:start position:0% +it +um + + align:start position:0% +um + + + align:start position:0% +um +essentially the argument is that + + align:start position:0% +essentially the argument is that + + + align:start position:0% +essentially the argument is that +behavior + + align:start position:0% + + + + align:start position:0% + +that you need to understand the space of + + align:start position:0% +that you need to understand the space of + + + align:start position:0% +that you need to understand the space of +the city before you can understand any + + align:start position:0% +the city before you can understand any + + + align:start position:0% +the city before you can understand any +of its elements the space of the city in + + align:start position:0% +of its elements the space of the city in + + + align:start position:0% +of its elements the space of the city in +the the application of this space + + align:start position:0% +the the application of this space + + + align:start position:0% +the the application of this space +syntax + + align:start position:0% +syntax + + + align:start position:0% +syntax +model is a theory based upon movement + + align:start position:0% +model is a theory based upon movement + + + align:start position:0% +model is a theory based upon movement +patterns cruly speaking they say that + + align:start position:0% +patterns cruly speaking they say that + + + align:start position:0% +patterns cruly speaking they say that +the movement pattern in a city is a + + align:start position:0% +the movement pattern in a city is a + + + align:start position:0% +the movement pattern in a city is a +function of the pattern that he shaped + + align:start position:0% +function of the pattern that he shaped + + + align:start position:0% +function of the pattern that he shaped +in order to cause the + + align:start position:0% +in order to cause the + + + align:start position:0% +in order to cause the +movement or allows the movement to take + + align:start position:0% +movement or allows the movement to take + + + align:start position:0% +movement or allows the movement to take +place so in a + + align:start position:0% + + + + align:start position:0% + +town which + + align:start position:0% + + + + align:start position:0% + +has space for + + align:start position:0% + + + + align:start position:0% + +movement + + align:start position:0% +movement + + + align:start position:0% +movement +the they can + + align:start position:0% +the they can + + + align:start position:0% +the they can +distinguish in what they call High + + align:start position:0% +distinguish in what they call High + + + align:start position:0% +distinguish in what they call High +correlation which is the number of moves + + align:start position:0% +correlation which is the number of moves + + + align:start position:0% +correlation which is the number of moves +that are the number of connections that + + align:start position:0% +that are the number of connections that + + + align:start position:0% +that are the number of connections that +are possible with a minimum number of + + align:start position:0% +are possible with a minimum number of + + + align:start position:0% +are possible with a minimum number of +separate moves and low + + align:start position:0% +separate moves and low + + + align:start position:0% +separate moves and low +correlation + + align:start position:0% + + + + align:start position:0% + +represents a change of + + align:start position:0% +represents a change of + + + align:start position:0% +represents a change of +pattern which involves the maximum + + align:start position:0% +pattern which involves the maximum + + + align:start position:0% +pattern which involves the maximum +number of + + align:start position:0% + + + + align:start position:0% + +moves I'm putting it rather crudely + + align:start position:0% + + + + align:start position:0% + +by this you can characterize the layout + + align:start position:0% +by this you can characterize the layout + + + align:start position:0% +by this you can characterize the layout +of a + + align:start position:0% +of a + + + align:start position:0% +of a +town in terms of this capacity of + + align:start position:0% +town in terms of this capacity of + + + align:start position:0% +town in terms of this capacity of +movement to + + align:start position:0% + + + + align:start position:0% + +flow the work correlate encounter + + align:start position:0% +flow the work correlate encounter + + + align:start position:0% +flow the work correlate encounter +rate with space + + align:start position:0% +rate with space + + + align:start position:0% +rate with space +syntax methodology in other words if you + + align:start position:0% +syntax methodology in other words if you + + + align:start position:0% +syntax methodology in other words if you +wish to create a system in which there + + align:start position:0% +wish to create a system in which there + + + align:start position:0% +wish to create a system in which there +are random encounter acts it was not + + align:start position:0% +are random encounter acts it was not + + + align:start position:0% +are random encounter acts it was not +only a function of density it's a + + align:start position:0% +only a function of density it's a + + + align:start position:0% +only a function of density it's a +function also of + + align:start position:0% + + + + align:start position:0% + +pattern it's also although they're a + + align:start position:0% +pattern it's also although they're a + + + align:start position:0% +pattern it's also although they're a +little unclear about this it's not so + + align:start position:0% +little unclear about this it's not so + + + align:start position:0% +little unclear about this it's not so +clearly a a result of a particular land + + align:start position:0% +clearly a a result of a particular land + + + align:start position:0% +clearly a a result of a particular land +use pattern if Marina ditri was singing + + align:start position:0% +use pattern if Marina ditri was singing + + + align:start position:0% +use pattern if Marina ditri was singing +tonight in East Boston I might + + align:start position:0% +tonight in East Boston I might + + + align:start position:0% +tonight in East Boston I might +go to East Boston I wouldn't normally go + + align:start position:0% +go to East Boston I wouldn't normally go + + + align:start position:0% +go to East Boston I wouldn't normally go +to East + + align:start position:0% +to East + + + align:start position:0% +to East +Boston + + align:start position:0% +Boston + + + align:start position:0% +Boston +uh but then the argument would be that + + align:start position:0% +uh but then the argument would be that + + + align:start position:0% +uh but then the argument would be that +Molina D would sing in a space which is + + align:start position:0% +Molina D would sing in a space which is + + + align:start position:0% +Molina D would sing in a space which is +easily available to + + align:start position:0% +easily available to + + + align:start position:0% +easily available to +me Andre seak who did his PhD two years + + align:start position:0% +me Andre seak who did his PhD two years + + + align:start position:0% +me Andre seak who did his PhD two years +ago has taken some elements of the space + + align:start position:0% +ago has taken some elements of the space + + + align:start position:0% +ago has taken some elements of the space +syntax model and correlated it with uh + + align:start position:0% +syntax model and correlated it with uh + + + align:start position:0% +syntax model and correlated it with uh +uh patterns of movement and Commercial + + align:start position:0% +uh patterns of movement and Commercial + + + align:start position:0% +uh patterns of movement and Commercial +location in + + align:start position:0% +location in + + + align:start position:0% +location in +Cambridge it's an it's a a branching off + + align:start position:0% +Cambridge it's an it's a a branching off + + + align:start position:0% +Cambridge it's an it's a a branching off +of space syntax it's not really space + + align:start position:0% +of space syntax it's not really space + + + align:start position:0% +of space syntax it's not really space +syntax because it doesn't develop + + align:start position:0% +syntax because it doesn't develop + + + align:start position:0% +syntax because it doesn't develop +theoretical + + align:start position:0% +theoretical + + + align:start position:0% +theoretical +models + + align:start position:0% +models + + + align:start position:0% +models +um he just bases it on observation very + + align:start position:0% +um he just bases it on observation very + + + align:start position:0% +um he just bases it on observation very +F detailed + + align:start position:0% +F detailed + + + align:start position:0% +F detailed +observation um + + align:start position:0% + + + + align:start position:0% + +the value of space and + + align:start position:0% +the value of space and + + + align:start position:0% +the value of space and +TX presumably is in its correlation with + + align:start position:0% +TX presumably is in its correlation with + + + align:start position:0% +TX presumably is in its correlation with +social good + + align:start position:0% +social good + + + align:start position:0% +social good +Dimensions so for instance + + align:start position:0% +Dimensions so for instance + + + align:start position:0% +Dimensions so for instance +their analysis of spatial patterns would + + align:start position:0% +their analysis of spatial patterns would + + + align:start position:0% +their analysis of spatial patterns would +suggest that crime rates are much lower + + align:start position:0% +suggest that crime rates are much lower + + + align:start position:0% +suggest that crime rates are much lower +where there is a lot of encoun high + + align:start position:0% +where there is a lot of encoun high + + + align:start position:0% +where there is a lot of encoun high +encounter rate + + align:start position:0% +encounter rate + + + align:start position:0% +encounter rate +so that housing Estates + + align:start position:0% +so that housing Estates + + + align:start position:0% +so that housing Estates +which turn their PS onto conventional + + align:start position:0% +which turn their PS onto conventional + + + align:start position:0% +which turn their PS onto conventional +streets and have access from private + + align:start position:0% +streets and have access from private + + + align:start position:0% +streets and have access from private +unguarded domains in the + + align:start position:0% +unguarded domains in the + + + align:start position:0% +unguarded domains in the +center are much more likely to be + + align:start position:0% +center are much more likely to be + + + align:start position:0% +center are much more likely to be +available + + align:start position:0% +available + + + align:start position:0% +available +for + + align:start position:0% +for + + + align:start position:0% +for +burglary than others and this + + align:start position:0% +burglary than others and this + + + align:start position:0% +burglary than others and this +correlates their work has expanded + + align:start position:0% +correlates their work has expanded + + + align:start position:0% +correlates their work has expanded +enormously they have now computer + + align:start position:0% +enormously they have now computer + + + align:start position:0% +enormously they have now computer +programs which you can buy and play + + align:start position:0% +programs which you can buy and play + + + align:start position:0% +programs which you can buy and play +yourself uh they consult all over the + + align:start position:0% +yourself uh they consult all over the + + + align:start position:0% +yourself uh they consult all over the +world + + align:start position:0% +world + + + align:start position:0% +world +they've I shown you one of the little + + align:start position:0% +they've I shown you one of the little + + + align:start position:0% +they've I shown you one of the little +projects in one drawing that's the + + align:start position:0% +projects in one drawing that's the + + + align:start position:0% +projects in one drawing that's the +traela + + align:start position:0% + + + + align:start position:0% + +square + + align:start position:0% +square + + + align:start position:0% +square +problem now you can say that everything + + align:start position:0% +problem now you can say that everything + + + align:start position:0% +problem now you can say that everything +that they + + align:start position:0% + + + + align:start position:0% + +theyve built as a Compu as a theoretical + + align:start position:0% +theyve built as a Compu as a theoretical + + + align:start position:0% +theyve built as a Compu as a theoretical +model and what they've actually found on + + align:start position:0% +model and what they've actually found on + + + align:start position:0% +model and what they've actually found on +the ground is something that you as an + + align:start position:0% +the ground is something that you as an + + + align:start position:0% +the ground is something that you as an +intelligent Observer could have + + align:start position:0% +intelligent Observer could have + + + align:start position:0% +intelligent Observer could have +told there's something obvious about + + align:start position:0% +told there's something obvious about + + + align:start position:0% +told there's something obvious about +what this enormous investment of energy + + align:start position:0% +what this enormous investment of energy + + + align:start position:0% +what this enormous investment of energy +and + + align:start position:0% +and + + + align:start position:0% +and +mind produces I was always told when I + + align:start position:0% +mind produces I was always told when I + + + align:start position:0% +mind produces I was always told when I +studied did a class in urban sociology + + align:start position:0% +studied did a class in urban sociology + + + align:start position:0% +studied did a class in urban sociology +at + + align:start position:0% +at + + + align:start position:0% +at +Yale uh that I should understand that + + align:start position:0% +Yale uh that I should understand that + + + align:start position:0% +Yale uh that I should understand that +sociology is about everyday + + align:start position:0% +sociology is about everyday + + + align:start position:0% +sociology is about everyday +things and that you shouldn't be + + align:start position:0% +things and that you shouldn't be + + + align:start position:0% +things and that you shouldn't be +surprised if + + align:start position:0% +surprised if + + + align:start position:0% +surprised if +sociological + + align:start position:0% +sociological + + + align:start position:0% +sociological +conclusions May accompany everyday + + align:start position:0% +conclusions May accompany everyday + + + align:start position:0% +conclusions May accompany everyday +observation I don't know it's uh it's a + + align:start position:0% +observation I don't know it's uh it's a + + + align:start position:0% +observation I don't know it's uh it's a +question which critics of say syntax + + align:start position:0% +question which critics of say syntax + + + align:start position:0% +question which critics of say syntax +have been very frequent to + + align:start position:0% +have been very frequent to + + + align:start position:0% +have been very frequent to +say why was the money on something which + + align:start position:0% +say why was the money on something which + + + align:start position:0% +say why was the money on something which +produces nothing new and just confirms + + align:start position:0% +produces nothing new and just confirms + + + align:start position:0% +produces nothing new and just confirms +what you intuitively + + align:start position:0% +what you intuitively + + + align:start position:0% +what you intuitively +know if there are obstacles to where + + align:start position:0% +know if there are obstacles to where + + + align:start position:0% +know if there are obstacles to where +people can walk people won't walk + + align:start position:0% +people can walk people won't walk + + + align:start position:0% +people can walk people won't walk +there uh so to reduce it to a rather + + align:start position:0% +there uh so to reduce it to a rather + + + align:start position:0% +there uh so to reduce it to a rather +sort of base level + + align:start position:0% + + + + align:start position:0% + +um it had a what did you think of the + + align:start position:0% +um it had a what did you think of the + + + align:start position:0% +um it had a what did you think of the +the presentation you had the one thing + + align:start position:0% +the presentation you had the one thing + + + align:start position:0% +the presentation you had the one thing +that I thought was interesting was + + align:start position:0% +that I thought was interesting was + + + align:start position:0% +that I thought was interesting was +towards the end he was talking about um + + align:start position:0% +towards the end he was talking about um + + + align:start position:0% +towards the end he was talking about um +like he was proposing that we're going + + align:start position:0% +like he was proposing that we're going + + + align:start position:0% +like he was proposing that we're going +to re if you were redevelop over the + + align:start position:0% +to re if you were redevelop over the + + + align:start position:0% +to re if you were redevelop over the +train yards in London and uh he showed + + align:start position:0% +train yards in London and uh he showed + + + align:start position:0% +train yards in London and uh he showed +if you just put a grid down uh like + + align:start position:0% +if you just put a grid down uh like + + + align:start position:0% +if you just put a grid down uh like +where the potential commercial streets + + align:start position:0% +where the potential commercial streets + + + align:start position:0% +where the potential commercial streets +would be you know because they they + + align:start position:0% +would be you know because they they + + + align:start position:0% +would be you know because they they +color M streets and he said but if you + + align:start position:0% +color M streets and he said but if you + + + align:start position:0% +color M streets and he said but if you +did this pattern you know then you could + + align:start position:0% +did this pattern you know then you could + + + align:start position:0% +did this pattern you know then you could +see oh this according to them would + + align:start position:0% +see oh this according to them would + + + align:start position:0% +see oh this according to them would +probably make uh you know a really good + + align:start position:0% +probably make uh you know a really good + + + align:start position:0% +probably make uh you know a really good +res or uh Commercial Street of these + + align:start position:0% +res or uh Commercial Street of these + + + align:start position:0% +res or uh Commercial Street of these +would be residential um and sort of a + + align:start position:0% +would be residential um and sort of a + + + align:start position:0% +would be residential um and sort of a +way to + + align:start position:0% +way to + + + align:start position:0% +way to +quantitatively under understand non-grid + + align:start position:0% +quantitatively under understand non-grid + + + align:start position:0% +quantitatively under understand non-grid +patterns um in a way that you could + + align:start position:0% +patterns um in a way that you could + + + align:start position:0% +patterns um in a way that you could +present it to yeah you know a planning + + align:start position:0% +present it to yeah you know a planning + + + align:start position:0% +present it to yeah you know a planning +border government yeah was + + align:start position:0% + + + + align:start position:0% + +interesting yeah I think the adjustments + + align:start position:0% +interesting yeah I think the adjustments + + + align:start position:0% +interesting yeah I think the adjustments +to the king's + + align:start position:0% +to the king's + + + align:start position:0% +to the king's +cross plan side plan were interesting + + align:start position:0% +cross plan side plan were interesting + + + align:start position:0% +cross plan side plan were interesting +I + + align:start position:0% +I + + + align:start position:0% +I +think a couple of things number one it + + align:start position:0% +think a couple of things number one it + + + align:start position:0% +think a couple of things number one it +satisfies me when somebody method + + align:start position:0% +satisfies me when somebody method + + + align:start position:0% +satisfies me when somebody method +methodologically shows that the form of + + align:start position:0% +methodologically shows that the form of + + + align:start position:0% +methodologically shows that the form of +things has + + align:start position:0% +things has + + + align:start position:0% +things has +meaning has + + align:start position:0% + + + + align:start position:0% + +value if you want if you think that + + align:start position:0% +value if you want if you think that + + + align:start position:0% +value if you want if you think that +encoun high encounter rates are good + + align:start position:0% +encoun high encounter rates are good + + + align:start position:0% +encoun high encounter rates are good +thing at least they will tell you how to + + align:start position:0% +thing at least they will tell you how to + + + align:start position:0% +thing at least they will tell you how to +accomplish it + + align:start position:0% +accomplish it + + + align:start position:0% +accomplish it +and that's not a bad set of + + align:start position:0% +and that's not a bad set of + + + align:start position:0% +and that's not a bad set of +propositions + + align:start position:0% +propositions + + + align:start position:0% +propositions +uh we understand + + align:start position:0% +uh we understand + + + align:start position:0% +uh we understand +actually very little about high + + align:start position:0% +actually very little about high + + + align:start position:0% +actually very little about high +encounter rates we assume them to be + + align:start position:0% +encounter rates we assume them to be + + + align:start position:0% +encounter rates we assume them to be +good man Anon has had a history of since + + align:start position:0% +good man Anon has had a history of since + + + align:start position:0% +good man Anon has had a history of since +its early days of making sure that side + + align:start position:0% +its early days of making sure that side + + + align:start position:0% +its early days of making sure that side +walks on its major Avenues are wide + + align:start position:0% +walks on its major Avenues are wide + + + align:start position:0% +walks on its major Avenues are wide +enough to take a lot of people Tokyo + + align:start position:0% +enough to take a lot of people Tokyo + + + align:start position:0% +enough to take a lot of people Tokyo +hasn't uh uh the street sidewalks are + + align:start position:0% +hasn't uh uh the street sidewalks are + + + align:start position:0% +hasn't uh uh the street sidewalks are +too narrow for The Pedestrian volume and + + align:start position:0% +too narrow for The Pedestrian volume and + + + align:start position:0% +too narrow for The Pedestrian volume and +uh one could imagine that encounter + + align:start position:0% + + + + align:start position:0% + +rates difficulty about our encounter + + align:start position:0% +rates difficulty about our encounter + + + align:start position:0% +rates difficulty about our encounter +rates is that often people use them be + + align:start position:0% +rates is that often people use them be + + + align:start position:0% +rates is that often people use them be +to believe that that is good Richard + + align:start position:0% +to believe that that is good Richard + + + align:start position:0% +to believe that that is good Richard +senet I think naively believes that is + + align:start position:0% +senet I think naively believes that is + + + align:start position:0% +senet I think naively believes that is +good uh for public + + align:start position:0% +good uh for public + + + align:start position:0% +good uh for public +relations when I walk down Fifth Avenue + + align:start position:0% +relations when I walk down Fifth Avenue + + + align:start position:0% +relations when I walk down Fifth Avenue +I don't stop and talk to a woman with a + + align:start position:0% +I don't stop and talk to a woman with a + + + align:start position:0% +I don't stop and talk to a woman with a +FK with a fur and a + + align:start position:0% +FK with a fur and a + + + align:start position:0% +FK with a fur and a +dog and probably be shot or be accused + + align:start position:0% +dog and probably be shot or be accused + + + align:start position:0% +dog and probably be shot or be accused +of you know um Crowds Are Not NE places + + align:start position:0% +of you know um Crowds Are Not NE places + + + align:start position:0% +of you know um Crowds Are Not NE places +in + + align:start position:0% +in + + + align:start position:0% +in +which uh enable often they don't enable + + align:start position:0% +which uh enable often they don't enable + + + align:start position:0% +which uh enable often they don't enable +human communication so encounter rates + + align:start position:0% +human communication so encounter rates + + + align:start position:0% +human communication so encounter rates +are in themselves not absolute Goods or + + align:start position:0% +are in themselves not absolute Goods or + + + align:start position:0% +are in themselves not absolute Goods or +absolute bads + + align:start position:0% +absolute bads + + + align:start position:0% +absolute bads +but certainly the notion that you + + align:start position:0% +but certainly the notion that you + + + align:start position:0% +but certainly the notion that you +feel when do you feel safer in all + + align:start position:0% +feel when do you feel safer in all + + + align:start position:0% +feel when do you feel safer in all +cultures when you are on streets with a + + align:start position:0% +cultures when you are on streets with a + + + align:start position:0% +cultures when you are on streets with a +lot of other people I can imagine I've + + align:start position:0% +lot of other people I can imagine I've + + + align:start position:0% +lot of other people I can imagine I've +been in places where I've been sh scared + + align:start position:0% +been in places where I've been sh scared + + + align:start position:0% +been in places where I've been sh scared +of being on a street with a lot of other + + align:start position:0% +of being on a street with a lot of other + + + align:start position:0% +of being on a street with a lot of other +people CU they all look like criminals + + align:start position:0% +people CU they all look like criminals + + + align:start position:0% +people CU they all look like criminals +to + + align:start position:0% +to + + + align:start position:0% +to +me uh cuz I couldn't read this situation + + align:start position:0% +me uh cuz I couldn't read this situation + + + align:start position:0% +me uh cuz I couldn't read this situation +well + + align:start position:0% +well + + + align:start position:0% +well +enough um the last set of stuff has a + + align:start position:0% +enough um the last set of stuff has a + + + align:start position:0% +enough um the last set of stuff has a +has a body of literature and I've only + + align:start position:0% +has a body of literature and I've only + + + align:start position:0% +has a body of literature and I've only +chosen one page from one of the + + align:start position:0% +chosen one page from one of the + + + align:start position:0% +chosen one page from one of the +documents it's there's a good book + + align:start position:0% +documents it's there's a good book + + + align:start position:0% +documents it's there's a good book +called Urban space and structures which + + align:start position:0% +called Urban space and structures which + + + align:start position:0% +called Urban space and structures which +those of you serious about becoming + + align:start position:0% +those of you serious about becoming + + + align:start position:0% +those of you serious about becoming +Urban designers need to + + align:start position:0% +Urban designers need to + + + align:start position:0% +Urban designers need to +read it's + + align:start position:0% + + + + align:start position:0% + +uh edited by Lesley Martin and Lionel + + align:start position:0% +uh edited by Lesley Martin and Lionel + + + align:start position:0% +uh edited by Lesley Martin and Lionel +Martin March Cambridge University press + + align:start position:0% + + + + align:start position:0% + +1972 the British have been interested in + + align:start position:0% +1972 the British have been interested in + + + align:start position:0% +1972 the British have been interested in +understanding spatial patterns largely + + align:start position:0% +understanding spatial patterns largely + + + align:start position:0% +understanding spatial patterns largely +through + + align:start position:0% + + + + align:start position:0% + +geometry + + align:start position:0% +geometry + + + align:start position:0% +geometry +um in the P piece that I've given to you + + align:start position:0% +um in the P piece that I've given to you + + + align:start position:0% +um in the P piece that I've given to you +today on the right hand side is a + + align:start position:0% +today on the right hand side is a + + + align:start position:0% +today on the right hand side is a +section of the grid of New York from + + align:start position:0% +section of the grid of New York from + + + align:start position:0% +section of the grid of New York from +42nd to 56 second and from 8th Avenue to + + align:start position:0% +42nd to 56 second and from 8th Avenue to + + + align:start position:0% +42nd to 56 second and from 8th Avenue to +Park + + align:start position:0% + + + + align:start position:0% + +Avenue the argument is relatively + + align:start position:0% +Avenue the argument is relatively + + + align:start position:0% +Avenue the argument is relatively +simple if you + + align:start position:0% +simple if you + + + align:start position:0% +simple if you +took the amount of gross square footage + + align:start position:0% +took the amount of gross square footage + + + align:start position:0% +took the amount of gross square footage +built on this parcel in the black + + align:start position:0% +built on this parcel in the black + + + align:start position:0% +built on this parcel in the black +areas + + align:start position:0% + + + + align:start position:0% + +today and you took away a number of the + + align:start position:0% +today and you took away a number of the + + + align:start position:0% +today and you took away a number of the +streets you took away every second + + align:start position:0% +streets you took away every second + + + align:start position:0% +streets you took away every second +Street more or less + + align:start position:0% +Street more or less + + + align:start position:0% +Street more or less +you could + + align:start position:0% +you could + + + align:start position:0% +you could +rebuild the same amount of square + + align:start position:0% +rebuild the same amount of square + + + align:start position:0% +rebuild the same amount of square +footage in the pattern on the right with + + align:start position:0% +footage in the pattern on the right with + + + align:start position:0% +footage in the pattern on the right with +only our maximum height of seven floors + + align:start position:0% +only our maximum height of seven floors + + + align:start position:0% +only our maximum height of seven floors +and large amounts of open space + + align:start position:0% + + + + align:start position:0% + +inside now no architecture student I + + align:start position:0% +inside now no architecture student I + + + align:start position:0% +inside now no architecture student I +know of would come to that conclusion + + align:start position:0% +know of would come to that conclusion + + + align:start position:0% +know of would come to that conclusion +automatically it's much like the use of + + align:start position:0% +automatically it's much like the use of + + + align:start position:0% +automatically it's much like the use of +the phrase nail + + align:start position:0% +the phrase nail + + + align:start position:0% +the phrase nail +lens in + + align:start position:0% + + + + align:start position:0% + +arguing population in a + + align:start position:0% + + + + align:start position:0% + +city as you go + + align:start position:0% +city as you go + + + align:start position:0% +city as you go +outwards if you want the same area of + + align:start position:0% +outwards if you want the same area of + + + align:start position:0% +outwards if you want the same area of +land as you get further out these bands + + align:start position:0% +land as you get further out these bands + + + align:start position:0% +land as you get further out these bands +need to become thinner because the area + + align:start position:0% +need to become thinner because the area + + + align:start position:0% +need to become thinner because the area +they cover is larger so the total + + align:start position:0% +they cover is larger so the total + + + align:start position:0% +they cover is larger so the total +population in the center of the city can + + align:start position:0% +population in the center of the city can + + + align:start position:0% +population in the center of the city can +be housed in a thin band on the + + align:start position:0% +be housed in a thin band on the + + + align:start position:0% +be housed in a thin band on the +out this is + + align:start position:0% + + + + align:start position:0% + +not there diminishing amount of width + + align:start position:0% +not there diminishing amount of width + + + align:start position:0% +not there diminishing amount of width +required in each band and as you go + + align:start position:0% +required in each band and as you go + + + align:start position:0% +required in each band and as you go +further out because the band becomes + + align:start position:0% +further out because the band becomes + + + align:start position:0% +further out because the band becomes +larger it's a simple geometric + + align:start position:0% +larger it's a simple geometric + + + align:start position:0% +larger it's a simple geometric +observation which they apply to some + + align:start position:0% +observation which they apply to some + + + align:start position:0% +observation which they apply to some +depict to some estimates of urban + + align:start position:0% + + + + align:start position:0% + +population the number of books published + + align:start position:0% +population the number of books published + + + align:start position:0% +population the number of books published +I will come back to the work of this + + align:start position:0% +I will come back to the work of this + + + align:start position:0% +I will come back to the work of this +group when we talk about prediction of + + align:start position:0% +group when we talk about prediction of + + + align:start position:0% +group when we talk about prediction of +growth and flexibility ability of + + align:start position:0% +growth and flexibility ability of + + + align:start position:0% +growth and flexibility ability of +building + + align:start position:0% +building + + + align:start position:0% +building +apparatus + + align:start position:0% +apparatus + + + align:start position:0% +apparatus +um uh a lot of this work came + + align:start position:0% +um uh a lot of this work came + + + align:start position:0% +um uh a lot of this work came +from a set of Investigations the British + + align:start position:0% +from a set of Investigations the British + + + align:start position:0% +from a set of Investigations the British +did after the 40 46 end of this 3946 war + + align:start position:0% +did after the 40 46 end of this 3946 war + + + align:start position:0% +did after the 40 46 end of this 3946 war +in the rebuilding of British + + align:start position:0% +in the rebuilding of British + + + align:start position:0% +in the rebuilding of British +infrastructure hospitals universities + + align:start position:0% +infrastructure hospitals universities + + + align:start position:0% +infrastructure hospitals universities +and so on I will do a set of case + + align:start position:0% +and so on I will do a set of case + + + align:start position:0% +and so on I will do a set of case +studies of a number of University plans + + align:start position:0% +studies of a number of University plans + + + align:start position:0% +studies of a number of University plans +showing + + align:start position:0% +showing + + + align:start position:0% +showing +how two + + align:start position:0% +how two + + + align:start position:0% +how two +factors + + align:start position:0% +factors + + + align:start position:0% +factors +one the idea that new groups of science + + align:start position:0% +one the idea that new groups of science + + + align:start position:0% +one the idea that new groups of science +new groups of knowledge disciplines Co + + align:start position:0% +new groups of knowledge disciplines Co + + + align:start position:0% +new groups of knowledge disciplines Co +my + + align:start position:0% +my + + + align:start position:0% +my +microbiology as opposed to micr physics + + align:start position:0% +microbiology as opposed to micr physics + + + align:start position:0% +microbiology as opposed to micr physics +uh biology and uh chemistry mixing + + align:start position:0% +uh biology and uh chemistry mixing + + + align:start position:0% +uh biology and uh chemistry mixing +together and so on how the these + + align:start position:0% +together and so on how the these + + + align:start position:0% +together and so on how the these +patterns could be + + align:start position:0% +patterns could be + + + align:start position:0% +patterns could be +accommodated in physical form which + + align:start position:0% +accommodated in physical form which + + + align:start position:0% +accommodated in physical form which +required the least adjustment over + + align:start position:0% +required the least adjustment over + + + align:start position:0% +required the least adjustment over +time we will look at the Technical + + align:start position:0% +time we will look at the Technical + + + align:start position:0% +time we will look at the Technical +University in Berlin we look at + + align:start position:0% +University in Berlin we look at + + + align:start position:0% +University in Berlin we look at +MIT as examples of these + + align:start position:0% +MIT as examples of these + + + align:start position:0% +MIT as examples of these +patterns which maintain which promote + + align:start position:0% +patterns which maintain which promote + + + align:start position:0% +patterns which maintain which promote +High degrees of + + align:start position:0% +High degrees of + + + align:start position:0% +High degrees of +flexibility also in the British writing + + align:start position:0% +flexibility also in the British writing + + + align:start position:0% +flexibility also in the British writing +about hospitals the research done in + + align:start position:0% +about hospitals the research done in + + + align:start position:0% +about hospitals the research done in +hospitals knowing that hos hospitals + + align:start position:0% +hospitals knowing that hos hospitals + + + align:start position:0% +hospitals knowing that hos hospitals +change Hospital science and + + align:start position:0% +change Hospital science and + + + align:start position:0% +change Hospital science and +administration changes rapidly how would + + align:start position:0% +administration changes rapidly how would + + + align:start position:0% +administration changes rapidly how would +you choose patterns which enabled the + + align:start position:0% +you choose patterns which enabled the + + + align:start position:0% +you choose patterns which enabled the +minimum disruption in in the trajectory + + align:start position:0% +minimum disruption in in the trajectory + + + align:start position:0% +minimum disruption in in the trajectory +of + + align:start position:0% +of + + + align:start position:0% +of +change so if any of you interested in + + align:start position:0% +change so if any of you interested in + + + align:start position:0% +change so if any of you interested in +this kind of work this is not the class + + align:start position:0% +this kind of work this is not the class + + + align:start position:0% +this kind of work this is not the class +to take I can just tell you we'll touch + + align:start position:0% +to take I can just tell you we'll touch + + + align:start position:0% +to take I can just tell you we'll touch +on some of this later on but in I can + + align:start position:0% +on some of this later on but in I can + + + align:start position:0% +on some of this later on but in I can +just read you some of the list of books + + align:start position:0% +just read you some of the list of books + + + align:start position:0% +just read you some of the list of books +that come from there's Philip stedman's + + align:start position:0% +that come from there's Philip stedman's + + + align:start position:0% +that come from there's Philip stedman's +book called architectural + + align:start position:0% +book called architectural + + + align:start position:0% +book called architectural +morphology these Philip stedman's book + + align:start position:0% +morphology these Philip stedman's book + + + align:start position:0% +morphology these Philip stedman's book +The Evolution of + + align:start position:0% +The Evolution of + + + align:start position:0% +The Evolution of +design these lonel March and Philip + + align:start position:0% +design these lonel March and Philip + + + align:start position:0% +design these lonel March and Philip +stepman Philip stedman's book The + + align:start position:0% +stepman Philip stedman's book The + + + align:start position:0% +stepman Philip stedman's book The +geometry of environment MIT press + + align:start position:0% + + + + align:start position:0% + +1974 those are a couple of the more + + align:start position:0% +1974 those are a couple of the more + + + align:start position:0% +1974 those are a couple of the more +General + + align:start position:0% +General + + + align:start position:0% +General +applied outcomes of much of this + + align:start position:0% + + + + align:start position:0% + +work we finished the first part of the + + align:start position:0% +work we finished the first part of the + + + align:start position:0% +work we finished the first part of the +three sections of this + + align:start position:0% +three sections of this + + + align:start position:0% +three sections of this +class this first part was just an + + align:start position:0% +class this first part was just an + + + align:start position:0% +class this first part was just an +attempt to bring you up to speed on some + + align:start position:0% +attempt to bring you up to speed on some + + + align:start position:0% +attempt to bring you up to speed on some +things which you might not have known + + align:start position:0% +things which you might not have known + + + align:start position:0% +things which you might not have known +about we start the serious work on th + + align:start position:0% +about we start the serious work on th + + + align:start position:0% +about we start the serious work on th +what is today + + align:start position:0% +what is today + + + align:start position:0% +what is today +Tuesday we start the serious work on + + align:start position:0% +Tuesday we start the serious work on + + + align:start position:0% +Tuesday we start the serious work on +Thursday who will start + + align:start position:0% +Thursday who will start + + + align:start position:0% +Thursday who will start +Excavating the the spatial pattern of + + align:start position:0% +Excavating the the spatial pattern of + + + align:start position:0% +Excavating the the spatial pattern of +existing cities after the Industrial + + align:start position:0% +existing cities after the Industrial + + + align:start position:0% +existing cities after the Industrial +Revolution uh will on + + align:start position:0% +Revolution uh will on + + + align:start position:0% +Revolution uh will on +Thursday try to make sense + + align:start position:0% +Thursday try to make sense + + + align:start position:0% +Thursday try to make sense +of what industrialism meant what it + + align:start position:0% +of what industrialism meant what it + + + align:start position:0% +of what industrialism meant what it +meant to special patterns in cities what + + align:start position:0% +meant to special patterns in cities what + + + align:start position:0% +meant to special patterns in cities what +it meant + + align:start position:0% +it meant + + + align:start position:0% +it meant +to knew the invention new instruments + + align:start position:0% +to knew the invention new instruments + + + align:start position:0% +to knew the invention new instruments +the mortgage system deficit + + align:start position:0% +the mortgage system deficit + + + align:start position:0% +the mortgage system deficit +spending uh and so + + align:start position:0% +spending uh and so + + + align:start position:0% +spending uh and so +on the Advent of poverty in + + align:start position:0% +on the Advent of poverty in + + + align:start position:0% +on the Advent of poverty in +accumulated situations in the west and + + align:start position:0% +accumulated situations in the west and + + + align:start position:0% +accumulated situations in the west and +so on and from that we will do my case + + align:start position:0% +so on and from that we will do my case + + + align:start position:0% +so on and from that we will do my case +studies of the major reactions London + + align:start position:0% +studies of the major reactions London + + + align:start position:0% +studies of the major reactions London +Paris Vienna Barcelona and + + align:start position:0% +Paris Vienna Barcelona and + + + align:start position:0% +Paris Vienna Barcelona and +Chicago so this is a comprehensive look + + align:start position:0% +Chicago so this is a comprehensive look + + + align:start position:0% +Chicago so this is a comprehensive look +at some very detailed aspects of + + align:start position:0% +at some very detailed aspects of + + + align:start position:0% +at some very detailed aspects of +existing + + align:start position:0% +existing + + + align:start position:0% +existing +Transformations hopefully by the time we + + align:start position:0% +Transformations hopefully by the time we + + + align:start position:0% +Transformations hopefully by the time we +get to the end of the class we'll be + + align:start position:0% +get to the end of the class we'll be + + + align:start position:0% +get to the end of the class we'll be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +make theoretical + + align:start position:0% +make theoretical + + + align:start position:0% +make theoretical +generalizations better than the ones + + align:start position:0% +generalizations better than the ones + + + align:start position:0% +generalizations better than the ones +I've explain to + + align:start position:0% +I've explain to + + + align:start position:0% +I've explain to +you so + + align:start position:0% +you so + + + align:start position:0% +you so +far Dy to to + + align:start position:0% +far Dy to to + + + align:start position:0% +far Dy to to +priest the remarkable thing is that we + + align:start position:0% +priest the remarkable thing is that we + + + align:start position:0% +priest the remarkable thing is that we +are building cities we build them + + align:start position:0% +are building cities we build them + + + align:start position:0% +are building cities we build them +perhaps not as well especially + + align:start position:0% +perhaps not as well especially + + + align:start position:0% +perhaps not as well especially +as we did 150 years ago or 300 years + + align:start position:0% +as we did 150 years ago or 300 years + + + align:start position:0% +as we did 150 years ago or 300 years +ago but there's no more + + align:start position:0% + + + + align:start position:0% + +colera because of the great invention in + + align:start position:0% +colera because of the great invention in + + + align:start position:0% +colera because of the great invention in +1854 in + + align:start position:0% +1854 in + + + align:start position:0% +1854 in +London causing the biggest + + align:start position:0% +London causing the biggest + + + align:start position:0% +London causing the biggest +transformation of London + + align:start position:0% + + + + align:start position:0% + +by siphoning of waste water on the nor + + align:start position:0% +by siphoning of waste water on the nor + + + align:start position:0% +by siphoning of waste water on the nor +on the East + + align:start position:0% +on the East + + + align:start position:0% +on the East +waste sides north and south of + + align:start position:0% +waste sides north and south of + + + align:start position:0% +waste sides north and south of +London all of this will build up Earth + + align:start position:0% +London all of this will build up Earth + + + align:start position:0% +London all of this will build up Earth +in story about the complexity of + + align:start position:0% +in story about the complexity of + + + align:start position:0% +in story about the complexity of +actual urban urban + + align:start position:0% +actual urban urban + + + align:start position:0% +actual urban urban +situation uh which I believe is better + + align:start position:0% +situation uh which I believe is better + + + align:start position:0% +situation uh which I believe is better +than too much time spending on abstract + + align:start position:0% +than too much time spending on abstract + + + align:start position:0% +than too much time spending on abstract +model + + align:start position:0% + + + + align:start position:0% + +I don't know if we'll ever have a theory + + align:start position:0% +I don't know if we'll ever have a theory + + + align:start position:0% +I don't know if we'll ever have a theory +of City form which university agreed + + align:start position:0% +of City form which university agreed + + + align:start position:0% +of City form which university agreed +upon able to be + + align:start position:0% +upon able to be + + + align:start position:0% +upon able to be +systematized some aspects of the + + align:start position:0% +systematized some aspects of the + + + align:start position:0% +systematized some aspects of the +performance of this field which are + + align:start position:0% +performance of this field which are + + + align:start position:0% +performance of this field which are +moving more and more in this direction + + align:start position:0% +moving more and more in this direction + + + align:start position:0% +moving more and more in this direction +we certainly know more about public + + align:start position:0% +we certainly know more about public + + + align:start position:0% +we certainly know more about public +transportation and it's engineering and + + align:start position:0% +transportation and it's engineering and + + + align:start position:0% +transportation and it's engineering and +science than ever before we we know very + + align:start position:0% +science than ever before we we know very + + + align:start position:0% +science than ever before we we know very +little about + + align:start position:0% +little about + + + align:start position:0% +little about +meaning we build pickle shaped tall + + align:start position:0% +meaning we build pickle shaped tall + + + align:start position:0% +meaning we build pickle shaped tall +buildings in + + align:start position:0% +buildings in + + + align:start position:0% +buildings in +London uh without him being able to + + align:start position:0% +London uh without him being able to + + + align:start position:0% +London uh without him being able to +measure the + + align:start position:0% +measure the + + + align:start position:0% +measure the +effect and the parts of the world which + + align:start position:0% +effect and the parts of the world which + + + align:start position:0% +effect and the parts of the world which +are looking + + align:start position:0% +are looking + + + align:start position:0% +are looking +to maintain to manifest Urban identity + + align:start position:0% +to maintain to manifest Urban identity + + + align:start position:0% +to maintain to manifest Urban identity +without building the tortois building in + + align:start position:0% +without building the tortois building in + + + align:start position:0% +without building the tortois building in +the world uh and a number of issues of + + align:start position:0% +the world uh and a number of issues of + + + align:start position:0% +the world uh and a number of issues of +that kind which are currently on the + + align:start position:0% +that kind which are currently on the + + + align:start position:0% +that kind which are currently on the +plate of herban + + align:start position:0% +plate of herban + + + align:start position:0% +plate of herban +designers okay I'll see you on Thursday + + align:start position:0% +designers okay I'll see you on Thursday + + + align:start position:0% +designers okay I'll see you on Thursday +have a good holiday \ No newline at end of file diff --git a/cNB2lADK3_s.txt b/cNB2lADK3_s.txt new file mode 100644 index 0000000000000000000000000000000000000000..e38767fff302d35327c76fea53445db38c1046d3 --- /dev/null +++ b/cNB2lADK3_s.txt @@ -0,0 +1,13776 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right good morning + + align:start position:0% +ocw.mit.edu all right good morning + + + align:start position:0% +ocw.mit.edu all right good morning +everyone let's get started a new new + + align:start position:0% +everyone let's get started a new new + + + align:start position:0% +everyone let's get started a new new +module today we're going to uh spend a + + align:start position:0% +module today we're going to uh spend a + + + align:start position:0% +module today we're going to uh spend a +few lectures on uh on randomized + + align:start position:0% +few lectures on uh on randomized + + + align:start position:0% +few lectures on uh on randomized +algorithms and so um not only will we + + align:start position:0% +algorithms and so um not only will we + + + align:start position:0% +algorithms and so um not only will we +look at U slightly different ways of + + align:start position:0% +look at U slightly different ways of + + + align:start position:0% +look at U slightly different ways of +solving old problems like + + align:start position:0% +solving old problems like + + + align:start position:0% +solving old problems like +sorting uh we'll also look at how we can + + align:start position:0% +sorting uh we'll also look at how we can + + + align:start position:0% +sorting uh we'll also look at how we can +analyze this new kind of algorithm that + + align:start position:0% +analyze this new kind of algorithm that + + + align:start position:0% +analyze this new kind of algorithm that +generates random numbers uh in order to + + align:start position:0% +generates random numbers uh in order to + + + align:start position:0% +generates random numbers uh in order to +actually make decisions as it's + + align:start position:0% +actually make decisions as it's + + + align:start position:0% +actually make decisions as it's +executing and uh we'll end up obviously + + align:start position:0% +executing and uh we'll end up obviously + + + align:start position:0% +executing and uh we'll end up obviously +uh with u analysis that uh gives us uh + + align:start position:0% +uh with u analysis that uh gives us uh + + + align:start position:0% +uh with u analysis that uh gives us uh +the expected runtime of the algorithm + + align:start position:0% +the expected runtime of the algorithm + + + align:start position:0% +the expected runtime of the algorithm +for + + align:start position:0% +for + + + align:start position:0% +for +example or uh whether the algorithm is + + align:start position:0% +example or uh whether the algorithm is + + + align:start position:0% +example or uh whether the algorithm is +going to produce the correct result or + + align:start position:0% +going to produce the correct result or + + + align:start position:0% +going to produce the correct result or +not with what probability will this + + align:start position:0% +not with what probability will this + + + align:start position:0% +not with what probability will this +algorithm produce a correct result so + + align:start position:0% +algorithm produce a correct result so + + + align:start position:0% +algorithm produce a correct result so +I'll talk a little bit about uh why + + align:start position:0% +I'll talk a little bit about uh why + + + align:start position:0% +I'll talk a little bit about uh why +we're interested in randomized + + align:start position:0% +we're interested in randomized + + + align:start position:0% +we're interested in randomized +algorithms in a in a couple of minutes + + align:start position:0% +algorithms in a in a couple of minutes + + + align:start position:0% +algorithms in a in a couple of minutes +but let me + + align:start position:0% +but let me + + + align:start position:0% +but let me +Define what uh a randomized algorithm or + + align:start position:0% +Define what uh a randomized algorithm or + + + align:start position:0% +Define what uh a randomized algorithm or +a probabilistic algorithm + + align:start position:0% +a probabilistic algorithm + + + align:start position:0% +a probabilistic algorithm +is to start things + + align:start position:0% + + + + align:start position:0% + +off and so randomized algorithm + + align:start position:0% +off and so randomized algorithm + + + align:start position:0% +off and so randomized algorithm +is something + + align:start position:0% + + + + align:start position:0% + +that generates a random + + align:start position:0% + + + + align:start position:0% + +number now this could be a coin + + align:start position:0% +number now this could be a coin + + + align:start position:0% +number now this could be a coin +flip but more often than not you're + + align:start position:0% +flip but more often than not you're + + + align:start position:0% +flip but more often than not you're +generating u a real + + align:start position:0% +generating u a real + + + align:start position:0% +generating u a real +number that comes from a certain + + align:start position:0% +number that comes from a certain + + + align:start position:0% +number that comes from a certain +range sometimes you're generating a + + align:start position:0% +range sometimes you're generating a + + + align:start position:0% +range sometimes you're generating a +vector you'll see a different uh a + + align:start position:0% +vector you'll see a different uh a + + + align:start position:0% +vector you'll see a different uh a +couple of different examples here in + + align:start position:0% +couple of different examples here in + + + align:start position:0% +couple of different examples here in +today's + + align:start position:0% +today's + + + align:start position:0% +today's +lecture uh and in and in + + align:start position:0% +lecture uh and in and in + + + align:start position:0% +lecture uh and in and in +section and it's going to make + + align:start position:0% +section and it's going to make + + + align:start position:0% +section and it's going to make +decisions based on this + + align:start position:0% + + + + align:start position:0% + +value based on + + align:start position:0% +value based on + + + align:start position:0% +value based on +R's actual value + + align:start position:0% + + + + align:start position:0% + +now you can imagine that an algorithm + + align:start position:0% +now you can imagine that an algorithm + + + align:start position:0% +now you can imagine that an algorithm +would be recursive and at every level of + + align:start position:0% +would be recursive and at every level of + + + align:start position:0% +would be recursive and at every level of +recursion it's going to generate a + + align:start position:0% +recursion it's going to generate a + + + align:start position:0% +recursion it's going to generate a +random R and so uh when you're executing + + align:start position:0% +random R and so uh when you're executing + + + align:start position:0% +random R and so uh when you're executing +at a particular level of recursion you + + align:start position:0% +at a particular level of recursion you + + + align:start position:0% +at a particular level of recursion you +may be doing different things uh based + + align:start position:0% +may be doing different things uh based + + + align:start position:0% +may be doing different things uh based +based on R and not only that if you + + align:start position:0% +based on R and not only that if you + + + align:start position:0% +based on R and not only that if you +rerun the algorithm again on the same + + align:start position:0% +rerun the algorithm again on the same + + + align:start position:0% +rerun the algorithm again on the same +input the execution will be different + + align:start position:0% +input the execution will be different + + + align:start position:0% +input the execution will be different +because U you're assuming a true random + + align:start position:0% +because U you're assuming a true random + + + align:start position:0% +because U you're assuming a true random +number generator as opposed to a a Pudo + + align:start position:0% +number generator as opposed to a a Pudo + + + align:start position:0% +number generator as opposed to a a Pudo +random one uh and and the RS that you're + + align:start position:0% +random one uh and and the RS that you're + + + align:start position:0% +random one uh and and the RS that you're +going to get at different levels of + + align:start position:0% +going to get at different levels of + + + align:start position:0% +going to get at different levels of +recursion or through the execution of + + align:start position:0% +recursion or through the execution of + + + align:start position:0% +recursion or through the execution of +the algorithm are going to be different + + align:start position:0% +the algorithm are going to be different + + + align:start position:0% +the algorithm are going to be different +from the first time to the second + + align:start position:0% +from the first time to the second + + + align:start position:0% +from the first time to the second +time so on the same + + align:start position:0% + + + + align:start position:0% + +input on different + + align:start position:0% +input on different + + + align:start position:0% +input on different +executions two things might + + align:start position:0% +executions two things might + + + align:start position:0% +executions two things might +happen um the algorithm may run for a + + align:start position:0% +happen um the algorithm may run for a + + + align:start position:0% +happen um the algorithm may run for a +different number number of + + align:start position:0% + + + + align:start position:0% + +steps so you might get lucky on the + + align:start position:0% +steps so you might get lucky on the + + + align:start position:0% +steps so you might get lucky on the +first execution and the algorithm + + align:start position:0% +first execution and the algorithm + + + align:start position:0% +first execution and the algorithm +finishes let's say in 100 time units the + + align:start position:0% +finishes let's say in 100 time units the + + + align:start position:0% +finishes let's say in 100 time units the +second time around it takes a a long + + align:start position:0% +second time around it takes a a long + + + align:start position:0% +second time around it takes a a long +time it takes 700 time units um our goal + + align:start position:0% +time it takes 700 time units um our goal + + + align:start position:0% +time it takes 700 time units um our goal +here is to try and analyze what this + + align:start position:0% +here is to try and analyze what this + + + align:start position:0% +here is to try and analyze what this +probabilistic runtime would be to ask + + align:start position:0% +probabilistic runtime would be to ask + + + align:start position:0% +probabilistic runtime would be to ask +for um an expectation to be able to + + align:start position:0% +for um an expectation to be able to + + + align:start position:0% +for um an expectation to be able to +compute an expectation + + align:start position:0% +compute an expectation + + + align:start position:0% +compute an expectation +for the runtime or if you're talking + + align:start position:0% +for the runtime or if you're talking + + + align:start position:0% +for the runtime or if you're talking +about a + + align:start position:0% +about a + + + align:start position:0% +about a +different scenario where different + + align:start position:0% +different scenario where different + + + align:start position:0% +different scenario where different +executions I could actually produce + + align:start position:0% +executions I could actually produce + + + align:start position:0% +executions I could actually produce +different in different + + align:start position:0% + + + + align:start position:0% + +outputs and in this case um it's + + align:start position:0% +outputs and in this case um it's + + + align:start position:0% +outputs and in this case um it's +possible that uh uh one or more of these + + align:start position:0% +possible that uh uh one or more of these + + + align:start position:0% +possible that uh uh one or more of these +outputs are incorrect you actually get + + align:start position:0% +outputs are incorrect you actually get + + + align:start position:0% +outputs are incorrect you actually get +the wrong answer uh and uh obviously uh + + align:start position:0% +the wrong answer uh and uh obviously uh + + + align:start position:0% +the wrong answer uh and uh obviously uh +that's going to happen with a certain + + align:start position:0% +that's going to happen with a certain + + + align:start position:0% +that's going to happen with a certain +probability we're going to have to + + align:start position:0% +probability we're going to have to + + + align:start position:0% +probability we're going to have to +u to decide or analyze what that + + align:start position:0% +u to decide or analyze what that + + + align:start position:0% +u to decide or analyze what that +probability is and uh generally speaking + + align:start position:0% +probability is and uh generally speaking + + + align:start position:0% +probability is and uh generally speaking +we won't be happy with a high + + align:start position:0% +we won't be happy with a high + + + align:start position:0% +we won't be happy with a high +probability of error as you can imagine + + align:start position:0% +probability of error as you can imagine + + + align:start position:0% +probability of error as you can imagine +and we'd like to set up an algorithm + + align:start position:0% +and we'd like to set up an algorithm + + + align:start position:0% +and we'd like to set up an algorithm +such that you can reduce that + + align:start position:0% +such that you can reduce that + + + align:start position:0% +such that you can reduce that +probability of incorrect output to be + + align:start position:0% +probability of incorrect output to be + + + align:start position:0% +probability of incorrect output to be +something really really small uh and + + align:start position:0% +something really really small uh and + + + align:start position:0% +something really really small uh and +it might take you uh longer to get to + + align:start position:0% +it might take you uh longer to get to + + + align:start position:0% +it might take you uh longer to get to +that that uh low level of uh incorrect + + align:start position:0% +that that uh low level of uh incorrect + + + align:start position:0% +that that uh low level of uh incorrect +error or incorrect output uh in one case + + align:start position:0% +error or incorrect output uh in one case + + + align:start position:0% +error or incorrect output uh in one case +uh for a certain set of inputs versus + + align:start position:0% +uh for a certain set of inputs versus + + + align:start position:0% +uh for a certain set of inputs versus +another case right so uh that's this + + align:start position:0% +another case right so uh that's this + + + align:start position:0% +another case right so uh that's this +setup here in terms of randomized um + + align:start position:0% +setup here in terms of randomized um + + + align:start position:0% +setup here in terms of randomized um +you're going to have algorithms that are + + align:start position:0% +you're going to have algorithms that are + + + align:start position:0% +you're going to have algorithms that are +uh you can think of them as uh probably + + align:start position:0% +uh you can think of them as uh probably + + + align:start position:0% +uh you can think of them as uh probably +correct okay so these are + + align:start position:0% +correct okay so these are + + + align:start position:0% +correct okay so these are +algorithms you want to think of them as + + align:start position:0% +algorithms you want to think of them as + + + align:start position:0% +algorithms you want to think of them as +probably correct and they do have a a + + align:start position:0% +probably correct and they do have a a + + + align:start position:0% +probably correct and they do have a a +name they're called Monte Carlo + + align:start position:0% +name they're called Monte Carlo + + + align:start position:0% +name they're called Monte Carlo +algorithms um and then you have + + align:start position:0% +algorithms um and then you have + + + align:start position:0% +algorithms um and then you have +algorithms that are probably + + align:start position:0% + + + + align:start position:0% + +fast + + align:start position:0% +fast + + + align:start position:0% +fast +so in the case of pro probably correct + + align:start position:0% +so in the case of pro probably correct + + + align:start position:0% +so in the case of pro probably correct +uh you you could you know have a + + align:start position:0% +uh you you could you know have a + + + align:start position:0% +uh you you could you know have a +constant probability that they're going + + align:start position:0% +constant probability that they're going + + + align:start position:0% +constant probability that they're going +to give you the correct answer + + align:start position:0% +to give you the correct answer + + + align:start position:0% +to give you the correct answer +99% uh and you could obviously try and + + align:start position:0% +99% uh and you could obviously try and + + + align:start position:0% +99% uh and you could obviously try and +parameterize that in the case of + + align:start position:0% +parameterize that in the case of + + + align:start position:0% +parameterize that in the case of +probably fast um you say things like it + + align:start position:0% +probably fast um you say things like it + + + align:start position:0% +probably fast um you say things like it +runs an expected polinomial time and um + + align:start position:0% +runs an expected polinomial time and um + + + align:start position:0% +runs an expected polinomial time and um +really what that means is that uh you + + align:start position:0% +really what that means is that uh you + + + align:start position:0% +really what that means is that uh you +may have to run it uh for more + + align:start position:0% +may have to run it uh for more + + + align:start position:0% +may have to run it uh for more +iterations so rather than taking uh 100 + + align:start position:0% +iterations so rather than taking uh 100 + + + align:start position:0% +iterations so rather than taking uh 100 +iterations or 100 uh steps to sort + + align:start position:0% +iterations or 100 uh steps to sort + + + align:start position:0% +iterations or 100 uh steps to sort +something it might take you 110 right + + align:start position:0% +something it might take you 110 right + + + align:start position:0% +something it might take you 110 right +but in the case of probably fast you do + + align:start position:0% +but in the case of probably fast you do + + + align:start position:0% +but in the case of probably fast you do +get the sorted result at the end and + + align:start position:0% +get the sorted result at the end and + + + align:start position:0% +get the sorted result at the end and +when the algorithm is finished execution + + align:start position:0% +when the algorithm is finished execution + + + align:start position:0% +when the algorithm is finished execution +you do get that sort of result at the + + align:start position:0% +you do get that sort of result at the + + + align:start position:0% +you do get that sort of result at the +end so correct and probably fast um or + + align:start position:0% +end so correct and probably fast um or + + + align:start position:0% +end so correct and probably fast um or +uh uh probably correct and uh + + align:start position:0% +uh uh probably correct and uh + + + align:start position:0% +uh uh probably correct and uh +deterministically fast okay and this is + + align:start position:0% +deterministically fast okay and this is + + + align:start position:0% +deterministically fast okay and this is +this is Las Vegas so you have Monte + + align:start position:0% +this is Las Vegas so you have Monte + + + align:start position:0% +this is Las Vegas so you have Monte +Carlo versus Las Vegas here um so I uh + + align:start position:0% +Carlo versus Las Vegas here um so I uh + + + align:start position:0% +Carlo versus Las Vegas here um so I uh +yesterday I and it occurred to me and + + align:start position:0% +yesterday I and it occurred to me and + + + align:start position:0% +yesterday I and it occurred to me and +I've thought this class A bunch of times + + align:start position:0% +I've thought this class A bunch of times + + + align:start position:0% +I've thought this class A bunch of times +but it occurred to me for the first time + + align:start position:0% +but it occurred to me for the first time + + + align:start position:0% +but it occurred to me for the first time +last night that there should be + + align:start position:0% +last night that there should be + + + align:start position:0% +last night that there should be +algorithms that are uh probably correct + + align:start position:0% +algorithms that are uh probably correct + + + align:start position:0% +algorithms that are uh probably correct +and probably fast which means that + + align:start position:0% +and probably fast which means that + + + align:start position:0% +and probably fast which means that +they're Incorrect and slow you know some + + align:start position:0% +they're Incorrect and slow you know some + + + align:start position:0% +they're Incorrect and slow you know some +of the time right so what do you think + + align:start position:0% +of the time right so what do you think + + + align:start position:0% +of the time right so what do you think +those algorithms are + + align:start position:0% +those algorithms are + + + align:start position:0% +those algorithms are +called sorry what the T the T oh oh that + + align:start position:0% +called sorry what the T the T oh oh that + + + align:start position:0% +called sorry what the T the T oh oh that +deserves a frisbee oh my + + align:start position:0% +deserves a frisbee oh my + + + align:start position:0% +deserves a frisbee oh my +goodness all right here you go there you + + align:start position:0% +goodness all right here you go there you + + + align:start position:0% +goodness all right here you go there you +go all right now they're not called the + + align:start position:0% +go all right now they're not called the + + + align:start position:0% +go all right now they're not called the +T okay so we should write that down for + + align:start position:0% +T okay so we should write that down for + + + align:start position:0% +T okay so we should write that down for +uh so so everyone knows uh probably + + align:start position:0% + + + + align:start position:0% + +correct and probably fast which is I + + align:start position:0% +correct and probably fast which is I + + + align:start position:0% +correct and probably fast which is I +guess yeah I I guess they don't get you + + align:start position:0% +guess yeah I I guess they don't get you + + + align:start position:0% +guess yeah I I guess they don't get you +anywhere I don't know what that means + + align:start position:0% +anywhere I don't know what that means + + + align:start position:0% +anywhere I don't know what that means +Incorrect and slow in the case of the T + + align:start position:0% +Incorrect and slow in the case of the T + + + align:start position:0% +Incorrect and slow in the case of the T +um uh so the MBTA huh okay now that's + + align:start position:0% +um uh so the MBTA huh okay now that's + + + align:start position:0% +um uh so the MBTA huh okay now that's +that's not the any guesses I mean think + + align:start position:0% +that's not the any guesses I mean think + + + align:start position:0% +that's not the any guesses I mean think +about uh what we have for uh for Monte + + align:start position:0% +about uh what we have for uh for Monte + + + align:start position:0% +about uh what we have for uh for Monte +Carlo Las Vegas you + + align:start position:0% +Carlo Las Vegas you + + + align:start position:0% +Carlo Las Vegas you +extrapolate these are the kinds of + + align:start position:0% +extrapolate these are the kinds of + + + align:start position:0% +extrapolate these are the kinds of +questions you're going to get on your + + align:start position:0% + + + + align:start position:0% + +quiz so what other you I guess you guys + + align:start position:0% +quiz so what other you I guess you guys + + + align:start position:0% +quiz so what other you I guess you guys +don't get you don't go to yeah yeah go + + align:start position:0% +don't get you don't go to yeah yeah go + + + align:start position:0% +don't get you don't go to yeah yeah go +ahead Atlantic City that deserves a + + align:start position:0% +ahead Atlantic City that deserves a + + + align:start position:0% +ahead Atlantic City that deserves a +frisbee yeah absolutely right there're + + align:start position:0% +frisbee yeah absolutely right there're + + + align:start position:0% +frisbee yeah absolutely right there're +actually it turns out Atlantic City uh + + align:start position:0% +actually it turns out Atlantic City uh + + + align:start position:0% +actually it turns out Atlantic City uh +isn't uh isn't a name that's really + + align:start position:0% +isn't uh isn't a name that's really + + + align:start position:0% +isn't uh isn't a name that's really +caught on uh but it was uh in terms of + + align:start position:0% +caught on uh but it was uh in terms of + + + align:start position:0% +caught on uh but it was uh in terms of +uh being used in this + + align:start position:0% +uh being used in this + + + align:start position:0% +uh being used in this +context uh most of the time if you do + + align:start position:0% +context uh most of the time if you do + + + align:start position:0% +context uh most of the time if you do +have a probably correct probably fast + + align:start position:0% +have a probably correct probably fast + + + align:start position:0% +have a probably correct probably fast +algorithm you can convert it into a + + align:start position:0% +algorithm you can convert it into a + + + align:start position:0% +algorithm you can convert it into a +Monte Carlo algorithm or a Las Vegas + + align:start position:0% +Monte Carlo algorithm or a Las Vegas + + + align:start position:0% +Monte Carlo algorithm or a Las Vegas +algorithm there are some uh Prime + + align:start position:0% +algorithm there are some uh Prime + + + align:start position:0% +algorithm there are some uh Prime +testing algorithms uh to test whether a + + align:start position:0% +testing algorithms uh to test whether a + + + align:start position:0% +testing algorithms uh to test whether a +particular number is a prime or not that + + align:start position:0% +particular number is a prime or not that + + + align:start position:0% +particular number is a prime or not that +run in probabilistic polinomial time and + + align:start position:0% +run in probabilistic polinomial time and + + + align:start position:0% +run in probabilistic polinomial time and +they may incorrectly tell you that uh + + align:start position:0% +they may incorrectly tell you that uh + + + align:start position:0% +they may incorrectly tell you that uh +the number is a prime so that's uh an + + align:start position:0% +the number is a prime so that's uh an + + + align:start position:0% +the number is a prime so that's uh an +example of an Atlantic City algorithm um + + align:start position:0% +example of an Atlantic City algorithm um + + + align:start position:0% +example of an Atlantic City algorithm um +we won't actually do Atlantic City uh + + align:start position:0% +we won't actually do Atlantic City uh + + + align:start position:0% +we won't actually do Atlantic City uh +what we'll do is we'll take a look at u + + align:start position:0% +what we'll do is we'll take a look at u + + + align:start position:0% +what we'll do is we'll take a look at u +a couple of different algorithms and and + + align:start position:0% +a couple of different algorithms and and + + + align:start position:0% +a couple of different algorithms and and +both of these will motivate why + + align:start position:0% +both of these will motivate why + + + align:start position:0% +both of these will motivate why +randomized algorithms are interesting + + align:start position:0% +randomized algorithms are interesting + + + align:start position:0% +randomized algorithms are interesting +the uh Monte Carlo example is is + + align:start position:0% +the uh Monte Carlo example is is + + + align:start position:0% +the uh Monte Carlo example is is +checking Matrix multiply so you've + + align:start position:0% +checking Matrix multiply so you've + + + align:start position:0% +checking Matrix multiply so you've +gotten a couple of square matrices both + + align:start position:0% +gotten a couple of square matrices both + + + align:start position:0% +gotten a couple of square matrices both +of them are n byn matrices and uh you + + align:start position:0% +of them are n byn matrices and uh you + + + align:start position:0% +of them are n byn matrices and uh you +multiplied them out a * B and you + + align:start position:0% +multiplied them out a * B and you + + + align:start position:0% +multiplied them out a * B and you +produce C and so you got the C Matrix + + align:start position:0% +produce C and so you got the C Matrix + + + align:start position:0% +produce C and so you got the C Matrix +and I rather than REM multiplying and + + align:start position:0% +and I rather than REM multiplying and + + + align:start position:0% +and I rather than REM multiplying and +checking the result you'd like to do + + align:start position:0% +checking the result you'd like to do + + + align:start position:0% +checking the result you'd like to do +something better uh you'd like to verify + + align:start position:0% +something better uh you'd like to verify + + + align:start position:0% +something better uh you'd like to verify +with some probability that you can + + align:start position:0% +with some probability that you can + + + align:start position:0% +with some probability that you can +parameterize that the output Matrix is + + align:start position:0% +parameterize that the output Matrix is + + + align:start position:0% +parameterize that the output Matrix is +in fact the product of the two input + + align:start position:0% +in fact the product of the two input + + + align:start position:0% +in fact the product of the two input +matrices and so that's a randomized + + align:start position:0% +matrices and so that's a randomized + + + align:start position:0% +matrices and so that's a randomized +algorithm that's Monte Carlo because + + align:start position:0% +algorithm that's Monte Carlo because + + + align:start position:0% +algorithm that's Monte Carlo because +you're not guaranteeing that that output + + align:start position:0% +you're not guaranteeing that that output + + + align:start position:0% +you're not guaranteeing that that output +Matrix is in fact the product of um the + + align:start position:0% +Matrix is in fact the product of um the + + + align:start position:0% +Matrix is in fact the product of um the +first two matrices or the operand + + align:start position:0% +first two matrices or the operand + + + align:start position:0% +first two matrices or the operand +matrices but you're getting a good sense + + align:start position:0% +matrices but you're getting a good sense + + + align:start position:0% +matrices but you're getting a good sense +of uh of uh How likely that is and you + + align:start position:0% +of uh of uh How likely that is and you + + + align:start position:0% +of uh of uh How likely that is and you +can kind of Squish that probability of + + align:start position:0% +can kind of Squish that probability of + + + align:start position:0% +can kind of Squish that probability of +error down to uh um how low you want it + + align:start position:0% +error down to uh um how low you want it + + + align:start position:0% +error down to uh um how low you want it +to uh be except you have run it run the + + align:start position:0% +to uh be except you have run it run the + + + align:start position:0% +to uh be except you have run it run the +algorithm for longer right so that's + + align:start position:0% +algorithm for longer right so that's + + + align:start position:0% +algorithm for longer right so that's +that's an example of Monte Carlo now + + align:start position:0% +that's an example of Monte Carlo now + + + align:start position:0% +that's an example of Monte Carlo now +quick sort it doesn't make sense to say + + align:start position:0% +quick sort it doesn't make sense to say + + + align:start position:0% +quick sort it doesn't make sense to say +you you I guess you could but it doesn't + + align:start position:0% +you you I guess you could but it doesn't + + + align:start position:0% +you you I guess you could but it doesn't +make too much sense to say that you have + + align:start position:0% +make too much sense to say that you have + + + align:start position:0% +make too much sense to say that you have +an almost sorted array right uh um what + + align:start position:0% +an almost sorted array right uh um what + + + align:start position:0% +an almost sorted array right uh um what +does that mean exactly you have to + + align:start position:0% +does that mean exactly you have to + + + align:start position:0% +does that mean exactly you have to +characterize that so quick sort is an + + align:start position:0% +characterize that so quick sort is an + + + align:start position:0% +characterize that so quick sort is an +example where you're guaranteed to get a + + align:start position:0% +example where you're guaranteed to get a + + + align:start position:0% +example where you're guaranteed to get a +sorted array at the end of it right so + + align:start position:0% +sorted array at the end of it right so + + + align:start position:0% +sorted array at the end of it right so +it's correct you will get a sorted array + + align:start position:0% +it's correct you will get a sorted array + + + align:start position:0% +it's correct you will get a sorted array +that's what you wanted descending order + + align:start position:0% +that's what you wanted descending order + + + align:start position:0% +that's what you wanted descending order +ascending order but uh it might not + + align:start position:0% +ascending order but uh it might not + + + align:start position:0% +ascending order but uh it might not +run in uh order log n log n time uh you + + align:start position:0% +run in uh order log n log n time uh you + + + align:start position:0% +run in uh order log n log n time uh you +can't that's expected time order n log n + + align:start position:0% +can't that's expected time order n log n + + + align:start position:0% +can't that's expected time order n log n +is expected time right so that's what + + align:start position:0% +is expected time right so that's what + + + align:start position:0% +is expected time right so that's what +probably fast uh would correspond to all + + align:start position:0% +probably fast uh would correspond to all + + + align:start position:0% +probably fast uh would correspond to all +right so uh so that's the setup uh you + + align:start position:0% +right so uh so that's the setup uh you + + + align:start position:0% +right so uh so that's the setup uh you +can kind of see why these are + + align:start position:0% +can kind of see why these are + + + align:start position:0% +can kind of see why these are +interesting because you could imagine + + align:start position:0% +interesting because you could imagine + + + align:start position:0% +interesting because you could imagine +that in Practical scenarios uh you might + + align:start position:0% +that in Practical scenarios uh you might + + + align:start position:0% +that in Practical scenarios uh you might +want to do some checking in a in a + + align:start position:0% +want to do some checking in a in a + + + align:start position:0% +want to do some checking in a in a +probabilistic way uh uh and uh you want + + align:start position:0% +probabilistic way uh uh and uh you want + + + align:start position:0% +probabilistic way uh uh and uh you want +to do that with having to redo all the + + align:start position:0% +to do that with having to redo all the + + + align:start position:0% +to do that with having to redo all the +work right you don't want to you you + + align:start position:0% +work right you don't want to you you + + + align:start position:0% +work right you don't want to you you +don't want obviously you don't want your + + align:start position:0% +don't want obviously you don't want your + + + align:start position:0% +don't want obviously you don't want your +checker for Matrix multiply to be as + + align:start position:0% +checker for Matrix multiply to be as + + + align:start position:0% +checker for Matrix multiply to be as +slow as multiplying the two matrices + + align:start position:0% +slow as multiplying the two matrices + + + align:start position:0% +slow as multiplying the two matrices +otherwise it makes no sense so let's + + align:start position:0% +otherwise it makes no sense so let's + + + align:start position:0% +otherwise it makes no sense so let's +dive into u a matrix product and our + + align:start position:0% +dive into u a matrix product and our + + + align:start position:0% +dive into u a matrix product and our +first example + + align:start position:0% +first example + + + align:start position:0% +first example +of a probably correct algorithm a Monte + + align:start position:0% +of a probably correct algorithm a Monte + + + align:start position:0% +of a probably correct algorithm a Monte +Carlo algorithm so what I want to do + + align:start position:0% +Carlo algorithm so what I want to do + + + align:start position:0% +Carlo algorithm so what I want to do +here is c equal a * B + + align:start position:0% +here is c equal a * B + + + align:start position:0% +here is c equal a * B +and the simple + + align:start position:0% +and the simple + + + align:start position:0% +and the simple +algorithm I guess those of us who went + + align:start position:0% +algorithm I guess those of us who went + + + align:start position:0% +algorithm I guess those of us who went +to high + + align:start position:0% + + + + align:start position:0% + +school myself + + align:start position:0% +school myself + + + align:start position:0% +school myself +included did my four + + align:start position:0% + + + + align:start position:0% + +years um know of an N cubed algorithm or + + align:start position:0% +years um know of an N cubed algorithm or + + + align:start position:0% +years um know of an N cubed algorithm or +learned it back then uh that it simply + + align:start position:0% +learned it back then uh that it simply + + + align:start position:0% +learned it back then uh that it simply +corresponds to uh taking rows and uh and + + align:start position:0% +corresponds to uh taking rows and uh and + + + align:start position:0% +corresponds to uh taking rows and uh and +and columns and uh uh you you get get an + + align:start position:0% +and columns and uh uh you you get get an + + + align:start position:0% +and columns and uh uh you you get get an +entry you have n Square uh entries that + + align:start position:0% +entry you have n Square uh entries that + + + align:start position:0% +entry you have n Square uh entries that +you need to compute corresponding to the + + align:start position:0% +you need to compute corresponding to the + + + align:start position:0% +you need to compute corresponding to the +output Matrix C and uh you're going to + + align:start position:0% +output Matrix C and uh you're going to + + + align:start position:0% +output Matrix C and uh you're going to +do um order and + + align:start position:0% +do um order and + + + align:start position:0% +do um order and +multiplications and additions but we're + + align:start position:0% +multiplications and additions but we're + + + align:start position:0% +multiplications and additions but we're +really going to consider multiplications + + align:start position:0% +really going to consider multiplications + + + align:start position:0% +really going to consider multiplications +here when I talk about n here it's not + + align:start position:0% +here when I talk about n here it's not + + + align:start position:0% +here when I talk about n here it's not +the total number of operations it's the + + align:start position:0% +the total number of operations it's the + + + align:start position:0% +the total number of operations it's the +number of multiplications and the reason + + align:start position:0% +number of multiplications and the reason + + + align:start position:0% +number of multiplications and the reason +for that is I this may have gone away a + + align:start position:0% +for that is I this may have gone away a + + + align:start position:0% +for that is I this may have gone away a +little bit but uh it's still probably + + align:start position:0% +little bit but uh it's still probably + + + align:start position:0% +little bit but uh it's still probably +true that multiplication is just uh in + + align:start position:0% +true that multiplication is just uh in + + + align:start position:0% +true that multiplication is just uh in +computer it takes longer uh to multiply + + align:start position:0% +computer it takes longer uh to multiply + + + align:start position:0% +computer it takes longer uh to multiply +two numbers uh integers or floating + + align:start position:0% +two numbers uh integers or floating + + + align:start position:0% +two numbers uh integers or floating +Point numbers than adding numbers um + + align:start position:0% +Point numbers than adding numbers um + + + align:start position:0% +Point numbers than adding numbers um +used to be much more dramatic the + + align:start position:0% +used to be much more dramatic the + + + align:start position:0% +used to be much more dramatic the +difference between a multiply and an add + + align:start position:0% +difference between a multiply and an add + + + align:start position:0% +difference between a multiply and an add +uh in in in uh uh computers but you know + + align:start position:0% +uh in in in uh uh computers but you know + + + align:start position:0% +uh in in in uh uh computers but you know +thanks to pipelining and lots of + + align:start position:0% +thanks to pipelining and lots of + + + align:start position:0% +thanks to pipelining and lots of +optimizations uh multiplies are actually + + align:start position:0% +optimizations uh multiplies are actually + + + align:start position:0% +optimizations uh multiplies are actually +very fast but uh they are obviously a + + align:start position:0% +very fast but uh they are obviously a + + + align:start position:0% +very fast but uh they are obviously a +more + + align:start position:0% +more + + + align:start position:0% +more +sophisticated operation than addition so + + align:start position:0% +sophisticated operation than addition so + + + align:start position:0% +sophisticated operation than addition so +we'll be counting multiplies right so so + + align:start position:0% +we'll be counting multiplies right so so + + + align:start position:0% +we'll be counting multiplies right so so +when you've seen CaRu + + align:start position:0% +when you've seen CaRu + + + align:start position:0% +when you've seen CaRu +divide and concer for multiply you know + + align:start position:0% +divide and concer for multiply you know + + + align:start position:0% +divide and concer for multiply you know +back in6 I remember that we were + + align:start position:0% +back in6 I remember that we were + + + align:start position:0% +back in6 I remember that we were +counting multiplications and we were + + align:start position:0% +counting multiplications and we were + + + align:start position:0% +counting multiplications and we were +actually trading off multiplications for + + align:start position:0% +actually trading off multiplications for + + + align:start position:0% +actually trading off multiplications for +additions we were trying to shrink that + + align:start position:0% +additions we were trying to shrink that + + + align:start position:0% +additions we were trying to shrink that +uh that number associated with the + + align:start position:0% +uh that number associated with the + + + align:start position:0% +uh that number associated with the +complexity of the algorithm when + + align:start position:0% +complexity of the algorithm when + + + align:start position:0% +complexity of the algorithm when +counting the number of multiplies and if + + align:start position:0% +counting the number of multiplies and if + + + align:start position:0% +counting the number of multiplies and if +you actually counted the number of + + align:start position:0% +you actually counted the number of + + + align:start position:0% +you actually counted the number of +additions they were they were going up + + align:start position:0% +additions they were they were going up + + + align:start position:0% +additions they were they were going up +at least from a constant Factor + + align:start position:0% +at least from a constant Factor + + + align:start position:0% +at least from a constant Factor +standpoint not necessarily from an ASM + + align:start position:0% +standpoint not necessarily from an ASM + + + align:start position:0% +standpoint not necessarily from an ASM +totic complexity standpoint um and so + + align:start position:0% +totic complexity standpoint um and so + + + align:start position:0% +totic complexity standpoint um and so +that's the simple algorithm um youve + + align:start position:0% +that's the simple algorithm um youve + + + align:start position:0% +that's the simple algorithm um youve +probably heard of Sten some of you might + + align:start position:0% +probably heard of Sten some of you might + + + align:start position:0% +probably heard of Sten some of you might +have seen it um Bas essentially what + + align:start position:0% +have seen it um Bas essentially what + + + align:start position:0% +have seen it um Bas essentially what +happens with Sten is you multiply two 2x + + align:start position:0% +happens with Sten is you multiply two 2x + + + align:start position:0% +happens with Sten is you multiply two 2x +two + + align:start position:0% + + + + align:start position:0% + +matrices um using seven multiplications + + align:start position:0% +matrices um using seven multiplications + + + align:start position:0% +matrices um using seven multiplications +as opposed to + + align:start position:0% + + + + align:start position:0% + +eight and so now if you do that and this + + align:start position:0% +eight and so now if you do that and this + + + align:start position:0% +eight and so now if you do that and this +is similar to the katuba analysis you + + align:start position:0% +is similar to the katuba analysis you + + + align:start position:0% +is similar to the katuba analysis you +get uh you can you can do this in N ra + + align:start position:0% +get uh you can you can do this in N ra + + + align:start position:0% +get uh you can you can do this in N ra +to log 27 time which is uh essentially n + + align:start position:0% +to log 27 time which is uh essentially n + + + align:start position:0% +to log 27 time which is uh essentially n +ra to + + align:start position:0% +ra to + + + align:start position:0% +ra to +2.81 time and so rather than n cubed you + + align:start position:0% +2.81 time and so rather than n cubed you + + + align:start position:0% +2.81 time and so rather than n cubed you +can go down to n uh n ra to + + align:start position:0% +can go down to n uh n ra to + + + align:start position:0% +can go down to n uh n ra to +2.81 now it turns out people have + + align:start position:0% +2.81 now it turns out people have + + + align:start position:0% +2.81 now it turns out people have +obviously uh not stopped with this uh + + align:start position:0% +obviously uh not stopped with this uh + + + align:start position:0% +obviously uh not stopped with this uh +you can go to n ra + + align:start position:0% +you can go to n ra + + + align:start position:0% +you can go to n ra +2.70 by doing something of the order of + + align:start position:0% +2.70 by doing something of the order of + + + align:start position:0% +2.70 by doing something of the order of +143,000 multiplications for 70 by 70 + + align:start position:0% +143,000 multiplications for 70 by 70 + + + align:start position:0% +143,000 multiplications for 70 by 70 +matrices right so you can play around + + align:start position:0% +matrices right so you can play around + + + align:start position:0% +matrices right so you can play around +just like you had tomb cook I don't know + + align:start position:0% +just like you had tomb cook I don't know + + + align:start position:0% +just like you had tomb cook I don't know +if you remember that or it got covered + + align:start position:0% +if you remember that or it got covered + + + align:start position:0% +if you remember that or it got covered +but you know caruba could get + + align:start position:0% +but you know caruba could get + + + align:start position:0% +but you know caruba could get +generalized into this thing called tomb + + align:start position:0% +generalized into this thing called tomb + + + align:start position:0% +generalized into this thing called tomb +cook and uh and the same thing Sten you + + align:start position:0% +cook and uh and the same thing Sten you + + + align:start position:0% +cook and uh and the same thing Sten you +could go off and and do uh uh divide and + + align:start position:0% +could go off and and do uh uh divide and + + + align:start position:0% +could go off and and do uh uh divide and +conquer that uh uh whose base case is + + align:start position:0% +conquer that uh uh whose base case is + + + align:start position:0% +conquer that uh uh whose base case is +not 2 by two but 70 by 70 and that + + align:start position:0% +not 2 by two but 70 by 70 and that + + + align:start position:0% +not 2 by two but 70 by 70 and that +improves things but it turns out uh you + + align:start position:0% +improves things but it turns out uh you + + + align:start position:0% +improves things but it turns out uh you +know there's other ways arithmetic + + align:start position:0% +know there's other ways arithmetic + + + align:start position:0% +know there's other ways arithmetic +series summation ways and so a famous + + align:start position:0% +series summation ways and so a famous + + + align:start position:0% +series summation ways and so a famous +algorithm that up until + + align:start position:0% +algorithm that up until + + + align:start position:0% +algorithm that up until +2010 was the uh was the best complexity + + align:start position:0% +2010 was the uh was the best complexity + + + align:start position:0% +2010 was the uh was the best complexity +uh algorithm known was copper Smith + + align:start position:0% +uh algorithm known was copper Smith + + + align:start position:0% +uh algorithm known was copper Smith +Winograd which is uh + + align:start position:0% +Winograd which is uh + + + align:start position:0% +Winograd which is uh +2376 and then at some point we had a + + align:start position:0% +2376 and then at some point we had a + + + align:start position:0% +2376 and then at some point we had a +faculty candidate here who uh who uh um + + align:start position:0% +faculty candidate here who uh who uh um + + + align:start position:0% +faculty candidate here who uh who uh um +uh uh you know shrunk this from 2.37 6 + + align:start position:0% +uh uh you know shrunk this from 2.37 6 + + + align:start position:0% +uh uh you know shrunk this from 2.37 6 +to + + align:start position:0% +to + + + align:start position:0% +to +2373 um and it turns out that uh there + + align:start position:0% +2373 um and it turns out that uh there + + + align:start position:0% +2373 um and it turns out that uh there +were two different uh researchers who + + align:start position:0% +were two different uh researchers who + + + align:start position:0% +were two different uh researchers who +came up with the 2373 but this + + align:start position:0% +came up with the 2373 but this + + + align:start position:0% +came up with the 2373 but this +particular candidate you know in the six + + align:start position:0% +particular candidate you know in the six + + + align:start position:0% +particular candidate you know in the six +decimal place won right so she had an + + align:start position:0% +decimal place won right so she had an + + + align:start position:0% +decimal place won right so she had an +eight and the other person had a nine or + + align:start position:0% +eight and the other person had a nine or + + + align:start position:0% +eight and the other person had a nine or +something but anyway all of these are + + align:start position:0% +something but anyway all of these are + + + align:start position:0% +something but anyway all of these are +impractical okay you you don't want to + + align:start position:0% +impractical okay you you don't want to + + + align:start position:0% +impractical okay you you don't want to +use them the the constant factors + + align:start position:0% +use them the the constant factors + + + align:start position:0% +use them the the constant factors +associated with these things are much + + align:start position:0% +associated with these things are much + + + align:start position:0% +associated with these things are much +larger uh than uh what you have here I + + align:start position:0% +larger uh than uh what you have here I + + + align:start position:0% +larger uh than uh what you have here I +mean the constant factors here are I + + align:start position:0% +mean the constant factors here are I + + + align:start position:0% +mean the constant factors here are I +guess it's one right make sense that it + + align:start position:0% +guess it's one right make sense that it + + + align:start position:0% +guess it's one right make sense that it +would be one yeah + + align:start position:0% +would be one yeah + + + align:start position:0% +would be one yeah +um so uh forgetting the additions of + + align:start position:0% +um so uh forgetting the additions of + + + align:start position:0% +um so uh forgetting the additions of +course right so if you have large + + align:start position:0% +course right so if you have large + + + align:start position:0% +course right so if you have large +constant factors then you need a billion + + align:start position:0% +constant factors then you need a billion + + + align:start position:0% +constant factors then you need a billion +by a billion Matrix in order to win and + + align:start position:0% +by a billion Matrix in order to win and + + + align:start position:0% +by a billion Matrix in order to win and +if you have you know billion by billion + + align:start position:0% +if you have you know billion by billion + + + align:start position:0% +if you have you know billion by billion +matrices that you want to multiply do + + align:start position:0% +matrices that you want to multiply do + + + align:start position:0% +matrices that you want to multiply do +something else okay uh you don't want to + + align:start position:0% +something else okay uh you don't want to + + + align:start position:0% +something else okay uh you don't want to +go there uh even in even even in the day + + align:start position:0% +go there uh even in even even in the day + + + align:start position:0% +go there uh even in even even in the day +of the Internet it's it's not going to + + align:start position:0% +of the Internet it's it's not going to + + + align:start position:0% +of the Internet it's it's not going to +work so uh what we'd like to do now is + + align:start position:0% +work so uh what we'd like to do now is + + + align:start position:0% +work so uh what we'd like to do now is +do something better so we will try given + + align:start position:0% +do something better so we will try given + + + align:start position:0% +do something better so we will try given +that I + + align:start position:0% +that I + + + align:start position:0% +that I +we are uh theoretical uh computer + + align:start position:0% +we are uh theoretical uh computer + + + align:start position:0% +we are uh theoretical uh computer +science class um it makes sense to say + + align:start position:0% +science class um it makes sense to say + + + align:start position:0% +science class um it makes sense to say +that our verification algorithm should + + align:start position:0% +that our verification algorithm should + + + align:start position:0% +that our verification algorithm should +be better than n raised to 2376 or 2.3 + + align:start position:0% +be better than n raised to 2376 or 2.3 + + + align:start position:0% +be better than n raised to 2376 or 2.3 +whatever right uh otherwise it you know + + align:start position:0% +whatever right uh otherwise it you know + + + align:start position:0% +whatever right uh otherwise it you know +it doesn't feel good right so um so what + + align:start position:0% +it doesn't feel good right so um so what + + + align:start position:0% +it doesn't feel good right so um so what +we'd like to do and we can do this is uh + + align:start position:0% +we'd like to do and we can do this is uh + + + align:start position:0% +we'd like to do and we can do this is uh +try and get um an order n Square + + align:start position:0% +try and get um an order n Square + + + align:start position:0% +try and get um an order n Square +algorithm + + align:start position:0% + + + + align:start position:0% + +uh that uh does this so it's um a + + align:start position:0% +uh that uh does this so it's um a + + + align:start position:0% +uh that uh does this so it's um a +probably correct Monte Carlo algorithm + + align:start position:0% +probably correct Monte Carlo algorithm + + + align:start position:0% +probably correct Monte Carlo algorithm +where if you have a * b equal + + align:start position:0% +where if you have a * b equal + + + align:start position:0% +where if you have a * b equal +C then the probability of the + + align:start position:0% +C then the probability of the + + + align:start position:0% +C then the probability of the +output equals + + align:start position:0% +output equals + + + align:start position:0% +output equals +yes is is one so in fact uh if you got + + align:start position:0% +yes is is one so in fact uh if you got + + + align:start position:0% +yes is is one so in fact uh if you got +it right then the verifier is going to + + align:start position:0% +it right then the verifier is going to + + + align:start position:0% +it right then the verifier is going to +not give you a a false negative right + + align:start position:0% +not give you a a false negative right + + + align:start position:0% +not give you a a false negative right +it's not going to say no you got it + + align:start position:0% +it's not going to say no you got it + + + align:start position:0% +it's not going to say no you got it +wrong when you got it right uh but it + + align:start position:0% +wrong when you got it right uh but it + + + align:start position:0% +wrong when you got it right uh but it +could give you a a false positive with + + align:start position:0% +could give you a a false positive with + + + align:start position:0% +could give you a a false positive with +some + + align:start position:0% + + + + align:start position:0% + +probability where you have the + + align:start position:0% +probability where you have the + + + align:start position:0% +probability where you have the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +of + + align:start position:0% +of + + + align:start position:0% +of +output equals yes and that's a false + + align:start position:0% +output equals yes and that's a false + + + align:start position:0% +output equals yes and that's a false +positive but you can bound that to be + + align:start position:0% +positive but you can bound that to be + + + align:start position:0% +positive but you can bound that to be +less than half okay so it's going to say + + align:start position:0% +less than half okay so it's going to say + + + align:start position:0% +less than half okay so it's going to say +yes so I mean obviously if the verifier + + align:start position:0% +yes so I mean obviously if the verifier + + + align:start position:0% +yes so I mean obviously if the verifier +kept saying yes all the time uh it you + + align:start position:0% +kept saying yes all the time uh it you + + + align:start position:0% +kept saying yes all the time uh it you +would't have this right it wouldn't be + + align:start position:0% +would't have this right it wouldn't be + + + align:start position:0% +would't have this right it wouldn't be +very interesting it would be constant + + align:start position:0% +very interesting it would be constant + + + align:start position:0% +very interesting it would be constant +time uh but uh it it wouldn't be very + + align:start position:0% +time uh but uh it it wouldn't be very + + + align:start position:0% +time uh but uh it it wouldn't be very +interesting uh what is interesting here + + align:start position:0% +interesting uh what is interesting here + + + align:start position:0% +interesting uh what is interesting here +is that uh uh when they're not equal uh + + align:start position:0% +is that uh uh when they're not equal uh + + + align:start position:0% +is that uh uh when they're not equal uh +you're going to get an incorrect result + + align:start position:0% +you're going to get an incorrect result + + + align:start position:0% +you're going to get an incorrect result +with with some upper bound on the + + align:start position:0% +with with some upper bound on the + + + align:start position:0% +with with some upper bound on the +probability right and so so you say well + + align:start position:0% +probability right and so so you say well + + + align:start position:0% +probability right and so so you say well +1 half it seems kind of high you know + + align:start position:0% +1 half it seems kind of high you know + + + align:start position:0% +1 half it seems kind of high you know +50% you know flipping a coin the good + + align:start position:0% +50% you know flipping a coin the good + + + align:start position:0% +50% you know flipping a coin the good +news is that uh you these algorithms can + + align:start position:0% +news is that uh you these algorithms can + + + align:start position:0% +news is that uh you these algorithms can +uh you can run them over and over you + + align:start position:0% +uh you can run them over and over you + + + align:start position:0% +uh you can run them over and over you +can run this Checker um over and over + + align:start position:0% +can run this Checker um over and over + + + align:start position:0% +can run this Checker um over and over +and as long as the executions are + + align:start position:0% +and as long as the executions are + + + align:start position:0% +and as long as the executions are +independent and you can certainly ensure + + align:start position:0% +independent and you can certainly ensure + + + align:start position:0% +independent and you can certainly ensure +that they're Independent by ensuring + + align:start position:0% +that they're Independent by ensuring + + + align:start position:0% +that they're Independent by ensuring +that the randomness from one execution + + align:start position:0% +that the randomness from one execution + + + align:start position:0% +that the randomness from one execution +to another the flipping of the coins are + + align:start position:0% +to another the flipping of the coins are + + + align:start position:0% +to another the flipping of the coins are +independent okay and so that's + + align:start position:0% +independent okay and so that's + + + align:start position:0% +independent okay and so that's +relatively easy to do and certainly in + + align:start position:0% +relatively easy to do and certainly in + + + align:start position:0% +relatively easy to do and certainly in +all of the scenarios we'll be looking at + + align:start position:0% +all of the scenarios we'll be looking at + + + align:start position:0% +all of the scenarios we'll be looking at +in know for six is relatively easy to do + + align:start position:0% +in know for six is relatively easy to do + + + align:start position:0% +in know for six is relatively easy to do +you can now drive this probability down + + align:start position:0% +you can now drive this probability down + + + align:start position:0% +you can now drive this probability down +to one quarter with two executions uh + + align:start position:0% +to one quarter with two executions uh + + + align:start position:0% +to one quarter with two executions uh +because you'll just check different + + align:start position:0% +because you'll just check different + + + align:start position:0% +because you'll just check different +things and then 1/ 18 with three and so + + align:start position:0% +things and then 1/ 18 with three and so + + + align:start position:0% +things and then 1/ 18 with three and so +on and so forth right so that's what's + + align:start position:0% +on and so forth right so that's what's + + + align:start position:0% +on and so forth right so that's what's +cool about it and now if you kind of + + align:start position:0% +cool about it and now if you kind of + + + align:start position:0% +cool about it and now if you kind of +look at the runtime you say well runtime + + align:start position:0% +look at the runtime you say well runtime + + + align:start position:0% +look at the runtime you say well runtime +is still order than Square now that's + + align:start position:0% +is still order than Square now that's + + + align:start position:0% +is still order than Square now that's +the beauty of this right because I'm + + align:start position:0% +the beauty of this right because I'm + + + align:start position:0% +the beauty of this right because I'm +just putting an extra constant Factor + + align:start position:0% +just putting an extra constant Factor + + + align:start position:0% +just putting an extra constant Factor +here where I have K and square right + + align:start position:0% +here where I have K and square right + + + align:start position:0% +here where I have K and square right +where K is a constant and I got this uh + + align:start position:0% +where K is a constant and I got this uh + + + align:start position:0% +where K is a constant and I got this uh +effectively I have this nice + + align:start position:0% +effectively I have this nice + + + align:start position:0% +effectively I have this nice +relationship in terms of the probability + + align:start position:0% +relationship in terms of the probability + + + align:start position:0% +relationship in terms of the probability +um of error going down to 1 / 2 raed to + + align:start position:0% +um of error going down to 1 / 2 raed to + + + align:start position:0% +um of error going down to 1 / 2 raed to +K right and what I have here is a KNN + + align:start position:0% +K right and what I have here is a KNN + + + align:start position:0% +K right and what I have here is a KNN +square right so so that's what's cool + + align:start position:0% +square right so so that's what's cool + + + align:start position:0% +square right so so that's what's cool +about it and obviously KNN square is + + align:start position:0% +about it and obviously KNN square is + + + align:start position:0% +about it and obviously KNN square is +still order n Square in a polinomial + + align:start position:0% +still order n Square in a polinomial + + + align:start position:0% +still order n Square in a polinomial +time and but the the probably correct + + align:start position:0% +time and but the the probably correct + + + align:start position:0% +time and but the the probably correct +aspect of it gets better and better okay + + align:start position:0% +aspect of it gets better and better okay + + + align:start position:0% +aspect of it gets better and better okay +um any questions so + + align:start position:0% + + + + align:start position:0% + +far all right right + + align:start position:0% + + + + align:start position:0% + +good so what we're going to do is uh + + align:start position:0% +good so what we're going to do is uh + + + align:start position:0% +good so what we're going to do is uh +this algorithm actually works uh for uh + + align:start position:0% +this algorithm actually works uh for uh + + + align:start position:0% +this algorithm actually works uh for uh +arbitrary matrices at the structure at + + align:start position:0% + + + + align:start position:0% + +least we're going to assume that the + + align:start position:0% +least we're going to assume that the + + + align:start position:0% +least we're going to assume that the +Matrix entries are are Boolean or we're + + align:start position:0% +Matrix entries are are Boolean or we're + + + align:start position:0% +Matrix entries are are Boolean or we're +going to work in the the finite field + + align:start position:0% +going to work in the the finite field + + + align:start position:0% +going to work in the the finite field +mod two and it's just an easier proof uh + + align:start position:0% +mod two and it's just an easier proof uh + + + align:start position:0% +mod two and it's just an easier proof uh +it's easier to see so uh the + + align:start position:0% +it's easier to see so uh the + + + align:start position:0% +it's easier to see so uh the +complexities are the same you're still + + align:start position:0% +complexities are the same you're still + + + align:start position:0% +complexities are the same you're still +multiplying numbers they happen to be + + align:start position:0% +multiplying numbers they happen to be + + + align:start position:0% +multiplying numbers they happen to be +small a multiplication costs you one + + align:start position:0% +small a multiplication costs you one + + + align:start position:0% +small a multiplication costs you one +operation and you need to do n cubed + + align:start position:0% +operation and you need to do n cubed + + + align:start position:0% +operation and you need to do n cubed +multiplies to actually get the C Matrix + + align:start position:0% +multiplies to actually get the C Matrix + + + align:start position:0% +multiplies to actually get the C Matrix +and you have to uh uh verify it in order + + align:start position:0% +and you have to uh uh verify it in order + + + align:start position:0% +and you have to uh uh verify it in order +and square time right and so the number + + align:start position:0% +and square time right and so the number + + + align:start position:0% +and square time right and so the number +of multiplies again that you want uh to + + align:start position:0% +of multiplies again that you want uh to + + + align:start position:0% +of multiplies again that you want uh to +use in your verification algorithm has + + align:start position:0% +use in your verification algorithm has + + + align:start position:0% +use in your verification algorithm has +to be order and square right we're + + align:start position:0% +to be order and square right we're + + + align:start position:0% +to be order and square right we're +ignoring the additions + + align:start position:0% +ignoring the additions + + + align:start position:0% +ignoring the additions +right um so uh that's that's what we'd + + align:start position:0% +right um so uh that's that's what we'd + + + align:start position:0% +right um so uh that's that's what we'd +like out of our Matrix uh product + + align:start position:0% +like out of our Matrix uh product + + + align:start position:0% +like out of our Matrix uh product +Checker and the algorithm we're going to + + align:start position:0% +Checker and the algorithm we're going to + + + align:start position:0% +Checker and the algorithm we're going to +look at is called free walls + + align:start position:0% + + + + align:start position:0% + +algorithm cute little algorithm that uh + + align:start position:0% +algorithm cute little algorithm that uh + + + align:start position:0% +algorithm cute little algorithm that uh +does uh the following so so the + + align:start position:0% +does uh the following so so the + + + align:start position:0% +does uh the following so so the +algorithm itself is very straightforward + + align:start position:0% +algorithm itself is very straightforward + + + align:start position:0% +algorithm itself is very straightforward +you know a couple of lines a minute or + + align:start position:0% +you know a couple of lines a minute or + + + align:start position:0% +you know a couple of lines a minute or +so to describe and the the the + + align:start position:0% +so to describe and the the the + + + align:start position:0% +so to describe and the the the +interesting aspect of it is the analysis + + align:start position:0% +interesting aspect of it is the analysis + + + align:start position:0% +interesting aspect of it is the analysis +the fact that uh you can show this + + align:start position:0% +the fact that uh you can show this + + + align:start position:0% +the fact that uh you can show this +that's that's the cool part if you could + + align:start position:0% +that's that's the cool part if you could + + + align:start position:0% +that's that's the cool part if you could +show that there's nothing cool about + + align:start position:0% +show that there's nothing cool about + + + align:start position:0% +show that there's nothing cool about +this + + align:start position:0% +this + + + align:start position:0% +this +algorithm so we're going to + + align:start position:0% +algorithm so we're going to + + + align:start position:0% +algorithm so we're going to +choose um a + + align:start position:0% +choose um a + + + align:start position:0% +choose um a +random binary Vector so there you + + align:start position:0% +random binary Vector so there you + + + align:start position:0% +random binary Vector so there you +go here's your + + align:start position:0% +go here's your + + + align:start position:0% +go here's your +Randomness and this binary Vector every + + align:start position:0% +Randomness and this binary Vector every + + + align:start position:0% +Randomness and this binary Vector every +time you run it as the K increases here + + align:start position:0% +time you run it as the K increases here + + + align:start position:0% +time you run it as the K increases here +the random binary Vector is different + + align:start position:0% +the random binary Vector is different + + + align:start position:0% +the random binary Vector is different +from one to another that's important you + + align:start position:0% +from one to another that's important you + + + align:start position:0% +from one to another that's important you +can't run the same thing again and then + + align:start position:0% +can't run the same thing again and then + + + align:start position:0% +can't run the same thing again and then +expect a different result right that's + + align:start position:0% +expect a different result right that's + + + align:start position:0% +expect a different result right that's +called Insanity U but uh + + align:start position:0% + + + + align:start position:0% + +you are going to assume that uh given + + align:start position:0% +you are going to assume that uh given + + + align:start position:0% +you are going to assume that uh given +that we're working in the + + align:start position:0% +that we're working in the + + + align:start position:0% +that we're working in the +space the binary space and this is a + + align:start position:0% +space the binary space and this is a + + + align:start position:0% +space the binary space and this is a +binary + + align:start position:0% +binary + + + align:start position:0% +binary +Vector + + align:start position:0% + + + + align:start position:0% + +uh you can assume that r i equal 1 is + + align:start position:0% +uh you can assume that r i equal 1 is + + + align:start position:0% +uh you can assume that r i equal 1 is +half + + align:start position:0% +half + + + align:start position:0% +half +independently for I = 1 through n and + + align:start position:0% +independently for I = 1 through n and + + + align:start position:0% +independently for I = 1 through n and +and the algorithm + + align:start position:0% +and the algorithm + + + align:start position:0% +and the algorithm +essentially is this we're going to do a + + align:start position:0% +essentially is this we're going to do a + + + align:start position:0% +essentially is this we're going to do a +bunch of Matrix Vector multiplies okay + + align:start position:0% +bunch of Matrix Vector multiplies okay + + + align:start position:0% +bunch of Matrix Vector multiplies okay +uh a matrix an N byn + + align:start position:0% +uh a matrix an N byn + + + align:start position:0% +uh a matrix an N byn +Matrix multiplied by an N byn + + align:start position:0% +Matrix multiplied by an N byn + + + align:start position:0% +Matrix multiplied by an N byn +Matrix gives you an N byn Matrix and + + align:start position:0% +Matrix gives you an N byn Matrix and + + + align:start position:0% +Matrix gives you an N byn Matrix and +that's your n cubed right so these are + + align:start position:0% +that's your n cubed right so these are + + + align:start position:0% +that's your n cubed right so these are +all I think I said this but I should + + align:start position:0% +all I think I said this but I should + + + align:start position:0% +all I think I said this but I should +have written this down these are all + + align:start position:0% +have written this down these are all + + + align:start position:0% +have written this down these are all +square matrices that are n byn and + + align:start position:0% +square matrices that are n byn and + + + align:start position:0% +square matrices that are n byn and +that's where you get your n Cube um a + + align:start position:0% +that's where you get your n Cube um a + + + align:start position:0% +that's where you get your n Cube um a +matrix Vector would be something where + + align:start position:0% +matrix Vector would be something where + + + align:start position:0% +matrix Vector would be something where +you have typically we have a column + + align:start position:0% +you have typically we have a column + + + align:start position:0% +you have typically we have a column +Vector here you're going to get + + align:start position:0% +Vector here you're going to get + + + align:start position:0% +Vector here you're going to get +something like that and uh you have n + + align:start position:0% +something like that and uh you have n + + + align:start position:0% +something like that and uh you have n +Square multiplications here right so + + align:start position:0% +Square multiplications here right so + + + align:start position:0% +Square multiplications here right so +each uh you you got to grab one of these + + align:start position:0% +each uh you you got to grab one of these + + + align:start position:0% +each uh you you got to grab one of these +uh and then multiply it by that and get + + align:start position:0% +uh and then multiply it by that and get + + + align:start position:0% +uh and then multiply it by that and get +an entry here and that obviously is um n + + align:start position:0% +an entry here and that obviously is um n + + + align:start position:0% +an entry here and that obviously is um n +multiplications uh but you only have n + + align:start position:0% +multiplications uh but you only have n + + + align:start position:0% +multiplications uh but you only have n +elements to produce here in this Vector + + align:start position:0% +elements to produce here in this Vector + + + align:start position:0% +elements to produce here in this Vector +so you only got n squ + + align:start position:0% +so you only got n squ + + + align:start position:0% +so you only got n squ +right that Mak sense um and so so what + + align:start position:0% +right that Mak sense um and so so what + + + align:start position:0% +right that Mak sense um and so so what +we're going to do is we're going to take + + align:start position:0% +we're going to do is we're going to take + + + align:start position:0% +we're going to do is we're going to take +this R and we're going to compute a * BR + + align:start position:0% +this R and we're going to compute a * BR + + + align:start position:0% +this R and we're going to compute a * BR +R and so the brackets are important + + align:start position:0% +R and so the brackets are important + + + align:start position:0% +R and so the brackets are important +because uh it says that you're going to + + align:start position:0% +because uh it says that you're going to + + + align:start position:0% +because uh it says that you're going to +compute what's inside the brackets first + + align:start position:0% +compute what's inside the brackets first + + + align:start position:0% +compute what's inside the brackets first +okay otherwise it' be a problem because + + align:start position:0% +okay otherwise it' be a problem because + + + align:start position:0% +okay otherwise it' be a problem because +you'd be multiplying a * B and obviously + + align:start position:0% +you'd be multiplying a * B and obviously + + + align:start position:0% +you'd be multiplying a * B and obviously +that's order n Cub right you don't want + + align:start position:0% +that's order n Cub right you don't want + + + align:start position:0% +that's order n Cub right you don't want +that so A * BR R equals CR + + align:start position:0% +that so A * BR R equals CR + + + align:start position:0% +that so A * BR R equals CR +okay so R remember is a is a column + + align:start position:0% +okay so R remember is a is a column + + + align:start position:0% +okay so R remember is a is a column +vector and C is an N byn Matrix as are A + + align:start position:0% +vector and C is an N byn Matrix as are A + + + align:start position:0% +vector and C is an N byn Matrix as are A +and B we're going to + + align:start position:0% +and B we're going to + + + align:start position:0% +and B we're going to +Output + + align:start position:0% + + + + align:start position:0% + +yes um + + align:start position:0% +yes um + + + align:start position:0% +yes um +else if if these two are not equal + + align:start position:0% +else if if these two are not equal + + + align:start position:0% +else if if these two are not equal +you're going to + + align:start position:0% +you're going to + + + align:start position:0% +you're going to +Output + + align:start position:0% +Output + + + align:start position:0% +Output +no + + align:start position:0% +no + + + align:start position:0% +no +okay and so that's it that's one + + align:start position:0% +okay and so that's it that's one + + + align:start position:0% +okay and so that's it that's one +run of the algorithm generate a random R + + align:start position:0% +run of the algorithm generate a random R + + + align:start position:0% +run of the algorithm generate a random R +and do the do the + + align:start position:0% +and do the do the + + + align:start position:0% +and do the do the +multiplication uh as you see here so + + align:start position:0% +multiplication uh as you see here so + + + align:start position:0% +multiplication uh as you see here so +let's uh uh be uh clear about complexity + + align:start position:0% +let's uh uh be uh clear about complexity + + + align:start position:0% +let's uh uh be uh clear about complexity +uh and uh let's make + + align:start position:0% +uh and uh let's make + + + align:start position:0% +uh and uh let's make +sure we understand the simpler aspects + + align:start position:0% +sure we understand the simpler aspects + + + align:start position:0% +sure we understand the simpler aspects +of the algorithm before we get into the + + align:start position:0% +of the algorithm before we get into the + + + align:start position:0% +of the algorithm before we get into the +analysis associated with bounding the + + align:start position:0% +analysis associated with bounding the + + + align:start position:0% +analysis associated with bounding the +false positive probability okay that the + + align:start position:0% +false positive probability okay that the + + + align:start position:0% +false positive probability okay that the +Heart part is going to be bounding the + + align:start position:0% +Heart part is going to be bounding the + + + align:start position:0% +Heart part is going to be bounding the +false positive probability um and so uh + + align:start position:0% +false positive probability um and so uh + + + align:start position:0% +false positive probability um and so uh +but the easy part is uh first the + + align:start position:0% +but the easy part is uh first the + + + align:start position:0% +but the easy part is uh first the +complexity right and uh so how many how + + align:start position:0% +complexity right and uh so how many how + + + align:start position:0% +complexity right and uh so how many how +many Matrix Vector products am I doing + + align:start position:0% +many Matrix Vector products am I doing + + + align:start position:0% +many Matrix Vector products am I doing +here how many Matrix Vector products am + + align:start position:0% +here how many Matrix Vector products am + + + align:start position:0% +here how many Matrix Vector products am +I doing here in this check on one ex + + align:start position:0% +I doing here in this check on one ex + + + align:start position:0% +I doing here in this check on one ex +iteration of the algorithm yeah three + + align:start position:0% +iteration of the algorithm yeah three + + + align:start position:0% +iteration of the algorithm yeah three +all right uh all right you need to stand + + align:start position:0% +all right uh all right you need to stand + + + align:start position:0% +all right uh all right you need to stand +up + + align:start position:0% +up + + + align:start position:0% +up +this is fun this is this is this is the + + align:start position:0% +this is fun this is this is this is the + + + align:start position:0% +this is fun this is this is this is the +the hardest throw I've had to make in + + align:start position:0% +the hardest throw I've had to make in + + + align:start position:0% +the hardest throw I've had to make in +6046 I got to put this down warm up a + + align:start position:0% +6046 I got to put this down warm up a + + + align:start position:0% +6046 I got to put this down warm up a +little bit right so yeah it's kind of + + align:start position:0% +little bit right so yeah it's kind of + + + align:start position:0% +little bit right so yeah it's kind of +cold you know what + + align:start position:0% +cold you know what + + + align:start position:0% +cold you know what +you whoa terrible all right uh you can + + align:start position:0% +you whoa terrible all right uh you can + + + align:start position:0% +you whoa terrible all right uh you can +the person who gets up and gets that + + align:start position:0% +the person who gets up and gets that + + + align:start position:0% +the person who gets up and gets that +owns it and we're going to do this again + + align:start position:0% +owns it and we're going to do this again + + + align:start position:0% +owns it and we're going to do this again +right all right let's let's see how long + + align:start position:0% +right all right let's let's see how long + + + align:start position:0% +right all right let's let's see how long +this takes is this yes well the first + + align:start position:0% +this takes is this yes well the first + + + align:start position:0% +this takes is this yes well the first +one fail you know false whatever right + + align:start position:0% +one fail you know false whatever right + + + align:start position:0% +one fail you know false whatever right +all right + + align:start position:0% + + + + align:start position:0% + +I got a few + + align:start position:0% +I got a few + + + align:start position:0% +I got a few +more all let me see I think I need to go + + align:start position:0% +more all let me see I think I need to go + + + align:start position:0% +more all let me see I think I need to go +here right this is good and I need to uh + + align:start position:0% +here right this is good and I need to uh + + + align:start position:0% +here right this is good and I need to uh +I need to + + align:start position:0% +I need to + + + align:start position:0% +I need to +be all right number three thank you + + align:start position:0% +be all right number three thank you + + + align:start position:0% +be all right number three thank you +thank you all right + + align:start position:0% + + + + align:start position:0% + +so so um it was three right three + + align:start position:0% +so so um it was three right three + + + align:start position:0% +so so um it was three right three +perfect uh three Matrix Vector products + + align:start position:0% +perfect uh three Matrix Vector products + + + align:start position:0% +perfect uh three Matrix Vector products +because I got to do this that's the + + align:start position:0% +because I got to do this that's the + + + align:start position:0% +because I got to do this that's the +Matrix Vector product remember I'm + + align:start position:0% +Matrix Vector product remember I'm + + + align:start position:0% +Matrix Vector product remember I'm +getting a column Vector out of this + + align:start position:0% +getting a column Vector out of this + + + align:start position:0% +getting a column Vector out of this +which is important and and then I'm + + align:start position:0% +which is important and and then I'm + + + align:start position:0% +which is important and and then I'm +going to multiply this Matrix with the + + align:start position:0% +going to multiply this Matrix with the + + + align:start position:0% +going to multiply this Matrix with the +column Vector Matrix Vector product + + align:start position:0% +column Vector Matrix Vector product + + + align:start position:0% +column Vector Matrix Vector product +number two and then there's a matri VOR + + align:start position:0% +number two and then there's a matri VOR + + + align:start position:0% +number two and then there's a matri VOR +Vector product over here right so then + + align:start position:0% +Vector product over here right so then + + + align:start position:0% +Vector product over here right so then +at that point remember I have a vector + + align:start position:0% +at that point remember I have a vector + + + align:start position:0% +at that point remember I have a vector +and a vector and checking the + + align:start position:0% +and a vector and checking the + + + align:start position:0% +and a vector and checking the +equivalence of two vectors is simply + + align:start position:0% +equivalence of two vectors is simply + + + align:start position:0% +equivalence of two vectors is simply +checking the equivalence of each element + + align:start position:0% +checking the equivalence of each element + + + align:start position:0% +checking the equivalence of each element +in the vector uh one by one so first one + + align:start position:0% +in the vector uh one by one so first one + + + align:start position:0% +in the vector uh one by one so first one +same as the first one second one the + + align:start position:0% +same as the first one second one the + + + align:start position:0% +same as the first one second one the +same as the second one + + align:start position:0% +same as the second one + + + align:start position:0% +same as the second one +Etc um and so so so this is order and + + align:start position:0% +Etc um and so so so this is order and + + + align:start position:0% +Etc um and so so so this is order and +square but three is is is something that + + align:start position:0% +square but three is is is something that + + + align:start position:0% +square but three is is is something that +is worth thinking about simply because + + align:start position:0% +is worth thinking about simply because + + + align:start position:0% +is worth thinking about simply because +every once in a while we're interested + + align:start position:0% +every once in a while we're interested + + + align:start position:0% +every once in a while we're interested +in constant factors and the other thing + + align:start position:0% +in constant factors and the other thing + + + align:start position:0% +in constant factors and the other thing +that's interesting about this um make + + align:start position:0% +that's interesting about this um make + + + align:start position:0% +that's interesting about this um make +sure I write this let + + align:start position:0% +sure I write this let + + + align:start position:0% +sure I write this let +me write this over here um + + align:start position:0% +me write this over here um + + + align:start position:0% +me write this over here um +that uh you are going to uh if um + + align:start position:0% +that uh you are going to uh if um + + + align:start position:0% +that uh you are going to uh if um +AB uh equals + + align:start position:0% +AB uh equals + + + align:start position:0% +AB uh equals +c uh then and uh there's no issue + + align:start position:0% +c uh then and uh there's no issue + + + align:start position:0% +c uh then and uh there's no issue +associated with uh error here right so + + align:start position:0% +associated with uh error here right so + + + align:start position:0% +associated with uh error here right so +there's no notion of a of a false + + align:start position:0% +there's no notion of a of a false + + + align:start position:0% +there's no notion of a of a false +negative because if AB equals c then uh + + align:start position:0% +negative because if AB equals c then uh + + + align:start position:0% +negative because if AB equals c then uh +you know thanks to the + + align:start position:0% +you know thanks to the + + + align:start position:0% +you know thanks to the +associativity of U matrix multiplication + + align:start position:0% +associativity of U matrix multiplication + + + align:start position:0% +associativity of U matrix multiplication +be it whether they're n byn matrices or + + align:start position:0% + + + + align:start position:0% + +um or columns you have + + align:start position:0% +um or columns you have + + + align:start position:0% +um or columns you have +uh this relationship here and I hope you + + align:start position:0% +uh this relationship here and I hope you + + + align:start position:0% +uh this relationship here and I hope you +can read it at the back essentially what + + align:start position:0% +can read it at the back essentially what + + + align:start position:0% +can read it at the back essentially what +I have here is if a equals c so if in + + align:start position:0% +I have here is if a equals c so if in + + + align:start position:0% +I have here is if a equals c so if in +fact uh The Matrix multiply happened + + align:start position:0% +fact uh The Matrix multiply happened + + + align:start position:0% +fact uh The Matrix multiply happened +correctly uh I'm in a situation where um + + align:start position:0% +correctly uh I'm in a situation where um + + + align:start position:0% +correctly uh I'm in a situation where um +it is clear that AB R equals uh this + + align:start position:0% +it is clear that AB R equals uh this + + + align:start position:0% +it is clear that AB R equals uh this +thanks to the associativity of a matrix + + align:start position:0% +thanks to the associativity of a matrix + + + align:start position:0% +thanks to the associativity of a matrix +multiply and that of course is exactly + + align:start position:0% +multiply and that of course is exactly + + + align:start position:0% +multiply and that of course is exactly +the same as as CR right so that should + + align:start position:0% +the same as as CR right so that should + + + align:start position:0% +the same as as CR right so that should +convince you uh thanks to associativity + + align:start position:0% +convince you uh thanks to associativity + + + align:start position:0% +convince you uh thanks to associativity +of Matrix multiply that you don't have + + align:start position:0% +of Matrix multiply that you don't have + + + align:start position:0% +of Matrix multiply that you don't have +any false negatives in this algorithm + + align:start position:0% +any false negatives in this algorithm + + + align:start position:0% +any false negatives in this algorithm +right make + + align:start position:0% +right make + + + align:start position:0% +right make +sense um so we're all good all we have + + align:start position:0% +sense um so we're all good all we have + + + align:start position:0% +sense um so we're all good all we have +to do uh given uh what we have with + + align:start position:0% +to do uh given uh what we have with + + + align:start position:0% +to do uh given uh what we have with +respect to freeall is to do this part + + align:start position:0% +respect to freeall is to do this part + + + align:start position:0% +respect to freeall is to do this part +here which is going to take a little bit + + align:start position:0% +here which is going to take a little bit + + + align:start position:0% +here which is going to take a little bit +of doing um and the challenge always + + align:start position:0% +of doing um and the challenge always + + + align:start position:0% +of doing um and the challenge always +with a simple algorithms is you don't + + align:start position:0% +with a simple algorithms is you don't + + + align:start position:0% +with a simple algorithms is you don't +quite know why they work and then of + + align:start position:0% +quite know why they work and then of + + + align:start position:0% +quite know why they work and then of +course you know you have sophisticated + + align:start position:0% +course you know you have sophisticated + + + align:start position:0% +course you know you have sophisticated +algorithms and you don't quite know + + align:start position:0% +algorithms and you don't quite know + + + align:start position:0% +algorithms and you don't quite know +where they + + align:start position:0% +where they + + + align:start position:0% +where they +work but + + align:start position:0% + + + + align:start position:0% + +so this will take a few minutes it's not + + align:start position:0% +so this will take a few minutes it's not + + + align:start position:0% +so this will take a few minutes it's not +super complicated there's a little + + align:start position:0% +super complicated there's a little + + + align:start position:0% +super complicated there's a little +insight as always with these things that + + align:start position:0% +insight as always with these things that + + + align:start position:0% +insight as always with these things that +are not immediately obvious uh but we'll + + align:start position:0% +are not immediately obvious uh but we'll + + + align:start position:0% +are not immediately obvious uh but we'll +have to um look at uh the number of + + align:start position:0% +have to um look at uh the number of + + + align:start position:0% +have to um look at uh the number of +RS uh the so you have an R Vector that + + align:start position:0% +RS uh the so you have an R Vector that + + + align:start position:0% +RS uh the so you have an R Vector that +you've generated randomly and it may be + + align:start position:0% +you've generated randomly and it may be + + + align:start position:0% +you've generated randomly and it may be +a bad Vector it may be a vector that + + align:start position:0% +a bad Vector it may be a vector that + + + align:start position:0% +a bad Vector it may be a vector that +doesn't show you that the two + + align:start position:0% +doesn't show you that the two + + + align:start position:0% +doesn't show you that the two +matrices or the product Matrix has an + + align:start position:0% +matrices or the product Matrix has an + + + align:start position:0% +matrices or the product Matrix has an +incorrect entry remember there's n + + align:start position:0% +incorrect entry remember there's n + + + align:start position:0% +incorrect entry remember there's n +Square entries in the in this Matrix + + align:start position:0% +Square entries in the in this Matrix + + + align:start position:0% +Square entries in the in this Matrix +exactly one of them may be wrong and you + + align:start position:0% +exactly one of them may be wrong and you + + + align:start position:0% +exactly one of them may be wrong and you +need to find it right uh uh and so there + + align:start position:0% +need to find it right uh uh and so there + + + align:start position:0% +need to find it right uh uh and so there +may be a lot of entries which are all + + align:start position:0% +may be a lot of entries which are all + + + align:start position:0% +may be a lot of entries which are all +correct but you got to find that one + + align:start position:0% +correct but you got to find that one + + + align:start position:0% +correct but you got to find that one +entry that's incorrect and so you could + + align:start position:0% +entry that's incorrect and so you could + + + align:start position:0% +entry that's incorrect and so you could +miss it a given R Vector might miss it + + align:start position:0% +miss it a given R Vector might miss it + + + align:start position:0% +miss it a given R Vector might miss it +and of course now if you keep generating + + align:start position:0% +and of course now if you keep generating + + + align:start position:0% +and of course now if you keep generating +the RS you'd like to find it uh and uh + + align:start position:0% +the RS you'd like to find it uh and uh + + + align:start position:0% +the RS you'd like to find it uh and uh +decare that the matrices Wen multiplied + + align:start position:0% +decare that the matrices Wen multiplied + + + align:start position:0% +decare that the matrices Wen multiplied +correctly uh and that probability is + + align:start position:0% +correctly uh and that probability is + + + align:start position:0% +correctly uh and that probability is +what we have to compute so uh we want to + + align:start position:0% +what we have to compute so uh we want to + + + align:start position:0% +what we have to compute so uh we want to +get + + align:start position:0% +get + + + align:start position:0% +get +this result where we're analyzing the + + align:start position:0% +this result where we're analyzing the + + + align:start position:0% +this result where we're analyzing the +correctness um in the case we've already + + align:start position:0% +correctness um in the case we've already + + + align:start position:0% +correctness um in the case we've already +analyzed the correctness uh in the case + + align:start position:0% +analyzed the correctness uh in the case + + + align:start position:0% +analyzed the correctness uh in the case +where um AB equals c but now we have to + + align:start position:0% +where um AB equals c but now we have to + + + align:start position:0% +where um AB equals c but now we have to +analyze the correctness in the case + + align:start position:0% +analyze the correctness in the case + + + align:start position:0% +analyze the correctness in the case +where AB is not equal to C right um and + + align:start position:0% +where AB is not equal to C right um and + + + align:start position:0% +where AB is not equal to C right um and +so uh the claim + + align:start position:0% +so uh the claim + + + align:start position:0% +so uh the claim +is that if a + + align:start position:0% +is that if a + + + align:start position:0% +is that if a +is not equal to + + align:start position:0% +is not equal to + + + align:start position:0% +is not equal to +C + + align:start position:0% +C + + + align:start position:0% +C +then the probability of a r not equal to + + align:start position:0% +then the probability of a r not equal to + + + align:start position:0% +then the probability of a r not equal to +C is greater than or equal to half right + + align:start position:0% +C is greater than or equal to half right + + + align:start position:0% +C is greater than or equal to half right +so this is greater than or equal to over + + align:start position:0% +so this is greater than or equal to over + + + align:start position:0% +so this is greater than or equal to over +there I'm just talking about the false + + align:start position:0% +there I'm just talking about the false + + + align:start position:0% +there I'm just talking about the false +negative probability where I'm actually + + align:start position:0% +negative probability where I'm actually + + + align:start position:0% +negative probability where I'm actually +getting an incorrect yes when you have + + align:start position:0% +getting an incorrect yes when you have + + + align:start position:0% +getting an incorrect yes when you have +uh the matrices being multiplied um uh + + align:start position:0% +uh the matrices being multiplied um uh + + + align:start position:0% +uh the matrices being multiplied um uh +uh wrongly incorrectly and so that's why + + align:start position:0% +uh wrongly incorrectly and so that's why + + + align:start position:0% +uh wrongly incorrectly and so that's why +I get uh this is what I want I want + + align:start position:0% +I get uh this is what I want I want + + + align:start position:0% +I get uh this is what I want I want +there to be a a greater than 1/2 + + align:start position:0% +there to be a a greater than 1/2 + + + align:start position:0% +there to be a a greater than 1/2 +probability for + + align:start position:0% +probability for + + + align:start position:0% +probability for +R to be + + align:start position:0% +R to be + + + align:start position:0% +R to be +um uh to have discovered that for for R + + align:start position:0% +um uh to have discovered that for for R + + + align:start position:0% +um uh to have discovered that for for R +to have discovered that okay uh I'll + + align:start position:0% +to have discovered that okay uh I'll + + + align:start position:0% +to have discovered that okay uh I'll +stop for questions in a second in case + + align:start position:0% +stop for questions in a second in case + + + align:start position:0% +stop for questions in a second in case +but let me do a little bit + + align:start position:0% +but let me do a little bit + + + align:start position:0% +but let me do a little bit +more I'm going to compute the difference + + align:start position:0% +more I'm going to compute the difference + + + align:start position:0% +more I'm going to compute the difference +Matrix uh and I'm not Computing this + + align:start position:0% +Matrix uh and I'm not Computing this + + + align:start position:0% +Matrix uh and I'm not Computing this +because obviously this would take a + + align:start position:0% +because obviously this would take a + + + align:start position:0% +because obviously this would take a +while to compute it's just for the + + align:start position:0% +while to compute it's just for the + + + align:start position:0% +while to compute it's just for the +purpose of analysis + + align:start position:0% +purpose of analysis + + + align:start position:0% +purpose of analysis +I'm going to look at this difference + + align:start position:0% +I'm going to look at this difference + + + align:start position:0% +I'm going to look at this difference +Matrix D equal a minus C because you + + align:start position:0% +Matrix D equal a minus C because you + + + align:start position:0% +Matrix D equal a minus C because you +want D to be zero and we're going to do + + align:start position:0% +want D to be zero and we're going to do + + + align:start position:0% +want D to be zero and we're going to do +some analysis that says we're going to + + align:start position:0% +some analysis that says we're going to + + + align:start position:0% +some analysis that says we're going to +try and find these nonzero entries in D + + align:start position:0% +try and find these nonzero entries in D + + + align:start position:0% +try and find these nonzero entries in D +because clearly the nonzero entries in d + + align:start position:0% +because clearly the nonzero entries in d + + + align:start position:0% +because clearly the nonzero entries in d +are tell you if there's non-zero entry + + align:start position:0% +are tell you if there's non-zero entry + + + align:start position:0% +are tell you if there's non-zero entry +in D you got a problem here the matrices + + align:start position:0% +in D you got a problem here the matrices + + + align:start position:0% +in D you got a problem here the matrices +we multiplied properly right so so + + align:start position:0% +we multiplied properly right so so + + + align:start position:0% +we multiplied properly right so so +that's why we have D here don't think of + + align:start position:0% +that's why we have D here don't think of + + + align:start position:0% +that's why we have D here don't think of +it as we're actually Computing that + + align:start position:0% +it as we're actually Computing that + + + align:start position:0% +it as we're actually Computing that +um so what we'd like is + + align:start position:0% + + + + align:start position:0% + +um uh is uh to as I said discover these + + align:start position:0% +um uh is uh to as I said discover these + + + align:start position:0% +um uh is uh to as I said discover these +entries where our hypothesis now is that + + align:start position:0% +entries where our hypothesis now is that + + + align:start position:0% +entries where our hypothesis now is that +D is not equal to zero because that's + + align:start position:0% +D is not equal to zero because that's + + + align:start position:0% +D is not equal to zero because that's +the case we're considering we know that + + align:start position:0% +the case we're considering we know that + + + align:start position:0% +the case we're considering we know that +D is not equal to Zer if the matrices + + align:start position:0% +D is not equal to Zer if the matrices + + + align:start position:0% +D is not equal to Zer if the matrices +were multiplied + + align:start position:0% +were multiplied + + + align:start position:0% +were multiplied +incorrectly and when I say d is not + + align:start position:0% +incorrectly and when I say d is not + + + align:start position:0% +incorrectly and when I say d is not +equal to zero it means that there are n + + align:start position:0% +equal to zero it means that there are n + + + align:start position:0% +equal to zero it means that there are n +Square entries in D and one of them is + + align:start position:0% +Square entries in D and one of them is + + + align:start position:0% +Square entries in D and one of them is +not zero right it they all have to be + + align:start position:0% +not zero right it they all have to be + + + align:start position:0% +not zero right it they all have to be +identically zero that's all it means d + + align:start position:0% +identically zero that's all it means d + + + align:start position:0% +identically zero that's all it means d +not equal to zero means one entry at + + align:start position:0% +not equal to zero means one entry at + + + align:start position:0% +not equal to zero means one entry at +least is not + + align:start position:0% +least is not + + + align:start position:0% +least is not +zero and so now what we need to do is we + + align:start position:0% +zero and so now what we need to do is we + + + align:start position:0% +zero and so now what we need to do is we +need to + + align:start position:0% + + + + align:start position:0% + +show + + align:start position:0% + + + + align:start position:0% + +that there are many R there's obviously + + align:start position:0% +that there are many R there's obviously + + + align:start position:0% +that there are many R there's obviously +uh it's a binary Vector of length n and + + align:start position:0% +uh it's a binary Vector of length n and + + + align:start position:0% +uh it's a binary Vector of length n and +you can obviously you think about 2 ra + + align:start position:0% +you can obviously you think about 2 ra + + + align:start position:0% +you can obviously you think about 2 ra +to n possibilities with respect to R and + + align:start position:0% +to n possibilities with respect to R and + + + align:start position:0% +to n possibilities with respect to R and +what we really want to show is that that + + align:start position:0% +what we really want to show is that that + + + align:start position:0% +what we really want to show is that that +there's a large fraction more than half + + align:start position:0% +there's a large fraction more than half + + + align:start position:0% +there's a large fraction more than half +of the RS are going to actually discover + + align:start position:0% +of the RS are going to actually discover + + + align:start position:0% +of the RS are going to actually discover +uh that that the matrices were were + + align:start position:0% +uh that that the matrices were were + + + align:start position:0% +uh that that the matrices were were +multiplied incorrectly okay so we want + + align:start position:0% +multiplied incorrectly okay so we want + + + align:start position:0% +multiplied incorrectly okay so we want +to we want to show that there many + + align:start position:0% +to we want to show that there many + + + align:start position:0% +to we want to show that there many +RS uh such that Dr is not equal to + + align:start position:0% + + + + align:start position:0% + +zero and because if Dr is not equal to + + align:start position:0% +zero and because if Dr is not equal to + + + align:start position:0% +zero and because if Dr is not equal to +zero then uh you're obviously going to + + align:start position:0% +zero then uh you're obviously going to + + + align:start position:0% +zero then uh you're obviously going to +discover that AB r + + align:start position:0% +discover that AB r + + + align:start position:0% +discover that AB r +is not equal to CR right so if a r is + + align:start position:0% +is not equal to CR right so if a r is + + + align:start position:0% +is not equal to CR right so if a r is +not equal to CR that's identical to + + align:start position:0% +not equal to CR that's identical to + + + align:start position:0% +not equal to CR that's identical to +saying that Dr is not equal to zero that + + align:start position:0% +saying that Dr is not equal to zero that + + + align:start position:0% +saying that Dr is not equal to zero that +Mak + + align:start position:0% +Mak + + + align:start position:0% +Mak +sense um + + align:start position:0% +sense um + + + align:start position:0% +sense um +so + + align:start position:0% +so + + + align:start position:0% +so +specifically if you look at the claim + + align:start position:0% +specifically if you look at the claim + + + align:start position:0% +specifically if you look at the claim +and writing it in terms of Dr we want to + + align:start position:0% +and writing it in terms of Dr we want to + + + align:start position:0% +and writing it in terms of Dr we want to +say that the + + align:start position:0% +say that the + + + align:start position:0% +say that the +probability of Dr not equal to zero is + + align:start position:0% +probability of Dr not equal to zero is + + + align:start position:0% +probability of Dr not equal to zero is +greater than or equal to + + align:start position:0% +greater than or equal to + + + align:start position:0% +greater than or equal to +half for a randomly chosen + + align:start position:0% + + + + align:start position:0% + +R okay this is + + align:start position:0% + + + + align:start position:0% + +looking and so that's it that's the + + align:start position:0% +looking and so that's it that's the + + + align:start position:0% +looking and so that's it that's the +setup uh that uh we have to show we have + + align:start position:0% +setup uh that uh we have to show we have + + + align:start position:0% +setup uh that uh we have to show we have +to do a counting argument corresponding + + align:start position:0% +to do a counting argument corresponding + + + align:start position:0% +to do a counting argument corresponding +to uh these R vectors that are being + + align:start position:0% +to uh these R vectors that are being + + + align:start position:0% +to uh these R vectors that are being +generated randomly so let's do + + align:start position:0% +generated randomly so let's do + + + align:start position:0% +generated randomly so let's do +that um + + align:start position:0% + + + + align:start position:0% + +so the general argument we're going to + + align:start position:0% +so the general argument we're going to + + + align:start position:0% +so the general argument we're going to +make here is simply that we're going to + + align:start position:0% +make here is simply that we're going to + + + align:start position:0% +make here is simply that we're going to +uh roughly speaking we're going to look + + align:start position:0% +uh roughly speaking we're going to look + + + align:start position:0% +uh roughly speaking we're going to look +at a bad R what's a bad r a bad R is + + align:start position:0% +at a bad R what's a bad r a bad R is + + + align:start position:0% +at a bad R what's a bad r a bad R is +something that doesn't Discover the + + align:start position:0% +something that doesn't Discover the + + + align:start position:0% +something that doesn't Discover the +incorrect + + align:start position:0% +incorrect + + + align:start position:0% +incorrect +multiplication right that's what a bad R + + align:start position:0% +multiplication right that's what a bad R + + + align:start position:0% +multiplication right that's what a bad R +is so um your your D is not equal to + + align:start position:0% +is so um your your D is not equal to + + + align:start position:0% +is so um your your D is not equal to +zero but Dr equals zero okay that's a + + align:start position:0% +zero but Dr equals zero okay that's a + + + align:start position:0% +zero but Dr equals zero okay that's a +bad R right it's quite possible that + + align:start position:0% +bad R right it's quite possible that + + + align:start position:0% +bad R right it's quite possible that +that would be the case um and so uh uh + + align:start position:0% +that would be the case um and so uh uh + + + align:start position:0% +that would be the case um and so uh uh +you you want to try and figure out how + + align:start position:0% +you you want to try and figure out how + + + align:start position:0% +you you want to try and figure out how +many of these bad RS are there because + + align:start position:0% +many of these bad RS are there because + + + align:start position:0% +many of these bad RS are there because +those are the ones that are causing the + + align:start position:0% +those are the ones that are causing the + + + align:start position:0% +those are the ones that are causing the +the false + + align:start position:0% +the false + + + align:start position:0% +the false +uh negatives right uh um + + align:start position:0% +uh negatives right uh um + + + align:start position:0% +uh negatives right uh um +so uh that counting argument is the Crux + + align:start position:0% +so uh that counting argument is the Crux + + + align:start position:0% +so uh that counting argument is the Crux +of uh the proof of the claim right so + + align:start position:0% +of uh the proof of the claim right so + + + align:start position:0% +of uh the proof of the claim right so +let's let's look at that um and what + + align:start position:0% +let's let's look at that um and what + + + align:start position:0% +let's let's look at that um and what +we're going to do is we're going to pick + + align:start position:0% +we're going to do is we're going to pick + + + align:start position:0% +we're going to do is we're going to pick +a bad R and we're going to say there + + align:start position:0% +a bad R and we're going to say there + + + align:start position:0% +a bad R and we're going to say there +these good RS that are associated with + + align:start position:0% +these good RS that are associated with + + + align:start position:0% +these good RS that are associated with +this bad R and for every bad R there's a + + align:start position:0% +this bad R and for every bad R there's a + + + align:start position:0% +this bad R and for every bad R there's a +good R right and a good R is something + + align:start position:0% +good R right and a good R is something + + + align:start position:0% +good R right and a good R is something +that actually discovers the incorrect + + align:start position:0% +that actually discovers the incorrect + + + align:start position:0% +that actually discovers the incorrect +multiply and and given that for every + + align:start position:0% +multiply and and given that for every + + + align:start position:0% +multiply and and given that for every +bad R there's a good R you know half of + + align:start position:0% +bad R there's a good R you know half of + + + align:start position:0% +bad R there's a good R you know half of +the RS are good RS right that's it so + + align:start position:0% +the RS are good RS right that's it so + + + align:start position:0% +the RS are good RS right that's it so +I'll write it out that's the essence of + + align:start position:0% +I'll write it out that's the essence of + + + align:start position:0% +I'll write it out that's the essence of +the argument and I'll go a little more + + align:start position:0% +the argument and I'll go a little more + + + align:start position:0% +the argument and I'll go a little more +slowly so hopefully you you'll get that + + align:start position:0% +slowly so hopefully you you'll get that + + + align:start position:0% +slowly so hopefully you you'll get that +but so let's look at the case where Dr + + align:start position:0% +but so let's look at the case where Dr + + + align:start position:0% +but so let's look at the case where Dr +equals zero case because that's the + + align:start position:0% +equals zero case because that's the + + + align:start position:0% +equals zero case because that's the +interesting case right that's the case + + align:start position:0% +interesting case right that's the case + + + align:start position:0% +interesting case right that's the case +where the r is bad even though we had an + + align:start position:0% +where the r is bad even though we had an + + + align:start position:0% +where the r is bad even though we had an +incorrect multiply and you get this um + + align:start position:0% +incorrect multiply and you get this um + + + align:start position:0% +incorrect multiply and you get this um +um uh this uh I should have said false U + + align:start position:0% +um uh this uh I should have said false U + + + align:start position:0% +um uh this uh I should have said false U +you get a false positive right so I'm + + align:start position:0% +you get a false positive right so I'm + + + align:start position:0% +you get a false positive right so I'm +sorry I think just before I I said false + + align:start position:0% +sorry I think just before I I said false + + + align:start position:0% +sorry I think just before I I said false +negative but I meant false positive + + align:start position:0% +negative but I meant false positive + + + align:start position:0% +negative but I meant false positive +right so you you have a false positive + + align:start position:0% +right so you you have a false positive + + + align:start position:0% +right so you you have a false positive +in this case um and D equal AB minus c + + align:start position:0% +in this case um and D equal AB minus c + + + align:start position:0% +in this case um and D equal AB minus c +not equal to zero implies there exists + + align:start position:0% +not equal to zero implies there exists + + + align:start position:0% +not equal to zero implies there exists +an i and J such that D J is not equal to + + align:start position:0% +an i and J such that D J is not equal to + + + align:start position:0% +an i and J such that D J is not equal to +zero okay um and there's just one entry + + align:start position:0% +zero okay um and there's just one entry + + + align:start position:0% +zero okay um and there's just one entry +at least if you say that Matrix is not + + align:start position:0% +at least if you say that Matrix is not + + + align:start position:0% +at least if you say that Matrix is not +equal to zero there's got to be an entry + + align:start position:0% +equal to zero there's got to be an entry + + + align:start position:0% +equal to zero there's got to be an entry +that's not equal to zero so let's take a + + align:start position:0% +that's not equal to zero so let's take a + + + align:start position:0% +that's not equal to zero so let's take a +look at that entry and let's just draw + + align:start position:0% +look at that entry and let's just draw + + + align:start position:0% +look at that entry and let's just draw +it out that's my D + + align:start position:0% +it out that's my D + + + align:start position:0% +it out that's my D +Matrix and there's going to be an an i + + align:start position:0% +Matrix and there's going to be an an i + + + align:start position:0% +Matrix and there's going to be an an i +and a + + align:start position:0% +and a + + + align:start position:0% +and a +j so that's my I row and my jth column + + align:start position:0% +j so that's my I row and my jth column + + + align:start position:0% +j so that's my I row and my jth column +and there you go I have an entry here + + align:start position:0% +and there you go I have an entry here + + + align:start position:0% +and there you go I have an entry here +which is D J and uh I'm just picking + + align:start position:0% +which is D J and uh I'm just picking + + + align:start position:0% +which is D J and uh I'm just picking +that I don't care what I and J are but + + align:start position:0% +that I don't care what I and J are but + + + align:start position:0% +that I don't care what I and J are but +there's got to be an entry that's not + + align:start position:0% +there's got to be an entry that's not + + + align:start position:0% +there's got to be an entry that's not +equal to zero now I'm going to create a + + align:start position:0% +equal to zero now I'm going to create a + + + align:start position:0% +equal to zero now I'm going to create a +vector v + + align:start position:0% +vector v + + + align:start position:0% +vector v +right so this Vector is a is is not R + + align:start position:0% +right so this Vector is a is is not R + + + align:start position:0% +right so this Vector is a is is not R +it's a vector v that is chosen uh + + align:start position:0% +it's a vector v that is chosen uh + + + align:start position:0% +it's a vector v that is chosen uh +deterministically given the DI where + + align:start position:0% +deterministically given the DI where + + + align:start position:0% +deterministically given the DI where +it's got zeros + + align:start position:0% + + + + align:start position:0% + +everywhere except at at + + align:start position:0% +everywhere except at at + + + align:start position:0% +everywhere except at at +VJ so if this is the if this is the J + + align:start position:0% +VJ so if this is the if this is the J + + + align:start position:0% +VJ so if this is the if this is the J +entry columnwise everywhere else you got + + align:start position:0% + + + + align:start position:0% + +zero and you just got the one uh + + align:start position:0% +zero and you just got the one uh + + + align:start position:0% +zero and you just got the one uh +associated with the uh The The J going + + align:start position:0% +associated with the uh The The J going + + + align:start position:0% +associated with the uh The The J going +downward The The J entry okay so it's a + + align:start position:0% +downward The The J entry okay so it's a + + + align:start position:0% +downward The The J entry okay so it's a +one hot Vector if you will it's got one + + align:start position:0% +one hot Vector if you will it's got one + + + align:start position:0% +one hot Vector if you will it's got one +one so now if you multiply these two + + align:start position:0% +one so now if you multiply these two + + + align:start position:0% +one so now if you multiply these two +things + + align:start position:0% +things + + + align:start position:0% +things +out you know that you're going to get + + align:start position:0% +out you know that you're going to get + + + align:start position:0% +out you know that you're going to get +something and we can call this uh + + align:start position:0% +something and we can call this uh + + + align:start position:0% +something and we can call this uh +DV right so you take D and you multiply + + align:start position:0% +DV right so you take D and you multiply + + + align:start position:0% +DV right so you take D and you multiply +it by V uh Matrix multiplied by a a + + align:start position:0% +it by V uh Matrix multiplied by a a + + + align:start position:0% +it by V uh Matrix multiplied by a a +vector um you're you're guaranteed given + + align:start position:0% +vector um you're you're guaranteed given + + + align:start position:0% +vector um you're you're guaranteed given +that all of these are zero when I do my + + align:start position:0% +that all of these are zero when I do my + + + align:start position:0% +that all of these are zero when I do my +this times that plus this times this + + align:start position:0% +this times that plus this times this + + + align:start position:0% +this times that plus this times this +plus this times this all of these are + + align:start position:0% +plus this times this all of these are + + + align:start position:0% +plus this times this all of these are +going to produce zero this times one is + + align:start position:0% +going to produce zero this times one is + + + align:start position:0% +going to produce zero this times one is +going to produce something that's non + + align:start position:0% +going to produce something that's non + + + align:start position:0% +going to produce something that's non +zero and then all the other ones are + + align:start position:0% +zero and then all the other ones are + + + align:start position:0% +zero and then all the other ones are +going to produce zero right so I'm just + + align:start position:0% +going to produce zero right so I'm just + + + align:start position:0% +going to produce zero right so I'm just +adding a bunch of zeros to this nonzero + + align:start position:0% +adding a bunch of zeros to this nonzero + + + align:start position:0% +adding a bunch of zeros to this nonzero +multiplied by one so I'm going to get + + align:start position:0% +multiplied by one so I'm going to get + + + align:start position:0% +multiplied by one so I'm going to get +something that's non zero right all make + + align:start position:0% +something that's non zero right all make + + + align:start position:0% +something that's non zero right all make +sense um so I'm going to see something + + align:start position:0% +sense um so I'm going to see something + + + align:start position:0% +sense um so I'm going to see something +here which is the J + + align:start position:0% +here which is the J + + + align:start position:0% +here which is the J +entry that's not equal to + + align:start position:0% +entry that's not equal to + + + align:start position:0% +entry that's not equal to +zero all and so that implies that DV is + + align:start position:0% +zero all and so that implies that DV is + + + align:start position:0% +zero all and so that implies that DV is +not equal to zero and in particular what + + align:start position:0% +not equal to zero and in particular what + + + align:start position:0% +not equal to zero and in particular what +I'm saying is um DV of J so if I just + + align:start position:0% +I'm saying is um DV of J so if I just + + + align:start position:0% +I'm saying is um DV of J so if I just +look at that entry that is + + align:start position:0% +look at that entry that is + + + align:start position:0% +look at that entry that is +identically D J which is not equal to + + align:start position:0% +identically D J which is not equal to + + + align:start position:0% +identically D J which is not equal to +zero because I'm multiplying it by one + + align:start position:0% +zero because I'm multiplying it by one + + + align:start position:0% +zero because I'm multiplying it by one +and I'm adding a bunch of zeros to + + align:start position:0% +and I'm adding a bunch of zeros to + + + align:start position:0% +and I'm adding a bunch of zeros to +that's it okay yeah question J or + + align:start position:0% +that's it okay yeah question J or + + + align:start position:0% +that's it okay yeah question J or +I um so I picked the J here so um I + + align:start position:0% +I um so I picked the J here so um I + + + align:start position:0% +I um so I picked the J here so um I +think I'm going J J + + align:start position:0% +think I'm going J J + + + align:start position:0% +think I'm going J J +right that make sense right so I go one + + align:start position:0% +right that make sense right so I go one + + + align:start position:0% +right that make sense right so I go one +if this was if J was seven and and this + + align:start position:0% +if this was if J was seven and and this + + + align:start position:0% +if this was if J was seven and and this +is seven down then I'm going it would be + + align:start position:0% +is seven down then I'm going it would be + + + align:start position:0% +is seven down then I'm going it would be +it would be the the the the the seventh + + align:start position:0% +it would be the the the the the seventh + + + align:start position:0% +it would be the the the the the seventh +would it because this is going to turn + + align:start position:0% +would it because this is going to turn + + + align:start position:0% +would it because this is going to turn +into + + align:start position:0% +into + + + align:start position:0% +into +that right + + align:start position:0% +that right + + + align:start position:0% +that right +okay um now either way I if I you know + + align:start position:0% +okay um now either way I if I you know + + + align:start position:0% +okay um now either way I if I you know +picked it in the middle uh it doesn't + + align:start position:0% +picked it in the middle uh it doesn't + + + align:start position:0% +picked it in the middle uh it doesn't +really matter the point is there's going + + align:start position:0% +really matter the point is there's going + + + align:start position:0% +really matter the point is there's going +to be one entry so hang in there there's + + align:start position:0% +to be one entry so hang in there there's + + + align:start position:0% +to be one entry so hang in there there's +going to be one entry that's non zero + + align:start position:0% +going to be one entry that's non zero + + + align:start position:0% +going to be one entry that's non zero +okay if you didn't quite get that um so + + align:start position:0% +okay if you didn't quite get that um so + + + align:start position:0% +okay if you didn't quite get that um so +di J is not zero and this is one more + + align:start position:0% +di J is not zero and this is one more + + + align:start position:0% +di J is not zero and this is one more +observation we're going to make in order + + align:start position:0% +observation we're going to make in order + + + align:start position:0% +observation we're going to make in order +to do the counting of these bad RS + + align:start position:0% +to do the counting of these bad RS + + + align:start position:0% +to do the counting of these bad RS +because this is a this is a bad r that + + align:start position:0% +because this is a this is a bad r that + + + align:start position:0% +because this is a this is a bad r that +we're looking at if you say that Dr + + align:start position:0% +we're looking at if you say that Dr + + + align:start position:0% +we're looking at if you say that Dr +equals zero um we've created a v that + + align:start position:0% +equals zero um we've created a v that + + + align:start position:0% +equals zero um we've created a v that +has nothing to do with r but we're going + + align:start position:0% +has nothing to do with r but we're going + + + align:start position:0% +has nothing to do with r but we're going +to use the V to go from a bad R which is + + align:start position:0% +to use the V to go from a bad R which is + + + align:start position:0% +to use the V to go from a bad R which is +our example here to a good one right + + align:start position:0% +our example here to a good one right + + + align:start position:0% +our example here to a good one right +that's pretty much it uh that's the last + + align:start position:0% +that's pretty much it uh that's the last + + + align:start position:0% +that's pretty much it uh that's the last +step here so what we're going to do is + + align:start position:0% +step here so what we're going to do is + + + align:start position:0% +step here so what we're going to do is +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +take any + + align:start position:0% +take any + + + align:start position:0% +take any +r that can be + + align:start position:0% + + + + align:start position:0% + +chosen by our + + align:start position:0% +chosen by our + + + align:start position:0% +chosen by our +algorithm and such that you know Dr + + align:start position:0% +algorithm and such that you know Dr + + + align:start position:0% +algorithm and such that you know Dr +equals zero because that's the case that + + align:start position:0% +equals zero because that's the case that + + + align:start position:0% +equals zero because that's the case that +we're looking at and um we're going to + + align:start position:0% +we're looking at and um we're going to + + + align:start position:0% +we're looking at and um we're going to +compute RP Prime which is r + V + + align:start position:0% +compute RP Prime which is r + V + + + align:start position:0% +compute RP Prime which is r + V +okay we're just going to and this + + align:start position:0% +okay we're just going to and this + + + align:start position:0% +okay we're just going to and this +remember this is mod 2 arithmetic uh + + align:start position:0% +remember this is mod 2 arithmetic uh + + + align:start position:0% +remember this is mod 2 arithmetic uh +you're only going to get zeros and ones + + align:start position:0% +you're only going to get zeros and ones + + + align:start position:0% +you're only going to get zeros and ones +so if you have 1 plus 1 it gives you + + align:start position:0% +so if you have 1 plus 1 it gives you + + + align:start position:0% +so if you have 1 plus 1 it gives you +zero obviously 0 plus 0 gives you zero + + align:start position:0% +zero obviously 0 plus 0 gives you zero + + + align:start position:0% +zero obviously 0 plus 0 gives you zero +and uh the other cases are clear and + + align:start position:0% +and uh the other cases are clear and + + + align:start position:0% +and uh the other cases are clear and +this plus here remember is also other + + align:start position:0% +this plus here remember is also other + + + align:start position:0% +this plus here remember is also other +thing that's important is this is not + + align:start position:0% +thing that's important is this is not + + + align:start position:0% +thing that's important is this is not +only mod 2 um these are all vectors so + + align:start position:0% +only mod 2 um these are all vectors so + + + align:start position:0% +only mod 2 um these are all vectors so +your R is a vector uh and you can think + + align:start position:0% +your R is a vector uh and you can think + + + align:start position:0% +your R is a vector uh and you can think +of it as a column Vector that's how I + + align:start position:0% +of it as a column Vector that's how I + + + align:start position:0% +of it as a column Vector that's how I +drew it uh you you're adding up + + align:start position:0% +drew it uh you you're adding up + + + align:start position:0% +drew it uh you you're adding up +a column Vector with a V that's a column + + align:start position:0% +a column Vector with a V that's a column + + + align:start position:0% +a column Vector with a V that's a column +Vector the way I drew that uh you could + + align:start position:0% +Vector the way I drew that uh you could + + + align:start position:0% +Vector the way I drew that uh you could +do this with rows if you like but it's + + align:start position:0% +do this with rows if you like but it's + + + align:start position:0% +do this with rows if you like but it's +just notation and you're going to + + align:start position:0% +just notation and you're going to + + + align:start position:0% +just notation and you're going to +compute an r r Prime here um what can + + align:start position:0% +compute an r r Prime here um what can + + + align:start position:0% +compute an r r Prime here um what can +you + + align:start position:0% +you + + + align:start position:0% +you +say + + align:start position:0% +say + + + align:start position:0% +say +about Dr R + + align:start position:0% +about Dr R + + + align:start position:0% +about Dr R +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +someone yeah go + + align:start position:0% +someone yeah go + + + align:start position:0% +someone yeah go +ahead it's not zero uh and and uh you'll + + align:start position:0% +ahead it's not zero uh and and uh you'll + + + align:start position:0% +ahead it's not zero uh and and uh you'll +get a I'll give you a frisbee but then + + align:start position:0% +get a I'll give you a frisbee but then + + + align:start position:0% +get a I'll give you a frisbee but then +you can explain I can you stand up I + + align:start position:0% +you can explain I can you stand up I + + + align:start position:0% +you can explain I can you stand up I +don't want to take this lady's head + + align:start position:0% +don't want to take this lady's head + + + align:start position:0% +don't want to take this lady's head +off um so can you explain + + align:start position:0% +off um so can you explain + + + align:start position:0% +off um so can you explain +why + + align:start position:0% + + + + align:start position:0% + +R absolutely right so essentially what + + align:start position:0% +R absolutely right so essentially what + + + align:start position:0% +R absolutely right so essentially what +we have is this is simply woo yellow um + + align:start position:0% +we have is this is simply woo yellow um + + + align:start position:0% +we have is this is simply woo yellow um +Dr + + + align:start position:0% +Dr + + + + align:start position:0% +Dr + +V uh + + align:start position:0% +V uh + + + align:start position:0% +V uh +highlights um 0+ + + align:start position:0% +highlights um 0+ + + + align:start position:0% +highlights um 0+ +DV not equal to zero all right do we + + align:start position:0% +DV not equal to zero all right do we + + + align:start position:0% +DV not equal to zero all right do we +like yellow or do we like + + align:start position:0% +like yellow or do we like + + + align:start position:0% +like yellow or do we like +white yellow is fine um so so that's + + align:start position:0% +white yellow is fine um so so that's + + + align:start position:0% +white yellow is fine um so so that's +pretty much it so what's cool about this + + align:start position:0% +pretty much it so what's cool about this + + + align:start position:0% +pretty much it so what's cool about this +is this final step which I think you've + + align:start position:0% +is this final step which I think you've + + + align:start position:0% +is this final step which I think you've +gotten but I'm just going to say it out + + align:start position:0% +gotten but I'm just going to say it out + + + align:start position:0% +gotten but I'm just going to say it out +loud now which is that um R to R + + align:start position:0% +loud now which is that um R to R + + + align:start position:0% +loud now which is that um R to R +Prime um is one: + + align:start position:0% +Prime um is one: + + + align:start position:0% +Prime um is one: +one for for any given R such that Dr + + align:start position:0% +one for for any given R such that Dr + + + align:start position:0% +one for for any given R such that Dr +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +um given the situation where you know + + align:start position:0% +um given the situation where you know + + + align:start position:0% +um given the situation where you know +capital D is not equal to zero and + + align:start position:0% +capital D is not equal to zero and + + + align:start position:0% +capital D is not equal to zero and +there's some Di and there could be many + + align:start position:0% +there's some Di and there could be many + + + align:start position:0% +there's some Di and there could be many +ds I just need one I've constructed + + align:start position:0% +ds I just need one I've constructed + + + align:start position:0% +ds I just need one I've constructed +based on that di this this V Vector + + align:start position:0% +based on that di this this V Vector + + + align:start position:0% +based on that di this this V Vector +which has the J entry corresponding to + + align:start position:0% +which has the J entry corresponding to + + + align:start position:0% +which has the J entry corresponding to +the V Vector being a one with all of the + + align:start position:0% +the V Vector being a one with all of the + + + align:start position:0% +the V Vector being a one with all of the +other entries being a zero but I can now + + align:start position:0% +other entries being a zero but I can now + + + align:start position:0% +other entries being a zero but I can now +create an R to r that is one to one in + + align:start position:0% +create an R to r that is one to one in + + + align:start position:0% +create an R to r that is one to one in +the sense that um if um R Prime equal = + + align:start position:0% +the sense that um if um R Prime equal = + + + align:start position:0% +the sense that um if um R Prime equal = +r + + + align:start position:0% +r + + + + align:start position:0% +r + +V and that equals R + + align:start position:0% +V and that equals R + + + align:start position:0% +V and that equals R +Prime + V right so if I ever have a + + align:start position:0% +Prime + V right so if I ever have a + + + align:start position:0% +Prime + V right so if I ever have a +situation where in order to show this + + align:start position:0% +situation where in order to show this + + + align:start position:0% +situation where in order to show this +one to one I want to say that it's not + + align:start position:0% +one to one I want to say that it's not + + + align:start position:0% +one to one I want to say that it's not +many to one right so or even two to one + + align:start position:0% +many to one right so or even two to one + + + align:start position:0% +many to one right so or even two to one +so if I have an R Prime that equals r + + + align:start position:0% +so if I have an R Prime that equals r + + + + align:start position:0% +so if I have an R Prime that equals r + +V and you tell me that RP Prime also + + align:start position:0% +V and you tell me that RP Prime also + + + align:start position:0% +V and you tell me that RP Prime also +equals R prime plus v i can make the the + + align:start position:0% +equals R prime plus v i can make the the + + + align:start position:0% +equals R prime plus v i can make the the +argument that R and R Prime + + align:start position:0% +argument that R and R Prime + + + align:start position:0% +argument that R and R Prime +are exactly the same right so + + align:start position:0% +are exactly the same right so + + + align:start position:0% +are exactly the same right so +then Ral R Prime right so what am I + + align:start position:0% +then Ral R Prime right so what am I + + + align:start position:0% +then Ral R Prime right so what am I +saying there um I'm just I'm just saying + + align:start position:0% +saying there um I'm just I'm just saying + + + align:start position:0% +saying there um I'm just I'm just saying +that um for any given any given R uh + + align:start position:0% +that um for any given any given R uh + + + align:start position:0% +that um for any given any given R uh +that this has Dr equals Zer I can + + align:start position:0% +that this has Dr equals Zer I can + + + align:start position:0% +that this has Dr equals Zer I can +twiddle at the J element of that R and + + align:start position:0% +twiddle at the J element of that R and + + + align:start position:0% +twiddle at the J element of that R and +go from 0 to 1 or 1 to zero if you tell + + align:start position:0% +go from 0 to 1 or 1 to zero if you tell + + + align:start position:0% +go from 0 to 1 or 1 to zero if you tell +me that there's a DI J somewhere in that + + align:start position:0% +me that there's a DI J somewhere in that + + + align:start position:0% +me that there's a DI J somewhere in that +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +that uh uh is non zero and I do that + + align:start position:0% +that uh uh is non zero and I do that + + + align:start position:0% +that uh uh is non zero and I do that +little twiddle remember it's all zeros + + align:start position:0% +little twiddle remember it's all zeros + + + align:start position:0% +little twiddle remember it's all zeros +and ones Boolean matrices so if I do one + + align:start position:0% +and ones Boolean matrices so if I do one + + + align:start position:0% +and ones Boolean matrices so if I do one +twiddle um it it's a one to one uh if I + + align:start position:0% +twiddle um it it's a one to one uh if I + + + align:start position:0% +twiddle um it it's a one to one uh if I +do two twiddles and I go you know one to + + align:start position:0% +do two twiddles and I go you know one to + + + align:start position:0% +do two twiddles and I go you know one to +zero I'm back to I'm back to one again + + align:start position:0% +zero I'm back to I'm back to one again + + + align:start position:0% +zero I'm back to I'm back to one again +and that's all this says because you + + align:start position:0% +and that's all this says because you + + + align:start position:0% +and that's all this says because you +have mod two that's all that says right + + align:start position:0% +have mod two that's all that says right + + + align:start position:0% +have mod two that's all that says right +so one little tweak um and I'm going to + + align:start position:0% +so one little tweak um and I'm going to + + + align:start position:0% +so one little tweak um and I'm going to +be able to take a bad R and turn it into + + align:start position:0% +be able to take a bad R and turn it into + + + align:start position:0% +be able to take a bad R and turn it into +a good R because the good R the r Prime + + align:start position:0% +a good R because the good R the r Prime + + + align:start position:0% +a good R because the good R the r Prime +in this case has Dr Prime not equal to + + align:start position:0% +in this case has Dr Prime not equal to + + + align:start position:0% +in this case has Dr Prime not equal to +zero okay and that's it that's my + + align:start position:0% +zero okay and that's it that's my + + + align:start position:0% +zero okay and that's it that's my +counting argument and All That Remains + + align:start position:0% +counting argument and All That Remains + + + align:start position:0% +counting argument and All That Remains +is to essentially close this by saying + + align:start position:0% +is to essentially close this by saying + + + align:start position:0% +is to essentially close this by saying +um just to write this out uh to get to + + align:start position:0% +um just to write this out uh to get to + + + align:start position:0% +um just to write this out uh to get to +the to get to the final + + align:start position:0% +the to get to the final + + + align:start position:0% +the to get to the final +claim and get the 1/2 the one: one + + align:start position:0% +claim and get the 1/2 the one: one + + + align:start position:0% +claim and get the 1/2 the one: one +essentially gives you the 1/2 half of at + + align:start position:0% +essentially gives you the 1/2 half of at + + + align:start position:0% +essentially gives you the 1/2 half of at +least half of these things are going to + + align:start position:0% +least half of these things are going to + + + align:start position:0% +least half of these things are going to +be good RS um if you had if you had a + + align:start position:0% + + + + align:start position:0% + +Dr if you had a Dr that's not equal to + + align:start position:0% +Dr if you had a Dr that's not equal to + + + align:start position:0% +Dr if you had a Dr that's not equal to +zero uh and that's that's the case that + + align:start position:0% +zero uh and that's that's the case that + + + align:start position:0% +zero uh and that's that's the case that +you have here um then we're going to + + align:start position:0% +you have here um then we're going to + + + align:start position:0% +you have here um then we're going to +discover an RP Prime such that the Dr + + align:start position:0% +discover an RP Prime such that the Dr + + + align:start position:0% +discover an RP Prime such that the Dr +Prime is not equal to zero and R to RP + + align:start position:0% +Prime is not equal to zero and R to RP + + + align:start position:0% +Prime is not equal to zero and R to RP +Prime is a one to one mapping + + align:start position:0% + + + + align:start position:0% + +um and so the number of R + + align:start position:0% + + + + align:start position:0% + +Prime for + + align:start position:0% +Prime for + + + align:start position:0% +Prime for +which Dr Prime is not equal to zero is + + align:start position:0% +which Dr Prime is not equal to zero is + + + align:start position:0% +which Dr Prime is not equal to zero is +greater than or equal to the + + align:start position:0% +greater than or equal to the + + + align:start position:0% +greater than or equal to the +number of + + align:start position:0% +number of + + + align:start position:0% +number of +R for + + align:start position:0% +R for + + + align:start position:0% +R for +which Dr equals z right and so that + + align:start position:0% +which Dr equals z right and so that + + + align:start position:0% +which Dr equals z right and so that +implies that the probability + + align:start position:0% +implies that the probability + + + align:start position:0% +implies that the probability +of + + align:start position:0% +of + + + align:start position:0% +of +Dr not equal to zero so if you just + + align:start position:0% +Dr not equal to zero so if you just + + + align:start position:0% +Dr not equal to zero so if you just +choose an R this is now a randomly + + align:start position:0% +choose an R this is now a randomly + + + align:start position:0% +choose an R this is now a randomly +chosen + + align:start position:0% +chosen + + + align:start position:0% +chosen +r i mean not that others weren't but I'm + + align:start position:0% +r i mean not that others weren't but I'm + + + align:start position:0% +r i mean not that others weren't but I'm +I'm treating it a little bit differently + + align:start position:0% +I'm treating it a little bit differently + + + align:start position:0% +I'm treating it a little bit differently +here this was a specific R for which Dr + + align:start position:0% +here this was a specific R for which Dr + + + align:start position:0% +here this was a specific R for which Dr +was equal to zero I made an argument + + align:start position:0% +was equal to zero I made an argument + + + align:start position:0% +was equal to zero I made an argument +that you can always get this R Prime 1 + + align:start position:0% +that you can always get this R Prime 1 + + + align:start position:0% +that you can always get this R Prime 1 +to one such that Dr Prime is not equal + + align:start position:0% +to one such that Dr Prime is not equal + + + align:start position:0% +to one such that Dr Prime is not equal +to zero and now going back to what I had + + align:start position:0% +to zero and now going back to what I had + + + align:start position:0% +to zero and now going back to what I had +initially with respect to the claim here + + align:start position:0% +initially with respect to the claim here + + + align:start position:0% +initially with respect to the claim here +the r here was a a randomly chosen R I'm + + align:start position:0% +the r here was a a randomly chosen R I'm + + + align:start position:0% +the r here was a a randomly chosen R I'm +I'm saying thanks to this little + + align:start position:0% +I'm saying thanks to this little + + + align:start position:0% +I'm saying thanks to this little +argument this line up up top I'm I'm + + align:start position:0% +argument this line up up top I'm I'm + + + align:start position:0% +argument this line up up top I'm I'm +going to be able to say this is greater + + align:start position:0% +going to be able to say this is greater + + + align:start position:0% +going to be able to say this is greater +than or equal to2 + + align:start position:0% +than or equal to2 + + + align:start position:0% +than or equal to2 +okay cool any questions + + align:start position:0% + + + + align:start position:0% + +yeahum on the last colum + + align:start position:0% +yeahum on the last colum + + + align:start position:0% +yeahum on the last colum +be this should be I + + align:start position:0% + + + + align:start position:0% + +yes people agree with that majority + + align:start position:0% +yes people agree with that majority + + + align:start position:0% +yes people agree with that majority +vote all right I'm good let's make that + + align:start position:0% +vote all right I'm good let's make that + + + align:start position:0% +vote all right I'm good let's make that +an + + align:start position:0% + + + + align:start position:0% + +ey oh yeah of course once you do that + + align:start position:0% +ey oh yeah of course once you do that + + + align:start position:0% +ey oh yeah of course once you do that +yeah once you do that you you you you + + align:start position:0% +yeah once you do that you you you you + + + align:start position:0% +yeah once you do that you you you you +have to have an eye there + + align:start position:0% +have to have an eye there + + + align:start position:0% +have to have an eye there +good um so you're looking at uh you're + + align:start position:0% +good um so you're looking at uh you're + + + align:start position:0% +good um so you're looking at uh you're +looking at a particular entry it it it + + align:start position:0% +looking at a particular entry it it it + + + align:start position:0% +looking at a particular entry it it it +makes a difference whether you used a + + align:start position:0% +makes a difference whether you used a + + + align:start position:0% +makes a difference whether you used a +column or a row if I done uh um now that + + align:start position:0% +column or a row if I done uh um now that + + + align:start position:0% +column or a row if I done uh um now that +I remember + + align:start position:0% +I remember + + + align:start position:0% +I remember +uh um if you think if you turn this into + + align:start position:0% +uh um if you think if you turn this into + + + align:start position:0% +uh um if you think if you turn this into +a a a row Matrix and this becomes a row + + align:start position:0% +a a a row Matrix and this becomes a row + + + align:start position:0% +a a a row Matrix and this becomes a row +Matrix you'll essentially get the dvj + + align:start position:0% +Matrix you'll essentially get the dvj + + + align:start position:0% +Matrix you'll essentially get the dvj +okay so it depends on which way you look + + align:start position:0% +okay so it depends on which way you look + + + align:start position:0% +okay so it depends on which way you look +at it but thanks for pointing that out + + align:start position:0% +at it but thanks for pointing that out + + + align:start position:0% +at it but thanks for pointing that out +um + + align:start position:0% +um + + + align:start position:0% +um +it's the specifics of I andj weren't + + align:start position:0% +it's the specifics of I andj weren't + + + align:start position:0% +it's the specifics of I andj weren't +particularly important to uh the proof + + align:start position:0% +particularly important to uh the proof + + + align:start position:0% +particularly important to uh the proof +itself uh the key thing is you zoom in + + align:start position:0% +itself uh the key thing is you zoom in + + + align:start position:0% +itself uh the key thing is you zoom in +on a particular entry that is not equal + + align:start position:0% +on a particular entry that is not equal + + + align:start position:0% +on a particular entry that is not equal +to zero uh and then you tweak uh that + + align:start position:0% +to zero uh and then you tweak uh that + + + align:start position:0% +to zero uh and then you tweak uh that +entry corresponding to the R so uh once + + align:start position:0% +entry corresponding to the R so uh once + + + align:start position:0% +entry corresponding to the R so uh once +you tweak that you make that zero or one + + align:start position:0% +you tweak that you make that zero or one + + + align:start position:0% +you tweak that you make that zero or one +or one to zero you can get this result + + align:start position:0% +or one to zero you can get this result + + + align:start position:0% +or one to zero you can get this result +um and uh uh I'm sorry I'm pointing the + + align:start position:0% +um and uh uh I'm sorry I'm pointing the + + + align:start position:0% +um and uh uh I'm sorry I'm pointing the +wrong spot this result uh and and then + + align:start position:0% +wrong spot this result uh and and then + + + align:start position:0% +wrong spot this result uh and and then +you get your you get your claim okay so + + align:start position:0% +you get your you get your claim okay so + + + align:start position:0% +you get your you get your claim okay so +summarize uh we have a bound we run it + + align:start position:0% +summarize uh we have a bound we run it + + + align:start position:0% +summarize uh we have a bound we run it +over and over uh and we get it to the + + align:start position:0% +over and over uh and we get it to the + + + align:start position:0% +over and over uh and we get it to the +point where we can have a 01 prob ility + + align:start position:0% +point where we can have a 01 prob ility + + + align:start position:0% +point where we can have a 01 prob ility +that uh if the matrices were multiplied + + align:start position:0% +that uh if the matrices were multiplied + + + align:start position:0% +that uh if the matrices were multiplied +uh incorrectly uh that you wouldn't + + align:start position:0% +uh incorrectly uh that you wouldn't + + + align:start position:0% +uh incorrectly uh that you wouldn't +discover that because you ran it long + + align:start position:0% +discover that because you ran it long + + + align:start position:0% +discover that because you ran it long +enough that for enough hours + + align:start position:0% +enough that for enough hours + + + align:start position:0% +enough that for enough hours +independently chosen that that + + align:start position:0% +independently chosen that that + + + align:start position:0% +independently chosen that that +probability becomes as low as possible + + align:start position:0% +probability becomes as low as possible + + + align:start position:0% +probability becomes as low as possible +okay so that was uh um Monte Carlo um + + align:start position:0% +okay so that was uh um Monte Carlo um + + + align:start position:0% +okay so that was uh um Monte Carlo um +let's do uh a Las Vegas algorithm and + + align:start position:0% +let's do uh a Las Vegas algorithm and + + + align:start position:0% +let's do uh a Las Vegas algorithm and +you guys are probably thinking my + + align:start position:0% +you guys are probably thinking my + + + align:start position:0% +you guys are probably thinking my +goodness another sorting algorithm uh + + align:start position:0% +goodness another sorting algorithm uh + + + align:start position:0% +goodness another sorting algorithm uh +after I don't know 17 different sorting + + align:start position:0% +after I don't know 17 different sorting + + + align:start position:0% +after I don't know 17 different sorting +algorithms but let me this all sorting + + align:start position:0% +algorithms but let me this all sorting + + + align:start position:0% +algorithms but let me this all sorting +algorithms that you've ever learned so + + align:start position:0% +algorithms that you've ever learned so + + + align:start position:0% +algorithms that you've ever learned so +far right so mer sort doesn't work um + + align:start position:0% +far right so mer sort doesn't work um + + + align:start position:0% +far right so mer sort doesn't work um +and the reason it doesn't work in + + align:start position:0% +and the reason it doesn't work in + + + align:start position:0% +and the reason it doesn't work in +practice uh if you're really into + + align:start position:0% +practice uh if you're really into + + + align:start position:0% +practice uh if you're really into +performance is because um is is because + + align:start position:0% +performance is because um is is because + + + align:start position:0% +performance is because um is is because +of um the auxiliary space that merge + + align:start position:0% +of um the auxiliary space that merge + + + align:start position:0% +of um the auxiliary space that merge +sort requires right so if you recall um + + align:start position:0% +sort requires right so if you recall um + + + align:start position:0% +sort requires right so if you recall um +there's uh the notion of uh in place + + align:start position:0% +there's uh the notion of uh in place + + + align:start position:0% +there's uh the notion of uh in place +sorting so let's uh move on to the next + + align:start position:0% +sorting so let's uh move on to the next + + + align:start position:0% +sorting so let's uh move on to the next +thing here which is + + align:start position:0% +thing here which is + + + align:start position:0% +thing here which is +um uh quick sort which is a new sorting + + align:start position:0% +um uh quick sort which is a new sorting + + + align:start position:0% +um uh quick sort which is a new sorting +algorithm and I want to motivate it for + + align:start position:0% +algorithm and I want to motivate it for + + + align:start position:0% +algorithm and I want to motivate it for +just a couple of + + align:start position:0% + + + + align:start position:0% + +minutes and the primary motivation + + align:start position:0% +minutes and the primary motivation + + + align:start position:0% +minutes and the primary motivation +really is + + align:start position:0% +really is + + + align:start position:0% +really is +practical performance not U asmic + + align:start position:0% +practical performance not U asmic + + + align:start position:0% +practical performance not U asmic +complexity so I I'll be uh upfront about + + align:start position:0% +complexity so I I'll be uh upfront about + + + align:start position:0% +complexity so I I'll be uh upfront about +that uh it's it's it's all about + + align:start position:0% +that uh it's it's it's all about + + + align:start position:0% +that uh it's it's it's all about +practical performance corresponding to + + align:start position:0% +practical performance corresponding to + + + align:start position:0% +practical performance corresponding to +quick sort uh and uh quick sort is divid + + align:start position:0% +quick sort uh and uh quick sort is divid + + + align:start position:0% +quick sort uh and uh quick sort is divid +and concer algorithm randomized + + align:start position:0% +and concer algorithm randomized + + + align:start position:0% +and concer algorithm randomized +algorithm invented in + + align:start position:0% +algorithm invented in + + + align:start position:0% +algorithm invented in +62 unlike merge + + align:start position:0% +62 unlike merge + + + align:start position:0% +62 unlike merge +sword it's got two interesting + + align:start position:0% +sword it's got two interesting + + + align:start position:0% +sword it's got two interesting +properties uh the first is that it's in + + align:start position:0% +properties uh the first is that it's in + + + align:start position:0% +properties uh the first is that it's in +place like I just said so no auxiliary + + align:start position:0% +place like I just said so no auxiliary + + + align:start position:0% +place like I just said so no auxiliary +space in merge + + align:start position:0% +space in merge + + + align:start position:0% +space in merge +sort um you can try and get around + + align:start position:0% +sort um you can try and get around + + + align:start position:0% +sort um you can try and get around +this uh no I should say order n + + align:start position:0% +this uh no I should say order n + + + align:start position:0% +this uh no I should say order n +auxiliary space you need U uh you need a + + align:start position:0% +auxiliary space you need U uh you need a + + + align:start position:0% +auxiliary space you need U uh you need a +little temporary + + align:start position:0% +little temporary + + + align:start position:0% +little temporary +uh variable in order to do swapping uh + + align:start position:0% +uh variable in order to do swapping uh + + + align:start position:0% +uh variable in order to do swapping uh +but uh you have uh you don't have the + + align:start position:0% +but uh you have uh you don't have the + + + align:start position:0% +but uh you have uh you don't have the +order and auxilary space so you don't + + align:start position:0% +order and auxilary space so you don't + + + align:start position:0% +order and auxilary space so you don't +have to constantly allocate and remember + + align:start position:0% +have to constantly allocate and remember + + + align:start position:0% +have to constantly allocate and remember +n could be large it could be in the + + align:start position:0% +n could be large it could be in the + + + align:start position:0% +n could be large it could be in the +billions or trillions so uh from that + + align:start position:0% +billions or trillions so uh from that + + + align:start position:0% +billions or trillions so uh from that +standpoint quick sort ends up winning + + align:start position:0% +standpoint quick sort ends up winning + + + align:start position:0% +standpoint quick sort ends up winning +simply because of relatively mundane + + align:start position:0% +simply because of relatively mundane + + + align:start position:0% +simply because of relatively mundane +things like memory allocation in uh uh + + align:start position:0% +things like memory allocation in uh uh + + + align:start position:0% +things like memory allocation in uh uh +your your computer uh and uh the other + + align:start position:0% +your your computer uh and uh the other + + + align:start position:0% +your your computer uh and uh the other +interesting thing about quick sort in + + align:start position:0% +interesting thing about quick sort in + + + align:start position:0% +interesting thing about quick sort in +relation to sord is that all the + + align:start position:0% + + + + align:start position:0% + +work is in the Divide + + align:start position:0% + + + + align:start position:0% + +step um so in merge s remember we just + + align:start position:0% +step um so in merge s remember we just + + + align:start position:0% +step um so in merge s remember we just +split and we recurse uh and what happens + + align:start position:0% +split and we recurse uh and what happens + + + align:start position:0% +split and we recurse uh and what happens +uh when you when you uh come back is you + + align:start position:0% +uh when you when you uh come back is you + + + align:start position:0% +uh when you when you uh come back is you +have to do the the the the finger + + align:start position:0% +have to do the the the the finger + + + align:start position:0% +have to do the the the the finger +merging algorithm uh by looking at the + + align:start position:0% +merging algorithm uh by looking at the + + + align:start position:0% +merging algorithm uh by looking at the +two sorted arrays and looking at what uh + + align:start position:0% +two sorted arrays and looking at what uh + + + align:start position:0% +two sorted arrays and looking at what uh +the new uh merge array is going to look + + align:start position:0% +the new uh merge array is going to look + + + align:start position:0% +the new uh merge array is going to look +like so the work is in the merge uh but + + align:start position:0% +like so the work is in the merge uh but + + + align:start position:0% +like so the work is in the merge uh but +uh in quick sort the work is going to be + + align:start position:0% +uh in quick sort the work is going to be + + + align:start position:0% +uh in quick sort the work is going to be +in the Divide because we're going to + + align:start position:0% +in the Divide because we're going to + + + align:start position:0% +in the Divide because we're going to +have to um do a bunch of work um + + align:start position:0% +have to um do a bunch of work um + + + align:start position:0% +have to um do a bunch of work um +associated with figuring out how to keep + + align:start position:0% +associated with figuring out how to keep + + + align:start position:0% +associated with figuring out how to keep +the partitions balanced and a little bit + + align:start position:0% +the partitions balanced and a little bit + + + align:start position:0% +the partitions balanced and a little bit +like uh we had to do when we did uh + + align:start position:0% +like uh we had to do when we did uh + + + align:start position:0% +like uh we had to do when we did uh +median finding back a couple of weeks + + align:start position:0% +median finding back a couple of weeks + + + align:start position:0% +median finding back a couple of weeks +ago um I'm going to talk about three + + align:start position:0% +ago um I'm going to talk about three + + + align:start position:0% +ago um I'm going to talk about three +different variants of quick sort the the + + align:start position:0% +different variants of quick sort the the + + + align:start position:0% +different variants of quick sort the the +variant that we're going to spend the + + align:start position:0% +variant that we're going to spend the + + + align:start position:0% +variant that we're going to spend the +most time on is the Las Vegas quick sort + + align:start position:0% +most time on is the Las Vegas quick sort + + + align:start position:0% +most time on is the Las Vegas quick sort +where we'd like to show that it's + + align:start position:0% +where we'd like to show that it's + + + align:start position:0% +where we'd like to show that it's +probably fast and uh make a statement + + align:start position:0% +probably fast and uh make a statement + + + align:start position:0% +probably fast and uh make a statement +about the expected + + align:start position:0% +about the expected + + + align:start position:0% +about the expected +runtime uh but we'll get to that uh by + + align:start position:0% +runtime uh but we'll get to that uh by + + + align:start position:0% +runtime uh but we'll get to that uh by +talking about a couple of other + + align:start position:0% +talking about a couple of other + + + align:start position:0% +talking about a couple of other +interesting variants and this will uh be + + align:start position:0% +interesting variants and this will uh be + + + align:start position:0% +interesting variants and this will uh be +uh elaborated on to some extent um in + + align:start position:0% +uh elaborated on to some extent um in + + + align:start position:0% +uh elaborated on to some extent um in +section + + align:start position:0% +section + + + align:start position:0% +section +tomorrow so before we get to variance of + + align:start position:0% +tomorrow so before we get to variance of + + + align:start position:0% +tomorrow so before we get to variance of +course let's try and set up the + + align:start position:0% +course let's try and set up the + + + align:start position:0% +course let's try and set up the +structure corresponding to quick + + align:start position:0% +structure corresponding to quick + + + align:start position:0% +structure corresponding to quick +sort and as always we have an N + + align:start position:0% +sort and as always we have an N + + + align:start position:0% +sort and as always we have an N +element + + align:start position:0% +element + + + align:start position:0% +element +array + + align:start position:0% +array + + + align:start position:0% +array +a you have + + align:start position:0% +a you have + + + align:start position:0% +a you have +divide that corresponds to + + align:start position:0% +divide that corresponds to + + + align:start position:0% +divide that corresponds to +picking a pivot + + align:start position:0% + + + + align:start position:0% + +element X in a and then we're going to a + + align:start position:0% +element X in a and then we're going to a + + + align:start position:0% +element X in a and then we're going to a +partition + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +array into a sub + + align:start position:0% + + + + align:start position:0% + +arrays and what we have here is uh this + + align:start position:0% +arrays and what we have here is uh this + + + align:start position:0% +arrays and what we have here is uh this +little picture should uh make things + + align:start position:0% +little picture should uh make things + + + align:start position:0% +little picture should uh make things +clear and you kind of saw this um in the + + align:start position:0% +clear and you kind of saw this um in the + + + align:start position:0% +clear and you kind of saw this um in the +median finding but here we go again + + align:start position:0% +median finding but here we go again + + + align:start position:0% +median finding but here we go again +let's assume all the array elements are + + align:start position:0% +let's assume all the array elements are + + + align:start position:0% +let's assume all the array elements are +unique um we have l e and G + + align:start position:0% +unique um we have l e and G + + + align:start position:0% +unique um we have l e and G +uh L is less than G is greater than and + + align:start position:0% +uh L is less than G is greater than and + + + align:start position:0% +uh L is less than G is greater than and +so your pivot element is going to break + + align:start position:0% +so your pivot element is going to break + + + align:start position:0% +so your pivot element is going to break +this array up into L and G where you got + + align:start position:0% +this array up into L and G where you got + + + align:start position:0% +this array up into L and G where you got +all the elements uh that are less on the + + align:start position:0% +all the elements uh that are less on the + + + align:start position:0% +all the elements uh that are less on the +left and all the elements that are + + align:start position:0% +left and all the elements that are + + + align:start position:0% +left and all the elements that are +greater on the right and you're going to + + align:start position:0% +greater on the right and you're going to + + + align:start position:0% +greater on the right and you're going to +recurse um on the + + align:start position:0% +recurse um on the + + + align:start position:0% +recurse um on the +LNG so recursively + + align:start position:0% + + + + align:start position:0% + +sort + + align:start position:0% + + + + align:start position:0% + +subarrays LNG + + align:start position:0% +subarrays LNG + + + align:start position:0% +subarrays LNG +um combine is + + align:start position:0% +um combine is + + + align:start position:0% +um combine is +Trivial or merge is Trivial because + + align:start position:0% +Trivial or merge is Trivial because + + + align:start position:0% +Trivial or merge is Trivial because +you've already broken things up thanks + + align:start position:0% +you've already broken things up thanks + + + align:start position:0% +you've already broken things up thanks +to the pivoting and uh you just + + align:start position:0% +to the pivoting and uh you just + + + align:start position:0% +to the pivoting and uh you just +concatenate those arrays and that's why + + align:start position:0% +concatenate those arrays and that's why + + + align:start position:0% +concatenate those arrays and that's why +you can do this in in place uh there's + + align:start position:0% +you can do this in in place uh there's + + + align:start position:0% +you can do this in in place uh there's +no issues uh you're really recursively + + align:start position:0% +no issues uh you're really recursively + + + align:start position:0% +no issues uh you're really recursively +sorting sub arrays you are moving things + + align:start position:0% +sorting sub arrays you are moving things + + + align:start position:0% +sorting sub arrays you are moving things +around a little bit uh when you do the + + align:start position:0% +around a little bit uh when you do the + + + align:start position:0% +around a little bit uh when you do the +partition obviously the initial array + + align:start position:0% +partition obviously the initial array + + + align:start position:0% +partition obviously the initial array +may have all the elements uh you may + + align:start position:0% +may have all the elements uh you may + + + align:start position:0% +may have all the elements uh you may +pick the pivot such that the pivot is + + align:start position:0% +pick the pivot such that the pivot is + + + align:start position:0% +pick the pivot such that the pivot is +all the way on on the on the right hand + + align:start position:0% +all the way on on the on the right hand + + + align:start position:0% +all the way on on the on the right hand +side in the sense that it's a large + + align:start position:0% +side in the sense that it's a large + + + align:start position:0% +side in the sense that it's a large +element uh that is not necessarily a + + align:start position:0% +element uh that is not necessarily a + + + align:start position:0% +element uh that is not necessarily a +good thing we'll talk about that but if + + align:start position:0% +good thing we'll talk about that but if + + + align:start position:0% +good thing we'll talk about that but if +you pick a an an interesting privot or a + + align:start position:0% +you pick a an an interesting privot or a + + + align:start position:0% +you pick a an an interesting privot or a +good pivot uh you're going to have to + + align:start position:0% +good pivot uh you're going to have to + + + align:start position:0% +good pivot uh you're going to have to +move the elements in the array U to the + + align:start position:0% +move the elements in the array U to the + + + align:start position:0% +move the elements in the array U to the +left of the pivot if they're less than + + align:start position:0% +left of the pivot if they're less than + + + align:start position:0% +left of the pivot if they're less than +the pivot and you got to move the + + align:start position:0% +the pivot and you got to move the + + + align:start position:0% +the pivot and you got to move the +elements to the right if they're to the + + align:start position:0% +elements to the right if they're to the + + + align:start position:0% +elements to the right if they're to the +right of the pivot um non-trivial piece + + align:start position:0% +right of the pivot um non-trivial piece + + + align:start position:0% +right of the pivot um non-trivial piece +of code not super complicated but you + + align:start position:0% +of code not super complicated but you + + + align:start position:0% +of code not super complicated but you +can look at U + + align:start position:0% +can look at U + + + align:start position:0% +can look at U +clrs at page 171 to look at in place uh + + align:start position:0% +clrs at page 171 to look at in place uh + + + align:start position:0% +clrs at page 171 to look at in place uh +partitioning uh where you don't have to + + align:start position:0% +partitioning uh where you don't have to + + + align:start position:0% +partitioning uh where you don't have to +use uh another order end space uh to + + align:start position:0% +use uh another order end space uh to + + + align:start position:0% +use uh another order end space uh to +move these elements around such that + + align:start position:0% +move these elements around such that + + + align:start position:0% +move these elements around such that +they look like that picture that I have + + align:start position:0% +they look like that picture that I have + + + align:start position:0% +they look like that picture that I have +up there starting from some random + + align:start position:0% +up there starting from some random + + + align:start position:0% +up there starting from some random +starting point right so you want to have + + align:start position:0% +starting point right so you want to have + + + align:start position:0% +starting point right so you want to have +your um uh the picture that you have + + align:start position:0% +your um uh the picture that you have + + + align:start position:0% +your um uh the picture that you have +here and you need to go from some well + + align:start position:0% +here and you need to go from some well + + + align:start position:0% +here and you need to go from some well +the very same array uh needs to and X is + + align:start position:0% +the very same array uh needs to and X is + + + align:start position:0% +the very same array uh needs to and X is +somewhere here and you know you got X+ + + align:start position:0% +somewhere here and you know you got X+ + + + align:start position:0% +somewhere here and you know you got X+ +one here and X plus xus one here for + + align:start position:0% +one here and X plus xus one here for + + + align:start position:0% +one here and X plus xus one here for +example uh you need to move those things + + align:start position:0% +example uh you need to move those things + + + align:start position:0% +example uh you need to move those things +around so they look like l e and G and U + + align:start position:0% +around so they look like l e and G and U + + + align:start position:0% +around so they look like l e and G and U +uh that's something that U that you can + + align:start position:0% +uh that's something that U that you can + + + align:start position:0% +uh that's something that U that you can +do in place and you can look at the code + + align:start position:0% +do in place and you can look at the code + + + align:start position:0% +do in place and you can look at the code +for that uh in clrs I won't I won't + + align:start position:0% +for that uh in clrs I won't I won't + + + align:start position:0% +for that uh in clrs I won't I won't +cover that here um so let's look at a + + align:start position:0% +cover that here um so let's look at a + + + align:start position:0% +cover that here um so let's look at a +bunch of different variants + + align:start position:0% +bunch of different variants + + + align:start position:0% +bunch of different variants +corresponding to quick sort um and + + align:start position:0% +corresponding to quick sort um and + + + align:start position:0% +corresponding to quick sort um and +there's some real simple ones each of + + align:start position:0% +there's some real simple ones each of + + + align:start position:0% +there's some real simple ones each of +these we can knock off with respect to U + + align:start position:0% +these we can knock off with respect to U + + + align:start position:0% +these we can knock off with respect to U +uh + + align:start position:0% +uh + + + align:start position:0% +uh +complexity uh and runtime uh fairly + + align:start position:0% +complexity uh and runtime uh fairly + + + align:start position:0% +complexity uh and runtime uh fairly +easily with with one exception that + + align:start position:0% +easily with with one exception that + + + align:start position:0% +easily with with one exception that +we'll spend some time on which is the + + align:start position:0% +we'll spend some time on which is the + + + align:start position:0% +we'll spend some time on which is the +Las Vegas uh quick sword but we'll call + + align:start position:0% +Las Vegas uh quick sword but we'll call + + + align:start position:0% +Las Vegas uh quick sword but we'll call +these different names let's talk about + + align:start position:0% +these different names let's talk about + + + align:start position:0% +these different names let's talk about +the basic quick sort which is also a + + align:start position:0% +the basic quick sort which is also a + + + align:start position:0% +the basic quick sort which is also a +useful algorithm that people use uh in + + align:start position:0% +useful algorithm that people use uh in + + + align:start position:0% +useful algorithm that people use uh in +practice and uh amazingly this algorithm + + align:start position:0% +practice and uh amazingly this algorithm + + + align:start position:0% +practice and uh amazingly this algorithm +uh is is simply something that says I'm + + align:start position:0% +uh is is simply something that says I'm + + + align:start position:0% +uh is is simply something that says I'm +just going to constantly pivot on either + + align:start position:0% +just going to constantly pivot on either + + + align:start position:0% +just going to constantly pivot on either +the first entry or the last entry so I'm + + align:start position:0% +the first entry or the last entry so I'm + + + align:start position:0% +the first entry or the last entry so I'm +going to pick my Pivot to be A1 and um + + align:start position:0% +going to pick my Pivot to be A1 and um + + + align:start position:0% +going to pick my Pivot to be A1 and um +when I pick my Pivot to be A1 it's a + + align:start position:0% +when I pick my Pivot to be A1 it's a + + + align:start position:0% +when I pick my Pivot to be A1 it's a +value that I'm talking about here x is a + + align:start position:0% +value that I'm talking about here x is a + + + align:start position:0% +value that I'm talking about here x is a +value it's not an index it's the A1 + + align:start position:0% +value it's not an index it's the A1 + + + align:start position:0% +value it's not an index it's the A1 +value maybe that's 75 then I'm going to + + align:start position:0% +value maybe that's 75 then I'm going to + + + align:start position:0% +value maybe that's 75 then I'm going to +create my L Matrix corresponding to this + + align:start position:0% +create my L Matrix corresponding to this + + + align:start position:0% +create my L Matrix corresponding to this +pivot where all the entries are strictly + + align:start position:0% +pivot where all the entries are strictly + + + align:start position:0% +pivot where all the entries are strictly +less than 75 and uh the G would be + + align:start position:0% +less than 75 and uh the G would be + + + align:start position:0% +less than 75 and uh the G would be +strictly greater than 75 and I could do + + align:start position:0% +strictly greater than 75 and I could do + + + align:start position:0% +strictly greater than 75 and I could do +that for A1 I could do that for a n so + + align:start position:0% +that for A1 I could do that for a n so + + + align:start position:0% +that for A1 I could do that for a n so +remember that the pivot is a + + align:start position:0% +remember that the pivot is a + + + align:start position:0% +remember that the pivot is a +value uh + + align:start position:0% +value uh + + + align:start position:0% +value uh +um uh now if I look at this I'm going to + + align:start position:0% +um uh now if I look at this I'm going to + + + align:start position:0% +um uh now if I look at this I'm going to +do the + + align:start position:0% + + + + align:start position:0% + +partition uh given X just like you saw + + align:start position:0% +partition uh given X just like you saw + + + align:start position:0% +partition uh given X just like you saw +there and this is going to be done in + + align:start position:0% +there and this is going to be done in + + + align:start position:0% +there and this is going to be done in +order end time it makes sense that + + align:start position:0% +order end time it makes sense that + + + align:start position:0% +order end time it makes sense that +you're going to look at every element + + align:start position:0% +you're going to look at every element + + + align:start position:0% +you're going to look at every element +and you're going to move it to an + + align:start position:0% +and you're going to move it to an + + + align:start position:0% +and you're going to move it to an +appropriate location to the left of X + + align:start position:0% +appropriate location to the left of X + + + align:start position:0% +appropriate location to the left of X +which is the E array or to the right and + + align:start position:0% +which is the E array or to the right and + + + align:start position:0% +which is the E array or to the right and +you do that that takes order end time + + align:start position:0% +you do that that takes order end time + + + align:start position:0% +you do that that takes order end time +and as I mention you can you can look at + + align:start position:0% +and as I mention you can you can look at + + + align:start position:0% +and as I mention you can you can look at +this to see uh how this is done um in + + align:start position:0% +this to see uh how this is done um in + + + align:start position:0% +this to see uh how this is done um in +place um so let's talk let's take a look + + align:start position:0% +place um so let's talk let's take a look + + + align:start position:0% +place um so let's talk let's take a look +at the analysis of uh of basic quick + + align:start position:0% +at the analysis of uh of basic quick + + + align:start position:0% +at the analysis of uh of basic quick +sort and what I'm interested in is of + + align:start position:0% +sort and what I'm interested in is of + + + align:start position:0% +sort and what I'm interested in is of +course is the worst case analysis and I + + align:start position:0% +course is the worst case analysis and I + + + align:start position:0% +course is the worst case analysis and I +asked this question I think uh before + + align:start position:0% +asked this question I think uh before + + + align:start position:0% +asked this question I think uh before +when we were doing median finding but um + + align:start position:0% +when we were doing median finding but um + + + align:start position:0% +when we were doing median finding but um +what is the worst case complexity of the + + align:start position:0% +what is the worst case complexity of the + + + align:start position:0% +what is the worst case complexity of the +basic quick sort algorithm that chooses + + align:start position:0% +basic quick sort algorithm that chooses + + + align:start position:0% +basic quick sort algorithm that chooses +the pivot as + + align:start position:0% +the pivot as + + + align:start position:0% +the pivot as +A1 what is the + + align:start position:0% +A1 what is the + + + align:start position:0% +A1 what is the +complexity order and square right it's + + align:start position:0% +complexity order and square right it's + + + align:start position:0% +complexity order and square right it's +order n square and the reason for that + + align:start position:0% +order n square and the reason for that + + + align:start position:0% +order n square and the reason for that +is that um you may have an array that is + + align:start position:0% +is that um you may have an array that is + + + align:start position:0% +is that um you may have an array that is +uh uh sorted uh or reverse sorted you + + align:start position:0% +uh uh sorted uh or reverse sorted you + + + align:start position:0% +uh uh sorted uh or reverse sorted you +know depending on whether you're picking + + align:start position:0% +know depending on whether you're picking + + + align:start position:0% +know depending on whether you're picking +A1 or a n you can have a worst case + + align:start position:0% +A1 or a n you can have a worst case + + + align:start position:0% +A1 or a n you can have a worst case +situation where one side + + align:start position:0% +situation where one side + + + align:start position:0% +situation where one side +uh L or G has n minus one + + align:start position:0% +uh L or G has n minus one + + + align:start position:0% +uh L or G has n minus one +elements and the other uh has zero + + align:start position:0% +elements and the other uh has zero + + + align:start position:0% +elements and the other uh has zero +elements um and so if you look at our + + align:start position:0% +elements um and so if you look at our + + + align:start position:0% +elements um and so if you look at our +recurrence associated with this you + + align:start position:0% +recurrence associated with this you + + + align:start position:0% +recurrence associated with this you +could have TN which is t 0 + TN + + align:start position:0% +could have TN which is t 0 + TN + + + align:start position:0% +could have TN which is t 0 + TN +minus1 plus Theta + + align:start position:0% +minus1 plus Theta + + + align:start position:0% +minus1 plus Theta +n right and why do I have a Theta n here + + align:start position:0% +n right and why do I have a Theta n here + + + align:start position:0% +n right and why do I have a Theta n here +well remember that I I still have to do + + align:start position:0% +well remember that I I still have to do + + + align:start position:0% +well remember that I I still have to do +this divide step or this partition step + + align:start position:0% +this divide step or this partition step + + + align:start position:0% +this divide step or this partition step +um in order to compute + + align:start position:0% +um in order to compute + + + align:start position:0% +um in order to compute +this uh unbalanced array so I do have to + + align:start position:0% +this uh unbalanced array so I do have to + + + align:start position:0% +this uh unbalanced array so I do have to +look at each of these elements and do + + align:start position:0% +look at each of these elements and do + + + align:start position:0% +look at each of these elements and do +the comparison uh and maybe you know I I + + align:start position:0% +the comparison uh and maybe you know I I + + + align:start position:0% +the comparison uh and maybe you know I I +don't actually have to move them but I + + align:start position:0% +don't actually have to move them but I + + + align:start position:0% +don't actually have to move them but I +have to do the comparison with the with + + align:start position:0% +have to do the comparison with the with + + + align:start position:0% +have to do the comparison with the with +the A1 which is the X pivot and uh + + align:start position:0% +the A1 which is the X pivot and uh + + + align:start position:0% +the A1 which is the X pivot and uh +that's going to do the uh and in some + + align:start position:0% +that's going to do the uh and in some + + + align:start position:0% +that's going to do the uh and in some +cases if I'm if I'm doing the wrong + + align:start position:0% +cases if I'm if I'm doing the wrong + + + align:start position:0% +cases if I'm if I'm doing the wrong +thing reverse sorted I also have to do + + align:start position:0% +thing reverse sorted I also have to do + + + align:start position:0% +thing reverse sorted I also have to do +the move either way I have a Theta n + + align:start position:0% +the move either way I have a Theta n + + + align:start position:0% +the move either way I have a Theta n +complexity associated with um The Divide + + align:start position:0% +complexity associated with um The Divide + + + align:start position:0% +complexity associated with um The Divide +step so if you go off and you look at + + align:start position:0% +step so if you go off and you look at + + + align:start position:0% +step so if you go off and you look at +what happens with um + + align:start position:0% +what happens with um + + + align:start position:0% +what happens with um +uh with this well you got uh + + align:start position:0% +uh with this well you got uh + + + align:start position:0% +uh with this well you got uh +TN = tnus 1 + Theta n which ends up with + + align:start position:0% +TN = tnus 1 + Theta n which ends up with + + + align:start position:0% +TN = tnus 1 + Theta n which ends up with +Theta n Square complexity so I hand + + align:start position:0% +Theta n Square complexity so I hand + + + align:start position:0% +Theta n Square complexity so I hand +waved a little bit you know two weeks + + align:start position:0% +waved a little bit you know two weeks + + + align:start position:0% +waved a little bit you know two weeks +ago uh for a similar analysis but you + + align:start position:0% +ago uh for a similar analysis but you + + + align:start position:0% +ago uh for a similar analysis but you +can kind of look at it a little more uh + + align:start position:0% +can kind of look at it a little more uh + + + align:start position:0% +can kind of look at it a little more uh +precisely here by writing the actual + + align:start position:0% +precisely here by writing the actual + + + align:start position:0% +precisely here by writing the actual +recurrence out and you see that you get + + align:start position:0% +recurrence out and you see that you get + + + align:start position:0% +recurrence out and you see that you get +the recurrence tnal tnus 1 plus Theta n + + align:start position:0% +the recurrence tnal tnus 1 plus Theta n + + + align:start position:0% +the recurrence tnal tnus 1 plus Theta n +which is a an N Square uh result or the + + align:start position:0% +which is a an N Square uh result or the + + + align:start position:0% +which is a an N Square uh result or the +the solution is n Square okay so basic + + align:start position:0% +the solution is n Square okay so basic + + + align:start position:0% +the solution is n Square okay so basic +quick sword looks bad it's got a worst + + align:start position:0% +quick sword looks bad it's got a worst + + + align:start position:0% +quick sword looks bad it's got a worst +case complexity of theta n Square uh it + + align:start position:0% +case complexity of theta n Square uh it + + + align:start position:0% +case complexity of theta n Square uh it +works well on random inputs in practice + + align:start position:0% +works well on random inputs in practice + + + align:start position:0% +works well on random inputs in practice +and it turns out that uh it's a fashion + + align:start position:0% +and it turns out that uh it's a fashion + + + align:start position:0% +and it turns out that uh it's a fashion +of algorithm partly because it's in + + align:start position:0% +of algorithm partly because it's in + + + align:start position:0% +of algorithm partly because it's in +place and it's easy to code that what + + align:start position:0% +place and it's easy to code that what + + + align:start position:0% +place and it's easy to code that what +people do is uh uh they take their + + align:start position:0% +people do is uh uh they take their + + + align:start position:0% +people do is uh uh they take their +inputs and they shuffle them uh they + + align:start position:0% +inputs and they shuffle them uh they + + + align:start position:0% +inputs and they shuffle them uh they +just kind of you might get a bad input + + align:start position:0% +just kind of you might get a bad input + + + align:start position:0% +just kind of you might get a bad input +and it might take you a long time to run + + align:start position:0% +and it might take you a long time to run + + + align:start position:0% +and it might take you a long time to run +but if you take an input and you Shuffle + + align:start position:0% +but if you take an input and you Shuffle + + + align:start position:0% +but if you take an input and you Shuffle +it and you do that in Theta n time uh + + align:start position:0% +it and you do that in Theta n time uh + + + align:start position:0% +it and you do that in Theta n time uh +you just move things around and + + align:start position:0% +you just move things around and + + + align:start position:0% +you just move things around and +randomize the input then effectively you + + align:start position:0% +randomize the input then effectively you + + + align:start position:0% +randomize the input then effectively you +have a random input and this thing uh + + align:start position:0% +have a random input and this thing uh + + + align:start position:0% +have a random input and this thing uh +works pretty well in practice right now + + align:start position:0% +works pretty well in practice right now + + + align:start position:0% +works pretty well in practice right now +what is pretty well well we're going to + + align:start position:0% +what is pretty well well we're going to + + + align:start position:0% +what is pretty well well we're going to +do an analysis that is going to um not + + align:start position:0% +do an analysis that is going to um not + + + align:start position:0% +do an analysis that is going to um not +be exactly the analysis that you'd have + + align:start position:0% +be exactly the analysis that you'd have + + + align:start position:0% +be exactly the analysis that you'd have +to do on basic quick sort with on on + + align:start position:0% +to do on basic quick sort with on on + + + align:start position:0% +to do on basic quick sort with on on +random inputs but essentially you can + + align:start position:0% +random inputs but essentially you can + + + align:start position:0% +random inputs but essentially you can +say that uh uh basic quick sort on + + align:start position:0% +say that uh uh basic quick sort on + + + align:start position:0% +say that uh uh basic quick sort on +random inputs is going to run in um + + align:start position:0% +random inputs is going to run in um + + + align:start position:0% +random inputs is going to run in um +expected Theta n log n time okay uh it + + align:start position:0% +expected Theta n log n time okay uh it + + + align:start position:0% +expected Theta n log n time okay uh it +it's uh uh it's something that you'll + + align:start position:0% +it's uh uh it's something that you'll + + + align:start position:0% +it's uh uh it's something that you'll +see a little bit of how to do that today + + align:start position:0% +see a little bit of how to do that today + + + align:start position:0% +see a little bit of how to do that today +and and in in section perhaps for median + + align:start position:0% +and and in in section perhaps for median + + + align:start position:0% +and and in in section perhaps for median +finding in section tomorrow uh but + + align:start position:0% +finding in section tomorrow uh but + + + align:start position:0% +finding in section tomorrow uh but +that's uh all I wanted to say about + + align:start position:0% +that's uh all I wanted to say about + + + align:start position:0% +that's uh all I wanted to say about +basic quick sort um it's a practical + + align:start position:0% +basic quick sort um it's a practical + + + align:start position:0% +basic quick sort um it's a practical +algorithm um it does require a little + + align:start position:0% +algorithm um it does require a little + + + align:start position:0% +algorithm um it does require a little +bit of shuffling up at the beginning and + + align:start position:0% +bit of shuffling up at the beginning and + + + align:start position:0% +bit of shuffling up at the beginning and +then you can simply use the pivot A1 and + + align:start position:0% +then you can simply use the pivot A1 and + + + align:start position:0% +then you can simply use the pivot A1 and +because you've done the shuffle uh + + align:start position:0% +because you've done the shuffle uh + + + align:start position:0% +because you've done the shuffle uh +generally you get balanced partitions + + align:start position:0% +generally you get balanced partitions + + + align:start position:0% +generally you get balanced partitions +the L and GS look balanced and you don't + + align:start position:0% +the L and GS look balanced and you don't + + + align:start position:0% +the L and GS look balanced and you don't +end up with Theta n square if you have + + align:start position:0% +end up with Theta n square if you have + + + align:start position:0% +end up with Theta n square if you have +any sort of balance associated with the + + align:start position:0% +any sort of balance associated with the + + + align:start position:0% +any sort of balance associated with the +two partitions L and G you're going to + + align:start position:0% +two partitions L and G you're going to + + + align:start position:0% +two partitions L and G you're going to +get a nice divide and concer which is + + align:start position:0% +get a nice divide and concer which is + + + align:start position:0% +get a nice divide and concer which is +going to give you your Theta n log n + + align:start position:0% +going to give you your Theta n log n + + + align:start position:0% +going to give you your Theta n log n +okay so so that's a basic quick sort um + + align:start position:0% +okay so so that's a basic quick sort um + + + align:start position:0% +okay so so that's a basic quick sort um +there's uh another way to do this and so + + align:start position:0% +there's uh another way to do this and so + + + align:start position:0% +there's uh another way to do this and so +this is a question for you guys suppose + + align:start position:0% +this is a question for you guys suppose + + + align:start position:0% +this is a question for you guys suppose +I wanted to use the quick sort strategy + + align:start position:0% +I wanted to use the quick sort strategy + + + align:start position:0% +I wanted to use the quick sort strategy +and get a uh a worst case Theta n log n + + align:start position:0% +and get a uh a worst case Theta n log n + + + align:start position:0% +and get a uh a worst case Theta n log n +through an + + align:start position:0% +through an + + + align:start position:0% +through an +intelligent pivot selection so I want to + + align:start position:0% +intelligent pivot selection so I want to + + + align:start position:0% +intelligent pivot selection so I want to +do a pivot + + align:start position:0% +do a pivot + + + align:start position:0% +do a pivot +selection + + align:start position:0% + + + + align:start position:0% + +intelligently okay so um how would I get + + align:start position:0% +intelligently okay so um how would I get + + + align:start position:0% +intelligently okay so um how would I get +under the structure of quick sort that + + align:start position:0% +under the structure of quick sort that + + + align:start position:0% +under the structure of quick sort that +you see up there uh on the left there + + align:start position:0% +you see up there uh on the left there + + + align:start position:0% +you see up there uh on the left there +how would I select a pivot such that I + + align:start position:0% +how would I select a pivot such that I + + + align:start position:0% +how would I select a pivot such that I +get worst case Theta n log n + + align:start position:0% + + + + align:start position:0% + +complexity go ahead linear median find + + align:start position:0% +complexity go ahead linear median find + + + align:start position:0% +complexity go ahead linear median find +linear median finding Perfect that's + + align:start position:0% +linear median finding Perfect that's + + + align:start position:0% +linear median finding Perfect that's +exactly right + + align:start position:0% +exactly right + + + align:start position:0% +exactly right +um there was a gentleman at the back who + + align:start position:0% +um there was a gentleman at the back who + + + align:start position:0% +um there was a gentleman at the back who +raised his hand and I decided I'd + + align:start position:0% +raised his hand and I decided I'd + + + align:start position:0% +raised his hand and I decided I'd +chicken + + align:start position:0% +chicken + + + align:start position:0% +chicken +out um I think one time to the back of + + align:start position:0% +out um I think one time to the back of + + + align:start position:0% +out um I think one time to the back of +the room is enough for a day right you + + align:start position:0% +the room is enough for a day right you + + + align:start position:0% +the room is enough for a day right you +can you can come have a frisbee left + + align:start position:0% +can you can come have a frisbee left + + + align:start position:0% +can you can come have a frisbee left +hopefully you can get one right um so U + + align:start position:0% +hopefully you can get one right um so U + + + align:start position:0% +hopefully you can get one right um so U +the intelligent pivot selection + + align:start position:0% +the intelligent pivot selection + + + align:start position:0% +the intelligent pivot selection +algorithm is the median finding + + align:start position:0% +algorithm is the median finding + + + align:start position:0% +algorithm is the median finding +algorithm because that's going to + + align:start position:0% +algorithm because that's going to + + + align:start position:0% +algorithm because that's going to +guarantee me that I'm going to get + + align:start position:0% +guarantee me that I'm going to get + + + align:start position:0% +guarantee me that I'm going to get +balanced partitions if you tell me that + + align:start position:0% +balanced partitions if you tell me that + + + align:start position:0% +balanced partitions if you tell me that +A1 and remember we're talking medians + + align:start position:0% +A1 and remember we're talking medians + + + align:start position:0% +A1 and remember we're talking medians +are values right so don't get confused + + align:start position:0% +are values right so don't get confused + + + align:start position:0% +are values right so don't get confused +with indices when I say something is a + + align:start position:0% +with indices when I say something is a + + + align:start position:0% +with indices when I say something is a +median I'm talking about the value that + + align:start position:0% +median I'm talking about the value that + + + align:start position:0% +median I'm talking about the value that +all of given its value that all these + + align:start position:0% +all of given its value that all these + + + align:start position:0% +all of given its value that all these +other n /2 uh values that are less than + + align:start position:0% +other n /2 uh values that are less than + + + align:start position:0% +other n /2 uh values that are less than +it uh uh roughly speaking and N over two + + align:start position:0% +it uh uh roughly speaking and N over two + + + align:start position:0% +it uh uh roughly speaking and N over two +values that are greater than it uh uh + + align:start position:0% +values that are greater than it uh uh + + + align:start position:0% +values that are greater than it uh uh +and so A1 I have no idea whether it's + + align:start position:0% +and so A1 I have no idea whether it's + + + align:start position:0% +and so A1 I have no idea whether it's +large or small and uh so I couldn't say + + align:start position:0% +large or small and uh so I couldn't say + + + align:start position:0% +large or small and uh so I couldn't say +much about it but if I want to be worst + + align:start position:0% +much about it but if I want to be worst + + + align:start position:0% +much about it but if I want to be worst +case and I want to guarantee that I I + + align:start position:0% +case and I want to guarantee that I I + + + align:start position:0% +case and I want to guarantee that I I +have balanced partitions I can choose + + align:start position:0% +have balanced partitions I can choose + + + align:start position:0% +have balanced partitions I can choose +the median and if I choose the median + + align:start position:0% +the median and if I choose the median + + + align:start position:0% +the median and if I choose the median +every time I'm going to get perfectly + + align:start position:0% +every time I'm going to get perfectly + + + align:start position:0% +every time I'm going to get perfectly +balanced partitions right they're going + + align:start position:0% +balanced partitions right they're going + + + align:start position:0% +balanced partitions right they're going +to be half on the left and half on the + + align:start position:0% +to be half on the left and half on the + + + align:start position:0% +to be half on the left and half on the +right um so and we do know a way + + align:start position:0% +right um so and we do know a way + + + align:start position:0% +right um so and we do know a way +of getting balanced partitions we can + + align:start position:0% +of getting balanced partitions we can + + + align:start position:0% +of getting balanced partitions we can +guarantee + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +balanced + + align:start position:0% +balanced + + + align:start position:0% +balanced +LNG using median + + align:start position:0% + + + + align:start position:0% + +selection that runs in Theta n time and + + align:start position:0% +selection that runs in Theta n time and + + + align:start position:0% +selection that runs in Theta n time and +we showed that a couple of weeks + + align:start position:0% +we showed that a couple of weeks + + + align:start position:0% +we showed that a couple of weeks +ago now that median selection algorithm + + align:start position:0% +ago now that median selection algorithm + + + align:start position:0% +ago now that median selection algorithm +was non-trivial okay uh it uh it it had + + align:start position:0% +was non-trivial okay uh it uh it it had + + + align:start position:0% +was non-trivial okay uh it uh it it had +this weird thing where you broke things + + align:start position:0% +this weird thing where you broke things + + + align:start position:0% +this weird thing where you broke things +up into + + align:start position:0% +up into + + + align:start position:0% +up into +five arrays of size subarrays of size + + align:start position:0% +five arrays of size subarrays of size + + + align:start position:0% +five arrays of size subarrays of size +five and you found a median of medians + + align:start position:0% +five and you found a median of medians + + + align:start position:0% +five and you found a median of medians +etc etc but we argued that the whole + + align:start position:0% +etc etc but we argued that the whole + + + align:start position:0% +etc etc but we argued that the whole +thing ran in Theta n time which is + + align:start position:0% +thing ran in Theta n time which is + + + align:start position:0% +thing ran in Theta n time which is +important and so now if you look at uh + + align:start position:0% +important and so now if you look at uh + + + align:start position:0% +important and so now if you look at uh +what happens with quick sort and if I + + align:start position:0% +what happens with quick sort and if I + + + align:start position:0% +what happens with quick sort and if I +write the recurrence for quick sort + + align:start position:0% +write the recurrence for quick sort + + + align:start position:0% +write the recurrence for quick sort +thanks to selecting a median I + + align:start position:0% +thanks to selecting a median I + + + align:start position:0% +thanks to selecting a median I +effectively have balanced partitions so + + align:start position:0% +effectively have balanced partitions so + + + align:start position:0% +effectively have balanced partitions so +I have 2 TN /2 this is + + align:start position:0% +I have 2 TN /2 this is + + + align:start position:0% +I have 2 TN /2 this is +thanks + + align:start position:0% +thanks + + + align:start position:0% +thanks +to the median pivot median based + + align:start position:0% +to the median pivot median based + + + align:start position:0% +to the median pivot median based +pivoting that's + + align:start position:0% +pivoting that's + + + align:start position:0% +pivoting that's +important otherwise it won't work and + + align:start position:0% +important otherwise it won't work and + + + align:start position:0% +important otherwise it won't work and +then uh just to be very clear here um I + + align:start position:0% +then uh just to be very clear here um I + + + align:start position:0% +then uh just to be very clear here um I +got two Theta n terms okay uh the first + + align:start position:0% +got two Theta n terms okay uh the first + + + align:start position:0% +got two Theta n terms okay uh the first +Theta n term is the + + align:start position:0% +Theta n term is the + + + align:start position:0% +Theta n term is the +recursive median selection + + align:start position:0% + + + + align:start position:0% + +um and then the second Thea end term is + + align:start position:0% +um and then the second Thea end term is + + + align:start position:0% +um and then the second Thea end term is +of course the divide or the + + align:start position:0% + + + + align:start position:0% + +partition but it's important to to + + align:start position:0% +partition but it's important to to + + + align:start position:0% +partition but it's important to to +realize that now I have a lot of work in + + align:start position:0% +realize that now I have a lot of work in + + + align:start position:0% +realize that now I have a lot of work in +the divide a lot of work I have to do an + + align:start position:0% +the divide a lot of work I have to do an + + + align:start position:0% +the divide a lot of work I have to do an +intelligence selection using this + + align:start position:0% +intelligence selection using this + + + align:start position:0% +intelligence selection using this +recursive median finding algorithm and I + + align:start position:0% +recursive median finding algorithm and I + + + align:start position:0% +recursive median finding algorithm and I +also have to do the moves comparing and + + align:start position:0% +also have to do the moves comparing and + + + align:start position:0% +also have to do the moves comparing and +then generate the L and the g arrays + + align:start position:0% +then generate the L and the g arrays + + + align:start position:0% +then generate the L and the g arrays +okay so those are the two Theta NS they + + align:start position:0% +okay so those are the two Theta NS they + + + align:start position:0% +okay so those are the two Theta NS they +obviously Theta n but but I wanted to + + align:start position:0% +obviously Theta n but but I wanted to + + + align:start position:0% +obviously Theta n but but I wanted to +make it clear that there's two things + + align:start position:0% +make it clear that there's two things + + + align:start position:0% +make it clear that there's two things +going on here right and we all know that + + align:start position:0% +going on here right and we all know that + + + align:start position:0% +going on here right and we all know that +that is Theta n log n worst case all + + align:start position:0% +that is Theta n log n worst case all + + + align:start position:0% +that is Theta n log n worst case all +right so there is a way of using the + + align:start position:0% +right so there is a way of using the + + + align:start position:0% +right so there is a way of using the +quick sort structure template and + + align:start position:0% +quick sort structure template and + + + align:start position:0% +quick sort structure template and +getting a Theta n log n worst case + + align:start position:0% +getting a Theta n log n worst case + + + align:start position:0% +getting a Theta n log n worst case +algorithm which doesn't work in practice + + align:start position:0% +algorithm which doesn't work in practice + + + align:start position:0% +algorithm which doesn't work in practice +uh because it's just too complicated + + align:start position:0% +uh because it's just too complicated + + + align:start position:0% +uh because it's just too complicated +right you know what's going on here is + + align:start position:0% +right you know what's going on here is + + + align:start position:0% +right you know what's going on here is +uh you have a recursion at every level + + align:start position:0% +uh you have a recursion at every level + + + align:start position:0% +uh you have a recursion at every level +of recursion you're going uh you know + + align:start position:0% +of recursion you're going uh you know + + + align:start position:0% +of recursion you're going uh you know +calling another recursive algorithm to + + align:start position:0% +calling another recursive algorithm to + + + align:start position:0% +calling another recursive algorithm to +find the median right so if you go code + + align:start position:0% +find the median right so if you go code + + + align:start position:0% +find the median right so if you go code +this up um it loses to merge sword uh in + + align:start position:0% +this up um it loses to merge sword uh in + + + align:start position:0% +this up um it loses to merge sword uh in +practice you can do all of this in place + + align:start position:0% +practice you can do all of this in place + + + align:start position:0% +practice you can do all of this in place +but because of all these recursive calls + + align:start position:0% +but because of all these recursive calls + + + align:start position:0% +but because of all these recursive calls +it doesn't work well in practice right + + align:start position:0% +it doesn't work well in practice right + + + align:start position:0% +it doesn't work well in practice right +but it's good to know and so this is an + + align:start position:0% +but it's good to know and so this is an + + + align:start position:0% +but it's good to know and so this is an +good example I think uh which we don't + + align:start position:0% +good example I think uh which we don't + + + align:start position:0% +good example I think uh which we don't +do a lot off in 046 where you get a + + align:start position:0% +do a lot off in 046 where you get a + + + align:start position:0% +do a lot off in 046 where you get a +sense of the difference between asmic + + align:start position:0% +sense of the difference between asmic + + + align:start position:0% +sense of the difference between asmic +complexity and performance so + + align:start position:0% +complexity and performance so + + + align:start position:0% +complexity and performance so +while uh the median finding algorithm + + align:start position:0% +while uh the median finding algorithm + + + align:start position:0% +while uh the median finding algorithm +has better asmic complexity where SK + + align:start position:0% +has better asmic complexity where SK + + + align:start position:0% +has better asmic complexity where SK +case it really loses in practice to the + + align:start position:0% +case it really loses in practice to the + + + align:start position:0% +case it really loses in practice to the +basic quick sort which essentially is a + + align:start position:0% +basic quick sort which essentially is a + + + align:start position:0% +basic quick sort which essentially is a +bit of a hack where you take an input + + align:start position:0% +bit of a hack where you take an input + + + align:start position:0% +bit of a hack where you take an input +and you randomize the input and you you + + align:start position:0% +and you randomize the input and you you + + + align:start position:0% +and you randomize the input and you you +run it with A1 as the pivot or a n as + + align:start position:0% +run it with A1 as the pivot or a n as + + + align:start position:0% +run it with A1 as the pivot or a n as +the pivot right so um is + + align:start position:0% +the pivot right so um is + + + align:start position:0% +the pivot right so um is +there is there a different way that um + + align:start position:0% +there is there a different way that um + + + align:start position:0% +there is there a different way that um +you can actually get to a Las Vegas + + align:start position:0% +you can actually get to a Las Vegas + + + align:start position:0% +you can actually get to a Las Vegas +algorithm and it turns out randomized + + align:start position:0% +algorithm and it turns out randomized + + + align:start position:0% +algorithm and it turns out randomized +quick sort is something that uh uh you + + align:start position:0% +quick sort is something that uh uh you + + + align:start position:0% +quick sort is something that uh uh you +can you can you can build and use which + + align:start position:0% +can you can you can build and use which + + + align:start position:0% +can you can you can build and use which +is a bit different from basic quick + + align:start position:0% +is a bit different from basic quick + + + align:start position:0% +is a bit different from basic quick +swort uh and certainly different from + + align:start position:0% +swort uh and certainly different from + + + align:start position:0% +swort uh and certainly different from +median finding but it kind of has a + + align:start position:0% +median finding but it kind of has a + + + align:start position:0% +median finding but it kind of has a +little bit in common with them and it's + + align:start position:0% +little bit in common with them and it's + + + align:start position:0% +little bit in common with them and it's +our uh example of a vas + + align:start position:0% +our uh example of a vas + + + align:start position:0% +our uh example of a vas +algorithm so what happens at randomized + + align:start position:0% +algorithm so what happens at randomized + + + align:start position:0% +algorithm so what happens at randomized +quick sort um X is + + align:start position:0% +quick sort um X is + + + align:start position:0% +quick sort um X is +chosen at + + align:start position:0% +chosen at + + + align:start position:0% +chosen at +random from the array a so you're not + + align:start position:0% +random from the array a so you're not + + + align:start position:0% +random from the array a so you're not +choosing A1 or a n you might just flip + + align:start position:0% +choosing A1 or a n you might just flip + + + align:start position:0% +choosing A1 or a n you might just flip +uh uh well effectively a an n-sided Dot + + align:start position:0% +uh uh well effectively a an n-sided Dot + + + align:start position:0% +uh uh well effectively a an n-sided Dot +and uh uh pick a particular index and + + align:start position:0% +and uh uh pick a particular index and + + + align:start position:0% +and uh uh pick a particular index and +then go grab the the pivot corresponding + + align:start position:0% +then go grab the the pivot corresponding + + + align:start position:0% +then go grab the the pivot corresponding +to the value at that index okay I mean + + align:start position:0% +to the value at that index okay I mean + + + align:start position:0% +to the value at that index okay I mean +you're not going to randomize over + + align:start position:0% +you're not going to randomize over + + + align:start position:0% +you're not going to randomize over +values you don't know what these values + + align:start position:0% +values you don't know what these values + + + align:start position:0% +values you don't know what these values +are but you can uh pick an a random + + align:start position:0% +are but you can uh pick an a random + + + align:start position:0% +are but you can uh pick an a random +index and then grab the pivot based on + + align:start position:0% +index and then grab the pivot based on + + + align:start position:0% +index and then grab the pivot based on +the value at that index um and so at + + align:start position:0% +the value at that index um and so at + + + align:start position:0% +the value at that index um and so at +each recursion a random choice is made + + align:start position:0% +each recursion a random choice is made + + + align:start position:0% +each recursion a random choice is made +and um the expected time so now we're + + align:start position:0% +and um the expected time so now we're + + + align:start position:0% +and um the expected time so now we're +saying something different we're making + + align:start position:0% +saying something different we're making + + + align:start position:0% +saying something different we're making +um a a stronger theoretic statement that + + align:start position:0% +um a a stronger theoretic statement that + + + align:start position:0% +um a a stronger theoretic statement that +the expected time when you do + + align:start position:0% +the expected time when you do + + + align:start position:0% +the expected time when you do +this um for all + + align:start position:0% +this um for all + + + align:start position:0% +this um for all +inputs arrays a is order order n log n + + align:start position:0% +inputs arrays a is order order n log n + + + align:start position:0% +inputs arrays a is order order n log n +and so now this is not worst case time + + align:start position:0% +and so now this is not worst case time + + + align:start position:0% +and so now this is not worst case time +it's expected time right so this is + + align:start position:0% +it's expected time right so this is + + + align:start position:0% +it's expected time right so this is +going to be our analysis um uh in the + + align:start position:0% +going to be our analysis um uh in the + + + align:start position:0% +going to be our analysis um uh in the +last few minutes here to um analyze not + + align:start position:0% +last few minutes here to um analyze not + + + align:start position:0% +last few minutes here to um analyze not +randomized quick sort uh but a slight + + align:start position:0% +randomized quick sort uh but a slight + + + align:start position:0% +randomized quick sort uh but a slight +variant of randomized quick sort uh that + + align:start position:0% +variant of randomized quick sort uh that + + + align:start position:0% +variant of randomized quick sort uh that +is going to show you that you can run uh + + align:start position:0% +is going to show you that you can run uh + + + align:start position:0% +is going to show you that you can run uh +randomized quick sort and this variant + + align:start position:0% +randomized quick sort and this variant + + + align:start position:0% +randomized quick sort and this variant +in order n log end time right so um not + + align:start position:0% +in order n log end time right so um not + + + align:start position:0% +in order n log end time right so um not +quite sure what's going to happen in + + align:start position:0% +quite sure what's going to happen in + + + align:start position:0% +quite sure what's going to happen in +section tomorrow but the full + + align:start position:0% +section tomorrow but the full + + + align:start position:0% +section tomorrow but the full +analysis um is in the book um you should + + align:start position:0% +analysis um is in the book um you should + + + align:start position:0% +analysis um is in the book um you should +you you should read it uh it's as you + + align:start position:0% +you you should read it uh it's as you + + + align:start position:0% +you you should read it uh it's as you +can see it's a it's a couple of pages uh + + align:start position:0% +can see it's a it's a couple of pages uh + + + align:start position:0% +can see it's a it's a couple of pages uh +that includes the description of quick + + align:start position:0% +that includes the description of quick + + + align:start position:0% +that includes the description of quick +sort uh that I have already uh but what + + align:start position:0% +sort uh that I have already uh but what + + + align:start position:0% +sort uh that I have already uh but what +we're going to do here is analyze uh s a + + align:start position:0% +we're going to do here is analyze uh s a + + + align:start position:0% +we're going to do here is analyze uh s a +variant quick sort which is a little bit + + align:start position:0% +variant quick sort which is a little bit + + + align:start position:0% +variant quick sort which is a little bit +easier to analyze and it gives you the + + align:start position:0% +easier to analyze and it gives you the + + + align:start position:0% +easier to analyze and it gives you the +sense of uh why in fact uh the + + align:start position:0% +sense of uh why in fact uh the + + + align:start position:0% +sense of uh why in fact uh the +randomized quick sort is going to run in + + align:start position:0% +randomized quick sort is going to run in + + + align:start position:0% +randomized quick sort is going to run in +expected time and this analysis is easy + + align:start position:0% +expected time and this analysis is easy + + + align:start position:0% +expected time and this analysis is easy +to do in a in in a few minutes so uh + + align:start position:0% +to do in a in in a few minutes so uh + + + align:start position:0% +to do in a in in a few minutes so uh +we'll do that and tomorrow you'll see + + align:start position:0% +we'll do that and tomorrow you'll see + + + align:start position:0% +we'll do that and tomorrow you'll see +either a median finding analysis that's + + align:start position:0% +either a median finding analysis that's + + + align:start position:0% +either a median finding analysis that's +similar to that analysis in + + align:start position:0% +similar to that analysis in + + + align:start position:0% +similar to that analysis in +clrs or precisely that analysis + + align:start position:0% +clrs or precisely that analysis + + + align:start position:0% +clrs or precisely that analysis +depending on what uh your ta want to do + + align:start position:0% +depending on what uh your ta want to do + + + align:start position:0% +depending on what uh your ta want to do +so this particular variant we're going + + align:start position:0% +so this particular variant we're going + + + align:start position:0% +so this particular variant we're going +to call paranoid quick sort right and so + + align:start position:0% +to call paranoid quick sort right and so + + + align:start position:0% +to call paranoid quick sort right and so +this quick sort um is U is paranoid in + + align:start position:0% +this quick sort um is U is paranoid in + + + align:start position:0% +this quick sort um is U is paranoid in +the sense that um it's going to be + + align:start position:0% +the sense that um it's going to be + + + align:start position:0% +the sense that um it's going to be +afraid of getting unbalanced partitions + + align:start position:0% +afraid of getting unbalanced partitions + + + align:start position:0% +afraid of getting unbalanced partitions +and it's going to keep trying to get + + align:start position:0% +and it's going to keep trying to get + + + align:start position:0% +and it's going to keep trying to get +balanced partitions so it's going to uh + + align:start position:0% +balanced partitions so it's going to uh + + + align:start position:0% +balanced partitions so it's going to uh +try to get a balanced partition it's + + align:start position:0% +try to get a balanced partition it's + + + align:start position:0% +try to get a balanced partition it's +going to check and then if it fails it's + + align:start position:0% +going to check and then if it fails it's + + + align:start position:0% +going to check and then if it fails it's +going to try again and so at the end of + + align:start position:0% +going to try again and so at the end of + + + align:start position:0% +going to try again and so at the end of +it I there's obviously a an expect + + align:start position:0% +it I there's obviously a an expect + + + align:start position:0% +it I there's obviously a an expect +expectation associated with the number + + align:start position:0% +expectation associated with the number + + + align:start position:0% +expectation associated with the number +of tries that you need in order to get a + + align:start position:0% +of tries that you need in order to get a + + + align:start position:0% +of tries that you need in order to get a +balanced partition but it just sort of + + align:start position:0% +balanced partition but it just sort of + + + align:start position:0% +balanced partition but it just sort of +flips the problem on its head and says + + align:start position:0% +flips the problem on its head and says + + + align:start position:0% +flips the problem on its head and says +you know what um I'm just going to + + align:start position:0% +you know what um I'm just going to + + + align:start position:0% +you know what um I'm just going to +guarantee a balanced partition from a + + align:start position:0% +guarantee a balanced partition from a + + + align:start position:0% +guarantee a balanced partition from a +probabilistic standpoint and it might + + align:start position:0% +probabilistic standpoint and it might + + + align:start position:0% +probabilistic standpoint and it might +take me a little bit longer to get there + + align:start position:0% +take me a little bit longer to get there + + + align:start position:0% +take me a little bit longer to get there +but that's what Las Vegas algorithms are + + align:start position:0% +but that's what Las Vegas algorithms are + + + align:start position:0% +but that's what Las Vegas algorithms are +all about uh it they're probably fast + + align:start position:0% +all about uh it they're probably fast + + + align:start position:0% +all about uh it they're probably fast +and once I get a balanced partition I'm + + align:start position:0% +and once I get a balanced partition I'm + + + align:start position:0% +and once I get a balanced partition I'm +in good shape because I can go do my + + align:start position:0% +in good shape because I can go do my + + + align:start position:0% +in good shape because I can go do my +recursion and I get uh my divide and + + align:start position:0% +recursion and I get uh my divide and + + + align:start position:0% +recursion and I get uh my divide and +conquer working properly right so what + + align:start position:0% +conquer working properly right so what + + + align:start position:0% +conquer working properly right so what +is paranoid quick sword absolutely + + align:start position:0% +is paranoid quick sword absolutely + + + align:start position:0% +is paranoid quick sword absolutely +straightforward you could probably guess + + align:start position:0% +straightforward you could probably guess + + + align:start position:0% +straightforward you could probably guess +given my description uh let's just + + align:start position:0% +given my description uh let's just + + + align:start position:0% +given my description uh let's just +choose uh a + + align:start position:0% +choose uh a + + + align:start position:0% +choose uh a +pivot uh to be a + + align:start position:0% +pivot uh to be a + + + align:start position:0% +pivot uh to be a +random + + align:start position:0% +random + + + align:start position:0% +random +element of + + align:start position:0% +element of + + + align:start position:0% +element of +a uh perform the + + align:start position:0% + + + + align:start position:0% + +partition and and then uh Val is a + + align:start position:0% +partition and and then uh Val is a + + + align:start position:0% +partition and and then uh Val is a +repeat uh so uh we're going to go off + + align:start position:0% +repeat uh so uh we're going to go off + + + align:start position:0% +repeat uh so uh we're going to go off +and we say + + align:start position:0% +and we say + + + align:start position:0% +and we say +until the + + align:start position:0% +until the + + + align:start position:0% +until the +resulting + + align:start position:0% +resulting + + + align:start position:0% +resulting +partition is such + + align:start position:0% +partition is such + + + align:start position:0% +partition is such +that the cardinality of L is less than + + align:start position:0% +that the cardinality of L is less than + + + align:start position:0% +that the cardinality of L is less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +3/4 of a cardinality of a and the + + align:start position:0% +3/4 of a cardinality of a and the + + + align:start position:0% +3/4 of a cardinality of a and the +cardinality of G is less than or equal + + align:start position:0% +cardinality of G is less than or equal + + + align:start position:0% +cardinality of G is less than or equal +to 3/4 the cardinality of a right so I'm + + align:start position:0% +to 3/4 the cardinality of a right so I'm + + + align:start position:0% +to 3/4 the cardinality of a right so I'm +allowing you a certain amount of + + align:start position:0% +allowing you a certain amount of + + + align:start position:0% +allowing you a certain amount of +imbalance but not a lot right um and and + + align:start position:0% +imbalance but not a lot right um and and + + + align:start position:0% +imbalance but not a lot right um and and +that's it that's recursive U uh I'm + + align:start position:0% +that's it that's recursive U uh I'm + + + align:start position:0% +that's it that's recursive U uh I'm +sorry a paranoid quick sort uh you + + align:start position:0% +sorry a paranoid quick sort uh you + + + align:start position:0% +sorry a paranoid quick sort uh you +obviously are doing that in each level + + align:start position:0% +obviously are doing that in each level + + + align:start position:0% +obviously are doing that in each level +of the recursion and at each level of + + align:start position:0% +of the recursion and at each level of + + + align:start position:0% +of the recursion and at each level of +the recursion your L and G are going to + + align:start position:0% +the recursion your L and G are going to + + + align:start position:0% +the recursion your L and G are going to +be at most a factor of three apart so + + align:start position:0% +be at most a factor of three apart so + + + align:start position:0% +be at most a factor of three apart so +you might get one quarter and 3/4 if + + align:start position:0% +you might get one quarter and 3/4 if + + + align:start position:0% +you might get one quarter and 3/4 if +you're lucky you'll get a half and a + + align:start position:0% +you're lucky you'll get a half and a + + + align:start position:0% +you're lucky you'll get a half and a +half uh but the worst case given uh that + + align:start position:0% +half uh but the worst case given uh that + + + align:start position:0% +half uh but the worst case given uh that +you're going to be exiting out of this + + align:start position:0% +you're going to be exiting out of this + + + align:start position:0% +you're going to be exiting out of this +Loop is one quarter and 3/ quter okay so + + align:start position:0% +Loop is one quarter and 3/ quter okay so + + + align:start position:0% +Loop is one quarter and 3/ quter okay so +uh as always you know you have a simple + + align:start position:0% +uh as always you know you have a simple + + + align:start position:0% +uh as always you know you have a simple +algorithm and it's uh not + + align:start position:0% +algorithm and it's uh not + + + align:start position:0% +algorithm and it's uh not +completely clear how you're going to get + + align:start position:0% +completely clear how you're going to get + + + align:start position:0% +completely clear how you're going to get +to um expected n log end time but uh + + align:start position:0% +to um expected n log end time but uh + + + align:start position:0% +to um expected n log end time but uh +it's not difficult uh basically what we + + align:start position:0% +it's not difficult uh basically what we + + + align:start position:0% +it's not difficult uh basically what we +have to do is we have to try and figure + + align:start position:0% +have to do is we have to try and figure + + + align:start position:0% +have to do is we have to try and figure +out what the probability of a good call + + align:start position:0% +out what the probability of a good call + + + align:start position:0% +out what the probability of a good call +is over here uh a good pivot choice and + + align:start position:0% +is over here uh a good pivot choice and + + + align:start position:0% +is over here uh a good pivot choice and +what the probability of a of a of a bad + + align:start position:0% +what the probability of a of a of a bad + + + align:start position:0% +what the probability of a of a of a bad +pivot choice is and we have to uh + + align:start position:0% +pivot choice is and we have to uh + + + align:start position:0% +pivot choice is and we have to uh +obviously given the uh potential + + align:start position:0% +obviously given the uh potential + + + align:start position:0% +obviously given the uh potential +imbalance we have to write the + + align:start position:0% +imbalance we have to write the + + + align:start position:0% +imbalance we have to write the +recurrence associated with that but + + align:start position:0% +recurrence associated with that but + + + align:start position:0% +recurrence associated with that but +let's take a look + + align:start position:0% +let's take a look + + + align:start position:0% +let's take a look +at uh the pivots here and um what can we + + align:start position:0% +at uh the pivots here and um what can we + + + align:start position:0% +at uh the pivots here and um what can we +say about uh the sizes of + + align:start position:0% +say about uh the sizes of + + + align:start position:0% +say about uh the sizes of +LG uh if you just did a random pivot + + align:start position:0% +LG uh if you just did a random pivot + + + align:start position:0% +LG uh if you just did a random pivot +well a bad call is + + align:start position:0% +well a bad call is + + + align:start position:0% +well a bad call is +when your you get uh + + align:start position:0% +when your you get uh + + + align:start position:0% +when your you get uh +uh something in L or G that is less than + + align:start position:0% +uh something in L or G that is less than + + + align:start position:0% +uh something in L or G that is less than +one + + align:start position:0% +one + + + align:start position:0% +one +quarter uh and a good call + + align:start position:0% +quarter uh and a good call + + + align:start position:0% +quarter uh and a good call +is when you get 1/2 somewhere between 1 + + align:start position:0% +is when you get 1/2 somewhere between 1 + + + align:start position:0% +is when you get 1/2 somewhere between 1 +half and um uh uh uh well roughly if you + + align:start position:0% +half and um uh uh uh well roughly if you + + + align:start position:0% +half and um uh uh uh well roughly if you +look at uh the choice of the pivot so + + align:start position:0% +look at uh the choice of the pivot so + + + align:start position:0% +look at uh the choice of the pivot so +what I have up here is is the choice of + + align:start position:0% +what I have up here is is the choice of + + + align:start position:0% +what I have up here is is the choice of +the pivot if my Pivot is out here I have + + align:start position:0% +the pivot if my Pivot is out here I have + + + align:start position:0% +the pivot if my Pivot is out here I have +um I have a very small L and all of the + + align:start position:0% +um I have a very small L and all of the + + + align:start position:0% +um I have a very small L and all of the +thing on the right is G if the pivot is + + align:start position:0% +thing on the right is G if the pivot is + + + align:start position:0% +thing on the right is G if the pivot is +here I have a relatively small l and a + + align:start position:0% +here I have a relatively small l and a + + + align:start position:0% +here I have a relatively small l and a +large G if the pivot is over here I'm + + align:start position:0% +large G if the pivot is over here I'm + + + align:start position:0% +large G if the pivot is over here I'm +good um I got one quarter uh and three + + align:start position:0% +good um I got one quarter uh and three + + + align:start position:0% +good um I got one quarter uh and three +qus the pivot is over here I got 1/2 and + + align:start position:0% +qus the pivot is over here I got 1/2 and + + + align:start position:0% +qus the pivot is over here I got 1/2 and +one2 and so on and so forth and so this + + align:start position:0% +one2 and so on and so forth and so this + + + align:start position:0% +one2 and so on and so forth and so this +part is bad this part is bad and the + + align:start position:0% +part is bad this part is bad and the + + + align:start position:0% +part is bad this part is bad and the +middle part is good right so that's all + + align:start position:0% +middle part is good right so that's all + + + align:start position:0% +middle part is good right so that's all +that this picture shows um so a + + align:start position:0% +that this picture shows um so a + + + align:start position:0% +that this picture shows um so a +call is good + + align:start position:0% +call is good + + + align:start position:0% +call is good +with what + + align:start position:0% +with what + + + align:start position:0% +with what +probability given that picture a call is + + align:start position:0% +probability given that picture a call is + + + align:start position:0% +probability given that picture a call is +good with what + + align:start position:0% +good with what + + + align:start position:0% +good with what +probability it's greater than or equal + + align:start position:0% +probability it's greater than or equal + + + align:start position:0% +probability it's greater than or equal +to 1/2 right + + align:start position:0% + + + + align:start position:0% + +so um and + + align:start position:0% +so um and + + + align:start position:0% +so um and +so what you can now write simply is uh + + align:start position:0% +so what you can now write simply is uh + + + align:start position:0% +so what you can now write simply is uh +if + + align:start position:0% +if + + + align:start position:0% +if +TN uh is the time required to sort the + + align:start position:0% +TN uh is the time required to sort the + + + align:start position:0% +TN uh is the time required to sort the +array um essentially what you can write + + align:start position:0% +array um essentially what you can write + + + align:start position:0% +array um essentially what you can write +is uh you can say TN is T of n / + + align:start position:0% +is uh you can say TN is T of n / + + + align:start position:0% +is uh you can say TN is T of n / +4+ T of 3 n / + + align:start position:0% +4+ T of 3 n / + + + align:start position:0% +4+ T of 3 n / + + align:start position:0% + + + align:start position:0% +plus + + align:start position:0% +plus + + + align:start position:0% +plus +expected number of + + align:start position:0% + + + + align:start position:0% + +iterations in terms of getting a good + + align:start position:0% +iterations in terms of getting a good + + + align:start position:0% +iterations in terms of getting a good +partition time C * n and there's a + + align:start position:0% +partition time C * n and there's a + + + align:start position:0% +partition time C * n and there's a +reason why I'm putting C in here as + + align:start position:0% +reason why I'm putting C in here as + + + align:start position:0% +reason why I'm putting C in here as +oppos to Theta that will become clear in + + align:start position:0% +oppos to Theta that will become clear in + + + align:start position:0% +oppos to Theta that will become clear in +just a second because I can't really + + align:start position:0% +just a second because I can't really + + + align:start position:0% +just a second because I can't really +apply the Master theorem to this uh + + align:start position:0% +apply the Master theorem to this uh + + + align:start position:0% +apply the Master theorem to this uh +given what I have with respect to TN /4 + + align:start position:0% +given what I have with respect to TN /4 + + + align:start position:0% +given what I have with respect to TN /4 +and 3n /4 right so so what I have here + + align:start position:0% +and 3n /4 right so so what I have here + + + align:start position:0% +and 3n /4 right so so what I have here +is I'm looking at the case + + align:start position:0% +is I'm looking at the case + + + align:start position:0% +is I'm looking at the case +where um I could get an imbalance + + align:start position:0% +where um I could get an imbalance + + + align:start position:0% +where um I could get an imbalance +partition but the imbalance is bounded + + align:start position:0% +partition but the imbalance is bounded + + + align:start position:0% +partition but the imbalance is bounded +so I could get I'd have n over4 on one + + align:start position:0% +so I could get I'd have n over4 on one + + + align:start position:0% +so I could get I'd have n over4 on one +side and 3 n over4 on the other side but + + align:start position:0% +side and 3 n over4 on the other side but + + + align:start position:0% +side and 3 n over4 on the other side but +I'm not going to have n over 5 and you + + align:start position:0% +I'm not going to have n over 5 and you + + + align:start position:0% +I'm not going to have n over 5 and you +know 4 n over 5 or what have you um and + + align:start position:0% +know 4 n over 5 or what have you um and + + + align:start position:0% +know 4 n over 5 or what have you um and +so that's the two recursive calls so + + align:start position:0% +so that's the two recursive calls so + + + align:start position:0% +so that's the two recursive calls so +that's hopefully uh easy to see uh the + + align:start position:0% +that's hopefully uh easy to see uh the + + + align:start position:0% +that's hopefully uh easy to see uh the +part that is new here is simply the + + align:start position:0% +part that is new here is simply the + + + align:start position:0% +part that is new here is simply the +complexity of this code that you see + + align:start position:0% +complexity of this code that you see + + + align:start position:0% +complexity of this code that you see +here which is obviously a the randomized + + align:start position:0% +here which is obviously a the randomized + + + align:start position:0% +here which is obviously a the randomized +algorithm that's exactly where the + + align:start position:0% +algorithm that's exactly where the + + + align:start position:0% +algorithm that's exactly where the +randomness comes in because you're + + align:start position:0% +randomness comes in because you're + + + align:start position:0% +randomness comes in because you're +picking a random pivot and you're + + align:start position:0% +picking a random pivot and you're + + + align:start position:0% +picking a random pivot and you're +checking it and so um this is going to + + align:start position:0% +checking it and so um this is going to + + + align:start position:0% +checking it and so um this is going to +run a certain number of times and U we + + align:start position:0% +run a certain number of times and U we + + + align:start position:0% +run a certain number of times and U we +can figure out what the expectation is + + align:start position:0% +can figure out what the expectation is + + + align:start position:0% +can figure out what the expectation is +in just a minute but I have C * n + + align:start position:0% +in just a minute but I have C * n + + + align:start position:0% +in just a minute but I have C * n +because uh this is constant time to + + align:start position:0% +because uh this is constant time to + + + align:start position:0% +because uh this is constant time to +choose the random number whe assume that + + align:start position:0% +choose the random number whe assume that + + + align:start position:0% +choose the random number whe assume that +performing the partition uh partition is + + align:start position:0% +performing the partition uh partition is + + + align:start position:0% +performing the partition uh partition is +is uh is C * n or Theta n and that's why + + align:start position:0% +is uh is C * n or Theta n and that's why + + + align:start position:0% +is uh is C * n or Theta n and that's why +I have this up there so this we're going + + align:start position:0% +I have this up there so this we're going + + + align:start position:0% +I have this up there so this we're going +to call as a + + align:start position:0% +to call as a + + + align:start position:0% +to call as a +CN um and so um expected number of + + align:start position:0% +CN um and so um expected number of + + + align:start position:0% +CN um and so um expected number of +iterations given what I have what can I + + align:start position:0% +iterations given what I have what can I + + + align:start position:0% +iterations given what I have what can I +say about the expected number of + + align:start position:0% +say about the expected number of + + + align:start position:0% +say about the expected number of +iterations using U using uh simple + + align:start position:0% +iterations using U using uh simple + + + align:start position:0% +iterations using U using uh simple +probability rules what is that two right + + align:start position:0% +probability rules what is that two right + + + align:start position:0% +probability rules what is that two right +one / P all of them are independent so + + align:start position:0% +one / P all of them are independent so + + + align:start position:0% +one / P all of them are independent so +this is this is two and so um uh what I + + align:start position:0% +this is this is two and so um uh what I + + + align:start position:0% +this is this is two and so um uh what I +have + + align:start position:0% +have + + + align:start position:0% +have +here uh is uh something that I think you + + align:start position:0% +here uh is uh something that I think you + + + align:start position:0% +here uh is uh something that I think you +might have seen this before uh but it's + + align:start position:0% +might have seen this before uh but it's + + + align:start position:0% +might have seen this before uh but it's +worth drawing the tree out and seeing it + + align:start position:0% +worth drawing the tree out and seeing it + + + align:start position:0% +worth drawing the tree out and seeing it +one more time in case uh um it didn't U + + align:start position:0% +one more time in case uh um it didn't U + + + align:start position:0% +one more time in case uh um it didn't U +fully registered the first time or you + + align:start position:0% +fully registered the first time or you + + + align:start position:0% +fully registered the first time or you +didn't actually see it uh in6 or + + align:start position:0% +didn't actually see it uh in6 or + + + align:start position:0% +didn't actually see it uh in6 or +regation but um what I now have is T of + + align:start position:0% +regation but um what I now have is T of + + + align:start position:0% +regation but um what I now have is T of +N I want to solve T of n n = t of n / 4 + + align:start position:0% +N I want to solve T of n n = t of n / 4 + + + align:start position:0% +N I want to solve T of n n = t of n / 4 ++ T of 3n / 4 + 2 * + + align:start position:0% ++ T of 3n / 4 + 2 * + + + align:start position:0% ++ T of 3n / 4 + 2 * +CN right um and um again like I said I + + align:start position:0% +CN right um and um again like I said I + + + align:start position:0% +CN right um and um again like I said I +didn't put Theta n in here because as + + align:start position:0% +didn't put Theta n in here because as + + + align:start position:0% +didn't put Theta n in here because as +you'll see when I draw this uh this tree + + align:start position:0% +you'll see when I draw this uh this tree + + + align:start position:0% +you'll see when I draw this uh this tree +out uh because it's not a master theorem + + align:start position:0% +out uh because it's not a master theorem + + + align:start position:0% +out uh because it's not a master theorem +uh invocation uh it's worth looking at + + align:start position:0% +uh invocation uh it's worth looking at + + + align:start position:0% +uh invocation uh it's worth looking at +it from a constant Factor standpoint to + + align:start position:0% +it from a constant Factor standpoint to + + + align:start position:0% +it from a constant Factor standpoint to +really get the sense of how all of this + + align:start position:0% +really get the sense of how all of this + + + align:start position:0% +really get the sense of how all of this +works out um and so if I draw the tree + + align:start position:0% +works out um and so if I draw the tree + + + align:start position:0% +works out um and so if I draw the tree +of execution I start counting um + + align:start position:0% +of execution I start counting um + + + align:start position:0% +of execution I start counting um +basically what I have is 2 CN up at the + + align:start position:0% +basically what I have is 2 CN up at the + + + align:start position:0% +basically what I have is 2 CN up at the +top I have 1 over4 * 2 CN over here I + + align:start position:0% +top I have 1 over4 * 2 CN over here I + + + align:start position:0% +top I have 1 over4 * 2 CN over here I +have 3 over4 * 2 CN over here and then + + align:start position:0% +have 3 over4 * 2 CN over here and then + + + align:start position:0% +have 3 over4 * 2 CN over here and then +this 1 over4 might go 1 over6 * 2 CN + + align:start position:0% +this 1 over4 might go 1 over6 * 2 CN + + + align:start position:0% +this 1 over4 might go 1 over6 * 2 CN +over here and this might go 3 over 16 * + + align:start position:0% +over here and this might go 3 over 16 * + + + align:start position:0% +over here and this might go 3 over 16 * +2 CN over here and and this would go um + + align:start position:0% +2 CN over here and and this would go um + + + align:start position:0% +2 CN over here and and this would go um +I guess it would be 3 over 16 * 2 CN and + + align:start position:0% +I guess it would be 3 over 16 * 2 CN and + + + align:start position:0% +I guess it would be 3 over 16 * 2 CN and +then uh 9 over 16 * 2 CN Etc so this is + + align:start position:0% +then uh 9 over 16 * 2 CN Etc so this is + + + align:start position:0% +then uh 9 over 16 * 2 CN Etc so this is +an unbalanced tree because you have uh + + align:start position:0% +an unbalanced tree because you have uh + + + align:start position:0% +an unbalanced tree because you have uh +an unbalanced partition up on top and + + align:start position:0% +an unbalanced partition up on top and + + + align:start position:0% +an unbalanced partition up on top and +now you want to count up all the work uh + + align:start position:0% +now you want to count up all the work uh + + + align:start position:0% +now you want to count up all the work uh +that this uh uh this tree does if you + + align:start position:0% +that this uh uh this tree does if you + + + align:start position:0% +that this uh uh this tree does if you +collect up all of the operations then + + align:start position:0% +collect up all of the operations then + + + align:start position:0% +collect up all of the operations then +that's going to tell you what T of n is + + align:start position:0% +that's going to tell you what T of n is + + + align:start position:0% +that's going to tell you what T of n is +because that's all the work that you + + align:start position:0% +because that's all the work that you + + + align:start position:0% +because that's all the work that you +have to do in order to uh finish up the + + align:start position:0% +have to do in order to uh finish up the + + + align:start position:0% +have to do in order to uh finish up the +top level of recursion and what you can + + align:start position:0% +top level of recursion and what you can + + + align:start position:0% +top level of recursion and what you can +say is if you look at this side here all + + align:start position:0% +say is if you look at this side here all + + + align:start position:0% +say is if you look at this side here all +the way to the right hand side you're + + align:start position:0% +the way to the right hand side you're + + + align:start position:0% +the way to the right hand side you're +going to have log + + align:start position:0% +going to have log + + + align:start position:0% +going to have log +of to the base 4 over3 * 2 CN levels + + align:start position:0% +of to the base 4 over3 * 2 CN levels + + + align:start position:0% +of to the base 4 over3 * 2 CN levels +right so that's just simply every time + + align:start position:0% +right so that's just simply every time + + + align:start position:0% +right so that's just simply every time +you're multiplying by 3 over 4 when do + + align:start position:0% +you're multiplying by 3 over 4 when do + + + align:start position:0% +you're multiplying by 3 over 4 when do +you get down to uh the number one and + + align:start position:0% +you get down to uh the number one and + + + align:start position:0% +you get down to uh the number one and +that's log of 4 over3 and then over here + + align:start position:0% +that's log of 4 over3 and then over here + + + align:start position:0% +that's log of 4 over3 and then over here +it's a little bit easier to think about + + align:start position:0% +it's a little bit easier to think about + + + align:start position:0% +it's a little bit easier to think about +because it's a power of two you're going + + align:start position:0% +because it's a power of two you're going + + + align:start position:0% +because it's a power of two you're going +to have log of four to the base 4 * 2 CN + + align:start position:0% +to have log of four to the base 4 * 2 CN + + + align:start position:0% +to have log of four to the base 4 * 2 CN +levels and really it doesn't really + + align:start position:0% +levels and really it doesn't really + + + align:start position:0% +levels and really it doesn't really +matter honestly when we go to astics but + + align:start position:0% +matter honestly when we go to astics but + + + align:start position:0% +matter honestly when we go to astics but +it's worth seeing I think uh just to get + + align:start position:0% +it's worth seeing I think uh just to get + + + align:start position:0% +it's worth seeing I think uh just to get +a sense of um why it all works out uh + + align:start position:0% +a sense of um why it all works out uh + + + align:start position:0% +a sense of um why it all works out uh +regardless of whether it's uh N4 or or + + align:start position:0% +regardless of whether it's uh N4 or or + + + align:start position:0% +regardless of whether it's uh N4 or or +or a different constant here or whether + + align:start position:0% +or a different constant here or whether + + + align:start position:0% +or a different constant here or whether +it's balanced or unbalanced the tree + + align:start position:0% +it's balanced or unbalanced the tree + + + align:start position:0% +it's balanced or unbalanced the tree +looks a little bit different um it it's + + align:start position:0% +looks a little bit different um it it's + + + align:start position:0% +looks a little bit different um it it's +sort of weird you know it's got a uh uh + + align:start position:0% +sort of weird you know it's got a uh uh + + + align:start position:0% +sort of weird you know it's got a uh uh +fewer levels here and and more levels + + align:start position:0% +fewer levels here and and more levels + + + align:start position:0% +fewer levels here and and more levels +there so s of tilted this way uh but uh + + align:start position:0% +there so s of tilted this way uh but uh + + + align:start position:0% +there so s of tilted this way uh but uh +eventually you get down to uh Theta 1 + + align:start position:0% +eventually you get down to uh Theta 1 + + + align:start position:0% +eventually you get down to uh Theta 1 +constants down + + align:start position:0% +constants down + + + align:start position:0% +constants down +below um and basically what you can see + + align:start position:0% +below um and basically what you can see + + + align:start position:0% +below um and basically what you can see +if you just add it up uh is 1 over4 + 3 + + align:start position:0% +if you just add it up uh is 1 over4 + 3 + + + align:start position:0% +if you just add it up uh is 1 over4 + 3 +over4 is 1 1 over 16 3 over 16 obviously + + align:start position:0% +over4 is 1 1 over 16 3 over 16 obviously + + + align:start position:0% +over4 is 1 1 over 16 3 over 16 obviously +those are all uh those are all uh end up + + align:start position:0% +those are all uh those are all uh end up + + + align:start position:0% +those are all uh those are all uh end up +end up being one so you have 2 + + align:start position:0% +end up being one so you have 2 + + + align:start position:0% +end up being one so you have 2 +CN + + align:start position:0% +CN + + + align:start position:0% +CN +work at each + + align:start position:0% +work at each + + + align:start position:0% +work at each +level and uh if you just go ahead and be + + align:start position:0% +level and uh if you just go ahead and be + + + align:start position:0% +level and uh if you just go ahead and be +pessimistic about it uh there's + + align:start position:0% +pessimistic about it uh there's + + + align:start position:0% +pessimistic about it uh there's +maximum of log 4 + + align:start position:0% +maximum of log 4 + + + align:start position:0% +maximum of log 4 +over3 times 2 CN + + align:start position:0% + + + + align:start position:0% + +levels + + align:start position:0% +levels + + + align:start position:0% +levels +and that's pretty much it um obviously + + align:start position:0% +and that's pretty much it um obviously + + + align:start position:0% +and that's pretty much it um obviously +now you can start ignoring the constants + + align:start position:0% +now you can start ignoring the constants + + + align:start position:0% +now you can start ignoring the constants +uh you just keep the log here you don't + + align:start position:0% +uh you just keep the log here you don't + + + align:start position:0% +uh you just keep the log here you don't +care what the Bas is you got an N here + + align:start position:0% +care what the Bas is you got an N here + + + align:start position:0% +care what the Bas is you got an N here +so drop the 2 C drop the 4 over3 drop + + align:start position:0% +so drop the 2 C drop the 4 over3 drop + + + align:start position:0% +so drop the 2 C drop the 4 over3 drop +the 2C and you get your end log app okay + + align:start position:0% +the 2C and you get your end log app okay + + + align:start position:0% +the 2C and you get your end log app okay +so that's pretty much it uh I'll uh + + align:start position:0% +so that's pretty much it uh I'll uh + + + align:start position:0% +so that's pretty much it uh I'll uh +stick around here for questions uh but + + align:start position:0% +stick around here for questions uh but + + + align:start position:0% +stick around here for questions uh but +you got an example of um of a Monte + + align:start position:0% +you got an example of um of a Monte + + + align:start position:0% +you got an example of um of a Monte +Carlo algorithm you got an example of a + + align:start position:0% +Carlo algorithm you got an example of a + + + align:start position:0% +Carlo algorithm you got an example of a +Las Vegas algorithm and tomorrow in + + align:start position:0% +Las Vegas algorithm and tomorrow in + + + align:start position:0% +Las Vegas algorithm and tomorrow in +section you'll see a slightly more + + align:start position:0% +section you'll see a slightly more + + + align:start position:0% +section you'll see a slightly more +involved analysis for something that + + align:start position:0% +involved analysis for something that + + + align:start position:0% +involved analysis for something that +looks a lot closer to the randomized + + align:start position:0% +looks a lot closer to the randomized + + + align:start position:0% +looks a lot closer to the randomized +quick sort so see you next time \ No newline at end of file diff --git a/cQntMUMQyRw.txt b/cQntMUMQyRw.txt new file mode 100644 index 0000000000000000000000000000000000000000..6dc85333164f44c156200c505a5d129d50deb81d --- /dev/null +++ b/cQntMUMQyRw.txt @@ -0,0 +1,3634 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation, or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hello. + +Welcome to the second +lecture in 6.01. + +I hope you had a good +time last week. + +Last lecture, we looked at +what is probably the most + +important theme in this course, +which is, how do you + +organize your thoughts, your +design, the things that you + +do, in order to manage +complexity when you're trying + +to build a complicated system? + +The mantra for this +class is PCAP-- + +primitives, combinations, +abstractions, and patterns. + +And last time, we saw how at +the very most elementary + +level, Python provides some +tools with which we can + +achieve this goal of defining +primitives, combining them + +into more complicated ideas, +abstracting the important + +information, and generating and +capturing new patterns. + +And so, for example, we saw +that Python has a defined + +statement that lets you +associate a sequence of + +operations with a name-- + +both of those things are +important, the sequence + +represents a combination, the +name represents a way that we + +can abstract the behavior of the +combination and treat it + +as though it were primitive +operation. + +We saw that we could do the same +sort of thing for data + +structures. + +And in particular, the list +structure in Python allows us + +to generate hierarchical +heterogeneous structures in + +much the same way. + +Then variables allow us to +associate names with those + +structures. + +And finally, we saw that classes +allow us to combine + +not only data, but also +procedures -- + +all into one object +of related things. + +So that's PCAP at the most +primitive level. + +What I want to do today +is talk about + +PCAP at higher levels. + +How do you build upon that +framework to continue this + +idea of building with +abstraction and modularity? + +How do you make-- + +how do you combine primitive +operations into powerful + +operations? + +How do you combine primitive +data into powerful data? + +And what I want to do is think +about the next level above the + +most rudimentary level +in Python. + +So we'll look first at some +programming styles, and how + +that affects your ability to +define useful abstractions. + +And then I'll look at something +much higher level, + +which is state machines, which +is the way that we will think + +about the construction +of robot controls. + +So I'll start with just a few +words about how you-- + +the different ways that you +could structure a program. + +The reason for doing this is +that the basic structure that + +you use can have an important +effect on + +your ability to abstract. + +We'll look at three different +methodologies for + +constructing a program. + +I'll refer to the first one as +imperative, also procedural. + +That's kind of the most basic +way you could think about + +writing a program. + +It's kind of a recipe. + +It's kind of like cooking +with a recipe. + +Take this, add this, stir this, +bake for 30 minutes, + +that kind of thing. + +So if you define a procedure, +if you organize the way you + +think about it in terms of step +by step instructions for, + +what should I do next? + +We refer to that kind of an +approach as imperative. + +We'll look at functional +programming. + +There, even though you implement +precisely the same + +algorithm, the perspective is +a little bit different. + +There, rather than focusing +quite so narrowly on the step + +by step, how do you get from A +to B, the idea is going to be, + +think about the structure of +the problem in terms of + +functions in a mathematical +sense. + +By which I mean, functions +that eat inputs, generate + +outputs, and don't have +side effects. + +Side effects are things like +setting variables that you can + +later look at. + +Then I'll look at +object-oriented programming. + +Again, you could be implementing +precisely the + +same algorithm by using an +object-oriented approach, but + +here the focus will be on +building collections of data + +with procedures that are +related, and organizing the + +solution to your problem in +terms of a hierarchy of such + +structures. + +So what I'd like to start off +today with is to look at an + +example problem and how you +could program it using any of + +these three approaches. + +So the example program is going +to be, find a sequence + +of operations-- + +by which I mean, an operation +is either + +increment or square-- + +the idea is that the operations +are things that we + +will do to integers. + +Find a sequence of operations, +either increment or square, + +that transforms one integer, +which is the initial value, i, + +into a goal, which +I'll call, g. + +So I want to think about +the problem of + +finding such sequences. + +So for example, the sequence +increment increment increment + +square, when applied to +1, would give 16. + +So I'm thinking about the first +increment increments 1 + +to give you 2. + +The second increment increments +2 to give you 3. + +The third increment increments +3 to give you 4. + +Then square squares +4 to give you 16. + +So I'll refer to this as having +found the sequence of + +operations, increment increment +increment square, + +that transforms 1 into 16. + +Everybody with me? + +OK, I'll be the judge of that. + +So, to prove that you're with +me, what's the minimum length + +sequence of increment and square +operations needed to + +transform 1 into 100. + +You've got thirty seconds to +discuss it with your neighbor, + +come to an agreement, and I'm +gonna ask you to raise your + +hands with a number of fingers, +(1), (2), (3), (4), + +or (5), indicating +the right answer. + +[AUDIENCE DISCUSSION] + +PROFESSOR: OK, everybody +raise your hand. + +Tell me a number of fingers +equal to the right answer, + +raise your hand, show me +a number of fingers. + +OK, I'm seeing-- + +OK. + +So keep in mind the number +of fingers is the + +thing before the colon. + +That avoids the awkward way +of saying less than 4. + +OK? + +So I want the number +before the colon. + +So what is the minimum +length sequence? + +Raise your hand, indicate +a number of fingers. + +OK, the answers are improving. + +Higher so I can see you. + +OK, it's about 90% +correct, I think. + +OK, most people said (3), which +is another name for 5. + +OK. + +So how do you get +the answer 5? + +What's the answer? + +Somebody explain that answer? + +Yeah. + +AUDIENCE: Increment increment +square increment square? + +PROFESSOR: That's +exactly right. + +So since I have two operators, +increments and squares, and + +since I'm trying to cover a big +distance, 1 to 100, square + +increases faster-- + +at least for bigger numbers, +than increment does. + +So what you'd like to do is +figure out a way of coercing + +as many squares as possible. + +So a good thing to do is to +start at the end, and you can + +take the square root of the +first one evenly, and that + +gives you 10. + +But then you can't take the +square root of 10, so you back + +off and you get 9, and then you +can take the square root + +of 9, et cetera. + +So there's any number of ways +you could solve this problem, + +the point is, that there's a +simple solution which is, the + +answer (3), which is +a pseudonym for 5. + +So 5 operations will get +you from 1 to 100. + +So what I want to do now-- + +now that you know the answer +to the question, I want to + +write a program to +find that answer. + +The most straightforward +approach that you could use is + +what we would call, imperative +or procedural. + +The idea is to solve the problem +by walking your way + +through it in some premeditated +fashion. + +A reasonable premeditated +fashion would be, think about + +the sequences and order +them by length. + +Think about all the sequences +of length + +one, see if they work. + +Think about all the sequences +of length + +two, see if they work. + +Three, see if they work. + +And just keep going until +you find one that works. + +That's a very reasonable-- + +that's a procedure. + +Start by thinking about short +sequences, and proceed by + +making them longer and longer +until you run into one that + +happens to solve your problem. + +So that's what's +going on here. + +First I gave a name to the +operator, increment. + +Then I give a name to the +operator, square-- + +that's just for convenience. + +Then what I want to do +is write a program-- + +find sequence, that will start +at some initial value, say 1, + +and go to some goal, say 100. + +And the way I'll do that is to +enumerate over the lengths of + +sequences that are possible -- + +1, 2, 3, et cetera. + +I'll represent each one of those +sequences of operations + +by this kind of a +representation, I'll make a + +tuple that has a string +that tells me in + +English, what did I do? + +And an integer that tells +me what the answer is + +after I've done that. + +So looking ahead, this is the +idea-- this is the program + +that I'm trying to construct. + +I would like the output of the +program to start by thinking + +about all sequences of length +one, then sequences of length + +two, then sequences of length +three, then sequences of + +length four. + +For each sequence of length one, +I'd like to think about, + +what are all the possible +sequences? + +Well, I could start with 1 and +increment it to get 2. + +Or I could start with 1 and +I could square it to 1. + +That's all the possible +sequences of length one. + +Then I go on to length two, +three, four, by the time I'm + +down here to length four, I +could start with 1, increment + +square square increment, and +that would give me 17. + +That's the structure +of the program that + +I'm trying to make. + +Everybody with it? + +So I'm going to define find +sequence, I'm going to loop + +over all those lengths, I'm +going to keep track of all the + +different sequences I found +as a list of tuples. + +After last week you're +supposed to be very + +comfortable with those +kinds of words. + +Each one of the sequences is a +tuple, a string and a final + +value, and the list is +all possibilities. + +And I'm going to try the ones of +length one, then I'm going + +to append to each one to make +sequences of two, and then I + +gonna append to that to make +sequences of three, four, + +five, and keep on going. + +So the point is, that this is a +very simple-minded, easy to + +conceive recipe for how to +search through a large number + +of sequences and find the one +with the minimum length. + +So when you write that program, +it iterates down + +until it finds number 5, the +5-length sequence here it came + +up with the answer 100, +so that's the answer. + +The point is, that it was an +easy way to write the program. + +We just think about telling +somebody with a pencil and + +paper, what would you do? + +And we tell Python, rather than +the person with the piece + +of paper, what to do. + +The approach is straightforward. + +The only ugliness is that +it ended up with + +three levels of loops. + +And the most common kind of +error in this kind of + +programming is you just +botch the indices. + +Because it's got three nested +layers of loops, it's very + +easy to lose track -- +when you're thinking + +of layer three -- + +about what's happening +in layer two. + +So that's the only difficulty +in this approach. + +The challenge is just to keep +all the indices consistent. + +But it works. + +There's nothing wrong +with this approach. + +It doesn't necessarily lead to +the most modular designs, but + +you can write functional +programs that work this way. + +A different way to structure the +program, I'll refer it-- + +here's a different version of +the same program, the same + +algorithm, but I'm going +to refer to this one as + +functional program. + +Here the idea is to focus on +procedures that implement + +functions of a mathematical +type. + +I want to recast the problem, +this time thinking about, how + +would I divide it up +into functions + +that calculate things. + +So rather than focusing on, +what's the set of nested loops + +that I have to make, I want +to ask, what would be a + +meaningful calculation that +I would want to do + +to solve this problem? + +So the first thing I might do, +focusing on this part, I might + +write a function, apply, +where apply -- + +I'm using the methodology of +functional programming -- + +apply is a pure function. + +It's going to eat some inputs, +generate an output, and have + +no side effects. + +So what I want it to do, I +want to feed it a list of + +functions and ask it, +what's the answer? + +So apply is going to have as its +first argument a list, but + +the list is going to be +a list of operations. + +It's not a list of strings, it's +not a list of integers, + +it's a list of functions. + +And what the procedure apply is +going to do is step through + +that list, applying +the functions + +one by one to argument. + +So the final goal is +written down here. + +If I apply nothing to 7, the +answer ought to be 7. + +If I apply increment to 7, +the answer ought to be 8. + +If I apply square to 7, the +answer ought to be 49. + +And if I apply increment +square to 7, the + +answer ought to be 64. + +There's a couple things you're +supposed to see here. + +First off, apply is +a pure function, + +it has no side effects. + +It eats its input, it does a +calculation, it tells you an + +answer, and it's done. + +There's no extra things that's +going on behind your back, + +it's not setting a variable, or +creating a list, or doing + +anything like that. + +It has inputs, from those inputs +it generates an output, + +and that's the end +of the story. + +Another thing that you should +see is that I'm treating + +procedures as first-class +objects. + +That's another tenet of +functional programming. + +Rather than sending the input +to apply as a list of text + +strings, or as a list of +integers, I'm giving it a list + +of function names. + +I'm treating functions just +as though it were any + +other kind of data. + +I'm making a list of functions +just the same as I could make + +a list of integers, or if I made +a list of strings, I'm + +just making a list +of functions. + +So another important feature +of this program is the idea + +that the functions +are being treated + +as first-class objects. + +The next procedure +is addLevel. + +addLevel is going to be a +second pure function. + +The idea there is that I'm +going to use addLevel to + +construct all the different +sequences of operations that + +are possible. + +Each sequence is going to be +a list, so the entire-- + +all possible sequences will +be a list of lists. + +So the idea in addLevel was +going to be that you take the + +list of lists and you generate +from that list of lists a new + +list of lists that has +one more element. + +So if the first list of lists +had four elements in it, how + +many lists are in the second +list of lists? + +Five. + +Four, five? + +The first list of lists +represents some number of + +different sequence +of operations. + +My second list of lists-- what +I want to do is think about + +all the different ways that +could be extended from a + +length-4 sequence to a +length-5 sequence. + +How many ways can you extend +a length-4 sequence to a + +length-5 sequence? + +Eight. + +So four becomes eight. + +Why does four become eight? + +AUDIENCE: You've got like +two possibilities. + +PROFESSOR: Because there's two +possibilities for the way that + +you could extend it. + +I could extend the length-4 +sequence by adding on an + +increment operator, or I could +extend it by adding on a + +square operator. + +So every time I addLevel, it's +going to create a new list of + +lists with double as many +elements in it as + +the old list of lists. + +Does that make sense? + +Other than that, the program +works very much the same-- + +I should illustrate that. + +So addLevel applied to the +list of lists, increment. + +I'm only considering one +sequence of length-1, so how + +many ways can I change that if +I'm willing to add procedures + +increment or square? + +Well, I could end up with +increment increment by taking + +that one and that one. + +Or I could end up with increment +square by taking + +that one and that one. + +So if I were to extend the +sequence, increment, two + +possible ways, by either +incrementing again or by + +squaring again, I end up with +two possibilities represented + +by this list of two +different lists. + +Is that clear? + +The important point is that I'm +treating functions as any + +other kind of data element that +could be added to a list. + +And when you run that program, +you get an answer that's very + +similar to the program that we +looked at previously, the + +imperative program. + +Except that the answer now +is a list of functions. + +So rather than generating a +text-string like the previous + +example did, this program +generates a list as the + +answer-- the program generates +a list, which + +is a list of functions. + +The first element in the list +is increment, the second + +element in the list is the +function increment, the third + +element is square increment +square. + +So it gave you the same answer, +it just represented it + +differently. + +Here I'm representing the answer +as a list of functions. + +That make sense? + +So there's a number of +advantages to this approach. + +One of them is that it kind of +automatically coerces you to + +think about modules. + +By specifically focusing my +attention on, how could I + +break up that problem by +defining functions? + +I end up with a bunch +of functions + +here, apply and addLevel. + +And being functions, +they're modules. + +They are things that are easy +to manipulate in other + +contexts, and in particular, +it's very easy to debug them. + +Especially in an interpretive +environment like Python. + +It's very easy to figure out +if your program works by + +figuring out if each +module works. + +That's one of the important +features of modular + +programming. + +When you have a module, it means +that you can use that + +module in multiple +different ways. + +It's easy to break apart the +debugging problem so that + +rather than trying to debug +the one, monolithic + +structure-- + +which was the procedural program +that we wrote in the + +first part, here we can debug +the individual components, + +which happen to be functions. + +So I can ask, what happens +when I apply the + +empty list to 7? + +Well, my answer better be 7. + +So that provides a +way of checking. + +So one of the features of +thinking about the algorithm + +as being broken up into a number +of functions is the + +greater modularity that +allows you, for + +example, easier debugging. + +A much more important reason for +thinking this way though, + +is the clarity of thought. + +And that can be derived from +another feature of the + +definition of apply. + +The particular way I +defined apply is + +what we call recursive. + +It's recursive in the sense that +the definition of apply + +calls apply. + +OK, that sounds like +a bad idea, right? + +How do I define something +in terms of itself? + +The idea is that each +application, every time apply + +calls itself-- + +the idea is to structure the +procedure so that the new + +incarnation is in some sense, +simpler than the previous one. + +If you can guarantee that, it +will reduce the complexity of + +the problem from something that +you don't know how to + +solve, to something that you +do know how to solve. + +And for that reason, it +represents a powerful way to + +think about structuring +programs. + +So as an example of that-- + +as an example of structuring +programs as recursions, think + +about raising a number to a +non-negative integer power. + +So if I'm trying to raise b to +the n, if n is 0, and if n is + +a non-negative integer-- well, +if n is 0, b to the n is 1. + +And if n is a non-negative +integer, then b to the n can + +be reduced to b times b +to the (n minus 1). + +Rewriting that functionally, if +I say that my function b to + +the n can be represented +by f of n. + +This statement is precisely +equivalent to saying that f of + +n is 1, if n is 0, or b times +f of (n minus 1) if n is + +bigger than 0. + +So the idea then, is that I may +not know how to raise 2 to + +the 10th, but I can use the rule +to say 2 to the 10th, oh, + +that must be 2 times +2 to the 9th. + +Great, I don't know how to +do 2 to the 9th, either. + +But 2 to the 9th is 2 +times 2 to the 8th. + +And eventually, I boil it down +to a case that I do know the + +answer to, in particular, +b to the 0 is 1. + +I would express that idea in +Python this way, define + +exponent of b, n. + +If n is 0, return 1, otherwise +return b times exponent of b, + +(n minus 1). + +OK, so what that does then +when you invoke it-- + +invoking exponent of 2, 6, in +fact, invokes exponent an + +additional six times. + +If I ask Python to evaluate +exponent of 2, 6 it will end + +up calling exponent of 2, 5. + +But to evaluate that, it will +call exponent of 2, 4-- + +3, 2, 1, 0. + +Then finally, it gets +to the base case. + +When it gets to the call +exponent of 2, 0 it falls into + +this case which returns +1 always. + +So now exponent of 2, 0 returns +1, but then that can + +pick up where call exponent +of 2, 1 left off. + +When I did 2, 1 it fell into +this case, where it was trying + +to take 2 times exponent of +2, 0 Now it knows the + +answer to 2, 0 is 1. + +So I can multiply by 2 and get +the answer is 2, and it backs + +out then all of the +other answers. + +So that's an example of how I +could use recursion to reduce + +a complicated case to a base +case-- a simple case that I + +know the answer to. + +Here, the recruitment with the +power of n causes a linear + +increase in the number of +invocations, so we would call + +that a linear process. + +So the idea then is that +recursion is a good way to + +reduce a complicated problem +to a simpler problem. + +Now that algorithm wasn't +particularly fast. + +If I imagine doing a big +number like 1024. + +Raising a number to the 1024 +power, that could take awhile. + +How long will it take? + +1024 is going to-- it will make +1024 calls to reduce it + +to the base case. + +Here's a way I could +speed it up. + +Here I'm trying to make +something called fast + +exponentiation, where I'm going +to take advantage of + +another rule for the way +exponentiation works. + +Not only is it true that I can +write b to the n as b times b + +to the n minus 1, but if n +happens to be even, there's + +another rule that I can use. + +If b is even, then I can raise +b to the n over 2, and square + +the answer. + +OK, that's more knowledge about +the way exponents work. + +The point is, that when I +think about the problem + +recursively, when I think +about the problem as a + +function, there's a natural way +to take advantage of that + +additional information. + +So what I can do then is +implement in Python in a + +scheme that looks very similar +to the one that I used for the + +simple exponentiation, +but it has a new + +rule embedded in there. + +So I can say, if n is 0 -- + +that was my original base +case, if n is 0 + +the answer is 1. + +If the modulus of n when divided +by 2 is 1, if it's + +odd, use the old rule-- + +which says b times the exponent +of b, n minus 1. + +However, if it's neither 0 nor +odd, then use this new rule. + +If I use that procedure compared +to the previous + +program, exponent, how many +invocations of fastExponent is + +generated by a call to +fastExponent of 2, 10? + +So talk to your neighbor, +figure out an + +answer, raise your hand. + +Use the number before the dot, +just to keep you alert. + +[AUDIENCE DISCUSSION] + +PROFESSOR: So how many +invocations of fastExponent is + +generated when you call it +with the arguments 2, 10? + +Everybody raise your hand, tell +me a number of fingers. + +OK, it's about 90%, something +like that. + +The most common answer is five, +how did you get five? + +So do you think of reducing +fastExponent of 2, 10? + +What happens the first call? + +AUDIENCE: It goes to +[UNINTELLIGIBLE] + +divided by 2 is 5. + +PROFESSOR: So the first thing +that happens, is that it + +realizes that the 10 is even, +so the 10 is not 0, it's not + +odd, it goes into this case. + +So it tries to run it with 5. + +Then when it tries to +run fastExponent + +with 5, what happens? + +OK, so 5 is not 0, so it's +not the base case. + +It is odd, so 5 gets +reduced to 4. + +4 gets reduced to 2. + +2 gets reduced to-- + +et cetera. + +So the idea is that we get a +faster convergence because, + +just like in the very first +example we did, we can do two + +different kinds of +operations-- + +either decrement, or in this +case half, and half works + +faster when the numbers are +bigger than decrement does, so + +it's the same idea as in +that first program. + +So the idea, then, is that this +requires 5 where we would + +have expected in the previous +exponent procedure, it would + +have required 10. + +And that difference just gets +bigger and bigger as we make n + +bigger and bigger. + +Much more importantly though, +than the fact that we can make + +something fast, is the idea +that this is expressive. + +The idea is that by structuring +the program this + +way, it was perfectly obvious +how to incorporate more + +knowledge about the way +exponents work. + +I could have done it by using +a procedural approach. + +Do this, then do this, +then do this. + +But then I have very complicated +indices. + +Check if it's-- check if it's +squared, check if it's + +whatever, and it's inside +the loop, right? + +So I complicate my looping +structure, where here-- + +because I'm using the functional +approach, it's very + +easy to understand that it just +introduces another case. + +It's nothing complicated. + +So it's much more important-- +the reason we think about + +recursion isn't so much that +it's fast, it's because it's + +expressive. + +It's a way to incorporate +knowledge about an answer into + +a solution, and that's +what we'd like to do. + +We want to have a way of making + +complicated things simply. + +Here's a way to incorporate +knowledge about a procedure in + +a very straightforward +fashion. + +All we have is a second case. + +Rather than making the loops +more complicated, all we have + +is a simple new case +in this statement. + +And that's especially important +when you think about + +harder problems. + +Here is a much harder problem. + +So Tower of Hanoi, you +probably played + +with this as a kid. + +I want to transfer all the disks +from Post A to Post B-- + +I have a typo on your +handout, by the way. + +I typed C on the handout, +and then I wrote the + +program the other way. + +That should have been a B. + +Transfer a stack of disks from +Post A to Post B by moving the + +disks one at a time, never +placing a bigger disk on top + +of a smaller disk. + +OK, that's kind of a challenging +problem. + +It's a very challenging +problem if you try to + +structure it as loops. + +If you try to structure it as +loops I would recommend that + +you do this gazillions of +times until you get the + +pattern stuck in your +head, because the + +pattern's not obvious. + +But the pattern is obvious +if you think + +about it as a recursion. + +I don't know how to move n from +Post A to Post B. How + +about this algorithm, take the +top n minus 1, move those to + +C-- get them out of the way. + +I don't know how you're going to +do that, but just trust me, + +just do it. + +So move n minus 1 of them off +the top, put them over on C, + +that exposes the bottom one. + +Move the bottom one to +B, which is where + +I'd like it to be. + +And then by this mysterious +process of moving n minus 1, + +bring the n minus 1 back from +C back on top of B. + +OK, what did I just do? + +I just started with a +problem that I don't + +know the answer to. + +How do I move n disks from +this post to that post? + +And I broke it into a sequence +of three operations, two of + +which I don't know how to do, +but one of which I know. + +The one will fortuitously +be the base case-- + +or at least similar +to the base case. + +So the idea is, if I want to +transfer the n, do two + +versions of the n minus 1 +problem and glue them together + +with this middle step. + +OK, well I don't know how to +do the n minus 1 problem + +either, just recurse. + +How do I do the n minus 1 one? + +Well, I'll do the +n minus 2 one. + +I don't know how to +do that either. + +Well, then do the +n minus 3 one. + +Keep going until I +get it down to 1. + +Because when I get down to 1, +I do know how to move 1. + +Does that make sense? + +This is supposed to illustrate +that the power of recursion is + +in thinking. + +Some algorithms are easy to +describe recursively. + +That set, is the set when the +hard problem can be reduced to + +a problem of the same type that +is in some sense simpler. + +Here simpler means taking the +index n, and turning it + +into n minus 1. + +If you write this simple little +Python snippet and run + +it, you get this procedure. + +And if you-- + +so the procedure means, take the +top disk off A, put it on + +B. Take the top disk off A, put +it on C. Take the top disk + +off B, put it on C. + +If you do that procedure, it +will magically do exactly the + +right thing. + +If you try to see the pattern +here, so that you were to + +write this in a procedural +approach, the pattern is very + +peculiar, but the algorithm for +doing it is very simple. + +So the idea-- + +one of the reasons that we like +recursion, is this idea + +of expressability. + +It makes it easy to express +what we're trying to do. + +OK, so that's a quick view of +the first two ways to do the + +first problem that +I talked about. + +We started thinking about a +sequence of operations, either + +increment or square, +that transforms an + +integer i into g. + +The first thing we looked at +was a procedural approach + +where I just gave +you a recipe-- + +do this, do this, do this. + +The issue there is that I ended +up with nested loops + +three deep. + +The issue there is keeping track +of the indices for all + +of the different loops. + +We just talked about a +functional approach. + +That can have an advantage, +especially whenever the + +functional approach has a very +simple implementation. + +The last approach I want to +talk about very briefly is + +object-oriented approach. + +Here-- + +I'm doing the same problem +again, find the sequence of + +operations that transforms +i into g, 1 into 100. + +Here I'm doing the same +algorithm again. + +I mean, I haven't really changed +the algorithm in going + +from the procedural approach to +the functional approach, to + +here, the object-oriented +approach. + +I have changed the +representation of the program, + +and that's the point. + +Here the representation +of the program + +is in terms of objects. + +Here what I'm going to do is +think about organizing all the + +sequences of operations that +are possible in a tree. + +So the sequences that I could +do, I could do no operation + +followed by increment +increment increment. + +Or I could do nothing increment +increment square. + +Or I could do nothing square +increment square. + +So I'm thinking about all the +possible sequences, but this + +time, I'm not thinking about it +is a text-string, I'm not + +thinking about it as a list of +functions that I need to call. + +I'm thinking about it as this +tree, this tree of objects. + +And in the object-oriented +approach, what I'm going to do + +is think about the solution in +terms of building up the tree + +until I find the answer. + +So the key in the +object-oriented approach is to + +think of a useful object. + +What would I like to remember +when I'm constructing the + +solution as this +kind of a tree? + +Well, if I call every circle a +node, I can define a class + +that will keep track of +all the important + +things about each node. + +And then I can structure my +program as creating nodes, + +connecting them up into +that tree, and + +looking for the answer. + +So each one of these nodes, +each one of these circles, + +ought to have a parent, they +ought to have an action, and + +they ought to have an answer. + +So, for example, let's say +that I started with the + +initial value i equals 1. + +Then this node right here +might say, whatever your + +answer was at this point, +the answer here was 1. + +So the answer here is going +to be 1 after it's been + +incremented, so answer +should be 2. + +So associated with each +one of these nodes is + +going to be a parent. + +The parent of this guy is this +guy, the parent of this guy is + +this guy, the parent of +this guy is that guy. + +Associated with each node is +going to be an action. + +When I'm here, my action +is to increment. + +When I'm here, my action +is to square. + +And associated with each node +is going to be the answer. + +So if I started at 1, by the +time I get here, the answer's + +going to be 2, 4, 16. + +So the idea is that I'm +structuring the + +problem as a tree. + +Each node has a couple things it +wants to remember, it wants + +to know who it's parent was. + +It wants to know, what's +the operation + +associated with this node? + +And it wants to know the +answer at this node. + +Also associated with each +node, a method. + +And the method will be to print +out the answer if this + +node is the answer. + +So the print routine is going to +have to say, OK, I ended up + +here and that happens +to be the answer. + +Well, how did I get here? + +Well, I have a parent, who has +a parent, who has a parent, + +who is none. + +So this routine is supposed to +figure out the sequence of + +operations that led me from the +initial value up at the + +top to the final answer that +just happens to be goal. + +Is that clear? + +So then I structure the program +in terms of building + +those node structures. + +I start off by making a node, +which is the top node. + +It has no parent, it has no +action, and the answer to the + +top node is 1. + +And then I just think through +loops that are very similar to + +the loops that I was +using before. + +They're structured similarly +to the way they were + +structured in the case of the +imperative program, except now + +the iterations are generating +new nodes. + +The iterations are simpler, +because each one just + +generates a node. + +It's not like in the imperative +case where I + +treated separately, what was +the ASCII string that + +represented the answer, +and what was + +the cumulative answer? + +Here I don't have two pieces +of things that I need to do + +inside my loop, I just +make a node. + +So the idea is that when I solve +the problem using this + +approach, what I'm trying to do +is build a representation + +for the solution out +of pieces that make + +sense for this problem. + +So the important idea that I +want to get across was to + +think about modularity at +the next higher level. + +We started last time with +modularity at the most + +microscopic level in Python, +and we saw how Python had + +primitives that allowed us +to build more complicated + +structures and simplified +our task of + +understanding complex designs. + +We looked at the most +primitive level + +in the first lecture. + +What I just went over was how +even within the structure of + +Python, you can structure +programs that are + +more or less modular. + +And the important point is that +the way you structure the + +program influences the degree +of modularity that you get. + +So the structure of the program +has a significant + +effect on how modular +your solution is. + +What I want to do for the rest +of the time today is jump one + +higher level yet. + +So last time, primitives +within Python. + +First half of this hour, +imperative programming, + +functional programming, +object-oriented programming, + +approaches that affect the +modularity of your solution. + +Now I want to go up one more +level and think about + +abstraction and modularity +at a much higher level. + +And there, I'm going to think +about programs that control + +the evolution of processes. + +What's a process? + +A process is some set +of procedures + +that evolve over time. + +An example was a bank account. + +OK, with the problems that we've +been thinking about so + +far, there was a clear answer. + +What's the minimum-length +sequence + +that blah, blah, blah. + +Right? + +There was a clear answer +to that problem. + +Here there isn't a clear answer +to the problem, what's + +the answer to the +bank account? + +The bank represents a process, +it's something that + +changes with time. + +There are transactions. + +Every time you make a deposit +or a withdrawal, you do a + +transaction that causes some +action to happen in the bank. + +So there isn't an answer, +there's an evolving answer. + +So those are the kinds +of problems I want + +to think about now. + +Graphical user interfaces. + +Again, there's no +answer to Excel. + +Right, you can't say calculate +the answer to Excel. + +Because whatever-- + +so the right answer for Excel +depends on, what's the + +sequence of buttons that you're +pressing, and what's + +the sequence of pull-down menus +that you're doing, and + +all that sort of stuff. + +So graphical user interfaces +are processes. + +They're things that +evolve over time. + +So they take a sequence of +inputs, and they generate a + +sequence of outputs, just +like a bank does. + +Controllers. + +How do you make a +robotic steerer? + +That's a process. + +There are inputs-- + +so for example, where are you +in the middle of the lane? + +What time is it? + +How many pedestrians are +you about to hit? + +There's all of those +kinds of inputs. + +And then there is things +that you output-- + +which is like, keep going. + +So some of the steering rules +are particularly simple. + +Other steering rules are you +know, avoid the guy this-- + +well, anyway. + +So the idea is that when you +were controlling processes, + +we're going to want to think +about other kinds of + +programming structures. + +And even though the programming +structures are + +going to be different, we're +still going to want to have + +this idea of modularity. + +We're going to want to be able +to think about, what are the + +primitives that we have, how can +we combine them, what are + +the important abstractions, +and how + +do we capture patterns? + +We're still going to +want to do PCAP. + +But we're going to want to do +PCAP at a much higher level. + +And the programming module that +I want to introduce is + +the idea of a state machine. + +A state machine is a very +convenient structure to + +capture the behavior +of a process. + +A state machine has an input, +a state, and an output. + +The idea is that +it's a process. + +It's operated upon in steps. + +Every step there's +a new input. + +From that input, the state +machine can calculate an + +output and the next state. + +By keeping track of the state, +this state machine can + +remember everything it needs +to know so that it can + +continue the process +into the future. + +So the idea is that this +is going to represent a + +fundamental programming element, +that we'll be able to + +use to construct things that +are like processes. + +And in particular, we use this +to represent the calculations + +that are done within +our robot. + +We'll think about the robot +as being a process. + +It's not got an answer, you +can't ask the question, what's + +the answer, to the robot. + +But you can answer the question, +if I were trying to + +steer and the sonar said +(x,y,z), how fast should you + +turn the wheels? + +You can think about that +as a state machine. + +There's some state +of the robot. + +There are some inputs-- + +which is what the sonars are +currently telling us, and + +there's some output-- + +which is how fast we're +driving the wheels. + +So we want to think about this +kind of a representation for + +processes that evolve +over time. + +OK, here's a very simple +example, a turnstile. + +So we can think about the +turnstile as a state machine. + +The turnstile has two states-- + +think about getting +onto the T-- + +either it's locked, or +it's not locked. + +Those are the two states +of the turnstile. + +There are some inputs. + +The inputs are, I put a coin +in it, or I walk through it + +and the turnstile turns, +or I don't do anything. + +And based on those inputs, and +based on the current state, + +the turnstile has +some outputs. + +So the turnstile can either +allow you to enter, + +or ask you to pay. + +So the output might be an LED +sign that says, please enter. + +Or it could have an LED sign +that says, please pay. + +So those are out all of the +elements of a state machine. + +And so we can think about a +graphical representation for + +the turnstile in terms +of states. + +Here I'm representing the +states as circles. + +There are two states in the +turnstile, the turnstiles is + +either locked or unlocked. + +You move between states +by getting inputs. + +So the inputs are represented +by the arcs-- + +it's the top identifier on each +arc is the input, the + +bottom identifier is the output, +and the special arrow + +says I start here. + +So the turnstiles start out +locked in the morning-- + +the turnstile is locked. + +If you drop a coin in it, you'll +move into the unlocked + +state and it will +output enter. + +It will tell you that it's OK to +enter because you've put a + +coin in it now. + +Then as long as you stay there +and do nothing, it'll continue + +to say enter-- + +none enter. + +Or if you keep dropping coins +in it, it'll say hey, keep + +going, and it'll continue to eat +your coins and continue to + +say enter-- + +being very nice. + +So in those cases it remains +unlocked, it continues to tell + +you that you can enter, and that +state persists until you + +turn the turnstile. + +When you turn the turnstile, +this particular turnstile + +forgets how many coins you gave +it and it simply locks + +and it tells you you've +got to pay more. + +So the idea is that we can +capture the desired behavior + +of the turnstile-- + +the turnstile is a process, +it's a thing that + +evolves over time. + +But we can capture the essence +of what we would like the + +turnstile to do in terms +of this diagram. + +We'll call this a +state diagram. + +And then we can think about +behaviors in terms of a set of + +outputs as a function of time. + +So imagine that as a +function of time-- + +say I started in the +state locked, and + +the input is nothing. + +So you wake up in the morning, +you go to the T, overnight the + +turnstiles have all +been locked. + +They all say that they're +locked, they all say, pay, as + +their output. + +If I don't do anything it just +sits there and it says pay. + +If I drop a coin, it says enter +and it moves into the + +unlocked state. + +If I don't do anything +enter persists + +and it stays unlocked. + +If I walk through it, it eats +the coin and it says, OK, you + +gotta pay now, and it locks. + +So you can think about the +evolution of this process-- + +the evolution of the turnstile +in terms of the diagram with + +regard to time. + +And the idea then is that this +is a kind of a representation + +that allows us to succinctly +capture the important + +information about how +processes work. + +One of the important features of +this representation is that + +it removes you one level away +from the looping structure. + +Somewhere somebody's keeping +track of the loop. + +Something's going from time 0 to +time 1, to time 2, to 3 -- + +we'll talk about that later. + +But for the time being, this +representation focuses on what + +do you do at each instance +in time? + +So it's a way of tearing apart +the time part from the state + +transition part. + +So separate out the loop from +the essence, it's very much + +like the functional example +that I did. + +The functions divorce themselves +from the looping + +structure that we saw in the +imperative approach, and you + +could define the functions +independent of the looping. + +We're doing the same +thing here. + +We can define the state +machine representation + +independent of the looping. + +And most importantly, +this idea of + +state machines is modular. + +Let me show you how that +plays out when we + +think about the robot. + +Think about the problem that I +showed you last time where + +we're trying to have the robot +go from point A to point B. + +Where, for example, it knows +where it is -- say it has GPS + +or something. + +It knows-- + +from a map say, where it wants +to be, but it has no idea of + +the obstacles between where it +is and where it wants to be. + +So we can think about that kind +of a problem-- we looked + +at this last time. + +It takes a step, it +uses its sonars-- + +which are depicted by these +lines, to infer that there are + +some walls-- + +that's the black dots. + +So it gets a reflection off the +sonar that tells it that + +there's some obstacle +in the way. + +That means it's not a good +idea to try to plow + +straightforward, so if I back +up, the original plan, it had + +no idea what was between it and +its destination, so its + +plan was just buzz +straight through. + +At the end of its first step, it +has got back sonar reports + +that tell it that there's a wall +here, and here, and here, + +and here, and here, and here. + +And based on where the wall is, +and the size of the robot, + +it can't get into any of +these red squares. + +It's too big. + +So it knows its original path, +which went from here to here, + +isn't going to work because +it can't fit through. + +So it computes a new path, +and then repeat. + +So the idea is that +we're solving a + +very complicated problem-- + +the robot 's solving a very +complicated problem, and what + +I'd like to do now is +think through a + +solution to that problem. + +As the robot's moving along, +on every step it's getting + +some new input-- + +it's behaving just like +a state machine. + +On every step it gets new +input from the sonars. + +Based on that new +input, it knows + +where there's new obstacles. + +Based on that knowledge, +it has a better idea of + +what the map is. + +Based on that knowledge, it has +a better idea of finding a + +plan that might work. + +And then based on that +knowledge, it knows how to + +tell the wheels to +move forward. + +So think about where +it is right now. + +It has done, logically, three +different things. + +It has figured out where +the walls are. + +That's the thing represented +in black and red. + +We'll call that -- +it made a map. + +Given the map, it +made a plan-- + +that's the blue thing. + +Given the plan, it figured out +how to turn the wheels. + +It's going straight ahead. + +So there are logically three +things going on, + +all at the same time. + +You can imagine writing an +imperative program to capture + +that behavior, but that's +complicated. + +Not impossible, you +would structure it + +as a bunch of loops. + +You know, it would-- + +unless you're a crack +programmer, and + +I'm sure you are-- + +it will end up being +an ugly program. + +The idea is, that by using the +state machine representation + +we'll be able to think +about how to pull + +apart those three pieces. + +So in particular, we can think +about the state machine for + +the robot-- + +which would take the sensory +input from the sonars and turn + +it into an action, which +is turning the wheels-- + +we can think about that as +having three modules. + +There's the mapmaker module, +which just looks at the + +sensory input. + +Doesn't care what the plan is, +doesn't care how it's turning + +the wheels right now. + +All it the cares about +is, what was the -- + +what's my current state? + +And what new information +can I infer about the + +map from the sonars? + +So given the sonars and my +current state, what's the most + +recent version of the map +likely to look like. + +Then there's a planner that +says, given the sonars and the + +map, how would I construct +this blue line? + +Given my current understanding +of the map of the world, how + +would I get from where I am, +to where I want to be? + +That's a plan. + +Then from that plan-- + +say the robot is here, from the +plan you can see that the + +thing the robot should do +is move straight ahead. + +So the mover can take +the heading-- + +the heading is just simply the +coordinates of the first + +destination point in the plan. + +So the mover can look at the +heading, the first destination + +point, and figure out how +to make the wheels turn. + +So the idea is that the state +machine representation will + +let us parse a very complicated +problem. + +A process-- + +the process by which the robot +gets from here to there, a + +very complicated process. + +We're going to be able to +break it up into pieces. + +The pieces are going +to be much easier. + +They're going to be modular. + +We will be able to write this +piece, and debug it and make + +sure that it all works, +independent + +of these other pieces. + +Because we just have it do any +arbitrary walk around task or + +no walk around at all and ask +whether the set of sensory + +inputs generates the +correct map. + +Similarly, this will +be a module. + +This will be something that we +can debug as well without + +having the other +pieces working. + +We'll be able to say, OK, well, +what if I fed a map that + +I hand constructed +to the robot-- + +ignore this, just forget +this, assume + +there is none of these-- + +I can hand make a map, feed it +to this guy, give it sensory + +input and see if it comes up +with the right heading. + +It's just like in that +functional approach example + +that I did. + +Having made the individual +functions, we were able to + +test them individually because +they were modules. + +Having made these individual +state machines, we'll be able + +to test them individually +because they're modules. + +Then at the end we'll be able to +paste them all together and + +get a very complicated +behavior-- + +much more complicated than you +would expect from the sum of + +the three programming +activities. + +That's what we want. + +That's how we want to +structure things. + +We want to be able to combine +simple things and get + +something that seems more +powerful than the linear + +combination, because it is. + +Okay, so that's the goal. + +To do that, we're going to +invent some new Python + +structures. + +And we're going to think about +the representation of the + +state machine in Python and +we will use objects. + +In fact, we use objects +at three levels. + +We'll think about the highest +level of abstraction of this + +problem as a state machine. + +So there's going to be +state machine class. + +The state machine class is going +to have all the things + +in it that all state machines +have to know about. + +All state machines, as we define +them, are going to have + +to know how to start, how to +make one step, and how to + +combine single steps into a +sequence of steps-- and we'll + +call that operation +of transduction. + +So if you give me a list of +inputs, transduce will make a + +list of outputs. + +So all state machines are +going to be able to-- + +all state machines are going to +have to know how to start, + +step, and transduce. + +Then for particular types +of state machines-- + +like the turnstile, we will +generate a subclass. + +The subclass of turnstiles are +going to have to know-- all of + +those are going to have to +do some other things. + +All turnstiles are going to have +to have a rule for what + +happens when you're in state +A and you get input i-- + +what should you do? + +Well there's going to be a +general pattern that all + +turnstiles will subscribe to. + +We'll put those in the +subclass, turnstile. + +Then individual turnstiles. + +The first one in the Kendall +stop, the second one in the + +Kendall stop, the first one in +the Central stop, the third + +one in the Harvard stop-- + +particular turnstiles +will be instances of + +the turnstile class. + +So the way this plays out, we'll +have a generic state + +machine class defined here. + +The state machine class will +have a method, start. + +Start will create the instance +variable, state. + +Every instance of a turnstile +has to remember where it is, + +that's an instance variable. + +That instance variable gets +created by the start routine. + +So the very first thing you do +if you want to talk about a + +new turnstile, is you have to +instantiate the turnstile. + +Then you have to make +an instance-- + +and you do that by +calling start. + +Every state machine has to +have a start routine. + +Every start routine will do +this-- it'll create an + +instance variable. + +Every state machine has to +know how to take a step. + +We will make a generic method +called, getNextValues, which + +will include all of the rules +for how the class turnstile + +generates a new output, and a +new state from the implant. + +And every subclass of state +machine will have to define + +what one of those looks like. + +The important thing here is that +every state machine has + +to have a step routine, and +the way we've decided to + +implement the step routine is +to call the getNextValues, + +that is particular to the +subclass of interest. + +So for example, the +getNextValues for a turnstile, + +might be different from the +getNextValues for a planner or + +a for a mapper. + +Then we will subclass state +machine according to the kind + +of state machine we're making. + +A planner, a mapper, a +mover, a turnstile. + +So a turnstile will be a class, +which is a subclass of + +state machine, and that's where +we'll define how do you + +do getNextValues. + +If you're a turnstile, here's +the way you ought to do + +getNextValues. + +When I call getNextValues, I'll +tell you your current + +state and the current input, and +from those two you ought + +to be able to figure out the +next state and the output. + +So the getNextValues method for +the turnstile class ought + +to take state and input-- + +the input, and the current +state, and it generates a + +tuple, which is the new +state and the output. + +And this is the rule by +which it happens. + +All turnstiles also have +the same start state. + +So if you look back again at +state machine, state machine + +created the instance +variable, state, by + +looking at start's state. + +All turnstiles have the +same start state, + +they all start locked. + +And then finally, the way we'll +use this, is we will + +instantiate a turnstile, we +will make an instance of + +turnstile, put it into TS, +turnstile, so this could be + +Central Square 16, +for example. + +And then that instance, we'll +be able to do things like + +start, step, and transduce. + +So if I transduced this the +input, none, coin, none, turn, + +turn, coin, coin, on a +particular turnstile, I'll + +generate some sequence +of outputs like so. + +So that's a complicated example +using turnstiles. + +Let me do something simpler +just to make + +sure you get the idea. + +Let's think about a simpler +class, a subclass of state + +machines, a subclass +called accumulator. + +That subclass always has a start +state of 0, and has a + +getNextValues that returns the +same value for the next state + +and for the output. + +It always adds the current +state to the input-- + +hence the name accumulator. + +It accumulates the input by +taking the current state, + +adding the currently input +to generate a new state-- + +that's just like +a bank account. + +The bank account would +accumulate transactions. + +So if the input to the +accumulator is 7, then the + +state gets incremented by 7, and +the output is the value of + +the new state. + +So that's what this says, the +starting state is always 0, + +the getNextValues always returns +for this new state-- + +state plus input, and for the +current output, the same thing + +as the current state. + +Everybody's clear? + +So the question is, what would +happen if I did this sequence + +of operations? + +Let's say that I have the state +machine class, I have + +the accumulator subclass. + +I make an instance A, I do some +stuff to A, I make an + +instance B. I do some stuff +to B, I do some stuff to + +A, and I type this. + +What gets printed? + +Take 30 seconds, talk to your +neighbor, figure out + +what the answer is. + +[AUDIENCE DISCUSSION] + +PROFESSOR: OK. + +What will get printed by +the print statement? + +Answer (1), (2), (3), +(4), or (5). + +Everybody raise your hand +with an answer. + +Excellent, excellent, +almost 100%. + +I don't think I see a +single wrong answer. + +So everybody seems +to be saying (2). + +(2), OK, so what's going on? + +So A is an accumulator, we +start it, we step it. + +B is an accumulator, we start +it, we step it, we step. + +So what is going to be A, +how did you get five? + +Well, A started at 0 that's +what the start + +method does, right? + +Stepping it stepped it to 7. + +B made a new one, we can ignore +that because it's a + +separate instance. + +The idea is that the state is +associated with the instance. + +So when we perturb the state of +B by doing B.step, we are + +touching the state of A-- + +because they're instance +variables. + +So that means when we +decrement it, we're + +decrementing the 7 to get 5. + +OK, seems reasonable. + +So the answer is either +(1), or (2), or none. + +Why is it the same (21, 21) (21, +21), when we called the + +A.getNextValues, and here we're +calling the B. Why are + +they the same? + +AUDIENCE: Because it sets +the state [INAUDIBLE]. + +PROFESSOR: So getNextValues +is a pure function. + +So it gets passed in the state, +the first number is the + +state, the second number +is the input. + +So it doesn't pay any attention +to the instance + +variable state, it uses the +thing they got passed in. + +Furthermore, the getNextValues +associated with A, is + +precisely the same as the +getNextValues associated with + +B, because getNextValues is +something that's in the + +accumulator subclass. + +So they're exactly the same +because it's the same method. + +So what should be in your +head, is a picture + +that looks like this. + +When we said create a state +machine, that was something we + +put in our library, and that +makes this environment. + +When we said subclass of state +machine to make accumulator, + +that made a new class, +a new environment. + +And then when we made A and +B by saying that A equals + +accumulator, and B equals + +accumulator, that made instances. + +The instances were initially +empty, but when I say A.start, + +that created the state variable +in the A instance, + +and in the B instance, and +associated values with them. + +So with the picture that you're +supposed to have in + +mind, is that there's an +environment associated with + +state machine. + +There's a separate environment +associated with accumulator, + +but just one of those. + +But there's two instances. + +So there's two sets of instance +variables, one + +associated with A and B. So +the answer was number (2). + +Now the robot example was +supposed to motivate this idea + +that what we're going to do +with state machines is put + +them together modularly. + +So what we're going to do-- and +you start to do that this + +week, and also continuing into +next week, we'll figure out + +how to compose state machine +M1 and M2 in a cascade. + +That means the output of the +first one becomes the input to + +the second one. + +We'll put things together in +parallel, we'll put things + +together with feedback. + +So what we'll do, is we'll +figure out operators. + +PCAP-- + +primitives, means +of combination, + +abstraction, patterns. + +The primitives are going to be +the state machines, the ways + +we combine them are going to be +these kinds of structures. + +Cascade them, put them in +parallel, that kind of stuff. + +And that's going to allow us to +make complicated brains out + +of simple ones. + +Here's a very simple example, +what if I had a state machine + +A, which is an accumulator, +so A is an instance of + +accumulator. + +B is an instance of accumulator, +there's two + +separate instances. + +And C is a new state composed +by cascading A and B. What + +would happen if I typed out +C.transduce so ([7, 3, 4])? + +What's the answer to C.transduce +([7,3,4])? + +[AUDIENCE DISCUSSION] + +PROFESSOR: So what happens +when I transduce C? + +Well C is a composition of A +and B. In particular, it's + +this composition. + +C is just the cascade of A into +B. What that means is + +that if I put some sequence of +inputs into the first machine, + +and if I put some sequence of +the inputs into C, it's the + +same as putting it into A. + +The output of the composite +machine is the output of B. + +And the input to B is the same +as the output of A. So the + +([7,3,4]) goes through A, which +is an accumulator, and + +comes out [7, 10, 14]. + +It accumulates, that's +what accumulators do. + +That clear? + +Then [7, 10, 14] + +goes into B and comes +out [7, 17, 31]. + +So C, which is the cascade of +two accumulators, ends up + +transforming [7, 3, 4] + +into [7, 17, 31]. + +So that's the idea for how +we're going to compose + +complicated behaviors out of +simple ones, and that's what + +the assignment is +for this week. \ No newline at end of file diff --git a/cSgaMRF4NlY.txt b/cSgaMRF4NlY.txt new file mode 100644 index 0000000000000000000000000000000000000000..30f71968b68620051ef6bba306678e642481c46f --- /dev/null +++ b/cSgaMRF4NlY.txt @@ -0,0 +1,17891 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +okay so what I want to talk about today + + align:start position:0% +okay so what I want to talk about today + + + align:start position:0% +okay so what I want to talk about today +is land markets and uh including the + + align:start position:0% +is land markets and uh including the + + + align:start position:0% +is land markets and uh including the +paper you guys read for today and + + align:start position:0% +paper you guys read for today and + + + align:start position:0% +paper you guys read for today and +broadly speaking we're going to cover I + + align:start position:0% +broadly speaking we're going to cover I + + + align:start position:0% +broadly speaking we're going to cover I +think two broad themes in that market so + + align:start position:0% +think two broad themes in that market so + + + align:start position:0% +think two broad themes in that market so +one is sort of why the allocation of + + align:start position:0% +one is sort of why the allocation of + + + align:start position:0% +one is sort of why the allocation of +land May matter + + align:start position:0% +land May matter + + + align:start position:0% +land May matter +um so that's moral hazard and + + align:start position:0% +um so that's moral hazard and + + + align:start position:0% +um so that's moral hazard and +sharecropping issues + + align:start position:0% +sharecropping issues + + + align:start position:0% +sharecropping issues +uh related to the paper you read today + + align:start position:0% +uh related to the paper you read today + + + align:start position:0% +uh related to the paper you read today +so I'll start with some basic kind of + + align:start position:0% +so I'll start with some basic kind of + + + align:start position:0% +so I'll start with some basic kind of +basic theory on this stuff + + align:start position:0% +basic theory on this stuff + + + align:start position:0% +basic theory on this stuff +and then the other question is sort of + + align:start position:0% +and then the other question is sort of + + + align:start position:0% +and then the other question is sort of +how do we think about + + align:start position:0% +how do we think about + + + align:start position:0% +how do we think about +um property rights and why do secure + + align:start position:0% +um property rights and why do secure + + + align:start position:0% +um property rights and why do secure +rights over property matter how do we + + align:start position:0% +rights over property matter how do we + + + align:start position:0% +rights over property matter how do we +think about the plan titling and things + + align:start position:0% +think about the plan titling and things + + + align:start position:0% +think about the plan titling and things +like that and the implications of those + + align:start position:0% +like that and the implications of those + + + align:start position:0% +like that and the implications of those +for investment decisions so mostly today + + align:start position:0% +for investment decisions so mostly today + + + align:start position:0% +for investment decisions so mostly today +is going to be like moral hazard and + + align:start position:0% +is going to be like moral hazard and + + + align:start position:0% +is going to be like moral hazard and +sharecropping I guess today's Wednesday + + align:start position:0% +sharecropping I guess today's Wednesday + + + align:start position:0% +sharecropping I guess today's Wednesday +so Monday will be uh primarily on uh + + align:start position:0% +so Monday will be uh primarily on uh + + + align:start position:0% +so Monday will be uh primarily on uh +investment decisions and + + align:start position:0% + + + + align:start position:0% + +and okay + + align:start position:0% +and okay + + + align:start position:0% +and okay +um + + align:start position:0% +um + + + align:start position:0% +um +okay so stepping way back right + + align:start position:0% +okay so stepping way back right + + + align:start position:0% +okay so stepping way back right +um + + align:start position:0% + + + + align:start position:0% + +very a very very very old subject it's + + align:start position:0% +very a very very very old subject it's + + + align:start position:0% +very a very very very old subject it's +been around for forever essentially or + + align:start position:0% +been around for forever essentially or + + + align:start position:0% +been around for forever essentially or +for a very very long time and that's + + align:start position:0% +for a very very long time and that's + + + align:start position:0% +for a very very long time and that's +been sort of laborers pay owners who + + align:start position:0% +been sort of laborers pay owners who + + + align:start position:0% +been sort of laborers pay owners who +share of the output okay + + align:start position:0% +share of the output okay + + + align:start position:0% +share of the output okay +so um sharecropping is is ubiquitous + + align:start position:0% +so um sharecropping is is ubiquitous + + + align:start position:0% +so um sharecropping is is ubiquitous +object and it's been thought about for a + + align:start position:0% +object and it's been thought about for a + + + align:start position:0% +object and it's been thought about for a +very long time you know going back like + + align:start position:0% +very long time you know going back like + + + align:start position:0% +very long time you know going back like +even to economists like Smith and + + align:start position:0% +even to economists like Smith and + + + align:start position:0% +even to economists like Smith and +Marshall were sort of talking about this + + align:start position:0% +Marshall were sort of talking about this + + + align:start position:0% +Marshall were sort of talking about this +issue and and not only just talking + + align:start position:0% +issue and and not only just talking + + + align:start position:0% +issue and and not only just talking +about it but recognizing that there may + + align:start position:0% +about it but recognizing that there may + + + align:start position:0% +about it but recognizing that there may +be an inefficiency from sharecropping + + align:start position:0% +be an inefficiency from sharecropping + + + align:start position:0% +be an inefficiency from sharecropping +right and the inefficiency is you don't + + align:start position:0% +right and the inefficiency is you don't + + + align:start position:0% +right and the inefficiency is you don't +get the full returns to your labor right + + align:start position:0% +get the full returns to your labor right + + + align:start position:0% +get the full returns to your labor right +because some share of it is going to the + + align:start position:0% +because some share of it is going to the + + + align:start position:0% +because some share of it is going to the +landlord so you know that could lead you + + align:start position:0% +landlord so you know that could lead you + + + align:start position:0% +landlord so you know that could lead you +to sort of not work as hard as you as + + align:start position:0% +to sort of not work as hard as you as + + + align:start position:0% +to sort of not work as hard as you as +you would otherwise right that's the + + align:start position:0% +you would otherwise right that's the + + + align:start position:0% +you would otherwise right that's the +basic issue okay + + align:start position:0% +basic issue okay + + + align:start position:0% +basic issue okay +um so here's just like a super duper + + align:start position:0% +um so here's just like a super duper + + + align:start position:0% +um so here's just like a super duper +duper simple like simple model to sort + + align:start position:0% +duper simple like simple model to sort + + + align:start position:0% +duper simple like simple model to sort +of make this very clear + + align:start position:0% +of make this very clear + + + align:start position:0% +of make this very clear +um so imagine that Barry's degree + + align:start position:0% +um so imagine that Barry's degree + + + align:start position:0% +um so imagine that Barry's degree +there's some output the the output is f + + align:start position:0% +there's some output the the output is f + + + align:start position:0% +there's some output the the output is f +of I that's where that's some input you + + align:start position:0% +of I that's where that's some input you + + + align:start position:0% +of I that's where that's some input you +know tenant pays some cost C could be + + align:start position:0% +know tenant pays some cost C could be + + + align:start position:0% +know tenant pays some cost C could be +their own labor whatever owner receives + + align:start position:0% +their own labor whatever owner receives + + + align:start position:0% +their own labor whatever owner receives +a share of alpha of the output so what's + + align:start position:0% +a share of alpha of the output so what's + + + align:start position:0% +a share of alpha of the output so what's +going to happen the tenant is going to + + align:start position:0% +going to happen the tenant is going to + + + align:start position:0% +going to happen the tenant is going to +solve you know um some problem they're + + align:start position:0% +solve you know um some problem they're + + + align:start position:0% +solve you know um some problem they're +gonna you know they get taxed + + align:start position:0% +gonna you know they get taxed + + + align:start position:0% +gonna you know they get taxed +essentially one minus Alpha on the + + align:start position:0% +essentially one minus Alpha on the + + + align:start position:0% +essentially one minus Alpha on the +output they pay the full costs the first + + align:start position:0% +output they pay the full costs the first + + + align:start position:0% +output they pay the full costs the first +order condition of that is just that the + + align:start position:0% +order condition of that is just that the + + + align:start position:0% +order condition of that is just that the +marginal product is equal to the + + align:start position:0% +marginal product is equal to the + + + align:start position:0% +marginal product is equal to the +marginal cost + + align:start position:0% +marginal cost + + + align:start position:0% +marginal cost +module of the tax rate right so uh if + + align:start position:0% +module of the tax rate right so uh if + + + align:start position:0% +module of the tax rate right so uh if +they're if they're being taxed that's + + align:start position:0% +they're if they're being taxed that's + + + align:start position:0% +they're if they're being taxed that's +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +um the the marginal product is going to + + align:start position:0% +um the the marginal product is going to + + + align:start position:0% +um the the marginal product is going to +be greater than than T and therefore if + + align:start position:0% +be greater than than T and therefore if + + + align:start position:0% +be greater than than T and therefore if +f is concave they're going to put it put + + align:start position:0% +f is concave they're going to put it put + + + align:start position:0% +f is concave they're going to put it put +less input than they would otherwise + + align:start position:0% +less input than they would otherwise + + + align:start position:0% +less input than they would otherwise +right that's like super duper duper + + align:start position:0% +right that's like super duper duper + + + align:start position:0% +right that's like super duper duper +basic like tax uh you know if you tax + + align:start position:0% +basic like tax uh you know if you tax + + + align:start position:0% +basic like tax uh you know if you tax +things people do less of them right + + align:start position:0% +things people do less of them right + + + align:start position:0% +things people do less of them right +um Okay so + + align:start position:0% +um Okay so + + + align:start position:0% +um Okay so +um + + align:start position:0% +um + + + align:start position:0% +um +is one thing that's worth noting + + align:start position:0% +is one thing that's worth noting + + + align:start position:0% +is one thing that's worth noting +actually that's very important is if you + + align:start position:0% +actually that's very important is if you + + + align:start position:0% +actually that's very important is if you +this is the key thing that's driving + + align:start position:0% +this is the key thing that's driving + + + align:start position:0% +this is the key thing that's driving +this Distortion is this is a tax on + + align:start position:0% +this Distortion is this is a tax on + + + align:start position:0% +this Distortion is this is a tax on +output not a tax on profits + + align:start position:0% +output not a tax on profits + + + align:start position:0% +output not a tax on profits +right + + align:start position:0% +right + + + align:start position:0% +right +um so if I if I wrote this exact same if + + align:start position:0% +um so if I if I wrote this exact same if + + + align:start position:0% +um so if I if I wrote this exact same if +I change this so that instead of having + + align:start position:0% +I change this so that instead of having + + + align:start position:0% +I change this so that instead of having +a tax on the output here I taxed your + + align:start position:0% +a tax on the output here I taxed your + + + align:start position:0% +a tax on the output here I taxed your +profits which is your you know F of I + + align:start position:0% +profits which is your you know F of I + + + align:start position:0% +profits which is your you know F of I +minus CL + + align:start position:0% +minus CL + + + align:start position:0% +minus CL +IP then in that case it's it wouldn't + + align:start position:0% +IP then in that case it's it wouldn't + + + align:start position:0% +IP then in that case it's it wouldn't +matter right you can just check that + + align:start position:0% +matter right you can just check that + + + align:start position:0% +matter right you can just check that +sort of you know this the the solution + + align:start position:0% +sort of you know this the the solution + + + align:start position:0% +sort of you know this the the solution +here + + align:start position:0% +here + + + align:start position:0% +here +um is the same as if there was no kind + + align:start position:0% +um is the same as if there was no kind + + + align:start position:0% +um is the same as if there was no kind +of I didn't have to share the output + + align:start position:0% +of I didn't have to share the output + + + align:start position:0% +of I didn't have to share the output +here + + align:start position:0% +here + + + align:start position:0% +here +okay and that's the general factors that + + align:start position:0% +okay and that's the general factors that + + + align:start position:0% +okay and that's the general factors that +that profit taxes are non-distortionary + + align:start position:0% +that profit taxes are non-distortionary + + + align:start position:0% +that profit taxes are non-distortionary +um and that's actually related to you + + align:start position:0% +um and that's actually related to you + + + align:start position:0% +um and that's actually related to you +know broader issues of like why are + + align:start position:0% +know broader issues of like why are + + + align:start position:0% +know broader issues of like why are +corporate income taxes for example taxes + + align:start position:0% +corporate income taxes for example taxes + + + align:start position:0% +corporate income taxes for example taxes +on profits not taxes on revenues it has + + align:start position:0% +on profits not taxes on revenues it has + + + align:start position:0% +on profits not taxes on revenues it has +to do with like these kinds of ideas + + align:start position:0% +to do with like these kinds of ideas + + + align:start position:0% +to do with like these kinds of ideas +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um of course the problem is is that what + + align:start position:0% +um of course the problem is is that what + + + align:start position:0% +um of course the problem is is that what +we can observe is your output + + align:start position:0% +we can observe is your output + + + align:start position:0% +we can observe is your output +right it's not it although as you talk + + align:start position:0% +right it's not it although as you talk + + + align:start position:0% +right it's not it although as you talk +about you saw in the paper even + + align:start position:0% +about you saw in the paper even + + + align:start position:0% +about you saw in the paper even +observing the output is hard but it's at + + align:start position:0% +observing the output is hard but it's at + + + align:start position:0% +observing the output is hard but it's at +least more plausible that you can + + align:start position:0% +least more plausible that you can + + + align:start position:0% +least more plausible that you can +observe the the output rather than + + align:start position:0% +observe the the output rather than + + + align:start position:0% +observe the the output rather than +observe your profits especially when if + + align:start position:0% +observe your profits especially when if + + + align:start position:0% +observe your profits especially when if +we think of like a agricultural uh like + + align:start position:0% +we think of like a agricultural uh like + + + align:start position:0% +we think of like a agricultural uh like +a you know uh self-employed farmer or + + align:start position:0% +a you know uh self-employed farmer or + + + align:start position:0% +a you know uh self-employed farmer or +something where a lot of their inputs + + align:start position:0% +something where a lot of their inputs + + + align:start position:0% +something where a lot of their inputs +are their own labor or things like that + + align:start position:0% +are their own labor or things like that + + + align:start position:0% +are their own labor or things like that +like that's very difficult to actually + + align:start position:0% +like that's very difficult to actually + + + align:start position:0% +like that's very difficult to actually +observe and and so the Distortion comes + + align:start position:0% +observe and and so the Distortion comes + + + align:start position:0% +observe and and so the Distortion comes +from the fact that we're taxing Revenue + + align:start position:0% +from the fact that we're taxing Revenue + + + align:start position:0% +from the fact that we're taxing Revenue +not taxing profits + + align:start position:0% +not taxing profits + + + align:start position:0% +not taxing profits +okay + + align:start position:0% +okay + + + align:start position:0% +okay +clear + + align:start position:0% +clear + + + align:start position:0% +clear +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so the the solution and actually I think + + align:start position:0% +so the the solution and actually I think + + + align:start position:0% +so the the solution and actually I think +one of you at least one of you sort of + + align:start position:0% +one of you at least one of you sort of + + + align:start position:0% +one of you at least one of you sort of +talked about this in your + + align:start position:0% +talked about this in your + + + align:start position:0% +talked about this in your +um in your uh in your reading response + + align:start position:0% +um in your uh in your reading response + + + align:start position:0% +um in your uh in your reading response +is the solution to this problem is a + + align:start position:0% +is the solution to this problem is a + + + align:start position:0% +is the solution to this problem is a +rental contract + + align:start position:0% +rental contract + + + align:start position:0% +rental contract +right so faced with this what should + + align:start position:0% +right so faced with this what should + + + align:start position:0% +right so faced with this what should +what should what do they do rather than + + align:start position:0% +what should what do they do rather than + + + align:start position:0% +what should what do they do rather than +have this extraordinary contract well + + align:start position:0% +have this extraordinary contract well + + + align:start position:0% +have this extraordinary contract well +what should happen is the tenant should + + align:start position:0% +what should happen is the tenant should + + + align:start position:0% +what should happen is the tenant should +rent the land from the landlord for a + + align:start position:0% +rent the land from the landlord for a + + + align:start position:0% +rent the land from the landlord for a +fixed rent r + + align:start position:0% +fixed rent r + + + align:start position:0% +fixed rent r +and keep all the output + + align:start position:0% +and keep all the output + + + align:start position:0% +and keep all the output +okay and so that contract would look + + align:start position:0% +okay and so that contract would look + + + align:start position:0% +okay and so that contract would look +like this + + align:start position:0% +like this + + + align:start position:0% +like this +right it would look they tenant would + + align:start position:0% +right it would look they tenant would + + + align:start position:0% +right it would look they tenant would +maximize I minus F sorry maximize over + + align:start position:0% +maximize I minus F sorry maximize over + + + align:start position:0% +maximize I minus F sorry maximize over +the inputs F of I minus CL minus r the + + align:start position:0% +the inputs F of I minus CL minus r the + + + align:start position:0% +the inputs F of I minus CL minus r the +fact that this r r is a lump sum here so + + align:start position:0% +fact that this r r is a lump sum here so + + + align:start position:0% +fact that this r r is a lump sum here so +it doesn't affect kind of the decisions + + align:start position:0% +it doesn't affect kind of the decisions + + + align:start position:0% +it doesn't affect kind of the decisions +so that gets us the first best + + align:start position:0% +so that gets us the first best + + + align:start position:0% +so that gets us the first best +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um that would in some sense that's the + + align:start position:0% +um that would in some sense that's the + + + align:start position:0% +um that would in some sense that's the +that's the Benchmark solution to all + + align:start position:0% +that's the Benchmark solution to all + + + align:start position:0% +that's the Benchmark solution to all +these problems is we should just you + + align:start position:0% +these problems is we should just you + + + align:start position:0% +these problems is we should just you +know the tenant should rent the contract + + align:start position:0% +know the tenant should rent the contract + + + align:start position:0% +know the tenant should rent the contract +rent the land for a fixed fee + + align:start position:0% +rent the land for a fixed fee + + + align:start position:0% +rent the land for a fixed fee +so why does that not happen + + align:start position:0% +so why does that not happen + + + align:start position:0% +so why does that not happen +okay so um there's a couple of reasons + + align:start position:0% +okay so um there's a couple of reasons + + + align:start position:0% +okay so um there's a couple of reasons +why this doesn't happen and that's kind + + align:start position:0% +why this doesn't happen and that's kind + + + align:start position:0% +why this doesn't happen and that's kind +of what I'm going to talk about for the + + align:start position:0% +of what I'm going to talk about for the + + + align:start position:0% +of what I'm going to talk about for the +next like I don't know half an hour or + + align:start position:0% +next like I don't know half an hour or + + + align:start position:0% +next like I don't know half an hour or +so right so one is kind of comes from + + align:start position:0% +so right so one is kind of comes from + + + align:start position:0% +so right so one is kind of comes from +stiglets + + align:start position:0% +stiglets + + + align:start position:0% +stiglets +and the the the idea is that there's a + + align:start position:0% +and the the the idea is that there's a + + + align:start position:0% +and the the the idea is that there's a +trade-off between incentives and risk + + align:start position:0% +trade-off between incentives and risk + + + align:start position:0% +trade-off between incentives and risk +sharing + + align:start position:0% +sharing + + + align:start position:0% +sharing +okay so the problem with this contract + + align:start position:0% +okay so the problem with this contract + + + align:start position:0% +okay so the problem with this contract +right is that if we imagine that the + + align:start position:0% +right is that if we imagine that the + + + align:start position:0% +right is that if we imagine that the +output is risky the land the tenant is + + align:start position:0% +output is risky the land the tenant is + + + align:start position:0% +output is risky the land the tenant is +bearing all the risk right and the + + align:start position:0% +bearing all the risk right and the + + + align:start position:0% +bearing all the risk right and the +landlord is kind of is is getting a + + align:start position:0% +landlord is kind of is is getting a + + + align:start position:0% +landlord is kind of is is getting a +fixed fee regardless + + align:start position:0% +fixed fee regardless + + + align:start position:0% +fixed fee regardless +you might imagine that the tenant is you + + align:start position:0% +you might imagine that the tenant is you + + + align:start position:0% +you might imagine that the tenant is you +know typically like a poor Farmer and + + align:start position:0% +know typically like a poor Farmer and + + + align:start position:0% +know typically like a poor Farmer and +the landlord might be a kind of Rich + + align:start position:0% +the landlord might be a kind of Rich + + + align:start position:0% +the landlord might be a kind of Rich +landlord + + align:start position:0% +landlord + + + align:start position:0% +landlord +um you know in that case you might + + align:start position:0% +um you know in that case you might + + + align:start position:0% +um you know in that case you might +imagine that the that the rich landlord + + align:start position:0% +imagine that the that the rich landlord + + + align:start position:0% +imagine that the that the rich landlord +might be less risk-averse than the sort + + align:start position:0% +might be less risk-averse than the sort + + + align:start position:0% +might be less risk-averse than the sort +of the poor tenant but even in fact + + align:start position:0% +of the poor tenant but even in fact + + + align:start position:0% +of the poor tenant but even in fact +either equally risk-averse you you know + + align:start position:0% +either equally risk-averse you you know + + + align:start position:0% +either equally risk-averse you you know +the optimal thing is not for one of them + + align:start position:0% +the optimal thing is not for one of them + + + align:start position:0% +the optimal thing is not for one of them +to Bear all the risk in the other to be + + align:start position:0% +to Bear all the risk in the other to be + + + align:start position:0% +to Bear all the risk in the other to be +totally insured the optimal thing is to + + align:start position:0% +totally insured the optimal thing is to + + + align:start position:0% +totally insured the optimal thing is to +share some of the the the + + align:start position:0% +share some of the the the + + + align:start position:0% +share some of the the the +um share the risk between them + + align:start position:0% +um share the risk between them + + + align:start position:0% +um share the risk between them +okay and once you share the risk between + + align:start position:0% +okay and once you share the risk between + + + align:start position:0% +okay and once you share the risk between +them then you end up in some kinds of + + align:start position:0% +them then you end up in some kinds of + + + align:start position:0% +them then you end up in some kinds of +contracts where you end up um that look + + align:start position:0% +contracts where you end up um that look + + + align:start position:0% +contracts where you end up um that look +more like sharecropping contracts okay + + align:start position:0% +more like sharecropping contracts okay + + + align:start position:0% +more like sharecropping contracts okay +and so that's kind of the the basic idea + + align:start position:0% +and so that's kind of the the basic idea + + + align:start position:0% +and so that's kind of the the basic idea +of this stiglitz + + align:start position:0% +of this stiglitz + + + align:start position:0% +of this stiglitz +cichlids model which was actually one of + + align:start position:0% +cichlids model which was actually one of + + + align:start position:0% +cichlids model which was actually one of +the kind of original moral hazard models + + align:start position:0% +the kind of original moral hazard models + + + align:start position:0% +the kind of original moral hazard models +actually develop with kind of + + align:start position:0% +actually develop with kind of + + + align:start position:0% +actually develop with kind of +sharecropping as kind of an example is + + align:start position:0% +sharecropping as kind of an example is + + + align:start position:0% +sharecropping as kind of an example is +to say Well we'd like to you know we end + + align:start position:0% +to say Well we'd like to you know we end + + + align:start position:0% +to say Well we'd like to you know we end +up in kind of these + + align:start position:0% +up in kind of these + + + align:start position:0% +up in kind of these +um inefficient these contracts that are + + align:start position:0% +um inefficient these contracts that are + + + align:start position:0% +um inefficient these contracts that are +productively inefficient uh because we + + align:start position:0% +productively inefficient uh because we + + + align:start position:0% +productively inefficient uh because we +we want to do some resharing + + align:start position:0% +we want to do some resharing + + + align:start position:0% +we want to do some resharing +okay so let me go through a little bit + + align:start position:0% +okay so let me go through a little bit + + + align:start position:0% +okay so let me go through a little bit +of that + + align:start position:0% +of that + + + align:start position:0% +of that +um + + align:start position:0% +um + + + align:start position:0% +um +and a little go through that a little + + align:start position:0% +and a little go through that a little + + + align:start position:0% +and a little go through that a little +bit of that any questions no + + align:start position:0% +bit of that any questions no + + + align:start position:0% +bit of that any questions no +clear + + align:start position:0% +clear + + + align:start position:0% +clear +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so that's basically what I what I uh + + align:start position:0% +um so that's basically what I what I uh + + + align:start position:0% +um so that's basically what I what I uh +what so to be clear the idea of this is + + align:start position:0% +what so to be clear the idea of this is + + + align:start position:0% +what so to be clear the idea of this is +that farming is going to be risky so + + align:start position:0% +that farming is going to be risky so + + + align:start position:0% +that farming is going to be risky so +we're going to put some some uncertainty + + align:start position:0% +we're going to put some some uncertainty + + + align:start position:0% +we're going to put some some uncertainty +on this + + align:start position:0% +on this + + + align:start position:0% +on this +um we have risk-averse agents want to be + + align:start position:0% +um we have risk-averse agents want to be + + + align:start position:0% +um we have risk-averse agents want to be +insured against this risk but the + + align:start position:0% +insured against this risk but the + + + align:start position:0% +insured against this risk but the +problem is if this effort choice is + + align:start position:0% +problem is if this effort choice is + + + align:start position:0% +problem is if this effort choice is +uncontractable that leads to to + + align:start position:0% +uncontractable that leads to to + + + align:start position:0% +uncontractable that leads to to +um to to inefficiencies + + align:start position:0% +um to to inefficiencies + + + align:start position:0% +um to to inefficiencies +okay so here's a a very simple + + align:start position:0% +okay so here's a a very simple + + + align:start position:0% +okay so here's a a very simple +like the simplest possible kind of moral + + align:start position:0% +like the simplest possible kind of moral + + + align:start position:0% +like the simplest possible kind of moral +simplest version of this of this model + + align:start position:0% +simplest version of this of this model + + + align:start position:0% +simplest version of this of this model +so let's consider + + align:start position:0% +so let's consider + + + align:start position:0% +so let's consider +a two-state version + + align:start position:0% +a two-state version + + + align:start position:0% +a two-state version +high and low output okay + + align:start position:0% +high and low output okay + + + align:start position:0% +high and low output okay +uh there's effort + + align:start position:0% +uh there's effort + + + align:start position:0% +uh there's effort +which is denoted by e + + align:start position:0% +which is denoted by e + + + align:start position:0% +which is denoted by e +the farmer chooses some effort but the + + align:start position:0% +the farmer chooses some effort but the + + + align:start position:0% +the farmer chooses some effort but the +landlord doesn't see e they only see + + align:start position:0% +landlord doesn't see e they only see + + + align:start position:0% +landlord doesn't see e they only see +output + + align:start position:0% +output + + + align:start position:0% +output +okay so we can't write con and the key + + align:start position:0% +okay so we can't write con and the key + + + align:start position:0% +okay so we can't write con and the key +point is we can't therefore write + + align:start position:0% +point is we can't therefore write + + + align:start position:0% +point is we can't therefore write +contracts over the level of effort e + + align:start position:0% +contracts over the level of effort e + + + align:start position:0% +contracts over the level of effort e +effort's going to be costly to the + + align:start position:0% +effort's going to be costly to the + + + align:start position:0% +effort's going to be costly to the +tenant with some cost one half c squared + + align:start position:0% +tenant with some cost one half c squared + + + align:start position:0% +tenant with some cost one half c squared +and the output is going to be stochastic + + align:start position:0% +and the output is going to be stochastic + + + align:start position:0% +and the output is going to be stochastic +um with uh the effort determining the + + align:start position:0% +um with uh the effort determining the + + + align:start position:0% +um with uh the effort determining the +probability of the high state + + align:start position:0% +probability of the high state + + + align:start position:0% +probability of the high state +so with probability e + + align:start position:0% +so with probability e + + + align:start position:0% +so with probability e +the output is high + + align:start position:0% +the output is high + + + align:start position:0% +the output is high +with probability 1 minus E the output is + + align:start position:0% +with probability 1 minus E the output is + + + align:start position:0% +with probability 1 minus E the output is +going to be zero + + align:start position:0% +going to be zero + + + align:start position:0% +going to be zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and the way we sort of think about these + + align:start position:0% +and the way we sort of think about these + + + align:start position:0% +and the way we sort of think about these +models is the farmer and landlord are + + align:start position:0% +models is the farmer and landlord are + + + align:start position:0% +models is the farmer and landlord are +going to write a contract + + align:start position:0% +going to write a contract + + + align:start position:0% +going to write a contract +which is going to specify a payment uh + + align:start position:0% +which is going to specify a payment uh + + + align:start position:0% +which is going to specify a payment uh +um to the farmer from the landlord I + + align:start position:0% +um to the farmer from the landlord I + + + align:start position:0% +um to the farmer from the landlord I +think that's the way I did it uh doesn't + + align:start position:0% +think that's the way I did it uh doesn't + + + align:start position:0% +think that's the way I did it uh doesn't +matter which way you write the payment + + align:start position:0% +matter which way you write the payment + + + align:start position:0% +matter which way you write the payment +um which is going to be a payment h a + + align:start position:0% +um which is going to be a payment h a + + + align:start position:0% +um which is going to be a payment h a +little H if the output is is Big H and a + + align:start position:0% +little H if the output is is Big H and a + + + align:start position:0% +little H if the output is is Big H and a +payment little L if the output is zero + + align:start position:0% +payment little L if the output is zero + + + align:start position:0% +payment little L if the output is zero +okay so we're gonna be interested in + + align:start position:0% +okay so we're gonna be interested in + + + align:start position:0% +okay so we're gonna be interested in +sort of what those little H's and little + + align:start position:0% +sort of what those little H's and little + + + align:start position:0% +sort of what those little H's and little +L's are okay so it's set up clear + + align:start position:0% +L's are okay so it's set up clear + + + align:start position:0% +L's are okay so it's set up clear +so just to be clear the key thing in + + align:start position:0% +so just to be clear the key thing in + + + align:start position:0% +so just to be clear the key thing in +this model is that the + + align:start position:0% +this model is that the + + + align:start position:0% +this model is that the +um the effort choice is going to drive + + align:start position:0% +um the effort choice is going to drive + + + align:start position:0% +um the effort choice is going to drive +the probability of the high State or the + + align:start position:0% +the probability of the high State or the + + + align:start position:0% +the probability of the high State or the +low state + + align:start position:0% +low state + + + align:start position:0% +low state +okay + + align:start position:0% + + + + align:start position:0% + +so what's the first best + + align:start position:0% +so what's the first best + + + align:start position:0% +so what's the first best +yeah + + align:start position:0% + + + + align:start position:0% + +output is observable what's right + + align:start position:0% +output is observable what's right + + + align:start position:0% +output is observable what's right +oh yes we're exactly we're going to + + align:start position:0% +oh yes we're exactly we're going to + + + align:start position:0% +oh yes we're exactly we're going to +write the output is observable we're + + align:start position:0% +write the output is observable we're + + + align:start position:0% +write the output is observable we're +going to write contracts on output but + + align:start position:0% +going to write contracts on output but + + + align:start position:0% +going to write contracts on output but +we can't write contracts on effort + + align:start position:0% +we can't write contracts on effort + + + align:start position:0% +we can't write contracts on effort +okay so so basically what so the way + + align:start position:0% +okay so so basically what so the way + + + align:start position:0% +okay so so basically what so the way +this model is going to work is the + + align:start position:0% +this model is going to work is the + + + align:start position:0% +this model is going to work is the +landlord is going to set up the contract + + align:start position:0% +landlord is going to set up the contract + + + align:start position:0% +landlord is going to set up the contract +here's the latest here's little L + + align:start position:0% +here's the latest here's little L + + + align:start position:0% +here's the latest here's little L +um + + align:start position:0% +um + + + align:start position:0% +um +which is our functions of what what the + + align:start position:0% +which is our functions of what what the + + + align:start position:0% +which is our functions of what what the +realized output is and then the tenant + + align:start position:0% +realized output is and then the tenant + + + align:start position:0% +realized output is and then the tenant +gets to sort of observe hnl and make + + align:start position:0% +gets to sort of observe hnl and make + + + align:start position:0% +gets to sort of observe hnl and make +their decisions about how much effort to + + align:start position:0% +their decisions about how much effort to + + + align:start position:0% +their decisions about how much effort to +put in + + align:start position:0% +put in + + + align:start position:0% +put in +and the landlord gets to set and the + + align:start position:0% +and the landlord gets to set and the + + + align:start position:0% +and the landlord gets to set and the +landlord in turn chooses a little agent + + align:start position:0% +landlord in turn chooses a little agent + + + align:start position:0% +landlord in turn chooses a little agent +little L knowing how the tenant will + + align:start position:0% +little L knowing how the tenant will + + + align:start position:0% +little L knowing how the tenant will +respond and make their contracts + + align:start position:0% +respond and make their contracts + + + align:start position:0% +respond and make their contracts +decisions + + align:start position:0% +decisions + + + align:start position:0% +decisions +okay it's a standard moral hazard set up + + align:start position:0% +okay it's a standard moral hazard set up + + + align:start position:0% +okay it's a standard moral hazard set up +but not everyone has seen this before so + + align:start position:0% +but not everyone has seen this before so + + + align:start position:0% +but not everyone has seen this before so +I want to go go through this + + align:start position:0% +I want to go go through this + + + align:start position:0% +I want to go go through this +okay clear + + align:start position:0% +okay clear + + + align:start position:0% +okay clear +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so what's the first best well the first + + align:start position:0% +so what's the first best well the first + + + align:start position:0% +so what's the first best well the first +best right would be + + align:start position:0% +best right would be + + + align:start position:0% +best right would be +um + + align:start position:0% +um + + + align:start position:0% +um +that so remember remember in the low + + align:start position:0% +that so remember remember in the low + + + align:start position:0% +that so remember remember in the low +State we get we get zero just by + + align:start position:0% +State we get we get zero just by + + + align:start position:0% +State we get we get zero just by +normalization so that's going to make + + align:start position:0% +normalization so that's going to make + + + align:start position:0% +normalization so that's going to make +our just make the math easier so what's + + align:start position:0% +our just make the math easier so what's + + + align:start position:0% +our just make the math easier so what's +the first best well the the sort of + + align:start position:0% +the first best well the the sort of + + + align:start position:0% +the first best well the the sort of +social Optimum right is to choose the + + align:start position:0% +social Optimum right is to choose the + + + align:start position:0% +social Optimum right is to choose the +level of effort such that the return the + + align:start position:0% +level of effort such that the return the + + + align:start position:0% +level of effort such that the return the +expected return which is the probability + + align:start position:0% +expected return which is the probability + + + align:start position:0% +expected return which is the probability +of getting a high return times the the + + align:start position:0% +of getting a high return times the the + + + align:start position:0% +of getting a high return times the the +value of a higher return you know your + + align:start position:0% +value of a higher return you know your + + + align:start position:0% +value of a higher return you know your +balance that against the cost of effort + + align:start position:0% +balance that against the cost of effort + + + align:start position:0% +balance that against the cost of effort +okay so we just take the derivative here + + align:start position:0% +okay so we just take the derivative here + + + align:start position:0% +okay so we just take the derivative here +and and uh e is equal to uh Capital H + + align:start position:0% +and and uh e is equal to uh Capital H + + + align:start position:0% +and and uh e is equal to uh Capital H +over C that's the optimal + + align:start position:0% +over C that's the optimal + + + align:start position:0% +over C that's the optimal +first best level of effort + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +it so that's the Benchmark right the + + align:start position:0% +it so that's the Benchmark right the + + + align:start position:0% +it so that's the Benchmark right the +question is are we going to get that + + align:start position:0% +question is are we going to get that + + + align:start position:0% +question is are we going to get that +level effort or not + + align:start position:0% +level effort or not + + + align:start position:0% +level effort or not +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what's going to happen so the + + align:start position:0% +so what's going to happen so the + + + align:start position:0% +so what's going to happen so the +question is + + align:start position:0% +question is + + + align:start position:0% +question is +can the landlord by the way if I'm going + + align:start position:0% +can the landlord by the way if I'm going + + + align:start position:0% +can the landlord by the way if I'm going +too fast like you should let me I Slow + + align:start position:0% +too fast like you should let me I Slow + + + align:start position:0% +too fast like you should let me I Slow +Me Down the problem with teaching on + + align:start position:0% +Me Down the problem with teaching on + + + align:start position:0% +Me Down the problem with teaching on +slides is teaching models on slides is + + align:start position:0% +slides is teaching models on slides is + + + align:start position:0% +slides is teaching models on slides is +you tend to go faster than people can + + align:start position:0% +you tend to go faster than people can + + + align:start position:0% +you tend to go faster than people can +write so if I'm going too fast just Slow + + align:start position:0% +write so if I'm going too fast just Slow + + + align:start position:0% +write so if I'm going too fast just Slow +Me Down + + align:start position:0% +Me Down + + + align:start position:0% +Me Down +so can the landlord implement this first + + align:start position:0% +so can the landlord implement this first + + + align:start position:0% +so can the landlord implement this first +best contract like what's going to + + align:start position:0% +best contract like what's going to + + + align:start position:0% +best contract like what's going to +actually happen okay so how do we solve + + align:start position:0% +actually happen okay so how do we solve + + + align:start position:0% +actually happen okay so how do we solve +this so the the problem for the landlord + + align:start position:0% +this so the the problem for the landlord + + + align:start position:0% +this so the the problem for the landlord +is is written as the following + + align:start position:0% +is is written as the following + + + align:start position:0% +is is written as the following +so the landlord + + align:start position:0% +so the landlord + + + align:start position:0% +so the landlord +is going to shoot has two choices what + + align:start position:0% +is going to shoot has two choices what + + + align:start position:0% +is going to shoot has two choices what +is little H and what is little l + + align:start position:0% +is little H and what is little l + + + align:start position:0% +is little H and what is little l +right + + align:start position:0% +right + + + align:start position:0% +right +and what does the landlord care about + + align:start position:0% +and what does the landlord care about + + + align:start position:0% +and what does the landlord care about +well with probability + + align:start position:0% +well with probability + + + align:start position:0% +well with probability +uh e which will be determined + + align:start position:0% +uh e which will be determined + + + align:start position:0% +uh e which will be determined +endogenously + + align:start position:0% +endogenously + + + align:start position:0% +endogenously +the landlord the output is Big H and the + + align:start position:0% +the landlord the output is Big H and the + + + align:start position:0% +the landlord the output is Big H and the +level has to make a payment little h + + align:start position:0% +level has to make a payment little h + + + align:start position:0% +level has to make a payment little h +okay so that's the landlord's return on + + align:start position:0% +okay so that's the landlord's return on + + + align:start position:0% +okay so that's the landlord's return on +the high state with probability one + + align:start position:0% +the high state with probability one + + + align:start position:0% +the high state with probability one +minus E we're in the low State and then + + align:start position:0% +minus E we're in the low State and then + + + align:start position:0% +minus E we're in the low State and then +later has to pay out and gets no output + + align:start position:0% +later has to pay out and gets no output + + + align:start position:0% +later has to pay out and gets no output +okay so that's the landlord's objective + + align:start position:0% +okay so that's the landlord's objective + + + align:start position:0% +okay so that's the landlord's objective +function this is by the way this is all + + align:start position:0% +function this is by the way this is all + + + align:start position:0% +function this is by the way this is all +going to be risk neutral as you'll see + + align:start position:0% +going to be risk neutral as you'll see + + + align:start position:0% +going to be risk neutral as you'll see +in a second but we can introduce risk + + align:start position:0% +in a second but we can introduce risk + + + align:start position:0% +in a second but we can introduce risk +aversion later but um so okay so that's + + align:start position:0% +aversion later but um so okay so that's + + + align:start position:0% +aversion later but um so okay so that's +the that's the uh landlord's problem + + align:start position:0% +the that's the uh landlord's problem + + + align:start position:0% +the that's the uh landlord's problem +and it has two constraints the the + + align:start position:0% +and it has two constraints the the + + + align:start position:0% +and it has two constraints the the +incentive compatibility constraint and + + align:start position:0% +incentive compatibility constraint and + + + align:start position:0% +incentive compatibility constraint and +the individual rationality constraint + + align:start position:0% +the individual rationality constraint + + + align:start position:0% +the individual rationality constraint +the incentive compatibility constraint + + align:start position:0% +the incentive compatibility constraint + + + align:start position:0% +the incentive compatibility constraint +says the landlord is going to solve this + + align:start position:0% +says the landlord is going to solve this + + + align:start position:0% +says the landlord is going to solve this +problem knowing that the tenant will in + + align:start position:0% +problem knowing that the tenant will in + + + align:start position:0% +problem knowing that the tenant will in +turn take the contract as uh as fixed + + align:start position:0% +turn take the contract as uh as fixed + + + align:start position:0% +turn take the contract as uh as fixed +and choose her level of effort + + align:start position:0% +and choose her level of effort + + + align:start position:0% +and choose her level of effort +accordingly + + align:start position:0% +accordingly + + + align:start position:0% +accordingly +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +the tenant here + + align:start position:0% +the tenant here + + + align:start position:0% +the tenant here +is going to solve uh for a level so the + + align:start position:0% +is going to solve uh for a level so the + + + align:start position:0% +is going to solve uh for a level so the +level of effort e is going to be chosen + + align:start position:0% +level of effort e is going to be chosen + + + align:start position:0% +level of effort e is going to be chosen +by the tenant to solve the tenant's own + + align:start position:0% +by the tenant to solve the tenant's own + + + align:start position:0% +by the tenant to solve the tenant's own +objective function which is well with + + align:start position:0% +objective function which is well with + + + align:start position:0% +objective function which is well with +probability E I get little payment I get + + align:start position:0% +probability E I get little payment I get + + + align:start position:0% +probability E I get little payment I get +payment little H with probability one + + align:start position:0% +payment little H with probability one + + + align:start position:0% +payment little H with probability one +minus E I get payment little L and I + + align:start position:0% +minus E I get payment little L and I + + + align:start position:0% +minus E I get payment little L and I +have to pay my cost of effort + + align:start position:0% +have to pay my cost of effort + + + align:start position:0% +have to pay my cost of effort +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and there's a third constraint which is + + align:start position:0% +and there's a third constraint which is + + + align:start position:0% +and there's a third constraint which is +the individual rationality constraint + + align:start position:0% +the individual rationality constraint + + + align:start position:0% +the individual rationality constraint +it's and the way to think about the + + align:start position:0% +it's and the way to think about the + + + align:start position:0% +it's and the way to think about the +individual rationality constraint is + + align:start position:0% +individual rationality constraint is + + + align:start position:0% +individual rationality constraint is +that the tenant has some outside option + + align:start position:0% +that the tenant has some outside option + + + align:start position:0% +that the tenant has some outside option +W bar and the tenant's net utility has + + align:start position:0% +W bar and the tenant's net utility has + + + align:start position:0% +W bar and the tenant's net utility has +to be at least equal to W bar + + align:start position:0% +to be at least equal to W bar + + + align:start position:0% +to be at least equal to W bar +Ely lower bar + + align:start position:0% +Ely lower bar + + + align:start position:0% +Ely lower bar +okay and that that's to say the tenant + + align:start position:0% +okay and that that's to say the tenant + + + align:start position:0% +okay and that that's to say the tenant +could like not take this contract and + + align:start position:0% +could like not take this contract and + + + align:start position:0% +could like not take this contract and +could walk away and just kind of you + + align:start position:0% +could walk away and just kind of you + + + align:start position:0% +could walk away and just kind of you +know get a job as a day laborer at some + + align:start position:0% +know get a job as a day laborer at some + + + align:start position:0% +know get a job as a day laborer at some +wage weight w so the net utility from + + align:start position:0% +wage weight w so the net utility from + + + align:start position:0% +wage weight w so the net utility from +the tenant so that's that's This this + + align:start position:0% +the tenant so that's that's This this + + + align:start position:0% +the tenant so that's that's This this +term here evaluated at the at the chosen + + align:start position:0% +term here evaluated at the at the chosen + + + align:start position:0% +term here evaluated at the at the chosen +e has to be at least as high as as or + + align:start position:0% +e has to be at least as high as as or + + + align:start position:0% +e has to be at least as high as as or +outside option + + align:start position:0% +outside option + + + align:start position:0% +outside option +okay so so this is this is the problem + + align:start position:0% +okay so so this is this is the problem + + + align:start position:0% +okay so so this is this is the problem +clear + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um and if those who have taken + + align:start position:0% +so um and if those who have taken + + + align:start position:0% +so um and if those who have taken +contract theory already this should be + + align:start position:0% +contract theory already this should be + + + align:start position:0% +contract theory already this should be +like very familiar right + + align:start position:0% +like very familiar right + + + align:start position:0% +like very familiar right +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so how do we solve this problem + + align:start position:0% +so how do we solve this problem + + + align:start position:0% +so how do we solve this problem +well we begin by take solving for the + + align:start position:0% +well we begin by take solving for the + + + align:start position:0% +well we begin by take solving for the +taking the farmer solution + + align:start position:0% +taking the farmer solution + + + align:start position:0% +taking the farmer solution +taking the contract the the IC is given + + align:start position:0% +taking the contract the the IC is given + + + align:start position:0% +taking the contract the the IC is given +okay so we basically say let's first + + align:start position:0% +okay so we basically say let's first + + + align:start position:0% +okay so we basically say let's first +solve the farmer's problem given a + + align:start position:0% +solve the farmer's problem given a + + + align:start position:0% +solve the farmer's problem given a +little H and little L what is the farmer + + align:start position:0% +little H and little L what is the farmer + + + align:start position:0% +little H and little L what is the farmer +going to do and then we'll plug that + + align:start position:0% +going to do and then we'll plug that + + + align:start position:0% +going to do and then we'll plug that +back in to the to the um to the + + align:start position:0% +back in to the to the um to the + + + align:start position:0% +back in to the to the um to the +landlord's problem right so what's the + + align:start position:0% +landlord's problem right so what's the + + + align:start position:0% +landlord's problem right so what's the +farmer's decision well the farmer is + + align:start position:0% +farmer's decision well the farmer is + + + align:start position:0% +farmer's decision well the farmer is +going to solve is going to maximize uh + + align:start position:0% +going to solve is going to maximize uh + + + align:start position:0% +going to solve is going to maximize uh +the same this objective function over + + align:start position:0% +the same this objective function over + + + align:start position:0% +the same this objective function over +here + + align:start position:0% +here + + + align:start position:0% +here +right remember she gets payment the late + + align:start position:0% +right remember she gets payment the late + + + align:start position:0% +right remember she gets payment the late +with probability e payment level + + align:start position:0% +with probability e payment level + + + align:start position:0% +with probability e payment level +probably one minus E she pays the cost + + align:start position:0% +probably one minus E she pays the cost + + + align:start position:0% +probably one minus E she pays the cost +of effort so her effort decision as you + + align:start position:0% +of effort so her effort decision as you + + + align:start position:0% +of effort so her effort decision as you +can see so right we can just take the + + align:start position:0% +can see so right we can just take the + + + align:start position:0% +can see so right we can just take the +derivative of the switch to e she's + + align:start position:0% +derivative of the switch to e she's + + + align:start position:0% +derivative of the switch to e she's +gonna the difference + + align:start position:0% +gonna the difference + + + align:start position:0% +gonna the difference +is she's going to get + + align:start position:0% +is she's going to get + + + align:start position:0% +is she's going to get +um H minus the sort of what additional e + + align:start position:0% +um H minus the sort of what additional e + + + align:start position:0% +um H minus the sort of what additional e +does is it increases the probability she + + align:start position:0% +does is it increases the probability she + + + align:start position:0% +does is it increases the probability she +gets H minus L right the difference in + + align:start position:0% +gets H minus L right the difference in + + + align:start position:0% +gets H minus L right the difference in +her her right the high the difference of + + align:start position:0% +her her right the high the difference of + + + align:start position:0% +her her right the high the difference of +the high status or difference in her + + align:start position:0% +the high status or difference in her + + + align:start position:0% +the high status or difference in her +payment and high State minus the + + align:start position:0% +payment and high State minus the + + + align:start position:0% +payment and high State minus the +difference in the payment the low State + + align:start position:0% +difference in the payment the low State + + + align:start position:0% +difference in the payment the low State +and just is equal to the marginal cost + + align:start position:0% +and just is equal to the marginal cost + + + align:start position:0% +and just is equal to the marginal cost +of effort okay so her choice is going to + + align:start position:0% +of effort okay so her choice is going to + + + align:start position:0% +of effort okay so her choice is going to +be easy e star is going to be equal to H + + align:start position:0% +be easy e star is going to be equal to H + + + align:start position:0% +be easy e star is going to be equal to H +minus little H minus little L over C + + align:start position:0% +minus little H minus little L over C + + + align:start position:0% +minus little H minus little L over C +okay so what you can immediately see + + align:start position:0% +okay so what you can immediately see + + + align:start position:0% +okay so what you can immediately see +here is this is a model where if there's + + align:start position:0% +here is this is a model where if there's + + + align:start position:0% +here is this is a model where if there's +no difference between the payment and + + align:start position:0% +no difference between the payment and + + + align:start position:0% +no difference between the payment and +the high State and the low state if + + align:start position:0% +the high State and the low state if + + + align:start position:0% +the high State and the low state if +she's fully insured she puts in no + + align:start position:0% +she's fully insured she puts in no + + + align:start position:0% +she's fully insured she puts in no +effort okay so there's gonna have to be + + align:start position:0% +effort okay so there's gonna have to be + + + align:start position:0% +effort okay so there's gonna have to be +some + + align:start position:0% +some + + + align:start position:0% +some +uh this is a model where there's if + + align:start position:0% +uh this is a model where there's if + + + align:start position:0% +uh this is a model where there's if +there's full insurance there's going to + + align:start position:0% +there's full insurance there's going to + + + align:start position:0% +there's full insurance there's going to +be no no no work + + align:start position:0% +be no no no work + + + align:start position:0% +be no no no work +so they have to provide some incentives + + align:start position:0% +so they have to provide some incentives + + + align:start position:0% +so they have to provide some incentives +um to in order to to to to get her to + + align:start position:0% +um to in order to to to to get her to + + + align:start position:0% +um to in order to to to to get her to +put in some effort right otherwise why + + align:start position:0% +put in some effort right otherwise why + + + align:start position:0% +put in some effort right otherwise why +would you do anything right because + + align:start position:0% +would you do anything right because + + + align:start position:0% +would you do anything right because +there's some cost of effort + + align:start position:0% +there's some cost of effort + + + align:start position:0% +there's some cost of effort +okay clear + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now + + align:start position:0% + + + + align:start position:0% + +the landlord so we can also see we all + + align:start position:0% +the landlord so we can also see we all + + + align:start position:0% +the landlord so we can also see we all +see immediately by the way + + align:start position:0% +see immediately by the way + + + align:start position:0% +see immediately by the way +that to get the first best right + + align:start position:0% +that to get the first best right + + + align:start position:0% +that to get the first best right +remember the first best effort + + align:start position:0% +remember the first best effort + + + align:start position:0% +remember the first best effort +first best effort was we like the + + align:start position:0% +first best effort was we like the + + + align:start position:0% +first best effort was we like the +landlord to uh with her we'd like the + + align:start position:0% +landlord to uh with her we'd like the + + + align:start position:0% +landlord to uh with her we'd like the +tenant to to put an effort equal to Big + + align:start position:0% +tenant to to put an effort equal to Big + + + align:start position:0% +tenant to to put an effort equal to Big +H over C + + align:start position:0% +H over C + + + align:start position:0% +H over C +so what does that mean well the contract + + align:start position:0% +so what does that mean well the contract + + + align:start position:0% +so what does that mean well the contract +any contract that's going to get the + + align:start position:0% +any contract that's going to get the + + + align:start position:0% +any contract that's going to get the +tenant to put in the full amount of + + align:start position:0% +tenant to put in the full amount of + + + align:start position:0% +tenant to put in the full amount of +effort + + align:start position:0% +effort + + + align:start position:0% +effort +that's going to imply right that the + + align:start position:0% +that's going to imply right that the + + + align:start position:0% +that's going to imply right that the +that little H minus little L is equal to + + align:start position:0% +that little H minus little L is equal to + + + align:start position:0% +that little H minus little L is equal to +Big H + + align:start position:0% +Big H + + + align:start position:0% +Big H +right + + align:start position:0% +right + + + align:start position:0% +right +another way of saying it is that the gap + + align:start position:0% +another way of saying it is that the gap + + + align:start position:0% +another way of saying it is that the gap +between what she gets in the high State + + align:start position:0% +between what she gets in the high State + + + align:start position:0% +between what she gets in the high State +and what she gets in a low state has to + + align:start position:0% +and what she gets in a low state has to + + + align:start position:0% +and what she gets in a low state has to +be equal to the Social and since it's + + align:start position:0% +be equal to the Social and since it's + + + align:start position:0% +be equal to the Social and since it's +the social return of being in the high + + align:start position:0% +the social return of being in the high + + + align:start position:0% +the social return of being in the high +State versus low state + + align:start position:0% +State versus low state + + + align:start position:0% +State versus low state +okay that's the only way to get her to + + align:start position:0% +okay that's the only way to get her to + + + align:start position:0% +okay that's the only way to get her to +put in full effort + + align:start position:0% +put in full effort + + + align:start position:0% +put in full effort +okay so you see that by saying look if + + align:start position:0% +okay so you see that by saying look if + + + align:start position:0% +okay so you see that by saying look if +we want this to equal to Big H over C we + + align:start position:0% +we want this to equal to Big H over C we + + + align:start position:0% +we want this to equal to Big H over C we +have to make the little the different + + align:start position:0% +have to make the little the different + + + align:start position:0% +have to make the little the different +little a little H and little L equal to + + align:start position:0% +little a little H and little L equal to + + + align:start position:0% +little a little H and little L equal to +Big H + + align:start position:0% +Big H + + + align:start position:0% +Big H +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +that is rental what is that that's a + + align:start position:0% +that is rental what is that that's a + + + align:start position:0% +that is rental what is that that's a +rental contract + + align:start position:0% +rental contract + + + align:start position:0% +rental contract +right we've just derived a rental + + align:start position:0% +right we've just derived a rental + + + align:start position:0% +right we've just derived a rental +contract why is that a rental contract + + align:start position:0% +contract why is that a rental contract + + + align:start position:0% +contract why is that a rental contract +because + + align:start position:0% +because + + + align:start position:0% +because +the tenant will make some some fixed + + align:start position:0% +the tenant will make some some fixed + + + align:start position:0% +the tenant will make some some fixed +payment to the landlord + + align:start position:0% +payment to the landlord + + + align:start position:0% +payment to the landlord +the other way of viewing any any + + align:start position:0% +the other way of viewing any any + + + align:start position:0% +the other way of viewing any any +contract where the difference between + + align:start position:0% +contract where the difference between + + + align:start position:0% +contract where the difference between +little H and little L is equal to to Big + + align:start position:0% +little H and little L is equal to to Big + + + align:start position:0% +little H and little L is equal to to Big +H is a contract where + + align:start position:0% +H is a contract where + + + align:start position:0% +H is a contract where +she makes some fixed payment to the + + align:start position:0% +she makes some fixed payment to the + + + align:start position:0% +she makes some fixed payment to the +landlord + + align:start position:0% +landlord + + + align:start position:0% +landlord +or maybe it goes the other way depending + + align:start position:0% +or maybe it goes the other way depending + + + align:start position:0% +or maybe it goes the other way depending +on what her I orchestrated but there's + + align:start position:0% +on what her I orchestrated but there's + + + align:start position:0% +on what her I orchestrated but there's +some fixed payment that goes one way or + + align:start position:0% +some fixed payment that goes one way or + + + align:start position:0% +some fixed payment that goes one way or +the other and then she keeps all the + + align:start position:0% +the other and then she keeps all the + + + align:start position:0% +the other and then she keeps all the +output uh that is produced okay so + + align:start position:0% +output uh that is produced okay so + + + align:start position:0% +output uh that is produced okay so +that's a rental contract + + align:start position:0% +that's a rental contract + + + align:start position:0% +that's a rental contract +Okay so we've just kind of derived the + + align:start position:0% +Okay so we've just kind of derived the + + + align:start position:0% +Okay so we've just kind of derived the +result that basically the another way of + + align:start position:0% +result that basically the another way of + + + align:start position:0% +result that basically the another way of +saying it is in this model the only way + + align:start position:0% +saying it is in this model the only way + + + align:start position:0% +saying it is in this model the only way +to get the the first best effort is to + + align:start position:0% +to get the the first best effort is to + + + align:start position:0% +to get the the first best effort is to +have a rental contract + + align:start position:0% +have a rental contract + + + align:start position:0% +have a rental contract +okay right which is basically what I + + align:start position:0% +okay right which is basically what I + + + align:start position:0% +okay right which is basically what I +just had a slide so why is that we need + + align:start position:0% +just had a slide so why is that we need + + + align:start position:0% +just had a slide so why is that we need +the worker to face a socially off + + align:start position:0% +the worker to face a socially off + + + align:start position:0% +the worker to face a socially off +emotion to effort so we need e Stars we + + align:start position:0% +emotion to effort so we need e Stars we + + + align:start position:0% +emotion to effort so we need e Stars we +need this + + align:start position:0% +need this + + + align:start position:0% +need this +right her her choice is effort to be + + align:start position:0% +right her her choice is effort to be + + + align:start position:0% +right her her choice is effort to be +equal to the socially optimal level the + + align:start position:0% +equal to the socially optimal level the + + + align:start position:0% +equal to the socially optimal level the +only way to do that is to set set H + + align:start position:0% +only way to do that is to set set H + + + align:start position:0% +only way to do that is to set set H +minus L equal to Big H which basically + + align:start position:0% +minus L equal to Big H which basically + + + align:start position:0% +minus L equal to Big H which basically +means she keeps all the the return on + + align:start position:0% +means she keeps all the the return on + + + align:start position:0% +means she keeps all the the return on +the margin + + align:start position:0% +the margin + + + align:start position:0% +the margin +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +in this contract + + align:start position:0% +in this contract + + + align:start position:0% +in this contract +how do that's pin now we've pinned down + + align:start position:0% +how do that's pin now we've pinned down + + + align:start position:0% +how do that's pin now we've pinned down +little H minus little l + + align:start position:0% +little H minus little l + + + align:start position:0% +little H minus little l +but we haven't pinned out but we can + + align:start position:0% +but we haven't pinned out but we can + + + align:start position:0% +but we haven't pinned out but we can +sort of Slide the level of those things + + align:start position:0% +sort of Slide the level of those things + + + align:start position:0% +sort of Slide the level of those things +up and down right that's the rent + + align:start position:0% +up and down right that's the rent + + + align:start position:0% +up and down right that's the rent +right and so how do we choose the rent + + align:start position:0% +right and so how do we choose the rent + + + align:start position:0% +right and so how do we choose the rent +we choose the rent so that the farmer is + + align:start position:0% +we choose the rent so that the farmer is + + + align:start position:0% +we choose the rent so that the farmer is +going to obtain W lower bar and + + align:start position:0% +going to obtain W lower bar and + + + align:start position:0% +going to obtain W lower bar and +expectation + + align:start position:0% +expectation + + + align:start position:0% +expectation +okay that's the IR constraint + + align:start position:0% +okay that's the IR constraint + + + align:start position:0% +okay that's the IR constraint +okay so the farmer's utility remember + + align:start position:0% +okay so the farmer's utility remember + + + align:start position:0% +okay so the farmer's utility remember +the farmer what was the farmer's utility + + align:start position:0% +the farmer what was the farmer's utility + + + align:start position:0% +the farmer what was the farmer's utility +the farmer's utility was + + align:start position:0% +the farmer's utility was + + + align:start position:0% +the farmer's utility was +um so now in in the first best contract + + align:start position:0% +um so now in in the first best contract + + + align:start position:0% +um so now in in the first best contract +with probability e the high State + + align:start position:0% +with probability e the high State + + + align:start position:0% +with probability e the high State +happens + + align:start position:0% +happens + + + align:start position:0% +happens +um + + align:start position:0% +um + + + align:start position:0% +um +she she and she gets h + + align:start position:0% +she she and she gets h + + + align:start position:0% +she she and she gets h +the rent gets paid either way right no + + align:start position:0% +the rent gets paid either way right no + + + align:start position:0% +the rent gets paid either way right no +matter what you pay the rent + + align:start position:0% +matter what you pay the rent + + + align:start position:0% +matter what you pay the rent +and you have to put in the cost of + + align:start position:0% +and you have to put in the cost of + + + align:start position:0% +and you have to put in the cost of +effort and We Know by the way that the + + align:start position:0% +effort and We Know by the way that the + + + align:start position:0% +effort and We Know by the way that the +the effort here is going to be equal to + + align:start position:0% +the effort here is going to be equal to + + + align:start position:0% +the effort here is going to be equal to +to Big H over C so we can sub in b a big + + align:start position:0% +to Big H over C so we can sub in b a big + + + align:start position:0% +to Big H over C so we can sub in b a big +H over C + + align:start position:0% +H over C + + + align:start position:0% +H over C +right so hurry so substituting in Big H + + align:start position:0% +right so hurry so substituting in Big H + + + align:start position:0% +right so hurry so substituting in Big H +over C here her utility is going to be + + align:start position:0% +over C here her utility is going to be + + + align:start position:0% +over C here her utility is going to be +um uh H Square over C minus a half H + + align:start position:0% +um uh H Square over C minus a half H + + + align:start position:0% +um uh H Square over C minus a half H +Square over C so we get a half an H + + align:start position:0% +Square over C so we get a half an H + + + align:start position:0% +Square over C so we get a half an H +Square over sorry uh + + align:start position:0% +Square over sorry uh + + + align:start position:0% +Square over sorry uh +yeah so we get a half an H Square over C + + align:start position:0% +yeah so we get a half an H Square over C + + + align:start position:0% +yeah so we get a half an H Square over C +minus the rent + + align:start position:0% +minus the rent + + + align:start position:0% +minus the rent +okay so that's her utility under this + + align:start position:0% +okay so that's her utility under this + + + align:start position:0% +okay so that's her utility under this +contract or expect you to look into this + + align:start position:0% +contract or expect you to look into this + + + align:start position:0% +contract or expect you to look into this +contract and that has to be equal to the + + align:start position:0% +contract and that has to be equal to the + + + align:start position:0% +contract and that has to be equal to the +outside option so we're going to set + + align:start position:0% +outside option so we're going to set + + + align:start position:0% +outside option so we're going to set +that equal to W lower bar + + align:start position:0% +that equal to W lower bar + + + align:start position:0% +that equal to W lower bar +right and so that's the rent that + + align:start position:0% +right and so that's the rent that + + + align:start position:0% +right and so that's the rent that +determines the rent so the rent is going + + align:start position:0% +determines the rent so the rent is going + + + align:start position:0% +determines the rent so the rent is going +to be the level uh where where she's + + align:start position:0% +to be the level uh where where she's + + + align:start position:0% +to be the level uh where where she's +exactly in different X ante + + align:start position:0% +exactly in different X ante + + + align:start position:0% +exactly in different X ante +okay and that's a general feature of the + + align:start position:0% +okay and that's a general feature of the + + + align:start position:0% +okay and that's a general feature of the +way that you sort of solve a lot of + + align:start position:0% +way that you sort of solve a lot of + + + align:start position:0% +way that you sort of solve a lot of +these problems is you figure out you + + align:start position:0% +these problems is you figure out you + + + align:start position:0% +these problems is you figure out you +first kind of solve for what the diff + + align:start position:0% +first kind of solve for what the diff + + + align:start position:0% +first kind of solve for what the diff +the IC constraint and sort of what what + + align:start position:0% +the IC constraint and sort of what what + + + align:start position:0% +the IC constraint and sort of what what +is the difference between the the you + + align:start position:0% +is the difference between the the you + + + align:start position:0% +is the difference between the the you +you sort of solve the problem to say + + align:start position:0% +you sort of solve the problem to say + + + align:start position:0% +you sort of solve the problem to say +what's the difference between the + + align:start position:0% +what's the difference between the + + + align:start position:0% +what's the difference between the +highest state and the low State payoff + + align:start position:0% +highest state and the low State payoff + + + align:start position:0% +highest state and the low State payoff +and then you slide the whole thing kind + + align:start position:0% +and then you slide the whole thing kind + + + align:start position:0% +and then you slide the whole thing kind +of up or down so that the the agent is + + align:start position:0% +of up or down so that the the agent is + + + align:start position:0% +of up or down so that the the agent is +exactly indifferent to their outside + + align:start position:0% +exactly indifferent to their outside + + + align:start position:0% +exactly indifferent to their outside +option in their IR constraint + + align:start position:0% +option in their IR constraint + + + align:start position:0% +option in their IR constraint +okay so that's that's the that's the + + align:start position:0% +okay so that's that's the that's the + + + align:start position:0% +okay so that's that's the that's the +general way you solve these moral hazard + + align:start position:0% +general way you solve these moral hazard + + + align:start position:0% +general way you solve these moral hazard +problems + + align:start position:0% +problems + + + align:start position:0% +problems +okay so that's the rent that pins down + + align:start position:0% +okay so that's the rent that pins down + + + align:start position:0% +okay so that's the rent that pins down +the rent + + align:start position:0% +the rent + + + align:start position:0% +the rent +okay + + align:start position:0% +okay + + + align:start position:0% +okay +clear + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's the final contract final + + align:start position:0% +so that's the final contract final + + + align:start position:0% +so that's the final contract final +contract now so now we know both the + + align:start position:0% +contract now so now we know both the + + + align:start position:0% +contract now so now we know both the +little H and the B and little l so + + align:start position:0% +little H and the B and little l so + + + align:start position:0% +little H and the B and little l so +little h + + align:start position:0% +little h + + + align:start position:0% +little h +so sorry so our our R here was H Square + + align:start position:0% +so sorry so our our R here was H Square + + + align:start position:0% +so sorry so our our R here was H Square +over 2C minus W bar + + align:start position:0% +over 2C minus W bar + + + align:start position:0% +over 2C minus W bar +so we can substitute in so we get + + align:start position:0% +so we can substitute in so we get + + + align:start position:0% +so we can substitute in so we get +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the so the the payment is like one minus + + align:start position:0% +the so the the payment is like one minus + + + align:start position:0% +the so the the payment is like one minus +the r right because it goes the other + + align:start position:0% +the r right because it goes the other + + + align:start position:0% +the r right because it goes the other +way so uh this is minus r + + align:start position:0% +way so uh this is minus r + + + align:start position:0% +way so uh this is minus r +right that happens in either state in + + align:start position:0% +right that happens in either state in + + + align:start position:0% +right that happens in either state in +either in either + + align:start position:0% +either in either + + + align:start position:0% +either in either +uh state of the world + + align:start position:0% +uh state of the world + + + align:start position:0% +uh state of the world +and the difference is she has to keep + + align:start position:0% +and the difference is she has to keep + + + align:start position:0% +and the difference is she has to keep +the the output so that's just another + + align:start position:0% +the the output so that's just another + + + align:start position:0% +the the output so that's just another +way of writing like there's a rental or + + align:start position:0% +way of writing like there's a rental or + + + align:start position:0% +way of writing like there's a rental or +rent equal to to H Square over 2C uh + + align:start position:0% +rent equal to to H Square over 2C uh + + + align:start position:0% +rent equal to to H Square over 2C uh +minus W bar that's the rent and then she + + align:start position:0% +minus W bar that's the rent and then she + + + align:start position:0% +minus W bar that's the rent and then she +keeps the return uh the gauge that's + + align:start position:0% +keeps the return uh the gauge that's + + + align:start position:0% +keeps the return uh the gauge that's +just sort of the way of expressing it + + align:start position:0% +just sort of the way of expressing it + + + align:start position:0% +just sort of the way of expressing it +kind of in this contract space + + align:start position:0% +kind of in this contract space + + + align:start position:0% +kind of in this contract space +okay is that all all clear so far + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this is a nice contract because the + + align:start position:0% +this is a nice contract because the + + + align:start position:0% +this is a nice contract because the +farmer is going to uh from you know the + + align:start position:0% +farmer is going to uh from you know the + + + align:start position:0% +farmer is going to uh from you know the +the farmer gets no rents right it's nice + + align:start position:0% +the farmer gets no rents right it's nice + + + align:start position:0% +the farmer gets no rents right it's nice +and from the protective of the landlord + + align:start position:0% +and from the protective of the landlord + + + align:start position:0% +and from the protective of the landlord +right the landlord likes his contract + + align:start position:0% +right the landlord likes his contract + + + align:start position:0% +right the landlord likes his contract +the farmer is getting no rents she's + + align:start position:0% +the farmer is getting no rents she's + + + align:start position:0% +the farmer is getting no rents she's +getting exactly equal to her outside + + align:start position:0% +getting exactly equal to her outside + + + align:start position:0% +getting exactly equal to her outside +option + + align:start position:0% +option + + + align:start position:0% +option +um in expectation + + align:start position:0% +um in expectation + + + align:start position:0% +um in expectation +so landlord is capturing all the Surplus + + align:start position:0% +so landlord is capturing all the Surplus + + + align:start position:0% +so landlord is capturing all the Surplus +and she puts it in full effort so that's + + align:start position:0% +and she puts it in full effort so that's + + + align:start position:0% +and she puts it in full effort so that's +like great landlord loves this contract + + align:start position:0% +like great landlord loves this contract + + + align:start position:0% +like great landlord loves this contract +problem is there's there's two uh + + align:start position:0% +problem is there's there's two uh + + + align:start position:0% +problem is there's there's two uh +challenges with this contract + + align:start position:0% +challenges with this contract + + + align:start position:0% +challenges with this contract +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the first challenge with this contract + + align:start position:0% +the first challenge with this contract + + + align:start position:0% +the first challenge with this contract +is the farmer is bearing all of the risk + + align:start position:0% +is the farmer is bearing all of the risk + + + align:start position:0% +is the farmer is bearing all of the risk +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +the second is that that's the first + + align:start position:0% +the second is that that's the first + + + align:start position:0% +the second is that that's the first +problem + + align:start position:0% +problem + + + align:start position:0% +problem +second problem + + align:start position:0% +second problem + + + align:start position:0% +second problem +is the farmer with positive probability + + align:start position:0% +is the farmer with positive probability + + + align:start position:0% +is the farmer with positive probability +is going to earn um uh this lower this + + align:start position:0% +is going to earn um uh this lower this + + + align:start position:0% +is going to earn um uh this lower this +this L + + align:start position:0% +this L + + + align:start position:0% +this L +um and that may be negative + + align:start position:0% +um and that may be negative + + + align:start position:0% +um and that may be negative +right + + align:start position:0% +right + + + align:start position:0% +right +so uh because you may get less than zero + + align:start position:0% +so uh because you may get less than zero + + + align:start position:0% +so uh because you may get less than zero +so what happens if the if if there's no + + align:start position:0% +so what happens if the if if there's no + + + align:start position:0% +so what happens if the if if there's no +money and can't pay + + align:start position:0% +money and can't pay + + + align:start position:0% +money and can't pay +right so then we have a second issue + + align:start position:0% +right so then we have a second issue + + + align:start position:0% +right so then we have a second issue +which is what we can think of what are + + align:start position:0% +which is what we can think of what are + + + align:start position:0% +which is what we can think of what are +called limited liability contracts where + + align:start position:0% +called limited liability contracts where + + + align:start position:0% +called limited liability contracts where +you're capped at zero + + align:start position:0% + + + + align:start position:0% + +From Below right you can't you can't + + align:start position:0% +From Below right you can't you can't + + + align:start position:0% +From Below right you can't you can't +ever go below zero if you have no money + + align:start position:0% +ever go below zero if you have no money + + + align:start position:0% +ever go below zero if you have no money +you can't pay the rent + + align:start position:0% +you can't pay the rent + + + align:start position:0% +you can't pay the rent +right + + align:start position:0% +right + + + align:start position:0% +right +and so this is so this one is kind of a + + align:start position:0% +and so this is so this one is kind of a + + + align:start position:0% +and so this is so this one is kind of a +this is like a risk an insurance issue + + align:start position:0% +this is like a risk an insurance issue + + + align:start position:0% +this is like a risk an insurance issue +and this is a limited liability issue + + align:start position:0% +and this is a limited liability issue + + + align:start position:0% +and this is a limited liability issue +and both of these can give rise to what + + align:start position:0% +and both of these can give rise to what + + + align:start position:0% +and both of these can give rise to what +looks like sharecropping Arrangements + + align:start position:0% +looks like sharecropping Arrangements + + + align:start position:0% +looks like sharecropping Arrangements +but the implications of them are going + + align:start position:0% +but the implications of them are going + + + align:start position:0% +but the implications of them are going +to be a little bit different + + align:start position:0% +to be a little bit different + + + align:start position:0% +to be a little bit different +okay so that's what I want to go through + + align:start position:0% +okay so that's what I want to go through + + + align:start position:0% +okay so that's what I want to go through +next is to say well how do we think + + align:start position:0% +next is to say well how do we think + + + align:start position:0% +next is to say well how do we think +about each of those and how could each + + align:start position:0% +about each of those and how could each + + + align:start position:0% +about each of those and how could each +of those different reasons + + align:start position:0% +of those different reasons + + + align:start position:0% +of those different reasons +um + + align:start position:0% +um + + + align:start position:0% +um +lead us to to a sharecropping + + align:start position:0% +lead us to to a sharecropping + + + align:start position:0% +lead us to to a sharecropping +arrangement + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +all clear yeah not just Liberty + + align:start position:0% +all clear yeah not just Liberty + + + align:start position:0% +all clear yeah not just Liberty +liability just means that I can't go I + + align:start position:0% +liability just means that I can't go I + + + align:start position:0% +liability just means that I can't go I +can only take I can't force you to take + + align:start position:0% +can only take I can't force you to take + + + align:start position:0% +can only take I can't force you to take +out + + align:start position:0% +out + + + align:start position:0% +out +yeah so um correct so it when so when + + align:start position:0% +yeah so um correct so it when so when + + + align:start position:0% +yeah so um correct so it when so when +might limited liability be a be a thing + + align:start position:0% +might limited liability be a be a thing + + + align:start position:0% +might limited liability be a be a thing +or might not be a thing so uh yes I + + align:start position:0% +or might not be a thing so uh yes I + + + align:start position:0% +or might not be a thing so uh yes I +right so you can't + + align:start position:0% +right so you can't + + + align:start position:0% +right so you can't +um + + align:start position:0% +um + + + align:start position:0% +um +so you're right it means we can't force + + align:start position:0% +so you're right it means we can't force + + + align:start position:0% +so you're right it means we can't force +you to go take out a loan to pay the + + align:start position:0% +you to go take out a loan to pay the + + + align:start position:0% +you to go take out a loan to pay the +rent for example + + align:start position:0% +rent for example + + + align:start position:0% +rent for example +um it um + + align:start position:0% + + + + align:start position:0% + +although even in in kind of um you know + + align:start position:0% +although even in in kind of um you know + + + align:start position:0% +although even in in kind of um you know +debt contracts right like why might that + + align:start position:0% +debt contracts right like why might that + + + align:start position:0% +debt contracts right like why might that +be why you could just like leave for + + align:start position:0% +be why you could just like leave for + + + align:start position:0% +be why you could just like leave for +example + + align:start position:0% +example + + + align:start position:0% +example +um uh you know it can be hard to um + + align:start position:0% +um uh you know it can be hard to um + + + align:start position:0% +um uh you know it can be hard to um +yeah so that's basically the the and + + align:start position:0% +yeah so that's basically the the and + + + align:start position:0% +yeah so that's basically the the and +we'll talk about those contracts limited + + align:start position:0% +we'll talk about those contracts limited + + + align:start position:0% +we'll talk about those contracts limited +liability also when we get to the credit + + align:start position:0% +liability also when we get to the credit + + + align:start position:0% +liability also when we get to the credit +lectures at the end of the semester + + align:start position:0% +lectures at the end of the semester + + + align:start position:0% +lectures at the end of the semester +where a lot of these same issues are + + align:start position:0% +where a lot of these same issues are + + + align:start position:0% +where a lot of these same issues are +going to come up + + align:start position:0% +going to come up + + + align:start position:0% +going to come up +um + + align:start position:0% +um + + + align:start position:0% +um +yeah but you could leave you could like + + align:start position:0% +yeah but you could leave you could like + + + align:start position:0% +yeah but you could leave you could like +it could be hard to enforce like there's + + align:start position:0% +it could be hard to enforce like there's + + + align:start position:0% +it could be hard to enforce like there's +a variety of reasons + + align:start position:0% +a variety of reasons + + + align:start position:0% +a variety of reasons +or you might right so you might have + + align:start position:0% +or you might right so you might have + + + align:start position:0% +or you might right so you might have +MasterCard yeah + + align:start position:0% +MasterCard yeah + + + align:start position:0% +MasterCard yeah +other questions + + align:start position:0% + + + + align:start position:0% + +okay so let's explore both of these + + align:start position:0% +okay so let's explore both of these + + + align:start position:0% +okay so let's explore both of these +so + + align:start position:0% +so + + + align:start position:0% +so +what happens when the farmer is + + align:start position:0% +what happens when the farmer is + + + align:start position:0% +what happens when the farmer is +risk-averse so now let's assume that the + + align:start position:0% +risk-averse so now let's assume that the + + + align:start position:0% +risk-averse so now let's assume that the +landlord is uh risk neutral + + align:start position:0% + + + + align:start position:0% + +okay but the farmer has utility has some + + align:start position:0% +okay but the farmer has utility has some + + + align:start position:0% +okay but the farmer has utility has some +utility function + + align:start position:0% +utility function + + + align:start position:0% +utility function +um which is concave over uh consumption + + align:start position:0% +um which is concave over uh consumption + + + align:start position:0% +um which is concave over uh consumption +in both States + + align:start position:0% +in both States + + + align:start position:0% +in both States +okay and and actually + + align:start position:0% +okay and and actually + + + align:start position:0% +okay and and actually +you can do this with as I said with both + + align:start position:0% +you can do this with as I said with both + + + align:start position:0% +you can do this with as I said with both +parties being risk neutral actually + + align:start position:0% +parties being risk neutral actually + + + align:start position:0% +parties being risk neutral actually +doesn't it's just the math gets more + + align:start position:0% +doesn't it's just the math gets more + + + align:start position:0% +doesn't it's just the math gets more +complicated uh actually all these moral + + align:start position:0% +complicated uh actually all these moral + + + align:start position:0% +complicated uh actually all these moral +hazard models actually the map gets like + + align:start position:0% +hazard models actually the map gets like + + + align:start position:0% +hazard models actually the map gets like +it can get a little a little uh + + align:start position:0% +it can get a little a little uh + + + align:start position:0% +it can get a little a little uh +unpleasant Ed you're nodding I can see + + align:start position:0% +unpleasant Ed you're nodding I can see + + + align:start position:0% +unpleasant Ed you're nodding I can see +you they're surprisingly like not pretty + + align:start position:0% +you they're surprisingly like not pretty + + + align:start position:0% +you they're surprisingly like not pretty +models for I think there's nothing + + align:start position:0% +models for I think there's nothing + + + align:start position:0% +models for I think there's nothing +I don't have a good reason why that is + + align:start position:0% +I don't have a good reason why that is + + + align:start position:0% +I don't have a good reason why that is +but that that's true so um okay so and + + align:start position:0% +but that that's true so um okay so and + + + align:start position:0% +but that that's true so um okay so and +and if anyone announce any proof of that + + align:start position:0% +and if anyone announce any proof of that + + + align:start position:0% +and if anyone announce any proof of that +go back and read sticklet 74 and uh + + align:start position:0% +go back and read sticklet 74 and uh + + + align:start position:0% +go back and read sticklet 74 and uh +you'll see it's not it's not it's not + + align:start position:0% +you'll see it's not it's not it's not + + + align:start position:0% +you'll see it's not it's not it's not +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +um + + align:start position:0% +um + + + align:start position:0% +um +okay I think it's just like carrying or + + align:start position:0% +okay I think it's just like carrying or + + + align:start position:0% +okay I think it's just like carrying or +solving all these contracts with all + + align:start position:0% +solving all these contracts with all + + + align:start position:0% +solving all these contracts with all +these concave utility functions just + + align:start position:0% +these concave utility functions just + + + align:start position:0% +these concave utility functions just +gets a little difficult anyway + + align:start position:0% +gets a little difficult anyway + + + align:start position:0% +gets a little difficult anyway +um + + align:start position:0% +um + + + align:start position:0% +um +so now + + align:start position:0% +so now + + + align:start position:0% +so now +what happens + + align:start position:0% +what happens + + + align:start position:0% +what happens +but but the key the key result actually + + align:start position:0% +but but the key the key result actually + + + align:start position:0% +but but the key the key result actually +is very easy to see + + align:start position:0% +is very easy to see + + + align:start position:0% +is very easy to see +so + + align:start position:0% +so + + + align:start position:0% +so +so this is exactly the same as before + + align:start position:0% +so this is exactly the same as before + + + align:start position:0% +so this is exactly the same as before +now + + align:start position:0% +now + + + align:start position:0% +now +the + + align:start position:0% +the + + + align:start position:0% +the +the farmer + + align:start position:0% +the farmer + + + align:start position:0% +the farmer +um has like this is concave you know + + align:start position:0% +um has like this is concave you know + + + align:start position:0% +um has like this is concave you know +we're maximizing e times U of H and one + + align:start position:0% +we're maximizing e times U of H and one + + + align:start position:0% +we're maximizing e times U of H and one +minus E times U of L as opposed to just + + align:start position:0% +minus E times U of L as opposed to just + + + align:start position:0% +minus E times U of L as opposed to just +uh h l directly + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +one thing to point out is if the + + align:start position:0% +one thing to point out is if the + + + align:start position:0% +one thing to point out is if the +landlord implemented the contract from + + align:start position:0% +landlord implemented the contract from + + + align:start position:0% +landlord implemented the contract from +before + + align:start position:0% +before + + + align:start position:0% +before +the farmer's utility is going to be + + align:start position:0% +the farmer's utility is going to be + + + align:start position:0% +the farmer's utility is going to be +strictly less than W lower bar + + align:start position:0% +strictly less than W lower bar + + + align:start position:0% +strictly less than W lower bar +right and okay because of the sort of + + align:start position:0% +right and okay because of the sort of + + + align:start position:0% +right and okay because of the sort of +the the + + align:start position:0% +the the + + + align:start position:0% +the the +or + + align:start position:0% +or + + + align:start position:0% +or +um + + align:start position:0% +um + + + align:start position:0% +um +I mean this is actually not totally + + align:start position:0% +I mean this is actually not totally + + + align:start position:0% +I mean this is actually not totally +precise oh sorry this is this is precise + + align:start position:0% +precise oh sorry this is this is precise + + + align:start position:0% +precise oh sorry this is this is precise +actually the uofw lower bar example + + align:start position:0% +actually the uofw lower bar example + + + align:start position:0% +actually the uofw lower bar example +right that's precise okay and and why is + + align:start position:0% +right that's precise okay and and why is + + + align:start position:0% +right that's precise okay and and why is +that that's just from concavity + + align:start position:0% +that that's just from concavity + + + align:start position:0% +that that's just from concavity +right that's just because + + align:start position:0% +right that's just because + + + align:start position:0% +right that's just because +um the so U of w lower bar right is the + + align:start position:0% +um the so U of w lower bar right is the + + + align:start position:0% +um the so U of w lower bar right is the +utility of the sort of expected + + align:start position:0% +utility of the sort of expected + + + align:start position:0% +utility of the sort of expected +um return + + align:start position:0% +um return + + + align:start position:0% +um return +and kind of what it what you what it + + align:start position:0% +and kind of what it what you what it + + + align:start position:0% +and kind of what it what you what it +means you risk averse or what concave + + align:start position:0% +means you risk averse or what concave + + + align:start position:0% +means you risk averse or what concave +utility functions give you is that the + + align:start position:0% +utility functions give you is that the + + + align:start position:0% +utility functions give you is that the +utility from the the expected utility is + + align:start position:0% +utility from the the expected utility is + + + align:start position:0% +utility from the the expected utility is +less than the utility of the certainty + + align:start position:0% +less than the utility of the certainty + + + align:start position:0% +less than the utility of the certainty +equivalent + + align:start position:0% +equivalent + + + align:start position:0% +equivalent +okay that's just what we get from + + align:start position:0% +okay that's just what we get from + + + align:start position:0% +okay that's just what we get from +concavity + + align:start position:0% +concavity + + + align:start position:0% +concavity +okay so that means that that so what + + align:start position:0% +okay so that means that that so what + + + align:start position:0% +okay so that means that that so what +does that mean practically right it + + align:start position:0% +does that mean practically right it + + + align:start position:0% +does that mean practically right it +means practically we took the contract + + align:start position:0% +means practically we took the contract + + + align:start position:0% +means practically we took the contract +from before + + align:start position:0% +from before + + + align:start position:0% +from before +like that's the worker is now below her + + align:start position:0% +like that's the worker is now below her + + + align:start position:0% +like that's the worker is now below her +IR constraint + + align:start position:0% +IR constraint + + + align:start position:0% +IR constraint +so we got to do something + + align:start position:0% +so we got to do something + + + align:start position:0% +so we got to do something +okay otherwise she'll walk away + + align:start position:0% +okay otherwise she'll walk away + + + align:start position:0% +okay otherwise she'll walk away +and what could we do well we could raise + + align:start position:0% +and what could we do well we could raise + + + align:start position:0% +and what could we do well we could raise +we could lower the rent we could raise + + align:start position:0% +we could lower the rent we could raise + + + align:start position:0% +we could lower the rent we could raise +kind of the fixed fee + + align:start position:0% +kind of the fixed fee + + + align:start position:0% +kind of the fixed fee +or we could provide some insurance and + + align:start position:0% +or we could provide some insurance and + + + align:start position:0% +or we could provide some insurance and +and and and reduce the gap between H + + align:start position:0% +and and and reduce the gap between H + + + align:start position:0% +and and and reduce the gap between H +minus l + + align:start position:0% +minus l + + + align:start position:0% +minus l +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +the question is Sir which should they + + align:start position:0% +the question is Sir which should they + + + align:start position:0% +the question is Sir which should they +what should landlord do should they like + + align:start position:0% +what should landlord do should they like + + + align:start position:0% +what should landlord do should they like +reduce the should they do it all on the + + align:start position:0% +reduce the should they do it all on the + + + align:start position:0% +reduce the should they do it all on the +fixed fee margin or should they do some + + align:start position:0% +fixed fee margin or should they do some + + + align:start position:0% +fixed fee margin or should they do some +of it on the on the other margin + + align:start position:0% +of it on the on the other margin + + + align:start position:0% +of it on the on the other margin +and one simple way to sort of see that + + align:start position:0% +and one simple way to sort of see that + + + align:start position:0% +and one simple way to sort of see that +they should do at least some of it at + + align:start position:0% +they should do at least some of it at + + + align:start position:0% +they should do at least some of it at +least a little bit of it on the eight on + + align:start position:0% +least a little bit of it on the eight on + + + align:start position:0% +least a little bit of it on the eight on +on reducing the H minus L uh Gap + + align:start position:0% +on reducing the H minus L uh Gap + + + align:start position:0% +on reducing the H minus L uh Gap +um is as follows right so + + align:start position:0% +um is as follows right so + + + align:start position:0% +um is as follows right so +um it basically just this argument here + + align:start position:0% +um it basically just this argument here + + + align:start position:0% +um it basically just this argument here +which is starting from like starting + + align:start position:0% +which is starting from like starting + + + align:start position:0% +which is starting from like starting +from the first best level of effort + + align:start position:0% +from the first best level of effort + + + align:start position:0% +from the first best level of effort +right the efficiency loss + + align:start position:0% +right the efficiency loss + + + align:start position:0% +right the efficiency loss +uh from reducing H minus L just a little + + align:start position:0% +uh from reducing H minus L just a little + + + align:start position:0% +uh from reducing H minus L just a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +is second order + + align:start position:0% +is second order + + + align:start position:0% +is second order +but the utilities right because we + + align:start position:0% +but the utilities right because we + + + align:start position:0% +but the utilities right because we +maximized that right so this is the loss + + align:start position:0% +maximized that right so this is the loss + + + align:start position:0% +maximized that right so this is the loss +there is second order but the utility + + align:start position:0% +there is second order but the utility + + + align:start position:0% +there is second order but the utility +gain for the agent is going to be first + + align:start position:0% +gain for the agent is going to be first + + + align:start position:0% +gain for the agent is going to be first +order + + align:start position:0% +order + + + align:start position:0% +order +okay so that's a simple argument which + + align:start position:0% +okay so that's a simple argument which + + + align:start position:0% +okay so that's a simple argument which +says + + align:start position:0% +says + + + align:start position:0% +says +the first the the solution to this + + align:start position:0% +the first the the solution to this + + + align:start position:0% +the first the the solution to this +problem can't have H minus L be equal to + + align:start position:0% +problem can't have H minus L be equal to + + + align:start position:0% +problem can't have H minus L be equal to +the full kind of uh + + align:start position:0% +the full kind of uh + + + align:start position:0% +the full kind of uh +um equal to cap h + + align:start position:0% +um equal to cap h + + + align:start position:0% +um equal to cap h +right we're going to do at least a + + align:start position:0% +right we're going to do at least a + + + align:start position:0% +right we're going to do at least a +little bit of this sort of reduction on + + align:start position:0% +little bit of this sort of reduction on + + + align:start position:0% +little bit of this sort of reduction on +the on the dimension of sort of + + align:start position:0% +the on the dimension of sort of + + + align:start position:0% +the on the dimension of sort of +providing a little bit of insurance + + align:start position:0% +providing a little bit of insurance + + + align:start position:0% +providing a little bit of insurance +because that's sort of second order in + + align:start position:0% +because that's sort of second order in + + + align:start position:0% +because that's sort of second order in +terms of the + + align:start position:0% +terms of the + + + align:start position:0% +terms of the +uh total kind of productivity loss but + + align:start position:0% +uh total kind of productivity loss but + + + align:start position:0% +uh total kind of productivity loss but +first Order gain in terms of the + + align:start position:0% +first Order gain in terms of the + + + align:start position:0% +first Order gain in terms of the +insurance value + + align:start position:0% +insurance value + + + align:start position:0% +insurance value +yeah Aaron um is that true when the + + align:start position:0% +yeah Aaron um is that true when the + + + align:start position:0% +yeah Aaron um is that true when the +landlord + + align:start position:0% +landlord + + + align:start position:0% +landlord +uh yes + + align:start position:0% +uh yes + + + align:start position:0% +uh yes +because another way of thinking about it + + align:start position:0% +because another way of thinking about it + + + align:start position:0% +because another way of thinking about it +is like the the landlord is bearing um + + align:start position:0% + + + + align:start position:0% + +let me think for one second yes it's + + align:start position:0% +let me think for one second yes it's + + + align:start position:0% +let me think for one second yes it's +true but let me just double check uh + + align:start position:0% + + + + align:start position:0% + +yeah I'm pretty sure it's true because + + align:start position:0% +yeah I'm pretty sure it's true because + + + align:start position:0% +yeah I'm pretty sure it's true because +it's gonna be I think because I think + + align:start position:0% +it's gonna be I think because I think + + + align:start position:0% +it's gonna be I think because I think +it's going to be a similar kind of + + align:start position:0% +it's going to be a similar kind of + + + align:start position:0% +it's going to be a similar kind of +argument that the landlord I was trying + + align:start position:0% +argument that the landlord I was trying + + + align:start position:0% +argument that the landlord I was trying +to think of whether the Indian narrator + + align:start position:0% +to think of whether the Indian narrator + + + align:start position:0% +to think of whether the Indian narrator +conditions I don't think so because I + + align:start position:0% +conditions I don't think so because I + + + align:start position:0% +conditions I don't think so because I +think that the landlord is going to be + + align:start position:0% +think that the landlord is going to be + + + align:start position:0% +think that the landlord is going to be +totally + + align:start position:0% +totally + + + align:start position:0% +totally +fully like go it's a simple argument + + align:start position:0% +fully like go it's a simple argument + + + align:start position:0% +fully like go it's a simple argument +going from fully insured to it to an + + align:start position:0% +going from fully insured to it to an + + + align:start position:0% +going from fully insured to it to an +Epsilon bit + + align:start position:0% +Epsilon bit + + + align:start position:0% +Epsilon bit +of risk is going to be less costly than + + align:start position:0% +of risk is going to be less costly than + + + align:start position:0% +of risk is going to be less costly than +sort of reducing the risk a little bit + + align:start position:0% +sort of reducing the risk a little bit + + + align:start position:0% +sort of reducing the risk a little bit +I'm pretty sure that's right + + align:start position:0% +I'm pretty sure that's right + + + align:start position:0% +I'm pretty sure that's right +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +um okay so on the other hand so the so + + align:start position:0% +um okay so on the other hand so the so + + + align:start position:0% +um okay so on the other hand so the so +that says look the optimal contract is + + align:start position:0% +that says look the optimal contract is + + + align:start position:0% +that says look the optimal contract is +not going to feature is not going to be + + align:start position:0% +not going to feature is not going to be + + + align:start position:0% +not going to feature is not going to be +the first best it's going to have at + + align:start position:0% +the first best it's going to have at + + + align:start position:0% +the first best it's going to have at +least a little bit of uh of a sharing + + align:start position:0% +least a little bit of uh of a sharing + + + align:start position:0% +least a little bit of uh of a sharing +feature + + align:start position:0% + + + + align:start position:0% + +on the other hand we also know + + align:start position:0% +on the other hand we also know + + + align:start position:0% +on the other hand we also know +that we can't fully insure the agent + + align:start position:0% +that we can't fully insure the agent + + + align:start position:0% +that we can't fully insure the agent +but then the agent will work + + align:start position:0% +but then the agent will work + + + align:start position:0% +but then the agent will work +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +kind of argument + + align:start position:0% +kind of argument + + + align:start position:0% +kind of argument +says that the optimal contract is going + + align:start position:0% +says that the optimal contract is going + + + align:start position:0% +says that the optimal contract is going +to look something like a share contract + + align:start position:0% +to look something like a share contract + + + align:start position:0% +to look something like a share contract +where there's I mean with maybe with a + + align:start position:0% +where there's I mean with maybe with a + + + align:start position:0% +where there's I mean with maybe with a +fixed fee but it's going to have some + + align:start position:0% +fixed fee but it's going to have some + + + align:start position:0% +fixed fee but it's going to have some +feature where the sort of the the share + + align:start position:0% +feature where the sort of the the share + + + align:start position:0% +feature where the sort of the the share +of the output that the agent keeps is + + align:start position:0% +of the output that the agent keeps is + + + align:start position:0% +of the output that the agent keeps is +less than the full output + + align:start position:0% +less than the full output + + + align:start position:0% +less than the full output +so some amount of the output I sort of + + align:start position:0% +so some amount of the output I sort of + + + align:start position:0% +so some amount of the output I sort of +shared with the landlord + + align:start position:0% +shared with the landlord + + + align:start position:0% +shared with the landlord +and that even though that has a + + align:start position:0% +and that even though that has a + + + align:start position:0% +and that even though that has a +productivity loss associated with doing + + align:start position:0% +productivity loss associated with doing + + + align:start position:0% +productivity loss associated with doing +that + + align:start position:0% +that + + + align:start position:0% +that +okay but it's not going to go all the + + align:start position:0% +okay but it's not going to go all the + + + align:start position:0% +okay but it's not going to go all the +way to the other dimension of full + + align:start position:0% +way to the other dimension of full + + + align:start position:0% +way to the other dimension of full +insurance either + + align:start position:0% +insurance either + + + align:start position:0% +insurance either +okay so that's kind of the that's in + + align:start position:0% +okay so that's kind of the that's in + + + align:start position:0% +okay so that's kind of the that's in +some sense the the this is the key + + align:start position:0% +some sense the the this is the key + + + align:start position:0% +some sense the the this is the key +uh insight + + align:start position:0% +uh insight + + + align:start position:0% +uh insight +um + + align:start position:0% +um + + + align:start position:0% +um +and this I said is the argument for + + align:start position:0% +and this I said is the argument for + + + align:start position:0% +and this I said is the argument for +sharecropping given by stiglets which is + + align:start position:0% +sharecropping given by stiglets which is + + + align:start position:0% +sharecropping given by stiglets which is +that landlords and peasants actually + + align:start position:0% +that landlords and peasants actually + + + align:start position:0% +that landlords and peasants actually +prefer so so the thickness argument + + align:start position:0% +prefer so so the thickness argument + + + align:start position:0% +prefer so so the thickness argument +actually kind of like + + align:start position:0% +actually kind of like + + + align:start position:0% +actually kind of like +um + + align:start position:0% +um + + + align:start position:0% +um +it's uh it's it's almost revolutionary + + align:start position:0% +it's uh it's it's almost revolutionary + + + align:start position:0% +it's uh it's it's almost revolutionary +in a sense it's say look like you know + + align:start position:0% +in a sense it's say look like you know + + + align:start position:0% +in a sense it's say look like you know +uh not revolutionary in the sense of + + align:start position:0% +uh not revolutionary in the sense of + + + align:start position:0% +uh not revolutionary in the sense of +like let's have the revolution but like + + align:start position:0% +like let's have the revolution but like + + + align:start position:0% +like let's have the revolution but like +Revolution + + align:start position:0% +Revolution + + + align:start position:0% +Revolution +revolutionary almost in the opposite + + align:start position:0% +revolutionary almost in the opposite + + + align:start position:0% +revolutionary almost in the opposite +sense actually to say look like you + + align:start position:0% +sense actually to say look like you + + + align:start position:0% +sense actually to say look like you +might be you might have sort of thought + + align:start position:0% +might be you might have sort of thought + + + align:start position:0% +might be you might have sort of thought +that like you know this this landlord + + align:start position:0% +that like you know this this landlord + + + align:start position:0% +that like you know this this landlord +the sharecropping thing was his total + + align:start position:0% +the sharecropping thing was his total + + + align:start position:0% +the sharecropping thing was his total +like exploitative thing and like if only + + align:start position:0% +like exploitative thing and like if only + + + align:start position:0% +like exploitative thing and like if only +the tenants could kind of get out from + + align:start position:0% +the tenants could kind of get out from + + + align:start position:0% +the tenants could kind of get out from +under it they would like be much happier + + align:start position:0% +under it they would like be much happier + + + align:start position:0% +under it they would like be much happier +right but actually he says no no + + align:start position:0% +right but actually he says no no + + + align:start position:0% +right but actually he says no no +actually the sharecropping is like + + align:start position:0% +actually the sharecropping is like + + + align:start position:0% +actually the sharecropping is like +preferred by the tenants in some sense + + align:start position:0% +preferred by the tenants in some sense + + + align:start position:0% +preferred by the tenants in some sense +to the full rental contract because + + align:start position:0% +to the full rental contract because + + + align:start position:0% +to the full rental contract because +they're they're getting some insurance + + align:start position:0% +they're they're getting some insurance + + + align:start position:0% +they're they're getting some insurance +value + + align:start position:0% +value + + + align:start position:0% +value +okay and otherwise because like life is + + align:start position:0% +okay and otherwise because like life is + + + align:start position:0% +okay and otherwise because like life is +really risky + + align:start position:0% +really risky + + + align:start position:0% +really risky +right and so so it's a way of providing + + align:start position:0% +right and so so it's a way of providing + + + align:start position:0% +right and so so it's a way of providing +some combination of providing insurance + + align:start position:0% +some combination of providing insurance + + + align:start position:0% +some combination of providing insurance +and and incentives + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yes + + align:start position:0% + + + + align:start position:0% + +does that change + + align:start position:0% +does that change + + + align:start position:0% +does that change +uh it doesn't change efficiency + + align:start position:0% +uh it doesn't change efficiency + + + align:start position:0% +uh it doesn't change efficiency +sorry so what happens in this let me + + align:start position:0% +sorry so what happens in this let me + + + align:start position:0% +sorry so what happens in this let me +think for a sec so you're saying what + + align:start position:0% +think for a sec so you're saying what + + + align:start position:0% +think for a sec so you're saying what +happens if you put in a restriction + + align:start position:0% +happens if you put in a restriction + + + align:start position:0% +happens if you put in a restriction +saying they're they have to get they + + align:start position:0% +saying they're they have to get they + + + align:start position:0% +saying they're they have to get they +have to give more rents yeah + + align:start position:0% + + + + align:start position:0% + +let me think for a sec + + align:start position:0% +let me think for a sec + + + align:start position:0% +let me think for a sec +um + + align:start position:0% +um + + + align:start position:0% +um +if I increase the rents + + align:start position:0% +if I increase the rents + + + align:start position:0% +if I increase the rents +will I + + align:start position:0% +will I + + + align:start position:0% +will I +don't know the answer off without my + + align:start position:0% +don't know the answer off without my + + + align:start position:0% +don't know the answer off without my +head so um + + align:start position:0% + + + + align:start position:0% + +like you're saying if I increase the + + align:start position:0% +like you're saying if I increase the + + + align:start position:0% +like you're saying if I increase the +rents will the landlord sort of like + + align:start position:0% +rents will the landlord sort of like + + + align:start position:0% +rents will the landlord sort of like +um compensate somehow + + align:start position:0% +um compensate somehow + + + align:start position:0% +um compensate somehow +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +I understand why so I think actually in + + align:start position:0% +I understand why so I think actually in + + + align:start position:0% +I understand why so I think actually in +this model + + align:start position:0% +this model + + + align:start position:0% +this model +um no + + align:start position:0% +um no + + + align:start position:0% +um no +um + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so I'm not totally sure and the bees are + + align:start position:0% +so I'm not totally sure and the bees are + + + align:start position:0% +so I'm not totally sure and the bees are +not totally sure is that I mean in + + align:start position:0% +not totally sure is that I mean in + + + align:start position:0% +not totally sure is that I mean in +general the way we solve these models is + + align:start position:0% +general the way we solve these models is + + + align:start position:0% +general the way we solve these models is +we figure out what the sort of the the + + align:start position:0% +we figure out what the sort of the the + + + align:start position:0% +we figure out what the sort of the the +Gap is and then sort of slide up and + + align:start position:0% +Gap is and then sort of slide up and + + + align:start position:0% +Gap is and then sort of slide up and +down to hit the rent floor and so if + + align:start position:0% +down to hit the rent floor and so if + + + align:start position:0% +down to hit the rent floor and so if +that's essentially what is the impact of + + align:start position:0% +that's essentially what is the impact of + + + align:start position:0% +that's essentially what is the impact of +raising the outside wage essentially and + + align:start position:0% +raising the outside wage essentially and + + + align:start position:0% +raising the outside wage essentially and +the reason I'm not 100 sure is it also + + align:start position:0% +the reason I'm not 100 sure is it also + + + align:start position:0% +the reason I'm not 100 sure is it also +affects the risk aversion and that's + + align:start position:0% +affects the risk aversion and that's + + + align:start position:0% +affects the risk aversion and that's +what's that's what's confusing that's + + align:start position:0% +what's that's what's confusing that's + + + align:start position:0% +what's that's what's confusing that's +why I'm not giving you a quick answer + + align:start position:0% +why I'm not giving you a quick answer + + + align:start position:0% +why I'm not giving you a quick answer +because you know in right if we in a + + align:start position:0% +because you know in right if we in a + + + align:start position:0% +because you know in right if we in a +concave model if I if I move the sort of + + align:start position:0% +concave model if I if I move the sort of + + + align:start position:0% +concave model if I if I move the sort of +overall payment up it makes me less + + align:start position:0% +overall payment up it makes me less + + + align:start position:0% +overall payment up it makes me less +risk-averse and so I'm not 100 sure + + align:start position:0% +risk-averse and so I'm not 100 sure + + + align:start position:0% +risk-averse and so I'm not 100 sure +actually does anyone else know the + + align:start position:0% +actually does anyone else know the + + + align:start position:0% +actually does anyone else know the +answer that question + + align:start position:0% +answer that question + + + align:start position:0% +answer that question +that would be a good problem with that + + align:start position:0% +that would be a good problem with that + + + align:start position:0% +that would be a good problem with that +question actually + + align:start position:0% +question actually + + + align:start position:0% +question actually +uh I don't know sorry + + align:start position:0% +uh I don't know sorry + + + align:start position:0% +uh I don't know sorry +um that's a good question yeah + + align:start position:0% + + + + align:start position:0% + +you can't write this directly + + align:start position:0% + + + + align:start position:0% + +like I said you couldn't write this + + align:start position:0% +like I said you couldn't write this + + + align:start position:0% +like I said you couldn't write this +contract because like uh + + align:start position:0% +contract because like uh + + + align:start position:0% +contract because like uh +or is it yes you could sure okay I mean + + align:start position:0% +or is it yes you could sure okay I mean + + + align:start position:0% +or is it yes you could sure okay I mean +well so + + align:start position:0% +well so + + + align:start position:0% +well so +um so that model didn't have any + + align:start position:0% +um so that model didn't have any + + + align:start position:0% +um so that model didn't have any +uncertainty + + align:start position:0% +uncertainty + + + align:start position:0% +uncertainty +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um + + align:start position:0% +um + + + align:start position:0% +um +okay so what is different in this model + + align:start position:0% +okay so what is different in this model + + + align:start position:0% +okay so what is different in this model +versus that model so that model had no + + align:start position:0% +versus that model so that model had no + + + align:start position:0% +versus that model so that model had no +uncertainty is the key thing and the + + align:start position:0% +uncertainty is the key thing and the + + + align:start position:0% +uncertainty is the key thing and the +other thing which is important is that + + align:start position:0% +other thing which is important is that + + + align:start position:0% +other thing which is important is that +the effort Choice here affects kind of + + align:start position:0% +the effort Choice here affects kind of + + + align:start position:0% +the effort Choice here affects kind of +the probability of the is related to the + + align:start position:0% +the probability of the is related to the + + + align:start position:0% +the probability of the is related to the +uncertainty so it is a bit of a + + align:start position:0% +uncertainty so it is a bit of a + + + align:start position:0% +uncertainty so it is a bit of a +different model in that sense + + align:start position:0% +different model in that sense + + + align:start position:0% +different model in that sense +but conceptually + + align:start position:0% +but conceptually + + + align:start position:0% +but conceptually +yes you can think of this as a bit of an + + align:start position:0% +yes you can think of this as a bit of an + + + align:start position:0% +yes you can think of this as a bit of an +as an app like like the the solution + + align:start position:0% +as an app like like the the solution + + + align:start position:0% +as an app like like the the solution +looks like an output attack + + align:start position:0% +looks like an output attack + + + align:start position:0% +looks like an output attack +it's just a percentage of output well I + + align:start position:0% +it's just a percentage of output well I + + + align:start position:0% +it's just a percentage of output well I +mean this is so sorry so in the in the + + align:start position:0% +mean this is so sorry so in the in the + + + align:start position:0% +mean this is so sorry so in the in the +uh continuous case so you can write + + align:start position:0% +uh continuous case so you can write + + + align:start position:0% +uh continuous case so you can write +there obviously are continuous moral + + align:start position:0% +there obviously are continuous moral + + + align:start position:0% +there obviously are continuous moral +hazard models + + align:start position:0% +hazard models + + + align:start position:0% +hazard models +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +in which which are even more difficult + + align:start position:0% +in which which are even more difficult + + + align:start position:0% +in which which are even more difficult +to work with + + align:start position:0% +to work with + + + align:start position:0% +to work with +um but you can solve them and if you + + align:start position:0% +um but you can solve them and if you + + + align:start position:0% +um but you can solve them and if you +take a contract theory class you will + + align:start position:0% +take a contract theory class you will + + + align:start position:0% +take a contract theory class you will +solve them + + align:start position:0% +solve them + + + align:start position:0% +solve them +um and in those models yes I think it + + align:start position:0% +um and in those models yes I think it + + + align:start position:0% +um and in those models yes I think it +will look like some you'll get some + + align:start position:0% +will look like some you'll get some + + + align:start position:0% +will look like some you'll get some +payment as a function of the output and + + align:start position:0% +payment as a function of the output and + + + align:start position:0% +payment as a function of the output and +it'll be it'll mean it'll be usually + + align:start position:0% +it'll be it'll mean it'll be usually + + + align:start position:0% +it'll be it'll mean it'll be usually +look like it will look like an output + + align:start position:0% +look like it will look like an output + + + align:start position:0% +look like it will look like an output +tax whether it will be a linear output + + align:start position:0% +tax whether it will be a linear output + + + align:start position:0% +tax whether it will be a linear output +tax I don't necessarily know that's + + align:start position:0% +tax I don't necessarily know that's + + + align:start position:0% +tax I don't necessarily know that's +always true + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +although although uh + + align:start position:0% +although although uh + + + align:start position:0% +although although uh +banked holmstrom has a well-known paper + + align:start position:0% +banked holmstrom has a well-known paper + + + align:start position:0% +banked holmstrom has a well-known paper +and contract theory that sort of shows + + align:start position:0% +and contract theory that sort of shows + + + align:start position:0% +and contract theory that sort of shows +under this what under what circumstances + + align:start position:0% +under this what under what circumstances + + + align:start position:0% +under this what under what circumstances +linear incentives are optimal so under I + + align:start position:0% +linear incentives are optimal so under I + + + align:start position:0% +linear incentives are optimal so under I +think that and I'm not remembering the + + align:start position:0% +think that and I'm not remembering the + + + align:start position:0% +think that and I'm not remembering the +details of these models off from my head + + align:start position:0% +details of these models off from my head + + + align:start position:0% +details of these models off from my head +but my understanding is the general + + align:start position:0% +but my understanding is the general + + + align:start position:0% +but my understanding is the general +class of in the general answer + + align:start position:0% +class of in the general answer + + + align:start position:0% +class of in the general answer +um it will not necessarily be a linear + + align:start position:0% +um it will not necessarily be a linear + + + align:start position:0% +um it will not necessarily be a linear +incentive function however uh what bank + + align:start position:0% +incentive function however uh what bank + + + align:start position:0% +incentive function however uh what bank +shows is that under some things under + + align:start position:0% +shows is that under some things under + + + align:start position:0% +shows is that under some things under +some various perturbations where you can + + align:start position:0% +some various perturbations where you can + + + align:start position:0% +some various perturbations where you can +sort of do some gaming or other things + + align:start position:0% +sort of do some gaming or other things + + + align:start position:0% +sort of do some gaming or other things +like that linear contracts often do + + align:start position:0% +like that linear contracts often do + + + align:start position:0% +like that linear contracts often do +emerge that's sort of my summary of that + + align:start position:0% +emerge that's sort of my summary of that + + + align:start position:0% +emerge that's sort of my summary of that +and you're nodding is it you know anyone + + align:start position:0% +and you're nodding is it you know anyone + + + align:start position:0% +and you're nodding is it you know anyone +else want to comment on that okay + + align:start position:0% +else want to comment on that okay + + + align:start position:0% +else want to comment on that okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +other comments + + align:start position:0% +other comments + + + align:start position:0% +other comments +so + + align:start position:0% +so + + + align:start position:0% +so +um I think I don't know if we still have + + align:start position:0% +um I think I don't know if we still have + + + align:start position:0% +um I think I don't know if we still have +an example in the problem set we should + + align:start position:0% +an example in the problem set we should + + + align:start position:0% +an example in the problem set we should +probably we should make sure we don't + + align:start position:0% +probably we should make sure we don't + + + align:start position:0% +probably we should make sure we don't +that's gone + + align:start position:0% +that's gone + + + align:start position:0% +that's gone +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +if you would like to work through an + + align:start position:0% +if you would like to work through an + + + align:start position:0% +if you would like to work through an +example of this I do think we have a + + align:start position:0% +example of this I do think we have a + + + align:start position:0% +example of this I do think we have a +previous problem set that we have put + + align:start position:0% +previous problem set that we have put + + + align:start position:0% +previous problem set that we have put +together on this problem that has an + + align:start position:0% +together on this problem that has an + + + align:start position:0% +together on this problem that has an +example of uh how to work through these + + align:start position:0% +example of uh how to work through these + + + align:start position:0% +example of uh how to work through these +moral hazard models + + align:start position:0% +moral hazard models + + + align:start position:0% +moral hazard models +um + + align:start position:0% +um + + + align:start position:0% +um +yes David just we should hear the the + + align:start position:0% +yes David just we should hear the the + + + align:start position:0% +yes David just we should hear the the +agents participation constraints yeah + + align:start position:0% +agents participation constraints yeah + + + align:start position:0% +agents participation constraints yeah +there's no service + + align:start position:0% +there's no service + + + align:start position:0% +there's no service +right yep yep they're still going to + + align:start position:0% +right yep yep they're still going to + + + align:start position:0% +right yep yep they're still going to +sort of slide at that they're still + + align:start position:0% +sort of slide at that they're still + + + align:start position:0% +sort of slide at that they're still +gonna it's still gonna be the case that + + align:start position:0% +gonna it's still gonna be the case that + + + align:start position:0% +gonna it's still gonna be the case that +the IR constraint is still gonna buy + + align:start position:0% +the IR constraint is still gonna buy + + + align:start position:0% +the IR constraint is still gonna buy +there's gonna be no Surplus here + + align:start position:0% +there's gonna be no Surplus here + + + align:start position:0% +there's gonna be no Surplus here +yeah + + align:start position:0% + + + + align:start position:0% + +anyways + + align:start position:0% + + + + align:start position:0% + +um do you see this kind of contracts + + align:start position:0% +um do you see this kind of contracts + + + align:start position:0% +um do you see this kind of contracts +like + + align:start position:0% + + + + align:start position:0% + +I will see both + + align:start position:0% +I will see both + + + align:start position:0% +I will see both +but yes with Uber you see a + + align:start position:0% +but yes with Uber you see a + + + align:start position:0% +but yes with Uber you see a +sharecropping contract + + align:start position:0% +sharecropping contract + + + align:start position:0% +sharecropping contract +I mean they don't call it share cropping + + align:start position:0% +I mean they don't call it share cropping + + + align:start position:0% +I mean they don't call it share cropping +but like + + align:start position:0% +but like + + + align:start position:0% +but like +you see a share contract right where + + align:start position:0% +you see a share contract right where + + + align:start position:0% +you see a share contract right where +where uh where it looks you know where + + align:start position:0% +where uh where it looks you know where + + + align:start position:0% +where uh where it looks you know where +Uber takes 30 of the or whatever the + + align:start position:0% +Uber takes 30 of the or whatever the + + + align:start position:0% +Uber takes 30 of the or whatever the +percentage is of the of the thing and + + align:start position:0% +percentage is of the of the thing and + + + align:start position:0% +percentage is of the of the thing and +they get to fix some share + + align:start position:0% + + + + align:start position:0% + +well I say sorry one other thing but in + + align:start position:0% +well I say sorry one other thing but in + + + align:start position:0% +well I say sorry one other thing but in +in the Uber contract it's observable and + + align:start position:0% +in the Uber contract it's observable and + + + align:start position:0% +in the Uber contract it's observable and +I think it may depend I think what I + + align:start position:0% +I think it may depend I think what I + + + align:start position:0% +I think it may depend I think what I +don't know the full + + align:start position:0% +don't know the full + + + align:start position:0% +don't know the full +economics of the taxi cab literature but + + align:start position:0% +economics of the taxi cab literature but + + + align:start position:0% +economics of the taxi cab literature but +I think it probably depends on to what + + align:start position:0% +I think it probably depends on to what + + + align:start position:0% +I think it probably depends on to what +degree you know certainly what degree + + align:start position:0% +degree you know certainly what degree + + + align:start position:0% +degree you know certainly what degree +effort is observable + + align:start position:0% +effort is observable + + + align:start position:0% +effort is observable +um you know uh would would affect kind + + align:start position:0% +um you know uh would would affect kind + + + align:start position:0% +um you know uh would would affect kind +of what these contracts looks like and + + align:start position:0% +of what these contracts looks like and + + + align:start position:0% +of what these contracts looks like and +you know Davey is nodding since Davey is + + align:start position:0% +you know Davey is nodding since Davey is + + + align:start position:0% +you know Davey is nodding since Davey is +sort of like actively sort of looking at + + align:start position:0% +sort of like actively sort of looking at + + + align:start position:0% +sort of like actively sort of looking at +exactly these issues of observability + + align:start position:0% +exactly these issues of observability + + + align:start position:0% +exactly these issues of observability +and sort of the endogenous contract + + align:start position:0% +and sort of the endogenous contract + + + align:start position:0% +and sort of the endogenous contract +choice in uh you know + + align:start position:0% +choice in uh you know + + + align:start position:0% +choice in uh you know +in uh + + align:start position:0% +in uh + + + align:start position:0% +in uh +in cultivar at the moment then we just + + align:start position:0% +in cultivar at the moment then we just + + + align:start position:0% +in cultivar at the moment then we just +lost my computer sorry go ahead while I + + align:start position:0% +lost my computer sorry go ahead while I + + + align:start position:0% +lost my computer sorry go ahead while I +get my computer back + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +exactly a like the first place kind of + + align:start position:0% +exactly a like the first place kind of + + + align:start position:0% +exactly a like the first place kind of +call Tracker so you would see so for + + align:start position:0% +call Tracker so you would see so for + + + align:start position:0% +call Tracker so you would see so for +example if you did if you had no + + align:start position:0% +example if you did if you had no + + + align:start position:0% +example if you did if you had no +observability of output then you would + + align:start position:0% +observability of output then you would + + + align:start position:0% +observability of output then you would +see + + align:start position:0% +see + + + align:start position:0% +see +um you would see a rental contract right + + align:start position:0% +um you would see a rental contract right + + + align:start position:0% +um you would see a rental contract right +so this contract requires that the + + align:start position:0% +so this contract requires that the + + + align:start position:0% +so this contract requires that the +principal to be able to condition the + + align:start position:0% +principal to be able to condition the + + + align:start position:0% +principal to be able to condition the +payment on the output + + align:start position:0% +payment on the output + + + align:start position:0% +payment on the output +for example + + align:start position:0% + + + + align:start position:0% + +or you also might think the taxi cab + + align:start position:0% +or you also might think the taxi cab + + + align:start position:0% +or you also might think the taxi cab +drivers may not be that risk-averse + + align:start position:0% +drivers may not be that risk-averse + + + align:start position:0% +drivers may not be that risk-averse +right so if the uncertainty is kind of + + align:start position:0% +right so if the uncertainty is kind of + + + align:start position:0% +right so if the uncertainty is kind of +day by day right that this is over a + + align:start position:0% +day by day right that this is over a + + + align:start position:0% +day by day right that this is over a +whole season right it's kind of one + + align:start position:0% +whole season right it's kind of one + + + align:start position:0% +whole season right it's kind of one +giant realization you really risk averse + + align:start position:0% +giant realization you really risk averse + + + align:start position:0% +giant realization you really risk averse +about that you know some days it rains + + align:start position:0% +about that you know some days it rains + + + align:start position:0% +about that you know some days it rains +and it doesn't rain like you know I may + + align:start position:0% +and it doesn't rain like you know I may + + + align:start position:0% +and it doesn't rain like you know I may +not be at risk-averse about that I might + + align:start position:0% +not be at risk-averse about that I might + + + align:start position:0% +not be at risk-averse about that I might +be able to smooth kind of over days so + + align:start position:0% +be able to smooth kind of over days so + + + align:start position:0% +be able to smooth kind of over days so +that's another reason might be different + + align:start position:0% + + + + align:start position:0% + +other questions comments yeah sure + + align:start position:0% + + + + align:start position:0% + +you're gonna have to speak up I can't + + align:start position:0% +you're gonna have to speak up I can't + + + align:start position:0% +you're gonna have to speak up I can't +really yeah + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah yeah sorry so when I say first best + + align:start position:0% +yeah yeah sorry so when I say first best + + + align:start position:0% +yeah yeah sorry so when I say first best +I meant first in terms of output but yes + + align:start position:0% +I meant first in terms of output but yes + + + align:start position:0% +I meant first in terms of output but yes +the the the optimal con the socially + + align:start position:0% +the the the optimal con the socially + + + align:start position:0% +the the the optimal con the socially +optimal contract includes sharing risk + + align:start position:0% +optimal contract includes sharing risk + + + align:start position:0% +optimal contract includes sharing risk +but it is not it does not get the first + + align:start position:0% +but it is not it does not get the first + + + align:start position:0% +but it is not it does not get the first +best level of output + + align:start position:0% +best level of output + + + align:start position:0% +best level of output +here tomorrow + + align:start position:0% +here tomorrow + + + align:start position:0% +here tomorrow +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +does it what sorry does it have a bite + + align:start position:0% +does it what sorry does it have a bite + + + align:start position:0% +does it what sorry does it have a bite +like because the fact that they can't + + align:start position:0% +like because the fact that they can't + + + align:start position:0% +like because the fact that they can't +observed + + align:start position:0% + + + + align:start position:0% + +no no so it no no so what would be that + + align:start position:0% +no no so it no no so what would be that + + + align:start position:0% +no no so it no no so what would be that +if we could observe effort what would be + + align:start position:0% +if we could observe effort what would be + + + align:start position:0% +if we could observe effort what would be +the first best contract first best + + align:start position:0% +the first best contract first best + + + align:start position:0% +the first best contract first best +contract would be we read a contract + + align:start position:0% +contract would be we read a contract + + + align:start position:0% +contract would be we read a contract +based on effort and we would observe + + align:start position:0% +based on effort and we would observe + + + align:start position:0% +based on effort and we would observe +your and we'd provide you full insurance + + align:start position:0% + + + + align:start position:0% + +so the first best contract would have + + align:start position:0% +so the first best contract would have + + + align:start position:0% +so the first best contract would have +like if we if we could Implement if we + + align:start position:0% +like if we if we could Implement if we + + + align:start position:0% +like if we if we could Implement if we +could contract an effort we would say + + align:start position:0% +could contract an effort we would say + + + align:start position:0% +could contract an effort we would say +you put in you know E equals Big H over + + align:start position:0% +you put in you know E equals Big H over + + + align:start position:0% +you put in you know E equals Big H over +C and I'll pay you H equals L equals the + + align:start position:0% +C and I'll pay you H equals L equals the + + + align:start position:0% +C and I'll pay you H equals L equals the +expected value equals you know W lower + + align:start position:0% +expected value equals you know W lower + + + align:start position:0% +expected value equals you know W lower +bar basically + + align:start position:0% +bar basically + + + align:start position:0% +bar basically +yeah that would be the first best + + align:start position:0% +yeah that would be the first best + + + align:start position:0% +yeah that would be the first best +contract + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so that's that's the risk + + align:start position:0% +all right so that's that's the risk + + + align:start position:0% +all right so that's that's the risk +conversion version + + align:start position:0% +conversion version + + + align:start position:0% +conversion version +so what about the limited liability + + align:start position:0% +so what about the limited liability + + + align:start position:0% +so what about the limited liability +version + + align:start position:0% +version + + + align:start position:0% +version +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's go back now to + + align:start position:0% +so let's go back now to + + + align:start position:0% +so let's go back now to +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% + + + + align:start position:0% + +um risk neutrality for a second + + align:start position:0% +um risk neutrality for a second + + + align:start position:0% +um risk neutrality for a second +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but let's impose limited liability + + align:start position:0% +but let's impose limited liability + + + align:start position:0% +but let's impose limited liability +so let's assume uh that we can't impose + + align:start position:0% +so let's assume uh that we can't impose + + + align:start position:0% +so let's assume uh that we can't impose +L Less Than Zero + + align:start position:0% +L Less Than Zero + + + align:start position:0% +L Less Than Zero +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now what happens to the optimal + + align:start position:0% +so now what happens to the optimal + + + align:start position:0% +so now what happens to the optimal +contract well now the landlord has lost + + align:start position:0% +contract well now the landlord has lost + + + align:start position:0% +contract well now the landlord has lost +a degree of freedom + + align:start position:0% +a degree of freedom + + + align:start position:0% +a degree of freedom +right the landlord before could choose + + align:start position:0% +right the landlord before could choose + + + align:start position:0% +right the landlord before could choose +little H and little L now they can now + + align:start position:0% +little H and little L now they can now + + + align:start position:0% +little H and little L now they can now +they have this problem that little H + + align:start position:0% +they have this problem that little H + + + align:start position:0% +they have this problem that little H +can't uh little L can't go below zero + + align:start position:0% +can't uh little L can't go below zero + + + align:start position:0% +can't uh little L can't go below zero +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% +um + + + align:start position:0% +um +so in the first best kind of contract we + + align:start position:0% +so in the first best kind of contract we + + + align:start position:0% +so in the first best kind of contract we +had this let's what happens suppose + + align:start position:0% +had this let's what happens suppose + + + align:start position:0% +had this let's what happens suppose +we're in the world where this thing is + + align:start position:0% +we're in the world where this thing is + + + align:start position:0% +we're in the world where this thing is +if this thing is positive then like + + align:start position:0% +if this thing is positive then like + + + align:start position:0% +if this thing is positive then like +great we have no problem + + align:start position:0% +great we have no problem + + + align:start position:0% +great we have no problem +right + + align:start position:0% +right + + + align:start position:0% +right +um but if this thing is negative + + align:start position:0% +um but if this thing is negative + + + align:start position:0% +um but if this thing is negative +right then we can't write that contract + + align:start position:0% +right then we can't write that contract + + + align:start position:0% +right then we can't write that contract +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +right because the in the low State they + + align:start position:0% +right because the in the low State they + + + align:start position:0% +right because the in the low State they +just won't pay + + align:start position:0% +just won't pay + + + align:start position:0% +just won't pay +another way of saying is they won't pay + + align:start position:0% +another way of saying is they won't pay + + + align:start position:0% +another way of saying is they won't pay +the rent right + + align:start position:0% +the rent right + + + align:start position:0% +the rent right +so what do we do where's limbo 2. okay + + align:start position:0% +so what do we do where's limbo 2. okay + + + align:start position:0% +so what do we do where's limbo 2. okay +so instead + + align:start position:0% +so instead + + + align:start position:0% +so instead +um so little L has to be equal to zero + + align:start position:0% +um so little L has to be equal to zero + + + align:start position:0% +um so little L has to be equal to zero +right because it can't be it's bounded + + align:start position:0% +right because it can't be it's bounded + + + align:start position:0% +right because it can't be it's bounded +by a limited liability + + align:start position:0% +by a limited liability + + + align:start position:0% +by a limited liability +so what happens to H + + align:start position:0% +so what happens to H + + + align:start position:0% +so what happens to H +so now what we know the optimal choice + + align:start position:0% +so now what we know the optimal choice + + + align:start position:0% +so now what we know the optimal choice +of effort so the landlord is going to + + align:start position:0% +of effort so the landlord is going to + + + align:start position:0% +of effort so the landlord is going to +say well I'm just going to shoot all all + + align:start position:0% +say well I'm just going to shoot all all + + + align:start position:0% +say well I'm just going to shoot all all +I'm ever going to get if the landlord is + + align:start position:0% +I'm ever going to get if the landlord is + + + align:start position:0% +I'm ever going to get if the landlord is +a payment in the high state I'm never + + align:start position:0% +a payment in the high state I'm never + + + align:start position:0% +a payment in the high state I'm never +going to get any money in the low state + + align:start position:0% +going to get any money in the low state + + + align:start position:0% +going to get any money in the low state +okay so my but I know still the Asian is + + align:start position:0% +okay so my but I know still the Asian is + + + align:start position:0% +okay so my but I know still the Asian is +only going to be incentivized based on + + align:start position:0% +only going to be incentivized based on + + + align:start position:0% +only going to be incentivized based on +the difference between between the + + align:start position:0% +the difference between between the + + + align:start position:0% +the difference between between the +little H and little l + + align:start position:0% +little H and little l + + + align:start position:0% +little H and little l +so now I'm I'm stuck solving this + + align:start position:0% +so now I'm I'm stuck solving this + + + align:start position:0% +so now I'm I'm stuck solving this +contract + + align:start position:0% +contract + + + align:start position:0% +contract +which is you know I'm going to maximize + + align:start position:0% +which is you know I'm going to maximize + + + align:start position:0% +which is you know I'm going to maximize +my return which is the probability of + + align:start position:0% +my return which is the probability of + + + align:start position:0% +my return which is the probability of +the high State times what I get paid in + + align:start position:0% +the high State times what I get paid in + + + align:start position:0% +the high State times what I get paid in +the high State and the low state is kind + + align:start position:0% +the high State and the low state is kind + + + align:start position:0% +the high State and the low state is kind +of a wash right I don't get anything on + + align:start position:0% +of a wash right I don't get anything on + + + align:start position:0% +of a wash right I don't get anything on +those state + + align:start position:0% +those state + + + align:start position:0% +those state +so that's this problem over here + + align:start position:0% +so that's this problem over here + + + align:start position:0% +so that's this problem over here +um this is H over C right we know that + + align:start position:0% +um this is H over C right we know that + + + align:start position:0% +um this is H over C right we know that +the we know that the the tenant is going + + align:start position:0% +the we know that the the tenant is going + + + align:start position:0% +the we know that the the tenant is going +to choose H minus L over C but there's L + + align:start position:0% +to choose H minus L over C but there's L + + + align:start position:0% +to choose H minus L over C but there's L +is equal to zero so the 10 instruction + + align:start position:0% +is equal to zero so the 10 instruction + + + align:start position:0% +is equal to zero so the 10 instruction +choose a little H over c times uh Big H + + align:start position:0% +choose a little H over c times uh Big H + + + align:start position:0% +choose a little H over c times uh Big H +over C and so the um + + align:start position:0% +over C and so the um + + + align:start position:0% +over C and so the um +uh the optimal Choice here for the + + align:start position:0% +uh the optimal Choice here for the + + + align:start position:0% +uh the optimal Choice here for the +effort is just for for the landlord is + + align:start position:0% +effort is just for for the landlord is + + + align:start position:0% +effort is just for for the landlord is +to choose + + align:start position:0% +to choose + + + align:start position:0% +to choose +um uh little H equal to Big H over two + + align:start position:0% +um uh little H equal to Big H over two + + + align:start position:0% +um uh little H equal to Big H over two +and + + align:start position:0% +and + + + align:start position:0% +and +um and therefore the optimal amount of + + align:start position:0% +um and therefore the optimal amount of + + + align:start position:0% +um and therefore the optimal amount of +effort is going to be big H over 2C + + align:start position:0% +effort is going to be big H over 2C + + + align:start position:0% +effort is going to be big H over 2C +okay everyone see that + + align:start position:0% +okay everyone see that + + + align:start position:0% +okay everyone see that +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +okay so again + + align:start position:0% +okay so again + + + align:start position:0% +okay so again +we have less than the first best amount + + align:start position:0% +we have less than the first best amount + + + align:start position:0% +we have less than the first best amount +of effort right first best amount of + + align:start position:0% +of effort right first best amount of + + + align:start position:0% +of effort right first best amount of +ever was Big H over C now we only have + + align:start position:0% +ever was Big H over C now we only have + + + align:start position:0% +ever was Big H over C now we only have +big H over 2C so we have half of the off + + align:start position:0% +big H over 2C so we have half of the off + + + align:start position:0% +big H over 2C so we have half of the off +the amount of effort + + align:start position:0% +the amount of effort + + + align:start position:0% +the amount of effort +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +so that so so we're also in a world here + + align:start position:0% +so that so so we're also in a world here + + + align:start position:0% +so that so so we're also in a world here +where uh sorry and so that's the point + + align:start position:0% +where uh sorry and so that's the point + + + align:start position:0% +where uh sorry and so that's the point +number one and point number two this is + + align:start position:0% +number one and point number two this is + + + align:start position:0% +number one and point number two this is +a sharecropping contract right because + + align:start position:0% +a sharecropping contract right because + + + align:start position:0% +a sharecropping contract right because +uh the in the high State you know you + + align:start position:0% +uh the in the high State you know you + + + align:start position:0% +uh the in the high State you know you +keep half I get the layer gets half ten + + align:start position:0% +keep half I get the layer gets half ten + + + align:start position:0% +keep half I get the layer gets half ten +it gets half and the low State uh nobody + + align:start position:0% +it gets half and the low State uh nobody + + + align:start position:0% +it gets half and the low State uh nobody +gets anything so this looks like a + + align:start position:0% +gets anything so this looks like a + + + align:start position:0% +gets anything so this looks like a +perfect share con in this simple example + + align:start position:0% +perfect share con in this simple example + + + align:start position:0% +perfect share con in this simple example +it's a share contract with a share equal + + align:start position:0% +it's a share contract with a share equal + + + align:start position:0% +it's a share contract with a share equal +to a half + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so now what happens if we have an IR + + align:start position:0% +so now what happens if we have an IR + + + align:start position:0% +so now what happens if we have an IR +constraint here well + + align:start position:0% +constraint here well + + + align:start position:0% +constraint here well +so what's the farmer's utility under + + align:start position:0% +so what's the farmer's utility under + + + align:start position:0% +so what's the farmer's utility under +this contract well we can solve the + + align:start position:0% +this contract well we can solve the + + + align:start position:0% +this contract well we can solve the +farmer's utility under the contract + + align:start position:0% +farmer's utility under the contract + + + align:start position:0% +farmer's utility under the contract +Farmers utility of the contract is + + align:start position:0% +Farmers utility of the contract is + + + align:start position:0% +Farmers utility of the contract is +um their choice of f we can just solve + + align:start position:0% +um their choice of f we can just solve + + + align:start position:0% +um their choice of f we can just solve +their choice of effort is going to be + + align:start position:0% +their choice of effort is going to be + + + align:start position:0% +their choice of effort is going to be +little H over c times uh + + align:start position:0% +little H over c times uh + + + align:start position:0% +little H over c times uh +and they're going to get to keep uh + + align:start position:0% +and they're going to get to keep uh + + + align:start position:0% +and they're going to get to keep uh +payment H in this state plus they have a + + align:start position:0% +payment H in this state plus they have a + + + align:start position:0% +payment H in this state plus they have a +cost of effort so if you solve this out + + align:start position:0% +cost of effort so if you solve this out + + + align:start position:0% +cost of effort so if you solve this out +it's 1 8 uh Big H square or over over C + + align:start position:0% +it's 1 8 uh Big H square or over over C + + + align:start position:0% +it's 1 8 uh Big H square or over over C +whatever it's all that out + + align:start position:0% +whatever it's all that out + + + align:start position:0% +whatever it's all that out +the the key point though is the + + align:start position:0% +the the key point though is the + + + align:start position:0% +the the key point though is the +following which is + + align:start position:0% + + + + align:start position:0% + +that's the landlord's utility that's + + align:start position:0% +that's the landlord's utility that's + + + align:start position:0% +that's the landlord's utility that's +that's sorry that's the tenants utility + + align:start position:0% +that's sorry that's the tenants utility + + + align:start position:0% +that's sorry that's the tenants utility +under this + + align:start position:0% +under this + + + align:start position:0% +under this +if the tenant + + align:start position:0% +if the tenant + + + align:start position:0% +if the tenant +is getting at least W lower bar + + align:start position:0% +is getting at least W lower bar + + + align:start position:0% +is getting at least W lower bar +than under this is with utility great + + align:start position:0% +than under this is with utility great + + + align:start position:0% +than under this is with utility great +we're done + + align:start position:0% +we're done + + + align:start position:0% +we're done +fine okay + + align:start position:0% +fine okay + + + align:start position:0% +fine okay +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% + + + + align:start position:0% + +in this case the tenant also is getting + + align:start position:0% +in this case the tenant also is getting + + + align:start position:0% +in this case the tenant also is getting +rents if this thing is exactly equal to + + align:start position:0% +rents if this thing is exactly equal to + + + align:start position:0% +rents if this thing is exactly equal to +the W lower bar fine + + align:start position:0% +the W lower bar fine + + + align:start position:0% +the W lower bar fine +but that's kind of like a knife edge + + align:start position:0% +but that's kind of like a knife edge + + + align:start position:0% +but that's kind of like a knife edge +case like generically like there there + + align:start position:0% +case like generically like there there + + + align:start position:0% +case like generically like there there +you may be a parameter values where you + + align:start position:0% +you may be a parameter values where you + + + align:start position:0% +you may be a parameter values where you +have to pay the tenant above her outside + + align:start position:0% +have to pay the tenant above her outside + + + align:start position:0% +have to pay the tenant above her outside +option in order to get her to work the + + align:start position:0% +option in order to get her to work the + + + align:start position:0% +option in order to get her to work the +optimal amount + + align:start position:0% +optimal amount + + + align:start position:0% +optimal amount +right and what's different here the + + align:start position:0% +right and what's different here the + + + align:start position:0% +right and what's different here the +difference is like in the other thing + + align:start position:0% +difference is like in the other thing + + + align:start position:0% +difference is like in the other thing +you could just sort of like Slide the + + align:start position:0% +you could just sort of like Slide the + + + align:start position:0% +you could just sort of like Slide the +whole contract up and down kind of + + align:start position:0% +whole contract up and down kind of + + + align:start position:0% +whole contract up and down kind of +arbitrarily so the expected value was + + align:start position:0% +arbitrarily so the expected value was + + + align:start position:0% +arbitrarily so the expected value was +equal to lower bar but now you can't + + align:start position:0% +equal to lower bar but now you can't + + + align:start position:0% +equal to lower bar but now you can't +because you sort of have this limited + + align:start position:0% +because you sort of have this limited + + + align:start position:0% +because you sort of have this limited +liability constraint From Below + + align:start position:0% +liability constraint From Below + + + align:start position:0% +liability constraint From Below +right so she may get rents here + + align:start position:0% +right so she may get rents here + + + align:start position:0% +right so she may get rents here +um + + align:start position:0% +um + + + align:start position:0% +um +and also the contract doesn't depend on + + align:start position:0% +and also the contract doesn't depend on + + + align:start position:0% +and also the contract doesn't depend on +W lower bar anymore in this in this + + align:start position:0% +W lower bar anymore in this in this + + + align:start position:0% +W lower bar anymore in this in this +state in this this piece of it + + align:start position:0% +state in this this piece of it + + + align:start position:0% +state in this this piece of it +right as long as it kind of we're as + + align:start position:0% +right as long as it kind of we're as + + + align:start position:0% +right as long as it kind of we're as +long as thing is well above all right + + align:start position:0% +long as thing is well above all right + + + align:start position:0% +long as thing is well above all right +bar up and down like the counter doesn't + + align:start position:0% +bar up and down like the counter doesn't + + + align:start position:0% +bar up and down like the counter doesn't +change whereas in the the more Hazard + + align:start position:0% +change whereas in the the more Hazard + + + align:start position:0% +change whereas in the the more Hazard +one like it was always kind of moving + + align:start position:0% +one like it was always kind of moving + + + align:start position:0% +one like it was always kind of moving +around so that she got W lower bar and + + align:start position:0% +around so that she got W lower bar and + + + align:start position:0% +around so that she got W lower bar and +expectation + + align:start position:0% +expectation + + + align:start position:0% +expectation +um + + align:start position:0% + + + + align:start position:0% + +now on the other hand if this thing is + + align:start position:0% +now on the other hand if this thing is + + + align:start position:0% +now on the other hand if this thing is +less than the W lower bar + + align:start position:0% +less than the W lower bar + + + align:start position:0% +less than the W lower bar +now the the tenant has to actually the + + align:start position:0% +now the the tenant has to actually the + + + align:start position:0% +now the the tenant has to actually the +landlord has to increase kind of the the + + align:start position:0% +landlord has to increase kind of the the + + + align:start position:0% +landlord has to increase kind of the the +the share that the tenant gets to keep + + align:start position:0% +the share that the tenant gets to keep + + + align:start position:0% +the share that the tenant gets to keep +in the high state so that she gets at + + align:start position:0% +in the high state so that she gets at + + + align:start position:0% +in the high state so that she gets at +least her outside her outside option + + align:start position:0% +least her outside her outside option + + + align:start position:0% +least her outside her outside option +expectation + + align:start position:0% +expectation + + + align:start position:0% +expectation +okay so what will happen in that case + + align:start position:0% +okay so what will happen in that case + + + align:start position:0% +okay so what will happen in that case +we'll just pick H such that sort of the + + align:start position:0% +we'll just pick H such that sort of the + + + align:start position:0% +we'll just pick H such that sort of the +expectation in the high state is just + + align:start position:0% +expectation in the high state is just + + + align:start position:0% +expectation in the high state is just +exactly equal to the sorry the expected + + align:start position:0% +exactly equal to the sorry the expected + + + align:start position:0% +exactly equal to the sorry the expected +value of the contract is exactly equal + + align:start position:0% +value of the contract is exactly equal + + + align:start position:0% +value of the contract is exactly equal +to the outside wage + + align:start position:0% + + + + align:start position:0% + +um and note that in this case increasing + + align:start position:0% +um and note that in this case increasing + + + align:start position:0% +um and note that in this case increasing +W lower bar actually increases effort + + align:start position:0% +W lower bar actually increases effort + + + align:start position:0% +W lower bar actually increases effort +because the the contract becomes you + + align:start position:0% +because the the contract becomes you + + + align:start position:0% +because the the contract becomes you +know as her outside option gets better + + align:start position:0% +know as her outside option gets better + + + align:start position:0% +know as her outside option gets better +the contract becomes more attractive + + align:start position:0% +the contract becomes more attractive + + + align:start position:0% +the contract becomes more attractive +okay + + align:start position:0% + + + + align:start position:0% + +clear + + align:start position:0% + + + + align:start position:0% + +Okay so + + align:start position:0% +Okay so + + + align:start position:0% +Okay so +both kind of key Point here is both + + align:start position:0% +both kind of key Point here is both + + + align:start position:0% +both kind of key Point here is both +moral hazard kind of insurance + + align:start position:0% +moral hazard kind of insurance + + + align:start position:0% +moral hazard kind of insurance +rationales + + align:start position:0% +rationales + + + align:start position:0% +rationales +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +limited liability rationales both + + align:start position:0% +limited liability rationales both + + + align:start position:0% +limited liability rationales both +generate what look like sharecropping + + align:start position:0% +generate what look like sharecropping + + + align:start position:0% +generate what look like sharecropping +contracts + + align:start position:0% +contracts + + + align:start position:0% +contracts +but they're a very different kind of + + align:start position:0% +but they're a very different kind of + + + align:start position:0% +but they're a very different kind of +like stories for what's going on and + + align:start position:0% +like stories for what's going on and + + + align:start position:0% +like stories for what's going on and +they have different implications + + align:start position:0% +they have different implications + + + align:start position:0% +they have different implications +okay and in particular + + align:start position:0% +okay and in particular + + + align:start position:0% +okay and in particular +so so both of these models generate the + + align:start position:0% +so so both of these models generate the + + + align:start position:0% +so so both of these models generate the +generate the fact that sort of + + align:start position:0% +generate the fact that sort of + + + align:start position:0% +generate the fact that sort of +sharecropping emerges effort is less + + align:start position:0% +sharecropping emerges effort is less + + + align:start position:0% +sharecropping emerges effort is less +than the first best + + align:start position:0% +than the first best + + + align:start position:0% +than the first best +right + + align:start position:0% +right + + + align:start position:0% +right +um but one thing that's really in + + align:start position:0% +um but one thing that's really in + + + align:start position:0% +um but one thing that's really in +particular kind of import interesting + + align:start position:0% +particular kind of import interesting + + + align:start position:0% +particular kind of import interesting +here is they differ in their + + align:start position:0% +here is they differ in their + + + align:start position:0% +here is they differ in their +implications for land reform + + align:start position:0% +implications for land reform + + + align:start position:0% +implications for land reform +so what do I so so as an aside I feel + + align:start position:0% +so what do I so so as an aside I feel + + + align:start position:0% +so what do I so so as an aside I feel +and I'll talk about this in like the + + align:start position:0% +and I'll talk about this in like the + + + align:start position:0% +and I'll talk about this in like the +next slide I feel like land reform + + align:start position:0% +next slide I feel like land reform + + + align:start position:0% +next slide I feel like land reform +is like a in my opinion like hugely kind + + align:start position:0% +is like a in my opinion like hugely kind + + + align:start position:0% +is like a in my opinion like hugely kind +of understudied + + align:start position:0% +of understudied + + + align:start position:0% +of understudied +topic it was like I feel like you know + + align:start position:0% +topic it was like I feel like you know + + + align:start position:0% +topic it was like I feel like you know +one of the Salient issues of the 20th + + align:start position:0% +one of the Salient issues of the 20th + + + align:start position:0% +one of the Salient issues of the 20th +century was sort of like should we do + + align:start position:0% +century was sort of like should we do + + + align:start position:0% +century was sort of like should we do +land reform in some sense that you can + + align:start position:0% +land reform in some sense that you can + + + align:start position:0% +land reform in some sense that you can +think of like the whole kind of like you + + align:start position:0% +think of like the whole kind of like you + + + align:start position:0% +think of like the whole kind of like you +know you could think of the whole kind + + align:start position:0% +know you could think of the whole kind + + + align:start position:0% +know you could think of the whole kind +of communist revolutions were really + + align:start position:0% +of communist revolutions were really + + + align:start position:0% +of communist revolutions were really +about this question of like should we do + + align:start position:0% +about this question of like should we do + + + align:start position:0% +about this question of like should we do +land reform or not many other things too + + align:start position:0% +land reform or not many other things too + + + align:start position:0% +land reform or not many other things too +but like should we sort of take away + + align:start position:0% +but like should we sort of take away + + + align:start position:0% +but like should we sort of take away +land from the landlords and give it to + + align:start position:0% +land from the landlords and give it to + + + align:start position:0% +land from the landlords and give it to +the farmers it was like a huge question + + align:start position:0% +the farmers it was like a huge question + + + align:start position:0% +the farmers it was like a huge question +kind of in the world in the 20th century + + align:start position:0% +kind of in the world in the 20th century + + + align:start position:0% +kind of in the world in the 20th century +and I feel like we don't have great I + + align:start position:0% +and I feel like we don't have great I + + + align:start position:0% +and I feel like we don't have great I +think the level of evidence we have is + + align:start position:0% +think the level of evidence we have is + + + align:start position:0% +think the level of evidence we have is +not commensurate with kind of how the + + align:start position:0% +not commensurate with kind of how the + + + align:start position:0% +not commensurate with kind of how the +importance of the question uh in in in + + align:start position:0% +importance of the question uh in in in + + + align:start position:0% +importance of the question uh in in in +my view + + align:start position:0% +my view + + + align:start position:0% +my view +um + + align:start position:0% +um + + + align:start position:0% +um +but any case these models differ a lot + + align:start position:0% +but any case these models differ a lot + + + align:start position:0% +but any case these models differ a lot +in terms of their the implications of + + align:start position:0% +in terms of their the implications of + + + align:start position:0% +in terms of their the implications of +land reform + + align:start position:0% +land reform + + + align:start position:0% +land reform +so what do I mean by that so + + align:start position:0% +so what do I mean by that so + + + align:start position:0% +so what do I mean by that so +in risk aversion + + align:start position:0% +in risk aversion + + + align:start position:0% +in risk aversion +in the risk aversion model + + align:start position:0% +in the risk aversion model + + + align:start position:0% +in the risk aversion model +we drew a land reform we say okay now + + align:start position:0% +we drew a land reform we say okay now + + + align:start position:0% +we drew a land reform we say okay now +tenant you're the owner of this land + + align:start position:0% +tenant you're the owner of this land + + + align:start position:0% +tenant you're the owner of this land +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% +um + + + align:start position:0% +um +that does make you wealthier and makes + + align:start position:0% +that does make you wealthier and makes + + + align:start position:0% +that does make you wealthier and makes +you maybe less risk-averse but other + + align:start position:0% +you maybe less risk-averse but other + + + align:start position:0% +you maybe less risk-averse but other +hand your risk is all kind of tied up in + + align:start position:0% +hand your risk is all kind of tied up in + + + align:start position:0% +hand your risk is all kind of tied up in +your your wealth all tied up in the + + align:start position:0% +your your wealth all tied up in the + + + align:start position:0% +your your wealth all tied up in the +Lance it's not easy that's not clear you + + align:start position:0% +Lance it's not easy that's not clear you + + + align:start position:0% +Lance it's not easy that's not clear you +can sort of get consumption smoothing + + align:start position:0% +can sort of get consumption smoothing + + + align:start position:0% +can sort of get consumption smoothing +benefits from from that maybe you can + + align:start position:0% +benefits from from that maybe you can + + + align:start position:0% +benefits from from that maybe you can +borrow maybe you can't + + align:start position:0% +borrow maybe you can't + + + align:start position:0% +borrow maybe you can't +um but you're still kind of + + align:start position:0% +um but you're still kind of + + + align:start position:0% +um but you're still kind of +would want some insurance + + align:start position:0% +would want some insurance + + + align:start position:0% +would want some insurance +right and so you might as a tenant + + align:start position:0% +right and so you might as a tenant + + + align:start position:0% +right and so you might as a tenant +say well I don't want to be in this + + align:start position:0% +say well I don't want to be in this + + + align:start position:0% +say well I don't want to be in this +position of uh you know + + align:start position:0% +position of uh you know + + + align:start position:0% +position of uh you know +uh being the owner and bearing all this + + align:start position:0% +uh being the owner and bearing all this + + + align:start position:0% +uh being the owner and bearing all this +risk I might prefer actually to be in a + + align:start position:0% +risk I might prefer actually to be in a + + + align:start position:0% +risk I might prefer actually to be in a +contract where I'm sharing some of the + + align:start position:0% +contract where I'm sharing some of the + + + align:start position:0% +contract where I'm sharing some of the +benefits some of the costs or sorry + + align:start position:0% +benefits some of the costs or sorry + + + align:start position:0% +benefits some of the costs or sorry +sharing some of the returns in return + + align:start position:0% +sharing some of the returns in return + + + align:start position:0% +sharing some of the returns in return +for some kind of insurance + + align:start position:0% +for some kind of insurance + + + align:start position:0% +for some kind of insurance +so you could imagine in a risk aversion + + align:start position:0% +so you could imagine in a risk aversion + + + align:start position:0% +so you could imagine in a risk aversion +model that some kind of these + + align:start position:0% +model that some kind of these + + + align:start position:0% +model that some kind of these +sharecropping Arrangements might might + + align:start position:0% +sharecropping Arrangements might might + + + align:start position:0% +sharecropping Arrangements might might +kind of uh emerge uh re-emerge + + align:start position:0% +kind of uh emerge uh re-emerge + + + align:start position:0% +kind of uh emerge uh re-emerge +endogenously right you can imagine for + + align:start position:0% +endogenously right you can imagine for + + + align:start position:0% +endogenously right you can imagine for +example a landlord might make you an + + align:start position:0% +example a landlord might make you an + + + align:start position:0% +example a landlord might make you an +offer and say I'll buy the land from you + + align:start position:0% +offer and say I'll buy the land from you + + + align:start position:0% +offer and say I'll buy the land from you +right and then I'll provide you a share + + align:start position:0% +right and then I'll provide you a share + + + align:start position:0% +right and then I'll provide you a share +contract and that might be better + + align:start position:0% +contract and that might be better + + + align:start position:0% +contract and that might be better +for you know including including the + + align:start position:0% +for you know including including the + + + align:start position:0% +for you know including including the +payment they get up front for the sort + + align:start position:0% +payment they get up front for the sort + + + align:start position:0% +payment they get up front for the sort +of value of land they may better off for + + align:start position:0% +of value of land they may better off for + + + align:start position:0% +of value of land they may better off for +that because they think they're getting + + align:start position:0% +that because they think they're getting + + + align:start position:0% +that because they think they're getting +some insurance values or later and + + align:start position:0% +some insurance values or later and + + + align:start position:0% +some insurance values or later and +there's a trade-off there but but + + align:start position:0% +there's a trade-off there but but + + + align:start position:0% +there's a trade-off there but but +because insurance is kind of helpful + + align:start position:0% +because insurance is kind of helpful + + + align:start position:0% +because insurance is kind of helpful +um + + align:start position:0% +um + + + align:start position:0% +um +it might emerge endogenously + + align:start position:0% +it might emerge endogenously + + + align:start position:0% +it might emerge endogenously +under limited liability no + + align:start position:0% +under limited liability no + + + align:start position:0% +under limited liability no +right under a limited liability model + + align:start position:0% +right under a limited liability model + + + align:start position:0% +right under a limited liability model +like the only reason we had the + + align:start position:0% +like the only reason we had the + + + align:start position:0% +like the only reason we had the +sharecropping was we couldn't pay that + + align:start position:0% +sharecropping was we couldn't pay that + + + align:start position:0% +sharecropping was we couldn't pay that +we couldn't make this payment from the + + align:start position:0% +we couldn't make this payment from the + + + align:start position:0% +we couldn't make this payment from the +tenant to the landlord in the in the low + + align:start position:0% +tenant to the landlord in the in the low + + + align:start position:0% +tenant to the landlord in the in the low +state but + + align:start position:0% +state but + + + align:start position:0% +state but +if I'm the owner like I'm good like I + + align:start position:0% +if I'm the owner like I'm good like I + + + align:start position:0% +if I'm the owner like I'm good like I +don't pay anybody so like uh and I'm not + + align:start position:0% +don't pay anybody so like uh and I'm not + + + align:start position:0% +don't pay anybody so like uh and I'm not +risk-averse in that model it was neutral + + align:start position:0% +risk-averse in that model it was neutral + + + align:start position:0% +risk-averse in that model it was neutral +model so + + align:start position:0% +model so + + + align:start position:0% +model so +the which of these models is important + + align:start position:0% +the which of these models is important + + + align:start position:0% +the which of these models is important +um would have implications for sort of + + align:start position:0% +um would have implications for sort of + + + align:start position:0% +um would have implications for sort of +what you would do in the context of a + + align:start position:0% +what you would do in the context of a + + + align:start position:0% +what you would do in the context of a +landlord + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +comments questions + + align:start position:0% + + + + align:start position:0% + +yeah gosh + + align:start position:0% +yeah gosh + + + align:start position:0% +yeah gosh +[Music] + + align:start position:0% + + + + align:start position:0% + +I'm going to talk about that in a few + + align:start position:0% +I'm going to talk about that in a few + + + align:start position:0% +I'm going to talk about that in a few +minutes I'm not gonna talk about much + + align:start position:0% +minutes I'm not gonna talk about much + + + align:start position:0% +minutes I'm not gonna talk about much +but I'm going to talk about a little bit + + align:start position:0% +but I'm going to talk about a little bit + + + align:start position:0% +but I'm going to talk about a little bit +um + + align:start position:0% +um + + + align:start position:0% +um +there are a couple papers I'm waiting + + align:start position:0% +there are a couple papers I'm waiting + + + align:start position:0% +there are a couple papers I'm waiting +for light I'm still waiting for like + + align:start position:0% +for light I'm still waiting for like + + + align:start position:0% +for light I'm still waiting for like +the great land reform paper + + align:start position:0% +the great land reform paper + + + align:start position:0% +the great land reform paper +like there are some that are there's + + align:start position:0% +like there are some that are there's + + + align:start position:0% +like there are some that are there's +some really nice papers that I'll talk + + align:start position:0% +some really nice papers that I'll talk + + + align:start position:0% +some really nice papers that I'll talk +about but I feel like they have that + + align:start position:0% +about but I feel like they have that + + + align:start position:0% +about but I feel like they have that +they're + + align:start position:0% +they're + + + align:start position:0% +they're +various challenges + + align:start position:0% +various challenges + + + align:start position:0% +various challenges +um I'll talk about a few of them uh in a + + align:start position:0% +um I'll talk about a few of them uh in a + + + align:start position:0% +um I'll talk about a few of them uh in a +couple slides yeah + + align:start position:0% + + + + align:start position:0% + +I'm sorry I didn't understand + + align:start position:0% +I'm sorry I didn't understand + + + align:start position:0% +I'm sorry I didn't understand +uh no I think you would do some uh + + align:start position:0% + + + + align:start position:0% + +let me think + + align:start position:0% +let me think + + + align:start position:0% +let me think +um + + align:start position:0% +um + + + align:start position:0% +um +yeah it's got to right because uh if + + align:start position:0% +yeah it's got to right because uh if + + + align:start position:0% +yeah it's got to right because uh if +you're capped at the whole limited + + align:start position:0% +you're capped at the whole limited + + + align:start position:0% +you're capped at the whole limited +liability thing uh + + align:start position:0% + + + + align:start position:0% + +if you have if you add risk aversion to + + align:start position:0% +if you have if you add risk aversion to + + + align:start position:0% +if you have if you add risk aversion to +the limited liability uh thing + + align:start position:0% + + + + align:start position:0% + +um yeah you're still gonna have a + + align:start position:0% +um yeah you're still gonna have a + + + align:start position:0% +um yeah you're still gonna have a +problem you can't pay the rent in the + + align:start position:0% +problem you can't pay the rent in the + + + align:start position:0% +problem you can't pay the rent in the +low state + + align:start position:0% +low state + + + align:start position:0% +low state +so yeah I think it's um I think if the + + align:start position:0% +so yeah I think it's um I think if the + + + align:start position:0% +so yeah I think it's um I think if the +if the if the thing is binding then you + + align:start position:0% +if the if the thing is binding then you + + + align:start position:0% +if the if the thing is binding then you +then that sort of limits your ability to + + align:start position:0% +then that sort of limits your ability to + + + align:start position:0% +then that sort of limits your ability to +sort of like trade off kind of a fixed + + align:start position:0% +sort of like trade off kind of a fixed + + + align:start position:0% +sort of like trade off kind of a fixed +fee for for insurance i o so yes + + align:start position:0% +fee for for insurance i o so yes + + + align:start position:0% +fee for for insurance i o so yes +I think so + + align:start position:0% + + + + align:start position:0% + +other questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now that kind of brings us to the + + align:start position:0% +so now that kind of brings us to the + + + align:start position:0% +so now that kind of brings us to the +paper you guys read for today + + align:start position:0% +paper you guys read for today + + + align:start position:0% +paper you guys read for today +which is uh + + align:start position:0% +which is uh + + + align:start position:0% +which is uh +um + + align:start position:0% +um + + + align:start position:0% +um +do we actually think that there so one + + align:start position:0% +do we actually think that there so one + + + align:start position:0% +do we actually think that there so one +one implication of these models is that + + align:start position:0% +one implication of these models is that + + + align:start position:0% +one implication of these models is that +the uh that there is kind of some that + + align:start position:0% +the uh that there is kind of some that + + + align:start position:0% +the uh that there is kind of some that +sort of the incentive the contract is + + align:start position:0% +sort of the incentive the contract is + + + align:start position:0% +sort of the incentive the contract is +going to + + align:start position:0% +going to + + + align:start position:0% +going to +um affect kind of the the effort choice + + align:start position:0% +um affect kind of the the effort choice + + + align:start position:0% +um affect kind of the the effort choice +right + + align:start position:0% +right + + + align:start position:0% +right +um and you don't actually need the full + + align:start position:0% +um and you don't actually need the full + + + align:start position:0% +um and you don't actually need the full +that's true under any of these models + + align:start position:0% +that's true under any of these models + + + align:start position:0% +that's true under any of these models +right that we talked about you can go + + align:start position:0% +right that we talked about you can go + + + align:start position:0% +right that we talked about you can go +back to the very simple one the two line + + align:start position:0% +back to the very simple one the two line + + + align:start position:0% +back to the very simple one the two line +one I put up in the very beginning but + + align:start position:0% +one I put up in the very beginning but + + + align:start position:0% +one I put up in the very beginning but +that's kind of a key kind of parameter + + align:start position:0% +that's kind of a key kind of parameter + + + align:start position:0% +that's kind of a key kind of parameter +that we need to sort of understand all + + align:start position:0% +that we need to sort of understand all + + + align:start position:0% +that we need to sort of understand all +this + + align:start position:0% +this + + + align:start position:0% +this +so + + align:start position:0% +so + + + align:start position:0% +so +um so before you actually got through an + + align:start position:0% +um so before you actually got through an + + + align:start position:0% +um so before you actually got through an +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +before we had an experiment if you + + align:start position:0% +before we had an experiment if you + + + align:start position:0% +before we had an experiment if you +didn't have an experiment with when we + + align:start position:0% +didn't have an experiment with when we + + + align:start position:0% +didn't have an experiment with when we +talked about how would you how would you + + align:start position:0% +talked about how would you how would you + + + align:start position:0% +talked about how would you how would you +go about estimating + + align:start position:0% +go about estimating + + + align:start position:0% +go about estimating +this thing like what would you want to + + align:start position:0% +this thing like what would you want to + + + align:start position:0% +this thing like what would you want to +estimate this + + align:start position:0% + + + + align:start position:0% + +what kind of regression would you want + + align:start position:0% +what kind of regression would you want + + + align:start position:0% +what kind of regression would you want +to run + + align:start position:0% + + + + align:start position:0% + +somebody yeah hello uh you may want + + align:start position:0% +somebody yeah hello uh you may want + + + align:start position:0% +somebody yeah hello uh you may want +something that's like output based on + + align:start position:0% +something that's like output based on + + + align:start position:0% +something that's like output based on +like what share of uh + + align:start position:0% +like what share of uh + + + align:start position:0% +like what share of uh +outputs that they have + + align:start position:0% + + + + align:start position:0% + +like you can't stop like individual + + align:start position:0% +like you can't stop like individual + + + align:start position:0% +like you can't stop like individual +Farmers what's that right so people on a + + align:start position:0% +Farmers what's that right so people on a + + + align:start position:0% +Farmers what's that right so people on a +regression where like yeah + + align:start position:0% +regression where like yeah + + + align:start position:0% +regression where like yeah +um + + align:start position:0% +um + + + align:start position:0% +um +we're half a variable is like the output + + align:start position:0% +we're half a variable is like the output + + + align:start position:0% +we're half a variable is like the output +of the farm and people have like an + + align:start position:0% +of the farm and people have like an + + + align:start position:0% +of the farm and people have like an +input of one of your aggressors + + align:start position:0% +input of one of your aggressors + + + align:start position:0% +input of one of your aggressors +um what share of output what profits + + align:start position:0% +um what share of output what profits + + + align:start position:0% +um what share of output what profits +they are getting + + align:start position:0% +they are getting + + + align:start position:0% +they are getting +alternative + + align:start position:0% +alternative + + + align:start position:0% +alternative +sorry I'm sorry I don't fully so say it + + align:start position:0% +sorry I'm sorry I don't fully so say it + + + align:start position:0% +sorry I'm sorry I don't fully so say it +again so you like yes you want to put + + align:start position:0% +again so you like yes you want to put + + + align:start position:0% +again so you like yes you want to put +output on the left hand side right what + + align:start position:0% +output on the left hand side right what + + + align:start position:0% +output on the left hand side right what +do you want to put on the right hand + + align:start position:0% +do you want to put on the right hand + + + align:start position:0% +do you want to put on the right hand +side + + align:start position:0% +side + + + align:start position:0% +side +um basically like terms of the contract + + align:start position:0% +um basically like terms of the contract + + + align:start position:0% +um basically like terms of the contract +right exactly right the same thing you + + align:start position:0% +right exactly right the same thing you + + + align:start position:0% +right exactly right the same thing you +do you like you'd like to regress what + + align:start position:0% +do you like you'd like to regress what + + + align:start position:0% +do you like you'd like to regress what +is the output on what are the terms of + + align:start position:0% +is the output on what are the terms of + + + align:start position:0% +is the output on what are the terms of +the contract right + + align:start position:0% +the contract right + + + align:start position:0% +the contract right +so the so you know but but the problem + + align:start position:0% +so the so you know but but the problem + + + align:start position:0% +so the so you know but but the problem +is of course that those like Farm those + + align:start position:0% +is of course that those like Farm those + + + align:start position:0% +is of course that those like Farm those +Farmers would be different okay so + + align:start position:0% +Farmers would be different okay so + + + align:start position:0% +Farmers would be different okay so +um one thing to do actually would be if + + align:start position:0% +um one thing to do actually would be if + + + align:start position:0% +um one thing to do actually would be if +you had multiple farmer so if you had + + align:start position:0% +you had multiple farmer so if you had + + + align:start position:0% +you had multiple farmer so if you had +Farmers with multiple plots so the basic + + align:start position:0% +Farmers with multiple plots so the basic + + + align:start position:0% +Farmers with multiple plots so the basic +problem with that regression is we have + + align:start position:0% +problem with that regression is we have + + + align:start position:0% +problem with that regression is we have +Farm there might be farmer + + align:start position:0% +Farm there might be farmer + + + align:start position:0% +Farm there might be farmer +characteristics that might be different + + align:start position:0% +characteristics that might be different + + + align:start position:0% +characteristics that might be different +right farmers who enter into those + + align:start position:0% +right farmers who enter into those + + + align:start position:0% +right farmers who enter into those +different contracts might be + + align:start position:0% +different contracts might be + + + align:start position:0% +different contracts might be +different people so one option would be + + align:start position:0% +different people so one option would be + + + align:start position:0% +different people so one option would be +to use farmers who have multiple plots + + align:start position:0% +to use farmers who have multiple plots + + + align:start position:0% +to use farmers who have multiple plots +some sharecrop and some owned right and + + align:start position:0% +some sharecrop and some owned right and + + + align:start position:0% +some sharecrop and some owned right and +run this regression with far more fixed + + align:start position:0% +run this regression with far more fixed + + + align:start position:0% +run this regression with far more fixed +effects and say are they putting in + + align:start position:0% +effects and say are they putting in + + + align:start position:0% +effects and say are they putting in +um more effort on the OWN on the owned + + align:start position:0% +um more effort on the OWN on the owned + + + align:start position:0% +um more effort on the OWN on the owned +plots compared to the shared plots for + + align:start position:0% +plots compared to the shared plots for + + + align:start position:0% +plots compared to the shared plots for +example or more inputs or whatever + + align:start position:0% +example or more inputs or whatever + + + align:start position:0% +example or more inputs or whatever +okay so would that be a good regression + + align:start position:0% +okay so would that be a good regression + + + align:start position:0% +okay so would that be a good regression +or a bad regression so that that + + align:start position:0% +or a bad regression so that that + + + align:start position:0% +or a bad regression so that that +regression would basically sorry I wake + + align:start position:0% +regression would basically sorry I wake + + + align:start position:0% +regression would basically sorry I wake +up + + align:start position:0% +up + + + align:start position:0% +up +go ahead you can ask your question oh uh + + align:start position:0% +go ahead you can ask your question oh uh + + + align:start position:0% +go ahead you can ask your question oh uh +could there could there be an issue with + + align:start position:0% +could there could there be an issue with + + + align:start position:0% +could there could there be an issue with +like some + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +absolutely yeah yes right so the problem + + align:start position:0% +absolutely yeah yes right so the problem + + + align:start position:0% +absolutely yeah yes right so the problem +with quality of the land right so it may + + align:start position:0% +with quality of the land right so it may + + + align:start position:0% +with quality of the land right so it may +be a different land is owned versus + + align:start position:0% +be a different land is owned versus + + + align:start position:0% +be a different land is owned versus +rented and therefore that could be that + + align:start position:0% +rented and therefore that could be that + + + align:start position:0% +rented and therefore that could be that +could be related to the issue and okay + + align:start position:0% +could be related to the issue and okay + + + align:start position:0% +could be related to the issue and okay +so in fact so so the regression you + + align:start position:0% +so in fact so so the regression you + + + align:start position:0% +so in fact so so the regression you +could run is some output as a function + + align:start position:0% +could run is some output as a function + + + align:start position:0% +could run is some output as a function +of sort of the whether it's its own or + + align:start position:0% +of sort of the whether it's its own or + + + align:start position:0% +of sort of the whether it's its own or +not with far more fixed effects + + align:start position:0% +not with far more fixed effects + + + align:start position:0% +not with far more fixed effects +um + + align:start position:0% +um + + + align:start position:0% +um +and this could be either inputs or + + align:start position:0% +and this could be either inputs or + + + align:start position:0% +and this could be either inputs or +outputs okay so the the problem is + + align:start position:0% +outputs okay so the the problem is + + + align:start position:0% +outputs okay so the the problem is +exactly this one that you mentioned of + + align:start position:0% +exactly this one that you mentioned of + + + align:start position:0% +exactly this one that you mentioned of +sort of quality so this is from an older + + align:start position:0% +sort of quality so this is from an older + + + align:start position:0% +sort of quality so this is from an older +paper and you can basically see that um + + align:start position:0% +paper and you can basically see that um + + + align:start position:0% +paper and you can basically see that um +they have + + align:start position:0% +they have + + + align:start position:0% +they have +looking among the owned plot this + + align:start position:0% +looking among the owned plot this + + + align:start position:0% +looking among the owned plot this +doesn't have a fixed effects but I think + + align:start position:0% +doesn't have a fixed effects but I think + + + align:start position:0% +doesn't have a fixed effects but I think +the same thing goes through the fixed + + align:start position:0% +the same thing goes through the fixed + + + align:start position:0% +the same thing goes through the fixed +facts if you compare the owned plots the + + align:start position:0% +facts if you compare the owned plots the + + + align:start position:0% +facts if you compare the owned plots the +sharecrop plots and the fixed rent plots + + align:start position:0% +sharecrop plots and the fixed rent plots + + + align:start position:0% +sharecrop plots and the fixed rent plots +the owned plots + + align:start position:0% +the owned plots + + + align:start position:0% +the owned plots +um look a lot better in terms of their + + align:start position:0% +um look a lot better in terms of their + + + align:start position:0% +um look a lot better in terms of their +uh say average value than the uh + + align:start position:0% +uh say average value than the uh + + + align:start position:0% +uh say average value than the uh +sharecropped plots actually in this case + + align:start position:0% +sharecropped plots actually in this case + + + align:start position:0% +sharecropped plots actually in this case +the fixed rent ones I think look kind of + + align:start position:0% +the fixed rent ones I think look kind of + + + align:start position:0% +the fixed rent ones I think look kind of +the worst of all + + align:start position:0% +the worst of all + + + align:start position:0% +the worst of all +um at least in some of the villages so + + align:start position:0% +um at least in some of the villages so + + + align:start position:0% +um at least in some of the villages so +the point though is that the you may + + align:start position:0% +the point though is that the you may + + + align:start position:0% +the point though is that the you may +have different uh and by the way this is + + align:start position:0% +have different uh and by the way this is + + + align:start position:0% +have different uh and by the way this is +too small to read that's why you have + + align:start position:0% +too small to read that's why you have + + + align:start position:0% +too small to read that's why you have +the handout + + align:start position:0% +the handout + + + align:start position:0% +the handout +um so if um + + align:start position:0% +um so if um + + + align:start position:0% +um so if um +so that's that's why this regression may + + align:start position:0% +so that's that's why this regression may + + + align:start position:0% +so that's that's why this regression may +be sort of challenging okay + + align:start position:0% +be sort of challenging okay + + + align:start position:0% +be sort of challenging okay +and so you know the original approach is + + align:start position:0% +and so you know the original approach is + + + align:start position:0% +and so you know the original approach is +before we had this RCT and the paper + + align:start position:0% +before we had this RCT and the paper + + + align:start position:0% +before we had this RCT and the paper +that we used to teach here was to say + + align:start position:0% +that we used to teach here was to say + + + align:start position:0% +that we used to teach here was to say +let's control for kind of really + + align:start position:0% +let's control for kind of really + + + align:start position:0% +let's control for kind of really +detailed plot characteristics okay + + align:start position:0% +detailed plot characteristics okay + + + align:start position:0% +detailed plot characteristics okay +um and the problem is that the problem + + align:start position:0% +um and the problem is that the problem + + + align:start position:0% +um and the problem is that the problem +here is that you know there may be sort + + align:start position:0% +here is that you know there may be sort + + + align:start position:0% +here is that you know there may be sort +of unobservable characteristics of the + + align:start position:0% +of unobservable characteristics of the + + + align:start position:0% +of unobservable characteristics of the +plot beyond the measurable plot + + align:start position:0% +plot beyond the measurable plot + + + align:start position:0% +plot beyond the measurable plot +characteristics + + align:start position:0% +characteristics + + + align:start position:0% +characteristics +um you know it's really hard to you know + + align:start position:0% +um you know it's really hard to you know + + + align:start position:0% +um you know it's really hard to you know +if you if you end up writing agriculture + + align:start position:0% +if you if you end up writing agriculture + + + align:start position:0% +if you if you end up writing agriculture +paper you'll go you know into the weeds + + align:start position:0% +paper you'll go you know into the weeds + + + align:start position:0% +paper you'll go you know into the weeds +so to speak uh and you will find like an + + align:start position:0% +so to speak uh and you will find like an + + + align:start position:0% +so to speak uh and you will find like an +incredible amount of + + align:start position:0% + + + + align:start position:0% + +D like how you describe a plot + + align:start position:0% +D like how you describe a plot + + + align:start position:0% +D like how you describe a plot +characteristics and soil quality and + + align:start position:0% +characteristics and soil quality and + + + align:start position:0% +characteristics and soil quality and +irrigate you know water quality and this + + align:start position:0% +irrigate you know water quality and this + + + align:start position:0% +irrigate you know water quality and this +that and everything is like it's like + + align:start position:0% +that and everything is like it's like + + + align:start position:0% +that and everything is like it's like +many many dimensional and so that + + align:start position:0% +many many dimensional and so that + + + align:start position:0% +many many dimensional and so that +approach is really hard to sort of get + + align:start position:0% +approach is really hard to sort of get + + + align:start position:0% +approach is really hard to sort of get +that right okay so what would be cool is + + align:start position:0% +that right okay so what would be cool is + + + align:start position:0% +that right okay so what would be cool is +um would be to have plot fixed effects + + align:start position:0% +um would be to have plot fixed effects + + + align:start position:0% +um would be to have plot fixed effects +right in this regression like maybe some + + align:start position:0% +right in this regression like maybe some + + + align:start position:0% +right in this regression like maybe some +plots change but then of course the + + align:start position:0% +plots change but then of course the + + + align:start position:0% +plots change but then of course the +question is why they're changing right + + align:start position:0% +question is why they're changing right + + + align:start position:0% +question is why they're changing right +so all of this basically uh actually I + + align:start position:0% +so all of this basically uh actually I + + + align:start position:0% +so all of this basically uh actually I +can't find a paper that does that uh + + align:start position:0% +can't find a paper that does that uh + + + align:start position:0% +can't find a paper that does that uh +because probably the contracts don't + + align:start position:0% +because probably the contracts don't + + + align:start position:0% +because probably the contracts don't +change I mean we don't know why they + + align:start position:0% +change I mean we don't know why they + + + align:start position:0% +change I mean we don't know why they +they don't change + + align:start position:0% +they don't change + + + align:start position:0% +they don't change +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +so so that all leads us to the paper you + + align:start position:0% +so so that all leads us to the paper you + + + align:start position:0% +so so that all leads us to the paper you +guys read for today which is I think why + + align:start position:0% +guys read for today which is I think why + + + align:start position:0% +guys read for today which is I think why +this paper uh even though as some of you + + align:start position:0% +this paper uh even though as some of you + + + align:start position:0% +this paper uh even though as some of you +guys noted the setting is a little + + align:start position:0% +guys noted the setting is a little + + + align:start position:0% +guys noted the setting is a little +unusual right it's these kind of um you + + align:start position:0% +unusual right it's these kind of um you + + + align:start position:0% +unusual right it's these kind of um you +know uh whoops + + align:start position:0% +know uh whoops + + + align:start position:0% +know uh whoops +um + + align:start position:0% +um + + + align:start position:0% +um +you know New farmers who are kind of + + align:start position:0% +you know New farmers who are kind of + + + align:start position:0% +you know New farmers who are kind of +interested in in farming is part of + + align:start position:0% +interested in in farming is part of + + + align:start position:0% +interested in in farming is part of +these kind of women's groups and sort of + + align:start position:0% +these kind of women's groups and sort of + + + align:start position:0% +these kind of women's groups and sort of +it's not the sort of the external + + align:start position:0% +it's not the sort of the external + + + align:start position:0% +it's not the sort of the external +validity of this may not necessarily be + + align:start position:0% +validity of this may not necessarily be + + + align:start position:0% +validity of this may not necessarily be +100 there the reason I think this paper + + align:start position:0% +100 there the reason I think this paper + + + align:start position:0% +100 there the reason I think this paper +is is + + align:start position:0% +is is + + + align:start position:0% +is is +you know got so much attention is it is + + align:start position:0% +you know got so much attention is it is + + + align:start position:0% +you know got so much attention is it is +kind of the the cleanest paper that we + + align:start position:0% +kind of the the cleanest paper that we + + + align:start position:0% +kind of the the cleanest paper that we +know that actually sort of like tests uh + + align:start position:0% +know that actually sort of like tests uh + + + align:start position:0% +know that actually sort of like tests uh +this so um + + align:start position:0% +this so um + + + align:start position:0% +this so um +so you know as you guys saw right what + + align:start position:0% +so you know as you guys saw right what + + + align:start position:0% +so you know as you guys saw right what +are they going to do they're going to + + align:start position:0% +are they going to do they're going to + + + align:start position:0% +are they going to do they're going to +work with tenant farmers in Uganda + + align:start position:0% +work with tenant farmers in Uganda + + + align:start position:0% +work with tenant farmers in Uganda +um randomize them to receive either 50 + + align:start position:0% +um randomize them to receive either 50 + + + align:start position:0% +um randomize them to receive either 50 +of their output so after they recruit + + align:start position:0% +of their output so after they recruit + + + align:start position:0% +of their output so after they recruit +them right so it's gonna be surprised + + align:start position:0% +them right so it's gonna be surprised + + + align:start position:0% +them right so it's gonna be surprised +randomization so there's no no selection + + align:start position:0% +randomization so there's no no selection + + + align:start position:0% +randomization so there's no no selection +issues right have either 50 so the + + align:start position:0% +issues right have either 50 so the + + + align:start position:0% +issues right have either 50 so the +Baseline is 50 of output or you can get + + align:start position:0% +Baseline is 50 of output or you can get + + + align:start position:0% +Baseline is 50 of output or you can get +to keep 75 of your output or 50 of your + + align:start position:0% +to keep 75 of your output or 50 of your + + + align:start position:0% +to keep 75 of your output or 50 of your +output plus an exogenous cash transfer + + align:start position:0% +output plus an exogenous cash transfer + + + align:start position:0% +output plus an exogenous cash transfer +calibrated to be equal to 25 percent of + + align:start position:0% +calibrated to be equal to 25 percent of + + + align:start position:0% +calibrated to be equal to 25 percent of +output and expectation either as a fixed + + align:start position:0% +output and expectation either as a fixed + + + align:start position:0% +output and expectation either as a fixed +fee or a risky contract + + align:start position:0% +fee or a risky contract + + + align:start position:0% +fee or a risky contract +okay so that's the basic design + + align:start position:0% +okay so that's the basic design + + + align:start position:0% +okay so that's the basic design +um + + align:start position:0% +um + + + align:start position:0% +um +okay so what do you guys + + align:start position:0% +okay so what do you guys + + + align:start position:0% +okay so what do you guys +I'm curious what do you guys think of + + align:start position:0% +I'm curious what do you guys think of + + + align:start position:0% +I'm curious what do you guys think of +this you like this you like this paper + + align:start position:0% +this you like this you like this paper + + + align:start position:0% +this you like this you like this paper +you have concerns about it like what do + + align:start position:0% +you have concerns about it like what do + + + align:start position:0% +you have concerns about it like what do +you think + + align:start position:0% + + + + align:start position:0% + +yeah Aaron so one I had was with the how + + align:start position:0% +yeah Aaron so one I had was with the how + + + align:start position:0% +yeah Aaron so one I had was with the how +they they're because they're trying to + + align:start position:0% +they they're because they're trying to + + + align:start position:0% +they they're because they're trying to +test for the fact that like these + + align:start position:0% +test for the fact that like these + + + align:start position:0% +test for the fact that like these +incentive effects do explain was after + + align:start position:0% +incentive effects do explain was after + + + align:start position:0% +incentive effects do explain was after +not income or risk um effects and so + + align:start position:0% +not income or risk um effects and so + + + align:start position:0% +not income or risk um effects and so +they kind of argue that their risky + + align:start position:0% +they kind of argue that their risky + + + align:start position:0% +they kind of argue that their risky +exogenous cast transfer is a way of + + align:start position:0% +exogenous cast transfer is a way of + + + align:start position:0% +exogenous cast transfer is a way of +making sure that these risk effects + + align:start position:0% +making sure that these risk effects + + + align:start position:0% +making sure that these risk effects +don't exist but what I thought was doing + + align:start position:0% +don't exist but what I thought was doing + + + align:start position:0% +don't exist but what I thought was doing +this they draw really heavily on this + + align:start position:0% +this they draw really heavily on this + + + align:start position:0% +this they draw really heavily on this +like um Marshalls kind of model + + align:start position:0% +like um Marshalls kind of model + + + align:start position:0% +like um Marshalls kind of model +um but that in that model what you see + + align:start position:0% +um but that in that model what you see + + + align:start position:0% +um but that in that model what you see +is that the probability of having like a + + align:start position:0% +is that the probability of having like a + + + align:start position:0% +is that the probability of having like a +high output is dependent on your inputs + + align:start position:0% +high output is dependent on your inputs + + + align:start position:0% +high output is dependent on your inputs +um whereas in theirs + + align:start position:0% +um whereas in theirs + + + align:start position:0% +um whereas in theirs +um for the for the risky + + align:start position:0% +um for the for the risky + + + align:start position:0% +um for the for the risky +exogenous piece it's not + + align:start position:0% +exogenous piece it's not + + + align:start position:0% +exogenous piece it's not +um like you it's whether or not you get + + align:start position:0% +um like you it's whether or not you get + + + align:start position:0% +um like you it's whether or not you get +a you get that additional 25 + + align:start position:0% +a you get that additional 25 + + + align:start position:0% +a you get that additional 25 +um in the risky case it's exhausting + + align:start position:0% +um in the risky case it's exhausting + + + align:start position:0% +um in the risky case it's exhausting +that's right yeah it doesn't depend on + + align:start position:0% +that's right yeah it doesn't depend on + + + align:start position:0% +that's right yeah it doesn't depend on +your inputs um versus in the 75 of + + align:start position:0% +your inputs um versus in the 75 of + + + align:start position:0% +your inputs um versus in the 75 of +output it's not actually 25 most + + align:start position:0% +output it's not actually 25 most + + + align:start position:0% +output it's not actually 25 most +certainly that + + align:start position:0% +certainly that + + + align:start position:0% +certainly that +um so what's the what's the concern + + align:start position:0% +um so what's the what's the concern + + + align:start position:0% +um so what's the what's the concern +there well so you know given that if + + align:start position:0% +there well so you know given that if + + + align:start position:0% +there well so you know given that if +your additional this additional 25 + + align:start position:0% +your additional this additional 25 + + + align:start position:0% +your additional this additional 25 +depends on your inputs or inputs are + + align:start position:0% +depends on your inputs or inputs are + + + align:start position:0% +depends on your inputs or inputs are +going to change versus if it is not and + + align:start position:0% +going to change versus if it is not and + + + align:start position:0% +going to change versus if it is not and +so I don't I don't understand how then + + align:start position:0% +so I don't I don't understand how then + + + align:start position:0% +so I don't I don't understand how then +you can you can say that risk does not + + align:start position:0% +you can you can say that risk does not + + + align:start position:0% +you can you can say that risk does not +account + + align:start position:0% +account + + + align:start position:0% +account +okay so does anyone else have any anyone + + align:start position:0% +okay so does anyone else have any anyone + + + align:start position:0% +okay so does anyone else have any anyone +want to respond to that + + align:start position:0% +want to respond to that + + + align:start position:0% +want to respond to that +James comment any any idea any thoughts + + align:start position:0% + + + + align:start position:0% + +two no damn yeah + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +the point rights the point of this one + + align:start position:0% +the point rights the point of this one + + + align:start position:0% +the point rights the point of this one +is not about insurance the point of this + + align:start position:0% +is not about insurance the point of this + + + align:start position:0% +is not about insurance the point of this +is an income effects + + align:start position:0% +is an income effects + + + align:start position:0% +is an income effects +right so the point of the point of this + + align:start position:0% +right so the point of the point of this + + + align:start position:0% +right so the point of the point of this +the point of the point of this one is to + + align:start position:0% +the point of the point of this one is to + + + align:start position:0% +the point of the point of this one is to +say well maybe they're like doing more + + align:start position:0% +say well maybe they're like doing more + + + align:start position:0% +say well maybe they're like doing more +stuff because they're richer in + + align:start position:0% +stuff because they're richer in + + + align:start position:0% +stuff because they're richer in +expectation like maybe somehow maybe + + align:start position:0% +expectation like maybe somehow maybe + + + align:start position:0% +expectation like maybe somehow maybe +they're I don't know not quite credit + + align:start position:0% +they're I don't know not quite credit + + + align:start position:0% +they're I don't know not quite credit +constrained but maybe they're sort of + + align:start position:0% +constrained but maybe they're sort of + + + align:start position:0% +constrained but maybe they're sort of +credit constraint you know maybe they + + align:start position:0% +credit constraint you know maybe they + + + align:start position:0% +credit constraint you know maybe they +only feel like they can afford to buy + + align:start position:0% +only feel like they can afford to buy + + + align:start position:0% +only feel like they can afford to buy +fertilizer if they're gonna get a higher + + align:start position:0% +fertilizer if they're gonna get a higher + + + align:start position:0% +fertilizer if they're gonna get a higher +payment at the end so that's what that's + + align:start position:0% +payment at the end so that's what that's + + + align:start position:0% +payment at the end so that's what that's +what this one is for is the is the level + + align:start position:0% +what this one is for is the is the level + + + align:start position:0% +what this one is for is the is the level +right + + align:start position:0% +right + + + align:start position:0% +right +well I think I think Aaron's concerned + + align:start position:0% +well I think I think Aaron's concerned + + + align:start position:0% +well I think I think Aaron's concerned +if I understand it correctly Aaron + + align:start position:0% +if I understand it correctly Aaron + + + align:start position:0% +if I understand it correctly Aaron +correct if I'm wrong was that the the + + align:start position:0% +correct if I'm wrong was that the the + + + align:start position:0% +correct if I'm wrong was that the the +issue with this one is that the + + align:start position:0% +issue with this one is that the + + + align:start position:0% +issue with this one is that the +payment here doesn't depend on your + + align:start position:0% +payment here doesn't depend on your + + + align:start position:0% +payment here doesn't depend on your +inputs but and so it doesn't exactly + + align:start position:0% +inputs but and so it doesn't exactly + + + align:start position:0% +inputs but and so it doesn't exactly +mirror the the riskiness you would have + + align:start position:0% +mirror the the riskiness you would have + + + align:start position:0% +mirror the the riskiness you would have +in the in in this contract because you + + align:start position:0% +in the in in this contract because you + + + align:start position:0% +in the in in this contract because you +would + + align:start position:0% +would + + + align:start position:0% +would +um + + align:start position:0% +um + + + align:start position:0% +um +yeah because here you would also be + + align:start position:0% +yeah because here you would also be + + + align:start position:0% +yeah because here you would also be +putting in more inputs and therefore + + align:start position:0% +putting in more inputs and therefore + + + align:start position:0% +putting in more inputs and therefore +your net returns would be different is + + align:start position:0% +your net returns would be different is + + + align:start position:0% +your net returns would be different is +that your point yeah so I think the way + + align:start position:0% +that your point yeah so I think the way + + + align:start position:0% +that your point yeah so I think the way +at least the way I think about this is + + align:start position:0% +at least the way I think about this is + + + align:start position:0% +at least the way I think about this is +to say + + align:start position:0% +to say + + + align:start position:0% +to say +this is this is actually testing a + + align:start position:0% +this is this is actually testing a + + + align:start position:0% +this is this is actually testing a +different issue which is to say look + + align:start position:0% +different issue which is to say look + + + align:start position:0% +different issue which is to say look +let's suppose that the + + align:start position:0% +let's suppose that the + + + align:start position:0% +let's suppose that the +there's two thoughts the first is say + + align:start position:0% +there's two thoughts the first is say + + + align:start position:0% +there's two thoughts the first is say +if you + + align:start position:0% +if you + + + align:start position:0% +if you +to first order + + align:start position:0% +to first order + + + align:start position:0% +to first order +is it + + align:start position:0% +is it + + + align:start position:0% +is it +this contract you know gives you a lot + + align:start position:0% +this contract you know gives you a lot + + + align:start position:0% +this contract you know gives you a lot +so sorry plus and minuses yeah I think + + align:start position:0% +so sorry plus and minuses yeah I think + + + align:start position:0% +so sorry plus and minuses yeah I think +what they're trying to say is yes this + + align:start position:0% +what they're trying to say is yes this + + + align:start position:0% +what they're trying to say is yes this +contract gives you gives you is just + + align:start position:0% +contract gives you gives you is just + + + align:start position:0% +contract gives you gives you is just +generally more risky than the other one + + align:start position:0% +generally more risky than the other one + + + align:start position:0% +generally more risky than the other one +and so if you thought that like what was + + align:start position:0% +and so if you thought that like what was + + + align:start position:0% +and so if you thought that like what was +happening as I was changing my behavior + + align:start position:0% +happening as I was changing my behavior + + + align:start position:0% +happening as I was changing my behavior +because I'm exposed to more risk in some + + align:start position:0% +because I'm exposed to more risk in some + + + align:start position:0% +because I'm exposed to more risk in some +general sense you would see things that + + align:start position:0% +general sense you would see things that + + + align:start position:0% +general sense you would see things that +look more similar between this and this + + align:start position:0% +look more similar between this and this + + + align:start position:0% +look more similar between this and this +so I agree with you that it is um + + align:start position:0% +so I agree with you that it is um + + + align:start position:0% +so I agree with you that it is um +it is different it's not exactly the + + align:start position:0% +it is different it's not exactly the + + + align:start position:0% +it is different it's not exactly the +same in a couple respects the first is + + align:start position:0% +same in a couple respects the first is + + + align:start position:0% +same in a couple respects the first is +um this risky contract + + align:start position:0% +um this risky contract + + + align:start position:0% +um this risky contract +is actually not as risky as this risky + + align:start position:0% +is actually not as risky as this risky + + + align:start position:0% +is actually not as risky as this risky +contract + + align:start position:0% +contract + + + align:start position:0% +contract +because this one I think if I were + + align:start position:0% +because this one I think if I were + + + align:start position:0% +because this one I think if I were +correctly is exogenous risk whereas this + + align:start position:0% +correctly is exogenous risk whereas this + + + align:start position:0% +correctly is exogenous risk whereas this +one is sorry and sort of like + + align:start position:0% +one is sorry and sort of like + + + align:start position:0% +one is sorry and sort of like +independent risk whereas this one is + + align:start position:0% +independent risk whereas this one is + + + align:start position:0% +independent risk whereas this one is +correlated with the rest of your risk + + align:start position:0% +correlated with the rest of your risk + + + align:start position:0% +correlated with the rest of your risk +right so actually to me the first order + + align:start position:0% +right so actually to me the first order + + + align:start position:0% +right so actually to me the first order +issue is that one which is sort of like + + align:start position:0% +issue is that one which is sort of like + + + align:start position:0% +issue is that one which is sort of like +the the this one is you know and I don't + + align:start position:0% +the the this one is you know and I don't + + + align:start position:0% +the the this one is you know and I don't +think this one if someone correct me I'm + + align:start position:0% +think this one if someone correct me I'm + + + align:start position:0% +think this one if someone correct me I'm +wrong this is just an exogenous risky + + align:start position:0% +wrong this is just an exogenous risky + + + align:start position:0% +wrong this is just an exogenous risky +payment right yeah it's like an eye like + + align:start position:0% +payment right yeah it's like an eye like + + + align:start position:0% +payment right yeah it's like an eye like +a random draw or anything right so one + + align:start position:0% +a random draw or anything right so one + + + align:start position:0% +a random draw or anything right so one +thing that might have been even slightly + + align:start position:0% +thing that might have been even slightly + + + align:start position:0% +thing that might have been even slightly +better to deal with this is not your + + align:start position:0% +better to deal with this is not your + + + align:start position:0% +better to deal with this is not your +issue but deal with this other issue + + align:start position:0% +issue but deal with this other issue + + + align:start position:0% +issue but deal with this other issue +might have been to say well I'm going to + + align:start position:0% +might have been to say well I'm going to + + + align:start position:0% +might have been to say well I'm going to +tie the risky contract to say average + + align:start position:0% +tie the risky contract to say average + + + align:start position:0% +tie the risky contract to say average +returns in the neighborhood + + align:start position:0% +returns in the neighborhood + + + align:start position:0% +returns in the neighborhood +like in your area so at least it becomes + + align:start position:0% +like in your area so at least it becomes + + + align:start position:0% +like in your area so at least it becomes +a correlated shock not not an + + align:start position:0% +a correlated shock not not an + + + align:start position:0% +a correlated shock not not an +independent shock because because + + align:start position:0% +independent shock because because + + + align:start position:0% +independent shock because because +otherwise this is like you know this + + align:start position:0% +otherwise this is like you know this + + + align:start position:0% +otherwise this is like you know this +risk is like less risky than this + + align:start position:0% +risk is like less risky than this + + + align:start position:0% +risk is like less risky than this +because like it's uh it's independent + + align:start position:0% +because like it's uh it's independent + + + align:start position:0% +because like it's uh it's independent +you see what I'm saying + + align:start position:0% +you see what I'm saying + + + align:start position:0% +you see what I'm saying +um it's not a correlated chalk + + align:start position:0% +um it's not a correlated chalk + + + align:start position:0% +um it's not a correlated chalk +to your point I don't know of a good way + + align:start position:0% +to your point I don't know of a good way + + + align:start position:0% +to your point I don't know of a good way +I see your point that sort of the net + + align:start position:0% +I see your point that sort of the net + + + align:start position:0% +I see your point that sort of the net +your point is if I write down the + + align:start position:0% +your point is if I write down the + + + align:start position:0% +your point is if I write down the +utility yet sort of under the things + + align:start position:0% +utility yet sort of under the things + + + align:start position:0% +utility yet sort of under the things +that the net risk is the same because I + + align:start position:0% +that the net risk is the same because I + + + align:start position:0% +that the net risk is the same because I +haven't put in the additional inputs I + + align:start position:0% +haven't put in the additional inputs I + + + align:start position:0% +haven't put in the additional inputs I +don't know of a good way to deal with + + align:start position:0% +don't know of a good way to deal with + + + align:start position:0% +don't know of a good way to deal with +that though like do you + + align:start position:0% + + + + align:start position:0% + +um what are some other like what other + + align:start position:0% +um what are some other like what other + + + align:start position:0% +um what are some other like what other +concerns did you guys have about this + + align:start position:0% +concerns did you guys have about this + + + align:start position:0% +concerns did you guys have about this +paper + + align:start position:0% + + + + align:start position:0% + +I know in general actually I haven't + + align:start position:0% +I know in general actually I haven't + + + align:start position:0% +I know in general actually I haven't +read all your comments you all pretty + + align:start position:0% +read all your comments you all pretty + + + align:start position:0% +read all your comments you all pretty +much liked it but like were there other + + align:start position:0% +much liked it but like were there other + + + align:start position:0% +much liked it but like were there other +concerns that you guys had looking over + + align:start position:0% +concerns that you guys had looking over + + + align:start position:0% +concerns that you guys had looking over +it + + align:start position:0% +it + + + align:start position:0% +it +or things you would have wanted them to + + align:start position:0% +or things you would have wanted them to + + + align:start position:0% +or things you would have wanted them to +do differently + + align:start position:0% + + + + align:start position:0% + +yeah I think that's like one of the + + align:start position:0% +yeah I think that's like one of the + + + align:start position:0% +yeah I think that's like one of the +things that I was thinking about was + + align:start position:0% +things that I was thinking about was + + + align:start position:0% +things that I was thinking about was +like in making this experiment like X + + align:start position:0% +like in making this experiment like X + + + align:start position:0% +like in making this experiment like X +auntie and like what but the outcome + + align:start position:0% +auntie and like what but the outcome + + + align:start position:0% +auntie and like what but the outcome +that you're going to get is either + + align:start position:0% +that you're going to get is either + + + align:start position:0% +that you're going to get is either +something along the lines of okay there + + align:start position:0% +something along the lines of okay there + + + align:start position:0% +something along the lines of okay there +it's mainly income effects or it's + + align:start position:0% +it's mainly income effects or it's + + + align:start position:0% +it's mainly income effects or it's +mainly these like incentive and moral + + align:start position:0% +mainly these like incentive and moral + + + align:start position:0% +mainly these like incentive and moral +hazard effects or like some combination + + align:start position:0% +hazard effects or like some combination + + + align:start position:0% +hazard effects or like some combination +of the two or neither of them + + align:start position:0% +of the two or neither of them + + + align:start position:0% +of the two or neither of them +so I think for me just in terms of like + + align:start position:0% +so I think for me just in terms of like + + + align:start position:0% +so I think for me just in terms of like +policy applications is like what is one + + align:start position:0% +policy applications is like what is one + + + align:start position:0% +policy applications is like what is one +supposed to get from this paper like had + + align:start position:0% +supposed to get from this paper like had + + + align:start position:0% +supposed to get from this paper like had +it been income effects I think there's a + + align:start position:0% +it been income effects I think there's a + + + align:start position:0% +it been income effects I think there's a +very clear like answer of just give of + + align:start position:0% +very clear like answer of just give of + + + align:start position:0% +very clear like answer of just give of +these tenants money and then you can be + + align:start position:0% +these tenants money and then you can be + + + align:start position:0% +these tenants money and then you can be +more productive but given that like the + + align:start position:0% +more productive but given that like the + + + align:start position:0% +more productive but given that like the +answer was this mainly a moral habit + + align:start position:0% +answer was this mainly a moral habit + + + align:start position:0% +answer was this mainly a moral habit +yeah so like what is going to be the + + align:start position:0% +yeah so like what is going to be the + + + align:start position:0% +yeah so like what is going to be the +reform that like a government or + + align:start position:0% +reform that like a government or + + + align:start position:0% +reform that like a government or +something does as an adult like it seems + + align:start position:0% +something does as an adult like it seems + + + align:start position:0% +something does as an adult like it seems +very hard to just tell everyone to + + align:start position:0% +very hard to just tell everyone to + + + align:start position:0% +very hard to just tell everyone to +change the terms with contracts of your + + align:start position:0% +change the terms with contracts of your + + + align:start position:0% +change the terms with contracts of your +tenants or things like that that's a + + align:start position:0% +tenants or things like that that's a + + + align:start position:0% +tenants or things like that that's a +good question + + align:start position:0% + + + + align:start position:0% + +in this + + align:start position:0% + + + + align:start position:0% + +oh I'm gonna take 50 of your output or + + align:start position:0% +oh I'm gonna take 50 of your output or + + + align:start position:0% +oh I'm gonna take 50 of your output or +only 25 of your output if you could have + + align:start position:0% +only 25 of your output if you could have + + + align:start position:0% +only 25 of your output if you could have +some sort of like staggered design in + + align:start position:0% +some sort of like staggered design in + + + align:start position:0% +some sort of like staggered design in +your contract you would say like I'll + + align:start position:0% +your contract you would say like I'll + + + align:start position:0% +your contract you would say like I'll +initially take 50 but like if you make + + align:start position:0% +initially take 50 but like if you make + + + align:start position:0% +initially take 50 but like if you make +above this amount in your output I'm + + align:start position:0% +above this amount in your output I'm + + + align:start position:0% +above this amount in your output I'm +gonna take less so then you have an + + align:start position:0% +gonna take less so then you have an + + + align:start position:0% +gonna take less so then you have an +incentive to keep producing more as you + + align:start position:0% +incentive to keep producing more as you + + + align:start position:0% +incentive to keep producing more as you +go along and I would be curious what + + align:start position:0% +go along and I would be curious what + + + align:start position:0% +go along and I would be curious what +that would actually look like + + align:start position:0% +that would actually look like + + + align:start position:0% +that would actually look like +implemented and if that would yeah so + + align:start position:0% +implemented and if that would yeah so + + + align:start position:0% +implemented and if that would yeah so +this gets back to this whole question of + + align:start position:0% +this gets back to this whole question of + + + align:start position:0% +this gets back to this whole question of +like our linear contracts optimal so you + + align:start position:0% +like our linear contracts optimal so you + + + align:start position:0% +like our linear contracts optimal so you +know I'm gonna I'm gonna not go into + + align:start position:0% +know I'm gonna I'm gonna not go into + + + align:start position:0% +know I'm gonna I'm gonna not go into +that in a lot of detail and refer you to + + align:start position:0% +that in a lot of detail and refer you to + + + align:start position:0% +that in a lot of detail and refer you to +a contract theory class for this + + align:start position:0% +a contract theory class for this + + + align:start position:0% +a contract theory class for this +question + + align:start position:0% +question + + + align:start position:0% +question +um but I think there's a couple of + + align:start position:0% +um but I think there's a couple of + + + align:start position:0% +um but I think there's a couple of +issues the first is I think the general + + align:start position:0% +issues the first is I think the general + + + align:start position:0% +issues the first is I think the general +issue with nonlinear contracts is you + + align:start position:0% +issue with nonlinear contracts is you + + + align:start position:0% +issue with nonlinear contracts is you +want to sort of put the + + align:start position:0% +want to sort of put the + + + align:start position:0% +want to sort of put the +um + + align:start position:0% +um + + + align:start position:0% +um +you want to put the part where you give + + align:start position:0% +you want to put the part where you give + + + align:start position:0% +you want to put the part where you give +them give people the most incentive at + + align:start position:0% +them give people the most incentive at + + + align:start position:0% +them give people the most incentive at +kind of the point where they're sort of + + align:start position:0% +kind of the point where they're sort of + + + align:start position:0% +kind of the point where they're sort of +motion elastic and figuring that out + + align:start position:0% +motion elastic and figuring that out + + + align:start position:0% +motion elastic and figuring that out +with heterogeneity across people can be + + align:start position:0% +with heterogeneity across people can be + + + align:start position:0% +with heterogeneity across people can be +tricky so you know it might be and if I + + align:start position:0% +tricky so you know it might be and if I + + + align:start position:0% +tricky so you know it might be and if I +put it in the wrong place then I can + + align:start position:0% +put it in the wrong place then I can + + + align:start position:0% +put it in the wrong place then I can +like so you sort of want to say I want + + align:start position:0% +like so you sort of want to say I want + + + align:start position:0% +like so you sort of want to say I want +to like you know so that can be kind of + + align:start position:0% +to like you know so that can be kind of + + + align:start position:0% +to like you know so that can be kind of +a tricky a tricky set of issues + + align:start position:0% +a tricky a tricky set of issues + + + align:start position:0% +a tricky a tricky set of issues +um uh and the other thing is you can + + align:start position:0% +um uh and the other thing is you can + + + align:start position:0% +um uh and the other thing is you can +also get kind of gaming if you can do + + align:start position:0% +also get kind of gaming if you can do + + + align:start position:0% +also get kind of gaming if you can do +things with across cross periods you + + align:start position:0% +things with across cross periods you + + + align:start position:0% +things with across cross periods you +might you can sometimes get gaming I + + align:start position:0% +might you can sometimes get gaming I + + + align:start position:0% +might you can sometimes get gaming I +don't know if that's a really issue in + + align:start position:0% +don't know if that's a really issue in + + + align:start position:0% +don't know if that's a really issue in +in sharecropping contracts and actually + + align:start position:0% +in sharecropping contracts and actually + + + align:start position:0% +in sharecropping contracts and actually +I don't know + + align:start position:0% +I don't know + + + align:start position:0% +I don't know +of a good + + align:start position:0% +of a good + + + align:start position:0% +of a good +I'm sure there is a paper I just can't + + align:start position:0% +I'm sure there is a paper I just can't + + + align:start position:0% +I'm sure there is a paper I just can't +think of it off the top of my head that + + align:start position:0% +think of it off the top of my head that + + + align:start position:0% +think of it off the top of my head that +has taken some of the like the the + + align:start position:0% +has taken some of the like the the + + + align:start position:0% +has taken some of the like the the +homestrom you know uh linear contract + + align:start position:0% +homestrom you know uh linear contract + + + align:start position:0% +homestrom you know uh linear contract +ideas and sort of said does this you + + align:start position:0% +ideas and sort of said does this you + + + align:start position:0% +ideas and sort of said does this you +know does do these kind of gaming or + + align:start position:0% +know does do these kind of gaming or + + + align:start position:0% +know does do these kind of gaming or +other sort of issues apply to kind of + + align:start position:0% +other sort of issues apply to kind of + + + align:start position:0% +other sort of issues apply to kind of +this share of behind us I don't know the + + align:start position:0% +this share of behind us I don't know the + + + align:start position:0% +this share of behind us I don't know the +answer that question + + align:start position:0% +answer that question + + + align:start position:0% +answer that question +um yeah we'll see + + align:start position:0% + + + + align:start position:0% + +what seems a little bit strange about + + align:start position:0% +what seems a little bit strange about + + + align:start position:0% +what seems a little bit strange about +this particular setting these would be + + align:start position:0% +this particular setting these would be + + + align:start position:0% +this particular setting these would be +like + + align:start position:0% +like + + + align:start position:0% +like +how to share property contracts actually + + align:start position:0% +how to share property contracts actually + + + align:start position:0% +how to share property contracts actually +work in practice + + align:start position:0% +work in practice + + + align:start position:0% +work in practice +is that bracket does not + + align:start position:0% +is that bracket does not + + + align:start position:0% +is that bracket does not +Brad does not care at his maximizing his + + align:start position:0% +Brad does not care at his maximizing his + + + align:start position:0% +Brad does not care at his maximizing his +profits and escaping as much on what we + + align:start position:0% +profits and escaping as much on what we + + + align:start position:0% +profits and escaping as much on what we +share property as it possibly can and so + + align:start position:0% +share property as it possibly can and so + + + align:start position:0% +share property as it possibly can and so +even if the result is that if you were + + align:start position:0% +even if the result is that if you were + + + align:start position:0% +even if the result is that if you were +to increase the like portion of the + + align:start position:0% +to increase the like portion of the + + + align:start position:0% +to increase the like portion of the +output that your share properties and + + align:start position:0% +output that your share properties and + + + align:start position:0% +output that your share properties and +you + + align:start position:0% +you + + + align:start position:0% +you +there's not really a way to like impose + + align:start position:0% +there's not really a way to like impose + + + align:start position:0% +there's not really a way to like impose +that on landlords who are looking to + + align:start position:0% +that on landlords who are looking to + + + align:start position:0% +that on landlords who are looking to +extract as much as they can out of their + + align:start position:0% +extract as much as they can out of their + + + align:start position:0% +extract as much as they can out of their +contract unless + + align:start position:0% +contract unless + + + align:start position:0% +contract unless +similar to what you were saying if there + + align:start position:0% +similar to what you were saying if there + + + align:start position:0% +similar to what you were saying if there +was like something coming back where a + + align:start position:0% +was like something coming back where a + + + align:start position:0% +was like something coming back where a +couple or if your landlord is a + + align:start position:0% +couple or if your landlord is a + + + align:start position:0% +couple or if your landlord is a +government who like doesn't particularly + + align:start position:0% +government who like doesn't particularly + + + align:start position:0% +government who like doesn't particularly +care about taking + + align:start position:0% + + + + align:start position:0% + +yeah so I mean I think so my own take on + + align:start position:0% +yeah so I mean I think so my own take on + + + align:start position:0% +yeah so I mean I think so my own take on +this is I don't necessarily think + + align:start position:0% +this is I don't necessarily think + + + align:start position:0% +this is I don't necessarily think +there's an obvious policy implication of + + align:start position:0% +there's an obvious policy implication of + + + align:start position:0% +there's an obvious policy implication of +this paper because + + align:start position:0% +this paper because + + + align:start position:0% +this paper because +it doesn't actually tell us if it's more + + align:start position:0% +it doesn't actually tell us if it's more + + + align:start position:0% +it doesn't actually tell us if it's more +if it's uh you know the insurance kind + + align:start position:0% +if it's uh you know the insurance kind + + + align:start position:0% +if it's uh you know the insurance kind +of insurance issue like it doesn't tell + + align:start position:0% +of insurance issue like it doesn't tell + + + align:start position:0% +of insurance issue like it doesn't tell +us kind of it tells us there's some + + align:start position:0% +us kind of it tells us there's some + + + align:start position:0% +us kind of it tells us there's some +inefficiency going on in terms of the + + align:start position:0% +inefficiency going on in terms of the + + + align:start position:0% +inefficiency going on in terms of the +the it says that the there's some + + align:start position:0% +the it says that the there's some + + + align:start position:0% +the it says that the there's some +inefficiency going on where sort of the + + align:start position:0% +inefficiency going on where sort of the + + + align:start position:0% +inefficiency going on where sort of the +share cropping is reducing effort but it + + align:start position:0% +share cropping is reducing effort but it + + + align:start position:0% +share cropping is reducing effort but it +doesn't say it doesn't address the + + align:start position:0% +doesn't say it doesn't address the + + + align:start position:0% +doesn't say it doesn't address the +questions we talked about before but + + align:start position:0% +questions we talked about before but + + + align:start position:0% +questions we talked about before but +like why is this emerging endogenously + + align:start position:0% +like why is this emerging endogenously + + + align:start position:0% +like why is this emerging endogenously +and like + + align:start position:0% +and like + + + align:start position:0% +and like +it's in the region of that in order to + + align:start position:0% +it's in the region of that in order to + + + align:start position:0% +it's in the region of that in order to +figure out the policy answer so I think + + align:start position:0% +figure out the policy answer so I think + + + align:start position:0% +figure out the policy answer so I think +this is to me this is an important piece + + align:start position:0% +this is to me this is an important piece + + + align:start position:0% +this is to me this is an important piece +of the puzzle it says like first point + + align:start position:0% +of the puzzle it says like first point + + + align:start position:0% +of the puzzle it says like first point +is yes these contracts are are have + + align:start position:0% +is yes these contracts are are have + + + align:start position:0% +is yes these contracts are are have +efficiency consequences so that's + + align:start position:0% +efficiency consequences so that's + + + align:start position:0% +efficiency consequences so that's +actually really important because if + + align:start position:0% +actually really important because if + + + align:start position:0% +actually really important because if +they didn't have efficiency consequence + + align:start position:0% +they didn't have efficiency consequence + + + align:start position:0% +they didn't have efficiency consequence +we were just like not worry about this + + align:start position:0% +we were just like not worry about this + + + align:start position:0% +we were just like not worry about this +whole set of issues uh from an aggregate + + align:start position:0% +whole set of issues uh from an aggregate + + + align:start position:0% +whole set of issues uh from an aggregate +welfare perspective aggregate + + align:start position:0% +welfare perspective aggregate + + + align:start position:0% +welfare perspective aggregate +productivity perspective + + align:start position:0% +productivity perspective + + + align:start position:0% +productivity perspective +the fact that it does say that there's + + align:start position:0% +the fact that it does say that there's + + + align:start position:0% +the fact that it does say that there's +like efficiency consequences it says to + + align:start position:0% +like efficiency consequences it says to + + + align:start position:0% +like efficiency consequences it says to +me that well okay now when you want to + + align:start position:0% +me that well okay now when you want to + + + align:start position:0% +me that well okay now when you want to +figure out like what's driving it and if + + align:start position:0% +figure out like what's driving it and if + + + align:start position:0% +figure out like what's driving it and if +you really thought that the issue was + + align:start position:0% +you really thought that the issue was + + + align:start position:0% +you really thought that the issue was +um about insurance value is there a way + + align:start position:0% +um about insurance value is there a way + + + align:start position:0% +um about insurance value is there a way +of providing insurance that doesn't have + + align:start position:0% +of providing insurance that doesn't have + + + align:start position:0% +of providing insurance that doesn't have +the same + + align:start position:0% +the same + + + align:start position:0% +the same +um moral hazard consequences and there + + align:start position:0% +um moral hazard consequences and there + + + align:start position:0% +um moral hazard consequences and there +is a small but kind of growing + + align:start position:0% +is a small but kind of growing + + + align:start position:0% +is a small but kind of growing +literature on agricultural insurance + + align:start position:0% +literature on agricultural insurance + + + align:start position:0% +literature on agricultural insurance +issues uh which and I'll tell you + + align:start position:0% +issues uh which and I'll tell you + + + align:start position:0% +issues uh which and I'll tell you +actually the main challenge with our + + align:start position:0% +actually the main challenge with our + + + align:start position:0% +actually the main challenge with our +cultural insurance is + + align:start position:0% +cultural insurance is + + + align:start position:0% +cultural insurance is +I don't want to write because of these + + align:start position:0% +I don't want to write because of these + + + align:start position:0% +I don't want to write because of these +more Hazard issues I can't ensure your + + align:start position:0% +more Hazard issues I can't ensure your + + + align:start position:0% +more Hazard issues I can't ensure your +output otherwise you don't work so what + + align:start position:0% +output otherwise you don't work so what + + + align:start position:0% +output otherwise you don't work so what +I do is I write insurance based on your + + align:start position:0% +I do is I write insurance based on your + + + align:start position:0% +I do is I write insurance based on your +predicted output which is essentially + + align:start position:0% +predicted output which is essentially + + + align:start position:0% +predicted output which is essentially +like I write insurance based on like the + + align:start position:0% +like I write insurance based on like the + + + align:start position:0% +like I write insurance based on like the +weather for example so actually you can + + align:start position:0% +weather for example so actually you can + + + align:start position:0% +weather for example so actually you can +buy in the US or in other places you can + + align:start position:0% +buy in the US or in other places you can + + + align:start position:0% +buy in the US or in other places you can +buy + + align:start position:0% +buy + + + align:start position:0% +buy +um weather Insurance essentially so if + + align:start position:0% +um weather Insurance essentially so if + + + align:start position:0% +um weather Insurance essentially so if +it's like a direct you can buy insurance + + align:start position:0% +it's like a direct you can buy insurance + + + align:start position:0% +it's like a direct you can buy insurance +against a drought that's an exogenous + + align:start position:0% +against a drought that's an exogenous + + + align:start position:0% +against a drought that's an exogenous +event that's going to like reduce your + + align:start position:0% +event that's going to like reduce your + + + align:start position:0% +event that's going to like reduce your +output so we can ensure you to some + + align:start position:0% +output so we can ensure you to some + + + align:start position:0% +output so we can ensure you to some +degree that way the problem with those + + align:start position:0% +degree that way the problem with those + + + align:start position:0% +degree that way the problem with those +insurance contracts is the + + align:start position:0% +insurance contracts is the + + + align:start position:0% +insurance contracts is the +the thing we're ensuring is not + + align:start position:0% +the thing we're ensuring is not + + + align:start position:0% +the thing we're ensuring is not +perfectly correlated with your shock and + + align:start position:0% +perfectly correlated with your shock and + + + align:start position:0% +perfectly correlated with your shock and +so they don't provide kind of as good + + align:start position:0% +so they don't provide kind of as good + + + align:start position:0% +so they don't provide kind of as good +insurance as you might like and that + + align:start position:0% +insurance as you might like and that + + + align:start position:0% +insurance as you might like and that +that issue is what's called basis risk + + align:start position:0% +that issue is what's called basis risk + + + align:start position:0% +that issue is what's called basis risk +that sort of the thing we're ensuring is + + align:start position:0% +that sort of the thing we're ensuring is + + + align:start position:0% +that sort of the thing we're ensuring is +not perfectly correlated with with your + + align:start position:0% +not perfectly correlated with with your + + + align:start position:0% +not perfectly correlated with with your +shocks and so if you're interested in + + align:start position:0% +shocks and so if you're interested in + + + align:start position:0% +shocks and so if you're interested in +that there are some papers that sort of + + align:start position:0% +that there are some papers that sort of + + + align:start position:0% +that there are some papers that sort of +have tried to think about that but if + + align:start position:0% +have tried to think about that but if + + + align:start position:0% +have tried to think about that but if +you thought that sort of the more that + + align:start position:0% +you thought that sort of the more that + + + align:start position:0% +you thought that sort of the more that +the the issue was kind of risk aversion + + align:start position:0% +the the issue was kind of risk aversion + + + align:start position:0% +the the issue was kind of risk aversion +um then you would be kind of heading in + + align:start position:0% +um then you would be kind of heading in + + + align:start position:0% +um then you would be kind of heading in +this insurance Direction and if you got + + align:start position:0% +this insurance Direction and if you got + + + align:start position:0% +this insurance Direction and if you got +the issue with limited liability then + + align:start position:0% +the issue with limited liability then + + + align:start position:0% +the issue with limited liability then +you might head in a different direction + + align:start position:0% +you might head in a different direction + + + align:start position:0% +you might head in a different direction +of kind of like you know can we like + + align:start position:0% +of kind of like you know can we like + + + align:start position:0% +of kind of like you know can we like +basically make some transfers to people + + align:start position:0% +basically make some transfers to people + + + align:start position:0% +basically make some transfers to people +so that they're kind of don't have as + + align:start position:0% +so that they're kind of don't have as + + + align:start position:0% +so that they're kind of don't have as +limited liability constraint + + align:start position:0% +limited liability constraint + + + align:start position:0% +limited liability constraint +or can we write can we help them + + align:start position:0% +or can we write can we help them + + + align:start position:0% +or can we write can we help them +facilitate them right you know we might + + align:start position:0% +facilitate them right you know we might + + + align:start position:0% +facilitate them right you know we might +be much without limited liability of an + + align:start position:0% +be much without limited liability of an + + + align:start position:0% +be much without limited liability of an +issue we might be much more interested + + align:start position:0% +issue we might be much more interested + + + align:start position:0% +issue we might be much more interested +in writing long-term things that look + + align:start position:0% +in writing long-term things that look + + + align:start position:0% +in writing long-term things that look +more like debt contracts for example and + + align:start position:0% +more like debt contracts for example and + + + align:start position:0% +more like debt contracts for example and +facilitating that sort of thing which + + align:start position:0% +facilitating that sort of thing which + + + align:start position:0% +facilitating that sort of thing which +might not be interested in + + align:start position:0% +might not be interested in + + + align:start position:0% +might not be interested in +in other if other things are important + + align:start position:0% +in other if other things are important + + + align:start position:0% +in other if other things are important +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +oh right guys + + align:start position:0% +oh right guys + + + align:start position:0% +oh right guys +um + + align:start position:0% +um + + + align:start position:0% +um +is there a benefit to + + align:start position:0% + + + + align:start position:0% + +staggered levels of incentives + + align:start position:0% +staggered levels of incentives + + + align:start position:0% +staggered levels of incentives +um + + align:start position:0% +um + + + align:start position:0% +um +from like getting a panel if that was + + align:start position:0% +from like getting a panel if that was + + + align:start position:0% +from like getting a panel if that was +possible as opposed to uh + + align:start position:0% + + + + align:start position:0% + +uh if you're trying to like back out + + align:start position:0% +uh if you're trying to like back out + + + align:start position:0% +uh if you're trying to like back out +what like certain types of workers might + + align:start position:0% +what like certain types of workers might + + + align:start position:0% +what like certain types of workers might +be and like how those elasticities might + + align:start position:0% +be and like how those elasticities might + + + align:start position:0% +be and like how those elasticities might +differ between groups work + + align:start position:0% +differ between groups work + + + align:start position:0% +differ between groups work +perspective of the + + align:start position:0% +perspective of the + + + align:start position:0% +perspective of the +for policy implications does that not in + + align:start position:0% +for policy implications does that not in + + + align:start position:0% +for policy implications does that not in +that matter + + align:start position:0% + + + + align:start position:0% + +so I don't think + + align:start position:0% +so I don't think + + + align:start position:0% +so I don't think +so so you're saying if we had a panel if + + align:start position:0% +so so you're saying if we had a panel if + + + align:start position:0% +so so you're saying if we had a panel if +we had panel and we sort of like Get + + align:start position:0% +we had panel and we sort of like Get + + + align:start position:0% +we had panel and we sort of like Get +Like repeated observations of you so + + align:start position:0% +Like repeated observations of you so + + + align:start position:0% +Like repeated observations of you so +huge yeah so I think it would be + + align:start position:0% +huge yeah so I think it would be + + + align:start position:0% +huge yeah so I think it would be +um + + align:start position:0% +um + + + align:start position:0% +um +yes so I think if you basically found + + align:start position:0% +yes so I think if you basically found + + + align:start position:0% +yes so I think if you basically found +that everybody was the same + + align:start position:0% +that everybody was the same + + + align:start position:0% +that everybody was the same +right if there was no heterogeneity in + + align:start position:0% +right if there was no heterogeneity in + + + align:start position:0% +right if there was no heterogeneity in +people's responsiveness at different + + align:start position:0% +people's responsiveness at different + + + align:start position:0% +people's responsiveness at different +points in the contract then you might be + + align:start position:0% +points in the contract then you might be + + + align:start position:0% +points in the contract then you might be +more willing to do some of those like + + align:start position:0% +more willing to do some of those like + + + align:start position:0% +more willing to do some of those like +non-linear funky contracts + + align:start position:0% +non-linear funky contracts + + + align:start position:0% +non-linear funky contracts +so yes in that sense yes but like uh + + align:start position:0% +so yes in that sense yes but like uh + + + align:start position:0% +so yes in that sense yes but like uh +mice is strong especially if you would + + align:start position:0% +mice is strong especially if you would + + + align:start position:0% +mice is strong especially if you would +you do that you'd find heterogeneity + + align:start position:0% +you do that you'd find heterogeneity + + + align:start position:0% +you do that you'd find heterogeneity +because you started doing most things in + + align:start position:0% +because you started doing most things in + + + align:start position:0% +because you started doing most things in +life and then so I'm not sure it's a + + align:start position:0% +life and then so I'm not sure it's a + + + align:start position:0% +life and then so I'm not sure it's a +practical matter it would make a huge + + align:start position:0% +practical matter it would make a huge + + + align:start position:0% +practical matter it would make a huge +difference + + align:start position:0% + + + + align:start position:0% + +is basically estimating the IC + + align:start position:0% +is basically estimating the IC + + + align:start position:0% +is basically estimating the IC +constraint or anything that you just + + align:start position:0% +constraint or anything that you just + + + align:start position:0% +constraint or anything that you just +problem and so but then like what is + + align:start position:0% +problem and so but then like what is + + + align:start position:0% +problem and so but then like what is +optimal will depend on like a bunch of + + align:start position:0% +optimal will depend on like a bunch of + + + align:start position:0% +optimal will depend on like a bunch of +other things yep yep yep yes + + align:start position:0% +other things yep yep yep yes + + + align:start position:0% +other things yep yep yep yes +yes I like that it's exactly it's + + align:start position:0% +yes I like that it's exactly it's + + + align:start position:0% +yes I like that it's exactly it's +exactly sort of saying we're randomly + + align:start position:0% +exactly sort of saying we're randomly + + + align:start position:0% +exactly sort of saying we're randomly +we're randomly varying the contract and + + align:start position:0% +we're randomly varying the contract and + + + align:start position:0% +we're randomly varying the contract and +looking at how the agent responds and + + align:start position:0% +looking at how the agent responds and + + + align:start position:0% +looking at how the agent responds and +it's just telling us that the fact that + + align:start position:0% +it's just telling us that the fact that + + + align:start position:0% +it's just telling us that the fact that +they usually + + align:start position:0% +they usually + + + align:start position:0% +they usually +is what like it's just it's telling us + + align:start position:0% +is what like it's just it's telling us + + + align:start position:0% +is what like it's just it's telling us +that that it's important + + align:start position:0% +that that it's important + + + align:start position:0% +that that it's important +yes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +other comments + + align:start position:0% +other comments + + + align:start position:0% +other comments +yeah right he knew there existed heters + + align:start position:0% +yeah right he knew there existed heters + + + align:start position:0% +yeah right he knew there existed heters +but then the person who's giving the + + align:start position:0% +but then the person who's giving the + + + align:start position:0% +but then the person who's giving the +contract could just like uh administers + + align:start position:0% +contract could just like uh administers + + + align:start position:0% +contract could just like uh administers +tests to you by varying your contract at + + align:start position:0% +tests to you by varying your contract at + + + align:start position:0% +tests to you by varying your contract at +the start of more like sharecropping + + align:start position:0% +the start of more like sharecropping + + + align:start position:0% +the start of more like sharecropping +relationship it's making a list of your + + align:start position:0% +relationship it's making a list of your + + + align:start position:0% +relationship it's making a list of your +time + + align:start position:0% + + + + align:start position:0% + +well yes except you would need to like + + align:start position:0% +well yes except you would need to like + + + align:start position:0% +well yes except you would need to like +um find incentive compatible ways of + + align:start position:0% +um find incentive compatible ways of + + + align:start position:0% +um find incentive compatible ways of +getting that information yeah yeah so + + align:start position:0% +getting that information yeah yeah so + + + align:start position:0% +getting that information yeah yeah so +you know I'm playing a game with my + + align:start position:0% +you know I'm playing a game with my + + + align:start position:0% +you know I'm playing a game with my +landlord and I know that the answers to + + align:start position:0% +landlord and I know that the answers to + + + align:start position:0% +landlord and I know that the answers to +my game are going to affect my contract + + align:start position:0% +my game are going to affect my contract + + + align:start position:0% +my game are going to affect my contract +may affect how I play the game + + align:start position:0% +may affect how I play the game + + + align:start position:0% +may affect how I play the game +right so + + align:start position:0% +right so + + + align:start position:0% +right so +um but I do no I think you're honestly + + align:start position:0% +um but I do no I think you're honestly + + + align:start position:0% +um but I do no I think you're honestly +this question is sort of like can we + + align:start position:0% +this question is sort of like can we + + + align:start position:0% +this question is sort of like can we +find incentive compatible mechanisms for + + align:start position:0% +find incentive compatible mechanisms for + + + align:start position:0% +find incentive compatible mechanisms for +getting like better contracts I don't + + align:start position:0% +getting like better contracts I don't + + + align:start position:0% +getting like better contracts I don't +know the answer to that but maybe yes + + align:start position:0% +know the answer to that but maybe yes + + + align:start position:0% +know the answer to that but maybe yes +it was like long term enough + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah so let me let me like I keep sort + + align:start position:0% +yeah so let me let me like I keep sort + + + align:start position:0% +yeah so let me let me like I keep sort +of referring you to contract theory + + align:start position:0% +of referring you to contract theory + + + align:start position:0% +of referring you to contract theory +classes like no in all seriously these + + align:start position:0% +classes like no in all seriously these + + + align:start position:0% +classes like no in all seriously these +questions are sort of like how do I + + align:start position:0% +questions are sort of like how do I + + + align:start position:0% +questions are sort of like how do I +design contracts and how do I get you to + + align:start position:0% +design contracts and how do I get you to + + + align:start position:0% +design contracts and how do I get you to +reveal information that are going to be + + align:start position:0% +reveal information that are going to be + + + align:start position:0% +reveal information that are going to be +um how do how do I design an incentive + + align:start position:0% +um how do how do I design an incentive + + + align:start position:0% +um how do how do I design an incentive +compatible mechanism that's going to + + align:start position:0% +compatible mechanism that's going to + + + align:start position:0% +compatible mechanism that's going to +have you reveal information that's going + + align:start position:0% +have you reveal information that's going + + + align:start position:0% +have you reveal information that's going +to let me get give you a better contract + + align:start position:0% +to let me get give you a better contract + + + align:start position:0% +to let me get give you a better contract +that + + align:start position:0% +that + + + align:start position:0% +that +sort of thinking about these things + + align:start position:0% +sort of thinking about these things + + + align:start position:0% +sort of thinking about these things +these models and more if you're + + align:start position:0% +these models and more if you're + + + align:start position:0% +these models and more if you're +interested in these models in more + + align:start position:0% +interested in these models in more + + + align:start position:0% +interested in these models in more +detail like that's + + align:start position:0% +detail like that's + + + align:start position:0% +detail like that's +where we explore them + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and I'm not a contract theorist although + + align:start position:0% +and I'm not a contract theorist although + + + align:start position:0% +and I'm not a contract theorist although +I did take that class many years ago so + + align:start position:0% +I did take that class many years ago so + + + align:start position:0% +I did take that class many years ago so +I I apologize for not having like all of + + align:start position:0% +I I apologize for not having like all of + + + align:start position:0% +I I apologize for not having like all of +the complicated all the answers off the + + align:start position:0% +the complicated all the answers off the + + + align:start position:0% +the complicated all the answers off the +top of my head but but some of them + + align:start position:0% +top of my head but but some of them + + + align:start position:0% +top of my head but but some of them +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +um + + align:start position:0% +um + + + align:start position:0% +um +all right + + align:start position:0% + + + + align:start position:0% + +okay a few other things I wanted to say + + align:start position:0% +okay a few other things I wanted to say + + + align:start position:0% +okay a few other things I wanted to say +about this paper + + align:start position:0% +about this paper + + + align:start position:0% +about this paper +um + + align:start position:0% + + + + align:start position:0% + +okay first point + + align:start position:0% +okay first point + + + align:start position:0% +okay first point +is uh + + align:start position:0% +is uh + + + align:start position:0% +is uh +so this is the 75 contract versus the 50 + + align:start position:0% +so this is the 75 contract versus the 50 + + + align:start position:0% +so this is the 75 contract versus the 50 +contract okay and nothing else really + + align:start position:0% +contract okay and nothing else really + + + align:start position:0% +contract okay and nothing else really +makes a big difference so also going + + align:start position:0% +makes a big difference so also going + + + align:start position:0% +makes a big difference so also going +back to I think Aaron your comment of + + align:start position:0% +back to I think Aaron your comment of + + + align:start position:0% +back to I think Aaron your comment of +like is the risky thing like + + align:start position:0% +like is the risky thing like + + + align:start position:0% +like is the risky thing like +you know it may not be exactly the same + + align:start position:0% +you know it may not be exactly the same + + + align:start position:0% +you know it may not be exactly the same +but it's certainly not the case that + + align:start position:0% +but it's certainly not the case that + + + align:start position:0% +but it's certainly not the case that +like this contract looks these results + + align:start position:0% +like this contract looks these results + + + align:start position:0% +like this contract looks these results +look anything like those results + + align:start position:0% +look anything like those results + + + align:start position:0% +look anything like those results +right so plus also you you actually + + align:start position:0% +right so plus also you you actually + + + align:start position:0% +right so plus also you you actually +might imagine it would go the other way + + align:start position:0% +might imagine it would go the other way + + + align:start position:0% +might imagine it would go the other way +like this like you know I'm making kind + + align:start position:0% +like this like you know I'm making kind + + + align:start position:0% +like this like you know I'm making kind +of the the world I might be I'm making + + align:start position:0% +of the the world I might be I'm making + + + align:start position:0% +of the the world I might be I'm making +myself more risky that you might + + align:start position:0% +myself more risky that you might + + + align:start position:0% +myself more risky that you might +actually think of anything this could be + + align:start position:0% +actually think of anything this could be + + + align:start position:0% +actually think of anything this could be +the opposite direction you actually + + align:start position:0% +the opposite direction you actually + + + align:start position:0% +the opposite direction you actually +might make me kind of more uh + + align:start position:0% +might make me kind of more uh + + + align:start position:0% +might make me kind of more uh +conservative in some sense but anyway + + align:start position:0% +conservative in some sense but anyway + + + align:start position:0% +conservative in some sense but anyway +it's certainly like to your point like I + + align:start position:0% +it's certainly like to your point like I + + + align:start position:0% +it's certainly like to your point like I +agree with you you're right but I think + + align:start position:0% +agree with you you're right but I think + + + align:start position:0% +agree with you you're right but I think +also let like + + align:start position:0% +also let like + + + align:start position:0% +also let like +you know it's it's a little bit not + + align:start position:0% +you know it's it's a little bit not + + + align:start position:0% +you know it's it's a little bit not +necessarily like it may not be perfectly + + align:start position:0% +necessarily like it may not be perfectly + + + align:start position:0% +necessarily like it may not be perfectly +right but to first order it's not like I + + align:start position:0% +right but to first order it's not like I + + + align:start position:0% +right but to first order it's not like I +look at this and I say oh it doesn't + + align:start position:0% +look at this and I say oh it doesn't + + + align:start position:0% +look at this and I say oh it doesn't +look like it's really the riskiness it's + + align:start position:0% +look like it's really the riskiness it's + + + align:start position:0% +look like it's really the riskiness it's +kind of like + + align:start position:0% +kind of like + + + align:start position:0% +kind of like +resulting + + align:start position:0% +resulting + + + align:start position:0% +resulting +so they're just like so different + + align:start position:0% +so they're just like so different + + + align:start position:0% +so they're just like so different +um + + align:start position:0% + + + + align:start position:0% + +several of you picked up in your in your + + align:start position:0% +several of you picked up in your in your + + + align:start position:0% +several of you picked up in your in your +response notes this question of + + align:start position:0% +response notes this question of + + + align:start position:0% +response notes this question of +randomization inference + + align:start position:0% +randomization inference + + + align:start position:0% +randomization inference +okay so uh + + align:start position:0% +okay so uh + + + align:start position:0% +okay so uh +how many of you have seen randomization + + align:start position:0% +how many of you have seen randomization + + + align:start position:0% +how many of you have seen randomization +inference before yes all of you great + + align:start position:0% +inference before yes all of you great + + + align:start position:0% +inference before yes all of you great +what's right + + align:start position:0% +what's right + + + align:start position:0% +what's right +great so I won't go into that in any + + align:start position:0% +great so I won't go into that in any + + + align:start position:0% +great so I won't go into that in any +more detail + + align:start position:0% +more detail + + + align:start position:0% +more detail +um + + align:start position:0% +um + + + align:start position:0% +um +great too awesome + + align:start position:0% +great too awesome + + + align:start position:0% +great too awesome +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +you see some effects on + + align:start position:0% +you see some effects on + + + align:start position:0% +you see some effects on +um + + align:start position:0% +um + + + align:start position:0% +um +the Intensive margin of capital usage of + + align:start position:0% +the Intensive margin of capital usage of + + + align:start position:0% +the Intensive margin of capital usage of +various inputs okay so it does look like + + align:start position:0% +various inputs okay so it does look like + + + align:start position:0% +various inputs okay so it does look like +some input so I do use more inputs + + align:start position:0% +some input so I do use more inputs + + + align:start position:0% +some input so I do use more inputs +um + + align:start position:0% +um + + + align:start position:0% +um +you also see some uh impacts on + + align:start position:0% +you also see some uh impacts on + + + align:start position:0% +you also see some uh impacts on +unpaid labor like family labor some of + + align:start position:0% +unpaid labor like family labor some of + + + align:start position:0% +unpaid labor like family labor some of +you have questions of kind of what this + + align:start position:0% +you have questions of kind of what this + + + align:start position:0% +you have questions of kind of what this +is like I think the idea is like we have + + align:start position:0% +is like I think the idea is like we have + + + align:start position:0% +is like I think the idea is like we have +lots of people in the household who also + + align:start position:0% +lots of people in the household who also + + + align:start position:0% +lots of people in the household who also +are kind of working on the farm and I'll + + align:start position:0% +are kind of working on the farm and I'll + + + align:start position:0% +are kind of working on the farm and I'll +talk about I'm going to talk a lot about + + align:start position:0% +talk about I'm going to talk a lot about + + + align:start position:0% +talk about I'm going to talk a lot about +um diff you know unpaid versus paid + + align:start position:0% +um diff you know unpaid versus paid + + + align:start position:0% +um diff you know unpaid versus paid +labor in the labor section so let me not + + align:start position:0% +labor in the labor section so let me not + + + align:start position:0% +labor in the labor section so let me not +answer the questions of kind of what do + + align:start position:0% +answer the questions of kind of what do + + + align:start position:0% +answer the questions of kind of what do +we mean about paid in unpaid labor now + + align:start position:0% +we mean about paid in unpaid labor now + + + align:start position:0% +we mean about paid in unpaid labor now +but like let me defer that to the + + align:start position:0% +but like let me defer that to the + + + align:start position:0% +but like let me defer that to the +there's a paper by Dan Benjamin that I'm + + align:start position:0% +there's a paper by Dan Benjamin that I'm + + + align:start position:0% +there's a paper by Dan Benjamin that I'm +going to talk about in like a lot of + + align:start position:0% +going to talk about in like a lot of + + + align:start position:0% +going to talk about in like a lot of +detail in like the first labor lecture + + align:start position:0% +detail in like the first labor lecture + + + align:start position:0% +detail in like the first labor lecture +which is going to like think about this + + align:start position:0% +which is going to like think about this + + + align:start position:0% +which is going to like think about this +issue like like why do we have why is + + align:start position:0% +issue like like why do we have why is + + + align:start position:0% +issue like like why do we have why is +there a difference actually between why + + align:start position:0% +there a difference actually between why + + + align:start position:0% +there a difference actually between why +might this respond and this not respond + + align:start position:0% +might this respond and this not respond + + + align:start position:0% +might this respond and this not respond +is like an enormous literature on that + + align:start position:0% +is like an enormous literature on that + + + align:start position:0% +is like an enormous literature on that +question and I'm going to talk about + + align:start position:0% +question and I'm going to talk about + + + align:start position:0% +question and I'm going to talk about +that I'm just going to push that over + + align:start position:0% +that I'm just going to push that over + + + align:start position:0% +that I'm just going to push that over +the land lecture okay but would you see + + align:start position:0% +the land lecture okay but would you see + + + align:start position:0% +the land lecture okay but would you see +that + + align:start position:0% +that + + + align:start position:0% +that +and the the third thing + + align:start position:0% +and the the third thing + + + align:start position:0% +and the the third thing +um we see is we see a change in the kind + + align:start position:0% +um we see is we see a change in the kind + + + align:start position:0% +um we see is we see a change in the kind +of crop so we see like you know Maize + + align:start position:0% +of crop so we see like you know Maize + + + align:start position:0% +of crop so we see like you know Maize +goes up and and tomatoes go up and I + + align:start position:0% +goes up and and tomatoes go up and I + + + align:start position:0% +goes up and and tomatoes go up and I +guess peanuts I think can go up with + + align:start position:0% +guess peanuts I think can go up with + + + align:start position:0% +guess peanuts I think can go up with +some of those specifications and you + + align:start position:0% +some of those specifications and you + + + align:start position:0% +some of those specifications and you +know they argue that sort of beans are + + align:start position:0% +know they argue that sort of beans are + + + align:start position:0% +know they argue that sort of beans are +kind of a safer crop on this contest the + + align:start position:0% +kind of a safer crop on this contest the + + + align:start position:0% +kind of a safer crop on this contest the +other ones are more whiskey crops and so + + align:start position:0% +other ones are more whiskey crops and so + + + align:start position:0% +other ones are more whiskey crops and so +I take kind of these more high-risk High + + align:start position:0% +I take kind of these more high-risk High + + + align:start position:0% +I take kind of these more high-risk High +return kind of kind of + + align:start position:0% +return kind of kind of + + + align:start position:0% +return kind of kind of +crop um which is not obvious + + align:start position:0% +crop um which is not obvious + + + align:start position:0% +crop um which is not obvious +but you know one thing I just wanted to + + align:start position:0% +but you know one thing I just wanted to + + + align:start position:0% +but you know one thing I just wanted to +point out was that the + + align:start position:0% +point out was that the + + + align:start position:0% +point out was that the +the more Hazard model had + + align:start position:0% +the more Hazard model had + + + align:start position:0% +the more Hazard model had +like kind of had this unobservable or at + + align:start position:0% +like kind of had this unobservable or at + + + align:start position:0% +like kind of had this unobservable or at +least non-contractable effort thing + + align:start position:0% +least non-contractable effort thing + + + align:start position:0% +least non-contractable effort thing +going on + + align:start position:0% +going on + + + align:start position:0% +going on +and I'm I wanted to ask + + align:start position:0% +and I'm I wanted to ask + + + align:start position:0% +and I'm I wanted to ask +what you thought in terms of if you + + align:start position:0% +what you thought in terms of if you + + + align:start position:0% +what you thought in terms of if you +think about the results + + align:start position:0% +think about the results + + + align:start position:0% +think about the results +like is it contract is the thing is the + + align:start position:0% +like is it contract is the thing is the + + + align:start position:0% +like is it contract is the thing is the +thing that's changing kind of + + align:start position:0% +thing that's changing kind of + + + align:start position:0% +thing that's changing kind of +contractable or non-contractable + + align:start position:0% + + + + align:start position:0% + +like you're sort of not trying to map + + align:start position:0% +like you're sort of not trying to map + + + align:start position:0% +like you're sort of not trying to map +the sort of results to the theory + + align:start position:0% + + + + align:start position:0% + +what do you think + + align:start position:0% +what do you think + + + align:start position:0% +what do you think +yes + + align:start position:0% + + + + align:start position:0% + +it seems like it right like seems like + + align:start position:0% +it seems like it right like seems like + + + align:start position:0% +it seems like it right like seems like +kind of crop is pretty darn observable + + align:start position:0% +kind of crop is pretty darn observable + + + align:start position:0% +kind of crop is pretty darn observable +right like are you planting like corn + + align:start position:0% +right like are you planting like corn + + + align:start position:0% +right like are you planting like corn +are you planting peanuts or you're + + align:start position:0% +are you planting peanuts or you're + + + align:start position:0% +are you planting peanuts or you're +planting beans like I can it's like + + align:start position:0% +planting beans like I can it's like + + + align:start position:0% +planting beans like I can it's like +pretty easy to sort of like + + align:start position:0% +pretty easy to sort of like + + + align:start position:0% +pretty easy to sort of like +figure out yeah how about some other + + align:start position:0% +figure out yeah how about some other + + + align:start position:0% +figure out yeah how about some other +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +maybe those are harder so to me in some + + align:start position:0% +maybe those are harder so to me in some + + + align:start position:0% +maybe those are harder so to me in some +sense one of the things that I think is + + align:start position:0% +sense one of the things that I think is + + + align:start position:0% +sense one of the things that I think is +a little surprising here is that like at + + align:start position:0% +a little surprising here is that like at + + + align:start position:0% +a little surprising here is that like at +least and they sort of do this + + align:start position:0% +least and they sort of do this + + + align:start position:0% +least and they sort of do this +decomposition thing right and they sort + + align:start position:0% +decomposition thing right and they sort + + + align:start position:0% +decomposition thing right and they sort +of about half of it is um + + align:start position:0% +of about half of it is um + + + align:start position:0% +of about half of it is um +uh actually sorry + + align:start position:0% +uh actually sorry + + + align:start position:0% +uh actually sorry +what's observable what's not observable + + align:start position:0% +what's observable what's not observable + + + align:start position:0% +what's observable what's not observable +let me not answer that but they sort of + + align:start position:0% +let me not answer that but they sort of + + + align:start position:0% +let me not answer that but they sort of +say what what are the obvious sort of + + align:start position:0% +say what what are the obvious sort of + + + align:start position:0% +say what what are the obvious sort of +the inputs of the production function + + align:start position:0% +the inputs of the production function + + + align:start position:0% +the inputs of the production function +like land labor capital is about half + + align:start position:0% +like land labor capital is about half + + + align:start position:0% +like land labor capital is about half +and crop choice is going to the other + + align:start position:0% +and crop choice is going to the other + + + align:start position:0% +and crop choice is going to the other +half + + align:start position:0% +half + + + align:start position:0% +half +to me actually crop Choice seems kind of + + align:start position:0% +to me actually crop Choice seems kind of + + + align:start position:0% +to me actually crop Choice seems kind of +the most observable or uncontractable of + + align:start position:0% +the most observable or uncontractable of + + + align:start position:0% +the most observable or uncontractable of +all this so it's not that that's a bit + + align:start position:0% +all this so it's not that that's a bit + + + align:start position:0% +all this so it's not that that's a bit +of a puzzle actually right like why + + align:start position:0% +of a puzzle actually right like why + + + align:start position:0% +of a puzzle actually right like why +can't we solve some of these problems by + + align:start position:0% +can't we solve some of these problems by + + + align:start position:0% +can't we solve some of these problems by +sort of Contracting on crop Choice + + align:start position:0% +sort of Contracting on crop Choice + + + align:start position:0% +sort of Contracting on crop Choice +um from compared to the model I think + + align:start position:0% +um from compared to the model I think + + + align:start position:0% +um from compared to the model I think +it's sort of a + + align:start position:0% +it's sort of a + + + align:start position:0% +it's sort of a +interesting question + + align:start position:0% +interesting question + + + align:start position:0% +interesting question +um + + align:start position:0% + + + + align:start position:0% + +other comments + + align:start position:0% +other comments + + + align:start position:0% +other comments +any other comments on that paper before + + align:start position:0% +any other comments on that paper before + + + align:start position:0% +any other comments on that paper before +I kind of move on yeah + + align:start position:0% + + + + align:start position:0% + +what's right + + align:start position:0% + + + + align:start position:0% + +in some ways but just because of it I + + align:start position:0% +in some ways but just because of it I + + + align:start position:0% +in some ways but just because of it I +don't know like the sharecropic + + align:start position:0% +don't know like the sharecropic + + + align:start position:0% +don't know like the sharecropic +contracts sometimes they're literally + + align:start position:0% +contracts sometimes they're literally + + + align:start position:0% +contracts sometimes they're literally +paid in kind + + align:start position:0% +paid in kind + + + align:start position:0% +paid in kind +um + + align:start position:0% +um + + + align:start position:0% +um +you know like literally like certainly + + align:start position:0% +you know like literally like certainly + + + align:start position:0% +you know like literally like certainly +I've seen examples where like you know + + align:start position:0% +I've seen examples where like you know + + + align:start position:0% +I've seen examples where like you know +you literally deliver like you know x x + + align:start position:0% +you literally deliver like you know x x + + + align:start position:0% +you literally deliver like you know x x +bushels of rice and then it's pretty + + align:start position:0% +bushels of rice and then it's pretty + + + align:start position:0% +bushels of rice and then it's pretty +observable kind of what the crop was + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +I think in general we want to monitor + + align:start position:0% +I think in general we want to monitor + + + align:start position:0% +I think in general we want to monitor +what the output is because in order to + + align:start position:0% +what the output is because in order to + + + align:start position:0% +what the output is because in order to +figure out the half so like I think that + + align:start position:0% +figure out the half so like I think that + + + align:start position:0% +figure out the half so like I think that +they pretty got permission yeah gosh + + align:start position:0% +they pretty got permission yeah gosh + + + align:start position:0% +they pretty got permission yeah gosh +cheating would have been nice to measure + + align:start position:0% +cheating would have been nice to measure + + + align:start position:0% +cheating would have been nice to measure +his preferences just directly + + align:start position:0% +his preferences just directly + + + align:start position:0% +his preferences just directly +I think that would have been interesting + + align:start position:0% +I think that would have been interesting + + + align:start position:0% +I think that would have been interesting +in some sense the the the paper although + + align:start position:0% +in some sense the the the paper although + + + align:start position:0% +in some sense the the the paper although +going to the previous point the paper is + + align:start position:0% +going to the previous point the paper is + + + align:start position:0% +going to the previous point the paper is +really about kind of the responsiveness + + align:start position:0% +really about kind of the responsiveness + + + align:start position:0% +really about kind of the responsiveness +to the contract it's about the IC + + align:start position:0% +to the contract it's about the IC + + + align:start position:0% +to the contract it's about the IC +constraint which doesn't really depend + + align:start position:0% +constraint which doesn't really depend + + + align:start position:0% +constraint which doesn't really depend +on your risk preferences as much + + align:start position:0% +on your risk preferences as much + + + align:start position:0% +on your risk preferences as much +right so if it was about if this was a + + align:start position:0% +right so if it was about if this was a + + + align:start position:0% +right so if it was about if this was a +paper about X ante + + align:start position:0% +paper about X ante + + + align:start position:0% +paper about X ante +what would be the optimal contract then + + align:start position:0% +what would be the optimal contract then + + + align:start position:0% +what would be the optimal contract then +for sure that seems really important + + align:start position:0% +for sure that seems really important + + + align:start position:0% +for sure that seems really important +uh it's it's not obvious it's not as + + align:start position:0% +uh it's it's not obvious it's not as + + + align:start position:0% +uh it's it's not obvious it's not as +obvious to me how how important that is + + align:start position:0% +obvious to me how how important that is + + + align:start position:0% +obvious to me how how important that is +given this is kind of about how the + + align:start position:0% +given this is kind of about how the + + + align:start position:0% +given this is kind of about how the +agent is responding you see what I'm + + align:start position:0% +agent is responding you see what I'm + + + align:start position:0% +agent is responding you see what I'm +saying + + align:start position:0% + + + + align:start position:0% + +I mean it's relevant vis-a-b they're + + align:start position:0% +I mean it's relevant vis-a-b they're + + + align:start position:0% +I mean it's relevant vis-a-b they're +doing it sort of the other way around by + + align:start position:0% +doing it sort of the other way around by + + + align:start position:0% +doing it sort of the other way around by +sort of making the contract is obviously + + align:start position:0% +sort of making the contract is obviously + + + align:start position:0% +sort of making the contract is obviously +more risky + + align:start position:0% +more risky + + + align:start position:0% +more risky +but that so you're right yes yes this + + align:start position:0% +but that so you're right yes yes this + + + align:start position:0% +but that so you're right yes yes this +contract does change the amount of risk + + align:start position:0% +contract does change the amount of risk + + + align:start position:0% +contract does change the amount of risk +they're exposed to but so so I do I mean + + align:start position:0% +they're exposed to but so so I do I mean + + + align:start position:0% +they're exposed to but so so I do I mean +it is kind of relevant but if we think + + align:start position:0% +it is kind of relevant but if we think + + + align:start position:0% +it is kind of relevant but if we think +back to kind of why do we care about + + align:start position:0% +back to kind of why do we care about + + + align:start position:0% +back to kind of why do we care about +risk aversion so much and all the models + + align:start position:0% +risk aversion so much and all the models + + + align:start position:0% +risk aversion so much and all the models +we went through today it was actually it + + align:start position:0% +we went through today it was actually it + + + align:start position:0% +we went through today it was actually it +was more of vis-a-vis the like the + + align:start position:0% +was more of vis-a-vis the like the + + + align:start position:0% +was more of vis-a-vis the like the +economy contract choice not about the + + align:start position:0% +economy contract choice not about the + + + align:start position:0% +economy contract choice not about the +sort of the IC constraint and I I liked + + align:start position:0% +sort of the IC constraint and I I liked + + + align:start position:0% +sort of the IC constraint and I I liked +whoever whoever sort of framed this is + + align:start position:0% +whoever whoever sort of framed this is + + + align:start position:0% +whoever whoever sort of framed this is +sort of saying this is about this is the + + align:start position:0% +sort of saying this is about this is the + + + align:start position:0% +sort of saying this is about this is the +paper with the IC constraint and sort of + + align:start position:0% +paper with the IC constraint and sort of + + + align:start position:0% +paper with the IC constraint and sort of +I think that that's right and the risk + + align:start position:0% +I think that that's right and the risk + + + align:start position:0% +I think that that's right and the risk +aversion yes I mean it does sort of + + align:start position:0% +aversion yes I mean it does sort of + + + align:start position:0% +aversion yes I mean it does sort of +matter there but but much less + + align:start position:0% + + + + align:start position:0% + +okay other questions we're basically out + + align:start position:0% +okay other questions we're basically out + + + align:start position:0% +okay other questions we're basically out +of time + + align:start position:0% +of time + + + align:start position:0% +of time +okay so we'll stop here and I'll pick up + + align:start position:0% +okay so we'll stop here and I'll pick up + + + align:start position:0% +okay so we'll stop here and I'll pick up +on Monday with the second half of this + + align:start position:0% +on Monday with the second half of this + + + align:start position:0% +on Monday with the second half of this +stuff which is all going to be talking + + align:start position:0% +stuff which is all going to be talking + + + align:start position:0% +stuff which is all going to be talking +about + + align:start position:0% +about + + + align:start position:0% +about +um + + align:start position:0% +um + + + align:start position:0% +um +primarily going to talk about + + align:start position:0% +primarily going to talk about + + + align:start position:0% +primarily going to talk about +um land tenure and I'll talk a little + + align:start position:0% +um land tenure and I'll talk a little + + + align:start position:0% +um land tenure and I'll talk a little +bit about some of the Land Reform papers + + align:start position:0% +bit about some of the Land Reform papers + + + align:start position:0% +bit about some of the Land Reform papers +uh just very briefly and then I'm mostly + + align:start position:0% +uh just very briefly and then I'm mostly + + + align:start position:0% +uh just very briefly and then I'm mostly +going to talk about sort of security + + align:start position:0% +going to talk about sort of security + + + align:start position:0% +going to talk about sort of security +property rights and investment decisions + + align:start position:0% +property rights and investment decisions + + + align:start position:0% +property rights and investment decisions +like that okay I'll see you all on + + align:start position:0% +like that okay I'll see you all on + + + align:start position:0% +like that okay I'll see you all on +Monday \ No newline at end of file diff --git a/cZAM2Co3tzo.txt b/cZAM2Co3tzo.txt new file mode 100644 index 0000000000000000000000000000000000000000..817e1ec37349f991937087152d2a9d12928e7b1b --- /dev/null +++ b/cZAM2Co3tzo.txt @@ -0,0 +1,211 @@ +align:start position:0% + +so during class I like to take a few + + align:start position:0% +so during class I like to take a few + + + align:start position:0% +so during class I like to take a few +minutes of break so so that that will + + align:start position:0% +minutes of break so so that that will + + + align:start position:0% +minutes of break so so that that will +allow the students to take some rest + + align:start position:0% +allow the students to take some rest + + + align:start position:0% +allow the students to take some rest +because when you ready the country is so + + align:start position:0% +because when you ready the country is so + + + align:start position:0% +because when you ready the country is so +intense such that people it takes some + + align:start position:0% +intense such that people it takes some + + + align:start position:0% +intense such that people it takes some +time for the students to actually digest + + align:start position:0% +time for the students to actually digest + + + align:start position:0% +time for the students to actually digest +and to understand the concepts covered + + align:start position:0% +and to understand the concepts covered + + + align:start position:0% +and to understand the concepts covered +in the first part of the lecture and + + align:start position:0% +in the first part of the lecture and + + + align:start position:0% +in the first part of the lecture and +also it gives them an opportunity to + + align:start position:0% +also it gives them an opportunity to + + + align:start position:0% +also it gives them an opportunity to +interact with me and that usually during + + align:start position:0% +interact with me and that usually during + + + align:start position:0% +interact with me and that usually during +the break they bring a lot of questions + + align:start position:0% +the break they bring a lot of questions + + + align:start position:0% +the break they bring a lot of questions +which we didn't anticipate before there + + align:start position:0% +which we didn't anticipate before there + + + align:start position:0% +which we didn't anticipate before there +are many many questions about + + align:start position:0% +are many many questions about + + + align:start position:0% +are many many questions about +mathematics and also physics concepts + + align:start position:0% +mathematics and also physics concepts + + + align:start position:0% +mathematics and also physics concepts +here you have del square e right and the + + align:start position:0% +here you have del square e right and the + + + align:start position:0% +here you have del square e right and the +term square you have one two three turn + + align:start position:0% +term square you have one two three turn + + + align:start position:0% +term square you have one two three turn +three operators and you are good you if + + align:start position:0% +three operators and you are good you if + + + align:start position:0% +three operators and you are good you if +you write everything explicitly so + + align:start position:0% +you write everything explicitly so + + + align:start position:0% +you write everything explicitly so +basically you this operator is going to + + align:start position:0% +basically you this operator is going to + + + align:start position:0% +basically you this operator is going to +be operating on e x ey + ZZ and we can + + align:start position:0% +be operating on e x ey + ZZ and we can + + + align:start position:0% +be operating on e x ey + ZZ and we can +actually solve them during the class and + + align:start position:0% +actually solve them during the class and + + + align:start position:0% +actually solve them during the class and +I can even cover part of the the + + align:start position:0% +I can even cover part of the the + + + align:start position:0% +I can even cover part of the the +question asked during the break so that + + align:start position:0% +question asked during the break so that + + + align:start position:0% +question asked during the break so that +everybody actually can benefit from + + align:start position:0% +everybody actually can benefit from + + + align:start position:0% +everybody actually can benefit from +those interesting questions people + + align:start position:0% +those interesting questions people + + + align:start position:0% +those interesting questions people +before I should bring up during the + + align:start position:0% +before I should bring up during the + + + align:start position:0% +before I should bring up during the +break \ No newline at end of file diff --git a/cvBHoCAUkD4.txt b/cvBHoCAUkD4.txt new file mode 100644 index 0000000000000000000000000000000000000000..9500432c541d20acb3740873432ee787bef07515 --- /dev/null +++ b/cvBHoCAUkD4.txt @@ -0,0 +1,9663 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +yeah so yeah I plan to split it in two + + align:start position:0% +yeah so yeah I plan to split it in two + + + align:start position:0% +yeah so yeah I plan to split it in two +parts so the first part is about + + align:start position:0% +parts so the first part is about + + + align:start position:0% +parts so the first part is about +ordinary differential equations so just + + align:start position:0% +ordinary differential equations so just + + + align:start position:0% +ordinary differential equations so just +a quick recap button ordinary + + align:start position:0% +a quick recap button ordinary + + + align:start position:0% +a quick recap button ordinary +differential equation actually is and + + align:start position:0% +differential equation actually is and + + + align:start position:0% +differential equation actually is and +then we go into this kind of sensitivity + + align:start position:0% +then we go into this kind of sensitivity + + + align:start position:0% +then we go into this kind of sensitivity +analysis so how to compute the + + align:start position:0% +analysis so how to compute the + + + align:start position:0% +analysis so how to compute the +derivatives of solutions of ordinary + + align:start position:0% +derivatives of solutions of ordinary + + + align:start position:0% +derivatives of solutions of ordinary +differential equations and specifically + + align:start position:0% +differential equations and specifically + + + align:start position:0% +differential equations and specifically +we'll pick out one very important of + + align:start position:0% +we'll pick out one very important of + + + align:start position:0% +we'll pick out one very important of +these methods + + align:start position:0% + + + + align:start position:0% + +so yeah ordinary differential equation + + align:start position:0% +so yeah ordinary differential equation + + + align:start position:0% +so yeah ordinary differential equation +is basically described by this kind of + + align:start position:0% +is basically described by this kind of + + + align:start position:0% +is basically described by this kind of +initial value problem where we have + + align:start position:0% +initial value problem where we have + + + align:start position:0% +initial value problem where we have +um the state at a given initial time t 0 + + align:start position:0% +um the state at a given initial time t 0 + + + align:start position:0% +um the state at a given initial time t 0 +is equal to u0 and then the Dynamics of + + align:start position:0% +is equal to u0 and then the Dynamics of + + + align:start position:0% +is equal to u0 and then the Dynamics of +this state is described by this kind of + + align:start position:0% +this state is described by this kind of + + + align:start position:0% +this state is described by this kind of +time Evolution so we have that the + + align:start position:0% +time Evolution so we have that the + + + align:start position:0% +time Evolution so we have that the +derivative of U is the time derivative + + align:start position:0% +derivative of U is the time derivative + + + align:start position:0% +derivative of U is the time derivative +of U is equal to this function f that + + align:start position:0% +of U is equal to this function f that + + + align:start position:0% +of U is equal to this function f that +can depend on time on the state itself + + align:start position:0% +can depend on time on the state itself + + + align:start position:0% +can depend on time on the state itself +and on some parameters p + + align:start position:0% +and on some parameters p + + + align:start position:0% +and on some parameters p +and the first natural question to ask is + + align:start position:0% +and the first natural question to ask is + + + align:start position:0% +and the first natural question to ask is +basically how do we solve such an ode + + align:start position:0% +basically how do we solve such an ode + + + align:start position:0% +basically how do we solve such an ode +and let's say the probably simplest ode + + align:start position:0% +and let's say the probably simplest ode + + + align:start position:0% +and let's say the probably simplest ode +I could imagine basically is one of a + + align:start position:0% +I could imagine basically is one of a + + + align:start position:0% +I could imagine basically is one of a +Free Falling particle or ball which is + + align:start position:0% +Free Falling particle or ball which is + + + align:start position:0% +Free Falling particle or ball which is +described by + + align:start position:0% +described by + + + align:start position:0% +described by +probably have all seen this + + align:start position:0% +probably have all seen this + + + align:start position:0% +probably have all seen this +um by Newton's law something like the + + align:start position:0% +um by Newton's law something like the + + + align:start position:0% +um by Newton's law something like the +acceleration is equal to minus the + + align:start position:0% +acceleration is equal to minus the + + + align:start position:0% +acceleration is equal to minus the +gravitational constant + + align:start position:0% +gravitational constant + + + align:start position:0% +gravitational constant +and for these kind of easy ordinary + + align:start position:0% +and for these kind of easy ordinary + + + align:start position:0% +and for these kind of easy ordinary +differential equations right we can + + align:start position:0% +differential equations right we can + + + align:start position:0% +differential equations right we can +solve that analytically so we simply + + align:start position:0% +solve that analytically so we simply + + + align:start position:0% +solve that analytically so we simply +integrate that equation twice right so + + align:start position:0% +integrate that equation twice right so + + + align:start position:0% +integrate that equation twice right so +we have that + + align:start position:0% +we have that + + + align:start position:0% +we have that +Z Prime is equal to + + align:start position:0% +Z Prime is equal to + + + align:start position:0% +Z Prime is equal to +some offset minus G + + align:start position:0% +some offset minus G + + + align:start position:0% +some offset minus G +T minus + + align:start position:0% +T minus + + + align:start position:0% +T minus +g0 and then we could integrate it a + + align:start position:0% +g0 and then we could integrate it a + + + align:start position:0% +g0 and then we could integrate it a +second time and we get like the full + + align:start position:0% +second time and we get like the full + + + align:start position:0% +second time and we get like the full +analytical solution of the + + align:start position:0% +analytical solution of the + + + align:start position:0% +analytical solution of the +height in that case + + align:start position:0% +height in that case + + + align:start position:0% +height in that case +um with respect to to time + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +here on the slide I did already + + align:start position:0% +here on the slide I did already + + + align:start position:0% +here on the slide I did already +something that's very meaningful like to + + align:start position:0% +something that's very meaningful like to + + + align:start position:0% +something that's very meaningful like to +solve Odes numerically and that's like + + align:start position:0% +solve Odes numerically and that's like + + + align:start position:0% +solve Odes numerically and that's like +we want to bring down this kind of + + align:start position:0% +we want to bring down this kind of + + + align:start position:0% +we want to bring down this kind of +Odes which are sometimes described like + + align:start position:0% +Odes which are sometimes described like + + + align:start position:0% +Odes which are sometimes described like +with second order derivatives to like + + align:start position:0% +with second order derivatives to like + + + align:start position:0% +with second order derivatives to like +just first order derivatives and the + + align:start position:0% +just first order derivatives and the + + + align:start position:0% +just first order derivatives and the +basic trick is to introduce this + + align:start position:0% +basic trick is to introduce this + + + align:start position:0% +basic trick is to introduce this +additional variable V right so the + + align:start position:0% +additional variable V right so the + + + align:start position:0% +additional variable V right so the +Velocity in that case which can be + + align:start position:0% +Velocity in that case which can be + + + align:start position:0% +Velocity in that case which can be +written as right so + + align:start position:0% +written as right so + + + align:start position:0% +written as right so +V of T is equal to + + align:start position:0% +V of T is equal to + + + align:start position:0% +V of T is equal to +DZ + + align:start position:0% +DZ + + + align:start position:0% +DZ +t + + align:start position:0% +t + + + align:start position:0% +t +t + + align:start position:0% +t + + + align:start position:0% +t +okay so for that kind of + + align:start position:0% +okay so for that kind of + + + align:start position:0% +okay so for that kind of +ode we know the analytical solution and + + align:start position:0% +ode we know the analytical solution and + + + align:start position:0% +ode we know the analytical solution and +it's basically easy to solve now coming + + align:start position:0% +it's basically easy to solve now coming + + + align:start position:0% +it's basically easy to solve now coming +back to the more General case + + align:start position:0% +back to the more General case + + + align:start position:0% +back to the more General case +where we have some + + align:start position:0% +where we have some + + + align:start position:0% +where we have some +nice function f but like solving for the + + align:start position:0% +nice function f but like solving for the + + + align:start position:0% +nice function f but like solving for the +analytical solution is tough right + + align:start position:0% +analytical solution is tough right + + + align:start position:0% +analytical solution is tough right +because so in integrating is already + + align:start position:0% +because so in integrating is already + + + align:start position:0% +because so in integrating is already +tough in solving these kind of initial + + align:start position:0% +tough in solving these kind of initial + + + align:start position:0% +tough in solving these kind of initial +value problems is even tougher we can + + align:start position:0% +value problems is even tougher we can + + + align:start position:0% +value problems is even tougher we can +fall back to some numerical routines + + align:start position:0% +fall back to some numerical routines + + + align:start position:0% +fall back to some numerical routines +basically to solve it + + align:start position:0% +basically to solve it + + + align:start position:0% +basically to solve it +and the easiest numerical routine is + + align:start position:0% +and the easiest numerical routine is + + + align:start position:0% +and the easiest numerical routine is +called Euler solver where we and + + align:start position:0% +called Euler solver where we and + + + align:start position:0% +called Euler solver where we and +probably all of us could have come up + + align:start position:0% +probably all of us could have come up + + + align:start position:0% +probably all of us could have come up +with that like by ourselves so we simply + + align:start position:0% +with that like by ourselves so we simply + + + align:start position:0% +with that like by ourselves so we simply +discretize time so we introduced this TN + + align:start position:0% +discretize time so we introduced this TN + + + align:start position:0% +discretize time so we introduced this TN +discrete time steps of our solution and + + align:start position:0% +discrete time steps of our solution and + + + align:start position:0% +discrete time steps of our solution and +then if we plugged it into the + + align:start position:0% +then if we plugged it into the + + + align:start position:0% +then if we plugged it into the +definition of the derivative we get + + align:start position:0% +definition of the derivative we get + + + align:start position:0% +definition of the derivative we get +something like this finite difference + + align:start position:0% +something like this finite difference + + + align:start position:0% +something like this finite difference +equations so right if we see here The Bu + + align:start position:0% +equations so right if we see here The Bu + + + align:start position:0% +equations so right if we see here The Bu +DT would be u n plus one at the so + + align:start position:0% +DT would be u n plus one at the so + + + align:start position:0% +DT would be u n plus one at the so +that's basically the state at the time t + + align:start position:0% +that's basically the state at the time t + + + align:start position:0% +that's basically the state at the time t +n plus 1 minus the state at the time t n + + align:start position:0% +n plus 1 minus the state at the time t n + + + align:start position:0% +n plus 1 minus the state at the time t n +divided by delta T and if we bring the + + align:start position:0% +divided by delta T and if we bring the + + + align:start position:0% +divided by delta T and if we bring the +delta T and the state to the other side + + align:start position:0% +delta T and the state to the other side + + + align:start position:0% +delta T and the state to the other side +we get this explicit Euler method + + align:start position:0% +we get this explicit Euler method + + + align:start position:0% +we get this explicit Euler method +last week we talked about client + + align:start position:0% +last week we talked about client + + + align:start position:0% +last week we talked about client +difference approximation so this is this + + align:start position:0% +difference approximation so this is this + + + align:start position:0% +difference approximation so this is this +is exactly taking that derivative and + + align:start position:0% +is exactly taking that derivative and + + + align:start position:0% +is exactly taking that derivative and +making a forward difference + + align:start position:0% +making a forward difference + + + align:start position:0% +making a forward difference +approximation yeah + + align:start position:0% +approximation yeah + + + align:start position:0% +approximation yeah +yeah exactly and you can have + + align:start position:0% +yeah exactly and you can have + + + align:start position:0% +yeah exactly and you can have +more sophisticated methods of course + + align:start position:0% +more sophisticated methods of course + + + align:start position:0% +more sophisticated methods of course +like to solve your ODS but for the rest + + align:start position:0% +like to solve your ODS but for the rest + + + align:start position:0% +like to solve your ODS but for the rest +of today it's basically enough to just + + align:start position:0% +of today it's basically enough to just + + + align:start position:0% +of today it's basically enough to just +think of we if we don't know the + + align:start position:0% +think of we if we don't know the + + + align:start position:0% +think of we if we don't know the +analytical solution we can use some + + align:start position:0% +analytical solution we can use some + + + align:start position:0% +analytical solution we can use some +numerical routine to solve for the state + + align:start position:0% +numerical routine to solve for the state + + + align:start position:0% +numerical routine to solve for the state +as a function of time + + align:start position:0% +as a function of time + + + align:start position:0% +as a function of time +and yeah actually I wanted to implement + + align:start position:0% +and yeah actually I wanted to implement + + + align:start position:0% +and yeah actually I wanted to implement +that very quickly with you like for the + + align:start position:0% +that very quickly with you like for the + + + align:start position:0% +that very quickly with you like for the +case of the Free Falling + + align:start position:0% + + + + align:start position:0% + +um well so like for that kind of old OD + + align:start position:0% + + + + align:start position:0% + +so lets you find some + + align:start position:0% +so lets you find some + + + align:start position:0% +so lets you find some +initial height some kind of um initial + + align:start position:0% +initial height some kind of um initial + + + align:start position:0% +initial height some kind of um initial +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +the gravitational constant + + align:start position:0% +the gravitational constant + + + align:start position:0% +the gravitational constant +and + + align:start position:0% +and + + + align:start position:0% +and +well maybe let's + + align:start position:0% +well maybe let's + + + align:start position:0% +well maybe let's +say that's basically our parameter + + align:start position:0% +say that's basically our parameter + + + align:start position:0% +say that's basically our parameter +G + + align:start position:0% +G + + + align:start position:0% +G +we can say our initial State I + + align:start position:0% +we can say our initial State I + + + align:start position:0% +we can say our initial State I +understand this + + align:start position:0% +understand this + + + align:start position:0% +understand this +Vector where we stack together initial + + align:start position:0% +Vector where we stack together initial + + + align:start position:0% +Vector where we stack together initial +height and initial velocity + + align:start position:0% + + + + align:start position:0% + +and we say maybe we in our task we want + + align:start position:0% +and we say maybe we in our task we want + + + align:start position:0% +and we say maybe we in our task we want +to integrate + + align:start position:0% +to integrate + + + align:start position:0% +to integrate +that equation from some initial time to + + align:start position:0% +that equation from some initial time to + + + align:start position:0% +that equation from some initial time to +some final time + + align:start position:0% + + + + align:start position:0% + +and we have to provide this kind of time + + align:start position:0% +and we have to provide this kind of time + + + align:start position:0% +and we have to provide this kind of time +discretization let's choose some + + align:start position:0% +discretization let's choose some + + + align:start position:0% +discretization let's choose some +some small time discretization + + align:start position:0% + + + + align:start position:0% + +everybody's happy with that so far + + align:start position:0% + + + + align:start position:0% + +so then we want to Define our + + align:start position:0% +so then we want to Define our + + + align:start position:0% +so then we want to Define our +ode function so which also called the + + align:start position:0% +ode function so which also called the + + + align:start position:0% +ode function so which also called the +vector field + + align:start position:0% +vector field + + + align:start position:0% +vector field +where we just insert the connections I + + align:start position:0% +where we just insert the connections I + + + align:start position:0% +where we just insert the connections I +had on the slide basically so we have + + align:start position:0% +had on the slide basically so we have + + + align:start position:0% +had on the slide basically so we have +that + + align:start position:0% +that + + + align:start position:0% +that +the derivative + + align:start position:0% +the derivative + + + align:start position:0% +the derivative +of the height with respect to time is + + align:start position:0% +of the height with respect to time is + + + align:start position:0% +of the height with respect to time is +the velocity right which you see in our + + align:start position:0% +the velocity right which you see in our + + + align:start position:0% +the velocity right which you see in our +case now the second component + + align:start position:0% +case now the second component + + + align:start position:0% +case now the second component +and we have that the derivative of the + + align:start position:0% +and we have that the derivative of the + + + align:start position:0% +and we have that the derivative of the +time is equal to the derivative of the + + align:start position:0% +time is equal to the derivative of the + + + align:start position:0% +time is equal to the derivative of the +Velocity with respect to time is equal + + align:start position:0% +Velocity with respect to time is equal + + + align:start position:0% +Velocity with respect to time is equal +to minus G which is on the right hand + + align:start position:0% +to minus G which is on the right hand + + + align:start position:0% +to minus G which is on the right hand +side of the bot + + align:start position:0% +side of the bot + + + align:start position:0% +side of the bot +and then we return basically + + align:start position:0% +and then we return basically + + + align:start position:0% +and then we return basically +the again the vector of these two we're + + align:start position:0% +the again the vector of these two we're + + + align:start position:0% +the again the vector of these two we're +going to get G from the parameters oh + + align:start position:0% +going to get G from the parameters oh + + + align:start position:0% +going to get G from the parameters oh +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +oh let's see like that thanks + + align:start position:0% + + + + align:start position:0% + +and so + + align:start position:0% +and so + + + align:start position:0% +and so +now we want to implement our + + align:start position:0% +now we want to implement our + + + align:start position:0% +now we want to implement our +our Euler solver which should take + + align:start position:0% +our Euler solver which should take + + + align:start position:0% +our Euler solver which should take +um well the kind of function that we + + align:start position:0% +um well the kind of function that we + + + align:start position:0% +um well the kind of function that we +want to solve + + align:start position:0% +want to solve + + + align:start position:0% +want to solve +we wanted to take + + align:start position:0% +we wanted to take + + + align:start position:0% +we wanted to take +um the initial condition + + align:start position:0% +um the initial condition + + + align:start position:0% +um the initial condition +let's write a bit more John + + align:start position:0% + + + + align:start position:0% + +the time span + + align:start position:0% +the time span + + + align:start position:0% +the time span +of the simulation + + align:start position:0% +of the simulation + + + align:start position:0% +of the simulation +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +the and the parameters + + align:start position:0% +the and the parameters + + + align:start position:0% +the and the parameters +and maybe even DT + + align:start position:0% + + + + align:start position:0% + +and let's say our time at the some point + + align:start position:0% +and let's say our time at the some point + + + align:start position:0% +and let's say our time at the some point +will be + + align:start position:0% +will be + + + align:start position:0% +will be +so we make a copy so we don't overwrite + + align:start position:0% +so we make a copy so we don't overwrite + + + align:start position:0% +so we make a copy so we don't overwrite +into the array so that this is preserved + + align:start position:0% +into the array so that this is preserved + + + align:start position:0% +into the array so that this is preserved +we make time grid + + align:start position:0% + + + + align:start position:0% + +this is actually big enough on the + + align:start position:0% +this is actually big enough on the + + + align:start position:0% +this is actually big enough on the +screen for everyone + + align:start position:0% + + + + align:start position:0% + +right we have to be be careful with the + + align:start position:0% +right we have to be be careful with the + + + align:start position:0% +right we have to be be careful with the +end point because we don't want to step + + align:start position:0% +end point because we don't want to step + + + align:start position:0% +end point because we don't want to step +one too far + + align:start position:0% + + + + align:start position:0% + +and then the update rule is basically + + align:start position:0% +and then the update rule is basically + + + align:start position:0% +and then the update rule is basically +would take you at a given time + + align:start position:0% + + + + align:start position:0% + +and that's whoops + + align:start position:0% + + + + align:start position:0% + +and you don't need the Deep copy since + + align:start position:0% +and you don't need the Deep copy since + + + align:start position:0% +and you don't need the Deep copy since +you're you're not overriding you in + + align:start position:0% +you're you're not overriding you in + + + align:start position:0% +you're you're not overriding you in +place anyway + + align:start position:0% +place anyway + + + align:start position:0% +place anyway +uh that's true I think I will need it + + align:start position:0% +uh that's true I think I will need it + + + align:start position:0% +uh that's true I think I will need it +later for one modification uh + + align:start position:0% +later for one modification uh + + + align:start position:0% +later for one modification uh +we don't need any copy uh + + align:start position:0% +we don't need any copy uh + + + align:start position:0% +we don't need any copy uh +that's also true okay + + align:start position:0% + + + + align:start position:0% + +and let's say I'm not interested in the + + align:start position:0% +and let's say I'm not interested in the + + + align:start position:0% +and let's say I'm not interested in the +full solution as a function of time but + + align:start position:0% +full solution as a function of time but + + + align:start position:0% +full solution as a function of time but +just in the end point of uh + + align:start position:0% + + + + align:start position:0% + +okay let's see if that works already + + align:start position:0% + + + + align:start position:0% + +you should be a t i for sure + + align:start position:0% + + + + align:start position:0% + +yeah we can check if that's the correct + + align:start position:0% +yeah we can check if that's the correct + + + align:start position:0% +yeah we can check if that's the correct +Solution by plugging it in into an + + align:start position:0% +Solution by plugging it in into an + + + align:start position:0% +Solution by plugging it in into an +analytical equation + + align:start position:0% +analytical equation + + + align:start position:0% +analytical equation +uh let me just close the phone + + align:start position:0% + + + + align:start position:0% + +right so so we have now written a + + align:start position:0% +right so so we have now written a + + + align:start position:0% +right so so we have now written a +numerical routine that spits out the + + align:start position:0% +numerical routine that spits out the + + + align:start position:0% +numerical routine that spits out the +state at a given time T and I think that + + align:start position:0% +state at a given time T and I think that + + + align:start position:0% +state at a given time T and I think that +looks actually good + + align:start position:0% +looks actually good + + + align:start position:0% +looks actually good +so we have t equal to zero so our Z + + align:start position:0% +so we have t equal to zero so our Z + + + align:start position:0% +so we have t equal to zero so our Z +should be + + align:start position:0% +should be + + + align:start position:0% +should be +zero minus + + align:start position:0% +zero minus + + + align:start position:0% +zero minus +G + + align:start position:0% + + + + align:start position:0% + +minus V 0 times + + align:start position:0% +minus V 0 times + + + align:start position:0% +minus V 0 times + + align:start position:0% + + + align:start position:0% +plus 3 0 times 1 + + align:start position:0% +plus 3 0 times 1 + + + align:start position:0% +plus 3 0 times 1 +minus one half times + + align:start position:0% +minus one half times + + + align:start position:0% +minus one half times +t + + align:start position:0% + + + + align:start position:0% + +and yeah that looks basically good + + align:start position:0% +and yeah that looks basically good + + + align:start position:0% +and yeah that looks basically good +that's a discretization error of the + + align:start position:0% +that's a discretization error of the + + + align:start position:0% +that's a discretization error of the +Euler method and we could check the same + + align:start position:0% +Euler method and we could check the same + + + align:start position:0% +Euler method and we could check the same +for the second component + + align:start position:0% +for the second component + + + align:start position:0% +for the second component +so the correct answer is + + align:start position:0% +so the correct answer is + + + align:start position:0% +so the correct answer is +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +exactly it's slightly off because we + + align:start position:0% +exactly it's slightly off because we + + + align:start position:0% +exactly it's slightly off because we +have not the most sophisticated + + align:start position:0% +have not the most sophisticated + + + align:start position:0% +have not the most sophisticated +numerical solver + + align:start position:0% +numerical solver + + + align:start position:0% +numerical solver +okay cool + + align:start position:0% +okay cool + + + align:start position:0% +okay cool +um so that's how we solve ode is + + align:start position:0% +um so that's how we solve ode is + + + align:start position:0% +um so that's how we solve ode is +numerically if we don't have an + + align:start position:0% +numerically if we don't have an + + + align:start position:0% +numerically if we don't have an +analytical solution + + align:start position:0% +analytical solution + + + align:start position:0% +analytical solution +and yeah now we get into the kind of + + align:start position:0% +and yeah now we get into the kind of + + + align:start position:0% +and yeah now we get into the kind of +sensitivity analysis if we have a + + align:start position:0% +sensitivity analysis if we have a + + + align:start position:0% +sensitivity analysis if we have a +numerical routine available + + align:start position:0% +numerical routine available + + + align:start position:0% +numerical routine available +so there are two different ways or + + align:start position:0% +so there are two different ways or + + + align:start position:0% +so there are two different ways or +fundamentally different ways to do + + align:start position:0% +fundamentally different ways to do + + + align:start position:0% +fundamentally different ways to do +sensitivity analysis one is called + + align:start position:0% +sensitivity analysis one is called + + + align:start position:0% +sensitivity analysis one is called +discrete sensitivity analysis and one is + + align:start position:0% +discrete sensitivity analysis and one is + + + align:start position:0% +discrete sensitivity analysis and one is +called continuous sensitivity analysis + + align:start position:0% +called continuous sensitivity analysis + + + align:start position:0% +called continuous sensitivity analysis +and the first one is basically you + + align:start position:0% +and the first one is basically you + + + align:start position:0% +and the first one is basically you +imagine that you wrote that solver that + + align:start position:0% +imagine that you wrote that solver that + + + align:start position:0% +imagine that you wrote that solver that +we just wrote in some language that's + + align:start position:0% +we just wrote in some language that's + + + align:start position:0% +we just wrote in some language that's +compatible with automatic + + align:start position:0% +compatible with automatic + + + align:start position:0% +compatible with automatic +differentiation and so we first this + + align:start position:0% +differentiation and so we first this + + + align:start position:0% +differentiation and so we first this +could type space gives a task and then + + align:start position:0% +could type space gives a task and then + + + align:start position:0% +could type space gives a task and then +we differentiate it and the second one + + align:start position:0% +we differentiate it and the second one + + + align:start position:0% +we differentiate it and the second one +is basically we write a custom rule for + + align:start position:0% +is basically we write a custom rule for + + + align:start position:0% +is basically we write a custom rule for +a sensitivity analysis and so we first + + align:start position:0% +a sensitivity analysis and so we first + + + align:start position:0% +a sensitivity analysis and so we first +approximate basically the gradient that + + align:start position:0% +approximate basically the gradient that + + + align:start position:0% +approximate basically the gradient that +we want to compute and then + + align:start position:0% +we want to compute and then + + + align:start position:0% +we want to compute and then +differentiated and then this discretize + + align:start position:0% +differentiated and then this discretize + + + align:start position:0% +differentiated and then this discretize +it + + align:start position:0% +it + + + align:start position:0% +it +and + + align:start position:0% +and + + + align:start position:0% +and +for each of these methods like these + + align:start position:0% +for each of these methods like these + + + align:start position:0% +for each of these methods like these +different paradigms basically of in + + align:start position:0% +different paradigms basically of in + + + align:start position:0% +different paradigms basically of in +either first discretizing and then + + align:start position:0% +either first discretizing and then + + + align:start position:0% +either first discretizing and then +differentiating or first differentiating + + align:start position:0% +differentiating or first differentiating + + + align:start position:0% +differentiating or first differentiating +and then discretizing there are two + + align:start position:0% +and then discretizing there are two + + + align:start position:0% +and then discretizing there are two +different modes that you also probably + + align:start position:0% +different modes that you also probably + + + align:start position:0% +different modes that you also probably +have covered in the lecture already + + align:start position:0% +have covered in the lecture already + + + align:start position:0% +have covered in the lecture already +you can either derive forward or also + + align:start position:0% +you can either derive forward or also + + + align:start position:0% +you can either derive forward or also +called tangent mode or reverse a joint + + align:start position:0% +called tangent mode or reverse a joint + + + align:start position:0% +called tangent mode or reverse a joint +modes and depending on if you have many + + align:start position:0% +modes and depending on if you have many + + + align:start position:0% +modes and depending on if you have many +input parameters and a small number of + + align:start position:0% +input parameters and a small number of + + + align:start position:0% +input parameters and a small number of +outputs one of these modes is basically + + align:start position:0% +outputs one of these modes is basically + + + align:start position:0% +outputs one of these modes is basically +preferred to each other so in the in the + + align:start position:0% +preferred to each other so in the in the + + + align:start position:0% +preferred to each other so in the in the +setting where you have many parameters + + align:start position:0% +setting where you have many parameters + + + align:start position:0% +setting where you have many parameters +with respect to which you want to + + align:start position:0% +with respect to which you want to + + + align:start position:0% +with respect to which you want to +compute a gradient or derivative you + + align:start position:0% +compute a gradient or derivative you + + + align:start position:0% +compute a gradient or derivative you +usually want to have some adjoint mode + + align:start position:0% +usually want to have some adjoint mode + + + align:start position:0% +usually want to have some adjoint mode +and if you have high memory demands you + + align:start position:0% +and if you have high memory demands you + + + align:start position:0% +and if you have high memory demands you +typically want to have like these + + align:start position:0% +typically want to have like these + + + align:start position:0% +typically want to have like these +continuous sensitivity methods so it's a + + align:start position:0% +continuous sensitivity methods so it's a + + + align:start position:0% +continuous sensitivity methods so it's a +very relevant case to consider these + + align:start position:0% +very relevant case to consider these + + + align:start position:0% +very relevant case to consider these +continuous adjoints basically + + align:start position:0% +continuous adjoints basically + + + align:start position:0% +continuous adjoints basically +and that's what we will do today + + align:start position:0% +and that's what we will do today + + + align:start position:0% +and that's what we will do today +so what are sensitivities good for just + + align:start position:0% +so what are sensitivities good for just + + + align:start position:0% +so what are sensitivities good for just +as a recap so sensitive analysis + + align:start position:0% +as a recap so sensitive analysis + + + align:start position:0% +as a recap so sensitive analysis +basically just + + align:start position:0% +basically just + + + align:start position:0% +basically just +um well describes what it says so we + + align:start position:0% +um well describes what it says so we + + + align:start position:0% +um well describes what it says so we +might be interested in just describing + + align:start position:0% +might be interested in just describing + + + align:start position:0% +might be interested in just describing +how maybe the height of our ball would + + align:start position:0% +how maybe the height of our ball would + + + align:start position:0% +how maybe the height of our ball would +change if we slightly perturb the + + align:start position:0% +change if we slightly perturb the + + + align:start position:0% +change if we slightly perturb the +parameter of the differential equation + + align:start position:0% +parameter of the differential equation + + + align:start position:0% +parameter of the differential equation +but we can also use the gradient of + + align:start position:0% +but we can also use the gradient of + + + align:start position:0% +but we can also use the gradient of +these Odes to do more fancy stuff as + + align:start position:0% +these Odes to do more fancy stuff as + + + align:start position:0% +these Odes to do more fancy stuff as +Steven mentioned like parameter + + align:start position:0% +Steven mentioned like parameter + + + align:start position:0% +Steven mentioned like parameter +estimation in what chemical reaction + + align:start position:0% +estimation in what chemical reaction + + + align:start position:0% +estimation in what chemical reaction +networks or so or like + + align:start position:0% +networks or so or like + + + align:start position:0% +networks or so or like +um control for whatever physical system + + align:start position:0% +um control for whatever physical system + + + align:start position:0% +um control for whatever physical system +or chemical system you have at hand + + align:start position:0% +or chemical system you have at hand + + + align:start position:0% +or chemical system you have at hand +so once again so for the Free Falling + + align:start position:0% +so once again so for the Free Falling + + + align:start position:0% +so once again so for the Free Falling +particle it might be the task that we + + align:start position:0% +particle it might be the task that we + + + align:start position:0% +particle it might be the task that we +have some terminal cost or so that could + + align:start position:0% +have some terminal cost or so that could + + + align:start position:0% +have some terminal cost or so that could +be this G of U at the final time and + + align:start position:0% +be this G of U at the final time and + + + align:start position:0% +be this G of U at the final time and +we're interested in maybe saying how the + + align:start position:0% +we're interested in maybe saying how the + + + align:start position:0% +we're interested in maybe saying how the +height changes respect to the + + align:start position:0% +height changes respect to the + + + align:start position:0% +height changes respect to the +gravitational constant and so the claim + + align:start position:0% +gravitational constant and so the claim + + + align:start position:0% +gravitational constant and so the claim +is that this is always easy if we can + + align:start position:0% +is that this is always easy if we can + + + align:start position:0% +is that this is always easy if we can +solve the ode analytically right so if + + align:start position:0% +solve the ode analytically right so if + + + align:start position:0% +solve the ode analytically right so if +we look at the solution there of the + + align:start position:0% +we look at the solution there of the + + + align:start position:0% +we look at the solution there of the +ode Can someone say what's the + + align:start position:0% +ode Can someone say what's the + + + align:start position:0% +ode Can someone say what's the +sensitivity that I wrote down like the + + align:start position:0% +sensitivity that I wrote down like the + + + align:start position:0% +sensitivity that I wrote down like the +sensitivity of the final height respect + + align:start position:0% +sensitivity of the final height respect + + + align:start position:0% +sensitivity of the final height respect +to + + align:start position:0% +to + + + align:start position:0% +to +G + + align:start position:0% + + + + align:start position:0% + +yeah exactly so and now we will + + align:start position:0% +yeah exactly so and now we will + + + align:start position:0% +yeah exactly so and now we will +basically cover how we do that if we + + align:start position:0% +basically cover how we do that if we + + + align:start position:0% +basically cover how we do that if we +don't have the analog solution available + + align:start position:0% +don't have the analog solution available + + + align:start position:0% +don't have the analog solution available +uh for this we will have to do some + + align:start position:0% +uh for this we will have to do some + + + align:start position:0% +uh for this we will have to do some +derivation + + align:start position:0% + + + + align:start position:0% + +so we do + + align:start position:0% +so we do + + + align:start position:0% +so we do +content + + align:start position:0% +content + + + align:start position:0% +content +news + + align:start position:0% +news + + + align:start position:0% +news +adjoints today + + align:start position:0% + + + + align:start position:0% + +so let's first write down one of these + + align:start position:0% +so let's first write down one of these + + + align:start position:0% +so let's first write down one of these +cost functions which I just had in a bit + + align:start position:0% +cost functions which I just had in a bit + + + align:start position:0% +cost functions which I just had in a bit +more General way so we have some cost + + align:start position:0% +more General way so we have some cost + + + align:start position:0% +more General way so we have some cost +that depends on the state as a function + + align:start position:0% +that depends on the state as a function + + + align:start position:0% +that depends on the state as a function +of time and P + + align:start position:0% +of time and P + + + align:start position:0% +of time and P +where + + align:start position:0% +where + + + align:start position:0% +where +the + + align:start position:0% +the + + + align:start position:0% +the +State itself of course also depends on + + align:start position:0% +State itself of course also depends on + + + align:start position:0% +State itself of course also depends on +the parameters + + align:start position:0% +the parameters + + + align:start position:0% +the parameters +and we say that this function can be + + align:start position:0% +and we say that this function can be + + + align:start position:0% +and we say that this function can be +written + + align:start position:0% +written + + + align:start position:0% +written +let's see + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +right so we say we can + + align:start position:0% +right so we say we can + + + align:start position:0% +right so we say we can +um we don't have maybe just the final + + align:start position:0% +um we don't have maybe just the final + + + align:start position:0% +um we don't have maybe just the final +value but we are interested in general + + align:start position:0% +value but we are interested in general + + + align:start position:0% +value but we are interested in general +as some functional of those on the + + align:start position:0% +as some functional of those on the + + + align:start position:0% +as some functional of those on the +solution of the differential equation + + align:start position:0% + + + + align:start position:0% + +uh yes yep yep + + align:start position:0% + + + + align:start position:0% + +and now comes basically the first nice + + align:start position:0% +and now comes basically the first nice + + + align:start position:0% +and now comes basically the first nice +trick in this kind of derivation + + align:start position:0% +trick in this kind of derivation + + + align:start position:0% +trick in this kind of derivation +and that's related to La Crosse + + align:start position:0% +and that's related to La Crosse + + + align:start position:0% +and that's related to La Crosse +multipliers + + align:start position:0% + + + + align:start position:0% + +assessments uh yeah probably a good idea + + align:start position:0% +assessments uh yeah probably a good idea + + + align:start position:0% +assessments uh yeah probably a good idea +all right + + align:start position:0% +all right + + + align:start position:0% +all right +instead + + align:start position:0% + + + + align:start position:0% + +oh I see + + align:start position:0% + + + + align:start position:0% + +okay so the first trick that we want to + + align:start position:0% +okay so the first trick that we want to + + + align:start position:0% +okay so the first trick that we want to +do is basically to add a zero to this + + align:start position:0% +do is basically to add a zero to this + + + align:start position:0% +do is basically to add a zero to this +kind of function + + align:start position:0% +kind of function + + + align:start position:0% +kind of function +[Music] + + align:start position:0% + + + + align:start position:0% + +and then we're going to compute a number + + align:start position:0% +and then we're going to compute a number + + + align:start position:0% +and then we're going to compute a number +at the end capital G + + align:start position:0% +at the end capital G + + + align:start position:0% +at the end capital G +by picking the odd solution and + + align:start position:0% +by picking the odd solution and + + + align:start position:0% +by picking the odd solution and +integrating some function literally that + + align:start position:0% +integrating some function literally that + + + align:start position:0% +integrating some function literally that +solution + + align:start position:0% +solution + + + align:start position:0% +solution +and the ode depends on some parameters + + align:start position:0% +and the ode depends on some parameters + + + align:start position:0% +and the ode depends on some parameters +and you want to find the derivative of + + align:start position:0% +and you want to find the derivative of + + + align:start position:0% +and you want to find the derivative of +this final output capital G with respect + + align:start position:0% +this final output capital G with respect + + + align:start position:0% +this final output capital G with respect +to all those parameters + + align:start position:0% + + + + align:start position:0% + +capital G might be the + + align:start position:0% +capital G might be the + + + align:start position:0% +capital G might be the +the integral of the square difference + + align:start position:0% +the integral of the square difference + + + align:start position:0% +the integral of the square difference +between the + + align:start position:0% +between the + + + align:start position:0% +between the +ode solution and like some experimental + + align:start position:0% +ode solution and like some experimental + + + align:start position:0% +ode solution and like some experimental +data on the chemical + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +react uh yeah exactly does everybody see + + align:start position:0% +react uh yeah exactly does everybody see + + + align:start position:0% +react uh yeah exactly does everybody see +why that's a zero + + align:start position:0% + + + + align:start position:0% + +right so why + + align:start position:0% +right so why + + + align:start position:0% +right so why +sorry I was talking about that + + align:start position:0% + + + + align:start position:0% + +right so because + + align:start position:0% +right so because + + + align:start position:0% +right so because +by definition basically our state + + align:start position:0% +by definition basically our state + + + align:start position:0% +by definition basically our state +fulfills this ordinary differential + + align:start position:0% +fulfills this ordinary differential + + + align:start position:0% +fulfills this ordinary differential +equation we can introduce this kind of + + align:start position:0% +equation we can introduce this kind of + + + align:start position:0% +equation we can introduce this kind of +like lacrosse multiplier and that term + + align:start position:0% +like lacrosse multiplier and that term + + + align:start position:0% +like lacrosse multiplier and that term +is zero so if we add that term to this + + align:start position:0% +is zero so if we add that term to this + + + align:start position:0% +is zero so if we add that term to this +kind of cost function we basically do + + align:start position:0% +kind of cost function we basically do + + + align:start position:0% +kind of cost function we basically do +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +but we have this free Lacross multiplier + + align:start position:0% +but we have this free Lacross multiplier + + + align:start position:0% +but we have this free Lacross multiplier +that we can choose later on so that will + + align:start position:0% +that we can choose later on so that will + + + align:start position:0% +that we can choose later on so that will +be kind of the trick that we will that + + align:start position:0% +be kind of the trick that we will that + + + align:start position:0% +be kind of the trick that we will that +we will play + + align:start position:0% +we will play + + + align:start position:0% +we will play +and now as Stephen already said so we're + + align:start position:0% +and now as Stephen already said so we're + + + align:start position:0% +and now as Stephen already said so we're +interested in + + align:start position:0% +interested in + + + align:start position:0% +interested in +computing + + align:start position:0% +computing + + + align:start position:0% +computing +DG over + + align:start position:0% +DG over + + + align:start position:0% +DG over +DP right so that's a kind of + + align:start position:0% +DP right so that's a kind of + + + align:start position:0% +DP right so that's a kind of +sensitivity gradient information that we + + align:start position:0% +sensitivity gradient information that we + + + align:start position:0% +sensitivity gradient information that we +that we want to want to have + + align:start position:0% + + + + align:start position:0% + +there will be a long line + + align:start position:0% +there will be a long line + + + align:start position:0% +there will be a long line +so what we basically do is just do + + align:start position:0% +so what we basically do is just do + + + align:start position:0% +so what we basically do is just do +another chain rule on that term and + + align:start position:0% +another chain rule on that term and + + + align:start position:0% +another chain rule on that term and +these terms + + align:start position:0% + + + + align:start position:0% + +in general could be a vector + + align:start position:0% +in general could be a vector + + + align:start position:0% +in general could be a vector +gradient instead + + align:start position:0% + + + + align:start position:0% + +probably this is a + + align:start position:0% + + + + align:start position:0% + +yeah it's a gradient transpose no that's + + align:start position:0% +yeah it's a gradient transpose no that's + + + align:start position:0% +yeah it's a gradient transpose no that's +what we were calling G Prime + + align:start position:0% + + + + align:start position:0% + +yeah let me quickly write it down + + align:start position:0% +yeah let me quickly write it down + + + align:start position:0% +yeah let me quickly write it down +because it's easy to do + + align:start position:0% +because it's easy to do + + + align:start position:0% +because it's easy to do +mistakes on that part + + align:start position:0% + + + + align:start position:0% + +from amongst people + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay I'll leave out the utp's to save + + align:start position:0% +okay I'll leave out the utp's to save + + + align:start position:0% +okay I'll leave out the utp's to save +some space but every U here depends on + + align:start position:0% +some space but every U here depends on + + + align:start position:0% +some space but every U here depends on +TMP + + align:start position:0% + + + + align:start position:0% + +I guess + + align:start position:0% +I guess + + + align:start position:0% +I guess +it's maybe hard to read at the end but + + align:start position:0% +it's maybe hard to read at the end but + + + align:start position:0% +it's maybe hard to read at the end but +there's a DT only missing here + + align:start position:0% + + + + align:start position:0% + +that's a readable for you on that side + + align:start position:0% +that's a readable for you on that side + + + align:start position:0% +that's a readable for you on that side +I know I will repeat that term in a + + align:start position:0% +I know I will repeat that term in a + + + align:start position:0% +I know I will repeat that term in a +second so it will you will see again + + align:start position:0% +second so it will you will see again + + + align:start position:0% +second so it will you will see again +what's that here + + align:start position:0% +what's that here + + + align:start position:0% +what's that here +um + + align:start position:0% + + + + align:start position:0% + +right so let's call that basically like + + align:start position:0% +right so let's call that basically like + + + align:start position:0% +right so let's call that basically like +the sensitivity + + align:start position:0% +the sensitivity + + + align:start position:0% +the sensitivity +called it and yet let's simplify a bit + + align:start position:0% +called it and yet let's simplify a bit + + + align:start position:0% +called it and yet let's simplify a bit +of notation so that's my small G I'm + + align:start position:0% +of notation so that's my small G I'm + + + align:start position:0% +of notation so that's my small G I'm +sorry my small G's and small F's look + + align:start position:0% +sorry my small G's and small F's look + + + align:start position:0% +sorry my small G's and small F's look +fairly similar + + align:start position:0% +fairly similar + + + align:start position:0% +fairly similar +that's small G + + align:start position:0% +that's small G + + + align:start position:0% +that's small G +U so I always denote by subscript the + + align:start position:0% +U so I always denote by subscript the + + + align:start position:0% +U so I always denote by subscript the +with respect to what we differentiate + + align:start position:0% + + + + align:start position:0% + +small GP + + align:start position:0% +small GP + + + align:start position:0% +small GP +and in this term + + align:start position:0% +and in this term + + + align:start position:0% +and in this term +what we can do here is basically swap + + align:start position:0% +what we can do here is basically swap + + + align:start position:0% +what we can do here is basically swap +the derivative respect to p and with + + align:start position:0% +the derivative respect to p and with + + + align:start position:0% +the derivative respect to p and with +respect to time so we get here + + align:start position:0% +respect to time so we get here + + + align:start position:0% +respect to time so we get here +S Prime + + align:start position:0% +S Prime + + + align:start position:0% +S Prime +right so because when we swap it we have + + align:start position:0% +right so because when we swap it we have + + + align:start position:0% +right so because when we swap it we have +the UDP which is s and then we have the + + align:start position:0% +the UDP which is s and then we have the + + + align:start position:0% +the UDP which is s and then we have the +time derivative + + align:start position:0% +time derivative + + + align:start position:0% +time derivative +and + + align:start position:0% +and + + + align:start position:0% +and +we have here some + + align:start position:0% + + + + align:start position:0% + +f u times s + + align:start position:0% +f u times s + + + align:start position:0% +f u times s +and the last term is + + align:start position:0% +and the last term is + + + align:start position:0% +and the last term is +if + + align:start position:0% +if + + + align:start position:0% +if +that last term is FP + + align:start position:0% + + + + align:start position:0% + +okay let me go to the center because I + + align:start position:0% +okay let me go to the center because I + + + align:start position:0% +okay let me go to the center because I +think it's probably better readable from + + align:start position:0% +think it's probably better readable from + + + align:start position:0% +think it's probably better readable from +there + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so yeah I write the second term which + + align:start position:0% +so yeah I write the second term which + + + align:start position:0% +so yeah I write the second term which +was probably hard to a little bit bigger + + align:start position:0% + + + + align:start position:0% + +so that's the second term on the right + + align:start position:0% +so that's the second term on the right + + + align:start position:0% +so that's the second term on the right +hand side + + align:start position:0% +hand side + + + align:start position:0% +hand side +and + + align:start position:0% +and + + + align:start position:0% +and +yeah + + align:start position:0% + + + + align:start position:0% + +it's all right so you have this function + + align:start position:0% +it's all right so you have this function + + + align:start position:0% +it's all right so you have this function +you're trying to differentiate + + align:start position:0% +you're trying to differentiate + + + align:start position:0% +you're trying to differentiate +if you just differentiate because P + + align:start position:0% +if you just differentiate because P + + + align:start position:0% +if you just differentiate because P +directly + + align:start position:0% +directly + + + align:start position:0% +directly +you get + + align:start position:0% +you get + + + align:start position:0% +you get +this term which is easy right if the + + align:start position:0% +this term which is easy right if the + + + align:start position:0% +this term which is easy right if the +function depends directly on the + + align:start position:0% +function depends directly on the + + + align:start position:0% +function depends directly on the +parameters you can take that derivative + + align:start position:0% +parameters you can take that derivative + + + align:start position:0% +parameters you can take that derivative +often that derivative is zero + + align:start position:0% +often that derivative is zero + + + align:start position:0% +often that derivative is zero +this term which is easy this is your + + align:start position:0% +this term which is easy this is your + + + align:start position:0% +this term which is easy this is your +cost function how does it depend on the + + align:start position:0% +cost function how does it depend on the + + + align:start position:0% +cost function how does it depend on the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +this term is hard + + align:start position:0% +this term is hard + + + align:start position:0% +this term is hard +how do you get the derivative of the + + align:start position:0% +how do you get the derivative of the + + + align:start position:0% +how do you get the derivative of the +solution with respect to parameters + + align:start position:0% +solution with respect to parameters + + + align:start position:0% +solution with respect to parameters +so the goal and adding zero here is + + align:start position:0% +so the goal and adding zero here is + + + align:start position:0% +so the goal and adding zero here is +going to be is going to give us this + + align:start position:0% +going to be is going to give us this + + + align:start position:0% +going to be is going to give us this +extra degree of Freedom Lambda that all + + align:start position:0% +extra degree of Freedom Lambda that all + + + align:start position:0% +extra degree of Freedom Lambda that all +if he's clever and how he chooses this + + align:start position:0% +if he's clever and how he chooses this + + + align:start position:0% +if he's clever and how he chooses this +gonna be a trick that allows him to + + align:start position:0% +gonna be a trick that allows him to + + + align:start position:0% +gonna be a trick that allows him to +cancel this term and get a a this term + + align:start position:0% +cancel this term and get a a this term + + + align:start position:0% +cancel this term and get a a this term +that's hard and get a differential + + align:start position:0% +that's hard and get a differential + + + align:start position:0% +that's hard and get a differential +equation for Lambda so that that's + + align:start position:0% +equation for Lambda so that that's + + + align:start position:0% +equation for Lambda so that that's +often good to sort of show there's kind + + align:start position:0% +often good to sort of show there's kind + + + align:start position:0% +often good to sort of show there's kind +of a magic step here where you add this + + align:start position:0% +of a magic step here where you add this + + + align:start position:0% +of a magic step here where you add this +landed term + + align:start position:0% +landed term + + + align:start position:0% +landed term +yeah sometimes good to not to build + + align:start position:0% +yeah sometimes good to not to build + + + align:start position:0% +yeah sometimes good to not to build +people in suspense why the hell did you + + align:start position:0% +people in suspense why the hell did you + + + align:start position:0% +people in suspense why the hell did you +have this term that's true + + align:start position:0% +have this term that's true + + + align:start position:0% +have this term that's true +yeah exactly yes one step before we can + + align:start position:0% +yeah exactly yes one step before we can + + + align:start position:0% +yeah exactly yes one step before we can +actually do that trick to eliminate the + + align:start position:0% +actually do that trick to eliminate the + + + align:start position:0% +actually do that trick to eliminate the +S and that's basically this S Prime that + + align:start position:0% +S and that's basically this S Prime that + + + align:start position:0% +S and that's basically this S Prime that +we got which we first have to + + align:start position:0% +we got which we first have to + + + align:start position:0% +we got which we first have to +get rid of anybody has an idea maybe how + + align:start position:0% +get rid of anybody has an idea maybe how + + + align:start position:0% +get rid of anybody has an idea maybe how +to how to do that like turning our plans + + align:start position:0% +to how to do that like turning our plans + + + align:start position:0% +to how to do that like turning our plans +to turn S Prime into an s + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +1801 question + + align:start position:0% +1801 question + + + align:start position:0% +1801 question +see the derivative in an integral you + + align:start position:0% +see the derivative in an integral you + + + align:start position:0% +see the derivative in an integral you +don't like like how can you get rid of + + align:start position:0% +don't like like how can you get rid of + + + align:start position:0% +don't like like how can you get rid of +it + + align:start position:0% + + + + align:start position:0% + +that's yep + + align:start position:0% +that's yep + + + align:start position:0% +that's yep +so we integrate that term by parts + + align:start position:0% +so we integrate that term by parts + + + align:start position:0% +so we integrate that term by parts +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% + + + + align:start position:0% + +right so that's from the integration by + + align:start position:0% +right so that's from the integration by + + + align:start position:0% +right so that's from the integration by +parts now the Prime on the Lambda + + align:start position:0% +parts now the Prime on the Lambda + + + align:start position:0% +parts now the Prime on the Lambda +which will be + + align:start position:0% +which will be + + + align:start position:0% +which will be +exactly going towards the + + align:start position:0% +exactly going towards the + + + align:start position:0% +exactly going towards the +ode that Stephen mentioned + + align:start position:0% + + + + align:start position:0% + +yes yes + + align:start position:0% + + + + align:start position:0% + +why is it transpose like what's the + + align:start position:0% +why is it transpose like what's the + + + align:start position:0% +why is it transpose like what's the +what's the size of this + + align:start position:0% +what's the size of this + + + align:start position:0% +what's the size of this +Lambda I will decide the size of this + + align:start position:0% +Lambda I will decide the size of this + + + align:start position:0% +Lambda I will decide the size of this +level so it's such that + + align:start position:0% +level so it's such that + + + align:start position:0% +level so it's such that +right this output should be + + align:start position:0% +right this output should be + + + align:start position:0% +right this output should be +a scalar + + align:start position:0% +a scalar + + + align:start position:0% +a scalar +right because we optimize the scalar + + align:start position:0% +right because we optimize the scalar + + + align:start position:0% +right because we optimize the scalar +cost function + + align:start position:0% +cost function + + + align:start position:0% +cost function +so the size of Lambda is basically in + + align:start position:0% +so the size of Lambda is basically in + + + align:start position:0% +so the size of Lambda is basically in +the + + align:start position:0% +the + + + align:start position:0% +the +well in the + + align:start position:0% +well in the + + + align:start position:0% +well in the +air joint space of + + align:start position:0% +air joint space of + + + align:start position:0% +air joint space of +F right of the of U Prime + + align:start position:0% +F right of the of U Prime + + + align:start position:0% +F right of the of U Prime +the solution here is it does not Escape + + align:start position:0% +the solution here is it does not Escape + + + align:start position:0% +the solution here is it does not Escape +U is not a scalar + + align:start position:0% + + + + align:start position:0% + +n equations + + align:start position:0% +n equations + + + align:start position:0% +n equations +and if Lambda is a column Vector with + + align:start position:0% +and if Lambda is a column Vector with + + + align:start position:0% +and if Lambda is a column Vector with +the same number + + align:start position:0% +the same number + + + align:start position:0% +the same number +so it has the same shape as U + + align:start position:0% + + + + align:start position:0% + +yeah so what we want to do next is + + align:start position:0% +yeah so what we want to do next is + + + align:start position:0% +yeah so what we want to do next is +basically insert back this term into + + align:start position:0% +basically insert back this term into + + + align:start position:0% +basically insert back this term into +that equation so we + + align:start position:0% +that equation so we + + + align:start position:0% +that equation so we +that was our theorem here and so we take + + align:start position:0% +that was our theorem here and so we take + + + align:start position:0% +that was our theorem here and so we take +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +this part inserted back and we're + + align:start position:0% +this part inserted back and we're + + + align:start position:0% +this part inserted back and we're +already going towards our goal and + + align:start position:0% +already going towards our goal and + + + align:start position:0% +already going towards our goal and +reorder all terms such that we have this + + align:start position:0% +reorder all terms such that we have this + + + align:start position:0% +reorder all terms such that we have this +s separated basically + + align:start position:0% + + + + align:start position:0% + +so what we end up is basically this DG + + align:start position:0% + + + + align:start position:0% + +DP + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + + align:start position:0% + +methods + + align:start position:0% +methods + + + align:start position:0% +methods +always called Lambda because it comes + + align:start position:0% + + + + align:start position:0% + +Prime here + + align:start position:0% + + + + align:start position:0% + +okay let's write that directly into one + + align:start position:0% + + + + align:start position:0% + +okay so not much happened here basically + + align:start position:0% +okay so not much happened here basically + + + align:start position:0% +okay so not much happened here basically +it's just looking at all the terms so we + + align:start position:0% +it's just looking at all the terms so we + + + align:start position:0% +it's just looking at all the terms so we +leave + + align:start position:0% +leave + + + align:start position:0% +leave +that term here + + align:start position:0% +that term here + + + align:start position:0% +that term here +this is that term + + align:start position:0% +this is that term + + + align:start position:0% +this is that term +that is that term we moved this term + + align:start position:0% +that is that term we moved this term + + + align:start position:0% +that is that term we moved this term +which doesn't depend on F to the front + + align:start position:0% +which doesn't depend on F to the front + + + align:start position:0% +which doesn't depend on F to the front +and we had another term that depended + + align:start position:0% +and we had another term that depended + + + align:start position:0% +and we had another term that depended +that was depending on S here which we + + align:start position:0% +that was depending on S here which we + + + align:start position:0% +that was depending on S here which we +moved to the back basically so these two + + align:start position:0% +moved to the back basically so these two + + + align:start position:0% +moved to the back basically so these two +terms were like + + align:start position:0% +terms were like + + + align:start position:0% +terms were like +well swapped + + align:start position:0% + + + + align:start position:0% + +the goal here is the S which is d u the + + align:start position:0% +the goal here is the S which is d u the + + + align:start position:0% +the goal here is the S which is d u the +derivative of the solution respective + + align:start position:0% +derivative of the solution respective + + + align:start position:0% +derivative of the solution respective +parameters that's the annoying term you + + align:start position:0% +parameters that's the annoying term you + + + align:start position:0% +parameters that's the annoying term you +don't know how to deal with it's going + + align:start position:0% +don't know how to deal with it's going + + + align:start position:0% +don't know how to deal with it's going +to try and group it all together and + + align:start position:0% +to try and group it all together and + + + align:start position:0% +to try and group it all together and +then + + align:start position:0% +then + + + align:start position:0% +then +make that term zero so you don't have to + + align:start position:0% +make that term zero so you don't have to + + + align:start position:0% +make that term zero so you don't have to +deal with it + + align:start position:0% +deal with it + + + align:start position:0% +deal with it +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so we are free + + align:start position:0% + + + + align:start position:0% + +to twos + + align:start position:0% + + + + align:start position:0% + +Lambda + + align:start position:0% +Lambda + + + align:start position:0% +Lambda +so we can choose Lambda to be whatever + + align:start position:0% +so we can choose Lambda to be whatever + + + align:start position:0% +so we can choose Lambda to be whatever +we want + + align:start position:0% +we want + + + align:start position:0% +we want +so why don't we + + align:start position:0% +so why don't we + + + align:start position:0% +so why don't we +take basically the choice + + align:start position:0% +take basically the choice + + + align:start position:0% +take basically the choice +Lambda Prime of T is equal to a minus + + align:start position:0% +Lambda Prime of T is equal to a minus + + + align:start position:0% +Lambda Prime of T is equal to a minus +Lambda t + + align:start position:0% +Lambda t + + + align:start position:0% +Lambda t +f u + + align:start position:0% +f u + + + align:start position:0% +f u +minus g u + + align:start position:0% +minus g u + + + align:start position:0% +minus g u +right if we take that choice + + align:start position:0% +right if we take that choice + + + align:start position:0% +right if we take that choice +we will have at this term vanishes + + align:start position:0% +we will have at this term vanishes + + + align:start position:0% +we will have at this term vanishes +and we can also since this is an ode + + align:start position:0% +and we can also since this is an ode + + + align:start position:0% +and we can also since this is an ode +specify + + align:start position:0% +specify + + + align:start position:0% +specify +uh well basically the initial condition + + align:start position:0% +uh well basically the initial condition + + + align:start position:0% +uh well basically the initial condition +so we can specify that Lambda + + align:start position:0% +so we can specify that Lambda + + + align:start position:0% +so we can specify that Lambda +of T should be equal to zero + + align:start position:0% +of T should be equal to zero + + + align:start position:0% +of T should be equal to zero +if we do that we have that + + align:start position:0% +if we do that we have that + + + align:start position:0% +if we do that we have that +this term cancels and one of the terms + + align:start position:0% +this term cancels and one of the terms + + + align:start position:0% +this term cancels and one of the terms +from this + + align:start position:0% +from this + + + align:start position:0% +from this +uh + + align:start position:0% +uh + + + align:start position:0% +uh +integration by parts also cancels + + align:start position:0% + + + + align:start position:0% + +then it's the question of + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +capital T to be that that would be + + align:start position:0% +capital T to be that that would be + + + align:start position:0% +capital T to be that that would be +capital T be zero yeah that's a the next + + align:start position:0% +capital T be zero yeah that's a the next + + + align:start position:0% +capital T be zero yeah that's a the next +question and that's because + + align:start position:0% +question and that's because + + + align:start position:0% +question and that's because +um + + align:start position:0% +um + + + align:start position:0% +um +basically what is s of t 0 which + + align:start position:0% +basically what is s of t 0 which + + + align:start position:0% +basically what is s of t 0 which +comes in into that term + + align:start position:0% +comes in into that term + + + align:start position:0% +comes in into that term +so we know that s of 2 to 0 + + align:start position:0% +so we know that s of 2 to 0 + + + align:start position:0% +so we know that s of 2 to 0 +right by definition of s + + align:start position:0% +right by definition of s + + + align:start position:0% +right by definition of s +it's a sensitivity + + align:start position:0% +it's a sensitivity + + + align:start position:0% +it's a sensitivity +of the initial state with respect to the + + align:start position:0% +of the initial state with respect to the + + + align:start position:0% +of the initial state with respect to the +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +and writing we know that the initial + + align:start position:0% +and writing we know that the initial + + + align:start position:0% +and writing we know that the initial +State doesn't depend on the parameter so + + align:start position:0% +State doesn't depend on the parameter so + + + align:start position:0% +State doesn't depend on the parameter so +that term could right it could but + + align:start position:0% +that term could right it could but + + + align:start position:0% +that term could right it could but +whatever it is you know what it is like + + align:start position:0% +whatever it is you know what it is like + + + align:start position:0% +whatever it is you know what it is like +you don't you have you have the initial + + align:start position:0% +you don't you have you have the initial + + + align:start position:0% +you don't you have you have the initial +condition in closed form + + align:start position:0% +condition in closed form + + + align:start position:0% +condition in closed form +right so even if it depends on some + + align:start position:0% +right so even if it depends on some + + + align:start position:0% +right so even if it depends on some +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +you know what it is but here here only + + align:start position:0% +you know what it is but here here only + + + align:start position:0% +you know what it is but here here only +the you're you're simplifying it to only + + align:start position:0% +the you're you're simplifying it to only + + + align:start position:0% +the you're you're simplifying it to only +the uh uh only the system of equations + + align:start position:0% +the uh uh only the system of equations + + + align:start position:0% +the uh uh only the system of equations +depends on the parameters + + align:start position:0% +depends on the parameters + + + align:start position:0% +depends on the parameters +yes yeah + + align:start position:0% +yes yeah + + + align:start position:0% +yes yeah +exactly so you know it's easy or it's uh + + align:start position:0% +exactly so you know it's easy or it's uh + + + align:start position:0% +exactly so you know it's easy or it's uh +what's zero basically + + align:start position:0% + + + + align:start position:0% + +yes nice so we have in the end that just + + align:start position:0% +yes nice so we have in the end that just + + + align:start position:0% +yes nice so we have in the end that just +this term basically survives so we have + + align:start position:0% +this term basically survives so we have + + + align:start position:0% +this term basically survives so we have +the DG + + align:start position:0% +the DG + + + align:start position:0% +the DG +um the derivative of G respect to the + + align:start position:0% +um the derivative of G respect to the + + + align:start position:0% +um the derivative of G respect to the +parameters or the gradient in this case + + align:start position:0% +parameters or the gradient in this case + + + align:start position:0% +parameters or the gradient in this case +is equal to that derivative which is + + align:start position:0% +is equal to that derivative which is + + + align:start position:0% +is equal to that derivative which is +easy compute + + align:start position:0% +easy compute + + + align:start position:0% +easy compute +it depends on this Lambda and it depends + + align:start position:0% +it depends on this Lambda and it depends + + + align:start position:0% +it depends on this Lambda and it depends +on the derivative of f respect to p + + align:start position:0% +on the derivative of f respect to p + + + align:start position:0% +on the derivative of f respect to p +oh that's a Jacobian basically + + align:start position:0% +oh that's a Jacobian basically + + + align:start position:0% +oh that's a Jacobian basically +so + + align:start position:0% +so + + + align:start position:0% +so +let me let this here right here + + align:start position:0% +let me let this here right here + + + align:start position:0% +let me let this here right here +so what's kind of the procedure that we + + align:start position:0% +so what's kind of the procedure that we + + + align:start position:0% +so what's kind of the procedure that we +need to do to solve it right so + + align:start position:0% +need to do to solve it right so + + + align:start position:0% +need to do to solve it right so +when we solve + + align:start position:0% +when we solve + + + align:start position:0% +when we solve +that integral we realized that we first + + align:start position:0% +that integral we realized that we first + + + align:start position:0% +that integral we realized that we first +have to solve + + align:start position:0% +have to solve + + + align:start position:0% +have to solve +this ordinary differential equation + + align:start position:0% +this ordinary differential equation + + + align:start position:0% +this ordinary differential equation +which gets a special name actually so + + align:start position:0% +which gets a special name actually so + + + align:start position:0% +which gets a special name actually so +this is the a joint ode + + align:start position:0% + + + + align:start position:0% + +but we also see that the forward + + align:start position:0% +but we also see that the forward + + + align:start position:0% +but we also see that the forward +solution is embedded in that ode right + + align:start position:0% +solution is embedded in that ode right + + + align:start position:0% +solution is embedded in that ode right +so to solve for the quantity which we're + + align:start position:0% +so to solve for the quantity which we're + + + align:start position:0% +so to solve for the quantity which we're +interested in we basically have a + + align:start position:0% +interested in we basically have a + + + align:start position:0% +interested in we basically have a +three-step procedure + + align:start position:0% +three-step procedure + + + align:start position:0% +three-step procedure +so we first + + align:start position:0% +so we first + + + align:start position:0% +so we first +solve + + align:start position:0% +solve + + + align:start position:0% +solve +for + + align:start position:0% +for + + + align:start position:0% +for +U of T + + align:start position:0% +U of T + + + align:start position:0% +U of T +oh that's at least the easiest way to + + align:start position:0% +oh that's at least the easiest way to + + + align:start position:0% +oh that's at least the easiest way to +think about we first would solve for the + + align:start position:0% +think about we first would solve for the + + + align:start position:0% +think about we first would solve for the +ode for U of T then we have that + + align:start position:0% +ode for U of T then we have that + + + align:start position:0% +ode for U of T then we have that +information in the next step we solve + + align:start position:0% +information in the next step we solve + + + align:start position:0% +information in the next step we solve +for + + align:start position:0% +for + + + align:start position:0% +for +Lambda of t + + align:start position:0% +Lambda of t + + + align:start position:0% +Lambda of t +my condolences and the Odes again and + + align:start position:0% +my condolences and the Odes again and + + + align:start position:0% +my condolences and the Odes again and +just these these steps just to summarize + + align:start position:0% +just these these steps just to summarize + + + align:start position:0% +just these these steps just to summarize +you solving an ode for U of T + + align:start position:0% + + + + align:start position:0% + +and write down the ode for Lambda Maybe + + align:start position:0% + + + + align:start position:0% + +maybe transpose it back so does Atlanta + + align:start position:0% +maybe transpose it back so does Atlanta + + + align:start position:0% +maybe transpose it back so does Atlanta +Prime + + align:start position:0% +Prime + + + align:start position:0% +Prime +usually usually you would transpose it + + align:start position:0% +usually usually you would transpose it + + + align:start position:0% +usually usually you would transpose it +right okay + + align:start position:0% + + + + align:start position:0% + +of course transposing both sides of that + + align:start position:0% +of course transposing both sides of that + + + align:start position:0% +of course transposing both sides of that +equation for Lambda + + align:start position:0% + + + + align:start position:0% + +Vu transmitter + + align:start position:0% + + + + align:start position:0% + +and there's an initial condition right + + align:start position:0% +and there's an initial condition right + + + align:start position:0% +and there's an initial condition right +so yeah + + align:start position:0% + + + + align:start position:0% + +right the initial condition is kind of + + align:start position:0% +right the initial condition is kind of + + + align:start position:0% +right the initial condition is kind of +important because we see the first ode + + align:start position:0% +important because we see the first ode + + + align:start position:0% +important because we see the first ode +we solve forwards in time and then the + + align:start position:0% +we solve forwards in time and then the + + + align:start position:0% +we solve forwards in time and then the +adjoint ode as you are now used to + + align:start position:0% +adjoint ode as you are now used to + + + align:start position:0% +adjoint ode as you are now used to +probably from reverse mode ad we have to + + align:start position:0% +probably from reverse mode ad we have to + + + align:start position:0% +probably from reverse mode ad we have to +solve backwards in time so we have also + + align:start position:0% +solve backwards in time so we have also + + + align:start position:0% +solve backwards in time so we have also +this forward equals workflow and then + + align:start position:0% +this forward equals workflow and then + + + align:start position:0% +this forward equals workflow and then +once we know U and Lambda we can + + align:start position:0% +once we know U and Lambda we can + + + align:start position:0% +once we know U and Lambda we can +actually solve the integration for + + align:start position:0% + + + + align:start position:0% + +uh EG + + align:start position:0% +uh EG + + + align:start position:0% +uh EG +PP can you write that out just because + + align:start position:0% +PP can you write that out just because + + + align:start position:0% +PP can you write that out just because +it's simplified it simplifies now so you + + align:start position:0% +it's simplified it simplifies now so you + + + align:start position:0% +it's simplified it simplifies now so you +you know several of the terms are + + align:start position:0% +you know several of the terms are + + + align:start position:0% +you know several of the terms are +dropped out shoes + + align:start position:0% +dropped out shoes + + + align:start position:0% +dropped out shoes +right big + + align:start position:0% + + + + align:start position:0% + +that's a no no wait there's no + + align:start position:0% +that's a no no wait there's no + + + align:start position:0% +that's a no no wait there's no +I thought you want to write in terms of + + align:start position:0% +I thought you want to write in terms of + + + align:start position:0% +I thought you want to write in terms of +Lambda oh yeah oh yeah there's no s + + align:start position:0% +Lambda oh yeah oh yeah there's no s + + + align:start position:0% +Lambda oh yeah oh yeah there's no s +anymore wait yeah + + align:start position:0% + + + + align:start position:0% + +yeah that should be right and then plus + + align:start position:0% +yeah that should be right and then plus + + + align:start position:0% +yeah that should be right and then plus +a boundary oh no the boundary term is + + align:start position:0% +a boundary oh no the boundary term is + + + align:start position:0% +a boundary oh no the boundary term is +zero in their case yeah I said it too + + align:start position:0% +zero in their case yeah I said it too + + + align:start position:0% +zero in their case yeah I said it too +so before you continue let me just + + align:start position:0% +so before you continue let me just + + + align:start position:0% +so before you continue let me just +compare this we talked about eye joint + + align:start position:0% +compare this we talked about eye joint + + + align:start position:0% +compare this we talked about eye joint +methods in class before but for solving + + align:start position:0% +methods in class before but for solving + + + align:start position:0% +methods in class before but for solving +like you know linear systems or + + align:start position:0% +like you know linear systems or + + + align:start position:0% +like you know linear systems or +nonlinear equations where you know where + + align:start position:0% +nonlinear equations where you know where + + + align:start position:0% +nonlinear equations where you know where +the dependence on parameter and it was + + align:start position:0% +the dependence on parameter and it was + + + align:start position:0% +the dependence on parameter and it was +at the same flavor sorry so first you + + align:start position:0% +at the same flavor sorry so first you + + + align:start position:0% +at the same flavor sorry so first you +solve the forward equations you solve ax + + align:start position:0% +solve the forward equations you solve ax + + + align:start position:0% +solve the forward equations you solve ax +equals B for X right and then we solved + + align:start position:0% +equals B for X right and then we solved + + + align:start position:0% +equals B for X right and then we solved +an adjoint equation that involved a + + align:start position:0% +an adjoint equation that involved a + + + align:start position:0% +an adjoint equation that involved a +transpose or a transpose of a Jacobian + + align:start position:0% +transpose or a transpose of a Jacobian + + + align:start position:0% +transpose or a transpose of a Jacobian +right but whatever the Adrian equation + + align:start position:0% +right but whatever the Adrian equation + + + align:start position:0% +right but whatever the Adrian equation +was of the same kind of + + align:start position:0% +was of the same kind of + + + align:start position:0% +was of the same kind of +same flavor and same size as the + + align:start position:0% +same flavor and same size as the + + + align:start position:0% +same flavor and same size as the +original problem but it was linear right + + align:start position:0% +original problem but it was linear right + + + align:start position:0% +original problem but it was linear right +and then once you have the forward + + align:start position:0% +and then once you have the forward + + + align:start position:0% +and then once you have the forward +solution the adjunct solution you just + + align:start position:0% +solution the adjunct solution you just + + + align:start position:0% +solution the adjunct solution you just +take some dot products so here you solve + + align:start position:0% +take some dot products so here you solve + + + align:start position:0% +take some dot products so here you solve +an ode right you're using whatever your + + align:start position:0% +an ode right you're using whatever your + + + align:start position:0% +an ode right you're using whatever your +favorite ode solver is then you solve an + + align:start position:0% +favorite ode solver is then you solve an + + + align:start position:0% +favorite ode solver is then you solve an +adjoint ode which is sort of transposed + + align:start position:0% +adjoint ode which is sort of transposed + + + align:start position:0% +adjoint ode which is sort of transposed +and it's linear now even if the original + + align:start position:0% +and it's linear now even if the original + + + align:start position:0% +and it's linear now even if the original +one was non-linear and it's backwards in + + align:start position:0% +one was non-linear and it's backwards in + + + align:start position:0% +one was non-linear and it's backwards in +time if the original one was forwards in + + align:start position:0% +time if the original one was forwards in + + + align:start position:0% +time if the original one was forwards in +time and then once you have the forward + + align:start position:0% +time and then once you have the forward + + + align:start position:0% +time and then once you have the forward +solution U of T and the adjuvant + + align:start position:0% +solution U of T and the adjuvant + + + align:start position:0% +solution U of T and the adjuvant +solution Lambda of T you take some dot + + align:start position:0% +solution Lambda of T you take some dot + + + align:start position:0% +solution Lambda of T you take some dot +products which for functions the analog + + align:start position:0% +products which for functions the analog + + + align:start position:0% +products which for functions the analog +of that is integrals right and so every + + align:start position:0% +of that is integrals right and so every + + + align:start position:0% +of that is integrals right and so every +everything in that sense becomes easy + + align:start position:0% +everything in that sense becomes easy + + + align:start position:0% +everything in that sense becomes easy +now independent even if you have ten + + align:start position:0% +now independent even if you have ten + + + align:start position:0% +now independent even if you have ten +thousand parameters you solve one + + align:start position:0% +thousand parameters you solve one + + + align:start position:0% +thousand parameters you solve one +forward OD one adjunct OD of the same + + align:start position:0% +forward OD one adjunct OD of the same + + + align:start position:0% +forward OD one adjunct OD of the same +size and then some dot products so this + + align:start position:0% +size and then some dot products so this + + + align:start position:0% +size and then some dot products so this +is why you can you can compute + + align:start position:0% +is why you can you can compute + + + align:start position:0% +is why you can you can compute +derivatives affect a huge number of + + align:start position:0% +derivatives affect a huge number of + + + align:start position:0% +derivatives affect a huge number of +parameters sufficiently + + align:start position:0% + + + + align:start position:0% + +and they're kind of always of the same + + align:start position:0% +and they're kind of always of the same + + + align:start position:0% +and they're kind of always of the same +flavor these adjoint reverse mode things + + align:start position:0% + + + + align:start position:0% + +efficiently or like different styles to + + align:start position:0% +efficiently or like different styles to + + + align:start position:0% +efficiently or like different styles to +evaluate that equation + + align:start position:0% +evaluate that equation + + + align:start position:0% +evaluate that equation +the first thing to notice is that + + align:start position:0% +the first thing to notice is that + + + align:start position:0% +the first thing to notice is that +basically that we don't necessarily for + + align:start position:0% +basically that we don't necessarily for + + + align:start position:0% +basically that we don't necessarily for +this continuous adjoint method have to + + align:start position:0% +this continuous adjoint method have to + + + align:start position:0% +this continuous adjoint method have to +store and compute the full continuous + + align:start position:0% +store and compute the full continuous + + + align:start position:0% +store and compute the full continuous +solution of U of T because an OD is + + align:start position:0% +solution of U of T because an OD is + + + align:start position:0% +solution of U of T because an OD is +basically reversible + + align:start position:0% +basically reversible + + + align:start position:0% +basically reversible +and so we can + + align:start position:0% +and so we can + + + align:start position:0% +and so we can +solve the ode forwards just save the + + align:start position:0% +solve the ode forwards just save the + + + align:start position:0% +solve the ode forwards just save the +final value of that ode and then solve + + align:start position:0% +final value of that ode and then solve + + + align:start position:0% +final value of that ode and then solve +it basically in log step backwards + + align:start position:0% +it basically in log step backwards + + + align:start position:0% +it basically in log step backwards +together with Lambda to have well to + + align:start position:0% +together with Lambda to have well to + + + align:start position:0% +together with Lambda to have well to +avoid this kind of storing The + + align:start position:0% +avoid this kind of storing The + + + align:start position:0% +avoid this kind of storing The +Continuous solution of U of T at all + + align:start position:0% +Continuous solution of U of T at all + + + align:start position:0% +Continuous solution of U of T at all +times + + align:start position:0% +times + + + align:start position:0% +times +and + + align:start position:0% +and + + + align:start position:0% +and +everybody happy with that kind of trick + + align:start position:0% +everybody happy with that kind of trick + + + align:start position:0% +everybody happy with that kind of trick +right so + + align:start position:0% +right so + + + align:start position:0% +right so +happy with that kind of trick if it's + + align:start position:0% +happy with that kind of trick if it's + + + align:start position:0% +happy with that kind of trick if it's +chaotic or or something like that so + + align:start position:0% +chaotic or or something like that so + + + align:start position:0% +chaotic or or something like that so +solving it might be expensive decaying + + align:start position:0% +solving it might be expensive decaying + + + align:start position:0% +solving it might be expensive decaying +and solving it backwards might be + + align:start position:0% +and solving it backwards might be + + + align:start position:0% +and solving it backwards might be +exponentially growing so that trick + + align:start position:0% +exponentially growing so that trick + + + align:start position:0% +exponentially growing so that trick +doesn't always work right yes exactly + + align:start position:0% +doesn't always work right yes exactly + + + align:start position:0% +doesn't always work right yes exactly +that trick has to be done with care and + + align:start position:0% +that trick has to be done with care and + + + align:start position:0% +that trick has to be done with care and +there are some right so that trick just + + align:start position:0% +there are some right so that trick just + + + align:start position:0% +there are some right so that trick just +to visualize it again it basically says + + align:start position:0% +to visualize it again it basically says + + + align:start position:0% +to visualize it again it basically says +if we have some + + align:start position:0% +if we have some + + + align:start position:0% +if we have some +ode at u20 and we solve it to some final + + align:start position:0% +ode at u20 and we solve it to some final + + + align:start position:0% +ode at u20 and we solve it to some final +time + + align:start position:0% +time + + + align:start position:0% +time +view of capital T + + align:start position:0% +view of capital T + + + align:start position:0% +view of capital T +I was saying you can just store this + + align:start position:0% +I was saying you can just store this + + + align:start position:0% +I was saying you can just store this +value and start solving it backwards but + + align:start position:0% +value and start solving it backwards but + + + align:start position:0% +value and start solving it backwards but +they are depending on your physical + + align:start position:0% +they are depending on your physical + + + align:start position:0% +they are depending on your physical +system + + align:start position:0% +system + + + align:start position:0% +system +well your trajectory might not because a + + align:start position:0% +well your trajectory might not because a + + + align:start position:0% +well your trajectory might not because a +numerical solver might not be reversible + + align:start position:0% +numerical solver might not be reversible + + + align:start position:0% +numerical solver might not be reversible +you might deviate from your true + + align:start position:0% +you might deviate from your true + + + align:start position:0% +you might deviate from your true +solution and then if you solve it for + + align:start position:0% +solution and then if you solve it for + + + align:start position:0% +solution and then if you solve it for +long times again backwards that might be + + align:start position:0% +long times again backwards that might be + + + align:start position:0% +long times again backwards that might be +numerically very bad and so the first + + align:start position:0% +numerically very bad and so the first + + + align:start position:0% +numerically very bad and so the first +thing people are usually doing is + + align:start position:0% +thing people are usually doing is + + + align:start position:0% +thing people are usually doing is +introducing so-called checkpoints which + + align:start position:0% +introducing so-called checkpoints which + + + align:start position:0% +introducing so-called checkpoints which +only means once you solve it back and + + align:start position:0% +only means once you solve it back and + + + align:start position:0% +only means once you solve it back and +you reach your checkpoint you basically + + align:start position:0% +you reach your checkpoint you basically + + + align:start position:0% +you reach your checkpoint you basically +reset your solution to + + align:start position:0% +reset your solution to + + + align:start position:0% +reset your solution to +the state which you head forwards so + + align:start position:0% +the state which you head forwards so + + + align:start position:0% +the state which you head forwards so +that reduces a bit the memory + + align:start position:0% +that reduces a bit the memory + + + align:start position:0% +that reduces a bit the memory +consumption and the second trick people + + align:start position:0% +consumption and the second trick people + + + align:start position:0% +consumption and the second trick people +are doing if it's really unstable and + + align:start position:0% +are doing if it's really unstable and + + + align:start position:0% +are doing if it's really unstable and +your ode server is not working then what + + align:start position:0% +your ode server is not working then what + + + align:start position:0% +your ode server is not working then what +you would do is maybe also have these + + align:start position:0% +you would do is maybe also have these + + + align:start position:0% +you would do is maybe also have these +checkpoints but always just store a + + align:start position:0% +checkpoints but always just store a + + + align:start position:0% +checkpoints but always just store a +continuous solution within the + + align:start position:0% +continuous solution within the + + + align:start position:0% +continuous solution within the +checkpoints that you solve forwards + + align:start position:0% +checkpoints that you solve forwards + + + align:start position:0% +checkpoints that you solve forwards +again in time + + align:start position:0% +again in time + + + align:start position:0% +again in time +just another comment on that so one + + align:start position:0% +just another comment on that so one + + + align:start position:0% +just another comment on that so one +thing we have to be always careful about + + align:start position:0% +thing we have to be always careful about + + + align:start position:0% +thing we have to be always careful about +in presenting things is explaining the + + align:start position:0% +in presenting things is explaining the + + + align:start position:0% +in presenting things is explaining the +solution before you explain the problem + + align:start position:0% +solution before you explain the problem + + + align:start position:0% +solution before you explain the problem +right so the the issue here that you're + + align:start position:0% +right so the the issue here that you're + + + align:start position:0% +right so the the issue here that you're +trying to solve with going backwards and + + align:start position:0% +trying to solve with going backwards and + + + align:start position:0% +trying to solve with going backwards and +reversing and so forth is so in + + align:start position:0% +reversing and so forth is so in + + + align:start position:0% +reversing and so forth is so in +principle You Solve It Forward right to + + align:start position:0% +principle You Solve It Forward right to + + + align:start position:0% +principle You Solve It Forward right to +find U of T and then you solve it + + align:start position:0% +find U of T and then you solve it + + + align:start position:0% +find U of T and then you solve it +backwards to find Lambda T and then you + + align:start position:0% +backwards to find Lambda T and then you + + + align:start position:0% +backwards to find Lambda T and then you +take some dot products right the the + + align:start position:0% +take some dot products right the the + + + align:start position:0% +take some dot products right the the +problem you can run into + + align:start position:0% +problem you can run into + + + align:start position:0% +problem you can run into +is that then you need to store U of T + + align:start position:0% +is that then you need to store U of T + + + align:start position:0% +is that then you need to store U of T +not just at the end point but at all the + + align:start position:0% +not just at the end point but at all the + + + align:start position:0% +not just at the end point but at all the +intermediate times which is fine if U of + + align:start position:0% +intermediate times which is fine if U of + + + align:start position:0% +intermediate times which is fine if U of +T is just a small number of parameters + + align:start position:0% +T is just a small number of parameters + + + align:start position:0% +T is just a small number of parameters +and you know you just stored at a bunch + + align:start position:0% +and you know you just stored at a bunch + + + align:start position:0% +and you know you just stored at a bunch +of points and then you like uh uh you + + align:start position:0% +of points and then you like uh uh you + + + align:start position:0% +of points and then you like uh uh you +basically can interpolate with + + align:start position:0% +basically can interpolate with + + + align:start position:0% +basically can interpolate with +polynomials in between right this is how + + align:start position:0% +polynomials in between right this is how + + + align:start position:0% +polynomials in between right this is how +ode solvers work right but this is a + + align:start position:0% +ode solvers work right but this is a + + + align:start position:0% +ode solvers work right but this is a +problem if you're solving a huge system + + align:start position:0% +problem if you're solving a huge system + + + align:start position:0% +problem if you're solving a huge system +of Odes where say it's really a + + align:start position:0% +of Odes where say it's really a + + + align:start position:0% +of Odes where say it's really a +discretized pde for example so you have + + align:start position:0% +discretized pde for example so you have + + + align:start position:0% +discretized pde for example so you have +U is say the electric field at every + + align:start position:0% +U is say the electric field at every + + + align:start position:0% +U is say the electric field at every +point in space as a function of time in + + align:start position:0% +point in space as a function of time in + + + align:start position:0% +point in space as a function of time in +some big computational cell then solving + + align:start position:0% +some big computational cell then solving + + + align:start position:0% +some big computational cell then solving +then usually when you solve it you march + + align:start position:0% +then usually when you solve it you march + + + align:start position:0% +then usually when you solve it you march +It Forward in time and you kind of just + + align:start position:0% +It Forward in time and you kind of just + + + align:start position:0% +It Forward in time and you kind of just +only store the solution at the current + + align:start position:0% +only store the solution at the current + + + align:start position:0% +only store the solution at the current +time but here you need to store all the + + align:start position:0% +time but here you need to store all the + + + align:start position:0% +time but here you need to store all the +solutions at all the intermediate times + + align:start position:0% +solutions at all the intermediate times + + + align:start position:0% +solutions at all the intermediate times +all the way until the end and then go + + align:start position:0% +all the way until the end and then go + + + align:start position:0% +all the way until the end and then go +backwards and you can run out of memory + + align:start position:0% +backwards and you can run out of memory + + + align:start position:0% +backwards and you can run out of memory +and so this is the the basic problem + + align:start position:0% +and so this is the the basic problem + + + align:start position:0% +and so this is the the basic problem +with adjuvant methods and uh when you + + align:start position:0% +with adjuvant methods and uh when you + + + align:start position:0% +with adjuvant methods and uh when you +have like evolving in time or going + + align:start position:0% +have like evolving in time or going + + + align:start position:0% +have like evolving in time or going +through big recurrences is you need to + + align:start position:0% +through big recurrences is you need to + + + align:start position:0% +through big recurrences is you need to +store all the intermediate ones and so + + align:start position:0% +store all the intermediate ones and so + + + align:start position:0% +store all the intermediate ones and so +there's all these tricks to try and Only + + align:start position:0% +there's all these tricks to try and Only + + + align:start position:0% +there's all these tricks to try and Only +store some of the intermediate values at + + align:start position:0% +store some of the intermediate values at + + + align:start position:0% +store some of the intermediate values at +some checkpoints and kind of reconstruct + + align:start position:0% +some checkpoints and kind of reconstruct + + + align:start position:0% +some checkpoints and kind of reconstruct +things on the fly as you as you + + align:start position:0% +things on the fly as you as you + + + align:start position:0% +things on the fly as you as you +integrate ODI integrate Lambda T + + align:start position:0% +integrate ODI integrate Lambda T + + + align:start position:0% +integrate ODI integrate Lambda T +backwards so that you don't need to + + align:start position:0% +backwards so that you don't need to + + + align:start position:0% +backwards so that you don't need to +store everything + + align:start position:0% +store everything + + + align:start position:0% +store everything +uh but that's that's that's sort of the + + align:start position:0% +uh but that's that's that's sort of the + + + align:start position:0% +uh but that's that's that's sort of the +issue that you're you're struggling with + + align:start position:0% +issue that you're you're struggling with + + + align:start position:0% +issue that you're you're struggling with +here but for a small OD easy to only + + align:start position:0% +here but for a small OD easy to only + + + align:start position:0% +here but for a small OD easy to only +have a few a few things you know getting + + align:start position:0% +have a few a few things you know getting + + + align:start position:0% +have a few a few things you know getting +in time you just you just store the + + align:start position:0% +in time you just you just store the + + + align:start position:0% +in time you just you just store the +whole solution it's not that hard right + + align:start position:0% +whole solution it's not that hard right + + + align:start position:0% +whole solution it's not that hard right +true + + align:start position:0% +true + + + align:start position:0% +true +um yeah or for small Odes that contains + + align:start position:0% +um yeah or for small Odes that contains + + + align:start position:0% +um yeah or for small Odes that contains +some parametric function that's very + + align:start position:0% +some parametric function that's very + + + align:start position:0% +some parametric function that's very +expensive to evaluate right like like + + align:start position:0% +expensive to evaluate right like like + + + align:start position:0% +expensive to evaluate right like like +what Chris is basically doing is putting + + align:start position:0% +what Chris is basically doing is putting + + + align:start position:0% +what Chris is basically doing is putting +a neural network inside the drift + + align:start position:0% +a neural network inside the drift + + + align:start position:0% +a neural network inside the drift +function so even if the ode itself looks + + align:start position:0% +function so even if the ode itself looks + + + align:start position:0% +function so even if the ode itself looks +very simple if you have a neural network + + align:start position:0% +very simple if you have a neural network + + + align:start position:0% +very simple if you have a neural network +in each time step you will have to store + + align:start position:0% +in each time step you will have to store + + + align:start position:0% +in each time step you will have to store +all intermediate computations also and + + align:start position:0% +all intermediate computations also and + + + align:start position:0% +all intermediate computations also and +outputs of that so yeah it makes the + + align:start position:0% +outputs of that so yeah it makes the + + + align:start position:0% +outputs of that so yeah it makes the +um it's continuous joint very meaningful + + align:start position:0% + + + + align:start position:0% + +yeah right so there's a third kind of + + align:start position:0% +yeah right so there's a third kind of + + + align:start position:0% +yeah right so there's a third kind of +trick to + + align:start position:0% +trick to + + + align:start position:0% +trick to +um + + align:start position:0% +um + + + align:start position:0% +um +to about which can be used to + + align:start position:0% +to about which can be used to + + + align:start position:0% +to about which can be used to +um + + align:start position:0% +um + + + align:start position:0% +um +simplify that workflow even a bit more + + align:start position:0% +simplify that workflow even a bit more + + + align:start position:0% +simplify that workflow even a bit more +um that's basically that's the first + + align:start position:0% +um that's basically that's the first + + + align:start position:0% +um that's basically that's the first +trick and as we now discussed it's not + + align:start position:0% +trick and as we now discussed it's not + + + align:start position:0% +trick and as we now discussed it's not +always applicable but if it's applicable + + align:start position:0% +always applicable but if it's applicable + + + align:start position:0% +always applicable but if it's applicable +um it can be nice and very efficient + + align:start position:0% +um it can be nice and very efficient + + + align:start position:0% +um it can be nice and very efficient +the third trick is basically to look at + + align:start position:0% +the third trick is basically to look at + + + align:start position:0% +the third trick is basically to look at +the at this integration term + + align:start position:0% +the at this integration term + + + align:start position:0% +the at this integration term +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% + + + + align:start position:0% + +basically realized that an integration + + align:start position:0% +basically realized that an integration + + + align:start position:0% +basically realized that an integration +can also be phrased as a solution to an + + align:start position:0% +can also be phrased as a solution to an + + + align:start position:0% +can also be phrased as a solution to an +ordinary differential equation + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +not sure if that was + + align:start position:0% +not sure if that was + + + align:start position:0% +not sure if that was +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +but yeah let's say I have a function + + align:start position:0% +but yeah let's say I have a function + + + align:start position:0% +but yeah let's say I have a function +f + + align:start position:0% +f + + + align:start position:0% +f +I want to integrate as a + + align:start position:0% +I want to integrate as a + + + align:start position:0% +I want to integrate as a +called find + + align:start position:0% + + + + align:start position:0% + +but everybody agrees that's kind of the + + align:start position:0% +but everybody agrees that's kind of the + + + align:start position:0% +but everybody agrees that's kind of the +same form so we have + + align:start position:0% +same form so we have + + + align:start position:0% +same form so we have +some some integration + + align:start position:0% +some some integration + + + align:start position:0% +some some integration +and now the claim is that we can write + + align:start position:0% +and now the claim is that we can write + + + align:start position:0% +and now the claim is that we can write +that as an ordinary differential + + align:start position:0% +that as an ordinary differential + + + align:start position:0% +that as an ordinary differential +equation + + align:start position:0% +equation + + + align:start position:0% +equation +um small F of t + + align:start position:0% +um small F of t + + + align:start position:0% +um small F of t +and yeah now we want to basically apply + + align:start position:0% +and yeah now we want to basically apply + + + align:start position:0% +and yeah now we want to basically apply +Euler's method to that + + align:start position:0% +Euler's method to that + + + align:start position:0% +Euler's method to that +and so if we apply Euler's method + + align:start position:0% +and so if we apply Euler's method + + + align:start position:0% +and so if we apply Euler's method +up here for a second so + + align:start position:0% +up here for a second so + + + align:start position:0% +up here for a second so +before you again give the solution so + + align:start position:0% +before you again give the solution so + + + align:start position:0% +before you again give the solution so +you're going to write a differential + + align:start position:0% +you're going to write a differential + + + align:start position:0% +you're going to write a differential +equation W Prime equals F of T right so + + align:start position:0% +equation W Prime equals F of T right so + + + align:start position:0% +equation W Prime equals F of T right so +uh WT is going to be a new variable + + align:start position:0% +uh WT is going to be a new variable + + + align:start position:0% +uh WT is going to be a new variable +what's the initial condition of that + + align:start position:0% +what's the initial condition of that + + + align:start position:0% +what's the initial condition of that +that you're going to want to use again + + align:start position:0% +that you're going to want to use again + + + align:start position:0% +that you're going to want to use again +at the end you're going to want to write + + align:start position:0% +at the end you're going to want to write + + + align:start position:0% +at the end you're going to want to write +down a differential equation whose + + align:start position:0% +down a differential equation whose + + + align:start position:0% +down a differential equation whose +solution gives that integral + + align:start position:0% +solution gives that integral + + + align:start position:0% +solution gives that integral +so what it is you're going to write a + + align:start position:0% +so what it is you're going to write a + + + align:start position:0% +so what it is you're going to write a +differential equation DWT DT equals + + align:start position:0% +differential equation DWT DT equals + + + align:start position:0% +differential equation DWT DT equals +little F of T what initial condition + + align:start position:0% +little F of T what initial condition + + + align:start position:0% +little F of T what initial condition +should you use + + align:start position:0% + + + + align:start position:0% + +any guesses + + align:start position:0% +any guesses + + + align:start position:0% +any guesses +to get to turn it back so its solution + + align:start position:0% +to get to turn it back so its solution + + + align:start position:0% +to get to turn it back so its solution +will give you the same thing as that + + align:start position:0% +will give you the same thing as that + + + align:start position:0% +will give you the same thing as that +definite integral from t 0 to T + + align:start position:0% + + + + align:start position:0% + +zero okay so put at what time + + align:start position:0% +zero okay so put at what time + + + align:start position:0% +zero okay so put at what time +at Tina so w t naught equals + + align:start position:0% +at Tina so w t naught equals + + + align:start position:0% +at Tina so w t naught equals +equals zero + + align:start position:0% +equals zero + + + align:start position:0% +equals zero +and then what's cap capital F of T + + align:start position:0% +and then what's cap capital F of T + + + align:start position:0% +and then what's cap capital F of T +equals what then so now the the integral + + align:start position:0% +equals what then so now the the integral + + + align:start position:0% +equals what then so now the the integral +you want the first line capital is that + + align:start position:0% +you want the first line capital is that + + + align:start position:0% +you want the first line capital is that +an i or an F I can't uh that's an F + + align:start position:0% +an i or an F I can't uh that's an F + + + align:start position:0% +an i or an F I can't uh that's an F +that's a capital f okay it has the uh + + align:start position:0% +that's a capital f okay it has the uh + + + align:start position:0% +that's a capital f okay it has the uh +the the second line going + + align:start position:0% +the the second line going + + + align:start position:0% +the the second line going +okay anyway so so your capital F of T + + align:start position:0% +okay anyway so so your capital F of T + + + align:start position:0% +okay anyway so so your capital F of T +your integral that you want is what in + + align:start position:0% +your integral that you want is what in + + + align:start position:0% +your integral that you want is what in +terms of w so if you have a differential + + align:start position:0% +terms of w so if you have a differential + + + align:start position:0% +terms of w so if you have a differential +equation it's initial condition to equal + + align:start position:0% +equation it's initial condition to equal + + + align:start position:0% +equation it's initial condition to equal +zero is zero a t zero is zero its + + align:start position:0% +zero is zero a t zero is zero its + + + align:start position:0% +zero is zero a t zero is zero its +derivative is is left of t + + align:start position:0% +derivative is is left of t + + + align:start position:0% +derivative is is left of t +so then the integral is what now + + align:start position:0% + + + + align:start position:0% + +yeah right so I can write that integral + + align:start position:0% +yeah right so I can write that integral + + + align:start position:0% +yeah right so I can write that integral +let me write one step in between + + align:start position:0% +let me write one step in between + + + align:start position:0% +let me write one step in between +basically + + align:start position:0% + + + + align:start position:0% + +you're kind of discretizing it first so + + align:start position:0% +you're kind of discretizing it first so + + + align:start position:0% +you're kind of discretizing it first so +before you discretize that I want to + + align:start position:0% +before you discretize that I want to + + + align:start position:0% +before you discretize that I want to +make sure they understand the connection + + align:start position:0% +make sure they understand the connection + + + align:start position:0% +make sure they understand the connection +between the ode and the integral so + + align:start position:0% +between the ode and the integral so + + + align:start position:0% +between the ode and the integral so +don't don't discretize it yet right this + + align:start position:0% +don't don't discretize it yet right this + + + align:start position:0% +don't don't discretize it yet right this +this is this is an exact relationship + + align:start position:0% +this is this is an exact relationship + + + align:start position:0% +this is this is an exact relationship +right oh so just once we've Plugged In + + align:start position:0% +right oh so just once we've Plugged In + + + align:start position:0% +right oh so just once we've Plugged In +The W yeah it's w of what + + align:start position:0% + + + + align:start position:0% + +no no there's no integral it's equal to + + align:start position:0% +no no there's no integral it's equal to + + + align:start position:0% +no no there's no integral it's equal to +W of + + align:start position:0% + + + + align:start position:0% + +it's it's w of capital T right that + + align:start position:0% +it's it's w of capital T right that + + + align:start position:0% +it's it's w of capital T right that +that's oh okay no I see what you want to + + align:start position:0% +that's oh okay no I see what you want to + + + align:start position:0% +that's oh okay no I see what you want to +screw it right + + align:start position:0% +screw it right + + + align:start position:0% +screw it right +so the point is if you have if you have + + align:start position:0% +so the point is if you have if you have + + + align:start position:0% +so the point is if you have if you have +a differential equation W primed equals + + align:start position:0% +a differential equation W primed equals + + + align:start position:0% +a differential equation W primed equals +ft the solution is just the integral W + + align:start position:0% +ft the solution is just the integral W + + + align:start position:0% +ft the solution is just the integral W +is just the integral of f which is what + + align:start position:0% +is just the integral of f which is what + + + align:start position:0% +is just the integral of f which is what +you want and then you put the initial + + align:start position:0% +you want and then you put the initial + + + align:start position:0% +you want and then you put the initial +condition t zero equals zero that's the + + align:start position:0% +condition t zero equals zero that's the + + + align:start position:0% +condition t zero equals zero that's the +left edge of the integral + + align:start position:0% +left edge of the integral + + + align:start position:0% +left edge of the integral +and then the final integral you want is + + align:start position:0% +and then the final integral you want is + + + align:start position:0% +and then the final integral you want is +just W of T so that's he's turning the + + align:start position:0% +just W of T so that's he's turning the + + + align:start position:0% +just W of T so that's he's turning the +the integral you want is just a + + align:start position:0% +the integral you want is just a + + + align:start position:0% +the integral you want is just a +differential equation + + align:start position:0% +differential equation + + + align:start position:0% +differential equation +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh is this differential equation now + + align:start position:0% +uh is this differential equation now + + + align:start position:0% +uh is this differential equation now +you're going to discretize it well + + align:start position:0% +you're going to discretize it well + + + align:start position:0% +you're going to discretize it well +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +right now if I'm discretizing it I will + + align:start position:0% +right now if I'm discretizing it I will + + + align:start position:0% +right now if I'm discretizing it I will +see the same basically as for + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +because not everyone here has done a lot + + align:start position:0% +because not everyone here has done a lot + + + align:start position:0% +because not everyone here has done a lot +of differential equations right or maybe + + align:start position:0% +of differential equations right or maybe + + + align:start position:0% +of differential equations right or maybe +hasn't done them recently so I want to + + align:start position:0% +hasn't done them recently so I want to + + + align:start position:0% +hasn't done them recently so I want to +make sure they understand + + align:start position:0% +make sure they understand + + + align:start position:0% +make sure they understand +okay + + align:start position:0% +okay + + + align:start position:0% +okay +understood that that trick + + align:start position:0% + + + + align:start position:0% + +s + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% +oh + + + align:start position:0% +oh +right so I'm basically writing down on + + align:start position:0% +right so I'm basically writing down on + + + align:start position:0% +right so I'm basically writing down on +the + + align:start position:0% +the + + + align:start position:0% +the +what the Euler steps would be in the + + align:start position:0% +what the Euler steps would be in the + + + align:start position:0% +what the Euler steps would be in the +discretization product integral + + align:start position:0% + + + + align:start position:0% + +that's the first and then I could just + + align:start position:0% +that's the first and then I could just + + + align:start position:0% +that's the first and then I could just +keep + + align:start position:0% + + + + align:start position:0% + +iterating + + align:start position:0% + + + + align:start position:0% + +well let's think of the moment for + + align:start position:0% + + + + align:start position:0% + +so these are n Euler steps + + align:start position:0% +so these are n Euler steps + + + align:start position:0% +so these are n Euler steps +iterate on the function + + align:start position:0% + + + + align:start position:0% + +there's an image probably some + + align:start position:0% + + + + align:start position:0% + +right because once I have my first step + + align:start position:0% +right because once I have my first step + + + align:start position:0% +right because once I have my first step +the time changes and then that's flag + + align:start position:0% +the time changes and then that's flag + + + align:start position:0% +the time changes and then that's flag +big uh also into the into the function + + align:start position:0% +big uh also into the into the function + + + align:start position:0% +big uh also into the into the function +it's really an approximation for the + + align:start position:0% +it's really an approximation for the + + + align:start position:0% +it's really an approximation for the +original thing right so you're writing + + align:start position:0% +original thing right so you're writing + + + align:start position:0% +original thing right so you're writing +equals here but + + align:start position:0% +equals here but + + + align:start position:0% +equals here but +just just to be clear right the original + + align:start position:0% +just just to be clear right the original + + + align:start position:0% +just just to be clear right the original +equation is you have an integral and the + + align:start position:0% +equation is you have an integral and the + + + align:start position:0% +equation is you have an integral and the +differential equation that that's an + + align:start position:0% +differential equation that that's an + + + align:start position:0% +differential equation that that's an +exact relationship and now you're going + + align:start position:0% +exact relationship and now you're going + + + align:start position:0% +exact relationship and now you're going +to write the discrete analog of that or + + align:start position:0% +to write the discrete analog of that or + + + align:start position:0% +to write the discrete analog of that or +discrete approximation so w t plus delta + + align:start position:0% +discrete approximation so w t plus delta + + + align:start position:0% +discrete approximation so w t plus delta +T is really approximately equal to W of + + align:start position:0% +T is really approximately equal to W of + + + align:start position:0% +T is really approximately equal to W of +t plus T delta T and this is + + align:start position:0% +t plus T delta T and this is + + + align:start position:0% +t plus T delta T and this is +approximately excuse me if I do again + + align:start position:0% +approximately excuse me if I do again + + + align:start position:0% +approximately excuse me if I do again +something like an Euler + + align:start position:0% +something like an Euler + + + align:start position:0% +something like an Euler +is it + + align:start position:0% + + + + align:start position:0% + +you can approximate the derivative by a + + align:start position:0% +you can approximate the derivative by a + + + align:start position:0% +you can approximate the derivative by a +difference and then the integral your + + align:start position:0% +difference and then the integral your + + + align:start position:0% +difference and then the integral your +proxy is essentially approximated by a + + align:start position:0% +proxy is essentially approximated by a + + + align:start position:0% +proxy is essentially approximated by a +sum + + align:start position:0% + + + + align:start position:0% + +right and so this now has then also the + + align:start position:0% +right and so this now has then also the + + + align:start position:0% +right and so this now has then also the +I mean the typical form + + align:start position:0% +I mean the typical form + + + align:start position:0% +I mean the typical form +of what you would do numerically to + + align:start position:0% +of what you would do numerically to + + + align:start position:0% +of what you would do numerically to +solve an integral right so it's a + + align:start position:0% +solve an integral right so it's a + + + align:start position:0% +solve an integral right so it's a +yeah you have to function value + + align:start position:0% +yeah you have to function value + + + align:start position:0% +yeah you have to function value +at different points and then with the + + align:start position:0% +at different points and then with the + + + align:start position:0% +at different points and then with the +discretization that you use and and sum + + align:start position:0% +discretization that you use and and sum + + + align:start position:0% +discretization that you use and and sum +it all up + + align:start position:0% +it all up + + + align:start position:0% +it all up +a way to do an approximate integral + + align:start position:0% +a way to do an approximate integral + + + align:start position:0% +a way to do an approximate integral +numerically just like oil or the + + align:start position:0% +numerically just like oil or the + + + align:start position:0% +numerically just like oil or the +integration for Odes and this + + align:start position:0% +integration for Odes and this + + + align:start position:0% +integration for Odes and this +approximate sum for an integral this is + + align:start position:0% +approximate sum for an integral this is + + + align:start position:0% +approximate sum for an integral this is +you should never ever do this in reality + + align:start position:0% +you should never ever do this in reality + + + align:start position:0% +you should never ever do this in reality +almost because there's + + align:start position:0% +almost because there's + + + align:start position:0% +almost because there's +exponentially more accurate ways to to + + align:start position:0% +exponentially more accurate ways to to + + + align:start position:0% +exponentially more accurate ways to to +integrate approximate integrals but it's + + align:start position:0% +integrate approximate integrals but it's + + + align:start position:0% +integrate approximate integrals but it's +a nice way to to Really simply think of + + align:start position:0% +a nice way to to Really simply think of + + + align:start position:0% +a nice way to to Really simply think of +an it if you're confused by integrals + + align:start position:0% +an it if you're confused by integrals + + + align:start position:0% +an it if you're confused by integrals +and derivatives that you can think of + + align:start position:0% +and derivatives that you can think of + + + align:start position:0% +and derivatives that you can think of +them as differences in sums or sums and + + align:start position:0% +them as differences in sums or sums and + + + align:start position:0% +them as differences in sums or sums and +differences all right + + align:start position:0% +differences all right + + + align:start position:0% +differences all right +yeah right let's say I mean it's true + + align:start position:0% +yeah right let's say I mean it's true + + + align:start position:0% +yeah right let's say I mean it's true +for both right the Euler server for + + align:start position:0% +for both right the Euler server for + + + align:start position:0% +for both right the Euler server for +Odes and the kind of derivation for the + + align:start position:0% +Odes and the kind of derivation for the + + + align:start position:0% +Odes and the kind of derivation for the +integral + + align:start position:0% + + + + align:start position:0% + +yeah that's actually the full derivation + + align:start position:0% +yeah that's actually the full derivation + + + align:start position:0% +yeah that's actually the full derivation +yeah so does everyone see that basically + + align:start position:0% +yeah so does everyone see that basically + + + align:start position:0% +yeah so does everyone see that basically +then if you plug in the initial T is + + align:start position:0% +then if you plug in the initial T is + + + align:start position:0% +then if you plug in the initial T is +zero wt0 is zero + + align:start position:0% +zero wt0 is zero + + + align:start position:0% +zero wt0 is zero +right so I mean once you take it one + + align:start position:0% +right so I mean once you take it one + + + align:start position:0% +right so I mean once you take it one +step further so then wt0 if WT 0 is 0 + + align:start position:0% +step further so then wt0 if WT 0 is 0 + + + align:start position:0% +step further so then wt0 if WT 0 is 0 +the first term is zero the second term + + align:start position:0% +the first term is zero the second term + + + align:start position:0% +the first term is zero the second term +is approximately + + align:start position:0% +is approximately + + + align:start position:0% +is approximately +the integral right so this is just + + align:start position:0% +the integral right so this is just + + + align:start position:0% +the integral right so this is just +restating the same thing just with sums + + align:start position:0% +restating the same thing just with sums + + + align:start position:0% +restating the same thing just with sums +and differences so this is + + align:start position:0% +and differences so this is + + + align:start position:0% +and differences so this is +so the solution of the ode is is really + + align:start position:0% +so the solution of the ode is is really + + + align:start position:0% +so the solution of the ode is is really +the integral + + align:start position:0% + + + + align:start position:0% + +yeah to summarize that so we can have + + align:start position:0% +yeah to summarize that so we can have + + + align:start position:0% +yeah to summarize that so we can have +them + + align:start position:0% +them + + + align:start position:0% +them +basically all the three methods above + + align:start position:0% +basically all the three methods above + + + align:start position:0% +basically all the three methods above +wait okay so can you finish and write it + + align:start position:0% +wait okay so can you finish and write it + + + align:start position:0% +wait okay so can you finish and write it +as I said the point what you're going to + + align:start position:0% +as I said the point what you're going to + + + align:start position:0% +as I said the point what you're going to +do then is just merge the solution of + + align:start position:0% +do then is just merge the solution of + + + align:start position:0% +do then is just merge the solution of +the adjoint ode with the with with that + + align:start position:0% +the adjoint ode with the with with that + + + align:start position:0% +the adjoint ode with the with with that +integral on the third step so instead of + + align:start position:0% +integral on the third step so instead of + + + align:start position:0% +integral on the third step so instead of +doing the separate steps so you can + + align:start position:0% +doing the separate steps so you can + + + align:start position:0% +doing the separate steps so you can +maybe just write down the the derivative + + align:start position:0% +maybe just write down the the derivative + + + align:start position:0% +maybe just write down the the derivative +it has a yeah so what's w w is now going + + align:start position:0% +it has a yeah so what's w w is now going + + + align:start position:0% +it has a yeah so what's w w is now going +to be is no no W is going to be Lambda + + align:start position:0% +to be is no no W is going to be Lambda + + + align:start position:0% +to be is no no W is going to be Lambda +and and + + align:start position:0% +and and + + + align:start position:0% +and and +okay it doesn't matter + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +yeah depending on you want to go in the + + align:start position:0% +yeah depending on you want to go in the + + + align:start position:0% +yeah depending on you want to go in the +other direction right + + align:start position:0% +other direction right + + + align:start position:0% +other direction right +probably want to solve it like that + + align:start position:0% +probably want to solve it like that + + + align:start position:0% +probably want to solve it like that +the point is you think of this as a + + align:start position:0% +the point is you think of this as a + + + align:start position:0% +the point is you think of this as a +coupled ode for w along with the I joint + + align:start position:0% +coupled ode for w along with the I joint + + + align:start position:0% +coupled ode for w along with the I joint +ode for Lambda Prime so if you write + + align:start position:0% +ode for Lambda Prime so if you write + + + align:start position:0% +ode for Lambda Prime so if you write +down the Lambda Prime underneath right + + align:start position:0% + + + + align:start position:0% + +oh + + align:start position:0% + + + + align:start position:0% + +so you can think of this as one system + + align:start position:0% +so you can think of this as one system + + + align:start position:0% +so you can think of this as one system +of ode's for a vector that contains + + align:start position:0% +of ode's for a vector that contains + + + align:start position:0% +of ode's for a vector that contains +W and and Lambda right so so you just + + align:start position:0% +W and and Lambda right so so you just + + + align:start position:0% +W and and Lambda right so so you just +you just do do the two things together + + align:start position:0% +you just do do the two things together + + + align:start position:0% +you just do do the two things together +instead of instead of a separate steps + + align:start position:0% +instead of instead of a separate steps + + + align:start position:0% +instead of instead of a separate steps +oh and and then I guess yeah you could + + align:start position:0% +oh and and then I guess yeah you could + + + align:start position:0% +oh and and then I guess yeah you could +also if you could also integrate the + + align:start position:0% +also if you could also integrate the + + + align:start position:0% +also if you could also integrate the +original equation backwards as well + + align:start position:0% + + + + align:start position:0% + +right so so now your unknowns are W + + align:start position:0% +right so so now your unknowns are W + + + align:start position:0% +right so so now your unknowns are W +Lambda and U it's like one big Vector of + + align:start position:0% +Lambda and U it's like one big Vector of + + + align:start position:0% +Lambda and U it's like one big Vector of +those three things stack together + + align:start position:0% + + + + align:start position:0% + +that's it + + align:start position:0% +that's it + + + align:start position:0% +that's it +and the advantage of this is that you + + align:start position:0% +and the advantage of this is that you + + + align:start position:0% +and the advantage of this is that you +don't need to store the lambdas I guess + + align:start position:0% +don't need to store the lambdas I guess + + + align:start position:0% +don't need to store the lambdas I guess +and maybe and maybe the use if you were + + align:start position:0% +and maybe and maybe the use if you were + + + align:start position:0% +and maybe and maybe the use if you were +able to integrate the whole thing + + align:start position:0% +able to integrate the whole thing + + + align:start position:0% +able to integrate the whole thing +backwards you don't need to store + + align:start position:0% +backwards you don't need to store + + + align:start position:0% +backwards you don't need to store +anything you just you just you just pass + + align:start position:0% +anything you just you just you just pass + + + align:start position:0% +anything you just you just you just pass +this to your ode integrator and it only + + align:start position:0% +this to your ode integrator and it only + + + align:start position:0% +this to your ode integrator and it only +keeps track of your current your current + + align:start position:0% +keeps track of your current your current + + + align:start position:0% +keeps track of your current your current +step and it just walks from beginning to + + align:start position:0% +step and it just walks from beginning to + + + align:start position:0% +step and it just walks from beginning to +end and at the end of the day your W is + + align:start position:0% +end and at the end of the day your W is + + + align:start position:0% +end and at the end of the day your W is +the is the integral that you want is + + align:start position:0% +the is the integral that you want is + + + align:start position:0% +the is the integral that you want is +this is the derivative + + align:start position:0% +this is the derivative + + + align:start position:0% +this is the derivative +so that's a most memory efficient one to + + align:start position:0% +so that's a most memory efficient one to + + + align:start position:0% +so that's a most memory efficient one to +basically solve photosensitive + + align:start position:0% +basically solve photosensitive + + + align:start position:0% +basically solve photosensitive +sensitivity DG DP in the end + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +we should maybe take a break ready or + + align:start position:0% +we should maybe take a break ready or + + + align:start position:0% +we should maybe take a break ready or +any minute but are you are you basically + + align:start position:0% +any minute but are you are you basically + + + align:start position:0% +any minute but are you are you basically +is this basically it or are you going to + + align:start position:0% +is this basically it or are you going to + + + align:start position:0% +is this basically it or are you going to +show some examples I would have the + + align:start position:0% +show some examples I would have the + + + align:start position:0% +show some examples I would have the +integration of that numerically but it + + align:start position:0% +integration of that numerically but it + + + align:start position:0% +integration of that numerically but it +takes another + + align:start position:0% +takes another + + + align:start position:0% +takes another +10-15 minutes at least um yeah I see + + align:start position:0% +10-15 minutes at least um yeah I see + + + align:start position:0% +10-15 minutes at least um yeah I see +when I show an example of uh yeah I mean + + align:start position:0% +when I show an example of uh yeah I mean + + + align:start position:0% +when I show an example of uh yeah I mean +we can do that after the break but maybe + + align:start position:0% +we can do that after the break but maybe + + + align:start position:0% +we can do that after the break but maybe +we can just take a okay to take a break + + align:start position:0% +we can just take a okay to take a break + + + align:start position:0% +we can just take a okay to take a break +for a couple of minutes now but do + + align:start position:0% +for a couple of minutes now but do + + + align:start position:0% +for a couple of minutes now but do +people have questions before we before + + align:start position:0% +people have questions before we before + + + align:start position:0% +people have questions before we before +about this step yeah forward OG adjoint + + align:start position:0% +about this step yeah forward OG adjoint + + + align:start position:0% +about this step yeah forward OG adjoint +ode and then adopt product which is + + align:start position:0% +ode and then adopt product which is + + + align:start position:0% +ode and then adopt product which is +based in the integral and then there's + + align:start position:0% +based in the integral and then there's + + + align:start position:0% +based in the integral and then there's +these tricks to try and basically + + align:start position:0% +these tricks to try and basically + + + align:start position:0% +these tricks to try and basically +combine them into one ode that you solve + + align:start position:0% +combine them into one ode that you solve + + + align:start position:0% +combine them into one ode that you solve +instead of having to store U of T store + + align:start position:0% +instead of having to store U of T store + + + align:start position:0% +instead of having to store U of T store +Lambda of T and then do the integral + + align:start position:0% + + + + align:start position:0% + +to some + + align:start position:0% +to some + + + align:start position:0% +to some +um + + align:start position:0% + + + + align:start position:0% + +so if the system's like not chaotic you + + align:start position:0% +so if the system's like not chaotic you + + + align:start position:0% +so if the system's like not chaotic you +probably want to start it like the final + + align:start position:0% +probably want to start it like the final + + + align:start position:0% +probably want to start it like the final +data point integrate backwards + + align:start position:0% +data point integrate backwards + + + align:start position:0% +data point integrate backwards +equations + + align:start position:0% +equations + + + align:start position:0% +equations +is + + align:start position:0% + + + + align:start position:0% + +yeah so suppose capital G maybe suppose + + align:start position:0% +yeah so suppose capital G maybe suppose + + + align:start position:0% +yeah so suppose capital G maybe suppose +capital G is a sum and not an integral + + align:start position:0% +capital G is a sum and not an integral + + + align:start position:0% +capital G is a sum and not an integral +right so so you're or you're you have a + + align:start position:0% +right so so you're or you're you have a + + + align:start position:0% +right so so you're or you're you have a +bunch of Delta functions another way of + + align:start position:0% +bunch of Delta functions another way of + + + align:start position:0% +bunch of Delta functions another way of +thinking about it right so basically + + align:start position:0% +thinking about it right so basically + + + align:start position:0% +thinking about it right so basically +you're comparing the solution U of T to + + align:start position:0% +you're comparing the solution U of T to + + + align:start position:0% +you're comparing the solution U of T to +say some known Solutions and measured + + align:start position:0% +say some known Solutions and measured + + + align:start position:0% +say some known Solutions and measured +data at only a discrete set of times so + + align:start position:0% +data at only a discrete set of times so + + + align:start position:0% +data at only a discrete set of times so +now G is a sum right so one way to do it + + align:start position:0% +now G is a sum right so one way to do it + + + align:start position:0% +now G is a sum right so one way to do it +would be to compute U of T Lambda of T + + align:start position:0% +would be to compute U of T Lambda of T + + + align:start position:0% +would be to compute U of T Lambda of T +and then just and then then just do the + + align:start position:0% +and then just and then then just do the + + + align:start position:0% +and then just and then then just do the +sum but is there a way to combine that + + align:start position:0% +sum but is there a way to combine that + + + align:start position:0% +sum but is there a way to combine that +into a single ode if now if now capital + + align:start position:0% +into a single ode if now if now capital + + + align:start position:0% +into a single ode if now if now capital +G is not an integral it's it's a + + align:start position:0% +G is not an integral it's it's a + + + align:start position:0% +G is not an integral it's it's a +discrete summation over a set of times + + align:start position:0% +discrete summation over a set of times + + + align:start position:0% +discrete summation over a set of times +yeah basically if you can write it go to + + align:start position:0% +yeah basically if you can write it go to + + + align:start position:0% +yeah basically if you can write it go to +this kind of discrete formulation the + + align:start position:0% +this kind of discrete formulation the + + + align:start position:0% +this kind of discrete formulation the +probably easiest way I think to think + + align:start position:0% +probably easiest way I think to think + + + align:start position:0% +probably easiest way I think to think +about it is that + + align:start position:0% +about it is that + + + align:start position:0% +about it is that +these describe the kind of continuous + + align:start position:0% +these describe the kind of continuous + + + align:start position:0% +these describe the kind of continuous +changes that you want to have on the on + + align:start position:0% +changes that you want to have on the on + + + align:start position:0% +changes that you want to have on the on +on uh in the cost function and so what + + align:start position:0% +on uh in the cost function and so what + + + align:start position:0% +on uh in the cost function and so what +you will have if you just have your cost + + align:start position:0% +you will have if you just have your cost + + + align:start position:0% +you will have if you just have your cost +function compared at discrete time + + align:start position:0% +function compared at discrete time + + + align:start position:0% +function compared at discrete time +points you know right you basically have + + align:start position:0% +points you know right you basically have + + + align:start position:0% +points you know right you basically have +your your solution and then at some + + align:start position:0% +your your solution and then at some + + + align:start position:0% +your your solution and then at some +point + + align:start position:0% +point + + + align:start position:0% +point +um + + align:start position:0% +um + + + align:start position:0% +um +you compare your cost and so what will + + align:start position:0% +you compare your cost and so what will + + + align:start position:0% +you compare your cost and so what will +happen is that you just sort of + + align:start position:0% +happen is that you just sort of + + + align:start position:0% +happen is that you just sort of +you will have a backward solution + + align:start position:0% +you will have a backward solution + + + align:start position:0% +you will have a backward solution +starting from + + align:start position:0% +starting from + + + align:start position:0% +starting from +here for for the for the a joint and for + + align:start position:0% +here for for the for the a joint and for + + + align:start position:0% +here for for the for the a joint and for +for you and then at these time points + + align:start position:0% +for you and then at these time points + + + align:start position:0% +for you and then at these time points +where you have your comparison you + + align:start position:0% +where you have your comparison you + + + align:start position:0% +where you have your comparison you +basically have to you can update your + + align:start position:0% +basically have to you can update your + + + align:start position:0% +basically have to you can update your +state + + align:start position:0% +state + + + align:start position:0% +state +by the change that comes in just from + + align:start position:0% +by the change that comes in just from + + + align:start position:0% +by the change that comes in just from +those notes basically so we'll just have + + align:start position:0% +those notes basically so we'll just have + + + align:start position:0% +those notes basically so we'll just have +like a + + align:start position:0% +like a + + + align:start position:0% +like a +partial derivatives added at those time + + align:start position:0% +partial derivatives added at those time + + + align:start position:0% +partial derivatives added at those time +points to your adjoin state + + align:start position:0% +points to your adjoin state + + + align:start position:0% +points to your adjoin state +yeah so I mean + + align:start position:0% +yeah so I mean + + + align:start position:0% +yeah so I mean +ode solvers you can tell them to stop at + + align:start position:0% +ode solvers you can tell them to stop at + + + align:start position:0% +ode solvers you can tell them to stop at +certain times so as you go backwards in + + align:start position:0% +certain times so as you go backwards in + + + align:start position:0% +certain times so as you go backwards in +time you could just have it stop at that + + align:start position:0% +time you could just have it stop at that + + + align:start position:0% +time you could just have it stop at that +time and then update something and + + align:start position:0% +time and then update something and + + + align:start position:0% +time and then update something and +that's not at that time and add + + align:start position:0% +that's not at that time and add + + + align:start position:0% +that's not at that time and add +something at the next time it adds + + align:start position:0% +something at the next time it adds + + + align:start position:0% +something at the next time it adds +something to your your accumulate your + + align:start position:0% +something to your your accumulate your + + + align:start position:0% +something to your your accumulate your +sum as you go along but like + + align:start position:0% +sum as you go along but like + + + align:start position:0% +sum as you go along but like +mathematically you could because + + align:start position:0% +mathematically you could because + + + align:start position:0% +mathematically you could because +basically think of it as jump conditions + + align:start position:0% +basically think of it as jump conditions + + + align:start position:0% +basically think of it as jump conditions +that occur at those times and so that's + + align:start position:0% +that occur at those times and so that's + + + align:start position:0% +that occur at those times and so that's +there's also ways to include those in uh + + align:start position:0% +there's also ways to include those in uh + + + align:start position:0% +there's also ways to include those in uh +in differential equation solvers where + + align:start position:0% +in differential equation solvers where + + + align:start position:0% +in differential equation solvers where +oh every every once in a while these + + align:start position:0% +oh every every once in a while these + + + align:start position:0% +oh every every once in a while these +these times something jumps + + align:start position:0% +these times something jumps + + + align:start position:0% +these times something jumps +um there's a discontinuity in the + + align:start position:0% +um there's a discontinuity in the + + + align:start position:0% +um there's a discontinuity in the +solution and and then in between it's + + align:start position:0% +solution and and then in between it's + + + align:start position:0% +solution and and then in between it's +not changing at all in this case + + align:start position:0% + + + + align:start position:0% + +probably it's easier just today to say + + align:start position:0% +probably it's easier just today to say + + + align:start position:0% +probably it's easier just today to say +let me integrate it and up to this time + + align:start position:0% +let me integrate it and up to this time + + + align:start position:0% +let me integrate it and up to this time +get that solution up to the next time + + align:start position:0% +get that solution up to the next time + + + align:start position:0% +get that solution up to the next time +and just have a call back at those + + align:start position:0% +and just have a call back at those + + + align:start position:0% +and just have a call back at those +discrete times and just accumulate the + + align:start position:0% +discrete times and just accumulate the + + + align:start position:0% +discrete times and just accumulate the +sum + + align:start position:0% + + + + align:start position:0% + +everything is still + + align:start position:0% +everything is still + + + align:start position:0% +everything is still +basically if you want to generalize it + + align:start position:0% +basically if you want to generalize it + + + align:start position:0% +basically if you want to generalize it +say you have a matrix valued ode then + + align:start position:0% +say you have a matrix valued ode then + + + align:start position:0% +say you have a matrix valued ode then +your your land that has become like some + + align:start position:0% +your your land that has become like some + + + align:start position:0% +your your land that has become like some +Matrix valued thing and so they just + + align:start position:0% +Matrix valued thing and so they just + + + align:start position:0% +Matrix valued thing and so they just +like basically live in the Dual space to + + align:start position:0% +like basically live in the Dual space to + + + align:start position:0% +like basically live in the Dual space to +whatever you want to take the relative + + align:start position:0% +whatever you want to take the relative + + + align:start position:0% +whatever you want to take the relative +and as long as it sort of makes sense + + align:start position:0% +and as long as it sort of makes sense + + + align:start position:0% +and as long as it sort of makes sense +the the + + align:start position:0% +the the + + + align:start position:0% +the the +Ode to get it come on at the other end + + align:start position:0% +Ode to get it come on at the other end + + + align:start position:0% +Ode to get it come on at the other end +that will give you like the light + + align:start position:0% +that will give you like the light + + + align:start position:0% +that will give you like the light +sensitivity is that yeah yeah so so if + + align:start position:0% +sensitivity is that yeah yeah so so if + + + align:start position:0% +sensitivity is that yeah yeah so so if +you have a more General space so you you + + align:start position:0% +you have a more General space so you you + + + align:start position:0% +you have a more General space so you you +lived in some arbitrary Vector space + + align:start position:0% +lived in some arbitrary Vector space + + + align:start position:0% +lived in some arbitrary Vector space +right then you have to replace the + + align:start position:0% +right then you have to replace the + + + align:start position:0% +right then you have to replace the +Lambda transpose there with with an + + align:start position:0% +Lambda transpose there with with an + + + align:start position:0% +Lambda transpose there with with an +inner product right and then the you + + align:start position:0% +inner product right and then the you + + + align:start position:0% +inner product right and then the you +know the the this Fu transpose is some + + align:start position:0% +know the the this Fu transpose is some + + + align:start position:0% +know the the this Fu transpose is some +more General adjoint uh agile and + + align:start position:0% +more General adjoint uh agile and + + + align:start position:0% +more General adjoint uh agile and +operator in that in that Hilbert space + + align:start position:0% +operator in that in that Hilbert space + + + align:start position:0% +operator in that in that Hilbert space +right so all of this this still works + + align:start position:0% +right so all of this this still works + + + align:start position:0% +right so all of this this still works +you can think of this as just it's + + align:start position:0% +you can think of this as just it's + + + align:start position:0% +you can think of this as just it's +literally the same derivation you can + + align:start position:0% +literally the same derivation you can + + + align:start position:0% +literally the same derivation you can +think of it as just a change it's just + + align:start position:0% +think of it as just a change it's just + + + align:start position:0% +think of it as just a change it's just +lab that transpose is now notation for + + align:start position:0% +lab that transpose is now notation for + + + align:start position:0% +lab that transpose is now notation for +for for that inner product and it just + + align:start position:0% +for for that inner product and it just + + + align:start position:0% +for for that inner product and it just +it just you have to you understand what + + align:start position:0% +it just you have to you understand what + + + align:start position:0% +it just you have to you understand what +the notation means in a more General + + align:start position:0% +the notation means in a more General + + + align:start position:0% +the notation means in a more General +sense but it's literally the same the + + align:start position:0% +sense but it's literally the same the + + + align:start position:0% +sense but it's literally the same the +same thing + + align:start position:0% +same thing + + + align:start position:0% +same thing +have you done anything where I guess + + align:start position:0% +have you done anything where I guess + + + align:start position:0% +have you done anything where I guess +you're doing Quantum systems so probably + + align:start position:0% +you're doing Quantum systems so probably + + + align:start position:0% +you're doing Quantum systems so probably +your your states are are living some + + align:start position:0% +your your states are are living some + + + align:start position:0% +your your states are are living some +more density matrices live in more + + align:start position:0% +more density matrices live in more + + + align:start position:0% +more density matrices live in more +General Hilbert spaces all the time yeah + + align:start position:0% + + + + align:start position:0% + +yeah numerical you can also then + + align:start position:0% +yeah numerical you can also then + + + align:start position:0% +yeah numerical you can also then +vectorize the density Matrix right and + + align:start position:0% +vectorize the density Matrix right and + + + align:start position:0% +vectorize the density Matrix right and +they have like + + align:start position:0% +they have like + + + align:start position:0% +they have like +yeah yeah we write but basically also + + align:start position:0% +yeah yeah we write but basically also + + + align:start position:0% +yeah yeah we write but basically also +the definitions of f + + align:start position:0% +the definitions of f + + + align:start position:0% +the definitions of f +um to deal with vectors depending on + + align:start position:0% +um to deal with vectors depending on + + + align:start position:0% +um to deal with vectors depending on +like your implementation but yeah right + + align:start position:0% +like your implementation but yeah right + + + align:start position:0% +like your implementation but yeah right +yeah so we talked about that as well so + + align:start position:0% +yeah so we talked about that as well so + + + align:start position:0% +yeah so we talked about that as well so +why one way of dealing with matrices and + + align:start position:0% +why one way of dealing with matrices and + + + align:start position:0% +why one way of dealing with matrices and +other things you just turn them into + + align:start position:0% +other things you just turn them into + + + align:start position:0% +other things you just turn them into +column vectors right but uh you know if + + align:start position:0% +column vectors right but uh you know if + + + align:start position:0% +column vectors right but uh you know if +it's more natural the institutional + + align:start position:0% +it's more natural the institutional + + + align:start position:0% +it's more natural the institutional +space to talk about + + align:start position:0% +space to talk about + + + align:start position:0% +space to talk about +matrices then you'd really rather deal + + align:start position:0% +matrices then you'd really rather deal + + + align:start position:0% +matrices then you'd really rather deal +with that Hilbert space directly and if + + align:start position:0% +with that Hilbert space directly and if + + + align:start position:0% +with that Hilbert space directly and if +these are pdes so U is now not is it + + align:start position:0% +these are pdes so U is now not is it + + + align:start position:0% +these are pdes so U is now not is it +like a function of space right of course + + align:start position:0% +like a function of space right of course + + + align:start position:0% +like a function of space right of course +on a computer you probably discretized + + align:start position:0% +on a computer you probably discretized + + + align:start position:0% +on a computer you probably discretized +it but it's it's nice conceptually to + + align:start position:0% +it but it's it's nice conceptually to + + + align:start position:0% +it but it's it's nice conceptually to +think about this as a function of space + + align:start position:0% +think about this as a function of space + + + align:start position:0% +think about this as a function of space +and this this inner product Lambda is + + align:start position:0% +and this this inner product Lambda is + + + align:start position:0% +and this this inner product Lambda is +also a function of space for example and + + align:start position:0% +also a function of space for example and + + + align:start position:0% +also a function of space for example and +then this inner product is some kind of + + align:start position:0% +then this inner product is some kind of + + + align:start position:0% +then this inner product is some kind of +integral over space + + align:start position:0% +integral over space + + + align:start position:0% +integral over space +um so it is really powerful to be able + + align:start position:0% +um so it is really powerful to be able + + + align:start position:0% +um so it is really powerful to be able +to to not have to turn everything into a + + align:start position:0% +to to not have to turn everything into a + + + align:start position:0% +to to not have to turn everything into a +column Vector when you want to do linear + + align:start position:0% +column Vector when you want to do linear + + + align:start position:0% +column Vector when you want to do linear +algebra + + align:start position:0% + + + + align:start position:0% + +a five minute break so we'll come back + + align:start position:0% +a five minute break so we'll come back + + + align:start position:0% +a five minute break so we'll come back +at 12 10 and and I could go then or if + + align:start position:0% +at 12 10 and and I could go then or if + + + align:start position:0% +at 12 10 and and I could go then or if +you want to show some more examples we + + align:start position:0% +you want to show some more examples we + + + align:start position:0% +you want to show some more examples we +can you can do that but \ No newline at end of file diff --git a/dAZ-i9MsbRM.txt b/dAZ-i9MsbRM.txt new file mode 100644 index 0000000000000000000000000000000000000000..f09e6f36d0b079a674ff71813eddab8afb450720 --- /dev/null +++ b/dAZ-i9MsbRM.txt @@ -0,0 +1,379 @@ +PROFESSOR: Today I'd like to +talk to you about a new method + +for solving circuits. + +Last time, we reviewed using +KVL, KCL, and Ohm's Law in + +order to solve circuits +in a general sense. + +This produced a lot of +equations, in particular, a + +lot of redundant equations or a +lot of dependent equations, + +that we don't necessarily need +for solving our circuit. + +Today I'm going to review the +Node Voltage Component Current + +method, which is very similar +to node analysis. + +So if you hear one versus the +other, know that you're + +talking about approximately +the same thing. + +And I'll review the difference +in a second. + +Once we know how to use the +NVCC method for solving + +circuits, we can express the +relationships between + +components in our circuit +more concisely and more + +effectively, and possibly solve +our equations faster, + +which is relevant when we're +working on a mid-term or in + +the general sense, just +trying to save time. + +Let's take a look at NVCC. + +As I said before NVCC, +stands for Node + +Voltage Component Current. + +And what that means is if you +have a very simple circuit-- + +let's say just a voltage source + +and a couple of resistors. + +Previously, with KVL, we were +interested in the voltage drop + +around the loop being +equivalent to 0. + +In this case, we're actually +going to look at the voltages + +associated with particular +nodes. + +To do that we're going to label +our nodes, which are + +anywhere our components +connect. + +We're also going to go after +the component current. + +When we're doing KCL, we +typically look at the flow in + +and out of a particular node. + +At this point, we're going to +look at the flow through a + +given component. + +So we're also going to label all +of the currents associated + +with our circuit. + +But when we approach NVCC +method, we're going to think + +about the currents flowing +through a particular component + +as opposed to and out of +a particular node. + +NVCC is sort of the opposite of +KVL and KCL in that sense, + +even though you're still going +to end up using the same + +relationships. + +So at this point, I've labeled +the currents going through-- + +I labeled one individual current +for every component in + +my circuit. + +The next step would be to +identify what I'm going to + +call ground, or in particular, +one of my nodes -- + +I'm going to assign to ground +or relative voltage 0. + +At that point, I'm going to +write out the relationships + +between the voltage drop across +particular components, + +the current flowing through that +particular component, and + +whatever relationship the +component requires the voltage + +and the current to have +to one another. + +That's a whirlwind review +of NVCC method. + +Node analysis is very similar. + +The main difference between node +analysis and NVCC method + +is when your component +is a voltage source. + +And there are multiple currents +flowing into that + +voltage source. + +You can treat this as +a single voltage. + +You can treat this as a single +voltage node, where this + +voltage it has value 0. + +And actually write your KCL +equations as though this point + +were collapsed. + +So current flowing in and +current flowing out, or vice + +versa, have to sum to 0. + +That's the major difference. + +Let's look at an example. + +You can find this example +repeated in + +6.4.3 of the reading. + +And I'm going to walk through +these directions. + +So the first thing I'm going +to do is label my + +nodes and my currents. + +People interchangeably +use e or n. + +It doesn't really matter. + +I guess n in particular could +refer to the node, while e in + +particular could refer +to the voltage + +associated with that node. + +Now I'm going to specify the +voltage drop across a + +particular component in terms +of the node voltages. + +I'm also going to assign +n0 to 0 as my ground. + +As a consequence, I know that +n1 is going to be 15 Volts. + +My voltage drop is typically +specified in the same + +direction as the current - +that I've also decided. + +So this convention +is arbitrary. + +But if you want to be consistent +in your work, and + +make it easier to get partial +credit or get help in office + +hours, et cetera, then assume +that the voltage drop occurs + +in the same direction +as the current. + +That's it for our relationship +associated with voltage drop. + +Now I'm going to go over KCL +for the relevant nodes. + +And in the last step I'm going +to combine the two into the + +equation that you're certainly +allowed to use to express your + +work on midterms. + +Or if you can skip +to the third step + +immediately, then that's OK. + +Just check your signs. + +Here's the second step. + +Flowing into n1 is i0 and +flowing out is i1. + +So i0 is going to +be equal to i1. + +Flowing into n2 is i1 and i3. + +And flowing out of n2 is i2. + +Flowing into n0 is i2, +and flowing out of + +n0 is i0 and i3. + +we're almost certainly +not going to end + +up using that equation. + +Because it's the last of our KCL +equations and is dependent + +upon the other equations +that we've already + +written out for KCL. + +I3 is equal to 10 Amperes. + +So we can go ahead and make +that substitution. + +I still have to work with +i1 and i2 though. + +And I can go after expressions +for them in terms of my node + +voltages and components by +using the equations for + +voltage drop I made earlier. + +This is the equation that you +can jump straight to, if you + +understand where this expression +comes from, as a + +consequence, of our KCL and also +our component voltages. + +I'm going to substitute in +15 Volts for n1 here. + +And now I have an expression +that only contains n2 and + +known values. + +So I can solve for n2. + +and I'll do that real +quickly right now. + +So first I'm just going +to copy this over. + +I'm going to multiply +through by 6 Ohms. + +And I solved for the voltage +associated with n2. + +At this point, I can solve +for i2 and i1. + +Sorry about that. + +What do I have left? + +i3 I know is 10 Amperes. + +i0 is equal to i1, which +is negative 1 Amperes. + +There's a voltage drop +associated with the 3 Ohm + +resistor, which is 15 minus +18, negative 3 Volts. + +And the voltage drop associated +with the 2 Ohm + +resistor is 18 Volts, +since n0 is ground. + +This concludes my introduction +to node voltage component + +current method or node analysis +without the ability + +to collapse voltage +sources for KCL. \ No newline at end of file diff --git a/dt5VhUIBY28.txt b/dt5VhUIBY28.txt new file mode 100644 index 0000000000000000000000000000000000000000..9743ae6b139e262f6f4d70e4628c41e1be5381b2 --- /dev/null +++ b/dt5VhUIBY28.txt @@ -0,0 +1,451 @@ +align:start position:0% + +charge induced in the ground plane by an + + align:start position:0% +charge induced in the ground plane by an + + + align:start position:0% +charge induced in the ground plane by an +overhead conductor illustrates the + + align:start position:0% +overhead conductor illustrates the + + + align:start position:0% +overhead conductor illustrates the +method of images and the superposition + + align:start position:0% +method of images and the superposition + + + align:start position:0% +method of images and the superposition +of fields due to line charges to satisfy + + align:start position:0% +of fields due to line charges to satisfy + + + align:start position:0% +of fields due to line charges to satisfy +boundary + + align:start position:0% + + + + align:start position:0% + +conditions in practice this circular + + align:start position:0% +conditions in practice this circular + + + align:start position:0% +conditions in practice this circular +conductor could be a high voltage power + + align:start position:0% +conductor could be a high voltage power + + + align:start position:0% +conductor could be a high voltage power +line and this conducting ground plane + + align:start position:0% +line and this conducting ground plane + + + align:start position:0% +line and this conducting ground plane +could be the Earth underneath + + align:start position:0% +could be the Earth underneath + + + align:start position:0% +could be the Earth underneath +the potential between the conductor and + + align:start position:0% +the potential between the conductor and + + + align:start position:0% +the potential between the conductor and +the ground plane is that of two line + + align:start position:0% +the ground plane is that of two line + + + align:start position:0% +the ground plane is that of two line +charges one just below the center of the + + align:start position:0% +charges one just below the center of the + + + align:start position:0% +charges one just below the center of the +conductor and the other its image + + align:start position:0% +conductor and the other its image + + + align:start position:0% +conductor and the other its image +symmetrically located below the ground + + align:start position:0% +symmetrically located below the ground + + + align:start position:0% +symmetrically located below the ground +plane we apply a volage from this 100 HZ + + align:start position:0% +plane we apply a volage from this 100 HZ + + + align:start position:0% +plane we apply a volage from this 100 HZ +source to the circular + + align:start position:0% + + + + align:start position:0% + +conductor the actual charges are induced + + align:start position:0% +conductor the actual charges are induced + + + align:start position:0% +conductor the actual charges are induced +on its surface in just such a way that + + align:start position:0% +on its surface in just such a way that + + + align:start position:0% +on its surface in just such a way that +every Point has the same potential as + + align:start position:0% +every Point has the same potential as + + + align:start position:0% +every Point has the same potential as +the + + align:start position:0% +the + + + align:start position:0% +the +source similarly charges are induced on + + align:start position:0% +source similarly charges are induced on + + + align:start position:0% +source similarly charges are induced on +the surface of the ground plane in just + + align:start position:0% +the surface of the ground plane in just + + + align:start position:0% +the surface of the ground plane in just +such a way as to make it have zero + + align:start position:0% +such a way as to make it have zero + + + align:start position:0% +such a way as to make it have zero +potential we can measure the charge + + align:start position:0% +potential we can measure the charge + + + align:start position:0% +potential we can measure the charge +induced on the ground plane with this + + align:start position:0% + + + + align:start position:0% + +probe the probe has a center section + + align:start position:0% +probe the probe has a center section + + + align:start position:0% +probe the probe has a center section +electrically insulating from the + + align:start position:0% +electrically insulating from the + + + align:start position:0% +electrically insulating from the +surrounding Shield which contacts the + + align:start position:0% +surrounding Shield which contacts the + + + align:start position:0% +surrounding Shield which contacts the +ground plane + + align:start position:0% + + + + align:start position:0% + +the surface charge density Distribution + + align:start position:0% +the surface charge density Distribution + + + align:start position:0% +the surface charge density Distribution +on the ground plane is proportional to + + align:start position:0% +on the ground plane is proportional to + + + align:start position:0% +on the ground plane is proportional to +the normal component of the electric + + align:start position:0% +the normal component of the electric + + + align:start position:0% +the normal component of the electric +field it is therefore proportional to + + align:start position:0% +field it is therefore proportional to + + + align:start position:0% +field it is therefore proportional to +the voltage of the + + align:start position:0% +the voltage of the + + + align:start position:0% +the voltage of the +cylinder conservation of charge requires + + align:start position:0% +cylinder conservation of charge requires + + + align:start position:0% +cylinder conservation of charge requires +that the probe current be the time rate + + align:start position:0% +that the probe current be the time rate + + + align:start position:0% +that the probe current be the time rate +of change of the charge on the probe + + align:start position:0% +of change of the charge on the probe + + + align:start position:0% +of change of the charge on the probe +surface it follows that the voltage + + align:start position:0% +surface it follows that the voltage + + + align:start position:0% +surface it follows that the voltage +induced across the internal resistance + + align:start position:0% +induced across the internal resistance + + + align:start position:0% +induced across the internal resistance +of the scope is proportional to the rate + + align:start position:0% +of the scope is proportional to the rate + + + align:start position:0% +of the scope is proportional to the rate +of change of the applied + + align:start position:0% +of change of the applied + + + align:start position:0% +of change of the applied +voltage the upper Trace is the applied + + align:start position:0% +voltage the upper Trace is the applied + + + align:start position:0% +voltage the upper Trace is the applied +volage the lower one is that of the + + align:start position:0% + + + + align:start position:0% + +probe because the probe volage is the + + align:start position:0% +probe because the probe volage is the + + + align:start position:0% +probe because the probe volage is the +time derivative of the applied volage + + align:start position:0% +time derivative of the applied volage + + + align:start position:0% +time derivative of the applied volage +the signals are 90° out of phase + + align:start position:0% + + + + align:start position:0% + +as the probe is moved out from under the + + align:start position:0% +as the probe is moved out from under the + + + align:start position:0% +as the probe is moved out from under the +conductor the lower scope tray shows the + + align:start position:0% +conductor the lower scope tray shows the + + + align:start position:0% +conductor the lower scope tray shows the +charge induced on its surface decreases + + align:start position:0% + + + + align:start position:0% + +electric fields at low frequency do not + + align:start position:0% +electric fields at low frequency do not + + + align:start position:0% +electric fields at low frequency do not +penetrate the body provided a person is + + align:start position:0% +penetrate the body provided a person is + + + align:start position:0% +penetrate the body provided a person is +grounded the hand effectively Shields + + align:start position:0% +grounded the hand effectively Shields + + + align:start position:0% +grounded the hand effectively Shields +the + + align:start position:0% + + + + align:start position:0% + +probe our experiment illustrates how the + + align:start position:0% +probe our experiment illustrates how the + + + align:start position:0% +probe our experiment illustrates how the +potential of two line charges can be + + align:start position:0% +potential of two line charges can be + + + align:start position:0% +potential of two line charges can be +used to predict the surface charged + + align:start position:0% +used to predict the surface charged + + + align:start position:0% +used to predict the surface charged +induced on a conducting surface \ No newline at end of file diff --git a/es6f90JcJ2k.txt b/es6f90JcJ2k.txt new file mode 100644 index 0000000000000000000000000000000000000000..a6652304193dee646759f8416b479228fd749c67 --- /dev/null +++ b/es6f90JcJ2k.txt @@ -0,0 +1,14915 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +I got an interesting question in the + + align:start position:0% +I got an interesting question in the + + + align:start position:0% +I got an interesting question in the +anonymous comment box and I want to see + + align:start position:0% +anonymous comment box and I want to see + + + align:start position:0% +anonymous comment box and I want to see +how many other people agree with it the + + align:start position:0% +how many other people agree with it the + + + align:start position:0% +how many other people agree with it the +comment when something like is + + align:start position:0% +comment when something like is + + + align:start position:0% +comment when something like is +everything in this field of nuclear + + align:start position:0% +everything in this field of nuclear + + + align:start position:0% +everything in this field of nuclear +science engineering computational in + + align:start position:0% +science engineering computational in + + + align:start position:0% +science engineering computational in +nature because so far we pretty much + + align:start position:0% +nature because so far we pretty much + + + align:start position:0% +nature because so far we pretty much +just thrown theory and simulations at + + align:start position:0% +just thrown theory and simulations at + + + align:start position:0% +just thrown theory and simulations at +you we haven't done any experiments so + + align:start position:0% +you we haven't done any experiments so + + + align:start position:0% +you we haven't done any experiments so +who shares this concern or wonder so one + + align:start position:0% +who shares this concern or wonder so one + + + align:start position:0% +who shares this concern or wonder so one +two three four funky five yeah so + + align:start position:0% +two three four funky five yeah so + + + align:start position:0% +two three four funky five yeah so +getting towards roughly half of you so I + + align:start position:0% +getting towards roughly half of you so I + + + align:start position:0% +getting towards roughly half of you so I +can confidently answer no this is not a + + align:start position:0% +can confidently answer no this is not a + + + align:start position:0% +can confidently answer no this is not a +purely computational field we just had + + align:start position:0% +purely computational field we just had + + + align:start position:0% +purely computational field we just had +to get you just enough science and + + align:start position:0% +to get you just enough science and + + + align:start position:0% +to get you just enough science and +physics so that you'd be able to + + align:start position:0% +physics so that you'd be able to + + + align:start position:0% +physics so that you'd be able to +understand some of the lab activities + + align:start position:0% +understand some of the lab activities + + + align:start position:0% +understand some of the lab activities +that we've got in store for you + + align:start position:0% +that we've got in store for you + + + align:start position:0% +that we've got in store for you +one of whom my games here from the + + align:start position:0% +one of whom my games here from the + + + align:start position:0% +one of whom my games here from the +nuclear reactor lab it's gonna be + + align:start position:0% +nuclear reactor lab it's gonna be + + + align:start position:0% +nuclear reactor lab it's gonna be +helping you with actually two of them + + align:start position:0% +helping you with actually two of them + + + align:start position:0% +helping you with actually two of them +he'll be helping with you + + align:start position:0% +he'll be helping with you + + + align:start position:0% +he'll be helping with you +yeah well the bananas and the thing that + + align:start position:0% +yeah well the bananas and the thing that + + + align:start position:0% +yeah well the bananas and the thing that +we dreamed up today so sure fill in what + + align:start position:0% +we dreamed up today so sure fill in what + + + align:start position:0% +we dreamed up today so sure fill in what +I get wrong also Mike's gonna talk about + + align:start position:0% +I get wrong also Mike's gonna talk about + + + align:start position:0% +I get wrong also Mike's gonna talk about +what we're going to do together which is + + align:start position:0% +what we're going to do together which is + + + align:start position:0% +what we're going to do together which is +called naa + + align:start position:0% +called naa + + + align:start position:0% +called naa +or nuclear activation analysis there are + + align:start position:0% +or nuclear activation analysis there are + + + align:start position:0% +or nuclear activation analysis there are +many many ways of measuring what sort of + + align:start position:0% +many many ways of measuring what sort of + + + align:start position:0% +many many ways of measuring what sort of +impurities may exist in materials and + + align:start position:0% +impurities may exist in materials and + + + align:start position:0% +impurities may exist in materials and +this is among the most sensitive we + + align:start position:0% +this is among the most sensitive we + + + align:start position:0% +this is among the most sensitive we +happen to have a nuclear reactor so what + + align:start position:0% +happen to have a nuclear reactor so what + + + align:start position:0% +happen to have a nuclear reactor so what +we will be doing what I'm gonna ask each + + align:start position:0% +we will be doing what I'm gonna ask each + + + align:start position:0% +we will be doing what I'm gonna ask each +of you guys to do for a special + + align:start position:0% +of you guys to do for a special + + + align:start position:0% +of you guys to do for a special +assignment it's not graded except you'll + + align:start position:0% +assignment it's not graded except you'll + + + align:start position:0% +assignment it's not graded except you'll +need it for the problem set so it kind + + align:start position:0% +need it for the problem set so it kind + + + align:start position:0% +need it for the problem set so it kind +of is is I want each of you to bring + + align:start position:0% +of is is I want each of you to bring + + + align:start position:0% +of is is I want each of you to bring +something into me that weighs about 50 + + align:start position:0% +something into me that weighs about 50 + + + align:start position:0% +something into me that weighs about 50 +milligrams in one piece fits in here is + + align:start position:0% +milligrams in one piece fits in here is + + + align:start position:0% +milligrams in one piece fits in here is +not fissionable so if you have uranium + + align:start position:0% +not fissionable so if you have uranium + + + align:start position:0% +not fissionable so if you have uranium +at home you know I shouldn't know about + + align:start position:0% +at home you know I shouldn't know about + + + align:start position:0% +at home you know I shouldn't know about +it and we also ask that you don't bring + + align:start position:0% +it and we also ask that you don't bring + + + align:start position:0% +it and we also ask that you don't bring +anything in that is too salty because + + align:start position:0% +anything in that is too salty because + + + align:start position:0% +anything in that is too salty because +sodium activates like crazy and each of + + align:start position:0% +sodium activates like crazy and each of + + + align:start position:0% +sodium activates like crazy and each of +you using your knowledge of radioactive + + align:start position:0% +you using your knowledge of radioactive + + + align:start position:0% +you using your knowledge of radioactive +decay that we learned Tuesday and today + + align:start position:0% +decay that we learned Tuesday and today + + + align:start position:0% +decay that we learned Tuesday and today +and the bateman equations and serious + + align:start position:0% +and the bateman equations and serious + + + align:start position:0% +and the bateman equations and serious +radioactive decay next Tuesday and + + align:start position:0% +radioactive decay next Tuesday and + + + align:start position:0% +radioactive decay next Tuesday and +Thursday are going to calculate what + + align:start position:0% +Thursday are going to calculate what + + + align:start position:0% +Thursday are going to calculate what +impurities exist in your sample what is + + align:start position:0% +impurities exist in your sample what is + + + align:start position:0% +impurities exist in your sample what is +your sample it's we're gonna make some + + align:start position:0% +your sample it's we're gonna make some + + + align:start position:0% +your sample it's we're gonna make some +estimates of the isotopes that you'll + + align:start position:0% +estimates of the isotopes that you'll + + + align:start position:0% +estimates of the isotopes that you'll +let us see the shorts yeah I know we're + + align:start position:0% +let us see the shorts yeah I know we're + + + align:start position:0% +let us see the shorts yeah I know we're +not gonna get every impurity right + + align:start position:0% + + + + align:start position:0% + +yes no but I will want your materials + + align:start position:0% +yes no but I will want your materials + + + align:start position:0% +yes no but I will want your materials +next week okay so by Tuesday I'd like + + align:start position:0% +next week okay so by Tuesday I'd like + + + align:start position:0% +next week okay so by Tuesday I'd like +each of you to come bring something in + + align:start position:0% +each of you to come bring something in + + + align:start position:0% +each of you to come bring something in +for which you'd like to know the + + align:start position:0% +for which you'd like to know the + + + align:start position:0% +for which you'd like to know the +elemental composition consisting of the + + align:start position:0% +elemental composition consisting of the + + + align:start position:0% +elemental composition consisting of the +following elements let's see + + align:start position:0% +following elements let's see + + + align:start position:0% +following elements let's see +problem sets I think I've got it right + + align:start position:0% +problem sets I think I've got it right + + + align:start position:0% +problem sets I think I've got it right +up here let me just clone the screen so + + align:start position:0% +up here let me just clone the screen so + + + align:start position:0% +up here let me just clone the screen so +you can see what we can look for so this + + align:start position:0% +you can see what we can look for so this + + + align:start position:0% +you can see what we can look for so this +is provided to me by Mike we're gonna do + + align:start position:0% +is provided to me by Mike we're gonna do + + + align:start position:0% +is provided to me by Mike we're gonna do +what's called a short nuclear activation + + align:start position:0% +what's called a short nuclear activation + + + align:start position:0% +what's called a short nuclear activation +analysis run looking for any of the + + align:start position:0% +analysis run looking for any of the + + + align:start position:0% +analysis run looking for any of the +elements up on this list shorts one with + + align:start position:0% +elements up on this list shorts one with + + + align:start position:0% +elements up on this list shorts one with +extremely short half-lives and shorts + + align:start position:0% +extremely short half-lives and shorts + + + align:start position:0% +extremely short half-lives and shorts +two with elements in the half-lives of + + align:start position:0% +two with elements in the half-lives of + + + align:start position:0% +two with elements in the half-lives of +hours and Mike I had a question for you + + align:start position:0% +hours and Mike I had a question for you + + + align:start position:0% +hours and Mike I had a question for you +now that we're live can we count arsenic + + align:start position:0% +now that we're live can we count arsenic + + + align:start position:0% +now that we're live can we count arsenic +in that list because it's 24 points + + align:start position:0% +in that list because it's 24 points + + + align:start position:0% +in that list because it's 24 points +something hours okay so if any of you + + align:start position:0% +something hours okay so if any of you + + + align:start position:0% +something hours okay so if any of you +guys have some food that you bought + + align:start position:0% +guys have some food that you bought + + + align:start position:0% +guys have some food that you bought +online and you don't know what sort of + + align:start position:0% +online and you don't know what sort of + + + align:start position:0% +online and you don't know what sort of +contaminants there are or if you've got + + align:start position:0% +contaminants there are or if you've got + + + align:start position:0% +contaminants there are or if you've got +a piece of your fingernail and want to + + align:start position:0% +a piece of your fingernail and want to + + + align:start position:0% +a piece of your fingernail and want to +see if you are what you eat or what + + align:start position:0% +see if you are what you eat or what + + + align:start position:0% +see if you are what you eat or what +about dog fingernails + + align:start position:0% +about dog fingernails + + + align:start position:0% +about dog fingernails +okay so clip your pets claws if you want + + align:start position:0% +okay so clip your pets claws if you want + + + align:start position:0% +okay so clip your pets claws if you want +to see if they are what they eat or + + align:start position:0% +to see if they are what they eat or + + + align:start position:0% +to see if they are what they eat or +don't tell me what nail the thing came + + align:start position:0% +don't tell me what nail the thing came + + + align:start position:0% +don't tell me what nail the thing came +from or you know get a you know slice up + + align:start position:0% +from or you know get a you know slice up + + + align:start position:0% +from or you know get a you know slice up +a piece of a peanut or whatever your + + align:start position:0% +a piece of a peanut or whatever your + + + align:start position:0% +a piece of a peanut or whatever your +favorite food is or if you want to see + + align:start position:0% +favorite food is or if you want to see + + + align:start position:0% +favorite food is or if you want to see +if there are any metal dyes used in your + + align:start position:0% +if there are any metal dyes used in your + + + align:start position:0% +if there are any metal dyes used in your +clothing cut out a little 50 milligram + + align:start position:0% +clothing cut out a little 50 milligram + + + align:start position:0% +clothing cut out a little 50 milligram +square it'll be like a fashion statement + + align:start position:0% +square it'll be like a fashion statement + + + align:start position:0% +square it'll be like a fashion statement +in an experiment at the same time right + + align:start position:0% +in an experiment at the same time right + + + align:start position:0% +in an experiment at the same time right +so we ask that it's about 50 milligrams + + align:start position:0% +so we ask that it's about 50 milligrams + + + align:start position:0% +so we ask that it's about 50 milligrams +it's got to fit in here it's got to be + + align:start position:0% +it's got to fit in here it's got to be + + + align:start position:0% +it's got to fit in here it's got to be +not that salty and not fissionable and + + align:start position:0% +not that salty and not fissionable and + + + align:start position:0% +not that salty and not fissionable and +we're going to pack a couple of these in + + align:start position:0% +we're going to pack a couple of these in + + + align:start position:0% +we're going to pack a couple of these in +one of these rabbits these polyethylene + + align:start position:0% +one of these rabbits these polyethylene + + + align:start position:0% +one of these rabbits these polyethylene +rabbits we call it those one because + + align:start position:0% +rabbits we call it those one because + + + align:start position:0% +rabbits we call it those one because +everything in nuclear is named after + + align:start position:0% +everything in nuclear is named after + + + align:start position:0% +everything in nuclear is named after +animals and farm implements for some + + align:start position:0% +animals and farm implements for some + + + align:start position:0% +animals and farm implements for some +reason did I go over that with you guys + + align:start position:0% +reason did I go over that with you guys + + + align:start position:0% +reason did I go over that with you guys +the first day of class barns shakes pigs + + align:start position:0% +the first day of class barns shakes pigs + + + align:start position:0% +the first day of class barns shakes pigs +rabbits okay so a rabbit is a little + + align:start position:0% +rabbits okay so a rabbit is a little + + + align:start position:0% +rabbits okay so a rabbit is a little +capsule oh you pop open or you screw it + + align:start position:0% +capsule oh you pop open or you screw it + + + align:start position:0% +capsule oh you pop open or you screw it +open oh yeah there's like a square nut + + align:start position:0% +open oh yeah there's like a square nut + + + align:start position:0% +open oh yeah there's like a square nut +at the top + + align:start position:0% +at the top + + + align:start position:0% +at the top +just a little capsule that goes through + + align:start position:0% +just a little capsule that goes through + + + align:start position:0% +just a little capsule that goes through +pneumatic tube kind of like the old bank + + align:start position:0% +pneumatic tube kind of like the old bank + + + align:start position:0% +pneumatic tube kind of like the old bank +machines and it'll go firing into the + + align:start position:0% +machines and it'll go firing into the + + + align:start position:0% +machines and it'll go firing into the +reactor sit there for a while and get + + align:start position:0% +reactor sit there for a while and get + + + align:start position:0% +reactor sit there for a while and get +pneumatically sucked back out so that we + + align:start position:0% +pneumatically sucked back out so that we + + + align:start position:0% +pneumatically sucked back out so that we +can calculate the activation and decay + + align:start position:0% +can calculate the activation and decay + + + align:start position:0% +can calculate the activation and decay +of the isotopes within and a pig is just + + align:start position:0% +of the isotopes within and a pig is just + + + align:start position:0% +of the isotopes within and a pig is just +a big heavy thing of lead where you keep + + align:start position:0% +a big heavy thing of lead where you keep + + + align:start position:0% +a big heavy thing of lead where you keep +pieces of things that you are radiated + + align:start position:0% +pieces of things that you are radiated + + + align:start position:0% +pieces of things that you are radiated +for shielding so if you notice the sort + + align:start position:0% +for shielding so if you notice the sort + + + align:start position:0% +for shielding so if you notice the sort +of methodology theme here Farms pigs + + align:start position:0% +of methodology theme here Farms pigs + + + align:start position:0% +of methodology theme here Farms pigs +rabbits barn shakes + + align:start position:0% +rabbits barn shakes + + + align:start position:0% +rabbits barn shakes +anyone else' know any other farm ii + + align:start position:0% +anyone else' know any other farm ii + + + align:start position:0% +anyone else' know any other farm ii +nuclear units + + align:start position:0% +nuclear units + + + align:start position:0% +nuclear units +yeah or farming anything so the + + align:start position:0% +yeah or farming anything so the + + + align:start position:0% +yeah or farming anything so the +detectors in NIF are called toads and + + align:start position:0% +detectors in NIF are called toads and + + + align:start position:0% +detectors in NIF are called toads and +bullfrogs why is that + + align:start position:0% + + + + align:start position:0% + +so they actually bullfrog stands for + + align:start position:0% +so they actually bullfrog stands for + + + align:start position:0% +so they actually bullfrog stands for +something that's pretty cool okay yeah + + align:start position:0% + + + + align:start position:0% + +oh yes the acronym for acronym as well + + align:start position:0% +oh yes the acronym for acronym as well + + + align:start position:0% +oh yes the acronym for acronym as well +as what I study which is crud or choc + + align:start position:0% +as what I study which is crud or choc + + + align:start position:0% +as what I study which is crud or choc +river unidentified deposits it's the + + align:start position:0% +river unidentified deposits it's the + + + align:start position:0% +river unidentified deposits it's the +gunk that builds up on fuel rods well I + + align:start position:0% +gunk that builds up on fuel rods well I + + + align:start position:0% +gunk that builds up on fuel rods well I +talked to a fellow from Chalk River who + + align:start position:0% +talked to a fellow from Chalk River who + + + align:start position:0% +talked to a fellow from Chalk River who +took extreme offense to this detriment + + align:start position:0% +took extreme offense to this detriment + + + align:start position:0% +took extreme offense to this detriment +in nuclear power plants being attributed + + align:start position:0% +in nuclear power plants being attributed + + + align:start position:0% +in nuclear power plants being attributed +to his fine laboratory Oh see that would + + align:start position:0% +to his fine laboratory Oh see that would + + + align:start position:0% +to his fine laboratory Oh see that would +work but they're not actually chromium + + align:start position:0% +work but they're not actually chromium + + + align:start position:0% +work but they're not actually chromium +rich yeah cool so Mike do you want to + + align:start position:0% +rich yeah cool so Mike do you want to + + + align:start position:0% +rich yeah cool so Mike do you want to +say anything else + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +mostly doing experiments these guys oh + + align:start position:0% +mostly doing experiments these guys oh + + + align:start position:0% +mostly doing experiments these guys oh +really + + align:start position:0% +really + + + align:start position:0% +really +samples in this the easiest thing for me + + align:start position:0% +samples in this the easiest thing for me + + + align:start position:0% +samples in this the easiest thing for me +to do without losing any of your samples + + align:start position:0% +to do without losing any of your samples + + + align:start position:0% +to do without losing any of your samples +is after something gets raided in this + + align:start position:0% +is after something gets raided in this + + + align:start position:0% +is after something gets raided in this +block and you probably can't see that + + align:start position:0% +block and you probably can't see that + + + align:start position:0% +block and you probably can't see that +there's a little poly bag I'll dump your + + align:start position:0% +there's a little poly bag I'll dump your + + + align:start position:0% +there's a little poly bag I'll dump your +sample into the poly bag so something + + align:start position:0% +sample into the poly bag so something + + + align:start position:0% +sample into the poly bag so something +that's like one piece works the best + + align:start position:0% +that's like one piece works the best + + + align:start position:0% +that's like one piece works the best +what I usually tell people is something + + align:start position:0% +what I usually tell people is something + + + align:start position:0% +what I usually tell people is something +that you could pick up reasonably easily + + align:start position:0% +that you could pick up reasonably easily + + + align:start position:0% +that you could pick up reasonably easily +with a pair of tweezers but that may + + align:start position:0% +with a pair of tweezers but that may + + + align:start position:0% +with a pair of tweezers but that may +give you good size we know nothing + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yep the list is posted on the stellar + + align:start position:0% +yep the list is posted on the stellar + + + align:start position:0% +yep the list is posted on the stellar +say yeah yeah yeah we'll see mostly + + align:start position:0% +say yeah yeah yeah we'll see mostly + + + align:start position:0% +say yeah yeah yeah we'll see mostly +these light elements the guys with the + + align:start position:0% +these light elements the guys with the + + + align:start position:0% +these light elements the guys with the +espera C's I don't see that well + + align:start position:0% + + + + align:start position:0% + +interesting we found gallium in your dog + + align:start position:0% +interesting we found gallium in your dog + + + align:start position:0% +interesting we found gallium in your dog +Claus or something yeah you know Mac + + align:start position:0% +Claus or something yeah you know Mac + + + align:start position:0% +Claus or something yeah you know Mac +they seem only titanium vanadium those + + align:start position:0% +they seem only titanium vanadium those + + + align:start position:0% +they seem only titanium vanadium those +are nice will come out nicely some of + + align:start position:0% +are nice will come out nicely some of + + + align:start position:0% +are nice will come out nicely some of +the elements of generally more interest + + align:start position:0% +the elements of generally more interest + + + align:start position:0% +the elements of generally more interest +down further down you know medium + + align:start position:0% +down further down you know medium + + + align:start position:0% +down further down you know medium +chromium + + align:start position:0% +chromium + + + align:start position:0% +chromium +those have longer half-life so I'm going + + align:start position:0% +those have longer half-life so I'm going + + + align:start position:0% +those have longer half-life so I'm going +to see those um you probably do like a + + align:start position:0% +to see those um you probably do like a + + + align:start position:0% +to see those um you probably do like a +five or ten minute irradiation + + align:start position:0% +five or ten minute irradiation + + + align:start position:0% +five or ten minute irradiation +let it decay for a little while and then + + align:start position:0% +let it decay for a little while and then + + + align:start position:0% +let it decay for a little while and then +do a couple of counts reactor we will be + + align:start position:0% +do a couple of counts reactor we will be + + + align:start position:0% +do a couple of counts reactor we will be +there a fair bit so what do you usually + + align:start position:0% +there a fair bit so what do you usually + + + align:start position:0% +there a fair bit so what do you usually +use naa for naa well the thing we've + + align:start position:0% +use naa for naa well the thing we've + + + align:start position:0% +use naa for naa well the thing we've +been using it for lately a lot is + + align:start position:0% +been using it for lately a lot is + + + align:start position:0% +been using it for lately a lot is +anything that's going to go in the core + + align:start position:0% +anything that's going to go in the core + + + align:start position:0% +anything that's going to go in the core +of the reactor we want to analyze to see + + align:start position:0% +of the reactor we want to analyze to see + + + align:start position:0% +of the reactor we want to analyze to see +if there's any surprise elements to see + + align:start position:0% +if there's any surprise elements to see + + + align:start position:0% +if there's any surprise elements to see +how much cobalt is in my past in doing + + align:start position:0% +how much cobalt is in my past in doing + + + align:start position:0% +how much cobalt is in my past in doing +naa was all environmental samples so we + + align:start position:0% +naa was all environmental samples so we + + + align:start position:0% +naa was all environmental samples so we +did a lot of trace element heavy metal + + align:start position:0% +did a lot of trace element heavy metal + + + align:start position:0% +did a lot of trace element heavy metal +chemistry sediments crude oil fly ash + + align:start position:0% +chemistry sediments crude oil fly ash + + + align:start position:0% +chemistry sediments crude oil fly ash +you know and so we would measure that + + align:start position:0% +you know and so we would measure that + + + align:start position:0% +you know and so we would measure that +whole stack elements cool that was my I + + align:start position:0% +whole stack elements cool that was my I + + + align:start position:0% +whole stack elements cool that was my I +don't know I think that's enough you + + align:start position:0% +don't know I think that's enough you + + + align:start position:0% +don't know I think that's enough you +want me back here next Tuesday or + + align:start position:0% +want me back here next Tuesday or + + + align:start position:0% +want me back here next Tuesday or +Thursday you have to explain a little + + align:start position:0% +Thursday you have to explain a little + + + align:start position:0% +Thursday you have to explain a little +bit more the specifics of the process + + align:start position:0% +bit more the specifics of the process + + + align:start position:0% +bit more the specifics of the process +and if you guys could depends on when + + align:start position:0% +and if you guys could depends on when + + + align:start position:0% +and if you guys could depends on when +you do them if it's early November then + + align:start position:0% +you do them if it's early November then + + + align:start position:0% +you do them if it's early November then +yes + + align:start position:0% + + + + align:start position:0% + +which you guys should see it's pretty + + align:start position:0% +which you guys should see it's pretty + + + align:start position:0% +which you guys should see it's pretty +cool and while those samples are + + align:start position:0% +cool and while those samples are + + + align:start position:0% +cool and while those samples are +counting I run another rap so you can + + align:start position:0% +counting I run another rap so you can + + + align:start position:0% +counting I run another rap so you can +almost come anytime during the day while + + align:start position:0% +almost come anytime during the day while + + + align:start position:0% +almost come anytime during the day while +I'm cool yeah thanks Mike so you heard + + align:start position:0% +I'm cool yeah thanks Mike so you heard + + + align:start position:0% +I'm cool yeah thanks Mike so you heard +the charge bring me your dog claws your + + align:start position:0% +the charge bring me your dog claws your + + + align:start position:0% +the charge bring me your dog claws your +head you know I browse your skin flakes + + align:start position:0% +head you know I browse your skin flakes + + + align:start position:0% +head you know I browse your skin flakes +your scabs your food pieces oh yeah so + + align:start position:0% +your scabs your food pieces oh yeah so + + + align:start position:0% +your scabs your food pieces oh yeah so +no hair staticy so don't bring us your + + align:start position:0% +no hair staticy so don't bring us your + + + align:start position:0% +no hair staticy so don't bring us your +hair but bring us your skin flakes your + + align:start position:0% +hair but bring us your skin flakes your + + + align:start position:0% +hair but bring us your skin flakes your +scabs your dog claws your food scraps + + align:start position:0% +scabs your dog claws your food scraps + + + align:start position:0% +scabs your dog claws your food scraps +your don't tell them get creative it + + align:start position:0% +your don't tell them get creative it + + + align:start position:0% +your don't tell them get creative it +doesn't have to be something that I said + + align:start position:0% +doesn't have to be something that I said + + + align:start position:0% +doesn't have to be something that I said +as long as it's not fissionable or salty + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +yeah but so let's figure it out by + + align:start position:0% +yeah but so let's figure it out by + + + align:start position:0% +yeah but so let's figure it out by +Tuesday that way if we have to veto we + + align:start position:0% +Tuesday that way if we have to veto we + + + align:start position:0% +Tuesday that way if we have to veto we +have a wild for you guys to find another + + align:start position:0% +have a wild for you guys to find another + + + align:start position:0% +have a wild for you guys to find another +sample we'll see we'll see what we can + + align:start position:0% +sample we'll see we'll see what we can + + + align:start position:0% +sample we'll see we'll see what we can +do thanks Mike so yeah so Mike's gonna + + align:start position:0% +do thanks Mike so yeah so Mike's gonna + + + align:start position:0% +do thanks Mike so yeah so Mike's gonna +be helping us do some nuclear activation + + align:start position:0% +be helping us do some nuclear activation + + + align:start position:0% +be helping us do some nuclear activation +analysis in an edition next week we're + + align:start position:0% +analysis in an edition next week we're + + + align:start position:0% +analysis in an edition next week we're +going to be counting our big bag of + + align:start position:0% +going to be counting our big bag of + + + align:start position:0% +going to be counting our big bag of +burnt bananas because now that you're + + align:start position:0% +burnt bananas because now that you're + + + align:start position:0% +burnt bananas because now that you're +learning about radioactivity and this + + align:start position:0% +learning about radioactivity and this + + + align:start position:0% +learning about radioactivity and this +when we go over activity and series + + align:start position:0% +when we go over activity and series + + + align:start position:0% +when we go over activity and series +decay you'll have enough of the science + + align:start position:0% +decay you'll have enough of the science + + + align:start position:0% +decay you'll have enough of the science +to understand to calculate how - what is + + align:start position:0% +to understand to calculate how - what is + + + align:start position:0% +to understand to calculate how - what is +the radioactivity of one banana and to + + align:start position:0% +the radioactivity of one banana and to + + + align:start position:0% +the radioactivity of one banana and to +do so we need like 500 bananas get + + align:start position:0% +do so we need like 500 bananas get + + + align:start position:0% +do so we need like 500 bananas get +enough statistics so we'll be going to + + align:start position:0% +enough statistics so we'll be going to + + + align:start position:0% +enough statistics so we'll be going to +the reactor for that we've also set it + + align:start position:0% +the reactor for that we've also set it + + + align:start position:0% +the reactor for that we've also set it +up so that next week and the week after + + align:start position:0% +up so that next week and the week after + + + align:start position:0% +up so that next week and the week after +words you guys are going to be + + align:start position:0% +words you guys are going to be + + + align:start position:0% +words you guys are going to be +manipulating the power levels of the + + align:start position:0% +manipulating the power levels of the + + + align:start position:0% +manipulating the power levels of the +reactor so you actually get to sit in + + align:start position:0% +reactor so you actually get to sit in + + + align:start position:0% +reactor so you actually get to sit in +the control seat raise and lower the + + align:start position:0% +the control seat raise and lower the + + + align:start position:0% +the control seat raise and lower the +control rods and watch the power of + + align:start position:0% +control rods and watch the power of + + + align:start position:0% +control rods and watch the power of +reactor change in ways you probably + + align:start position:0% +reactor change in ways you probably + + + align:start position:0% +reactor change in ways you probably +won't expect unless you're getting + + align:start position:0% +won't expect unless you're getting + + + align:start position:0% +won't expect unless you're getting +operator training and all of that stuff + + align:start position:0% +operator training and all of that stuff + + + align:start position:0% +operator training and all of that stuff +is going to be used in the lab + + align:start position:0% +is going to be used in the lab + + + align:start position:0% +is going to be used in the lab +components of the problem sets so you + + align:start position:0% +components of the problem sets so you + + + align:start position:0% +components of the problem sets so you +might guys might have noticed there was + + align:start position:0% +might guys might have noticed there was + + + align:start position:0% +might guys might have noticed there was +some spin thoris cope thing on problems + + align:start position:0% +some spin thoris cope thing on problems + + + align:start position:0% +some spin thoris cope thing on problems +at three radiation protection did not + + align:start position:0% +at three radiation protection did not + + + align:start position:0% +at three radiation protection did not +want me taking smoke detectors apart and + + align:start position:0% +want me taking smoke detectors apart and + + + align:start position:0% +want me taking smoke detectors apart and +giving them all to you because that's + + align:start position:0% +giving them all to you because that's + + + align:start position:0% +giving them all to you because that's +distributing open radioactive radiation + + align:start position:0% +distributing open radioactive radiation + + + align:start position:0% +distributing open radioactive radiation +sources and probably shouldn't do that + + align:start position:0% +sources and probably shouldn't do that + + + align:start position:0% +sources and probably shouldn't do that +but we've got plenty of lab stuff for + + align:start position:0% +but we've got plenty of lab stuff for + + + align:start position:0% +but we've got plenty of lab stuff for +you to do to see what is actually + + align:start position:0% +you to do to see what is actually + + + align:start position:0% +you to do to see what is actually +hands-on in this field and if you do + + align:start position:0% +hands-on in this field and if you do + + + align:start position:0% +hands-on in this field and if you do +want to know what else is hands-on I + + align:start position:0% +want to know what else is hands-on I + + + align:start position:0% +want to know what else is hands-on I +have an experimental group and you're + + align:start position:0% +have an experimental group and you're + + + align:start position:0% +have an experimental group and you're +always welcome to come see what we do + + align:start position:0% +always welcome to come see what we do + + + align:start position:0% +always welcome to come see what we do +with the lab there usually isn't an + + align:start position:0% +with the lab there usually isn't an + + + align:start position:0% +with the lab there usually isn't an +explosion happening but there's usually + + align:start position:0% +explosion happening but there's usually + + + align:start position:0% +explosion happening but there's usually +something at a thousand to fifteen + + align:start position:0% +something at a thousand to fifteen + + + align:start position:0% +something at a thousand to fifteen +hundred Celsius temperature blue uranium + + align:start position:0% +hundred Celsius temperature blue uranium + + + align:start position:0% +hundred Celsius temperature blue uranium +fluoride salts you know nano Newton + + align:start position:0% +fluoride salts you know nano Newton + + + align:start position:0% +fluoride salts you know nano Newton +forces extreme pressures or what have + + align:start position:0% +forces extreme pressures or what have + + + align:start position:0% +forces extreme pressures or what have +you we do a lot of it so I wanted to + + align:start position:0% +you we do a lot of it so I wanted to + + + align:start position:0% +you we do a lot of it so I wanted to +give a quick review of where we were in + + align:start position:0% +give a quick review of where we were in + + + align:start position:0% +give a quick review of where we were in +radioactive decay last time I think we + + align:start position:0% +radioactive decay last time I think we + + + align:start position:0% +radioactive decay last time I think we +left off somewhere around particle + + align:start position:0% +left off somewhere around particle + + + align:start position:0% +left off somewhere around particle +physics telescope explodes was my + + align:start position:0% +physics telescope explodes was my + + + align:start position:0% +physics telescope explodes was my +favorite BBC headline ever when we were + + align:start position:0% +favorite BBC headline ever when we were + + + align:start position:0% +favorite BBC headline ever when we were +talking about we've already gone over + + align:start position:0% +talking about we've already gone over + + + align:start position:0% +talking about we've already gone over +alpha decay we've gone over beta decay + + align:start position:0% +alpha decay we've gone over beta decay + + + align:start position:0% +alpha decay we've gone over beta decay +we started talking about positron decay + + align:start position:0% +we started talking about positron decay + + + align:start position:0% +we started talking about positron decay +and the neutrinos that come out of that + + align:start position:0% +and the neutrinos that come out of that + + + align:start position:0% +and the neutrinos that come out of that +and this kamiokande detector that is set + + align:start position:0% +and this kamiokande detector that is set + + + align:start position:0% +and this kamiokande detector that is set +up with lots of expensive photo tubes to + + align:start position:0% +up with lots of expensive photo tubes to + + + align:start position:0% +up with lots of expensive photo tubes to +detect the cones of light left as + + align:start position:0% +detect the cones of light left as + + + align:start position:0% +detect the cones of light left as +neutrinos pass faster than the speed of + + align:start position:0% +neutrinos pass faster than the speed of + + + align:start position:0% +neutrinos pass faster than the speed of +light in water through water and then + + align:start position:0% +light in water through water and then + + + align:start position:0% +light in water through water and then +there is my favorite headline and I + + align:start position:0% +there is my favorite headline and I + + + align:start position:0% +there is my favorite headline and I +believe we made it up to the end of + + align:start position:0% +believe we made it up to the end of + + + align:start position:0% +believe we made it up to the end of +positron annihilation spectroscopy or + + align:start position:0% +positron annihilation spectroscopy or + + + align:start position:0% +positron annihilation spectroscopy or +ways that you can actually use positron + + align:start position:0% +ways that you can actually use positron + + + align:start position:0% +ways that you can actually use positron +emission to look at the number and types + + align:start position:0% +emission to look at the number and types + + + align:start position:0% +emission to look at the number and types +of atomic defects in crystalline + + align:start position:0% +of atomic defects in crystalline + + + align:start position:0% +of atomic defects in crystalline +materials and yep that's where we left + + align:start position:0% +materials and yep that's where we left + + + align:start position:0% +materials and yep that's where we left +off interested in pas lots of papers to + + align:start position:0% +off interested in pas lots of papers to + + + align:start position:0% +off interested in pas lots of papers to +check out in the meantime let's look at + + align:start position:0% +check out in the meantime let's look at + + + align:start position:0% +check out in the meantime let's look at +one of the competing mechanisms for + + align:start position:0% +one of the competing mechanisms for + + + align:start position:0% +one of the competing mechanisms for +positron emission which is electron + + align:start position:0% +positron emission which is electron + + + align:start position:0% +positron emission which is electron +capture in this case so I will warn you + + align:start position:0% +capture in this case so I will warn you + + + align:start position:0% +capture in this case so I will warn you +it's sometimes a little easy to get + + align:start position:0% +it's sometimes a little easy to get + + + align:start position:0% +it's sometimes a little easy to get +mixed up between electron capture + + align:start position:0% +mixed up between electron capture + + + align:start position:0% +mixed up between electron capture +internal conversion isomeric transition + + align:start position:0% +internal conversion isomeric transition + + + align:start position:0% +internal conversion isomeric transition +so I've left these slides on here and I + + align:start position:0% +so I've left these slides on here and I + + + align:start position:0% +so I've left these slides on here and I +also took pictures of the board from + + align:start position:0% +also took pictures of the board from + + + align:start position:0% +also took pictures of the board from +last time and posted them on the stellar + + align:start position:0% +last time and posted them on the stellar + + + align:start position:0% +last time and posted them on the stellar +site + + align:start position:0% +site + + + align:start position:0% +site +so all the blackboards where we filled + + align:start position:0% +so all the blackboards where we filled + + + align:start position:0% +so all the blackboards where we filled +the board's there's pictures of those + + align:start position:0% +the board's there's pictures of those + + + align:start position:0% +the board's there's pictures of those +and I want to keep doing that so if + + align:start position:0% +and I want to keep doing that so if + + + align:start position:0% +and I want to keep doing that so if +you've learned better just by looking + + align:start position:0% +you've learned better just by looking + + + align:start position:0% +you've learned better just by looking +and listening rather than writing + + align:start position:0% +and listening rather than writing + + + align:start position:0% +and listening rather than writing +everything feel free if you want to + + align:start position:0% +everything feel free if you want to + + + align:start position:0% +everything feel free if you want to +write stuff down also feel free so an + + align:start position:0% +write stuff down also feel free so an + + + align:start position:0% +write stuff down also feel free so an +electron capture another way of well + + align:start position:0% +electron capture another way of well + + + align:start position:0% +electron capture another way of well +destroying positive charge would be for + + align:start position:0% +destroying positive charge would be for + + + align:start position:0% +destroying positive charge would be for +the nucleus to capture an electron so + + align:start position:0% +the nucleus to capture an electron so + + + align:start position:0% +the nucleus to capture an electron so +either it can emit a positron giving + + align:start position:0% +either it can emit a positron giving + + + align:start position:0% +either it can emit a positron giving +away some positive charge or it can + + align:start position:0% +away some positive charge or it can + + + align:start position:0% +away some positive charge or it can +capture an electron destroying one of + + align:start position:0% +capture an electron destroying one of + + + align:start position:0% +capture an electron destroying one of +the positive charges and these case here + + align:start position:0% +the positive charges and these case here + + + align:start position:0% +the positive charges and these case here +we've got a proton that becomes a + + align:start position:0% +we've got a proton that becomes a + + + align:start position:0% +we've got a proton that becomes a +neutron and a something I won't be + + align:start position:0% +neutron and a something I won't be + + + align:start position:0% +neutron and a something I won't be +specific as to which one because + + align:start position:0% +specific as to which one because + + + align:start position:0% +specific as to which one because +positron and electron capture well two + + align:start position:0% +positron and electron capture well two + + + align:start position:0% +positron and electron capture well two +different but similar kind of decay + + align:start position:0% +different but similar kind of decay + + + align:start position:0% +different but similar kind of decay +mechanisms and then what you get is this + + align:start position:0% +mechanisms and then what you get is this + + + align:start position:0% +mechanisms and then what you get is this +hole where the electron used to be and + + align:start position:0% +hole where the electron used to be and + + + align:start position:0% +hole where the electron used to be and +that's not a very stable configuration + + align:start position:0% +that's not a very stable configuration + + + align:start position:0% +that's not a very stable configuration +for an atom to have let's say one fewer + + align:start position:0% +for an atom to have let's say one fewer + + + align:start position:0% +for an atom to have let's say one fewer +electron than protons and especially to + + align:start position:0% +electron than protons and especially to + + + align:start position:0% +electron than protons and especially to +have a hole in the inner shell so you + + align:start position:0% +have a hole in the inner shell so you + + + align:start position:0% +have a hole in the inner shell so you +get this cascade from straight up from + + align:start position:0% +get this cascade from straight up from + + + align:start position:0% +get this cascade from straight up from +high school chemistry of electrons + + align:start position:0% +high school chemistry of electrons + + + align:start position:0% +high school chemistry of electrons +falling from one shell to the next and + + align:start position:0% +falling from one shell to the next and + + + align:start position:0% +falling from one shell to the next and +giving off characteristic x-rays that's + + align:start position:0% +giving off characteristic x-rays that's + + + align:start position:0% +giving off characteristic x-rays that's +me that crossed that out there because + + align:start position:0% +me that crossed that out there because + + + align:start position:0% +me that crossed that out there because +you will find misinformation all over + + align:start position:0% +you will find misinformation all over + + + align:start position:0% +you will find misinformation all over +the place online and someone might make + + align:start position:0% +the place online and someone might make + + + align:start position:0% +the place online and someone might make +a great figure and mislabel an electron + + align:start position:0% +a great figure and mislabel an electron + + + align:start position:0% +a great figure and mislabel an electron +emitted photon as a gamma ray and + + align:start position:0% +emitted photon as a gamma ray and + + + align:start position:0% +emitted photon as a gamma ray and +remember we said game has come from the + + align:start position:0% +remember we said game has come from the + + + align:start position:0% +remember we said game has come from the +nucleus otherwise they're + + align:start position:0% +nucleus otherwise they're + + + align:start position:0% +nucleus otherwise they're +indistinguishable photons and so an + + align:start position:0% +indistinguishable photons and so an + + + align:start position:0% +indistinguishable photons and so an +electron captured you don't need much of + + align:start position:0% +electron captured you don't need much of + + + align:start position:0% +electron captured you don't need much of +an energy difference between the parents + + align:start position:0% +an energy difference between the parents + + + align:start position:0% +an energy difference between the parents +and the daughters unlike positron decay + + align:start position:0% +and the daughters unlike positron decay + + + align:start position:0% +and the daughters unlike positron decay +where for positron decay to happen you + + align:start position:0% +where for positron decay to happen you + + + align:start position:0% +where for positron decay to happen you +have to have Q at least equal to 1.0 to + + align:start position:0% +have to have Q at least equal to 1.0 to + + + align:start position:0% +have to have Q at least equal to 1.0 to +2 MeV which is the same as 2 times the + + align:start position:0% +2 MeV which is the same as 2 times the + + + align:start position:0% +2 MeV which is the same as 2 times the +rest mass of the electron for electron + + align:start position:0% +rest mass of the electron for electron + + + align:start position:0% +rest mass of the electron for electron +capture you don't this can happen at + + align:start position:0% +capture you don't this can happen at + + + align:start position:0% +capture you don't this can happen at +just about any energy as long as you can + + align:start position:0% +just about any energy as long as you can + + + align:start position:0% +just about any energy as long as you can +overcome just the binding energy of the + + align:start position:0% +overcome just the binding energy of the + + + align:start position:0% +overcome just the binding energy of the +electron which is negligible compared to + + align:start position:0% +electron which is negligible compared to + + + align:start position:0% +electron which is negligible compared to +these sort of nuclear energy levels and + + align:start position:0% +these sort of nuclear energy levels and + + + align:start position:0% +these sort of nuclear energy levels and +so this is the Q equation keep in mind + + align:start position:0% +so this is the Q equation keep in mind + + + align:start position:0% +so this is the Q equation keep in mind +these deltas here are excess masses so + + align:start position:0% +these deltas here are excess masses so + + + align:start position:0% +these deltas here are excess masses so +I'll put this up again the excess mass + + align:start position:0% +I'll put this up again the excess mass + + + align:start position:0% +I'll put this up again the excess mass +is the real mass minus the terrible + + align:start position:0% +is the real mass minus the terrible + + + align:start position:0% +is the real mass minus the terrible +approximation of a nucleoid mass and + + align:start position:0% +approximation of a nucleoid mass and + + + align:start position:0% +approximation of a nucleoid mass and +this way excess mass and real mass are + + align:start position:0% +this way excess mass and real mass are + + + align:start position:0% +this way excess mass and real mass are +directly related so you could plug in + + align:start position:0% +directly related so you could plug in + + + align:start position:0% +directly related so you could plug in +masses here you could plug in binding + + align:start position:0% +masses here you could plug in binding + + + align:start position:0% +masses here you could plug in binding +jeez by making everything with a minus + + align:start position:0% +jeez by making everything with a minus + + + align:start position:0% +jeez by making everything with a minus +sign and so on I think I've repeated + + align:start position:0% +sign and so on I think I've repeated + + + align:start position:0% +sign and so on I think I've repeated +myself enough for the Q equation stuff + + align:start position:0% +myself enough for the Q equation stuff + + + align:start position:0% +myself enough for the Q equation stuff +would you guys agree yeah okay and so + + align:start position:0% +would you guys agree yeah okay and so + + + align:start position:0% +would you guys agree yeah okay and so +these are actually two competing + + align:start position:0% +these are actually two competing + + + align:start position:0% +these are actually two competing +mechanisms so shown here is the decay of + + align:start position:0% +mechanisms so shown here is the decay of + + + align:start position:0% +mechanisms so shown here is the decay of +sodium 22 which we don't want to happen + + align:start position:0% +sodium 22 which we don't want to happen + + + align:start position:0% +sodium 22 which we don't want to happen +in our nuclear activation analysis + + align:start position:0% +in our nuclear activation analysis + + + align:start position:0% +in our nuclear activation analysis +because it gets pretty toasty + + align:start position:0% +because it gets pretty toasty + + + align:start position:0% +because it gets pretty toasty +it can either proceed there's a kind of + + align:start position:0% +it can either proceed there's a kind of + + + align:start position:0% +it can either proceed there's a kind of +hidden part of the diagram that I drew + + align:start position:0% +hidden part of the diagram that I drew + + + align:start position:0% +hidden part of the diagram that I drew +in to make a little more sense you start + + align:start position:0% +in to make a little more sense you start + + + align:start position:0% +in to make a little more sense you start +off with a nucleus at 2 point 8 MeV + + align:start position:0% +off with a nucleus at 2 point 8 MeV + + + align:start position:0% +off with a nucleus at 2 point 8 MeV +above the neon nucleuses energy level + + align:start position:0% +above the neon nucleuses energy level + + + align:start position:0% +above the neon nucleuses energy level +you need 1.0 to 2 MeV to create the + + align:start position:0% +you need 1.0 to 2 MeV to create the + + + align:start position:0% +you need 1.0 to 2 MeV to create the +positron electron pair at which point + + align:start position:0% +positron electron pair at which point + + + align:start position:0% +positron electron pair at which point +you can emit the positron with a certain + + align:start position:0% +you can emit the positron with a certain + + + align:start position:0% +you can emit the positron with a certain +energy you're left at an excited state + + align:start position:0% +energy you're left at an excited state + + + align:start position:0% +energy you're left at an excited state +and the next thing we'll go over is + + align:start position:0% +and the next thing we'll go over is + + + align:start position:0% +and the next thing we'll go over is +gamma decay your isomeric transitions or + + align:start position:0% +gamma decay your isomeric transitions or + + + align:start position:0% +gamma decay your isomeric transitions or +i.t + + align:start position:0% +i.t + + + align:start position:0% +i.t +that's the next method of decay we'll + + align:start position:0% +that's the next method of decay we'll + + + align:start position:0% +that's the next method of decay we'll +talk about or the nucleus can just + + align:start position:0% +talk about or the nucleus can just + + + align:start position:0% +talk about or the nucleus can just +capture an electron getting to that same + + align:start position:0% +capture an electron getting to that same + + + align:start position:0% +capture an electron getting to that same +energy level and emitting the same gamma + + align:start position:0% +energy level and emitting the same gamma + + + align:start position:0% +energy level and emitting the same gamma +ray so these are two competing + + align:start position:0% +ray so these are two competing + + + align:start position:0% +ray so these are two competing +mechanisms of decay and then you might + + align:start position:0% +mechanisms of decay and then you might + + + align:start position:0% +mechanisms of decay and then you might +ask well when is one gonna happen and + + align:start position:0% +ask well when is one gonna happen and + + + align:start position:0% +ask well when is one gonna happen and +not the other well chances are the lower + + align:start position:0% +not the other well chances are the lower + + + align:start position:0% +not the other well chances are the lower +energy that transition is the more + + align:start position:0% +energy that transition is the more + + + align:start position:0% +energy that transition is the more +likely a electron capture is going to + + align:start position:0% +likely a electron capture is going to + + + align:start position:0% +likely a electron capture is going to +happen so when you look at these energy + + align:start position:0% +happen so when you look at these energy + + + align:start position:0% +happen so when you look at these energy +diagrams you can see that as the + + align:start position:0% +diagrams you can see that as the + + + align:start position:0% +diagrams you can see that as the +transitions get bigger the probability + + align:start position:0% +transitions get bigger the probability + + + align:start position:0% +transitions get bigger the probability +of positron decay goes up and up and up + + align:start position:0% +of positron decay goes up and up and up + + + align:start position:0% +of positron decay goes up and up and up +so you need 1.0 to 2 MeV to make the + + align:start position:0% +so you need 1.0 to 2 MeV to make the + + + align:start position:0% +so you need 1.0 to 2 MeV to make the +positron and electron but the + + align:start position:0% +positron and electron but the + + + align:start position:0% +positron and electron but the +probability of positron decay very close + + align:start position:0% +probability of positron decay very close + + + align:start position:0% +probability of positron decay very close +to this is far is fairly low possible + + align:start position:0% +to this is far is fairly low possible + + + align:start position:0% +to this is far is fairly low possible +but unlikely is everyone clear on these + + align:start position:0% +but unlikely is everyone clear on these + + + align:start position:0% +but unlikely is everyone clear on these +two competing mechanisms so one way of + + align:start position:0% +two competing mechanisms so one way of + + + align:start position:0% +two competing mechanisms so one way of +reducing the number of protons is emit a + + align:start position:0% +reducing the number of protons is emit a + + + align:start position:0% +reducing the number of protons is emit a +positron another is gobble up an + + align:start position:0% +positron another is gobble up an + + + align:start position:0% +positron another is gobble up an +electron in the end they make the same + + align:start position:0% +electron in the end they make the same + + + align:start position:0% +electron in the end they make the same +daughter products but they go by + + align:start position:0% +daughter products but they go by + + + align:start position:0% +daughter products but they go by +different mechanisms and they give off + + align:start position:0% +different mechanisms and they give off + + + align:start position:0% +different mechanisms and they give off +different bits of radiation which we can + + align:start position:0% +different bits of radiation which we can + + + align:start position:0% +different bits of radiation which we can +actually sense and measure cool so onto + + align:start position:0% +actually sense and measure cool so onto + + + align:start position:0% +actually sense and measure cool so onto +gamma decay or isomeric transition these + + align:start position:0% +gamma decay or isomeric transition these + + + align:start position:0% +gamma decay or isomeric transition these +range from the dead simple like + + align:start position:0% +range from the dead simple like + + + align:start position:0% +range from the dead simple like +technetium-99 metastable giving off a + + align:start position:0% +technetium-99 metastable giving off a + + + align:start position:0% +technetium-99 metastable giving off a +characteristic 140 ke V gamma ray for + + align:start position:0% +characteristic 140 ke V gamma ray for + + + align:start position:0% +characteristic 140 ke V gamma ray for +technetium that's the medical imaging + + align:start position:0% +technetium that's the medical imaging + + + align:start position:0% +technetium that's the medical imaging +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +we've talked a lot about to the + + align:start position:0% +we've talked a lot about to the + + + align:start position:0% +we've talked a lot about to the +ridiculously complex like americium-241 + + align:start position:0% +ridiculously complex like americium-241 + + + align:start position:0% +ridiculously complex like americium-241 +which has a lot a lot a lot of different + + align:start position:0% +which has a lot a lot a lot of different + + + align:start position:0% +which has a lot a lot a lot of different +nuclear energy states all of which + + align:start position:0% +nuclear energy states all of which + + + align:start position:0% +nuclear energy states all of which +release anywhere between one and a lot + + align:start position:0% +release anywhere between one and a lot + + + align:start position:0% +release anywhere between one and a lot +of gamma rays and this is what's + + align:start position:0% +of gamma rays and this is what's + + + align:start position:0% +of gamma rays and this is what's +referred to as + + align:start position:0% +referred to as + + + align:start position:0% +referred to as +isomeric transition so we'll say gamma + + align:start position:0% +isomeric transition so we'll say gamma + + + align:start position:0% +isomeric transition so we'll say gamma +or isomeric transition is like the same + + align:start position:0% +or isomeric transition is like the same + + + align:start position:0% +or isomeric transition is like the same +thing they're just different words for + + align:start position:0% +thing they're just different words for + + + align:start position:0% +thing they're just different words for +it these are called isomers they've got + + align:start position:0% +it these are called isomers they've got + + + align:start position:0% +it these are called isomers they've got +the same number of protons and neutrons + + align:start position:0% +the same number of protons and neutrons + + + align:start position:0% +the same number of protons and neutrons +so it's the same nuclide but at an + + align:start position:0% +so it's the same nuclide but at an + + + align:start position:0% +so it's the same nuclide but at an +excited state and we call it gamma decay + + align:start position:0% +excited state and we call it gamma decay + + + align:start position:0% +excited state and we call it gamma decay +because we emit gamma rays or photons I + + align:start position:0% +because we emit gamma rays or photons I + + + align:start position:0% +because we emit gamma rays or photons I +think this one is the easiest one to + + align:start position:0% +think this one is the easiest one to + + + align:start position:0% +think this one is the easiest one to +understand because the reaction goes + + align:start position:0% +understand because the reaction goes + + + align:start position:0% +understand because the reaction goes +something like let's say we have a + + align:start position:0% +something like let's say we have a + + + align:start position:0% +something like let's say we have a +parent nucleus with Z protons and a + + align:start position:0% +parent nucleus with Z protons and a + + + align:start position:0% +parent nucleus with Z protons and a +neutrons nothing happens it's about the + + align:start position:0% +neutrons nothing happens it's about the + + + align:start position:0% +neutrons nothing happens it's about the +easiest nuclear reaction there is except + + align:start position:0% +easiest nuclear reaction there is except + + + align:start position:0% +easiest nuclear reaction there is except +you do give off a gamma ray and we'll + + align:start position:0% +you do give off a gamma ray and we'll + + + align:start position:0% +you do give off a gamma ray and we'll +usually put a star or something to + + align:start position:0% +usually put a star or something to + + + align:start position:0% +usually put a star or something to +denote an excited state so when you see + + align:start position:0% +denote an excited state so when you see + + + align:start position:0% +denote an excited state so when you see +a star in the reading over there on a + + align:start position:0% +a star in the reading over there on a + + + align:start position:0% +a star in the reading over there on a +nuclide where the charge would be that's + + align:start position:0% +nuclide where the charge would be that's + + + align:start position:0% +nuclide where the charge would be that's +an excited energy state that will likely + + align:start position:0% +an excited energy state that will likely + + + align:start position:0% +an excited energy state that will likely +decay by i.t or gamma decay there is + + align:start position:0% +decay by i.t or gamma decay there is + + + align:start position:0% +decay by i.t or gamma decay there is +also a competing mechanism for isomeric + + align:start position:0% +also a competing mechanism for isomeric + + + align:start position:0% +also a competing mechanism for isomeric +transition or gamma decay and that's + + align:start position:0% +transition or gamma decay and that's + + + align:start position:0% +transition or gamma decay and that's +what's called internal conversion in + + align:start position:0% +what's called internal conversion in + + + align:start position:0% +what's called internal conversion in +this case you can kind of think of it + + align:start position:0% +this case you can kind of think of it + + + align:start position:0% +this case you can kind of think of it +this isn't the correct physical + + align:start position:0% +this isn't the correct physical + + + align:start position:0% +this isn't the correct physical +explanation but it's a perfectly good + + align:start position:0% +explanation but it's a perfectly good + + + align:start position:0% +explanation but it's a perfectly good +mental model that the gamma ray I would + + align:start position:0% +mental model that the gamma ray I would + + + align:start position:0% +mental model that the gamma ray I would +either just be emitted from the nucleus + + align:start position:0% +either just be emitted from the nucleus + + + align:start position:0% +either just be emitted from the nucleus +at which point you would see it and the + + align:start position:0% +at which point you would see it and the + + + align:start position:0% +at which point you would see it and the +energy of the gamma is the same as that + + align:start position:0% +energy of the gamma is the same as that + + + align:start position:0% +energy of the gamma is the same as that +Q or it kind of hits an electron on its + + align:start position:0% +Q or it kind of hits an electron on its + + + align:start position:0% +Q or it kind of hits an electron on its +way out + + align:start position:0% +way out + + + align:start position:0% +way out +ejecting that electron so instead of + + align:start position:0% +ejecting that electron so instead of + + + align:start position:0% +ejecting that electron so instead of +finding a gamma ray you may just get an + + align:start position:0% +finding a gamma ray you may just get an + + + align:start position:0% +finding a gamma ray you may just get an +electron emitted at an energy very very + + align:start position:0% +electron emitted at an energy very very + + + align:start position:0% +electron emitted at an energy very very +close to that gamma ray the difference + + align:start position:0% +close to that gamma ray the difference + + + align:start position:0% +close to that gamma ray the difference +between the gamma ray energy and the + + align:start position:0% +between the gamma ray energy and the + + + align:start position:0% +between the gamma ray energy and the +electron energy is it's binding energy + + align:start position:0% +electron energy is it's binding energy + + + align:start position:0% +electron energy is it's binding energy +because if a gamma hits an electron on + + align:start position:0% +because if a gamma hits an electron on + + + align:start position:0% +because if a gamma hits an electron on +the way out it has to overcome the + + align:start position:0% +the way out it has to overcome the + + + align:start position:0% +the way out it has to overcome the +binding energy of that electron at which + + align:start position:0% +binding energy of that electron at which + + + align:start position:0% +binding energy of that electron at which +point the rest of the energy is just its + + align:start position:0% +point the rest of the energy is just its + + + align:start position:0% +point the rest of the energy is just its +kinetic energy so again + + align:start position:0% +kinetic energy so again + + + align:start position:0% +kinetic energy so again +I don't think that's the precise + + align:start position:0% +I don't think that's the precise + + + align:start position:0% +I don't think that's the precise +physical mechanism but it's a perfectly + + align:start position:0% +physical mechanism but it's a perfectly + + + align:start position:0% +physical mechanism but it's a perfectly +good mental model to remember what this + + align:start position:0% +good mental model to remember what this + + + align:start position:0% +good mental model to remember what this +is a gamma can either just get out on + + align:start position:0% +is a gamma can either just get out on + + + align:start position:0% +is a gamma can either just get out on +its own or it can hit an electron on its + + align:start position:0% +its own or it can hit an electron on its + + + align:start position:0% +its own or it can hit an electron on its +way out if you hit the electron on your + + align:start position:0% +way out if you hit the electron on your + + + align:start position:0% +way out if you hit the electron on your +way out just like an electron capture + + align:start position:0% +way out just like an electron capture + + + align:start position:0% +way out just like an electron capture +then you get a large larger shell + + align:start position:0% +then you get a large larger shell + + + align:start position:0% +then you get a large larger shell +electron falling down to the inner shell + + align:start position:0% +electron falling down to the inner shell + + + align:start position:0% +electron falling down to the inner shell +emitting an x-ray just like before and + + align:start position:0% +emitting an x-ray just like before and + + + align:start position:0% +emitting an x-ray just like before and +then there's one other process I want + + align:start position:0% +then there's one other process I want + + + align:start position:0% +then there's one other process I want +you guys to be aware of has anyone here + + align:start position:0% +you guys to be aware of has anyone here + + + align:start position:0% +you guys to be aware of has anyone here +here ever heard of oj electron emission + + align:start position:0% +here ever heard of oj electron emission + + + align:start position:0% +here ever heard of oj electron emission +or yeah so in this case instead of + + align:start position:0% +or yeah so in this case instead of + + + align:start position:0% +or yeah so in this case instead of +sending out an x-ray you can think of it + + align:start position:0% +sending out an x-ray you can think of it + + + align:start position:0% +sending out an x-ray you can think of it +like the x-ray kind of hits the another + + align:start position:0% +like the x-ray kind of hits the another + + + align:start position:0% +like the x-ray kind of hits the another +electron on its way out + + align:start position:0% +electron on its way out + + + align:start position:0% +electron on its way out +that's not the actual process that + + align:start position:0% +that's not the actual process that + + + align:start position:0% +that's not the actual process that +happens but let's just think of it like + + align:start position:0% +happens but let's just think of it like + + + align:start position:0% +happens but let's just think of it like +that and then that electron is ejected + + align:start position:0% +that and then that electron is ejected + + + align:start position:0% +that and then that electron is ejected +usually from a much outer shell and we + + align:start position:0% +usually from a much outer shell and we + + + align:start position:0% +usually from a much outer shell and we +can actually use these ój electrons + + align:start position:0% +can actually use these ój electrons + + + align:start position:0% +can actually use these ój electrons +because they have specific but very low + + align:start position:0% +because they have specific but very low + + + align:start position:0% +because they have specific but very low +binding energies to do imaging and + + align:start position:0% +binding energies to do imaging and + + + align:start position:0% +binding energies to do imaging and +elemental analysis of materials so this + + align:start position:0% +elemental analysis of materials so this + + + align:start position:0% +elemental analysis of materials so this +is another one of those things where the + + align:start position:0% +is another one of those things where the + + + align:start position:0% +is another one of those things where the +stuff you're learning today is used in + + align:start position:0% +stuff you're learning today is used in + + + align:start position:0% +stuff you're learning today is used in +an ogee electron microscope up in + + align:start position:0% +an ogee electron microscope up in + + + align:start position:0% +an ogee electron microscope up in +building 13 to do combined imaging and + + align:start position:0% +building 13 to do combined imaging and + + + align:start position:0% +building 13 to do combined imaging and +elemental analysis of materials I want + + align:start position:0% +elemental analysis of materials I want + + + align:start position:0% +elemental analysis of materials I want +to skip back a sec because let's say we + + align:start position:0% +to skip back a sec because let's say we + + + align:start position:0% +to skip back a sec because let's say we +have this decay diagram right here a + + align:start position:0% +have this decay diagram right here a + + + align:start position:0% +have this decay diagram right here a +pretty simple one cesium 137 that + + align:start position:0% +pretty simple one cesium 137 that + + + align:start position:0% +pretty simple one cesium 137 that +isotope that everyone was worried about + + align:start position:0% +isotope that everyone was worried about + + + align:start position:0% +isotope that everyone was worried about +from the release from Fukushima can + + align:start position:0% +from the release from Fukushima can + + + align:start position:0% +from the release from Fukushima can +either proceed by just beta decay or + + align:start position:0% +either proceed by just beta decay or + + + align:start position:0% +either proceed by just beta decay or +beta decay followed by an isomeric + + align:start position:0% +beta decay followed by an isomeric + + + align:start position:0% +beta decay followed by an isomeric +transition and shown here as a spectrum + + align:start position:0% +transition and shown here as a spectrum + + + align:start position:0% +transition and shown here as a spectrum +of all the different electron energies + + align:start position:0% +of all the different electron energies + + + align:start position:0% +of all the different electron energies +that you'll get out if you remember from + + align:start position:0% +that you'll get out if you remember from + + + align:start position:0% +that you'll get out if you remember from +last time when we talked about let's say + + align:start position:0% +last time when we talked about let's say + + + align:start position:0% +last time when we talked about let's say +the energy of a beta particle emitted + + align:start position:0% +the energy of a beta particle emitted + + + align:start position:0% +the energy of a beta particle emitted +versus let's say the number of those + + align:start position:0% +versus let's say the number of those + + + align:start position:0% +versus let's say the number of those +particles emitted if this is the Q value + + align:start position:0% +particles emitted if this is the Q value + + + align:start position:0% +particles emitted if this is the Q value +for that reaction you don't always get a + + align:start position:0% +for that reaction you don't always get a + + + align:start position:0% +for that reaction you don't always get a +beta particle out at the Q value in fact + + align:start position:0% +beta particle out at the Q value in fact + + + align:start position:0% +beta particle out at the Q value in fact +you never do it looks something like + + align:start position:0% +you never do it looks something like + + + align:start position:0% +you never do it looks something like +this where they'll be some let's say + + align:start position:0% +this where they'll be some let's say + + + align:start position:0% +this where they'll be some let's say +average or some most likely beta energy + + align:start position:0% +average or some most likely beta energy + + + align:start position:0% +average or some most likely beta energy +which is about + + align:start position:0% +which is about + + + align:start position:0% +which is about +one third queue depends on the reaction + + align:start position:0% +one third queue depends on the reaction + + + align:start position:0% +one third queue depends on the reaction +but that's a good rule of thumb so if + + align:start position:0% +but that's a good rule of thumb so if + + + align:start position:0% +but that's a good rule of thumb so if +you've got a 1.1 74 MeV beta particle + + align:start position:0% +you've got a 1.1 74 MeV beta particle + + + align:start position:0% +you've got a 1.1 74 MeV beta particle +you're gonna see a spectrum of electron + + align:start position:0% +you're gonna see a spectrum of electron + + + align:start position:0% +you're gonna see a spectrum of electron +energies ranging from zero to one point + + align:start position:0% +energies ranging from zero to one point + + + align:start position:0% +energies ranging from zero to one point +one seven four and you've got this other + + align:start position:0% +one seven four and you've got this other + + + align:start position:0% +one seven four and you've got this other +beta transition possible at about half + + align:start position:0% +beta transition possible at about half + + + align:start position:0% +beta transition possible at about half +an MeV so you're gonna see that same + + align:start position:0% +an MeV so you're gonna see that same + + + align:start position:0% +an MeV so you're gonna see that same +spectrum right there and then there's + + align:start position:0% +spectrum right there and then there's + + + align:start position:0% +spectrum right there and then there's +these two what's called the conversion + + align:start position:0% +these two what's called the conversion + + + align:start position:0% +these two what's called the conversion +electrons that's evidence of the + + align:start position:0% +electrons that's evidence of the + + + align:start position:0% +electrons that's evidence of the +competing process with gamma decay which + + align:start position:0% +competing process with gamma decay which + + + align:start position:0% +competing process with gamma decay which +is to say that this gamma decay can + + align:start position:0% +is to say that this gamma decay can + + + align:start position:0% +is to say that this gamma decay can +either just get out at which point you + + align:start position:0% +either just get out at which point you + + + align:start position:0% +either just get out at which point you +see a gamma ray of that energy or that + + align:start position:0% +see a gamma ray of that energy or that + + + align:start position:0% +see a gamma ray of that energy or that +gamma hits an electron on its way out + + align:start position:0% +gamma hits an electron on its way out + + + align:start position:0% +gamma hits an electron on its way out +knocking those electrons out does anyone + + align:start position:0% +knocking those electrons out does anyone + + + align:start position:0% +knocking those electrons out does anyone +know here what it means by K shell or L + + align:start position:0% +know here what it means by K shell or L + + + align:start position:0% +know here what it means by K shell or L +shell if you do just shout it out so + + align:start position:0% +shell if you do just shout it out so + + + align:start position:0% +shell if you do just shout it out so +that there depends on the that's correct + + align:start position:0% +that there depends on the that's correct + + + align:start position:0% +that there depends on the that's correct +it's it's the energy level so let's say + + align:start position:0% +it's it's the energy level so let's say + + + align:start position:0% +it's it's the energy level so let's say +we'll draw a kind of a Bohr model of a + + align:start position:0% +we'll draw a kind of a Bohr model of a + + + align:start position:0% +we'll draw a kind of a Bohr model of a +nucleus we'll call it N and let's give + + align:start position:0% +nucleus we'll call it N and let's give + + + align:start position:0% +nucleus we'll call it N and let's give +it three electron energy levels and + + align:start position:0% +it three electron energy levels and + + + align:start position:0% +it three electron energy levels and +let's say there's a couple electrons in + + align:start position:0% +let's say there's a couple electrons in + + + align:start position:0% +let's say there's a couple electrons in +the first shell and some electrons and + + align:start position:0% +the first shell and some electrons and + + + align:start position:0% +the first shell and some electrons and +the outer shells and let's say this + + align:start position:0% +the outer shells and let's say this + + + align:start position:0% +the outer shells and let's say this +electron was struck on its way out by a + + align:start position:0% +electron was struck on its way out by a + + + align:start position:0% +electron was struck on its way out by a +gamma ray so it's gone at this point you + + align:start position:0% +gamma ray so it's gone at this point you + + + align:start position:0% +gamma ray so it's gone at this point you +might have an electron fall from let's + + align:start position:0% +might have an electron fall from let's + + + align:start position:0% +might have an electron fall from let's +call this level two to level one and so + + align:start position:0% +call this level two to level one and so + + + align:start position:0% +call this level two to level one and so +this two to one transition is called the + + align:start position:0% +this two to one transition is called the + + + align:start position:0% +this two to one transition is called the +K transition don't ask me why the + + align:start position:0% +K transition don't ask me why the + + + align:start position:0% +K transition don't ask me why the +letters are the way they are I probably + + align:start position:0% +letters are the way they are I probably + + + align:start position:0% +letters are the way they are I probably +have read it and have forgotten it + + align:start position:0% +have read it and have forgotten it + + + align:start position:0% +have read it and have forgotten it +because it wasn't that intuitive but + + align:start position:0% +because it wasn't that intuitive but + + + align:start position:0% +because it wasn't that intuitive but +this is referred to as a K transition so + + align:start position:0% +this is referred to as a K transition so + + + align:start position:0% +this is referred to as a K transition so +you may have what's called the K alpha + + align:start position:0% +you may have what's called the K alpha + + + align:start position:0% +you may have what's called the K alpha +or a K beta line that depends on if you + + align:start position:0% +or a K beta line that depends on if you + + + align:start position:0% +or a K beta line that depends on if you +have an even higher energy shell but + + align:start position:0% +have an even higher energy shell but + + + align:start position:0% +have an even higher energy shell but +whatever this letter is it tells you + + align:start position:0% +whatever this letter is it tells you + + + align:start position:0% +whatever this letter is it tells you +what energy level the electron is going + + align:start position:0% +what energy level the electron is going + + + align:start position:0% +what energy level the electron is going +to so the K lines would be here the L + + align:start position:0% +to so the K lines would be here the L + + + align:start position:0% +to so the K lines would be here the L +line yeah I'm sorry let me let me back + + align:start position:0% +line yeah I'm sorry let me let me back + + + align:start position:0% +line yeah I'm sorry let me let me back +up and say that again so the idea here + + align:start position:0% +up and say that again so the idea here + + + align:start position:0% +up and say that again so the idea here +is that if this is the + + align:start position:0% +is that if this is the + + + align:start position:0% +is that if this is the +let's see which one is this point six + + align:start position:0% +let's see which one is this point six + + + align:start position:0% +let's see which one is this point six +six two so if the gamma-ray is at point + + align:start position:0% +six two so if the gamma-ray is at point + + + align:start position:0% +six two so if the gamma-ray is at point +six six 2 MeV which would be about there + + align:start position:0% +six six 2 MeV which would be about there + + + align:start position:0% +six six 2 MeV which would be about there +notice that these cash L and L shell + + align:start position:0% +notice that these cash L and L shell + + + align:start position:0% +notice that these cash L and L shell +lines aren't quite point six six two + + align:start position:0% +lines aren't quite point six six two + + + align:start position:0% +lines aren't quite point six six two +that's because they have to overcome the + + align:start position:0% +that's because they have to overcome the + + + align:start position:0% +that's because they have to overcome the +binding energy of the electron to get + + align:start position:0% +binding energy of the electron to get + + + align:start position:0% +binding energy of the electron to get +out so to jump back to this diagram + + align:start position:0% +out so to jump back to this diagram + + + align:start position:0% +out so to jump back to this diagram +right here the gamma ray loses a little + + align:start position:0% +right here the gamma ray loses a little + + + align:start position:0% +right here the gamma ray loses a little +bit of energy in freeing the electron + + align:start position:0% +bit of energy in freeing the electron + + + align:start position:0% +bit of energy in freeing the electron +the rest of which can become kinetic + + align:start position:0% +the rest of which can become kinetic + + + align:start position:0% +the rest of which can become kinetic +energy which is why you can see that the + + align:start position:0% +energy which is why you can see that the + + + align:start position:0% +energy which is why you can see that the +electron let's say was ejected from the + + align:start position:0% +electron let's say was ejected from the + + + align:start position:0% +electron let's say was ejected from the +K shell here and yeah I will I will say + + align:start position:0% +K shell here and yeah I will I will say + + + align:start position:0% +K shell here and yeah I will I will say +that internal conversion you can imagine + + align:start position:0% +that internal conversion you can imagine + + + align:start position:0% +that internal conversion you can imagine +a mental model of the gamma ray hits an + + align:start position:0% +a mental model of the gamma ray hits an + + + align:start position:0% +a mental model of the gamma ray hits an +electron on its way out physically it's + + align:start position:0% +electron on its way out physically it's + + + align:start position:0% +electron on its way out physically it's +more complicated yes yeah yep so if you + + align:start position:0% +more complicated yes yeah yep so if you + + + align:start position:0% +more complicated yes yeah yep so if you +want to remember like what's what I + + align:start position:0% +want to remember like what's what I + + + align:start position:0% +want to remember like what's what I +would say just remember this diagram + + align:start position:0% +would say just remember this diagram + + + align:start position:0% +would say just remember this diagram +right here yeah Kristin just you'd you + + align:start position:0% +right here yeah Kristin just you'd you + + + align:start position:0% +right here yeah Kristin just you'd you +get just the electron good question is + + align:start position:0% +get just the electron good question is + + + align:start position:0% +get just the electron good question is +the gamma rays effectively absorbed in + + align:start position:0% +the gamma rays effectively absorbed in + + + align:start position:0% +the gamma rays effectively absorbed in +freeing the electron from its bound + + align:start position:0% +freeing the electron from its bound + + + align:start position:0% +freeing the electron from its bound +shell and then imparting kinetic energy + + align:start position:0% +shell and then imparting kinetic energy + + + align:start position:0% +shell and then imparting kinetic energy +yep + + align:start position:0% + + + + align:start position:0% + +that's right so that's correct + + align:start position:0% +that's right so that's correct + + + align:start position:0% +that's right so that's correct +so we'll I'll spend the next couple + + align:start position:0% +so we'll I'll spend the next couple + + + align:start position:0% +so we'll I'll spend the next couple +slides going over what O'Shea electron + + align:start position:0% +slides going over what O'Shea electron + + + align:start position:0% +slides going over what O'Shea electron +emission is but not till we finish the + + align:start position:0% +emission is but not till we finish the + + + align:start position:0% +emission is but not till we finish the +the easier stuff because OJ's a little + + align:start position:0% +the easier stuff because OJ's a little + + + align:start position:0% +the easier stuff because OJ's a little +complicated did I see another question + + align:start position:0% +complicated did I see another question + + + align:start position:0% +complicated did I see another question +out here cool so again all the competing + + align:start position:0% +out here cool so again all the competing + + + align:start position:0% +out here cool so again all the competing +methods for a gamma decay won the game + + align:start position:0% +methods for a gamma decay won the game + + + align:start position:0% +methods for a gamma decay won the game +it can just get out to the gamma can + + align:start position:0% +it can just get out to the gamma can + + + align:start position:0% +it can just get out to the gamma can +knock out an electron from let's say the + + align:start position:0% +knock out an electron from let's say the + + + align:start position:0% +knock out an electron from let's say the +K shell or the L shell or the M shell + + align:start position:0% +K shell or the L shell or the M shell + + + align:start position:0% +K shell or the L shell or the M shell +and so on and so on depending on what + + align:start position:0% +and so on and so on depending on what + + + align:start position:0% +and so on and so on depending on what +elements you have so I'll just label + + align:start position:0% +elements you have so I'll just label + + + align:start position:0% +elements you have so I'll just label +these like this would be like the K + + align:start position:0% +these like this would be like the K + + + align:start position:0% +these like this would be like the K +shell would be the L shell this would be + + align:start position:0% +shell would be the L shell this would be + + + align:start position:0% +shell would be the L shell this would be +the M shell now I want you to notice + + align:start position:0% +the M shell now I want you to notice + + + align:start position:0% +the M shell now I want you to notice +something to the K shell electron + + align:start position:0% +something to the K shell electron + + + align:start position:0% +something to the K shell electron +ejected from the innermost electron is + + align:start position:0% +ejected from the innermost electron is + + + align:start position:0% +ejected from the innermost electron is +slightly lower than the L shell electron + + align:start position:0% +slightly lower than the L shell electron + + + align:start position:0% +slightly lower than the L shell electron +why do you guys think that is well let's + + align:start position:0% +why do you guys think that is well let's + + + align:start position:0% +why do you guys think that is well let's +let's look at the energetics for this + + align:start position:0% +let's look at the energetics for this + + + align:start position:0% +let's look at the energetics for this +process right the electron energy level + + align:start position:0% +process right the electron energy level + + + align:start position:0% +process right the electron energy level +is whatever the gamma ray level is minus + + align:start position:0% +is whatever the gamma ray level is minus + + + align:start position:0% +is whatever the gamma ray level is minus +the binding energy which of these two + + align:start position:0% +the binding energy which of these two + + + align:start position:0% +the binding energy which of these two +electrons that the K shell or the L + + align:start position:0% +electrons that the K shell or the L + + + align:start position:0% +electrons that the K shell or the L +shell do you think is going to be more + + align:start position:0% +shell do you think is going to be more + + + align:start position:0% +shell do you think is going to be more +tightly bound the K shell the innermost + + align:start position:0% +tightly bound the K shell the innermost + + + align:start position:0% +tightly bound the K shell the innermost +electron is more bound so it takes away + + align:start position:0% +electron is more bound so it takes away + + + align:start position:0% +electron is more bound so it takes away +more energy from that gamma ray let's + + align:start position:0% +more energy from that gamma ray let's + + + align:start position:0% +more energy from that gamma ray let's +say this is the gamma it takes more + + align:start position:0% +say this is the gamma it takes more + + + align:start position:0% +say this is the gamma it takes more +energy to eject an electron from the K + + align:start position:0% +energy to eject an electron from the K + + + align:start position:0% +energy to eject an electron from the K +shell than the L shell or in other words + + align:start position:0% +shell than the L shell or in other words + + + align:start position:0% +shell than the L shell or in other words +the gamma loses less energy ejecting a + + align:start position:0% +the gamma loses less energy ejecting a + + + align:start position:0% +the gamma loses less energy ejecting a +less bound electron so that's why you + + align:start position:0% +less bound electron so that's why you + + + align:start position:0% +less bound electron so that's why you +see these if there were an M shell there + + align:start position:0% +see these if there were an M shell there + + + align:start position:0% +see these if there were an M shell there +I don't know what element this was drawn + + align:start position:0% +I don't know what element this was drawn + + + align:start position:0% +I don't know what element this was drawn +for but let's say o for cesium so there + + align:start position:0% +for but let's say o for cesium so there + + + align:start position:0% +for but let's say o for cesium so there +probably is an M shell it's just that as + + align:start position:0% +probably is an M shell it's just that as + + + align:start position:0% +probably is an M shell it's just that as +you get down in energy levels the + + align:start position:0% +you get down in energy levels the + + + align:start position:0% +you get down in energy levels the +probability of finding an electron from + + align:start position:0% +probability of finding an electron from + + + align:start position:0% +probability of finding an electron from +these outer and outer energy levels gets + + align:start position:0% +these outer and outer energy levels gets + + + align:start position:0% +these outer and outer energy levels gets +way in way less likely + + align:start position:0% +way in way less likely + + + align:start position:0% +way in way less likely +so you'd usually just see a K or an L + + align:start position:0% +so you'd usually just see a K or an L + + + align:start position:0% +so you'd usually just see a K or an L +shell electron and if I ask you to draw + + align:start position:0% +shell electron and if I ask you to draw + + + align:start position:0% +shell electron and if I ask you to draw +one of these on a problem set or an exam + + align:start position:0% +one of these on a problem set or an exam + + + align:start position:0% +one of these on a problem set or an exam +just drawing the K and the L shells is + + align:start position:0% +just drawing the K and the L shells is + + + align:start position:0% +just drawing the K and the L shells is +perfectly sufficient because that way at + + align:start position:0% +perfectly sufficient because that way at + + + align:start position:0% +perfectly sufficient because that way at +least you'll know that there's a couple + + align:start position:0% +least you'll know that there's a couple + + + align:start position:0% +least you'll know that there's a couple +possibilities yeah + + align:start position:0% +possibilities yeah + + + align:start position:0% +possibilities yeah +on this one so these two curves + + align:start position:0% +on this one so these two curves + + + align:start position:0% +on this one so these two curves +represent the probability of finding an + + align:start position:0% +represent the probability of finding an + + + align:start position:0% +represent the probability of finding an +electron emitted at that energy so this + + align:start position:0% +electron emitted at that energy so this + + + align:start position:0% +electron emitted at that energy so this +curve right here where you get a maximum + + align:start position:0% +curve right here where you get a maximum + + + align:start position:0% +curve right here where you get a maximum +beta energy of 512 ke V comes from that + + align:start position:0% +beta energy of 512 ke V comes from that + + + align:start position:0% +beta energy of 512 ke V comes from that +beta decay and the maximum for the 1.17 + + align:start position:0% +beta decay and the maximum for the 1.17 + + + align:start position:0% +beta decay and the maximum for the 1.17 +4 comes from this beta decay so the + + align:start position:0% +4 comes from this beta decay so the + + + align:start position:0% +4 comes from this beta decay so the +total curve would be the sum of each of + + align:start position:0% +total curve would be the sum of each of + + + align:start position:0% +total curve would be the sum of each of +these 4 things if I just said draw the + + align:start position:0% +these 4 things if I just said draw the + + + align:start position:0% +these 4 things if I just said draw the +total probability of detecting an + + align:start position:0% +total probability of detecting an + + + align:start position:0% +total probability of detecting an +electron at that temperature you just + + align:start position:0% +electron at that temperature you just + + + align:start position:0% +electron at that temperature you just +add those up I saw two other questions + + align:start position:0% +add those up I saw two other questions + + + align:start position:0% +add those up I saw two other questions +or were they the same thing yeah + + align:start position:0% + + + + align:start position:0% + +ah so that so the question was is the + + align:start position:0% +ah so that so the question was is the + + + align:start position:0% +ah so that so the question was is the +area under each of these curves one not + + align:start position:0% +area under each of these curves one not + + + align:start position:0% +area under each of these curves one not +with this scale here we're just showing + + align:start position:0% +with this scale here we're just showing + + + align:start position:0% +with this scale here we're just showing +a relative number of electrons so if you + + align:start position:0% +a relative number of electrons so if you + + + align:start position:0% +a relative number of electrons so if you +want to find what's the total + + align:start position:0% +want to find what's the total + + + align:start position:0% +want to find what's the total +probability that CCM will emit an + + align:start position:0% +probability that CCM will emit an + + + align:start position:0% +probability that CCM will emit an +electron of each energy if you integrate + + align:start position:0% +electron of each energy if you integrate + + + align:start position:0% +electron of each energy if you integrate +under all of these curves that will sum + + align:start position:0% +under all of these curves that will sum + + + align:start position:0% +under all of these curves that will sum +to one if you're looking at just one of + + align:start position:0% +to one if you're looking at just one of + + + align:start position:0% +to one if you're looking at just one of +these decays and you're saying if cesium + + align:start position:0% +these decays and you're saying if cesium + + + align:start position:0% +these decays and you're saying if cesium +undergoes this decay what's the + + align:start position:0% +undergoes this decay what's the + + + align:start position:0% +undergoes this decay what's the +probability of each of these energy + + align:start position:0% +probability of each of these energy + + + align:start position:0% +probability of each of these energy +levels then you only integrate under the + + align:start position:0% +levels then you only integrate under the + + + align:start position:0% +levels then you only integrate under the +relevant curve + + align:start position:0% +relevant curve + + + align:start position:0% +relevant curve +what's more practical is usually what's + + align:start position:0% +what's more practical is usually what's + + + align:start position:0% +what's more practical is usually what's +the probability of finding any electron + + align:start position:0% +the probability of finding any electron + + + align:start position:0% +the probability of finding any electron +at any energy from cesium then you take + + align:start position:0% +at any energy from cesium then you take + + + align:start position:0% +at any energy from cesium then you take +into account all the possible decays + + align:start position:0% +into account all the possible decays + + + align:start position:0% +into account all the possible decays +draw all the curves independently add + + align:start position:0% +draw all the curves independently add + + + align:start position:0% +draw all the curves independently add +them up and you get the total + + align:start position:0% +them up and you get the total + + + align:start position:0% +them up and you get the total +probability function whose area will be + + align:start position:0% +probability function whose area will be + + + align:start position:0% +probability function whose area will be +one yes + + align:start position:0% + + + + align:start position:0% + +what can you say the last part again + + align:start position:0% + + + + align:start position:0% + +that's correct so the L shell electron + + align:start position:0% +that's correct so the L shell electron + + + align:start position:0% +that's correct so the L shell electron +in the second shell is less tightly + + align:start position:0% +in the second shell is less tightly + + + align:start position:0% +in the second shell is less tightly +bound than the first one which is why + + align:start position:0% +bound than the first one which is why + + + align:start position:0% +bound than the first one which is why +it's ejected with more energy it doesn't + + align:start position:0% +it's ejected with more energy it doesn't + + + align:start position:0% +it's ejected with more energy it doesn't +take as much of the game as energy to + + align:start position:0% +take as much of the game as energy to + + + align:start position:0% +take as much of the game as energy to +get it out if you were to get let's say + + align:start position:0% +get it out if you were to get let's say + + + align:start position:0% +get it out if you were to get let's say +the outermost electrons ejected which + + align:start position:0% +the outermost electrons ejected which + + + align:start position:0% +the outermost electrons ejected which +happens in O'Shay which we'll go over + + align:start position:0% +happens in O'Shay which we'll go over + + + align:start position:0% +happens in O'Shay which we'll go over +next it can take up anywhere from like + + align:start position:0% +next it can take up anywhere from like + + + align:start position:0% +next it can take up anywhere from like +one to seven + + align:start position:0% +one to seven + + + align:start position:0% +one to seven +evie really really low energies that's + + align:start position:0% +evie really really low energies that's + + + align:start position:0% +evie really really low energies that's +what we call the work function or the + + align:start position:0% +what we call the work function or the + + + align:start position:0% +what we call the work function or the +the energy required to iron to take the + + align:start position:0% +the energy required to iron to take the + + + align:start position:0% +the energy required to iron to take the +outermost electron out so any other + + align:start position:0% +outermost electron out so any other + + + align:start position:0% +outermost electron out so any other +questions on this before I go to Jose + + align:start position:0% +questions on this before I go to Jose + + + align:start position:0% +questions on this before I go to Jose +and show you that process cool so then + + align:start position:0% +and show you that process cool so then + + + align:start position:0% +and show you that process cool so then +let's get into what is Jose electron + + align:start position:0% +let's get into what is Jose electron + + + align:start position:0% +let's get into what is Jose electron +emission it's exactly luca's of what you + + align:start position:0% +emission it's exactly luca's of what you + + + align:start position:0% +emission it's exactly luca's of what you +said you're asking about it yeah so it's + + align:start position:0% +said you're asking about it yeah so it's + + + align:start position:0% +said you're asking about it yeah so it's +exactly like what Luke said normally if + + align:start position:0% +exactly like what Luke said normally if + + + align:start position:0% +exactly like what Luke said normally if +you have a hole in a lower level energy + + align:start position:0% +you have a hole in a lower level energy + + + align:start position:0% +you have a hole in a lower level energy +shell an electron from a higher shell + + align:start position:0% +shell an electron from a higher shell + + + align:start position:0% +shell an electron from a higher shell +will fall down to fill it meaning an + + align:start position:0% +will fall down to fill it meaning an + + + align:start position:0% +will fall down to fill it meaning an +x-ray a competing process for this is + + align:start position:0% +x-ray a competing process for this is + + + align:start position:0% +x-ray a competing process for this is +another electron from a very similar + + align:start position:0% +another electron from a very similar + + + align:start position:0% +another electron from a very similar +energy shell will get ejected instead + + align:start position:0% +energy shell will get ejected instead + + + align:start position:0% +energy shell will get ejected instead +the mental model for this which again is + + align:start position:0% +the mental model for this which again is + + + align:start position:0% +the mental model for this which again is +not the true physical picture but it's + + align:start position:0% +not the true physical picture but it's + + + align:start position:0% +not the true physical picture but it's +perfectly fine to think of it like this + + align:start position:0% +perfectly fine to think of it like this + + + align:start position:0% +perfectly fine to think of it like this +the x-ray hits another electron on its + + align:start position:0% +the x-ray hits another electron on its + + + align:start position:0% +the x-ray hits another electron on its +way out and you can look at the + + align:start position:0% +way out and you can look at the + + + align:start position:0% +way out and you can look at the +energetics accordingly where for Jose + + align:start position:0% +energetics accordingly where for Jose + + + align:start position:0% +energetics accordingly where for Jose +emission let's say the kinetic energy + + align:start position:0% +emission let's say the kinetic energy + + + align:start position:0% +emission let's say the kinetic energy +the Jose electron is the difference in + + align:start position:0% +the Jose electron is the difference in + + + align:start position:0% +the Jose electron is the difference in +the final and initial electron energy + + align:start position:0% +the final and initial electron energy + + + align:start position:0% +the final and initial electron energy +States minus the binding energy of the + + align:start position:0% +States minus the binding energy of the + + + align:start position:0% +States minus the binding energy of the +Jose electron which will usually be very + + align:start position:0% +Jose electron which will usually be very + + + align:start position:0% +Jose electron which will usually be very +low because the Jose electron that's + + align:start position:0% +low because the Jose electron that's + + + align:start position:0% +low because the Jose electron that's +emitted is usually one of the outer + + align:start position:0% +emitted is usually one of the outer + + + align:start position:0% +emitted is usually one of the outer +shell electrons so to help make this a + + align:start position:0% +shell electrons so to help make this a + + + align:start position:0% +shell electrons so to help make this a +little more concrete I wanted to show + + align:start position:0% +little more concrete I wanted to show + + + align:start position:0% +little more concrete I wanted to show +will do a little calculation example + + align:start position:0% +will do a little calculation example + + + align:start position:0% +will do a little calculation example +it's just addition so it's not that hard + + align:start position:0% +it's just addition so it's not that hard + + + align:start position:0% +it's just addition so it's not that hard +so let's say we were measuring I don't + + align:start position:0% +so let's say we were measuring I don't + + + align:start position:0% +so let's say we were measuring I don't +even know what this is and we started to + + align:start position:0% +even know what this is and we started to + + + align:start position:0% +even know what this is and we started to +see some characteristic Jose electrons + + align:start position:0% +see some characteristic Jose electrons + + + align:start position:0% +see some characteristic Jose electrons +for a copper platinum carbon and oxygen + + align:start position:0% +for a copper platinum carbon and oxygen + + + align:start position:0% +for a copper platinum carbon and oxygen +and the question is why do we see oxygen + + align:start position:0% +and the question is why do we see oxygen + + + align:start position:0% +and the question is why do we see oxygen +coming out right there at about 501 easy + + align:start position:0% +coming out right there at about 501 easy + + + align:start position:0% +coming out right there at about 501 easy +very very low energy compared to what + + align:start position:0% +very very low energy compared to what + + + align:start position:0% +very very low energy compared to what +we've been talking about + + align:start position:0% +we've been talking about + + + align:start position:0% +we've been talking about +we can actually look at the binding + + align:start position:0% +we can actually look at the binding + + + align:start position:0% +we can actually look at the binding +energies of some of the different + + align:start position:0% +energies of some of the different + + + align:start position:0% +energies of some of the different +electrons in oxygen luckily there aren't + + align:start position:0% +electrons in oxygen luckily there aren't + + + align:start position:0% +electrons in oxygen luckily there aren't +that many electrons in oxygen + + align:start position:0% +that many electrons in oxygen + + + align:start position:0% +that many electrons in oxygen +the first the only will the only k + + align:start position:0% +the first the only will the only k + + + align:start position:0% +the first the only will the only k +electrons let's say have a binding + + align:start position:0% +electrons let's say have a binding + + + align:start position:0% +electrons let's say have a binding +energy of 532 Eevee the l1 is 24 and + + align:start position:0% +energy of 532 Eevee the l1 is 24 and + + + align:start position:0% +energy of 532 Eevee the l1 is 24 and +then the l3 something else and one of + + align:start position:0% +then the l3 something else and one of + + + align:start position:0% +then the l3 something else and one of +the other P orbitals is 70 V and so the + + align:start position:0% +the other P orbitals is 70 V and so the + + + align:start position:0% +the other P orbitals is 70 V and so the +formula is pretty simple it's just 532 + + align:start position:0% +formula is pretty simple it's just 532 + + + align:start position:0% +formula is pretty simple it's just 532 +minus 24 that's the difference between + + align:start position:0% +minus 24 that's the difference between + + + align:start position:0% +minus 24 that's the difference between +the final and initial energy levels - + + align:start position:0% +the final and initial energy levels - + + + align:start position:0% +the final and initial energy levels - +the seven - free that outer electron + + align:start position:0% +the seven - free that outer electron + + + align:start position:0% +the seven - free that outer electron +comes to 501 evey which is exactly where + + align:start position:0% +comes to 501 evey which is exactly where + + + align:start position:0% +comes to 501 evey which is exactly where +you see the oj line for oxygen so when I + + align:start position:0% +you see the oj line for oxygen so when I + + + align:start position:0% +you see the oj line for oxygen so when I +ask you what are all the possible things + + align:start position:0% +ask you what are all the possible things + + + align:start position:0% +ask you what are all the possible things +that you could see during the decay of + + align:start position:0% +that you could see during the decay of + + + align:start position:0% +that you could see during the decay of +something something something if I were + + align:start position:0% +something something something if I were + + + align:start position:0% +something something something if I were +to show you this curve and ask you + + align:start position:0% +to show you this curve and ask you + + + align:start position:0% +to show you this curve and ask you +what's missing what would you do + + align:start position:0% + + + + align:start position:0% + +where would you draw the oj electrons on + + align:start position:0% +where would you draw the oj electrons on + + + align:start position:0% +where would you draw the oj electrons on +this curve yep yep 500 evey would be + + align:start position:0% +this curve yep yep 500 evey would be + + + align:start position:0% +this curve yep yep 500 evey would be +like I don't know one pixel away on this + + align:start position:0% +like I don't know one pixel away on this + + + align:start position:0% +like I don't know one pixel away on this +graph but if you want a complete answer + + align:start position:0% +graph but if you want a complete answer + + + align:start position:0% +graph but if you want a complete answer +to this question you've got to take into + + align:start position:0% +to this question you've got to take into + + + align:start position:0% +to this question you've got to take into +account all the possible beta energies + + align:start position:0% +account all the possible beta energies + + + align:start position:0% +account all the possible beta energies +for all the possible beta decay + + align:start position:0% +for all the possible beta decay + + + align:start position:0% +for all the possible beta decay +mechanisms all of the possible + + align:start position:0% +mechanisms all of the possible + + + align:start position:0% +mechanisms all of the possible +conversion electrons for whatever gammas + + align:start position:0% +conversion electrons for whatever gammas + + + align:start position:0% +conversion electrons for whatever gammas +come out in this case there's only one + + align:start position:0% +come out in this case there's only one + + + align:start position:0% +come out in this case there's only one +gamma and oj electrons which could + + align:start position:0% +gamma and oj electrons which could + + + align:start position:0% +gamma and oj electrons which could +compete with x-ray emission so everyone + + align:start position:0% +compete with x-ray emission so everyone + + + align:start position:0% +compete with x-ray emission so everyone +clear on that + + align:start position:0% +clear on that + + + align:start position:0% +clear on that +yeah + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +so the question is if you if you eject + + align:start position:0% +so the question is if you if you eject + + + align:start position:0% +so the question is if you if you eject +an electron from one of the inner shells + + align:start position:0% +an electron from one of the inner shells + + + align:start position:0% +an electron from one of the inner shells +does that eventually create a no J + + align:start position:0% +does that eventually create a no J + + + align:start position:0% +does that eventually create a no J +electron right + + align:start position:0% +electron right + + + align:start position:0% +electron right +it can these are competing processes so + + align:start position:0% +it can these are competing processes so + + + align:start position:0% +it can these are competing processes so +either the x-ray can just escape during + + align:start position:0% +either the x-ray can just escape during + + + align:start position:0% +either the x-ray can just escape during +that transition or will assume that it + + align:start position:0% +that transition or will assume that it + + + align:start position:0% +that transition or will assume that it +hits another electron on its way out and + + align:start position:0% +hits another electron on its way out and + + + align:start position:0% +hits another electron on its way out and +emits a no J electron so these are also + + align:start position:0% +emits a no J electron so these are also + + + align:start position:0% +emits a no J electron so these are also +competing processes so you'll see one or + + align:start position:0% +competing processes so you'll see one or + + + align:start position:0% +competing processes so you'll see one or +the other in reality you'll see a lot of + + align:start position:0% +the other in reality you'll see a lot of + + + align:start position:0% +the other in reality you'll see a lot of +both with different probabilities + + align:start position:0% +both with different probabilities + + + align:start position:0% +both with different probabilities +because they're usually not looking at + + align:start position:0% +because they're usually not looking at + + + align:start position:0% +because they're usually not looking at +one atom it's usually looking at a lot + + align:start position:0% +one atom it's usually looking at a lot + + + align:start position:0% +one atom it's usually looking at a lot +cool any other questions on i.t as an + + align:start position:0% +cool any other questions on i.t as an + + + align:start position:0% +cool any other questions on i.t as an +isomeric transition or internal + + align:start position:0% +isomeric transition or internal + + + align:start position:0% +isomeric transition or internal +conversion or Oh J what this is all + + align:start position:0% +conversion or Oh J what this is all + + + align:start position:0% +conversion or Oh J what this is all +about who wanted to give you one note to + + align:start position:0% +about who wanted to give you one note to + + + align:start position:0% +about who wanted to give you one note to +that these Oh J electrons are really + + align:start position:0% +that these Oh J electrons are really + + + align:start position:0% +that these Oh J electrons are really +really low energy which means the only + + align:start position:0% +really low energy which means the only + + + align:start position:0% +really low energy which means the only +ones that get out of the material are in + + align:start position:0% +ones that get out of the material are in + + + align:start position:0% +ones that get out of the material are in +the top like tens or so of nanometers of + + align:start position:0% +the top like tens or so of nanometers of + + + align:start position:0% +the top like tens or so of nanometers of +the material so it's a very surface + + align:start position:0% +the material so it's a very surface + + + align:start position:0% +the material so it's a very surface +sensitive technique so if you want to do + + align:start position:0% +sensitive technique so if you want to do + + + align:start position:0% +sensitive technique so if you want to do +really detailed surface analysis or + + align:start position:0% +really detailed surface analysis or + + + align:start position:0% +really detailed surface analysis or +profiling you can scan an electron beam + + align:start position:0% +profiling you can scan an electron beam + + + align:start position:0% +profiling you can scan an electron beam +across the sample and then collect the + + align:start position:0% +across the sample and then collect the + + + align:start position:0% +across the sample and then collect the +o'shea electrons that come out skipping + + align:start position:0% +o'shea electrons that come out skipping + + + align:start position:0% +o'shea electrons that come out skipping +ahead our calculation and get like an + + align:start position:0% +ahead our calculation and get like an + + + align:start position:0% +ahead our calculation and get like an +elemental profile that'll tell you how + + align:start position:0% +elemental profile that'll tell you how + + + align:start position:0% +elemental profile that'll tell you how +much of each element is where depending + + align:start position:0% +much of each element is where depending + + + align:start position:0% +much of each element is where depending +on how many of its Oh J electrons you + + align:start position:0% +on how many of its Oh J electrons you + + + align:start position:0% +on how many of its Oh J electrons you +can count and it's pretty it's a pretty + + align:start position:0% +can count and it's pretty it's a pretty + + + align:start position:0% +can count and it's pretty it's a pretty +cool technique they're just machines + + align:start position:0% +cool technique they're just machines + + + align:start position:0% +cool technique they're just machines +that do this now any interest in seeing + + align:start position:0% +that do this now any interest in seeing + + + align:start position:0% +that do this now any interest in seeing +one of these at the Center for material + + align:start position:0% +one of these at the Center for material + + + align:start position:0% +one of these at the Center for material +science and engineering because we could + + align:start position:0% +science and engineering because we could + + + align:start position:0% +science and engineering because we could +try to arrange that - cool okay I'll see + + align:start position:0% +try to arrange that - cool okay I'll see + + + align:start position:0% +try to arrange that - cool okay I'll see +what I can do that'd be fun and the last + + align:start position:0% +what I can do that'd be fun and the last + + + align:start position:0% +what I can do that'd be fun and the last +decay that we haven't talked about and + + align:start position:0% +decay that we haven't talked about and + + + align:start position:0% +decay that we haven't talked about and +did not show up in our generalized decay + + align:start position:0% +did not show up in our generalized decay + + + align:start position:0% +did not show up in our generalized decay +diagram from last time we did talk about + + align:start position:0% +diagram from last time we did talk about + + + align:start position:0% +diagram from last time we did talk about +Neutron decay there's one other one that + + align:start position:0% +Neutron decay there's one other one that + + + align:start position:0% +Neutron decay there's one other one that +probably wouldn't fit on this diagrams + + align:start position:0% +probably wouldn't fit on this diagrams + + + align:start position:0% +probably wouldn't fit on this diagrams +anyone know what it is spontaneous + + align:start position:0% +anyone know what it is spontaneous + + + align:start position:0% +anyone know what it is spontaneous +fission so this can tap that's right + + align:start position:0% +fission so this can tap that's right + + + align:start position:0% +fission so this can tap that's right +this happens with very heavy elements + + align:start position:0% +this happens with very heavy elements + + + align:start position:0% +this happens with very heavy elements +then usually the heavier it is or the + + align:start position:0% +then usually the heavier it is or the + + + align:start position:0% +then usually the heavier it is or the +less stable it is the higher probability + + align:start position:0% +less stable it is the higher probability + + + align:start position:0% +less stable it is the higher probability +this is at which the nucleus can once in + + align:start position:0% +this is at which the nucleus can once in + + + align:start position:0% +this is at which the nucleus can once in +a while it nuclei just explodes + + align:start position:0% +a while it nuclei just explodes + + + align:start position:0% +a while it nuclei just explodes +sometimes giving off to fission products + + align:start position:0% +sometimes giving off to fission products + + + align:start position:0% +sometimes giving off to fission products +any + + align:start position:0% +any + + + align:start position:0% +any +number of neutrons usually between one + + align:start position:0% +number of neutrons usually between one + + + align:start position:0% +number of neutrons usually between one +and three a couple of gamma-rays some + + align:start position:0% +and three a couple of gamma-rays some + + + align:start position:0% +and three a couple of gamma-rays some +anti neutrinos and a whole bunch of + + align:start position:0% +anti neutrinos and a whole bunch of + + + align:start position:0% +anti neutrinos and a whole bunch of +other craziness and so that of course + + align:start position:0% +other craziness and so that of course + + + align:start position:0% +other craziness and so that of course +doesn't fit on the diagram but it is + + align:start position:0% +doesn't fit on the diagram but it is + + + align:start position:0% +doesn't fit on the diagram but it is +another type of decay that I'll ask you + + align:start position:0% +another type of decay that I'll ask you + + + align:start position:0% +another type of decay that I'll ask you +guys to analyze on the homework and + + align:start position:0% +guys to analyze on the homework and + + + align:start position:0% +guys to analyze on the homework and +here's a hint you already analyzed part + + align:start position:0% +here's a hint you already analyzed part + + + align:start position:0% +here's a hint you already analyzed part +of it in problem set one I'll ask you to + + align:start position:0% +of it in problem set one I'll ask you to + + + align:start position:0% +of it in problem set one I'll ask you to +go a little deeper in problem set three + + align:start position:0% +go a little deeper in problem set three + + + align:start position:0% +go a little deeper in problem set three +so anyone have a question I saw okay + + align:start position:0% +so anyone have a question I saw okay + + + align:start position:0% +so anyone have a question I saw okay +bear with me because I skipped back to + + align:start position:0% +bear with me because I skipped back to + + + align:start position:0% +bear with me because I skipped back to +like slide really far away oh cool + + align:start position:0% +like slide really far away oh cool + + + align:start position:0% +like slide really far away oh cool +actually works right to the summary so + + align:start position:0% +actually works right to the summary so + + + align:start position:0% +actually works right to the summary so +in summary the radioactive decay + + align:start position:0% +in summary the radioactive decay + + + align:start position:0% +in summary the radioactive decay +processes are more I think the + + align:start position:0% +processes are more I think the + + + align:start position:0% +processes are more I think the +energetics are pretty easy the formulas + + align:start position:0% +energetics are pretty easy the formulas + + + align:start position:0% +energetics are pretty easy the formulas +aren't that hard to remember because + + align:start position:0% +aren't that hard to remember because + + + align:start position:0% +aren't that hard to remember because +most of them are just parents - + + align:start position:0% +most of them are just parents - + + + align:start position:0% +most of them are just parents - +daughters - something and what I do want + + align:start position:0% +daughters - something and what I do want + + + align:start position:0% +daughters - something and what I do want +you to remember is which mechanisms + + align:start position:0% +you to remember is which mechanisms + + + align:start position:0% +you to remember is which mechanisms +compete with which other ones and why + + align:start position:0% +compete with which other ones and why + + + align:start position:0% +compete with which other ones and why +and if I were to tell you draw me a + + align:start position:0% +and if I were to tell you draw me a + + + align:start position:0% +and if I were to tell you draw me a +spectrum of photons that you may see + + align:start position:0% +spectrum of photons that you may see + + + align:start position:0% +spectrum of photons that you may see +from the decay of caesium-137 or draw me + + align:start position:0% +from the decay of caesium-137 or draw me + + + align:start position:0% +from the decay of caesium-137 or draw me +a spectrum of electrons you'd be able to + + align:start position:0% +a spectrum of electrons you'd be able to + + + align:start position:0% +a spectrum of electrons you'd be able to +draw what that is so that when you go do + + align:start position:0% +draw what that is so that when you go do + + + align:start position:0% +draw what that is so that when you go do +lap number 4 and we count our big bag of + + align:start position:0% +lap number 4 and we count our big bag of + + + align:start position:0% +lap number 4 and we count our big bag of +burnt bananas and you know that there's + + align:start position:0% +burnt bananas and you know that there's + + + align:start position:0% +burnt bananas and you know that there's +potassium-40 in there you know what + + align:start position:0% +potassium-40 in there you know what + + + align:start position:0% +potassium-40 in there you know what +Peaks to start looking for because + + align:start position:0% +Peaks to start looking for because + + + align:start position:0% +Peaks to start looking for because +you're not just going to see looks let's + + align:start position:0% +you're not just going to see looks let's + + + align:start position:0% +you're not just going to see looks let's +let's do a little flash-forward two + + align:start position:0% +let's do a little flash-forward two + + + align:start position:0% +let's do a little flash-forward two +detectors now and some other stuff that + + align:start position:0% +detectors now and some other stuff that + + + align:start position:0% +detectors now and some other stuff that +nuclear engineers actually do on a daily + + align:start position:0% +nuclear engineers actually do on a daily + + + align:start position:0% +nuclear engineers actually do on a daily +basis let's say you're counting the + + align:start position:0% +basis let's say you're counting the + + + align:start position:0% +basis let's say you're counting the +energy of photons as a function of let's + + align:start position:0% +energy of photons as a function of let's + + + align:start position:0% +energy of photons as a function of let's +say the number of photons that you count + + align:start position:0% +say the number of photons that you count + + + align:start position:0% +say the number of photons that you count +you're never you're almost never just + + align:start position:0% +you're never you're almost never just + + + align:start position:0% +you're never you're almost never just +going to see a lone potassium-40 + + align:start position:0% +going to see a lone potassium-40 + + + align:start position:0% +going to see a lone potassium-40 +peak like that it's very very rare that + + align:start position:0% +peak like that it's very very rare that + + + align:start position:0% +peak like that it's very very rare that +you would just capture the gamma ray as + + align:start position:0% +you would just capture the gamma ray as + + + align:start position:0% +you would just capture the gamma ray as +is there's gonna be a lot of other + + align:start position:0% +is there's gonna be a lot of other + + + align:start position:0% +is there's gonna be a lot of other +things that will go into it which I'm + + align:start position:0% +things that will go into it which I'm + + + align:start position:0% +things that will go into it which I'm +not going to give away yet because we're + + align:start position:0% +not going to give away yet because we're + + + align:start position:0% +not going to give away yet because we're +gonna go over photon interactions in + + align:start position:0% +gonna go over photon interactions in + + + align:start position:0% +gonna go over photon interactions in +like a week or two but you do have to + + align:start position:0% +like a week or two but you do have to + + + align:start position:0% +like a week or two but you do have to +think about well what other x-rays might + + align:start position:0% +think about well what other x-rays might + + + align:start position:0% +think about well what other x-rays might +you see what if the gamma what if this + + align:start position:0% +you see what if the gamma what if this + + + align:start position:0% +you see what if the gamma what if this +gamma ray hits an electron on the way + + align:start position:0% +gamma ray hits an electron on the way + + + align:start position:0% +gamma ray hits an electron on the way +out and then you end up with some x-rays + + align:start position:0% +out and then you end up with some x-rays + + + align:start position:0% +out and then you end up with some x-rays +let's say you might have some K level + + align:start position:0% +let's say you might have some K level + + + align:start position:0% +let's say you might have some K level +x-rays and some L level x-rays and maybe + + align:start position:0% +x-rays and some L level x-rays and maybe + + + align:start position:0% +x-rays and some L level x-rays and maybe +some M s these could all be possible as + + align:start position:0% +some M s these could all be possible as + + + align:start position:0% +some M s these could all be possible as +well + + align:start position:0% +well + + + align:start position:0% +well +I'll just label those real quick does + + align:start position:0% +I'll just label those real quick does + + + align:start position:0% +I'll just label those real quick does +anyone know how to find these energies + + align:start position:0% +anyone know how to find these energies + + + align:start position:0% +anyone know how to find these energies +what those x-ray levels are anyone ever + + align:start position:0% +what those x-ray levels are anyone ever + + + align:start position:0% +what those x-ray levels are anyone ever +heard of the Lyman series the emission + + align:start position:0% +heard of the Lyman series the emission + + + align:start position:0% +heard of the Lyman series the emission +lines from ionized hydrogen or anything + + align:start position:0% +lines from ionized hydrogen or anything + + + align:start position:0% +lines from ionized hydrogen or anything +like that that's kind of the the simpler + + align:start position:0% +like that that's kind of the the simpler + + + align:start position:0% +like that that's kind of the the simpler +case of it the idea here is if you want + + align:start position:0% +case of it the idea here is if you want + + + align:start position:0% +case of it the idea here is if you want +to figure out what's the wavelength of + + align:start position:0% +to figure out what's the wavelength of + + + align:start position:0% +to figure out what's the wavelength of +light that's going to be emitted it'll + + align:start position:0% +light that's going to be emitted it'll + + + align:start position:0% +light that's going to be emitted it'll +be that's this thing called the Rydberg + + align:start position:0% +be that's this thing called the Rydberg + + + align:start position:0% +be that's this thing called the Rydberg +constant a more complex formula for + + align:start position:0% +constant a more complex formula for + + + align:start position:0% +constant a more complex formula for +which I have in the notes times one over + + align:start position:0% +which I have in the notes times one over + + + align:start position:0% +which I have in the notes times one over +your final shell squared minus one over + + align:start position:0% +your final shell squared minus one over + + + align:start position:0% +your final shell squared minus one over +your initial shell squared so the idea + + align:start position:0% +your initial shell squared so the idea + + + align:start position:0% +your initial shell squared so the idea +here is that you can look up these this + + align:start position:0% +here is that you can look up these this + + + align:start position:0% +here is that you can look up these this +Rydberg constant for any element that + + align:start position:0% +Rydberg constant for any element that + + + align:start position:0% +Rydberg constant for any element that +you have and there's actually there's + + align:start position:0% +you have and there's actually there's + + + align:start position:0% +you have and there's actually there's +what's called an R infinity constant and + + align:start position:0% +what's called an R infinity constant and + + + align:start position:0% +what's called an R infinity constant and +I think you just multiplied by Z I + + align:start position:0% +I think you just multiplied by Z I + + + align:start position:0% +I think you just multiplied by Z I +forget what power it is but I will get + + align:start position:0% +forget what power it is but I will get + + + align:start position:0% +forget what power it is but I will get +it for you next time and then it's just + + align:start position:0% +it for you next time and then it's just + + + align:start position:0% +it for you next time and then it's just +a matter of the squares between the + + align:start position:0% +a matter of the squares between the + + + align:start position:0% +a matter of the squares between the +final and the initial shell levels where + + align:start position:0% +final and the initial shell levels where + + + align:start position:0% +final and the initial shell levels where +n can vary from one to theoretically + + align:start position:0% +n can vary from one to theoretically + + + align:start position:0% +n can vary from one to theoretically +infinity realistically I've never heard + + align:start position:0% +infinity realistically I've never heard + + + align:start position:0% +infinity realistically I've never heard +of anything beyond a G orbital so let's + + align:start position:0% +of anything beyond a G orbital so let's + + + align:start position:0% +of anything beyond a G orbital so let's +just say it's that or something like + + align:start position:0% +just say it's that or something like + + + align:start position:0% +just say it's that or something like +that + + align:start position:0% +that + + + align:start position:0% +that +oh but they'll all leave the Infinity + + align:start position:0% +oh but they'll all leave the Infinity + + + align:start position:0% +oh but they'll all leave the Infinity +there that's technically correct okay + + align:start position:0% +there that's technically correct okay + + + align:start position:0% +there that's technically correct okay +and so all you need to do is either look + + align:start position:0% +and so all you need to do is either look + + + align:start position:0% +and so all you need to do is either look +up or calculate this constant for your + + align:start position:0% +up or calculate this constant for your + + + align:start position:0% +up or calculate this constant for your +element and then plug in the numbers of + + align:start position:0% +element and then plug in the numbers of + + + align:start position:0% +element and then plug in the numbers of +the shells and you know what sort of + + align:start position:0% +the shells and you know what sort of + + + align:start position:0% +the shells and you know what sort of +photon energy you're going to get out + + align:start position:0% +photon energy you're going to get out + + + align:start position:0% +photon energy you're going to get out +and to make that easier for you I think + + align:start position:0% +and to make that easier for you I think + + + align:start position:0% +and to make that easier for you I think +now is a good time to introduce the NIST + + align:start position:0% +now is a good time to introduce the NIST + + + align:start position:0% +now is a good time to introduce the NIST +x-ray tables so I want to make sure you + + align:start position:0% +x-ray tables so I want to make sure you + + + align:start position:0% +x-ray tables so I want to make sure you +can see my screen and I'm going to show + + align:start position:0% +can see my screen and I'm going to show + + + align:start position:0% +can see my screen and I'm going to show +you something that's on the stellar site + + align:start position:0% +you something that's on the stellar site + + + align:start position:0% +you something that's on the stellar site +which will help you figure this stuff + + align:start position:0% +which will help you figure this stuff + + + align:start position:0% +which will help you figure this stuff +out + + align:start position:0% + + + + align:start position:0% + +22:01 good you can see probably will + + align:start position:0% +22:01 good you can see probably will + + + align:start position:0% +22:01 good you can see probably will +make me login + + align:start position:0% + + + + align:start position:0% + +and all the way at the bottom of the + + align:start position:0% +and all the way at the bottom of the + + + align:start position:0% +and all the way at the bottom of the +material section there's the nist x-ray + + align:start position:0% +material section there's the nist x-ray + + + align:start position:0% +material section there's the nist x-ray +transition energy database so for + + align:start position:0% +transition energy database so for + + + align:start position:0% +transition energy database so for +example you can look at I don't know we + + align:start position:0% +example you can look at I don't know we + + + align:start position:0% +example you can look at I don't know we +were looking at cesium right let's find + + align:start position:0% +were looking at cesium right let's find + + + align:start position:0% +were looking at cesium right let's find +cesium and you can start to look at all + + align:start position:0% +cesium and you can start to look at all + + + align:start position:0% +cesium and you can start to look at all +transitions let's look at the simplest + + align:start position:0% +transitions let's look at the simplest + + + align:start position:0% +transitions let's look at the simplest +one KL one an electron going from shell + + align:start position:0% +one KL one an electron going from shell + + + align:start position:0% +one KL one an electron going from shell +number two - shell number one get + + align:start position:0% +number two - shell number one get + + + align:start position:0% +number two - shell number one get +transitions and you end up with a table + + align:start position:0% +transitions and you end up with a table + + + align:start position:0% +transitions and you end up with a table +of these energies in electron volts so + + align:start position:0% +of these energies in electron volts so + + + align:start position:0% +of these energies in electron volts so +if I were to ask you let's say what sort + + align:start position:0% +if I were to ask you let's say what sort + + + align:start position:0% +if I were to ask you let's say what sort +of gamma rays might you see coming off + + align:start position:0% +of gamma rays might you see coming off + + + align:start position:0% +of gamma rays might you see coming off +of cesium that would be the most likely + + align:start position:0% +of cesium that would be the most likely + + + align:start position:0% +of cesium that would be the most likely +one where you're more likely to eject an + + align:start position:0% +one where you're more likely to eject an + + + align:start position:0% +one where you're more likely to eject an +inner shell electron and it's most + + align:start position:0% +inner shell electron and it's most + + + align:start position:0% +inner shell electron and it's most +likely that a number two shell electron + + align:start position:0% +likely that a number two shell electron + + + align:start position:0% +likely that a number two shell electron +will fall down to a number one or from + + align:start position:0% +will fall down to a number one or from + + + align:start position:0% +will fall down to a number one or from +the L shell to the K shell whatever you + + align:start position:0% +the L shell to the K shell whatever you + + + align:start position:0% +the L shell to the K shell whatever you +want to call it or the some level + + align:start position:0% +want to call it or the some level + + + align:start position:0% +want to call it or the some level +orbitals some other lows there seems to + + align:start position:0% +orbitals some other lows there seems to + + + align:start position:0% +orbitals some other lows there seems to +be like eight different letters have + + align:start position:0% +be like eight different letters have + + + align:start position:0% +be like eight different letters have +described the same thing I hope you guys + + align:start position:0% +described the same thing I hope you guys + + + align:start position:0% +described the same thing I hope you guys +get the idea if you want to look at all + + align:start position:0% +get the idea if you want to look at all + + + align:start position:0% +get the idea if you want to look at all +the possible transitions I have to zoom + + align:start position:0% +the possible transitions I have to zoom + + + align:start position:0% +the possible transitions I have to zoom +back out again yeah let's just scroll + + align:start position:0% +back out again yeah let's just scroll + + + align:start position:0% +back out again yeah let's just scroll +through it but what I want you to notice + + align:start position:0% +through it but what I want you to notice + + + align:start position:0% +through it but what I want you to notice +is that all of the KL transitions are + + align:start position:0% +is that all of the KL transitions are + + + align:start position:0% +is that all of the KL transitions are +within like a couple hundred Evie from + + align:start position:0% +within like a couple hundred Evie from + + + align:start position:0% +within like a couple hundred Evie from +each other so this is like the first or + + align:start position:0% +each other so this is like the first or + + + align:start position:0% +each other so this is like the first or +second or third L shell electron falling + + align:start position:0% +second or third L shell electron falling + + + align:start position:0% +second or third L shell electron falling +to the K level so they call it the KL + + align:start position:0% +to the K level so they call it the KL + + + align:start position:0% +to the K level so they call it the KL +one KL - KL three they're all from the L + + align:start position:0% +one KL - KL three they're all from the L + + + align:start position:0% +one KL - KL three they're all from the L +shell they all just might be one of the + + align:start position:0% +shell they all just might be one of the + + + align:start position:0% +shell they all just might be one of the +different electrons occupying that shell + + align:start position:0% +different electrons occupying that shell + + + align:start position:0% +different electrons occupying that shell +which is why they're not that different + + align:start position:0% +which is why they're not that different + + + align:start position:0% +which is why they're not that different +so if I asked you draw all of the all of + + align:start position:0% +so if I asked you draw all of the all of + + + align:start position:0% +so if I asked you draw all of the all of +the x-rays and gamma is coming out I + + align:start position:0% +the x-rays and gamma is coming out I + + + align:start position:0% +the x-rays and gamma is coming out I +don't want to see a line for every + + align:start position:0% +don't want to see a line for every + + + align:start position:0% +don't want to see a line for every +single level I'm very happy for you just + + align:start position:0% +single level I'm very happy for you just + + + align:start position:0% +single level I'm very happy for you just +to say this line represents the KL + + align:start position:0% +to say this line represents the KL + + + align:start position:0% +to say this line represents the KL +series this line represents the km + + align:start position:0% +series this line represents the km + + + align:start position:0% +series this line represents the km +series all the things from shell 3 to + + align:start position:0% +series all the things from shell 3 to + + + align:start position:0% +series all the things from shell 3 to +shell 1 notice also that because it's + + align:start position:0% +shell 1 notice also that because it's + + + align:start position:0% +shell 1 notice also that because it's +final minus initial squared which I + + align:start position:0% +final minus initial squared which I + + + align:start position:0% +final minus initial squared which I +covered up falling from an even further + + align:start position:0% +covered up falling from an even further + + + align:start position:0% +covered up falling from an even further +outer shell to the same inner shell + + align:start position:0% +outer shell to the same inner shell + + + align:start position:0% +outer shell to the same inner shell +should give you a higher energy which it + + align:start position:0% +should give you a higher energy which it + + + align:start position:0% +should give you a higher energy which it +does by like five ke V and then the KN + + align:start position:0% +does by like five ke V and then the KN + + + align:start position:0% +does by like five ke V and then the KN +levels another 500 evie up they don't + + align:start position:0% +levels another 500 evie up they don't + + + align:start position:0% +levels another 500 evie up they don't +have Kos interesting but they have the K + + align:start position:0% +have Kos interesting but they have the K + + + align:start position:0% +have Kos interesting but they have the K +edge does anyone know what the K edges + + align:start position:0% + + + + align:start position:0% + +exactly it's it's level infinity which + + align:start position:0% +exactly it's it's level infinity which + + + align:start position:0% +exactly it's it's level infinity which +would mean an electron from somewhere + + align:start position:0% +would mean an electron from somewhere + + + align:start position:0% +would mean an electron from somewhere +else right so this in effect is like the + + align:start position:0% +else right so this in effect is like the + + + align:start position:0% +else right so this in effect is like the +energy it takes to ionize a K electron + + align:start position:0% +energy it takes to ionize a K electron + + + align:start position:0% +energy it takes to ionize a K electron +or the x-ray that you would get from an + + align:start position:0% +or the x-ray that you would get from an + + + align:start position:0% +or the x-ray that you would get from an +electron falling all the way into the K + + align:start position:0% +electron falling all the way into the K + + + align:start position:0% +electron falling all the way into the K +shell so this is your kind of level + + align:start position:0% +shell so this is your kind of level + + + align:start position:0% +shell so this is your kind of level +infinity notice that's not that + + align:start position:0% +infinity notice that's not that + + + align:start position:0% +infinity notice that's not that +different from level 5 that's why I + + align:start position:0% +different from level 5 that's why I + + + align:start position:0% +different from level 5 that's why I +wrote 6 I erased it for theoretical + + align:start position:0% +wrote 6 I erased it for theoretical + + + align:start position:0% +wrote 6 I erased it for theoretical +correctness but in prom practicality you + + align:start position:0% +correctness but in prom practicality you + + + align:start position:0% +correctness but in prom practicality you +won't see much else someone have a + + align:start position:0% +won't see much else someone have a + + + align:start position:0% +won't see much else someone have a +question that I saw hand ok let's look + + align:start position:0% +question that I saw hand ok let's look + + + align:start position:0% +question that I saw hand ok let's look +at the L Series oh yes yep yeah that's + + align:start position:0% +at the L Series oh yes yep yeah that's + + + align:start position:0% +at the L Series oh yes yep yeah that's +another exactly yep there's the L alphas + + align:start position:0% +another exactly yep there's the L alphas + + + align:start position:0% +another exactly yep there's the L alphas +the albedo's or you may see L alpha 1 + + align:start position:0% +the albedo's or you may see L alpha 1 + + + align:start position:0% +the albedo's or you may see L alpha 1 +and 2 and L beta 1 & 2 so L designates + + align:start position:0% +and 2 and L beta 1 & 2 so L designates + + + align:start position:0% +and 2 and L beta 1 & 2 so L designates +that it's going to shell level 2 alpha + + align:start position:0% +that it's going to shell level 2 alpha + + + align:start position:0% +that it's going to shell level 2 alpha +or beta is like LM or L n again I I + + align:start position:0% +or beta is like LM or L n again I I + + + align:start position:0% +or beta is like LM or L n again I I +think I've ranted about notations before + + align:start position:0% +think I've ranted about notations before + + + align:start position:0% +think I've ranted about notations before +physics is notorious because whoever + + align:start position:0% +physics is notorious because whoever + + + align:start position:0% +physics is notorious because whoever +does that student and gets enough people + + align:start position:0% +does that student and gets enough people + + + align:start position:0% +does that student and gets enough people +to in fact with the notation that you + + align:start position:0% +to in fact with the notation that you + + + align:start position:0% +to in fact with the notation that you +decide it sticks but the main patterns + + align:start position:0% +decide it sticks but the main patterns + + + align:start position:0% +decide it sticks but the main patterns +to look at then there's let's say the L + + align:start position:0% +to look at then there's let's say the L + + + align:start position:0% +to look at then there's let's say the L +1 M whatever this is from level 3 to + + align:start position:0% +1 M whatever this is from level 3 to + + + align:start position:0% +1 M whatever this is from level 3 to +level 2 notice how much lower and energy + + align:start position:0% +level 2 notice how much lower and energy + + + align:start position:0% +level 2 notice how much lower and energy +these are and the L edge 5kv compared to + + align:start position:0% +these are and the L edge 5kv compared to + + + align:start position:0% +these are and the L edge 5kv compared to +like 36 KETV and all of these are two + + align:start position:0% +like 36 KETV and all of these are two + + + align:start position:0% +like 36 KETV and all of these are two +different transitions you can calculate + + align:start position:0% +different transitions you can calculate + + + align:start position:0% +different transitions you can calculate +with this formula so this is just kind + + align:start position:0% +with this formula so this is just kind + + + align:start position:0% +with this formula so this is just kind +of tabulated this formula for you so + + align:start position:0% +of tabulated this formula for you so + + + align:start position:0% +of tabulated this formula for you so +whatever you're more comfortable doing + + align:start position:0% +whatever you're more comfortable doing + + + align:start position:0% +whatever you're more comfortable doing +is putting this in Excel look it up on + + align:start position:0% +is putting this in Excel look it up on + + + align:start position:0% +is putting this in Excel look it up on +NIST your choice yep + + align:start position:0% + + + + align:start position:0% + +Oh what is the largest enough you mean + + align:start position:0% +Oh what is the largest enough you mean + + + align:start position:0% +Oh what is the largest enough you mean +yeah for that I'll put my practical + + align:start position:0% +yeah for that I'll put my practical + + + align:start position:0% +yeah for that I'll put my practical +thing back there you'll never see it + + align:start position:0% +thing back there you'll never see it + + + align:start position:0% +thing back there you'll never see it +much higher than six unless you're + + align:start position:0% +much higher than six unless you're + + + align:start position:0% +much higher than six unless you're +talking about actinides and super heavy + + align:start position:0% +talking about actinides and super heavy + + + align:start position:0% +talking about actinides and super heavy +elements with even crazier shell levels + + align:start position:0% +elements with even crazier shell levels + + + align:start position:0% +elements with even crazier shell levels +but you'll put the integer shell number + + align:start position:0% +but you'll put the integer shell number + + + align:start position:0% +but you'll put the integer shell number +regardless of whether they call it L or + + align:start position:0% +regardless of whether they call it L or + + + align:start position:0% +regardless of whether they call it L or +s or whatever they put the number here + + align:start position:0% +s or whatever they put the number here + + + align:start position:0% +s or whatever they put the number here +and that will give you the a pretty good + + align:start position:0% +and that will give you the a pretty good + + + align:start position:0% +and that will give you the a pretty good +approximation of the energy transition + + align:start position:0% +approximation of the energy transition + + + align:start position:0% +approximation of the energy transition +does anyone remember this from high + + align:start position:0% +does anyone remember this from high + + + align:start position:0% +does anyone remember this from high +school I hope they're teaching this now + + align:start position:0% +school I hope they're teaching this now + + + align:start position:0% +school I hope they're teaching this now +well they did in five eleven one oh + + align:start position:0% +well they did in five eleven one oh + + + align:start position:0% +well they did in five eleven one oh +that's good to hear what about three oh + + align:start position:0% +that's good to hear what about three oh + + + align:start position:0% +that's good to hear what about three oh +nine one anyone take that no one took + + align:start position:0% +nine one anyone take that no one took + + + align:start position:0% +nine one anyone take that no one took +four you're nine one Wow okay usually + + align:start position:0% +four you're nine one Wow okay usually + + + align:start position:0% +four you're nine one Wow okay usually +it's like half and half raised oh cool + + align:start position:0% +it's like half and half raised oh cool + + + align:start position:0% +it's like half and half raised oh cool +and let's see how far does it go all the + + align:start position:0% +and let's see how far does it go all the + + + align:start position:0% +and let's see how far does it go all the +way to the L 3 ends in the L 3 edge so + + align:start position:0% +way to the L 3 ends in the L 3 edge so + + + align:start position:0% +way to the L 3 ends in the L 3 edge so +that's the biggest element they have + + align:start position:0% +that's the biggest element they have + + + align:start position:0% +that's the biggest element they have +talking about ridiculous transitions + + align:start position:0% + + + + align:start position:0% + +yeah so notice also as you go up in + + align:start position:0% +yeah so notice also as you go up in + + + align:start position:0% +yeah so notice also as you go up in +that's that that's number a hundred so + + align:start position:0% +that's that that's number a hundred so + + + align:start position:0% +that's that that's number a hundred so +this is the heaviest one they have so + + align:start position:0% +this is the heaviest one they have so + + + align:start position:0% +this is the heaviest one they have so +most likely to have the largest number + + align:start position:0% +most likely to have the largest number + + + align:start position:0% +most likely to have the largest number +of levels so here the KL one is like 114 + + align:start position:0% +of levels so here the KL one is like 114 + + + align:start position:0% +of levels so here the KL one is like 114 +ke V sometimes indistinguishable from + + align:start position:0% +ke V sometimes indistinguishable from + + + align:start position:0% +ke V sometimes indistinguishable from +some of these smaller nuclear energy + + align:start position:0% +some of these smaller nuclear energy + + + align:start position:0% +some of these smaller nuclear energy +level transitions so remember I said + + align:start position:0% +level transitions so remember I said + + + align:start position:0% +level transitions so remember I said +before chemistry and nuclear differ by + + align:start position:0% +before chemistry and nuclear differ by + + + align:start position:0% +before chemistry and nuclear differ by +about a factor of a million well not so + + align:start position:0% +about a factor of a million well not so + + + align:start position:0% +about a factor of a million well not so +if you're talking about weak gammas + + align:start position:0% +if you're talking about weak gammas + + + align:start position:0% +if you're talking about weak gammas +versus heavy elements K shell + + align:start position:0% +versus heavy elements K shell + + + align:start position:0% +versus heavy elements K shell +transitions or their K edges let's see + + align:start position:0% +transitions or their K edges let's see + + + align:start position:0% +transitions or their K edges let's see +the Lea the largest X rayed expect would + + align:start position:0% +the Lea the largest X rayed expect would + + + align:start position:0% +the Lea the largest X rayed expect would +be the K edge at a hundred and forty two + + align:start position:0% +be the K edge at a hundred and forty two + + + align:start position:0% +be the K edge at a hundred and forty two +ke V and the technetium-99 gamma ray + + align:start position:0% +ke V and the technetium-99 gamma ray + + + align:start position:0% +ke V and the technetium-99 gamma ray +comes out of one hundred forty KETV how + + align:start position:0% +comes out of one hundred forty KETV how + + + align:start position:0% +comes out of one hundred forty KETV how +do you know if it's a game or an x-ray + + align:start position:0% +do you know if it's a game or an x-ray + + + align:start position:0% +do you know if it's a game or an x-ray +you don't unless you have really really + + align:start position:0% +you don't unless you have really really + + + align:start position:0% +you don't unless you have really really +good energy resolution and you can tell + + align:start position:0% +good energy resolution and you can tell + + + align:start position:0% +good energy resolution and you can tell +them apart yep + + align:start position:0% + + + + align:start position:0% + +correct + + align:start position:0% +correct + + + align:start position:0% +correct +this thing's get quantum so the question + + align:start position:0% +this thing's get quantum so the question + + + align:start position:0% +this thing's get quantum so the question +was this formula in this chart yes this + + align:start position:0% +was this formula in this chart yes this + + + align:start position:0% +was this formula in this chart yes this +is only for x-rays and electron shells + + align:start position:0% +is only for x-rays and electron shells + + + align:start position:0% +is only for x-rays and electron shells +there are probably equivalent + + align:start position:0% +there are probably equivalent + + + align:start position:0% +there are probably equivalent +calculations for nuclear energy levels I + + align:start position:0% +calculations for nuclear energy levels I + + + align:start position:0% +calculations for nuclear energy levels I +will say that's a 22:02 and far beyond + + align:start position:0% +will say that's a 22:02 and far beyond + + + align:start position:0% +will say that's a 22:02 and far beyond +topic for the nuclear energy levels just + + align:start position:0% +topic for the nuclear energy levels just + + + align:start position:0% +topic for the nuclear energy levels just +use the decay diagrams to find those + + align:start position:0% +use the decay diagrams to find those + + + align:start position:0% +use the decay diagrams to find those +yeah the object the table of nuclides + + align:start position:0% +yeah the object the table of nuclides + + + align:start position:0% +yeah the object the table of nuclides +and all there are different diagrams + + align:start position:0% +and all there are different diagrams + + + align:start position:0% +and all there are different diagrams +cool how far do we go here L and yep + + align:start position:0% +cool how far do we go here L and yep + + + align:start position:0% +cool how far do we go here L and yep +there's no OHS so they never talk about + + align:start position:0% +there's no OHS so they never talk about + + + align:start position:0% +there's no OHS so they never talk about +anything beyond shell level for even for + + align:start position:0% +anything beyond shell level for even for + + + align:start position:0% +anything beyond shell level for even for +fermium so huh I stand corrected okay + + align:start position:0% +fermium so huh I stand corrected okay + + + align:start position:0% +fermium so huh I stand corrected okay +cool + + align:start position:0% +cool + + + align:start position:0% +cool +so what I wanted to show you quickly is + + align:start position:0% +so what I wanted to show you quickly is + + + align:start position:0% +so what I wanted to show you quickly is +is that series of hydrogen emission + + align:start position:0% +is that series of hydrogen emission + + + align:start position:0% +is that series of hydrogen emission +lines so how familiar does this look to + + align:start position:0% +lines so how familiar does this look to + + + align:start position:0% +lines so how familiar does this look to +folks where you can have a transition + + align:start position:0% +folks where you can have a transition + + + align:start position:0% +folks where you can have a transition +from level 3 to level 2 level 4 to level + + align:start position:0% +from level 3 to level 2 level 4 to level + + + align:start position:0% +from level 3 to level 2 level 4 to level +2 and you can actually this is a kind of + + align:start position:0% +2 and you can actually this is a kind of + + + align:start position:0% +2 and you can actually this is a kind of +neat thing to verify I don't have it as + + align:start position:0% +neat thing to verify I don't have it as + + + align:start position:0% +neat thing to verify I don't have it as +a problem set question because it's not + + align:start position:0% +a problem set question because it's not + + + align:start position:0% +a problem set question because it's not +very nuclear but you can try this on + + align:start position:0% +very nuclear but you can try this on + + + align:start position:0% +very nuclear but you can try this on +your own and verify that you can + + align:start position:0% +your own and verify that you can + + + align:start position:0% +your own and verify that you can +actually calculate the expected + + align:start position:0% +actually calculate the expected + + + align:start position:0% +actually calculate the expected +wavelength of these photons coming off + + align:start position:0% +wavelength of these photons coming off + + + align:start position:0% +wavelength of these photons coming off +of excited hydrogen also notice here it + + align:start position:0% +of excited hydrogen also notice here it + + + align:start position:0% +of excited hydrogen also notice here it +goes all the way out to 9 and out to + + align:start position:0% +goes all the way out to 9 and out to + + + align:start position:0% +goes all the way out to 9 and out to +infinity because this is electronic + + align:start position:0% +infinity because this is electronic + + + align:start position:0% +infinity because this is electronic +excitation you won't usually get the + + align:start position:0% +excitation you won't usually get the + + + align:start position:0% +excitation you won't usually get the +ejection of anything beyond an M or an N + + align:start position:0% +ejection of anything beyond an M or an N + + + align:start position:0% +ejection of anything beyond an M or an N +electron even in the largest elements + + align:start position:0% +electron even in the largest elements + + + align:start position:0% +electron even in the largest elements +from let's say from I see what is it + + align:start position:0% +from let's say from I see what is it + + + align:start position:0% +from let's say from I see what is it +from internal conversion but you can + + align:start position:0% +from internal conversion but you can + + + align:start position:0% +from internal conversion but you can +electronically excite them to whatever + + align:start position:0% +electronically excite them to whatever + + + align:start position:0% +electronically excite them to whatever +energy level to the point of even + + align:start position:0% +energy level to the point of even + + + align:start position:0% +energy level to the point of even +ionizing them that's what the Infinity + + align:start position:0% +ionizing them that's what the Infinity + + + align:start position:0% +ionizing them that's what the Infinity +comes in cool so it's like two of five + + align:start position:0% +comes in cool so it's like two of five + + + align:start position:0% +comes in cool so it's like two of five +of so I want to open this up to any + + align:start position:0% +of so I want to open this up to any + + + align:start position:0% +of so I want to open this up to any +questions about decay before we move + + align:start position:0% +questions about decay before we move + + + align:start position:0% +questions about decay before we move +upstairs to talk about activity + + align:start position:0% +upstairs to talk about activity + + + align:start position:0% +upstairs to talk about activity +half-life and series radioactive decay + + align:start position:0% +half-life and series radioactive decay + + + align:start position:0% +half-life and series radioactive decay +which is what nuclear activation + + align:start position:0% +which is what nuclear activation + + + align:start position:0% +which is what nuclear activation +analysis is all about so anything here + + align:start position:0% + + + + align:start position:0% + +yep correct in our pre in in our other + + align:start position:0% +yep correct in our pre in in our other + + + align:start position:0% +yep correct in our pre in in our other +notation this would be known as an LM + + align:start position:0% +notation this would be known as an LM + + + align:start position:0% +notation this would be known as an LM +electron and probably l1 m1 because + + align:start position:0% +electron and probably l1 m1 because + + + align:start position:0% +electron and probably l1 m1 because +there's only one electron in hydrogen + + align:start position:0% +there's only one electron in hydrogen + + + align:start position:0% +there's only one electron in hydrogen +yep so don't let the notations trip you + + align:start position:0% +yep so don't let the notations trip you + + + align:start position:0% +yep so don't let the notations trip you +up as long as you've I'm sure someone's + + align:start position:0% +up as long as you've I'm sure someone's + + + align:start position:0% +up as long as you've I'm sure someone's +got a chart of L you know l equals two + + align:start position:0% +got a chart of L you know l equals two + + + align:start position:0% +got a chart of L you know l equals two +equals whatever other Greek letter + + align:start position:0% +equals whatever other Greek letter + + + align:start position:0% +equals whatever other Greek letter +someone has designated it for there's + + align:start position:0% +someone has designated it for there's + + + align:start position:0% +someone has designated it for there's +just different ways of saying the same + + align:start position:0% +just different ways of saying the same + + + align:start position:0% +just different ways of saying the same +thing so as long as you know the physics + + align:start position:0% +thing so as long as you know the physics + + + align:start position:0% +thing so as long as you know the physics +looking up the notation is just kind of + + align:start position:0% +looking up the notation is just kind of + + + align:start position:0% +looking up the notation is just kind of +a little pain any other questions on + + align:start position:0% +a little pain any other questions on + + + align:start position:0% +a little pain any other questions on +radioactive decay or competing + + align:start position:0% +radioactive decay or competing + + + align:start position:0% +radioactive decay or competing +mechanisms cool let's take a 10-minute + + align:start position:0% +mechanisms cool let's take a 10-minute + + + align:start position:0% +mechanisms cool let's take a 10-minute +break so I'll see you guys upstairs in + + align:start position:0% +break so I'll see you guys upstairs in + + + align:start position:0% +break so I'll see you guys upstairs in +room 307 in ten minutes + + align:start position:0% +room 307 in ten minutes + + + align:start position:0% +room 307 in ten minutes +there's no projector there so we'll do + + align:start position:0% +there's no projector there so we'll do + + + align:start position:0% +there's no projector there so we'll do +it all on the board all right so I want + + align:start position:0% +it all on the board all right so I want + + + align:start position:0% +it all on the board all right so I want +to start off the second half of today's + + align:start position:0% +to start off the second half of today's + + + align:start position:0% +to start off the second half of today's +class by posing and answering a question + + align:start position:0% +class by posing and answering a question + + + align:start position:0% +class by posing and answering a question +who's still mentally having trouble + + align:start position:0% +who's still mentally having trouble + + + align:start position:0% +who's still mentally having trouble +grasping this idea what did I tell you + + align:start position:0% +grasping this idea what did I tell you + + + align:start position:0% +grasping this idea what did I tell you +yeah so whoever I said it to I said at + + align:start position:0% +yeah so whoever I said it to I said at + + + align:start position:0% +yeah so whoever I said it to I said at +least half the class is right there with + + align:start position:0% +least half the class is right there with + + + align:start position:0% +least half the class is right there with +you it's true so in a sentence it's this + + align:start position:0% +you it's true so in a sentence it's this + + + align:start position:0% +you it's true so in a sentence it's this +Q is the conversion of mass to energy + + align:start position:0% +Q is the conversion of mass to energy + + + align:start position:0% +Q is the conversion of mass to energy +that's all and the whole point of doing + + align:start position:0% +that's all and the whole point of doing + + + align:start position:0% +that's all and the whole point of doing +this nuclear reaction energetics to find + + align:start position:0% +this nuclear reaction energetics to find + + + align:start position:0% +this nuclear reaction energetics to find +out if things are aren't allowed if + + align:start position:0% +out if things are aren't allowed if + + + align:start position:0% +out if things are aren't allowed if +they're x over endothermic is to see how + + align:start position:0% +they're x over endothermic is to see how + + + align:start position:0% +they're x over endothermic is to see how +much mass is converted to energy or how + + align:start position:0% +much mass is converted to energy or how + + + align:start position:0% +much mass is converted to energy or how +much energy has to be converted to mass + + align:start position:0% +much energy has to be converted to mass + + + align:start position:0% +much energy has to be converted to mass +and if you have trouble remembering just + + align:start position:0% +and if you have trouble remembering just + + + align:start position:0% +and if you have trouble remembering just +go back to the equation that I see on + + align:start position:0% +go back to the equation that I see on + + + align:start position:0% +go back to the equation that I see on +everybody's t-shirts and like I said on + + align:start position:0% +everybody's t-shirts and like I said on + + + align:start position:0% +everybody's t-shirts and like I said on +the first day of class everyone's got it + + align:start position:0% +the first day of class everyone's got it + + + align:start position:0% +the first day of class everyone's got it +on their shirts and no one quite + + align:start position:0% +on their shirts and no one quite + + + align:start position:0% +on their shirts and no one quite +understands it not even the nuclear + + align:start position:0% +understands it not even the nuclear + + + align:start position:0% +understands it not even the nuclear +engineers because it's very difficult + + align:start position:0% +engineers because it's very difficult + + + align:start position:0% +engineers because it's very difficult +mentally to grasp the idea that energy + + align:start position:0% +mentally to grasp the idea that energy + + + align:start position:0% +mentally to grasp the idea that energy +and matter are two sides of the same + + align:start position:0% +and matter are two sides of the same + + + align:start position:0% +and matter are two sides of the same +coin or two different forms of the same + + align:start position:0% +coin or two different forms of the same + + + align:start position:0% +coin or two different forms of the same +thing so for a nuclear reaction where Q + + align:start position:0% +thing so for a nuclear reaction where Q + + + align:start position:0% +thing so for a nuclear reaction where Q +is greater than zero or exothermic all + + align:start position:0% +is greater than zero or exothermic all + + + align:start position:0% +is greater than zero or exothermic all +that means is that energy is + + align:start position:0% +that means is that energy is + + + align:start position:0% +that means is that energy is +spontaneously created from the + + align:start position:0% +spontaneously created from the + + + align:start position:0% +spontaneously created from the +destruction of mass that's all + + align:start position:0% +destruction of mass that's all + + + align:start position:0% +destruction of mass that's all +and for aq less than zero reaction or + + align:start position:0% +and for aq less than zero reaction or + + + align:start position:0% +and for aq less than zero reaction or +endothermic when you inject energy into + + align:start position:0% +endothermic when you inject energy into + + + align:start position:0% +endothermic when you inject energy into +the system it is absorbed and mass is + + align:start position:0% +the system it is absorbed and mass is + + + align:start position:0% +the system it is absorbed and mass is +created straight from this equation so + + align:start position:0% +created straight from this equation so + + + align:start position:0% +created straight from this equation so +does this make more sense to the folks + + align:start position:0% +does this make more sense to the folks + + + align:start position:0% +does this make more sense to the folks +that raised their hands which was almost + + align:start position:0% +that raised their hands which was almost + + + align:start position:0% +that raised their hands which was almost +everybody Q is nothing but a + + align:start position:0% +everybody Q is nothing but a + + + align:start position:0% +everybody Q is nothing but a +quantification of the amount of matter + + align:start position:0% +quantification of the amount of matter + + + align:start position:0% +quantification of the amount of matter +and energy that turned from one to the + + align:start position:0% +and energy that turned from one to the + + + align:start position:0% +and energy that turned from one to the +other and all the balanced stuff we'd + + align:start position:0% +other and all the balanced stuff we'd + + + align:start position:0% +other and all the balanced stuff we'd +been doing for almost the last month has + + align:start position:0% +been doing for almost the last month has + + + align:start position:0% +been doing for almost the last month has +been to conserve to quantify and to + + align:start position:0% +been to conserve to quantify and to + + + align:start position:0% +been to conserve to quantify and to +predict it so hope that helps I know + + align:start position:0% +predict it so hope that helps I know + + + align:start position:0% +predict it so hope that helps I know +that MIT students have this gift for + + align:start position:0% +that MIT students have this gift for + + + align:start position:0% +that MIT students have this gift for +being able to hide behind the math and I + + align:start position:0% +being able to hide behind the math and I + + + align:start position:0% +being able to hide behind the math and I +know that's true because I used to be + + align:start position:0% +know that's true because I used to be + + + align:start position:0% +know that's true because I used to be +one myself and you could get through the + + align:start position:0% +one myself and you could get through the + + + align:start position:0% +one myself and you could get through the +day or get through the class getting the + + align:start position:0% +day or get through the class getting the + + + align:start position:0% +day or get through the class getting the +math right without really understanding + + align:start position:0% +math right without really understanding + + + align:start position:0% +math right without really understanding +the physics or the mechanism behind + + align:start position:0% +the physics or the mechanism behind + + + align:start position:0% +the physics or the mechanism behind +what's going on so everything we've done + + align:start position:0% +what's going on so everything we've done + + + align:start position:0% +what's going on so everything we've done +for the last three weeks can be summed + + align:start position:0% +for the last three weeks can be summed + + + align:start position:0% +for the last three weeks can be summed +up in one sentence mass and energy of + + align:start position:0% +up in one sentence mass and energy of + + + align:start position:0% +up in one sentence mass and energy of +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +we've just had a lot of math to get + + align:start position:0% +we've just had a lot of math to get + + + align:start position:0% +we've just had a lot of math to get +there and be able to yeah it still kind + + align:start position:0% +there and be able to yeah it still kind + + + align:start position:0% +there and be able to yeah it still kind +of makes your head want to explode right + + align:start position:0% +of makes your head want to explode right + + + align:start position:0% +of makes your head want to explode right +do you think about it if you make a net + + align:start position:0% +do you think about it if you make a net + + + align:start position:0% +do you think about it if you make a net +we want to make an endothermic reaction + + align:start position:0% +we want to make an endothermic reaction + + + align:start position:0% +we want to make an endothermic reaction +happen you have to put kinetic energy + + align:start position:0% +happen you have to put kinetic energy + + + align:start position:0% +happen you have to put kinetic energy +into one of the particles and that + + align:start position:0% +into one of the particles and that + + + align:start position:0% +into one of the particles and that +system in the just barely allowed state + + align:start position:0% +system in the just barely allowed state + + + align:start position:0% +system in the just barely allowed state +the nuclei won't really be moving or at + + align:start position:0% +the nuclei won't really be moving or at + + + align:start position:0% +the nuclei won't really be moving or at +least the set yeah the nuclei won't + + align:start position:0% +least the set yeah the nuclei won't + + + align:start position:0% +least the set yeah the nuclei won't +really be moving afterwards because + + align:start position:0% +really be moving afterwards because + + + align:start position:0% +really be moving afterwards because +you'll have turned energy into matter so + + align:start position:0% +you'll have turned energy into matter so + + + align:start position:0% +you'll have turned energy into matter so +that kinetic Energy's turned into mass + + align:start position:0% +that kinetic Energy's turned into mass + + + align:start position:0% +that kinetic Energy's turned into mass +energy just like you can turn potential + + align:start position:0% +energy just like you can turn potential + + + align:start position:0% +energy just like you can turn potential +into kinetic or thermal into mechanical + + align:start position:0% +into kinetic or thermal into mechanical + + + align:start position:0% +into kinetic or thermal into mechanical +or vice-versa it's other forms of energy + + align:start position:0% +or vice-versa it's other forms of energy + + + align:start position:0% +or vice-versa it's other forms of energy +kind of mind-blowing well anyways so now + + align:start position:0% +kind of mind-blowing well anyways so now + + + align:start position:0% +kind of mind-blowing well anyways so now +that we finished radioactive decay I + + align:start position:0% +that we finished radioactive decay I + + + align:start position:0% +that we finished radioactive decay I +want to get into the concept of activity + + align:start position:0% +want to get into the concept of activity + + + align:start position:0% +want to get into the concept of activity +half-life and then we're gonna start but + + align:start position:0% +half-life and then we're gonna start but + + + align:start position:0% +half-life and then we're gonna start but +not finish cereal radioactive creation + + align:start position:0% +not finish cereal radioactive creation + + + align:start position:0% +not finish cereal radioactive creation +and destruction in your readings you'll + + align:start position:0% +and destruction in your readings you'll + + + align:start position:0% +and destruction in your readings you'll +see an equation that looks something + + align:start position:0% +see an equation that looks something + + + align:start position:0% +see an equation that looks something +like this + + align:start position:0% +like this + + + align:start position:0% +like this +where we're gonna be at the end of the + + align:start position:0% +where we're gonna be at the end of the + + + align:start position:0% +where we're gonna be at the end of the +day today if you want to show off how + + align:start position:0% +day today if you want to show off how + + + align:start position:0% +day today if you want to show off how +much of some isotope and one exists as a + + align:start position:0% +much of some isotope and one exists as a + + + align:start position:0% +much of some isotope and one exists as a +function of time you may have seen + + align:start position:0% +function of time you may have seen + + + align:start position:0% +function of time you may have seen +something that looks like this we're + + align:start position:0% +something that looks like this we're + + + align:start position:0% +something that looks like this we're +going to be able to understand how these + + align:start position:0% +going to be able to understand how these + + + align:start position:0% +going to be able to understand how these +equations are created and because this + + align:start position:0% +equations are created and because this + + + align:start position:0% +equations are created and because this +is MIT we're going to take it further + + align:start position:0% +is MIT we're going to take it further + + + align:start position:0% +is MIT we're going to take it further +and add specifically driven mechanisms + + align:start position:0% +and add specifically driven mechanisms + + + align:start position:0% +and add specifically driven mechanisms +like can you create an isotope not just + + align:start position:0% +like can you create an isotope not just + + + align:start position:0% +like can you create an isotope not just +by decay from one isotope to another but + + align:start position:0% +by decay from one isotope to another but + + + align:start position:0% +by decay from one isotope to another but +by intentionally making it which is + + align:start position:0% +by intentionally making it which is + + + align:start position:0% +by intentionally making it which is +exactly how naa or nuclear activation + + align:start position:0% +exactly how naa or nuclear activation + + + align:start position:0% +exactly how naa or nuclear activation +analysis works you fire neutrons into a + + align:start position:0% +analysis works you fire neutrons into a + + + align:start position:0% +analysis works you fire neutrons into a +material they turn into something else + + align:start position:0% +material they turn into something else + + + align:start position:0% +material they turn into something else +and start decaying in series this is + + align:start position:0% +and start decaying in series this is + + + align:start position:0% +and start decaying in series this is +what we're going to be working out the + + align:start position:0% +what we're going to be working out the + + + align:start position:0% +what we're going to be working out the +math for but I want to make sure it + + align:start position:0% +math for but I want to make sure it + + + align:start position:0% +math for but I want to make sure it +every step that we get the physics right + + align:start position:0% +every step that we get the physics right + + + align:start position:0% +every step that we get the physics right +so first a very quick primer on where + + align:start position:0% +so first a very quick primer on where + + + align:start position:0% +so first a very quick primer on where +what what is activity and where does + + align:start position:0% +what what is activity and where does + + + align:start position:0% +what what is activity and where does +half-life come from so we define the a + + align:start position:0% +half-life come from so we define the a + + + align:start position:0% +half-life come from so we define the a +the activity of a substance as pretty + + align:start position:0% +the activity of a substance as pretty + + + align:start position:0% +the activity of a substance as pretty +simple it depends on the amount of the + + align:start position:0% +simple it depends on the amount of the + + + align:start position:0% +simple it depends on the amount of the +substance that's there and it depends on + + align:start position:0% +substance that's there and it depends on + + + align:start position:0% +substance that's there and it depends on +what's called this decay constant so + + align:start position:0% +what's called this decay constant so + + + align:start position:0% +what's called this decay constant so +this amount let's just say like atoms + + align:start position:0% +this amount let's just say like atoms + + + align:start position:0% +this amount let's just say like atoms +and this decay constant is in units of 1 + + align:start position:0% +and this decay constant is in units of 1 + + + align:start position:0% +and this decay constant is in units of 1 +over second an activity is in let's say + + align:start position:0% +over second an activity is in let's say + + + align:start position:0% +over second an activity is in let's say +atoms destroyed or decays for a second + + align:start position:0% +atoms destroyed or decays for a second + + + align:start position:0% +atoms destroyed or decays for a second +that thing right there is called the + + align:start position:0% +that thing right there is called the + + + align:start position:0% +that thing right there is called the +decay constant lambda and if we want to + + align:start position:0% +decay constant lambda and if we want to + + + align:start position:0% +decay constant lambda and if we want to +see let's say how much of a substance is + + align:start position:0% +see let's say how much of a substance is + + + align:start position:0% +see let's say how much of a substance is +decaying at a certain time or what's its + + align:start position:0% +decaying at a certain time or what's its + + + align:start position:0% +decaying at a certain time or what's its +activity and get a measure of how + + align:start position:0% +activity and get a measure of how + + + align:start position:0% +activity and get a measure of how +quickly does it take to decay away we + + align:start position:0% +quickly does it take to decay away we + + + align:start position:0% +quickly does it take to decay away we +can start by saying well this in effect + + align:start position:0% +can start by saying well this in effect + + + align:start position:0% +can start by saying well this in effect +is a destruction rate of isotope n so we + + align:start position:0% +is a destruction rate of isotope n so we + + + align:start position:0% +is a destruction rate of isotope n so we +can make the simplest of differential + + align:start position:0% +can make the simplest of differential + + + align:start position:0% +can make the simplest of differential +equations and say the amount of + + align:start position:0% +equations and say the amount of + + + align:start position:0% +equations and say the amount of +substance n is a function of time is + + align:start position:0% +substance n is a function of time is + + + align:start position:0% +substance n is a function of time is +just - its activity which equals minus + + align:start position:0% +just - its activity which equals minus + + + align:start position:0% +just - its activity which equals minus +lambda n + + align:start position:0% +lambda n + + + align:start position:0% +lambda n +I hope I don't have to explain how to + + align:start position:0% +I hope I don't have to explain how to + + + align:start position:0% +I hope I don't have to explain how to +excel this differential equation so I'm + + align:start position:0% +excel this differential equation so I'm + + + align:start position:0% +excel this differential equation so I'm +going to go through it pretty quickly + + align:start position:0% +going to go through it pretty quickly + + + align:start position:0% +going to go through it pretty quickly +what's the method you use for this to + + align:start position:0% +what's the method you use for this to + + + align:start position:0% +what's the method you use for this to +get n as a function of T yes you're all + + align:start position:0% +get n as a function of T yes you're all + + + align:start position:0% +get n as a function of T yes you're all +in 1803 or have finished 1803 right this + + align:start position:0% +in 1803 or have finished 1803 right this + + + align:start position:0% +in 1803 or have finished 1803 right this +should have been day one so we'll just + + align:start position:0% +should have been day one so we'll just + + + align:start position:0% +should have been day one so we'll just +separate variables divide each side by n + + align:start position:0% +separate variables divide each side by n + + + align:start position:0% +separate variables divide each side by n +multiplied it side by DT so we get DN + + align:start position:0% +multiplied it side by DT so we get DN + + + align:start position:0% +multiplied it side by DT so we get DN +over N equals negative lambda DT you can + + align:start position:0% +over N equals negative lambda DT you can + + + align:start position:0% +over N equals negative lambda DT you can +integrate both sides and we get the + + align:start position:0% +integrate both sides and we get the + + + align:start position:0% +integrate both sides and we get the +natural log of n equals minus lambda T + + align:start position:0% +natural log of n equals minus lambda T + + + align:start position:0% +natural log of n equals minus lambda T +plus some integration constant we're + + align:start position:0% +plus some integration constant we're + + + align:start position:0% +plus some integration constant we're +gonna do a little bit of trickery and to + + align:start position:0% +gonna do a little bit of trickery and to + + + align:start position:0% +gonna do a little bit of trickery and to +make things in a nice form that we can + + align:start position:0% +make things in a nice form that we can + + + align:start position:0% +make things in a nice form that we can +deal with let's just call this log of + + align:start position:0% +deal with let's just call this log of + + + align:start position:0% +deal with let's just call this log of +and not they're just numbers right we + + align:start position:0% +and not they're just numbers right we + + + align:start position:0% +and not they're just numbers right we +haven't defined what this constant of + + align:start position:0% +haven't defined what this constant of + + + align:start position:0% +haven't defined what this constant of +integration is every one clue cool with + + align:start position:0% +integration is every one clue cool with + + + align:start position:0% +integration is every one clue cool with +us doing that so then we can subtract + + align:start position:0% +us doing that so then we can subtract + + + align:start position:0% +us doing that so then we can subtract +log of n naught from each side and we + + align:start position:0% +log of n naught from each side and we + + + align:start position:0% +log of n naught from each side and we +get log n minus log of n naught equals + + align:start position:0% +get log n minus log of n naught equals + + + align:start position:0% +get log n minus log of n naught equals +minus lambda T so this is like saying + + align:start position:0% +minus lambda T so this is like saying + + + align:start position:0% +minus lambda T so this is like saying +log of n over N naught equals minus + + align:start position:0% +log of n over N naught equals minus + + + align:start position:0% +log of n over N naught equals minus +lambda T well take e to the power of + + align:start position:0% +lambda T well take e to the power of + + + align:start position:0% +lambda T well take e to the power of +both sides and we get n over N naught + + align:start position:0% +both sides and we get n over N naught + + + align:start position:0% +both sides and we get n over N naught +equals e to the minus lambda T and right + + align:start position:0% +equals e to the minus lambda T and right + + + align:start position:0% +equals e to the minus lambda T and right +there you've got your exponential decay + + align:start position:0% +there you've got your exponential decay + + + align:start position:0% +there you've got your exponential decay +equation this is the easy part and what + + align:start position:0% +equation this is the easy part and what + + + align:start position:0% +equation this is the easy part and what +this tells you is it is a larger decay + + align:start position:0% +this tells you is it is a larger decay + + + align:start position:0% +this tells you is it is a larger decay +constant well let me ask you a question + + align:start position:0% +constant well let me ask you a question + + + align:start position:0% +constant well let me ask you a question +then what a larger decay constant mean a + + align:start position:0% +then what a larger decay constant mean a + + + align:start position:0% +then what a larger decay constant mean a +faster or a slower decaying isotope a + + align:start position:0% + + + + align:start position:0% + +larger decay constant correct means that + + align:start position:0% +larger decay constant correct means that + + + align:start position:0% +larger decay constant correct means that +you've got more of these decays + + align:start position:0% +you've got more of these decays + + + align:start position:0% +you've got more of these decays +happening per second so a larger lambda + + align:start position:0% +happening per second so a larger lambda + + + align:start position:0% +happening per second so a larger lambda +means faster decay + + align:start position:0% + + + + align:start position:0% + +and we also can define a quantity called + + align:start position:0% +and we also can define a quantity called + + + align:start position:0% +and we also can define a quantity called +the half-life which means n at T 1/2 + + align:start position:0% +the half-life which means n at T 1/2 + + + align:start position:0% +the half-life which means n at T 1/2 +equals 1/2 and not so forth at all you + + align:start position:0% +equals 1/2 and not so forth at all you + + + align:start position:0% +equals 1/2 and not so forth at all you +have to do is plug in T 1/2 for T and + + align:start position:0% +have to do is plug in T 1/2 for T and + + + align:start position:0% +have to do is plug in T 1/2 for T and +1/2 and not for n naught and you + + align:start position:0% +1/2 and not for n naught and you + + + align:start position:0% +1/2 and not for n naught and you +actually get this relation where the + + align:start position:0% +actually get this relation where the + + + align:start position:0% +actually get this relation where the +half-life is just log of 2 over lambda + + align:start position:0% +half-life is just log of 2 over lambda + + + align:start position:0% +half-life is just log of 2 over lambda +better known as 0.693 but we'll just + + align:start position:0% +better known as 0.693 but we'll just + + + align:start position:0% +better known as 0.693 but we'll just +leave it as log of 2 for exactness and + + align:start position:0% +leave it as log of 2 for exactness and + + + align:start position:0% +leave it as log of 2 for exactness and +that's all there really is for decay in + + align:start position:0% +that's all there really is for decay in + + + align:start position:0% +that's all there really is for decay in +half-life so I'll told another question + + align:start position:0% +half-life so I'll told another question + + + align:start position:0% +half-life so I'll told another question +to you something with a larger decay + + align:start position:0% +to you something with a larger decay + + + align:start position:0% +to you something with a larger decay +constant will it have a larger or a + + align:start position:0% +constant will it have a larger or a + + + align:start position:0% +constant will it have a larger or a +smaller half-life smaller because + + align:start position:0% +smaller half-life smaller because + + + align:start position:0% +smaller half-life smaller because +they're inversely related + + align:start position:0% + + + + align:start position:0% + +so I'd say from this quick derivation + + align:start position:0% +so I'd say from this quick derivation + + + align:start position:0% +so I'd say from this quick derivation +these are the two things to note is that + + align:start position:0% +these are the two things to note is that + + + align:start position:0% +these are the two things to note is that +something with a larger decay constant + + align:start position:0% +something with a larger decay constant + + + align:start position:0% +something with a larger decay constant +decays faster and therefore has a + + align:start position:0% +decays faster and therefore has a + + + align:start position:0% +decays faster and therefore has a +shorter half-life so when we were + + align:start position:0% +shorter half-life so when we were + + + align:start position:0% +shorter half-life so when we were +separating out our isotopes in nuclear + + align:start position:0% +separating out our isotopes in nuclear + + + align:start position:0% +separating out our isotopes in nuclear +activation analysis into what might call + + align:start position:0% +activation analysis into what might call + + + align:start position:0% +activation analysis into what might call +the shorts and the lungs + + align:start position:0% +the shorts and the lungs + + + align:start position:0% +the shorts and the lungs +he was separating them by half-life to + + align:start position:0% +he was separating them by half-life to + + + align:start position:0% +he was separating them by half-life to +say that left fer let's say the same + + align:start position:0% +say that left fer let's say the same + + + align:start position:0% +say that left fer let's say the same +amount of activation or the same amount + + align:start position:0% +amount of activation or the same amount + + + align:start position:0% +amount of activation or the same amount +of creation the ones with shorter + + align:start position:0% +of creation the ones with shorter + + + align:start position:0% +of creation the ones with shorter +half-lives will be hotter more + + align:start position:0% +half-lives will be hotter more + + + align:start position:0% +half-lives will be hotter more +radioactive but for less time and so + + align:start position:0% +radioactive but for less time and so + + + align:start position:0% +radioactive but for less time and so +what we're gonna be doing is what's + + align:start position:0% +what we're gonna be doing is what's + + + align:start position:0% +what we're gonna be doing is what's +called short nuclear activation analysis + + align:start position:0% +called short nuclear activation analysis + + + align:start position:0% +called short nuclear activation analysis +because we don't want to count for like + + align:start position:0% +because we don't want to count for like + + + align:start position:0% +because we don't want to count for like +days or weeks or months yep the decay + + align:start position:0% +days or weeks or months yep the decay + + + align:start position:0% +days or weeks or months yep the decay +constant is a property of the given + + align:start position:0% +constant is a property of the given + + + align:start position:0% +constant is a property of the given +isotope specific to that type of decay + + align:start position:0% +isotope specific to that type of decay + + + align:start position:0% +isotope specific to that type of decay +so if we were to draw that generalized + + align:start position:0% +so if we were to draw that generalized + + + align:start position:0% +so if we were to draw that generalized +radioactivity diagram let's say we have + + align:start position:0% +radioactivity diagram let's say we have + + + align:start position:0% +radioactivity diagram let's say we have +potassium-40 + + align:start position:0% +potassium-40 + + + align:start position:0% +potassium-40 +which can either go by beta decay to + + align:start position:0% +which can either go by beta decay to + + + align:start position:0% +which can either go by beta decay to +what comes in beta what comes after + + align:start position:0% +what comes in beta what comes after + + + align:start position:0% +what comes in beta what comes after +I think it's calcium for T or it can go + + align:start position:0% +I think it's calcium for T or it can go + + + align:start position:0% +I think it's calcium for T or it can go +by positron or electron capture + + align:start position:0% +by positron or electron capture + + + align:start position:0% +by positron or electron capture +to argon-40 each of these processes has + + align:start position:0% +to argon-40 each of these processes has + + + align:start position:0% +to argon-40 each of these processes has +a different half-life and then in that + + align:start position:0% +a different half-life and then in that + + + align:start position:0% +a different half-life and then in that +chain remember let's let's do the + + align:start position:0% +chain remember let's let's do the + + + align:start position:0% +chain remember let's let's do the +americium-241 and I'm gonna channel my + + align:start position:0% +americium-241 and I'm gonna channel my + + + align:start position:0% +americium-241 and I'm gonna channel my +one-year-old son and drawing this decay + + align:start position:0% +one-year-old son and drawing this decay + + + align:start position:0% +one-year-old son and drawing this decay +diagram looks something like that with + + align:start position:0% +diagram looks something like that with + + + align:start position:0% +diagram looks something like that with +all sorts of transitions I didn't scream + + align:start position:0% +all sorts of transitions I didn't scream + + + align:start position:0% +all sorts of transitions I didn't scream +like he usually does but you know + + align:start position:0% +like he usually does but you know + + + align:start position:0% +like he usually does but you know +whatever we're on camera + + align:start position:0% +whatever we're on camera + + + align:start position:0% +whatever we're on camera +each of these decay each of these + + align:start position:0% +each of these decay each of these + + + align:start position:0% +each of these decay each of these +transitions may also have its own + + align:start position:0% +transitions may also have its own + + + align:start position:0% +transitions may also have its own +half-life so between isomeric + + align:start position:0% +half-life so between isomeric + + + align:start position:0% +half-life so between isomeric +transitions they're usually very very + + align:start position:0% +transitions they're usually very very + + + align:start position:0% +transitions they're usually very very +fast but once in a while they're not + + align:start position:0% + + + + align:start position:0% + +like technetium-99 metastable to + + align:start position:0% +like technetium-99 metastable to + + + align:start position:0% +like technetium-99 metastable to +technetium-99 has a half-life of around + + align:start position:0% +technetium-99 has a half-life of around + + + align:start position:0% +technetium-99 has a half-life of around +six days which is why it's so useful as + + align:start position:0% +six days which is why it's so useful as + + + align:start position:0% +six days which is why it's so useful as +a medical isotope so when you see + + align:start position:0% +a medical isotope so when you see + + + align:start position:0% +a medical isotope so when you see +something marked m4 metastable all that + + align:start position:0% +something marked m4 metastable all that + + + align:start position:0% +something marked m4 metastable all that +means is there some sort of a gamma also + + align:start position:0% +means is there some sort of a gamma also + + + align:start position:0% +means is there some sort of a gamma also +known as an IT transition with a + + align:start position:0% +known as an IT transition with a + + + align:start position:0% +known as an IT transition with a +particularly long half-life everyone + + align:start position:0% +particularly long half-life everyone + + + align:start position:0% +particularly long half-life everyone +clear and what all that means + + align:start position:0% + + + + align:start position:0% + +cool well there'll be some time for it + + align:start position:0% +cool well there'll be some time for it + + + align:start position:0% +cool well there'll be some time for it +to sink in because with these + + align:start position:0% +to sink in because with these + + + align:start position:0% +to sink in because with these +definitions in hand I want to pose a + + align:start position:0% +definitions in hand I want to pose a + + + align:start position:0% +definitions in hand I want to pose a +problem to you guys let's say I start + + align:start position:0% +problem to you guys let's say I start + + + align:start position:0% +problem to you guys let's say I start +off with some amount of an isotope N 1 + + align:start position:0% +off with some amount of an isotope N 1 + + + align:start position:0% +off with some amount of an isotope N 1 +and it decays by some mechanism we don't + + align:start position:0% +and it decays by some mechanism we don't + + + align:start position:0% +and it decays by some mechanism we don't +care what two isotope n 2 and it decays + + align:start position:0% +care what two isotope n 2 and it decays + + + align:start position:0% +care what two isotope n 2 and it decays +to some isotope n 3 with decay constants + + align:start position:0% +to some isotope n 3 with decay constants + + + align:start position:0% +to some isotope n 3 with decay constants +lambda 1 and lambda 2 this is what we + + align:start position:0% +lambda 1 and lambda 2 this is what we + + + align:start position:0% +lambda 1 and lambda 2 this is what we +call serial radioactive decay + + align:start position:0% + + + + align:start position:0% + +how do we construct a system of + + align:start position:0% +how do we construct a system of + + + align:start position:0% +how do we construct a system of +equations to tell us what is n1 as a + + align:start position:0% +equations to tell us what is n1 as a + + + align:start position:0% +equations to tell us what is n1 as a +function of time what is n2 is a + + align:start position:0% +function of time what is n2 is a + + + align:start position:0% +function of time what is n2 is a +function of time and what is n3 as a + + align:start position:0% +function of time and what is n3 as a + + + align:start position:0% +function of time and what is n3 as a +function of time where do we begin in a + + align:start position:0% +function of time where do we begin in a + + + align:start position:0% +function of time where do we begin in a +general sense okay so let's start with + + align:start position:0% +general sense okay so let's start with + + + align:start position:0% +general sense okay so let's start with +n1 we kind of have an expression for n1 + + align:start position:0% +n1 we kind of have an expression for n1 + + + align:start position:0% +n1 we kind of have an expression for n1 +already but let's start out with a + + align:start position:0% +already but let's start out with a + + + align:start position:0% +already but let's start out with a +differential equation so the form of all + + align:start position:0% +differential equation so the form of all + + + align:start position:0% +differential equation so the form of all +of these equations for everything cereal + + align:start position:0% +of these equations for everything cereal + + + align:start position:0% +of these equations for everything cereal +radioactive decay and burning isotopes + + align:start position:0% +radioactive decay and burning isotopes + + + align:start position:0% +radioactive decay and burning isotopes +in a reactor and creating isotopes in a + + align:start position:0% +in a reactor and creating isotopes in a + + + align:start position:0% +in a reactor and creating isotopes in a +reactor is going to take the following + + align:start position:0% +reactor is going to take the following + + + align:start position:0% +reactor is going to take the following +form + + align:start position:0% +form + + + align:start position:0% +form +the general equation is simple the + + align:start position:0% +the general equation is simple the + + + align:start position:0% +the general equation is simple the +change equals creation - destruction or + + align:start position:0% +change equals creation - destruction or + + + align:start position:0% +change equals creation - destruction or +the simple thing is let's say the the + + align:start position:0% +the simple thing is let's say the the + + + align:start position:0% +the simple thing is let's say the the +change is a source - a sink and we'll + + align:start position:0% +change is a source - a sink and we'll + + + align:start position:0% +change is a source - a sink and we'll +have to come up for every one of these + + align:start position:0% +have to come up for every one of these + + + align:start position:0% +have to come up for every one of these +isotopes for a mathematical way to + + align:start position:0% +isotopes for a mathematical way to + + + align:start position:0% +isotopes for a mathematical way to +describe what's the source and what's + + align:start position:0% +describe what's the source and what's + + + align:start position:0% +describe what's the source and what's +the sink so if we want to measure the + + align:start position:0% +the sink so if we want to measure the + + + align:start position:0% +the sink so if we want to measure the +change in n 1 as a function of time what + + align:start position:0% +change in n 1 as a function of time what + + + align:start position:0% +change in n 1 as a function of time what +are the sources of isotope N 1 yeah no + + align:start position:0% +are the sources of isotope N 1 yeah no + + + align:start position:0% +are the sources of isotope N 1 yeah no +sources we're starting off with some + + align:start position:0% +sources we're starting off with some + + + align:start position:0% +sources we're starting off with some +fixed quantity of N 1 let's just call it + + align:start position:0% +fixed quantity of N 1 let's just call it + + + align:start position:0% +fixed quantity of N 1 let's just call it +N 1 not but you're right there's no + + align:start position:0% +N 1 not but you're right there's no + + + align:start position:0% +N 1 not but you're right there's no +continuous source of isotope N 1 what + + align:start position:0% +continuous source of isotope N 1 what + + + align:start position:0% +continuous source of isotope N 1 what +about its destruction + + align:start position:0% + + + + align:start position:0% + +yeah decay to n2 so we've got the + + align:start position:0% +yeah decay to n2 so we've got the + + + align:start position:0% +yeah decay to n2 so we've got the +equation for that right there it depends + + align:start position:0% +equation for that right there it depends + + + align:start position:0% +equation for that right there it depends +on the decay constant of number one and + + align:start position:0% +on the decay constant of number one and + + + align:start position:0% +on the decay constant of number one and +the amount of number one so what we're + + align:start position:0% +the amount of number one so what we're + + + align:start position:0% +the amount of number one so what we're +doing here I love how this course is + + align:start position:0% +doing here I love how this course is + + + align:start position:0% +doing here I love how this course is +timed with 1803 because you're learning + + align:start position:0% +timed with 1803 because you're learning + + + align:start position:0% +timed with 1803 because you're learning +ordinary differential equations in 1803 + + align:start position:0% +ordinary differential equations in 1803 + + + align:start position:0% +ordinary differential equations in 1803 +and we're gonna be solving order + + align:start position:0% +and we're gonna be solving order + + + align:start position:0% +and we're gonna be solving order +ordinary differential equations for a + + align:start position:0% +ordinary differential equations for a + + + align:start position:0% +ordinary differential equations for a +fair bit of this course so it's one of + + align:start position:0% +fair bit of this course so it's one of + + + align:start position:0% +fair bit of this course so it's one of +those rare times and you get to like + + align:start position:0% +those rare times and you get to like + + + align:start position:0% +those rare times and you get to like +learn math and put it to use at the same + + align:start position:0% +learn math and put it to use at the same + + + align:start position:0% +learn math and put it to use at the same +time instead of six years later just + + align:start position:0% +time instead of six years later just + + + align:start position:0% +time instead of six years later just +kind of nice so that's easy let's go to + + align:start position:0% +kind of nice so that's easy let's go to + + + align:start position:0% +kind of nice so that's easy let's go to +the more challenging one what is the + + align:start position:0% +the more challenging one what is the + + + align:start position:0% +the more challenging one what is the +source of isotope n to decay from n 1 so + + align:start position:0% +source of isotope n to decay from n 1 so + + + align:start position:0% +source of isotope n to decay from n 1 so +how would I mathematically write that + + align:start position:0% + + + + align:start position:0% + +just lambda 1 N 1 and what is the + + align:start position:0% +just lambda 1 N 1 and what is the + + + align:start position:0% +just lambda 1 N 1 and what is the +destruction of isotope and and to anyone + + align:start position:0% +destruction of isotope and and to anyone + + + align:start position:0% +destruction of isotope and and to anyone +else takes the same form it depends on + + align:start position:0% +else takes the same form it depends on + + + align:start position:0% +else takes the same form it depends on +the decay constant of isotope 2 in the + + align:start position:0% +the decay constant of isotope 2 in the + + + align:start position:0% +the decay constant of isotope 2 in the +amount of isotope two that's there + + align:start position:0% + + + + align:start position:0% + +how about isotope 3 where does that come + + align:start position:0% +how about isotope 3 where does that come + + + align:start position:0% +how about isotope 3 where does that come +from + + align:start position:0% + + + + align:start position:0% + +that's it the source is lambda two and + + align:start position:0% +that's it the source is lambda two and + + + align:start position:0% +that's it the source is lambda two and +two what are the sinks or the + + align:start position:0% +two what are the sinks or the + + + align:start position:0% +two what are the sinks or the +destruction nothing so we have a rarely + + align:start position:0% +destruction nothing so we have a rarely + + + align:start position:0% +destruction nothing so we have a rarely +very simple set of posed differential + + align:start position:0% +very simple set of posed differential + + + align:start position:0% +very simple set of posed differential +equations to describe the production and + + align:start position:0% +equations to describe the production and + + + align:start position:0% +equations to describe the production and +the destruction of these three isotopes + + align:start position:0% +the destruction of these three isotopes + + + align:start position:0% +the destruction of these three isotopes +so let's imagine now that n1 was let's + + align:start position:0% +so let's imagine now that n1 was let's + + + align:start position:0% +so let's imagine now that n1 was let's +say radium which exists all throughout + + align:start position:0% +say radium which exists all throughout + + + align:start position:0% +say radium which exists all throughout +the soil and rocks and two is radon the + + align:start position:0% +the soil and rocks and two is radon the + + + align:start position:0% +the soil and rocks and two is radon the +gas that's produced from radium decay + + align:start position:0% +gas that's produced from radium decay + + + align:start position:0% +gas that's produced from radium decay +and then n3 could be let's say this one + + align:start position:0% +and then n3 could be let's say this one + + + align:start position:0% +and then n3 could be let's say this one +of the stable daughter products of radon + + align:start position:0% +of the stable daughter products of radon + + + align:start position:0% +of the stable daughter products of radon +so these are the sorts of calculations + + align:start position:0% +so these are the sorts of calculations + + + align:start position:0% +so these are the sorts of calculations +that are done all the time in real life + + align:start position:0% +that are done all the time in real life + + + align:start position:0% +that are done all the time in real life +to see if you know how much radians in + + align:start position:0% +to see if you know how much radians in + + + align:start position:0% +to see if you know how much radians in +the rock how much radon do you expect to + + align:start position:0% +the rock how much radon do you expect to + + + align:start position:0% +the rock how much radon do you expect to +breathe in because at the same time + + align:start position:0% +breathe in because at the same time + + + align:start position:0% +breathe in because at the same time +you're producing radon from radium decay + + align:start position:0% +you're producing radon from radium decay + + + align:start position:0% +you're producing radon from radium decay +and the radon is decaying itself so you + + align:start position:0% +and the radon is decaying itself so you + + + align:start position:0% +and the radon is decaying itself so you +can't just say oh the activity of the + + align:start position:0% +can't just say oh the activity of the + + + align:start position:0% +can't just say oh the activity of the +radium equals the amount of radon + + align:start position:0% +radium equals the amount of radon + + + align:start position:0% +radium equals the amount of radon +because it's being created and destroyed + + align:start position:0% +because it's being created and destroyed + + + align:start position:0% +because it's being created and destroyed +all at the same time and it depends on + + align:start position:0% +all at the same time and it depends on + + + align:start position:0% +all at the same time and it depends on +how much there is around same thing with + + align:start position:0% +how much there is around same thing with + + + align:start position:0% +how much there is around same thing with +nuclear activation analysis you'll let's + + align:start position:0% +nuclear activation analysis you'll let's + + + align:start position:0% +nuclear activation analysis you'll let's +say you'd start off with sodium 21 you + + align:start position:0% +say you'd start off with sodium 21 you + + + align:start position:0% +say you'd start off with sodium 21 you +can create sodium 22 sodium 22 will + + align:start position:0% +can create sodium 22 sodium 22 will + + + align:start position:0% +can create sodium 22 sodium 22 will +decay by positron emission what comes + + align:start position:0% +decay by positron emission what comes + + + align:start position:0% +decay by positron emission what comes +before sodium probably neon I think 22 + + align:start position:0% +before sodium probably neon I think 22 + + + align:start position:0% +before sodium probably neon I think 22 +that's my guess yeah so if you want to + + align:start position:0% +that's my guess yeah so if you want to + + + align:start position:0% +that's my guess yeah so if you want to +say how much sodium 22 is there well + + align:start position:0% +say how much sodium 22 is there well + + + align:start position:0% +say how much sodium 22 is there well +you're both creating it from sodium 21 + + align:start position:0% +you're both creating it from sodium 21 + + + align:start position:0% +you're both creating it from sodium 21 +from Neutron absorption and you're + + align:start position:0% +from Neutron absorption and you're + + + align:start position:0% +from Neutron absorption and you're +decaying it naturally by positron + + align:start position:0% +decaying it naturally by positron + + + align:start position:0% +decaying it naturally by positron +emission among other processes we're + + align:start position:0% +emission among other processes we're + + + align:start position:0% +emission among other processes we're +gonna get back into how do we deal with + + align:start position:0% +gonna get back into how do we deal with + + + align:start position:0% +gonna get back into how do we deal with +the neutrons thing probably on Tuesday + + align:start position:0% +the neutrons thing probably on Tuesday + + + align:start position:0% +the neutrons thing probably on Tuesday +but for now let's work on solving this + + align:start position:0% +but for now let's work on solving this + + + align:start position:0% +but for now let's work on solving this +system of equations so I think n1 is + + align:start position:0% +system of equations so I think n1 is + + + align:start position:0% +system of equations so I think n1 is +pretty easy because we already have the + + align:start position:0% +pretty easy because we already have the + + + align:start position:0% +pretty easy because we already have the +solution for it so I'll just write it + + align:start position:0% + + + + align:start position:0% + +the harder one is end - so what can we + + align:start position:0% +the harder one is end - so what can we + + + align:start position:0% +the harder one is end - so what can we +start by doing we've got an ordinary + + align:start position:0% +start by doing we've got an ordinary + + + align:start position:0% +start by doing we've got an ordinary +differential equation with it's just + + align:start position:0% +differential equation with it's just + + + align:start position:0% +differential equation with it's just +first order but there's two variables so + + align:start position:0% +first order but there's two variables so + + + align:start position:0% +first order but there's two variables so +how do we deal + + align:start position:0% + + + + align:start position:0% + +we do well we have other equations so + + align:start position:0% +we do well we have other equations so + + + align:start position:0% +we do well we have other equations so +actually got this one yes + + align:start position:0% +actually got this one yes + + + align:start position:0% +actually got this one yes +substitute n1 in here so we get + + align:start position:0% +substitute n1 in here so we get + + + align:start position:0% +substitute n1 in here so we get +everything in terms of n2 and constants + + align:start position:0% +everything in terms of n2 and constants + + + align:start position:0% +everything in terms of n2 and constants +in time so we'll rewrite this equation + + align:start position:0% +in time so we'll rewrite this equation + + + align:start position:0% +in time so we'll rewrite this equation +as d + 2 DT which I'm also just going to + + align:start position:0% +as d + 2 DT which I'm also just going to + + + align:start position:0% +as d + 2 DT which I'm also just going to +write as n 2 Prime I'm going to use this + + align:start position:0% +write as n 2 Prime I'm going to use this + + + align:start position:0% +write as n 2 Prime I'm going to use this +little bit of notation that I'll leave + + align:start position:0% +little bit of notation that I'll leave + + + align:start position:0% +little bit of notation that I'll leave +up there on the board because it's gonna + + align:start position:0% +up there on the board because it's gonna + + + align:start position:0% +up there on the board because it's gonna +be a lot faster in writing which equals + + align:start position:0% +be a lot faster in writing which equals + + + align:start position:0% +be a lot faster in writing which equals +lambda 1 and 10 e to the minus lambda 1 + + align:start position:0% +lambda 1 and 10 e to the minus lambda 1 + + + align:start position:0% +lambda 1 and 10 e to the minus lambda 1 +t minus lambda 2 and 2 can we separate + + align:start position:0% +t minus lambda 2 and 2 can we separate + + + align:start position:0% +t minus lambda 2 and 2 can we separate +variables here I don't see an easy way + + align:start position:0% +variables here I don't see an easy way + + + align:start position:0% +variables here I don't see an easy way +so 1803 experts how do we solve this + + align:start position:0% +so 1803 experts how do we solve this + + + align:start position:0% +so 1803 experts how do we solve this +type of first-order differential + + align:start position:0% +type of first-order differential + + + align:start position:0% +type of first-order differential +equations and I'll give you I'll won't + + align:start position:0% +equations and I'll give you I'll won't + + + align:start position:0% +equations and I'll give you I'll won't +give you a hint I'll give you a little + + align:start position:0% +give you a hint I'll give you a little + + + align:start position:0% +give you a hint I'll give you a little +bit of consolation no one from last year + + align:start position:0% +bit of consolation no one from last year + + + align:start position:0% +bit of consolation no one from last year +knew how to approach this so if you + + align:start position:0% +knew how to approach this so if you + + + align:start position:0% +knew how to approach this so if you +don't know I won't be disappointed + + align:start position:0% +don't know I won't be disappointed + + + align:start position:0% +don't know I won't be disappointed +yep + + align:start position:0% + + + + align:start position:0% + +mm-hmm Aadland the two and two to both + + align:start position:0% +mm-hmm Aadland the two and two to both + + + align:start position:0% +mm-hmm Aadland the two and two to both +sides I think you're on to what I'm + + align:start position:0% +sides I think you're on to what I'm + + + align:start position:0% +sides I think you're on to what I'm +thinking about also if you can't read + + align:start position:0% +thinking about also if you can't read + + + align:start position:0% +thinking about also if you can't read +something I write please stop me and let + + align:start position:0% +something I write please stop me and let + + + align:start position:0% +something I write please stop me and let +me know and I'll be happy to erase it I + + align:start position:0% +me know and I'll be happy to erase it I + + + align:start position:0% +me know and I'll be happy to erase it I +don't think I've said that yet but it + + align:start position:0% +don't think I've said that yet but it + + + align:start position:0% +don't think I've said that yet but it +takes a lot of control for me to get my + + align:start position:0% +takes a lot of control for me to get my + + + align:start position:0% +takes a lot of control for me to get my +handwriting legible on the board let + + align:start position:0% +handwriting legible on the board let + + + align:start position:0% +handwriting legible on the board let +alone on a piece of paper so if you + + align:start position:0% +alone on a piece of paper so if you + + + align:start position:0% +alone on a piece of paper so if you +can't read please let me know okay so + + align:start position:0% +can't read please let me know okay so + + + align:start position:0% +can't read please let me know okay so +now we've got the N twos separate from + + align:start position:0% +now we've got the N twos separate from + + + align:start position:0% +now we've got the N twos separate from +the N ones what do we do next okay let's + + align:start position:0% +the N ones what do we do next okay let's + + + align:start position:0% +the N ones what do we do next okay let's +try this assume n two has the form e to + + align:start position:0% +try this assume n two has the form e to + + + align:start position:0% +try this assume n two has the form e to +the what negative has the form e to the + + align:start position:0% +the what negative has the form e to the + + + align:start position:0% +the what negative has the form e to the +lambda negative 1t with an a some + + align:start position:0% +lambda negative 1t with an a some + + + align:start position:0% +lambda negative 1t with an a some +constant in front what makes you say + + align:start position:0% +constant in front what makes you say + + + align:start position:0% +constant in front what makes you say +that + + align:start position:0% + + + + align:start position:0% + +mmm-hmm cool so that is one way to do it + + align:start position:0% +mmm-hmm cool so that is one way to do it + + + align:start position:0% +mmm-hmm cool so that is one way to do it +it's gonna get a little messy though + + align:start position:0% +it's gonna get a little messy though + + + align:start position:0% +it's gonna get a little messy though +there's another method specifically for + + align:start position:0% +there's another method specifically for + + + align:start position:0% +there's another method specifically for +equations of the form let's call it Y + + align:start position:0% +equations of the form let's call it Y + + + align:start position:0% +equations of the form let's call it Y +prime plus I'm gonna use notation they + + align:start position:0% +prime plus I'm gonna use notation they + + + align:start position:0% +prime plus I'm gonna use notation they +may have used in 1803 I hear a couple of + + align:start position:0% +may have used in 1803 I hear a couple of + + + align:start position:0% +may have used in 1803 I hear a couple of +AHA anything look familiar about this + + align:start position:0% +AHA anything look familiar about this + + + align:start position:0% +AHA anything look familiar about this +type of equation okay what is it it's + + align:start position:0% +type of equation okay what is it it's + + + align:start position:0% +type of equation okay what is it it's +not that hard anyone remember the word + + align:start position:0% +not that hard anyone remember the word + + + align:start position:0% +not that hard anyone remember the word +integrating factor and it was probably + + align:start position:0% +integrating factor and it was probably + + + align:start position:0% +integrating factor and it was probably +done horribly and unlike six math boards + + align:start position:0% +done horribly and unlike six math boards + + + align:start position:0% +done horribly and unlike six math boards +or whatever so I'm gonna show you the + + align:start position:0% +or whatever so I'm gonna show you the + + + align:start position:0% +or whatever so I'm gonna show you the +simpler way to do this the idea here is + + align:start position:0% +simpler way to do this the idea here is + + + align:start position:0% +simpler way to do this the idea here is +we want to multiply everything by some + + align:start position:0% +we want to multiply everything by some + + + align:start position:0% +we want to multiply everything by some +by something so I some function mu what + + align:start position:0% +by something so I some function mu what + + + align:start position:0% +by something so I some function mu what +am you there put am you there put am you + + align:start position:0% +am you there put am you there put am you + + + align:start position:0% +am you there put am you there put am you +there I think that's the notation that's + + align:start position:0% +there I think that's the notation that's + + + align:start position:0% +there I think that's the notation that's +usually used in differential equations + + align:start position:0% +usually used in differential equations + + + align:start position:0% +usually used in differential equations +such that this thing right here is + + align:start position:0% +such that this thing right here is + + + align:start position:0% +such that this thing right here is +shrinkable through the product rule or + + align:start position:0% +shrinkable through the product rule or + + + align:start position:0% +shrinkable through the product rule or +the product rule just I'm not assuming + + align:start position:0% +the product rule just I'm not assuming + + + align:start position:0% +the product rule just I'm not assuming +everyone remembers says that let's say + + align:start position:0% +everyone remembers says that let's say + + + align:start position:0% +everyone remembers says that let's say +you have some function a of T B of T + + align:start position:0% +you have some function a of T B of T + + + align:start position:0% +you have some function a of T B of T +prime is like a prime times B plus a + + align:start position:0% +prime is like a prime times B plus a + + + align:start position:0% +prime is like a prime times B plus a +times B prime so we're kind of getting + + align:start position:0% +times B prime so we're kind of getting + + + align:start position:0% +times B prime so we're kind of getting +around to the method that Luke was + + align:start position:0% +around to the method that Luke was + + + align:start position:0% +around to the method that Luke was +talking about but we're gonna do it via + + align:start position:0% +talking about but we're gonna do it via + + + align:start position:0% +talking about but we're gonna do it via +a little bit of a cleaner way we + + align:start position:0% +a little bit of a cleaner way we + + + align:start position:0% +a little bit of a cleaner way we +multiply every term by some function mu + + align:start position:0% +multiply every term by some function mu + + + align:start position:0% +multiply every term by some function mu +such that this part is one of these + + align:start position:0% +such that this part is one of these + + + align:start position:0% +such that this part is one of these +perfect product rules at which point we + + align:start position:0% +perfect product rules at which point we + + + align:start position:0% +perfect product rules at which point we +can shrink and integrate the expression + + align:start position:0% +can shrink and integrate the expression + + + align:start position:0% +can shrink and integrate the expression +without going through the derivation of + + align:start position:0% +without going through the derivation of + + + align:start position:0% +without going through the derivation of +how integrating factors are done I'll + + align:start position:0% +how integrating factors are done I'll + + + align:start position:0% +how integrating factors are done I'll +just let you know that this function mu + + align:start position:0% +just let you know that this function mu + + + align:start position:0% +just let you know that this function mu +ends up being e to the integral of P + + align:start position:0% + + + + align:start position:0% + +that is our integrating factor so that's + + align:start position:0% +that is our integrating factor so that's + + + align:start position:0% +that is our integrating factor so that's +the end result of what was probably six + + align:start position:0% +the end result of what was probably six + + + align:start position:0% +the end result of what was probably six +boards of 1803 am I am I right or am I + + align:start position:0% +boards of 1803 am I am I right or am I + + + align:start position:0% +boards of 1803 am I am I right or am I +mistaken Wow things haven't changed in + + align:start position:0% +mistaken Wow things haven't changed in + + + align:start position:0% +mistaken Wow things haven't changed in +15 years cool okay so what is mu for + + align:start position:0% +15 years cool okay so what is mu for + + + align:start position:0% +15 years cool okay so what is mu for +this equation + + align:start position:0% +this equation + + + align:start position:0% +this equation +luckily P of T is pretty simple + + align:start position:0% +luckily P of T is pretty simple + + + align:start position:0% +luckily P of T is pretty simple +which part of this equation right here + + align:start position:0% +which part of this equation right here + + + align:start position:0% +which part of this equation right here +is our P of T like term actually just + + align:start position:0% +is our P of T like term actually just + + + align:start position:0% +is our P of T like term actually just +lambda two because we've got our + + align:start position:0% +lambda two because we've got our + + + align:start position:0% +lambda two because we've got our +variable right here that right there is + + align:start position:0% +variable right here that right there is + + + align:start position:0% +variable right here that right there is +our P of T so we'll just say that mu + + align:start position:0% +our P of T so we'll just say that mu + + + align:start position:0% +our P of T so we'll just say that mu +equals e to the integral of ya of lambda + + align:start position:0% +equals e to the integral of ya of lambda + + + align:start position:0% +equals e to the integral of ya of lambda +2 DT which is just e to the lambda 2 T + + align:start position:0% +2 DT which is just e to the lambda 2 T + + + align:start position:0% +2 DT which is just e to the lambda 2 T +that's our integrating factor right + + align:start position:0% +that's our integrating factor right + + + align:start position:0% +that's our integrating factor right +there so we'll multiply every term right + + align:start position:0% +there so we'll multiply every term right + + + align:start position:0% +there so we'll multiply every term right +here by that + + align:start position:0% +here by that + + + align:start position:0% +here by that +so we'll say e to the lambda 2 T times M + + align:start position:0% +so we'll say e to the lambda 2 T times M + + + align:start position:0% +so we'll say e to the lambda 2 T times M +2 prime plus lambda 2 e to the lambda 2 + + align:start position:0% +2 prime plus lambda 2 e to the lambda 2 + + + align:start position:0% +2 prime plus lambda 2 e to the lambda 2 +T anyone see what's going on here + + align:start position:0% +T anyone see what's going on here + + + align:start position:0% +T anyone see what's going on here +there's the product rule thing going on + + align:start position:0% +there's the product rule thing going on + + + align:start position:0% +there's the product rule thing going on +times n 2 plus e to the lambda 2 T times + + align:start position:0% +times n 2 plus e to the lambda 2 T times + + + align:start position:0% +times n 2 plus e to the lambda 2 T times +lambda 1 and 10 e to the minus lambda 1 + + align:start position:0% +lambda 1 and 10 e to the minus lambda 1 + + + align:start position:0% +lambda 1 and 10 e to the minus lambda 1 +T equals 0 and we have successfully + + align:start position:0% +T equals 0 and we have successfully + + + align:start position:0% +T equals 0 and we have successfully +created something here that could be + + align:start position:0% +created something here that could be + + + align:start position:0% +created something here that could be +shrunk up with a product rule yep + + align:start position:0% + + + + align:start position:0% + +oh yeah there's an equal sign there + + align:start position:0% +oh yeah there's an equal sign there + + + align:start position:0% +oh yeah there's an equal sign there +isn't it that's what tripped me up thank + + align:start position:0% +isn't it that's what tripped me up thank + + + align:start position:0% +isn't it that's what tripped me up thank +you so there is indeed a minus sign + + align:start position:0% +you so there is indeed a minus sign + + + align:start position:0% +you so there is indeed a minus sign +there because I skipped a step putting + + align:start position:0% +there because I skipped a step putting + + + align:start position:0% +there because I skipped a step putting +everything on one side of the equation + + align:start position:0% +everything on one side of the equation + + + align:start position:0% +everything on one side of the equation +yep where you replace one variable with + + align:start position:0% +yep where you replace one variable with + + + align:start position:0% +yep where you replace one variable with +a or replace a couple of variables with + + align:start position:0% +a or replace a couple of variables with + + + align:start position:0% +a or replace a couple of variables with +another one yeah there are there are + + align:start position:0% +another one yeah there are there are + + + align:start position:0% +another one yeah there are there are +lots of ways of solving a first-order OD + + align:start position:0% +lots of ways of solving a first-order OD + + + align:start position:0% +lots of ways of solving a first-order OD +II like this sure so this would work + + align:start position:0% +II like this sure so this would work + + + align:start position:0% +II like this sure so this would work +with variation of parameters it would + + align:start position:0% +with variation of parameters it would + + + align:start position:0% +with variation of parameters it would +work with what Luke's talking about it + + align:start position:0% +work with what Luke's talking about it + + + align:start position:0% +work with what Luke's talking about it +works with this one this just happened + + align:start position:0% +works with this one this just happened + + + align:start position:0% +works with this one this just happened +to be a particularly simple one because + + align:start position:0% +to be a particularly simple one because + + + align:start position:0% +to be a particularly simple one because +the integrating factor is so simple so + + align:start position:0% +the integrating factor is so simple so + + + align:start position:0% +the integrating factor is so simple so +let's cram this up right here + + align:start position:0% +let's cram this up right here + + + align:start position:0% +let's cram this up right here +so this is like saying n 2 times e to + + align:start position:0% +so this is like saying n 2 times e to + + + align:start position:0% +so this is like saying n 2 times e to +the lambda 2 T prime minus and we've got + + align:start position:0% +the lambda 2 T prime minus and we've got + + + align:start position:0% +the lambda 2 T prime minus and we've got +2 e to the some things that we can + + align:start position:0% +2 e to the some things that we can + + + align:start position:0% +2 e to the some things that we can +combine right here so I'll just say + + align:start position:0% +combine right here so I'll just say + + + align:start position:0% +combine right here so I'll just say +lambda 1 and 10 e to the lambda 2 minus + + align:start position:0% +lambda 1 and 10 e to the lambda 2 minus + + + align:start position:0% +lambda 1 and 10 e to the lambda 2 minus +lambda 1 T equals zero so now I will put + + align:start position:0% +lambda 1 T equals zero so now I will put + + + align:start position:0% +lambda 1 T equals zero so now I will put +this term back on the other side by + + align:start position:0% +this term back on the other side by + + + align:start position:0% +this term back on the other side by +doing that and now we just integrate + + align:start position:0% +doing that and now we just integrate + + + align:start position:0% +doing that and now we just integrate +both sides and we get + 2 e to the + + align:start position:0% +both sides and we get + 2 e to the + + + align:start position:0% +both sides and we get + 2 e to the +lambda 2 T equals let's see comes lambda + + align:start position:0% +lambda 2 T equals let's see comes lambda + + + align:start position:0% +lambda 2 T equals let's see comes lambda +1 and 10 over lambda 2 minus lambda 1 e + + align:start position:0% +1 and 10 over lambda 2 minus lambda 1 e + + + align:start position:0% +1 and 10 over lambda 2 minus lambda 1 e +to the lambda 2 minus lambda 1 T plus + + align:start position:0% +to the lambda 2 minus lambda 1 T plus + + + align:start position:0% +to the lambda 2 minus lambda 1 T plus +some integration constant C and in this + + align:start position:0% +some integration constant C and in this + + + align:start position:0% +some integration constant C and in this +case our initial condition well how much + + align:start position:0% +case our initial condition well how much + + + align:start position:0% +case our initial condition well how much +of isotope n 2 did we start with have we + + align:start position:0% +of isotope n 2 did we start with have we + + + align:start position:0% +of isotope n 2 did we start with have we +specified that yet no let's make it + + align:start position:0% +specified that yet no let's make it + + + align:start position:0% +specified that yet no let's make it +simple + + align:start position:0% +simple + + + align:start position:0% +simple +let's assume that the initial amount of + + align:start position:0% +let's assume that the initial amount of + + + align:start position:0% +let's assume that the initial amount of +isotope n2 equals zero we put some + + align:start position:0% +isotope n2 equals zero we put some + + + align:start position:0% +isotope n2 equals zero we put some +isotope in the reactor or started off + + align:start position:0% +isotope in the reactor or started off + + + align:start position:0% +isotope in the reactor or started off +with some amount of isotope like radium + + align:start position:0% +with some amount of isotope like radium + + + align:start position:0% +with some amount of isotope like radium +didn't start off with and it didn't + + align:start position:0% +didn't start off with and it didn't + + + align:start position:0% +didn't start off with and it didn't +start off with any radon and just kept + + align:start position:0% +start off with any radon and just kept + + + align:start position:0% +start off with any radon and just kept +going so then all we have to do is + + align:start position:0% +going so then all we have to do is + + + align:start position:0% +going so then all we have to do is +divide each side by e to the lambda 2 T + + align:start position:0% + + + + align:start position:0% + +and that cancels those that cancels that + + align:start position:0% +and that cancels those that cancels that + + + align:start position:0% +and that cancels those that cancels that +and that and we end up with n 2 as a + + align:start position:0% +and that and we end up with n 2 as a + + + align:start position:0% +and that and we end up with n 2 as a +function of time equals lambda 1 n 1 + + align:start position:0% +function of time equals lambda 1 n 1 + + + align:start position:0% +function of time equals lambda 1 n 1 +naught over lambda 2 minus lambda 1 + + align:start position:0% +naught over lambda 2 minus lambda 1 + + + align:start position:0% +naught over lambda 2 minus lambda 1 +times e to the minus lambda 1 T ok and + + align:start position:0% +times e to the minus lambda 1 T ok and + + + align:start position:0% +times e to the minus lambda 1 T ok and +we've got an expression for n 2 + + align:start position:0% +we've got an expression for n 2 + + + align:start position:0% +we've got an expression for n 2 +how about n 3 do we even have to solve + + align:start position:0% +how about n 3 do we even have to solve + + + align:start position:0% +how about n 3 do we even have to solve +this one see a couple people shaking + + align:start position:0% +this one see a couple people shaking + + + align:start position:0% +this one see a couple people shaking +their heads no why is that well not + + align:start position:0% +their heads no why is that well not + + + align:start position:0% +their heads no why is that well not +quite because we are we hope well yeah I + + align:start position:0% +quite because we are we hope well yeah I + + + align:start position:0% +quite because we are we hope well yeah I +guess we've kind of solved it for n 1 + + align:start position:0% +guess we've kind of solved it for n 1 + + + align:start position:0% +guess we've kind of solved it for n 1 +but now we take this expression for n 2 + + align:start position:0% +but now we take this expression for n 2 + + + align:start position:0% +but now we take this expression for n 2 +stick it in here and then solve that + + align:start position:0% +stick it in here and then solve that + + + align:start position:0% +stick it in here and then solve that +it's going to get messy so I'm going to + + align:start position:0% +it's going to get messy so I'm going to + + + align:start position:0% +it's going to get messy so I'm going to +show you something + + align:start position:0% +show you something + + + align:start position:0% +show you something +mathematically now that I'll show you + + align:start position:0% +mathematically now that I'll show you + + + align:start position:0% +mathematically now that I'll show you +graphically later there's a conservation + + align:start position:0% +graphically later there's a conservation + + + align:start position:0% +graphically later there's a conservation +equation that we're missing here if we + + align:start position:0% +equation that we're missing here if we + + + align:start position:0% +equation that we're missing here if we +sum up isotopes n 1 + 2 + 3 equals what + + align:start position:0% +sum up isotopes n 1 + 2 + 3 equals what + + + align:start position:0% +sum up isotopes n 1 + 2 + 3 equals what +conserving total number of atoms exactly + + align:start position:0% +conserving total number of atoms exactly + + + align:start position:0% +conserving total number of atoms exactly +and 1 not in this situation where we + + align:start position:0% +and 1 not in this situation where we + + + align:start position:0% +and 1 not in this situation where we +started off with some known quantity of + + align:start position:0% +started off with some known quantity of + + + align:start position:0% +started off with some known quantity of +isotope 1 only you can't change the + + align:start position:0% +isotope 1 only you can't change the + + + align:start position:0% +isotope 1 only you can't change the +number of atoms here you can only change + + align:start position:0% +number of atoms here you can only change + + + align:start position:0% +number of atoms here you can only change +the type of atoms so we don't have to + + align:start position:0% +the type of atoms so we don't have to + + + align:start position:0% +the type of atoms so we don't have to +solve for e 3 oh sorry for n 3 because n + + align:start position:0% +solve for e 3 oh sorry for n 3 because n + + + align:start position:0% +solve for e 3 oh sorry for n 3 because n +3 is just N 1 not minus N 1 minus n 2 + + align:start position:0% +3 is just N 1 not minus N 1 minus n 2 + + + align:start position:0% +3 is just N 1 not minus N 1 minus n 2 +and that takes like an extra 10 minutes + + align:start position:0% +and that takes like an extra 10 minutes + + + align:start position:0% +and that takes like an extra 10 minutes +out of the today's lecture so later on + + align:start position:0% +out of the today's lecture so later on + + + align:start position:0% +out of the today's lecture so later on +when we have a projector on + + align:start position:0% +when we have a projector on + + + align:start position:0% +when we have a projector on +Tuesday I will show you these equations + + align:start position:0% +Tuesday I will show you these equations + + + align:start position:0% +Tuesday I will show you these equations +graphed out where I've actually I'll + + align:start position:0% +graphed out where I've actually I'll + + + align:start position:0% +graphed out where I've actually I'll +share this with you did I tell you guys + + align:start position:0% +share this with you did I tell you guys + + + align:start position:0% +share this with you did I tell you guys +about the decimals graphical calculator + + align:start position:0% +about the decimals graphical calculator + + + align:start position:0% +about the decimals graphical calculator +or have I shown this to you yet go here + + align:start position:0% +or have I shown this to you yet go here + + + align:start position:0% +or have I shown this to you yet go here +for all of your graphing needs it's free + + align:start position:0% +for all of your graphing needs it's free + + + align:start position:0% +for all of your graphing needs it's free +and the best part that I like is at any + + align:start position:0% +and the best part that I like is at any + + + align:start position:0% +and the best part that I like is at any +time you define some parameter it + + align:start position:0% +time you define some parameter it + + + align:start position:0% +time you define some parameter it +automatically makes a slider bar so you + + align:start position:0% +automatically makes a slider bar so you + + + align:start position:0% +automatically makes a slider bar so you +can play with the equations and you can + + align:start position:0% +can play with the equations and you can + + + align:start position:0% +can play with the equations and you can +just say like well what if L 1 and L + + align:start position:0% +just say like well what if L 1 and L + + + align:start position:0% +just say like well what if L 1 and L +lambda 1 and L 2 are equal what if they + + align:start position:0% +lambda 1 and L 2 are equal what if they + + + align:start position:0% +lambda 1 and L 2 are equal what if they +were way different and it just graphs + + align:start position:0% +were way different and it just graphs + + + align:start position:0% +were way different and it just graphs +the solutions for you it's pretty useful + + align:start position:0% +the solutions for you it's pretty useful + + + align:start position:0% +the solutions for you it's pretty useful +so I'll show you some of that on Tuesday + + align:start position:0% +so I'll show you some of that on Tuesday + + + align:start position:0% +so I'll show you some of that on Tuesday +when we actually have a screen let me + + align:start position:0% +when we actually have a screen let me + + + align:start position:0% +when we actually have a screen let me +see what time it is + + align:start position:0% +see what time it is + + + align:start position:0% +see what time it is +oh sweet we've got plenty of time so now + + align:start position:0% +oh sweet we've got plenty of time so now + + + align:start position:0% +oh sweet we've got plenty of time so now +I want to pose the following questions + + align:start position:0% +I want to pose the following questions + + + align:start position:0% +I want to pose the following questions +to you guys I'm going to erase stuff + + align:start position:0% +to you guys I'm going to erase stuff + + + align:start position:0% +to you guys I'm going to erase stuff +from here because we still have some + + align:start position:0% +from here because we still have some + + + align:start position:0% +from here because we still have some +space how do we model nuclear activation + + align:start position:0% +space how do we model nuclear activation + + + align:start position:0% +space how do we model nuclear activation +analysis using this kind of equation + + align:start position:0% +analysis using this kind of equation + + + align:start position:0% +analysis using this kind of equation +we'll start off with the same equation + + align:start position:0% +we'll start off with the same equation + + + align:start position:0% +we'll start off with the same equation +so let's say we'll have a minus lambda 1 + + align:start position:0% +so let's say we'll have a minus lambda 1 + + + align:start position:0% +so let's say we'll have a minus lambda 1 +N 1 we'll have n 2 minus lambda 2 n 2 + + align:start position:0% +N 1 we'll have n 2 minus lambda 2 n 2 + + + align:start position:0% +N 1 we'll have n 2 minus lambda 2 n 2 +minus something 3 equals something let's + + align:start position:0% +minus something 3 equals something let's + + + align:start position:0% +minus something 3 equals something let's +see there's a lambda 1 N 1 + + align:start position:0% +see there's a lambda 1 N 1 + + + align:start position:0% +see there's a lambda 1 N 1 +there's a lambda 2 n 2 minus something + + align:start position:0% +there's a lambda 2 n 2 minus something + + + align:start position:0% +there's a lambda 2 n 2 minus something +I've left some trailing minus signs to + + align:start position:0% +I've left some trailing minus signs to + + + align:start position:0% +I've left some trailing minus signs to +indicate that where you don't have + + align:start position:0% +indicate that where you don't have + + + align:start position:0% +indicate that where you don't have +complete equations for this yet so for + + align:start position:0% +complete equations for this yet so for + + + align:start position:0% +complete equations for this yet so for +the case of nuclear activation analysis + + align:start position:0% +the case of nuclear activation analysis + + + align:start position:0% +the case of nuclear activation analysis +where we have some imposed flux flux of + + align:start position:0% +where we have some imposed flux flux of + + + align:start position:0% +where we have some imposed flux flux of +neutrons + + align:start position:0% + + + + align:start position:0% + +does anyone remember from some of our + + align:start position:0% +does anyone remember from some of our + + + align:start position:0% +does anyone remember from some of our +previous flash-forwards how do we turn + + align:start position:0% +previous flash-forwards how do we turn + + + align:start position:0% +previous flash-forwards how do we turn +these into creation and destruction + + align:start position:0% +these into creation and destruction + + + align:start position:0% +these into creation and destruction +rates of these different isotopes yep + + align:start position:0% +rates of these different isotopes yep + + + align:start position:0% +rates of these different isotopes yep +so let's say we are we've now stuck n 1 + + align:start position:0% +so let's say we are we've now stuck n 1 + + + align:start position:0% +so let's say we are we've now stuck n 1 +in the reactor and we're now using the + + align:start position:0% +in the reactor and we're now using the + + + align:start position:0% +in the reactor and we're now using the +reactor to create different isotopes + + align:start position:0% +reactor to create different isotopes + + + align:start position:0% +reactor to create different isotopes +like n 2 and n 3 but at the same time + + align:start position:0% +like n 2 and n 3 but at the same time + + + align:start position:0% +like n 2 and n 3 but at the same time +they're in the reactor they're getting + + align:start position:0% +they're in the reactor they're getting + + + align:start position:0% +they're in the reactor they're getting +cooked as well by some imposed flux of + + align:start position:0% +cooked as well by some imposed flux of + + + align:start position:0% +cooked as well by some imposed flux of +neutrons how do we set up and not solve + + align:start position:0% +neutrons how do we set up and not solve + + + align:start position:0% +neutrons how do we set up and not solve +the system of equations to describe this + + align:start position:0% + + + + align:start position:0% + +they're getting destroyed and whatnot oh + + align:start position:0% + + + + align:start position:0% + +that depends on the isotope so let's + + align:start position:0% +that depends on the isotope so let's + + + align:start position:0% +that depends on the isotope so let's +define what the system that system is + + align:start position:0% +define what the system that system is + + + align:start position:0% +define what the system that system is +let's say we stuck in some other isotope + + align:start position:0% +let's say we stuck in some other isotope + + + align:start position:0% +let's say we stuck in some other isotope +and not and we put it in and we're gonna + + align:start position:0% +and not and we put it in and we're gonna + + + align:start position:0% +and not and we put it in and we're gonna +have to say it's if we have n not prime + + align:start position:0% +have to say it's if we have n not prime + + + align:start position:0% +have to say it's if we have n not prime +so minus some creation term and in this + + align:start position:0% +so minus some creation term and in this + + + align:start position:0% +so minus some creation term and in this +case n naught can absorb a neutron to + + align:start position:0% +case n naught can absorb a neutron to + + + align:start position:0% +case n naught can absorb a neutron to +become n one and one is decaying to n 2 + + align:start position:0% +become n one and one is decaying to n 2 + + + align:start position:0% +become n one and one is decaying to n 2 +and 2 is decaying to n 3 but also N 1 + + align:start position:0% +and 2 is decaying to n 3 but also N 1 + + + align:start position:0% +and 2 is decaying to n 3 but also N 1 +can be burned by neutrons and n 2 can be + + align:start position:0% +can be burned by neutrons and n 2 can be + + + align:start position:0% +can be burned by neutrons and n 2 can be +burned by neutrons and n 3 can be burned + + align:start position:0% +burned by neutrons and n 3 can be burned + + + align:start position:0% +burned by neutrons and n 3 can be burned +by neutrons so here I've given you kind + + align:start position:0% +by neutrons so here I've given you kind + + + align:start position:0% +by neutrons so here I've given you kind +of a simplistic situation that doesn't + + align:start position:0% +of a simplistic situation that doesn't + + + align:start position:0% +of a simplistic situation that doesn't +usually exist here I've given you a + + align:start position:0% +usually exist here I've given you a + + + align:start position:0% +usually exist here I've given you a +situation that you can replicate in the + + align:start position:0% +situation that you can replicate in the + + + align:start position:0% +situation that you can replicate in the +reactor how do we model this nuclear + + align:start position:0% +reactor how do we model this nuclear + + + align:start position:0% +reactor how do we model this nuclear +activation analysis process well first + + align:start position:0% +activation analysis process well first + + + align:start position:0% +activation analysis process well first +of all what's the creation rate of n-not + + align:start position:0% +of all what's the creation rate of n-not + + + align:start position:0% +of all what's the creation rate of n-not +the stuff we put in the reactor are we + + align:start position:0% +the stuff we put in the reactor are we + + + align:start position:0% +the stuff we put in the reactor are we +creating any + + align:start position:0% + + + + align:start position:0% + +no Luke it could be so if we had this + + align:start position:0% +no Luke it could be so if we had this + + + align:start position:0% +no Luke it could be so if we had this +fall the following nuclear reaction now + + align:start position:0% +fall the following nuclear reaction now + + + align:start position:0% +fall the following nuclear reaction now +it's getting crazy we can model that too + + align:start position:0% +it's getting crazy we can model that too + + + align:start position:0% +it's getting crazy we can model that too +let's do it okay I was gonna say no but + + align:start position:0% +let's do it okay I was gonna say no but + + + align:start position:0% +let's do it okay I was gonna say no but +let's do it we can let so I'm what I'm + + align:start position:0% +let's do it we can let so I'm what I'm + + + align:start position:0% +let's do it we can let so I'm what I'm +trying to do here is give you the + + align:start position:0% +trying to do here is give you the + + + align:start position:0% +trying to do here is give you the +mathematical tools to model any real + + align:start position:0% +mathematical tools to model any real + + + align:start position:0% +mathematical tools to model any real +physical situation usually in this class + + align:start position:0% +physical situation usually in this class + + + align:start position:0% +physical situation usually in this class +like when I took it the discussion + + align:start position:0% +like when I took it the discussion + + + align:start position:0% +like when I took it the discussion +stopped here we got to start looking at + + align:start position:0% +stopped here we got to start looking at + + + align:start position:0% +stopped here we got to start looking at +different graphs of secular versus + + align:start position:0% +different graphs of secular versus + + + align:start position:0% +different graphs of secular versus +transient equilibrium like in the + + align:start position:0% +transient equilibrium like in the + + + align:start position:0% +transient equilibrium like in the +reading but I want you guys to have the + + align:start position:0% +reading but I want you guys to have the + + + align:start position:0% +reading but I want you guys to have the +intuition to say all right let's take + + align:start position:0% +intuition to say all right let's take + + + align:start position:0% +intuition to say all right let's take +any crazy decay diagram right and n 3 + + align:start position:0% +any crazy decay diagram right and n 3 + + + align:start position:0% +any crazy decay diagram right and n 3 +becomes n 1 let's just go nuts how do we + + align:start position:0% +becomes n 1 let's just go nuts how do we + + + align:start position:0% +becomes n 1 let's just go nuts how do we +set up the differential equations for + + align:start position:0% +set up the differential equations for + + + align:start position:0% +set up the differential equations for +this assuming that computers consultant + + align:start position:0% +this assuming that computers consultant + + + align:start position:0% +this assuming that computers consultant +in every case whereas by long pointer go + + align:start position:0% +in every case whereas by long pointer go + + + align:start position:0% +in every case whereas by long pointer go +back to this here the change is the + + align:start position:0% +back to this here the change is the + + + align:start position:0% +back to this here the change is the +creation - the destruction so what are + + align:start position:0% +creation - the destruction so what are + + + align:start position:0% +creation - the destruction so what are +all the creation sources in our new + + align:start position:0% +all the creation sources in our new + + + align:start position:0% +all the creation sources in our new +scenario for n naught + + align:start position:0% + + + + align:start position:0% + +well I'll pose you a simpler question if + + align:start position:0% +well I'll pose you a simpler question if + + + align:start position:0% +well I'll pose you a simpler question if +there is no isotope n - can you create + + align:start position:0% +there is no isotope n - can you create + + + align:start position:0% +there is no isotope n - can you create +any and not no because the only way to + + align:start position:0% +any and not no because the only way to + + + align:start position:0% +any and not no because the only way to +make and not is to start with n - so we + + align:start position:0% +make and not is to start with n - so we + + + align:start position:0% +make and not is to start with n - so we +know its creation term is gonna have an + + align:start position:0% +know its creation term is gonna have an + + + align:start position:0% +know its creation term is gonna have an +N 2 in it what else does it depend on I + + align:start position:0% + + + + align:start position:0% + +heard both of the pieces of the answer + + align:start position:0% +heard both of the pieces of the answer + + + align:start position:0% +heard both of the pieces of the answer +correct at the same time it depends on + + align:start position:0% +correct at the same time it depends on + + + align:start position:0% +correct at the same time it depends on +the flux of neutrons and it depends on + + align:start position:0% +the flux of neutrons and it depends on + + + align:start position:0% +the flux of neutrons and it depends on +the cross section this macroscopic cross + + align:start position:0% +the cross section this macroscopic cross + + + align:start position:0% +the cross section this macroscopic cross +section right here okay I'm sorry + + align:start position:0% +section right here okay I'm sorry + + + align:start position:0% +section right here okay I'm sorry +no no it depends on the microscopic + + align:start position:0% +no no it depends on the microscopic + + + align:start position:0% +no no it depends on the microscopic +cross section because we have an amount + + align:start position:0% +cross section because we have an amount + + + align:start position:0% +cross section because we have an amount +of n - but it does depend on how many + + align:start position:0% +of n - but it does depend on how many + + + align:start position:0% +of n - but it does depend on how many +neutrons you throw at it + + align:start position:0% +neutrons you throw at it + + + align:start position:0% +neutrons you throw at it +and what is the probability that each of + + align:start position:0% +and what is the probability that each of + + + align:start position:0% +and what is the probability that each of +those neutrons make some n not so what + + align:start position:0% +those neutrons make some n not so what + + + align:start position:0% +those neutrons make some n not so what +we've got right here is a reaction rate + + align:start position:0% +we've got right here is a reaction rate + + + align:start position:0% +we've got right here is a reaction rate +so who remembers from the like second or + + align:start position:0% +so who remembers from the like second or + + + align:start position:0% +so who remembers from the like second or +third lecture we said a reaction rate + + align:start position:0% +third lecture we said a reaction rate + + + align:start position:0% +third lecture we said a reaction rate +can be expressed like macroscopic cross + + align:start position:0% +can be expressed like macroscopic cross + + + align:start position:0% +can be expressed like macroscopic cross +section times a flux which is the same + + align:start position:0% +section times a flux which is the same + + + align:start position:0% +section times a flux which is the same +as a microscopic cross section times + + align:start position:0% +as a microscopic cross section times + + + align:start position:0% +as a microscopic cross section times +number density times flux but this is + + align:start position:0% +number density times flux but this is + + + align:start position:0% +number density times flux but this is +better known as a macroscopic cross + + align:start position:0% +better known as a macroscopic cross + + + align:start position:0% +better known as a macroscopic cross +section member I kind of showed this to + + align:start position:0% +section member I kind of showed this to + + + align:start position:0% +section member I kind of showed this to +you very briefly when we talked about + + align:start position:0% +you very briefly when we talked about + + + align:start position:0% +you very briefly when we talked about +cross sections now is where we actually + + align:start position:0% +cross sections now is where we actually + + + align:start position:0% +cross sections now is where we actually +use them so the cross sections like the + + align:start position:0% +use them so the cross sections like the + + + align:start position:0% +use them so the cross sections like the +probability that a neutron coming in to + + align:start position:0% +probability that a neutron coming in to + + + align:start position:0% +probability that a neutron coming in to +atom n is going to react with it the + + align:start position:0% +atom n is going to react with it the + + + align:start position:0% +atom n is going to react with it the +macroscopic cross section in units of + + align:start position:0% +macroscopic cross section in units of + + + align:start position:0% +macroscopic cross section in units of +let's say 1 over centimeters is the + + align:start position:0% +let's say 1 over centimeters is the + + + align:start position:0% +let's say 1 over centimeters is the +total let's say the total probability + + align:start position:0% +total let's say the total probability + + + align:start position:0% +total let's say the total probability +accounting for how many are there and + + align:start position:0% +accounting for how many are there and + + + align:start position:0% +accounting for how many are there and +the flux is in neutrons per centimeter + + align:start position:0% +the flux is in neutrons per centimeter + + + align:start position:0% +the flux is in neutrons per centimeter +squared per second combine these + + align:start position:0% +squared per second combine these + + + align:start position:0% +squared per second combine these +together and you get a reaction rate in + + align:start position:0% +together and you get a reaction rate in + + + align:start position:0% +together and you get a reaction rate in +atoms per centimeter cubed for a second + + align:start position:0% +atoms per centimeter cubed for a second + + + align:start position:0% +atoms per centimeter cubed for a second +a volumetric reaction rate there we go + + align:start position:0% +a volumetric reaction rate there we go + + + align:start position:0% +a volumetric reaction rate there we go +so n1 can be created let's give this + + align:start position:0% +so n1 can be created let's give this + + + align:start position:0% +so n1 can be created let's give this +cross-section a designation from n2 to + + align:start position:0% +cross-section a designation from n2 to + + + align:start position:0% +cross-section a designation from n2 to +n-not so let's call it cross-section to + + align:start position:0% +n-not so let's call it cross-section to + + + align:start position:0% +n-not so let's call it cross-section to +0 how can n does not be destroyed + + align:start position:0% + + + + align:start position:0% + +I'll give you a hint it looks very + + align:start position:0% +I'll give you a hint it looks very + + + align:start position:0% +I'll give you a hint it looks very +similar to this term anyone want to take + + align:start position:0% +similar to this term anyone want to take + + + align:start position:0% +similar to this term anyone want to take +a guess yeah we haven't specified that + + align:start position:0% +a guess yeah we haven't specified that + + + align:start position:0% +a guess yeah we haven't specified that +I'm going to I'm gonna cut the craziness + + align:start position:0% +I'm going to I'm gonna cut the craziness + + + align:start position:0% +I'm going to I'm gonna cut the craziness +it there I think but just look at the + + align:start position:0% +it there I think but just look at the + + + align:start position:0% +it there I think but just look at the +reactions right here and not can absorb + + align:start position:0% +reactions right here and not can absorb + + + align:start position:0% +reactions right here and not can absorb +a neutron and become n1 so how do we + + align:start position:0% +a neutron and become n1 so how do we + + + align:start position:0% +a neutron and become n1 so how do we +mathematically write that minus the + + align:start position:0% +mathematically write that minus the + + + align:start position:0% +mathematically write that minus the +cross-section of let's say zero going to + + align:start position:0% +cross-section of let's say zero going to + + + align:start position:0% +cross-section of let's say zero going to +1 let's just call it that times the + + align:start position:0% +1 let's just call it that times the + + + align:start position:0% +1 let's just call it that times the +neutron flux times what times the amount + + align:start position:0% +neutron flux times what times the amount + + + align:start position:0% +neutron flux times what times the amount +that's there and not so this is your + + align:start position:0% +that's there and not so this is your + + + align:start position:0% +that's there and not so this is your +destruction term using this pattern we + + align:start position:0% +destruction term using this pattern we + + + align:start position:0% +destruction term using this pattern we +can fill in all the remaining terms for + + align:start position:0% +can fill in all the remaining terms for + + + align:start position:0% +can fill in all the remaining terms for +all the remaining isotopes so what are + + align:start position:0% +all the remaining isotopes so what are + + + align:start position:0% +all the remaining isotopes so what are +the creation mechanisms for isotope n1 + + align:start position:0% + + + + align:start position:0% + +well just follow the arrows mm-hmm yep + + align:start position:0% +well just follow the arrows mm-hmm yep + + + align:start position:0% +well just follow the arrows mm-hmm yep +there's this one right here we can edit + + align:start position:0% +there's this one right here we can edit + + + align:start position:0% +there's this one right here we can edit +this but flip the sign because it's + + align:start position:0% +this but flip the sign because it's + + + align:start position:0% +this but flip the sign because it's +creation + + align:start position:0% +creation + + + align:start position:0% +creation +so Sigma oh one flux and not and what + + align:start position:0% +so Sigma oh one flux and not and what + + + align:start position:0% +so Sigma oh one flux and not and what +else can create n1 because we're just + + align:start position:0% +else can create n1 because we're just + + + align:start position:0% +else can create n1 because we're just +going crazy today and three can create + + align:start position:0% +going crazy today and three can create + + + align:start position:0% +going crazy today and three can create +and one because we said so but yeah cuz + + align:start position:0% +and one because we said so but yeah cuz + + + align:start position:0% +and one because we said so but yeah cuz +we said so so now we'll say also will + + align:start position:0% +we said so so now we'll say also will + + + align:start position:0% +we said so so now we'll say also will +have this cross-section for three + + align:start position:0% +have this cross-section for three + + + align:start position:0% +have this cross-section for three +turning into one times flux times n 3 + + align:start position:0% +turning into one times flux times n 3 + + + align:start position:0% +turning into one times flux times n 3 +minus the decay of n1 using our activity + + align:start position:0% +minus the decay of n1 using our activity + + + align:start position:0% +minus the decay of n1 using our activity +expression - what else + + align:start position:0% + + + + align:start position:0% + +I heard some yep croc there will be the + + align:start position:0% +I heard some yep croc there will be the + + + align:start position:0% +I heard some yep croc there will be the +cross-section of n1 let's call it going + + align:start position:0% +cross-section of n1 let's call it going + + + align:start position:0% +cross-section of n1 let's call it going +to some isotope we don't care about + + align:start position:0% +to some isotope we don't care about + + + align:start position:0% +to some isotope we don't care about +times the flux times n1 so as long as + + align:start position:0% +times the flux times n1 so as long as + + + align:start position:0% +times the flux times n1 so as long as +you can draw a like arrow decay and + + align:start position:0% +you can draw a like arrow decay and + + + align:start position:0% +you can draw a like arrow decay and +destruction reduction diagram we can put + + align:start position:0% +destruction reduction diagram we can put + + + align:start position:0% +destruction reduction diagram we can put +this to meth that's the crazy thing + + align:start position:0% +this to meth that's the crazy thing + + + align:start position:0% +this to meth that's the crazy thing +let's finish it up how about n2 we know + + align:start position:0% +let's finish it up how about n2 we know + + + align:start position:0% +let's finish it up how about n2 we know +that n1 can decay to end - what are the + + align:start position:0% +that n1 can decay to end - what are the + + + align:start position:0% +that n1 can decay to end - what are the +other production mechanisms for n2 + + align:start position:0% +other production mechanisms for n2 + + + align:start position:0% +other production mechanisms for n2 +follow the arrows that's it that's + + align:start position:0% +follow the arrows that's it that's + + + align:start position:0% +follow the arrows that's it that's +because we're not changing anything at + + align:start position:0% +because we're not changing anything at + + + align:start position:0% +because we're not changing anything at +this point what are all the destruction + + align:start position:0% +this point what are all the destruction + + + align:start position:0% +this point what are all the destruction +mechanisms for n2 yep it can decay it + + align:start position:0% +mechanisms for n2 yep it can decay it + + + align:start position:0% +mechanisms for n2 yep it can decay it +can be absorbed by a neutron to become + + align:start position:0% +can be absorbed by a neutron to become + + + align:start position:0% +can be absorbed by a neutron to become +something we don't care about see let's + + align:start position:0% +something we don't care about see let's + + + align:start position:0% +something we don't care about see let's +call it cross-section to know times flux + + align:start position:0% +call it cross-section to know times flux + + + align:start position:0% +call it cross-section to know times flux +times n2 - the cross-section from 2 to 0 + + align:start position:0% +times n2 - the cross-section from 2 to 0 + + + align:start position:0% +times n2 - the cross-section from 2 to 0 +just this term with a minus sign + + align:start position:0% + + + + align:start position:0% + +how about n3 what are all the ways we + + align:start position:0% +how about n3 what are all the ways we + + + align:start position:0% +how about n3 what are all the ways we +can make n3 so you see it a little + + align:start position:0% +can make n3 so you see it a little + + + align:start position:0% +can make n3 so you see it a little +louder only from decay again just see + + align:start position:0% +louder only from decay again just see + + + align:start position:0% +louder only from decay again just see +what ours are pointing at it and what + + align:start position:0% +what ours are pointing at it and what + + + align:start position:0% +what ours are pointing at it and what +about the destruction mechanisms friend + + align:start position:0% +about the destruction mechanisms friend + + + align:start position:0% +about the destruction mechanisms friend +3 yep so there's some probability it + + align:start position:0% +3 yep so there's some probability it + + + align:start position:0% +3 yep so there's some probability it +decays let's say cross-section 3 no + + align:start position:0% +decays let's say cross-section 3 no + + + align:start position:0% +decays let's say cross-section 3 no +times flux times n3 - this arrow going + + align:start position:0% +times flux times n3 - this arrow going + + + align:start position:0% +times flux times n3 - this arrow going +back to n1 running out of space too many + + align:start position:0% +back to n1 running out of space too many + + + align:start position:0% +back to n1 running out of space too many +units from 3 to 1 flux and 3 so the + + align:start position:0% +units from 3 to 1 flux and 3 so the + + + align:start position:0% +units from 3 to 1 flux and 3 so the +point of accepting the escalation of + + align:start position:0% +point of accepting the escalation of + + + align:start position:0% +point of accepting the escalation of +this problem into something crazy is + + align:start position:0% +this problem into something crazy is + + + align:start position:0% +this problem into something crazy is +that it doesn't matter how crazy it gets + + align:start position:0% +that it doesn't matter how crazy it gets + + + align:start position:0% +that it doesn't matter how crazy it gets +as long as you have like an arrow based + + align:start position:0% +as long as you have like an arrow based + + + align:start position:0% +as long as you have like an arrow based +diagram or a flowchart to say which + + align:start position:0% +diagram or a flowchart to say which + + + align:start position:0% +diagram or a flowchart to say which +isotopes become which other isotopes by + + align:start position:0% +isotopes become which other isotopes by + + + align:start position:0% +isotopes become which other isotopes by +which other means you can pose and + + align:start position:0% +which other means you can pose and + + + align:start position:0% +which other means you can pose and +correctly write the set of equations + + align:start position:0% +correctly write the set of equations + + + align:start position:0% +correctly write the set of equations +that define + + align:start position:0% +that define + + + align:start position:0% +that define +them this is when I would bring in + + align:start position:0% +them this is when I would bring in + + + align:start position:0% +them this is when I would bring in +MATLAB or Mathematica I could make you + + align:start position:0% +MATLAB or Mathematica I could make you + + + align:start position:0% +MATLAB or Mathematica I could make you +do this analytically but this isn't a + + align:start position:0% +do this analytically but this isn't a + + + align:start position:0% +do this analytically but this isn't a +course 18 class and yeah we don't go + + align:start position:0% +course 18 class and yeah we don't go + + + align:start position:0% +course 18 class and yeah we don't go +there cool so I think I guess it's + + align:start position:0% +there cool so I think I guess it's + + + align:start position:0% +there cool so I think I guess it's +probably getting towards 10 of 10 of + + align:start position:0% +probably getting towards 10 of 10 of + + + align:start position:0% +probably getting towards 10 of 10 of +close enough it's like 3 of 10 of so I'd + + align:start position:0% +close enough it's like 3 of 10 of so I'd + + + align:start position:0% +close enough it's like 3 of 10 of so I'd +like to open it up to any questions + + align:start position:0% +like to open it up to any questions + + + align:start position:0% +like to open it up to any questions +because we let this I let this escalate + + align:start position:0% +because we let this I let this escalate + + + align:start position:0% +because we let this I let this escalate +freely to prove the point that as long + + align:start position:0% +freely to prove the point that as long + + + align:start position:0% +freely to prove the point that as long +as you know what decays into what or + + align:start position:0% +as you know what decays into what or + + + align:start position:0% +as you know what decays into what or +what creates or destroys what you can + + align:start position:0% +what creates or destroys what you can + + + align:start position:0% +what creates or destroys what you can +set up the equations correctly and what + + align:start position:0% +set up the equations correctly and what + + + align:start position:0% +set up the equations correctly and what +we'll be doing on Tuesday is graphing + + align:start position:0% +we'll be doing on Tuesday is graphing + + + align:start position:0% +we'll be doing on Tuesday is graphing +this where we can pose an arbitrarily + + align:start position:0% +this where we can pose an arbitrarily + + + align:start position:0% +this where we can pose an arbitrarily +complex set of equations and you can + + align:start position:0% +complex set of equations and you can + + + align:start position:0% +complex set of equations and you can +start looking at well the change in one + + align:start position:0% +start looking at well the change in one + + + align:start position:0% +start looking at well the change in one +depends on the amount of the other and + + align:start position:0% +depends on the amount of the other and + + + align:start position:0% +depends on the amount of the other and +you can almost graphically solve these + + align:start position:0% +you can almost graphically solve these + + + align:start position:0% +you can almost graphically solve these +on paper + + align:start position:0% +on paper + + + align:start position:0% +on paper +forget Mathematica or MATLAB if you look + + align:start position:0% +forget Mathematica or MATLAB if you look + + + align:start position:0% +forget Mathematica or MATLAB if you look +at last year's exam I actually posed a + + align:start position:0% +at last year's exam I actually posed a + + + align:start position:0% +at last year's exam I actually posed a +more complex set of beasts and said draw + + align:start position:0% +more complex set of beasts and said draw + + + align:start position:0% +more complex set of beasts and said draw +the solution and I'm gonna we're going + + align:start position:0% +the solution and I'm gonna we're going + + + align:start position:0% +the solution and I'm gonna we're going +to show you how to do that but any + + align:start position:0% +to show you how to do that but any + + + align:start position:0% +to show you how to do that but any +question on how we formed these yep so + + align:start position:0% +question on how we formed these yep so + + + align:start position:0% +question on how we formed these yep so +we just said let's say n 3 2 care to sum + + align:start position:0% +we just said let's say n 3 2 care to sum + + + align:start position:0% +we just said let's say n 3 2 care to sum +the case that some isotope we don't care + + align:start position:0% +the case that some isotope we don't care + + + align:start position:0% +the case that some isotope we don't care +about that's how I initially had it and + + align:start position:0% +about that's how I initially had it and + + + align:start position:0% +about that's how I initially had it and +then I think Luke said well can n to + + align:start position:0% +then I think Luke said well can n to + + + align:start position:0% +then I think Luke said well can n to +become n 0 and I said yeah sure so there + + align:start position:0% +become n 0 and I said yeah sure so there + + + align:start position:0% +become n 0 and I said yeah sure so there +can be a cross section for every type of + + align:start position:0% +can be a cross section for every type of + + + align:start position:0% +can be a cross section for every type of +reaction so in reality you might have + + align:start position:0% +reaction so in reality you might have + + + align:start position:0% +reaction so in reality you might have +any reaction under the Sun right one + + align:start position:0% +any reaction under the Sun right one + + + align:start position:0% +any reaction under the Sun right one +isotope could absorb a neutron and decay + + align:start position:0% +isotope could absorb a neutron and decay + + + align:start position:0% +isotope could absorb a neutron and decay +by like any of three or four different + + align:start position:0% +by like any of three or four different + + + align:start position:0% +by like any of three or four different +mechanisms into something else you may + + align:start position:0% +mechanisms into something else you may + + + align:start position:0% +mechanisms into something else you may +have different probabilities for each of + + align:start position:0% +have different probabilities for each of + + + align:start position:0% +have different probabilities for each of +these + + align:start position:0% + + + + align:start position:0% + +yep + + align:start position:0% + + + + align:start position:0% + +the only time I'd expect you to find + + align:start position:0% +the only time I'd expect you to find + + + align:start position:0% +the only time I'd expect you to find +these decay constants is if I told you + + align:start position:0% +these decay constants is if I told you + + + align:start position:0% +these decay constants is if I told you +what these isotopes were those are also + + align:start position:0% +what these isotopes were those are also + + + align:start position:0% +what these isotopes were those are also +listed on the table of nuclides as and + + align:start position:0% +listed on the table of nuclides as and + + + align:start position:0% +listed on the table of nuclides as and +they give you the half-life and you know + + align:start position:0% +they give you the half-life and you know + + + align:start position:0% +they give you the half-life and you know +from this half-life relation what the + + align:start position:0% +from this half-life relation what the + + + align:start position:0% +from this half-life relation what the +decay constant is if I didn't tell you + + align:start position:0% +decay constant is if I didn't tell you + + + align:start position:0% +decay constant is if I didn't tell you +what these isotopes were I would just + + align:start position:0% +what these isotopes were I would just + + + align:start position:0% +what these isotopes were I would just +have you keep these symbols as lambda 1 + + align:start position:0% +have you keep these symbols as lambda 1 + + + align:start position:0% +have you keep these symbols as lambda 1 +lambda 2 and I might pose a question + + align:start position:0% +lambda 2 and I might pose a question + + + align:start position:0% +lambda 2 and I might pose a question +which will solve graphically on Tuesday + + align:start position:0% +which will solve graphically on Tuesday + + + align:start position:0% +which will solve graphically on Tuesday +like let's say solve this set of + + align:start position:0% +like let's say solve this set of + + + align:start position:0% +like let's say solve this set of +equations for lambda 2 is much greater + + align:start position:0% +equations for lambda 2 is much greater + + + align:start position:0% +equations for lambda 2 is much greater +than lambda 1 I don't care what the + + align:start position:0% +than lambda 1 I don't care what the + + + align:start position:0% +than lambda 1 I don't care what the +numbers are let's just look at that + + align:start position:0% +numbers are let's just look at that + + + align:start position:0% +numbers are let's just look at that +general relation and all the graphs for + + align:start position:0% +general relation and all the graphs for + + + align:start position:0% +general relation and all the graphs for +that sort of situation will follow the + + align:start position:0% +that sort of situation will follow the + + + align:start position:0% +that sort of situation will follow the +same pattern cool any other questions on + + align:start position:0% +same pattern cool any other questions on + + + align:start position:0% +same pattern cool any other questions on +how we constructed this set of + + align:start position:0% +how we constructed this set of + + + align:start position:0% +how we constructed this set of +differential equations and know that + + align:start position:0% +differential equations and know that + + + align:start position:0% +differential equations and know that +I'll never ask you to solve them + + align:start position:0% +I'll never ask you to solve them + + + align:start position:0% +I'll never ask you to solve them +numerically or analytically yeah that's + + align:start position:0% +numerically or analytically yeah that's + + + align:start position:0% +numerically or analytically yeah that's +why we have computers and this is the + + align:start position:0% +why we have computers and this is the + + + align:start position:0% +why we have computers and this is the +future these I might expect you to know + + align:start position:0% +future these I might expect you to know + + + align:start position:0% +future these I might expect you to know +how to derive but this is the simplest + + align:start position:0% +how to derive but this is the simplest + + + align:start position:0% +how to derive but this is the simplest +possible case cool + + align:start position:0% +possible case cool + + + align:start position:0% +possible case cool +all right if there's no questions and + + align:start position:0% +all right if there's no questions and + + + align:start position:0% +all right if there's no questions and +let's take another 10-minute break and + + align:start position:0% +let's take another 10-minute break and + + + align:start position:0% +let's take another 10-minute break and +I'll be here for recitation to go over + + align:start position:0% +I'll be here for recitation to go over + + + align:start position:0% +I'll be here for recitation to go over +whatever problems you guys would like to + + align:start position:0% +whatever problems you guys would like to + + + align:start position:0% +whatever problems you guys would like to +do + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/euqZK85cQwo.txt b/euqZK85cQwo.txt new file mode 100644 index 0000000000000000000000000000000000000000..fce695c00ad7c768d677d7b235127a87497afbda --- /dev/null +++ b/euqZK85cQwo.txt @@ -0,0 +1,410 @@ +Hi, In this problem, we'll +be looking at the PDF the + +absolute value of x. + +So if we know a random variable, +x, and we know it's + +PDF, how can we use that +information to help us find + +the PDF of another random +variable-- the + +absolute value of x? + +And so throughout this problem, +we'll define a new + +random variable called y. + +And we'll define that y to be +equal to the absolute value of + +x, just to make things +simpler. + +So we'll do a couple of concrete +examples, and then + +we'll try to generalize +at the end. + +The first example that we'll +deal with in part A is + +this PDF for x. + +So we're told that the PDF of +x is 1/3 between negative 2 + +and 1, and 0 otherwise. + +And here's a picture of +what it looks like. + +It's just a rectangle from +negative 2 to 1. + +So now we want to find out +what is the PDF of the + +absolute value of x, which +we've called y? + +And at this point, it may be +helpful to step back and think + +about this problem from the +discrete point of view again. + +So if x were a discrete random +variable, the problem would + +be, what is the probability that +the absolute value of x + +is equal to, say, 1/2? + +Well, the probability that +the absolute value of + +x is equal to 1/2-- + +that can occur in two +different ways. + +One is that x itself is 1/2. + +Or x could be negative 1/2, in +which case, the absolute value + +of x would still be 1/2. + +So those two events are +mutually exclusive. + +And so the probability of either +one of them happening + +is you can just add them up. + +And so the probability of the +absolute value of x being 1/2 + +would have two contributions, +one from x being 1/2, and one + +from x being negative 1/2. + + + +The analogous idea carries over +to the continuous case, + +when you have a PDF. + +So now let's say that we're +interested in the case where + +we want to know the +PDF of y at 1/2. + +Well, that again, is going to +have two contributions, one + +from where x is 1/2, and one +from where x is minus 1/2. + +And so you can just imagine that +each one of these values + +for y-- and remember, y has to +be non-negative, because it's + +an absolute value-- + +has two contributions, one from +the right side of 0, and + +one from the left, or +negative, side of 0. + +So you can come up and write +an algebraic expression for + +this, and we'll do that in Part +C. But you can also look + +at this from a visual +point of view. + +And you can take the PDF diagram +itself and imagine + +transforming it to find out what +the PDF of the absolute + +value of x would look like. + +So the way to do it would be +you take what's on the + +negative side. + +You flip it over and take the +mirror image, and then you + +stack it on top of what you have +on the right-hand side, + +or the positive side. + +So take this, flip it over, +and stack it on top. + +You can imagine just taking this +block, flipping it over. + +And just think of it as like a +Tetris block that's falling + +down from above. + +And it stacks on top of +wherever it lands. + +So it'll turn it into something + +that looks like this. + + + +So there's already a block of +height 1/3 from 0 to 1. + +That's from the original 1. + +And now we take this, and flip +it over, and drop it on top. + +Well, this part is going to +fall on top of the segment + +from 0 to 1. + +And then this part gets +flipped over and + +dropped over here. + +And it falls down here. + +And so the final PDF actually +looks like this kind of + +staircase, where this is 2/3 +now, because this has two + +contributions of 1/3 each, +and this is 1/3. + + + +So that is the graphical way +of approaching this. + +And the PDF for completeness, +the PDF of y would be 2/3 for + +y between 0 and 1, 1/3 for y +from 1 to 2, and 0 otherwise. + + + +All right, so let's move +on to part B, and + +get some more practice. + +Part B, we're given that this +PDF of x now is 2 times e to + +the negative 2x for x positive, +and 0 otherwise. + +Now you may just recognize this +as an exponential random + +variable with a parameter +of 2. + +And again, we can graph this +and see what it looks like. + + + +And it turns out that it's going +to start out at 2 and + +fall off exponentially. + + + +So in this case, this is +actually quite simple. + +Because if you look at it, +x is already positive. + +It doesn't have any +negative parts. + +So in fact, the absolute value +of x is the same as x itself, + +because x is never negative. + +And so y is just the +same thing as x. + +And so in this case, actually, +the PDF of y is exactly the + +same as the PDF of x. + +It's just 2e to the +minus 2y, for y + +positive and zero otherwise. + +Now you can also see this +graphically also, because to + +the left of 0, the negative +part, there is no PDF. + +The PDF is 0. + +And so if you were to take this, +flip it over, and drop + +it on top, you wouldn't get +anything, because there's + +nothing there. + +And so the entire PDF, even +after you take the absolute + +value, is just the +original one. + +So to generalize, what I said +at the beginning was that, + +remember, the probability in +the discrete case, if you + +wanted the probability that the +absolute value of a random + +variable equals something, +that would just be the + +probability that the random +variable equals that value of + +little x, or the random +variable equals + +negative little x. + +In either of those two +cases, the absolute + +value would equal x. + +So you get those two +contributions. + +And so to generalize in the +continuous case with PDFs, you + +get something that looks +very similar. + +So in this case, the PDF or y +is just the PDF of x at y. + +So this is the case where x is +just equal to y, plus the PDF + +of x evaluated negative y. + +So you, again, have both of +these two contributions. + +And we can rewrite this +top one to make + +it look more similar. + +So the PMF of some discrete +[? number ?] y, where this is + +a discrete random variable +that's equal to the absolute + +value of x, would be the PMF of +x evaluated at y, plus the + +PMF of x evaluated +at negative y. + +So in both the discrete and +continuous cases, you have the + +same thing. + +So the overall summary of this +problem is that, when you take + +a transformation-- + +in this case, an absolute +value-- + +you can reason about it and +figure out how to decompose + +that into arguments about the +original random variable, just + +plain old x. + +And for the specific case of +the absolute value, it just + +becomes taking a mirror image +and popping it on top of what + +you originally had. + +So remember, you always have +these two contributions. + +And so if you ever have a random +variable that you need + +to take an absolute value of, +you don't have to be scared. + +All you have to do is consider +both of these contributions + +and add them up, and you have +the PDF that you want. + +So I'll see you next time. \ No newline at end of file diff --git a/gMf_fpHF5rE.txt b/gMf_fpHF5rE.txt new file mode 100644 index 0000000000000000000000000000000000000000..9eac48f995bfa0b7ca27bf4fffaf584ddabeec19 --- /dev/null +++ b/gMf_fpHF5rE.txt @@ -0,0 +1,15779 @@ +align:start position:0% + +so today I'm G to + + align:start position:0% + + + + align:start position:0% + +do um empirical literature on entry and + + align:start position:0% +do um empirical literature on entry and + + + align:start position:0% +do um empirical literature on entry and +I wanted to start with this uh you know + + align:start position:0% +I wanted to start with this uh you know + + + align:start position:0% +I wanted to start with this uh you know +really classic paper by bran and Reese + + align:start position:0% +really classic paper by bran and Reese + + + align:start position:0% +really classic paper by bran and Reese +um and you know bre H it's actually it's + + align:start position:0% +um and you know bre H it's actually it's + + + align:start position:0% +um and you know bre H it's actually it's +an entry paper but it's really a a + + align:start position:0% +an entry paper but it's really a a + + + align:start position:0% +an entry paper but it's really a a +static competition paper so the research + + align:start position:0% +static competition paper so the research + + + align:start position:0% +static competition paper so the research +question here is how empirically does + + align:start position:0% +question here is how empirically does + + + align:start position:0% +question here is how empirically does +level markups and competition change + + align:start position:0% +level markups and competition change + + + align:start position:0% +level markups and competition change +when you have more firms in Market you + + align:start position:0% +when you have more firms in Market you + + + align:start position:0% +when you have more firms in Market you +know is it true that I guess maybe it is + + align:start position:0% +know is it true that I guess maybe it is + + + align:start position:0% +know is it true that I guess maybe it is +the entry graph you know once this graph + + align:start position:0% +the entry graph you know once this graph + + + align:start position:0% +the entry graph you know once this graph +look + + align:start position:0% +look + + + align:start position:0% +look +like + + align:start position:0% +like + + + align:start position:0% +like +uh you what does the sort of price cost + + align:start position:0% +uh you what does the sort of price cost + + + align:start position:0% +uh you what does the sort of price cost +margin look like as a number of firms + + align:start position:0% +margin look like as a number of firms + + + align:start position:0% +margin look like as a number of firms +uh or the profit look like as a number + + align:start position:0% +uh or the profit look like as a number + + + align:start position:0% +uh or the profit look like as a number +of firms + + align:start position:0% +of firms + + + align:start position:0% +of firms +enters um and you know rest anies are + + align:start position:0% +enters um and you know rest anies are + + + align:start position:0% +enters um and you know rest anies are +starting from this classic neio approach + + align:start position:0% +starting from this classic neio approach + + + align:start position:0% +starting from this classic neio approach +of thinking that it's very hard to + + align:start position:0% +of thinking that it's very hard to + + + align:start position:0% +of thinking that it's very hard to +estimate profits because it's very hard + + align:start position:0% +estimate profits because it's very hard + + + align:start position:0% +estimate profits because it's very hard +to estimate costs you know in many + + align:start position:0% +to estimate costs you know in many + + + align:start position:0% +to estimate costs you know in many +businesses there are lots of sort of + + align:start position:0% +businesses there are lots of sort of + + + align:start position:0% +businesses there are lots of sort of +incal costs and you can't just buy an + + align:start position:0% +incal costs and you can't just buy an + + + align:start position:0% +incal costs and you can't just buy an +account and get that so we want to use + + align:start position:0% +account and get that so we want to use + + + align:start position:0% +account and get that so we want to use +something that's readily observable idea + + align:start position:0% +something that's readily observable idea + + + align:start position:0% +something that's readily observable idea +is that entry is very clearly + + align:start position:0% +is that entry is very clearly + + + align:start position:0% +is that entry is very clearly +a f cost or not + + align:start position:0% +a f cost or not + + + align:start position:0% +a f cost or not +um the other idea in bre hand ree is + + align:start position:0% +um the other idea in bre hand ree is + + + align:start position:0% +um the other idea in bre hand ree is +that you know it's in a one of the + + align:start position:0% +that you know it's in a one of the + + + align:start position:0% +that you know it's in a one of the +challengs always how do you get a cross + + align:start position:0% +challengs always how do you get a cross + + + align:start position:0% +challengs always how do you get a cross +set enough a big enough cross-section of + + align:start position:0% +set enough a big enough cross-section of + + + align:start position:0% +set enough a big enough cross-section of +observations to + + align:start position:0% +observations to + + + align:start position:0% +observations to +run significant stal estimates and Brean + + align:start position:0% +run significant stal estimates and Brean + + + align:start position:0% +run significant stal estimates and Brean +ree had this idea of looking at isolated + + align:start position:0% +ree had this idea of looking at isolated + + + align:start position:0% +ree had this idea of looking at isolated +small towns and so you know if you look + + align:start position:0% +small towns and so you know if you look + + + align:start position:0% +small towns and so you know if you look +at the United States one thing that's + + align:start position:0% +at the United States one thing that's + + + align:start position:0% +at the United States one thing that's +nice about the United States is it's + + align:start position:0% +nice about the United States is it's + + + align:start position:0% +nice about the United States is it's +very very big and there are many parts + + align:start position:0% +very very big and there are many parts + + + align:start position:0% +very very big and there are many parts +of it where there aren't a lot of people + + align:start position:0% +of it where there aren't a lot of people + + + align:start position:0% +of it where there aren't a lot of people +and so that gives you a lot of towns + + align:start position:0% +and so that gives you a lot of towns + + + align:start position:0% +and so that gives you a lot of towns +where there towns and then there's very + + align:start position:0% +where there towns and then there's very + + + align:start position:0% +where there towns and then there's very +little around them and so if you think + + align:start position:0% +little around them and so if you think + + + align:start position:0% +little around them and so if you think +about you know you go to search around + + align:start position:0% +about you know you go to search around + + + align:start position:0% +about you know you go to search around +the United States it's a big enough + + align:start position:0% +the United States it's a big enough + + + align:start position:0% +the United States it's a big enough +country that you can if you want towns + + align:start position:0% +country that you can if you want towns + + + align:start position:0% +country that you can if you want towns +and breast an re's case they're looking + + align:start position:0% +and breast an re's case they're looking + + + align:start position:0% +and breast an re's case they're looking +for is you know I the cut offs are um + + align:start position:0% +for is you know I the cut offs are um + + + align:start position:0% +for is you know I the cut offs are um +but you know you have towns that have at + + align:start position:0% +but you know you have towns that have at + + + align:start position:0% +but you know you have towns that have at +least uh you know you have cities that + + align:start position:0% +least uh you know you have cities that + + + align:start position:0% +least uh you know you have cities that +are isolated in the sense of I think + + align:start position:0% +are isolated in the sense of I think + + + align:start position:0% +are isolated in the sense of I think +they're all 100,000 miles from any city + + align:start position:0% +they're all 100,000 miles from any city + + + align:start position:0% +they're all 100,000 miles from any city +of 100 100 miles from any City 100,000 + + align:start position:0% +of 100 100 miles from any City 100,000 + + + align:start position:0% +of 100 100 miles from any City 100,000 +people and they're at least 20 miles + + align:start position:0% +people and they're at least 20 miles + + + align:start position:0% +people and they're at least 20 miles +through any city of 1,000 people so + + align:start position:0% +through any city of 1,000 people so + + + align:start position:0% +through any city of 1,000 people so +these are all towns that are just + + align:start position:0% +these are all towns that are just + + + align:start position:0% +these are all towns that are just +completely isolated from anything else + + align:start position:0% +completely isolated from anything else + + + align:start position:0% +completely isolated from anything else +that you would any other population + + align:start position:0% +that you would any other population + + + align:start position:0% +that you would any other population +centers and they knowe that there are a + + align:start position:0% +centers and they knowe that there are a + + + align:start position:0% +centers and they knowe that there are a +lot of them and in fact I think uh you + + align:start position:0% +lot of them and in fact I think uh you + + + align:start position:0% +lot of them and in fact I think uh you +know + + align:start position:0% +know + + + align:start position:0% +know +they Peter tells stories of driving + + align:start position:0% +they Peter tells stories of driving + + + align:start position:0% +they Peter tells stories of driving +around and wanting to verify the data by + + align:start position:0% +around and wanting to verify the data by + + + align:start position:0% +around and wanting to verify the data by +just sort of driving around to all of + + align:start position:0% +just sort of driving around to all of + + + align:start position:0% +just sort of driving around to all of +these small towns and then asking them + + align:start position:0% +these small towns and then asking them + + + align:start position:0% +these small towns and then asking them +you know where can I get a pummer in + + align:start position:0% +you know where can I get a pummer in + + + align:start position:0% +you know where can I get a pummer in +this town where can I get where can I + + align:start position:0% +this town where can I get where can I + + + align:start position:0% +this town where can I get where can I +buy tires for my car whatever and so + + align:start position:0% +buy tires for my car whatever and so + + + align:start position:0% +buy tires for my car whatever and so +what they did is you know most of the + + align:start position:0% +what they did is you know most of the + + + align:start position:0% +what they did is you know most of the +data collection was done through + + align:start position:0% +data collection was done through + + + align:start position:0% +data collection was done through +business directories they basically just + + align:start position:0% +business directories they basically just + + + align:start position:0% +business directories they basically just +looked at a US map found places that + + align:start position:0% +looked at a US map found places that + + + align:start position:0% +looked at a US map found places that +were completely isolated and then used + + align:start position:0% +were completely isolated and then used + + + align:start position:0% +were completely isolated and then used +to have this thing called yemo Pages + + align:start position:0% +to have this thing called yemo Pages + + + align:start position:0% +to have this thing called yemo Pages +which was like a phone directory where + + align:start position:0% +which was like a phone directory where + + + align:start position:0% +which was like a phone directory where +you would look up phone numbers in a + + align:start position:0% +you would look up phone numbers in a + + + align:start position:0% +you would look up phone numbers in a +book and so people would use these books + + align:start position:0% +book and so people would use these books + + + align:start position:0% +book and so people would use these books +to look up phone numbers they would find + + align:start position:0% +to look up phone numbers they would find + + + align:start position:0% +to look up phone numbers they would find +out who is advertising as a Plummer in + + align:start position:0% +out who is advertising as a Plummer in + + + align:start position:0% +out who is advertising as a Plummer in +each of these towns they also used just + + align:start position:0% +each of these towns they also used just + + + align:start position:0% +each of these towns they also used just +uh business to ref frees and then they + + align:start position:0% +uh business to ref frees and then they + + + align:start position:0% +uh business to ref frees and then they +visited them sort of see you know does + + align:start position:0% +visited them sort of see you know does + + + align:start position:0% +visited them sort of see you know does +this dat be accurately collected + + align:start position:0% +this dat be accurately collected + + + align:start position:0% +this dat be accurately collected +um you know the paper it's it's a single + + align:start position:0% +um you know the paper it's it's a single + + + align:start position:0% +um you know the paper it's it's a single +crosssection they don't observe firms + + align:start position:0% +crosssection they don't observe firms + + + align:start position:0% +crosssection they don't observe firms +entering in or exiting but what they're + + align:start position:0% +entering in or exiting but what they're + + + align:start position:0% +entering in or exiting but what they're +going to infer is that sometime prior to + + align:start position:0% +going to infer is that sometime prior to + + + align:start position:0% +going to infer is that sometime prior to +the point at which they're collecting + + align:start position:0% +the point at which they're collecting + + + align:start position:0% +the point at which they're collecting +the data this you know uh + + align:start position:0% +the data this you know uh + + + align:start position:0% +the data this you know uh +firms you classic games you know firms + + align:start position:0% +firms you classic games you know firms + + + align:start position:0% +firms you classic games you know firms +choose in slash out then firms choose + + align:start position:0% +choose in slash out then firms choose + + + align:start position:0% +choose in slash out then firms choose +you know prices for quantities star of n + + align:start position:0% +you know prices for quantities star of n + + + align:start position:0% +you know prices for quantities star of n +qar of n + + align:start position:0% + + + + align:start position:0% + +then they pay the fixed costs they + + align:start position:0% +then they pay the fixed costs they + + + align:start position:0% +then they pay the fixed costs they +assume that this game has been played at + + align:start position:0% +assume that this game has been played at + + + align:start position:0% +assume that this game has been played at +some point in the past and so what we're + + align:start position:0% +some point in the past and so what we're + + + align:start position:0% +some point in the past and so what we're +observing in each market is what's the + + align:start position:0% +observing in each market is what's the + + + align:start position:0% +observing in each market is what's the +equilibrium number of firms in that + + align:start position:0% + + + + align:start position:0% + +market okay the basic thing the paper + + align:start position:0% +market okay the basic thing the paper + + + align:start position:0% +market okay the basic thing the paper +then tries to do is say if we can + + align:start position:0% +then tries to do is say if we can + + + align:start position:0% +then tries to do is say if we can +observe the number of firms in a large + + align:start position:0% +observe the number of firms in a large + + + align:start position:0% +observe the number of firms in a large +cross-section of markets that's going to + + align:start position:0% +cross-section of markets that's going to + + + align:start position:0% +cross-section of markets that's going to +give us a means to estimate profit + + align:start position:0% +give us a means to estimate profit + + + align:start position:0% +give us a means to estimate profit +levels without any data on prices or on + + align:start position:0% +levels without any data on prices or on + + + align:start position:0% +levels without any data on prices or on +costs or on + + align:start position:0% +costs or on + + + align:start position:0% +costs or on +demand and so you know consider this + + align:start position:0% +demand and so you know consider this + + + align:start position:0% +demand and so you know consider this +sort of basic model you have an entry + + align:start position:0% +sort of basic model you have an entry + + + align:start position:0% +sort of basic model you have an entry +decision you have a firm that has fixed + + align:start position:0% +decision you have a firm that has fixed + + + align:start position:0% +decision you have a firm that has fixed +cost F there's going to be symmetric + + align:start position:0% +cost F there's going to be symmetric + + + align:start position:0% +cost F there's going to be symmetric +competition so if they're n firms in a + + align:start position:0% +competition so if they're n firms in a + + + align:start position:0% +competition so if they're n firms in a +market with s + + align:start position:0% +market with s + + + align:start position:0% +market with s +people you're going to get S Over N so + + align:start position:0% +people you're going to get S Over N so + + + align:start position:0% +people you're going to get S Over N so +the total number of customers divided by + + align:start position:0% +the total number of customers divided by + + + align:start position:0% +the total number of customers divided by +the number of firms times PN minus CD of + + align:start position:0% +the number of firms times PN minus CD of + + + align:start position:0% +the number of firms times PN minus CD of +PN and so they're going to call that s + + align:start position:0% +PN and so they're going to call that s + + + align:start position:0% +PN and so they're going to call that s +over n * pi n so Pi n is the like per + + align:start position:0% +over n * pi n so Pi n is the like per + + + align:start position:0% +over n * pi n so Pi n is the like per +population + + align:start position:0% +population + + + align:start position:0% +population +profit per you know per population + + align:start position:0% +profit per you know per population + + + align:start position:0% +profit per you know per population +served um profit in this market you it + + align:start position:0% +served um profit in this market you it + + + align:start position:0% +served um profit in this market you it +reflects both sales you make to each + + align:start position:0% +reflects both sales you make to each + + + align:start position:0% +reflects both sales you make to each +customer you know like there's obviously + + align:start position:0% +customer you know like there's obviously + + + align:start position:0% +customer you know like there's obviously +only some fraction that consumers are + + align:start position:0% +only some fraction that consumers are + + + align:start position:0% +only some fraction that consumers are +buying from you and so this is profit + + align:start position:0% +buying from you and so this is profit + + + align:start position:0% +buying from you and so this is profit +per person that's in your your part of + + align:start position:0% +per person that's in your your part of + + + align:start position:0% +per person that's in your your part of +the market so you have a town and + + align:start position:0% +the market so you have a town and + + + align:start position:0% +the market so you have a town and +roughly it's divided like this and each + + align:start position:0% +roughly it's divided like this and each + + + align:start position:0% +roughly it's divided like this and each +firm gets one quarter of the market if + + align:start position:0% +firm gets one quarter of the market if + + + align:start position:0% +firm gets one quarter of the market if +your per customer profit in the quarter + + align:start position:0% +your per customer profit in the quarter + + + align:start position:0% +your per customer profit in the quarter +of the market that you serve uh we're + + align:start position:0% +of the market that you serve uh we're + + + align:start position:0% +of the market that you serve uh we're +going to have end firms in equilibrium + + align:start position:0% +going to have end firms in equilibrium + + + align:start position:0% +going to have end firms in equilibrium +if s over n * pi n is bigger than the + + align:start position:0% +if s over n * pi n is bigger than the + + + align:start position:0% +if s over n * pi n is bigger than the +fixed cost but s over n + 1 * pi n+ 1 + + align:start position:0% +fixed cost but s over n + 1 * pi n+ 1 + + + align:start position:0% +fixed cost but s over n + 1 * pi n+ 1 +would be less than the fixed cost and + + align:start position:0% +would be less than the fixed cost and + + + align:start position:0% +would be less than the fixed cost and +obviously this is decre this is smaller + + align:start position:0% +obviously this is decre this is smaller + + + align:start position:0% +obviously this is decre this is smaller +than this both because you're dividing + + align:start position:0% +than this both because you're dividing + + + align:start position:0% +than this both because you're dividing +the city into more um fractions and the + + align:start position:0% +the city into more um fractions and the + + + align:start position:0% +the city into more um fractions and the +per customer profit goes down because + + align:start position:0% +per customer profit goes down because + + + align:start position:0% +per customer profit goes down because +the price goes + + align:start position:0% +the price goes + + + align:start position:0% +the price goes +down and we're going to say is let SN be + + align:start position:0% +down and we're going to say is let SN be + + + align:start position:0% +down and we're going to say is let SN be +the minimum size in which um so for + + align:start position:0% +the minimum size in which um so for + + + align:start position:0% +the minimum size in which um so for +instance like you know let's put n on + + align:start position:0% +instance like you know let's put n on + + + align:start position:0% +instance like you know let's put n on +this a + + align:start position:0% +this a + + + align:start position:0% +this a +and then you can put the number of + + align:start position:0% +and then you can put the number of + + + align:start position:0% +and then you can put the number of +doctors in a town on this + + align:start position:0% +doctors in a town on this + + + align:start position:0% +doctors in a town on this +axis and what you would observe if you + + align:start position:0% +axis and what you would observe if you + + + align:start position:0% +axis and what you would observe if you +could draw this graph is towns that have + + align:start position:0% +could draw this graph is towns that have + + + align:start position:0% +could draw this graph is towns that have +no that are very small don't have a + + align:start position:0% +no that are very small don't have a + + + align:start position:0% +no that are very small don't have a +doctor and then there's some threshold + + align:start position:0% +doctor and then there's some threshold + + + align:start position:0% +doctor and then there's some threshold +you know maybe it's like 800 people + + align:start position:0% +you know maybe it's like 800 people + + + align:start position:0% +you know maybe it's like 800 people +where now there's a doctor in the + + align:start position:0% +where now there's a doctor in the + + + align:start position:0% +where now there's a doctor in the +town and then you know some other + + align:start position:0% +town and then you know some other + + + align:start position:0% +town and then you know some other +threshold where uh you know 2,000 people + + align:start position:0% +threshold where uh you know 2,000 people + + + align:start position:0% +threshold where uh you know 2,000 people +were now you have t to have two doctors + + align:start position:0% +were now you have t to have two doctors + + + align:start position:0% +were now you have t to have two doctors +and then some other threshold where you + + align:start position:0% +and then some other threshold where you + + + align:start position:0% +and then some other threshold where you +tend to have three + + align:start position:0% +tend to have three + + + align:start position:0% +tend to have three +[Music] + + align:start position:0% + + + + align:start position:0% + +doctors two + + align:start position:0% +doctors two + + + align:start position:0% +doctors two +three and so the idea is that you know + + align:start position:0% +three and so the idea is that you know + + + align:start position:0% +three and so the idea is that you know +we can estimate these cut we can + + align:start position:0% +we can estimate these cut we can + + + align:start position:0% +we can estimate these cut we can +estimate these curves obviously in + + align:start position:0% +estimate these curves obviously in + + + align:start position:0% +estimate these curves obviously in +practice you know you're going to see a + + align:start position:0% +practice you know you're going to see a + + + align:start position:0% +practice you know you're going to see a +lot of zeros you may see some doctors + + align:start position:0% +lot of zeros you may see some doctors + + + align:start position:0% +lot of zeros you may see some doctors +even in very small + + align:start position:0% +even in very small + + + align:start position:0% +even in very small +towns you'll still see some towns + + align:start position:0% +towns you'll still see some towns + + + align:start position:0% +towns you'll still see some towns +without doctors here but you'll see a + + align:start position:0% +without doctors here but you'll see a + + + align:start position:0% +without doctors here but you'll see a +lot of a lot of ones and maybe you'll + + align:start position:0% +lot of a lot of ones and maybe you'll + + + align:start position:0% +lot of a lot of ones and maybe you'll +even see some + + align:start position:0% +even see some + + + align:start position:0% +even see some +twos but there's going to be sort of in + + align:start position:0% +twos but there's going to be sort of in + + + align:start position:0% +twos but there's going to be sort of in +en some some curve like this where this + + align:start position:0% +en some some curve like this where this + + + align:start position:0% +en some some curve like this where this +is + + align:start position:0% +is + + + align:start position:0% +is +typically you need to have + + align:start position:0% + + + + align:start position:0% + +S1 customers to have one doctor you need + + align:start position:0% +S1 customers to have one doctor you need + + + align:start position:0% +S1 customers to have one doctor you need +S2 to have two doctors and out here you + + align:start position:0% +S2 to have two doctors and out here you + + + align:start position:0% +S2 to have two doctors and out here you +need S3 to have three doctors and so + + align:start position:0% +need S3 to have three doctors and so + + + align:start position:0% +need S3 to have three doctors and so +they want to do is estimate what does + + align:start position:0% +they want to do is estimate what does + + + align:start position:0% +they want to do is estimate what does +this look like how many people do you + + align:start position:0% +this look like how many people do you + + + align:start position:0% +this look like how many people do you +need to have before the first doctor + + align:start position:0% +need to have before the first doctor + + + align:start position:0% +need to have before the first doctor +comes in how many you need to have + + align:start position:0% +comes in how many you need to have + + + align:start position:0% +comes in how many you need to have +before the second doctor comes in how + + align:start position:0% +before the second doctor comes in how + + + align:start position:0% +before the second doctor comes in how +many you need to have before the third + + align:start position:0% +many you need to have before the third + + + align:start position:0% +many you need to have before the third +doctor comes in + + align:start position:0% +doctor comes in + + + align:start position:0% +doctor comes in +and you know possibly you can estimate + + align:start position:0% +and you know possibly you can estimate + + + align:start position:0% +and you know possibly you can estimate +this just by put plotting the cities put + + align:start position:0% +this just by put plotting the cities put + + + align:start position:0% +this just by put plotting the cities put +the population the x-axis number of + + align:start position:0% +the population the x-axis number of + + + align:start position:0% +the population the x-axis number of +doctors in the y- axis bit a curve that + + align:start position:0% +doctors in the y- axis bit a curve that + + + align:start position:0% +doctors in the y- axis bit a curve that +looks like this through the see where + + align:start position:0% +looks like this through the see where + + + align:start position:0% +looks like this through the see where +the jump points + + align:start position:0% +the jump points + + + align:start position:0% +the jump points +are + + align:start position:0% +are + + + align:start position:0% +are +um so you know if you assume that the + + align:start position:0% +um so you know if you assume that the + + + align:start position:0% +um so you know if you assume that the +fixed costs don't vary with n then SN + + align:start position:0% +fixed costs don't vary with n then SN + + + align:start position:0% +fixed costs don't vary with n then SN +Over N is going to be Pi n times pi n is + + align:start position:0% +Over N is going to be Pi n times pi n is + + + align:start position:0% +Over N is going to be Pi n times pi n is +going to be F and also SN + 1/ n +1 Pi n + + align:start position:0% +going to be F and also SN + 1/ n +1 Pi n + + + align:start position:0% +going to be F and also SN + 1/ n +1 Pi n ++ 1 is going to be F so both at this + + align:start position:0% ++ 1 is going to be F so both at this + + + align:start position:0% ++ 1 is going to be F so both at this +point you know at this point you know + + align:start position:0% +point you know at this point you know + + + align:start position:0% +point you know at this point you know +the second doctor is just indifferent to + + align:start position:0% +the second doctor is just indifferent to + + + align:start position:0% +the second doctor is just indifferent to +entering or not because if it was + + align:start position:0% +entering or not because if it was + + + align:start position:0% +entering or not because if it was +smaller he wouldn't enter if it was + + align:start position:0% +smaller he wouldn't enter if it was + + + align:start position:0% +smaller he wouldn't enter if it was +bigger he would enter here we're the + + align:start position:0% +bigger he would enter here we're the + + + align:start position:0% +bigger he would enter here we're the +Third Doctor is indifferent to entering + + align:start position:0% +Third Doctor is indifferent to entering + + + align:start position:0% +Third Doctor is indifferent to entering +or not so both of these The Profit that + + align:start position:0% +or not so both of these The Profit that + + + align:start position:0% +or not so both of these The Profit that +you get if you do come in is exactly + + align:start position:0% +you get if you do come in is exactly + + + align:start position:0% +you get if you do come in is exactly +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +F and so if you just set this equal to + + align:start position:0% +F and so if you just set this equal to + + + align:start position:0% +F and so if you just set this equal to +this and then you divide the you bring + + align:start position:0% +this and then you divide the you bring + + + align:start position:0% +this and then you divide the you bring +the pi end down here denominator you get + + align:start position:0% +the pi end down here denominator you get + + + align:start position:0% +the pi end down here denominator you get +that the profit with n plus1 firms + + align:start position:0% +that the profit with n plus1 firms + + + align:start position:0% +that the profit with n plus1 firms +divided the profit with n firms is n +1 + + align:start position:0% +divided the profit with n firms is n +1 + + + align:start position:0% +divided the profit with n firms is n +1 +/n SN over SN + one you know I could + + align:start position:0% +/n SN over SN + one you know I could + + + align:start position:0% +/n SN over SN + one you know I could +also write that as + + align:start position:0% +also write that as + + + align:start position:0% +also write that as +uh Pi n + 1 Pi n + + align:start position:0% +uh Pi n + 1 Pi n + + + align:start position:0% +uh Pi n + 1 Pi n +equals + + align:start position:0% +equals + + + align:start position:0% +equals +snn / SN + 1 over n + + + align:start position:0% + + + + align:start position:0% + +1 you know so the the idea here is that + + align:start position:0% +1 you know so the the idea here is that + + + align:start position:0% +1 you know so the the idea here is that +imagine it takes uh 1,000 people in a + + align:start position:0% +imagine it takes uh 1,000 people in a + + + align:start position:0% +imagine it takes uh 1,000 people in a +market to have one + + align:start position:0% +market to have one + + + align:start position:0% +market to have one +doctor and S2 is + + align:start position:0% + + + + align:start position:0% + +4,000 then this is S1 over one is 1,000 + + align:start position:0% +4,000 then this is S1 over one is 1,000 + + + align:start position:0% +4,000 then this is S1 over one is 1,000 +you need 1,000 patients in order to be + + align:start position:0% +you need 1,000 patients in order to be + + + align:start position:0% +you need 1,000 patients in order to be +worthwhile to open a doctor's office but + + align:start position:0% +worthwhile to open a doctor's office but + + + align:start position:0% +worthwhile to open a doctor's office but +then here S2 over2 is 2,000 so that + + align:start position:0% +then here S2 over2 is 2,000 so that + + + align:start position:0% +then here S2 over2 is 2,000 so that +would say you need 2,000 people to make + + align:start position:0% +would say you need 2,000 people to make + + + align:start position:0% +would say you need 2,000 people to make +it work you need 2,000 patients for the + + align:start position:0% +it work you need 2,000 patients for the + + + align:start position:0% +it work you need 2,000 patients for the +new doctor make it worthwhile to have a + + align:start position:0% +new doctor make it worthwhile to have a + + + align:start position:0% +new doctor make it worthwhile to have a +second doctor's office and from that we + + align:start position:0% +second doctor's office and from that we + + + align:start position:0% +second doctor's office and from that we +infer that it must be that you know Pi 2 + + align:start position:0% +infer that it must be that you know Pi 2 + + + align:start position:0% +infer that it must be that you know Pi 2 +is just 1 half pi + + align:start position:0% +is just 1 half pi + + + align:start position:0% +is just 1 half pi +one so this ratio of this to this is how + + align:start position:0% +one so this ratio of this to this is how + + + align:start position:0% +one so this ratio of this to this is how +much profits per person must have + + align:start position:0% +much profits per person must have + + + align:start position:0% +much profits per person must have +declined for the second doctor to not + + align:start position:0% +declined for the second doctor to not + + + align:start position:0% +declined for the second doctor to not +come in the second doctors who get many + + align:start position:0% +come in the second doctors who get many + + + align:start position:0% +come in the second doctors who get many +more patients than the first doctor + + align:start position:0% + + + + align:start position:0% + +got and so anyway that so that's that's + + align:start position:0% +got and so anyway that so that's that's + + + align:start position:0% +got and so anyway that so that's that's +the really sort of powerful idea of this + + align:start position:0% +the really sort of powerful idea of this + + + align:start position:0% +the really sort of powerful idea of this +paper we don't have to have any data at + + align:start position:0% +paper we don't have to have any data at + + + align:start position:0% +paper we don't have to have any data at +all on prices or quantities and yet we + + align:start position:0% +all on prices or quantities and yet we + + + align:start position:0% +all on prices or quantities and yet we +can tell how the ratio of profits + + align:start position:0% +can tell how the ratio of profits + + + align:start position:0% +can tell how the ratio of profits +declines as more firms enter the market + + align:start position:0% +declines as more firms enter the market + + + align:start position:0% +declines as more firms enter the market +by just looking at how many more + + align:start position:0% +by just looking at how many more + + + align:start position:0% +by just looking at how many more +customers have to be there for the + + align:start position:0% +customers have to be there for the + + + align:start position:0% +customers have to be there for the +second firm to want to come + + align:start position:0% + + + + align:start position:0% + +in question about that basic + + align:start position:0% +in question about that basic + + + align:start position:0% +in question about that basic +idea okay U you know the previous slide + + align:start position:0% +idea okay U you know the previous slide + + + align:start position:0% +idea okay U you know the previous slide +suggested with r Henry's we're going to + + align:start position:0% +suggested with r Henry's we're going to + + + align:start position:0% +suggested with r Henry's we're going to +do is + + align:start position:0% +do is + + + align:start position:0% +do is +put population on the xaxis number of + + align:start position:0% +put population on the xaxis number of + + + align:start position:0% +put population on the xaxis number of +doctors in the Y AIS and then just draw + + align:start position:0% +doctors in the Y AIS and then just draw + + + align:start position:0% +doctors in the Y AIS and then just draw +a curve like this that best fit the data + + align:start position:0% +a curve like this that best fit the data + + + align:start position:0% +a curve like this that best fit the data +uh that's not exactly what they do + + align:start position:0% +uh that's not exactly what they do + + + align:start position:0% +uh that's not exactly what they do +because they want to have a lot of + + align:start position:0% +because they want to have a lot of + + + align:start position:0% +because they want to have a lot of +co-variants in the regression that are + + align:start position:0% +co-variants in the regression that are + + + align:start position:0% +co-variants in the regression that are +also affecting all of the elements + + align:start position:0% +also affecting all of the elements + + + align:start position:0% +also affecting all of the elements +so basic way they set up the model is + + align:start position:0% +so basic way they set up the model is + + + align:start position:0% +so basic way they set up the model is +first they have something they call the + + align:start position:0% +first they have something they call the + + + align:start position:0% +first they have something they call the +effective + + align:start position:0% +effective + + + align:start position:0% +effective +population um the effective population + + align:start position:0% +population um the effective population + + + align:start position:0% +population um the effective population +in cityi is its actual + + align:start position:0% +in cityi is its actual + + + align:start position:0% +in cityi is its actual +population plus some uh X up some + + align:start position:0% +population plus some uh X up some + + + align:start position:0% +population plus some uh X up some +explanatory variables x times some + + align:start position:0% +explanatory variables x times some + + + align:start position:0% +explanatory variables x times some +coefficients + + align:start position:0% +coefficients + + + align:start position:0% +coefficients +gamma you know those X's they use for + + align:start position:0% +gamma you know those X's they use for + + + align:start position:0% +gamma you know those X's they use for +things like the rural population within + + align:start position:0% +things like the rural population within + + + align:start position:0% +things like the rural population within +five miles of the city the rural + + align:start position:0% +five miles of the city the rural + + + align:start position:0% +five miles of the city the rural +population within 10 miles of the city + + align:start position:0% +population within 10 miles of the city + + + align:start position:0% +population within 10 miles of the city +the growth rate of the population I + + align:start position:0% +the growth rate of the population I + + + align:start position:0% +the growth rate of the population I +forget what else goes in there but they + + align:start position:0% +forget what else goes in there but they + + + align:start position:0% +forget what else goes in there but they +have the actual population in the city + + align:start position:0% +have the actual population in the city + + + align:start position:0% +have the actual population in the city +plus some controls for nearby + + align:start position:0% +plus some controls for nearby + + + align:start position:0% +plus some controls for nearby +population um per consumer profits again + + align:start position:0% +population um per consumer profits again + + + align:start position:0% +population um per consumer profits again +the idea is that you would have per + + align:start position:0% +the idea is that you would have per + + + align:start position:0% +the idea is that you would have per +consumer profits Alpha One under a + + align:start position:0% +consumer profits Alpha One under a + + + align:start position:0% +consumer profits Alpha One under a +monopoly profits + + align:start position:0% +monopoly profits + + + align:start position:0% +monopoly profits +Alpha One + + align:start position:0% +Alpha One + + + align:start position:0% +Alpha One +Monopoly uh Alpha 2 would be duopoly + + align:start position:0% +Monopoly uh Alpha 2 would be duopoly + + + align:start position:0% +Monopoly uh Alpha 2 would be duopoly +profits alha three three + + align:start position:0% +profits alha three three + + + align:start position:0% +profits alha three three +firms but then you're going to have + + align:start position:0% +firms but then you're going to have + + + align:start position:0% +firms but then you're going to have +other variables that affect the + + align:start position:0% +other variables that affect the + + + align:start position:0% +other variables that affect the +profitability of a market those + + align:start position:0% +profitability of a market those + + + align:start position:0% +profitability of a market those +variables can include the per capita + + align:start position:0% +variables can include the per capita + + + align:start position:0% +variables can include the per capita +income in the city the age distribution + + align:start position:0% +income in the city the age distribution + + + align:start position:0% +income in the city the age distribution +maybe higher income cities you earn more + + align:start position:0% +maybe higher income cities you earn more + + + align:start position:0% +maybe higher income cities you earn more +profits per customer things like that um + + align:start position:0% +profits per customer things like that um + + + align:start position:0% +profits per customer things like that um +the fixed costs again it's mostly a + + align:start position:0% +the fixed costs again it's mostly a + + + align:start position:0% +the fixed costs again it's mostly a +fixed cost they do allow there to be + + align:start position:0% +fixed cost they do allow there to be + + + align:start position:0% +fixed cost they do allow there to be +co-variants that affect the fixed costs + + align:start position:0% +co-variants that affect the fixed costs + + + align:start position:0% +co-variants that affect the fixed costs +across cities so for instance cities + + align:start position:0% +across cities so for instance cities + + + align:start position:0% +across cities so for instance cities +that have more valuable agricultural + + align:start position:0% +that have more valuable agricultural + + + align:start position:0% +that have more valuable agricultural +land it may be more expensive to open up + + align:start position:0% +land it may be more expensive to open up + + + align:start position:0% +land it may be more expensive to open up +atire dealership than in places with + + align:start position:0% +atire dealership than in places with + + + align:start position:0% +atire dealership than in places with +cheaper agricultural land because the + + align:start position:0% +cheaper agricultural land because the + + + align:start position:0% +cheaper agricultural land because the +land that you need to buy in setad of + + align:start position:0% +land that you need to buy in setad of + + + align:start position:0% +land that you need to buy in setad of +your tire shop cost more so they allow + + align:start position:0% +your tire shop cost more so they allow + + + align:start position:0% +your tire shop cost more so they allow +the fixed cost to also vary with some + + align:start position:0% +the fixed cost to also vary with some + + + align:start position:0% +the fixed cost to also vary with some +co-variants + + align:start position:0% +co-variants + + + align:start position:0% +co-variants +um and then the basic thought is that so + + align:start position:0% +um and then the basic thought is that so + + + align:start position:0% +um and then the basic thought is that so +I have all these elements i' I've + + align:start position:0% +I have all these elements i' I've + + + align:start position:0% +I have all these elements i' I've +redefined SI pi and fi be there no + + align:start position:0% +redefined SI pi and fi be there no + + + align:start position:0% +redefined SI pi and fi be there no +variant and then my model + + align:start position:0% +variant and then my model + + + align:start position:0% +variant and then my model +is if there were n firms in the market + + align:start position:0% +is if there were n firms in the market + + + align:start position:0% +is if there were n firms in the market +the profits would be SI Over N Pi i n + + align:start position:0% +the profits would be SI Over N Pi i n + + + align:start position:0% +the profits would be SI Over N Pi i n +minus fi plus Epsilon I where Epsilon I + + align:start position:0% +minus fi plus Epsilon I where Epsilon I + + + align:start position:0% +minus fi plus Epsilon I where Epsilon I +is just the normally distributed random + + align:start position:0% +is just the normally distributed random + + + align:start position:0% +is just the normally distributed random +variable and so in this model when are + + align:start position:0% +variable and so in this model when are + + + align:start position:0% +variable and so in this model when are +we going to observe n firms we're going + + align:start position:0% +we going to observe n firms we're going + + + align:start position:0% +we going to observe n firms we're going +to observe n firms if um SI + + align:start position:0% +to observe n firms if um SI + + + align:start position:0% +to observe n firms if um SI +n sorry SI over n + + align:start position:0% +n sorry SI over n + + + align:start position:0% +n sorry SI over n +nus + + align:start position:0% +nus + + + align:start position:0% +nus +f i is greater than zero and Si i n + + + align:start position:0% +f i is greater than zero and Si i n + + + + align:start position:0% +f i is greater than zero and Si i n + +1 I I + 1us + + align:start position:0% +1 I I + 1us + + + align:start position:0% +1 I I + 1us +fi + + align:start position:0% + + + + align:start position:0% + +I okay so we have these two things that + + align:start position:0% +I okay so we have these two things that + + + align:start position:0% +I okay so we have these two things that +have to both be true for there to be + + align:start position:0% +have to both be true for there to be + + + align:start position:0% +have to both be true for there to be +exactly n firms in the market but you + + align:start position:0% +exactly n firms in the market but you + + + align:start position:0% +exactly n firms in the market but you +could write the first one as Epsilon is + + align:start position:0% +could write the first one as Epsilon is + + + align:start position:0% +could write the first one as Epsilon is +bigger than something and the second one + + align:start position:0% +bigger than something and the second one + + + align:start position:0% +bigger than something and the second one +is Epsilon is less than something so if + + align:start position:0% +is Epsilon is less than something so if + + + align:start position:0% +is Epsilon is less than something so if +you view Epsilon as a random variable + + align:start position:0% +you view Epsilon as a random variable + + + align:start position:0% +you view Epsilon as a random variable +here a random shop to fix + + align:start position:0% +here a random shop to fix + + + align:start position:0% +here a random shop to fix +costs we're going to observe n firms + + align:start position:0% +costs we're going to observe n firms + + + align:start position:0% +costs we're going to observe n firms +whenever Epsilon is in this interval + + align:start position:0% +whenever Epsilon is in this interval + + + align:start position:0% +whenever Epsilon is in this interval +it's between this and this and so you + + align:start position:0% +it's between this and this and so you + + + align:start position:0% +it's between this and this and so you +know given the param given all the data + + align:start position:0% +know given the param given all the data + + + align:start position:0% +know given the param given all the data +and the parameters um you can compute + + align:start position:0% +and the parameters um you can compute + + + align:start position:0% +and the parameters um you can compute +the likelihood of this as just the + + align:start position:0% +the likelihood of this as just the + + + align:start position:0% +the likelihood of this as just the +normal CDF evaluated at this point minus + + align:start position:0% +normal CDF evaluated at this point minus + + + align:start position:0% +normal CDF evaluated at this point minus +the normal CDF evaluated at this point + + align:start position:0% +the normal CDF evaluated at this point + + + align:start position:0% +the normal CDF evaluated at this point +and so then you can estimate all the + + align:start position:0% +and so then you can estimate all the + + + align:start position:0% +and so then you can estimate all the +parameters gamma beta Alpha + + align:start position:0% +parameters gamma beta Alpha + + + align:start position:0% +parameters gamma beta Alpha +Delta um + + align:start position:0% +Delta um + + + align:start position:0% +Delta um +gamma Lambda you can estimate all of + + align:start position:0% +gamma Lambda you can estimate all of + + + align:start position:0% +gamma Lambda you can estimate all of +those by um maximum likelihood and + + align:start position:0% +those by um maximum likelihood and + + + align:start position:0% +those by um maximum likelihood and +that's the sort of basic estimation + + align:start position:0% +that's the sort of basic estimation + + + align:start position:0% +that's the sort of basic estimation +technique in the paper you know people I + + align:start position:0% +technique in the paper you know people I + + + align:start position:0% +technique in the paper you know people I +know we still teach ordered probit + + align:start position:0% +know we still teach ordered probit + + + align:start position:0% +know we still teach ordered probit +models in econometrics this what people + + align:start position:0% +models in econometrics this what people + + + align:start position:0% +models in econometrics this what people +refer to as ordered probate model where + + align:start position:0% +refer to as ordered probate model where + + + align:start position:0% +refer to as ordered probate model where +you have discrete data produced by you + + align:start position:0% +you have discrete data produced by you + + + align:start position:0% +you have discrete data produced by you +know the discritization of something + + align:start position:0% +know the discritization of something + + + align:start position:0% +know the discritization of something +that has a normal error in + + align:start position:0% + + + + align:start position:0% + +it and obviously you know the main + + align:start position:0% +it and obviously you know the main + + + align:start position:0% +it and obviously you know the main +things of interest here coming out of + + align:start position:0% +things of interest here coming out of + + + align:start position:0% +things of interest here coming out of +this estimation are alpha one you know + + align:start position:0% +this estimation are alpha one you know + + + align:start position:0% +this estimation are alpha one you know +these were the objects interest what is + + align:start position:0% +these were the objects interest what is + + + align:start position:0% +these were the objects interest what is +the per customer profits under + + align:start position:0% + + + + align:start position:0% + +Monopoly what are the per customer + + align:start position:0% +Monopoly what are the per customer + + + align:start position:0% +Monopoly what are the per customer +profits under Monopoly duopoly whatever + + align:start position:0% +profits under Monopoly duopoly whatever + + + align:start position:0% +profits under Monopoly duopoly whatever +but somehow in the paper you know like + + align:start position:0% +but somehow in the paper you know like + + + align:start position:0% +but somehow in the paper you know like +they they really like the idea of the s + + align:start position:0% +they they really like the idea of the s + + + align:start position:0% +they they really like the idea of the s +as the thresholds and so they basically + + align:start position:0% +as the thresholds and so they basically + + + align:start position:0% +as the thresholds and so they basically +estimate these things and then they + + align:start position:0% +estimate these things and then they + + + align:start position:0% +estimate these things and then they +convert from all the They convert from + + align:start position:0% +convert from all the They convert from + + + align:start position:0% +convert from all the They convert from +all the parameters back to what is the + + align:start position:0% +all the parameters back to what is the + + + align:start position:0% +all the parameters back to what is the +mean S1 s mean S2 mean S3 holding all + + align:start position:0% +mean S1 s mean S2 mean S3 holding all + + + align:start position:0% +mean S1 s mean S2 mean S3 holding all +the covariates that their sample means + + align:start position:0% +the covariates that their sample means + + + align:start position:0% +the covariates that their sample means +uh and then they sort of do a lot of the + + align:start position:0% +uh and then they sort of do a lot of the + + + align:start position:0% +uh and then they sort of do a lot of the +presentation just talking about what are + + align:start position:0% +presentation just talking about what are + + + align:start position:0% +presentation just talking about what are +the + + align:start position:0% + + + + align:start position:0% + +s's okay anyway so data sample as I said + + align:start position:0% +s's okay anyway so data sample as I said + + + align:start position:0% +s's okay anyway so data sample as I said +they've got data on a whole bunch of + + align:start position:0% +they've got data on a whole bunch of + + + align:start position:0% +they've got data on a whole bunch of +businesses um gathered from 20 two small + + align:start position:0% +businesses um gathered from 20 two small + + + align:start position:0% +businesses um gathered from 20 two small +towns in the western us these are small + + align:start position:0% +towns in the western us these are small + + + align:start position:0% +towns in the western us these are small +places the mean population is + + align:start position:0% +places the mean population is + + + align:start position:0% +places the mean population is +3,740 uh and as I said they're all at + + align:start position:0% +3,740 uh and as I said they're all at + + + align:start position:0% +3,740 uh and as I said they're all at +least 20 miles away from any place that + + align:start position:0% +least 20 miles away from any place that + + + align:start position:0% +least 20 miles away from any place that +has a thousand people in + + align:start position:0% + + + + align:start position:0% + +it college with a guy from Wyoming uh + + align:start position:0% +it college with a guy from Wyoming uh + + + align:start position:0% +it college with a guy from Wyoming uh +who said he was 90 miles from the + + align:start position:0% +who said he was 90 miles from the + + + align:start position:0% +who said he was 90 miles from the +nearest movie + + align:start position:0% +nearest movie + + + align:start position:0% +nearest movie +theater so there parts of the United + + align:start position:0% +theater so there parts of the United + + + align:start position:0% +theater so there parts of the United +States they're already back + + align:start position:0% +States they're already back + + + align:start position:0% +States they're already back +um okay here is the + + align:start position:0% +um okay here is the + + + align:start position:0% +um okay here is the +data sample showing the full set of uh + + align:start position:0% +data sample showing the full set of uh + + + align:start position:0% +data sample showing the full set of uh +full set of occupation or businesses + + align:start position:0% +full set of occupation or businesses + + + align:start position:0% +full set of occupation or businesses +they started with and the number of + + align:start position:0% +they started with and the number of + + + align:start position:0% +they started with and the number of +firms they get um they end up focusing + + align:start position:0% +firms they get um they end up focusing + + + align:start position:0% +firms they get um they end up focusing +on the ones on the top part of the table + + align:start position:0% +on the ones on the top part of the table + + + align:start position:0% +on the ones on the top part of the table +there are some paper some results in the + + align:start position:0% +there are some paper some results in the + + + align:start position:0% +there are some paper some results in the +papers about things farther down on the + + align:start position:0% +papers about things farther down on the + + + align:start position:0% +papers about things farther down on the +paper but you know what they wanted in + + align:start position:0% +paper but you know what they wanted in + + + align:start position:0% +paper but you know what they wanted in +some sense if you want to talk about how + + align:start position:0% +some sense if you want to talk about how + + + align:start position:0% +some sense if you want to talk about how +the competition changes with a number of + + align:start position:0% +the competition changes with a number of + + + align:start position:0% +the competition changes with a number of +firms you want there to be a significant + + align:start position:0% +firms you want there to be a significant + + + align:start position:0% +firms you want there to be a significant +number of cities that have zero firms + + align:start position:0% +number of cities that have zero firms + + + align:start position:0% +number of cities that have zero firms +one two three four or whatever and a lot + + align:start position:0% +one two three four or whatever and a lot + + + align:start position:0% +one two three four or whatever and a lot +of these businesses it turns out you + + align:start position:0% +of these businesses it turns out you + + + align:start position:0% +of these businesses it turns out you +never get you know a lot of these + + align:start position:0% +never get you know a lot of these + + + align:start position:0% +never get you know a lot of these +businesses are apparently two big + + align:start position:0% +businesses are apparently two big + + + align:start position:0% +businesses are apparently two big +businesses have many of them in in the + + align:start position:0% +businesses have many of them in in the + + + align:start position:0% +businesses have many of them in in the +towns that they're working with uh so + + align:start position:0% +towns that they're working with uh so + + + align:start position:0% +towns that they're working with uh so +they don't get much Beyond n equals to + + align:start position:0% +they don't get much Beyond n equals to + + + align:start position:0% +they don't get much Beyond n equals to +but if you look at the the druggists I + + align:start position:0% +but if you look at the the druggists I + + + align:start position:0% +but if you look at the the druggists I +assume this means pharmacies um you know + + align:start position:0% +assume this means pharmacies um you know + + + align:start position:0% +assume this means pharmacies um you know +they're very they're relatively rare to + + align:start position:0% +they're very they're relatively rare to + + + align:start position:0% +they're very they're relatively rare to +have no no Pharmacy but then you do get + + align:start position:0% +have no no Pharmacy but then you do get + + + align:start position:0% +have no no Pharmacy but then you do get +one two three and some fours and fives + + align:start position:0% +one two three and some fours and fives + + + align:start position:0% +one two three and some fours and fives +and Beyond um same things with the + + align:start position:0% +and Beyond um same things with the + + + align:start position:0% +and Beyond um same things with the +doctors dentist pumers tired is you some + + align:start position:0% +doctors dentist pumers tired is you some + + + align:start position:0% +doctors dentist pumers tired is you some +sense they focus on these because they + + align:start position:0% +sense they focus on these because they + + + align:start position:0% +sense they focus on these because they +all have at least some number of markets + + align:start position:0% +all have at least some number of markets + + + align:start position:0% +all have at least some number of markets +with three and some number of markets + + align:start position:0% +with three and some number of markets + + + align:start position:0% +with three and some number of markets +with + + align:start position:0% +with + + + align:start position:0% +with +four there was also sort of a question + + align:start position:0% +four there was also sort of a question + + + align:start position:0% +four there was also sort of a question +of how well defined are these markets + + align:start position:0% +of how well defined are these markets + + + align:start position:0% +of how well defined are these markets +you know like the um some of these + + align:start position:0% +you know like the um some of these + + + align:start position:0% +you know like the um some of these +things like The Barbers or whatever you + + align:start position:0% +things like The Barbers or whatever you + + + align:start position:0% +things like The Barbers or whatever you +know people who are not Barbers can cut + + align:start position:0% +know people who are not Barbers can cut + + + align:start position:0% +know people who are not Barbers can cut +people's hair and so there sort of it + + align:start position:0% +people's hair and so there sort of it + + + align:start position:0% +people's hair and so there sort of it +gets harder to count how many Barbers or + + align:start position:0% +gets harder to count how many Barbers or + + + align:start position:0% +gets harder to count how many Barbers or +beauticians there are in a town because + + align:start position:0% +beauticians there are in a town because + + + align:start position:0% +beauticians there are in a town because +it's just somebody who works somewhere + + align:start position:0% +it's just somebody who works somewhere + + + align:start position:0% +it's just somebody who works somewhere +else also Cuts Hair people know they can + + align:start position:0% +else also Cuts Hair people know they can + + + align:start position:0% +else also Cuts Hair people know they can +go to that person or whatever so hard to + + align:start position:0% +go to that person or whatever so hard to + + + align:start position:0% +go to that person or whatever so hard to +you know whereas things like um dentists + + align:start position:0% +you know whereas things like um dentists + + + align:start position:0% +you know whereas things like um dentists +are I guess are easier to identify that + + align:start position:0% +are I guess are easier to identify that + + + align:start position:0% +are I guess are easier to identify that +someone is a dentist if you don't get + + align:start position:0% +someone is a dentist if you don't get + + + align:start position:0% +someone is a dentist if you don't get +just guys who come up with drill holes + + align:start position:0% +just guys who come up with drill holes + + + align:start position:0% +just guys who come up with drill holes +in your teeth weekends + + align:start position:0% +in your teeth weekends + + + align:start position:0% +in your teeth weekends +um uh okay um so what are the entry + + align:start position:0% +um uh okay um so what are the entry + + + align:start position:0% +um uh okay um so what are the entry +thresholds look like + + align:start position:0% +thresholds look like + + + align:start position:0% +thresholds look like +so again the numbers I put up on the + + align:start position:0% +so again the numbers I put up on the + + + align:start position:0% +so again the numbers I put up on the +board over there are um most of these + + align:start position:0% +board over there are um most of these + + + align:start position:0% +board over there are um most of these +businesses tend to start to exist in + + align:start position:0% +businesses tend to start to exist in + + + align:start position:0% +businesses tend to start to exist in +towns when they have fewer than a + + align:start position:0% +towns when they have fewer than a + + + align:start position:0% +towns when they have fewer than a +thousand people + + align:start position:0% +thousand people + + + align:start position:0% +thousand people +um so the doctors the cut off is 880 + + align:start position:0% +um so the doctors the cut off is 880 + + + align:start position:0% +um so the doctors the cut off is 880 +people the dentists the cut off is 710 + + align:start position:0% +people the dentists the cut off is 710 + + + align:start position:0% +people the dentists the cut off is 710 +people far the druggist it's 530 people + + align:start position:0% +people far the druggist it's 530 people + + + align:start position:0% +people far the druggist it's 530 people +the tire dealers is + + align:start position:0% +the tire dealers is + + + align:start position:0% +the tire dealers is +490 people you need to be bigger to have + + align:start position:0% +490 people you need to be bigger to have + + + align:start position:0% +490 people you need to be bigger to have +a plumber that's over 1,400 people + + align:start position:0% +a plumber that's over 1,400 people + + + align:start position:0% +a plumber that's over 1,400 people +um but then you know if if you look at + + align:start position:0% +um but then you know if if you look at + + + align:start position:0% +um but then you know if if you look at +let's like just look at the the + + align:start position:0% +let's like just look at the the + + + align:start position:0% +let's like just look at the the +druggists um this one of the most Stark + + align:start position:0% +druggists um this one of the most Stark + + + align:start position:0% +druggists um this one of the most Stark +examples it seems like you need 500 + + align:start position:0% +examples it seems like you need 500 + + + align:start position:0% +examples it seems like you need 500 +people to have one uh you need 2,000 + + align:start position:0% +people to have one uh you need 2,000 + + + align:start position:0% +people to have one uh you need 2,000 +people to have two so that's when you + + align:start position:0% +people to have two so that's when you + + + align:start position:0% +people to have two so that's when you +have a thousand customers per per + + align:start position:0% +have a thousand customers per per + + + align:start position:0% +have a thousand customers per per +drugstore um to have three you need + + align:start position:0% +drugstore um to have three you need + + + align:start position:0% +drugstore um to have three you need +5,000 so that's like 16600 people per + + align:start position:0% +5,000 so that's like 16600 people per + + + align:start position:0% +5,000 so that's like 16600 people per +druggist um and you know they put the + + align:start position:0% +druggist um and you know they put the + + + align:start position:0% +druggist um and you know they put the +ratios over here make it + + align:start position:0% +ratios over here make it + + + align:start position:0% +ratios over here make it +clear like the S2 over S1 ratio this is + + align:start position:0% +clear like the S2 over S1 ratio this is + + + align:start position:0% +clear like the S2 over S1 ratio this is +you know how many customers per firm you + + align:start position:0% +you know how many customers per firm you + + + align:start position:0% +you know how many customers per firm you +need to have to have so this is this is + + align:start position:0% +need to have to have so this is this is + + + align:start position:0% +need to have to have so this is this is +you they + + align:start position:0% +you they + + + align:start position:0% +you they +use little SN to be Capital SN n which + + align:start position:0% +use little SN to be Capital SN n which + + + align:start position:0% +use little SN to be Capital SN n which +is always tough for when you're putting + + align:start position:0% +is always tough for when you're putting + + + align:start position:0% +is always tough for when you're putting +things on slides that are small so + + align:start position:0% +things on slides that are small so + + + align:start position:0% +things on slides that are small so +anyway these are these are the ratio of + + align:start position:0% +anyway these are these are the ratio of + + + align:start position:0% +anyway these are these are the ratio of +the per + + align:start position:0% +the per + + + align:start position:0% +the per +customer uh the per firm number of + + align:start position:0% +customer uh the per firm number of + + + align:start position:0% +customer uh the per firm number of +customers which you can think of as this + + align:start position:0% +customers which you can think of as this + + + align:start position:0% +customers which you can think of as this +is the thing that's supposed to estimate + + align:start position:0% +is the thing that's supposed to estimate + + + align:start position:0% +is the thing that's supposed to estimate +pi over pi plus one so this is supposed + + align:start position:0% +pi over pi plus one so this is supposed + + + align:start position:0% +pi over pi plus one so this is supposed +to be um uh Pi 1 over Pi 2 and so what + + align:start position:0% +to be um uh Pi 1 over Pi 2 and so what + + + align:start position:0% +to be um uh Pi 1 over Pi 2 and so what +this is saying is that in many of these + + align:start position:0% +this is saying is that in many of these + + + align:start position:0% +this is saying is that in many of these +industries profits are dropping almost + + align:start position:0% +industries profits are dropping almost + + + align:start position:0% +industries profits are dropping almost +in half when you have have when you have + + align:start position:0% +in half when you have have when you have + + + align:start position:0% +in half when you have have when you have +a second firm or per customer profits + + align:start position:0% +a second firm or per customer profits + + + align:start position:0% +a second firm or per customer profits +dropping almost in half it's like you + + align:start position:0% +dropping almost in half it's like you + + + align:start position:0% +dropping almost in half it's like you +know profits divide you divide it by + + align:start position:0% +know profits divide you divide it by + + + align:start position:0% +know profits divide you divide it by +either 1.9 or by 1.8 that's like a 45 + + align:start position:0% +either 1.9 or by 1.8 that's like a 45 + + + align:start position:0% +either 1.9 or by 1.8 that's like a 45 +50% drop in profit from the second firm + + align:start position:0% +50% drop in profit from the second firm + + + align:start position:0% +50% drop in profit from the second firm +comes in uh the one exception appears to + + align:start position:0% +comes in uh the one exception appears to + + + align:start position:0% +comes in uh the one exception appears to +be plumers where we don't get the first + + align:start position:0% +be plumers where we don't get the first + + + align:start position:0% +be plumers where we don't get the first +pummer for a while and so it seems that + + align:start position:0% +pummer for a while and so it seems that + + + align:start position:0% +pummer for a while and so it seems that +you know the second pummer is also + + align:start position:0% +you know the second pummer is also + + + align:start position:0% +you know the second pummer is also +serving 15 you know like you get one + + align:start position:0% +serving 15 you know like you get one + + + align:start position:0% +serving 15 you know like you get one +pummer when you have, 1400 people for + + align:start position:0% +pummer when you have, 1400 people for + + + align:start position:0% +pummer when you have, 1400 people for +the pummer deserve a second P you have + + align:start position:0% +the pummer deserve a second P you have + + + align:start position:0% +the pummer deserve a second P you have +1500 um + + align:start position:0% +1500 um + + + align:start position:0% +1500 um +if you look at what happens when you go + + align:start position:0% +if you look at what happens when you go + + + align:start position:0% +if you look at what happens when you go +so one firm to two it's a big drop in + + align:start position:0% +so one firm to two it's a big drop in + + + align:start position:0% +so one firm to two it's a big drop in +profit when you go from two firms to + + align:start position:0% +profit when you go from two firms to + + + align:start position:0% +profit when you go from two firms to +three it varies by industry but most of + + align:start position:0% +three it varies by industry but most of + + + align:start position:0% +three it varies by industry but most of +them other than the plumbers you know we + + align:start position:0% +them other than the plumbers you know we + + + align:start position:0% +them other than the plumbers you know we +have a a 1 point you know 10% drop 30% + + align:start position:0% +have a a 1 point you know 10% drop 30% + + + align:start position:0% +have a a 1 point you know 10% drop 30% +drop 60% drop or whatever so it it again + + align:start position:0% +drop 60% drop or whatever so it it again + + + align:start position:0% +drop 60% drop or whatever so it it again +is a one over 1.6 + + align:start position:0% +is a one over 1.6 + + + align:start position:0% +is a one over 1.6 +so you know again you get sort of + + align:start position:0% +so you know again you get sort of + + + align:start position:0% +so you know again you get sort of +substantial drops often going from two + + align:start position:0% +substantial drops often going from two + + + align:start position:0% +substantial drops often going from two +to three um by the time you're out here + + align:start position:0% +to three um by the time you're out here + + + align:start position:0% +to three um by the time you're out here +though the S5 over S4 numbers here it + + align:start position:0% +though the S5 over S4 numbers here it + + + align:start position:0% +though the S5 over S4 numbers here it +seems like competition whatever + + align:start position:0% +seems like competition whatever + + + align:start position:0% +seems like competition whatever +competition you're going to get is all + + align:start position:0% +competition you're going to get is all + + + align:start position:0% +competition you're going to get is all +done by the time you have four firms + + align:start position:0% +done by the time you have four firms + + + align:start position:0% +done by the time you have four firms +like four firms are getting you just as + + align:start position:0% +like four firms are getting you just as + + + align:start position:0% +like four firms are getting you just as +much competition as five firms is G is + + align:start position:0% +much competition as five firms is G is + + + align:start position:0% +much competition as five firms is G is +giving you um so the conclusion here of + + align:start position:0% +giving you um so the conclusion here of + + + align:start position:0% +giving you um so the conclusion here of +how you know basics of competition seems + + align:start position:0% +how you know basics of competition seems + + + align:start position:0% +how you know basics of competition seems +to work is there's a big difference + + align:start position:0% +to work is there's a big difference + + + align:start position:0% +to work is there's a big difference +between Monopoly and two firms it seems + + align:start position:0% +between Monopoly and two firms it seems + + + align:start position:0% +between Monopoly and two firms it seems +like prices keep going down from two to + + align:start position:0% +like prices keep going down from two to + + + align:start position:0% +like prices keep going down from two to +three and then it seems like we asmt + + align:start position:0% +three and then it seems like we asmt + + + align:start position:0% +three and then it seems like we asmt +pretty quickly um to things are not + + align:start position:0% +pretty quickly um to things are not + + + align:start position:0% +pretty quickly um to things are not +getting any any more + + align:start position:0% + + + + align:start position:0% + +competitive + + align:start position:0% + + + + align:start position:0% + +questions okay I mean I think it's a + + align:start position:0% +questions okay I mean I think it's a + + + align:start position:0% +questions okay I mean I think it's a +it's a you know a fantastic paper and + + align:start position:0% +it's a you know a fantastic paper and + + + align:start position:0% +it's a you know a fantastic paper and +that this idea of Entry telling us about + + align:start position:0% +that this idea of Entry telling us about + + + align:start position:0% +that this idea of Entry telling us about +profit levels and that being an + + align:start position:0% +profit levels and that being an + + + align:start position:0% +profit levels and that being an +optimality condition we can use has just + + align:start position:0% +optimality condition we can use has just + + + align:start position:0% +optimality condition we can use has just +been tremendously + + align:start position:0% +been tremendously + + + align:start position:0% +been tremendously +influential as far as the applied + + align:start position:0% +influential as far as the applied + + + align:start position:0% +influential as far as the applied +results going I would sort of say the + + align:start position:0% +results going I would sort of say the + + + align:start position:0% +results going I would sort of say the +biggest difficulty with this about with + + align:start position:0% +biggest difficulty with this about with + + + align:start position:0% +biggest difficulty with this about with +regard to this is an applied result is + + align:start position:0% +regard to this is an applied result is + + + align:start position:0% +regard to this is an applied result is +you know this model was interpreting + + align:start position:0% +you know this model was interpreting + + + align:start position:0% +you know this model was interpreting +what we're seeing as the equilibrium end + + align:start position:0% +what we're seeing as the equilibrium end + + + align:start position:0% +what we're seeing as the equilibrium end +star of this + + align:start position:0% +star of this + + + align:start position:0% +star of this +game so the equili end star of that game + + align:start position:0% +game so the equili end star of that game + + + align:start position:0% +game so the equili end star of that game +implies in part that everybody who's + + align:start position:0% +implies in part that everybody who's + + + align:start position:0% +implies in part that everybody who's +there is happy they're there and + + align:start position:0% +there is happy they're there and + + + align:start position:0% +there is happy they're there and +everyone who's not there is happy + + align:start position:0% +everyone who's not there is happy + + + align:start position:0% +everyone who's not there is happy +they're not there I think the happy + + align:start position:0% +they're not there I think the happy + + + align:start position:0% +they're not there I think the happy +they're not there part I'm very H I'm + + align:start position:0% +they're not there part I'm very H I'm + + + align:start position:0% +they're not there part I'm very H I'm +very I think is very clear the question + + align:start position:0% +very I think is very clear the question + + + align:start position:0% +very I think is very clear the question +is what do we make of all these doctors + + align:start position:0% +is what do we make of all these doctors + + + align:start position:0% +is what do we make of all these doctors +in counts of 800 people + + align:start position:0% +in counts of 800 people + + + align:start position:0% +in counts of 800 people +is the doctor in the town of 800 people + + align:start position:0% +is the doctor in the town of 800 people + + + align:start position:0% +is the doctor in the town of 800 people +because the doctor is Happy serving 800 + + align:start position:0% +because the doctor is Happy serving 800 + + + align:start position:0% +because the doctor is Happy serving 800 +patients or is the doctor in the town of + + align:start position:0% +patients or is the doctor in the town of + + + align:start position:0% +patients or is the doctor in the town of +800 people because it was a town of 1500 + + align:start position:0% +800 people because it was a town of 1500 + + + align:start position:0% +800 people because it was a town of 1500 +people in a thriving farming town in the + + align:start position:0% +people in a thriving farming town in the + + + align:start position:0% +people in a thriving farming town in the +1950s when the doctor moved there and + + align:start position:0% +1950s when the doctor moved there and + + + align:start position:0% +1950s when the doctor moved there and +the doctor is now 75 years old and + + align:start position:0% +the doctor is now 75 years old and + + + align:start position:0% +the doctor is now 75 years old and +doesn't want to leave the patients the + + align:start position:0% +doesn't want to leave the patients the + + + align:start position:0% +doesn't want to leave the patients the +doctor has had for 40 years even though + + align:start position:0% +doctor has had for 40 years even though + + + align:start position:0% +doctor has had for 40 years even though +the number of patients is dwindling + + align:start position:0% +the number of patients is dwindling + + + align:start position:0% +the number of patients is dwindling +relative to what it was when the doctor + + align:start position:0% +relative to what it was when the doctor + + + align:start position:0% +relative to what it was when the doctor +got there um and you know if you think + + align:start position:0% +got there um and you know if you think + + + align:start position:0% +got there um and you know if you think +about it right if there's this sort of + + align:start position:0% +about it right if there's this sort of + + + align:start position:0% +about it right if there's this sort of +you pay this sunk cost to enter and you + + align:start position:0% +you pay this sunk cost to enter and you + + + align:start position:0% +you pay this sunk cost to enter and you +don't get your sunk cost back when you + + align:start position:0% +don't get your sunk cost back when you + + + align:start position:0% +don't get your sunk cost back when you +leave it could be that people enter you + + align:start position:0% +leave it could be that people enter you + + + align:start position:0% +leave it could be that people enter you +know the entry the things that we're + + align:start position:0% +know the entry the things that we're + + + align:start position:0% +know the entry the things that we're +seeing are not entry thresholds they're + + align:start position:0% +seeing are not entry thresholds they're + + + align:start position:0% +seeing are not entry thresholds they're +sort of exit we're seeing like ENT exit + + align:start position:0% +sort of exit we're seeing like ENT exit + + + align:start position:0% +sort of exit we're seeing like ENT exit +thresholds um and the exit thresholds + + align:start position:0% +thresholds um and the exit thresholds + + + align:start position:0% +thresholds um and the exit thresholds +might not be sort of re counting all fix + + align:start position:0% +might not be sort of re counting all fix + + + align:start position:0% +might not be sort of re counting all fix +costs um you another potential issue is + + align:start position:0% +costs um you another potential issue is + + + align:start position:0% +costs um you another potential issue is +just that you know counting firms is + + align:start position:0% +just that you know counting firms is + + + align:start position:0% +just that you know counting firms is +more difficult in their application than + + align:start position:0% +more difficult in their application than + + + align:start position:0% +more difficult in their application than +in other you know how do you count + + align:start position:0% +in other you know how do you count + + + align:start position:0% +in other you know how do you count +someone who does some plumming on the + + align:start position:0% +someone who does some plumming on the + + + align:start position:0% +someone who does some plumming on the +side or someone who does some hair + + align:start position:0% +side or someone who does some hair + + + align:start position:0% +side or someone who does some hair +cutting so you know I think the ones in + + align:start position:0% +cutting so you know I think the ones in + + + align:start position:0% +cutting so you know I think the ones in +the licensed professions like the + + align:start position:0% +the licensed professions like the + + + align:start position:0% +the licensed professions like the +dentists and doctors are probably better + + align:start position:0% +dentists and doctors are probably better + + + align:start position:0% +dentists and doctors are probably better +with that but you know the ones that are + + align:start position:0% +with that but you know the ones that are + + + align:start position:0% +with that but you know the ones that are +more like the businesses we normally + + align:start position:0% +more like the businesses we normally + + + align:start position:0% +more like the businesses we normally +think about price competition operating + + align:start position:0% +think about price competition operating + + + align:start position:0% +think about price competition operating +in some of those have this issue of it's + + align:start position:0% +in some of those have this issue of it's + + + align:start position:0% +in some of those have this issue of it's +going to be hard to ident it's going to + + align:start position:0% +going to be hard to ident it's going to + + + align:start position:0% +going to be hard to ident it's going to +be hard to identify businesses be sure + + align:start position:0% +be hard to identify businesses be sure + + + align:start position:0% +be hard to identify businesses be sure +that we're we're for instance the result + + align:start position:0% +that we're we're for instance the result + + + align:start position:0% +that we're we're for instance the result +on pumers could be + + align:start position:0% +on pumers could be + + + align:start position:0% +on pumers could be +that you don't get a lot of Market power + + align:start position:0% +that you don't get a lot of Market power + + + align:start position:0% +that you don't get a lot of Market power +with one pummer because there's always + + align:start position:0% +with one pummer because there's always + + + align:start position:0% +with one pummer because there's always +somebody else in count who you can call + + align:start position:0% +somebody else in count who you can call + + + align:start position:0% +somebody else in count who you can call +who just owns wrenches and can come over + + align:start position:0% +who just owns wrenches and can come over + + + align:start position:0% +who just owns wrenches and can come over +and fix stuff for you even if they're + + align:start position:0% +and fix stuff for you even if they're + + + align:start position:0% +and fix stuff for you even if they're +not officially + + align:start position:0% + + + + align:start position:0% + +public + + align:start position:0% + + + + align:start position:0% + +questions okay so you next I wanted to + + align:start position:0% +questions okay so you next I wanted to + + + align:start position:0% +questions okay so you next I wanted to +go to was uh bar wall um so this is you + + align:start position:0% +go to was uh bar wall um so this is you + + + align:start position:0% +go to was uh bar wall um so this is you +know very much following up on this sort + + align:start position:0% +know very much following up on this sort + + + align:start position:0% +know very much following up on this sort +of theory of efficiency of Entry I did + + align:start position:0% +of theory of efficiency of Entry I did + + + align:start position:0% +of theory of efficiency of Entry I did +last class and so you know as I said + + align:start position:0% +last class and so you know as I said + + + align:start position:0% +last class and so you know as I said +there are reasons why entry is going to + + align:start position:0% +there are reasons why entry is going to + + + align:start position:0% +there are reasons why entry is going to +be higher or lower than we would like it + + align:start position:0% +be higher or lower than we would like it + + + align:start position:0% +be higher or lower than we would like it +to be and bar and W are trying to say + + align:start position:0% +to be and bar and W are trying to say + + + align:start position:0% +to be and bar and W are trying to say +let's pick an industry let's say in this + + align:start position:0% +let's pick an industry let's say in this + + + align:start position:0% +let's pick an industry let's say in this +industry how does it work out are there + + align:start position:0% +industry how does it work out are there + + + align:start position:0% +industry how does it work out are there +more firms that we would like or fewer + + align:start position:0% +more firms that we would like or fewer + + + align:start position:0% +more firms that we would like or fewer +firms how big are the welfare losses + + align:start position:0% +firms how big are the welfare losses + + + align:start position:0% +firms how big are the welfare losses +from the number of firms that we observe + + align:start position:0% +from the number of firms that we observe + + + align:start position:0% +from the number of firms that we observe +uh the industry that they pick is + + align:start position:0% +uh the industry that they pick is + + + align:start position:0% +uh the industry that they pick is +um uh commercial radio and you know I + + align:start position:0% +um uh commercial radio and you know I + + + align:start position:0% +um uh commercial radio and you know I +think the argument is that there's you + + align:start position:0% +think the argument is that there's you + + + align:start position:0% +think the argument is that there's you +know you need a license to you need a + + align:start position:0% +know you need a license to you need a + + + align:start position:0% +know you need a license to you need a +license to sort of open a radio station + + align:start position:0% +license to sort of open a radio station + + + align:start position:0% +license to sort of open a radio station +there are some places where you might + + align:start position:0% +there are some places where you might + + + align:start position:0% +there are some places where you might +where there's a you know you can't open + + align:start position:0% +where there's a you know you can't open + + + align:start position:0% +where there's a you know you can't open +a radio station and broadcast on any + + align:start position:0% +a radio station and broadcast on any + + + align:start position:0% +a radio station and broadcast on any +band because you'd be interfering with + + align:start position:0% +band because you'd be interfering with + + + align:start position:0% +band because you'd be interfering with +the stations right around you but in + + align:start position:0% +the stations right around you but in + + + align:start position:0% +the stations right around you but in +most cities in the United States there + + align:start position:0% +most cities in the United States there + + + align:start position:0% +most cities in the United States there +are bands that are available you know + + align:start position:0% +are bands that are available you know + + + align:start position:0% +are bands that are available you know +there's obviously a fixed cost of + + align:start position:0% +there's obviously a fixed cost of + + + align:start position:0% +there's obviously a fixed cost of +applying for the government license and + + align:start position:0% +applying for the government license and + + + align:start position:0% +applying for the government license and +opening up and just putting up a + + align:start position:0% +opening up and just putting up a + + + align:start position:0% +opening up and just putting up a +transmission tower but that's fine you + + align:start position:0% +transmission tower but that's fine you + + + align:start position:0% +transmission tower but that's fine you +know that's exactly all the F uh and so + + align:start position:0% +know that's exactly all the F uh and so + + + align:start position:0% +know that's exactly all the F uh and so +this is an example of an industry where + + align:start position:0% +this is an example of an industry where + + + align:start position:0% +this is an example of an industry where +we think there is a substantial F + + align:start position:0% +we think there is a substantial F + + + align:start position:0% +we think there is a substantial F +because to have a radio station you need + + align:start position:0% +because to have a radio station you need + + + align:start position:0% +because to have a radio station you need +equipment you need people there um but + + align:start position:0% +equipment you need people there um but + + + align:start position:0% +equipment you need people there um but +then we can think about how how are the + + align:start position:0% +then we can think about how how are the + + + align:start position:0% +then we can think about how how are the +is a price is affected um now you know + + align:start position:0% +is a price is affected um now you know + + + align:start position:0% +is a price is affected um now you know +Radio is free so in some sense the price + + align:start position:0% +Radio is free so in some sense the price + + + align:start position:0% +Radio is free so in some sense the price +you're used to think about for radio is + + align:start position:0% +you're used to think about for radio is + + + align:start position:0% +you're used to think about for radio is +zero um but you know radio is a platform + + align:start position:0% +zero um but you know radio is a platform + + + align:start position:0% +zero um but you know radio is a platform +market so there are two types of + + align:start position:0% +market so there are two types of + + + align:start position:0% +market so there are two types of +customers of radio stations there are + + align:start position:0% +customers of radio stations there are + + + align:start position:0% +customers of radio stations there are +listeners who different pay zero to + + align:start position:0% +listeners who different pay zero to + + + align:start position:0% +listeners who different pay zero to +listen but then there are advertisers + + align:start position:0% +listen but then there are advertisers + + + align:start position:0% +listen but then there are advertisers +who pay money to put commercials on and + + align:start position:0% +who pay money to put commercials on and + + + align:start position:0% +who pay money to put commercials on and +so the standard way that you know + + align:start position:0% +so the standard way that you know + + + align:start position:0% +so the standard way that you know +because the price is free the standard + + align:start position:0% +because the price is free the standard + + + align:start position:0% +because the price is free the standard +way that like the FTC or antitrust + + align:start position:0% +way that like the FTC or antitrust + + + align:start position:0% +way that like the FTC or antitrust +Regulators tend creete radio is to focus + + align:start position:0% +Regulators tend creete radio is to focus + + + align:start position:0% +Regulators tend creete radio is to focus +on the business of producing advertising + + align:start position:0% +on the business of producing advertising + + + align:start position:0% +on the business of producing advertising +so they think of as a radio station is a + + align:start position:0% +so they think of as a radio station is a + + + align:start position:0% +so they think of as a radio station is a +they have this technology where they buy + + align:start position:0% +they have this technology where they buy + + + align:start position:0% +they have this technology where they buy +rights to music they play that music + + align:start position:0% +rights to music they play that music + + + align:start position:0% +rights to music they play that music +that music produces ears to people and + + align:start position:0% +that music produces ears to people and + + + align:start position:0% +that music produces ears to people and +then they they sell those ears of people + + align:start position:0% +then they they sell those ears of people + + + align:start position:0% +then they they sell those ears of people +to advertisers want to advertise to them + + align:start position:0% +to advertisers want to advertise to them + + + align:start position:0% +to advertisers want to advertise to them +so when we're thinking about price in + + align:start position:0% +so when we're thinking about price in + + + align:start position:0% +so when we're thinking about price in +this market we should be thinking about + + align:start position:0% +this market we should be thinking about + + + align:start position:0% +this market we should be thinking about +price of advertisers or the price of you + + align:start position:0% +price of advertisers or the price of you + + + align:start position:0% +price of advertisers or the price of you +know think of the price as the price of + + align:start position:0% +know think of the price as the price of + + + align:start position:0% +know think of the price as the price of +a listener and think of the firms as + + align:start position:0% +a listener and think of the firms as + + + align:start position:0% +a listener and think of the firms as +having a technology for producing + + align:start position:0% +having a technology for producing + + + align:start position:0% +having a technology for producing +listeners so there technology for + + align:start position:0% +listeners so there technology for + + + align:start position:0% +listeners so there technology for +producing listeners involves something + + align:start position:0% +producing listeners involves something + + + align:start position:0% +producing listeners involves something +about radio music quality or content + + align:start position:0% +about radio music quality or content + + + align:start position:0% +about radio music quality or content +quality and then that that produces + + align:start position:0% +quality and then that that produces + + + align:start position:0% +quality and then that that produces +people that they then sell to the + + align:start position:0% +people that they then sell to the + + + align:start position:0% +people that they then sell to the +advertisers so the the advertisers the + + align:start position:0% +advertisers so the the advertisers the + + + align:start position:0% +advertisers so the the advertisers the +consumers the people are sort of B work + + align:start position:0% +consumers the people are sort of B work + + + align:start position:0% +consumers the people are sort of B work +and you know one thing you might know if + + align:start position:0% +and you know one thing you might know if + + + align:start position:0% +and you know one thing you might know if +if that's your view of radio You' be + + align:start position:0% +if that's your view of radio You' be + + + align:start position:0% +if that's your view of radio You' be +like wait wouldn't that mean like + + align:start position:0% +like wait wouldn't that mean like + + + align:start position:0% +like wait wouldn't that mean like +whenever two radio stations are + + align:start position:0% +whenever two radio stations are + + + align:start position:0% +whenever two radio stations are +proposing merging what would be + + align:start position:0% +proposing merging what would be + + + align:start position:0% +proposing merging what would be +considered bad is if by merging the + + align:start position:0% +considered bad is if by merging the + + + align:start position:0% +considered bad is if by merging the +radio stations are going to raise the + + align:start position:0% +radio stations are going to raise the + + + align:start position:0% +radio stations are going to raise the +price of advertising and show have fewer + + align:start position:0% +price of advertising and show have fewer + + + align:start position:0% +price of advertising and show have fewer +commercials per hour and play music + + align:start position:0% +commercials per hour and play music + + + align:start position:0% +commercials per hour and play music +instead and that actually tends to be + + align:start position:0% +instead and that actually tends to be + + + align:start position:0% +instead and that actually tends to be +how us anti trust authorities have + + align:start position:0% +how us anti trust authorities have + + + align:start position:0% +how us anti trust authorities have +largely conceptualized radio that is if + + align:start position:0% +largely conceptualized radio that is if + + + align:start position:0% +largely conceptualized radio that is if +there's something going on that's going + + align:start position:0% +there's something going on that's going + + + align:start position:0% +there's something going on that's going +to result in fewer commercials per hour + + align:start position:0% +to result in fewer commercials per hour + + + align:start position:0% +to result in fewer commercials per hour +and more music or more news then they're + + align:start position:0% +and more music or more news then they're + + + align:start position:0% +and more music or more news then they're +skeptical of it if it's something that's + + align:start position:0% +skeptical of it if it's something that's + + + align:start position:0% +skeptical of it if it's something that's +going to result even more commercials + + align:start position:0% +going to result even more commercials + + + align:start position:0% +going to result even more commercials +per hour that's good because that's + + align:start position:0% +per hour that's good because that's + + + align:start position:0% +per hour that's good because that's +stopping the dead weight loss to the on + + align:start position:0% +stopping the dead weight loss to the on + + + align:start position:0% +stopping the dead weight loss to the on +The Advertiser side you know obviously + + align:start position:0% +The Advertiser side you know obviously + + + align:start position:0% +The Advertiser side you know obviously +you and you know Barry wal fol will + + align:start position:0% +you and you know Barry wal fol will + + + align:start position:0% +you and you know Barry wal fol will +mostly adopt that they they they are + + align:start position:0% +mostly adopt that they they they are + + + align:start position:0% +mostly adopt that they they they are +clearly well aware that radio is also + + align:start position:0% +clearly well aware that radio is also + + + align:start position:0% +clearly well aware that radio is also +something people listen to when they + + align:start position:0% +something people listen to when they + + + align:start position:0% +something people listen to when they +talk about that at the end but all the + + align:start position:0% +talk about that at the end but all the + + + align:start position:0% +talk about that at the end but all the +analysis is done thinking about radio + + align:start position:0% +analysis is done thinking about radio + + + align:start position:0% +analysis is done thinking about radio +stations as things that produce + + align:start position:0% +stations as things that produce + + + align:start position:0% +stations as things that produce +advertising to sell to + + align:start position:0% + + + + align:start position:0% + +advertisers um okay anyway so we've got + + align:start position:0% +advertisers um okay anyway so we've got + + + align:start position:0% +advertisers um okay anyway so we've got +135 us markets we're trying to compare + + align:start position:0% +135 us markets we're trying to compare + + + align:start position:0% +135 us markets we're trying to compare +with what would be socially efficient + + align:start position:0% +with what would be socially efficient + + + align:start position:0% +with what would be socially efficient +and talk about the welfare losses we're + + align:start position:0% +and talk about the welfare losses we're + + + align:start position:0% +and talk about the welfare losses we're +going to focus on the uh radio stations + + align:start position:0% +going to focus on the uh radio stations + + + align:start position:0% +going to focus on the uh radio stations +as firms that have advertisers as + + align:start position:0% +as firms that have advertisers as + + + align:start position:0% +as firms that have advertisers as +customers um they're going to assume + + align:start position:0% +customers um they're going to assume + + + align:start position:0% +customers um they're going to assume +they're starting with the very first + + align:start position:0% +they're starting with the very first + + + align:start position:0% +they're starting with the very first +model of Entry that I did so they're + + align:start position:0% +model of Entry that I did so they're + + + align:start position:0% +model of Entry that I did so they're +assuming that the ears that are being + + align:start position:0% +assuming that the ears that are being + + + align:start position:0% +assuming that the ears that are being +produced are homogeneous good so every + + align:start position:0% +produced are homogeneous good so every + + + align:start position:0% +produced are homogeneous good so every +listener is worth exactly the same + + align:start position:0% +listener is worth exactly the same + + + align:start position:0% +listener is worth exactly the same +amount to every + + align:start position:0% +amount to every + + + align:start position:0% +amount to every +Advertiser you know in practice + + align:start position:0% +Advertiser you know in practice + + + align:start position:0% +Advertiser you know in practice +obviously you know you know they going + + align:start position:0% +obviously you know you know they going + + + align:start position:0% +obviously you know you know they going +to be stations produ you know you know + + align:start position:0% +to be stations produ you know you know + + + align:start position:0% +to be stations produ you know you know +stations playing music in the 1950s + + align:start position:0% +stations playing music in the 1950s + + + align:start position:0% +stations playing music in the 1950s +where they have lots of ads for reverse + + align:start position:0% +where they have lots of ads for reverse + + + align:start position:0% +where they have lots of ads for reverse +mortgages you know they're going to be + + align:start position:0% +mortgages you know they're going to be + + + align:start position:0% +mortgages you know they're going to be +stations you + + align:start position:0% +stations you + + + align:start position:0% +stations you +know playing much more upto-date music + + align:start position:0% +know playing much more upto-date music + + + align:start position:0% +know playing much more upto-date music +that are sort of advertising concert + + align:start position:0% +that are sort of advertising concert + + + align:start position:0% +that are sort of advertising concert +tickets you know somehow they just they + + align:start position:0% +tickets you know somehow they just they + + + align:start position:0% +tickets you know somehow they just they +just abstract away from that it's just + + align:start position:0% +just abstract away from that it's just + + + align:start position:0% +just abstract away from that it's just +they're just going to go to PE listeners + + align:start position:0% +they're just going to go to PE listeners + + + align:start position:0% +they're just going to go to PE listeners +are homogeneous effect there's a just a + + align:start position:0% +are homogeneous effect there's a just a + + + align:start position:0% +are homogeneous effect there's a just a +downward sloping demand curve for the + + align:start position:0% +downward sloping demand curve for the + + + align:start position:0% +downward sloping demand curve for the +more listeners you have the price or the + + align:start position:0% +more listeners you have the price or the + + + align:start position:0% +more listeners you have the price or the +more listeners you the more commercial + + align:start position:0% +more listeners you the more commercial + + + align:start position:0% +more listeners you the more commercial +slots you have to sell uh the lower is + + align:start position:0% +slots you have to sell uh the lower is + + + align:start position:0% +slots you have to sell uh the lower is +in price per commercial slot and that's + + align:start position:0% +in price per commercial slot and that's + + + align:start position:0% +in price per commercial slot and that's +how that Market's going to work anyway + + align:start position:0% +how that Market's going to work anyway + + + align:start position:0% +how that Market's going to work anyway +so the and you know what's also good + + align:start position:0% +so the and you know what's also good + + + align:start position:0% +so the and you know what's also good +here is they have sort of purely fixed + + align:start position:0% +here is they have sort of purely fixed + + + align:start position:0% +here is they have sort of purely fixed +costs and no marginal costs of producing + + align:start position:0% +costs and no marginal costs of producing + + + align:start position:0% +costs and no marginal costs of producing +listeners so you get even simpler + + align:start position:0% +listeners so you get even simpler + + + align:start position:0% +listeners so you get even simpler +welfare function what I talked about + + align:start position:0% +welfare function what I talked about + + + align:start position:0% +welfare function what I talked about +before so the welfare if you have n + + align:start position:0% +before so the welfare if you have n + + + align:start position:0% +before so the welfare if you have n +radio + + align:start position:0% +radio + + + align:start position:0% +radio +stations it's going to be the integral + + align:start position:0% +stations it's going to be the integral + + + align:start position:0% +stations it's going to be the integral +from zero so lar of n is be the number + + align:start position:0% +from zero so lar of n is be the number + + + align:start position:0% +from zero so lar of n is be the number +of listeners per station when you have n + + align:start position:0% +of listeners per station when you have n + + + align:start position:0% +of listeners per station when you have n +stations so it's just the integral from + + align:start position:0% +stations so it's just the integral from + + + align:start position:0% +stations so it's just the integral from +zero to n lar of n p of x X the + + align:start position:0% +zero to n lar of n p of x X the + + + align:start position:0% +zero to n lar of n p of x X the +willingness to pay for the very first + + align:start position:0% +willingness to pay for the very first + + + align:start position:0% +willingness to pay for the very first +for each listener integrated out of the + + align:start position:0% +for each listener integrated out of the + + + align:start position:0% +for each listener integrated out of the +total number of listeners so this is the + + align:start position:0% +total number of listeners so this is the + + + align:start position:0% +total number of listeners so this is the +advertiser willingness to pay for + + align:start position:0% +advertiser willingness to pay for + + + align:start position:0% +advertiser willingness to pay for +listeners just this is the gross Surplus + + align:start position:0% +listeners just this is the gross Surplus + + + align:start position:0% +listeners just this is the gross Surplus +is just the area under that + + align:start position:0% +is just the area under that + + + align:start position:0% +is just the area under that +curve um minus the fixed cost that are + + align:start position:0% +curve um minus the fixed cost that are + + + align:start position:0% +curve um minus the fixed cost that are +occurred generating all those listeners + + align:start position:0% +occurred generating all those listeners + + + align:start position:0% +occurred generating all those listeners +and so the things that we need to + + align:start position:0% +and so the things that we need to + + + align:start position:0% +and so the things that we need to +estimate are this per firm listening + + align:start position:0% +estimate are this per firm listening + + + align:start position:0% +estimate are this per firm listening +function lar of n we need the advertiser + + align:start position:0% +function lar of n we need the advertiser + + + align:start position:0% +function lar of n we need the advertiser +inverse demand function + + align:start position:0% +inverse demand function + + + align:start position:0% +inverse demand function +L and we need to fix cost F so sort of + + align:start position:0% +L and we need to fix cost F so sort of + + + align:start position:0% +L and we need to fix cost F so sort of +evaluate welfare in this perspective you + + align:start position:0% +evaluate welfare in this perspective you + + + align:start position:0% +evaluate welfare in this perspective you +just need to elocate those three + + align:start position:0% + + + + align:start position:0% + +objects how are we doing this so the + + align:start position:0% +objects how are we doing this so the + + + align:start position:0% +objects how are we doing this so the +first one I'm listening you know this is + + align:start position:0% +first one I'm listening you know this is + + + align:start position:0% +first one I'm listening you know this is +where you get the sort of sense of how + + align:start position:0% +where you get the sort of sense of how + + + align:start position:0% +where you get the sort of sense of how +much in iio people like um uh discrete + + align:start position:0% +much in iio people like um uh discrete + + + align:start position:0% +much in iio people like um uh discrete +Choice models and discret you know + + align:start position:0% +Choice models and discret you know + + + align:start position:0% +Choice models and discret you know +discrete Choice resp estimating things + + align:start position:0% +discrete Choice resp estimating things + + + align:start position:0% +discrete Choice resp estimating things +because you know they don't have any + + align:start position:0% +because you know they don't have any + + + align:start position:0% +because you know they don't have any +price variation they're not actually + + align:start position:0% +price variation they're not actually + + + align:start position:0% +price variation they're not actually +trying to estimate consumer preferences + + align:start position:0% +trying to estimate consumer preferences + + + align:start position:0% +trying to estimate consumer preferences +despite not trying to estimate the + + align:start position:0% +despite not trying to estimate the + + + align:start position:0% +despite not trying to estimate the +consumer preferences they're still using + + align:start position:0% +consumer preferences they're still using + + + align:start position:0% +consumer preferences they're still using +a model with consumers having discrete + + align:start position:0% +a model with consumers having discrete + + + align:start position:0% +a model with consumers having discrete +Choice preferences choosing among + + align:start position:0% +Choice preferences choosing among + + + align:start position:0% +Choice preferences choosing among +stations or the outside good to generate + + align:start position:0% +stations or the outside good to generate + + + align:start position:0% +stations or the outside good to generate +their listening + + align:start position:0% +their listening + + + align:start position:0% +their listening +function um so this is um people know + + align:start position:0% +function um so this is um people know + + + align:start position:0% +function um so this is um people know +what Nest vet models + + align:start position:0% +what Nest vet models + + + align:start position:0% +what Nest vet models +are so okay okay so anyway this is a + + align:start position:0% +are so okay okay so anyway this is a + + + align:start position:0% +are so okay okay so anyway this is a +what we call a nested loit model you + + align:start position:0% +what we call a nested loit model you + + + align:start position:0% +what we call a nested loit model you +remember I sort of we went with the sort + + align:start position:0% +remember I sort of we went with the sort + + + align:start position:0% +remember I sort of we went with the sort +of standard loic model the utility that + + align:start position:0% +of standard loic model the utility that + + + align:start position:0% +of standard loic model the utility that +consumer I gets from listening to to + + align:start position:0% +consumer I gets from listening to to + + + align:start position:0% +consumer I gets from listening to to +station J is Delta J which is like the + + align:start position:0% +station J is Delta J which is like the + + + align:start position:0% +station J is Delta J which is like the +quality of station J plus Epsilon i j + + align:start position:0% +quality of station J plus Epsilon i j + + + align:start position:0% +quality of station J plus Epsilon i j +which is like the loit type okay + + align:start position:0% +which is like the loit type okay + + + align:start position:0% +which is like the loit type okay +um in the nest ofit model you add a + + align:start position:0% +um in the nest ofit model you add a + + + align:start position:0% +um in the nest ofit model you add a +second shock so the Epsilon i j is this + + align:start position:0% +second shock so the Epsilon i j is this + + + align:start position:0% +second shock so the Epsilon i j is this +sort of shock that's independent across + + align:start position:0% +sort of shock that's independent across + + + align:start position:0% +sort of shock that's independent across +stations I like the music on this + + align:start position:0% +stations I like the music on this + + + align:start position:0% +stations I like the music on this +station I don't like music on this + + align:start position:0% +station I don't like music on this + + + align:start position:0% +station I don't like music on this +station that's additive to my + + align:start position:0% +station that's additive to my + + + align:start position:0% +station that's additive to my +preferences but then there's also a + + align:start position:0% +preferences but then there's also a + + + align:start position:0% +preferences but then there's also a +common shock + + align:start position:0% +common shock + + + align:start position:0% +common shock +VI and the vi is a random variable it's + + align:start position:0% +VI and the vi is a random variable it's + + + align:start position:0% +VI and the vi is a random variable it's +drawn randomly at the level of the + + align:start position:0% +drawn randomly at the level of the + + + align:start position:0% +drawn randomly at the level of the +customer not at the station and it is + + align:start position:0% +customer not at the station and it is + + + align:start position:0% +customer not at the station and it is +their taste for music as a whole versus + + align:start position:0% +their taste for music as a whole versus + + + align:start position:0% +their taste for music as a whole versus +not listening to the radio so we have + + align:start position:0% +not listening to the radio so we have + + + align:start position:0% +not listening to the radio so we have +these two shocks one common shock that + + align:start position:0% +these two shocks one common shock that + + + align:start position:0% +these two shocks one common shock that +customer ey gets + + align:start position:0% +customer ey gets + + + align:start position:0% +customer ey gets +regardless of which station they listen + + align:start position:0% +regardless of which station they listen + + + align:start position:0% +regardless of which station they listen +to and then one set of and then a set of + + align:start position:0% +to and then one set of and then a set of + + + align:start position:0% +to and then one set of and then a set of +idiosyncratic shocks that are + + align:start position:0% +idiosyncratic shocks that are + + + align:start position:0% +idiosyncratic shocks that are +independent across stations that you get + + align:start position:0% +independent across stations that you get + + + align:start position:0% +independent across stations that you get +if and only if you listen to that + + align:start position:0% +if and only if you listen to that + + + align:start position:0% +if and only if you listen to that +particular station and the idea here is + + align:start position:0% +particular station and the idea here is + + + align:start position:0% +particular station and the idea here is +by having a sigma that can vary between + + align:start position:0% +by having a sigma that can vary between + + + align:start position:0% +by having a sigma that can vary between +zero and one so Sigma equals z is the + + align:start position:0% +zero and one so Sigma equals z is the + + + align:start position:0% +zero and one so Sigma equals z is the +pure loic model where when you you know + + align:start position:0% +pure loic model where when you you know + + + align:start position:0% +pure loic model where when you you know +add another station it draws customers + + align:start position:0% +add another station it draws customers + + + align:start position:0% +add another station it draws customers +equally from all of the other stations + + align:start position:0% +equally from all of the other stations + + + align:start position:0% +equally from all of the other stations +and from the non-listeners and in radio + + align:start position:0% +and from the non-listeners and in radio + + + align:start position:0% +and from the non-listeners and in radio +non-listeners are most people you know + + align:start position:0% +non-listeners are most people you know + + + align:start position:0% +non-listeners are most people you know +in most half hours most people in the + + align:start position:0% +in most half hours most people in the + + + align:start position:0% +in most half hours most people in the +United States are not listening to the + + align:start position:0% +United States are not listening to the + + + align:start position:0% +United States are not listening to the +radio I mean it's actually surprisingly + + align:start position:0% +radio I mean it's actually surprisingly + + + align:start position:0% +radio I mean it's actually surprisingly +do it's about I think it's like + + align:start position:0% +do it's about I think it's like + + + align:start position:0% +do it's about I think it's like +85% so typical half hour 85% of people + + align:start position:0% +85% so typical half hour 85% of people + + + align:start position:0% +85% so typical half hour 85% of people +un states are not listening to the radio + + align:start position:0% +un states are not listening to the radio + + + align:start position:0% +un states are not listening to the radio +uh but so then if you're if you if you + + align:start position:0% +uh but so then if you're if you if you + + + align:start position:0% +uh but so then if you're if you if you +have the pure loic that means when you a + + align:start position:0% +have the pure loic that means when you a + + + align:start position:0% +have the pure loic that means when you a +new station attracts someone it's 85% + + align:start position:0% +new station attracts someone it's 85% + + + align:start position:0% +new station attracts someone it's 85% +chance they're expanding the market and + + align:start position:0% +chance they're expanding the market and + + + align:start position:0% +chance they're expanding the market and +choosing someone who wasn't listening to + + align:start position:0% +choosing someone who wasn't listening to + + + align:start position:0% +choosing someone who wasn't listening to +the radio to begin with the Other + + align:start position:0% +the radio to begin with the Other + + + align:start position:0% +the radio to begin with the Other +Extreme Sigma equals one this shock goes + + align:start position:0% +Extreme Sigma equals one this shock goes + + + align:start position:0% +Extreme Sigma equals one this shock goes +away it's all the common + + align:start position:0% +away it's all the common + + + align:start position:0% +away it's all the common +shock and when it's all the common shock + + align:start position:0% +shock and when it's all the common shock + + + align:start position:0% +shock and when it's all the common shock +then it's 100% business stealing if you + + align:start position:0% +then it's 100% business stealing if you + + + align:start position:0% +then it's 100% business stealing if you +only have common shocks no and the EOS + + align:start position:0% +only have common shocks no and the EOS + + + align:start position:0% +only have common shocks no and the EOS +cratic things are essentially zero + + align:start position:0% +cratic things are essentially zero + + + align:start position:0% +cratic things are essentially zero +you add a new station it's just going to + + align:start position:0% +you add a new station it's just going to + + + align:start position:0% +you add a new station it's just going to +pull people away from the other station + + align:start position:0% +pull people away from the other station + + + align:start position:0% +pull people away from the other station +it's only the people who have the VIS + + align:start position:0% +it's only the people who have the VIS + + + align:start position:0% +it's only the people who have the VIS +that are big enough to overcome Delta + + align:start position:0% +that are big enough to overcome Delta + + + align:start position:0% +that are big enough to overcome Delta +that will that will listen to that will + + align:start position:0% +that will that will listen to that will + + + align:start position:0% +that will that will listen to that will +listen to radio with + + align:start position:0% +listen to radio with + + + align:start position:0% +listen to radio with +arless anyway so this you know they have + + align:start position:0% +arless anyway so this you know they have + + + align:start position:0% +arless anyway so this you know they have +this model it's got this free preter + + align:start position:0% +this model it's got this free preter + + + align:start position:0% +this model it's got this free preter +Sigma and that's going to let them say + + align:start position:0% +Sigma and that's going to let them say + + + align:start position:0% +Sigma and that's going to let them say +how important business dealing is and + + align:start position:0% +how important business dealing is and + + + align:start position:0% +how important business dealing is and +it's very important to have that because + + align:start position:0% +it's very important to have that because + + + align:start position:0% +it's very important to have that because +if business dealing you know we know + + align:start position:0% +if business dealing you know we know + + + align:start position:0% +if business dealing you know we know +that there's a lot of business dealing + + align:start position:0% +that there's a lot of business dealing + + + align:start position:0% +that there's a lot of business dealing +there's too much entry if there's very + + align:start position:0% +there's too much entry if there's very + + + align:start position:0% +there's too much entry if there's very +little business dealing then we might + + align:start position:0% +little business dealing then we might + + + align:start position:0% +little business dealing then we might +have insufficient entry + + align:start position:0% +have insufficient entry + + + align:start position:0% +have insufficient entry +um you know if you have a totally if + + align:start position:0% +um you know if you have a totally if + + + align:start position:0% +um you know if you have a totally if +this model was totally symmetric if all + + align:start position:0% +this model was totally symmetric if all + + + align:start position:0% +this model was totally symmetric if all +the Deltas were the same if all the + + align:start position:0% +the Deltas were the same if all the + + + align:start position:0% +the Deltas were the same if all the +stations were exactly the same quality + + align:start position:0% +stations were exactly the same quality + + + align:start position:0% +stations were exactly the same quality +then the nested loit model um n lar of n + + align:start position:0% +then the nested loit model um n lar of n + + + align:start position:0% +then the nested loit model um n lar of n +would be n 1 minus Sigma power over eus + + align:start position:0% +would be n 1 minus Sigma power over eus + + + align:start position:0% +would be n 1 minus Sigma power over eus +Delta plus n 1 minus Sigma so again for + + align:start position:0% +Delta plus n 1 minus Sigma so again for + + + align:start position:0% +Delta plus n 1 minus Sigma so again for +Sigma equals 1 total listenership is + + align:start position:0% +Sigma equals 1 total listenership is + + + align:start position:0% +Sigma equals 1 total listenership is +just completely fixed at 1 over 1 plus e + + align:start position:0% +just completely fixed at 1 over 1 plus e + + + align:start position:0% +just completely fixed at 1 over 1 plus e +minus Delta regardless of the number of + + align:start position:0% +minus Delta regardless of the number of + + + align:start position:0% +minus Delta regardless of the number of +consumers but when uh Sigma is you know + + align:start position:0% +consumers but when uh Sigma is you know + + + align:start position:0% +consumers but when uh Sigma is you know +Sigma goes to zero this thing is like + + align:start position:0% +Sigma goes to zero this thing is like + + + align:start position:0% +Sigma goes to zero this thing is like +you know it's ASM toting towards one but + + align:start position:0% +you know it's ASM toting towards one but + + + align:start position:0% +you know it's ASM toting towards one but +it's sort of going up initially linearly + + align:start position:0% +it's sort of going up initially linearly + + + align:start position:0% +it's sort of going up initially linearly +in right so it's like n to n to the + + align:start position:0% +in right so it's like n to n to the + + + align:start position:0% +in right so it's like n to n to the +first over this plus something small so + + align:start position:0% +first over this plus something small so + + + align:start position:0% +first over this plus something small so +it's it's going up by + + align:start position:0% +it's it's going up by + + + align:start position:0% +it's it's going up by +again + + align:start position:0% + + + + align:start position:0% + +uh okay anyway so they estimate this you + + align:start position:0% +uh okay anyway so they estimate this you + + + align:start position:0% +uh okay anyway so they estimate this you +know they're estimating this using the + + align:start position:0% +know they're estimating this using the + + + align:start position:0% +know they're estimating this using the +data on how many people listen as a + + align:start position:0% +data on how many people listen as a + + + align:start position:0% +data on how many people listen as a +function of N and they have an IV + + align:start position:0% +function of N and they have an IV + + + align:start position:0% +function of N and they have an IV +approach where they use population like + + align:start position:0% +approach where they use population like + + + align:start position:0% +approach where they use population like +you might overest underestimate the + + align:start position:0% +you might overest underestimate the + + + align:start position:0% +you might overest underestimate the +effect of n on markets because you'll + + align:start position:0% +effect of n on markets because you'll + + + align:start position:0% +effect of n on markets because you'll +see a lot of or overestimate it because + + align:start position:0% +see a lot of or overestimate it because + + + align:start position:0% +see a lot of or overestimate it because +you'd see a lot of stations entering the + + align:start position:0% +you'd see a lot of stations entering the + + + align:start position:0% +you'd see a lot of stations entering the +markets that have a lot of demand like + + align:start position:0% +markets that have a lot of demand like + + + align:start position:0% +markets that have a lot of demand like +if there's some cities people like the + + align:start position:0% +if there's some cities people like the + + + align:start position:0% +if there's some cities people like the +radio like Nashville and some like + + align:start position:0% +radio like Nashville and some like + + + align:start position:0% +radio like Nashville and some like +Boston where they don't then you might + + align:start position:0% +Boston where they don't then you might + + + align:start position:0% +Boston where they don't then you might +get more firms in Nashville than in + + align:start position:0% +get more firms in Nashville than in + + + align:start position:0% +get more firms in Nashville than in +Boston because they're meeting the + + align:start position:0% +Boston because they're meeting the + + + align:start position:0% +Boston because they're meeting the +demand and so the instrument for the + + align:start position:0% +demand and so the instrument for the + + + align:start position:0% +demand and so the instrument for the +number of firms uh they use the + + align:start position:0% +number of firms uh they use the + + + align:start position:0% +number of firms uh they use the +population as an instrument for the + + align:start position:0% +population as an instrument for the + + + align:start position:0% +population as an instrument for the +number of firms and so there's some + + align:start position:0% +number of firms and so there's some + + + align:start position:0% +number of firms and so there's some +sense looking at how does uh listening + + align:start position:0% +sense looking at how does uh listening + + + align:start position:0% +sense looking at how does uh listening +compare in in cities with a lot of + + align:start position:0% +compare in in cities with a lot of + + + align:start position:0% +compare in in cities with a lot of +people versus few + + align:start position:0% +people versus few + + + align:start position:0% +people versus few +people um then the second thing they do + + align:start position:0% +people um then the second thing they do + + + align:start position:0% +people um then the second thing they do +is just they want to estimate this + + align:start position:0% +is just they want to estimate this + + + align:start position:0% +is just they want to estimate this +downward sloping advertising demand + + align:start position:0% +downward sloping advertising demand + + + align:start position:0% +downward sloping advertising demand +curve uh you know they're going to + + align:start position:0% +curve uh you know they're going to + + + align:start position:0% +curve uh you know they're going to +assume that the advertising prices + + align:start position:0% +assume that the advertising prices + + + align:start position:0% +assume that the advertising prices +depend on the share of people listening + + align:start position:0% +depend on the share of people listening + + + align:start position:0% +depend on the share of people listening +to the radio and Market K and so it's + + align:start position:0% +to the radio and Market K and so it's + + + align:start position:0% +to the radio and Market K and so it's +just the log of um price of advertising + + align:start position:0% +just the log of um price of advertising + + + align:start position:0% +just the log of um price of advertising +in Market K is equal to some + + align:start position:0% +in Market K is equal to some + + + align:start position:0% +in Market K is equal to some +characteristics of the + + align:start position:0% +characteristics of the + + + align:start position:0% +characteristics of the +city uh plus something that you have a + + align:start position:0% +city uh plus something that you have a + + + align:start position:0% +city uh plus something that you have a +downward sloping demand in the number of + + align:start position:0% +downward sloping demand in the number of + + + align:start position:0% +downward sloping demand in the number of +listeners listener hours that there are + + align:start position:0% +listeners listener hours that there are + + + align:start position:0% +listeners listener hours that there are +plus Omega K so again the idea is the + + align:start position:0% +plus Omega K so again the idea is the + + + align:start position:0% +plus Omega K so again the idea is the +more listener hours you have more + + align:start position:0% +more listener hours you have more + + + align:start position:0% +more listener hours you have more +listener hours you have the lower is the + + align:start position:0% +listener hours you have the lower is the + + + align:start position:0% +listener hours you have the lower is the +willingness to pay per listener hour to + + align:start position:0% +willingness to pay per listener hour to + + + align:start position:0% +willingness to pay per listener hour to +be for the + + align:start position:0% + + + + align:start position:0% + +commercials and then the fixed costs you + + align:start position:0% +commercials and then the fixed costs you + + + align:start position:0% +commercials and then the fixed costs you +know in some sense uh this is like a + + align:start position:0% +know in some sense uh this is like a + + + align:start position:0% +know in some sense uh this is like a +breast to hand and Reese kind of + + align:start position:0% +breast to hand and Reese kind of + + + align:start position:0% +breast to hand and Reese kind of +approach that you just you know you are + + align:start position:0% +approach that you just you know you are + + + align:start position:0% +approach that you just you know you are +trying to rationalize the number of + + align:start position:0% +trying to rationalize the number of + + + align:start position:0% +trying to rationalize the number of +radio stations in every Market as you + + align:start position:0% +radio stations in every Market as you + + + align:start position:0% +radio stations in every Market as you +rationalize it by assuming that there + + align:start position:0% +rationalize it by assuming that there + + + align:start position:0% +rationalize it by assuming that there +are these errors um they this case they + + align:start position:0% +are these errors um they this case they + + + align:start position:0% +are these errors um they this case they +do errors drawn from a long normal + + align:start position:0% +do errors drawn from a long normal + + + align:start position:0% +do errors drawn from a long normal +distribution instead of from a normal + + align:start position:0% +distribution instead of from a normal + + + align:start position:0% +distribution instead of from a normal +distribution and they they do the sort + + align:start position:0% +distribution and they they do the sort + + + align:start position:0% +distribution and they they do the sort +of uh estimate two parameters the mean + + align:start position:0% +of uh estimate two parameters the mean + + + align:start position:0% +of uh estimate two parameters the mean +and variance of the laog normal + + align:start position:0% +and variance of the laog normal + + + align:start position:0% +and variance of the laog normal +distribution um but uh anyway that's + + align:start position:0% +distribution um but uh anyway that's + + + align:start position:0% +distribution um but uh anyway that's +just like breast + + align:start position:0% +just like breast + + + align:start position:0% +just like breast +Ree and you know the data have + + align:start position:0% +Ree and you know the data have + + + align:start position:0% +Ree and you know the data have +information about 3285 stations 135 + + align:start position:0% +information about 3285 stations 135 + + + align:start position:0% +information about 3285 stations 135 +markets so they have individual station + + align:start position:0% +markets so they have individual station + + + align:start position:0% +markets so they have individual station +characteristics that they're using in + + align:start position:0% +characteristics that they're using in + + + align:start position:0% +characteristics that they're using in +some places um these regressions like + + align:start position:0% +some places um these regressions like + + + align:start position:0% +some places um these regressions like +the advertising demand regressions those + + align:start position:0% +the advertising demand regressions those + + + align:start position:0% +the advertising demand regressions those +are just run their advertising data is + + align:start position:0% +are just run their advertising data is + + + align:start position:0% +are just run their advertising data is +purely at the market level it's not at + + align:start position:0% +purely at the market level it's not at + + + align:start position:0% +purely at the market level it's not at +the station Market level so there + + align:start position:0% +the station Market level so there + + + align:start position:0% +the station Market level so there +they're just using Market level + + align:start position:0% +they're just using Market level + + + align:start position:0% +they're just using Market level +advertising prices they get from some + + align:start position:0% +advertising prices they get from some + + + align:start position:0% +advertising prices they get from some +consulting firm that provides adver in + + align:start position:0% +consulting firm that provides adver in + + + align:start position:0% +consulting firm that provides adver in +prices I think it actually come from the + + align:start position:0% +prices I think it actually come from the + + + align:start position:0% +prices I think it actually come from the +revenues of radio you it's it comes with + + align:start position:0% +revenues of radio you it's it comes with + + + align:start position:0% +revenues of radio you it's it comes with +the radio it comes with the radio + + align:start position:0% +the radio it comes with the radio + + + align:start position:0% +the radio it comes with the radio +station advertising report and + + align:start position:0% +station advertising report and + + + align:start position:0% +station advertising report and +advertising revenues okay um the raw + + align:start position:0% +advertising revenues okay um the raw + + + align:start position:0% +advertising revenues okay um the raw +data which is going to tell you a lot + + align:start position:0% +data which is going to tell you a lot + + + align:start position:0% +data which is going to tell you a lot +about what the results come out is is is + + align:start position:0% +about what the results come out is is is + + + align:start position:0% +about what the results come out is is is +here in the paper so this graph is as + + align:start position:0% +here in the paper so this graph is as + + + align:start position:0% +here in the paper so this graph is as +the number of stations in the market + + align:start position:0% +the number of stations in the market + + + align:start position:0% +the number of stations in the market +increases how does listening go up and + + align:start position:0% +increases how does listening go up and + + + align:start position:0% +increases how does listening go up and +you might say okay I definitely see that + + align:start position:0% +you might say okay I definitely see that + + + align:start position:0% +you might say okay I definitely see that +positive slope more radio stations more + + align:start position:0% +positive slope more radio stations more + + + align:start position:0% +positive slope more radio stations more +listening but you look at this graph you + + align:start position:0% +listening but you look at this graph you + + + align:start position:0% +listening but you look at this graph you +know this scale is really running from + + align:start position:0% +know this scale is really running from + + + align:start position:0% +know this scale is really running from +0.1 to 0.18 or 0.12 to 0.18 so when you + + align:start position:0% +0.1 to 0.18 or 0.12 to 0.18 so when you + + + align:start position:0% +0.1 to 0.18 or 0.12 to 0.18 so when you +have 15 radio stations it's looking like + + align:start position:0% +have 15 radio stations it's looking like + + + align:start position:0% +have 15 radio stations it's looking like +you're getting 14% of the people + + align:start position:0% +you're getting 14% of the people + + + align:start position:0% +you're getting 14% of the people +listening to the + + align:start position:0% +listening to the + + + align:start position:0% +listening to the +radio when you have 45 radio stations + + align:start position:0% +radio when you have 45 radio stations + + + align:start position:0% +radio when you have 45 radio stations +you're getting like 15 or 16 so you know + + align:start position:0% +you're getting like 15 or 16 so you know + + + align:start position:0% +you're getting like 15 or 16 so you know +we're tripling the number of radio + + align:start position:0% +we're tripling the number of radio + + + align:start position:0% +we're tripling the number of radio +stations in the market and listening is + + align:start position:0% +stations in the market and listening is + + + align:start position:0% +stations in the market and listening is +going from 14% to 16% or something like + + align:start position:0% +going from 14% to 16% or something like + + + align:start position:0% +going from 14% to 16% or something like +that so this is saying that it does seem + + align:start position:0% +that so this is saying that it does seem + + + align:start position:0% +that so this is saying that it does seem +like radio station entry is mostly + + align:start position:0% +like radio station entry is mostly + + + align:start position:0% +like radio station entry is mostly +business stealing and you know again we + + align:start position:0% +business stealing and you know again we + + + align:start position:0% +business stealing and you know again we +think that this graph if you draw the OS + + align:start position:0% +think that this graph if you draw the OS + + + align:start position:0% +think that this graph if you draw the OS +might be overstated how much Market + + align:start position:0% +might be overstated how much Market + + + align:start position:0% +might be overstated how much Market +expansion there is um so when you're R + + align:start position:0% +expansion there is um so when you're R + + + align:start position:0% +expansion there is um so when you're R +the IV it's it's not surprising that it + + align:start position:0% +the IV it's it's not surprising that it + + + align:start position:0% +the IV it's it's not surprising that it +says yes there's an awful lot of + + align:start position:0% +says yes there's an awful lot of + + + align:start position:0% +says yes there's an awful lot of +business dealing + + align:start position:0% +business dealing + + + align:start position:0% +business dealing +here uh and then okay this is just sort + + align:start position:0% +here uh and then okay this is just sort + + + align:start position:0% +here uh and then okay this is just sort +of showing you what the where the + + align:start position:0% +of showing you what the where the + + + align:start position:0% +of showing you what the where the +instrument comes from that is that it is + + align:start position:0% +instrument comes from that is that it is + + + align:start position:0% +instrument comes from that is that it is +true that the cities that are small the + + align:start position:0% +true that the cities that are small the + + + align:start position:0% +true that the cities that are small the +cities of of a few hundred thousand tend + + align:start position:0% +cities of of a few hundred thousand tend + + + align:start position:0% +cities of of a few hundred thousand tend +to have only 10 or 15 radio station and + + align:start position:0% +to have only 10 or 15 radio station and + + + align:start position:0% +to have only 10 or 15 radio station and +as markets get bigger you're getting + + align:start position:0% +as markets get bigger you're getting + + + align:start position:0% +as markets get bigger you're getting +more radio stations that's sort that's + + align:start position:0% +more radio stations that's sort that's + + + align:start position:0% +more radio stations that's sort that's +the first + + align:start position:0% + + + + align:start position:0% + +stage and then the advertising + + align:start position:0% + + + + align:start position:0% + +prices you as the listening share + + align:start position:0% +prices you as the listening share + + + align:start position:0% +prices you as the listening share +increases the this is a you know per + + align:start position:0% +increases the this is a you know per + + + align:start position:0% +increases the this is a you know per +listener hour advertising price or + + align:start position:0% +listener hour advertising price or + + + align:start position:0% +listener hour advertising price or +advertising Revenue advertising revenues + + align:start position:0% +advertising Revenue advertising revenues + + + align:start position:0% +advertising Revenue advertising revenues +per listener hour are are clearly + + align:start position:0% +per listener hour are are clearly + + + align:start position:0% +per listener hour are are clearly +declining as the listening share is + + align:start position:0% +declining as the listening share is + + + align:start position:0% +declining as the listening share is +going up + + align:start position:0% + + + + align:start position:0% + +and you know r model for this would be + + align:start position:0% +and you know r model for this would be + + + align:start position:0% +and you know r model for this would be +there's some things that you need to + + align:start position:0% +there's some things that you need to + + + align:start position:0% +there's some things that you need to +advertise in the radio and so if there's + + align:start position:0% +advertise in the radio and so if there's + + + align:start position:0% +advertise in the radio and so if there's +very few radio commercial slots + + align:start position:0% +very few radio commercial slots + + + align:start position:0% +very few radio commercial slots +available we pay a lot for them and then + + align:start position:0% +available we pay a lot for them and then + + + align:start position:0% +available we pay a lot for them and then +beyond that you're just left with plank + + align:start position:0% +beyond that you're just left with plank + + + align:start position:0% +beyond that you're just left with plank +radio ads for things that you could + + align:start position:0% +radio ads for things that you could + + + align:start position:0% +radio ads for things that you could +advertise anywhere else and The + + align:start position:0% +advertise anywhere else and The + + + align:start position:0% +advertise anywhere else and The +Advertiser there's just fewer + + align:start position:0% +Advertiser there's just fewer + + + align:start position:0% +Advertiser there's just fewer +advertisers who really want those ads + + align:start position:0% +advertisers who really want those ads + + + align:start position:0% +advertisers who really want those ads +off the prices have to go + + align:start position:0% + + + + align:start position:0% + +fine + + align:start position:0% +fine + + + align:start position:0% +fine +um um so what do they get so anyway the + + align:start position:0% +um um so what do they get so anyway the + + + align:start position:0% +um um so what do they get so anyway the +estimate close to one entry is mostly + + align:start position:0% +estimate close to one entry is mostly + + + align:start position:0% +estimate close to one entry is mostly +business dealing therefore there's going + + align:start position:0% +business dealing therefore there's going + + + align:start position:0% +business dealing therefore there's going +to be too much entry um almost sort of + + align:start position:0% +to be too much entry um almost sort of + + + align:start position:0% +to be too much entry um almost sort of +shocking results there's a wealth on how + + align:start position:0% +shocking results there's a wealth on how + + + align:start position:0% +shocking results there's a wealth on how +much excessive entry there is so welfare + + align:start position:0% +much excessive entry there is so welfare + + + align:start position:0% +much excessive entry there is so welfare +under free entry is5 + + align:start position:0% +under free entry is5 + + + align:start position:0% +under free entry is5 +billion uh a social planner could + + align:start position:0% +billion uh a social planner could + + + align:start position:0% +billion uh a social planner could +increase uh social welfare by almost 40% + + align:start position:0% +increase uh social welfare by almost 40% + + + align:start position:0% +increase uh social welfare by almost 40% +by restricting the number of radio + + align:start position:0% +by restricting the number of radio + + + align:start position:0% +by restricting the number of radio +stations if we even had a monopolist so + + align:start position:0% +stations if we even had a monopolist so + + + align:start position:0% +stations if we even had a monopolist so +there was just one firm that had unique + + align:start position:0% +there was just one firm that had unique + + + align:start position:0% +there was just one firm that had unique +license to operate all radio station in + + align:start position:0% +license to operate all radio station in + + + align:start position:0% +license to operate all radio station in +each market and that monopolist could + + align:start position:0% +each market and that monopolist could + + + align:start position:0% +each market and that monopolist could +operate as many stations as it wanted it + + align:start position:0% +operate as many stations as it wanted it + + + align:start position:0% +operate as many stations as it wanted it +would say we would do almost as well + + align:start position:0% +would say we would do almost as well + + + align:start position:0% +would say we would do almost as well +under monopolist as we do Under the + + align:start position:0% +under monopolist as we do Under the + + + align:start position:0% +under monopolist as we do Under the +social planner their estimates sort of + + align:start position:0% +social planner their estimates sort of + + + align:start position:0% +social planner their estimates sort of +imply that we want very few radio + + align:start position:0% +imply that we want very few radio + + + align:start position:0% +imply that we want very few radio +stations you know monopis wouldn't open + + align:start position:0% +stations you know monopis wouldn't open + + + align:start position:0% +stations you know monopis wouldn't open +just one a monopolis would open you know + + align:start position:0% +just one a monopolis would open you know + + + align:start position:0% +just one a monopolis would open you know +three or four or uh F you know five + + align:start position:0% +three or four or uh F you know five + + + align:start position:0% +three or four or uh F you know five +stations per Market but you know in some + + align:start position:0% +stations per Market but you know in some + + + align:start position:0% +stations per Market but you know in some +sense of ble saying that there's just an + + align:start position:0% +sense of ble saying that there's just an + + + align:start position:0% +sense of ble saying that there's just an +awful lot of wasteful duplication of + + align:start position:0% +awful lot of wasteful duplication of + + + align:start position:0% +awful lot of wasteful duplication of +fixed cost and we you get by with many + + align:start position:0% +fixed cost and we you get by with many + + + align:start position:0% +fixed cost and we you get by with many +fewer radio stations um so in their data + + align:start position:0% +fewer radio stations um so in their data + + + align:start position:0% +fewer radio stations um so in their data +set there's + + align:start position:0% +set there's + + + align:start position:0% +set there's +259 within Metro station uh stations and + + align:start position:0% +259 within Metro station uh stations and + + + align:start position:0% +259 within Metro station uh stations and +they basically estimate that we have + + align:start position:0% +they basically estimate that we have + + + align:start position:0% +they basically estimate that we have +four times as many as we want um that + + align:start position:0% +four times as many as we want um that + + + align:start position:0% +four times as many as we want um that +optimal would be only have 649 + + align:start position:0% +optimal would be only have 649 + + + align:start position:0% +optimal would be only have 649 +stations um what would happen in this + + align:start position:0% +stations um what would happen in this + + + align:start position:0% +stations um what would happen in this +world where three qus of the radio + + align:start position:0% +world where three qus of the radio + + + align:start position:0% +world where three qus of the radio +stations disappeared um advertising + + align:start position:0% +stations disappeared um advertising + + + align:start position:0% +stations disappeared um advertising +price would go from 277 to 326 so it + + align:start position:0% +price would go from 277 to 326 so it + + + align:start position:0% +price would go from 277 to 326 so it +goes up but only + + align:start position:0% +goes up but only + + + align:start position:0% +goes up but only +moderately um + + align:start position:0% +moderately um + + + align:start position:0% +moderately um +uh listening share would go from 12.9% + + align:start position:0% +uh listening share would go from 12.9% + + + align:start position:0% +uh listening share would go from 12.9% +of the population to 9.3 so it is true + + align:start position:0% +of the population to 9.3 so it is true + + + align:start position:0% +of the population to 9.3 so it is true +that uh you know more than a quarter of + + align:start position:0% +that uh you know more than a quarter of + + + align:start position:0% +that uh you know more than a quarter of +all radio listening would stop when all + + align:start position:0% +all radio listening would stop when all + + + align:start position:0% +all radio listening would stop when all +stations disappeared um but the big + + align:start position:0% +stations disappeared um but the big + + + align:start position:0% +stations disappeared um but the big +social welfare gain is the fixed cost of + + align:start position:0% +social welfare gain is the fixed cost of + + + align:start position:0% +social welfare gain is the fixed cost of +operating all these radio stations drops + + align:start position:0% +operating all these radio stations drops + + + align:start position:0% +operating all these radio stations drops +from $5 billion to $1 + + align:start position:0% +from $5 billion to $1 + + + align:start position:0% +from $5 billion to $1 +billion so I just make you know this + + align:start position:0% +billion so I just make you know this + + + align:start position:0% +billion so I just make you know this +does make you wonder a little bit about + + align:start position:0% +does make you wonder a little bit about + + + align:start position:0% +does make you wonder a little bit about +this does it seem like you know + + align:start position:0% +this does it seem like you know + + + align:start position:0% +this does it seem like you know +some Marvel superhero movie where + + align:start position:0% +some Marvel superhero movie where + + + align:start position:0% +some Marvel superhero movie where +there's this evil guy who's like I'm + + align:start position:0% +there's this evil guy who's like I'm + + + align:start position:0% +there's this evil guy who's like I'm +going to destroy three4 of all the + + align:start position:0% +going to destroy three4 of all the + + + align:start position:0% +going to destroy three4 of all the +people on Earth and then everyone's + + align:start position:0% +people on Earth and then everyone's + + + align:start position:0% +people on Earth and then everyone's +going to be better off somehow you so + + align:start position:0% +going to be better off somehow you so + + + align:start position:0% +going to be better off somehow you so +he's guys you know their rest Barry wal + + align:start position:0% +he's guys you know their rest Barry wal + + + align:start position:0% +he's guys you know their rest Barry wal +fol are going to destroy three quarters + + align:start position:0% +fol are going to destroy three quarters + + + align:start position:0% +fol are going to destroy three quarters +of all the radio stations and yes few + + align:start position:0% +of all the radio stations and yes few + + + align:start position:0% +of all the radio stations and yes few +people are going to listen but we're + + align:start position:0% +people are going to listen but we're + + + align:start position:0% +people are going to listen but we're +going to sort of save all this money and + + align:start position:0% +going to sort of save all this money and + + + align:start position:0% +going to sort of save all this money and +we're all going to be better off here um + + align:start position:0% +we're all going to be better off here um + + + align:start position:0% +we're all going to be better off here um +one thing they note is that you know it + + align:start position:0% +one thing they note is that you know it + + + align:start position:0% +one thing they note is that you know it +is true that the advertising listening + + align:start position:0% +is true that the advertising listening + + + align:start position:0% +is true that the advertising listening +share goes down from 12.9 to 9.3% you + + align:start position:0% +share goes down from 12.9 to 9.3% you + + + align:start position:0% +share goes down from 12.9 to 9.3% you +again remember this is a calculation + + align:start position:0% +again remember this is a calculation + + + align:start position:0% +again remember this is a calculation +where there are only two two two types + + align:start position:0% +where there are only two two two types + + + align:start position:0% +where there are only two two two types +of people in the world there are + + align:start position:0% +of people in the world there are + + + align:start position:0% +of people in the world there are +radio stations and there advertisers and + + align:start position:0% +radio stations and there advertisers and + + + align:start position:0% +radio stations and there advertisers and +the people are just intermediaries who + + align:start position:0% +the people are just intermediaries who + + + align:start position:0% +the people are just intermediaries who +are just being used to generate ad + + align:start position:0% +are just being used to generate ad + + + align:start position:0% +are just being used to generate ad +Revenue um they sort of ask what + + align:start position:0% +Revenue um they sort of ask what + + + align:start position:0% +Revenue um they sort of ask what +happened would how important would + + align:start position:0% +happened would how important would + + + align:start position:0% +happened would how important would +people have to be and people's enjoyment + + align:start position:0% +people have to be and people's enjoyment + + + align:start position:0% +people have to be and people's enjoyment +of radio have to be in order to not want + + align:start position:0% +of radio have to be in order to not want + + + align:start position:0% +of radio have to be in order to not want +to kill three quarters of the radio + + align:start position:0% +to kill three quarters of the radio + + + align:start position:0% +to kill three quarters of the radio +stations and you know my take on the + + align:start position:0% +stations and you know my take on the + + + align:start position:0% +stations and you know my take on the +number is that it's really kind of small + + align:start position:0% +number is that it's really kind of small + + + align:start position:0% +number is that it's really kind of small +so the advertiser Revenue um per + + align:start position:0% +so the advertiser Revenue um per + + + align:start position:0% +so the advertiser Revenue um per +listener hour if I'm reading the data + + align:start position:0% +listener hour if I'm reading the data + + + align:start position:0% +listener hour if I'm reading the data +correctly is about 4.2 cents per + + align:start position:0% +correctly is about 4.2 cents per + + + align:start position:0% +correctly is about 4.2 cents per +listener hour that is if you think about + + align:start position:0% +listener hour that is if you think about + + + align:start position:0% +listener hour that is if you think about +like you listen to radio how often you + + align:start position:0% +like you listen to radio how often you + + + align:start position:0% +like you listen to radio how often you +actually buy anything that you hear in a + + align:start position:0% +actually buy anything that you hear in a + + + align:start position:0% +actually buy anything that you hear in a +radio ad how much someone be willing to + + align:start position:0% +radio ad how much someone be willing to + + + align:start position:0% +radio ad how much someone be willing to +pay to have you hear those radio ads the + + align:start position:0% +pay to have you hear those radio ads the + + + align:start position:0% +pay to have you hear those radio ads the +answer is almost nothing so to offset + + align:start position:0% +answer is almost nothing so to offset + + + align:start position:0% +answer is almost nothing so to offset +all these losses you would need consumer + + align:start position:0% +all these losses you would need consumer + + + align:start position:0% +all these losses you would need consumer +surplus to be about 13 and a half cents + + align:start position:0% +surplus to be about 13 and a half cents + + + align:start position:0% +surplus to be about 13 and a half cents +per listener hour to say we don't want + + align:start position:0% +per listener hour to say we don't want + + + align:start position:0% +per listener hour to say we don't want +to kill three4 of radio stations in the + + align:start position:0% +to kill three4 of radio stations in the + + + align:start position:0% +to kill three4 of radio stations in the +United States and again I you know you + + align:start position:0% +United States and again I you know you + + + align:start position:0% +United States and again I you know you +know again I don't know how much people + + align:start position:0% +know again I don't know how much people + + + align:start position:0% +know again I don't know how much people +are willing to pay for to listen to the + + align:start position:0% +are willing to pay for to listen to the + + + align:start position:0% +are willing to pay for to listen to the +radio you know it is true that like + + align:start position:0% +radio you know it is true that like + + + align:start position:0% +radio you know it is true that like +satellite radio doesn't get that + + align:start position:0% +satellite radio doesn't get that + + + align:start position:0% +satellite radio doesn't get that +customers and I know how much Spotify + + align:start position:0% +customers and I know how much Spotify + + + align:start position:0% +customers and I know how much Spotify +charges per listener hour but 13 and a + + align:start position:0% +charges per listener hour but 13 and a + + + align:start position:0% +charges per listener hour but 13 and a +half cents is not such a big number and + + align:start position:0% +half cents is not such a big number and + + + align:start position:0% +half cents is not such a big number and +so in some sense you wouldn't need + + align:start position:0% +so in some sense you wouldn't need + + + align:start position:0% +so in some sense you wouldn't need +customers be all that important to not + + align:start position:0% +customers be all that important to not + + + align:start position:0% +customers be all that important to not +want to get rid of all the firms in this + + align:start position:0% + + + + align:start position:0% + +way any questions on + + align:start position:0% +way any questions on + + + align:start position:0% +way any questions on +um oh these are just yeah had the graphs + + align:start position:0% +um oh these are just yeah had the graphs + + + align:start position:0% +um oh these are just yeah had the graphs +up there so yeah so the monopis + + align:start position:0% +up there so yeah so the monopis + + + align:start position:0% +up there so yeah so the monopis +different numbers like mist is nearly as + + align:start position:0% +different numbers like mist is nearly as + + + align:start position:0% +different numbers like mist is nearly as +good in the market the M get all the way + + align:start position:0% +good in the market the M get all the way + + + align:start position:0% +good in the market the M get all the way +down to just + + align:start position:0% +down to just + + + align:start position:0% +down to just +341 uh radio stations and 13 five cities + + align:start position:0% +341 uh radio stations and 13 five cities + + + align:start position:0% +341 uh radio stations and 13 five cities +so we're going down to literally less + + align:start position:0% +so we're going down to literally less + + + align:start position:0% +so we're going down to literally less +than three radio stations uh per City + + align:start position:0% +than three radio stations uh per City + + + align:start position:0% +than three radio stations uh per City +and again the listening + + align:start position:0% +and again the listening + + + align:start position:0% +and again the listening +share drop substantially under + + align:start position:0% + + + + align:start position:0% + +Monopoly so some you know comments I + + align:start position:0% +Monopoly so some you know comments I + + + align:start position:0% +Monopoly so some you know comments I +wanted to make it um in some sense I + + align:start position:0% +wanted to make it um in some sense I + + + align:start position:0% +wanted to make it um in some sense I +didn't need to actually do this paper do + + align:start position:0% +didn't need to actually do this paper do + + + align:start position:0% +didn't need to actually do this paper do +the empirics this paper you know this is + + align:start position:0% +the empirics this paper you know this is + + + align:start position:0% +the empirics this paper you know this is +a as I said they modeled as a + + align:start position:0% +a as I said they modeled as a + + + align:start position:0% +a as I said they modeled as a +homogeneous good I already gave that + + align:start position:0% +homogeneous good I already gave that + + + align:start position:0% +homogeneous good I already gave that +theorem that once when you have a + + align:start position:0% +theorem that once when you have a + + + align:start position:0% +theorem that once when you have a +homogeneous good entry is always + + align:start position:0% +homogeneous good entry is always + + + align:start position:0% +homogeneous good entry is always +excessive so whatever parameter Sigma + + align:start position:0% +excessive so whatever parameter Sigma + + + align:start position:0% +excessive so whatever parameter Sigma +and Gamma and whatever they've estimate + + align:start position:0% +and Gamma and whatever they've estimate + + + align:start position:0% +and Gamma and whatever they've estimate +they've estimated we know that this + + align:start position:0% +they've estimated we know that this + + + align:start position:0% +they've estimated we know that this +model is going to say there's too much + + align:start position:0% +model is going to say there's too much + + + align:start position:0% +model is going to say there's too much +entry if the advertisers if the people + + align:start position:0% +entry if the advertisers if the people + + + align:start position:0% +entry if the advertisers if the people +are homogeneous Goods being sold to + + align:start position:0% +are homogeneous Goods being sold to + + + align:start position:0% +are homogeneous Goods being sold to +advertisers um you know it's definitely + + align:start position:0% +advertisers um you know it's definitely + + + align:start position:0% +advertisers um you know it's definitely +true that they're estimating how + + align:start position:0% +true that they're estimating how + + + align:start position:0% +true that they're estimating how +excessive It Is by estimating that Sigma + + align:start position:0% +excessive It Is by estimating that Sigma + + + align:start position:0% +excessive It Is by estimating that Sigma +parameter and if that Sigma parameter + + align:start position:0% +parameter and if that Sigma parameter + + + align:start position:0% +parameter and if that Sigma parameter +had come not to be zero they would have + + align:start position:0% +had come not to be zero they would have + + + align:start position:0% +had come not to be zero they would have +gotten a much less excessive entry but + + align:start position:0% +gotten a much less excessive entry but + + + align:start position:0% +gotten a much less excessive entry but +the model is always saying that entry is + + align:start position:0% +the model is always saying that entry is + + + align:start position:0% +the model is always saying that entry is +excessive and doesn't have estimates of + + align:start position:0% +excessive and doesn't have estimates of + + + align:start position:0% +excessive and doesn't have estimates of +the things that would let you say + + align:start position:0% +the things that would let you say + + + align:start position:0% +the things that would let you say +there's insufficient entry what would + + align:start position:0% +there's insufficient entry what would + + + align:start position:0% +there's insufficient entry what would +those things be for instance you know if + + align:start position:0% +those things be for instance you know if + + + align:start position:0% +those things be for instance you know if +you could estimate how differentiated + + align:start position:0% +you could estimate how differentiated + + + align:start position:0% +you could estimate how differentiated +are the goods are people who listen to + + align:start position:0% +are the goods are people who listen to + + + align:start position:0% +are the goods are people who listen to +classical music versus top 40 music + + align:start position:0% +classical music versus top 40 music + + + align:start position:0% +classical music versus top 40 music +valued differently by different + + align:start position:0% +valued differently by different + + + align:start position:0% +valued differently by different +advertisers do the advertisers gain from + + align:start position:0% +advertisers do the advertisers gain from + + + align:start position:0% +advertisers do the advertisers gain from +match quality that would be one thing + + align:start position:0% +match quality that would be one thing + + + align:start position:0% +match quality that would be one thing +leading us to want more stations besides + + align:start position:0% +leading us to want more stations besides + + + align:start position:0% +leading us to want more stations besides +the consumer + + align:start position:0% +the consumer + + + align:start position:0% +the consumer +surplus um you know the paper also is + + align:start position:0% +surplus um you know the paper also is + + + align:start position:0% +surplus um you know the paper also is +also very limited in letting quality + + align:start position:0% +also very limited in letting quality + + + align:start position:0% +also very limited in letting quality +vary across stations you know I think it + + align:start position:0% +vary across stations you know I think it + + + align:start position:0% +vary across stations you know I think it +is true that there are big stations that + + align:start position:0% +is true that there are big stations that + + + align:start position:0% +is true that there are big stations that +have very big fixed costs there are a + + align:start position:0% +have very big fixed costs there are a + + + align:start position:0% +have very big fixed costs there are a +lot of like College radio stations that + + align:start position:0% +lot of like College radio stations that + + + align:start position:0% +lot of like College radio stations that +have very small fixed costs and very low + + align:start position:0% +have very small fixed costs and very low + + + align:start position:0% +have very small fixed costs and very low +powerered antennas and you imagine that + + align:start position:0% +powerered antennas and you imagine that + + + align:start position:0% +powerered antennas and you imagine that +it's not the case that sort of we cut + + align:start position:0% +it's not the case that sort of we cut + + + align:start position:0% +it's not the case that sort of we cut +out three quarters of stations we cut + + align:start position:0% +out three quarters of stations we cut + + + align:start position:0% +out three quarters of stations we cut +out three quarters the fixed costs it + + align:start position:0% +out three quarters the fixed costs it + + + align:start position:0% +out three quarters the fixed costs it +may be that all those little stations + + align:start position:0% +may be that all those little stations + + + align:start position:0% +may be that all those little stations +that no one's listening to also are + + align:start position:0% +that no one's listening to also are + + + align:start position:0% +that no one's listening to also are +there because they all have very little + + align:start position:0% +there because they all have very little + + + align:start position:0% +there because they all have very little +fixed costs and we would like to do that + + align:start position:0% +fixed costs and we would like to do that + + + align:start position:0% +fixed costs and we would like to do that +um the other thing that I think they you + + align:start position:0% +um the other thing that I think they you + + + align:start position:0% +um the other thing that I think they you +know they don't have the data to do but + + align:start position:0% +know they don't have the data to do but + + + align:start position:0% +know they don't have the data to do but +it would be you know I think a big + + align:start position:0% +it would be you know I think a big + + + align:start position:0% +it would be you know I think a big +question in these media markets is what + + align:start position:0% +question in these media markets is what + + + align:start position:0% +question in these media markets is what +is the number of advertising minutes per + + align:start position:0% +is the number of advertising minutes per + + + align:start position:0% +is the number of advertising minutes per +hour and how is that optimal relative to + + align:start position:0% +hour and how is that optimal relative to + + + align:start position:0% +hour and how is that optimal relative to +Consumer preferences and Advertiser + + align:start position:0% +Consumer preferences and Advertiser + + + align:start position:0% +Consumer preferences and Advertiser +preferences and you know it would be you + + align:start position:0% +preferences and you know it would be you + + + align:start position:0% +preferences and you know it would be you +know be very nice to do sort of have + + align:start position:0% +know be very nice to do sort of have + + + align:start position:0% +know be very nice to do sort of have +more on know more about you know how do + + align:start position:0% +more on know more about you know how do + + + align:start position:0% +more on know more about you know how do +advertisers choose the number of minutes + + align:start position:0% +advertisers choose the number of minutes + + + align:start position:0% +advertisers choose the number of minutes +per how do radio stations choose the + + align:start position:0% +per how do radio stations choose the + + + align:start position:0% +per how do radio stations choose the +number of minutes per hour and what is + + align:start position:0% +number of minutes per hour and what is + + + align:start position:0% +number of minutes per hour and what is +the tradeoff on that look like and you + + align:start position:0% +the tradeoff on that look like and you + + + align:start position:0% +the tradeoff on that look like and you +know you can imagine that we don't get + + align:start position:0% +know you can imagine that we don't get + + + align:start position:0% +know you can imagine that we don't get +we don't get price variation on the + + align:start position:0% +we don't get price variation on the + + + align:start position:0% +we don't get price variation on the +consumer side but you do get minutes of + + align:start position:0% +consumer side but you do get minutes of + + + align:start position:0% +consumer side but you do get minutes of +advertising variation on the consumer + + align:start position:0% +advertising variation on the consumer + + + align:start position:0% +advertising variation on the consumer +side and you could imagine that + + align:start position:0% +side and you could imagine that + + + align:start position:0% +side and you could imagine that +exploiting that minute of advertising + + align:start position:0% +exploiting that minute of advertising + + + align:start position:0% +exploiting that minute of advertising +variation can be an be an interesting + + align:start position:0% +variation can be an be an interesting + + + align:start position:0% +variation can be an be an interesting +way um to sort of get get better at sort + + align:start position:0% +way um to sort of get get better at sort + + + align:start position:0% +way um to sort of get get better at sort +of what are the what's the consumer + + align:start position:0% +of what are the what's the consumer + + + align:start position:0% +of what are the what's the consumer +surplus of the consumers were listening + + align:start position:0% +surplus of the consumers were listening + + + align:start position:0% +surplus of the consumers were listening +to the free radio and you know should + + align:start position:0% +to the free radio and you know should + + + align:start position:0% +to the free radio and you know should +say there there are a number of papers + + align:start position:0% +say there there are a number of papers + + + align:start position:0% +say there there are a number of papers +that sort of do have advertising data + + align:start position:0% +that sort of do have advertising data + + + align:start position:0% +that sort of do have advertising data +try to address some of these questions + + align:start position:0% +try to address some of these questions + + + align:start position:0% +try to address some of these questions +but I think it's still an area for more + + align:start position:0% +but I think it's still an area for more + + + align:start position:0% +but I think it's still an area for more +some interesting work okay so then the + + align:start position:0% +some interesting work okay so then the + + + align:start position:0% +some interesting work okay so then the +final thing I want to do is is cover a + + align:start position:0% +final thing I want to do is is cover a + + + align:start position:0% +final thing I want to do is is cover a +couple papers that + + align:start position:0% +couple papers that + + + align:start position:0% +couple papers that +are some sense arguing that often these + + align:start position:0% +are some sense arguing that often these + + + align:start position:0% +are some sense arguing that often these +entry models are doing the wrong model + + align:start position:0% +entry models are doing the wrong model + + + align:start position:0% +entry models are doing the wrong model +of Entry um these most of the models of + + align:start position:0% +of Entry um these most of the models of + + + align:start position:0% +of Entry um these most of the models of +Entry that I discussed in th's textbook + + align:start position:0% +Entry that I discussed in th's textbook + + + align:start position:0% +Entry that I discussed in th's textbook +are this variety we have n you know we + + align:start position:0% +are this variety we have n you know we + + + align:start position:0% +are this variety we have n you know we +have some large population of firms M + + align:start position:0% +have some large population of firms M + + + align:start position:0% +have some large population of firms M +they're all choosing in or out paying a + + align:start position:0% +they're all choosing in or out paying a + + + align:start position:0% +they're all choosing in or out paying a +fixed cost and then once they enter + + align:start position:0% +fixed cost and then once they enter + + + align:start position:0% +fixed cost and then once they enter +there's this symmetric competition + + align:start position:0% +there's this symmetric competition + + + align:start position:0% +there's this symmetric competition +between them you know I think we know + + align:start position:0% +between them you know I think we know + + + align:start position:0% +between them you know I think we know +though that like on the radio is an + + align:start position:0% +though that like on the radio is an + + + align:start position:0% +though that like on the radio is an +example that it's not symmetric + + align:start position:0% +example that it's not symmetric + + + align:start position:0% +example that it's not symmetric +competition there's some big firms + + align:start position:0% +competition there's some big firms + + + align:start position:0% +competition there's some big firms +there's some small firms uh and what's + + align:start position:0% +there's some small firms uh and what's + + + align:start position:0% +there's some small firms uh and what's +in these next two papers is is thinking + + align:start position:0% +in these next two papers is is thinking + + + align:start position:0% +in these next two papers is is thinking +about um even when you have products + + align:start position:0% +about um even when you have products + + + align:start position:0% +about um even when you have products +that like in radio we think they're like + + align:start position:0% +that like in radio we think they're like + + + align:start position:0% +that like in radio we think they're like +high quality or there's popular music + + align:start position:0% +high quality or there's popular music + + + align:start position:0% +high quality or there's popular music +stations that lots of people listen to + + align:start position:0% +stations that lots of people listen to + + + align:start position:0% +stations that lots of people listen to +and then they're in esoteric stations + + align:start position:0% +and then they're in esoteric stations + + + align:start position:0% +and then they're in esoteric stations +that not a lot of people listen to with + + align:start position:0% +that not a lot of people listen to with + + + align:start position:0% +that not a lot of people listen to with +low power even when you look at products + + align:start position:0% +low power even when you look at products + + + align:start position:0% +low power even when you look at products +that seem like they should be + + align:start position:0% +that seem like they should be + + + align:start position:0% +that seem like they should be +homogeneous it seems like symmetry of + + align:start position:0% +homogeneous it seems like symmetry of + + + align:start position:0% +homogeneous it seems like symmetry of +competition is not a correct answer so + + align:start position:0% +competition is not a correct answer so + + + align:start position:0% +competition is not a correct answer so +these papers on Entry they're again also + + align:start position:0% +these papers on Entry they're again also + + + align:start position:0% +these papers on Entry they're again also +papers really about competition arguing + + align:start position:0% +papers really about competition arguing + + + align:start position:0% +papers really about competition arguing +that this model of entry and then + + align:start position:0% +that this model of entry and then + + + align:start position:0% +that this model of entry and then +symmetric competition seems like it + + align:start position:0% +symmetric competition seems like it + + + align:start position:0% +symmetric competition seems like it +doesn't fit the data very well so anyway + + align:start position:0% +doesn't fit the data very well so anyway + + + align:start position:0% +doesn't fit the data very well so anyway +you know example homogeneous product + + align:start position:0% +you know example homogeneous product + + + align:start position:0% +you know example homogeneous product +mayonnaise you know I've heard that if + + align:start position:0% +mayonnaise you know I've heard that if + + + align:start position:0% +mayonnaise you know I've heard that if +you do blind paste tests people have a + + align:start position:0% +you do blind paste tests people have a + + + align:start position:0% +you do blind paste tests people have a +very hard time telling one brand of + + align:start position:0% +very hard time telling one brand of + + + align:start position:0% +very hard time telling one brand of +mayonnaise apart from another brand of + + align:start position:0% +mayonnaise apart from another brand of + + + align:start position:0% +mayonnaise apart from another brand of +mayonnaise shouldn't mayonnaise just be + + align:start position:0% +mayonnaise shouldn't mayonnaise just be + + + align:start position:0% +mayonnaise shouldn't mayonnaise just be +a homogeneous good where there's a + + align:start position:0% +a homogeneous good where there's a + + + align:start position:0% +a homogeneous good where there's a +quantity of mayonnaise market cing price + + align:start position:0% +quantity of mayonnaise market cing price + + + align:start position:0% +quantity of mayonnaise market cing price +in mayonnaise anyway it turns out + + align:start position:0% +in mayonnaise anyway it turns out + + + align:start position:0% +in mayonnaise anyway it turns out +empirically that that's actually that's + + align:start position:0% +empirically that that's actually that's + + + align:start position:0% +empirically that that's actually that's +not true well that that it's not true + + align:start position:0% +not true well that that it's not true + + + align:start position:0% +not true well that that it's not true +that mayonnaise does all taste the same + + align:start position:0% +that mayonnaise does all taste the same + + + align:start position:0% +that mayonnaise does all taste the same +it's not what's not true is that people + + align:start position:0% +it's not what's not true is that people + + + align:start position:0% +it's not what's not true is that people +treat may like just product they're + + align:start position:0% +treat may like just product they're + + + align:start position:0% +treat may like just product they're +deciding what to buy in the + + align:start position:0% +deciding what to buy in the + + + align:start position:0% +deciding what to buy in the +supermarket um so in particular uh one + + align:start position:0% +supermarket um so in particular uh one + + + align:start position:0% +supermarket um so in particular uh one +of the things that's + + align:start position:0% +of the things that's + + + align:start position:0% +of the things that's +uh you so there's a you know paper by + + align:start position:0% +uh you so there's a you know paper by + + + align:start position:0% +uh you so there's a you know paper by +Golder and tell us that's you know few + + align:start position:0% +Golder and tell us that's you know few + + + align:start position:0% +Golder and tell us that's you know few +decades old now noting that there are + + align:start position:0% +decades old now noting that there are + + + align:start position:0% +decades old now noting that there are +many many leading brands that have been + + align:start position:0% +many many leading brands that have been + + + align:start position:0% +many many leading brands that have been +leaders for a very very long time you + + align:start position:0% +leaders for a very very long time you + + + align:start position:0% +leaders for a very very long time you +look like when did Coca-Cola become the + + align:start position:0% +look like when did Coca-Cola become the + + + align:start position:0% +look like when did Coca-Cola become the +leading Cola in the United States it's + + align:start position:0% +leading Cola in the United States it's + + + align:start position:0% +leading Cola in the United States it's +something years ago and like many of the + + align:start position:0% +something years ago and like many of the + + + align:start position:0% +something years ago and like many of the +thing products you can think + + align:start position:0% +thing products you can think + + + align:start position:0% +thing products you can think +of have been the same you know the same + + align:start position:0% +of have been the same you know the same + + + align:start position:0% +of have been the same you know the same +leader has been there for a for a + + align:start position:0% +leader has been there for a for a + + + align:start position:0% +leader has been there for a for a +decades and decades and decades and um + + align:start position:0% +decades and decades and decades and um + + + align:start position:0% +decades and decades and decades and um +you know ever ready batteries or + + align:start position:0% +you know ever ready batteries or + + + align:start position:0% +you know ever ready batteries or +whatever like you know the Pampers + + align:start position:0% +whatever like you know the Pampers + + + align:start position:0% +whatever like you know the Pampers +diapers you know these same firms just + + align:start position:0% +diapers you know these same firms just + + + align:start position:0% +diapers you know these same firms just +persist for decade after decade after + + align:start position:0% +persist for decade after decade after + + + align:start position:0% +persist for decade after decade after +decade um interesting fact that sort of + + align:start position:0% +decade um interesting fact that sort of + + + align:start position:0% +decade um interesting fact that sort of +Ron Dar and do B were bring out their + + align:start position:0% +Ron Dar and do B were bring out their + + + align:start position:0% +Ron Dar and do B were bring out their +paper is that not only is it true that + + align:start position:0% +paper is that not only is it true that + + + align:start position:0% +paper is that not only is it true that +in many consumer goods there are Market + + align:start position:0% +in many consumer goods there are Market + + + align:start position:0% +in many consumer goods there are Market +leaders but those Market leaders differ + + align:start position:0% +leaders but those Market leaders differ + + + align:start position:0% +leaders but those Market leaders differ +in similar markets so this is the + + align:start position:0% +in similar markets so this is the + + + align:start position:0% +in similar markets so this is the +mayonnaise graph from their paper so + + align:start position:0% +mayonnaise graph from their paper so + + + align:start position:0% +mayonnaise graph from their paper so +there're you know two main mayonnaise + + align:start position:0% +there're you know two main mayonnaise + + + align:start position:0% +there're you know two main mayonnaise +firms in the United States um at least + + align:start position:0% +firms in the United States um at least + + + align:start position:0% +firms in the United States um at least +in the I probably in the South um + + align:start position:0% +in the I probably in the South um + + + align:start position:0% +in the I probably in the South um +there's craft and there's + + align:start position:0% +there's craft and there's + + + align:start position:0% +there's craft and there's +Unilever uh and craft produces uh craft + + align:start position:0% +Unilever uh and craft produces uh craft + + + align:start position:0% +Unilever uh and craft produces uh craft +mayonnaise um Unilever produces two + + align:start position:0% +mayonnaise um Unilever produces two + + + align:start position:0% +mayonnaise um Unilever produces two +Brands depending on what city you're in + + align:start position:0% +Brands depending on what city you're in + + + align:start position:0% +Brands depending on what city you're in +they produce something called helman's + + align:start position:0% +they produce something called helman's + + + align:start position:0% +they produce something called helman's +real mayonnaise they also produce + + align:start position:0% +real mayonnaise they also produce + + + align:start position:0% +real mayonnaise they also produce +something called Best Foods mayonnaise + + align:start position:0% +something called Best Foods mayonnaise + + + align:start position:0% +something called Best Foods mayonnaise +you can tell from the jars that helmens + + align:start position:0% +you can tell from the jars that helmens + + + align:start position:0% +you can tell from the jars that helmens +and Best Foods mayonnaise is are they're + + align:start position:0% +and Best Foods mayonnaise is are they're + + + align:start position:0% +and Best Foods mayonnaise is are they're +they're the same mayonnaise produced by + + align:start position:0% +they're the same mayonnaise produced by + + + align:start position:0% +they're the same mayonnaise produced by +Unilever just in some cities they sell + + align:start position:0% +Unilever just in some cities they sell + + + align:start position:0% +Unilever just in some cities they sell +it as helmond in some cities they sell + + align:start position:0% +it as helmond in some cities they sell + + + align:start position:0% +it as helmond in some cities they sell +it as Best Foods mayonnaise um but then + + align:start position:0% +it as Best Foods mayonnaise um but then + + + align:start position:0% +it as Best Foods mayonnaise um but then +what's striking is this is data on you + + align:start position:0% +what's striking is this is data on you + + + align:start position:0% +what's striking is this is data on you +know over the course of half a year I + + align:start position:0% +know over the course of half a year I + + + align:start position:0% +know over the course of half a year I +think on what's the market share by week + + align:start position:0% +think on what's the market share by week + + + align:start position:0% +think on what's the market share by week +of craft mayonnaise versus un mayonnaise + + align:start position:0% +of craft mayonnaise versus un mayonnaise + + + align:start position:0% +of craft mayonnaise versus un mayonnaise +in Denver and you can see in Denver like + + align:start position:0% +in Denver and you can see in Denver like + + + align:start position:0% +in Denver and you can see in Denver like +65 70% of people buy craft + + align:start position:0% +65 70% of people buy craft + + + align:start position:0% +65 70% of people buy craft +mayonnaise and 15 to 20% of the people + + align:start position:0% +mayonnaise and 15 to 20% of the people + + + align:start position:0% +mayonnaise and 15 to 20% of the people +buy the Unilever + + align:start position:0% +buy the Unilever + + + align:start position:0% +buy the Unilever +mayonnaise and then you go to Los + + align:start position:0% +mayonnaise and then you go to Los + + + align:start position:0% +mayonnaise and then you go to Los +Angeles and in Los Angeles only 25% of + + align:start position:0% +Angeles and in Los Angeles only 25% of + + + align:start position:0% +Angeles and in Los Angeles only 25% of +the people are buying craft mayonnaise + + align:start position:0% +the people are buying craft mayonnaise + + + align:start position:0% +the people are buying craft mayonnaise +and 60% I think it's the best foods M so + + align:start position:0% +and 60% I think it's the best foods M so + + + align:start position:0% +and 60% I think it's the best foods M so +the west coast and so it's sort of + + align:start position:0% +the west coast and so it's sort of + + + align:start position:0% +the west coast and so it's sort of +striking that like in some + + align:start position:0% +striking that like in some + + + align:start position:0% +striking that like in some +sense in Denver craft is the clear May + + align:start position:0% +sense in Denver craft is the clear May + + + align:start position:0% +sense in Denver craft is the clear May +is + + align:start position:0% +is + + + align:start position:0% +is +leer and in Los Angeles uh uner is the + + align:start position:0% +leer and in Los Angeles uh uner is the + + + align:start position:0% +leer and in Los Angeles uh uner is the +mayonnaise leader and so there are these + + align:start position:0% +mayonnaise leader and so there are these + + + align:start position:0% +mayonnaise leader and so there are these +different Market leaders and they've + + align:start position:0% +different Market leaders and they've + + + align:start position:0% +different Market leaders and they've +been different leaders and it seems + + align:start position:0% +been different leaders and it seems + + + align:start position:0% +been different leaders and it seems +quite stable that there's a leading + + align:start position:0% +quite stable that there's a leading + + + align:start position:0% +quite stable that there's a leading +mayonnaise that everyone buys and then + + align:start position:0% +mayonnaise that everyone buys and then + + + align:start position:0% +mayonnaise that everyone buys and then +there's a second mayonnaise that some + + align:start position:0% +there's a second mayonnaise that some + + + align:start position:0% +there's a second mayonnaise that some +people + + align:start position:0% +people + + + align:start position:0% +people +buy um they give other examples in the + + align:start position:0% +buy um they give other examples in the + + + align:start position:0% +buy um they give other examples in the +paper if you look at you know ground + + align:start position:0% +paper if you look at you know ground + + + align:start position:0% +paper if you look at you know ground +coffee I think it was another fairly + + align:start position:0% +coffee I think it was another fairly + + + align:start position:0% +coffee I think it was another fairly +undifferentiated product I don't know if + + align:start position:0% +undifferentiated product I don't know if + + + align:start position:0% +undifferentiated product I don't know if +you guys + + align:start position:0% +you guys + + + align:start position:0% +you guys +are wealthy enough that you don't drink + + align:start position:0% +are wealthy enough that you don't drink + + + align:start position:0% +are wealthy enough that you don't drink +eat frozen drink frozen ground coffee + + align:start position:0% +eat frozen drink frozen ground coffee + + + align:start position:0% +eat frozen drink frozen ground coffee +and you buy F Starbucks whatever but you + + align:start position:0% +and you buy F Starbucks whatever but you + + + align:start position:0% +and you buy F Starbucks whatever but you +know you buy the FR ground coffee in a + + align:start position:0% +know you buy the FR ground coffee in a + + + align:start position:0% +know you buy the FR ground coffee in a +can I don't know how different the + + align:start position:0% +can I don't know how different the + + + align:start position:0% +can I don't know how different the +different cans are um but anyway folder + + align:start position:0% +different cans are um but anyway folder + + + align:start position:0% +different cans are um but anyway folder +share ranges from 16% in New York to 59% + + align:start position:0% +share ranges from 16% in New York to 59% + + + align:start position:0% +share ranges from 16% in New York to 59% +in De Iowa Maxwell House's share is only + + align:start position:0% +in De Iowa Maxwell House's share is only + + + align:start position:0% +in De Iowa Maxwell House's share is only +4% in Seattle but it's 46% in Pittsburgh + + align:start position:0% +4% in Seattle but it's 46% in Pittsburgh + + + align:start position:0% +4% in Seattle but it's 46% in Pittsburgh +and again you know these shares seem to + + align:start position:0% +and again you know these shares seem to + + + align:start position:0% +and again you know these shares seem to +be persistent in the + + align:start position:0% + + + + align:start position:0% + +data um so what uh BR du to do to sort + + align:start position:0% +data um so what uh BR du to do to sort + + + align:start position:0% +data um so what uh BR du to do to sort +of talk about this is they just + + align:start position:0% +of talk about this is they just + + + align:start position:0% +of talk about this is they just +investigate this as being + + align:start position:0% +investigate this as being + + + align:start position:0% +investigate this as being +a really really long time span echo of + + align:start position:0% +a really really long time span echo of + + + align:start position:0% +a really really long time span echo of +what happened when these products were + + align:start position:0% +what happened when these products were + + + align:start position:0% +what happened when these products were +introduced and so their idea is that you + + align:start position:0% +introduced and so their idea is that you + + + align:start position:0% +introduced and so their idea is that you +know in consumer packaged good + + align:start position:0% +know in consumer packaged good + + + align:start position:0% +know in consumer packaged good +markets people just you know somehow + + align:start position:0% +markets people just you know somehow + + + align:start position:0% +markets people just you know somehow +there's some model where people learn to + + align:start position:0% +there's some model where people learn to + + + align:start position:0% +there's some model where people learn to +buy a brand they buy that brand and + + align:start position:0% +buy a brand they buy that brand and + + + align:start position:0% +buy a brand they buy that brand and +either they buy that brand and they get + + align:start position:0% +either they buy that brand and they get + + + align:start position:0% +either they buy that brand and they get +used to exactly what that brand tastes + + align:start position:0% +used to exactly what that brand tastes + + + align:start position:0% +used to exactly what that brand tastes +like and that's what they think mayona + + align:start position:0% +like and that's what they think mayona + + + align:start position:0% +like and that's what they think mayona +should taste like or they just know that + + align:start position:0% +should taste like or they just know that + + + align:start position:0% +should taste like or they just know that +I buy craft mayonnaise my mother bought + + align:start position:0% +I buy craft mayonnaise my mother bought + + + align:start position:0% +I buy craft mayonnaise my mother bought +craft mayonnaise her mother bought craft + + align:start position:0% +craft mayonnaise her mother bought craft + + + align:start position:0% +craft mayonnaise her mother bought craft +mayonnaise before her when you go to + + align:start position:0% +mayonnaise before her when you go to + + + align:start position:0% +mayonnaise before her when you go to +mayonnaise you've seen your mother buy + + align:start position:0% +mayonnaise you've seen your mother buy + + + align:start position:0% +mayonnaise you've seen your mother buy +craft mayonnaise you buy craft + + align:start position:0% +craft mayonnaise you buy craft + + + align:start position:0% +craft mayonnaise you buy craft +mayonnaise um so we're you know anyway + + align:start position:0% +mayonnaise um so we're you know anyway + + + align:start position:0% +mayonnaise um so we're you know anyway +that's the sort of story that they're + + align:start position:0% +that's the sort of story that they're + + + align:start position:0% +that's the sort of story that they're +thinking of is there's just something + + align:start position:0% +thinking of is there's just something + + + align:start position:0% +thinking of is there's just something +about people toring taste you know it + + align:start position:0% +about people toring taste you know it + + + align:start position:0% +about people toring taste you know it +could also be something that's less + + align:start position:0% +could also be something that's less + + + align:start position:0% +could also be something that's less +um it could be something that's less + + align:start position:0% +um it could be something that's less + + + align:start position:0% +um it could be something that's less +taste based it could also be there's + + align:start position:0% +taste based it could also be there's + + + align:start position:0% +taste based it could also be there's +some advantages to dominance like if + + align:start position:0% +some advantages to dominance like if + + + align:start position:0% +some advantages to dominance like if +you're the dominant mayonnaise you can + + align:start position:0% +you're the dominant mayonnaise you can + + + align:start position:0% +you're the dominant mayonnaise you can +go to the supermarket and tell + + align:start position:0% +go to the supermarket and tell + + + align:start position:0% +go to the supermarket and tell +Albertson's I want my mayonnaise at eye + + align:start position:0% +Albertson's I want my mayonnaise at eye + + + align:start position:0% +Albertson's I want my mayonnaise at eye +level I want you to put that un lever + + align:start position:0% +level I want you to put that un lever + + + align:start position:0% +level I want you to put that un lever +mayonnaise down on the bottom shelf and + + align:start position:0% +mayonnaise down on the bottom shelf and + + + align:start position:0% +mayonnaise down on the bottom shelf and +that somehow the dominant mayonnaise + + align:start position:0% +that somehow the dominant mayonnaise + + + align:start position:0% +that somehow the dominant mayonnaise +gets put at ey level the second + + align:start position:0% +gets put at ey level the second + + + align:start position:0% +gets put at ey level the second +mayonnaise gets put on the lower shelf + + align:start position:0% +mayonnaise gets put on the lower shelf + + + align:start position:0% +mayonnaise gets put on the lower shelf +and then people are just always seeing + + align:start position:0% +and then people are just always seeing + + + align:start position:0% +and then people are just always seeing +the ey level mayonnaise and that's what + + align:start position:0% +the ey level mayonnaise and that's what + + + align:start position:0% +the ey level mayonnaise and that's what +they buy um and so there's just some you + + align:start position:0% +they buy um and so there's just some you + + + align:start position:0% +they buy um and so there's just some you +know some sense this is a you know story + + align:start position:0% +know some sense this is a you know story + + + align:start position:0% +know some sense this is a you know story +of dominance producing dominance and and + + align:start position:0% +of dominance producing dominance and and + + + align:start position:0% +of dominance producing dominance and and +some kind of you know Market power being + + align:start position:0% +some kind of you know Market power being + + + align:start position:0% +some kind of you know Market power being +produced by large market + + align:start position:0% +produced by large market + + + align:start position:0% +produced by large market +share but so anyway what they've done is + + align:start position:0% +share but so anyway what they've done is + + + align:start position:0% +share but so anyway what they've done is +they they go back to um you know they go + + align:start position:0% +they they go back to um you know they go + + + align:start position:0% +they they go back to um you know they go +back a 100 years and so all these + + align:start position:0% +back a 100 years and so all these + + + align:start position:0% +back a 100 years and so all these +products like the helman's mayonnaise or + + align:start position:0% +products like the helman's mayonnaise or + + + align:start position:0% +products like the helman's mayonnaise or +the craft mayonnaise um they find where + + align:start position:0% +the craft mayonnaise um they find where + + + align:start position:0% +the craft mayonnaise um they find where +those products were first introduced in + + align:start position:0% +those products were first introduced in + + + align:start position:0% +those products were first introduced in +the early 20th century uh and sometimes + + align:start position:0% +the early 20th century uh and sometimes + + + align:start position:0% +the early 20th century uh and sometimes +in the 19th + + align:start position:0% +in the 19th + + + align:start position:0% +in the 19th +century uh and then they run a couple + + align:start position:0% +century uh and then they run a couple + + + align:start position:0% +century uh and then they run a couple +they do two things so this is their sort + + align:start position:0% +they do two things so this is their sort + + + align:start position:0% +they do two things so this is their sort +of main analysis where they have 40 + + align:start position:0% +of main analysis where they have 40 + + + align:start position:0% +of main analysis where they have 40 +Brands which they could find these uh + + align:start position:0% +Brands which they could find these uh + + + align:start position:0% +Brands which they could find these uh +Origins and they regress the market + + align:start position:0% +Origins and they regress the market + + + align:start position:0% +Origins and they regress the market +share that brand I is getting in City M + + align:start position:0% +share that brand I is getting in City M + + + align:start position:0% +share that brand I is getting in City M +forget about the Seas um it's a constant + + align:start position:0% +forget about the Seas um it's a constant + + + align:start position:0% +forget about the Seas um it's a constant +so like you know helmet is better than + + align:start position:0% +so like you know helmet is better than + + + align:start position:0% +so like you know helmet is better than +craft plus these coefficients based on + + align:start position:0% +craft plus these coefficients based on + + + align:start position:0% +craft plus these coefficients based on +your distance to the origin city are you + + align:start position:0% +your distance to the origin city are you + + + align:start position:0% +your distance to the origin city are you +the origin city are you 50 miles from + + align:start position:0% +the origin city are you 50 miles from + + + align:start position:0% +the origin city are you 50 miles from +the origin city are you 100 miles 200 + + align:start position:0% +the origin city are you 100 miles 200 + + + align:start position:0% +the origin city are you 100 miles 200 +miles 1,000 miles the thought being that + + align:start position:0% +miles 1,000 miles the thought being that + + + align:start position:0% +miles 1,000 miles the thought being that +they don't know when all these + + align:start position:0% +they don't know when all these + + + align:start position:0% +they don't know when all these +mayonnaise has got to all these + + align:start position:0% +mayonnaise has got to all these + + + align:start position:0% +mayonnaise has got to all these +different places but their idea would be + + align:start position:0% +different places but their idea would be + + + align:start position:0% +different places but their idea would be +that you know there's uh uh if we look + + align:start position:0% +that you know there's uh uh if we look + + + align:start position:0% +that you know there's uh uh if we look +at United States um so anyway I have + + align:start position:0% +at United States um so anyway I have + + + align:start position:0% +at United States um so anyway I have +have map United States and then there's + + align:start position:0% +have map United States and then there's + + + align:start position:0% +have map United States and then there's +just sort of like craft mayonnaise gets + + align:start position:0% +just sort of like craft mayonnaise gets + + + align:start position:0% +just sort of like craft mayonnaise gets +invented here the year + + align:start position:0% +invented here the year + + + align:start position:0% +invented here the year +1895 and then their thought is that it + + align:start position:0% +1895 and then their thought is that it + + + align:start position:0% +1895 and then their thought is that it +probably just spread like this and so by + + align:start position:0% +probably just spread like this and so by + + + align:start position:0% +probably just spread like this and so by +like you know 1910 it was here by 1930 + + align:start position:0% +like you know 1910 it was here by 1930 + + + align:start position:0% +like you know 1910 it was here by 1930 +it was here and so we're sort of seeing + + align:start position:0% +it was here and so we're sort of seeing + + + align:start position:0% +it was here and so we're sort of seeing +the craft spreading and we're seeing + + align:start position:0% +the craft spreading and we're seeing + + + align:start position:0% +the craft spreading and we're seeing +helmets + + align:start position:0% +helmets + + + align:start position:0% +helmets +spreading and so the how far you are + + align:start position:0% +spreading and so the how far you are + + + align:start position:0% +spreading and so the how far you are +from where it started is going to sort + + align:start position:0% +from where it started is going to sort + + + align:start position:0% +from where it started is going to sort +of be how many other mayonnaise were + + align:start position:0% +of be how many other mayonnaise were + + + align:start position:0% +of be how many other mayonnaise were +there before you and so if you were near + + align:start position:0% +there before you and so if you were near + + + align:start position:0% +there before you and so if you were near +the origin you were there and got to + + align:start position:0% +the origin you were there and got to + + + align:start position:0% +the origin you were there and got to +establish the early lead and now + + align:start position:0% +establish the early lead and now + + + align:start position:0% +establish the early lead and now +dominate if you're far from the origin + + align:start position:0% +dominate if you're far from the origin + + + align:start position:0% +dominate if you're far from the origin +you know by the time this mayonnaise + + align:start position:0% +you know by the time this mayonnaise + + + align:start position:0% +you know by the time this mayonnaise +gets to California people were eating + + align:start position:0% +gets to California people were eating + + + align:start position:0% +gets to California people were eating +several other mayonnaise and so it's + + align:start position:0% +several other mayonnaise and so it's + + + align:start position:0% +several other mayonnaise and so it's +stayed + + align:start position:0% + + + + align:start position:0% + +behind so that's their sort of main + + align:start position:0% +behind so that's their sort of main + + + align:start position:0% +behind so that's their sort of main +analysis because they were able to do + + align:start position:0% +analysis because they were able to do + + + align:start position:0% +analysis because they were able to do +this for 40 products the second thing + + align:start position:0% +this for 40 products the second thing + + + align:start position:0% +this for 40 products the second thing +they did is there were six products + + align:start position:0% +they did is there were six products + + + align:start position:0% +they did is there were six products +where they were actually able to + + align:start position:0% +where they were actually able to + + + align:start position:0% +where they were actually able to +identify + + align:start position:0% +identify + + + align:start position:0% +identify +at the City by City level when did + + align:start position:0% +at the City by City level when did + + + align:start position:0% +at the City by City level when did +Miller beer get to Milwaukee when did + + align:start position:0% +Miller beer get to Milwaukee when did + + + align:start position:0% +Miller beer get to Milwaukee when did +Miller beer get to Chicago when did + + align:start position:0% +Miller beer get to Chicago when did + + + align:start position:0% +Miller beer get to Chicago when did +Miller beer get to Indianapolis when did + + align:start position:0% +Miller beer get to Indianapolis when did + + + align:start position:0% +Miller beer get to Indianapolis when did +it get to Philadelphia when did it get + + align:start position:0% +it get to Philadelphia when did it get + + + align:start position:0% +it get to Philadelphia when did it get +to Miami so they actually were able to + + align:start position:0% +to Miami so they actually were able to + + + align:start position:0% +to Miami so they actually were able to +track when each of the brands enter all + + align:start position:0% +track when each of the brands enter all + + + align:start position:0% +track when each of the brands enter all +the different cities and then they can + + align:start position:0% +the different cities and then they can + + + align:start position:0% +the different cities and then they can +regress City specific market shares on + + align:start position:0% +regress City specific market shares on + + + align:start position:0% +regress City specific market shares on +the ENT on dummies for entry order were + + align:start position:0% +the ENT on dummies for entry order were + + + align:start position:0% +the ENT on dummies for entry order were +you there before your arrival you know + + align:start position:0% +you there before your arrival you know + + + align:start position:0% +you there before your arrival you know +which mayona got to Phoenix First the + + align:start position:0% +which mayona got to Phoenix First the + + + align:start position:0% +which mayona got to Phoenix First the +regression + + align:start position:0% + + + + align:start position:0% + +anyway so here's the uh you know what + + align:start position:0% +anyway so here's the uh you know what + + + align:start position:0% +anyway so here's the uh you know what +their data sample looks like so again + + align:start position:0% +their data sample looks like so again + + + align:start position:0% +their data sample looks like so again +this is you know 40 products and so for + + align:start position:0% +this is you know 40 products and so for + + + align:start position:0% +this is you know 40 products and so for +each of these 40 products like let's go + + align:start position:0% +each of these 40 products like let's go + + + align:start position:0% +each of these 40 products like let's go +to CRA mayonnaise down at the bottom + + align:start position:0% +to CRA mayonnaise down at the bottom + + + align:start position:0% +to CRA mayonnaise down at the bottom +mayonnaise at the very bottom craft + + align:start position:0% +mayonnaise at the very bottom craft + + + align:start position:0% +mayonnaise at the very bottom craft +mayonnaise oh I was I was just about + + align:start position:0% +mayonnaise oh I was I was just about + + + align:start position:0% +mayonnaise oh I was I was just about +right craft mayonnaise started in Salem + + align:start position:0% +right craft mayonnaise started in Salem + + + align:start position:0% +right craft mayonnaise started in Salem +Illinois and it started Salem Illinois + + align:start position:0% +Illinois and it started Salem Illinois + + + align:start position:0% +Illinois and it started Salem Illinois +in + + align:start position:0% +in + + + align:start position:0% +in +1931 uh and Unilever mayonnaise which is + + align:start position:0% +1931 uh and Unilever mayonnaise which is + + + align:start position:0% +1931 uh and Unilever mayonnaise which is +um Helman on the East Coast helman's + + align:start position:0% +um Helman on the East Coast helman's + + + align:start position:0% +um Helman on the East Coast helman's +mayonnaise started New York City in the + + align:start position:0% +mayonnaise started New York City in the + + + align:start position:0% +mayonnaise started New York City in the +year + + align:start position:0% +year + + + align:start position:0% +year +1905 and so what they're looking at is + + align:start position:0% +1905 and so what they're looking at is + + + align:start position:0% +1905 and so what they're looking at is +how do how does the share of Unilever + + align:start position:0% +how do how does the share of Unilever + + + align:start position:0% +how do how does the share of Unilever +versus um craft depend on your distance + + align:start position:0% +versus um craft depend on your distance + + + align:start position:0% +versus um craft depend on your distance +relative to these two points of + + align:start position:0% + + + + align:start position:0% + +origin okay so distance the origin + + align:start position:0% +origin okay so distance the origin + + + align:start position:0% +origin okay so distance the origin +analysis finds that current market + + align:start position:0% +analysis finds that current market + + + align:start position:0% +analysis finds that current market +shares are 18 percentage points higher + + align:start position:0% +shares are 18 percentage points higher + + + align:start position:0% +shares are 18 percentage points higher +in the closest cities than the most dist + + align:start position:0% +in the closest cities than the most dist + + + align:start position:0% +in the closest cities than the most dist +cities so you know the mean share of + + align:start position:0% +cities so you know the mean share of + + + align:start position:0% +cities so you know the mean share of +these products is like 22% so this is + + align:start position:0% +these products is like 22% so this is + + + align:start position:0% +these products is like 22% so this is +saying that you get like you know you + + align:start position:0% +saying that you get like you know you + + + align:start position:0% +saying that you get like you know you +could think of the 18 difference is + + align:start position:0% +could think of the 18 difference is + + + align:start position:0% +could think of the 18 difference is +being you know you get + + align:start position:0% +being you know you get + + + align:start position:0% +being you know you get +31% + + align:start position:0% + + + + align:start position:0% + +um yeah you're young + + align:start position:0% +um yeah you're young + + + align:start position:0% +um yeah you're young +uh let's see so it's you get like 31% in + + align:start position:0% +uh let's see so it's you get like 31% in + + + align:start position:0% +uh let's see so it's you get like 31% in +the closest cities and you get 133% in + + align:start position:0% +the closest cities and you get 133% in + + + align:start position:0% +the closest cities and you get 133% in +the farthest away cities so your market + + align:start position:0% +the farthest away cities so your market + + + align:start position:0% +the farthest away cities so your market +share is just dramatically higher in the + + align:start position:0% +share is just dramatically higher in the + + + align:start position:0% +share is just dramatically higher in the +cities near where you started right + + align:start position:0% +cities near where you started right + + + align:start position:0% +cities near where you started right +where you started than cities farther + + align:start position:0% +where you started than cities farther + + + align:start position:0% +where you started than cities farther +away where you started we get this sort + + align:start position:0% +away where you started we get this sort + + + align:start position:0% +away where you started we get this sort +of you know big effect for your origin + + align:start position:0% +of you know big effect for your origin + + + align:start position:0% +of you know big effect for your origin +City and then it's declining as we get + + align:start position:0% +City and then it's declining as we get + + + align:start position:0% +City and then it's declining as we get +to 250 miles 500 miles a thousand miles + + align:start position:0% +to 250 miles 500 miles a thousand miles + + + align:start position:0% +to 250 miles 500 miles a thousand miles +it then seems to be fairly flat and then + + align:start position:0% +it then seems to be fairly flat and then + + + align:start position:0% +it then seems to be fairly flat and then +it goes down a lot when you get to the + + align:start position:0% +it goes down a lot when you get to the + + + align:start position:0% +it goes down a lot when you get to the +opposite coast of the United States so + + align:start position:0% +opposite coast of the United States so + + + align:start position:0% +opposite coast of the United States so +it's like East Coast Products are + + align:start position:0% +it's like East Coast Products are + + + align:start position:0% +it's like East Coast Products are +selling noticeably Less on the West + + align:start position:0% +selling noticeably Less on the West + + + align:start position:0% +selling noticeably Less on the West +Coast West Coast Products are selling no + + align:start position:0% +Coast West Coast Products are selling no + + + align:start position:0% +Coast West Coast Products are selling no +or West Coast Products so notably Less + + align:start position:0% +or West Coast Products so notably Less + + + align:start position:0% +or West Coast Products so notably Less +on the East + + align:start position:0% +on the East + + + align:start position:0% +on the East +Coast so you know you may think that + + align:start position:0% +Coast so you know you may think that + + + align:start position:0% +Coast so you know you may think that +like you know our politics that the + + align:start position:0% +like you know our politics that the + + + align:start position:0% +like you know our politics that the +coasts are actually similar similar to + + align:start position:0% +coasts are actually similar similar to + + + align:start position:0% +coasts are actually similar similar to +each other and it's the middle of the + + align:start position:0% +each other and it's the middle of the + + + align:start position:0% +each other and it's the middle of the +country that's different I think this + + align:start position:0% +country that's different I think this + + + align:start position:0% +country that's different I think this +graph is saying no it's actually the it + + align:start position:0% +graph is saying no it's actually the it + + + align:start position:0% +graph is saying no it's actually the it +really is the distance it's like there + + align:start position:0% +really is the distance it's like there + + + align:start position:0% +really is the distance it's like there +East Coast mayonnaise and they West + + align:start position:0% +East Coast mayonnaise and they West + + + align:start position:0% +East Coast mayonnaise and they West +Coast mayonnaises they East Coast Bagels + + align:start position:0% +Coast mayonnaises they East Coast Bagels + + + align:start position:0% +Coast mayonnaises they East Coast Bagels +and West Coast Bagels and the market + + align:start position:0% +and West Coast Bagels and the market + + + align:start position:0% +and West Coast Bagels and the market +shares are most different on the + + align:start position:0% +shares are most different on the + + + align:start position:0% +shares are most different on the +opposite coast of the + + align:start position:0% +opposite coast of the + + + align:start position:0% +opposite coast of the +country and then the second uh ADV + + align:start position:0% +country and then the second uh ADV + + + align:start position:0% +country and then the second uh ADV +second part of the analysis about you + + align:start position:0% +second part of the analysis about you + + + align:start position:0% +second part of the analysis about you +know + + align:start position:0% +know + + + align:start position:0% +know +just is your market share higher or low + + align:start position:0% +just is your market share higher or low + + + align:start position:0% +just is your market share higher or low +you know higher in the cities that you + + align:start position:0% +you know higher in the cities that you + + + align:start position:0% +you know higher in the cities that you +reached first versus second relative to + + align:start position:0% +reached first versus second relative to + + + align:start position:0% +reached first versus second relative to +your main RI biggest rival and these + + align:start position:0% +your main RI biggest rival and these + + + align:start position:0% +your main RI biggest rival and these +numbers are are more moderate um they + + align:start position:0% +numbers are are more moderate um they + + + align:start position:0% +numbers are are more moderate um they +range across products so like the + + align:start position:0% +range across products so like the + + + align:start position:0% +range across products so like the +buttweiser versus Miller beer um there's + + align:start position:0% +buttweiser versus Miller beer um there's + + + align:start position:0% +buttweiser versus Miller beer um there's +not that much difference between bud and + + align:start position:0% +not that much difference between bud and + + + align:start position:0% +not that much difference between bud and +Miller market shares in the United + + align:start position:0% +Miller market shares in the United + + + align:start position:0% +Miller market shares in the United +States um on average whoever got their + + align:start position:0% +States um on average whoever got their + + + align:start position:0% +States um on average whoever got their +first is doing a 1.3% Point better than + + align:start position:0% +first is doing a 1.3% Point better than + + + align:start position:0% +first is doing a 1.3% Point better than +than whoever got their second um in the + + align:start position:0% +than whoever got their second um in the + + + align:start position:0% +than whoever got their second um in the +main a example who got their first + + align:start position:0% +main a example who got their first + + + align:start position:0% +main a example who got their first +versus second is uh 6.3 percentage + + align:start position:0% + + + + align:start position:0% + +points questions so it is I think fairly + + align:start position:0% +points questions so it is I think fairly + + + align:start position:0% +points questions so it is I think fairly +strong evidence especially that first + + align:start position:0% +strong evidence especially that first + + + align:start position:0% +strong evidence especially that first +part of there just are these asymmetries + + align:start position:0% +part of there just are these asymmetries + + + align:start position:0% +part of there just are these asymmetries +and remember these are events 100 years + + align:start position:0% +and remember these are events 100 years + + + align:start position:0% +and remember these are events 100 years +ago and right so it does seem like + + align:start position:0% +ago and right so it does seem like + + + align:start position:0% +ago and right so it does seem like +there's very very longlasting Market + + align:start position:0% +there's very very longlasting Market + + + align:start position:0% +there's very very longlasting Market +leadership advantages and we if we're + + align:start position:0% +leadership advantages and we if we're + + + align:start position:0% +leadership advantages and we if we're +thinking about entrance you know you + + align:start position:0% +thinking about entrance you know you + + + align:start position:0% +thinking about entrance you know you +know it's not like you enter in one year + + align:start position:0% +know it's not like you enter in one year + + + align:start position:0% +know it's not like you enter in one year +later you're G to be on even footing + + align:start position:0% +later you're G to be on even footing + + + align:start position:0% +later you're G to be on even footing +it's like you're going to enter in 100 + + align:start position:0% +it's like you're going to enter in 100 + + + align:start position:0% +it's like you're going to enter in 100 +years later you're still G to + + align:start position:0% +years later you're still G to + + + align:start position:0% +years later you're still G to +have fraction of the share that the + + align:start position:0% +have fraction of the share that the + + + align:start position:0% +have fraction of the share that the +leading firm had 100 years ago on + + align:start position:0% +leading firm had 100 years ago on + + + align:start position:0% +leading firm had 100 years ago on +something like mayonnaise whereas + + align:start position:0% +something like mayonnaise whereas + + + align:start position:0% +something like mayonnaise whereas +clearly it's not like their mayonnaise + + align:start position:0% +clearly it's not like their mayonnaise + + + align:start position:0% +clearly it's not like their mayonnaise +just been better for 100 + + align:start position:0% + + + + align:start position:0% + +years okay so then final pap going to + + align:start position:0% +years okay so then final pap going to + + + align:start position:0% +years okay so then final pap going to +cover today bronberg Dubay Jens cow um + + align:start position:0% +cover today bronberg Dubay Jens cow um + + + align:start position:0% +cover today bronberg Dubay Jens cow um +so this is really digging into where do + + align:start position:0% +so this is really digging into where do + + + align:start position:0% +so this is really digging into where do +Long Live advantages come from they draw + + align:start position:0% +Long Live advantages come from they draw + + + align:start position:0% +Long Live advantages come from they draw +two main distinctions for where to think + + align:start position:0% +two main distinctions for where to think + + + align:start position:0% +two main distinctions for where to think +of two main types of stories one is what + + align:start position:0% +of two main types of stories one is what + + + align:start position:0% +of two main types of stories one is what +they'll call demand side stories or + + align:start position:0% +they'll call demand side stories or + + + align:start position:0% +they'll call demand side stories or +preference side preference based Stories + + align:start position:0% +preference side preference based Stories + + + align:start position:0% +preference side preference based Stories +the preference based stories are people + + align:start position:0% +the preference based stories are people + + + align:start position:0% +the preference based stories are people +develop case for + + align:start position:0% +develop case for + + + align:start position:0% +develop case for +products that they consume growing up + + align:start position:0% +products that they consume growing up + + + align:start position:0% +products that they consume growing up +they're like you know I I I'm just used + + align:start position:0% +they're like you know I I I'm just used + + + align:start position:0% +they're like you know I I I'm just used +to this product I like the taste of this + + align:start position:0% +to this product I like the taste of this + + + align:start position:0% +to this product I like the taste of this +product or I've just learned from my + + align:start position:0% +product or I've just learned from my + + + align:start position:0% +product or I've just learned from my +parents that this is the right product + + align:start position:0% +parents that this is the right product + + + align:start position:0% +parents that this is the right product +to buy I just I have preferences about + + align:start position:0% +to buy I just I have preferences about + + + align:start position:0% +to buy I just I have preferences about +what this product + + align:start position:0% +what this product + + + align:start position:0% +what this product +is the supply side stories are the ones + + align:start position:0% +is the supply side stories are the ones + + + align:start position:0% +is the supply side stories are the ones +I talked about about like things like + + align:start position:0% +I talked about about like things like + + + align:start position:0% +I talked about about like things like +shelf space or advertising where if + + align:start position:0% +shelf space or advertising where if + + + align:start position:0% +shelf space or advertising where if +you're dominant you get the premier + + align:start position:0% +you're dominant you get the premier + + + align:start position:0% +you're dominant you get the premier +shelf space or if you're dominant it + + align:start position:0% +shelf space or if you're dominant it + + + align:start position:0% +shelf space or if you're dominant it +pays you to put on TV commercials you + + align:start position:0% +pays you to put on TV commercials you + + + align:start position:0% +pays you to put on TV commercials you +put on TV commercials that reinforces + + align:start position:0% +put on TV commercials that reinforces + + + align:start position:0% +put on TV commercials that reinforces +people's love for your type for your + + align:start position:0% +people's love for your type for your + + + align:start position:0% +people's love for your type for your +product and so what + + align:start position:0% +product and so what + + + align:start position:0% +product and so what +rber dub and Jens kind want to do is + + align:start position:0% +rber dub and Jens kind want to do is + + + align:start position:0% +rber dub and Jens kind want to do is +sort of say does it look like demand + + align:start position:0% +sort of say does it look like demand + + + align:start position:0% +sort of say does it look like demand +side or does it look like supply side + + align:start position:0% +side or does it look like supply side + + + align:start position:0% +side or does it look like supply side +and they have this sort of very + + align:start position:0% +and they have this sort of very + + + align:start position:0% +and they have this sort of very +thoughtful idea which is how about to + + align:start position:0% +thoughtful idea which is how about to + + + align:start position:0% +thoughtful idea which is how about to +investigate this looks look at people + + align:start position:0% +investigate this looks look at people + + + align:start position:0% +investigate this looks look at people +when they move and so like right many of + + align:start position:0% +when they move and so like right many of + + + align:start position:0% +when they move and so like right many of +you have moved to Boston and the + + align:start position:0% +you have moved to Boston and the + + + align:start position:0% +you have moved to Boston and the +question is once you've moved to Boston + + align:start position:0% +question is once you've moved to Boston + + + align:start position:0% +question is once you've moved to Boston +do you guys buy now the Boston + + align:start position:0% +do you guys buy now the Boston + + + align:start position:0% +do you guys buy now the Boston +mayonnaise brand or do you guys buy the + + align:start position:0% +mayonnaise brand or do you guys buy the + + + align:start position:0% +mayonnaise brand or do you guys buy the +mayonnaise brand that was big where you + + align:start position:0% +mayonnaise brand that was big where you + + + align:start position:0% +mayonnaise brand that was big where you +grew up so you know many of you probably + + align:start position:0% +grew up so you know many of you probably + + + align:start position:0% +grew up so you know many of you probably +I think + + align:start position:0% +I think + + + align:start position:0% +I think +I'd have to guess that Boston is a + + align:start position:0% +I'd have to guess that Boston is a + + + align:start position:0% +I'd have to guess that Boston is a +helman's mayonnaise city um given that + + align:start position:0% +helman's mayonnaise city um given that + + + align:start position:0% +helman's mayonnaise city um given that +you know again Helman started in New + + align:start position:0% +you know again Helman started in New + + + align:start position:0% +you know again Helman started in New +York and craft started in Illinois again + + align:start position:0% +York and craft started in Illinois again + + + align:start position:0% +York and craft started in Illinois again +there was a six percentage Point + + align:start position:0% +there was a six percentage Point + + + align:start position:0% +there was a six percentage Point +difference um but anyway I would guess + + align:start position:0% +difference um but anyway I would guess + + + align:start position:0% +difference um but anyway I would guess +that Helman is the Boston mayonnaise and + + align:start position:0% +that Helman is the Boston mayonnaise and + + + align:start position:0% +that Helman is the Boston mayonnaise and +the question is do you guys when you + + align:start position:0% +the question is do you guys when you + + + align:start position:0% +the question is do you guys when you +move here I don't know I guess not that + + align:start position:0% +move here I don't know I guess not that + + + align:start position:0% +move here I don't know I guess not that +many from West either um but you know + + align:start position:0% +many from West either um but you know + + + align:start position:0% +many from West either um but you know +when you guys move here did you start + + align:start position:0% +when you guys move here did you start + + + align:start position:0% +when you guys move here did you start +buying helman's mayonnaise and give up + + align:start position:0% +buying helman's mayonnaise and give up + + + align:start position:0% +buying helman's mayonnaise and give up +your craft mayonnaise or did you + + align:start position:0% +your craft mayonnaise or did you + + + align:start position:0% +your craft mayonnaise or did you +continue to buy the Craft mayonnaise + + align:start position:0% +continue to buy the Craft mayonnaise + + + align:start position:0% +continue to buy the Craft mayonnaise +which is you know totally aable in Star + + align:start position:0% +which is you know totally aable in Star + + + align:start position:0% +which is you know totally aable in Star +Market Whole Foods and whatever not + + align:start position:0% +Market Whole Foods and whatever not + + + align:start position:0% +Market Whole Foods and whatever not +Whole Foods um uh but anyway that's + + align:start position:0% +Whole Foods um uh but anyway that's + + + align:start position:0% +Whole Foods um uh but anyway that's +their idea and you might think well + + align:start position:0% +their idea and you might think well + + + align:start position:0% +their idea and you might think well +that's a great idea how would I ever + + align:start position:0% +that's a great idea how would I ever + + + align:start position:0% +that's a great idea how would I ever +find this out and this is where you know + + align:start position:0% +find this out and this is where you know + + + align:start position:0% +find this out and this is where you know +again this you get the sort of + + align:start position:0% +again this you get the sort of + + + align:start position:0% +again this you get the sort of +recognition of the importance in our + + align:start position:0% +recognition of the importance in our + + + align:start position:0% +recognition of the importance in our +profession of being very well funded and + + align:start position:0% +profession of being very well funded and + + + align:start position:0% +profession of being very well funded and +well connected sometimes um so what um + + align:start position:0% +well connected sometimes um so what um + + + align:start position:0% +well connected sometimes um so what um +you know University of Chicago has a + + align:start position:0% +you know University of Chicago has a + + + align:start position:0% +you know University of Chicago has a +long-standing relationship with uh + + align:start position:0% +long-standing relationship with uh + + + align:start position:0% +long-standing relationship with uh +neelon um + + align:start position:0% +neelon um + + + align:start position:0% +neelon um +you know NE firms like neelon besides + + align:start position:0% +you know NE firms like neelon besides + + + align:start position:0% +you know NE firms like neelon besides +doing things for people they have + + align:start position:0% +doing things for people they have + + + align:start position:0% +doing things for people they have +relationships with also do things for + + align:start position:0% +relationships with also do things for + + + align:start position:0% +relationships with also do things for +people who have money to pay them to do + + align:start position:0% +people who have money to pay them to do + + + align:start position:0% +people who have money to pay them to do +things uh and so what um BR jow got + + align:start position:0% +things uh and so what um BR jow got + + + align:start position:0% +things uh and so what um BR jow got +neelson to do is you know so I talked + + align:start position:0% +neelson to do is you know so I talked + + + align:start position:0% +neelson to do is you know so I talked +about neelson home scam panel okay + + align:start position:0% +about neelson home scam panel okay + + + align:start position:0% +about neelson home scam panel okay +neelon home scan panel if you want it's + + align:start position:0% +neelon home scan panel if you want it's + + + align:start position:0% +neelon home scan panel if you want it's +it's actually a lot of this data is + + align:start position:0% +it's actually a lot of this data is + + + align:start position:0% +it's actually a lot of this data is +available for free through the + + align:start position:0% +available for free through the + + + align:start position:0% +available for free through the +University of Chicago website um uh but + + align:start position:0% +University of Chicago website um uh but + + + align:start position:0% +University of Chicago website um uh but +anyway neon home scan panel is they + + align:start position:0% +anyway neon home scan panel is they + + + align:start position:0% +anyway neon home scan panel is they +they've got a panel of thousands of + + align:start position:0% +they've got a panel of thousands of + + + align:start position:0% +they've got a panel of thousands of +people across the United States + + align:start position:0% +people across the United States + + + align:start position:0% +people across the United States +and what these thousands of people do is + + align:start position:0% +and what these thousands of people do is + + + align:start position:0% +and what these thousands of people do is +they all have a part-time job their + + align:start position:0% +they all have a part-time job their + + + align:start position:0% +they all have a part-time job their +part-time job is recording everything + + align:start position:0% +part-time job is recording everything + + + align:start position:0% +part-time job is recording everything +that they buy and they're employed by + + align:start position:0% +that they buy and they're employed by + + + align:start position:0% +that they buy and they're employed by +neelon to do that and so like they're + + align:start position:0% +neelon to do that and so like they're + + + align:start position:0% +neelon to do that and so like they're +given like a supermarket scanner so like + + align:start position:0% +given like a supermarket scanner so like + + + align:start position:0% +given like a supermarket scanner so like +you go to the supermarket you buy stuff + + align:start position:0% +you go to the supermarket you buy stuff + + + align:start position:0% +you go to the supermarket you buy stuff +you scan it all on the scanner when + + align:start position:0% +you scan it all on the scanner when + + + align:start position:0% +you scan it all on the scanner when +you're there and then you bring it home + + align:start position:0% +you're there and then you bring it home + + + align:start position:0% +you're there and then you bring it home +and as you take it out of the bag you + + align:start position:0% +and as you take it out of the bag you + + + align:start position:0% +and as you take it out of the bag you +scan it again and you just scan it in so + + align:start position:0% +scan it again and you just scan it in so + + + align:start position:0% +scan it again and you just scan it in so +that neelon knows everything that you + + align:start position:0% +that neelon knows everything that you + + + align:start position:0% +that neelon knows everything that you +bought and you're supposed to do this + + align:start position:0% +bought and you're supposed to do this + + + align:start position:0% +bought and you're supposed to do this +everywhere you go you go to Target you + + align:start position:0% +everywhere you go you go to Target you + + + align:start position:0% +everywhere you go you go to Target you +come back you scan it you go to the CVS + + align:start position:0% +come back you scan it you go to the CVS + + + align:start position:0% +come back you scan it you go to the CVS +you come back you scan it you go to the + + align:start position:0% +you come back you scan it you go to the + + + align:start position:0% +you come back you scan it you go to the +supermarket you come back you scan it + + align:start position:0% +supermarket you come back you scan it + + + align:start position:0% +supermarket you come back you scan it +you basically just home scan so what + + align:start position:0% +you basically just home scan so what + + + align:start position:0% +you basically just home scan so what +these people do is they they buy stuff + + align:start position:0% +these people do is they they buy stuff + + + align:start position:0% +these people do is they they buy stuff +and then they just record everything + + align:start position:0% +and then they just record everything + + + align:start position:0% +and then they just record everything +that they got and then you know they're + + align:start position:0% +that they got and then you know they're + + + align:start position:0% +that they got and then you know they're +also recording where they got it and so + + align:start position:0% +also recording where they got it and so + + + align:start position:0% +also recording where they got it and so +because because neelon is already in the + + align:start position:0% +because because neelon is already in the + + + align:start position:0% +because because neelon is already in the +Star Market and nilson's already in the + + align:start position:0% +Star Market and nilson's already in the + + + align:start position:0% +Star Market and nilson's already in the +Whole Foods you bring it home you scan + + align:start position:0% +Whole Foods you bring it home you scan + + + align:start position:0% +Whole Foods you bring it home you scan +it they know what you PID for it because + + align:start position:0% +it they know what you PID for it because + + + align:start position:0% +it they know what you PID for it because +they know where you bought it and they + + align:start position:0% +they know where you bought it and they + + + align:start position:0% +they know where you bought it and they +know what that store of charging for it + + align:start position:0% +know what that store of charging for it + + + align:start position:0% +know what that store of charging for it +so you get this sort of data set of you + + align:start position:0% +so you get this sort of data set of you + + + align:start position:0% +so you get this sort of data set of you +know uh what is it that what is it that + + align:start position:0% +know uh what is it that what is it that + + + align:start position:0% +know uh what is it that what is it that +you know people at the individual level + + align:start position:0% +you know people at the individual level + + + align:start position:0% +you know people at the individual level +are are purchasing and you can also get + + align:start position:0% +are are purchasing and you can also get + + + align:start position:0% +are are purchasing and you can also get +you know aggregate market shares out of + + align:start position:0% +you know aggregate market shares out of + + + align:start position:0% +you know aggregate market shares out of +this um neelen home scan panel did not + + align:start position:0% +this um neelen home scan panel did not + + + align:start position:0% +this um neelen home scan panel did not +tell them you know it tells you where + + align:start position:0% +tell them you know it tells you where + + + align:start position:0% +tell them you know it tells you where +the people are located that this person + + align:start position:0% +the people are located that this person + + + align:start position:0% +the people are located that this person +is in Boston it doesn't tell you that um + + align:start position:0% +is in Boston it doesn't tell you that um + + + align:start position:0% +is in Boston it doesn't tell you that um +they grew up in Illinois and moved to + + align:start position:0% +they grew up in Illinois and moved to + + + align:start position:0% +they grew up in Illinois and moved to +Boston when they went to college at age + + align:start position:0% +Boston when they went to college at age + + + align:start position:0% +Boston when they went to college at age +of 19 okay so what they got neelon to do + + align:start position:0% +of 19 okay so what they got neelon to do + + + align:start position:0% +of 19 okay so what they got neelon to do +is survey the members of the home scan + + align:start position:0% +is survey the members of the home scan + + + align:start position:0% +is survey the members of the home scan +panel and ask them so + + align:start position:0% +panel and ask them so + + + align:start position:0% +panel and ask them so +What state were you born in when did you + + align:start position:0% +What state were you born in when did you + + + align:start position:0% +What state were you born in when did you +leave your state of birth um when did + + align:start position:0% +leave your state of birth um when did + + + align:start position:0% +leave your state of birth um when did +you how long have you been in your + + align:start position:0% +you how long have you been in your + + + align:start position:0% +you how long have you been in your +current um how long have youve been in + + align:start position:0% +current um how long have youve been in + + + align:start position:0% +current um how long have youve been in +your current location and ask you other + + align:start position:0% +your current location and ask you other + + + align:start position:0% +your current location and ask you other +questions like you know what's your + + align:start position:0% +questions like you know what's your + + + align:start position:0% +questions like you know what's your +gender what's your is SL education + + align:start position:0% +gender what's your is SL education + + + align:start position:0% +gender what's your is SL education +completed and so on um you know normally + + align:start position:0% +completed and so on um you know normally + + + align:start position:0% +completed and so on um you know normally +you would think you send a survey like + + align:start position:0% +you would think you send a survey like + + + align:start position:0% +you would think you send a survey like +that to people it's very hard to get + + align:start position:0% +that to people it's very hard to get + + + align:start position:0% +that to people it's very hard to get +them to respond but since this sort of + + align:start position:0% +them to respond but since this sort of + + + align:start position:0% +them to respond but since this sort of +survey was sponsored by homescan who is + + align:start position:0% +survey was sponsored by homescan who is + + + align:start position:0% +survey was sponsored by homescan who is +like an employer of all the homescan + + align:start position:0% +like an employer of all the homescan + + + align:start position:0% +like an employer of all the homescan +people um they got a 65 % response rate + + align:start position:0% +people um they got a 65 % response rate + + + align:start position:0% +people um they got a 65 % response rate +on their survey asking this information + + align:start position:0% +on their survey asking this information + + + align:start position:0% +on their survey asking this information +they're able to merge that information + + align:start position:0% +they're able to merge that information + + + align:start position:0% +they're able to merge that information +together with the people's purchasing + + align:start position:0% +together with the people's purchasing + + + align:start position:0% +together with the people's purchasing +patterns uh and they get this you know + + align:start position:0% +patterns uh and they get this you know + + + align:start position:0% +patterns uh and they get this you know +remarkable data set of 880,000 + + align:start position:0% +remarkable data set of 880,000 + + + align:start position:0% +remarkable data set of 880,000 +individuals living in 49,000 households + + align:start position:0% +individuals living in 49,000 households + + + align:start position:0% +individuals living in 49,000 households +uh and they know their sort of life + + align:start position:0% +uh and they know their sort of life + + + align:start position:0% +uh and they know their sort of life +history of moving and then they can + + align:start position:0% +history of moving and then they can + + + align:start position:0% +history of moving and then they can +examine what those people + + align:start position:0% +examine what those people + + + align:start position:0% +examine what those people +purchased I think it's just it's a + + align:start position:0% +purchased I think it's just it's a + + + align:start position:0% +purchased I think it's just it's a +interesting contrast with resent Han and + + align:start position:0% +interesting contrast with resent Han and + + + align:start position:0% +interesting contrast with resent Han and +Reese where we have like you know we're + + align:start position:0% +Reese where we have like you know we're + + + align:start position:0% +Reese where we have like you know we're +opening up the phone books we're + + align:start position:0% +opening up the phone books we're + + + align:start position:0% +opening up the phone books we're +counting there are three dentists or + + align:start position:0% +counting there are three dentists or + + + align:start position:0% +counting there are three dentists or +whatever and that's you know 200 + + align:start position:0% +whatever and that's you know 200 + + + align:start position:0% +whatever and that's you know 200 +different cities versus this 80,000 + + align:start position:0% +different cities versus this 80,000 + + + align:start position:0% +different cities versus this 80,000 +people you've got basically their + + align:start position:0% +people you've got basically their + + + align:start position:0% +people you've got basically their +shopping lives laid out in front of you + + align:start position:0% +shopping lives laid out in front of you + + + align:start position:0% +shopping lives laid out in front of you +as well as something real life history + + align:start position:0% +as well as something real life history + + + align:start position:0% +as well as something real life history +um okay um you know neelon classifies + + align:start position:0% +um okay um you know neelon classifies + + + align:start position:0% +um okay um you know neelon classifies +UPC codes by product category and brand + + align:start position:0% +UPC codes by product category and brand + + + align:start position:0% +UPC codes by product category and brand +um in this paper they've sort of picked + + align:start position:0% +um in this paper they've sort of picked + + + align:start position:0% +um in this paper they've sort of picked +238 different modules so a module could + + align:start position:0% +238 different modules so a module could + + + align:start position:0% +238 different modules so a module could +be + + align:start position:0% +be + + + align:start position:0% +be +mayonnaise so they picked 23 modules + + align:start position:0% +mayonnaise so they picked 23 modules + + + align:start position:0% +mayonnaise so they picked 23 modules +they pick modules where they have at + + align:start position:0% +they pick modules where they have at + + + align:start position:0% +they pick modules where they have at +least 5,000 households purchasing that + + align:start position:0% +least 5,000 households purchasing that + + + align:start position:0% +least 5,000 households purchasing that +item uh and where the top two brands are + + align:start position:0% +item uh and where the top two brands are + + + align:start position:0% +item uh and where the top two brands are +owned by different firms so for instance + + align:start position:0% +owned by different firms so for instance + + + align:start position:0% +owned by different firms so for instance +in the cream cheese module the number + + align:start position:0% +in the cream cheese module the number + + + align:start position:0% +in the cream cheese module the number +one cream cheese is Philadelphia Cream + + align:start position:0% +one cream cheese is Philadelphia Cream + + + align:start position:0% +one cream cheese is Philadelphia Cream +Cheese the number two cream cheese is + + align:start position:0% +Cheese the number two cream cheese is + + + align:start position:0% +Cheese the number two cream cheese is +Philadelphia light cream cheese so they + + align:start position:0% +Philadelphia light cream cheese so they + + + align:start position:0% +Philadelphia light cream cheese so they +would throw out cream cheese but in + + align:start position:0% +would throw out cream cheese but in + + + align:start position:0% +would throw out cream cheese but in +mayonnaise number one mayonnaise is is + + align:start position:0% +mayonnaise number one mayonnaise is is + + + align:start position:0% +mayonnaise number one mayonnaise is is +unever mayonnaise number two mayonnaise + + align:start position:0% +unever mayonnaise number two mayonnaise + + + align:start position:0% +unever mayonnaise number two mayonnaise +is craft mayonnaise they keep + + align:start position:0% +is craft mayonnaise they keep + + + align:start position:0% +is craft mayonnaise they keep +mayonnaise um + + align:start position:0% +mayonnaise um + + + align:start position:0% +mayonnaise um +anyway the current market share data is + + align:start position:0% +anyway the current market share data is + + + align:start position:0% +anyway the current market share data is +also supplemented with historical data + + align:start position:0% +also supplemented with historical data + + + align:start position:0% +also supplemented with historical data +at the state level that's obtained from + + align:start position:0% +at the state level that's obtained from + + + align:start position:0% +at the state level that's obtained from +some published surveys that ask people + + align:start position:0% +some published surveys that ask people + + + align:start position:0% +some published surveys that ask people +about what brand of mayonnaise do you + + align:start position:0% +about what brand of mayonnaise do you + + + align:start position:0% +about what brand of mayonnaise do you +normally Buy and they found these sort + + align:start position:0% +normally Buy and they found these sort + + + align:start position:0% +normally Buy and they found these sort +of archival things from the 40s up to + + align:start position:0% +of archival things from the 40s up to + + + align:start position:0% +of archival things from the 40s up to +the 60s I won't talk so much about that + + align:start position:0% +the 60s I won't talk so much about that + + + align:start position:0% +the 60s I won't talk so much about that +part though actually they also do + + align:start position:0% +part though actually they also do + + + align:start position:0% +part though actually they also do +advertising data I'm not going to talk + + align:start position:0% +advertising data I'm not going to talk + + + align:start position:0% +advertising data I'm not going to talk +so much about what they do with the + + align:start position:0% +so much about what they do with the + + + align:start position:0% +so much about what they do with the +advertising + + align:start position:0% +advertising + + + align:start position:0% +advertising +data but anyway so here is part of their + + align:start position:0% +data but anyway so here is part of their + + + align:start position:0% +data but anyway so here is part of their +product list and again it's it's 23 38 + + align:start position:0% +product list and again it's it's 23 38 + + + align:start position:0% +product list and again it's it's 23 38 +things long um but so all of these are + + align:start position:0% +things long um but so all of these are + + + align:start position:0% +things long um but so all of these are +um well let's see down here at the + + align:start position:0% +um well let's see down here at the + + + align:start position:0% +um well let's see down here at the +bottom I've got beer I talked about beer + + align:start position:0% +bottom I've got beer I talked about beer + + + align:start position:0% +bottom I've got beer I talked about beer +before so the number one beer is + + align:start position:0% +before so the number one beer is + + + align:start position:0% +before so the number one beer is +Budweiser uh number two beer is + + align:start position:0% +Budweiser uh number two beer is + + + align:start position:0% +Budweiser uh number two beer is +Miller um what they do is they record + + align:start position:0% +Miller um what they do is they record + + + align:start position:0% +Miller um what they do is they record +the aggregate purchase share so + + align:start position:0% +the aggregate purchase share so + + + align:start position:0% +the aggregate purchase share so +aggregate share here means share of + + align:start position:0% +aggregate share here means share of + + + align:start position:0% +aggregate share here means share of +product one aggregate purchase share is + + align:start position:0% +product one aggregate purchase share is + + + align:start position:0% +product one aggregate purchase share is +share of BD wise or a fraction people + + align:start position:0% +share of BD wise or a fraction people + + + align:start position:0% +share of BD wise or a fraction people +buy Budweiser or Miller so 60% of 4% of + + align:start position:0% +buy Budweiser or Miller so 60% of 4% of + + + align:start position:0% +buy Budweiser or Miller so 60% of 4% of +people buy Budweiser or Miller buy + + align:start position:0% +people buy Budweiser or Miller buy + + + align:start position:0% +people buy Budweiser or Miller buy +Miller and then you again these are the + + align:start position:0% +Miller and then you again these are the + + + align:start position:0% +Miller and then you again these are the +cross state standard deviation so it's + + align:start position:0% +cross state standard deviation so it's + + + align:start position:0% +cross state standard deviation so it's +64 on average but in different states + + align:start position:0% +64 on average but in different states + + + align:start position:0% +64 on average but in different states +it's different so it's 64 plus or minus + + align:start position:0% +it's different so it's 64 plus or minus + + + align:start position:0% +it's different so it's 64 plus or minus +19 for Budweiser versus Miller um some + + align:start position:0% +19 for Budweiser versus Miller um some + + + align:start position:0% +19 for Budweiser versus Miller um some +of the products like you know this sort + + align:start position:0% +of the products like you know this sort + + + align:start position:0% +of the products like you know this sort +of + + align:start position:0% +of + + + align:start position:0% +of +red um nature Zone versus serly soft and + + align:start position:0% +red um nature Zone versus serly soft and + + + align:start position:0% +red um nature Zone versus serly soft and +smooth it's like 50/50 between those two + + align:start position:0% +smooth it's like 50/50 between those two + + + align:start position:0% +smooth it's like 50/50 between those two +plus or minus + + align:start position:0% +plus or minus + + + align:start position:0% +plus or minus +32 um + + align:start position:0% + + + + align:start position:0% + +some of them there's very little + + align:start position:0% +some of them there's very little + + + align:start position:0% +some of them there's very little +variation so Hand acids pyc rollad of + + align:start position:0% +variation so Hand acids pyc rollad of + + + align:start position:0% +variation so Hand acids pyc rollad of +the top two an acids pyc has a 71% share + + align:start position:0% +the top two an acids pyc has a 71% share + + + align:start position:0% +the top two an acids pyc has a 71% share +in that comparison um you it's a more + + align:start position:0% +in that comparison um you it's a more + + + align:start position:0% +in that comparison um you it's a more +effective drug I guess and it's 71 plus + + align:start position:0% +effective drug I guess and it's 71 plus + + + align:start position:0% +effective drug I guess and it's 71 plus +or minus + + align:start position:0% + + + + align:start position:0% + +8 you know I look at some of these and + + align:start position:0% +8 you know I look at some of these and + + + align:start position:0% +8 you know I look at some of these and +they seem like things that are very + + align:start position:0% +they seem like things that are very + + + align:start position:0% +they seem like things that are very +similar products you know like I think I + + align:start position:0% +similar products you know like I think I + + + align:start position:0% +similar products you know like I think I +would be shocked if Comet abrasive + + align:start position:0% +would be shocked if Comet abrasive + + + align:start position:0% +would be shocked if Comet abrasive +cleaning powder and Ajax abrasive + + align:start position:0% +cleaning powder and Ajax abrasive + + + align:start position:0% +cleaning powder and Ajax abrasive +cleaning powder very different some of + + align:start position:0% +cleaning powder very different some of + + + align:start position:0% +cleaning powder very different some of +them like the bakery products maybe it + + align:start position:0% +them like the bakery products maybe it + + + align:start position:0% +them like the bakery products maybe it +seems like they're not as homogeneous as + + align:start position:0% +seems like they're not as homogeneous as + + + align:start position:0% +seems like they're not as homogeneous as +as some of the other + + align:start position:0% +as some of the other + + + align:start position:0% +as some of the other +things + + align:start position:0% + + + + align:start position:0% + +um so what what is shoppers home scan at + + align:start position:0% +um so what what is shoppers home scan at + + + align:start position:0% +um so what what is shoppers home scan at +least home home scan Shoppers in the + + align:start position:0% +least home home scan Shoppers in the + + + align:start position:0% +least home home scan Shoppers in the +United States look like I don't know how + + align:start position:0% +United States look like I don't know how + + + align:start position:0% +United States look like I don't know how +this compares to the US population as a + + align:start position:0% +this compares to the US population as a + + + align:start position:0% +this compares to the US population as a +whole someone must know that um about + + align:start position:0% +whole someone must know that um about + + + align:start position:0% +whole someone must know that um about +27% of the uh households and their + + align:start position:0% +27% of the uh households and their + + + align:start position:0% +27% of the uh households and their +sample are migrants um you know I guess + + align:start position:0% +sample are migrants um you know I guess + + + align:start position:0% +sample are migrants um you know I guess +obviously almost everybody I know is a + + align:start position:0% +obviously almost everybody I know is a + + + align:start position:0% +obviously almost everybody I know is a +migrant which I guess tells me that + + align:start position:0% +migrant which I guess tells me that + + + align:start position:0% +migrant which I guess tells me that +migrants are unusual you that we're + + align:start position:0% +migrants are unusual you that we're + + + align:start position:0% +migrants are unusual you that we're +we're we're some unusual relative to US + + align:start position:0% +we're we're some unusual relative to US + + + align:start position:0% +we're we're some unusual relative to US +population um but so 27% of the + + align:start position:0% +population um but so 27% of the + + + align:start position:0% +population um but so 27% of the +households were born in a different um + + align:start position:0% +households were born in a different um + + + align:start position:0% +households were born in a different um +state where they now reside uh 16% were + + align:start position:0% +state where they now reside uh 16% were + + + align:start position:0% +state where they now reside uh 16% were +born in a different census region so + + align:start position:0% +born in a different census region so + + + align:start position:0% +born in a different census region so +conditional on having moved States many + + align:start position:0% +conditional on having moved States many + + + align:start position:0% +conditional on having moved States many +people have moved fairly far um you know + + align:start position:0% +people have moved fairly far um you know + + + align:start position:0% +people have moved fairly far um you know +obviously you know this is um you know + + align:start position:0% +obviously you know this is um you know + + + align:start position:0% +obviously you know this is um you know +you'll notice like people don't really + + align:start position:0% +you'll notice like people don't really + + + align:start position:0% +you'll notice like people don't really +move to the Northeast people are born in + + align:start position:0% +move to the Northeast people are born in + + + align:start position:0% +move to the Northeast people are born in +the Northeast and they stay in the + + align:start position:0% +the Northeast and they stay in the + + + align:start position:0% +the Northeast and they stay in the +Northeast very few people especially + + align:start position:0% +Northeast very few people especially + + + align:start position:0% +Northeast very few people especially +from the West move to the Northeast + + align:start position:0% +from the West move to the Northeast + + + align:start position:0% +from the West move to the Northeast +given the weather um PE more people in + + align:start position:0% +given the weather um PE more people in + + + align:start position:0% +given the weather um PE more people in +the South move to the south from the + + align:start position:0% +the South move to the south from the + + + align:start position:0% +the South move to the south from the +from the northeast or from the + + align:start position:0% +from the northeast or from the + + + align:start position:0% +from the northeast or from the +Midwest + + align:start position:0% +Midwest + + + align:start position:0% +Midwest +um ages you know the people in their + + align:start position:0% +um ages you know the people in their + + + align:start position:0% +um ages you know the people in their +sample tend to be in their in their 40s + + align:start position:0% +sample tend to be in their in their 40s + + + align:start position:0% +sample tend to be in their in their 40s +50s 60s um you get very few people in + + align:start position:0% +50s 60s um you get very few people in + + + align:start position:0% +50s 60s um you get very few people in +their 20s who want to have a scanner and + + align:start position:0% +their 20s who want to have a scanner and + + + align:start position:0% +their 20s who want to have a scanner and +scan everything they buy at the grocery + + align:start position:0% +scan everything they buy at the grocery + + + align:start position:0% +scan everything they buy at the grocery +store um uh age leaving state of birth + + align:start position:0% +store um uh age leaving state of birth + + + align:start position:0% +store um uh age leaving state of birth +there's an awful lot of variation in it + + align:start position:0% +there's an awful lot of variation in it + + + align:start position:0% +there's an awful lot of variation in it +you get a lot of people who left before + + align:start position:0% +you get a lot of people who left before + + + align:start position:0% +you get a lot of people who left before +they were 10 years old a lot of people + + align:start position:0% +they were 10 years old a lot of people + + + align:start position:0% +they were 10 years old a lot of people +who move in their 20s not surprisingly + + align:start position:0% +who move in their 20s not surprisingly + + + align:start position:0% +who move in their 20s not surprisingly +or uh and then you do get people who + + align:start position:0% +or uh and then you do get people who + + + align:start position:0% +or uh and then you do get people who +also move in their 60s uh when they're + + align:start position:0% +also move in their 60s uh when they're + + + align:start position:0% +also move in their 60s uh when they're +retiring okay so what's the main + + align:start position:0% +retiring okay so what's the main + + + align:start position:0% +retiring okay so what's the main +analysis the the main thing is to ask + + align:start position:0% +analysis the the main thing is to ask + + + align:start position:0% +analysis the the main thing is to ask +let's look at these people and ask when + + align:start position:0% +let's look at these people and ask when + + + align:start position:0% +let's look at these people and ask when +they move how far do they move from + + align:start position:0% +they move how far do they move from + + + align:start position:0% +they move how far do they move from +their birth place purchasing patterns + + align:start position:0% +their birth place purchasing patterns + + + align:start position:0% +their birth place purchasing patterns +their + + align:start position:0% +their + + + align:start position:0% +their +destination purchasing patterns and so I + + align:start position:0% +destination purchasing patterns and so I + + + align:start position:0% +destination purchasing patterns and so I +they write usj for the share of people + + align:start position:0% +they write usj for the share of people + + + align:start position:0% +they write usj for the share of people +who never the share of non-migrants in + + align:start position:0% +who never the share of non-migrants in + + + align:start position:0% +who never the share of non-migrants in +state s who buy product + + align:start position:0% +state s who buy product + + + align:start position:0% +state s who buy product +J and then m s Prime J is the people in + + align:start position:0% +J and then m s Prime J is the people in + + + align:start position:0% +J and then m s Prime J is the people in +state S Prime who never move what + + align:start position:0% +state S Prime who never move what + + + align:start position:0% +state S Prime who never move what +fraction of them buy product J and so + + align:start position:0% +fraction of them buy product J and so + + + align:start position:0% +fraction of them buy product J and so +what I'm doing is I'm thinking of + + align:start position:0% +what I'm doing is I'm thinking of + + + align:start position:0% +what I'm doing is I'm thinking of +someone who moves from State s State S + + align:start position:0% +someone who moves from State s State S + + + align:start position:0% +someone who moves from State s State S +Prime and + + align:start position:0% +Prime and + + + align:start position:0% +Prime and +saying how does their purchasing compare + + align:start position:0% +saying how does their purchasing compare + + + align:start position:0% +saying how does their purchasing compare +to how far in the direction of S Prime + + align:start position:0% +to how far in the direction of S Prime + + + align:start position:0% +to how far in the direction of S Prime +has their purchasing how far along way + + align:start position:0% +has their purchasing how far along way + + + align:start position:0% +has their purchasing how far along way +from us from us Prime has their + + align:start position:0% +from us from us Prime has their + + + align:start position:0% +from us from us Prime has their +purchasing moved assuming they started + + align:start position:0% +purchasing moved assuming they started + + + align:start position:0% +purchasing moved assuming they started +at + + align:start position:0% +at + + + align:start position:0% +at +usj uh when they were in before they + + align:start position:0% +usj uh when they were in before they + + + align:start position:0% +usj uh when they were in before they +moved you know 20 years ago when I did + + align:start position:0% +moved you know 20 years ago when I did + + + align:start position:0% +moved you know 20 years ago when I did +don't observe that so this question is + + align:start position:0% +don't observe that so this question is + + + align:start position:0% +don't observe that so this question is +you know if this if you still purchase + + align:start position:0% +you know if this if you still purchase + + + align:start position:0% +you know if this if you still purchase +if if these migrants still still + + align:start position:0% +if if these migrants still still + + + align:start position:0% +if if these migrants still still +purchase exactly what they + + align:start position:0% +purchase exactly what they + + + align:start position:0% +purchase exactly what they +purchased uh well if they were + + align:start position:0% +purchased uh well if they were + + + align:start position:0% +purchased uh well if they were +representative of the population in + + align:start position:0% +representative of the population in + + + align:start position:0% +representative of the population in +state s and still purchase what they + + align:start position:0% +state s and still purchase what they + + + align:start position:0% +state s and still purchase what they +purchased before they left beta would be + + align:start position:0% +purchased before they left beta would be + + + align:start position:0% +purchased before they left beta would be +zero if they all purchase are exactly + + align:start position:0% +zero if they all purchase are exactly + + + align:start position:0% +zero if they all purchase are exactly +representative of the non-migrants in + + align:start position:0% +representative of the non-migrants in + + + align:start position:0% +representative of the non-migrants in +their new home and purchase what what + + align:start position:0% +their new home and purchase what what + + + align:start position:0% +their new home and purchase what what +people in the new home purchase uh beta + + align:start position:0% +people in the new home purchase uh beta + + + align:start position:0% +people in the new home purchase uh beta +would be one so beta is like what + + align:start position:0% +would be one so beta is like what + + + align:start position:0% +would be one so beta is like what +fraction of the way have people moveed + + align:start position:0% +fraction of the way have people moveed + + + align:start position:0% +fraction of the way have people moveed +from looking like where they were born + + align:start position:0% +from looking like where they were born + + + align:start position:0% +from looking like where they were born +people to where they now live people + + align:start position:0% +people to where they now live people + + + align:start position:0% +people to where they now live people +and we're going to a basically have a + + align:start position:0% +and we're going to a basically have a + + + align:start position:0% +and we're going to a basically have a +regression estimating beta J as a + + align:start position:0% +regression estimating beta J as a + + + align:start position:0% +regression estimating beta J as a +function of + + align:start position:0% +function of + + + align:start position:0% +function of +um the age that you were when you moved + + align:start position:0% +um the age that you were when you moved + + + align:start position:0% +um the age that you were when you moved +and the time that you've been in your + + align:start position:0% +and the time that you've been in your + + + align:start position:0% +and the time that you've been in your +new location so you might think if you + + align:start position:0% +new location so you might think if you + + + align:start position:0% +new location so you might think if you +moved when you were one year old and + + align:start position:0% +moved when you were one year old and + + + align:start position:0% +moved when you were one year old and +you've been in your location for 60 + + align:start position:0% +you've been in your location for 60 + + + align:start position:0% +you've been in your location for 60 +years you want to look like people who + + align:start position:0% +years you want to look like people who + + + align:start position:0% +years you want to look like people who +grew up in that location where you moved + + align:start position:0% +grew up in that location where you moved + + + align:start position:0% +grew up in that location where you moved +when you were Oney old other than maybe + + align:start position:0% +when you were Oney old other than maybe + + + align:start position:0% +when you were Oney old other than maybe +you know your parents talking about what + + align:start position:0% +you know your parents talking about what + + + align:start position:0% +you know your parents talking about what +pays to buy um whereas if you're sort of + + align:start position:0% +pays to buy um whereas if you're sort of + + + align:start position:0% +pays to buy um whereas if you're sort of +you know 60 years old and you moved at + + align:start position:0% +you know 60 years old and you moved at + + + align:start position:0% +you know 60 years old and you moved at +age if you moved at age 60 and you've + + align:start position:0% +age if you moved at age 60 and you've + + + align:start position:0% +age if you moved at age 60 and you've +been there for 6 months you might expect + + align:start position:0% +been there for 6 months you might expect + + + align:start position:0% +been there for 6 months you might expect +that those people would look more like + + align:start position:0% +that those people would look more like + + + align:start position:0% +that those people would look more like +the origin people at least on the case + + align:start position:0% + + + + align:start position:0% + +side and then they do this via weighted + + align:start position:0% +side and then they do this via weighted + + + align:start position:0% +side and then they do this via weighted +Le squares you think about it like you + + align:start position:0% +Le squares you think about it like you + + + align:start position:0% +Le squares you think about it like you +know if s if us and US Prime are almost + + align:start position:0% +know if s if us and US Prime are almost + + + align:start position:0% +know if s if us and US Prime are almost +identical we're getting almost no + + align:start position:0% +identical we're getting almost no + + + align:start position:0% +identical we're getting almost no +information from that market and it's + + align:start position:0% +information from that market and it's + + + align:start position:0% +information from that market and it's +where us and US Prime are very different + + align:start position:0% +where us and US Prime are very different + + + align:start position:0% +where us and US Prime are very different +that we're getting information so they + + align:start position:0% +that we're getting information so they + + + align:start position:0% +that we're getting information so they +do a weight of Le squares estimate + + align:start position:0% +do a weight of Le squares estimate + + + align:start position:0% +do a weight of Le squares estimate +waiting the behavior of people who are + + align:start position:0% +waiting the behavior of people who are + + + align:start position:0% +waiting the behavior of people who are +who may moves from more to more + + align:start position:0% +who may moves from more to more + + + align:start position:0% +who may moves from more to more +different + + align:start position:0% +different + + + align:start position:0% +different +places anyways they've got a few figures + + align:start position:0% +places anyways they've got a few figures + + + align:start position:0% +places anyways they've got a few figures +in paper they've got this one you know + + align:start position:0% +in paper they've got this one you know + + + align:start position:0% +in paper they've got this one you know +and sometimes they're they're estimating + + align:start position:0% +and sometimes they're they're estimating + + + align:start position:0% +and sometimes they're they're estimating +this coefficient separately it's it's + + align:start position:0% +this coefficient separately it's it's + + + align:start position:0% +this coefficient separately it's it's +again you've got 880,000 people you've + + align:start position:0% +again you've got 880,000 people you've + + + align:start position:0% +again you've got 880,000 people you've +got a lot of people who move at age 15 + + align:start position:0% +got a lot of people who move at age 15 + + + align:start position:0% +got a lot of people who move at age 15 +and have been there for 35 years so they + + align:start position:0% +and have been there for 35 years so they + + + align:start position:0% +and have been there for 35 years so they +have separate coefficients for every age + + align:start position:0% +have separate coefficients for every age + + + align:start position:0% +have separate coefficients for every age +at move and every uh year since move + + align:start position:0% +at move and every uh year since move + + + align:start position:0% +at move and every uh year since move +um I find this one hard to see though in + + align:start position:0% +um I find this one hard to see though in + + + align:start position:0% +um I find this one hard to see though in +three dimensions it's hard to see how + + align:start position:0% +three dimensions it's hard to see how + + + align:start position:0% +three dimensions it's hard to see how +high these things are versus the slope + + align:start position:0% +high these things are versus the slope + + + align:start position:0% +high these things are versus the slope +so easier to read is these ones here + + align:start position:0% +so easier to read is these ones here + + + align:start position:0% +so easier to read is these ones here +that just go they collapse it down to + + align:start position:0% +that just go they collapse it down to + + + align:start position:0% +that just go they collapse it down to +one dimension um and what this is saying + + align:start position:0% +one dimension um and what this is saying + + + align:start position:0% +one dimension um and what this is saying +is that uh an awful lot of it seems to + + align:start position:0% +is that uh an awful lot of it seems to + + + align:start position:0% +is that uh an awful lot of it seems to +be supply + + align:start position:0% +be supply + + + align:start position:0% +be supply +side because if you look at people who + + align:start position:0% +side because if you look at people who + + + align:start position:0% +side because if you look at people who +have just moved so it's 0 to four years + + align:start position:0% +have just moved so it's 0 to four years + + + align:start position:0% +have just moved so it's 0 to four years +since their move um there's immediately + + align:start position:0% +since their move um there's immediately + + + align:start position:0% +since their move um there's immediately +like something per of the way to the new + + align:start position:0% +like something per of the way to the new + + + align:start position:0% +like something per of the way to the new +purchasing + + align:start position:0% +purchasing + + + align:start position:0% +purchasing +patterns when you look at people who + + align:start position:0% +patterns when you look at people who + + + align:start position:0% +patterns when you look at people who +Moved 40 or 50 years ago they are like + + align:start position:0% +Moved 40 or 50 years ago they are like + + + align:start position:0% +Moved 40 or 50 years ago they are like +80 or 90% of the way to the purching + + align:start position:0% +80 or 90% of the way to the purching + + + align:start position:0% +80 or 90% of the way to the purching +patterns so it it if it you know it + + align:start position:0% +patterns so it it if it you know it + + + align:start position:0% +patterns so it it if it you know it +seems like there's a big supply side + + align:start position:0% +seems like there's a big supply side + + + align:start position:0% +seems like there's a big supply side +element that makes you immediately on + + align:start position:0% +element that makes you immediately on + + + align:start position:0% +element that makes you immediately on +moving here to Boston you start buying + + align:start position:0% +moving here to Boston you start buying + + + align:start position:0% +moving here to Boston you start buying +helmets + + align:start position:0% +helmets + + + align:start position:0% +helmets +bayonnaise but there is something that's + + align:start position:0% +bayonnaise but there is something that's + + + align:start position:0% +bayonnaise but there is something that's +longer term and so this could be the + + align:start position:0% +longer term and so this could be the + + + align:start position:0% +longer term and so this could be the +advertising playing on you over 40 years + + align:start position:0% +advertising playing on you over 40 years + + + align:start position:0% +advertising playing on you over 40 years +or this could just be the um your tastes + + align:start position:0% +or this could just be the um your tastes + + + align:start position:0% +or this could just be the um your tastes +adapt you know you go to friends houses + + align:start position:0% +adapt you know you go to friends houses + + + align:start position:0% +adapt you know you go to friends houses +they serve helmet's mayonnaise you think + + align:start position:0% +they serve helmet's mayonnaise you think + + + align:start position:0% +they serve helmet's mayonnaise you think +wow that helmet is good I should buy + + align:start position:0% +wow that helmet is good I should buy + + + align:start position:0% +wow that helmet is good I should buy +that myself um so there's adaptation + + align:start position:0% +that myself um so there's adaptation + + + align:start position:0% +that myself um so there's adaptation +over time but a lot of it happens on day + + align:start position:0% +over time but a lot of it happens on day + + + align:start position:0% +over time but a lot of it happens on day +one um and then you know here's the age + + align:start position:0% +one um and then you know here's the age + + + align:start position:0% +one um and then you know here's the age +at move graph the people who Moved when + + align:start position:0% +at move graph the people who Moved when + + + align:start position:0% +at move graph the people who Moved when +they were children obviously the people + + align:start position:0% +they were children obviously the people + + + align:start position:0% +they were children obviously the people +moved when they were children have + + align:start position:0% +moved when they were children have + + + align:start position:0% +moved when they were children have +already um had to have lived for quite a + + align:start position:0% +already um had to have lived for quite a + + + align:start position:0% +already um had to have lived for quite a +while in new location because they + + align:start position:0% +while in new location because they + + + align:start position:0% +while in new location because they +they're only surveying adults but the + + align:start position:0% +they're only surveying adults but the + + + align:start position:0% +they're only surveying adults but the +people who Moved at children + + align:start position:0% +people who Moved at children + + + align:start position:0% +people who Moved at children +you know you moved at age one you do + + align:start position:0% +you know you moved at age one you do + + + align:start position:0% +you know you moved at age one you do +retain something of your birth + + align:start position:0% +retain something of your birth + + + align:start position:0% +retain something of your birth +mayonnaise so this is this is you're + + align:start position:0% +mayonnaise so this is this is you're + + + align:start position:0% +mayonnaise so this is this is you're +getting something about mayonnaise from + + align:start position:0% +getting something about mayonnaise from + + + align:start position:0% +getting something about mayonnaise from +your parents um because it can't be that + + align:start position:0% +your parents um because it can't be that + + + align:start position:0% +your parents um because it can't be that +you moved at age one therefore you you + + align:start position:0% +you moved at age one therefore you you + + + align:start position:0% +you moved at age one therefore you you +you know you that you remember the + + align:start position:0% +you know you that you remember the + + + align:start position:0% +you know you that you remember the +mayonnaise of your of your babyhood you + + align:start position:0% +mayonnaise of your of your babyhood you + + + align:start position:0% +mayonnaise of your of your babyhood you +know so there is something that you're + + align:start position:0% +know so there is something that you're + + + align:start position:0% +know so there is something that you're +getting it's only + + align:start position:0% +getting it's only + + + align:start position:0% +getting it's only +0.9 uh but then it it it declines in the + + align:start position:0% +0.9 uh but then it it it declines in the + + + align:start position:0% +0.9 uh but then it it it declines in the +age it moves um but it STS that you know + + align:start position:0% +age it moves um but it STS that you know + + + align:start position:0% +age it moves um but it STS that you know +even people who people who moved in + + align:start position:0% +even people who people who moved in + + + align:start position:0% +even people who people who moved in +their 60s they're mostly adjusting to + + align:start position:0% +their 60s they're mostly adjusting to + + + align:start position:0% +their 60s they're mostly adjusting to +the + + align:start position:0% + + + + align:start position:0% + +newes okay so what do I have here this + + align:start position:0% +newes okay so what do I have here this + + + align:start position:0% +newes okay so what do I have here this +to say um so anyway people instantly + + align:start position:0% +to say um so anyway people instantly + + + align:start position:0% +to say um so anyway people instantly +move 60% of the way this suggests that + + align:start position:0% +move 60% of the way this suggests that + + + align:start position:0% +move 60% of the way this suggests that +it's it it is a lot of sort of supply + + align:start position:0% +it's it it is a lot of sort of supply + + + align:start position:0% +it's it it is a lot of sort of supply +side + + align:start position:0% +side + + + align:start position:0% +side +stuff um yeah people become more similar + + align:start position:0% +stuff um yeah people become more similar + + + align:start position:0% +stuff um yeah people become more similar +over time I said that datas are related + + align:start position:0% +over time I said that datas are related + + + align:start position:0% +over time I said that datas are related +to age and move so age 60 plus you're + + align:start position:0% +to age and move so age 60 plus you're + + + align:start position:0% +to age and move so age 60 plus you're +still getting a baby movement people + + align:start position:0% +still getting a baby movement people + + + align:start position:0% +still getting a baby movement people +learn new things um oh number four data + + align:start position:0% +learn new things um oh number four data + + + align:start position:0% +learn new things um oh number four data +on pre-move migrants again there's this + + align:start position:0% +on pre-move migrants again there's this + + + align:start position:0% +on pre-move migrants again there's this +sort of thing of you guys move to Boston + + align:start position:0% +sort of thing of you guys move to Boston + + + align:start position:0% +sort of thing of you guys move to Boston +because you're not the + + align:start position:0% +because you're not the + + + align:start position:0% +because you're not the +typical people where you grew up right + + align:start position:0% +typical people where you grew up right + + + align:start position:0% +typical people where you grew up right +and you probably don't drink the same + + align:start position:0% +and you probably don't drink the same + + + align:start position:0% +and you probably don't drink the same +coffee that people where you um grew up + + align:start position:0% +coffee that people where you um grew up + + + align:start position:0% +coffee that people where you um grew up +drink you probably don't drink the same + + align:start position:0% +drink you probably don't drink the same + + + align:start position:0% +drink you probably don't drink the same +beer that people where you grew up drink + + align:start position:0% +beer that people where you grew up drink + + + align:start position:0% +beer that people where you grew up drink +you know probably don't maybe don't have + + align:start position:0% +you know probably don't maybe don't have + + + align:start position:0% +you know probably don't maybe don't have +the same name up um so the question is + + align:start position:0% +the same name up um so the question is + + + align:start position:0% +the same name up um so the question is +like is this in part is this like 60% + + align:start position:0% +like is this in part is this like 60% + + + align:start position:0% +like is this in part is this like 60% +figure because the + + align:start position:0% +figure because the + + + align:start position:0% +figure because the +people you know right remember in most + + align:start position:0% +people you know right remember in most + + + align:start position:0% +people you know right remember in most +the analysis are only observing where + + align:start position:0% +the analysis are only observing where + + + align:start position:0% +the analysis are only observing where +people are today so the 60% figure is + + align:start position:0% +people are today so the 60% figure is + + + align:start position:0% +people are today so the 60% figure is +the people living in Boston maybe it's + + align:start position:0% +the people living in Boston maybe it's + + + align:start position:0% +the people living in Boston maybe it's +that like you know you become you know + + align:start position:0% +that like you know you become you know + + + align:start position:0% +that like you know you become you know +it's like you were different therefore + + align:start position:0% +it's like you were different therefore + + + align:start position:0% +it's like you were different therefore +you get your coffee at Starbucks whereas + + align:start position:0% +you get your coffee at Starbucks whereas + + + align:start position:0% +you get your coffee at Starbucks whereas +people you grew up with didn't go to + + align:start position:0% +people you grew up with didn't go to + + + align:start position:0% +people you grew up with didn't go to +Starbucks or something like that and you + + align:start position:0% +Starbucks or something like that and you + + + align:start position:0% +Starbucks or something like that and you +moved to Boston because you were like + + align:start position:0% +moved to Boston because you were like + + + align:start position:0% +moved to Boston because you were like +the Starbucks type person say um they + + align:start position:0% +the Starbucks type person say um they + + + align:start position:0% +the Starbucks type person say um they +have evidence though like they actually + + align:start position:0% +have evidence though like they actually + + + align:start position:0% +have evidence though like they actually +have look at this sort of month by Monon + + align:start position:0% +have look at this sort of month by Monon + + + align:start position:0% +have look at this sort of month by Monon +data you know they don't can't track you + + align:start position:0% +data you know they don't can't track you + + + align:start position:0% +data you know they don't can't track you +precisely but they're ask they did their + + align:start position:0% +precisely but they're ask they did their + + + align:start position:0% +precisely but they're ask they did their +survey in October of + + align:start position:0% + + + + align:start position:0% + +20077 and then um no sorry they did + + align:start position:0% +20077 and then um no sorry they did + + + align:start position:0% +20077 and then um no sorry they did +their survey in September of 2008 and + + align:start position:0% +their survey in September of 2008 and + + + align:start position:0% +their survey in September of 2008 and +they asked people you know like they + + align:start position:0% +they asked people you know like they + + + align:start position:0% +they asked people you know like they +asked people how long have you been in + + align:start position:0% +asked people how long have you been in + + + align:start position:0% +asked people how long have you been in +your current state and one of the answer + + align:start position:0% +your current state and one of the answer + + + align:start position:0% +your current state and one of the answer +the answers are integers so it's less + + align:start position:0% +the answers are integers so it's less + + + align:start position:0% +the answers are integers so it's less +than one one to two two to three + + align:start position:0% +than one one to two two to three + + + align:start position:0% +than one one to two two to three +whatever so all the people who said less + + align:start position:0% +whatever so all the people who said less + + + align:start position:0% +whatever so all the people who said less +than I'm I'm living in some state in + + align:start position:0% +than I'm I'm living in some state in + + + align:start position:0% +than I'm I'm living in some state in +September 2008 I've been here less than + + align:start position:0% +September 2008 I've been here less than + + + align:start position:0% +September 2008 I've been here less than +a year they know that they moved + + align:start position:0% +a year they know that they moved + + + align:start position:0% +a year they know that they moved +sometime between October of 2007 and + + align:start position:0% +sometime between October of 2007 and + + + align:start position:0% +sometime between October of 2007 and +September of 2008 they didn't ask for + + align:start position:0% +September of 2008 they didn't ask for + + + align:start position:0% +September of 2008 they didn't ask for +the month of the mo but what they can + + align:start position:0% +the month of the mo but what they can + + + align:start position:0% +the month of the mo but what they can +then do is say look at these people who + + align:start position:0% +then do is say look at these people who + + + align:start position:0% +then do is say look at these people who +moved here within the past year and look + + align:start position:0% +moved here within the past year and look + + + align:start position:0% +moved here within the past year and look +at what Mayas did they eat before they + + align:start position:0% +at what Mayas did they eat before they + + + align:start position:0% +at what Mayas did they eat before they +moved and what they find is that before + + align:start position:0% +moved and what they find is that before + + + align:start position:0% +moved and what they find is that before +they + + align:start position:0% +they + + + align:start position:0% +they +moved over this year you know it's + + align:start position:0% +moved over this year you know it's + + + align:start position:0% +moved over this year you know it's +looking to me like the people were only + + align:start position:0% +looking to me like the people were only + + + align:start position:0% +looking to me like the people were only +like 10% of the way to their new + + align:start position:0% +like 10% of the way to their new + + + align:start position:0% +like 10% of the way to their new +destination so maybe they were more + + align:start position:0% +destination so maybe they were more + + + align:start position:0% +destination so maybe they were more +worldly maybe they already had more boss + + align:start position:0% +worldly maybe they already had more boss + + + align:start position:0% +worldly maybe they already had more boss +kind of tastes but they're only maybe + + align:start position:0% +kind of tastes but they're only maybe + + + align:start position:0% +kind of tastes but they're only maybe +10% Boston taste people and then you + + align:start position:0% +10% Boston taste people and then you + + + align:start position:0% +10% Boston taste people and then you +look at them as they move through the + + align:start position:0% +look at them as they move through the + + + align:start position:0% +look at them as they move through the +year and by the time they moved like + + align:start position:0% +year and by the time they moved like + + + align:start position:0% +year and by the time they moved like +that 60% 1 to four years isn't 60% Z to + + align:start position:0% +that 60% 1 to four years isn't 60% Z to + + + align:start position:0% +that 60% 1 to four years isn't 60% Z to +four years that's that's 60% like in + + align:start position:0% +four years that's that's 60% like in + + + align:start position:0% +four years that's that's 60% like in +within the first 12 months after you get + + align:start position:0% +within the first 12 months after you get + + + align:start position:0% +within the first 12 months after you get +there so some of these people have only + + align:start position:0% +there so some of these people have only + + + align:start position:0% +there so some of these people have only +been here one month and already buying + + align:start position:0% +been here one month and already buying + + + align:start position:0% +been here one month and already buying +the new mayonnaise some have been here + + align:start position:0% +the new mayonnaise some have been here + + + align:start position:0% +the new mayonnaise some have been here +six or nine months but it seems that + + align:start position:0% +six or nine months but it seems that + + + align:start position:0% +six or nine months but it seems that +this 65% thing is looks like a causal + + align:start position:0% +this 65% thing is looks like a causal + + + align:start position:0% +this 65% thing is looks like a causal +effect of moving and it looks like or + + align:start position:0% +effect of moving and it looks like or + + + align:start position:0% +effect of moving and it looks like or +maybe 80% of it's a cause of effective + + align:start position:0% +maybe 80% of it's a cause of effective + + + align:start position:0% +maybe 80% of it's a cause of effective +moving some part of it is like a + + align:start position:0% +moving some part of it is like a + + + align:start position:0% +moving some part of it is like a +pre-existing underlying heterogen but + + align:start position:0% +pre-existing underlying heterogen but + + + align:start position:0% +pre-existing underlying heterogen but +then there's this + + align:start position:0% +then there's this + + + align:start position:0% +then there's this +[Music] + + align:start position:0% + + + + align:start position:0% + +big and again you know it's just so just + + align:start position:0% +big and again you know it's just so just + + + align:start position:0% +big and again you know it's just so just +80,000 is a good like 80,000 data points + + align:start position:0% +80,000 is a good like 80,000 data points + + + align:start position:0% +80,000 is a good like 80,000 data points +is a good thing and you know 80,000 data + + align:start position:0% +is a good thing and you know 80,000 data + + + align:start position:0% +is a good thing and you know 80,000 data +points times 238 products is good thing + + align:start position:0% +points times 238 products is good thing + + + align:start position:0% +points times 238 products is good thing +and just you know sort of this is + + align:start position:0% +and just you know sort of this is + + + align:start position:0% +and just you know sort of this is +Vantage + + align:start position:0% +Vantage + + + align:start position:0% +Vantage +data scale as you can do these things + + align:start position:0% +data scale as you can do these things + + + align:start position:0% +data scale as you can do these things +that would be very very hard to do with + + align:start position:0% + + + + align:start position:0% + +small so um yeah that is what I've got + + align:start position:0% +small so um yeah that is what I've got + + + align:start position:0% +small so um yeah that is what I've got +today so um next week again is uh you + + align:start position:0% +today so um next week again is uh you + + + align:start position:0% +today so um next week again is uh you +Theory Monday empirics Wednesday next + + align:start position:0% +Theory Monday empirics Wednesday next + + + align:start position:0% +Theory Monday empirics Wednesday next +week the theory topic is Strategic + + align:start position:0% +week the theory topic is Strategic + + + align:start position:0% +week the theory topic is Strategic +investment uh again it's it's this is + + align:start position:0% +investment uh again it's it's this is + + + align:start position:0% +investment uh again it's it's this is +going to be a very to Old textbook kind + + align:start position:0% +going to be a very to Old textbook kind + + + align:start position:0% +going to be a very to Old textbook kind +of lecture on Monday it's you'll get + + align:start position:0% +of lecture on Monday it's you'll get + + + align:start position:0% +of lecture on Monday it's you'll get +chapter eight of throlls book it's the + + align:start position:0% +chapter eight of throlls book it's the + + + align:start position:0% +chapter eight of throlls book it's the +longest chapter in the book so I will + + align:start position:0% +longest chapter in the book so I will + + + align:start position:0% +longest chapter in the book so I will +just try to go over the basics of + + align:start position:0% +just try to go over the basics of + + + align:start position:0% +just try to go over the basics of +Strategic investment Strategic + + align:start position:0% +Strategic investment Strategic + + + align:start position:0% +Strategic investment Strategic +investment is about thinking of things + + align:start position:0% +investment is about thinking of things + + + align:start position:0% +investment is about thinking of things +firms do to affect entry and markets + + align:start position:0% +firms do to affect entry and markets + + + align:start position:0% +firms do to affect entry and markets +because if entry really is the primary + + align:start position:0% +because if entry really is the primary + + + align:start position:0% +because if entry really is the primary +determin of markups really should want + + align:start position:0% +determin of markups really should want + + + align:start position:0% +determin of markups really should want +to affect entry and keep firms out + + align:start position:0% + + + + align:start position:0% + +of see you on + + align:start position:0% + + + + align:start position:0% + +Monday e \ No newline at end of file diff --git a/goT94BheP3E.txt b/goT94BheP3E.txt new file mode 100644 index 0000000000000000000000000000000000000000..fcb4d558f1ca848732d7b33510308911fe281a5c --- /dev/null +++ b/goT94BheP3E.txt @@ -0,0 +1,3848 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: OK, I guess we might +as well start a minute + +early since those of you +who are here are here. + +We're coming to the +end of course. + +We're deep in chapter 7 now +talking about random walks and + +detection theory. + +We'll get into martingales +sometime next week. + +There are four more lectures +after this one. + +The schedule was passed out at +the beginning of the term. + +I don't know how I did it, but +I somehow left off the last + +Wednesday of class. + +The final is going to +be on Wednesday + +morning at the ice rink. + +I don't know what the +ice rink is like. + +It doesn't sound like an ideal +place to take a final, but I + +assume they must have desks +there and all that stuff. + +We will send out a notice +about that. + +This is the last homework set +that you will have to turn in. + +We will probably have another +set of practice problems and + +problems on-- + +but not things you +should turn in. + +We will try to get solutions +out on them + +fairly quickly, also. + +So you can do them, but also +look at the answers right + +after you do them. + +OK, so let's get back +to random walks. + +And remember what we were +doing last time. + +A random walk, by definition, +you have a sequence of IID + +random variables. + +You have partial sums of +those random variables. + +S sub n is a sum of +the first n of + +those IID random variables. + +And the sequence of partial sums +S1, S2, S3, and so forth, + +that sequence is called +a random walk. + +And if you graph the random +walk, it's something which + +wanders up and down usually. + +And sometimes, if the mean of X +is positive, it wanders off + +to infinity. + +If the mean of X is negative, +it wanders + +off to minus infinity. + +If the mean of X is 0, it simply +diffuses somewhat as + +time goes on. + +And what we're trying to find +that is exactly how do these + +things work. + +So our focus here is +going to be on + +threshold-crossing problems. + +Namely, what's the probability +that this random walk is going + +to cross some threshold by or at +some particular value of n? + +If you have two thresholds, +one above and one below, + +what's the probability it's +going to cross the one above? + +What's the probability it's +going to cross the one below? + +And if it crosses one of these, +when does it cross it? + +If it crosses it, how much +of an overshoot is there? + +All of those problems just come +in naturally by looking + +at a sum of IID random +variables. + +But here we're going to be +trying to study them in some + +consistent manner looking at the +thresholds particularly. + +We've talked a little bit +about two particularly + +important applications. + +One is [? GG1Qs ?]. + +And even far more important than +that is this question of + +detection, or making decisions, +or hypothesis + +testing, all of which +are the same thing. + +You remember we did show that +there was at least one + +threshold-crossing problem +that was very, very easy. + +It's the threshold problem where +the underlying random + +variable is binary. + +You either go up by 1 or you +go down by 1 on each step. + +And the question is, what's the +probability that you will + +cross some threshold at +some k greater than 0? + +And it turns out that since +you can only go up 1 each + +time, the probability of getting +up to some point k is + +the probability you +ever got up to 1. + +Given that you got up to 1, it's +the probability that you + +ever got up to 2. + +Given you got up to 2, it's +the probability you + +ever got up to 3. + +That doesn't mean that you +go directly from 2 to 3. + +After you go to 2, you wander +all around, and eventually you + +make it up to 3. + +If you do, then the question is, +do you ever get from 3 to + +4, and so forth. + +And we found that the solution +to that problem was p over 1 + +minus p to the k-th power of p +is less than or equal to 1/2. + +And we solved that problem, if +you remember, back when we + +were talking about stop when +you're ahead if you're playing + +coin tossing with somebody. + +And so let's go further and +look particularly at this + +problem of detection, and +decisions, and hypothesis + +testing, which is really not a +particularly hard problem. + +But it's made particularly hard +by statisticians who have + +so many special rules, peculiar +cases, and almost + +mythology about making +decisions. + +And you can imagine why because +as long as you talk + +about probability, everybody +knows you're talking about an + +abstraction. + +As soon as you start talking +about making a decision, it + +suddenly becomes real. + +I mean, you look at a +bunch of data and + +you have to do something. + +You look at a bunch of +candidates for a job, you have + +to choose one. + +That's always very difficult +because you might not choose + +the right one. + +You might choose a +very poor one. + +But you have to do your best. + +If you're investing in stocks, +you look at all the statistics + +of everything. + +And finally you say, +that's where I'm + +going to put my money. + +Or if you're looking for a job +you say, that's where I'm + +going to work, and you +hope that that's + +going to work out well. + +There are all these situations +where you can evaluate + +probabilities until you're +sick in the head. + +They don't mean anything. + +It's only when you make a +decision and actually do + +something with it that it +really means something. + +So it becomes important +at this point. + +The model we use for this, +since we're studying + +probability theory-- + +well, actually, we're studying +random processes. + +But we're really studying +probability theory. + +You probably noticed +that by now. + +Since we're studying +probability, we study all + +these problems in terms of +a probabilistic model. + +And in the probabilistic model, +there's a discrete and, + +in most cases, binary random +variable, H, which is called + +the hypothesis random +variable. + +The sample values of H, +you might as well + +call them 0 and 1. + +That's the easiest things +to call binary things. + +They're called the alternative +hypotheses. + +They have marginal probabilities +because it's a + +probability model. + +You have a random variable. + +It can only take on the value +0 and 1, so it has to have + +probabilities of +being 0 and 1. + +Along with that, there +are all sorts of + +other random variables. + +The situation might be as +complicated as you want. + +But since we're making +decisions, we're making + +decisions on the basis of some +set of alternatives. + +And here, since we're trying +to talk about random walks, + +and martingales, and things like +that, also we restrict + +our attention to particular +kinds of observations. + +And the particular kind of +observation that we restrict + +attention to here is a sequence +of random variables, + +which we call the observation. + +You observe Y1. + +You observe Y2. + +You observe Y3, and so forth. + +In other words, you observe a +sample value of each of those + +random variables. + +There are a whole sequence +of them. + +And we assume, to make life +simple for ourselves, that + +each of these are independent, +conditional on the hypothesis. + +And they're identically +distributed conditional on the + +hypothesis. + +That's what this says +right here. + +This makes one more assumption +that assumes that these + +observations are continuous +random variables. + +That doesn't make much +difference, there are just a + +few peculiarities that +come in if these are + +discrete random variables. + +There also a few peculiarities +that come in when they're + +continuous. + +And there are a lot of +peculiarities that come in + +when they're absolutely +arbitrary. + +But for the time being, just +imagine each of these are + +continuous random variables. + +So for each value of n, we +look at n observations. + +We can calculate the probability +density that those + +observations would occur +conditional on hypothesis 0. + +We can find the conditional +probability they could occur + +conditional on hypothesis 1. + +And since they're IID, that's +equal to this product here. + +Excuse me, they are not IID, +they are conditionally ID. + +Conditional on the hypothesis. + +Namely, the idea is the world +is one way or the world is + +another way. + +If the world is this way, +then all of these + +hypotheses are IID. + +You're doing the same experiment +again and again and + +again, but it's based on the +same underlying hypothesis. + +Or, the underlying hypothesis +is this over here. + +You make the number of +observations all based on this + +same hypothesis, and you make +as many of these IID + +observations conditional +on that + +observation as you choose. + +And when you're all done, +what do you do? + +You have to make +your decision. + +OK, so this is a very +simple-minded model of this + +very complicated and very +important problem. + +But it's close enough to the +truth that we can get a lot of + +observations from it. + +Now, I spent a lot last time +talking about this. + +Spend a lot of time this time +talking about it because when + +we use a probability model for +this, when we say that we're + +studying probability theory. + +And therefore, we're going to +use probability, we have + +suddenly allied ourselves +completely with people called + +Bayesian statisticians or +Bayesian probabilists. + +And we have gone against, turned +our back on people + +called Non-Bayesians, or +sometimes classical. + +I hate using the word +"classical" because I like the + +word "classics." I like the +classics for such an unusual + +point of view. + +And the unusual point of view +is that we refuse to take a + +probability model. + +We accept the fact that on all +the observations, all the + +observations are +probabilistic. + +We assume we have a nice model +for them, which makes sense. + +We can do whatever we want +with that model. + +We can change the model. + +We can do whatever we +want with a model. + +But if you once assume that +these two hypotheses that + +you're trying to choose between, +that they have a + +priori probabilities, then +people get very upset about it + +because they say, well, +if what the a priori + +probabilities are, why do you +have to do a hypothesis test? + +You already understand +everything there is to know + +about the problem. + +And they feel this +is very strange. + +It's not strange because you +use probability models. + +You use models to try to +understand certain things + +about reality. + +And you assume as many +things as you want to + +assume about it. + +And when you get all done, you +either use all the assumptions + +or you don't use them. + +What we're going to find today +is that when you use this + +assumption of a probability +model, you can answer the + +questions that these classical +statisticians go to great + +pains to answer. + +And you can ask them +very, very simply. + +So that after we assume the a +priori probabilities, we can + +calculate certain things which +don't depend on those a priori + +probabilities. + +And therefore, we +know two things. + +One, we know that if we +did know the a priori + +probabilities, it wouldn't +make any difference. + +And two, we know that if we +can estimate the a priori + +probabilities, it makes a great +deal of difference. + +And three-- + +and this is the most +important point-- + +you make 100 observations +of something. + +Somebody else says, I don't +believe you, and comes in and + +makes another 100 +observations. + +Somebody else makes another +100 observations. + +Now, even if the second person +doesn't believe what the first + +person has done, it doesn't make +sense as a scientist to + +completely eliminate all of +that from consideration. + +Namely, what you would like to +do is say well, since this + +person has found such and +such, the a priori + +probabilities have changed. + +And then I can go on and make +my 100 observations. + +I can either make a hypothesis +test based on my 100 + +observations or I can make a +hypothesis test assuming that + +the other person did +their work well. + +I can make it based on all +of these observations. + +If you try to do that those +two things in a classical + +formulation, you run into +a lot of trouble. + +If you try to do them in this +probabilistic formulation, + +it's all perfectly +straightforward. + +Because you can either start +out with a model in which + +you're taking 200 observations +or you can start out with a + +model in which you take +100 observations. + +And then suddenly, the +world changes. + +This hypothesis takes on, +perhaps a different value. + +You take another hundred +observations. + +So you do whatever you want +to within a probabilistic + +formulation. + +But the other thing is, all of +you that patiently have lived + +with this idea of studying +probabilistic + +models all term long. + +You might as well keep +on living with it. + +The fact that we're now +interested in making decisions + +should not make you think that +everything you've learned up + +until this point is baloney. + +And to move from here to +a classical statistical + +formulation of the world would +really be saying, I don't + +believe in probability theory. + +It's that bad. + +So here we go. + +I'm sorry, we did that. + +We were there. + +Assume that on the basis of +observing a sample value of + +this sequence of observations, +we have to make a decision + +about H. We have to choose +H equals 0 or H equals 1. + +We have to detect whether +or not H is 1. + +When you do this detection, you +would think in the real + +world that you've detected +something. + +If you've made a decision about +something, that you've + +tested a hypothesis and you +found that which is correct. + +Not at all. + +When you make decisions, +you can make errors. + +And the question of what kinds +of errors you're making is a + +major part of trying +to make decisions. + +I mean, those people who make +decisions and then can't + +believe that they might have +made the wrong decision are + +the worst kind of fools. + +And you see them in politics. + +You see them in business. + +You see them in academia. + +You see them all +over the place. + +When you make a decision and +you've made a mistake, you get + +some more evidence. + +You see that it's a mistake +and you change. + +The whole 19th century +was taken up with-- + +I mean, the scientific community +was driven by + +physicists in those days. + +And the idea of Newton's +laws was the most + +sacred thing they had. + +Everybody believed in Newtonian + +mechanics in those days. + +When quantum mechanics came +along, this wasn't just a + +minor perturbation in physics. + +This was a most crucial thing. + +This said, everything we've +known goes out the window. + +We can't rely on anything +anymore. + +But the physicists said, OK, +I guess we made a mistake. + +We'll make new observations. + +We have new observations +that can be made. + +We now see that Newtonian +mechanics works over a certain + +range of things. + +It doesn't work in another +ranges of things. + +And they go on and +find new things. + +That's the same thing +we do here. + +We take these models. + +We evaluate our error +probabilities. + +And evaluating them, we then +say, well, we've got to go on + +and take some more +measurements. + +Or we say we're going +to live with it. + +But we face the fact that there +are errors involved. + +And in doing that, you have to +take a probabilistic model. + +If you don't take a +probabilistic model, it's very + +hard for you to talk honestly +about what error + +probabilities are. + +So both ways-- + +well, I'm preaching +and I'm sorry. + +But I've lived for a long time +with many statisticians, many + +of whom get into my own +field and who cause a + +great deal of trouble. + +So the only thing I can do it +urge you all to be cautious + +about this. + +And to think the matter +through on your own. + +I'm not telling you to take +my point of view on it. + +I'm telling you, don't take +other people's point of view + +without thinking it through. + +The probability experiment +here really-- + +I mean, every probability model +we view in terms of the + +real world, as you have this set +of probabilities, a set of + +possible events. + +You do the experiment. + +There's one sample point +that comes out. + +And after the one sample point +comes out, then you know what + +the result of the +experiment is. + +Here, the experiment consists +both of what you normally view + +as the experiment. + +Namely, taking the +observations. + +And it also involves a +choice of hypotheses. + +Namely, there's not a correct +hypothesis to start with. + +The experiment involves +God throws his dice. + +Einstein didn't believe that +God threw dice, but I do. + +And after throwing the dice, +one or the other of these + +hypotheses turns +out to be true. + +All of these observations point +to that or they point to + +the other and you +make a decision. + +OK, so the experiment consists +both on choosing the + +hypothesis and on taking +a whole sequence of + +observations. + +Now, the other thing to +not forget in this-- + +because you really have to get +this model in your mind or + +you're going to get very +confused with all + +the things we do. + +The experiment consists +on a whole sequence of + +observations, but only one +choice of hypothesis. + +Namely, you do the experiment. + +There's a hypothesis that +occurs, and there's a whole + +sequence of observations which +are all IID conditional on + +that particular hypothesis. + +So that's the model we're +going to be using. + +And now life is quite +simple once we've + +explained the model. + +We can talk about the +probability that H is equal to + +either 0 or 1, conditional +on the + +sample point we've observed. + +It's equal to the a priori +probability of that hypothesis + +times the density of the +observation conditional on the + +hypothesis divided by just +a normalization factor. + +Namely, the overall probability +of that + +observation period, which is the +sum of probability that 0 + +is a correct hypothesis times +this plus probability that 1 + +is a correct hypothesis times +the density given 1. + +This denominator here +is a pain in the + +neck, as you can see. + +But you can avoid ever dealing +with a denominator if you take + +this for H equals 0, divide by +this for H equals 1, and then + +you have this term divided by +this term all divided by this + +term for l equals 1 divided +by the same thing. + +So the ratio, the probability +that H equals 0 given y over + +the probability that +H is 1 equals y is + +just this ratio here. + +Now, what's the probability of +error if we make a decision at + +this point? + +If I've got in this particular +sequence Y, this quantity here + +is, in fact, the probability +that hypothesis 0 is correct + +in the model that +we have chosen. + +So this is the probability that +H is equal to 0 given Y. + +If we select 1 under these +conditions, if we select + +hypothesis 1, if we make a +decision and say, I'm going to + +guess that 1 is the +right decision. + +That means that this +is the probability + +you've made a mistake. + +Because this is the probability +that H is actually + +0 rather than 1. + +This quantity here is the +probability that you've made a + +mistake given that 1 is the +correct hypothesis. + +So here we are sitting +here with these + +probabilities of error. + +We don't have to do any +calculations for them. + +Well, you might have to do a +great deal of calculation to + +calculate this and to +calculate this. + +But otherwise, the whole thing +is just sitting there for you. + +So what do you do if you +want to minimize the + +probability of error? + +This was the probability that +you're going to make an error + +if you choose 1. + +This is the probability of +error if you choose 0. + +We want to minimize the +probability of error and we + +see the observation Y, we want +to pick the one of these which + +is largest. + +And that's all there is to it. + +This is the decision rule +that minimizes the + +probability of an error. + +It's based on knowing +what P0 and P1 is. + +But otherwise, probability that +H equals l is the correct + +hypothesis given the observation +is probability + +that H equals L given Y. We +maximize the a posteriori + +probability of choosing +correctly by choosing the + +maximum over l of probability +that H equals l given Y. + +This choosing directly, +maximizing the a posteriori + +probability is called the MAP +rule, Maximum A posteriori + +Probability. + +You can only solve the MAP +problem if you assume that you + +know P0 P1. + +We do know P0 and P1 if we've +selected a probability model. + +So when we select this +probability model, we've + +already assumed what these a +priori probabilities are, so + +we now make our observation. + +And after making our + +observation, we make a decision. + +And at that point, we have an a +posteriori probability that + +each of the hypotheses +is correct. + +Anybody has any issues +with this? + +I mean, it looks painfully +simple when you + +look at this way. + +And if it doesn't look painfully +simple, please ask + +now or forever hold your +peace as they say. + +Yeah? + +AUDIENCE: So can you explain +how you get the equation? + +Can you explain how you +get the equation + +on the first line? + +PROFESSOR: On the first +line right up here? + +Yes, I use Bayes' law. + +AUDIENCE: So what is that? + +So that's P of A given B is +equal to P of B given A? + +PROFESSOR: Yes. + +AUDIENCE: I don't quite +see how to-- + +P of A given B is equal to P +of B given A times P of A + +divided by P of A and B. + +If you take this over +there then it's-- + +am I stating Bayes' law +in a funny way? + +AUDIENCE: So the thing on +the bottom is P of B? + +OK. + +PROFESSOR: What? + +AUDIENCE: OK, I get it. + +PROFESSOR: I mean, I might +not be explained it well. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Except if you start +out with P of A given B is + +equal to P of B given A times P +of B divided by P of A. This + +quantity here is P of Y. So we +have probability that H equals + +l times probability of Y given +l divided by the probability + +of l to start with. + +OK, so you maximize the a +posteriori probability by + +choosing the maximum of these. + +It's called the MAP rule. + +And it doesn't require you to +calculate this quantity, which + +is sometimes a mess. + +All it requires you to do +is to compare these two + +quantities, which means you +have to compare these two + +quantities. + +AUDIENCE: It's 10 o'clock. + +PROFESSOR: Well, excuse me. + +Yes. + +Yes, I know. + +These things become clearer if +you state them in terms of + +what you call the likelihood +ratio. + +Likelihood ratio only works when +you have two hypotheses. + +When you have two hypotheses, +you call the ratio of one of + +them to the other one the +likelihood ratio. + +Why do I put 0 up here +and 1 down here? + +Absolutely no reason at all, +it's just convention. + +And unfortunately, it's +a convention that + +not everybody follows. + +So some people have one +convention and some people + +have another convention. + +If you want to use the other +convention, just imagine + +switching 1 and 1 +in your mind. + +They're both just +binary numbers. + +Then, when you want to look at +this MAP rule, the MAP rule is + +choosing the larger of +these two things, + +which we had back here. + +That's choosing whether this is +larger than this, or vice + +versa, which is choosing whether +this ratio here is + +greater than the ratio +of P1 to P0. + +So that's the same, that's +the same thing. + +So the MAP rule is to calculate +the likelihood ratio + +for this given observation y. + +And if this is greater +than P1 over P0, you + +select H equals 0. + +If it's less than or equal to +P1 over P0, you select H1. + +Why do I put the strict equality +here and the strict + +inequality here? + +Again, no reason whatsoever. + +When you have equality, it +doesn't make any difference + +which you choose. + +So you could flip a coin. + +It's a little easier if you just +say, we're going to do + +this under this condition. + +So we state condition +this way. + +We calculate the likelihood +ratio. + +We compare it with +a threshold. + +The threshold here +is P1 over P0. + +And then we select something. + +Why did I put a little +hat over this? + +AUDIENCE: Estimation. + +PROFESSOR: What? + +AUDIENCE: Because it's +an estimation. + +PROFESSOR: What? + +AUDIENCE: It's an estimation? + +PROFESSOR: Well, it's not +really an estimation. + +It's a detection. + +I mean, estimation you usually +view as being analog. + +Detection you usually view +as being digital. + +And thanks for bringing +that up because it's + +an important point. + +But in this model, H is either +0 or 1 in the result of this + +experiment. + +We don't know which it is. + +This is what we've chosen. + +So H hat is 0 does not mean +that H itself is 0. + +So this is our choice. + +It might be wrong or +it might be right. + +Many decision rules, including +the most common and the most + +sensible, are rules that compare +lambda of y to a fixed + +threshold, say, eta, is P1 over +P0, which is independent + +of y, which is just +a fixed threshold. + +The decision rules then vary +only in the way that you + +choose the threshold. + +Now, what happens as soon +as I call this eta + +instead of P1 over P0? + +My test becomes independent of +these a priori probabilities + +that statisticians have thought +about for so long. + +Namely, after a couple of lines +of fiddling around with + +these things, suddenly all +of that has disappeared. + +We have a threshold test. + +The threshold test says, +take this ratio-- + +everybody agrees that there's +such a ratio that exists-- + +and compare it with something. + +And if it's bigger than that +something, you choose 0. + +If it's less than that +thing, you choose 1. + +And that's the end of it. + +OK, so we have two questions. + +One, do we always want to use a +threshold test or are there + +cases where we should +use things other + +than a threshold test? + +And the second question is, if +we're going to use a threshold + +test, where should we +set the threshold? + +I mean, there's nothing that +says that you really want to + +minimize the probability +of error. + +I mean, suppose your test +is to see whether-- + +I mean, something in +the news today. + +I mean, you'd like to take an +experiment to see whether your + +nuclear plant is going +to explode or not. + +So you come up with +one decision, it's + +not going to explode. + +Or another decision, you +decide it will explode. + +Presumably on the basis of +that decision, you do all + +sorts of things. + +Do you really want to make +it a maximum a posteriori + +probability decision? + +No. + +You recognize that if it's +going to explode, and you + +choose that it's not going to +explode and you don't do + +anything, there is a humongous +cost associated with that. + +If you decide the other way, +there's a pretty large cost + +associated with that also. + +But there's not really much +comparison between the two. + +But anyway, you want to do +something which takes those + +costs into account. + +One of the problems in the +homework does that. + +It's really almost trivial to +readjust this problem, so that + +you set the threshold to +involve the costs also. + +So if you have arbitrary costs +in making errors, then you + +change the threshold +a little bit. + +But you still use a +threshold test. + +There's something called maximum +likelihood that people + +like for making decisions. + +And maximum likelihood +says you calculate + +the likelihood ratio. + +And if the likelihood +ratio is bigger than + +1, you go this way. + +If it's less than 1, +you go this way. + +It's the MAP test if +the two a priori + +probabilities are equal. + +But in many cases, you want to +use it whether or not the a + +priori probabilities +are equal. + +It's a standard test, +and there are many + +reasons for using it. + +Aside from the fact that the a +priori probabilities might be + +chosen that way. + +So anyway, that's one +other choice. + +When we go a little further +day, we'll talk about a + +Neyman-Pearson test. + +The Neyman-Pearson test says, +for some reason or other, I + +want to make sure that the +probability that my nuclear + +plant doesn't blow up is +less than, say, 10 + +to the minus fifth. + +Why 10 to the minus fifth? + +Pull it out of the air. + +Maybe 10 to the minus sixth, +that point our probabilities + +don't make much sense anymore. + +But however we choose it, we +choose our test to say, we + +can't make the probability of +error under one hypothesis + +bigger than some certain amount +alpha than what test + +will minimize the probability +of error under the other + +hypothesis. + +Namely, if I have to get one +thing right, or I have to get + +it right almost all the time, +what's the best I can do on + +the other alternative? + +And that's the Neyman-Pearson +test. + +That is a favorite test among +the non-Bayesians because it + +doesn't involve the a priori +probabilities anymore. + +So it's a nice one +in that way. + +But we'll see, we get +it anyway using + +a probability model. + +OK, let's go back to random +walks just a little bit to see + +why we're doing what +we're doing. + +The logarithm of the threshold +ratio is logarithm of this + +lambda of y. + +I'm taking m observations. + +I'm putting that in explicitly, +is the sum from N + +equals 1 to m of the log of +the individual ratio. + +In other words, when you-- + +under hypothesis 0, if I +calculate the probability of + +vector y given H equals 0, I'm +finding the probability of n + +things which are IID. + +So what I'm going to find this +probability density is taking + +the product of the probabilities +of each of the + +observations. + +Most of you know now that +any time you look at a + +probability, which is a product +of observations, what + +you'd really like to do is to +take the logarithm of it. + +So you're talking about a sum +of things rather than a + +product of things because +we all know how to add + +independent random variables. + +So the log of this likelihood +ratio, which is called the log + +likelihood ratio as you might +guess, is just a sum of these + +likelihood ratios. + +If we look at this for each m +greater than or equal to 1, + +then given H equals 0, +it's a random walk. + +And given H equals 1, it's +another random walk. + +It's the same sequence of sample +values in both cases. + +Namely, as an experimentalist, +we're taking these + +observations. + +We don't know whether H equals +0 or H equals 1 is what the + +result of the experiment +is going to be. + +But what we do know is we know +what those values are. + +We can calculate this sum. + +And now, if we condition this +on H equals 0, then this + +quantity, which is fixed, +has a particular + +probability of occurring. + +So this is a random variable +then under the + +hypothesis H equals 0. + +It's a random variable under +the hypothesis H equals 1. + +And this sum of random variables +behaves in a very + +different way under these +two hypotheses. + +What's going to happen is that +under one hypothesis, the + +expected value of this log +likelihood ratio is going to + +linearly increase with n. + +If we look at it under the other +hypothesis, it's going + +to linearly decrease +as we increase n. + +And a nifty test at that point +is to say, as soon as it + +crosses a threshold up here or +a threshold down here, we're + +going to make a decision. + +And that's called a sequential +test in that case because you + +haven't specified ahead of time, +I'm going to take 100 + +tests and then make +up my mind. + +You've specified that I'm going +to take as many tests as + +I need to be relatively sure +that I'm getting the right + +decision, which is what +you do in real life. + +I mean, there's nothing fancy +about doing sequential tests. + +Those are the obvious things to +do, except they're a little + +more tricky to talk about using +probability theory. + +But anyway, that's where +we're headed. + +That's why we're talking about +hypothesis testing. + +Because when you look at it in +this formulation, we get a + +random walk. + +And it gives us a nice example +of when you want to use random + +walks crossing a threshold as +a way of making decisions. + +OK, so that's why we're doing +what we're doing. + +Now, let's go back and look at +threshold tests again, and try + +to see how we're going to make +threshold tests, what the + +error probabilities will be, +and try to analyze them a + +little more than just saying, +well, a MAP test does this. + +Because as soon as you see that +a MAP test does this, you + +say, well, suppose I use +some other test. + +And what am I going to +suffer from that? + +What am I going to gain by it? + +So it's worthwhile to, instead +of looking at even just + +threshold tests, to say, +well, let's look at + +any old test at all. + +Now, any test means +the following. + +I have this probability model. + +I've already bludgeoned you into +accepting the fact that's + +the probability model we're +going to be looking at. + +And we have this-- + +well, we have the likelihood +ratio, but we don't care about + +that for the moment. + +But we make this observation. + +We got to make a decision. + +And our decision is going +to be either 1 or 0. + +How do we characterize +that mathematically? + +Or how do we calculate it if +we want a computer to make + +that decision for us? + +The systematic way to do it is +for every possible sequence of + +y to say ahead of time to give a +formula, which sequences get + +mapped into 1 and which +sequences get mapped into 0. + +So we're going to call a set A +the set of sample sequences + +that get mapped into +hypothesis 1. + +That's the most general binary +hypothesis test you can do. + +That includes all +possible ways of + +choosing either 1 or 0. + +You're forced to hire somebody +or not hire somebody. + +You can't get them to work for +you for two weeks, and then + +make a decision at that point. + +Well, sometimes you +can in this world. + +But if it's somebody you really +want and other people + +want them, too, then you've got +to decide, I'm going to go + +with this person or I'm not +going to go with them. + +So under all observations that +you've made, you need some way + +to decide which ones make +you go to decision 1. + +Which ones make you +go to decision 0. + +So we will just say arbitrarily, +there's a set A + +of sample sequences that +map into hypothesis 1. + +And the error probability for +each hypothesis using test A + +is given by-- and we'll just +call Q sub 0 of A-- + +this is our name for the +error probability. + +Have I twisted this up? + +No. + +Q sub 0 of A is the probability + +that I actually choose-- + +it's the probability that I +choose A given that the + +hypothesis is 0. + +Q sub 1 of A is the probability +that I choose 1. + +Blah, let me start +that over again. + +Q0 of A is the probability +that I'm going to choose + +hypothesis 1 given that +hypothesis 0 was the correct + +hypothesis. + +It's the probability that Y is +in A. That means that H hat is + +equal to 1 given that +H is actually 0. + +So that's the probability we +make an error given the + +hypothesis, the correct +hypothesis is 0. + +Q1 of A is the probability of +making an error given that the + +correct hypothesis is 1. + +If I have a priori +probabilities, I'm going back + +to assuming a priori +probabilities again. + +The probability of error is? + +It's P0 times the probability +I make an error given that H + +equals zero. + +P1 a priori probability +of 1 given that I make + +an error given 1. + +I add these two up. + +I can write it this way. + +Don't ask for the time being. + +I'll just take the P0 out, so +it's Q0 of A plus P1 over P0 + +Q1 of A. So that's what I've +called eta times Q1 of A. + +For the threshold test based +on eta, the probability of + +error is the same thing. + +But that A there is an eta. + +I hope you can imagine that +quantity there is an eta. + +This is an eta. + +So it's P0 times Q0 of eta +plus eta times Q1 of eta. + +So the eta probability, under +this crazy test that you've + +designed, is P0 times +this quantity. + +Under the MAP test, probability +of error is this + +quantity here. + +What do we know about +the MAP test? + +It minimizes the error +probability under those a + +priori probabilities. + +So what we know about it is +that this quantity is less + +than or equal to +this quantity. + +Take out the P0's and it says +that this quantity is less + +than or equal to +this quantity. + +Pretty simple. + +Let's draw a picture that +shows what that means. + +Here's a result that we have. + +We know because of maximum a +posteriori probability for the + +threshold test that this is less +than or equal to this. + +This is the minimum +error probability. + +This is the error probability +you get with + +whatever test you like. + +So let's draw a picture on a +graph where the probability of + +error given H equals 1 is +on the horizontal axis. + +The probability of error +conditional on H equals 0 is + +on this axis. + +So I can list the probability +of error for the threshold + +test, which sits here. + +I can list the probability of +error for this arbitrary test, + +which sits here. + +And I know that this quantity +is greater than or equal to + +this quantity. + +So the only thing I have to do +now is to sort out using plain + +geometry, why these numbers +are what they are. + +This number here is Q0 of eta +plus eta times Q1 of eta. + +Here's Q1 of eta. + +This distance here +is Q1 of eta. + +We have a line of slope minus +eta there that we've drawn. + +So this point here is, in fact, +Q0 of eta plus eta times + +Q1 of eta . + +That's just plain geometry. + +This point is Q0 of A plus eta +times Q1 of A. Another line of + +slope minus et. + +What we've shown is that this is +less than or equal to this. + +That's because of +the MAP rule. + +This has to be less than +or equal to that. + +So what have we shown here? + +We've shown that for every test +A you can imagine, when + +you draw that test on this +two-dimensional plot of error + +probability given H equals 1 +versus error probability given + +H equals 0. + +Every test in the world lies +Northeast of this line here. + +Yeah? + +AUDIENCE: Can you say +again exactly what + +axis represents what? + +PROFESSOR: This axis here +represents the error + +probability given that H +equals 1 is the correct + +hypothesis. + +This axis is the error +probability given that 0 is + +the correct hypothesis. + +So we've defined Q1 of eta and +Q0 of eta as those two error + +probabilities. + +Using the threshold test, or +using the MAP test where eta + +is equal to P0 over P1. + +And this point here is whatever +it happens to be for + +any test that you +happen to like. + +You might have a supervisor who +wants to hire somebody and + +you view that person is a threat +to yourself, so you've + +taken all your observations and +you then make a decision. + +If the person is any good, +you say, don't hire him. + +If the person is good +you say, hire them. + +So just the opposite of +what you should do. + +But whatever you do, this says +this is less than or equal to + +this because of the MAP rule. + +And therefore, this point lies +up in that direction + +of this line here. + +You can do this for any eta that +you want to do it for. + +So for every eta that we want +to use, we get some value of + +Q0 of eta and Q1 of eta. + +These go along here +in some way. + +You can do the same +argument again. + +For every threshold test, every +point lies Northeast of + +the line of slope minus eta +through that threshold test. + +We get a whole family of curves +when eta is very big, + +the curve of slope minus +eta goes like this. + +When eta is very small, +it goes like this. + +We just think of ourselves +plotting all these curves, + +taking the upper envelope of +them because every test has to + +lie Northeast of every +one of those lines. + +So we take the upper envelope of +all of these lines, and we + +get something that +looks like this. + +We call this the error curve. + +And this is the upper envelope +of the straight lines of slope + +minus eta that go through the +threshold tests at eta. + +You get something else +from that, too. + +This curve is convex. + +Why is the curve convex? + +Well, you might like to take the +second derivative of it, + +but that's a pain in the neck. + +But the fundamental definition +of convexity is that a + +one-dimensional curve is convex +if all of its tangents + +lie underneath the curve. + +That's the way we've +constructed this. + +It's the upper envelope of a +bunch of straight lines. + +Yes? + +AUDIENCE: Can you please +explain, what is u of alpha? + +PROFESSOR: U of alpha +is just what I've + +called this upper envelope. + +This upper envelope +is now a function. + +AUDIENCE: What's +the definition? + +PROFESSOR: What? + +AUDIENCE: What is +the definition? + +PROFESSOR: The definition is +the upper envelope of all + +these straight lines. + +AUDIENCE: For changing eta? + +PROFESSOR: What? + +AUDIENCE: For changing eta? + +PROFESSOR: Yes. + +As eta changes, I get a whole +bunch of these points. + +I got a whole bunch +of these points. + +I take the upper envelope of all +of these straight lines. + +I mean, yes, you'd rather +see an equation. + +But if you see an equation +it's terribly ugly. + +I mean, you can program +a computer to do this. + +as easily as you can +program it to + +follow a bunch of equations. + +But anyway, I'm not interested +in actually solving for this + +curve in particular. + +I am particularly interested +in the fact that this upper + +envelope is, in fact, a convex +curve and that the threshold + +tests lie on the curve. + +The other tests lie Northeast +of the curve. + +And that's the reason you want +to use threshold tests. + +And it has nothing to do with a +priori probabilities at all. + +So you see, the thing we've done +is to start out assuming + +a priori probabilities. + +We've derived this neat result +using a priori probabilities. + +But now we have this +error curve. + +Well, to give you a better +definition of what u of alpha + +is, u of alpha is the error +probability under hypothesis 1 + +if the error probability under +hypothesis 0 was alpha. + +You pick an error probability +here. + +You go up to that point here. + +There's a threshold +test there. + +You read over there. + +And at that point, you find the +probability of error given + +H equals 1. + +AUDIENCE: How do you know +that the threshold + +tests lie on the curve? + +PROFESSOR: Well, this threshold +test here is + +Southwest of all tests. + +And therefore, it can't lie +above this upper envelope. + +Now, I've cheated you +in one small way. + +If you have a discrete test, +what you're going to wind up + +with is just a finite set of +these possible points here. + +So you're going to wind up with +the upper envelope of a + +finite set of straight lines. + +So the straight line is +actually going to be-- + +it's still convex, but it's +piecewise linear. + +And it's piecewise linear, and +the threshold tests are at the + +points of that curve. + +And in between those points, +you don't quite + +know what to do. + +So since you don't quite know +what to do in between those + +points, as far as the maximum a +posteriori probability test + +goes, you can reach any one of +those points, sometimes using + +one test on one corner of-- + +I guess it's easier +if I draw it. + +And I didn't want to get into +this particularly because it's + +a little messier. + +So you could have this +kind of curve. + +And the notes talk about +this in detail. + +So the threshold test correspond +to this point. + +This point says always +decide one. + +Don't pay any attention to the +tests at all, just say I think + +one is the right hypothesis. + +I mean, this is the testing +philosophy of people who don't + +believe in experimentalism. + +They've already made +up their mind. + +They look at the results. + +They say, that's very +interesting. + +And then they say, I'm +going to choose this. + +These other points are our +particular threshold tests. + +If you want to get error +probabilities in the middle + +here, what do you do? + +You use a randomized test. + +Sometimes you use this. + +Sometimes you use this. + +You flip a coin and choose +whichever one of these you + +want to choose. + +So what this says is the +Neyman-Pearson test, which is + +the test that says pick some +alpha, which is the error + +probability under hypothesis +1 that + +you're willing to tolerate. + +So you pick alpha. + +And then it says, minimize the +error probability of the other + +kind, so you read over there. + +And the Neyman-Pearson test, +what it does is it minimizes + +the error probability under +the other hypothesis. + +Now, when this curve is +piecewise linear, the + +Neyman-Pearson test is not a +threshold test, but it's a + +randomized threshold test. + +Sometimes when you're at a point +like this, you have to + +use this test and this +test sometimes. + +For most of the tests that you +deal with, Neyman-Pearson test + +is just the threshold +test that's at + +that particular point. + +Any questions about that? + +This is probably one of these +things you have to think about + +a little bit. + +Yes? + +AUDIENCE: When you say you have +to use this test or this + +test, are you talking about +threshold or are you talking + +about-- because this is always-- +it's either H equals + +0 or H equal 1, right? + +What do you mean when you say +you have to randomize between + +the two tests? + +I mean threshold tests-- + +if I have a finite set of +alternatives, and I'm doing a + +threshold test on that finite +set of alternatives, I only + +have a finite number +of things I can do. + +As I increase the threshold, +I suddenly get to the point + +where this ratio of likelihoods + +includes one more point. + +And then it gets to the point +where it includes one other + +point and so forth. + +So that what happens is that +this upper envelope is just + +the upper envelope of a finite +number of points. + +And this upper envelope of a +finite number of points, the + +threshold tests are just +the corners there. + +So I sometimes have to randomize +between them. + +If you don't like +that, ignore it. + +Because for most tests you deal +with, almost all books on + +statistics that I've ever +seen, it just says the + +Neyman-Pearson test looks at the +threshold curve, at this + +error curve. + +And it chooses accordingly. + +Yes? + +AUDIENCE: You can put the +previous slide back? + +You told us that because +of maximum a posteriori + +probability, if eta is equal to +P0 divided by P1, then the + +probability of error +is minimized. + +And so the errors of the +test A are [INAUDIBLE]. + +But if we start changing eta +from 0 to infinity, it doesn't + +have to be anymore. + +[INAUDIBLE], which means +the error is + +not necessarily minimized. + +So the argument doesn't +hold anymore. + +PROFESSOR: As I change eta, I'm +changing P1 and P0 also. + +In other words, now what I'm +doing is I'm saying, let's + +look at this threshold test, +and let's visualize what + +happens as I change the a +priori probabilities. + +So I'm suddenly becoming a +classical statistician instead + +of a Bayesian one. + +But I know what the answers +are from looking at the + +Bayesian case. + +OK, so let's move on. + +I mean, we now sort of see +that these tests-- + +well, one thing we've seen is +when you have to make a + +decision under this kind of +probabilistic model we've been + +talking about-- namely, two +hypotheses, IID random + +variable is conditional +on each hypothesis. + +Those hypothesis testing +problems turn + +into random walk problems. + +We also saw that +the [? GG1Q ?] + +when I started looking at when +the system becomes empty, and + +how long it takes to start to +fill up again, that problem is + +a random walk problem. + +So now I want to start to ask +the question, what's the + +probability that a random walk +will cross a threshold? + +I'm going to apply the +Chernoff bound to it. + +You remember the +Chernoff bound? + +We talked about it a little +bit back on the + +second week of the term. + +We were talking about the Markov +inequality and the + +Chebyshev inequality. + +And we said that the Chernoff +inequality was the same sort + +of thing, except it was based +on e to the rZ rather than x + +or x squared. + +And we talked a little bit +about its properties. + +The major thing one uses the +Chernoff bound for is to get + +good estimates very, very +far away from the mean. + +In other words, good estimates +of probabilities that are + +very, very small. + +I've grown up using these all +my life because I've been + +concerned with error +probabilities in + +communication systems. + +You typically want error +probabilities that run between + +10 to the minus fifth and +10 to the minus eighth. + +So you want to look at points +which are quite far away. + +I mean, you take a +large number of-- + +you take a sum of a large number +of variables, which + +correspond to a code. + +And you look at error +probabilities for this rather + +complicated thing. + +But you're looking very, very +far away from the mean, and + +you're looking at very large +numbers of observations. + +So instead of the kinds of +things where we deal with + +things like the central limit +theorem where you're trying to + +figure out what goes on close +to the mean, here you're + +trying to figure out what goes +on very far from the mean. + +OK, so what the Chernoff bound +says is that the probability + +that a random variable Z is +greater than or equal to some + +constant b. + +We don't even need sums of +random variables here, it's + +just a Chernoff bound is a +bound on the tail of a + +distribution. + +Is less than or equal to the +moment generating function of + +that random variable. + +g sub Z of r is the expected +value of e to the rZ. + +These generating functions, +you can calculate + +them if you want to. + +Times e to the minus rb. + +This is the Markov inequality +for the random + +variable e to the rZ. + +And go back and review +chapter 1. + +I think it's section +1.43 or something. + +It's the section that deals with +the Markov inequality, + +the Chebyshev inequality, +and the Chernoff bound. + +And as I told you once when we +talked about these things, + +Chernoff is still +alive and well. + +He's a statistician +at Harvard. + +He was somewhat embarrassed by +this inequality becoming so + +famous because he did it as sort +of a throw-off thing in a + +paper where he was trying to +do something which was much + +more mathematically +sophisticated. + +And now the poor guy is only +known for this thing that he + +views as being trivial. + +But what the bound says is the +probability of Z is greater + +than or equal to b is +this inequality. + +Strangely enough, the +probability that Z is less + +than or equal to b is bounded +by the same inequality. + +But one of them, r +is bigger than 0. + +And the other one, +r is less than 0. + +And you have to go back and +read that section to + +understand why. + +Now, this is most useful when +it's applied to a sum of + +random variables. + +I don't know of any applications +for it otherwise. + +So if the moment-generating +function-- + +oh, incidentally, also. + +When most people talk about +moment-generating functions, + +and certainly when people talked +about moment-generating + +functions before the 1950s or +so, what they were always + +interested in is the fact that +if you take derivatives of the + +moment-generating functions, +you generate the moments of + +the random variable. + +If you take the derivative of +this with respect to r, + +evaluate it at r equals 0, you +get the expected value of Z. + +If you take the second +derivative evaluated at r + +equals 0, you get the +expected value of Z + +squared, and so forth. + +You can see that by just taking +the derivative of that. + +Here, we're looking +at something else. + +We're not looking at what goes +on around r equals 0. + +We're trying to figure out what +goes on way on the far + +tails of these distributions. + +So if gX of r is e to the rX, +then e to the e to the r Sn-- + +Sn is the sum of these +random variables-- + +is the expected value of the +product of e to the rXi. + +Namely, it's e to the r. + +Some of Xi. + +So that turns into a product. + +The expected value of a product +of a finite number of + +terms is the product of +the expected value. + +So it's gX or r to +the n-th power. + +So if I want to write this, now +I'm applying the Chernoff + +bound to the random +variable S sub n. + +What's the probability that S +sub n is greater than or equal + +to n times a? + +It's gX to the n of r times +e to the minus rna. + +That's what the Chernoff +bound says. + +This is the Chernoff bound over +on the other side of the + +distribution. + +This only makes sense and has +interesting values when a is + +bigger than the mean or when +a is less than the mean. + +And when r is greater than 0 for +this one and less than 0 + +for this one. + +Now, this is easier to +interpret and it's + +easier to work with. + +If you take that product of +terms g to the r to the n-th + +power and you visualize the +logarithm of g to the X. + +Visualize the logarithm of g +to the X, then you get this + +quantity up here. + +You get the probability that Sn +is greater than or equal to + +na is this e to the n times +gamma x of r minus ra. + +Gamma is the logarithm of the +moment-generating function. + +The logarithm of the +moment-generating function is + +always called the +semi-invariant + +moment-generating function. + +The name is, again, because +people were originally + +interested in the +moment-generating properties + +of these random variables. + +If you sit down and take +the derivatives, I can + +probably do it here. + +It's simple enough that +I won't get confused. + +The derivative with respect to +r of the logarithm of g of r + +is first derivative of +r divided by g of r. + +And the second derivative +is then the + +natural log of g of r. + +Taking the derivative of that is +equal to g double prime of + +r over g of r squared. + +Tell me if I'm making a mistake +here because I usually + +do when I do this. + +Minus g of r and g prime of r. + +Probably divided by +this squared. + +Let's see. + +Is this right? + +Who can take derivatives here? + +AUDIENCE: First term doesn't +have a square in it. + +PROFESSOR: What? + +AUDIENCE: First term doesn't +have a square in the + +denominator. + +PROFESSOR: First term? + +Yeah. + +Oh, the first thing doesn't +have a square. + +No, you're right. + +AUDIENCE: Second one +doesn't have-- + +PROFESSOR: And the second +one, let's see. + +We have-- + +we just have g prime +of r squared + +divided by g of r squared. + +And we evaluate this +at r equals 0. + +This term becomes 1. + +This term becomes 1. + +This term becomes the second +moment x squared bar. + +And this term becomes +x bar squared. + +And this whole thing becomes the +variance of the moment of + +the random variable rather +than the second moment. + +All of these terms might be +wrong, but this term is right. + +And I'm sure all of you can +rewrite that and evaluate it + +at r equals 0. + +So that's why it's called +the semi-invariant + +moment-generating function. + +It doesn't make any difference +for what we're interested in. + +The thing that we're interested +in is that this + +exponent here-- + +as you visualize doing this +experiment and taking + +additional observations, what +happens is the probability + +that you exceed na-- + +that the n-th sum exceeds n +times some fixed quantity a is + +going down exponentially +with [? the a. ?] + +Now, is this bound any good? + +Well, if you optimize it over +r, It's essentially + +exponentially tight. + +So, in fact, it is good. + +What does it mean to be +exponentially tight? + +That's what I don't want +to define carefully. + +There's a theorem in the notes +that says what exponentially + +tight means. + +And it takes you half an hour to +read it because it's being + +stated very carefully. + +What it says essentially is that +if I take this quantity + +here and I subtract-- + +I add an epsilon to it. + +Namely, e to the n times this +quantity minus epsilon. + +So I have an e to the +minus n epsilon, see + +it sitting in there? + +When I take this exponent and I +reduce it just a little bit, + +I get a bound that isn't true. + +This is greater than +or equal to the + +quantity with an epsilon. + +In other words, you can't make +an exponent that's any + +smaller than this. + +You can take coefficients and +play with them, but you can't + +make the exponent any smaller. + +OK, all of these things you +can do them by pictures. + +I know many of you don't like +doing things by pictures. + +I keep doing them by pictures +because I keep trying to + +convince you that pictures +are more rigorous + +than equations are. + +At least, many times. + +If you want to show that +something is convex, you try + +to show that the second +derivative is positive. + +That works sometimes and it +doesn't work sometimes. + +I mean, it works as a function +is continuous and has a + +continuous first derivative. + +It doesn't work. otherwise. + +When you start taking tangents +of the curve, and you say the + +upper envelope of the tangents +to the curve all lie below the + +function, then it +works perfectly. + +That's what a convex function +is by definition. + +How do we derive +all this stuff? + +What we're trying to +do is to find-- + +I mean, this inequality here is +true for all r, for all r + +greater than 0 so long as a is +greater than the mean of X. + +It's true for all r for which +this moment-generating + +function exists. + +Moment-generating functions can +sometimes blow up, so they + +don't exist everywhere. + +So it's true wherever the + +moment-generating function exists. + +So we like to find the r for +which this bound is tightest. + +So what I'm going to do is draw +a picture and show you + +where it's tightest in +terms of the picture. + +What I've drawn here is +the semi-invariant + +moment-generating function. + +Why didn't I put that down? + +This is gamma of r. + +Gamma of r at 0, it's the log +of the moment-generating + +function at 0, which is 0. + +It's convex. + +You take its second +derivative. + +Its second derivative at r +equals 0 is pretty easy. + +Its second derivative of other +values or r you have to + +struggle with it. + +But when you struggle a little +bit, it is convex. + +If you've got a curve that goes +down like this, then it + +goes back up again. + +Sometimes goes off +towards infinity. + +Might do whatever +it wants to do. + +Sometimes at a certain value +of r, it stops existing. + +Suppose I take the +simplest random + +variable you know about. + +You only know two simple +random variables. + +One of them is a binary +random variable. + +The other one's an exponential +random variable. + +Suppose I take the exponential +random variable with density + +alpha times e to the minus +alpha X. Where does this + +moment-generating +function exist? + +You take alpha and I multiply +it by e to the rX when I + +integrate it. + +Where does this exist? + +I mean, don't bother +to integrate it. + +If r is bigger than alpha, this +exponent is bigger than + +this exponent. + +And this thing takes off +towards infinity. + +If r is less than a, the +whole thing goes to 0. + +gX of r exists for r less +than alpha in this case. + +And in general, if you look at +a moment-generating function, + +if the tail of that distribution +function is going + +to 0 exponentially, you find the +rate at which it's going + +to 0 exponentially. + +And that's where the +moment-generating + +function cuts off. + +It has to cut off. + +You can't show a result like +this, which says something is + +going to 0, faster than it could +possibly be going to 0. + +So we have to have that +kind of result. + +But anyway, we draw +this curve. + +This is mu sub X of r. + +And then we say, how do we +graphically minimize gamma of + +r minus r times a? + +Well, what I do because I've +done this before and I know + +how to do it-- + +I mean, it's not the kind of +thing where if you sat down + +you would immediately +settle on this. + +I look at some particular +value of r. + +If I take a line of slope gamma +prime of r, that's a + +tangent to this curve because +this curve is convex. + +So if I take a line through here +of this slope and I look + +at where this line hits here, +where does it hit? + +It hits at gamma sub X of +r, this point here, + +minus gamma X of r-- + +oh. + +Well, what I've done is I've +already optimized the problem. + +I'm trying to find the +probability that Sn is greater + +than or equal to na. + +I'm trying to minimize this +exponent here, gamma + +X of r minus ra. + +Unfortunately, I really start +out by taking the derivative + +of that and setting it equal to +0, which is what you would + +all do, too. + +When I set the derivative of +this equal to 0, I get gamma + +prime of r minus a is equal to +0, which is what this says. + +So then we take a line of slope +gamma x of r equals 0. + +It's tangent at this +point here. + +You look at this point over here +and you get the minimum + +value of the gamma X +of r minus r0 a. + +So what this says is when you +vary a, you can go through + +this maximization tilting +this curve around. + +I mean, a determines the slope +of this line here. + +If I use a smaller value of +a, the slope is smaller. + +It hits in here. + +If I take a larger value of a, +it comes in further down and + +the exponent gets bigger. + +That's not surprising. + +I want to find out the +probability that S sub n is + +greater than or equal to a. + +As I increase a, I expect this +exponent to keep going down as + +I make a bigger and bigger +because it's harder and harder + +for it to be greater +than or equal to a. + +So anyway, when you optimize +this, you get something + +exponentially tight. + +And this is what +it's equal to. + +And I would recommend that you +go back and read the section + +of chapter 1, which goes through +all of this in a + +little more detail. + +Let me go passed that. + +Don't want to talk about that. + +Well, when I do this +optimization, if what I'm + +looking at is the probability +that S sub n is greater than + +or equal to some alpha rather +than n times a when I'm do + +this optimization and I'm +looking at what happens at + +different values of n, it turns +out that when n is very + +big, you get something which +is tangent there. + +As n gets smaller, you get these +tangents that come down + +that comes in to there, +and then it starts + +going back out again. + +This e to the r star is the +tightest the bound ever gets. + +That's the n at which errors +in the hypothesis testing + +usually occur. + +It's the point at which-- + +it's the n for which Sn greater +than or equal to alpha + +is most likely to occur. + +And if you evaluate that for +our friendly binary case + +again, X equals 1 or X equals +minus 1, what you find when + +you evaluate that point alpha r +star is that r star is equal + +to log 1 minus P over P. And our +bound of probability union + +of Sn is greater than or equal +to alpha is approximately e to + +the minus alpha r star +is 1 minus P over P + +to the minus alpha. + +I mean, why do I torture +you with this? + +Because we solved this problem +at the beginning of the + +lecture, remember? + +The probability that the sum +S sub n for this binary + +experiment is greater than or +equal to k is equal to 1 minus + +P over P to the minus k. + +That's what it's equal +to exactly. + +When I go through all of this +Chernoff bound stuff, I get + +the same answer. + +Now, this is a much harder way +to do it, but this is a + +general way of doing it. + +And that's a very specialized +way of doing it. + +So we'll talk more about +this next time. \ No newline at end of file diff --git a/gpZu5N1FFq0.txt b/gpZu5N1FFq0.txt new file mode 100644 index 0000000000000000000000000000000000000000..f725fd637a81f366f7e5652072efb3260550b6c8 --- /dev/null +++ b/gpZu5N1FFq0.txt @@ -0,0 +1,5979 @@ 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materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi today we're going to conclude our + + align:start position:0% +hi today we're going to conclude our + + + align:start position:0% +hi today we're going to conclude our +survey of complex variables and a rather + + align:start position:0% +survey of complex variables and a rather + + + align:start position:0% +survey of complex variables and a rather +fitting topic I imagine would be what it + + align:start position:0% +fitting topic I imagine would be what it + + + align:start position:0% +fitting topic I imagine would be what it +means to integrate a complex valued + + align:start position:0% +means to integrate a complex valued + + + align:start position:0% +means to integrate a complex valued +function of a complex variable and I + + align:start position:0% +function of a complex variable and I + + + align:start position:0% +function of a complex variable and I +thought that that's what we would talk + + align:start position:0% +thought that that's what we would talk + + + align:start position:0% +thought that that's what we would talk +about today and in fact let's just call + + align:start position:0% +about today and in fact let's just call + + + align:start position:0% +about today and in fact let's just call +today's lecture integrating complex + + align:start position:0% +today's lecture integrating complex + + + align:start position:0% +today's lecture integrating complex +functions but let me emphasize I really + + align:start position:0% +functions but let me emphasize I really + + + align:start position:0% +functions but let me emphasize I really +do mean by a complex function the thing + + align:start position:0% +do mean by a complex function the thing + + + align:start position:0% +do mean by a complex function the thing +that we've been stressing throughout the + + align:start position:0% +that we've been stressing throughout the + + + align:start position:0% +that we've been stressing throughout the +course a complex valued function of a + + align:start position:0% +course a complex valued function of a + + + align:start position:0% +course a complex valued function of a +complex variable the idea being that if + + align:start position:0% +complex variable the idea being that if + + + align:start position:0% +complex variable the idea being that if +you have a complex function of a real + + align:start position:0% +you have a complex function of a real + + + align:start position:0% +you have a complex function of a real +variable essentially this breaks down as + + align:start position:0% +variable essentially this breaks down as + + + align:start position:0% +variable essentially this breaks down as +we've seen in the previous assignment + + align:start position:0% +we've seen in the previous assignment + + + align:start position:0% +we've seen in the previous assignment +into studying uh regular functions of a + + align:start position:0% +into studying uh regular functions of a + + + align:start position:0% +into studying uh regular functions of a +single real variable in other words if + + align:start position:0% +single real variable in other words if + + + align:start position:0% +single real variable in other words if +you have U of T plus I V of t uh where T + + align:start position:0% +you have U of T plus I V of t uh where T + + + align:start position:0% +you have U of T plus I V of t uh where T +is a real variable this really gives us + + align:start position:0% +is a real variable this really gives us + + + align:start position:0% +is a real variable this really gives us +no problem this is sort of like the + + align:start position:0% +no problem this is sort of like the + + + align:start position:0% +no problem this is sort of like the +vector Vector treatment a vector + + align:start position:0% +vector Vector treatment a vector + + + align:start position:0% +vector Vector treatment a vector +function of a scal of variable Etc so + + align:start position:0% +function of a scal of variable Etc so + + + align:start position:0% +function of a scal of variable Etc so +what I'm saying here though is let's + + align:start position:0% +what I'm saying here though is let's + + + align:start position:0% +what I'm saying here though is let's +make sure that it's clear that we're + + align:start position:0% +make sure that it's clear that we're + + + align:start position:0% +make sure that it's clear that we're +still talking about mappings that map + + align:start position:0% +still talking about mappings that map + + + align:start position:0% +still talking about mappings that map +complex numbers into complex numbers now + + align:start position:0% +complex numbers into complex numbers now + + + align:start position:0% +complex numbers into complex numbers now +by way of review how did we Define the + + align:start position:0% +by way of review how did we Define the + + + align:start position:0% +by way of review how did we Define the +definite integral in the case of a + + align:start position:0% +definite integral in the case of a + + + align:start position:0% +definite integral in the case of a +single real variable we Define the + + align:start position:0% +single real variable we Define the + + + align:start position:0% +single real variable we Define the +integral from x0 to X1 F ofx DX to be a + + align:start position:0% +integral from x0 to X1 F ofx DX to be a + + + align:start position:0% +integral from x0 to X1 F ofx DX to be a +certain limit namely we partition the + + align:start position:0% +certain limit namely we partition the + + + align:start position:0% +certain limit namely we partition the +interval from x0 into X to X1 into n + + align:start position:0% +interval from x0 into X to X1 into n + + + align:start position:0% +interval from x0 into X to X1 into n +pieces calling the pieces Delta X1 up to + + align:start position:0% +pieces calling the pieces Delta X1 up to + + + align:start position:0% +pieces calling the pieces Delta X1 up to +Delta xn we took a number say C subk + + align:start position:0% +Delta xn we took a number say C subk + + + align:start position:0% +Delta xn we took a number say C subk +star in the K potition formed the sum F + + align:start position:0% +star in the K potition formed the sum F + + + align:start position:0% +star in the K potition formed the sum F +of C subk star Delta x k as K went from + + align:start position:0% +of C subk star Delta x k as K went from + + + align:start position:0% +of C subk star Delta x k as K went from +1 to n and took that limit as the + + align:start position:0% +1 to n and took that limit as the + + + align:start position:0% +1 to n and took that limit as the +maximum sized interval the maximum Delta + + align:start position:0% +maximum sized interval the maximum Delta + + + align:start position:0% +maximum sized interval the maximum Delta +x sub K went to zero and if that limit + + align:start position:0% +x sub K went to zero and if that limit + + + align:start position:0% +x sub K went to zero and if that limit +existed that was defined to be the + + align:start position:0% +existed that was defined to be the + + + align:start position:0% +existed that was defined to be the +definite integral now we did see a few + + align:start position:0% +definite integral now we did see a few + + + align:start position:0% +definite integral now we did see a few +other things along the way but this is + + align:start position:0% +other things along the way but this is + + + align:start position:0% +other things along the way but this is +the main definition see this is the + + align:start position:0% +the main definition see this is the + + + align:start position:0% +the main definition see this is the +definition that we're using some of the + + align:start position:0% +definition that we're using some of the + + + align:start position:0% +definition that we're using some of the +consequences of this definition were one + + align:start position:0% +consequences of this definition were one + + + align:start position:0% +consequences of this definition were one +if we could find a function capital F + + align:start position:0% +if we could find a function capital F + + + align:start position:0% +if we could find a function capital F +whose derivative was little F then this + + align:start position:0% +whose derivative was little F then this + + + align:start position:0% +whose derivative was little F then this +integral was simply capital F of X1 + + align:start position:0% +integral was simply capital F of X1 + + + align:start position:0% +integral was simply capital F of X1 +minus capital F of + + align:start position:0% +minus capital F of + + + align:start position:0% +minus capital F of +x0 and we also saw that if we wished and + + align:start position:0% +x0 and we also saw that if we wished and + + + align:start position:0% +x0 and we also saw that if we wished and +we didn't have to but if we wished we + + align:start position:0% +we didn't have to but if we wished we + + + align:start position:0% +we didn't have to but if we wished we +could view this thing geometrically by + + align:start position:0% +could view this thing geometrically by + + + align:start position:0% +could view this thing geometrically by +observing that the x- axis was the + + align:start position:0% +observing that the x- axis was the + + + align:start position:0% +observing that the x- axis was the +domain of f the Y AIS was the range of f + + align:start position:0% +domain of f the Y AIS was the range of f + + + align:start position:0% +domain of f the Y AIS was the range of f +we could then plot the curve yal f ofx + + align:start position:0% +we could then plot the curve yal f ofx + + + align:start position:0% +we could then plot the curve yal f ofx +look at the area of the region R between + + align:start position:0% +look at the area of the region R between + + + align:start position:0% +look at the area of the region R between +x0 and X1 and the area of the region R + + align:start position:0% +x0 and X1 and the area of the region R + + + align:start position:0% +x0 and X1 and the area of the region R +was the value of this definite integral + + align:start position:0% +was the value of this definite integral + + + align:start position:0% +was the value of this definite integral +but the important point is what that the + + align:start position:0% +but the important point is what that the + + + align:start position:0% +but the important point is what that the +definition of the integral is as a limit + + align:start position:0% +definition of the integral is as a limit + + + align:start position:0% +definition of the integral is as a limit +of an infinite sum and now the question + + align:start position:0% +of an infinite sum and now the question + + + align:start position:0% +of an infinite sum and now the question +is how shall we Define the analogous + + align:start position:0% +is how shall we Define the analogous + + + align:start position:0% +is how shall we Define the analogous +thing for a complex valued function of a + + align:start position:0% +thing for a complex valued function of a + + + align:start position:0% +thing for a complex valued function of a +complex variable in other words what + + align:start position:0% +complex variable in other words what + + + align:start position:0% +complex variable in other words what +shall we mean by integral from z0 to Z1 + + align:start position:0% +shall we mean by integral from z0 to Z1 + + + align:start position:0% +shall we mean by integral from z0 to Z1 +F of Z DZ and because we've been so + + align:start position:0% +F of Z DZ and because we've been so + + + align:start position:0% +F of Z DZ and because we've been so +successful with this technique in the + + align:start position:0% +successful with this technique in the + + + align:start position:0% +successful with this technique in the +past it would seem that the simplest + + align:start position:0% +past it would seem that the simplest + + + align:start position:0% +past it would seem that the simplest +thing to do would be to Simply replace X + + align:start position:0% +thing to do would be to Simply replace X + + + align:start position:0% +thing to do would be to Simply replace X +by Z every place in this definition in + + align:start position:0% +by Z every place in this definition in + + + align:start position:0% +by Z every place in this definition in +other words let's simply do this let's + + align:start position:0% +other words let's simply do this let's + + + align:start position:0% +other words let's simply do this let's +define the integral z0 to Z1 F of zdz to + + align:start position:0% +define the integral z0 to Z1 F of zdz to + + + align:start position:0% +define the integral z0 to Z1 F of zdz to +be the limit as the maximum Delta Z subk + + align:start position:0% +be the limit as the maximum Delta Z subk + + + align:start position:0% +be the limit as the maximum Delta Z subk +approaches zero summation K goes from 1 + + align:start position:0% +approaches zero summation K goes from 1 + + + align:start position:0% +approaches zero summation K goes from 1 +to n f of C subk star time Delta Z subk + + align:start position:0% +to n f of C subk star time Delta Z subk + + + align:start position:0% +to n f of C subk star time Delta Z subk +where all we have done is replaced X's + + align:start position:0% +where all we have done is replaced X's + + + align:start position:0% +where all we have done is replaced X's +every place by Z's wherever they + + align:start position:0% +every place by Z's wherever they + + + align:start position:0% +every place by Z's wherever they +appeared now the reason I've put + + align:start position:0% +appeared now the reason I've put + + + align:start position:0% +appeared now the reason I've put +question marks here is that all of a + + align:start position:0% +question marks here is that all of a + + + align:start position:0% +question marks here is that all of a +sudden a problem occurs that never + + align:start position:0% +sudden a problem occurs that never + + + align:start position:0% +sudden a problem occurs that never +occurred in the real case you see the + + align:start position:0% +occurred in the real case you see the + + + align:start position:0% +occurred in the real case you see the +key reason that these problems are going + + align:start position:0% +key reason that these problems are going + + + align:start position:0% +key reason that these problems are going +to occur as I'll explain in a moment + + align:start position:0% +to occur as I'll explain in a moment + + + align:start position:0% +to occur as I'll explain in a moment +hinges on the fact that in the real case + + align:start position:0% +hinges on the fact that in the real case + + + align:start position:0% +hinges on the fact that in the real case +the domain of f was onedimensional it + + align:start position:0% +the domain of f was onedimensional it + + + align:start position:0% +the domain of f was onedimensional it +was an axis the x axis in the complex + + align:start position:0% +was an axis the x axis in the complex + + + align:start position:0% +was an axis the x axis in the complex +variable case the domain of f is + + align:start position:0% +variable case the domain of f is + + + align:start position:0% +variable case the domain of f is +two-dimensional it's the entire XY plane + + align:start position:0% +two-dimensional it's the entire XY plane + + + align:start position:0% +two-dimensional it's the entire XY plane +the agon diagram you see the problem is + + align:start position:0% +the agon diagram you see the problem is + + + align:start position:0% +the agon diagram you see the problem is +simply this what do you mean by Delta Z + + align:start position:0% +simply this what do you mean by Delta Z + + + align:start position:0% +simply this what do you mean by Delta Z +subk intuitively it certainly should + + align:start position:0% +subk intuitively it certainly should + + + align:start position:0% +subk intuitively it certainly should +seem to mean what the line that joins + + align:start position:0% +seem to mean what the line that joins + + + align:start position:0% +seem to mean what the line that joins +the point in the Aon diagram Zu subk + + align:start position:0% +the point in the Aon diagram Zu subk + + + align:start position:0% +the point in the Aon diagram Zu subk +minus1 to the point Z subk in other + + align:start position:0% +minus1 to the point Z subk in other + + + align:start position:0% +minus1 to the point Z subk in other +words remember we view complex numbers + + align:start position:0% +words remember we view complex numbers + + + align:start position:0% +words remember we view complex numbers +as being vectors they have a magnitude + + align:start position:0% +as being vectors they have a magnitude + + + align:start position:0% +as being vectors they have a magnitude +and a Direction so Delta Z subk can be + + align:start position:0% +and a Direction so Delta Z subk can be + + + align:start position:0% +and a Direction so Delta Z subk can be +viewed as the vector which joins these + + align:start position:0% +viewed as the vector which joins these + + + align:start position:0% +viewed as the vector which joins these +two points the trouble is this let's + + align:start position:0% +two points the trouble is this let's + + + align:start position:0% +two points the trouble is this let's +take a look in the agon diagram and + + align:start position:0% +take a look in the agon diagram and + + + align:start position:0% +take a look in the agon diagram and +locate the points z0 and Z1 his z0 his + + align:start position:0% +locate the points z0 and Z1 his z0 his + + + align:start position:0% +locate the points z0 and Z1 his z0 his +Z1 that's all that's given where shall + + align:start position:0% +Z1 that's all that's given where shall + + + align:start position:0% +Z1 that's all that's given where shall +these intermediary points zuub you know + + align:start position:0% +these intermediary points zuub you know + + + align:start position:0% +these intermediary points zuub you know +where should these intermediary points + + align:start position:0% +where should these intermediary points + + + align:start position:0% +where should these intermediary points +that are going to give rise to Delta z + + align:start position:0% +that are going to give rise to Delta z + + + align:start position:0% +that are going to give rise to Delta z +subk b in other words there seem to be + + align:start position:0% +subk b in other words there seem to be + + + align:start position:0% +subk b in other words there seem to be +many points that we can pick for a + + align:start position:0% +many points that we can pick for a + + + align:start position:0% +many points that we can pick for a +partition in particular it would seem + + align:start position:0% +partition in particular it would seem + + + align:start position:0% +partition in particular it would seem +that the most natural definition would + + align:start position:0% +that the most natural definition would + + + align:start position:0% +that the most natural definition would +be to specify a particular curve C and + + align:start position:0% +be to specify a particular curve C and + + + align:start position:0% +be to specify a particular curve C and +then look at Delta Z subk in terms of + + align:start position:0% +then look at Delta Z subk in terms of + + + align:start position:0% +then look at Delta Z subk in terms of +the curve C because you see once the + + align:start position:0% +the curve C because you see once the + + + align:start position:0% +the curve C because you see once the +curve C is specified if I partition + + align:start position:0% +curve C is specified if I partition + + + align:start position:0% +curve C is specified if I partition +things now notice that the Delta Z subk + + align:start position:0% +things now notice that the Delta Z subk + + + align:start position:0% +things now notice that the Delta Z subk +do not connect random points but rather + + align:start position:0% +do not connect random points but rather + + + align:start position:0% +do not connect random points but rather +points on the curve C the difficult + + align:start position:0% +points on the curve C the difficult + + + align:start position:0% +points on the curve C the difficult +point is that there are many different + + align:start position:0% +point is that there are many different + + + align:start position:0% +point is that there are many different +curves that join z0 to Z1 so perhaps the + + align:start position:0% +curves that join z0 to Z1 so perhaps the + + + align:start position:0% +curves that join z0 to Z1 so perhaps the +first thing that we should do is keeping + + align:start position:0% +first thing that we should do is keeping + + + align:start position:0% +first thing that we should do is keeping +in mind this ambiguity maybe we should + + align:start position:0% +in mind this ambiguity maybe we should + + + align:start position:0% +in mind this ambiguity maybe we should +come back to this definition and put in + + align:start position:0% +come back to this definition and put in + + + align:start position:0% +come back to this definition and put in +a c to indicate that we're going to talk + + align:start position:0% +a c to indicate that we're going to talk + + + align:start position:0% +a c to indicate that we're going to talk +about the integral of f of zdz from the + + align:start position:0% +about the integral of f of zdz from the + + + align:start position:0% +about the integral of f of zdz from the +point z0 to the point Z1 along the curve + + align:start position:0% +point z0 to the point Z1 along the curve + + + align:start position:0% +point z0 to the point Z1 along the curve +C keeping in mind you + + align:start position:0% +C keeping in mind you + + + align:start position:0% +C keeping in mind you +see that the reason that we have to + + align:start position:0% +see that the reason that we have to + + + align:start position:0% +see that the reason that we have to +specify the curve here is that z0 and Z1 + + align:start position:0% +specify the curve here is that z0 and Z1 + + + align:start position:0% +specify the curve here is that z0 and Z1 +are in the plane you see going back to + + align:start position:0% +are in the plane you see going back to + + + align:start position:0% +are in the plane you see going back to +this example here notice that here when + + align:start position:0% +this example here notice that here when + + + align:start position:0% +this example here notice that here when +we said let's go from x0 to X1 there was + + align:start position:0% +we said let's go from x0 to X1 there was + + + align:start position:0% +we said let's go from x0 to X1 there was +only one direction in which you could go + + align:start position:0% +only one direction in which you could go + + + align:start position:0% +only one direction in which you could go +from x0 to X1 namely since the domain of + + align:start position:0% +from x0 to X1 namely since the domain of + + + align:start position:0% +from x0 to X1 namely since the domain of +definition of f was the x- axis the + + align:start position:0% +definition of f was the x- axis the + + + align:start position:0% +definition of f was the x- axis the +direction had to be in the direction of + + align:start position:0% +direction had to be in the direction of + + + align:start position:0% +direction had to be in the direction of +the x-axis you see in the Aon diagram + + align:start position:0% +the x-axis you see in the Aon diagram + + + align:start position:0% +the x-axis you see in the Aon diagram +case I can go along any curve in the + + align:start position:0% +case I can go along any curve in the + + + align:start position:0% +case I can go along any curve in the +plane provid that plane connects that + + align:start position:0% +plane provid that plane connects that + + + align:start position:0% +plane provid that plane connects that +the curve connects the two points in + + align:start position:0% +the curve connects the two points in + + + align:start position:0% +the curve connects the two points in +question now the other question that I + + align:start position:0% +question now the other question that I + + + align:start position:0% +question now the other question that I +think I should point out here even + + align:start position:0% +think I should point out here even + + + align:start position:0% +think I should point out here even +though it may be bringing up a question + + align:start position:0% +though it may be bringing up a question + + + align:start position:0% +though it may be bringing up a question +that you might not have anticipated + + align:start position:0% +that you might not have anticipated + + + align:start position:0% +that you might not have anticipated +notice that when I interpret the + + align:start position:0% +notice that when I interpret the + + + align:start position:0% +notice that when I interpret the +definite integral as an area here notice + + align:start position:0% +definite integral as an area here notice + + + align:start position:0% +definite integral as an area here notice +that + + align:start position:0% +that + + + align:start position:0% +that +the lower bound is the domain of f + + align:start position:0% +the lower bound is the domain of f + + + align:start position:0% +the lower bound is the domain of f +itself and the upper bound is already + + align:start position:0% +itself and the upper bound is already + + + align:start position:0% +itself and the upper bound is already +from the curve yal F ofx that the upper + + align:start position:0% +from the curve yal F ofx that the upper + + + align:start position:0% +from the curve yal F ofx that the upper +curve brings out the function here you + + align:start position:0% +curve brings out the function here you + + + align:start position:0% +curve brings out the function here you +see the X x axis is the domain the Y AIS + + align:start position:0% +see the X x axis is the domain the Y AIS + + + align:start position:0% +see the X x axis is the domain the Y AIS +is the range I would like you to observe + + align:start position:0% +is the range I would like you to observe + + + align:start position:0% +is the range I would like you to observe +that there is no similar interpretation + + align:start position:0% +that there is no similar interpretation + + + align:start position:0% +that there is no similar interpretation +along the curve C in other words if we + + align:start position:0% +along the curve C in other words if we + + + align:start position:0% +along the curve C in other words if we +were to drop perpendiculars from z0 to + + align:start position:0% +were to drop perpendiculars from z0 to + + + align:start position:0% +were to drop perpendiculars from z0 to +Z1 down to the x-axis and talk about + + align:start position:0% +Z1 down to the x-axis and talk about + + + align:start position:0% +Z1 down to the x-axis and talk about +that area that would be the wrong area + + align:start position:0% +that area that would be the wrong area + + + align:start position:0% +that area that would be the wrong area +to talk about because you see the point + + align:start position:0% +to talk about because you see the point + + + align:start position:0% +to talk about because you see the point +is that that region is determined just + + align:start position:0% +is that that region is determined just + + + align:start position:0% +is that that region is determined just +by our domain notice that this curve and + + align:start position:0% +by our domain notice that this curve and + + + align:start position:0% +by our domain notice that this curve and +this is very very crucial that the curve + + align:start position:0% +this is very very crucial that the curve + + + align:start position:0% +this is very very crucial that the curve +that we're talking about about here C + + align:start position:0% +that we're talking about about here C + + + align:start position:0% +that we're talking about about here C +has absolutely nothing in the world to + + align:start position:0% +has absolutely nothing in the world to + + + align:start position:0% +has absolutely nothing in the world to +do with this F of Z just like when we + + align:start position:0% +do with this F of Z just like when we + + + align:start position:0% +do with this F of Z just like when we +computed Mass using density the density + + align:start position:0% +computed Mass using density the density + + + align:start position:0% +computed Mass using density the density +had nothing to do with the region that + + align:start position:0% +had nothing to do with the region that + + + align:start position:0% +had nothing to do with the region that +you were integrating with respect to the + + align:start position:0% +you were integrating with respect to the + + + align:start position:0% +you were integrating with respect to the +point to observe here is that we're + + align:start position:0% +point to observe here is that we're + + + align:start position:0% +point to observe here is that we're +observ we're assuming that F of Z is + + align:start position:0% +observ we're assuming that F of Z is + + + align:start position:0% +observ we're assuming that F of Z is +defined every place in the plane F of Z + + align:start position:0% +defined every place in the plane F of Z + + + align:start position:0% +defined every place in the plane F of Z +is defined here it's defined here it's + + align:start position:0% +is defined here it's defined here it's + + + align:start position:0% +is defined here it's defined here it's +defined here it's also defined on the + + align:start position:0% +defined here it's also defined on the + + + align:start position:0% +defined here it's also defined on the +curve C notice that F in this case + + align:start position:0% +curve C notice that F in this case + + + align:start position:0% +curve C notice that F in this case +is a complex number which means that it + + align:start position:0% +is a complex number which means that it + + + align:start position:0% +is a complex number which means that it +has a real and imaginary Part F is no + + align:start position:0% +has a real and imaginary Part F is no + + + align:start position:0% +has a real and imaginary Part F is no +place in this diagram and to plot what F + + align:start position:0% +place in this diagram and to plot what F + + + align:start position:0% +place in this diagram and to plot what F +does I would have to use the UV plane + + align:start position:0% +does I would have to use the UV plane + + + align:start position:0% +does I would have to use the UV plane +because F itself is two-dimensional in + + align:start position:0% +because F itself is two-dimensional in + + + align:start position:0% +because F itself is two-dimensional in +other words I would need two dimensions + + align:start position:0% +other words I would need two dimensions + + + align:start position:0% +other words I would need two dimensions +for the domain and two dimensions for + + align:start position:0% +for the domain and two dimensions for + + + align:start position:0% +for the domain and two dimensions for +the range and I hope that that part is + + align:start position:0% +the range and I hope that that part is + + + align:start position:0% +the range and I hope that that part is +fairly clear to you now don't confuse + + align:start position:0% +fairly clear to you now don't confuse + + + align:start position:0% +fairly clear to you now don't confuse +the path of integration with the + + align:start position:0% +the path of integration with the + + + align:start position:0% +the path of integration with the +integrand F of Z they are entirely + + align:start position:0% +integrand F of Z they are entirely + + + align:start position:0% +integrand F of Z they are entirely +different concepts + + align:start position:0% +different concepts + + + align:start position:0% +different concepts +okay at any rate I hope that this does + + align:start position:0% +okay at any rate I hope that this does + + + align:start position:0% +okay at any rate I hope that this does +suggest the concept of a line integral + + align:start position:0% +suggest the concept of a line integral + + + align:start position:0% +suggest the concept of a line integral +in some sense what I'm saying now is + + align:start position:0% +in some sense what I'm saying now is + + + align:start position:0% +in some sense what I'm saying now is +okay I want to integrate this from z0 to + + align:start position:0% +okay I want to integrate this from z0 to + + + align:start position:0% +okay I want to integrate this from z0 to +Z1 that means I want to compute a + + align:start position:0% +Z1 that means I want to compute a + + + align:start position:0% +Z1 that means I want to compute a +particular limit I pick the curve that + + align:start position:0% +particular limit I pick the curve that + + + align:start position:0% +particular limit I pick the curve that +joins z0 to Z1 let's assume that in + + align:start position:0% +joins z0 to Z1 let's assume that in + + + align:start position:0% +joins z0 to Z1 let's assume that in +cartisian coordinates that curve + + align:start position:0% +cartisian coordinates that curve + + + align:start position:0% +cartisian coordinates that curve +parametrically has the form X as some + + align:start position:0% +parametrically has the form X as some + + + align:start position:0% +parametrically has the form X as some +function of t y is some function of T + + align:start position:0% +function of t y is some function of T + + + align:start position:0% +function of t y is some function of T +where T is a real variable that's + + align:start position:0% +where T is a real variable that's + + + align:start position:0% +where T is a real variable that's +important T is a re real variable by the + + align:start position:0% +important T is a re real variable by the + + + align:start position:0% +important T is a re real variable by the +way as we mentioned when we were + + align:start position:0% +way as we mentioned when we were + + + align:start position:0% +way as we mentioned when we were +studying vectors if I want to introduce + + align:start position:0% +studying vectors if I want to introduce + + + align:start position:0% +studying vectors if I want to introduce +Vector notation the radius vector and + + align:start position:0% +Vector notation the radius vector and + + + align:start position:0% +Vector notation the radius vector and +write the curve C in Vector form notice + + align:start position:0% +write the curve C in Vector form notice + + + align:start position:0% +write the curve C in Vector form notice +that the curve C also has the form that + + align:start position:0% +that the curve C also has the form that + + + align:start position:0% +that the curve C also has the form that +R is X of t plus y of TJ and finally if + + align:start position:0% +R is X of t plus y of TJ and finally if + + + align:start position:0% +R is X of t plus y of TJ and finally if +I now want to write the curve in terms + + align:start position:0% +I now want to write the curve in terms + + + align:start position:0% +I now want to write the curve in terms +of complex numbers after all the Aon + + align:start position:0% +of complex numbers after all the Aon + + + align:start position:0% +of complex numbers after all the Aon +diagram now is the domain of the complex + + align:start position:0% +diagram now is the domain of the complex + + + align:start position:0% +diagram now is the domain of the complex +numbers what is the connection between + + align:start position:0% +numbers what is the connection between + + + align:start position:0% +numbers what is the connection between +the XY plane and the Aon diagram the X + + align:start position:0% +the XY plane and the Aon diagram the X + + + align:start position:0% +the XY plane and the Aon diagram the X +AIS names the real part the Y AIS the + + align:start position:0% +AIS names the real part the Y AIS the + + + align:start position:0% +AIS names the real part the Y AIS the +imaginary part in other words the unit + + align:start position:0% +imaginary part in other words the unit + + + align:start position:0% +imaginary part in other words the unit +know we think of the I Vector as + + align:start position:0% +know we think of the I Vector as + + + align:start position:0% +know we think of the I Vector as +representing the real part the J Vector + + align:start position:0% +representing the real part the J Vector + + + align:start position:0% +representing the real part the J Vector +as the imaginary part notice that + + align:start position:0% +as the imaginary part notice that + + + align:start position:0% +as the imaginary part notice that +changing this notation into the language + + align:start position:0% +changing this notation into the language + + + align:start position:0% +changing this notation into the language +of the Aon diagram results in this + + align:start position:0% +of the Aon diagram results in this + + + align:start position:0% +of the Aon diagram results in this +equation being replaced by Z equal x of + + align:start position:0% +equation being replaced by Z equal x of + + + align:start position:0% +equation being replaced by Z equal x of +t plus I Y of T we notice now that Z is + + align:start position:0% +t plus I Y of T we notice now that Z is + + + align:start position:0% +t plus I Y of T we notice now that Z is +a complex valued function of the real + + align:start position:0% +a complex valued function of the real + + + align:start position:0% +a complex valued function of the real +variable T and T of course goes from + + align:start position:0% +variable T and T of course goes from + + + align:start position:0% +variable T and T of course goes from +some fixed value t0 to some fix value T1 + + align:start position:0% +some fixed value t0 to some fix value T1 + + + align:start position:0% +some fixed value t0 to some fix value T1 +because after all what we're saying is + + align:start position:0% +because after all what we're saying is + + + align:start position:0% +because after all what we're saying is +that the curve Z equals x of t + i y of + + align:start position:0% +that the curve Z equals x of t + i y of + + + align:start position:0% +that the curve Z equals x of t + i y of +T is being traced out in terms of T when + + align:start position:0% +T is being traced out in terms of T when + + + align:start position:0% +T is being traced out in terms of T when +T t0 corresponds to being at z0 T1 + + align:start position:0% +T t0 corresponds to being at z0 T1 + + + align:start position:0% +T t0 corresponds to being at z0 T1 +corresponds to being at Z1 the idea now + + align:start position:0% +corresponds to being at Z1 the idea now + + + align:start position:0% +corresponds to being at Z1 the idea now +is + + align:start position:0% +is + + + align:start position:0% +is +this we go back to our definition + + align:start position:0% +this we go back to our definition + + + align:start position:0% +this we go back to our definition +of what the definite integral meant in + + align:start position:0% +of what the definite integral meant in + + + align:start position:0% +of what the definite integral meant in +terms of a limit we observe that we'll + + align:start position:0% +terms of a limit we observe that we'll + + + align:start position:0% +terms of a limit we observe that we'll +assume that we'll make the further + + align:start position:0% +assume that we'll make the further + + + align:start position:0% +assume that we'll make the further +restriction that our curves are smooth + + align:start position:0% +restriction that our curves are smooth + + + align:start position:0% +restriction that our curves are smooth +so that dzdt will exist what we now do + + align:start position:0% +so that dzdt will exist what we now do + + + align:start position:0% +so that dzdt will exist what we now do +is go back to our infinite sum and + + align:start position:0% +is go back to our infinite sum and + + + align:start position:0% +is go back to our infinite sum and +multiply and divide by delta T subk the + + align:start position:0% +multiply and divide by delta T subk the + + + align:start position:0% +multiply and divide by delta T subk the +idea being notice that this is what a + + align:start position:0% +idea being notice that this is what a + + + align:start position:0% +idea being notice that this is what a +complex valued function of a real + + align:start position:0% +complex valued function of a real + + + align:start position:0% +complex valued function of a real +variable it nowes because I can handle + + align:start position:0% +variable it nowes because I can handle + + + align:start position:0% +variable it nowes because I can handle +complex valued function of a real + + align:start position:0% +complex valued function of a real + + + align:start position:0% +complex valued function of a real +variable namely I just break them down + + align:start position:0% +variable namely I just break them down + + + align:start position:0% +variable namely I just break them down +into real and imaginary parts and use + + align:start position:0% +into real and imaginary parts and use + + + align:start position:0% +into real and imaginary parts and use +the same calculus that we used in part + + align:start position:0% +the same calculus that we used in part + + + align:start position:0% +the same calculus that we used in part +one of this course the idea is that with + + align:start position:0% +one of this course the idea is that with + + + align:start position:0% +one of this course the idea is that with +this suggestive notation and remembering + + align:start position:0% +this suggestive notation and remembering + + + align:start position:0% +this suggestive notation and remembering +how the definite integral gave rise to + + align:start position:0% +how the definite integral gave rise to + + + align:start position:0% +how the definite integral gave rise to +the the infinite sum gave rise to the + + align:start position:0% +the the infinite sum gave rise to the + + + align:start position:0% +the the infinite sum gave rise to the +integral notation looking at this you + + align:start position:0% +integral notation looking at this you + + + align:start position:0% +integral notation looking at this you +see we arrive at the fact that the + + align:start position:0% +see we arrive at the fact that the + + + align:start position:0% +see we arrive at the fact that the +integral from z0 to Z1 along the curve c + + align:start position:0% +integral from z0 to Z1 along the curve c + + + align:start position:0% +integral from z0 to Z1 along the curve c +f of zdz if we want to write that that + + align:start position:0% +f of zdz if we want to write that that + + + align:start position:0% +f of zdz if we want to write that that +in terms of an integral involving a real + + align:start position:0% +in terms of an integral involving a real + + + align:start position:0% +in terms of an integral involving a real +variable T is simply what the integral + + align:start position:0% +variable T is simply what the integral + + + align:start position:0% +variable T is simply what the integral +from t0 to T1 F of Z of T in other words + + align:start position:0% +from t0 to T1 F of Z of T in other words + + + align:start position:0% +from t0 to T1 F of Z of T in other words +we're assuming that Z is a function of T + + align:start position:0% +we're assuming that Z is a function of T + + + align:start position:0% +we're assuming that Z is a function of T +along along the curve C we know what Z + + align:start position:0% +along along the curve C we know what Z + + + align:start position:0% +along along the curve C we know what Z +looks like along the curve C in terms of + + align:start position:0% +looks like along the curve C in terms of + + + align:start position:0% +looks like along the curve C in terms of +T times the derivative of Z with respect + + align:start position:0% +T times the derivative of Z with respect + + + align:start position:0% +T times the derivative of Z with respect +to t z Prime of T time DT and we'll have + + align:start position:0% +to t z Prime of T time DT and we'll have + + + align:start position:0% +to t z Prime of T time DT and we'll have +plenty of exercises including one in + + align:start position:0% +plenty of exercises including one in + + + align:start position:0% +plenty of exercises including one in +this lecture to show you how we use this + + align:start position:0% +this lecture to show you how we use this + + + align:start position:0% +this lecture to show you how we use this +particular result on the other hand keep + + align:start position:0% +particular result on the other hand keep + + + align:start position:0% +particular result on the other hand keep +in mind that this is just what one way + + align:start position:0% +in mind that this is just what one way + + + align:start position:0% +in mind that this is just what one way +of visualizing what the infinite sum is + + align:start position:0% +of visualizing what the infinite sum is + + + align:start position:0% +of visualizing what the infinite sum is +a second way to visualize the same + + align:start position:0% +a second way to visualize the same + + + align:start position:0% +a second way to visualize the same +problem is to recall that we very + + align:start position:0% +problem is to recall that we very + + + align:start position:0% +problem is to recall that we very +frequently like things in terms of u and + + align:start position:0% +frequently like things in terms of u and + + + align:start position:0% +frequently like things in terms of u and +v components coordinates the idea is + + align:start position:0% +v components coordinates the idea is + + + align:start position:0% +v components coordinates the idea is +that if we now want to introduce u and v + + align:start position:0% +that if we now want to introduce u and v + + + align:start position:0% +that if we now want to introduce u and v +in the usual manner F of Z is then U + + align:start position:0% +in the usual manner F of Z is then U + + + align:start position:0% +in the usual manner F of Z is then U +plus IV Delta Z is Delta X plus I Delta + + align:start position:0% +plus IV Delta Z is Delta X plus I Delta + + + align:start position:0% +plus IV Delta Z is Delta X plus I Delta +Y and coming back to our basic + + align:start position:0% +Y and coming back to our basic + + + align:start position:0% +Y and coming back to our basic +definition over here + + align:start position:0% +definition over here + + + align:start position:0% +definition over here +you see what we can now do is rewrite f + + align:start position:0% +you see what we can now do is rewrite f + + + align:start position:0% +you see what we can now do is rewrite f +as u+ I V rewrite Delta Z subk as Delta + + align:start position:0% +as u+ I V rewrite Delta Z subk as Delta + + + align:start position:0% +as u+ I V rewrite Delta Z subk as Delta +X subk plus I Delta y + + align:start position:0% +X subk plus I Delta y + + + align:start position:0% +X subk plus I Delta y +subk multiply this thing out pick off + + align:start position:0% +subk multiply this thing out pick off + + + align:start position:0% +subk multiply this thing out pick off +the real and the imaginary Parts write + + align:start position:0% +the real and the imaginary Parts write + + + align:start position:0% +the real and the imaginary Parts write +this as two separate sums Etc and take + + align:start position:0% +this as two separate sums Etc and take + + + align:start position:0% +this as two separate sums Etc and take +the limit separately what this leads to + + align:start position:0% +the limit separately what this leads to + + + align:start position:0% +the limit separately what this leads to +if you want to go through the whole + + align:start position:0% +if you want to go through the whole + + + align:start position:0% +if you want to go through the whole +rigorous process quickly just coming up + + align:start position:0% +rigorous process quickly just coming up + + + align:start position:0% +rigorous process quickly just coming up +with the right answer is that + + align:start position:0% +with the right answer is that + + + align:start position:0% +with the right answer is that +essentially what we do is given this + + align:start position:0% +essentially what we do is given this + + + align:start position:0% +essentially what we do is given this +this particular integral we write f as + + align:start position:0% +this particular integral we write f as + + + align:start position:0% +this particular integral we write f as +u+ I V we write DZ as DX plus I Dy we + + align:start position:0% +u+ I V we write DZ as DX plus I Dy we + + + align:start position:0% +u+ I V we write DZ as DX plus I Dy we +then multiply the way we ordinarily + + align:start position:0% +then multiply the way we ordinarily + + + align:start position:0% +then multiply the way we ordinarily +would with complex numbers see udx minus + + align:start position:0% +would with complex numbers see udx minus + + + align:start position:0% +would with complex numbers see udx minus +vdy and the imaginary PO is vdx plus udy + + align:start position:0% +vdy and the imaginary PO is vdx plus udy + + + align:start position:0% +vdy and the imaginary PO is vdx plus udy +break this up as two separate integrals + + align:start position:0% +break this up as two separate integrals + + + align:start position:0% +break this up as two separate integrals +and the key point is notice that both of + + align:start position:0% +and the key point is notice that both of + + + align:start position:0% +and the key point is notice that both of +these integrals forgetting about the + + align:start position:0% +these integrals forgetting about the + + + align:start position:0% +these integrals forgetting about the +coefficient of here being I this is the + + align:start position:0% +coefficient of here being I this is the + + + align:start position:0% +coefficient of here being I this is the +only place where I appears is notice + + align:start position:0% +only place where I appears is notice + + + align:start position:0% +only place where I appears is notice +that both integrals are now ordinary + + align:start position:0% +that both integrals are now ordinary + + + align:start position:0% +that both integrals are now ordinary +line integrals you see U is a real + + align:start position:0% +line integrals you see U is a real + + + align:start position:0% +line integrals you see U is a real +valued function of X and Y V is a real + + align:start position:0% +valued function of X and Y V is a real + + + align:start position:0% +valued function of X and Y V is a real +valued function of X and Y along the + + align:start position:0% +valued function of X and Y along the + + + align:start position:0% +valued function of X and Y along the +curve C X and Y are functions of T + + align:start position:0% +curve C X and Y are functions of T + + + align:start position:0% +curve C X and Y are functions of T +remember the equation of the curve C was + + align:start position:0% +remember the equation of the curve C was + + + align:start position:0% +remember the equation of the curve C was +X was some function of t y was some + + align:start position:0% +X was some function of t y was some + + + align:start position:0% +X was some function of t y was some +function of T in other words again this + + align:start position:0% +function of T in other words again this + + + align:start position:0% +function of T in other words again this +is not only a line integral but if you + + align:start position:0% +is not only a line integral but if you + + + align:start position:0% +is not only a line integral but if you +want to use this parametric form both of + + align:start position:0% +want to use this parametric form both of + + + align:start position:0% +want to use this parametric form both of +these integral + + align:start position:0% +these integral + + + align:start position:0% +these integral +involve real integrals of real variables + + align:start position:0% +involve real integrals of real variables + + + align:start position:0% +involve real integrals of real variables +in other words both u v DX and Dy are + + align:start position:0% +in other words both u v DX and Dy are + + + align:start position:0% +in other words both u v DX and Dy are +all expressible in terms of T and DT and + + align:start position:0% +all expressible in terms of T and DT and + + + align:start position:0% +all expressible in terms of T and DT and +we can integrate this expression in the + + align:start position:0% +we can integrate this expression in the + + + align:start position:0% +we can integrate this expression in the +usual way but the reason I like the u + + align:start position:0% +usual way but the reason I like the u + + + align:start position:0% +usual way but the reason I like the u +and v form is that we've stressed what + + align:start position:0% +and v form is that we've stressed what + + + align:start position:0% +and v form is that we've stressed what +it means for a function to be analytic + + align:start position:0% +it means for a function to be analytic + + + align:start position:0% +it means for a function to be analytic +in terms of the real and imaginary Parts + + align:start position:0% +in terms of the real and imaginary Parts + + + align:start position:0% +in terms of the real and imaginary Parts +Etc remember keep an eye on this + + align:start position:0% +Etc remember keep an eye on this + + + align:start position:0% +Etc remember keep an eye on this +remember this particular expression here + + align:start position:0% +remember this particular expression here + + + align:start position:0% +remember this particular expression here +and here's the key point if if it turns + + align:start position:0% +and here's the key point if if it turns + + + align:start position:0% +and here's the key point if if it turns +out that u and v are the real and + + align:start position:0% +out that u and v are the real and + + + align:start position:0% +out that u and v are the real and +imaginary parts of an analytic function + + align:start position:0% +imaginary parts of an analytic function + + + align:start position:0% +imaginary parts of an analytic function +in other words If U plus IV is some + + align:start position:0% +in other words If U plus IV is some + + + align:start position:0% +in other words If U plus IV is some +analytic function f remember that the Ki + + align:start position:0% +analytic function f remember that the Ki + + + align:start position:0% +analytic function f remember that the Ki +reman conditions told us that the + + align:start position:0% +reman conditions told us that the + + + align:start position:0% +reman conditions told us that the +partial of U respect to X is equal to + + align:start position:0% +partial of U respect to X is equal to + + + align:start position:0% +partial of U respect to X is equal to +the partial of V respect to Y the + + align:start position:0% +the partial of V respect to Y the + + + align:start position:0% +the partial of V respect to Y the +partial of U respect to Y is minus the + + align:start position:0% +partial of U respect to Y is minus the + + + align:start position:0% +partial of U respect to Y is minus the +partial of V respect to X and if you + + align:start position:0% +partial of V respect to X and if you + + + align:start position:0% +partial of V respect to X and if you +look at these two conditions coupled + + align:start position:0% +look at these two conditions coupled + + + align:start position:0% +look at these two conditions coupled +with a definition of what it meant for a + + align:start position:0% +with a definition of what it meant for a + + + align:start position:0% +with a definition of what it meant for a +real differential in two variables to be + + align:start position:0% +real differential in two variables to be + + + align:start position:0% +real differential in two variables to be +exact noce + + align:start position:0% +exact noce + + + align:start position:0% +exact noce +that this condition here tells us that + + align:start position:0% +that this condition here tells us that + + + align:start position:0% +that this condition here tells us that +this is exact and this condition here + + align:start position:0% +this is exact and this condition here + + + align:start position:0% +this is exact and this condition here +tells us that this is exact in other + + align:start position:0% +tells us that this is exact in other + + + align:start position:0% +tells us that this is exact in other +words both of these ordinary line + + align:start position:0% +words both of these ordinary line + + + align:start position:0% +words both of these ordinary line +integrals are exact If U plus IV is + + align:start position:0% +integrals are exact If U plus IV is + + + align:start position:0% +integrals are exact If U plus IV is +analytic and again if you want to leave + + align:start position:0% +analytic and again if you want to leave + + + align:start position:0% +analytic and again if you want to leave +the complex number part out of this if + + align:start position:0% +the complex number part out of this if + + + align:start position:0% +the complex number part out of this if +all we know is that the partial of the + + align:start position:0% +all we know is that the partial of the + + + align:start position:0% +all we know is that the partial of the +real function U with respect to x equals + + align:start position:0% +real function U with respect to x equals + + + align:start position:0% +real function U with respect to x equals +the partial of the real valued function + + align:start position:0% +the partial of the real valued function + + + align:start position:0% +the partial of the real valued function +V respect to Y + + align:start position:0% +V respect to Y + + + align:start position:0% +V respect to Y +Etc and in particular then because this + + align:start position:0% +Etc and in particular then because this + + + align:start position:0% +Etc and in particular then because this +is exact what what happened when a + + align:start position:0% +is exact what what happened when a + + + align:start position:0% +is exact what what happened when a +differential was exact remember if the + + align:start position:0% +differential was exact remember if the + + + align:start position:0% +differential was exact remember if the +differential was exact the line + + align:start position:0% +differential was exact the line + + + align:start position:0% +differential was exact the line +integral was what dependent only on the + + align:start position:0% +integral was what dependent only on the + + + align:start position:0% +integral was what dependent only on the +end points but not on the path that + + align:start position:0% +end points but not on the path that + + + align:start position:0% +end points but not on the path that +connected the end points or stated in + + align:start position:0% +connected the end points or stated in + + + align:start position:0% +connected the end points or stated in +still other words if the integrand was + + align:start position:0% +still other words if the integrand was + + + align:start position:0% +still other words if the integrand was +exact the line integral around the + + align:start position:0% +exact the line integral around the + + + align:start position:0% +exact the line integral around the +closed curve was zero so what we're + + align:start position:0% +closed curve was zero so what we're + + + align:start position:0% +closed curve was zero so what we're +saying in summary is that notice that if + + align:start position:0% +saying in summary is that notice that if + + + align:start position:0% +saying in summary is that notice that if +fals U plus IV is analytic then the + + align:start position:0% +fals U plus IV is analytic then the + + + align:start position:0% +fals U plus IV is analytic then the +integral from z0 to Z1 F of zdz is + + align:start position:0% +integral from z0 to Z1 F of zdz is + + + align:start position:0% +integral from z0 to Z1 F of zdz is +independent of C it depends only on z0 + + align:start position:0% +independent of C it depends only on z0 + + + align:start position:0% +independent of C it depends only on z0 +and Z1 and in that case I do not have to + + align:start position:0% +and Z1 and in that case I do not have to + + + align:start position:0% +and Z1 and in that case I do not have to +specify what curve C is joining z0 and + + align:start position:0% +specify what curve C is joining z0 and + + + align:start position:0% +specify what curve C is joining z0 and +Z1 and in particular if F of Z happens + + align:start position:0% +Z1 and in particular if F of Z happens + + + align:start position:0% +Z1 and in particular if F of Z happens +to be exact analytic so that this is + + align:start position:0% +to be exact analytic so that this is + + + align:start position:0% +to be exact analytic so that this is +exact then the integral around a closed + + align:start position:0% +exact then the integral around a closed + + + align:start position:0% +exact then the integral around a closed +curve is zero for all closed curve C and + + align:start position:0% +curve is zero for all closed curve C and + + + align:start position:0% +curve is zero for all closed curve C and +that means again in particular if I know + + align:start position:0% +that means again in particular if I know + + + align:start position:0% +that means again in particular if I know +that F of Z is analytic I do not have to + + align:start position:0% +that F of Z is analytic I do not have to + + + align:start position:0% +that F of Z is analytic I do not have to +indicate the curve that I'm forming the + + align:start position:0% +indicate the curve that I'm forming the + + + align:start position:0% +indicate the curve that I'm forming the +Contour integral around you see but I do + + align:start position:0% +Contour integral around you see but I do + + + align:start position:0% +Contour integral around you see but I do +have to put this in here if the function + + align:start position:0% +have to put this in here if the function + + + align:start position:0% +have to put this in here if the function +is not analytic okay by the way let me + + align:start position:0% +is not analytic okay by the way let me + + + align:start position:0% +is not analytic okay by the way let me +just make one more remark in passing and + + align:start position:0% +just make one more remark in passing and + + + align:start position:0% +just make one more remark in passing and +we'll emphasize this more in the + + align:start position:0% +we'll emphasize this more in the + + + align:start position:0% +we'll emphasize this more in the +learning + + align:start position:0% +learning + + + align:start position:0% +learning +exercises not only is it true that + + align:start position:0% +exercises not only is it true that + + + align:start position:0% +exercises not only is it true that +integral z0 to Z1 F of zdz Depends only + + align:start position:0% +integral z0 to Z1 F of zdz Depends only + + + align:start position:0% +integral z0 to Z1 F of zdz Depends only +on the end points if f is analytical + + align:start position:0% +on the end points if f is analytical + + + align:start position:0% +on the end points if f is analytical +but the parallel structure that is + + align:start position:0% +but the parallel structure that is + + + align:start position:0% +but the parallel structure that is +obeyed in the real case also is true + + align:start position:0% +obeyed in the real case also is true + + + align:start position:0% +obeyed in the real case also is true +here namely if f is analytic not only + + align:start position:0% +here namely if f is analytic not only + + + align:start position:0% +here namely if f is analytic not only +does the integral from z0 to Z1 F of zdz + + align:start position:0% +does the integral from z0 to Z1 F of zdz + + + align:start position:0% +does the integral from z0 to Z1 F of zdz +not depend on the path but it can be + + align:start position:0% +not depend on the path but it can be + + + align:start position:0% +not depend on the path but it can be +evaluated very simply just by Computing + + align:start position:0% +evaluated very simply just by Computing + + + align:start position:0% +evaluated very simply just by Computing +capital F of Z1 minus capital F of z0 + + align:start position:0% +capital F of Z1 minus capital F of z0 + + + align:start position:0% +capital F of Z1 minus capital F of z0 +where capital F is any function whose + + align:start position:0% +where capital F is any function whose + + + align:start position:0% +where capital F is any function whose +derivative is little F the same + + align:start position:0% +derivative is little F the same + + + align:start position:0% +derivative is little F the same +structure as before but and this is + + align:start position:0% +structure as before but and this is + + + align:start position:0% +structure as before but and this is +extremely important to note the integral + + align:start position:0% +extremely important to note the integral + + + align:start position:0% +extremely important to note the integral +around the closed curve c f of + + align:start position:0% +around the closed curve c f of + + + align:start position:0% +around the closed curve c f of +zdz need not be zero if f is not + + align:start position:0% +zdz need not be zero if f is not + + + align:start position:0% +zdz need not be zero if f is not +analytic and I think the best way to + + align:start position:0% +analytic and I think the best way to + + + align:start position:0% +analytic and I think the best way to +show you that is by means of an example + + align:start position:0% +show you that is by means of an example + + + align:start position:0% +show you that is by means of an example +let's compute the integral around the + + align:start position:0% +let's compute the integral around the + + + align:start position:0% +let's compute the integral around the +Clos curve C DZ over Z where C is the + + align:start position:0% +Clos curve C DZ over Z where C is the + + + align:start position:0% +Clos curve C DZ over Z where C is the +circle in the Aon diagram centered at + + align:start position:0% +circle in the Aon diagram centered at + + + align:start position:0% +circle in the Aon diagram centered at +the origin with radius equal to R and + + align:start position:0% +the origin with radius equal to R and + + + align:start position:0% +the origin with radius equal to R and +again to emphasize what I said to you + + align:start position:0% +again to emphasize what I said to you + + + align:start position:0% +again to emphasize what I said to you +earlier in the lesson do not confuse the + + align:start position:0% +earlier in the lesson do not confuse the + + + align:start position:0% +earlier in the lesson do not confuse the +integrand with the path C notice that + + align:start position:0% +integrand with the path C notice that + + + align:start position:0% +integrand with the path C notice that +the integrand here is what what is the + + align:start position:0% +the integrand here is what what is the + + + align:start position:0% +the integrand here is what what is the +integrant it's 1 / Z notice that one/ Z + + align:start position:0% +integrant it's 1 / Z notice that one/ Z + + + align:start position:0% +integrant it's 1 / Z notice that one/ Z +is defined at any point in the Aon plane + + align:start position:0% +is defined at any point in the Aon plane + + + align:start position:0% +is defined at any point in the Aon plane +all right notice also from our previous + + align:start position:0% +all right notice also from our previous + + + align:start position:0% +all right notice also from our previous +lecture on derivatives that 1 / Z is + + align:start position:0% +lecture on derivatives that 1 / Z is + + + align:start position:0% +lecture on derivatives that 1 / Z is +analytic except when Z equals z in which + + align:start position:0% +analytic except when Z equals z in which + + + align:start position:0% +analytic except when Z equals z in which +case one / Z isn't even defined you see + + align:start position:0% +case one / Z isn't even defined you see + + + align:start position:0% +case one / Z isn't even defined you see +what we're saying is notice that on the + + align:start position:0% +what we're saying is notice that on the + + + align:start position:0% +what we're saying is notice that on the +curve C I can talk about F of 1 / Z for + + align:start position:0% +curve C I can talk about F of 1 / Z for + + + align:start position:0% +curve C I can talk about F of 1 / Z for +each point on the curve I can talk about + + align:start position:0% +each point on the curve I can talk about + + + align:start position:0% +each point on the curve I can talk about +1 / Z for every Point inside the curve I + + align:start position:0% +1 / Z for every Point inside the curve I + + + align:start position:0% +1 / Z for every Point inside the curve I +can talk about 1 / Z for every Point + + align:start position:0% +can talk about 1 / Z for every Point + + + align:start position:0% +can talk about 1 / Z for every Point +outside the curve what I want to compute + + align:start position:0% +outside the curve what I want to compute + + + align:start position:0% +outside the curve what I want to compute +here is the integral as I move along + + align:start position:0% +here is the integral as I move along + + + align:start position:0% +here is the integral as I move along +this curve 1 / Z DZ notice by the way + + align:start position:0% +this curve 1 / Z DZ notice by the way + + + align:start position:0% +this curve 1 / Z DZ notice by the way +that inside the interval inside this + + align:start position:0% +that inside the interval inside this + + + align:start position:0% +that inside the interval inside this +circle F of Z is not analytic F of Z has + + align:start position:0% +circle F of Z is not analytic F of Z has + + + align:start position:0% +circle F of Z is not analytic F of Z has +a bad point namely 1 / Z is trouble when + + align:start position:0% +a bad point namely 1 / Z is trouble when + + + align:start position:0% +a bad point namely 1 / Z is trouble when +Z equals zero and notice that Z equals 0 + + align:start position:0% +Z equals zero and notice that Z equals 0 + + + align:start position:0% +Z equals zero and notice that Z equals 0 +is inside my region in other words + + align:start position:0% +is inside my region in other words + + + align:start position:0% +is inside my region in other words +notice that my function f of Z is + + align:start position:0% +notice that my function f of Z is + + + align:start position:0% +notice that my function f of Z is +analytic on the circle but it's not + + align:start position:0% +analytic on the circle but it's not + + + align:start position:0% +analytic on the circle but it's not +analytic every place inside the circle + + align:start position:0% +analytic every place inside the circle + + + align:start position:0% +analytic every place inside the circle +the one bad spot is when Z is zero so I + + align:start position:0% +the one bad spot is when Z is zero so I + + + align:start position:0% +the one bad spot is when Z is zero so I +do have a case where what the integrand + + align:start position:0% +do have a case where what the integrand + + + align:start position:0% +do have a case where what the integrand +which is 1/ z is not analytic in the + + align:start position:0% +which is 1/ z is not analytic in the + + + align:start position:0% +which is 1/ z is not analytic in the +entire region even though it does happen + + align:start position:0% +entire region even though it does happen + + + align:start position:0% +entire region even though it does happen +to be analytic on the boundary you see + + align:start position:0% +to be analytic on the boundary you see + + + align:start position:0% +to be analytic on the boundary you see +the boundary is made up of points none + + align:start position:0% +the boundary is made up of points none + + + align:start position:0% +the boundary is made up of points none +of which is the origin because this is a + + align:start position:0% +of which is the origin because this is a + + + align:start position:0% +of which is the origin because this is a +circle of positive radius R centered at + + align:start position:0% +circle of positive radius R centered at + + + align:start position:0% +circle of positive radius R centered at +the origin and again keep in mind that F + + align:start position:0% +the origin and again keep in mind that F + + + align:start position:0% +the origin and again keep in mind that F +does not appear in this diagram anywhere + + align:start position:0% +does not appear in this diagram anywhere + + + align:start position:0% +does not appear in this diagram anywhere +if I wanted to plot one / Z I have to + + align:start position:0% +if I wanted to plot one / Z I have to + + + align:start position:0% +if I wanted to plot one / Z I have to +use the UV plane if I want to think of + + align:start position:0% +use the UV plane if I want to think of + + + align:start position:0% +use the UV plane if I want to think of +this in terms of a real interpretation + + align:start position:0% +this in terms of a real interpretation + + + align:start position:0% +this in terms of a real interpretation +what I'm saying is visualize a force + + align:start position:0% +what I'm saying is visualize a force + + + align:start position:0% +what I'm saying is visualize a force +which when written in the language of + + align:start position:0% +which when written in the language of + + + align:start position:0% +which when written in the language of +complex variables is 1 / Z we don't have + + align:start position:0% +complex variables is 1 / Z we don't have + + + align:start position:0% +complex variables is 1 / Z we don't have +to worry about what that means it what + + align:start position:0% +to worry about what that means it what + + + align:start position:0% +to worry about what that means it what +it really means is write the real and + + align:start position:0% +it really means is write the real and + + + align:start position:0% +it really means is write the real and +the imaginary parts of this and U is the + + align:start position:0% +the imaginary parts of this and U is the + + + align:start position:0% +the imaginary parts of this and U is the +real part and V is the imaginary part + + align:start position:0% +real part and V is the imaginary part + + + align:start position:0% +real part and V is the imaginary part +it's like Computing the work as you go + + align:start position:0% +it's like Computing the work as you go + + + align:start position:0% +it's like Computing the work as you go +along this circle under the influence of + + align:start position:0% +along this circle under the influence of + + + align:start position:0% +along this circle under the influence of +that particular force and the force has + + align:start position:0% +that particular force and the force has + + + align:start position:0% +that particular force and the force has +two components you see an i and a j + + align:start position:0% +two components you see an i and a j + + + align:start position:0% +two components you see an i and a j +component in terms of the Aon diagram a + + align:start position:0% +component in terms of the Aon diagram a + + + align:start position:0% +component in terms of the Aon diagram a +real and an imaginary component so I + + align:start position:0% +real and an imaginary component so I + + + align:start position:0% +real and an imaginary component so I +can't stress that point too much + + align:start position:0% +can't stress that point too much + + + align:start position:0% +can't stress that point too much +separate the integrand from the path + + align:start position:0% +separate the integrand from the path + + + align:start position:0% +separate the integrand from the path +that you're integrating with respect ECT + + align:start position:0% +that you're integrating with respect ECT + + + align:start position:0% +that you're integrating with respect ECT +to now what I claim is is that if I + + align:start position:0% +to now what I claim is is that if I + + + align:start position:0% +to now what I claim is is that if I +integrate 1 / Z along the curve + + align:start position:0% +integrate 1 / Z along the curve + + + align:start position:0% +integrate 1 / Z along the curve +C from beginning to end let's say for + + align:start position:0% +C from beginning to end let's say for + + + align:start position:0% +C from beginning to end let's say for +the sake of definiteness I start at the + + align:start position:0% +the sake of definiteness I start at the + + + align:start position:0% +the sake of definiteness I start at the +at at the point one over here and go + + align:start position:0% +at at the point one over here and go + + + align:start position:0% +at at the point one over here and go +around this at the point R and go around + + align:start position:0% +around this at the point R and go around + + + align:start position:0% +around this at the point R and go around +like this I claim that this integral + + align:start position:0% +like this I claim that this integral + + + align:start position:0% +like this I claim that this integral +will not be zero and I'm going to do it + + align:start position:0% +will not be zero and I'm going to do it + + + align:start position:0% +will not be zero and I'm going to do it +two ways for you one which emphasizes + + align:start position:0% +two ways for you one which emphasizes + + + align:start position:0% +two ways for you one which emphasizes +the UV definition of derivative of of + + align:start position:0% +the UV definition of derivative of of + + + align:start position:0% +the UV definition of derivative of of +integral and one that emphasizes the F + + align:start position:0% +integral and one that emphasizes the F + + + align:start position:0% +integral and one that emphasizes the F +of z f Prime d t definition method one + + align:start position:0% +of z f Prime d t definition method one + + + align:start position:0% +of z f Prime d t definition method one +is what to compute this particular + + align:start position:0% +is what to compute this particular + + + align:start position:0% +is what to compute this particular +integral you simply write the integrand + + align:start position:0% +integral you simply write the integrand + + + align:start position:0% +integral you simply write the integrand +in terms of its real and imaginary parts + + align:start position:0% +in terms of its real and imaginary parts + + + align:start position:0% +in terms of its real and imaginary parts +and write DZ as DX plus I Dy if I do + + align:start position:0% +and write DZ as DX plus I Dy if I do + + + align:start position:0% +and write DZ as DX plus I Dy if I do +that I mechanically get from here to + + align:start position:0% +that I mechanically get from here to + + + align:start position:0% +that I mechanically get from here to +here remembering that to get into the + + align:start position:0% +here remembering that to get into the + + + align:start position:0% +here remembering that to get into the +standard form of a real plus I * a real + + align:start position:0% +standard form of a real plus I * a real + + + align:start position:0% +standard form of a real plus I * a real +I must multiply the denominator by its + + align:start position:0% +I must multiply the denominator by its + + + align:start position:0% +I must multiply the denominator by its +complex conjugate I multiply numerator + + align:start position:0% +complex conjugate I multiply numerator + + + align:start position:0% +complex conjugate I multiply numerator +denominator here by xus i y + + align:start position:0% +denominator here by xus i y + + + align:start position:0% +denominator here by xus i y +I then get this expression you see x + i + + align:start position:0% +I then get this expression you see x + i + + + align:start position:0% +I then get this expression you see x + i +y * x - i y being x^2 + y^2 I now pick + + align:start position:0% +y * x - i y being x^2 + y^2 I now pick + + + align:start position:0% +y * x - i y being x^2 + y^2 I now pick +off the real and the imaginary Parts the + + align:start position:0% +off the real and the imaginary Parts the + + + align:start position:0% +off the real and the imaginary Parts the +real part here is X DX plus ydy because + + align:start position:0% +real part here is X DX plus ydy because + + + align:start position:0% +real part here is X DX plus ydy because +minus I * I is + 1 the imaginary part is + + align:start position:0% +minus I * I is + 1 the imaginary part is + + + align:start position:0% +minus I * I is + 1 the imaginary part is +going to be minus ydx plus xdy and so in + + align:start position:0% +going to be minus ydx plus xdy and so in + + + align:start position:0% +going to be minus ydx plus xdy and so in +terms of u and v components this is the + + align:start position:0% +terms of u and v components this is the + + + align:start position:0% +terms of u and v components this is the +integral that I'm evaluating and you see + + align:start position:0% +integral that I'm evaluating and you see + + + align:start position:0% +integral that I'm evaluating and you see +notice that both both of the integrand + + align:start position:0% +notice that both both of the integrand + + + align:start position:0% +notice that both both of the integrand +are line integrals real line integrals + + align:start position:0% +are line integrals real line integrals + + + align:start position:0% +are line integrals real line integrals +okay now notice that on C how do I + + align:start position:0% +okay now notice that on C how do I + + + align:start position:0% +okay now notice that on C how do I +describe the curve C remember I'm trying + + align:start position:0% +describe the curve C remember I'm trying + + + align:start position:0% +describe the curve C remember I'm trying +to go so that my area always stays to + + align:start position:0% +to go so that my area always stays to + + + align:start position:0% +to go so that my area always stays to +the left I'm starting at this point so + + align:start position:0% +the left I'm starting at this point so + + + align:start position:0% +the left I'm starting at this point so +why not write this parametrically as xal + + align:start position:0% +why not write this parametrically as xal + + + align:start position:0% +why not write this parametrically as xal +capital r cosine Theta and yal capital r + + align:start position:0% +capital r cosine Theta and yal capital r + + + align:start position:0% +capital r cosine Theta and yal capital r +sin Theta you see that puts me at here + + align:start position:0% +sin Theta you see that puts me at here + + + align:start position:0% +sin Theta you see that puts me at here +when Theta is zero brings me around in + + align:start position:0% +when Theta is zero brings me around in + + + align:start position:0% +when Theta is zero brings me around in +the counterclock wise Direction back to + + align:start position:0% +the counterclock wise Direction back to + + + align:start position:0% +the counterclock wise Direction back to +the same point when Theta is 2 pi in + + align:start position:0% +the same point when Theta is 2 pi in + + + align:start position:0% +the same point when Theta is 2 pi in +other words parametrically the curve C + + align:start position:0% +other words parametrically the curve C + + + align:start position:0% +other words parametrically the curve C +is given how X is our cosine Theta Y is + + align:start position:0% +is given how X is our cosine Theta Y is + + + align:start position:0% +is given how X is our cosine Theta Y is +our sin Theta I could have used T in + + align:start position:0% +our sin Theta I could have used T in + + + align:start position:0% +our sin Theta I could have used T in +here if I wanted to but why bother DX is + + align:start position:0% +here if I wanted to but why bother DX is + + + align:start position:0% +here if I wanted to but why bother DX is +just minus r sin Theta D Theta Dy is R + + align:start position:0% +just minus r sin Theta D Theta Dy is R + + + align:start position:0% +just minus r sin Theta D Theta Dy is R +cosine Theta D Theta x^2 + y^2 on C is + + align:start position:0% +cosine Theta D Theta x^2 + y^2 on C is + + + align:start position:0% +cosine Theta D Theta x^2 + y^2 on C is +just R 2 and Theta goes continuously + + align:start position:0% +just R 2 and Theta goes continuously + + + align:start position:0% +just R 2 and Theta goes continuously +from 0 to 2 pi so you see if I now put + + align:start position:0% +from 0 to 2 pi so you see if I now put + + + align:start position:0% +from 0 to 2 pi so you see if I now put +all of information into here see X DX is + + align:start position:0% +all of information into here see X DX is + + + align:start position:0% +all of information into here see X DX is +what it's - r^ 2 sin Theta cosine Theta + + align:start position:0% +what it's - r^ 2 sin Theta cosine Theta + + + align:start position:0% +what it's - r^ 2 sin Theta cosine Theta +D Theta y Dy is + + align:start position:0% +D Theta y Dy is + + + align:start position:0% +D Theta y Dy is +minus uh yd Y is plus r^ 2 sin Theta + + align:start position:0% +minus uh yd Y is plus r^ 2 sin Theta + + + align:start position:0% +minus uh yd Y is plus r^ 2 sin Theta +cosine Theta D Theta so therefore the + + align:start position:0% +cosine Theta D Theta so therefore the + + + align:start position:0% +cosine Theta D Theta so therefore the +sum is zero so therefore this integral + + align:start position:0% +sum is zero so therefore this integral + + + align:start position:0% +sum is zero so therefore this integral +will be zero because the integrant is + + align:start position:0% +will be zero because the integrant is + + + align:start position:0% +will be zero because the integrant is +zero on the other hand minus y DX is - R + + align:start position:0% +zero on the other hand minus y DX is - R + + + align:start position:0% +zero on the other hand minus y DX is - R +sin thet * - R sin Theta D Theta that's + + align:start position:0% +sin thet * - R sin Theta D Theta that's + + + align:start position:0% +sin thet * - R sin Theta D Theta that's +r^ 2 sin^2 thet D Theta X Dy is r^ 2 + + align:start position:0% +r^ 2 sin^2 thet D Theta X Dy is r^ 2 + + + align:start position:0% +r^ 2 sin^2 thet D Theta X Dy is r^ 2 +cine 2 thet D Theta so I add those + + align:start position:0% +cine 2 thet D Theta so I add those + + + align:start position:0% +cine 2 thet D Theta so I add those +together and then I divide by R 2 and + + align:start position:0% +together and then I divide by R 2 and + + + align:start position:0% +together and then I divide by R 2 and +Theta I've now converted this in terms + + align:start position:0% +Theta I've now converted this in terms + + + align:start position:0% +Theta I've now converted this in terms +of theta so the interal goes from 0 to 2 + + align:start position:0% +of theta so the interal goes from 0 to 2 + + + align:start position:0% +of theta so the interal goes from 0 to 2 +pi the same as we did you see with + + align:start position:0% +pi the same as we did you see with + + + align:start position:0% +pi the same as we did you see with +ordinary line integrals and to summarize + + align:start position:0% +ordinary line integrals and to summarize + + + align:start position:0% +ordinary line integrals and to summarize +this for you because I may have talked + + align:start position:0% +this for you because I may have talked + + + align:start position:0% +this for you because I may have talked +kind of fast all we're saying is that + + align:start position:0% +kind of fast all we're saying is that + + + align:start position:0% +kind of fast all we're saying is that +the integral around the closed curve C + + align:start position:0% +the integral around the closed curve C + + + align:start position:0% +the integral around the closed curve C +DZ over Z is the real part is zero and + + align:start position:0% +DZ over Z is the real part is zero and + + + align:start position:0% +DZ over Z is the real part is zero and +the imaginary part the coefficient of I + + align:start position:0% +the imaginary part the coefficient of I + + + align:start position:0% +the imaginary part the coefficient of I +is integral from 0 to 2 pi r 2 sin 2 + + align:start position:0% +is integral from 0 to 2 pi r 2 sin 2 + + + align:start position:0% +is integral from 0 to 2 pi r 2 sin 2 +thet plus cosine 2 Theta D Theta over R + + align:start position:0% +thet plus cosine 2 Theta D Theta over R + + + align:start position:0% +thet plus cosine 2 Theta D Theta over R +2 notice that R cannot be zero because C + + align:start position:0% +2 notice that R cannot be zero because C + + + align:start position:0% +2 notice that R cannot be zero because C +is the circle of radius R centered at + + align:start position:0% +is the circle of radius R centered at + + + align:start position:0% +is the circle of radius R centered at +the origin on that Circle I mean r is a + + align:start position:0% +the origin on that Circle I mean r is a + + + align:start position:0% +the origin on that Circle I mean r is a +positive number here so it's just not + + align:start position:0% +positive number here so it's just not + + + align:start position:0% +positive number here so it's just not +zero the I can cancel the RS because the + + align:start position:0% +zero the I can cancel the RS because the + + + align:start position:0% +zero the I can cancel the RS because the +radius of a circle can't be zero + + align:start position:0% +radius of a circle can't be zero + + + align:start position:0% +radius of a circle can't be zero +and all I'm left with is sin^2 thet plus + + align:start position:0% +and all I'm left with is sin^2 thet plus + + + align:start position:0% +and all I'm left with is sin^2 thet plus +cosine s thet which is 1 the integral D + + align:start position:0% +cosine s thet which is 1 the integral D + + + align:start position:0% +cosine s thet which is 1 the integral D +Theta from 0 to 2 pi is just 2 pi so + + align:start position:0% +Theta from 0 to 2 pi is just 2 pi so + + + align:start position:0% +Theta from 0 to 2 pi is just 2 pi so +this integral is just 2 pi I all right + + align:start position:0% +this integral is just 2 pi I all right + + + align:start position:0% +this integral is just 2 pi I all right +and the second method is to use the + + align:start position:0% +and the second method is to use the + + + align:start position:0% +and the second method is to use the +formula what F of integral F of Z DZ is + + align:start position:0% +formula what F of integral F of Z DZ is + + + align:start position:0% +formula what F of integral F of Z DZ is +the integral F of Z of theta DZ D Theta + + align:start position:0% +the integral F of Z of theta DZ D Theta + + + align:start position:0% +the integral F of Z of theta DZ D Theta +time D Theta in this case notice that + + align:start position:0% +time D Theta in this case notice that + + + align:start position:0% +time D Theta in this case notice that +the Circle Center at the origin with + + align:start position:0% +the Circle Center at the origin with + + + align:start position:0% +the Circle Center at the origin with +radius r is given in polar complex form + + align:start position:0% +radius r is given in polar complex form + + + align:start position:0% +radius r is given in polar complex form +by zal re e to the I Theta remember in + + align:start position:0% +by zal re e to the I Theta remember in + + + align:start position:0% +by zal re e to the I Theta remember in +polar form R is the magnitude and Theta + + align:start position:0% +polar form R is the magnitude and Theta + + + align:start position:0% +polar form R is the magnitude and Theta +is the angle to say that you're on the + + align:start position:0% +is the angle to say that you're on the + + + align:start position:0% +is the angle to say that you're on the +circle of radius R Center at the origin + + align:start position:0% +circle of radius R Center at the origin + + + align:start position:0% +circle of radius R Center at the origin +simply says that the magnitude of the + + align:start position:0% +simply says that the magnitude of the + + + align:start position:0% +simply says that the magnitude of the +point must be R the radius and the angle + + align:start position:0% +point must be R the radius and the angle + + + align:start position:0% +point must be R the radius and the angle +can be any angle whatsoever between 0 + + align:start position:0% +can be any angle whatsoever between 0 + + + align:start position:0% +can be any angle whatsoever between 0 +and 2 pi if you want to Traverse the + + align:start position:0% +and 2 pi if you want to Traverse the + + + align:start position:0% +and 2 pi if you want to Traverse the +Region C just the curve C just one time + + align:start position:0% +Region C just the curve C just one time + + + align:start position:0% +Region C just the curve C just one time +at any rate from this notice that DZ D + + align:start position:0% +at any rate from this notice that DZ D + + + align:start position:0% +at any rate from this notice that DZ D +Theta is simply what i e to the I Theta + + align:start position:0% +Theta is simply what i e to the I Theta + + + align:start position:0% +Theta is simply what i e to the I Theta +therefore DZ over Z around C is just the + + align:start position:0% +therefore DZ over Z around C is just the + + + align:start position:0% +therefore DZ over Z around C is just the +integral from 0 to 2 pi F of Z of T in + + align:start position:0% +integral from 0 to 2 pi F of Z of T in + + + align:start position:0% +integral from 0 to 2 pi F of Z of T in +this case that's F of Z of theta that's + + align:start position:0% +this case that's F of Z of theta that's + + + align:start position:0% +this case that's F of Z of theta that's +one over Z of theta Z of theta is re to + + align:start position:0% +one over Z of theta Z of theta is re to + + + align:start position:0% +one over Z of theta Z of theta is re to +the I Theta DZ D Theta which is this + + align:start position:0% +the I Theta DZ D Theta which is this + + + align:start position:0% +the I Theta DZ D Theta which is this +times D Theta you see I've now converted + + align:start position:0% +times D Theta you see I've now converted + + + align:start position:0% +times D Theta you see I've now converted +this into a complex valued function of a + + align:start position:0% +this into a complex valued function of a + + + align:start position:0% +this into a complex valued function of a +real variable at any rate making all of + + align:start position:0% +real variable at any rate making all of + + + align:start position:0% +real variable at any rate making all of +these substitutions and simplifying DZ D + + align:start position:0% +these substitutions and simplifying DZ D + + + align:start position:0% +these substitutions and simplifying DZ D +Theta being i e to the I Theta and Z + + align:start position:0% +Theta being i e to the I Theta and Z + + + align:start position:0% +Theta being i e to the I Theta and Z +being r e to the I Theta these cancel + + align:start position:0% +being r e to the I Theta these cancel + + + align:start position:0% +being r e to the I Theta these cancel +leaving only a factor of I the I comes + + align:start position:0% +leaving only a factor of I the I comes + + + align:start position:0% +leaving only a factor of I the I comes +outside I have I integral 0 to 2 pi D + + align:start position:0% +outside I have I integral 0 to 2 pi D + + + align:start position:0% +outside I have I integral 0 to 2 pi D +Theta which is just 2 pi I again notice + + align:start position:0% +Theta which is just 2 pi I again notice + + + align:start position:0% +Theta which is just 2 pi I again notice +the answers are the same because the + + align:start position:0% +the answers are the same because the + + + align:start position:0% +the answers are the same because the +techniques are equivalent which of the + + align:start position:0% +techniques are equivalent which of the + + + align:start position:0% +techniques are equivalent which of the +two ways is better it depends on + + align:start position:0% +two ways is better it depends on + + + align:start position:0% +two ways is better it depends on +yourself as to which way you feel more + + align:start position:0% +yourself as to which way you feel more + + + align:start position:0% +yourself as to which way you feel more +comfortable with it depends on the + + align:start position:0% +comfortable with it depends on the + + + align:start position:0% +comfortable with it depends on the +particular problem that you're dealing + + align:start position:0% +particular problem that you're dealing + + + align:start position:0% +particular problem that you're dealing +with and the like we'll emphasize these + + align:start position:0% +with and the like we'll emphasize these + + + align:start position:0% +with and the like we'll emphasize these +things in the exercises but for the time + + align:start position:0% +things in the exercises but for the time + + + align:start position:0% +things in the exercises but for the time +being I just hope that you have a + + align:start position:0% +being I just hope that you have a + + + align:start position:0% +being I just hope that you have a +feeling as to what we mean by + + align:start position:0% +feeling as to what we mean by + + + align:start position:0% +feeling as to what we mean by +integrating a complex valued function + + align:start position:0% +integrating a complex valued function + + + align:start position:0% +integrating a complex valued function +around a particular Contra and by the + + align:start position:0% +around a particular Contra and by the + + + align:start position:0% +around a particular Contra and by the +way the subject called topology finds a + + align:start position:0% +way the subject called topology finds a + + + align:start position:0% +way the subject called topology finds a +natural inroad to the study of complex + + align:start position:0% +natural inroad to the study of complex + + + align:start position:0% +natural inroad to the study of complex +variables from this point of view namely + + align:start position:0% +variables from this point of view namely + + + align:start position:0% +variables from this point of view namely +I call this rubber sheet geometry simply + + align:start position:0% +I call this rubber sheet geometry simply + + + align:start position:0% +I call this rubber sheet geometry simply +because of a property that I'll mention + + align:start position:0% +because of a property that I'll mention + + + align:start position:0% +because of a property that I'll mention +for you in a few moments but the idea is + + align:start position:0% +for you in a few moments but the idea is + + + align:start position:0% +for you in a few moments but the idea is +this one of the very interesting factors + + align:start position:0% +this one of the very interesting factors + + + align:start position:0% +this one of the very interesting factors +about what we've just done one of the + + align:start position:0% +about what we've just done one of the + + + align:start position:0% +about what we've just done one of the +interesting byproducts is this let's + + align:start position:0% +interesting byproducts is this let's + + + align:start position:0% +interesting byproducts is this let's +suppose I'm integrating F of zdz along a + + align:start position:0% +suppose I'm integrating F of zdz along a + + + align:start position:0% +suppose I'm integrating F of zdz along a +simple curve C1 and let's suppose that + + align:start position:0% +simple curve C1 and let's suppose that + + + align:start position:0% +simple curve C1 and let's suppose that +C2 is another curve that encloses C1 and + + align:start position:0% +C2 is another curve that encloses C1 and + + + align:start position:0% +C2 is another curve that encloses C1 and +let's suppose that f is analytic on the + + align:start position:0% +let's suppose that f is analytic on the + + + align:start position:0% +let's suppose that f is analytic on the +boundaries C1 and C2 and also in the + + align:start position:0% +boundaries C1 and C2 and also in the + + + align:start position:0% +boundaries C1 and C2 and also in the +region between them okay in other words + + align:start position:0% +region between them okay in other words + + + align:start position:0% +region between them okay in other words +I'm Computing I want to compute F of zdz + + align:start position:0% +I'm Computing I want to compute F of zdz + + + align:start position:0% +I'm Computing I want to compute F of zdz +along C1 I want to compute F of zdz + + align:start position:0% +along C1 I want to compute F of zdz + + + align:start position:0% +along C1 I want to compute F of zdz +along C2 and all I know is is that F of + + align:start position:0% +along C2 and all I know is is that F of + + + align:start position:0% +along C2 and all I know is is that F of +Z is analytic on and between C1 and C2 + + align:start position:0% +Z is analytic on and between C1 and C2 + + + align:start position:0% +Z is analytic on and between C1 and C2 +then the amazing result is that the + + align:start position:0% +then the amazing result is that the + + + align:start position:0% +then the amazing result is that the +integral around C1 F of + + align:start position:0% +integral around C1 F of + + + align:start position:0% +integral around C1 F of +zdz is equal to the integral around C2 F + + align:start position:0% +zdz is equal to the integral around C2 F + + + align:start position:0% +zdz is equal to the integral around C2 F +of zdz that's where the word rubber + + align:start position:0% +of zdz that's where the word rubber + + + align:start position:0% +of zdz that's where the word rubber +sheet geometry comes in which is saying + + align:start position:0% +sheet geometry comes in which is saying + + + align:start position:0% +sheet geometry comes in which is saying +is that if there are no bad spots + + align:start position:0% +is that if there are no bad spots + + + align:start position:0% +is that if there are no bad spots +between the two curves if I were to + + align:start position:0% +between the two curves if I were to + + + align:start position:0% +between the two curves if I were to +visualize this curve as being a rubber + + align:start position:0% +visualize this curve as being a rubber + + + align:start position:0% +visualize this curve as being a rubber +band by stretching that rubber band I + + align:start position:0% +band by stretching that rubber band I + + + align:start position:0% +band by stretching that rubber band I +could make it take the form of the curve + + align:start position:0% +could make it take the form of the curve + + + align:start position:0% +could make it take the form of the curve +C2 and what you're saying is given any + + align:start position:0% +C2 and what you're saying is given any + + + align:start position:0% +C2 and what you're saying is given any +curve that you're integrating around if + + align:start position:0% +curve that you're integrating around if + + + align:start position:0% +curve that you're integrating around if +I can stretch that curve out into any + + align:start position:0% +I can stretch that curve out into any + + + align:start position:0% +I can stretch that curve out into any +position I want without breaking it I + + align:start position:0% +position I want without breaking it I + + + align:start position:0% +position I want without breaking it I +stretch that curve out in such a way + + align:start position:0% +stretch that curve out in such a way + + + align:start position:0% +stretch that curve out in such a way +that as that curve is being stretched it + + align:start position:0% +that as that curve is being stretched it + + + align:start position:0% +that as that curve is being stretched it +never goes through any points at which F + + align:start position:0% +never goes through any points at which F + + + align:start position:0% +never goes through any points at which F +of Z fails to be anal + + align:start position:0% +of Z fails to be anal + + + align:start position:0% +of Z fails to be anal +then it turns out that the integral + + align:start position:0% +then it turns out that the integral + + + align:start position:0% +then it turns out that the integral +around the new curve is the same as the + + align:start position:0% +around the new curve is the same as the + + + align:start position:0% +around the new curve is the same as the +integral around the old curve and the + + align:start position:0% +integral around the old curve and the + + + align:start position:0% +integral around the old curve and the +easiest way to prove this is by the + + align:start position:0% +easiest way to prove this is by the + + + align:start position:0% +easiest way to prove this is by the +method of making Cuts here remember we + + align:start position:0% +method of making Cuts here remember we + + + align:start position:0% +method of making Cuts here remember we +showed in our lecture on greens theorem + + align:start position:0% +showed in our lecture on greens theorem + + + align:start position:0% +showed in our lecture on greens theorem +that I could make a cut actually in the + + align:start position:0% +that I could make a cut actually in the + + + align:start position:0% +that I could make a cut actually in the +lecture on greens theorem I made two + + align:start position:0% +lecture on greens theorem I made two + + + align:start position:0% +lecture on greens theorem I made two +cuts so that I could vividly show you + + align:start position:0% +cuts so that I could vividly show you + + + align:start position:0% +cuts so that I could vividly show you +the two separate pieces all you need is + + align:start position:0% +the two separate pieces all you need is + + + align:start position:0% +the two separate pieces all you need is +one cut see let me cut the region this + + align:start position:0% +one cut see let me cut the region this + + + align:start position:0% +one cut see let me cut the region this +way and to emphasize what I've done here + + align:start position:0% +way and to emphasize what I've done here + + + align:start position:0% +way and to emphasize what I've done here +I'll pull this apart just so that we can + + align:start position:0% +I'll pull this apart just so that we can + + + align:start position:0% +I'll pull this apart just so that we can +see what's happening here you see I've + + align:start position:0% +see what's happening here you see I've + + + align:start position:0% +see what's happening here you see I've +made the cut and now here's what I'm + + align:start position:0% +made the cut and now here's what I'm + + + align:start position:0% +made the cut and now here's what I'm +saying this SNF stands for start and + + align:start position:0% +saying this SNF stands for start and + + + align:start position:0% +saying this SNF stands for start and +finish you see I'm going to start at + + align:start position:0% +finish you see I'm going to start at + + + align:start position:0% +finish you see I'm going to start at +this point here I am going to go along + + align:start position:0% +this point here I am going to go along + + + align:start position:0% +this point here I am going to go along +I'm going to go along the connected the + + align:start position:0% +I'm going to go along the connected the + + + align:start position:0% +I'm going to go along the connected the +Simply Connected + + align:start position:0% +Simply Connected + + + align:start position:0% +Simply Connected +region that I have here so this is a + + align:start position:0% +region that I have here so this is a + + + align:start position:0% +region that I have here so this is a +simply once I make the cut this is a + + align:start position:0% +simply once I make the cut this is a + + + align:start position:0% +simply once I make the cut this is a +Simply Connected region notice that if I + + align:start position:0% +Simply Connected region notice that if I + + + align:start position:0% +Simply Connected region notice that if I +go along here I am doing what I am + + align:start position:0% +go along here I am doing what I am + + + align:start position:0% +go along here I am doing what I am +integrating a complex valued function + + align:start position:0% +integrating a complex valued function + + + align:start position:0% +integrating a complex valued function +over a Simply Connected region where the + + align:start position:0% +over a Simply Connected region where the + + + align:start position:0% +over a Simply Connected region where the +function is analytic consequently + + align:start position:0% +function is analytic consequently + + + align:start position:0% +function is analytic consequently +whatever this integral turns out to be + + align:start position:0% +whatever this integral turns out to be + + + align:start position:0% +whatever this integral turns out to be +in other words the integral F of zdz + + align:start position:0% +in other words the integral F of zdz + + + align:start position:0% +in other words the integral F of zdz +along this particular Contour must be + + align:start position:0% +along this particular Contour must be + + + align:start position:0% +along this particular Contour must be +Zero by our previous result that if a + + align:start position:0% +Zero by our previous result that if a + + + align:start position:0% +Zero by our previous result that if a +function is analytic the integral around + + align:start position:0% +function is analytic the integral around + + + align:start position:0% +function is analytic the integral around +the closed curve is zero now here's the + + align:start position:0% +the closed curve is zero now here's the + + + align:start position:0% +the closed curve is zero now here's the +point notice that with this cut in here + + align:start position:0% +point notice that with this cut in here + + + align:start position:0% +point notice that with this cut in here +when I look at the line integral I + + align:start position:0% +when I look at the line integral I + + + align:start position:0% +when I look at the line integral I +Traverse the cut twice once in one Sense + + align:start position:0% +Traverse the cut twice once in one Sense + + + align:start position:0% +Traverse the cut twice once in one Sense +Once in the opposite sense so that + + align:start position:0% +Once in the opposite sense so that + + + align:start position:0% +Once in the opposite sense so that +cancels see that that part cancels out + + align:start position:0% +cancels see that that part cancels out + + + align:start position:0% +cancels see that that part cancels out +no notice that this + + align:start position:0% +no notice that this + + + align:start position:0% +no notice that this +integral around here this part is just + + align:start position:0% +integral around here this part is just + + + align:start position:0% +integral around here this part is just +the integral around the closed curve of + + align:start position:0% +the integral around the closed curve of + + + align:start position:0% +the integral around the closed curve of +C2 F of zdz because after all we're + + align:start position:0% +C2 F of zdz because after all we're + + + align:start position:0% +C2 F of zdz because after all we're +assuming that this is together I've just + + align:start position:0% +assuming that this is together I've just + + + align:start position:0% +assuming that this is together I've just +separated it here so that we can see + + align:start position:0% +separated it here so that we can see + + + align:start position:0% +separated it here so that we can see +what's happening notice that the inner + + align:start position:0% +what's happening notice that the inner + + + align:start position:0% +what's happening notice that the inner +curve is C1 but in the opposite + + align:start position:0% +curve is C1 but in the opposite + + + align:start position:0% +curve is C1 but in the opposite +orientation you see C1 is traversed in + + align:start position:0% +orientation you see C1 is traversed in + + + align:start position:0% +orientation you see C1 is traversed in +this sense but the inner curve here is + + align:start position:0% +this sense but the inner curve here is + + + align:start position:0% +this sense but the inner curve here is +traversed in the opposite sense so this + + align:start position:0% +traversed in the opposite sense so this + + + align:start position:0% +traversed in the opposite sense so this +integrand is just minus the integral C1 + + align:start position:0% +integrand is just minus the integral C1 + + + align:start position:0% +integrand is just minus the integral C1 +F of Z DZ so if we put this whole thing + + align:start position:0% +F of Z DZ so if we put this whole thing + + + align:start position:0% +F of Z DZ so if we put this whole thing +together what we have is that this + + align:start position:0% +together what we have is that this + + + align:start position:0% +together what we have is that this +integral with the cut along c is on the + + align:start position:0% +integral with the cut along c is on the + + + align:start position:0% +integral with the cut along c is on the +one hand zero on the other hand it's the + + align:start position:0% +one hand zero on the other hand it's the + + + align:start position:0% +one hand zero on the other hand it's the +integral around C2 F of zdz minus the + + align:start position:0% +integral around C2 F of zdz minus the + + + align:start position:0% +integral around C2 F of zdz minus the +integral around C1 F of zdz because this + + align:start position:0% +integral around C1 F of zdz because this + + + align:start position:0% +integral around C1 F of zdz because this +expression is zero it means that this + + align:start position:0% +expression is zero it means that this + + + align:start position:0% +expression is zero it means that this +equals this and that proves the result + + align:start position:0% +equals this and that proves the result + + + align:start position:0% +equals this and that proves the result +that we wanted in other words this must + + align:start position:0% +that we wanted in other words this must + + + align:start position:0% +that we wanted in other words this must +equal this because the difference is + + align:start position:0% +equal this because the difference is + + + align:start position:0% +equal this because the difference is +zero how is this useful in the theory of + + align:start position:0% +zero how is this useful in the theory of + + + align:start position:0% +zero how is this useful in the theory of +complex integration well let me give you + + align:start position:0% +complex integration well let me give you + + + align:start position:0% +complex integration well let me give you +an example let's go back to our old + + align:start position:0% +an example let's go back to our old + + + align:start position:0% +an example let's go back to our old +friend integrating DZ over Z along the + + align:start position:0% +friend integrating DZ over Z along the + + + align:start position:0% +friend integrating DZ over Z along the +Clos curve C but now the Clos curve C is + + align:start position:0% +Clos curve C but now the Clos curve C is + + + align:start position:0% +Clos curve C but now the Clos curve C is +going to be much messier than before + + align:start position:0% +going to be much messier than before + + + align:start position:0% +going to be much messier than before +it's not going to be a nice Circle the + + align:start position:0% +it's not going to be a nice Circle the + + + align:start position:0% +it's not going to be a nice Circle the +close curve C is going to be something + + align:start position:0% +close curve C is going to be something + + + align:start position:0% +close curve C is going to be something +like this and what I'd like to do is to + + align:start position:0% +like this and what I'd like to do is to + + + align:start position:0% +like this and what I'd like to do is to +find the value of this integral along + + align:start position:0% +find the value of this integral along + + + align:start position:0% +find the value of this integral along +the curve + + align:start position:0% +the curve + + + align:start position:0% +the curve +C now the point is I could get into a + + align:start position:0% +C now the point is I could get into a + + + align:start position:0% +C now the point is I could get into a +mess trying to expl exess C + + align:start position:0% +mess trying to expl exess C + + + align:start position:0% +mess trying to expl exess C +parametrically but the beauty is what + + align:start position:0% +parametrically but the beauty is what + + + align:start position:0% +parametrically but the beauty is what +first of all notice that if C doesn't + + align:start position:0% +first of all notice that if C doesn't + + + align:start position:0% +first of all notice that if C doesn't +enclose the origin the integral is just + + align:start position:0% +enclose the origin the integral is just + + + align:start position:0% +enclose the origin the integral is just +zero because the only place that the + + align:start position:0% +zero because the only place that the + + + align:start position:0% +zero because the only place that the +integrant 1 / Z fails to be analytic is + + align:start position:0% +integrant 1 / Z fails to be analytic is + + + align:start position:0% +integrant 1 / Z fails to be analytic is +when Z is zero consequently if I were to + + align:start position:0% +when Z is zero consequently if I were to + + + align:start position:0% +when Z is zero consequently if I were to +take a region like this see call this my + + align:start position:0% +take a region like this see call this my + + + align:start position:0% +take a region like this see call this my +C if I take a region like this notice + + align:start position:0% +C if I take a region like this notice + + + align:start position:0% +C if I take a region like this notice +that the integral around here would just + + align:start position:0% +that the integral around here would just + + + align:start position:0% +that the integral around here would just +be zero because in and on this region + + align:start position:0% +be zero because in and on this region + + + align:start position:0% +be zero because in and on this region +the function 1 / Z is analytic at any + + align:start position:0% +the function 1 / Z is analytic at any + + + align:start position:0% +the function 1 / Z is analytic at any +rate I know that I'm I'm in a bad + + align:start position:0% +rate I know that I'm I'm in a bad + + + align:start position:0% +rate I know that I'm I'm in a bad +situation here because my function fails + + align:start position:0% +situation here because my function fails + + + align:start position:0% +situation here because my function fails +to be analytic over here the integral + + align:start position:0% +to be analytic over here the integral + + + align:start position:0% +to be analytic over here the integral +around the closed curve doesn't have to + + align:start position:0% +around the closed curve doesn't have to + + + align:start position:0% +around the closed curve doesn't have to +be zero however what I do know is how to + + align:start position:0% +be zero however what I do know is how to + + + align:start position:0% +be zero however what I do know is how to +find the integral around this very nice + + align:start position:0% +find the integral around this very nice + + + align:start position:0% +find the integral around this very nice +curve C1 where C1 happens to be a circle + + align:start position:0% +curve C1 where C1 happens to be a circle + + + align:start position:0% +curve C1 where C1 happens to be a circle +centered at the origin you see the + + align:start position:0% +centered at the origin you see the + + + align:start position:0% +centered at the origin you see the +integral around C1 was just 2 pi I we + + align:start position:0% +integral around C1 was just 2 pi I we + + + align:start position:0% +integral around C1 was just 2 pi I we +did that in our earlier example the + + align:start position:0% +did that in our earlier example the + + + align:start position:0% +did that in our earlier example the +important point is to observe that + + align:start position:0% +important point is to observe that + + + align:start position:0% +important point is to observe that +between the circle C1 and the given + + align:start position:0% +between the circle C1 and the given + + + align:start position:0% +between the circle C1 and the given +curve C in that particular region + + align:start position:0% +curve C in that particular region + + + align:start position:0% +curve C in that particular region +including the two curves C and C1 the + + align:start position:0% +including the two curves C and C1 the + + + align:start position:0% +including the two curves C and C1 the +function 1 / Z is analytic consequently + + align:start position:0% +function 1 / Z is analytic consequently + + + align:start position:0% +function 1 / Z is analytic consequently +the integral DZ over Z along the curve C + + align:start position:0% +the integral DZ over Z along the curve C + + + align:start position:0% +the integral DZ over Z along the curve C +is the same as the integral DZ over Z + + align:start position:0% +is the same as the integral DZ over Z + + + align:start position:0% +is the same as the integral DZ over Z +along the curve C1 and therefore its + + align:start position:0% +along the curve C1 and therefore its + + + align:start position:0% +along the curve C1 and therefore its +value will also be 2 pi I now at any + + align:start position:0% +value will also be 2 pi I now at any + + + align:start position:0% +value will also be 2 pi I now at any +rate all I've tried to show you in this + + align:start position:0% +rate all I've tried to show you in this + + + align:start position:0% +rate all I've tried to show you in this +particular + + align:start position:0% +particular + + + align:start position:0% +particular +lecture and I hope this part has come + + align:start position:0% +lecture and I hope this part has come + + + align:start position:0% +lecture and I hope this part has come +through fairly clearly is the fact that + + align:start position:0% +through fairly clearly is the fact that + + + align:start position:0% +through fairly clearly is the fact that +we can handle complex valued functions + + align:start position:0% +we can handle complex valued functions + + + align:start position:0% +we can handle complex valued functions +in terms of integration and it this + + align:start position:0% +in terms of integration and it this + + + align:start position:0% +in terms of integration and it this +leads to a treatment of line integrals + + align:start position:0% +leads to a treatment of line integrals + + + align:start position:0% +leads to a treatment of line integrals +it leads to uh examining certain types + + align:start position:0% +it leads to uh examining certain types + + + align:start position:0% +it leads to uh examining certain types +of line integrals along certain regions + + align:start position:0% +of line integrals along certain regions + + + align:start position:0% +of line integrals along certain regions +in the XY plane which we can call the + + align:start position:0% +in the XY plane which we can call the + + + align:start position:0% +in the XY plane which we can call the +Aon diagram we will save applications + + align:start position:0% +Aon diagram we will save applications + + + align:start position:0% +Aon diagram we will save applications +our identifications with the real world + + align:start position:0% +our identifications with the real world + + + align:start position:0% +our identifications with the real world +for the exercises but all I hope by now + + align:start position:0% +for the exercises but all I hope by now + + + align:start position:0% +for the exercises but all I hope by now +is that we have had a little bit of + + align:start position:0% +is that we have had a little bit of + + + align:start position:0% +is that we have had a little bit of +insight to the various aspects of + + align:start position:0% +insight to the various aspects of + + + align:start position:0% +insight to the various aspects of +mathematical analysis as it applies to + + align:start position:0% +mathematical analysis as it applies to + + + align:start position:0% +mathematical analysis as it applies to +complex variables this winds up our + + align:start position:0% +complex variables this winds up our + + + align:start position:0% +complex variables this winds up our +treatment of complex variables as far as + + align:start position:0% +treatment of complex variables as far as + + + align:start position:0% +treatment of complex variables as far as +this course is concerned and next time + + align:start position:0% +this course is concerned and next time + + + align:start position:0% +this course is concerned and next time +we will begin a new block of material + + align:start position:0% +we will begin a new block of material + + + align:start position:0% +we will begin a new block of material +and begin again a survey type + + align:start position:0% +and begin again a survey type + + + align:start position:0% +and begin again a survey type +investigation of the subject known as + + align:start position:0% +investigation of the subject known as + + + align:start position:0% +investigation of the subject known as +ordinary differential equations at any + + align:start position:0% +ordinary differential equations at any + + + align:start position:0% +ordinary differential equations at any +rate then until next time goodbye + + align:start position:0% + + + + align:start position:0% + +funding for the publication of this + + align:start position:0% +funding for the publication of this + + + align:start position:0% +funding for the publication of this +video was provided by the Gabriella and + + align:start position:0% +video was provided by the Gabriella and + + + align:start position:0% +video was provided by the Gabriella and +Paul rosenbom + + align:start position:0% +Paul rosenbom + + + align:start position:0% +Paul rosenbom +foundation help ocw continue to provide + + align:start position:0% +foundation help ocw continue to provide + + + align:start position:0% +foundation help ocw continue to provide +free and open access to MIT courses by + + align:start position:0% +free and open access to MIT courses by + + + align:start position:0% +free and open access to MIT courses by +making a donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/hl4c1P9D8IY.txt b/hl4c1P9D8IY.txt new file mode 100644 index 0000000000000000000000000000000000000000..5dc91e6ca1b93a59e10d7d46fc3e4270f226fe30 --- /dev/null +++ b/hl4c1P9D8IY.txt @@ -0,0 +1,3199 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high-quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Begin +with a new topic, + +which is breakdown of classical +statistical mechanics. + +So we developed a formalism +to probabilistically describe + +collections of large particles. + +And once we have that, from that +formalism calculate properties + +of matter that have to do +with heat, temperature, + +et cetera, and things +coming to equilibrium. + +So question is, is this +formalism always successful? + +And by the time you come to +the end of the 19th Century, + +there were several things +that were hanging around that + +had to do with thermal +properties of the matter + +where this formalism +was having difficulties. + +And the difficulties +ultimately pointed out + +to emergence of +quantum mechanics. + +So essentially, understanding +the relationship + +between thermodynamics, +statistical mechanics, + +and properties of matter was +very important to development + +of quantum mechanics. + +And in particular, I will +mention three difficulties. + +The most important one +that really originally set + +the first stone for +quantum mechanics + +is the spectrum of +black body radiation. + +And it's basically +the observation + +that you heat something. + +And when it becomes hot, +it starts to radiate. + +And typically, the color of +the radiation that you get + +is a function of +temperature, but does not + +depend on the properties of the +material that you are heating. + +So that has to do with heat. + +And you should be +able to explain + +that using +statistical mechanics. + +Another thing that we +have already mentioned + +has to do with the third +law of thermodynamics. + +And let's say the heat capacity +of materials such as solids. + +We mentioned this +Nernst theorem that + +was the third law +of thermodynamics + +based on observation. + +Consequence of it was that +heat capacity of most things + +that you can measure go to 0 +as you go to 0 temperature. + +We should be able to +explain that again, + +based on the phenomena of +statistical-- the phenomenology + +of thermodynamics and the +rules of statistical mechanics. + +Now, a third thing that +is less often mentioned + +but is also important has +to do with heat capacity + +of the atomic gases such as +the air in this room, which + +is composed of, say, +oxygen and nitrogen that + +are diatomic gases. + +So probably, historically they +were answered and discussed + +and resolving the order +that I have drawn for you. + +But I will go backwards. + +so we will first +talk about this one, + +then about number two-- +heat capacity of solids-- + +and number three about +black body radiation. + +OK. + +Part of the reason is that +throughout the course, + +we have been using our +understanding of the gas + +as the sort of measure +of how well we understand + +thermal properties +of the matter. + +And so let's stick with +the gas and ask, what do I + +know about the heat capacity +of the gas in this room? + +So let's think +about heat capacity + +of dilute diatomic gas. + +It is a gas that is sufficiently +dilute that it is practically + +having ideal gas law. + +So PV is roughly +proportional to temperature. + +But rather than thinking +about its pressure, + +I want to make sure I +understand something + +about the heat capacity, another +quantity that I can measure. + +So what's going on here? + +I have, let's say, a box. + +And within this box, +we have a whole bunch + +of these diatomic molecules. + +Let's stick to the +canonical ensemble. + +So I tell you the volume +of this gas, the number + +of diatomic molecules, +and the temperature. + +And in this formalism, I +would calculate the partition + +function. + +Out of that, I should +be able to calculate + +the energy, heat +capacity, et cetera. + +So what do I have to do? + +I have to integrate over all +possible coordinates that + +occur in this system. + +To all intents and purposes, +the different molecules + +are identical. + +So I divide by the +phase space that + +is assigned to each one of them. + +And I said it is dilute +enough that for all intents + +and purposes, the pressure is +proportional to temperature. + +And that occur, I +know, when I can + +ignore the interactions +between particles. + +So if I can ignore the +interactions between particles, + +then the partition function +for the entire system + +would be the product of +the partition functions + +that I would write for +the individual molecules, + +or one of them raised +to the N power. + +So what's the Z1 that +I have to calculate? + +Z1 is obtained by +integrating over + +the coordinates and momenta +of a single diatomic particle. + +So I have a factor of d cubed p. + +I have a factor of d cubed q. + +But I have two particles, so +I have d cubed p1, d cubed q1, + +d cubed p2, d cubed +q 2, and I have + +six pairs of coordinate momenta. + +So I divide it by h cubed. + +I have e to the minus beta +times the energy of this system, + +which is p1 squared over +2m p2 squared over 2m. + +And some potential +of interaction + +that is responsible for bringing +and binding these things + +together. + +So there is some V that +is function of q1 and q2 + +that binds the two particles +together and does not + +allow them to become separate. + +All right, so what +do we do here? + +We realize that immediately for +one of these particle,s there + +is a center of mass that +can go all over the place. + +So we change +coordinates to, let's + +say, Q, which is +q1 plus q2 over 2. + +And corresponding to the +center of mass position, + +there is also a center +of mass momentum, P, + +which is related to p1 minus p2. + +But when I make the change +of variables from these + +coordinates to these +coordinates, what I will get + +is that I will have +a simple integral + +over the relative coordinates. + +So I have d cubed Q d +cubed big P h cubed. + +And the only thing that +I have over there is + +e to the minus beta p squared +divided by 2 big M. Big M + +being the sum total +of the two masses. + +If the two masses are +identical, it would be 2M. + +Otherwise, it would +be M1 plus M2. + +And then I have an integration +over the relative coordinate. + +Let's call that q +relative momentum p + +h cubed e to the minus +beta p squared over 2 times + +the reduced mass here. + +And then, the +potential which only + +is a function of the +relative coordinate. + +Point is that what I have done +is I have separated out this 6 + +degrees of freedom that +make up-- or actually, + +the 3 degrees of freedom and +their conjugate momenta that + +make up a single molecule into +some degrees of freedom that + +correspond to the center of +mass and some degrees of freedom + +that correspond to +the relative motion. + +Furthermore, for +the relative motion + +I expect that the +form of this potential + +as a function of the separation +has a form that is a minimum. + +Basically, the particles +at 0 temperature + +would be sitting +where this minimum is. + +So essentially, the shape +of this diatomic molecule + +would be something like this +if I find its minimum energy + +configuration. + +But then, I can allow +it to move with respect + +to, say, the minimum energy. + +Let's say it occurs +at some distance d. + +It can oscillate around +this minimum value. + +If it oscillates around +this minimum value, + +it basically will explore +the bottom of this potential. + +So I can basically think of +this center of mass contribution + +to the partition function. + +And this contribution +has a part that + +comes from these oscillations +around the center of mass. + +Let's call that u. + +Then, there is the +corresponding momentum. + +I don't know, let's call it pi. + +I divide by h and I +have e to the minus beta + +pi squared over 2 mu. + +And then I have minus beta. + +Well, to the lowest +order, I have + +v of d, which is a constant. + +And then I have some +frequency, some curvature + +at the bottom of +this potential that I + +choose to write as +mu omega squared + +over 2 multiplying by u squared. + +Essentially, what +I want to do is + +to say that really, there is a +vibrational degree of freedom + +and there is a harmonic +oscillator that describes that. + +The frequency of that is +related to the curvature + +that I have at the +bottom of this potential. + +So this degree of freedom +corresponds to vibrations. + +But that's not the end of this +story because here I had three + +q's. + +One of them became the +amplitude of this oscillation. + +So basically, the relative +coordinate is a vector. + +One degree of freedom +corresponds to stretching, + +but there are two +other components of it. + +those two other +components correspond + +to essentially keeping +the length of this fixed + +but moving in the +other directions. + +What do they correspond to? + +They correspond to rotations. + +So then there is essentially +another partition function + +that I want right here. + +That corresponds to the +rotational degrees of freedom. + +Now, the rotational +degrees of freedom + +have a momentum contribution +because this p is also + +three components. + +One component went +in to the vibrations. + +There are two more +components that + +really combine to tell +you about the angular + +momentum and the energy that +is proportional to the square + +of the angular momentum. + +But there is no +restoring force for them. + +There is no corresponding +term that is like this. + +So maybe I will just write +that as an integral over angles + +that I can rotate this thing. + +An integral over +the two components + +of the angular momentum +divided by h squared. + +There's actually two angles. + +And the contribution is e +to the minus beta angular + +momentum squared over 2I. + +So I wrote the entire thing. + +So essentially, +all I have done is + +I have taken the +Hamiltonian that + +corresponds to +two particles that + +are bound together and +broken it into three pieces + +corresponding to the center +of mass, to the vibrations, + +and to the rotations. + +Now, the thing is +that if I now ask, + +what is the energy that I would +get for this one particle-- + +I guess I'll call this Z1-- what +is the contribution of the one + +particular to the energy +of the entire system? + +I have minus the log Z1 +with respect to beta. + +That's the usual formula +to calculate energies. + +So I go and look at +this entire thing. + +And where do the beta +dependencies come from? + +Well, let's see. + +So my Z1 has a part that comes +from this center of mass. + +It gives me a V. We expect that. + +And then from the +integration over the momenta, + +I will get something like 2 pi +m over beta h squared to the 3/2 + +power. + +From the vibrations-- +OK, what do I have? + +I have e to the minus beta V +of d, which is the constant. + +We really don't care. + +But there are these +two components + +that give me root 2 +pi mu divided by beta. + +There is a +corresponding thing that + +comes from the variance that +goes with this object, which + +is square root of 2 pi divided +by beta mu omega squared. + +The entire thing +has a factor of 1/h. + +So this is the vibrations. + +And for the rotations, +what do I get? + +I will get a 4 pi +from integrating + +over all orientations. + +Divided by h squared. + +I have essentially the two +components of angular momentum. + +So I get essentially, the square +of 2 pi I divided by beta. + +So this is rotations. + +And this is center of mass. + +We can see that if +I take that formula, + +take its log divide by-- take +a derivative with respect + +to beta. + +First of all, I will +get this constant + +that is the energy of the +bond state at 0 temperature. + +But the more interesting +things are the things + +that I take from the derivatives +of the various factors of beta. + +Essentially, for each factor +of beta in the denominator, + +log Z will have a +minus log of beta. + +I take a derivative, I will +get a factor of 1 over beta. + +So from here, I will get 3/2 +1 over beta, which is 3/2 kT. + +So this is the center of mass. + +From here, I have two +factors of beta to the 1/2. + +So they combine to give +me one factor of kT. + +This is for vibrations. + +And similarly, I have +two factors of beta + +to the 1/2, which correspond +to 1 kT for rotations. + +So then I say that the heat +capacity at constant volume + +is simply-- per particle +is related to d e1 by dT. + +And I see that that amounts +to kb times 3/2 plus 1 plus 1, + +or I should get 7/2 kb. + +Per particle, which says that +if you go and calculate the heat + +capacity of the +gas in this room, + +divide by the +number of molecules + +that we have-- doesn't +matter whether they + +are oxygens or nitrogen. + +They would basically give +the same contribution + +because you can see +that the masses and all + +the other properties +of the molecule + +do not appear in +the heat capacity. + +That as a function +of temperature, + +I should get a value of 7/2. + +So basically, C in units of kb. + +So I divide by kb. + +And my predictions is +that I should see 7/2. + +So you go and do a measurement +and what do you get? + +What you get is actually 5/2. + +So something is not quite right. + +We are not getting the +7/2 that we predicted. + +Except that I really +mentioned that you + +are getting this measurement +when you do measurements + +at room temperature, +you get this value. + +So when we measure +the heat capacity + +of the gas in this +room, we will get 5/2. + +But if we heat it +up, by the time + +we get to temperatures of a +few thousand degrees Kelvin. + +So if you heat the room +by a factor of 5 to 10, + +you will actually +get the value of 7/2. + +And if you cool +it, by the time you + +get to the order of +10 degrees or fewer, + +then you will find that +the heat capacity actually + +goes even further. + +It goes all the way to 3/2. + +And the 3/2 is +the thing that you + +would have predicted +for a gas that + +had monatomic particles, +no internal structure. + +Because then the only thing +that you would have gotten + +is the center of +mass contribution. + +So it seems like by going +to low temperatures, + +you somehow freeze +the degrees of freedom + +that correspond to vibrations +and rotations of the gas. + +And by going to really +high temperatures, + +you are able to liberate all +of these degrees of freedom + +and store energy in them. + +Heat capacity is the +measure of the ability + +to store heat and energy +into these molecules. + +So what is happening? + +Well, by 1905, +Planck Had already + +proposed that there is some +underlying quantization + +for heat that you have +in the black body case. + +And in 1905, Einstein +said, well, maybe we + +should think about the +vibrational degrees + +of the molecule also as +being similarly quantized. + +So quantize vibrations. + +It's totally a +phenomenological statement. + +We have to justify it later. + +But the statement is that for +the case where classically we + +had a harmonic oscillator. + +And let's say in +this case we would + +have said that +its energy depends + +on its momentum and its +position or displacement-- + +I guess I called it u-- +through a formula such as this. + +Certainly, you can pick +lots of values of u and p + +that are compatible with +any value of the energy + +that you choose. + +But to get the +black body spectrum + +to work, Planck had proposed +that really what you should do + +is rather than thinking of +this harmonic oscillator + +as being able to take all +possible values, that somehow + +the values of energy that +it can take are quantized. + +And furthermore, he +had proposed that they + +are proportional to +the frequency involved. + +And how did he guess that? + +Ultimately, it was +related to what + +I said about black +body radiation. + +That as you heat +up the body, you + +will find that there's +a light that comes out + +and the frequency of +that light is somehow + +related to temperature +and nothing else. + +And based on that, +he had proposed + +that frequencies should come +up in certain packages that + +are proportional +to-- the energies + +of the particular frequencies +should come in packages that + +are proportional +to that frequency. + +So there is an integer +here n that tells you + +about the number +of these packets. + +And not that it really matters +for what we are doing now, + +but just to be consistent +with what we currently know + +with quantum mechanics, +let me add the 0 point + +energy of the harmonic +oscillator here. + +So then, to calculate +the contribution + +of a system in which energy +is in quantized packages, + +you would say, OK, +I will calculate + +a Z1 for these +vibrational levels, + +assuming this +quantization of energy. + +And so that says that +the possible states + +of my harmonic +oscillator have energies + +that are in these units +h bar omega n plus 1/2. + +And if I still continue to +believe statistical mechanics, + +I would say that +at a temperature t, + +the probability that I +will be in a state that + +is characterized by +integer n is e to the minus + +beta times the energy that +corresponds to that integer n. + +And then I can go and sum +over all possible energies + +and that would be +the normalization + +of the probability that +I'm in one of these states. + +So this is e to the minus +beta h bar omega over 2 + +from the ground +state contribution. + +The rest of it is simply +a geometric series. + +Geometric series, we can sum +very easily to get 1 minus e + +to the minus beta h bar omega. + +And the interesting thing-- +or a few interesting things + +about this expression +is that if I + +evaluate this in the +limit of low temperatures. + +Well, actually, let's go +first to the high temperature + +where beta goes to 0. + +So t goes to become +large, beta goes to 0. + +Numerator goes to 1, denominator +I can expand the exponential. + +And to lowest order, I will +get 1 over beta h bar omega. + +Now, compare this result +with the classical result + +that we have over here +for the vibration. + +Contribution of a harmonic +oscillator to the partition + +function. + +You can see that +the mu's cancel out. + +I will get 1 over beta. + +I will get h divided by 2 pi. + +So if I call h divided +by 2 pi to be h bar, + +then I will get +exactly this limit. + +So somehow this constant +that we had introduced + +that had dimensions +of action made + +to make our calculations +of partition function + +to be dimensionless +will be related + +to this h bar that +quantizes the energy + +levels through the +usual formula of h being + +h bar-- h bar being h over 2 pi. + +So basically, this +quantization of energy + +clearly does not affect +the high temperature limit. + +This oscillator at +high temperature + +behaves exactly like what we +had calculated classically. + +Yes? + +AUDIENCE: Is it h +equals h bar over 2 pi? + +Or is it the other way, based +on your definitions above? + +PROFESSOR: Thank you. + +Good. + +All right? + +So this is, I guess, the +corresponding formula. + +Now, when you go to low +temperature, what do you get? + +You essentially get the first +few terms in the series. + +Because at the +lowest temperature + +you get the term that +corresponds to n equals to 0, + +and then you will +get corrections + +from subsequent terms. + +Now, what this does is that +it affects the heat capacity + +profoundly. + +So let's see how that happens. + +So the contribution of 1 +degrees of freedom to the energy + +in this quantized fashion +d log Z by d beta. + +So if I just take the +log of this expression, + +log of this expression will get +this factor of minus beta h bar + +omega over 2 from the numerator. + +The derivative of that will +give you this ground state + +energy, which is always there. + +And then you'll have +to take the derivative + +of the log of what +is coming out here. + +Taking a derivative +with respect to beta, + +we'll always pick out a +factor of h bar omega. + +Indeed, it will pick out +a factor of h bar omega + +e to the minus beta h bar omega. + +And then in the denominator, +because I took the log, + +I will get this expression back. + +So again, in this +expression, if I + +take the limit where beta +goes to 0, what do I get? + +I will get this h +bar omega over 2. + +It's always there. + +Expanding these results here, +I will have a beta h bar omega. + +It will cancel this and it +will give me a 1 over beta. + +I will get this kT +that I had before. + +Indeed, if I am correct +to the right order, + +I will just simply +get 1 over beta. + +Whereas, if I go to +large beta, what I get + +is this h bar omega +over 2 plus a correction + +from here, which is h bar omega +e to the minus beta h bar. + +And that will be reflected +in the heat capacity, which + +is dE by dT. + +This h bar omega over 2 does +not continue to heat capacity, + +not surprisingly. + +From here, I have to take +derivatives with temperatures. + +They appear in the combination +h bar omega over kT. + +So what happens is +I will get something + +that is of the order +of h bar omega. + +And then from here, I +will get another h bar + +omega divided by kb T squared. + +I will write it in this fashion +and put the kb out here. + +And then the rest +of these objects + +will give me a +contribution that is minus + +h bar omega over kT +divided by 1 minus e + +to the minus h bar +omega over kT squared. + +The important thing +is the following-- + +If I plot the heat +capacity that I + +get from one of +these oscillators-- + +and the natural +units of all heat + +capacities are kb, essentially. + +Energy divided by temperature, +as kb has that units. + +At high temperatures, +what I can see + +is that the energy is +proportional to kT. + +So heat capacity of the +vibrational degree of freedom + +will be in these +units going to 1. + +At low temperatures, however, it +becomes this exponentially hard + +problem to create excitations. + +Because of that, you +will get a contribution + +that as T goes to 0 will +exponentially go to 0. + +So the shape of the heat +capacity that you would get + +will be something like this. + +The natural way to +draw this figure + +is actually what I +made the vertical axis + +to be dimensionless. + +So it goes between 0 and 1. + +I can make the +horizontal axis to be + +dimensionless by introducing +a theta of vibrations, + +so that all of the exponential +terms are of the form e + +to the minus T over this +theta of vibrations, which + +means that this +theta of vibration + +is h bar omega over kb. + +That is, you tell me what the +frequency of your oscillator + +is. + +I can calculate the +corresponding temperature, + +theta. + +And then the heat capacity +of a harmonic oscillator + +is this universal +function there, presumably + +at some value that +is of the order of 1. + +It switches from +being of the order + +of 1 to going +exponentially to 0. + +So basically, the dependence +down here to leading order + +is e to the minus T +over theta vibration. + +OK. + +So you say, OK, +Planck has given us + +some estimate of what +this h bar is based + +on looking at the spectrum +of black body radiation. + +We can, more or, less +estimate the typical energies + +of interactions of molecules. + +And from that, we +can estimate what + +this frequency of vibration is. + +So we should be able to +get an order of magnitude + +estimate of what +this theta y is. + +And what you find is that +theta y is of the order of 10 + +to the 3 degrees Kelvin. + +It depends, of course, on +what gas you are looking at, + +et cetera. + +But as an order of magnitude, +it is something like that. + +So we can now transport this +curve that we have over here + +and more or less get this +first part of the curve + +that we have over here. + +So essentially, in this +picture what we have + +is that there is no vibrations. + +The vibrations have +been frozen out. + +And here you have vibrations. + +Of course, in all +of the cases, you + +have the kinetic energy +of the center of mass. + +And presumably since we are +getting the right answer + +at very high temperatures now, +we also have the rotations. + +And it makes sense +that essentially + +what happened as we go +to very low temperatures + +is that the rotations +are also frozen out. + +Now, that's part of +the story-- actually, + +you would think that among all +of the examples that I gave + +you, this last one should be +the simplest thing because it's + +really a two-body problem. + +Whereas, solids you +have many things. + +Radiation, you +have to think about + +the electromagnetic +waves, et cetera. + +That somehow, +historically, this would + +be the one that +is resolved first. + +And indeed, as I said +in 1905, Einstein + +figured out +something about this. + +But this part dealing with the +rotational degrees of freedom + +and quantizing +them appropriately + +had to really wait until you +had developed quantum mechanics + +beyond the statement +that harmonic oscillators + +are quantized in energy. + +You had to know something more. + +So since in retrospect we +do know something more, + +let's finish and +give that answer + +before going on +to something else. + +OK? + +So the next part of the +story of the diatomic gas + +is quantizing rotations. + +So currently what I have is that +there is an energy classically + +for rotations that is +simply the kinetic energy + +of rotational +degrees of freedom. + +So there is an +angular momentum L, + +and then there's +L squared over 2I. + +It looks pretty much +like P squared over 2M, + +except that the +degrees of freedom + +for translation and +motion are positions. + +They can be all over the place. + +Whereas, the degrees +of freedom that you + +have to think in +terms of rotations + +are angles that go +between 0, 2 pi, + +or on the surface of +a sphere, et cetera. + +So once we figure out how +to do quantum mechanics, + +we find that the +allowed values of this + +are of the form h bar squared +over 2I l, l plus 1, where + +l now is the number that gives +you the discrete values that + +are possible for the square +of the angular momentum. + +So you say OK, let's calculate +a Z for the rotational degrees + +of freedom assuming this +kind of quantization. + +So what I have to do, like I +did for the harmonic oscillator, + +is I sum over all possible +values of l that are allowed. + +The energy e to the minus +beta h bar squared over 2I + +l, l plus 1. + +Except that there +is one other thing, + +which is that these +different values of l + +have degeneracy +that is 2l plus 1. + +And so you have to multiply by +the corresponding degeneracy. + +So what am I doing over here? + +I have to do a sum over +different values of l, + +contributions that are +really the probability that I + +am in these different values of +the index l-- 0, 1, 2, 3, 4, 5, + +6. + +And I have to add all +of these contributions. + +Now, the first +thing that I will do + +is I ask whether the limit +of high temperatures that I + +had calculated before is +correctly reproduced or not. + +So I have to go to the limit +where temperature is high + +or beta goes to 0. + +If beta goes to 0, +you can see that going + +from one l to another +l, it is multiply + +this exponent by a small number. + +So what does that mean? + +It means that the values from +one point to another point + +of what am I summing over is +not really that different. + +And I can think of a +continuous curve that + +goes through all +of these points. + +So if I do that, then +I can essentially + +replace the sum +with an integral. + +In fact, you can systematically +calculate corrections + +to replacing the sum with +an integral mathematically + +and you have a problem set +that shows you how to do that. + +But now what I can do is I +can call this combination l, l + +plus 1 x. + +And then dx will +simply be 2l plus 1 dl. + +So essentially, the +degeneracy works out precisely + +so that when I go to the +continuum limit, whatever + +quantization I had for +these angular momenta + +corresponds to the +weight or measure + +that I would have in stepping +around the l-directions. + +And then, this is something +that I can easily do. + +It's just an integral dx +e to the minus alpha x. + +The answer is going to be 1 over +alpha, or the answer to this + +is simply 2I beta h bar squared. + +So this is the classical +limit of the expression + +that we had over here. + +Let's go and see what we had +when we did things classically. + +So when we did +things classically, + +I had two factors of +h and 2 pi and 4 pi. + +So I can write the whole +thing as h bar squared and 2. + +I have I, and then I have beta. + +And you can see that +this is exactly what we + +have over there. + +So once more, properly +accounting for phase space, + +measure, productive p +q's being dimension-- + +made dimensionless +by this quantity h + +is equivalent to the +high temperature limit + +that you would get +in quantum mechanics + +where things are discretized. + +Yes. + +AUDIENCE: When you're +talking about the quantum + +interpretations, then h +bar is the precise value + +of Planck's constant, which +can be an experimental measure. + +PROFESSOR: Right. + +AUDIENCE: But when +you're talking + +about the classical derivations, +h is just some factor + +that we mention of +curve dimension. + +PROFESSOR: That's correct. + +AUDIENCE: So if you're +comparing the limits + +of large temperatures, +how can you + +be sure to establish the +h bar in two places means + +the same thing? + +PROFESSOR: So far, +I haven't told + +you anything to justify that. + +So when we were doing +things classically, + +we said that just to make +things dimensionless, + +let's introduce this +quantity that we call h. + +Now, I have shown you +two examples where + +if you do things quantum +mechanically properly + +and take the limit of +going to high temperatures, + +you will see that the +h that you would get-- + +because the quantum +mechanical partition functions + +are dimensionless +quantities, right? + +So these are +dimensionless quantities. + +They have to be made +dimensionless by something. + +They're made dimensionless +by Boltzmann's constant. + +By a Planck's constant, h bar. + +And we can see +that as long as we + +are consistent with this +measure of phase space, + +the same constant shows up both +for the case of the vibrations, + +for the case of the rotations. + +And very soon, we will +see that it will also + +arise in the case of +the center of mass. + +And so there is certainly +something in the transcriptions + +that we ultimately will make +between quantum mechanics + +and classical mechanics +that must account for this. + +And somehow in the limit where +quantum mechanics is dealing + +with large energies, +it is indistinguishable + +from classical mechanics. + +And quantum partition +functions are-- + +all of the countings that we do +in quantum mechanics are kind + +of unambiguous because we are +dealing with discrete levels. + +So if you remember the +original part of the difficulty + +was that we could define +things like entropy only + +properly when we +had discrete levels. + +If we had a continuum +probability distribution + +and if we made a +change of variable, + +then the entropy was changed. + +But in quantum mechanics, +we don't have that problem. + +We have discretized values +for the different states. + +Probabilities will be-- once +we deal with them appropriately + +be discretized. + +And all of the things +here are dimensionless. + +And somehow they reproduce the +correct classical dynamics. + +Quantum mechanics goes +to classical mechanics + +in the appropriate +high-energy limit. + +And what we find is that what +happens is that this shows up. + +If you like, another +way of achieving-- + +why is there this +correspondence? + +In classical +statistical mechanics, + +I emphasize that I should really +write h in units of p and q. + +And it was only when I +calculated partition functions + +in coordinates p and q that were +canonically conjugate that I + +was getting results +that were meaningful. + +One way of constructing +quantum mechanics + +is that you take the +Hamiltonian and you change these + +into operators. + +And you have to impose these +kinds of commutation relations. + +So you can see that somehow +the same prescription in terms + +of phase space appears both +in statistical mechanics, + +in calculating measures +of partition function, + +in quantum mechanics. + +And not surprisingly, you have +introduced in quantum mechanics + +some unit for phase space p, q. + +It shows up in +classical mechanics + +as the quantity [INAUDIBLE]. + +But there is, indeed, +a little bit more work + +than I have shown you +here that one can do. + +Once we have developed +the appropriate formalism + +for quantum statistical +mechanics, which + +is this [INAUDIBLE] performed +and appropriate quantities + +defined for partition +functions, et cetera, + +in quantum statistical +mechanics that we + +will do in a couple of lectures. + +Then if you take the +limit h bar goes to 0, + +you should get the classical +integration over phase space + +with this factor +of h showing up. + +But right now, we +are just giving you + +some heuristic response. + +If I go, however, in +the other limit, where + +beta is much larger +than 1, what do I get? + +Basically, then +all of the weight + +is going to be in the +lowest energy level, 0, 1. + +And then the rest of them +will be exponentially small. + +I cannot replace the +sum with an integral, + +so basically I will get a +contribution that starts with 1 + +for l equals to 0. + +And then I will get +3e to the minus beta h + +bar squared divided by 2I. + +l being 1, this will +give me 1 times 2. + +So I will have a 2 here. + +And then, higher-order terms. + +So once you have the +partition function, + +you go through +the same procedure + +as we described before. + +You calculate the energy, +which is d log Z by d beta. + +What do you get? + +Again, in the high +temperature limit + +you will get the same +answer as before. + +So you will get beta goes to 0. + +You will get kT. + +If you go to the low +temperature limit-- well, + +let's be more precise. + +What do I mean by +low temperatures? + +Beta larger than what? + +Clearly, the unit that +is appearing everywhere + +is this beta h bar squared +over 2I, which has units of 1 + +over temperature from beta. + +So I can introduce a +theta for rotations + +to make this demonstrate +that this is dimensionless. + +So the theta that +goes with rotations + +is h bar squared over 2I kb. + +And so what I mean by going +to the low temperatures + +is that I go for +temperatures that + +are much less than the +theta of these rotations. + +And then what happens is +that essentially this state + +will occur with exponentially +small probability + +and will contribute to +the energy and amount that + +is of the order of h +bar squared 2I times 2. + +That's the energy of +the l equals to 1 state. + +There are three of them, and +they occur with probability e + +to the minus theta +rotation divided + +by T times a factor of 2. + +All of those factors is +not particularly important. + +Really, the only thing +that is important + +is that if I look now at the +rotational heat capacity, which + +again should properly +have units of kb, + +as a function of temperature. + +Well, temperatures +I have to make + +dimensionless by dividing by +this rotational heat capacity. + +I say that at +high, temperature I + +get the classical result back. + +So basically, I will get +to 1 at high temperatures. + +At low temperatures, again +I have this situation + +that there is a gap in +the allowed energies. + +So there is the lowest +energy, which is 0. + +The next one, the first type of +rotational mode that is allowed + +has a finite energy +that is larger than that + +by an amount that is of the +order of h bar squared over I. + +And if I am at these +temperatures that + +are less than this +theta of rotation, + +I simply don't +have enough energy + +from thermal fluctuations +to get to that level. + +So the occupation of that level +will be exponentially small. + +And so I will have a curve that +will, in fact, look something + +like this. + +So again, you basically +go over at a temperature + +of the order of 1 +from heat capacity + +that is order of 1 to heat +capacity that is exponentially + +small when you get to +temperatures that are lower + +than this rotational +temperature. + +AUDIENCE: Is that +over-shooting, or is that-- + +PROFESSOR: Yes. + +So you have a +problem set where you + +calculate the next correction. + +So there is the summation +replacing the sum + +with an integral. + +This gives you this +to the first order, + +and then there's a correction. + +And you will show that +the correction is such + +that there is actually +the approach to one + +for the case of the rotational +heat capacity is from above. + +Whereas, for the +vibrational heat capacity, + +it is from below. + +So there is, indeed, +a small bump. + +OK? + +So you can ask, well, I +know the typical size of one + +of these oxygen molecules. + +I know the mass. + +I can figure out what the +moment of inertia I is. + +I put it over here and I figure +out what the theta of rotation + +is. + +And you find that, again, as a +matter of order of magnitudes, + +theta of rotations is of +the order of 10 degrees + +K. So this kind of accounts for +why when you go to sufficiently + +low temperatures for the +heat capacity of the gas + +in this room, we +see that essentially + +the rotational degrees of +freedom are also frozen out. + +OK. + +So now let's go to the +second item that we have, + +which is the heat +capacity of the solid. + +So what do I mean? + +So this is item 2, +heat capacity of solid. + +And you measure heat +capacities for some solid + +as a function of temperature. + +And what you find is +that the heat capacity + +has a behavior such as this. + +So it seems to +vanish as you to go + +to lower and lower temperatures. + +So what's going on here? + +Again, Einstein looked at +this and said, well, it's + +another case of the story of +vibrations and some things + +that we have looked at here. + +And in fact, I really don't +have to do any calculation. + +I'll do the following. + +Let's imagine that this is +what we have for the solid. + +It's some regular arrangement +of atoms or molecules. + +And presumably, this +is the situation + +that I have at 0 temperature. + +Everybody is +sitting nicely where + +they should be to +minimize the energy. + +If I go to finite temperature, +then these atoms and molecules + +start to vibrate. + +And he said, well, +basically, I can + +estimate the frequencies +of vibrations. + +And what I will do is I +will say that each atom is + +in a cage by its neighbors. + +That is, this particular atom +here, if it wants to move, + +it find that its distance to +the neighbors has been changed. + +And if I imagine +that there are kind + +of springs that are +connecting this atom only + +to its neighbors, +moving around there + +will be some kind of +a restoring force. + +So it's like it is +sitting in some kind + +of a harmonic potential. + +And if it tries to +move, it will experience + +this restoring force. + +And so it will have some +kind of a frequency. + +So each atom vibrates +at some frequency. + +Let's call it omega E. + +Now, in principle, +in this picture + +if this cage is not +exactly symmetric, + +you may imagine that +oscillations in the three + +different directions could +give you different frequencies. + +But let's ignore that and let's +imagine that the frequencies is + +the same in all of these. + +So what have we done? + +We have reduced the problem +of the excitation energy + +that you can put in the +atoms of the solid to be + +the same now as 3N harmonic +oscillators of frequency omega. + +Why 3N? + +Because each atom +essentially sees restoring + +force in three directions. + +And forgetting about +boundary effects, + +it's basically +three per particle. + +So you would have said that +the heat capacity that I would + +calculate per particle +in units of kb + +should essentially be exactly +what we have over here, + +except that I multiply by 3 +because each particular has + +3 possible degrees of freedom. + +So all I need to do is +to take that green curve + +and multiply it +by a factor of 3. + +And indeed, the limiting value +that you get over here is 3. + +Except that if I just +take that green curve + +and superpose it on +this, what I will get + +is something like this. + +So this is 3 times +harmonic oscillator. + +What do I mean by that, is +I try to sort of do my best + +to match the +temperature at which you + +go from one to the other. + +But then what I find is that +as we had established before, + +the green curve goes +to 0 exponentially. + +So there is going to be +some theta associated + +with this frequency. + +Let's call it theta +Einstein divided by T. + +And so the prediction +of this model + +is that the heat capacities +should vanish very rapidly + +as this form of exponential. + +Whereas, what is actually +observed in the experiment + +is that it is going +to 0 proportional + +to T cubed, which is a +much slower type of decay. + +OK? + +AUDIENCE: That's +negative [INAUDIBLE]? + +PROFESSOR: As T goes to 0, +the heat capacity goes to 0. + +T to the third power. + +So it's the limit-- did I +make a mistake somewhere else? + +All right. + +So what's happening here? + +OK, so what's happening +is the following. + +In some average +sense, it is correct + +that if you try to oscillate +some atom in the crystal, + +it's going to have some +characteristic restoring force. + +The characteristic +restoring force + +will give you some +corresponding typical scale + +for the frequencies +of the vibrations. + +Yes? + +AUDIENCE: Is this the +historical progression? + +PROFESSOR: Yes. + +AUDIENCE: I mean, it seems +interesting that they + +would know that-- like this +cage hypothesis is very good, + +considering where a +quantum [INAUDIBLE] exists. + +I don't understand how +that's the logic based-- + +if what we know is the +top board over there, + +the logical progression is that +you would have-- I don't know. + +PROFESSOR: No. + +At that time, the proposal +was that essentially + +if you have oscillator +of frequency omega, + +its energy is quantized +in multiples of omega. + +So that's really the only +aspect of quantum mechanics. + +So I actually jumped the +historical development + +where I gave you the +rotational degrees of freedom. + +So as I said, historically this +was resolved last in this part + +because they didn't know +what to do with rotations. + +But now I'm saying that +you know about rotations, + +you know that the heat +capacity goes to 0. + +You say, well, +solid is composed. + +The way that you put +heat into the system, + +enhance its heat capacity, is +because there is kinetic energy + +that you put in the +atoms of the solid. + +And as you try to +put kinetic energy, + +there is this cage model +and there's restoring force. + +The thing that is +wrong about this model + +is that, basically, if you ask +how easy it is to give energy + +to the system, if rather +than having one frequency + +you have multiple frequencies, +then at low temperatures + +you would put energy +in the lower frequency. + +Because the typical scale we +saw for connecting temperature + +and frequency, they are kind +of proportional to each other. + +So if you want to go +to low temperature, + +you are bound to excite things +that have lower frequency. + +So the thing is that +it is true that there + +is a typical frequency. + +But the typical frequency +becomes less and less important + +as you go to low temperature. + +The issue is, what are +the lowest frequencies + +of excitation? + +And basically, the +correct picture + +of excitations of the solid +is that you bang on something + +and you generate +these sound waves. + +So what you have is that +oscillations or vibrations + +of solid are characterized +by wavelength and wave number + +k, 2 pi over lambda. + +So if I really take a +better model of the solid + +in which I have springs that +connect all of these things + +together and ask, what are +the normal modes of vibration? + +I find that the normal +modes can be characterized + +by some wave number k. + +As I said, it's the +inverse of the wavelength. + +And frequency depends +on wave number. + +In a manner that when you go +to 0k, frequency goes to 0. + +And why is that? + +Essentially, what I'm +saying is that if you + +look at particles +that are along a line + +and may be connected by springs. + +So a kind of one-dimensional +version of a solid. + +Then, the normal modes +are characterized + +by distortions that have +some particular wavelength. + +And in the limit +where the wavelength + +goes to 0, essentially-- + +Sorry, in the limit +where the wavelength goes + +to infinity or k +goes to 0, it looks + +like I am taking +all of the particles + +and translating them together. + +And if I take the entire +solid here and translate it, + +there is no restoring force. + +So omega has to go to +0 as your k goes to 0, + +or wavelength goes to infinity. + +And there is a symmetry +between k and minus k, + +in fact, that forces +the restoring force + +to be proportional to k squared. + +And when you take the +square root of that, + +you get the frequency. + +You always get a linear +behavior as k goes to 0. + +So essentially, +that's the observation + +that whatever you +do with your solid, + +no matter how complicated, +you have sound modes. + +And sound modes are +things that happen + +in the limit where you +have long wavelengths + +and there is a relationship +between omega and k + +through some kind of +velocity of sound. + +Now, to be precise +there are really + +three types of sound waves. + +If I choose the +direction k along which + +I want to create an +oscillation, the distortions + +can be either along that +direction or perpendicular + +to that. + +They can either be +longitudinal or transfers. + +So there could be one +or two other branches. + +So there could, in principle, +be different straight lines + +as k goes to 0. + +And the other +thing is that there + +is a shortest wavelength +that you can think about. + +So if these particles +are a distance a apart, + +there is no sense in +going to wave numbers that + +are larger than pi over a. + +So you have some +limit to these curves. + +And indeed, when you +approach the boundary, + +this linear dependence +can shift and change + +in all kinds of possible ways. + +And calculating the +frequency inside one + +of these units that is +called a Brillouin zone + +is a nice thing +to do for the case + +of using methods of solid state. + +And you've probably seen that. + +And there is a whole +spectrum of frequencies + +as a function of +wave number that + +correctly characterize a solid. + +So it may be that somewhere +in the middle of this spectrum + +is a typical frequency +omega E. But the point is + +that as you go to lower +and lower temperatures, + +because of these factors of e +to the minus beta h bar omega, + +you can see that as you go to +lower and lower temperature, + +the only things that get +excited are omegas that are also + +going to 0 +proportionately to kT. + +So I can draw a line here that +corresponds to frequencies that + +are of the order +of kT over h bar. + +All of the harmonic +oscillators that + +have these larger frequencies +that occur at short wavelengths + +are unimportant. + +They're kind of frozen, +just like the vibrations + +of the oxygen molecules +in this room are frozen. + +You cannot put energy in them. + +They don't contribute +to heat capacity. + +But all of these +long wavelength modes + +down here have +frequencies that go to 0. + +Their excitation +possibility is large. + +And it, indeed, +these long wavelength + +modes that are easy to excite +and continue to heat capacity. + +I'll do maybe the precise +calculation next time, + +but even within this +picture we can figure out + +why the answer should be +proportional to T cubed. + +So what I need to do, +rather than counting + +all harmonic oscillators-- +the factor of 3n-- + +I have to count how many +oscillators have frequencies + +that are less than +this kT over h bar. + +So I claim that number of modes +with frequency less than kT + +over h bar goes like +kT over h bar cubed V. + +Essentially, what +I have to do is + +to do a summation over all k +that is less than some k max. + +This k max is set +by this condition + +that Vk max is of the +order of kT over h bar. + +So this k max is of the +order of kT over h bar V. + +So actually, to be more +precise I have to put a V here. + +So I have to count +all of the modes. + +Now, this separation +between these modes-- + +if you have a box of +size l is 2 pi over l. + +So maybe we will +discuss that later on. + +But the summations +over k you will always + +replace with +integrations over k times + +the density of state, which +is V divided by 2 pi cubed. + +So this has to go +between 0 and k max. + +And so this is +proportional to V k max + +cubed, which is what +I wrote over there. + +So as I go to lower +and lower temperature, + +there are fewer and +fewer oscillators. + +The number of those +oscillators grows like T cubed. + +Each one of those +oscillators is fully excited + +as energy kT contributes +1 unit to heat capacity. + +Since the number of oscillators +goes to 0 as T cubed, + +the heat capacity that +they contribute also + +goes to 0 as T cubed. + +So you don't really need +to know-- this is actually + +an interesting thing to ponder. + +So rather than doing +the calculations, + +maybe just think about this. + +That somehow the solid could +be arbitrarily complicated. + +So it could be +composed of molecules + +that have some particular shape. + +They are forming +some strange lattice + +of some form, et cetera. + +And given the complicated +nature of the molecules, + +the spectrum that you have +for potential frequencies + +that a solid can +take, because of all + +of the different +vibrations, et cetera, + +could be arbitrary complicated. + +You can have kinds of +oscillations such as the ones + +that I have indicated. + +However, if you go +to low temperature, + +you are only interested +in vibrations + +that are very low in frequency. + +Vibrations that are +very low in frequencies + +must correspond +to the formations + +that are very long wavelength. + +And when you are +looking at things + +that are long wavelength, +this is, again, + +another thing that has +statistical in character. + +That is, rather you +are here looking + +at things that span thousands +of atoms or molecules. + +However, as you go to lower +and lower temperature, + +more and more atoms +and molecules. + +And so again, some kind of +averaging is taking place. + +All of the details, +et cetera, wash out. + +You really see some +global characteristic. + +The global characteristic +that you see + +is set by this symmetry. + +Just the fact that when I +go to exactly k equals to 0, + +I am translating. + +I have 0 frequency. + +So when I'm doing something +that is long wavelength, + +the frequency should +somehow be proportional + +to that wavelength. + +So that's just a statement +of continuity if you like. + +Once I have made that +statement, then it's + +just a calculation of how +many modes are possible. + +The number of modes will +be proportional to T cubed. + +And I will get this T +cubed law irrespective + +of how complicated the solid is. + +All of the solids will have +the same T cubed behavior. + +The place where they come +from the classical behavior + +to this quantum +behavior will depend + +on the details of +the solid, et cetera. + +But the low temperature +law, this T cubed law, + +is something that is universal. + +OK, so next time around, +we will do this calculation + +in more detail, and then +see also its connection + +to the blackbody radius. \ No newline at end of file diff --git a/i8rnEl8O-r0.txt b/i8rnEl8O-r0.txt new file mode 100644 index 0000000000000000000000000000000000000000..c571ef3f6e1243978b59cec224e5e9803891e2e6 --- /dev/null +++ b/i8rnEl8O-r0.txt @@ -0,0 +1,1483 @@ +align:start position:0% + +okay uh this is heat equation video so + + align:start position:0% +okay uh this is heat equation video so + + + align:start position:0% +okay uh this is heat equation video so +this is the second of the + + align:start position:0% +this is the second of the + + + align:start position:0% +this is the second of the +three basic partial differential + + align:start position:0% +three basic partial differential + + + align:start position:0% +three basic partial differential +equations we had llosa's equation that + + align:start position:0% +equations we had llosa's equation that + + + align:start position:0% +equations we had llosa's equation that +was time was not there now time comes + + align:start position:0% +was time was not there now time comes + + + align:start position:0% +was time was not there now time comes +into the heat equation we have a Time + + align:start position:0% +into the heat equation we have a Time + + + align:start position:0% +into the heat equation we have a Time +derivative and + + align:start position:0% +derivative and + + + align:start position:0% +derivative and +two matching with two space derivatives + + align:start position:0% +two matching with two space derivatives + + + align:start position:0% +two matching with two space derivatives +so I have my function my my solution + + align:start position:0% +so I have my function my my solution + + + align:start position:0% +so I have my function my my solution +depends on T and on X and I hope I can + + align:start position:0% +depends on T and on X and I hope I can + + + align:start position:0% +depends on T and on X and I hope I can +separate those two parts this is exactly + + align:start position:0% +separate those two parts this is exactly + + + align:start position:0% +separate those two parts this is exactly +like the way we + + align:start position:0% +like the way we + + + align:start position:0% +like the way we +solved ordinary systems of differential + + align:start position:0% +solved ordinary systems of differential + + + align:start position:0% +solved ordinary systems of differential +equations we pulled out uh an e to the + + align:start position:0% +equations we pulled out uh an e to the + + + align:start position:0% +equations we pulled out uh an e to the +Lambda T where Lambda was the I value + + align:start position:0% +Lambda T where Lambda was the I value + + + align:start position:0% +Lambda T where Lambda was the I value +and then we had the igen vector here + + align:start position:0% +and then we had the igen vector here + + + align:start position:0% +and then we had the igen vector here +it's an igen function because it depends + + align:start position:0% +it's an igen function because it depends + + + align:start position:0% +it's an igen function because it depends +on X we didn't have X before but now now + + align:start position:0% +on X we didn't have X before but now now + + + align:start position:0% +on X we didn't have X before but now now +we have partial differential equations X + + align:start position:0% +we have partial differential equations X + + + align:start position:0% +we have partial differential equations X +is also a coordinate here and this so I + + align:start position:0% +is also a coordinate here and this so I + + + align:start position:0% +is also a coordinate here and this so I +look for Solutions like that and just as + + align:start position:0% +look for Solutions like that and just as + + + align:start position:0% +look for Solutions like that and just as +always I substitute that into the + + align:start position:0% +always I substitute that into the + + + align:start position:0% +always I substitute that into the +differential equation and and to + + align:start position:0% +differential equation and and to + + + align:start position:0% +differential equation and and to +discover what the what determines s s of + + align:start position:0% +discover what the what determines s s of + + + align:start position:0% +discover what the what determines s s of +X okay the time derivative brings down a + + align:start position:0% +X okay the time derivative brings down a + + + align:start position:0% +X okay the time derivative brings down a +Lambda the space derivative + + align:start position:0% +Lambda the space derivative + + + align:start position:0% +Lambda the space derivative +brings down has two two space + + align:start position:0% +brings down has two two space + + + align:start position:0% +brings down has two two space +derivatives so that's what I get when I + + align:start position:0% +derivatives so that's what I get when I + + + align:start position:0% +derivatives so that's what I get when I +substitute e the Lambda TS I value times + + align:start position:0% +substitute e the Lambda TS I value times + + + align:start position:0% +substitute e the Lambda TS I value times +I function into the equation and always + + align:start position:0% +I function into the equation and always + + + align:start position:0% +I function into the equation and always +I cancel e to the Lambda T that's the + + align:start position:0% +I cancel e to the Lambda T that's the + + + align:start position:0% +I cancel e to the Lambda T that's the +beauty of it and I have an igen value + + align:start position:0% +beauty of it and I have an igen value + + + align:start position:0% +beauty of it and I have an igen value +equation or an i an I'm looking again + + align:start position:0% +equation or an i an I'm looking again + + + align:start position:0% +equation or an i an I'm looking again +for a function so so the second + + align:start position:0% +for a function so so the second + + + align:start position:0% +for a function so so the second +derivative of my function is Lambda some + + align:start position:0% +derivative of my function is Lambda some + + + align:start position:0% +derivative of my function is Lambda some +number times my function okay what I'm + + align:start position:0% +number times my function okay what I'm + + + align:start position:0% +number times my function okay what I'm +looking for for functions s there'll be + + align:start position:0% +looking for for functions s there'll be + + + align:start position:0% +looking for for functions s there'll be +S functions s will be s s ofx will be + + align:start position:0% +S functions s will be s s ofx will be + + + align:start position:0% +S functions s will be s s ofx will be +the S of K pi x the S of x the sign of + + align:start position:0% +the S of K pi x the S of x the sign of + + + align:start position:0% +the S of K pi x the S of x the sign of +something time x what's the IG + + align:start position:0% +something time x what's the IG + + + align:start position:0% +something time x what's the IG +value put take two derivatives of this I + + align:start position:0% +value put take two derivatives of this I + + + align:start position:0% +value put take two derivatives of this I +get back sine K pix which is so that's + + align:start position:0% +get back sine K pix which is so that's + + + align:start position:0% +get back sine K pix which is so that's +great it's an igen function and out + + align:start position:0% +great it's an igen function and out + + + align:start position:0% +great it's an igen function and out +comes the I value Lambda is well when I + + align:start position:0% +comes the I value Lambda is well when I + + + align:start position:0% +comes the I value Lambda is well when I +take two derivatives K Pi comes out + + align:start position:0% +take two derivatives K Pi comes out + + + align:start position:0% +take two derivatives K Pi comes out +twice with a minus sign so it's minus k^ + + align:start position:0% +twice with a minus sign so it's minus k^ + + + align:start position:0% +twice with a minus sign so it's minus k^ +2k^ + + align:start position:0% +2k^ + + + align:start position:0% +2k^ +2 so I have found a bunch of igen + + align:start position:0% +2 so I have found a bunch of igen + + + align:start position:0% +2 so I have found a bunch of igen +vectors igen functions and the igen + + align:start position:0% +vectors igen functions and the igen + + + align:start position:0% +vectors igen functions and the igen +values so now so this was a simple pair + + align:start position:0% +values so now so this was a simple pair + + + align:start position:0% +values so now so this was a simple pair +but now General + + align:start position:0% + + + + align:start position:0% + +solution the general solution U of TX + + align:start position:0% +solution the general solution U of TX + + + align:start position:0% +solution the general solution U of TX +will + + align:start position:0% +will + + + align:start position:0% +will +be if I know several Solutions and I + + align:start position:0% +be if I know several Solutions and I + + + align:start position:0% +be if I know several Solutions and I +have a linear equation I just take + + align:start position:0% +have a linear equation I just take + + + align:start position:0% +have a linear equation I just take +combinations that's always our way take + + align:start position:0% +combinations that's always our way take + + + align:start position:0% +combinations that's always our way take +combinations of those basic Solutions so + + align:start position:0% +combinations of those basic Solutions so + + + align:start position:0% +combinations of those basic Solutions so +I'll have a + + align:start position:0% +I'll have a + + + align:start position:0% +I'll have a +sum K going from 1 to Infinity in + + align:start position:0% +sum K going from 1 to Infinity in + + + align:start position:0% +sum K going from 1 to Infinity in +differential equ partial differential + + align:start position:0% +differential equ partial differential + + + align:start position:0% +differential equ partial differential +equations I need a big sum here of some + + align:start position:0% +equations I need a big sum here of some + + + align:start position:0% +equations I need a big sum here of some +coefficients let me call them + + align:start position:0% +coefficients let me call them + + + align:start position:0% +coefficients let me call them +BK times this this solution e to the + + align:start position:0% +BK times this this solution e to the + + + align:start position:0% +BK times this this solution e to the +Lambda what was Lambda - k^ 2 pk^ 2 T * + + align:start position:0% +Lambda what was Lambda - k^ 2 pk^ 2 T * + + + align:start position:0% +Lambda what was Lambda - k^ 2 pk^ 2 T * +s s number K I should have given this + + align:start position:0% +s s number K I should have given this + + + align:start position:0% +s s number K I should have given this +igen + + align:start position:0% +igen + + + align:start position:0% +igen +function uh its number k + + align:start position:0% +function uh its number k + + + align:start position:0% +function uh its number k +so there's the IG there this is my + + align:start position:0% +so there's the IG there this is my + + + align:start position:0% +so there's the IG there this is my +family of igen functions and igen values + + align:start position:0% +family of igen functions and igen values + + + align:start position:0% +family of igen functions and igen values +and then this is the combination of + + align:start position:0% +and then this is the combination of + + + align:start position:0% +and then this is the combination of +these Solutions there's the general + + align:start position:0% +these Solutions there's the general + + + align:start position:0% +these Solutions there's the general +solution and for SK I should have + + align:start position:0% +solution and for SK I should have + + + align:start position:0% +solution and for SK I should have +written in sin K pix so that's the + + align:start position:0% +written in sin K pix so that's the + + + align:start position:0% +written in sin K pix so that's the +dependence on T let's have a look at + + align:start position:0% +dependence on T let's have a look at + + + align:start position:0% +dependence on T let's have a look at +this so the dependence on T is fast + + align:start position:0% +this so the dependence on T is fast + + + align:start position:0% +this so the dependence on T is fast +Decay and if k is as K gets + + align:start position:0% +Decay and if k is as K gets + + + align:start position:0% +Decay and if k is as K gets +larger later terms in this sum the Decay + + align:start position:0% +larger later terms in this sum the Decay + + + align:start position:0% +larger later terms in this sum the Decay +is really fast so the the the term that + + align:start position:0% +is really fast so the the the term that + + + align:start position:0% +is really fast so the the the term that +decays most slowly k equal 1 there will + + align:start position:0% +decays most slowly k equal 1 there will + + + align:start position:0% +decays most slowly k equal 1 there will +be a B1 and e to the minus Pi s + + align:start position:0% +be a B1 and e to the minus Pi s + + + align:start position:0% +be a B1 and e to the minus Pi s +t that's decaying already pretty fast + + align:start position:0% +t that's decaying already pretty fast + + + align:start position:0% +t that's decaying already pretty fast +the when I'm talking about Decay What's + + align:start position:0% +the when I'm talking about Decay What's + + + align:start position:0% +the when I'm talking about Decay What's +Happening Here I I have a + + align:start position:0% +Happening Here I I have a + + + align:start position:0% +Happening Here I I have a +bar the of uh uh uh a material bar the + + align:start position:0% +bar the of uh uh uh a material bar the + + + align:start position:0% +bar the of uh uh uh a material bar the +ends of the bar + + align:start position:0% +ends of the bar + + + align:start position:0% +ends of the bar +are kept at temperature + + align:start position:0% +are kept at temperature + + + align:start position:0% +are kept at temperature +zero they're + + align:start position:0% +zero they're + + + align:start position:0% +zero they're +frozen and heat is in the bar heat is + + align:start position:0% +frozen and heat is in the bar heat is + + + align:start position:0% +frozen and heat is in the bar heat is +Flowing around in the bar and where to + + align:start position:0% +Flowing around in the bar and where to + + + align:start position:0% +Flowing around in the bar and where to +where is it going it's flowing out the + + align:start position:0% +where is it going it's flowing out the + + + align:start position:0% +where is it going it's flowing out the +ends the the temp the bar is approaching + + align:start position:0% +ends the the temp the bar is approaching + + + align:start position:0% +ends the the temp the bar is approaching +freezing the the ends are kept at + + align:start position:0% +freezing the the ends are kept at + + + align:start position:0% +freezing the the ends are kept at +freezing and the inside of the bar + + align:start position:0% +freezing and the inside of the bar + + + align:start position:0% +freezing and the inside of the bar +whatever Heat is there at the beginning + + align:start position:0% +whatever Heat is there at the beginning + + + align:start position:0% +whatever Heat is there at the beginning +is going to flow out the ends so you see + + align:start position:0% +is going to flow out the ends so you see + + + align:start position:0% +is going to flow out the ends so you see +that I have these s + + align:start position:0% +that I have these s + + + align:start position:0% +that I have these s +functions when X is + + align:start position:0% +functions when X is + + + align:start position:0% +functions when X is +zero the sign is zero so that's frozen + + align:start position:0% +zero the sign is zero so that's frozen + + + align:start position:0% +zero the sign is zero so that's frozen +at one end when X is + + align:start position:0% +at one end when X is + + + align:start position:0% +at one end when X is +one I have a s of K Pi which is again + + align:start position:0% +one I have a s of K Pi which is again + + + align:start position:0% +one I have a s of K Pi which is again +zero so it's frozen at the other end so + + align:start position:0% +zero so it's frozen at the other end so + + + align:start position:0% +zero so it's frozen at the other end so +I'm freezing it at both ends the + + align:start position:0% +I'm freezing it at both ends the + + + align:start position:0% +I'm freezing it at both ends the +temperature is escaping out of the out + + align:start position:0% +temperature is escaping out of the out + + + align:start position:0% +temperature is escaping out of the out +of the uh Center so so the solution so + + align:start position:0% +of the uh Center so so the solution so + + + align:start position:0% +of the uh Center so so the solution so +let me graph the + + align:start position:0% +let me graph the + + + align:start position:0% +let me graph the +solution so maybe I start with here's my + + align:start position:0% +solution so maybe I start with here's my + + + align:start position:0% +solution so maybe I start with here's my +bar from 0 to one and I'm keeping it + + align:start position:0% +bar from 0 to one and I'm keeping it + + + align:start position:0% +bar from 0 to one and I'm keeping it +Frozen f for Frozen f for Frozen at that + + align:start position:0% +Frozen f for Frozen f for Frozen at that + + + align:start position:0% +Frozen f for Frozen f for Frozen at that +end maybe I maybe I start off with a + + align:start position:0% +end maybe I maybe I start off with a + + + align:start position:0% +end maybe I maybe I start off with a +warm bar so u u u at zero and X I'll say + + align:start position:0% +warm bar so u u u at zero and X I'll say + + + align:start position:0% +warm bar so u u u at zero and X I'll say +it B one this way is X + + align:start position:0% +it B one this way is X + + + align:start position:0% +it B one this way is X +so I have an ordinary heated + + align:start position:0% +so I have an ordinary heated + + + align:start position:0% +so I have an ordinary heated +bar and I put it in the freezer + + align:start position:0% +bar and I put it in the freezer + + + align:start position:0% +bar and I put it in the freezer +so I insulate the side so it's The + + align:start position:0% +so I insulate the side so it's The + + + align:start position:0% +so I insulate the side so it's The +Temper the heat is escaping out the two + + align:start position:0% +Temper the heat is escaping out the two + + + align:start position:0% +Temper the heat is escaping out the two +ends out the end x equals 0 and at the + + align:start position:0% +ends out the end x equals 0 and at the + + + align:start position:0% +ends out the end x equals 0 and at the +end xal 1 and the solution will + + align:start position:0% +end xal 1 and the solution will + + + align:start position:0% +end xal 1 and the solution will +be uh this let me + + align:start position:0% +be uh this let me + + + align:start position:0% +be uh this let me +remember what the general solution + + align:start position:0% +remember what the general solution + + + align:start position:0% +remember what the general solution +looked like and I have to find these + + align:start position:0% +looked like and I have to find these + + + align:start position:0% +looked like and I have to find these +numbers okay so and those numbers of + + align:start position:0% +numbers okay so and those numbers of + + + align:start position:0% +numbers okay so and those numbers of +course the numbers are always found by + + align:start position:0% +course the numbers are always found by + + + align:start position:0% +course the numbers are always found by +matching the initial condition this is + + align:start position:0% +matching the initial condition this is + + + align:start position:0% +matching the initial condition this is +the initial this is the initial + + align:start position:0% + + + + align:start position:0% + +picture okay so I have to match that by + + align:start position:0% +picture okay so I have to match that by + + + align:start position:0% +picture okay so I have to match that by +so this is t equal 0 I have to match the + + align:start position:0% +so this is t equal 0 I have to match the + + + align:start position:0% +so this is t equal 0 I have to match the +sum of BK this is K going from 1 to + + align:start position:0% +sum of BK this is K going from 1 to + + + align:start position:0% +sum of BK this is K going from 1 to +Infinity when T is is when T is zero + + align:start position:0% +Infinity when T is is when T is zero + + + align:start position:0% +Infinity when T is is when T is zero +this is one and I just have the SK the + + align:start position:0% +this is one and I just have the SK the + + + align:start position:0% +this is one and I just have the SK the +sign of K pi x that has to + + align:start position:0% +sign of K pi x that has to + + + align:start position:0% +sign of K pi x that has to +match the + + align:start position:0% + + + + align:start position:0% + +one and when I that that from that I + + align:start position:0% +one and when I that that from that I + + + align:start position:0% +one and when I that that from that I +find the bks and then the the the final + + align:start position:0% +find the bks and then the the the final + + + align:start position:0% +find the bks and then the the the final +solution T greater than zero is uh uses + + align:start position:0% +solution T greater than zero is uh uses + + + align:start position:0% +solution T greater than zero is uh uses +those + + align:start position:0% +those + + + align:start position:0% +those +bks and we're again faced with a fora + + align:start position:0% +bks and we're again faced with a fora + + + align:start position:0% +bks and we're again faced with a fora +series problem anytime I have to find + + align:start position:0% +series problem anytime I have to find + + + align:start position:0% +series problem anytime I have to find +these coefficients this is a Fier sign + + align:start position:0% +these coefficients this is a Fier sign + + + align:start position:0% +these coefficients this is a Fier sign +series I I have only signs not cosiness + + align:start position:0% +series I I have only signs not cosiness + + + align:start position:0% +series I I have only signs not cosiness +here uh and I'm finding the coefficients + + align:start position:0% +here uh and I'm finding the coefficients + + + align:start position:0% +here uh and I'm finding the coefficients +so that they'll this will match one the + + align:start position:0% +so that they'll this will match one the + + + align:start position:0% +so that they'll this will match one the +initial condition and then for T greater + + align:start position:0% +initial condition and then for T greater + + + align:start position:0% +initial condition and then for T greater +than zero the solution U will + + align:start position:0% +than zero the solution U will + + + align:start position:0% +than zero the solution U will +be as we said a sum of these + + align:start position:0% +be as we said a sum of these + + + align:start position:0% +be as we said a sum of these +bks which come from the initial + + align:start position:0% +bks which come from the initial + + + align:start position:0% +bks which come from the initial +conditions come from this fora + + align:start position:0% +conditions come from this fora + + + align:start position:0% +conditions come from this fora +coefficients we still have to do that + + align:start position:0% +coefficients we still have to do that + + + align:start position:0% +coefficients we still have to do that +video on fora series to know what these + + align:start position:0% +video on fora series to know what these + + + align:start position:0% +video on fora series to know what these +numbers will come out to be uh times the + + align:start position:0% +numbers will come out to be uh times the + + + align:start position:0% +numbers will come out to be uh times the +e to the minus k 2 pk^ 2 T * the S of k + + align:start position:0% +e to the minus k 2 pk^ 2 T * the S of k + + + align:start position:0% +e to the minus k 2 pk^ 2 T * the S of k +piun x + + align:start position:0% +piun x + + + align:start position:0% +piun x +X you may think well that's a pretty + + align:start position:0% +X you may think well that's a pretty + + + align:start position:0% +X you may think well that's a pretty +messy solution because it's an infinite + + align:start position:0% +messy solution because it's an infinite + + + align:start position:0% +messy solution because it's an infinite +sum but it's not bad for partial + + align:start position:0% +sum but it's not bad for partial + + + align:start position:0% +sum but it's not bad for partial +differential equations we have numbers + + align:start position:0% +differential equations we have numbers + + + align:start position:0% +differential equations we have numbers +we have something depending on time and + + align:start position:0% +we have something depending on time and + + + align:start position:0% +we have something depending on time and +de decaying rapidly and something + + align:start position:0% +de decaying rapidly and something + + + align:start position:0% +de decaying rapidly and something +depending on X so that at at at uh at + + align:start position:0% +depending on X so that at at at uh at + + + align:start position:0% +depending on X so that at at at uh at +time one if I drew a picture suppose so + + align:start position:0% +time one if I drew a picture suppose so + + + align:start position:0% +time one if I drew a picture suppose so +there the heat is the temperature is + + align:start position:0% +there the heat is the temperature is + + + align:start position:0% +there the heat is the temperature is +starts out through the the whole bar at + + align:start position:0% +starts out through the the whole bar at + + + align:start position:0% +starts out through the the whole bar at +one but with these with this kind of + + align:start position:0% +one but with these with this kind of + + + align:start position:0% +one but with these with this kind of +time Decay a little later in time the + + align:start position:0% +time Decay a little later in time the + + + align:start position:0% +time Decay a little later in time the +the temperature is going to be something + + align:start position:0% +the temperature is going to be something + + + align:start position:0% +the temperature is going to be something +like that it'll be way down at the ends + + align:start position:0% +like that it'll be way down at the ends + + + align:start position:0% +like that it'll be way down at the ends +pretty low in the middle and so at some + + align:start position:0% +pretty low in the middle and so at some + + + align:start position:0% +pretty low in the middle and so at some +time T the temperature will look like + + align:start position:0% +time T the temperature will look like + + + align:start position:0% +time T the temperature will look like +that and then soon after that the + + align:start position:0% +that and then soon after that the + + + align:start position:0% +that and then soon after that the +temperature will go down to here and the + + align:start position:0% +temperature will go down to here and the + + + align:start position:0% +temperature will go down to here and the +steady state of course is the whole + + align:start position:0% +steady state of course is the whole + + + align:start position:0% +steady state of course is the whole +thing is at temperature zero so that's + + align:start position:0% +thing is at temperature zero so that's + + + align:start position:0% +thing is at temperature zero so that's +what + + align:start position:0% +what + + + align:start position:0% +what +solutions to + + align:start position:0% +solutions to + + + align:start position:0% +solutions to +the heat equation look like and this is + + align:start position:0% +the heat equation look like and this is + + + align:start position:0% +the heat equation look like and this is +the step of finding the which I didn't + + align:start position:0% +the step of finding the which I didn't + + + align:start position:0% +the step of finding the which I didn't +take this is the Fier series step of + + align:start position:0% +take this is the Fier series step of + + + align:start position:0% +take this is the Fier series step of +finding the coefficients in our infinite + + align:start position:0% +finding the coefficients in our infinite + + + align:start position:0% +finding the coefficients in our infinite +series of solutions once again we have + + align:start position:0% +series of solutions once again we have + + + align:start position:0% +series of solutions once again we have +infinitely many solutions we're talking + + align:start position:0% +infinitely many solutions we're talking + + + align:start position:0% +infinitely many solutions we're talking +about a partial differential equation we + + align:start position:0% +about a partial differential equation we + + + align:start position:0% +about a partial differential equation we +have a whole function to match so we + + align:start position:0% +have a whole function to match so we + + + align:start position:0% +have a whole function to match so we +need all of those and 4A series is is + + align:start position:0% +need all of those and 4A series is is + + + align:start position:0% +need all of those and 4A series is is +the is the mat it g tells us how to do + + align:start position:0% +the is the mat it g tells us how to do + + + align:start position:0% +the is the mat it g tells us how to do +that matching how to find these bks so + + align:start position:0% +that matching how to find these bks so + + + align:start position:0% +that matching how to find these bks so +that's a separate and important question + + align:start position:0% +that's a separate and important question + + + align:start position:0% +that's a separate and important question +for EA series thank you \ No newline at end of file diff --git a/ikaTTZEY5VE.txt b/ikaTTZEY5VE.txt new file mode 100644 index 0000000000000000000000000000000000000000..c8afe473883ec92235fd83bf304b01439721cc0a --- /dev/null +++ b/ikaTTZEY5VE.txt @@ -0,0 +1,8883 @@ +align:start position:0% + +okay so what I wanted to + + align:start position:0% +okay so what I wanted to + + + align:start position:0% +okay so what I wanted to +do uh for the next few lectures is talk + + align:start position:0% +do uh for the next few lectures is talk + + + align:start position:0% +do uh for the next few lectures is talk +a bit about control of power converters + + align:start position:0% +a bit about control of power converters + + + align:start position:0% +a bit about control of power converters +okay and actually I'm more going to talk + + align:start position:0% +okay and actually I'm more going to talk + + + align:start position:0% +okay and actually I'm more going to talk +about modeling of power converters than + + align:start position:0% +about modeling of power converters than + + + align:start position:0% +about modeling of power converters than +control of power converters because I + + align:start position:0% +control of power converters because I + + + align:start position:0% +control of power converters because I +can't really teach te you know control + + align:start position:0% +can't really teach te you know control + + + align:start position:0% +can't really teach te you know control +theory in this class if you haven't had + + align:start position:0% +theory in this class if you haven't had + + + align:start position:0% +theory in this class if you haven't had +a control class yet um it's really time + + align:start position:0% +a control class yet um it's really time + + + align:start position:0% +a control class yet um it's really time +to go out and take one because matter + + align:start position:0% +to go out and take one because matter + + + align:start position:0% +to go out and take one because matter +what you're going to do you're really + + align:start position:0% +what you're going to do you're really + + + align:start position:0% +what you're going to do you're really +probably going to need to uh understand + + align:start position:0% +probably going to need to uh understand + + + align:start position:0% +probably going to need to uh understand +feedback control but what we can do in + + align:start position:0% +feedback control but what we can do in + + + align:start position:0% +feedback control but what we can do in +this class is show you how one can model + + align:start position:0% +this class is show you how one can model + + + align:start position:0% +this class is show you how one can model +power converters to put them to get a + + align:start position:0% +power converters to put them to get a + + + align:start position:0% +power converters to put them to get a +model in the format that you can use it + + align:start position:0% +model in the format that you can use it + + + align:start position:0% +model in the format that you can use it +for feedback control and do basic + + align:start position:0% +for feedback control and do basic + + + align:start position:0% +for feedback control and do basic +control okay so let's think about + + align:start position:0% +control okay so let's think about + + + align:start position:0% +control okay so let's think about +a power converter let's start off with + + align:start position:0% +a power converter let's start off with + + + align:start position:0% +a power converter let's start off with +you know our our friendly neighborhood + + align:start position:0% +you know our our friendly neighborhood + + + align:start position:0% +you know our our friendly neighborhood +boost converter right so maybe I have + + align:start position:0% +boost converter right so maybe I have + + + align:start position:0% +boost converter right so maybe I have +some input voltage + + align:start position:0% +some input voltage + + + align:start position:0% +some input voltage +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +VN I'll switch it with some switching + + align:start position:0% +VN I'll switch it with some switching + + + align:start position:0% +VN I'll switch it with some switching +waveform Q of + + align:start position:0% +waveform Q of + + + align:start position:0% +waveform Q of +T and then I'm going to have a diode I + + align:start position:0% +T and then I'm going to have a diode I + + + align:start position:0% +T and then I'm going to have a diode I +will have a capacitor and the converter + + align:start position:0% +will have a capacitor and the converter + + + align:start position:0% +will have a capacitor and the converter +ends here and then somewhere you know we + + align:start position:0% +ends here and then somewhere you know we + + + align:start position:0% +ends here and then somewhere you know we +usually + + align:start position:0% +usually + + + align:start position:0% +usually +show RL right and I have my input + + align:start position:0% +show RL right and I have my input + + + align:start position:0% +show RL right and I have my input +voltage and I have my output voltage V + + align:start position:0% +voltage and I have my output voltage V + + + align:start position:0% +voltage and I have my output voltage V +out okay + + align:start position:0% +out okay + + + align:start position:0% +out okay +now I usually in my examples just just + + align:start position:0% +now I usually in my examples just just + + + align:start position:0% +now I usually in my examples just just +by way of an aside I usually show a + + align:start position:0% +by way of an aside I usually show a + + + align:start position:0% +by way of an aside I usually show a +resistive load a lot of loads are + + align:start position:0% +resistive load a lot of loads are + + + align:start position:0% +resistive load a lot of loads are +resistive right but there's no guarantee + + align:start position:0% +resistive right but there's no guarantee + + + align:start position:0% +resistive right but there's no guarantee +that you know in an actual application + + align:start position:0% +that you know in an actual application + + + align:start position:0% +that you know in an actual application +your load looks like a resistor right it + + align:start position:0% +your load looks like a resistor right it + + + align:start position:0% +your load looks like a resistor right it +could look like + + align:start position:0% +could look like + + + align:start position:0% +could look like +whatever uh maybe a lot of + + align:start position:0% +whatever uh maybe a lot of + + + align:start position:0% +whatever uh maybe a lot of +loads you know you might represent as + + align:start position:0% +loads you know you might represent as + + + align:start position:0% +loads you know you might represent as +some maybe Norton equivalent right where + + align:start position:0% +some maybe Norton equivalent right where + + + align:start position:0% +some maybe Norton equivalent right where +there's some constant current component + + align:start position:0% +there's some constant current component + + + align:start position:0% +there's some constant current component +and some resistive current component + + align:start position:0% +and some resistive current component + + + align:start position:0% +and some resistive current component +right and I'm just doing the simplified + + align:start position:0% +right and I'm just doing the simplified + + + align:start position:0% +right and I'm just doing the simplified +case where the Norton source is zero and + + align:start position:0% +case where the Norton source is zero and + + + align:start position:0% +case where the Norton source is zero and +the resistance is RL okay but I that's + + align:start position:0% +the resistance is RL okay but I that's + + + align:start position:0% +the resistance is RL okay but I that's +just a way of saying in general you know + + align:start position:0% +just a way of saying in general you know + + + align:start position:0% +just a way of saying in general you know +you would worry about exactly what the + + align:start position:0% +you would worry about exactly what the + + + align:start position:0% +you would worry about exactly what the +load looks like not just in terms of how + + align:start position:0% +load looks like not just in terms of how + + + align:start position:0% +load looks like not just in terms of how +much current does it draw but exactly + + align:start position:0% +much current does it draw but exactly + + + align:start position:0% +much current does it draw but exactly +what the Lo look like can affect the + + align:start position:0% +what the Lo look like can affect the + + + align:start position:0% +what the Lo look like can affect the +Dynamics okay but for Simplicity let's + + align:start position:0% +Dynamics okay but for Simplicity let's + + + align:start position:0% +Dynamics okay but for Simplicity let's +just talk about resistive loads which is + + align:start position:0% +just talk about resistive loads which is + + + align:start position:0% +just talk about resistive loads which is +a very common case + + align:start position:0% +a very common case + + + align:start position:0% +a very common case +Okay um all right uh you know what do we + + align:start position:0% +Okay um all right uh you know what do we + + + align:start position:0% +Okay um all right uh you know what do we +have to do in a typical power converter + + align:start position:0% +have to do in a typical power converter + + + align:start position:0% +have to do in a typical power converter +application right we want to usually + + align:start position:0% +application right we want to usually + + + align:start position:0% +application right we want to usually +regulate the output voltage to be + + align:start position:0% +regulate the output voltage to be + + + align:start position:0% +regulate the output voltage to be +something we want okay so we want to + + align:start position:0% + + + + align:start position:0% + +make you know V out go to + + align:start position:0% +make you know V out go to + + + align:start position:0% +make you know V out go to +some reference voltage that I'll call + + align:start position:0% +some reference voltage that I'll call + + + align:start position:0% +some reference voltage that I'll call +vref okay vref might be fixed it might + + align:start position:0% +vref okay vref might be fixed it might + + + align:start position:0% +vref okay vref might be fixed it might +be you know I want 12 volts output all + + align:start position:0% +be you know I want 12 volts output all + + + align:start position:0% +be you know I want 12 volts output all +day long or it may be something that you + + align:start position:0% +day long or it may be something that you + + + align:start position:0% +day long or it may be something that you +dynamically vary based on some other + + align:start position:0% +dynamically vary based on some other + + + align:start position:0% +dynamically vary based on some other +consideration that we're not going to + + align:start position:0% +consideration that we're not going to + + + align:start position:0% +consideration that we're not going to +talk about right so it could be a fixed + + align:start position:0% +talk about right so it could be a fixed + + + align:start position:0% +talk about right so it could be a fixed +or a variable reference but for the + + align:start position:0% +or a variable reference but for the + + + align:start position:0% +or a variable reference but for the +present time let's just assume I want to + + align:start position:0% +present time let's just assume I want to + + + align:start position:0% +present time let's just assume I want to +get my output in my converter to be some + + align:start position:0% +get my output in my converter to be some + + + align:start position:0% +get my output in my converter to be some +fixed value that I would like it to be + + align:start position:0% +fixed value that I would like it to be + + + align:start position:0% +fixed value that I would like it to be +you know if I'm creating a 12vt power I + + align:start position:0% +you know if I'm creating a 12vt power I + + + align:start position:0% +you know if I'm creating a 12vt power I +want it to be 12 volts okay and we have + + align:start position:0% +want it to be 12 volts okay and we have + + + align:start position:0% +want it to be 12 volts okay and we have +to keep the output voltage closer at the + + align:start position:0% +to keep the output voltage closer at the + + + align:start position:0% +to keep the output voltage closer at the +reference voltage under a wide variety + + align:start position:0% +reference voltage under a wide variety + + + align:start position:0% +reference voltage under a wide variety +of conditions and this is where Power + + align:start position:0% +of conditions and this is where Power + + + align:start position:0% +of conditions and this is where Power +Electronics is challenging + + align:start position:0% +Electronics is challenging + + + align:start position:0% +Electronics is challenging +firstly for variations in + + align:start position:0% + + + + align:start position:0% + +load so maybe I would have RL + + align:start position:0% +load so maybe I would have RL + + + align:start position:0% +load so maybe I would have RL +Min less than what RL is less than RL + + align:start position:0% +Min less than what RL is less than RL + + + align:start position:0% +Min less than what RL is less than RL +Max right right so this would sort of be + + align:start position:0% +Max right right so this would sort of be + + + align:start position:0% +Max right right so this would sort of be +heavy + + align:start position:0% + + + + align:start position:0% + +load right because the lowest resistance + + align:start position:0% +load right because the lowest resistance + + + align:start position:0% +load right because the lowest resistance +gives me the highest power and this + + align:start position:0% +gives me the highest power and this + + + align:start position:0% +gives me the highest power and this +might be light + + align:start position:0% + + + + align:start position:0% + +load okay I also need to keep V out near + + align:start position:0% +load okay I also need to keep V out near + + + align:start position:0% +load okay I also need to keep V out near +V reference in terms of for + + align:start position:0% + + + + align:start position:0% + +variations in VN so maybe there's a VN + + align:start position:0% +variations in VN so maybe there's a VN + + + align:start position:0% +variations in VN so maybe there's a VN +Min less than VN less than VN + + align:start position:0% +Min less than VN less than VN + + + align:start position:0% +Min less than VN less than VN +Max right that I got to deal with why + + align:start position:0% +Max right that I got to deal with why + + + align:start position:0% +Max right that I got to deal with why +why do I have to worry about those well + + align:start position:0% +why do I have to worry about those well + + + align:start position:0% +why do I have to worry about those well +you know my load's not always going to + + align:start position:0% +you know my load's not always going to + + + align:start position:0% +you know my load's not always going to +be the same maybe this is controlling a + + align:start position:0% +be the same maybe this is controlling a + + + align:start position:0% +be the same maybe this is controlling a +voltage which goes to a bunch of + + align:start position:0% +voltage which goes to a bunch of + + + align:start position:0% +voltage which goes to a bunch of +microprocessors or other things or + + align:start position:0% +microprocessors or other things or + + + align:start position:0% +microprocessors or other things or +actuators and they're turning on and off + + align:start position:0% +actuators and they're turning on and off + + + align:start position:0% +actuators and they're turning on and off +so the effective resistance the effect + + align:start position:0% +so the effective resistance the effect + + + align:start position:0% +so the effective resistance the effect +of power I have to supply varies even at + + align:start position:0% +of power I have to supply varies even at + + + align:start position:0% +of power I have to supply varies even at +fixed voltage and here you know maybe + + align:start position:0% +fixed voltage and here you know maybe + + + align:start position:0% +fixed voltage and here you know maybe +I'm powered from a battery and the + + align:start position:0% +I'm powered from a battery and the + + + align:start position:0% +I'm powered from a battery and the +battery discharges over time or I'm + + align:start position:0% +battery discharges over time or I'm + + + align:start position:0% +battery discharges over time or I'm +charging or whatever so there's going to + + align:start position:0% +charging or whatever so there's going to + + + align:start position:0% +charging or whatever so there's going to +be some input range input voltage range + + align:start position:0% +be some input range input voltage range + + + align:start position:0% +be some input range input voltage range +over which this converter is designed to + + align:start position:0% +over which this converter is designed to + + + align:start position:0% +over which this converter is designed to +reject that as a disturbance and just + + align:start position:0% +reject that as a disturbance and just + + + align:start position:0% +reject that as a disturbance and just +keep the output where I want it + + align:start position:0% +keep the output where I want it + + + align:start position:0% +keep the output where I want it +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now so far we've spent a lot of time + + align:start position:0% +now so far we've spent a lot of time + + + align:start position:0% +now so far we've spent a lot of time +talking about the steady state operation + + align:start position:0% +talking about the steady state operation + + + align:start position:0% +talking about the steady state operation +right and that's usually always the + + align:start position:0% +right and that's usually always the + + + align:start position:0% +right and that's usually always the +first thing I look at because it tells + + align:start position:0% +first thing I look at because it tells + + + align:start position:0% +first thing I look at because it tells +me when things are sitting at some place + + align:start position:0% +me when things are sitting at some place + + + align:start position:0% +me when things are sitting at some place +you know some load resistance some input + + align:start position:0% +you know some load resistance some input + + + align:start position:0% +you know some load resistance some input +voltage what's it going to do and we + + align:start position:0% +voltage what's it going to do and we + + + align:start position:0% +voltage what's it going to do and we +said for the Boost converter what I get + + align:start position:0% +said for the Boost converter what I get + + + align:start position:0% +said for the Boost converter what I get +is uh V out is equal to V in over 1 + + align:start position:0% +is uh V out is equal to V in over 1 + + + align:start position:0% +is uh V out is equal to V in over 1 +minus d right so this is the steady + + align:start position:0% +minus d right so this is the steady + + + align:start position:0% +minus d right so this is the steady +state relationship this is n + + align:start position:0% +state relationship this is n + + + align:start position:0% +state relationship this is n +PSS right in periodic steady state once + + align:start position:0% +PSS right in periodic steady state once + + + align:start position:0% +PSS right in periodic steady state once +we've settled down this converter ought + + align:start position:0% +we've settled down this converter ought + + + align:start position:0% +we've settled down this converter ought +to do this so if I control the duty + + align:start position:0% +to do this so if I control the duty + + + align:start position:0% +to do this so if I control the duty +ratio of my switch Q of t + + align:start position:0% +ratio of my switch Q of t + + + align:start position:0% +ratio of my switch Q of t +to this value this is what I should get + + align:start position:0% +to this value this is what I should get + + + align:start position:0% +to this value this is what I should get +for an output voltage + + align:start position:0% +for an output voltage + + + align:start position:0% +for an output voltage +okay so um you might think okay maybe I + + align:start position:0% +okay so um you might think okay maybe I + + + align:start position:0% +okay so um you might think okay maybe I +could just measure the input + + align:start position:0% +could just measure the input + + + align:start position:0% +could just measure the input +voltage set a duty ratio and get the + + align:start position:0% +voltage set a duty ratio and get the + + + align:start position:0% +voltage set a duty ratio and get the +output voltage I want and you know + + align:start position:0% +output voltage I want and you know + + + align:start position:0% +output voltage I want and you know +that's sort of the end of the day but + + align:start position:0% +that's sort of the end of the day but + + + align:start position:0% +that's sort of the end of the day but +there's two problems with that one is + + align:start position:0% +there's two problems with that one is + + + align:start position:0% +there's two problems with that one is +this is only in periodic steady state + + align:start position:0% +this is only in periodic steady state + + + align:start position:0% +this is only in periodic steady state +and it doesn't say how things will + + align:start position:0% +and it doesn't say how things will + + + align:start position:0% +and it doesn't say how things will +change transiently in between periodic C + + align:start position:0% +change transiently in between periodic C + + + align:start position:0% +change transiently in between periodic C +State conditions and I really care about + + align:start position:0% +State conditions and I really care about + + + align:start position:0% +State conditions and I really care about +that because if the voltage goes you + + align:start position:0% +that because if the voltage goes you + + + align:start position:0% +that because if the voltage goes you +know if I if I decide to change the load + + align:start position:0% +know if I if I decide to change the load + + + align:start position:0% +know if I if I decide to change the load +the voltage goes wild until it settles + + align:start position:0% +the voltage goes wild until it settles + + + align:start position:0% +the voltage goes wild until it settles +down I'm probably not going to be happy + + align:start position:0% +down I'm probably not going to be happy + + + align:start position:0% +down I'm probably not going to be happy +uh the other thing about this is this is + + align:start position:0% +uh the other thing about this is this is + + + align:start position:0% +uh the other thing about this is this is +an idealized relationship right when we + + align:start position:0% +an idealized relationship right when we + + + align:start position:0% +an idealized relationship right when we +derived this we did it by volt seconds + + align:start position:0% +derived this we did it by volt seconds + + + align:start position:0% +derived this we did it by volt seconds +balance across this inductor I pretended + + align:start position:0% +balance across this inductor I pretended + + + align:start position:0% +balance across this inductor I pretended +the inductor had no resistance I ignored + + align:start position:0% +the inductor had no resistance I ignored + + + align:start position:0% +the inductor had no resistance I ignored +the diode drop I ignored a whole bunch + + align:start position:0% +the diode drop I ignored a whole bunch + + + align:start position:0% +the diode drop I ignored a whole bunch +of things which don't matter for getting + + align:start position:0% +of things which don't matter for getting + + + align:start position:0% +of things which don't matter for getting +in a Pro imate relationship but they do + + align:start position:0% +in a Pro imate relationship but they do + + + align:start position:0% +in a Pro imate relationship but they do +matter if I need to control this to you + + align:start position:0% +matter if I need to control this to you + + + align:start position:0% +matter if I need to control this to you +know 12 Vols plus or minus + + align:start position:0% +know 12 Vols plus or minus + + + align:start position:0% +know 12 Vols plus or minus +2% the model's just not good enough + + align:start position:0% +2% the model's just not good enough + + + align:start position:0% +2% the model's just not good enough +right I need some better way to get my + + align:start position:0% +right I need some better way to get my + + + align:start position:0% +right I need some better way to get my +converter to get where I want it to be + + align:start position:0% +converter to get where I want it to be + + + align:start position:0% +converter to get where I want it to be +all right and maintain it there under + + align:start position:0% +all right and maintain it there under + + + align:start position:0% +all right and maintain it there under +variations like this okay any questions + + align:start position:0% +variations like this okay any questions + + + align:start position:0% +variations like this okay any questions +about + + align:start position:0% + + + + align:start position:0% + +that just to illustrate that what I've + + align:start position:0% +that just to illustrate that what I've + + + align:start position:0% +that just to illustrate that what I've +got here is a spice + + align:start position:0% + + + + align:start position:0% + +simulation of a boost + + align:start position:0% +simulation of a boost + + + align:start position:0% +simulation of a boost +converter uh which is undergoing a load + + align:start position:0% +converter uh which is undergoing a load + + + align:start position:0% +converter uh which is undergoing a load +transient okay so what's happening in + + align:start position:0% +transient okay so what's happening in + + + align:start position:0% +transient okay so what's happening in +this is here at some time actually 1.4 + + align:start position:0% +this is here at some time actually 1.4 + + + align:start position:0% +this is here at some time actually 1.4 +milliseconds we had a 5 ohm we + + align:start position:0% +milliseconds we had a 5 ohm we + + + align:start position:0% +milliseconds we had a 5 ohm we +originally had a 5 ohm load on the + + align:start position:0% +originally had a 5 ohm load on the + + + align:start position:0% +originally had a 5 ohm load on the +converter and we put in another 5 ohm + + align:start position:0% +converter and we put in another 5 ohm + + + align:start position:0% +converter and we put in another 5 ohm +load right so it's like some new load + + align:start position:0% +load right so it's like some new load + + + align:start position:0% +load right so it's like some new load +has come in and I and I'm I'm in this + + align:start position:0% +has come in and I and I'm I'm in this + + + align:start position:0% +has come in and I and I'm I'm in this +example we're just holding the duty + + align:start position:0% +example we're just holding the duty + + + align:start position:0% +example we're just holding the duty +ratio of the converter constant right so + + align:start position:0% +ratio of the converter constant right so + + + align:start position:0% +ratio of the converter constant right so +we kind of expect that barring a lot of + + align:start position:0% +we kind of expect that barring a lot of + + + align:start position:0% +we kind of expect that barring a lot of +second order effects the output voltage + + align:start position:0% +second order effects the output voltage + + + align:start position:0% +second order effects the output voltage +should go back to the same thing in + + align:start position:0% +should go back to the same thing in + + + align:start position:0% +should go back to the same thing in +periodic steady state but clearly if the + + align:start position:0% +periodic steady state but clearly if the + + + align:start position:0% +periodic steady state but clearly if the +output voltage is going to be the + + align:start position:0% +output voltage is going to be the + + + align:start position:0% +output voltage is going to be the +same and I've got smaller net resistance + + align:start position:0% +same and I've got smaller net resistance + + + align:start position:0% +same and I've got smaller net resistance +on it because I've have the net + + align:start position:0% +on it because I've have the net + + + align:start position:0% +on it because I've have the net +resistance the power has to go up the + + align:start position:0% +resistance the power has to go up the + + + align:start position:0% +resistance the power has to go up the +current has to go up right so things + + align:start position:0% +current has to go up right so things + + + align:start position:0% +current has to go up right so things +have to change and that's what we see + + align:start position:0% +have to change and that's what we see + + + align:start position:0% +have to change and that's what we see +happening right so this Trace down here + + align:start position:0% +happening right so this Trace down here + + + align:start position:0% +happening right so this Trace down here +is the input current so the input + + align:start position:0% +is the input current so the input + + + align:start position:0% +is the input current so the input +current was sitting on average around + + align:start position:0% +current was sitting on average around + + + align:start position:0% +current was sitting on average around +you know 12 amps I go through some + + align:start position:0% +you know 12 amps I go through some + + + align:start position:0% +you know 12 amps I go through some +transient and I end up around 24 amps + + align:start position:0% +transient and I end up around 24 amps + + + align:start position:0% +transient and I end up around 24 amps +okay the output voltage had been sitting + + align:start position:0% +okay the output voltage had been sitting + + + align:start position:0% +okay the output voltage had been sitting +at like 22 volts goes through some + + align:start position:0% +at like 22 volts goes through some + + + align:start position:0% +at like 22 volts goes through some +transient and I get back to sort of 22 + + align:start position:0% +transient and I get back to sort of 22 + + + align:start position:0% +transient and I get back to sort of 22 +volts right because it's running it + + align:start position:0% +volts right because it's running it + + + align:start position:0% +volts right because it's running it +fixed Duty ratio all + + align:start position:0% +fixed Duty ratio all + + + align:start position:0% +fixed Duty ratio all +right so what we see here is the the + + align:start position:0% +right so what we see here is the the + + + align:start position:0% +right so what we see here is the the +sort of the stuff we we've skipped over + + align:start position:0% +sort of the stuff we we've skipped over + + + align:start position:0% +sort of the stuff we we've skipped over +so far right we we know we could + + align:start position:0% +so far right we we know we could + + + align:start position:0% +so far right we we know we could +calculate based on periodic St say you + + align:start position:0% +calculate based on periodic St say you + + + align:start position:0% +calculate based on periodic St say you +know say the the output capacitor + + align:start position:0% +know say the the output capacitor + + + align:start position:0% +know say the the output capacitor +voltage and the average inductor current + + align:start position:0% +voltage and the average inductor current + + + align:start position:0% +voltage and the average inductor current +in both conditions but we haven't + + align:start position:0% +in both conditions but we haven't + + + align:start position:0% +in both conditions but we haven't +accounted for how does it trans + + align:start position:0% +accounted for how does it trans + + + align:start position:0% +accounted for how does it trans +transiently go between those conditions + + align:start position:0% +transiently go between those conditions + + + align:start position:0% +transiently go between those conditions +okay and that's what we have to know um + + align:start position:0% +okay and that's what we have to know um + + + align:start position:0% +okay and that's what we have to know um +in order to sort of make our system + + align:start position:0% +in order to sort of make our system + + + align:start position:0% +in order to sort of make our system +happy okay and so that's what we're + + align:start position:0% +happy okay and so that's what we're + + + align:start position:0% +happy okay and so that's what we're +going to focus on and i' and I'd like + + align:start position:0% +going to focus on and i' and I'd like + + + align:start position:0% +going to focus on and i' and I'd like +you to um notice that this resp response + + align:start position:0% +you to um notice that this resp response + + + align:start position:0% +you to um notice that this resp response +looks like sort of like a second order + + align:start position:0% +looks like sort of like a second order + + + align:start position:0% +looks like sort of like a second order +system + + align:start position:0% +system + + + align:start position:0% +system +right kind of has a looks sort of like a + + align:start position:0% +right kind of has a looks sort of like a + + + align:start position:0% +right kind of has a looks sort of like a +damp LC oscillation sort of which is not + + align:start position:0% +damp LC oscillation sort of which is not + + + align:start position:0% +damp LC oscillation sort of which is not +surprising right because I've got one C + + align:start position:0% +surprising right because I've got one C + + + align:start position:0% +surprising right because I've got one C +and one L so and you know there's load + + align:start position:0% +and one L so and you know there's load + + + align:start position:0% +and one L so and you know there's load +on it so Energy's been taken out of it + + align:start position:0% +on it so Energy's been taken out of it + + + align:start position:0% +on it so Energy's been taken out of it +so maybe that's not surprising the + + align:start position:0% +so maybe that's not surprising the + + + align:start position:0% +so maybe that's not surprising the +question is you know what is this thing + + align:start position:0% +question is you know what is this thing + + + align:start position:0% +question is you know what is this thing +look like + + align:start position:0% +look like + + + align:start position:0% +look like +okay so how would I control this thing + + align:start position:0% +okay so how would I control this thing + + + align:start position:0% +okay so how would I control this thing +in the real world I'd use feedback + + align:start position:0% +in the real world I'd use feedback + + + align:start position:0% +in the real world I'd use feedback +control + + align:start position:0% +control + + + align:start position:0% +control +okay so what are we going to do we're + + align:start position:0% +okay so what are we going to do we're + + + align:start position:0% +okay so what are we going to do we're +going to say I have some reference + + align:start position:0% +going to say I have some reference + + + align:start position:0% +going to say I have some reference +voltage + + align:start position:0% + + + + align:start position:0% + +vref that I want my converter to go to + + align:start position:0% +vref that I want my converter to go to + + + align:start position:0% +vref that I want my converter to go to +and I provide that voltage reference and + + align:start position:0% +and I provide that voltage reference and + + + align:start position:0% +and I provide that voltage reference and +I'm going to compare that voltage + + align:start position:0% +I'm going to compare that voltage + + + align:start position:0% +I'm going to compare that voltage +reference to the output voltage V + + align:start position:0% +reference to the output voltage V + + + align:start position:0% +reference to the output voltage V +out right and I'm going to generate an + + align:start position:0% +out right and I'm going to generate an + + + align:start position:0% +out right and I'm going to generate an +error + + align:start position:0% + + + + align:start position:0% + +between those + + align:start position:0% +between those + + + align:start position:0% +between those +two I'll take that error and feed it + + align:start position:0% +two I'll take that error and feed it + + + align:start position:0% +two I'll take that error and feed it +into a high gain + + align:start position:0% + + + + align:start position:0% + +compensator maybe I could represent that + + align:start position:0% +compensator maybe I could represent that + + + align:start position:0% +compensator maybe I could represent that +with a transfer function GC of s this + + align:start position:0% +with a transfer function GC of s this + + + align:start position:0% +with a transfer function GC of s this +might be for example a uh Pi D + + align:start position:0% + + + + align:start position:0% + +controller or something + + align:start position:0% +controller or something + + + align:start position:0% +controller or something +fancier depends on the topology right + + align:start position:0% +fancier depends on the topology right + + + align:start position:0% +fancier depends on the topology right +this is where + + align:start position:0% +this is where + + + align:start position:0% +this is where +having a control class but you might + + align:start position:0% +having a control class but you might + + + align:start position:0% +having a control class but you might +think what this does is if I have error + + align:start position:0% +think what this does is if I have error + + + align:start position:0% +think what this does is if I have error +I amplify that error by some amount + + align:start position:0% +I amplify that error by some amount + + + align:start position:0% +I amplify that error by some amount +either proportionally or look at the + + align:start position:0% +either proportionally or look at the + + + align:start position:0% +either proportionally or look at the +integral of the error something like + + align:start position:0% +integral of the error something like + + + align:start position:0% +integral of the error something like +that and generate an output which I'm + + align:start position:0% +that and generate an output which I'm + + + align:start position:0% +that and generate an output which I'm +going to call + + align:start position:0% + + + + align:start position:0% + +VD what is this signal this is usually a + + align:start position:0% +VD what is this signal this is usually a + + + align:start position:0% +VD what is this signal this is usually a +voltage although I could represent it + + align:start position:0% +voltage although I could represent it + + + align:start position:0% +voltage although I could represent it +with a + + align:start position:0% +with a + + + align:start position:0% +with a +current it's a + + align:start position:0% +current it's a + + + align:start position:0% +current it's a +voltage representing + + align:start position:0% + + + + align:start position:0% + +the duty ratio I + + align:start position:0% +the duty ratio I + + + align:start position:0% +the duty ratio I +want okay this then now I have a voltage + + align:start position:0% +want okay this then now I have a voltage + + + align:start position:0% +want okay this then now I have a voltage +representing Duty ratio I have to put + + align:start position:0% +representing Duty ratio I have to put + + + align:start position:0% +representing Duty ratio I have to put +this into some pwm circuit pulse withth + + align:start position:0% +this into some pwm circuit pulse withth + + + align:start position:0% +this into some pwm circuit pulse withth +modulation circuit that's going to give + + align:start position:0% +modulation circuit that's going to give + + + align:start position:0% +modulation circuit that's going to give +me Q of + + align:start position:0% + + + + align:start position:0% + +T right because if I look at up there + + align:start position:0% +T right because if I look at up there + + + align:start position:0% +T right because if I look at up there +I'm talking about in terms of Duty ratio + + align:start position:0% +I'm talking about in terms of Duty ratio + + + align:start position:0% +I'm talking about in terms of Duty ratio +but the actual signal going to my switch + + align:start position:0% +but the actual signal going to my switch + + + align:start position:0% +but the actual signal going to my switch +is some qft or or some Amplified version + + align:start position:0% +is some qft or or some Amplified version + + + align:start position:0% +is some qft or or some Amplified version +of qft from a gate drive that's turning + + align:start position:0% +of qft from a gate drive that's turning + + + align:start position:0% +of qft from a gate drive that's turning +the switch on and off at the right Duty + + align:start position:0% +the switch on and off at the right Duty + + + align:start position:0% +the switch on and off at the right Duty +ratio so the input of this is some value + + align:start position:0% +ratio so the input of this is some value + + + align:start position:0% +ratio so the input of this is some value +of Duty ratio I want the output of this + + align:start position:0% +of Duty ratio I want the output of this + + + align:start position:0% +of Duty ratio I want the output of this +is some pwm waveform switching at period + + align:start position:0% +is some pwm waveform switching at period + + + align:start position:0% +is some pwm waveform switching at period +t with an on + + align:start position:0% +t with an on + + + align:start position:0% +t with an on +time that's + + align:start position:0% +time that's + + + align:start position:0% +time that's +DT okay this then goes into my actual + + align:start position:0% + + + + align:start position:0% + +converter which also you know if you + + align:start position:0% +converter which also you know if you + + + align:start position:0% +converter which also you know if you +think about it has inputs of VN + + align:start position:0% +think about it has inputs of VN + + + align:start position:0% +think about it has inputs of VN +and it's being affected by what the RL + + align:start position:0% +and it's being affected by what the RL + + + align:start position:0% +and it's being affected by what the RL +is right and then you know its state + + align:start position:0% +is right and then you know its state + + + align:start position:0% +is right and then you know its state +variables are the inductor current and + + align:start position:0% +variables are the inductor current and + + + align:start position:0% +variables are the inductor current and +the output voltage which is also the + + align:start position:0% +the output voltage which is also the + + + align:start position:0% +the output voltage which is also the +capacitor voltage V out and that's what + + align:start position:0% +capacitor voltage V out and that's what + + + align:start position:0% +capacitor voltage V out and that's what +I'm feeding around back here okay so + + align:start position:0% +I'm feeding around back here okay so + + + align:start position:0% +I'm feeding around back here okay so +this is a typical closed loop control + + align:start position:0% +this is a typical closed loop control + + + align:start position:0% +this is a typical closed loop control +system right if V out gets smaller than + + align:start position:0% +system right if V out gets smaller than + + + align:start position:0% +system right if V out gets smaller than +the reference voltage vrra goes up I + + align:start position:0% +the reference voltage vrra goes up I + + + align:start position:0% +the reference voltage vrra goes up I +amplify that my duty ratio goes up and + + align:start position:0% +amplify that my duty ratio goes up and + + + align:start position:0% +amplify that my duty ratio goes up and +when my duty ratio goes up my output + + align:start position:0% +when my duty ratio goes up my output + + + align:start position:0% +when my duty ratio goes up my output +voltage goes up and you know I close the + + align:start position:0% +voltage goes up and you know I close the + + + align:start position:0% +voltage goes up and you know I close the +loop and eventually hopefully this + + align:start position:0% +loop and eventually hopefully this + + + align:start position:0% +loop and eventually hopefully this +settles to V Out close to + + align:start position:0% +settles to V Out close to + + + align:start position:0% +settles to V Out close to +vref okay any questions about that + + align:start position:0% + + + + align:start position:0% + +picture just out of curiosity how many + + align:start position:0% +picture just out of curiosity how many + + + align:start position:0% +picture just out of curiosity how many +people here have had either a classical + + align:start position:0% +people here have had either a classical + + + align:start position:0% +people here have had either a classical +or state space control + + align:start position:0% +or state space control + + + align:start position:0% +or state space control +class all right good good fraction good + + align:start position:0% +class all right good good fraction good + + + align:start position:0% +class all right good good fraction good +let's make that fraction 100% next year + + align:start position:0% +let's make that fraction 100% next year + + + align:start position:0% +let's make that fraction 100% next year +because you really you really want to + + align:start position:0% +because you really you really want to + + + align:start position:0% +because you really you really want to +know this no matter what you do + + align:start position:0% +know this no matter what you do + + + align:start position:0% +know this no matter what you do +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um what you know this is a standard kind + + align:start position:0% +um what you know this is a standard kind + + + align:start position:0% +um what you know this is a standard kind +of feedback + + align:start position:0% +of feedback + + + align:start position:0% +of feedback +system okay what we need to do this + + align:start position:0% +system okay what we need to do this + + + align:start position:0% +system okay what we need to do this +right if I put in the wrong compensator + + align:start position:0% +right if I put in the wrong compensator + + + align:start position:0% +right if I put in the wrong compensator +and I put feedback I could make this + + align:start position:0% +and I put feedback I could make this + + + align:start position:0% +and I put feedback I could make this +thing oscillate and go + + align:start position:0% +thing oscillate and go + + + align:start position:0% +thing oscillate and go +unstable right we we've all seen the + + align:start position:0% +unstable right we we've all seen the + + + align:start position:0% +unstable right we we've all seen the +effects of um bad feedback like when you + + align:start position:0% +effects of um bad feedback like when you + + + align:start position:0% +effects of um bad feedback like when you +put your microphone too close to your + + align:start position:0% +put your microphone too close to your + + + align:start position:0% +put your microphone too close to your +speaker right and suddenly the thing + + align:start position:0% +speaker right and suddenly the thing + + + align:start position:0% +speaker right and suddenly the thing +goes crazy right and you can certainly + + align:start position:0% +goes crazy right and you can certainly + + + align:start position:0% +goes crazy right and you can certainly +make a power converter go crazy if + + align:start position:0% +make a power converter go crazy if + + + align:start position:0% +make a power converter go crazy if +you're not careful right um and what we + + align:start position:0% +you're not careful right um and what we + + + align:start position:0% +you're not careful right um and what we +need to know in order to make this work + + align:start position:0% +need to know in order to make this work + + + align:start position:0% +need to know in order to make this work +is some + + align:start position:0% +is some + + + align:start position:0% +is some +model that basically + + align:start position:0% +model that basically + + + align:start position:0% +model that basically +says you know as I'm changing my duty + + align:start position:0% +says you know as I'm changing my duty + + + align:start position:0% +says you know as I'm changing my duty +Ratio or something else like the load + + align:start position:0% +Ratio or something else like the load + + + align:start position:0% +Ratio or something else like the load +resistor how does the this dynamically + + align:start position:0% +resistor how does the this dynamically + + + align:start position:0% +resistor how does the this dynamically +vary right if I know that then I can + + align:start position:0% +vary right if I know that then I can + + + align:start position:0% +vary right if I know that then I can +design a control Loop for the thing + + align:start position:0% +design a control Loop for the thing + + + align:start position:0% +design a control Loop for the thing +okay and so what I'd like to talk about + + align:start position:0% +okay and so what I'd like to talk about + + + align:start position:0% +okay and so what I'd like to talk about +is how do we build this model this + + align:start position:0% +is how do we build this model this + + + align:start position:0% +is how do we build this model this +Dynamic model instead of a periodic + + align:start position:0% +Dynamic model instead of a periodic + + + align:start position:0% +Dynamic model instead of a periodic +state state model what does the dynamic + + align:start position:0% +state state model what does the dynamic + + + align:start position:0% +state state model what does the dynamic +model of this thing look like okay from + + align:start position:0% +model of this thing look like okay from + + + align:start position:0% +model of this thing look like okay from +variations in Duty ratio for example to + + align:start position:0% +variations in Duty ratio for example to + + + align:start position:0% +variations in Duty ratio for example to +the variations in the output voltage + + align:start position:0% +the variations in the output voltage + + + align:start position:0% +the variations in the output voltage +okay and coming back to this picture + + align:start position:0% +okay and coming back to this picture + + + align:start position:0% +okay and coming back to this picture +right we can see that what we have here + + align:start position:0% +right we can see that what we have here + + + align:start position:0% +right we can see that what we have here +is a bunch of switching here's the + + align:start position:0% +is a bunch of switching here's the + + + align:start position:0% +is a bunch of switching here's the +switching Ripple the Triangular Ripple + + align:start position:0% +switching Ripple the Triangular Ripple + + + align:start position:0% +switching Ripple the Triangular Ripple +current in the inductor and you know + + align:start position:0% +current in the inductor and you know + + + align:start position:0% +current in the inductor and you know +goes through some oscillations and then + + align:start position:0% +goes through some oscillations and then + + + align:start position:0% +goes through some oscillations and then +it settles down and same thing with the + + align:start position:0% +it settles down and same thing with the + + + align:start position:0% +it settles down and same thing with the +capacitor voltage + + align:start position:0% +capacitor voltage + + + align:start position:0% +capacitor voltage +well I'm not particularly interested in + + align:start position:0% +well I'm not particularly interested in + + + align:start position:0% +well I'm not particularly interested in +this switching + + align:start position:0% +this switching + + + align:start position:0% +this switching +Ripple right why am I not interested in + + align:start position:0% +Ripple right why am I not interested in + + + align:start position:0% +Ripple right why am I not interested in +it is because notice that the sort of + + align:start position:0% +it is because notice that the sort of + + + align:start position:0% +it is because notice that the sort of +the dynamical behavior is at a very low + + align:start position:0% +the dynamical behavior is at a very low + + + align:start position:0% +the dynamical behavior is at a very low +frequency compared to the switching + + align:start position:0% +frequency compared to the switching + + + align:start position:0% +frequency compared to the switching +Ripple okay and I can't really do + + align:start position:0% +Ripple okay and I can't really do + + + align:start position:0% +Ripple okay and I can't really do +anything about the switching Ripple + + align:start position:0% +anything about the switching Ripple + + + align:start position:0% +anything about the switching Ripple +anyways right in other words that's + + align:start position:0% +anyways right in other words that's + + + align:start position:0% +anyways right in other words that's +that's intrinsic to the converter right + + align:start position:0% +that's intrinsic to the converter right + + + align:start position:0% +that's intrinsic to the converter right +I'm going to put some energy in I'm + + align:start position:0% +I'm going to put some energy in I'm + + + align:start position:0% +I'm going to put some energy in I'm +going to process through I'm going to + + align:start position:0% +going to process through I'm going to + + + align:start position:0% +going to process through I'm going to +take it out if I'm trying to say vary my + + align:start position:0% +take it out if I'm trying to say vary my + + + align:start position:0% +take it out if I'm trying to say vary my +duty ratio on the time scale of this + + align:start position:0% +duty ratio on the time scale of this + + + align:start position:0% +duty ratio on the time scale of this +switching I'm like very very fast I'm + + align:start position:0% +switching I'm like very very fast I'm + + + align:start position:0% +switching I'm like very very fast I'm +probably going to make the converter do + + align:start position:0% +probably going to make the converter do + + + align:start position:0% +probably going to make the converter do +unhappy things right my whole my whole + + align:start position:0% +unhappy things right my whole my whole + + + align:start position:0% +unhappy things right my whole my whole +notion was that at least within a cycle + + align:start position:0% +notion was that at least within a cycle + + + align:start position:0% +notion was that at least within a cycle +Duty ratio is not something that I'm + + align:start position:0% +Duty ratio is not something that I'm + + + align:start position:0% +Duty ratio is not something that I'm +swinging around wildly right so I'm + + align:start position:0% +swinging around wildly right so I'm + + + align:start position:0% +swinging around wildly right so I'm +interested in the behavior of this + + align:start position:0% +interested in the behavior of this + + + align:start position:0% +interested in the behavior of this +circuit for frequencies relatively low + + align:start position:0% +circuit for frequencies relatively low + + + align:start position:0% +circuit for frequencies relatively low +compared to the switching frequency okay + + align:start position:0% +compared to the switching frequency okay + + + align:start position:0% +compared to the switching frequency okay +so what I want to do is generate models + + align:start position:0% +so what I want to do is generate models + + + align:start position:0% +so what I want to do is generate models +that sort of capture this sort of + + align:start position:0% +that sort of capture this sort of + + + align:start position:0% +that sort of capture this sort of +average Behavior like how you know these + + align:start position:0% +average Behavior like how you know these + + + align:start position:0% +average Behavior like how you know these +low frequency oscillations and ignore + + align:start position:0% +low frequency oscillations and ignore + + + align:start position:0% +low frequency oscillations and ignore +the switching Ripple okay every + + align:start position:0% +the switching Ripple okay every + + + align:start position:0% +the switching Ripple okay every +Everybody follow + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +okay so let me think about this in a + + align:start position:0% +okay so let me think about this in a + + + align:start position:0% +okay so let me think about this in a +couple of pieces well first of all let's + + align:start position:0% +couple of pieces well first of all let's + + + align:start position:0% +couple of pieces well first of all let's +just talk about this pwm block we've + + align:start position:0% +just talk about this pwm block we've + + + align:start position:0% +just talk about this pwm block we've +talked about this before this isn't part + + align:start position:0% +talked about this before this isn't part + + + align:start position:0% +talked about this before this isn't part +of the average model but essentially you + + align:start position:0% +of the average model but essentially you + + + align:start position:0% +of the average model but essentially you +know what would the pwm block look + + align:start position:0% +know what would the pwm block look + + + align:start position:0% +know what would the pwm block look +like um you know basically what I would + + align:start position:0% +like um you know basically what I would + + + align:start position:0% +like um you know basically what I would +have is + + align:start position:0% +have is + + + align:start position:0% +have is +um maybe I would generate some triangle + + align:start position:0% +um maybe I would generate some triangle + + + align:start position:0% +um maybe I would generate some triangle +wave this could be a saw tooth for + + align:start position:0% +wave this could be a saw tooth for + + + align:start position:0% +wave this could be a saw tooth for +example with a period + + align:start position:0% + + + + align:start position:0% + +T right and I'll just generate this and + + align:start position:0% +T right and I'll just generate this and + + + align:start position:0% +T right and I'll just generate this and +maybe for Simplicity I'll just say this + + align:start position:0% +maybe for Simplicity I'll just say this + + + align:start position:0% +maybe for Simplicity I'll just say this +is a 1V + + align:start position:0% +is a 1V + + + align:start position:0% +is a 1V +signal right and I will compare that to + + align:start position:0% +signal right and I will compare that to + + + align:start position:0% +signal right and I will compare that to +this Duty ratio signal so here's + + align:start position:0% + + + + align:start position:0% + +VD right and VD is you know maybe it's + + align:start position:0% +VD right and VD is you know maybe it's + + + align:start position:0% +VD right and VD is you know maybe it's +changing but it's changing very slowly + + align:start position:0% +changing but it's changing very slowly + + + align:start position:0% +changing but it's changing very slowly +so here's + + align:start position:0% +so here's + + + align:start position:0% +so here's +VD right and I'm just going to run this + + align:start position:0% +VD right and I'm just going to run this + + + align:start position:0% +VD right and I'm just going to run this +into a comparator right I'm going to + + align:start position:0% +into a comparator right I'm going to + + + align:start position:0% +into a comparator right I'm going to +call this you know + + align:start position:0% +call this you know + + + align:start position:0% +call this you know +vry and I'll compare V + + align:start position:0% +vry and I'll compare V + + + align:start position:0% +vry and I'll compare V +Tri to + + align:start position:0% +Tri to + + + align:start position:0% +Tri to +VD and generate Q of + + align:start position:0% +VD and generate Q of + + + align:start position:0% +VD and generate Q of +T right so all I'm going to do is at the + + align:start position:0% +T right so all I'm going to do is at the + + + align:start position:0% +T right so all I'm going to do is at the +beginning of each cycle what you can + + align:start position:0% +beginning of each cycle what you can + + + align:start position:0% +beginning of each cycle what you can +kind of see is if this is + + align:start position:0% +kind of see is if this is + + + align:start position:0% +kind of see is if this is +time at the beginning of each cycle Q of + + align:start position:0% +time at the beginning of each cycle Q of + + + align:start position:0% +time at the beginning of each cycle Q of +is going to go + + align:start position:0% +is going to go + + + align:start position:0% +is going to go +high + + align:start position:0% +high + + + align:start position:0% +high +until the triangle exceeds + + align:start position:0% +until the triangle exceeds + + + align:start position:0% +until the triangle exceeds +the v subd in which case I'll go low and + + align:start position:0% +the v subd in which case I'll go low and + + + align:start position:0% +the v subd in which case I'll go low and +then I'll go high at the beginning of + + align:start position:0% +then I'll go high at the beginning of + + + align:start position:0% +then I'll go high at the beginning of +the next + + align:start position:0% +the next + + + align:start position:0% +the next +cycle and + + align:start position:0% +cycle and + + + align:start position:0% +cycle and +I'll stay high until I hit the end until + + align:start position:0% +I'll stay high until I hit the end until + + + align:start position:0% +I'll stay high until I hit the end until +I hit the comparison and so forth same + + align:start position:0% +I hit the comparison and so forth same + + + align:start position:0% +I hit the comparison and so forth same +again in the next + + align:start position:0% + + + + align:start position:0% + +cycle and so forth all right so by + + align:start position:0% +cycle and so forth all right so by + + + align:start position:0% +cycle and so forth all right so by +comparing my V subd to a linearly rising + + align:start position:0% +comparing my V subd to a linearly rising + + + align:start position:0% +comparing my V subd to a linearly rising +element I can generate something where + + align:start position:0% +element I can generate something where + + + align:start position:0% +element I can generate something where +this is you know whatever V subd was + + align:start position:0% +this is you know whatever V subd was + + + align:start position:0% +this is you know whatever V subd was +here that's represents some Duty ratio + + align:start position:0% +here that's represents some Duty ratio + + + align:start position:0% +here that's represents some Duty ratio +that's going to be DT at this point I'm + + align:start position:0% +that's going to be DT at this point I'm + + + align:start position:0% +that's going to be DT at this point I'm +going to have DT at this point which + + align:start position:0% +going to have DT at this point which + + + align:start position:0% +going to have DT at this point which +might be different Etc in each cycle I + + align:start position:0% +might be different Etc in each cycle I + + + align:start position:0% +might be different Etc in each cycle I +kind of get a duty ratio that's related + + align:start position:0% +kind of get a duty ratio that's related + + + align:start position:0% +kind of get a duty ratio that's related +to V ofd during that cycle assuming vcd + + align:start position:0% +to V ofd during that cycle assuming vcd + + + align:start position:0% +to V ofd during that cycle assuming vcd +doesn't vary very quickly okay so this + + align:start position:0% +doesn't vary very quickly okay so this + + + align:start position:0% +doesn't vary very quickly okay so this +is how I build the pwm generator that's + + align:start position:0% +is how I build the pwm generator that's + + + align:start position:0% +is how I build the pwm generator that's +this block here okay that's not how I + + align:start position:0% +this block here okay that's not how I + + + align:start position:0% +this block here okay that's not how I +model it that's just how I implement it + + align:start position:0% +model it that's just how I implement it + + + align:start position:0% +model it that's just how I implement it +so from a mental perspective we can + + align:start position:0% +so from a mental perspective we can + + + align:start position:0% +so from a mental perspective we can +worry about going from some desired Duty + + align:start position:0% +worry about going from some desired Duty + + + align:start position:0% +worry about going from some desired Duty +ratio to some response or the local + + align:start position:0% +ratio to some response or the local + + + align:start position:0% +ratio to some response or the local +average Duty ratio to sum response we're + + align:start position:0% +average Duty ratio to sum response we're + + + align:start position:0% +average Duty ratio to sum response we're +I'm assuming that VD is only varying + + align:start position:0% +I'm assuming that VD is only varying + + + align:start position:0% +I'm assuming that VD is only varying +very slow within any given switching + + align:start position:0% +very slow within any given switching + + + align:start position:0% +very slow within any given switching +cycle okay and if your compensator lets + + align:start position:0% +cycle okay and if your compensator lets + + + align:start position:0% +cycle okay and if your compensator lets +it very very quickly you're probably + + align:start position:0% +it very very quickly you're probably + + + align:start position:0% +it very very quickly you're probably +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +unhappy + + align:start position:0% +unhappy + + + align:start position:0% +unhappy +okay all right so that gives me a way to + + align:start position:0% +okay all right so that gives me a way to + + + align:start position:0% +okay all right so that gives me a way to +implement this and I should say by the + + align:start position:0% +implement this and I should say by the + + + align:start position:0% +implement this and I should say by the +way that if I go buy a pwm chip for a + + align:start position:0% +way that if I go buy a pwm chip for a + + + align:start position:0% +way that if I go buy a pwm chip for a +typical dcddc converter or controller + + align:start position:0% +typical dcddc converter or controller + + + align:start position:0% +typical dcddc converter or controller +chip I'll usually get a + + align:start position:0% +chip I'll usually get a + + + align:start position:0% +chip I'll usually get a +reference some kind of error amplifier + + align:start position:0% +reference some kind of error amplifier + + + align:start position:0% +reference some kind of error amplifier +opamp and other things things to + + align:start position:0% +opamp and other things things to + + + align:start position:0% +opamp and other things things to +generate the compensator I'll get the + + align:start position:0% +generate the compensator I'll get the + + + align:start position:0% +generate the compensator I'll get the +pwm chip and in fact this triangle also + + align:start position:0% +pwm chip and in fact this triangle also + + + align:start position:0% +pwm chip and in fact this triangle also +serves as my clock so I can set the + + align:start position:0% +serves as my clock so I can set the + + + align:start position:0% +serves as my clock so I can set the +clock frequency I can set T and then you + + align:start position:0% +clock frequency I can set T and then you + + + align:start position:0% +clock frequency I can set T and then you +know maybe it gives me a gate driver so + + align:start position:0% +know maybe it gives me a gate driver so + + + align:start position:0% +know maybe it gives me a gate driver so +I kind of get all this stuff in one chip + + align:start position:0% +I kind of get all this stuff in one chip + + + align:start position:0% +I kind of get all this stuff in one chip +very often for a simple design okay of + + align:start position:0% +very often for a simple design okay of + + + align:start position:0% +very often for a simple design okay of +course you can also do a lot of this + + align:start position:0% +course you can also do a lot of this + + + align:start position:0% +course you can also do a lot of this +stuff digitally these days depending + + align:start position:0% +stuff digitally these days depending + + + align:start position:0% +stuff digitally these days depending +upon what kind of processor you + + align:start position:0% +upon what kind of processor you + + + align:start position:0% +upon what kind of processor you +use okay but this doesn't tell me you + + align:start position:0% +use okay but this doesn't tell me you + + + align:start position:0% +use okay but this doesn't tell me you +know this tells me how did I get from + + align:start position:0% +know this tells me how did I get from + + + align:start position:0% +know this tells me how did I get from +Duty ratio to the Q ofd but it doesn't + + align:start position:0% +Duty ratio to the Q ofd but it doesn't + + + align:start position:0% +Duty ratio to the Q ofd but it doesn't +tell me how I model this whole + + align:start position:0% +tell me how I model this whole + + + align:start position:0% +tell me how I model this whole +block okay and that's what I'd like to + + align:start position:0% +block okay and that's what I'd like to + + + align:start position:0% +block okay and that's what I'd like to +talk about + + align:start position:0% +talk about + + + align:start position:0% +talk about +now and we said we are not interested in + + align:start position:0% +now and we said we are not interested in + + + align:start position:0% +now and we said we are not interested in +this high frequency Ripple but only the + + align:start position:0% +this high frequency Ripple but only the + + + align:start position:0% +this high frequency Ripple but only the +low frequency + + align:start position:0% +low frequency + + + align:start position:0% +low frequency +Behavior okay and towards that end I'd + + align:start position:0% +Behavior okay and towards that end I'd + + + align:start position:0% +Behavior okay and towards that end I'd +like to introduce what's known as a + + align:start position:0% +like to introduce what's known as a + + + align:start position:0% +like to introduce what's known as a +local average so the local average + + align:start position:0% +local average so the local average + + + align:start position:0% +local average so the local average +operator + + align:start position:0% + + + + align:start position:0% + +is this it's if I had some signal for + + align:start position:0% +is this it's if I had some signal for + + + align:start position:0% +is this it's if I had some signal for +for any signal X of T some time varying + + align:start position:0% +for any signal X of T some time varying + + + align:start position:0% +for any signal X of T some time varying +waveform X of T could be a voltage could + + align:start position:0% +waveform X of T could be a voltage could + + + align:start position:0% +waveform X of T could be a voltage could +be a current whatever I + + align:start position:0% +be a current whatever I + + + align:start position:0% +be a current whatever I +wanted I can define a local average xar + + align:start position:0% +wanted I can define a local average xar + + + align:start position:0% +wanted I can define a local average xar +of + + align:start position:0% +of + + + align:start position:0% +of +T is defined as being equal to 1/ + + align:start position:0% +T is defined as being equal to 1/ + + + align:start position:0% +T is defined as being equal to 1/ +T integral between T minus capital T and + + align:start position:0% +T integral between T minus capital T and + + + align:start position:0% +T integral between T minus capital T and +T of X of to D to + + align:start position:0% +T of X of to D to + + + align:start position:0% +T of X of to D to +okay this is the local average of + + align:start position:0% +okay this is the local average of + + + align:start position:0% +okay this is the local average of +signal and what is this local average + + align:start position:0% +signal and what is this local average + + + align:start position:0% +signal and what is this local average +it's just sort of a moving average okay + + align:start position:0% +it's just sort of a moving average okay + + + align:start position:0% +it's just sort of a moving average okay +so if I'm at my signal time right now at + + align:start position:0% +so if I'm at my signal time right now at + + + align:start position:0% +so if I'm at my signal time right now at +time T what I'm going to look do is I'm + + align:start position:0% +time T what I'm going to look do is I'm + + + align:start position:0% +time T what I'm going to look do is I'm +going to look back over + + align:start position:0% +going to look back over + + + align:start position:0% +going to look back over +one um capital T and take the average of + + align:start position:0% +one um capital T and take the average of + + + align:start position:0% +one um capital T and take the average of +the waveform just over that time and + + align:start position:0% +the waveform just over that time and + + + align:start position:0% +the waveform just over that time and +then if I'm at another time I'll look + + align:start position:0% +then if I'm at another time I'll look + + + align:start position:0% +then if I'm at another time I'll look +back and I'll take the average over at + + align:start position:0% +back and I'll take the average over at + + + align:start position:0% +back and I'll take the average over at +that time okay so if I had some you know + + align:start position:0% +that time okay so if I had some you know + + + align:start position:0% +that time okay so if I had some you know +time varying with form X of + + align:start position:0% +time varying with form X of + + + align:start position:0% +time varying with form X of +T right and I said okay here's + + align:start position:0% + + + + align:start position:0% + +T1 maybe I'd go back and here's T1 minus + + align:start position:0% +T1 maybe I'd go back and here's T1 minus + + + align:start position:0% +T1 maybe I'd go back and here's T1 minus +capital T maybe I would take the average + + align:start position:0% +capital T maybe I would take the average + + + align:start position:0% +capital T maybe I would take the average +of this waveform over that time and then + + align:start position:0% +of this waveform over that time and then + + + align:start position:0% +of this waveform over that time and then +if I'm at some other time + + align:start position:0% + + + + align:start position:0% + +T2 I'd go back one + + align:start position:0% +T2 I'd go back one + + + align:start position:0% +T2 I'd go back one +cycle and this is T minus T2 uh T2 minus + + align:start position:0% +cycle and this is T minus T2 uh T2 minus + + + align:start position:0% +cycle and this is T minus T2 uh T2 minus +capital T and I'd look at the average + + align:start position:0% +capital T and I'd look at the average + + + align:start position:0% +capital T and I'd look at the average +over this time period Etc so at any + + align:start position:0% +over this time period Etc so at any + + + align:start position:0% +over this time period Etc so at any +given point I'm going to look + + align:start position:0% +given point I'm going to look + + + align:start position:0% +given point I'm going to look +at what I've been doing over the last + + align:start position:0% +at what I've been doing over the last + + + align:start position:0% +at what I've been doing over the last +capital T okay and take that average why + + align:start position:0% +capital T okay and take that average why + + + align:start position:0% +capital T okay and take that average why +am I doing that well because if I set + + align:start position:0% +am I doing that well because if I set + + + align:start position:0% +am I doing that well because if I set +capital T to be my switching period I + + align:start position:0% +capital T to be my switching period I + + + align:start position:0% +capital T to be my switching period I +can kind of look at what the average of + + align:start position:0% +can kind of look at what the average of + + + align:start position:0% +can kind of look at what the average of +this variable + + align:start position:0% +this variable + + + align:start position:0% +this variable +is over one switching + + align:start position:0% +is over one switching + + + align:start position:0% +is over one switching +cycle okay at any point + + align:start position:0% +cycle okay at any point + + + align:start position:0% +cycle okay at any point +time all + + align:start position:0% +time all + + + align:start position:0% +time all +right and we can think of this as + + align:start position:0% +right and we can think of this as + + + align:start position:0% +right and we can think of this as +basically tracking the low frequency + + align:start position:0% +basically tracking the low frequency + + + align:start position:0% +basically tracking the low frequency +variations and rejecting the switching + + align:start position:0% +variations and rejecting the switching + + + align:start position:0% +variations and rejecting the switching +Ripple okay we can think about it + + align:start position:0% +Ripple okay we can think about it + + + align:start position:0% +Ripple okay we can think about it +qualitatively and we can think about it + + align:start position:0% +qualitatively and we can think about it + + + align:start position:0% +qualitatively and we can think about it +quantitatively okay any questions about + + align:start position:0% +quantitatively okay any questions about + + + align:start position:0% +quantitatively okay any questions about +the idea or what we want to do with this + + align:start position:0% + + + + align:start position:0% + +operator okay so what are the properties + + align:start position:0% +operator okay so what are the properties + + + align:start position:0% +operator okay so what are the properties +of this operator + + align:start position:0% +of this operator + + + align:start position:0% +of this operator +okay um the first is that it's + + align:start position:0% + + + + align:start position:0% + +LTI linear and timing variance so when I + + align:start position:0% +LTI linear and timing variance so when I + + + align:start position:0% +LTI linear and timing variance so when I +say it's + + align:start position:0% + + + + align:start position:0% + +linear I mean the following that if I + + align:start position:0% +linear I mean the following that if I + + + align:start position:0% +linear I mean the following that if I +took a * X of t plus b * y of + + align:start position:0% +took a * X of t plus b * y of + + + align:start position:0% +took a * X of t plus b * y of +t Okay and then I took the local average + + align:start position:0% +t Okay and then I took the local average + + + align:start position:0% +t Okay and then I took the local average +of this whole + + align:start position:0% +of this whole + + + align:start position:0% +of this whole +signal right what I would get is + + align:start position:0% +signal right what I would get is + + + align:start position:0% +signal right what I would get is +a * xar of + + align:start position:0% +a * xar of + + + align:start position:0% +a * xar of +t plus b * Y Bar of + + align:start position:0% +t plus b * Y Bar of + + + align:start position:0% +t plus b * Y Bar of +T + + align:start position:0% +T + + + align:start position:0% +T +okay that's nice it's also Time + + align:start position:0% + + + + align:start position:0% + +invariant by which I mean if I took a + + align:start position:0% +invariant by which I mean if I took a + + + align:start position:0% +invariant by which I mean if I took a +signal X and shifted it by some time T + + align:start position:0% +signal X and shifted it by some time T + + + align:start position:0% +signal X and shifted it by some time T +KN and then I took the local average of + + align:start position:0% +KN and then I took the local average of + + + align:start position:0% +KN and then I took the local average of +that shifted + + align:start position:0% +that shifted + + + align:start position:0% +that shifted +signal it's equal + + align:start position:0% +signal it's equal + + + align:start position:0% +signal it's equal +to xar shifted it's equal to xar of T + + align:start position:0% +to xar shifted it's equal to xar of T + + + align:start position:0% +to xar shifted it's equal to xar of T +shifted by T so the local average of the + + align:start position:0% +shifted by T so the local average of the + + + align:start position:0% +shifted by T so the local average of the +shift is the shift of the local average + + align:start position:0% +shift is the shift of the local average + + + align:start position:0% +shift is the shift of the local average +okay that make sense + + align:start position:0% +okay that make sense + + + align:start position:0% +okay that make sense +everybody so now why am I worrying that + + align:start position:0% +everybody so now why am I worrying that + + + align:start position:0% +everybody so now why am I worrying that +it's a Lo a linear time invariant + + align:start position:0% +it's a Lo a linear time invariant + + + align:start position:0% +it's a Lo a linear time invariant +operator that means I can actually + + align:start position:0% +operator that means I can actually + + + align:start position:0% +operator that means I can actually +represent this thing with a transfer + + align:start position:0% +represent this thing with a transfer + + + align:start position:0% +represent this thing with a transfer +function okay as an operator it's + + align:start position:0% +function okay as an operator it's + + + align:start position:0% +function okay as an operator it's +basically a filter that I can put on my + + align:start position:0% +basically a filter that I can put on my + + + align:start position:0% +basically a filter that I can put on my +circuit so this is + + align:start position:0% +circuit so this is + + + align:start position:0% +circuit so this is +just you know a way of describing a + + align:start position:0% +just you know a way of describing a + + + align:start position:0% +just you know a way of describing a +filter here's what the filter transfer + + align:start position:0% +filter here's what the filter transfer + + + align:start position:0% +filter here's what the filter transfer +function looks like here's the operator + + align:start position:0% +function looks like here's the operator + + + align:start position:0% +function looks like here's the operator +definition in time domain here's what it + + align:start position:0% +definition in time domain here's what it + + + align:start position:0% +definition in time domain here's what it +looks like in the frequency domain what + + align:start position:0% +looks like in the frequency domain what + + + align:start position:0% +looks like in the frequency domain what +we can see is that at low frequencies + + align:start position:0% +we can see is that at low frequencies + + + align:start position:0% +we can see is that at low frequencies +near DC it has a gain of one it passes + + align:start position:0% +near DC it has a gain of one it passes + + + align:start position:0% +near DC it has a gain of one it passes +through the low frequency + + align:start position:0% +through the low frequency + + + align:start position:0% +through the low frequency +content but this particular filter just + + align:start position:0% +content but this particular filter just + + + align:start position:0% +content but this particular filter just +happens to have zero amplitudes at the + + align:start position:0% +happens to have zero amplitudes at the + + + align:start position:0% +happens to have zero amplitudes at the +switching frequency twice the switching + + align:start position:0% +switching frequency twice the switching + + + align:start position:0% +switching frequency twice the switching +frequency three times Etc so it very + + align:start position:0% +frequency three times Etc so it very + + + align:start position:0% +frequency three times Etc so it very +prec pris L keeps the low frequency + + align:start position:0% +prec pris L keeps the low frequency + + + align:start position:0% +prec pris L keeps the low frequency +stuff and murders all the switching + + align:start position:0% +stuff and murders all the switching + + + align:start position:0% +stuff and murders all the switching +ripples okay now could I pick some other + + align:start position:0% +ripples okay now could I pick some other + + + align:start position:0% +ripples okay now could I pick some other +filter that kind of captures this idea + + align:start position:0% +filter that kind of captures this idea + + + align:start position:0% +filter that kind of captures this idea +sure right but we just happen to pick + + align:start position:0% +sure right but we just happen to pick + + + align:start position:0% +sure right but we just happen to pick +this one because it's a good one for our + + align:start position:0% +this one because it's a good one for our + + + align:start position:0% +this one because it's a good one for our +purpose which is to keep the low + + align:start position:0% +purpose which is to keep the low + + + align:start position:0% +purpose which is to keep the low +frequency content and get rid of the + + align:start position:0% +frequency content and get rid of the + + + align:start position:0% +frequency content and get rid of the +switching Ripple and its + + align:start position:0% +switching Ripple and its + + + align:start position:0% +switching Ripple and its +harmonics + + align:start position:0% +harmonics + + + align:start position:0% +harmonics +okay you'll also notice that the phase + + align:start position:0% +okay you'll also notice that the phase + + + align:start position:0% +okay you'll also notice that the phase +of this thing is basically representing + + align:start position:0% +of this thing is basically representing + + + align:start position:0% +of this thing is basically representing +you know it's a linear phase response + + align:start position:0% +you know it's a linear phase response + + + align:start position:0% +you know it's a linear phase response +space delay of half a cycle why because + + align:start position:0% +space delay of half a cycle why because + + + align:start position:0% +space delay of half a cycle why because +if I'm looking now I'm really asking + + align:start position:0% +if I'm looking now I'm really asking + + + align:start position:0% +if I'm looking now I'm really asking +what was what's my signal over the last + + align:start position:0% +what was what's my signal over the last + + + align:start position:0% +what was what's my signal over the last +capital T so I'm sort of on average + + align:start position:0% +capital T so I'm sort of on average + + + align:start position:0% +capital T so I'm sort of on average +looking back half a t in + + align:start position:0% +looking back half a t in + + + align:start position:0% +looking back half a t in +duration okay if I didn't like that I + + align:start position:0% +duration okay if I didn't like that I + + + align:start position:0% +duration okay if I didn't like that I +could make my local average you know + + align:start position:0% +could make my local average you know + + + align:start position:0% +could make my local average you know +between T minus t over2 and t plus T + + align:start position:0% +between T minus t over2 and t plus T + + + align:start position:0% +between T minus t over2 and t plus T +over2 capital T over2 and then I + + align:start position:0% +over2 capital T over2 and then I + + + align:start position:0% +over2 capital T over2 and then I +wouldn't have any delay in it but I also + + align:start position:0% +wouldn't have any delay in it but I also + + + align:start position:0% +wouldn't have any delay in it but I also +wouldn't be causal right now I'm not + + align:start position:0% +wouldn't be causal right now I'm not + + + align:start position:0% +wouldn't be causal right now I'm not +saying we're actually going to physic + + align:start position:0% +saying we're actually going to physic + + + align:start position:0% +saying we're actually going to physic +build a + + align:start position:0% +build a + + + align:start position:0% +build a +filter but this is sort of an operator + + align:start position:0% +filter but this is sort of an operator + + + align:start position:0% +filter but this is sort of an operator +that lets me think about how I'd process + + align:start position:0% +that lets me think about how I'd process + + + align:start position:0% +that lets me think about how I'd process +my sim signals so that I could keep the + + align:start position:0% +my sim signals so that I could keep the + + + align:start position:0% +my sim signals so that I could keep the +low frequency content and get rid of the + + align:start position:0% +low frequency content and get rid of the + + + align:start position:0% +low frequency content and get rid of the +switching + + align:start position:0% +switching + + + align:start position:0% +switching +rle any questions about + + align:start position:0% + + + + align:start position:0% + +that okay so we're going to see how to + + align:start position:0% +that okay so we're going to see how to + + + align:start position:0% +that okay so we're going to see how to +use this um kind of filter to do + + align:start position:0% +use this um kind of filter to do + + + align:start position:0% +use this um kind of filter to do +interesting things + + align:start position:0% + + + + align:start position:0% + +um there's a few ways we can use it okay + + align:start position:0% +um there's a few ways we can use it okay + + + align:start position:0% +um there's a few ways we can use it okay +um and they they kind of give similar + + align:start position:0% +um and they they kind of give similar + + + align:start position:0% +um and they they kind of give similar +results but they're they're + + align:start position:0% +results but they're they're + + + align:start position:0% +results but they're they're +useful but let me just lastly talk about + + align:start position:0% +useful but let me just lastly talk about + + + align:start position:0% +useful but let me just lastly talk about +a couple of other properties of this uh + + align:start position:0% +a couple of other properties of this uh + + + align:start position:0% +a couple of other properties of this uh +operator and the first that's a very + + align:start position:0% +operator and the first that's a very + + + align:start position:0% +operator and the first that's a very +useful property is the differentiation + + align:start position:0% +useful property is the differentiation + + + align:start position:0% +useful property is the differentiation +property + + align:start position:0% + + + + align:start position:0% + +right and this is this is one of the + + align:start position:0% +right and this is this is one of the + + + align:start position:0% +right and this is this is one of the +reasons why we picked this particular + + align:start position:0% +reasons why we picked this particular + + + align:start position:0% +reasons why we picked this particular +filter if I took some signal + + align:start position:0% +filter if I took some signal + + + align:start position:0% +filter if I took some signal +dxdt right so so some time varying + + align:start position:0% +dxdt right so so some time varying + + + align:start position:0% +dxdt right so so some time varying +signal I looked at its derivative and I + + align:start position:0% +signal I looked at its derivative and I + + + align:start position:0% +signal I looked at its derivative and I +said give me the local average of the + + align:start position:0% +said give me the local average of the + + + align:start position:0% +said give me the local average of the +derivative of this + + align:start position:0% +derivative of this + + + align:start position:0% +derivative of this +signal it's pretty easy to show that + + align:start position:0% +signal it's pretty easy to show that + + + align:start position:0% +signal it's pretty easy to show that +this is the same as the + + align:start position:0% +this is the same as the + + + align:start position:0% +this is the same as the +derivative of xar of T that is the + + align:start position:0% +derivative of xar of T that is the + + + align:start position:0% +derivative of xar of T that is the +derivative of the local average is the + + align:start position:0% +derivative of the local average is the + + + align:start position:0% +derivative of the local average is the +local average of the + + align:start position:0% +local average of the + + + align:start position:0% +local average of the +derivative okay or the local average of + + align:start position:0% +derivative okay or the local average of + + + align:start position:0% +derivative okay or the local average of +the derivative is the derivative of the + + align:start position:0% +the derivative is the derivative of the + + + align:start position:0% +the derivative is the derivative of the +local average why is that true because + + align:start position:0% +local average why is that true because + + + align:start position:0% +local average why is that true because +basically I'm taking the derivative of + + align:start position:0% +basically I'm taking the derivative of + + + align:start position:0% +basically I'm taking the derivative of +this thing I can interchange the order + + align:start position:0% +this thing I can interchange the order + + + align:start position:0% +this thing I can interchange the order +of differentiation integration I get + + align:start position:0% +of differentiation integration I get + + + align:start position:0% +of differentiation integration I get +back the same thing okay and this + + align:start position:0% +back the same thing okay and this + + + align:start position:0% +back the same thing okay and this +property turns out to be a very useful + + align:start position:0% +property turns out to be a very useful + + + align:start position:0% +property turns out to be a very useful +one for modeling as we'll see in a + + align:start position:0% +one for modeling as we'll see in a + + + align:start position:0% +one for modeling as we'll see in a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +okay so how might I + + align:start position:0% +okay so how might I + + + align:start position:0% +okay so how might I +use this um + + align:start position:0% + + + + align:start position:0% + +average model or or average + + align:start position:0% +average model or or average + + + align:start position:0% +average model or or average +operator and the way I'd like to sh Show + + align:start position:0% +operator and the way I'd like to sh Show + + + align:start position:0% +operator and the way I'd like to sh Show +you to use it today is on a circuit + + align:start position:0% +you to use it today is on a circuit + + + align:start position:0% +you to use it today is on a circuit +itself so suppose I came up and I gave + + align:start position:0% +itself so suppose I came up and I gave + + + align:start position:0% +itself so suppose I came up and I gave +you a boost converter and I said well + + align:start position:0% +you a boost converter and I said well + + + align:start position:0% +you a boost converter and I said well +gee could I apply that average model to + + align:start position:0% +gee could I apply that average model to + + + align:start position:0% +gee could I apply that average model to +the Boost converter itself to the + + align:start position:0% +the Boost converter itself to the + + + align:start position:0% +the Boost converter itself to the +Circuit okay and let's think about what + + align:start position:0% +Circuit okay and let's think about what + + + align:start position:0% +Circuit okay and let's think about what +that + + align:start position:0% +that + + + align:start position:0% +that +means if I thought about any + + align:start position:0% +means if I thought about any + + + align:start position:0% +means if I thought about any +circuit what the defines its topology + + align:start position:0% +circuit what the defines its topology + + + align:start position:0% +circuit what the defines its topology +what defines its topology what's + + align:start position:0% +what defines its topology what's + + + align:start position:0% +what defines its topology what's +connected to what the structure of it is + + align:start position:0% +connected to what the structure of it is + + + align:start position:0% +connected to what the structure of it is +really the set of kbl and KCl + + align:start position:0% +really the set of kbl and KCl + + + align:start position:0% +really the set of kbl and KCl +equations that exist for that circuit + + align:start position:0% +equations that exist for that circuit + + + align:start position:0% +equations that exist for that circuit +right so any circuit has some set of + + align:start position:0% +right so any circuit has some set of + + + align:start position:0% +right so any circuit has some set of +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +kvl right has some set of kvl equations + + align:start position:0% +kvl right has some set of kvl equations + + + align:start position:0% +kvl right has some set of kvl equations +which essentially are the sum of VI J is + + align:start position:0% +which essentially are the sum of VI J is + + + align:start position:0% +which essentially are the sum of VI J is +equal to zero around a bunch of Loops + + align:start position:0% +equal to zero around a bunch of Loops + + + align:start position:0% +equal to zero around a bunch of Loops +there's a whole bunch of equations that + + align:start position:0% +there's a whole bunch of equations that + + + align:start position:0% +there's a whole bunch of equations that +have this form right + + align:start position:0% +have this form right + + + align:start position:0% +have this form right +right and likewise there's a set of KCl + + align:start position:0% +right and likewise there's a set of KCl + + + align:start position:0% +right and likewise there's a set of KCl +equations the sum of I subk that are + + align:start position:0% +equations the sum of I subk that are + + + align:start position:0% +equations the sum of I subk that are +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +zero okay so I could take any + + align:start position:0% +zero okay so I could take any + + + align:start position:0% +zero okay so I could take any +circuit and write down a list of kvl and + + align:start position:0% +circuit and write down a list of kvl and + + + align:start position:0% +circuit and write down a list of kvl and +KCl equations that pertain to that + + align:start position:0% +KCl equations that pertain to that + + + align:start position:0% +KCl equations that pertain to that +circuit one you know one for every + + align:start position:0% +circuit one you know one for every + + + align:start position:0% +circuit one you know one for every +voltage one for every voltage Loop one + + align:start position:0% +voltage one for every voltage Loop one + + + align:start position:0% +voltage one for every voltage Loop one +for every node and we can go back and + + align:start position:0% +for every node and we can go back and + + + align:start position:0% +for every node and we can go back and +say figure out which ones of those are + + align:start position:0% +say figure out which ones of those are + + + align:start position:0% +say figure out which ones of those are +independent and so forth okay + + align:start position:0% +independent and so forth okay + + + align:start position:0% +independent and so forth okay +well what happens if I came up and said + + align:start position:0% +well what happens if I came up and said + + + align:start position:0% +well what happens if I came up and said +okay let me take a kvl or KCl equation + + align:start position:0% +okay let me take a kvl or KCl equation + + + align:start position:0% +okay let me take a kvl or KCl equation +or more generally the ones that + + align:start position:0% +or more generally the ones that + + + align:start position:0% +or more generally the ones that +represent my circuit and average those + + align:start position:0% +represent my circuit and average those + + + align:start position:0% +represent my circuit and average those +things okay well all I would do is if I + + align:start position:0% +things okay well all I would do is if I + + + align:start position:0% +things okay well all I would do is if I +took this and I averaged + + align:start position:0% +took this and I averaged + + + align:start position:0% +took this and I averaged +it when I say average it I mean apply + + align:start position:0% +it when I say average it I mean apply + + + align:start position:0% +it when I say average it I mean apply +this + + align:start position:0% +this + + + align:start position:0% +this +operator okay what would I do i' take + + align:start position:0% +operator okay what would I do i' take + + + align:start position:0% +operator okay what would I do i' take +the local average of each side the local + + align:start position:0% +the local average of each side the local + + + align:start position:0% +the local average of each side the local +average of 0 is0 + + align:start position:0% +average of 0 is0 + + + align:start position:0% +average of 0 is0 +this is just the local average of the + + align:start position:0% +this is just the local average of the + + + align:start position:0% +this is just the local average of the +sum right which I already said because + + align:start position:0% +sum right which I already said because + + + align:start position:0% +sum right which I already said because +of linearity is the sum of the local + + align:start position:0% +of linearity is the sum of the local + + + align:start position:0% +of linearity is the sum of the local +averages so this gives me if I average + + align:start position:0% +averages so this gives me if I average + + + align:start position:0% +averages so this gives me if I average +it the sum of VI + + align:start position:0% +it the sum of VI + + + align:start position:0% +it the sum of VI +J local average is equal to zero and + + align:start position:0% +J local average is equal to zero and + + + align:start position:0% +J local average is equal to zero and +this gives me the sum of I sub K local + + align:start position:0% +this gives me the sum of I sub K local + + + align:start position:0% +this gives me the sum of I sub K local +average which is + + align:start position:0% +average which is + + + align:start position:0% +average which is +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so what I'm really saying here is + + align:start position:0% +okay so what I'm really saying here is + + + align:start position:0% +okay so what I'm really saying here is +if I have some circuit like my Boost + + align:start position:0% +if I have some circuit like my Boost + + + align:start position:0% +if I have some circuit like my Boost +converter up there + + align:start position:0% +converter up there + + + align:start position:0% +converter up there +I could apply averaging to that circuit + + align:start position:0% +I could apply averaging to that circuit + + + align:start position:0% +I could apply averaging to that circuit +right or all the kvl and KCl equations + + align:start position:0% +right or all the kvl and KCl equations + + + align:start position:0% +right or all the kvl and KCl equations +and I could get another circuit that's + + align:start position:0% +and I could get another circuit that's + + + align:start position:0% +and I could get another circuit that's +average that has the same Connections in + + align:start position:0% +average that has the same Connections in + + + align:start position:0% +average that has the same Connections in +it why because for every kvl equation in + + align:start position:0% +it why because for every kvl equation in + + + align:start position:0% +it why because for every kvl equation in +this circuit there's an identical kvl + + align:start position:0% +this circuit there's an identical kvl + + + align:start position:0% +this circuit there's an identical kvl +equation in this circuit it just has + + align:start position:0% +equation in this circuit it just has + + + align:start position:0% +equation in this circuit it just has +average voltages and likewise every KCl + + align:start position:0% +average voltages and likewise every KCl + + + align:start position:0% +average voltages and likewise every KCl +in this circuit generates a new KCl + + align:start position:0% +in this circuit generates a new KCl + + + align:start position:0% +in this circuit generates a new KCl +circuit just with average currents so I + + align:start position:0% +circuit just with average currents so I + + + align:start position:0% +circuit just with average currents so I +can get a new circuit with the same + + align:start position:0% +can get a new circuit with the same + + + align:start position:0% +can get a new circuit with the same +topology for which averages + + align:start position:0% +topology for which averages + + + align:start position:0% +topology for which averages +pertain + + align:start position:0% +pertain + + + align:start position:0% +pertain +okay why does this work this is the sort + + align:start position:0% +okay why does this work this is the sort + + + align:start position:0% +okay why does this work this is the sort +of similar to what we were saying + + align:start position:0% +of similar to what we were saying + + + align:start position:0% +of similar to what we were saying +remember we talked about well there's + + align:start position:0% +remember we talked about well there's + + + align:start position:0% +remember we talked about well there's +average kvl and average KCl over all + + align:start position:0% +average kvl and average KCl over all + + + align:start position:0% +average kvl and average KCl over all +time right from periodic St State well I + + align:start position:0% +time right from periodic St State well I + + + align:start position:0% +time right from periodic St State well I +can also talk about it over a cycle + + align:start position:0% +can also talk about it over a cycle + + + align:start position:0% +can also talk about it over a cycle +right if kvl holds instantaneously then + + align:start position:0% +right if kvl holds instantaneously then + + + align:start position:0% +right if kvl holds instantaneously then +it ought to hold for the local averages + + align:start position:0% +it ought to hold for the local averages + + + align:start position:0% +it ought to hold for the local averages +likewise if KCl into a circuit node + + align:start position:0% +likewise if KCl into a circuit node + + + align:start position:0% +likewise if KCl into a circuit node +holds instantaneously would all to hold + + align:start position:0% +holds instantaneously would all to hold + + + align:start position:0% +holds instantaneously would all to hold +you know average over the last cycle + + align:start position:0% +you know average over the last cycle + + + align:start position:0% +you know average over the last cycle +right so it sort of makes sense that you + + align:start position:0% +right so it sort of makes sense that you + + + align:start position:0% +right so it sort of makes sense that you +should be able to do this and the key + + align:start position:0% +should be able to do this and the key + + + align:start position:0% +should be able to do this and the key +Point here is because these equations + + align:start position:0% +Point here is because these equations + + + align:start position:0% +Point here is because these equations +have the same form as these equations + + align:start position:0% +have the same form as these equations + + + align:start position:0% +have the same form as these equations +you get the same exact circuit back the + + align:start position:0% +you get the same exact circuit back the + + + align:start position:0% +you get the same exact circuit back the +same exact circuit topology back what + + align:start position:0% +same exact circuit topology back what + + + align:start position:0% +same exact circuit topology back what +the elements in that circuit topology do + + align:start position:0% +the elements in that circuit topology do + + + align:start position:0% +the elements in that circuit topology do +is another question right we haven't + + align:start position:0% +is another question right we haven't + + + align:start position:0% +is another question right we haven't +said how are voltages and currents of + + align:start position:0% +said how are voltages and currents of + + + align:start position:0% +said how are voltages and currents of +the elements + + align:start position:0% +the elements + + + align:start position:0% +the elements +related all we've said is that the + + align:start position:0% +related all we've said is that the + + + align:start position:0% +related all we've said is that the +circuit topology stays the same okay any + + align:start position:0% +circuit topology stays the same okay any + + + align:start position:0% +circuit topology stays the same okay any +questions about + + align:start position:0% + + + + align:start position:0% + +that okay let's start talking about + + align:start position:0% +that okay let's start talking about + + + align:start position:0% +that okay let's start talking about +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +elements what do I have in this + + align:start position:0% +elements what do I have in this + + + align:start position:0% +elements what do I have in this +circuit you know if I come back and look + + align:start position:0% +circuit you know if I come back and look + + + align:start position:0% +circuit you know if I come back and look +at my Boost cver I have inductors + + align:start position:0% +at my Boost cver I have inductors + + + align:start position:0% +at my Boost cver I have inductors +capacitors resistors and then switches + + align:start position:0% +capacitors resistors and then switches + + + align:start position:0% +capacitors resistors and then switches +and S sources and switches right well + + align:start position:0% +and S sources and switches right well + + + align:start position:0% +and S sources and switches right well +the the the local average of a source is + + align:start position:0% +the the the local average of a source is + + + align:start position:0% +the the the local average of a source is +just the local average of a source right + + align:start position:0% +just the local average of a source right + + + align:start position:0% +just the local average of a source right +so VN would become VN + + align:start position:0% +so VN would become VN + + + align:start position:0% +so VN would become VN +bar but what about a resistor what about + + align:start position:0% +bar but what about a resistor what about + + + align:start position:0% +bar but what about a resistor what about +my load resistor + + align:start position:0% +my load resistor + + + align:start position:0% +my load resistor +if I took my load + + align:start position:0% +if I took my load + + + align:start position:0% +if I took my load +resistor what I really have is uh V I + + align:start position:0% +resistor what I really have is uh V I + + + align:start position:0% +resistor what I really have is uh V I +have I subr and V + + align:start position:0% +have I subr and V + + + align:start position:0% +have I subr and V +subr and what I get is V subr is equal + + align:start position:0% +subr and what I get is V subr is equal + + + align:start position:0% +subr and what I get is V subr is equal +to I subr * R right well what happens if + + align:start position:0% +to I subr * R right well what happens if + + + align:start position:0% +to I subr * R right well what happens if +I take the local average of that guy I'm + + align:start position:0% +I take the local average of that guy I'm + + + align:start position:0% +I take the local average of that guy I'm +just going to take the local average of + + align:start position:0% +just going to take the local average of + + + align:start position:0% +just going to take the local average of +this equation right so I'll come over + + align:start position:0% +this equation right so I'll come over + + + align:start position:0% +this equation right so I'll come over +here and I'll average the left and I'll + + align:start position:0% +here and I'll average the left and I'll + + + align:start position:0% +here and I'll average the left and I'll +average to the right and I can pull R + + align:start position:0% +average to the right and I can pull R + + + align:start position:0% +average to the right and I can pull R +out of the equation right so then my + + align:start position:0% +out of the equation right so then my + + + align:start position:0% +out of the equation right so then my +averaged element ought to just be this + + align:start position:0% +averaged element ought to just be this + + + align:start position:0% +averaged element ought to just be this +right I have V subr + + align:start position:0% +right I have V subr + + + align:start position:0% +right I have V subr +bar I subr bar and R right because my + + align:start position:0% +bar I subr bar and R right because my + + + align:start position:0% +bar I subr bar and R right because my +relationship is simply V subar bar is + + align:start position:0% +relationship is simply V subar bar is + + + align:start position:0% +relationship is simply V subar bar is +equal to I subar bar R which is exactly + + align:start position:0% +equal to I subar bar R which is exactly + + + align:start position:0% +equal to I subar bar R which is exactly +the relation of a + + align:start position:0% +the relation of a + + + align:start position:0% +the relation of a +resistor okay so that just says if I had + + align:start position:0% +resistor okay so that just says if I had + + + align:start position:0% +resistor okay so that just says if I had +a resistor in my original circuit and I + + align:start position:0% +a resistor in my original circuit and I + + + align:start position:0% +a resistor in my original circuit and I +look at the local average of the + + align:start position:0% +look at the local average of the + + + align:start position:0% +look at the local average of the +constitutive relation of the two things + + align:start position:0% +constitutive relation of the two things + + + align:start position:0% +constitutive relation of the two things +connecting the nodes if it's a resistor + + align:start position:0% +connecting the nodes if it's a resistor + + + align:start position:0% +connecting the nodes if it's a resistor +it just stays being a + + align:start position:0% +it just stays being a + + + align:start position:0% +it just stays being a +resistor that make + + align:start position:0% +resistor that make + + + align:start position:0% +resistor that make +sense well what happens if I have an + + align:start position:0% +sense well what happens if I have an + + + align:start position:0% +sense well what happens if I have an +inductor right I have + + align:start position:0% +inductor right I have + + + align:start position:0% +inductor right I have +vabel Isabel and the relationship is + + align:start position:0% +vabel Isabel and the relationship is + + + align:start position:0% +vabel Isabel and the relationship is +vabel is equal to l d Isabel DT right + + align:start position:0% +vabel is equal to l d Isabel DT right + + + align:start position:0% +vabel is equal to l d Isabel DT right +well if I average this guy + + align:start position:0% +well if I average this guy + + + align:start position:0% +well if I average this guy +okay I'm going to take the local average + + align:start position:0% +okay I'm going to take the local average + + + align:start position:0% +okay I'm going to take the local average +here and the local average here right + + align:start position:0% +here and the local average here right + + + align:start position:0% +here and the local average here right +this shouldn't have been a local average + + align:start position:0% +this shouldn't have been a local average + + + align:start position:0% +this shouldn't have been a local average +right and this would give me what well + + align:start position:0% +right and this would give me what well + + + align:start position:0% +right and this would give me what well +the relationship is V sub L + + align:start position:0% +the relationship is V sub L + + + align:start position:0% +the relationship is V sub L +bar now I can pull the L out because of + + align:start position:0% +bar now I can pull the L out because of + + + align:start position:0% +bar now I can pull the L out because of +linearity and the local average of the + + align:start position:0% +linearity and the local average of the + + + align:start position:0% +linearity and the local average of the +derivative becomes the derivative of + + align:start position:0% +derivative becomes the derivative of + + + align:start position:0% +derivative becomes the derivative of +local average I said that was my + + align:start position:0% +local average I said that was my + + + align:start position:0% +local average I said that was my +property over here and what I get is + + align:start position:0% +property over here and what I get is + + + align:start position:0% +property over here and what I get is +then is equal to l d DT of I bar which + + align:start position:0% +then is equal to l d DT of I bar which + + + align:start position:0% +then is equal to l d DT of I bar which +is just an induct value + + align:start position:0% + + + + align:start position:0% + +L does that make + + align:start position:0% +L does that make + + + align:start position:0% +L does that make +sense I could do the same thing with a + + align:start position:0% +sense I could do the same thing with a + + + align:start position:0% +sense I could do the same thing with a +capacitor so the beautiful thing here is + + align:start position:0% +capacitor so the beautiful thing here is + + + align:start position:0% +capacitor so the beautiful thing here is +if I go to average my circuit the + + align:start position:0% +if I go to average my circuit the + + + align:start position:0% +if I go to average my circuit the +resistors inductors capacitors sources + + align:start position:0% +resistors inductors capacitors sources + + + align:start position:0% +resistors inductors capacitors sources +just + + align:start position:0% +just + + + align:start position:0% +just +become the local averages of + + align:start position:0% +become the local averages of + + + align:start position:0% +become the local averages of +themselves okay well that's nice + + align:start position:0% +themselves okay well that's nice + + + align:start position:0% +themselves okay well that's nice +because what I'm suggesting is I can + + align:start position:0% +because what I'm suggesting is I can + + + align:start position:0% +because what I'm suggesting is I can +come to this circuit and take its local + + align:start position:0% +come to this circuit and take its local + + + align:start position:0% +come to this circuit and take its local +average and come up with a new circuit + + align:start position:0% +average and come up with a new circuit + + + align:start position:0% +average and come up with a new circuit +that does the same thing but without + + align:start position:0% +that does the same thing but without + + + align:start position:0% +that does the same thing but without +switching + + align:start position:0% +switching + + + align:start position:0% +switching +Ripple that make sense + + align:start position:0% + + + + align:start position:0% + +everybody let me see how I would do + + align:start position:0% +everybody let me see how I would do + + + align:start position:0% +everybody let me see how I would do +this + + align:start position:0% +this + + + align:start position:0% +this +here + + align:start position:0% +here + + + align:start position:0% +here +um but in order to do it what I haven't + + align:start position:0% +um but in order to do it what I haven't + + + align:start position:0% +um but in order to do it what I haven't +said is what happens to the + + align:start position:0% +said is what happens to the + + + align:start position:0% +said is what happens to the +switches right and that's a little + + align:start position:0% +switches right and that's a little + + + align:start position:0% +switches right and that's a little +trickier to think about + + align:start position:0% +trickier to think about + + + align:start position:0% +trickier to think about +all right + + align:start position:0% + + + + align:start position:0% + +um but let me to do that let me make + + align:start position:0% +um but let me to do that let me make + + + align:start position:0% +um but let me to do that let me make +something that's a little bit sort of + + align:start position:0% +something that's a little bit sort of + + + align:start position:0% +something that's a little bit sort of +circuit model + + align:start position:0% +circuit model + + + align:start position:0% +circuit model +friendly okay so let me come up with a + + align:start position:0% +friendly okay so let me come up with a + + + align:start position:0% +friendly okay so let me come up with a +different model for my Boost converter + + align:start position:0% +different model for my Boost converter + + + align:start position:0% +different model for my Boost converter +my Boost converter + + align:start position:0% +my Boost converter + + + align:start position:0% +my Boost converter +had an input + + align:start position:0% +had an input + + + align:start position:0% +had an input +voltage an + + align:start position:0% +voltage an + + + align:start position:0% +voltage an +inductor L that with a current + + align:start position:0% +inductor L that with a current + + + align:start position:0% +inductor L that with a current +I and then it had a capacitor + + align:start position:0% +I and then it had a capacitor + + + align:start position:0% +I and then it had a capacitor +c and a resistor r with an output + + align:start position:0% +c and a resistor r with an output + + + align:start position:0% +c and a resistor r with an output +voltage V out on it okay and then it had + + align:start position:0% +voltage V out on it okay and then it had + + + align:start position:0% +voltage V out on it okay and then it had +the switch in the + + align:start position:0% +the switch in the + + + align:start position:0% +the switch in the +diode okay and I could represent + + align:start position:0% +diode okay and I could represent + + + align:start position:0% +diode okay and I could represent +everything with the switch in the diode + + align:start position:0% +everything with the switch in the diode + + + align:start position:0% +everything with the switch in the diode +but maybe it would be easier from a + + align:start position:0% +but maybe it would be easier from a + + + align:start position:0% +but maybe it would be easier from a +modeling perspective if I just came back + + align:start position:0% +modeling perspective if I just came back + + + align:start position:0% +modeling perspective if I just came back +and modeled the switch and diode with + + align:start position:0% +and modeled the switch and diode with + + + align:start position:0% +and modeled the switch and diode with +equivalent dependent + + align:start position:0% +equivalent dependent + + + align:start position:0% +equivalent dependent +sources okay and here's how I'm going to + + align:start position:0% +sources okay and here's how I'm going to + + + align:start position:0% +sources okay and here's how I'm going to +argue and let me let me there's a couple + + align:start position:0% +argue and let me let me there's a couple + + + align:start position:0% +argue and let me let me there's a couple +ways I could do this + + align:start position:0% + + + + align:start position:0% + +maybe the switch sort of you like I have + + align:start position:0% +maybe the switch sort of you like I have + + + align:start position:0% +maybe the switch sort of you like I have +to worry about what's the voltage VX + + align:start position:0% +to worry about what's the voltage VX + + + align:start position:0% +to worry about what's the voltage VX +here and the current iix at this node + + align:start position:0% +here and the current iix at this node + + + align:start position:0% +here and the current iix at this node +maybe this is I this is VX and this is + + align:start position:0% +maybe this is I this is VX and this is + + + align:start position:0% +maybe this is I this is VX and this is +IX + + align:start position:0% +IX + + + align:start position:0% +IX +okay maybe I would model + + align:start position:0% +okay maybe I would model + + + align:start position:0% +okay maybe I would model +this as a dependent voltage source so + + align:start position:0% +this as a dependent voltage source so + + + align:start position:0% +this as a dependent voltage source so +what would this voltage source be this + + align:start position:0% +what would this voltage source be this + + + align:start position:0% +what would this voltage source be this +would I could write this voltage source + + align:start position:0% +would I could write this voltage source + + + align:start position:0% +would I could write this voltage source +dependent source is being sort of 1 - + + align:start position:0% +dependent source is being sort of 1 - + + + align:start position:0% +dependent source is being sort of 1 - +Q * V + + align:start position:0% +Q * V + + + align:start position:0% +Q * V +out okay because notice right this + + align:start position:0% +out okay because notice right this + + + align:start position:0% +out okay because notice right this +voltage VX pulsates when the switch is + + align:start position:0% +voltage VX pulsates when the switch is + + + align:start position:0% +voltage VX pulsates when the switch is +on when Q is high it's zero when it + + align:start position:0% +on when Q is high it's zero when it + + + align:start position:0% +on when Q is high it's zero when it +switches off it's equal to V out right + + align:start position:0% +switches off it's equal to V out right + + + align:start position:0% +switches off it's equal to V out right +so in continuous conduction mode this is + + align:start position:0% +so in continuous conduction mode this is + + + align:start position:0% +so in continuous conduction mode this is +a perfectly legitimate representation of + + align:start position:0% +a perfectly legitimate representation of + + + align:start position:0% +a perfectly legitimate representation of +what the voltage is doing there right so + + align:start position:0% +what the voltage is doing there right so + + + align:start position:0% +what the voltage is doing there right so +I'm replacing the switch with something + + align:start position:0% +I'm replacing the switch with something + + + align:start position:0% +I'm replacing the switch with something +that generates the same voltage VX as + + align:start position:0% +that generates the same voltage VX as + + + align:start position:0% +that generates the same voltage VX as +the switch + + align:start position:0% +the switch + + + align:start position:0% +the switch +does I'm going to replace the curent + + align:start position:0% +does I'm going to replace the curent + + + align:start position:0% +does I'm going to replace the curent +diode with a dependent current + + align:start position:0% +diode with a dependent current + + + align:start position:0% +diode with a dependent current +source that equals ID and that would be + + align:start position:0% +source that equals ID and that would be + + + align:start position:0% +source that equals ID and that would be +1us Q * iil right when the switch is on + + align:start position:0% +1us Q * iil right when the switch is on + + + align:start position:0% +1us Q * iil right when the switch is on +this current is zero because the diode's + + align:start position:0% +this current is zero because the diode's + + + align:start position:0% +this current is zero because the diode's +off when the switch is off this + + align:start position:0% +off when the switch is off this + + + align:start position:0% +off when the switch is off this +dependent current source is equal to + + align:start position:0% +dependent current source is equal to + + + align:start position:0% +dependent current source is equal to +I right so I've sort of got one + + align:start position:0% +I right so I've sort of got one + + + align:start position:0% +I right so I've sort of got one +dependent voltage source from one + + align:start position:0% +dependent voltage source from one + + + align:start position:0% +dependent voltage source from one +dependent current source which impos the + + align:start position:0% +dependent current source which impos the + + + align:start position:0% +dependent current source which impos the +same constraints as what's happening at + + align:start position:0% +same constraints as what's happening at + + + align:start position:0% +same constraints as what's happening at +this node as the original switch and + + align:start position:0% +this node as the original switch and + + + align:start position:0% +this node as the original switch and +diode any questions about + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +yeahi + + align:start position:0% + + + + align:start position:0% + +your + + align:start position:0% +your + + + align:start position:0% +your +No in fact I could have modeled this + + align:start position:0% +No in fact I could have modeled this + + + align:start position:0% +No in fact I could have modeled this +with a dependent current source and that + + align:start position:0% +with a dependent current source and that + + + align:start position:0% +with a dependent current source and that +with a dependent voltage source it would + + align:start position:0% +with a dependent voltage source it would + + + align:start position:0% +with a dependent voltage source it would +have been totally fine would have done + + align:start position:0% +have been totally fine would have done + + + align:start position:0% +have been totally fine would have done +the same thing + + align:start position:0% +the same thing + + + align:start position:0% +the same thing +right there's a lot of ways I could do + + align:start position:0% +right there's a lot of ways I could do + + + align:start position:0% +right there's a lot of ways I could do +this and in fact I don't even have to do + + align:start position:0% +this and in fact I don't even have to do + + + align:start position:0% +this and in fact I don't even have to do +it I could operate everything I was + + align:start position:0% +it I could operate everything I was + + + align:start position:0% +it I could operate everything I was +going to say with the switches but + + align:start position:0% +going to say with the switches but + + + align:start position:0% +going to say with the switches but +really what I'm interested in is how + + align:start position:0% +really what I'm interested in is how + + + align:start position:0% +really what I'm interested in is how +does the switch in the diode control the + + align:start position:0% +does the switch in the diode control the + + + align:start position:0% +does the switch in the diode control the +waveforms in the circuit and and cause + + align:start position:0% +waveforms in the circuit and and cause + + + align:start position:0% +waveforms in the circuit and and cause +currents to be fed to the capacitor and + + align:start position:0% +currents to be fed to the capacitor and + + + align:start position:0% +currents to be fed to the capacitor and +voltages to be fed to the inductor and + + align:start position:0% +voltages to be fed to the inductor and + + + align:start position:0% +voltages to be fed to the inductor and +this is just a simpler way to get + + align:start position:0% +this is just a simpler way to get + + + align:start position:0% +this is just a simpler way to get +it okay does that make sense + + align:start position:0% +it okay does that make sense + + + align:start position:0% +it okay does that make sense +everybody so + + align:start position:0% +everybody so + + + align:start position:0% +everybody so +this is still a switching circuit right + + align:start position:0% +this is still a switching circuit right + + + align:start position:0% +this is still a switching circuit right +in fact if I simulated this circuit and + + align:start position:0% +in fact if I simulated this circuit and + + + align:start position:0% +in fact if I simulated this circuit and +I knew Q of from some like I ran a + + align:start position:0% +I knew Q of from some like I ran a + + + align:start position:0% +I knew Q of from some like I ran a +controller and I had some Q oft I could + + align:start position:0% +controller and I had some Q oft I could + + + align:start position:0% +controller and I had some Q oft I could +simulate this and it would generate + + align:start position:0% +simulate this and it would generate + + + align:start position:0% +simulate this and it would generate +exactly right this switching wave form + + align:start position:0% +exactly right this switching wave form + + + align:start position:0% +exactly right this switching wave form +if I told you Q of T and that Q oft is + + align:start position:0% +if I told you Q of T and that Q oft is + + + align:start position:0% +if I told you Q of T and that Q oft is +the constant Duty ratio here and I + + align:start position:0% +the constant Duty ratio here and I + + + align:start position:0% +the constant Duty ratio here and I +simulated this circuit with with that Q + + align:start position:0% +simulated this circuit with with that Q + + + align:start position:0% +simulated this circuit with with that Q +oft I would and I change the load + + align:start position:0% +oft I would and I change the load + + + align:start position:0% +oft I would and I change the load +resistance I would get exactly that + + align:start position:0% +resistance I would get exactly that + + + align:start position:0% +resistance I would get exactly that +response okay so as long as I'm in + + align:start position:0% +response okay so as long as I'm in + + + align:start position:0% +response okay so as long as I'm in +continuous conduction mode this model + + align:start position:0% +continuous conduction mode this model + + + align:start position:0% +continuous conduction mode this model +represents that + + align:start position:0% +represents that + + + align:start position:0% +represents that +circuit but I want to get rid of the + + align:start position:0% +circuit but I want to get rid of the + + + align:start position:0% +circuit but I want to get rid of the +switching right so let me just go + + align:start position:0% +switching right so let me just go + + + align:start position:0% +switching right so let me just go +average this circuit I'm going to apply + + align:start position:0% +average this circuit I'm going to apply + + + align:start position:0% +average this circuit I'm going to apply +that operator to that circuit and what + + align:start position:0% +that operator to that circuit and what + + + align:start position:0% +that operator to that circuit and what +do I know well I know that if I apply + + align:start position:0% +do I know well I know that if I apply + + + align:start position:0% +do I know well I know that if I apply +the operator to the Circuit the topology + + align:start position:0% +the operator to the Circuit the topology + + + align:start position:0% +the operator to the Circuit the topology +of the new circuit doesn't + + align:start position:0% +of the new circuit doesn't + + + align:start position:0% +of the new circuit doesn't +change + + align:start position:0% +change + + + align:start position:0% +change +why because when I apply averaging I get + + align:start position:0% +why because when I apply averaging I get + + + align:start position:0% +why because when I apply averaging I get +the same set of kvl and KL equation so + + align:start position:0% +the same set of kvl and KL equation so + + + align:start position:0% +the same set of kvl and KL equation so +the topology ought to be the same okay + + align:start position:0% +the topology ought to be the same okay + + + align:start position:0% +the topology ought to be the same okay +and what that means is I can take the + + align:start position:0% +and what that means is I can take the + + + align:start position:0% +and what that means is I can take the +same circuit and I can just replace V in + + align:start position:0% +same circuit and I can just replace V in + + + align:start position:0% +same circuit and I can just replace V in +by V in bar I by iil + + align:start position:0% +by V in bar I by iil + + + align:start position:0% +by V in bar I by iil +bar uh V out by V out bar and L C and R + + align:start position:0% +bar uh V out by V out bar and L C and R + + + align:start position:0% +bar uh V out by V out bar and L C and R +all stay the same because I've told you + + align:start position:0% +all stay the same because I've told you + + + align:start position:0% +all stay the same because I've told you +what happens to the to the uh to the IV + + align:start position:0% +what happens to the to the uh to the IV + + + align:start position:0% +what happens to the to the uh to the IV +characteristics of my linear time inv + + align:start position:0% +characteristics of my linear time inv + + + align:start position:0% +characteristics of my linear time inv +varing components right the only thing I + + align:start position:0% +varing components right the only thing I + + + align:start position:0% +varing components right the only thing I +haven't said what Happ happens is to + + align:start position:0% +haven't said what Happ happens is to + + + align:start position:0% +haven't said what Happ happens is to +these two components I've drawn in pink + + align:start position:0% +these two components I've drawn in pink + + + align:start position:0% +these two components I've drawn in pink +and so what I really have to do is take + + align:start position:0% +and so what I really have to do is take + + + align:start position:0% +and so what I really have to do is take +the local average of the product of V + + align:start position:0% +the local average of the product of V + + + align:start position:0% +the local average of the product of V +out and the switching + + align:start position:0% +out and the switching + + + align:start position:0% +out and the switching +waveform and iil in the switching wave + + align:start position:0% +waveform and iil in the switching wave + + + align:start position:0% +waveform and iil in the switching wave +form all right and that's kind of ugly + + align:start position:0% +form all right and that's kind of ugly + + + align:start position:0% +form all right and that's kind of ugly +because now I have the local average of + + align:start position:0% +because now I have the local average of + + + align:start position:0% +because now I have the local average of +a product right and I got to go think + + align:start position:0% +a product right and I got to go think + + + align:start position:0% +a product right and I got to go think +about that a little + + align:start position:0% +about that a little + + + align:start position:0% +about that a little +bit now let me tell you something about + + align:start position:0% +bit now let me tell you something about + + + align:start position:0% +bit now let me tell you something about +the local average of products right okay + + align:start position:0% +the local average of products right okay + + + align:start position:0% +the local average of products right okay +um one property that this operator + + align:start position:0% +um one property that this operator + + + align:start position:0% +um one property that this operator +doesn't have in general is that + + align:start position:0% +doesn't have in general is that + + + align:start position:0% +doesn't have in general is that +typically if I have uh X of + + align:start position:0% +typically if I have uh X of + + + align:start position:0% +typically if I have uh X of +t y of + + align:start position:0% +t y of + + + align:start position:0% +t y of +T and I take the local average of that + + align:start position:0% +T and I take the local average of that + + + align:start position:0% +T and I take the local average of that +in + + align:start position:0% + + + + align:start position:0% + +general is not equal to xar of + + align:start position:0% +general is not equal to xar of + + + align:start position:0% +general is not equal to xar of +t y bar of + + align:start position:0% +t y bar of + + + align:start position:0% +t y bar of +T okay you can't just arbitrarily do + + align:start position:0% +T okay you can't just arbitrarily do + + + align:start position:0% +T okay you can't just arbitrarily do +that how can I prove it to you suppose I + + align:start position:0% +that how can I prove it to you suppose I + + + align:start position:0% +that how can I prove it to you suppose I +had two + + align:start position:0% +had two + + + align:start position:0% +had two +signals um that were like this here's X + + align:start position:0% +signals um that were like this here's X + + + align:start position:0% +signals um that were like this here's X +of + + align:start position:0% + + + + align:start position:0% + +T suppose X oft is just a 50% Duty ratio + + align:start position:0% +T suppose X oft is just a 50% Duty ratio + + + align:start position:0% +T suppose X oft is just a 50% Duty ratio +Square wave like this here + + align:start position:0% +Square wave like this here + + + align:start position:0% +Square wave like this here +0.5t here's T this is X of + + align:start position:0% +0.5t here's T this is X of + + + align:start position:0% +0.5t here's T this is X of +T right what is xar of t for that + + align:start position:0% +T right what is xar of t for that + + + align:start position:0% +T right what is xar of t for that +signal and suppose this goes on + + align:start position:0% +signal and suppose this goes on + + + align:start position:0% +signal and suppose this goes on +forever and this height one yeah it's + + align:start position:0% +forever and this height one yeah it's + + + align:start position:0% +forever and this height one yeah it's +just going to be half right any given + + align:start position:0% +just going to be half right any given + + + align:start position:0% +just going to be half right any given +time if I slide a window over this and I + + align:start position:0% +time if I slide a window over this and I + + + align:start position:0% +time if I slide a window over this and I +take the average I've always got it high + + align:start position:0% +take the average I've always got it high + + + align:start position:0% +take the average I've always got it high +half the time so xar of + + align:start position:0% +half the time so xar of + + + align:start position:0% +half the time so xar of +T is just equal to + + align:start position:0% +T is just equal to + + + align:start position:0% +T is just equal to +0.5 okay well what happens if I made its + + align:start position:0% +0.5 okay well what happens if I made its + + + align:start position:0% +0.5 okay well what happens if I made its +complement Y Bar of t + + align:start position:0% + + + + align:start position:0% + +right here's y I'm sorry here's y of T + + align:start position:0% +right here's y I'm sorry here's y of T + + + align:start position:0% +right here's y I'm sorry here's y of T +right y of T is exactly the complement + + align:start position:0% +right y of T is exactly the complement + + + align:start position:0% +right y of T is exactly the complement +of X of T so what I would argue is that + + align:start position:0% +of X of T so what I would argue is that + + + align:start position:0% +of X of T so what I would argue is that +Y Bar of + + align:start position:0% + + + + align:start position:0% + +T is also equal to 0.5 right it just + + align:start position:0% +T is also equal to 0.5 right it just + + + align:start position:0% +T is also equal to 0.5 right it just +happens to be out of + + align:start position:0% + + + + align:start position:0% + +phase well what's X of t y of + + align:start position:0% + + + + align:start position:0% + +T I think I heard somebody say that it's + + align:start position:0% +T I think I heard somebody say that it's + + + align:start position:0% +T I think I heard somebody say that it's +zero right one of them is zero all the + + align:start position:0% +zero right one of them is zero all the + + + align:start position:0% +zero right one of them is zero all the +time and that's zip so if I took the + + align:start position:0% +time and that's zip so if I took the + + + align:start position:0% +time and that's zip so if I took the +local average of + + align:start position:0% +local average of + + + align:start position:0% +local average of +xar if I took the local average of x * y + + align:start position:0% +xar if I took the local average of x * y + + + align:start position:0% +xar if I took the local average of x * y +that would have to be equal to zero but + + align:start position:0% +that would have to be equal to zero but + + + align:start position:0% +that would have to be equal to zero but +if I took xar + + align:start position:0% +if I took xar + + + align:start position:0% +if I took xar +Yar that would actually be equal to + + align:start position:0% +Yar that would actually be equal to + + + align:start position:0% +Yar that would actually be equal to +0.25 right so that's proof that in + + align:start position:0% +0.25 right so that's proof that in + + + align:start position:0% +0.25 right so that's proof that in +general I can't just take the local + + align:start position:0% +general I can't just take the local + + + align:start position:0% +general I can't just take the local +average of the product and expect it to + + align:start position:0% +average of the product and expect it to + + + align:start position:0% +average of the product and expect it to +be the product of the local averages + + align:start position:0% +be the product of the local averages + + + align:start position:0% +be the product of the local averages +that just doesn't work + + align:start position:0% +that just doesn't work + + + align:start position:0% +that just doesn't work +generally okay and I care because I have + + align:start position:0% +generally okay and I care because I have + + + align:start position:0% +generally okay and I care because I have +this kind of local average of a product + + align:start position:0% +this kind of local average of a product + + + align:start position:0% +this kind of local average of a product +over here + + align:start position:0% +over here + + + align:start position:0% +over here +but imagine the reason this kind of + + align:start position:0% +but imagine the reason this kind of + + + align:start position:0% +but imagine the reason this kind of +failed was because when y was high X was + + align:start position:0% +failed was because when y was high X was + + + align:start position:0% +failed was because when y was high X was +low and vice versa right they were both + + align:start position:0% +low and vice versa right they were both + + + align:start position:0% +low and vice versa right they were both +kind of doing crazy + + align:start position:0% +kind of doing crazy + + + align:start position:0% +kind of doing crazy +stuff what happens if perhaps one of X + + align:start position:0% +stuff what happens if perhaps one of X + + + align:start position:0% +stuff what happens if perhaps one of X +of T and Y of T sort of look like a + + align:start position:0% +of T and Y of T sort of look like a + + + align:start position:0% +of T and Y of T sort of look like a +constant roughly speaking + + align:start position:0% +constant roughly speaking + + + align:start position:0% +constant roughly speaking +and what I what do I mean by constant I + + align:start position:0% +and what I what do I mean by constant I + + + align:start position:0% +and what I what do I mean by constant I +mean that it has two properties + + align:start position:0% +mean that it has two properties + + + align:start position:0% +mean that it has two properties +if x or + + align:start position:0% +if x or + + + align:start position:0% +if x or +y + + align:start position:0% +y + + + align:start position:0% +y +has one a small + + align:start position:0% + + + + align:start position:0% + +Ripple in other words it's not sort of + + align:start position:0% +Ripple in other words it's not sort of + + + align:start position:0% +Ripple in other words it's not sort of +varying full scale within the + + align:start position:0% +varying full scale within the + + + align:start position:0% +varying full scale within the +cycle and two slow + + align:start position:0% + + + + align:start position:0% + +variation meaning it's not one thing in + + align:start position:0% +variation meaning it's not one thing in + + + align:start position:0% +variation meaning it's not one thing in +one cycle in jumping to some massive + + align:start position:0% +one cycle in jumping to some massive + + + align:start position:0% +one cycle in jumping to some massive +thing in another cycle massively + + align:start position:0% +thing in another cycle massively + + + align:start position:0% +thing in another cycle massively +different another cycle it's just sort + + align:start position:0% +different another cycle it's just sort + + + align:start position:0% +different another cycle it's just sort +of the two waveforms just sort of like + + align:start position:0% +of the two waveforms just sort of like + + + align:start position:0% +of the two waveforms just sort of like +one of the two just it may move but it + + align:start position:0% +one of the two just it may move but it + + + align:start position:0% +one of the two just it may move but it +only moves a little bit okay uh + + align:start position:0% +only moves a little bit okay uh + + + align:start position:0% +only moves a little bit okay uh +then I can kind of think of within any + + align:start position:0% +then I can kind of think of within any + + + align:start position:0% +then I can kind of think of within any +given + + align:start position:0% +given + + + align:start position:0% +given +interval one of those two is sort of + + align:start position:0% +interval one of those two is sort of + + + align:start position:0% +interval one of those two is sort of +constant and then like linearity right + + align:start position:0% +constant and then like linearity right + + + align:start position:0% +constant and then like linearity right +then then I can just take the product of + + align:start position:0% +then then I can just take the product of + + + align:start position:0% +then then I can just take the product of +the local averages right so in this case + + align:start position:0% +the local averages right so in this case + + + align:start position:0% +the local averages right so in this case +I can have x y Y Bar is approximately + + align:start position:0% +I can have x y Y Bar is approximately + + + align:start position:0% +I can have x y Y Bar is approximately +equal to xar Y Bar right so the only + + align:start position:0% +equal to xar Y Bar right so the only + + + align:start position:0% +equal to xar Y Bar right so the only +reason this failed is because they're + + align:start position:0% +reason this failed is because they're + + + align:start position:0% +reason this failed is because they're +both flapping up and down in + + align:start position:0% +both flapping up and down in + + + align:start position:0% +both flapping up and down in +Counterpoint if only one of them's + + align:start position:0% +Counterpoint if only one of them's + + + align:start position:0% +Counterpoint if only one of them's +flapping up and down the other sort of + + align:start position:0% +flapping up and down the other sort of + + + align:start position:0% +flapping up and down the other sort of +constant at least constant you know not + + align:start position:0% +constant at least constant you know not + + + align:start position:0% +constant at least constant you know not +changing that much in in the given + + align:start position:0% +changing that much in in the given + + + align:start position:0% +changing that much in in the given +capital T interval I could make that + + align:start position:0% +capital T interval I could make that + + + align:start position:0% +capital T interval I could make that +approximation does that make sense + + align:start position:0% +approximation does that make sense + + + align:start position:0% +approximation does that make sense +everybody + + align:start position:0% +everybody + + + align:start position:0% +everybody +so this might be true of If X or Y is + + align:start position:0% +so this might be true of If X or Y is + + + align:start position:0% +so this might be true of If X or Y is +an inductor current or a capacitor + + align:start position:0% +an inductor current or a capacitor + + + align:start position:0% +an inductor current or a capacitor +voltage right we know that you know even + + align:start position:0% +voltage right we know that you know even + + + align:start position:0% +voltage right we know that you know even +in that example I was showing you yeah + + align:start position:0% +in that example I was showing you yeah + + + align:start position:0% +in that example I was showing you yeah +there's some Ripple but it's you know on + + align:start position:0% +there's some Ripple but it's you know on + + + align:start position:0% +there's some Ripple but it's you know on +top of a big DC + + align:start position:0% +top of a big DC + + + align:start position:0% +top of a big DC +offset it's not going to it's not really + + align:start position:0% +offset it's not going to it's not really + + + align:start position:0% +offset it's not going to it's not really +violating that approximate approximation + + align:start position:0% +violating that approximate approximation + + + align:start position:0% +violating that approximate approximation +very much so here maybe I could say that + + align:start position:0% +very much so here maybe I could say that + + + align:start position:0% +very much so here maybe I could say that +uh 1 minus Q time the product of 1 minus + + align:start position:0% +uh 1 minus Q time the product of 1 minus + + + align:start position:0% +uh 1 minus Q time the product of 1 minus +Q times uh v v out is approximately + + align:start position:0% +Q times uh v v out is approximately + + + align:start position:0% +Q times uh v v out is approximately +equal to 1 - Q * V out bar and 1 - Q * I + + align:start position:0% +equal to 1 - Q * V out bar and 1 - Q * I + + + align:start position:0% +equal to 1 - Q * V out bar and 1 - Q * I +is approximately equal to 1 - Q Bar * I + + align:start position:0% +is approximately equal to 1 - Q Bar * I + + + align:start position:0% +is approximately equal to 1 - Q Bar * I +bar + + align:start position:0% +bar + + + align:start position:0% +bar +okay um let me Define d as being equal + + align:start position:0% +okay um let me Define d as being equal + + + align:start position:0% +okay um let me Define d as being equal +to Q Bar of + + align:start position:0% + + + + align:start position:0% + +T right in any given cycle if I'm + + align:start position:0% +T right in any given cycle if I'm + + + align:start position:0% +T right in any given cycle if I'm +assuming my duty ratio is changing + + align:start position:0% +assuming my duty ratio is changing + + + align:start position:0% +assuming my duty ratio is changing +slowly it's about equal to the local + + align:start position:0% +slowly it's about equal to the local + + + align:start position:0% +slowly it's about equal to the local +average of qft because that's what my + + align:start position:0% +average of qft because that's what my + + + align:start position:0% +average of qft because that's what my +pwm modulator over there was doing right + + align:start position:0% +pwm modulator over there was doing right + + + align:start position:0% +pwm modulator over there was doing right +it was giving me a duty ratio now this + + align:start position:0% +it was giving me a duty ratio now this + + + align:start position:0% +it was giving me a duty ratio now this +is precisely only true when I'm looking + + align:start position:0% +is precisely only true when I'm looking + + + align:start position:0% +is precisely only true when I'm looking +at capital T and I look back and I get D + + align:start position:0% +at capital T and I look back and I get D + + + align:start position:0% +at capital T and I look back and I get D +for that cycle is exactly here if I did + + align:start position:0% +for that cycle is exactly here if I did + + + align:start position:0% +for that cycle is exactly here if I did +my local average right here but if D of + + align:start position:0% +my local average right here but if D of + + + align:start position:0% +my local average right here but if D of +T is changing only slowly that's a + + align:start position:0% +T is changing only slowly that's a + + + align:start position:0% +T is changing only slowly that's a +pretty good model to within half a cycle + + align:start position:0% +pretty good model to within half a cycle + + + align:start position:0% +pretty good model to within half a cycle +okay so then + + align:start position:0% +okay so then + + + align:start position:0% +okay so then +I could replace this I could say 1 - Q + + align:start position:0% +I could replace this I could say 1 - Q + + + align:start position:0% +I could replace this I could say 1 - Q +is equal + + align:start position:0% +is equal + + + align:start position:0% +is equal +to 1 - D * V out bar and this is equal + + align:start position:0% +to 1 - D * V out bar and this is equal + + + align:start position:0% +to 1 - D * V out bar and this is equal +to 1us D * I bar right and I can average + + align:start position:0% +to 1us D * I bar right and I can average + + + align:start position:0% +to 1us D * I bar right and I can average +this circuit and what I'm going to get + + align:start position:0% +this circuit and what I'm going to get + + + align:start position:0% +this circuit and what I'm going to get +is + + align:start position:0% +is + + + align:start position:0% +is +this the + + align:start position:0% + + + + align:start position:0% + +Nar iil + + align:start position:0% +Nar iil + + + align:start position:0% +Nar iil +bar this becomes a source + + align:start position:0% +bar this becomes a source + + + align:start position:0% +bar this becomes a source +1 minus D times v v out bar and this + + align:start position:0% +1 minus D times v v out bar and this + + + align:start position:0% +1 minus D times v v out bar and this +becomes 1 minus D * I + + align:start position:0% + + + + align:start position:0% + +bar + + align:start position:0% +bar + + + align:start position:0% +bar +c + + align:start position:0% +c + + + align:start position:0% +c +r v bar okay this circuit has no + + align:start position:0% +r v bar okay this circuit has no + + + align:start position:0% +r v bar okay this circuit has no +switching D is a continuously varying + + align:start position:0% +switching D is a continuously varying + + + align:start position:0% +switching D is a continuously varying +variable that my controller might + + align:start position:0% +variable that my controller might + + + align:start position:0% +variable that my controller might +generate there's no switching left in + + align:start position:0% +generate there's no switching left in + + + align:start position:0% +generate there's no switching left in +this circuit + + align:start position:0% +this circuit + + + align:start position:0% +this circuit +it does vary in time it's a dynamic + + align:start position:0% +it does vary in time it's a dynamic + + + align:start position:0% +it does vary in time it's a dynamic +circuit has an l and a c and if D + + align:start position:0% +circuit has an l and a c and if D + + + align:start position:0% +circuit has an l and a c and if D +changes over time the voltages and + + align:start position:0% +changes over time the voltages and + + + align:start position:0% +changes over time the voltages and +currents in this will change but I've + + align:start position:0% +currents in this will change but I've + + + align:start position:0% +currents in this will change but I've +sort of killed the switching Ripple + + align:start position:0% +sort of killed the switching Ripple + + + align:start position:0% +sort of killed the switching Ripple +essentially applying my local average + + align:start position:0% +essentially applying my local average + + + align:start position:0% +essentially applying my local average +operator to the + + align:start position:0% +operator to the + + + align:start position:0% +operator to the +Circuit all + + align:start position:0% +Circuit all + + + align:start position:0% +Circuit all +right that make sense + + align:start position:0% +right that make sense + + + align:start position:0% +right that make sense +everybody let's take a look at what + + align:start position:0% +everybody let's take a look at what + + + align:start position:0% +everybody let's take a look at what +happens if I do that this is a + + align:start position:0% +happens if I do that this is a + + + align:start position:0% +happens if I do that this is a +simulation of this exact circuit + + align:start position:0% +simulation of this exact circuit + + + align:start position:0% +simulation of this exact circuit +okay um for the same transient except + + align:start position:0% +okay um for the same transient except + + + align:start position:0% +okay um for the same transient except +that I'm simulating this thing it's in + + align:start position:0% +that I'm simulating this thing it's in + + + align:start position:0% +that I'm simulating this thing it's in +that little box that says average model + + align:start position:0% +that little box that says average model + + + align:start position:0% +that little box that says average model +okay there is a diode there that diode + + align:start position:0% +okay there is a diode there that diode + + + align:start position:0% +okay there is a diode there that diode +is just providing a constant drop + + align:start position:0% +is just providing a constant drop + + + align:start position:0% +is just providing a constant drop +because keep in mind my approximate + + align:start position:0% +because keep in mind my approximate + + + align:start position:0% +because keep in mind my approximate +models didn't really include constant + + align:start position:0% +models didn't really include constant + + + align:start position:0% +models didn't really include constant +diode drops or anything like that so + + align:start position:0% +diode drops or anything like that so + + + align:start position:0% +diode drops or anything like that so +that that diode there is not doing any + + align:start position:0% +that that diode there is not doing any + + + align:start position:0% +that that diode there is not doing any +switching it's providing a constant DC + + align:start position:0% +switching it's providing a constant DC + + + align:start position:0% +switching it's providing a constant DC +offset but this is the transit you get + + align:start position:0% +offset but this is the transit you get + + + align:start position:0% +offset but this is the transit you get +when you change the resistance in that + + align:start position:0% +when you change the resistance in that + + + align:start position:0% +when you change the resistance in that +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +here's the voltage and here's the + + align:start position:0% +here's the voltage and here's the + + + align:start position:0% +here's the voltage and here's the +current it's sort of right up the middle + + align:start position:0% +current it's sort of right up the middle + + + align:start position:0% +current it's sort of right up the middle +right so basically I've got a circuit + + align:start position:0% +right so basically I've got a circuit + + + align:start position:0% +right so basically I've got a circuit +that has second order response and it + + align:start position:0% +that has second order response and it + + + align:start position:0% +that has second order response and it +tracks the average values of my + + align:start position:0% +tracks the average values of my + + + align:start position:0% +tracks the average values of my +waveforms got gotten rid of the + + align:start position:0% +waveforms got gotten rid of the + + + align:start position:0% +waveforms got gotten rid of the +switching so this + + align:start position:0% + + + + align:start position:0% + +circuit could + + align:start position:0% +circuit could + + + align:start position:0% +circuit could +be it's not in a controller form but + + align:start position:0% +be it's not in a controller form but + + + align:start position:0% +be it's not in a controller form but +it's a circuit that tracks this whole + + align:start position:0% +it's a circuit that tracks this whole + + + align:start position:0% +it's a circuit that tracks this whole +thing without any + + align:start position:0% + + + + align:start position:0% + +switching questions about + + align:start position:0% + + + + align:start position:0% + +that now we're going to take this up + + align:start position:0% +that now we're going to take this up + + + align:start position:0% +that now we're going to take this up +next + + align:start position:0% +next + + + align:start position:0% +next +class okay but I wanted to show you + + align:start position:0% +class okay but I wanted to show you + + + align:start position:0% +class okay but I wanted to show you +um kind of the the basis for um doing + + align:start position:0% +um kind of the the basis for um doing + + + align:start position:0% +um kind of the the basis for um doing +this I want to say this is really useful + + align:start position:0% +this I want to say this is really useful + + + align:start position:0% +this I want to say this is really useful +for building control models for + + align:start position:0% +for building control models for + + + align:start position:0% +for building control models for +converters because now I have something + + align:start position:0% +converters because now I have something + + + align:start position:0% +converters because now I have something +that I've gotten rid of all the + + align:start position:0% +that I've gotten rid of all the + + + align:start position:0% +that I've gotten rid of all the +complicated switching stuff but it still + + align:start position:0% +complicated switching stuff but it still + + + align:start position:0% +complicated switching stuff but it still +gives me the low frequency dynamics that + + align:start position:0% +gives me the low frequency dynamics that + + + align:start position:0% +gives me the low frequency dynamics that +I want to deal with my + + align:start position:0% +I want to deal with my + + + align:start position:0% +I want to deal with my +controller I will warn you that this + + align:start position:0% +controller I will warn you that this + + + align:start position:0% +controller I will warn you that this +system is + + align:start position:0% +system is + + + align:start position:0% +system is +nonlinear okay why because you notice D + + align:start position:0% +nonlinear okay why because you notice D + + + align:start position:0% +nonlinear okay why because you notice D +is my control variable here and it + + align:start position:0% +is my control variable here and it + + + align:start position:0% +is my control variable here and it +multiplies the output voltage and it + + align:start position:0% +multiplies the output voltage and it + + + align:start position:0% +multiplies the output voltage and it +multiplies the inductor current so I + + align:start position:0% +multiplies the inductor current so I + + + align:start position:0% +multiplies the inductor current so I +have a product of my control input my + + align:start position:0% +have a product of my control input my + + + align:start position:0% +have a product of my control input my +state variables this is not a linear + + align:start position:0% +state variables this is not a linear + + + align:start position:0% +state variables this is not a linear +system from in terms of going from Duty + + align:start position:0% +system from in terms of going from Duty + + + align:start position:0% +system from in terms of going from Duty +ratio to Output + + align:start position:0% +ratio to Output + + + align:start position:0% +ratio to Output +so I I still have nonlinearity I have to + + align:start position:0% +so I I still have nonlinearity I have to + + + align:start position:0% +so I I still have nonlinearity I have to +deal with and that's just life okay + + align:start position:0% +deal with and that's just life okay + + + align:start position:0% +deal with and that's just life okay +we'll talk about how to deal with that + + align:start position:0% +we'll talk about how to deal with that + + + align:start position:0% +we'll talk about how to deal with that +um it's very good for doing low + + align:start position:0% +um it's very good for doing low + + + align:start position:0% +um it's very good for doing low +frequency controller + + align:start position:0% +frequency controller + + + align:start position:0% +frequency controller +modeling okay it's not useful for other + + align:start position:0% +modeling okay it's not useful for other + + + align:start position:0% +modeling okay it's not useful for other +things so for example if I asked you to + + align:start position:0% +things so for example if I asked you to + + + align:start position:0% +things so for example if I asked you to +ver calculate power dissipation of + + align:start position:0% +ver calculate power dissipation of + + + align:start position:0% +ver calculate power dissipation of +components you cannot use this + + align:start position:0% +components you cannot use this + + + align:start position:0% +components you cannot use this +model why because what would the power + + align:start position:0% +model why because what would the power + + + align:start position:0% +model why because what would the power +dissipation in the switch be the power + + align:start position:0% +dissipation in the switch be the power + + + align:start position:0% +dissipation in the switch be the power +dissipation in the switch would be the + + align:start position:0% +dissipation in the switch would be the + + + align:start position:0% +dissipation in the switch would be the +switch voltage times the switch current + + align:start position:0% +switch voltage times the switch current + + + align:start position:0% +switch voltage times the switch current +both of which are pulsing up and down + + align:start position:0% +both of which are pulsing up and down + + + align:start position:0% +both of which are pulsing up and down +together it violates this assumption I + + align:start position:0% +together it violates this assumption I + + + align:start position:0% +together it violates this assumption I +was talking about right in fact the + + align:start position:0% +was talking about right in fact the + + + align:start position:0% +was talking about right in fact the +voltage and current on the switch + + align:start position:0% +voltage and current on the switch + + + align:start position:0% +voltage and current on the switch +actually look a lot like that so I can + + align:start position:0% +actually look a lot like that so I can + + + align:start position:0% +actually look a lot like that so I can +use this average model to do things like + + align:start position:0% +use this average model to do things like + + + align:start position:0% +use this average model to do things like +control Dynamics that's perfect for it I + + align:start position:0% +control Dynamics that's perfect for it I + + + align:start position:0% +control Dynamics that's perfect for it I +can't use it to ask answer questions + + align:start position:0% +can't use it to ask answer questions + + + align:start position:0% +can't use it to ask answer questions +like dissipation or other kinds of + + align:start position:0% +like dissipation or other kinds of + + + align:start position:0% +like dissipation or other kinds of +things so I am well out of time today uh + + align:start position:0% +things so I am well out of time today uh + + + align:start position:0% +things so I am well out of time today uh +but we will take up the notion of + + align:start position:0% +but we will take up the notion of + + + align:start position:0% +but we will take up the notion of +control modeling next class have a great + + align:start position:0% +control modeling next class have a great + + + align:start position:0% +control modeling next class have a great +day okay \ No newline at end of file diff --git a/j3CaKev2GnQ.txt b/j3CaKev2GnQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..dd49a8b65fa5d273cc16ac43a4a1105f128a37b1 --- /dev/null +++ b/j3CaKev2GnQ.txt @@ -0,0 +1,579 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT opencourseware continue to + + align:start position:0% +will help MIT opencourseware continue to + + + align:start position:0% +will help MIT opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +this is a course about meaning + + align:start position:0% +this is a course about meaning + + + align:start position:0% +this is a course about meaning +the idea is to understand first what the + + align:start position:0% +the idea is to understand first what the + + + align:start position:0% +the idea is to understand first what the +standard model is for understanding how + + align:start position:0% +standard model is for understanding how + + + align:start position:0% +standard model is for understanding how +it is that we can use language to + + align:start position:0% +it is that we can use language to + + + align:start position:0% +it is that we can use language to +communicate to transfer information + + align:start position:0% +communicate to transfer information + + + align:start position:0% +communicate to transfer information +between us + + align:start position:0% +between us + + + align:start position:0% +between us +the second part of the course + + align:start position:0% +the second part of the course + + + align:start position:0% +the second part of the course +is to understand why vagueness spells + + align:start position:0% +is to understand why vagueness spells + + + align:start position:0% +is to understand why vagueness spells +disaster for the standard model + + align:start position:0% +disaster for the standard model + + + align:start position:0% +disaster for the standard model +sometimes when people teach a graduate + + align:start position:0% +sometimes when people teach a graduate + + + align:start position:0% +sometimes when people teach a graduate +course on vagueness they do so in a very + + align:start position:0% +course on vagueness they do so in a very + + + align:start position:0% +course on vagueness they do so in a very +puzzle oriented way this is not how I + + align:start position:0% +puzzle oriented way this is not how I + + + align:start position:0% +puzzle oriented way this is not how I +teach the course I think of it as a big + + align:start position:0% +teach the course I think of it as a big + + + align:start position:0% +teach the course I think of it as a big +picture course in the philosophy of + + align:start position:0% +picture course in the philosophy of + + + align:start position:0% +picture course in the philosophy of +language the idea is to use vagueness to + + align:start position:0% +language the idea is to use vagueness to + + + align:start position:0% +language the idea is to use vagueness to +understand how meaning works + + align:start position:0% + + + + align:start position:0% + +affairs something one might call the + + align:start position:0% +affairs something one might call the + + + align:start position:0% +affairs something one might call the +standard model + + align:start position:0% +standard model + + + align:start position:0% +standard model +a picture whereby sentences have + + align:start position:0% +a picture whereby sentences have + + + align:start position:0% +a picture whereby sentences have +meanings and we can use these meanings + + align:start position:0% +meanings and we can use these meanings + + + align:start position:0% +meanings and we can use these meanings +in etherea communication to explain how + + align:start position:0% +in etherea communication to explain how + + + align:start position:0% +in etherea communication to explain how +it is that language works + + align:start position:0% +it is that language works + + + align:start position:0% +it is that language works +the way I see vagueness it + + align:start position:0% +the way I see vagueness it + + + align:start position:0% +the way I see vagueness it +draws the standard model + + align:start position:0% +draws the standard model + + + align:start position:0% +draws the standard model +so I think of the course as an effort to + + align:start position:0% +so I think of the course as an effort to + + + align:start position:0% +so I think of the course as an effort to +First understand why the standard model + + align:start position:0% +First understand why the standard model + + + align:start position:0% +First understand why the standard model +is threatened by vagueness and secondly + + align:start position:0% +is threatened by vagueness and secondly + + + align:start position:0% +is threatened by vagueness and secondly +to try and find an alternate model that + + align:start position:0% +to try and find an alternate model that + + + align:start position:0% +to try and find an alternate model that +can explain how communication Works in + + align:start position:0% +can explain how communication Works in + + + align:start position:0% +can explain how communication Works in +spite of fakeness + + align:start position:0% +spite of fakeness + + + align:start position:0% +spite of fakeness +a typical class session will consist of + + align:start position:0% +a typical class session will consist of + + + align:start position:0% +a typical class session will consist of +overall discussion + + align:start position:0% +overall discussion + + + align:start position:0% +overall discussion +amongst everyone in the seminar so there + + align:start position:0% +amongst everyone in the seminar so there + + + align:start position:0% +amongst everyone in the seminar so there +is very little lecture what happens is + + align:start position:0% +is very little lecture what happens is + + + align:start position:0% +is very little lecture what happens is +we've all read a text + + align:start position:0% +we've all read a text + + + align:start position:0% +we've all read a text +and + + align:start position:0% +and + + + align:start position:0% +and +I might say a few words to get the + + align:start position:0% +I might say a few words to get the + + + align:start position:0% +I might say a few words to get the +discussion warmed up and after that + + align:start position:0% +discussion warmed up and after that + + + align:start position:0% +discussion warmed up and after that +people bring up problems we discuss the + + align:start position:0% +people bring up problems we discuss the + + + align:start position:0% +people bring up problems we discuss the +problems and it's in these interactions + + align:start position:0% +problems and it's in these interactions + + + align:start position:0% +problems and it's in these interactions +that we acquire an understanding of + + align:start position:0% +that we acquire an understanding of + + + align:start position:0% +that we acquire an understanding of +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +in teaching a course about vagueness one + + align:start position:0% +in teaching a course about vagueness one + + + align:start position:0% +in teaching a course about vagueness one +faces a challenge because the literature + + align:start position:0% +faces a challenge because the literature + + + align:start position:0% +faces a challenge because the literature +is enormous + + align:start position:0% +is enormous + + + align:start position:0% +is enormous +so one has to either + + align:start position:0% +so one has to either + + + align:start position:0% +so one has to either +discuss many texts and not too much + + align:start position:0% +discuss many texts and not too much + + + align:start position:0% +discuss many texts and not too much +detail or discuss a few in a lot of + + align:start position:0% +detail or discuss a few in a lot of + + + align:start position:0% +detail or discuss a few in a lot of +detail and I choose the latter approach + + align:start position:0% +detail and I choose the latter approach + + + align:start position:0% +detail and I choose the latter approach +so + + align:start position:0% +so + + + align:start position:0% +so +I've picked maybe 10 or 12 texts which I + + align:start position:0% +I've picked maybe 10 or 12 texts which I + + + align:start position:0% +I've picked maybe 10 or 12 texts which I +think are especially illuminated and we + + align:start position:0% +think are especially illuminated and we + + + align:start position:0% +think are especially illuminated and we +spent a lot of time getting to + + align:start position:0% +spent a lot of time getting to + + + align:start position:0% +spent a lot of time getting to +understand each of them really well + + align:start position:0% +understand each of them really well + + + align:start position:0% +understand each of them really well +I think this would be a difficult course + + align:start position:0% +I think this would be a difficult course + + + align:start position:0% +I think this would be a difficult course +to take on one's own + + align:start position:0% +to take on one's own + + + align:start position:0% +to take on one's own +uh if someone wanted to take it from a + + align:start position:0% +uh if someone wanted to take it from a + + + align:start position:0% +uh if someone wanted to take it from a +distance what I would recommend is + + align:start position:0% +distance what I would recommend is + + + align:start position:0% +distance what I would recommend is +finding a partner finding someone to do + + align:start position:0% +finding a partner finding someone to do + + + align:start position:0% +finding a partner finding someone to do +the readings with and discuss them + + align:start position:0% +the readings with and discuss them + + + align:start position:0% +the readings with and discuss them +I want to ask someone to talk these + + align:start position:0% +I want to ask someone to talk these + + + align:start position:0% +I want to ask someone to talk these +things through with it makes a big + + align:start position:0% +things through with it makes a big + + + align:start position:0% +things through with it makes a big +difference because the issues are subtle + + align:start position:0% +difference because the issues are subtle + + + align:start position:0% +difference because the issues are subtle +and it's often difficult to identify + + align:start position:0% +and it's often difficult to identify + + + align:start position:0% +and it's often difficult to identify +them on a first reading \ No newline at end of file diff --git a/kr8Hn8y3sEg.txt b/kr8Hn8y3sEg.txt new file mode 100644 index 0000000000000000000000000000000000000000..af8a6c663e86e604e1df957fe836d411cd5bc960 --- /dev/null +++ b/kr8Hn8y3sEg.txt @@ -0,0 +1,7331 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT opencourseware continue to + + align:start position:0% +will help MIT opencourseware continue to + + + align:start position:0% +will help MIT opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +today we're going to talk about + + align:start position:0% +today we're going to talk about + + + align:start position:0% +today we're going to talk about +Evolution the earliest nervous systems + + align:start position:0% + + + + align:start position:0% + +nervous systems so important with + + align:start position:0% +nervous systems so important with + + + align:start position:0% +nervous systems so important with +multicellular organisms + + align:start position:0% + + + + align:start position:0% + +single cell organisms + + align:start position:0% +single cell organisms + + + align:start position:0% +single cell organisms +can do a lot and they don't have nervous + + align:start position:0% +can do a lot and they don't have nervous + + + align:start position:0% +can do a lot and they don't have nervous +systems + + align:start position:0% +systems + + + align:start position:0% +systems +but remember they have the Primitive + + align:start position:0% +but remember they have the Primitive + + + align:start position:0% +but remember they have the Primitive +cellular mechanisms they respond to + + align:start position:0% +cellular mechanisms they respond to + + + align:start position:0% +cellular mechanisms they respond to +inputs say + + align:start position:0% + + + + align:start position:0% + +the effects of inputs are conducted + + align:start position:0% +the effects of inputs are conducted + + + align:start position:0% +the effects of inputs are conducted +throughout the cell + + align:start position:0% +throughout the cell + + + align:start position:0% +throughout the cell +they respond to cells + + align:start position:0% + + + + align:start position:0% + +they do a lot of things multi-sellular + + align:start position:0% +they do a lot of things multi-sellular + + + align:start position:0% +they do a lot of things multi-sellular +organisms do + + align:start position:0% +organisms do + + + align:start position:0% +organisms do +but as soon as you start putting a lot + + align:start position:0% +but as soon as you start putting a lot + + + align:start position:0% +but as soon as you start putting a lot +of cells together then you have the + + align:start position:0% +of cells together then you have the + + + align:start position:0% +of cells together then you have the +problem of integration one part of the + + align:start position:0% +problem of integration one part of the + + + align:start position:0% +problem of integration one part of the +organism with another + + align:start position:0% +organism with another + + + align:start position:0% +organism with another +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +what are some + + align:start position:0% +what are some + + + align:start position:0% +what are some +multi-purpose actions that every animal + + align:start position:0% +multi-purpose actions that every animal + + + align:start position:0% +multi-purpose actions that every animal +even one cell organisms must be able to + + align:start position:0% +even one cell organisms must be able to + + + align:start position:0% +even one cell organisms must be able to +perform + + align:start position:0% + + + + align:start position:0% + +I teach animal behavior and so this to + + align:start position:0% +I teach animal behavior and so this to + + + align:start position:0% +I teach animal behavior and so this to +me + + align:start position:0% +me + + + align:start position:0% +me +even though it's emitted by a lot of + + align:start position:0% +even though it's emitted by a lot of + + + align:start position:0% +even though it's emitted by a lot of +Behavioral + + align:start position:0% +Behavioral + + + align:start position:0% +Behavioral +textbooks and teachers to me you've got + + align:start position:0% +textbooks and teachers to me you've got + + + align:start position:0% +textbooks and teachers to me you've got +to start with the fundamentals what is + + align:start position:0% +to start with the fundamentals what is + + + align:start position:0% +to start with the fundamentals what is +what do Power animals do + + align:start position:0% + + + + align:start position:0% + +Locomotion big one + + align:start position:0% +Locomotion big one + + + align:start position:0% +Locomotion big one +you know what do they use Locomotion for + + align:start position:0% + + + + align:start position:0% + +escape from things to get away from + + align:start position:0% +escape from things to get away from + + + align:start position:0% +escape from things to get away from +things + + align:start position:0% +things + + + align:start position:0% +things +and to grab things + + align:start position:0% +and to grab things + + + align:start position:0% +and to grab things +either attack them and kill them and eat + + align:start position:0% +either attack them and kill them and eat + + + align:start position:0% +either attack them and kill them and eat +them or find food in some other way + + align:start position:0% +them or find food in some other way + + + align:start position:0% +them or find food in some other way +requires Locomotion unless there are a + + align:start position:0% +requires Locomotion unless there are a + + + align:start position:0% +requires Locomotion unless there are a +few Exceptions there are animals that + + align:start position:0% +few Exceptions there are animals that + + + align:start position:0% +few Exceptions there are animals that +have been have evolved at least at + + align:start position:0% +have been have evolved at least at + + + align:start position:0% +have been have evolved at least at +certain stages of their life sessile + + align:start position:0% +certain stages of their life sessile + + + align:start position:0% +certain stages of their life sessile +forms where they just sit but most + + align:start position:0% +forms where they just sit but most + + + align:start position:0% +forms where they just sit but most +organisms have to locomotive cords are + + align:start position:0% +organisms have to locomotive cords are + + + align:start position:0% +organisms have to locomotive cords are +away from things what else + + align:start position:0% +away from things what else + + + align:start position:0% +away from things what else +what is another multi-purpose action + + align:start position:0% + + + + align:start position:0% + +reproduction very basic but reproduction + + align:start position:0% +reproduction very basic but reproduction + + + align:start position:0% +reproduction very basic but reproduction +that's a that's a a broader thing I'm + + align:start position:0% +that's a that's a a broader thing I'm + + + align:start position:0% +that's a that's a a broader thing I'm +talking about fundamental action + + align:start position:0% +talking about fundamental action + + + align:start position:0% +talking about fundamental action +patterns so let's go back from + + align:start position:0% +patterns so let's go back from + + + align:start position:0% +patterns so let's go back from +reproduction + + align:start position:0% +reproduction + + + align:start position:0% +reproduction +but these things we're talking about are + + align:start position:0% +but these things we're talking about are + + + align:start position:0% +but these things we're talking about are +involved in reproduction you're + + align:start position:0% +involved in reproduction you're + + + align:start position:0% +involved in reproduction you're +absolutely right and that's particularly + + align:start position:0% +absolutely right and that's particularly + + + align:start position:0% +absolutely right and that's particularly +fundamental because + + align:start position:0% +fundamental because + + + align:start position:0% +fundamental because +that's what drives Evolution uh yeah + + align:start position:0% + + + + align:start position:0% + +responding to a stimulus very basic but + + align:start position:0% +responding to a stimulus very basic but + + + align:start position:0% +responding to a stimulus very basic but +I want the action how do they respond to + + align:start position:0% +I want the action how do they respond to + + + align:start position:0% +I want the action how do they respond to +the students + + align:start position:0% +the students + + + align:start position:0% +the students +besides locomotive + + align:start position:0% +besides locomotive + + + align:start position:0% +besides locomotive +yes + + align:start position:0% +yes + + + align:start position:0% +yes +oriented turning + + align:start position:0% +oriented turning + + + align:start position:0% +oriented turning +animals have to respond to where things + + align:start position:0% +animals have to respond to where things + + + align:start position:0% +animals have to respond to where things +are + + align:start position:0% +are + + + align:start position:0% +are +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +Locomotion approaching for orienting + + align:start position:0% +Locomotion approaching for orienting + + + align:start position:0% +Locomotion approaching for orienting +towards or away again + + align:start position:0% +towards or away again + + + align:start position:0% +towards or away again +um and then I've added here exploring or + + align:start position:0% +um and then I've added here exploring or + + + align:start position:0% +um and then I've added here exploring or +foraging or seeking + + align:start position:0% +foraging or seeking + + + align:start position:0% +foraging or seeking +but you see that's just includes the + + align:start position:0% +but you see that's just includes the + + + align:start position:0% +but you see that's just includes the +first two but what is included in + + align:start position:0% +first two but what is included in + + + align:start position:0% +first two but what is included in +foraging that's not + + align:start position:0% +foraging that's not + + + align:start position:0% +foraging that's not +necessarily in those first two + + align:start position:0% +necessarily in those first two + + + align:start position:0% +necessarily in those first two +Locomotion and Orient there's an element + + align:start position:0% +Locomotion and Orient there's an element + + + align:start position:0% +Locomotion and Orient there's an element +that's involved I think I probably asked + + align:start position:0% +that's involved I think I probably asked + + + align:start position:0% +that's involved I think I probably asked +that yeah here that's the next question + + align:start position:0% +that yeah here that's the next question + + + align:start position:0% +that yeah here that's the next question +okay a portion of related to flight + + align:start position:0% +okay a portion of related to flight + + + align:start position:0% +okay a portion of related to flight +movements are controlled by sensory + + align:start position:0% +movements are controlled by sensory + + + align:start position:0% +movements are controlled by sensory +inputs Plus + + align:start position:0% +inputs Plus + + + align:start position:0% +inputs Plus +one other thing one other important + + align:start position:0% +one other thing one other important + + + align:start position:0% +one other thing one other important +thing what is that other thing + + align:start position:0% +thing what is that other thing + + + align:start position:0% +thing what is that other thing +it's very important in the evolution of + + align:start position:0% +it's very important in the evolution of + + + align:start position:0% +it's very important in the evolution of +the CNS + + align:start position:0% +the CNS + + + align:start position:0% +the CNS +grasping is part of we'll include yeah + + align:start position:0% +grasping is part of we'll include yeah + + + align:start position:0% +grasping is part of we'll include yeah +grasping is actually a third fundamental + + align:start position:0% +grasping is actually a third fundamental + + + align:start position:0% +grasping is actually a third fundamental +action but grasping is it's always + + align:start position:0% +action but grasping is it's always + + + align:start position:0% +action but grasping is it's always +I'm thinking of something else + + align:start position:0% + + + + align:start position:0% + +anybody + + align:start position:0% +anybody + + + align:start position:0% +anybody +yes + + align:start position:0% + + + + align:start position:0% + +motivation the internal drive something + + align:start position:0% +motivation the internal drive something + + + align:start position:0% +motivation the internal drive something +that comes from inside + + align:start position:0% +that comes from inside + + + align:start position:0% +that comes from inside +I mean why they why are they locomoting + + align:start position:0% +I mean why they why are they locomoting + + + align:start position:0% +I mean why they why are they locomoting +in One Direction now in another + + align:start position:0% +in One Direction now in another + + + align:start position:0% +in One Direction now in another +direction another time why are they + + align:start position:0% +direction another time why are they + + + align:start position:0% +direction another time why are they +trying to get to food one time to a mate + + align:start position:0% +trying to get to food one time to a mate + + + align:start position:0% +trying to get to food one time to a mate +another time and so on and so forth + + align:start position:0% +another time and so on and so forth + + + align:start position:0% +another time and so on and so forth +depends on internal States all right + + align:start position:0% +depends on internal States all right + + + align:start position:0% +depends on internal States all right +and then as I mentioned + + align:start position:0% +and then as I mentioned + + + align:start position:0% +and then as I mentioned +in that earlier slide we didn't get + + align:start position:0% +in that earlier slide we didn't get + + + align:start position:0% +in that earlier slide we didn't get +through everything there but I asked a + + align:start position:0% +through everything there but I asked a + + + align:start position:0% +through everything there but I asked a +question about it here what are the + + align:start position:0% +question about it here what are the + + + align:start position:0% +question about it here what are the +ongoing ongoing maintenance activities + + align:start position:0% +ongoing ongoing maintenance activities + + + align:start position:0% +ongoing ongoing maintenance activities +or background activities + + align:start position:0% +or background activities + + + align:start position:0% +or background activities +that are happening all the time + + align:start position:0% +that are happening all the time + + + align:start position:0% +that are happening all the time +while The Locomotion is happening well + + align:start position:0% +while The Locomotion is happening well + + + align:start position:0% +while The Locomotion is happening well +the orienting is happening you know + + align:start position:0% +the orienting is happening you know + + + align:start position:0% +the orienting is happening you know +whatever the motivation it's independent + + align:start position:0% +whatever the motivation it's independent + + + align:start position:0% +whatever the motivation it's independent +of motivation what are the ongoing + + align:start position:0% +of motivation what are the ongoing + + + align:start position:0% +of motivation what are the ongoing +background activities and what kind of + + align:start position:0% +background activities and what kind of + + + align:start position:0% +background activities and what kind of +nervous system mechanisms involved yes + + align:start position:0% + + + + align:start position:0% + +yeah things that are maintained need to + + align:start position:0% +yeah things that are maintained need to + + + align:start position:0% +yeah things that are maintained need to +be maintained in a constant state that's + + align:start position:0% +be maintained in a constant state that's + + + align:start position:0% +be maintained in a constant state that's +good + + align:start position:0% +good + + + align:start position:0% +good +can anybody think of other things + + align:start position:0% + + + + align:start position:0% + +think of when you're + + align:start position:0% +think of when you're + + + align:start position:0% +think of when you're +you're doing one of these fundamental + + align:start position:0% +you're doing one of these fundamental + + + align:start position:0% +you're doing one of these fundamental +things you're locomotive you're going to + + align:start position:0% +things you're locomotive you're going to + + + align:start position:0% +things you're locomotive you're going to +your next class what are the background + + align:start position:0% +your next class what are the background + + + align:start position:0% +your next class what are the background +things going on + + align:start position:0% +things going on + + + align:start position:0% +things going on +what is your body doing what what's it + + align:start position:0% +what is your body doing what what's it + + + align:start position:0% +what is your body doing what what's it +maintaining in homeostasis your + + align:start position:0% +maintaining in homeostasis your + + + align:start position:0% +maintaining in homeostasis your +temperature for example + + align:start position:0% +temperature for example + + + align:start position:0% +temperature for example +even protists will seek places of the + + align:start position:0% +even protists will seek places of the + + + align:start position:0% +even protists will seek places of the +right temperature + + align:start position:0% +right temperature + + + align:start position:0% +right temperature +they may not have much internal + + align:start position:0% +they may not have much internal + + + align:start position:0% +they may not have much internal +they're not endothermic + + align:start position:0% +they're not endothermic + + + align:start position:0% +they're not endothermic +okay but like we are but they still have + + align:start position:0% +okay but like we are but they still have + + + align:start position:0% +okay but like we are but they still have +some kind of Regulation + + align:start position:0% +some kind of Regulation + + + align:start position:0% +some kind of Regulation +they still have to eliminate they still + + align:start position:0% +they still have to eliminate they still + + + align:start position:0% +they still have to eliminate they still +have to + + align:start position:0% +have to + + + align:start position:0% +have to +you know + + align:start position:0% +you know + + + align:start position:0% +you know +what about a quadruped now like or two + + align:start position:0% +what about a quadruped now like or two + + + align:start position:0% +what about a quadruped now like or two +or four-legged animal + + align:start position:0% +or four-legged animal + + + align:start position:0% +or four-legged animal +what does he do when he's locomoting + + align:start position:0% +what does he do when he's locomoting + + + align:start position:0% +what does he do when he's locomoting +what is the maintenance + + align:start position:0% +what is the maintenance + + + align:start position:0% +what is the maintenance +balance yeah across here this happened + + align:start position:0% +balance yeah across here this happened + + + align:start position:0% +balance yeah across here this happened +what are the mechanisms now that control + + align:start position:0% +what are the mechanisms now that control + + + align:start position:0% +what are the mechanisms now that control +these background picks + + align:start position:0% +these background picks + + + align:start position:0% +these background picks +what do we call them they're lower level + + align:start position:0% +what do we call them they're lower level + + + align:start position:0% +what do we call them they're lower level +mechanisms for the most part + + align:start position:0% +mechanisms for the most part + + + align:start position:0% +mechanisms for the most part +many of them are spinal mechanisms as + + align:start position:0% +many of them are spinal mechanisms as + + + align:start position:0% +many of them are spinal mechanisms as +we'll be talking about yes + + align:start position:0% +we'll be talking about yes + + + align:start position:0% +we'll be talking about yes +a lot of them are reflexes very simple + + align:start position:0% +a lot of them are reflexes very simple + + + align:start position:0% +a lot of them are reflexes very simple +local Pathways that's exactly right + + align:start position:0% +local Pathways that's exactly right + + + align:start position:0% +local Pathways that's exactly right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +simple reflexes and simple programs that + + align:start position:0% +simple reflexes and simple programs that + + + align:start position:0% +simple reflexes and simple programs that +are ongoing so they don't heart race one + + align:start position:0% +are ongoing so they don't heart race one + + + align:start position:0% +are ongoing so they don't heart race one +the heart of course + + align:start position:0% +the heart of course + + + align:start position:0% +the heart of course +has its own ganglion that's regulating + + align:start position:0% +has its own ganglion that's regulating + + + align:start position:0% +has its own ganglion that's regulating +it + + align:start position:0% +it + + + align:start position:0% +it +but it's enforced by the central nervous + + align:start position:0% +but it's enforced by the central nervous + + + align:start position:0% +but it's enforced by the central nervous +system also to suggested + + align:start position:0% +system also to suggested + + + align:start position:0% +system also to suggested +because you need a lot more blood flow + + align:start position:0% +because you need a lot more blood flow + + + align:start position:0% +because you need a lot more blood flow +when you're running than you do when + + align:start position:0% +when you're running than you do when + + + align:start position:0% +when you're running than you do when +you're not running and things like that + + align:start position:0% +you're not running and things like that + + + align:start position:0% +you're not running and things like that +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so now let's start talking about + + align:start position:0% +so now let's start talking about + + + align:start position:0% +so now let's start talking about +conduction get to nervous nervous cells + + align:start position:0% +conduction get to nervous nervous cells + + + align:start position:0% +conduction get to nervous nervous cells +nerve cells how can conduction between + + align:start position:0% +nerve cells how can conduction between + + + align:start position:0% +nerve cells how can conduction between +cells occur without synaptic connections + + align:start position:0% +cells occur without synaptic connections + + + align:start position:0% +cells occur without synaptic connections +we find such conduct conduction before + + align:start position:0% +we find such conduct conduction before + + + align:start position:0% +we find such conduct conduction before +we find real nerves + + align:start position:0% +we find real nerves + + + align:start position:0% +we find real nerves +it's found in sponges even + + align:start position:0% +it's found in sponges even + + + align:start position:0% +it's found in sponges even +as well as in this nadarians like Hydra + + align:start position:0% +as well as in this nadarians like Hydra + + + align:start position:0% +as well as in this nadarians like Hydra +most of these things I'm going to talk + + align:start position:0% +most of these things I'm going to talk + + + align:start position:0% +most of these things I'm going to talk +about are found in little creatures like + + align:start position:0% +about are found in little creatures like + + + align:start position:0% +about are found in little creatures like +Hydra + + align:start position:0% +Hydra + + + align:start position:0% +Hydra +we used to call them ritual entries + + align:start position:0% + + + + align:start position:0% + +that's been revised + + align:start position:0% + + + + align:start position:0% + +even sponges have conduction between + + align:start position:0% +even sponges have conduction between + + + align:start position:0% +even sponges have conduction between +cells if you touch a sponge + + align:start position:0% +cells if you touch a sponge + + + align:start position:0% +cells if you touch a sponge +it's just not the cells that you're + + align:start position:0% +it's just not the cells that you're + + + align:start position:0% +it's just not the cells that you're +touching that are responding other cells + + align:start position:0% +touching that are responding other cells + + + align:start position:0% +touching that are responding other cells +respond too + + align:start position:0% + + + + align:start position:0% + +like + + align:start position:0% + + + + align:start position:0% + +yeah there are there is a kind of + + align:start position:0% +yeah there are there is a kind of + + + align:start position:0% +yeah there are there is a kind of +electrical conduction this + + align:start position:0% +electrical conduction this + + + align:start position:0% +electrical conduction this +this people sometimes call this + + align:start position:0% +this people sometimes call this + + + align:start position:0% +this people sometimes call this +conduction myoid and neuroid just + + align:start position:0% +conduction myoid and neuroid just + + + align:start position:0% +conduction myoid and neuroid just +meaning it's like conduction between + + align:start position:0% +meaning it's like conduction between + + + align:start position:0% +meaning it's like conduction between +muscle cells its light conduction + + align:start position:0% +muscle cells its light conduction + + + align:start position:0% +muscle cells its light conduction +between nerve cells but it's not really + + align:start position:0% +between nerve cells but it's not really + + + align:start position:0% +between nerve cells but it's not really +the same as an advanced organisms + + align:start position:0% +the same as an advanced organisms + + + align:start position:0% +the same as an advanced organisms +it's a term used in mauda and the + + align:start position:0% +it's a term used in mauda and the + + + align:start position:0% +it's a term used in mauda and the +prototype's book and it's used in + + align:start position:0% +prototype's book and it's used in + + + align:start position:0% +prototype's book and it's used in +by others to talk about + + align:start position:0% +by others to talk about + + + align:start position:0% +by others to talk about +primitive conductive mechanisms + + align:start position:0% +primitive conductive mechanisms + + + align:start position:0% +primitive conductive mechanisms +and it's been in the study of the + + align:start position:0% +and it's been in the study of the + + + align:start position:0% +and it's been in the study of the +anatomy of those creatures that we get + + align:start position:0% +anatomy of those creatures that we get + + + align:start position:0% +anatomy of those creatures that we get +ideas about earliest stages of nervous + + align:start position:0% +ideas about earliest stages of nervous + + + align:start position:0% +ideas about earliest stages of nervous +system evolution + + align:start position:0% +system evolution + + + align:start position:0% +system evolution +I've taken these pictures that I put in + + align:start position:0% +I've taken these pictures that I put in + + + align:start position:0% +I've taken these pictures that I put in +the book + + align:start position:0% +the book + + + align:start position:0% +the book +not uh + + align:start position:0% +not uh + + + align:start position:0% +not uh +not from + + align:start position:0% +not from + + + align:start position:0% +not from +let's + + align:start position:0% +let's + + + align:start position:0% +let's +part George Park or at Yale who's the + + align:start position:0% +part George Park or at Yale who's the + + + align:start position:0% +part George Park or at Yale who's the +guy who first tried to do it but Mackie + + align:start position:0% +guy who first tried to do it but Mackie + + + align:start position:0% +guy who first tried to do it but Mackie +George Mackey who updated it + + align:start position:0% +George Mackey who updated it + + + align:start position:0% +George Mackey who updated it +wrote a nice paper in the quarterly + + align:start position:0% +wrote a nice paper in the quarterly + + + align:start position:0% +wrote a nice paper in the quarterly +quarterly reviewed biology in the 1970. + + align:start position:0% +quarterly reviewed biology in the 1970. + + + align:start position:0% +quarterly reviewed biology in the 1970. +this is his earliest stage there you + + align:start position:0% +this is his earliest stage there you + + + align:start position:0% +this is his earliest stage there you +have contractile cells that are also + + align:start position:0% +have contractile cells that are also + + + align:start position:0% +have contractile cells that are also +sensory + + align:start position:0% +sensory + + + align:start position:0% +sensory +so there's sense fan motor they're + + align:start position:0% +so there's sense fan motor they're + + + align:start position:0% +so there's sense fan motor they're +responding to the environment they can + + align:start position:0% +responding to the environment they can + + + align:start position:0% +responding to the environment they can +contract but he shows + + align:start position:0% +contract but he shows + + + align:start position:0% +contract but he shows +this + + align:start position:0% + + + + align:start position:0% + +he indicates this dashed line where the + + align:start position:0% +he indicates this dashed line where the + + + align:start position:0% +he indicates this dashed line where the +membranes are against each other that + + align:start position:0% +membranes are against each other that + + + align:start position:0% +membranes are against each other that +simply means Gap Junctions is something + + align:start position:0% +simply means Gap Junctions is something + + + align:start position:0% +simply means Gap Junctions is something +equivalent to Gap Junctions in our own + + align:start position:0% +equivalent to Gap Junctions in our own + + + align:start position:0% +equivalent to Gap Junctions in our own +nervous systems it's electrical + + align:start position:0% +nervous systems it's electrical + + + align:start position:0% +nervous systems it's electrical +conductive work charged ions can flow + + align:start position:0% +conductive work charged ions can flow + + + align:start position:0% +conductive work charged ions can flow +from one cell to the other + + align:start position:0% +from one cell to the other + + + align:start position:0% +from one cell to the other +so an electrical change that starts here + + align:start position:0% +so an electrical change that starts here + + + align:start position:0% +so an electrical change that starts here +can spread down the line + + align:start position:0% +can spread down the line + + + align:start position:0% +can spread down the line +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and here's the second stage where there + + align:start position:0% +and here's the second stage where there + + + align:start position:0% +and here's the second stage where there +are some contractual cells now + + align:start position:0% +are some contractual cells now + + + align:start position:0% +are some contractual cells now +that are no longer directly responsive + + align:start position:0% +that are no longer directly responsive + + + align:start position:0% +that are no longer directly responsive +to the environment + + align:start position:0% +to the environment + + + align:start position:0% +to the environment +because some protomyocytes they separate + + align:start position:0% +because some protomyocytes they separate + + + align:start position:0% +because some protomyocytes they separate +from the epithelium they're below the + + align:start position:0% +from the epithelium they're below the + + + align:start position:0% +from the epithelium they're below the +epithelium but you can see they're still + + align:start position:0% + + + + align:start position:0% + +joined to these epithelial cells by + + align:start position:0% +joined to these epithelial cells by + + + align:start position:0% +joined to these epithelial cells by +these Gap Junction type uh + + align:start position:0% + + + + align:start position:0% + +contacts that allow the electrical + + align:start position:0% +contacts that allow the electrical + + + align:start position:0% +contacts that allow the electrical +changes in one cell to influence the + + align:start position:0% +changes in one cell to influence the + + + align:start position:0% +changes in one cell to influence the +next the cell that is next to + + align:start position:0% + + + + align:start position:0% + +it's not like external axonal conduction + + align:start position:0% +it's not like external axonal conduction + + + align:start position:0% +it's not like external axonal conduction +the effect doesn't always spread to in + + align:start position:0% +the effect doesn't always spread to in + + + align:start position:0% +the effect doesn't always spread to in +the entire organism that often + + align:start position:0% +the entire organism that often + + + align:start position:0% +the entire organism that often +diminishes the further you get + + align:start position:0% +diminishes the further you get + + + align:start position:0% +diminishes the further you get +from the source + + align:start position:0% +from the source + + + align:start position:0% +from the source +and here + + align:start position:0% + + + + align:start position:0% + +the contractile cells are no longer + + align:start position:0% +the contractile cells are no longer + + + align:start position:0% +the contractile cells are no longer +directly connected to most of these + + align:start position:0% +directly connected to most of these + + + align:start position:0% +directly connected to most of these +cells there is there are neurons in the + + align:start position:0% +cells there is there are neurons in the + + + align:start position:0% +cells there is there are neurons in the +epithelium that are like neurons in that + + align:start position:0% +epithelium that are like neurons in that + + + align:start position:0% +epithelium that are like neurons in that +they have an accent a process an + + align:start position:0% +they have an accent a process an + + + align:start position:0% +they have an accent a process an +excellent like process that extends down + + align:start position:0% +excellent like process that extends down + + + align:start position:0% +excellent like process that extends down +to the muscle cells the connections are + + align:start position:0% +to the muscle cells the connections are + + + align:start position:0% +to the muscle cells the connections are +still all electrical in nature there's + + align:start position:0% +still all electrical in nature there's + + + align:start position:0% +still all electrical in nature there's +no chemical secretion yet triggering a + + align:start position:0% +no chemical secretion yet triggering a + + + align:start position:0% +no chemical secretion yet triggering a +response in the next cell + + align:start position:0% + + + + align:start position:0% + +it calls them proto-neurons + + align:start position:0% +it calls them proto-neurons + + + align:start position:0% +it calls them proto-neurons +you know + + align:start position:0% +you know + + + align:start position:0% +you know +they are epithelial cells + + align:start position:0% +they are epithelial cells + + + align:start position:0% +they are epithelial cells +we have some + + align:start position:0% +we have some + + + align:start position:0% +we have some +primary central neurons that are just + + align:start position:0% +primary central neurons that are just + + + align:start position:0% +primary central neurons that are just +like this we'll talk about that in a + + align:start position:0% +like this we'll talk about that in a + + + align:start position:0% +like this we'll talk about that in a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +and there is a electrical contact with + + align:start position:0% +and there is a electrical contact with + + + align:start position:0% +and there is a electrical contact with +the contractile cell + + align:start position:0% +the contractile cell + + + align:start position:0% +the contractile cell +which are now + + align:start position:0% +which are now + + + align:start position:0% +which are now +you know completely sub-epithelial note + + align:start position:0% +you know completely sub-epithelial note + + + align:start position:0% +you know completely sub-epithelial note +the only context with the epithelium is + + align:start position:0% +the only context with the epithelium is + + + align:start position:0% +the only context with the epithelium is +through that exact sunlight accent like + + align:start position:0% +through that exact sunlight accent like + + + align:start position:0% +through that exact sunlight accent like +processes and then he has + + align:start position:0% +processes and then he has + + + align:start position:0% +processes and then he has +real neurons appearing motor neurons + + align:start position:0% +real neurons appearing motor neurons + + + align:start position:0% +real neurons appearing motor neurons +with a chemical chemical synapse + + align:start position:0% +with a chemical chemical synapse + + + align:start position:0% +with a chemical chemical synapse +when he looked at Hydra he found things + + align:start position:0% +when he looked at Hydra he found things + + + align:start position:0% +when he looked at Hydra he found things +like this evidence for chemical synapses + + align:start position:0% +like this evidence for chemical synapses + + + align:start position:0% +like this evidence for chemical synapses +contacting the contractual cells and it + + align:start position:0% +contacting the contractual cells and it + + + align:start position:0% +contacting the contractual cells and it +was those cells then that got input from + + align:start position:0% +was those cells then that got input from + + + align:start position:0% +was those cells then that got input from +the epithelia + + align:start position:0% + + + + align:start position:0% + +now you can call it a primary sensory + + align:start position:0% +now you can call it a primary sensory + + + align:start position:0% +now you can call it a primary sensory +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +so now you've got a + + align:start position:0% +so now you've got a + + + align:start position:0% +so now you've got a +two synapse + + align:start position:0% +two synapse + + + align:start position:0% +two synapse +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +what was missing now to study + + align:start position:0% +what was missing now to study + + + align:start position:0% +what was missing now to study +the earlier is not the he knew mackie's + + align:start position:0% +the earlier is not the he knew mackie's + + + align:start position:0% +the earlier is not the he knew mackie's +work he knew that George Parker would + + align:start position:0% +work he knew that George Parker would + + + align:start position:0% +work he knew that George Parker would +decides me and Parker + + align:start position:0% +decides me and Parker + + + align:start position:0% +decides me and Parker +but he realized there's something missed + + align:start position:0% +but he realized there's something missed + + + align:start position:0% +but he realized there's something missed +there's no intermediate Network + + align:start position:0% +there's no intermediate Network + + + align:start position:0% +there's no intermediate Network +and so and that's what I've added I + + align:start position:0% +and so and that's what I've added I + + + align:start position:0% +and so and that's what I've added I +added to the question here the addition + + align:start position:0% +added to the question here the addition + + + align:start position:0% +added to the question here the addition +emphasized by now and I'm sorry I + + align:start position:0% +emphasized by now and I'm sorry I + + + align:start position:0% +emphasized by now and I'm sorry I +answered before you this is the picture + + align:start position:0% +answered before you this is the picture + + + align:start position:0% +answered before you this is the picture +again that now it adds so now this book + + align:start position:0% +again that now it adds so now this book + + + align:start position:0% +again that now it adds so now this book +he has those earlier stages + + align:start position:0% +he has those earlier stages + + + align:start position:0% +he has those earlier stages +uh and then he has + + align:start position:0% +uh and then he has + + + align:start position:0% +uh and then he has +cells in between the sensory neuron + + align:start position:0% +cells in between the sensory neuron + + + align:start position:0% +cells in between the sensory neuron +he has the axon now not directly + + align:start position:0% +he has the axon now not directly + + + align:start position:0% +he has the axon now not directly +contacting either a muscle cell or a + + align:start position:0% +contacting either a muscle cell or a + + + align:start position:0% +contacting either a muscle cell or a +motor neuron but contacting a neuron in + + align:start position:0% +motor neuron but contacting a neuron in + + + align:start position:0% +motor neuron but contacting a neuron in +between + + align:start position:0% +between + + + align:start position:0% +between +so this is a neuron now that's not + + align:start position:0% +so this is a neuron now that's not + + + align:start position:0% +so this is a neuron now that's not +in direct contact with the environment + + align:start position:0% +in direct contact with the environment + + + align:start position:0% +in direct contact with the environment +outside and it's not connecting + + align:start position:0% +outside and it's not connecting + + + align:start position:0% +outside and it's not connecting +contractor cells it is really an + + align:start position:0% +contractor cells it is really an + + + align:start position:0% +contractor cells it is really an +intermediate neuron + + align:start position:0% +intermediate neuron + + + align:start position:0% +intermediate neuron +so we would Define this as a motor + + align:start position:0% +so we would Define this as a motor + + + align:start position:0% +so we would Define this as a motor +neuron and of course the muscle cell + + align:start position:0% +neuron and of course the muscle cell + + + align:start position:0% +neuron and of course the muscle cell +this is we could call plantar sensory + + align:start position:0% +this is we could call plantar sensory + + + align:start position:0% +this is we could call plantar sensory +but then these are the intermediate and + + align:start position:0% +but then these are the intermediate and + + + align:start position:0% +but then these are the intermediate and +that's the beginning of what now it + + align:start position:0% +that's the beginning of what now it + + + align:start position:0% +that's the beginning of what now it +refers to as the great intermediate + + align:start position:0% +refers to as the great intermediate + + + align:start position:0% +refers to as the great intermediate +Network + + align:start position:0% + + + + align:start position:0% + +so now let's define + + align:start position:0% +so now let's define + + + align:start position:0% +so now let's define +for every every nervous system + + align:start position:0% +for every every nervous system + + + align:start position:0% +for every every nervous system +including mammalian primary sensory + + align:start position:0% +including mammalian primary sensory + + + align:start position:0% +including mammalian primary sensory +neuron secondary sensory neuron motor + + align:start position:0% +neuron secondary sensory neuron motor + + + align:start position:0% +neuron secondary sensory neuron motor +neuron and intermediate Network neuron + + align:start position:0% +neuron and intermediate Network neuron + + + align:start position:0% +neuron and intermediate Network neuron +just summer I've said I've done it in a + + align:start position:0% +just summer I've said I've done it in a + + + align:start position:0% +just summer I've said I've done it in a +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +but can you define them now + + align:start position:0% +but can you define them now + + + align:start position:0% +but can you define them now +remember I want you to read before you + + align:start position:0% +remember I want you to read before you + + + align:start position:0% +remember I want you to read before you +come to class you should already be able + + align:start position:0% +come to class you should already be able + + + align:start position:0% +come to class you should already be able +to do this + + align:start position:0% +to do this + + + align:start position:0% +to do this +there's one person three two people + + align:start position:0% +there's one person three two people + + + align:start position:0% +there's one person three two people +there have not said anything yet + + align:start position:0% + + + + align:start position:0% + +so speak up + + align:start position:0% +so speak up + + + align:start position:0% +so speak up +Define just one of these what's a motor + + align:start position:0% +Define just one of these what's a motor + + + align:start position:0% +Define just one of these what's a motor +nerve or yeah + + align:start position:0% +nerve or yeah + + + align:start position:0% +nerve or yeah +to find Define any of them + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +very + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay the primary Center + + align:start position:0% +okay the primary Center + + + align:start position:0% +okay the primary Center +and what is it contact you + + align:start position:0% +and what is it contact you + + + align:start position:0% +and what is it contact you +where it is it's + + align:start position:0% +where it is it's + + + align:start position:0% +where it is it's +axon go + + align:start position:0% + + + + align:start position:0% + +to a secondary sensory neuron and where + + align:start position:0% +to a secondary sensory neuron and where + + + align:start position:0% +to a secondary sensory neuron and where +is that one + + align:start position:0% +is that one + + + align:start position:0% +is that one +is it also in the periphery + + align:start position:0% + + + + align:start position:0% + +no + + align:start position:0% +no + + + align:start position:0% +no +secondary sensory neuron + + align:start position:0% +secondary sensory neuron + + + align:start position:0% +secondary sensory neuron +is in the CNS the primary sensory neuron + + align:start position:0% +is in the CNS the primary sensory neuron + + + align:start position:0% +is in the CNS the primary sensory neuron +is not + + align:start position:0% +is not + + + align:start position:0% +is not +major difference between those two types + + align:start position:0% +major difference between those two types + + + align:start position:0% +major difference between those two types +otherwise what you said is completely + + align:start position:0% +otherwise what you said is completely + + + align:start position:0% +otherwise what you said is completely +right okay now what about the motor + + align:start position:0% +right okay now what about the motor + + + align:start position:0% +right okay now what about the motor +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +I've declined it maybe three times so + + align:start position:0% +I've declined it maybe three times so + + + align:start position:0% +I've declined it maybe three times so +far in the class in the corner what is + + align:start position:0% +far in the class in the corner what is + + + align:start position:0% +far in the class in the corner what is +the motor neuron + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% + + + + align:start position:0% + +okay okay well if you don't want to + + align:start position:0% +okay okay well if you don't want to + + + align:start position:0% +okay okay well if you don't want to +answer it somebody else but if you come + + align:start position:0% +answer it somebody else but if you come + + + align:start position:0% +answer it somebody else but if you come +to the class I do expect you to be able + + align:start position:0% +to the class I do expect you to be able + + + align:start position:0% +to the class I do expect you to be able +to answer some questions okay so uh + + align:start position:0% +to answer some questions okay so uh + + + align:start position:0% +to answer some questions okay so uh +somebody else + + align:start position:0% +somebody else + + + align:start position:0% +somebody else +you want to go on + + align:start position:0% + + + + align:start position:0% + +so Define it again the motor neuron + + align:start position:0% +so Define it again the motor neuron + + + align:start position:0% +so Define it again the motor neuron +where is the cell body of the motor + + align:start position:0% +where is the cell body of the motor + + + align:start position:0% +where is the cell body of the motor +neuron + + align:start position:0% + + + + align:start position:0% + +in the central nervous system + + align:start position:0% +in the central nervous system + + + align:start position:0% +in the central nervous system +accent goes out in contact some muscles + + align:start position:0% +accent goes out in contact some muscles + + + align:start position:0% +accent goes out in contact some muscles +so exactly so that's how I came up with + + align:start position:0% +so exactly so that's how I came up with + + + align:start position:0% +so exactly so that's how I came up with +this diagram there's one other cell type + + align:start position:0% +this diagram there's one other cell type + + + align:start position:0% +this diagram there's one other cell type +in here though it's not primary sensor + + align:start position:0% +in here though it's not primary sensor + + + align:start position:0% +in here though it's not primary sensor +neuron it's not secondary sensory neuron + + align:start position:0% +neuron it's not secondary sensory neuron + + + align:start position:0% +neuron it's not secondary sensory neuron +it's not a motor neuron because actually + + align:start position:0% +it's not a motor neuron because actually + + + align:start position:0% +it's not a motor neuron because actually +there's two others + + align:start position:0% +there's two others + + + align:start position:0% +there's two others +place + + align:start position:0% +place + + + align:start position:0% +place +itself like this + + align:start position:0% + + + + align:start position:0% + +and even the secondary sensory neuron is + + align:start position:0% +and even the secondary sensory neuron is + + + align:start position:0% +and even the secondary sensory neuron is +sometimes included in that intermediate + + align:start position:0% +sometimes included in that intermediate + + + align:start position:0% +sometimes included in that intermediate +Network okay but since we Define + + align:start position:0% +Network okay but since we Define + + + align:start position:0% +Network okay but since we Define +secondary sensory already we'll include + + align:start position:0% +secondary sensory already we'll include + + + align:start position:0% +secondary sensory already we'll include +all the rest + + align:start position:0% +all the rest + + + align:start position:0% +all the rest +that are not motor nerves as + + align:start position:0% +that are not motor nerves as + + + align:start position:0% +that are not motor nerves as +intermediate Network neurons + + align:start position:0% + + + + align:start position:0% + +and I should point out this is a good + + align:start position:0% +and I should point out this is a good + + + align:start position:0% +and I should point out this is a good +way to do it right now that many + + align:start position:0% +way to do it right now that many + + + align:start position:0% +way to do it right now that many +neuronatomists when they talk about an + + align:start position:0% +neuronatomists when they talk about an + + + align:start position:0% +neuronatomists when they talk about an +interneuron they always mean a short + + align:start position:0% +interneuron they always mean a short + + + align:start position:0% +interneuron they always mean a short +axon from neuron like these of course + + align:start position:0% +axon from neuron like these of course + + + align:start position:0% +axon from neuron like these of course +I've greatly simplified + + align:start position:0% +I've greatly simplified + + + align:start position:0% +I've greatly simplified +not showing the dendrites simplifying + + align:start position:0% +not showing the dendrites simplifying + + + align:start position:0% +not showing the dendrites simplifying +the axon but still basically that's the + + align:start position:0% +the axon but still basically that's the + + + align:start position:0% +the axon but still basically that's the +way a short axon interneuron connects + + align:start position:0% + + + + align:start position:0% + +but broadly speaking all these are all + + align:start position:0% +but broadly speaking all these are all + + + align:start position:0% +but broadly speaking all these are all +interneurons if they're not primary + + align:start position:0% +interneurons if they're not primary + + + align:start position:0% +interneurons if they're not primary +sensory and they're not motor + + align:start position:0% +sensory and they're not motor + + + align:start position:0% +sensory and they're not motor +everything else is an interneuron we + + align:start position:0% +everything else is an interneuron we + + + align:start position:0% +everything else is an interneuron we +Define secondary sensory + + align:start position:0% +Define secondary sensory + + + align:start position:0% +Define secondary sensory +separately + + align:start position:0% +separately + + + align:start position:0% +separately +most neuron atoms would talk about the + + align:start position:0% +most neuron atoms would talk about the + + + align:start position:0% +most neuron atoms would talk about the +long Axon + + align:start position:0% +long Axon + + + align:start position:0% +long Axon +ourselves in the central nervous system + + align:start position:0% +ourselves in the central nervous system + + + align:start position:0% +ourselves in the central nervous system +they usually don't bother to call them + + align:start position:0% +they usually don't bother to call them + + + align:start position:0% +they usually don't bother to call them +internounds but they actually are they + + align:start position:0% +internounds but they actually are they + + + align:start position:0% +internounds but they actually are they +just have much stronger actions okay now + + align:start position:0% +just have much stronger actions okay now + + + align:start position:0% +just have much stronger actions okay now +we've got an another cell type here + + align:start position:0% +we've got an another cell type here + + + align:start position:0% +we've got an another cell type here +it's not in the central nervous system + + align:start position:0% +it's not in the central nervous system + + + align:start position:0% +it's not in the central nervous system +it's in contact with a motor neuron at + + align:start position:0% +it's in contact with a motor neuron at + + + align:start position:0% +it's in contact with a motor neuron at +least it's a neuron that looks like a + + align:start position:0% +least it's a neuron that looks like a + + + align:start position:0% +least it's a neuron that looks like a +motor neuron because its axon is leaving + + align:start position:0% +motor neuron because its axon is leaving + + + align:start position:0% +motor neuron because its axon is leaving +the central nervous system + + align:start position:0% +the central nervous system + + + align:start position:0% +the central nervous system +what is it + + align:start position:0% +what is it + + + align:start position:0% +what is it +gets in a peripheral ganglion + + align:start position:0% +gets in a peripheral ganglion + + + align:start position:0% +gets in a peripheral ganglion +it's part of the + + align:start position:0% +it's part of the + + + align:start position:0% +it's part of the +it's a mo it's a preganglionic motor + + align:start position:0% +it's a mo it's a preganglionic motor + + + align:start position:0% +it's a mo it's a preganglionic motor +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +here and a ganglionic motor neuron here + + align:start position:0% +here and a ganglionic motor neuron here + + + align:start position:0% +here and a ganglionic motor neuron here +and the ganglionic motor neurons contact + + align:start position:0% +and the ganglionic motor neurons contact + + + align:start position:0% +and the ganglionic motor neurons contact +the smooth muscle or gland cells causing + + align:start position:0% +the smooth muscle or gland cells causing + + + align:start position:0% +the smooth muscle or gland cells causing +glandular secretions causing contraction + + align:start position:0% +glandular secretions causing contraction + + + align:start position:0% +glandular secretions causing contraction +of the gut or some other organ + + align:start position:0% + + + + align:start position:0% + +no they are not we don't we call these + + align:start position:0% +no they are not we don't we call these + + + align:start position:0% +no they are not we don't we call these +into neurons + + align:start position:0% +into neurons + + + align:start position:0% +into neurons +here of course is the type of + + align:start position:0% +here of course is the type of + + + align:start position:0% +here of course is the type of +interneuron but it's defined as a motor + + align:start position:0% +interneuron but it's defined as a motor + + + align:start position:0% +interneuron but it's defined as a motor +neuron in contact with the central + + align:start position:0% +neuron in contact with the central + + + align:start position:0% +neuron in contact with the central +nervous system through a preganglionic + + align:start position:0% +nervous system through a preganglionic + + + align:start position:0% +nervous system through a preganglionic +motor neuron we call this a motor neuron + + align:start position:0% +motor neuron we call this a motor neuron + + + align:start position:0% +motor neuron we call this a motor neuron +because it's got an axon that causes + + align:start position:0% +because it's got an axon that causes + + + align:start position:0% +because it's got an axon that causes +some kind of movement or contraction or + + align:start position:0% +some kind of movement or contraction or + + + align:start position:0% +some kind of movement or contraction or +secretion secretion is considered an + + align:start position:0% +secretion secretion is considered an + + + align:start position:0% +secretion secretion is considered an +output okay + + align:start position:0% +output okay + + + align:start position:0% +output okay +so it's an output neuron but it + + align:start position:0% +so it's an output neuron but it + + + align:start position:0% +so it's an output neuron but it +it exerts its action through a Purple + + align:start position:0% +it exerts its action through a Purple + + + align:start position:0% +it exerts its action through a Purple +Gang + + align:start position:0% +Gang + + + align:start position:0% +Gang +so a sympathetic ganglion a repair + + align:start position:0% +so a sympathetic ganglion a repair + + + align:start position:0% +so a sympathetic ganglion a repair +synthetic gangrian itself + + align:start position:0% +synthetic gangrian itself + + + align:start position:0% +synthetic gangrian itself +which we will be defining in more detail + + align:start position:0% +which we will be defining in more detail + + + align:start position:0% +which we will be defining in more detail +soon okay + + align:start position:0% + + + + align:start position:0% + +so what just + + align:start position:0% +so what just + + + align:start position:0% +so what just +remember for me now the answer to + + align:start position:0% +remember for me now the answer to + + + align:start position:0% +remember for me now the answer to +question five Where are neuronal cell + + align:start position:0% +question five Where are neuronal cell + + + align:start position:0% +question five Where are neuronal cell +bodies of the peripheral nervous system + + align:start position:0% +bodies of the peripheral nervous system + + + align:start position:0% +bodies of the peripheral nervous system +located + + align:start position:0% +located + + + align:start position:0% +located +if you have cell bodies and they're in + + align:start position:0% +if you have cell bodies and they're in + + + align:start position:0% +if you have cell bodies and they're in +the periphery + + align:start position:0% +the periphery + + + align:start position:0% +the periphery +we say they are in + + align:start position:0% +we say they are in + + + align:start position:0% +we say they are in +a ganglion + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +what about these words + + align:start position:0% +what about these words + + + align:start position:0% +what about these words +what is a nerve and what is a tract and + + align:start position:0% +what is a nerve and what is a tract and + + + align:start position:0% +what is a nerve and what is a tract and +there's some other names we could add to + + align:start position:0% +there's some other names we could add to + + + align:start position:0% +there's some other names we could add to +that + + align:start position:0% +that + + + align:start position:0% +that +but just figure out just take those two + + align:start position:0% +but just figure out just take those two + + + align:start position:0% +but just figure out just take those two +nerve and tract + + align:start position:0% +nerve and tract + + + align:start position:0% +nerve and tract +Define nerve for me + + align:start position:0% + + + + align:start position:0% + +anybody want to try + + align:start position:0% + + + + align:start position:0% + +that's very good + + align:start position:0% +that's very good + + + align:start position:0% +that's very good +except + + align:start position:0% +except + + + align:start position:0% +except +it's not always true + + align:start position:0% +it's not always true + + + align:start position:0% +it's not always true +many nerves don't have a common origin + + align:start position:0% +many nerves don't have a common origin + + + align:start position:0% +many nerves don't have a common origin +they can be mixed they can come from + + align:start position:0% +they can be mixed they can come from + + + align:start position:0% +they can be mixed they can come from +various sources + + align:start position:0% +various sources + + + align:start position:0% +various sources +in fact they might not even end up at + + align:start position:0% +in fact they might not even end up at + + + align:start position:0% +in fact they might not even end up at +the same place + + align:start position:0% +the same place + + + align:start position:0% +the same place +that's not what defines them + + align:start position:0% +that's not what defines them + + + align:start position:0% +that's not what defines them +first of all where is a nerve + + align:start position:0% +first of all where is a nerve + + + align:start position:0% +first of all where is a nerve +in the periphery we don't if you hear + + align:start position:0% +in the periphery we don't if you hear + + + align:start position:0% +in the periphery we don't if you hear +people talking about nerves in the brain + + align:start position:0% +people talking about nerves in the brain + + + align:start position:0% +people talking about nerves in the brain +or spinal cord you'll know that they're + + align:start position:0% +or spinal cord you'll know that they're + + + align:start position:0% +or spinal cord you'll know that they're +not neuroanatalous and they've never had + + align:start position:0% +not neuroanatalous and they've never had + + + align:start position:0% +not neuroanatalous and they've never had +this class okay because we don't call + + align:start position:0% +this class okay because we don't call + + + align:start position:0% +this class okay because we don't call +them nerves unless they're in the + + align:start position:0% +them nerves unless they're in the + + + align:start position:0% +them nerves unless they're in the +periphery okay + + align:start position:0% +periphery okay + + + align:start position:0% +periphery okay +in the central nervous system we call + + align:start position:0% +in the central nervous system we call + + + align:start position:0% +in the central nervous system we call +them + + align:start position:0% +them + + + align:start position:0% +them +attract + + align:start position:0% +attract + + + align:start position:0% +attract +or we give them some other name we call + + align:start position:0% +or we give them some other name we call + + + align:start position:0% +or we give them some other name we call +them a bundle a tract a fasciculus a + + align:start position:0% +them a bundle a tract a fasciculus a + + + align:start position:0% +them a bundle a tract a fasciculus a +meniscus + + align:start position:0% +meniscus + + + align:start position:0% +meniscus +all very descriptive terms of what these + + align:start position:0% +all very descriptive terms of what these + + + align:start position:0% +all very descriptive terms of what these +are like bundle that's clear + + align:start position:0% +are like bundle that's clear + + + align:start position:0% +are like bundle that's clear +okay + + align:start position:0% + + + + align:start position:0% + +lemniscus means ribbon + + align:start position:0% +lemniscus means ribbon + + + align:start position:0% +lemniscus means ribbon +so there are rhythm of Fighters + + align:start position:0% +so there are rhythm of Fighters + + + align:start position:0% +so there are rhythm of Fighters +fasciculus basically a term meaning a + + align:start position:0% +fasciculus basically a term meaning a + + + align:start position:0% +fasciculus basically a term meaning a +group a bundle of axes okay + + align:start position:0% + + + + align:start position:0% + +they all mean bundles of axons but + + align:start position:0% +they all mean bundles of axons but + + + align:start position:0% +they all mean bundles of axons but +you've got to keep separate the terms we + + align:start position:0% +you've got to keep separate the terms we + + + align:start position:0% +you've got to keep separate the terms we +use for central nervous system and + + align:start position:0% +use for central nervous system and + + + align:start position:0% +use for central nervous system and +peripheral nervous system + + align:start position:0% +peripheral nervous system + + + align:start position:0% +peripheral nervous system +so on this slide I just poured a bunch + + align:start position:0% +so on this slide I just poured a bunch + + + align:start position:0% +so on this slide I just poured a bunch +of these things they're all defined in + + align:start position:0% +of these things they're all defined in + + + align:start position:0% +of these things they're all defined in +chapter three + + align:start position:0% +chapter three + + + align:start position:0% +chapter three +there's a few things we haven't + + align:start position:0% +there's a few things we haven't + + + align:start position:0% +there's a few things we haven't +mentioned like the different cell groups + + align:start position:0% +mentioned like the different cell groups + + + align:start position:0% +mentioned like the different cell groups +we call them ganglia outside the central + + align:start position:0% +we call them ganglia outside the central + + + align:start position:0% +we call them ganglia outside the central +nervous system that in the central + + align:start position:0% +nervous system that in the central + + + align:start position:0% +nervous system that in the central +nervous system yes we violate our rules + + align:start position:0% +nervous system yes we violate our rules + + + align:start position:0% +nervous system yes we violate our rules +sometimes when we talk about the basal + + align:start position:0% +sometimes when we talk about the basal + + + align:start position:0% +sometimes when we talk about the basal +ganglia + + align:start position:0% +ganglia + + + align:start position:0% +ganglia +that has to do with the history of the + + align:start position:0% +that has to do with the history of the + + + align:start position:0% +that has to do with the history of the +field but usually in the South and + + align:start position:0% +field but usually in the South and + + + align:start position:0% +field but usually in the South and +nervous system groups of cells + + align:start position:0% + + + + align:start position:0% + +that are functionally distinct and are + + align:start position:0% +that are functionally distinct and are + + + align:start position:0% +that are functionally distinct and are +anatomically distinct or usually both + + align:start position:0% +anatomically distinct or usually both + + + align:start position:0% +anatomically distinct or usually both +we call them nuclei just to confuse you + + align:start position:0% +we call them nuclei just to confuse you + + + align:start position:0% +we call them nuclei just to confuse you +more because it doesn't mean nucleus to + + align:start position:0% +more because it doesn't mean nucleus to + + + align:start position:0% +more because it doesn't mean nucleus to +the Cell at all + + align:start position:0% +the Cell at all + + + align:start position:0% +the Cell at all +it's a grouping of cells + + align:start position:0% + + + + align:start position:0% + +and we give them various specific names + + align:start position:0% +and we give them various specific names + + + align:start position:0% +and we give them various specific names +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we'll get to know the chord and neural + + align:start position:0% +we'll get to know the chord and neural + + + align:start position:0% +we'll get to know the chord and neural +tube and very soon + + align:start position:0% +tube and very soon + + + align:start position:0% +tube and very soon +what's the animal + + align:start position:0% +what's the animal + + + align:start position:0% +what's the animal +that is called in my book the simplest + + align:start position:0% +that is called in my book the simplest + + + align:start position:0% +that is called in my book the simplest +living chordate + + align:start position:0% +living chordate + + + align:start position:0% +living chordate +there are others in the group The + + align:start position:0% +there are others in the group The + + + align:start position:0% +there are others in the group The +cephalochordates + + align:start position:0% + + + + align:start position:0% + +they have a similar structure but + + align:start position:0% +they have a similar structure but + + + align:start position:0% +they have a similar structure but +there's this particular one + + align:start position:0% + + + + align:start position:0% + +sorry what did I do + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +what's the animal that's pointed at both + + align:start position:0% +what's the animal that's pointed at both + + + align:start position:0% +what's the animal that's pointed at both +ends + + align:start position:0% +ends + + + align:start position:0% +ends +and theoxis okay and and + + align:start position:0% +and theoxis okay and and + + + align:start position:0% +and theoxis okay and and +that little antioxidants can be found + + align:start position:0% +that little antioxidants can be found + + + align:start position:0% +that little antioxidants can be found +even in waters around here uh + + align:start position:0% +even in waters around here uh + + + align:start position:0% +even in waters around here uh +it's very common uh + + align:start position:0% +it's very common uh + + + align:start position:0% +it's very common uh +I I may have said in the book that it + + align:start position:0% +I I may have said in the book that it + + + align:start position:0% +I I may have said in the book that it +was most southern Waters but we do now + + align:start position:0% +was most southern Waters but we do now + + + align:start position:0% +was most southern Waters but we do now +find them fairly far north as well + + align:start position:0% +find them fairly far north as well + + + align:start position:0% +find them fairly far north as well +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it has another name that's more common + + align:start position:0% +it has another name that's more common + + + align:start position:0% +it has another name that's more common +from a scientific by outdoor + + align:start position:0% +from a scientific by outdoor + + + align:start position:0% +from a scientific by outdoor +systematic people who do systems of + + align:start position:0% +systematic people who do systems of + + + align:start position:0% +systematic people who do systems of +biology + + align:start position:0% +biology + + + align:start position:0% +biology +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +well chordate is the phylum they are + + align:start position:0% +well chordate is the phylum they are + + + align:start position:0% +well chordate is the phylum they are +called the simplest living quarter the + + align:start position:0% +called the simplest living quarter the + + + align:start position:0% +called the simplest living quarter the +branch is the other name so when you + + align:start position:0% +branch is the other name so when you + + + align:start position:0% +branch is the other name so when you +look things up on amphioxus you want to + + align:start position:0% +look things up on amphioxus you want to + + + align:start position:0% +look things up on amphioxus you want to +try searching both but because + + align:start position:0% +try searching both but because + + + align:start position:0% +try searching both but because +antioxidants is so popular because it's + + align:start position:0% +antioxidants is so popular because it's + + + align:start position:0% +antioxidants is so popular because it's +so descriptive + + align:start position:0% +so descriptive + + + align:start position:0% +so descriptive +meaning sharp at both ends it's still + + align:start position:0% +meaning sharp at both ends it's still + + + align:start position:0% +meaning sharp at both ends it's still +both use so I use more + + align:start position:0% +both use so I use more + + + align:start position:0% +both use so I use more +you can see it is sort of sharp at both + + align:start position:0% +you can see it is sort of sharp at both + + + align:start position:0% +you can see it is sort of sharp at both +ends this is a picture of its nervous + + align:start position:0% +ends this is a picture of its nervous + + + align:start position:0% +ends this is a picture of its nervous +system + + align:start position:0% +system + + + align:start position:0% +system +notice + + align:start position:0% +notice + + + align:start position:0% +notice +it's not much bigger there than it is + + align:start position:0% +it's not much bigger there than it is + + + align:start position:0% +it's not much bigger there than it is +anywhere + + align:start position:0% +anywhere + + + align:start position:0% +anywhere +okay + + align:start position:0% + + + + align:start position:0% + +is equating + + align:start position:0% + + + + align:start position:0% + +so what is a chordate + + align:start position:0% +so what is a chordate + + + align:start position:0% +so what is a chordate +what defines according + + align:start position:0% +what defines according + + + align:start position:0% +what defines according +we are a chordate + + align:start position:0% + + + + align:start position:0% + +this is I basically simplified a + + align:start position:0% +this is I basically simplified a + + + align:start position:0% +this is I basically simplified a +reconstruction done of ambians + + align:start position:0% +reconstruction done of ambians + + + align:start position:0% +reconstruction done of ambians +uh + + align:start position:0% + + + + align:start position:0% + +it has along the back + + align:start position:0% +it has along the back + + + align:start position:0% +it has along the back +a nerve put + + align:start position:0% +a nerve put + + + align:start position:0% +a nerve put +that is its central nervous system + + align:start position:0% +that is its central nervous system + + + align:start position:0% +that is its central nervous system +you can see it runs almost the entirely + + align:start position:0% +you can see it runs almost the entirely + + + align:start position:0% +you can see it runs almost the entirely +I've indicated just to emphasize there + + align:start position:0% +I've indicated just to emphasize there + + + align:start position:0% +I've indicated just to emphasize there +very slightly something different way at + + align:start position:0% +very slightly something different way at + + + align:start position:0% +very slightly something different way at +the front end yes it does have a brain + + align:start position:0% +the front end yes it does have a brain + + + align:start position:0% +the front end yes it does have a brain +it's a little hard to make out you don't + + align:start position:0% +it's a little hard to make out you don't + + + align:start position:0% +it's a little hard to make out you don't +study it + + align:start position:0% +study it + + + align:start position:0% +study it +with the microscope but what is that + + align:start position:0% +with the microscope but what is that + + + align:start position:0% +with the microscope but what is that +it has no skeleton except that + + align:start position:0% +it has no skeleton except that + + + align:start position:0% +it has no skeleton except that +see another chord + + align:start position:0% +see another chord + + + align:start position:0% +see another chord +it's not a nerve cord + + align:start position:0% +it's not a nerve cord + + + align:start position:0% +it's not a nerve cord +okay it's cartilage + + align:start position:0% +okay it's cartilage + + + align:start position:0% +okay it's cartilage +okay it's called a notochord + + align:start position:0% +okay it's called a notochord + + + align:start position:0% +okay it's called a notochord +all chordates at some stage in their + + align:start position:0% +all chordates at some stage in their + + + align:start position:0% +all chordates at some stage in their +development + + align:start position:0% +development + + + align:start position:0% +development +usually at least early in development + + align:start position:0% +usually at least early in development + + + align:start position:0% +usually at least early in development +have a notochord along the dorsal side + + align:start position:0% +have a notochord along the dorsal side + + + align:start position:0% +have a notochord along the dorsal side +okay that's the note accord + + align:start position:0% +okay that's the note accord + + + align:start position:0% +okay that's the note accord +and the dorsal nerve cord or Central + + align:start position:0% +and the dorsal nerve cord or Central + + + align:start position:0% +and the dorsal nerve cord or Central +nerve assistant develops + + align:start position:0% +nerve assistant develops + + + align:start position:0% +nerve assistant develops +in all quarters + + align:start position:0% + + + + align:start position:0% + +just above or just endorsing + + align:start position:0% +just above or just endorsing + + + align:start position:0% +just above or just endorsing +to that + + align:start position:0% +to that + + + align:start position:0% +to that +notochord + + align:start position:0% +notochord + + + align:start position:0% +notochord +notice it's got an odd spelling it's a + + align:start position:0% +notice it's got an odd spelling it's a + + + align:start position:0% +notice it's got an odd spelling it's a +looks like music no record but that is + + align:start position:0% +looks like music no record but that is + + + align:start position:0% +looks like music no record but that is +the way it's spelled okay + + align:start position:0% + + + + align:start position:0% + +so what is that central nervous system + + align:start position:0% +so what is that central nervous system + + + align:start position:0% +so what is that central nervous system +that nerve cord look like + + align:start position:0% +that nerve cord look like + + + align:start position:0% +that nerve cord look like +this is another picture I simplified + + align:start position:0% +this is another picture I simplified + + + align:start position:0% +this is another picture I simplified +from Earth a recent study and I've shown + + align:start position:0% +from Earth a recent study and I've shown + + + align:start position:0% +from Earth a recent study and I've shown +in blue there + + align:start position:0% +in blue there + + + align:start position:0% +in blue there +the central nervous system + + align:start position:0% +the central nervous system + + + align:start position:0% +the central nervous system +it's basically a tube with somewhat + + align:start position:0% +it's basically a tube with somewhat + + + align:start position:0% +it's basically a tube with somewhat +thickened walls + + align:start position:0% +thickened walls + + + align:start position:0% +thickened walls +okay that's so that's the neural two + + align:start position:0% +okay that's so that's the neural two + + + align:start position:0% +okay that's so that's the neural two +with a ventricle in the middle you can't + + align:start position:0% +with a ventricle in the middle you can't + + + align:start position:0% +with a ventricle in the middle you can't +really see there very well + + align:start position:0% +really see there very well + + + align:start position:0% +really see there very well +but you do see + + align:start position:0% +but you do see + + + align:start position:0% +but you do see +peripheral nerves + + align:start position:0% +peripheral nerves + + + align:start position:0% +peripheral nerves +that are extending into the + + align:start position:0% +that are extending into the + + + align:start position:0% +that are extending into the +that and earthquake + + align:start position:0% +that and earthquake + + + align:start position:0% +that and earthquake +you also see outputs + + align:start position:0% +you also see outputs + + + align:start position:0% +you also see outputs +from on mostly on the ventral side here + + align:start position:0% +from on mostly on the ventral side here + + + align:start position:0% +from on mostly on the ventral side here +and note that they're unlike + + align:start position:0% +and note that they're unlike + + + align:start position:0% +and note that they're unlike +all the vertebrates + + align:start position:0% + + + + align:start position:0% + +and we didn't know this in the early + + align:start position:0% +and we didn't know this in the early + + + align:start position:0% +and we didn't know this in the early +studies now they didn't know it actually + + align:start position:0% +studies now they didn't know it actually + + + align:start position:0% +studies now they didn't know it actually +because the electron microscopic + + align:start position:0% +because the electron microscopic + + + align:start position:0% +because the electron microscopic +reconstructions hadn't been done + + align:start position:0% +reconstructions hadn't been done + + + align:start position:0% +reconstructions hadn't been done +these are muscle cells these are groups + + align:start position:0% +these are muscle cells these are groups + + + align:start position:0% +these are muscle cells these are groups +of muscles and these are muscle + + align:start position:0% +of muscles and these are muscle + + + align:start position:0% +of muscles and these are muscle +processes that extend right up to the + + align:start position:0% +processes that extend right up to the + + + align:start position:0% +processes that extend right up to the +nerve cord and they poke right into the + + align:start position:0% +nerve cord and they poke right into the + + + align:start position:0% +nerve cord and they poke right into the +nerve Clerk and they directly contact + + align:start position:0% +nerve Clerk and they directly contact + + + align:start position:0% +nerve Clerk and they directly contact +the motor neurons + + align:start position:0% +the motor neurons + + + align:start position:0% +the motor neurons +eventual parts of that miracle + + align:start position:0% +eventual parts of that miracle + + + align:start position:0% +eventual parts of that miracle +that's a peculiarity of amphioxus + + align:start position:0% + + + + align:start position:0% + +okay what's the Belmonte law + + align:start position:0% +okay what's the Belmonte law + + + align:start position:0% +okay what's the Belmonte law +there's something in what I was just + + align:start position:0% +there's something in what I was just + + + align:start position:0% +there's something in what I was just +saying was almost getting to that + + align:start position:0% +saying was almost getting to that + + + align:start position:0% +saying was almost getting to that +the Belmonte law what is it + + align:start position:0% +the Belmonte law what is it + + + align:start position:0% +the Belmonte law what is it +what do we usually call it more + + align:start position:0% +what do we usually call it more + + + align:start position:0% +what do we usually call it more +popularly + + align:start position:0% +popularly + + + align:start position:0% +popularly +and less historically + + align:start position:0% +and less historically + + + align:start position:0% +and less historically +discovered by Charles Bell + + align:start position:0% +discovered by Charles Bell + + + align:start position:0% +discovered by Charles Bell +and Prince of margin d + + align:start position:0% +and Prince of margin d + + + align:start position:0% +and Prince of margin d +Bell 1811. + + align:start position:0% +Bell 1811. + + + align:start position:0% +Bell 1811. +imagine the 1823. + + align:start position:0% +imagine the 1823. + + + align:start position:0% +imagine the 1823. +even though + + align:start position:0% + + + + align:start position:0% + +it was a discovery about mammals + + align:start position:0% +it was a discovery about mammals + + + align:start position:0% +it was a discovery about mammals +about the nerves that come in and attach + + align:start position:0% +about the nerves that come in and attach + + + align:start position:0% +about the nerves that come in and attach +to the central nervous system the spinal + + align:start position:0% +to the central nervous system the spinal + + + align:start position:0% +to the central nervous system the spinal +cord + + align:start position:0% +cord + + + align:start position:0% +cord +they always divide into a dorsal root + + align:start position:0% +they always divide into a dorsal root + + + align:start position:0% +they always divide into a dorsal root +and a ventral root as they approach the + + align:start position:0% +and a ventral root as they approach the + + + align:start position:0% +and a ventral root as they approach the +cord + + align:start position:0% +cord + + + align:start position:0% +cord +the dorsal root + + align:start position:0% +the dorsal root + + + align:start position:0% +the dorsal root +contains actually the dorsity of + + align:start position:0% +contains actually the dorsity of + + + align:start position:0% +contains actually the dorsity of +ganglion cells + + align:start position:0% +ganglion cells + + + align:start position:0% +ganglion cells +so we'll see pictures of that in a + + align:start position:0% +so we'll see pictures of that in a + + + align:start position:0% +so we'll see pictures of that in a +minute + + align:start position:0% +minute + + + align:start position:0% +minute +sensory fibers the inputs come in Dorset + + align:start position:0% +sensory fibers the inputs come in Dorset + + + align:start position:0% +sensory fibers the inputs come in Dorset +the outputs those axons of the motor + + align:start position:0% +the outputs those axons of the motor + + + align:start position:0% +the outputs those axons of the motor +neurons remember in the picture of kahal + + align:start position:0% +neurons remember in the picture of kahal + + + align:start position:0% +neurons remember in the picture of kahal +I showed you the axes were going out + + align:start position:0% +I showed you the axes were going out + + + align:start position:0% +I showed you the axes were going out +eventually okay + + align:start position:0% +eventually okay + + + align:start position:0% +eventually okay +that's the ventral root it's motor + + align:start position:0% + + + + align:start position:0% + +but then I ask you here so that's the + + align:start position:0% +but then I ask you here so that's the + + + align:start position:0% +but then I ask you here so that's the +law Roots the Belmont shouldn't be left + + align:start position:0% +law Roots the Belmont shouldn't be left + + + align:start position:0% +law Roots the Belmont shouldn't be left +is it always true + + align:start position:0% + + + + align:start position:0% + +responsibly true here I mean yeah + + align:start position:0% +responsibly true here I mean yeah + + + align:start position:0% +responsibly true here I mean yeah +they're not actual axons going out but + + align:start position:0% +they're not actual axons going out but + + + align:start position:0% +they're not actual axons going out but +those the motor outputs are going out + + align:start position:0% +those the motor outputs are going out + + + align:start position:0% +those the motor outputs are going out +ventrally + + align:start position:0% +ventrally + + + align:start position:0% +ventrally +the sensory inputs are coming endorsing + + align:start position:0% + + + + align:start position:0% + +but one thing really odd about + + align:start position:0% +but one thing really odd about + + + align:start position:0% +but one thing really odd about +antioxidants one level of the nervous + + align:start position:0% +antioxidants one level of the nervous + + + align:start position:0% +antioxidants one level of the nervous +system this + + align:start position:0% +system this + + + align:start position:0% +system this +the nerves come in + + align:start position:0% +the nerves come in + + + align:start position:0% +the nerves come in +on one side and they go up the other + + align:start position:0% +on one side and they go up the other + + + align:start position:0% +on one side and they go up the other +side you go to the the next nerve it + + align:start position:0% +side you go to the the next nerve it + + + align:start position:0% +side you go to the the next nerve it +does have multiple nerves you see here + + align:start position:0% +does have multiple nerves you see here + + + align:start position:0% +does have multiple nerves you see here +are the different roots + + align:start position:0% + + + + align:start position:0% + +if you the next segment down you would + + align:start position:0% +if you the next segment down you would + + + align:start position:0% +if you the next segment down you would +find + + align:start position:0% +find + + + align:start position:0% +find +the input the Nerf from the periphery + + align:start position:0% +the input the Nerf from the periphery + + + align:start position:0% +the input the Nerf from the periphery +coming in dorsally + + align:start position:0% +coming in dorsally + + + align:start position:0% +coming in dorsally +and the muscles + + align:start position:0% +and the muscles + + + align:start position:0% +and the muscles +being driven from a the ventral part of + + align:start position:0% +being driven from a the ventral part of + + + align:start position:0% +being driven from a the ventral part of +the core + + align:start position:0% +the core + + + align:start position:0% +the core +so it alternates + + align:start position:0% +so it alternates + + + align:start position:0% +so it alternates +not only that + + align:start position:0% +not only that + + + align:start position:0% +not only that +there are a few motor axons in that + + align:start position:0% +there are a few motor axons in that + + + align:start position:0% +there are a few motor axons in that +dorsity + + align:start position:0% +dorsity + + + align:start position:0% +dorsity +there are violations and if you study + + align:start position:0% +there are violations and if you study + + + align:start position:0% +there are violations and if you study +other creatures in great detail you will + + align:start position:0% +other creatures in great detail you will + + + align:start position:0% +other creatures in great detail you will +find even in higher vertebrates you'll + + align:start position:0% +find even in higher vertebrates you'll + + + align:start position:0% +find even in higher vertebrates you'll +find a few exceptions to the law groups + + align:start position:0% +find a few exceptions to the law groups + + + align:start position:0% +find a few exceptions to the law groups +but for the most part + + align:start position:0% +but for the most part + + + align:start position:0% +but for the most part +and when you know in neuroanatomy it's + + align:start position:0% +and when you know in neuroanatomy it's + + + align:start position:0% +and when you know in neuroanatomy it's +it's not quite like physics + + align:start position:0% +it's not quite like physics + + + align:start position:0% +it's not quite like physics +in case you're from physics or + + align:start position:0% +in case you're from physics or + + + align:start position:0% +in case you're from physics or +engineering you know there are a lot of + + align:start position:0% +engineering you know there are a lot of + + + align:start position:0% +engineering you know there are a lot of +exceptions + + align:start position:0% +exceptions + + + align:start position:0% +exceptions +and that's a lot of times what we're + + align:start position:0% +and that's a lot of times what we're + + + align:start position:0% +and that's a lot of times what we're +describing is + + align:start position:0% +describing is + + + align:start position:0% +describing is +by and large food + + align:start position:0% + + + + align:start position:0% + +so think of the Belmont and be that law + + align:start position:0% +so think of the Belmont and be that law + + + align:start position:0% +so think of the Belmont and be that law +that way it's it's usually true + + align:start position:0% +that way it's it's usually true + + + align:start position:0% +that way it's it's usually true +what is meant by primary brain vesicles + + align:start position:0% + + + + align:start position:0% + +I indicated something odd here about the + + align:start position:0% +I indicated something odd here about the + + + align:start position:0% +I indicated something odd here about the +very front end that's his brain + + align:start position:0% +very front end that's his brain + + + align:start position:0% +very front end that's his brain +the antioxis does have the beginning of + + align:start position:0% +the antioxis does have the beginning of + + + align:start position:0% +the antioxis does have the beginning of +primary brain vesicles what are they + + align:start position:0% +primary brain vesicles what are they + + + align:start position:0% +primary brain vesicles what are they +we defined it before + + align:start position:0% +we defined it before + + + align:start position:0% +we defined it before +I don't expect you necessarily to + + align:start position:0% +I don't expect you necessarily to + + + align:start position:0% +I don't expect you necessarily to +remember it but now you've read about it + + align:start position:0% +remember it but now you've read about it + + + align:start position:0% +remember it but now you've read about it +again because in chapter 3 + + align:start position:0% + + + + align:start position:0% + +what are the three primary brain + + align:start position:0% +what are the three primary brain + + + align:start position:0% +what are the three primary brain +vesicles + + align:start position:0% +vesicles + + + align:start position:0% +vesicles +see now I've added I've told you there's + + align:start position:0% +see now I've added I've told you there's + + + align:start position:0% +see now I've added I've told you there's +three of them + + align:start position:0% + + + + align:start position:0% + +mind brain midbrain + + align:start position:0% +mind brain midbrain + + + align:start position:0% +mind brain midbrain +okay those are the primary brain + + align:start position:0% +okay those are the primary brain + + + align:start position:0% +okay those are the primary brain +testicles + + align:start position:0% +testicles + + + align:start position:0% +testicles +they generally are vests in the basement + + align:start position:0% +they generally are vests in the basement + + + align:start position:0% +they generally are vests in the basement +well a little bit they're a little bit + + align:start position:0% +well a little bit they're a little bit + + + align:start position:0% +well a little bit they're a little bit +bigger than the spinal cord below + + align:start position:0% +bigger than the spinal cord below + + + align:start position:0% +bigger than the spinal cord below +and + + align:start position:0% +and + + + align:start position:0% +and +they usually get a little smaller at + + align:start position:0% +they usually get a little smaller at + + + align:start position:0% +they usually get a little smaller at +their boundary + + align:start position:0% +their boundary + + + align:start position:0% +their boundary +so you can see a distinct enduring + + align:start position:0% +so you can see a distinct enduring + + + align:start position:0% +so you can see a distinct enduring +development + + align:start position:0% +development + + + align:start position:0% +development +of human and just about every other + + align:start position:0% +of human and just about every other + + + align:start position:0% +of human and just about every other +vertebrae you do see three at least + + align:start position:0% +vertebrae you do see three at least + + + align:start position:0% +vertebrae you do see three at least +early in development + + align:start position:0% + + + + align:start position:0% + +now number 10 there asks for a little + + align:start position:0% +now number 10 there asks for a little + + + align:start position:0% +now number 10 there asks for a little +more detail + + align:start position:0% +more detail + + + align:start position:0% +more detail +but this is another question that the + + align:start position:0% +but this is another question that the + + + align:start position:0% +but this is another question that the +answer would be the same for amphioaxis + + align:start position:0% +answer would be the same for amphioaxis + + + align:start position:0% +answer would be the same for amphioaxis +and for mammals + + align:start position:0% +and for mammals + + + align:start position:0% +and for mammals +in what subdivision of the CNS do visual + + align:start position:0% +in what subdivision of the CNS do visual + + + align:start position:0% +in what subdivision of the CNS do visual +input Center + + align:start position:0% +input Center + + + align:start position:0% +input Center +describe her name the two visual inputs + + align:start position:0% +describe her name the two visual inputs + + + align:start position:0% +describe her name the two visual inputs +found in many qualities + + align:start position:0% + + + + align:start position:0% + +the diencephalum yeah the tween brain + + align:start position:0% +the diencephalum yeah the tween brain + + + align:start position:0% +the diencephalum yeah the tween brain +which of the brain vesicles is + + align:start position:0% +which of the brain vesicles is + + + align:start position:0% +which of the brain vesicles is +diencephalon in + + align:start position:0% + + + + align:start position:0% + +part of the floor brain okay it's the + + align:start position:0% +part of the floor brain okay it's the + + + align:start position:0% +part of the floor brain okay it's the +caudal part of the foreign + + align:start position:0% +caudal part of the foreign + + + align:start position:0% +caudal part of the foreign +it's not part of the cerebral + + align:start position:0% +it's not part of the cerebral + + + align:start position:0% +it's not part of the cerebral +hemispheres they balloon out from the + + align:start position:0% +hemispheres they balloon out from the + + + align:start position:0% +hemispheres they balloon out from the +diencephalon okay + + align:start position:0% + + + + align:start position:0% + +so here's the antioxidants this is from + + align:start position:0% +so here's the antioxidants this is from + + + align:start position:0% +so here's the antioxidants this is from +almond and he shows the arrangement of + + align:start position:0% +almond and he shows the arrangement of + + + align:start position:0% +almond and he shows the arrangement of +cells + + align:start position:0% +cells + + + align:start position:0% +cells +near there a little pigmented area and + + align:start position:0% +near there a little pigmented area and + + + align:start position:0% +near there a little pigmented area and +you see right at the front end of the + + align:start position:0% +you see right at the front end of the + + + align:start position:0% +you see right at the front end of the +animal + + align:start position:0% + + + + align:start position:0% + +and these are pigmented cells next to + + align:start position:0% +and these are pigmented cells next to + + + align:start position:0% +and these are pigmented cells next to +them + + align:start position:0% + + + + align:start position:0% + +our receptor cells responding to light + + align:start position:0% +our receptor cells responding to light + + + align:start position:0% +our receptor cells responding to light +next to them + + align:start position:0% +next to them + + + align:start position:0% +next to them +are neurons that have axons + + align:start position:0% +are neurons that have axons + + + align:start position:0% +are neurons that have axons +that travel to other parts of the + + align:start position:0% +that travel to other parts of the + + + align:start position:0% +that travel to other parts of the +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +the arrangement that Arrangement very + + align:start position:0% +the arrangement that Arrangement very + + + align:start position:0% +the arrangement that Arrangement very +simple Arrangement and antioxus was very + + align:start position:0% +simple Arrangement and antioxus was very + + + align:start position:0% +simple Arrangement and antioxus was very +much like the developing retina and + + align:start position:0% +much like the developing retina and + + + align:start position:0% +much like the developing retina and +vertebrates + + align:start position:0% +vertebrates + + + align:start position:0% +vertebrates +Pig here's the pigment epithelium + + align:start position:0% + + + + align:start position:0% + +here the receptor cells + + align:start position:0% +here the receptor cells + + + align:start position:0% +here the receptor cells +here are the neurons + + align:start position:0% + + + + align:start position:0% + +receptor cells sometimes they're really + + align:start position:0% +receptor cells sometimes they're really + + + align:start position:0% +receptor cells sometimes they're really +primary Sensory neurons + + align:start position:0% +primary Sensory neurons + + + align:start position:0% +primary Sensory neurons +very specialized for responding to light + + align:start position:0% +very specialized for responding to light + + + align:start position:0% +very specialized for responding to light +energy + + align:start position:0% +energy + + + align:start position:0% +energy +and then runs in the retina besides the + + align:start position:0% +and then runs in the retina besides the + + + align:start position:0% +and then runs in the retina besides the +interneurons the main ones are the + + align:start position:0% +interneurons the main ones are the + + + align:start position:0% +interneurons the main ones are the +bipolar cells in the retinal gang cells + + align:start position:0% +bipolar cells in the retinal gang cells + + + align:start position:0% +bipolar cells in the retinal gang cells +and it's the ganglion cells + + align:start position:0% +and it's the ganglion cells + + + align:start position:0% +and it's the ganglion cells +that give rise to these long accidents + + align:start position:0% +that give rise to these long accidents + + + align:start position:0% +that give rise to these long accidents +just like these cells in the + + align:start position:0% +just like these cells in the + + + align:start position:0% +just like these cells in the +antioxidants + + align:start position:0% +antioxidants + + + align:start position:0% +antioxidants +okay now these are cartoons of + + align:start position:0% +okay now these are cartoons of + + + align:start position:0% +okay now these are cartoons of +antioxidants on top + + align:start position:0% +antioxidants on top + + + align:start position:0% +antioxidants on top +putting the vertebrae from the bottom + + align:start position:0% +putting the vertebrae from the bottom + + + align:start position:0% +putting the vertebrae from the bottom +it was based originally just on + + align:start position:0% +it was based originally just on + + + align:start position:0% +it was based originally just on +structural studies but gene expression + + align:start position:0% +structural studies but gene expression + + + align:start position:0% +structural studies but gene expression +Studies have shown now and confirmed + + align:start position:0% +Studies have shown now and confirmed + + + align:start position:0% +Studies have shown now and confirmed +that antioxis + + align:start position:0% +that antioxis + + + align:start position:0% +that antioxis +has a region that's expresses the genes + + align:start position:0% +has a region that's expresses the genes + + + align:start position:0% +has a region that's expresses the genes +of the spinal cord + + align:start position:0% + + + + align:start position:0% + +he has a small region that expresses the + + align:start position:0% +he has a small region that expresses the + + + align:start position:0% +he has a small region that expresses the +genes of the midbrain + + align:start position:0% +genes of the midbrain + + + align:start position:0% +genes of the midbrain +segments of their brain mainly one + + align:start position:0% +segments of their brain mainly one + + + align:start position:0% +segments of their brain mainly one +segment invertebrates + + align:start position:0% +segment invertebrates + + + align:start position:0% +segment invertebrates +and then more rasterly + + align:start position:0% +and then more rasterly + + + align:start position:0% +and then more rasterly +the rest of it is like the tween brain + + align:start position:0% +the rest of it is like the tween brain + + + align:start position:0% +the rest of it is like the tween brain +but he doesn't have + + align:start position:0% +but he doesn't have + + + align:start position:0% +but he doesn't have +the end brain + + align:start position:0% +the end brain + + + align:start position:0% +the end brain +or an olfactory both + + align:start position:0% +or an olfactory both + + + align:start position:0% +or an olfactory both +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the olfactory bulb is part of the end + + align:start position:0% +the olfactory bulb is part of the end + + + align:start position:0% +the olfactory bulb is part of the end +brain + + align:start position:0% +brain + + + align:start position:0% +brain +invertebrates + + align:start position:0% + + + + align:start position:0% + +and notice here there you see the retina + + align:start position:0% +and notice here there you see the retina + + + align:start position:0% +and notice here there you see the retina +ballooning out + + align:start position:0% +ballooning out + + + align:start position:0% +ballooning out +another kind of out poaching like the + + align:start position:0% +another kind of out poaching like the + + + align:start position:0% +another kind of out poaching like the +hemispheres but now it's it remains part + + align:start position:0% +hemispheres but now it's it remains part + + + align:start position:0% +hemispheres but now it's it remains part +of the diet suffering that's the retina + + align:start position:0% +of the diet suffering that's the retina + + + align:start position:0% +of the diet suffering that's the retina +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so there you have that visual area + + align:start position:0% +so there you have that visual area + + + align:start position:0% +so there you have that visual area +of antioxidants here you have it in a + + align:start position:0% +of antioxidants here you have it in a + + + align:start position:0% +of antioxidants here you have it in a +vertebrate + + align:start position:0% +vertebrate + + + align:start position:0% +vertebrate +here is the other area remember I said + + align:start position:0% +here is the other area remember I said + + + align:start position:0% +here is the other area remember I said +there were two + + align:start position:0% +there were two + + + align:start position:0% +there were two +well + + align:start position:0% +well + + + align:start position:0% +well +the at the opposite side of the tween + + align:start position:0% +the at the opposite side of the tween + + + align:start position:0% +the at the opposite side of the tween +brings we have what we call an + + align:start position:0% +brings we have what we call an + + + align:start position:0% +brings we have what we call an +epithalamus it's another the most caudal + + align:start position:0% +epithalamus it's another the most caudal + + + align:start position:0% +epithalamus it's another the most caudal +segment of the developing + + align:start position:0% +segment of the developing + + + align:start position:0% +segment of the developing +tween brain okay + + align:start position:0% +tween brain okay + + + align:start position:0% +tween brain okay +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that's where many + + align:start position:0% +that's where many + + + align:start position:0% +that's where many +chordates have a pine needle eye + + align:start position:0% +chordates have a pine needle eye + + + align:start position:0% +chordates have a pine needle eye +an eye on top of the hip responds to + + align:start position:0% +an eye on top of the hip responds to + + + align:start position:0% +an eye on top of the hip responds to +lightness involved in + + align:start position:0% +lightness involved in + + + align:start position:0% +lightness involved in +control of + + align:start position:0% +control of + + + align:start position:0% +control of +photoperiodic behavior + + align:start position:0% +photoperiodic behavior + + + align:start position:0% +photoperiodic behavior +and even in us that region controls + + align:start position:0% +and even in us that region controls + + + align:start position:0% +and even in us that region controls +the + + align:start position:0% +the + + + align:start position:0% +the +daily cycle of secretion of melatonin + + align:start position:0% +daily cycle of secretion of melatonin + + + align:start position:0% +daily cycle of secretion of melatonin +even though it doesn't directly respond + + align:start position:0% +even though it doesn't directly respond + + + align:start position:0% +even though it doesn't directly respond +to light anymore you know the animals we + + align:start position:0% +to light anymore you know the animals we + + + align:start position:0% +to light anymore you know the animals we +use in the lab like the mouse + + align:start position:0% +use in the lab like the mouse + + + align:start position:0% +use in the lab like the mouse +the red the mouse has got a pretty thin + + align:start position:0% +the red the mouse has got a pretty thin + + + align:start position:0% +the red the mouse has got a pretty thin +Stone and he's got cells here that + + align:start position:0% +Stone and he's got cells here that + + + align:start position:0% +Stone and he's got cells here that +actually do directly respond to light + + align:start position:0% +actually do directly respond to light + + + align:start position:0% +actually do directly respond to light +the distance but the main inputs come + + align:start position:0% +the distance but the main inputs come + + + align:start position:0% +the distance but the main inputs come +through the lateral eyes + + align:start position:0% +through the lateral eyes + + + align:start position:0% +through the lateral eyes +These Eyes through an indirect pathway + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +you should be able to summarize the + + align:start position:0% +you should be able to summarize the + + + align:start position:0% +you should be able to summarize the +basic rules of evolution + + align:start position:0% +basic rules of evolution + + + align:start position:0% +basic rules of evolution +I do it on the next slide here + + align:start position:0% +I do it on the next slide here + + + align:start position:0% +I do it on the next slide here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you should know the basic processes that + + align:start position:0% +you should know the basic processes that + + + align:start position:0% +you should know the basic processes that +govern Evolution and it's all right if + + align:start position:0% +govern Evolution and it's all right if + + + align:start position:0% +govern Evolution and it's all right if +you assume the natural selection just + + align:start position:0% +you assume the natural selection just + + + align:start position:0% +you assume the natural selection just +like Darwin believed is the major factor + + align:start position:0% +like Darwin believed is the major factor + + + align:start position:0% +like Darwin believed is the major factor +that causes Gene sorting + + align:start position:0% + + + + align:start position:0% + +survival of some genes and not of others + + align:start position:0% +survival of some genes and not of others + + + align:start position:0% +survival of some genes and not of others +or decrease in the frequency of sun + + align:start position:0% +or decrease in the frequency of sun + + + align:start position:0% +or decrease in the frequency of sun +genes increase in the frequency of + + align:start position:0% +genes increase in the frequency of + + + align:start position:0% +genes increase in the frequency of +others + + align:start position:0% +others + + + align:start position:0% +others +okay so I just summarized that and I + + align:start position:0% +okay so I just summarized that and I + + + align:start position:0% +okay so I just summarized that and I +write it out in a pretty straightforward + + align:start position:0% +write it out in a pretty straightforward + + + align:start position:0% +write it out in a pretty straightforward +way in the book + + align:start position:0% +way in the book + + + align:start position:0% +way in the book +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in the animal behavior class I do talk a + + align:start position:0% +in the animal behavior class I do talk a + + + align:start position:0% +in the animal behavior class I do talk a +little bit about other mechanisms of + + align:start position:0% +little bit about other mechanisms of + + + align:start position:0% +little bit about other mechanisms of +genetic change + + align:start position:0% +genetic change + + + align:start position:0% +genetic change +can result result in changes outside of + + align:start position:0% +can result result in changes outside of + + + align:start position:0% +can result result in changes outside of +natural selection that still are + + align:start position:0% +natural selection that still are + + + align:start position:0% +natural selection that still are +important in evolution + + align:start position:0% +important in evolution + + + align:start position:0% +important in evolution +various argument about just how + + align:start position:0% +various argument about just how + + + align:start position:0% +various argument about just how +important these things are + + align:start position:0% + + + + align:start position:0% + +so when you think now about that very + + align:start position:0% +so when you think now about that very + + + align:start position:0% +so when you think now about that very +simple neural tooth the beginning of the + + align:start position:0% +simple neural tooth the beginning of the + + + align:start position:0% +simple neural tooth the beginning of the +central nervous system you've got to say + + align:start position:0% +central nervous system you've got to say + + + align:start position:0% +central nervous system you've got to say +well what how did that little worm-like + + align:start position:0% +well what how did that little worm-like + + + align:start position:0% +well what how did that little worm-like +animal + + align:start position:0% +animal + + + align:start position:0% +animal +or animals liked it + + align:start position:0% +or animals liked it + + + align:start position:0% +or animals liked it +how did that end up evolving primates + + align:start position:0% + + + + align:start position:0% + +you've got to think about the highest + + align:start position:0% +you've got to think about the highest + + + align:start position:0% +you've got to think about the highest +priorities in evolution and I've + + align:start position:0% +priorities in evolution and I've + + + align:start position:0% +priorities in evolution and I've +consistently done that through the book + + align:start position:0% + + + + align:start position:0% + +and I I've taken this a nice phrase from + + align:start position:0% +and I I've taken this a nice phrase from + + + align:start position:0% +and I I've taken this a nice phrase from +Chandler Elliott who wrote this book in + + align:start position:0% +Chandler Elliott who wrote this book in + + + align:start position:0% +Chandler Elliott who wrote this book in +69. + + align:start position:0% +69. + + + align:start position:0% +69. +he has this phrase in there at the + + align:start position:0% +he has this phrase in there at the + + + align:start position:0% +he has this phrase in there at the +beginning of the book every brain system + + align:start position:0% +beginning of the book every brain system + + + align:start position:0% +beginning of the book every brain system +grows logically from the tooth what he + + align:start position:0% +grows logically from the tooth what he + + + align:start position:0% +grows logically from the tooth what he +simply meant was that by small steps by + + align:start position:0% +simply meant was that by small steps by + + + align:start position:0% +simply meant was that by small steps by +processes of natural selection + + align:start position:0% +processes of natural selection + + + align:start position:0% +processes of natural selection +sent that neural tube developed the way + + align:start position:0% +sent that neural tube developed the way + + + align:start position:0% +sent that neural tube developed the way +we have it + + align:start position:0% +we have it + + + align:start position:0% +we have it +into into print + + align:start position:0% +into into print + + + align:start position:0% +into into print +species + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +it's mostly speculation + + align:start position:0% +it's mostly speculation + + + align:start position:0% +it's mostly speculation +and these are the questions I was + + align:start position:0% +and these are the questions I was + + + align:start position:0% +and these are the questions I was +following + + align:start position:0% +following + + + align:start position:0% +following +just looking across existing animals + + align:start position:0% +just looking across existing animals + + + align:start position:0% +just looking across existing animals +and also using some paleo ontologies so + + align:start position:0% +and also using some paleo ontologies so + + + align:start position:0% +and also using some paleo ontologies so +that's what we're going to do next time + + align:start position:0% +that's what we're going to do next time + + + align:start position:0% +that's what we're going to do next time +we're going to + + align:start position:0% +we're going to + + + align:start position:0% +we're going to +talk about the ancestors of mammals the + + align:start position:0% +talk about the ancestors of mammals the + + + align:start position:0% +talk about the ancestors of mammals the +sketch is simple premammalian brain well + + align:start position:0% +sketch is simple premammalian brain well + + + align:start position:0% +sketch is simple premammalian brain well +how could I guess what a premium alien + + align:start position:0% +how could I guess what a premium alien + + + align:start position:0% +how could I guess what a premium alien +brain is like it's actually based mostly + + align:start position:0% +brain is like it's actually based mostly + + + align:start position:0% +brain is like it's actually based mostly +on an amphibian brain + + align:start position:0% +on an amphibian brain + + + align:start position:0% +on an amphibian brain +okay but we we do have skulls + + align:start position:0% +okay but we we do have skulls + + + align:start position:0% +okay but we we do have skulls +of the group of animals that led to the + + align:start position:0% +of the group of animals that led to the + + + align:start position:0% +of the group of animals that led to the +evolution of mammals + + align:start position:0% +evolution of mammals + + + align:start position:0% +evolution of mammals +they were + + align:start position:0% +they were + + + align:start position:0% +they were +running around the forest floor at the + + align:start position:0% +running around the forest floor at the + + + align:start position:0% +running around the forest floor at the +time of the big dinosaurs + + align:start position:0% +time of the big dinosaurs + + + align:start position:0% +time of the big dinosaurs +they evolved with the dinosaurs + + align:start position:0% +they evolved with the dinosaurs + + + align:start position:0% +they evolved with the dinosaurs +they were the synodonts okay + + align:start position:0% + + + + align:start position:0% + +we'll talk about that other stuff next + + align:start position:0% +we'll talk about that other stuff next + + + align:start position:0% +we'll talk about that other stuff next +time these are the sign of dots + + align:start position:0% +time these are the sign of dots + + + align:start position:0% +time these are the sign of dots +okay this is just a few of them + + align:start position:0% +okay this is just a few of them + + + align:start position:0% +okay this is just a few of them +reconstructed we don't really know their + + align:start position:0% +reconstructed we don't really know their + + + align:start position:0% +reconstructed we don't really know their +colors we just have the skulls but we do + + align:start position:0% +colors we just have the skulls but we do + + + align:start position:0% +colors we just have the skulls but we do +know a little about their brain because + + align:start position:0% +know a little about their brain because + + + align:start position:0% +know a little about their brain because +the skull the inside of the skull + + align:start position:0% +the skull the inside of the skull + + + align:start position:0% +the skull the inside of the skull +preserves the shape of the central + + align:start position:0% +preserves the shape of the central + + + align:start position:0% +preserves the shape of the central +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +just like the you find the vertebrae we + + align:start position:0% +just like the you find the vertebrae we + + + align:start position:0% +just like the you find the vertebrae we +know how big the spinal cord was we know + + align:start position:0% +know how big the spinal cord was we know + + + align:start position:0% +know how big the spinal cord was we know +in brontosaurus his + + align:start position:0% +in brontosaurus his + + + align:start position:0% +in brontosaurus his +lumbar enlargement + + align:start position:0% +lumbar enlargement + + + align:start position:0% +lumbar enlargement +probably bigger than his brain + + align:start position:0% +probably bigger than his brain + + + align:start position:0% +probably bigger than his brain +but he was a very very large animal and + + align:start position:0% +but he was a very very large animal and + + + align:start position:0% +but he was a very very large animal and +had a needed a lot of neurons there just + + align:start position:0% +had a needed a lot of neurons there just + + + align:start position:0% +had a needed a lot of neurons there just +control those enormous rear legs + + align:start position:0% +control those enormous rear legs + + + align:start position:0% +control those enormous rear legs +but okay so we'll be talking about a + + align:start position:0% +but okay so we'll be talking about a + + + align:start position:0% +but okay so we'll be talking about a +brain that we'll assume is + + align:start position:0% +brain that we'll assume is + + + align:start position:0% +brain that we'll assume is +if you don't like thinking in terms of + + align:start position:0% +if you don't like thinking in terms of + + + align:start position:0% +if you don't like thinking in terms of +evolution you can think of it as an + + align:start position:0% +evolution you can think of it as an + + + align:start position:0% +evolution you can think of it as an +amphibian + + align:start position:0% +amphibian + + + align:start position:0% +amphibian +but we think it's something like the + + align:start position:0% +but we think it's something like the + + + align:start position:0% +but we think it's something like the +early sign Advance because the early + + align:start position:0% +early sign Advance because the early + + + align:start position:0% +early sign Advance because the early +sign of Dance by the time you have the + + align:start position:0% +sign of Dance by the time you have the + + + align:start position:0% +sign of Dance by the time you have the +sign of dogs they're pretty similar to + + align:start position:0% +sign of dogs they're pretty similar to + + + align:start position:0% +sign of dogs they're pretty similar to +mammoths okay + + align:start position:0% +mammoths okay + + + align:start position:0% +mammoths okay +so that's what we'll be doing next time + + align:start position:0% + + + + align:start position:0% + +and that's all the time we have + + align:start position:0% + + + + align:start position:0% + +foreign \ No newline at end of file diff --git a/lLdUm6AU0aw.txt b/lLdUm6AU0aw.txt new file mode 100644 index 0000000000000000000000000000000000000000..aa571a08cede8376b782bc24d8e45897d74f0d33 --- /dev/null +++ b/lLdUm6AU0aw.txt @@ -0,0 +1,2319 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So, any +questions from last time? + +We started doing +reaction mechanisms. + +We did first order +parallel reactions. + +So one of the things +that we'll be stressing + +is that the mechanisms +that we write down + +are ways to try to understand +a complicated chemical process. + +And you take data, you can +find intermediates sometimes. + +And you get rate +laws from the data. + +You infer rate laws. + +And from these rate +laws, you think up + +of a reaction mechanism and you +make sure that what you measure + +is consistent with +your mechanism + +that you make up to explain the +complicated chemical process. + +And one really important +thing to remember + +is that when you come +up with a mechanism + +and you've got a bunch of data +that supports it, it's great. + +But it doesn't mean that +you've solve the problem. + +It doesn't mean +that you've proven + +that the way that the +chemistry proceeds + +is really the way it proceeds. + +Because there's +always the possibility + +that there's an intermediate +somewhere in there + +that you haven't +been able to measure. + +And a lot of people +got tripped up + +over the course of +the last century, + +of making up mechanisms, getting +a lot of data that supports + +the mechanism and missing +something really important. + +So it's a common +mistake, that people + +think they've proven +a particular chemical + +mechanism just because they +have data that supports it. + +It's up to a certain point +that you know what you have. + +And we'll see examples +of that today, probably. + +And then certainly +next time when + +we start making approximations +in our kinetics. + +And see where things +can really go wrong + +if you don't have enough data. + +If you don't try +to fish out really, + +really, tiny intermediates +somewhere along the way. + +So last time we did then +parallel first order reactions. + +And today we're going +to march through and do + +parallel first and second order. + +So one is first order, the +other one is second order. + +Things are going to +get more complicated. + +And what you're going +to get is a flavor + +of how to solve the problems. + +Setting up the problems. + +We're not going to do a lot of +the algebra here on the board, + +because otherwise we +would spend the next three + +weeks doing algebra. + +And that would be no fun at all. + +That doesn't mean +that you're not + +going to be doing any +algebra on the homework. + +Because part of it is +figuring how to do it. + +So, we have a reaction +where A goes to B plus C. + +And the first thing we did +was, the first mechanism + +we wrote was a parallel +mechanism where + +we had A goes B and A goes +to C. That's the mechanism. + +And one other way to write +it is A goes to B or C, + +in a way that is more, +sort of describes + +the branching +process, that when we + +talk about a branching ratio, +the ratio of amount of B to C, + +this looks like the branching +out of two different paths. + +And this time we're going to +do where this is first order + +and this is second order. + +With the rate k1 and a rate k2. + +And the way that you +do all these problems, + +you have to be very +systematic about it. + +The first thing +you do is you have + +to write down all +your rate laws. + +And make sure that you +include everything. + +So you start by writing the rate +law for the destruction of A. + +And then the rate law for the +appearance of B and for C. + +So for a, we have dA/dt. + +And again, I'm dropping +the brackets around the A, + +because I don't want to carry +around all these extra symbols. + +So we destroy A by making B. So +that's going to be first order. + +And then we also +destroy A by making C, + +and that's second order. + +So we have two paths out +of A. To get rid of A. + +Then we write down the +appearance of B, dB/dt. + +It's only through one +path, first order in A, + +and then the appearance +of C, only one path + +which is second order. + +And these are all our +differential equations. + +And now the trick is, how do you +solve these three differential + +equations in a way that you +get meaningful information out. + +Well, the first +thing to do is to, + +so these two here depend on +A. So the appearance of B + +depends on A, the appearance +of C depends on A. + +But this one here only +depends on A by itself. + +So this is the first one +you're going to start out with. + +Because you can +put all of the A's + +on one side and all the time on +the other side and integrate. + +So then you solve, and +you can rewrite this + +as minus dA/dt is equal to +k1 times A times one plus k2 + +over k1 times A. And then you +put all the A's on one side, + +all the t's on the other side. + +And integrate from A0 to A minus +dA over A times one plus k2 + +over k1 times A. That is +equal to k1 from zero to t dt. + +And then you have to +solve this integral here. + +And there's a reason why +I factored out the A here. + +It's because this +is of the form you + +can use to use the trick +of partial fractions, which + +we mentioned this before. + +So you use partial +fractions to solve this. + +And I'm not going to +do it on the board. + +You turn the crank, +you basically + +write one over A times +one plus k2 over k1 A + +is equal to n1 of A plus +n2 over this part here, + +and you solve for n1 and +n2 and you plug it back in, + +and you redo your +integral, et cetera. + +And you get your answer. + +Which I'm going to +write down because I'm + +going to use it +later. k1 A0 over e + +to the k1 times +t, k1 plus k2 A0. + +So one of the things +we immediately see + +is even though this mechanism +isn't very complicated, + +just two paths, one first order, +one second order, the solutions + +start to get not so +simple pretty quickly. + +So it depends, there's an +exponential on the bottom here. + +Depends on the initial +concentrations and both rate + +constants are in there. + +The first thing +you want to do is + +you want to look +at limiting cases. + +Just like before. + +We did, and the +first limiting case + +we're going to look at, +so interesting to look at + +is this guy right +here. k1 and k2 A here. + +If one is bigger than the other, +then things will cancel out. + +And we can get some intuition. + +So the first limiting case +we're going to look at + +is where k2 A0, this term right +here, is much smaller than k1. + +Now, we want to make sure +that in these limiting cases + +that when I write something like +this, that the units actually + +make sense. + +That I'm not +saying, three apples + +are less than four oranges. + +So k1, it's first +order, so the units + +are one over second. k2, it's +a second order rate constant, + +so the units are one over second +molar, times moles per liter. + +So the moles per +liters cancel out + +and I have one over our second +is less than one over second, + +so things are great. + +It I'm making the right +kind of approximation here. + +What else is this +approximation saying? + +This is saying that the +rate into B, so this one is + +the faster one. k1, the rate +into B, is the rate into, + +is k1, is faster than k2 times +A, which is basically the rate + +into C. So this is saying that +the rate into B, to form B, + +is faster than into C. So +we can write down a sketch. + +We can sketch what we expect +this approximation to be, then. + +And we know it's going to +look something like this. + +We know that A is going to +come down, exponentially. + +Without any structure to it. + +It's going to go either +into B or into C, + +in some branching fractions. + +And we know that the rate +into B is faster than into C, + +so B is going to +come up like this. + +And C is going to +come up, but slower. + +And there's going to be a +ratio between these two guys. + +So we know the slope here +is going to be slower + +then the slope for B. And +we can check that out, + +within our approximation. + +We can write, at t +equals zero, find out + +what these initial slopes are. + +For the creation of +B and C. So dB/dt + +is the slope of the creation +of B at the beginning. + +At t equals zero. + +And that's just the +rate law. dB/dt at t + +equals zero is k1 A0. + +And dC/dt, the initial slope, t +equals zero, is k1 A0 squared. + +Or k2 A0 squared, rather. + +So I'm going to write it as +k2 A0 squared, like this. + +We said k1 is much +bigger than k2 times A0. + +There's the same A0 here. + +So we see, just by +writing this down, + +that our intuition that +because the rate into B + +is much faster than into A, +that it should look like this. + +Well it's borne out just +like this very simple sort + +of looking at the initial +rate where the slope here + +is much smaller +than the slope here. + +And then we can take the +approximation in here. + +And see what it implies. + +So let me do that here, let me +just use my green chalk here. + +So k2 A0 is much less than k1. + +So this is going to go away. +k2 A0 is much less than k1. + +Well, this is +building up from zero. + +So this is always +bigger than one here. + +So I can get rid +of this as well. + +Because there's the +k1 sitting here. + +And k1 is much +bigger than k2 A0. + +Once I got rid of all these two +guys, then the k1's cancel out. + +And this is looking very nice. + +Because now I can take that e +to the k1 t and put it upstairs. + +A is equal to approximately +A0 e to the minus k1 times + +time in this approximation. + +It looks like it's +first order coming down, + +with a rate constant k1. + +It looks like basically +the branching into C + +is nonexistent as far as, at +least in this approximation, + +as far A is concerned. + +It's going to look +like this thing here. + +It's going to look +like first order + +A goes to B with +rate constant k1. + +So if you didn't +know, if you didn't + +know that there was +another substance, C, + +that was being formed along the +way, if you didn't measure it, + +if you didn't do the analytical +chemistry and sort of fish it + +out, and you just looked at the +two major components, A and B, + +in this case here, you'd +measure a rate out of A, + +it would look like +it's first order. + +It's great. + +Got my mechanism. + +A goes to B, period. + +And you would know there +was a minor component that + +was being formed +at the same time. + +OK, let's do another +approximation. + +Let's do the other case, where +k2 A0 is much bigger than k1. + +And, in this case +here, you have to be + +a little bit more careful. + +You have to add +that you're going + +to look at this at early times. + +And we're going to see why +early times is important here. + +In just five minutes. + +And early times, and how +you define early times. + +What does it mean for things to +be close to time equals zero? + +Well, we have to have +a reference time scale. + +The reactions, I'm +going at a certain rate. + +And one second may be very slow. + +Or it may be very fast. + +Depending on the +rate of the reaction. + +So k1 here defines the +time scale of the problem. + +It's one over second, +unit of one over second. + +And early times means that +the times that I'm looking at + +compare to this rate, +it's very small. + +So k1 t is less than one. + +That means that the time, +during the time period that I'm + +looking at, hardly anything has +happened to the branching of A + +to B. That that's what +I mean by early time. + +So B is hardly being built +up yet. k1 is our reference + +time. k1 is units +of one over second. + +This has units of seconds. + +So it's all working out fine. + +In other words, I would have no +idea how to define early times. + +I could say, it's in +a year, it could be, + +if you're looking +at plutonium decay, + +it's a 100,000 year half-life. + +A year would be an early time. + +So it would be really fast, +compared to the process. + +But if you're looking +at a reaction that + +takes a few nanoseconds than a +year would be very, very long. + +So you really need +your reference time + +somewhere in there. + +So this approximation means +that essentially, no B + +is being created. + +While we're looking +at the process. + +And so we might then +very well expect + +that if we look at A and +C, that the answer is going + +to be that we're going to see +something that's second order. + +So we expect that the form +of A, the way to write it + +is going to be one over +A equals k1 t plus A0. + +So let's go ahead and +take our complete solution + +and write it in the way that we +might expect the answer to be. + +In terms of one over +A rather than A here. + +So let's just invert it. e to +the k1 times time, k1 plus k2 + +A0, minus k2 A0 over k1 A0. + +This should be a +minus sign here. + +There should be a +minus sign here. + +It didn't matter for +our approximation + +because we got rid +of it anyway, but it + +would be a proper +sign here is minus. + +And so now we need to +make our approximation + +and figure out what this here. + +So if we take the approximation +that k1 t is small, less + +than one, then what that +should trigger in your mind + +if that if you have e to +the something that small + +you should use a Taylor series. + +And expand this into +a Taylor series. + +So we're going to see +this multiple times. + +So we take e to the k1 t +and expand it out as one + +plus k1 t plus et cetera. + +We're going to keep the +first order terms in there. + +So we're going to plug this +approximation into here. + +That's this approximation there. + +And then we're going +to expand it out. + +So plug it in here, and, keeping +it to first order in time, + +and multiplying it +out, and I'm not + +going to do the +intermediate steps, + +I'm just going to give +you the stuff after doing + +the multiplications, +we get k1 t squared. + +So that's basically k1 +times one plus k1 t, + +and then you have +plus k1 k2 A0 times t. + +That's this term here. k1 +k2 A0 times t times that. + +And the k2 A0 times +one gets subtracted out + +from this minus k2 A0 here. + +So that's all we have on top. + +And then there are terms +of higher order in time. + +But we're not going +to worry about this. + +We're going to stick +to first order in time. + +Divided by k1 A0. + +And now you do +your cancellations. + +We have our +approximation at k1 times + +time is much less than one. + +So here we have k1 +times k1 times time. + +So this term here means it's +much less than this term + +here, because of +our approximations. + +So we can get rid +of this term here. + +Get rid of that. + +There's no reason for us to +get rid of this one here. + +Because we've got k2 A0 there, +which is much larger than k1. + +And so when you expand this out, +all the k1's cancel out here. + +So so k1 cancels out that +k1, we have one plus one. + +So this is basically +one over A0. + +And then we have plus +k2 A0 time over A0, + +so this ends up being equal to +one over A0 plus k2 times time. + +Exactly what we expected. + +That if you put in the right +approximation in the math, + +it behaves as your +intuition would tell you. + +Which is that the branching +into B nonexistent. + +And that you're looking +at everything going to C. + +It looks second order +in C. But in this case + +here, it's only early times. + +So if you keep +going, what happens? + +If you keep going in +time, beyond the time + +scale of this first +order rate constant, + +and you wait long enough, +then the amount of A + +keeps decreasing. + +Keeps getting +smaller and smaller. + +So if you start the clock +again, a little bit later, + +where A is much +smaller, then k2 times + +the amount of A you +have there, is no longer + +going to be much +greater than k1. + +At some point along +the way, k2 times A + +is going to be +much less than k1. + +So at some point +along the way, it's + +not going to be this +approximation any more. + +It's going to be the +previous one that we did. + +The one up there. + +So at early times we +start with something + +that may look second order for +A. Time goes on, time goes on, + +time goes on, A gets depleted. + +A gets depleted, and +the rate k2 times + +A, which is sitting right +here, this part here + +becomes smaller and smaller. + +And pretty soon this part wins. + +And it becomes first order. + +So what you'd +expect to see, then, + +is if you were to plot +as a function of A, + +you expect to see something +that starts out as first order + +and then as A gets depleted, +switches over to second order. + +Something that's +second order here. + +And first order. + +This is the concentration of +A. So if you were to plot it, + +here you're plotting +the concentration of A. + +If you were to plot the log, +of the concentration of A, + +at long times you'd expect +it to be first order. + +So something linear. + +But at early times you'd +expect it to be second order. + +So you'd expect to see +something that's nonlinear, + +then switching to +something linear. + +And if you were to +plot it as one over A, + +then you'd expect to start off +with something that's linear, + +at second order, early times. + +But instead of keeping, +being second order, + +as you deplete the amount +of A, the branching into B + +becomes important. + +And you become second order. + +So this is second +order at the beginning. + +And this becomes first order. + +So, any questions here? + +The importance of +doing this problem + +here was to lay out +basically a systematic way + +of looking at the problem. + +You lay out your rate equations. + +Like this. + +You solve what you can, in +this case you solve for A. + +And it's complicated. + +So you want to learn +something about what + +the data might look like. + +And you look at limiting cases. + +Two obvious limiting cases. + +One rate is faster +than the other. + +You pick the first one +first, then go through it. + +And then use your intuition. + +Every point along the +way, your intuition + +can tell you what you +expect the result to be. + +So in this case +here, our intuition + +told us that if we +took the rate into B + +to be much faster +than that into C, + +than we expected +to see something + +that was largely first order. + +And when you we +the approximation + +in our exact solution, +in fact it does + +look like it's first order. + +So always use your intuition. + +Because the math is going +to get pretty hairy. + +The algebra might +make it complicated. + +And it's really easy +to make a plus sign + +into a minus sign +somewhere along the way. + +Just like I did here. + +So if I hadn't fixed +my mistake here, + +and I had gone and put +in my Taylor series here, + +I would have gotten in trouble. + +Because this minus sign +would have been a plus. + +And these k2 A0's would +not have canceled out. + +And I wouldn't have gotten +the right result, which + +my intuition had told me should +be a second order process. + +And so if you have a problem, +let's say you're on an exam + +and you're doing algebra, +you're trying to, + +and you end up +with a result that + +doesn't match what your +intuition tells you, + +and you don't have +time to fix it. + +Tell us. + +You know, I know this +is wrong because I + +know it's supposed +to be second order. + +But I don't know +where I went wrong. + +And that's really important. + +Just tell us. + +That means that you're thinking. + +Let's get a little +bit more complicated. + +Any questions? + +Consecutive series reactions. + +These were parallel +reactions and now. + +Basically what +we're doing here is + +we're building up a toolkit +of simple mechanisms. + +And then we'll be able to +put these mechanisms together + +to make something +more complicated. + +So the next kind of mechanism, +series mechanism, series + +reactions, so we +have our reaction. + +Which is A goes to +C. And the mechanism + +that's been thought +for this reaction + +is that there's an intermediate. + +That first you have A goes to +B, some intermediate, which gets + +used up to form the final +product, C, with a rate, k2, + +here. + +And we can either write +the mechanism in two steps. + +Or we can write it as A goes +to B goes to C, like this. + +And see both ways of writing it. + +And we want to solve this. + +And we want to look +at special cases, + +and we just want to +understand the implications + +of this mechanism. + +So the first thing to do, +just like we did before, + +is to write all the rate laws. + +Before we got going +solving anything. + +So we start with A, minus dA/dt. + +There's only one way +that gets used up. + +Through the formation of B +in a first order process. + +Easy. + +This is easy to solve. + +We know the answer is going +to be exponential in it. + +For B, dB/dt is +equal to, well it + +can be formed through +my first order in A, + +so that's k1 times +A. But it also + +could get destroyed +by forming C. + +So we've got to get +all the paths out + +of A, here on the right +side of this equation. + +So it can be destroyed +in a process, which + +is first order in +B. So we're going + +to take both k1 and k2 to +be first order initially. + +Then we'll make one of them +second order and things will + +become very complicated and +we'll throw up our hands. + +But for now, let's not throw +up our hands quite yet. + +OK and for dC/dt, +there's only one way + +it can be formed is first +order by destroying B. + +And we have a couple of +differential equations here. + +This differential equation +for C, depends on B here. + +The differential for +B depends on A here. + +So that means that things are +going to get a little bit more + +complicated. + +The easy one to solve is +always the first one here. + +That's first order. + +So we just write +down the answer. + +A is equal to A0, e +to the minus k1 t. + +We know the answer to that one. + +Then we have to work +on B. So we want + +to find out integrated rate laws +for every one of these chemical + +species. + +And always there +are tricks involved. + +Partial fractions, whatever. + +So we write down +B now. dB/dt plus, + +let me rearrange it a little +bit, plus k2 times B, putting + +the minus k2 B on +the other side here. + +Is equal to k1 +times A. But I'm not + +going to keep this A +there, because now I + +know what A is in terms of time. + +And a constant. k1 times A0 +e to the minus k1 times time. + +OK, that's my +differential equation + +for B. Got to solve this thing. + +Well, the last time I did +differential equations + +in college was a century ago. + +And I wasn't kidding. + +It really was last century. + +In fact, it was last millennium. + +That was a long time ago. + +So how do you do this? + +Well, the trick here, +there's a trick. + +And the trick is to multiply the +whole thing, both sides, by e + +to the k2 t. + +And you multiply this +side by e to the k2 t + +and you multiply this +side by e to the k2 t, + +to solve this equation. + +So once you do +that, then you have + +e to the k2 t times dB/dt plus +k2 times B. This side here. + +And then you have is equal to +k1 times A0 e to the minus, e + +to the k2 minus k1 times time. + +OK, so the reason +why this trick works + +is because this guy right +here can be nicely written + +as d/dt of B times +e to the k2 t. + +It's in nice simple form, +so when you integrate, + +it'll be very easy to integrate. + +And then the other +side, you still + +have k1 A0 e to the k2 +minus k1 times the time. + +So now you integrate +both sides with respect + +to time, The integral of +something d/dt with respect + +to time, it's just going +to be itself right here. + +So it's very simple. + +So you integrate both sides +from zero to time, dt. + +Zero to t, dt on both sides. + +And on this side here, +you end up with B, + +e to the k2 times time minus +B, e to the k2 times zero. + +Just taking the upper limit +minus the lower limit. + +And that's just equal to +B0, at time to equal zero. + +And so, and at +time to equal zero, + +B0 is equal to zero because we +haven't made any intermediates. + +So this goes away. + +And then we have an equals sign. + +And on the other side, we +have k1 A0 over k2 minus k1, + +it's just the integral +of this thing, + +here with a k2 minus k1 +goes in the denominator. e + +to the k2 minus k1 +times time minus one. + +So now you have your integral +form for the amount of B + +that gets created at any time. + +And I want to keep +that on the board. + +Because I'm going +to use it later. + +k1 A0 over k1 minus k2 times +e to the minus k1 times + +time minus e to the +minus k2 times time. + +OK, we're two thirds +of the way through. + +Now we've got to find C. +And for the last component, + +you don't want to be +doing this kind of stuff. + +You don't want to waste your +time solving differential + +equations, because +stoichiometry can help you out. + +At the end of the day, +you know that everything + +that started out as A, +in terms of quantities, + +is going to end up at C. +You know that if you end up + +with a concentration +A0 at the beginning, + +at the end of the process +the concentration of C, + +at infinite time, is +also going to be A0. + +If you know that +there's a correlation, + +there's a stoichiometry that +relates A and C together. + +And B. You have conservation +of mass here, basically. + +Conservation of atoms. + +That has to come into play + +So, for C, we're just going to +do algebra instead of calculus. + +So let's write down +the stoichiometry here. + +The amount of C at +any time is what + +it's going to be at the end. + +Which is A0, very +end of the process. + +It's going to be A0. + +But before we get +to the end, there's + +still stuff that's +left in A and B. + +And that's going to +decrease the amount of C. + +So minus whatever's +still in A and B. + +That's the stoichiometry. + +That's one way of writing it. + +You could also write +it in a different way. + +Which is that the amount of +C is equal to the amount of A + +that you have used up. + +A0 is what you started out with. + +A is what's left over. + +So this is the +amount of A used up. + +It's not all quite in C yet. + +Some of it is stuck in B. + +So it's the amount of A used +up, minus the amount that's + +stuck in B. Those +two are the same. + +I hope. + +A0 minus A, yeah, that's right. + +Minus B, yeah, that's right. + +So this is used up. + +And then stuck in B. +That's the hard part. + +Putting down the stoichiometry. + +Once you've done +the hard part, then + +if you solve the other +two then it's easy. + +You just plug in. + +It's just algebra. + +And you get something +complicated. + +C is equal to complicated. + +It's in the notes, I'm not +going to write it down. + +So we've solved the +problem exactly. + +And now you're going +to do an experiment. + +And the experiment +you're going to do + +is not going to follow +this whole thing, exactly. + +It's going to look +at limited cases. + +That's what you can do. + +And so the first +thing to look at + +is to look at the initial times. + +The very beginning +of the process, + +how are things appearing. + +And then we'll look +at the late times. + +So initial times. + +Near t equals zero. + +Well, every one of these things +has an exponential in it. + +And whenever we see exponentials +and we look at something + +at the early times, times that +are faster than one over k1, + +or faster than one over k2, it +tells us use a Taylor series. + +So use the approximation +e to the minus kt + +is approximately equal to +one minus kt plus kt squared + +over two plus et cetera. + +And keep as many terms as +you need in the Taylor series + +to get something sensible. + +So if everything comes +out of zero at the end, + +you know you haven't +kept enough terms in t. + +Things have canceled +out too much. + +And you want something +that is time dependent. + +Because you've got a +change in time, right? + +It's a very common mistake +to say only keep one here + +and then everything +cancels out you get zero, + +and you say, well, B is +equal to zero at all times. + +That's nonsensical. + +And I don't know a priori +how much time to keep. + +So let's go to second order. + +So if you plug this +Taylor series into A, + +and get something +that's time dependent, + +you only need to +go to first order. + +One minus k1 times +time plus et cetera. + +Plug it into b, plug your +Taylor series into these two + +guys here, get k1 +A0 over k2 minus k1, + +you only need it to +go to first order. + +The one's cancel out but +the times don't cancel out. + +Minus k1 plus k2, that is, +unless k1 and k2 are the same. + +So we're making +the approximation + +that k1 is different than k2. + +Times the time. + +And when we look at C, +this complicated thing + +that I didn't write +down, if you were just + +to stop at first order in +C, you get C equals zero. + +You know that can't be right. + +You know that C is going +to increase in time. + +It can't be equal to +zero at all times. + +So we have to go to +second order for C0. + +And it's approximately equal to +A0 times k1 k2 over two times + +the time squared. + +Let me rewrite this a +little bit closer in, + +because I need some room here. + +So c is approximately +equal to A0 k1 + +is k2 over two +times time squared. + +OK, and then we can +start plotting out + +what this is going +to look like then. + +So we have the concentrations +time on the axis here. + +Let's start with the +concentrating of A. A + +is dropping down +linearly in time. + +It's dropping down +linearly in time here. + +B is increasing linearly +in time, at the beginning. + +So B is going up linearly +in time, like this. + +And C is increasing +quadratically in time. + +So it's pretty flat, +coming up first. + +And then it starts to curve up. + +It's our first approximation. + +Then, we go to late +times. t equals infinity. + +So t equals infinity where +am I going to write this? + +Have to move this up. + +Let's go, t goes to infinity. + +Well, here I know that +I'm allowed to go to zero. + +Or allowed to go to constant, +because infinity is forever. + +So at t infinity, I know that +I'm going to use up all of A. + +So I know that A is +going to be equal to 0. + +I know I'm going +to use up all of B. + +So I know B is +going to go to zero. + +Somehow. + +And I know that C is +going to go to A0. + +So C is going to go +to A0 at infinity. + +So now on my graph here, +I know that at infinity, A + +is going to go down to +zero like this, somehow. + +Probably exponentially, because +it is exponential in time. + +So it's going to go +to zero exponentially. + +B is going to go down +to zero exponentially. + +There are the +exponentials right here. + +So B is going to go down +to zero exponentially. + +Something like this. + +And C is going to +saturate to A0. + +Exponentially rise up to A0. + +So this was A0 right here. + +It's going to go like this. + +So then I connect the dots. + +And I know that C is going +to start quadratically. + +And then it's going to rise +up an exponent like this. + +I know that B is going +to start off linearly, + +and then it has to go to zero. + +So it has to go through +some sort of maximum. + +And A is going to go +down exponentially, + +exponentially like this. + +So the interesting +part of this diagram + +is that B goes to a maximum. + +There is some point, +there's some time, + +that we can call t sub B +max, where B is a maxima. + +And that's an interesting point. + +That's something that we can +try to figure out experimentally + +what it is. + +And we could get +some parameters, + +we could maybe extract +some information. + +There's a maximum B, +concentration of B, + +that gets formed. + +And how do you solve that? + +You set dB/dt equal to zero. + +So you have your equation +for B right here. + +You set it equal to +zero. and you solve. + +You get your maximum time. + +It's made up of rate constant. + +You get your maximum +concentration, + +which is also made +up of rate constants. + +And you can get rate +constants out of this. + +Question. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yes. + +STUDENT: [INAUDIBLE] + +PROFESSOR: That +is a coincidence. + +That is my poor sketching. + +It should probably be somewhere +like, in the middle here. + +Actually, it completely +depends on the rates. + +And we're going to +see limiting cases + +where this maximum +can occur here, + +or it can occur +somewhere down here. + +So this is the complete case. + +So, limiting cases. the +important limiting cases. + +We've made an +approximation along the way + +that k1 is different than k2. + +So that has to be a case +that needs to be worked out. + +And it's likely to be easier +than the full solution. + +So one of the limiting +cases is k1 is equal to k2 + +and I'll leave +that for homework. + +You can do that yourselves. + +It's good exercise. + +What about another +limiting case? + +Well, you have two +other limiting cases. + +One, you've got two rates. + +So, one is bigger +than the other. + +No information on +this board here. + +You start off with one case. + +So k1 greater than k2. +k1 greater than k2. + +What does it mean? +k1 greater than k2. + +It means that the +rate determining + +step, or the limiting +step, in this reaction, + +is the second step. k2 is +very slow compared to k1. + +And sometimes I like to think +of these things as pipes. + +And connecting vessels. + +So let's say we have +the amount of liquid + +in the top vessel is +the concentration of A. + +The amount of liquid +in the middle vessel, + +let me get my color scheme +to be consistent here. + +Then we have a +middle vessel, which + +is the concentration of B, +and a final vessel, which + +is the concentration +of C. And we start out + +with some sort of +amount of A in here. + +Started with a lot of A, +and then these vessels + +are connecting with pipes. + +So there's a very +thick, big pipe + +that connects A and B together. + +The rate is fast, +going from A to B. + +And the rate going +from B to C is slow, + +so there's a skinny pipe +connecting B and C together. + +Then I turn on the +system, I set time + +to equal zero, +poof, what happens? + +There's the big pipe +connecting A and B. + +The whole amount of a here gets +transferred to B, suddenly. + +Then it gets stuck here. + +And then it dribbles +out from B to C. + +So what do we expect, +if we were to plot + +our quantities as +a function of time. + +What we'd expect +then, then we're + +going to make sure that +the math works out, + +is that A is going to +decrease really fast. + +It's going to go, poof. + +First order in time +with a very fast rate. + +And all of this is going +to go straight into B. + +So we expect B to go linearly. + +Remember, at the +beginning it's linear. + +Linear goes up. + +Almost all the way up to A0. + +Because it can't hardly get out. + +Reaches its maximum, +then it goes from B to C + +through this +skinny, skinny pipe. + +First order rate, +with a rate k2, + +so we're exponentially going +down, slowly, slowly, slowly, + +with a rate k2. + +And then C starts quadratically. + +And then very quickly, +once everything's into B, + +A is forgotten. + +A doesn't matter any more. + +Basically what you're +looking at is a transfer of B + +into C through this little pipe. + +And you know that's going +to be a first order of rate. + +First order of process, +B to C's first order + +of process with rate k2. + +So you expect, then, C to +go up in the first order + +process to A0 with rate k2. + +There's the rate k2 here. + +And the rate k1 here. + +So when you turn the crank on +your approximation in the math, + +what you'd better see +is that at the end, + +B as a function of +time should look + +like a first order +process with rate k2. + +C as a function of time +should look like a first order + +process with rate +k2, going to A0. + +And you can write +the answer, you + +should be able to +write the answer, + +for C, it's going to +be C is approximately, + +it's going to go to A0, +there's no other choice. + +Everything that was in A gets +transferred to B0, so at time + +is infinity it's going +to be A0, and it's + +going to be a first order +process with rate k2. + +One minus e to the +minus k2 times times. + +I don't even have +to do the math. + +I know that's the answer. + +If you don't believe +me, then do the math. + +You should do it. + +But that's the answer. + +It has to be the answer. + +And if you look at +B, the answer has + +to be that it's approximately +looking like B is disappearing + +with a rate constant that's +k2, e to the minus k2, + +and the maximum here +is very close to A0. + +So I'm going to be +putting A0 here. + +Close enough. + +So as long as I ignore the +very initial time where + +A suddenly dumps into B, then +everything after that very + +early time here is just +looking like B goes to C. + +This is not zero, this is t. + +And A just disappears quickly. + +And we can write it as A is +equal to A0 e to the minus + +k1 times the time. + +That's an easy approximation. + +And you've just got to +make sure that this fits. + +So the other limiting +case, which I'm also + +going to leave as a +homework, because it's + +so straightforward, is to +have k2 greater than k1, + +and you should make sure +that you can predict it. + +and that the math works out. + +OK, any questions? + +Next time we'll do +reversible reactions. + +And some more approximations. \ No newline at end of file diff --git a/lnZR0TVNh2k.txt b/lnZR0TVNh2k.txt new file mode 100644 index 0000000000000000000000000000000000000000..cc882c0a64255ff68367bc367eb5e4e13b15fc1a --- /dev/null +++ b/lnZR0TVNh2k.txt @@ -0,0 +1,3271 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Very good. + +So today, we'll +begin with a study + +of one dimensional potentials +and the energy eigenstates + +or properties. + +And we'll discuss this for +about half of the lecture. + +And then go into the +variational principle. + +So let me go back then to +our discussion of last time, + +where we were talking +about energy eigenstates + +and the Schrodinger +equation in one dimension. + +So there's a term that +we use all the time. + +This term is called +the bound state. + +And bound state seems something +sort of very non-trivial. + +But mathematically, we can +say quite clearly what it is. + +A bound state is +something that is not + +spread all over +space, basically. + +And the way we therefore use +the terminology for bound + +state it that we only +speak of bound states + +when there are +energy eigenstates. + +So an energy eigenstate may +or may not be a bound state, + +but any bound state is +an energy eigenstate. + +So an energy eigenstate +is a bound state + +if the wave function +goes to zero + +when you go +sufficiently far away. + +So it's a simple +definition, but it + +helps us understand +that the basic idea is + +at the state is just not +spread all over the world. + +Now remember we're trying +to find energy eigenstates, + +and that is to find +wave functions, time + +independent wave functions, +that solve the time + +independent +Schrodinger equation. + +Which I have written +there for convenience. + +This is the same equation +we wrote last time. + +For a time +independent potential, + +so that the full +wave function can + +be written as a +phase that contains + +the information of the +energy times a function of x, + +sine of x. + +That still may be complex, but +it doesn't have to be complex. + +As you can see, this +is a real equation. + +Now in order to clean up some of +the constants in this equation, + +it's-- yes? + +AUDIENCE: Why is +it not V x minus e? + +PROFESSOR: Well you have to +look back at the Schrodinger + +equation, and bring the +things to the other side, + +and take care of the signs. + +It is correct as stated. + +Check it. + +Now we have, in order +to do this and just + +to write things with +a little more clarity, + +we scale the energy. + +So we define a +calligraphic energy, + +which is 2m over h squared times +energy E. And a calligraphic V + +with the same scaling factor. + +So that the Schrodinger +equation then takes the form-- + +this same equation-- sine. + +And I'll use the double prime +notation for two derivatives. + +Plus now E minus cal +of x sine equals zero. + +So this is how our +equation looks. + +It's relatively simple. + +And can be treated +without carrying constants + +all over the place. + +Now we're going to +discuss a few results that + +are extremely important that +you keep in mind for the future. + +It helps you think clearly. + +So these results are +little theorems that I'm + +going to state. + +And the proofs are +given in the notes. + +I will skip some of +the proofs, although I + +will tell you what the +strategy is for the proofs + +and then show how +the theorem implies, + +as a corollary, +interesting things that + +could easily be misconstrued. + +So let me give you +the first theorem. + +Theorem one. + +This is just the +statement that if you + +are talking about bound states +in one dimensional potentials, + +there are no degeneracies. + +So let's write it. + +There is no degeneracy +for bound states of one + +dimensional potentials. + +So it's a fundamental result. + +We'll see some way to +understand it a little later. + +And you have seen this +in 804, I believe. + +So what is a +strategy to a proof? + +So we want a rigorous proof. + +So what is a strategy? + +I will not go through the proof. + +The strategy is to assume +there is a degeneracy. + +So strategy, assume +a degeneracy. + +So sine 1 and sine 2 different +with the same energy. + +And then you write this +equation for sine 1 and sine 2, + +and they have the same energy. + +Then you take the two equations, +and you multiply the first + +by something, the +second by another thing. + +Subtract it. + +Do a bit of algebra. + +And you suddenly can +prove that one solution + +is equal to a constant +times the other solution. + +So you do the work, and +that's what comes out. + +Once you've shown that one +is proportional to the other, + +we've declared in +quantum mechanics + +that two wave functions +that differ by a constant + +have exactly the same physics. + +You can normalize it, +and normalize them. + +And the constant +can be just a phase, + +but the phase doesn't matter. + +So those two wave functions +are really the same. + +So you get a contradiction. + +You thought they were different. + +But the difference +is just too trivial, + +and therefore they are really +the same wave function. + +Because we've said that +two wave functions that + +differ by a constant +should be identified. + +So that's this theorem. + +And it's a key theorem. + +Let's go to the next theorem +that is also important. + +So theorem two. + +Energy eigenstates sine f of +x can be chosen to be real. + +So here it is. + +We mentioned that this +differential equation + +allows for real solutions. + +There's no contradiction, +because there's no i in there. + +But now we say more. + +That even if you find +a complex solution, + +you can work with +real solutions. + +So what is the strategy here? + +Again strategy. + +To have you get a +complex solution. + +Sine f of x. + +And then you go about +to prove that actually + +this complex solution +implies the existence of two + +real solutions. + +So this complex solution +implies existence + +of two real solutions. + +And moreover, two real-- I +should say it better here-- + +degenerate solutions. + +How could you prove that? + +Well, it probably +would occur to you + +that you would take a solution +and say, oh, this solves it. + +Then you would show that sine +star also solves this equation. + +And then by linearity of +the Schrodinger equation, + +you could form what we would +call the real solution formed + +by taking sine plus sine +star and adding them. + +Or the real solution that +comes from the imaginary part. + +You see the real and imaginary +parts of a complex number + +are real. + +So is the case here as well. + +That they can take sine and +sine star that are different. + +And the sum is real +by construction. + +You put the star, and +recalling that star of star + +gives nothing, you see that this +function is equal to its star. + +So it's real. + +So is this one. + +This function, which is the +imaginary part of the solution + +that you had, is also real. + +So you get two real solutions. + +Moreover, you can show +that sine and sine star + +have the same energy. + +Therefore sine r and sine +m have the same energy. + +So I'm really +skipping very little. + +But I don't want to +clutter the blackboard + +with the whole derivation +at this moment. + +So here is the strategy. + +A complex solution implies +two real solutions. + +And therefore, since +you have real solutions, + +you can always choose +them to be real. + +No loss of generality. + +You had a complex solution. + +You say, I like +just real solutions. + +And you chose your +two real solutions. + +You give them. + +You've given the whole thing. + +But then there is +a nice corollary + +for the case of one +dimension bound states. + +So this is the part that is +perhaps somewhat interesting. + +And the corollary +is that if you're + +talking bound states +of one dimension, + +any solution is equal to a +real solution up to a constant. + +You may say, well +what's the difference? + +Let's write it down +and look at it. + +Corollary for bound states of +one dimensional potentials. + +Any solution is, up to a phase, +equal to a real solution. + +So how does that go? + +Maybe we can use more +of this blackboard. + +Why would any solution +be, up to a phase, + +equal to a real solution? + +OK. + +Suppose you have these +two solutions here. + +Well this is real, so +that's trivially true. + +And this is real. + +But what if I put a linear +combination of them? + +Or take the original +complex solution? + +Why would it be, up to a phase, +equal to a real solution? + +The answer is the following. + +Because of theorem and, +that there's no degeneracy, + +you've got two +solutions that claim + +to be different and degenerate. + +But that can't be. + +So by theorem one, you must +have that-- in the notations, + +I have here-- sine +imaginary of x + +must be equal to a constant +times sine real of x. + +Now if these function's +anyway are real, + +the constant here must be real. + +Therefore, even if you form +the original complex solution, + +sine, which is sine real +plus i sine imaginary. + +You can check that. + +It's clear by definition that +that's the way it should be. + +If you think this, this +is equal to 1 plus i times + +c times sine real of x. + +Therefore this is equal +to a constant times + +the phase of-- this +is a complex number. + +So this is yet another +constant that we + +could say, the norm of 1 plus +i c times some phase times sine + +r of x. + +So you see that any solution, +any linear combination, + +in fact, with any numbers of +sine r and sine imaginary, + +will be a constant times +a phase times this thing. + +So it is really +just real anyway. + +So you can just +have one solution. + +And any solution +that you may write, + +that represents a bound +state, is, up to a phase, + +equal to a real solution. + +OK. + +So that's our theorem two. + +Theorem three. + +It's also very famous. + +If the potential V of x is +even-- that is, V of minus x + +is equal to V of x-- the +eigenstate can be chosen + +to be even or odd +under x2 minus x. + +OK. + +So here is another claim. + +So the potential is even. + +There's no theorem for +all the potentials. + +No clear theorems, no simple +theorems for all the-- + +but if the potential +is even, the claim + +is that you can choose +eigenstates to be even or odd. + +The word chosen is +very important here. + +Otherwise, this would not +be a precise statement. + +You cannot say the +eigenstates are even or odd. + +You can choose them to be. + +So how does the proof go? + +Strategy begin with +a wave function, + +sine of x, that is +neither even nor odd. + +And then you do a little work +with the Schrodinger equation. + +Take the Schrodinger +equation, change all x's + +to minus x's and show that, +in fact, not only is sine + +of x a solution, but sine of +minus x is also a solution. + +With the same energy. + +So prove that sine of +minus x is a solution + +with the same energy. + +And in this case, of +course, we can already + +have shown that we +can choose these wave + +functions to be real. + +So we can choose all of these +wave functions to be real. + +And what do we do next? + +If we have these two solutions +with the same energy, + +then you can build +of sine s, which + +is 1/2 of sine of x +plus sine of minus x. + +And of sine a. + +s for symmetric, and +a for anti-symmetric. + +And of sine a, +that is 1/2 of sine + +of x minus sine of minus x. + +And this tool +would be this even, + +under the exchange +of x for minus x. + +This one odd, under the +exchange of x for minus x. + +And both would be +solutions by superposition. + +And both would have +the same energy. + +So that's the end of the theorem +because then these things are + +even or odd and have +the same energy. + +So the solutions can be chosen +to be even or odd under x. + +So if you've proven this, +you've got it already. + +But now we get the corollary. + +For bound states +in one dimension, + +the solutions not +anymore the word chosen. + +We can delete the word chosen. + +The solutions are +either odd or even. + +So it's a lot stronger. + +It's not anymore, you +can choose them to be, + +but a general one is +neither odd nor even. + +No. + +You try to find the solution +that is neither odd nor even, + +and you can't find it. + +So it's very strong. + +Yes? + +AUDIENCE: Is this +for even potentials? + +PROFESSOR: Even potentials. + +Yes. + +For bound states in one +dimension with even potentials. + +V of x. + +V of minus x equal V of x. + +Yes. + +So how do we show that? + +Well, again, you've +got two solutions here + +that are degenerate that +have the same energy. + +Sine of x and sine of minus x. + +So given that there's +no degeneracy in one + +dimensional problems, this thing +that they have the same energy, + +the only thing that +can be happening + +is that sine of minus x is equal +to a constant times sine of x. + +Where this constant is real. + +Why real? + +Because we said already +by the previously theorem, + +wave functions can +be chosen to be real. + +So you've got this thing +already that this is true. + +Sine of minus x is equal +to c times sine of x. + +Which, if you use this +property again by saying, + +oh, but sine of x is equal +to c times sine of minus x. + +Basically, what this says +is that you can change + +the sign of the argument +by putting an extra c. + +So you do it again, sine +of x is equal to this. + +So this is c squared +times sine of minus x. + +So c squared must be equal to 1. + +And therefore c is equal +to either plus or minus 1. + +No other option. + +So the functions are +either even or odd, + +but they can't be arbitrary. + +This point is +sufficiently settled + +that part two +general exam at MIT + +10 years ago had a +question like that. + +And the person that +invented the problem + +claimed that there +would be a solution that + +could be neither even nor odd. + +So even faculty members at +MIT sometimes get this wrong. + +It's not as weak as +this, that can be chosen. + +But it's really either +or other in the case + +you have one dimension. + +OK. + +So these are our main theorems. + +And we're going to +proceed now by clarifying + +a little more the +nature of the spectrum. + +So are there questions? + +Yes? + +AUDIENCE: Can you give +an example of state + +that's not bound? + +PROFESSOR: OK. + +The question is can +I give an example + +of a state that is not bound? + +Yes. + +We can give such state. + +You have a potential like this. + +And you have an +energy like that. + +And then the wave function +could look like this. + +Then do something like that. + +And then look like that. + +It just doesn't vanish +when you go to infinity. + +AUDIENCE: So that +can't be normalized? + +PROFESSOR: Can't be normalized. + +That's right. + +If it's not bound, it +can't be normalized. + +Other questions? + +Yes? + +AUDIENCE: So you can't really +represent-- it's doesn't really + +represent single particles, +more like a stream of particles? + +PROFESSOR: Yes. + +So it doesn't represent +a single particle. + +Now trying to interpret it +as a stream of particles + +is a little delicate. + +So what we usually do is +we build superpositions + +of those states that can +represent a localized thing. + +But it's true that, +morally speaking, + +it seems to represent +more than one particle. + +OK. + +So now we talk a little about +the nature of the spectrum. + +So what do we want to say here? + +We want to go back to the +Schrodinger equation here. + +And just move one term +to the right hand side. + +And just see what +can happen in terms + +of singularities +and discontinuities. + +So first of all, we +always begin with the idea + +that sine must be continuous. + +And the reason sine +must be continuous is + +that we don't want +singularities worse + +than delta functions +in potentials. + +If a function is +continuous, the derivative + +might be discontinuous, +and the second derivative + +would have a delta function. + +So the second derivative +would have a delta function. + +But if the function is +not even continuous, + +the second derivative would have +derivatives of delta functions. + +So somehow the potential +would have to have that. + +And we don't want it. + +So to simplify our life, we say +that sine must be continuous. + +Now if sine is +continuous, we will + +consider several possibilities, +possibilities for V, + +possibilities for V of x. + +So first possibility-- +one, V is continuous. + +So psi is continuous, +and V is continuous. + +If psi is continuous +and V is continuous, + +this product is continuous. + +Psi double prime is continuous. + +And psi prime is continuous. + +Two, V has finite jumps. + +Well, if V has finite jumps, +and psi is continuous, + +this product has finite jumps. + +So psi double prime +has finite jumps. + +If psi prime has +finite jumps, the worst + +is that psi prime still +must be continuous. + +But it changes. + +Psi prime could look like +that, could have a corner. + +But it cannot be +worse than that. + +Because if V has finite +jumps, if psi double + +prime has finite jumps, and if +psi prime is not continuous, + +it would have delta functions. + +So for these two conditions, +continuous or even + +finite jumps, psi prime +is still continuous. + +Things change qualitatively if +three, V has delta functions. + +If V has a delta +function, then psi + +double prime has +a delta function. + +And psi prime therefore jumps. + +Psi prime is not continuous. + +Psi prime jumps. + +This may be reminiscent +to you whenever + +you had to solve the +problem of a bound state + +of a delta function, +you got a wave function + +that looked like this in +which psi prime jumps. + +And it has to jump. + +Because psi double prime +has a delta function. + +Another case in +which psi prime jumps + +is for if V has a hard wall. + +That is, the potential suddenly +at one point becomes infinite, + +and it prevents the +particle from moving across. + +A hard wall is a +place, as you remember + +in the infinite square +well, in which the wave + +function vanishes, but the +derivative doesn't vanish. + +So you could say that +psi is 0 here outside. + +Psi prime, then, jumps +in that it's non-0 here + +and it's 0 afterwards. + +So now, you could +object to what I'm + +saying by explaining that, +well, we shouldn't talk + +about the wave function +beyond the hard wall. + +And in some sense, you're right. + +But suppose we do and we say +the wave function is just + +0 everywhere, we see +that psi prime jumps. + +So really, psi prime jumps. + +So this is as bad +as things can get. + +So we can summarize this +in just one sentence. + +And the sentence reads, +psi and psi prime + +are continuous unless V has +delta functions or hard walls, + +in which case psi prime +can have finite jumps. + +So basically, psi and +psi prime, continuous. + +Exceptions-- delta functions +and hard walls, and psi prime + +can change. + +So questions. + +There was a question before. + +Maybe it's still there. + +Yes. + +AUDIENCE: Do you absolutely +need that function [INAUDIBLE]? + +Or do we just assume +that [INAUDIBLE]? + +PROFESSOR: We assume it-- +so the question is, do I + +need that in absolute generality +to do quantum mechanics? + +I don't think so. + +I presume you could discuss +some potentials that + +lead to psi that +are not continuous + +and still make sense. + +But we will not discuss them. + +And actually, I don't think +I've encountered any of those. + +Yes. + +AUDIENCE: Can you +give an example + +of a physical system whose +potential is well approximated + +by a delta function [INAUDIBLE]? + +PROFESSOR: Yes, there +are systems like that. + +For example, this one +that is somewhat well + +approximated by +a delta function. + +For example, a +nucleus sometimes is + +considered to be like a +spherical cavity in which + +particles are bound by a deep +potential and don't escape. + +So the nuclei are moving +like that and don't escape. + +In that case, it would be +a three dimensional delta + +function that vanishes +at the origin. + +I presume there +are many examples. + +Any potential that +sort of begins + +like a finite square well +that is sufficiently deep + +will start to look like a +delta function after awhile. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Well, it's again +neither-- yeah, I guess so. + +But it depends how +big is this psi. + +So yeah, probably you're right. + +This looks a little more like +an analog of a hard wall. + +But if a hard wall is +very narrow and very deep, + +it looks like a delta function. + +So it's idealizations for sure. + +But I'm sure we could +get a better example. + +And I'll try to find one. + +Now, the next +thing we want to do + +is give you intuition for +this incredible result + +that there's no degeneratives +in one dimensional potentials. + +That is not to say that the +proof is not good enough. + +It is just to say that +we can illustrate that + +without going into a +mathematical proof that + +is more complicated. + +So how do we do that? + +We'll consider the following +case, a simple case, + +an example of a +potential of this form. + +V of x-- this is x. + +And here is V of x. + +And we will try to find a +solution with some energy that + +is like that, an energy that is +right there below the barrier. + +So this would be a bound state. + +Why? + +Because solutions +here are exponentials + +that decay, +exponentials that decay. + +And here, the wave +function would + +be oscillating presumably. + +So the wave functions +go to 0 and infinity. + +You could get a bound state. + +So let's see how we +get a bound state. + +Now, the argument +I'm going to follow + +is just an elaboration +of something + +you can read in Shankar. + +And it's a nice and +simple argument. + +So we want to understand why we +would get here no degeneracies. + +Or even more-- in fact +not just no degeneracies, + +but the spectrum is quantized. + +That is, you find one energy, +and then another energy maybe, + +and another energy. + +So how do we see that? + +Well, you look at the way +you can write solutions + +and count the parameters +of the solutions + +and try to see how many +conditions you have to satisfy. + +So here, the wave function +would be a decay in exponential. + +A decay in exponential +is of the form + +alpha e to the K, kappa, x. + +Because x here is negative. + +So this decays as x +goes to minus infinity + +if kappa is positive. + +And that's how a solution looks. + +You need one coefficient here +to determine this solutions. + +So I'll put a 1 here. + +Now, in here, the +solution is oscillatory. + +So it's a sine plus cosine. + +So you need two coefficients. + +In here, the solution +must again be decaying. + +And therefore, you just +need one coefficient. + +Again, this time it would +be a beta e to the minus Kx. + +The fact that this +potential looks + +symmetric-- I'm +not assuming it is. + +Yes. + +AUDIENCE: Won't one +of the coefficients + +be unconstrained +by normalization? + +Isn't one just the +normalization factor? + +PROFESSOR: OK, how +about normalization? + +Indeed, we have one, +two, and two and one, so + +a total of four coefficients, +four parameters. + +But indeed, suppose you +wrote your whole solution. + +You could say, look, let me +divide this solution by 3. + +That's an equivalent solution. + +I'm just checking if it solves +the Schrodinger equation. + +That's all I have to check. + +I don't have to +check normalization. + +Normalization, in fact, is +sort of irrelevant here. + +You just need to know +if a bound state exists. + +So indeed, even though you have +these four parameters, given + +that you can multiply the +solution by a constant, + +there's just three +constants to fix. + +Four parameters +via normalization + +or the multiplication by +any constant-- just three + +constants to fix. + +But this potential +is nice enough + +that psi and psi prime +must be continuous. + +So you get two conditions +here and two conditions here. + +So four conditions-- continuity +of psi and psi prime, + +continuity of psi and psi +prime, four conditions. + +So what did we get? + +We got in trouble. + +We've shown that this is +unsolvable in general. + +Because there are more +conditions than parameters. + +Now, this equation could +to be a little peculiar. + +Maybe this is not +completely general. + +But you seem to have more +conditions than parameters. + +But here comes the catch. + +The solution really +is determined. + +Like kappa-- do you know kappa? + +Well, you know kappa if you +know the energy of the solution. + +Kappa is determined by the +energy of the solution. + +So some parameters in the +solution depend on the energy. + +So the way we have +to think of this + +is that in fact three constants +to fix, but four conditions. + +So we really need +four constants to fix. + +And the fourth +constant is the energy. + +So the energy is the +fourth constant to fix. + +And with four conditions, +these three constants + +that we had there and the +energy, they can just be fixed. + +So the solution +should fix the energy + +and should fix this coefficient. + +So the solution exists for +some energy, or possibly + +some values of the energies, but +not all values of the energy. + +So this shows, or at least +very clearly illustrates, + +that you are going to find sets +of energies for which you have + +solutions depending on +how the equations look, + +and one solution each time. + +So you get what is called +a discrete non-degenerate + +spectrum. + +Now, there are more +cases to discuss, + +the case in which you +have just the step, + +or the case in which you +have three bound states. + +And I will not do them +but state the results. + +Again, all that I +don't do explicitly + +can be found in the notes. + +So you would look at them later. + +And so here is the second +case, a potential like this + +and an energy like +that, energy level. + +And what you get here is that +in fact, doing the counting + +and analyzing the +boundary conditions, + +you should do it by yourselves. + +But you will see the +answers in the notes. + +You get here continuous +spectrum, non-degenerate. + +So you will get a +solution for every value + +of the energy-- that's to mean, +continuous spectrum-- and one + +solution each time. + +Finally, this case-- if you +have an energy like this, + +e, you get continuous spectrum +and doubly degenerate, + +so two solutions. + +Now, after this, +there's one more result + +that qualifies as a theorem. + +And it's hard to +prove rigorously. + +I will not attempt to prove +it here nor even in the notes. + +It's hard enough. + +So this theorem has +to do with nodes. + +Theorem-- so if you have +the discrete bound state + +spectrum of a one +dimensional potential, + +and you list the energies +E1 less than E2 less than E3 + +like that, E1 is the +ground state energy. + +Remember, this +spectrum is discrete. + +So this is less than +E2, less than E3, + +and it goes on like that, +the ground state energy. + +Then, you have associated wave +functions, energy eigenstates + +psi 1 of x, psi 2 +of x, psi 3 of x. + +Here is the theorem. + +The theorem tells you something +about the vanishing of the wave + +function. + +It says that psi 1 has no nodes. + +Psi 2 has one node. + +Psi 3 has two nodes. + +And so it goes so that psi +n has n minus one node. + +So psi n is greater +than-- well, it's correct. + +Any n greater or equal +to 1 has n minus 1 nodes. + +Now, there are several +ways people show this. + +Mathematicians show it in +a rather delicate analysis. + +Physicists have an +argument as well + +for this, which is based on +approximating any potential + +by infinite square +wells to begin with. + +So suppose you have a +potential like that. + +Well, think of it as first being +a little potential like that, + +an infinite square well. + +And you start making the window +of the square well bigger. + +The argument-- it's +a neat argument. + +Maybe you can discuss +it in recitation. + +I would suggest that. + +It's a good argument. + +But it's not rigorous. + +But still, one can do +something like that. + +You make it grow. + +And what you know is that +the infinite square well, + +the first wave +function has no node. + +And as you change the screen to +make the potential really what + +it's supposed to be and not +just that of a square well, + +the wave function +cannot gain a node. + +On the other hand, what you +will show in the homework + +is something that is +a partial result which + +says that the +solution with n plus 1 + +has at least one more node +than the solution with n. + +So it's part of +what you can show. + +And it doesn't take +too much effort. + +And you can prove it rigorously. + +So we will assign +that eventually + +for a homework to do. + +In the homework that you +have for the first homework, + +you also have a problem +with delta functions. + +And I suggest that you +read the notes that + +will be posted today. + +Because there's an example +there with delta functions. + +If you study that +example, you'll + +find the problem +quite easy to solve. + +You may have solved already. + +Some of you are very eager to +get going with the homework. + +So it's something you +can study first, and then + +make your life a little easier. + +So what we're going to do now +for the rest of the lecture + +is consider the +variational problem, which + +is something you probably +haven't seen before, + +the variational problem. + +This problem has to do with +calculus of variations. + +Now, calculus of +variations is something + +considered fairly advanced. + +And therefore, as +you will see, we + +will avoid some of the major +difficulties of calculus + +of variations in our discussion +of the variational principle. + +But I wanted to mention a +little story about this problem. + +So this calculus of variations +is a more complicated version + +of maxima and minima in which in +maxima and minima of functions + +you look at the function. + +And if you could plot it, you +could say, here's a maximum, + +here's a minimum. + +If you want to figure out +where they are, you know. + +You take a derivative, +set it equal to 0, + +you find the maxima and minima. + +So the typical +calculus problem is + +one in which you +have a function, + +and you want the +maxima and minima. + +The variational +problem is a problem + +in which you want to maximize +or minimize something. + +But what you don't know is not +where the maximum or minimum + +occurs, but which +kind of function + +will give you this +maximum or minimum. + +So your unknown is +not a point where + +there's a maximum or a +minimum but a function where + +there is a maximum +and a minimum. + +So it's slightly +more complicated. + +So this is the +calculus of variations. + +And people wonder +when did it start. + +It actually seems to have +first been discussed by Newton. + +And it's quite an +interesting story. + +Newton was trying to +understand apparently + +the following problem. + +If you would have a cross +sectional area like this, + +he asked the question, +how should you + +make a solid out of this +by tapering it and ending + +with this, tapering +it, in such a way + +that as it moves +in a viscous fluid, + +the resistance is the minimum +possible-- very complicated + +problem. + +And as you can imagine, this +is a complicated problem + +because you're trying to find +a shape-- not just a maximum + +or a minimum of a +function but what + +shape maximizes +or minimizes this. + +So apparently, he +solved the problem + +and wrote it in Principia but +didn't explain his solution. + +And people for years were +trying to figure it out. + +And nobody could figure +out how he did it. + +Then, the story goes that this +mathematician Johann Bernoulli + +in 1696 came up with a +challenge to all mathematicians. + +At that time, people +would announce a problem + +and challenge to +see who's smart, + +who can solve this problem. + +So Johann Bernoulli +in around 1696 + +poses a problem of, you're +given two points in the plane, + +in the vertical plane like +this blackboard, point this, A, + +and point B in here. + +You must design the +curve of shortest time + +for fall, so some curve here. + +If you put an object +and let it fall, + +it will get the fastest +to that point, so maybe + +something that looks like this. + +It's a complicated curve, or +at least not all that simple. + +And he asked all the +people to solve it, + +gave them one year to solve it. + +So who was around at that time? + +Well, one person that got +the letter was Leibniz. + +He got it on the 9th of +June of that year, 1696. + +And he answered it, +sent an email back, + +by the 16th of +June with a letter + +with a complete solution. + +It's a funny thing that actually +apparently Newton was very busy + +and didn't receive this letter. + +Or something happened, +and he got it one day, + +and he actually solved +the problem in one night. + +It took him one full +night to solve it. + +Now, you say, well, +how brilliant. + +And true, but given that +he had solved this problem, + +he was criticized as being +really slow and-- how come + +you took 12 hours to +solve this problem? + +So it's quite amazing. + +There's a lot of Bernoullis. + +And apparently, this +question by Jacob Bernoulli, + +the main purpose +of this question + +was to demonstrate to everybody +that his older brother, + +Jacob Bernoulli, who had +invented the Bernoulli numbers, + +was actually an +incompetent person that + +could not solve this problem. + +So that was apparently +what he wanted to do. + +It's a rather famous family. + +But they obviously +didn't get along. + +But apparently, Jacob did +manage to solve the problem. + +So Jacob Bernoulli, Leibniz, and +Newton all solved the problem. + +Johann Bernoulli, the one that +started this problem-- and I + +think it's maybe +with a double N, + +I'm sorry-- his son +is Daniel Bernoulli. + +And engineers know +him, because that's + +the Bernoulli of the Bernoulli +fluid dynamics stuff. + +So the problem is +not all that easy. + +And calculus of variations +determines this shape. + +So the calculus of variation +applied to quantum mechanics + +asks, here, this function is +determined by the principle + +that it minimizes time. + +So you have the +Schrodinger Equation. + +And you could ask, you have +all these Eigenfunctions. + +What do they minimize? + +Is there something +they're minimize? + +And the answer is yes. + +And this is what +you'll understand + +in the next few minutes. + +So what is the problem +we want to solve? + +We want to solve the +problem h psi equal e psi. + +So some Hamiltonian. + +Now my notation +will be such that it + +applies to three +dimensions as well. + +So I'll put just +arrows on top of it, + +and you would have to write +the proper Hamiltonian. + +It will not be necessary for +you to know the Hamiltonian. + +So I'll put psi +of x here, meaning + +that this is equally valid +for more than one dimension. + +Now we want to find +solutions of this equation. + +And you can say, what do +they maximize or minimize? + +Well we won't get to +it until 15 minutes. + +First let's try +something simpler. + +How about, can we +learn something + +about the ground state +energy of the system? + +So let's try to think about +the ground state energy. + +State energy. + +Now consider ground +state energy and we'll + +consider an +arbitrary-- arbitrary + +is the most +important word here-- + +psi of x that is normalized. + +Is normalized. + +So integral the x of psi +squared is equal to 1. + +And here comes the claim. + +The first claim +that we can make. + +You see, this wave +function doesn't + +solve the Schrodinger equation. + +That's what we +mean by arbitrary. + +It's just any function of +space that is normalizable. + +Doesn't solve the +Schrodinger equation. + +Never the less, +you are commanded + +to compute the +following quantity. + +This quantity is +also by definition + +what we call the +expectation value + +of the Hamiltonian +in the state psi. + +I love the fact, the +remarkable fact that we're + +going to show now, is +that this thing provides + +an upper bound for the ground +state energy for all psi. + +So let me try to make +sure we understand + +what's happening here. + +Here it says you don't know +the ground state energy + +but you're going to +learn something about it. + +Something that's +interesting is if you + +know that it has an upper bound, +so the ground state energy + +is definitely not +higher than this one, + +so you learn something. + +Would be ideal if you +had also lower bound + +so you knew it's in this range. + +But an upper bound is +a nice thing to have. + +And the claim here is that +each time you try an arbitrary + +function, you put anything +here, you ever write, + +you've got an upper bound. + +So how is this used? + +You try arbitrary functions +that you think look possibly + +like the wave function +of a bound state. + +And you get numbers +and you already + +know that the ground +state energy smaller + +than some number. + +So it's a rather nice way +of getting some information + +about the ground state energy. + +So this psi effects is +called a trial wave function. + +Is a trial wave function. + +So is the statement +of this theorem clear? + +Not the proof, +but the statement. + +Do we have questions? + +Yes. + +AUDIENCE: Is there any +statement about how + +using the wave +function will give us + +how accurate an +estimate [INAUDIBLE] + +PROFESSOR: No. + +We're going to become +good and figure out + +some nice way of choosing +wave functions, but no. + +Once you tried you +got some information. + +And you may not know +so easily whether you + +could go much lower. + +You can try a little, but +there's no clear way to know. + +This is just some +partial information. + +OK. + +So let me first prove this. + +We'll prove it and then explain +a little more what it all + +means. + +So the proof. + +Now it's a proof +under quotation marks. + +I will make a few assumptions. + +Basically, that I don't +have a continuous spectrum. + +Now that assumption is done for +me to write a simpler proof, + +not because the +result doesn't hold. + +So the proof is +good, but I will just + +consider for notational +purposes no continuous spectrum. + +So we'll have a +ground state energy + +which is e1 that is maybe less +than or equal to e2 less than + +or equal e3 like that. + +So you even may consider +the [? genorisies. ?] + +And we have h psi n +is equal to en psi n. + +So what do we have? + +We have a trial wave function. + +So your trial wave +function since it's + +an arbitrary +function of x should + +be expandable by completeness +as a serious or a superb + +position of the +energy eigenstates. + +Let me clarify this point. + +This is a trial wave function. + +Doesn't solve the +Schrodinger equation. + +So this Doesn't solve this +energy eigenstate equation. + +So in fact, it doesn't +solve it because this + +is a superb position +of many in here. + +So that's consistent +with this, and the fact + +that this wave function +as given in here + +just can be represented +using the energy eigenstates. + +But being a superb +position, it's + +not an energy eigenstate which +is true because a trial wave + +function is something that +you invent out of your head. + +It's not a solution. + +If you had a solution, +you wouldn't need this. + +So you don't have a solution. + +You invent the trial wave +function, and you have this. + +A couple of things. + +The psi squared +integral being one. + +You can do that +integral, that condition, + +is the sum of their +bn-2nd is equal to 1. + +This I use the orthonormality. + +You can elevate this. + +It's sort of the kinds of +things we're doing last time. + +Please make sure you +know how to do that. + +Then there's the +other computation + +that we also have +sketched last time, which + +is that the integral +of psi star h + +psi which is what +we want to compute, + +h hat psi is actually bn-2nd en. + +So that was +something we're doing + +towards the end of last lecture. + +And this computation takes a +few lines, but it was there. + +It's in the notes. + +And now comes the kind +of thing we want to say. + +Look at this sum. + +It has b1, e1, b2, e2, +b3, e3, but e2, e3, e4, + +all those are bigger, +or at most, equal to e1. + +So if I did, here, +the following bad joke + +of substituting en for e1, which +is not the same, if I put here + +bn squared n equals +1 to infinity. + +I put here e1, +well this is bigger + +than that because e2 is +possibly bigger than e1, + +e3 is bigger than e1. + +But it may be equal. + +But at this moment, e1 +can go out of the sum. + +So this is e1 times +this sum which + +is 1 because bn is equal to 1. + +And e1 is the ground state +energy by definition. + +So the ground state +energy is less + +than this which +is the expectation + +value of the Hamiltonian. + +Pretty simple, in +fact, the proof + +is really a little too simple. + +Where do we go from now? + +Well let's make a +more general statement + +of the variational principal. + +Again, sometimes +it's not all that + +convenient to have +normalized wave functions. + +So recall that if psi +of x is not normalized, + +psi of x over the square root +of integral of psi-2nd dx is. + +Therefore if you +hand me an arbitrary + +psi of x that is +really arbitrary. + +You don't even bother +to normalize it. + +Then when I plug +here in this formula + +it is supposed to be normalized. + +So I plug the second +expression there. + +So therefore I get +that egs less than + +or equal to the +integral of psi star h + +psi the x over integral +of psi star psi the x. + +This is actually +nicer in one way + +because you don't have to work +with normalized wave functions. + +And that result +must be true still. + +Yes? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Sure. + +It cannot be +completely arbitrary, + +the function should +we normalizable. + +Doesn't have to be +normalized but normalizable. + +So here you got. + +And here let me introduce +just a little name. + +f of psi. + +f of psi is what is +called a functional. + +f of is a functional. + +What is a functional? + +A functional is a +machine or an expression + +whose input is a function +and whose output is a number. + +So here f of psi +is a functional. + +And maybe I should use brackets. + +Many times people with brackets +denote that, watch out, + +this is not a function, +it's a functional. + +And here it is. + +No dash there. + +You give me a psi of +x, which is a function, + +and then this is a +number because you've + +done the integrals. + +So that is like the +Brachistochrone problem, that + +a funny name for it. + +Here it is. + +There is a function +now which is the time + +that it takes to go here. + +You give me a path, +a function, and I + +can calculate the time it will +take the mass to get here. + +So this was the issue of +finding a critical point + +of a functional. + +So actually we start to see, +it seems that the ground state + +energy is the minimum +of this functional. + +And what this +interesting as well + +is that when you get the +minimum you will have gotten + +a ground state wave function. + +So the ground state +wave function actually + +is the thing that +minimizes this functional + +and gives you some value, +the ground state energy. + +A little more in a +couple of minutes. + +Let's do an example. + +How do we use this so now if +you think about this carefully + +it's kind of dizzying because +what is sell functional, + +really? + +It's, in some sense, a function +in an infinite dimensional + +space because a function +itself is specified + +by infinitely many numbers +that you can change. + +So how many dimensions +you have is how many ways + +you can move your hands, but +they are linearly independent. + +But if you have a function, +and you can change it, + +you can change it here, +you can change it there, + +or you can change it +there, and those are all + +orthogonal directions. + +You're finding a critical point. + +When you find the +critical point, + +you should imagine that you're +plotting a function that is not + +one dimensional function or +two dimensional function, + +but it's infinitely +dimensional function. + +Direction one, direction two, +infinitely many directions. + +And suddenly in this +infinitely many directions + +you find the critical point. + +It's really incredible that +one can do these things. + +So you're at that +critical point, + +and you can deform +the energy eigenstate + +by making it a little +fatter here or thinner + +here or up there. + +And those are the +infinite directions + +in any direction that +you will the energy + +goes up because you're +at the global minimum + +it's pretty amazing. + +Something that you will +prove in the homework + +is that actually it's even more. + +Every single eigenstate +is a critical point + +of this functional. + +So you've got the +lowest energy state + +and in that infinite dimensional +space in every direction + +that you move you go up. + +The first excited state +is another critical point. + +But it will not be +an absolute minimum. + +It will be a [? saddle ?] +an infinite dimensional + +[? saddle ?] which +are infinitely + +many directions in +which you go up. + +There's one direction +in which you go down + +because you could flow +towards the ground state. + +So the first excited state +is the [? saddle ?] but these + +are all stationary points +of this functional. + +So we'll conclude by +doing this example. + +Sorry, what is the question? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: I didn't assume +it's non-degenerate. + +So if you have two things that +have the same ground state, + +the functional will have, in +fact, the degeneracy there + +will be two solutions +that have the same energy. + +And any linear combination of +them will have the same energy. + +The proof that I did here +doesn't assume non-degeneracy, + +it's even true with +degenerate things. + +So the example is an +example for illustration, + +not for solving something +that you can't do otherwise. + +So it's a delta +function potential. + +v of x is minus alpha delta +of x with alpha positive. + +And the ground state +energy is well known. + +It's minus m alpha +squared over 2h-2nd. + +You've solved this +problem many times in 804. + +So trial wave function. + +Well you know how +it should look, + +but let's assume you don't. + +And you say, it's some +sort of [INAUDIBLE]. + +So trial. + +It would be psi of x equals +e to the minus x squared. + +While this would do, +you're going to work hard + +and you're not going to +reap all the benefits + +of this calculation. + +So what you should do at this +moment is put a constant here. + +Minus beta squared x squared +and I'll put the minus one half. + +This is our trial wave function. + +You see, by this, you're +going to get an expression. + +You calculate this +number, and you're + +going to get the +function of beta. + +Beta is not going to disappear. + +And therefore, you're going +to know that the ground state + +energy is less than +this function of beta. + +And then you can adjust +beta to get the best bound. + +So beta is put as a +parameter to begin with, + +and we hope to use it. + +So note that integral of +psi squared dx in this case + +is equal to square +root of pi over beta. + +So we have to calculate +this whole functional. + +So this integral +of psi star-- well + +I don't have to bother with +psi star because it's real. + +h psi over psi psi, +and what do we get? + +Well the denominator is easy. + +So we beta over +square root of pi, + +and let me write the +whole thing here. + +dx the psi would have +e to the minus one half + +beta squared x squared +minus h squared + +over 2m d-2nd dx2nd +minus alpha delta of x. + +And another wave function, +e to the minus one + +half beta squared x-2nd. + +OK. + +So you have to evaluate that. + +And that's the part +that is not so much fun. + +For any integral +that you have in 805, + +we believe that you can use +Mathematica or Maple or MATLAB + +or whatever and do it. + +The only reason not to +use any of these things + +is if you think you could +not do the integral. + +But once you realize, +oh, this is an integral, + +I know how to do, +don't waste time. + +Use any of those programs. + +Now, this part of the +integral is kind of easy + +because the delta function +just picks the value of 0. + +So this part of the +integral gives you + +minus beta alpha over +square root of pi. + +The other part of the +integral, however, + +is a little more complicated. + +Believe it or not, it +makes a big difference + +whether you take +the two derivatives + +of this function or +you integrate by parts. + +If you integrate by parts, +you save a lot of work. + +So let me integrate by parts. + +This becomes, plus beta +over square root of h, + +h-2nd over 2m, +integral dx of ddx of e + +to the minus one half beta +squared x-2nd squared. + +So you integrate by +parts one of the ddx + +and then you have the other +ddx, so it's the thing squared. + +And that's an easier +integral to do. + +We don't want to +bother with this, + +but this whole +thing then becomes + +minus beta over square root of +pi, alpha plus beta squared h + +squared over 4m. + +That's the whole +answer And that's + +the valuation of +this whole thing. + +So look what you get. + +You got a function +of beta indeed. + +So how does that +function of beta look? + +It's 0 for beta equals 0 is 0 +for some other possible beta, + +it's going to look like this. + +So there's a point at +which this function is + +going to have a minimum, and +we should choose that point + +to get the best upper +bound on the function. + +Our claim is that following +from the variational theorem + +that we've proven +is that the e ground + +state is less than or equal +than the minimum value over beta + +of this beta squared +h squared over 4m + +minus beta square +root of pie alpha. + +So you minimize over beta, +and yet still the ground state + +energy must be a little +smaller than that. + +Well what do you get? + +You do this, this minimization +gives beta equal 2m + +alpha over h squared +square root of pi. + +It's a little messy +but not terrible. + +And you substitute, and you +get that e ground state is + +less than or equal than m alpha +squared over pi h squared. + +And to better write it as 2 +over pi times minus m alpha + +squared over 2h-2nd which is +the true ground state energy. + +So let's just make sure we +understand what has happened. + +Here is the energy. + +Here is zero. + +Energy as just a vertical +plot here is zero. + +The true ground state +energy of this problem + +is this one, let's call +it egs, is negative. + +And we go 2 over pi times that. + +2 over pi is about 0.64. + +So the bound says +that here is 0.64 egs. + +So that's what the +bound told you. + +The bound state energy must +be lower than this quantity. + +We got close. + +Not impressively +close, but the work + +functional was not +all that bad either. + +Question? + +AUDIENCE: [INAUDIBLE] +always going + +to be a constant times +incorrect energy value + +or is it just the +closest approximation? + +PROFESSOR: Is it +going to be what? + +AUDIENCE: Is it +always going to be + +a constant times the correct +energy value or is it just-- + +PROFESSOR: Well it +typically is like that + +because of dimensional units. + +You're looking for a +constant because you're not + +looking for the function. + +So you will get a number times +a correct value, yes, indeed. + +That's an illustration of the +problem of wave functions. + +You know the variational +principle tells you + +things about the +ground state but allows + +you to find the first +excited state as well + +if the potential is symmetric, +will allow you to prove + +that any attractive +potential has a bound state. + +And you will prove +in the homework + +that stationary points of these +things are the eigenfunctions. + +See you next Monday. \ No newline at end of file diff --git a/mQSp6VmfakA.txt b/mQSp6VmfakA.txt new file mode 100644 index 0000000000000000000000000000000000000000..429ff37f2403f9ea133d2794c8619f45021d51e2 --- /dev/null +++ b/mQSp6VmfakA.txt @@ -0,0 +1,9715 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay then let's start with + + align:start position:0% +ocw.mit.edu okay then let's start with + + + align:start position:0% +ocw.mit.edu okay then let's start with +problems and as we find pro as we find + + align:start position:0% +problems and as we find pro as we find + + + align:start position:0% +problems and as we find pro as we find +concept issues we'll get to concept + + align:start position:0% +concept issues we'll get to concept + + + align:start position:0% +concept issues we'll get to concept +issues so we talked about about shortest + + align:start position:0% +issues so we talked about about shortest + + + align:start position:0% +issues so we talked about about shortest +path but we talked about shortest path + + align:start position:0% +path but we talked about shortest path + + + align:start position:0% +path but we talked about shortest path +in a very odd way right I'm a coder so + + align:start position:0% +in a very odd way right I'm a coder so + + + align:start position:0% +in a very odd way right I'm a coder so +for me I'm used to all right I go to one + + align:start position:0% +for me I'm used to all right I go to one + + + align:start position:0% +for me I'm used to all right I go to one +of these lectures I hear a problem then + + align:start position:0% +of these lectures I hear a problem then + + + align:start position:0% +of these lectures I hear a problem then +I get out of the lecture with an + + align:start position:0% +I get out of the lecture with an + + + align:start position:0% +I get out of the lecture with an +algorithm and the running time right + + align:start position:0% +algorithm and the running time right + + + align:start position:0% +algorithm and the running time right +this time we got out of the lecture with + + align:start position:0% +this time we got out of the lecture with + + + align:start position:0% +this time we got out of the lecture with +no algorithm and no running time so + + align:start position:0% +no algorithm and no running time so + + + align:start position:0% +no algorithm and no running time so +what's the point the point is that we + + align:start position:0% +what's the point the point is that we + + + align:start position:0% +what's the point the point is that we +learned some analysis tricks that we can + + align:start position:0% +learned some analysis tricks that we can + + + align:start position:0% +learned some analysis tricks that we can +use for any shortest path algorithm and + + align:start position:0% +use for any shortest path algorithm and + + + align:start position:0% +use for any shortest path algorithm and +the advantage of knowing that by the way + + align:start position:0% +the advantage of knowing that by the way + + + align:start position:0% +the advantage of knowing that by the way +it's really easy to forget at least + + align:start position:0% +it's really easy to forget at least + + + align:start position:0% +it's really easy to forget at least +until you the first wheel algorithms if + + align:start position:0% +until you the first wheel algorithms if + + + align:start position:0% +until you the first wheel algorithms if +you know that if you have to modify an + + align:start position:0% +you know that if you have to modify an + + + align:start position:0% +you know that if you have to modify an +algorithm you can still use the same + + align:start position:0% +algorithm you can still use the same + + + align:start position:0% +algorithm you can still use the same +analysis to prove that your new + + align:start position:0% +analysis to prove that your new + + + align:start position:0% +analysis to prove that your new +algorithm is going to be correct and + + align:start position:0% +algorithm is going to be correct and + + + align:start position:0% +algorithm is going to be correct and +that is going to be fast so they're + + align:start position:0% +that is going to be fast so they're + + + align:start position:0% +that is going to be fast so they're +really nice tools to have especially if + + align:start position:0% +really nice tools to have especially if + + + align:start position:0% +really nice tools to have especially if +you have to do that on a problem set or + + align:start position:0% +you have to do that on a problem set or + + + align:start position:0% +you have to do that on a problem set or +on an interview or who knows maybe even + + align:start position:0% +on an interview or who knows maybe even + + + align:start position:0% +on an interview or who knows maybe even +on a quiz so we'll see if that happens + + align:start position:0% +on a quiz so we'll see if that happens + + + align:start position:0% +on a quiz so we'll see if that happens +or not so we didn't talk about any + + align:start position:0% +or not so we didn't talk about any + + + align:start position:0% +or not so we didn't talk about any +shortest path algorithms so we're not + + align:start position:0% +shortest path algorithms so we're not + + + align:start position:0% +shortest path algorithms so we're not +going to assume shortest path algorithms + + align:start position:0% +going to assume shortest path algorithms + + + align:start position:0% +going to assume shortest path algorithms +instead we're going to use them as if we + + align:start position:0% +instead we're going to use them as if we + + + align:start position:0% +instead we're going to use them as if we +had them + + align:start position:0% + + + + align:start position:0% + +no wait I don't like that uh that's kind + + align:start position:0% +no wait I don't like that uh that's kind + + + align:start position:0% +no wait I don't like that uh that's kind +of annoying let's let's not do that + + align:start position:0% +of annoying let's let's not do that + + + align:start position:0% +of annoying let's let's not do that +let's do something else we didn't talk + + align:start position:0% +let's do something else we didn't talk + + + align:start position:0% +let's do something else we didn't talk +about the shortest path algorithm in + + align:start position:0% +about the shortest path algorithm in + + + align:start position:0% +about the shortest path algorithm in +lecture let's build one right now how + + align:start position:0% +lecture let's build one right now how + + + align:start position:0% +lecture let's build one right now how +about that let's start with a + + align:start position:0% +about that let's start with a + + + align:start position:0% +about that let's start with a +graph vertices and edges + + align:start position:0% + + + + align:start position:0% + +right let's see if I can make this + + align:start position:0% +right let's see if I can make this + + + align:start position:0% +right let's see if I can make this +work a c d e + + align:start position:0% + + + + align:start position:0% + +okay so suppose we have a graph we have + + align:start position:0% +okay so suppose we have a graph we have + + + align:start position:0% +okay so suppose we have a graph we have +V vertices e + + align:start position:0% +V vertices e + + + align:start position:0% +V vertices e +edges and all the edges have a weight + + align:start position:0% +edges and all the edges have a weight + + + align:start position:0% +edges and all the edges have a weight +that's non negative sorry that's let's + + align:start position:0% +that's non negative sorry that's let's + + + align:start position:0% +that's non negative sorry that's let's +make it positive just to make things + + align:start position:0% +make it positive just to make things + + + align:start position:0% +make it positive just to make things +easy + + align:start position:0% +easy + + + align:start position:0% +easy +it's smaller than W so it's not too + + align:start position:0% +it's smaller than W so it's not too + + + align:start position:0% +it's smaller than W so it's not too +big and they're all + + align:start position:0% +big and they're all + + + align:start position:0% +big and they're all +integers + + align:start position:0% + + + + align:start position:0% + +go there's Brute Force there's Brute + + align:start position:0% +go there's Brute Force there's Brute + + + align:start position:0% +go there's Brute Force there's Brute +Force okay so brute force would mean + + align:start position:0% +Force okay so brute force would mean + + + align:start position:0% +Force okay so brute force would mean +what enumerate all the paths okay uh + + align:start position:0% +what enumerate all the paths okay uh + + + align:start position:0% +what enumerate all the paths okay uh +let's go for something a little bit + + align:start position:0% + + + + align:start position:0% + +better does anyone remember the + + align:start position:0% +better does anyone remember the + + + align:start position:0% +better does anyone remember the +algorithm that was Tau in class class + + align:start position:0% +algorithm that was Tau in class class + + + align:start position:0% +algorithm that was Tau in class class +the structure no so class mentioned dtra + + align:start position:0% +the structure no so class mentioned dtra + + + align:start position:0% +the structure no so class mentioned dtra +and mentioned bman + + align:start position:0% +and mentioned bman + + + align:start position:0% +and mentioned bman +Ford let's write them up + + align:start position:0% + + + + align:start position:0% + +here bman Ford and it gave us the + + align:start position:0% +here bman Ford and it gave us the + + + align:start position:0% +here bman Ford and it gave us the +running times which we'll try to + + align:start position:0% +running times which we'll try to + + + align:start position:0% +running times which we'll try to +remember in a bit but we don't know the + + align:start position:0% +remember in a bit but we don't know the + + + align:start position:0% +remember in a bit but we don't know the +algorithms + + align:start position:0% +algorithms + + + align:start position:0% +algorithms +so no D no well for for + + align:start position:0% +so no D no well for for + + + align:start position:0% +so no D no well for for +us what do we + + align:start position:0% +us what do we + + + align:start position:0% +us what do we +know let's start with a simpler case + + align:start position:0% +know let's start with a simpler case + + + align:start position:0% +know let's start with a simpler case +what if there were no weights here what + + align:start position:0% +what if there were no weights here what + + + align:start position:0% +what if there were no weights here what +if the graph looked like + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +a you're making my life + + align:start position:0% + + + + align:start position:0% + +hard like + + align:start position:0% +hard like + + + align:start position:0% +hard like +this no cost all the edges have the same + + align:start position:0% +this no cost all the edges have the same + + + align:start position:0% +this no cost all the edges have the same +cost what would we do to solve the + + align:start position:0% +cost what would we do to solve the + + + align:start position:0% +cost what would we do to solve the +problem say we want the shortest path + + align:start position:0% +problem say we want the shortest path + + + align:start position:0% +problem say we want the shortest path +from a to + + align:start position:0% + + + + align:start position:0% + +e + + align:start position:0% +e + + + align:start position:0% +e +BFS how's everyone feeling about + + align:start position:0% +BFS how's everyone feeling about + + + align:start position:0% +BFS how's everyone feeling about +BFS so what does BFS do really + + align:start position:0% +BFS so what does BFS do really + + + align:start position:0% +BFS so what does BFS do really +quick how do you run BFS take a starting + + align:start position:0% +quick how do you run BFS take a starting + + + align:start position:0% +quick how do you run BFS take a starting +Noe and then you search all its + + align:start position:0% +Noe and then you search all its + + + align:start position:0% +Noe and then you search all its +neighbors okay so take a starting + + align:start position:0% +neighbors okay so take a starting + + + align:start position:0% +neighbors okay so take a starting +Noe then look at its neighbors mhm and + + align:start position:0% +Noe then look at its neighbors mhm and + + + align:start position:0% +Noe then look at its neighbors mhm and +then then youate through each of it + + align:start position:0% +then then youate through each of it + + + align:start position:0% +then then youate through each of it +neighbors to find it + + align:start position:0% + + + + align:start position:0% + +neighbors sounds an awful lot like DFS + + align:start position:0% +neighbors sounds an awful lot like DFS + + + align:start position:0% +neighbors sounds an awful lot like DFS +what's the difference between them well + + align:start position:0% +what's the difference between them well + + + align:start position:0% +what's the difference between them well +um you go through all of a neighbors + + align:start position:0% +um you go through all of a neighbors + + + align:start position:0% +um you go through all of a neighbors +before you start going through any of I + + align:start position:0% +before you start going through any of I + + + align:start position:0% +before you start going through any of I +mean you go through all a neighbors + + align:start position:0% +mean you go through all a neighbors + + + align:start position:0% +mean you go through all a neighbors +before you take a neighbor and go + + align:start position:0% +before you take a neighbor and go + + + align:start position:0% +before you take a neighbor and go +through all its neighbors okay that's + + align:start position:0% +through all its neighbors okay that's + + + align:start position:0% +through all its neighbors okay that's +the difference and it makes a huge + + align:start position:0% +the difference and it makes a huge + + + align:start position:0% +the difference and it makes a huge +difference as we've seen in top logical + + align:start position:0% +difference as we've seen in top logical + + + align:start position:0% +difference as we've seen in top logical +sorting last time so we have a list and + + align:start position:0% +sorting last time so we have a list and + + + align:start position:0% +sorting last time so we have a list and +we're going to use it to keep track of + + align:start position:0% +we're going to use it to keep track of + + + align:start position:0% +we're going to use it to keep track of +the noes that we need to visit we start + + align:start position:0% +the noes that we need to visit we start + + + align:start position:0% +the noes that we need to visit we start +with a we enumerate all of A's neighbors + + align:start position:0% +with a we enumerate all of A's neighbors + + + align:start position:0% +with a we enumerate all of A's neighbors +and the ones that haven't se haven't + + align:start position:0% +and the ones that haven't se haven't + + + align:start position:0% +and the ones that haven't se haven't +been seen get stuck at the end of the + + align:start position:0% +been seen get stuck at the end of the + + + align:start position:0% +been seen get stuck at the end of the +list a b c a is out of the list then we + + align:start position:0% +list a b c a is out of the list then we + + + align:start position:0% +list a b c a is out of the list then we +take out the first node from the + + align:start position:0% +take out the first node from the + + + align:start position:0% +take out the first node from the +list B in this case we enumerate all its + + align:start position:0% +list B in this case we enumerate all its + + + align:start position:0% +list B in this case we enumerate all its +neighbors a CDE e out of all these we + + align:start position:0% +neighbors a CDE e out of all these we + + + align:start position:0% +neighbors a CDE e out of all these we +take the neighbors that we haven't seen + + align:start position:0% +take the neighbors that we haven't seen + + + align:start position:0% +take the neighbors that we haven't seen +and we put them at the end of the list + + align:start position:0% + + + + align:start position:0% + +took out B we take out C we look at all + + align:start position:0% +took out B we take out C we look at all + + + align:start position:0% +took out B we take out C we look at all +its neighbors we've seen them we take + + align:start position:0% +its neighbors we've seen them we take + + + align:start position:0% +its neighbors we've seen them we take +out D we look at all its neighbors we've + + align:start position:0% +out D we look at all its neighbors we've + + + align:start position:0% +out D we look at all its neighbors we've +seen them we take out T we look at all + + align:start position:0% +seen them we take out T we look at all + + + align:start position:0% +seen them we take out T we look at all +its neighbors we've seen them so this is + + align:start position:0% +its neighbors we've seen them so this is + + + align:start position:0% +its neighbors we've seen them so this is +BFS BFS has this concept of levels and + + align:start position:0% +BFS BFS has this concept of levels and + + + align:start position:0% +BFS BFS has this concept of levels and +another way to look at levels is if you + + align:start position:0% +another way to look at levels is if you + + + align:start position:0% +another way to look at levels is if you +start at a and you draw a circus of + + align:start position:0% +start at a and you draw a circus of + + + align:start position:0% +start at a and you draw a circus of +radius + + align:start position:0% +radius + + + align:start position:0% +radius +one it's going to have all the nodes + + align:start position:0% +one it's going to have all the nodes + + + align:start position:0% +one it's going to have all the nodes +that are a distance one from a right + + align:start position:0% +that are a distance one from a right + + + align:start position:0% +that are a distance one from a right +exactly one Edge then you draw a circus + + align:start position:0% +exactly one Edge then you draw a circus + + + align:start position:0% +exactly one Edge then you draw a circus +of radius + + align:start position:0% +of radius + + + align:start position:0% +of radius +two and you get all the nodes that you + + align:start position:0% +two and you get all the nodes that you + + + align:start position:0% +two and you get all the nodes that you +can reach in two + + align:start position:0% +can reach in two + + + align:start position:0% +can reach in two +edges and BFS called these circles + + align:start position:0% +edges and BFS called these circles + + + align:start position:0% +edges and BFS called these circles +levels so a is at level zero this is + + align:start position:0% +levels so a is at level zero this is + + + align:start position:0% +levels so a is at level zero this is +level one this is level two and if you + + align:start position:0% +level one this is level two and if you + + + align:start position:0% +level one this is level two and if you +look at this list and you write down the + + align:start position:0% +look at this list and you write down the + + + align:start position:0% +look at this list and you write down the +levels you have 0 1 1 2 two if you add + + align:start position:0% +levels you have 0 1 1 2 two if you add + + + align:start position:0% +levels you have 0 1 1 2 two if you add +another node out here say + + align:start position:0% +another node out here say + + + align:start position:0% +another node out here say +F this would be discovered when we get + + align:start position:0% +F this would be discovered when we get + + + align:start position:0% +F this would be discovered when we get +to + + align:start position:0% +to + + + align:start position:0% +to +D so it would go all the way here at the + + align:start position:0% +D so it would go all the way here at the + + + align:start position:0% +D so it would go all the way here at the +end and this is level three so in BFS + + align:start position:0% +end and this is level three so in BFS + + + align:start position:0% +end and this is level three so in BFS +the levels are always + + align:start position:0% +the levels are always + + + align:start position:0% +the levels are always +increasing so if you keep track of + + align:start position:0% +increasing so if you keep track of + + + align:start position:0% +increasing so if you keep track of +parent pointers the parent pointer of a + + align:start position:0% +parent pointers the parent pointer of a + + + align:start position:0% +parent pointers the parent pointer of a +node at some level will always point to + + align:start position:0% +node at some level will always point to + + + align:start position:0% +node at some level will always point to +a node at the previous + + align:start position:0% +a node at the previous + + + align:start position:0% +a node at the previous +level so in BFS we get the shortest path + + align:start position:0% +level so in BFS we get the shortest path + + + align:start position:0% +level so in BFS we get the shortest path +in terms of edge + + align:start position:0% + + + + align:start position:0% + +count make sense this is recall right + + align:start position:0% +count make sense this is recall right + + + align:start position:0% +count make sense this is recall right +it's not new stuff everyone happy with + + align:start position:0% +it's not new stuff everyone happy with + + + align:start position:0% +it's not new stuff everyone happy with +it + + align:start position:0% +it + + + align:start position:0% +it +so if we wouldn't have costs we could + + align:start position:0% +so if we wouldn't have costs we could + + + align:start position:0% +so if we wouldn't have costs we could +use BFS to compute shortest + + align:start position:0% +use BFS to compute shortest + + + align:start position:0% +use BFS to compute shortest +paths but we have costs how do we how do + + align:start position:0% +paths but we have costs how do we how do + + + align:start position:0% +paths but we have costs how do we how do +we deal with + + align:start position:0% +we deal with + + + align:start position:0% +we deal with +that intuitively I'd like to make BFS go + + align:start position:0% +that intuitively I'd like to make BFS go + + + align:start position:0% +that intuitively I'd like to make BFS go +across this Edge faster than it would go + + align:start position:0% +across this Edge faster than it would go + + + align:start position:0% +across this Edge faster than it would go +across this Edge right if I could do + + align:start position:0% +across this Edge right if I could do + + + align:start position:0% +across this Edge right if I could do +that if this guy could get stuck in the + + align:start position:0% +that if this guy could get stuck in the + + + align:start position:0% +that if this guy could get stuck in the +queue before this guy I would be happy + + align:start position:0% +queue before this guy I would be happy + + + align:start position:0% +queue before this guy I would be happy +so intuitively that's what I'd like to + + align:start position:0% +so intuitively that's what I'd like to + + + align:start position:0% +so intuitively that's what I'd like to +do how do we do that + + align:start position:0% + + + + align:start position:0% + +sort sort + + align:start position:0% +sort sort + + + align:start position:0% +sort sort +neighbor sort okay so what if you kept + + align:start position:0% +neighbor sort okay so what if you kept + + + align:start position:0% +neighbor sort okay so what if you kept +track of + + align:start position:0% +track of + + + align:start position:0% +track of +it track of + + align:start position:0% +it track of + + + align:start position:0% +it track of +your as a priority congratulations you + + align:start position:0% +your as a priority congratulations you + + + align:start position:0% +your as a priority congratulations you +deserve a touring award you have + + align:start position:0% +deserve a touring award you have + + + align:start position:0% +deserve a touring award you have +discovered the + + align:start position:0% + + + + align:start position:0% + +extra okay let's go for something + + align:start position:0% +extra okay let's go for something + + + align:start position:0% +extra okay let's go for something +simpler so what you just said is the + + align:start position:0% +simpler so what you just said is the + + + align:start position:0% +simpler so what you just said is the +extra you we'll talk about it in lecture + + align:start position:0% +extra you we'll talk about it in lecture + + + align:start position:0% +extra you we'll talk about it in lecture +on Tuesday very + + align:start position:0% + + + + align:start position:0% + +good I have an adjacency list and I + + align:start position:0% +good I have an adjacency list and I + + + align:start position:0% +good I have an adjacency list and I +think using what you said um just sort + + align:start position:0% +think using what you said um just sort + + + align:start position:0% +think using what you said um just sort +it by C okay so let's see how this would + + align:start position:0% +it by C okay so let's see how this would + + + align:start position:0% +it by C okay so let's see how this would +work so we have + + align:start position:0% +work so we have + + + align:start position:0% +work so we have +a and we're pulling a out of the list + + align:start position:0% +a and we're pulling a out of the list + + + align:start position:0% +a and we're pulling a out of the list +and we see its neighbors are C and B + + align:start position:0% +and we see its neighbors are C and B + + + align:start position:0% +and we see its neighbors are C and B +right the distance to C is two the + + align:start position:0% +right the distance to C is two the + + + align:start position:0% +right the distance to C is two the +distance to B is four so we start with + + align:start position:0% +distance to B is four so we start with + + + align:start position:0% +distance to B is four so we start with +a so does this mean that I'm going to + + align:start position:0% +a so does this mean that I'm going to + + + align:start position:0% +a so does this mean that I'm going to +put in B before c and then so I'm going + + align:start position:0% +put in B before c and then so I'm going + + + align:start position:0% +put in B before c and then so I'm going +to put in C and then + + align:start position:0% + + + + align:start position:0% + +B I guess add the cost like associate + + align:start position:0% +B I guess add the cost like associate + + + align:start position:0% +B I guess add the cost like associate +the cost + + align:start position:0% +the cost + + + align:start position:0% +the cost +of within + + align:start position:0% +of within + + + align:start position:0% +of within +your okay so that's how we would keep + + align:start position:0% +your okay so that's how we would keep + + + align:start position:0% +your okay so that's how we would keep +track of costs right one way for the key + + align:start position:0% +track of costs right one way for the key + + + align:start position:0% +track of costs right one way for the key +would be a and then the value would be + + align:start position:0% +would be a and then the value would be + + + align:start position:0% +would be a and then the value would be +like a t of B and cost and of c and its + + align:start position:0% +like a t of B and cost and of c and its + + + align:start position:0% +like a t of B and cost and of c and its +cost okay so you're saying that what I + + align:start position:0% +cost okay so you're saying that what I + + + align:start position:0% +cost okay so you're saying that what I +would would have in this list is B with + + align:start position:0% +would would have in this list is B with + + + align:start position:0% +would would have in this list is B with +a cost of + + align:start position:0% +a cost of + + + align:start position:0% +a cost of +four and C with a cost + + align:start position:0% +four and C with a cost + + + align:start position:0% +four and C with a cost +of two presumably in the other other way + + align:start position:0% +of two presumably in the other other way + + + align:start position:0% +of two presumably in the other other way +around right C goes + + align:start position:0% + + + + align:start position:0% + +first like this and then I take out c i + + align:start position:0% +first like this and then I take out c i + + + align:start position:0% +first like this and then I take out c i +explore the neighbor so on so + + align:start position:0% +explore the neighbor so on so + + + align:start position:0% +explore the neighbor so on so +forth the moment I did this I already + + align:start position:0% +forth the moment I did this I already + + + align:start position:0% +forth the moment I did this I already +lost the battle because + + align:start position:0% + + + + align:start position:0% + +see this path uh AC CB length three if I + + align:start position:0% +see this path uh AC CB length three if I + + + align:start position:0% +see this path uh AC CB length three if I +put both of them in the Q then the + + align:start position:0% +put both of them in the Q then the + + + align:start position:0% +put both of them in the Q then the +parent pointers are going to look like + + align:start position:0% +parent pointers are going to look like + + + align:start position:0% +parent pointers are going to look like +this so I'll already have a bad path + + align:start position:0% +this so I'll already have a bad path + + + align:start position:0% +this so I'll already have a bad path +from B to a okay well don't add that + + align:start position:0% +from B to a okay well don't add that + + + align:start position:0% +from B to a okay well don't add that +note + + align:start position:0% +note + + + align:start position:0% +note +then okay then how how do we do + + align:start position:0% +then okay then how how do we do + + + align:start position:0% +then okay then how how do we do +it well you can you can talk to each of + + align:start position:0% +it well you can you can talk to each of + + + align:start position:0% +it well you can you can talk to each of +them see lower and then only add that + + align:start position:0% +them see lower and then only add that + + + align:start position:0% +them see lower and then only add that +one if it's the lowest and then you so + + align:start position:0% +one if it's the lowest and then you so + + + align:start position:0% +one if it's the lowest and then you so +it's more like death first search then + + align:start position:0% +it's more like death first search then + + + align:start position:0% +it's more like death first search then +well you two need to talk together + + align:start position:0% +well you two need to talk together + + + align:start position:0% +well you two need to talk together +because that you're getting to the extra + + align:start position:0% +because that you're getting to the extra + + + align:start position:0% +because that you're getting to the extra +too you're you're both gonna ReDiscover + + align:start position:0% +too you're you're both gonna ReDiscover + + + align:start position:0% +too you're you're both gonna ReDiscover +the extra so so that's great but I'm + + align:start position:0% +the extra so so that's great but I'm + + + align:start position:0% +the extra so so that's great but I'm +looking for something simple so this is + + align:start position:0% +looking for something simple so this is + + + align:start position:0% +looking for something simple so this is +too complicated if you're if you're + + align:start position:0% +too complicated if you're if you're + + + align:start position:0% +too complicated if you're if you're +going to do the extra now then what are + + align:start position:0% +going to do the extra now then what are + + + align:start position:0% +going to do the extra now then what are +we going to do on lecture on Tuesday + + align:start position:0% +we going to do on lecture on Tuesday + + + align:start position:0% +we going to do on lecture on Tuesday +more extra + + align:start position:0% +more extra + + + align:start position:0% +more extra +problems well I I think Shi wants to + + align:start position:0% +problems well I I think Shi wants to + + + align:start position:0% +problems well I I think Shi wants to +talk about D extra so let's not get + + align:start position:0% +talk about D extra so let's not get + + + align:start position:0% +talk about D extra so let's not get +there how do you do this without doing + + align:start position:0% +there how do you do this without doing + + + align:start position:0% +there how do you do this without doing +dtra good that that's exactly what I + + align:start position:0% +dtra good that that's exactly what I + + + align:start position:0% +dtra good that that's exactly what I +want to know + + align:start position:0% + + + + align:start position:0% + +so let me give you another hint so the + + align:start position:0% +so let me give you another hint so the + + + align:start position:0% +so let me give you another hint so the +first hint was that I want to go through + + align:start position:0% +first hint was that I want to go through + + + align:start position:0% +first hint was that I want to go through +this Edge faster than I would go through + + align:start position:0% +this Edge faster than I would go through + + + align:start position:0% +this Edge faster than I would go through +this Edge the other hint is that we're + + align:start position:0% +this Edge the other hint is that we're + + + align:start position:0% +this Edge the other hint is that we're +allowed to change the + + align:start position:0% +allowed to change the + + + align:start position:0% +allowed to change the +graph so I mean for each not is this + + align:start position:0% +graph so I mean for each not is this + + + align:start position:0% +graph so I mean for each not is this +what we're talking about lecture are you + + align:start position:0% +what we're talking about lecture are you + + + align:start position:0% +what we're talking about lecture are you +thinking something else what uh he might + + align:start position:0% +thinking something else what uh he might + + + align:start position:0% +thinking something else what uh he might +have uh talked about that at the end of + + align:start position:0% +have uh talked about that at the end of + + + align:start position:0% +have uh talked about that at the end of +lecture I mean where where you're + + align:start position:0% +lecture I mean where where you're + + + align:start position:0% +lecture I mean where where you're +putting the current wave for each inside + + align:start position:0% +putting the current wave for each inside + + + align:start position:0% +putting the current wave for each inside +the circles no + + align:start position:0% + + + + align:start position:0% + +you could add it and then just you find + + align:start position:0% +you could add it and then just you find + + + align:start position:0% +you could add it and then just you find +a better path to B if you're always + + align:start position:0% +a better path to B if you're always + + + align:start position:0% +a better path to B if you're always +relative to a and you can just delete + + align:start position:0% +relative to a and you can just delete + + + align:start position:0% +relative to a and you can just delete +that + + align:start position:0% +that + + + align:start position:0% +that +path so the beginning add them all but + + align:start position:0% +path so the beginning add them all but + + + align:start position:0% +path so the beginning add them all but +then you're risking to have exponential + + align:start position:0% +then you're risking to have exponential + + + align:start position:0% +then you're risking to have exponential +running + + align:start position:0% + + + + align:start position:0% + +time those are all valid optimizations + + align:start position:0% +time those are all valid optimizations + + + align:start position:0% +time those are all valid optimizations +under some constraints like this one's + + align:start position:0% +under some constraints like this one's + + + align:start position:0% +under some constraints like this one's +good if you're willing if you don't have + + align:start position:0% +good if you're willing if you don't have + + + align:start position:0% +good if you're willing if you don't have +too much memory but the time goes + + align:start position:0% +too much memory but the time goes + + + align:start position:0% +too much memory but the time goes +up so I Want My Graph to have edges with + + align:start position:0% +up so I Want My Graph to have edges with + + + align:start position:0% +up so I Want My Graph to have edges with +no costs as if I have costs this is not + + align:start position:0% +no costs as if I have costs this is not + + + align:start position:0% +no costs as if I have costs this is not +going to work BFS is not going to + + align:start position:0% +going to work BFS is not going to + + + align:start position:0% +going to work BFS is not going to +work we can't tweak it if we could tweak + + align:start position:0% +work we can't tweak it if we could tweak + + + align:start position:0% +work we can't tweak it if we could tweak +it then that would be another touring a + + align:start position:0% +it then that would be another touring a + + + align:start position:0% +it then that would be another touring a +word so like create doodes create domy + + align:start position:0% +word so like create doodes create domy + + + align:start position:0% +word so like create doodes create domy +noes how do I do + + align:start position:0% + + + + align:start position:0% + +that a random between a and C okay why + + align:start position:0% +that a random between a and C okay why + + + align:start position:0% +that a random between a and C okay why +am I doing + + align:start position:0% + + + + align:start position:0% + +this so now I have two edges and they + + align:start position:0% +this so now I have two edges and they + + + align:start position:0% +this so now I have two edges and they +have cost + + align:start position:0% + + + + align:start position:0% + +put + + align:start position:0% + + + + align:start position:0% + +okay and now here I have four edges + + align:start position:0% +okay and now here I have four edges + + + align:start position:0% +okay and now here I have four edges +rights one one one one there was a four + + align:start position:0% +rights one one one one there was a four + + + align:start position:0% +rights one one one one there was a four +here before and there was a two here + + align:start position:0% +here before and there was a two here + + + align:start position:0% +here before and there was a two here +before do you guys see what's happening + + align:start position:0% +before do you guys see what's happening + + + align:start position:0% +before do you guys see what's happening +so instead of one edge of cost C I have + + align:start position:0% +so instead of one edge of cost C I have + + + align:start position:0% +so instead of one edge of cost C I have +C edges so now BFS is going to take C + + align:start position:0% +C edges so now BFS is going to take C + + + align:start position:0% +C edges so now BFS is going to take C +steps to go through that edge + + align:start position:0% +steps to go through that edge + + + align:start position:0% +steps to go through that edge +and all the edges now have the same cost + + align:start position:0% +and all the edges now have the same cost + + + align:start position:0% +and all the edges now have the same cost +so this looks like a problem that BFS + + align:start position:0% +so this looks like a problem that BFS + + + align:start position:0% +so this looks like a problem that BFS +can solve we know it can solve we prove + + align:start position:0% +can solve we know it can solve we prove + + + align:start position:0% +can solve we know it can solve we prove +that it can solve it well CLR is De we + + align:start position:0% +that it can solve it well CLR is De we + + + align:start position:0% +that it can solve it well CLR is De we +take their word for granted sort + + align:start position:0% +take their word for granted sort + + + align:start position:0% +take their word for granted sort +of + + align:start position:0% +of + + + align:start position:0% +of +so this works right is everyone happy + + align:start position:0% +so this works right is everyone happy + + + align:start position:0% +so this works right is everyone happy +with it does it make sense so basically + + align:start position:0% +with it does it make sense so basically + + + align:start position:0% +with it does it make sense so basically +you get to you get to B before you ever + + align:start position:0% +you get to you get to B before you ever + + + align:start position:0% +you get to you get to B before you ever +get to I mean through C before you'll + + align:start position:0% +get to I mean through C before you'll + + + align:start position:0% +get to I mean through C before you'll +get to B on path yep so this is a path + + align:start position:0% +get to B on path yep so this is a path + + + align:start position:0% +get to B on path yep so this is a path +of L three so this node is going to get + + align:start position:0% +of L three so this node is going to get + + + align:start position:0% +of L three so this node is going to get +in the Q first then this node then these + + align:start position:0% +in the Q first then this node then these + + + align:start position:0% +in the Q first then this node then these +two nodes and they're going to get in + + align:start position:0% +two nodes and they're going to get in + + + align:start position:0% +two nodes and they're going to get in +the Q from + + align:start position:0% +the Q from + + + align:start position:0% +the Q from +C so let's see what happened here so + + align:start position:0% +C so let's see what happened here so + + + align:start position:0% +C so let's see what happened here so +this is really important because this is + + align:start position:0% +this is really important because this is + + + align:start position:0% +this is really important because this is +what you're going to be doing in real + + align:start position:0% +what you're going to be doing in real + + + align:start position:0% +what you're going to be doing in real +life chances of having to build a new + + align:start position:0% +life chances of having to build a new + + + align:start position:0% +life chances of having to build a new +algorithm kind of slim why don't you + + align:start position:0% +algorithm kind of slim why don't you + + + align:start position:0% +algorithm kind of slim why don't you +want to do that so you take D exra and + + align:start position:0% +want to do that so you take D exra and + + + align:start position:0% +want to do that so you take D exra and +you tweak it a little bit if you did + + align:start position:0% +you tweak it a little bit if you did + + + align:start position:0% +you tweak it a little bit if you did +that you have to go through the analysis + + align:start position:0% +that you have to go through the analysis + + + align:start position:0% +that you have to go through the analysis +and prove the running time again prove + + align:start position:0% +and prove the running time again prove + + + align:start position:0% +and prove the running time again prove +the correctness again time consuming + + align:start position:0% +the correctness again time consuming + + + align:start position:0% +the correctness again time consuming +error prone it's really hard however + + align:start position:0% +error prone it's really hard however + + + align:start position:0% +error prone it's really hard however +what happened here is that we have some + + align:start position:0% +what happened here is that we have some + + + align:start position:0% +what happened here is that we have some +problem that we want to solve say we + + align:start position:0% +problem that we want to solve say we + + + align:start position:0% +problem that we want to solve say we +have the raw input for that problem that + + align:start position:0% +have the raw input for that problem that + + + align:start position:0% +have the raw input for that problem that +we're trying to + + align:start position:0% +we're trying to + + + align:start position:0% +we're trying to +solve that is this graph that I drew on + + align:start position:0% +solve that is this graph that I drew on + + + align:start position:0% +solve that is this graph that I drew on +the + + align:start position:0% + + + + align:start position:0% + +board and we apply some + + align:start position:0% +board and we apply some + + + align:start position:0% +board and we apply some +transform and we get an input that's + + align:start position:0% +transform and we get an input that's + + + align:start position:0% +transform and we get an input that's +suitable for an algorithm that we + + align:start position:0% +suitable for an algorithm that we + + + align:start position:0% +suitable for an algorithm that we +already know + + align:start position:0% + + + + align:start position:0% + +and I'm I'm going to take a shortcut + + align:start position:0% +and I'm I'm going to take a shortcut + + + align:start position:0% +and I'm I'm going to take a shortcut +here because I + + align:start position:0% + + + + align:start position:0% + +don't so we apply the transform right we + + align:start position:0% +don't so we apply the transform right we + + + align:start position:0% +don't so we apply the transform right we +took this graph and we built a new graph + + align:start position:0% +took this graph and we built a new graph + + + align:start position:0% +took this graph and we built a new graph +in and this is hopefully easy right take + + align:start position:0% +in and this is hopefully easy right take + + + align:start position:0% +in and this is hopefully easy right take +a take an edge and split it up put in + + align:start position:0% +a take an edge and split it up put in + + + align:start position:0% +a take an edge and split it up put in +fake noes this is easy we know how to + + align:start position:0% +fake noes this is easy we know how to + + + align:start position:0% +fake noes this is easy we know how to +code + + align:start position:0% +code + + + align:start position:0% +code +that and now we have this algorithm that + + align:start position:0% +that and now we have this algorithm that + + + align:start position:0% +that and now we have this algorithm that +we already know and treating it like a + + align:start position:0% +we already know and treating it like a + + + align:start position:0% +we already know and treating it like a +black + + align:start position:0% + + + + align:start position:0% + +box we know it's correct we know it's + + align:start position:0% +box we know it's correct we know it's + + + align:start position:0% +box we know it's correct we know it's +running time we're not questioning them + + align:start position:0% +running time we're not questioning them + + + align:start position:0% +running time we're not questioning them +we're taking them straight from the + + align:start position:0% +we're taking them straight from the + + + align:start position:0% +we're taking them straight from the +textbook they have to be right by the + + align:start position:0% +textbook they have to be right by the + + + align:start position:0% +textbook they have to be right by the +way what's the running time of + + align:start position:0% + + + + align:start position:0% + +BFS U and + + align:start position:0% +BFS U and + + + align:start position:0% +BFS U and +sorry very good can hear you very + + align:start position:0% + + + + align:start position:0% + +well so then BFS is going to give us a + + align:start position:0% +well so then BFS is going to give us a + + + align:start position:0% +well so then BFS is going to give us a +path right and the path is going to look + + align:start position:0% +path right and the path is going to look + + + align:start position:0% +path right and the path is going to look +like this it's going to + + align:start position:0% +like this it's going to + + + align:start position:0% +like this it's going to +be uh a fake node c + + align:start position:0% +be uh a fake node c + + + align:start position:0% +be uh a fake node c +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +d fake node + + align:start position:0% +d fake node + + + align:start position:0% +d fake node +e if you give this back to the guy who + + align:start position:0% +e if you give this back to the guy who + + + align:start position:0% +e if you give this back to the guy who +gave you the problem they're going to be + + align:start position:0% +gave you the problem they're going to be + + + align:start position:0% +gave you the problem they're going to be +like what are these fake nodes I don't + + align:start position:0% +like what are these fake nodes I don't + + + align:start position:0% +like what are these fake nodes I don't +know anything about them this doesn't + + align:start position:0% +know anything about them this doesn't + + + align:start position:0% +know anything about them this doesn't +make sense so you need to take + + align:start position:0% +make sense so you need to take + + + align:start position:0% +make sense so you need to take +this raw output and you need to + + align:start position:0% +this raw output and you need to + + + align:start position:0% +this raw output and you need to +transform it again based on what you did + + align:start position:0% +transform it again based on what you did + + + align:start position:0% +transform it again based on what you did +on this transformation you have to read + + align:start position:0% +on this transformation you have to read + + + align:start position:0% +on this transformation you have to read +out the output you have to interpret it + + align:start position:0% +out the output you have to interpret it + + + align:start position:0% +out the output you have to interpret it +so this is either interpret or read out + + align:start position:0% +so this is either interpret or read out + + + align:start position:0% +so this is either interpret or read out +and then you get a nice + + align:start position:0% +and then you get a nice + + + align:start position:0% +and then you get a nice +output that's the output to your + + align:start position:0% +output that's the output to your + + + align:start position:0% +output that's the output to your +original + + align:start position:0% +original + + + align:start position:0% +original +problem this process here is the most + + align:start position:0% +problem this process here is the most + + + align:start position:0% +problem this process here is the most +likely way in which you'll use your 66 + + align:start position:0% +likely way in which you'll use your 66 + + + align:start position:0% +likely way in which you'll use your 66 +knowledge and this is replaced by any + + align:start position:0% +knowledge and this is replaced by any + + + align:start position:0% +knowledge and this is replaced by any +algorithm that we taught this is + + align:start position:0% +algorithm that we taught this is + + + align:start position:0% +algorithm that we taught this is +replaced by any real life problem that + + align:start position:0% +replaced by any real life problem that + + + align:start position:0% +replaced by any real life problem that +you'll + + align:start position:0% +you'll + + + align:start position:0% +you'll +encounter okay + + align:start position:0% +encounter okay + + + align:start position:0% +encounter okay +so there's one missing step here we know + + align:start position:0% +so there's one missing step here we know + + + align:start position:0% +so there's one missing step here we know +the running time for this let's find out + + align:start position:0% +the running time for this let's find out + + + align:start position:0% +the running time for this let's find out +the running time for the + + align:start position:0% +the running time for the + + + align:start position:0% +the running time for the +whole thing so in order to do that we + + align:start position:0% +whole thing so in order to do that we + + + align:start position:0% +whole thing so in order to do that we +have to figure out given this original + + align:start position:0% +have to figure out given this original + + + align:start position:0% +have to figure out given this original +graph let's say that now in the original + + align:start position:0% +graph let's say that now in the original + + + align:start position:0% +graph let's say that now in the original +graph we have V Prime vertices e Prime + + align:start position:0% +graph we have V Prime vertices e Prime + + + align:start position:0% +graph we have V Prime vertices e Prime +edges and W Prime + + align:start position:0% +edges and W Prime + + + align:start position:0% +edges and W Prime +weights we have to convert this into V + + align:start position:0% +weights we have to convert this into V + + + align:start position:0% +weights we have to convert this into V +plus e so we have to see when we make + + align:start position:0% +plus e so we have to see when we make + + + align:start position:0% +plus e so we have to see when we make +this transform how many vertices do we + + align:start position:0% +this transform how many vertices do we + + + align:start position:0% +this transform how many vertices do we +get how many edges do we get in terms of + + align:start position:0% +get how many edges do we get in terms of + + + align:start position:0% +get how many edges do we get in terms of +the original graph so that we can + + align:start position:0% +the original graph so that we can + + + align:start position:0% +the original graph so that we can +compute the running + + align:start position:0% +compute the running + + + align:start position:0% +compute the running +time so in the original graph V Prime + + align:start position:0% +time so in the original graph V Prime + + + align:start position:0% +time so in the original graph V Prime +vertices e Prime edges W Prime weights + + align:start position:0% +vertices e Prime edges W Prime weights + + + align:start position:0% +vertices e Prime edges W Prime weights +in this new graph how many edges do I + + align:start position:0% +in this new graph how many edges do I + + + align:start position:0% +in this new graph how many edges do I +have at + + align:start position:0% + + + + align:start position:0% + +most + + align:start position:0% +most + + + align:start position:0% +most +sorry yep + + align:start position:0% + + + + align:start position:0% + +perfect so each Edge has at most W so + + align:start position:0% +perfect so each Edge has at most W so + + + align:start position:0% +perfect so each Edge has at most W so +that means we're going to split it up + + align:start position:0% +that means we're going to split it up + + + align:start position:0% +that means we're going to split it up +into at most W + + align:start position:0% +into at most W + + + align:start position:0% +into at most W +edges how many vertices are we going to + + align:start position:0% + + + + align:start position:0% + +have W Prime e + + align:start position:0% +have W Prime e + + + align:start position:0% +have W Prime e +prime plus b Prime don't forget about + + align:start position:0% +prime plus b Prime don't forget about + + + align:start position:0% +prime plus b Prime don't forget about +the original ones they're still + + align:start position:0% +the original ones they're still + + + align:start position:0% +the original ones they're still +there okay so total running time for BFS + + align:start position:0% +there okay so total running time for BFS + + + align:start position:0% +there okay so total running time for BFS +on the new graph + + align:start position:0% + + + + align:start position:0% + +is okay I'll put it the other way around + + align:start position:0% +is okay I'll put it the other way around + + + align:start position:0% +is okay I'll put it the other way around +plus W Prime e + + align:start position:0% + + + + align:start position:0% + +Prime okay so this is the running time + + align:start position:0% +Prime okay so this is the running time + + + align:start position:0% +Prime okay so this is the running time +that we have now does anyone remember + + align:start position:0% +that we have now does anyone remember + + + align:start position:0% +that we have now does anyone remember +the extra's running time and B for + + align:start position:0% +the extra's running time and B for + + + align:start position:0% +the extra's running time and B for +running + + align:start position:0% + + + + align:start position:0% + +time so what's the running time for + + align:start position:0% + + + + align:start position:0% + +dtra uh + + align:start position:0% +dtra uh + + + align:start position:0% +dtra uh +almost oh wait oh yeah I think you're + + align:start position:0% +almost oh wait oh yeah I think you're + + + align:start position:0% +almost oh wait oh yeah I think you're +right V log V + + align:start position:0% + + + + align:start position:0% + +plus are you reading this from + + align:start position:0% +plus are you reading this from + + + align:start position:0% +plus are you reading this from +clrs or is this what we got what they + + align:start position:0% +clrs or is this what we got what they + + + align:start position:0% +clrs or is this what we got what they +you need to use a fancy Hep to get this + + align:start position:0% +you need to use a fancy Hep to get this + + + align:start position:0% +you need to use a fancy Hep to get this +running + + align:start position:0% +running + + + align:start position:0% +running +time yeah you can get this but you need + + align:start position:0% +time yeah you can get this but you need + + + align:start position:0% +time yeah you can get this but you need +a real fancy data structure for it in + + align:start position:0% +a real fancy data structure for it in + + + align:start position:0% +a real fancy data structure for it in +real life the running time looks more + + align:start position:0% +real life the running time looks more + + + align:start position:0% +real life the running time looks more +like e log + + align:start position:0% +like e log + + + align:start position:0% +like e log +V okay and how about B + + align:start position:0% + + + + align:start position:0% + +for okay so let's take this running time + + align:start position:0% +for okay so let's take this running time + + + align:start position:0% +for okay so let's take this running time +for D extra because this is what you're + + align:start position:0% +for D extra because this is what you're + + + align:start position:0% +for D extra because this is what you're +going to implement in real life and we + + align:start position:0% +going to implement in real life and we + + + align:start position:0% +going to implement in real life and we +can argue about that after next lecture + + align:start position:0% +can argue about that after next lecture + + + align:start position:0% +can argue about that after next lecture +for now take my word for it and let's + + align:start position:0% +for now take my word for it and let's + + + align:start position:0% +for now take my word for it and let's +compare it to what we got + + align:start position:0% +compare it to what we got + + + align:start position:0% +compare it to what we got +here V is smaller than e in most saying + + align:start position:0% +here V is smaller than e in most saying + + + align:start position:0% +here V is smaller than e in most saying +cases so let's say that this is actually + + align:start position:0% +cases so let's say that this is actually + + + align:start position:0% +cases so let's say that this is actually +W Prime e Prime so if you compare this + + align:start position:0% +W Prime e Prime so if you compare this + + + align:start position:0% +W Prime e Prime so if you compare this +with + + align:start position:0% +with + + + align:start position:0% +with +this you'll see that if W is smaller + + align:start position:0% +this you'll see that if W is smaller + + + align:start position:0% +this you'll see that if W is smaller +than log + + align:start position:0% +than log + + + align:start position:0% +than log +V well smaller or equal then this Al + + align:start position:0% +V well smaller or equal then this Al + + + align:start position:0% +V well smaller or equal then this Al +algorithm is not worse than D extra it's + + align:start position:0% +algorithm is not worse than D extra it's + + + align:start position:0% +algorithm is not worse than D extra it's +on onar with the + + align:start position:0% +on onar with the + + + align:start position:0% +on onar with the +extra so for graphs with small costs we + + align:start position:0% +extra so for graphs with small costs we + + + align:start position:0% +extra so for graphs with small costs we +discovered an algorithm that solves + + align:start position:0% +discovered an algorithm that solves + + + align:start position:0% +discovered an algorithm that solves +shortest paths we W in walked in this + + align:start position:0% +shortest paths we W in walked in this + + + align:start position:0% +shortest paths we W in walked in this +restation knowing no algorithm to solve + + align:start position:0% +restation knowing no algorithm to solve + + + align:start position:0% +restation knowing no algorithm to solve +shortest paths now we have an algorithm + + align:start position:0% +shortest paths now we have an algorithm + + + align:start position:0% +shortest paths now we have an algorithm +already in a much better position right + + align:start position:0% +already in a much better position right + + + align:start position:0% +already in a much better position right +and we didn't invent anything new we + + align:start position:0% +and we didn't invent anything new we + + + align:start position:0% +and we didn't invent anything new we +don't have to prove correctness all we + + align:start position:0% +don't have to prove correctness all we + + + align:start position:0% +don't have to prove correctness all we +did was one of these + + align:start position:0% +did was one of these + + + align:start position:0% +did was one of these +Transformations okay how's everyone + + align:start position:0% +Transformations okay how's everyone + + + align:start position:0% +Transformations okay how's everyone +feeling do things make sense everyone + + align:start position:0% + + + + align:start position:0% + +happy okay let's talk about another + + align:start position:0% +happy okay let's talk about another + + + align:start position:0% +happy okay let's talk about another +problem that uh also uses this + + align:start position:0% + + + + align:start position:0% + +structure so suppose we have the same + + align:start position:0% +structure so suppose we have the same + + + align:start position:0% +structure so suppose we have the same +graph that we had before or actually any + + align:start position:0% +graph that we had before or actually any + + + align:start position:0% +graph that we had before or actually any +graph with v vertices e edges now we + + align:start position:0% +graph with v vertices e edges now we + + + align:start position:0% +graph with v vertices e edges now we +know how to compute shortest path so we + + align:start position:0% +know how to compute shortest path so we + + + align:start position:0% +know how to compute shortest path so we +can assume these as black + + align:start position:0% + + + + align:start position:0% + +boxes so we're going to use these as + + align:start position:0% +boxes so we're going to use these as + + + align:start position:0% +boxes so we're going to use these as +they are so we have a graph with v + + align:start position:0% +they are so we have a graph with v + + + align:start position:0% +they are so we have a graph with v +vertices and E + + align:start position:0% + + + + align:start position:0% + +edges a b c d + + align:start position:0% +edges a b c d + + + align:start position:0% +edges a b c d +e and let me copy the cost really + + align:start position:0% +e and let me copy the cost really + + + align:start position:0% +e and let me copy the cost really +quickly 4 2 one + + align:start position:0% +quickly 4 2 one + + + align:start position:0% +quickly 4 2 one +two + + align:start position:0% + + + + align:start position:0% + +one so suppose this is a highway system + + align:start position:0% +one so suppose this is a highway system + + + align:start position:0% +one so suppose this is a highway system +right like in Google Maps + + align:start position:0% +right like in Google Maps + + + align:start position:0% +right like in Google Maps +and we have two brothers they start off + + align:start position:0% +and we have two brothers they start off + + + align:start position:0% +and we have two brothers they start off +from a place and they have to end up in + + align:start position:0% +from a place and they have to end up in + + + align:start position:0% +from a place and they have to end up in +another place they're going to drive + + align:start position:0% +another place they're going to drive + + + align:start position:0% +another place they're going to drive +together uh they want this to be sort of + + align:start position:0% +together uh they want this to be sort of + + + align:start position:0% +together uh they want this to be sort of +fair so every time they go between two + + align:start position:0% +fair so every time they go between two + + + align:start position:0% +fair so every time they go between two +cities they're going to switch seats so + + align:start position:0% +cities they're going to switch seats so + + + align:start position:0% +cities they're going to switch seats so +that none of them drives too much so say + + align:start position:0% +that none of them drives too much so say + + + align:start position:0% +that none of them drives too much so say +the brothers are Tim and + + align:start position:0% +the brothers are Tim and + + + align:start position:0% +the brothers are Tim and +Jim the names are wrong this is actually + + align:start position:0% +Jim the names are wrong this is actually + + + align:start position:0% +Jim the names are wrong this is actually +a problem for from last year's quiz so + + align:start position:0% +a problem for from last year's quiz so + + + align:start position:0% +a problem for from last year's quiz so +by the way real problem you can pay + + align:start position:0% +by the way real problem you can pay + + + align:start position:0% +by the way real problem you can pay +attention now + + align:start position:0% +attention now + + + align:start position:0% +attention now +so these are two + + align:start position:0% +so these are two + + + align:start position:0% +so these are two +brothers they they're going to alternate + + align:start position:0% +brothers they they're going to alternate + + + align:start position:0% +brothers they they're going to alternate +right one of them is going to drive + + align:start position:0% +right one of them is going to drive + + + align:start position:0% +right one of them is going to drive +across one road then the other one then + + align:start position:0% +across one road then the other one then + + + align:start position:0% +across one road then the other one then +the first one then the second one so on + + align:start position:0% +the first one then the second one so on + + + align:start position:0% +the first one then the second one so on +so forth now Tim has a much better sense + + align:start position:0% +so forth now Tim has a much better sense + + + align:start position:0% +so forth now Tim has a much better sense +of direction than + + align:start position:0% +of direction than + + + align:start position:0% +of direction than +Jim that's just how things are and if + + align:start position:0% +Jim that's just how things are and if + + + align:start position:0% +Jim that's just how things are and if +you ever driven long + + align:start position:0% +you ever driven long + + + align:start position:0% +you ever driven long +distances the hardest thing to do is to + + align:start position:0% +distances the hardest thing to do is to + + + align:start position:0% +distances the hardest thing to do is to +get from the city to the highway so like + + align:start position:0% +get from the city to the highway so like + + + align:start position:0% +get from the city to the highway so like +if you have to drive from here to New + + align:start position:0% +if you have to drive from here to New + + + align:start position:0% +if you have to drive from here to New +York hardest thing to do get out of + + align:start position:0% +York hardest thing to do get out of + + + align:start position:0% +York hardest thing to do get out of +Boston and onto the highway then at the + + align:start position:0% +Boston and onto the highway then at the + + + align:start position:0% +Boston and onto the highway then at the +end hardest thing to do get from the + + align:start position:0% +end hardest thing to do get from the + + + align:start position:0% +end hardest thing to do get from the +highway into where you want to go + + align:start position:0% +highway into where you want to go + + + align:start position:0% +highway into where you want to go +through New York traffic everything else + + align:start position:0% +through New York traffic everything else + + + align:start position:0% +through New York traffic everything else +piece of cake so we want Tim to handle + + align:start position:0% +piece of cake so we want Tim to handle + + + align:start position:0% +piece of cake so we want Tim to handle +both of these situations so the driving + + align:start position:0% +both of these situations so the driving + + + align:start position:0% +both of these situations so the driving +path must start with Tim and must end + + align:start position:0% +path must start with Tim and must end + + + align:start position:0% +path must start with Tim and must end +with Tim otherwise God knows they're + + align:start position:0% +with Tim otherwise God knows they're + + + align:start position:0% +with Tim otherwise God knows they're +going to + + align:start position:0% +going to + + + align:start position:0% +going to +crash so let's first off let's convert + + align:start position:0% +crash so let's first off let's convert + + + align:start position:0% +crash so let's first off let's convert +this into graph terms and then let's + + align:start position:0% +this into graph terms and then let's + + + align:start position:0% +this into graph terms and then let's +solve it + + align:start position:0% + + + + align:start position:0% + +well so this I have this constraint that + + align:start position:0% +well so this I have this constraint that + + + align:start position:0% +well so this I have this constraint that +they're going to switch seats and that + + align:start position:0% +they're going to switch seats and that + + + align:start position:0% +they're going to switch seats and that +Tim has to start and Tim has to end how + + align:start position:0% +Tim has to start and Tim has to end how + + + align:start position:0% +Tim has to start and Tim has to end how +do I phrase this in mathy terms in graph + + align:start position:0% + + + + align:start position:0% + +terms um we're starting at where ending + + align:start position:0% +terms um we're starting at where ending + + + align:start position:0% +terms um we're starting at where ending +where we're given where in the graph so + + align:start position:0% +where we're given where in the graph so + + + align:start position:0% +where we're given where in the graph so +so we're starting at s ending at T some + + align:start position:0% +so we're starting at s ending at T some + + + align:start position:0% +so we're starting at s ending at T some +points in the + + align:start position:0% +points in the + + + align:start position:0% +points in the +graph + + align:start position:0% +graph + + + align:start position:0% +graph +and people have to drive an entire Edge + + align:start position:0% +and people have to drive an entire Edge + + + align:start position:0% +and people have to drive an entire Edge +is that true yeah okay so then so + + align:start position:0% + + + + align:start position:0% + +basically Jim has to wait whoever the + + align:start position:0% +basically Jim has to wait whoever the + + + align:start position:0% +basically Jim has to wait whoever the +good driver has to drive on the edge + + align:start position:0% +good driver has to drive on the edge + + + align:start position:0% +good driver has to drive on the edge +that's adjacent to and S yep + + align:start position:0% +that's adjacent to and S yep + + + align:start position:0% +that's adjacent to and S yep +okay basically need an odd number yep so + + align:start position:0% +okay basically need an odd number yep so + + + align:start position:0% +okay basically need an odd number yep so +I want the shortest path with an odd + + align:start position:0% +I want the shortest path with an odd + + + align:start position:0% +I want the shortest path with an odd +number of edges + + align:start position:0% +number of edges + + + align:start position:0% +number of edges +why a number of edges if we look at the + + align:start position:0% +why a number of edges if we look at the + + + align:start position:0% +why a number of edges if we look at the +edges Tim's going to take the first one + + align:start position:0% +edges Tim's going to take the first one + + + align:start position:0% +edges Tim's going to take the first one +then Jim then Tim then Jim then Tim then + + align:start position:0% +then Jim then Tim then Jim then Tim then + + + align:start position:0% +then Jim then Tim then Jim then Tim then +Jim and no matter how many I have here + + align:start position:0% +Jim and no matter how many I have here + + + align:start position:0% +Jim and no matter how many I have here +it has to end with Tim so I'm going to + + align:start position:0% +it has to end with Tim so I'm going to + + + align:start position:0% +it has to end with Tim so I'm going to +have an odd number of letters here + + align:start position:0% +have an odd number of letters here + + + align:start position:0% +have an odd number of letters here +therefore odd number of edges right so I + + align:start position:0% +therefore odd number of edges right so I + + + align:start position:0% +therefore odd number of edges right so I +want the shortest + + align:start position:0% +want the shortest + + + align:start position:0% +want the shortest +path that has + + align:start position:0% +path that has + + + align:start position:0% +path that has +an odd number of + + align:start position:0% + + + + align:start position:0% + +edges and as the hint we're gonna use + + align:start position:0% +edges and as the hint we're gonna use + + + align:start position:0% +edges and as the hint we're gonna use +that trick over there so yes but the + + align:start position:0% +that trick over there so yes but the + + + align:start position:0% +that trick over there so yes but the +shortest path isn't necessarily like the + + align:start position:0% +shortest path isn't necessarily like the + + + align:start position:0% +shortest path isn't necessarily like the +fair in terms of + + align:start position:0% +fair in terms of + + + align:start position:0% +fair in terms of +Distributing + + align:start position:0% +Distributing + + + align:start position:0% +Distributing +driving one of them is going to drive + + align:start position:0% +driving one of them is going to drive + + + align:start position:0% +driving one of them is going to drive +one more Road such as life well sorry + + align:start position:0% +one more Road such as life well sorry + + + align:start position:0% +one more Road such as life well sorry +one more Edge segment so Tim's gonna + + align:start position:0% +one more Edge segment so Tim's gonna + + + align:start position:0% +one more Edge segment so Tim's gonna +drive say Tim's gonna drive three times + + align:start position:0% +drive say Tim's gonna drive three times + + + align:start position:0% +drive say Tim's gonna drive three times +Jim is gonna drive two times but in + + align:start position:0% +Jim is gonna drive two times but in + + + align:start position:0% +Jim is gonna drive two times but in +terms of the weights oh yeah we don't + + align:start position:0% +terms of the weights oh yeah we don't + + + align:start position:0% +terms of the weights oh yeah we don't +care about that + + align:start position:0% +care about that + + + align:start position:0% +care about that +oh Jim doesn't know he going anyways a + + align:start position:0% +oh Jim doesn't know he going anyways a + + + align:start position:0% +oh Jim doesn't know he going anyways a +minimum link through path right we don't + + align:start position:0% +minimum link through path right we don't + + + align:start position:0% +minimum link through path right we don't +just want Tim to get out to the highway + + align:start position:0% +just want Tim to get out to the highway + + + align:start position:0% +just want Tim to get out to the highway +and be like oh look our journey is not + + align:start position:0% +and be like oh look our journey is not + + + align:start position:0% +and be like oh look our journey is not +that far and then so I want the shortest + + align:start position:0% +that far and then so I want the shortest + + + align:start position:0% +that far and then so I want the shortest +so I want the path of the smallest cost + + align:start position:0% +so I want the path of the smallest cost + + + align:start position:0% +so I want the path of the smallest cost +okay so smallest total weight but I mean + + align:start position:0% +okay so smallest total weight but I mean + + + align:start position:0% +okay so smallest total weight but I mean +like in theory it could be length two + + align:start position:0% +like in theory it could be length two + + + align:start position:0% +like in theory it could be length two +right cuz well if it's length two then + + align:start position:0% +right cuz well if it's length two then + + + align:start position:0% +right cuz well if it's length two then +it's not going to be good because + + align:start position:0% +it's not going to be good because + + + align:start position:0% +it's not going to be good because +they're going to crash well no like Tim + + align:start position:0% +they're going to crash well no like Tim + + + align:start position:0% +they're going to crash well no like Tim +would oh I see they have to switch every + + align:start position:0% +would oh I see they have to switch every + + + align:start position:0% +would oh I see they have to switch every +time y Tim can't drive for two exective + + align:start position:0% +time y Tim can't drive for two exective + + + align:start position:0% +time y Tim can't drive for two exective +edits + + align:start position:0% + + + + align:start position:0% + +okay I me you could use breath search + + align:start position:0% +okay I me you could use breath search + + + align:start position:0% +okay I me you could use breath search +and um once you get to the end point + + align:start position:0% +and um once you get to the end point + + + align:start position:0% +and um once you get to the end point +eliminate all paths that are um you know + + align:start position:0% +eliminate all paths that are um you know + + + align:start position:0% +eliminate all paths that are um you know +an even length and then of those paths + + align:start position:0% +an even length and then of those paths + + + align:start position:0% +an even length and then of those paths +go through them to see if which one's + + align:start position:0% +go through them to see if which one's + + + align:start position:0% +go through them to see if which one's +the lowest cost so you're thinking you + + align:start position:0% +the lowest cost so you're thinking you + + + align:start position:0% +the lowest cost so you're thinking you +numeral Paths of even length + + align:start position:0% +numeral Paths of even length + + + align:start position:0% +numeral Paths of even length +no just to make sure I got it so this is + + align:start position:0% +no just to make sure I got it so this is + + + align:start position:0% +no just to make sure I got it so this is +cool because it it lets me show + + align:start position:0% +cool because it it lets me show + + + align:start position:0% +cool because it it lets me show +something else that's cool so I'll + + align:start position:0% +something else that's cool so I'll + + + align:start position:0% +something else that's cool so I'll +enumerate all Paths of even length um + + align:start position:0% +enumerate all Paths of even length um + + + align:start position:0% +enumerate all Paths of even length um +something else I heard enumerate all the + + align:start position:0% +something else I heard enumerate all the + + + align:start position:0% +something else I heard enumerate all the +shortest path for both of these let's + + align:start position:0% +shortest path for both of these let's + + + align:start position:0% +shortest path for both of these let's +look at this + + align:start position:0% +look at this + + + align:start position:0% +look at this +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +graph s t all the paths have length one + + align:start position:0% + + + + align:start position:0% + +how many ways are there to get from s to + + align:start position:0% + + + + align:start position:0% + +T two the three two ways to go across + + align:start position:0% +T two the three two ways to go across + + + align:start position:0% +T two the three two ways to go across +this diamond two way to go across ways + + align:start position:0% +this diamond two way to go across ways + + + align:start position:0% +this diamond two way to go across ways +to go across this one two ways to go + + align:start position:0% +to go across this one two ways to go + + + align:start position:0% +to go across this one two ways to go +across this one right 2 * 2 * 2 8 if I + + align:start position:0% +across this one right 2 * 2 * 2 8 if I + + + align:start position:0% +across this one right 2 * 2 * 2 8 if I +add another + + align:start position:0% +add another + + + align:start position:0% +add another +Diamond how many + + align:start position:0% +Diamond how many + + + align:start position:0% +Diamond how many +pads one more + + align:start position:0% +pads one more + + + align:start position:0% +pads one more +okay so the number of even paths or the + + align:start position:0% +okay so the number of even paths or the + + + align:start position:0% +okay so the number of even paths or the +number of shortest paths the number + + align:start position:0% +number of shortest paths the number + + + align:start position:0% +number of shortest paths the number +of whatever paths I can think about is + + align:start position:0% +of whatever paths I can think about is + + + align:start position:0% +of whatever paths I can think about is +order + + align:start position:0% + + + + align:start position:0% + +of come on guys + + align:start position:0% +of come on guys + + + align:start position:0% +of come on guys +math + + align:start position:0% +math + + + align:start position:0% +math +go two the number of diamonds okay which + + align:start position:0% + + + + align:start position:0% + +is roughly two to the vertices right + + align:start position:0% +is roughly two to the vertices right + + + align:start position:0% +is roughly two to the vertices right +exponential in the number vertices not + + align:start position:0% +exponential in the number vertices not + + + align:start position:0% +exponential in the number vertices not +very good not very good we can't do + + align:start position:0% +very good not very good we can't do + + + align:start position:0% +very good not very good we can't do +this so it's better that we talked about + + align:start position:0% +this so it's better that we talked about + + + align:start position:0% +this so it's better that we talked about +it here than then you try to do it on + + align:start position:0% +it here than then you try to do it on + + + align:start position:0% +it here than then you try to do it on +the quiz and you have to discover this + + align:start position:0% +the quiz and you have to discover this + + + align:start position:0% +the quiz and you have to discover this +on your own right so good comment didn't + + align:start position:0% +on your own right so good comment didn't + + + align:start position:0% +on your own right so good comment didn't +understand what you meant by that + + align:start position:0% +understand what you meant by that + + + align:start position:0% +understand what you meant by that +lecture so that makes sense that's + + align:start position:0% +lecture so that makes sense that's + + + align:start position:0% +lecture so that makes sense that's +completely different that's another the + + align:start position:0% +completely different that's another the + + + align:start position:0% +completely different that's another the +thing he was talking about that's + + align:start position:0% +thing he was talking about that's + + + align:start position:0% +thing he was talking about that's +different that was + + align:start position:0% +different that was + + + align:start position:0% +different that was +okay yeah that's that's where relaxation + + align:start position:0% +okay yeah that's that's where relaxation + + + align:start position:0% +okay yeah that's that's where relaxation +can go wrong so he show that if you + + align:start position:0% +can go wrong so he show that if you + + + align:start position:0% +can go wrong so he show that if you +relax the edges in a random order you + + align:start position:0% +relax the edges in a random order you + + + align:start position:0% +relax the edges in a random order you +can have an exponential number of + + align:start position:0% + + + + align:start position:0% + +steps this shows that there are an + + align:start position:0% +steps this shows that there are an + + + align:start position:0% +steps this shows that there are an +exponential number of paths for any + + align:start position:0% +exponential number of paths for any + + + align:start position:0% +exponential number of paths for any +graph no matter how good your algorithm + + align:start position:0% +graph no matter how good your algorithm + + + align:start position:0% +graph no matter how good your algorithm +is okay so we're not going to be able to + + align:start position:0% +is okay so we're not going to be able to + + + align:start position:0% +is okay so we're not going to be able to +enumerate them let's try something + + align:start position:0% + + + + align:start position:0% + +else + + align:start position:0% +else + + + align:start position:0% +else +suggestion uh look at all yeah so so + + align:start position:0% +suggestion uh look at all yeah so so + + + align:start position:0% +suggestion uh look at all yeah so so +you're doing this right you're looking + + align:start position:0% +you're doing this right you're looking + + + align:start position:0% +you're doing this right you're looking +here you're everyone's looking here how + + align:start position:0% +here you're everyone's looking here how + + + align:start position:0% +here you're everyone's looking here how +about + + align:start position:0% + + + + align:start position:0% + +this should do that there there's that + + align:start position:0% +this should do that there there's that + + + align:start position:0% +this should do that there there's that +right there's a transform you need to + + align:start position:0% +right there's a transform you need to + + + align:start position:0% +right there's a transform you need to +transform your graph in some way and + + align:start position:0% +transform your graph in some way and + + + align:start position:0% +transform your graph in some way and +then run the algorithm and then reading + + align:start position:0% +then run the algorithm and then reading + + + align:start position:0% +then run the algorithm and then reading +off the output should be easy I claim + + align:start position:0% +off the output should be easy I claim + + + align:start position:0% +off the output should be easy I claim +that the hard step is the transform step + + align:start position:0% +that the hard step is the transform step + + + align:start position:0% +that the hard step is the transform step +not the Roff + + align:start position:0% + + + + align:start position:0% + +step okay so let me give you one more + + align:start position:0% +step okay so let me give you one more + + + align:start position:0% +step okay so let me give you one more +piece of intuition + + align:start position:0% + + + + align:start position:0% + +so we're going to keep track of State + + align:start position:0% +so we're going to keep track of State + + + align:start position:0% +so we're going to keep track of State +somehow so remember Rubik's Cube we had + + align:start position:0% +somehow so remember Rubik's Cube we had + + + align:start position:0% +somehow so remember Rubik's Cube we had +one vertex for each state right a state + + align:start position:0% +one vertex for each state right a state + + + align:start position:0% +one vertex for each state right a state +represented a configuration of the + + align:start position:0% +represented a configuration of the + + + align:start position:0% +represented a configuration of the +cube here suppose I got from I'm looking + + align:start position:0% +cube here suppose I got from I'm looking + + + align:start position:0% +cube here suppose I got from I'm looking +at a path from s to D the problem that I + + align:start position:0% +at a path from s to D the problem that I + + + align:start position:0% +at a path from s to D the problem that I +have with this is + + align:start position:0% +have with this is + + + align:start position:0% +have with this is +that if I have an algorithm that tells + + align:start position:0% +that if I have an algorithm that tells + + + align:start position:0% +that if I have an algorithm that tells +me the shortest path from s to D is + + align:start position:0% +me the shortest path from s to D is + + + align:start position:0% +me the shortest path from s to D is +something + + align:start position:0% +something + + + align:start position:0% +something +I don't know if it's even or if it's odd + + align:start position:0% +I don't know if it's even or if it's odd + + + align:start position:0% +I don't know if it's even or if it's odd +it's not keeping track of that so it's + + align:start position:0% +it's not keeping track of that so it's + + + align:start position:0% +it's not keeping track of that so it's +missing some State the state that it's + + align:start position:0% +missing some State the state that it's + + + align:start position:0% +missing some State the state that it's +missing is whether the path that I used + + align:start position:0% +missing is whether the path that I used + + + align:start position:0% +missing is whether the path that I used +to get here is even or odd length so I + + align:start position:0% +to get here is even or odd length so I + + + align:start position:0% +to get here is even or odd length so I +should do something to the graph to keep + + align:start position:0% +should do something to the graph to keep + + + align:start position:0% +should do something to the graph to keep +track of the + + align:start position:0% + + + + align:start position:0% + +state so can + + align:start position:0% + + + + align:start position:0% + +you so cuz if you BFS once then you know + + align:start position:0% +you so cuz if you BFS once then you know + + + align:start position:0% +you so cuz if you BFS once then you know +that B and C are all like one way and + + align:start position:0% +that B and C are all like one way and + + + align:start position:0% +that B and C are all like one way and +then you know two + + align:start position:0% +then you know two + + + align:start position:0% +then you know two +away + + align:start position:0% +away + + + align:start position:0% +away +uh well B might be to away if I take + + align:start position:0% +uh well B might be to away if I take + + + align:start position:0% +uh well B might be to away if I take +this + + align:start position:0% +this + + + align:start position:0% +this +path so it might be one away it might be + + align:start position:0% +path so it might be one away it might be + + + align:start position:0% +path so it might be one away it might be +two + + align:start position:0% + + + + align:start position:0% + +away but this is good so this is what + + align:start position:0% +away but this is good so this is what + + + align:start position:0% +away but this is good so this is what +you'll do on a quiz right you come up + + align:start position:0% +you'll do on a quiz right you come up + + + align:start position:0% +you'll do on a quiz right you come up +with an idea and then you're going to + + align:start position:0% +with an idea and then you're going to + + + align:start position:0% +with an idea and then you're going to +think about it for a bit if you get + + align:start position:0% +think about it for a bit if you get + + + align:start position:0% +think about it for a bit if you get +stuck try to convince yourself that it's + + align:start position:0% +stuck try to convince yourself that it's + + + align:start position:0% +stuck try to convince yourself that it's +wrong or just if things get too hard + + align:start position:0% +wrong or just if things get too hard + + + align:start position:0% +wrong or just if things get too hard +discard and look somewhere else so this + + align:start position:0% +discard and look somewhere else so this + + + align:start position:0% +discard and look somewhere else so this +is thought process right you + + align:start position:0% +is thought process right you + + + align:start position:0% +is thought process right you +think of something backtrack backtrack + + align:start position:0% +think of something backtrack backtrack + + + align:start position:0% +think of something backtrack backtrack +backtrack and eventually you get to the + + align:start position:0% +backtrack and eventually you get to the + + + align:start position:0% +backtrack and eventually you get to the +right + + align:start position:0% + + + + align:start position:0% + +solution so let's go over the solution + + align:start position:0% +solution so let's go over the solution + + + align:start position:0% +solution so let's go over the solution +for this one and then I'll give you a + + align:start position:0% +for this one and then I'll give you a + + + align:start position:0% +for this one and then I'll give you a +hard one that is sort of like this and + + align:start position:0% +hard one that is sort of like this and + + + align:start position:0% +hard one that is sort of like this and +then I'll want the solution from you for + + align:start position:0% +then I'll want the solution from you for + + + align:start position:0% +then I'll want the solution from you for +that one so I'm going to draw this graph + + align:start position:0% +that one so I'm going to draw this graph + + + align:start position:0% +that one so I'm going to draw this graph +in a bigger version so I'll have to + + align:start position:0% +in a bigger version so I'll have to + + + align:start position:0% +in a bigger version so I'll have to +erase this + + align:start position:0% +erase this + + + align:start position:0% +erase this +so this is a cool + + align:start position:0% +so this is a cool + + + align:start position:0% +so this is a cool +concept you will be able to do a lot of + + align:start position:0% +concept you will be able to do a lot of + + + align:start position:0% +concept you will be able to do a lot of +things with + + align:start position:0% +things with + + + align:start position:0% +things with +it is this Sol by D + + align:start position:0% +it is this Sol by D + + + align:start position:0% +it is this Sol by D +yeah yeah we'll run dyra on it after we + + align:start position:0% +yeah yeah we'll run dyra on it after we + + + align:start position:0% +yeah yeah we'll run dyra on it after we +transform + + align:start position:0% + + + + align:start position:0% + +it these are Big nodes right why am I + + align:start position:0% +it these are Big nodes right why am I + + + align:start position:0% +it these are Big nodes right why am I +doing it this + + align:start position:0% +doing it this + + + align:start position:0% +doing it this +way like Seattle Portland s Francisco + + align:start position:0% +way like Seattle Portland s Francisco + + + align:start position:0% +way like Seattle Portland s Francisco +well it's because I'm going to need room + + align:start position:0% +well it's because I'm going to need room + + + align:start position:0% +well it's because I'm going to need room +for copies I'm going to make a copy of + + align:start position:0% +for copies I'm going to make a copy of + + + align:start position:0% +for copies I'm going to make a copy of +each node to keep track of + + align:start position:0% +each node to keep track of + + + align:start position:0% +each node to keep track of +state so instead of one node I'll have + + align:start position:0% +state so instead of one node I'll have + + + align:start position:0% +state so instead of one node I'll have +two nodes for each node and I have two + + align:start position:0% +two nodes for each node and I have two + + + align:start position:0% +two nodes for each node and I have two +nodes because this is what lets me keep + + align:start position:0% +nodes because this is what lets me keep + + + align:start position:0% +nodes because this is what lets me keep +track of State odd path or even + + align:start position:0% + + + + align:start position:0% + +path let me erase the edges because + + align:start position:0% +path let me erase the edges because + + + align:start position:0% +path let me erase the edges because +that's not how it's going to work + + align:start position:0% + + + + align:start position:0% + +actually so instead of having a node a + + align:start position:0% +actually so instead of having a node a + + + align:start position:0% +actually so instead of having a node a +I'm going to have a + + align:start position:0% +I'm going to have a + + + align:start position:0% +I'm going to have a +node a even and I'm going to have a + + align:start position:0% +node a even and I'm going to have a + + + align:start position:0% +node a even and I'm going to have a +copy a + + align:start position:0% +copy a + + + align:start position:0% +copy a +odd B even I'm going to have a + + align:start position:0% +odd B even I'm going to have a + + + align:start position:0% +odd B even I'm going to have a +copy B + + align:start position:0% +copy B + + + align:start position:0% +copy B +odd C even copi to C odd D + + align:start position:0% + + + + align:start position:0% + +even make a copy to the odd uh wait this + + align:start position:0% +even make a copy to the odd uh wait this + + + align:start position:0% +even make a copy to the odd uh wait this +is e sorry sorry my + + align:start position:0% + + + + align:start position:0% + +bad okay so suppose I got to a using an + + align:start position:0% +bad okay so suppose I got to a using an + + + align:start position:0% +bad okay so suppose I got to a using an +eval length + + align:start position:0% +eval length + + + align:start position:0% +eval length +path if I take the edge from A to B I + + align:start position:0% +path if I take the edge from A to B I + + + align:start position:0% +path if I take the edge from A to B I +will get to B using an even length path + + align:start position:0% +will get to B using an even length path + + + align:start position:0% +will get to B using an even length path +or an odd length + + align:start position:0% +or an odd length + + + align:start position:0% +or an odd length +path so if I get to a using an even + + align:start position:0% +path so if I get to a using an even + + + align:start position:0% +path so if I get to a using an even +length path then from there I'll get to + + align:start position:0% +length path then from there I'll get to + + + align:start position:0% +length path then from there I'll get to +be using an odd length + + align:start position:0% +be using an odd length + + + align:start position:0% +be using an odd length +path sorry for using this exact + + align:start position:0% + + + + align:start position:0% + +road that that's a nice way to name it + + align:start position:0% +road that that's a nice way to name it + + + align:start position:0% +road that that's a nice way to name it +I've heard worse so if I get to a using + + align:start position:0% +I've heard worse so if I get to a using + + + align:start position:0% +I've heard worse so if I get to a using +an odd number of + + align:start position:0% +an odd number of + + + align:start position:0% +an odd number of +edges how many edges will I have when I + + align:start position:0% +edges how many edges will I have when I + + + align:start position:0% +edges how many edges will I have when I +get to + + align:start position:0% + + + + align:start position:0% + +B + + align:start position:0% +B + + + align:start position:0% +B +okay so this Edge became these edges + + align:start position:0% +okay so this Edge became these edges + + + align:start position:0% +okay so this Edge became these edges +here + + align:start position:0% +here + + + align:start position:0% +here +okay now let's do the edge between B and + + align:start position:0% +okay now let's do the edge between B and + + + align:start position:0% +okay now let's do the edge between B and +E I get to be using an even number of + + align:start position:0% +E I get to be using an even number of + + + align:start position:0% +E I get to be using an even number of +edges I take + + align:start position:0% +edges I take + + + align:start position:0% +edges I take +B do I get to even to or to e odd + + align:start position:0% +B do I get to even to or to e odd + + + align:start position:0% +B do I get to even to or to e odd +odd okay I get to be using an odd + + align:start position:0% + + + + align:start position:0% + +path what are the length of these + + align:start position:0% + + + + align:start position:0% + +paths + + align:start position:0% +paths + + + align:start position:0% +paths +okay + + align:start position:0% +okay + + + align:start position:0% +okay +cool uh God this is starting look uglier + + align:start position:0% +cool uh God this is starting look uglier + + + align:start position:0% +cool uh God this is starting look uglier +right uh let's do AC and stop there um a + + align:start position:0% +right uh let's do AC and stop there um a + + + align:start position:0% +right uh let's do AC and stop there um a +even is connected + + align:start position:0% +even is connected + + + align:start position:0% +even is connected +to C odd by a path of + + align:start position:0% +to C odd by a path of + + + align:start position:0% +to C odd by a path of +length and a OD is connected to C by a + + align:start position:0% +length and a OD is connected to C by a + + + align:start position:0% +length and a OD is connected to C by a +path of + + align:start position:0% + + + + align:start position:0% + +length okay is this starting to make + + align:start position:0% + + + + align:start position:0% + +sense I mean you want just so all the + + align:start position:0% +sense I mean you want just so all the + + + align:start position:0% +sense I mean you want just so all the +edges are going to look like this so are + + align:start position:0% +edges are going to look like this so are + + + align:start position:0% +edges are going to look like this so are +those like two + + align:start position:0% +those like two + + + align:start position:0% +those like two +independent uh well I have well I have + + align:start position:0% +independent uh well I have well I have + + + align:start position:0% +independent uh well I have well I have +edges connecting them but I I like your + + align:start position:0% +edges connecting them but I I like your + + + align:start position:0% +edges connecting them but I I like your +question so the reason this is ugly is + + align:start position:0% +question so the reason this is ugly is + + + align:start position:0% +question so the reason this is ugly is +because I'm looking at a 2d projection + + align:start position:0% +because I'm looking at a 2d projection + + + align:start position:0% +because I'm looking at a 2d projection +of a 3D graph if I had a holographic + + align:start position:0% +of a 3D graph if I had a holographic + + + align:start position:0% +of a 3D graph if I had a holographic +display which would be a lot nicer then + + align:start position:0% +display which would be a lot nicer then + + + align:start position:0% +display which would be a lot nicer then +I would do something along these lines I + + align:start position:0% +I would do something along these lines I + + + align:start position:0% +I would do something along these lines I +would + + align:start position:0% +would + + + align:start position:0% +would +say two pieces of + + align:start position:0% +say two pieces of + + + align:start position:0% +say two pieces of +paper I would draw the graph I would + + align:start position:0% +paper I would draw the graph I would + + + align:start position:0% +paper I would draw the graph I would +draw the original graph and call it the + + align:start position:0% +draw the original graph and call it the + + + align:start position:0% +draw the original graph and call it the +even graph graph put it here I would + + align:start position:0% +even graph graph put it here I would + + + align:start position:0% +even graph graph put it here I would +draw the graph again call it the odd + + align:start position:0% +draw the graph again call it the odd + + + align:start position:0% +draw the graph again call it the odd +graph and put it + + align:start position:0% +graph and put it + + + align:start position:0% +graph and put it +here so this is my 2D graph this is my + + align:start position:0% +here so this is my 2D graph this is my + + + align:start position:0% +here so this is my 2D graph this is my +map the original map and this is State + + align:start position:0% +map the original map and this is State + + + align:start position:0% +map the original map and this is State +the third dimension is state so when I + + align:start position:0% +the third dimension is state so when I + + + align:start position:0% +the third dimension is state so when I +start when I when I'm at a node and I + + align:start position:0% +start when I when I'm at a node and I + + + align:start position:0% +start when I when I'm at a node and I +used an even number of edges to get + + align:start position:0% +used an even number of edges to get + + + align:start position:0% +used an even number of edges to get +here I'm going to go take one Edge and + + align:start position:0% +here I'm going to go take one Edge and + + + align:start position:0% +here I'm going to go take one Edge and +go to another node using an odd number + + align:start position:0% +go to another node using an odd number + + + align:start position:0% +go to another node using an odd number +of edges so all the edges are going to + + align:start position:0% +of edges so all the edges are going to + + + align:start position:0% +of edges so all the edges are going to +go from here to here and from here to + + align:start position:0% + + + + align:start position:0% + +here does it Mak more sense now so the + + align:start position:0% +here does it Mak more sense now so the + + + align:start position:0% +here does it Mak more sense now so the +reason that looks ugly is because you're + + align:start position:0% +reason that looks ugly is because you're + + + align:start position:0% +reason that looks ugly is because you're +seeing the graph like this if you could + + align:start position:0% +seeing the graph like this if you could + + + align:start position:0% +seeing the graph like this if you could +see like this and maybe play with it a + + align:start position:0% +see like this and maybe play with it a + + + align:start position:0% +see like this and maybe play with it a +little bit it would make more sense it + + align:start position:0% +little bit it would make more sense it + + + align:start position:0% +little bit it would make more sense it +wouldn't look as + + align:start position:0% + + + + align:start position:0% + +ugly so there are two graphs the even + + align:start position:0% +ugly so there are two graphs the even + + + align:start position:0% +ugly so there are two graphs the even +graph and the odd graph and the edges + + align:start position:0% +graph and the odd graph and the edges + + + align:start position:0% +graph and the odd graph and the edges +between them represent you doing + + align:start position:0% +between them represent you doing + + + align:start position:0% +between them represent you doing +something so when you transition when + + align:start position:0% +something so when you transition when + + + align:start position:0% +something so when you transition when +you take a highway you transition from + + align:start position:0% +you take a highway you transition from + + + align:start position:0% +you take a highway you transition from +an even state to an odd State and from + + align:start position:0% +an even state to an odd State and from + + + align:start position:0% +an even state to an odd State and from +an odd state to an even state so that's + + align:start position:0% +an odd state to an even state so that's + + + align:start position:0% +an odd state to an even state so that's +why the edges are the way they + + align:start position:0% +why the edges are the way they + + + align:start position:0% +why the edges are the way they +are okay so now let me see if you guys + + align:start position:0% +are okay so now let me see if you guys + + + align:start position:0% +are okay so now let me see if you guys +get it what node do I start from what + + align:start position:0% +get it what node do I start from what + + + align:start position:0% +get it what node do I start from what +node do I want to end up + + align:start position:0% +node do I want to end up + + + align:start position:0% +node do I want to end up +in + + align:start position:0% + + + + align:start position:0% + +you're + + align:start position:0% +you're + + + align:start position:0% +you're +okay oh there's two + + align:start position:0% +okay oh there's two + + + align:start position:0% +okay oh there's two +yeah okay so I heard three answers one + + align:start position:0% +yeah okay so I heard three answers one + + + align:start position:0% +yeah okay so I heard three answers one +of them is correct do we want to vote or + + align:start position:0% +of them is correct do we want to vote or + + + align:start position:0% +of them is correct do we want to vote or +do you guys want to figure it out talk + + align:start position:0% +do you guys want to figure it out talk + + + align:start position:0% +do you guys want to figure it out talk +it out + + align:start position:0% +it out + + + align:start position:0% +it out +fight + + align:start position:0% +fight + + + align:start position:0% +fight +okay we start from a even and we end up + + align:start position:0% +okay we start from a even and we end up + + + align:start position:0% +okay we start from a even and we end up +at e OD why do I start at a + + align:start position:0% + + + + align:start position:0% + +even yep so the original path has length + + align:start position:0% +even yep so the original path has length + + + align:start position:0% +even yep so the original path has length +zero which happens to be even and we + + align:start position:0% +zero which happens to be even and we + + + align:start position:0% +zero which happens to be even and we +want to end up with an odd length path + + align:start position:0% +want to end up with an odd length path + + + align:start position:0% +want to end up with an odd length path +so if we go from here to here see how + + align:start position:0% +so if we go from here to here see how + + + align:start position:0% +so if we go from here to here see how +because we have two instead of each + + align:start position:0% +because we have two instead of each + + + align:start position:0% +because we have two instead of each +original node the path is going to + + align:start position:0% +original node the path is going to + + + align:start position:0% +original node the path is going to +alternate between even and odd and it's + + align:start position:0% +alternate between even and odd and it's + + + align:start position:0% +alternate between even and odd and it's +going to keep track of the state that I + + align:start position:0% +going to keep track of the state that I + + + align:start position:0% +going to keep track of the state that I +didn't have before and it's going to + + align:start position:0% +didn't have before and it's going to + + + align:start position:0% +didn't have before and it's going to +just do the right + + align:start position:0% +just do the right + + + align:start position:0% +just do the right +thing it's magic it + + align:start position:0% +thing it's magic it + + + align:start position:0% +thing it's magic it +works so let's see what's the running + + align:start position:0% +works so let's see what's the running + + + align:start position:0% +works so let's see what's the running +time of this new algorithm how many uh + + align:start position:0% +time of this new algorithm how many uh + + + align:start position:0% +time of this new algorithm how many uh +say my original graph had V and D how + + align:start position:0% +say my original graph had V and D how + + + align:start position:0% +say my original graph had V and D how +many new vertices do I + + align:start position:0% + + + + align:start position:0% + +have how many edges + + align:start position:0% + + + + align:start position:0% + +each Edge is copied exactly twice which + + align:start position:0% +each Edge is copied exactly twice which + + + align:start position:0% +each Edge is copied exactly twice which +algorithm am I going to use all my + + align:start position:0% +algorithm am I going to use all my + + + align:start position:0% +algorithm am I going to use all my +weights are positive because they're the + + align:start position:0% +weights are positive because they're the + + + align:start position:0% +weights are positive because they're the +time it takes to drive somewhere the + + align:start position:0% +time it takes to drive somewhere the + + + align:start position:0% +time it takes to drive somewhere the +distance or something so which algorithm + + align:start position:0% +distance or something so which algorithm + + + align:start position:0% +distance or something so which algorithm +do I + + align:start position:0% + + + + align:start position:0% + +use + + align:start position:0% + + + + align:start position:0% + +can't um we can't use bread for search + + align:start position:0% +can't um we can't use bread for search + + + align:start position:0% +can't um we can't use bread for search +because you have + + align:start position:0% +because you have + + + align:start position:0% +because you have +weights so bre for search is not going + + align:start position:0% +weights so bre for search is not going + + + align:start position:0% +weights so bre for search is not going +to find the right answer oh you you want + + align:start position:0% +to find the right answer oh you you want + + + align:start position:0% +to find the right answer oh you you want +to use this thing well so we don't have + + align:start position:0% +to use this thing well so we don't have + + + align:start position:0% +to use this thing well so we don't have +to worry about that because now we put + + align:start position:0% +to worry about that because now we put + + + align:start position:0% +to worry about that because now we put +the shortest path algorithm in a black + + align:start position:0% +the shortest path algorithm in a black + + + align:start position:0% +the shortest path algorithm in a black +box and we have them also we can use + + align:start position:0% +box and we have them also we can use + + + align:start position:0% +box and we have them also we can use +yeah so we use these black boxes but + + align:start position:0% +yeah so we use these black boxes but + + + align:start position:0% +yeah so we use these black boxes but +what we need to know is when do you use + + align:start position:0% +what we need to know is when do you use + + + align:start position:0% +what we need to know is when do you use +this black box and when you use this + + align:start position:0% +this black box and when you use this + + + align:start position:0% +this black box and when you use this +black box which box is faster by the + + align:start position:0% +black box which box is faster by the + + + align:start position:0% +black box which box is faster by the +way please please give me the right + + align:start position:0% +way please please give me the right + + + align:start position:0% +way please please give me the right +answer exay all right the xtray is + + align:start position:0% +answer exay all right the xtray is + + + align:start position:0% +answer exay all right the xtray is +faster so whenever we can use the extra + + align:start position:0% +faster so whenever we can use the extra + + + align:start position:0% +faster so whenever we can use the extra +we will use the extra when can't we use + + align:start position:0% +we will use the extra when can't we use + + + align:start position:0% +we will use the extra when can't we use +the + + align:start position:0% +the + + + align:start position:0% +the +extra negative + + align:start position:0% + + + + align:start position:0% + +negative negative + + align:start position:0% +negative negative + + + align:start position:0% +negative negative +weights so if I have weights greater or + + align:start position:0% +weights so if I have weights greater or + + + align:start position:0% +weights so if I have weights greater or +equal to zero I'm happy I can use the + + align:start position:0% +equal to zero I'm happy I can use the + + + align:start position:0% +equal to zero I'm happy I can use the +extra if I have weights that are smaller + + align:start position:0% +extra if I have weights that are smaller + + + align:start position:0% +extra if I have weights that are smaller +than zero well whatever it's going to be + + align:start position:0% +than zero well whatever it's going to be + + + align:start position:0% +than zero well whatever it's going to be +slower but I can still solve it it's + + align:start position:0% +slower but I can still solve it it's + + + align:start position:0% +slower but I can still solve it it's +like + + align:start position:0% +like + + + align:start position:0% +like +arbitary + + align:start position:0% +arbitary + + + align:start position:0% +arbitary +yep arbitrary negative + + align:start position:0% + + + + align:start position:0% + +weights so all the edges here are + + align:start position:0% +weights so all the edges here are + + + align:start position:0% +weights so all the edges here are +positive I'm going to + + align:start position:0% +positive I'm going to + + + align:start position:0% +positive I'm going to +use ttra ttra very good so the running + + align:start position:0% +use ttra ttra very good so the running + + + align:start position:0% +use ttra ttra very good so the running +time will be order + + align:start position:0% + + + + align:start position:0% + +of V log V plus e if you're a theory + + align:start position:0% +of V log V plus e if you're a theory + + + align:start position:0% +of V log V plus e if you're a theory +person if you're in real life it's e log + + align:start position:0% +person if you're in real life it's e log + + + align:start position:0% +person if you're in real life it's e log +V so hey this is exactly the running + + align:start position:0% +V so hey this is exactly the running + + + align:start position:0% +V so hey this is exactly the running +time for the original graph so the + + align:start position:0% +time for the original graph so the + + + align:start position:0% +time for the original graph so the +transformation only increase the graph + + align:start position:0% +transformation only increase the graph + + + align:start position:0% +transformation only increase the graph +size by a constant Factor so same + + align:start position:0% +size by a constant Factor so same + + + align:start position:0% +size by a constant Factor so same +running time pretty good + + align:start position:0% + + + + align:start position:0% + +right okay let's do one more problem + + align:start position:0% +right okay let's do one more problem + + + align:start position:0% +right okay let's do one more problem +let's do the hard problem + + align:start position:0% + + + + align:start position:0% + +now are you guys getting ready for the + + align:start position:0% +now are you guys getting ready for the + + + align:start position:0% +now are you guys getting ready for the +hard + + align:start position:0% + + + + align:start position:0% + +problem seen this we probably wouldn't + + align:start position:0% +problem seen this we probably wouldn't + + + align:start position:0% +problem seen this we probably wouldn't +have thought of it yeah how would we + + align:start position:0% +have thought of it yeah how would we + + + align:start position:0% +have thought of it yeah how would we +think about this well that's why that's + + align:start position:0% +think about this well that's why that's + + + align:start position:0% +think about this well that's why that's +why we thought that's why we T you this + + align:start position:0% +why we thought that's why we T you this + + + align:start position:0% +why we thought that's why we T you this +so I wanted to do two things I wanted to + + align:start position:0% +so I wanted to do two things I wanted to + + + align:start position:0% +so I wanted to do two things I wanted to +show you that trick which is a cool + + align:start position:0% +show you that trick which is a cool + + + align:start position:0% +show you that trick which is a cool +trick keep track of state by doubling or + + align:start position:0% +trick keep track of state by doubling or + + + align:start position:0% +trick keep track of state by doubling or +by multiplying the vertices that you + + align:start position:0% +by multiplying the vertices that you + + + align:start position:0% +by multiplying the vertices that you +have and I wanted to go through some + + align:start position:0% +have and I wanted to go through some + + + align:start position:0% +have and I wanted to go through some +wrong Solutions and figure out why + + align:start position:0% +wrong Solutions and figure out why + + + align:start position:0% +wrong Solutions and figure out why +they're wrong so you can develop an + + align:start position:0% +they're wrong so you can develop an + + + align:start position:0% +they're wrong so you can develop an +intuition because when you're going to + + align:start position:0% +intuition because when you're going to + + + align:start position:0% +intuition because when you're going to +get a new problem you're going to think + + align:start position:0% +get a new problem you're going to think + + + align:start position:0% +get a new problem you're going to think +of something unless you're really good + + align:start position:0% +of something unless you're really good + + + align:start position:0% +of something unless you're really good +unless you're destined to win a turing + + align:start position:0% +unless you're destined to win a turing + + + align:start position:0% +unless you're destined to win a turing +Award of some sort the first solution + + align:start position:0% +Award of some sort the first solution + + + align:start position:0% +Award of some sort the first solution +will probably be wrong even if you're + + align:start position:0% +will probably be wrong even if you're + + + align:start position:0% +will probably be wrong even if you're +destined to win a touring a work the + + align:start position:0% +destined to win a touring a work the + + + align:start position:0% +destined to win a touring a work the +first thing that comes to mind will + + align:start position:0% +first thing that comes to mind will + + + align:start position:0% +first thing that comes to mind will +probably be wrong I'm willing to bet the + + align:start position:0% +probably be wrong I'm willing to bet the + + + align:start position:0% +probably be wrong I'm willing to bet the +extra didn't think of the extra off the + + align:start position:0% +extra didn't think of the extra off the + + + align:start position:0% +extra didn't think of the extra off the +top of his head when he heard about the + + align:start position:0% +top of his head when he heard about the + + + align:start position:0% +top of his head when he heard about the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so what you want to do is get an + + align:start position:0% +so what you want to do is get an + + + align:start position:0% +so what you want to do is get an +intuition so when you think of a + + align:start position:0% +intuition so when you think of a + + + align:start position:0% +intuition so when you think of a +solution and it starts getting + + align:start position:0% +solution and it starts getting + + + align:start position:0% +solution and it starts getting +complicated or things start looking + + align:start position:0% +complicated or things start looking + + + align:start position:0% +complicated or things start looking +wrong you want to back out and think of + + align:start position:0% +wrong you want to back out and think of + + + align:start position:0% +wrong you want to back out and think of +something else the more things you can + + align:start position:0% +something else the more things you can + + + align:start position:0% +something else the more things you can +consider higher chances that you're + + align:start position:0% +consider higher chances that you're + + + align:start position:0% +consider higher chances that you're +going to stumble upon the correct + + align:start position:0% +going to stumble upon the correct + + + align:start position:0% +going to stumble upon the correct +solution so that's why we're building an + + align:start position:0% +solution so that's why we're building an + + + align:start position:0% +solution so that's why we're building an +intuition for bad + + align:start position:0% +intuition for bad + + + align:start position:0% +intuition for bad +Solutions I'm not I'm not just saying + + align:start position:0% +Solutions I'm not I'm not just saying + + + align:start position:0% +Solutions I'm not I'm not just saying +hey give me a solution and now I'll tell + + align:start position:0% +hey give me a solution and now I'll tell + + + align:start position:0% +hey give me a solution and now I'll tell +you it's wrong it's not just to EMB + + align:start position:0% +you it's wrong it's not just to EMB + + + align:start position:0% +you it's wrong it's not just to EMB +embarrass you or something there's that + + align:start position:0% +embarrass you or something there's that + + + align:start position:0% +embarrass you or something there's that +intuition building step that's really + + align:start position:0% +intuition building step that's really + + + align:start position:0% +intuition building step that's really +important okay so there's this network + + align:start position:0% +important okay so there's this network + + + align:start position:0% +important okay so there's this network +that we keep talking + + align:start position:0% +that we keep talking + + + align:start position:0% +that we keep talking +about there's this highway Network + + align:start position:0% +about there's this highway Network + + + align:start position:0% +about there's this highway Network +except this time it's a bit more + + align:start position:0% + + + + align:start position:0% + +complicated so for each + + align:start position:0% +complicated so for each + + + align:start position:0% +complicated so for each +Edge I have two things I have a fuel + + align:start position:0% +Edge I have two things I have a fuel + + + align:start position:0% +Edge I have two things I have a fuel +cost which is constant so a fuel cost is + + align:start position:0% +cost which is constant so a fuel cost is + + + align:start position:0% +cost which is constant so a fuel cost is +a function of the length of the road but + + align:start position:0% +a function of the length of the road but + + + align:start position:0% +a function of the length of the road but +now I have these realistic highways + + align:start position:0% +now I have these realistic highways + + + align:start position:0% +now I have these realistic highways +where I have traffic if you try to go + + align:start position:0% +where I have traffic if you try to go + + + align:start position:0% +where I have traffic if you try to go +from Boston to New York 2: a.m. 3 hours + + align:start position:0% +from Boston to New York 2: a.m. 3 hours + + + align:start position:0% +from Boston to New York 2: a.m. 3 hours +Rush Hour 6 hours so we have to keep + + align:start position:0% +Rush Hour 6 hours so we have to keep + + + align:start position:0% +Rush Hour 6 hours so we have to keep +track of this in some way well we're + + align:start position:0% +track of this in some way well we're + + + align:start position:0% +track of this in some way well we're +going to split up the day into + + align:start position:0% +going to split up the day into + + + align:start position:0% +going to split up the day into +minutes say you have M minutes in a day + + align:start position:0% +minutes say you have M minutes in a day + + + align:start position:0% +minutes say you have M minutes in a day +can anyone tell me what m is really + + align:start position:0% +can anyone tell me what m is really + + + align:start position:0% +can anyone tell me what m is really +quickly not a number a formula something + + align:start position:0% +quickly not a number a formula something + + + align:start position:0% +quickly not a number a formula something +what's is it what's 3600 * + + align:start position:0% + + + + align:start position:0% + +24 okay 6 all right so this is how many + + align:start position:0% +24 okay 6 all right so this is how many + + + align:start position:0% +24 okay 6 all right so this is how many +minutes in a + + align:start position:0% + + + + align:start position:0% + +day so this is how many minutes we have + + align:start position:0% +day so this is how many minutes we have + + + align:start position:0% +day so this is how many minutes we have +in a day right okay so we're going for + + align:start position:0% +in a day right okay so we're going for + + + align:start position:0% +in a day right okay so we're going for +each Edge we're going to have a function + + align:start position:0% +each Edge we're going to have a function + + + align:start position:0% +each Edge we're going to have a function +that's the time cost of the edge so it's + + align:start position:0% +that's the time cost of the edge so it's + + + align:start position:0% +that's the time cost of the edge so it's +the time cost of this Edge and it's + + align:start position:0% +the time cost of this Edge and it's + + + align:start position:0% +the time cost of this Edge and it's +going to say if I start at a certain + + align:start position:0% +going to say if I start at a certain + + + align:start position:0% +going to say if I start at a certain +time it's going to take this many + + align:start position:0% +time it's going to take this many + + + align:start position:0% +time it's going to take this many +minutes to go across the + + align:start position:0% +minutes to go across the + + + align:start position:0% +minutes to go across the +edge so for each Street I know how much + + align:start position:0% +edge so for each Street I know how much + + + align:start position:0% +edge so for each Street I know how much +time it's sorry each highway I know know + + align:start position:0% +time it's sorry each highway I know know + + + align:start position:0% +time it's sorry each highway I know know +how much time it's going to take to go + + align:start position:0% +how much time it's going to take to go + + + align:start position:0% +how much time it's going to take to go +across it given when I + + align:start position:0% +across it given when I + + + align:start position:0% +across it given when I +start and I know how much fuel I'm going + + align:start position:0% +start and I know how much fuel I'm going + + + align:start position:0% +start and I know how much fuel I'm going +to consume by the way edges are directed + + align:start position:0% +to consume by the way edges are directed + + + align:start position:0% +to consume by the way edges are directed +now just to make our life easy so this + + align:start position:0% +now just to make our life easy so this + + + align:start position:0% +now just to make our life easy so this +is this graph is going to + + align:start position:0% +is this graph is going to + + + align:start position:0% +is this graph is going to +be like this let's see if I can get this + + align:start position:0% +be like this let's see if I can get this + + + align:start position:0% +be like this let's see if I can get this +right it's actually like aw they've got + + align:start position:0% +right it's actually like aw they've got + + + align:start position:0% +right it's actually like aw they've got +one ways + + align:start position:0% +one ways + + + align:start position:0% +one ways +everywhere well so the real reason I'm + + align:start position:0% +everywhere well so the real reason I'm + + + align:start position:0% +everywhere well so the real reason I'm +having this is um the the time to go + + align:start position:0% +having this is um the the time to go + + + align:start position:0% +having this is um the the time to go +across the street might be different + + align:start position:0% +across the street might be different + + + align:start position:0% +across the street might be different +across Highway might be different + + align:start position:0% +across Highway might be different + + + align:start position:0% +across Highway might be different +depending which way you go oh getting + + align:start position:0% +depending which way you go oh getting + + + align:start position:0% +depending which way you go oh getting +into Boston in the morning versus + + align:start position:0% +into Boston in the morning versus + + + align:start position:0% +into Boston in the morning versus +getting into Boston in the evening which + + align:start position:0% +getting into Boston in the evening which + + + align:start position:0% +getting into Boston in the evening which +one's easier sorry versus getting out of + + align:start position:0% +one's easier sorry versus getting out of + + + align:start position:0% +one's easier sorry versus getting out of +bus in the + + align:start position:0% +bus in the + + + align:start position:0% +bus in the +morning intuitively I say it's probably + + align:start position:0% +morning intuitively I say it's probably + + + align:start position:0% +morning intuitively I say it's probably +harder to get in in the morning because + + align:start position:0% +harder to get in in the morning because + + + align:start position:0% +harder to get in in the morning because +people are going to work and it's easier + + align:start position:0% +people are going to work and it's easier + + + align:start position:0% +people are going to work and it's easier +to get out but yeah I don't know either + + align:start position:0% +to get out but yeah I don't know either + + + align:start position:0% +to get out but yeah I don't know either +no the 95s are + + align:start position:0% +no the 95s are + + + align:start position:0% +no the 95s are +brutal okay we have an + + align:start position:0% +brutal okay we have an + + + align:start position:0% +brutal okay we have an +answer okay so our edges are going to be + + align:start position:0% +answer okay so our edges are going to be + + + align:start position:0% +answer okay so our edges are going to be +oriented and I want the road that so I + + align:start position:0% +oriented and I want the road that so I + + + align:start position:0% +oriented and I want the road that so I +want the final itary that gives me that + + align:start position:0% +want the final itary that gives me that + + + align:start position:0% +want the final itary that gives me that +satisfies two + + align:start position:0% + + + + align:start position:0% + +constraints yeah that's not good right + + align:start position:0% +constraints yeah that's not good right + + + align:start position:0% +constraints yeah that's not good right +okay New York and New York + + align:start position:0% +okay New York and New York + + + align:start position:0% +okay New York and New York +so if so I want to see how fast I can + + align:start position:0% +so if so I want to see how fast I can + + + align:start position:0% +so if so I want to see how fast I can +get to my destination that's my top + + align:start position:0% +get to my destination that's my top + + + align:start position:0% +get to my destination that's my top +priority if I can get if I can get to B + + align:start position:0% +priority if I can get if I can get to B + + + align:start position:0% +priority if I can get if I can get to B +to New York at 5:00 p.m I want to get + + align:start position:0% +to New York at 5:00 p.m I want to get + + + align:start position:0% +to New York at 5:00 p.m I want to get +there at 5:00 p.m. but if I have three I + + align:start position:0% +there at 5:00 p.m. but if I have three I + + + align:start position:0% +there at 5:00 p.m. but if I have three I +don't want to get there at 501 for + + align:start position:0% +don't want to get there at 501 for + + + align:start position:0% +don't want to get there at 501 for +example but if I have three ways to get + + align:start position:0% +example but if I have three ways to get + + + align:start position:0% +example but if I have three ways to get +there at 5:00 p.m. I want to choose the + + align:start position:0% +there at 5:00 p.m. I want to choose the + + + align:start position:0% +there at 5:00 p.m. I want to choose the +way that's the most eco-friendly so + + align:start position:0% +way that's the most eco-friendly so + + + align:start position:0% +way that's the most eco-friendly so +least amount of + + align:start position:0% +least amount of + + + align:start position:0% +least amount of +fuel so out of all possible ways the + + align:start position:0% +fuel so out of all possible ways the + + + align:start position:0% +fuel so out of all possible ways the +fastest way out of all possible fastest + + align:start position:0% +fastest way out of all possible fastest + + + align:start position:0% +fastest way out of all possible fastest +ways the way that consumes the less fuel + + align:start position:0% +ways the way that consumes the less fuel + + + align:start position:0% +ways the way that consumes the less fuel +Le + + align:start position:0% +Le + + + align:start position:0% +Le +fuel + + align:start position:0% +fuel + + + align:start position:0% +fuel +go you have two + + align:start position:0% +go you have two + + + align:start position:0% +go you have two +minutes maybe five the same cost for the + + align:start position:0% +minutes maybe five the same cost for the + + + align:start position:0% +minutes maybe five the same cost for the +so each Edge always has the same fuel + + align:start position:0% +so each Edge always has the same fuel + + + align:start position:0% +so each Edge always has the same fuel +cost oh but depending on when you start + + align:start position:0% +cost oh but depending on when you start + + + align:start position:0% +cost oh but depending on when you start +going across it it's going to take a + + align:start position:0% +going across it it's going to take a + + + align:start position:0% +going across it it's going to take a +different time to we don't know what + + align:start position:0% +different time to we don't know what + + + align:start position:0% +different time to we don't know what +those times are they're going to be + + align:start position:0% +those times are they're going to be + + + align:start position:0% +those times are they're going to be +different for each Edge one guess take D + + align:start position:0% +different for each Edge one guess take D + + + align:start position:0% +different for each Edge one guess take D +stra find the shorts path length and + + align:start position:0% +stra find the shorts path length and + + + align:start position:0% +stra find the shorts path length and +look for all path LS that length I don't + + align:start position:0% +look for all path LS that length I don't + + + align:start position:0% +look for all path LS that length I don't +know uh so we have the issue that I I + + align:start position:0% +know uh so we have the issue that I I + + + align:start position:0% +know uh so we have the issue that I I +might still have it oh no never mind + + align:start position:0% +might still have it oh no never mind + + + align:start position:0% +might still have it oh no never mind +sorry I erased it so it's not on your + + align:start position:0% +sorry I erased it so it's not on your + + + align:start position:0% +sorry I erased it so it's not on your +mind anymore we have those diamonds that + + align:start position:0% +mind anymore we have those diamonds that + + + align:start position:0% +mind anymore we have those diamonds that +show you that there're there might be an + + align:start position:0% +show you that there're there might be an + + + align:start position:0% +show you that there're there might be an +exponential number of paths with the + + align:start position:0% +exponential number of paths with the + + + align:start position:0% +exponential number of paths with the +same length or the same distance and it + + align:start position:0% +same length or the same distance and it + + + align:start position:0% +same length or the same distance and it +doesn't help that we know so we should + + align:start position:0% +doesn't help that we know so we should + + + align:start position:0% +doesn't help that we know so we should +cut off it nope yeah so we need to do + + align:start position:0% +cut off it nope yeah so we need to do + + + align:start position:0% +cut off it nope yeah so we need to do +the process that I just erased so + + align:start position:0% +the process that I just erased so + + + align:start position:0% +the process that I just erased so +transform the graph in right so the + + align:start position:0% +transform the graph in right so the + + + align:start position:0% +transform the graph in right so the +thing is now you're missing state right + + align:start position:0% +thing is now you're missing state right + + + align:start position:0% +thing is now you're missing state right +this misses State this tells you how + + align:start position:0% +this misses State this tells you how + + + align:start position:0% +this misses State this tells you how +many edges you have to get from source + + align:start position:0% +many edges you have to get from source + + + align:start position:0% +many edges you have to get from source +of destination but we're not keeping + + align:start position:0% +of destination but we're not keeping + + + align:start position:0% +of destination but we're not keeping +track of some state that is vital so + + align:start position:0% +track of some state that is vital so + + + align:start position:0% +track of some state that is vital so +transform the the graph to keep track of + + align:start position:0% +transform the the graph to keep track of + + + align:start position:0% +transform the the graph to keep track of +state run say dtop and then interpret + + align:start position:0% +state run say dtop and then interpret + + + align:start position:0% +state run say dtop and then interpret +the + + align:start position:0% + + + + align:start position:0% + +output so what state do we need let's + + align:start position:0% +output so what state do we need let's + + + align:start position:0% +output so what state do we need let's +think of that + + align:start position:0% +think of that + + + align:start position:0% +think of that +cross sorry is the same for each + + align:start position:0% +cross sorry is the same for each + + + align:start position:0% +cross sorry is the same for each +Edge just the time is different on + + align:start position:0% +Edge just the time is different on + + + align:start position:0% +Edge just the time is different on +traffic but like don't we want to keep + + align:start position:0% +traffic but like don't we want to keep + + + align:start position:0% +traffic but like don't we want to keep +because like once we have found the + + align:start position:0% +because like once we have found the + + + align:start position:0% +because like once we have found the +fastest spot then we want to like see + + align:start position:0% +fastest spot then we want to like see + + + align:start position:0% +fastest spot then we want to like see +like according to our Fiel cost right do + + align:start position:0% +like according to our Fiel cost right do + + + align:start position:0% +like according to our Fiel cost right do +we wanted + + align:start position:0% +we wanted + + + align:start position:0% +we wanted +to take so won't we like so like + + align:start position:0% +to take so won't we like so like + + + align:start position:0% +to take so won't we like so like +thinking about the priority our priority + + align:start position:0% +thinking about the priority our priority + + + align:start position:0% +thinking about the priority our priority +is + + align:start position:0% +is + + + align:start position:0% +is +y so we want to like save fuel I feel + + align:start position:0% +y so we want to like save fuel I feel + + + align:start position:0% +y so we want to like save fuel I feel +like as a state to check it + + align:start position:0% +like as a state to check it + + + align:start position:0% +like as a state to check it +uh so the problem is I don't even know + + align:start position:0% +uh so the problem is I don't even know + + + align:start position:0% +uh so the problem is I don't even know +if fuel costs are integers I can't keep + + align:start position:0% +if fuel costs are integers I can't keep + + + align:start position:0% +if fuel costs are integers I can't keep +fuel as a + + align:start position:0% +fuel as a + + + align:start position:0% +fuel as a +state so how many copies would I have + + align:start position:0% +state so how many copies would I have + + + align:start position:0% +state so how many copies would I have +for each verx how many copies would I + + align:start position:0% +for each verx how many copies would I + + + align:start position:0% +for each verx how many copies would I +have is fuel is a state who + + align:start position:0% +have is fuel is a state who + + + align:start position:0% +have is fuel is a state who +knows so let's try something else but + + align:start position:0% +knows so let's try something else but + + + align:start position:0% +knows so let's try something else but +you're on the right track let's take a + + align:start position:0% +you're on the right track let's take a + + + align:start position:0% +you're on the right track let's take a +variable and make it state + + align:start position:0% + + + + align:start position:0% + +so for every vertex can + + align:start position:0% +so for every vertex can + + + align:start position:0% +so for every vertex can +you keep track + + align:start position:0% + + + + align:start position:0% + +of how what's the shortest time it took + + align:start position:0% +of how what's the shortest time it took + + + align:start position:0% +of how what's the shortest time it took +to get + + align:start position:0% +to get + + + align:start position:0% +to get +there what's the shortest time it took + + align:start position:0% +there what's the shortest time it took + + + align:start position:0% +there what's the shortest time it took +to get there uh so how would you keep + + align:start position:0% +to get there uh so how would you keep + + + align:start position:0% +to get there uh so how would you keep +track of that would you make that state + + align:start position:0% +track of that would you make that state + + + align:start position:0% +track of that would you make that state +or how do you keep track of that + + align:start position:0% + + + + align:start position:0% + +I'm not disagreeing I'm trying to + + align:start position:0% +I'm not disagreeing I'm trying to + + + align:start position:0% +I'm not disagreeing I'm trying to +understand your so like for example + + align:start position:0% +understand your so like for example + + + align:start position:0% +understand your so like for example +like let's say if you have B right like + + align:start position:0% +like let's say if you have B right like + + + align:start position:0% +like let's say if you have B right like +say at vertex B if you let's say it + + align:start position:0% +say at vertex B if you let's say it + + + align:start position:0% +say at vertex B if you let's say it +takes like one hour to go from A to B + + align:start position:0% +takes like one hour to go from A to B + + + align:start position:0% +takes like one hour to go from A to B +and so when you when you so it depends + + align:start position:0% +and so when you when you so it depends + + + align:start position:0% +and so when you when you so it depends +when you start by the way so how much + + align:start position:0% +when you start by the way so how much + + + align:start position:0% +when you start by the way so how much +time it takes depends on when you start + + align:start position:0% +time it takes depends on when you start + + + align:start position:0% +time it takes depends on when you start +so like if you start at 8:00 a.m. it + + align:start position:0% +so like if you start at 8:00 a.m. it + + + align:start position:0% +so like if you start at 8:00 a.m. it +might be an hour if you start at 8 at + + align:start position:0% +might be an hour if you start at 8 at + + + align:start position:0% +might be an hour if you start at 8 at +9:00 a.m. it might be two hours right do + + align:start position:0% +9:00 a.m. it might be two hours right do + + + align:start position:0% +9:00 a.m. it might be two hours right do +you need to have a finite number of + + align:start position:0% +you need to have a finite number of + + + align:start position:0% +you need to have a finite number of +states + + align:start position:0% +states + + + align:start position:0% +states +uh it's nice if it's not infinite but it + + align:start position:0% +uh it's nice if it's not infinite but it + + + align:start position:0% +uh it's nice if it's not infinite but it +doesn't have to be constant like we had + + align:start position:0% +doesn't have to be constant like we had + + + align:start position:0% +doesn't have to be constant like we had +before it can be more than constant for + + align:start position:0% +before it can be more than constant for + + + align:start position:0% +before it can be more than constant for +sure so what are you + + align:start position:0% +sure so what are you + + + align:start position:0% +sure so what are you +thinking I want to use time as a state I + + align:start position:0% +thinking I want to use time as a state I + + + align:start position:0% +thinking I want to use time as a state I +like that idea let's try to do it so + + align:start position:0% +like that idea let's try to do it so + + + align:start position:0% +like that idea let's try to do it so +we're going to use time as a state how + + align:start position:0% +we're going to use time as a state how + + + align:start position:0% +we're going to use time as a state how +many vertices am I going to have for + + align:start position:0% +many vertices am I going to have for + + + align:start position:0% +many vertices am I going to have for +each + + align:start position:0% +each + + + align:start position:0% +each +vertex so for each original verx how + + align:start position:0% +vertex so for each original verx how + + + align:start position:0% +vertex so for each original verx how +many vertices am I going to have in my + + align:start position:0% +many vertices am I going to have in my + + + align:start position:0% +many vertices am I going to have in my +new + + align:start position:0% + + + + align:start position:0% + +graph three + + align:start position:0% +graph three + + + align:start position:0% +graph three +I feel + + align:start position:0% + + + + align:start position:0% + +expon so if if I say hey I'm at this + + align:start position:0% +expon so if if I say hey I'm at this + + + align:start position:0% +expon so if if I say hey I'm at this +vertex at this time then I'm going to + + align:start position:0% +vertex at this time then I'm going to + + + align:start position:0% +vertex at this time then I'm going to +have M vertices for each original vertex + + align:start position:0% +have M vertices for each original vertex + + + align:start position:0% +have M vertices for each original vertex +right right so I promise that the + + align:start position:0% +right right so I promise that the + + + align:start position:0% +right right so I promise that the +resolution of time is minutes so I + + align:start position:0% +resolution of time is minutes so I + + + align:start position:0% +resolution of time is minutes so I +promise that this thing gives you an + + align:start position:0% +promise that this thing gives you an + + + align:start position:0% +promise that this thing gives you an +integer number of + + align:start position:0% +integer number of + + + align:start position:0% +integer number of +minutes can it + + align:start position:0% +minutes can it + + + align:start position:0% +minutes can it +be in the days + + align:start position:0% +be in the days + + + align:start position:0% +be in the days +though suppose uh suppose we can get + + align:start position:0% +though suppose uh suppose we can get + + + align:start position:0% +though suppose uh suppose we can get +from source to destination in one + + align:start position:0% +from source to destination in one + + + align:start position:0% +from source to destination in one +day so let's see how it build this graph + + align:start position:0% +day so let's see how it build this graph + + + align:start position:0% +day so let's see how it build this graph +first and then we can uh figure out the + + align:start position:0% +first and then we can uh figure out the + + + align:start position:0% +first and then we can uh figure out the +rest of the things so for each node I'm + + align:start position:0% +rest of the things so for each node I'm + + + align:start position:0% +rest of the things so for each node I'm +going to make M copies of it so suppose + + align:start position:0% +going to make M copies of it so suppose + + + align:start position:0% +going to make M copies of it so suppose +in my original graph I had a node I'm + + align:start position:0% +in my original graph I had a node I'm + + + align:start position:0% +in my original graph I had a node I'm +going to have M copies of that node and + + align:start position:0% +going to have M copies of that node and + + + align:start position:0% +going to have M copies of that node and +each copy has the original vertex and + + align:start position:0% +each copy has the original vertex and + + + align:start position:0% +each copy has the original vertex and +the time when I'm there right so there + + align:start position:0% +the time when I'm there right so there + + + align:start position:0% +the time when I'm there right so there +are V of these and there are M of these + + align:start position:0% +are V of these and there are M of these + + + align:start position:0% +are V of these and there are M of these +yes makes sense it's a great idea yeah + + align:start position:0% +yes makes sense it's a great idea yeah + + + align:start position:0% +yes makes sense it's a great idea yeah +you had it great idea so far so good and + + align:start position:0% +you had it great idea so far so good and + + + align:start position:0% +you had it great idea so far so good and +then connect it to the appropriate next + + align:start position:0% +then connect it to the appropriate next + + + align:start position:0% +then connect it to the appropriate next +one yeah so let's see how we do that + + align:start position:0% +one yeah so let's see how we do that + + + align:start position:0% +one yeah so let's see how we do that +let's do that so um suppose we have an + + align:start position:0% +let's do that so um suppose we have an + + + align:start position:0% +let's do that so um suppose we have an +edge from U + + align:start position:0% +edge from U + + + align:start position:0% +edge from U +Tov + + align:start position:0% +Tov + + + align:start position:0% +Tov +and uh yeah how are we going to connect + + align:start position:0% +and uh yeah how are we going to connect + + + align:start position:0% +and uh yeah how are we going to connect +this how are we going to transform + + align:start position:0% +this how are we going to transform + + + align:start position:0% +this how are we going to transform +this how many edges are we going to make + + align:start position:0% +this how many edges are we going to make + + + align:start position:0% +this how many edges are we going to make +from that edge so you need + + align:start position:0% +from that edge so you need + + + align:start position:0% +from that edge so you need +you should only + + align:start position:0% +you should only + + + align:start position:0% +you should only +make oh my goodness do you have to do it + + align:start position:0% +make oh my goodness do you have to do it + + + align:start position:0% +make oh my goodness do you have to do it +from every start time I guess yeah so + + align:start position:0% +from every start time I guess yeah so + + + align:start position:0% +from every start time I guess yeah so +you m EDG okay M edges so from U and a + + align:start position:0% +you m EDG okay M edges so from U and a + + + align:start position:0% +you m EDG okay M edges so from U and a +start time + + align:start position:0% +start time + + + align:start position:0% +start time +to V and + + align:start position:0% +to V and + + + align:start position:0% +to V and +what uh t plus TC of t t plus TC of + + align:start position:0% +what uh t plus TC of t t plus TC of + + + align:start position:0% +what uh t plus TC of t t plus TC of +going through that edge right TC of + + align:start position:0% +going through that edge right TC of + + + align:start position:0% +going through that edge right TC of +going from U to V at this + + align:start position:0% + + + + align:start position:0% + +time yeah yeah like + + align:start position:0% +time yeah yeah like + + + align:start position:0% +time yeah yeah like +this so you start from a time so the + + align:start position:0% +this so you start from a time so the + + + align:start position:0% +this so you start from a time so the +edge points from the time that you start + + align:start position:0% +edge points from the time that you start + + + align:start position:0% +edge points from the time that you start +up until the time when You' be able to + + align:start position:0% +up until the time when You' be able to + + + align:start position:0% +up until the time when You' be able to +finish so up until the time where you'd + + align:start position:0% +finish so up until the time where you'd + + + align:start position:0% +finish so up until the time where you'd +be off the highway and done in the next + + align:start position:0% +be off the highway and done in the next + + + align:start position:0% +be off the highway and done in the next +city and we need one more type of edges + + align:start position:0% +city and we need one more type of edges + + + align:start position:0% +city and we need one more type of edges +there's one more tiny trick so if I'm + + align:start position:0% +there's one more tiny trick so if I'm + + + align:start position:0% +there's one more tiny trick so if I'm +somewhere in Massachusetts and I know + + align:start position:0% +somewhere in Massachusetts and I know + + + align:start position:0% +somewhere in Massachusetts and I know +that it's really bad now I might prefer + + align:start position:0% +that it's really bad now I might prefer + + + align:start position:0% +that it's really bad now I might prefer +to wait out for a few minutes go to a + + align:start position:0% +to wait out for a few minutes go to a + + + align:start position:0% +to wait out for a few minutes go to a +bar and then come and drive okay not to + + align:start position:0% +bar and then come and drive okay not to + + + align:start position:0% +bar and then come and drive okay not to +a bar go to a food place and then drive + + align:start position:0% +a bar go to a food place and then drive + + + align:start position:0% +a bar go to a food place and then drive +later so vertical edges that represent + + align:start position:0% +later so vertical edges that represent + + + align:start position:0% +later so vertical edges that represent +waiting have one minute between them + + align:start position:0% +waiting have one minute between them + + + align:start position:0% +waiting have one minute between them +okay so how do I do that so from a from + + align:start position:0% +okay so how do I do that so from a from + + + align:start position:0% +okay so how do I do that so from a from +U to U okay with a cost of one from U to + + align:start position:0% +U to U okay with a cost of one from U to + + + align:start position:0% +U to U okay with a cost of one from U to +U uh well so from U and at time T to + + align:start position:0% +U uh well so from U and at time T to + + + align:start position:0% +U uh well so from U and at time T to +youu at time t plus one okay I like this + + align:start position:0% +youu at time t plus one okay I like this + + + align:start position:0% +youu at time t plus one okay I like this +better and what's the fuel cost of + + align:start position:0% +better and what's the fuel cost of + + + align:start position:0% +better and what's the fuel cost of +this okay so here if this Edge had fuel + + align:start position:0% +this okay so here if this Edge had fuel + + + align:start position:0% +this okay so here if this Edge had fuel +cost FC then the near is going to have + + align:start position:0% +cost FC then the near is going to have + + + align:start position:0% +cost FC then the near is going to have +fuel + + align:start position:0% +fuel + + + align:start position:0% +fuel +cost for the ones on the + + align:start position:0% +cost for the ones on the + + + align:start position:0% +cost for the ones on the +top is it proportional to minutes speed + + align:start position:0% +top is it proportional to minutes speed + + + align:start position:0% +top is it proportional to minutes speed +it's the same FC so FC stays the same no + + align:start position:0% +it's the same FC so FC stays the same no + + + align:start position:0% +it's the same FC so FC stays the same no +matter when we go through the highway FC + + align:start position:0% +matter when we go through the highway FC + + + align:start position:0% +matter when we go through the highway FC +is a function of the distance of the + + align:start position:0% +is a function of the distance of the + + + align:start position:0% +is a function of the distance of the +road so this Edge becomes M edges with + + align:start position:0% +road so this Edge becomes M edges with + + + align:start position:0% +road so this Edge becomes M edges with +the same cost and then I have to have + + align:start position:0% +the same cost and then I have to have + + + align:start position:0% +the same cost and then I have to have +vertical waiting + + align:start position:0% +vertical waiting + + + align:start position:0% +vertical waiting +edges so if we have the if we had the + + align:start position:0% +edges so if we have the if we had the + + + align:start position:0% +edges so if we have the if we had the +Hol graphic display that I talked about + + align:start position:0% +Hol graphic display that I talked about + + + align:start position:0% +Hol graphic display that I talked about +earlier you'd have M sheets of paper + + align:start position:0% +earlier you'd have M sheets of paper + + + align:start position:0% +earlier you'd have M sheets of paper +this time you start at Time Zero at your + + align:start position:0% +this time you start at Time Zero at your + + + align:start position:0% +this time you start at Time Zero at your +source and then your edges go represent + + align:start position:0% +source and then your edges go represent + + + align:start position:0% +source and then your edges go represent +the moves that you could make so you + + align:start position:0% +the moves that you could make so you + + + align:start position:0% +the moves that you could make so you +could start in Boston at 8: a.m. and you + + align:start position:0% +could start in Boston at 8: a.m. and you + + + align:start position:0% +could start in Boston at 8: a.m. and you +could take I90 and end up in I don't + + align:start position:0% +could take I90 and end up in I don't + + + align:start position:0% +could take I90 and end up in I don't +know I don't know Massachusetts city + + align:start position:0% +know I don't know Massachusetts city + + + align:start position:0% +know I don't know Massachusetts city +names Alber + + align:start position:0% +names Alber + + + align:start position:0% +names Alber +at 9:00 a.m. okay I don't know sorry I + + align:start position:0% +at 9:00 a.m. okay I don't know sorry I + + + align:start position:0% +at 9:00 a.m. okay I don't know sorry I +don't Amherst okay so you started Boston + + align:start position:0% +don't Amherst okay so you started Boston + + + align:start position:0% +don't Amherst okay so you started Boston +8: a.m. you end up at Amhurst at I don't + + align:start position:0% +8: a.m. you end up at Amhurst at I don't + + + align:start position:0% +8: a.m. you end up at Amhurst at I don't +know 9:10 a.m. right so this is one Edge + + align:start position:0% +know 9:10 a.m. right so this is one Edge + + + align:start position:0% +know 9:10 a.m. right so this is one Edge +so the edges represent the moves that + + align:start position:0% +so the edges represent the moves that + + + align:start position:0% +so the edges represent the moves that +you could make in this + + align:start position:0% + + + + align:start position:0% + +graph does this make sense wa I + + align:start position:0% +graph does this make sense wa I + + + align:start position:0% +graph does this make sense wa I +understand the two last lines there what + + align:start position:0% +understand the two last lines there what + + + align:start position:0% +understand the two last lines there what +was the I don't really get what we were + + align:start position:0% +was the I don't really get what we were + + + align:start position:0% +was the I don't really get what we were +doing okay so let's see what we're + + align:start position:0% +doing okay so let's see what we're + + + align:start position:0% +doing okay so let's see what we're +trying to do here so saying that if I'm + + align:start position:0% +trying to do here so saying that if I'm + + + align:start position:0% +trying to do here so saying that if I'm +a node you m and I'm starting at time T + + align:start position:0% +a node you m and I'm starting at time T + + + align:start position:0% +a node you m and I'm starting at time T +yeah so it's like one one paper yep okay + + align:start position:0% +yeah so it's like one one paper yep okay + + + align:start position:0% +yeah so it's like one one paper yep okay +so this is I'm going to go on a road + + align:start position:0% +so this is I'm going to go on a road + + + align:start position:0% +so this is I'm going to go on a road +right I'm going to go on the road from U + + align:start position:0% +right I'm going to go on the road from U + + + align:start position:0% +right I'm going to go on the road from U +to v m so where am I going to + + align:start position:0% +to v m so where am I going to + + + align:start position:0% +to v m so where am I going to +arrive at some time so now we have to + + align:start position:0% +arrive at some time so now we have to + + + align:start position:0% +arrive at some time so now we have to +figure out what time we're going to + + align:start position:0% +figure out what time we're going to + + + align:start position:0% +figure out what time we're going to +arrive at so the time that we arrive at + + align:start position:0% +arrive at so the time that we arrive at + + + align:start position:0% +arrive at so the time that we arrive at +is the original time plus whatever time + + align:start position:0% +is the original time plus whatever time + + + align:start position:0% +is the original time plus whatever time +I'm going to spend on the road what's + + align:start position:0% +I'm going to spend on the road what's + + + align:start position:0% +I'm going to spend on the road what's +the time I spend on the road it's not + + align:start position:0% +the time I spend on the road it's not + + + align:start position:0% +the time I spend on the road it's not +constant because I have the that + + align:start position:0% +constant because I have the that + + + align:start position:0% +constant because I have the that +timetable that includes traffic yeah so + + align:start position:0% +timetable that includes traffic yeah so + + + align:start position:0% +timetable that includes traffic yeah so +this is what this tells me this is what + + align:start position:0% +this is what this tells me this is what + + + align:start position:0% +this is what this tells me this is what +this big ugly formula is all about it + + align:start position:0% +this big ugly formula is all about it + + + align:start position:0% +this big ugly formula is all about it +says the timetable for this Edge + + align:start position:0% +says the timetable for this Edge + + + align:start position:0% +says the timetable for this Edge +assuming you start at time T that's all + + align:start position:0% +assuming you start at time T that's all + + + align:start position:0% +assuming you start at time T that's all +there is nothing else what's the second + + align:start position:0% +there is nothing else what's the second + + + align:start position:0% +there is nothing else what's the second +line so the second line is + + align:start position:0% +line so the second line is + + + align:start position:0% +line so the second line is +waiting so if I don't have this then I'm + + align:start position:0% +waiting so if I don't have this then I'm + + + align:start position:0% +waiting so if I don't have this then I'm +constrained in that I have to drive all + + align:start position:0% +constrained in that I have to drive all + + + align:start position:0% +constrained in that I have to drive all +the time right I go from here to emmer + + align:start position:0% +the time right I go from here to emmer + + + align:start position:0% +the time right I go from here to emmer +then I have to go from ammer to + + align:start position:0% +then I have to go from ammer to + + + align:start position:0% +then I have to go from ammer to +somewhere else and keep going keep going + + align:start position:0% +somewhere else and keep going keep going + + + align:start position:0% +somewhere else and keep going keep going +keep going saying use so this is the + + align:start position:0% +keep going saying use so this is the + + + align:start position:0% +keep going saying use so this is the +this is the pausing yeah this is where I + + align:start position:0% +this is the pausing yeah this is where I + + + align:start position:0% +this is the pausing yeah this is where I +wait for a minute okay so if I wait for + + align:start position:0% +wait for a minute okay so if I wait for + + + align:start position:0% +wait for a minute okay so if I wait for +a minute I don't consume any fuel and I + + align:start position:0% +a minute I don't consume any fuel and I + + + align:start position:0% +a minute I don't consume any fuel and I +go from time T time t + + + align:start position:0% +go from time T time t + + + + align:start position:0% +go from time T time t + +one okay does this make + + align:start position:0% +one okay does this make + + + align:start position:0% +one okay does this make +sense uh do we want to analyze the + + align:start position:0% +sense uh do we want to analyze the + + + align:start position:0% +sense uh do we want to analyze the +running time for this really quickly + + align:start position:0% +running time for this really quickly + + + align:start position:0% +running time for this really quickly +sure so how many + + align:start position:0% + + + + align:start position:0% + +edges e * m okay let's do vertices + + align:start position:0% +edges e * m okay let's do vertices + + + align:start position:0% +edges e * m okay let's do vertices +because vertices is quick you TR okay so + + align:start position:0% +because vertices is quick you TR okay so + + + align:start position:0% +because vertices is quick you TR okay so +Ed + + align:start position:0% +Ed + + + align:start position:0% +Ed +is you're saying e * + + align:start position:0% +is you're saying e * + + + align:start position:0% +is you're saying e * +m almost pause there okay so there's the + + align:start position:0% +m almost pause there okay so there's the + + + align:start position:0% +m almost pause there okay so there's the +pause right how many pause edges do I + + align:start position:0% +pause right how many pause edges do I + + + align:start position:0% +pause right how many pause edges do I +have + + align:start position:0% +have + + + align:start position:0% +have +um oh + + align:start position:0% +um oh + + + align:start position:0% +um oh +b um + + align:start position:0% + + + + align:start position:0% + +M okay so this is how many vertices this + + align:start position:0% +M okay so this is how many vertices this + + + align:start position:0% +M okay so this is how many vertices this +is how many edges plug this into which + + align:start position:0% +is how many edges plug this into which + + + align:start position:0% +is how many edges plug this into which +algorithm D extra or B + + align:start position:0% +algorithm D extra or B + + + align:start position:0% +algorithm D extra or B +for it's all positive + + align:start position:0% +for it's all positive + + + align:start position:0% +for it's all positive +done yeah we solved the hard problem how + + align:start position:0% +done yeah we solved the hard problem how + + + align:start position:0% +done yeah we solved the hard problem how +how do you ensure that the time's right + + align:start position:0% +how do you ensure that the time's right + + + align:start position:0% +how do you ensure that the time's right +so do you have to go through and see if + + align:start position:0% +so do you have to go through and see if + + + align:start position:0% +so do you have to go through and see if +there's a path how do we read the + + align:start position:0% +there's a path how do we read the + + + align:start position:0% +there's a path how do we read the +solution that's good that's a good + + align:start position:0% +solution that's good that's a good + + + align:start position:0% +solution that's good that's a good +question I like that so we're going to + + align:start position:0% +question I like that so we're going to + + + align:start position:0% +question I like that so we're going to +have M vertices at the destination right + + align:start position:0% +have M vertices at the destination right + + + align:start position:0% +have M vertices at the destination right +let's see how they're going to look like + + align:start position:0% +let's see how they're going to look like + + + align:start position:0% +let's see how they're going to look like +first off if you start at 8:00 a.m. + + align:start position:0% +first off if you start at 8:00 a.m. + + + align:start position:0% +first off if you start at 8:00 a.m. +maybe you're not going to make it to New + + align:start position:0% +maybe you're not going to make it to New + + + align:start position:0% +maybe you're not going to make it to New +York at 8:01 a.m. so the vert the vertex + + align:start position:0% +York at 8:01 a.m. so the vert the vertex + + + align:start position:0% +York at 8:01 a.m. so the vert the vertex +that says New York at8 to 1 a.m. is + + align:start position:0% +that says New York at8 to 1 a.m. is + + + align:start position:0% +that says New York at8 to 1 a.m. is +probably going to have a cost of plus + + align:start position:0% +probably going to have a cost of plus + + + align:start position:0% +probably going to have a cost of plus +infinity so first off the really early + + align:start position:0% +infinity so first off the really early + + + align:start position:0% +infinity so first off the really early +times are going to have a cost of plus + + align:start position:0% +times are going to have a cost of plus + + + align:start position:0% +times are going to have a cost of plus +infinity not going to happen then at + + align:start position:0% +infinity not going to happen then at + + + align:start position:0% +infinity not going to happen then at +some point the cost is going to become + + align:start position:0% +some point the cost is going to become + + + align:start position:0% +some point the cost is going to become +finite that's the fastest way you can + + align:start position:0% +finite that's the fastest way you can + + + align:start position:0% +finite that's the fastest way you can +get from Boston to New York and in the + + align:start position:0% +get from Boston to New York and in the + + + align:start position:0% +get from Boston to New York and in the +shortest time sorry using the least + + align:start position:0% +shortest time sorry using the least + + + align:start position:0% +shortest time sorry using the least +amount of fuel so the cost that you have + + align:start position:0% +amount of fuel so the cost that you have + + + align:start position:0% +amount of fuel so the cost that you have +there is the answer to our + + align:start position:0% +there is the answer to our + + + align:start position:0% +there is the answer to our +problem so basically when you get the + + align:start position:0% +problem so basically when you get the + + + align:start position:0% +problem so basically when you get the +result you have to iterate through all + + align:start position:0% +result you have to iterate through all + + + align:start position:0% +result you have to iterate through all +and all and vertices that correspond to + + align:start position:0% +and all and vertices that correspond to + + + align:start position:0% +and all and vertices that correspond to +the destination okay so what I like + + align:start position:0% +the destination okay so what I like + + + align:start position:0% +the destination okay so what I like +about this is + + align:start position:0% +about this is + + + align:start position:0% +about this is +so the costs are going to look like this + + align:start position:0% +so the costs are going to look like this + + + align:start position:0% +so the costs are going to look like this +they're going to be infinity infinity + + align:start position:0% +they're going to be infinity infinity + + + align:start position:0% +they're going to be infinity infinity +infinity all the way up until some point + + align:start position:0% +infinity all the way up until some point + + + align:start position:0% +infinity all the way up until some point +and here you're going to have your final + + align:start position:0% +and here you're going to have your final + + + align:start position:0% +and here you're going to have your final +answer the cost to get there the fastest + + align:start position:0% +answer the cost to get there the fastest + + + align:start position:0% +answer the cost to get there the fastest +say you can get there at 3 p.m. this is + + align:start position:0% +say you can get there at 3 p.m. this is + + + align:start position:0% +say you can get there at 3 p.m. this is +how much fuel you're willing to you have + + align:start position:0% +how much fuel you're willing to you have + + + align:start position:0% +how much fuel you're willing to you have +to spend together at 3 p.m. but if you + + align:start position:0% +to spend together at 3 p.m. but if you + + + align:start position:0% +to spend together at 3 p.m. but if you +want if you're willing to wait until + + align:start position:0% +want if you're willing to wait until + + + align:start position:0% +want if you're willing to wait until +3:01 p.m. you're going to have the cost + + align:start position:0% +3:01 p.m. you're going to have the cost + + + align:start position:0% +3:01 p.m. you're going to have the cost +the fastest cost you can have for that + + align:start position:0% +the fastest cost you can have for that + + + align:start position:0% +the fastest cost you can have for that +if you're willing to wait until + + align:start position:0% +if you're willing to wait until + + + align:start position:0% +if you're willing to wait until +302 you're going to have the answer for + + align:start position:0% +302 you're going to have the answer for + + + align:start position:0% +302 you're going to have the answer for +that too so here you're going to get the + + align:start position:0% +that too so here you're going to get the + + + align:start position:0% +that too so here you're going to get the +whole trade-off curve of if you're + + align:start position:0% +whole trade-off curve of if you're + + + align:start position:0% +whole trade-off curve of if you're +willing to wait for a few minutes or if + + align:start position:0% +willing to wait for a few minutes or if + + + align:start position:0% +willing to wait for a few minutes or if +you're willing to wait for an extra hour + + align:start position:0% +you're willing to wait for an extra hour + + + align:start position:0% +you're willing to wait for an extra hour +how much fuel you can + + align:start position:0% + + + + align:start position:0% + +save so I think that's cool about that's + + align:start position:0% +save so I think that's cool about that's + + + align:start position:0% +save so I think that's cool about that's +cool about your question okay you other + + align:start position:0% +cool about your question okay you other + + + align:start position:0% +cool about your question okay you other +question too uh why did we have V * m in + + align:start position:0% +question too uh why did we have V * m in + + + align:start position:0% +question too uh why did we have V * m in +the E Prime + + align:start position:0% +the E Prime + + + align:start position:0% +the E Prime +expression so first off we have etimes M + + align:start position:0% +expression so first off we have etimes M + + + align:start position:0% +expression so first off we have etimes M +right we're good with these These are + + align:start position:0% +right we're good with these These are + + + align:start position:0% +right we're good with these These are +the waiting edges + + align:start position:0% +the waiting edges + + + align:start position:0% +the waiting edges +so we are waiting like after every + + align:start position:0% +so we are waiting like after every + + + align:start position:0% +so we are waiting like after every +minute or what so the waiting edges are + + align:start position:0% +minute or what so the waiting edges are + + + align:start position:0% +minute or what so the waiting edges are +vertex time to verx time plus one how + + align:start position:0% +vertex time to verx time plus one how + + + align:start position:0% +vertex time to verx time plus one how +many + + align:start position:0% +many + + + align:start position:0% +many +vertices V how many + + align:start position:0% +vertices V how many + + + align:start position:0% +vertices V how many +times okay so it's V * + + align:start position:0% +times okay so it's V * + + + align:start position:0% +times okay so it's V * +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +m because at each minute you can be at a + + align:start position:0% +m because at each minute you can be at a + + + align:start position:0% +m because at each minute you can be at a +certain city and decide to wait one more + + align:start position:0% +certain city and decide to wait one more + + + align:start position:0% +certain city and decide to wait one more +minute to stay in the same + + align:start position:0% + + + + align:start position:0% + +city okay does this make sense thank you + + align:start position:0% +city okay does this make sense thank you + + + align:start position:0% +city okay does this make sense thank you +guys I'm really happy we solved the hard + + align:start position:0% +guys I'm really happy we solved the hard + + + align:start position:0% +guys I'm really happy we solved the hard +problem that's good \ No newline at end of file diff --git a/moyD_yeviMY.txt b/moyD_yeviMY.txt new file mode 100644 index 0000000000000000000000000000000000000000..b08d8cfe574d9f28210166b0a233aaebbf160d87 --- /dev/null +++ b/moyD_yeviMY.txt @@ -0,0 +1,3785 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, starting again. + +I want to begin +with a quick review + +of what we said last time. + +This time will be +quicker than usual + +because we're not really +continuing from there, + +we'll be starting a +completely new topic today. + +But I thought I'd +remind you, nonetheless, + +that we had a last lecture-- +the universe was not + +created between then and now. + +And what we talked +about last time + +was the spacetime +geodesic equation, + +which is written this way. + +It's a completely +identical to the equation + +we derived for geodesics +in pure spatial situations. + +The only difference really, +is a difference in notation. + +Instead of using i +and j the tradition + +is to use mu, nu, et cetera +for the spacetime indices which + +are sum from 0 to 3, where +x super 0 is identical to t. + +And in addition, the parameter +which is sometimes called s + +when we're talking about +space, is called tau + +when we're talking +about time because what + +the parameter refers +to is the proper time + +along the trajectory of the +object whose geodesic we're + +calculating. + +We then introduced the +Schwarzschild metric, + +which we did not +derive, but we claimed + +it describes the metric for +any spherically symmetric mass + +distribution as long +as you're talking + +about the region outside +where the masses are located. + +And here M is the total +mass of the object, which + +is the only thing the +metric really depends on, + +G is Newton's constant, and C +is of course the speed of light. + +The metric has an +interesting feature + +that the coefficients +of both the dt + +squared term and to dr squared +term becomes singular either 0 + +or infinity, depending on +which one you're looking at, + +a particular value of the +radius called the Schwarzschild + +radius, given by this formula +2 GM divided by c squared. + +The bigger the mass the bigger +the Schwarzschild radius, + +they're proportional +to each other. + +The metric is singular +at those points, + +but I mentioned +but did not prove, + +that that particular +singularity is + +in fact what is referred to +as a coordinate singularity. + +It's a singularity that's +there only because of the way + +the coordinates were chosen. + +So there are other ways of +choosing the coordinates where + +that singularity disappears. + +There's also singularity +at r equals zero, + +and that singularity +is real, there's + +no way to remove +that singularity + +by a change of coordinates. + +However, although r sub s +is not a true singularity, + +it is a horizon. + +And by that we mean that if any +particle or even a light beam + +gets inside the Schwarzschild +radius, it can never get out. + +There's no geodesic which will +take it out of the horizon. + +And it's not even a +matter of geodesics, + +there are no +time-like paths even + +if you have a rocket which +would then not follow geodesic. + +There's no way to get out +from inside a black hole. + +We didn't show that, but +that fact is claimed. + +Then we calculated the geodesic +for our radially falling + +object. + +We solve the problem +of an object that + +is released from rest at +some initial value r sub 0, + +and just let fall straight +down towards the center + +of the sphere. + +And the the equation +describing the geodesic + +is just a special case +of the general equation + +that we had a few slides ago. + +And we need only look +at the radial component + +if we want to track how the +radius changes with time. + +So there was a free index +mu in the generic form + +of the equation, we're setting +mu equal to the r variable. + +And then the equation +reduces to this form + +and we know what these G sub +t t's and G sub r r's are, + +they come from the equation +for the Schwarzschild metric + +on the previous slide. + +And that equation +can be manipulated + +and eventually it simplifies +to something extraordinarily + +simple. + +It's just the statement that +d squared r d tau squared is + +equal to minus GM over r +squared, which looks exactly + +like the Newtonian equation +for something falling + +in a spherically symmetric +gravitational field. + +But it's not really +the same equation, + +it just looks like it's the same +equation, because the variables + +both a different +meanings. r and tau + +both have different meanings +from the r and t that + +would have appeared in +the Newtonian calculation. + +The r variable that +appears here is not really + +the distance from the origin. + +If you wanted to know the +distance from the origin + +you'd have to integrate +the metric singular even-- + +if not even a well defined +distance to the origin + +because the origin singular. + +And the tau that appears +here is a time variable, + +but it's not the time that would +be read on any fixed clock, + +rather it's the +time that would be + +read on the wristwatch +of the person falling + +into the spherically symmetric +object, which we might consider + +to be a black hole. + +And we were able to +solve this equation + +by using essentially +conservation of energy + +techniques, or at least what +would be called conservation + +of energy if we were doing +the Newtonian version + +of the problem, which is +the same equation even + +though the variables have +a different interpretation. + +So we were able to calculate +not r as a function of tau, + +but at least tau +a function of r. + +And we got that equation, +which is a little complicated, + +but the interesting +thing about it + +is that it gives finite answers +for every value of r going + +all the way down +to r equals zero. + +So it means that in a +finite amount of time, + +as seen by the person +falling into the black hole, + +the person would reach r +equals zero, at which point + +he would disappear +into the singularity. + +He'd actually be ripped +apart as he approached + +the singularity +because of tidal forces + +which pull more strongly +on the front part of him + +than on the back part of him, +stretching the object out + +in the radial direction. + +However, curiously, +if one calculates + +what this trajectory +looks like as a function + +of the coordinate time, +t, we did actually + +do that calculation +but we looked + +at how it would +behave in the limit + +as you approached-- as +the particle approached + +the Schwarzschild horizon. + +And we discovered it would take +an infinite amount of time, + +as seen from the outside, +for the in falling object + +to reach the horizon, let +go through the horizon + +and get to r equals zero. + +So from the outside, it +looks like the object never + +actually falls into +the black hole, + +but just gets closer and closer +and closer as t approaches + +infinity. + +So it's an example of a very +highly distorted spacetime, + +where you can see very +different pictures depending + +on which observer you're +trying to describe + +the observations of. + +And I think that's it. + +Any questions about any of that? + +I guess I'll put that back up. + +OK. + +On your homework you'll be +applying this geodesic equation + +to a model universe, to +Robertson-Walker universe, + +and this will serve only as an +example for those calculations. + +I guess there's also a homework +problem about the Schwarzschild + +metric, that orbits in +the Schwarzschild metric + +that you'll be working at. + +It's all in principal +straightforward + +if you just look at +equations and follow + +what the equations tell +you, thinking carefully + +about what the variables mean. + +OK. + +In that case, let's get +started on today's work, + +which is a change of gear. + +We're now going to be +talking about black body + +radiation and its +effect on the universe. + +I should say that +my original plan was + +to get into this set +of lectures notes-- + +lecture notes six, which have +not been handed out yet-- + +to get into those last time +and to finish them today. + +I don't think that's +going to be possible + +because I didn't get +into them last time, + +and I don't think I'll be +able to finish them today. + +But I would like today to be +sort of the closing for what's + +needed for the problem set +due Monday and for the quiz + +next week. + +So, shortly after +today's lecture + +I will send you an +email telling you + +where the cutoff is +as far as the reading + +and the lecture notes. + +And I also hope to post the +lecture notes by tomorrow. + +And I also will be posting +a set of review problems + +as we had for quiz one. + +And I hope to get +that done by tomorrow. + +You may have noticed that not +all of my hopes are filled, + +but I do my best, and I'll try. + +OK are there any logistic +questions or anything + +before we go on? + +Yes. + +AUDIENCE: Can you +post the solutions + +to the previous +problem set, the one + +that we turned in on Friday? + +PROFESSOR: Oh, um, +yes I can, I should. + +OK I will. + +OK, that's a third item I +should try to get done today. + +Thanks for reminding me. + +And the solutions +to the problem set + +that you'll be +handing in Monday will + +be posted very shortly +after you hand them in + +so that people can +start talking about them + +and prepare for the quiz. + +Yes. + +AUDIENCE: Do we have any day at +which the videos might be up? + +PROFESSOR: Ah, I've request +about that and all I was told + +was that they're +doing their best. + +So, I did look into it, but +I don't know the answer. + +I hope that you'll have all +the videos available to study + +for the quiz, but I don't +know if that's going to happen + +or not. + +OK. + +in that case, the new topic +is Blackbody Radiation + +and the Early History +of the Universe. + +So far we've dealt +with a universe which + +contains only +non-relativistic matter + +and that, as we said +from the beginning, + +describes our universe for +the bulk of its history. + +But in the early +period, the universe + +was in fact dominated +by radiation, + +as we will now be calculating. + +And in the more recent +period, the universe + +is dominated by +dark energy, which + +we'll be talking about +immediately after we + +finish talking about radiation. + +So the important point here is +that even though we don't think + +of light as having +mass, light certainly + +has energy and +relativistically we + +know that energy and +mass are equivalent. + +The key equation that actually +dominates today's lecture + +is perhaps the most +famous equation physics, + +E equals MC squared, energy +and mass are equivalent. + +And the numbers-- +I'll just give you + +some numbers for this equation. + +You've probably already +aware that the numbers + +are kind of out of sight. + +One kilogram, a point +to that equation, + +is equivalent to-- I don't +have any figures to give you-- + +8.9876, in case you really want +to know it accurately, times 10 + +to the 16th, most important +to know the exponent there, + +joules. + +And it's also perhaps +interesting to translate this + +into the kind of +energy units that + +are use when we talk +about power consumption + +in practical situations. + +It corresponds to 2.497 times +10 to the 10th kilowatt hours, + +which is a lot of +kilowatt hours. + +An interesting comparison, is +the total power consumption + +of the world, which +turns out to be + +comparable to a kilograms +worth of things. + +I looked things up +in the Wikipedia, + +and it told me that +in 2008-- which + +is the most recent year +it had numbers for, + +which is a little surprising, +that's so far in the past-- + +the total world +power consumption + +for the year equaled about, +I'm rounding off here, + +about 150 petawatt hours. + +Now, I always have to look +up peta when I see it, + +I haven't quite learned +what peta means yet. + +But they translated this, this +means 150 trillion kilowatt + +hours. + +So 150 times 10 to the +12th kilowatt hours. + +And if we divide this by the +number of hours in the year-- + +to ask how much +is per hour, which + +is I think a natural thing to +think about if you're using + +kilowatt hours to measure the +power, especially the energy-- + +the power that goes with +this is about 17 times 10 + +to the ninth kilowatts. + +And therefore 17 times 10 to +the 9th kilowatt hours per hour. + +And if you compare +these two numbers, + +it means that if you could +convert one kilogram per hour + +into pure energy, +that would be about + +equal to 1.5 times the +world's power usage in 2008. + +So if you could convert +matter completely to energy, + +as they do on Star +Trek, it would + +mean that you could +fill up your tank + +of your typical +American car and power + +the world for about two days. + +But of course we +can't undo this, + +that's the important +fact concerning power. + +Only a small +fraction of the mass + +of the uranium in +a nuclear reactor + +is actually converted as +power, a fraction of a percent. + +So you don't get +nearly as much power + +as this calculation +would indicate, + +but in principle +this much energy + +is contained in the matter that +we have around us all the time. + +OK. + +I want to introduce +a few formulas which + +we'll be using sooner +or later concerning + +the relativistic treatment +of momentum and energy, + +which is what we're +getting into here. + +And we're not trying to derive +relativity in this course, + +so I'm just trying to quote the +results that we'll be needing. + +So, it is useful to introduce +an energy momentum four-vector, + +which has a 0-th component +and an i-th component, + +where i refers to the +spatial indices 1, 2, and 3. + +And sometimes I might +write this as p zero p + +with a vector sign over it, +where the vector sign indicates + +the three components 1, 2, 3. + +The momentum here +is the momentum. + +It differs in its +relationship to velocity + +from what we have +from Newton, and I'll + +write that in a minute, +but this momentum + +is the conserved physical +momentum of an object. + +And p0 is also conserved. + +p0 is just an abbreviation +for the energy divided by C. + +And this quantity forms +a four dimensional + +vector in special relativity. + +And when we say that +it's a four-vector, + +we're actually making +a definite statement + +about how it transforms from +one Lorentz frame to another. + +a four-vector is +something which transforms + +in exactly the same way as x +super mu, four spatial and time + +coordinates transform. + +And in particular, +we learned that there + +was an invariant associated with +spacetime transformations this + +s squared, which was x squared +plus y squared plus z squared + +minus C squared t squared. + +And the same thing +will happen here. + +p squared, which means +the Lorentz invariant + +square of the four-vector is the +Lorentz [INAUDIBLE] again here, + +and it's again equal to the +sum of the squares of the 3 + +spatial components minus the +square of the time component. + +And that can be written out as +the square of the momentum-- + +spatial momentum-- minus +E squared C squared. + +And the claim is that this +is also Lorentz invariant. + +And we could figure out what +Lorentz invariant quantity + +it's equal to by +having knowledge + +that this is the +same in all frames. + +We can evaluate it in +the simplest frame. + +And the simplest frame would be +the rest frame of the object. + +In the rest frame of the +object the p would be zero + +and this would then just be +minus E squared over C squared. + +E squared would be M +squared C to the fourth, + +so that implies that this is +equal to minus M0 C squared + +squared where M0 is often +called the rest mass. + +And when I say it's often called +the the rest mass, what I mean + +is that nobody ever +mistakes the word "rest + +mass" to mean anything else, +if anybody says "rest mass," + +and he knows what he's +talking about, he means this. + +But this is often sometimes +just called the mass + +because sometimes people +only talk about masses + +as being rest masses. + +But I'll try to +call this the rest + +mass because I will use the +word mass in other ways. + +We could also relate this +momentum to the velocity, + +and in doing that we will again +encounter this factor of gamma + +that we found +kinematically earlier. + +AUDIENCE: Yes, question. + +Did you forget to divide +by C squared there? + +PROFESSOR: Um, yes. + +There's too many C's here. + +Absolutely. + +It should have +units of momentum. + +So it should have units of +mass times velocity squared. + +Thank you. + +Thank you. + +So, the quantity gamma, +is the same quantity + +we encounter at the +beginning of the course + +when we talked about +time dilation and Lorentz + +contraction, it just depends +on the velocity and approaches + +infinity as the velocity +approaches the speed of light. + +And the physical momentum of +a particle, relativistically + +is equal to gamma +times M sub 0 times V. + +Where V is the ordinary +velocity-- this + +is special relativity, +we're not concerned + +with coordinate velocity +versus physical velocity yet-- + +and gamma is that factor. + +So the momentum is larger than +what you would get a la Newton. + +The energy can also +be written down. + +And this formula +is one expression + +we can use to find the energy +in terms of the momentum. + +The energy in terms +of the momentum + +is M0 C squared squared +plus p squared C squared. + +And it also can be written +in terms of the velocity + +as just gamma times M0 C squared +where the velocity appears + +in the gamma. + +And a special case of this is +when the particle is at rest. + +Might as well write this, the +energy of a particle at rest, + +which we might call E0, is just +M0 C squared, which gets us + +back to where we started +with E equals MC squared. + +Now, I might just +say a quick word + +about where these formulas come +from, what idea underlies them. + +I'm not going to +make any attempt + +to derive them because +we just don't have time. + +It'd be easy to drive them, +but we want to do other things. + +But logically, +where they come from + +is simply the observation, +by Einstein originally, + +that if one has the Lorentz +transformations relating + +what one inertial observer sees +to another inertial observer, + +if one used those +transformations but used + +the Newtonian definitions +of energy and momentum, + +then you would find immediately +that if energy and momentum + +were conserved in one frame you +then know how to calculate what + +happens in other frames by +using the transformations, + +you'd find it would not +be conserved other frames. + +So if the conservation +of energy and momentum + +are to be a universal principle +of physics, which Einstein + +wanted to maintain, it would +be necessary to redefine + +energy and momentum. + +Now they're defined in +ways so that they approach + +the Newtonian values +for small velocities, + +but for velocities of the +order of the speed of light + +they're different. + +And they have the property-- +not completely obvious from what + +we wrote, well it is actually +completely obvious from what + +we wrote-- they +have the property + +that if it's +conserved in on frame, + +it's conserved in all frames. + +And what makes it +obvious-- maybe + +the connections between +these different formulas + +are not obvious-- +but I did tell you + +that p super mu transforms +as a four-vector, + +meaning it transforms the same +way as x super mu transforms, + +which are linear +transformations. + +And that's enough to guarantee +that if p mu is conserved + +in one frame, it has to +be conserved in all frames + +because delta p mu, +the change in p mu, + +would also be a four-vector, +and if a four-vector vanishes + +in one frame, it +vanishes in all frames. + +OK. + +Well I wanted to give you +sort of a quick example of how + +this works in practice. + +So I to just talk about the +energetics of a hydrogen atom. + +A hydrogen atom +consists of a proton, + +with a mass that we'll call +M sub p, and an electron, + +with the mass that +we'll call M sub + +E. And, as, if you imagine +starting with the electron + +and proton arbitrarily far +apart and bring them together, + +what you can discover +experimentally-- of if you know + +quantum mechanics +you can calculate + +theoretically-- +energy is released, + +because you're releasing +potential energy as you + +bring the electron +into the atom. + +And the amount of +energy released + +is 13.6 electron volts. + +And the important +E equals MC squared + +implication which I +want to point out here + +is that loss of energy. + +This energy would be +extracted from the system + +as you made the hydrogen atom. + +The fact that you've extracted +energy from the system + +means that now the system +should have less energy + +than it had to start with. + +Initially it had the +rest energy of the proton + +and the rest of electronic, M +sub p C squared and M sub E C + +squared. + +Now it has less +energy by delta E, + +and that means it also +has to have less mass. + +So the mass of a +hydrogen atom is not + +the sum of the mass of +the proton and electron, + +as it would be in +Newtonian mechanics, + +but is less by an +amount proportional + +to this energy given off, +delta E, 13.6 electron volts. + +And just putting in +the C squares in I + +hope the right places, the +mass of a hydrogen atom + +will be equal to +the mass of a proton + +plus the mass of an +electron, but then + +minus the binding energy +expressed in mass units-- delta + +E over C squared. + +OK. + +So I guess, just +probably one more topic + +I want to talk about in terms of +just basic special relativity, + +and this actually get's +into general relativity. + +I wanted to find the +relativistic mass + +of any system just being its +energy divided by C squared. + +And this means that the +relativistic mass of a particle + +increases with its velocity. + +The energy of a +single moving particle + +is gamma times M0 C squared. + +That would say the +by this definition + +the relativistic mass of that +particle is gamma times M0. + +And I might mention that this +concept of relativistic mass + +is disparaged in many books +on special relativity. + +It's certainly a concept +that you can do without, + +so people who emotionally +are bothered by it + +can get along without +it because it is just + +the energy divided by C squared. + +And in fact a lot of work +in special relativity + +is done in units +where C is equal to 1 + +and then it is just the energy. + +Especially if you +use C equals 1 you + +could dispense with this +concept of relativistic mass. + +We're not going to +be using C equals 1, + +so the phrase +relativistic mass will + +allow us to abbreviate +E divided by E + +squared in a convenient way. + +But the important thing +is not the definitions, + +the important thing +is what properties + +does this relativistic +mass have, + +whether or not one chooses +to call it relativistic mass + +or E divided by C squared. + +And it as an important +property concerning + +the gravitational field +created by matter. + +Now the gravitational field +of a single moving object + +is complicated. + +If we were talking +about, say, a moving star + +that was moving at a +velocity large enough + +so we care about relativity, the +way we calculate that actually + +as we start with the +Schwarzschild metric, which + +will describe the metric of +the star outside of the matter + +if it were stationary. + +And then you can just +make a transformation + +to a moving frame. + +You're allowed to +use any coordinates + +you want in general +relativity, so transforming + +to coordinates that describe +the moving frame is no problem. + +But it distorts the field in a +complicated way, nonetheless, + +a way that you can deal with. + +And what you find, of +course, is that what + +you get would be asymmetric +once you transform to the moving + +frame, it would show the +signs of the velocity + +that you used to transform +from the original spherically + +symmetric Schwarzschild +metric to the new frame. + +So the bottom line is that the +gravitational field of a moving + +object is not isotropic, it's +more complicated than that, + +just as the electric +field would be. + +But if we have a +gas of particles, + +which is pretty much what we +have in the early universe. + +If we have a gas of particles +in a box moving every which way, + +then if we thought of this +box as being an object + +that we're only going to +look at from the outside-- + +a black box in the +classic use of the phrase + +black box-- the mass +of the black box + +really would just be the sum +of the relativistic masses + +of the particles. + +And the isotropy of the metric +that any one particle would + +generate would be canceled +by averaging or summing + +over all the particles going +every which direction, because + +on average the velocity of +particles inside the box is 0. + +So this relativistic mass, when +you're talking about a gas, + +really is the mass per particle. + +And if you divide +that by the volume + +really you do get +the mass density, + +which is a relevant +mass density in terms + +of talking about how +this matter would + +generate gravitational fields. + +Yes. + +AUDIENCE: So why +do some people have + +emotional problems with it? + +PROFESSOR: I think some people +have emotional problems with it + +because when one thinks +about pedagogy in a course, + +for example, one worries +about people confusing it + +with the rest mass. + +I think that's the reason. + +And I guess there are other +possible sources of confusion, + +so your question is a good one. + +Another source of confusion +is that this mass does not + +fit into an F +equals ma equation. + +So in calling this +the mass you might + +suggest to students who aren't +paying attention to every word + +that you say, you might +go ahead and put F equals + +ma for this mass, +that does not work. + +So it has some of the +properties of a mass, + +but not-- by no +means all of them. + +But in particular +for us is important + +because we're going to be +interested in the gravitational + +field of a gas +and then it really + +is the mass that +determines that. + +In the more formal language +in general relativity, + +it's the mass-- it's +the energy density, that + +appears in the equations that +produce gravitational fields, + +and then this really +is the energy density + +except for a factor +of C squared. + +OK, any questions? + +Because now I'm going +to leave this formalism + +and get into what role +this radiation could + +play in the early universe. + +So now I'd like to talk about +radiation in particular, + +and for now I mean +electromagnetic radiation + +just ordinary photons. + +And we're not accustomed +to thinking of light + +as having mass, +but we know light + +has energy and energy is +related to mass by a factor of C + +squared. + +So we can write down +the formula that + +says that rho is equal to +u divided by C squared. + +Where u is the +energy density, which + +we know electromagnetic +fields have. + +And rho will be the mass +density of radiation. + +Now, photons have +zero rest mass, + +so if we apply for example +this formula for a photon + +we would set M sub 0 equal to 0. + +And we said that photons +have zero rest mass what + +we mean is that +there's no lower limit + +to the energy a photon can have. + +In general, the +rest mass determines + +the lowest possible energy +a particle could have, + +which is when it's at rest. + +Photon can never +be rest and there's + +no lower limit to what +its energy can be. + +So for photons, M0 is +equal to 0 and that + +implies that the +energy of the photon + +is just C times the +magnitude of its momentum. + +And this formula one can derive +just for electromagnetic waves + +is purely classical +EM-- you don't + +have to be talking +about photons, + +but since it's true for a +classical electromagnetic wave + +it had better also be true +for photons because we think + +of this classical +electromagnetic waves + +as really being +made out of photons. + +So the energy that +exists in the universe + +in the form of +electromagnetic radiation + +will have an energy density, +which we know how to calculate. + +And we know to calculate the +momentum of any given photon. + +Now that will average +to zero, but nonetheless + +if we imagine talking about +a box of photons, which + +are bouncing off +the walls, the fact + +that each photon +carries momentum + +means that there will be +a pressure on the walls. + +And we will be interested +in that pressure, + +we'll be calculating a +formula for it in a minute. + +So, what we now +want to talk about + +is what happens when we put a +photon gas into the universe + +and allow the +universe to expand. + +What happens to the +radiation energy density, + +or equivalently mass density, +as the universe expands? + +This turns out to be +a very easy question + +to answer if we +think of the energy + +as being made out of photons. + +We would get an equivalent +identical answer + +if we use classical +Maxwell's equations + +and talked about how +energy density is + +a [INAUDIBLE] of +electromagnetic fields behaved. + +It would be more work +actually do it that way, + +but we would get +the same answer. + +In terms of photos, +we could simply + +notice that the number +density of photons-- photons + +are not going to disappear +as the universe expands, + +the number density +will just keep + +the same number of photons, +but as the universe expands + +those photons will +occupy a larger volume. + +So it's exactly +the same as what we + +said about +non-relativistic matter, + +the number density of +photons will fall like 1 + +over the cube of the +scale factor, which just + +says that photons are conserved. + +And the volume of any +region grows like a cubed. + +I should also mention +that I'm using gamma here. + +Gamma of course also +sometimes meant 1 + +over the square-root of 1 +minus V squared over C squared, + +but besides that +use, gamma is also + +just a label that means photons. + +It comes from the +idea of gamma rays, + +but it's actually +used in this context + +for any kind of a +photon no matter + +what its frequency +is, whether it's + +a gamma ray or an x-ray or +visible light, or infrared. + +Yes. + +AUDIENCE: Is this +assumed for time average? + +Because photons can +be absorbed, right? + +I mean, at least like +in a small [? slice ?] + +can't there be a decided +non-relativistic matter? + +PROFESSOR: Is this +true on the--? + +Well, the validity of +this formula-- you're + +right this formula's not +exact, photons can be absorbed. + +But in terms of what happens +as the universe evolves, + +that's a very, very, +very minor process, + +especially when we're talking +about the early universe + +when there isn't really +anything around to absorb them. + +So, especially for the early +universe and even pretty well + +today, if we're talking +about the cosmic background + +radiation, which is the +bulk of the photons, + +this formula's a very +good approximation. + +Yes. + +AUDIENCE: Even though the +photons in the early universe + +created a lot of +massive particles, + +[INAUDIBLE] didn't that +affect the expansion? + +PROFESSOR: Are you're +asking, will the photons + +be important if there's a +lot of mass of particles? + +Is that your question? + +AUDIENCE: Would the +photons, won't they + +decay into matter antimatter? + +PROFESSOR: Will the photon +decay into matter antimatter? + +No, not really. + +It is, in principle, +possible for two photons + +to collide and produce an +electron positron pair. + +It's actually a rather small +cross section for that. + +And all of these processes +in the early universe + +will rapidly reach +an equilibrium, + +which we'll be talking about +more a little later, where + +there'll be just as many +photons converting into E plus E + +minus pairs as there will be +E plus E minus pairs colliding + +and making photons. + +So the early universe is +assumed to reach equilibrium + +very quickly, and all the +description we'll be giving + +will be a description +of the universe that's + +in thermal equilibrium +with these processes will + +tend to iron out. + +We will learn that +they don't always + +cancel each other because +the universe is cooling, + +and that means it can't be +exactly in thermal equilibrium. + +And there are some cases where +the effect of that cooling + +is significant and we'll +be talking about those. + +But for the most part, +if the cooling is slow, + +which it is for the most part +compared to other processes, + +everything stays in +thermal equilibrium. + +OK. + +Those are good questions. + +We've gotten a little ahead of +what I wanted to talk about. + +So for now I'm just +imagining a free photon gas, + +which is an excellent +approximation + +for the early universe. + +And those photons +just continue to exist + +as the universe expands, +so their number density + +falls off as 1 over a cubed. + +But there's another +affect that goes + +on which is that the +photons are redshifting. + +And we already know +about that, but now we're + +going to take it into account +in terms of the energy balances. + +So we know that the frequency +of a photon at some time t2 + +divide by its frequency +at some time t1, + +and here nu equals +frequency, is just + +diluted by the expansion +of the universe. + +This ratio is 1 +over 1 plus z, where + +z is the redshift +between these two times. + +But written out in +more detail which + +is a formula we'll +actually be using, + +is just a of t1 +divided by a of t2. + +When the scale factor doubles, +all the frequency is half. + +And that means that all +the photons are lowering + +in frequency, and we also know +that photons are quantized. + +The energy of a photon +can't be any old thing, + +but in fact, the energy of a +photon is equal to h times nu. + +Where little h is what's +called Planck's constant. + +And numerically there +are various units + +you could express it +in, but it's 4.136 times + +10 to the minus 15th +electron volt seconds. + +So if you measure a +frequency an inverse seconds, + +you get an energy in electron +volts from that formula. + +The important thing +for now though is + +that this says that the +energy of each photon-- being + +proportional to its frequency, +and the frequency being + +proportional to 1 over +the scale factor-- + +the energy of each photons is +proportional to 1 over a of t. + +And then the total +energy density + +of photons in +photon on gas which + +I'll call u sub gamma, the +energy density of the gas, + +can be thought of as the +number density of photons + +times the energy of each photon. + +And the number +density is falling off + +like 1 over a cubed, the energy +is falling off like 1 over a. + +And therefore, this +is proportional to 1 + +over a to the fourth. + +So as the universe +expands, the density + +of non-relativistic matter +falls off like 1 over a cubed-- + +as we've been talking +about some time now-- + +but the energy of +radiation falls off faster, + +like 1 over a to +the fourth because + +of the red shifting +of the photons. + +OK, now once we know +this, we can ask ourselves + +what happens if we look at +our universe going backwards, + +knowing where we are +now where we come from? + +And if the energy +density of photons + +is falling off faster than +the energy density of matter, + +it would mean that the +ratio is getting smaller + +as we go forward in time. + +But that of course +implies that the ratio + +gets larger as we go +backwards in time. + +So as we go backwards +in time, the radiation + +becomes more and more +important, and there actually + +is going to be a time when the +radiation will equal the matter + +and at earlier times the +radiation will dominate. + +Today I'll just give +you a number for now, + +we'll learn later +how to calculate it, + +but for today the +total radiation energy + +density in the universe +is equal to 7.01 times 10 + +to the minus 14 joules +per meter cubed. + +And this actually includes +two kinds of radiation, + +it includes photons +and also neutrinos, + +which at least in +the early universe + +behaved just like radiation. + +And we'll be talking more about +neutrinos later so don't worry + +if you don't have any +idea what a neutrino is. + +But for now it's just another +contribution to the radiation, + +and we can measure +basically this is all + +based on measuring +the temperature + +of the cosmic microwave +background radiation-- + +and we'll learn later how +to make that conversion. + +But once you measure +the temperature + +of the cosmic +background radiation + +and have a theory about how +many neutrinos there should be, + +that's actually all +theoretical and we'll + +talk about that later as well. + +One can determine +what the energy + +density of that radiation is. + +And it corresponds to a mass +density just dividing by C + +squared of 7.80 times 10 to the +minus 31 kilograms per meter + +cubed. + +And when I think +of mass densities + +I always like to think of in +centimeters per-- excuse me, + +grams per centimeter +cubed because I'm + +used to the density of water +being one gram per centimeter + +cubed and I like to be able +to make that comparison. + +So just making that conversion, +usually I use SI units, + +but some things just seem to +make more sense in other units. + +So it's 10 to the minus 34 +grams per centimeter cubed, + +so 10 to the minus 34, or +maybe 10 to the minus 33, + +times the density of water. + +And this is incredibly +low even compared + +to the critical density +of our universe, + +and the actual +density we know is + +very near this critical density. + +Let me remind you that +the critical density + +we derived a formula for, +and when we put numbers + +into that formula +we found that was + +equal to 1.88 times +little h0 squared, + +which is Hubble's units-- +Hubble's constant in units + +of 100 kilometers per +second per megaparsec-- + +I'll write that in +a second-- times 10 + +to the minus 29 grams +per centimeter cubed. + +So just writing down the +equation for little h sub 0 + +is where capital H sub 0, +Hubble's expansion rate, + +is equal to 100 +times little h sub 0 + +kilometers per second +per megaparsec. + +Yep. + +AUDIENCE: What's +the, I guess, what's + +the motivation of +normalizing the Hubble + +constant in this way? + +PROFESSOR: Well, I think +the real motivation is + +that the astronomers like these +peculiar units of kilometers + +per second per megaparsec, but +if your favorite unit is called + +a kilometer per +second per megaparsec + +you don't want to have to +say those units very often. + +So H0 is dimensionless, so +it's a dimensionless way + +of talking about +the Hubble constant. + +But that's the only +importance, there's + +no real-- no deep +significance to it. + +But it's a standard notation, +so it's worth knowing. + +And then finally, +we can write down + +how much the radiation +contributes to omega-- omega + +sub r, r is going to +indicate radiation. + +The notation, by +the way, will be-- + +and I realized I've already +violated that notation. + +This really should have been r. + +Well, I'm not going to change +it, it'll get too messy. + +But I'm going to start using the +notation where gamma indicates + +photons and little r +indicates radiation. + +And the difference is that there +are other kinds of radiation + +besides photons, in +particular we've already + +added in neutrinos in part of +what we're calling radiation. + +So omega sub r, which now +includes photons and neutrinos, + +is just defined to be the +mass density radiation divided + +by the critical density. + +And that turns out, when +you combine these numbers, + +to be 4.15 times 10 to the minus +5 little h0 to the minus 2. + +And then for h0 equals 0.67, +which is the Planck satellite + +value for little +h0, we finally get + +omega sub r is equal to 9.2 +times 10 to the minus 5. + +So roughly 10 to the minus 4. + +The fraction of the mass +density, or energy density + +today is about 10 to the minus +4 fraction and radiation. + +And actually as I write +this, this actually + +calls to mind another reason for +defining little h sub 0, which + +is that if you write formulas +in terms of little h sub 0, + +they remain valid between +one year and next year. + +The observational value +of the Hubble parameter + +is still floating +around and differs, + +for example, every time +I teach this course. + +So the formulas in +terms of little h sub 0 + +stay, and then you plug in the +current value of little h sub 0 + +to get the best value that +one can currently write down. + +Now we know the Hubble constant +to within a few percent, which + +is much better than it used to +be, but it's still floating. + +The Planck value was somewhat +lower than the previous except + +a value, which was about 0.70. + +OK. + +So we know enough information +to extrapolate backwards + +and calculate when +this radiation would've + +equaled the energy +density of matter. + +Because we know how +the ratio changes. + +It changes by a factor +of a, the scale factor, + +because the energy density +of non-relativistic matter + +is falling off like +1 over a cubed. + +The energy density of +radiation is flowing off like 1 + +over a to the fourth. + +So the ratio between +them just changes + +by a factor of a, +decreasing as a gets larger. + +So we can write RHO radiation +of t divided by RHO matter of t. + +The m there means +non-relativistic matter. + +This is just equal +to the current value. + +And the current value is +gotten by taking that number + +and, where I forgot to write +down is that omega matter today + +is about 0.30. + +So the ratio of the two, omega +radiation over omega matter, + +which is the same as RHO +radiation over RHO matter, + +is about 3.1 times +10 to the minus 4. + +And that number is about +to appear in this equation. + +If we want the ratio +as a function of time, + +we start with this value today, +3.1 times 10 to the minus 4, + +and then we can just multiply +that by the scale factor + +today divided by the +scale factor at the time + +that we want to know it, because +we know it falls off as 1 + +over the scale factor. + +And by putting an a +of t0 here, this just + +guarantees that if +we let t equal t0, + +we get this number, which is +the right ratio for today. + +OK. + +Now it's just a +matter of arithmetic. + +We also know that for a +matter-dominated universe. + +And for now, we're going to +estimate when the radiation + +energy will equal +the matter density. + +This will only be an estimate. + +We're going to +estimate it by assuming + +that we can approximate the +universe as matter dominated + +between now, all the way +back until that time. + +There are two errors +in that calculation. + +We're not taking into account +here the era of acceleration + +where dark energy is +playing a significant role. + +We'll learn later +how to do that. + +And also, as we approach +this time when they're + +making equal contributions, +we will run into a regime + +where the contribution +of the radiation + +itself will be relevant. + +So this is only an estimate. + +But what we're +going to do is we're + +going to assume that +we can treat this + +as a matter-dominated universe +with a of t proportional + +to the 2/3. + +And then we can plug +numbers into this formula + +and ask, when was the ratio 1? + +And when the ratio +was 1, we call + +that the time of equality, using +the subscript EQ for equality + +to indicate anything having to +do with that crossing point. + +And what we find is +that the z of equality, + +and z is just the ratio +of the a's, is-- according + +to this calculation, it +would be 3.1 times 10 + +to the minus 4 minus 1. + +I fibbed when I said that +z is the ratio of the a's. + +It's offset by a little bit. + +It's 1 plus z that's +the ratio of the a's. + +And that's why there's +a minus 1 there. + +And numerically, this is +about equal to 32,000. + +So if we look back in the +history of the universe, + +we can define looking back +in terms of the redshift. + +If you look back to a redshift +of 3,200, we get to the time + +when matter and radiation +had the same energy density. + +And we can know what time +that is if we assume t + +to the 2/3, which again is +only a crude approximation. + +We don't necessarily expect +to get the right answer here. + +But we expect to get the +right order of magnitude. + +So t-equality, according +to this situation, + +would be about 75,000 years +after the Big Bang-- just + +converting the scale +factor that we just + +calculated to a time using that +formula, treating this as t + +to the 2/3. + +So this says that about +75,000 years after the Big + +Bang, the energy densities +of matter and radiation + +were equal. + +In the earlier +times, the universe + +was radiation dominated. + +The radiation exceeded the +matter in its energy density. + +Yes? + +AUDIENCE: It seems like +zEQ is relatively about 31 + +[INAUDIBLE]. + +PROFESSOR: You might be +right if we would just + +look to these formulas. + +When I calculated +this at home, I + +kept more decimal +places all the way + +and rounded off each answer +to one significant figure. + +And that's not the same as +taking the answer to one + +significant figure +and calculating + +and then rounding off +to ones in every figure. + +So I think there's always an +ambiguity of, roughly speaking, + +1 in the last decimal +place whenever + +you're rounding numbers off. + +AUDIENCE: So we just +plug that [INAUDIBLE] + +PROFESSOR: 3,220-- +starting with this + +or starting with a more +accurate number than the 3.1. + +AUDIENCE: Just 1/3.1. + +PROFESSOR: 1/3.1. + +OK. + +So, OK? + +AUDIENCE: Sorry. + +AUDIENCE: Wait no, +[INAUDIBLE] like we have 1 + +over 3 times 10 negative 4. + +That's 3 times 10-- + +PROFESSOR: It's 3.1. + +AUDIENCE: You have 1 over 3.1. + +PROFESSOR: 1 over 3.1. + +So you have to divide. + +AUDIENCE:I do that all the time. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: So apparently +it's even right + +if you just calculate with that. + +But there is actually +some ambiguity. + +The numbers I'm +giving you probably + +have some uncertainty +of 1 in the last digit, + +depending on how you calculate. + +But the number they +give you, I think + +they're the ones that +you get if you start + +using this and the 0.67 and +from then on do everything + +to large numbers +in decimal places + +and round off at each stage. + +You'll get the numbers +I've given you. + +In any case, all these +are really, at best, + +order of magnitude estimates. + +So worrying about whether or +not the last figure is accurate + +is not a big deal. + +Yes? + +AUDIENCE: I don't +really understand + +how you got t [INAUDIBLE] +without telling was a of t dot + +is [INAUDIBLE]. + +PROFESSOR: I'm sorry. + +There is actually a +piece of information + +I used I forgot to write here. + +You're absolutely right. + +I used t0 is equal to 13.8 +times 10 to the nine years. + +And then everything +can be related to t0 + +if you know how things +are proportional to t. + +You're absolute right. + +I did not give you +all the information + +necessary for that calculation. + +Now I think I have. + +I haven't done the +arithmetic for you. + +But otherwise it's all there. + +OK. + +Now I might mention +that in Ryden's book, + +she does the calculation taking +into account everything-- + +matter, radiation, +cosmological constants. + +And her number for +t-equality is 47,000 years, + +which verifies that we have +the right order of magnitude. + +And actually, the +biggest difference + +between her number +and my number is not + +that she's taken into account +these more sophisticated + +things, but rather that +she used a different value + +for the Hubble expansion +rate than I'm using. + +She's using a value that was +current at the time she wrote + +her book, which was +like '72, I think. + +h0 equals 0.72 instead +of [INAUDIBLE] 0.67. + +And that does make a +significant difference here. + +But either of these numbers +are, I think, probably + +within the range of uncertainty +of when it really happened. + +But it's on that scale, on the +scale of 50,000 years, 100,000 + +years, something of that order. + +So there was a +significantly long period + +compared to human lifetime +when the universe was + +radiation dominated. + +But it's a very small fraction +of the overall history + +of the universe, +but nonetheless does + +have important features that +happened during that time + +period. + +Now, if we want to +understand those features, + +we have to understand how a +radiation-dominated universe + +evolves, which is what +we're going to get to next. + +OK. + +The next little +chapter than I'm going + +to be talking +about-- the dynamics + +of a radiation-dominated +universe. + +This is a chapter +that you more or less + +get to work out the +equations for yourself + +on one of the homework problems. + +That's part of this week's set. + +So I will try here +to outline the logic. + +But because all the calculations +are in the homework, + +I will basically skip the +calculations themselves, + +and let you do +them for yourselves + +as part of the homework. + +But where we start is we have +written down Friedman equations + +for the matter-dominated case. + +And I'll start by reminding +us what those were. + +And then in addition to +these two equations, which + +describe our expanding universe, +which we've derived sometime + +ago for-- and to +remind us here, this + +is for a matter-dominated +universe. + +And matter-dominated means +non-relativistic matter + +dominated. + +And going along with +these equations, + +we also know that RHO of t +for non-relativistic matter + +falls off like one +over a cubed of t. + +This can be converted into a +differential equation for RHO. + +That is, we can calculate +Rho dot from this equation. + +And the way to see that +is probably most easily + +to start on a new blackboard +and write that equation not as + +a proportionality, since +it's hard to differentiate + +a proportionality, +but we can write it + +in an arbitrary constant +of proportionality. + +And then it becomes an equality. + +So I'm going to write +the equation as RHO of t + +is equal to some constant, +b, divided by a cubed of t. + +And this we know how +to differentiate. + +We can write Rho dot is +equal to minus b over a + +to the fourth of t times a dot. + +And that is equal to minus 3. + +I'm sorry--there's a 3 here. + +Minus 3 times a dot over +a times the original RHO. + +So we can forget the +intermediate steps, + +and we just arrived +at the equation + +that RHO dot is equal to minus +3 a dot over a times RHO. + +And we can think of +that as going along + +with equations one and two. + +Maybe I'll even +give that a number. + +Equation three +will be RHO dot is + +equal to minus 3 a +dot over a times RHO. + +Now for radiation, +there will be a 4 here. + +The 4 will arrive the same +way as the 3 arrives there. + +It's just the power that +appeared in the factor of a. + +So for radiation, this +last formula we know + +is going to be modified, +which is the key point. + +Note that these three +formulas are not + +independent of each other. + +If we know, for example, +equation one, which + +is an equation for +a dot, we could + +differentiate that +with respect to time + +and get an equation +for a double dot. + +When we do that, everything +has to be differentiated. + +So it involves +differentiating a, + +but that just expresses things +in terms of derivatives of a. + +But the new quantity that +gets introduced is RHO. + +If we wanted to differentiate +this equation with respect + +to time, we have to +know what RHO dot is. + +But we do. + +That's what equation +three tells us. + +So we can differentiate equation +one, use equation three, + +and we can derive an +equation for a double dot. + +And if these equations +are consistent, + +it'd better be equation two. + +And it will be. + +You can check it. + +And actually, I think any +two of these equations + +can be used to derive the third. + +Those equations +just are-- really + +a set of two +independent equations + +and one dependent equation. + +You can shuffle it +any way you want. + +But, now what we want +to do is to consider + +a different kind of matter. + +Instead of +non-relativistic matter, + +we're considering photon matter. + +And in particular, +we know that it's + +going to change equation three. + +So for radiation, +3 gets modified + +into 3 prime, which +is the equation that + +says that RHO dot is equal to +minus 4 a dot over a times RHO. + +So how are we going to +fix these equations? + +Now they're inconsistent. + +If we change three and don't +change either one or two, + +we know that we're +inconsistent, because any two + +of those equations can be +used to derive the third. + +So we're in trouble. + +Either equations +one or two will also + +have to be modified if we're +going to modify equation three. + +OK. + +Before we go on, I'd like to +say a little more about why + +this equation is different +from that equation. + +One might think +that it should just + +be governed by the +conservation of energy. + +After all, we just +write down an equation + +for RHO dot-- how energy +density changes with time. + +Shouldn't conservation +of energy determine that? + +It does. + +But there is an extra element +to conservation of energy + +that we need to +take into account, + +and that is the pressure +of the gas affects + +what happens to its +energy as it expands. + +So before we get back +to the early universe, + +I just want to consider a +gas in a piston chamber. + +And I'm going to let the piston +have an area a, and inside + +we're going to have a volume +v. Just to define our notation. + +If we have a gas +inside a piston chamber + +and let the piston chamber +enlarge by pulling out + +on the piston, the gas has +a pressure, in general, + +and that pressure will +exert a force on the piston. + +So if I allow the piston +to move to the right, + +that gas will be +exerting a force + +on the piston in the +direction that it's moving. + +And that means the gas will +be doing work on the piston. + +So, by our ordinary notions +of Newtonian conservation + +of energy, we would know that +the gas would lose energy, + +and we can even calculate +how much energy it loses. + +And the formula is easy enough +to get in a Newtonian context. + +It's just du is equal +to minus the pressure + +of the gas times the +change in volume. + +A famous formula. + +And this just comes +about by saying + +that the work that's done is +the force times the distance. + +The force is the +pressure times the area. + +And the volume is the +area times the distance. + +And putting those +things together, + +you get this +formula immediately. + +Now this formula is +actually much more general + +than the quasi derivation +that I just showed. + +It works no matter what +the shape of the gas is. + +If you put a gas in +any kind of a container + +and let that container enlarge, +even in an irregular way, + +the work that the gas +will do will always + +be equal to minus the +pressure of the gas + +times the change in the volume. + +We can apply this to +the early universe. + +It actually works. + +The difference +between our two cases + +is that our non-relativistic +matter has no pressure at all. + +We're just talking about +particles sitting at rest. + +They're not bouncing +off of any walls. + +They're not creating +any pressure, + +while the photons are +moving around all the time. + +And if you imagine +a box of them, + +they'd be hitting against +the walls of that box, + +exerting a pressure. + +And we're now in a position +to relate the pressure + +to the difference between +the 3's and the 4's that + +appear in those two equations +for RHO dot in the two cases. + +To apply this naive idea +to a piece of the universe, + +we can imagine choosing-- we're +going to choose some fixed + +volume in our co-moving +coordinate system. + +So our box, the volume +that we're talking about + +will actually be expanding +with the universe + +but be fixed in +co-moving coordinates. + +And the physical volume +therefore of our box + +will be a cubed of t times +the coordinate volume + +of the box-- the volume +and not just cubed. + +And this volume will +be independent of time. + +There's time dependents there. + +There's time dependents there. + +The physical volume of +our box will be enlarging. + +The total energy in our +box, the total gas energy, + +which I'll call +capital U, will just + +be the physical volume +times the energy density. + +The energy density is +energy per physical volume. + +And we can now +apply this formula + +using this U and this v. + +And here again is one +of these cases where + +I'm going to be skipping +steps because you're + +going to be doing it in +detail on the homework. + +But by putting these +equations together, + +what you'll find is that d dt +of a cubed times RHO times c + +squared-- this is just d dt +of a cubed times the energy + +density-- basically, +the left hand side + +of that equation divided by dt +and divided by v coordinates-- + +is equal to minus p +times d dt of a cubed. + +And this is just the PDV +term from the right hand side + +of that equation rewritten +in terms of the variables. + +And you'll be doing +this for homework. + +I'm just getting +straight the factors + +to make sure I have them right. + +OK. + +Reshuffling that +equation-- and again, this + +is a homework problem-- +you can turn that + +into an equation for RHO dot. + +And what you'll get +is minus 3 a dot + +over a times RHO plus +p over c squared. + +And now we can see how +our two cases emerge. + +If the pressure is 0, +we get minus 3 a dot + +over 8 times RHO, +which is what we + +had for non-relativistic matter. + +And the photon gas is +going to have a pressure, + +and we could read +off from this formula + +to know what the pressure has +to be to turn the 3 into a 4. + +The pressure has to be +a factor of a third. + +So you determine for this +that the pressure for light + +is 1/3 of the energy density, +or 1/3 times RHO c squared. + +And that's what you need +to turn the 3 into a 4. + +So we now have indirectly +calculated the pressure + +of light, and this agrees +with any other calculation + +for the pressure of +light that you might do. + +It's by no means the +only way to calculate it. + +And now finally, +we're in a position-- + +and we'll just do +this quickly to decide + +how to modify these equations. + +Now, we're not in a position +to determine that rigorously. + +It can be determined rigorously +by doing general relativity, + +which we're not +doing at that level. + +But we can still +motivate the answer. + +One of these two +equations is going + +to have to be changed +to accommodate + +a more general +expression for RHO dot. + +The top equation +we know is really + +an equation for +conservation of energy. + +That's how we got it +in the Newtonian case + +where little k ended up +being partial to the energy + +in the Newtonian case. + +But this is basically +a conservation + +of energy equation. + +And that's what you +expect, just given + +your general notion +of mechanics as well. + +If you have a second +order equation, + +a second order differential +is with respect to time. + +That's the force equation. + +And if you have a first +order differential + +equation with respect to time, +1/2 mv squared plus v of r + +equals constant. + +That's energy conservation. + +Same thing here. + +And we know that energy +cannot suddenly change. + +If we imagine-- I guess the +first experiment I want to do + +is imagining somehow +there's an explosion + +throughout all of space. + +I imagine putting pieces +of TNT throughout space + +and arranging for, at the same +cosmic time, for all of them + +to be ignited. + +And that would suddenly change +the pressure of the universe, + +but it would not change +the energy density. + +The energy density +would be conserved. + +So the bottom line is +that pressures can change + +discontinuously, but +energy densities cannot. + +And since this equation is +the conservation of energy + +equation, we'd expected that +nothing can change suddenly + +here, that the pressure +term cannot contribute here, + +because if it did, the pressure +term would changed suddenly. + +Nothing else in this equation +would change suddenly. + +There would be no way the +equation could be satisfied. + +But if we added a pressure +term to the second equation, + +that would allow the pressure +to change discontinuously + +as the TNT went off. + +And that would change a +double dot discontinuously. + +And there's nothing wrong +with a double dot changing + +discontinuously. + +If you suddenly the apply +a new force to a particle, + +you suddenly change its second +derivative of its motion. + +You suddenly change +its acceleration. + +So that's OK. + +So any pressure to +this term make sense. + +Adding pressure to this +equation does not make sense. + +And then we can just +ask, what do you + +have to do to this equation if +we're going to add a pressure + +term to make all +three equations now + +consistent with the new +equation for RHO dot? + +It's your homework problem +to answer that question, + +but the homework +tells you the answer, + +and I'll write the answer +on the board right now, + +and then we'll consider +today's lecture over. + +The bottom line is that +equation number one + +has to be modified +into one prime, which + +says that equation number +two has to be modified. + +What am I talking about? + +And the new equation +is a double dot + +is equal to minus 4 +pi over 3 G times RHO + +plus 3p over c squared times a. + +And now we have a consistent +set of Friedman equations, + +and these are the +Friedman equations + +that we would have gotten +if we had done everything + +using general relativity +from the beginning. + +And we'll stop there. + +And we will meet +again next Tuesday. + +And I'll send you an +email about-- there + +will be at least one homework +problem on the problems set + +that will have to be held over +to the following problems set. + +I'll send you an +email about that + +and post it on the website. \ No newline at end of file diff --git a/nHhQeCdbxoE.txt b/nHhQeCdbxoE.txt new file mode 100644 index 0000000000000000000000000000000000000000..393b0edb79cb703bf4d0d2669fd995ed7d6ddc49 --- /dev/null +++ b/nHhQeCdbxoE.txt @@ -0,0 +1,8571 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so let me just start out by + + align:start position:0% +ocw.mit.edu so let me just start out by + + + align:start position:0% +ocw.mit.edu so let me just start out by +giving you a quick uh overv of what + + align:start position:0% +giving you a quick uh overv of what + + + align:start position:0% +giving you a quick uh overv of what +we're going to be doing today what how + + align:start position:0% +we're going to be doing today what how + + + align:start position:0% +we're going to be doing today what how +what the plan is um I'm going to spend + + align:start position:0% +what the plan is um I'm going to spend + + + align:start position:0% +what the plan is um I'm going to spend +the first maybe third or so of the time + + align:start position:0% +the first maybe third or so of the time + + + align:start position:0% +the first maybe third or so of the time +or maybe hopefully less than that + + align:start position:0% +or maybe hopefully less than that + + + align:start position:0% +or maybe hopefully less than that +talking very generally about basic + + align:start position:0% +talking very generally about basic + + + align:start position:0% +talking very generally about basic +camera Concepts and if you have some + + align:start position:0% +camera Concepts and if you have some + + + align:start position:0% +camera Concepts and if you have some +video experience or if you have some + + align:start position:0% +video experience or if you have some + + + align:start position:0% +video experience or if you have some +still photography experience they're + + align:start position:0% +still photography experience they're + + + align:start position:0% +still photography experience they're +going to be pretty familiar to to you + + align:start position:0% +going to be pretty familiar to to you + + + align:start position:0% +going to be pretty familiar to to you +I'm going to keep it fairly General and + + align:start position:0% +I'm going to keep it fairly General and + + + align:start position:0% +I'm going to keep it fairly General and +we're going to go through fairly quickly + + align:start position:0% +we're going to go through fairly quickly + + + align:start position:0% +we're going to go through fairly quickly +some basic + + align:start position:0% +some basic + + + align:start position:0% +some basic +things uh in order to sort of lay the + + align:start position:0% +things uh in order to sort of lay the + + + align:start position:0% +things uh in order to sort of lay the +groundwork for the more exciting and + + align:start position:0% +groundwork for the more exciting and + + + align:start position:0% +groundwork for the more exciting and +interesting part which is actually going + + align:start position:0% +interesting part which is actually going + + + align:start position:0% +interesting part which is actually going +out and and shooting um so but after I + + align:start position:0% +out and and shooting um so but after I + + + align:start position:0% +out and and shooting um so but after I +finish that then Dave is going to take + + align:start position:0% +finish that then Dave is going to take + + + align:start position:0% +finish that then Dave is going to take +over and he's going to provide you with + + align:start position:0% +over and he's going to provide you with + + + align:start position:0% +over and he's going to provide you with +a very quick introduction to our camera + + align:start position:0% +a very quick introduction to our camera + + + align:start position:0% +a very quick introduction to our camera +uh where the controls are how things are + + align:start position:0% +uh where the controls are how things are + + + align:start position:0% +uh where the controls are how things are +set up how to sort do some of the the + + align:start position:0% +set up how to sort do some of the the + + + align:start position:0% +set up how to sort do some of the the +the things that I'm talking about + + align:start position:0% +the things that I'm talking about + + + align:start position:0% +the things that I'm talking about +specifically with our camera and then uh + + align:start position:0% +specifically with our camera and then uh + + + align:start position:0% +specifically with our camera and then uh +we're all going to go out and have a + + align:start position:0% +we're all going to go out and have a + + + align:start position:0% +we're all going to go out and have a +chance to actually shoot some stuff + + align:start position:0% +chance to actually shoot some stuff + + + align:start position:0% +chance to actually shoot some stuff +which should be a lot of fun uh so + + align:start position:0% +which should be a lot of fun uh so + + + align:start position:0% +which should be a lot of fun uh so +that's the story and uh I'm just going + + align:start position:0% +that's the story and uh I'm just going + + + align:start position:0% +that's the story and uh I'm just going +to jump right in um + + align:start position:0% +to jump right in um + + + align:start position:0% +to jump right in um +although I guess I should ask first does + + align:start position:0% +although I guess I should ask first does + + + align:start position:0% +although I guess I should ask first does +anyone have any questions or thoughts + + align:start position:0% +anyone have any questions or thoughts + + + align:start position:0% +anyone have any questions or thoughts +from Wednesday + + align:start position:0% + + + + align:start position:0% + +night okay well what we're trying to do + + align:start position:0% +night okay well what we're trying to do + + + align:start position:0% +night okay well what we're trying to do +is is build uh every session on the last + + align:start position:0% +is is build uh every session on the last + + + align:start position:0% +is is build uh every session on the last +one and so I'm going to start out by by + + align:start position:0% +one and so I'm going to start out by by + + + align:start position:0% +one and so I'm going to start out by by +uh referencing something that that I + + align:start position:0% +uh referencing something that that I + + + align:start position:0% +uh referencing something that that I +talked about last time sort of the way + + align:start position:0% +talked about last time sort of the way + + + align:start position:0% +talked about last time sort of the way +that we began which was looking at + + align:start position:0% +that we began which was looking at + + + align:start position:0% +that we began which was looking at +another visual art right painting and um + + align:start position:0% +another visual art right painting and um + + + align:start position:0% +another visual art right painting and um +if I asked you what the tools and the + + align:start position:0% +if I asked you what the tools and the + + + align:start position:0% +if I asked you what the tools and the +medium of a of a painter was were uh you + + align:start position:0% +medium of a of a painter was were uh you + + + align:start position:0% +medium of a of a painter was were uh you +would have a pretty easy answer right I + + align:start position:0% +would have a pretty easy answer right I + + + align:start position:0% +would have a pretty easy answer right I +mean it's paint it's canvas uh it's the + + align:start position:0% +mean it's paint it's canvas uh it's the + + + align:start position:0% +mean it's paint it's canvas uh it's the +stuff that you do use to make a painting + + align:start position:0% +stuff that you do use to make a painting + + + align:start position:0% +stuff that you do use to make a painting +same with sculpture you know Stone steel + + align:start position:0% +same with sculpture you know Stone steel + + + align:start position:0% +same with sculpture you know Stone steel +mud bricks whatever it may be uh so the + + align:start position:0% +mud bricks whatever it may be uh so the + + + align:start position:0% +mud bricks whatever it may be uh so the +question then is what's the medium for + + align:start position:0% +question then is what's the medium for + + + align:start position:0% +question then is what's the medium for +film and what what are the tools of film + + align:start position:0% +film and what what are the tools of film + + + align:start position:0% +film and what what are the tools of film +Timor obvious + + align:start position:0% +Timor obvious + + + align:start position:0% +Timor obvious +obviously the camera exactly that's + + align:start position:0% +obviously the camera exactly that's + + + align:start position:0% +obviously the camera exactly that's +that's kind of the brush you know I mean + + align:start position:0% +that's kind of the brush you know I mean + + + align:start position:0% +that's kind of the brush you know I mean +not exactly but but it's that's the + + align:start position:0% +not exactly but but it's that's the + + + align:start position:0% +not exactly but but it's that's the +basic tool um but what else what are the + + align:start position:0% +basic tool um but what else what are the + + + align:start position:0% +basic tool um but what else what are the +other tools of the + + align:start position:0% +other tools of the + + + align:start position:0% +other tools of the +filmmaker light + + align:start position:0% + + + + align:start position:0% + +others so the the actual what you record + + align:start position:0% +others so the the actual what you record + + + align:start position:0% +others so the the actual what you record +on exactly and how you manipulate that + + align:start position:0% +on exactly and how you manipulate that + + + align:start position:0% +on exactly and how you manipulate that +um but there are lots of others as well + + align:start position:0% +um but there are lots of others as well + + + align:start position:0% +um but there are lots of others as well +and a concept that I find really useful + + align:start position:0% +and a concept that I find really useful + + + align:start position:0% +and a concept that I find really useful +and interesting in just thinking about + + align:start position:0% +and interesting in just thinking about + + + align:start position:0% +and interesting in just thinking about +kind of what you do as a filmmaker or a + + align:start position:0% +kind of what you do as a filmmaker or a + + + align:start position:0% +kind of what you do as a filmmaker or a +video maker and I'm going to use those + + align:start position:0% +video maker and I'm going to use those + + + align:start position:0% +video maker and I'm going to use those +terms interchangeably as I said on + + align:start position:0% +terms interchangeably as I said on + + + align:start position:0% +terms interchangeably as I said on +Wednesday um are what we call or can be + + align:start position:0% +Wednesday um are what we call or can be + + + align:start position:0% +Wednesday um are what we call or can be +called the plastic elements of film and + + align:start position:0% +called the plastic elements of film and + + + align:start position:0% +called the plastic elements of film and +by that I just mean the elements that + + align:start position:0% +by that I just mean the elements that + + + align:start position:0% +by that I just mean the elements that +you as the artist the filmmaker have + + align:start position:0% +you as the artist the filmmaker have + + + align:start position:0% +you as the artist the filmmaker have +control over and that you can change uh + + align:start position:0% +control over and that you can change uh + + + align:start position:0% +control over and that you can change uh +at will uh so the camera what you choose + + align:start position:0% +at will uh so the camera what you choose + + + align:start position:0% +at will uh so the camera what you choose +to do with the camera is obviously + + align:start position:0% +to do with the camera is obviously + + + align:start position:0% +to do with the camera is obviously +extremely important and in fact Central + + align:start position:0% +extremely important and in fact Central + + + align:start position:0% +extremely important and in fact Central +to uh to the outcome and to what you + + align:start position:0% +to uh to the outcome and to what you + + + align:start position:0% +to uh to the outcome and to what you +want to do as an artist or as a + + align:start position:0% +want to do as an artist or as a + + + align:start position:0% +want to do as an artist or as a +documentarian lighting again whether + + align:start position:0% +documentarian lighting again whether + + + align:start position:0% +documentarian lighting again whether +you're actually adding lights setting up + + align:start position:0% +you're actually adding lights setting up + + + align:start position:0% +you're actually adding lights setting up +lights doing very complex lighting + + align:start position:0% +lights doing very complex lighting + + + align:start position:0% +lights doing very complex lighting +setups or just using available light how + + align:start position:0% +setups or just using available light how + + + align:start position:0% +setups or just using available light how +you choose to place your subject in + + align:start position:0% +you choose to place your subject in + + + align:start position:0% +you choose to place your subject in +relation to the sun how you choose to + + align:start position:0% +relation to the sun how you choose to + + + align:start position:0% +relation to the sun how you choose to +light uh you know turn light the uh + + align:start position:0% +light uh you know turn light the uh + + + align:start position:0% +light uh you know turn light the uh +lights in a room these fluorescent + + align:start position:0% +lights in a room these fluorescent + + + align:start position:0% +lights in a room these fluorescent +lights above us uh we're taping this + + align:start position:0% +lights above us uh we're taping this + + + align:start position:0% +lights above us uh we're taping this +this for open courseware and before + + align:start position:0% +this for open courseware and before + + + align:start position:0% +this for open courseware and before +everyone came we tried a couple of + + align:start position:0% +everyone came we tried a couple of + + + align:start position:0% +everyone came we tried a couple of +different settings uh for the overhead + + align:start position:0% +different settings uh for the overhead + + + align:start position:0% +different settings uh for the overhead +lights and so that is again a plastic + + align:start position:0% +lights and so that is again a plastic + + + align:start position:0% +lights and so that is again a plastic +element um but there are others too can + + align:start position:0% +element um but there are others too can + + + align:start position:0% +element um but there are others too can +can you think of + + align:start position:0% +can you think of + + + align:start position:0% +can you think of +others the lens yeah what what lens you + + align:start position:0% +others the lens yeah what what lens you + + + align:start position:0% +others the lens yeah what what lens you +use to shoot with exactly + + align:start position:0% + + + + align:start position:0% + +others yeah exactly the scene the + + align:start position:0% +others yeah exactly the scene the + + + align:start position:0% +others yeah exactly the scene the +setting uh could be the location another + + align:start position:0% +setting uh could be the location another + + + align:start position:0% +setting uh could be the location another +way of thinking about it so if you're + + align:start position:0% +way of thinking about it so if you're + + + align:start position:0% +way of thinking about it so if you're +doing and that's obviously true of a + + align:start position:0% +doing and that's obviously true of a + + + align:start position:0% +doing and that's obviously true of a +fiction film but it's also true of a + + align:start position:0% +fiction film but it's also true of a + + + align:start position:0% +fiction film but it's also true of a +documentary if you're uh interviewing + + align:start position:0% +documentary if you're uh interviewing + + + align:start position:0% +documentary if you're uh interviewing +somebody where do you choose to put them + + align:start position:0% +somebody where do you choose to put them + + + align:start position:0% +somebody where do you choose to put them +and what does where you choose to put + + align:start position:0% +and what does where you choose to put + + + align:start position:0% +and what does where you choose to put +them say about your subject what do you + + align:start position:0% +them say about your subject what do you + + + align:start position:0% +them say about your subject what do you +want it to say you have control over + + align:start position:0% +want it to say you have control over + + + align:start position:0% +want it to say you have control over +that uh and you have in a lot of ways + + align:start position:0% +that uh and you have in a lot of ways + + + align:start position:0% +that uh and you have in a lot of ways +you have as much or as little control as + + align:start position:0% +you have as much or as little control as + + + align:start position:0% +you have as much or as little control as +you want because you can uh be very + + align:start position:0% +you want because you can uh be very + + + align:start position:0% +you want because you can uh be very +interventionist and place them exactly + + align:start position:0% +interventionist and place them exactly + + + align:start position:0% +interventionist and place them exactly +where you want them or you can just sort + + align:start position:0% +where you want them or you can just sort + + + align:start position:0% +where you want them or you can just sort +of do whatever happens you know if you + + align:start position:0% +of do whatever happens you know if you + + + align:start position:0% +of do whatever happens you know if you +went to interview a professor here at + + align:start position:0% +went to interview a professor here at + + + align:start position:0% +went to interview a professor here at +MIT and you found them in their office + + align:start position:0% +MIT and you found them in their office + + + align:start position:0% +MIT and you found them in their office +you just could do it right there and + + align:start position:0% +you just could do it right there and + + + align:start position:0% +you just could do it right there and +that would say something about them as + + align:start position:0% +that would say something about them as + + + align:start position:0% +that would say something about them as +well um you know do you clean the office + + align:start position:0% +well um you know do you clean the office + + + align:start position:0% +well um you know do you clean the office +uh or do you not clean the office that's + + align:start position:0% +uh or do you not clean the office that's + + + align:start position:0% +uh or do you not clean the office that's +another thing um so so if you think + + align:start position:0% +another thing um so so if you think + + + align:start position:0% +another thing um so so if you think +about it like that then suddenly this + + align:start position:0% +about it like that then suddenly this + + + align:start position:0% +about it like that then suddenly this +whole world of elements opens up right + + align:start position:0% +whole world of elements opens up right + + + align:start position:0% +whole world of elements opens up right +props how you arrange things in a scene + + align:start position:0% +props how you arrange things in a scene + + + align:start position:0% +props how you arrange things in a scene +whe you know whether you kind of dress + + align:start position:0% +whe you know whether you kind of dress + + + align:start position:0% +whe you know whether you kind of dress +the set and again whether it's a + + align:start position:0% +the set and again whether it's a + + + align:start position:0% +the set and again whether it's a +documentary or a fiction film it's still + + align:start position:0% +documentary or a fiction film it's still + + + align:start position:0% +documentary or a fiction film it's still +it's still applies um sound how you + + align:start position:0% +it's still applies um sound how you + + + align:start position:0% +it's still applies um sound how you +record the sound whether you record the + + align:start position:0% +record the sound whether you record the + + + align:start position:0% +record the sound whether you record the +sound what you do in editing in order to + + align:start position:0% +sound what you do in editing in order to + + + align:start position:0% +sound what you do in editing in order to +uh change things if you add music if you + + align:start position:0% +uh change things if you add music if you + + + align:start position:0% +uh change things if you add music if you +mix the sound if you add sound effects + + align:start position:0% +mix the sound if you add sound effects + + + align:start position:0% +mix the sound if you add sound effects +um and editing itself is a plastic + + align:start position:0% +um and editing itself is a plastic + + + align:start position:0% +um and editing itself is a plastic +element that's almost as important as + + align:start position:0% +element that's almost as important as + + + align:start position:0% +element that's almost as important as +the + + align:start position:0% +the + + + align:start position:0% +the +camera uh it's it's a central sort of + + align:start position:0% +camera uh it's it's a central sort of + + + align:start position:0% +camera uh it's it's a central sort of +tool for for the filmmaker how you edit + + align:start position:0% +tool for for the filmmaker how you edit + + + align:start position:0% +tool for for the filmmaker how you edit +a piece so there are any number and + + align:start position:0% +a piece so there are any number and + + + align:start position:0% +a piece so there are any number and +these are just a few uh any number of + + align:start position:0% +these are just a few uh any number of + + + align:start position:0% +these are just a few uh any number of +plastic elements that you can control + + align:start position:0% +plastic elements that you can control + + + align:start position:0% +plastic elements that you can control +and I think this is just like a central + + align:start position:0% +and I think this is just like a central + + + align:start position:0% +and I think this is just like a central +idea that sort of seems obvious but it's + + align:start position:0% +idea that sort of seems obvious but it's + + + align:start position:0% +idea that sort of seems obvious but it's +also something that you want to + + align:start position:0% +also something that you want to + + + align:start position:0% +also something that you want to +continually remind yourself because uh I + + align:start position:0% +continually remind yourself because uh I + + + align:start position:0% +continually remind yourself because uh I +know that in you know in my experience + + align:start position:0% +know that in you know in my experience + + + align:start position:0% +know that in you know in my experience +uh as a producer or a director and doing + + align:start position:0% +uh as a producer or a director and doing + + + align:start position:0% +uh as a producer or a director and doing +a lot of other things in film as well + + align:start position:0% +a lot of other things in film as well + + + align:start position:0% +a lot of other things in film as well +you you can sometimes forget that you + + align:start position:0% +you you can sometimes forget that you + + + align:start position:0% +you you can sometimes forget that you +have the ability to change things + + align:start position:0% +have the ability to change things + + + align:start position:0% +have the ability to change things +because sometimes you're rushed you + + align:start position:0% +because sometimes you're rushed you + + + align:start position:0% +because sometimes you're rushed you +don't have time or something kind of you + + align:start position:0% +don't have time or something kind of you + + + align:start position:0% +don't have time or something kind of you +know fate deals you a blow that that you + + align:start position:0% +know fate deals you a blow that that you + + + align:start position:0% +know fate deals you a blow that that you +know you sort of sort of feel you have + + align:start position:0% +know you sort of sort of feel you have + + + align:start position:0% +know you sort of sort of feel you have +to accept but you just remember that + + align:start position:0% +to accept but you just remember that + + + align:start position:0% +to accept but you just remember that +that you know you can take the + + align:start position:0% +that you know you can take the + + + align:start position:0% +that you know you can take the +initiative and change something so you + + align:start position:0% +initiative and change something so you + + + align:start position:0% +initiative and change something so you +know the location doesn't work the + + align:start position:0% +know the location doesn't work the + + + align:start position:0% +know the location doesn't work the +beautiful idea you had is not going to + + align:start position:0% +beautiful idea you had is not going to + + + align:start position:0% +beautiful idea you had is not going to +not going to happen improvise and think + + align:start position:0% +not going to happen improvise and think + + + align:start position:0% +not going to happen improvise and think +think of something else you have the + + align:start position:0% +think of something else you have the + + + align:start position:0% +think of something else you have the +power to change a lot of these things um + + align:start position:0% +power to change a lot of these things um + + + align:start position:0% +power to change a lot of these things um +so today we're going to talk about + + align:start position:0% +so today we're going to talk about + + + align:start position:0% +so today we're going to talk about +camera which is in many ways for first + + align:start position:0% +camera which is in many ways for first + + + align:start position:0% +camera which is in many ways for first +and foremost the plastic element it's + + align:start position:0% +and foremost the plastic element it's + + + align:start position:0% +and foremost the plastic element it's +the first one that that was mentioned + + align:start position:0% +the first one that that was mentioned + + + align:start position:0% +the first one that that was mentioned +here when I asked you about what kinds + + align:start position:0% +here when I asked you about what kinds + + + align:start position:0% +here when I asked you about what kinds +of things you you use as a tool and it's + + align:start position:0% +of things you you use as a tool and it's + + + align:start position:0% +of things you you use as a tool and it's +sort of obviously the fundamental thing + + align:start position:0% +sort of obviously the fundamental thing + + + align:start position:0% +sort of obviously the fundamental thing +because everything is passing through + + align:start position:0% +because everything is passing through + + + align:start position:0% +because everything is passing through +the lens um and I want to uh just + + align:start position:0% +the lens um and I want to uh just + + + align:start position:0% +the lens um and I want to uh just +provide a very very brief introduction + + align:start position:0% +provide a very very brief introduction + + + align:start position:0% +provide a very very brief introduction +to some of the really basic ideas in uh + + align:start position:0% +to some of the really basic ideas in uh + + + align:start position:0% +to some of the really basic ideas in uh +film making which are very similar in + + align:start position:0% +film making which are very similar in + + + align:start position:0% +film making which are very similar in +many ways to uh some of the basic ideas + + align:start position:0% +many ways to uh some of the basic ideas + + + align:start position:0% +many ways to uh some of the basic ideas +in still photography if you've done that + + align:start position:0% +in still photography if you've done that + + + align:start position:0% +in still photography if you've done that +uh and they're uh one way to think about + + align:start position:0% +uh and they're uh one way to think about + + + align:start position:0% +uh and they're uh one way to think about +them when way I like to think about them + + align:start position:0% +them when way I like to think about them + + + align:start position:0% +them when way I like to think about them +are as the four FS f- stop or exposure + + align:start position:0% +are as the four FS f- stop or exposure + + + align:start position:0% +are as the four FS f- stop or exposure +Focus focal length and + + align:start position:0% +Focus focal length and + + + align:start position:0% +Focus focal length and +framing uh and there are others but they + + align:start position:0% +framing uh and there are others but they + + + align:start position:0% +framing uh and there are others but they +don't start with f so I like you know I + + align:start position:0% +don't start with f so I like you know I + + + align:start position:0% +don't start with f so I like you know I +like to start with these um and uh + + align:start position:0% +like to start with these um and uh + + + align:start position:0% +like to start with these um and uh +f-stop is also maybe a bit simplistic + + align:start position:0% +f-stop is also maybe a bit simplistic + + + align:start position:0% +f-stop is also maybe a bit simplistic +when you're talking about exposure but + + align:start position:0% +when you're talking about exposure but + + + align:start position:0% +when you're talking about exposure but +it's just a way to remember them f-stop + + align:start position:0% +it's just a way to remember them f-stop + + + align:start position:0% +it's just a way to remember them f-stop +Focus focal length Framing and I'm just + + align:start position:0% +Focus focal length Framing and I'm just + + + align:start position:0% +Focus focal length Framing and I'm just +going to spend a couple of minutes on + + align:start position:0% +going to spend a couple of minutes on + + + align:start position:0% +going to spend a couple of minutes on +each one uh and don't expect to sort of + + align:start position:0% +each one uh and don't expect to sort of + + + align:start position:0% +each one uh and don't expect to sort of +absorb it all right now it's the kind of + + align:start position:0% +absorb it all right now it's the kind of + + + align:start position:0% +absorb it all right now it's the kind of +thing that's going to make a lot more + + align:start position:0% +thing that's going to make a lot more + + + align:start position:0% +thing that's going to make a lot more +sense when you're filming so I'm not + + align:start position:0% +sense when you're filming so I'm not + + + align:start position:0% +sense when you're filming so I'm not +going to get really hung up on a lot of + + align:start position:0% +going to get really hung up on a lot of + + + align:start position:0% +going to get really hung up on a lot of +details this isn't a class on Optics or + + align:start position:0% +details this isn't a class on Optics or + + + align:start position:0% +details this isn't a class on Optics or +the physics of light or anything like + + align:start position:0% +the physics of light or anything like + + + align:start position:0% +the physics of light or anything like +that but I want to just introduce a + + align:start position:0% +that but I want to just introduce a + + + align:start position:0% +that but I want to just introduce a +couple of + + align:start position:0% +couple of + + + align:start position:0% +couple of +terms so first exposure f-stop or + + align:start position:0% +terms so first exposure f-stop or + + + align:start position:0% +terms so first exposure f-stop or +aperture is one of the basic things that + + align:start position:0% +aperture is one of the basic things that + + + align:start position:0% +aperture is one of the basic things that +controls how you know what your exposure + + align:start position:0% +controls how you know what your exposure + + + align:start position:0% +controls how you know what your exposure +of your camera is and that is basically + + align:start position:0% +of your camera is and that is basically + + + align:start position:0% +of your camera is and that is basically +uh in simplistic terms or in simple + + align:start position:0% +uh in simplistic terms or in simple + + + align:start position:0% +uh in simplistic terms or in simple +terms how much light is entering the + + align:start position:0% +terms how much light is entering the + + + align:start position:0% +terms how much light is entering the +camera lens how much light is hitting + + align:start position:0% +camera lens how much light is hitting + + + align:start position:0% +camera lens how much light is hitting +the sensor that's recording the image uh + + align:start position:0% +the sensor that's recording the image uh + + + align:start position:0% +the sensor that's recording the image uh +and lenses are equipped with an aperture + + align:start position:0% +and lenses are equipped with an aperture + + + align:start position:0% +and lenses are equipped with an aperture +that is adjustable so you see at the top + + align:start position:0% +that is adjustable so you see at the top + + + align:start position:0% +that is adjustable so you see at the top +there uh there's an aperture that's very + + align:start position:0% +there uh there's an aperture that's very + + + align:start position:0% +there uh there's an aperture that's very +wide it's very open which uh in terms of + + align:start position:0% +wide it's very open which uh in terms of + + + align:start position:0% +wide it's very open which uh in terms of +f-stop is a very low number + + align:start position:0% +f-stop is a very low number + + + align:start position:0% +f-stop is a very low number +F2 uh and at the bottom that very same + + align:start position:0% +F2 uh and at the bottom that very same + + + align:start position:0% +F2 uh and at the bottom that very same +lens the aperture is almost completely + + align:start position:0% +lens the aperture is almost completely + + + align:start position:0% +lens the aperture is almost completely +shut it's just almost a pinhole and that + + align:start position:0% +shut it's just almost a pinhole and that + + + align:start position:0% +shut it's just almost a pinhole and that +corresponds to a very high F number f s + + align:start position:0% +corresponds to a very high F number f s + + + align:start position:0% +corresponds to a very high F number f s +F22 and lenses you'll see that the + + align:start position:0% +F22 and lenses you'll see that the + + + align:start position:0% +F22 and lenses you'll see that the +lenses on our cameras can be adjusted uh + + align:start position:0% +lenses on our cameras can be adjusted uh + + + align:start position:0% +lenses on our cameras can be adjusted uh +you can either adjust leave it in Auto + + align:start position:0% +you can either adjust leave it in Auto + + + align:start position:0% +you can either adjust leave it in Auto +and let the camera choose what the + + align:start position:0% +and let the camera choose what the + + + align:start position:0% +and let the camera choose what the +exposure should be or you can choose it + + align:start position:0% +exposure should be or you can choose it + + + align:start position:0% +exposure should be or you can choose it +and obviously uh the more light you have + + align:start position:0% +and obviously uh the more light you have + + + align:start position:0% +and obviously uh the more light you have +in a scene the more stop down or the + + align:start position:0% +in a scene the more stop down or the + + + align:start position:0% +in a scene the more stop down or the +smaller the aperture would be in order + + align:start position:0% +smaller the aperture would be in order + + + align:start position:0% +smaller the aperture would be in order +to get the correct exposure in other + + align:start position:0% +to get the correct exposure in other + + + align:start position:0% +to get the correct exposure in other +words in order to have enough light + + align:start position:0% +words in order to have enough light + + + align:start position:0% +words in order to have enough light +hitting your sensor but not too much + + align:start position:0% +hitting your sensor but not too much + + + align:start position:0% +hitting your sensor but not too much +light in order to get a good a + + align:start position:0% +light in order to get a good a + + + align:start position:0% +light in order to get a good a +good-looking image um just uh just also + + align:start position:0% +good-looking image um just uh just also + + + align:start position:0% +good-looking image um just uh just also +quickly f-stop is not the only way to + + align:start position:0% +quickly f-stop is not the only way to + + + align:start position:0% +quickly f-stop is not the only way to +adjust exposure you do have other + + align:start position:0% +adjust exposure you do have other + + + align:start position:0% +adjust exposure you do have other +controls you have the shutter speed the + + align:start position:0% +controls you have the shutter speed the + + + align:start position:0% +controls you have the shutter speed the +shutter speed is basically uh + + align:start position:0% +shutter speed is basically uh + + + align:start position:0% +shutter speed is basically uh +determining uh how much time each frame + + align:start position:0% +determining uh how much time each frame + + + align:start position:0% +determining uh how much time each frame +of your video or your film is exposed to + + align:start position:0% +of your video or your film is exposed to + + + align:start position:0% +of your video or your film is exposed to +light as it goes by um and you can + + align:start position:0% +light as it goes by um and you can + + + align:start position:0% +light as it goes by um and you can +adjust it but in video uh and film you + + align:start position:0% +adjust it but in video uh and film you + + + align:start position:0% +adjust it but in video uh and film you +normally aren't going to adjust it you + + align:start position:0% +normally aren't going to adjust it you + + + align:start position:0% +normally aren't going to adjust it you +normally want to keep it for sort of + + align:start position:0% +normally want to keep it for sort of + + + align:start position:0% +normally want to keep it for sort of +normal appearing motion at about 160th + + align:start position:0% +normal appearing motion at about 160th + + + align:start position:0% +normal appearing motion at about 160th +of a second so in Practical terms unless + + align:start position:0% +of a second so in Practical terms unless + + + align:start position:0% +of a second so in Practical terms unless +you're shooting something that's a very + + align:start position:0% +you're shooting something that's a very + + + align:start position:0% +you're shooting something that's a very +highp speed activity or or some kind of + + align:start position:0% +highp speed activity or or some kind of + + + align:start position:0% +highp speed activity or or some kind of +special situation or you're maybe in in + + align:start position:0% +special situation or you're maybe in in + + + align:start position:0% +special situation or you're maybe in in +a very very low light situation you + + align:start position:0% +a very very low light situation you + + + align:start position:0% +a very very low light situation you +don't want to use the shutter as an + + align:start position:0% +don't want to use the shutter as an + + + align:start position:0% +don't want to use the shutter as an +exposure control mainly you're going to + + align:start position:0% +exposure control mainly you're going to + + + align:start position:0% +exposure control mainly you're going to +keep it at 160 um sorry it's it's + + align:start position:0% +keep it at 160 um sorry it's it's + + + align:start position:0% +keep it at 160 um sorry it's it's +usually double the frame rate so if it's + + align:start position:0% +usually double the frame rate so if it's + + + align:start position:0% +usually double the frame rate so if it's +like if you're shooting 24 frames per + + align:start position:0% +like if you're shooting 24 frames per + + + align:start position:0% +like if you're shooting 24 frames per +second it would be uh one over 48 like + + align:start position:0% +second it would be uh one over 48 like + + + align:start position:0% +second it would be uh one over 48 like +you know 48 and we're shooting 30 frames + + align:start position:0% +you know 48 and we're shooting 30 frames + + + align:start position:0% +you know 48 and we're shooting 30 frames +a second so that's why 60 160th yeah um + + align:start position:0% +a second so that's why 60 160th yeah um + + + align:start position:0% +a second so that's why 60 160th yeah um +the second thing is the camera + + align:start position:0% +the second thing is the camera + + + align:start position:0% +the second thing is the camera +sensitivity itself different cameras + + align:start position:0% +sensitivity itself different cameras + + + align:start position:0% +sensitivity itself different cameras +have a different sensitivity to light + + align:start position:0% +have a different sensitivity to light + + + align:start position:0% +have a different sensitivity to light +and you'll very quickly come to uh both + + align:start position:0% +and you'll very quickly come to uh both + + + align:start position:0% +and you'll very quickly come to uh both +appreciate and hate some of the quirks + + align:start position:0% +appreciate and hate some of the quirks + + + align:start position:0% +appreciate and hate some of the quirks +of our camera uh it is sensitive in + + align:start position:0% +of our camera uh it is sensitive in + + + align:start position:0% +of our camera uh it is sensitive in +compared to some and not as others so it + + align:start position:0% +compared to some and not as others so it + + + align:start position:0% +compared to some and not as others so it +depends on what you may be expecting um + + align:start position:0% +depends on what you may be expecting um + + + align:start position:0% +depends on what you may be expecting um +you can also however uh there there are + + align:start position:0% +you can also however uh there there are + + + align:start position:0% +you can also however uh there there are +adjustments to camera + + align:start position:0% +adjustments to camera + + + align:start position:0% +adjustments to camera +uh and video cameras basically it's + + align:start position:0% +uh and video cameras basically it's + + + align:start position:0% +uh and video cameras basically it's +called the gain control so the if the if + + align:start position:0% +called the gain control so the if the if + + + align:start position:0% +called the gain control so the if the if +the light lighting situation is very + + align:start position:0% +the light lighting situation is very + + + align:start position:0% +the light lighting situation is very +poor you don't have a lot of light the + + align:start position:0% +poor you don't have a lot of light the + + + align:start position:0% +poor you don't have a lot of light the +gain can can be raised but the trade-off + + align:start position:0% +gain can can be raised but the trade-off + + + align:start position:0% +gain can can be raised but the trade-off +is that the image gets very very uh + + align:start position:0% +is that the image gets very very uh + + + align:start position:0% +is that the image gets very very uh +fuzzy much lower resolution uh but there + + align:start position:0% +fuzzy much lower resolution uh but there + + + align:start position:0% +fuzzy much lower resolution uh but there +is that sensitivity and then finally of + + align:start position:0% +is that sensitivity and then finally of + + + align:start position:0% +is that sensitivity and then finally of +course there are + + align:start position:0% +course there are + + + align:start position:0% +course there are +lights uh you can add add light either + + align:start position:0% +lights uh you can add add light either + + + align:start position:0% +lights uh you can add add light either +by changing the location uh going from + + align:start position:0% +by changing the location uh going from + + + align:start position:0% +by changing the location uh going from +you know if this one room is too dark + + align:start position:0% +you know if this one room is too dark + + + align:start position:0% +you know if this one room is too dark +and the Next Room isn't you can change + + align:start position:0% +and the Next Room isn't you can change + + + align:start position:0% +and the Next Room isn't you can change +the rooms if you have lights you can add + + align:start position:0% +the rooms if you have lights you can add + + + align:start position:0% +the rooms if you have lights you can add +them uh we actually are be for this + + align:start position:0% +them uh we actually are be for this + + + align:start position:0% +them uh we actually are be for this +class we're shooting available light for + + align:start position:0% +class we're shooting available light for + + + align:start position:0% +class we're shooting available light for +the most part there will be one class on + + align:start position:0% +the most part there will be one class on + + + align:start position:0% +the most part there will be one class on +lighting but we don't have lighting + + align:start position:0% +lighting but we don't have lighting + + + align:start position:0% +lighting but we don't have lighting +packages that are going to be generally + + align:start position:0% +packages that are going to be generally + + + align:start position:0% +packages that are going to be generally +available but there are ways to um uh + + align:start position:0% +available but there are ways to um uh + + + align:start position:0% +available but there are ways to um uh +overcome that uh clip lights regular you + + align:start position:0% +overcome that uh clip lights regular you + + + align:start position:0% +overcome that uh clip lights regular you +know sort of consumer lights and people + + align:start position:0% +know sort of consumer lights and people + + + align:start position:0% +know sort of consumer lights and people +in this class have done interesting + + align:start position:0% +in this class have done interesting + + + align:start position:0% +in this class have done interesting +things with those those kinds of things + + align:start position:0% +things with those those kinds of things + + + align:start position:0% +things with those those kinds of things +in the past so anyway lots of ways to + + align:start position:0% +in the past so anyway lots of ways to + + + align:start position:0% +in the past so anyway lots of ways to +control exposure the essential basic one + + align:start position:0% +control exposure the essential basic one + + + align:start position:0% +control exposure the essential basic one +is the f- stoer + + align:start position:0% +is the f- stoer + + + align:start position:0% +is the f- stoer +aperture so let's go on to focus the + + align:start position:0% +aperture so let's go on to focus the + + + align:start position:0% +aperture so let's go on to focus the +second f um first thing to know is that + + align:start position:0% +second f um first thing to know is that + + + align:start position:0% +second f um first thing to know is that +just like with exposure uh this camera + + align:start position:0% +just like with exposure uh this camera + + + align:start position:0% +just like with exposure uh this camera +and almost all video cameras have two + + align:start position:0% +and almost all video cameras have two + + + align:start position:0% +and almost all video cameras have two +settings Auto and manual uh manual focus + + align:start position:0% +settings Auto and manual uh manual focus + + + align:start position:0% +settings Auto and manual uh manual focus +is almost always preferred because uh + + align:start position:0% +is almost always preferred because uh + + + align:start position:0% +is almost always preferred because uh +just as with exposure uh the auto uh + + align:start position:0% +just as with exposure uh the auto uh + + + align:start position:0% +just as with exposure uh the auto uh +setting can be fooled uh it will breathe + + align:start position:0% +setting can be fooled uh it will breathe + + + align:start position:0% +setting can be fooled uh it will breathe +so you know like it'll sort of change + + align:start position:0% +so you know like it'll sort of change + + + align:start position:0% +so you know like it'll sort of change +its mind and focus on something else in + + align:start position:0% +its mind and focus on something else in + + + align:start position:0% +its mind and focus on something else in +the middle of a shot which can be very + + align:start position:0% +the middle of a shot which can be very + + + align:start position:0% +the middle of a shot which can be very +distracting and annoying so in almost + + align:start position:0% +distracting and annoying so in almost + + + align:start position:0% +distracting and annoying so in almost +all situations you're going going to + + align:start position:0% +all situations you're going going to + + + align:start position:0% +all situations you're going going to +want to stay manual both for f- stop and + + align:start position:0% +want to stay manual both for f- stop and + + + align:start position:0% +want to stay manual both for f- stop and +for Focus but you do have that option + + align:start position:0% +for Focus but you do have that option + + + align:start position:0% +for Focus but you do have that option +you do have Auto as a choice and there + + align:start position:0% +you do have Auto as a choice and there + + + align:start position:0% +you do have Auto as a choice and there +are situations you know where it's + + align:start position:0% +are situations you know where it's + + + align:start position:0% +are situations you know where it's +better to be in Auto than to be in + + align:start position:0% +better to be in Auto than to be in + + + align:start position:0% +better to be in Auto than to be in +nothing right I mean if if you grab the + + align:start position:0% +nothing right I mean if if you grab the + + + align:start position:0% +nothing right I mean if if you grab the +camera because uh you know there's a + + align:start position:0% +camera because uh you know there's a + + + align:start position:0% +camera because uh you know there's a +flying saucer landing outside and you + + align:start position:0% +flying saucer landing outside and you + + + align:start position:0% +flying saucer landing outside and you +want to get the shot if it's an auto + + align:start position:0% +want to get the shot if it's an auto + + + align:start position:0% +want to get the shot if it's an auto +it's much better to have something than + + align:start position:0% +it's much better to have something than + + + align:start position:0% +it's much better to have something than +to have nothing and to you know to be + + align:start position:0% +to have nothing and to you know to be + + + align:start position:0% +to have nothing and to you know to be +adjusting um but generally we discourage + + align:start position:0% +adjusting um but generally we discourage + + + align:start position:0% +adjusting um but generally we discourage +the use of of uh autofocus and Auto + + align:start position:0% +the use of of uh autofocus and Auto + + + align:start position:0% +the use of of uh autofocus and Auto +Iris uh second thing to think about with + + align:start position:0% +Iris uh second thing to think about with + + + align:start position:0% +Iris uh second thing to think about with +focus is um the depth of field depth of + + align:start position:0% +focus is um the depth of field depth of + + + align:start position:0% +focus is um the depth of field depth of +field is basically uh a term that refers + + align:start position:0% +field is basically uh a term that refers + + + align:start position:0% +field is basically uh a term that refers +to how much of your image in terms of + + align:start position:0% +to how much of your image in terms of + + + align:start position:0% +to how much of your image in terms of +the depth is in Focus so if you're + + align:start position:0% +the depth is in Focus so if you're + + + align:start position:0% +the depth is in Focus so if you're +shooting me sitting here talking as uh + + align:start position:0% +shooting me sitting here talking as uh + + + align:start position:0% +shooting me sitting here talking as uh +our camera person is hopefully I'm in + + align:start position:0% +our camera person is hopefully I'm in + + + align:start position:0% +our camera person is hopefully I'm in +Focus the background behind me doesn't + + align:start position:0% +Focus the background behind me doesn't + + + align:start position:0% +Focus the background behind me doesn't +have to be in focus and it might or + + align:start position:0% +have to be in focus and it might or + + + align:start position:0% +have to be in focus and it might or +might not be in Focus depending on the + + align:start position:0% +might not be in Focus depending on the + + + align:start position:0% +might not be in Focus depending on the +aperture that the camera is set at so uh + + align:start position:0% +aperture that the camera is set at so uh + + + align:start position:0% +aperture that the camera is set at so uh +a very wide aperture because it's a low + + align:start position:0% +a very wide aperture because it's a low + + + align:start position:0% +a very wide aperture because it's a low +light situation means that you have very + + align:start position:0% +light situation means that you have very + + + align:start position:0% +light situation means that you have very +shallow focus and the background may be + + align:start position:0% +shallow focus and the background may be + + + align:start position:0% +shallow focus and the background may be +out of focus the the smaller the + + align:start position:0% +out of focus the the smaller the + + + align:start position:0% +out of focus the the smaller the +aperture gets the deeper your focus is + + align:start position:0% +aperture gets the deeper your focus is + + + align:start position:0% +aperture gets the deeper your focus is +so that the background suddenly could + + align:start position:0% +so that the background suddenly could + + + align:start position:0% +so that the background suddenly could +become in focus and this is something + + align:start position:0% +become in focus and this is something + + + align:start position:0% +become in focus and this is something +that you can it's an aesthetic Choice + + align:start position:0% +that you can it's an aesthetic Choice + + + align:start position:0% +that you can it's an aesthetic Choice +it's not just sort of determined by by + + align:start position:0% +it's not just sort of determined by by + + + align:start position:0% +it's not just sort of determined by by +uh your lighting although that's + + align:start position:0% +uh your lighting although that's + + + align:start position:0% +uh your lighting although that's +obviously something you have to deal + + align:start position:0% +obviously something you have to deal + + + align:start position:0% +obviously something you have to deal +with but you can actually make choices + + align:start position:0% +with but you can actually make choices + + + align:start position:0% +with but you can actually make choices +about what's in focus and what's not and + + align:start position:0% +about what's in focus and what's not and + + + align:start position:0% +about what's in focus and what's not and +how deep the focus is and it and it um + + align:start position:0% +how deep the focus is and it and it um + + + align:start position:0% +how deep the focus is and it and it um +and it has an impact on how people read + + align:start position:0% +and it has an impact on how people read + + + align:start position:0% +and it has an impact on how people read +the images that you create um I don't + + align:start position:0% +the images that you create um I don't + + + align:start position:0% +the images that you create um I don't +know if anybody here is nearsighted but + + align:start position:0% +know if anybody here is nearsighted but + + + align:start position:0% +know if anybody here is nearsighted but +if you want to get a sense of how depth + + align:start position:0% +if you want to get a sense of how depth + + + align:start position:0% +if you want to get a sense of how depth +a field is determined by the aperture um + + align:start position:0% +a field is determined by the aperture um + + + align:start position:0% +a field is determined by the aperture um +you can take your glasses off and you + + align:start position:0% +you can take your glasses off and you + + + align:start position:0% +you can take your glasses off and you +can actually do this and the smaller you + + align:start position:0% +can actually do this and the smaller you + + + align:start position:0% +can actually do this and the smaller you +make the pinhole that you're looking + + align:start position:0% +make the pinhole that you're looking + + + align:start position:0% +make the pinhole that you're looking +through the more + + align:start position:0% +through the more + + + align:start position:0% +through the more +Focus you are or that what you're seeing + + align:start position:0% +Focus you are or that what you're seeing + + + align:start position:0% +Focus you are or that what you're seeing +is and it doesn't really work if you're + + align:start position:0% +is and it doesn't really work if you're + + + align:start position:0% +is and it doesn't really work if you're +everything's always in focus for you but + + align:start position:0% +everything's always in focus for you but + + + align:start position:0% +everything's always in focus for you but +uh for me it works really well so if I + + align:start position:0% +uh for me it works really well so if I + + + align:start position:0% +uh for me it works really well so if I +don't have my glasses on in the morning + + align:start position:0% +don't have my glasses on in the morning + + + align:start position:0% +don't have my glasses on in the morning +I can look at you and I can see that + + align:start position:0% +I can look at you and I can see that + + + align:start position:0% +I can look at you and I can see that +you're quite sharp if I make the pinhole + + align:start position:0% +you're quite sharp if I make the pinhole + + + align:start position:0% +you're quite sharp if I make the pinhole +small out it's so anyway it's kind of a + + align:start position:0% +small out it's so anyway it's kind of a + + + align:start position:0% +small out it's so anyway it's kind of a +cool effect and it gives you a sense + + align:start position:0% +cool effect and it gives you a sense + + + align:start position:0% +cool effect and it gives you a sense +that basically what's happening is that + + align:start position:0% +that basically what's happening is that + + + align:start position:0% +that basically what's happening is that +the smaller the the the the aperture + + align:start position:0% +the smaller the the the the aperture + + + align:start position:0% +the smaller the the the the aperture +that the light is passing through the + + align:start position:0% +that the light is passing through the + + + align:start position:0% +that the light is passing through the +more uh aligned and again I'm not this + + align:start position:0% +more uh aligned and again I'm not this + + + align:start position:0% +more uh aligned and again I'm not this +is not an Optics class and you know I'm + + align:start position:0% +is not an Optics class and you know I'm + + + align:start position:0% +is not an Optics class and you know I'm +not going to go too far down this road + + align:start position:0% +not going to go too far down this road + + + align:start position:0% +not going to go too far down this road +that I don't know much about but the the + + align:start position:0% +that I don't know much about but the the + + + align:start position:0% +that I don't know much about but the the +light is more is is more aligned there's + + align:start position:0% +light is more is is more aligned there's + + + align:start position:0% +light is more is is more aligned there's +less + + align:start position:0% +less + + + align:start position:0% +less +scatter and that makes everything uh in + + align:start position:0% +scatter and that makes everything uh in + + + align:start position:0% +scatter and that makes everything uh in +sharper Focus so again uh focus is + + align:start position:0% +sharper Focus so again uh focus is + + + align:start position:0% +sharper Focus so again uh focus is +something that is extremely important so + + align:start position:0% +something that is extremely important so + + + align:start position:0% +something that is extremely important so +is so is exposure they're sort of + + align:start position:0% +is so is exposure they're sort of + + + align:start position:0% +is so is exposure they're sort of +non-negotiable uh you know the first two + + align:start position:0% +non-negotiable uh you know the first two + + + align:start position:0% +non-negotiable uh you know the first two +FS are either you did it or you didn't + + align:start position:0% +FS are either you did it or you didn't + + + align:start position:0% +FS are either you did it or you didn't +you're either in Focus or you're not and + + align:start position:0% +you're either in Focus or you're not and + + + align:start position:0% +you're either in Focus or you're not and +you pretty much want to be in focus and + + align:start position:0% +you pretty much want to be in focus and + + + align:start position:0% +you pretty much want to be in focus and +you pretty much want to be properly + + align:start position:0% +you pretty much want to be properly + + + align:start position:0% +you pretty much want to be properly +exposed you don't want to have too much + + align:start position:0% +exposed you don't want to have too much + + + align:start position:0% +exposed you don't want to have too much +light hitting your image you don't want + + align:start position:0% +light hitting your image you don't want + + + align:start position:0% +light hitting your image you don't want +to have too little um even if you want + + align:start position:0% +to have too little um even if you want + + + align:start position:0% +to have too little um even if you want +to manipulate Focus or exposure later um + + align:start position:0% +to manipulate Focus or exposure later um + + + align:start position:0% +to manipulate Focus or exposure later um +because you want to actually have things + + align:start position:0% +because you want to actually have things + + + align:start position:0% +because you want to actually have things +appear out of focus it's much better to + + align:start position:0% +appear out of focus it's much better to + + + align:start position:0% +appear out of focus it's much better to +do it in in editing and post-production + + align:start position:0% +do it in in editing and post-production + + + align:start position:0% +do it in in editing and post-production +than to do it when you're shooting + + align:start position:0% +than to do it when you're shooting + + + align:start position:0% +than to do it when you're shooting +because you can't change it back you + + align:start position:0% +because you can't change it back you + + + align:start position:0% +because you can't change it back you +can't make a a blurry image sharp you + + align:start position:0% +can't make a a blurry image sharp you + + + align:start position:0% +can't make a a blurry image sharp you +can make a sharp image blurry you can + + align:start position:0% +can make a sharp image blurry you can + + + align:start position:0% +can make a sharp image blurry you can +take a a very well exposed image and + + align:start position:0% +take a a very well exposed image and + + + align:start position:0% +take a a very well exposed image and +make it dark or bright but but you can't + + align:start position:0% +make it dark or bright but but you can't + + + align:start position:0% +make it dark or bright but but you can't +very easily take a dark image and make + + align:start position:0% +very easily take a dark image and make + + + align:start position:0% +very easily take a dark image and make +it properly exposed so these first two I + + align:start position:0% +it properly exposed so these first two I + + + align:start position:0% +it properly exposed so these first two I +as I said I usually refer to them as the + + align:start position:0% +as I said I usually refer to them as the + + + align:start position:0% +as I said I usually refer to them as the +non-negotiable + + align:start position:0% +non-negotiable + + + align:start position:0% +non-negotiable +to um the next two however um are + + align:start position:0% +to um the next two however um are + + + align:start position:0% +to um the next two however um are +infinitely + + align:start position:0% +infinitely + + + align:start position:0% +infinitely +negotiable uh focal length uh refers to + + align:start position:0% +negotiable uh focal length uh refers to + + + align:start position:0% +negotiable uh focal length uh refers to +uh whether you're shooting something in + + align:start position:0% +uh whether you're shooting something in + + + align:start position:0% +uh whether you're shooting something in +a wide angle or a telephoto or a normal + + align:start position:0% +a wide angle or a telephoto or a normal + + + align:start position:0% +a wide angle or a telephoto or a normal +setting and again you may have you know + + align:start position:0% +setting and again you may have you know + + + align:start position:0% +setting and again you may have you know +some experience with this with still + + align:start position:0% +some experience with this with still + + + align:start position:0% +some experience with this with still +photography wideangle lens are the the + + align:start position:0% +photography wideangle lens are the the + + + align:start position:0% +photography wideangle lens are the the +lenses that are a smaller number of + + align:start position:0% +lenses that are a smaller number of + + + align:start position:0% +lenses that are a smaller number of +millimeters you know like like the 12 mm + + align:start position:0% +millimeters you know like like the 12 mm + + + align:start position:0% +millimeters you know like like the 12 mm +millimet lens the 6 mm lens uh you know + + align:start position:0% +millimet lens the 6 mm lens uh you know + + + align:start position:0% +millimet lens the 6 mm lens uh you know +the 16 mm lens telephoto are the big + + align:start position:0% +the 16 mm lens telephoto are the big + + + align:start position:0% +the 16 mm lens telephoto are the big +numbers 200 300 + + align:start position:0% +numbers 200 300 + + + align:start position:0% +numbers 200 300 +150 um and each of them uh give you very + + align:start position:0% +150 um and each of them uh give you very + + + align:start position:0% +150 um and each of them uh give you very +very very different feeling uh kinds of + + align:start position:0% +very very different feeling uh kinds of + + + align:start position:0% +very very different feeling uh kinds of +images uh the wide angle lens gives you + + align:start position:0% +images uh the wide angle lens gives you + + + align:start position:0% +images uh the wide angle lens gives you +a much wider angle of view obious + + align:start position:0% +a much wider angle of view obious + + + align:start position:0% +a much wider angle of view obious +obviously so uh if you're filming + + align:start position:0% +obviously so uh if you're filming + + + align:start position:0% +obviously so uh if you're filming +Landscapes uh you could put a wide angle + + align:start position:0% +Landscapes uh you could put a wide angle + + + align:start position:0% +Landscapes uh you could put a wide angle +lens on your camera and from the same + + align:start position:0% +lens on your camera and from the same + + + align:start position:0% +lens on your camera and from the same +position get a much wider field uh it + + align:start position:0% +position get a much wider field uh it + + + align:start position:0% +position get a much wider field uh it +also gives you much deeper Focus uh to + + align:start position:0% +also gives you much deeper Focus uh to + + + align:start position:0% +also gives you much deeper Focus uh to +go back to the idea of of depth of field + + align:start position:0% +go back to the idea of of depth of field + + + align:start position:0% +go back to the idea of of depth of field +with a wide angle lens it's much easier + + align:start position:0% +with a wide angle lens it's much easier + + + align:start position:0% +with a wide angle lens it's much easier +to get everything in focus from the + + align:start position:0% +to get everything in focus from the + + + align:start position:0% +to get everything in focus from the +foreground to the background telephoto + + align:start position:0% +foreground to the background telephoto + + + align:start position:0% +foreground to the background telephoto +lenses on the on the other hand are a + + align:start position:0% +lenses on the on the other hand are a + + + align:start position:0% +lenses on the on the other hand are a +much narrower angle of view so if I'm + + align:start position:0% +much narrower angle of view so if I'm + + + align:start position:0% +much narrower angle of view so if I'm +standing in the same place filming the + + align:start position:0% +standing in the same place filming the + + + align:start position:0% +standing in the same place filming the +same thing I'm seeing a much narrower + + align:start position:0% +same thing I'm seeing a much narrower + + + align:start position:0% +same thing I'm seeing a much narrower +field um which is can also be thought of + + align:start position:0% +field um which is can also be thought of + + + align:start position:0% +field um which is can also be thought of +as magnification right so same image but + + align:start position:0% +as magnification right so same image but + + + align:start position:0% +as magnification right so same image but +now if I'm filming the camera person + + align:start position:0% +now if I'm filming the camera person + + + align:start position:0% +now if I'm filming the camera person +who's filming me I'm + + align:start position:0% +who's filming me I'm + + + align:start position:0% +who's filming me I'm +seeing just his face instead of the + + align:start position:0% +seeing just his face instead of the + + + align:start position:0% +seeing just his face instead of the +whole the whole field uh and the focus + + align:start position:0% +whole the whole field uh and the focus + + + align:start position:0% +whole the whole field uh and the focus +the depth of field is much shallower so + + align:start position:0% +the depth of field is much shallower so + + + align:start position:0% +the depth of field is much shallower so +it's much easier to get a nice soft + + align:start position:0% +it's much easier to get a nice soft + + + align:start position:0% +it's much easier to get a nice soft +background on a telephoto lens um just + + align:start position:0% +background on a telephoto lens um just + + + align:start position:0% +background on a telephoto lens um just +one one other note about focal length + + align:start position:0% +one one other note about focal length + + + align:start position:0% +one one other note about focal length +again it's it's something that is + + align:start position:0% +again it's it's something that is + + + align:start position:0% +again it's it's something that is +infinitely uh variable and you can + + align:start position:0% +infinitely uh variable and you can + + + align:start position:0% +infinitely uh variable and you can +choose as a filmmaker what kinds of uh + + align:start position:0% +choose as a filmmaker what kinds of uh + + + align:start position:0% +choose as a filmmaker what kinds of uh +focal lengths you use but don't confuse + + align:start position:0% +focal lengths you use but don't confuse + + + align:start position:0% +focal lengths you use but don't confuse +a wideangle lens with a wide shot or a + + align:start position:0% +a wideangle lens with a wide shot or a + + + align:start position:0% +a wideangle lens with a wide shot or a +telephoto lens with a closeup it's + + align:start position:0% +telephoto lens with a closeup it's + + + align:start position:0% +telephoto lens with a closeup it's +easier to get a close-up with a + + align:start position:0% +easier to get a close-up with a + + + align:start position:0% +easier to get a close-up with a +telephoto lens and it's easier to get a + + align:start position:0% +telephoto lens and it's easier to get a + + + align:start position:0% +telephoto lens and it's easier to get a +wide shot with a wide angle lens but + + align:start position:0% +wide shot with a wide angle lens but + + + align:start position:0% +wide shot with a wide angle lens but +it's certainly possible to do uh a wide + + align:start position:0% +it's certainly possible to do uh a wide + + + align:start position:0% +it's certainly possible to do uh a wide +shot with a telephoto lens you just have + + align:start position:0% +shot with a telephoto lens you just have + + + align:start position:0% +shot with a telephoto lens you just have +to be much farther away from your + + align:start position:0% +to be much farther away from your + + + align:start position:0% +to be much farther away from your +subject and vice versa it's much it's + + align:start position:0% +subject and vice versa it's much it's + + + align:start position:0% +subject and vice versa it's much it's +very possible to do a close-up with a + + align:start position:0% +very possible to do a close-up with a + + + align:start position:0% +very possible to do a close-up with a +wide-angle lens you just have to get + + align:start position:0% +wide-angle lens you just have to get + + + align:start position:0% +wide-angle lens you just have to get +much closer but but they'll feel very + + align:start position:0% +much closer but but they'll feel very + + + align:start position:0% +much closer but but they'll feel very +very different and um I'll show you some + + align:start position:0% +very different and um I'll show you some + + + align:start position:0% +very different and um I'll show you some +extreme examples in here in a minute so + + align:start position:0% +extreme examples in here in a minute so + + + align:start position:0% +extreme examples in here in a minute so +this is an extreme wide angle lens uh + + align:start position:0% +this is an extreme wide angle lens uh + + + align:start position:0% +this is an extreme wide angle lens uh +what's what we call a fisheye lens and + + align:start position:0% +what's what we call a fisheye lens and + + + align:start position:0% +what's what we call a fisheye lens and +you'll see you know first of all that + + align:start position:0% +you'll see you know first of all that + + + align:start position:0% +you'll see you know first of all that +that it's very distorted but you're + + align:start position:0% +that it's very distorted but you're + + + align:start position:0% +that it's very distorted but you're +seeing a very very wide field of view so + + align:start position:0% +seeing a very very wide field of view so + + + align:start position:0% +seeing a very very wide field of view so +wide in fact that that the only way to + + align:start position:0% +wide in fact that that the only way to + + + align:start position:0% +wide in fact that that the only way to +accommodate is the Distortion uh you're + + align:start position:0% +accommodate is the Distortion uh you're + + + align:start position:0% +accommodate is the Distortion uh you're +also seeing incredible depth of field + + align:start position:0% +also seeing incredible depth of field + + + align:start position:0% +also seeing incredible depth of field +the background the infinite distance is + + align:start position:0% +the background the infinite distance is + + + align:start position:0% +the background the infinite distance is +is sharp and so is the hand that's not + + align:start position:0% +is sharp and so is the hand that's not + + + align:start position:0% +is sharp and so is the hand that's not +that far away from the from the camera + + align:start position:0% +that far away from the from the camera + + + align:start position:0% +that far away from the from the camera +but also uh wideangle lenses and this is + + align:start position:0% +but also uh wideangle lenses and this is + + + align:start position:0% +but also uh wideangle lenses and this is +an extreme example wide angle lenses + + align:start position:0% +an extreme example wide angle lenses + + + align:start position:0% +an extreme example wide angle lenses +tend to distort and elongate the + + align:start position:0% +tend to distort and elongate the + + + align:start position:0% +tend to distort and elongate the +distance between objects so that hand is + + align:start position:0% +distance between objects so that hand is + + + align:start position:0% +distance between objects so that hand is +much closer to the camera than it might + + align:start position:0% +much closer to the camera than it might + + + align:start position:0% +much closer to the camera than it might +appear and the distance between the hand + + align:start position:0% +appear and the distance between the hand + + + align:start position:0% +appear and the distance between the hand +and and you know every other element + + align:start position:0% +and and you know every other element + + + align:start position:0% +and and you know every other element +going back is somewhat elongated so uh + + align:start position:0% +going back is somewhat elongated so uh + + + align:start position:0% +going back is somewhat elongated so uh +it makes small rooms feel much bigger uh + + align:start position:0% +it makes small rooms feel much bigger uh + + + align:start position:0% +it makes small rooms feel much bigger uh +it makes distances seem much + + align:start position:0% +it makes distances seem much + + + align:start position:0% +it makes distances seem much +greater telephoto lens which you know + + align:start position:0% +greater telephoto lens which you know + + + align:start position:0% +greater telephoto lens which you know +you know the long lens because they're + + align:start position:0% +you know the long lens because they're + + + align:start position:0% +you know the long lens because they're +long do the opposite so here we have a + + align:start position:0% +long do the opposite so here we have a + + + align:start position:0% +long do the opposite so here we have a +telephoto shot of a of a of a bird and + + align:start position:0% +telephoto shot of a of a of a bird and + + + align:start position:0% +telephoto shot of a of a of a bird and +you see first of all that the background + + align:start position:0% +you see first of all that the background + + + align:start position:0% +you see first of all that the background +is is very very soft even though it's + + align:start position:0% +is is very very soft even though it's + + + align:start position:0% +is is very very soft even though it's +not that far you know really behind the + + align:start position:0% +not that far you know really behind the + + + align:start position:0% +not that far you know really behind the +bird uh and things are very compressed + + align:start position:0% +bird uh and things are very compressed + + + align:start position:0% +bird uh and things are very compressed +so the distance between the bird and the + + align:start position:0% +so the distance between the bird and the + + + align:start position:0% +so the distance between the bird and the +background feels like there you know + + align:start position:0% +background feels like there you know + + + align:start position:0% +background feels like there you know +there's not much distance at all even + + align:start position:0% +there's not much distance at all even + + + align:start position:0% +there's not much distance at all even +though there might actually be quite a + + align:start position:0% +though there might actually be quite a + + + align:start position:0% +though there might actually be quite a +lot um one of the things about telephoto + + align:start position:0% +lot um one of the things about telephoto + + + align:start position:0% +lot um one of the things about telephoto +lenses is that sometimes the the depth + + align:start position:0% +lenses is that sometimes the the depth + + + align:start position:0% +lenses is that sometimes the the depth +of field is so shallow that you can + + align:start position:0% +of field is so shallow that you can + + + align:start position:0% +of field is so shallow that you can +literally have uh you know like the eye + + align:start position:0% +literally have uh you know like the eye + + + align:start position:0% +literally have uh you know like the eye +of the bird in focus and uh you know the + + align:start position:0% +of the bird in focus and uh you know the + + + align:start position:0% +of the bird in focus and uh you know the +the background that you know of the the + + align:start position:0% +the background that you know of the the + + + align:start position:0% +the background that you know of the the +plant that it's standing on completely + + align:start position:0% +plant that it's standing on completely + + + align:start position:0% +plant that it's standing on completely +soft here you the plant is actually in + + align:start position:0% +soft here you the plant is actually in + + + align:start position:0% +soft here you the plant is actually in +Focus um but if you're doing an + + align:start position:0% +Focus um but if you're doing an + + + align:start position:0% +Focus um but if you're doing an +interview like the a human eye might be + + align:start position:0% +interview like the a human eye might be + + + align:start position:0% +interview like the a human eye might be +in focus and their ear might be out of + + align:start position:0% +in focus and their ear might be out of + + + align:start position:0% +in focus and their ear might be out of +focus at a at an extreme telephoto uh + + align:start position:0% +focus at a at an extreme telephoto uh + + + align:start position:0% +focus at a at an extreme telephoto uh +lens so this is actually you know + + align:start position:0% +lens so this is actually you know + + + align:start position:0% +lens so this is actually you know +aesthetically really pleasing because + + align:start position:0% +aesthetically really pleasing because + + + align:start position:0% +aesthetically really pleasing because +the foreground jumps out at you you know + + align:start position:0% +the foreground jumps out at you you know + + + align:start position:0% +the foreground jumps out at you you know +our eye goes immediately to the bird and + + align:start position:0% +our eye goes immediately to the bird and + + + align:start position:0% +our eye goes immediately to the bird and +the background just drops off into this + + align:start position:0% +the background just drops off into this + + + align:start position:0% +the background just drops off into this +very soft nice kind of kind of uh back + + align:start position:0% +very soft nice kind of kind of uh back + + + align:start position:0% +very soft nice kind of kind of uh back +plate so uh again I could shoot a wide + + align:start position:0% +plate so uh again I could shoot a wide + + + align:start position:0% +plate so uh again I could shoot a wide +shot like this but it would look + + align:start position:0% +shot like this but it would look + + + align:start position:0% +shot like this but it would look +extremely different than shooting a wide + + align:start position:0% +extremely different than shooting a wide + + + align:start position:0% +extremely different than shooting a wide +shot with with a wide angle + + align:start position:0% + + + + align:start position:0% + +lens so now let's talk about framing um + + align:start position:0% +lens so now let's talk about framing um + + + align:start position:0% +lens so now let's talk about framing um +and framing this is this is really + + align:start position:0% +and framing this is this is really + + + align:start position:0% +and framing this is this is really +really you know once you sort of master + + align:start position:0% +really you know once you sort of master + + + align:start position:0% +really you know once you sort of master +the basics of the camera framing is kind + + align:start position:0% +the basics of the camera framing is kind + + + align:start position:0% +the basics of the camera framing is kind +of a catch-all term for sort of + + align:start position:0% +of a catch-all term for sort of + + + align:start position:0% +of a catch-all term for sort of +everything else you know about how you + + align:start position:0% +everything else you know about how you + + + align:start position:0% +everything else you know about how you +choose to shoot things uh you know do + + align:start position:0% +choose to shoot things uh you know do + + + align:start position:0% +choose to shoot things uh you know do +you choose to shoot close-ups do you + + align:start position:0% +you choose to shoot close-ups do you + + + align:start position:0% +you choose to shoot close-ups do you +choose to shoot wide shots what's the + + align:start position:0% +choose to shoot wide shots what's the + + + align:start position:0% +choose to shoot wide shots what's the +grammar of film and we're not going to + + align:start position:0% +grammar of film and we're not going to + + + align:start position:0% +grammar of film and we're not going to +uh do any kind of exhaustive um talk + + align:start position:0% +uh do any kind of exhaustive um talk + + + align:start position:0% +uh do any kind of exhaustive um talk +about that right now um but it's an + + align:start position:0% +about that right now um but it's an + + + align:start position:0% +about that right now um but it's an +infinitely sort of uh interesting and uh + + align:start position:0% +infinitely sort of uh interesting and uh + + + align:start position:0% +infinitely sort of uh interesting and uh +inexhaustible subject um Sabrina you + + align:start position:0% +inexhaustible subject um Sabrina you + + + align:start position:0% +inexhaustible subject um Sabrina you +mention you know that that uh on + + align:start position:0% +mention you know that that uh on + + + align:start position:0% +mention you know that that uh on +Wednesday night when we were looking at + + align:start position:0% +Wednesday night when we were looking at + + + align:start position:0% +Wednesday night when we were looking at +those very early films everything was + + align:start position:0% +those very early films everything was + + + align:start position:0% +those very early films everything was +filmed head to toe and that was because + + align:start position:0% +filmed head to toe and that was because + + + align:start position:0% +filmed head to toe and that was because +I mean there really hadn't been a + + align:start position:0% +I mean there really hadn't been a + + + align:start position:0% +I mean there really hadn't been a +grammar of film developed at that point + + align:start position:0% +grammar of film developed at that point + + + align:start position:0% +grammar of film developed at that point +they were just thinking about them as + + align:start position:0% +they were just thinking about them as + + + align:start position:0% +they were just thinking about them as +stage plays so people would walk in head + + align:start position:0% +stage plays so people would walk in head + + + align:start position:0% +stage plays so people would walk in head +to toe and they do their thing and + + align:start position:0% +to toe and they do their thing and + + + align:start position:0% +to toe and they do their thing and +they'd walk out um but you know a few + + align:start position:0% +they'd walk out um but you know a few + + + align:start position:0% +they'd walk out um but you know a few +years after that people started filming + + align:start position:0% +years after that people started filming + + + align:start position:0% +years after that people started filming +close-ups and that was a huge uh + + align:start position:0% +close-ups and that was a huge uh + + + align:start position:0% +close-ups and that was a huge uh +Revolution they started filming shots of + + align:start position:0% +Revolution they started filming shots of + + + align:start position:0% +Revolution they started filming shots of +the hands of people doing things they + + align:start position:0% +the hands of people doing things they + + + align:start position:0% +the hands of people doing things they +started moving the camera so that it + + align:start position:0% +started moving the camera so that it + + + align:start position:0% +started moving the camera so that it +would pan from one person to another and + + align:start position:0% +would pan from one person to another and + + + align:start position:0% +would pan from one person to another and +back they started filming shots with + + align:start position:0% +back they started filming shots with + + + align:start position:0% +back they started filming shots with +someone in the foreground and someone in + + align:start position:0% +someone in the foreground and someone in + + + align:start position:0% +someone in the foreground and someone in +the background and then they do a + + align:start position:0% +the background and then they do a + + + align:start position:0% +the background and then they do a +reverse with this person in the + + align:start position:0% +reverse with this person in the + + + align:start position:0% +reverse with this person in the +foreground and this person in the + + align:start position:0% +foreground and this person in the + + + align:start position:0% +foreground and this person in the +background and and that kind of opened + + align:start position:0% +background and and that kind of opened + + + align:start position:0% +background and and that kind of opened +up this whole language that all of us + + align:start position:0% +up this whole language that all of us + + + align:start position:0% +up this whole language that all of us +you know we're used to reading this + + align:start position:0% +you know we're used to reading this + + + align:start position:0% +you know we're used to reading this +language because we've been doing it our + + align:start position:0% +language because we've been doing it our + + + align:start position:0% +language because we've been doing it our +entire lives but at that point it was + + align:start position:0% +entire lives but at that point it was + + + align:start position:0% +entire lives but at that point it was +extremely new you know what shot works + + align:start position:0% +extremely new you know what shot works + + + align:start position:0% +extremely new you know what shot works +with this shot what's confusing what's + + align:start position:0% +with this shot what's confusing what's + + + align:start position:0% +with this shot what's confusing what's +not confusing how do we understand a + + align:start position:0% +not confusing how do we understand a + + + align:start position:0% +not confusing how do we understand a +scene and all of that is is uh related + + align:start position:0% +scene and all of that is is uh related + + + align:start position:0% +scene and all of that is is uh related +to to framing so uh we're going to be + + align:start position:0% +to to framing so uh we're going to be + + + align:start position:0% +to to framing so uh we're going to be +looking at a lot of films in this class + + align:start position:0% +looking at a lot of films in this class + + + align:start position:0% +looking at a lot of films in this class +we're going to be talking about why they + + align:start position:0% +we're going to be talking about why they + + + align:start position:0% +we're going to be talking about why they +were shot the way they were shot uh both + + align:start position:0% +were shot the way they were shot uh both + + + align:start position:0% +were shot the way they were shot uh both +in terms of the sort of the social terms + + align:start position:0% +in terms of the sort of the social terms + + + align:start position:0% +in terms of the sort of the social terms +uh and the the technical terms the + + align:start position:0% +uh and the the technical terms the + + + align:start position:0% +uh and the the technical terms the +technological terms but also in terms of + + align:start position:0% +technological terms but also in terms of + + + align:start position:0% +technological terms but also in terms of +the framing and the grammar of them and + + align:start position:0% +the framing and the grammar of them and + + + align:start position:0% +the framing and the grammar of them and +uh it's something that uh you're going + + align:start position:0% +uh it's something that uh you're going + + + align:start position:0% +uh it's something that uh you're going +to gain a lot of experience and + + align:start position:0% +to gain a lot of experience and + + + align:start position:0% +to gain a lot of experience and +understanding of as you as you make your + + align:start position:0% +understanding of as you as you make your + + + align:start position:0% +understanding of as you as you make your +own + + align:start position:0% + + + + align:start position:0% + +films um + + align:start position:0% +films um + + + align:start position:0% +films um +um but just for starters um you know I'm + + align:start position:0% +um but just for starters um you know I'm + + + align:start position:0% +um but just for starters um you know I'm +going to talk a little bit about + + align:start position:0% +going to talk a little bit about + + + align:start position:0% +going to talk a little bit about +um just some basic kind of ideas and + + align:start position:0% +um just some basic kind of ideas and + + + align:start position:0% +um just some basic kind of ideas and +Concepts that you might want to think + + align:start position:0% +Concepts that you might want to think + + + align:start position:0% +Concepts that you might want to think +about as as you as you frame a scene um + + align:start position:0% +about as as you as you frame a scene um + + + align:start position:0% +about as as you as you frame a scene um +let's take this class for instance uh + + align:start position:0% +let's take this class for instance uh + + + align:start position:0% +let's take this class for instance uh +how would I film this + + align:start position:0% +how would I film this + + + align:start position:0% +how would I film this +class there are an infinite number of + + align:start position:0% +class there are an infinite number of + + + align:start position:0% +class there are an infinite number of +ways that I could do it it's being + + align:start position:0% +ways that I could do it it's being + + + align:start position:0% +ways that I could do it it's being +filmed right now for a very particular + + align:start position:0% +filmed right now for a very particular + + + align:start position:0% +filmed right now for a very particular +reason a very particular purpose open + + align:start position:0% +reason a very particular purpose open + + + align:start position:0% +reason a very particular purpose open +course whereare is filming it and the + + align:start position:0% +course whereare is filming it and the + + + align:start position:0% +course whereare is filming it and the +way they're filming It Is by focusing on + + align:start position:0% +way they're filming It Is by focusing on + + + align:start position:0% +way they're filming It Is by focusing on +me because I'm the one talking and on + + align:start position:0% +me because I'm the one talking and on + + + align:start position:0% +me because I'm the one talking and on +the slides because it's information that + + align:start position:0% +the slides because it's information that + + + align:start position:0% +the slides because it's information that +they're trying to + + align:start position:0% +they're trying to + + + align:start position:0% +they're trying to +capture uh if we were filming it for + + align:start position:0% +capture uh if we were filming it for + + + align:start position:0% +capture uh if we were filming it for +other purposes we could have a + + align:start position:0% +other purposes we could have a + + + align:start position:0% +other purposes we could have a +completely different approach we could + + align:start position:0% +completely different approach we could + + + align:start position:0% +completely different approach we could +film it uh as a a documentary Cinema ver + + align:start position:0% +film it uh as a a documentary Cinema ver + + + align:start position:0% +film it uh as a a documentary Cinema ver +direct Cinema style which is if you + + align:start position:0% +direct Cinema style which is if you + + + align:start position:0% +direct Cinema style which is if you +remember the the the scene uh the John F + + align:start position:0% +remember the the the scene uh the John F + + + align:start position:0% +remember the the the scene uh the John F +Kennedy documentary about uh the primary + + align:start position:0% +Kennedy documentary about uh the primary + + + align:start position:0% +Kennedy documentary about uh the primary +in Wisconsin that we watched the clip of + + align:start position:0% +in Wisconsin that we watched the clip of + + + align:start position:0% +in Wisconsin that we watched the clip of +on Wednesday night uh that was all about + + align:start position:0% +on Wednesday night uh that was all about + + + align:start position:0% +on Wednesday night uh that was all about +the experience of being there and it had + + align:start position:0% +the experience of being there and it had + + + align:start position:0% +the experience of being there and it had +a very particular point of view the + + align:start position:0% +a very particular point of view the + + + align:start position:0% +a very particular point of view the +experience of uh Jackie Kennedy and JFK + + align:start position:0% +experience of uh Jackie Kennedy and JFK + + + align:start position:0% +experience of uh Jackie Kennedy and JFK +in that room shaking a million hands + + align:start position:0% +in that room shaking a million hands + + + align:start position:0% +in that room shaking a million hands +being kind of pushed by the crowd so if + + align:start position:0% +being kind of pushed by the crowd so if + + + align:start position:0% +being kind of pushed by the crowd so if +we were going to film this class in that + + align:start position:0% +we were going to film this class in that + + + align:start position:0% +we were going to film this class in that +way we could use a handheld camera the + + align:start position:0% +way we could use a handheld camera the + + + align:start position:0% +way we could use a handheld camera the +camera could be completely mobile you + + align:start position:0% +camera could be completely mobile you + + + align:start position:0% +camera could be completely mobile you +you could be bar you know if I'm not + + align:start position:0% +you could be bar you know if I'm not + + + align:start position:0% +you could be bar you know if I'm not +what's important to the fil fil maker I + + align:start position:0% +what's important to the fil fil maker I + + + align:start position:0% +what's important to the fil fil maker I +could I might barely be in it you know + + align:start position:0% +could I might barely be in it you know + + + align:start position:0% +could I might barely be in it you know +maybe it's a film about you and they're + + align:start position:0% +maybe it's a film about you and they're + + + align:start position:0% +maybe it's a film about you and they're +following you in your day and I'm just + + align:start position:0% +following you in your day and I'm just + + + align:start position:0% +following you in your day and I'm just +this sort of droning voice in the + + align:start position:0% +this sort of droning voice in the + + + align:start position:0% +this sort of droning voice in the +background what they're interested in is + + align:start position:0% +background what they're interested in is + + + align:start position:0% +background what they're interested in is +your response to the environment and how + + align:start position:0% +your response to the environment and how + + + align:start position:0% +your response to the environment and how +to capture that so there'd be a + + align:start position:0% +to capture that so there'd be a + + + align:start position:0% +to capture that so there'd be a +completely different completely + + align:start position:0% +completely different completely + + + align:start position:0% +completely different completely +different uh way of filming this and the + + align:start position:0% +different uh way of filming this and the + + + align:start position:0% +different uh way of filming this and the +framing and the shot choices would be + + align:start position:0% +framing and the shot choices would be + + + align:start position:0% +framing and the shot choices would be +completely different than what we're + + align:start position:0% +completely different than what we're + + + align:start position:0% +completely different than what we're +doing right now um we could film it with + + align:start position:0% +doing right now um we could film it with + + + align:start position:0% +doing right now um we could film it with +multiple cameras we could film you know + + align:start position:0% +multiple cameras we could film you know + + + align:start position:0% +multiple cameras we could film you know +as we did the other night we could have + + align:start position:0% +as we did the other night we could have + + + align:start position:0% +as we did the other night we could have +have a camera that you know pointing at + + align:start position:0% +have a camera that you know pointing at + + + align:start position:0% +have a camera that you know pointing at +the students camera in the background we + + align:start position:0% +the students camera in the background we + + + align:start position:0% +the students camera in the background we +could edit it together um what how how + + align:start position:0% +could edit it together um what how how + + + align:start position:0% +could edit it together um what how how +we you know how we shoot people whether + + align:start position:0% +we you know how we shoot people whether + + + align:start position:0% +we you know how we shoot people whether +we're shooting them in close-ups or wide + + align:start position:0% +we're shooting them in close-ups or wide + + + align:start position:0% +we're shooting them in close-ups or wide +shots all has a really significant + + align:start position:0% +shots all has a really significant + + + align:start position:0% +shots all has a really significant +impact on the story that we're telling + + align:start position:0% +impact on the story that we're telling + + + align:start position:0% +impact on the story that we're telling +and uh one of the things with + + align:start position:0% +and uh one of the things with + + + align:start position:0% +and uh one of the things with +documentary film is that you're you as a + + align:start position:0% +documentary film is that you're you as a + + + align:start position:0% +documentary film is that you're you as a +as a camera person like again let's say + + align:start position:0% +as a camera person like again let's say + + + align:start position:0% +as a camera person like again let's say +that that we're doing you know a day in + + align:start position:0% +that that we're doing you know a day in + + + align:start position:0% +that that we're doing you know a day in +the life of Sabrina um as the uh + + align:start position:0% +the life of Sabrina um as the uh + + + align:start position:0% +the life of Sabrina um as the uh +as the story unfolds we're constantly + + align:start position:0% +as the story unfolds we're constantly + + + align:start position:0% +as the story unfolds we're constantly +making adjustments we're constantly + + align:start position:0% +making adjustments we're constantly + + + align:start position:0% +making adjustments we're constantly +making new choices about what to film so + + align:start position:0% +making new choices about what to film so + + + align:start position:0% +making new choices about what to film so +uh if we're filming your experience of + + align:start position:0% +uh if we're filming your experience of + + + align:start position:0% +uh if we're filming your experience of +being in this class as that experience + + align:start position:0% +being in this class as that experience + + + align:start position:0% +being in this class as that experience +changes as a camera person you you would + + align:start position:0% +changes as a camera person you you would + + + align:start position:0% +changes as a camera person you you would +you know the camera person would need to + + align:start position:0% +you know the camera person would need to + + + align:start position:0% +you know the camera person would need to +be sensitive to that change so uh you + + align:start position:0% +be sensitive to that change so uh you + + + align:start position:0% +be sensitive to that change so uh you +know let's say you got in into a a + + align:start position:0% +know let's say you got in into a a + + + align:start position:0% +know let's say you got in into a a +discussion and a disagreement with Dave + + align:start position:0% +discussion and a disagreement with Dave + + + align:start position:0% +discussion and a disagreement with Dave +R ta you know because you didn't agree + + align:start position:0% +R ta you know because you didn't agree + + + align:start position:0% +R ta you know because you didn't agree +with his interpretation of something + + align:start position:0% +with his interpretation of something + + + align:start position:0% +with his interpretation of something +um which will happen no I won't no I + + align:start position:0% +um which will happen no I won't no I + + + align:start position:0% +um which will happen no I won't no I +won't um so suddenly we we would be + + align:start position:0% +won't um so suddenly we we would be + + + align:start position:0% +won't um so suddenly we we would be +focusing on Dave and your response to + + align:start position:0% +focusing on Dave and your response to + + + align:start position:0% +focusing on Dave and your response to +Dave so you know we would be in + + align:start position:0% +Dave so you know we would be in + + + align:start position:0% +Dave so you know we would be in +close-ups on you listening to Dave + + align:start position:0% +close-ups on you listening to Dave + + + align:start position:0% +close-ups on you listening to Dave +looking unhappy arguing back suddenly + + align:start position:0% +looking unhappy arguing back suddenly + + + align:start position:0% +looking unhappy arguing back suddenly +we're on Dave Dave is talking back and + + align:start position:0% +we're on Dave Dave is talking back and + + + align:start position:0% +we're on Dave Dave is talking back and +forth back and forth and you know me the + + align:start position:0% +forth back and forth and you know me the + + + align:start position:0% +forth back and forth and you know me the +instructor who's being filmed right now + + align:start position:0% +instructor who's being filmed right now + + + align:start position:0% +instructor who's being filmed right now +I'm not even in the picture it doesn't + + align:start position:0% +I'm not even in the picture it doesn't + + + align:start position:0% +I'm not even in the picture it doesn't +matter what I what I'm saying or + + align:start position:0% +matter what I what I'm saying or + + + align:start position:0% +matter what I what I'm saying or +thinking or doing you know that maybe + + align:start position:0% +thinking or doing you know that maybe + + + align:start position:0% +thinking or doing you know that maybe +then you know we're the camera person + + align:start position:0% +then you know we're the camera person + + + align:start position:0% +then you know we're the camera person +starts looking for closeup reaction + + align:start position:0% +starts looking for closeup reaction + + + align:start position:0% +starts looking for closeup reaction +shots of other students you know does + + align:start position:0% +shots of other students you know does + + + align:start position:0% +shots of other students you know does +everyone agree with you or does everyone + + align:start position:0% +everyone agree with you or does everyone + + + align:start position:0% +everyone agree with you or does everyone +agree with Dave and think you're wrong + + align:start position:0% +agree with Dave and think you're wrong + + + align:start position:0% +agree with Dave and think you're wrong +you know and and as and and as you make + + align:start position:0% +you know and and as and and as you make + + + align:start position:0% +you know and and as and and as you make +that choice as a camera person it's + + align:start position:0% +that choice as a camera person it's + + + align:start position:0% +that choice as a camera person it's +going to impact who you choose to film + + align:start position:0% +going to impact who you choose to film + + + align:start position:0% +going to impact who you choose to film +so um you know we went we we we touched + + align:start position:0% +so um you know we went we we we touched + + + align:start position:0% +so um you know we went we we we touched +on the idea of fairness and accuracy in + + align:start position:0% +on the idea of fairness and accuracy in + + + align:start position:0% +on the idea of fairness and accuracy in +the documentary film you know what you + + align:start position:0% +the documentary film you know what you + + + align:start position:0% +the documentary film you know what you +choose to frame and how you choose to + + align:start position:0% +choose to frame and how you choose to + + + align:start position:0% +choose to frame and how you choose to +frame it has a huge huge impact on the + + align:start position:0% +frame it has a huge huge impact on the + + + align:start position:0% +frame it has a huge huge impact on the +story that you tell so you can walk into + + align:start position:0% +story that you tell so you can walk into + + + align:start position:0% +story that you tell so you can walk into +that situation I just described and film + + align:start position:0% +that situation I just described and film + + + align:start position:0% +that situation I just described and film +it with an agenda like you know we want + + align:start position:0% +it with an agenda like you know we want + + + align:start position:0% +it with an agenda like you know we want +to make Sabrina look like the smartest + + align:start position:0% +to make Sabrina look like the smartest + + + align:start position:0% +to make Sabrina look like the smartest +person in the room so then you film it + + align:start position:0% +person in the room so then you film it + + + align:start position:0% +person in the room so then you film it +in a certain way or you know we want to + + align:start position:0% +in a certain way or you know we want to + + + align:start position:0% +in a certain way or you know we want to +just we want to show how you know how + + align:start position:0% +just we want to show how you know how + + + align:start position:0% +just we want to show how you know how +completely isolated she is film it in in + + align:start position:0% +completely isolated she is film it in in + + + align:start position:0% +completely isolated she is film it in in +a different way uh or you could be very + + align:start position:0% +a different way uh or you could be very + + + align:start position:0% +a different way uh or you could be very +sensitive and open to the the situation + + align:start position:0% +sensitive and open to the the situation + + + align:start position:0% +sensitive and open to the the situation +and adjust and try to be make an + + align:start position:0% +and adjust and try to be make an + + + align:start position:0% +and adjust and try to be make an +accurate or Fair representation of + + align:start position:0% +accurate or Fair representation of + + + align:start position:0% +accurate or Fair representation of +what's actually happening and believe me + + align:start position:0% +what's actually happening and believe me + + + align:start position:0% +what's actually happening and believe me +that's that both are common in in + + align:start position:0% +that's that both are common in in + + + align:start position:0% +that's that both are common in in +documentary film I mean going in with an + + align:start position:0% +documentary film I mean going in with an + + + align:start position:0% +documentary film I mean going in with an +agenda is extremely common and that's + + align:start position:0% +agenda is extremely common and that's + + + align:start position:0% +agenda is extremely common and that's +not the same as you know lying quote + + align:start position:0% +not the same as you know lying quote + + + align:start position:0% +not the same as you know lying quote +unquote manipulating although there is + + align:start position:0% +unquote manipulating although there is + + + align:start position:0% +unquote manipulating although there is +an element of manipulation to it uh but + + align:start position:0% +an element of manipulation to it uh but + + + align:start position:0% +an element of manipulation to it uh but +but generally we do go in with pre + + align:start position:0% +but generally we do go in with pre + + + align:start position:0% +but generally we do go in with pre +preconceived notions and it impacts how + + align:start position:0% +preconceived notions and it impacts how + + + align:start position:0% +preconceived notions and it impacts how +we how we frame things and how we shoot + + align:start position:0% +we how we frame things and how we shoot + + + align:start position:0% +we how we frame things and how we shoot +things um so anyway that's kind of the + + align:start position:0% +things um so anyway that's kind of the + + + align:start position:0% +things um so anyway that's kind of the +overall thing we're not going to talk + + align:start position:0% +overall thing we're not going to talk + + + align:start position:0% +overall thing we're not going to talk +about a lot of film grammar right now + + align:start position:0% +about a lot of film grammar right now + + + align:start position:0% +about a lot of film grammar right now +because I could go on for the rest of + + align:start position:0% +because I could go on for the rest of + + + align:start position:0% +because I could go on for the rest of +the time and I'd rather get on to the + + align:start position:0% +the time and I'd rather get on to the + + + align:start position:0% +the time and I'd rather get on to the +actual camera work um but I am going to + + align:start position:0% +actual camera work um but I am going to + + + align:start position:0% +actual camera work um but I am going to +I am going to uh just raise a couple of + + align:start position:0% +I am going to uh just raise a couple of + + + align:start position:0% +I am going to uh just raise a couple of +things to think about since you'll very + + align:start position:0% +things to think about since you'll very + + + align:start position:0% +things to think about since you'll very +soon have cameras in your hands and um + + align:start position:0% +soon have cameras in your hands and um + + + align:start position:0% +soon have cameras in your hands and um +you know just just basic kind of kinds + + align:start position:0% +you know just just basic kind of kinds + + + align:start position:0% +you know just just basic kind of kinds +of things to think about as you choose + + align:start position:0% +of things to think about as you choose + + + align:start position:0% +of things to think about as you choose +the shots that you that you're going to + + align:start position:0% +the shots that you that you're going to + + + align:start position:0% +the shots that you that you're going to +um going to film um first of all there's + + align:start position:0% +um going to film um first of all there's + + + align:start position:0% +um going to film um first of all there's +a real tendency when you get a camera + + align:start position:0% +a real tendency when you get a camera + + + align:start position:0% +a real tendency when you get a camera +the F you know for the first time and I + + align:start position:0% +the F you know for the first time and I + + + align:start position:0% +the F you know for the first time and I +mean I'm sure everyone at this point has + + align:start position:0% +mean I'm sure everyone at this point has + + + align:start position:0% +mean I'm sure everyone at this point has +filmed something you know with a video + + align:start position:0% +filmed something you know with a video + + + align:start position:0% +filmed something you know with a video +camera um there's a real tendency to + + align:start position:0% +camera um there's a real tendency to + + + align:start position:0% +camera um there's a real tendency to +want to capture everything right so + + align:start position:0% +want to capture everything right so + + + align:start position:0% +want to capture everything right so +we're we're in this room we're + + align:start position:0% +we're we're in this room we're + + + align:start position:0% +we're we're in this room we're +filming and you sort of think like oh + + align:start position:0% +filming and you sort of think like oh + + + align:start position:0% +filming and you sort of think like oh +I'm going to get everything and you + + align:start position:0% +I'm going to get everything and you + + + align:start position:0% +I'm going to get everything and you +start doing this which is basically + + align:start position:0% +start doing this which is basically + + + align:start position:0% +start doing this which is basically +moving continually because that's how we + + align:start position:0% +moving continually because that's how we + + + align:start position:0% +moving continually because that's how we +our eyes work right you know I'm I'm + + align:start position:0% +our eyes work right you know I'm I'm + + + align:start position:0% +our eyes work right you know I'm I'm +just looking around I see everything so + + align:start position:0% +just looking around I see everything so + + + align:start position:0% +just looking around I see everything so +you just assume the camera works that + + align:start position:0% +you just assume the camera works that + + + align:start position:0% +you just assume the camera works that +way too but what you end up doing is + + align:start position:0% +way too but what you end up doing is + + + align:start position:0% +way too but what you end up doing is +capturing nothing because with the + + align:start position:0% +capturing nothing because with the + + + align:start position:0% +capturing nothing because with the +camera you have to you have to sort of + + align:start position:0% +camera you have to you have to sort of + + + align:start position:0% +camera you have to you have to sort of +fake the way your eye works and the way + + align:start position:0% +fake the way your eye works and the way + + + align:start position:0% +fake the way your eye works and the way +your eye works is I I'm really I'm doing + + align:start position:0% +your eye works is I I'm really I'm doing + + + align:start position:0% +your eye works is I I'm really I'm doing +this I'm seeing everything but I'm also + + align:start position:0% +this I'm seeing everything but I'm also + + + align:start position:0% +this I'm seeing everything but I'm also +continuously you know my brain is + + align:start position:0% +continuously you know my brain is + + + align:start position:0% +continuously you know my brain is +continuously picking out things and + + align:start position:0% +continuously picking out things and + + + align:start position:0% +continuously picking out things and +making closeups out of the stuff that I + + align:start position:0% +making closeups out of the stuff that I + + + align:start position:0% +making closeups out of the stuff that I +see making different angles so when I + + align:start position:0% +see making different angles so when I + + + align:start position:0% +see making different angles so when I +was talking about you suddenly there was + + align:start position:0% +was talking about you suddenly there was + + + align:start position:0% +was talking about you suddenly there was +a close-up of you even though I saw + + align:start position:0% +a close-up of you even though I saw + + + align:start position:0% +a close-up of you even though I saw +everything else too um when I talked + + align:start position:0% +everything else too um when I talked + + + align:start position:0% +everything else too um when I talked +about Dave suddenly there was a close-up + + align:start position:0% +about Dave suddenly there was a close-up + + + align:start position:0% +about Dave suddenly there was a close-up +of Dave in my head right so the camera + + align:start position:0% +of Dave in my head right so the camera + + + align:start position:0% +of Dave in my head right so the camera +has to do that and you have to make it + + align:start position:0% +has to do that and you have to make it + + + align:start position:0% +has to do that and you have to make it +do that which means that you know what + + align:start position:0% +do that which means that you know what + + + align:start position:0% +do that which means that you know what +what they call H down the room which is + + align:start position:0% +what they call H down the room which is + + + align:start position:0% +what they call H down the room which is +this kind of continual sort of well I + + align:start position:0% +this kind of continual sort of well I + + + align:start position:0% +this kind of continual sort of well I +don't want to you know I don't want to + + align:start position:0% +don't want to you know I don't want to + + + align:start position:0% +don't want to you know I don't want to +miss anything so I'm just going to keep + + align:start position:0% +miss anything so I'm just going to keep + + + align:start position:0% +miss anything so I'm just going to keep +doing + + align:start position:0% +doing + + + align:start position:0% +doing +this it just ends up with with mush and + + align:start position:0% +this it just ends up with with mush and + + + align:start position:0% +this it just ends up with with mush and +and you're not telling a story and + + align:start position:0% +and you're not telling a story and + + + align:start position:0% +and you're not telling a story and +you're not really getting any shots that + + align:start position:0% +you're not really getting any shots that + + + align:start position:0% +you're not really getting any shots that +you're able to edit so you know you want + + align:start position:0% +you're able to edit so you know you want + + + align:start position:0% +you're able to edit so you know you want +to be deliberate about what you're + + align:start position:0% +to be deliberate about what you're + + + align:start position:0% +to be deliberate about what you're +shooting and you want to think about + + align:start position:0% +shooting and you want to think about + + + align:start position:0% +shooting and you want to think about +what you're shooting you know what story + + align:start position:0% +what you're shooting you know what story + + + align:start position:0% +what you're shooting you know what story +am I telling and what what images do I + + align:start position:0% +am I telling and what what images do I + + + align:start position:0% +am I telling and what what images do I +need to tell that story you know do I + + align:start position:0% +need to tell that story you know do I + + + align:start position:0% +need to tell that story you know do I +need to focus on on you do I need to + + align:start position:0% +need to focus on on you do I need to + + + align:start position:0% +need to focus on on you do I need to +focus on Dave do I need to shoot a wide + + align:start position:0% +focus on Dave do I need to shoot a wide + + + align:start position:0% +focus on Dave do I need to shoot a wide +shot that establishes the geography of + + align:start position:0% +shot that establishes the geography of + + + align:start position:0% +shot that establishes the geography of +the room so that I know where people are + + align:start position:0% +the room so that I know where people are + + + align:start position:0% +the room so that I know where people are +sitting um second thing uh is very basic + + align:start position:0% +sitting um second thing uh is very basic + + + align:start position:0% +sitting um second thing uh is very basic +thing hold your + + align:start position:0% +thing hold your + + + align:start position:0% +thing hold your +shots um you know there's also a + + align:start position:0% +shots um you know there's also a + + + align:start position:0% +shots um you know there's also a +tendency that that goes along with this + + align:start position:0% +tendency that that goes along with this + + + align:start position:0% +tendency that that goes along with this +this posing down the room to never + + align:start position:0% +this posing down the room to never + + + align:start position:0% +this posing down the room to never +really hold on anything so uh I'm + + align:start position:0% +really hold on anything so uh I'm + + + align:start position:0% +really hold on anything so uh I'm +filming Sabrina but then suddenly I want + + align:start position:0% +filming Sabrina but then suddenly I want + + + align:start position:0% +filming Sabrina but then suddenly I want +to go over here and then I want to go + + align:start position:0% +to go over here and then I want to go + + + align:start position:0% +to go over here and then I want to go +back and then I end up with nothing + + align:start position:0% +back and then I end up with nothing + + + align:start position:0% +back and then I end up with nothing +again uh so you you know you want to you + + align:start position:0% +again uh so you you know you want to you + + + align:start position:0% +again uh so you you know you want to you +want to uh make a choice and then stick + + align:start position:0% +want to uh make a choice and then stick + + + align:start position:0% +want to uh make a choice and then stick +with it for long enough that you + + align:start position:0% +with it for long enough that you + + + align:start position:0% +with it for long enough that you +actually get something so if I'm + + align:start position:0% +actually get something so if I'm + + + align:start position:0% +actually get something so if I'm +shooting a close-up of Chris listening + + align:start position:0% +shooting a close-up of Chris listening + + + align:start position:0% +shooting a close-up of Chris listening +to me + + align:start position:0% +to me + + + align:start position:0% +to me +skeptically I want to hold on + + align:start position:0% +skeptically I want to hold on + + + align:start position:0% +skeptically I want to hold on +for a certain number of seconds and then + + align:start position:0% +for a certain number of seconds and then + + + align:start position:0% +for a certain number of seconds and then +go back to the next thing that I want to + + align:start position:0% +go back to the next thing that I want to + + + align:start position:0% +go back to the next thing that I want to +shoot and it can be hard sometimes + + align:start position:0% +shoot and it can be hard sometimes + + + align:start position:0% +shoot and it can be hard sometimes +because you know suddenly something + + align:start position:0% +because you know suddenly something + + + align:start position:0% +because you know suddenly something +really interesting is happening over + + align:start position:0% +really interesting is happening over + + + align:start position:0% +really interesting is happening over +there and you want to run over and get + + align:start position:0% +there and you want to run over and get + + + align:start position:0% +there and you want to run over and get +it and you need to be responsive to that + + align:start position:0% +it and you need to be responsive to that + + + align:start position:0% +it and you need to be responsive to that +and and obviously pay attention to it + + align:start position:0% +and and obviously pay attention to it + + + align:start position:0% +and and obviously pay attention to it +but if you get sort of too caught up in + + align:start position:0% +but if you get sort of too caught up in + + + align:start position:0% +but if you get sort of too caught up in +the moment you end up with nothing and + + align:start position:0% +the moment you end up with nothing and + + + align:start position:0% +the moment you end up with nothing and +and this is something that is a real + + align:start position:0% +and this is something that is a real + + + align:start position:0% +and this is something that is a real +struggle even for professional camera + + align:start position:0% +struggle even for professional camera + + + align:start position:0% +struggle even for professional camera +people sometimes because they they have + + align:start position:0% +people sometimes because they they have + + + align:start position:0% +people sometimes because they they have +all this sort of information bombarding + + align:start position:0% +all this sort of information bombarding + + + align:start position:0% +all this sort of information bombarding +them about what they want to do and they + + align:start position:0% +them about what they want to do and they + + + align:start position:0% +them about what they want to do and they +some of them especially people who come + + align:start position:0% +some of them especially people who come + + + align:start position:0% +some of them especially people who come +from still photography maybe don't hold + + align:start position:0% +from still photography maybe don't hold + + + align:start position:0% +from still photography maybe don't hold +the shots long enough um you know + + align:start position:0% +the shots long enough um you know + + + align:start position:0% +the shots long enough um you know +there's kind of a rule of you know like + + align:start position:0% +there's kind of a rule of you know like + + + align:start position:0% +there's kind of a rule of you know like +the nice long slow count to 10 before + + align:start position:0% +the nice long slow count to 10 before + + + align:start position:0% +the nice long slow count to 10 before +you then pan away to something else + + align:start position:0% +you then pan away to something else + + + align:start position:0% +you then pan away to something else +could be count to five if the action is + + align:start position:0% +could be count to five if the action is + + + align:start position:0% +could be count to five if the action is +a little faster um but just remember you + + align:start position:0% +a little faster um but just remember you + + + align:start position:0% +a little faster um but just remember you +know frame something up hold the shot + + align:start position:0% +know frame something up hold the shot + + + align:start position:0% +know frame something up hold the shot +and then move on um and then you know + + align:start position:0% +and then move on um and then you know + + + align:start position:0% +and then move on um and then you know +the idea also when you're moving the + + align:start position:0% +the idea also when you're moving the + + + align:start position:0% +the idea also when you're moving the +camera is is think about why you're + + align:start position:0% +camera is is think about why you're + + + align:start position:0% +camera is is think about why you're +moving the camera uh why would you move + + align:start position:0% +moving the camera uh why would you move + + + align:start position:0% +moving the camera uh why would you move +it why would you move the camera rather + + align:start position:0% +it why would you move the camera rather + + + align:start position:0% +it why would you move the camera rather +than just to hose down the + + align:start position:0% +than just to hose down the + + + align:start position:0% +than just to hose down the +room any basic + + align:start position:0% + + + + align:start position:0% + +ideas well like no if I'm moving if I if + + align:start position:0% +ideas well like no if I'm moving if I if + + + align:start position:0% +ideas well like no if I'm moving if I if +if I have a + + align:start position:0% +if I have a + + + align:start position:0% +if I have a +camera why would I actually start doing + + align:start position:0% +camera why would I actually start doing + + + align:start position:0% +camera why would I actually start doing +this why would I actually move + + align:start position:0% + + + + align:start position:0% + +well compared to compared to um just + + align:start position:0% +well compared to compared to um just + + + align:start position:0% +well compared to compared to um just +moving like this randomly or not moving + + align:start position:0% +moving like this randomly or not moving + + + align:start position:0% +moving like this randomly or not moving +at all you know what would motivate me + + align:start position:0% +at all you know what would motivate me + + + align:start position:0% +at all you know what would motivate me +to move the camera around talking + + align:start position:0% +to move the camera around talking + + + align:start position:0% +to move the camera around talking +somebody right yep exactly so following + + align:start position:0% +somebody right yep exactly so following + + + align:start position:0% +somebody right yep exactly so following +an action and it might be an actually a + + align:start position:0% +an action and it might be an actually a + + + align:start position:0% +an action and it might be an actually a +physical action I mean if I'm if I'm + + align:start position:0% +physical action I mean if I'm if I'm + + + align:start position:0% +physical action I mean if I'm if I'm +profiling Chris and suddenly she gets up + + align:start position:0% +profiling Chris and suddenly she gets up + + + align:start position:0% +profiling Chris and suddenly she gets up +and goes over and you know to like you + + align:start position:0% +and goes over and you know to like you + + + align:start position:0% +and goes over and you know to like you +know really get in Dave's face to really + + align:start position:0% +know really get in Dave's face to really + + + align:start position:0% +know really get in Dave's face to really +argue with him I I you know I'd want to + + align:start position:0% +argue with him I I you know I'd want to + + + align:start position:0% +argue with him I I you know I'd want to +follow that right but if they're just + + align:start position:0% +follow that right but if they're just + + + align:start position:0% +follow that right but if they're just +talking even cordially I don't know why + + align:start position:0% +talking even cordially I don't know why + + + align:start position:0% +talking even cordially I don't know why +I always bring you into conflict Dave I + + align:start position:0% +I always bring you into conflict Dave I + + + align:start position:0% +I always bring you into conflict Dave I +don't know apologize that's just who I + + align:start position:0% +don't know apologize that's just who I + + + align:start position:0% +don't know apologize that's just who I +am um yeah you just draw you know you + + align:start position:0% +am um yeah you just draw you know you + + + align:start position:0% +am um yeah you just draw you know you +just draw it out of people um but you + + align:start position:0% +just draw it out of people um but you + + + align:start position:0% +just draw it out of people um but you +know even if even if they're just + + align:start position:0% +know even if even if they're just + + + align:start position:0% +know even if even if they're just +they're speaking as you say I would be + + align:start position:0% +they're speaking as you say I would be + + + align:start position:0% +they're speaking as you say I would be +panning back and forth and at some point + + align:start position:0% +panning back and forth and at some point + + + align:start position:0% +panning back and forth and at some point +I might come over + + align:start position:0% + + + + align:start position:0% + +here and film Dave and start filming + + align:start position:0% +here and film Dave and start filming + + + align:start position:0% +here and film Dave and start filming +from his point of + + align:start position:0% +from his point of + + + align:start position:0% +from his point of +view so that's the you know that's the + + align:start position:0% +view so that's the you know that's the + + + align:start position:0% +view so that's the you know that's the +situation uh you you try to we want to + + align:start position:0% +situation uh you you try to we want to + + + align:start position:0% +situation uh you you try to we want to +try to make your moves motivated by + + align:start position:0% +try to make your moves motivated by + + + align:start position:0% +try to make your moves motivated by +something not just by kind of random + + align:start position:0% +something not just by kind of random + + + align:start position:0% +something not just by kind of random +hosing down of the room so that's again + + align:start position:0% +hosing down of the room so that's again + + + align:start position:0% +hosing down of the room so that's again +just a really basic concept + + align:start position:0% +just a really basic concept + + + align:start position:0% +just a really basic concept +and all of this is you know it's going + + align:start position:0% +and all of this is you know it's going + + + align:start position:0% +and all of this is you know it's going +to make a lot more sense when you start + + align:start position:0% +to make a lot more sense when you start + + + align:start position:0% +to make a lot more sense when you start +shooting and it's really going to make + + align:start position:0% +shooting and it's really going to make + + + align:start position:0% +shooting and it's really going to make +sense when you start editing because + + align:start position:0% +sense when you start editing because + + + align:start position:0% +sense when you start editing because +editing is the part where you really + + align:start position:0% +editing is the part where you really + + + align:start position:0% +editing is the part where you really +learn how to shoot I think all people + + align:start position:0% +learn how to shoot I think all people + + + align:start position:0% +learn how to shoot I think all people +who shoot should edit even if they don't + + align:start position:0% +who shoot should edit even if they don't + + + align:start position:0% +who shoot should edit even if they don't +want to be editors because that's when + + align:start position:0% +want to be editors because that's when + + + align:start position:0% +want to be editors because that's when +you really learn what's working and + + align:start position:0% +you really learn what's working and + + + align:start position:0% +you really learn what's working and +what's not working in your + + align:start position:0% +what's not working in your + + + align:start position:0% +what's not working in your +shooting + + align:start position:0% +shooting + + + align:start position:0% +shooting +um couple of other uh quick tips uh + + align:start position:0% +um couple of other uh quick tips uh + + + align:start position:0% +um couple of other uh quick tips uh +remember that although film is a + + align:start position:0% +remember that although film is a + + + align:start position:0% +remember that although film is a +two-dimensional art form and your images + + align:start position:0% +two-dimensional art form and your images + + + align:start position:0% +two-dimensional art form and your images +are all 2D you're you're representing a + + align:start position:0% +are all 2D you're you're representing a + + + align:start position:0% +are all 2D you're you're representing a +3D World and that means that you want to + + align:start position:0% +3D World and that means that you want to + + + align:start position:0% +3D World and that means that you want to +think about ways to create depth in your + + align:start position:0% +think about ways to create depth in your + + + align:start position:0% +think about ways to create depth in your +frame uh which means essentially + + align:start position:0% +frame uh which means essentially + + + align:start position:0% +frame uh which means essentially +different planes of action um so again + + align:start position:0% +different planes of action um so again + + + align:start position:0% +different planes of action um so again +if I'm filming Chris and + + align:start position:0% +if I'm filming Chris and + + + align:start position:0% +if I'm filming Chris and +Dave if I come around like this and I + + align:start position:0% +Dave if I come around like this and I + + + align:start position:0% +Dave if I come around like this and I +shoot Chris's shoulder in the foreground + + align:start position:0% +shoot Chris's shoulder in the foreground + + + align:start position:0% +shoot Chris's shoulder in the foreground +and Dave in the far background that's + + align:start position:0% +and Dave in the far background that's + + + align:start position:0% +and Dave in the far background that's +kind of a nice deep shot because we're + + align:start position:0% +kind of a nice deep shot because we're + + + align:start position:0% +kind of a nice deep shot because we're +we got a sense of the room we got a + + align:start position:0% +we got a sense of the room we got a + + + align:start position:0% +we got a sense of the room we got a +sense that there's depth that there's + + align:start position:0% +sense that there's depth that there's + + + align:start position:0% +sense that there's depth that there's +kind of a a dimensionality to to the + + align:start position:0% +kind of a a dimensionality to to the + + + align:start position:0% +kind of a a dimensionality to to the +conversation and then I can go over and + + align:start position:0% +conversation and then I can go over and + + + align:start position:0% +conversation and then I can go over and +I can do the same this way you know I + + align:start position:0% +I can do the same this way you know I + + + align:start position:0% +I can do the same this way you know I +also might still shoot close-ups and + + align:start position:0% +also might still shoot close-ups and + + + align:start position:0% +also might still shoot close-ups and +edit it all together um but you know + + align:start position:0% +edit it all together um but you know + + + align:start position:0% +edit it all together um but you know +what would be kind of weird and and + + align:start position:0% +what would be kind of weird and and + + + align:start position:0% +what would be kind of weird and and +orienting would be is again if they're + + align:start position:0% +orienting would be is again if they're + + + align:start position:0% +orienting would be is again if they're +having a conversation and I just filmed + + align:start position:0% +having a conversation and I just filmed + + + align:start position:0% +having a conversation and I just filmed +a close-up of + + align:start position:0% +a close-up of + + + align:start position:0% +a close-up of +Chris and then I went over and I filmed + + align:start position:0% +Chris and then I went over and I filmed + + + align:start position:0% +Chris and then I went over and I filmed +the close-up of Dave and I never had any + + align:start position:0% +the close-up of Dave and I never had any + + + align:start position:0% +the close-up of Dave and I never had any +sense of like the relationship in space + + align:start position:0% +sense of like the relationship in space + + + align:start position:0% +sense of like the relationship in space +or what the room was like or anything + + align:start position:0% +or what the room was like or anything + + + align:start position:0% +or what the room was like or anything +else because then you would just have + + align:start position:0% +else because then you would just have + + + align:start position:0% +else because then you would just have +this sort of head floating in space over + + align:start position:0% +this sort of head floating in space over + + + align:start position:0% +this sort of head floating in space over +here head floating in space over there + + align:start position:0% +here head floating in space over there + + + align:start position:0% +here head floating in space over there +with no kind of relationship between + + align:start position:0% +with no kind of relationship between + + + align:start position:0% +with no kind of relationship between +them and no kind of + + align:start position:0% +them and no kind of + + + align:start position:0% +them and no kind of +three-dimensionality so again using + + align:start position:0% +three-dimensionality so again using + + + align:start position:0% +three-dimensionality so again using +depth of field using even if something's + + align:start position:0% +depth of field using even if something's + + + align:start position:0% +depth of field using even if something's +out of focus in the background or in the + + align:start position:0% +out of focus in the background or in the + + + align:start position:0% +out of focus in the background or in the +foreground you know you you could also + + align:start position:0% +foreground you know you you could also + + + align:start position:0% +foreground you know you you could also +have the foreground be out of focus so + + align:start position:0% +have the foreground be out of focus so + + + align:start position:0% +have the foreground be out of focus so +you know if I if there was something on + + align:start position:0% +you know if I if there was something on + + + align:start position:0% +you know if I if there was something on +this computer that was really really + + align:start position:0% +this computer that was really really + + + align:start position:0% +this computer that was really really +interesting and I wanted to have Dave as + + align:start position:0% +interesting and I wanted to have Dave as + + + align:start position:0% +interesting and I wanted to have Dave as +well I could have this be out of focus + + align:start position:0% +well I could have this be out of focus + + + align:start position:0% +well I could have this be out of focus +and Dave in focus it doesn't have to be + + align:start position:0% +and Dave in focus it doesn't have to be + + + align:start position:0% +and Dave in focus it doesn't have to be +that the foreground is the one the thing + + align:start position:0% +that the foreground is the one the thing + + + align:start position:0% +that the foreground is the one the thing +that's in + + align:start position:0% +that's in + + + align:start position:0% +that's in +Focus um and then the last tip and then + + align:start position:0% +Focus um and then the last tip and then + + + align:start position:0% +Focus um and then the last tip and then +I'm going to turn it over to Dave and + + align:start position:0% +I'm going to turn it over to Dave and + + + align:start position:0% +I'm going to turn it over to Dave and +again I understand that this is all kind + + align:start position:0% +again I understand that this is all kind + + + align:start position:0% +again I understand that this is all kind +of you know abstract at this point but + + align:start position:0% +of you know abstract at this point but + + + align:start position:0% +of you know abstract at this point but +it's just kind of I want to put ideas + + align:start position:0% +it's just kind of I want to put ideas + + + align:start position:0% +it's just kind of I want to put ideas +out there that will hopefully kind of + + align:start position:0% +out there that will hopefully kind of + + + align:start position:0% +out there that will hopefully kind of +inform uh some of the shot choices that + + align:start position:0% +inform uh some of the shot choices that + + + align:start position:0% +inform uh some of the shot choices that +you'll may be making later um but the + + align:start position:0% +you'll may be making later um but the + + + align:start position:0% +you'll may be making later um but the +last thing I want to mention is framing + + align:start position:0% +last thing I want to mention is framing + + + align:start position:0% +last thing I want to mention is framing +in terms of centering things or not + + align:start position:0% +in terms of centering things or not + + + align:start position:0% +in terms of centering things or not +centering things um we tend to think put + + align:start position:0% +centering things um we tend to think put + + + align:start position:0% +centering things um we tend to think put +things off + + align:start position:0% +things off + + + align:start position:0% +things off +center this is a an interview that we + + align:start position:0% +center this is a an interview that we + + + align:start position:0% +center this is a an interview that we +did uh with Joel Dawson a professor in + + align:start position:0% +did uh with Joel Dawson a professor in + + + align:start position:0% +did uh with Joel Dawson a professor in +electrical engineering here kind of dark + + align:start position:0% +electrical engineering here kind of dark + + + align:start position:0% +electrical engineering here kind of dark +on the screen but um you see that he's + + align:start position:0% +on the screen but um you see that he's + + + align:start position:0% +on the screen but um you see that he's +off off center + + align:start position:0% +off off center + + + align:start position:0% +off off center +and there's a lot of negative space on + + align:start position:0% +and there's a lot of negative space on + + + align:start position:0% +and there's a lot of negative space on +the left which is where he's looking and + + align:start position:0% +the left which is where he's looking and + + + align:start position:0% +the left which is where he's looking and +that tends to be and and I'm talking + + align:start position:0% +that tends to be and and I'm talking + + + align:start position:0% +that tends to be and and I'm talking +about sort of very conventional Kinds of + + align:start position:0% +about sort of very conventional Kinds of + + + align:start position:0% +about sort of very conventional Kinds of +Kinds of Kinds of filming that tends to + + align:start position:0% +Kinds of Kinds of filming that tends to + + + align:start position:0% +Kinds of Kinds of filming that tends to +be something that's a little more + + align:start position:0% +be something that's a little more + + + align:start position:0% +be something that's a little more +pleasing because it gives this the the + + align:start position:0% +pleasing because it gives this the the + + + align:start position:0% +pleasing because it gives this the the +uh the frame some more + + align:start position:0% +uh the frame some more + + + align:start position:0% +uh the frame some more +energy uh psychologically I'm not + + align:start position:0% +energy uh psychologically I'm not + + + align:start position:0% +energy uh psychologically I'm not +exactly sure why that's true but it + + align:start position:0% +exactly sure why that's true but it + + + align:start position:0% +exactly sure why that's true but it +might be that there's sort of space for + + align:start position:0% +might be that there's sort of space for + + + align:start position:0% +might be that there's sort of space for +him to potentially move into rather than + + align:start position:0% +him to potentially move into rather than + + + align:start position:0% +him to potentially move into rather than +being lined up right in the center of + + align:start position:0% +being lined up right in the center of + + + align:start position:0% +being lined up right in the center of +the frame so there's so there he's + + align:start position:0% +the frame so there's so there he's + + + align:start position:0% +the frame so there's so there he's +looking kind of into space SP that he + + align:start position:0% +looking kind of into space SP that he + + + align:start position:0% +looking kind of into space SP that he +could sort of potentially occupy also + + align:start position:0% +could sort of potentially occupy also + + + align:start position:0% +could sort of potentially occupy also +just as an a side notice that the + + align:start position:0% +just as an a side notice that the + + + align:start position:0% +just as an a side notice that the +background is is very very soft it's + + align:start position:0% +background is is very very soft it's + + + align:start position:0% +background is is very very soft it's +it's shot with a quite a long lens uh + + align:start position:0% +it's shot with a quite a long lens uh + + + align:start position:0% +it's shot with a quite a long lens uh +which is nice because you know the the + + align:start position:0% +which is nice because you know the the + + + align:start position:0% +which is nice because you know the the +interview subject pops out number one + + align:start position:0% +interview subject pops out number one + + + align:start position:0% +interview subject pops out number one +and also number two it was this very + + align:start position:0% +and also number two it was this very + + + align:start position:0% +and also number two it was this very +very uh unattractive lab and it just + + align:start position:0% +very uh unattractive lab and it just + + + align:start position:0% +very uh unattractive lab and it just +goes away it's very nice um the other + + align:start position:0% +goes away it's very nice um the other + + + align:start position:0% +goes away it's very nice um the other +thing about about uh filming things off + + align:start position:0% +thing about about uh filming things off + + + align:start position:0% +thing about about uh filming things off +center like this is that um uh you you + + align:start position:0% +center like this is that um uh you you + + + align:start position:0% +center like this is that um uh you you +want to think about in terms of Framing + + align:start position:0% +want to think about in terms of Framing + + + align:start position:0% +want to think about in terms of Framing +and this is again kind of classic + + align:start position:0% +and this is again kind of classic + + + align:start position:0% +and this is again kind of classic +composition um think about your frame in + + align:start position:0% +composition um think about your frame in + + + align:start position:0% +composition um think about your frame in +thirds uh the the the the the the third + + align:start position:0% +thirds uh the the the the the the third + + + align:start position:0% +thirds uh the the the the the the third +dividing lines you know if you take a a + + align:start position:0% +dividing lines you know if you take a a + + + align:start position:0% +dividing lines you know if you take a a +line and and divide it vertically in + + align:start position:0% +line and and divide it vertically in + + + align:start position:0% +line and and divide it vertically in +thirds and then there's one line missing + + align:start position:0% +thirds and then there's one line missing + + + align:start position:0% +thirds and then there's one line missing +here but horizontally in thirds the + + align:start position:0% +here but horizontally in thirds the + + + align:start position:0% +here but horizontally in thirds the +intersections of the lines tend to be + + align:start position:0% +intersections of the lines tend to be + + + align:start position:0% +intersections of the lines tend to be +kind of powerful places in the frame and + + align:start position:0% +kind of powerful places in the frame and + + + align:start position:0% +kind of powerful places in the frame and +you notice here again it's very kind of + + align:start position:0% +you notice here again it's very kind of + + + align:start position:0% +you notice here again it's very kind of +classic kind of framing his eye + + align:start position:0% +classic kind of framing his eye + + + align:start position:0% +classic kind of framing his eye +lines up exactly with one of those third + + align:start position:0% +lines up exactly with one of those third + + + align:start position:0% +lines up exactly with one of those third +places one of those + + align:start position:0% +places one of those + + + align:start position:0% +places one of those +intersections um that's why when you + + align:start position:0% +intersections um that's why when you + + + align:start position:0% +intersections um that's why when you +have close-ups of people in movies and + + align:start position:0% +have close-ups of people in movies and + + + align:start position:0% +have close-ups of people in movies and +it gets really really close they tend to + + align:start position:0% +it gets really really close they tend to + + + align:start position:0% +it gets really really close they tend to +chop the top of the head off because + + align:start position:0% +chop the top of the head off because + + + align:start position:0% +chop the top of the head off because +they're keeping the ey line roughly in + + align:start position:0% +they're keeping the ey line roughly in + + + align:start position:0% +they're keeping the ey line roughly in +the top third of the frame you notice + + align:start position:0% +the top third of the frame you notice + + + align:start position:0% +the top third of the frame you notice +again he's centered this way so there's + + align:start position:0% +again he's centered this way so there's + + + align:start position:0% +again he's centered this way so there's +a lot of negative space over there could + + align:start position:0% +a lot of negative space over there could + + + align:start position:0% +a lot of negative space over there could +you could just as easily put him over + + align:start position:0% +you could just as easily put him over + + + align:start position:0% +you could just as easily put him over +here looking kind of this way into the + + align:start position:0% +here looking kind of this way into the + + + align:start position:0% +here looking kind of this way into the +negative space and his eye could be + + align:start position:0% +negative space and his eye could be + + + align:start position:0% +negative space and his eye could be +lined up with that um if his was a wider + + align:start position:0% +lined up with that um if his was a wider + + + align:start position:0% +lined up with that um if his was a wider +shot like a very wide shot maybe a head + + align:start position:0% +shot like a very wide shot maybe a head + + + align:start position:0% +shot like a very wide shot maybe a head +to body shot and we saw the entire frame + + align:start position:0% +to body shot and we saw the entire frame + + + align:start position:0% +to body shot and we saw the entire frame +you know you would probably if again if + + align:start position:0% +you know you would probably if again if + + + align:start position:0% +you know you would probably if again if +it was classic uh classic framing his + + align:start position:0% +it was classic uh classic framing his + + + align:start position:0% +it was classic uh classic framing his +head would end up being kind of in one + + align:start position:0% +head would end up being kind of in one + + + align:start position:0% +head would end up being kind of in one +of these third spaces as well so you + + align:start position:0% +of these third spaces as well so you + + + align:start position:0% +of these third spaces as well so you +know imagine a whole body with a head + + align:start position:0% +know imagine a whole body with a head + + + align:start position:0% +know imagine a whole body with a head +here or here and if they were walking + + align:start position:0% +here or here and if they were walking + + + align:start position:0% +here or here and if they were walking +and you were panning with them you know + + align:start position:0% +and you were panning with them you know + + + align:start position:0% +and you were panning with them you know +if he was walking this way you would + + align:start position:0% +if he was walking this way you would + + + align:start position:0% +if he was walking this way you would +probably frame him up kind of on that + + align:start position:0% +probably frame him up kind of on that + + + align:start position:0% +probably frame him up kind of on that +line with his head there which would + + align:start position:0% +line with his head there which would + + + align:start position:0% +line with his head there which would +give him plenty of space to walk into + + align:start position:0% +give him plenty of space to walk into + + + align:start position:0% +give him plenty of space to walk into +and then you would continue to pan with + + align:start position:0% +and then you would continue to pan with + + + align:start position:0% +and then you would continue to pan with +him always giving more space here which + + align:start position:0% +him always giving more space here which + + + align:start position:0% +him always giving more space here which +because again that gives you kind of + + align:start position:0% +because again that gives you kind of + + + align:start position:0% +because again that gives you kind of +this this energetic frame in the sense + + align:start position:0% +this this energetic frame in the sense + + + align:start position:0% +this this energetic frame in the sense +that the person is walking and you're + + align:start position:0% +that the person is walking and you're + + + align:start position:0% +that the person is walking and you're +following so that's the very very kind + + align:start position:0% +following so that's the very very kind + + + align:start position:0% +following so that's the very very kind +of quick tour of some things to think + + align:start position:0% +of quick tour of some things to think + + + align:start position:0% +of quick tour of some things to think +about when you frame and and choose + + align:start position:0% +about when you frame and and choose + + + align:start position:0% +about when you frame and and choose +shots and we will be spending a lot of + + align:start position:0% +shots and we will be spending a lot of + + + align:start position:0% +shots and we will be spending a lot of +time on this in this in this class so + + align:start position:0% +time on this in this in this class so + + + align:start position:0% +time on this in this in this class so +don't think that you know you needed to + + align:start position:0% +don't think that you know you needed to + + + align:start position:0% +don't think that you know you needed to +sort of absorb it all right now but um + + align:start position:0% +sort of absorb it all right now but um + + + align:start position:0% +sort of absorb it all right now but um +go ahead and + + align:start position:0% + + + + align:start position:0% + +one I was the future becomes a chance + + align:start position:0% +one I was the future becomes a chance + + + align:start position:0% +one I was the future becomes a chance +that after you've been playing around + + align:start position:0% +that after you've been playing around + + + align:start position:0% +that after you've been playing around +with the camera some point you can go + + align:start position:0% +with the camera some point you can go + + + align:start position:0% +with the camera some point you can go +back and to + + align:start position:0% + + + + align:start position:0% + +this this will this will make the most + + align:start position:0% +this this will this will make the most + + + align:start position:0% +this this will this will make the most +sense when you've as I said not only + + align:start position:0% +sense when you've as I said not only + + + align:start position:0% +sense when you've as I said not only +done some shooting but also done some + + align:start position:0% +done some shooting but also done some + + + align:start position:0% +done some shooting but also done some +editing and um you know between now and + + align:start position:0% +editing and um you know between now and + + + align:start position:0% +editing and um you know between now and +then we will definitely be going back to + + align:start position:0% +then we will definitely be going back to + + + align:start position:0% +then we will definitely be going back to +talk more about film language and film + + align:start position:0% +talk more about film language and film + + + align:start position:0% +talk more about film language and film +grammar and the shot kinds of shots that + + align:start position:0% +grammar and the shot kinds of shots that + + + align:start position:0% +grammar and the shot kinds of shots that +cut together and the kinds of shots that + + align:start position:0% +cut together and the kinds of shots that + + + align:start position:0% +cut together and the kinds of shots that +don't cut together um I'm going to turn + + align:start position:0% +don't cut together um I'm going to turn + + + align:start position:0% +don't cut together um I'm going to turn +it over to Dave in just a minute um but + + align:start position:0% +it over to Dave in just a minute um but + + + align:start position:0% +it over to Dave in just a minute um but +I want to say one last word about + + align:start position:0% +I want to say one last word about + + + align:start position:0% +I want to say one last word about +formats uh so formats in video are + + align:start position:0% +formats uh so formats in video are + + + align:start position:0% +formats uh so formats in video are +proliferating like crazy there are an + + align:start position:0% +proliferating like crazy there are an + + + align:start position:0% +proliferating like crazy there are an +endless number of of + + align:start position:0% +endless number of of + + + align:start position:0% +endless number of of +HD uh SD but at this point primarily HD + + align:start position:0% +HD uh SD but at this point primarily HD + + + align:start position:0% +HD uh SD but at this point primarily HD +High defition formats the one we're + + align:start position:0% +High defition formats the one we're + + + align:start position:0% +High defition formats the one we're +filming in or using in this class is hdv + + align:start position:0% +filming in or using in this class is hdv + + + align:start position:0% +filming in or using in this class is hdv +1080i 1440 x 1080 which is basically a + + align:start position:0% +1080i 1440 x 1080 which is basically a + + + align:start position:0% +1080i 1440 x 1080 which is basically a +compressed version of full h which is + + align:start position:0% +compressed version of full h which is + + + align:start position:0% +compressed version of full h which is +1920 by 1080 and you may know something + + align:start position:0% +1920 by 1080 and you may know something + + + align:start position:0% +1920 by 1080 and you may know something +about what those things mean you may + + align:start position:0% +about what those things mean you may + + + align:start position:0% +about what those things mean you may +know nothing about what they mean but I + + align:start position:0% +know nothing about what they mean but I + + + align:start position:0% +know nothing about what they mean but I +want you to kind of write them down and + + align:start position:0% +want you to kind of write them down and + + + align:start position:0% +want you to kind of write them down and +you'll absorb them later uh if that + + align:start position:0% +you'll absorb them later uh if that + + + align:start position:0% +you'll absorb them later uh if that +makes sense basically um 1920 by 1080 + + align:start position:0% +makes sense basically um 1920 by 1080 + + + align:start position:0% +makes sense basically um 1920 by 1080 +refers to the size of the frame it's + + align:start position:0% +refers to the size of the frame it's + + + align:start position:0% +refers to the size of the frame it's +1,920 pixels wide by 1,80 pixels High + + align:start position:0% +1,920 pixels wide by 1,80 pixels High + + + align:start position:0% +1,920 pixels wide by 1,80 pixels High +which again if we go back to this Frame + + align:start position:0% +which again if we go back to this Frame + + + align:start position:0% +which again if we go back to this Frame +that gives you basically that aspect + + align:start position:0% +that gives you basically that aspect + + + align:start position:0% +that gives you basically that aspect +ratio so you know it's wider than it is + + align:start position:0% +ratio so you know it's wider than it is + + + align:start position:0% +ratio so you know it's wider than it is +high and that's you know 16 by9 + + align:start position:0% +high and that's you know 16 by9 + + + align:start position:0% +high and that's you know 16 by9 +televisions as opposed to standard + + align:start position:0% +televisions as opposed to standard + + + align:start position:0% +televisions as opposed to standard +definition Square televisions um our + + align:start position:0% +definition Square televisions um our + + + align:start position:0% +definition Square televisions um our +data rate is 25 megabits per second uh + + align:start position:0% +data rate is 25 megabits per second uh + + + align:start position:0% +data rate is 25 megabits per second uh +and that boils down to approximately + + align:start position:0% +and that boils down to approximately + + + align:start position:0% +and that boils down to approximately +more or less 10 gigabits gigabytes per + + align:start position:0% +more or less 10 gigabits gigabytes per + + + align:start position:0% +more or less 10 gigabits gigabytes per +hour and what that means obviously is + + align:start position:0% +hour and what that means obviously is + + + align:start position:0% +hour and what that means obviously is +that the file sizes are very very large + + align:start position:0% +that the file sizes are very very large + + + align:start position:0% +that the file sizes are very very large +there's a lot of data uh the camera's + + align:start position:0% +there's a lot of data uh the camera's + + + align:start position:0% +there's a lot of data uh the camera's +capturing a lot of data the the computer + + align:start position:0% +capturing a lot of data the the computer + + + align:start position:0% +capturing a lot of data the the computer +you edit on is expected to process a lot + + align:start position:0% +you edit on is expected to process a lot + + + align:start position:0% +you edit on is expected to process a lot +of data and one of the things that we + + align:start position:0% +of data and one of the things that we + + + align:start position:0% +of data and one of the things that we +will be talking about later in the class + + align:start position:0% +will be talking about later in the class + + + align:start position:0% +will be talking about later in the class +is how you know the it revolution has + + align:start position:0% +is how you know the it revolution has + + + align:start position:0% +is how you know the it revolution has +really enabled video documentaries and + + align:start position:0% +really enabled video documentaries and + + + align:start position:0% +really enabled video documentaries and +completely changed the game and enabled + + align:start position:0% +completely changed the game and enabled + + + align:start position:0% +completely changed the game and enabled +things like this class to happen um + + align:start position:0% +things like this class to happen um + + + align:start position:0% +things like this class to happen um +Point here is mainly just so that you're + + align:start position:0% +Point here is mainly just so that you're + + + align:start position:0% +Point here is mainly just so that you're +kind of aware of the format that that + + align:start position:0% +kind of aware of the format that that + + + align:start position:0% +kind of aware of the format that that +these cameras shoot and uh what the file + + align:start position:0% +these cameras shoot and uh what the file + + + align:start position:0% +these cameras shoot and uh what the file +sizes are are going to be that's also + + align:start position:0% +sizes are are going to be that's also + + + align:start position:0% +sizes are are going to be that's also +why we give each of you a hard drive so + + align:start position:0% +why we give each of you a hard drive so + + + align:start position:0% +why we give each of you a hard drive so +that you don't have to you know worry + + align:start position:0% +that you don't have to you know worry + + + align:start position:0% +that you don't have to you know worry +about how you're going to store a + + align:start position:0% +about how you're going to store a + + + align:start position:0% +about how you're going to store a +terabyte worth of material on your own + + align:start position:0% +terabyte worth of material on your own + + + align:start position:0% +terabyte worth of material on your own +so uh any quick questions before I turn + + align:start position:0% +so uh any quick questions before I turn + + + align:start position:0% +so uh any quick questions before I turn +it over to + + align:start position:0% + + + + align:start position:0% + +Dave + + align:start position:0% + + + + align:start position:0% + +yeah shape yeah it's basically squeezed + + align:start position:0% +yeah shape yeah it's basically squeezed + + + align:start position:0% +yeah shape yeah it's basically squeezed +uh but you never see it squeezed they it + + align:start position:0% +uh but you never see it squeezed they it + + + align:start position:0% +uh but you never see it squeezed they it +actually then gets get uncompressed + + align:start position:0% +actually then gets get uncompressed + + + align:start position:0% +actually then gets get uncompressed +automatically when it's viewed so we see + + align:start position:0% +automatically when it's viewed so we see + + + align:start position:0% +automatically when it's viewed so we see +that 1920 yes yeah you see the same it + + align:start position:0% +that 1920 yes yeah you see the same it + + + align:start position:0% +that 1920 yes yeah you see the same it +looks like 1920 by 1080 and the reason + + align:start position:0% +looks like 1920 by 1080 and the reason + + + align:start position:0% +looks like 1920 by 1080 and the reason +that they compress it like that is to + + align:start position:0% +that they compress it like that is to + + + align:start position:0% +that they compress it like that is to +save uh save space so the 25 megabits + + align:start position:0% +save uh save space so the 25 megabits + + + align:start position:0% +save uh save space so the 25 megabits +per second data rate is very very low + + align:start position:0% +per second data rate is very very low + + + align:start position:0% +per second data rate is very very low +for high + + align:start position:0% +for high + + + align:start position:0% +for high +defition you know video uh most most + + align:start position:0% +defition you know video uh most most + + + align:start position:0% +defition you know video uh most most +data rates are higher than that like 35 + + align:start position:0% +data rates are higher than that like 35 + + + align:start position:0% +data rates are higher than that like 35 +50 55 or for completely uncompressed HD + + align:start position:0% +50 55 or for completely uncompressed HD + + + align:start position:0% +50 55 or for completely uncompressed HD +really I forget it's really really high + + align:start position:0% +really I forget it's really really high + + + align:start position:0% +really I forget it's really really high +um so so it's just a strategy for for + + align:start position:0% +um so so it's just a strategy for for + + + align:start position:0% +um so so it's just a strategy for for +giving less data but still having a nice + + align:start position:0% +giving less data but still having a nice + + + align:start position:0% +giving less data but still having a nice +HD + + align:start position:0% +HD + + + align:start position:0% +HD +image yeah you never actually see that + + align:start position:0% +image yeah you never actually see that + + + align:start position:0% +image yeah you never actually see that +unless you make a mistake in Final Cut + + align:start position:0% +unless you make a mistake in Final Cut + + + align:start position:0% +unless you make a mistake in Final Cut +which we'll we can talk about later and + + align:start position:0% +which we'll we can talk about later and + + + align:start position:0% +which we'll we can talk about later and +just one word about why we're using tape + + align:start position:0% +just one word about why we're using tape + + + align:start position:0% +just one word about why we're using tape +in this era of cards and files um one + + align:start position:0% +in this era of cards and files um one + + + align:start position:0% +in this era of cards and files um one +reason is that the cameras are a couple + + align:start position:0% +reason is that the cameras are a couple + + + align:start position:0% +reason is that the cameras are a couple +of years old but but there's actually + + align:start position:0% +of years old but but there's actually + + + align:start position:0% +of years old but but there's actually +another reason too which is that this + + align:start position:0% +another reason too which is that this + + + align:start position:0% +another reason too which is that this +provides a very cheap and easy backup + + align:start position:0% +provides a very cheap and easy backup + + + align:start position:0% +provides a very cheap and easy backup +for you uh file + + align:start position:0% +for you uh file + + + align:start position:0% +for you uh file +management as wonderful as cards are and + + align:start position:0% +management as wonderful as cards are and + + + align:start position:0% +management as wonderful as cards are and +as much as it speeds the process and I'm + + align:start position:0% +as much as it speeds the process and I'm + + + align:start position:0% +as much as it speeds the process and I'm +a big fan of them uh in a student + + align:start position:0% +a big fan of them uh in a student + + + align:start position:0% +a big fan of them uh in a student +situation if you want to do cheap + + align:start position:0% +situation if you want to do cheap + + + align:start position:0% +situation if you want to do cheap +backups there's you know tape is is + + align:start position:0% +backups there's you know tape is is + + + align:start position:0% +backups there's you know tape is is +great you can stick them in your sock + + align:start position:0% +great you can stick them in your sock + + + align:start position:0% +great you can stick them in your sock +drawer and not have to worry about your + + align:start position:0% +drawer and not have to worry about your + + + align:start position:0% +drawer and not have to worry about your +hard drive crashing or something \ No newline at end of file diff --git a/nNqnivVl8WI.txt b/nNqnivVl8WI.txt new file mode 100644 index 0000000000000000000000000000000000000000..4f9891aead40f107678456603a454d2f2621ffae --- /dev/null +++ b/nNqnivVl8WI.txt @@ -0,0 +1,8139 @@ +align:start position:0% + +okay let's uh let's start so today we're + + align:start position:0% +okay let's uh let's start so today we're + + + align:start position:0% +okay let's uh let's start so today we're +going to talk about technological + + align:start position:0% +going to talk about technological + + + align:start position:0% +going to talk about technological +progress and economic growth + + align:start position:0% +progress and economic growth + + + align:start position:0% +progress and economic growth +um I mean that's it's a big topic + + align:start position:0% +um I mean that's it's a big topic + + + align:start position:0% +um I mean that's it's a big topic +certainly at MIT + + align:start position:0% +certainly at MIT + + + align:start position:0% +certainly at MIT +perhaps this is one of the main ways we + + align:start position:0% +perhaps this is one of the main ways we + + + align:start position:0% +perhaps this is one of the main ways we +contribute + + align:start position:0% + + + + align:start position:0% + +to human well-being no um but before I + + align:start position:0% +to human well-being no um but before I + + + align:start position:0% +to human well-being no um but before I +do that let me let me H do a brief + + align:start position:0% +do that let me let me H do a brief + + + align:start position:0% +do that let me let me H do a brief +review of of the things I did the second + + align:start position:0% +review of of the things I did the second + + + align:start position:0% +review of of the things I did the second +half of the the previous + + align:start position:0% +half of the the previous + + + align:start position:0% +half of the the previous +lecture for two reasons I want to do + + align:start position:0% +lecture for two reasons I want to do + + + align:start position:0% +lecture for two reasons I want to do +that Brief Review first um is as after + + align:start position:0% +that Brief Review first um is as after + + + align:start position:0% +that Brief Review first um is as after +spring break so I assume there is some + + align:start position:0% +spring break so I assume there is some + + + align:start position:0% +spring break so I assume there is some +depreciation of knowledge H since the + + align:start position:0% +depreciation of knowledge H since the + + + align:start position:0% +depreciation of knowledge H since the +last time and and the second is that + + align:start position:0% +last time and and the second is that + + + align:start position:0% +last time and and the second is that +that while the equations I show you at + + align:start position:0% +that while the equations I show you at + + + align:start position:0% +that while the equations I show you at +the end with population growth are + + align:start position:0% +the end with population growth are + + + align:start position:0% +the end with population growth are +correct I think I said something which + + align:start position:0% +correct I think I said something which + + + align:start position:0% +correct I think I said something which +is not correct I think I kept saying I + + align:start position:0% +is not correct I think I kept saying I + + + align:start position:0% +is not correct I think I kept saying I +don't know why but I kept saying look if + + align:start position:0% +don't know why but I kept saying look if + + + align:start position:0% +don't know why but I kept saying look if +x is small 1/ 1 plus X is approximately + + align:start position:0% +x is small 1/ 1 plus X is approximately + + + align:start position:0% +x is small 1/ 1 plus X is approximately +equal to Min - x no no it's + + align:start position:0% +equal to Min - x no no it's + + + align:start position:0% +equal to Min - x no no it's +approximately equal to 1 - x not Min - x + + align:start position:0% +approximately equal to 1 - x not Min - x + + + align:start position:0% +approximately equal to 1 - x not Min - x +but uh so I wanted to correct that that + + align:start position:0% +but uh so I wanted to correct that that + + + align:start position:0% +but uh so I wanted to correct that that +typle so let me remind you what what we + + align:start position:0% +typle so let me remind you what what we + + + align:start position:0% +typle so let me remind you what what we +had U so we had we started with a + + align:start position:0% +had U so we had we started with a + + + align:start position:0% +had U so we had we started with a +production function one of an important + + align:start position:0% +production function one of an important + + + align:start position:0% +production function one of an important +part of economic growth is we're going + + align:start position:0% +part of economic growth is we're going + + + align:start position:0% +part of economic growth is we're going +to capital accumulation will be sort of + + align:start position:0% +to capital accumulation will be sort of + + + align:start position:0% +to capital accumulation will be sort of +a very important variable here and so we + + align:start position:0% +a very important variable here and so we + + + align:start position:0% +a very important variable here and so we +hadn't talked about capital in the + + align:start position:0% +hadn't talked about capital in the + + + align:start position:0% +hadn't talked about capital in the +production function in the previous uh + + align:start position:0% +production function in the previous uh + + + align:start position:0% +production function in the previous uh +part of the course but now we we were + + align:start position:0% +part of the course but now we we were + + + align:start position:0% +part of the course but now we we were +explicit about it and we start with a + + align:start position:0% +explicit about it and we start with a + + + align:start position:0% +explicit about it and we start with a +production function that constant + + align:start position:0% +production function that constant + + + align:start position:0% +production function that constant +returns to scale h on Capital and labor + + align:start position:0% +returns to scale h on Capital and labor + + + align:start position:0% +returns to scale h on Capital and labor +H and here remember in this part of the + + align:start position:0% +H and here remember in this part of the + + + align:start position:0% +H and here remember in this part of the +course we're not talking about + + align:start position:0% +course we're not talking about + + + align:start position:0% +course we're not talking about +unemployment or anything like that so + + align:start position:0% +unemployment or anything like that so + + + align:start position:0% +unemployment or anything like that so +whenever I say labor I also mean + + align:start position:0% +whenever I say labor I also mean + + + align:start position:0% +whenever I say labor I also mean +population I mean labor force all of + + align:start position:0% +population I mean labor force all of + + + align:start position:0% +population I mean labor force all of +them together you know the distinction + + align:start position:0% +them together you know the distinction + + + align:start position:0% +them together you know the distinction +between each of these Concepts but + + align:start position:0% +between each of these Concepts but + + + align:start position:0% +between each of these Concepts but +they're not that important for growth + + align:start position:0% +they're not that important for growth + + + align:start position:0% +they're not that important for growth +matters mostly because all of those + + align:start position:0% +matters mostly because all of those + + + align:start position:0% +matters mostly because all of those +Aggregates sort of move in tandem over + + align:start position:0% +Aggregates sort of move in tandem over + + + align:start position:0% +Aggregates sort of move in tandem over +the long run no it's very difficult for + + align:start position:0% +the long run no it's very difficult for + + + align:start position:0% +the long run no it's very difficult for +for a + + align:start position:0% +for a + + + align:start position:0% +for a +population and the labor force to + + align:start position:0% +population and the labor force to + + + align:start position:0% +population and the labor force to +diverge for a very long period of time + + align:start position:0% +diverge for a very long period of time + + + align:start position:0% +diverge for a very long period of time +you know there may be fluctuations and + + align:start position:0% +you know there may be fluctuations and + + + align:start position:0% +you know there may be fluctuations and +so on but then tend to move together + + align:start position:0% +so on but then tend to move together + + + align:start position:0% +so on but then tend to move together +um so but we decided that we wanted to + + align:start position:0% +um so but we decided that we wanted to + + + align:start position:0% +um so but we decided that we wanted to +look at things normalized by by + + align:start position:0% +look at things normalized by by + + + align:start position:0% +look at things normalized by by +population and so output per per person + + align:start position:0% +population and so output per per person + + + align:start position:0% +population and so output per per person +is is an increasing function of capital + + align:start position:0% +is is an increasing function of capital + + + align:start position:0% +is is an increasing function of capital +per person but also is is increasing at + + align:start position:0% +per person but also is is increasing at + + + align:start position:0% +per person but also is is increasing at +a decreasing rate no there's decreasing + + align:start position:0% +a decreasing rate no there's decreasing + + + align:start position:0% +a decreasing rate no there's decreasing +returns with respect to uh the capital + + align:start position:0% +returns with respect to uh the capital + + + align:start position:0% +returns with respect to uh the capital +labor ratio and so output per capital + + align:start position:0% +labor ratio and so output per capital + + + align:start position:0% +labor ratio and so output per capital +grows as capital per as the economy + + align:start position:0% +grows as capital per as the economy + + + align:start position:0% +grows as capital per as the economy +becomes more Capital intensive that is + + align:start position:0% +becomes more Capital intensive that is + + + align:start position:0% +becomes more Capital intensive that is +you have more Capital per worker + + align:start position:0% +you have more Capital per worker + + + align:start position:0% +you have more Capital per worker +H but it grows at a decreasing rate the + + align:start position:0% +H but it grows at a decreasing rate the + + + align:start position:0% +H but it grows at a decreasing rate the +second key equation of the our model was + + align:start position:0% +second key equation of the our model was + + + align:start position:0% +second key equation of the our model was +that that assumed we're say in this part + + align:start position:0% +that that assumed we're say in this part + + + align:start position:0% +that that assumed we're say in this part +of the course we're going to assume that + + align:start position:0% +of the course we're going to assume that + + + align:start position:0% +of the course we're going to assume that +the government is not running any fiscal + + align:start position:0% +the government is not running any fiscal + + + align:start position:0% +the government is not running any fiscal +deficit or anything like that and the + + align:start position:0% +deficit or anything like that and the + + + align:start position:0% +deficit or anything like that and the +econom is closed which is an assumption + + align:start position:0% +econom is closed which is an assumption + + + align:start position:0% +econom is closed which is an assumption +we have maintain and we will keep + + align:start position:0% +we have maintain and we will keep + + + align:start position:0% +we have maintain and we will keep +assuming until three lectures from now + + align:start position:0% +assuming until three lectures from now + + + align:start position:0% +assuming until three lectures from now +and so in close economy no fiscal + + align:start position:0% +and so in close economy no fiscal + + + align:start position:0% +and so in close economy no fiscal +deficit we have that + + align:start position:0% +deficit we have that + + + align:start position:0% +deficit we have that +investment is equal to saving and we + + align:start position:0% +investment is equal to saving and we + + + align:start position:0% +investment is equal to saving and we +made an extra step to assume that the + + align:start position:0% +made an extra step to assume that the + + + align:start position:0% +made an extra step to assume that the +saving is proportional to income okay so + + align:start position:0% +saving is proportional to income okay so + + + align:start position:0% +saving is proportional to income okay so +s proportional to income so with all + + align:start position:0% +s proportional to income so with all + + + align:start position:0% +s proportional to income so with all +these things together putting this two + + align:start position:0% +these things together putting this two + + + align:start position:0% +these things together putting this two +things together H we got to our a very + + align:start position:0% +things together H we got to our a very + + + align:start position:0% +things together H we got to our a very +important equation in any growth model + + align:start position:0% +important equation in any growth model + + + align:start position:0% +important equation in any growth model +which is the capital accumulation + + align:start position:0% +which is the capital accumulation + + + align:start position:0% +which is the capital accumulation +equation and this equation says well the + + align:start position:0% +equation and this equation says well the + + + align:start position:0% +equation and this equation says well the +Capital stock tomorrow tomorrow means in + + align:start position:0% +Capital stock tomorrow tomorrow means in + + + align:start position:0% +Capital stock tomorrow tomorrow means in +the next unit time next year or whatever + + align:start position:0% +the next unit time next year or whatever + + + align:start position:0% +the next unit time next year or whatever +H H is equal to the current stock of + + align:start position:0% +H H is equal to the current stock of + + + align:start position:0% +H H is equal to the current stock of +capital minus the depreciation of that + + align:start position:0% +capital minus the depreciation of that + + + align:start position:0% +capital minus the depreciation of that +stock of capital minus Delta time KT + + align:start position:0% +stock of capital minus Delta time KT + + + align:start position:0% +stock of capital minus Delta time KT +plus investment but investment is equal + + align:start position:0% +plus investment but investment is equal + + + align:start position:0% +plus investment but investment is equal +to saving and saving is equal to H uh is + + align:start position:0% +to saving and saving is equal to H uh is + + + align:start position:0% +to saving and saving is equal to H uh is +proportional to to Output okay so that + + align:start position:0% +proportional to to Output okay so that + + + align:start position:0% +proportional to to Output okay so that +was the that was common across all the + + align:start position:0% +was the that was common across all the + + + align:start position:0% +was the that was common across all the +things we did in the previous lectur is + + align:start position:0% +things we did in the previous lectur is + + + align:start position:0% +things we did in the previous lectur is +there any question about these equations + + align:start position:0% +there any question about these equations + + + align:start position:0% +there any question about these equations +no no good okay so the next step was to + + align:start position:0% +no no good okay so the next step was to + + + align:start position:0% +no no good okay so the next step was to +say okay and and I did remember all the + + align:start position:0% +say okay and and I did remember all the + + + align:start position:0% +say okay and and I did remember all the +initial derivations I assumed that n was + + align:start position:0% +initial derivations I assumed that n was + + + align:start position:0% +initial derivations I assumed that n was +constant population was constant + + align:start position:0% +constant population was constant + + + align:start position:0% +constant population was constant +and + + align:start position:0% +and + + + align:start position:0% +and +so and the next step was I divided by a + + align:start position:0% +so and the next step was I divided by a + + + align:start position:0% +so and the next step was I divided by a +constant here so we did everything in + + align:start position:0% +constant here so we did everything in + + + align:start position:0% +constant here so we did everything in +terms of capital output per per person + + align:start position:0% +terms of capital output per per person + + + align:start position:0% +terms of capital output per per person +but actually since population was + + align:start position:0% +but actually since population was + + + align:start position:0% +but actually since population was +constant the per person part was just + + align:start position:0% +constant the per person part was just + + + align:start position:0% +constant the per person part was just +the tri we just divide it by a constant + + align:start position:0% +the tri we just divide it by a constant + + + align:start position:0% +the tri we just divide it by a constant +the last thing I did though in the + + align:start position:0% +the last thing I did though in the + + + align:start position:0% +the last thing I did though in the +previous lecture was to say okay what if + + align:start position:0% +previous lecture was to say okay what if + + + align:start position:0% +previous lecture was to say okay what if +not if that's not the case what if + + align:start position:0% +not if that's not the case what if + + + align:start position:0% +not if that's not the case what if +population is growing over time as well + + align:start position:0% +population is growing over time as well + + + align:start position:0% +population is growing over time as well +how does our analy change and so I did + + align:start position:0% +how does our analy change and so I did + + + align:start position:0% +how does our analy change and so I did +this no I said well okay let's try let's + + align:start position:0% +this no I said well okay let's try let's + + + align:start position:0% +this no I said well okay let's try let's +start by dividing everything by NT + one + + align:start position:0% +start by dividing everything by NT + one + + + align:start position:0% +start by dividing everything by NT + one +so then we get Capital per uh person at + + align:start position:0% +so then we get Capital per uh person at + + + align:start position:0% +so then we get Capital per uh person at +t+ one problem is I said is when I + + align:start position:0% +t+ one problem is I said is when I + + + align:start position:0% +t+ one problem is I said is when I +divide the right hand side by NT plus + + align:start position:0% +divide the right hand side by NT plus + + + align:start position:0% +divide the right hand side by NT plus +one I don't get what I want I want + + align:start position:0% +one I don't get what I want I want + + + align:start position:0% +one I don't get what I want I want +Capital at T divided by population of T + + align:start position:0% +Capital at T divided by population of T + + + align:start position:0% +Capital at T divided by population of T +I want output at T divide by population + + align:start position:0% +I want output at T divide by population + + + align:start position:0% +I want output at T divide by population +of T not at t+ one okay so what I did is + + align:start position:0% +of T not at t+ one okay so what I did is + + + align:start position:0% +of T not at t+ one okay so what I did is +I multiply and divide by n T both of + + align:start position:0% +I multiply and divide by n T both of + + + align:start position:0% +I multiply and divide by n T both of +these so I multiply by one NT over NT is + + align:start position:0% +these so I multiply by one NT over NT is + + + align:start position:0% +these so I multiply by one NT over NT is +one so I multiply by one everything and + + align:start position:0% +one so I multiply by one everything and + + + align:start position:0% +one so I multiply by one everything and +then rearrange terms so I got + + align:start position:0% +then rearrange terms so I got + + + align:start position:0% +then rearrange terms so I got +expressions like this no I got what I + + align:start position:0% +expressions like this no I got what I + + + align:start position:0% +expressions like this no I got what I +wanted here which is capital per ER + + align:start position:0% +wanted here which is capital per ER + + + align:start position:0% +wanted here which is capital per ER +person at the same point in time and but + + align:start position:0% +person at the same point in time and but + + + align:start position:0% +person at the same point in time and but +now it's multiply by NT over NT + one + + align:start position:0% +now it's multiply by NT over NT + one + + + align:start position:0% +now it's multiply by NT over NT + one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +H um and the same I can do for this uh + + align:start position:0% +H um and the same I can do for this uh + + + align:start position:0% +H um and the same I can do for this uh +another expression + + align:start position:0% +another expression + + + align:start position:0% +another expression +here okay so so this is what I'm using + + align:start position:0% +here okay so so this is what I'm using + + + align:start position:0% +here okay so so this is what I'm using +the approximation here in which X is + + align:start position:0% +the approximation here in which X is + + + align:start position:0% +the approximation here in which X is +equal to GN okay this in here is just 1 + + align:start position:0% +equal to GN okay this in here is just 1 + + + align:start position:0% +equal to GN okay this in here is just 1 +over 1 plus GN and I'm saying this is + + align:start position:0% +over 1 plus GN and I'm saying this is + + + align:start position:0% +over 1 plus GN and I'm saying this is +approximately equal I can approximate if + + align:start position:0% +approximately equal I can approximate if + + + align:start position:0% +approximately equal I can approximate if +GN is a small number this is + + align:start position:0% +GN is a small number this is + + + align:start position:0% +GN is a small number this is +approximately equal to 1 minus GN okay + + align:start position:0% +approximately equal to 1 minus GN okay + + + align:start position:0% +approximately equal to 1 minus GN okay +so that's what we have and this is a + + align:start position:0% +so that's what we have and this is a + + + align:start position:0% +so that's what we have and this is a +second + + align:start position:0% +second + + + align:start position:0% +second +approximation going from this line to + + align:start position:0% +approximation going from this line to + + + align:start position:0% +approximation going from this line to +this line in which we did the following + + align:start position:0% +this line in which we did the following + + + align:start position:0% +this line in which we did the following +it said okay + + align:start position:0% +it said okay + + + align:start position:0% +it said okay +you know this is equal to uh 1us + + align:start position:0% +you know this is equal to uh 1us + + + align:start position:0% +you know this is equal to uh 1us +Delta uh minus + + align:start position:0% +Delta uh minus + + + align:start position:0% +Delta uh minus +GN + + align:start position:0% +GN + + + align:start position:0% +GN +plus Delta * GN but the Delta time G is + + align:start position:0% +plus Delta * GN but the Delta time G is + + + align:start position:0% +plus Delta * GN but the Delta time G is +the multiplication of two small numbers + + align:start position:0% +the multiplication of two small numbers + + + align:start position:0% +the multiplication of two small numbers +so I said assume that is close to zero + + align:start position:0% +so I said assume that is close to zero + + + align:start position:0% +so I said assume that is close to zero +and the same we had here we had saving + + align:start position:0% +and the same we had here we had saving + + + align:start position:0% +and the same we had here we had saving +rate * 1 + GN you get you get the saving + + align:start position:0% +rate * 1 + GN you get you get the saving + + + align:start position:0% +rate * 1 + GN you get you get the saving +rate h plus the saving rate times GN but + + align:start position:0% +rate h plus the saving rate times GN but + + + align:start position:0% +rate h plus the saving rate times GN but +the saving rate times GN is also small + + align:start position:0% +the saving rate times GN is also small + + + align:start position:0% +the saving rate times GN is also small +number so we also drop okay so those are + + align:start position:0% +number so we also drop okay so those are + + + align:start position:0% +number so we also drop okay so those are +the more explicit steps of what I did in + + align:start position:0% +the more explicit steps of what I did in + + + align:start position:0% +the more explicit steps of what I did in +the previous lecture and I think the + + align:start position:0% +the previous lecture and I think the + + + align:start position:0% +the previous lecture and I think the +final equation I showed you was this but + + align:start position:0% +final equation I showed you was this but + + + align:start position:0% +final equation I showed you was this but +it comes from again two approximations + + align:start position:0% +it comes from again two approximations + + + align:start position:0% +it comes from again two approximations +the one down here which I use here and + + align:start position:0% +the one down here which I use here and + + + align:start position:0% +the one down here which I use here and +then the fact that I dropped the second + + align:start position:0% +then the fact that I dropped the second + + + align:start position:0% +then the fact that I dropped the second +order terms okay that's it and then I + + align:start position:0% +order terms okay that's it and then I + + + align:start position:0% +order terms okay that's it and then I +just rearrange things I move K KT over n + + align:start position:0% +just rearrange things I move K KT over n + + + align:start position:0% +just rearrange things I move K KT over n +to the left hand side and so we have the + + align:start position:0% +to the left hand side and so we have the + + + align:start position:0% +to the left hand side and so we have the +change in the stock of capital per + + align:start position:0% +change in the stock of capital per + + + align:start position:0% +change in the stock of capital per +person is an increasing function of + + align:start position:0% +person is an increasing function of + + + align:start position:0% +person is an increasing function of +investment uh per person which is this + + align:start position:0% +investment uh per person which is this + + + align:start position:0% +investment uh per person which is this +because this is saving per person and I + + align:start position:0% +because this is saving per person and I + + + align:start position:0% +because this is saving per person and I +can replace this by the production + + align:start position:0% +can replace this by the production + + + align:start position:0% +can replace this by the production +function no which is f of K Over N and + + align:start position:0% +function no which is f of K Over N and + + + align:start position:0% +function no which is f of K Over N and +so what I have here is a difference + + align:start position:0% +so what I have here is a difference + + + align:start position:0% +so what I have here is a difference +equation in capital per + + align:start position:0% + + + + align:start position:0% + +person why is this so so what so this is + + align:start position:0% +person why is this so so what so this is + + + align:start position:0% +person why is this so so what so this is +investment so the Capital stock per + + align:start position:0% +investment so the Capital stock per + + + align:start position:0% +investment so the Capital stock per +person will be growing as we + + align:start position:0% +person will be growing as we + + + align:start position:0% +person will be growing as we +invest the it shrinks with the passage + + align:start position:0% +invest the it shrinks with the passage + + + align:start position:0% +invest the it shrinks with the passage +of time just because of depreciation + + align:start position:0% +of time just because of depreciation + + + align:start position:0% +of time just because of depreciation +some things break down that reduces the + + align:start position:0% +some things break down that reduces the + + + align:start position:0% +some things break down that reduces the +stock of capital but the new term that + + align:start position:0% +stock of capital but the new term that + + + align:start position:0% +stock of capital but the new term that +we introduce at the end of last lecture + + align:start position:0% +we introduce at the end of last lecture + + + align:start position:0% +we introduce at the end of last lecture +is is that that now this ratio also + + align:start position:0% +is is that that now this ratio also + + + align:start position:0% +is is that that now this ratio also +declines H with population growth and so + + align:start position:0% +declines H with population growth and so + + + align:start position:0% +declines H with population growth and so +who can explain why we get this ter + + align:start position:0% + + + + align:start position:0% + +you know I'm saying look suppose that + + align:start position:0% +you know I'm saying look suppose that + + + align:start position:0% +you know I'm saying look suppose that +that that + + align:start position:0% +that that + + + align:start position:0% +that that +H that we have take a given amount of + + align:start position:0% +H that we have take a given amount of + + + align:start position:0% +H that we have take a given amount of +investment we take as given depreciation + + align:start position:0% +investment we take as given depreciation + + + align:start position:0% +investment we take as given depreciation +but now we I I say well if if GN Rises + + align:start position:0% +but now we I I say well if if GN Rises + + + align:start position:0% +but now we I I say well if if GN Rises +and all the rest remains constant + + align:start position:0% +and all the rest remains constant + + + align:start position:0% +and all the rest remains constant +then the left hand side will start + + align:start position:0% +then the left hand side will start + + + align:start position:0% +then the left hand side will start +declining or will grow less rapidly than + + align:start position:0% +declining or will grow less rapidly than + + + align:start position:0% +declining or will grow less rapidly than +what going to grow before a increase GN + + align:start position:0% +what going to grow before a increase GN + + + align:start position:0% +what going to grow before a increase GN +why is what do the case but + + align:start position:0% +why is what do the case but + + + align:start position:0% +why is what do the case but +sometimes it's counter inuitive that's + + align:start position:0% +sometimes it's counter inuitive that's + + + align:start position:0% +sometimes it's counter inuitive that's +the reason I want I I thought I rush in + + align:start position:0% +the reason I want I I thought I rush in + + + align:start position:0% +the reason I want I I thought I rush in +the previous lecture over that and I + + align:start position:0% +the previous lecture over that and I + + + align:start position:0% +the previous lecture over that and I +since it's going to be an important + + align:start position:0% +since it's going to be an important + + + align:start position:0% +since it's going to be an important +intermediate step into the next one + + align:start position:0% +intermediate step into the next one + + + align:start position:0% +intermediate step into the next one +which is when introduce technological + + align:start position:0% +which is when introduce technological + + + align:start position:0% +which is when introduce technological +progress I want us to understand why + + align:start position:0% +progress I want us to understand why + + + align:start position:0% +progress I want us to understand why +that GN appears with a negative sign + + align:start position:0% + + + + align:start position:0% + +there + + align:start position:0% +there + + + align:start position:0% +there +yep for the same amount of capital that + + align:start position:0% +yep for the same amount of capital that + + + align:start position:0% +yep for the same amount of capital that +increased + + align:start position:0% + + + + align:start position:0% + +inor that that + + align:start position:0% +inor that that + + + align:start position:0% +inor that that +term + + align:start position:0% +term + + + align:start position:0% +term +ER is going to be captured + + align:start position:0% +ER is going to be captured + + + align:start position:0% +ER is going to be captured +here and it's going to play a role but + + align:start position:0% +here and it's going to play a role but + + + align:start position:0% +here and it's going to play a role but +this one comes from something much more + + align:start position:0% +this one comes from something much more + + + align:start position:0% +this one comes from something much more +mechanical than + + align:start position:0% + + + + align:start position:0% + +that hint observe what I have on the + + align:start position:0% +that hint observe what I have on the + + + align:start position:0% +that hint observe what I have on the +left hand side I don't have on the left + + align:start position:0% +left hand side I don't have on the left + + + align:start position:0% +left hand side I don't have on the left +hand side the change in the stock of + + align:start position:0% +hand side the change in the stock of + + + align:start position:0% +hand side the change in the stock of +capital I have the change in the stock + + align:start position:0% +capital I have the change in the stock + + + align:start position:0% +capital I have the change in the stock +of capital per + + align:start position:0% +of capital per + + + align:start position:0% +of capital per +person so suppose I don't change the + + align:start position:0% +person so suppose I don't change the + + + align:start position:0% +person so suppose I don't change the +stock of capital at all from this period + + align:start position:0% +stock of capital at all from this period + + + align:start position:0% +stock of capital at all from this period +to the next but population grows what + + align:start position:0% +to the next but population grows what + + + align:start position:0% +to the next but population grows what +happens to this expression + + align:start position:0% +happens to this expression + + + align:start position:0% +happens to this expression +here decreases it becomes negative + + align:start position:0% +here decreases it becomes negative + + + align:start position:0% +here decreases it becomes negative +because I haven't changed the Capital + + align:start position:0% +because I haven't changed the Capital + + + align:start position:0% +because I haven't changed the Capital +stock but the denominator is growing + + align:start position:0% +stock but the denominator is growing + + + align:start position:0% +stock but the denominator is growing +that's the GM part and that means this + + align:start position:0% +that's the GM part and that means this + + + align:start position:0% +that's the GM part and that means this +turns negative and that's what this term + + align:start position:0% +turns negative and that's what this term + + + align:start position:0% +turns negative and that's what this term +is is here for is to capture the fact + + align:start position:0% +is is here for is to capture the fact + + + align:start position:0% +is is here for is to capture the fact +that the denominator now is also moving + + align:start position:0% +that the denominator now is also moving + + + align:start position:0% +that the denominator now is also moving +on the left hand side variable and and + + align:start position:0% +on the left hand side variable and and + + + align:start position:0% +on the left hand side variable and and +you say so what but I at the end of the + + align:start position:0% +you say so what but I at the end of the + + + align:start position:0% +you say so what but I at the end of the +day I care about the capital capital why + + align:start position:0% +day I care about the capital capital why + + + align:start position:0% +day I care about the capital capital why +why do I care about Capital per person + + align:start position:0% +why do I care about Capital per person + + + align:start position:0% +why do I care about Capital per person +well for all my analysis I told you it's + + align:start position:0% +well for all my analysis I told you it's + + + align:start position:0% +well for all my analysis I told you it's +much easier if I do it on something + + align:start position:0% +much easier if I do it on something + + + align:start position:0% +much easier if I do it on something +which it has a steady state that's the + + align:start position:0% +which it has a steady state that's the + + + align:start position:0% +which it has a steady state that's the +reason I'm looking for this + + align:start position:0% +reason I'm looking for this + + + align:start position:0% +reason I'm looking for this +normalization but once I look at the + + align:start position:0% +normalization but once I look at the + + + align:start position:0% +normalization but once I look at the +dynamic equation of accumulation of + + align:start position:0% +dynamic equation of accumulation of + + + align:start position:0% +dynamic equation of accumulation of +capital in + + align:start position:0% +capital in + + + align:start position:0% +capital in +this divided by population then I need + + align:start position:0% +this divided by population then I need + + + align:start position:0% +this divided by population then I need +to take into account the fact that my + + align:start position:0% +to take into account the fact that my + + + align:start position:0% +to take into account the fact that my +denominator is also moving okay so + + align:start position:0% +denominator is also moving okay so + + + align:start position:0% +denominator is also moving okay so +that's the reason that GN is there and + + align:start position:0% +that's the reason that GN is there and + + + align:start position:0% +that's the reason that GN is there and +and again the reason I wanted to pause + + align:start position:0% +and again the reason I wanted to pause + + + align:start position:0% +and again the reason I wanted to pause +on this is because when we introduce + + align:start position:0% +on this is because when we introduce + + + align:start position:0% +on this is because when we introduce +technological progress we're going to + + align:start position:0% +technological progress we're going to + + + align:start position:0% +technological progress we're going to +have a similar effect and and and so I + + align:start position:0% +have a similar effect and and and so I + + + align:start position:0% +have a similar effect and and and so I +want you to it's going to be counter + + align:start position:0% +want you to it's going to be counter + + + align:start position:0% +want you to it's going to be counter +intuitive because it sounds like + + align:start position:0% +intuitive because it sounds like + + + align:start position:0% +intuitive because it sounds like +technological progress is something + + align:start position:0% +technological progress is something + + + align:start position:0% +technological progress is something +negative no it's not + + align:start position:0% +negative no it's not + + + align:start position:0% +negative no it's not +negative but but in this space it turns + + align:start position:0% +negative but but in this space it turns + + + align:start position:0% +negative but but in this space it turns +out that if population grows very fast + + align:start position:0% +out that if population grows very fast + + + align:start position:0% +out that if population grows very fast +then you need a lot of investment to + + align:start position:0% +then you need a lot of investment to + + + align:start position:0% +then you need a lot of investment to +keep up the the capital labor ratio + + align:start position:0% +keep up the the capital labor ratio + + + align:start position:0% +keep up the the capital labor ratio +constant okay that's the idea if + + align:start position:0% +constant okay that's the idea if + + + align:start position:0% +constant okay that's the idea if +population is not growing I don't need + + align:start position:0% +population is not growing I don't need + + + align:start position:0% +population is not growing I don't need +need a lot of investment to keep the + + align:start position:0% +need a lot of investment to keep the + + + align:start position:0% +need a lot of investment to keep the +capital labor ratio constant but if + + align:start position:0% +capital labor ratio constant but if + + + align:start position:0% +capital labor ratio constant but if +population is growing very fast then I + + align:start position:0% +population is growing very fast then I + + + align:start position:0% +population is growing very fast then I +need a lot of investment to really keep + + align:start position:0% +need a lot of investment to really keep + + + align:start position:0% +need a lot of investment to really keep +that ratio constant that's what this is + + align:start position:0% +that ratio constant that's what this is + + + align:start position:0% +that ratio constant that's what this is +capturing there + + align:start position:0% +capturing there + + + align:start position:0% +capturing there +so to repeat if if this guy is is is + + align:start position:0% +so to repeat if if this guy is is is + + + align:start position:0% +so to repeat if if this guy is is is +very large then I need a lot of + + align:start position:0% +very large then I need a lot of + + + align:start position:0% +very large then I need a lot of +investment here to make this thing equal + + align:start position:0% +investment here to make this thing equal + + + align:start position:0% +investment here to make this thing equal +to zero so the Capital stock per person + + align:start position:0% +to zero so the Capital stock per person + + + align:start position:0% +to zero so the Capital stock per person +is not declining that's idea + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good okay so now ah and then I said okay + + align:start position:0% +good okay so now ah and then I said okay + + + align:start position:0% +good okay so now ah and then I said okay +this is where we finish then I said okay + + align:start position:0% +this is where we finish then I said okay + + + align:start position:0% +this is where we finish then I said okay +so let's go uh back to our diagram I can + + align:start position:0% +so let's go uh back to our diagram I can + + + align:start position:0% +so let's go uh back to our diagram I can +once I have everything in this space K + + align:start position:0% +once I have everything in this space K + + + align:start position:0% +once I have everything in this space K +Over N I can go back to our diagram + + align:start position:0% +Over N I can go back to our diagram + + + align:start position:0% +Over N I can go back to our diagram +assume that GA is equal to zero you + + align:start position:0% +assume that GA is equal to zero you + + + align:start position:0% +assume that GA is equal to zero you +don't even know what A is for the time + + align:start position:0% +don't even know what A is for the time + + + align:start position:0% +don't even know what A is for the time +being you will know in five minutes but + + align:start position:0% +being you will know in five minutes but + + + align:start position:0% +being you will know in five minutes but +assume GA is equal to zero then that's + + align:start position:0% +assume GA is equal to zero then that's + + + align:start position:0% +assume GA is equal to zero then that's +exactly the model we had before + + align:start position:0% +exactly the model we had before + + + align:start position:0% +exactly the model we had before +so and remember this this is exactly the + + align:start position:0% +so and remember this this is exactly the + + + align:start position:0% +so and remember this this is exactly the +same diagram it looked the same at least + + align:start position:0% +same diagram it looked the same at least + + + align:start position:0% +same diagram it looked the same at least +that we had when population was not + + align:start position:0% +that we had when population was not + + + align:start position:0% +that we had when population was not +growing I'm saying I can use the same + + align:start position:0% +growing I'm saying I can use the same + + + align:start position:0% +growing I'm saying I can use the same +diagram when population is growing as + + align:start position:0% +diagram when population is growing as + + + align:start position:0% +diagram when population is growing as +well but there is one important + + align:start position:0% +well but there is one important + + + align:start position:0% +well but there is one important +difference which is this this curve + + align:start position:0% +difference which is this this curve + + + align:start position:0% +difference which is this this curve +looks exactly the same this is just + + align:start position:0% +looks exactly the same this is just + + + align:start position:0% +looks exactly the same this is just +output H per per worker okay that's the + + align:start position:0% +output H per per worker okay that's the + + + align:start position:0% +output H per per worker okay that's the +Blue Line the green line looks exactly + + align:start position:0% +Blue Line the green line looks exactly + + + align:start position:0% +Blue Line the green line looks exactly +the same as in the basic model it's just + + align:start position:0% +the same as in the basic model it's just + + + align:start position:0% +the same as in the basic model it's just +little s times that the blue line so + + align:start position:0% +little s times that the blue line so + + + align:start position:0% +little s times that the blue line so +that's exactly the same but this line is + + align:start position:0% +that's exactly the same but this line is + + + align:start position:0% +that's exactly the same but this line is +different what happens to this red line + + align:start position:0% +different what happens to this red line + + + align:start position:0% +different what happens to this red line +as as GN goes up so what happens to this + + align:start position:0% +as as GN goes up so what happens to this + + + align:start position:0% +as as GN goes up so what happens to this +line as GN goes + + align:start position:0% +line as GN goes + + + align:start position:0% +line as GN goes +up becomes steeper no yeah so it rotates + + align:start position:0% +up becomes steeper no yeah so it rotates + + + align:start position:0% +up becomes steeper no yeah so it rotates +up okay goes up and that can sound + + align:start position:0% +up okay goes up and that can sound + + + align:start position:0% +up okay goes up and that can sound +counterintuitive sometimes because you + + align:start position:0% +counterintuitive sometimes because you + + + align:start position:0% +counterintuitive sometimes because you +say look look what happens here let's + + align:start position:0% +say look look what happens here let's + + + align:start position:0% +say look look what happens here let's +spend time on + + align:start position:0% +spend time on + + + align:start position:0% +spend time on +this suppose that we are at some St + + align:start position:0% +this suppose that we are at some St + + + align:start position:0% +this suppose that we are at some St +state say this + + align:start position:0% +state say this + + + align:start position:0% +state say this +one and now population growth + + align:start position:0% + + + + align:start position:0% + +Rises okay it sounds like Ireland in you + + align:start position:0% +Rises okay it sounds like Ireland in you + + + align:start position:0% +Rises okay it sounds like Ireland in you +know 2000s and + + align:start position:0% +know 2000s and + + + align:start position:0% +know 2000s and +so so population growth Rises a + + align:start position:0% +so so population growth Rises a + + + align:start position:0% +so so population growth Rises a +lot what happens in this diagram so + + align:start position:0% +lot what happens in this diagram so + + + align:start position:0% +lot what happens in this diagram so +suppose we're at the state state + + align:start position:0% +suppose we're at the state state + + + align:start position:0% +suppose we're at the state state +here no and that the state + + align:start position:0% +here no and that the state + + + align:start position:0% +here no and that the state +investment uh saving which is equal to + + align:start position:0% +investment uh saving which is equal to + + + align:start position:0% +investment uh saving which is equal to +investment is exactly what you need to + + align:start position:0% +investment is exactly what you need to + + + align:start position:0% +investment is exactly what you need to +maintain the stock of capital per person + + align:start position:0% +maintain the stock of capital per person + + + align:start position:0% +maintain the stock of capital per person +constant okay that's what the red line + + align:start position:0% +constant okay that's what the red line + + + align:start position:0% +constant okay that's what the red line +tells us no that here so that's the Gap + + align:start position:0% +tells us no that here so that's the Gap + + + align:start position:0% +tells us no that here so that's the Gap +here is this is a gap between investment + + align:start position:0% +here is this is a gap between investment + + + align:start position:0% +here is this is a gap between investment +and what you need to maintain the stock + + align:start position:0% +and what you need to maintain the stock + + + align:start position:0% +and what you need to maintain the stock +of capital per person constant so when + + align:start position:0% +of capital per person constant so when + + + align:start position:0% +of capital per person constant so when +the Gap is zero then then this equation + + align:start position:0% +the Gap is zero then then this equation + + + align:start position:0% +the Gap is zero then then this equation +this left hand side is equal to zero + + align:start position:0% +this left hand side is equal to zero + + + align:start position:0% +this left hand side is equal to zero +okay that's the red line that's the + + align:start position:0% +okay that's the red line that's the + + + align:start position:0% +okay that's the red line that's the +green line when this is equal to Z + + align:start position:0% +green line when this is equal to Z + + + align:start position:0% +green line when this is equal to Z +that's equal to that that's exactly that + + align:start position:0% +that's equal to that that's exactly that + + + align:start position:0% +that's equal to that that's exactly that +point okay but I'm saying suppose we are + + align:start position:0% +point okay but I'm saying suppose we are + + + align:start position:0% +point okay but I'm saying suppose we are +at that point and + + align:start position:0% +at that point and + + + align:start position:0% +at that point and +now population growth + + align:start position:0% +now population growth + + + align:start position:0% +now population growth +Rises so what moves in that diagram does + + align:start position:0% +Rises so what moves in that diagram does + + + align:start position:0% +Rises so what moves in that diagram does +a blue line + + align:start position:0% + + + + align:start position:0% + +move I don't see GN in the blue line so + + align:start position:0% +move I don't see GN in the blue line so + + + align:start position:0% +move I don't see GN in the blue line so +the Blue Line doesn't move if the Blue + + align:start position:0% +the Blue Line doesn't move if the Blue + + + align:start position:0% +the Blue Line doesn't move if the Blue +Line doesn't move and the saving rate + + align:start position:0% +Line doesn't move and the saving rate + + + align:start position:0% +Line doesn't move and the saving rate +hasn't changed then the green line + + align:start position:0% +hasn't changed then the green line + + + align:start position:0% +hasn't changed then the green line +doesn't move move + + align:start position:0% +doesn't move move + + + align:start position:0% +doesn't move move +either so for this diagram to be + + align:start position:0% +either so for this diagram to be + + + align:start position:0% +either so for this diagram to be +interesting what moves assum has to move + + align:start position:0% +interesting what moves assum has to move + + + align:start position:0% +interesting what moves assum has to move +so the only thing that has that can move + + align:start position:0% +so the only thing that has that can move + + + align:start position:0% +so the only thing that has that can move +here is the is the red line and the red + + align:start position:0% +here is the is the red line and the red + + + align:start position:0% +here is the is the red line and the red +line we already said if GM goes up it's + + align:start position:0% +line we already said if GM goes up it's + + + align:start position:0% +line we already said if GM goes up it's +going to rotate + + align:start position:0% +going to rotate + + + align:start position:0% +going to rotate +upwards that + + align:start position:0% +upwards that + + + align:start position:0% +upwards that +means say so now we have that line there + + align:start position:0% +means say so now we have that line there + + + align:start position:0% +means say so now we have that line there +so what happens at the at the at the + + align:start position:0% +so what happens at the at the at the + + + align:start position:0% +so what happens at the at the at the +previous St State stock of capital per + + align:start position:0% +previous St State stock of capital per + + + align:start position:0% +previous St State stock of capital per +worker at this level what happens is + + align:start position:0% +worker at this level what happens is + + + align:start position:0% +worker at this level what happens is +that a new state + + align:start position:0% + + + + align:start position:0% + +state no but what happens in particular + + align:start position:0% +state no but what happens in particular + + + align:start position:0% +state no but what happens in particular +what is it so I'm saying suppose that + + align:start position:0% +what is it so I'm saying suppose that + + + align:start position:0% +what is it so I'm saying suppose that +you're here and now I rotate the red + + align:start position:0% +you're here and now I rotate the red + + + align:start position:0% +you're here and now I rotate the red +line + + align:start position:0% +line + + + align:start position:0% +line +up okay so that means the red line that + + align:start position:0% +up okay so that means the red line that + + + align:start position:0% +up okay so that means the red line that +represents the amount of capital I need + + align:start position:0% +represents the amount of capital I need + + + align:start position:0% +represents the amount of capital I need +to maintain the stock of capital + + align:start position:0% +to maintain the stock of capital + + + align:start position:0% +to maintain the stock of capital +constant is greater than how much + + align:start position:0% +constant is greater than how much + + + align:start position:0% +constant is greater than how much +Society saving and therefore investing + + align:start position:0% +Society saving and therefore investing + + + align:start position:0% +Society saving and therefore investing +so what will happen to Capital per + + align:start position:0% +so what will happen to Capital per + + + align:start position:0% +so what will happen to Capital per +worker + + align:start position:0% + + + + align:start position:0% + +decrease exactly because you need more + + align:start position:0% +decrease exactly because you need more + + + align:start position:0% +decrease exactly because you need more +than you're investing so the Capital + + align:start position:0% +than you're investing so the Capital + + + align:start position:0% +than you're investing so the Capital +stock has to decline and that's what + + align:start position:0% +stock has to decline and that's what + + + align:start position:0% +stock has to decline and that's what +will happen the new state state is going + + align:start position:0% +will happen the new state state is going + + + align:start position:0% +will happen the new state state is going +to be to the left of that point + + align:start position:0% +to be to the left of that point + + + align:start position:0% +to be to the left of that point +there that sounds very + + align:start position:0% +there that sounds very + + + align:start position:0% +there that sounds very +weird how can it be that you know after + + align:start position:0% +weird how can it be that you know after + + + align:start position:0% +weird how can it be that you know after +all labor contributes to Output how can + + align:start position:0% +all labor contributes to Output how can + + + align:start position:0% +all labor contributes to Output how can +it be that we end up with a + + align:start position:0% +it be that we end up with a + + + align:start position:0% +it be that we end up with a +lower ER output per per worker when we + + align:start position:0% +lower ER output per per worker when we + + + align:start position:0% +lower ER output per per worker when we +increase popul population growth is + + align:start position:0% +increase popul population growth is + + + align:start position:0% +increase popul population growth is +population growth bad in a sense for + + align:start position:0% +population growth bad in a sense for + + + align:start position:0% +population growth bad in a sense for +growth itself for + + align:start position:0% + + + + align:start position:0% + +output well the answer is no it's it's + + align:start position:0% +output well the answer is no it's it's + + + align:start position:0% +output well the answer is no it's it's +true that the new state state will have + + align:start position:0% +true that the new state state will have + + + align:start position:0% +true that the new state state will have +lower output per person so in that sense + + align:start position:0% +lower output per person so in that sense + + + align:start position:0% +lower output per person so in that sense +it's bad you have lots of population if + + align:start position:0% +it's bad you have lots of population if + + + align:start position:0% +it's bad you have lots of population if +you if if you don't change the saving + + align:start position:0% +you if if you don't change the saving + + + align:start position:0% +you if if you don't change the saving +rate or something then output per person + + align:start position:0% +rate or something then output per person + + + align:start position:0% +rate or something then output per person +will be lower but output will be higher + + align:start position:0% +will be lower but output will be higher + + + align:start position:0% +will be lower but output will be higher +than it used to be at any point in time + + align:start position:0% +than it used to be at any point in time + + + align:start position:0% +than it used to be at any point in time +it just happens that in the transition + + align:start position:0% +it just happens that in the transition + + + align:start position:0% +it just happens that in the transition +the growth of output so so the growth + + align:start position:0% +the growth of output so so the growth + + + align:start position:0% +the growth of output so so the growth +the growth of output in this model is + + align:start position:0% +the growth of output in this model is + + + align:start position:0% +the growth of output in this model is +going to be equal to the growth of + + align:start position:0% +going to be equal to the growth of + + + align:start position:0% +going to be equal to the growth of +population okay that's if you have a St + + align:start position:0% +population okay that's if you have a St + + + align:start position:0% +population okay that's if you have a St +state where population is growing and + + align:start position:0% +state where population is growing and + + + align:start position:0% +state where population is growing and +output per worker or per person is not + + align:start position:0% +output per worker or per person is not + + + align:start position:0% +output per worker or per person is not +growing that means output is growing at + + align:start position:0% +growing that means output is growing at + + + align:start position:0% +growing that means output is growing at +the same rate as population so that + + align:start position:0% +the same rate as population so that + + + align:start position:0% +the same rate as population so that +means that if I increase the rate of + + align:start position:0% +means that if I increase the rate of + + + align:start position:0% +means that if I increase the rate of +population growth the rate of growth + + align:start position:0% +population growth the rate of growth + + + align:start position:0% +population growth the rate of growth +output will + + align:start position:0% +output will + + + align:start position:0% +output will +increase together with the rate of + + align:start position:0% +increase together with the rate of + + + align:start position:0% +increase together with the rate of +growth of population but in the + + align:start position:0% +growth of population but in the + + + align:start position:0% +growth of population but in the +transition as the output per capita goes + + align:start position:0% +transition as the output per capita goes + + + align:start position:0% +transition as the output per capita goes +lower output will grow less than + + align:start position:0% +lower output will grow less than + + + align:start position:0% +lower output will grow less than +population that's what is happening here + + align:start position:0% +population that's what is happening here + + + align:start position:0% +population that's what is happening here +okay but output is growing if you + + align:start position:0% +okay but output is growing if you + + + align:start position:0% +okay but output is growing if you +population starts growing if you + + align:start position:0% +population starts growing if you + + + align:start position:0% +population starts growing if you +increase migration you're going to see + + align:start position:0% +increase migration you're going to see + + + align:start position:0% +increase migration you're going to see +output grow but output per person will + + align:start position:0% +output grow but output per person will + + + align:start position:0% +output grow but output per person will +start declining until you get to New + + align:start position:0% +start declining until you get to New + + + align:start position:0% +start declining until you get to New +State and then you'll get the same + + align:start position:0% +State and then you'll get the same + + + align:start position:0% +State and then you'll get the same +ER you'll get the higher rate of growth + + align:start position:0% +ER you'll get the higher rate of growth + + + align:start position:0% +ER you'll get the higher rate of growth +you continue with population growth with + + align:start position:0% +you continue with population growth with + + + align:start position:0% +you continue with population growth with +the high population growth but output + + align:start position:0% +the high population growth but output + + + align:start position:0% +the high population growth but output +per worker would be slightly lower rate + + align:start position:0% + + + + align:start position:0% + +okay anyways this may have been fast the + + align:start position:0% +okay anyways this may have been fast the + + + align:start position:0% +okay anyways this may have been fast the +last part but since I'm going to repeat + + align:start position:0% +last part but since I'm going to repeat + + + align:start position:0% +last part but since I'm going to repeat +it now in the context of technological + + align:start position:0% +it now in the context of technological + + + align:start position:0% +it now in the context of technological +progress we should be fine okay so if + + align:start position:0% +progress we should be fine okay so if + + + align:start position:0% +progress we should be fine okay so if +you're a little confused now it's okay + + align:start position:0% +you're a little confused now it's okay + + + align:start position:0% +you're a little confused now it's okay +if you're a little confused at the end + + align:start position:0% +if you're a little confused at the end + + + align:start position:0% +if you're a little confused at the end +of the lecture it's not okay because + + align:start position:0% +of the lecture it's not okay because + + + align:start position:0% +of the lecture it's not okay because +that's I'm counting with you sort of + + align:start position:0% +that's I'm counting with you sort of + + + align:start position:0% +that's I'm counting with you sort of +getting it in the second pass okay + + align:start position:0% +getting it in the second pass okay + + + align:start position:0% +getting it in the second pass okay +second try Okay so next step is is f so + + align:start position:0% +second try Okay so next step is is f so + + + align:start position:0% +second try Okay so next step is is f so +here we assume already population growth + + align:start position:0% +here we assume already population growth + + + align:start position:0% +here we assume already population growth +where we assume that technology so the + + align:start position:0% +where we assume that technology so the + + + align:start position:0% +where we assume that technology so the +production function sort of stay put for + + align:start position:0% +production function sort of stay put for + + + align:start position:0% +production function sort of stay put for +any combination of capital and labor the + + align:start position:0% +any combination of capital and labor the + + + align:start position:0% +any combination of capital and labor the +next step is to think what happens when + + align:start position:0% +next step is to think what happens when + + + align:start position:0% +next step is to think what happens when +the technology itself is getting better + + align:start position:0% +the technology itself is getting better + + + align:start position:0% +the technology itself is getting better +over time and that's what we call + + align:start position:0% +over time and that's what we call + + + align:start position:0% +over time and that's what we call +technological progress okay this is tfp + + align:start position:0% +technological progress okay this is tfp + + + align:start position:0% +technological progress okay this is tfp +let me not get into to specifics at the + + align:start position:0% +let me not get into to specifics at the + + + align:start position:0% +let me not get into to specifics at the +end I'll say a little more but P tfp + + align:start position:0% +end I'll say a little more but P tfp + + + align:start position:0% +end I'll say a little more but P tfp +stands for total Factor productivity and + + align:start position:0% +stands for total Factor productivity and + + + align:start position:0% +stands for total Factor productivity and +this index here captures the level of + + align:start position:0% +this index here captures the level of + + + align:start position:0% +this index here captures the level of +tfp in the + + align:start position:0% +tfp in the + + + align:start position:0% +tfp in the +US over time and it's clearly growing so + + align:start position:0% +US over time and it's clearly growing so + + + align:start position:0% +US over time and it's clearly growing so +technolog is getting better and better + + align:start position:0% +technolog is getting better and better + + + align:start position:0% +technolog is getting better and better +over time what that means well it I say + + align:start position:0% +over time what that means well it I say + + + align:start position:0% +over time what that means well it I say +a little more not a lot more but but + + align:start position:0% +a little more not a lot more but but + + + align:start position:0% +a little more not a lot more but but +it's getting + + align:start position:0% +it's getting + + + align:start position:0% +it's getting +better no h and so the question we have + + align:start position:0% +better no h and so the question we have + + + align:start position:0% +better no h and so the question we have +here is I'm going when to address next + + align:start position:0% +here is I'm going when to address next + + + align:start position:0% +here is I'm going when to address next +is how does this so now we're going to + + align:start position:0% +is how does this so now we're going to + + + align:start position:0% +is how does this so now we're going to +put together our entire economic growth + + align:start position:0% +put together our entire economic growth + + + align:start position:0% +put together our entire economic growth +model we're going to have population + + align:start position:0% +model we're going to have population + + + align:start position:0% +model we're going to have population +growth we're want to have also + + align:start position:0% +growth we're want to have also + + + align:start position:0% +growth we're want to have also +technology growing up to now the only + + align:start position:0% +technology growing up to now the only + + + align:start position:0% +technology growing up to now the only +reason you could + + align:start position:0% +reason you could + + + align:start position:0% +reason you could +grow a you could grow output per per + + align:start position:0% +grow a you could grow output per per + + + align:start position:0% +grow a you could grow output per per +worker was because you were accumulating + + align:start position:0% +worker was because you were accumulating + + + align:start position:0% +worker was because you were accumulating +lots of capital you were catching up + + align:start position:0% +lots of capital you were catching up + + + align:start position:0% +lots of capital you were catching up +with you're a steady state that's what + + align:start position:0% +with you're a steady state that's what + + + align:start position:0% +with you're a steady state that's what +would make you grow faster but then + + align:start position:0% +would make you grow faster but then + + + align:start position:0% +would make you grow faster but then +there was nothing else tfp is going to + + align:start position:0% +there was nothing else tfp is going to + + + align:start position:0% +there was nothing else tfp is going to +be the only growth in technology is + + align:start position:0% +be the only growth in technology is + + + align:start position:0% +be the only growth in technology is +going to be the only thing that will + + align:start position:0% +going to be the only thing that will + + + align:start position:0% +going to be the only thing that will +give you sustainable growth in the long + + align:start position:0% +give you sustainable growth in the long + + + align:start position:0% +give you sustainable growth in the long +run an output per person okay so this is + + align:start position:0% +run an output per person okay so this is + + + align:start position:0% +run an output per person okay so this is +a very important component of of H of + + align:start position:0% +a very important component of of H of + + + align:start position:0% +a very important component of of H of +growth again it's the only thing that + + align:start position:0% +growth again it's the only thing that + + + align:start position:0% +growth again it's the only thing that +will make you grow in a sustainable + + align:start position:0% +will make you grow in a sustainable + + + align:start position:0% +will make you grow in a sustainable +manner in in per person terms okay the + + align:start position:0% +manner in in per person terms okay the + + + align:start position:0% +manner in in per person terms okay the +previous model didn't have that in the + + align:start position:0% +previous model didn't have that in the + + + align:start position:0% +previous model didn't have that in the +previous model we had a steady + + align:start position:0% +previous model we had a steady + + + align:start position:0% +previous model we had a steady +state ER on on output per worker so in + + align:start position:0% +state ER on on output per worker so in + + + align:start position:0% +state ER on on output per worker so in +the previous model we didn't have growth + + align:start position:0% +the previous model we didn't have growth + + + align:start position:0% +the previous model we didn't have growth +in output per worker in the St state + + align:start position:0% +in output per worker in the St state + + + align:start position:0% +in output per worker in the St state +we could have transitional growth when + + align:start position:0% +we could have transitional growth when + + + align:start position:0% +we could have transitional growth when +we were catching up no if you if you + + align:start position:0% +we were catching up no if you if you + + + align:start position:0% +we were catching up no if you if you +started + + align:start position:0% +started + + + align:start position:0% +started +here then you were going to have growth + + align:start position:0% +here then you were going to have growth + + + align:start position:0% +here then you were going to have growth +fast growth but eventually will pet it + + align:start position:0% +fast growth but eventually will pet it + + + align:start position:0% +fast growth but eventually will pet it +out okay out work so so up to now we + + align:start position:0% +out okay out work so so up to now we + + + align:start position:0% +out okay out work so so up to now we +don't have a reason for why to to to + + align:start position:0% +don't have a reason for why to to to + + + align:start position:0% +don't have a reason for why to to to +explain why we see that output per + + align:start position:0% +explain why we see that output per + + + align:start position:0% +explain why we see that output per +worker grows in most economies in the + + align:start position:0% +worker grows in most economies in the + + + align:start position:0% +worker grows in most economies in the +world and the answer will be this this + + align:start position:0% +world and the answer will be this this + + + align:start position:0% +world and the answer will be this this +is the reason really how output per + + align:start position:0% +is the reason really how output per + + + align:start position:0% +is the reason really how output per +worker can grow in a sustained manner + + align:start position:0% +worker can grow in a sustained manner + + + align:start position:0% +worker can grow in a sustained manner +it's technolog is getting better and + + align:start position:0% +it's technolog is getting better and + + + align:start position:0% +it's technolog is getting better and +better over time so let's let's see so + + align:start position:0% +better over time so let's let's see so + + + align:start position:0% +better over time so let's let's see so +the question is let's now see what this + + align:start position:0% +the question is let's now see what this + + + align:start position:0% +the question is let's now see what this +does to the model we + + align:start position:0% +does to the model we + + + align:start position:0% +does to the model we +have now in practice technological + + align:start position:0% +have now in practice technological + + + align:start position:0% +have now in practice technological +progress takes many many forms er + + align:start position:0% +progress takes many many forms er + + + align:start position:0% +progress takes many many forms er +um it in at most basic level means that + + align:start position:0% +um it in at most basic level means that + + + align:start position:0% +um it in at most basic level means that +you can produce larger quantities output + + align:start position:0% +you can produce larger quantities output + + + align:start position:0% +you can produce larger quantities output +and that's really the meaning we're + + align:start position:0% +and that's really the meaning we're + + + align:start position:0% +and that's really the meaning we're +going to have here larger quantities of + + align:start position:0% +going to have here larger quantities of + + + align:start position:0% +going to have here larger quantities of +output for the same amount of capital + + align:start position:0% +output for the same amount of capital + + + align:start position:0% +output for the same amount of capital +and + + align:start position:0% +and + + + align:start position:0% +and +labor okay so you have 10 machines 10 + + align:start position:0% +labor okay so you have 10 machines 10 + + + align:start position:0% +labor okay so you have 10 machines 10 +workers technological progress means + + align:start position:0% +workers technological progress means + + + align:start position:0% +workers technological progress means +well you used to produce 12 units now + + align:start position:0% +well you used to produce 12 units now + + + align:start position:0% +well you used to produce 12 units now +we're going to produce 12 14 15 and so + + align:start position:0% +we're going to produce 12 14 15 and so + + + align:start position:0% +we're going to produce 12 14 15 and so +on so forth that's that's a one way of + + align:start position:0% +on so forth that's that's a one way of + + + align:start position:0% +on so forth that's that's a one way of +techn that one of the main ways + + align:start position:0% +techn that one of the main ways + + + align:start position:0% +techn that one of the main ways +technological progress shows up we can + + align:start position:0% +technological progress shows up we can + + + align:start position:0% +technological progress shows up we can +do more with the same if you will second + + align:start position:0% +do more with the same if you will second + + + align:start position:0% +do more with the same if you will second +dimension is better product so it's not + + align:start position:0% +dimension is better product so it's not + + + align:start position:0% +dimension is better product so it's not +that you produce more cars but you + + align:start position:0% +that you produce more cars but you + + + align:start position:0% +that you produce more cars but you +produce better cars better computers and + + align:start position:0% +produce better cars better computers and + + + align:start position:0% +produce better cars better computers and +so on okay that's another dimension of + + align:start position:0% +so on okay that's another dimension of + + + align:start position:0% +so on okay that's another dimension of +technal prod you can produce new + + align:start position:0% +technal prod you can produce new + + + align:start position:0% +technal prod you can produce new +products things that didn't even exist + + align:start position:0% +products things that didn't even exist + + + align:start position:0% +products things that didn't even exist +but now you + + align:start position:0% +but now you + + + align:start position:0% +but now you +have that counts more than having one + + align:start position:0% +have that counts more than having one + + + align:start position:0% +have that counts more than having one +more unit of good it counts more because + + align:start position:0% +more unit of good it counts more because + + + align:start position:0% +more unit of good it counts more because +you have you know things that you + + align:start position:0% +you have you know things that you + + + align:start position:0% +you have you know things that you +couldn't even satisfy in the past you + + align:start position:0% +couldn't even satisfy in the past you + + + align:start position:0% +couldn't even satisfy in the past you +can satisfy now because you have the + + align:start position:0% +can satisfy now because you have the + + + align:start position:0% +can satisfy now because you have the +certain kind of goods that DNX is before + + align:start position:0% +certain kind of goods that DNX is before + + + align:start position:0% +certain kind of goods that DNX is before +that's a very important dimension of + + align:start position:0% +that's a very important dimension of + + + align:start position:0% +that's a very important dimension of +technological progress is just create no + + align:start position:0% +technological progress is just create no + + + align:start position:0% +technological progress is just create no +new sort of forms of inputs of + + align:start position:0% +new sort of forms of inputs of + + + align:start position:0% +new sort of forms of inputs of +production and Technologies think of AI + + align:start position:0% +production and Technologies think of AI + + + align:start position:0% +production and Technologies think of AI +what that will do to to technology in + + align:start position:0% +what that will do to to technology in + + + align:start position:0% +what that will do to to technology in +general and to consumption very + + align:start position:0% +general and to consumption very + + + align:start position:0% +general and to consumption very +directly ER and that's what I mean even + + align:start position:0% +directly ER and that's what I mean even + + + align:start position:0% +directly ER and that's what I mean even +within a product you you can get more + + align:start position:0% +within a product you you can get more + + + align:start position:0% +within a product you you can get more +variety and more variety you know + + align:start position:0% +variety and more variety you know + + + align:start position:0% +variety and more variety you know +improves welfare because you can align + + align:start position:0% +improves welfare because you can align + + + align:start position:0% +improves welfare because you can align +better the needs H with with the product + + align:start position:0% +better the needs H with with the product + + + align:start position:0% +better the needs H with with the product +and so on but we're going to make it + + align:start position:0% +and so on but we're going to make it + + + align:start position:0% +and so on but we're going to make it +very simple in this in this in this + + align:start position:0% +very simple in this in this in this + + + align:start position:0% +very simple in this in this in this +course we're going to we're going to + + align:start position:0% +course we're going to we're going to + + + align:start position:0% +course we're going to we're going to +model technological progress as if it + + align:start position:0% +model technological progress as if it + + + align:start position:0% +model technological progress as if it +was + + align:start position:0% +was + + + align:start position:0% +was +workers okay so + + align:start position:0% +workers okay so + + + align:start position:0% +workers okay so +uh we're going to capture technology + + align:start position:0% +uh we're going to capture technology + + + align:start position:0% +uh we're going to capture technology +with this Con with this variable a which + + align:start position:0% +with this Con with this variable a which + + + align:start position:0% +with this Con with this variable a which +is going to be we're going to model it + + align:start position:0% +is going to be we're going to model it + + + align:start position:0% +is going to be we're going to model it +as labor equivalent that is if a grows + + align:start position:0% +as labor equivalent that is if a grows + + + align:start position:0% +as labor equivalent that is if a grows +it's going to count for us as if we had + + align:start position:0% +it's going to count for us as if we had + + + align:start position:0% +it's going to count for us as if we had +more + + align:start position:0% +more + + + align:start position:0% +more +workers okay that's just one way of + + align:start position:0% +workers okay that's just one way of + + + align:start position:0% +workers okay that's just one way of +model it I mean I can I can do it in + + align:start position:0% +model it I mean I can I can do it in + + + align:start position:0% +model it I mean I can I can do it in +many different ways andan some many of + + align:start position:0% +many different ways andan some many of + + + align:start position:0% +many different ways andan some many of +these are equivalent but that's a very + + align:start position:0% +these are equivalent but that's a very + + + align:start position:0% +these are equivalent but that's a very +very nice way of modeling so we can use + + align:start position:0% +very nice way of modeling so we can use + + + align:start position:0% +very nice way of modeling so we can use +exactly the same diagrams we have and so + + align:start position:0% +exactly the same diagrams we have and so + + + align:start position:0% +exactly the same diagrams we have and so +okay so you can think of technological + + align:start position:0% +okay so you can think of technological + + + align:start position:0% +okay so you can think of technological +progress the way I'm going to model this + + align:start position:0% +progress the way I'm going to model this + + + align:start position:0% +progress the way I'm going to model this +here is you can think of technological + + align:start position:0% +here is you can think of technological + + + align:start position:0% +here is you can think of technological +progress as if this economy was + + align:start position:0% +progress as if this economy was + + + align:start position:0% +progress as if this economy was +receiving more + + align:start position:0% +receiving more + + + align:start position:0% +receiving more +workers okay or a more accurate + + align:start position:0% +workers okay or a more accurate + + + align:start position:0% +workers okay or a more accurate +description is with the same workers it + + align:start position:0% +description is with the same workers it + + + align:start position:0% +description is with the same workers it +can produce is as if he had more labor + + align:start position:0% +can produce is as if he had more labor + + + align:start position:0% +can produce is as if he had more labor +input okay that's that's one way of + + align:start position:0% +input okay that's that's one way of + + + align:start position:0% +input okay that's that's one way of +capturing technology technological + + align:start position:0% +capturing technology technological + + + align:start position:0% +capturing technology technological +progress so now that means that I'm + + align:start position:0% +progress so now that means that I'm + + + align:start position:0% +progress so now that means that I'm +going to refer to this term a n as + + align:start position:0% +going to refer to this term a n as + + + align:start position:0% +going to refer to this term a n as +effective labor you know so with the + + align:start position:0% +effective labor you know so with the + + + align:start position:0% +effective labor you know so with the +same number of n bodies I may get more + + align:start position:0% +same number of n bodies I may get more + + + align:start position:0% +same number of n bodies I may get more +effective label because each worker can + + align:start position:0% +effective label because each worker can + + + align:start position:0% +effective label because each worker can +produce more things it's a better input + + align:start position:0% +produce more things it's a better input + + + align:start position:0% +produce more things it's a better input +of production factor of production + + align:start position:0% +of production factor of production + + + align:start position:0% +of production factor of production +okay so it and I like to mod it this way + + align:start position:0% +okay so it and I like to mod it this way + + + align:start position:0% +okay so it and I like to mod it this way +because now I can use exactly the same + + align:start position:0% +because now I can use exactly the same + + + align:start position:0% +because now I can use exactly the same +diagrams we had before but rather than + + align:start position:0% +diagrams we had before but rather than + + + align:start position:0% +diagrams we had before but rather than +normalizing by population I'm going to + + align:start position:0% +normalizing by population I'm going to + + + align:start position:0% +normalizing by population I'm going to +normalize by effective labor by a n + + align:start position:0% +normalize by effective labor by a n + + + align:start position:0% +normalize by effective labor by a n +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let me do that so recall that we had + + align:start position:0% +so let me do that so recall that we had + + + align:start position:0% +so let me do that so recall that we had +our production function with constant + + align:start position:0% +our production function with constant + + + align:start position:0% +our production function with constant +return so this hold I'm going to set + + align:start position:0% +return so this hold I'm going to set + + + align:start position:0% +return so this hold I'm going to set +this x now as 1/ a n we used to have 1/ + + align:start position:0% +this x now as 1/ a n we used to have 1/ + + + align:start position:0% +this x now as 1/ a n we used to have 1/ +n I'm going to have 1/ a n and so I'm + + align:start position:0% +n I'm going to have 1/ a n and so I'm + + + align:start position:0% +n I'm going to have 1/ a n and so I'm +going to now have output per effective + + align:start position:0% +going to now have output per effective + + + align:start position:0% +going to now have output per effective +worker is going to be also the same + + align:start position:0% +worker is going to be also the same + + + align:start position:0% +worker is going to be also the same +little function f of capital per + + align:start position:0% +little function f of capital per + + + align:start position:0% +little function f of capital per +effective + + align:start position:0% +effective + + + align:start position:0% +effective +worker okay and what is nice of this is + + align:start position:0% +worker okay and what is nice of this is + + + align:start position:0% +worker okay and what is nice of this is +that now here rather than plotting y + + align:start position:0% +that now here rather than plotting y + + + align:start position:0% +that now here rather than plotting y +Over N I'm going to PL plot y over a n + + align:start position:0% +Over N I'm going to PL plot y over a n + + + align:start position:0% +Over N I'm going to PL plot y over a n +rather than plotting K Over N here I'm + + align:start position:0% +rather than plotting K Over N here I'm + + + align:start position:0% +rather than plotting K Over N here I'm +going to plot K over a n and I have the + + align:start position:0% +going to plot K over a n and I have the + + + align:start position:0% +going to plot K over a n and I have the +blue line looks exactly like it used to + + align:start position:0% +blue line looks exactly like it used to + + + align:start position:0% +blue line looks exactly like it used to +look it's just I'm dividing by a Over N + + align:start position:0% +look it's just I'm dividing by a Over N + + + align:start position:0% +look it's just I'm dividing by a Over N +remember the trick in all these models + + align:start position:0% +remember the trick in all these models + + + align:start position:0% +remember the trick in all these models +is to find the right normalization that + + align:start position:0% +is to find the right normalization that + + + align:start position:0% +is to find the right normalization that +is to find the right X so I can find + + align:start position:0% +is to find the right X so I can find + + + align:start position:0% +is to find the right X so I can find +find a steady state in my diagram I + + align:start position:0% +find a steady state in my diagram I + + + align:start position:0% +find a steady state in my diagram I +don't want these curves to be moving + + align:start position:0% +don't want these curves to be moving + + + align:start position:0% +don't want these curves to be moving +around I want this to have a a steady + + align:start position:0% +around I want this to have a a steady + + + align:start position:0% +around I want this to have a a steady +state something a point that that we're + + align:start position:0% +state something a point that that we're + + + align:start position:0% +state something a point that that we're +going to converge to after enough time + + align:start position:0% +going to converge to after enough time + + + align:start position:0% +going to converge to after enough time +has passed okay and I know that that the + + align:start position:0% +has passed okay and I know that that the + + + align:start position:0% +has passed okay and I know that that the +thing that will do it in a model in + + align:start position:0% +thing that will do it in a model in + + + align:start position:0% +thing that will do it in a model in +which I have popul effective workers + + align:start position:0% +which I have popul effective workers + + + align:start position:0% +which I have popul effective workers +growing is one in which I divide + + align:start position:0% +growing is one in which I divide + + + align:start position:0% +growing is one in which I divide +everything by effective + + align:start position:0% +everything by effective + + + align:start position:0% +everything by effective +workers okay so that's what I'm doing + + align:start position:0% +workers okay so that's what I'm doing + + + align:start position:0% +workers okay so that's what I'm doing +here I'm going to build a diagram that + + align:start position:0% +here I'm going to build a diagram that + + + align:start position:0% +here I'm going to build a diagram that +looks like the other one that has a nice + + align:start position:0% +looks like the other one that has a nice + + + align:start position:0% +looks like the other one that has a nice +steady state as the previous one had + + align:start position:0% +steady state as the previous one had + + + align:start position:0% +steady state as the previous one had +okay so I have my blue line you I have + + align:start position:0% +okay so I have my blue line you I have + + + align:start position:0% +okay so I have my blue line you I have +my blue line I know I have my green line + + align:start position:0% +my blue line I know I have my green line + + + align:start position:0% +my blue line I know I have my green line +no because the green line was just + + align:start position:0% +no because the green line was just + + + align:start position:0% +no because the green line was just +little s times the blue line so I have + + align:start position:0% +little s times the blue line so I have + + + align:start position:0% +little s times the blue line so I have +that the last thing I need and I already + + align:start position:0% +that the last thing I need and I already + + + align:start position:0% +that the last thing I need and I already +show you that but I'm going to show it + + align:start position:0% +show you that but I'm going to show it + + + align:start position:0% +show you that but I'm going to show it +again is is the is the red line okay but + + align:start position:0% +again is is the is the red line okay but + + + align:start position:0% +again is is the is the red line okay but +for the red line I need to find this + + align:start position:0% +for the red line I need to find this + + + align:start position:0% +for the red line I need to find this +term the term remember the red line + + align:start position:0% +term the term remember the red line + + + align:start position:0% +term the term remember the red line +represents the capital we need to + + align:start position:0% +represents the capital we need to + + + align:start position:0% +represents the capital we need to +maintain the current stock of capital + + align:start position:0% +maintain the current stock of capital + + + align:start position:0% +maintain the current stock of capital +per effective worker constant that's + + align:start position:0% +per effective worker constant that's + + + align:start position:0% +per effective worker constant that's +what I need my red line for so let's get + + align:start position:0% +what I need my red line for so let's get + + + align:start position:0% +what I need my red line for so let's get +there and it always start from this + + align:start position:0% +there and it always start from this + + + align:start position:0% +there and it always start from this +equation so this equation is still the + + align:start position:0% +equation so this equation is still the + + + align:start position:0% +equation so this equation is still the +same as it used to be that doesn't + + align:start position:0% +same as it used to be that doesn't + + + align:start position:0% +same as it used to be that doesn't +change but what I'm going to do now is + + align:start position:0% +change but what I'm going to do now is + + + align:start position:0% +change but what I'm going to do now is +rather than dividing by n I'm going to + + align:start position:0% +rather than dividing by n I'm going to + + + align:start position:0% +rather than dividing by n I'm going to +divide by a * n so the same as I did + + align:start position:0% +divide by a * n so the same as I did + + + align:start position:0% +divide by a * n so the same as I did +earlier in this lecture I now want to + + align:start position:0% +earlier in this lecture I now want to + + + align:start position:0% +earlier in this lecture I now want to +divide by a Over N so I get Capital per + + align:start position:0% +divide by a Over N so I get Capital per + + + align:start position:0% +divide by a Over N so I get Capital per +effective work on the left hand side I + + align:start position:0% +effective work on the left hand side I + + + align:start position:0% +effective work on the left hand side I +don't like what I get here but you know + + align:start position:0% +don't like what I get here but you know + + + align:start position:0% +don't like what I get here but you know +that I can divide and multiply by a n n + + align:start position:0% +that I can divide and multiply by a n n + + + align:start position:0% +that I can divide and multiply by a n n +over a n so I can write the right hand + + align:start position:0% +over a n so I can write the right hand + + + align:start position:0% +over a n so I can write the right hand +side after do all my substitutions as + + align:start position:0% +side after do all my substitutions as + + + align:start position:0% +side after do all my substitutions as +this + + align:start position:0% +this + + + align:start position:0% +this +okay you know so I first step one I + + align:start position:0% +okay you know so I first step one I + + + align:start position:0% +okay you know so I first step one I +divided everything by a t + 1 * NT + 1 + + align:start position:0% +divided everything by a t + 1 * NT + 1 + + + align:start position:0% +divided everything by a t + 1 * NT + 1 +step two I multiply each of these terms + + align:start position:0% +step two I multiply each of these terms + + + align:start position:0% +step two I multiply each of these terms +by a and t i multiply by AT and T divide + + align:start position:0% +by a and t i multiply by AT and T divide + + + align:start position:0% +by a and t i multiply by AT and T divide +by AT and T and T okay and then I + + align:start position:0% +by AT and T and T okay and then I + + + align:start position:0% +by AT and T and T okay and then I +regroup things so I end up with that + + align:start position:0% +regroup things so I end up with that + + + align:start position:0% +regroup things so I end up with that +well this using the approximation we + + align:start position:0% +well this using the approximation we + + + align:start position:0% +well this using the approximation we +have here here is equal to approximately + + align:start position:0% +have here here is equal to approximately + + + align:start position:0% +have here here is equal to approximately +equal to 1 minus g + + align:start position:0% +equal to 1 minus g + + + align:start position:0% +equal to 1 minus g +n and g + + align:start position:0% + + + + align:start position:0% + +n is equal to + + align:start position:0% +n is equal to + + + align:start position:0% +n is equal to +GA plus + + align:start position:0% + + + + align:start position:0% + +GN okay so I already show you that that + + align:start position:0% +GN okay so I already show you that that + + + align:start position:0% +GN okay so I already show you that that +case for the case in which GA was equal + + align:start position:0% +case for the case in which GA was equal + + + align:start position:0% +case for the case in which GA was equal +to zero I'm doing now the same thing but + + align:start position:0% +to zero I'm doing now the same thing but + + + align:start position:0% +to zero I'm doing now the same thing but +but you know since I renormalize things + + align:start position:0% +but you know since I renormalize things + + + align:start position:0% +but you know since I renormalize things +by effective workers effective labor + + align:start position:0% +by effective workers effective labor + + + align:start position:0% +by effective workers effective labor +rather than actual label I need to use a + + align:start position:0% +rather than actual label I need to use a + + + align:start position:0% +rather than actual label I need to use a +n rather than + + align:start position:0% +n rather than + + + align:start position:0% +n rather than +n okay and then by the same + + align:start position:0% +n okay and then by the same + + + align:start position:0% +n okay and then by the same +approximation I had before which is that + + align:start position:0% +approximation I had before which is that + + + align:start position:0% +approximation I had before which is that +you know these products are close to + + align:start position:0% +you know these products are close to + + + align:start position:0% +you know these products are close to +zero then I get to the equation I want + + align:start position:0% +zero then I get to the equation I want + + + align:start position:0% +zero then I get to the equation I want +and if I write it in first difference + + align:start position:0% +and if I write it in first difference + + + align:start position:0% +and if I write it in first difference +then I get my Red Line This is my red + + align:start position:0% +then I get my Red Line This is my red + + + align:start position:0% +then I get my Red Line This is my red +line + + align:start position:0% +line + + + align:start position:0% +line +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +good + + align:start position:0% +good + + + align:start position:0% +good +so H in um this tells me that when the + + align:start position:0% +so H in um this tells me that when the + + + align:start position:0% +so H in um this tells me that when the +ER the green line green line is equal to + + align:start position:0% +ER the green line green line is equal to + + + align:start position:0% +ER the green line green line is equal to +the red line then I have a steady state + + align:start position:0% +the red line then I have a steady state + + + align:start position:0% +the red line then I have a steady state +capital perfective worker is constant + + align:start position:0% +capital perfective worker is constant + + + align:start position:0% +capital perfective worker is constant +that this this is equal to zero that's + + align:start position:0% +that this this is equal to zero that's + + + align:start position:0% +that this this is equal to zero that's +the way I find my steady state if I ask + + align:start position:0% +the way I find my steady state if I ask + + + align:start position:0% +the way I find my steady state if I ask +you a question find the steady state of + + align:start position:0% +you a question find the steady state of + + + align:start position:0% +you a question find the steady state of +this economy what you'll do is you'll + + align:start position:0% +this economy what you'll do is you'll + + + align:start position:0% +this economy what you'll do is you'll +set this equal to zero and find the + + align:start position:0% +set this equal to zero and find the + + + align:start position:0% +set this equal to zero and find the +Capital stock that gives you this equal + + align:start position:0% +Capital stock that gives you this equal + + + align:start position:0% +Capital stock that gives you this equal +to zero that's the way you do it okay + + align:start position:0% +to zero that's the way you do it okay + + + align:start position:0% +to zero that's the way you do it okay +so so that's that's that and then we get + + align:start position:0% +so so that's that's that and then we get + + + align:start position:0% +so so that's that's that and then we get +back to + + align:start position:0% +back to + + + align:start position:0% +back to +um well this is this is the same as we + + align:start position:0% +um well this is this is the same as we + + + align:start position:0% +um well this is this is the same as we +had + + align:start position:0% +had + + + align:start position:0% +had +before that's what I just said that's + + align:start position:0% +before that's what I just said that's + + + align:start position:0% +before that's what I just said that's +the way you find the stud State okay and + + align:start position:0% +the way you find the stud State okay and + + + align:start position:0% +the way you find the stud State okay and +then we get back to the diagram I + + align:start position:0% +then we get back to the diagram I + + + align:start position:0% +then we get back to the diagram I +started with in this lecture okay but + + align:start position:0% +started with in this lecture okay but + + + align:start position:0% +started with in this lecture okay but +now we have here a a n and now in in in + + align:start position:0% +now we have here a a n and now in in in + + + align:start position:0% +now we have here a a n and now in in in +the first part I said assume this G ga + + align:start position:0% +the first part I said assume this G ga + + + align:start position:0% +the first part I said assume this G ga +GA is equal to zero now the main actor + + align:start position:0% +GA is equal to zero now the main actor + + + align:start position:0% +GA is equal to zero now the main actor +is GA positive okay and and we get this + + align:start position:0% +is GA positive okay and and we get this + + + align:start position:0% +is GA positive okay and and we get this +diagram so now I can ask you the + + align:start position:0% +diagram so now I can ask you the + + + align:start position:0% +diagram so now I can ask you the +question that that that I asked you + + align:start position:0% +question that that that I asked you + + + align:start position:0% +question that that that I asked you +before with population growth and see + + align:start position:0% +before with population growth and see + + + align:start position:0% +before with population growth and see +how much I can confuse you suppose that + + align:start position:0% +how much I can confuse you suppose that + + + align:start position:0% +how much I can confuse you suppose that +GA goes up that sounds like a good thing + + align:start position:0% +GA goes up that sounds like a good thing + + + align:start position:0% +GA goes up that sounds like a good thing +no I mean ER suppose that we're at the + + align:start position:0% +no I mean ER suppose that we're at the + + + align:start position:0% +no I mean ER suppose that we're at the +steady state here and I mean this + + align:start position:0% +steady state here and I mean this + + + align:start position:0% +steady state here and I mean this +diagram has too much stuff let me + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +okay so we're + + align:start position:0% + + + + align:start position:0% + +here that's our initial + + align:start position:0% +here that's our initial + + + align:start position:0% +here that's our initial +State um + + align:start position:0% + + + + align:start position:0% + +zero and and this line here is Delta + + align:start position:0% +zero and and this line here is Delta + + + align:start position:0% +zero and and this line here is Delta +plus + + align:start position:0% +plus + + + align:start position:0% +plus +GA plus + + align:start position:0% + + + + align:start position:0% + +GN * K over a n okay + + align:start position:0% +GN * K over a n okay + + + align:start position:0% +GN * K over a n okay +so the question well first let's let's + + align:start position:0% +so the question well first let's let's + + + align:start position:0% +so the question well first let's let's +so suppose we're at the say + + align:start position:0% + + + + align:start position:0% + +state is output constant there I mean + + align:start position:0% +state is output constant there I mean + + + align:start position:0% +state is output constant there I mean +that's it's a state state it's output + + align:start position:0% +that's it's a state state it's output + + + align:start position:0% +that's it's a state state it's output +output constant there so suppose we are + + align:start position:0% +output constant there so suppose we are + + + align:start position:0% +output constant there so suppose we are +at that + + align:start position:0% + + + + align:start position:0% + +point here here we know that investment + + align:start position:0% +point here here we know that investment + + + align:start position:0% +point here here we know that investment +exactly how much we need to maintain the + + align:start position:0% +exactly how much we need to maintain the + + + align:start position:0% +exactly how much we need to maintain the +stock of capital per effective worker + + align:start position:0% +stock of capital per effective worker + + + align:start position:0% +stock of capital per effective worker +constant that's what what the state + + align:start position:0% +constant that's what what the state + + + align:start position:0% +constant that's what what the state +state + + align:start position:0% +state + + + align:start position:0% +state +means question is output constant + + align:start position:0% +means question is output constant + + + align:start position:0% +means question is output constant +there state + + align:start position:0% + + + + align:start position:0% + +state + + align:start position:0% +state + + + align:start position:0% +state +no this only says + + align:start position:0% +no this only says + + + align:start position:0% +no this only says +that Capital per effective work + + align:start position:0% +that Capital per effective work + + + align:start position:0% +that Capital per effective work +is constant that means that if effective + + align:start position:0% +is constant that means that if effective + + + align:start position:0% +is constant that means that if effective +workers or labor is growing then capital + + align:start position:0% +workers or labor is growing then capital + + + align:start position:0% +workers or labor is growing then capital +is growing at the same rate and + + align:start position:0% +is growing at the same rate and + + + align:start position:0% +is growing at the same rate and +therefore output is growing at the same + + align:start position:0% +therefore output is growing at the same + + + align:start position:0% +therefore output is growing at the same +rate as effective workers okay that's + + align:start position:0% +rate as effective workers okay that's + + + align:start position:0% +rate as effective workers okay that's +the reason remember the whole trick so + + align:start position:0% +the reason remember the whole trick so + + + align:start position:0% +the reason remember the whole trick so +the curves would not be moving around is + + align:start position:0% +the curves would not be moving around is + + + align:start position:0% +the curves would not be moving around is +I find the right normalization so + + align:start position:0% +I find the right normalization so + + + align:start position:0% +I find the right normalization so +everything is growing at the same rate + + align:start position:0% +everything is growing at the same rate + + + align:start position:0% +everything is growing at the same rate +in that St + + align:start position:0% +in that St + + + align:start position:0% +in that St +State okay + + align:start position:0% + + + + align:start position:0% + +so let me actually show you that and + + align:start position:0% +so let me actually show you that and + + + align:start position:0% +so let me actually show you that and +then I'm going to go over the experiment + + align:start position:0% +then I'm going to go over the experiment + + + align:start position:0% +then I'm going to go over the experiment +I want to have so this is what is + + align:start position:0% +I want to have so this is what is + + + align:start position:0% +I want to have so this is what is +happening in that steady + + align:start position:0% +happening in that steady + + + align:start position:0% +happening in that steady +state so Capital per effective worker at + + align:start position:0% +state so Capital per effective worker at + + + align:start position:0% +state so Capital per effective worker at +the steady state so at that point + + align:start position:0% +the steady state so at that point + + + align:start position:0% +the steady state so at that point +there is zero no that's a stady that's + + align:start position:0% +there is zero no that's a stady that's + + + align:start position:0% +there is zero no that's a stady that's +my definition of a steady state okay + + align:start position:0% +my definition of a steady state okay + + + align:start position:0% +my definition of a steady state okay +output effective worker is also growing + + align:start position:0% +output effective worker is also growing + + + align:start position:0% +output effective worker is also growing +at at at the rate zero that's that one + + align:start position:0% +at at at the rate zero that's that one + + + align:start position:0% +at at at the rate zero that's that one +over there + + align:start position:0% +over there + + + align:start position:0% +over there +sorry that's my state level of output + + align:start position:0% +sorry that's my state level of output + + + align:start position:0% +sorry that's my state level of output +per effective worker + + align:start position:0% + + + + align:start position:0% + +okay so these are constant that's a say + + align:start position:0% +okay so these are constant that's a say + + + align:start position:0% +okay so these are constant that's a say +State those are constant this ratio is + + align:start position:0% +State those are constant this ratio is + + + align:start position:0% +State those are constant this ratio is +constant each of those components is + + align:start position:0% +constant each of those components is + + + align:start position:0% +constant each of those components is +not + + align:start position:0% +not + + + align:start position:0% +not +so that's what I'm plotting there so + + align:start position:0% +so that's what I'm plotting there so + + + align:start position:0% +so that's what I'm plotting there so +that's those are not growing Capital per + + align:start position:0% +that's those are not growing Capital per + + + align:start position:0% +that's those are not growing Capital per +worker what about that well you you see + + align:start position:0% +worker what about that well you you see + + + align:start position:0% +worker what about that well you you see +there explain why why so claim Capital + + align:start position:0% +there explain why why so claim Capital + + + align:start position:0% +there explain why why so claim Capital +per worker is growing at the rate GA how + + align:start position:0% +per worker is growing at the rate GA how + + + align:start position:0% +per worker is growing at the rate GA how +do I know that + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so the question I'm asking + + align:start position:0% +so the question I'm asking + + + align:start position:0% +so the question I'm asking +there is what is the rate of + + align:start position:0% +there is what is the rate of + + + align:start position:0% +there is what is the rate of +growth of k/ + + align:start position:0% + + + + align:start position:0% + +n Pro given that I already know that the + + align:start position:0% +n Pro given that I already know that the + + + align:start position:0% +n Pro given that I already know that the +rate of growth of K over a + + align:start position:0% + + + + align:start position:0% + +n is equal to zero + + align:start position:0% + + + + align:start position:0% + +well this the rate of growth of K Over N + + align:start position:0% +well this the rate of growth of K Over N + + + align:start position:0% +well this the rate of growth of K Over N +is the rate of growth of K over a n plus + + align:start position:0% +is the rate of growth of K over a n plus + + + align:start position:0% +is the rate of growth of K over a n plus +the rate of growth of + + align:start position:0% +the rate of growth of + + + align:start position:0% +the rate of growth of +a + + align:start position:0% +a + + + align:start position:0% +a +no I mean if a is growing and this ratio + + align:start position:0% +no I mean if a is growing and this ratio + + + align:start position:0% +no I mean if a is growing and this ratio +is + + align:start position:0% +is + + + align:start position:0% +is +constant that means that k/ n must be + + align:start position:0% +constant that means that k/ n must be + + + align:start position:0% +constant that means that k/ n must be +growing + + align:start position:0% +growing + + + align:start position:0% +growing +and it has to be growing at exactly the + + align:start position:0% +and it has to be growing at exactly the + + + align:start position:0% +and it has to be growing at exactly the +same rate as this a is growing otherwise + + align:start position:0% +same rate as this a is growing otherwise + + + align:start position:0% +same rate as this a is growing otherwise +I wouldn't be able to maintain that + + align:start position:0% +I wouldn't be able to maintain that + + + align:start position:0% +I wouldn't be able to maintain that +ratio + + align:start position:0% +ratio + + + align:start position:0% +ratio +constant + + align:start position:0% +constant + + + align:start position:0% +constant +okay and the same logic applies + + align:start position:0% +okay and the same logic applies + + + align:start position:0% +okay and the same logic applies +to Output per worker because in that + + align:start position:0% +to Output per worker because in that + + + align:start position:0% +to Output per worker because in that +steady state output per effective worker + + align:start position:0% +steady state output per effective worker + + + align:start position:0% +steady state output per effective worker +is + + align:start position:0% +is + + + align:start position:0% +is +constant but a is growing so output per + + align:start position:0% +constant but a is growing so output per + + + align:start position:0% +constant but a is growing so output per +worker must be growing at the same rate + + align:start position:0% +worker must be growing at the same rate + + + align:start position:0% +worker must be growing at the same rate +as a is growing and that's + + align:start position:0% +as a is growing and that's + + + align:start position:0% +as a is growing and that's +G okay + + align:start position:0% +G okay + + + align:start position:0% +G okay +good labor well labor is exogenous which + + align:start position:0% +good labor well labor is exogenous which + + + align:start position:0% +good labor well labor is exogenous which +say population is growing at the rate n + + align:start position:0% +say population is growing at the rate n + + + align:start position:0% +say population is growing at the rate n +that's given what about + + align:start position:0% +that's given what about + + + align:start position:0% +that's given what about +Capital an output well claim capital and + + align:start position:0% +Capital an output well claim capital and + + + align:start position:0% +Capital an output well claim capital and +output are growing at the rate GA plus + + align:start position:0% + + + + align:start position:0% + +GN and I can do the same as I was in + + align:start position:0% +GN and I can do the same as I was in + + + align:start position:0% +GN and I can do the same as I was in +here I'm asking you the question GK what + + align:start position:0% +here I'm asking you the question GK what + + + align:start position:0% +here I'm asking you the question GK what +is the rate of growth of GK + + align:start position:0% +is the rate of growth of GK + + + align:start position:0% +is the rate of growth of GK +well is going to be equal to the rate of + + align:start position:0% +well is going to be equal to the rate of + + + align:start position:0% +well is going to be equal to the rate of +growth of k/ + + align:start position:0% +growth of k/ + + + align:start position:0% +growth of k/ +n plus the rate of growth of + + align:start position:0% + + + + align:start position:0% + +n okay this is equal to + + align:start position:0% + + + + align:start position:0% + +GA so it's G Plus + + align:start position:0% +GA so it's G Plus + + + align:start position:0% +GA so it's G Plus +GN and the same happens for uh + + align:start position:0% +GN and the same happens for uh + + + align:start position:0% +GN and the same happens for uh +um for + + align:start position:0% +um for + + + align:start position:0% +um for +output + + align:start position:0% +output + + + align:start position:0% +output +okay so that's what is remember I said + + align:start position:0% +okay so that's what is remember I said + + + align:start position:0% +okay so that's what is remember I said +earlier on that + + align:start position:0% +earlier on that + + + align:start position:0% +earlier on that +that if an economy has more population + + align:start position:0% +that if an economy has more population + + + align:start position:0% +that if an economy has more population +growth it will grow + + align:start position:0% +growth it will grow + + + align:start position:0% +growth it will grow +more okay there's no doubt of that + + align:start position:0% +more okay there's no doubt of that + + + align:start position:0% +more okay there's no doubt of that +obviously output per worker will not + + align:start position:0% +obviously output per worker will not + + + align:start position:0% +obviously output per worker will not +grow more because population growth + + align:start position:0% +grow more because population growth + + + align:start position:0% +grow more because population growth +grows more in the new state G doesn't + + align:start position:0% +grows more in the new state G doesn't + + + align:start position:0% +grows more in the new state G doesn't +show up + + align:start position:0% +show up + + + align:start position:0% +show up +there okay but the only thing that will + + align:start position:0% +there okay but the only thing that will + + + align:start position:0% +there okay but the only thing that will +make output per + + align:start position:0% +make output per + + + align:start position:0% +make output per +worker grow is technological progress so + + align:start position:0% +worker grow is technological progress so + + + align:start position:0% +worker grow is technological progress so +it's + + align:start position:0% +it's + + + align:start position:0% +it's +G that was my claim + + align:start position:0% + + + + align:start position:0% + +earlier there's another we're going to + + align:start position:0% +earlier there's another we're going to + + + align:start position:0% +earlier there's another we're going to +use this later + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +um no I'm not going to do this myself + + align:start position:0% +um no I'm not going to do this myself + + + align:start position:0% +um no I'm not going to do this myself +now we're I'm going to get back to what + + align:start position:0% +now we're I'm going to get back to what + + + align:start position:0% +now we're I'm going to get back to what +I wanted to do now because I need to + + align:start position:0% +I wanted to do now because I need to + + + align:start position:0% +I wanted to do now because I need to +tell you a little bit more about the + + align:start position:0% +tell you a little bit more about the + + + align:start position:0% +tell you a little bit more about the +production function to do growth + + align:start position:0% +production function to do growth + + + align:start position:0% +production function to do growth +accounting um which is what I wanted to + + align:start position:0% +accounting um which is what I wanted to + + + align:start position:0% +accounting um which is what I wanted to +do so but this is clear I mean this is + + align:start position:0% +do so but this is clear I mean this is + + + align:start position:0% +do so but this is clear I mean this is +important + + align:start position:0% +important + + + align:start position:0% +important +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good so this is the reason GA is such an + + align:start position:0% +good so this is the reason GA is such an + + + align:start position:0% +good so this is the reason GA is such an +important variable what you guys do here + + align:start position:0% +important variable what you guys do here + + + align:start position:0% +important variable what you guys do here +at MIT is very important afterwards very + + align:start position:0% +at MIT is very important afterwards very + + + align:start position:0% +at MIT is very important afterwards very +important + + align:start position:0% +important + + + align:start position:0% +important +okay that's the only thing that can + + align:start position:0% +okay that's the only thing that can + + + align:start position:0% +okay that's the only thing that can +drive really growth in the long run in + + align:start position:0% +drive really growth in the long run in + + + align:start position:0% +drive really growth in the long run in +per + + align:start position:0% + + + + align:start position:0% + +capita this GM plays also role I mean + + align:start position:0% +capita this GM plays also role I mean + + + align:start position:0% +capita this GM plays also role I mean +you look at countries not only the + + align:start position:0% +you look at countries not only the + + + align:start position:0% +you look at countries not only the +growth in per capita output you'll tend + + align:start position:0% +growth in per capita output you'll tend + + + align:start position:0% +growth in per capita output you'll tend +to look at growth a total growth one of + + align:start position:0% +to look at growth a total growth one of + + + align:start position:0% +to look at growth a total growth one of +the big concerns in big parts of Asia + + align:start position:0% +the big concerns in big parts of Asia + + + align:start position:0% +the big concerns in big parts of Asia +now in Europe as well as I said earlier + + align:start position:0% +now in Europe as well as I said earlier + + + align:start position:0% +now in Europe as well as I said earlier +in the course is that g is turning + + align:start position:0% +in the course is that g is turning + + + align:start position:0% +in the course is that g is turning +negative that's not going to affect + + align:start position:0% +negative that's not going to affect + + + align:start position:0% +negative that's not going to affect +output per worker growth but it does + + align:start position:0% +output per worker growth but it does + + + align:start position:0% +output per worker growth but it does +affect output growth in general okay and + + align:start position:0% +affect output growth in general okay and + + + align:start position:0% +affect output growth in general okay and +you can see it here so if G goes down + + align:start position:0% +you can see it here so if G goes down + + + align:start position:0% +you can see it here so if G goes down +that will reduce the rate of growth of + + align:start position:0% +that will reduce the rate of growth of + + + align:start position:0% +that will reduce the rate of growth of +output doesn't reduce the rate of growth + + align:start position:0% +output doesn't reduce the rate of growth + + + align:start position:0% +output doesn't reduce the rate of growth +output of worker but it does reduce the + + align:start position:0% +output of worker but it does reduce the + + + align:start position:0% +output of worker but it does reduce the +rate of growth of + + align:start position:0% +rate of growth of + + + align:start position:0% +rate of growth of +output + + align:start position:0% + + + + align:start position:0% + +good so what happens remember we did in + + align:start position:0% +good so what happens remember we did in + + + align:start position:0% +good so what happens remember we did in +the in the in the in the basic model we + + align:start position:0% +the in the in the in the basic model we + + + align:start position:0% +the in the in the in the basic model we +did an experiment in which we increase + + align:start position:0% +did an experiment in which we increase + + + align:start position:0% +did an experiment in which we increase +the saving rate so we can do the same + + align:start position:0% +the saving rate so we can do the same + + + align:start position:0% +the saving rate so we can do the same +here what happens if we get an increase + + align:start position:0% +here what happens if we get an increase + + + align:start position:0% +here what happens if we get an increase +in the saving rate do we get more growth + + align:start position:0% +in the saving rate do we get more growth + + + align:start position:0% +in the saving rate do we get more growth +in the long run and the answer is for + + align:start position:0% +in the long run and the answer is for + + + align:start position:0% +in the long run and the answer is for +the same reasons we had before no + + align:start position:0% +the same reasons we had before no + + + align:start position:0% +the same reasons we had before no +if we increase the saving rate in this + + align:start position:0% +if we increase the saving rate in this + + + align:start position:0% +if we increase the saving rate in this +now this full model all that happens is + + align:start position:0% +now this full model all that happens is + + + align:start position:0% +now this full model all that happens is +that this green line moves up it means + + align:start position:0% +that this green line moves up it means + + + align:start position:0% +that this green line moves up it means +that at initial St State now we have + + align:start position:0% +that at initial St State now we have + + + align:start position:0% +that at initial St State now we have +more saving and therefore more + + align:start position:0% +more saving and therefore more + + + align:start position:0% +more saving and therefore more +investment than we need to maintain the + + align:start position:0% +investment than we need to maintain the + + + align:start position:0% +investment than we need to maintain the +stock of capital per effective worker + + align:start position:0% +stock of capital per effective worker + + + align:start position:0% +stock of capital per effective worker +constant which means that we're going to + + align:start position:0% +constant which means that we're going to + + + align:start position:0% +constant which means that we're going to +get transitional growth Capital per + + align:start position:0% +get transitional growth Capital per + + + align:start position:0% +get transitional growth Capital per +effective worker will start growing for + + align:start position:0% +effective worker will start growing for + + + align:start position:0% +effective worker will start growing for +a while and as that happens output per + + align:start position:0% +a while and as that happens output per + + + align:start position:0% +a while and as that happens output per +effective worker will also start + + align:start position:0% +effective worker will also start + + + align:start position:0% +effective worker will also start +growing okay but eventually the + + align:start position:0% +growing okay but eventually the + + + align:start position:0% +growing okay but eventually the +increasing returns will kick in here as + + align:start position:0% +increasing returns will kick in here as + + + align:start position:0% +increasing returns will kick in here as +well and we are going to that + + align:start position:0% +well and we are going to that + + + align:start position:0% +well and we are going to that +transitional growth will stop and H will + + align:start position:0% +transitional growth will stop and H will + + + align:start position:0% +transitional growth will stop and H will +end up at a higher level of output per + + align:start position:0% +end up at a higher level of output per + + + align:start position:0% +end up at a higher level of output per +effective worker and a higher level of + + align:start position:0% +effective worker and a higher level of + + + align:start position:0% +effective worker and a higher level of +capital per effective worker but the + + align:start position:0% +capital per effective worker but the + + + align:start position:0% +capital per effective worker but the +rate of growth in the long run will not + + align:start position:0% +rate of growth in the long run will not + + + align:start position:0% +rate of growth in the long run will not +be affected by the saving rate we'll get + + align:start position:0% +be affected by the saving rate we'll get + + + align:start position:0% +be affected by the saving rate we'll get +more transitional growth but we will not + + align:start position:0% +more transitional growth but we will not + + + align:start position:0% +more transitional growth but we will not +get a faster long-term + + align:start position:0% +get a faster long-term + + + align:start position:0% +get a faster long-term +growth a lot of the Asian Miracle that's + + align:start position:0% +growth a lot of the Asian Miracle that's + + + align:start position:0% +growth a lot of the Asian Miracle that's +that the Southeast Asian milon in + + align:start position:0% +that the Southeast Asian milon in + + + align:start position:0% +that the Southeast Asian milon in +particular we saw very fast rates of + + align:start position:0% +particular we saw very fast rates of + + + align:start position:0% +particular we saw very fast rates of +growth in many economies of + + align:start position:0% +growth in many economies of + + + align:start position:0% +growth in many economies of +Asia was a lot of that kind meaning was + + align:start position:0% +Asia was a lot of that kind meaning was + + + align:start position:0% +Asia was a lot of that kind meaning was +a combination of what we had before + + align:start position:0% +a combination of what we had before + + + align:start position:0% +a combination of what we had before +economies that were relatively poor had + + align:start position:0% +economies that were relatively poor had + + + align:start position:0% +economies that were relatively poor had +low Capital per work early on in which a + + align:start position:0% +low Capital per work early on in which a + + + align:start position:0% +low Capital per work early on in which a +saving rate increased enormously and + + align:start position:0% +saving rate increased enormously and + + + align:start position:0% +saving rate increased enormously and +that combination gave them + + align:start position:0% +that combination gave them + + + align:start position:0% +that combination gave them +enormous a transitional growth so rate + + align:start position:0% +enormous a transitional growth so rate + + + align:start position:0% +enormous a transitional growth so rate +of growth of 10 12% that was Japan and + + align:start position:0% +of growth of 10 12% that was Japan and + + + align:start position:0% +of growth of 10 12% that was Japan and +then it was Korea Taiwan and so on all + + align:start position:0% +then it was Korea Taiwan and so on all + + + align:start position:0% +then it was Korea Taiwan and so on all +those economies had very fast rates of + + align:start position:0% +those economies had very fast rates of + + + align:start position:0% +those economies had very fast rates of +growth as a result of that China later + + align:start position:0% +growth as a result of that China later + + + align:start position:0% +growth as a result of that China later +on and China was a big thing for the + + align:start position:0% +on and China was a big thing for the + + + align:start position:0% +on and China was a big thing for the +world because it was much bigger at the + + align:start position:0% +world because it was much bigger at the + + + align:start position:0% +world because it was much bigger at the +same time but it was mostly a + + align:start position:0% +same time but it was mostly a + + + align:start position:0% +same time but it was mostly a +combination of those two things it was + + align:start position:0% +combination of those two things it was + + + align:start position:0% +combination of those two things it was +being having a low stock of capital + + align:start position:0% +being having a low stock of capital + + + align:start position:0% +being having a low stock of capital +early on combined with for a variety of + + align:start position:0% +early on combined with for a variety of + + + align:start position:0% +early on combined with for a variety of +reasons and increasing the saving rate + + align:start position:0% +reasons and increasing the saving rate + + + align:start position:0% +reasons and increasing the saving rate +and that combination so gave them very + + align:start position:0% +and that combination so gave them very + + + align:start position:0% +and that combination so gave them very +fast transitional growth but they're all + + align:start position:0% +fast transitional growth but they're all + + + align:start position:0% +fast transitional growth but they're all +getting a little stuck now and they're + + align:start position:0% +getting a little stuck now and they're + + + align:start position:0% +getting a little stuck now and they're +very concerned with that well they're + + align:start position:0% +very concerned with that well they're + + + align:start position:0% +very concerned with that well they're +fighting against this model there's lots + + align:start position:0% +fighting against this model there's lots + + + align:start position:0% +fighting against this model there's lots +of concerns of what is happening to + + align:start position:0% +of concerns of what is happening to + + + align:start position:0% +of concerns of what is happening to +China are we going to follow the Japan + + align:start position:0% +China are we going to follow the Japan + + + align:start position:0% +China are we going to follow the Japan +path and so on well they're following + + align:start position:0% +path and so on well they're following + + + align:start position:0% +path and so on well they're following +this model that's what's happening to + + align:start position:0% +this model that's what's happening to + + + align:start position:0% +this model that's what's happening to +aair + + align:start position:0% + + + + align:start position:0% + +order I I'll say a little bit more later + + align:start position:0% +order I I'll say a little bit more later + + + align:start position:0% +order I I'll say a little bit more later +on about that so in this particular case + + align:start position:0% +on about that so in this particular case + + + align:start position:0% +on about that so in this particular case +no what what what I have done is in log + + align:start position:0% +no what what what I have done is in log + + + align:start position:0% +no what what what I have done is in log +space so I can have linear things when + + align:start position:0% +space so I can have linear things when + + + align:start position:0% +space so I can have linear things when +it's growing in log space this economy + + align:start position:0% +it's growing in log space this economy + + + align:start position:0% +it's growing in log space this economy +with the the low saving rate was + + align:start position:0% +with the the low saving rate was + + + align:start position:0% +with the the low saving rate was +growing here the slope of this was this + + align:start position:0% +growing here the slope of this was this + + + align:start position:0% +growing here the slope of this was this +is output so the slope of this was GA + + align:start position:0% +is output so the slope of this was GA + + + align:start position:0% +is output so the slope of this was GA +plus GN remember in a stady state output + + align:start position:0% +plus GN remember in a stady state output + + + align:start position:0% +plus GN remember in a stady state output +is growing at GA plus GN if the saving + + align:start position:0% +is growing at GA plus GN if the saving + + + align:start position:0% +is growing at GA plus GN if the saving +rate now increases then output starts + + align:start position:0% +rate now increases then output starts + + + align:start position:0% +rate now increases then output starts +growing transitionally faster than GA + + align:start position:0% +growing transitionally faster than GA + + + align:start position:0% +growing transitionally faster than GA +plus GN that's the reason sort of output + + align:start position:0% +plus GN that's the reason sort of output + + + align:start position:0% +plus GN that's the reason sort of output +grows faster than G here is all is + + align:start position:0% +grows faster than G here is all is + + + align:start position:0% +grows faster than G here is all is +growing faster than G here is very fast + + align:start position:0% +growing faster than G here is very fast + + + align:start position:0% +growing faster than G here is very fast +okay this is when we saw in Asia the + + align:start position:0% +okay this is when we saw in Asia the + + + align:start position:0% +okay this is when we saw in Asia the +rate of growth of 12% and stuff like + + align:start position:0% +rate of growth of 12% and stuff like + + + align:start position:0% +rate of growth of 12% and stuff like +that we were there moving there and and + + align:start position:0% +that we were there moving there and and + + + align:start position:0% +that we were there moving there and and +and but eventually it sort of PS out you + + align:start position:0% +and but eventually it sort of PS out you + + + align:start position:0% +and but eventually it sort of PS out you +end up with a higher level of output per + + align:start position:0% +end up with a higher level of output per + + + align:start position:0% +end up with a higher level of output per +capita per + + align:start position:0% +capita per + + + align:start position:0% +capita per +worker a higher sort of path no it's an + + align:start position:0% +worker a higher sort of path no it's an + + + align:start position:0% +worker a higher sort of path no it's an +entire path the rate of growth goes back + + align:start position:0% +entire path the rate of growth goes back + + + align:start position:0% +entire path the rate of growth goes back +to GA plus + + align:start position:0% +to GA plus + + + align:start position:0% +to GA plus +GN er uh but but you get this + + align:start position:0% +GN er uh but but you get this + + + align:start position:0% +GN er uh but but you get this +transitional growth which is very + + align:start position:0% +transitional growth which is very + + + align:start position:0% +transitional growth which is very +strong and once you're here once you all + + align:start position:0% +strong and once you're here once you all + + + align:start position:0% +strong and once you're here once you all +you run out of sort of the high saving + + align:start position:0% +you run out of sort of the high saving + + + align:start position:0% +you run out of sort of the high saving +and the catching up growth and so on + + align:start position:0% +and the catching up growth and so on + + + align:start position:0% +and the catching up growth and so on +there is little the only way you're + + align:start position:0% +there is little the only way you're + + + align:start position:0% +there is little the only way you're +going to really change your rate of + + align:start position:0% +going to really change your rate of + + + align:start position:0% +going to really change your rate of +growth in a sustained manner is doing + + align:start position:0% + + + + align:start position:0% + +what once you have used the tool of you + + align:start position:0% +what once you have used the tool of you + + + align:start position:0% +what once you have used the tool of you +know of catching up with the world of + + align:start position:0% +know of catching up with the world of + + + align:start position:0% +know of catching up with the world of +increasing your saving rate sometimes to + + align:start position:0% +increasing your saving rate sometimes to + + + align:start position:0% +increasing your saving rate sometimes to +levels incredibly High you still want to + + align:start position:0% +levels incredibly High you still want to + + + align:start position:0% +levels incredibly High you still want to +keep growing very fast what is the only + + align:start position:0% +keep growing very fast what is the only + + + align:start position:0% +keep growing very fast what is the only +option you have according to this model + + align:start position:0% + + + + align:start position:0% + +particularly let me bring even more ER + + align:start position:0% +particularly let me bring even more ER + + + align:start position:0% +particularly let me bring even more ER +realism to the story particular if GN is + + align:start position:0% +realism to the story particular if GN is + + + align:start position:0% +realism to the story particular if GN is +dropping and you still want to keep your + + align:start position:0% +dropping and you still want to keep your + + + align:start position:0% +dropping and you still want to keep your +growth high and your GN now you sort of + + align:start position:0% +growth high and your GN now you sort of + + + align:start position:0% +growth high and your GN now you sort of +use the catching up growth you use the + + align:start position:0% +use the catching up growth you use the + + + align:start position:0% +use the catching up growth you use the +higher saving rate which gives you + + align:start position:0% +higher saving rate which gives you + + + align:start position:0% +higher saving rate which gives you +transitional growth but it doesn't give + + align:start position:0% +transitional growth but it doesn't give + + + align:start position:0% +transitional growth but it doesn't give +you permanently higher rate of growth + + align:start position:0% +you permanently higher rate of growth + + + align:start position:0% +you permanently higher rate of growth +and on top of that for reasons you don't + + align:start position:0% +and on top of that for reasons you don't + + + align:start position:0% +and on top of that for reasons you don't +control population growth is declining + + align:start position:0% +control population growth is declining + + + align:start position:0% +control population growth is declining +even turning negative in some + + align:start position:0% +even turning negative in some + + + align:start position:0% +even turning negative in some +cases but suppose you still want to keep + + align:start position:0% +cases but suppose you still want to keep + + + align:start position:0% +cases but suppose you still want to keep +the rate of growth very high what is the + + align:start position:0% +the rate of growth very high what is the + + + align:start position:0% +the rate of growth very high what is the +only option you + + align:start position:0% + + + + align:start position:0% + +have increase G exactly technological + + align:start position:0% +have increase G exactly technological + + + align:start position:0% +have increase G exactly technological +progress that's the only option you have + + align:start position:0% +progress that's the only option you have + + + align:start position:0% +progress that's the only option you have +so it makes sense you see that you know + + align:start position:0% +so it makes sense you see that you know + + + align:start position:0% +so it makes sense you see that you know +in the case of china they're obsessed + + align:start position:0% +in the case of china they're obsessed + + + align:start position:0% +in the case of china they're obsessed +about technology and so on they + + align:start position:0% +about technology and so on they + + + align:start position:0% +about technology and so on they +understand the solo model okay if you + + align:start position:0% +understand the solo model okay if you + + + align:start position:0% +understand the solo model okay if you +want to maintain growth at a high Pace + + align:start position:0% +want to maintain growth at a high Pace + + + align:start position:0% +want to maintain growth at a high Pace +you you're going to need to work on that + + align:start position:0% +you you're going to need to work on that + + + align:start position:0% +you you're going to need to work on that +side a lot now it doesn't have to be you + + align:start position:0% +side a lot now it doesn't have to be you + + + align:start position:0% +side a lot now it doesn't have to be you +necessarily it's the world as a whole + + align:start position:0% +necessarily it's the world as a whole + + + align:start position:0% +necessarily it's the world as a whole +because technology you know moves around + + align:start position:0% +because technology you know moves around + + + align:start position:0% +because technology you know moves around +the world but but GA is at the end what + + align:start position:0% +the world but but GA is at the end what + + + align:start position:0% +the world but but GA is at the end what +puts the limits of what we can + + align:start position:0% + + + + align:start position:0% + +do ah what I what I was going to do is + + align:start position:0% +do ah what I what I was going to do is + + + align:start position:0% +do ah what I what I was going to do is +that's what I was drawing this diagram + + align:start position:0% +that's what I was drawing this diagram + + + align:start position:0% +that's what I was drawing this diagram +for is say well suppose that in this D + + align:start position:0% +for is say well suppose that in this D + + + align:start position:0% +for is say well suppose that in this D +this situation we are in a state state + + align:start position:0% +this situation we are in a state state + + + align:start position:0% +this situation we are in a state state +and we do increase + + align:start position:0% +and we do increase + + + align:start position:0% +and we do increase +GA what happens if we increase ga a well + + align:start position:0% +GA what happens if we increase ga a well + + + align:start position:0% +GA what happens if we increase ga a well +this + + align:start position:0% +this + + + align:start position:0% +this +curve rotates up no and at that point + + align:start position:0% +curve rotates up no and at that point + + + align:start position:0% +curve rotates up no and at that point +it's clear that that if if GA grows + + align:start position:0% +it's clear that that if if GA grows + + + align:start position:0% +it's clear that that if if GA grows +you're going to start growing at a + + align:start position:0% +you're going to start growing at a + + + align:start position:0% +you're going to start growing at a +faster rate but transitionally actually + + align:start position:0% +faster rate but transitionally actually + + + align:start position:0% +faster rate but transitionally actually +you're going to grow less than in your + + align:start position:0% +you're going to grow less than in your + + + align:start position:0% +you're going to grow less than in your +long-term rate of growth why is that the + + align:start position:0% + + + + align:start position:0% + +case so my claim is suppose we manage to + + align:start position:0% +case so my claim is suppose we manage to + + + align:start position:0% +case so my claim is suppose we manage to +increase GA so now we know that this + + align:start position:0% +increase GA so now we know that this + + + align:start position:0% +increase GA so now we know that this +line here now going to a um be steeper + + align:start position:0% +line here now going to a um be steeper + + + align:start position:0% +line here now going to a um be steeper +or say this we were in this line + + align:start position:0% +or say this we were in this line + + + align:start position:0% +or say this we were in this line +whatever we were in this line and now we + + align:start position:0% +whatever we were in this line and now we + + + align:start position:0% +whatever we were in this line and now we +make it a steeper so we're want to start + + align:start position:0% +make it a steeper so we're want to start + + + align:start position:0% +make it a steeper so we're want to start +growing faster eventually in the new + + align:start position:0% +growing faster eventually in the new + + + align:start position:0% +growing faster eventually in the new +state state and my claim now is that in + + align:start position:0% +state state and my claim now is that in + + + align:start position:0% +state state and my claim now is that in +the + + align:start position:0% +the + + + align:start position:0% +the +transition growth is less than the new + + align:start position:0% +transition growth is less than the new + + + align:start position:0% +transition growth is less than the new +rate of growth in the new in the new + + align:start position:0% +rate of growth in the new in the new + + + align:start position:0% +rate of growth in the new in the new +state state rate of + + align:start position:0% +state state rate of + + + align:start position:0% +state state rate of +growth is higher than the rate of growth + + align:start position:0% +growth is higher than the rate of growth + + + align:start position:0% +growth is higher than the rate of growth +of the previous St state but it's lower + + align:start position:0% +of the previous St state but it's lower + + + align:start position:0% +of the previous St state but it's lower +than the long run how do I see that I + + align:start position:0% +than the long run how do I see that I + + + align:start position:0% +than the long run how do I see that I +need another diagram you + + align:start position:0% + + + + align:start position:0% + +think so let me + + align:start position:0% +think so let me + + + align:start position:0% +think so let me +just put the the s y curve + + align:start position:0% + + + + align:start position:0% + +here so we were + + align:start position:0% +here so we were + + + align:start position:0% +here so we were +here at this state if I increase GA the + + align:start position:0% +here at this state if I increase GA the + + + align:start position:0% +here at this state if I increase GA the +only thing that will move here and + + align:start position:0% +only thing that will move here and + + + align:start position:0% +only thing that will move here and +remember the output equation is there + + align:start position:0% +remember the output equation is there + + + align:start position:0% +remember the output equation is there +but I don't want to put it the only + + align:start position:0% +but I don't want to put it the only + + + align:start position:0% +but I don't want to put it the only +thing I do is I rotate this curve + + align:start position:0% +thing I do is I rotate this curve + + + align:start position:0% +thing I do is I rotate this curve +up okay so this moves + + align:start position:0% + + + + align:start position:0% + +up do you see yes so this curves moves + + align:start position:0% +up do you see yes so this curves moves + + + align:start position:0% +up do you see yes so this curves moves +up when + + align:start position:0% +up when + + + align:start position:0% +up when +GA goes up so at the oldest steady state + + align:start position:0% +GA goes up so at the oldest steady state + + + align:start position:0% +GA goes up so at the oldest steady state +what I have now is a gap between the + + align:start position:0% +what I have now is a gap between the + + + align:start position:0% +what I have now is a gap between the +saving this economy investment and how + + align:start position:0% +saving this economy investment and how + + + align:start position:0% +saving this economy investment and how +much I need in order to maintain Capital + + align:start position:0% +much I need in order to maintain Capital + + + align:start position:0% +much I need in order to maintain Capital +per effective worker constant + + align:start position:0% +per effective worker constant + + + align:start position:0% +per effective worker constant +which means that I'm going to start + + align:start position:0% +which means that I'm going to start + + + align:start position:0% +which means that I'm going to start +moving in this direction until I reach + + align:start position:0% +moving in this direction until I reach + + + align:start position:0% +moving in this direction until I reach +the new stady + + align:start position:0% +the new stady + + + align:start position:0% +the new stady +state okay during this transition I'm + + align:start position:0% +state okay during this transition I'm + + + align:start position:0% +state okay during this transition I'm +growing at a lower Pace than in the new + + align:start position:0% +growing at a lower Pace than in the new + + + align:start position:0% +growing at a lower Pace than in the new +steady state in this new steady state I + + align:start position:0% +steady state in this new steady state I + + + align:start position:0% +steady state in this new steady state I +be + + align:start position:0% + + + + align:start position:0% + +growing much faster than in this state + + align:start position:0% +growing much faster than in this state + + + align:start position:0% +growing much faster than in this state +how much faster well equal to Delta GA + + align:start position:0% +how much faster well equal to Delta GA + + + align:start position:0% +how much faster well equal to Delta GA +but in the transition I will grow faster + + align:start position:0% +but in the transition I will grow faster + + + align:start position:0% +but in the transition I will grow faster +than that but not as fast as in the new + + align:start position:0% +than that but not as fast as in the new + + + align:start position:0% +than that but not as fast as in the new +today St that's the name was + + align:start position:0% + + + + align:start position:0% + +making H okay + + align:start position:0% + + + + align:start position:0% + +good do I you know i' rather discuss + + align:start position:0% +good do I you know i' rather discuss + + + align:start position:0% +good do I you know i' rather discuss +this with more time so questions about + + align:start position:0% +this with more time so questions about + + + align:start position:0% +this with more time so questions about +what we have done up to now + + align:start position:0% + + + + align:start position:0% + +is it clear or is it very unclear and + + align:start position:0% +is it clear or is it very unclear and + + + align:start position:0% +is it clear or is it very unclear and +probably + + align:start position:0% + + + + align:start position:0% + +both so let me I I I want to let me keep + + align:start position:0% +both so let me I I I want to let me keep + + + align:start position:0% +both so let me I I I want to let me keep +this for the next the next lecture + + align:start position:0% +this for the next the next lecture + + + align:start position:0% +this for the next the next lecture +because going to take a little time just + + align:start position:0% +because going to take a little time just + + + align:start position:0% +because going to take a little time just +play okay \ No newline at end of file diff --git a/oOya3cFmAMc.txt b/oOya3cFmAMc.txt new file mode 100644 index 0000000000000000000000000000000000000000..23dc3d0fb7e2ad71b6b76f967ba094360a558ee3 --- /dev/null +++ b/oOya3cFmAMc.txt @@ -0,0 +1,8651 @@ +align:start position:0% + +so gonna be a great lecture today it's + + align:start position:0% +so gonna be a great lecture today it's + + + align:start position:0% +so gonna be a great lecture today it's +about proteins I love proteins don't + + align:start position:0% +about proteins I love proteins don't + + + align:start position:0% +about proteins I love proteins don't +forget the handout yeah okay so I'm + + align:start position:0% +forget the handout yeah okay so I'm + + + align:start position:0% +forget the handout yeah okay so I'm +going to briefly wrap up the lecture we + + align:start position:0% +going to briefly wrap up the lecture we + + + align:start position:0% +going to briefly wrap up the lecture we +were doing on Friday because there were + + align:start position:0% +were doing on Friday because there were + + + align:start position:0% +were doing on Friday because there were +a couple of things that I wanted to make + + align:start position:0% +a couple of things that I wanted to make + + + align:start position:0% +a couple of things that I wanted to make +a note of and then we'll move on to + + align:start position:0% +a note of and then we'll move on to + + + align:start position:0% +a note of and then we'll move on to +section 2.3 about amino acids peptides + + align:start position:0% +section 2.3 about amino acids peptides + + + align:start position:0% +section 2.3 about amino acids peptides +and proteins now in the last class I + + align:start position:0% +and proteins now in the last class I + + + align:start position:0% +and proteins now in the last class I +introduced you to the lipid ik molecules + + align:start position:0% +introduced you to the lipid ik molecules + + + align:start position:0% +introduced you to the lipid ik molecules +and you can pick them out of a lineup + + align:start position:0% +and you can pick them out of a lineup + + + align:start position:0% +and you can pick them out of a lineup +because they are rich in carbon carbon + + align:start position:0% +because they are rich in carbon carbon + + + align:start position:0% +because they are rich in carbon carbon +and carbon hydrogen bonds as you can see + + align:start position:0% +and carbon hydrogen bonds as you can see + + + align:start position:0% +and carbon hydrogen bonds as you can see +here in these line angle drawings the + + align:start position:0% +here in these line angle drawings the + + + align:start position:0% +here in these line angle drawings the +majority of a lot of these molecules is + + align:start position:0% +majority of a lot of these molecules is + + + align:start position:0% +majority of a lot of these molecules is +carbon carbon or carbon hydrogen they + + align:start position:0% +carbon carbon or carbon hydrogen they + + + align:start position:0% +carbon carbon or carbon hydrogen they +are molecules that are mostly + + align:start position:0% +are molecules that are mostly + + + align:start position:0% +are molecules that are mostly +hydrophobic so there are some + + align:start position:0% +hydrophobic so there are some + + + align:start position:0% +hydrophobic so there are some +terminologies here what's hydrophobic + + align:start position:0% +terminologies here what's hydrophobic + + + align:start position:0% +terminologies here what's hydrophobic +which can also be referred to as + + align:start position:0% +which can also be referred to as + + + align:start position:0% +which can also be referred to as +lipophilic you either you can heat water + + align:start position:0% +lipophilic you either you can heat water + + + align:start position:0% +lipophilic you either you can heat water +and love fatty acid or fatty types of + + align:start position:0% +and love fatty acid or fatty types of + + + align:start position:0% +and love fatty acid or fatty types of +materials so there's both terms are + + align:start position:0% +materials so there's both terms are + + + align:start position:0% +materials so there's both terms are +synonymous and some of the lipids are + + align:start position:0% +synonymous and some of the lipids are + + + align:start position:0% +synonymous and some of the lipids are +what are known as an three Pathak and + + align:start position:0% +what are known as an three Pathak and + + + align:start position:0% +what are known as an three Pathak and +they include hydrophilic and hydrophobic + + align:start position:0% +they include hydrophilic and hydrophobic + + + align:start position:0% +they include hydrophilic and hydrophobic +components there are a couple of tiny + + align:start position:0% +components there are a couple of tiny + + + align:start position:0% +components there are a couple of tiny +terms that I didn't mention explicitly + + align:start position:0% +terms that I didn't mention explicitly + + + align:start position:0% +terms that I didn't mention explicitly +so I just want to go ahead and do that + + align:start position:0% +so I just want to go ahead and do that + + + align:start position:0% +so I just want to go ahead and do that +now for example in this phospholipid + + align:start position:0% +now for example in this phospholipid + + + align:start position:0% +now for example in this phospholipid +structure and we'll talk about these + + align:start position:0% +structure and we'll talk about these + + + align:start position:0% +structure and we'll talk about these +they have long-chain fatty acids + + align:start position:0% +they have long-chain fatty acids + + + align:start position:0% +they have long-chain fatty acids +attached via esters to this glycerol + + align:start position:0% +attached via esters to this glycerol + + + align:start position:0% +attached via esters to this glycerol +unit so there's one here and the second + + align:start position:0% +unit so there's one here and the second + + + align:start position:0% +unit so there's one here and the second +one here and then what's known as the + + align:start position:0% +one here and then what's known as the + + + align:start position:0% +one here and then what's known as the +polar head group in those fatty acids + + align:start position:0% +polar head group in those fatty acids + + + align:start position:0% +polar head group in those fatty acids +they could be fully saturated it means + + align:start position:0% +they could be fully saturated it means + + + align:start position:0% +they could be fully saturated it means +they have no double bonds in the + + align:start position:0% +they have no double bonds in the + + + align:start position:0% +they have no double bonds in the +structure so that term saturated is + + align:start position:0% +structure so that term saturated is + + + align:start position:0% +structure so that term saturated is +equivalent to no double bonds so no + + align:start position:0% +equivalent to no double bonds so no + + + align:start position:0% +equivalent to no double bonds so no +carbon-carbon double bonds or they could + + align:start position:0% +carbon-carbon double bonds or they could + + + align:start position:0% +carbon-carbon double bonds or they could +be unsaturated where there is a double + + align:start position:0% +be unsaturated where there is a double + + + align:start position:0% +be unsaturated where there is a double +bond within it so that's one or more + + align:start position:0% +bond within it so that's one or more + + + align:start position:0% +bond within it so that's one or more +double bonds and those double bonds take + + align:start position:0% +double bonds and those double bonds take + + + align:start position:0% +double bonds and those double bonds take +on a particular shape because there's + + align:start position:0% +on a particular shape because there's + + + align:start position:0% +on a particular shape because there's +not freedom of rotation around double + + align:start position:0% +not freedom of rotation around double + + + align:start position:0% +not freedom of rotation around double +bonds the same way there is around + + align:start position:0% +bonds the same way there is around + + + align:start position:0% +bonds the same way there is around +single bonds so those single bonds you + + align:start position:0% +single bonds so those single bonds you + + + align:start position:0% +single bonds so those single bonds you +can twist them around and twist them + + align:start position:0% +can twist them around and twist them + + + align:start position:0% +can twist them around and twist them +around but the double bond geometry is + + align:start position:0% +around but the double bond geometry is + + + align:start position:0% +around but the double bond geometry is +fixed and so double bonds we refer to + + align:start position:0% +fixed and so double bonds we refer to + + + align:start position:0% +fixed and so double bonds we refer to +them as either trans where the two + + align:start position:0% +them as either trans where the two + + + align:start position:0% +them as either trans where the two +groups are on opposite sides leaving the + + align:start position:0% +groups are on opposite sides leaving the + + + align:start position:0% +groups are on opposite sides leaving the +double bond or we refer to them as sis + + align:start position:0% +double bond or we refer to them as sis + + + align:start position:0% +double bond or we refer to them as sis +where the two groups are on the same + + align:start position:0% +where the two groups are on the same + + + align:start position:0% +where the two groups are on the same +side and we tend to use that sis and + + align:start position:0% +side and we tend to use that sis and + + + align:start position:0% +side and we tend to use that sis and +trans sort of naming system in a lot of + + align:start position:0% +trans sort of naming system in a lot of + + + align:start position:0% +trans sort of naming system in a lot of +other contexts as well but you might + + align:start position:0% +other contexts as well but you might + + + align:start position:0% +other contexts as well but you might +almost always want to remember the trans + + align:start position:0% +almost always want to remember the trans + + + align:start position:0% +almost always want to remember the trans +is as far away as possible + + align:start position:0% +is as far away as possible + + + align:start position:0% +is as far away as possible +sis is closer than trans alright so I'm + + align:start position:0% +sis is closer than trans alright so I'm + + + align:start position:0% +sis is closer than trans alright so I'm +just gonna take you forward to the + + align:start position:0% +just gonna take you forward to the + + + align:start position:0% +just gonna take you forward to the +phospholipid structure this is a very + + align:start position:0% +phospholipid structure this is a very + + + align:start position:0% +phospholipid structure this is a very +important semipermeable membranes I made + + align:start position:0% +important semipermeable membranes I made + + + align:start position:0% +important semipermeable membranes I made +up through the non covalent super + + align:start position:0% +up through the non covalent super + + + align:start position:0% +up through the non covalent super +molecular Association of phospholipid + + align:start position:0% +molecular Association of phospholipid + + + align:start position:0% +molecular Association of phospholipid +monomer units here's a monomer unit up + + align:start position:0% +monomer units here's a monomer unit up + + + align:start position:0% +monomer units here's a monomer unit up +here you see it has an amphipathic + + align:start position:0% +here you see it has an amphipathic + + + align:start position:0% +here you see it has an amphipathic +structure with a lot of hydrophobicity + + align:start position:0% +structure with a lot of hydrophobicity + + + align:start position:0% +structure with a lot of hydrophobicity +but also hydrophilicity and these + + align:start position:0% +but also hydrophilicity and these + + + align:start position:0% +but also hydrophilicity and these +molecules assemble into super molecular + + align:start position:0% +molecules assemble into super molecular + + + align:start position:0% +molecules assemble into super molecular +structures that form the boundaries of + + align:start position:0% +structures that form the boundaries of + + + align:start position:0% +structures that form the boundaries of +your cells saying they are semi + + align:start position:0% +your cells saying they are semi + + + align:start position:0% +your cells saying they are semi +permeable tells us a little bit about + + align:start position:0% +permeable tells us a little bit about + + + align:start position:0% +permeable tells us a little bit about +what can go through them if they were + + align:start position:0% +what can go through them if they were + + + align:start position:0% +what can go through them if they were +fully permeable anything could come and + + align:start position:0% +fully permeable anything could come and + + + align:start position:0% +fully permeable anything could come and +go and they wouldn't be much use frankly + + align:start position:0% +go and they wouldn't be much use frankly + + + align:start position:0% +go and they wouldn't be much use frankly +it's like leaving the door open the + + align:start position:0% +it's like leaving the door open the + + + align:start position:0% +it's like leaving the door open the +whole time but because they are semi + + align:start position:0% +whole time but because they are semi + + + align:start position:0% +whole time but because they are semi +permeable only a few things can come and + + align:start position:0% +permeable only a few things can come and + + + align:start position:0% +permeable only a few things can come and +go without extra help and other things + + align:start position:0% +go without extra help and other things + + + align:start position:0% +go without extra help and other things +need active mechanisms to to go through + + align:start position:0% +need active mechanisms to to go through + + + align:start position:0% +need active mechanisms to to go through +so let's take a look at the boundary + + align:start position:0% +so let's take a look at the boundary + + + align:start position:0% +so let's take a look at the boundary +here so when you see a membrane bilayer + + align:start position:0% +here so when you see a membrane bilayer + + + align:start position:0% +here so when you see a membrane bilayer +they are they're often shown looking + + align:start position:0% +they are they're often shown looking + + + align:start position:0% +they are they're often shown looking +like this where every one of these units + + align:start position:0% +like this where every one of these units + + + align:start position:0% +like this where every one of these units +is a phospholipid + + align:start position:0% +is a phospholipid + + + align:start position:0% +is a phospholipid +and there's water on both sides of the + + align:start position:0% +and there's water on both sides of the + + + align:start position:0% +and there's water on both sides of the +phospholipid because that polar head + + align:start position:0% +phospholipid because that polar head + + + align:start position:0% +phospholipid because that polar head +group is interacting with water on both + + align:start position:0% +group is interacting with water on both + + + align:start position:0% +group is interacting with water on both +sides so down here could be the inside + + align:start position:0% +sides so down here could be the inside + + + align:start position:0% +sides so down here could be the inside +of the cell up here could be the outside + + align:start position:0% +of the cell up here could be the outside + + + align:start position:0% +of the cell up here could be the outside +of the cell and a lot of cells + + align:start position:0% +of the cell and a lot of cells + + + align:start position:0% +of the cell and a lot of cells +especially eukaryotic cells the ones + + align:start position:0% +especially eukaryotic cells the ones + + + align:start position:0% +especially eukaryotic cells the ones +that make us up have a lot of endo + + align:start position:0% +that make us up have a lot of endo + + + align:start position:0% +that make us up have a lot of endo +membranes membranes with + + align:start position:0% +membranes membranes with + + + align:start position:0% +membranes membranes with +in the cells for example forming the + + align:start position:0% +in the cells for example forming the + + + align:start position:0% +in the cells for example forming the +boundary to the nucleus or to the + + align:start position:0% +boundary to the nucleus or to the + + + align:start position:0% +boundary to the nucleus or to the +mitochondria yes oh this guy must be so + + align:start position:0% +mitochondria yes oh this guy must be so + + + align:start position:0% +mitochondria yes oh this guy must be so +this looks like it's probably a + + align:start position:0% +this looks like it's probably a + + + align:start position:0% +this looks like it's probably a +saturated fatty acid so what do you + + align:start position:0% +saturated fatty acid so what do you + + + align:start position:0% +saturated fatty acid so what do you +think this one might be folks + + align:start position:0% +think this one might be folks + + + align:start position:0% +think this one might be folks +unsaturated and what's the double bond + + align:start position:0% +unsaturated and what's the double bond + + + align:start position:0% +unsaturated and what's the double bond +geometry sis so yeah it is it's like a + + align:start position:0% +geometry sis so yeah it is it's like a + + + align:start position:0% +geometry sis so yeah it is it's like a +it looks like a ballerina or something + + align:start position:0% +it looks like a ballerina or something + + + align:start position:0% +it looks like a ballerina or something +okay so we're you have a lot of concerns + + align:start position:0% +okay so we're you have a lot of concerns + + + align:start position:0% +okay so we're you have a lot of concerns +and we'll see later about how things get + + align:start position:0% +and we'll see later about how things get + + + align:start position:0% +and we'll see later about how things get +in and out of cells but most commonly + + align:start position:0% +in and out of cells but most commonly + + + align:start position:0% +in and out of cells but most commonly +things like oxygen or water and other + + align:start position:0% +things like oxygen or water and other + + + align:start position:0% +things like oxygen or water and other +small hydrophobic molecules can pass + + align:start position:0% +small hydrophobic molecules can pass + + + align:start position:0% +small hydrophobic molecules can pass +readily in and out through the semi + + align:start position:0% +readily in and out through the semi + + + align:start position:0% +readily in and out through the semi +permeable barrier but other things + + align:start position:0% +permeable barrier but other things + + + align:start position:0% +permeable barrier but other things +things that are charged things that are + + align:start position:0% +things that are charged things that are + + + align:start position:0% +things that are charged things that are +big need a different mechanism to get in + + align:start position:0% +big need a different mechanism to get in + + + align:start position:0% +big need a different mechanism to get in +and out and we will see later on how + + align:start position:0% +and out and we will see later on how + + + align:start position:0% +and out and we will see later on how +proteins provide the opportunities to + + align:start position:0% +proteins provide the opportunities to + + + align:start position:0% +proteins provide the opportunities to +Cargo things into cells or out of cells + + align:start position:0% +Cargo things into cells or out of cells + + + align:start position:0% +Cargo things into cells or out of cells +even very large entities and there are + + align:start position:0% +even very large entities and there are + + + align:start position:0% +even very large entities and there are +certain mechanisms whereby that happens + + align:start position:0% +certain mechanisms whereby that happens + + + align:start position:0% +certain mechanisms whereby that happens +through a semi permeable membrane okay I + + align:start position:0% +through a semi permeable membrane okay I + + + align:start position:0% +through a semi permeable membrane okay I +want to show you the other feature of + + align:start position:0% +want to show you the other feature of + + + align:start position:0% +want to show you the other feature of +membranes they are self-healing what + + align:start position:0% +membranes they are self-healing what + + + align:start position:0% +membranes they are self-healing what +this means is if you poke them you poke + + align:start position:0% +this means is if you poke them you poke + + + align:start position:0% +this means is if you poke them you poke +a hole in a cellular membrane you + + align:start position:0% +a hole in a cellular membrane you + + + align:start position:0% +a hole in a cellular membrane you +basically push apart those non-covalent + + align:start position:0% +basically push apart those non-covalent + + + align:start position:0% +basically push apart those non-covalent +forces once you take the thing away be + + align:start position:0% +forces once you take the thing away be + + + align:start position:0% +forces once you take the thing away be +it a needle or a very fine glass + + align:start position:0% +it a needle or a very fine glass + + + align:start position:0% +it a needle or a very fine glass +capillary they seal right back up to + + align:start position:0% +capillary they seal right back up to + + + align:start position:0% +capillary they seal right back up to +close to close the hole in the cell wall + + align:start position:0% +close to close the hole in the cell wall + + + align:start position:0% +close to close the hole in the cell wall +so that kind of tells us that they're + + align:start position:0% +so that kind of tells us that they're + + + align:start position:0% +so that kind of tells us that they're +non covalent forces so this is a really + + align:start position:0% +non covalent forces so this is a really + + + align:start position:0% +non covalent forces so this is a really +cool video of someone doing micro + + align:start position:0% +cool video of someone doing micro + + + align:start position:0% +cool video of someone doing micro +injection into eukaryotic cells the + + align:start position:0% +injection into eukaryotic cells the + + + align:start position:0% +injection into eukaryotic cells the +needle points to the cell approaches the + + align:start position:0% +needle points to the cell approaches the + + + align:start position:0% +needle points to the cell approaches the +surface you can drop something into the + + align:start position:0% +surface you can drop something into the + + + align:start position:0% +surface you can drop something into the +cell and then the cell closes and + + align:start position:0% +cell and then the cell closes and + + + align:start position:0% +cell and then the cell closes and +maintained regains its mackay its + + align:start position:0% +maintained regains its mackay its + + + align:start position:0% +maintained regains its mackay its +integrity of the barrier so this is a + + align:start position:0% +integrity of the barrier so this is a + + + align:start position:0% +integrity of the barrier so this is a +very cool + + align:start position:0% +very cool + + + align:start position:0% +very cool +a nation people do this they have to not + + align:start position:0% +a nation people do this they have to not + + + align:start position:0% +a nation people do this they have to not +drink too much coffee because it's quite + + align:start position:0% +drink too much coffee because it's quite + + + align:start position:0% +drink too much coffee because it's quite +complicated to do a lot of + + align:start position:0% +complicated to do a lot of + + + align:start position:0% +complicated to do a lot of +microinjection because you can really + + align:start position:0% +microinjection because you can really + + + align:start position:0% +microinjection because you can really +cause carnage and your cell population + + align:start position:0% +cause carnage and your cell population + + + align:start position:0% +cause carnage and your cell population +if you're if you're not very dexterous + + align:start position:0% +if you're if you're not very dexterous + + + align:start position:0% +if you're if you're not very dexterous +with microinjection + + align:start position:0% +with microinjection + + + align:start position:0% +with microinjection +but people have they can be very good at + + align:start position:0% +but people have they can be very good at + + + align:start position:0% +but people have they can be very good at +it so I just want to ask a couple of + + align:start position:0% +it so I just want to ask a couple of + + + align:start position:0% +it so I just want to ask a couple of +questions before you a couple of things + + align:start position:0% +questions before you a couple of things + + + align:start position:0% +questions before you a couple of things +to think about before we close up the + + align:start position:0% +to think about before we close up the + + + align:start position:0% +to think about before we close up the +lipids so here's a typical lipid bilayer + + align:start position:0% +lipids so here's a typical lipid bilayer + + + align:start position:0% +lipids so here's a typical lipid bilayer +where I've highlighted a single lipid in + + align:start position:0% +where I've highlighted a single lipid in + + + align:start position:0% +where I've highlighted a single lipid in +the colors those are the head groups and + + align:start position:0% +the colors those are the head groups and + + + align:start position:0% +the colors those are the head groups and +all in white and gray are the + + align:start position:0% +all in white and gray are the + + + align:start position:0% +all in white and gray are the +hydrophilic components and just one of + + align:start position:0% +hydrophilic components and just one of + + + align:start position:0% +hydrophilic components and just one of +the phospholipids is highlighted and + + align:start position:0% +the phospholipids is highlighted and + + + align:start position:0% +the phospholipids is highlighted and +that would be this molecular structure + + align:start position:0% +that would be this molecular structure + + + align:start position:0% +that would be this molecular structure +here so first of all what do you think + + align:start position:0% +here so first of all what do you think + + + align:start position:0% +here so first of all what do you think +the non covalent forces at that membrane + + align:start position:0% +the non covalent forces at that membrane + + + align:start position:0% +the non covalent forces at that membrane +interface may be that is what's going on + + align:start position:0% +interface may be that is what's going on + + + align:start position:0% +interface may be that is what's going on +here at the interface what are the types + + align:start position:0% +here at the interface what are the types + + + align:start position:0% +here at the interface what are the types +of interactions that you might have + + align:start position:0% +of interactions that you might have + + + align:start position:0% +of interactions that you might have +there give you a minute to think about + + align:start position:0% +there give you a minute to think about + + + align:start position:0% +there give you a minute to think about +it and I want to show you that I'm + + align:start position:0% +it and I want to show you that I'm + + + align:start position:0% +it and I want to show you that I'm +actually giving you a clue here because + + align:start position:0% +actually giving you a clue here because + + + align:start position:0% +actually giving you a clue here because +you can see the structure negative + + align:start position:0% +you can see the structure negative + + + align:start position:0% +you can see the structure negative +charge positive charge but also remember + + align:start position:0% +charge positive charge but also remember + + + align:start position:0% +charge positive charge but also remember +this is a barrier to water so there are + + align:start position:0% +this is a barrier to water so there are + + + align:start position:0% +this is a barrier to water so there are +other things going on with the solvent + + align:start position:0% +other things going on with the solvent + + + align:start position:0% +other things going on with the solvent +that the membrane is sitting in because + + align:start position:0% +that the membrane is sitting in because + + + align:start position:0% +that the membrane is sitting in because +there's water surrounding that barrier + + align:start position:0% +there's water surrounding that barrier + + + align:start position:0% +there's water surrounding that barrier +layer anyone want to tell me what the + + align:start position:0% +layer anyone want to tell me what the + + + align:start position:0% +layer anyone want to tell me what the +answer is and why yeah did you yeah yeah + + align:start position:0% +answer is and why yeah did you yeah yeah + + + align:start position:0% +answer is and why yeah did you yeah yeah +between what and what + + align:start position:0% + + + + align:start position:0% + +in + + align:start position:0% + + + + align:start position:0% + +right so water so that what is a good + + align:start position:0% +right so water so that what is a good + + + align:start position:0% +right so water so that what is a good +hydrogen bond donor and acceptor so + + align:start position:0% +hydrogen bond donor and acceptor so + + + align:start position:0% +hydrogen bond donor and acceptor so +there will be hydrogen bonding + + align:start position:0% +there will be hydrogen bonding + + + align:start position:0% +there will be hydrogen bonding +what about amongst all those lipid head + + align:start position:0% +what about amongst all those lipid head + + + align:start position:0% +what about amongst all those lipid head +groups what's the other major force yeah + + align:start position:0% +groups what's the other major force yeah + + + align:start position:0% +groups what's the other major force yeah +between the different charges so the + + align:start position:0% +between the different charges so the + + + align:start position:0% +between the different charges so the +correct answer here is both of them + + align:start position:0% +correct answer here is both of them + + + align:start position:0% +correct answer here is both of them +don't think it's just electrostatic it's + + align:start position:0% +don't think it's just electrostatic it's + + + align:start position:0% +don't think it's just electrostatic it's +both it's electrostatic amongst the head + + align:start position:0% +both it's electrostatic amongst the head + + + align:start position:0% +both it's electrostatic amongst the head +groups hydrogen bonding between all that + + align:start position:0% +groups hydrogen bonding between all that + + + align:start position:0% +groups hydrogen bonding between all that +sort of dense bunch of charge and the + + align:start position:0% +sort of dense bunch of charge and the + + + align:start position:0% +sort of dense bunch of charge and the +water and then the other question what + + align:start position:0% +water and then the other question what + + + align:start position:0% +water and then the other question what +type of molecules can get across I've + + align:start position:0% +type of molecules can get across I've + + + align:start position:0% +type of molecules can get across I've +already answered that question to you + + align:start position:0% +already answered that question to you + + + align:start position:0% +already answered that question to you +salts are gonna need ways to get in and + + align:start position:0% +salts are gonna need ways to get in and + + + align:start position:0% +salts are gonna need ways to get in and +out small proteins are too big to + + align:start position:0% +out small proteins are too big to + + + align:start position:0% +out small proteins are too big to +dissolve in that membrane through + + align:start position:0% +dissolve in that membrane through + + + align:start position:0% +dissolve in that membrane through +passive mechanisms so we're gonna have + + align:start position:0% +passive mechanisms so we're gonna have + + + align:start position:0% +passive mechanisms so we're gonna have +to figure out how to get proteins in and + + align:start position:0% +to figure out how to get proteins in and + + + align:start position:0% +to figure out how to get proteins in and +out of cells + + align:start position:0% +out of cells + + + align:start position:0% +out of cells +neurotransmitters such as this this is + + align:start position:0% +neurotransmitters such as this this is + + + align:start position:0% +neurotransmitters such as this this is +gaba or gamma amino butyric acid it's + + align:start position:0% +gaba or gamma amino butyric acid it's + + + align:start position:0% +gaba or gamma amino butyric acid it's +charged it just can't get through + + align:start position:0% +charged it just can't get through + + + align:start position:0% +charged it just can't get through +without a transporter of some kind and + + align:start position:0% +without a transporter of some kind and + + + align:start position:0% +without a transporter of some kind and +it's actually proteins that end up doing + + align:start position:0% +it's actually proteins that end up doing + + + align:start position:0% +it's actually proteins that end up doing +the heavy lifting of the transport + + align:start position:0% +the heavy lifting of the transport + + + align:start position:0% +the heavy lifting of the transport +processes that we'll see okay so this + + align:start position:0% +processes that we'll see okay so this + + + align:start position:0% +processes that we'll see okay so this +section will it be about the building + + align:start position:0% +section will it be about the building + + + align:start position:0% +section will it be about the building +blocks of your protein macromolecules + + align:start position:0% +blocks of your protein macromolecules + + + align:start position:0% +blocks of your protein macromolecules +which I want to remind you comprise 50% + + align:start position:0% +which I want to remind you comprise 50% + + + align:start position:0% +which I want to remind you comprise 50% +of all of the macromolecules so that + + align:start position:0% +of all of the macromolecules so that + + + align:start position:0% +of all of the macromolecules so that +suggests it's a pretty important class + + align:start position:0% +suggests it's a pretty important class + + + align:start position:0% +suggests it's a pretty important class +of macromolecules that has a lot of + + align:start position:0% +of macromolecules that has a lot of + + + align:start position:0% +of macromolecules that has a lot of +different functions + + align:start position:0% +different functions + + + align:start position:0% +different functions +now the amino acid building lock blocks + + align:start position:0% +now the amino acid building lock blocks + + + align:start position:0% +now the amino acid building lock blocks +look pretty simple they're called amino + + align:start position:0% +look pretty simple they're called amino + + + align:start position:0% +look pretty simple they're called amino +acids because they have an amine the + + align:start position:0% +acids because they have an amine the + + + align:start position:0% +acids because they have an amine the +carboxylic acid and there's a carbon + + align:start position:0% +carboxylic acid and there's a carbon + + + align:start position:0% +carboxylic acid and there's a carbon +that is tetrahedral between the + + align:start position:0% +that is tetrahedral between the + + + align:start position:0% +that is tetrahedral between the +carboxylic acid and the amine and the + + align:start position:0% +carboxylic acid and the amine and the + + + align:start position:0% +carboxylic acid and the amine and the +simplest of those is when those are both + + align:start position:0% +simplest of those is when those are both + + + align:start position:0% +simplest of those is when those are both +hydrogen but most of the amino acids are + + align:start position:0% +hydrogen but most of the amino acids are + + + align:start position:0% +hydrogen but most of the amino acids are +differentiated from that this one I + + align:start position:0% +differentiated from that this one I + + + align:start position:0% +differentiated from that this one I +showed you on the board this amino acid + + align:start position:0% +showed you on the board this amino acid + + + align:start position:0% +showed you on the board this amino acid +is glycine usually when it's just a + + align:start position:0% +is glycine usually when it's just a + + + align:start position:0% +is glycine usually when it's just a +lonely amino acid in aqueous solution + + align:start position:0% +lonely amino acid in aqueous solution + + + align:start position:0% +lonely amino acid in aqueous solution +it's in a different charged form + + align:start position:0% +it's in a different charged form + + + align:start position:0% +it's in a different charged form +just in consistent with what we talked + + align:start position:0% +just in consistent with what we talked + + + align:start position:0% +just in consistent with what we talked +about in the last class so this is + + align:start position:0% +about in the last class so this is + + + align:start position:0% +about in the last class so this is +glycine it's one of the 20 encoded amino + + align:start position:0% +glycine it's one of the 20 encoded amino + + + align:start position:0% +glycine it's one of the 20 encoded amino +acids that means the amino acids that + + align:start position:0% +acids that means the amino acids that + + + align:start position:0% +acids that means the amino acids that +are made through ribosomal biosynthesis + + align:start position:0% +are made through ribosomal biosynthesis + + + align:start position:0% +are made through ribosomal biosynthesis +through a code that's provided by the + + align:start position:0% +through a code that's provided by the + + + align:start position:0% +through a code that's provided by the +messenger RNA so they are encoded by + + align:start position:0% +messenger RNA so they are encoded by + + + align:start position:0% +messenger RNA so they are encoded by +messenger RNA RNA and later on you'll + + align:start position:0% +messenger RNA RNA and later on you'll + + + align:start position:0% +messenger RNA RNA and later on you'll +see all of the beautiful mechanics of + + align:start position:0% +see all of the beautiful mechanics of + + + align:start position:0% +see all of the beautiful mechanics of +those processes now this table looks + + align:start position:0% +those processes now this table looks + + + align:start position:0% +those processes now this table looks +pretty complicated so I'm going to + + align:start position:0% +pretty complicated so I'm going to + + + align:start position:0% +pretty complicated so I'm going to +deconstruct it a bit but what I first of + + align:start position:0% +deconstruct it a bit but what I first of + + + align:start position:0% +deconstruct it a bit but what I first of +all want to assure you is that these + + align:start position:0% +all want to assure you is that these + + + align:start position:0% +all want to assure you is that these +twenty you will always get a handout + + align:start position:0% +twenty you will always get a handout + + + align:start position:0% +twenty you will always get a handout +with these structures on them we are not + + align:start position:0% +with these structures on them we are not + + + align:start position:0% +with these structures on them we are not +asking you to remember these structures + + align:start position:0% +asking you to remember these structures + + + align:start position:0% +asking you to remember these structures +you might become familiar with some of + + align:start position:0% +you might become familiar with some of + + + align:start position:0% +you might become familiar with some of +them but you do not have to remember + + align:start position:0% +them but you do not have to remember + + + align:start position:0% +them but you do not have to remember +them you'll have a table that shows them + + align:start position:0% +them you'll have a table that shows them + + + align:start position:0% +them you'll have a table that shows them +but on that table I won't necessarily + + align:start position:0% +but on that table I won't necessarily + + + align:start position:0% +but on that table I won't necessarily +give you the information on what their + + align:start position:0% +give you the information on what their + + + align:start position:0% +give you the information on what their +properties are because those are things + + align:start position:0% +properties are because those are things + + + align:start position:0% +properties are because those are things +that you should be able to spot by + + align:start position:0% +that you should be able to spot by + + + align:start position:0% +that you should be able to spot by +looking at their chemical structures all + + align:start position:0% +looking at their chemical structures all + + + align:start position:0% +looking at their chemical structures all +right so that's important so these are + + align:start position:0% +right so that's important so these are + + + align:start position:0% +right so that's important so these are +all line angle drawings so you see the + + align:start position:0% +all line angle drawings so you see the + + + align:start position:0% +all line angle drawings so you see the +carbon the hydrogen's aren't shown in + + align:start position:0% +carbon the hydrogen's aren't shown in + + + align:start position:0% +carbon the hydrogen's aren't shown in +there the charges are shown for what's + + align:start position:0% +there the charges are shown for what's + + + align:start position:0% +there the charges are shown for what's +called the sidechain because most of the + + align:start position:0% +called the sidechain because most of the + + + align:start position:0% +called the sidechain because most of the +amino acids + + align:start position:0% + + + + align:start position:0% + +have a sigh change the amino acids are + + align:start position:0% +have a sigh change the amino acids are + + + align:start position:0% +have a sigh change the amino acids are +also chiral but you'll learn more than + + align:start position:0% +also chiral but you'll learn more than + + + align:start position:0% +also chiral but you'll learn more than +you ever wanted to know about chirality + + align:start position:0% +you ever wanted to know about chirality + + + align:start position:0% +you ever wanted to know about chirality +in 512 so I won't weigh you down with + + align:start position:0% +in 512 so I won't weigh you down with + + + align:start position:0% +in 512 so I won't weigh you down with +any of those properties so there is a + + align:start position:0% +any of those properties so there is a + + + align:start position:0% +any of those properties so there is a +side chain that dictates the properties + + align:start position:0% +side chain that dictates the properties + + + align:start position:0% +side chain that dictates the properties +of the amino acids one tiny detail the + + align:start position:0% +of the amino acids one tiny detail the + + + align:start position:0% +of the amino acids one tiny detail the +amino acids that are encoded in our + + align:start position:0% +amino acids that are encoded in our + + + align:start position:0% +amino acids that are encoded in our +proteins are all what are known as alpha + + align:start position:0% +proteins are all what are known as alpha + + + align:start position:0% +proteins are all what are known as alpha +amino acids there are other amino acids + + align:start position:0% +amino acids there are other amino acids + + + align:start position:0% +amino acids there are other amino acids +GABA that I showed you on the previous + + align:start position:0% +GABA that I showed you on the previous + + + align:start position:0% +GABA that I showed you on the previous +slide is not an alpha amino acid + + align:start position:0% +slide is not an alpha amino acid + + + align:start position:0% +slide is not an alpha amino acid +actually it's a gamma amino acid these + + align:start position:0% +actually it's a gamma amino acid these + + + align:start position:0% +actually it's a gamma amino acid these +are called amino acids because the amine + + align:start position:0% +are called amino acids because the amine + + + align:start position:0% +are called amino acids because the amine +group is at the Alpha position relative + + align:start position:0% +group is at the Alpha position relative + + + align:start position:0% +group is at the Alpha position relative +to the carboxyl don't need to know a lot + + align:start position:0% +to the carboxyl don't need to know a lot + + + align:start position:0% +to the carboxyl don't need to know a lot +more about that with respect to that so + + align:start position:0% +more about that with respect to that so + + + align:start position:0% +more about that with respect to that so +let's take a look at this set of amino + + align:start position:0% +let's take a look at this set of amino + + + align:start position:0% +let's take a look at this set of amino +acids and what you see is amino acid + + align:start position:0% +acids and what you see is amino acid + + + align:start position:0% +acids and what you see is amino acid +side chains with rather different + + align:start position:0% +side chains with rather different + + + align:start position:0% +side chains with rather different +properties I've amassed here's glycine + + align:start position:0% +properties I've amassed here's glycine + + + align:start position:0% +properties I've amassed here's glycine +at the very top all amino acids have a + + align:start position:0% +at the very top all amino acids have a + + + align:start position:0% +at the very top all amino acids have a +three-letter code or a one letter code I + + align:start position:0% +three-letter code or a one letter code I + + + align:start position:0% +three-letter code or a one letter code I +particularly enjoy using one letter + + align:start position:0% +particularly enjoy using one letter + + + align:start position:0% +particularly enjoy using one letter +codes and spelling out people's names in + + align:start position:0% +codes and spelling out people's names in + + + align:start position:0% +codes and spelling out people's names in +peptides and things like that I'll let + + align:start position:0% +peptides and things like that I'll let + + + align:start position:0% +peptides and things like that I'll let +you do that in privacy of your own room + + align:start position:0% +you do that in privacy of your own room + + + align:start position:0% +you do that in privacy of your own room +it's kind of amusing to see if your name + + align:start position:0% +it's kind of amusing to see if your name + + + align:start position:0% +it's kind of amusing to see if your name +actually spells out a peptide some some + + align:start position:0% +actually spells out a peptide some some + + + align:start position:0% +actually spells out a peptide some some +of us get I get a little stuck with + + align:start position:0% +of us get I get a little stuck with + + + align:start position:0% +of us get I get a little stuck with +Barbara because there are no B amino + + align:start position:0% +Barbara because there are no B amino + + + align:start position:0% +Barbara because there are no B amino +acid 1 letters with a B the next most + + align:start position:0% +acid 1 letters with a B the next most + + + align:start position:0% +acid 1 letters with a B the next most +abundant type of amino acid have + + align:start position:0% +abundant type of amino acid have + + + align:start position:0% +abundant type of amino acid have +hydrophobic side chains what that means + + align:start position:0% +hydrophobic side chains what that means + + + align:start position:0% +hydrophobic side chains what that means +is they have a lot of CHS are not a lot + + align:start position:0% +is they have a lot of CHS are not a lot + + + align:start position:0% +is they have a lot of CHS are not a lot +else right so take a look at them + + align:start position:0% +else right so take a look at them + + + align:start position:0% +else right so take a look at them +alanine has a methyl group for example + + align:start position:0% +alanine has a methyl group for example + + + align:start position:0% +alanine has a methyl group for example +where I've shown they are that would be + + align:start position:0% +where I've shown they are that would be + + + align:start position:0% +where I've shown they are that would be +Aladin and they get increasingly big + + align:start position:0% +Aladin and they get increasingly big + + + align:start position:0% +Aladin and they get increasingly big +they're quite large some of them have + + align:start position:0% +they're quite large some of them have + + + align:start position:0% +they're quite large some of them have +quite extended side chains are the ones + + align:start position:0% +quite extended side chains are the ones + + + align:start position:0% +quite extended side chains are the ones +have side chains with rings with double + + align:start position:0% +have side chains with rings with double + + + align:start position:0% +have side chains with rings with double +bonds in them those are what we would + + align:start position:0% +bonds in them those are what we would + + + align:start position:0% +bonds in them those are what we would +designate in organic chemistry is + + align:start position:0% +designate in organic chemistry is + + + align:start position:0% +designate in organic chemistry is +aromatic they show slit they're still + + align:start position:0% +aromatic they show slit they're still + + + align:start position:0% +aromatic they show slit they're still +hydrophobic but they show different + + align:start position:0% +hydrophobic but they show different + + + align:start position:0% +hydrophobic but they show different +properties to the to this other set of + + align:start position:0% +properties to the to this other set of + + + align:start position:0% +properties to the to this other set of +amino acids some of these amino + + align:start position:0% +amino acids some of these amino + + + align:start position:0% +amino acids some of these amino +may actually have hula groups in them + + align:start position:0% +may actually have hula groups in them + + + align:start position:0% +may actually have hula groups in them +but their major feature is that they're + + align:start position:0% +but their major feature is that they're + + + align:start position:0% +but their major feature is that they're +hydrophobic but in an amino acids such + + align:start position:0% +hydrophobic but in an amino acids such + + + align:start position:0% +hydrophobic but in an amino acids such +as tyrosine you could not only have + + align:start position:0% +as tyrosine you could not only have + + + align:start position:0% +as tyrosine you could not only have +hydrophobic interactions with that ring + + align:start position:0% +hydrophobic interactions with that ring + + + align:start position:0% +hydrophobic interactions with that ring +system but also hydrogen bonding with + + align:start position:0% +system but also hydrogen bonding with + + + align:start position:0% +system but also hydrogen bonding with +the O H on the tyrosine so some of the + + align:start position:0% +the O H on the tyrosine so some of the + + + align:start position:0% +the O H on the tyrosine so some of the +amino acids can do a few different + + align:start position:0% +amino acids can do a few different + + + align:start position:0% +amino acids can do a few different +things the next set of amino acids are + + align:start position:0% +things the next set of amino acids are + + + align:start position:0% +things the next set of amino acids are +those that are polar and charged and + + align:start position:0% +those that are polar and charged and + + + align:start position:0% +those that are polar and charged and +I've shown you the most common state of + + align:start position:0% +I've shown you the most common state of + + + align:start position:0% +I've shown you the most common state of +all of those amino acids but you already + + align:start position:0% +all of those amino acids but you already + + + align:start position:0% +all of those amino acids but you already +know that the amine of lysine is likely + + align:start position:0% +know that the amine of lysine is likely + + + align:start position:0% +know that the amine of lysine is likely +to be charged this guanidinium group of + + align:start position:0% +to be charged this guanidinium group of + + + align:start position:0% +to be charged this guanidinium group of +arginine take my word for it it's + + align:start position:0% +arginine take my word for it it's + + + align:start position:0% +arginine take my word for it it's +charged it's a bit more complicated to + + align:start position:0% +charged it's a bit more complicated to + + + align:start position:0% +charged it's a bit more complicated to +draw histidine is also one of those + + align:start position:0% +draw histidine is also one of those + + + align:start position:0% +draw histidine is also one of those +that's annoying to draw but the + + align:start position:0% +that's annoying to draw but the + + + align:start position:0% +that's annoying to draw but the +negatively charged side chains with a + + align:start position:0% +negatively charged side chains with a + + + align:start position:0% +negatively charged side chains with a +carboxylate are both negatively charged + + align:start position:0% +carboxylate are both negatively charged + + + align:start position:0% +carboxylate are both negatively charged +and that's something you would remember + + align:start position:0% +and that's something you would remember + + + align:start position:0% +and that's something you would remember +from the previous class hopefully and + + align:start position:0% +from the previous class hopefully and + + + align:start position:0% +from the previous class hopefully and +then finally their amino acids with + + align:start position:0% +then finally their amino acids with + + + align:start position:0% +then finally their amino acids with +polar uncharged side chains such as + + align:start position:0% +polar uncharged side chains such as + + + align:start position:0% +polar uncharged side chains such as +those shown here now this doesn't look + + align:start position:0% +those shown here now this doesn't look + + + align:start position:0% +those shown here now this doesn't look +like a very exciting set of building + + align:start position:0% +like a very exciting set of building + + + align:start position:0% +like a very exciting set of building +blocks how can life run on things made + + align:start position:0% +blocks how can life run on things made + + + align:start position:0% +blocks how can life run on things made +of twenty relatively simple building + + align:start position:0% +of twenty relatively simple building + + + align:start position:0% +of twenty relatively simple building +blocks with functional groups and it's + + align:start position:0% +blocks with functional groups and it's + + + align:start position:0% +blocks with functional groups and it's +that the building blocks are not + + align:start position:0% +that the building blocks are not + + + align:start position:0% +that the building blocks are not +functional themselves it is the polymers + + align:start position:0% +functional themselves it is the polymers + + + align:start position:0% +functional themselves it is the polymers +that are made up of amino acids and I'll + + align:start position:0% +that are made up of amino acids and I'll + + + align:start position:0% +that are made up of amino acids and I'll +always call them AAS because it's easier + + align:start position:0% +always call them AAS because it's easier + + + align:start position:0% +always call them AAS because it's easier +for me the polymers of amino acids are + + align:start position:0% +for me the polymers of amino acids are + + + align:start position:0% +for me the polymers of amino acids are +hetero polymers that means they're made + + align:start position:0% +hetero polymers that means they're made + + + align:start position:0% +hetero polymers that means they're made +up of a bunch of different monomer units + + align:start position:0% +up of a bunch of different monomer units + + + align:start position:0% +up of a bunch of different monomer units +when they're called hetero polymers and + + align:start position:0% +when they're called hetero polymers and + + + align:start position:0% +when they're called hetero polymers and +the other important thing about these + + align:start position:0% +the other important thing about these + + + align:start position:0% +the other important thing about these +polymers is that they are of defined + + align:start position:0% + + + + align:start position:0% + +sequence what is the sequence it's the + + align:start position:0% +sequence what is the sequence it's the + + + align:start position:0% +sequence what is the sequence it's the +order in which the amino acids appear so + + align:start position:0% +order in which the amino acids appear so + + + align:start position:0% +order in which the amino acids appear so +I'm right and all the functions of + + align:start position:0% +I'm right and all the functions of + + + align:start position:0% +I'm right and all the functions of +proteins are dictated by the order of + + align:start position:0% +proteins are dictated by the order of + + + align:start position:0% +proteins are dictated by the order of +the amino acids let's take a look at the + + align:start position:0% +the amino acids let's take a look at the + + + align:start position:0% +the amino acids let's take a look at the +side bar here so once again + + align:start position:0% +side bar here so once again + + + align:start position:0% +side bar here so once again +remember a couple of things that we will + + align:start position:0% +remember a couple of things that we will + + + align:start position:0% +remember a couple of things that we will +always give you this table to think + + align:start position:0% +always give you this table to think + + + align:start position:0% +always give you this table to think +about come back there were a couple of + + align:start position:0% +about come back there were a couple of + + + align:start position:0% +about come back there were a couple of +outliers I just want to mention quickly + + align:start position:0% +outliers I just want to mention quickly + + + align:start position:0% +outliers I just want to mention quickly +so I've talked to you about luck glycine + + align:start position:0% +so I've talked to you about luck glycine + + + align:start position:0% +so I've talked to you about luck glycine +the simplest amino acid with no + + align:start position:0% +the simplest amino acid with no + + + align:start position:0% +the simplest amino acid with no +elaborate side chain prolene is a little + + align:start position:0% +elaborate side chain prolene is a little + + + align:start position:0% +elaborate side chain prolene is a little +odd because it's side chain is kind of + + align:start position:0% +odd because it's side chain is kind of + + + align:start position:0% +odd because it's side chain is kind of +in a cyclic structure and towards the + + align:start position:0% +in a cyclic structure and towards the + + + align:start position:0% +in a cyclic structure and towards the +end of the class I'll talk to you about + + align:start position:0% +end of the class I'll talk to you about + + + align:start position:0% +end of the class I'll talk to you about +collagen whose structure is totally + + align:start position:0% +collagen whose structure is totally + + + align:start position:0% +collagen whose structure is totally +dependent on the involvement of prolene + + align:start position:0% +dependent on the involvement of prolene + + + align:start position:0% +dependent on the involvement of prolene +in the sequence of the amino acids that + + align:start position:0% +in the sequence of the amino acids that + + + align:start position:0% +in the sequence of the amino acids that +make up collagen and then the last sort + + align:start position:0% +make up collagen and then the last sort + + + align:start position:0% +make up collagen and then the last sort +of unusual amino acid is cysteine it has + + align:start position:0% +of unusual amino acid is cysteine it has + + + align:start position:0% +of unusual amino acid is cysteine it has +a file and the one clever thing about + + align:start position:0% +a file and the one clever thing about + + + align:start position:0% +a file and the one clever thing about +cysteine I'm just gonna put a bit of a + + align:start position:0% +cysteine I'm just gonna put a bit of a + + + align:start position:0% +cysteine I'm just gonna put a bit of a +peptide here one cysteine and then I'm + + align:start position:0% +peptide here one cysteine and then I'm + + + align:start position:0% +peptide here one cysteine and then I'm +gonna put a second cysteine and these + + align:start position:0% +gonna put a second cysteine and these + + + align:start position:0% +gonna put a second cysteine and these +are going to be deemed in a peptide ik + + align:start position:0% +are going to be deemed in a peptide ik + + + align:start position:0% +are going to be deemed in a peptide ik +structure what cysteine can do is it can + + align:start position:0% +structure what cysteine can do is it can + + + align:start position:0% +structure what cysteine can do is it can +exist either with the file sidechain SH + + align:start position:0% +exist either with the file sidechain SH + + + align:start position:0% +exist either with the file sidechain SH +or it can be at a different oxidation + + align:start position:0% +or it can be at a different oxidation + + + align:start position:0% +or it can be at a different oxidation +state where the two sulfur's are joined + + align:start position:0% +state where the two sulfur's are joined + + + align:start position:0% +state where the two sulfur's are joined +to each other so for the most part your + + align:start position:0% +to each other so for the most part your + + + align:start position:0% +to each other so for the most part your +linear arrangement of amino acids that + + align:start position:0% +linear arrangement of amino acids that + + + align:start position:0% +linear arrangement of amino acids that +dictates this sequence is solely held by + + align:start position:0% +dictates this sequence is solely held by + + + align:start position:0% +dictates this sequence is solely held by +it together by the Coulomb covalent + + align:start position:0% +it together by the Coulomb covalent + + + align:start position:0% +it together by the Coulomb covalent +bonds in the peptide backbone that we'll + + align:start position:0% +bonds in the peptide backbone that we'll + + + align:start position:0% +bonds in the peptide backbone that we'll +talk about in a minute but occasionally + + align:start position:0% +talk about in a minute but occasionally + + + align:start position:0% +talk about in a minute but occasionally +in folded structures if two cysteines + + align:start position:0% +in folded structures if two cysteines + + + align:start position:0% +in folded structures if two cysteines +are close to each other and the + + align:start position:0% +are close to each other and the + + + align:start position:0% +are close to each other and the +environment is oxidizing they will form + + align:start position:0% +environment is oxidizing they will form + + + align:start position:0% +environment is oxidizing they will form +a cross-linked but they're not what + + align:start position:0% +a cross-linked but they're not what + + + align:start position:0% +a cross-linked but they're not what +drives folding they kind of fall into + + align:start position:0% +drives folding they kind of fall into + + + align:start position:0% +drives folding they kind of fall into +place later on but that just sort of + + align:start position:0% +place later on but that just sort of + + + align:start position:0% +place later on but that just sort of +sets cysteine apart a little bit for its + + align:start position:0% +sets cysteine apart a little bit for its + + + align:start position:0% +sets cysteine apart a little bit for its +properties + + align:start position:0% +properties + + + align:start position:0% +properties +all right okay so coming down the side + + align:start position:0% +all right okay so coming down the side + + + align:start position:0% +all right okay so coming down the side +here amino acids are assembled in a + + align:start position:0% +here amino acids are assembled in a + + + align:start position:0% +here amino acids are assembled in a +unique linear polymer of defined order + + align:start position:0% +unique linear polymer of defined order + + + align:start position:0% +unique linear polymer of defined order +and we designate that defined sequence + + align:start position:0% +and we designate that defined sequence + + + align:start position:0% +and we designate that defined sequence +the primary sequence + + align:start position:0% + + + + align:start position:0% + +and proteins can be a thousand amino + + align:start position:0% +and proteins can be a thousand amino + + + align:start position:0% +and proteins can be a thousand amino +acids fifteen hundred a hundred amino + + align:start position:0% +acids fifteen hundred a hundred amino + + + align:start position:0% +acids fifteen hundred a hundred amino +acids they can be various lengths where + + align:start position:0% +acids they can be various lengths where + + + align:start position:0% +acids they can be various lengths where +they you know we would generally + + align:start position:0% +they you know we would generally + + + align:start position:0% +they you know we would generally +consider the smallest protein to be back + + align:start position:0% +consider the smallest protein to be back + + + align:start position:0% +consider the smallest protein to be back +about four hundred amino acids and you + + align:start position:0% +about four hundred amino acids and you + + + align:start position:0% +about four hundred amino acids and you +might go up to thousands of amino acids + + align:start position:0% +might go up to thousands of amino acids + + + align:start position:0% +might go up to thousands of amino acids +I'm gonna write two thousand or more + + align:start position:0% +I'm gonna write two thousand or more + + + align:start position:0% +I'm gonna write two thousand or more +here when the proteins are smaller they + + align:start position:0% +here when the proteins are smaller they + + + align:start position:0% +here when the proteins are smaller they +are not capable of adopting too much + + align:start position:0% +are not capable of adopting too much + + + align:start position:0% +are not capable of adopting too much +ordered structure and we mostly call + + align:start position:0% +ordered structure and we mostly call + + + align:start position:0% +ordered structure and we mostly call +them peptides peptides are sort of + + align:start position:0% +them peptides peptides are sort of + + + align:start position:0% +them peptides peptides are sort of +shorter sequences so peptide sequences + + align:start position:0% +shorter sequences so peptide sequences + + + align:start position:0% +shorter sequences so peptide sequences +so this would be a protein and peptides + + align:start position:0% + + + + align:start position:0% + +probably two to thirty nine amino acids + + align:start position:0% +probably two to thirty nine amino acids + + + align:start position:0% +probably two to thirty nine amino acids +for these breakpoints are a little a + + align:start position:0% +for these breakpoints are a little a + + + align:start position:0% +for these breakpoints are a little a +little bit more vague so the primary + + align:start position:0% +little bit more vague so the primary + + + align:start position:0% +little bit more vague so the primary +sequence will define the structure of a + + align:start position:0% +sequence will define the structure of a + + + align:start position:0% +sequence will define the structure of a +protein and we're gonna start to talk + + align:start position:0% +protein and we're gonna start to talk + + + align:start position:0% +protein and we're gonna start to talk +about the hierarchical structure of + + align:start position:0% +about the hierarchical structure of + + + align:start position:0% +about the hierarchical structure of +proteins that's put in place so and + + align:start position:0% +proteins that's put in place so and + + + align:start position:0% +proteins that's put in place so and +that's the primary sequence and that + + align:start position:0% +that's the primary sequence and that + + + align:start position:0% +that's the primary sequence and that +primary sequence is kind of a cool thing + + align:start position:0% +primary sequence is kind of a cool thing + + + align:start position:0% +primary sequence is kind of a cool thing +because it's very specific it defines + + align:start position:0% +because it's very specific it defines + + + align:start position:0% +because it's very specific it defines +it's got encoded into its structure the + + align:start position:0% +it's got encoded into its structure the + + + align:start position:0% +it's got encoded into its structure the +three-dimensional fold of the protein + + align:start position:0% +three-dimensional fold of the protein + + + align:start position:0% +three-dimensional fold of the protein +okay all the information for the folded + + align:start position:0% +okay all the information for the folded + + + align:start position:0% +okay all the information for the folded +compact globular structure that's + + align:start position:0% +compact globular structure that's + + + align:start position:0% +compact globular structure that's +functional is encoded in that primary + + align:start position:0% +functional is encoded in that primary + + + align:start position:0% +functional is encoded in that primary +sequence it's a cryptic code we may may + + align:start position:0% +sequence it's a cryptic code we may may + + + align:start position:0% +sequence it's a cryptic code we may may +not be able to tell by looking at it + + align:start position:0% +not be able to tell by looking at it + + + align:start position:0% +not be able to tell by looking at it +what it really looks like but all the + + align:start position:0% +what it really looks like but all the + + + align:start position:0% +what it really looks like but all the +information is there in order to program + + align:start position:0% +information is there in order to program + + + align:start position:0% +information is there in order to program +the folding into a globular structure so + + align:start position:0% +the folding into a globular structure so + + + align:start position:0% +the folding into a globular structure so +the primary sequence determines the fold + + align:start position:0% +the primary sequence determines the fold + + + align:start position:0% +the primary sequence determines the fold +and it's the fold of the protein that + + align:start position:0% +and it's the fold of the protein that + + + align:start position:0% +and it's the fold of the protein that +mandates its function it's not the + + align:start position:0% +mandates its function it's not the + + + align:start position:0% +mandates its function it's not the +sequence of the protein the sequence + + align:start position:0% +sequence of the protein the sequence + + + align:start position:0% +sequence of the protein the sequence +defines the fold the fold the + + align:start position:0% +defines the fold the fold the + + + align:start position:0% +defines the fold the fold the +three-dimensional form defines the + + align:start position:0% +three-dimensional form defines the + + + align:start position:0% +three-dimensional form defines the +function okay so that's very important + + align:start position:0% +function okay so that's very important + + + align:start position:0% +function okay so that's very important +and I think it's absolutely amazing that + + align:start position:0% +and I think it's absolutely amazing that + + + align:start position:0% +and I think it's absolutely amazing that +with a relatively limited set of + + align:start position:0% +with a relatively limited set of + + + align:start position:0% +with a relatively limited set of +building blocks we can define so many + + align:start position:0% +building blocks we can define so many + + + align:start position:0% +building blocks we can define so many +different functions of all the proteins + + align:start position:0% +different functions of all the proteins + + + align:start position:0% +different functions of all the proteins +in our body that may be structural they + + align:start position:0% +in our body that may be structural they + + + align:start position:0% +in our body that may be structural they +may be catalysts they may be things that + + align:start position:0% +may be catalysts they may be things that + + + align:start position:0% +may be catalysts they may be things that +transfer information from the outside to + + align:start position:0% +transfer information from the outside to + + + align:start position:0% +transfer information from the outside to +the inside of the cell all of that is + + align:start position:0% +the inside of the cell all of that is + + + align:start position:0% +the inside of the cell all of that is +programmed with this rather limited set + + align:start position:0% +programmed with this rather limited set + + + align:start position:0% +programmed with this rather limited set +of building blocks + + align:start position:0% +of building blocks + + + align:start position:0% +of building blocks +okay now let's now talk about peptides + + align:start position:0% +okay now let's now talk about peptides + + + align:start position:0% +okay now let's now talk about peptides +because one gets a little frustrated + + align:start position:0% +because one gets a little frustrated + + + align:start position:0% +because one gets a little frustrated +looking at single amino acids they don't + + align:start position:0% +looking at single amino acids they don't + + + align:start position:0% +looking at single amino acids they don't +tell us so much about the peptide ik + + align:start position:0% +tell us so much about the peptide ik + + + align:start position:0% +tell us so much about the peptide ik +structure so I'm going to draw two amino + + align:start position:0% +structure so I'm going to draw two amino + + + align:start position:0% +structure so I'm going to draw two amino +acids and then I'm going to tell you one + + align:start position:0% +acids and then I'm going to tell you one + + + align:start position:0% +acids and then I'm going to tell you one +important thing so let's put our 1 and + + align:start position:0% +important thing so let's put our 1 and + + + align:start position:0% +important thing so let's put our 1 and +I'm going to draw another amino acid and + + align:start position:0% +I'm going to draw another amino acid and + + + align:start position:0% +I'm going to draw another amino acid and +I'm putting it in a particular + + align:start position:0% +I'm putting it in a particular + + + align:start position:0% +I'm putting it in a particular +orientation or two because that + + align:start position:0% +orientation or two because that + + + align:start position:0% +orientation or two because that +designates that these might be different + + align:start position:0% +designates that these might be different + + + align:start position:0% +designates that these might be different +amino acids for example if our one is H + + align:start position:0% +amino acids for example if our one is H + + + align:start position:0% +amino acids for example if our one is H +there's an implied hydrogen here that + + align:start position:0% +there's an implied hydrogen here that + + + align:start position:0% +there's an implied hydrogen here that +would be glycine if our two is a methyl + + align:start position:0% +would be glycine if our two is a methyl + + + align:start position:0% +would be glycine if our two is a methyl +group there's an implied hydrogen there + + align:start position:0% +group there's an implied hydrogen there + + + align:start position:0% +group there's an implied hydrogen there +that would be alanine all right when + + align:start position:0% +that would be alanine all right when + + + align:start position:0% +that would be alanine all right when +nature bonds all these amino acids + + align:start position:0% +nature bonds all these amino acids + + + align:start position:0% +nature bonds all these amino acids +together it carries out a condensation + + align:start position:0% +together it carries out a condensation + + + align:start position:0% +together it carries out a condensation +reaction to form a peptide bond between + + align:start position:0% +reaction to form a peptide bond between + + + align:start position:0% +reaction to form a peptide bond between +these two components of the amino acid + + align:start position:0% +these two components of the amino acid + + + align:start position:0% +these two components of the amino acid +the amine and the carboxylic acid now + + align:start position:0% +the amine and the carboxylic acid now + + + align:start position:0% +the amine and the carboxylic acid now +I'm going to draw you the first of the + + align:start position:0% +I'm going to draw you the first of the + + + align:start position:0% +I'm going to draw you the first of the +dipeptides that you'll meet there are so + + align:start position:0% +dipeptides that you'll meet there are so + + + align:start position:0% +dipeptides that you'll meet there are so +many things to tell you about these + + align:start position:0% +many things to tell you about these + + + align:start position:0% +many things to tell you about these +structures it sort of drives me crazy + + align:start position:0% +structures it sort of drives me crazy + + + align:start position:0% +structures it sort of drives me crazy +thinking about oh I must remember to + + align:start position:0% +thinking about oh I must remember to + + + align:start position:0% +thinking about oh I must remember to +tell them that oh I got to remember to + + align:start position:0% +tell them that oh I got to remember to + + + align:start position:0% +tell them that oh I got to remember to +tell them that because the structures + + align:start position:0% +tell them that because the structures + + + align:start position:0% +tell them that because the structures +are cool r1 okay so this is a dipeptide + + align:start position:0% +are cool r1 okay so this is a dipeptide + + + align:start position:0% +are cool r1 okay so this is a dipeptide +two amino acids and there are some + + align:start position:0% +two amino acids and there are some + + + align:start position:0% +two amino acids and there are some +characteristics I want you to remember + + align:start position:0% +characteristics I want you to remember + + + align:start position:0% +characteristics I want you to remember +when we write out peptides we always + + align:start position:0% +when we write out peptides we always + + + align:start position:0% +when we write out peptides we always +write them in 2c so in that peptide this + + align:start position:0% +write them in 2c so in that peptide this + + + align:start position:0% +write them in 2c so in that peptide this +would be the carboxyl term + + align:start position:0% + + + + align:start position:0% + +and this would be the amino terminus if + + align:start position:0% +and this would be the amino terminus if + + + align:start position:0% +and this would be the amino terminus if +you don't always remember to write + + align:start position:0% +you don't always remember to write + + + align:start position:0% +you don't always remember to write +things in this order and you tell your + + align:start position:0% +things in this order and you tell your + + + align:start position:0% +things in this order and you tell your +friend oh go and get this peptide made + + align:start position:0% +friend oh go and get this peptide made + + + align:start position:0% +friend oh go and get this peptide made +and you put it down in the wrong order + + align:start position:0% +and you put it down in the wrong order + + + align:start position:0% +and you put it down in the wrong order +they'll make the wrong peptide so you + + align:start position:0% +they'll make the wrong peptide so you + + + align:start position:0% +they'll make the wrong peptide so you +always there's basically an agreement + + align:start position:0% +always there's basically an agreement + + + align:start position:0% +always there's basically an agreement +amongst everyone that we always write + + align:start position:0% +amongst everyone that we always write + + + align:start position:0% +amongst everyone that we always write +from left to right the sequence of + + align:start position:0% +from left to right the sequence of + + + align:start position:0% +from left to right the sequence of +peptides the next important thing about + + align:start position:0% +peptides the next important thing about + + + align:start position:0% +peptides the next important thing about +this structure as you look at it there + + align:start position:0% +this structure as you look at it there + + + align:start position:0% +this structure as you look at it there +are several bonds joining the polymeric + + align:start position:0% +are several bonds joining the polymeric + + + align:start position:0% +are several bonds joining the polymeric +structure many of these bonds show free + + align:start position:0% +structure many of these bonds show free + + + align:start position:0% +structure many of these bonds show free +rotations you can twist them around + + align:start position:0% +rotations you can twist them around + + + align:start position:0% +rotations you can twist them around +there's nothing stopping that conversion + + align:start position:0% +there's nothing stopping that conversion + + + align:start position:0% +there's nothing stopping that conversion +all of these show freedom of rotation so + + align:start position:0% +all of these show freedom of rotation so + + + align:start position:0% +all of these show freedom of rotation so +the image or peptide bond is unique in + + align:start position:0% +the image or peptide bond is unique in + + + align:start position:0% +the image or peptide bond is unique in +that there's restricted rotation about + + align:start position:0% +that there's restricted rotation about + + + align:start position:0% +that there's restricted rotation about +that bond so it's as if you've got a + + align:start position:0% +that bond so it's as if you've got a + + + align:start position:0% +that bond so it's as if you've got a +linear polymer but every third bond has + + align:start position:0% +linear polymer but every third bond has + + + align:start position:0% +linear polymer but every third bond has +kind of stuck in a particular + + align:start position:0% +kind of stuck in a particular + + + align:start position:0% +kind of stuck in a particular +orientation which starts to define a lot + + align:start position:0% +orientation which starts to define a lot + + + align:start position:0% +orientation which starts to define a lot +of details about protein tertiary + + align:start position:0% +of details about protein tertiary + + + align:start position:0% +of details about protein tertiary +structure it's not complete spaghetti + + align:start position:0% +structure it's not complete spaghetti + + + align:start position:0% +structure it's not complete spaghetti +it's like spaghetti with little bits + + align:start position:0% +it's like spaghetti with little bits + + + align:start position:0% +it's like spaghetti with little bits +that haven't been cooked they're stiffer + + align:start position:0% +that haven't been cooked they're stiffer + + + align:start position:0% +that haven't been cooked they're stiffer +than the rest of the sequence and the + + align:start position:0% +than the rest of the sequence and the + + + align:start position:0% +than the rest of the sequence and the +other really important thing about the + + align:start position:0% +other really important thing about the + + + align:start position:0% +other really important thing about the +peptide structure is that embedded + + align:start position:0% +peptide structure is that embedded + + + align:start position:0% +peptide structure is that embedded +within that structure there is the + + align:start position:0% +within that structure there is the + + + align:start position:0% +within that structure there is the +amador peptide functional group where + + align:start position:0% +amador peptide functional group where + + + align:start position:0% +amador peptide functional group where +remember this can be a hydrogen bond + + align:start position:0% +remember this can be a hydrogen bond + + + align:start position:0% +remember this can be a hydrogen bond +acceptor and this can be a hydrogen bond + + align:start position:0% +acceptor and this can be a hydrogen bond + + + align:start position:0% +acceptor and this can be a hydrogen bond +donor once you know that the next few + + align:start position:0% +donor once you know that the next few + + + align:start position:0% +donor once you know that the next few +slides will make a lot of sense as we + + align:start position:0% +slides will make a lot of sense as we + + + align:start position:0% +slides will make a lot of sense as we +talk about higher order structure of + + align:start position:0% +talk about higher order structure of + + + align:start position:0% +talk about higher order structure of +proteins so let's just take a look at + + align:start position:0% +proteins so let's just take a look at + + + align:start position:0% +proteins so let's just take a look at +that with a slightly longer peptide by + + align:start position:0% +that with a slightly longer peptide by + + + align:start position:0% +that with a slightly longer peptide by +convention if I'm going to draw a + + align:start position:0% +convention if I'm going to draw a + + + align:start position:0% +convention if I'm going to draw a +peptide that's methionine isoleucine + + align:start position:0% +peptide that's methionine isoleucine + + + align:start position:0% +peptide that's methionine isoleucine +threonine you can look up that names on + + align:start position:0% +threonine you can look up that names on + + + align:start position:0% +threonine you can look up that names on +those names on the chart that would be + + align:start position:0% +those names on the chart that would be + + + align:start position:0% +those names on the chart that would be +the MIT peptide these are the three + + align:start position:0% +the MIT peptide these are the three + + + align:start position:0% +the MIT peptide these are the three +amino acid + + align:start position:0% +amino acid + + + align:start position:0% +amino acid +I'm going to condense them into a + + align:start position:0% +I'm going to condense them into a + + + align:start position:0% +I'm going to condense them into a +tripeptide when I condense three amino + + align:start position:0% +tripeptide when I condense three amino + + + align:start position:0% +tripeptide when I condense three amino +acids I spit out two molecules of water + + align:start position:0% +acids I spit out two molecules of water + + + align:start position:0% +acids I spit out two molecules of water +and I put in place two Amador peptide + + align:start position:0% +and I put in place two Amador peptide + + + align:start position:0% +and I put in place two Amador peptide +bonds if I go down this backbone every + + align:start position:0% +bonds if I go down this backbone every + + + align:start position:0% +bonds if I go down this backbone every +third bond is going to be fixed fairly + + align:start position:0% +third bond is going to be fixed fairly + + + align:start position:0% +third bond is going to be fixed fairly +fixed there's not freedom of rotation + + align:start position:0% +fixed there's not freedom of rotation + + + align:start position:0% +fixed there's not freedom of rotation +around it and every third bond is going + + align:start position:0% +around it and every third bond is going + + + align:start position:0% +around it and every third bond is going +to have the capacity to be involved in + + align:start position:0% +to have the capacity to be involved in + + + align:start position:0% +to have the capacity to be involved in +hydrogen bonding interactions as I've + + align:start position:0% +hydrogen bonding interactions as I've + + + align:start position:0% +hydrogen bonding interactions as I've +suggested here all right what else is + + align:start position:0% +suggested here all right what else is + + + align:start position:0% +suggested here all right what else is +there here when when I write the MIT + + align:start position:0% +there here when when I write the MIT + + + align:start position:0% +there here when when I write the MIT +peptide I write n first I second T third + + align:start position:0% +peptide I write n first I second T third + + + align:start position:0% +peptide I write n first I second T third +if I wrote gim it would be a completely + + align:start position:0% +if I wrote gim it would be a completely + + + align:start position:0% +if I wrote gim it would be a completely +different chemical structure with + + align:start position:0% +different chemical structure with + + + align:start position:0% +different chemical structure with +different chemical properties so the + + align:start position:0% +different chemical properties so the + + + align:start position:0% +different chemical properties so the +directionality is important to + + align:start position:0% +directionality is important to + + + align:start position:0% +directionality is important to +understand and there you have it so now + + align:start position:0% +understand and there you have it so now + + + align:start position:0% +understand and there you have it so now +you can go home and practice your name + + align:start position:0% +you can go home and practice your name + + + align:start position:0% +you can go home and practice your name +in amino acids and draw them out if you + + align:start position:0% +in amino acids and draw them out if you + + + align:start position:0% +in amino acids and draw them out if you +draw them out fairly sort of sharply + + align:start position:0% +draw them out fairly sort of sharply + + + align:start position:0% +draw them out fairly sort of sharply +then you'll never get confused about + + align:start position:0% +then you'll never get confused about + + + align:start position:0% +then you'll never get confused about +what ends what and what where the + + align:start position:0% +what ends what and what where the + + + align:start position:0% +what ends what and what where the +substituents are but it's important to + + align:start position:0% +substituents are but it's important to + + + align:start position:0% +substituents are but it's important to +remember as you're making a dipeptide i + + align:start position:0% +remember as you're making a dipeptide i + + + align:start position:0% +remember as you're making a dipeptide i +forget this doesn't work as you're + + align:start position:0% +forget this doesn't work as you're + + + align:start position:0% +forget this doesn't work as you're +condensing a dipeptide + + align:start position:0% +condensing a dipeptide + + + align:start position:0% +condensing a dipeptide +when you're putting these R groups on + + align:start position:0% +when you're putting these R groups on + + + align:start position:0% +when you're putting these R groups on +one goes up one goes down but these are + + align:start position:0% +one goes up one goes down but these are + + + align:start position:0% +one goes up one goes down but these are +nuances of the structure that may may be + + align:start position:0% +nuances of the structure that may may be + + + align:start position:0% +nuances of the structure that may may be +lit for a good for a later discussion so + + align:start position:0% +lit for a good for a later discussion so + + + align:start position:0% +lit for a good for a later discussion so +here is now a longer linear peptide and + + align:start position:0% +here is now a longer linear peptide and + + + align:start position:0% +here is now a longer linear peptide and +the suggestion of a globular structure + + align:start position:0% +the suggestion of a globular structure + + + align:start position:0% +the suggestion of a globular structure +that might be found if that peptide was + + align:start position:0% +that might be found if that peptide was + + + align:start position:0% +that might be found if that peptide was +folded up so and the primary sequence + + align:start position:0% +folded up so and the primary sequence + + + align:start position:0% +folded up so and the primary sequence +here defines the globular structure and + + align:start position:0% +here defines the globular structure and + + + align:start position:0% +here defines the globular structure and +the process whereby you go from the + + align:start position:0% +the process whereby you go from the + + + align:start position:0% +the process whereby you go from the +extended primary sequence to the folded + + align:start position:0% +extended primary sequence to the folded + + + align:start position:0% +extended primary sequence to the folded +structure is called protein folding + + align:start position:0% + + + + align:start position:0% + +and physical chemists and physicists and + + align:start position:0% +and physical chemists and physicists and + + + align:start position:0% +and physical chemists and physicists and +computational chemists have for years + + align:start position:0% +computational chemists have for years + + + align:start position:0% +computational chemists have for years +try to understand how we could predict + + align:start position:0% +try to understand how we could predict + + + align:start position:0% +try to understand how we could predict +the folded structure from the primary + + align:start position:0% +the folded structure from the primary + + + align:start position:0% +the folded structure from the primary +sequence it's not simple because what + + align:start position:0% +sequence it's not simple because what + + + align:start position:0% +sequence it's not simple because what +you're doing is you're solving a massive + + align:start position:0% +you're doing is you're solving a massive + + + align:start position:0% +you're doing is you're solving a massive +energy diagram where as you fold a + + align:start position:0% +energy diagram where as you fold a + + + align:start position:0% +energy diagram where as you fold a +structure up you're trying to maximize + + align:start position:0% +structure up you're trying to maximize + + + align:start position:0% +structure up you're trying to maximize +all those covet non-covalent forces for + + align:start position:0% +all those covet non-covalent forces for + + + align:start position:0% +all those covet non-covalent forces for +maximum maximum thermodynamic stability + + align:start position:0% +maximum maximum thermodynamic stability + + + align:start position:0% +maximum maximum thermodynamic stability +right it's kind of a three dimensional + + align:start position:0% +right it's kind of a three dimensional + + + align:start position:0% +right it's kind of a three dimensional +puzzle where you're trying to have as + + align:start position:0% +puzzle where you're trying to have as + + + align:start position:0% +puzzle where you're trying to have as +many hydrogen bonds electrostatic + + align:start position:0% +many hydrogen bonds electrostatic + + + align:start position:0% +many hydrogen bonds electrostatic +interactions and so on as you can + + align:start position:0% +interactions and so on as you can + + + align:start position:0% +interactions and so on as you can +possibly make + + align:start position:0% +possibly make + + + align:start position:0% +possibly make +so when computational chemists try to + + align:start position:0% +so when computational chemists try to + + + align:start position:0% +so when computational chemists try to +fold proteins they're basically solving + + align:start position:0% +fold proteins they're basically solving + + + align:start position:0% +fold proteins they're basically solving +a three-dimensional puzzle where they + + align:start position:0% +a three-dimensional puzzle where they + + + align:start position:0% +a three-dimensional puzzle where they +are maximizing interactions and there + + align:start position:0% +are maximizing interactions and there + + + align:start position:0% +are maximizing interactions and there +are a lot of initio immaculate I nameks + + align:start position:0% +are a lot of initio immaculate I nameks + + + align:start position:0% +are a lot of initio immaculate I nameks +programs that are now starting to be + + align:start position:0% +programs that are now starting to be + + + align:start position:0% +programs that are now starting to be +able to fold proteins into fairly + + align:start position:0% +able to fold proteins into fairly + + + align:start position:0% +able to fold proteins into fairly +reliable structures but they don't + + align:start position:0% +reliable structures but they don't + + + align:start position:0% +reliable structures but they don't +always get them right because they they + + align:start position:0% +always get them right because they they + + + align:start position:0% +always get them right because they they +haven't gotten all the clues yet and + + align:start position:0% +haven't gotten all the clues yet and + + + align:start position:0% +haven't gotten all the clues yet and +also while they may be able to do ab + + align:start position:0% +also while they may be able to do ab + + + align:start position:0% +also while they may be able to do ab +initio or computational folding with + + align:start position:0% +initio or computational folding with + + + align:start position:0% +initio or computational folding with +small structures the headache gets way + + align:start position:0% +small structures the headache gets way + + + align:start position:0% +small structures the headache gets way +bigger the larger the structures gets so + + align:start position:0% +bigger the larger the structures gets so + + + align:start position:0% +bigger the larger the structures gets so +the the predictors aren't very good at + + align:start position:0% +the the predictors aren't very good at + + + align:start position:0% +the the predictors aren't very good at +predicting big structures they're + + align:start position:0% +predicting big structures they're + + + align:start position:0% +predicting big structures they're +getting better or predicting small + + align:start position:0% +getting better or predicting small + + + align:start position:0% +getting better or predicting small +structures and so just to reinforce to + + align:start position:0% +structures and so just to reinforce to + + + align:start position:0% +structures and so just to reinforce to +you the primary sequence is established + + align:start position:0% +you the primary sequence is established + + + align:start position:0% +you the primary sequence is established +by covalent bonds the peptide bonds but + + align:start position:0% +by covalent bonds the peptide bonds but + + + align:start position:0% +by covalent bonds the peptide bonds but +the globular tertiary structure is based + + align:start position:0% +the globular tertiary structure is based + + + align:start position:0% +the globular tertiary structure is based +on non covalent covalent interactions + + align:start position:0% +on non covalent covalent interactions + + + align:start position:0% +on non covalent covalent interactions +okay now I want to ask you this I love + + align:start position:0% +okay now I want to ask you this I love + + + align:start position:0% +okay now I want to ask you this I love +cartoons with science in them but you + + align:start position:0% +cartoons with science in them but you + + + align:start position:0% +cartoons with science in them but you +know 1020 percent of the time they get + + align:start position:0% +know 1020 percent of the time they get + + + align:start position:0% +know 1020 percent of the time they get +they make mistakes and I thought this + + align:start position:0% +they make mistakes and I thought this + + + align:start position:0% +they make mistakes and I thought this +one was particularly pertinent it's a + + align:start position:0% +one was particularly pertinent it's a + + + align:start position:0% +one was particularly pertinent it's a +bunch of guys lugging around in a lab + + align:start position:0% +bunch of guys lugging around in a lab + + + align:start position:0% +bunch of guys lugging around in a lab +and says well we finished the genome app + + align:start position:0% +and says well we finished the genome app + + + align:start position:0% +and says well we finished the genome app +now we've just have to figure out how to + + align:start position:0% +now we've just have to figure out how to + + + align:start position:0% +now we've just have to figure out how to +fold it what is wrong with that cartoon + + align:start position:0% + + + + align:start position:0% + +what fault yeah + + align:start position:0% +what fault yeah + + + align:start position:0% +what fault yeah +yeah yeah the genome doesn't fold his + + align:start position:0% +yeah yeah the genome doesn't fold his + + + align:start position:0% +yeah yeah the genome doesn't fold his +double helical duplex DNA or something + + align:start position:0% +double helical duplex DNA or something + + + align:start position:0% +double helical duplex DNA or something +you're actually folding proteins so the + + align:start position:0% +you're actually folding proteins so the + + + align:start position:0% +you're actually folding proteins so the +cartoon is not quite right but it's sort + + align:start position:0% +cartoon is not quite right but it's sort + + + align:start position:0% +cartoon is not quite right but it's sort +of kind of cute all right now when we + + align:start position:0% +of kind of cute all right now when we + + + align:start position:0% +of kind of cute all right now when we +talk about the non covalent forces that + + align:start position:0% +talk about the non covalent forces that + + + align:start position:0% +talk about the non covalent forces that +hold proteins together I just want you + + align:start position:0% +hold proteins together I just want you + + + align:start position:0% +hold proteins together I just want you +to remember from last time this set of + + align:start position:0% +to remember from last time this set of + + + align:start position:0% +to remember from last time this set of +non covalent forces because if you + + align:start position:0% +non covalent forces because if you + + + align:start position:0% +non covalent forces because if you +understand them and recognize them + + align:start position:0% +understand them and recognize them + + + align:start position:0% +understand them and recognize them +you'll understand how they may occur in + + align:start position:0% +you'll understand how they may occur in + + + align:start position:0% +you'll understand how they may occur in +folded protein structures all right so + + align:start position:0% +folded protein structures all right so + + + align:start position:0% +folded protein structures all right so +here's a peptide sequence here's a + + align:start position:0% +here's a peptide sequence here's a + + + align:start position:0% +here's a peptide sequence here's a +puzzle for you you can go back and + + align:start position:0% +puzzle for you you can go back and + + + align:start position:0% +puzzle for you you can go back and +figure out what the one letter code + + align:start position:0% +figure out what the one letter code + + + align:start position:0% +figure out what the one letter code +spells there just take out your um your + + align:start position:0% +spells there just take out your um your + + + align:start position:0% +spells there just take out your um your +table with all the amino acids it's a + + align:start position:0% +table with all the amino acids it's a + + + align:start position:0% +table with all the amino acids it's a +pendent to the back of your p-set and + + align:start position:0% +pendent to the back of your p-set and + + + align:start position:0% +pendent to the back of your p-set and +you'll be able to see what that very + + align:start position:0% +you'll be able to see what that very + + + align:start position:0% +you'll be able to see what that very +large peptide spells all right and then + + align:start position:0% +large peptide spells all right and then + + + align:start position:0% +large peptide spells all right and then +when you're working that out while + + align:start position:0% +when you're working that out while + + + align:start position:0% +when you're working that out while +you're here you got to listen to me for + + align:start position:0% +you're here you got to listen to me for + + + align:start position:0% +you're here you got to listen to me for +the time being okay so the first order + + align:start position:0% + + + + align:start position:0% + +we get it there's a primary sequence the + + align:start position:0% +we get it there's a primary sequence the + + + align:start position:0% +we get it there's a primary sequence the +next thing to think about is what's + + align:start position:0% +next thing to think about is what's + + + align:start position:0% +next thing to think about is what's +known as secondary structure it's higher + + align:start position:0% +known as secondary structure it's higher + + + align:start position:0% +known as secondary structure it's higher +order than just the primary sequence and + + align:start position:0% +order than just the primary sequence and + + + align:start position:0% +order than just the primary sequence and +it's established by non covalent bonds + + align:start position:0% +it's established by non covalent bonds + + + align:start position:0% +it's established by non covalent bonds +and it's called secondary my writings + + align:start position:0% +and it's called secondary my writings + + + align:start position:0% +and it's called secondary my writings +horrid today secondary structure and + + align:start position:0% +horrid today secondary structure and + + + align:start position:0% +horrid today secondary structure and +those are interactions that are put in + + align:start position:0% +those are interactions that are put in + + + align:start position:0% +those are interactions that are put in +place exclusively by interactions + + align:start position:0% +place exclusively by interactions + + + align:start position:0% +place exclusively by interactions +between the peptide bonds of what's + + align:start position:0% +between the peptide bonds of what's + + + align:start position:0% +between the peptide bonds of what's +known as the peptide backbone so if we + + align:start position:0% +known as the peptide backbone so if we + + + align:start position:0% +known as the peptide backbone so if we +look at this structure these are the + + align:start position:0% +look at this structure these are the + + + align:start position:0% +look at this structure these are the +side chains the peptide backbone is this + + align:start position:0% +side chains the peptide backbone is this + + + align:start position:0% +side chains the peptide backbone is this +continuous linear sequence that's what + + align:start position:0% +continuous linear sequence that's what + + + align:start position:0% +continuous linear sequence that's what +we would call the peptide backbone and + + align:start position:0% +we would call the peptide backbone and + + + align:start position:0% +we would call the peptide backbone and +the secondary structure is put in place + + align:start position:0% +the secondary structure is put in place + + + align:start position:0% +the secondary structure is put in place +by hydrogen bonding between components + + align:start position:0% +by hydrogen bonding between components + + + align:start position:0% +by hydrogen bonding between components +of the peptide backbone so for example + + align:start position:0% +of the peptide backbone so for example + + + align:start position:0% +of the peptide backbone so for example +hydrogen bonds such as that + + align:start position:0% + + + + align:start position:0% + +or a different hydrogen bonding + + align:start position:0% +or a different hydrogen bonding + + + align:start position:0% +or a different hydrogen bonding +interaction such as that between the + + align:start position:0% +interaction such as that between the + + + align:start position:0% +interaction such as that between the +atoms that have lone pairs of electrons + + align:start position:0% +atoms that have lone pairs of electrons + + + align:start position:0% +atoms that have lone pairs of electrons +and the other atoms had heavy atoms that + + align:start position:0% +and the other atoms had heavy atoms that + + + align:start position:0% +and the other atoms had heavy atoms that +hold a hydrogen that's quite acidic and + + align:start position:0% +hold a hydrogen that's quite acidic and + + + align:start position:0% +hold a hydrogen that's quite acidic and +there are a couple of major forms of + + align:start position:0% +there are a couple of major forms of + + + align:start position:0% +there are a couple of major forms of +secondary structure what I'm showing you + + align:start position:0% +secondary structure what I'm showing you + + + align:start position:0% +secondary structure what I'm showing you +here is what's known as the alpha helix + + align:start position:0% +here is what's known as the alpha helix + + + align:start position:0% +here is what's known as the alpha helix +first deduced by Pauling in fact through + + align:start position:0% +first deduced by Pauling in fact through + + + align:start position:0% +first deduced by Pauling in fact through +model building he said proteins could + + align:start position:0% +model building he said proteins could + + + align:start position:0% +model building he said proteins could +form these ordered structures and an + + align:start position:0% +form these ordered structures and an + + + align:start position:0% +form these ordered structures and an +alpha helix is an ordered structure + + align:start position:0% +alpha helix is an ordered structure + + + align:start position:0% +alpha helix is an ordered structure +exclusively made up from the hydrogen + + align:start position:0% +exclusively made up from the hydrogen + + + align:start position:0% +exclusively made up from the hydrogen +bonding interactions of the peptide + + align:start position:0% +bonding interactions of the peptide + + + align:start position:0% +bonding interactions of the peptide +backbone and you can look at this + + align:start position:0% +backbone and you can look at this + + + align:start position:0% +backbone and you can look at this +helical structure it's a continuous + + align:start position:0% +helical structure it's a continuous + + + align:start position:0% +helical structure it's a continuous +strand of peptide but there are hydrogen + + align:start position:0% +strand of peptide but there are hydrogen + + + align:start position:0% +strand of peptide but there are hydrogen +bonds between cos and NH s all the way + + align:start position:0% +bonds between cos and NH s all the way + + + align:start position:0% +bonds between cos and NH s all the way +through the backbone such that this + + align:start position:0% +through the backbone such that this + + + align:start position:0% +through the backbone such that this +strand of polypeptide can fold up into a + + align:start position:0% +strand of polypeptide can fold up into a + + + align:start position:0% +strand of polypeptide can fold up into a +cylindrical helical structure where all + + align:start position:0% +cylindrical helical structure where all + + + align:start position:0% +cylindrical helical structure where all +those are groups side chains of the + + align:start position:0% +those are groups side chains of the + + + align:start position:0% +those are groups side chains of the +amino acids on the perimeter of that + + align:start position:0% +amino acids on the perimeter of that + + + align:start position:0% +amino acids on the perimeter of that +helix so this secondary structure is an + + align:start position:0% +helix so this secondary structure is an + + + align:start position:0% +helix so this secondary structure is an +important one because it's very + + align:start position:0% +important one because it's very + + + align:start position:0% +important one because it's very +prevalent in a lot of proteins the next + + align:start position:0% +prevalent in a lot of proteins the next + + + align:start position:0% +prevalent in a lot of proteins the next +secondary structure is also held + + align:start position:0% +secondary structure is also held + + + align:start position:0% +secondary structure is also held +together by hydrogen bonding and it's + + align:start position:0% +together by hydrogen bonding and it's + + + align:start position:0% +together by hydrogen bonding and it's +interactions between stretched out + + align:start position:0% +interactions between stretched out + + + align:start position:0% +interactions between stretched out +strands of polypeptides that may not be + + align:start position:0% +strands of polypeptides that may not be + + + align:start position:0% +strands of polypeptides that may not be +close to each other in the primary + + align:start position:0% +close to each other in the primary + + + align:start position:0% +close to each other in the primary +sequence but they align in in the folded + + align:start position:0% +sequence but they align in in the folded + + + align:start position:0% +sequence but they align in in the folded +structure and so for example what I've + + align:start position:0% +structure and so for example what I've + + + align:start position:0% +structure and so for example what I've +shown you here is what's known as this + + align:start position:0% +shown you here is what's known as this + + + align:start position:0% +shown you here is what's known as this +sir this guy is enter C this is an anti + + align:start position:0% +sir this guy is enter C this is an anti + + + align:start position:0% +sir this guy is enter C this is an anti +parallel beta sheet and across that + + align:start position:0% +parallel beta sheet and across that + + + align:start position:0% +parallel beta sheet and across that +sheet there are continuous opportunities + + align:start position:0% +sheet there are continuous opportunities + + + align:start position:0% +sheet there are continuous opportunities +for hydrogen bonding interaction if the + + align:start position:0% +for hydrogen bonding interaction if the + + + align:start position:0% +for hydrogen bonding interaction if the +strands run in opposite directions its + + align:start position:0% +strands run in opposite directions its + + + align:start position:0% +strands run in opposite directions its +anti parallel if they're in the same + + align:start position:0% +anti parallel if they're in the same + + + align:start position:0% +anti parallel if they're in the same +direction is parallel these two + + align:start position:0% +direction is parallel these two + + + align:start position:0% +direction is parallel these two +secondary structure elements make up a + + align:start position:0% +secondary structure elements make up a + + + align:start position:0% +secondary structure elements make up a +lot of the sort of basics of how + + align:start position:0% +lot of the sort of basics of how + + + align:start position:0% +lot of the sort of basics of how +proteins start to fold their key non + + align:start position:0% +proteins start to fold their key non + + + align:start position:0% +proteins start to fold their key non +covalent forces and they're also other + + align:start position:0% +covalent forces and they're also other + + + align:start position:0% +covalent forces and they're also other +smaller motifs one is called a beta turn + + align:start position:0% +smaller motifs one is called a beta turn + + + align:start position:0% +smaller motifs one is called a beta turn +where the the peptide sequence may go + + align:start position:0% +where the the peptide sequence may go + + + align:start position:0% +where the the peptide sequence may go +through a chain reversal so the sequence + + align:start position:0% +through a chain reversal so the sequence + + + align:start position:0% +through a chain reversal so the sequence +would look like this I'm gonna just + + align:start position:0% +would look like this I'm gonna just + + + align:start position:0% +would look like this I'm gonna just +throw it and I'll talk to you in a + + align:start position:0% +throw it and I'll talk to you in a + + + align:start position:0% +throw it and I'll talk to you in a +moment about ribbon diagrams and this + + align:start position:0% +moment about ribbon diagrams and this + + + align:start position:0% +moment about ribbon diagrams and this +piece here would be the turn whereas + + align:start position:0% +piece here would be the turn whereas + + + align:start position:0% +piece here would be the turn whereas +that would be the interactions enforced + + align:start position:0% +that would be the interactions enforced + + + align:start position:0% +that would be the interactions enforced +by the sheep these are the ordered + + align:start position:0% +by the sheep these are the ordered + + + align:start position:0% +by the sheep these are the ordered +elements of secondary structure you + + align:start position:0% +elements of secondary structure you + + + align:start position:0% +elements of secondary structure you +don't have to be able to figure them out + + align:start position:0% +don't have to be able to figure them out + + + align:start position:0% +don't have to be able to figure them out +but you have to be able to pick them out + + align:start position:0% +but you have to be able to pick them out + + + align:start position:0% +but you have to be able to pick them out +in order to understand the structure + + align:start position:0% +in order to understand the structure + + + align:start position:0% +in order to understand the structure +okay so even those simple elements still + + align:start position:0% +okay so even those simple elements still + + + align:start position:0% +okay so even those simple elements still +it's hard to make big enough structures + + align:start position:0% +it's hard to make big enough structures + + + align:start position:0% +it's hard to make big enough structures +to have functions so as I mentioned in a + + align:start position:0% +to have functions so as I mentioned in a + + + align:start position:0% +to have functions so as I mentioned in a +continuation of the theme the protein + + align:start position:0% +continuation of the theme the protein + + + align:start position:0% +continuation of the theme the protein +folding is hierarchical you can start to + + align:start position:0% +folding is hierarchical you can start to + + + align:start position:0% +folding is hierarchical you can start to +put together elements of secondary + + align:start position:0% +put together elements of secondary + + + align:start position:0% +put together elements of secondary +structure to make things that are a + + align:start position:0% +structure to make things that are a + + + align:start position:0% +structure to make things that are a +little larger helix turn helix helix + + align:start position:0% +little larger helix turn helix helix + + + align:start position:0% +little larger helix turn helix helix +with a different kind of turn may be put + + align:start position:0% +with a different kind of turn may be put + + + align:start position:0% +with a different kind of turn may be put +in place by a metal iron or something or + + align:start position:0% +in place by a metal iron or something or + + + align:start position:0% +in place by a metal iron or something or +a strand turn strand or now something + + align:start position:0% +a strand turn strand or now something + + + align:start position:0% +a strand turn strand or now something +that's a composite of these two major + + align:start position:0% +that's a composite of these two major + + + align:start position:0% +that's a composite of these two major +types of cell secondary structure the + + align:start position:0% +types of cell secondary structure the + + + align:start position:0% +types of cell secondary structure the +helix and the turn and these really + + align:start position:0% +helix and the turn and these really + + + align:start position:0% +helix and the turn and these really +start to be proteins that might be big + + align:start position:0% +start to be proteins that might be big + + + align:start position:0% +start to be proteins that might be big +enough to be able to do something but + + align:start position:0% +enough to be able to do something but + + + align:start position:0% +enough to be able to do something but +they're all exclusively held together by + + align:start position:0% +they're all exclusively held together by + + + align:start position:0% +they're all exclusively held together by +non-covalent forces between the amides + + align:start position:0% +non-covalent forces between the amides + + + align:start position:0% +non-covalent forces between the amides +or peptide bonds in the backbone of the + + align:start position:0% +or peptide bonds in the backbone of the + + + align:start position:0% +or peptide bonds in the backbone of the +protein okay not very exciting just yet + + align:start position:0% +protein okay not very exciting just yet + + + align:start position:0% +protein okay not very exciting just yet +now one other little clue that people + + align:start position:0% +now one other little clue that people + + + align:start position:0% +now one other little clue that people +will you might see and you might be + + align:start position:0% +will you might see and you might be + + + align:start position:0% +will you might see and you might be +confused people sometimes when they're + + align:start position:0% +confused people sometimes when they're + + + align:start position:0% +confused people sometimes when they're +drawing sort of a quick picture of a + + align:start position:0% +drawing sort of a quick picture of a + + + align:start position:0% +drawing sort of a quick picture of a +protein they might draw a helix but + + align:start position:0% +protein they might draw a helix but + + + align:start position:0% +protein they might draw a helix but +instead of really showing it in detail + + align:start position:0% +instead of really showing it in detail + + + align:start position:0% +instead of really showing it in detail +they might show it as a cylinder so you + + align:start position:0% +they might show it as a cylinder so you + + + align:start position:0% +they might show it as a cylinder so you +might need to pick that out of a + + align:start position:0% +might need to pick that out of a + + + align:start position:0% +might need to pick that out of a +structure and then I want to call your + + align:start position:0% +structure and then I want to call your + + + align:start position:0% +structure and then I want to call your +attention to the fact that in all those + + align:start position:0% +attention to the fact that in all those + + + align:start position:0% +attention to the fact that in all those +motifs when you join one helix to + + align:start position:0% +motifs when you join one helix to + + + align:start position:0% +motifs when you join one helix to +another you might need a turn a strand + + align:start position:0% +another you might need a turn a strand + + + align:start position:0% +another you might need a turn a strand +to another strand you need a turn and so + + align:start position:0% +to another strand you need a turn and so + + + align:start position:0% +to another strand you need a turn and so +on okay so this is like taking your very + + align:start position:0% +on okay so this is like taking your very + + + align:start position:0% +on okay so this is like taking your very +extended sort of polymer knowing there + + align:start position:0% +extended sort of polymer knowing there + + + align:start position:0% +extended sort of polymer knowing there +are different kinks in it because of the + + align:start position:0% +are different kinks in it because of the + + + align:start position:0% +are different kinks in it because of the +back bow bonds but folding it up in a + + align:start position:0% +back bow bonds but folding it up in a + + + align:start position:0% +back bow bonds but folding it up in a +structure that + + align:start position:0% +structure that + + + align:start position:0% +structure that +maximizing the opportunity for another + + align:start position:0% +maximizing the opportunity for another + + + align:start position:0% +maximizing the opportunity for another +order of structure which we'll talk + + align:start position:0% +order of structure which we'll talk + + + align:start position:0% +order of structure which we'll talk +about now all right so we've seen + + align:start position:0% +about now all right so we've seen + + + align:start position:0% +about now all right so we've seen +primary/secondary is just with backbone + + align:start position:0% +primary/secondary is just with backbone + + + align:start position:0% +primary/secondary is just with backbone +and things start to get much more + + align:start position:0% +and things start to get much more + + + align:start position:0% +and things start to get much more +interesting when we get to tertiary + + align:start position:0% +interesting when we get to tertiary + + + align:start position:0% +interesting when we get to tertiary +structure because tertiary structure is + + align:start position:0% +structure because tertiary structure is + + + align:start position:0% +structure because tertiary structure is +enabled by all these other interactions + + align:start position:0% +enabled by all these other interactions + + + align:start position:0% +enabled by all these other interactions +electrostatic hydrogen bonding + + align:start position:0% +electrostatic hydrogen bonding + + + align:start position:0% +electrostatic hydrogen bonding +hydrophobic forces that can be put in + + align:start position:0% +hydrophobic forces that can be put in + + + align:start position:0% +hydrophobic forces that can be put in +place due to the side chains of the + + align:start position:0% +place due to the side chains of the + + + align:start position:0% +place due to the side chains of the +amino acids interacting with each other + + align:start position:0% +amino acids interacting with each other + + + align:start position:0% +amino acids interacting with each other +or with the backbone structure so I'm + + align:start position:0% +or with the backbone structure so I'm + + + align:start position:0% +or with the backbone structure so I'm +going to walk you through this so you + + align:start position:0% +going to walk you through this so you + + + align:start position:0% +going to walk you through this so you +can sort of get a sense of how these + + align:start position:0% +can sort of get a sense of how these + + + align:start position:0% +can sort of get a sense of how these +three dimensional puzzles work on a very + + align:start position:0% +three dimensional puzzles work on a very + + + align:start position:0% +three dimensional puzzles work on a very +small scale so look here that's a very + + align:start position:0% +small scale so look here that's a very + + + align:start position:0% +small scale so look here that's a very +small motif and what I'm going to call + + align:start position:0% +small motif and what I'm going to call + + + align:start position:0% +small motif and what I'm going to call +your attention to is when you fold up + + align:start position:0% +your attention to is when you fold up + + + align:start position:0% +your attention to is when you fold up +these motifs when the secondary + + align:start position:0% +these motifs when the secondary + + + align:start position:0% +these motifs when the secondary +structure is in place a lot of the side + + align:start position:0% +structure is in place a lot of the side + + + align:start position:0% +structure is in place a lot of the side +chains are near each other and they can + + align:start position:0% +chains are near each other and they can + + + align:start position:0% +chains are near each other and they can +engage in long distance contacts and so + + align:start position:0% +engage in long distance contacts and so + + + align:start position:0% +engage in long distance contacts and so +for example I'm going to show you + + align:start position:0% +for example I'm going to show you + + + align:start position:0% +for example I'm going to show you +interactions between side chains between + + align:start position:0% +interactions between side chains between + + + align:start position:0% +interactions between side chains between +side chains and the peptide backbone or + + align:start position:0% +side chains and the peptide backbone or + + + align:start position:0% +side chains and the peptide backbone or +side chains and water but what I want + + align:start position:0% +side chains and water but what I want + + + align:start position:0% +side chains and water but what I want +you do is take a look at this and see + + align:start position:0% +you do is take a look at this and see + + + align:start position:0% +you do is take a look at this and see +can you can you put any of those + + align:start position:0% +can you can you put any of those + + + align:start position:0% +can you can you put any of those +potential interactions on the drawing + + align:start position:0% +potential interactions on the drawing + + + align:start position:0% +potential interactions on the drawing +that's on your handout it's pretty + + align:start position:0% +that's on your handout it's pretty + + + align:start position:0% +that's on your handout it's pretty +obvious where there's a an electrostatic + + align:start position:0% +obvious where there's a an electrostatic + + + align:start position:0% +obvious where there's a an electrostatic +interaction right okay between plus get + + align:start position:0% +interaction right okay between plus get + + + align:start position:0% +interaction right okay between plus get +those out the way those are the easy + + align:start position:0% +those out the way those are the easy + + + align:start position:0% +those out the way those are the easy +ones and then interactions between + + align:start position:0% +ones and then interactions between + + + align:start position:0% +ones and then interactions between +hydrophobic groups where they want to + + align:start position:0% +hydrophobic groups where they want to + + + align:start position:0% +hydrophobic groups where they want to +amass that lipophilic structures so it's + + align:start position:0% +amass that lipophilic structures so it's + + + align:start position:0% +amass that lipophilic structures so it's +not exposed as much to water so they + + align:start position:0% +not exposed as much to water so they + + + align:start position:0% +not exposed as much to water so they +cluster so those are easy and then you + + align:start position:0% +cluster so those are easy and then you + + + align:start position:0% +cluster so those are easy and then you +can start thinking about what are all + + align:start position:0% +can start thinking about what are all + + + align:start position:0% +can start thinking about what are all +the hydrogen bonds you could draw here + + align:start position:0% +the hydrogen bonds you could draw here + + + align:start position:0% +the hydrogen bonds you could draw here +I've shown one between side chains + + align:start position:0% +I've shown one between side chains + + + align:start position:0% +I've shown one between side chains +between side chains and backbone between + + align:start position:0% +between side chains and backbone between + + + align:start position:0% +between side chains and backbone between +side chains and water and those may all + + align:start position:0% +side chains and water and those may all + + + align:start position:0% +side chains and water and those may all +contribute to the ultimate thermodynamic + + align:start position:0% +contribute to the ultimate thermodynamic + + + align:start position:0% +contribute to the ultimate thermodynamic +stability make sure you get your + + align:start position:0% +stability make sure you get your + + + align:start position:0% +stability make sure you get your +hydrogen bonds right remember two donors + + align:start position:0% +hydrogen bonds right remember two donors + + + align:start position:0% +hydrogen bonds right remember two donors +don't interact with a it's with each + + align:start position:0% +don't interact with a it's with each + + + align:start position:0% +don't interact with a it's with each +other and two acceptors don't so this + + align:start position:0% +other and two acceptors don't so this + + + align:start position:0% +other and two acceptors don't so this +might describe the folding possibilities + + align:start position:0% +might describe the folding possibilities + + + align:start position:0% +might describe the folding possibilities +of that small + + align:start position:0% +of that small + + + align:start position:0% +of that small +Lutie now what I want to show you is an + + align:start position:0% +Lutie now what I want to show you is an + + + align:start position:0% +Lutie now what I want to show you is an +ab initio simulation of a folding + + align:start position:0% +ab initio simulation of a folding + + + align:start position:0% +ab initio simulation of a folding +process so let me just get that a little + + align:start position:0% +process so let me just get that a little + + + align:start position:0% +process so let me just get that a little +bigger on the screen so this is + + align:start position:0% +bigger on the screen so this is + + + align:start position:0% +bigger on the screen so this is +computing gb1 is a very small protein + + align:start position:0% +computing gb1 is a very small protein + + + align:start position:0% +computing gb1 is a very small protein +that folds reversibly under appropriate + + align:start position:0% +that folds reversibly under appropriate + + + align:start position:0% +that folds reversibly under appropriate +conditions and what I'm going to do is + + align:start position:0% +conditions and what I'm going to do is + + + align:start position:0% +conditions and what I'm going to do is +forward you through this video this is a + + align:start position:0% +forward you through this video this is a + + + align:start position:0% +forward you through this video this is a +simulation this is all computation it's + + align:start position:0% +simulation this is all computation it's + + + align:start position:0% +simulation this is all computation it's +not looking at anything by spectroscopy + + align:start position:0% +not looking at anything by spectroscopy + + + align:start position:0% +not looking at anything by spectroscopy +or in solution or anything like that and + + align:start position:0% +or in solution or anything like that and + + + align:start position:0% +or in solution or anything like that and +what I'm gonna do is I'm gonna forward + + align:start position:0% +what I'm gonna do is I'm gonna forward + + + align:start position:0% +what I'm gonna do is I'm gonna forward +you through the structure this is multi + + align:start position:0% +you through the structure this is multi + + + align:start position:0% +you through the structure this is multi +scale modeling it's got its got a lot of + + align:start position:0% +scale modeling it's got its got a lot of + + + align:start position:0% +scale modeling it's got its got a lot of +details in how it's done but the + + align:start position:0% +details in how it's done but the + + + align:start position:0% +details in how it's done but the +starting point is a very denatured + + align:start position:0% +starting point is a very denatured + + + align:start position:0% +starting point is a very denatured +protein all stretched out right and what + + align:start position:0% +protein all stretched out right and what + + + align:start position:0% +protein all stretched out right and what +I'm gonna do is just show you for a few + + align:start position:0% +I'm gonna do is just show you for a few + + + align:start position:0% +I'm gonna do is just show you for a few +seconds you know this thing's like + + align:start position:0% +seconds you know this thing's like + + + align:start position:0% +seconds you know this thing's like +trying to find its thermodynamic minimum + + align:start position:0% +trying to find its thermodynamic minimum + + + align:start position:0% +trying to find its thermodynamic minimum +and it's actually failing pretty badly + + align:start position:0% +and it's actually failing pretty badly + + + align:start position:0% +and it's actually failing pretty badly +and it it does that for about 3060 + + align:start position:0% +and it it does that for about 3060 + + + align:start position:0% +and it it does that for about 3060 +seconds of the simulation so I made a + + align:start position:0% +seconds of the simulation so I made a + + + align:start position:0% +seconds of the simulation so I made a +point to myself to take you to about + + align:start position:0% +point to myself to take you to about + + + align:start position:0% +point to myself to take you to about +minute 1 where things start to get + + align:start position:0% +minute 1 where things start to get + + + align:start position:0% +minute 1 where things start to get +fairly interesting you're saying well + + align:start position:0% +fairly interesting you're saying well + + + align:start position:0% +fairly interesting you're saying well +what's interesting about that you see + + align:start position:0% +what's interesting about that you see + + + align:start position:0% +what's interesting about that you see +that nascent helix in the background and + + align:start position:0% +that nascent helix in the background and + + + align:start position:0% +that nascent helix in the background and +the red and the blue is starting to form + + align:start position:0% +the red and the blue is starting to form + + + align:start position:0% +the red and the blue is starting to form +strands that are a little bit aligned + + align:start position:0% +strands that are a little bit aligned + + + align:start position:0% +strands that are a little bit aligned +and it's trying to find as many + + align:start position:0% +and it's trying to find as many + + + align:start position:0% +and it's trying to find as many +connections as possible to satisfy a + + align:start position:0% +connections as possible to satisfy a + + + align:start position:0% +connections as possible to satisfy a +stable structure at a certain point in + + align:start position:0% +stable structure at a certain point in + + + align:start position:0% +stable structure at a certain point in +the simulation five of the hydrophobic + + align:start position:0% +the simulation five of the hydrophobic + + + align:start position:0% +the simulation five of the hydrophobic +groups are in a little team they're in a + + align:start position:0% +groups are in a little team they're in a + + + align:start position:0% +groups are in a little team they're in a +little hydrophobic cluster and that's a + + align:start position:0% +little hydrophobic cluster and that's a + + + align:start position:0% +little hydrophobic cluster and that's a +breakpoint in the folding process + + align:start position:0% +breakpoint in the folding process + + + align:start position:0% +breakpoint in the folding process +because that gets everything glued + + align:start position:0% +because that gets everything glued + + + align:start position:0% +because that gets everything glued +together better so that the rest of it + + align:start position:0% +together better so that the rest of it + + + align:start position:0% +together better so that the rest of it +now can start to really find its final + + align:start position:0% +now can start to really find its final + + + align:start position:0% +now can start to really find its final +place in the folded structure these + + align:start position:0% +place in the folded structure these + + + align:start position:0% +place in the folded structure these +early structures are known as molten + + align:start position:0% +early structures are known as molten + + + align:start position:0% +early structures are known as molten +globules a lot of the interactions are + + align:start position:0% +globules a lot of the interactions are + + + align:start position:0% +globules a lot of the interactions are +not yet in place but the hydrophobic + + align:start position:0% +not yet in place but the hydrophobic + + + align:start position:0% +not yet in place but the hydrophobic +cluster is critical but then after that + + align:start position:0% +cluster is critical but then after that + + + align:start position:0% +cluster is critical but then after that +it's almost as if you're sliding + + align:start position:0% +it's almost as if you're sliding + + + align:start position:0% +it's almost as if you're sliding +downhill to get all the remaining + + align:start position:0% +downhill to get all the remaining + + + align:start position:0% +downhill to get all the remaining +interactions in place to fold the + + align:start position:0% +interactions in place to fold the + + + align:start position:0% +interactions in place to fold the +protein ok so protein folding is a + + align:start position:0% +protein ok so protein folding is a + + + align:start position:0% +protein ok so protein folding is a +puzzle + + align:start position:0% +puzzle + + + align:start position:0% +puzzle +that can be solved computationally by + + align:start position:0% +that can be solved computationally by + + + align:start position:0% +that can be solved computationally by +maximizing thermodynamic interactions so + + align:start position:0% +maximizing thermodynamic interactions so + + + align:start position:0% +maximizing thermodynamic interactions so +it's Sigma this some of this some of + + align:start position:0% +it's Sigma this some of this some of + + + align:start position:0% +it's Sigma this some of this some of +this some of that that's gonna get + + align:start position:0% +this some of that that's gonna get + + + align:start position:0% +this some of that that's gonna get +difficult the larger the protein gets + + align:start position:0% +difficult the larger the protein gets + + + align:start position:0% +difficult the larger the protein gets +but for small proteins those simulations + + align:start position:0% +but for small proteins those simulations + + + align:start position:0% +but for small proteins those simulations +really start to make sense okay all + + align:start position:0% +really start to make sense okay all + + + align:start position:0% +really start to make sense okay all +right so let's just move on here last + + align:start position:0% +right so let's just move on here last + + + align:start position:0% +right so let's just move on here last +good what did you think of the + + align:start position:0% +good what did you think of the + + + align:start position:0% +good what did you think of the +simulation it's kind of cool right so + + align:start position:0% +simulation it's kind of cool right so + + + align:start position:0% +simulation it's kind of cool right so +you can find the link in the sidebar so + + align:start position:0% +you can find the link in the sidebar so + + + align:start position:0% +you can find the link in the sidebar so +just pop these back on now and that's + + align:start position:0% +just pop these back on now and that's + + + align:start position:0% +just pop these back on now and that's +the folded structure all right so with + + align:start position:0% +the folded structure all right so with + + + align:start position:0% +the folded structure all right so with +many proteins they're much more complex + + align:start position:0% +many proteins they're much more complex + + + align:start position:0% +many proteins they're much more complex +than that so for example here's cyclin a + + align:start position:0% +than that so for example here's cyclin a + + + align:start position:0% +than that so for example here's cyclin a +it's involved in cell cycle and you can + + align:start position:0% +it's involved in cell cycle and you can + + + align:start position:0% +it's involved in cell cycle and you can +see it's alpha helical structure + + align:start position:0% +see it's alpha helical structure + + + align:start position:0% +see it's alpha helical structure +dominantly very clearly all those + + align:start position:0% +dominantly very clearly all those + + + align:start position:0% +dominantly very clearly all those +beautiful alpha helixes next to it is + + align:start position:0% +beautiful alpha helixes next to it is + + + align:start position:0% +beautiful alpha helixes next to it is +the green fluorescent protein which is a + + align:start position:0% +the green fluorescent protein which is a + + + align:start position:0% +the green fluorescent protein which is a +cylindrical structure made up of a C + + align:start position:0% +cylindrical structure made up of a C + + + align:start position:0% +cylindrical structure made up of a C +parallel beta sheets what's really cool + + align:start position:0% +parallel beta sheets what's really cool + + + align:start position:0% +parallel beta sheets what's really cool +is when you sort of rotated you can see + + align:start position:0% +is when you sort of rotated you can see + + + align:start position:0% +is when you sort of rotated you can see +all those sheets but then it does this + + align:start position:0% +all those sheets but then it does this + + + align:start position:0% +all those sheets but then it does this +little sort of curtsy to the audience + + align:start position:0% +little sort of curtsy to the audience + + + align:start position:0% +little sort of curtsy to the audience +and you can look down into the barrel + + align:start position:0% +and you can look down into the barrel + + + align:start position:0% +and you can look down into the barrel +and then in some cases proteins may be a + + align:start position:0% +and then in some cases proteins may be a + + + align:start position:0% +and then in some cases proteins may be a +mixture of secondary structure elements + + align:start position:0% +mixture of secondary structure elements + + + align:start position:0% +mixture of secondary structure elements +here's a little hard to tell this is + + align:start position:0% +here's a little hard to tell this is + + + align:start position:0% +here's a little hard to tell this is +triose phosphate isomerase but if you + + align:start position:0% +triose phosphate isomerase but if you + + + align:start position:0% +triose phosphate isomerase but if you +look down it you can see the Gila C's + + align:start position:0% +look down it you can see the Gila C's + + + align:start position:0% +look down it you can see the Gila C's +and there's also a group of beta strands + + align:start position:0% +and there's also a group of beta strands + + + align:start position:0% +and there's also a group of beta strands +that are held together so in that + + align:start position:0% +that are held together so in that + + + align:start position:0% +that are held together so in that +protein it's a mixture of alpha helix + + align:start position:0% +protein it's a mixture of alpha helix + + + align:start position:0% +protein it's a mixture of alpha helix +and beta sheet now I'm not going to tell + + align:start position:0% +and beta sheet now I'm not going to tell + + + align:start position:0% +and beta sheet now I'm not going to tell +you much about pulling up protein + + align:start position:0% +you much about pulling up protein + + + align:start position:0% +you much about pulling up protein +databank files right now because I want + + align:start position:0% +databank files right now because I want + + + align:start position:0% +databank files right now because I want +to cover the next topic and then when we + + align:start position:0% +to cover the next topic and then when we + + + align:start position:0% +to cover the next topic and then when we +have a few minutes later on I'll show + + align:start position:0% +have a few minutes later on I'll show + + + align:start position:0% +have a few minutes later on I'll show +you but wherever I show you a structure + + align:start position:0% +you but wherever I show you a structure + + + align:start position:0% +you but wherever I show you a structure +I'm trying to show you the protein data + + align:start position:0% +I'm trying to show you the protein data + + + align:start position:0% +I'm trying to show you the protein data +bank code and in the website you can see + + align:start position:0% +bank code and in the website you can see + + + align:start position:0% +bank code and in the website you can see +there is a free download of Pi mall + + align:start position:0% +there is a free download of Pi mall + + + align:start position:0% +there is a free download of Pi mall +which is the program I used to create + + align:start position:0% +which is the program I used to create + + + align:start position:0% +which is the program I used to create +all these structures and movies so you + + align:start position:0% +all these structures and movies so you + + + align:start position:0% +all these structures and movies so you +can really look at things and believe me + + align:start position:0% +can really look at things and believe me + + + align:start position:0% +can really look at things and believe me +it took me about three years to learn + + align:start position:0% +it took me about three years to learn + + + align:start position:0% +it took me about three years to learn +how to use it probably take you about a + + align:start position:0% +how to use it probably take you about a + + + align:start position:0% +how to use it probably take you about a +week or maybe a couple of days so if I + + align:start position:0% +week or maybe a couple of days so if I + + + align:start position:0% +week or maybe a couple of days so if I +can learn it you can certainly learn it + + align:start position:0% +can learn it you can certainly learn it + + + align:start position:0% +can learn it you can certainly learn it +now there is one final element of + + align:start position:0% +now there is one final element of + + + align:start position:0% +now there is one final element of +protein structure the people get kind of + + align:start position:0% +protein structure the people get kind of + + + align:start position:0% +protein structure the people get kind of +hung up on and it's what's called put + + align:start position:0% +hung up on and it's what's called put + + + align:start position:0% +hung up on and it's what's called put +ternary structure it's like aren't we + + align:start position:0% +ternary structure it's like aren't we + + + align:start position:0% +ternary structure it's like aren't we +done yet so in addition to all of these + + align:start position:0% +done yet so in addition to all of these + + + align:start position:0% +done yet so in addition to all of these +let's say I have a folded motif and + + align:start position:0% +let's say I have a folded motif and + + + align:start position:0% +let's say I have a folded motif and +there's its structure that would be have + + align:start position:0% +there's its structure that would be have + + + align:start position:0% +there's its structure that would be have +primary secondary between the strands or + + align:start position:0% +primary secondary between the strands or + + + align:start position:0% +primary secondary between the strands or +the helix and tertiary structure right + + align:start position:0% +the helix and tertiary structure right + + + align:start position:0% +the helix and tertiary structure right +but in some cases proteins pulled up to + + align:start position:0% +but in some cases proteins pulled up to + + + align:start position:0% +but in some cases proteins pulled up to +quaternary structure where it's multiple + + align:start position:0% +quaternary structure where it's multiple + + + align:start position:0% +quaternary structure where it's multiple +of these units joined together I could + + align:start position:0% +of these units joined together I could + + + align:start position:0% +of these units joined together I could +have picked a simpler fold but doesn't + + align:start position:0% +have picked a simpler fold but doesn't + + + align:start position:0% +have picked a simpler fold but doesn't +get you the general gist of it all right + + align:start position:0% +get you the general gist of it all right + + + align:start position:0% +get you the general gist of it all right +where these are actually associated by + + align:start position:0% +where these are actually associated by + + + align:start position:0% +where these are actually associated by +non covalent forces so there's more than + + align:start position:0% +non covalent forces so there's more than + + + align:start position:0% +non covalent forces so there's more than +one polypeptide chain in fact here would + + align:start position:0% +one polypeptide chain in fact here would + + + align:start position:0% +one polypeptide chain in fact here would +be four polypeptide chains coming + + align:start position:0% +be four polypeptide chains coming + + + align:start position:0% +be four polypeptide chains coming +together in a higher order structure + + align:start position:0% +together in a higher order structure + + + align:start position:0% +together in a higher order structure +that's made up of four of those units + + align:start position:0% +that's made up of four of those units + + + align:start position:0% +that's made up of four of those units +the prototypic example of this is the + + align:start position:0% +the prototypic example of this is the + + + align:start position:0% +the prototypic example of this is the +protein that carries oxygen around in + + align:start position:0% +protein that carries oxygen around in + + + align:start position:0% +protein that carries oxygen around in +your blood which is hemoglobin and it + + align:start position:0% +your blood which is hemoglobin and it + + + align:start position:0% +your blood which is hemoglobin and it +has four primary sequences that have + + align:start position:0% +has four primary sequences that have + + + align:start position:0% +has four primary sequences that have +come together in a tetrameric quaternary + + align:start position:0% +come together in a tetrameric quaternary + + + align:start position:0% +come together in a tetrameric quaternary +structure hemoglobin is kind of + + align:start position:0% +structure hemoglobin is kind of + + + align:start position:0% +structure hemoglobin is kind of +interesting because it's made up of two + + align:start position:0% +interesting because it's made up of two + + + align:start position:0% +interesting because it's made up of two +alpha and two beta subunits if all these + + align:start position:0% +alpha and two beta subunits if all these + + + align:start position:0% +alpha and two beta subunits if all these +subunits were identical they would be + + align:start position:0% +subunits were identical they would be + + + align:start position:0% +subunits were identical they would be +called homo oligomers all the same + + align:start position:0% +called homo oligomers all the same + + + align:start position:0% +called homo oligomers all the same +pieces if they are different they are + + align:start position:0% +pieces if they are different they are + + + align:start position:0% +pieces if they are different they are +called hetero oligomers we'll see a + + align:start position:0% +called hetero oligomers we'll see a + + + align:start position:0% +called hetero oligomers we'll see a +little bit more about this when i talk + + align:start position:0% +little bit more about this when i talk + + + align:start position:0% +little bit more about this when i talk +about hemoglobin in the next class + + align:start position:0% +about hemoglobin in the next class + + + align:start position:0% +about hemoglobin in the next class +because the the features of the + + align:start position:0% +because the the features of the + + + align:start position:0% +because the the features of the +quaternary structure are very very + + align:start position:0% +quaternary structure are very very + + + align:start position:0% +quaternary structure are very very +important for the proper transport of + + align:start position:0% +important for the proper transport of + + + align:start position:0% +important for the proper transport of +oxygen and single mutations can really + + align:start position:0% +oxygen and single mutations can really + + + align:start position:0% +oxygen and single mutations can really +mess things up and you'll you'll see + + align:start position:0% +mess things up and you'll you'll see + + + align:start position:0% +mess things up and you'll you'll see +more about that in the in the next class + + align:start position:0% +more about that in the in the next class + + + align:start position:0% +more about that in the in the next class +so just to wrap that little bit up + + align:start position:0% +so just to wrap that little bit up + + + align:start position:0% +so just to wrap that little bit up +proteins are condensation polymers of + + align:start position:0% +proteins are condensation polymers of + + + align:start position:0% +proteins are condensation polymers of +amino acids each protein sequence is + + align:start position:0% +amino acids each protein sequence is + + + align:start position:0% +amino acids each protein sequence is +defined by covalent bonding native + + align:start position:0% +defined by covalent bonding native + + + align:start position:0% +defined by covalent bonding native +proteins most of them that are not don't + + align:start position:0% +proteins most of them that are not don't + + + align:start position:0% +proteins most of them that are not don't +have quaternary structure of + + align:start position:0% +have quaternary structure of + + + align:start position:0% +have quaternary structure of +through secondary and tertiary + + align:start position:0% +through secondary and tertiary + + + align:start position:0% +through secondary and tertiary +interactions these things that we + + align:start position:0% +interactions these things that we + + + align:start position:0% +interactions these things that we +already talked about and foldings + + align:start position:0% +already talked about and foldings + + + align:start position:0% +already talked about and foldings +defined by how to maximize all those + + align:start position:0% +defined by how to maximize all those + + + align:start position:0% +defined by how to maximize all those +non-covalent forces to get the maximum + + align:start position:0% +non-covalent forces to get the maximum + + + align:start position:0% +non-covalent forces to get the maximum +thermodynamic stability with the maximum + + align:start position:0% +thermodynamic stability with the maximum + + + align:start position:0% +thermodynamic stability with the maximum +number of interactions and subunits may + + align:start position:0% +number of interactions and subunits may + + + align:start position:0% +number of interactions and subunits may +also come together through quaternary + + align:start position:0% +also come together through quaternary + + + align:start position:0% +also come together through quaternary +structure okay so I'm going to talk to + + align:start position:0% +structure okay so I'm going to talk to + + + align:start position:0% +structure okay so I'm going to talk to +you about several proteins throughout + + align:start position:0% +you about several proteins throughout + + + align:start position:0% +you about several proteins throughout +the course but for now I want to focus + + align:start position:0% +the course but for now I want to focus + + + align:start position:0% +the course but for now I want to focus +you in on a structural protein that + + align:start position:0% +you in on a structural protein that + + + align:start position:0% +you in on a structural protein that +provides mechanical support for tissues + + align:start position:0% +provides mechanical support for tissues + + + align:start position:0% +provides mechanical support for tissues +in the next class we'll talk about + + align:start position:0% +in the next class we'll talk about + + + align:start position:0% +in the next class we'll talk about +transporters and enzymes and as we move + + align:start position:0% +transporters and enzymes and as we move + + + align:start position:0% +transporters and enzymes and as we move +on to signaling things like receptors + + align:start position:0% +on to signaling things like receptors + + + align:start position:0% +on to signaling things like receptors +and membrane proteins and so on so the + + align:start position:0% +and membrane proteins and so on so the + + + align:start position:0% +and membrane proteins and so on so the +protein I'm gonna describe to you is + + align:start position:0% +protein I'm gonna describe to you is + + + align:start position:0% +protein I'm gonna describe to you is +collagen it is the most abundant protein + + align:start position:0% +collagen it is the most abundant protein + + + align:start position:0% +collagen it is the most abundant protein +in the human body + + align:start position:0% +in the human body + + + align:start position:0% +in the human body +it plays enormous roles it's not an + + align:start position:0% +it plays enormous roles it's not an + + + align:start position:0% +it plays enormous roles it's not an +enzyme it's not a catalyst it's not a + + align:start position:0% +enzyme it's not a catalyst it's not a + + + align:start position:0% +enzyme it's not a catalyst it's not a +transporter it is one of those + + align:start position:0% +transporter it is one of those + + + align:start position:0% +transporter it is one of those +structural proteins where the structure + + align:start position:0% +structural proteins where the structure + + + align:start position:0% +structural proteins where the structure +of collagen has evolved to provide a + + align:start position:0% +of collagen has evolved to provide a + + + align:start position:0% +of collagen has evolved to provide a +mechanical stability to lot of essential + + align:start position:0% +mechanical stability to lot of essential + + + align:start position:0% +mechanical stability to lot of essential +components of complex organisms and + + align:start position:0% +components of complex organisms and + + + align:start position:0% +components of complex organisms and +there are many different types of + + align:start position:0% +there are many different types of + + + align:start position:0% +there are many different types of +collagen that are found in different + + align:start position:0% +collagen that are found in different + + + align:start position:0% +collagen that are found in different +parts of the body for example bone + + align:start position:0% +parts of the body for example bone + + + align:start position:0% +parts of the body for example bone +tendon cartilage and so on they are all + + align:start position:0% +tendon cartilage and so on they are all + + + align:start position:0% +tendon cartilage and so on they are all +collagen structures but they have subtle + + align:start position:0% +collagen structures but they have subtle + + + align:start position:0% +collagen structures but they have subtle +differences maybe some have different + + align:start position:0% +differences maybe some have different + + + align:start position:0% +differences maybe some have different +slightly different mechanical properties + + align:start position:0% +slightly different mechanical properties + + + align:start position:0% +slightly different mechanical properties +to adapt the functions that they perform + + align:start position:0% +to adapt the functions that they perform + + + align:start position:0% +to adapt the functions that they perform +okay a signal and what I'm going to show + + align:start position:0% +okay a signal and what I'm going to show + + + align:start position:0% +okay a signal and what I'm going to show +you is that a single amino acid change + + align:start position:0% +you is that a single amino acid change + + + align:start position:0% +you is that a single amino acid change +in the primary sequence of collagen can + + align:start position:0% +in the primary sequence of collagen can + + + align:start position:0% +in the primary sequence of collagen can +destabilize the structure so it is no + + align:start position:0% +destabilize the structure so it is no + + + align:start position:0% +destabilize the structure so it is no +longer viable and no disease type I'm + + align:start position:0% +longer viable and no disease type I'm + + + align:start position:0% +longer viable and no disease type I'm +going to talk to you about is a doozy a + + align:start position:0% +going to talk to you about is a doozy a + + + align:start position:0% +going to talk to you about is a doozy a +set of diseases known as collagen AAPA + + align:start position:0% +set of diseases known as collagen AAPA + + + align:start position:0% +set of diseases known as collagen AAPA +thiis and the particular one is called + + align:start position:0% +thiis and the particular one is called + + + align:start position:0% +thiis and the particular one is called +osteogenesis imperfecta osteo always + + align:start position:0% +osteogenesis imperfecta osteo always + + + align:start position:0% +osteogenesis imperfecta osteo always +refers to bone because collagen plays a + + align:start position:0% +refers to bone because collagen plays a + + + align:start position:0% +refers to bone because collagen plays a +critical role in the structure of bone + + align:start position:0% +critical role in the structure of bone + + + align:start position:0% +critical role in the structure of bone +bone isn't just bone it's collagen + + align:start position:0% +bone isn't just bone it's collagen + + + align:start position:0% +bone isn't just bone it's collagen +involved in it and it's also this + + align:start position:0% +involved in it and it's also this + + + align:start position:0% +involved in it and it's also this +disease is called brittle bone syndrome + + align:start position:0% +disease is called brittle bone syndrome + + + align:start position:0% +disease is called brittle bone syndrome +and here's the x-ray of a baby born with + + align:start position:0% +and here's the x-ray of a baby born with + + + align:start position:0% +and here's the x-ray of a baby born with +brittle bone syndrome and you'll see + + align:start position:0% +brittle bone syndrome and you'll see + + + align:start position:0% +brittle bone syndrome and you'll see +that the long bones in the upper arm are + + align:start position:0% +that the long bones in the upper arm are + + + align:start position:0% +that the long bones in the upper arm are +all irregular because the bones are + + align:start position:0% +all irregular because the bones are + + + align:start position:0% +all irregular because the bones are +brittle and they'll they'll break even + + align:start position:0% +brittle and they'll they'll break even + + + align:start position:0% +brittle and they'll they'll break even +in utero + + align:start position:0% +in utero + + + align:start position:0% +in utero +a lot of babies with this defect can't + + align:start position:0% +a lot of babies with this defect can't + + + align:start position:0% +a lot of babies with this defect can't +even be born through the birth canal + + align:start position:0% +even be born through the birth canal + + + align:start position:0% +even be born through the birth canal +because it would crush the bones and + + align:start position:0% +because it would crush the bones and + + + align:start position:0% +because it would crush the bones and +many of them don't survive very long at + + align:start position:0% +many of them don't survive very long at + + + align:start position:0% +many of them don't survive very long at +all + + align:start position:0% +all + + + align:start position:0% +all +some survive with different kinds of + + align:start position:0% +some survive with different kinds of + + + align:start position:0% +some survive with different kinds of +cases but their lives are greatly + + align:start position:0% +cases but their lives are greatly + + + align:start position:0% +cases but their lives are greatly +impacted and they could just sort of hit + + align:start position:0% +impacted and they could just sort of hit + + + align:start position:0% +impacted and they could just sort of hit +a table and the bones would break all + + align:start position:0% +a table and the bones would break all + + + align:start position:0% +a table and the bones would break all +right there are other sort of serious + + align:start position:0% +right there are other sort of serious + + + align:start position:0% +right there are other sort of serious +situations where parents are actually + + align:start position:0% +situations where parents are actually + + + align:start position:0% +situations where parents are actually +accused of abuse to the child but the + + align:start position:0% +accused of abuse to the child but the + + + align:start position:0% +accused of abuse to the child but the +child actually had brittle bone syndrome + + align:start position:0% +child actually had brittle bone syndrome + + + align:start position:0% +child actually had brittle bone syndrome +and it was just through you know helping + + align:start position:0% +and it was just through you know helping + + + align:start position:0% +and it was just through you know helping +them put their clothes on or taking them + + align:start position:0% +them put their clothes on or taking them + + + align:start position:0% +them put their clothes on or taking them +upstairs the bones got broken very + + align:start position:0% +upstairs the bones got broken very + + + align:start position:0% +upstairs the bones got broken very +readily + + align:start position:0% +readily + + + align:start position:0% +readily +so osteogenesis imperfecta really + + align:start position:0% +so osteogenesis imperfecta really + + + align:start position:0% +so osteogenesis imperfecta really +describes a collection of these defects + + align:start position:0% +describes a collection of these defects + + + align:start position:0% +describes a collection of these defects +now the collagen tertiary structure is + + align:start position:0% +now the collagen tertiary structure is + + + align:start position:0% +now the collagen tertiary structure is +shown here it's actually made up of a + + align:start position:0% +shown here it's actually made up of a + + + align:start position:0% +shown here it's actually made up of a +type of helix it's not an alpha helix + + align:start position:0% +type of helix it's not an alpha helix + + + align:start position:0% +type of helix it's not an alpha helix +it's a poly prolene helix where the + + align:start position:0% +it's a poly prolene helix where the + + + align:start position:0% +it's a poly prolene helix where the +individual subunits in that tersh in the + + align:start position:0% +individual subunits in that tersh in the + + + align:start position:0% +individual subunits in that tersh in the +structure are fairly long and extended + + align:start position:0% +structure are fairly long and extended + + + align:start position:0% +structure are fairly long and extended +and I show you three strands in this + + align:start position:0% +and I show you three strands in this + + + align:start position:0% +and I show you three strands in this +polymeric structure yellow a red and a + + align:start position:0% +polymeric structure yellow a red and a + + + align:start position:0% +polymeric structure yellow a red and a +green + + align:start position:0% +green + + + align:start position:0% +green +and these roll together into a three + + align:start position:0% +and these roll together into a three + + + align:start position:0% +and these roll together into a three +helix bundle that has a fibrillar + + align:start position:0% +helix bundle that has a fibrillar + + + align:start position:0% +helix bundle that has a fibrillar +structure and then all these structures + + align:start position:0% +structure and then all these structures + + + align:start position:0% +structure and then all these structures +come together to make the macromolecular + + align:start position:0% +come together to make the macromolecular + + + align:start position:0% +come together to make the macromolecular +structure that is collagen it's not just + + align:start position:0% +structure that is collagen it's not just + + + align:start position:0% +structure that is collagen it's not just +one of those peoples it's bundles of + + align:start position:0% +one of those peoples it's bundles of + + + align:start position:0% +one of those peoples it's bundles of +those fibrillar very organized pattern + + align:start position:0% +those fibrillar very organized pattern + + + align:start position:0% +those fibrillar very organized pattern +where you could even see that patterning + + align:start position:0% +where you could even see that patterning + + + align:start position:0% +where you could even see that patterning +in an electron microscopy and there are + + align:start position:0% +in an electron microscopy and there are + + + align:start position:0% +in an electron microscopy and there are +many genetic defects of collagen and + + align:start position:0% +many genetic defects of collagen and + + + align:start position:0% +many genetic defects of collagen and +what's so important to think about this + + align:start position:0% +what's so important to think about this + + + align:start position:0% +what's so important to think about this +if you have a defect in one strand that + + align:start position:0% +if you have a defect in one strand that + + + align:start position:0% +if you have a defect in one strand that +defect will propagate through every + + align:start position:0% +defect will propagate through every + + + align:start position:0% +defect will propagate through every +single strand if this is one strand made + + align:start position:0% +single strand if this is one strand made + + + align:start position:0% +single strand if this is one strand made +up of three polypeptide chains it + + align:start position:0% +up of three polypeptide chains it + + + align:start position:0% +up of three polypeptide chains it +propagates all the way through the + + align:start position:0% +propagates all the way through the + + + align:start position:0% +propagates all the way through the +structure and I believe I have a little + + align:start position:0% +structure and I believe I have a little + + + align:start position:0% +structure and I believe I have a little +time to just show you here's the + + align:start position:0% +time to just show you here's the + + + align:start position:0% +time to just show you here's the +collagen structure I'm just showing you + + align:start position:0% +collagen structure I'm just showing you + + + align:start position:0% +collagen structure I'm just showing you +how its extended those are three + + align:start position:0% +how its extended those are three + + + align:start position:0% +how its extended those are three +independent strands and there's a set of + + align:start position:0% +independent strands and there's a set of + + + align:start position:0% +independent strands and there's a set of +magenta residues in the middle which + + align:start position:0% +magenta residues in the middle which + + + align:start position:0% +magenta residues in the middle which +come from a defect + + align:start position:0% +come from a defect + + + align:start position:0% +come from a defect +in the sequence where a glycine has been + + align:start position:0% +in the sequence where a glycine has been + + + align:start position:0% +in the sequence where a glycine has been +changed to an alanine and that so I'm + + align:start position:0% +changed to an alanine and that so I'm + + + align:start position:0% +changed to an alanine and that so I'm +gonna show you this movie because it + + align:start position:0% +gonna show you this movie because it + + + align:start position:0% +gonna show you this movie because it +shows you right at the center of the + + align:start position:0% +shows you right at the center of the + + + align:start position:0% +shows you right at the center of the +structure there are residues painted in + + align:start position:0% +structure there are residues painted in + + + align:start position:0% +structure there are residues painted in +pink and what I'm going to do is show + + align:start position:0% +pink and what I'm going to do is show + + + align:start position:0% +pink and what I'm going to do is show +you close-up of that segment if you look + + align:start position:0% +you close-up of that segment if you look + + + align:start position:0% +you close-up of that segment if you look +at those HeLa sees they're all nicely + + align:start position:0% +at those HeLa sees they're all nicely + + + align:start position:0% +at those HeLa sees they're all nicely +organized except where that defect is + + align:start position:0% +organized except where that defect is + + + align:start position:0% +organized except where that defect is +and that defect is caused by the change + + align:start position:0% +and that defect is caused by the change + + + align:start position:0% +and that defect is caused by the change +of a hydrogen to a methyl group on three + + align:start position:0% +of a hydrogen to a methyl group on three + + + align:start position:0% +of a hydrogen to a methyl group on three +residues that come together and that + + align:start position:0% +residues that come together and that + + + align:start position:0% +residues that come together and that +bulges out that fibrillar structure and + + align:start position:0% +bulges out that fibrillar structure and + + + align:start position:0% +bulges out that fibrillar structure and +makes it not as compact and beautiful as + + align:start position:0% +makes it not as compact and beautiful as + + + align:start position:0% +makes it not as compact and beautiful as +it should be + + align:start position:0% +it should be + + + align:start position:0% +it should be +in the version that's got the glycine + + align:start position:0% +in the version that's got the glycine + + + align:start position:0% +in the version that's got the glycine +there so if you look at it you can even + + align:start position:0% +there so if you look at it you can even + + + align:start position:0% +there so if you look at it you can even +see that helix gets bulged out and is + + align:start position:0% +see that helix gets bulged out and is + + + align:start position:0% +see that helix gets bulged out and is +not as well aligned as the rest of the + + align:start position:0% +not as well aligned as the rest of the + + + align:start position:0% +not as well aligned as the rest of the +structure and then that defect gets + + align:start position:0% +structure and then that defect gets + + + align:start position:0% +structure and then that defect gets +propagated into all the fibrin results + + align:start position:0% +propagated into all the fibrin results + + + align:start position:0% +propagated into all the fibrin results +in the weakening of the bones either the + + align:start position:0% +in the weakening of the bones either the + + + align:start position:0% +in the weakening of the bones either the +collagen fails to form properly or the + + align:start position:0% +collagen fails to form properly or the + + + align:start position:0% +collagen fails to form properly or the +collagen when it forms it has much less + + align:start position:0% +collagen when it forms it has much less + + + align:start position:0% +collagen when it forms it has much less +mechanical stability so I think that's a + + align:start position:0% +mechanical stability so I think that's a + + + align:start position:0% +mechanical stability so I think that's a +good place to stop and now pick up next + + align:start position:0% +good place to stop and now pick up next + + + align:start position:0% +good place to stop and now pick up next +time with hemoglobin oh one last little + + align:start position:0% +time with hemoglobin oh one last little + + + align:start position:0% +time with hemoglobin oh one last little +thing a couple of things for you to do + + align:start position:0% +thing a couple of things for you to do + + + align:start position:0% +thing a couple of things for you to do +there's a great link on the website to + + align:start position:0% +there's a great link on the website to + + + align:start position:0% +there's a great link on the website to +the protein databank to see how enzymes + + align:start position:0% +the protein databank to see how enzymes + + + align:start position:0% +the protein databank to see how enzymes +work and if you have a little time it + + align:start position:0% +work and if you have a little time it + + + align:start position:0% +work and if you have a little time it +would be awesome if you could just take + + align:start position:0% +would be awesome if you could just take + + + align:start position:0% +would be awesome if you could just take +a quick flick through those parts of the + + align:start position:0% +a quick flick through those parts of the + + + align:start position:0% +a quick flick through those parts of the +text these slides are posted with these + + align:start position:0% +text these slides are posted with these + + + align:start position:0% +text these slides are posted with these +are reading assignments and they're + + align:start position:0% +are reading assignments and they're + + + align:start position:0% +are reading assignments and they're +posted in color if you want to look at + + align:start position:0% +posted in color if you want to look at + + + align:start position:0% +posted in color if you want to look at +them again + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/ozbtgvLKAqE.txt b/ozbtgvLKAqE.txt new file mode 100644 index 0000000000000000000000000000000000000000..3208c49f040c0ef7088dac9184ce3ab655c7ed6d --- /dev/null +++ b/ozbtgvLKAqE.txt @@ -0,0 +1,1003 @@ +align:start position:0% + +we will now consider an operation that + + align:start position:0% +we will now consider an operation that + + + align:start position:0% +we will now consider an operation that +is in some sense the opposite of merging + + align:start position:0% +is in some sense the opposite of merging + + + align:start position:0% +is in some sense the opposite of merging +we have a node and traffic arrives to + + align:start position:0% +we have a node and traffic arrives to + + + align:start position:0% +we have a node and traffic arrives to +that node and each time that we have an + + align:start position:0% +that node and each time that we have an + + + align:start position:0% +that node and each time that we have an +arrival we flip a coin and with + + align:start position:0% +arrival we flip a coin and with + + + align:start position:0% +arrival we flip a coin and with +probability Q we send that arrival to + + align:start position:0% +probability Q we send that arrival to + + + align:start position:0% +probability Q we send that arrival to +one particular stream and with + + align:start position:0% +one particular stream and with + + + align:start position:0% +one particular stream and with +probability 1 minus Q we send the + + align:start position:0% +probability 1 minus Q we send the + + + align:start position:0% +probability 1 minus Q we send the +arrival to another stream so we get two + + align:start position:0% +arrival to another stream so we get two + + + align:start position:0% +arrival to another stream so we get two +streams that are formed by taking the + + align:start position:0% +streams that are formed by taking the + + + align:start position:0% +streams that are formed by taking the +original stream and splitting it into + + align:start position:0% +original stream and splitting it into + + + align:start position:0% +original stream and splitting it into +two pieces and as an example these might + + align:start position:0% +two pieces and as an example these might + + + align:start position:0% +two pieces and as an example these might +be arrivals at the department store and + + align:start position:0% +be arrivals at the department store and + + + align:start position:0% +be arrivals at the department store and +the one stream corresponds the people + + align:start position:0% +the one stream corresponds the people + + + align:start position:0% +the one stream corresponds the people +who go to the clothes section of the + + align:start position:0% +who go to the clothes section of the + + + align:start position:0% +who go to the clothes section of the +department store whereas the other + + align:start position:0% +department store whereas the other + + + align:start position:0% +department store whereas the other +stream corresponds to the people that go + + align:start position:0% +stream corresponds to the people that go + + + align:start position:0% +stream corresponds to the people that go +to all of the other sections of the + + align:start position:0% +to all of the other sections of the + + + align:start position:0% +to all of the other sections of the +store so let us now make our model a + + align:start position:0% +store so let us now make our model a + + + align:start position:0% +store so let us now make our model a +little more precise we have a Bernoulli + + align:start position:0% +little more precise we have a Bernoulli + + + align:start position:0% +little more precise we have a Bernoulli +process which is independent across time + + align:start position:0% +process which is independent across time + + + align:start position:0% +process which is independent across time +we also use independent coin flips an + + align:start position:0% +we also use independent coin flips an + + + align:start position:0% +we also use independent coin flips an +independent coin flip to deal with each + + align:start position:0% +independent coin flip to deal with each + + + align:start position:0% +independent coin flip to deal with each +one of the arrivals but we will also + + align:start position:0% +one of the arrivals but we will also + + + align:start position:0% +one of the arrivals but we will also +make one additional assumption namely + + align:start position:0% +make one additional assumption namely + + + align:start position:0% +make one additional assumption namely +that the Bernoulli process is also + + align:start position:0% +that the Bernoulli process is also + + + align:start position:0% +that the Bernoulli process is also +independent from the process of coin + + align:start position:0% +independent from the process of coin + + + align:start position:0% +independent from the process of coin +flips with this assumption in place let + + align:start position:0% +flips with this assumption in place let + + + align:start position:0% +flips with this assumption in place let +us now continue and let us draw a + + align:start position:0% +us now continue and let us draw a + + + align:start position:0% +us now continue and let us draw a +picture we have a Bernoulli process with + + align:start position:0% +picture we have a Bernoulli process with + + + align:start position:0% +picture we have a Bernoulli process with +parameter P and arrivals get recorded at + + align:start position:0% +parameter P and arrivals get recorded at + + + align:start position:0% +parameter P and arrivals get recorded at +certain times each time that there is an + + align:start position:0% +certain times each time that there is an + + + align:start position:0% +certain times each time that there is an +arrival we will flip a coin and with + + align:start position:0% +arrival we will flip a coin and with + + + align:start position:0% +arrival we will flip a coin and with +probability Q the arrival will be sent + + align:start position:0% +probability Q the arrival will be sent + + + align:start position:0% +probability Q the arrival will be sent +to that stream with probability 1 minus + + align:start position:0% +to that stream with probability 1 minus + + + align:start position:0% +to that stream with probability 1 minus +Q the arrival will be sent to the other + + align:start position:0% +Q the arrival will be sent to the other + + + align:start position:0% +Q the arrival will be sent to the other +stream so one possible outcome of the + + align:start position:0% +stream so one possible outcome of the + + + align:start position:0% +stream so one possible outcome of the +experiment might be this one word these + + align:start position:0% +experiment might be this one word these + + + align:start position:0% +experiment might be this one word these +two arrivals were sent to the stream and + + align:start position:0% +two arrivals were sent to the stream and + + + align:start position:0% +two arrivals were sent to the stream and +these two arrivals were sent to the top + + align:start position:0% +these two arrivals were sent to the top + + + align:start position:0% +these two arrivals were sent to the top +stream and we have these probabilities Q + + align:start position:0% +stream and we have these probabilities Q + + + align:start position:0% +stream and we have these probabilities Q +and 1 minus Q of sending the arrivals to + + align:start position:0% +and 1 minus Q of sending the arrivals to + + + align:start position:0% +and 1 minus Q of sending the arrivals to +one or the other stream what kind of + + align:start position:0% +one or the other stream what kind of + + + align:start position:0% +one or the other stream what kind of +process is this one we argue that it is + + align:start position:0% +process is this one we argue that it is + + + align:start position:0% +process is this one we argue that it is +a Bernoulli process + + align:start position:0% +a Bernoulli process + + + align:start position:0% +a Bernoulli process +first we need to check independence here + + align:start position:0% +first we need to check independence here + + + align:start position:0% +first we need to check independence here +the argument is more or less the same as + + align:start position:0% +the argument is more or less the same as + + + align:start position:0% +the argument is more or less the same as +in the case when we studied the merging + + align:start position:0% +in the case when we studied the merging + + + align:start position:0% +in the case when we studied the merging +of processes for example if we look at + + align:start position:0% +of processes for example if we look at + + + align:start position:0% +of processes for example if we look at +two different slots and we ask how is + + align:start position:0% +two different slots and we ask how is + + + align:start position:0% +two different slots and we ask how is +the event at that slot and that slot + + align:start position:0% +the event at that slot and that slot + + + align:start position:0% +the event at that slot and that slot +determined well what happens in this + + align:start position:0% +determined well what happens in this + + + align:start position:0% +determined well what happens in this +slot is determined by whether we had an + + align:start position:0% +slot is determined by whether we had an + + + align:start position:0% +slot is determined by whether we had an +arrival here and what happened to the + + align:start position:0% +arrival here and what happened to the + + + align:start position:0% +arrival here and what happened to the +outcome of the coin flip at that time + + align:start position:0% +outcome of the coin flip at that time + + + align:start position:0% +outcome of the coin flip at that time +what happens in this slot is determined + + align:start position:0% +what happens in this slot is determined + + + align:start position:0% +what happens in this slot is determined +by whether we had an arrival here and + + align:start position:0% +by whether we had an arrival here and + + + align:start position:0% +by whether we had an arrival here and +what happened to the coin flip at that + + align:start position:0% +what happened to the coin flip at that + + + align:start position:0% +what happened to the coin flip at that +time now the coin flips are independent + + align:start position:0% +time now the coin flips are independent + + + align:start position:0% +time now the coin flips are independent +from the original Bernoulli process and + + align:start position:0% +from the original Bernoulli process and + + + align:start position:0% +from the original Bernoulli process and +for either the coin flips or the + + align:start position:0% +for either the coin flips or the + + + align:start position:0% +for either the coin flips or the +Bernoulli process we have independence + + align:start position:0% +Bernoulli process we have independence + + + align:start position:0% +Bernoulli process we have independence +across time so all of the four random + + align:start position:0% +across time so all of the four random + + + align:start position:0% +across time so all of the four random +variables involved here that determines + + align:start position:0% +variables involved here that determines + + + align:start position:0% +variables involved here that determines +what happens in these two slots are + + align:start position:0% +what happens in these two slots are + + + align:start position:0% +what happens in these two slots are +independent of each other so what + + align:start position:0% +independent of each other so what + + + align:start position:0% +independent of each other so what +happens in this slot is a function of + + align:start position:0% +happens in this slot is a function of + + + align:start position:0% +happens in this slot is a function of +two random variables here which are + + align:start position:0% +two random variables here which are + + + align:start position:0% +two random variables here which are +independent from the two random + + align:start position:0% +independent from the two random + + + align:start position:0% +independent from the two random +variables that determine what happens in + + align:start position:0% +variables that determine what happens in + + + align:start position:0% +variables that determine what happens in +that slot so what happens in these two + + align:start position:0% +that slot so what happens in these two + + + align:start position:0% +that slot so what happens in these two +slots are independent events and this + + align:start position:0% +slots are independent events and this + + + align:start position:0% +slots are independent events and this +argument goes through more generally + + align:start position:0% +argument goes through more generally + + + align:start position:0% +argument goes through more generally +when we consider multiple distinct slots + + align:start position:0% +when we consider multiple distinct slots + + + align:start position:0% +when we consider multiple distinct slots +so this is the argument for the + + align:start position:0% +so this is the argument for the + + + align:start position:0% +so this is the argument for the +independence of the different slots in + + align:start position:0% +independence of the different slots in + + + align:start position:0% +independence of the different slots in +this particular process and then during + + align:start position:0% +this particular process and then during + + + align:start position:0% +this particular process and then during +each slot what happens is that we will + + align:start position:0% +each slot what happens is that we will + + + align:start position:0% +each slot what happens is that we will +have an arrival if and only if this + + align:start position:0% +have an arrival if and only if this + + + align:start position:0% +have an arrival if and only if this +process records an arrival which happens + + align:start position:0% +process records an arrival which happens + + + align:start position:0% +process records an arrival which happens +with probability P and the corresponding + + align:start position:0% +with probability P and the corresponding + + + align:start position:0% +with probability P and the corresponding +coin flip happened to send the arrival + + align:start position:0% +coin flip happened to send the arrival + + + align:start position:0% +coin flip happened to send the arrival +in this direction which happens with + + align:start position:0% +in this direction which happens with + + + align:start position:0% +in this direction which happens with +probability Q and so the conclusion is + + align:start position:0% +probability Q and so the conclusion is + + + align:start position:0% +probability Q and so the conclusion is +that this process is a Bernoulli process + + align:start position:0% +that this process is a Bernoulli process + + + align:start position:0% +that this process is a Bernoulli process +with parameter P times Q by a similar + + align:start position:0% +with parameter P times Q by a similar + + + align:start position:0% +with parameter P times Q by a similar +argument the other process that we + + align:start position:0% +argument the other process that we + + + align:start position:0% +argument the other process that we +obtain will also be Bernoulli but with + + align:start position:0% +obtain will also be Bernoulli but with + + + align:start position:0% +obtain will also be Bernoulli but with +probability P times 1 minus Q and the + + align:start position:0% +probability P times 1 minus Q and the + + + align:start position:0% +probability P times 1 minus Q and the +final question are these two processes + + align:start position:0% +final question are these two processes + + + align:start position:0% +final question are these two processes +that we get after the splitting + + align:start position:0% +that we get after the splitting + + + align:start position:0% +that we get after the splitting +independent of each other this is a + + align:start position:0% +independent of each other this is a + + + align:start position:0% +independent of each other this is a +question that we can answer by reasoning + + align:start position:0% +question that we can answer by reasoning + + + align:start position:0% +question that we can answer by reasoning +into it + + align:start position:0% +into it + + + align:start position:0% +into it +if I tell you that there was an arrival + + align:start position:0% +if I tell you that there was an arrival + + + align:start position:0% +if I tell you that there was an arrival +in this slot what can you infer from + + align:start position:0% +in this slot what can you infer from + + + align:start position:0% +in this slot what can you infer from +this well it tells me that there was an + + align:start position:0% +this well it tells me that there was an + + + align:start position:0% +this well it tells me that there was an +arrival in the original stream which was + + align:start position:0% +arrival in the original stream which was + + + align:start position:0% +arrival in the original stream which was +sent here but since it was sent in this + + align:start position:0% +sent here but since it was sent in this + + + align:start position:0% +sent here but since it was sent in this +direction it means that it was not sent + + align:start position:0% +direction it means that it was not sent + + + align:start position:0% +direction it means that it was not sent +in the other direction and so we do not + + align:start position:0% +in the other direction and so we do not + + + align:start position:0% +in the other direction and so we do not +have an arrival in this slot knowing + + align:start position:0% +have an arrival in this slot knowing + + + align:start position:0% +have an arrival in this slot knowing +that we have an arrival here means that + + align:start position:0% +that we have an arrival here means that + + + align:start position:0% +that we have an arrival here means that +we do not have an arrival there so + + align:start position:0% +we do not have an arrival there so + + + align:start position:0% +we do not have an arrival there so +information about one of the streams + + align:start position:0% +information about one of the streams + + + align:start position:0% +information about one of the streams +gives us information about what happened + + align:start position:0% +gives us information about what happened + + + align:start position:0% +gives us information about what happened +in the other stream and therefore we do + + align:start position:0% +in the other stream and therefore we do + + + align:start position:0% +in the other stream and therefore we do +not have independence so this is what + + align:start position:0% +not have independence so this is what + + + align:start position:0% +not have independence so this is what +happens when we split to Bernoulli + + align:start position:0% +happens when we split to Bernoulli + + + align:start position:0% +happens when we split to Bernoulli +processes and earlier we saw what + + align:start position:0% +processes and earlier we saw what + + + align:start position:0% +processes and earlier we saw what +happens when we merge two independent + + align:start position:0% +happens when we merge two independent + + + align:start position:0% +happens when we merge two independent +Bernoulli processes these two operations + + align:start position:0% +Bernoulli processes these two operations + + + align:start position:0% +Bernoulli processes these two operations +of merging and splitting are quite + + align:start position:0% +of merging and splitting are quite + + + align:start position:0% +of merging and splitting are quite +common in constructing more complex + + align:start position:0% +common in constructing more complex + + + align:start position:0% +common in constructing more complex +models using Bernoulli processes as the + + align:start position:0% +models using Bernoulli processes as the + + + align:start position:0% +models using Bernoulli processes as the +elements of those models they are often + + align:start position:0% +elements of those models they are often + + + align:start position:0% +elements of those models they are often +useful models either in transportation + + align:start position:0% +useful models either in transportation + + + align:start position:0% +useful models either in transportation +systems where you have streams of + + align:start position:0% +systems where you have streams of + + + align:start position:0% +systems where you have streams of +traffic that merge or split also in + + align:start position:0% +traffic that merge or split also in + + + align:start position:0% +traffic that merge or split also in +models of computer networks or any other + + align:start position:0% +models of computer networks or any other + + + align:start position:0% +models of computer networks or any other +kind of chewing system and these same + + align:start position:0% +kind of chewing system and these same + + + align:start position:0% +kind of chewing system and these same +operations of merging and splitting will + + align:start position:0% +operations of merging and splitting will + + + align:start position:0% +operations of merging and splitting will +also show up when we study the + + align:start position:0% +also show up when we study the + + + align:start position:0% +also show up when we study the +continuous-time analogue of the + + align:start position:0% +continuous-time analogue of the + + + align:start position:0% +continuous-time analogue of the +Bernoulli process namely the Poisson + + align:start position:0% +Bernoulli process namely the Poisson + + + align:start position:0% +Bernoulli process namely the Poisson +process \ No newline at end of file diff --git a/p12HLN9jw6s.txt b/p12HLN9jw6s.txt new file mode 100644 index 0000000000000000000000000000000000000000..3ec530e9b6b34f52146e65712bea17ad5a6c86dc --- /dev/null +++ b/p12HLN9jw6s.txt @@ -0,0 +1,11187 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common license. Your support + + align:start position:0% +a Creative Common license. Your support + + + align:start position:0% +a Creative Common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mit.edu. + + align:start position:0% + + + + align:start position:0% + +Good evening people. I want to uh + + align:start position:0% +Good evening people. I want to uh + + + align:start position:0% +Good evening people. I want to uh +continue our discussion of the end of + + align:start position:0% +continue our discussion of the end of + + + align:start position:0% +continue our discussion of the end of +the studio + + align:start position:0% +the studio + + + align:start position:0% +the studio +era. The advent of the kind of much + + align:start position:0% +era. The advent of the kind of much + + + align:start position:0% +era. The advent of the kind of much +freer, more independent, + + align:start position:0% +freer, more independent, + + + align:start position:0% +freer, more independent, +more politically and even morally + + align:start position:0% +more politically and even morally + + + align:start position:0% +more politically and even morally +liberated movies that appear after the + + align:start position:0% +liberated movies that appear after the + + + align:start position:0% +liberated movies that appear after the +Hollywood dispensation has subsided. uh + + align:start position:0% +Hollywood dispensation has subsided. uh + + + align:start position:0% +Hollywood dispensation has subsided. uh +but remember that I've also been + + align:start position:0% +but remember that I've also been + + + align:start position:0% +but remember that I've also been +suggesting to you that even though there + + align:start position:0% +suggesting to you that even though there + + + align:start position:0% +suggesting to you that even though there +is there's a certain sense in which a + + align:start position:0% +is there's a certain sense in which a + + + align:start position:0% +is there's a certain sense in which a +kind of artistic freedom was now granted + + align:start position:0% +kind of artistic freedom was now granted + + + align:start position:0% +kind of artistic freedom was now granted +to directors and to and to American + + align:start position:0% +to directors and to and to American + + + align:start position:0% +to directors and to and to American +films and on balance I think most view + + align:start position:0% +films and on balance I think most view + + + align:start position:0% +films and on balance I think most view +mo most uh uh folks look most scholars + + align:start position:0% +mo most uh uh folks look most scholars + + + align:start position:0% +mo most uh uh folks look most scholars +and and film buffs looking at the 1970s + + align:start position:0% +and and film buffs looking at the 1970s + + + align:start position:0% +and and film buffs looking at the 1970s +would certainly share my sense that it's + + align:start position:0% +would certainly share my sense that it's + + + align:start position:0% +would certainly share my sense that it's +a very remarkable decade but I think + + align:start position:0% +a very remarkable decade but I think + + + align:start position:0% +a very remarkable decade but I think +they might also share my sense that the + + align:start position:0% +they might also share my sense that the + + + align:start position:0% +they might also share my sense that the +films had given up more than they + + align:start position:0% +films had given up more than they + + + align:start position:0% +films had given up more than they +realized certainly more than they were + + align:start position:0% +realized certainly more than they were + + + align:start position:0% +realized certainly more than they were +conscious of that the shift in the in + + align:start position:0% +conscious of that the shift in the in + + + align:start position:0% +conscious of that the shift in the in +the in the what we might call the media + + align:start position:0% +the in the what we might call the media + + + align:start position:0% +the in the what we might call the media +ecology of the + + align:start position:0% +ecology of the + + + align:start position:0% +ecology of the +society which enabled this level of + + align:start position:0% +society which enabled this level of + + + align:start position:0% +society which enabled this level of +freedom for movies also carried with it + + align:start position:0% +freedom for movies also carried with it + + + align:start position:0% +freedom for movies also carried with it +a tremendous cost and remember how + + align:start position:0% +a tremendous cost and remember how + + + align:start position:0% +a tremendous cost and remember how +decisive the numbers are I've mentioned + + align:start position:0% +decisive the numbers are I've mentioned + + + align:start position:0% +decisive the numbers are I've mentioned +them a few times in this course at the + + align:start position:0% +them a few times in this course at the + + + align:start position:0% +them a few times in this course at the +height of the studio era twothirds of + + align:start position:0% +height of the studio era twothirds of + + + align:start position:0% +height of the studio era twothirds of +the country is going to the movies every + + align:start position:0% +the country is going to the movies every + + + align:start position:0% +the country is going to the movies every +week it's an habitual experience for + + align:start position:0% +week it's an habitual experience for + + + align:start position:0% +week it's an habitual experience for +most Americans both adults and children + + align:start position:0% +most Americans both adults and children + + + align:start position:0% +most Americans both adults and children +really by the time this system comes to + + align:start position:0% +really by the time this system comes to + + + align:start position:0% +really by the time this system comes to +an end after in this uh by the time the + + align:start position:0% +an end after in this uh by the time the + + + align:start position:0% +an end after in this uh by the time the +movies have been as I've suggested + + align:start position:0% +movies have been as I've suggested + + + align:start position:0% +movies have been as I've suggested +several times in the course supplanted + + align:start position:0% +several times in the course supplanted + + + align:start position:0% +several times in the course supplanted +by television as the new central + + align:start position:0% +by television as the new central + + + align:start position:0% +by television as the new central +storytelling system of the society by + + align:start position:0% +storytelling system of the society by + + + align:start position:0% +storytelling system of the society by +the time that occurs at the end of the + + align:start position:0% +the time that occurs at the end of the + + + align:start position:0% +the time that occurs at the end of the +60s most Americans are going to the + + align:start position:0% +60s most Americans are going to the + + + align:start position:0% +60s most Americans are going to the +movies only once a once a year and it's + + align:start position:0% +movies only once a once a year and it's + + + align:start position:0% +movies only once a once a year and it's +only particular + + align:start position:0% +only particular + + + align:start position:0% +only particular +subcultures teenagers for example who + + align:start position:0% +subcultures teenagers for example who + + + align:start position:0% +subcultures teenagers for example who +make a regular habit of going to the + + align:start position:0% +make a regular habit of going to the + + + align:start position:0% +make a regular habit of going to the +movies and a good deal of the triviality + + align:start position:0% +movies and a good deal of the triviality + + + align:start position:0% +movies and a good deal of the triviality +and + + align:start position:0% +and + + + align:start position:0% +and +superficiality of movies of the of many + + align:start position:0% +superficiality of movies of the of many + + + align:start position:0% +superficiality of movies of the of many +of the box office successes of the 80s + + align:start position:0% +of the box office successes of the 80s + + + align:start position:0% +of the box office successes of the 80s +and 90s from the American film industry + + align:start position:0% +and 90s from the American film industry + + + align:start position:0% +and 90s from the American film industry +is a direct function of the fact that + + align:start position:0% +is a direct function of the fact that + + + align:start position:0% +is a direct function of the fact that +the audience had dwindled from the whole + + align:start position:0% +the audience had dwindled from the whole + + + align:start position:0% +the audience had dwindled from the whole +society to particular subsets of the + + align:start position:0% +society to particular subsets of the + + + align:start position:0% +society to particular subsets of the +society. uh and the consequences the + + align:start position:0% +society. uh and the consequences the + + + align:start position:0% +society. uh and the consequences the +consequences for the uh nature of the + + align:start position:0% +consequences for the uh nature of the + + + align:start position:0% +consequences for the uh nature of the +the movie's sense of its connection to + + align:start position:0% +the movie's sense of its connection to + + + align:start position:0% +the movie's sense of its connection to +the society + + align:start position:0% +the society + + + align:start position:0% +the society +are powerful are + + align:start position:0% +are powerful are + + + align:start position:0% +are powerful are +profound. Well, we're going to explore + + align:start position:0% +profound. Well, we're going to explore + + + align:start position:0% +profound. Well, we're going to explore +aspects finally our final exploration of + + align:start position:0% +aspects finally our final exploration of + + + align:start position:0% +aspects finally our final exploration of +aspects of this topic comes in tonight's + + align:start position:0% +aspects of this topic comes in tonight's + + + align:start position:0% +aspects of this topic comes in tonight's +lecture and especially in the + + align:start position:0% +lecture and especially in the + + + align:start position:0% +lecture and especially in the +exemplary early 1970s film McCabe and + + align:start position:0% +exemplary early 1970s film McCabe and + + + align:start position:0% +exemplary early 1970s film McCabe and +Mrs. Miller that we're going to uh + + align:start position:0% +Mrs. Miller that we're going to uh + + + align:start position:0% +Mrs. Miller that we're going to uh +screen for you after my lecture. I want + + align:start position:0% +screen for you after my lecture. I want + + + align:start position:0% +screen for you after my lecture. I want +to begin by talking a little bit about + + align:start position:0% +to begin by talking a little bit about + + + align:start position:0% +to begin by talking a little bit about +Robert Alman's career. And uh I'll + + align:start position:0% +Robert Alman's career. And uh I'll + + + align:start position:0% +Robert Alman's career. And uh I'll +actually look at certain specific films + + align:start position:0% +actually look at certain specific films + + + align:start position:0% +actually look at certain specific films +and say a few things about them in a + + align:start position:0% +and say a few things about them in a + + + align:start position:0% +and say a few things about them in a +minute. But first, let me talk about + + align:start position:0% +minute. But first, let me talk about + + + align:start position:0% +minute. But first, let me talk about +what I take to be some of his not only + + align:start position:0% +what I take to be some of his not only + + + align:start position:0% +what I take to be some of his not only +the only ones, but some of his defining + + align:start position:0% +the only ones, but some of his defining + + + align:start position:0% +the only ones, but some of his defining +qualities as a director, signature + + align:start position:0% +qualities as a director, signature + + + align:start position:0% +qualities as a director, signature +features of his work. The first and most + + align:start position:0% +features of his work. The first and most + + + align:start position:0% +features of his work. The first and most +obvious to me is what we might call his + + align:start position:0% +obvious to me is what we might call his + + + align:start position:0% +obvious to me is what we might call his +moral skepticism. He really is in some + + align:start position:0% +moral skepticism. He really is in some + + + align:start position:0% +moral skepticism. He really is in some +respects temperamentally an outsider. + + align:start position:0% +respects temperamentally an outsider. + + + align:start position:0% +respects temperamentally an outsider. +And it's interesting to speculate, I + + align:start position:0% +And it's interesting to speculate, I + + + align:start position:0% +And it's interesting to speculate, I +think, about what might have happened to + + align:start position:0% +think, about what might have happened to + + + align:start position:0% +think, about what might have happened to +Robert Alman, a immensely gifted uh + + align:start position:0% +Robert Alman, a immensely gifted uh + + + align:start position:0% +Robert Alman, a immensely gifted uh +natural filmmaker, had he been born a + + align:start position:0% +natural filmmaker, had he been born a + + + align:start position:0% +natural filmmaker, had he been born a +generation earlier and had to actually + + align:start position:0% +generation earlier and had to actually + + + align:start position:0% +generation earlier and had to actually +to struggle with the requirements and + + align:start position:0% +to struggle with the requirements and + + + align:start position:0% +to struggle with the requirements and +responsibilities, the confinements of + + align:start position:0% +responsibilities, the confinements of + + + align:start position:0% +responsibilities, the confinements of +the studio system. But he luckily for + + align:start position:0% +the studio system. But he luckily for + + + align:start position:0% +the studio system. But he luckily for +Alman he emerges in a time when the + + align:start position:0% +Alman he emerges in a time when the + + + align:start position:0% +Alman he emerges in a time when the +tyranny of the studios and also the + + align:start position:0% +tyranny of the studios and also the + + + align:start position:0% +tyranny of the studios and also the +creative input of the studios has long + + align:start position:0% +creative input of the studios has long + + + align:start position:0% +creative input of the studios has long +has has has disappeared has gone away. + + align:start position:0% +has has has disappeared has gone away. + + + align:start position:0% +has has has disappeared has gone away. +Um and and and in that sense in that + + align:start position:0% +Um and and and in that sense in that + + + align:start position:0% +Um and and and in that sense in that +sense he represents a new kind of + + align:start position:0% +sense he represents a new kind of + + + align:start position:0% +sense he represents a new kind of +independent spirit uh in film making and + + align:start position:0% +independent spirit uh in film making and + + + align:start position:0% +independent spirit uh in film making and +and he resembles some of the other + + align:start position:0% +and he resembles some of the other + + + align:start position:0% +and he resembles some of the other +directors who come of age uh at roughly + + align:start position:0% +directors who come of age uh at roughly + + + align:start position:0% +directors who come of age uh at roughly +the same time. directors, some of whom I + + align:start position:0% +the same time. directors, some of whom I + + + align:start position:0% +the same time. directors, some of whom I +mentioned this afternoon like Scorsesei + + align:start position:0% +mentioned this afternoon like Scorsesei + + + align:start position:0% +mentioned this afternoon like Scorsesei +or Copala or Alan Pecula. + + align:start position:0% +or Copala or Alan Pecula. + + + align:start position:0% +or Copala or Alan Pecula. +Um, a second so, so one of his defining + + align:start position:0% +Um, a second so, so one of his defining + + + align:start position:0% +Um, a second so, so one of his defining +qualities is a kind of moral skepticism, + + align:start position:0% +qualities is a kind of moral skepticism, + + + align:start position:0% +qualities is a kind of moral skepticism, +a kind of sympathy we might call it, + + align:start position:0% +a kind of sympathy we might call it, + + + align:start position:0% +a kind of sympathy we might call it, +which is connected to his what we might + + align:start position:0% +which is connected to his what we might + + + align:start position:0% +which is connected to his what we might +call his sympathy for the marginal. Over + + align:start position:0% +call his sympathy for the marginal. Over + + + align:start position:0% +call his sympathy for the marginal. Over +and over again in Altman's films, we + + align:start position:0% +and over again in Altman's films, we + + + align:start position:0% +and over again in Altman's films, we +focus on either marginal figures in + + align:start position:0% +focus on either marginal figures in + + + align:start position:0% +focus on either marginal figures in +a who are part of a who are reluctantly + + align:start position:0% +a who are part of a who are reluctantly + + + align:start position:0% +a who are part of a who are reluctantly +or inadequately part of a larger + + align:start position:0% +or inadequately part of a larger + + + align:start position:0% +or inadequately part of a larger +community. uh or we focus on a community + + align:start position:0% +community. uh or we focus on a community + + + align:start position:0% +community. uh or we focus on a community +that itself is so dubious as a + + align:start position:0% +that itself is so dubious as a + + + align:start position:0% +that itself is so dubious as a +community, so damaged as a community, so + + align:start position:0% +community, so damaged as a community, so + + + align:start position:0% +community, so damaged as a community, so +infeebled and unlike the traditional + + align:start position:0% +infeebled and unlike the traditional + + + align:start position:0% +infeebled and unlike the traditional +communities that it's as if the + + align:start position:0% +communities that it's as if the + + + align:start position:0% +communities that it's as if the +community he treats itself, the + + align:start position:0% +community he treats itself, the + + + align:start position:0% +community he treats itself, the +societies or groupings that he finds + + align:start position:0% +societies or groupings that he finds + + + align:start position:0% +societies or groupings that he finds +interesting are full of are also in some + + align:start position:0% +interesting are full of are also in some + + + align:start position:0% +interesting are full of are also in some +deep way non-traditional communities. Uh + + align:start position:0% +deep way non-traditional communities. Uh + + + align:start position:0% +deep way non-traditional communities. Uh +and in fact in McCabe and Mrs. Miller uh + + align:start position:0% +and in fact in McCabe and Mrs. Miller uh + + + align:start position:0% +and in fact in McCabe and Mrs. Miller uh +most of the supporting cast were were + + align:start position:0% +most of the supporting cast were were + + + align:start position:0% +most of the supporting cast were were +literally members of a commune. they + + align:start position:0% +literally members of a commune. they + + + align:start position:0% +literally members of a commune. they +were members of a count of the + + align:start position:0% +were members of a count of the + + + align:start position:0% +were members of a count of the +counterculture. uh the ballad that is + + align:start position:0% +counterculture. uh the ballad that is + + + align:start position:0% +counterculture. uh the ballad that is +sung by the by by the great ballader and + + align:start position:0% +sung by the by by the great ballader and + + + align:start position:0% +sung by the by by the great ballader and +American singer Leonard Conn in the + + align:start position:0% +American singer Leonard Conn in the + + + align:start position:0% +American singer Leonard Conn in the +beginning of the film would have struck + + align:start position:0% +beginning of the film would have struck + + + align:start position:0% +beginning of the film would have struck +knowledgeable viewers as a deeply + + align:start position:0% +knowledgeable viewers as a deeply + + + align:start position:0% +knowledgeable viewers as a deeply +subversive gesture because think how + + align:start position:0% +subversive gesture because think how + + + align:start position:0% +subversive gesture because think how +often the western begins with a wi-i + + align:start position:0% +often the western begins with a wi-i + + + align:start position:0% +often the western begins with a wi-i +with a with a ballad with someone + + align:start position:0% +with a with a ballad with someone + + + align:start position:0% +with a with a ballad with someone +singing about as if you know the stories + + align:start position:0% +singing about as if you know the stories + + + align:start position:0% +singing about as if you know the stories +of the west have become so mythological + + align:start position:0% +of the west have become so mythological + + + align:start position:0% +of the west have become so mythological +that they're part of our song tradition + + align:start position:0% +that they're part of our song tradition + + + align:start position:0% +that they're part of our song tradition +our musical tradition which is true as + + align:start position:0% +our musical tradition which is true as + + + align:start position:0% +our musical tradition which is true as +well as our narrative tradition uh and + + align:start position:0% +well as our narrative tradition uh and + + + align:start position:0% +well as our narrative tradition uh and +many many uh classic westerns begin with + + align:start position:0% +many many uh classic westerns begin with + + + align:start position:0% +many many uh classic westerns begin with +a with a with a ballot of some kind. + + align:start position:0% +a with a with a ballot of some kind. + + + align:start position:0% +a with a with a ballot of some kind. +Uh, The Searchers has such a ballot, in + + align:start position:0% +Uh, The Searchers has such a ballot, in + + + align:start position:0% +Uh, The Searchers has such a ballot, in +fact, uh, as I as I as I hope you + + align:start position:0% +fact, uh, as I as I as I hope you + + + align:start position:0% +fact, uh, as I as I as I hope you +notice. Well, McCabe and Mrs. Miller + + align:start position:0% +notice. Well, McCabe and Mrs. Miller + + + align:start position:0% +notice. Well, McCabe and Mrs. Miller +begins with a ballot, as you'll see, but + + align:start position:0% +begins with a ballot, as you'll see, but + + + align:start position:0% +begins with a ballot, as you'll see, but +it's a subversive ballot. It's sung by a + + align:start position:0% +it's a subversive ballot. It's sung by a + + + align:start position:0% +it's a subversive ballot. It's sung by a +man, Leonard Conn, who's deeply + + align:start position:0% +man, Leonard Conn, who's deeply + + + align:start position:0% +man, Leonard Conn, who's deeply +associated with marijuana, with the with + + align:start position:0% +associated with marijuana, with the with + + + align:start position:0% +associated with marijuana, with the with +the counterculture, with striking out + + align:start position:0% +the counterculture, with striking out + + + align:start position:0% +the counterculture, with striking out +against authority, with writing anti-war + + align:start position:0% +against authority, with writing anti-war + + + align:start position:0% +against authority, with writing anti-war +songs. uh and uh there's a kind of of + + align:start position:0% +songs. uh and uh there's a kind of of + + + align:start position:0% +songs. uh and uh there's a kind of of +countercultural ambiencece, a kind of + + align:start position:0% +countercultural ambiencece, a kind of + + + align:start position:0% +countercultural ambiencece, a kind of +countercultural skepticism and sympathy + + align:start position:0% +countercultural skepticism and sympathy + + + align:start position:0% +countercultural skepticism and sympathy +for the margins in nearly all of Robert + + align:start position:0% +for the margins in nearly all of Robert + + + align:start position:0% +for the margins in nearly all of Robert +Alman's work. Uh a third quality. So, so + + align:start position:0% +Alman's work. Uh a third quality. So, so + + + align:start position:0% +Alman's work. Uh a third quality. So, so +his moral skepticism then uh could be + + align:start position:0% +his moral skepticism then uh could be + + + align:start position:0% +his moral skepticism then uh could be +said to have at least two dimensions. + + align:start position:0% +said to have at least two dimensions. + + + align:start position:0% +said to have at least two dimensions. +One is a what we might call an aesthetic + + align:start position:0% +One is a what we might call an aesthetic + + + align:start position:0% +One is a what we might call an aesthetic +dimension in which he is skeptical about + + align:start position:0% +dimension in which he is skeptical about + + + align:start position:0% +dimension in which he is skeptical about +the inherited strategies, belief + + align:start position:0% +the inherited strategies, belief + + + align:start position:0% +the inherited strategies, belief +systems, and even structures of earlier + + align:start position:0% +systems, and even structures of earlier + + + align:start position:0% +systems, and even structures of earlier +movies. And he actually we is in that + + align:start position:0% +movies. And he actually we is in that + + + align:start position:0% +movies. And he actually we is in that +sense aesthetically subversive, although + + align:start position:0% +sense aesthetically subversive, although + + + align:start position:0% +sense aesthetically subversive, although +very subtly so as I hope you'll see in + + align:start position:0% +very subtly so as I hope you'll see in + + + align:start position:0% +very subtly so as I hope you'll see in +tonight's film. He'll very often give + + align:start position:0% +tonight's film. He'll very often give + + + align:start position:0% +tonight's film. He'll very often give +you a film that seems on the surface to + + align:start position:0% +you a film that seems on the surface to + + + align:start position:0% +you a film that seems on the surface to +sustain and to recreate all the classic + + align:start position:0% +sustain and to recreate all the classic + + + align:start position:0% +sustain and to recreate all the classic +conventions of the genre in which he's + + align:start position:0% +conventions of the genre in which he's + + + align:start position:0% +conventions of the genre in which he's +working. And it's only when you look a + + align:start position:0% +working. And it's only when you look a + + + align:start position:0% +working. And it's only when you look a +little bit more closely that you realize + + align:start position:0% +little bit more closely that you realize + + + align:start position:0% +little bit more closely that you realize +that although the structural elements + + align:start position:0% +that although the structural elements + + + align:start position:0% +that although the structural elements +are there, they have been perverted or + + align:start position:0% +are there, they have been perverted or + + + align:start position:0% +are there, they have been perverted or +inverted so that so that they have in + + align:start position:0% +inverted so that so that they have in + + + align:start position:0% +inverted so that so that they have in +some sense enacted some a kind of moral + + align:start position:0% +some sense enacted some a kind of moral + + + align:start position:0% +some sense enacted some a kind of moral +uh migration uh and stand for virtually + + align:start position:0% +uh migration uh and stand for virtually + + + align:start position:0% +uh migration uh and stand for virtually +alternative beliefs, assumptions or + + align:start position:0% +alternative beliefs, assumptions or + + + align:start position:0% +alternative beliefs, assumptions or +values from what they might have what + + align:start position:0% +values from what they might have what + + + align:start position:0% +values from what they might have what +from what they normally are taken to + + align:start position:0% +from what they normally are taken to + + + align:start position:0% +from what they normally are taken to +stand for in the classic genre films on + + align:start position:0% +stand for in the classic genre films on + + + align:start position:0% +stand for in the classic genre films on +which Alman is borrowing or against + + align:start position:0% +which Alman is borrowing or against + + + align:start position:0% +which Alman is borrowing or against +which he is engaged in in a kind of in a + + align:start position:0% +which he is engaged in in a kind of in a + + + align:start position:0% +which he is engaged in in a kind of in a +kind of mockery or or at least uh + + align:start position:0% +kind of mockery or or at least uh + + + align:start position:0% +kind of mockery or or at least uh +hostile action of some kind. And I I + + align:start position:0% +hostile action of some kind. And I I + + + align:start position:0% +hostile action of some kind. And I I +think that McCabe and Mrs. Miller + + align:start position:0% +think that McCabe and Mrs. Miller + + + align:start position:0% +think that McCabe and Mrs. Miller +demonstrates this very dramatically + + align:start position:0% +demonstrates this very dramatically + + + align:start position:0% +demonstrates this very dramatically +although most of Alman's films have + + align:start position:0% +although most of Alman's films have + + + align:start position:0% +although most of Alman's films have +these qualities in some degree. The + + align:start position:0% +these qualities in some degree. The + + + align:start position:0% +these qualities in some degree. The +second quality of his moral skepticism + + align:start position:0% +second quality of his moral skepticism + + + align:start position:0% +second quality of his moral skepticism +is uh uh would be not + + align:start position:0% +is uh uh would be not + + + align:start position:0% +is uh uh would be not +now related to his tr to his aesthetic + + align:start position:0% +now related to his tr to his aesthetic + + + align:start position:0% +now related to his tr to his aesthetic +principles to his filmmaking practice + + align:start position:0% +principles to his filmmaking practice + + + align:start position:0% +principles to his filmmaking practice +but uh would be more broadly associated + + align:start position:0% +but uh would be more broadly associated + + + align:start position:0% +but uh would be more broadly associated +with his with his with his politics with + + align:start position:0% +with his with his with his politics with + + + align:start position:0% +with his with his with his politics with +his general ideological view of the + + align:start position:0% +his general ideological view of the + + + align:start position:0% +his general ideological view of the +world and even there especially there + + align:start position:0% +world and even there especially there + + + align:start position:0% +world and even there especially there +maybe Alman styled himself a rebel uh + + align:start position:0% +maybe Alman styled himself a rebel uh + + + align:start position:0% +maybe Alman styled himself a rebel uh +even when he was successful in Hollywood + + align:start position:0% +even when he was successful in Hollywood + + + align:start position:0% +even when he was successful in Hollywood +in his early in his early career when he + + align:start position:0% +in his early in his early career when he + + + align:start position:0% +in his early in his early career when he +was so mash was a box off of success in + + align:start position:0% +was so mash was a box off of success in + + + align:start position:0% +was so mash was a box off of success in +the the period of the the decade of 1970 + + align:start position:0% +the the period of the the decade of 1970 + + + align:start position:0% +the the period of the the decade of 1970 +through 80 is probably the richest + + align:start position:0% +through 80 is probably the richest + + + align:start position:0% +through 80 is probably the richest +decade of Alman's of Alman's career uh + + align:start position:0% +decade of Alman's of Alman's career uh + + + align:start position:0% +decade of Alman's of Alman's career uh +and and and in that time um um even + + align:start position:0% +and and and in that time um um even + + + align:start position:0% +and and and in that time um um even +though Alman was very successful and + + align:start position:0% +though Alman was very successful and + + + align:start position:0% +though Alman was very successful and +later he fell into disfavor with the + + align:start position:0% +later he fell into disfavor with the + + + align:start position:0% +later he fell into disfavor with the +Hollywood bosses and he spent some + + align:start position:0% +Hollywood bosses and he spent some + + + align:start position:0% +Hollywood bosses and he spent some +period of his career certain underground + + align:start position:0% +period of his career certain underground + + + align:start position:0% +period of his career certain underground +in a way not either not making movies at + + align:start position:0% +in a way not either not making movies at + + + align:start position:0% +in a way not either not making movies at +all directing plays in various places or + + align:start position:0% +all directing plays in various places or + + + align:start position:0% +all directing plays in various places or +making documentary films other or + + align:start position:0% +making documentary films other or + + + align:start position:0% +making documentary films other or +private films that were not released + + align:start position:0% +private films that were not released + + + align:start position:0% +private films that were not released +commercially. Uh then he makes he has a + + align:start position:0% +commercially. Uh then he makes he has a + + + align:start position:0% +commercially. Uh then he makes he has a +resurgence later before his before the + + align:start position:0% +resurgence later before his before the + + + align:start position:0% +resurgence later before his before the +end of his life. The last 10 or 15 years + + align:start position:0% +end of his life. The last 10 or 15 years + + + align:start position:0% +end of his life. The last 10 or 15 years +of his life are are are again successes + + align:start position:0% +of his life are are are again successes + + + align:start position:0% +of his life are are are again successes +involve successes at the box office. Um + + align:start position:0% +involve successes at the box office. Um + + + align:start position:0% +involve successes at the box office. Um +so so the the second aspect of his moral + + align:start position:0% +so so the the second aspect of his moral + + + align:start position:0% +so so the the second aspect of his moral +skepticism might be a kind of political + + align:start position:0% +skepticism might be a kind of political + + + align:start position:0% +skepticism might be a kind of political +skepticism and a skepticism a political + + align:start position:0% +skepticism and a skepticism a political + + + align:start position:0% +skepticism and a skepticism a political +skepticism both against the Hollywood + + align:start position:0% +skepticism both against the Hollywood + + + align:start position:0% +skepticism both against the Hollywood +system and then against the larger + + align:start position:0% +system and then against the larger + + + align:start position:0% +system and then against the larger +political structures of the society. Now + + align:start position:0% +political structures of the society. Now + + + align:start position:0% +political structures of the society. Now +remember his his subver his political + + align:start position:0% +remember his his subver his political + + + align:start position:0% +remember his his subver his political +subversiveness comes at a time when many + + align:start position:0% +subversiveness comes at a time when many + + + align:start position:0% +subversiveness comes at a time when many +honorable and normal people including + + align:start position:0% +honorable and normal people including + + + align:start position:0% +honorable and normal people including +your professor were subversive in some + + align:start position:0% +your professor were subversive in some + + + align:start position:0% +your professor were subversive in some +sense because it was a time when the + + align:start position:0% +sense because it was a time when the + + + align:start position:0% +sense because it was a time when the +country was at war in a war that many + + align:start position:0% +country was at war in a war that many + + + align:start position:0% +country was at war in a war that many +people in the country thought was uh + + align:start position:0% +people in the country thought was uh + + + align:start position:0% +people in the country thought was uh +unreasonable and wrong. Many people went + + align:start position:0% +unreasonable and wrong. Many people went + + + align:start position:0% +unreasonable and wrong. Many people went +to jail or or or or protested uh the the + + align:start position:0% +to jail or or or or protested uh the the + + + align:start position:0% +to jail or or or or protested uh the the +war and Alman was on the side of the + + align:start position:0% +war and Alman was on the side of the + + + align:start position:0% +war and Alman was on the side of the +anti-war forces. He was on the he was on + + align:start position:0% +anti-war forces. He was on the he was on + + + align:start position:0% +anti-war forces. He was on the he was on +the morally skeptical side about uh wars + + align:start position:0% +the morally skeptical side about uh wars + + + align:start position:0% +the morally skeptical side about uh wars +in about wars of choice in foreign in in + + align:start position:0% +in about wars of choice in foreign in in + + + align:start position:0% +in about wars of choice in foreign in in +in foreign environments. So he was both + + align:start position:0% +in foreign environments. So he was both + + + align:start position:0% +in foreign environments. So he was both +politically and uh um culturally a + + align:start position:0% +politically and uh um culturally a + + + align:start position:0% +politically and uh um culturally a +skeptic and aesthetically a skeptic and + + align:start position:0% +skeptic and aesthetically a skeptic and + + + align:start position:0% +skeptic and aesthetically a skeptic and +both qualities show up in his films in + + align:start position:0% +both qualities show up in his films in + + + align:start position:0% +both qualities show up in his films in +all kinds of remarkable ways. uh uh I've + + align:start position:0% +all kinds of remarkable ways. uh uh I've + + + align:start position:0% +all kinds of remarkable ways. uh uh I've +talked about how that leads to a kind of + + align:start position:0% +talked about how that leads to a kind of + + + align:start position:0% +talked about how that leads to a kind of +sympathy for marginality for the + + align:start position:0% +sympathy for marginality for the + + + align:start position:0% +sympathy for marginality for the +condition of marginality and for + + align:start position:0% +condition of marginality and for + + + align:start position:0% +condition of marginality and for +characters who belong on the margins of + + align:start position:0% +characters who belong on the margins of + + + align:start position:0% +characters who belong on the margins of +the society who live on the margins and + + align:start position:0% +the society who live on the margins and + + + align:start position:0% +the society who live on the margins and +he loved to make films often about about + + align:start position:0% +he loved to make films often about about + + + align:start position:0% +he loved to make films often about about +certain kinds of uh uh human communities + + align:start position:0% +certain kinds of uh uh human communities + + + align:start position:0% +certain kinds of uh uh human communities +subsets about human small versions of + + align:start position:0% +subsets about human small versions of + + + align:start position:0% +subsets about human small versions of +human society comprised entirely of + + align:start position:0% +human society comprised entirely of + + + align:start position:0% +human society comprised entirely of +misfits and marginal characters. He had + + align:start position:0% +misfits and marginal characters. He had + + + align:start position:0% +misfits and marginal characters. He had +a great and so and and he he even has a + + align:start position:0% +a great and so and and he he even has a + + + align:start position:0% +a great and so and and he he even has a +sympathy for what we might think of as + + align:start position:0% +sympathy for what we might think of as + + + align:start position:0% +sympathy for what we might think of as +unconventional appearance. So that you + + align:start position:0% +unconventional appearance. So that you + + + align:start position:0% +unconventional appearance. So that you +know many of the actors and especially + + align:start position:0% +know many of the actors and especially + + + align:start position:0% +know many of the actors and especially +the secondary background actors in his + + align:start position:0% +the secondary background actors in his + + + align:start position:0% +the secondary background actors in his +films might actually be in uh uh in ads + + align:start position:0% +films might actually be in uh uh in ads + + + align:start position:0% +films might actually be in uh uh in ads +for grotescery. He loves the grotesque + + align:start position:0% +for grotescery. He loves the grotesque + + + align:start position:0% +for grotescery. He loves the grotesque +uh and he often and and and at least his + + align:start position:0% +uh and he often and and and at least his + + + align:start position:0% +uh and he often and and and at least his +background characters often have a sort + + align:start position:0% +background characters often have a sort + + + align:start position:0% +background characters often have a sort +of grotesque element in them. There's a + + align:start position:0% +of grotesque element in them. There's a + + + align:start position:0% +of grotesque element in them. There's a +there's a there's a uh a a love of the + + align:start position:0% +there's a there's a uh a a love of the + + + align:start position:0% +there's a there's a uh a a love of the +non of the of of the of the weird and + + align:start position:0% +non of the of of the of the weird and + + + align:start position:0% +non of the of of the of the weird and +the strange in Altman that you can feel + + align:start position:0% +the strange in Altman that you can feel + + + align:start position:0% +the strange in Altman that you can feel +in his in in in in his films in his + + align:start position:0% +in his in in in in his films in his + + + align:start position:0% +in his in in in in his films in his +casting and in his subject + + align:start position:0% +casting and in his subject + + + align:start position:0% +casting and in his subject +matter. Another aspect of another thing + + align:start position:0% +matter. Another aspect of another thing + + + align:start position:0% +matter. Another aspect of another thing +that I would identify as a kind of + + align:start position:0% +that I would identify as a kind of + + + align:start position:0% +that I would identify as a kind of +defining quality for Robert Alman is the + + align:start position:0% +defining quality for Robert Alman is the + + + align:start position:0% +defining quality for Robert Alman is the +u relation in his films especially his + + align:start position:0% +u relation in his films especially his + + + align:start position:0% +u relation in his films especially his +mature films between plot and character. + + align:start position:0% +mature films between plot and character. + + + align:start position:0% +mature films between plot and character. +There's a tendency in it's an aspect of + + align:start position:0% +There's a tendency in it's an aspect of + + + align:start position:0% +There's a tendency in it's an aspect of +his skepticism. He doesn't like + + align:start position:0% +his skepticism. He doesn't like + + + align:start position:0% +his skepticism. He doesn't like +structures that control him. And from + + align:start position:0% +structures that control him. And from + + + align:start position:0% +structures that control him. And from +one angle, if you think about + + align:start position:0% +one angle, if you think about + + + align:start position:0% +one angle, if you think about +storytelling or narrative, uh the uh + + align:start position:0% +storytelling or narrative, uh the uh + + + align:start position:0% +storytelling or narrative, uh the uh +plot is a kind of controlling feature. + + align:start position:0% +plot is a kind of controlling feature. + + + align:start position:0% +plot is a kind of controlling feature. +It it it it it especially if you allow + + align:start position:0% +It it it it it especially if you allow + + + align:start position:0% +It it it it it especially if you allow +the plot to take to take take the + + align:start position:0% +the plot to take to take take the + + + align:start position:0% +the plot to take to take take the +foreground of the to to assume a + + align:start position:0% +foreground of the to to assume a + + + align:start position:0% +foreground of the to to assume a +position in the foreground of the text, + + align:start position:0% +position in the foreground of the text, + + + align:start position:0% +position in the foreground of the text, +the the plot can become a kind of iron + + align:start position:0% +the the plot can become a kind of iron + + + align:start position:0% +the the plot can become a kind of iron +hand controlling the choices the + + align:start position:0% +hand controlling the choices the + + + align:start position:0% +hand controlling the choices the +director make makes controlling what can + + align:start position:0% +director make makes controlling what can + + + align:start position:0% +director make makes controlling what can +happen to the characters. uh and certain + + align:start position:0% +happen to the characters. uh and certain + + + align:start position:0% +happen to the characters. uh and certain +forms of action adventure. What happens + + align:start position:0% +forms of action adventure. What happens + + + align:start position:0% +forms of action adventure. What happens +next? The sequence of events and the + + align:start position:0% +next? The sequence of events and the + + + align:start position:0% +next? The sequence of events and the +visual excitement of watching those + + align:start position:0% +visual excitement of watching those + + + align:start position:0% +visual excitement of watching those +events is virtually the only interest + + align:start position:0% +events is virtually the only interest + + + align:start position:0% +events is virtually the only interest +you have in such in in in film. Those + + align:start position:0% +you have in such in in in film. Those + + + align:start position:0% +you have in such in in in film. Those +totally ploted films uh tend to have + + align:start position:0% +totally ploted films uh tend to have + + + align:start position:0% +totally ploted films uh tend to have +stereotyped or flat characters in them. + + align:start position:0% +stereotyped or flat characters in them. + + + align:start position:0% +stereotyped or flat characters in them. +But Alman, even when he embraces certain + + align:start position:0% +But Alman, even when he embraces certain + + + align:start position:0% +But Alman, even when he embraces certain +genre principles that require what looks + + align:start position:0% +genre principles that require what looks + + + align:start position:0% +genre principles that require what looks +like a conventional linear plot, is + + align:start position:0% +like a conventional linear plot, is + + + align:start position:0% +like a conventional linear plot, is +often tries to subvert the linearity of + + align:start position:0% +often tries to subvert the linearity of + + + align:start position:0% +often tries to subvert the linearity of +his plot. There's a kind of digressive + + align:start position:0% +his plot. There's a kind of digressive + + + align:start position:0% +his plot. There's a kind of digressive +or or + + align:start position:0% +or or + + + align:start position:0% +or or +or + + align:start position:0% +or + + + align:start position:0% +or +dissenting uh nonlinear tendency in + + align:start position:0% +dissenting uh nonlinear tendency in + + + align:start position:0% +dissenting uh nonlinear tendency in +Altman's work. You can sense it in + + align:start position:0% +Altman's work. You can sense it in + + + align:start position:0% +Altman's work. You can sense it in +McCabe and Mrs. Miller, although it + + align:start position:0% +McCabe and Mrs. Miller, although it + + + align:start position:0% +McCabe and Mrs. Miller, although it +doesn't emerge really totally fully + + align:start position:0% +doesn't emerge really totally fully + + + align:start position:0% +doesn't emerge really totally fully +until later in his career, especially a + + align:start position:0% +until later in his career, especially a + + + align:start position:0% +until later in his career, especially a +little bit later in his career. The + + align:start position:0% +little bit later in his career. The + + + align:start position:0% +little bit later in his career. The +fullest embodiment of this non-plot + + align:start position:0% +fullest embodiment of this non-plot + + + align:start position:0% +fullest embodiment of this non-plot +principle of this preference for + + align:start position:0% +principle of this preference for + + + align:start position:0% +principle of this preference for +character over plot I think is probably + + align:start position:0% +character over plot I think is probably + + + align:start position:0% +character over plot I think is probably +the film Nashville 1975 + + align:start position:0% +the film Nashville 1975 + + + align:start position:0% +the film Nashville 1975 +uh in which you see an in which Alman + + align:start position:0% +uh in which you see an in which Alman + + + align:start position:0% +uh in which you see an in which Alman +displays an immense range of characters + + align:start position:0% +displays an immense range of characters + + + align:start position:0% +displays an immense range of characters +to us and skips from one character to + + align:start position:0% +to us and skips from one character to + + + align:start position:0% +to us and skips from one character to +another to another. There are certain + + align:start position:0% +another to another. There are certain + + + align:start position:0% +another to another. There are certain +centers of interest. They seem to have + + align:start position:0% +centers of interest. They seem to have + + + align:start position:0% +centers of interest. They seem to have +no connection to each other. And you sit + + align:start position:0% +no connection to each other. And you sit + + + align:start position:0% +no connection to each other. And you sit +there in the film, when the film first + + align:start position:0% +there in the film, when the film first + + + align:start position:0% +there in the film, when the film first +came out, it actually elicited a number + + align:start position:0% +came out, it actually elicited a number + + + align:start position:0% +came out, it actually elicited a number +of negative reviews from reviewers who + + align:start position:0% +of negative reviews from reviewers who + + + align:start position:0% +of negative reviews from reviewers who +were angry about the fact that it that + + align:start position:0% +were angry about the fact that it that + + + align:start position:0% +were angry about the fact that it that +the film took virtually its whole length + + align:start position:0% +the film took virtually its whole length + + + align:start position:0% +the film took virtually its whole length +to make clear that in fact there was a + + align:start position:0% +to make clear that in fact there was a + + + align:start position:0% +to make clear that in fact there was a +connection between these characters. The + + align:start position:0% +connection between these characters. The + + + align:start position:0% +connection between these characters. The +complaint against the film was it was + + align:start position:0% +complaint against the film was it was + + + align:start position:0% +complaint against the film was it was +plotless. Well, that wasn't exactly + + align:start position:0% +plotless. Well, that wasn't exactly + + + align:start position:0% +plotless. Well, that wasn't exactly +true. It wasn't plotless. In fact, all + + align:start position:0% +true. It wasn't plotless. In fact, all + + + align:start position:0% +true. It wasn't plotless. In fact, all +the lines of the plot do come together + + align:start position:0% +the lines of the plot do come together + + + align:start position:0% +the lines of the plot do come together +toward the end of the film. But the + + align:start position:0% +toward the end of the film. But the + + + align:start position:0% +toward the end of the film. But the +truth is that Alman is at least as + + align:start position:0% +truth is that Alman is at least as + + + align:start position:0% +truth is that Alman is at least as +interested in digression as he is as he + + align:start position:0% +interested in digression as he is as he + + + align:start position:0% +interested in digression as he is as he +is in linear in linear progression. And + + align:start position:0% +is in linear in linear progression. And + + + align:start position:0% +is in linear in linear progression. And +there is a sense in which his films like + + align:start position:0% +there is a sense in which his films like + + + align:start position:0% +there is a sense in which his films like +to pause and savor what's going on + + align:start position:0% +to pause and savor what's going on + + + align:start position:0% +to pause and savor what's going on +around them. And if you as you're + + align:start position:0% +around them. And if you as you're + + + align:start position:0% +around them. And if you as you're +watching McCabe and Mrs. Miller, one of + + align:start position:0% +watching McCabe and Mrs. Miller, one of + + + align:start position:0% +watching McCabe and Mrs. Miller, one of +the things you might ask yourself at at + + align:start position:0% +the things you might ask yourself at at + + + align:start position:0% +the things you might ask yourself at at +a certain level is what's the what's the + + align:start position:0% +a certain level is what's the what's the + + + align:start position:0% +a certain level is what's the what's the +throughine of the story? I mean, and in + + align:start position:0% +throughine of the story? I mean, and in + + + align:start position:0% +throughine of the story? I mean, and in +fact, it feels when you're watching + + align:start position:0% +fact, it feels when you're watching + + + align:start position:0% +fact, it feels when you're watching +McCabe and Mrs. Miller as if it doesn't + + align:start position:0% +McCabe and Mrs. Miller as if it doesn't + + + align:start position:0% +McCabe and Mrs. Miller as if it doesn't +have at least a conventional western + + align:start position:0% +have at least a conventional western + + + align:start position:0% +have at least a conventional western +plot. As the film goes on, you begin to + + align:start position:0% +plot. As the film goes on, you begin to + + + align:start position:0% +plot. As the film goes on, you begin to +realize, yes, there is the story here is + + align:start position:0% +realize, yes, there is the story here is + + + align:start position:0% +realize, yes, there is the story here is +about the growth of this town. It's + + align:start position:0% +about the growth of this town. It's + + + align:start position:0% +about the growth of this town. It's +really the it's really in that sense the + + align:start position:0% +really the it's really in that sense the + + + align:start position:0% +really the it's really in that sense the +film the the film really is a a founding + + align:start position:0% +film the the film really is a a founding + + + align:start position:0% +film the the film really is a a founding +myth, an ironic mocking founding myth. + + align:start position:0% +myth, an ironic mocking founding myth. + + + align:start position:0% +myth, an ironic mocking founding myth. +But there's a long while you're watching + + align:start position:0% +But there's a long while you're watching + + + align:start position:0% +But there's a long while you're watching +the film, you're interested in McCabe + + align:start position:0% +the film, you're interested in McCabe + + + align:start position:0% +the film, you're interested in McCabe +and you're interested in some of the + + align:start position:0% +and you're interested in some of the + + + align:start position:0% +and you're interested in some of the +other minor characters in the town, but + + align:start position:0% +other minor characters in the town, but + + + align:start position:0% +other minor characters in the town, but +it's hard to identify what the actual + + align:start position:0% +it's hard to identify what the actual + + + align:start position:0% +it's hard to identify what the actual +subject of the film is at first. Well, + + align:start position:0% +subject of the film is at first. Well, + + + align:start position:0% +subject of the film is at first. Well, +Alman likes to leave his audiences uh in + + align:start position:0% +Alman likes to leave his audiences uh in + + + align:start position:0% +Alman likes to leave his audiences uh in +a little bit of confusion of that sort. + + align:start position:0% +a little bit of confusion of that sort. + + + align:start position:0% +a little bit of confusion of that sort. +In other words, he doesn't like to he + + align:start position:0% +In other words, he doesn't like to he + + + align:start position:0% +In other words, he doesn't like to he +doesn't like to satisfy the narrow + + align:start position:0% +doesn't like to satisfy the narrow + + + align:start position:0% +doesn't like to satisfy the narrow +desire to have a clear linear plot. Uh + + align:start position:0% +desire to have a clear linear plot. Uh + + + align:start position:0% +desire to have a clear linear plot. Uh +he he prefers some principles of + + align:start position:0% +he he prefers some principles of + + + align:start position:0% +he he prefers some principles of +digression. And one of the reasons that + + align:start position:0% +digression. And one of the reasons that + + + align:start position:0% +digression. And one of the reasons that +he does apart from the fact that he + + align:start position:0% +he does apart from the fact that he + + + align:start position:0% +he does apart from the fact that he +wants to savor the experience of the + + align:start position:0% +wants to savor the experience of the + + + align:start position:0% +wants to savor the experience of the +world and he he's uh attentive to so + + align:start position:0% +world and he he's uh attentive to so + + + align:start position:0% +world and he he's uh attentive to so +many aspects of experience that he wants + + align:start position:0% +many aspects of experience that he wants + + + align:start position:0% +many aspects of experience that he wants +to often bring all of them into the film + + align:start position:0% +to often bring all of them into the film + + + align:start position:0% +to often bring all of them into the film +he's very interested in sound for + + align:start position:0% +he's very interested in sound for + + + align:start position:0% +he's very interested in sound for +example in this in the in the way sound + + align:start position:0% +example in this in the in the way sound + + + align:start position:0% +example in this in the in the way sound +operates in the world. Uh and he does + + align:start position:0% +operates in the world. Uh and he does + + + align:start position:0% +operates in the world. Uh and he does +odd things with his soundtrack as you'll + + align:start position:0% +odd things with his soundtrack as you'll + + + align:start position:0% +odd things with his soundtrack as you'll +see in McCabe and Mrs. Miller. I'll come + + align:start position:0% +see in McCabe and Mrs. Miller. I'll come + + + align:start position:0% +see in McCabe and Mrs. Miller. I'll come +back to this in a minute. Uh + + align:start position:0% +back to this in a minute. Uh + + + align:start position:0% +back to this in a minute. Uh +so + + align:start position:0% +so + + + align:start position:0% +so +he he he his his + + align:start position:0% +he he he his his + + + align:start position:0% +he he he his his +his preoccupation then is with trying to + + align:start position:0% +his preoccupation then is with trying to + + + align:start position:0% +his preoccupation then is with trying to +create a situation in which character + + align:start position:0% +create a situation in which character + + + align:start position:0% +create a situation in which character +unfolds and he'll always sacrifice what + + align:start position:0% +unfolds and he'll always sacrifice what + + + align:start position:0% +unfolds and he'll always sacrifice what +might what what a what a more + + align:start position:0% +might what what a what a more + + + align:start position:0% +might what what a what a more +actionoriented director might think was + + align:start position:0% +actionoriented director might think was + + + align:start position:0% +actionoriented director might think was +the most important thing in order to + + align:start position:0% +the most important thing in order to + + + align:start position:0% +the most important thing in order to +explore character more fully. Now, one + + align:start position:0% +explore character more fully. Now, one + + + align:start position:0% +explore character more fully. Now, one +one can say that one one very broad way + + align:start position:0% +one can say that one one very broad way + + + align:start position:0% +one can say that one one very broad way +of dividing narratives, as I may have + + align:start position:0% +of dividing narratives, as I may have + + + align:start position:0% +of dividing narratives, as I may have +suggested earlier in the semester to you + + align:start position:0% +suggested earlier in the semester to you + + + align:start position:0% +suggested earlier in the semester to you +is is a distinction between plot- driven + + align:start position:0% +is is a distinction between plot- driven + + + align:start position:0% +is is a distinction between plot- driven +and character-driven stories. And one of + + align:start position:0% +and character-driven stories. And one of + + + align:start position:0% +and character-driven stories. And one of +the things one can see happening in + + align:start position:0% +the things one can see happening in + + + align:start position:0% +the things one can see happening in +Altman's film, again, it's another + + align:start position:0% +Altman's film, again, it's another + + + align:start position:0% +Altman's film, again, it's another +marker of the fact that Altman is + + align:start position:0% +marker of the fact that Altman is + + + align:start position:0% +marker of the fact that Altman is +operating in a in a uh cinematic + + align:start position:0% +operating in a in a uh cinematic + + + align:start position:0% +operating in a in a uh cinematic +environment that no longer has + + align:start position:0% +environment that no longer has + + + align:start position:0% +environment that no longer has +the conservative aesthetic constraints + + align:start position:0% +the conservative aesthetic constraints + + + align:start position:0% +the conservative aesthetic constraints +that are placed upon a consensus system. + + align:start position:0% +that are placed upon a consensus system. + + + align:start position:0% +that are placed upon a consensus system. +So he's he can explore these kinds of + + align:start position:0% +So he's he can explore these kinds of + + + align:start position:0% +So he's he can explore these kinds of +possibilities more fully than than uh or + + align:start position:0% +possibilities more fully than than uh or + + + align:start position:0% +possibilities more fully than than uh or +or can explore them at all. In fact, in + + align:start position:0% +or can explore them at all. In fact, in + + + align:start position:0% +or can explore them at all. In fact, in +some cases, he couldn't have even have + + align:start position:0% +some cases, he couldn't have even have + + + align:start position:0% +some cases, he couldn't have even have +looked down these territories, look + + align:start position:0% +looked down these territories, look + + + align:start position:0% +looked down these territories, look +looked down these pathways if he'd been + + align:start position:0% +looked down these pathways if he'd been + + + align:start position:0% +looked down these pathways if he'd been +a conventional um uh studio director. Um + + align:start position:0% +a conventional um uh studio director. Um + + + align:start position:0% +a conventional um uh studio director. Um +so so uh a distinctive feature then of + + align:start position:0% +so so uh a distinctive feature then of + + + align:start position:0% +so so uh a distinctive feature then of +the way he works is this tension between + + align:start position:0% +the way he works is this tension between + + + align:start position:0% +the way he works is this tension between +plot and character and the and the + + align:start position:0% +plot and character and the and the + + + align:start position:0% +plot and character and the and the +emphasis that that Alman will almost + + align:start position:0% +emphasis that that Alman will almost + + + align:start position:0% +emphasis that that Alman will almost +always put on character. the way he'll + + align:start position:0% +always put on character. the way he'll + + + align:start position:0% +always put on character. the way he'll +even subvert your interest in what is + + align:start position:0% +even subvert your interest in what is + + + align:start position:0% +even subvert your interest in what is +going to happen next sometime in the + + align:start position:0% +going to happen next sometime in the + + + align:start position:0% +going to happen next sometime in the +film. And as you're watching McCabe, you + + align:start position:0% +film. And as you're watching McCabe, you + + + align:start position:0% +film. And as you're watching McCabe, you +might sort of think about that what's + + align:start position:0% +might sort of think about that what's + + + align:start position:0% +might sort of think about that what's +you don't ever feel that the film is + + align:start position:0% +you don't ever feel that the film is + + + align:start position:0% +you don't ever feel that the film is +flagging. You always are interested in + + align:start position:0% +flagging. You always are interested in + + + align:start position:0% +flagging. You always are interested in +what happens, but after a while, you + + align:start position:0% +what happens, but after a while, you + + + align:start position:0% +what happens, but after a while, you +suddenly realize that you're not being + + align:start position:0% +suddenly realize that you're not being + + + align:start position:0% +suddenly realize that you're not being +carried along by the momentum of story + + align:start position:0% +carried along by the momentum of story + + + align:start position:0% +carried along by the momentum of story +itself in the way you are in a normal + + align:start position:0% +itself in the way you are in a normal + + + align:start position:0% +itself in the way you are in a normal +film or in what you would think of as a + + align:start position:0% +film or in what you would think of as a + + + align:start position:0% +film or in what you would think of as a +conventional film. And McCabe is only a + + align:start position:0% +conventional film. And McCabe is only a + + + align:start position:0% +conventional film. And McCabe is only a +minor version of this. As I say, + + align:start position:0% +minor version of this. As I say, + + + align:start position:0% +minor version of this. As I say, +Nashville is a much more dramatic is a + + align:start position:0% +Nashville is a much more dramatic is a + + + align:start position:0% +Nashville is a much more dramatic is a +much more dramatic instance of this. Um, + + align:start position:0% +much more dramatic instance of this. Um, + + + align:start position:0% +much more dramatic instance of this. Um, +finally, another distinctive, not + + align:start position:0% +finally, another distinctive, not + + + align:start position:0% +finally, another distinctive, not +unique, but distinctive feature of + + align:start position:0% +unique, but distinctive feature of + + + align:start position:0% +unique, but distinctive feature of +Alman's work, and this occurs especially + + align:start position:0% +Alman's work, and this occurs especially + + + align:start position:0% +Alman's work, and this occurs especially +uh powerfully as his career uh + + align:start position:0% +uh powerfully as his career uh + + + align:start position:0% +uh powerfully as his career uh +continues. It's part it's really a kind + + align:start position:0% +continues. It's part it's really a kind + + + align:start position:0% +continues. It's part it's really a kind +of you can sense it earlier, but it + + align:start position:0% +of you can sense it earlier, but it + + + align:start position:0% +of you can sense it earlier, but it +actually becomes a dominant topic later + + align:start position:0% +actually becomes a dominant topic later + + + align:start position:0% +actually becomes a dominant topic later +in his career after he's very + + align:start position:0% +in his career after he's very + + + align:start position:0% +in his career after he's very +successful. He has great confidence in + + align:start position:0% +successful. He has great confidence in + + + align:start position:0% +successful. He has great confidence in +him. by the end of his last decade of + + align:start position:0% +him. by the end of his last decade of + + + align:start position:0% +him. by the end of his last decade of +his life he's conceived of I think as a + + align:start position:0% +his life he's conceived of I think as a + + + align:start position:0% +his life he's conceived of I think as a +kind of master movie maker and he finds + + align:start position:0% +kind of master movie maker and he finds + + + align:start position:0% +kind of master movie maker and he finds +it very easy to get people to appear in + + align:start position:0% +it very easy to get people to appear in + + + align:start position:0% +it very easy to get people to appear in +his films and uh that's where this + + align:start position:0% +his films and uh that's where this + + + align:start position:0% +his films and uh that's where this +principle comes in most fully he's + + align:start position:0% +principle comes in most fully he's + + + align:start position:0% +principle comes in most fully he's +interested in the in blurring the + + align:start position:0% +interested in the in blurring the + + + align:start position:0% +interested in the in blurring the +distinction between fiction and reality + + align:start position:0% +distinction between fiction and reality + + + align:start position:0% +distinction between fiction and reality +and there and and in fact in some of his + + align:start position:0% +and there and and in fact in some of his + + + align:start position:0% +and there and and in fact in some of his +films I think Nashville is the first one + + align:start position:0% +films I think Nashville is the first one + + + align:start position:0% +films I think Nashville is the first one +in which this happens and then he he + + align:start position:0% +in which this happens and then he he + + + align:start position:0% +in which this happens and then he he +returns to this this trick or this + + align:start position:0% +returns to this this trick or this + + + align:start position:0% +returns to this this trick or this +strategy much later in his career in a + + align:start position:0% +strategy much later in his career in a + + + align:start position:0% +strategy much later in his career in a +whole series films in Nashville. There + + align:start position:0% +whole series films in Nashville. There + + + align:start position:0% +whole series films in Nashville. There +are some performers who are playing + + align:start position:0% +are some performers who are playing + + + align:start position:0% +are some performers who are playing +themselves. They're not fictional + + align:start position:0% +themselves. They're not fictional + + + align:start position:0% +themselves. They're not fictional +characters. Uh some of some of them are + + align:start position:0% +characters. Uh some of some of them are + + + align:start position:0% +characters. Uh some of some of them are +famous singers and so forth. And they + + align:start position:0% +famous singers and so forth. And they + + + align:start position:0% +famous singers and so forth. And they +they they appear as themselves. + + align:start position:0% +they they appear as themselves. + + + align:start position:0% +they they appear as themselves. +Nashville is about the American music + + align:start position:0% +Nashville is about the American music + + + align:start position:0% +Nashville is about the American music +scene and also about the turmoil of + + align:start position:0% +scene and also about the turmoil of + + + align:start position:0% +scene and also about the turmoil of +American society in the 1970s. Uh and so + + align:start position:0% +American society in the 1970s. Uh and so + + + align:start position:0% +American society in the 1970s. Uh and so +many of the people who many of the + + align:start position:0% +many of the people who many of the + + + align:start position:0% +many of the people who many of the +people who appear in the film uh are + + align:start position:0% +people who appear in the film uh are + + + align:start position:0% +people who appear in the film uh are +playing musicians, singers and so or uh + + align:start position:0% +playing musicians, singers and so or uh + + + align:start position:0% +playing musicians, singers and so or uh +songwriters, performers. Uh but there + + align:start position:0% +songwriters, performers. Uh but there + + + align:start position:0% +songwriters, performers. Uh but there +are actually some real performers who + + align:start position:0% +are actually some real performers who + + + align:start position:0% +are actually some real performers who +are recognized by the audience because + + align:start position:0% +are recognized by the audience because + + + align:start position:0% +are recognized by the audience because +they're relatively famous who play + + align:start position:0% +they're relatively famous who play + + + align:start position:0% +they're relatively famous who play +themselves. Well, this mingling of this + + align:start position:0% +themselves. Well, this mingling of this + + + align:start position:0% +themselves. Well, this mingling of this +or this blurring of the distinction of + + align:start position:0% +or this blurring of the distinction of + + + align:start position:0% +or this blurring of the distinction of +the difference between fiction and + + align:start position:0% +the difference between fiction and + + + align:start position:0% +the difference between fiction and +reality. This this um uh mingling of + + align:start position:0% +reality. This this um uh mingling of + + + align:start position:0% +reality. This this um uh mingling of +fictional with real characters becomes a + + align:start position:0% +fictional with real characters becomes a + + + align:start position:0% +fictional with real characters becomes a +very distinctive feature of Altman's + + align:start position:0% +very distinctive feature of Altman's + + + align:start position:0% +very distinctive feature of Altman's +work later in his career. And very + + align:start position:0% +work later in his career. And very + + + align:start position:0% +work later in his career. And very +quickly then, what I'd like to do is + + align:start position:0% +quickly then, what I'd like to do is + + + align:start position:0% +quickly then, what I'd like to do is +show you a list of some of his films. + + align:start position:0% +show you a list of some of his films. + + + align:start position:0% +show you a list of some of his films. +You can put that up now, Greg. Um and I + + align:start position:0% +You can put that up now, Greg. Um and I + + + align:start position:0% +You can put that up now, Greg. Um and I +want to say not something about all of + + align:start position:0% +want to say not something about all of + + + align:start position:0% +want to say not something about all of +them. This is not a list a full list of + + align:start position:0% +them. This is not a list a full list of + + + align:start position:0% +them. This is not a list a full list of +his films and you can see there's a long + + align:start position:0% +his films and you can see there's a long + + + align:start position:0% +his films and you can see there's a long +interregnum of almost a decade where he + + align:start position:0% +interregnum of almost a decade where he + + + align:start position:0% +interregnum of almost a decade where he +makes some films. I just haven't + + align:start position:0% +makes some films. I just haven't + + + align:start position:0% +makes some films. I just haven't +bothered to list them. This is not a + + align:start position:0% +bothered to list them. This is not a + + + align:start position:0% +bothered to list them. This is not a +complete listing of his films although I + + align:start position:0% +complete listing of his films although I + + + align:start position:0% +complete listing of his films although I +think it is a complete listing of his + + align:start position:0% +think it is a complete listing of his + + + align:start position:0% +think it is a complete listing of his +films made in the 1970s. And I did that + + align:start position:0% +films made in the 1970s. And I did that + + + align:start position:0% +films made in the 1970s. And I did that +partly because I wanted you to see what + + align:start position:0% +partly because I wanted you to see what + + + align:start position:0% +partly because I wanted you to see what +a prolific and productive decade this + + align:start position:0% +a prolific and productive decade this + + + align:start position:0% +a prolific and productive decade this +was for Alman. But also because I + + align:start position:0% +was for Alman. But also because I + + + align:start position:0% +was for Alman. But also because I +thought you might be interested in + + align:start position:0% +thought you might be interested in + + + align:start position:0% +thought you might be interested in +seeing how many titles register with + + align:start position:0% +seeing how many titles register with + + + align:start position:0% +seeing how many titles register with +you. Even if you've not seen the films, + + align:start position:0% +you. Even if you've not seen the films, + + + align:start position:0% +you. Even if you've not seen the films, +you probably have heard of some of these + + align:start position:0% +you probably have heard of some of these + + + align:start position:0% +you probably have heard of some of these +films because they're among the most + + align:start position:0% +films because they're among the most + + + align:start position:0% +films because they're among the most +innovative and important films of the + + align:start position:0% +innovative and important films of the + + + align:start position:0% +innovative and important films of the +second American films of the second half + + align:start position:0% +second American films of the second half + + + align:start position:0% +second American films of the second half +of the 20th century. I want to say a + + align:start position:0% +of the 20th century. I want to say a + + + align:start position:0% +of the 20th century. I want to say a +couple of things about some of these + + align:start position:0% +couple of things about some of these + + + align:start position:0% +couple of things about some of these +films. Um, you you've already seen the + + align:start position:0% +films. Um, you you've already seen the + + + align:start position:0% +films. Um, you you've already seen the +ending of The Long Goodbye and you know + + align:start position:0% +ending of The Long Goodbye and you know + + + align:start position:0% +ending of The Long Goodbye and you know +what a deeply subversive version of the + + align:start position:0% +what a deeply subversive version of the + + + align:start position:0% +what a deeply subversive version of the +detective genre that film is. Uh, I want + + align:start position:0% +detective genre that film is. Uh, I want + + + align:start position:0% +detective genre that film is. Uh, I want +to say a word about California Split + + align:start position:0% +to say a word about California Split + + + align:start position:0% +to say a word about California Split +because in some ways it's a film that + + align:start position:0% +because in some ways it's a film that + + + align:start position:0% +because in some ways it's a film that +most fully embodies this principle of + + align:start position:0% +most fully embodies this principle of + + + align:start position:0% +most fully embodies this principle of +being interested in the marginal. Uh, + + align:start position:0% +being interested in the marginal. Uh, + + + align:start position:0% +being interested in the marginal. Uh, +California Split is a gamblers movie and + + align:start position:0% +California Split is a gamblers movie and + + + align:start position:0% +California Split is a gamblers movie and +u Elliot Ghoul that sort of shooken and + + align:start position:0% +u Elliot Ghoul that sort of shooken and + + + align:start position:0% +u Elliot Ghoul that sort of shooken and +jiven + + align:start position:0% +jiven + + + align:start position:0% +jiven +uh figure of anti-heroic irony that you + + align:start position:0% +uh figure of anti-heroic irony that you + + + align:start position:0% +uh figure of anti-heroic irony that you +saw at the end of of uh the long goodbye + + align:start position:0% +saw at the end of of uh the long goodbye + + + align:start position:0% +saw at the end of of uh the long goodbye +is the star of California Split as well. + + align:start position:0% +is the star of California Split as well. + + + align:start position:0% +is the star of California Split as well. +And almost the entire film, a large part + + align:start position:0% +And almost the entire film, a large part + + + align:start position:0% +And almost the entire film, a large part +of the film actually takes place at the + + align:start position:0% +of the film actually takes place at the + + + align:start position:0% +of the film actually takes place at the +racetrack and in gambling environments. + + align:start position:0% +racetrack and in gambling environments. + + + align:start position:0% +racetrack and in gambling environments. +The the the climax of the film is a trip + + align:start position:0% +The the the climax of the film is a trip + + + align:start position:0% +The the the climax of the film is a trip +to Las Vegas where our our uh hero has a + + align:start position:0% +to Las Vegas where our our uh hero has a + + + align:start position:0% +to Las Vegas where our our uh hero has a +tremendous run of + + align:start position:0% +tremendous run of + + + align:start position:0% +tremendous run of +luck near nearly breaks the bank. Um and + + align:start position:0% +luck near nearly breaks the bank. Um and + + + align:start position:0% +luck near nearly breaks the bank. Um and +and uh um California Split follows the + + align:start position:0% +and uh um California Split follows the + + + align:start position:0% +and uh um California Split follows the +fortunes of these two gamblers. + + align:start position:0% +fortunes of these two gamblers. + + + align:start position:0% +fortunes of these two gamblers. +Uh it's hard even fully to follow the + + align:start position:0% +Uh it's hard even fully to follow the + + + align:start position:0% +Uh it's hard even fully to follow the +the chronology of the film. Sometimes + + align:start position:0% +the chronology of the film. Sometimes + + + align:start position:0% +the chronology of the film. Sometimes +you lose sense of how many how much time + + align:start position:0% +you lose sense of how many how much time + + + align:start position:0% +you lose sense of how many how much time +has passed. Uh there are many things + + align:start position:0% +has passed. Uh there are many things + + + align:start position:0% +has passed. Uh there are many things +about the characters that are vague and + + align:start position:0% +about the characters that are vague and + + + align:start position:0% +about the characters that are vague and +and unclear. It's also a film + + align:start position:0% +and unclear. It's also a film + + + align:start position:0% +and unclear. It's also a film +parathetically show you a kind of this + + align:start position:0% +parathetically show you a kind of this + + + align:start position:0% +parathetically show you a kind of this +is a trivial detail but it's always + + align:start position:0% +is a trivial detail but it's always + + + align:start position:0% +is a trivial detail but it's always +struck me as a mark of of of Altman's + + align:start position:0% +struck me as a mark of of of Altman's + + + align:start position:0% +struck me as a mark of of of Altman's +perversity. Every woman in the film is + + align:start position:0% +perversity. Every woman in the film is + + + align:start position:0% +perversity. Every woman in the film is +named + + align:start position:0% +named + + + align:start position:0% +named +Barbara. I I I especially noticed this + + align:start position:0% +Barbara. I I I especially noticed this + + + align:start position:0% +Barbara. I I I especially noticed this +because my wife is named Barbara. But + + align:start position:0% +because my wife is named Barbara. But + + + align:start position:0% +because my wife is named Barbara. But +um it's all and I think the perversity + + align:start position:0% +um it's all and I think the perversity + + + align:start position:0% +um it's all and I think the perversity +had to do with Alman's idea that uh u he + + align:start position:0% +had to do with Alman's idea that uh u he + + + align:start position:0% +had to do with Alman's idea that uh u he +I'm creating a kind of slice of life + + align:start position:0% +I'm creating a kind of slice of life + + + align:start position:0% +I'm creating a kind of slice of life +movie. Thieves Like us uh is is a + + align:start position:0% +movie. Thieves Like us uh is is a + + + align:start position:0% +movie. Thieves Like us uh is is a +particularly characteristic Alman film + + align:start position:0% +particularly characteristic Alman film + + + align:start position:0% +particularly characteristic Alman film +not only because it has a kind of + + align:start position:0% +not only because it has a kind of + + + align:start position:0% +not only because it has a kind of +plotless amorphousness to it when you + + align:start position:0% +plotless amorphousness to it when you + + + align:start position:0% +plotless amorphousness to it when you +first look at it even though it it has + + align:start position:0% +first look at it even though it it has + + + align:start position:0% +first look at it even though it it has +great excitement in it and a great + + align:start position:0% +great excitement in it and a great + + + align:start position:0% +great excitement in it and a great +emphasis on character and a great + + align:start position:0% +emphasis on character and a great + + + align:start position:0% +emphasis on character and a great +emphasis on marginal weird people who + + align:start position:0% +emphasis on marginal weird people who + + + align:start position:0% +emphasis on marginal weird people who +sort of are not solid citizens in any + + align:start position:0% +sort of are not solid citizens in any + + + align:start position:0% +sort of are not solid citizens in any +way. But it also uh carries another + + align:start position:0% +way. But it also uh carries another + + + align:start position:0% +way. But it also uh carries another +signature feature of Alman's uh work + + align:start position:0% +signature feature of Alman's uh work + + + align:start position:0% +signature feature of Alman's uh work +which I did not list on the on my + + align:start position:0% +which I did not list on the on my + + + align:start position:0% +which I did not list on the on my +outline and that is he was very prone to + + align:start position:0% +outline and that is he was very prone to + + + align:start position:0% +outline and that is he was very prone to +allow his actors to improvise when they + + align:start position:0% +allow his actors to improvise when they + + + align:start position:0% +allow his actors to improvise when they +got in front of the camera or not + + align:start position:0% +got in front of the camera or not + + + align:start position:0% +got in front of the camera or not +literally when he was shooting but they + + align:start position:0% +literally when he was shooting but they + + + align:start position:0% +literally when he was shooting but they +would improvise work something out he + + align:start position:0% +would improvise work something out he + + + align:start position:0% +would improvise work something out he +didn't work from a set script or he + + align:start position:0% +didn't work from a set script or he + + + align:start position:0% +didn't work from a set script or he +would allow departures from his script + + align:start position:0% +would allow departures from his script + + + align:start position:0% +would allow departures from his script +very that's one of very s easily and + + align:start position:0% +very that's one of very s easily and + + + align:start position:0% +very that's one of very s easily and +quickly one of the reasons he loved to + + align:start position:0% +quickly one of the reasons he loved to + + + align:start position:0% +quickly one of the reasons he loved to +work with with Elliot Gould was Elliot + + align:start position:0% +work with with Elliot Gould was Elliot + + + align:start position:0% +work with with Elliot Gould was Elliot +Gould was a particularly gifted + + align:start position:0% +Gould was a particularly gifted + + + align:start position:0% +Gould was a particularly gifted +improvisational actor + + align:start position:0% +improvisational actor + + + align:start position:0% +improvisational actor +and and there's a kind of authenticity + + align:start position:0% +and and there's a kind of authenticity + + + align:start position:0% +and and there's a kind of authenticity +in the performances in most of Altman's + + align:start position:0% +in the performances in most of Altman's + + + align:start position:0% +in the performances in most of Altman's +films that partly come from the fact + + align:start position:0% +films that partly come from the fact + + + align:start position:0% +films that partly come from the fact +that he was deeply interested in trying + + align:start position:0% +that he was deeply interested in trying + + + align:start position:0% +that he was deeply interested in trying +to create an illusion of authenticity + + align:start position:0% +to create an illusion of authenticity + + + align:start position:0% +to create an illusion of authenticity +that was much more intense and much more + + align:start position:0% +that was much more intense and much more + + + align:start position:0% +that was much more intense and much more +compelling than what the traditional + + align:start position:0% +compelling than what the traditional + + + align:start position:0% +compelling than what the traditional +Hollywood movie offers. He really wasn't + + align:start position:0% +Hollywood movie offers. He really wasn't + + + align:start position:0% +Hollywood movie offers. He really wasn't +interested in the in the u uh fancy + + align:start position:0% +interested in the in the u uh fancy + + + align:start position:0% +interested in the in the u uh fancy +lighting and the ver and and and the + + align:start position:0% +lighting and the ver and and and the + + + align:start position:0% +lighting and the ver and and and the +very elaborate patterning uh of the + + align:start position:0% +very elaborate patterning uh of the + + + align:start position:0% +very elaborate patterning uh of the +Hollywood film. There was something he + + align:start position:0% +Hollywood film. There was something he + + + align:start position:0% +Hollywood film. There was something he +he he liked grit and dirt and and uh + + align:start position:0% +he he liked grit and dirt and and uh + + + align:start position:0% +he he liked grit and dirt and and uh +imperfection and you can feel these + + align:start position:0% +imperfection and you can feel these + + + align:start position:0% +imperfection and you can feel these +elements in uh in his work and you can + + align:start position:0% +elements in uh in his work and you can + + + align:start position:0% +elements in uh in his work and you can +especially feel it in the often in the + + align:start position:0% +especially feel it in the often in the + + + align:start position:0% +especially feel it in the often in the +performances of his of his actors who + + align:start position:0% +performances of his of his actors who + + + align:start position:0% +performances of his of his actors who +loved working the the ones who liked + + align:start position:0% +loved working the the ones who liked + + + align:start position:0% +loved working the the ones who liked +working with him really loved it because + + align:start position:0% +working with him really loved it because + + + align:start position:0% +working with him really loved it because +it gave them a significant creative a + + align:start position:0% +it gave them a significant creative a + + + align:start position:0% +it gave them a significant creative a +part uh in the film itself. So th + + align:start position:0% +part uh in the film itself. So th + + + align:start position:0% +part uh in the film itself. So th +Thieves Like Us is a relatively minor + + align:start position:0% +Thieves Like Us is a relatively minor + + + align:start position:0% +Thieves Like Us is a relatively minor +Altman film in certain ways, but it + + align:start position:0% +Altman film in certain ways, but it + + + align:start position:0% +Altman film in certain ways, but it +shows his interest in character, his + + align:start position:0% +shows his interest in character, his + + + align:start position:0% +shows his interest in character, his +lack of interest in plot, and his love + + align:start position:0% +lack of interest in plot, and his love + + + align:start position:0% +lack of interest in plot, and his love +of the marginal and of and of course of + + align:start position:0% +of the marginal and of and of course of + + + align:start position:0% +of the marginal and of and of course of +improvisational uh performance. I've + + align:start position:0% +improvisational uh performance. I've + + + align:start position:0% +improvisational uh performance. I've +mentioned Nashville already. Maybe I + + align:start position:0% +mentioned Nashville already. Maybe I + + + align:start position:0% +mentioned Nashville already. Maybe I +should say a little bit more about it + + align:start position:0% +should say a little bit more about it + + + align:start position:0% +should say a little bit more about it +simply because it really was an + + align:start position:0% +simply because it really was an + + + align:start position:0% +simply because it really was an +unbelievably influential film. This film + + align:start position:0% +unbelievably influential film. This film + + + align:start position:0% +unbelievably influential film. This film +seemed to desert conventional plot uh + + align:start position:0% +seemed to desert conventional plot uh + + + align:start position:0% +seemed to desert conventional plot uh +and and uh almost in an arbitrary way + + align:start position:0% +and and uh almost in an arbitrary way + + + align:start position:0% +and and uh almost in an arbitrary way +for its first half simply to look at + + align:start position:0% +for its first half simply to look at + + + align:start position:0% +for its first half simply to look at +various characters who had musical + + align:start position:0% +various characters who had musical + + + align:start position:0% +various characters who had musical +ambitions and were bound for Nashville. + + align:start position:0% +ambitions and were bound for Nashville. + + + align:start position:0% +ambitions and were bound for Nashville. +That was sort of the only through line + + align:start position:0% +That was sort of the only through line + + + align:start position:0% +That was sort of the only through line +in the film. Everyone's going to + + align:start position:0% +in the film. Everyone's going to + + + align:start position:0% +in the film. Everyone's going to +Nashville. But and and you really + + align:start position:0% +Nashville. But and and you really + + + align:start position:0% +Nashville. But and and you really +wondered as you were watching the film, + + align:start position:0% +wondered as you were watching the film, + + + align:start position:0% +wondered as you were watching the film, +what could these characters possibly + + align:start position:0% +what could these characters possibly + + + align:start position:0% +what could these characters possibly +have to do with each other? Will they + + align:start position:0% +have to do with each other? Will they + + + align:start position:0% +have to do with each other? Will they +ever come together? Uh should they come + + align:start position:0% +ever come together? Uh should they come + + + align:start position:0% +ever come together? Uh should they come +together? And it's a very artful film in + + align:start position:0% +together? And it's a very artful film in + + + align:start position:0% +together? And it's a very artful film in +part because of the way it plays with + + align:start position:0% +part because of the way it plays with + + + align:start position:0% +part because of the way it plays with +the reader's frustration about a about a + + align:start position:0% +the reader's frustration about a about a + + + align:start position:0% +the reader's frustration about a about a +linear plot. And and in fact the re one + + align:start position:0% +linear plot. And and in fact the re one + + + align:start position:0% +linear plot. And and in fact the re one +of the things one of the things the + + align:start position:0% +of the things one of the things the + + + align:start position:0% +of the things one of the things the +movie does is it makes you aware as a + + align:start position:0% +movie does is it makes you aware as a + + + align:start position:0% +movie does is it makes you aware as a +viewer of the of the extent to which uh + + align:start position:0% +viewer of the of the extent to which uh + + + align:start position:0% +viewer of the of the extent to which uh +a linear plot is a kind of crutch you + + align:start position:0% +a linear plot is a kind of crutch you + + + align:start position:0% +a linear plot is a kind of crutch you +lean on when you're watching a movie. It + + align:start position:0% +lean on when you're watching a movie. It + + + align:start position:0% +lean on when you're watching a movie. It +helps you sort of get through the film. + + align:start position:0% +helps you sort of get through the film. + + + align:start position:0% +helps you sort of get through the film. +If you're confused about other stuff, + + align:start position:0% +If you're confused about other stuff, + + + align:start position:0% +If you're confused about other stuff, +you always have that sort of through + + align:start position:0% +you always have that sort of through + + + align:start position:0% +you always have that sort of through +line to grasp onto. And when Alman takes + + align:start position:0% +line to grasp onto. And when Alman takes + + + align:start position:0% +line to grasp onto. And when Alman takes +that away from you or seems to take it + + align:start position:0% +that away from you or seems to take it + + + align:start position:0% +that away from you or seems to take it +away from you, he immerses you in the in + + align:start position:0% +away from you, he immerses you in the in + + + align:start position:0% +away from you, he immerses you in the in +the moral texture of his movie, in the + + align:start position:0% +the moral texture of his movie, in the + + + align:start position:0% +the moral texture of his movie, in the +psychological and political meanings of + + align:start position:0% +psychological and political meanings of + + + align:start position:0% +psychological and political meanings of +his movies in a way that would not be + + align:start position:0% +his movies in a way that would not be + + + align:start position:0% +his movies in a way that would not be +true if you were fixated on what happens + + align:start position:0% +true if you were fixated on what happens + + + align:start position:0% +true if you were fixated on what happens +next, what happens next, what happens + + align:start position:0% +next, what happens next, what happens + + + align:start position:0% +next, what happens next, what happens +next. Um, I want to say a couple of + + align:start position:0% +next. Um, I want to say a couple of + + + align:start position:0% +next. Um, I want to say a couple of +words. I I've mentioned Buffalo Bill and + + align:start position:0% +words. I I've mentioned Buffalo Bill and + + + align:start position:0% +words. I I've mentioned Buffalo Bill and +the Indians to you earlier, and it's + + align:start position:0% +the Indians to you earlier, and it's + + + align:start position:0% +the Indians to you earlier, and it's +it's one of his most subversive + + align:start position:0% +it's one of his most subversive + + + align:start position:0% +it's one of his most subversive +westerns. It's interesting that he went + + align:start position:0% +westerns. It's interesting that he went + + + align:start position:0% +westerns. It's interesting that he went +back to the western genre uh in this + + align:start position:0% +back to the western genre uh in this + + + align:start position:0% +back to the western genre uh in this +very creative period of his career and I + + align:start position:0% +very creative period of his career and I + + + align:start position:0% +very creative period of his career and I +think one of the reasons was he + + align:start position:0% +think one of the reasons was he + + + align:start position:0% +think one of the reasons was he +understood that there were aspects of + + align:start position:0% +understood that there were aspects of + + + align:start position:0% +understood that there were aspects of +the genre he hadn't made made enough fun + + align:start position:0% +the genre he hadn't made made enough fun + + + align:start position:0% +the genre he hadn't made made enough fun +of. There are aspects of he hadn't quite + + align:start position:0% +of. There are aspects of he hadn't quite + + + align:start position:0% +of. There are aspects of he hadn't quite +destroyed all he hadn't quite ruined all + + align:start position:0% +destroyed all he hadn't quite ruined all + + + align:start position:0% +destroyed all he hadn't quite ruined all +the sacred truths to you use a phrase + + align:start position:0% +the sacred truths to you use a phrase + + + align:start position:0% +the sacred truths to you use a phrase +that I'm going to refer to later when we + + align:start position:0% +that I'm going to refer to later when we + + + align:start position:0% +that I'm going to refer to later when we +that I have on my outline for McCabe and + + align:start position:0% +that I have on my outline for McCabe and + + + align:start position:0% +that I have on my outline for McCabe and +Mrs. Miller. So he wanted to return + + align:start position:0% +Mrs. Miller. So he wanted to return + + + align:start position:0% +Mrs. Miller. So he wanted to return +again. And that of course is the film + + align:start position:0% +again. And that of course is the film + + + align:start position:0% +again. And that of course is the film +that has uh uh that of course is the + + align:start position:0% +that has uh uh that of course is the + + + align:start position:0% +that has uh uh that of course is the +story uh about those Wild West shows I + + align:start position:0% +story uh about those Wild West shows I + + + align:start position:0% +story uh about those Wild West shows I +spoke about last week. And it uh the + + align:start position:0% +spoke about last week. And it uh the + + + align:start position:0% +spoke about last week. And it uh the +episode he uh dramatizes actually + + align:start position:0% +episode he uh dramatizes actually + + + align:start position:0% +episode he uh dramatizes actually +involves a comical and also very + + align:start position:0% +involves a comical and also very + + + align:start position:0% +involves a comical and also very +disturbing confrontation or interaction + + align:start position:0% +disturbing confrontation or interaction + + + align:start position:0% +disturbing confrontation or interaction +between great chief Sitting Bull and a + + align:start position:0% +between great chief Sitting Bull and a + + + align:start position:0% +between great chief Sitting Bull and a +drunken Buffalo Bill and an an + + align:start position:0% +drunken Buffalo Bill and an an + + + align:start position:0% +drunken Buffalo Bill and an an +absolutely corrupt drunken morally + + align:start position:0% +absolutely corrupt drunken morally + + + align:start position:0% +absolutely corrupt drunken morally +muddled uh uh uh uh Indian hero. uh the + + align:start position:0% +muddled uh uh uh uh Indian hero. uh the + + + align:start position:0% +muddled uh uh uh uh Indian hero. uh the +played by incidentally played by Paul + + align:start position:0% +played by incidentally played by Paul + + + align:start position:0% +played by incidentally played by Paul +Newman who had played you know upright + + align:start position:0% +Newman who had played you know upright + + + align:start position:0% +Newman who had played you know upright +upright heroes uh frequently before + + align:start position:0% +upright heroes uh frequently before + + + align:start position:0% +upright heroes uh frequently before +um and uh let me jump down a little bit + + align:start position:0% +um and uh let me jump down a little bit + + + align:start position:0% +um and uh let me jump down a little bit +and say one word the films I've listed + + align:start position:0% +and say one word the films I've listed + + + align:start position:0% +and say one word the films I've listed +from 88 on are are are more recent films + + align:start position:0% +from 88 on are are are more recent films + + + align:start position:0% +from 88 on are are are more recent films +all of them relative successes uh my + + align:start position:0% +all of them relative successes uh my + + + align:start position:0% +all of them relative successes uh my +view is that his greatest work is in the + + align:start position:0% +view is that his greatest work is in the + + + align:start position:0% +view is that his greatest work is in the +70s but these later films I've listed + + align:start position:0% +70s but these later films I've listed + + + align:start position:0% +70s but these later films I've listed +are interesting but I wanted to say a + + align:start position:0% +are interesting but I wanted to say a + + + align:start position:0% +are interesting but I wanted to say a +word about Tanner and Tanner on Tanner + + align:start position:0% +word about Tanner and Tanner on Tanner + + + align:start position:0% +word about Tanner and Tanner on Tanner +because they show how imaginative and + + align:start position:0% +because they show how imaginative and + + + align:start position:0% +because they show how imaginative and +experimental. He remained even in his + + align:start position:0% +experimental. He remained even in his + + + align:start position:0% +experimental. He remained even in his +later years as a director. As some of + + align:start position:0% +later years as a director. As some of + + + align:start position:0% +later years as a director. As some of +you may know, Tanner is not a movie. It + + align:start position:0% +you may know, Tanner is not a movie. It + + + align:start position:0% +you may know, Tanner is not a movie. It +was a television series. And it was a + + align:start position:0% +was a television series. And it was a + + + align:start position:0% +was a television series. And it was a +very interesting television series in + + align:start position:0% +very interesting television series in + + + align:start position:0% +very interesting television series in +which we could see Robert Alman further + + align:start position:0% +which we could see Robert Alman further + + + align:start position:0% +which we could see Robert Alman further +developing this interest he had in this + + align:start position:0% +developing this interest he had in this + + + align:start position:0% +developing this interest he had in this +confusion between reality and fiction. + + align:start position:0% +confusion between reality and fiction. + + + align:start position:0% +confusion between reality and fiction. +He uh uh he see I think he was he was + + align:start position:0% +He uh uh he see I think he was he was + + + align:start position:0% +He uh uh he see I think he was he was +right about this in some ways. He felt + + align:start position:0% +right about this in some ways. He felt + + + align:start position:0% +right about this in some ways. He felt +that I mean partly I think he felt that + + align:start position:0% +that I mean partly I think he felt that + + + align:start position:0% +that I mean partly I think he felt that +uh that because we live in such a media + + align:start position:0% +uh that because we live in such a media + + + align:start position:0% +uh that because we live in such a media +saturated culture the difference and + + align:start position:0% +saturated culture the difference and + + + align:start position:0% +saturated culture the difference and +because of the power that celebrity + + align:start position:0% +because of the power that celebrity + + + align:start position:0% +because of the power that celebrity +seems to exercise in our culture. This + + align:start position:0% +seems to exercise in our culture. This + + + align:start position:0% +seems to exercise in our culture. This +celebrity was always one of often one of + + align:start position:0% +celebrity was always one of often one of + + + align:start position:0% +celebrity was always one of often one of +Robert Alman's subplots. It's a key uh + + align:start position:0% +Robert Alman's subplots. It's a key uh + + + align:start position:0% +Robert Alman's subplots. It's a key uh +subject in in in uh in Nashville and he + + align:start position:0% +subject in in in uh in Nashville and he + + + align:start position:0% +subject in in in uh in Nashville and he +returns to it uh in a in in a number of + + align:start position:0% +returns to it uh in a in in a number of + + + align:start position:0% +returns to it uh in a in in a number of +his later films as well. + + align:start position:0% + + + + align:start position:0% + +Um, the trick of Tanner is that it + + align:start position:0% +Um, the trick of Tanner is that it + + + align:start position:0% +Um, the trick of Tanner is that it +purports to be a + + align:start position:0% +purports to be a + + + align:start position:0% +purports to be a +documentary following a presidential a + + align:start position:0% +documentary following a presidential a + + + align:start position:0% +documentary following a presidential a +Democratic presidential candidate in the + + align:start position:0% +Democratic presidential candidate in the + + + align:start position:0% +Democratic presidential candidate in the +Democratic primaries of what 1988 and + + align:start position:0% +Democratic primaries of what 1988 and + + + align:start position:0% +Democratic primaries of what 1988 and +the and he got an actor, one of his + + align:start position:0% +the and he got an actor, one of his + + + align:start position:0% +the and he got an actor, one of his +favorite actors. He actually has a the + + align:start position:0% +favorite actors. He actually has a the + + + align:start position:0% +favorite actors. He actually has a the +actor, this actor, I think his name is + + align:start position:0% +actor, this actor, I think his name is + + + align:start position:0% +actor, this actor, I think his name is +Michael Murphy. He has a role in McCabe + + align:start position:0% +Michael Murphy. He has a role in McCabe + + + align:start position:0% +Michael Murphy. He has a role in McCabe +and Mrs. Miller. is one of the he's the + + align:start position:0% +and Mrs. Miller. is one of the he's the + + + align:start position:0% +and Mrs. Miller. is one of the he's the +younger company representative who comes + + align:start position:0% +younger company representative who comes + + + align:start position:0% +younger company representative who comes +near the end of the film to negotiate + + align:start position:0% +near the end of the film to negotiate + + + align:start position:0% +near the end of the film to negotiate +with McCabe about selling his interest + + align:start position:0% +with McCabe about selling his interest + + + align:start position:0% +with McCabe about selling his interest +in the town and uh he's a wonderful + + align:start position:0% +in the town and uh he's a wonderful + + + align:start position:0% +in the town and uh he's a wonderful +actor this guy Michael Murphy and and + + align:start position:0% +actor this guy Michael Murphy and and + + + align:start position:0% +actor this guy Michael Murphy and and +like many of the actors who appear in + + align:start position:0% +like many of the actors who appear in + + + align:start position:0% +like many of the actors who appear in +Alman's films you have a sense if you've + + align:start position:0% +Alman's films you have a sense if you've + + + align:start position:0% +Alman's films you have a sense if you've +watched Alman's films over your over the + + align:start position:0% +watched Alman's films over your over the + + + align:start position:0% +watched Alman's films over your over the +whole of his career that there was a + + align:start position:0% +whole of his career that there was a + + + align:start position:0% +whole of his career that there was a +repatory company that kept coming back + + align:start position:0% +repatory company that kept coming back + + + align:start position:0% +repatory company that kept coming back +to work with him again and again Elliot + + align:start position:0% +to work with him again and again Elliot + + + align:start position:0% +to work with him again and again Elliot +Gould must be in six or seven of his + + align:start position:0% +Gould must be in six or seven of his + + + align:start position:0% +Gould must be in six or seven of his +movies. Michael Murphy in at least three + + align:start position:0% +movies. Michael Murphy in at least three + + + align:start position:0% +movies. Michael Murphy in at least three +or four. Uh he he has favorite actresses + + align:start position:0% +or four. Uh he he has favorite actresses + + + align:start position:0% +or four. Uh he he has favorite actresses +too who love to work with them. I think + + align:start position:0% +too who love to work with them. I think + + + align:start position:0% +too who love to work with them. I think +Julie Christie is one uh the star of + + align:start position:0% +Julie Christie is one uh the star of + + + align:start position:0% +Julie Christie is one uh the star of +tonight's film. Uh Warren Batty is + + align:start position:0% +tonight's film. Uh Warren Batty is + + + align:start position:0% +tonight's film. Uh Warren Batty is +another of his favorite actors although + + align:start position:0% +another of his favorite actors although + + + align:start position:0% +another of his favorite actors although +Batty was such a big star that could + + align:start position:0% +Batty was such a big star that could + + + align:start position:0% +Batty was such a big star that could +generate his own films he didn't need + + align:start position:0% +generate his own films he didn't need + + + align:start position:0% +generate his own films he didn't need +Alman as much as some of these others + + align:start position:0% +Alman as much as some of these others + + + align:start position:0% +Alman as much as some of these others +actors did. Uh in any case, what what + + align:start position:0% +actors did. Uh in any case, what what + + + align:start position:0% +actors did. Uh in any case, what what +the trick of Tanner, the strategy of + + align:start position:0% +the trick of Tanner, the strategy of + + + align:start position:0% +the trick of Tanner, the strategy of +Tanner, the really memorable thing about + + align:start position:0% +Tanner, the really memorable thing about + + + align:start position:0% +Tanner, the really memorable thing about +Tanner, it was I think a very + + align:start position:0% +Tanner, it was I think a very + + + align:start position:0% +Tanner, it was I think a very +significant television event uh is that + + align:start position:0% +significant television event uh is that + + + align:start position:0% +significant television event uh is that +is that the fictional Tanner played by + + align:start position:0% +is that the fictional Tanner played by + + + align:start position:0% +is that the fictional Tanner played by +this guy Michael Murphy u um who and + + align:start position:0% +this guy Michael Murphy u um who and + + + align:start position:0% +this guy Michael Murphy u um who and +treated with complete seriousness. I + + align:start position:0% +treated with complete seriousness. I + + + align:start position:0% +treated with complete seriousness. I +mostly saw him through the eyes of his + + align:start position:0% +mostly saw him through the eyes of his + + + align:start position:0% +mostly saw him through the eyes of his +press managers, his press handlers. So + + align:start position:0% +press managers, his press handlers. So + + + align:start position:0% +press managers, his press handlers. So +there was a great cynicism about the + + align:start position:0% +there was a great cynicism about the + + + align:start position:0% +there was a great cynicism about the +political process uh and the gossip of + + align:start position:0% +political process uh and the gossip of + + + align:start position:0% +political process uh and the gossip of +the journalists about the presidential + + align:start position:0% +the journalists about the presidential + + + align:start position:0% +the journalists about the presidential +candidate. But the + + align:start position:0% +candidate. But the + + + align:start position:0% +candidate. But the +real genius of Tanner was that we saw + + align:start position:0% +real genius of Tanner was that we saw + + + align:start position:0% +real genius of Tanner was that we saw +Tanner on the stump with the real + + align:start position:0% +Tanner on the stump with the real + + + align:start position:0% +Tanner on the stump with the real +presidential candidates and they + + align:start position:0% +presidential candidates and they + + + align:start position:0% +presidential candidates and they +cooperated. The real presidential + + align:start position:0% +cooperated. The real presidential + + + align:start position:0% +cooperated. The real presidential +candidates cooperated in the making of + + align:start position:0% +candidates cooperated in the making of + + + align:start position:0% +candidates cooperated in the making of +the film and there were actually scenes + + align:start position:0% +the film and there were actually scenes + + + align:start position:0% +the film and there were actually scenes +in which the fictional Tanner gets into + + align:start position:0% +in which the fictional Tanner gets into + + + align:start position:0% +in which the fictional Tanner gets into +a conversation with Michael Dukakus + + align:start position:0% +a conversation with Michael Dukakus + + + align:start position:0% +a conversation with Michael Dukakus +who's who's also running to be president + + align:start position:0% +who's who's also running to be president + + + align:start position:0% +who's who's also running to be president +there. and and then there's an interview + + align:start position:0% +there. and and then there's an interview + + + align:start position:0% +there. and and then there's an interview +with Michael Dukakus in which Michael + + align:start position:0% +with Michael Dukakus in which Michael + + + align:start position:0% +with Michael Dukakus in which Michael +Dukakus assesses the danger that that + + align:start position:0% +Dukakus assesses the danger that that + + + align:start position:0% +Dukakus assesses the danger that that +Tanner represents to his candidacy. So + + align:start position:0% +Tanner represents to his candidacy. So + + + align:start position:0% +Tanner represents to his candidacy. So +what what what and when when he returned + + align:start position:0% +what what what and when when he returned + + + align:start position:0% +what what what and when when he returned +to Tanner on Tanner in 2004, he + + align:start position:0% +to Tanner on Tanner in 2004, he + + + align:start position:0% +to Tanner on Tanner in 2004, he +elaborated this theory. Now Tanner is a + + align:start position:0% +elaborated this theory. Now Tanner is a + + + align:start position:0% +elaborated this theory. Now Tanner is a +retired politician and he's helping his + + align:start position:0% +retired politician and he's helping his + + + align:start position:0% +retired politician and he's helping his +daughter who's a documentary filmmaker + + align:start position:0% +daughter who's a documentary filmmaker + + + align:start position:0% +daughter who's a documentary filmmaker +do a new political film, but now it's + + align:start position:0% +do a new political film, but now it's + + + align:start position:0% +do a new political film, but now it's +about the contemporary the the the it + + align:start position:0% +about the contemporary the the the it + + + align:start position:0% +about the contemporary the the the it +was about the the last election about + + align:start position:0% +was about the the last election about + + + align:start position:0% +was about the the last election about +the the the last or the nomination the + + align:start position:0% +the the the last or the nomination the + + + align:start position:0% +the the the last or the nomination the +the the the nomination just I guess it + + align:start position:0% +the the the nomination just I guess it + + + align:start position:0% +the the the nomination just I guess it +was the the the first Bush election was + + align:start position:0% +was the the the first Bush election was + + + align:start position:0% +was the the the first Bush election was +what it was about. And it's very + + align:start position:0% +what it was about. And it's very + + + align:start position:0% +what it was about. And it's very +interesting he brings back many of the + + align:start position:0% +interesting he brings back many of the + + + align:start position:0% +interesting he brings back many of the +characters. Well, both of these texts, + + align:start position:0% +characters. Well, both of these texts, + + + align:start position:0% +characters. Well, both of these texts, +like some of his other films, are really + + align:start position:0% +like some of his other films, are really + + + align:start position:0% +like some of his other films, are really +preoccupied with the question of this of + + align:start position:0% +preoccupied with the question of this of + + + align:start position:0% +preoccupied with the question of this of +the blurred boundaries between what we + + align:start position:0% +the blurred boundaries between what we + + + align:start position:0% +the blurred boundaries between what we +between the fictional worlds we live in + + align:start position:0% +between the fictional worlds we live in + + + align:start position:0% +between the fictional worlds we live in +and the actual worlds we eat and breathe + + align:start position:0% +and the actual worlds we eat and breathe + + + align:start position:0% +and the actual worlds we eat and breathe +in. Uh, and the extent to which our + + align:start position:0% +in. Uh, and the extent to which our + + + align:start position:0% +in. Uh, and the extent to which our +media saturated culture has created a + + align:start position:0% +media saturated culture has created a + + + align:start position:0% +media saturated culture has created a +kind of virtual reality that we watch on + + align:start position:0% +kind of virtual reality that we watch on + + + align:start position:0% +kind of virtual reality that we watch on +television and now of course we watch on + + align:start position:0% +television and now of course we watch on + + + align:start position:0% +television and now of course we watch on +our computer screens that competes with + + align:start position:0% +our computer screens that competes with + + + align:start position:0% +our computer screens that competes with +the actual reality we live every day. + + align:start position:0% +the actual reality we live every day. + + + align:start position:0% +the actual reality we live every day. +Well, uh uh Alman loved playing games + + align:start position:0% +Well, uh uh Alman loved playing games + + + align:start position:0% +Well, uh uh Alman loved playing games +with that question, raising questions + + align:start position:0% +with that question, raising questions + + + align:start position:0% +with that question, raising questions +about it and and and uh the first Tanner + + align:start position:0% +about it and and and uh the first Tanner + + + align:start position:0% +about it and and and uh the first Tanner +series is among other things a powerful + + align:start position:0% +series is among other things a powerful + + + align:start position:0% +series is among other things a powerful +meditation on the macity and the + + align:start position:0% +meditation on the macity and the + + + align:start position:0% +meditation on the macity and the +stupidity of the political process in + + align:start position:0% +stupidity of the political process in + + + align:start position:0% +stupidity of the political process in +our country. It showed people trying to + + align:start position:0% +our country. It showed people trying to + + + align:start position:0% +our country. It showed people trying to +raise money, candidates scrabbling to + + align:start position:0% +raise money, candidates scrabbling to + + + align:start position:0% +raise money, candidates scrabbling to +get five minutes in front of the uh in + + align:start position:0% +get five minutes in front of the uh in + + + align:start position:0% +get five minutes in front of the uh in +front of the news cameras just just at + + align:start position:0% +front of the news cameras just just at + + + align:start position:0% +front of the news cameras just just at +the moment when the evening news is + + align:start position:0% +the moment when the evening news is + + + align:start position:0% +the moment when the evening news is +going to break, that sort of thing. very + + align:start position:0% +going to break, that sort of thing. very + + + align:start position:0% +going to break, that sort of thing. very +wonderfully uh accurate, cynical account + + align:start position:0% +wonderfully uh accurate, cynical account + + + align:start position:0% +wonderfully uh accurate, cynical account +of American politics. And it might be + + align:start position:0% +of American politics. And it might be + + + align:start position:0% +of American politics. And it might be +worth mentioning that the writer of this + + align:start position:0% +worth mentioning that the writer of this + + + align:start position:0% +worth mentioning that the writer of this +episode uh the writer of this series who + + align:start position:0% +episode uh the writer of this series who + + + align:start position:0% +episode uh the writer of this series who +returned also to help on Tanner on + + align:start position:0% +returned also to help on Tanner on + + + align:start position:0% +returned also to help on Tanner on +Tanner is the famous comic strip genius + + align:start position:0% +Tanner is the famous comic strip genius + + + align:start position:0% +Tanner is the famous comic strip genius +Gary + + align:start position:0% +Gary + + + align:start position:0% +Gary +Trudeau. Um uh and Trudeau's + + align:start position:0% +Trudeau. Um uh and Trudeau's + + + align:start position:0% +Trudeau. Um uh and Trudeau's +collaboration with + + align:start position:0% +collaboration with + + + align:start position:0% +collaboration with +um this director + + align:start position:0% +um this director + + + align:start position:0% +um this director +uh he has sometimes said was a a a + + align:start position:0% +uh he has sometimes said was a a a + + + align:start position:0% +uh he has sometimes said was a a a +uh an enlarging experience for him and I + + align:start position:0% +uh an enlarging experience for him and I + + + align:start position:0% +uh an enlarging experience for him and I +mean it was it wasn't too long I think + + align:start position:0% +mean it was it wasn't too long I think + + + align:start position:0% +mean it was it wasn't too long I think +after this that Trudeau Trudeau stopped + + align:start position:0% +after this that Trudeau Trudeau stopped + + + align:start position:0% +after this that Trudeau Trudeau stopped +his regular work I mean as if I mean and + + align:start position:0% +his regular work I mean as if I mean and + + + align:start position:0% +his regular work I mean as if I mean and +and in fact I think that Trudeau began + + align:start position:0% +and in fact I think that Trudeau began + + + align:start position:0% +and in fact I think that Trudeau began +himself to have larger ambitions in in + + align:start position:0% +himself to have larger ambitions in in + + + align:start position:0% +himself to have larger ambitions in in +part because of his collaboration with + + align:start position:0% +part because of his collaboration with + + + align:start position:0% +part because of his collaboration with +with Robert Alman. Okay. So, uh Altman + + align:start position:0% +with Robert Alman. Okay. So, uh Altman + + + align:start position:0% +with Robert Alman. Okay. So, uh Altman +is a distinctive and interesting uh + + align:start position:0% +is a distinctive and interesting uh + + + align:start position:0% +is a distinctive and interesting uh +director and his films are interesting + + align:start position:0% +director and his films are interesting + + + align:start position:0% +director and his films are interesting +throughout the range of his career. Uh + + align:start position:0% +throughout the range of his career. Uh + + + align:start position:0% +throughout the range of his career. Uh +even though most people would say his + + align:start position:0% +even though most people would say his + + + align:start position:0% +even though most people would say his +most energetic and powerful films come + + align:start position:0% +most energetic and powerful films come + + + align:start position:0% +most energetic and powerful films come +come earlier. Well, let me turn now to + + align:start position:0% +come earlier. Well, let me turn now to + + + align:start position:0% +come earlier. Well, let me turn now to +McCabe and Mrs. Miller and try to + + align:start position:0% +McCabe and Mrs. Miller and try to + + + align:start position:0% +McCabe and Mrs. Miller and try to +concretize some of what I've been saying + + align:start position:0% +concretize some of what I've been saying + + + align:start position:0% +concretize some of what I've been saying +with specific reference to this + + align:start position:0% +with specific reference to this + + + align:start position:0% +with specific reference to this +remarkable film. Um, ruin the sacred + + align:start position:0% +remarkable film. Um, ruin the sacred + + + align:start position:0% +remarkable film. Um, ruin the sacred +truths, a line that I that I have + + align:start position:0% +truths, a line that I that I have + + + align:start position:0% +truths, a line that I that I have +plagiarized from the uh, Yale literary + + align:start position:0% +plagiarized from the uh, Yale literary + + + align:start position:0% +plagiarized from the uh, Yale literary +critic and scholar Harold Bloom, who + + align:start position:0% +critic and scholar Harold Bloom, who + + + align:start position:0% +critic and scholar Harold Bloom, who +uses it to describe the enterprise of + + align:start position:0% +uses it to describe the enterprise of + + + align:start position:0% +uses it to describe the enterprise of +certain romantic poets who are said to + + align:start position:0% +certain romantic poets who are said to + + + align:start position:0% +certain romantic poets who are said to +aim to whose aim was said in Bloom's + + align:start position:0% +aim to whose aim was said in Bloom's + + + align:start position:0% +aim to whose aim was said in Bloom's +terms uh, to be to ruin the inherited + + align:start position:0% +terms uh, to be to ruin the inherited + + + align:start position:0% +terms uh, to be to ruin the inherited +truths of the society, to attack them, + + align:start position:0% +truths of the society, to attack them, + + + align:start position:0% +truths of the society, to attack them, +to assault them. And in a certain sense, + + align:start position:0% +to assault them. And in a certain sense, + + + align:start position:0% +to assault them. And in a certain sense, +one could say that that's Altman's + + align:start position:0% +one could say that that's Altman's + + + align:start position:0% +one could say that that's Altman's +ambition as well, to ruin, to expose, to + + align:start position:0% +ambition as well, to ruin, to expose, to + + + align:start position:0% +ambition as well, to ruin, to expose, to +undermine, to to uh uh drench in irony + + align:start position:0% +undermine, to to uh uh drench in irony + + + align:start position:0% +undermine, to to uh uh drench in irony +uh the sacred truths that have come down + + align:start position:0% +uh the sacred truths that have come down + + + align:start position:0% +uh the sacred truths that have come down +to us from cinematic tradition and maybe + + align:start position:0% +to us from cinematic tradition and maybe + + + align:start position:0% +to us from cinematic tradition and maybe +from our political and moral culture as + + align:start position:0% +from our political and moral culture as + + + align:start position:0% +from our political and moral culture as +well. Uh and we can see this in many + + align:start position:0% +well. Uh and we can see this in many + + + align:start position:0% +well. Uh and we can see this in many +different aspects of uh of Altman's of + + align:start position:0% +different aspects of uh of Altman's of + + + align:start position:0% +different aspects of uh of Altman's of +Altman's movie of of uh of many of his + + align:start position:0% +Altman's movie of of uh of many of his + + + align:start position:0% +Altman's movie of of uh of many of his +films. We feel these pre these elements + + align:start position:0% +films. We feel these pre these elements + + + align:start position:0% +films. We feel these pre these elements +but especially powerfully and especially + + align:start position:0% +but especially powerfully and especially + + + align:start position:0% +but especially powerfully and especially +clearly I think in McCabe and Mrs. + + align:start position:0% +clearly I think in McCabe and Mrs. + + + align:start position:0% +clearly I think in McCabe and Mrs. +Miller. One might say in fact that the + + align:start position:0% +Miller. One might say in fact that the + + + align:start position:0% +Miller. One might say in fact that the +whole energy of McCabe and Mrs. Miller. + + align:start position:0% +whole energy of McCabe and Mrs. Miller. + + + align:start position:0% +whole energy of McCabe and Mrs. Miller. +Uh the whole energy of the film resides + + align:start position:0% +Uh the whole energy of the film resides + + + align:start position:0% +Uh the whole energy of the film resides +in a kind of tension or clash between + + align:start position:0% +in a kind of tension or clash between + + + align:start position:0% +in a kind of tension or clash between +the conventional expectations that we + + align:start position:0% +the conventional expectations that we + + + align:start position:0% +the conventional expectations that we +have about westerns and even the + + align:start position:0% +have about westerns and even the + + + align:start position:0% +have about westerns and even the +conventional expectations as they have + + align:start position:0% +conventional expectations as they have + + + align:start position:0% +conventional expectations as they have +been complicated by the serious and + + align:start position:0% +been complicated by the serious and + + + align:start position:0% +been complicated by the serious and +enlarging and already ironic westerns of + + align:start position:0% +enlarging and already ironic westerns of + + + align:start position:0% +enlarging and already ironic westerns of +the late 50s and early 60s. a kind of + + align:start position:0% +the late 50s and early 60s. a kind of + + + align:start position:0% +the late 50s and early 60s. a kind of +tension or class between the + + align:start position:0% +tension or class between the + + + align:start position:0% +tension or class between the +expectations we have about traditional + + align:start position:0% +expectations we have about traditional + + + align:start position:0% +expectations we have about traditional +westerns, no matter how ironic they + + align:start position:0% +westerns, no matter how ironic they + + + align:start position:0% +westerns, no matter how ironic they +might have been, and the gritty, + + align:start position:0% +might have been, and the gritty, + + + align:start position:0% +might have been, and the gritty, +comical, uglified, and humanized reality + + align:start position:0% +comical, uglified, and humanized reality + + + align:start position:0% +comical, uglified, and humanized reality +that Altman actually presents us with. + + align:start position:0% +that Altman actually presents us with. + + + align:start position:0% +that Altman actually presents us with. +And almost every element of the film has + + align:start position:0% +And almost every element of the film has + + + align:start position:0% +And almost every element of the film has +this kind of shock of recognition in it. + + align:start position:0% +this kind of shock of recognition in it. + + + align:start position:0% +this kind of shock of recognition in it. +Let's take the question, watch, for + + align:start position:0% +Let's take the question, watch, for + + + align:start position:0% +Let's take the question, watch, for +example, how the film um how the film + + align:start position:0% +example, how the film um how the film + + + align:start position:0% +example, how the film um how the film +treats uh both the soundtrack and what + + align:start position:0% +treats uh both the soundtrack and what + + + align:start position:0% +treats uh both the soundtrack and what +you visually see. Um + + align:start position:0% +you visually see. Um + + + align:start position:0% +you visually see. Um +what one of the thing when the film + + align:start position:0% +what one of the thing when the film + + + align:start position:0% +what one of the thing when the film +first came out some reviewers complained + + align:start position:0% +first came out some reviewers complained + + + align:start position:0% +first came out some reviewers complained +that they had trouble making out the + + align:start position:0% +that they had trouble making out the + + + align:start position:0% +that they had trouble making out the +dialogue and they weren't lying about + + align:start position:0% +dialogue and they weren't lying about + + + align:start position:0% +dialogue and they weren't lying about +this. It's because when Alman takes his + + align:start position:0% +this. It's because when Alman takes his + + + align:start position:0% +this. It's because when Alman takes his +uh camera inside in in inside the dingy + + align:start position:0% +uh camera inside in in inside the dingy + + + align:start position:0% +uh camera inside in in inside the dingy +saloon in which some of the action early + + align:start position:0% +saloon in which some of the action early + + + align:start position:0% +saloon in which some of the action early +in the film begins and to which it + + align:start position:0% +in the film begins and to which it + + + align:start position:0% +in the film begins and to which it +returns periodically as the film goes + + align:start position:0% +returns periodically as the film goes + + + align:start position:0% +returns periodically as the film goes +on. Uh Alman does not tamp down the + + align:start position:0% +on. Uh Alman does not tamp down the + + + align:start position:0% +on. Uh Alman does not tamp down the +ambient noise in the bar. You hear the + + align:start position:0% +ambient noise in the bar. You hear the + + + align:start position:0% +ambient noise in the bar. You hear the +conversation of other people. You hear + + align:start position:0% +conversation of other people. You hear + + + align:start position:0% +conversation of other people. You hear +bodies moving. You hear various kinds of + + align:start position:0% +bodies moving. You hear various kinds of + + + align:start position:0% +bodies moving. You hear various kinds of +noise. And sometimes if the if the + + align:start position:0% +noise. And sometimes if the if the + + + align:start position:0% +noise. And sometimes if the if the +people who are in the foreground of the + + align:start position:0% +people who are in the foreground of the + + + align:start position:0% +people who are in the foreground of the +frame are talking in very low voices, + + align:start position:0% +frame are talking in very low voices, + + + align:start position:0% +frame are talking in very low voices, +their voices are blotted out by the + + align:start position:0% +their voices are blotted out by the + + + align:start position:0% +their voices are blotted out by the +sounds around them. And in fact, Alman's + + align:start position:0% +sounds around them. And in fact, Alman's + + + align:start position:0% +sounds around them. And in fact, Alman's +treatment of sound all the way through + + align:start position:0% +treatment of sound all the way through + + + align:start position:0% +treatment of sound all the way through +the film has an has a an energetic + + align:start position:0% +the film has an has a an energetic + + + align:start position:0% +the film has an has a an energetic +realism in it. And it's a it's a strange + + align:start position:0% +realism in it. And it's a it's a strange + + + align:start position:0% +realism in it. And it's a it's a strange +and ultimately I think very satisfying + + align:start position:0% +and ultimately I think very satisfying + + + align:start position:0% +and ultimately I think very satisfying +aspect of the film. the way in which + + align:start position:0% +aspect of the film. the way in which + + + align:start position:0% +aspect of the film. the way in which +Alman seems to try to create a a + + align:start position:0% +Alman seems to try to create a a + + + align:start position:0% +Alman seems to try to create a a +grittier, more accurate account of the + + align:start position:0% +grittier, more accurate account of the + + + align:start position:0% +grittier, more accurate account of the +way sound operates in our world. I mean, + + align:start position:0% +way sound operates in our world. I mean, + + + align:start position:0% +way sound operates in our world. I mean, +the fact is when when uh when we're in + + align:start position:0% +the fact is when when uh when we're in + + + align:start position:0% +the fact is when when uh when we're in +in actuality and we address someone in a + + align:start position:0% +in actuality and we address someone in a + + + align:start position:0% +in actuality and we address someone in a +crowded room, it's not quiet. the only + + align:start position:0% +crowded room, it's not quiet. the only + + + align:start position:0% +crowded room, it's not quiet. the only +thing you you can hear a lot of other + + align:start position:0% +thing you you can hear a lot of other + + + align:start position:0% +thing you you can hear a lot of other +Alman wants to sort of recreate that and + + align:start position:0% +Alman wants to sort of recreate that and + + + align:start position:0% +Alman wants to sort of recreate that and +sometimes it almost seems as if that + + align:start position:0% +sometimes it almost seems as if that + + + align:start position:0% +sometimes it almost seems as if that +tendency that that digressive tendency + + align:start position:0% +tendency that that digressive tendency + + + align:start position:0% +tendency that that digressive tendency +that I've said is characteristic of + + align:start position:0% +that I've said is characteristic of + + + align:start position:0% +that I've said is characteristic of +Alman's imagination uh may even be + + align:start position:0% +Alman's imagination uh may even be + + + align:start position:0% +Alman's imagination uh may even be +expressing itself in the way he uses the + + align:start position:0% +expressing itself in the way he uses the + + + align:start position:0% +expressing itself in the way he uses the +soundtrack because it's almost as if he + + align:start position:0% +soundtrack because it's almost as if he + + + align:start position:0% +soundtrack because it's almost as if he +the soundtrack may sometimes be more + + align:start position:0% +the soundtrack may sometimes be more + + + align:start position:0% +the soundtrack may sometimes be more +interested in the words or sounds coming + + align:start position:0% +interested in the words or sounds coming + + + align:start position:0% +interested in the words or sounds coming +from the margins of the frame rather + + align:start position:0% +from the margins of the frame rather + + + align:start position:0% +from the margins of the frame rather +than from the center of the frame. So + + align:start position:0% +than from the center of the frame. So + + + align:start position:0% +than from the center of the frame. So +there are these elements of potential + + align:start position:0% +there are these elements of potential + + + align:start position:0% +there are these elements of potential +distraction that you always have to + + align:start position:0% +distraction that you always have to + + + align:start position:0% +distraction that you always have to +contend with when you're watching + + align:start position:0% +contend with when you're watching + + + align:start position:0% +contend with when you're watching +Altman's film uh Altman's films. Uh the + + align:start position:0% +Altman's film uh Altman's films. Uh the + + + align:start position:0% +Altman's film uh Altman's films. Uh the +same thing in a from another angle could + + align:start position:0% +same thing in a from another angle could + + + align:start position:0% +same thing in a from another angle could +also be said to be true in some degree + + align:start position:0% +also be said to be true in some degree + + + align:start position:0% +also be said to be true in some degree +of the way uh the images work in the + + align:start position:0% +of the way uh the images work in the + + + align:start position:0% +of the way uh the images work in the +film. Watch especially for the for the + + align:start position:0% +film. Watch especially for the for the + + + align:start position:0% +film. Watch especially for the for the +color palette that Alman uses. He plays + + align:start position:0% +color palette that Alman uses. He plays + + + align:start position:0% +color palette that Alman uses. He plays +around with light and dark with certain + + align:start position:0% +around with light and dark with certain + + + align:start position:0% +around with light and dark with certain +kinds of with with a certain kind of uh + + align:start position:0% +kinds of with with a certain kind of uh + + + align:start position:0% +kinds of with with a certain kind of uh +cold uh uh uh dark damp feeling. And he + + align:start position:0% +cold uh uh uh dark damp feeling. And he + + + align:start position:0% +cold uh uh uh dark damp feeling. And he +contrasts that uh with a a kind of + + align:start position:0% +contrasts that uh with a a kind of + + + align:start position:0% +contrasts that uh with a a kind of +lighting that that suggests not not + + align:start position:0% +lighting that that suggests not not + + + align:start position:0% +lighting that that suggests not not +incredibly bright sunlight but a kind of + + align:start position:0% +incredibly bright sunlight but a kind of + + + align:start position:0% +incredibly bright sunlight but a kind of +nostalgic golden sunset kind of imagery. + + align:start position:0% +nostalgic golden sunset kind of imagery. + + + align:start position:0% +nostalgic golden sunset kind of imagery. +Uh and and if you watch uh if you watch + + align:start position:0% +Uh and and if you watch uh if you watch + + + align:start position:0% +Uh and and if you watch uh if you watch +the film in the very beginning of the + + align:start position:0% +the film in the very beginning of the + + + align:start position:0% +the film in the very beginning of the +film, one of the things that happens is + + align:start position:0% +film, one of the things that happens is + + + align:start position:0% +film, one of the things that happens is +that sometimes this golden sort of light + + align:start position:0% +that sometimes this golden sort of light + + + align:start position:0% +that sometimes this golden sort of light +appears indoors and the outdoors seems + + align:start position:0% +appears indoors and the outdoors seems + + + align:start position:0% +appears indoors and the outdoors seems +gloomy and dank and dark. And then later + + align:start position:0% +gloomy and dank and dark. And then later + + + align:start position:0% +gloomy and dank and dark. And then later +in the film, this this this uh + + align:start position:0% +in the film, this this this uh + + + align:start position:0% +in the film, this this this uh +uh division between light and dark uh + + align:start position:0% +uh division between light and dark uh + + + align:start position:0% +uh division between light and dark uh +under goes an alteration. And you might + + align:start position:0% +under goes an alteration. And you might + + + align:start position:0% +under goes an alteration. And you might +ask yourself why. In one of the most + + align:start position:0% +ask yourself why. In one of the most + + + align:start position:0% +ask yourself why. In one of the most +dramatic moments toward the end of the + + align:start position:0% +dramatic moments toward the end of the + + + align:start position:0% +dramatic moments toward the end of the +film, there is a a a group of murderers, + + align:start position:0% +film, there is a a a group of murderers, + + + align:start position:0% +film, there is a a a group of murderers, +assassins, sort of a ride into the town + + align:start position:0% +assassins, sort of a ride into the town + + + align:start position:0% +assassins, sort of a ride into the town +and they ride in accompanied by this + + align:start position:0% +and they ride in accompanied by this + + + align:start position:0% +and they ride in accompanied by this +kind of with its sun behind them, + + align:start position:0% +kind of with its sun behind them, + + + align:start position:0% +kind of with its sun behind them, +accompanied by this sort of golden haze + + align:start position:0% +accompanied by this sort of golden haze + + + align:start position:0% +accompanied by this sort of golden haze +that Alman has ironically associated + + align:start position:0% +that Alman has ironically associated + + + align:start position:0% +that Alman has ironically associated +with with comfort and and uh and and + + align:start position:0% +with with comfort and and uh and and + + + align:start position:0% +with with comfort and and uh and and +pleasure earlier earlier in the film. So + + align:start position:0% +pleasure earlier earlier in the film. So + + + align:start position:0% +pleasure earlier earlier in the film. So +u both in terms of the sound and the + + align:start position:0% +u both in terms of the sound and the + + + align:start position:0% +u both in terms of the sound and the +image we we we we're we're engaged in + + align:start position:0% +image we we we we're we're engaged in + + + align:start position:0% +image we we we we're we're engaged in +something new here and maybe I also in + + align:start position:0% +something new here and maybe I also in + + + align:start position:0% +something new here and maybe I also in +considering the word image I should also + + align:start position:0% +considering the word image I should also + + + align:start position:0% +considering the word image I should also +mention Altman's montage Alman's habits + + align:start position:0% +mention Altman's montage Alman's habits + + + align:start position:0% +mention Altman's montage Alman's habits +of editing. Uh he's capable of the most + + align:start position:0% +of editing. Uh he's capable of the most + + + align:start position:0% +of editing. Uh he's capable of the most +fluid and and uh + + align:start position:0% +fluid and and uh + + + align:start position:0% +fluid and and uh +um uh undistracted editing if he wants + + align:start position:0% +um uh undistracted editing if he wants + + + align:start position:0% +um uh undistracted editing if he wants +to do it. But he is actually fonder of + + align:start position:0% +to do it. But he is actually fonder of + + + align:start position:0% +to do it. But he is actually fonder of +forms of editing that are abrupt uh that + + align:start position:0% +forms of editing that are abrupt uh that + + + align:start position:0% +forms of editing that are abrupt uh that +are disconcerting that are mildly + + align:start position:0% +are disconcerting that are mildly + + + align:start position:0% +are disconcerting that are mildly +disorienting. And that style is part I + + align:start position:0% +disorienting. And that style is part I + + + align:start position:0% +disorienting. And that style is part I +don't mean he does this at all moments + + align:start position:0% +don't mean he does this at all moments + + + align:start position:0% +don't mean he does this at all moments +of the film but that style I think is + + align:start position:0% +of the film but that style I think is + + + align:start position:0% +of the film but that style I think is +part or sometimes he'll use abrupt cuts + + align:start position:0% +part or sometimes he'll use abrupt cuts + + + align:start position:0% +part or sometimes he'll use abrupt cuts +uh that style is part of his uh of his + + align:start position:0% +uh that style is part of his uh of his + + + align:start position:0% +uh that style is part of his uh of his +art I think but it's also part of this + + align:start position:0% +art I think but it's also part of this + + + align:start position:0% +art I think but it's also part of this +sort of desire not to have things too + + align:start position:0% +sort of desire not to have things too + + + align:start position:0% +sort of desire not to have things too +smooth not to have things too neat. his + + align:start position:0% +smooth not to have things too neat. his + + + align:start position:0% +smooth not to have things too neat. his +love of the his love of the im of the + + align:start position:0% +love of the his love of the im of the + + + align:start position:0% +love of the his love of the im of the +apparently imperfect is part of what's + + align:start position:0% +apparently imperfect is part of what's + + + align:start position:0% +apparently imperfect is part of what's +is part of what's operating there. + + align:start position:0% +is part of what's operating there. + + + align:start position:0% +is part of what's operating there. +Um a and even a third element of what + + align:start position:0% +Um a and even a third element of what + + + align:start position:0% +Um a and even a third element of what +I'm calling his special or his new + + align:start position:0% +I'm calling his special or his new + + + align:start position:0% +I'm calling his special or his new +realism uh might have to do even with + + align:start position:0% +realism uh might have to do even with + + + align:start position:0% +realism uh might have to do even with +the way he treats not just the physical + + align:start position:0% +the way he treats not just the physical + + + align:start position:0% +the way he treats not just the physical +spaces that you see but even the + + align:start position:0% +spaces that you see but even the + + + align:start position:0% +spaces that you see but even the +weather. Watch how lousy the weather is + + align:start position:0% +weather. Watch how lousy the weather is + + + align:start position:0% +weather. Watch how lousy the weather is +in this film and how much damage it does + + align:start position:0% +in this film and how much damage it does + + + align:start position:0% +in this film and how much damage it does +to people. What an unpleasant thing the + + align:start position:0% +to people. What an unpleasant thing the + + + align:start position:0% +to people. What an unpleasant thing the +weather actually is. Snow really matters + + align:start position:0% +weather actually is. Snow really matters + + + align:start position:0% +weather actually is. Snow really matters +in this film. Bad weather really matters + + align:start position:0% +in this film. Bad weather really matters + + + align:start position:0% +in this film. Bad weather really matters +in this film. It affects the outcome of + + align:start position:0% +in this film. It affects the outcome of + + + align:start position:0% +in this film. It affects the outcome of +the plot in certain ways as you'll see. + + align:start position:0% +the plot in certain ways as you'll see. + + + align:start position:0% +the plot in certain ways as you'll see. +So it so so this this uh this messy + + align:start position:0% +So it so so this this uh this messy + + + align:start position:0% +So it so so this this uh this messy +realism I'm talking about even extends + + align:start position:0% +realism I'm talking about even extends + + + align:start position:0% +realism I'm talking about even extends +to the way in which the film treats the + + align:start position:0% +to the way in which the film treats the + + + align:start position:0% +to the way in which the film treats the +weather as you'll a as you'll as you'll + + align:start position:0% +weather as you'll a as you'll as you'll + + + align:start position:0% +weather as you'll a as you'll as you'll +see as the film as the film proceeds. + + align:start position:0% +see as the film as the film proceeds. + + + align:start position:0% +see as the film as the film proceeds. +um the central features of the + + align:start position:0% +um the central features of the + + + align:start position:0% +um the central features of the +traditional western, the hero savior + + align:start position:0% +traditional western, the hero savior + + + align:start position:0% +traditional western, the hero savior +figure, the protagonist figure, uh the + + align:start position:0% +figure, the protagonist figure, uh the + + + align:start position:0% +figure, the protagonist figure, uh the +gal from the east who is often a a + + align:start position:0% +gal from the east who is often a a + + + align:start position:0% +gal from the east who is often a a +school momm who falls in love with the + + align:start position:0% +school momm who falls in love with the + + + align:start position:0% +school momm who falls in love with the +hero. Uh and the idea that the western + + align:start position:0% +hero. Uh and the idea that the western + + + align:start position:0% +hero. Uh and the idea that the western +as a as a text, as I've said many times + + align:start position:0% +as a as a text, as I've said many times + + + align:start position:0% +as a as a text, as I've said many times +already, is always a kind of founding + + align:start position:0% +already, is always a kind of founding + + + align:start position:0% +already, is always a kind of founding +story about the creation of a community. + + align:start position:0% +story about the creation of a community. + + + align:start position:0% +story about the creation of a community. +All of those + + align:start position:0% +All of those + + + align:start position:0% +All of those +conventional structures remain in McCabe + + align:start position:0% +conventional structures remain in McCabe + + + align:start position:0% +conventional structures remain in McCabe +and Mrs. Miller, but they're inverted. + + align:start position:0% +and Mrs. Miller, but they're inverted. + + + align:start position:0% +and Mrs. Miller, but they're inverted. +They're weird. Let's take for let me + + align:start position:0% +They're weird. Let's take for let me + + + align:start position:0% +They're weird. Let's take for let me +just a quick example the the character + + align:start position:0% +just a quick example the the character + + + align:start position:0% +just a quick example the the character +played by Warren Batty. He's a he's he + + align:start position:0% +played by Warren Batty. He's a he's he + + + align:start position:0% +played by Warren Batty. He's a he's he +he really is in some sense the founder + + align:start position:0% +he really is in some sense the founder + + + align:start position:0% +he really is in some sense the founder +of the town. Uh there's a miserable + + align:start position:0% +of the town. Uh there's a miserable + + + align:start position:0% +of the town. Uh there's a miserable +mining not even a it's a mining camp. It + + align:start position:0% +mining not even a it's a mining camp. It + + + align:start position:0% +mining not even a it's a mining camp. It +just has a saloon in it uh when the film + + align:start position:0% +just has a saloon in it uh when the film + + + align:start position:0% +just has a saloon in it uh when the film +opens and McCabe arrives. He's the great + + align:start position:0% +opens and McCabe arrives. He's the great + + + align:start position:0% +opens and McCabe arrives. He's the great +gambler. He's actually a visionary + + align:start position:0% +gambler. He's actually a visionary + + + align:start position:0% +gambler. He's actually a visionary +entrepreneur in a certain way. Although + + align:start position:0% +entrepreneur in a certain way. Although + + + align:start position:0% +entrepreneur in a certain way. Although +in a very ironic sense and the story is + + align:start position:0% +in a very ironic sense and the story is + + + align:start position:0% +in a very ironic sense and the story is +an ironic entrepreneur story, a Horatio + + align:start position:0% +an ironic entrepreneur story, a Horatio + + + align:start position:0% +an ironic entrepreneur story, a Horatio +Algeria story. This this gambler McCabe + + align:start position:0% +Algeria story. This this gambler McCabe + + + align:start position:0% +Algeria story. This this gambler McCabe +comes to town, looks the place over, + + align:start position:0% +comes to town, looks the place over, + + + align:start position:0% +comes to town, looks the place over, +gambles for a while with these poor with + + align:start position:0% +gambles for a while with these poor with + + + align:start position:0% +gambles for a while with these poor with +these poor schlubs who are suffering on + + align:start position:0% +these poor schlubs who are suffering on + + + align:start position:0% +these poor schlubs who are suffering on +the very margins of civilization and + + align:start position:0% +the very margins of civilization and + + + align:start position:0% +the very margins of civilization and +then goes away. And when he comes back, + + align:start position:0% +then goes away. And when he comes back, + + + align:start position:0% +then goes away. And when he comes back, +he's bringing prostitutes with him. This + + align:start position:0% +he's bringing prostitutes with him. This + + + align:start position:0% +he's bringing prostitutes with him. This +town is not built by noble intentions. + + align:start position:0% +town is not built by noble intentions. + + + align:start position:0% +town is not built by noble intentions. +It's built by a whoremonger who brings a + + align:start position:0% +It's built by a whoremonger who brings a + + + align:start position:0% +It's built by a whoremonger who brings a +bunch of uh of prostitutes into the town + + align:start position:0% +bunch of uh of prostitutes into the town + + + align:start position:0% +bunch of uh of prostitutes into the town +and sets up the town's first house of + + align:start position:0% +and sets up the town's first house of + + + align:start position:0% +and sets up the town's first house of +prostitution. And in fact, McKay becomes + + align:start position:0% +prostitution. And in fact, McKay becomes + + + align:start position:0% +prostitution. And in fact, McKay becomes +the biggest land owner and the richest + + align:start position:0% +the biggest land owner and the richest + + + align:start position:0% +the biggest land owner and the richest +man in town. Not be not because he has + + align:start position:0% +man in town. Not be not because he has + + + align:start position:0% +man in town. Not be not because he has +the entrepreneurial vision of an Andrew + + align:start position:0% +the entrepreneurial vision of an Andrew + + + align:start position:0% +the entrepreneurial vision of an Andrew +Carnegie, although actually if we look + + align:start position:0% +Carnegie, although actually if we look + + + align:start position:0% +Carnegie, although actually if we look +closely at Andrew Carnegiey's life, we + + align:start position:0% +closely at Andrew Carnegiey's life, we + + + align:start position:0% +closely at Andrew Carnegiey's life, we +might find he more resembles Mabe than + + align:start position:0% +might find he more resembles Mabe than + + + align:start position:0% +might find he more resembles Mabe than +his biographers have acknowledged. + + align:start position:0% +his biographers have acknowledged. + + + align:start position:0% +his biographers have acknowledged. +Right? But in other words, it's as if + + align:start position:0% +Right? But in other words, it's as if + + + align:start position:0% +Right? But in other words, it's as if +what m what what Alman is doing is he's + + align:start position:0% +what m what what Alman is doing is he's + + + align:start position:0% +what m what what Alman is doing is he's +telling a kind of ironic or mocking or + + align:start position:0% +telling a kind of ironic or mocking or + + + align:start position:0% +telling a kind of ironic or mocking or +anti-heroic Horatio Algeria story, + + align:start position:0% +anti-heroic Horatio Algeria story, + + + align:start position:0% +anti-heroic Horatio Algeria story, +right? And a and as the story unfolds, + + align:start position:0% +right? And a and as the story unfolds, + + + align:start position:0% +right? And a and as the story unfolds, +something certain lovely things begin to + + align:start position:0% +something certain lovely things begin to + + + align:start position:0% +something certain lovely things begin to +happen. One thing that begins to happen + + align:start position:0% +happen. One thing that begins to happen + + + align:start position:0% +happen. One thing that begins to happen +is we begin to see a soft or a or a or a + + align:start position:0% +is we begin to see a soft or a or a or a + + + align:start position:0% +is we begin to see a soft or a or a or a +vulnerable side to m to the McCabe + + align:start position:0% +vulnerable side to m to the McCabe + + + align:start position:0% +vulnerable side to m to the McCabe +character. And when the schoolm from the + + align:start position:0% +character. And when the schoolm from the + + + align:start position:0% +character. And when the schoolm from the +east figure arrives, she's really from + + align:start position:0% +east figure arrives, she's really from + + + align:start position:0% +east figure arrives, she's really from +the east. She's not even from the east + + align:start position:0% +the east. She's not even from the east + + + align:start position:0% +the east. She's not even from the east +of the United States. She has an English + + align:start position:0% +of the United States. She has an English + + + align:start position:0% +of the United States. She has an English +accent, right? It's Julie Christie, but + + align:start position:0% +accent, right? It's Julie Christie, but + + + align:start position:0% +accent, right? It's Julie Christie, but +she's not a school momm. She's a retired + + align:start position:0% +she's not a school momm. She's a retired + + + align:start position:0% +she's not a school momm. She's a retired + who was now a who was now a + + align:start position:0% + who was now a who was now a + + + align:start position:0% + who was now a who was now a +manager of She's a she she's a + + align:start position:0% +manager of She's a she she's a + + + align:start position:0% +manager of She's a she she's a +she's a mistress, an expert in + + align:start position:0% +she's a mistress, an expert in + + + align:start position:0% +she's a mistress, an expert in +running And in fact, as soon as + + align:start position:0% +running And in fact, as soon as + + + align:start position:0% +running And in fact, as soon as +she arrives in town and partners with + + align:start position:0% +she arrives in town and partners with + + + align:start position:0% +she arrives in town and partners with +McCabe, McCabe really begins to make + + align:start position:0% +McCabe, McCabe really begins to make + + + align:start position:0% +McCabe, McCabe really begins to make +money. And what we begin to realize is + + align:start position:0% +money. And what we begin to realize is + + + align:start position:0% +money. And what we begin to realize is +McCabe really doesn't know what he's + + align:start position:0% +McCabe really doesn't know what he's + + + align:start position:0% +McCabe really doesn't know what he's +doing. McCabe had a kind of vision, but + + align:start position:0% +doing. McCabe had a kind of vision, but + + + align:start position:0% +doing. McCabe had a kind of vision, but +he doesn't really even know. And there's + + align:start position:0% +he doesn't really even know. And there's + + + align:start position:0% +he doesn't really even know. And there's +a wonderful scene over a over a over a + + align:start position:0% +a wonderful scene over a over a over a + + + align:start position:0% +a wonderful scene over a over a over a +meal in which the Julie Christie + + align:start position:0% +meal in which the Julie Christie + + + align:start position:0% +meal in which the Julie Christie +character who wolfs down her food like + + align:start position:0% +character who wolfs down her food like + + + align:start position:0% +character who wolfs down her food like +some John Wayne character while the Mabe + + align:start position:0% +some John Wayne character while the Mabe + + + align:start position:0% +some John Wayne character while the Mabe +characters looks very a scance at her. + + align:start position:0% +characters looks very a scance at her. + + + align:start position:0% +characters looks very a scance at her. +There's a scene in which the Julie + + align:start position:0% +There's a scene in which the Julie + + + align:start position:0% +There's a scene in which the Julie +Christine in effect explains to McCabe + + align:start position:0% +Christine in effect explains to McCabe + + + align:start position:0% +Christine in effect explains to McCabe +how little he knows about how to take + + align:start position:0% +how little he knows about how to take + + + align:start position:0% +how little he knows about how to take +care how to manage women. And then what + + align:start position:0% +care how to manage women. And then what + + + align:start position:0% +care how to manage women. And then what +develops is a kind of love affair + + align:start position:0% +develops is a kind of love affair + + + align:start position:0% +develops is a kind of love affair +between Mabe and this and this um uh + + align:start position:0% +between Mabe and this and this um uh + + + align:start position:0% +between Mabe and this and this um uh +prostitute. Uh and and what one begins + + align:start position:0% +prostitute. Uh and and what one begins + + + align:start position:0% +prostitute. Uh and and what one begins +to realize is first of all the woman is + + align:start position:0% +to realize is first of all the woman is + + + align:start position:0% +to realize is first of all the woman is +much smarter than the man and you can + + align:start position:0% +much smarter than the man and you can + + + align:start position:0% +much smarter than the man and you can +see her despair being generated as the + + align:start position:0% +see her despair being generated as the + + + align:start position:0% +see her despair being generated as the +story unfolds and McCabe is manipulated + + align:start position:0% +story unfolds and McCabe is manipulated + + + align:start position:0% +story unfolds and McCabe is manipulated +by other people. She knows the powerful + + align:start position:0% +by other people. She knows the powerful + + + align:start position:0% +by other people. She knows the powerful +forces that Mabe will be up against by + + align:start position:0% +forces that Mabe will be up against by + + + align:start position:0% +forces that Mabe will be up against by +the end of the film. And she tries to + + align:start position:0% +the end of the film. And she tries to + + + align:start position:0% +the end of the film. And she tries to +discourage him and help him but he's too + + align:start position:0% +discourage him and help him but he's too + + + align:start position:0% +discourage him and help him but he's too +caught up in his sort of macho idea of + + align:start position:0% +caught up in his sort of macho idea of + + + align:start position:0% +caught up in his sort of macho idea of +what a man is to allow himself to see + + align:start position:0% +what a man is to allow himself to see + + + align:start position:0% +what a man is to allow himself to see +the wisdom of what she's saying. and + + align:start position:0% +the wisdom of what she's saying. and + + + align:start position:0% +the wisdom of what she's saying. and +he's actually sometimes embarrassed by + + align:start position:0% +he's actually sometimes embarrassed by + + + align:start position:0% +he's actually sometimes embarrassed by +the fact that she seems to know more + + align:start position:0% +the fact that she seems to know more + + + align:start position:0% +the fact that she seems to know more +than she more than he does. Uh uh well, + + align:start position:0% +than she more than he does. Uh uh well, + + + align:start position:0% +than she more than he does. Uh uh well, +the relation between McCabe and Mrs. + + align:start position:0% +the relation between McCabe and Mrs. + + + align:start position:0% +the relation between McCabe and Mrs. +Miller inverts the normal love affair + + align:start position:0% +Miller inverts the normal love affair + + + align:start position:0% +Miller inverts the normal love affair +relationship. It shows us a woman who's + + align:start position:0% +relationship. It shows us a woman who's + + + align:start position:0% +relationship. It shows us a woman who's +stronger and smarter, although also much + + align:start position:0% +stronger and smarter, although also much + + + align:start position:0% +stronger and smarter, although also much +more cynical and desparing than her man. + + align:start position:0% +more cynical and desparing than her man. + + + align:start position:0% +more cynical and desparing than her man. +But McCabe's optimism and sense of + + align:start position:0% +But McCabe's optimism and sense of + + + align:start position:0% +But McCabe's optimism and sense of +self-confidence, which he loses pretty + + align:start position:0% +self-confidence, which he loses pretty + + + align:start position:0% +self-confidence, which he loses pretty +quickly, uh is shown in the film to be a + + align:start position:0% +quickly, uh is shown in the film to be a + + + align:start position:0% +quickly, uh is shown in the film to be a +to be a function of his ignorance and + + align:start position:0% +to be a function of his ignorance and + + + align:start position:0% +to be a function of his ignorance and +his innocence. Uh so so the treatment of + + align:start position:0% +his innocence. Uh so so the treatment of + + + align:start position:0% +his innocence. Uh so so the treatment of +the love story and the treatment of the + + align:start position:0% +the love story and the treatment of the + + + align:start position:0% +the love story and the treatment of the +hero savior figure in the film is deeply + + align:start position:0% +hero savior figure in the film is deeply + + + align:start position:0% +hero savior figure in the film is deeply +humanizing and deeply ironic. They're + + align:start position:0% +humanizing and deeply ironic. They're + + + align:start position:0% +humanizing and deeply ironic. They're +actually more credible psychologically + + align:start position:0% +actually more credible psychologically + + + align:start position:0% +actually more credible psychologically +complex characters, these two, McCabe + + align:start position:0% +complex characters, these two, McCabe + + + align:start position:0% +complex characters, these two, McCabe +and Mrs. Miller, most of their + + align:start position:0% +and Mrs. Miller, most of their + + + align:start position:0% +and Mrs. Miller, most of their +predecessors in earlier westerns, but + + align:start position:0% +predecessors in earlier westerns, but + + + align:start position:0% +predecessors in earlier westerns, but +they're also deeply ironic embodiment of + + align:start position:0% +they're also deeply ironic embodiment of + + + align:start position:0% +they're also deeply ironic embodiment of +their much nobler ancestors. And the + + align:start position:0% +their much nobler ancestors. And the + + + align:start position:0% +their much nobler ancestors. And the +same thing is that I've just been saying + + align:start position:0% +same thing is that I've just been saying + + + align:start position:0% +same thing is that I've just been saying +about about the hero and the heroine uh + + align:start position:0% +about about the hero and the heroine uh + + + align:start position:0% +about about the hero and the heroine uh +about the love story and the savior + + align:start position:0% +about the love story and the savior + + + align:start position:0% +about the love story and the savior +story is also true of the founding myth + + align:start position:0% +story is also true of the founding myth + + + align:start position:0% +story is also true of the founding myth +itself. The name of this town is + + align:start position:0% +itself. The name of this town is + + + align:start position:0% +itself. The name of this town is +Presbyterian + + align:start position:0% +Presbyterian + + + align:start position:0% +Presbyterian +Church. Very good name, isn't it? And it + + align:start position:0% +Church. Very good name, isn't it? And it + + + align:start position:0% +Church. Very good name, isn't it? And it +takes its name from the steeple of an + + align:start position:0% +takes its name from the steeple of an + + + align:start position:0% +takes its name from the steeple of an +unfinished church. And I think the + + align:start position:0% +unfinished church. And I think the + + + align:start position:0% +unfinished church. And I think the +illusion to unfinished churches in + + align:start position:0% +illusion to unfinished churches in + + + align:start position:0% +illusion to unfinished churches in +earlier traditional westerns is + + align:start position:0% +earlier traditional westerns is + + + align:start position:0% +earlier traditional westerns is +certainly intentional. uh it takes his + + align:start position:0% +certainly intentional. uh it takes his + + + align:start position:0% +certainly intentional. uh it takes his +name from the unfinished from the from + + align:start position:0% +name from the unfinished from the from + + + align:start position:0% +name from the unfinished from the from +the unfinished church in the in in the + + align:start position:0% +the unfinished church in the in in the + + + align:start position:0% +the unfinished church in the in in the +town. And in fact, as you will see, the + + align:start position:0% +town. And in fact, as you will see, the + + + align:start position:0% +town. And in fact, as you will see, the +church is never finished. You might + + align:start position:0% +church is never finished. You might + + + align:start position:0% +church is never finished. You might +watch how in the plot that works out and + + align:start position:0% +watch how in the plot that works out and + + + align:start position:0% +watch how in the plot that works out and +why it works out and what role the + + align:start position:0% +why it works out and what role the + + + align:start position:0% +why it works out and what role the +church and especially the minister who + + align:start position:0% +church and especially the minister who + + + align:start position:0% +church and especially the minister who +is hanging out at the church plays in + + align:start position:0% +is hanging out at the church plays in + + + align:start position:0% +is hanging out at the church plays in +the outcome of the story. Does the + + align:start position:0% +the outcome of the story. Does the + + + align:start position:0% +the outcome of the story. Does the +church does implicitly therefore does + + align:start position:0% +church does implicitly therefore does + + + align:start position:0% +church does implicitly therefore does +religion play a constructive or a + + align:start position:0% +religion play a constructive or a + + + align:start position:0% +religion play a constructive or a +destructive role in the film? I'm not + + align:start position:0% +destructive role in the film? I'm not + + + align:start position:0% +destructive role in the film? I'm not +giving too much away to tell you it's + + align:start position:0% +giving too much away to tell you it's + + + align:start position:0% +giving too much away to tell you it's +obvious. It's obvious which answer is + + align:start position:0% +obvious. It's obvious which answer is + + + align:start position:0% +obvious. It's obvious which answer is +appropriate. It plays a destructive + + align:start position:0% +appropriate. It plays a destructive + + + align:start position:0% +appropriate. It plays a destructive +role. Just as it's hostile to certain + + align:start position:0% +role. Just as it's hostile to certain + + + align:start position:0% +role. Just as it's hostile to certain +political myths about the founding of + + align:start position:0% +political myths about the founding of + + + align:start position:0% +political myths about the founding of +the west, the film is also hostile to + + align:start position:0% +the west, the film is also hostile to + + + align:start position:0% +the west, the film is also hostile to +our pieties and complacencies about the + + align:start position:0% +our pieties and complacencies about the + + + align:start position:0% +our pieties and complacencies about the +role of religious institutions in our + + align:start position:0% +role of religious institutions in our + + + align:start position:0% +role of religious institutions in our +and especially in the founding of our + + align:start position:0% +and especially in the founding of our + + + align:start position:0% +and especially in the founding of our +society. So uh watch how it works itself + + align:start position:0% +society. So uh watch how it works itself + + + align:start position:0% +society. So uh watch how it works itself +out and how the uh uh and how that + + align:start position:0% +out and how the uh uh and how that + + + align:start position:0% +out and how the uh uh and how that +traditional icon of the of of the + + align:start position:0% +traditional icon of the of of the + + + align:start position:0% +traditional icon of the of of the +conventional western uh has its meanings + + align:start position:0% +conventional western uh has its meanings + + + align:start position:0% +conventional western uh has its meanings +and its significance inverted uh and + + align:start position:0% +and its significance inverted uh and + + + align:start position:0% +and its significance inverted uh and +subverted uh in in this in this film. + + align:start position:0% + + + + align:start position:0% + +Um there's + + align:start position:0% +Um there's + + + align:start position:0% +Um there's +one crucial film conventional western to + + align:start position:0% +one crucial film conventional western to + + + align:start position:0% +one crucial film conventional western to +which this film directly alludes I think + + align:start position:0% +which this film directly alludes I think + + + align:start position:0% +which this film directly alludes I think +or at least implicitly directly alludes + + align:start position:0% +or at least implicitly directly alludes + + + align:start position:0% +or at least implicitly directly alludes +uh one of it alludes to other films as + + align:start position:0% +uh one of it alludes to other films as + + + align:start position:0% +uh one of it alludes to other films as +well but there's one especially um and + + align:start position:0% +well but there's one especially um and + + + align:start position:0% +well but there's one especially um and +and I want to show you a show you a clip + + align:start position:0% +and I want to show you a show you a clip + + + align:start position:0% +and I want to show you a show you a clip +from it because it has its own + + align:start position:0% +from it because it has its own + + + align:start position:0% +from it because it has its own +distinction uh and it reminds you about + + align:start position:0% +distinction uh and it reminds you about + + + align:start position:0% +distinction uh and it reminds you about +the not only about the sort of ballad + + align:start position:0% +the not only about the sort of ballad + + + align:start position:0% +the not only about the sort of ballad +dimensions of of the western, but the + + align:start position:0% +dimensions of of the western, but the + + + align:start position:0% +dimensions of of the western, but the +but how stylized and and uh heroic in a + + align:start position:0% +but how stylized and and uh heroic in a + + + align:start position:0% +but how stylized and and uh heroic in a +certain way the conventional western is. + + align:start position:0% +certain way the conventional western is. + + + align:start position:0% +certain way the conventional western is. +And it'll give it it'll be a it'll be a + + align:start position:0% +And it'll give it it'll be a it'll be a + + + align:start position:0% +And it'll give it it'll be a it'll be a +nice contrast with the anti-heroic uh + + align:start position:0% +nice contrast with the anti-heroic uh + + + align:start position:0% +nice contrast with the anti-heroic uh +qualities of McCabe and Mrs. Miller. Uh + + align:start position:0% +qualities of McCabe and Mrs. Miller. Uh + + + align:start position:0% +qualities of McCabe and Mrs. Miller. Uh +and this is a a scene from from the very + + align:start position:0% +and this is a a scene from from the very + + + align:start position:0% +and this is a a scene from from the very +beginning of a film made in the early + + align:start position:0% +beginning of a film made in the early + + + align:start position:0% +beginning of a film made in the early +50s called High Noon, starring the + + align:start position:0% +50s called High Noon, starring the + + + align:start position:0% +50s called High Noon, starring the +traditional the most icon the the first + + align:start position:0% +traditional the most icon the the first + + + align:start position:0% +traditional the most icon the the first +or second most iconic of Western heroes. + + align:start position:0% +or second most iconic of Western heroes. + + + align:start position:0% +or second most iconic of Western heroes. +If John Wayne was the first, then Gary + + align:start position:0% +If John Wayne was the first, then Gary + + + align:start position:0% +If John Wayne was the first, then Gary +Cooper was the second. And this stars + + align:start position:0% +Cooper was the second. And this stars + + + align:start position:0% +Cooper was the second. And this stars +Gary Cooper. But the main reason I want + + align:start position:0% +Gary Cooper. But the main reason I want + + + align:start position:0% +Gary Cooper. But the main reason I want +you to see the film, see this opening of + + align:start position:0% +you to see the film, see this opening of + + + align:start position:0% +you to see the film, see this opening of +the film, is because it's very important + + align:start position:0% +the film, is because it's very important + + + align:start position:0% +the film, is because it's very important +to McCabe and Mrs. Miller. And there's + + align:start position:0% +to McCabe and Mrs. Miller. And there's + + + align:start position:0% +to McCabe and Mrs. Miller. And there's +no doubt that Altman expects his + + align:start position:0% +no doubt that Altman expects his + + + align:start position:0% +no doubt that Altman expects his +audience not only to be thinking about + + align:start position:0% +audience not only to be thinking about + + + align:start position:0% +audience not only to be thinking about +many prior westerns to contrast with + + align:start position:0% +many prior westerns to contrast with + + + align:start position:0% +many prior westerns to contrast with +what happens in this western, but he + + align:start position:0% +what happens in this western, but he + + + align:start position:0% +what happens in this western, but he +certainly expects his audience to + + align:start position:0% +certainly expects his audience to + + + align:start position:0% +certainly expects his audience to +remember + + align:start position:0% +remember + + + align:start position:0% +remember +specifically the beginning of Highoon + + align:start position:0% +specifically the beginning of Highoon + + + align:start position:0% +specifically the beginning of Highoon +and the way Highoon plays itself out the + + align:start position:0% +and the way Highoon plays itself out the + + + align:start position:0% +and the way Highoon plays itself out the +and and perhaps per perhaps also uh um + + align:start position:0% +and and perhaps per perhaps also uh um + + + align:start position:0% +and and perhaps per perhaps also uh um +certain other uh uh westerns play maybe + + align:start position:0% +certain other uh uh westerns play maybe + + + align:start position:0% +certain other uh uh westerns play maybe +as significant almost as significant a + + align:start position:0% +as significant almost as significant a + + + align:start position:0% +as significant almost as significant a +role in the film, but it's But but high + + align:start position:0% +role in the film, but it's But but high + + + align:start position:0% +role in the film, but it's But but high +noon especially and the main reason that + + align:start position:0% +noon especially and the main reason that + + + align:start position:0% +noon especially and the main reason that +Highoon is so important to McCabe and + + align:start position:0% +Highoon is so important to McCabe and + + + align:start position:0% +Highoon is so important to McCabe and +Mrs. Miller is that it's also a a drama + + align:start position:0% +Mrs. Miller is that it's also a a drama + + + align:start position:0% +Mrs. Miller is that it's also a a drama +that takes place in the physical spaces + + align:start position:0% +that takes place in the physical spaces + + + align:start position:0% +that takes place in the physical spaces +of the town. High Noon is a begins + + align:start position:0% +of the town. High Noon is a begins + + + align:start position:0% +of the town. High Noon is a begins +brilliantly uh with bad guys riding into + + align:start position:0% +brilliantly uh with bad guys riding into + + + align:start position:0% +brilliantly uh with bad guys riding into +town and in the and + + align:start position:0% +town and in the and + + + align:start position:0% +town and in the and +in we hardly see the hero until the + + align:start position:0% +in we hardly see the hero until the + + + align:start position:0% +in we hardly see the hero until the +final images of the sequence I'm going + + align:start position:0% +final images of the sequence I'm going + + + align:start position:0% +final images of the sequence I'm going +to show you the Gary Cooper figure bad + + align:start position:0% +to show you the Gary Cooper figure bad + + + align:start position:0% +to show you the Gary Cooper figure bad +guy a man a man's been released from + + align:start position:0% +guy a man a man's been released from + + + align:start position:0% +guy a man a man's been released from +prison who's going to take vengeance on + + align:start position:0% +prison who's going to take vengeance on + + + align:start position:0% +prison who's going to take vengeance on +the town marshall it's the day of the + + align:start position:0% +the town marshall it's the day of the + + + align:start position:0% +the town marshall it's the day of the +town marshall's wedding right when the + + align:start position:0% +town marshall's wedding right when the + + + align:start position:0% +town marshall's wedding right when the +bad guys are coming into town to take + + align:start position:0% +bad guys are coming into town to take + + + align:start position:0% +bad guys are coming into town to take +their revenge the film itself + + align:start position:0% +their revenge the film itself + + + align:start position:0% +their revenge the film itself +incidentally is a parable of the + + align:start position:0% +incidentally is a parable of the + + + align:start position:0% +incidentally is a parable of the +McCarthy era of the early 1950s uh it's + + align:start position:0% +McCarthy era of the early 1950s uh it's + + + align:start position:0% +McCarthy era of the early 1950s uh it's +even like many westerns, and we've + + align:start position:0% +even like many westerns, and we've + + + align:start position:0% +even like many westerns, and we've +talked about this, like many westerns, + + align:start position:0% +talked about this, like many westerns, + + + align:start position:0% +talked about this, like many westerns, +it's a disguised form of social and + + align:start position:0% +it's a disguised form of social and + + + align:start position:0% +it's a disguised form of social and +political commentary on the present. Uh, + + align:start position:0% +political commentary on the present. Uh, + + + align:start position:0% +political commentary on the present. Uh, +and in this case, the the marshall's + + align:start position:0% +and in this case, the the marshall's + + + align:start position:0% +and in this case, the the marshall's +endangered. A lot of bad guys are coming + + align:start position:0% +endangered. A lot of bad guys are coming + + + align:start position:0% +endangered. A lot of bad guys are coming +after him. He goes around the town + + align:start position:0% +after him. He goes around the town + + + align:start position:0% +after him. He goes around the town +asking for help to set up a posi to help + + align:start position:0% +asking for help to set up a posi to help + + + align:start position:0% +asking for help to set up a posi to help +him defend the town. Nobody wants to + + align:start position:0% +him defend the town. Nobody wants to + + + align:start position:0% +him defend the town. Nobody wants to +help him. He's left on his own, and he + + align:start position:0% +help him. He's left on his own, and he + + + align:start position:0% +help him. He's left on his own, and he +has to fight against these guys on his + + align:start position:0% +has to fight against these guys on his + + + align:start position:0% +has to fight against these guys on his +own. Right? And that's so and the the + + align:start position:0% +own. Right? And that's so and the the + + + align:start position:0% +own. Right? And that's so and the the +drama of the film has to do with this + + align:start position:0% +drama of the film has to do with this + + + align:start position:0% +drama of the film has to do with this +where it's and as you'll see, McCabe and + + align:start position:0% +where it's and as you'll see, McCabe and + + + align:start position:0% +where it's and as you'll see, McCabe and +Mrs. Miller ends on a similar note in + + align:start position:0% +Mrs. Miller ends on a similar note in + + + align:start position:0% +Mrs. Miller ends on a similar note in +which McCabe is up against a force of + + align:start position:0% +which McCabe is up against a force of + + + align:start position:0% +which McCabe is up against a force of +men far larger than he he and also + + align:start position:0% +men far larger than he he and also + + + align:start position:0% +men far larger than he he and also +professional killers. Right? And in that + + align:start position:0% +professional killers. Right? And in that + + + align:start position:0% +professional killers. Right? And in that +sense, the end of McCabe in which McCabe + + align:start position:0% +sense, the end of McCabe in which McCabe + + + align:start position:0% +sense, the end of McCabe in which McCabe +has to the lost the whole last section + + align:start position:0% +has to the lost the whole last section + + + align:start position:0% +has to the lost the whole last section +of McCabe, which involves McCabe + + align:start position:0% +of McCabe, which involves McCabe + + + align:start position:0% +of McCabe, which involves McCabe +defending himself against assassins who + + align:start position:0% +defending himself against assassins who + + + align:start position:0% +defending himself against assassins who +have been dispatched by a corporation + + align:start position:0% +have been dispatched by a corporation + + + align:start position:0% +have been dispatched by a corporation +that has tried to buy McCabe out and + + align:start position:0% +that has tried to buy McCabe out and + + + align:start position:0% +that has tried to buy McCabe out and +when he's refused to sell, they've said, + + align:start position:0% +when he's refused to sell, they've said, + + + align:start position:0% +when he's refused to sell, they've said, +"Okay, we'll take another route. We + + align:start position:0% +"Okay, we'll take another route. We + + + align:start position:0% +"Okay, we'll take another route. We +we'll eliminate him." Right? This so + + align:start position:0% +we'll eliminate him." Right? This so + + + align:start position:0% +we'll eliminate him." Right? This so +Altman's telling the story of of + + align:start position:0% +Altman's telling the story of of + + + align:start position:0% +Altman's telling the story of of +capitalism at its most at its most + + align:start position:0% +capitalism at its most at its most + + + align:start position:0% +capitalism at its most at its most +aggressively evil. Right? instead of the + + align:start position:0% +aggressively evil. Right? instead of the + + + align:start position:0% +aggressively evil. Right? instead of the +kind of fairy tales that were told about + + align:start position:0% +kind of fairy tales that were told about + + + align:start position:0% +kind of fairy tales that were told about +how the west was made by by uh certain + + align:start position:0% +how the west was made by by uh certain + + + align:start position:0% +how the west was made by by uh certain +mythological uh u optimistically + + align:start position:0% +mythological uh u optimistically + + + align:start position:0% +mythological uh u optimistically +mythological westerns. Um so so um + + align:start position:0% +mythological westerns. Um so so um + + + align:start position:0% +mythological westerns. Um so so um +when when mabe defends himself at the + + align:start position:0% +when when mabe defends himself at the + + + align:start position:0% +when when mabe defends himself at the +very end against these larger forces, + + align:start position:0% +very end against these larger forces, + + + align:start position:0% +very end against these larger forces, +one of the things that gives him an + + align:start position:0% +one of the things that gives him an + + + align:start position:0% +one of the things that gives him an +advantage and one of the most + + align:start position:0% +advantage and one of the most + + + align:start position:0% +advantage and one of the most +interesting moments in the passages in + + align:start position:0% +interesting moments in the passages in + + + align:start position:0% +interesting moments in the passages in +the film occurs here has to do with his + + align:start position:0% +the film occurs here has to do with his + + + align:start position:0% +the film occurs here has to do with his +knowledge of the town. He helped build + + align:start position:0% +knowledge of the town. He helped build + + + align:start position:0% +knowledge of the town. He helped build +the town. So, he knows every nook and + + align:start position:0% +the town. So, he knows every nook and + + + align:start position:0% +the town. So, he knows every nook and +cranny of the town. And he's able in + + align:start position:0% +cranny of the town. And he's able in + + + align:start position:0% +cranny of the town. And he's able in +part to hold his own against four other + + align:start position:0% +part to hold his own against four other + + + align:start position:0% +part to hold his own against four other +men who are actually much better with + + align:start position:0% +men who are actually much better with + + + align:start position:0% +men who are actually much better with +with violence than he is because of his + + align:start position:0% +with violence than he is because of his + + + align:start position:0% +with violence than he is because of his +knowledge of the town. Something of that + + align:start position:0% +knowledge of the town. Something of that + + + align:start position:0% +knowledge of the town. Something of that +same kind of thing happens at the end of + + align:start position:0% +same kind of thing happens at the end of + + + align:start position:0% +same kind of thing happens at the end of +Highoon. The beginning of High Noon is + + align:start position:0% +Highoon. The beginning of High Noon is + + + align:start position:0% +Highoon. The beginning of High Noon is +exciting because what it shows is the + + align:start position:0% +exciting because what it shows is the + + + align:start position:0% +exciting because what it shows is the +film is exploring the territory that it + + align:start position:0% +film is exploring the territory that it + + + align:start position:0% +film is exploring the territory that it +will later return to. So, so, uh, I'm + + align:start position:0% +will later return to. So, so, uh, I'm + + + align:start position:0% +will later return to. So, so, uh, I'm +showing it to you because I think in + + align:start position:0% +showing it to you because I think in + + + align:start position:0% +showing it to you because I think in +part it's interesting. It's a nice + + align:start position:0% +part it's interesting. It's a nice + + + align:start position:0% +part it's interesting. It's a nice +contrast. There's no question that Alman + + align:start position:0% +contrast. There's no question that Alman + + + align:start position:0% +contrast. There's no question that Alman +expects us to have this film in our + + align:start position:0% +expects us to have this film in our + + + align:start position:0% +expects us to have this film in our +minds when we're watching McCabe. Okay, + + align:start position:0% +minds when we're watching McCabe. Okay, + + + align:start position:0% +minds when we're watching McCabe. Okay, +great. + + align:start position:0% + + + + align:start position:0% + +Any of you recognize this actor? His + + align:start position:0% +Any of you recognize this actor? His + + + align:start position:0% +Any of you recognize this actor? His +name is Lee Ben Cle. He played bad guys + + align:start position:0% +name is Lee Ben Cle. He played bad guys + + + align:start position:0% +name is Lee Ben Cle. He played bad guys +for most of his career and then when the + + align:start position:0% +for most of his career and then when the + + + align:start position:0% +for most of his career and then when the +spaghetti westerns came in, he started + + align:start position:0% +spaghetti westerns came in, he started + + + align:start position:0% +spaghetti westerns came in, he started +to he was reversed and he began to + + align:start position:0% +to he was reversed and he began to + + + align:start position:0% +to he was reversed and he began to +play less evil characters. But he he's + + align:start position:0% +play less evil characters. But he he's + + + align:start position:0% +play less evil characters. But he he's +an actor who was associated with evil + + align:start position:0% +an actor who was associated with evil + + + align:start position:0% +an actor who was associated with evil +roles in a series of westerns. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +The singer is is is text Ritter. And I + + align:start position:0% +The singer is is is text Ritter. And I + + + align:start position:0% +The singer is is is text Ritter. And I +must face the deadly + + align:start position:0% + + + + align:start position:0% + +killer. All + + align:start position:0% +killer. All + + + align:start position:0% +killer. All +[Music] + + align:start position:0% + + + + align:start position:0% + +I am a cow in my grave. + + align:start position:0% + + + + align:start position:0% + +I lose + + align:start position:0% +I lose + + + align:start position:0% +I lose +my + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +hand. I'm not afraid of I also wanted + + align:start position:0% +hand. I'm not afraid of I also wanted + + + align:start position:0% +hand. I'm not afraid of I also wanted +you to see this beginning so you could + + align:start position:0% +you to see this beginning so you could + + + align:start position:0% +you to see this beginning so you could +hear this ballad and contrast it with + + align:start position:0% +hear this ballad and contrast it with + + + align:start position:0% +hear this ballad and contrast it with +Leonard + + align:start position:0% +Leonard + + + align:start position:0% +Leonard +Conn's stoned area. Leonard Conn sounds + + align:start position:0% +Conn's stoned area. Leonard Conn sounds + + + align:start position:0% +Conn's stoned area. Leonard Conn sounds +like he's singing out of the + + align:start position:0% +like he's singing out of the + + + align:start position:0% +like he's singing out of the +counterculture and + + align:start position:0% +counterculture and + + + align:start position:0% +counterculture and +What? Watch the different subject + + align:start position:0% +What? Watch the different subject + + + align:start position:0% +What? Watch the different subject +matter. + + align:start position:0% +matter. + + + align:start position:0% +matter. +[Music] + + align:start position:0% + + + + align:start position:0% + +Although + + align:start position:0% +Although + + + align:start position:0% +Although +you + + align:start position:0% +you + + + align:start position:0% +you +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +can't + + align:start position:0% + + + + align:start position:0% + +you wait + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +long only someone who had never seen a + + align:start position:0% +long only someone who had never seen a + + + align:start position:0% +long only someone who had never seen a +movie would fail to recognize that these + + align:start position:0% +movie would fail to recognize that these + + + align:start position:0% +movie would fail to recognize that these +are bad guys. Now, how do you know + + align:start position:0% +are bad guys. Now, how do you know + + + align:start position:0% +are bad guys. Now, how do you know +they're bad guys? They're unshaven. They + + align:start position:0% +they're bad guys? They're unshaven. They + + + align:start position:0% +they're bad guys? They're unshaven. They +have black hats, right? There's a kind + + align:start position:0% +have black hats, right? There's a kind + + + align:start position:0% +have black hats, right? There's a kind +of implicit symbolism that the + + align:start position:0% +of implicit symbolism that the + + + align:start position:0% +of implicit symbolism that the +conventional western, even subtle ones + + align:start position:0% +conventional western, even subtle ones + + + align:start position:0% +conventional western, even subtle ones +like this one, which is a grown-up + + align:start position:0% +like this one, which is a grown-up + + + align:start position:0% +like this one, which is a grown-up +western. It's an adult western, still + + align:start position:0% +western. It's an adult western, still + + + align:start position:0% +western. It's an adult western, still +make use of. Alman will throw all those + + align:start position:0% +make use of. Alman will throw all those + + + align:start position:0% +make use of. Alman will throw all those +kinds of markers out. He thinks they're + + align:start position:0% +kinds of markers out. He thinks they're + + + align:start position:0% +kinds of markers out. He thinks they're +foolish. Another church + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +Think that's + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +heavy-handed? So, you see how what's + + align:start position:0% +heavy-handed? So, you see how what's + + + align:start position:0% +heavy-handed? So, you see how what's +happening here is a kind of visit + + align:start position:0% +happening here is a kind of visit + + + align:start position:0% +happening here is a kind of visit +through the town. It isn't until later + + align:start position:0% +through the town. It isn't until later + + + align:start position:0% +through the town. It isn't until later +in the film that you realize that every + + align:start position:0% +in the film that you realize that every + + + align:start position:0% +in the film that you realize that every +space you go by should have registered + + align:start position:0% +space you go by should have registered + + + align:start position:0% +space you go by should have registered +with you because the later action of the + + align:start position:0% +with you because the later action of the + + + align:start position:0% +with you because the later action of the +film will take place on these streets, + + align:start position:0% +film will take place on these streets, + + + align:start position:0% +film will take place on these streets, +in these in these barns, on these + + align:start position:0% +in these in these barns, on these + + + align:start position:0% +in these in these barns, on these +balconies. + + align:start position:0% +balconies. + + + align:start position:0% +balconies. +Come on, open up. We're going to have a + + align:start position:0% +Come on, open up. We're going to have a + + + align:start position:0% +Come on, open up. We're going to have a +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +big in a hurry. Yeah, I sure am. You're + + align:start position:0% +big in a hurry. Yeah, I sure am. You're + + + align:start position:0% +big in a hurry. Yeah, I sure am. You're +a fool. Come on. + + align:start position:0% +a fool. Come on. + + + align:start position:0% +a fool. Come on. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Now watch this shot. All right. All + + align:start position:0% +Now watch this shot. All right. All + + + align:start position:0% +Now watch this shot. All right. All +right, ladies and gentlemen, let us + + align:start position:0% +right, ladies and gentlemen, let us + + + align:start position:0% +right, ladies and gentlemen, let us +begin. And there's Gary Cooper, the + + align:start position:0% +begin. And there's Gary Cooper, the + + + align:start position:0% +begin. And there's Gary Cooper, the +bride and groom step forward, who will + + align:start position:0% +bride and groom step forward, who will + + + align:start position:0% +bride and groom step forward, who will +be our hero. And in fact, he's marrying + + align:start position:0% +be our hero. And in fact, he's marrying + + + align:start position:0% +be our hero. And in fact, he's marrying +Grace Kelly, who in this film is a + + align:start position:0% +Grace Kelly, who in this film is a + + + align:start position:0% +Grace Kelly, who in this film is a +Quaker. And guess what? One of the + + align:start position:0% +Quaker. And guess what? One of the + + + align:start position:0% +Quaker. And guess what? One of the +climactic events in the film invi is the + + align:start position:0% +climactic events in the film invi is the + + + align:start position:0% +climactic events in the film invi is the +Quaker lady fires a gun to save her + + align:start position:0% +Quaker lady fires a gun to save her + + + align:start position:0% +Quaker lady fires a gun to save her +beloved, violates her moral principles, + + align:start position:0% +beloved, violates her moral principles, + + + align:start position:0% +beloved, violates her moral principles, +and kills someone to save her man. + + align:start position:0% +and kills someone to save her man. + + + align:start position:0% +and kills someone to save her man. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Now, I I don't want I I don't want you + + align:start position:0% +Now, I I don't want I I don't want you + + + align:start position:0% +Now, I I don't want I I don't want you +to think that my Can we have the lights + + align:start position:0% +to think that my Can we have the lights + + + align:start position:0% +to think that my Can we have the lights +again, Greg? I don't want you to think + + align:start position:0% +again, Greg? I don't want you to think + + + align:start position:0% +again, Greg? I don't want you to think +that I'm suggesting that High Noon is + + align:start position:0% +that I'm suggesting that High Noon is + + + align:start position:0% +that I'm suggesting that High Noon is +not a remarkable movie. It is. It's It's + + align:start position:0% +not a remarkable movie. It is. It's It's + + + align:start position:0% +not a remarkable movie. It is. It's It's +one of the very very good westerns + + align:start position:0% +one of the very very good westerns + + + align:start position:0% +one of the very very good westerns +there. It it has great uh uh subtlety + + align:start position:0% +there. It it has great uh uh subtlety + + + align:start position:0% +there. It it has great uh uh subtlety +and power in its own way. Uh but I think + + align:start position:0% +and power in its own way. Uh but I think + + + align:start position:0% +and power in its own way. Uh but I think +that Alman definitely wanted us to think + + align:start position:0% +that Alman definitely wanted us to think + + + align:start position:0% +that Alman definitely wanted us to think +about the radical differences between + + align:start position:0% +about the radical differences between + + + align:start position:0% +about the radical differences between +the universe imagined in McCabe and Mrs. + + align:start position:0% +the universe imagined in McCabe and Mrs. + + + align:start position:0% +the universe imagined in McCabe and Mrs. +Miller and the world as it's uh uh + + align:start position:0% +Miller and the world as it's uh uh + + + align:start position:0% +Miller and the world as it's uh uh +imagined in even even subtle adult 50s + + align:start position:0% +imagined in even even subtle adult 50s + + + align:start position:0% +imagined in even even subtle adult 50s +westerns. So uh many of these things are + + align:start position:0% +westerns. So uh many of these things are + + + align:start position:0% +westerns. So uh many of these things are +crystallized for us in the remarkable + + align:start position:0% +crystallized for us in the remarkable + + + align:start position:0% +crystallized for us in the remarkable +conclusion of the film. + + align:start position:0% +conclusion of the film. + + + align:start position:0% +conclusion of the film. +Um, and I hope that you'll pay a lot of + + align:start position:0% +Um, and I hope that you'll pay a lot of + + + align:start position:0% +Um, and I hope that you'll pay a lot of +attention to that. It's an extended + + align:start position:0% +attention to that. It's an extended + + + align:start position:0% +attention to that. It's an extended +sequence and it's it's a it it operates + + align:start position:0% +sequence and it's it's a it it operates + + + align:start position:0% +sequence and it's it's a it it operates +according to a principle of parallel + + align:start position:0% +according to a principle of parallel + + + align:start position:0% +according to a principle of parallel +action. The church I mentioned earlier + + align:start position:0% +action. The church I mentioned earlier + + + align:start position:0% +action. The church I mentioned earlier +catches fire. Watch why it catches fire. + + align:start position:0% +catches fire. Watch why it catches fire. + + + align:start position:0% +catches fire. Watch why it catches fire. +It's connected to the plot. Uh, and + + align:start position:0% +It's connected to the plot. Uh, and + + + align:start position:0% +It's connected to the plot. Uh, and +while the church is burning, most of the + + align:start position:0% +while the church is burning, most of the + + + align:start position:0% +while the church is burning, most of the +town gets together in a kind of comic + + align:start position:0% +town gets together in a kind of comic + + + align:start position:0% +town gets together in a kind of comic +bucket brigade to put this to put the + + align:start position:0% +bucket brigade to put this to put the + + + align:start position:0% +bucket brigade to put this to put the +fire out. Uh, they are partly aided by a + + align:start position:0% +fire out. Uh, they are partly aided by a + + + align:start position:0% +fire out. Uh, they are partly aided by a +new fire engine, a mark of the town's + + align:start position:0% +new fire engine, a mark of the town's + + + align:start position:0% +new fire engine, a mark of the town's +growth, right? that arrives at a certain + + align:start position:0% +growth, right? that arrives at a certain + + + align:start position:0% +growth, right? that arrives at a certain +point uh in the history of the town. The + + align:start position:0% +point uh in the history of the town. The + + + align:start position:0% +point uh in the history of the town. The +fire engine, I believe, arrives at the + + align:start position:0% +fire engine, I believe, arrives at the + + + align:start position:0% +fire engine, I believe, arrives at the +same time that Mrs. Miller arrives in + + align:start position:0% +same time that Mrs. Miller arrives in + + + align:start position:0% +same time that Mrs. Miller arrives in +town. They're both equally important + + align:start position:0% +town. They're both equally important + + + align:start position:0% +town. They're both equally important +historical events for the town's future. + + align:start position:0% +historical events for the town's future. + + + align:start position:0% +historical events for the town's future. +Uh but the arrival of the engine + + align:start position:0% +Uh but the arrival of the engine + + + align:start position:0% +Uh but the arrival of the engine +suggests of the coming of civilization, + + align:start position:0% +suggests of the coming of civilization, + + + align:start position:0% +suggests of the coming of civilization, +right? And there's a certain sense in + + align:start position:0% +right? And there's a certain sense in + + + align:start position:0% +right? And there's a certain sense in +which the act the the the fighting of + + align:start position:0% +which the act the the the fighting of + + + align:start position:0% +which the act the the the fighting of +the of the fire, it's actually almost + + align:start position:0% +the of the fire, it's actually almost + + + align:start position:0% +the of the fire, it's actually almost +treated like a slapstick event. Uh, real + + align:start position:0% +treated like a slapstick event. Uh, real + + + align:start position:0% +treated like a slapstick event. Uh, real +film buffs would actually recognize + + align:start position:0% +film buffs would actually recognize + + + align:start position:0% +film buffs would actually recognize +visual illusions or references to the + + align:start position:0% +visual illusions or references to the + + + align:start position:0% +visual illusions or references to the +Keystone Cops era. Uh, I I don't want to + + align:start position:0% +Keystone Cops era. Uh, I I don't want to + + + align:start position:0% +Keystone Cops era. Uh, I I don't want to +exaggerate this, but you'll see it. I + + align:start position:0% +exaggerate this, but you'll see it. I + + + align:start position:0% +exaggerate this, but you'll see it. I +mean, there actually is someone carrying + + align:start position:0% +mean, there actually is someone carrying + + + align:start position:0% +mean, there actually is someone carrying +a bucket that has a hole in it, water's + + align:start position:0% +a bucket that has a hole in it, water's + + + align:start position:0% +a bucket that has a hole in it, water's +falling out, that kind of thing. And + + align:start position:0% +falling out, that kind of thing. And + + + align:start position:0% +falling out, that kind of thing. And +they're incredibly ineffectual in their + + align:start position:0% +they're incredibly ineffectual in their + + + align:start position:0% +they're incredibly ineffectual in their +trying to put out the fire. I don't + + align:start position:0% +trying to put out the fire. I don't + + + align:start position:0% +trying to put out the fire. I don't +think they succeed very well. The church + + align:start position:0% +think they succeed very well. The church + + + align:start position:0% +think they succeed very well. The church +essentially is destroyed, or at least + + align:start position:0% +essentially is destroyed, or at least + + + align:start position:0% +essentially is destroyed, or at least +the steeple is destroyed. But what + + align:start position:0% +the steeple is destroyed. But what + + + align:start position:0% +the steeple is destroyed. But what +happens nonetheless is the town has come + + align:start position:0% +happens nonetheless is the town has come + + + align:start position:0% +happens nonetheless is the town has come +together and it's actually a moment in + + align:start position:0% +together and it's actually a moment in + + + align:start position:0% +together and it's actually a moment in +which you actually feel that the town's + + align:start position:0% +which you actually feel that the town's + + + align:start position:0% +which you actually feel that the town's +identity is being forged as these + + align:start position:0% +identity is being forged as these + + + align:start position:0% +identity is being forged as these +disperate people, the and the + + align:start position:0% +disperate people, the and the + + + align:start position:0% +disperate people, the and the +barbers and the respectable people and + + align:start position:0% +barbers and the respectable people and + + + align:start position:0% +barbers and the respectable people and +the saloonkeeper all get together to try + + align:start position:0% +the saloonkeeper all get together to try + + + align:start position:0% +the saloonkeeper all get together to try +to put the fire out. So it is a moment + + align:start position:0% +to put the fire out. So it is a moment + + + align:start position:0% +to put the fire out. So it is a moment +in which the town is really a burning + + align:start position:0% +in which the town is really a burning + + + align:start position:0% +in which the town is really a burning +right while that is happening. McCabe is + + align:start position:0% +right while that is happening. McCabe is + + + align:start position:0% +right while that is happening. McCabe is +being stalked by the assassins. the + + align:start position:0% +being stalked by the assassins. the + + + align:start position:0% +being stalked by the assassins. the +creator of the town, the founder of the + + align:start position:0% +creator of the town, the founder of the + + + align:start position:0% +creator of the town, the founder of the +town is in a in a fight for his life + + align:start position:0% +town is in a in a fight for his life + + + align:start position:0% +town is in a in a fight for his life +while they're while this slapstick + + align:start position:0% +while they're while this slapstick + + + align:start position:0% +while they're while this slapstick +firefighting is going on. Watch how that + + align:start position:0% +firefighting is going on. Watch how that + + + align:start position:0% +firefighting is going on. Watch how that +works itself out. Watch how and then pay + + align:start position:0% +works itself out. Watch how and then pay + + + align:start position:0% +works itself out. Watch how and then pay +a special attention to the profound + + align:start position:0% +a special attention to the profound + + + align:start position:0% +a special attention to the profound +disturbing ambiguities of the ending. + + align:start position:0% +disturbing ambiguities of the ending. + + + align:start position:0% +disturbing ambiguities of the ending. +One of the reasons I admire McCabe and + + align:start position:0% +One of the reasons I admire McCabe and + + + align:start position:0% +One of the reasons I admire McCabe and +Mrs. Miller so much is that it seems in + + align:start position:0% +Mrs. Miller so much is that it seems in + + + align:start position:0% +Mrs. Miller so much is that it seems in +many ways to satisfy the desires one has + + align:start position:0% +many ways to satisfy the desires one has + + + align:start position:0% +many ways to satisfy the desires one has +the desire one has + + align:start position:0% +the desire one has + + + align:start position:0% +the desire one has +for the trappings of a conventional + + align:start position:0% +for the trappings of a conventional + + + align:start position:0% +for the trappings of a conventional +western. They're all all of the elements + + align:start position:0% +western. They're all all of the elements + + + align:start position:0% +western. They're all all of the elements +that you think of should that you think + + align:start position:0% +that you think of should that you think + + + align:start position:0% +that you think of should that you think +should belong to a serious western are + + align:start position:0% +should belong to a serious western are + + + align:start position:0% +should belong to a serious western are +present but they're present in such + + align:start position:0% +present but they're present in such + + + align:start position:0% +present but they're present in such +ironized such damage such inverted form + + align:start position:0% +ironized such damage such inverted form + + + align:start position:0% +ironized such damage such inverted form +that they make you rethink not only + + align:start position:0% +that they make you rethink not only + + + align:start position:0% +that they make you rethink not only +those particular conventions but the + + align:start position:0% +those particular conventions but the + + + align:start position:0% +those particular conventions but the +larger mythological and ideological + + align:start position:0% +larger mythological and ideological + + + align:start position:0% +larger mythological and ideological +uh work that western that the western + + align:start position:0% +uh work that western that the western + + + align:start position:0% +uh work that western that the western +mythology has performed in American + + align:start position:0% +mythology has performed in American + + + align:start position:0% +mythology has performed in American +society up to this time. So it makes + + align:start position:0% +society up to this time. So it makes + + + align:start position:0% +society up to this time. So it makes +McCabe and Mrs. Miller not just a + + align:start position:0% +McCabe and Mrs. Miller not just a + + + align:start position:0% +McCabe and Mrs. Miller not just a +wonderfully entertaining film. full of + + align:start position:0% +wonderfully entertaining film. full of + + + align:start position:0% +wonderfully entertaining film. full of +comic moments and brilliant + + align:start position:0% +comic moments and brilliant + + + align:start position:0% +comic moments and brilliant +performances. It is in its own right an + + align:start position:0% +performances. It is in its own right an + + + align:start position:0% +performances. It is in its own right an +a great work of imaginative uh + + align:start position:0% +a great work of imaginative uh + + + align:start position:0% +a great work of imaginative uh +intelligence. But it is an even larger + + align:start position:0% +intelligence. But it is an even larger + + + align:start position:0% +intelligence. But it is an even larger +thing it seems to me because of the + + align:start position:0% +thing it seems to me because of the + + + align:start position:0% +thing it seems to me because of the +intelligence with which it engages in + + align:start position:0% +intelligence with which it engages in + + + align:start position:0% +intelligence with which it engages in +this systematic conversation with its + + align:start position:0% +this systematic conversation with its + + + align:start position:0% +this systematic conversation with its +aesthetic and moral ancestry in the + + align:start position:0% +aesthetic and moral ancestry in the + + + align:start position:0% +aesthetic and moral ancestry in the +great founding story of the western + + align:start position:0% +great founding story of the western + + + align:start position:0% +great founding story of the western +which I suppose must be identified as + + align:start position:0% +which I suppose must be identified as + + + align:start position:0% +which I suppose must be identified as +America's most distinctive and in some + + align:start position:0% +America's most distinctive and in some + + + align:start position:0% +America's most distinctive and in some +ways most disturbingly + + align:start position:0% +ways most disturbingly + + + align:start position:0% +ways most disturbingly +revealing story about + + align:start position:0% +revealing story about + + + align:start position:0% +revealing story about +itself. See you next week. \ No newline at end of file diff --git a/pSdxdfBnu0I.txt b/pSdxdfBnu0I.txt new file mode 100644 index 0000000000000000000000000000000000000000..74520dc6f144b26ee544c9c861a4dfa286fc72bd --- /dev/null +++ b/pSdxdfBnu0I.txt @@ -0,0 +1,2265 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Ladies and gentlemen, +welcome to + +lecture number 11. + +In this lecture, I would like +to continue discussing with + +you the solution of the dynamic +equilibrium equations. + +We discussed the solution of +dynamic equilibrium equations + +already in lecture number 10. + +In that lecture, we consider +direct integration methods. + +In this lecture, I would like to +consider with you, discuss + +with you the mode superposition +analysis. + +The basic idea in the mode +superposition analysis is the + +transformation from the U +displacements into a set of + +new displacements, X. + +P is an n by n matrix, +which is nonsingular. + +If P is nonsingular, we should +recognize that the vector U of + +lengths n is uniquely given +when we have the vector X, + +also of lengths n +and vice versa. + +In other words, if we have the +vector X, we can calculate U. + +Or if we have U, we can +calculate X. P, of course, has + +to be a nonsingular matrix. + +We call this a transformation +matrix. + +And we call the X displacement, +that I will be + +talking about, the generalized +displacement. + +Now, if we use this +transformation, we find that + +if we substitute this +transformation into this + +equation for U, and we postulate +that P shall not be + +a function of time. + +So that when we find the +derivative of U, + +with respect to time-- + +let me denote it +by a dot here-- + +we simply obtain that U dot +is equal to P times X dot. + +And similarly, U double dot is +equal to P times X double dot. + +If we then substitute for U, +U dot, and U double dot-- + +in other words, for the +displacements, velocities, and + +accelerations-- + +into this equation, we obtain +this equation, provided-- + +and now, there's one +additional step-- + +after the substitution for the +displacements, velocities, and + +accelerations, we also +premultiply the total equation + +by a P transposed. + +In other words, what we do is +we take a P transposed here, + +and we are substituting for +these vectors here from that + +relation here. + +The P transposed, of course, +gives us, also, a P transposed + +R on the right-hand side. + +So R curl here is defined +as shown down here. + +Notice that M curl, C +curl, and K curl are + +given as shown here. + +And they involve, of course, +the M, C, and K matrices. + +And this P here comes via this + +substitution into these vectors. + +This P transposed comes from +that P transposed here. + +Now, what have we been +doing so far? + +Basically, what we have +been doing is we + +have changed bases. + +We have come from the +displacement defined by the + +finite elements-- + +by the finite element +nodal points-- + +to generalized displacements. + +The generalized displacements +now govern the equilibrium of + +the system. + +Now, this transformation is +effective if we find that our + +M curl, C curl, and K curl have +a better structure than + +the matrices, M, C, and K. +And, of course, if it is + +simpler to find the P matrix +or a P matrix. + +Let's look at a very +simple case. + +If, for example, M curl, C curl, +and K curl would all be + +diagonal matrices, then the +solution of this set of + +equations would be +very simple. + +In fact, this is +our objective. + +It is our objective to come up +with a P matrix, which when + +used in this transformation, +gives us an M curl, C curl, + +and K curl matrix that +are all diagonal. + +And, of course, in addition we +want to find the P matrix with + +a minimum amount of effort. + +Once we have diagonal matrices +here on the left-hand side-- + +in other words, M curl, +C curl, and K curl-- + +then, we can use our direct time +integration schemes, the + +Newmark method, or the essential +difference method. + +Usually we use the +Newmark method. + +Or we might even be able to +solve the decoupled equations. + +They're decoupled because M +curl, CK curl, are diagonal. + +We might even solve these +equations in closed form. + +The question then is how do we +find P or [UNINTELLIGIBLE] + +P? + +We want to find it cheaply. + +It shall be economical to +calculate P. And we want to, + +of course, have that M curl, +C curl, K curl are ideally + +diagonal matrices. + +Well, the P matrix can +be constructed-- + +or a P matrix can be +constructed, effectively, by + +looking at the free vibration +equilibrium + +equations of the system. + +If we look at these equilibrium +equations here, in + +which we neglect damping and we +neglect the right-hand side + +forces-- we're looking at the +equilibrium equations of the + +dynamic system without damping +and without forces applied. + +And if we look for a solution +to this system, then, we can + +assume a solution +of this form. + +U, of course, being our +displacement vector. + +Phi being all the vector that +is independent now of time. + +And here is the time dependency, +sin, omega, omega + +is a radiant per second +circular frequency. + +t, of course, being the time. + +And t 0 is a time shift. + +If we make this assumption, +substitute into here-- + +when we do substitute, of +course, remember we have to + +take the second derivative of +this function here with + +respect to time because we're +taking the second + +derivative of U here. + +And that gives us a minus omega +squared sin, omega t + +minus t 0, substituting +from here into there. + +We immediately get this equation +because we can cancel + +out sin omega t minus +t 0 on both sides. + +This is the resulting +equation. + +So what we now want +is to solve for + +phi and omega squared. + +This is the generalized +eigenvalue problem. + +The generalized eigenvalue +problem because M is a matrix + +other than the identity +matrix in general. + +And we know that they are n +solutions to this problem if K + +and M are n by n matrices. + +There are n solutions +to this problem. + +We call these solutions +the eigensolutions. + +And we call omega 1 squared, +I should say, and phi 1 the + +first eigenpair. + +This is the second eigenpair, +this is the nth eigenpair. + +There are n such eigenpairs. + +Each of these eigenpairs +satisfies this equation here. + +Therefore, these are +a solution-- + +we call it an eigensolution-- + +to this equation. + +And in addition, we also can +prove-- we can show-- + +that the phi I vectors-- +these vectors here-- + +are M orthogonal. + +M orthogonal because phi +I transposed M phi j-- + +for example, phi 1 transposed +M phi 2 is equal to 0. + +And phi 1 transposed M phi j-- + +sorry phi 1 transposed M +phi 1 is equal to 1. + +And because it's equal to 1, +they're not only M orthogonal, + +they're indeed even +M ortho normal. + +What we find is that if we look +at this eigenproblem, and + +we notice that a certain +vector satisfies this + +eigenproblem, then also a +multiple of that vector + +satisfies the eigenproblem. + +And we determine this constant, +this undetermined + +constant, in such a way as to +have phi I transposed M phi I + +equal to 1. + +So these are the eigenpairs and +the eigenvectors, phi 1 to + +phi n, satisfy this relation. + +The eigenvalues, omega 1 squared +to omega n squared can + +be ordered in this way where +we find that we might have + +multiple eigenvalues. + +Omega 1 might be equal +to omega 2. + +But if we do, we still have only +a total number of n such + +eigenvalues. + +I will discuss in the next +lecture with you the solution + +techniques that we're using to +calculate these eigenpairs. + +Let's for the moment assume that +we have calculated them. + +And we want to use them. + +Well, if we now define +the following + +matrix, phi capital phi. + +It's a capital phi because +we see crossbars + +top and bottom here. + +If we define this matrix +as phi 1 to phi n-- + +in other words, we're taking +the first eigenvector, and + +list it as a first column +of this matrix here. + +The second eigenvector, we list +as the second column in + +this matrix and so on. + +So that we find, of course, that +this matrix here is an n + +by n matrix. + +And if we define a diagonal +matrix, omega squared. + +This is a capital omega. + +Omega squared, being +equal to 0s in the + +off diagonal elements. + +But the diagonal elements +being omega 1 + +squared to omega n squared. + +Then, we can write the solutions +to the eigenproblem. + +The solutions to the +eigenproblem-- + +and I'm still talking +about this + +eigenproblem problem here. + +We can write the solutions to +this e eigenproblem in the + +following form. + +Notice that this omega squared +here has to be on the back of + +the capital phi. + +In other words, this is the +solution to the problem, K phi + +equals omega squared M phi, +where the omega squared is a + +scalar and appears +here in front. + +We usually write it in front. + +Of course, we can put +it also at the back + +because it's a scalar. + +We can put in front +or the back. + +However, when we have listed the +solutions to this problem + +in this way, then, we have to +put the capital omega squared + +at the back of M times phi. + +You can verify that by simply +multiplying out + +the right-hand side. + +We also have this relationship +here, which is the M ortho + +normality, the phi ortho +normality with M. In other + +words, this here says nothing +else and phi I transposed M + +phi j is equal to delta I j. + +We call this the +chronica delta. + +And this chronica delta +is equal to 1 for I + +being equal to j. + +And it's 0 otherwise. + +So we are having this +relationship here. + +And if we use this relationship, +and we are + +premultiplying this equation by +phi transposed to capital + +phi transposed now, +both sides. + +We are finding that we +are getting here + +the identity matrix. + +And therefore, we're having that +this left-hand side is + +equal to omega squared. + +This matrix here. + +And this is an important fact. + +In other words, we find +that the vectors-- + +the eigenvectors-- + +satisfy these two +relationships. + +Now, if we look back at what +we started off with in our + +multiple position analysis +discussion, we wanted a matrix + +that we call P, which is such +that P transposed M, P ideally + +is a diagonal matrix. + +Well, we have no +such a matrix. + +If we take phi being equal to P. +Then, phi transposed M phi + +is in fact a diagonal matrix. + +In fact, a very nice diagonal +matrix, the identity matrix, + +which is a matrix that +is diagonal. + +It has just once on +the diagonal. + +Similarly, we wondered here +that P transposed KP is a + +diagonal matrix. + +Well, we have achieved that +by this phi matrix. + +So the phi matrix is, indeed, +a particular P + +matrix that we can use. + +So what we are then saying is +let us use a multiple position + +analysis this particular +P matrix. + +The P matrix, which is equal +to the phi matrix and phi + +storing the eigenvectors of the +generalized eigenproblem. + +Well, substituting from here, as +before, into the governing + +dynamic equilibrium +equations, we + +directly obtain this equation. + +However, we notice now that this +matrix here, in general, + +is not yet a diagonal matrix. + +We call that our C curl. + +And our C curl has not been +diagonalized yet. + +We will have to deal with that +matrix still a little later. + +How do we solve these +equations? + +Well, if we solve these +equations, we have to also + +recognize, of course, that we +have to include the initial + +conditions to the problem. + +And the initial conditions +mean that the initial + +displacements are defined +and the initial + +velocities are defined. + +These, of course, are the +initial conditions that are + +used in the direct integration +solution of the governing + +dynamic equilibrium equations. + +Well, if we are now performing +the solution of this set of + +equations, we will have to +transform these initial + +conditions to initial conditions +on the generalized + +displacements. + +And that is achieved via +these relations here. + +Let us see how we +derive these. + +Well, if we look at this +equation here, and if we + +notice that, of course, +this equation must be + +applicable 4 times 0. + +We can simply put a 0 there. + +And we put a 0 there. + +Then, of course, we also +recognize that we can + +premultiply this equation +with this relation here. + +And if we do that on the +right-hand side, we notice + +that phi transposed M +times that phi is + +the identity matrix. + +And so we have this relation +directly obtained. + +The left-hand side in this +equation is the right-hand + +side in this equation. + +And the right-hand side here +is simply this 0 x now. + +The same holds also for +the initial velocity. + +We can simply put dots on top +of the U here and of the X. + +And therefore, we have +this relation here. + +So the solution of this set of +equations and with these + +initial conditions subject to +these initial conditions, + +gives us a solution to of +the dynamic response. + +Now, I should mention here that +we still have to deal + +with the damping matrix. + +The damping matrix here needs +particular attention. + +We do not have, in general, +a diagonal matrix here. + +And we will want to construct +specific damping matrices with + +which we can deal, +effectively. + +And yet, of course, these +matrices must make, + +physically, sense. + +Let us look now, however, first +at the case where we + +neglect damping. + +When we neglect damping, we have +this set of equations and + +individual equations +of this form. + +Notice that these are individual +equations because + +this is a vector. + +This is a diagonal matrix. + +And on the right-hand side, we +simply have a vector off load, + +of course, time dependent. + +So we can look at the first row +in this matrix relation. + +And the first row in that matrix +relation will be this + +equation here with +I equal to 1. + +The I-th row in this relation +here is the + +I-th equation here. + +In other words, I subscripts +on the [UNINTELLIGIBLE]. + +And, in general therefore, +we want to + +solve n such equations. + +I going from 1 to n, with this +being the load vector and, of + +course, with the initial +conditions. + +These initial conditions are +obtained by simply looking at + +this equation here and +extracting the I-th row from + +each of these two relations. + +So this is then the problem. + +Notice the following that if we +solve all n equations with + +these initial conditions, then, +if we use, for example, + +the Newmark direct integration +method on these equations, we + +would obtain exactly the same +solution as if we had solved + +the fully coupled equations. + +The fully coupled equations-- +let me write them down once + +more here-- + +plus KU equals R. + +In other words, whether we +apply the Newmark time + +integration scheme, a direct +integration scheme, to this + +set of equations with the +initial conditions on U and U + +dot or apply the Newmark direct +time integration scheme + +to this set of equations, or +rather this one here with + +these initial conditions, we +obtain exactly the same + +response provided we use the +same time step, delta t in + +both integrations. + +There has been no assumption +so far. + +All we have done is a +transformation from the U + +displacements to the +X displacements. + +And this transformation is +effective if we can find the + +phi matrix that we're using +in the transformation very + +cheaply, very economically. + +Well, the effectiveness, really, +of multiple position + +goes beyond what I have +just described. + +The important point in multiple +position analysis is + +that we do not need to solve +all of these equations. + +That we do not need to solve +and look at all of the + +decoupled equations. + +But let us look first once also +at how we can solve the + +decoupled equations +now exactly. + +Where we can solve them exactly +for example using a + +Duhamel integral formulation +as shown here. + +X i of t is given via +this relation here. + +And we would, of course, +substitute our ri of tau where + +we now assume that this part +here is given, directly. + +In a computer program, very +frequently r i would only be + +given as a segment of +straight lines. + +And if that is the case, then, +of course, we might have to + +still evaluate all of this +here numerically if the + +segment is very complicated, +complex, like + +an earthquake analysis. + +ri might be varying +very rapidly. + +And then, we might still want to +evaluate this, numerically. + +However in general, we can +evaluate here this + +relationship analytically. + +And we don't need to use +numerical integration. + +Having got xi, of course, we get +our U of t as shown here + +by our transforming back. + +Well, the important point that +I now would like to get back + +to you and discuss with you for +a little while is that we + +do not need to use or to solve +all of these equations in + +multiple position analysis. + +In fact, multiple position +analysis is only effective + +when we do not need +to look at all of + +these decoupled equations. + +If we have to solve all +decoupled equations, then, we + +would have to calculate, course, +first all eigenvalues + +and eigenvectors, which can +be an enormous expense. + +And then, the multiple +position analysis + +would not be effective. + +I would like to repeat, however, +if we do solve all + +decoupled equations, using a +specific time integration + +scheme with a specific +data t time step. + +Then, if we use the same time +integration scheme on + +decoupled equations with the +same time step, we must get + +exactly the same response. + +Then there has been no +assumption so far. + +Well, however, if we then +do neglect some of + +the equations here. + +We do not solve some +of the equations. + +Then, of course, our response +will be different that we are + +predicting via this approach +when we compare with the + +response predicted by solving +these equations. + +Well, let us look once at this +graph again, which we already + +looked at briefly in +the last lecture. + +And I would like to explain +to you now why it is not + +necessary to solve all of the +decoupled equations in + +multiple position analysis. + +Why it is not, in general, +not necessary? + +Well, if we look at a +single oscillator + +equation, as given here. + +I include a damp in here, +of course, side + +can be equal to 0. + +Where P is the driving +frequency, omega is the + +frequency of the oscillator +itself. + +And if we plot the maximum +dynamic response observed, + +which we define if the dynamic +load factor when we divide + +that maximum dynamic response by +the static response, we get + +this set of curves. + +Let us look at say the curved +side equal to 0 + +a little bit closer. + +If we do that, and if we +solve this equation + +with side equals 0. + +This term now not being there. + +For certain values of P over +omega, we are getting this + +curve here and that +curve here. + +What do we notice? + +Well, we notice that when P over +omega is equal to 0, we + +are getting the static +response. + +Or P over omega very +small, we're + +getting the static response. + +This means, of course, that +omega, the system frequency, + +is much larger than the applied +frequency, which means + +really that this oscillator +is extremely stiff. + +Well, when compared to the +frequency of load application. + +So then, we are in this range. + +And we notice that say P over +omega in this range here, + +smaller than a certain value, +and this is here 0.5 say, + +smaller than 0.2. + +We would see that basically, the +maximum dynamic response + +is really just nothing else +than the static response. + +So we are talking in this +region here really about + +static response. + +And in this region here, we +are talking about a truly + +dynamic response. + +Now what does that mean? + +Well, if we look at our +decoupled equations here, it + +means that if i consist of +frequencies, basically, which + +when measured on the system of +the oscillator frequency are + +very small, we, basically, would +have a static solution. + +You would, basically, have a +static solution for this + +equilibrium equation. + +A truly dynamic solution will +only be obtained when P, in + +other words, the frequency of +the load divided by omega, + +falls into this range here. + +Well, this is what we +are using in most + +superposition analysis. + +We only need to consider those +frequencies of the system. + +And these are the frequencies +of the systems, the omegas, + +which are truly excited +by the dynamic loads. + +We only need to look at those +decoupled equilibrium + +equations for which we have that +the frequencies in the + +decoupled equations are truly +excited by the dynamic loads. + +Now, I only talked about +the P value here. + +Of course, in an actual +analysis, we would find that + +ri of P contains a number of +frequencies, a spectrum of + +frequencies. + +Well, what we have to do is look +at the highest frequency + +that is contained in ri. + +And we measure that highest +frequency on the frequencies + +of the system. + +If that highest frequency +divided by the frequency of + +the system is falling into +this range here, we are + +talking about a static +response, basically. + +And we do not need to consider +those equilibrium equations in + +are multiple position +analysis. + +Well, so what we are then saying +is let us all solve + +these equations not from i +equals 1 to n but from i + +equals 1 to P. And then, instead +of obtaining the true + +response, the "exact" response, +we are obtaining a + +response U P. i equals 1 to P. +Phi i, x i gives us U P, where + +U P is an approximation now +to the U displacements. + +And the U displacements, once +again, are the solution to + +this system of equations. + +How can we find out the error? + +Well, if U P is an approximate +solution to the system of + +equations that we want to solve, +then, let us substitute + +back into that system +of equations. + +Let me write it down +once more here. + +We have MU double dot +plus KU equals R + +that we want to solve. + +Well, we can also write that, of +course, MU double dot plus + +KU minus R. And this +shall be 0. + +So if we have an approximate +solution to this set of + +equations, why not just +substitute that approximate + +solution in here and see how +large the right-hand side is. + +If it's exactly 0, well, then +we have that our U P is, + +indeed, very close to U. And if +it's exactly 0 because U P + +would be equal to U. + +We will not find this to be 0. + +We will never find it to be 0 +because in a computer, we + +would, of course, use finite +digit arithmetic to evaluate + +the left-hand side. + +And we would have at +least round off. + +But what we want is at the +right-hand side calculated, + +which we now might call some +value shall be close to 0. + +And that means really what +we want to measure + +is this part here. + +Now what have I written +down here? + +I have here epsilon P of t +being this vector here. + +This is a vector. + +And we can call this an out of +balance load vector divided by + +the applied load vector. + +Notice that what I'm doing here, +I take the norm of this + +vector because I want to +get a single number. + +I want to get a single number +here, which is representative + +of all the elements +in that vector. + +The same applies here. + +This norm is calculated by +taking each value in this + +vector, squaring that value, +adding the squares of the + +values up, and then, taking +a square root out + +of that final value. + +In other words, if we write it +down here, quickly, what we do + +is if we have a vector a, and +we want to find this norm. + +What we do is we take a 1 +squared plus a 2 squared, et + +cetera, add all the individual +entries up + +of that vector here-- + +squares of the entries up-- + +and then, take the square +root out of it. + +And that gives us a single +number, which is + +representative of all the +elements in that vector. + +Notice that if one element is +large, well then, this value + +must be large, too, because +that one element will make + +this value large here. + +Well, if epsilon t is close to +0, assuming that r of t is not + +0, of course. + +Otherwise, you couldn't +use this. + +You would have to use some +equivalent approach. + +If epsilon P is close to 0, +then, we know that our + +equilibrium equation has been +solved quite accurately. + +In general, we might find that +it's not close to 0. + +And what we want to do is +a static correction. + +This static correction takes +into account the fact that we + +have neglected the +higher modes. + +And in the higher modes, of +course, we know we have + +basically static response. + +that's why we did not include +those equations in the + +multiple position analysis. + +So what do we do in that +static correction? + +We recognize that R could +be written in this form. + +This RI is exactly the value +that I defined earlier. + +M phi i is a vector. + +You see, I can take M and +multiply it by phi i, and I + +get a vector. + +Now they are in such +a vectors. + +We might not have calculated +all n. + +But you can say that indeed, +in theory there are n. + +So we can write this down. + +We also then can calculate the +delta R, which is that amount + +of the load vector, which has +not been included in the + +multiple position analysis. + +How do we obtain it? + +Well, we know R is the +total load vector. + +And if we now sum instead of i +equals 1 to n, only from i + +equals 1 to P, we are getting +this part here. + +But this part is exactly what +we have included in the + +multiple position analysis +already. + +So we are left with a vector on +the left-hand side, which + +we have not included in the +multiple position analysis. + +And we did not include it +because we knew at most, we + +can have static response, +corresponding to these loads. + +Let us now calculate that +static response. + +That's done right down here. + +Now, this static response has +to be added to the response + +which we predicted in the +multiple position analysis. + +Let us now go to the case +with damping included. + +So far we neglected that. + +Now, with damping included, we +have this part here, too. + +Notice phi transpose C +phi, in general, is + +not a diagonal matrix. + +And that's why I considered +first the + +case without damping. + +However, if we have +proportionate damping, and in + +structural analysis, frequently, +all that is + +necessary is to include +proportionate damping. + +Which we postulate to +be of this form. + +2 omega i xi i. + +Delta ij is again the chronica +delta, which is equal to 1 + +when i is equal to j and is +equal to 0 otherwise. + +So if we are postulating +this, where omega i, + +of course, is given. + +That is the free vibration +frequency, which is stored in + +this matrix here. + +xi i is a value, which +we are not given yet. + +We have not discussed it yet. + +But if we postulate that this +matrix here, basically, or + +each entry in that matrix can +be written in this way. + +Then, indeed, we would have +decoupled equations. + +It turns out that in practice, +as I mentioned already, this + +is all that is necessary to +include damping appropriately. + +Well, if we know these xi i +values, then, we can also + +construct a C matrix with +the xi i values given. + +The xi i values are frequently +obtained from experiments. + +In other words, the structure +is taken, its vibrated, it's + +excited into certain +vibration modes. + +And from these experiments +then, we + +obtain the xi i value. + +So once we have the xi +i value given, we can + +calculate the C matrix. + +And one way of calculating is +to use the Caughey series. + +Here we have the Caughey series, +which was proposed for + +calculating the C matrix, which +satisfies this criteria. + +In other words, damping +is proportional. + +Well, if the psi i values are +given, we can calculate the + +omega i, of course +are also given. + +We can calculate using this +equation, the constants a 0 to + +ap minus 1. + +Once we have these constants, +we can substitute them into + +here and be coming up +with a C matrix. + +And this C matrix here, +indeed, satisfies the + +normality property shown here. + +So, in other words, given the +psi i values from experimental + +results, given the omega i +values, we can calculate a C + +matrix that, in fact, gives us +a diagonal matrix when we + +carry out phi i transposed +C phi j. + +A special case of this C matrix +is Rayleigh damping, + +used abundantly in practice. + +Where we just include the first +two terms, alpha and + +beta being constants now. + +Let us go through a particular +example. + +Let's say that we know the +critical damping psi 1 is 0.02 + +and psi 2 is 0.10. + +In other words, 10% critical +damping in the second mode and + +2% critical damping +in the first mode. + +The corresponding frequencies +are 1 and 3. + +We want to calculate +our friend, beta. + +Well, what we do is use this C +matrix in the relation, phi i + +transposed, C times phi i. + +And that should give +us 2 omega psi i. + +Of course, we have two +i values, i equals 1 + +and i equals 2. + +So we can apply this +equation twice. + +Well, when we calculate +it out, we get this. + +Applying it twice, we directly +obtain these + +two equations here. + +And we solve these two equations +for alpha and beta. + +Having alpha and beta, we can +substitute now back into this + +equation here and have +our C matrix. + +This would be, for example, a C +matrix that we could use in + +a direct integration analysis. + +You see, if we are performing a +multiple position analysis, + +we might know, from experience, +from experimental + +results, that psi 1 and psi +2 are of these two values. + +And then, if we know that we +have so much critical damping + +or so much damping in the first +and second vibration + +mode, and we want to perform +a step-by-step direct + +integration analysis, we would +have to construct a C matrix. + +And this is the procedure +to construct a C matrix. + +Then, of course, we would have +to ask ourselves well, knowing + +these psi values for omega 1 and +omega 2, what are now the + +psi values that we are +implicitly using for the + +higher modes when we employ +this specific C matrix? + +And we use now, this +equation here. + +This is the equation, which we +already derived on this view + +graph here by looking +at this relation. + +You are now using this equation +because this equation + +must be applicable not just for +psi 1 and psi 2 but for + +all psi values. + +Well, then using this equation, +we can solve for the + +psi values. + +And, of course, psi 1 and psi 2, +substituting alpha and beta + +in here and omega 1 and omega +2 would, indeed, be just 2% + +and 10%, 0.02 and 0.10. + +However, we can now use +this equation to + +get the high xi values. + +And there's something to be +observed, which is quite + +important, namely we notice that +the beta value that we + +calculated is associated +with the high + +frequencies, basically. + +And the alpha value goes away. + +Or this contribution goes away +when we're looking at the high + +frequencies. + +For high frequencies therefore, +the beta value is a + +dominant factor. + +And for low frequencies, +the alpha value is + +the dominant factor. + +In other words, once again, +looking at this equation here, + +in the high frequency response, +beta K, really, will + +determine the damping. + +And in the low frequency, the +response is really the alpha + +value that determines +the damping. + +Well, the response solution +now would be performed in + +exactly the same +way as before. + +As in the case of +no damping, we + +solve now again P equations. + +P equations only. + +And we are doing that by looking +at this equation and + +with, of course, ri being given +as shown here and the + +initial conditions +being given here. + +Solving this equation here via +numerical integration or exact + +integration, using, for +something, Duhamel integral, + +we obtain the xi values +as a function of time. + +We substitute into here to +get our U P, which is an + +approximation to the +solution of the + +dynamic equilibrium equations. + +The dynamic equilibrium +equations now being MU double + +dot plus CU dot plus KU, +being equal to r. + +Notice we have a C matrix +in here now. + +However, and this is an +important point, we have a + +specific C matrix constructed +such that the phi i transposed + +C phi j gives us a diagonal +matrix with the diagonal + +elements being equal to +2 omega i, psi i. + +And one of these matrices, +for example, would be + +the Rayleigh matrix. + +The matrix obtained using +Rayleigh damping, rather. + +The important point is, once +again, that all we have been + +doing so far is to make a +change of bases from the + +finite element coordinates +to the generalized + +displacements, xi. + +That was the first step. + +The second step was that we +are neglecting the modes P + +plus 1 to n by only solving the +first P equations here and + +using this as an approximation +to the actual solution. + +The important point, of course, +is now that we have to + +ask ourselves when is +multiple position + +analysis really effective? + +Some considerations I have here +summarized on the last + +view graph. + +The multiple position analysis +is effective when the response + +lies in only a few modes. + +What does this mean? + +It means that if we look at our +eigenvalue problem, K phi + +equals omega squared M phi. + +We only need to solve this +eigenvalue problem + +for a very few modes. + +In other words, P being much +smaller than M, I will only + +have to solve for phi 1 up to +phi P and omega 1 squared up + +to omega P squared. + +This is a very important +point. + +I assumed here that we are +taking the lowest frequencies, + +omega 1 to omega P. Of course, +in general analysis, it might + +just be necessary to calculate +certain frequencies, say omega + +10 to omega 20. + +We only want to find the +frequencies in a certain range + +because we know that the +excitation frequency only lies + +in a particular range. + +That would be, for example, +the case in vibration + +excitation analysis. + +This then is a requirement for +multiple position analysis, + +really, to be effective. + +When the response is obtained +over many time intervals, then + +multiple position analysis +also becomes effective. + +We should remember here that +if we perform a direct + +integration analysis, and if +that is an implicit direct + +integration analysis, using the + +Newmark method, for example. + +Then, the number of operations +that we talked about in the + +Newmark method was +1/2 nm squared. + +That is the initial triangular +factorization + +that we have to perform. + +m being the half bandwidth. + +Plus 2 nm. + +n is the order, of course, +of the system. + +m is the half bandwidth, +once again. + +Times t, the number +of time steps. + +This is an initial expense that +we have to perform, using + +the direct integration Newmark +method, for example. + +The same holds for the +Wilson Theta method. + +or the Houbolt method. + +This is an initial expense. + +And then, we perform this +number of operations + +for each time step. + +Now, if we have to run 5,000 +time steps, then direct + +integration would be + +extremely, extremely expensive. + +And, in fact, you might not be +able to afford it, using + +implicit direct integration. + +Well, therefore, you can see +directed by looking at this + +operation column. + +What should make the analysis +more effective is to bring + +down the bandwidths. + +And, of course, this is exactly +what we're doing in + +multiple position analysis. + +We are going from a bandwidth +of m to a bandwidth of 0. + +You are having a diagonal +matrix. + +Remember, the bandwidths we +defined to be the number of + +off diagonal elements here +that we are having. + +We did not include +the diagonal. + +That is a half bandwidth. + +If you look at the +total band here-- + +that total band here was +equal to 2m plus 1. + +So if we are reducing the +bandwidths, as we do in + +multiple position analysis, then +we can see immediately + +that this number of operations +here, which is directly + +proportional to the number +of times steps goes down. + +And that is exactly the +objective in multiple position + +analysis that I talked +about earlier. + +That is the first important +objective. + +We want to reduce the bandwidths +for the direct + +integration analysis. + +The second objective, of course, +is that we do not need + +to even consider all +of the equations. + +So looking at n. + +We are reducing n, also. + +We are not looking anymore +at n equations. + +We are looking at P equations. + +And we are reducing the +bandwidths as I said earlier. + +m goes to 0. + +And n goes to P. Of +course, this is an + +approximate count here. + +So basically, you can see that +in the solution using multiple + +position analysis, the number +of operations in the time + +integration of the decoupled +equations is + +relatively small, is little. + +And, in fact, this solution +here can be obtained very, + +very effectively. + +The time integration of the +decoupled equations is very + +effective in an actual +practical analysis. + +Where the expense lies in +multiple position is really in + +the calculation of the required + +frequencies and motions. + +And, of course, this is exactly +the subject of the + +next lecture where I want to +discuss with you the effective + +solution techniques for +calculating these vectors and + +frequencies. + +Multiple position analysis is +effective, altogether only, + +when we can calculate these +eigenvalues and eigenvectors + +in an effective way. + +I should also finally, once +again, emphasize that it may + +be important to calculate the +error, epsilon pt that I + +referred to. + +Or to add a static correction +to the predicted response in + +the multiple position analysis +when P is, of course, much + +smaller than n. + +We have neglected the high +frequency response here. + +That high frequency response +is a static + +response, in general. + +And should be taken into +account via say static + +correction, as I have been +discussing with you. + +This is all I wanted to +say in this lecture. + +Thank you very much for +your attention. \ No newline at end of file diff --git a/pYZMNOuRwk0.txt b/pYZMNOuRwk0.txt new file mode 100644 index 0000000000000000000000000000000000000000..f625d37abce1a709be61784f7225f272bd8424f4 --- /dev/null +++ b/pYZMNOuRwk0.txt @@ -0,0 +1,4339 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right let's start off + + align:start position:0% +ocw.mit.edu all right let's start off + + + align:start position:0% +ocw.mit.edu all right let's start off +with a quick list of important concepts + + align:start position:0% +with a quick list of important concepts + + + align:start position:0% +with a quick list of important concepts +for the week + + align:start position:0% + + + + align:start position:0% + +just and and I'm going to push you right + + align:start position:0% +just and and I'm going to push you right + + + align:start position:0% +just and and I'm going to push you right +along today I want to get to something + + align:start position:0% +along today I want to get to something + + + align:start position:0% +along today I want to get to something +what do you + + align:start position:0% +what do you + + + align:start position:0% +what do you +got static equilibrium okay so + + align:start position:0% + + + + align:start position:0% + +eom + + align:start position:0% +eom + + + align:start position:0% +eom +from + + align:start position:0% +from + + + align:start position:0% +from +ecstatic okay + + align:start position:0% +ecstatic okay + + + align:start position:0% +ecstatic okay +good another concept for the week + + align:start position:0% + + + + align:start position:0% + +damping damping + + align:start position:0% +damping damping + + + align:start position:0% +damping damping +yeah and what have we been talking about + + align:start position:0% +yeah and what have we been talking about + + + align:start position:0% +yeah and what have we been talking about +all week vibration vibration okay so + + align:start position:0% + + + + align:start position:0% + +vibration + + align:start position:0% + + + + align:start position:0% + +damping okay more + + align:start position:0% + + + + align:start position:0% + +what's the whole General subject that + + align:start position:0% +what's the whole General subject that + + + align:start position:0% +what's the whole General subject that +we've encase vibration in it's an + + align:start position:0% +we've encase vibration in it's an + + + align:start position:0% +we've encase vibration in it's an +introduction to + + align:start position:0% + + + + align:start position:0% + +what we have to make it we've been + + align:start position:0% +what we have to make it we've been + + + align:start position:0% +what we have to make it we've been +making an assumption that we haven't + + align:start position:0% +making an assumption that we haven't + + + align:start position:0% +making an assumption that we haven't +made + + align:start position:0% + + + + align:start position:0% + +before yeah linear we have been studying + + align:start position:0% +before yeah linear we have been studying + + + align:start position:0% +before yeah linear we have been studying +this has been an intro to + + align:start position:0% + + + + align:start position:0% + +linear + + align:start position:0% + + + + align:start position:0% + +systems we can only do things like + + align:start position:0% +systems we can only do things like + + + align:start position:0% +systems we can only do things like +transfer functions that sort of thing + + align:start position:0% +transfer functions that sort of thing + + + align:start position:0% +transfer functions that sort of thing +with by assuming linearity anything + + align:start position:0% +with by assuming linearity anything + + + align:start position:0% +with by assuming linearity anything +else what have I just spent the last two + + align:start position:0% +else what have I just spent the last two + + + align:start position:0% +else what have I just spent the last two +lectures deriving for you and showing + + align:start position:0% +lectures deriving for you and showing + + + align:start position:0% +lectures deriving for you and showing +you transfer functions + + align:start position:0% + + + + align:start position:0% + +in fact I've shown you + + align:start position:0% + + + + align:start position:0% + +three all right all right that's that + + align:start position:0% +three all right all right that's that + + + align:start position:0% +three all right all right that's that +beginning to get at what we've been + + align:start position:0% +beginning to get at what we've been + + + align:start position:0% +beginning to get at what we've been +talking about so introduction to linear + + align:start position:0% +talking about so introduction to linear + + + align:start position:0% +talking about so introduction to linear +systems we've been studying vibration as + + align:start position:0% +systems we've been studying vibration as + + + align:start position:0% +systems we've been studying vibration as +one a one uh implementation or + + align:start position:0% +one a one uh implementation or + + + align:start position:0% +one a one uh implementation or +application of linear systems we've been + + align:start position:0% +application of linear systems we've been + + + align:start position:0% +application of linear systems we've been +looking at single degree of Freedom + + align:start position:0% +looking at single degree of Freedom + + + align:start position:0% +looking at single degree of Freedom +vibration problems only so far and we've + + align:start position:0% +vibration problems only so far and we've + + + align:start position:0% +vibration problems only so far and we've +found frequency response + + align:start position:0% +found frequency response + + + align:start position:0% +found frequency response +functions these frequency response + + align:start position:0% +functions these frequency response + + + align:start position:0% +functions these frequency response +function tell you the response of a + + align:start position:0% +function tell you the response of a + + + align:start position:0% +function tell you the response of a +system to what kind of an + + align:start position:0% + + + + align:start position:0% + +input what are the characteristics of + + align:start position:0% +input what are the characteristics of + + + align:start position:0% +input what are the characteristics of +the input that we've been looking at har + + align:start position:0% +the input that we've been looking at har + + + align:start position:0% +the input that we've been looking at har +what we call harmonic single frequency + + align:start position:0% +what we call harmonic single frequency + + + align:start position:0% +what we call harmonic single frequency +cosine Omega T like input cosine Omega T + + align:start position:0% +cosine Omega T like input cosine Omega T + + + align:start position:0% +cosine Omega T like input cosine Omega T +sin Omega t e to the I Omega t one + + align:start position:0% +sin Omega t e to the I Omega t one + + + align:start position:0% +sin Omega t e to the I Omega t one +frequency repetitive it's called a + + align:start position:0% +frequency repetitive it's called a + + + align:start position:0% +frequency repetitive it's called a +harmonic input so for a linear + + align:start position:0% + + + + align:start position:0% + +system we've also were talking about + + align:start position:0% +system we've also were talking about + + + align:start position:0% +system we've also were talking about +what we call the steady state response + + align:start position:0% +what we call the steady state response + + + align:start position:0% +what we call the steady state response +what's that + + align:start position:0% + + + + align:start position:0% + +mean what is okay put that in the + + align:start position:0% + + + + align:start position:0% + +words so you turn the motor on the whole + + align:start position:0% +words so you turn the motor on the whole + + + align:start position:0% +words so you turn the motor on the whole +building Shake settles down and just has + + align:start position:0% +building Shake settles down and just has + + + align:start position:0% +building Shake settles down and just has +a steady vibration you're dealing with + + align:start position:0% +a steady vibration you're dealing with + + + align:start position:0% +a steady vibration you're dealing with +so after any startup transients of died + + align:start position:0% +so after any startup transients of died + + + align:start position:0% +so after any startup transients of died +out it's a steady state response so if + + align:start position:0% +out it's a steady state response so if + + + align:start position:0% +out it's a steady state response so if +you're doing if you have + + align:start position:0% + + + + align:start position:0% + +a linear system and you're putting in + + align:start position:0% +a linear system and you're putting in + + + align:start position:0% +a linear system and you're putting in +some f e to the I Omega T + + align:start position:0% +some f e to the I Omega T + + + align:start position:0% +some f e to the I Omega T +Force real part of steady state + + align:start position:0% +Force real part of steady state + + + align:start position:0% +Force real part of steady state +response what is the frequency of the + + align:start position:0% + + + + align:start position:0% + +response right so for systems the steady + + align:start position:0% +response right so for systems the steady + + + align:start position:0% +response right so for systems the steady +state response the frequency of the + + align:start position:0% + + + + align:start position:0% + +output always it's a property of a + + align:start position:0% +output always it's a property of a + + + align:start position:0% +output always it's a property of a +linear system okay so a couple really + + align:start position:0% +linear system okay so a couple really + + + align:start position:0% +linear system okay so a couple really +important things to remember here good + + align:start position:0% + + + + align:start position:0% + +now we're going to move on to a problem + + align:start position:0% +now we're going to move on to a problem + + + align:start position:0% +now we're going to move on to a problem +oh and what other thing I usually do ask + + align:start position:0% +oh and what other thing I usually do ask + + + align:start position:0% +oh and what other thing I usually do ask +of you is are there any major questions + + align:start position:0% +of you is are there any major questions + + + align:start position:0% +of you is are there any major questions +something left over from lecture + + align:start position:0% +something left over from lecture + + + align:start position:0% +something left over from lecture +something we've done in the last week it + + align:start position:0% +something we've done in the last week it + + + align:start position:0% +something we've done in the last week it +just isn't going + + align:start position:0% + + + + align:start position:0% + +down gravity + + align:start position:0% +down gravity + + + align:start position:0% +down gravity +goes how how do you get gravity to go + + align:start position:0% +goes how how do you get gravity to go + + + align:start position:0% +goes how how do you get gravity to go +away in the equation actually this is + + align:start position:0% +away in the equation actually this is + + + align:start position:0% +away in the equation actually this is +the most common question that's been + + align:start position:0% +the most common question that's been + + + align:start position:0% +the most common question that's been +asked of the TA this week of Professor + + align:start position:0% +asked of the TA this week of Professor + + + align:start position:0% +asked of the TA this week of Professor +Gossard of me so the still seems to be a + + align:start position:0% +Gossard of me so the still seems to be a + + + align:start position:0% +Gossard of me so the still seems to be a +little bit of a misunderstanding about + + align:start position:0% +little bit of a misunderstanding about + + + align:start position:0% +little bit of a misunderstanding about +and this is the subject of static + + align:start position:0% +and this is the subject of static + + + align:start position:0% +and this is the subject of static +equilibrium versus uh unstretched spring + + align:start position:0% +equilibrium versus uh unstretched spring + + + align:start position:0% +equilibrium versus uh unstretched spring +kind of positions okay okay uh I think + + align:start position:0% +kind of positions okay okay uh I think + + + align:start position:0% +kind of positions okay okay uh I think +I'll just deal with that right + + align:start position:0% + + + + align:start position:0% + +away you're familiar with this problem + + align:start position:0% +away you're familiar with this problem + + + align:start position:0% +away you're familiar with this problem +you know k c m and you're and most of + + align:start position:0% +you know k c m and you're and most of + + + align:start position:0% +you know k c m and you're and most of +you're comfortable with the notion of + + align:start position:0% +you're comfortable with the notion of + + + align:start position:0% +you're comfortable with the notion of +measuring X from the unstretched spring + + align:start position:0% +measuring X from the unstretched spring + + + align:start position:0% +measuring X from the unstretched spring +position right so that's what I've done + + align:start position:0% +position right so that's what I've done + + + align:start position:0% +position right so that's what I've done +right here now you add gravity though + + align:start position:0% +right here now you add gravity though + + + align:start position:0% +right here now you add gravity though +and and let it find its equilibrium + + align:start position:0% +and and let it find its equilibrium + + + align:start position:0% +and and let it find its equilibrium +position under Gravity it's going to be + + align:start position:0% +position under Gravity it's going to be + + + align:start position:0% +position under Gravity it's going to be +at some other location right and I'm + + align:start position:0% +at some other location right and I'm + + + align:start position:0% +at some other location right and I'm +just going to call that + + align:start position:0% +just going to call that + + + align:start position:0% +just going to call that +xstatic that static + + align:start position:0% +xstatic that static + + + align:start position:0% +xstatic that static +displacement now when you turn on the ex + + align:start position:0% +displacement now when you turn on the ex + + + align:start position:0% +displacement now when you turn on the ex +the harmonic + + align:start position:0% +the harmonic + + + align:start position:0% +the harmonic +excitation or even grab it and let it go + + align:start position:0% +excitation or even grab it and let it go + + + align:start position:0% +excitation or even grab it and let it go +from initial condition where will it + + align:start position:0% +from initial condition where will it + + + align:start position:0% +from initial condition where will it +vibrate + + align:start position:0% + + + + align:start position:0% + +around it's going to vibrate with around + + align:start position:0% +around it's going to vibrate with around + + + align:start position:0% +around it's going to vibrate with around +the static equil equilibrium position so + + align:start position:0% +the static equil equilibrium position so + + + align:start position:0% +the static equil equilibrium position so +I'm going I'm here's my + + align:start position:0% +I'm going I'm here's my + + + align:start position:0% +I'm going I'm here's my +system here's my free body diagram got + + align:start position:0% +system here's my free body diagram got + + + align:start position:0% +system here's my free body diagram got +all the gravities and cxs and kx's and X + + align:start position:0% +all the gravities and cxs and kx's and X + + + align:start position:0% +all the gravities and cxs and kx's and X +dots and so forth in it complete + + align:start position:0% +dots and so forth in it complete + + + align:start position:0% +dots and so forth in it complete +right I can write it equation of motion + + align:start position:0% +right I can write it equation of motion + + + align:start position:0% +right I can write it equation of motion +for that system which you've done lots + + align:start position:0% +for that system which you've done lots + + + align:start position:0% +for that system which you've done lots +of times and it has gravity in + + align:start position:0% + + + + align:start position:0% + +it but now I'm going to say look here's + + align:start position:0% +it but now I'm going to say look here's + + + align:start position:0% +it but now I'm going to say look here's +my x coordinate it stretches down + + align:start position:0% +my x coordinate it stretches down + + + align:start position:0% +my x coordinate it stretches down +xstatic and on top of that I'm going to + + align:start position:0% +xstatic and on top of that I'm going to + + + align:start position:0% +xstatic and on top of that I'm going to +add a little Dynamic + + align:start position:0% +add a little Dynamic + + + align:start position:0% +add a little Dynamic +motion and I'm going to describe that as + + align:start position:0% +motion and I'm going to describe that as + + + align:start position:0% +motion and I'm going to describe that as +x equal xstatic a a constant plus the + + align:start position:0% +x equal xstatic a a constant plus the + + + align:start position:0% +x equal xstatic a a constant plus the +dynamic movement with respect to + + align:start position:0% + + + + align:start position:0% + +xstatic take the time derivative of it + + align:start position:0% +xstatic take the time derivative of it + + + align:start position:0% +xstatic take the time derivative of it +because this is constant it goes away + + align:start position:0% +because this is constant it goes away + + + align:start position:0% +because this is constant it goes away +and two time derivatives so x dot is X + + align:start position:0% +and two time derivatives so x dot is X + + + align:start position:0% +and two time derivatives so x dot is X +do D and x dot is xou dot the dynamic + + align:start position:0% +do D and x dot is xou dot the dynamic + + + align:start position:0% +do D and x dot is xou dot the dynamic +quantity take these three and plug them + + align:start position:0% +quantity take these three and plug them + + + align:start position:0% +quantity take these three and plug them +into here + + align:start position:0% + + + + align:start position:0% + +mxd dot cxd dot but the K term you still + + align:start position:0% +mxd dot cxd dot but the K term you still + + + align:start position:0% +mxd dot cxd dot but the K term you still +have xstatic in it don't + + align:start position:0% +have xstatic in it don't + + + align:start position:0% +have xstatic in it don't +you the original KX breaks into two + + align:start position:0% +you the original KX breaks into two + + + align:start position:0% +you the original KX breaks into two +pieces and on the right hand side is my + + align:start position:0% +pieces and on the right hand side is my + + + align:start position:0% +pieces and on the right hand side is my +mg plus F of T like + + align:start position:0% +mg plus F of T like + + + align:start position:0% +mg plus F of T like +before but K exatic is must be equal to + + align:start position:0% +before but K exatic is must be equal to + + + align:start position:0% +before but K exatic is must be equal to +mg in order for static equilibrium to + + align:start position:0% +mg in order for static equilibrium to + + + align:start position:0% +mg in order for static equilibrium to +have + + align:start position:0% + + + + align:start position:0% + +existed everybody agree with that + + align:start position:0% +existed everybody agree with that + + + align:start position:0% +existed everybody agree with that +another way to see that is let's say + + align:start position:0% +another way to see that is let's say + + + align:start position:0% +another way to see that is let's say +there's no Dynamic motion this term goes + + align:start position:0% +there's no Dynamic motion this term goes + + + align:start position:0% +there's no Dynamic motion this term goes +away this term goes away this term goes + + align:start position:0% +away this term goes away this term goes + + + align:start position:0% +away this term goes away this term goes +away turn off the excitation you left + + align:start position:0% +away turn off the excitation you left + + + align:start position:0% +away turn off the excitation you left +with that equals this and that's what + + align:start position:0% +with that equals this and that's what + + + align:start position:0% +with that equals this and that's what +says it sits in the static equilibrium + + align:start position:0% +says it sits in the static equilibrium + + + align:start position:0% +says it sits in the static equilibrium +position if those two are equal they + + align:start position:0% +position if those two are equal they + + + align:start position:0% +position if those two are equal they +cancel leaving you with + + align:start position:0% + + + + align:start position:0% + +this so if you had understood this in + + align:start position:0% +this so if you had understood this in + + + align:start position:0% +this so if you had understood this in +the + + align:start position:0% +the + + + align:start position:0% +the +beginning you could have said let + + align:start position:0% +beginning you could have said let + + + align:start position:0% +beginning you could have said let +let's start let's make our inertial + + align:start position:0% +let's start let's make our inertial + + + align:start position:0% +let's start let's make our inertial +coordinate from the static equilibrium + + align:start position:0% + + + + align:start position:0% + +position just let the thing find its + + align:start position:0% +position just let the thing find its + + + align:start position:0% +position just let the thing find its +static equilibri equilibrium position + + align:start position:0% +static equilibri equilibrium position + + + align:start position:0% +static equilibri equilibrium position +set the inertial coordinate measured + + align:start position:0% +set the inertial coordinate measured + + + align:start position:0% +set the inertial coordinate measured +from + + align:start position:0% +from + + + align:start position:0% +from +there and you would direct you would get + + align:start position:0% +there and you would direct you would get + + + align:start position:0% +there and you would direct you would get +to this + + align:start position:0% +to this + + + align:start position:0% +to this +equation with the possible + + align:start position:0% +equation with the possible + + + align:start position:0% +equation with the possible +confusion of having to deal with the + + align:start position:0% +confusion of having to deal with the + + + align:start position:0% +confusion of having to deal with the +free body diagram because the free body + + align:start position:0% +free body diagram because the free body + + + align:start position:0% +free body diagram because the free body +diagram still has on it + + align:start position:0% +diagram still has on it + + + align:start position:0% +diagram still has on it +mg and the spring force that comes from + + align:start position:0% +mg and the spring force that comes from + + + align:start position:0% +mg and the spring force that comes from +the static position right so if I were + + align:start position:0% +the static position right so if I were + + + align:start position:0% +the static position right so if I were +drawing a free if I were doing this and + + align:start position:0% +drawing a free if I were doing this and + + + align:start position:0% +drawing a free if I were doing this and +just say I want to go directly to this + + align:start position:0% +just say I want to go directly to this + + + align:start position:0% +just say I want to go directly to this +equation I would draw the free body + + align:start position:0% +equation I would draw the free body + + + align:start position:0% +equation I would draw the free body +diagram that would + + align:start position:0% +diagram that would + + + align:start position:0% +diagram that would +have + + align:start position:0% + + + + align:start position:0% + +kxd cxd + + align:start position:0% +kxd cxd + + + align:start position:0% +kxd cxd +dot f + + align:start position:0% + + + + align:start position:0% + +mg but then I would also just put in + + align:start position:0% +mg but then I would also just put in + + + align:start position:0% +mg but then I would also just put in +here there's one more Force + + align:start position:0% +here there's one more Force + + + align:start position:0% +here there's one more Force +K times ecstatic or Delta or whatever + + align:start position:0% +K times ecstatic or Delta or whatever + + + align:start position:0% +K times ecstatic or Delta or whatever +you want to call it you know there's + + align:start position:0% +you want to call it you know there's + + + align:start position:0% +you want to call it you know there's +some ecstatic and you know because + + align:start position:0% +some ecstatic and you know because + + + align:start position:0% +some ecstatic and you know because +you're doing this because you know this + + align:start position:0% +you're doing this because you know this + + + align:start position:0% +you're doing this because you know this +about the problem you know this cancels + + align:start position:0% +about the problem you know this cancels + + + align:start position:0% +about the problem you know this cancels +that and it won't appear in the equation + + align:start position:0% +that and it won't appear in the equation + + + align:start position:0% +that and it won't appear in the equation +of + + align:start position:0% + + + + align:start position:0% + +motion so to be able to do anytime + + align:start position:0% +motion so to be able to do anytime + + + align:start position:0% +motion so to be able to do anytime +you're confronted with a problem that + + align:start position:0% +you're confronted with a problem that + + + align:start position:0% +you're confronted with a problem that +has um gravity + + align:start position:0% +has um gravity + + + align:start position:0% +has um gravity +which causes a static + + align:start position:0% +which causes a static + + + align:start position:0% +which causes a static +deflection or results in a static + + align:start position:0% +deflection or results in a static + + + align:start position:0% +deflection or results in a static +equilibrium position it might be zero in + + align:start position:0% +equilibrium position it might be zero in + + + align:start position:0% +equilibrium position it might be zero in +your coordinate like + + align:start position:0% +your coordinate like + + + align:start position:0% +your coordinate like +pendulum uh you look at it and you say + + align:start position:0% +pendulum uh you look at it and you say + + + align:start position:0% +pendulum uh you look at it and you say +now in the equation of motion that you + + align:start position:0% +now in the equation of motion that you + + + align:start position:0% +now in the equation of motion that you +derive from the unstretched spring Force + + align:start position:0% +derive from the unstretched spring Force + + + align:start position:0% +derive from the unstretched spring Force +position is the mg term a function of + + align:start position:0% +position is the mg term a function of + + + align:start position:0% +position is the mg term a function of +the motion + + align:start position:0% +the motion + + + align:start position:0% +the motion +coordinate and in this + + align:start position:0% +coordinate and in this + + + align:start position:0% +coordinate and in this +case it is not so it doesn't matter what + + align:start position:0% +case it is not so it doesn't matter what + + + align:start position:0% +case it is not so it doesn't matter what +x comes this this Force stays constant + + align:start position:0% +x comes this this Force stays constant + + + align:start position:0% +x comes this this Force stays constant +it doesn't enter into the Dynamics of + + align:start position:0% +it doesn't enter into the Dynamics of + + + align:start position:0% +it doesn't enter into the Dynamics of +the + + align:start position:0% +the + + + align:start position:0% +the +problem and so if you can find the right + + align:start position:0% +problem and so if you can find the right + + + align:start position:0% +problem and so if you can find the right +if you ever write an equation of motion + + align:start position:0% +if you ever write an equation of motion + + + align:start position:0% +if you ever write an equation of motion +and you come with an mg term that + + align:start position:0% +and you come with an mg term that + + + align:start position:0% +and you come with an mg term that +doesn't have a Theta or an X or any + + align:start position:0% +doesn't have a Theta or an X or any + + + align:start position:0% +doesn't have a Theta or an X or any +variable in it you know that there's + + align:start position:0% +variable in it you know that there's + + + align:start position:0% +variable in it you know that there's +another way to write that equation about + + align:start position:0% +another way to write that equation about + + + align:start position:0% +another way to write that equation about +static equilibrium and you'll be able to + + align:start position:0% +static equilibrium and you'll be able to + + + align:start position:0% +static equilibrium and you'll be able to +get rid of it and and simplify the math + + align:start position:0% +get rid of it and and simplify the math + + + align:start position:0% +get rid of it and and simplify the math +basically okay now we got to move want + + align:start position:0% +basically okay now we got to move want + + + align:start position:0% +basically okay now we got to move want +to move on to + + align:start position:0% +to move on to + + + align:start position:0% +to move on to +the problem of the + + align:start position:0% +the problem of the + + + align:start position:0% +the problem of the +day and the problem of the day I've + + align:start position:0% +day and the problem of the day I've + + + align:start position:0% +day and the problem of the day I've +written up + + align:start position:0% + + + + align:start position:0% + +here that's the last classes list um + + align:start position:0% +here that's the last classes list um + + + align:start position:0% +here that's the last classes list um +you've got a motor fan or something it's + + align:start position:0% +you've got a motor fan or something it's + + + align:start position:0% +you've got a motor fan or something it's +got a rotating + + align:start position:0% +got a rotating + + + align:start position:0% +got a rotating +imbalance it's got a flexible + + align:start position:0% + + + + align:start position:0% + +base it's got a lot of vertical by + + align:start position:0% +base it's got a lot of vertical by + + + align:start position:0% +base it's got a lot of vertical by +vibration driving you crazy the rotation + + align:start position:0% +vibration driving you crazy the rotation + + + align:start position:0% +vibration driving you crazy the rotation +rate this is a you know a pump or + + align:start position:0% +rate this is a you know a pump or + + + align:start position:0% +rate this is a you know a pump or +something with a + + align:start position:0% +something with a + + + align:start position:0% +something with a +rotating some rotating Mass inside has + + align:start position:0% +rotating some rotating Mass inside has + + + align:start position:0% +rotating some rotating Mass inside has +some eccentricity so it's causing some + + align:start position:0% +some eccentricity so it's causing some + + + align:start position:0% +some eccentricity so it's causing some +external Force causing a VI force that + + align:start position:0% +external Force causing a VI force that + + + align:start position:0% +external Force causing a VI force that +results in vertical vibration the + + align:start position:0% +results in vertical vibration the + + + align:start position:0% +results in vertical vibration the +rotation rate of that fan is 1750 + + align:start position:0% + + + + align:start position:0% + +RPM the weight of this motor sitting on + + align:start position:0% +RPM the weight of this motor sitting on + + + align:start position:0% +RPM the weight of this motor sitting on +this Frame is 500 lb + + align:start position:0% + + + + align:start position:0% + +when you set this motor and bolt it down + + align:start position:0% +when you set this motor and bolt it down + + + align:start position:0% +when you set this motor and bolt it down +on that frame the frame deflects 026 + + align:start position:0% + + + + align:start position:0% + +in and this thing's vibrating like crazy + + align:start position:0% +in and this thing's vibrating like crazy + + + align:start position:0% +in and this thing's vibrating like crazy +now your assistant comes in and says I + + align:start position:0% +now your assistant comes in and says I + + + align:start position:0% +now your assistant comes in and says I +got a solution for this we're going to + + align:start position:0% + + + + align:start position:0% + +put braces in + + align:start position:0% + + + + align:start position:0% + +here and those braces will double the K + + align:start position:0% +here and those braces will double the K + + + align:start position:0% +here and those braces will double the K +the spring constant of the of the thing + + align:start position:0% +the spring constant of the of the thing + + + align:start position:0% +the spring constant of the of the thing +and he or she asserts that it he thinks + + align:start position:0% +and he or she asserts that it he thinks + + + align:start position:0% +and he or she asserts that it he thinks +it will cut the amplitude of response in + + align:start position:0% +it will cut the amplitude of response in + + + align:start position:0% +it will cut the amplitude of response in +half cut the vibration amplitude in half + + align:start position:0% +half cut the vibration amplitude in half + + + align:start position:0% +half cut the vibration amplitude in half +so you're going to do the calculations + + align:start position:0% +so you're going to do the calculations + + + align:start position:0% +so you're going to do the calculations +today to see whether or not this is a + + align:start position:0% +today to see whether or not this is a + + + align:start position:0% +today to see whether or not this is a +good + + align:start position:0% +good + + + align:start position:0% +good +idea and we're going to begin so + + align:start position:0% +idea and we're going to begin so + + + align:start position:0% +idea and we're going to begin so +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +one is come up with a + + align:start position:0% +one is come up with a + + + align:start position:0% +one is come up with a +simple lump parameter model masses + + align:start position:0% +simple lump parameter model masses + + + align:start position:0% +simple lump parameter model masses +Springs Dash pots of this system so that + + align:start position:0% +Springs Dash pots of this system so that + + + align:start position:0% +Springs Dash pots of this system so that +you can model + + align:start position:0% +you can model + + + align:start position:0% +you can model +it and so we've only been doing single + + align:start position:0% +it and so we've only been doing single + + + align:start position:0% +it and so we've only been doing single +degree Freedom systems it's probably + + align:start position:0% +degree Freedom systems it's probably + + + align:start position:0% +degree Freedom systems it's probably +going to look something like that so + + align:start position:0% +going to look something like that so + + + align:start position:0% +going to look something like that so +come up with a lump parameter model of + + align:start position:0% +come up with a lump parameter model of + + + align:start position:0% +come up with a lump parameter model of +that and we've got what + + align:start position:0% +that and we've got what + + + align:start position:0% +that and we've got what +four 8 12 we could do four groups easily + + align:start position:0% +four 8 12 we could do four groups easily + + + align:start position:0% +four 8 12 we could do four groups easily +here of four or five each so break into + + align:start position:0% +here of four or five each so break into + + + align:start position:0% +here of four or five each so break into +four groups come up first with the uh + + align:start position:0% +four groups come up first with the uh + + + align:start position:0% +four groups come up first with the uh +find and group one we'll we'll put group + + align:start position:0% +find and group one we'll we'll put group + + + align:start position:0% +find and group one we'll we'll put group +one right here and group two here and + + align:start position:0% +one right here and group two here and + + + align:start position:0% +one right here and group two here and +three and four there so come when you + + align:start position:0% +three and four there so come when you + + + align:start position:0% +three and four there so come when you +got when your group figure is out and we + + align:start position:0% +got when your group figure is out and we + + + align:start position:0% +got when your group figure is out and we +got to move right along because there's + + align:start position:0% +got to move right along because there's + + + align:start position:0% +got to move right along because there's +several parts of this come up sketch + + align:start position:0% +several parts of this come up sketch + + + align:start position:0% +several parts of this come up sketch +your model that you're going to do it + + align:start position:0% +your model that you're going to do it + + + align:start position:0% +your model that you're going to do it +with and then part two right after that + + align:start position:0% +with and then part two right after that + + + align:start position:0% +with and then part two right after that +is to compute the natural frequency of + + align:start position:0% +is to compute the natural frequency of + + + align:start position:0% +is to compute the natural frequency of +the + + align:start position:0% +the + + + align:start position:0% +the +system we're going to eventually have to + + align:start position:0% +system we're going to eventually have to + + + align:start position:0% +system we're going to eventually have to +compute the transfer functions and then + + align:start position:0% +compute the transfer functions and then + + + align:start position:0% +compute the transfer functions and then +try out the fix and see if the fix makes + + align:start position:0% +try out the fix and see if the fix makes + + + align:start position:0% +try out the fix and see if the fix makes +things better or worse so let's uh come + + align:start position:0% +things better or worse so let's uh come + + + align:start position:0% +things better or worse so let's uh come +first first assignment come up with the + + align:start position:0% +first first assignment come up with the + + + align:start position:0% +first first assignment come up with the +lump parameter model and find the + + align:start position:0% +lump parameter model and find the + + + align:start position:0% +lump parameter model and find the +natural + + align:start position:0% +natural + + + align:start position:0% +natural +frequency form your groups and get + + align:start position:0% + + + + align:start position:0% + +talking what about who is this you guys + + align:start position:0% +talking what about who is this you guys + + + align:start position:0% +talking what about who is this you guys +what about the + + align:start position:0% + + + + align:start position:0% + +force + + align:start position:0% + + + + align:start position:0% + +it and it's really some me e Omega + + align:start position:0% +it and it's really some me e Omega + + + align:start position:0% +it and it's really some me e Omega +squared + + align:start position:0% +squared + + + align:start position:0% +squared +Co Omega + + align:start position:0% +Co Omega + + + align:start position:0% +Co Omega +T and this comes from the equivalent + + align:start position:0% +T and this comes from the equivalent + + + align:start position:0% +T and this comes from the equivalent +little Mass on some arm East going round + + align:start position:0% +little Mass on some arm East going round + + + align:start position:0% +little Mass on some arm East going round +and round inside this is the equivalent + + align:start position:0% +and round inside this is the equivalent + + + align:start position:0% +and round inside this is the equivalent +uh unbalanced Mass here okay so keep + + align:start position:0% +uh unbalanced Mass here okay so keep + + + align:start position:0% +uh unbalanced Mass here okay so keep +coming up put your models up here yeah + + align:start position:0% +coming up put your models up here yeah + + + align:start position:0% +coming up put your models up here yeah +how do you get + + align:start position:0% +how do you get + + + align:start position:0% +how do you get +that well let's go back we've done this + + align:start position:0% +that well let's go back we've done this + + + align:start position:0% +that well let's go back we've done this +problem about four times over the course + + align:start position:0% +problem about four times over the course + + + align:start position:0% +problem about four times over the course +of homework in the term you know block + + align:start position:0% +of homework in the term you know block + + + align:start position:0% +of homework in the term you know block +with an arm with a mass on the end the E + + align:start position:0% +with an arm with a mass on the end the E + + + align:start position:0% +with an arm with a mass on the end the E +is the little L is the length the arm + + align:start position:0% +is the little L is the length the arm + + + align:start position:0% +is the little L is the length the arm +and the mass on the end is essentially + + align:start position:0% +and the mass on the end is essentially + + + align:start position:0% +and the mass on the end is essentially +the location of the center of mass of + + align:start position:0% +the location of the center of mass of + + + align:start position:0% +the location of the center of mass of +the rotating part okay all + + align:start position:0% + + + + align:start position:0% + +right so the other three groups need to + + align:start position:0% +right so the other three groups need to + + + align:start position:0% +right so the other three groups need to +draw a model up and come up with a + + align:start position:0% +draw a model up and come up with a + + + align:start position:0% +draw a model up and come up with a +natural + + align:start position:0% + + + + align:start position:0% + +frequency one of the annoyances this + + align:start position:0% +frequency one of the annoyances this + + + align:start position:0% +frequency one of the annoyances this +problem has nasty English units + + align:start position:0% + + + + align:start position:0% + +y all remember what G is in English + + align:start position:0% + + + + align:start position:0% + +units I want radians per + + align:start position:0% + + + + align:start position:0% + +second yeah but why do you convert + + align:start position:0% +second yeah but why do you convert + + + align:start position:0% +second yeah but why do you convert +English inches to feet and and you're + + align:start position:0% +English inches to feet and and you're + + + align:start position:0% +English inches to feet and and you're +done because you know G and feed per + + align:start position:0% +done because you know G and feed per + + + align:start position:0% +done because you know G and feed per +second + + align:start position:0% +second + + + align:start position:0% +second +squared so rather than do three + + align:start position:0% +squared so rather than do three + + + align:start position:0% +squared so rather than do three +conversions do + + align:start position:0% +conversions do + + + align:start position:0% +conversions do +one + + align:start position:0% +one + + + align:start position:0% +one +just well that's one and then you know G + + align:start position:0% +just well that's one and then you know G + + + align:start position:0% +just well that's one and then you know G +so you could do it that way sure I don't + + align:start position:0% +so you could do it that way sure I don't + + + align:start position:0% +so you could do it that way sure I don't +care I just want them I want the + + align:start position:0% + + + + align:start position:0% + +result you guys got a + + align:start position:0% +result you guys got a + + + align:start position:0% +result you guys got a +number which which group + + align:start position:0% +number which which group + + + align:start position:0% +number which which group +one you guys are one got a number you + + align:start position:0% +one you guys are one got a number you + + + align:start position:0% +one you guys are one got a number you +can give + + align:start position:0% +can give + + + align:start position:0% +can give +me how many MIT students is it take to + + align:start position:0% +me how many MIT students is it take to + + + align:start position:0% +me how many MIT students is it take to +convert from inches to feet we got that + + align:start position:0% +convert from inches to feet we got that + + + align:start position:0% +convert from inches to feet we got that +but we're not sure if we're gettings or + + align:start position:0% +but we're not sure if we're gettings or + + + align:start position:0% +but we're not sure if we're gettings or +radi + + align:start position:0% +radi + + + align:start position:0% +radi +after well in this this equation does it + + align:start position:0% +after well in this this equation does it + + + align:start position:0% +after well in this this equation does it +give you Hertz or + + align:start position:0% + + + + align:start position:0% + +radians + + align:start position:0% +radians + + + align:start position:0% +radians +H sure and you just made this + + align:start position:0% +H sure and you just made this + + + align:start position:0% +H sure and you just made this +substitution in here so it hasn't done + + align:start position:0% +substitution in here so it hasn't done + + + align:start position:0% +substitution in here so it hasn't done +anything to change + + align:start position:0% + + + + align:start position:0% + +hurts + + align:start position:0% +hurts + + + align:start position:0% +hurts +12 write that + + align:start position:0% + + + + align:start position:0% + +down what a struggle + + align:start position:0% +down what a struggle + + + align:start position:0% +down what a struggle +[Laughter] + + align:start position:0% + + + + align:start position:0% + +okay good that's good you can leave it + + align:start position:0% +okay good that's good you can leave it + + + align:start position:0% +okay good that's good you can leave it +all right we've all converged to about + + align:start position:0% +all right we've all converged to about + + + align:start position:0% +all right we've all converged to about +121 right that was quite a struggle was + + align:start position:0% +121 right that was quite a struggle was + + + align:start position:0% +121 right that was quite a struggle was +it the units or was partly it was Hertz + + align:start position:0% +it the units or was partly it was Hertz + + + align:start position:0% +it the units or was partly it was Hertz +and you guys haven't had you know we're + + align:start position:0% +and you guys haven't had you know we're + + + align:start position:0% +and you guys haven't had you know we're +dealing with nothing but equations for + + align:start position:0% +dealing with nothing but equations for + + + align:start position:0% +dealing with nothing but equations for +weeks and they actually have to do real + + align:start position:0% +weeks and they actually have to do real + + + align:start position:0% +weeks and they actually have to do real +engineering numbers has thrown you a + + align:start position:0% +engineering numbers has thrown you a + + + align:start position:0% +engineering numbers has thrown you a +little bit um but so it's about + + align:start position:0% +little bit um but so it's about + + + align:start position:0% +little bit um but so it's about +121 and that g over Delta thing is + + align:start position:0% +121 and that g over Delta thing is + + + align:start position:0% +121 and that g over Delta thing is +really handy you know um now we want now + + align:start position:0% +really handy you know um now we want now + + + align:start position:0% +really handy you know um now we want now +I want to know what is the response of + + align:start position:0% +I want to know what is the response of + + + align:start position:0% +I want to know what is the response of +this system to this input given the + + align:start position:0% +this system to this input given the + + + align:start position:0% +this system to this input given the +frequency of the input is 1750 + + align:start position:0% +frequency of the input is 1750 + + + align:start position:0% +frequency of the input is 1750 +RPM and RPM n is often + + align:start position:0% + + + + align:start position:0% + +written how's it related to frequency in + + align:start position:0% +written how's it related to frequency in + + + align:start position:0% +written how's it related to frequency in +hertz or cycles per second anybody know + + align:start position:0% +hertz or cycles per second anybody know + + + align:start position:0% +hertz or cycles per second anybody know +this is revolutions per minute what + + align:start position:0% +this is revolutions per minute what + + + align:start position:0% +this is revolutions per minute what +would be reol utions per second is that + + align:start position:0% +would be reol utions per second is that + + + align:start position:0% +would be reol utions per second is that +the same thing as Hertz so Revolution is + + align:start position:0% +the same thing as Hertz so Revolution is + + + align:start position:0% +the same thing as Hertz so Revolution is +something going around one full time + + align:start position:0% +something going around one full time + + + align:start position:0% +something going around one full time +around is 2 pi it's one cycle so if you + + align:start position:0% +around is 2 pi it's one cycle so if you + + + align:start position:0% +around is 2 pi it's one cycle so if you +do 60 Cycles in a minute how many do you + + align:start position:0% +do 60 Cycles in a minute how many do you + + + align:start position:0% +do 60 Cycles in a minute how many do you +in a second one so this RPM divided by + + align:start position:0% +in a second one so this RPM divided by + + + align:start position:0% +in a second one so this RPM divided by +60 equals F in cycles per + + align:start position:0% +60 equals F in cycles per + + + align:start position:0% +60 equals F in cycles per +second or + + align:start position:0% +second or + + + align:start position:0% +second or +Hertz okay + + align:start position:0% +Hertz okay + + + align:start position:0% +Hertz okay +RPM divided by 60 gives you revolutions + + align:start position:0% +RPM divided by 60 gives you revolutions + + + align:start position:0% +RPM divided by 60 gives you revolutions +per + + align:start position:0% +per + + + align:start position:0% +per +second RPS well excuse me uh I was + + align:start position:0% +second RPS well excuse me uh I was + + + align:start position:0% +second RPS well excuse me uh I was +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about we'll do that just get rid of that + + align:start position:0% +about we'll do that just get rid of that + + + align:start position:0% +about we'll do that just get rid of that +that's the relation you want and what's + + align:start position:0% +that's the relation you want and what's + + + align:start position:0% +that's the relation you want and what's +the relationship between Omega and + + align:start position:0% + + + + align:start position:0% + +F for every cycle you get two Pi + + align:start position:0% +F for every cycle you get two Pi + + + align:start position:0% +F for every cycle you get two Pi +radians okay so now compute I want to + + align:start position:0% +radians okay so now compute I want to + + + align:start position:0% +radians okay so now compute I want to +give me an estimate find um pose my + + align:start position:0% +give me an estimate find um pose my + + + align:start position:0% +give me an estimate find um pose my +problem + + align:start position:0% +problem + + + align:start position:0% +problem +here so part one you've done part two + + align:start position:0% +here so part one you've done part two + + + align:start position:0% +here so part one you've done part two +here is + + align:start position:0% +here is + + + align:start position:0% +here is +to get an estimate of the magnitude of + + align:start position:0% +to get an estimate of the magnitude of + + + align:start position:0% +to get an estimate of the magnitude of +the steady state + + align:start position:0% + + + + align:start position:0% + +response and we've been talking about + + align:start position:0% +response and we've been talking about + + + align:start position:0% +response and we've been talking about +transfer functions so it's probably a + + align:start position:0% +transfer functions so it's probably a + + + align:start position:0% +transfer functions so it's probably a +app applying a transfer function + + align:start position:0% + + + + align:start position:0% + +here I would put your symbolic answer up + + align:start position:0% +here I would put your symbolic answer up + + + align:start position:0% +here I would put your symbolic answer up +first would be a terrific + + align:start position:0% +first would be a terrific + + + align:start position:0% +first would be a terrific +idea think you all when you think you + + align:start position:0% +idea think you all when you think you + + + align:start position:0% +idea think you all when you think you +have kind of a symbolic Sol approach to + + align:start position:0% +have kind of a symbolic Sol approach to + + + align:start position:0% +have kind of a symbolic Sol approach to +this go write it up and we'll that way I + + align:start position:0% +this go write it up and we'll that way I + + + align:start position:0% +this go write it up and we'll that way I +can know where you need a little help if + + align:start position:0% +can know where you need a little help if + + + align:start position:0% +can know where you need a little help if +any + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% + + + + align:start position:0% + +okay so you don't know + + align:start position:0% +okay so you don't know + + + align:start position:0% +okay so you don't know +K so just just leave that as a + + align:start position:0% +K so just just leave that as a + + + align:start position:0% +K so just just leave that as a +undetermined quantity F not a what it + + align:start position:0% +undetermined quantity F not a what it + + + align:start position:0% +undetermined quantity F not a what it +what is well well let you guys keep + + align:start position:0% +what is well well let you guys keep + + + align:start position:0% +what is well well let you guys keep +working for a second then we'll talk + + align:start position:0% +working for a second then we'll talk + + + align:start position:0% +working for a second then we'll talk +about it so you don't know okay so just + + align:start position:0% +about it so you don't know okay so just + + + align:start position:0% +about it so you don't know okay so just +leave it as an + + align:start position:0% + + + + align:start position:0% + +unknown uh don't do that just call it + + align:start position:0% +unknown uh don't do that just call it + + + align:start position:0% +unknown uh don't do that just call it +FN but now plug in some numbers for what + + align:start position:0% +FN but now plug in some numbers for what + + + align:start position:0% +FN but now plug in some numbers for what +you do + + align:start position:0% + + + + align:start position:0% + +know so one quantity you're going to + + align:start position:0% +know so one quantity you're going to + + + align:start position:0% +know so one quantity you're going to +needs Omega over Omega n right so write + + align:start position:0% +needs Omega over Omega n right so write + + + align:start position:0% +needs Omega over Omega n right so write +that one down when you get it what's + + align:start position:0% +that one down when you get it what's + + + align:start position:0% +that one down when you get it what's +Omega over Omega n and + + align:start position:0% +Omega over Omega n and + + + align:start position:0% +Omega over Omega n and +then move on from + + align:start position:0% + + + + align:start position:0% + +there now there's a little Pitfall here + + align:start position:0% +there now there's a little Pitfall here + + + align:start position:0% +there now there's a little Pitfall here +that you're all running into and that is + + align:start position:0% +that you're all running into and that is + + + align:start position:0% +that you're all running into and that is +you're taking the positive square root + + align:start position:0% +you're taking the positive square root + + + align:start position:0% +you're taking the positive square root +is written it's that whole quantity down + + align:start position:0% +is written it's that whole quantity down + + + align:start position:0% +is written it's that whole quantity down +there squared square root and you're + + align:start position:0% +there squared square root and you're + + + align:start position:0% +there squared square root and you're +writing it 1 minus Omega squar and this + + align:start position:0% +writing it 1 minus Omega squar and this + + + align:start position:0% +writing it 1 minus Omega squar and this +thing's going to turn out negative on + + align:start position:0% +thing's going to turn out negative on + + + align:start position:0% +thing's going to turn out negative on +you if you're not careful but it you can + + align:start position:0% +you if you're not careful but it you can + + + align:start position:0% +you if you're not careful but it you can +flip it around it's really the absolute + + align:start position:0% +flip it around it's really the absolute + + + align:start position:0% +flip it around it's really the absolute +value of that quantity because it's a + + align:start position:0% +value of that quantity because it's a + + + align:start position:0% +value of that quantity because it's a +that quantity squared square root so it + + align:start position:0% +that quantity squared square root so it + + + align:start position:0% +that quantity squared square root so it +can be plus or + + align:start position:0% + + + + align:start position:0% + +minus so you got 1.5 for 1.5 what + + align:start position:0% +minus so you got 1.5 for 1.5 what + + + align:start position:0% +minus so you got 1.5 for 1.5 what +sorry 1.5 is your ratio okay write it + + align:start position:0% +sorry 1.5 is your ratio okay write it + + + align:start position:0% +sorry 1.5 is your ratio okay write it +down just write the ratio that's what + + align:start position:0% +down just write the ratio that's what + + + align:start position:0% +down just write the ratio that's what +you + + align:start position:0% + + + + align:start position:0% + +need 1.5 + + align:start position:0% + + + + align:start position:0% + +and you got this is four fifths here + + align:start position:0% +and you got this is four fifths here + + + align:start position:0% +and you got this is four fifths here +that's what you guys that worked out + + align:start position:0% +that's what you guys that worked out + + + align:start position:0% +that's what you guys that worked out +okay so like + + align:start position:0% + + + + align:start position:0% + +08 they took calculate Omega over Omega + + align:start position:0% +08 they took calculate Omega over Omega + + + align:start position:0% +08 they took calculate Omega over Omega +n you have a 183 divided by what was + + align:start position:0% +n you have a 183 divided by what was + + + align:start position:0% +n you have a 183 divided by what was +your Omega + + align:start position:0% +your Omega + + + align:start position:0% +your Omega +n oh 60 okay not 60 no no I mean it's + + align:start position:0% +n oh 60 okay not 60 no no I mean it's + + + align:start position:0% +n oh 60 okay not 60 no no I mean it's +it's it's like 360s over 260 yeah well + + align:start position:0% +it's it's like 360s over 260 yeah well + + + align:start position:0% +it's it's like 360s over 260 yeah well +you got to divide 1750 by 60 to get F + + align:start position:0% +you got to divide 1750 by 60 to get F + + + align:start position:0% +you got to divide 1750 by 60 to get F +and then you got to multiply by 2 pi + + align:start position:0% +and then you got to multiply by 2 pi + + + align:start position:0% +and then you got to multiply by 2 pi +right I'm doing it for the benefit of + + align:start position:0% +right I'm doing it for the benefit of + + + align:start position:0% +right I'm doing it for the benefit of +everybody in the room + + align:start position:0% + + + + align:start position:0% + +here8 F not over K all right now we're + + align:start position:0% +here8 F not over K all right now we're + + + align:start position:0% +here8 F not over K all right now we're +getting + + align:start position:0% +getting + + + align:start position:0% +getting +somewhere 08 point8 what do you you guys + + align:start position:0% +somewhere 08 point8 what do you you guys + + + align:start position:0% +somewhere 08 point8 what do you you guys +have here you got one over 1.3 how's + + align:start position:0% +have here you got one over 1.3 how's + + + align:start position:0% +have here you got one over 1.3 how's +that work + + align:start position:0% +that work + + + align:start position:0% +that work +out all right so about + + align:start position:0% +out all right so about + + + align:start position:0% +out all right so about +08 okay so you've come to the conclusion + + align:start position:0% +08 okay so you've come to the conclusion + + + align:start position:0% +08 okay so you've come to the conclusion +that the magnitude of that steady state + + align:start position:0% +that the magnitude of that steady state + + + align:start position:0% +that the magnitude of that steady state +response is about 08 F over K and we + + align:start position:0% +response is about 08 F over K and we + + + align:start position:0% +response is about 08 F over K and we +call that FN over K we you know in + + align:start position:0% +call that FN over K we you know in + + + align:start position:0% +call that FN over K we you know in +lecture I call it the static response + + align:start position:0% +lecture I call it the static response + + + align:start position:0% +lecture I call it the static response +the book calls it the static response is + + align:start position:0% +the book calls it the static response is + + + align:start position:0% +the book calls it the static response is +it is this it is it the same static + + align:start position:0% +it is this it is it the same static + + + align:start position:0% +it is this it is it the same static +respones we're talking about here + + align:start position:0% +respones we're talking about here + + + align:start position:0% +respones we're talking about here +don't confuse the two this was the + + align:start position:0% +don't confuse the two this was the + + + align:start position:0% +don't confuse the two this was the +effect of gravity on the system static + + align:start position:0% +effect of gravity on the system static + + + align:start position:0% +effect of gravity on the system static +response we're talking about here is if + + align:start position:0% +response we're talking about here is if + + + align:start position:0% +response we're talking about here is if +the frequency of this excitation went to + + align:start position:0% +the frequency of this excitation went to + + + align:start position:0% +the frequency of this excitation went to +zero then the response this would + + align:start position:0% +zero then the response this would + + + align:start position:0% +zero then the response this would +stretch that Spring by the amount we're + + align:start position:0% +stretch that Spring by the amount we're + + + align:start position:0% +stretch that Spring by the amount we're +calling xstatic FN over K all right so + + align:start position:0% +calling xstatic FN over K all right so + + + align:start position:0% +calling xstatic FN over K all right so +now you know that you're operating at a + + align:start position:0% +now you know that you're operating at a + + + align:start position:0% +now you know that you're operating at a +frequency what's the Frequency ratio + + align:start position:0% +frequency what's the Frequency ratio + + + align:start position:0% +frequency what's the Frequency ratio +that you found Omega over Omega + + align:start position:0% +that you found Omega over Omega + + + align:start position:0% +that you found Omega over Omega +n you had that was an intermediate step + + align:start position:0% +n you had that was an intermediate step + + + align:start position:0% +n you had that was an intermediate step +here all right + + align:start position:0% +here all right + + + align:start position:0% +here all right +1.5 all right now you're going to the + + align:start position:0% +1.5 all right now you're going to the + + + align:start position:0% +1.5 all right now you're going to the +proposed fixed is to double the + + align:start position:0% +proposed fixed is to double the + + + align:start position:0% +proposed fixed is to double the +stiffness double the + + align:start position:0% +stiffness double the + + + align:start position:0% +stiffness double the +stiffness and somebody so you're going + + align:start position:0% +stiffness and somebody so you're going + + + align:start position:0% +stiffness and somebody so you're going +from what's the we want now we want to + + align:start position:0% +from what's the we want now we want to + + + align:start position:0% +from what's the we want now we want to +compute this + + align:start position:0% +compute this + + + align:start position:0% +compute this +result if you double the stiffness and + + align:start position:0% +result if you double the stiffness and + + + align:start position:0% +result if you double the stiffness and +the person who proposed that thinks it's + + align:start position:0% +the person who proposed that thinks it's + + + align:start position:0% +the person who proposed that thinks it's +going to have the response that's the + + align:start position:0% +going to have the response that's the + + + align:start position:0% +going to have the response that's the +proposal so double the stiffness and in + + align:start position:0% +proposal so double the stiffness and in + + + align:start position:0% +proposal so double the stiffness and in +order to get finished here what effect + + align:start position:0% +order to get finished here what effect + + + align:start position:0% +order to get finished here what effect +does changing the the stiffness have on + + align:start position:0% +does changing the the stiffness have on + + + align:start position:0% +does changing the the stiffness have on +this + + align:start position:0% + + + + align:start position:0% + +system well you're jumping to An Answer + + align:start position:0% +system well you're jumping to An Answer + + + align:start position:0% +system well you're jumping to An Answer +intermediate step here what does it due + + align:start position:0% +intermediate step here what does it due + + + align:start position:0% +intermediate step here what does it due +to the natural + + align:start position:0% +to the natural + + + align:start position:0% +to the natural +frequency there's a natural frequency + + align:start position:0% +frequency there's a natural frequency + + + align:start position:0% +frequency there's a natural frequency +change if you change the + + align:start position:0% +change if you change the + + + align:start position:0% +change if you change the +stiffness okay so the natural frequency + + align:start position:0% +stiffness okay so the natural frequency + + + align:start position:0% +stiffness okay so the natural frequency +is + + align:start position:0% + + + + align:start position:0% + +normally some kind of K Over M right now + + align:start position:0% +normally some kind of K Over M right now + + + align:start position:0% +normally some kind of K Over M right now +we also know it's G over + + align:start position:0% + + + + align:start position:0% + +Delta but we're going to double the + + align:start position:0% +Delta but we're going to double the + + + align:start position:0% +Delta but we're going to double the +stiffness so what does that do to the + + align:start position:0% +stiffness so what does that do to the + + + align:start position:0% +stiffness so what does that do to the +natural frequency does the M change okay + + align:start position:0% +natural frequency does the M change okay + + + align:start position:0% +natural frequency does the M change okay +so what's the this is Omega n before + + align:start position:0% +so what's the this is Omega n before + + + align:start position:0% +so what's the this is Omega n before +Omega n + + align:start position:0% +Omega n + + + align:start position:0% +Omega n +after + + align:start position:0% + + + + align:start position:0% + +equals right okay and that is what does + + align:start position:0% +equals right okay and that is what does + + + align:start position:0% +equals right okay and that is what does +that do to your frequency + + align:start position:0% + + + + align:start position:0% + +ratio so your fre the effect of changing + + align:start position:0% +ratio so your fre the effect of changing + + + align:start position:0% +ratio so your fre the effect of changing +the stiffness changes the natural + + align:start position:0% +the stiffness changes the natural + + + align:start position:0% +the stiffness changes the natural +frequency and that changes the ratio of + + align:start position:0% +frequency and that changes the ratio of + + + align:start position:0% +frequency and that changes the ratio of +the input frequency to the natural + + align:start position:0% +the input frequency to the natural + + + align:start position:0% +the input frequency to the natural +frequency and that will change this + + align:start position:0% +frequency and that will change this + + + align:start position:0% +frequency and that will change this +calculation here right so come up with a + + align:start position:0% +calculation here right so come up with a + + + align:start position:0% +calculation here right so come up with a +new value for + + align:start position:0% + + + + align:start position:0% + +this anybody got a number what's the + + align:start position:0% +this anybody got a number what's the + + + align:start position:0% +this anybody got a number what's the +Frequency ratio + + align:start position:0% + + + + align:start position:0% + +after oh oh um + + align:start position:0% +after oh oh um + + + align:start position:0% +after oh oh um +um I was doing the squ + + align:start position:0% + + + + align:start position:0% + +ter I want to know the frequency ratio + + align:start position:0% +ter I want to know the frequency ratio + + + align:start position:0% +ter I want to know the frequency ratio +this is uh after is equal to the + + align:start position:0% +this is uh after is equal to the + + + align:start position:0% +this is uh after is equal to the +frequency ratio that with something to + + align:start position:0% +frequency ratio that with something to + + + align:start position:0% +frequency ratio that with something to +do with root2 here the natural frequency + + align:start position:0% +do with root2 here the natural frequency + + + align:start position:0% +do with root2 here the natural frequency +is going to go up or down by factor of + + align:start position:0% +is going to go up or down by factor of + + + align:start position:0% +is going to go up or down by factor of +root2 if you double k the natural + + align:start position:0% +root2 if you double k the natural + + + align:start position:0% +root2 if you double k the natural +frequency go up by a sare < TK of + + align:start position:0% +frequency go up by a sare < TK of + + + align:start position:0% +frequency go up by a sare < TK of +two so the frequency ratio after the + + align:start position:0% +two so the frequency ratio after the + + + align:start position:0% +two so the frequency ratio after the +natural frequency goes up by the sare < + + align:start position:0% +natural frequency goes up by the sare < + + + align:start position:0% +natural frequency goes up by the sare < +TK of two that's the same as < tk2 over2 + + align:start position:0% +TK of two that's the same as < tk2 over2 + + + align:start position:0% +TK of two that's the same as < tk2 over2 +here so the whole thing drops down so + + align:start position:0% +here so the whole thing drops down so + + + align:start position:0% +here so the whole thing drops down so +1.5 * < TK of 2 over two what is it 1 + + align:start position:0% +1.5 * < TK of 2 over two what is it 1 + + + align:start position:0% +1.5 * < TK of 2 over two what is it 1 +all right + + align:start position:0% +all right + + + align:start position:0% +all right +1.07 now what is figure out this + + align:start position:0% + + + + align:start position:0% + +quantity pardon + + align:start position:0% +quantity pardon + + + align:start position:0% +quantity pardon +got + + align:start position:0% +got + + + align:start position:0% +got +3.4 and and did you put in a two here + + align:start position:0% +3.4 and and did you put in a two here + + + align:start position:0% +3.4 and and did you put in a two here +right + + align:start position:0% + + + + align:start position:0% + +so this is the this is the this is the + + align:start position:0% +so this is the this is the this is the + + + align:start position:0% +so this is the this is the this is the +correct expression to be using but now + + align:start position:0% +correct expression to be using but now + + + align:start position:0% +correct expression to be using but now +in this new problem this was before in + + align:start position:0% +in this new problem this was before in + + + align:start position:0% +in this new problem this was before in +this in this problem afterwards x a + + align:start position:0% +this in this problem afterwards x a + + + align:start position:0% +this in this problem afterwards x a +steady state is f not over 2K if double + + align:start position:0% +steady state is f not over 2K if double + + + align:start position:0% +steady state is f not over 2K if double +the stiffness all over this + + align:start position:0% +the stiffness all over this + + + align:start position:0% +the stiffness all over this +quantity Omega 2 over Omega n^ 2 -1 + + align:start position:0% +quantity Omega 2 over Omega n^ 2 -1 + + + align:start position:0% +quantity Omega 2 over Omega n^ 2 -1 +but with the new frequency ratio this is + + align:start position:0% +but with the new frequency ratio this is + + + align:start position:0% +but with the new frequency ratio this is +now + + align:start position:0% +now + + + align:start position:0% +now +1.07 you do this number what do you + + align:start position:0% +1.07 you do this number what do you + + + align:start position:0% +1.07 you do this number what do you +get 3 point what you say 3.4 + + align:start position:0% +get 3 point what you say 3.4 + + + align:start position:0% +get 3 point what you say 3.4 +roughly fnot over K so so you have + + align:start position:0% +roughly fnot over K so so you have + + + align:start position:0% +roughly fnot over K so so you have +apples and apples you got to want to + + align:start position:0% +apples and apples you got to want to + + + align:start position:0% +apples and apples you got to want to +compare the F not over K before to after + + align:start position:0% +compare the F not over K before to after + + + align:start position:0% +compare the F not over K before to after +you end up with a factor of 3.4 so + + align:start position:0% +you end up with a factor of 3.4 so + + + align:start position:0% +you end up with a factor of 3.4 so +should you make the + + align:start position:0% +should you make the + + + align:start position:0% +should you make the +change no it was a bad idea what if you + + align:start position:0% +change no it was a bad idea what if you + + + align:start position:0% +change no it was a bad idea what if you +so you run into a situation like this + + align:start position:0% +so you run into a situation like this + + + align:start position:0% +so you run into a situation like this +before going all that trouble of cutting + + align:start position:0% +before going all that trouble of cutting + + + align:start position:0% +before going all that trouble of cutting +steel and getting out the torch you know + + align:start position:0% +steel and getting out the torch you know + + + align:start position:0% +steel and getting out the torch you know +the welding system take yourself a great + + align:start position:0% +the welding system take yourself a great + + + align:start position:0% +the welding system take yourself a great +big weight and walk up and thump some + + align:start position:0% +big weight and walk up and thump some + + + align:start position:0% +big weight and walk up and thump some +weight on top of this thing and see if + + align:start position:0% +weight on top of this thing and see if + + + align:start position:0% +weight on top of this thing and see if +it gets better or worse because if I + + align:start position:0% +it gets better or worse because if I + + + align:start position:0% +it gets better or worse because if I +doubled the mass of the system what + + align:start position:0% +doubled the mass of the system what + + + align:start position:0% +doubled the mass of the system what +would + + align:start position:0% + + + + align:start position:0% + +happen it's going to go the other + + align:start position:0% +happen it's going to go the other + + + align:start position:0% +happen it's going to go the other +direction right this this will go up by + + align:start position:0% +direction right this this will go up by + + + align:start position:0% +direction right this this will go up by +a factor of < tk2 and then this this + + align:start position:0% +a factor of < tk2 and then this this + + + align:start position:0% +a factor of < tk2 and then this this +denominator you're getting pushing it f + + align:start position:0% +denominator you're getting pushing it f + + + align:start position:0% +denominator you're getting pushing it f +F out and you instead of being at 08 + + align:start position:0% +F out and you instead of being at 08 + + + align:start position:0% +F out and you instead of being at 08 +you'll be down further \ No newline at end of file diff --git a/qJOQOkJ7rI8.txt b/qJOQOkJ7rI8.txt new file mode 100644 index 0000000000000000000000000000000000000000..097468546a91438f90ef2545334e9015f8d86bae --- /dev/null +++ b/qJOQOkJ7rI8.txt @@ -0,0 +1,1555 @@ +align:start position:0% + +Okay, I want to talk about a slightly + + align:start position:0% +Okay, I want to talk about a slightly + + + align:start position:0% +Okay, I want to talk about a slightly +different way to solve a linear first + + align:start position:0% +different way to solve a linear first + + + align:start position:0% +different way to solve a linear first +order equation. And if you look at the + + align:start position:0% +order equation. And if you look at the + + + align:start position:0% +order equation. And if you look at the +equation, I'll I'll I'll do an example. + + align:start position:0% +equation, I'll I'll I'll do an example. + + + align:start position:0% +equation, I'll I'll I'll do an example. +That's the best. Do you notice what's + + align:start position:0% +That's the best. Do you notice what's + + + align:start position:0% +That's the best. Do you notice what's +different from our favorite equation? + + align:start position:0% +different from our favorite equation? + + + align:start position:0% +different from our favorite equation? +The change is 2T. The interest rate + + align:start position:0% +The change is 2T. The interest rate + + + align:start position:0% +The change is 2T. The interest rate +A is increasing with time. Changing with + + align:start position:0% +A is increasing with time. Changing with + + + align:start position:0% +A is increasing with time. Changing with +time. So we still have a linear equation + + align:start position:0% +time. So we still have a linear equation + + + align:start position:0% +time. So we still have a linear equation +still just y but the coefficient is + + align:start position:0% +still just y but the coefficient is + + + align:start position:0% +still just y but the coefficient is +varying we have a variable coefficient + + align:start position:0% +varying we have a variable coefficient + + + align:start position:0% +varying we have a variable coefficient +2t and in real if we're thinking of + + align:start position:0% +2t and in real if we're thinking of + + + align:start position:0% +2t and in real if we're thinking of +applications to economy to banks uh that + + align:start position:0% +applications to economy to banks uh that + + + align:start position:0% +applications to economy to banks uh that +would be a rampant inflation interest + + align:start position:0% +would be a rampant inflation interest + + + align:start position:0% +would be a rampant inflation interest +rate 2t climbing and climbing forever + + align:start position:0% +rate 2t climbing and climbing forever + + + align:start position:0% +rate 2t climbing and climbing forever +but we want to see that This is a class + + align:start position:0% +but we want to see that This is a class + + + align:start position:0% +but we want to see that This is a class +of equations that we can solve. Okay. + + align:start position:0% +of equations that we can solve. Okay. + + + align:start position:0% +of equations that we can solve. Okay. +And and the new new method is called an + + align:start position:0% +And and the new new method is called an + + + align:start position:0% +And and the new new method is called an +integrating factor. It's a magic factor + + align:start position:0% +integrating factor. It's a magic factor + + + align:start position:0% +integrating factor. It's a magic factor +that makes the equation simple. So + + align:start position:0% +that makes the equation simple. So + + + align:start position:0% +that makes the equation simple. So +that's a another nice way to solve all + + align:start position:0% +that's a another nice way to solve all + + + align:start position:0% +that's a another nice way to solve all +the problems that we've dealt with so + + align:start position:0% +the problems that we've dealt with so + + + align:start position:0% +the problems that we've dealt with so +far plus this new one. So what is this + + align:start position:0% +far plus this new one. So what is this + + + align:start position:0% +far plus this new one. So what is this +factor? Well, for + + align:start position:0% +factor? Well, for + + + align:start position:0% +factor? Well, for +this + + align:start position:0% +this + + + align:start position:0% +this +2T problem, the right factor is e to the + + align:start position:0% +2T problem, the right factor is e to the + + + align:start position:0% +2T problem, the right factor is e to the +minus t ^2. And why is that the right + + align:start position:0% +minus t ^2. And why is that the right + + + align:start position:0% +minus t ^2. And why is that the right +factor? This this is the factor that I'm + + align:start position:0% +factor? This this is the factor that I'm + + + align:start position:0% +factor? This this is the factor that I'm +going to multiply the equation by and + + align:start position:0% +going to multiply the equation by and + + + align:start position:0% +going to multiply the equation by and +make it simple. The right the reason + + align:start position:0% +make it simple. The right the reason + + + align:start position:0% +make it simple. The right the reason +that's the right choice is that the + + align:start position:0% +that's the right choice is that the + + + align:start position:0% +that's the right choice is that the +derivative of + + align:start position:0% +derivative of + + + align:start position:0% +derivative of +this you you remember how to take the + + align:start position:0% +this you you remember how to take the + + + align:start position:0% +this you you remember how to take the +derivative by the chain rule. The + + align:start position:0% +derivative by the chain rule. The + + + align:start position:0% +derivative by the chain rule. The +derivative will be the same eus t ^2 the + + align:start position:0% +derivative will be the same eus t ^2 the + + + align:start position:0% +derivative will be the same eus t ^2 the +same i times the derivative + + align:start position:0% +same i times the derivative + + + align:start position:0% +same i times the derivative +of the + + align:start position:0% +of the + + + align:start position:0% +of the +exponent and the derivative of that + + align:start position:0% +exponent and the derivative of that + + + align:start position:0% +exponent and the derivative of that +exponent exponent is - 2t - t ^2 becomes + + align:start position:0% +exponent exponent is - 2t - t ^2 becomes + + + align:start position:0% +exponent exponent is - 2t - t ^2 becomes +- 2t. So it's that + + align:start position:0% +- 2t. So it's that + + + align:start position:0% +- 2t. So it's that +little device that gives us an + + align:start position:0% +little device that gives us an + + + align:start position:0% +little device that gives us an +integrating factor that makes the + + align:start position:0% +integrating factor that makes the + + + align:start position:0% +integrating factor that makes the +equation simple. And now I want to look + + align:start position:0% +equation simple. And now I want to look + + + align:start position:0% +equation simple. And now I want to look +at the equation. What I want to look at + + align:start position:0% +at the equation. What I want to look at + + + align:start position:0% +at the equation. What I want to look at +is the derivative of I * Y. Instead of + + align:start position:0% +is the derivative of I * Y. Instead of + + + align:start position:0% +is the derivative of I * Y. Instead of +just dydt, let me look at the derivative + + align:start position:0% +just dydt, let me look at the derivative + + + align:start position:0% +just dydt, let me look at the derivative +of I * Y. So I have a product here. Got + + align:start position:0% +of I * Y. So I have a product here. Got + + + align:start position:0% +of I * Y. So I have a product here. Got +to use the product rule. So that will be + + align:start position:0% +to use the product rule. So that will be + + + align:start position:0% +to use the product rule. So that will be +I. So I dydt. + + align:start position:0% + + + + align:start position:0% + +But d okay dydt + + align:start position:0% +But d okay dydt + + + align:start position:0% +But d okay dydt +is we can take dydt from the equation i + + align:start position:0% +is we can take dydt from the equation i + + + align:start position:0% +is we can take dydt from the equation i +* 2 t + + align:start position:0% +* 2 t + + + align:start position:0% +* 2 t +y + q of + + align:start position:0% + + + + align:start position:0% + +t. So + + align:start position:0% + + + + align:start position:0% + +that's and now I have to add + + align:start position:0% +that's and now I have to add + + + align:start position:0% +that's and now I have to add +on + + align:start position:0% +on + + + align:start position:0% +on +dt + + align:start position:0% + + + + align:start position:0% + +y. + + align:start position:0% +y. + + + align:start position:0% +y. +Good. So it's the product rule. I * the + + align:start position:0% +Good. So it's the product rule. I * the + + + align:start position:0% +Good. So it's the product rule. I * the +derivative of y plus the derivative of i + + align:start position:0% +derivative of y plus the derivative of i + + + align:start position:0% +derivative of y plus the derivative of i +* y. But now look + + align:start position:0% +* y. But now look + + + align:start position:0% +* y. But now look +dt we know is minus 2ti. So that dt now + + align:start position:0% +dt we know is minus 2ti. So that dt now + + + align:start position:0% +dt we know is minus 2ti. So that dt now +I'm using the key fact about i that min + + align:start position:0% +I'm using the key fact about i that min + + + align:start position:0% +I'm using the key fact about i that min +-2 t i y. Look - 2ti y cancels 2 + + align:start position:0% +-2 t i y. Look - 2ti y cancels 2 + + + align:start position:0% +-2 t i y. Look - 2ti y cancels 2 +tiy. So I have a nice equation now. The + + align:start position:0% +tiy. So I have a nice equation now. The + + + align:start position:0% +tiy. So I have a nice equation now. The +derivative of + + align:start position:0% +derivative of + + + align:start position:0% +derivative of +iy is + + align:start position:0% +iy is + + + align:start position:0% +iy is +iq. The derivative of iy is iq. I can + + align:start position:0% +iq. The derivative of iy is iq. I can + + + align:start position:0% +iq. The derivative of iy is iq. I can +just integrate both sides. And that's + + align:start position:0% +just integrate both sides. And that's + + + align:start position:0% +just integrate both sides. And that's +the key. That's the key. If I integrate + + align:start position:0% +the key. That's the key. If I integrate + + + align:start position:0% +the key. That's the key. If I integrate +the left hand side, so I'll just move + + align:start position:0% +the left hand side, so I'll just move + + + align:start position:0% +the left hand side, so I'll just move +this + + align:start position:0% +this + + + align:start position:0% +this +up. Integrate the derivative. Of course, + + align:start position:0% +up. Integrate the derivative. Of course, + + + align:start position:0% +up. Integrate the derivative. Of course, +the integral of the derivative is the + + align:start position:0% +the integral of the derivative is the + + + align:start position:0% +the integral of the derivative is the +function + + align:start position:0% +function + + + align:start position:0% +function +at time + + align:start position:0% +at time + + + align:start position:0% +at time +t. I y at time t minus iy at time z. y + + align:start position:0% +t. I y at time t minus iy at time z. y + + + align:start position:0% +t. I y at time t minus iy at time z. y +of z. Because notice that I at + + align:start position:0% +of z. Because notice that I at + + + align:start position:0% +of z. Because notice that I at +t=0. Can I just mention that I at 0 is + + align:start position:0% +t=0. Can I just mention that I at 0 is + + + align:start position:0% +t=0. Can I just mention that I at 0 is +1. When t is zero, I have e to the 0 + + align:start position:0% +1. When t is zero, I have e to the 0 + + + align:start position:0% +1. When t is zero, I have e to the 0 +power, which is + + align:start position:0% +power, which is + + + align:start position:0% +power, which is +1. So that i of 0 is 1. So that's the + + align:start position:0% +1. So that i of 0 is 1. So that's the + + + align:start position:0% +1. So that i of 0 is 1. So that's the +integral of the derivative. And on the + + align:start position:0% +integral of the derivative. And on the + + + align:start position:0% +integral of the derivative. And on the +right hand side I have the integral from + + align:start position:0% +right hand side I have the integral from + + + align:start position:0% +right hand side I have the integral from +0 to 2 T + + align:start position:0% +0 to 2 T + + + align:start position:0% +0 to 2 T +of I * + + align:start position:0% +of I * + + + align:start position:0% +of I * +Q I. So I'll put in I yeah E to the + + align:start position:0% +Q I. So I'll put in I yeah E to the + + + align:start position:0% +Q I. So I'll put in I yeah E to the +minus S^2 + + align:start position:0% +minus S^2 + + + align:start position:0% +minus S^2 +q of S + + align:start position:0% +q of S + + + align:start position:0% +q of S +d I've introduced a inte variable of + + align:start position:0% +d I've introduced a inte variable of + + + align:start position:0% +d I've introduced a inte variable of +integration s going from zero to t. + + align:start position:0% +integration s going from zero to t. + + + align:start position:0% +integration s going from zero to t. +You remember this type of formula? The + + align:start position:0% +You remember this type of formula? The + + + align:start position:0% +You remember this type of formula? The +the uh input is continuous over time and + + align:start position:0% +the uh input is continuous over time and + + + align:start position:0% +the uh input is continuous over time and +I'm looking at the resulting output at + + align:start position:0% +I'm looking at the resulting output at + + + align:start position:0% +I'm looking at the resulting output at +time t. So all the inputs go in, they're + + align:start position:0% +time t. So all the inputs go in, they're + + + align:start position:0% +time t. So all the inputs go in, they're +all multiplied by some factor and + + align:start position:0% +all multiplied by some factor and + + + align:start position:0% +all multiplied by some factor and +integrate integrated gives the total + + align:start position:0% +integrate integrated gives the total + + + align:start position:0% +integrate integrated gives the total +result from those inputs. Okay, I'm I'm + + align:start position:0% +result from those inputs. Okay, I'm I'm + + + align:start position:0% +result from those inputs. Okay, I'm I'm +I'm almost here. I just want to remember + + align:start position:0% +I'm almost here. I just want to remember + + + align:start position:0% +I'm almost here. I just want to remember +uh I have I want to divide by I of T. So + + align:start position:0% +uh I have I want to divide by I of T. So + + + align:start position:0% +uh I have I want to divide by I of T. So +I have a formula for Y. Okay. So my + + align:start position:0% +I have a formula for Y. Okay. So my + + + align:start position:0% +I have a formula for Y. Okay. So my +formula for + + align:start position:0% +formula for + + + align:start position:0% +formula for +Y when I divide by I of + + align:start position:0% +Y when I divide by I of + + + align:start position:0% +Y when I divide by I of +T, don't forget what I of T is. Let me + + align:start position:0% +T, don't forget what I of T is. Let me + + + align:start position:0% +T, don't forget what I of T is. Let me +put it again here. Let me remind myself. + + align:start position:0% +put it again here. Let me remind myself. + + + align:start position:0% +put it again here. Let me remind myself. +I of T is E to the minus T ^2. That was + + align:start position:0% +I of T is E to the minus T ^2. That was + + + align:start position:0% +I of T is E to the minus T ^2. That was +the magic integration factor. Okay. So + + align:start position:0% +the magic integration factor. Okay. So + + + align:start position:0% +the magic integration factor. Okay. So +I'm going to divide by that which means + + align:start position:0% +I'm going to divide by that which means + + + align:start position:0% +I'm going to divide by that which means +I'll multiply by e to the t ^2. So that + + align:start position:0% +I'll multiply by e to the t ^2. So that + + + align:start position:0% +I'll multiply by e to the t ^2. So that +will knock out the i here. I'll put this + + align:start position:0% +will knock out the i here. I'll put this + + + align:start position:0% +will knock out the i here. I'll put this +on the other side of the equation. y of + + align:start position:0% +on the other side of the equation. y of + + + align:start position:0% +on the other side of the equation. y of +0. y of 0 and it'll be multiplied by the + + align:start position:0% +0. y of 0 and it'll be multiplied by the + + + align:start position:0% +0. y of 0 and it'll be multiplied by the +e to the t ^2. And this thing will be + + align:start position:0% +e to the t ^2. And this thing will be + + + align:start position:0% +e to the t ^2. And this thing will be +multiplied by e t ^2. the integral from + + align:start position:0% +multiplied by e t ^2. the integral from + + + align:start position:0% +multiplied by e t ^2. the integral from +0 to t of e to the t^2 - s^2 + + align:start position:0% +0 to t of e to the t^2 - s^2 + + + align:start position:0% +0 to t of e to the t^2 - s^2 +q of s d s. That's my + + align:start position:0% +q of s d s. That's my + + + align:start position:0% +q of s d s. That's my +answer. Let's look at it. I + + align:start position:0% +answer. Let's look at it. I + + + align:start position:0% +answer. Let's look at it. I +have y of t. This is what comes out of y + + align:start position:0% +have y of t. This is what comes out of y + + + align:start position:0% +have y of t. This is what comes out of y +of zero. You see that the growth + + align:start position:0% +of zero. You see that the growth + + + align:start position:0% +of zero. You see that the growth +factor has changed from our old e to the + + align:start position:0% +factor has changed from our old e to the + + + align:start position:0% +factor has changed from our old e to the +a that was the growth at constant rate + + align:start position:0% +a that was the growth at constant rate + + + align:start position:0% +a that was the growth at constant rate +interest rate a to e to the t^2 that's + + align:start position:0% +interest rate a to e to the t^2 that's + + + align:start position:0% +interest rate a to e to the t^2 that's +our growth from an increasing interest + + align:start position:0% +our growth from an increasing interest + + + align:start position:0% +our growth from an increasing interest +rate and over here I'm seeing the result + + align:start position:0% +rate and over here I'm seeing the result + + + align:start position:0% +rate and over here I'm seeing the result +the output from the input Q and from all + + align:start position:0% +the output from the input Q and from all + + + align:start position:0% +the output from the input Q and from all +the inputs between zero and t each input + + align:start position:0% +the inputs between zero and t each input + + + align:start position:0% +the inputs between zero and t each input +is multiplied by now that + + align:start position:0% +is multiplied by now that + + + align:start position:0% +is multiplied by now that +factor is the + + align:start position:0% +factor is the + + + align:start position:0% +factor is the +growth not from zero to t. This is the + + align:start position:0% +growth not from zero to t. This is the + + + align:start position:0% +growth not from zero to t. This is the +growth from zero to t. This is the + + align:start position:0% +growth from zero to t. This is the + + + align:start position:0% +growth from zero to t. This is the +growth from s to t because the input + + align:start position:0% +growth from s to t because the input + + + align:start position:0% +growth from s to t because the input +went in at time s and it had the shorter + + align:start position:0% +went in at time s and it had the shorter + + + align:start position:0% +went in at time s and it had the shorter +time t minus s to grow. So that's the + + align:start position:0% +time t minus s to grow. So that's the + + + align:start position:0% +time t minus s to grow. So that's the +formula for the answer. If if you give + + align:start position:0% +formula for the answer. If if you give + + + align:start position:0% +formula for the answer. If if you give +me any particular Q of S, I just do the + + align:start position:0% +me any particular Q of S, I just do the + + + align:start position:0% +me any particular Q of S, I just do the +integral and I find the solution to the + + align:start position:0% +integral and I find the solution to the + + + align:start position:0% +integral and I find the solution to the +differential equation. So that + + align:start position:0% +differential equation. So that + + + align:start position:0% +differential equation. So that +integrating factor has made things work. + + align:start position:0% +integrating factor has made things work. + + + align:start position:0% +integrating factor has made things work. +Maybe I should say what the integrating + + align:start position:0% +Maybe I should say what the integrating + + + align:start position:0% +Maybe I should say what the integrating +factor would be in general. + + align:start position:0% +factor would be in general. + + + align:start position:0% +factor would be in general. +So let + + align:start position:0% +So let + + + align:start position:0% +So let +me pay a + + align:start position:0% +me pay a + + + align:start position:0% +me pay a +moment to see that that this was an + + align:start position:0% +moment to see that that this was an + + + align:start position:0% +moment to see that that this was an +example. This was an example with a of t + + align:start position:0% +example. This was an example with a of t + + + align:start position:0% +example. This was an example with a of t +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +2t. What's what's the general + + align:start position:0% +2t. What's what's the general + + + align:start position:0% +2t. What's what's the general +integrating factor? We always want the + + align:start position:0% +integrating factor? We always want the + + + align:start position:0% +integrating factor? We always want the +integrating factor to so we always want + + align:start position:0% +integrating factor to so we always want + + + align:start position:0% +integrating factor to so we always want +the integrating + + align:start position:0% +the integrating + + + align:start position:0% +the integrating +factor the our construction rule is that + + align:start position:0% +factor the our construction rule is that + + + align:start position:0% +factor the our construction rule is that +it should be it should give us the + + align:start position:0% +it should be it should give us the + + + align:start position:0% +it should be it should give us the +derivative should be minus a of t * i + + align:start position:0% +derivative should be minus a of t * i + + + align:start position:0% +derivative should be minus a of t * i +itself. That's how we chose the e the + + align:start position:0% +itself. That's how we chose the e the + + + align:start position:0% +itself. That's how we chose the e the +minus t ^ + + align:start position:0% +minus t ^ + + + align:start position:0% +minus t ^ +2 when a of t was 2t. + + align:start position:0% +2 when a of t was 2t. + + + align:start position:0% +2 when a of t was 2t. +Now I want to give the general rule + + align:start position:0% +Now I want to give the general rule + + + align:start position:0% +Now I want to give the general rule +general the rule for the integrating + + align:start position:0% +general the rule for the integrating + + + align:start position:0% +general the rule for the integrating +factor + + align:start position:0% +factor + + + align:start position:0% +factor +is the solution to that + + align:start position:0% +is the solution to that + + + align:start position:0% +is the solution to that +equation. The solution to that equation + + align:start position:0% +equation. The solution to that equation + + + align:start position:0% +equation. The solution to that equation +is giving us the e to the t ^2 in the + + align:start position:0% +is giving us the e to the t ^2 in the + + + align:start position:0% +is giving us the e to the t ^2 in the +example. This was the example. But now I + + align:start position:0% +example. This was the example. But now I + + + align:start position:0% +example. This was the example. But now I +want a formula just to close off the + + align:start position:0% +want a formula just to close off the + + + align:start position:0% +want a formula just to close off the +entire case of varying interest rate. I + + align:start position:0% +entire case of varying interest rate. I + + + align:start position:0% +entire case of varying interest rate. I +want to find the solution to that + + align:start position:0% +want to find the solution to that + + + align:start position:0% +want to find the solution to that +equation and it is. So here's the + + align:start position:0% +equation and it is. So here's the + + + align:start position:0% +equation and it is. So here's the +integrating factor. It's + + align:start position:0% +integrating factor. It's + + + align:start position:0% +integrating factor. It's +e to the minus because of that minus + + align:start position:0% +e to the minus because of that minus + + + align:start position:0% +e to the minus because of that minus +sign. Now I'm wanting a to come down + + align:start position:0% +sign. Now I'm wanting a to come down + + + align:start position:0% +sign. Now I'm wanting a to come down +when I take a + + align:start position:0% +when I take a + + + align:start position:0% +when I take a +derivative. So what I'll I'll put up + + align:start position:0% +derivative. So what I'll I'll put up + + + align:start position:0% +derivative. So what I'll I'll put up +here the integral of a of + + align:start position:0% +here the integral of a of + + + align:start position:0% +here the integral of a of +tdt say from zero to t. Now let me just + + align:start position:0% +tdt say from zero to t. Now let me just + + + align:start position:0% +tdt say from zero to t. Now let me just +do again this + + align:start position:0% +do again this + + + align:start position:0% +do again this +example just to see. I have e to the + + align:start position:0% +example just to see. I have e to the + + + align:start position:0% +example just to see. I have e to the +minus the integral of + + align:start position:0% + + + + align:start position:0% + +2t which is e to the minus t + + align:start position:0% + + + + align:start position:0% + +^2. That's how we get t ^2 as the right + + align:start position:0% +^2. That's how we get t ^2 as the right + + + align:start position:0% +^2. That's how we get t ^2 as the right +choice for our example. And the general + + align:start position:0% +choice for our example. And the general + + + align:start position:0% +choice for our example. And the general +rule is there. That's the integrating + + align:start position:0% +rule is there. That's the integrating + + + align:start position:0% +rule is there. That's the integrating +factor. And finally, finally, if a is a + + align:start position:0% +factor. And finally, finally, if a is a + + + align:start position:0% +factor. And finally, finally, if a is a +constant, which is the most common case, + + align:start position:0% +constant, which is the most common case, + + + align:start position:0% +constant, which is the most common case, +the only case we've had until this + + align:start position:0% +the only case we've had until this + + + align:start position:0% +the only case we've had until this +video, if a is a constant, then the + + align:start position:0% +video, if a is a constant, then the + + + align:start position:0% +video, if a is a constant, then the +integral of a from 0 to t is just a * t. + + align:start position:0% +integral of a from 0 to t is just a * t. + + + align:start position:0% +integral of a from 0 to t is just a * t. +So, sec number one example, number zero + + align:start position:0% +So, sec number one example, number zero + + + align:start position:0% +So, sec number one example, number zero +example would be e to the minus a t. + + align:start position:0% +example would be e to the minus a t. + + + align:start position:0% +example would be e to the minus a t. +that would + + align:start position:0% +that would + + + align:start position:0% +that would +be the correct integrating factor if we + + align:start position:0% +be the correct integrating factor if we + + + align:start position:0% +be the correct integrating factor if we +had constant a and I'll create some uh + + align:start position:0% +had constant a and I'll create some uh + + + align:start position:0% +had constant a and I'll create some uh +examples some problems just to go + + align:start position:0% +examples some problems just to go + + + align:start position:0% +examples some problems just to go +through the steps in that best case of + + align:start position:0% +through the steps in that best case of + + + align:start position:0% +through the steps in that best case of +all with constant integrating factor but + + align:start position:0% +all with constant integrating factor but + + + align:start position:0% +all with constant integrating factor but +now we can solve it with a varying + + align:start position:0% +now we can solve it with a varying + + + align:start position:0% +now we can solve it with a varying +uh interest rate. Good. Thank you. \ No newline at end of file diff --git a/qOAs4HVCR48.txt b/qOAs4HVCR48.txt new file mode 100644 index 0000000000000000000000000000000000000000..2723dcdeaa1702d221b3c15c2a8eaebecb3eec7b --- /dev/null +++ b/qOAs4HVCR48.txt @@ -0,0 +1,6285 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mit.edu. + + align:start position:0% + + + + align:start position:0% + +Okay, so today we're going to talk about + + align:start position:0% +Okay, so today we're going to talk about + + + align:start position:0% +Okay, so today we're going to talk about +RKR and a few other things. + + align:start position:0% +RKR and a few other things. + + + align:start position:0% +RKR and a few other things. +Um before I start though, I want to + + align:start position:0% +Um before I start though, I want to + + + align:start position:0% +Um before I start though, I want to +refer you to uh two wonderful + + align:start position:0% +refer you to uh two wonderful + + + align:start position:0% +refer you to uh two wonderful +uh documents that are uh that are + + align:start position:0% +uh documents that are uh that are + + + align:start position:0% +uh documents that are uh that are +produced by Bob Loy. Um, and you can get + + align:start position:0% +produced by Bob Loy. Um, and you can get + + + align:start position:0% +produced by Bob Loy. Um, and you can get +them at to his + + align:start position:0% + + + + align:start position:0% + +website and the two that I have here, + + align:start position:0% +website and the two that I have here, + + + align:start position:0% +website and the two that I have here, +one is a program called is a document + + align:start position:0% +one is a program called is a document + + + align:start position:0% +one is a program called is a document +called RKR1. I don't know whether it's + + align:start position:0% +called RKR1. I don't know whether it's + + + align:start position:0% +called RKR1. I don't know whether it's +RKR1 now because this is dated + + align:start position:0% +RKR1 now because this is dated + + + align:start position:0% +RKR1 now because this is dated +1992 but uh it is the definitive RKR + + align:start position:0% +1992 but uh it is the definitive RKR + + + align:start position:0% +1992 but uh it is the definitive RKR +program uh and you can download it and + + align:start position:0% +program uh and you can download it and + + + align:start position:0% +program uh and you can download it and +whatever it it it contains a write up of + + align:start position:0% +whatever it it it contains a write up of + + + align:start position:0% +whatever it it it contains a write up of +what the RKR is which is nominally the + + align:start position:0% +what the RKR is which is nominally the + + + align:start position:0% +what the RKR is which is nominally the +purpose of this lecture but also it's a + + align:start position:0% +purpose of this lecture but also it's a + + + align:start position:0% +purpose of this lecture but also it's a +program that + + align:start position:0% +program that + + + align:start position:0% +program that +works and there's also a thing called + + align:start position:0% +works and there's also a thing called + + + align:start position:0% +works and there's also a thing called +level and level among other things + + align:start position:0% +level and level among other things + + + align:start position:0% +level and level among other things +starts starts with the uh the potential + + align:start position:0% +starts starts with the uh the potential + + + align:start position:0% +starts starts with the uh the potential +and calculates uh uh the vibrational + + align:start position:0% +and calculates uh uh the vibrational + + + align:start position:0% +and calculates uh uh the vibrational +wave + + align:start position:0% +wave + + + align:start position:0% +wave +function and anything else that you + + align:start position:0% +function and anything else that you + + + align:start position:0% +function and anything else that you +would would calculate from expectation + + align:start position:0% +would would calculate from expectation + + + align:start position:0% +would would calculate from expectation +values or overlaps of vibrational wave + + align:start position:0% +values or overlaps of vibrational wave + + + align:start position:0% +values or overlaps of vibrational wave +functions. And again, this is the + + align:start position:0% +functions. And again, this is the + + + align:start position:0% +functions. And again, this is the +definitive numerical integration routine + + align:start position:0% +definitive numerical integration routine + + + align:start position:0% +definitive numerical integration routine +for diatomic molecules. And so these are + + align:start position:0% +for diatomic molecules. And so these are + + + align:start position:0% +for diatomic molecules. And so these are +two incredibly important uh tools in + + align:start position:0% +two incredibly important uh tools in + + + align:start position:0% +two incredibly important uh tools in +diatomic molecule spectroscopy and Bob + + align:start position:0% +diatomic molecule spectroscopy and Bob + + + align:start position:0% +diatomic molecule spectroscopy and Bob +Loy really owns them. And there are a + + align:start position:0% +Loy really owns them. And there are a + + + align:start position:0% +Loy really owns them. And there are a +couple other areas that uh Loy is the uh + + align:start position:0% +couple other areas that uh Loy is the uh + + + align:start position:0% +couple other areas that uh Loy is the uh +the key person. And so it would be a + + align:start position:0% +the key person. And so it would be a + + + align:start position:0% +the key person. And so it would be a +good idea to uh obtain these documents. + + align:start position:0% +good idea to uh obtain these documents. + + + align:start position:0% +good idea to uh obtain these documents. +And in previous years, I would always + + align:start position:0% +And in previous years, I would always + + + align:start position:0% +And in previous years, I would always +assign some kind of a problem where you + + align:start position:0% +assign some kind of a problem where you + + + align:start position:0% +assign some kind of a problem where you +would have to use both of those + + align:start position:0% +would have to use both of those + + + align:start position:0% +would have to use both of those +programs. And I I don't have the heart + + align:start position:0% +programs. And I I don't have the heart + + + align:start position:0% +programs. And I I don't have the heart +to do that this year. So I'm just going + + align:start position:0% +to do that this year. So I'm just going + + + align:start position:0% +to do that this year. So I'm just going +to say look at them and maybe use them. + + align:start position:0% +to say look at them and maybe use them. + + + align:start position:0% +to say look at them and maybe use them. +Okay. + + align:start position:0% + + + + align:start position:0% + +So you + + align:start position:0% +So you + + + align:start position:0% +So you +have approached the energy levels of + + align:start position:0% +have approached the energy levels of + + + align:start position:0% +have approached the energy levels of +diatomic molecules using perturbation + + align:start position:0% +diatomic molecules using perturbation + + + align:start position:0% +diatomic molecules using perturbation +theory. And part of the reason that I + + align:start position:0% +theory. And part of the reason that I + + + align:start position:0% +theory. And part of the reason that I +spent a lot of time uh on this kind of + + align:start position:0% +spent a lot of time uh on this kind of + + + align:start position:0% +spent a lot of time uh on this kind of +perturbation theory treatment is that + + align:start position:0% +perturbation theory treatment is that + + + align:start position:0% +perturbation theory treatment is that +everything you do using perturbation + + align:start position:0% +everything you do using perturbation + + + align:start position:0% +everything you do using perturbation +theory + + align:start position:0% +theory + + + align:start position:0% +theory +uh on diatomic molecules transfers to + + align:start position:0% +uh on diatomic molecules transfers to + + + align:start position:0% +uh on diatomic molecules transfers to +polyatomic molecules. + + align:start position:0% +polyatomic molecules. + + + align:start position:0% +polyatomic molecules. +There is an exact procedure for relating + + align:start position:0% +There is an exact procedure for relating + + + align:start position:0% +There is an exact procedure for relating +the energy levels to the potential + + align:start position:0% +the energy levels to the potential + + + align:start position:0% +the energy levels to the potential +energy curve in diatomic molecules and + + align:start position:0% +energy curve in diatomic molecules and + + + align:start position:0% +energy curve in diatomic molecules and +that's called + + align:start position:0% +that's called + + + align:start position:0% +that's called +RKR and that does not transfer to + + align:start position:0% +RKR and that does not transfer to + + + align:start position:0% +RKR and that does not transfer to +polyatomic + + align:start position:0% +polyatomic + + + align:start position:0% +polyatomic +molecules. So it's a little bit of a + + align:start position:0% +molecules. So it's a little bit of a + + + align:start position:0% +molecules. So it's a little bit of a +bait and switch if I were to to tell you + + align:start position:0% +bait and switch if I were to to tell you + + + align:start position:0% +bait and switch if I were to to tell you +only use RKR because it works and is + + align:start position:0% +only use RKR because it works and is + + + align:start position:0% +only use RKR because it works and is +wonderful + + align:start position:0% +wonderful + + + align:start position:0% +wonderful +uh because you won't be able to take it + + align:start position:0% +uh because you won't be able to take it + + + align:start position:0% +uh because you won't be able to take it +over. And so I I that's why I invested + + align:start position:0% +over. And so I I that's why I invested + + + align:start position:0% +over. And so I I that's why I invested +so much in perturbation theory. + + align:start position:0% + + + + align:start position:0% + +Um now one reason you would not just use + + align:start position:0% +Um now one reason you would not just use + + + align:start position:0% +Um now one reason you would not just use +perturbation theory on diatomics is + + align:start position:0% +perturbation theory on diatomics is + + + align:start position:0% +perturbation theory on diatomics is +because they're not accurate enough. + + align:start position:0% +because they're not accurate enough. + + + align:start position:0% +because they're not accurate enough. +uh that uh you really want to represent + + align:start position:0% +uh that uh you really want to represent + + + align:start position:0% +uh that uh you really want to represent +uh all observable properties and + + align:start position:0% +uh all observable properties and + + + align:start position:0% +uh all observable properties and +relationships between them uh as + + align:start position:0% +relationships between them uh as + + + align:start position:0% +relationships between them uh as +accurately as possible through one + + align:start position:0% +accurately as possible through one + + + align:start position:0% +accurately as possible through one +common thing and that is the potential + + align:start position:0% +common thing and that is the potential + + + align:start position:0% +common thing and that is the potential +energy curve. And uh if you use + + align:start position:0% +energy curve. And uh if you use + + + align:start position:0% +energy curve. And uh if you use +perturbation theory, you you you make a + + align:start position:0% +perturbation theory, you you you make a + + + align:start position:0% +perturbation theory, you you you make a +good approximation to the potential + + align:start position:0% +good approximation to the potential + + + align:start position:0% +good approximation to the potential +energy curve near the bottom. And the + + align:start position:0% +energy curve near the bottom. And the + + + align:start position:0% +energy curve near the bottom. And the +higher up you go, the more uh uh you + + align:start position:0% +higher up you go, the more uh uh you + + + align:start position:0% +higher up you go, the more uh uh you +don't really know how good it is what + + align:start position:0% +don't really know how good it is what + + + align:start position:0% +don't really know how good it is what +you've + + align:start position:0% +you've + + + align:start position:0% +you've +built. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So + + align:start position:0% +So + + + align:start position:0% +So +RKR Redberg Klein + + align:start position:0% +RKR Redberg Klein + + + align:start position:0% +RKR Redberg Klein +Ree is a direct product of + + align:start position:0% +Ree is a direct product of + + + align:start position:0% +Ree is a direct product of +WKB Wel Kmer's Brew. This is a + + align:start position:0% +WKB Wel Kmer's Brew. This is a + + + align:start position:0% +WKB Wel Kmer's Brew. This is a +semiclassical approach. It is a + + align:start position:0% +semiclassical approach. It is a + + + align:start position:0% +semiclassical approach. It is a +fantastic thing, fantastic tool and it + + align:start position:0% +fantastic thing, fantastic tool and it + + + align:start position:0% +fantastic thing, fantastic tool and it +is relevant at least in little in little + + align:start position:0% +is relevant at least in little in little + + + align:start position:0% +is relevant at least in little in little +bits of analysis for polyatomic + + align:start position:0% +bits of analysis for polyatomic + + + align:start position:0% +bits of analysis for polyatomic +molecules. you are able to determine the + + align:start position:0% +molecules. you are able to determine the + + + align:start position:0% +molecules. you are able to determine the +shape of the wave function qualitative + + align:start position:0% +shape of the wave function qualitative + + + align:start position:0% +shape of the wave function qualitative +features of the wave function without + + align:start position:0% +features of the wave function without + + + align:start position:0% +features of the wave function without +solving a shortening equation. So the + + align:start position:0% +solving a shortening equation. So the + + + align:start position:0% +solving a shortening equation. So the +basically all you need to know is uh + + align:start position:0% +basically all you need to know is uh + + + align:start position:0% +basically all you need to know is uh +what is the uh kinetic energy at a + + align:start position:0% +what is the uh kinetic energy at a + + + align:start position:0% +what is the uh kinetic energy at a +particular point in space. Now that's + + align:start position:0% +particular point in space. Now that's + + + align:start position:0% +particular point in space. Now that's +not a quantum mechanical idea. That's an + + align:start position:0% +not a quantum mechanical idea. That's an + + + align:start position:0% +not a quantum mechanical idea. That's an +a quantum mechanical impossibility. But + + align:start position:0% +a quantum mechanical impossibility. But + + + align:start position:0% +a quantum mechanical impossibility. But +classically you can ask well what is the + + align:start position:0% +classically you can ask well what is the + + + align:start position:0% +classically you can ask well what is the +momentum anywhere uh in space or what is + + align:start position:0% +momentum anywhere uh in space or what is + + + align:start position:0% +momentum anywhere uh in space or what is +the kinetic energy and now for a + + align:start position:0% +the kinetic energy and now for a + + + align:start position:0% +the kinetic energy and now for a +diatomic molecule + + align:start position:0% +diatomic molecule + + + align:start position:0% +diatomic molecule +uh kinetic energy is a scalar quantity + + align:start position:0% +uh kinetic energy is a scalar quantity + + + align:start position:0% +uh kinetic energy is a scalar quantity +momentum is a vector quantity and one + + align:start position:0% +momentum is a vector quantity and one + + + align:start position:0% +momentum is a vector quantity and one +can ignore the fact because there's only + + align:start position:0% +can ignore the fact because there's only + + + align:start position:0% +can ignore the fact because there's only +one direction but in a polyatomic + + align:start position:0% +one direction but in a polyatomic + + + align:start position:0% +one direction but in a polyatomic +molecule uh what you really want is + + align:start position:0% +molecule uh what you really want is + + + align:start position:0% +molecule uh what you really want is +momentum and that's a vector quantity or + + align:start position:0% +momentum and that's a vector quantity or + + + align:start position:0% +momentum and that's a vector quantity or +it's and uh and what you have really is + + align:start position:0% +it's and uh and what you have really is + + + align:start position:0% +it's and uh and what you have really is +the distance of your + + align:start position:0% +the distance of your + + + align:start position:0% +the distance of your +uh the energy above the potential + + align:start position:0% +uh the energy above the potential + + + align:start position:0% +uh the energy above the potential +surface and that's a kinetic energy and + + align:start position:0% +surface and that's a kinetic energy and + + + align:start position:0% +surface and that's a kinetic energy and +so you have to be careful but let's + + align:start position:0% +so you have to be careful but let's + + + align:start position:0% +so you have to be careful but let's +let's uh uh look at WKB for a little + + align:start position:0% +let's uh uh look at WKB for a little + + + align:start position:0% +let's uh uh look at WKB for a little +while because uh uh this is such a + + align:start position:0% +while because uh uh this is such a + + + align:start position:0% +while because uh uh this is such a +wonderful thing. + + align:start position:0% + + + + align:start position:0% + +Okay. So semiclassical means + + align:start position:0% +Okay. So semiclassical means + + + align:start position:0% +Okay. So semiclassical means +that we can define momentum + + align:start position:0% +that we can define momentum + + + align:start position:0% +that we can define momentum +uh + + align:start position:0% +uh + + + align:start position:0% +uh +classically and and this is not the + + align:start position:0% +classically and and this is not the + + + align:start position:0% +classically and and this is not the +quantum mechanical momentum but it's a + + align:start position:0% +quantum mechanical momentum but it's a + + + align:start position:0% +quantum mechanical momentum but it's a +function. It's a perfectly legitimate + + align:start position:0% +function. It's a perfectly legitimate + + + align:start position:0% +function. It's a perfectly legitimate +function. We could calculate expectation + + align:start position:0% +function. We could calculate expectation + + + align:start position:0% +function. We could calculate expectation +values of it. Uh but uh the momentum is + + align:start position:0% + + + + align:start position:0% + +uh well the + + align:start position:0% + + + + align:start position:0% + +uh the kinetic energy is p ^2 over + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +mu. Right? This is the reduced mass. And + + align:start position:0% +mu. Right? This is the reduced mass. And + + + align:start position:0% +mu. Right? This is the reduced mass. And +uh so to get + + align:start position:0% +uh so to get + + + align:start position:0% +uh so to get +uh P you have 2 mu E minus V of + + align:start position:0% + + + + align:start position:0% + +R. So that's the classical momentum + + align:start position:0% + + + + align:start position:0% + +function. the WKB wave + + align:start position:0% + + + + align:start position:0% + +function which you can derive by making + + align:start position:0% +function which you can derive by making + + + align:start position:0% +function which you can derive by making +some clever uh uh uh expansion where you + + align:start position:0% +some clever uh uh uh expansion where you + + + align:start position:0% +some clever uh uh uh expansion where you +know basically you get quantum mechanics + + align:start position:0% +know basically you get quantum mechanics + + + align:start position:0% +know basically you get quantum mechanics +classical mechanics if h is + + align:start position:0% +classical mechanics if h is + + + align:start position:0% +classical mechanics if h is +uh zero and uh + + align:start position:0% +uh zero and uh + + + align:start position:0% +uh zero and uh +uh and you get quantum + + align:start position:0% +uh and you get quantum + + + align:start position:0% +uh and you get quantum +mechanics otherwise uh The WKB wave + + align:start position:0% + + + + align:start position:0% + +function as this minus a half. + + align:start position:0% + + + + align:start position:0% + +Okay, so this is an envelope + + align:start position:0% +Okay, so this is an envelope + + + align:start position:0% +Okay, so this is an envelope +function and this is the oscilly + + align:start position:0% +function and this is the oscilly + + + align:start position:0% +function and this is the oscilly +function. Okay, and this is a turning + + align:start position:0% +function. Okay, and this is a turning + + + align:start position:0% +function. Okay, and this is a turning +point. Uh and uh so uh you're + + align:start position:0% +point. Uh and uh so uh you're + + + align:start position:0% +point. Uh and uh so uh you're +integrating + + align:start position:0% +integrating + + + align:start position:0% +integrating +this classical momentum function in from + + align:start position:0% +this classical momentum function in from + + + align:start position:0% +this classical momentum function in from +a turning point to where you want to + + align:start position:0% +a turning point to where you want to + + + align:start position:0% +a turning point to where you want to +look at the wave function. + + align:start position:0% +look at the wave function. + + + align:start position:0% +look at the wave function. +And the larger this p is, the faster + + align:start position:0% +And the larger this p is, the faster + + + align:start position:0% +And the larger this p is, the faster +this + + align:start position:0% +this + + + align:start position:0% +this +uh exponential + + align:start position:0% +uh exponential + + + align:start position:0% +uh exponential +wiggles. And if you have functions that + + align:start position:0% +wiggles. And if you have functions that + + + align:start position:0% +wiggles. And if you have functions that +are oscillating rapidly and you have + + align:start position:0% +are oscillating rapidly and you have + + + align:start position:0% +are oscillating rapidly and you have +integrals involving functions that are + + align:start position:0% +integrals involving functions that are + + + align:start position:0% +integrals involving functions that are +oscillating rapidly, the only place + + align:start position:0% +oscillating rapidly, the only place + + + align:start position:0% +oscillating rapidly, the only place +where the integral accumulates is where + + align:start position:0% +where the integral accumulates is where + + + align:start position:0% +where the integral accumulates is where +the two things are oscillating rapidly + + align:start position:0% +the two things are oscillating rapidly + + + align:start position:0% +the two things are oscillating rapidly +at the same frequency. And so this is an + + align:start position:0% +at the same frequency. And so this is an + + + align:start position:0% +at the same frequency. And so this is an +extremely important thing because it + + align:start position:0% +extremely important thing because it + + + align:start position:0% +extremely important thing because it +gives you causality. It gives you this + + align:start position:0% +gives you causality. It gives you this + + + align:start position:0% +gives you causality. It gives you this +is where a react is something is you + + align:start position:0% +is where a react is something is you + + + align:start position:0% +is where a react is something is you +know if you're using these kinds of wave + + align:start position:0% +know if you're using these kinds of wave + + + align:start position:0% +know if you're using these kinds of wave +functions and you're calculating the + + align:start position:0% +functions and you're calculating the + + + align:start position:0% +functions and you're calculating the +expectation value of something you can + + align:start position:0% +expectation value of something you can + + + align:start position:0% +expectation value of something you can +think that the expectation value of + + align:start position:0% +think that the expectation value of + + + align:start position:0% +think that the expectation value of +something is due to something that + + align:start position:0% +something is due to something that + + + align:start position:0% +something is due to something that +occurred in a particular region of + + align:start position:0% +occurred in a particular region of + + + align:start position:0% +occurred in a particular region of +space. And this is the way we think + + align:start position:0% +space. And this is the way we think + + + align:start position:0% +space. And this is the way we think +about the classical world. And so this + + align:start position:0% +about the classical world. And so this + + + align:start position:0% +about the classical world. And so this +oscilly thing is amazingly important + + align:start position:0% +oscilly thing is amazingly important + + + align:start position:0% +oscilly thing is amazingly important +because it gets you back to classical + + align:start position:0% + + + + align:start position:0% + +mechanisms and + + align:start position:0% +mechanisms and + + + align:start position:0% +mechanisms and +uh you've heard of + + align:start position:0% +uh you've heard of + + + align:start position:0% +uh you've heard of +u I won't talk about that and this uh + + align:start position:0% +u I won't talk about that and this uh + + + align:start position:0% +u I won't talk about that and this uh +this is the envelope. So the faster + + align:start position:0% +this is the envelope. So the faster + + + align:start position:0% +this is the envelope. So the faster +something is moving the smaller this + + align:start position:0% +something is moving the smaller this + + + align:start position:0% +something is moving the smaller this +factor is. And again that that comes out + + align:start position:0% +factor is. And again that that comes out + + + align:start position:0% +factor is. And again that that comes out +of a probabilistic uh idea. If you if + + align:start position:0% +of a probabilistic uh idea. If you if + + + align:start position:0% +of a probabilistic uh idea. If you if +something is moving fast it doesn't + + align:start position:0% +something is moving fast it doesn't + + + align:start position:0% +something is moving fast it doesn't +spend much time in a particular place + + align:start position:0% +spend much time in a particular place + + + align:start position:0% +spend much time in a particular place +and you can actually work out what the + + align:start position:0% +and you can actually work out what the + + + align:start position:0% +and you can actually work out what the +uh envelope function ought to be based + + align:start position:0% +uh envelope function ought to be based + + + align:start position:0% +uh envelope function ought to be based +on calculating. Okay. Suppose you + + align:start position:0% + + + + align:start position:0% + +have we have motion in a potential. You + + align:start position:0% +have we have motion in a potential. You + + + align:start position:0% +have we have motion in a potential. You +if you can calculate what the the period + + align:start position:0% +if you can calculate what the the period + + + align:start position:0% +if you can calculate what the the period +of oscillation is + + align:start position:0% +of oscillation is + + + align:start position:0% +of oscillation is +uh and you can calculate say how long it + + align:start position:0% +uh and you can calculate say how long it + + + align:start position:0% +uh and you can calculate say how long it +takes to go through a particular region + + align:start position:0% +takes to go through a particular region + + + align:start position:0% +takes to go through a particular region +of space. If you know the momentum at + + align:start position:0% +of space. If you know the momentum at + + + align:start position:0% +of space. If you know the momentum at +that point, you can calculate how long + + align:start position:0% +that point, you can calculate how long + + + align:start position:0% +that point, you can calculate how long +it takes to go through this and the + + align:start position:0% +it takes to go through this and the + + + align:start position:0% +it takes to go through this and the +ratio of that time to the period or to + + align:start position:0% +ratio of that time to the period or to + + + align:start position:0% +ratio of that time to the period or to +half the period tells you the + + align:start position:0% +half the period tells you the + + + align:start position:0% +half the period tells you the +probability of finding the system in + + align:start position:0% +probability of finding the system in + + + align:start position:0% +probability of finding the system in +this point in this region. And so uh the + + align:start position:0% +this point in this region. And so uh the + + + align:start position:0% +this point in this region. And so uh the +probability is + + align:start position:0% +probability is + + + align:start position:0% +probability is +uh proportional to one over the + + align:start position:0% +uh proportional to one over the + + + align:start position:0% +uh proportional to one over the +momentum and the uh probability + + align:start position:0% +momentum and the uh probability + + + align:start position:0% +momentum and the uh probability +amplitude which is what what the wave + + align:start position:0% +amplitude which is what what the wave + + + align:start position:0% +amplitude which is what what the wave +function is pro is square root of that. + + align:start position:0% +function is pro is square root of that. + + + align:start position:0% +function is pro is square root of that. +So we have something that tells you what + + align:start position:0% +So we have something that tells you what + + + align:start position:0% +So we have something that tells you what +is the probability of finding a system + + align:start position:0% +is the probability of finding a system + + + align:start position:0% +is the probability of finding a system +in a particular region of space and how + + align:start position:0% +in a particular region of space and how + + + align:start position:0% +in a particular region of space and how +it oscillates and these two are enough + + align:start position:0% +it oscillates and these two are enough + + + align:start position:0% +it oscillates and these two are enough +to build an incredible amount of + + align:start position:0% +to build an incredible amount of + + + align:start position:0% +to build an incredible amount of +insight. Okay. So + + align:start position:0% + + + + align:start position:0% + +now we have a + + align:start position:0% +now we have a + + + align:start position:0% +now we have a +um we have a problem + + align:start position:0% +um we have a problem + + + align:start position:0% +um we have a problem +that we're at some energy and we have a + + align:start position:0% +that we're at some energy and we have a + + + align:start position:0% +that we're at some energy and we have a +wave function the WKB wave function + + align:start position:0% +wave function the WKB wave function + + + align:start position:0% +wave function the WKB wave function +which uh it turns out + + align:start position:0% +which uh it turns out + + + align:start position:0% +which uh it turns out +uh is valid away in a region of space + + align:start position:0% +uh is valid away in a region of space + + + align:start position:0% +uh is valid away in a region of space +not near a turning point. + + align:start position:0% +not near a turning point. + + + align:start position:0% +not near a turning point. +because at a turning point the + + align:start position:0% +because at a turning point the + + + align:start position:0% +because at a turning point the +uh the momentum is + + align:start position:0% +uh the momentum is + + + align:start position:0% +uh the momentum is +zero and uh this blows up and that's + + align:start position:0% +zero and uh this blows up and that's + + + align:start position:0% +zero and uh this blows up and that's +unphysical. And + + align:start position:0% +unphysical. And + + + align:start position:0% +unphysical. And +so if we wanted to use + + align:start position:0% +so if we wanted to use + + + align:start position:0% +so if we wanted to use +WKB to describe energy + + align:start position:0% +WKB to describe energy + + + align:start position:0% +WKB to describe energy +levels, we have a little bit of a + + align:start position:0% +levels, we have a little bit of a + + + align:start position:0% +levels, we have a little bit of a +problem. We're okay outside in the + + align:start position:0% +problem. We're okay outside in the + + + align:start position:0% +problem. We're okay outside in the +non-class region of the + + align:start position:0% +non-class region of the + + + align:start position:0% +non-class region of the +potential. And uh but in the non-class + + align:start position:0% +potential. And uh but in the non-class + + + align:start position:0% +potential. And uh but in the non-class +region, the the wave function has to go + + align:start position:0% +region, the the wave function has to go + + + align:start position:0% +region, the the wave function has to go +to zero at infinity. And that's a + + align:start position:0% +to zero at infinity. And that's a + + + align:start position:0% +to zero at infinity. And that's a +boundary condition. Uh and we're okay + + align:start position:0% +boundary condition. Uh and we're okay + + + align:start position:0% +boundary condition. Uh and we're okay +inside. And but we have we have wave + + align:start position:0% +inside. And but we have we have wave + + + align:start position:0% +inside. And but we have we have wave +functions + + align:start position:0% +functions + + + align:start position:0% +functions +propagating inside and they have to meet + + align:start position:0% +propagating inside and they have to meet + + + align:start position:0% +propagating inside and they have to meet +and be uh and and where these two wave + + align:start position:0% +and be uh and and where these two wave + + + align:start position:0% +and be uh and and where these two wave +functions meet they have to the wave + + align:start position:0% +functions meet they have to the wave + + + align:start position:0% +functions meet they have to the wave +function has to be + + align:start position:0% +function has to be + + + align:start position:0% +function has to be +continuous. And so, okay, first of + + align:start position:0% +continuous. And so, okay, first of + + + align:start position:0% +continuous. And so, okay, first of +all, the way you deal with this uh gap + + align:start position:0% +all, the way you deal with this uh gap + + + align:start position:0% +all, the way you deal with this uh gap +at the boundary is that you discover + + align:start position:0% +at the boundary is that you discover + + + align:start position:0% +at the boundary is that you discover +that you can approximate this region + + align:start position:0% +that you can approximate this region + + + align:start position:0% +that you can approximate this region +here as a linear potential if you're + + align:start position:0% +here as a linear potential if you're + + + align:start position:0% +here as a linear potential if you're +close to it. And then you have wave + + align:start position:0% +close to it. And then you have wave + + + align:start position:0% +close to it. And then you have wave +functions that are uh well, they're + + align:start position:0% +functions that are uh well, they're + + + align:start position:0% +functions that are uh well, they're +functions. Are functions are the correct + + align:start position:0% +functions. Are functions are the correct + + + align:start position:0% +functions. Are functions are the correct +wave function for a linear potential. + + align:start position:0% +wave function for a linear potential. + + + align:start position:0% +wave function for a linear potential. +And so with area functions you can go + + align:start position:0% +And so with area functions you can go + + + align:start position:0% +And so with area functions you can go +across this region and you join up these + + align:start position:0% +across this region and you join up these + + + align:start position:0% +across this region and you join up these +two things. The uh the wave function + + align:start position:0% +two things. The uh the wave function + + + align:start position:0% +two things. The uh the wave function +having to go to infin go to zero at + + align:start position:0% +having to go to infin go to zero at + + + align:start position:0% +having to go to infin go to zero at +infinity positive and negative infinity + + align:start position:0% +infinity positive and negative infinity + + + align:start position:0% +infinity positive and negative infinity +imply imposes a definite phase. And what + + align:start position:0% +imply imposes a definite phase. And what + + + align:start position:0% +imply imposes a definite phase. And what +you end up discovering is that the wave + + align:start position:0% +you end up discovering is that the wave + + + align:start position:0% +you end up discovering is that the wave +function at a at a point where the WKB + + align:start position:0% +function at a at a point where the WKB + + + align:start position:0% +function at a at a point where the WKB +is valid on the inside of the potential + + align:start position:0% +is valid on the inside of the potential + + + align:start position:0% +is valid on the inside of the potential +uh is the WKB wave function you would + + align:start position:0% +uh is the WKB wave function you would + + + align:start position:0% +uh is the WKB wave function you would +have calculated from here but it's not + + align:start position:0% +have calculated from here but it's not + + + align:start position:0% +have calculated from here but it's not +valid here plus pi over4 with a phase of + + align:start position:0% +valid here plus pi over4 with a phase of + + + align:start position:0% +valid here plus pi over4 with a phase of +pi + + align:start position:0% +pi + + + align:start position:0% +pi +over4. So the it's a long complicated + + align:start position:0% +over4. So the it's a long complicated + + + align:start position:0% +over4. So the it's a long complicated +lecture explaining how you join the wave + + align:start position:0% +lecture explaining how you join the wave + + + align:start position:0% +lecture explaining how you join the wave +fun you you get the correct wave + + align:start position:0% +fun you you get the correct wave + + + align:start position:0% +fun you you get the correct wave +function and joining across the boundary + + align:start position:0% +function and joining across the boundary + + + align:start position:0% +function and joining across the boundary +is a is a really important piece of that + + align:start position:0% +is a is a really important piece of that + + + align:start position:0% +is a is a really important piece of that +I won't do + + align:start position:0% +I won't do + + + align:start position:0% +I won't do +that then the continuity that leads to + + align:start position:0% +that then the continuity that leads to + + + align:start position:0% +that then the continuity that leads to +what's called the quantization condition + + align:start position:0% +what's called the quantization condition + + + align:start position:0% +what's called the quantization condition +because the only way wave functions + + align:start position:0% +because the only way wave functions + + + align:start position:0% +because the only way wave functions +which go to go to zero at infinity + + align:start position:0% +which go to go to zero at infinity + + + align:start position:0% +which go to go to zero at infinity +correctly can uh be legitimate solutions + + align:start position:0% +correctly can uh be legitimate solutions + + + align:start position:0% +correctly can uh be legitimate solutions +is if the two- wave functions are + + align:start position:0% +is if the two- wave functions are + + + align:start position:0% +is if the two- wave functions are +continuous and the derivative is + + align:start position:0% +continuous and the derivative is + + + align:start position:0% +continuous and the derivative is +continuous. And so you end up getting a + + align:start position:0% +continuous. And so you end up getting a + + + align:start position:0% +continuous. And so you end up getting a +quantization condition. And the + + align:start position:0% +quantization condition. And the + + + align:start position:0% +quantization condition. And the +quantization condition + + align:start position:0% + + + + align:start position:0% + +is I'm going to put the + + align:start position:0% + + + + align:start position:0% + +So this is the quantization + + align:start position:0% +So this is the quantization + + + align:start position:0% +So this is the quantization +condition. This is an integral. This + + align:start position:0% +condition. This is an integral. This + + + align:start position:0% +condition. This is an integral. This +this quantity is + + align:start position:0% +this quantity is + + + align:start position:0% +this quantity is +uh did I blow a + + align:start position:0% +uh did I blow a + + + align:start position:0% +uh did I blow a +sign? No, that's + + align:start position:0% +sign? No, that's + + + align:start position:0% +sign? No, that's +right. This is the classical + + align:start position:0% +right. This is the classical + + + align:start position:0% +right. This is the classical +momentum. So, it's an integral P dQ or + + align:start position:0% +momentum. So, it's an integral P dQ or + + + align:start position:0% +momentum. So, it's an integral P dQ or +PDR. This P Q has the dimension of H. + + align:start position:0% + + + + align:start position:0% + +It's also a quantity that is known as + + align:start position:0% +It's also a quantity that is known as + + + align:start position:0% +It's also a quantity that is known as +action. Now, a personal + + align:start position:0% +action. Now, a personal + + + align:start position:0% +action. Now, a personal +story. I was an undergraduate at Ammerst + + align:start position:0% +story. I was an undergraduate at Ammerst + + + align:start position:0% +story. I was an undergraduate at Ammerst +College and we all write thesis and and + + align:start position:0% +College and we all write thesis and and + + + align:start position:0% +College and we all write thesis and and +we we have a thesis defense and at my + + align:start position:0% +we we have a thesis defense and at my + + + align:start position:0% +we we have a thesis defense and at my +thesis defense uh Dick Frink who uh was + + align:start position:0% +thesis defense uh Dick Frink who uh was + + + align:start position:0% +thesis defense uh Dick Frink who uh was +a young assistant professor at the time + + align:start position:0% +a young assistant professor at the time + + + align:start position:0% +a young assistant professor at the time +asked me a question which was what is + + align:start position:0% +asked me a question which was what is + + + align:start position:0% +asked me a question which was what is +the unit of H? + + align:start position:0% +the unit of H? + + + align:start position:0% +the unit of H? +And I said, "Energy times + + align:start position:0% +And I said, "Energy times + + + align:start position:0% +And I said, "Energy times +time." And I was right. But he didn't + + align:start position:0% +time." And I was right. But he didn't + + + align:start position:0% +time." And I was right. But he didn't +want that. He wanted action. And we went + + align:start position:0% +want that. He wanted action. And we went + + + align:start position:0% +want that. He wanted action. And we went +around for half an hour. I was + + align:start position:0% +around for half an hour. I was + + + align:start position:0% +around for half an hour. I was +absolutely certain that I knew what the + + align:start position:0% +absolutely certain that I knew what the + + + align:start position:0% +absolutely certain that I knew what the +units of H were. And and and he was + + align:start position:0% +units of H were. And and and he was + + + align:start position:0% +units of H were. And and and he was +determined to get action and we never + + align:start position:0% +determined to get action and we never + + + align:start position:0% +determined to get action and we never +converged. Um but anyway, this is an + + align:start position:0% +converged. Um but anyway, this is an + + + align:start position:0% +converged. Um but anyway, this is an +action + + align:start position:0% +action + + + align:start position:0% +action +integral and basically the quantization + + align:start position:0% +integral and basically the quantization + + + align:start position:0% +integral and basically the quantization +condition says there's a certain allowed + + align:start position:0% +condition says there's a certain allowed + + + align:start position:0% +condition says there's a certain allowed +amount of action that uh at each energy + + align:start position:0% +amount of action that uh at each energy + + + align:start position:0% +amount of action that uh at each energy +level the action integral is uh an + + align:start position:0% +level the action integral is uh an + + + align:start position:0% +level the action integral is uh an +integral number of + + align:start position:0% +integral number of + + + align:start position:0% +integral number of +uh so if we if we kill the the uh the + + align:start position:0% +uh so if we if we kill the the uh the + + + align:start position:0% +uh so if we if we kill the the uh the +the so if we make this just h over two + + align:start position:0% +the so if we make this just h over two + + + align:start position:0% +the so if we make this just h over two +to V + 1 or H * V + a half. Uh, that + + align:start position:0% +to V + 1 or H * V + a half. Uh, that + + + align:start position:0% +to V + 1 or H * V + a half. Uh, that +looks a little more familiar. So, + + align:start position:0% +looks a little more familiar. So, + + + align:start position:0% +looks a little more familiar. So, +there's a half integer amount of + + align:start position:0% +there's a half integer amount of + + + align:start position:0% +there's a half integer amount of +action when you evaluate the action + + align:start position:0% +action when you evaluate the action + + + align:start position:0% +action when you evaluate the action +integral um at uh + + align:start position:0% +integral um at uh + + + align:start position:0% +integral um at uh +um the energy of a energy level. And + + align:start position:0% +um the energy of a energy level. And + + + align:start position:0% +um the energy of a energy level. And +there's also you get for each additional + + align:start position:0% +there's also you get for each additional + + + align:start position:0% +there's also you get for each additional +level there's another h of + + align:start position:0% +level there's another h of + + + align:start position:0% +level there's another h of +action. And so this is a a very useful + + align:start position:0% +action. And so this is a a very useful + + + align:start position:0% +action. And so this is a a very useful +quantity and the + + align:start position:0% +quantity and the + + + align:start position:0% +quantity and the +RKR RKR is built on the action + + align:start position:0% +RKR RKR is built on the action + + + align:start position:0% +RKR RKR is built on the action +integral. Okay. + + align:start position:0% + + + + align:start position:0% + +So the derivation of the RKR method is + + align:start position:0% +So the derivation of the RKR method is + + + align:start position:0% +So the derivation of the RKR method is +mathematically opaque especially when I + + align:start position:0% +mathematically opaque especially when I + + + align:start position:0% +mathematically opaque especially when I +have to present it in a lecture. Um and + + align:start position:0% +have to present it in a lecture. Um and + + + align:start position:0% +have to present it in a lecture. Um and +there are many different ways of uh + + align:start position:0% +there are many different ways of uh + + + align:start position:0% +there are many different ways of uh +motivating + + align:start position:0% +motivating + + + align:start position:0% +motivating +it. They all say let's start with some + + align:start position:0% +it. They all say let's start with some + + + align:start position:0% +it. They all say let's start with some +function of energy and + + align:start position:0% +function of energy and + + + align:start position:0% +function of energy and +rotation and + + align:start position:0% + + + + align:start position:0% + +um the the lecture not these lecture + + align:start position:0% +um the the lecture not these lecture + + + align:start position:0% +um the the lecture not these lecture +notes were written in + + align:start position:0% +notes were written in + + + align:start position:0% +notes were written in +1975 and revised over the years. My book + + align:start position:0% +1975 and revised over the years. My book + + + align:start position:0% +1975 and revised over the years. My book +was written in + + align:start position:0% +was written in + + + align:start position:0% +was written in +199 2004 sorry and uh it's better in my + + align:start position:0% +199 2004 sorry and uh it's better in my + + + align:start position:0% +199 2004 sorry and uh it's better in my +book and I don't know why I uh didn't do + + align:start position:0% +book and I don't know why I uh didn't do + + + align:start position:0% +book and I don't know why I uh didn't do +this uh earlier. So we can describe this + + align:start position:0% +this uh earlier. So we can describe this + + + align:start position:0% +this uh earlier. So we can describe this +function uh by the quantity that appears + + align:start position:0% +function uh by the quantity that appears + + + align:start position:0% +function uh by the quantity that appears +uh on as + + align:start position:0% +uh on as + + + align:start position:0% +uh on as +uh where is + + align:start position:0% + + + + align:start position:0% + +it? Equation 22 on page four. + + align:start position:0% +it? Equation 22 on page four. + + + align:start position:0% +it? Equation 22 on page four. +So we can just define a as this function + + align:start position:0% +So we can just define a as this function + + + align:start position:0% +So we can just define a as this function +2 mu over h bar 2 + + align:start position:0% +2 mu over h bar 2 + + + align:start position:0% +2 mu over h bar 2 +square<unk> 1 / + + align:start position:0% +square<unk> 1 / + + + align:start position:0% +square<unk> 1 / +i r - r + + align:start position:0% +i r - r + + + align:start position:0% +i r - r ++ + + align:start position:0% ++ + + + align:start position:0% ++ +and these are functions of energy. + + align:start position:0% +and these are functions of energy. + + + align:start position:0% +and these are functions of energy. +Um E minus U + + align:start position:0% +Um E minus U + + + align:start position:0% +Um E minus U +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +R minus H bar 2 / 2 mu R 2 JJ + + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +Br. Okay. So this what is this? + + align:start position:0% +Br. Okay. So this what is this? + + + align:start position:0% +Br. Okay. So this what is this? +This here + + align:start position:0% +This here + + + align:start position:0% +This here +um I is uh the centrifugal potential. + + align:start position:0% +um I is uh the centrifugal potential. + + + align:start position:0% +um I is uh the centrifugal potential. +This is V of J of + + align:start position:0% +This is V of J of + + + align:start position:0% +This is V of J of +R. Okay, this + + align:start position:0% +R. Okay, this + + + align:start position:0% +R. Okay, this +combination. And so you you have the + + align:start position:0% +combination. And so you you have the + + + align:start position:0% +combination. And so you you have the +bare potential and you have the + + align:start position:0% +bare potential and you have the + + + align:start position:0% +bare potential and you have the +centrifugal correction. And so this + + align:start position:0% +centrifugal correction. And so this + + + align:start position:0% +centrifugal correction. And so this +difference is the energy. + + align:start position:0% +difference is the energy. + + + align:start position:0% +difference is the energy. +So if we have the potential like this, + + align:start position:0% +So if we have the potential like this, + + + align:start position:0% +So if we have the potential like this, +this is the energy. A is just the + + align:start position:0% + + + + align:start position:0% + +area. That's why it's called A. Now + + align:start position:0% +area. That's why it's called A. Now + + + align:start position:0% +area. That's why it's called A. Now +there's some other stuff to make it + + align:start position:0% +there's some other stuff to make it + + + align:start position:0% +there's some other stuff to make it +dimensionally consistent. So we have a + + align:start position:0% +dimensionally consistent. So we have a + + + align:start position:0% +dimensionally consistent. So we have a +function that we are going to play with + + align:start position:0% +function that we are going to play with + + + align:start position:0% +function that we are going to play with +two different ways. + + align:start position:0% +two different ways. + + + align:start position:0% +two different ways. +one way gives + + align:start position:0% +one way gives + + + align:start position:0% +one way gives +us R minus and R plus at + + align:start position:0% + + + + align:start position:0% + +E. So if we knew what A + + align:start position:0% +E. So if we knew what A + + + align:start position:0% +E. So if we knew what A +was then we could do something and + + align:start position:0% +was then we could do something and + + + align:start position:0% +was then we could do something and +derive values for the turning points + + align:start position:0% +derive values for the turning points + + + align:start position:0% +derive values for the turning points +from + + align:start position:0% +from + + + align:start position:0% +from +it. And the other way of processing this + + align:start position:0% +it. And the other way of processing this + + + align:start position:0% +it. And the other way of processing this +is to find out how what A is based on + + align:start position:0% +is to find out how what A is based on + + + align:start position:0% +is to find out how what A is based on +what we know from spectra which are the + + align:start position:0% +what we know from spectra which are the + + + align:start position:0% +what we know from spectra which are the +vibrational and + + align:start position:0% +vibrational and + + + align:start position:0% +vibrational and +rotational + + align:start position:0% +rotational + + + align:start position:0% +rotational +constants. So we determine this from the + + align:start position:0% +constants. So we determine this from the + + + align:start position:0% +constants. So we determine this from the +spectrum. G of V is you know omega V + + align:start position:0% +spectrum. G of V is you know omega V + + + align:start position:0% +spectrum. G of V is you know omega V +plus a half etc etc. And this is be E + + align:start position:0% +plus a half etc etc. And this is be E + + + align:start position:0% +plus a half etc etc. And this is be E +minus uh alpha E V plus a half + + align:start position:0% +minus uh alpha E V plus a half + + + align:start position:0% +minus uh alpha E V plus a half +plus whatever. And + + align:start position:0% +plus whatever. And + + + align:start position:0% +plus whatever. And +so we take this thing and we approach it + + align:start position:0% +so we take this thing and we approach it + + + align:start position:0% +so we take this thing and we approach it +two different ways. One gives us turning + + align:start position:0% +two different ways. One gives us turning + + + align:start position:0% +two different ways. One gives us turning +points if we knew that and the other + + align:start position:0% +points if we knew that and the other + + + align:start position:0% +points if we knew that and the other +gives us that if we knew + + align:start position:0% + + + + align:start position:0% + +this. So this to that is where we want + + align:start position:0% +this. So this to that is where we want + + + align:start position:0% +this. So this to that is where we want +to go. + + align:start position:0% + + + + align:start position:0% + +Okay, Bob + + align:start position:0% +Okay, Bob + + + align:start position:0% +Okay, Bob +Loy + + align:start position:0% +Loy + + + align:start position:0% +Loy +says that the best way to learn about + + align:start position:0% +says that the best way to learn about + + + align:start position:0% +says that the best way to learn about +RKR is to read Klein's + + align:start position:0% +RKR is to read Klein's + + + align:start position:0% +RKR is to read Klein's +paper probably in German from + + align:start position:0% +paper probably in German from + + + align:start position:0% +paper probably in German from +1932 and that uh + + align:start position:0% +1932 and that uh + + + align:start position:0% +1932 and that uh +uh he says also that there's a paper by + + align:start position:0% +uh he says also that there's a paper by + + + align:start position:0% +uh he says also that there's a paper by +Kersner and Watson. This is Jim Watson + + align:start position:0% +Kersner and Watson. This is Jim Watson + + + align:start position:0% +Kersner and Watson. This is Jim Watson +who is as close to God and spectroscopy + + align:start position:0% +who is as close to God and spectroscopy + + + align:start position:0% +who is as close to God and spectroscopy +as you can get. uh um he says that this + + align:start position:0% +as you can get. uh um he says that this + + + align:start position:0% +as you can get. uh um he says that this +was rediscovered. In other words, Watson + + align:start position:0% +was rediscovered. In other words, Watson + + + align:start position:0% +was rediscovered. In other words, Watson +and Kersner wrote basically Klein's + + align:start position:0% +and Kersner wrote basically Klein's + + + align:start position:0% +and Kersner wrote basically Klein's +paper again in + + align:start position:0% +paper again in + + + align:start position:0% +paper again in +1992. Uh and so it might be almost as + + align:start position:0% +1992. Uh and so it might be almost as + + + align:start position:0% +1992. Uh and so it might be almost as +good to read the Kersner and Watson + + align:start position:0% +good to read the Kersner and Watson + + + align:start position:0% +good to read the Kersner and Watson +paper. But anyway uh and what and Loy + + align:start position:0% +paper. But anyway uh and what and Loy + + + align:start position:0% +paper. But anyway uh and what and Loy +does not like the way I develop this uh + + align:start position:0% +does not like the way I develop this uh + + + align:start position:0% +does not like the way I develop this uh +by saying okay let's consider this + + align:start position:0% +by saying okay let's consider this + + + align:start position:0% +by saying okay let's consider this +function and process it two different + + align:start position:0% +function and process it two different + + + align:start position:0% +function and process it two different +ways but I've been doing this all my + + align:start position:0% +ways but I've been doing this all my + + + align:start position:0% +ways but I've been doing this all my +life and I'm just I'm just unable to + + align:start position:0% +life and I'm just I'm just unable to + + + align:start position:0% +life and I'm just I'm just unable to +escape that. Now + + align:start position:0% +escape that. Now + + + align:start position:0% +escape that. Now +there's given this + + align:start position:0% +there's given this + + + align:start position:0% +there's given this +function it's an exceedingly easy thing + + align:start position:0% +function it's an exceedingly easy thing + + + align:start position:0% +function it's an exceedingly easy thing +to make the connection between this and + + align:start position:0% +to make the connection between this and + + + align:start position:0% +to make the connection between this and +that. That's a a a couple of + + align:start position:0% +that. That's a a a couple of + + + align:start position:0% +that. That's a a a couple of +steps. The other thing of showing how + + align:start position:0% +steps. The other thing of showing how + + + align:start position:0% +steps. The other thing of showing how +you can build these two things in to + + align:start position:0% +you can build these two things in to + + + align:start position:0% +you can build these two things in to +determine that is mathematically tedious + + align:start position:0% +determine that is mathematically tedious + + + align:start position:0% +determine that is mathematically tedious +and involves all sorts of stuff and I'm + + align:start position:0% +and involves all sorts of stuff and I'm + + + align:start position:0% +and involves all sorts of stuff and I'm +not going to do that. But you know the + + align:start position:0% +not going to do that. But you know the + + + align:start position:0% +not going to do that. But you know the +the lecture notes do do that. Okay. So + + align:start position:0% +the lecture notes do do that. Okay. So + + + align:start position:0% +the lecture notes do do that. Okay. So +uh let's just take a look at this + + align:start position:0% +uh let's just take a look at this + + + align:start position:0% +uh let's just take a look at this +function and uh suppose we uh take the + + align:start position:0% +function and uh suppose we uh take the + + + align:start position:0% +function and uh suppose we uh take the +derivative the partial derivative of + + align:start position:0% +derivative the partial derivative of + + + align:start position:0% +derivative the partial derivative of +a with respect to + + align:start position:0% + + + + align:start position:0% + +e. Okay. + + align:start position:0% + + + + align:start position:0% + +So, so we get all sorts of garbage out + + align:start position:0% +So, so we get all sorts of garbage out + + + align:start position:0% +So, so we get all sorts of garbage out +in + + align:start position:0% +in + + + align:start position:0% +in +front. And now we have uh an + + align:start position:0% +front. And now we have uh an + + + align:start position:0% +front. And now we have uh an +integral um and so we're going to take + + align:start position:0% +integral um and so we're going to take + + + align:start position:0% +integral um and so we're going to take +the derivative and this this isn't e + + align:start position:0% +the derivative and this this isn't e + + + align:start position:0% +the derivative and this this isn't e +that's e that we take the derivative + + align:start position:0% +that's e that we take the derivative + + + align:start position:0% +that's e that we take the derivative +that's one. So we get the constants out + + align:start position:0% +that's one. So we get the constants out + + + align:start position:0% +that's one. So we get the constants out +in front and then we have integral r + r + + align:start position:0% +in front and then we have integral r + r + + + align:start position:0% +in front and then we have integral r + r +minus the + + align:start position:0% + + + + align:start position:0% + +r that's pretty easy integral even I can + + align:start position:0% +r that's pretty easy integral even I can + + + align:start position:0% +r that's pretty easy integral even I can +do that one and so that gives us this + + align:start position:0% +do that one and so that gives us this + + + align:start position:0% +do that one and so that gives us this +constant times r plus of + + align:start position:0% +constant times r plus of + + + align:start position:0% +constant times r plus of +e minus r minus of + + align:start position:0% + + + + align:start position:0% + +e. So the first + + align:start position:0% +e. So the first + + + align:start position:0% +e. So the first +integral or the first uh equation uh we + + align:start position:0% +integral or the first uh equation uh we + + + align:start position:0% +integral or the first uh equation uh we +get the + + align:start position:0% +get the + + + align:start position:0% +get the +derivative the this derivative of this + + align:start position:0% +derivative the this derivative of this + + + align:start position:0% +derivative the this derivative of this +area area just gives us the difference + + align:start position:0% +area area just gives us the difference + + + align:start position:0% +area area just gives us the difference +in turning + + align:start position:0% + + + + align:start position:0% + +points which is a nice + + align:start position:0% +points which is a nice + + + align:start position:0% +points which is a nice +thing. Okay. And now let's look at the + + align:start position:0% +thing. Okay. And now let's look at the + + + align:start position:0% +thing. Okay. And now let's look at the +partial derivative of a with respect to + + align:start position:0% +partial derivative of a with respect to + + + align:start position:0% +partial derivative of a with respect to +j. + + align:start position:0% + + + + align:start position:0% + +Well, where's J? J only appears here. + + align:start position:0% +Well, where's J? J only appears here. + + + align:start position:0% +Well, where's J? J only appears here. +So, these two terms go away and we get 2 + + align:start position:0% +So, these two terms go away and we get 2 + + + align:start position:0% +So, these two terms go away and we get 2 +J + 1 times that. So we get all that + + align:start position:0% +J + 1 times that. So we get all that + + + align:start position:0% +J + 1 times that. So we get all that +constant stuff and we have uh an + + align:start position:0% +constant stuff and we have uh an + + + align:start position:0% +constant stuff and we have uh an +integral uh and we can take + + align:start position:0% + + + + align:start position:0% + +uh minus h + + align:start position:0% +uh minus h + + + align:start position:0% +uh minus h +bar squar over 2 mu out and we can take + + align:start position:0% +bar squar over 2 mu out and we can take + + + align:start position:0% +bar squar over 2 mu out and we can take +2 j + 1 out and we have now the integral + + align:start position:0% +2 j + 1 out and we have now the integral + + + align:start position:0% +2 j + 1 out and we have now the integral +from r minus to R + of 1 / R^2 D + + align:start position:0% + + + + align:start position:0% + +R and this gives us um this integral + + align:start position:0% +R and this gives us um this integral + + + align:start position:0% +R and this gives us um this integral +gives us one + + align:start position:0% +gives us one + + + align:start position:0% +gives us one +over so this is equal to + + align:start position:0% + + + + align:start position:0% + +uh minus 1 / R + - 1 / R + + align:start position:0% + + + + align:start position:0% + +us right I'm very bad at integration + + align:start position:0% +us right I'm very bad at integration + + + align:start position:0% +us right I'm very bad at integration +even something simple like this uh so we + + align:start position:0% +even something simple like this uh so we + + + align:start position:0% +even something simple like this uh so we +have minus sign cancelling that the + + align:start position:0% +have minus sign cancelling that the + + + align:start position:0% +have minus sign cancelling that the +minus sign I took out here and we get + + align:start position:0% +minus sign I took out here and we get + + + align:start position:0% +minus sign I took out here and we get +now an integral + + align:start position:0% +now an integral + + + align:start position:0% +now an integral +uh that involves so we have one integral + + align:start position:0% +uh that involves so we have one integral + + + align:start position:0% +uh that involves so we have one integral +that's the difference in r the + + align:start position:0% +that's the difference in r the + + + align:start position:0% +that's the difference in r the +difference in turning points at e and + + align:start position:0% +difference in turning points at e and + + + align:start position:0% +difference in turning points at e and +this is the difference in the reciprocal + + align:start position:0% +this is the difference in the reciprocal + + + align:start position:0% +this is the difference in the reciprocal +of the two turning points points at E. + + align:start position:0% +of the two turning points points at E. + + + align:start position:0% +of the two turning points points at E. +Two unknowns, two + + align:start position:0% +Two unknowns, two + + + align:start position:0% +Two unknowns, two +equations. Bam, we've got it. And so if + + align:start position:0% +equations. Bam, we've got it. And so if + + + align:start position:0% +equations. Bam, we've got it. And so if +we can know A of + + align:start position:0% +we can know A of + + + align:start position:0% +we can know A of +EJ, we can determine the turning + + align:start position:0% +EJ, we can determine the turning + + + align:start position:0% +EJ, we can determine the turning +points R plus of E J and R minus of E + + align:start position:0% + + + + align:start position:0% + +Z. And that's what RKR is. Okay. + + align:start position:0% + + + + align:start position:0% + +So I won't + + align:start position:0% + + + + align:start position:0% + +uh I won't go through the derivation + + align:start position:0% +uh I won't go through the derivation + + + align:start position:0% +uh I won't go through the derivation +because it's I don't like it. It's + + align:start position:0% +because it's I don't like it. It's + + + align:start position:0% +because it's I don't like it. It's +tedious. It involves a change of + + align:start position:0% +tedious. It involves a change of + + + align:start position:0% +tedious. It involves a change of +variable and integration by parts and + + align:start position:0% +variable and integration by parts and + + + align:start position:0% +variable and integration by parts and +all sorts of stuff that you can do and + + align:start position:0% +all sorts of stuff that you can do and + + + align:start position:0% +all sorts of stuff that you can do and +it you wouldn't want to see that on a + + align:start position:0% +it you wouldn't want to see that on a + + + align:start position:0% +it you wouldn't want to see that on a +blackboard from someone who is + + align:start position:0% +blackboard from someone who is + + + align:start position:0% +blackboard from someone who is +uncomfortable doing it. And so what you + + align:start position:0% +uncomfortable doing it. And so what you + + + align:start position:0% +uncomfortable doing it. And so what you +discover is that r + - r + + align:start position:0% +discover is that r + - r + + + align:start position:0% +discover is that r + - r +minus is equal to 2 h bar 2 over 2 + + align:start position:0% +minus is equal to 2 h bar 2 over 2 + + + align:start position:0% +minus is equal to 2 h bar 2 over 2 +mu square root + + align:start position:0% + + + + align:start position:0% + +integral over the vibrational quantum + + align:start position:0% + + + + align:start position:0% + +number. + + align:start position:0% +number. + + + align:start position:0% +number. +Um, that's + + align:start position:0% + + + + align:start position:0% + +J. + + align:start position:0% +J. + + + align:start position:0% +J. +So the difference in two turning points + + align:start position:0% +So the difference in two turning points + + + align:start position:0% +So the difference in two turning points +is given by uh at E and E can be treated + + align:start position:0% +is given by uh at E and E can be treated + + + align:start position:0% +is given by uh at E and E can be treated +as continuous. This is the inversion of + + align:start position:0% +as continuous. This is the inversion of + + + align:start position:0% +as continuous. This is the inversion of +E of V. And so this can also be treated + + align:start position:0% +E of V. And so this can also be treated + + + align:start position:0% +E of V. And so this can also be treated +as a continuous function. So you can + + align:start position:0% +as a continuous function. So you can + + + align:start position:0% +as a continuous function. So you can +determine R + minus R minus as a + + align:start position:0% +determine R + minus R minus as a + + + align:start position:0% +determine R + minus R minus as a +continuous function of + + align:start position:0% +continuous function of + + + align:start position:0% +continuous function of +V if you know + + align:start position:0% +V if you know + + + align:start position:0% +V if you know +uh G of + + align:start position:0% +uh G of + + + align:start position:0% +uh G of +V or a continuous function of E. So this + + align:start position:0% +V or a continuous function of E. So this + + + align:start position:0% +V or a continuous function of E. So this +is one thing and so you do do that and + + align:start position:0% +is one thing and so you do do that and + + + align:start position:0% +is one thing and so you do do that and +you can have something like this from + + align:start position:0% +you can have something like this from + + + align:start position:0% +you can have something like this from +polyatomic molecules + + align:start position:0% +polyatomic molecules + + + align:start position:0% +polyatomic molecules +too. So what is this doing? It's telling + + align:start position:0% +too. So what is this doing? It's telling + + + align:start position:0% +too. So what is this doing? It's telling +you what is + + align:start position:0% +you what is + + + align:start position:0% +you what is +the the width of the + + align:start position:0% + + + + align:start position:0% + +potential and that's mostly what you + + align:start position:0% +potential and that's mostly what you + + + align:start position:0% +potential and that's mostly what you +want to + + align:start position:0% +want to + + + align:start position:0% +want to +know. It would be nice to know where + + align:start position:0% +know. It would be nice to know where + + + align:start position:0% +know. It would be nice to know where +this is and where this is. But the + + align:start position:0% +this is and where this is. But the + + + align:start position:0% +this is and where this is. But the +difference between them is the most + + align:start position:0% +difference between them is the most + + + align:start position:0% +difference between them is the most +important thing because + + align:start position:0% +important thing because + + + align:start position:0% +important thing because +often you're willing to say I'm going to + + align:start position:0% +often you're willing to say I'm going to + + + align:start position:0% +often you're willing to say I'm going to +use a model not a model to that's + + align:start position:0% +use a model not a model to that's + + + align:start position:0% +use a model not a model to that's +completely free. A model that is uh + + align:start position:0% +completely free. A model that is uh + + + align:start position:0% +completely free. A model that is uh +saying what is the qualitative form of + + align:start position:0% +saying what is the qualitative form of + + + align:start position:0% +saying what is the qualitative form of +the potential and the difference between + + align:start position:0% +the potential and the difference between + + + align:start position:0% +the potential and the difference between +the two turning points is all you need + + align:start position:0% +the two turning points is all you need + + + align:start position:0% +the two turning points is all you need +in order to pin down the model and that + + align:start position:0% +in order to pin down the model and that + + + align:start position:0% +in order to pin down the model and that +could be done for polyatomic molecules. + + align:start position:0% +could be done for polyatomic molecules. + + + align:start position:0% +could be done for polyatomic molecules. +One of the problems is what is the + + align:start position:0% +One of the problems is what is the + + + align:start position:0% +One of the problems is what is the +potential? Uh what are the coordinates? + + align:start position:0% +potential? Uh what are the coordinates? + + + align:start position:0% +potential? Uh what are the coordinates? +Uh because you know you + + align:start position:0% +Uh because you know you + + + align:start position:0% +Uh because you know you +are observing energy + + align:start position:0% +are observing energy + + + align:start position:0% +are observing energy +levels there energy levels or they're + + align:start position:0% +levels there energy levels or they're + + + align:start position:0% +levels there energy levels or they're +levels in state space. There is nothing + + align:start position:0% +levels in state space. There is nothing + + + align:start position:0% +levels in state space. There is nothing +about the coordinates. And so, uh, + + align:start position:0% +about the coordinates. And so, uh, + + + align:start position:0% +about the coordinates. And so, uh, +there's all sorts of problems of saying, + + align:start position:0% +there's all sorts of problems of saying, + + + align:start position:0% +there's all sorts of problems of saying, +okay, well, we have a we would like a + + align:start position:0% +okay, well, we have a we would like a + + + align:start position:0% +okay, well, we have a we would like a +one-dimensional cut through a potential + + align:start position:0% +one-dimensional cut through a potential + + + align:start position:0% +one-dimensional cut through a potential +surface, but there's all sorts of issues + + align:start position:0% +surface, but there's all sorts of issues + + + align:start position:0% +surface, but there's all sorts of issues +of, well, yeah, we could determine the + + align:start position:0% +of, well, yeah, we could determine the + + + align:start position:0% +of, well, yeah, we could determine the +width of the potential along some + + align:start position:0% +width of the potential along some + + + align:start position:0% +width of the potential along some +one-dimensional cut, but we don't know + + align:start position:0% +one-dimensional cut, but we don't know + + + align:start position:0% +one-dimensional cut, but we don't know +what the coordinates are. So, this is + + align:start position:0% +what the coordinates are. So, this is + + + align:start position:0% +what the coordinates are. So, this is +interesting, and it's kind of an area + + align:start position:0% +interesting, and it's kind of an area + + + align:start position:0% +interesting, and it's kind of an area +where some insight might be gotten for + + align:start position:0% +where some insight might be gotten for + + + align:start position:0% +where some insight might be gotten for +polyatomic molecules. + + align:start position:0% +polyatomic molecules. + + + align:start position:0% +polyatomic molecules. +Okay. And the other one is 1 / r + 1 / r + + align:start position:0% +Okay. And the other one is 1 / r + 1 / r + + + align:start position:0% +Okay. And the other one is 1 / r + 1 / r +minus. And that's again we got this same + + align:start position:0% +minus. And that's again we got this same + + + align:start position:0% +minus. And that's again we got this same +kind of stuff. I don't know + + align:start position:0% +kind of stuff. I don't know + + + align:start position:0% +kind of stuff. I don't know +whether except the + + align:start position:0% +whether except the + + + align:start position:0% +whether except the +two mu or h bar + + align:start position:0% +two mu or h bar + + + align:start position:0% +two mu or h bar +squared square root. And now we have + + align:start position:0% + + + + align:start position:0% + +So here is an integral involving a + + align:start position:0% +So here is an integral involving a + + + align:start position:0% +So here is an integral involving a +combination of the rotational constant + + align:start position:0% +combination of the rotational constant + + + align:start position:0% +combination of the rotational constant +function and the vibrational + + align:start position:0% +function and the vibrational + + + align:start position:0% +function and the vibrational +energies. And again, if you know these + + align:start position:0% +energies. And again, if you know these + + + align:start position:0% +energies. And again, if you know these +functions and you can pretend that + + align:start position:0% +functions and you can pretend that + + + align:start position:0% +functions and you can pretend that +they're a continuous variable, a + + align:start position:0% +they're a continuous variable, a + + + align:start position:0% +they're a continuous variable, a +continuous function of v + + align:start position:0% +continuous function of v + + + align:start position:0% +continuous function of v +uh it's determined pointwise, but so you + + align:start position:0% +uh it's determined pointwise, but so you + + + align:start position:0% +uh it's determined pointwise, but so you +can determine uh this integral as as a + + align:start position:0% +can determine uh this integral as as a + + + align:start position:0% +can determine uh this integral as as a +at any uh energy. And so you have this + + align:start position:0% +at any uh energy. And so you have this + + + align:start position:0% +at any uh energy. And so you have this +difference of turning points at any + + align:start position:0% +difference of turning points at any + + + align:start position:0% +difference of turning points at any +energy. And so between the two, you've + + align:start position:0% +energy. And so between the two, you've + + + align:start position:0% +energy. And so between the two, you've +got it. Now, this is why you can't even + + align:start position:0% +got it. Now, this is why you can't even + + + align:start position:0% +got it. Now, this is why you can't even +think about using this for polyatomic + + align:start position:0% +think about using this for polyatomic + + + align:start position:0% +think about using this for polyatomic +molecules because this is the rotational + + align:start position:0% +molecules because this is the rotational + + + align:start position:0% +molecules because this is the rotational +constant for a one-dimensional + + align:start position:0% +constant for a one-dimensional + + + align:start position:0% +constant for a one-dimensional +oscillator. And for a polyatomic + + align:start position:0% +oscillator. And for a polyatomic + + + align:start position:0% +oscillator. And for a polyatomic +molecule, you have three rotational + + align:start position:0% +molecule, you have three rotational + + + align:start position:0% +molecule, you have three rotational +constants. They're all a function of + + align:start position:0% +constants. They're all a function of + + + align:start position:0% +constants. They're all a function of +uh displacements. uh they're they're all + + align:start position:0% +uh displacements. uh they're they're all + + + align:start position:0% +uh displacements. uh they're they're all +affected in different ways by + + align:start position:0% +affected in different ways by + + + align:start position:0% +affected in different ways by +displacements along normal coordinates. + + align:start position:0% +displacements along normal coordinates. + + + align:start position:0% +displacements along normal coordinates. +You can take derivatives of the uh uh + + align:start position:0% +You can take derivatives of the uh uh + + + align:start position:0% +You can take derivatives of the uh uh +the uh a b and c uh or the uh inertial + + align:start position:0% +the uh a b and c uh or the uh inertial + + + align:start position:0% +the uh a b and c uh or the uh inertial +constants in the a b and c directions. + + align:start position:0% +constants in the a b and c directions. + + + align:start position:0% +constants in the a b and c directions. +And so you can show how the rotational + + align:start position:0% +And so you can show how the rotational + + + align:start position:0% +And so you can show how the rotational +constant + + align:start position:0% +constant + + + align:start position:0% +constant +uh constants would change with respect + + align:start position:0% +uh constants would change with respect + + + align:start position:0% +uh constants would change with respect +to vibrational exitation. But you can't + + align:start position:0% +to vibrational exitation. But you can't + + + align:start position:0% +to vibrational exitation. But you can't +do something like this. There is no + + align:start position:0% +do something like this. There is no + + + align:start position:0% +do something like this. There is no +sensible way. Yes. What if you have like + + align:start position:0% +sensible way. Yes. What if you have like + + + align:start position:0% +sensible way. Yes. What if you have like +a settling where there is only one + + align:start position:0% +a settling where there is only one + + + align:start position:0% +a settling where there is only one +rotational constant ground state? + + align:start position:0% +rotational constant ground state? + + + align:start position:0% +rotational constant ground state? +Yes. But uh you have you still have uh + + align:start position:0% +Yes. But uh you have you still have uh + + + align:start position:0% +Yes. But uh you have you still have uh +seven vibrational degrees of freedom of + + align:start position:0% +seven vibrational degrees of freedom of + + + align:start position:0% +seven vibrational degrees of freedom of +which uh and so + + align:start position:0% +which uh and so + + + align:start position:0% +which uh and so +uh what potential are you sampling? + + align:start position:0% +uh what potential are you sampling? + + + align:start position:0% +uh what potential are you sampling? +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So you can sort of do this. You can't do + + align:start position:0% +So you can sort of do this. You can't do + + + align:start position:0% +So you can sort of do this. You can't do +that. This might be + + align:start position:0% + + + + align:start position:0% + +useful. Okay. + + align:start position:0% +useful. Okay. + + + align:start position:0% +useful. Okay. +Now there are all sorts of issues with + + align:start position:0% +Now there are all sorts of issues with + + + align:start position:0% +Now there are all sorts of issues with +uh these kinds of functions. Um + + align:start position:0% + + + + align:start position:0% + +uh at the upper turning point here + + align:start position:0% +uh at the upper turning point here + + + align:start position:0% +uh at the upper turning point here +uh the energy is equal to + + align:start position:0% +uh the energy is equal to + + + align:start position:0% +uh the energy is equal to +uh the vibrational energy and so + + align:start position:0% +uh the vibrational energy and so + + + align:start position:0% +uh the vibrational energy and so +this is zero. The integrant goes to + + align:start position:0% +this is zero. The integrant goes to + + + align:start position:0% +this is zero. The integrant goes to +infinity. + + align:start position:0% +infinity. + + + align:start position:0% +infinity. +And so there's a singularity in this + + align:start position:0% +And so there's a singularity in this + + + align:start position:0% +And so there's a singularity in this +integral at the upper limit of + + align:start position:0% +integral at the upper limit of + + + align:start position:0% +integral at the upper limit of +integration. No + + align:start position:0% +integration. No + + + align:start position:0% +integration. No +problem. But it's something people worry + + align:start position:0% +problem. But it's something people worry + + + align:start position:0% +problem. But it's something people worry +about. But there is one thing that + + align:start position:0% +about. But there is one thing that + + + align:start position:0% +about. But there is one thing that +happens very commonly when you do RKR. + + align:start position:0% +happens very commonly when you do RKR. + + + align:start position:0% +happens very commonly when you do RKR. +You generate a potential curve that + + align:start position:0% +You generate a potential curve that + + + align:start position:0% +You generate a potential curve that +instead of looking like this looks like + + align:start position:0% +instead of looking like this looks like + + + align:start position:0% +instead of looking like this looks like +that. The inner wall tends to hook. And + + align:start position:0% +that. The inner wall tends to hook. And + + + align:start position:0% +that. The inner wall tends to hook. And +this is this is a common problem and it + + align:start position:0% +this is this is a common problem and it + + + align:start position:0% +this is this is a common problem and it +comes from uh blindly using BV and G of + + align:start position:0% +comes from uh blindly using BV and G of + + + align:start position:0% +comes from uh blindly using BV and G of +V. Keep in mind that you're determining + + align:start position:0% +V. Keep in mind that you're determining + + + align:start position:0% +V. Keep in mind that you're determining +the outer wall is moving very + + align:start position:0% +the outer wall is moving very + + + align:start position:0% +the outer wall is moving very +fast. So you're you're sampling the + + align:start position:0% +fast. So you're you're sampling the + + + align:start position:0% +fast. So you're you're sampling the +energy levels and the outer wall is + + align:start position:0% +energy levels and the outer wall is + + + align:start position:0% +energy levels and the outer wall is +changing its uh uh it its position + + align:start position:0% +changing its uh uh it its position + + + align:start position:0% +changing its uh uh it its position +rapidly with V. The inner wall is mostly + + align:start position:0% +rapidly with V. The inner wall is mostly + + + align:start position:0% +rapidly with V. The inner wall is mostly +going up slowly. I mean, it's going up + + align:start position:0% +going up slowly. I mean, it's going up + + + align:start position:0% +going up slowly. I mean, it's going up +vertically. It not changing much. And + + align:start position:0% +vertically. It not changing much. And + + + align:start position:0% +vertically. It not changing much. And +you So all of the RKR is being stressed + + align:start position:0% +you So all of the RKR is being stressed + + + align:start position:0% +you So all of the RKR is being stressed +by trying to determine this rapidly + + align:start position:0% +by trying to determine this rapidly + + + align:start position:0% +by trying to determine this rapidly +changing function with perhaps + + align:start position:0% +changing function with perhaps + + + align:start position:0% +changing function with perhaps +incomplete, perhaps uh defective data. + + align:start position:0% +incomplete, perhaps uh defective data. + + + align:start position:0% +incomplete, perhaps uh defective data. +And you almost always get a hook. And so + + align:start position:0% +And you almost always get a hook. And so + + + align:start position:0% +And you almost always get a hook. And so +what you do is you say, okay, what is + + align:start position:0% +what you do is you say, okay, what is + + + align:start position:0% +what you do is you say, okay, what is +the functional form for the inner wall? + + align:start position:0% +the functional form for the inner wall? + + + align:start position:0% +the functional form for the inner wall? +and you for constrain the RKR to have + + align:start position:0% +and you for constrain the RKR to have + + + align:start position:0% +and you for constrain the RKR to have +the right inner wall and that gives + + align:start position:0% +the right inner wall and that gives + + + align:start position:0% +the right inner wall and that gives +better potentials. There are other + + align:start position:0% +better potentials. There are other + + + align:start position:0% +better potentials. There are other +things that people do to uh improve on + + align:start position:0% +things that people do to uh improve on + + + align:start position:0% +things that people do to uh improve on +RKR potentials. + + align:start position:0% +RKR potentials. + + + align:start position:0% +RKR potentials. +One of the best tests is okay we have V + + align:start position:0% +One of the best tests is okay we have V + + + align:start position:0% +One of the best tests is okay we have V +of R and we automatically get the J + + align:start position:0% +of R and we automatically get the J + + + align:start position:0% +of R and we automatically get the J +dependence of it and so we should be + + align:start position:0% +dependence of it and so we should be + + + align:start position:0% +dependence of it and so we should be +able to calculate + + align:start position:0% +able to calculate + + + align:start position:0% +able to calculate +uh from + + align:start position:0% +uh from + + + align:start position:0% +uh from +it G of V, B of V, D of V and many other + + align:start position:0% +it G of V, B of V, D of V and many other + + + align:start position:0% +it G of V, B of V, D of V and many other +things. + + align:start position:0% + + + + align:start position:0% + +And + + align:start position:0% +And + + + align:start position:0% +And +now RKR used G of E and B of E to + + align:start position:0% +now RKR used G of E and B of E to + + + align:start position:0% +now RKR used G of E and B of E to +determine this. + + align:start position:0% +determine this. + + + align:start position:0% +determine this. +But we have the potential now we do + + align:start position:0% +But we have the potential now we do + + + align:start position:0% +But we have the potential now we do +numerical integration of the we solve + + align:start position:0% +numerical integration of the we solve + + + align:start position:0% +numerical integration of the we solve +for the you know you have a potential + + align:start position:0% +for the you know you have a potential + + + align:start position:0% +for the you know you have a potential +you find where the energy levels are not + + align:start position:0% +you find where the energy levels are not + + + align:start position:0% +you find where the energy levels are not +by uh semiclassical methods but by + + align:start position:0% +by uh semiclassical methods but by + + + align:start position:0% +by uh semiclassical methods but by +integration of the shorter equation and + + align:start position:0% +integration of the shorter equation and + + + align:start position:0% +integration of the shorter equation and +so you can then + + align:start position:0% +so you can then + + + align:start position:0% +so you can then +uh solve the problem by numerical + + align:start position:0% +uh solve the problem by numerical + + + align:start position:0% +uh solve the problem by numerical +integration and ask well do the + + align:start position:0% +integration and ask well do the + + + align:start position:0% +integration and ask well do the +calculated values of quantities + + align:start position:0% +calculated values of quantities + + + align:start position:0% +calculated values of quantities +uh obtained from the potential are they + + align:start position:0% +uh obtained from the potential are they + + + align:start position:0% +uh obtained from the potential are they +equal to the input values? + + align:start position:0% +equal to the input values? + + + align:start position:0% +equal to the input values? +It's not a + + align:start position:0% +It's not a + + + align:start position:0% +It's not a +circle. If you uh you are using + + align:start position:0% +circle. If you uh you are using + + + align:start position:0% +circle. If you uh you are using +semiclassical methods to get this and + + align:start position:0% +semiclassical methods to get this and + + + align:start position:0% +semiclassical methods to get this and +strictly quantum mechanical numerical + + align:start position:0% +strictly quantum mechanical numerical + + + align:start position:0% +strictly quantum mechanical numerical +integration methods to to invert back to + + align:start position:0% +integration methods to to invert back to + + + align:start position:0% +integration methods to to invert back to +the spectrum and the agreement is + + align:start position:0% +the spectrum and the agreement is + + + align:start position:0% +the spectrum and the agreement is +astonishing and + + align:start position:0% +astonishing and + + + align:start position:0% +astonishing and +uh so that's that's an important uh + + align:start position:0% +uh so that's that's an important uh + + + align:start position:0% +uh so that's that's an important uh +characteristic of RKR. It it works. It's + + align:start position:0% +characteristic of RKR. It it works. It's + + + align:start position:0% +characteristic of RKR. It it works. It's +a trivial program. it uh even in + + align:start position:0% +a trivial program. it uh even in + + + align:start position:0% +a trivial program. it uh even in +1970 it took uh seconds to run + + align:start position:0% +1970 it took uh seconds to run + + + align:start position:0% +1970 it took uh seconds to run +uh and on a big computer but you know + + align:start position:0% +uh and on a big computer but you know + + + align:start position:0% +uh and on a big computer but you know +big computer in those days yes you don't + + align:start position:0% +big computer in those days yes you don't + + + align:start position:0% +big computer in those days yes you don't +they were pretty slow comp whereas Frank + + align:start position:0% +they were pretty slow comp whereas Frank + + + align:start position:0% +they were pretty slow comp whereas Frank +Conan or the numerical integration takes + + align:start position:0% +Conan or the numerical integration takes + + + align:start position:0% +Conan or the numerical integration takes +hundreds of times + + align:start position:0% +hundreds of times + + + align:start position:0% +hundreds of times +longer now both take no time at all on + + align:start position:0% +longer now both take no time at all on + + + align:start position:0% +longer now both take no time at all on +little on on your uh laptops. + + align:start position:0% +little on on your uh laptops. + + + align:start position:0% +little on on your uh laptops. +So, it's a wonderful procedure and it + + align:start position:0% +So, it's a wonderful procedure and it + + + align:start position:0% +So, it's a wonderful procedure and it +makes using models in diatomic + + align:start position:0% +makes using models in diatomic + + + align:start position:0% +makes using models in diatomic +molecules completely stupid unless you + + align:start position:0% +molecules completely stupid unless you + + + align:start position:0% +molecules completely stupid unless you +have essentially no data and you want to + + align:start position:0% +have essentially no data and you want to + + + align:start position:0% +have essentially no data and you want to +take a little fraction, you know, + + align:start position:0% +take a little fraction, you know, + + + align:start position:0% +take a little fraction, you know, +fragmentaryary data and get a little bit + + align:start position:0% +fragmentaryary data and get a little bit + + + align:start position:0% +fragmentaryary data and get a little bit +of leverage to extrapolate or + + align:start position:0% +of leverage to extrapolate or + + + align:start position:0% +of leverage to extrapolate or +interpolate hoping to find more so that + + align:start position:0% +interpolate hoping to find more so that + + + align:start position:0% +interpolate hoping to find more so that +you can verify things. But you the RKR + + align:start position:0% +you can verify things. But you the RKR + + + align:start position:0% +you can verify things. But you the RKR +is just a wonderful thing. And often you + + align:start position:0% +is just a wonderful thing. And often you + + + align:start position:0% +is just a wonderful thing. And often you +see people still writing papers + + align:start position:0% +see people still writing papers + + + align:start position:0% +see people still writing papers +questioning the validity of RKR + + align:start position:0% +questioning the validity of RKR + + + align:start position:0% +questioning the validity of RKR +potentials and saying well uh you really + + align:start position:0% +potentials and saying well uh you really + + + align:start position:0% +potentials and saying well uh you really +ought to take this to a higher order of + + align:start position:0% +ought to take this to a higher order of + + + align:start position:0% +ought to take this to a higher order of +WKB and you can do that. And in fact + + align:start position:0% +WKB and you can do that. And in fact + + + align:start position:0% +WKB and you can do that. And in fact +that's built into Loyy's programs. So I + + align:start position:0% +that's built into Loyy's programs. So I + + + align:start position:0% +that's built into Loyy's programs. So I +it's not it's not time to quit yet but + + align:start position:0% +it's not it's not time to quit yet but + + + align:start position:0% +it's not it's not time to quit yet but +u uh it's time for you to ask a + + align:start position:0% +u uh it's time for you to ask a + + + align:start position:0% +u uh it's time for you to ask a +question. Yes. + + align:start position:0% +question. Yes. + + + align:start position:0% +question. Yes. +So, WB + + align:start position:0% +So, WB + + + align:start position:0% +So, WB +uh wave + + align:start position:0% +uh wave + + + align:start position:0% +uh wave +functions are are are harmonic. + + align:start position:0% +functions are are are harmonic. + + + align:start position:0% +functions are are are harmonic. +No. No. + + align:start position:0% +No. No. + + + align:start position:0% +No. No. +Why do you say they're harmonic? Well, + + align:start position:0% +Why do you say they're harmonic? Well, + + + align:start position:0% +Why do you say they're harmonic? Well, +so are way if you have a harmonic + + align:start position:0% +so are way if you have a harmonic + + + align:start position:0% +so are way if you have a harmonic +potential. Yes. You'll be exactly right. + + align:start position:0% +potential. Yes. You'll be exactly right. + + + align:start position:0% +potential. Yes. You'll be exactly right. +It turns out that + + align:start position:0% +It turns out that + + + align:start position:0% +It turns out that +WKB is uh invalid near turning + + align:start position:0% +WKB is uh invalid near turning + + + align:start position:0% +WKB is uh invalid near turning +points at the bottom of the potential V + + align:start position:0% +points at the bottom of the potential V + + + align:start position:0% +points at the bottom of the potential V +equals Z. You've got two turning points + + align:start position:0% +equals Z. You've got two turning points + + + align:start position:0% +equals Z. You've got two turning points +close together. So you say, well, if + + align:start position:0% +close together. So you say, well, if + + + align:start position:0% +close together. So you say, well, if +there's ever going to be a problem, it's + + align:start position:0% +there's ever going to be a problem, it's + + + align:start position:0% +there's ever going to be a problem, it's +going to be here. However, near the + + align:start position:0% +going to be here. However, near the + + + align:start position:0% +going to be here. However, near the +bottom of every potential, it's a good + + align:start position:0% +bottom of every potential, it's a good + + + align:start position:0% +bottom of every potential, it's a good +to very good approximation. It is + + align:start position:0% +to very good approximation. It is + + + align:start position:0% +to very good approximation. It is +harmonic. + + align:start position:0% +harmonic. + + + align:start position:0% +harmonic. +WKB + + align:start position:0% +WKB + + + align:start position:0% +WKB +works everywhere for harmonic + + align:start position:0% +works everywhere for harmonic + + + align:start position:0% +works everywhere for harmonic +oscillator. There is no Okay. So that + + align:start position:0% +oscillator. There is no Okay. So that + + + align:start position:0% +oscillator. There is no Okay. So that +that that that that's kind of what what + + align:start position:0% +that that that that's kind of what what + + + align:start position:0% +that that that that's kind of what what +I right but uh at very high exitation + + align:start position:0% +I right but uh at very high exitation + + + align:start position:0% +I right but uh at very high exitation +you have enormous anharmonic + + align:start position:0% +you have enormous anharmonic + + + align:start position:0% +you have enormous anharmonic +contributions from a real potential. As + + align:start position:0% +contributions from a real potential. As + + + align:start position:0% +contributions from a real potential. As +long as the potential doesn't have kinks + + align:start position:0% +long as the potential doesn't have kinks + + + align:start position:0% +long as the potential doesn't have kinks +or is not double valued you're okay. I + + align:start position:0% +or is not double valued you're okay. I + + + align:start position:0% +or is not double valued you're okay. I +mean this WK + + align:start position:0% +mean this WK + + + align:start position:0% +mean this WK +RKR does not give you the correct energy + + align:start position:0% +RKR does not give you the correct energy + + + align:start position:0% +RKR does not give you the correct energy +levels for this sort of a problem. + + align:start position:0% +levels for this sort of a problem. + + + align:start position:0% +levels for this sort of a problem. +That has nothing to do with WKB. Right. + + align:start position:0% +That has nothing to do with WKB. Right. + + + align:start position:0% +That has nothing to do with WKB. Right. +Right. Right. No. Right. Sure. Sure. But + + align:start position:0% +Right. Right. No. Right. Sure. Sure. But + + + align:start position:0% +Right. Right. No. Right. Sure. Sure. But +R but RVR is scarily correct for very + + align:start position:0% +R but RVR is scarily correct for very + + + align:start position:0% +R but RVR is scarily correct for very +anharmonic potentials. It does + + align:start position:0% +anharmonic potentials. It does + + + align:start position:0% +anharmonic potentials. It does +absolutely you know the the scary point + + align:start position:0% +absolutely you know the the scary point + + + align:start position:0% +absolutely you know the the scary point +is down here. + + align:start position:0% +is down here. + + + align:start position:0% +is down here. +everything else, you know, as long as + + align:start position:0% +everything else, you know, as long as + + + align:start position:0% +everything else, you know, as long as +there's there's no + + align:start position:0% +there's there's no + + + align:start position:0% +there's there's no +twiddles. + + align:start position:0% +twiddles. + + + align:start position:0% +twiddles. +Uh it's valid. The higher you go, the + + align:start position:0% +Uh it's valid. The higher you go, the + + + align:start position:0% +Uh it's valid. The higher you go, the +better it is. That's another thing about + + align:start position:0% +better it is. That's another thing about + + + align:start position:0% +better it is. That's another thing about +semiclass. The higher you go, + + align:start position:0% +semiclass. The higher you go, + + + align:start position:0% +semiclass. The higher you go, +uh uh the closer it approach + + align:start position:0% +uh uh the closer it approach + + + align:start position:0% +uh uh the closer it approach +approaches you semiclassical. Yes. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% + + + + align:start position:0% + +um the problems with RKR this one is the + + align:start position:0% +um the problems with RKR this one is the + + + align:start position:0% +um the problems with RKR this one is the +most commonly encountered and it's not a + + align:start position:0% +most commonly encountered and it's not a + + + align:start position:0% +most commonly encountered and it's not a +problem with the semiclassical method. + + align:start position:0% +problem with the semiclassical method. + + + align:start position:0% +problem with the semiclassical method. +It's a problem that you're trying to + + align:start position:0% +It's a problem that you're trying to + + + align:start position:0% +It's a problem that you're trying to +determine + + align:start position:0% +determine + + + align:start position:0% +determine +uh a very rapidly changing function with + + align:start position:0% +uh a very rapidly changing function with + + + align:start position:0% +uh a very rapidly changing function with +incomplete data and and it doesn't know + + align:start position:0% +incomplete data and and it doesn't know + + + align:start position:0% +incomplete data and and it doesn't know +any difference between inner and outer + + align:start position:0% +any difference between inner and outer + + + align:start position:0% +any difference between inner and outer +turning points and it just pulls it it + + align:start position:0% +turning points and it just pulls it it + + + align:start position:0% +turning points and it just pulls it it +nails the difference but uh the the + + align:start position:0% +nails the difference but uh the the + + + align:start position:0% +nails the difference but uh the the +rotational constants uh are what's + + align:start position:0% +rotational constants uh are what's + + + align:start position:0% +rotational constants uh are what's +determining the absolute positions and + + align:start position:0% +determining the absolute positions and + + + align:start position:0% +determining the absolute positions and +that just gets overpowered. + + align:start position:0% +that just gets overpowered. + + + align:start position:0% +that just gets overpowered. +So is there are there + + align:start position:0% +So is there are there + + + align:start position:0% +So is there are there +other questions? Should I come up with a + + align:start position:0% +other questions? Should I come up with a + + + align:start position:0% +other questions? Should I come up with a +problem that forces you to use the AR uh + + align:start position:0% +problem that forces you to use the AR uh + + + align:start position:0% +problem that forces you to use the AR uh +Loyy's programs? The problem with that + + align:start position:0% +Loyy's programs? The problem with that + + + align:start position:0% +Loyy's programs? The problem with that +I've discovered in asking people to use + + align:start position:0% +I've discovered in asking people to use + + + align:start position:0% +I've discovered in asking people to use +Loyy's programs is Loy writes programs + + align:start position:0% +Loyy's programs is Loy writes programs + + + align:start position:0% +Loyy's programs is Loy writes programs +in + + align:start position:0% +in + + + align:start position:0% +in +forrren which is the only language that + + align:start position:0% +forrren which is the only language that + + + align:start position:0% +forrren which is the only language that +I understand and nobody knows for + + align:start position:0% +I understand and nobody knows for + + + align:start position:0% +I understand and nobody knows for +anymore. + + align:start position:0% +anymore. + + + align:start position:0% +anymore. +So uh that makes for terrible + + align:start position:0% +So uh that makes for terrible + + + align:start position:0% +So uh that makes for terrible +difficulties in using his programs. + + align:start position:0% +difficulties in using his programs. + + + align:start position:0% +difficulties in using his programs. +However, in these publications + + align:start position:0% +However, in these publications + + + align:start position:0% +However, in these publications +he gives detailed discussion of the + + align:start position:0% +he gives detailed discussion of the + + + align:start position:0% +he gives detailed discussion of the +structure of the input files and the + + align:start position:0% +structure of the input files and the + + + align:start position:0% +structure of the input files and the +output files. And so basically you can + + align:start position:0% +output files. And so basically you can + + + align:start position:0% +output files. And so basically you can +use them as a black box as long as you + + align:start position:0% +use them as a black box as long as you + + + align:start position:0% +use them as a black box as long as you +believe in RKR which I think is a very + + align:start position:0% +believe in RKR which I think is a very + + + align:start position:0% +believe in RKR which I think is a very +you know there are many more many other + + align:start position:0% +you know there are many more many other + + + align:start position:0% +you know there are many more many other +things that you would not want to + + align:start position:0% +things that you would not want to + + + align:start position:0% +things that you would not want to +believe in. uh this is you can pretty + + align:start position:0% +believe in. uh this is you can pretty + + + align:start position:0% +believe in. uh this is you can pretty +much take it for + + align:start position:0% +much take it for + + + align:start position:0% +much take it for +granted. So + + align:start position:0% + + + + align:start position:0% + +uh I I urge you all to download these + + align:start position:0% +uh I I urge you all to download these + + + align:start position:0% +uh I I urge you all to download these +things and have a functioning numerical + + align:start position:0% +things and have a functioning numerical + + + align:start position:0% +things and have a functioning numerical +integration program and an RKR program + + align:start position:0% +integration program and an RKR program + + + align:start position:0% +integration program and an RKR program +in your computers and it would be a good + + align:start position:0% +in your computers and it would be a good + + + align:start position:0% +in your computers and it would be a good +idea to do something with them but I'm + + align:start position:0% +idea to do something with them but I'm + + + align:start position:0% +idea to do something with them but I'm +not going to ask you to to hand hand it + + align:start position:0% +not going to ask you to to hand hand it + + + align:start position:0% +not going to ask you to to hand hand it +in. Uh it might be a good idea to look + + align:start position:0% +in. Uh it might be a good idea to look + + + align:start position:0% +in. Uh it might be a good idea to look +at the paper by Mance and at all that I + + align:start position:0% +at the paper by Mance and at all that I + + + align:start position:0% +at the paper by Mance and at all that I +cite in the no notes and and take the + + align:start position:0% +cite in the no notes and and take the + + + align:start position:0% +cite in the no notes and and take the +data set that he uses and just reproduce + + align:start position:0% +data set that he uses and just reproduce + + + align:start position:0% +data set that he uses and just reproduce +his results to show that yes in fact it + + align:start position:0% +his results to show that yes in fact it + + + align:start position:0% +his results to show that yes in fact it +does reproduce B of V and G of V as to + + align:start position:0% +does reproduce B of V and G of V as to + + + align:start position:0% +does reproduce B of V and G of V as to +the accuracy to about a parton 10 to the + + align:start position:0% +the accuracy to about a parton 10 to the + + + align:start position:0% +the accuracy to about a parton 10 to the +sixth or maybe pardon to the eth. What + + align:start position:0% +sixth or maybe pardon to the eth. What + + + align:start position:0% +sixth or maybe pardon to the eth. What +paper do you uh M yeah that man at all + + align:start position:0% +paper do you uh M yeah that man at all + + + align:start position:0% +paper do you uh M yeah that man at all +that's actually man etc etc is there + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +um so I recommend doing that and if + + align:start position:0% +um so I recommend doing that and if + + + align:start position:0% +um so I recommend doing that and if +that's it then I'm \ No newline at end of file diff --git a/qbyeQum8qTE.txt b/qbyeQum8qTE.txt new file mode 100644 index 0000000000000000000000000000000000000000..7efdc939e55e5128862c1da5c29ad22d191498cf --- /dev/null +++ b/qbyeQum8qTE.txt @@ -0,0 +1,1783 @@ +align:start position:0% + +Welcome to this recitation on matrix + + align:start position:0% +Welcome to this recitation on matrix + + + align:start position:0% +Welcome to this recitation on matrix +exponential. So here we're given matrix + + align:start position:0% +exponential. So here we're given matrix + + + align:start position:0% +exponential. So here we're given matrix +A with entry + + align:start position:0% +A with entry + + + align:start position:0% +A with entry +6512 and we're asked to compute the + + align:start position:0% +6512 and we're asked to compute the + + + align:start position:0% +6512 and we're asked to compute the +matrix exponential exponential a t and + + align:start position:0% +matrix exponential exponential a t and + + + align:start position:0% +matrix exponential exponential a t and +to use it to solve the initial value + + align:start position:0% +to use it to solve the initial value + + + align:start position:0% +to use it to solve the initial value +problem u u prime of tals a ut where + + align:start position:0% +problem u u prime of tals a ut where + + + align:start position:0% +problem u u prime of tals a ut where +here u are basically vectors with + + align:start position:0% +here u are basically vectors with + + + align:start position:0% +here u are basically vectors with +initial condition u of 0= 41. So, why + + align:start position:0% +initial condition u of 0= 41. So, why + + + align:start position:0% +initial condition u of 0= 41. So, why +don't you pause the video, work through + + align:start position:0% +don't you pause the video, work through + + + align:start position:0% +don't you pause the video, work through +the problem, and I'll be right + + align:start position:0% + + + + align:start position:0% + +back. Welcome back. Okay, so first to uh + + align:start position:0% +back. Welcome back. Okay, so first to uh + + + align:start position:0% +back. Welcome back. Okay, so first to uh +go ahead and compute the matrix + + align:start position:0% +go ahead and compute the matrix + + + align:start position:0% +go ahead and compute the matrix +exponential, we need to identify the aen + + align:start position:0% +exponential, we need to identify the aen + + + align:start position:0% +exponential, we need to identify the aen +values of the matrix A and its AEN + + align:start position:0% +values of the matrix A and its AEN + + + align:start position:0% +values of the matrix A and its AEN +vectors. So this is a + + align:start position:0% +vectors. So this is a + + + align:start position:0% +vectors. So this is a +matrix just rewrite it + + align:start position:0% +matrix just rewrite it + + + align:start position:0% +matrix just rewrite it +here that we saw before and it's a + + align:start position:0% + + + + align:start position:0% + +values are again solution of 6 - lambda + + align:start position:0% +values are again solution of 6 - lambda + + + align:start position:0% +values are again solution of 6 - lambda +5 1 2 - lambda = 0 which gives us + + align:start position:0% +5 1 2 - lambda = 0 which gives us + + + align:start position:0% +5 1 2 - lambda = 0 which gives us +6 2 - lambda - 5 = + + align:start position:0% +6 2 - lambda - 5 = + + + align:start position:0% +6 2 - lambda - 5 = +0 lambda square - 8 lambda and we have a + + align:start position:0% +0 lambda square - 8 lambda and we have a + + + align:start position:0% +0 lambda square - 8 lambda and we have a +12 - + + align:start position:0% +12 - + + + align:start position:0% +12 - +5. So you can verify that the two egg + + align:start position:0% +5. So you can verify that the two egg + + + align:start position:0% +5. So you can verify that the two egg +values be 1 and + + align:start position:0% +values be 1 and + + + align:start position:0% +values be 1 and +7. So + + align:start position:0% +7. So + + + align:start position:0% +7. So +yeah plus or minus just write + + align:start position:0% +yeah plus or minus just write + + + align:start position:0% +yeah plus or minus just write +them la 1 = to 1 and lda 2 = to 7. So + + align:start position:0% +them la 1 = to 1 and lda 2 = to 7. So + + + align:start position:0% +them la 1 = to 1 and lda 2 = to 7. So +now we need to seek the AEN vectors + + align:start position:0% +now we need to seek the AEN vectors + + + align:start position:0% +now we need to seek the AEN vectors +associated to each one of the AEN + + align:start position:0% +associated to each one of the AEN + + + align:start position:0% +associated to each one of the AEN +values. So the idea here is to basically + + align:start position:0% +values. So the idea here is to basically + + + align:start position:0% +values. So the idea here is to basically +move toward a diagonalization of the + + align:start position:0% +move toward a diagonalization of the + + + align:start position:0% +move toward a diagonalization of the +matrix A. So let's seek the AEN vectors + + align:start position:0% +matrix A. So let's seek the AEN vectors + + + align:start position:0% +matrix A. So let's seek the AEN vectors +and here I'm + + align:start position:0% +and here I'm + + + align:start position:0% +and here I'm +just going to give them to you and you + + align:start position:0% +just going to give them to you and you + + + align:start position:0% +just going to give them to you and you +can verify the the the calculation. Uh + + align:start position:0% +can verify the the the calculation. Uh + + + align:start position:0% +can verify the the the calculation. Uh +and this calculation was performed in a + + align:start position:0% +and this calculation was performed in a + + + align:start position:0% +and this calculation was performed in a +previous recitation. So the aen vectors + + align:start position:0% +previous recitation. So the aen vectors + + + align:start position:0% +previous recitation. So the aen vectors +v1 associated to the aen value lambda + + align:start position:0% + + + + align:start position:0% + +1 was for example one minus + + align:start position:0% +1 was for example one minus + + + align:start position:0% +1 was for example one minus +one and the other + + align:start position:0% + + + + align:start position:0% + +one that we found again this is one form + + align:start position:0% +one that we found again this is one form + + + align:start position:0% +one that we found again this is one form +of the aen vector was one and + + align:start position:0% +of the aen vector was one and + + + align:start position:0% +of the aen vector was one and +five minus five five and + + align:start position:0% + + + + align:start position:0% + +So these are from the notes of the + + align:start position:0% +So these are from the notes of the + + + align:start position:0% +So these are from the notes of the +previous recitation. So you can verify + + align:start position:0% +previous recitation. So you can verify + + + align:start position:0% +previous recitation. So you can verify +that these are the two agon vectors and + + align:start position:0% +that these are the two agon vectors and + + + align:start position:0% +that these are the two agon vectors and +uh from this point then we can rewrite + + align:start position:0% +uh from this point then we can rewrite + + + align:start position:0% +uh from this point then we can rewrite +the solution if if you recall I'm just + + align:start position:0% +the solution if if you recall I'm just + + + align:start position:0% +the solution if if you recall I'm just +going to go through the steps toward + + align:start position:0% +going to go through the steps toward + + + align:start position:0% +going to go through the steps toward +getting to the definition of the + + align:start position:0% +getting to the definition of the + + + align:start position:0% +getting to the definition of the +exponential matrix. So here if we didn't + + align:start position:0% +exponential matrix. So here if we didn't + + + align:start position:0% +exponential matrix. So here if we didn't +know anything about the exponential + + align:start position:0% +know anything about the exponential + + + align:start position:0% +know anything about the exponential +matrix we'd be able to write this + + align:start position:0% +matrix we'd be able to write this + + + align:start position:0% +matrix we'd be able to write this +solution as C1 + + align:start position:0% +solution as C1 + + + align:start position:0% +solution as C1 +exponential T + + align:start position:0% +exponential T + + + align:start position:0% +exponential T +v1 plus + + align:start position:0% +v1 plus + + + align:start position:0% +v1 plus +C2 exponential + + align:start position:0% +C2 exponential + + + align:start position:0% +C2 exponential + + align:start position:0% + + + align:start position:0% +V2 which basically gives + + align:start position:0% +V2 which basically gives + + + align:start position:0% +V2 which basically gives +us here if I write it in this form for + + align:start position:0% +us here if I write it in this form for + + + align:start position:0% +us here if I write it in this form for +example uh an exponential + + align:start position:0% +example uh an exponential + + + align:start position:0% +example uh an exponential +t minus exponential + + align:start position:0% + + + + align:start position:0% + +t and an + + align:start position:0% +t and an + + + align:start position:0% +t and an +exponential 5t multiplied by the entry + + align:start position:0% +exponential 5t multiplied by the entry + + + align:start position:0% +exponential 5t multiplied by the entry +of this vector an + + align:start position:0% +of this vector an + + + align:start position:0% +of this vector an +exponential 70t here + + align:start position:0% +exponential 70t here + + + align:start position:0% +exponential 70t here +multiplying c1 c2. So this is where the + + align:start position:0% +multiplying c1 c2. So this is where the + + + align:start position:0% +multiplying c1 c2. So this is where the +idea of the um of the um matrix + + align:start position:0% +idea of the um of the um matrix + + + align:start position:0% +idea of the um of the um matrix +exponential come from. We're basically + + align:start position:0% + + + + align:start position:0% + +introducing a matrix f of t for which we + + align:start position:0% +introducing a matrix f of t for which we + + + align:start position:0% +introducing a matrix f of t for which we +can write u equals 5 oft multiply by the + + align:start position:0% +can write u equals 5 oft multiply by the + + + align:start position:0% +can write u equals 5 oft multiply by the +c1 c2 uh general + + align:start position:0% +c1 c2 uh general + + + align:start position:0% +c1 c2 uh general +constants. So f of + + align:start position:0% +constants. So f of + + + align:start position:0% +constants. So f of +t would then be equal to this matrix. + + align:start position:0% +t would then be equal to this matrix. + + + align:start position:0% +t would then be equal to this matrix. +But what we + + align:start position:0% +But what we + + + align:start position:0% +But what we +want is an in is to be able to solve an + + align:start position:0% +want is an in is to be able to solve an + + + align:start position:0% +want is an in is to be able to solve an +initial value + + align:start position:0% +initial value + + + align:start position:0% +initial value +problem for which + + align:start position:0% +problem for which + + + align:start position:0% +problem for which +um so let me just for which e of a of + + align:start position:0% +um so let me just for which e of a of + + + align:start position:0% +um so let me just for which e of a of +zero applied to our initial conditions + + align:start position:0% +zero applied to our initial conditions + + + align:start position:0% +zero applied to our initial conditions +would give us + + align:start position:0% +would give us + + + align:start position:0% +would give us +back our initial + + align:start position:0% +back our initial + + + align:start position:0% +back our initial +condition. Okay. So we're seeking for a + + align:start position:0% +condition. Okay. So we're seeking for a + + + align:start position:0% +condition. Okay. So we're seeking for a +form for this exponential matrix that + + align:start position:0% +form for this exponential matrix that + + + align:start position:0% +form for this exponential matrix that +would allow us to do this. + + align:start position:0% +would allow us to do this. + + + align:start position:0% +would allow us to do this. +So the way that + + align:start position:0% +So the way that + + + align:start position:0% +So the way that +we define the exponential the matrix + + align:start position:0% +we define the exponential the matrix + + + align:start position:0% +we define the exponential the matrix +exponential give us exponential + + align:start position:0% +exponential give us exponential + + + align:start position:0% +exponential give us exponential +a and I won't go into the proof but + + align:start position:0% +a and I won't go into the proof but + + + align:start position:0% +a and I won't go into the proof but +we're just going to check it together + + align:start position:0% +we're just going to check it together + + + align:start position:0% +we're just going to check it together +multiplied by 5 of 0 minus one. So let's + + align:start position:0% +multiplied by 5 of 0 minus one. So let's + + + align:start position:0% +multiplied by 5 of 0 minus one. So let's +check that if we use this form of the + + align:start position:0% +check that if we use this form of the + + + align:start position:0% +check that if we use this form of the +exponential matrix exponential we would + + align:start position:0% +exponential matrix exponential we would + + + align:start position:0% +exponential matrix exponential we would +have + + align:start position:0% + + + + align:start position:0% + +e we would have that at + + align:start position:0% +e we would have that at + + + align:start position:0% +e we would have that at +zero applied to + + align:start position:0% +zero applied to + + + align:start position:0% +zero applied to +u0 we + + align:start position:0% +u0 we + + + align:start position:0% +u0 we +have 5 + + align:start position:0% +have 5 + + + align:start position:0% +have 5 +0 5 0 - + + align:start position:0% +0 5 0 - + + + align:start position:0% +0 5 0 - +1 applied to u 0. This is a matrix with + + align:start position:0% +1 applied to u 0. This is a matrix with + + + align:start position:0% +1 applied to u 0. This is a matrix with +its inverse which gives us the identity + + align:start position:0% +its inverse which gives us the identity + + + align:start position:0% +its inverse which gives us the identity +and so basically this gives us back + + align:start position:0% +and so basically this gives us back + + + align:start position:0% +and so basically this gives us back +u of zero. So basically just as a quick + + align:start position:0% +u of zero. So basically just as a quick + + + align:start position:0% +u of zero. So basically just as a quick +I mean you don't need to do that when + + align:start position:0% +I mean you don't need to do that when + + + align:start position:0% +I mean you don't need to do that when +you're asked to find the matrix + + align:start position:0% +you're asked to find the matrix + + + align:start position:0% +you're asked to find the matrix +exponential but just as to remember + + align:start position:0% +exponential but just as to remember + + + align:start position:0% +exponential but just as to remember +where it's coming from you have the you + + align:start position:0% +where it's coming from you have the you + + + align:start position:0% +where it's coming from you have the you +write down your system in in matrix form + + align:start position:0% +write down your system in in matrix form + + + align:start position:0% +write down your system in in matrix form +you identify the matrix 5 of t and then + + align:start position:0% +you identify the matrix 5 of t and then + + + align:start position:0% +you identify the matrix 5 of t and then +you recall why you + + align:start position:0% +you recall why you + + + align:start position:0% +you recall why you +want the matrix exponential to have this + + align:start position:0% +want the matrix exponential to have this + + + align:start position:0% +want the matrix exponential to have this +form basically to be able to solve + + align:start position:0% +form basically to be able to solve + + + align:start position:0% +form basically to be able to solve +initial value problems for which the + + align:start position:0% +initial value problems for which the + + + align:start position:0% +initial value problems for which the +value u of t is uh projected to u of + + align:start position:0% +value u of t is uh projected to u of + + + align:start position:0% +value u of t is uh projected to u of +zero when u we take t equals z for the + + align:start position:0% +zero when u we take t equals z for the + + + align:start position:0% +zero when u we take t equals z for the +matrix + + align:start position:0% +matrix + + + align:start position:0% +matrix +exponential. Okay. So now let's go back + + align:start position:0% +exponential. Okay. So now let's go back + + + align:start position:0% +exponential. Okay. So now let's go back +to our problem. So let's compute this + + align:start position:0% +to our problem. So let's compute this + + + align:start position:0% +to our problem. So let's compute this +matrix exponential. We have five of t. + + align:start position:0% +matrix exponential. We have five of t. + + + align:start position:0% +matrix exponential. We have five of t. +So now from this formula we know that we + + align:start position:0% +So now from this formula we know that we + + + align:start position:0% +So now from this formula we know that we +need five of + + align:start position:0% +need five of + + + align:start position:0% +need five of +zero. So that's give us basically + + align:start position:0% +zero. So that's give us basically + + + align:start position:0% +zero. So that's give us basically +exponential of + + align:start position:0% +exponential of + + + align:start position:0% +exponential of +zero + + align:start position:0% +zero + + + align:start position:0% +zero +five minus + + align:start position:0% +five minus + + + align:start position:0% +five minus +one and + + align:start position:0% +one and + + + align:start position:0% +one and +one. We need to find its inverse. So + + align:start position:0% +one. We need to find its inverse. So + + + align:start position:0% +one. We need to find its inverse. So +recall + + align:start position:0% + + + + align:start position:0% + +that the inverse of a 2x two matrix is + + align:start position:0% +that the inverse of a 2x two matrix is + + + align:start position:0% +that the inverse of a 2x two matrix is +basically just the + + align:start position:0% + + + + align:start position:0% + +determinant minus b minus c and + + align:start position:0% +determinant minus b minus c and + + + align:start position:0% +determinant minus b minus c and +reversing the diagonal entries. Okay. So + + align:start position:0% +reversing the diagonal entries. Okay. So + + + align:start position:0% +reversing the diagonal entries. Okay. So +we can just apply + + align:start position:0% +we can just apply + + + align:start position:0% +we can just apply +this to get our five of 0 minus + + align:start position:0% +this to get our five of 0 minus + + + align:start position:0% +this to get our five of 0 minus +one. So here our determinant is + + align:start position:0% +one. So here our determinant is + + + align:start position:0% +one. So here our determinant is +basically + + align:start position:0% +basically + + + align:start position:0% +basically +1 + 5 which is 1 / + + align:start position:0% +1 + 5 which is 1 / + + + align:start position:0% +1 + 5 which is 1 / +6 and then the entries are simply 1 + + align:start position:0% +6 and then the entries are simply 1 + + + align:start position:0% +6 and then the entries are simply 1 +one minus 5 and one. So now we're just + + align:start position:0% +one minus 5 and one. So now we're just + + + align:start position:0% +one minus 5 and one. So now we're just +left with a multiplication of two + + align:start position:0% +left with a multiplication of two + + + align:start position:0% +left with a multiplication of two +matrices to get our matrix exponential. + + align:start position:0% +matrices to get our matrix exponential. + + + align:start position:0% +matrices to get our matrix exponential. +Okay, so a matrix + + align:start position:0% + + + + align:start position:0% + +exponential would give us this 16. + + align:start position:0% +exponential would give us this 16. + + + align:start position:0% +exponential would give us this 16. +And we now have to multiply the entries. + + align:start position:0% +And we now have to multiply the entries. + + + align:start position:0% +And we now have to multiply the entries. +So I'm not going to rewrite everything. + + align:start position:0% +So I'm not going to rewrite everything. + + + align:start position:0% +So I'm not going to rewrite everything. +I'm just going to use the space here. So + + align:start position:0% +I'm just going to use the space here. So + + + align:start position:0% +I'm just going to use the space here. So +we have exponential + + align:start position:0% +we have exponential + + + align:start position:0% +we have exponential +t multiplying + + align:start position:0% +t multiplying + + + align:start position:0% +t multiplying +one + 5 exponential + + align:start position:0% + + + + align:start position:0% + +70. Yeah. 70. Then we have exponential t + + align:start position:0% +70. Yeah. 70. Then we have exponential t + + + align:start position:0% +70. Yeah. 70. Then we have exponential t +minus 5 for this entry. + + align:start position:0% + + + + align:start position:0% + +Five exponential tiping our one + + align:start position:0% + + + + align:start position:0% + +uh 70. Thank you. Uh then for the second + + align:start position:0% +uh 70. Thank you. Uh then for the second + + + align:start position:0% +uh 70. Thank you. Uh then for the second +entry we basically have minus + + align:start position:0% +entry we basically have minus + + + align:start position:0% +entry we basically have minus +exponential + + align:start position:0% + + + + align:start position:0% + +t1 exponential + + align:start position:0% + + + + align:start position:0% + +71 minus exponential t minus + + align:start position:0% + + + + align:start position:0% + +5 and exponential 71. + + align:start position:0% + + + + align:start position:0% + +Okay, so we're done with the matrix + + align:start position:0% +Okay, so we're done with the matrix + + + align:start position:0% +Okay, so we're done with the matrix +exponential. So now we were asked to + + align:start position:0% +exponential. So now we were asked to + + + align:start position:0% +exponential. So now we were asked to +solve for the initial value problem with + + align:start position:0% +solve for the initial value problem with + + + align:start position:0% +solve for the initial value problem with +initial condition one uh four and one. + + align:start position:0% +initial condition one uh four and one. + + + align:start position:0% +initial condition one uh four and one. +So how do we go about that? Well, recall + + align:start position:0% +So how do we go about that? Well, recall + + + align:start position:0% +So how do we go about that? Well, recall +that I just reminded you what what did + + align:start position:0% +that I just reminded you what what did + + + align:start position:0% +that I just reminded you what what did +we want to use this matrix exponential + + align:start position:0% +we want to use this matrix exponential + + + align:start position:0% +we want to use this matrix exponential +for? And what we wanted it for is to be + + align:start position:0% +for? And what we wanted it for is to be + + + align:start position:0% +for? And what we wanted it for is to be +able to basically project an initial + + align:start position:0% +able to basically project an initial + + + align:start position:0% +able to basically project an initial +condition into a solution u t times + + align:start position:0% +condition into a solution u t times + + + align:start position:0% +condition into a solution u t times +later. And we constructed this matrix to + + align:start position:0% +later. And we constructed this matrix to + + + align:start position:0% +later. And we constructed this matrix to +be able to basically give us this + + align:start position:0% +be able to basically give us this + + + align:start position:0% +be able to basically give us this +solution by just multiplying the matrix + + align:start position:0% +solution by just multiplying the matrix + + + align:start position:0% +solution by just multiplying the matrix +by the initial value vector. So + + align:start position:0% +by the initial value vector. So + + + align:start position:0% +by the initial value vector. So +basically to find the solution of this + + align:start position:0% +basically to find the solution of this + + + align:start position:0% +basically to find the solution of this +initial value problem, we simply need to + + align:start position:0% +initial value problem, we simply need to + + + align:start position:0% +initial value problem, we simply need to +multiply this matrix by the initial ve + + align:start position:0% +multiply this matrix by the initial ve + + + align:start position:0% +multiply this matrix by the initial ve +vector uh that we were given. And I'm + + align:start position:0% +vector uh that we were given. And I'm + + + align:start position:0% +vector uh that we were given. And I'm +just going + + align:start position:0% +just going + + + align:start position:0% +just going +to write it here to not have to rewrite + + align:start position:0% +to write it here to not have to rewrite + + + align:start position:0% +to write it here to not have to rewrite +everything. And it was four and one. And + + align:start position:0% +everything. And it was four and one. And + + + align:start position:0% +everything. And it was four and one. And +this is + + align:start position:0% +this is + + + align:start position:0% +this is +u of + + align:start position:0% +u of + + + align:start position:0% +u of +zero. Uh so let me just do a dash here + + align:start position:0% +zero. Uh so let me just do a dash here + + + align:start position:0% +zero. Uh so let me just do a dash here +just so that we can do the computation + + align:start position:0% +just so that we can do the computation + + + align:start position:0% +just so that we can do the computation +and we would end up with a + + align:start position:0% +and we would end up with a + + + align:start position:0% +and we would end up with a +solution of t. I'm going to keep it in + + align:start position:0% +solution of t. I'm going to keep it in + + + align:start position:0% +solution of t. I'm going to keep it in +matrix form for + + align:start position:0% +matrix form for + + + align:start position:0% +matrix form for +now. So we end up with exponential t + + align:start position:0% +now. So we end up with exponential t + + + align:start position:0% +now. So we end up with exponential t +four exponential + + align:start position:0% +four exponential + + + align:start position:0% +four exponential +t minus 5 exponential t. So minus one + + align:start position:0% +t minus 5 exponential t. So minus one + + + align:start position:0% +t minus 5 exponential t. So minus one +exponential t and we have 16. + + align:start position:0% +exponential t and we have 16. + + + align:start position:0% +exponential t and we have 16. +Here five exponential 70 multiply. So we + + align:start position:0% +Here five exponential 70 multiply. So we + + + align:start position:0% +Here five exponential 70 multiply. So we +have 20 + 5 so + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +exponential + + align:start position:0% +exponential + + + align:start position:0% +exponential +70. Uh then for the for the second entry + + align:start position:0% +70. Uh then for the for the second entry + + + align:start position:0% +70. Uh then for the for the second entry +of the vector solution we have minus + + align:start position:0% +of the vector solution we have minus + + + align:start position:0% +of the vector solution we have minus +exponential here minus 4 that we add to + + align:start position:0% +exponential here minus 4 that we add to + + + align:start position:0% +exponential here minus 4 that we add to +a + + align:start position:0% +a + + + align:start position:0% +a +five and here a seven multiplied by four + + align:start position:0% +five and here a seven multiplied by four + + + align:start position:0% +five and here a seven multiplied by four +that we add to a one. So we have + + align:start position:0% +that we add to a one. So we have + + + align:start position:0% +that we add to a one. So we have +basically + + + align:start position:0% +basically + + + + align:start position:0% +basically + + + align:start position:0% + + + align:start position:0% +exponential 7T and that basically gives + + align:start position:0% +exponential 7T and that basically gives + + + align:start position:0% +exponential 7T and that basically gives +us one way of writing the solution and + + align:start position:0% +us one way of writing the solution and + + + align:start position:0% +us one way of writing the solution and +we can split this then if we + + align:start position:0% +we can split this then if we + + + align:start position:0% +we can split this then if we +will into two solutions two two + + align:start position:0% + + + + align:start position:0% + +vectors yeah plus t minus + + align:start position:0% +vectors yeah plus t minus + + + align:start position:0% +vectors yeah plus t minus +one + + align:start position:0% +one + + + align:start position:0% +one + + align:start position:0% + + + align:start position:0% +25 but this form is as valid. Yes, thank + + align:start position:0% +25 but this form is as valid. Yes, thank + + + align:start position:0% +25 but this form is as valid. Yes, thank +you. Okay, so that ends the library's + + align:start position:0% +you. Okay, so that ends the library's + + + align:start position:0% +you. Okay, so that ends the library's +calculations but basically the key point + + align:start position:0% +calculations but basically the key point + + + align:start position:0% +calculations but basically the key point +here was just to remember where is the + + align:start position:0% +here was just to remember where is the + + + align:start position:0% +here was just to remember where is the +matrix exponential coming from uh + + align:start position:0% +matrix exponential coming from uh + + + align:start position:0% +matrix exponential coming from uh +basically from the the the aen values + + align:start position:0% +basically from the the the aen values + + + align:start position:0% +basically from the the the aen values +and vectors of the original matrix + + align:start position:0% +and vectors of the original matrix + + + align:start position:0% +and vectors of the original matrix +present in the system. And where is the + + align:start position:0% +present in the system. And where is the + + + align:start position:0% +present in the system. And where is the +definition coming from? Why do we define + + align:start position:0% +definition coming from? Why do we define + + + align:start position:0% +definition coming from? Why do we define +it as five of t 5 minus one of zero and + + align:start position:0% +it as five of t 5 minus one of zero and + + + align:start position:0% +it as five of t 5 minus one of zero and +how to use it then to compute the + + align:start position:0% +how to use it then to compute the + + + align:start position:0% +how to use it then to compute the +solutions given an initial value uh to + + align:start position:0% +solutions given an initial value uh to + + + align:start position:0% +solutions given an initial value uh to +basically answer give the solution to an + + align:start position:0% +basically answer give the solution to an + + + align:start position:0% +basically answer give the solution to an +initial value problem. So that ends this + + align:start position:0% +initial value problem. So that ends this + + + align:start position:0% +initial value problem. So that ends this +recitation. \ No newline at end of file diff --git a/taCtV7gVKdI.txt b/taCtV7gVKdI.txt new file mode 100644 index 0000000000000000000000000000000000000000..3eb2d288fb92d66e2206567506678afa8a389446 --- /dev/null +++ b/taCtV7gVKdI.txt @@ -0,0 +1,1263 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high-quality +educational resources for free. + +To make a donation, or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +BOGDAN FEDELES: Greetings, +and welcome to 5.07 + +Biochemistry online. + +I'm Dr. Bogden Fedeles. + +Let's metabolize some problems. + +I have a good problem +for you today. + +This is problem one, +from problem set nine. + +It is a problem in +which we're going + +to calculate how much energy +we get from metabolizing + +a molecule of fat, +more specifically, + +a molecule of triacylglycerol. + +Here is a structural +representation + +of the triacylglycerol. + +Recognize the glycerol +molecule in the middle + +here, that it's holding +together three fatty acids. + +Now notice, I picked a +short-chain fatty acid, + +a long-chain fatty acid, +and a fatty acid that + +actually has a double bond. + +Now when this molecule +gets metabolized, + +it's going to be acted upon by +an enzyme called the lipase. + +It's going to hydrolyze the +molecule into its constituents. + +Obviously the lipase is +going to use water molecules, + +and it's going to break it +down into glycerol, shown here. + +Glycerol. + +Then, this fatty acid that has +two, four, six, C6 fatty acid. + +This fatty acid has two, four, +six, eight, 10, 12, 14, 16, + +C16 fatty acid. + +And this one, it's an +unsaturated fatty acid, + +has a double bond, and +if you count the carbons + +it should add up to 15 carbons. + +So not only it +has a double bond, + +but also it's an +odd-numbered fatty acid. + +In order to figure out how much +energy we can get from this one + +molecule of fat, we will +look at how much energy + +we get from each one +of these constituents-- + +namely, the glycerol and +the three fatty acids-- + +and calculate what is +the maximum amount of ATP + +we can generate +when we metabolize + +each one of these molecules +completely to CO2 and water. + +In order to keep track +of how much energy we + +get from each of +the molecules, let's + +make a handy table right here. + +So we're going to put glycerol +and the C6 fatty acid, + +and the C16 fatty acid, +and C15 fatty acid. + +All right. + +And each one of these, we're +going to follow the metabolism, + +and see how much ATP we're going +to need to put in or generate. + +Also, the redox cofactors +in ADH or FADH2. + +Also, for fatty +acids, we're going + +to be dealing with +beta-oxidation. + +And pretty much every +single molecule, + +when it's going to +be born completely, + +it's going to generate +first acetyl-CoA. + +All right. + +And here, we're going to tally +up the total amount of ATP + +for each one of them. + +And then we're going to tally +up for the entire molecule. + +So let's start with +the glycerol molecule. + +Now, if you have watched +the problem set seven, + +you might recognize +the following pathway. + +As we just discussed, +triacylglyceride + +can be hydrolyzed +to form glycerol. + +And the glycerol, then, +is first phosphorylated + +by glycerol kinase, and +oxidized by glycerol phosphate + +dehydrogenase, to generate +dihydro acetyl phosphate, which + +can then enter the +glycolysis, and follow + +glycolysis all the way to +pyruvate, and then acetyl-CoA. + +From then, acetyl-CoA can +go into the TCA cycle. + +So let's tally up +how much energy + +we can get from one +molecule of glycerol. + +Let's take a look +specifically at the steps + +where we are generating ATP, +or generating redox cofactors, + +such as NADH or FADH2. + +First, we need to put in ATP. + +Neglect glycerol kinase. + +But we're going to +get back one ATP + +in the phosphoglycerate +kinase step, + +and one ATP in the +pyruvate kinase step. + +So the net ATP formation is one. + +Now in the +glycolysis, we're also + +going to generate one NADH, +in the pyruvate dehydrogenase + +another NADH, and the +glycerol-3-phosphate + +dehydrogenase will +generate also an NADH. + +Now, keep in mind, +this NADH is going + +to be outside the +mitochondria, so we're + +going to have to use a +shuttle to bring it in. + +But we're considering +that we're using + +an efficient shuttle, that gives +us the full amount of energy + +for this NADH. + +So, once again, the +total, it's going + +to be three molecules of NADH. + +So, going back to +our table, we said + +the glycerol is going to give +us a net one molecule of ATP, + +three molecules of NADH. + +There's going to be no +FADH2, no beta-oxidation, + +and we're going to get one +molecule of acetyl-CoA. + +As you've seen by +this point many times, + +acetyl-CoA will +enter the TCA cycle, + +where it's going to be +completely oxidized to two CO2 + +molecules, and in the +process is going to generate + +the equivalent of 12 ATPs. + +Let's take a look at where +those are coming from. + +Here is a schematic +of the TCA cycle. + +And one acetyl-CoA +molecule comes in, + +and it's going to generate one, +two, three molecules of NADH, + +one molecule of FADH2, +and one molecule of GTP. + +Now, if we keep in mind +that for every FADH2 + +we generate about two +ATPs, and for every NADH + +we generate three ATPs, that's +a total of, 3 times 3 is 9, + +plus 2 is 11, plus a GDP +is equivalent to an ATP. + +That's about 12 molecules of +ATP per molecule of acetyl-CoA + +that enters the TCA cycle. + +So now let's tally +up how much energy + +we can get from one +molecule of glycerol. + +So we know we get +one ATP, three NADHs, + +now each NADH is going to give +us three molecules of ATP. + +Now FADH2, we know these +give two molecules of ATP. + +We don't have any +beta-oxidation-- + +we're going to be talking +more about fatty acids-- + +and acetyl-CoA we just talked +about, we get 12 molecules + +of ATP per acetyl-CoA. + +So, the total here +is 12 plus 9, plus 1, + +that's going to be 22 ATPs +from one molecule of glycerol. + +Now let's talk about +the fatty acids. + +In order to metabolize +them, first we + +need to activate +them into thioesters. + +These are going to be thioesters +formed with coenzyme A, or CoA. + +Here's an overview of +the activation process + +by which fatty acids become +fatty acid thioesters. + +Of course, this is written +for the C6 fatty acid, + +but would occur for +any other fatty acid, + +regardless of the chain length. + +Now this process is catalyzed +by acetyl-CoA synthetase, that + +uses ATP to first generate +this mixed anhydride, with AMP. + +This process is +called adenylation. + +So this activates +the acid, which + +then reacts with +coenzyme A shown here, + +HS-CoA, which will generate the +thioester of the fatty acid. + +Now, here we are using +one molecule of ATP, + +but we're breaking it into +alpha-phosphate to generate + +pyrophosphate, which is +then broken down into two + +inorganic phosphates. + +And the energy in this +reaction, catalyzed + +by inorganic +pyrophosphatase, drives + +the reaction towards the right. + +Now, since we're generating +AMP in the second step, + +we need a second molecule of +ATP to convert this AMP back + +to ADP. + +So, overall, this process +requires two molecules of ATP + +to generate one molecule of +the fatty acid thioester. + +Once a fatty acid is +activated into a thioester + +with coenzyme A, it can +now undergo beta-oxidation. + +This is a set of reactions in +which the fatty acid is broken + +down into a shorter fatty acid +and one molecule of acetyl-CoA. + +The process then can +repeat over and over, + +until the entire fatty +acid is broken down + +into acetyl-CoA molecules. + +So let's take a look at +how beta-oxidation works. + +Here is an overview of +beta-oxidation pathway. + +We're starting with a fatty +acyl-CoA thioester that + +has "n" carbons, and by +the end of the process, + +we're going to get a thioester +that has "n" minus 2 carbons, + +and the remaining +two carbons are + +going to be in the +form of acetyl-CoA. + +Now, this beta-oxidation +involves four steps. + +In the first step, we're +going to use a dehydrogenase + +to oxidize this single +bond between the alpha + +and beta carbons, and +make a trans double bond. + +So this is the alpha carbon, +this is the beta carbon. + +So these fatty acyl-CoA +dehydrogenases, + +there are actually +several of them, + +and they have +different specificities + +for short, medium, +long, and very + +long chain fatty acyl-CoAs. + +But regardless, there +will be some dehydrogenase + +to act on any length +fatty acyl-CoA, + +and introduce this +trans double bond. + +In the next step, we +add one water molecule + +to generate a +beta-hydroxyacyl-CoA, which + +is subsequently oxidized to +generate a beta-ketoacyl-CoA. + +In this oxidation, +we're going to use NAD, + +generating one molecule NADH. + +Finally, the thiolase, or +beta-ketoacyl thiolase, + +is going to break down this +bond between the alpha and beta + +carbons, in a reverse +Claisen reaction, + +to generate one +molecule of acetyl-CoA. + +And the remainder of the fatty +acid is another thioester. + +So one round of +beta-oxidation is + +going to generate one +molecule of FADH2, + +and one molecule +of NADH, as well + +as one molecule of acetyl-CoA. + +Now let's update our table +with the information we just + +learned. + +So, as we just said, +for every fatty acid + +we need to expend +two molecules of ATP, + +to transform them +into the thioesters. + +That's why I put here minus +2 for each one of the three + +fatty acids. + +We also learned that +in beta-oxidation, we + +generate one molecule of FADH2, +and one molecule of NADH. + +So, for every beta-oxidation, +we generate the equivalent + +of five ATP. + +Now we're ready to +calculate how much energy we + +can get from each of the three +fatty acids in our problem. + +Now, for the C6 fatty acid +that's what's represented here, + +we discussed, we're +going to activate it, + +we're going to need to +use two ATP molecules + +and coenzyme A. We're going +to form the thioester. + +And then we're going +to do beta-oxidation + +Now, for a fatty acid +that has six carbons, + +we're going to do +the beta-oxidation, + +and the molecule is +going to cleave there, + +and we're going to +do it one more time, + +the molecule is going +to be cleaved there. + +So we're going to do two +rounds of beta-oxidation. + +And each one of +these two carbons + +is going to become +an acetyl-CoA. + +So we're going to generate +three acetyl-CoAs. + +Now, similarly, for +the C16 fatty acid-- + +two, four, six, +eight, 10, 12, 14, 16. + +All right, it's going to first +activate two molecules of ATP + +and coenzyme A to form the +thioester, with 16 carbons. + +And this will undergo +beta-oxidation. + +And we're going to do it one, +two, three, four, five, six, + +seven times. + +OK, so seven rounds +of beta-oxidation + +is going to generate eight +molecules of acetyl-CoA. + +Now let's go back and put +in all this information + +into our table. + +So for the C6 fatty acid, we +expended two molecules of ATP + +to activate it, and then we did +two rounds of beta-oxidation, + +and we generated three +molecules of acetyl-CoA. + +For the C16 fatty +acid, again, we + +activated then we did seven +rounds beta-oxidation, + +and we generated eight +molecules of acetyl-CoA. + +So for the C6 fatty acid, +we have a grand total of, + +3 times 12 is 36, plus 2 +times 5, 10, is 46, minus 2, + +is 44 molecules of ATP. + +For the C16 fatty +acid, well, 8 times 12 + +is 96, plus 35, minus 2, +that's 129 molecules of ATP. + +Now the C15 fatty acid is +going to be a little bit more + +complicated, because on one +hand, it has a double bond, + +so we need to figure out +how to deal with that. + +On the other hand, it's +an odd chain fatty acid, + +and as you imagine, the +beta-oxidation breaks off + +two carbons at a time. + +So the last time we +do beta-oxidation, + +we're going to be left +with three carbons. + +That's called +propionyl-CoA, and we'll + +have to figure out +what to do with that. + +Just as with the +other fatty acids, + +the C15 fatty acid +is going to need + +to be activated into +a thioester with CoA. + +So this is going to cost two +ATP molecules, and, of course, + +we need to add the CoA. + +And now, this is the thioester +of our C15 fatty acid. + +Now, since the double +bond is pretty far away + +from the business-end +of the molecule, + +we can do a number of +rounds of beta-oxidation. + +In fact, we can do +beta-oxidation once, twice. + +So two rounds of +beta-oxidation is + +going to give us this molecule. + +Two rounds beta-oxidation. + +In each one of +these rounds we're + +going to generate one +molecule of acetyl-CoA, + +so two acetyl-CoA. + +So we get this fatty +acid taiyo thioester, + +which contains a +beta-gamma double bond. + +Now, it turns out +there is an enzyme that + +can isomerize this double bond +into an alpha-beta double bond. + +So this is what is +going to happen next. + +The double bond moves from the +beta-gamma to the alpha-beta. + +Now, this looks a lot +like an intermediate + +in the beta-oxidation. + +Once again, this reaction is +catalyzed by am isomerase. + +And this alpha-beta +unsaturated thioester + +can continue in a manner +similar to beta-oxidation. + +So, first it's going to add +water to form a hydroxyl here + +at the beta position. + +Then that hydroxyl is getting +oxidized to form a keto group. + +And the thiolase is going +to generate acetyl-CoA, + +and another +thioester shown here. + +So, from here, we're going to +generate one molecule of NADH, + +and one molecule of acetyl-CoA. + +All right, now +this is a thioester + +of a completely +saturated fatty acid. + +Now of course, it's +still odd chained, + +so we have one, six, +seven, eight, nine carbons. + +So we can do beta-oxidation +actually three times. + +So, three rounds +of beta-oxidation. + +And it's going to take us to +three molecules of acetyl-CoA. + +And the last portion +of the molecule + +is going to be this molecule, +which we call propionyl-CoA, + +is a three carbon thioester. + +So far we have generated +two, three, and another three + +here, six molecule +of acetyl-CoA. + +And we've done, +two, another three, + +five rounds of beta-oxidation. + +And we also generated an +additional NADH molecule. + +So now let's update our +table with this information, + +and then we're +going to figure out + +what happens to propionyl-CoA. + +As we just discussed, +the C15 fatty acid + +is going to get activated, +so we need to ATPs there. + +Then it's going to undergo +five rounds of beta-oxidation. + +And we generated a total of +six molecules of acetyl-CoA, + +and one additional +molecule of NADH. + +Let's now take a look +at propionyl-CoA, + +and see how we metabolize +it, and how much energy + +we can generate from it. + +It turns out the first step is +to expand from a three carbon + +molecule to a four +carbon molecule. + +This happens by adding one CO2. + +Of course, this +process will require + +the expense of an ATP molecule. + +We generate this +methylmalonyl-CoA, + +which is a branched four +carbon chain molecule. + +And another enzyme, +racemase, is going + +to interconvert +this stereocenter + +from the S-configuaration +to the R-configuration. + +Finally, this +methylmalonyl-CoA is + +going to undergo a +rearrangement of the groups + +to generate a linear +molecule, succinyl-CoA. + +Now, this is one of the most +fascinating transformations + +in the whole +biochemistry, and involves + +an enzyme called +methylmalonyl-CoA mutase, which + +requires cobalamin, or +the coenzyme derived + +from vitamin B12. + +This unusual +transformation catalyzed + +by the methylmalonyl-CoA +mutase, the enzyme that + +requires vitamin +B12 cofactor, it's + +fascinating because it +involves a carbon skeletal + +rearrangement of the molecule. + +And this reaction occurs +via a radical mechanism. + +The radical is obtained by +breaking a carbon metal bond. + +In this case, it's a +carbon-cobalt bond. + +Now succinyl-CoA is +a familiar molecule, + +you've encountered +it in the TCA cycle. + +However, we cannot use the TCA +cycle directly to completely + +metabolize succinyl-CoA, as all +the intermediates in the TCA + +cycle are in fact in +catalytic amounts. + +So, we're going to use +just part of the TCA cycle, + +to generate a molecule, +malate, which then + +can be converted into pyruvate. + +And pyruvate can then +generate acetyl-CoA + +to re-enter the TCA cycle and +be completely metabolized. + +Here is the TCA cycle, +to refresh your memory. + +And this is +succinyl-CoA that we can + +generate from the +methylmalonyl-CoA mutase. + +Now, as we said, +succinyl-CoA is going + +to be converted to malate. + +Malate can then escape +the mitochondria + +and continue its transformation +towards pyruvate. + +So, in this process, +succinyl-CoA + +is going to generate +one molecule of GTP + +to form succinate. + +And succinate to fumartate +is going to give us + +one more molecule of FADH2. + +Then malate will escape +the mitochondria. + +So to summarize what +happens in the TCA cycle, + +succinyl-CoA is going to +give us a molecule of GTP, + +and then one more +molecule of FADH2. + +And it's going to +make it to malate, + +and then malate is going +to be converted to pyruvate + +using the malic enzyme. + +Now, this is an oxidation +and decarboxylation + +that happens in one step. + +For the oxidation, +we're going to need + +NADP, instead of the usual NAD. + +So we're going to generate +one molecule of NADPH. + +Now for the purpose +of this problem, + +we're going to treat NADPH +as equivalent to NADH. + +So malate, via the malic enzyme, +is going to form pyruvate. + +And then pyruvate, in the +pyruvate dehydrogenase, + +is going to lose one +CO2 and form acetyl-CoA. + +In the process we'll also +generate one more NADH, + +and now acetyl-CoA can +re-enter the TCA cycle + +and be completely +metabolized, generating + +in the process about +12 ATP equivalents. + +So now let's go back, +and update our table + +with all this information +that we found out + +about propionyl-CoA. + +So as we said, propionyl-CoA +required first the loss + +of another ATP to activate it, +to form the methylmalonyl-CoA. + +But then methylmalonyl-CoA +converted to succinyl-CoA. + +Succinyl-CoA generated +one molecule of GTP, + +so we're going to +put plus 1 back here. + +Then we're going to get +one molecule of FADH2 + +the generating +succinate, from going + +from succinate to fumarate. + +And then, we're +going to generate + +two more molecules of NADH, +one at the malate enzyme step, + +and one at the pyruvate +dehydrogenase step, + +so we have plus 2 here. + +And, of course, in the end, +we get one more molecule + +of acetyl-CoA as well. + +So now we have a total of +seven molecules of acetyl-CoA, + +five rounds of beta-oxidation, +one FADH2, three NADHs, + +and at a loss of two ATPs. + +So this totals up to 118 +ATPs for the C15 fatty acid. + +Now we can tally the entire +ATP yield of a molecule of fat, + +of this triacylglyceride, +and that's + +going to be 313 +molecules of ATP. + +Now that's a lot of energy from +one single molecule of fat. + +Now, this problem has +an additional question, + +and it asked us to contrast how +much energy we get from a six + +carbon fatty acid +and compare that + +to how much energy would get +from one molecule of glucose, + +which also has six carbons. + +Let's take a look +at our table here. + +The six carbon fatty acid +generates about 44 molecules + +of ATP when completely oxidized. + +By contrast, one +molecule of glucose + +would generate only about +34 to 36 molecules of ATP. + +If you want to follow the same +analysis that we did here-- + +remember glucose, well, we need +to spend two molecules of ATP + +to activate it, but +then we're going + +to generate four molecules +of ATP going to pyruvate. + +And then there's going to be +two molecules of NADH generated, + +one at the GAPDH step, one +at the pyruvate dehydrogenase + +step, and finally, +we're going to generate + +two molecules of acetyl-CoA. + +So the total is going to be, 2 +times 12 is 24, plus 4 times 3 + +is 12, is 36, plus 2, is 38. + +So as you guys can +see, the C6 fatty acid + +generates actually more ATP +than one molecule of glucose. + +And that's probably reasonable, +because the C6 fatty acids + +have a lot more C-H bonds. + +In other words, the +carbons are more reduced. + +In glucose, we have +a lot of hydroxyls, + +so the carbons are in a +slightly higher oxidation state. + +Therefore, there's less +energy generated total. + +Of course, one +molecule of glucose + +pales in comparison +with one molecule + +of fat, which has +hundreds of ATP generated, + +as we thought in part +A of this problem. + +Well, that sums up this problem. + +I hope it helped you realize why +fats, or triacylglycerides, are + +so much more energy dense than +other nutrients, such as sugars + +or amino acids. \ No newline at end of file diff --git a/ucPrWHF_5Lc.txt b/ucPrWHF_5Lc.txt new file mode 100644 index 0000000000000000000000000000000000000000..d5268097597b4dad623fa311987a340354797808 --- /dev/null +++ b/ucPrWHF_5Lc.txt @@ -0,0 +1,9211 @@ +align:start position:0% + +Let's uh let's start with the Mandel + + align:start position:0% +Let's uh let's start with the Mandel + + + align:start position:0% +Let's uh let's start with the Mandel +flaming mold now this is a mold that + + align:start position:0% +flaming mold now this is a mold that + + + align:start position:0% +flaming mold now this is a mold that +that I think is extremely + + align:start position:0% +that I think is extremely + + + align:start position:0% +that I think is extremely +useful H and in the short term it will + + align:start position:0% +useful H and in the short term it will + + + align:start position:0% +useful H and in the short term it will +be important for because probably 70% of + + align:start position:0% +be important for because probably 70% of + + + align:start position:0% +be important for because probably 70% of +the quiz will be related to things that + + align:start position:0% +the quiz will be related to things that + + + align:start position:0% +the quiz will be related to things that +to this mod meaning you know we're going + + align:start position:0% +to this mod meaning you know we're going + + + align:start position:0% +to this mod meaning you know we're going +to use this model for different things + + align:start position:0% +to use this model for different things + + + align:start position:0% +to use this model for different things +but but but uh if you understand it well + + align:start position:0% +but but but uh if you understand it well + + + align:start position:0% +but but but uh if you understand it well +you probably have 70% of the last quiz + + align:start position:0% +you probably have 70% of the last quiz + + + align:start position:0% +you probably have 70% of the last quiz +under control so I'm going to go very + + align:start position:0% +under control so I'm going to go very + + + align:start position:0% +under control so I'm going to go very +slowly over it and please stop me if + + align:start position:0% +slowly over it and please stop me if + + + align:start position:0% +slowly over it and please stop me if +there is any step you don't understand I + + align:start position:0% +there is any step you don't understand I + + + align:start position:0% +there is any step you don't understand I +I put steps into myself so I don't rush + + align:start position:0% +I put steps into myself so I don't rush + + + align:start position:0% +I put steps into myself so I don't rush +because again I think it's + + align:start position:0% +because again I think it's + + + align:start position:0% +because again I think it's +important um to understand things + + align:start position:0% +important um to understand things + + + align:start position:0% +important um to understand things +so here you have uh the exchange rate + + align:start position:0% +so here you have uh the exchange rate + + + align:start position:0% +so here you have uh the exchange rate +two exchange rates uh the the the wide + + align:start position:0% +two exchange rates uh the the the wide + + + align:start position:0% +two exchange rates uh the the the wide +one is + + align:start position:0% +one is + + + align:start position:0% +one is +the the the the euro dollar exchange + + align:start position:0% +the the the the euro dollar exchange + + + align:start position:0% +the the the the euro dollar exchange +rate I'm quoting it the opposite of the + + align:start position:0% +rate I'm quoting it the opposite of the + + + align:start position:0% +rate I'm quoting it the opposite of the +way it's normally quoted there are some + + align:start position:0% +way it's normally quoted there are some + + + align:start position:0% +way it's normally quoted there are some +conventions in FX markets but this is as + + align:start position:0% +conventions in FX markets but this is as + + + align:start position:0% +conventions in FX markets but this is as +we have defined in this courses if it + + align:start position:0% +we have defined in this courses if it + + + align:start position:0% +we have defined in this courses if it +goes up it means an appreciation of a + + align:start position:0% +goes up it means an appreciation of a + + + align:start position:0% +goes up it means an appreciation of a +local currency that is the + + align:start position:0% +local currency that is the + + + align:start position:0% +local currency that is the +dollar that is you get more of the + + align:start position:0% +dollar that is you get more of the + + + align:start position:0% +dollar that is you get more of the +foreign currency per unit of the + + align:start position:0% +foreign currency per unit of the + + + align:start position:0% +foreign currency per unit of the +domestic currency when it goes up and + + align:start position:0% +domestic currency when it goes up and + + + align:start position:0% +domestic currency when it goes up and +down is a + + align:start position:0% +down is a + + + align:start position:0% +down is a +depreciation and and you see there that + + align:start position:0% +depreciation and and you see there that + + + align:start position:0% +depreciation and and you see there that +so this is the the dollar became a gain + + align:start position:0% +so this is the the dollar became a gain + + + align:start position:0% +so this is the the dollar became a gain +value relative to the euro through all + + align:start position:0% +value relative to the euro through all + + + align:start position:0% +value relative to the euro through all +this period and then it has lost quite a + + align:start position:0% +this period and then it has lost quite a + + + align:start position:0% +this period and then it has lost quite a +bit of value H since sort of late + + align:start position:0% +bit of value H since sort of late + + + align:start position:0% +bit of value H since sort of late +2022 for for with respect to the + + align:start position:0% +2022 for for with respect to the + + + align:start position:0% +2022 for for with respect to the +Japanese Yen that's a blue line it's was + + align:start position:0% +Japanese Yen that's a blue line it's was + + + align:start position:0% +Japanese Yen that's a blue line it's was +the whole cycle is even more dramatic no + + align:start position:0% +the whole cycle is even more dramatic no + + + align:start position:0% +the whole cycle is even more dramatic no +big appreciation of the dollar + + align:start position:0% +big appreciation of the dollar + + + align:start position:0% +big appreciation of the dollar +depreciation of the Yen H and and a + + align:start position:0% +depreciation of the Yen H and and a + + + align:start position:0% +depreciation of the Yen H and and a +reversal since late 2022 and so so what + + align:start position:0% +reversal since late 2022 and so so what + + + align:start position:0% +reversal since late 2022 and so so what +is behind this these big + + align:start position:0% +is behind this these big + + + align:start position:0% +is behind this these big +fluctuations many things effects are + + align:start position:0% +fluctuations many things effects are + + + align:start position:0% +fluctuations many things effects are +volatile like almost any asset price but + + align:start position:0% +volatile like almost any asset price but + + + align:start position:0% +volatile like almost any asset price but +one of the main drivers of this uh of of + + align:start position:0% +one of the main drivers of this uh of of + + + align:start position:0% +one of the main drivers of this uh of of +of these fluctuations is perceptions + + align:start position:0% +of these fluctuations is perceptions + + + align:start position:0% +of these fluctuations is perceptions +about interest rate policy in the + + align:start position:0% +about interest rate policy in the + + + align:start position:0% +about interest rate policy in the +different parts of the world okay so uh + + align:start position:0% +different parts of the world okay so uh + + + align:start position:0% +different parts of the world okay so uh +the risk Reon we have seen a lot of this + + align:start position:0% +the risk Reon we have seen a lot of this + + + align:start position:0% +the risk Reon we have seen a lot of this +decline here so the reason for the rise + + align:start position:0% +decline here so the reason for the rise + + + align:start position:0% +decline here so the reason for the rise +here of the dollar is mostly because + + align:start position:0% +here of the dollar is mostly because + + + align:start position:0% +here of the dollar is mostly because +investors in general perceived that the + + align:start position:0% +investors in general perceived that the + + + align:start position:0% +investors in general perceived that the +US was more advanced in its business + + align:start position:0% +US was more advanced in its business + + + align:start position:0% +US was more advanced in its business +cycle it began to tighten interest rate + + align:start position:0% +cycle it began to tighten interest rate + + + align:start position:0% +cycle it began to tighten interest rate +before the rest of the world and since + + align:start position:0% +before the rest of the world and since + + + align:start position:0% +before the rest of the world and since +interest rates were rising in in the US + + align:start position:0% +interest rates were rising in in the US + + + align:start position:0% +interest rates were rising in in the US +that led to an appreciation of the + + align:start position:0% +that led to an appreciation of the + + + align:start position:0% +that led to an appreciation of the +Dollar by a mechanism they describe at + + align:start position:0% +Dollar by a mechanism they describe at + + + align:start position:0% +Dollar by a mechanism they describe at +the end of the previous lecture but I'm + + align:start position:0% +the end of the previous lecture but I'm + + + align:start position:0% +the end of the previous lecture but I'm +going to repeat today remember when I + + align:start position:0% +going to repeat today remember when I + + + align:start position:0% +going to repeat today remember when I +talk about the uncover in part condition + + align:start position:0% +talk about the uncover in part condition + + + align:start position:0% +talk about the uncover in part condition +but it's related to what I'm talking + + align:start position:0% +but it's related to what I'm talking + + + align:start position:0% +but it's related to what I'm talking +about here I'm going to again go go + + align:start position:0% +about here I'm going to again go go + + + align:start position:0% +about here I'm going to again go go +again over that and a big reason for the + + align:start position:0% +again over that and a big reason for the + + + align:start position:0% +again over that and a big reason for the +decline more recently is simply that + + align:start position:0% +decline more recently is simply that + + + align:start position:0% +decline more recently is simply that +there is a sense that monetary policy is + + align:start position:0% +there is a sense that monetary policy is + + + align:start position:0% +there is a sense that monetary policy is +piing in the US in terms of tightness + + align:start position:0% +piing in the US in terms of tightness + + + align:start position:0% +piing in the US in terms of tightness +while the rest of the world is catching + + align:start position:0% +while the rest of the world is catching + + + align:start position:0% +while the rest of the world is catching +up ER and in the case of Europe more + + align:start position:0% +up ER and in the case of Europe more + + + align:start position:0% +up ER and in the case of Europe more +than catching up because they have + + align:start position:0% +than catching up because they have + + + align:start position:0% +than catching up because they have +further Supply shocks coming from energy + + align:start position:0% +further Supply shocks coming from energy + + + align:start position:0% +further Supply shocks coming from energy +shocks and so on so if you look for + + align:start position:0% +shocks and so on so if you look for + + + align:start position:0% +shocks and so on so if you look for +example at the expected in policy rate + + align:start position:0% +example at the expected in policy rate + + + align:start position:0% +example at the expected in policy rate +path in the case of the US nowadays it + + align:start position:0% +path in the case of the US nowadays it + + + align:start position:0% +path in the case of the US nowadays it +looks like this so the still markets + + align:start position:0% +looks like this so the still markets + + + align:start position:0% +looks like this so the still markets +expect some hike some hikes in the US + + align:start position:0% +expect some hike some hikes in the US + + + align:start position:0% +expect some hike some hikes in the US +but a limited amount of hikes and then + + align:start position:0% +but a limited amount of hikes and then + + + align:start position:0% +but a limited amount of hikes and then +they expect quickly the FED to start + + align:start position:0% +they expect quickly the FED to start + + + align:start position:0% +they expect quickly the FED to start +undoing that okay that's what this path + + align:start position:0% +undoing that okay that's what this path + + + align:start position:0% +undoing that okay that's what this path +is telling you this is expected policy + + align:start position:0% +is telling you this is expected policy + + + align:start position:0% +is telling you this is expected policy +rate path what the market thinks now the + + align:start position:0% +rate path what the market thinks now the + + + align:start position:0% +rate path what the market thinks now the +policy rate will be in the next meeting + + align:start position:0% +policy rate will be in the next meeting + + + align:start position:0% +policy rate will be in the next meeting +two meetings from now three meetings + + align:start position:0% +two meetings from now three meetings + + + align:start position:0% +two meetings from now three meetings +from now for meetings meetings of the + + align:start position:0% +from now for meetings meetings of the + + + align:start position:0% +from now for meetings meetings of the +fomc from now okay well if you look at + + align:start position:0% +fomc from now okay well if you look at + + + align:start position:0% +fomc from now okay well if you look at +the same picture in Europe it looks like + + align:start position:0% +the same picture in Europe it looks like + + + align:start position:0% +the same picture in Europe it looks like +that it's clear that there there are + + align:start position:0% +that it's clear that there there are + + + align:start position:0% +that it's clear that there there are +still there's more ahead and and and you + + align:start position:0% +still there's more ahead and and and you + + + align:start position:0% +still there's more ahead and and and you +see sort of that that's what the market + + align:start position:0% +see sort of that that's what the market + + + align:start position:0% +see sort of that that's what the market +perceive at this point whether that ends + + align:start position:0% +perceive at this point whether that ends + + + align:start position:0% +perceive at this point whether that ends +up being true or not doesn't matter at + + align:start position:0% +up being true or not doesn't matter at + + + align:start position:0% +up being true or not doesn't matter at +any point in time the exchanger is + + align:start position:0% +any point in time the exchanger is + + + align:start position:0% +any point in time the exchanger is +determined by what the markets think so + + align:start position:0% +determined by what the markets think so + + + align:start position:0% +determined by what the markets think so +so what actually happens is less + + align:start position:0% +so what actually happens is less + + + align:start position:0% +so what actually happens is less +important for an asset price an asset + + align:start position:0% +important for an asset price an asset + + + align:start position:0% +important for an asset price an asset +price is a lot about pricing today + + align:start position:0% +price is a lot about pricing today + + + align:start position:0% +price is a lot about pricing today +things that you expect to happen in the + + align:start position:0% +things that you expect to happen in the + + + align:start position:0% +things that you expect to happen in the +future what expects what you expect is + + align:start position:0% +future what expects what you expect is + + + align:start position:0% +future what expects what you expect is +what matter not what actually happens + + align:start position:0% +what matter not what actually happens + + + align:start position:0% +what matter not what actually happens +and at this moment the the market expect + + align:start position:0% +and at this moment the the market expect + + + align:start position:0% +and at this moment the the market expect +a the Euro area to go through a a sort + + align:start position:0% +a the Euro area to go through a a sort + + + align:start position:0% +a the Euro area to go through a a sort +of a more prolonged periods of hiking + + align:start position:0% +of a more prolonged periods of hiking + + + align:start position:0% +of a more prolonged periods of hiking +interest rate hiking Japan hasn't had + + align:start position:0% +interest rate hiking Japan hasn't had + + + align:start position:0% +interest rate hiking Japan hasn't had +hikes in interest rates for three three + + align:start position:0% +hikes in interest rates for three three + + + align:start position:0% +hikes in interest rates for three three +decades but even now you start you begin + + align:start position:0% +decades but even now you start you begin + + + align:start position:0% +decades but even now you start you begin +to see some you know the scale here is + + align:start position:0% +to see some you know the scale here is + + + align:start position:0% +to see some you know the scale here is +very small these are a few basis points + + align:start position:0% +very small these are a few basis points + + + align:start position:0% +very small these are a few basis points +but even the point I'm trying to make is + + align:start position:0% +but even the point I'm trying to make is + + + align:start position:0% +but even the point I'm trying to make is +that certainly people expect interest + + align:start position:0% +that certainly people expect interest + + + align:start position:0% +that certainly people expect interest +rates in the US to go down relative to + + align:start position:0% +rates in the US to go down relative to + + + align:start position:0% +rates in the US to go down relative to +interest rates in Japan not to say say + + align:start position:0% +interest rates in Japan not to say say + + + align:start position:0% +interest rates in Japan not to say say +that the interest rate in the US will be + + align:start position:0% +that the interest rate in the US will be + + + align:start position:0% +that the interest rate in the US will be +lower than the interest rate in Japan + + align:start position:0% +lower than the interest rate in Japan + + + align:start position:0% +lower than the interest rate in Japan +but the direction of the change isn't + + align:start position:0% +but the direction of the change isn't + + + align:start position:0% +but the direction of the change isn't +that way so relative to where we're at + + align:start position:0% +that way so relative to where we're at + + + align:start position:0% +that way so relative to where we're at +now the direction of the change is is is + + align:start position:0% +now the direction of the change is is is + + + align:start position:0% +now the direction of the change is is is +is towards the US loosening monetary + + align:start position:0% +is towards the US loosening monetary + + + align:start position:0% +is towards the US loosening monetary +policy H before the rest of the world + + align:start position:0% +policy H before the rest of the world + + + align:start position:0% +policy H before the rest of the world +does okay and and that's what is leading + + align:start position:0% +does okay and and that's what is leading + + + align:start position:0% +does okay and and that's what is leading +to this big + + align:start position:0% +to this big + + + align:start position:0% +to this big +swings as I said before you know this is + + align:start position:0% +swings as I said before you know this is + + + align:start position:0% +swings as I said before you know this is +a period in which the US had to start + + align:start position:0% +a period in which the US had to start + + + align:start position:0% +a period in which the US had to start +tightening before the rest and and the + + align:start position:0% +tightening before the rest and and the + + + align:start position:0% +tightening before the rest and and the +currency appreciated a lot especially + + align:start position:0% +currency appreciated a lot especially + + + align:start position:0% +currency appreciated a lot especially +with respect to the Yen because again + + align:start position:0% +with respect to the Yen because again + + + align:start position:0% +with respect to the Yen because again +the Yen has been against the zero lower + + align:start position:0% +the Yen has been against the zero lower + + + align:start position:0% +the Yen has been against the zero lower +Bound for a very long time so nobody + + align:start position:0% +Bound for a very long time so nobody + + + align:start position:0% +Bound for a very long time so nobody +expected the yen to move to follow the + + align:start position:0% +expected the yen to move to follow the + + + align:start position:0% +expected the yen to move to follow the +US and and and while with respect to + + align:start position:0% +US and and and while with respect to + + + align:start position:0% +US and and and while with respect to +Europe well Europe was having + + align:start position:0% +Europe well Europe was having + + + align:start position:0% +Europe well Europe was having +inflationary problems and so on as well + + align:start position:0% +inflationary problems and so on as well + + + align:start position:0% +inflationary problems and so on as well +so people expected it to follow the us + + align:start position:0% +so people expected it to follow the us + + + align:start position:0% +so people expected it to follow the us +at some point for Japan there was + + align:start position:0% +at some point for Japan there was + + + align:start position:0% +at some point for Japan there was +nothing like that and that's what led to + + align:start position:0% +nothing like that and that's what led to + + + align:start position:0% +nothing like that and that's what led to +the massive depreciation of the Gen + + align:start position:0% +the massive depreciation of the Gen + + + align:start position:0% +the massive depreciation of the Gen +appreciation of the US dollar Visa gen + + align:start position:0% +appreciation of the US dollar Visa gen + + + align:start position:0% +appreciation of the US dollar Visa gen +okay so what we the Mandel flaming model + + align:start position:0% +okay so what we the Mandel flaming model + + + align:start position:0% +okay so what we the Mandel flaming model +is about is about first connecting these + + align:start position:0% +is about is about first connecting these + + + align:start position:0% +is about is about first connecting these +things trying to understand what moves + + align:start position:0% +things trying to understand what moves + + + align:start position:0% +things trying to understand what moves +exchange rate how the different monetary + + align:start position:0% +exchange rate how the different monetary + + + align:start position:0% +exchange rate how the different monetary +policies in different places or + + align:start position:0% +policies in different places or + + + align:start position:0% +policies in different places or +different policies in different places + + align:start position:0% +different policies in different places + + + align:start position:0% +different policies in different places +of the world affect exchange rate and + + align:start position:0% +of the world affect exchange rate and + + + align:start position:0% +of the world affect exchange rate and +then it's about understanding how those + + align:start position:0% +then it's about understanding how those + + + align:start position:0% +then it's about understanding how those +exchange rate movements affect real + + align:start position:0% +exchange rate movements affect real + + + align:start position:0% +exchange rate movements affect real +activity okay in the short run that's + + align:start position:0% +activity okay in the short run that's + + + align:start position:0% +activity okay in the short run that's +what the Mandel flaming model is so it + + align:start position:0% +what the Mandel flaming model is so it + + + align:start position:0% +what the Mandel flaming model is so it +is really we're going to go back to our + + align:start position:0% +is really we're going to go back to our + + + align:start position:0% +is really we're going to go back to our +old islm model very short run we're + + align:start position:0% +old islm model very short run we're + + + align:start position:0% +old islm model very short run we're +going to even fix nominal prices and so + + align:start position:0% +going to even fix nominal prices and so + + + align:start position:0% +going to even fix nominal prices and so +on so back to that environment but we're + + align:start position:0% +on so back to that environment but we're + + + align:start position:0% +on so back to that environment but we're +going to do in an open economy so we're + + align:start position:0% +going to do in an open economy so we're + + + align:start position:0% +going to do in an open economy so we're +going to have a new variable floating + + align:start position:0% +going to have a new variable floating + + + align:start position:0% +going to have a new variable floating +around which is the exchange rate and + + align:start position:0% +around which is the exchange rate and + + + align:start position:0% +around which is the exchange rate and +and and we need to understand how the + + align:start position:0% +and and we need to understand how the + + + align:start position:0% +and and we need to understand how the +exchange rate moves when you different + + align:start position:0% +exchange rate moves when you different + + + align:start position:0% +exchange rate moves when you different +things happen in different countries and + + align:start position:0% +things happen in different countries and + + + align:start position:0% +things happen in different countries and +the and and what is the impact of that + + align:start position:0% +the and and what is the impact of that + + + align:start position:0% +the and and what is the impact of that +on aggregate demand and hence in on + + align:start position:0% +on aggregate demand and hence in on + + + align:start position:0% +on aggregate demand and hence in on +output we're talking about the very + + align:start position:0% +output we're talking about the very + + + align:start position:0% +output we're talking about the very +short run in the different parts of the + + align:start position:0% +short run in the different parts of the + + + align:start position:0% +short run in the different parts of the +world okay so that's a plan that's what + + align:start position:0% +world okay so that's a plan that's what + + + align:start position:0% +world okay so that's a plan that's what +we intend to do so let's start with the + + align:start position:0% +we intend to do so let's start with the + + + align:start position:0% +we intend to do so let's start with the +this Mandel flaming model remember we we + + align:start position:0% +this Mandel flaming model remember we we + + + align:start position:0% +this Mandel flaming model remember we we +wrote down the equilibrium in the Goods + + align:start position:0% +wrote down the equilibrium in the Goods + + + align:start position:0% +wrote down the equilibrium in the Goods +Market Market in the previous lecture + + align:start position:0% +Market Market in the previous lecture + + + align:start position:0% +Market Market in the previous lecture +and and and that's that's I'm just + + align:start position:0% +and and and that's that's I'm just + + + align:start position:0% +and and and that's that's I'm just +reproducing what I wrote in the previous + + align:start position:0% +reproducing what I wrote in the previous + + + align:start position:0% +reproducing what I wrote in the previous +lecture so it looks exactly like the + + align:start position:0% +lecture so it looks exactly like the + + + align:start position:0% +lecture so it looks exactly like the +close economy output is be determined by + + align:start position:0% +close economy output is be determined by + + + align:start position:0% +close economy output is be determined by +aggregate demand but it's aggregate + + align:start position:0% +aggregate demand but it's aggregate + + + align:start position:0% +aggregate demand but it's aggregate +demand for domestically produced Goods + + align:start position:0% +demand for domestically produced Goods + + + align:start position:0% +demand for domestically produced Goods +domestic produced Goods is now the is + + align:start position:0% +domestic produced Goods is now the is + + + align:start position:0% +domestic produced Goods is now the is +not the same as domestic demand for + + align:start position:0% +not the same as domestic demand for + + + align:start position:0% +not the same as domestic demand for +goods which is this because now there's + + align:start position:0% +goods which is this because now there's + + + align:start position:0% +goods which is this because now there's +a net export term so part of the things + + align:start position:0% +a net export term so part of the things + + + align:start position:0% +a net export term so part of the things +that that residents sort of demand they + + align:start position:0% +that that residents sort of demand they + + + align:start position:0% +that that residents sort of demand they +they demand from the rest of the world + + align:start position:0% +they demand from the rest of the world + + + align:start position:0% +they demand from the rest of the world +not from Dom domestic producers and at + + align:start position:0% +not from Dom domestic producers and at + + + align:start position:0% +not from Dom domestic producers and at +the same time part of the amount + + align:start position:0% +the same time part of the amount + + + align:start position:0% +the same time part of the amount +perceived by domestic producers comes + + align:start position:0% +perceived by domestic producers comes + + + align:start position:0% +perceived by domestic producers comes +from the rest of the world from exports + + align:start position:0% +from the rest of the world from exports + + + align:start position:0% +from the rest of the world from exports +not from domestic producers so that's + + align:start position:0% +not from domestic producers so that's + + + align:start position:0% +not from domestic producers so that's +the reason we got an extra term here + + align:start position:0% +the reason we got an extra term here + + + align:start position:0% +the reason we got an extra term here +which is this net exports and we said + + align:start position:0% +which is this net exports and we said + + + align:start position:0% +which is this net exports and we said +this net exports is a function of three + + align:start position:0% +this net exports is a function of three + + + align:start position:0% +this net exports is a function of three +things it's a function of + + align:start position:0% +things it's a function of + + + align:start position:0% +things it's a function of +output + + align:start position:0% +output + + + align:start position:0% +output +okay and it's a it's a decreasing + + align:start position:0% +okay and it's a it's a decreasing + + + align:start position:0% +okay and it's a it's a decreasing +function of output why is that of + + align:start position:0% +function of output why is that of + + + align:start position:0% +function of output why is that of +domestic + + align:start position:0% + + + + align:start position:0% + +output domestic output domestic income + + align:start position:0% +output domestic output domestic income + + + align:start position:0% +output domestic output domestic income +why is it a decreasing function of + + align:start position:0% +why is it a decreasing function of + + + align:start position:0% +why is it a decreasing function of +domestic + + align:start position:0% + + + + align:start position:0% + +income why do net exports decline when + + align:start position:0% +income why do net exports decline when + + + align:start position:0% +income why do net exports decline when +domestic income + + align:start position:0% + + + + align:start position:0% + +Rises import they they import more they + + align:start position:0% +Rises import they they import more they + + + align:start position:0% +Rises import they they import more they +consume everything more but part of that + + align:start position:0% +consume everything more but part of that + + + align:start position:0% +consume everything more but part of that +is import and so part of that energy of + + align:start position:0% +is import and so part of that energy of + + + align:start position:0% +is import and so part of that energy of +the extra demand goes to foreign goods + + align:start position:0% +the extra demand goes to foreign goods + + + align:start position:0% +the extra demand goes to foreign goods +and that's what deteriorates net exports + + align:start position:0% +and that's what deteriorates net exports + + + align:start position:0% +and that's what deteriorates net exports +okay and that's the reason with had had + + align:start position:0% +okay and that's the reason with had had + + + align:start position:0% +okay and that's the reason with had had +we just stopped there made the net + + align:start position:0% +we just stopped there made the net + + + align:start position:0% +we just stopped there made the net +export function just a function of + + align:start position:0% +export function just a function of + + + align:start position:0% +export function just a function of +output we would have not needed all + + align:start position:0% +output we would have not needed all + + + align:start position:0% +output we would have not needed all +these extra Paratus that I'm about to + + align:start position:0% +these extra Paratus that I'm about to + + + align:start position:0% +these extra Paratus that I'm about to +build because all that would have meant + + align:start position:0% +build because all that would have meant + + + align:start position:0% +build because all that would have meant +is that just we have a smaller + + align:start position:0% +is that just we have a smaller + + + align:start position:0% +is that just we have a smaller +multiplier it would have been exactly + + align:start position:0% +multiplier it would have been exactly + + + align:start position:0% +multiplier it would have been exactly +the same as we did in the close economy + + align:start position:0% +the same as we did in the close economy + + + align:start position:0% +the same as we did in the close economy +but with a smaller multiplier because + + align:start position:0% +but with a smaller multiplier because + + + align:start position:0% +but with a smaller multiplier because +you know every time output goes up now + + align:start position:0% +you know every time output goes up now + + + align:start position:0% +you know every time output goes up now +part of the demand goes to foreign Goods + + align:start position:0% +part of the demand goes to foreign Goods + + + align:start position:0% +part of the demand goes to foreign Goods +rather than domestic + + align:start position:0% +rather than domestic + + + align:start position:0% +rather than domestic +Goods but it's not + + align:start position:0% +Goods but it's not + + + align:start position:0% +Goods but it's not +so first because we have an extra + + align:start position:0% +so first because we have an extra + + + align:start position:0% +so first because we have an extra +another in income that matters here + + align:start position:0% +another in income that matters here + + + align:start position:0% +another in income that matters here +which is the income of the rest of the + + align:start position:0% +which is the income of the rest of the + + + align:start position:0% +which is the income of the rest of the +world but more important because we also + + align:start position:0% +world but more important because we also + + + align:start position:0% +world but more important because we also +have an exchanger but let's start from + + align:start position:0% +have an exchanger but let's start from + + + align:start position:0% +have an exchanger but let's start from +this sign so net export is increasing in + + align:start position:0% +this sign so net export is increasing in + + + align:start position:0% +this sign so net export is increasing in +the income of the rest of the world why + + align:start position:0% +the income of the rest of the world why + + + align:start position:0% +the income of the rest of the world why +is + + align:start position:0% + + + + align:start position:0% + +that that this demand for domestically + + align:start position:0% +that that this demand for domestically + + + align:start position:0% +that that this demand for domestically +produced good Rises when foreign income + + align:start position:0% +produced good Rises when foreign income + + + align:start position:0% +produced good Rises when foreign income +goes + + align:start position:0% +goes + + + align:start position:0% +goes +up foreign output foreign income goes up + + align:start position:0% +up foreign output foreign income goes up + + + align:start position:0% +up foreign output foreign income goes up +why is + + align:start position:0% + + + + align:start position:0% + +that it's a symmetric argument no if + + align:start position:0% +that it's a symmetric argument no if + + + align:start position:0% +that it's a symmetric argument no if +with with Imports well our exports are + + align:start position:0% +with with Imports well our exports are + + + align:start position:0% +with with Imports well our exports are +the Imports of the other country so if + + align:start position:0% +the Imports of the other country so if + + + align:start position:0% +the Imports of the other country so if +the income in the other country goes up + + align:start position:0% +the income in the other country goes up + + + align:start position:0% +the income in the other country goes up +then their their Imports will go up + + align:start position:0% +then their their Imports will go up + + + align:start position:0% +then their their Imports will go up +which is our exports that go up that's + + align:start position:0% +which is our exports that go up that's + + + align:start position:0% +which is our exports that go up that's +the reason n + + align:start position:0% +the reason n + + + align:start position:0% +the reason n +exports goes + + align:start position:0% +exports goes + + + align:start position:0% +exports goes +up and the last term remember is that + + align:start position:0% +up and the last term remember is that + + + align:start position:0% +up and the last term remember is that +says that net exports is declining on + + align:start position:0% +says that net exports is declining on + + + align:start position:0% +says that net exports is declining on +the real exchange rate + + align:start position:0% +the real exchange rate + + + align:start position:0% +the real exchange rate +why is + + align:start position:0% + + + + align:start position:0% + +that what happen when the real exchanger + + align:start position:0% +that what happen when the real exchanger + + + align:start position:0% +that what happen when the real exchanger +goes up it makes our Goods more + + align:start position:0% +goes up it makes our Goods more + + + align:start position:0% +goes up it makes our Goods more +expensive relative to foreign Goods + + align:start position:0% +expensive relative to foreign Goods + + + align:start position:0% +expensive relative to foreign Goods +exactly our Goods become more expensive + + align:start position:0% +exactly our Goods become more expensive + + + align:start position:0% +exactly our Goods become more expensive +relative to foreign good and that + + align:start position:0% +relative to foreign good and that + + + align:start position:0% +relative to foreign good and that +affects us from two Dimensions first our + + align:start position:0% +affects us from two Dimensions first our + + + align:start position:0% +affects us from two Dimensions first our +exports will tend to decline because our + + align:start position:0% +exports will tend to decline because our + + + align:start position:0% +exports will tend to decline because our +goods are more expensive and also our + + align:start position:0% +goods are more expensive and also our + + + align:start position:0% +goods are more expensive and also our +Imports are going to tend to increase + + align:start position:0% +Imports are going to tend to increase + + + align:start position:0% +Imports are going to tend to increase +because foreign goods are cheaper okay + + align:start position:0% +because foreign goods are cheaper okay + + + align:start position:0% +because foreign goods are cheaper okay +and so that's the reason this is + + align:start position:0% +and so that's the reason this is + + + align:start position:0% +and so that's the reason this is +decreasing with respect to the exchange + + align:start position:0% +decreasing with respect to the exchange + + + align:start position:0% +decreasing with respect to the exchange +the big thing of the Mandel flaming + + align:start position:0% +the big thing of the Mandel flaming + + + align:start position:0% +the big thing of the Mandel flaming +model really comes from the fact that + + align:start position:0% +model really comes from the fact that + + + align:start position:0% +model really comes from the fact that +this guy is there we had we not had the + + align:start position:0% +this guy is there we had we not had the + + + align:start position:0% +this guy is there we had we not had the +exchange rate there again we could have + + align:start position:0% +exchange rate there again we could have + + + align:start position:0% +exchange rate there again we could have +used exactly the same apparatus as we + + align:start position:0% +used exactly the same apparatus as we + + + align:start position:0% +used exactly the same apparatus as we +used earlier on but we're going to have + + align:start position:0% +used earlier on but we're going to have + + + align:start position:0% +used earlier on but we're going to have +an exchange rate floating around and + + align:start position:0% +an exchange rate floating around and + + + align:start position:0% +an exchange rate floating around and +that will require us that to to build + + align:start position:0% +that will require us that to to build + + + align:start position:0% +that will require us that to to build +more a little more we need an extra + + align:start position:0% +more a little more we need an extra + + + align:start position:0% +more a little more we need an extra +equation you know because we have an + + align:start position:0% +equation you know because we have an + + + align:start position:0% +equation you know because we have an +extra endogenous variable now what I'm + + align:start position:0% +extra endogenous variable now what I'm + + + align:start position:0% +extra endogenous variable now what I'm +going to assume here as we did in the + + align:start position:0% +going to assume here as we did in the + + + align:start position:0% +going to assume here as we did in the +first part of the course is that both + + align:start position:0% +first part of the course is that both + + + align:start position:0% +first part of the course is that both +the domestic and foreign prices are + + align:start position:0% +the domestic and foreign prices are + + + align:start position:0% +the domestic and foreign prices are +completely fixed so I'm going to ignore + + align:start position:0% +completely fixed so I'm going to ignore + + + align:start position:0% +completely fixed so I'm going to ignore +Philips curve inflation expected + + align:start position:0% +Philips curve inflation expected + + + align:start position:0% +Philips curve inflation expected +inflation and all that okay assume all + + align:start position:0% +inflation and all that okay assume all + + + align:start position:0% +inflation and all that okay assume all +that is zero expected inflation + + align:start position:0% +that is zero expected inflation + + + align:start position:0% +that is zero expected inflation +inflation zero when I do that the same + + align:start position:0% +inflation zero when I do that the same + + + align:start position:0% +inflation zero when I do that the same +equation the equilibrium in the goods + + align:start position:0% +equation the equilibrium in the goods + + + align:start position:0% +equation the equilibrium in the goods +markets changes a little bit I mean it's + + align:start position:0% +markets changes a little bit I mean it's + + + align:start position:0% +markets changes a little bit I mean it's +the same equation but now I don't need + + align:start position:0% +the same equation but now I don't need + + + align:start position:0% +the same equation but now I don't need +to differentiate between real interest + + align:start position:0% +to differentiate between real interest + + + align:start position:0% +to differentiate between real interest +rate and nominal interest rate because + + align:start position:0% +rate and nominal interest rate because + + + align:start position:0% +rate and nominal interest rate because +inflation is zero so nominal interest is + + align:start position:0% +inflation is zero so nominal interest is + + + align:start position:0% +inflation is zero so nominal interest is +equal to the real interest rate so I'm + + align:start position:0% +equal to the real interest rate so I'm + + + align:start position:0% +equal to the real interest rate so I'm +going to stick in here the nominal + + align:start position:0% +going to stick in here the nominal + + + align:start position:0% +going to stick in here the nominal +interest rate second I really don't need + + align:start position:0% +interest rate second I really don't need + + + align:start position:0% +interest rate second I really don't need +to differentiate between real exchange + + align:start position:0% +to differentiate between real exchange + + + align:start position:0% +to differentiate between real exchange +rate and nominal exchange rate because + + align:start position:0% +rate and nominal exchange rate because + + + align:start position:0% +rate and nominal exchange rate because +the relative prices the prices + + align:start position:0% +the relative prices the prices + + + align:start position:0% +the relative prices the prices +themselves are not changing and so all + + align:start position:0% +themselves are not changing and so all + + + align:start position:0% +themselves are not changing and so all +that will move the the re exchang is the + + align:start position:0% +that will move the the re exchang is the + + + align:start position:0% +that will move the the re exchang is the +nominal exchanger okay so that's the + + align:start position:0% +nominal exchanger okay so that's the + + + align:start position:0% +nominal exchanger okay so that's the +reason I'm going to write here the the + + align:start position:0% +reason I'm going to write here the the + + + align:start position:0% +reason I'm going to write here the the +nominal exchange rate is because it's + + align:start position:0% +nominal exchange rate is because it's + + + align:start position:0% +nominal exchange rate is because it's +the only thing that will move this + + align:start position:0% +the only thing that will move this + + + align:start position:0% +the only thing that will move this +variable around given that prices are + + align:start position:0% +variable around given that prices are + + + align:start position:0% +variable around given that prices are +fixed okay so that's my our equilibrium + + align:start position:0% +fixed okay so that's my our equilibrium + + + align:start position:0% +fixed okay so that's my our equilibrium +in the Goods Market and this is a thing + + align:start position:0% +in the Goods Market and this is a thing + + + align:start position:0% +in the Goods Market and this is a thing +you need to compare with you know + + align:start position:0% +you need to compare with you know + + + align:start position:0% +you need to compare with you know +lecture three or something like that and + + align:start position:0% +lecture three or something like that and + + + align:start position:0% +lecture three or something like that and +as I said this part here only lowers the + + align:start position:0% +as I said this part here only lowers the + + + align:start position:0% +as I said this part here only lowers the +multiplier so not a big change this one + + align:start position:0% +multiplier so not a big change this one + + + align:start position:0% +multiplier so not a big change this one +here is an extra parameter that shift + + align:start position:0% +here is an extra parameter that shift + + + align:start position:0% +here is an extra parameter that shift +agre demand up and down so you can treat + + align:start position:0% +agre demand up and down so you can treat + + + align:start position:0% +agre demand up and down so you can treat +it almost like we treated c0 remember if + + align:start position:0% +it almost like we treated c0 remember if + + + align:start position:0% +it almost like we treated c0 remember if +the consumer confident goes up then + + align:start position:0% +the consumer confident goes up then + + + align:start position:0% +the consumer confident goes up then +aggre demand goes up well here we have + + align:start position:0% +aggre demand goes up well here we have + + + align:start position:0% +aggre demand goes up well here we have +sort of the rest of the walls output + + align:start position:0% +sort of the rest of the walls output + + + align:start position:0% +sort of the rest of the walls output +goes up it does exactly the same the + + align:start position:0% +goes up it does exactly the same the + + + align:start position:0% +goes up it does exactly the same the +same analysis the problem we have though + + align:start position:0% +same analysis the problem we have though + + + align:start position:0% +same analysis the problem we have though +is that we have an extra variable here + + align:start position:0% +is that we have an extra variable here + + + align:start position:0% +is that we have an extra variable here +which is the exchange rate and that's an + + align:start position:0% +which is the exchange rate and that's an + + + align:start position:0% +which is the exchange rate and that's an +endogenous variable okay so we're going + + align:start position:0% +endogenous variable okay so we're going + + + align:start position:0% +endogenous variable okay so we're going +to have to come up with some other + + align:start position:0% +to have to come up with some other + + + align:start position:0% +to have to come up with some other +equation to solve for that equation here + + align:start position:0% +equation to solve for that equation here + + + align:start position:0% +equation to solve for that equation here +in in lecture three or four what we did + + align:start position:0% +in in lecture three or four what we did + + + align:start position:0% +in in lecture three or four what we did +is okay we said we have two endogenous + + align:start position:0% +is okay we said we have two endogenous + + + align:start position:0% +is okay we said we have two endogenous +variable output and the interest rate + + align:start position:0% +variable output and the interest rate + + + align:start position:0% +variable output and the interest rate +output and the interest rate we need one + + align:start position:0% +output and the interest rate we need one + + + align:start position:0% +output and the interest rate we need one +more equation well the other equation + + align:start position:0% +more equation well the other equation + + + align:start position:0% +more equation well the other equation +was just monetary policy that set the + + align:start position:0% +was just monetary policy that set the + + + align:start position:0% +was just monetary policy that set the +nominal interest rate here that's not + + align:start position:0% +nominal interest rate here that's not + + + align:start position:0% +nominal interest rate here that's not +going to be enough because we also have + + align:start position:0% +going to be enough because we also have + + + align:start position:0% +going to be enough because we also have +an exchange floting okay so and we need + + align:start position:0% +an exchange floting okay so and we need + + + align:start position:0% +an exchange floting okay so and we need +to bring another equation here er er to + + align:start position:0% +to bring another equation here er er to + + + align:start position:0% +to bring another equation here er er to +deal with this this new endogenous + + align:start position:0% +deal with this this new endogenous + + + align:start position:0% +deal with this this new endogenous +variable what is that extra + + align:start position:0% +variable what is that extra + + + align:start position:0% +variable what is that extra +equation well is the uncovering + + align:start position:0% +equation well is the uncovering + + + align:start position:0% +equation well is the uncovering +transparity condition remember it's the + + align:start position:0% +transparity condition remember it's the + + + align:start position:0% +transparity condition remember it's the +last expression we had in in in the + + align:start position:0% +last expression we had in in in the + + + align:start position:0% +last expression we had in in in the +previous + + align:start position:0% +previous + + + align:start position:0% +previous +lecture H that takes this + + align:start position:0% +lecture H that takes this + + + align:start position:0% +lecture H that takes this +form okay it + + align:start position:0% +form okay it + + + align:start position:0% +form okay it +says I before I simplify lots of things + + align:start position:0% +says I before I simplify lots of things + + + align:start position:0% +says I before I simplify lots of things +I wrote this down and it says that the + + align:start position:0% +I wrote this down and it says that the + + + align:start position:0% +I wrote this down and it says that the +exchange rate is um is equal to to that + + align:start position:0% +exchange rate is um is equal to to that + + + align:start position:0% +exchange rate is um is equal to to that +okay now what what is this where does + + align:start position:0% +okay now what what is this where does + + + align:start position:0% +okay now what what is this where does +this equation come + + align:start position:0% +this equation come + + + align:start position:0% +this equation come +from what is it trying to + + align:start position:0% +from what is it trying to + + + align:start position:0% +from what is it trying to +do remember we talk we we talk about + + align:start position:0% +do remember we talk we we talk about + + + align:start position:0% +do remember we talk we we talk about +this in the context and say well you + + align:start position:0% +this in the context and say well you + + + align:start position:0% +this in the context and say well you +know when you open Goods markets then + + align:start position:0% +know when you open Goods markets then + + + align:start position:0% +know when you open Goods markets then +you need a relative price to decide + + align:start position:0% +you need a relative price to decide + + + align:start position:0% +you need a relative price to decide +where you're going to buy that's what + + align:start position:0% +where you're going to buy that's what + + + align:start position:0% +where you're going to buy that's what +what a ER the real exchange did and and + + align:start position:0% +what a ER the real exchange did and and + + + align:start position:0% +what a ER the real exchange did and and +and now then then we open the capital + + align:start position:0% +and now then then we open the capital + + + align:start position:0% +and now then then we open the capital +account and then you need to people need + + align:start position:0% +account and then you need to people need + + + align:start position:0% +account and then you need to people need +to decide where they're going to invest + + align:start position:0% +to decide where they're going to invest + + + align:start position:0% +to decide where they're going to invest +money and that equation was related to + + align:start position:0% +money and that equation was related to + + + align:start position:0% +money and that equation was related to +that expected return has to be the same + + align:start position:0% +that expected return has to be the same + + + align:start position:0% +that expected return has to be the same +like exactly it's what equalizes the + + align:start position:0% +like exactly it's what equalizes the + + + align:start position:0% +like exactly it's what equalizes the +Spector rate of an equilibrium that has + + align:start position:0% +Spector rate of an equilibrium that has + + + align:start position:0% +Spector rate of an equilibrium that has +to happen okay again in reality there is + + align:start position:0% +to happen okay again in reality there is + + + align:start position:0% +to happen okay again in reality there is +risk adjustment there's lots of other + + align:start position:0% +risk adjustment there's lots of other + + + align:start position:0% +risk adjustment there's lots of other +factors that we're removing from here + + align:start position:0% +factors that we're removing from here + + + align:start position:0% +factors that we're removing from here +but absent those other factors the the + + align:start position:0% +but absent those other factors the the + + + align:start position:0% +but absent those other factors the the +returns have to be similar in both + + align:start position:0% +returns have to be similar in both + + + align:start position:0% +returns have to be similar in both +places because if one asset is given + + align:start position:0% +places because if one asset is given + + + align:start position:0% +places because if one asset is given +more return than the other expected + + align:start position:0% +more return than the other expected + + + align:start position:0% +more return than the other expected +return then then then people are going + + align:start position:0% +return then then then people are going + + + align:start position:0% +return then then then people are going +to invest all the portfolios in that + + align:start position:0% +to invest all the portfolios in that + + + align:start position:0% +to invest all the portfolios in that +asset and what happens is those flows + + align:start position:0% +asset and what happens is those flows + + + align:start position:0% +asset and what happens is those flows +that try to go to the those assets that + + align:start position:0% +that try to go to the those assets that + + + align:start position:0% +that try to go to the those assets that +give the highest return end up + + align:start position:0% +give the highest return end up + + + align:start position:0% +give the highest return end up +equalizing expected return in + + align:start position:0% +equalizing expected return in + + + align:start position:0% +equalizing expected return in +equilibrium and that's equation that + + align:start position:0% +equilibrium and that's equation that + + + align:start position:0% +equilibrium and that's equation that +does that exactly that how do I know + + align:start position:0% +does that exactly that how do I know + + + align:start position:0% +does that exactly that how do I know +that well remember h i can divide this + + align:start position:0% +that well remember h i can divide this + + + align:start position:0% +that well remember h i can divide this +by the exchange rate on both sides and + + align:start position:0% +by the exchange rate on both sides and + + + align:start position:0% +by the exchange rate on both sides and +then what you get is one equal to a + + align:start position:0% +then what you get is one equal to a + + + align:start position:0% +then what you get is one equal to a +numerator that has the nominal exchange + + align:start position:0% +numerator that has the nominal exchange + + + align:start position:0% +numerator that has the nominal exchange +rate times the expected appreciation of + + align:start position:0% +rate times the expected appreciation of + + + align:start position:0% +rate times the expected appreciation of +the currency Plus + + align:start position:0% +the currency Plus + + + align:start position:0% +the currency Plus +and in the denominator you have the the + + align:start position:0% +and in the denominator you have the the + + + align:start position:0% +and in the denominator you have the the +the foreign interest rate and so you + + align:start position:0% +the foreign interest rate and so you + + + align:start position:0% +the foreign interest rate and so you +have to when you compare the two you + + align:start position:0% +have to when you compare the two you + + + align:start position:0% +have to when you compare the two you +have to compare one base interest rate + + align:start position:0% +have to compare one base interest rate + + + align:start position:0% +have to compare one base interest rate +either the domestic or the foreign plus + + align:start position:0% +either the domestic or the foreign plus + + + align:start position:0% +either the domestic or the foreign plus +expected appreciation or depreciation of + + align:start position:0% +expected appreciation or depreciation of + + + align:start position:0% +expected appreciation or depreciation of +that currency and that's what this term + + align:start position:0% +that currency and that's what this term + + + align:start position:0% +that currency and that's what this term +is doing here this divided by that + + align:start position:0% +is doing here this divided by that + + + align:start position:0% +is doing here this divided by that +okay good so what do we get out of this + + align:start position:0% +okay good so what do we get out of this + + + align:start position:0% +okay good so what do we get out of this +uh one thing we're going to do for for + + align:start position:0% +uh one thing we're going to do for for + + + align:start position:0% +uh one thing we're going to do for for +quite a while because it will simplify + + align:start position:0% +quite a while because it will simplify + + + align:start position:0% +quite a while because it will simplify +things a lot but sometimes also lead to + + align:start position:0% +things a lot but sometimes also lead to + + + align:start position:0% +things a lot but sometimes also lead to +confusion in in in in + + align:start position:0% +confusion in in in in + + + align:start position:0% +confusion in in in in +in in the way we understand why Curren + + align:start position:0% +in in the way we understand why Curren + + + align:start position:0% +in in the way we understand why Curren +is depreciated or appreciate but we + + align:start position:0% +is depreciated or appreciate but we + + + align:start position:0% +is depreciated or appreciate but we +we'll pause and I'll remind you of this + + align:start position:0% +we'll pause and I'll remind you of this + + + align:start position:0% +we'll pause and I'll remind you of this +repeatedly we're going to assume for now + + align:start position:0% +repeatedly we're going to assume for now + + + align:start position:0% +repeatedly we're going to assume for now +that the expected exchange rate for t+ + + align:start position:0% +that the expected exchange rate for t+ + + + align:start position:0% +that the expected exchange rate for t+ +one is + + align:start position:0% +one is + + + align:start position:0% +one is +fixed okay and and until I tell you + + align:start position:0% +fixed okay and and until I tell you + + + align:start position:0% +fixed okay and and until I tell you +otherwise we're going to make this + + align:start position:0% + + + + align:start position:0% + +assumption now that's a huge + + align:start position:0% +assumption now that's a huge + + + align:start position:0% +assumption now that's a huge +simplification completely unrealistic + + align:start position:0% +simplification completely unrealistic + + + align:start position:0% +simplification completely unrealistic +and so on but it will help me explain + + align:start position:0% +and so on but it will help me explain + + + align:start position:0% +and so on but it will help me explain +the mechanism I mean one of the things + + align:start position:0% +the mechanism I mean one of the things + + + align:start position:0% +the mechanism I mean one of the things +that moves exchang a lot is that people + + align:start position:0% +that moves exchang a lot is that people + + + align:start position:0% +that moves exchang a lot is that people +have lots of expectations about future + + align:start position:0% +have lots of expectations about future + + + align:start position:0% +have lots of expectations about future +exchange rate we'll get to that later + + align:start position:0% +exchange rate we'll get to that later + + + align:start position:0% +exchange rate we'll get to that later +but for now so you understand the + + align:start position:0% +but for now so you understand the + + + align:start position:0% +but for now so you understand the +mechanism how the Mandel flaming mod + + align:start position:0% +mechanism how the Mandel flaming mod + + + align:start position:0% +mechanism how the Mandel flaming mod +works I'm going to assume that we all + + align:start position:0% +works I'm going to assume that we all + + + align:start position:0% +works I'm going to assume that we all +know what the expected exchange rate we + + align:start position:0% +know what the expected exchange rate we + + + align:start position:0% +know what the expected exchange rate we +we all have a common expected exchange + + align:start position:0% +we all have a common expected exchange + + + align:start position:0% +we all have a common expected exchange +rate and it's + + align:start position:0% +rate and it's + + + align:start position:0% +rate and it's +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +okay we may move it as a parameter but I + + align:start position:0% +okay we may move it as a parameter but I + + + align:start position:0% +okay we may move it as a parameter but I +was trying to say I'm not going to + + align:start position:0% +was trying to say I'm not going to + + + align:start position:0% +was trying to say I'm not going to +endogenize that I'm going to take it as + + align:start position:0% +endogenize that I'm going to take it as + + + align:start position:0% +endogenize that I'm going to take it as +fixed and I I may move it around to show + + align:start position:0% +fixed and I I may move it around to show + + + align:start position:0% +fixed and I I may move it around to show +you what happens when that changes but + + align:start position:0% +you what happens when that changes but + + + align:start position:0% +you what happens when that changes but +I'm not going to endogenize it + + align:start position:0% +I'm not going to endogenize it + + + align:start position:0% +I'm not going to endogenize it +okay otherwise I need more equations one + + align:start position:0% +okay otherwise I need more equations one + + + align:start position:0% +okay otherwise I need more equations one +more I want to stop this this this + + align:start position:0% +more I want to stop this this this + + + align:start position:0% +more I want to stop this this this +sequence of equations that I would be + + align:start position:0% +sequence of equations that I would be + + + align:start position:0% +sequence of equations that I would be +have to build + + align:start position:0% +have to build + + + align:start position:0% +have to build +but later we'll understand more of that + + align:start position:0% +but later we'll understand more of that + + + align:start position:0% +but later we'll understand more of that +what I just said but but for now just + + align:start position:0% +what I just said but but for now just + + + align:start position:0% +what I just said but but for now just +take this as fixed so if I take this as + + align:start position:0% +take this as fixed so if I take this as + + + align:start position:0% +take this as fixed so if I take this as +fixed now I have an equation remember I + + align:start position:0% +fixed now I have an equation remember I + + + align:start position:0% +fixed now I have an equation remember I +was looking for an equation here for my + + align:start position:0% +was looking for an equation here for my + + + align:start position:0% +was looking for an equation here for my +exchange rate + + align:start position:0% +exchange rate + + + align:start position:0% +exchange rate +once I do that then I have what I want I + + align:start position:0% +once I do that then I have what I want I + + + align:start position:0% +once I do that then I have what I want I +have an equation from my exchange today + + align:start position:0% +have an equation from my exchange today + + + align:start position:0% +have an equation from my exchange today +it's just function of domestic interest + + align:start position:0% +it's just function of domestic interest + + + align:start position:0% +it's just function of domestic interest +rate International interest rate and the + + align:start position:0% +rate International interest rate and the + + + align:start position:0% +rate International interest rate and the +expected exchange rate okay so I know + + align:start position:0% +expected exchange rate okay so I know + + + align:start position:0% +expected exchange rate okay so I know +the following for example I know that an + + align:start position:0% +the following for example I know that an + + + align:start position:0% +the following for example I know that an +increase in the domestic interest rate + + align:start position:0% +increase in the domestic interest rate + + + align:start position:0% +increase in the domestic interest rate +other things equal appreciates exchange + + align:start position:0% +other things equal appreciates exchange + + + align:start position:0% +other things equal appreciates exchange +rate you know I can see it in the + + align:start position:0% +rate you know I can see it in the + + + align:start position:0% +rate you know I can see it in the +equation if I move the domestic interest + + align:start position:0% +equation if I move the domestic interest + + + align:start position:0% +equation if I move the domestic interest +rate up the exchanger goes up that's an + + align:start position:0% +rate up the exchanger goes up that's an + + + align:start position:0% +rate up the exchanger goes up that's an +appreciation the dollar becomes more + + align:start position:0% +appreciation the dollar becomes more + + + align:start position:0% +appreciation the dollar becomes more +expensive even simpler suppose we start + + align:start position:0% +expensive even simpler suppose we start + + + align:start position:0% +expensive even simpler suppose we start +with a situation in which the domestic + + align:start position:0% +with a situation in which the domestic + + + align:start position:0% +with a situation in which the domestic +and the international interest rate were + + align:start position:0% +and the international interest rate were + + + align:start position:0% +and the international interest rate were +the same and now I increase the + + align:start position:0% +the same and now I increase the + + + align:start position:0% +the same and now I increase the +international interest rate and I'm + + align:start position:0% +international interest rate and I'm + + + align:start position:0% +international interest rate and I'm +saying the exchanger will + + align:start position:0% +saying the exchanger will + + + align:start position:0% +saying the exchanger will +appreciate well first of + + align:start position:0% +appreciate well first of + + + align:start position:0% +appreciate well first of +all let let me start for something even + + align:start position:0% +all let let me start for something even + + + align:start position:0% +all let let me start for something even +simpler suppose that suppose that that + + align:start position:0% +simpler suppose that suppose that that + + + align:start position:0% +simpler suppose that suppose that that +this interest rate is equal to + + align:start position:0% +this interest rate is equal to + + + align:start position:0% +this interest rate is equal to +International interest rate before + + align:start position:0% +International interest rate before + + + align:start position:0% +International interest rate before +analyzing the change I'm about to + + align:start position:0% +analyzing the change I'm about to + + + align:start position:0% +analyzing the change I'm about to +analyze then from this equation what do + + align:start position:0% +analyze then from this equation what do + + + align:start position:0% +analyze then from this equation what do +I I know about the exchange rate what is + + align:start position:0% +I I know about the exchange rate what is + + + align:start position:0% +I I know about the exchange rate what is +it equal to if the domestic interest + + align:start position:0% +it equal to if the domestic interest + + + align:start position:0% +it equal to if the domestic interest +rate is equal to International interest + + align:start position:0% +rate is equal to International interest + + + align:start position:0% +rate is equal to International interest +rate what is the exchange rate today + + align:start position:0% +rate what is the exchange rate today + + + align:start position:0% +rate what is the exchange rate today +equal + + align:start position:0% + + + + align:start position:0% + +to the expected exchange next year if I + + align:start position:0% +to the expected exchange next year if I + + + align:start position:0% +to the expected exchange next year if I +have the same interest rates I cannot + + align:start position:0% +have the same interest rates I cannot + + + align:start position:0% +have the same interest rates I cannot +expect a capital gain or loss from the + + align:start position:0% +expect a capital gain or loss from the + + + align:start position:0% +expect a capital gain or loss from the +currency position because I have already + + align:start position:0% +currency position because I have already + + + align:start position:0% +currency position because I have already +an equal interest rate in the two bonds + + align:start position:0% +an equal interest rate in the two bonds + + + align:start position:0% +an equal interest rate in the two bonds +okay so then I'm starting from a + + align:start position:0% +okay so then I'm starting from a + + + align:start position:0% +okay so then I'm starting from a +situation where the current exchange + + align:start position:0% +situation where the current exchange + + + align:start position:0% +situation where the current exchange +rate is equal to the expected exchange + + align:start position:0% +rate is equal to the expected exchange + + + align:start position:0% +rate is equal to the expected exchange +rate and these two are equal and now I'm + + align:start position:0% +rate and these two are equal and now I'm + + + align:start position:0% +rate and these two are equal and now I'm +going to increase the interest rate the + + align:start position:0% +going to increase the interest rate the + + + align:start position:0% +going to increase the interest rate the +domestic interest rate and it's very + + align:start position:0% +domestic interest rate and it's very + + + align:start position:0% +domestic interest rate and it's very +easy for you to read from here that the + + align:start position:0% +easy for you to read from here that the + + + align:start position:0% +easy for you to read from here that the +exchanger will go up the currency will + + align:start position:0% +exchanger will go up the currency will + + + align:start position:0% +exchanger will go up the currency will +appreciate + + align:start position:0% +appreciate + + + align:start position:0% +appreciate +why this is not an easy thing to answer + + align:start position:0% +why this is not an easy thing to answer + + + align:start position:0% +why this is not an easy thing to answer +unless you know where unless you have + + align:start position:0% +unless you know where unless you have + + + align:start position:0% +unless you know where unless you have +read the book or + + align:start position:0% + + + + align:start position:0% + +something if the interest rate goes up + + align:start position:0% +something if the interest rate goes up + + + align:start position:0% +something if the interest rate goes up +then like money supply should go down + + align:start position:0% +then like money supply should go down + + + align:start position:0% +then like money supply should go down +which would generally increase the value + + align:start position:0% +which would generally increase the value + + + align:start position:0% +which would generally increase the value +of money no no money here + + align:start position:0% +of money no no money here + + + align:start position:0% +of money no no money here +that money is only related to the + + align:start position:0% +that money is only related to the + + + align:start position:0% +that money is only related to the +mechanism we use to increase interest + + align:start position:0% +mechanism we use to increase interest + + + align:start position:0% +mechanism we use to increase interest +rate but I'm saying just use that + + align:start position:0% +rate but I'm saying just use that + + + align:start position:0% +rate but I'm saying just use that +equation and the logic behind that + + align:start position:0% +equation and the logic behind that + + + align:start position:0% +equation and the logic behind that +equation the uncover parity why is it + + align:start position:0% +equation the uncover parity why is it + + + align:start position:0% +equation the uncover parity why is it +that if I you know we went to from a + + align:start position:0% +that if I you know we went to from a + + + align:start position:0% +that if I you know we went to from a +situation which inter were the same now + + align:start position:0% +situation which inter were the same now + + + align:start position:0% +situation which inter were the same now +I increase the domestic interest rate + + align:start position:0% +I increase the domestic interest rate + + + align:start position:0% +I increase the domestic interest rate +I'm saying the The Exchange has to + + align:start position:0% + + + + align:start position:0% + +appreciate no no but that's a + + align:start position:0% +appreciate no no but that's a + + + align:start position:0% +appreciate no no but that's a +description of yeah that's that we know + + align:start position:0% +description of yeah that's that we know + + + align:start position:0% +description of yeah that's that we know +that the question is work what is the + + align:start position:0% + + + + align:start position:0% + +logic yeah we we have we know the result + + align:start position:0% +logic yeah we we have we know the result + + + align:start position:0% +logic yeah we we have we know the result +what I'm asking is for an economic + + align:start position:0% +what I'm asking is for an economic + + + align:start position:0% +what I'm asking is for an economic +explanation for that + + align:start position:0% + + + + align:start position:0% + +result more people want to invest in the + + align:start position:0% +result more people want to invest in the + + + align:start position:0% +result more people want to invest in the +currency like using + + align:start position:0% +currency like using + + + align:start position:0% +currency like using +Curren well if you go to Wall Street to + + align:start position:0% +Curren well if you go to Wall Street to + + + align:start position:0% +Curren well if you go to Wall Street to +do an ARR they will explain it in those + + align:start position:0% +do an ARR they will explain it in those + + + align:start position:0% +do an ARR they will explain it in those +terms it's not the right explanation but + + align:start position:0% +terms it's not the right explanation but + + + align:start position:0% +terms it's not the right explanation but +they will explain on those ter and there + + align:start position:0% +they will explain on those ter and there + + + align:start position:0% +they will explain on those ter and there +is some logic behind that because this + + align:start position:0% +is some logic behind that because this + + + align:start position:0% +is some logic behind that because this +equation assumes that the arit happens + + align:start position:0% +equation assumes that the arit happens + + + align:start position:0% +equation assumes that the arit happens +instantaneously immediately things move + + align:start position:0% +instantaneously immediately things move + + + align:start position:0% +instantaneously immediately things move +but but before that happens you know + + align:start position:0% +but but before that happens you know + + + align:start position:0% +but but before that happens you know +some people will start buying more the + + align:start position:0% +some people will start buying more the + + + align:start position:0% +some people will start buying more the +the one that has more R but this + + align:start position:0% +the one that has more R but this + + + align:start position:0% +the one that has more R but this +equation already solve all that and + + align:start position:0% +equation already solve all that and + + + align:start position:0% +equation already solve all that and +that's when this + + align:start position:0% +that's when this + + + align:start position:0% +that's when this +assumption matters and and is a little + + align:start position:0% +assumption matters and and is a little + + + align:start position:0% +assumption matters and and is a little +Annoying it bothers me for a variet of + + align:start position:0% +Annoying it bothers me for a variet of + + + align:start position:0% +Annoying it bothers me for a variet of +reason but but we're going to use it to + + align:start position:0% +reason but but we're going to use it to + + + align:start position:0% +reason but but we're going to use it to +understand the mechanism you see if if I + + align:start position:0% +understand the mechanism you see if if I + + + align:start position:0% +understand the mechanism you see if if I +keep the exchange rate fixed we started + + align:start position:0% +keep the exchange rate fixed we started + + + align:start position:0% +keep the exchange rate fixed we started +with a situation where the exchange rate + + align:start position:0% +with a situation where the exchange rate + + + align:start position:0% +with a situation where the exchange rate +was equal to the expected exchange rate + + align:start position:0% +was equal to the expected exchange rate + + + align:start position:0% +was equal to the expected exchange rate +if I keep it fix and I appreciate the + + align:start position:0% +if I keep it fix and I appreciate the + + + align:start position:0% +if I keep it fix and I appreciate the +currency today then what do I expect to + + align:start position:0% +currency today then what do I expect to + + + align:start position:0% +currency today then what do I expect to +happen to the dollar let's talk about + + align:start position:0% +happen to the dollar let's talk about + + + align:start position:0% +happen to the dollar let's talk about +the dollar from this period to the next + + align:start position:0% +the dollar from this period to the next + + + align:start position:0% +the dollar from this period to the next +one remember we start from a situation + + align:start position:0% +one remember we start from a situation + + + align:start position:0% +one remember we start from a situation +where the exchange rate was equal to the + + align:start position:0% +where the exchange rate was equal to the + + + align:start position:0% +where the exchange rate was equal to the +spected exchange rate now I increase the + + align:start position:0% +spected exchange rate now I increase the + + + align:start position:0% +spected exchange rate now I increase the +interest rate and I said the exchange + + align:start position:0% +interest rate and I said the exchange + + + align:start position:0% +interest rate and I said the exchange +rate + + align:start position:0% +rate + + + align:start position:0% +rate +appreciate then what do you expect the + + align:start position:0% +appreciate then what do you expect the + + + align:start position:0% +appreciate then what do you expect the +the exchange rate to do over the next + + align:start position:0% +the exchange rate to do over the next + + + align:start position:0% +the exchange rate to do over the next +period if I haven't move expected + + align:start position:0% +period if I haven't move expected + + + align:start position:0% +period if I haven't move expected +exchange rate and now the exchange move + + align:start position:0% +exchange rate and now the exchange move + + + align:start position:0% +exchange rate and now the exchange move +above the expected exchange rate what do + + align:start position:0% +above the expected exchange rate what do + + + align:start position:0% +above the expected exchange rate what do +you expect exchange rate to + + align:start position:0% + + + + align:start position:0% + +do exactly has to + + align:start position:0% +do exactly has to + + + align:start position:0% +do exactly has to +depreciate so the reason the + + align:start position:0% +depreciate so the reason the + + + align:start position:0% +depreciate so the reason the +appreciation happens here is because you + + align:start position:0% +appreciation happens here is because you + + + align:start position:0% +appreciation happens here is because you +need to expect to depreciate the dollar + + align:start position:0% +need to expect to depreciate the dollar + + + align:start position:0% +need to expect to depreciate the dollar +from this period to the next one why do + + align:start position:0% +from this period to the next one why do + + + align:start position:0% +from this period to the next one why do +I need to expect the exchange rate to + + align:start position:0% + + + + align:start position:0% + +depreciate so I'm appreciating the + + align:start position:0% +depreciate so I'm appreciating the + + + align:start position:0% +depreciate so I'm appreciating the +currency because I need in equilibrium I + + align:start position:0% +currency because I need in equilibrium I + + + align:start position:0% +currency because I need in equilibrium I +need to expect to depreciate that is I + + align:start position:0% +need to expect to depreciate that is I + + + align:start position:0% +need to expect to depreciate that is I +need to expect to lose money money on + + align:start position:0% +need to expect to lose money money on + + + align:start position:0% +need to expect to lose money money on +the currency part of the trade why is + + align:start position:0% +the currency part of the trade why is + + + align:start position:0% +the currency part of the trade why is +that confusion is good you you learn + + align:start position:0% +that confusion is good you you learn + + + align:start position:0% +that confusion is good you you learn +from + + align:start position:0% +from + + + align:start position:0% +from +that and this can be very confusing I + + align:start position:0% + + + + align:start position:0% + +know what is it this equation trying to + + align:start position:0% + + + + align:start position:0% + +do we are trying to make the Spectre + + align:start position:0% +do we are trying to make the Spectre + + + align:start position:0% +do we are trying to make the Spectre +Returns the same that's the whole idea + + align:start position:0% +Returns the same that's the whole idea + + + align:start position:0% +Returns the same that's the whole idea +of this so if I now I'm now telling you + + align:start position:0% +of this so if I now I'm now telling you + + + align:start position:0% +of this so if I now I'm now telling you +that one bond is paying a higher + + align:start position:0% +that one bond is paying a higher + + + align:start position:0% +that one bond is paying a higher +interest than the other one I need to + + align:start position:0% +interest than the other one I need to + + + align:start position:0% +interest than the other one I need to +offset that somehow how do I offset it + + align:start position:0% +offset that somehow how do I offset it + + + align:start position:0% +offset that somehow how do I offset it +by expecting a depreciation of the + + align:start position:0% +by expecting a depreciation of the + + + align:start position:0% +by expecting a depreciation of the +currency of the bond that is you know of + + align:start position:0% +currency of the bond that is you know of + + + align:start position:0% +currency of the bond that is you know of +of the bond that is + + align:start position:0% +of the bond that is + + + align:start position:0% +of the bond that is +denominated in the currency that + + align:start position:0% +denominated in the currency that + + + align:start position:0% +denominated in the currency that +expected to depreciate so what I need to + + align:start position:0% +expected to depreciate so what I need to + + + align:start position:0% +expected to depreciate so what I need to +do is compensate for the interest rate + + align:start position:0% +do is compensate for the interest rate + + + align:start position:0% +do is compensate for the interest rate +differential with an expected + + align:start position:0% +differential with an expected + + + align:start position:0% +differential with an expected +depreciation of the currency that is + + align:start position:0% +depreciation of the currency that is + + + align:start position:0% +depreciation of the currency that is +paying a higher interest rate so that's + + align:start position:0% +paying a higher interest rate so that's + + + align:start position:0% +paying a higher interest rate so that's +what in this model when I fix expected + + align:start position:0% +what in this model when I fix expected + + + align:start position:0% +what in this model when I fix expected +exchange rate the only way I can do that + + align:start position:0% +exchange rate the only way I can do that + + + align:start position:0% +exchange rate the only way I can do that +is by appreciating the currency today so + + align:start position:0% +is by appreciating the currency today so + + + align:start position:0% +is by appreciating the currency today so +I can expect it to depreciate in the + + align:start position:0% +I can expect it to depreciate in the + + + align:start position:0% +I can expect it to depreciate in the +future that's the logic okay now how + + align:start position:0% +future that's the logic okay now how + + + align:start position:0% +future that's the logic okay now how +what is the connection with qu in wall + + align:start position:0% +what is the connection with qu in wall + + + align:start position:0% +what is the connection with qu in wall +stre they will tell you is to say well + + align:start position:0% +stre they will tell you is to say well + + + align:start position:0% +stre they will tell you is to say well +before this may happen not + + align:start position:0% +before this may happen not + + + align:start position:0% +before this may happen not +instantaneously it happens somewhat + + align:start position:0% +instantaneously it happens somewhat + + + align:start position:0% +instantaneously it happens somewhat +slowly so Traders immediately will go to + + align:start position:0% +slowly so Traders immediately will go to + + + align:start position:0% +slowly so Traders immediately will go to +the US + + align:start position:0% +the US + + + align:start position:0% +the US +dollar Bond because they see that they + + align:start position:0% +dollar Bond because they see that they + + + align:start position:0% +dollar Bond because they see that they +have a higher return and it will be the + + align:start position:0% +have a higher return and it will be the + + + align:start position:0% +have a higher return and it will be the +case until the currency really + + align:start position:0% +case until the currency really + + + align:start position:0% +case until the currency really +appreciates once the currency + + align:start position:0% +appreciates once the currency + + + align:start position:0% +appreciates once the currency +appreciates enough then that that + + align:start position:0% +appreciates enough then that that + + + align:start position:0% +appreciates enough then that that +Advantage disappeared that's what this + + align:start position:0% +Advantage disappeared that's what this + + + align:start position:0% +Advantage disappeared that's what this +condition is doing it's making the + + align:start position:0% +condition is doing it's making the + + + align:start position:0% +condition is doing it's making the +Spector return the same but in the + + align:start position:0% +Spector return the same but in the + + + align:start position:0% +Spector return the same but in the +process of the exchanger going from the + + align:start position:0% +process of the exchanger going from the + + + align:start position:0% +process of the exchanger going from the +initial exchange rate to to to the new + + align:start position:0% +initial exchange rate to to to the new + + + align:start position:0% +initial exchange rate to to to the new +equilibrium exchange rate there may be + + align:start position:0% +equilibrium exchange rate there may be + + + align:start position:0% +equilibrium exchange rate there may be +an opportunity there and that's when you + + align:start position:0% +an opportunity there and that's when you + + + align:start position:0% +an opportunity there and that's when you +start seeing these flows okay that + + align:start position:0% +start seeing these flows okay that + + + align:start position:0% +start seeing these flows okay that +happens very very fast but that's when + + align:start position:0% +happens very very fast but that's when + + + align:start position:0% +happens very very fast but that's when +you can see some of those + + align:start position:0% + + + + align:start position:0% + +flows I mean in these markets that + + align:start position:0% +flows I mean in these markets that + + + align:start position:0% +flows I mean in these markets that +happens very very quickly so what is + + align:start position:0% +happens very very quickly so what is + + + align:start position:0% +happens very very quickly so what is +typically wrong is that then analyst + + align:start position:0% +typically wrong is that then analyst + + + align:start position:0% +typically wrong is that then analyst +comes and tells you explains the story + + align:start position:0% +comes and tells you explains the story + + + align:start position:0% +comes and tells you explains the story +why the changes if want to continue to + + align:start position:0% +why the changes if want to continue to + + + align:start position:0% +why the changes if want to continue to +appreciate well that's just way too late + + align:start position:0% +appreciate well that's just way too late + + + align:start position:0% +appreciate well that's just way too late +you're already in this environment you + + align:start position:0% +you're already in this environment you + + + align:start position:0% +you're already in this environment you +lost the trade + + align:start position:0% + + + + align:start position:0% + +okay okay what about an increaseing the + + align:start position:0% +okay okay what about an increaseing the + + + align:start position:0% +okay okay what about an increaseing the +foreign interest rate I + + align:start position:0% +foreign interest rate I + + + align:start position:0% +foreign interest rate I +star so an increaseing the foreign + + align:start position:0% +star so an increaseing the foreign + + + align:start position:0% +star so an increaseing the foreign +interest rate let's start from the same + + align:start position:0% +interest rate let's start from the same + + + align:start position:0% +interest rate let's start from the same +situation we had before we start from + + align:start position:0% +situation we had before we start from + + + align:start position:0% +situation we had before we start from +interest rate equal to International + + align:start position:0% +interest rate equal to International + + + align:start position:0% +interest rate equal to International +interest rate therefore the exchange + + align:start position:0% +interest rate therefore the exchange + + + align:start position:0% +interest rate therefore the exchange +rate is equal to spected exchange rate + + align:start position:0% +rate is equal to spected exchange rate + + + align:start position:0% +rate is equal to spected exchange rate +and now the + + align:start position:0% +and now the + + + align:start position:0% +and now the +foreign interest rate goes + + align:start position:0% +foreign interest rate goes + + + align:start position:0% +foreign interest rate goes +up okay what is going on now in the US + + align:start position:0% +up okay what is going on now in the US + + + align:start position:0% +up okay what is going on now in the US +the US is sort of stabilizing here and + + align:start position:0% +the US is sort of stabilizing here and + + + align:start position:0% +the US is sort of stabilizing here and +and Europe is beginning to hike a little + + align:start position:0% +and Europe is beginning to hike a little + + + align:start position:0% +and Europe is beginning to hike a little +more than the us + + align:start position:0% +more than the us + + + align:start position:0% +more than the us +so we know from the equation that that + + align:start position:0% +so we know from the equation that that + + + align:start position:0% +so we know from the equation that that +means the exchange will fall that is + + align:start position:0% +means the exchange will fall that is + + + align:start position:0% +means the exchange will fall that is +will drop here so that that means the + + align:start position:0% +will drop here so that that means the + + + align:start position:0% +will drop here so that that means the +exchange rate is depreciating the dollar + + align:start position:0% +exchange rate is depreciating the dollar + + + align:start position:0% +exchange rate is depreciating the dollar +is + + align:start position:0% +is + + + align:start position:0% +is +depreciating why is the dollar + + align:start position:0% +depreciating why is the dollar + + + align:start position:0% +depreciating why is the dollar +depreciating + + align:start position:0% + + + + align:start position:0% + +yeah that's + + align:start position:0% +yeah that's + + + align:start position:0% +yeah that's +correct I mean the the issue here in + + align:start position:0% +correct I mean the the issue here in + + + align:start position:0% +correct I mean the the issue here in +terms of the economics is that remember + + align:start position:0% +terms of the economics is that remember + + + align:start position:0% +terms of the economics is that remember +if we start from the same interest and + + align:start position:0% +if we start from the same interest and + + + align:start position:0% +if we start from the same interest and +now all the lines I'm giving you doesn't + + align:start position:0% +now all the lines I'm giving you doesn't + + + align:start position:0% +now all the lines I'm giving you doesn't +need to start for the same interest it + + align:start position:0% +need to start for the same interest it + + + align:start position:0% +need to start for the same interest it +just a lot simpler to start from from + + align:start position:0% +just a lot simpler to start from from + + + align:start position:0% +just a lot simpler to start from from +the same interest but suppose we start + + align:start position:0% +the same interest but suppose we start + + + align:start position:0% +the same interest but suppose we start +with the same interest rate and now we + + align:start position:0% +with the same interest rate and now we + + + align:start position:0% +with the same interest rate and now we +increase this one then that means the + + align:start position:0% +increase this one then that means the + + + align:start position:0% +increase this one then that means the +foreign bond is playing a high interest + + align:start position:0% +foreign bond is playing a high interest + + + align:start position:0% +foreign bond is playing a high interest +rate than the domestic Bond I need to + + align:start position:0% +rate than the domestic Bond I need to + + + align:start position:0% +rate than the domestic Bond I need to +equalize expected Returns the only way I + + align:start position:0% +equalize expected Returns the only way I + + + align:start position:0% +equalize expected Returns the only way I +can do that is by having an expected + + align:start position:0% +can do that is by having an expected + + + align:start position:0% +can do that is by having an expected +appreciation of the + + align:start position:0% +appreciation of the + + + align:start position:0% +appreciation of the +dollar since the expected exchange and + + align:start position:0% +dollar since the expected exchange and + + + align:start position:0% +dollar since the expected exchange and +we fix it here the only way I can give + + align:start position:0% +we fix it here the only way I can give + + + align:start position:0% +we fix it here the only way I can give +you an expected appreciation of the + + align:start position:0% +you an expected appreciation of the + + + align:start position:0% +you an expected appreciation of the +dollar is to by depreciating the dollar + + align:start position:0% + + + + align:start position:0% + +today so it's the same mechanism the + + align:start position:0% +today so it's the same mechanism the + + + align:start position:0% +today so it's the same mechanism the +same logic is + + align:start position:0% +same logic is + + + align:start position:0% +same logic is +symmetric that's that's the + + align:start position:0% +symmetric that's that's the + + + align:start position:0% +symmetric that's that's the +mechanism now is this true that in the + + align:start position:0% +mechanism now is this true that in the + + + align:start position:0% +mechanism now is this true that in the +very short run when when I start goes up + + align:start position:0% +very short run when when I start goes up + + + align:start position:0% +very short run when when I start goes up +and and I doesn't move then lots of + + align:start position:0% +and and I doesn't move then lots of + + + align:start position:0% +and and I doesn't move then lots of +people go and buy foreign bonds and that + + align:start position:0% +people go and buy foreign bonds and that + + + align:start position:0% +people go and buy foreign bonds and that +produces sort of you know demand for + + align:start position:0% +produces sort of you know demand for + + + align:start position:0% +produces sort of you know demand for +euros and blah blah blah blah but that's + + align:start position:0% +euros and blah blah blah blah but that's + + + align:start position:0% +euros and blah blah blah blah but that's +very quick machines do it for you now so + + align:start position:0% +very quick machines do it for you now so + + + align:start position:0% +very quick machines do it for you now so +it happens very + + align:start position:0% +it happens very + + + align:start position:0% +it happens very +quickly so this equation shows you what + + align:start position:0% +quickly so this equation shows you what + + + align:start position:0% +quickly so this equation shows you what +happens after all that mess has already + + align:start position:0% +happens after all that mess has already + + + align:start position:0% +happens after all that mess has already +clear which happens in + + align:start position:0% + + + + align:start position:0% + +milliseconds + + align:start position:0% +milliseconds + + + align:start position:0% +milliseconds +okay what what if I change the spect to + + align:start position:0% +okay what what if I change the spect to + + + align:start position:0% +okay what what if I change the spect to +rate so again I'm fixing it but I can + + align:start position:0% +rate so again I'm fixing it but I can + + + align:start position:0% +rate so again I'm fixing it but I can +move it around I'm treating as a + + align:start position:0% +move it around I'm treating as a + + + align:start position:0% +move it around I'm treating as a +parameter that when I say if I fix it I + + align:start position:0% +parameter that when I say if I fix it I + + + align:start position:0% +parameter that when I say if I fix it I +just don't want to endogenize I don't + + align:start position:0% +just don't want to endogenize I don't + + + align:start position:0% +just don't want to endogenize I don't +want to make it another endogenous + + align:start position:0% +want to make it another endogenous + + + align:start position:0% +want to make it another endogenous +variable so what happens here if the + + align:start position:0% +variable so what happens here if the + + + align:start position:0% +variable so what happens here if the +exchange rate we start with the same + + align:start position:0% +exchange rate we start with the same + + + align:start position:0% +exchange rate we start with the same +situation we had before now the Spector + + align:start position:0% +situation we had before now the Spector + + + align:start position:0% +situation we had before now the Spector +exchanger goes up well from the equation + + align:start position:0% +exchanger goes up well from the equation + + + align:start position:0% +exchanger goes up well from the equation +is very clear the current exchanges + + align:start position:0% +is very clear the current exchanges + + + align:start position:0% +is very clear the current exchanges +immediately + + align:start position:0% +immediately + + + align:start position:0% +immediately +Rises one for one in fact okay if I have + + align:start position:0% +Rises one for one in fact okay if I have + + + align:start position:0% +Rises one for one in fact okay if I have +the these two interest are the same and + + align:start position:0% +the these two interest are the same and + + + align:start position:0% +the these two interest are the same and +now I move the spect change itate up + + align:start position:0% +now I move the spect change itate up + + + align:start position:0% +now I move the spect change itate up +then the current exchange immediately + + align:start position:0% +then the current exchange immediately + + + align:start position:0% +then the current exchange immediately +jumps so is if we expect the dollar to + + align:start position:0% +jumps so is if we expect the dollar to + + + align:start position:0% +jumps so is if we expect the dollar to +appreciate in the future then it + + align:start position:0% +appreciate in the future then it + + + align:start position:0% +appreciate in the future then it +appreciate today why is + + align:start position:0% +appreciate today why is + + + align:start position:0% +appreciate today why is +that expectations are very powerful in + + align:start position:0% +that expectations are very powerful in + + + align:start position:0% +that expectations are very powerful in +financial Assets in general this is the + + align:start position:0% +financial Assets in general this is the + + + align:start position:0% +financial Assets in general this is the +first time you come out but and we'll + + align:start position:0% +first time you come out but and we'll + + + align:start position:0% +first time you come out but and we'll +talk a lot more about that in the next + + align:start position:0% +talk a lot more about that in the next + + + align:start position:0% +talk a lot more about that in the next +week but but you can see it here so if I + + align:start position:0% +week but but you can see it here so if I + + + align:start position:0% +week but but you can see it here so if I +move the exchange rate today + + align:start position:0% +move the exchange rate today + + + align:start position:0% +move the exchange rate today +up the expected exchange rate means + + align:start position:0% +up the expected exchange rate means + + + align:start position:0% +up the expected exchange rate means +which expect the changer to be you know + + align:start position:0% +which expect the changer to be you know + + + align:start position:0% +which expect the changer to be you know +today the dollar is is 90 cents on 90 + + align:start position:0% +today the dollar is is 90 cents on 90 + + + align:start position:0% +today the dollar is is 90 cents on 90 +Cent + + align:start position:0% +Cent + + + align:start position:0% +Cent +9 Euros per dollar well suppose I expect + + align:start position:0% +9 Euros per dollar well suppose I expect + + + align:start position:0% +9 Euros per dollar well suppose I expect +one Euro for dollar in the next period + + align:start position:0% +one Euro for dollar in the next period + + + align:start position:0% +one Euro for dollar in the next period +what will happen to the CH today will it + + align:start position:0% +what will happen to the CH today will it + + + align:start position:0% +what will happen to the CH today will it +jumps today to + + align:start position:0% +jumps today to + + + align:start position:0% +jumps today to +one why is + + align:start position:0% + + + + align:start position:0% + +that the dollar will be more expensive + + align:start position:0% +that the dollar will be more expensive + + + align:start position:0% +that the dollar will be more expensive +to BU there so people + + align:start position:0% +to BU there so people + + + align:start position:0% +to BU there so people +okay that's that's your friend the + + align:start position:0% +okay that's that's your friend the + + + align:start position:0% +okay that's that's your friend the +trader there okay + + align:start position:0% +trader there okay + + + align:start position:0% +trader there okay +but + + align:start position:0% +but + + + align:start position:0% +but +um + + align:start position:0% +um + + + align:start position:0% +um +yes that's + + align:start position:0% + + + + align:start position:0% + +true that's true what does it + + align:start position:0% +true that's true what does it + + + align:start position:0% +true that's true what does it +mean though it is true it's more + + align:start position:0% +mean though it is true it's more + + + align:start position:0% +mean though it is true it's more +expensive but why would why did you want + + align:start position:0% +expensive but why would why did you want + + + align:start position:0% +expensive but why would why did you want +to buy it to start with I mean who cares + + align:start position:0% +to buy it to start with I mean who cares + + + align:start position:0% +to buy it to start with I mean who cares +that something it's more expensive you + + align:start position:0% +that something it's more expensive you + + + align:start position:0% +that something it's more expensive you +are not planning to buy it + + align:start position:0% + + + + align:start position:0% + +um because the the current price is + + align:start position:0% +um because the the current price is + + + align:start position:0% +um because the the current price is +something also has to take into account + + align:start position:0% +something also has to take into account + + + align:start position:0% +something also has to take into account +future price that's what the question + + align:start position:0% +future price that's what the question + + + align:start position:0% +future price that's what the question +says yes because part of because its + + align:start position:0% +says yes because part of because its + + + align:start position:0% +says yes because part of because its +value at the present moment takes into + + align:start position:0% +value at the present moment takes into + + + align:start position:0% +value at the present moment takes into +account some of value I I you know + + align:start position:0% +account some of value I I you know + + + align:start position:0% +account some of value I I you know +whenever we we this is an Arbitrage type + + align:start position:0% +whenever we we this is an Arbitrage type + + + align:start position:0% +whenever we we this is an Arbitrage type +relationship and what I suggest is + + align:start position:0% +relationship and what I suggest is + + + align:start position:0% +relationship and what I suggest is +whenever you come across an Arbitrage + + align:start position:0% +whenever you come across an Arbitrage + + + align:start position:0% +whenever you come across an Arbitrage +type argument you ask a question well + + align:start position:0% +type argument you ask a question well + + + align:start position:0% +type argument you ask a question well +suppose not suppose this didn't happen + + align:start position:0% +suppose not suppose this didn't happen + + + align:start position:0% +suppose not suppose this didn't happen +What would then happen What would look + + align:start position:0% +What would then happen What would look + + + align:start position:0% +What would then happen What would look +odd okay that's almost any arbitr that's + + align:start position:0% +odd okay that's almost any arbitr that's + + + align:start position:0% +odd okay that's almost any arbitr that's +a good way of thinking about this say + + align:start position:0% +a good way of thinking about this say + + + align:start position:0% +a good way of thinking about this say +okay the equation tells me that the + + align:start position:0% +okay the equation tells me that the + + + align:start position:0% +okay the equation tells me that the +exchanger has to jump right + + align:start position:0% +exchanger has to jump right + + + align:start position:0% +exchanger has to jump right +away well suppose not what goes + + align:start position:0% +away well suppose not what goes + + + align:start position:0% +away well suppose not what goes +wrong that's I think that's the way the + + align:start position:0% +wrong that's I think that's the way the + + + align:start position:0% +wrong that's I think that's the way the +the easiest way to think about any of + + align:start position:0% +the easiest way to think about any of + + + align:start position:0% +the easiest way to think about any of +this asset pricing in general by the + + align:start position:0% +this asset pricing in general by the + + + align:start position:0% +this asset pricing in general by the +way well suppose not suppose the + + align:start position:0% +way well suppose not suppose the + + + align:start position:0% +way well suppose not suppose the +expected exchange rate goes up the + + align:start position:0% +expected exchange rate goes up the + + + align:start position:0% +expected exchange rate goes up the +interest rates haven't changed and the + + align:start position:0% +interest rates haven't changed and the + + + align:start position:0% +interest rates haven't changed and the +exchange rate today doesn't move what + + align:start position:0% +exchange rate today doesn't move what + + + align:start position:0% +exchange rate today doesn't move what +happens then remember we s a situation + + align:start position:0% +happens then remember we s a situation + + + align:start position:0% +happens then remember we s a situation +which both interest rates are the same + + align:start position:0% +which both interest rates are the same + + + align:start position:0% +which both interest rates are the same +now the spect exchanger went up by 10% + + align:start position:0% +now the spect exchanger went up by 10% + + + align:start position:0% +now the spect exchanger went up by 10% +say and er the current exchanger hasn't + + align:start position:0% +say and er the current exchanger hasn't + + + align:start position:0% +say and er the current exchanger hasn't +move I'm sure between the two of you can + + align:start position:0% +move I'm sure between the two of you can + + + align:start position:0% +move I'm sure between the two of you can +design this tra okay what do you + + align:start position:0% + + + + align:start position:0% + +do everyone would buy foreign Bonds in + + align:start position:0% +do everyone would buy foreign Bonds in + + + align:start position:0% +do everyone would buy foreign Bonds in +like the next period + + align:start position:0% +like the next period + + + align:start position:0% +like the next period +now in the first + + align:start position:0% + + + + align:start position:0% + +period er no no but what do you do + + align:start position:0% + + + + align:start position:0% + +today suppos you're a Trader and and + + align:start position:0% +today suppos you're a Trader and and + + + align:start position:0% +today suppos you're a Trader and and +then now you see whoops The Exchange the + + align:start position:0% +then now you see whoops The Exchange the + + + align:start position:0% +then now you see whoops The Exchange the +dollar will appreciate 10% the interest + + align:start position:0% +dollar will appreciate 10% the interest + + + align:start position:0% +dollar will appreciate 10% the interest +rates are the same and the CH is not + + align:start position:0% +rates are the same and the CH is not + + + align:start position:0% +rates are the same and the CH is not +moving today what do you do + + align:start position:0% + + + + align:start position:0% + +which Bond do you + + align:start position:0% + + + + align:start position:0% + +buy of course because you have a 10% + + align:start position:0% +buy of course because you have a 10% + + + align:start position:0% +buy of course because you have a 10% +expected capital gain from buying that + + align:start position:0% +expected capital gain from buying that + + + align:start position:0% +expected capital gain from buying that +bone if that doesn't happen the both the + + align:start position:0% +bone if that doesn't happen the both the + + + align:start position:0% +bone if that doesn't happen the both the +two bones are paying the same interest + + align:start position:0% +two bones are paying the same interest + + + align:start position:0% +two bones are paying the same interest +rate and now I tell you well yeah but + + align:start position:0% +rate and now I tell you well yeah but + + + align:start position:0% +rate and now I tell you well yeah but +one is on appreciate by 10% relative to + + align:start position:0% +one is on appreciate by 10% relative to + + + align:start position:0% +one is on appreciate by 10% relative to +the other okay so clearly that you go + + align:start position:0% +the other okay so clearly that you go + + + align:start position:0% +the other okay so clearly that you go +short massively the foreign bone and you + + align:start position:0% +short massively the foreign bone and you + + + align:start position:0% +short massively the foreign bone and you +go very long the US Bond that's what you + + align:start position:0% +go very long the US Bond that's what you + + + align:start position:0% +go very long the US Bond that's what you +do we all want to do the same so it + + align:start position:0% +do we all want to do the same so it + + + align:start position:0% +do we all want to do the same so it +happens very quickly + + align:start position:0% +happens very quickly + + + align:start position:0% +happens very quickly +and exchanges appre today up to a point + + align:start position:0% +and exchanges appre today up to a point + + + align:start position:0% +and exchanges appre today up to a point +in which that that incentive is no + + align:start position:0% +in which that that incentive is no + + + align:start position:0% +in which that that incentive is no +longer there and that in this particular + + align:start position:0% +longer there and that in this particular + + + align:start position:0% +longer there and that in this particular +case if the interest are the same that + + align:start position:0% +case if the interest are the same that + + + align:start position:0% +case if the interest are the same that +will happen only if the exchange today + + align:start position:0% +will happen only if the exchange today + + + align:start position:0% +will happen only if the exchange today +jumps exactly by the same amount as + + align:start position:0% +jumps exactly by the same amount as + + + align:start position:0% +jumps exactly by the same amount as +expected appreciation of the as expected + + align:start position:0% +expected appreciation of the as expected + + + align:start position:0% +expected appreciation of the as expected +value of the dollar change in the future + + align:start position:0% +value of the dollar change in the future + + + align:start position:0% +value of the dollar change in the future +okay good think about this play with + + align:start position:0% +okay good think about this play with + + + align:start position:0% +okay good think about this play with +these things I know it can be confusing + + align:start position:0% +these things I know it can be confusing + + + align:start position:0% +these things I know it can be confusing +but and I always start with let me move + + align:start position:0% +but and I always start with let me move + + + align:start position:0% +but and I always start with let me move +some + + align:start position:0% +some + + + align:start position:0% +some +the equation tells me this is what has + + align:start position:0% +the equation tells me this is what has + + + align:start position:0% +the equation tells me this is what has +to happen to the exchange rate well + + align:start position:0% +to happen to the exchange rate well + + + align:start position:0% +to happen to the exchange rate well +suppose that didn't happen to The + + align:start position:0% +suppose that didn't happen to The + + + align:start position:0% +suppose that didn't happen to The +Exchange and then you say oh then I + + align:start position:0% +Exchange and then you say oh then I + + + align:start position:0% +Exchange and then you say oh then I +clearly invest in this one this + + align:start position:0% +clearly invest in this one this + + + align:start position:0% +clearly invest in this one this +dominates the other one well that + + align:start position:0% +dominates the other one well that + + + align:start position:0% +dominates the other one well that +condition tells you no no in equilibrium + + align:start position:0% +condition tells you no no in equilibrium + + + align:start position:0% +condition tells you no no in equilibrium +you have to be different so so the only + + align:start position:0% +you have to be different so so the only + + + align:start position:0% +you have to be different so so the only +thing you can move is exchange rate and + + align:start position:0% +thing you can move is exchange rate and + + + align:start position:0% +thing you can move is exchange rate and +the exchange has to move until you are + + align:start position:0% +the exchange has to move until you are + + + align:start position:0% +the exchange has to move until you are +in different again after you have done + + align:start position:0% +in different again after you have done + + + align:start position:0% +in different again after you have done +some change some argument on the right + + align:start position:0% +some change some argument on the right + + + align:start position:0% +some change some argument on the right +hand side okay that's the way you need + + align:start position:0% +hand side okay that's the way you need + + + align:start position:0% +hand side okay that's the way you need +to think about it + + align:start position:0% +to think about it + + + align:start position:0% +to think about it +so I here I'm just + + align:start position:0% +so I here I'm just + + + align:start position:0% +so I here I'm just +plotting uh this this + + align:start position:0% +plotting uh this this + + + align:start position:0% +plotting uh this this +relationship in the space of exchange + + align:start position:0% +relationship in the space of exchange + + + align:start position:0% +relationship in the space of exchange +rate in the x-axis and the domestic + + align:start position:0% +rate in the x-axis and the domestic + + + align:start position:0% +rate in the x-axis and the domestic +interest rate here okay so that's an + + align:start position:0% +interest rate here okay so that's an + + + align:start position:0% +interest rate here okay so that's an +upward sloping relationship you can see + + align:start position:0% +upward sloping relationship you can see + + + align:start position:0% +upward sloping relationship you can see +here that I move the interest rate up or + + align:start position:0% +here that I move the interest rate up or + + + align:start position:0% +here that I move the interest rate up or +the other way around but anyways if I + + align:start position:0% +the other way around but anyways if I + + + align:start position:0% +the other way around but anyways if I +move the interest rate up the exchange + + align:start position:0% +move the interest rate up the exchange + + + align:start position:0% +move the interest rate up the exchange +is going up so that's a positive + + align:start position:0% +is going up so that's a positive + + + align:start position:0% +is going up so that's a positive +relationship I can do it the other way + + align:start position:0% +relationship I can do it the other way + + + align:start position:0% +relationship I can do it the other way +around they move the chain rate up then + + align:start position:0% +around they move the chain rate up then + + + align:start position:0% +around they move the chain rate up then +the domestic has to go up I'm taking as + + align:start position:0% +the domestic has to go up I'm taking as + + + align:start position:0% +the domestic has to go up I'm taking as +parameters the foreign interest rate and + + align:start position:0% +parameters the foreign interest rate and + + + align:start position:0% +parameters the foreign interest rate and +and and the expected exchange if I take + + align:start position:0% +and and the expected exchange if I take + + + align:start position:0% +and and the expected exchange if I take +as parameter this and that then I have a + + align:start position:0% +as parameter this and that then I have a + + + align:start position:0% +as parameter this and that then I have a +positive relationship between the + + align:start position:0% +positive relationship between the + + + align:start position:0% +positive relationship between the +exchange rate and the domestic interest + + align:start position:0% +exchange rate and the domestic interest + + + align:start position:0% +exchange rate and the domestic interest +rate okay so that's going to be the U + + align:start position:0% +rate okay so that's going to be the U + + + align:start position:0% +rate okay so that's going to be the U +I'm plotting the uip and covering + + align:start position:0% +I'm plotting the uip and covering + + + align:start position:0% +I'm plotting the uip and covering +transparity condition notice this point + + align:start position:0% +transparity condition notice this point + + + align:start position:0% +transparity condition notice this point +here is interesting this points tells + + align:start position:0% +here is interesting this points tells + + + align:start position:0% +here is interesting this points tells +you that when the domestic interest rate + + align:start position:0% +you that when the domestic interest rate + + + align:start position:0% +you that when the domestic interest rate +I is equal to the international interest + + align:start position:0% +I is equal to the international interest + + + align:start position:0% +I is equal to the international interest +rate + + align:start position:0% +rate + + + align:start position:0% +rate +then the exchange rate has to be equal + + align:start position:0% +then the exchange rate has to be equal + + + align:start position:0% +then the exchange rate has to be equal +to the expected exchange rate which is + + align:start position:0% +to the expected exchange rate which is + + + align:start position:0% +to the expected exchange rate which is +the question I asked before remember I + + align:start position:0% +the question I asked before remember I + + + align:start position:0% +the question I asked before remember I +ask you a question well suppose that we + + align:start position:0% +ask you a question well suppose that we + + + align:start position:0% +ask you a question well suppose that we +start with an interest rate that is + + align:start position:0% +start with an interest rate that is + + + align:start position:0% +start with an interest rate that is +equal to the international interest + + align:start position:0% +equal to the international interest + + + align:start position:0% +equal to the international interest +rate what the exchange what is the + + align:start position:0% +rate what the exchange what is the + + + align:start position:0% +rate what the exchange what is the +exchange rate and you said the answer + + align:start position:0% +exchange rate and you said the answer + + + align:start position:0% +exchange rate and you said the answer +was well it has to be equal to the + + align:start position:0% +was well it has to be equal to the + + + align:start position:0% +was well it has to be equal to the +expected exchange rate that's that point + + align:start position:0% +expected exchange rate that's that point + + + align:start position:0% +expected exchange rate that's that point +here okay if the interest rate domestic + + align:start position:0% +here okay if the interest rate domestic + + + align:start position:0% +here okay if the interest rate domestic +interest rate is above that the intern + + align:start position:0% +interest rate is above that the intern + + + align:start position:0% +interest rate is above that the intern +National interest rate then the exchange + + align:start position:0% +National interest rate then the exchange + + + align:start position:0% +National interest rate then the exchange +rate today has to be above the expected + + align:start position:0% +rate today has to be above the expected + + + align:start position:0% +rate today has to be above the expected +exchange rate because that will give you + + align:start position:0% +exchange rate because that will give you + + + align:start position:0% +exchange rate because that will give you +expected depreciation of the currency + + align:start position:0% +expected depreciation of the currency + + + align:start position:0% +expected depreciation of the currency +which will compensate for the fact that + + align:start position:0% +which will compensate for the fact that + + + align:start position:0% +which will compensate for the fact that +the domestic bond is paying a higher + + align:start position:0% +the domestic bond is paying a higher + + + align:start position:0% +the domestic bond is paying a higher +interest rate than international bond + + align:start position:0% +interest rate than international bond + + + align:start position:0% +interest rate than international bond +okay conversely if if the domestic bond + + align:start position:0% +okay conversely if if the domestic bond + + + align:start position:0% +okay conversely if if the domestic bond +is paying a lower interest rate then the + + align:start position:0% +is paying a lower interest rate then the + + + align:start position:0% +is paying a lower interest rate then the +exchange rate today is very depreciated + + align:start position:0% +exchange rate today is very depreciated + + + align:start position:0% +exchange rate today is very depreciated +because you have to expect it to + + align:start position:0% +because you have to expect it to + + + align:start position:0% +because you have to expect it to +appreciate in order to compensate for + + align:start position:0% +appreciate in order to compensate for + + + align:start position:0% +appreciate in order to compensate for +the interest rate differential + + align:start position:0% +the interest rate differential + + + align:start position:0% +the interest rate differential +okay probably not + + align:start position:0% +okay probably not + + + align:start position:0% +okay probably not +but this requires practice I tell you + + align:start position:0% + + + + align:start position:0% + +ER okay so but now we have a an equation + + align:start position:0% +ER okay so but now we have a an equation + + + align:start position:0% +ER okay so but now we have a an equation +for the exchange rate at least so I can + + align:start position:0% +for the exchange rate at least so I can + + + align:start position:0% +for the exchange rate at least so I can +go back to my is is is the is equation + + align:start position:0% +go back to my is is is the is equation + + + align:start position:0% +go back to my is is is the is equation +in the open economy and I have an + + align:start position:0% +in the open economy and I have an + + + align:start position:0% +in the open economy and I have an +equation for the exchanger so I can + + align:start position:0% +equation for the exchanger so I can + + + align:start position:0% +equation for the exchanger so I can +replace it this is nice because I I have + + align:start position:0% +replace it this is nice because I I have + + + align:start position:0% +replace it this is nice because I I have +two new parameters expected exchange + + align:start position:0% +two new parameters expected exchange + + + align:start position:0% +two new parameters expected exchange +rate and international interest rate but + + align:start position:0% +rate and international interest rate but + + + align:start position:0% +rate and international interest rate but +now this is also a function of the + + align:start position:0% +now this is also a function of the + + + align:start position:0% +now this is also a function of the +interest rate so at this moment I have + + align:start position:0% +interest rate so at this moment I have + + + align:start position:0% +interest rate so at this moment I have +one equation in two unknowns really + + align:start position:0% +one equation in two unknowns really + + + align:start position:0% +one equation in two unknowns really +after I solve out for the exchang it I + + align:start position:0% +after I solve out for the exchang it I + + + align:start position:0% +after I solve out for the exchang it I +have one equation and two unknowns the + + align:start position:0% +have one equation and two unknowns the + + + align:start position:0% +have one equation and two unknowns the +two unknowns are output and the domestic + + align:start position:0% +two unknowns are output and the domestic + + + align:start position:0% +two unknowns are output and the domestic +interest rate all the rest are + + align:start position:0% +interest rate all the rest are + + + align:start position:0% +interest rate all the rest are +parameters so that's the same situation + + align:start position:0% +parameters so that's the same situation + + + align:start position:0% +parameters so that's the same situation +we're at in lecture three or so so then + + align:start position:0% +we're at in lecture three or so so then + + + align:start position:0% +we're at in lecture three or so so then +we need an extra + + align:start position:0% +we need an extra + + + align:start position:0% +we need an extra +equation the extra equation was monetary + + align:start position:0% +equation the extra equation was monetary + + + align:start position:0% +equation the extra equation was monetary +policy the LM + + align:start position:0% +policy the LM + + + align:start position:0% +policy the LM +we're going to do exactly the same here + + align:start position:0% +we're going to do exactly the same here + + + align:start position:0% +we're going to do exactly the same here +okay the Lim is the same it's a domestic + + align:start position:0% +okay the Lim is the same it's a domestic + + + align:start position:0% +okay the Lim is the same it's a domestic +Central Bank sets the interest rate so + + align:start position:0% +Central Bank sets the interest rate so + + + align:start position:0% +Central Bank sets the interest rate so +now I'm + + align:start position:0% +now I'm + + + align:start position:0% +now I'm +set now we have the islm model in the + + align:start position:0% +set now we have the islm model in the + + + align:start position:0% +set now we have the islm model in the +open economy this is the Mandel flaming + + align:start position:0% +open economy this is the Mandel flaming + + + align:start position:0% +open economy this is the Mandel flaming +model okay that's what the Mandel + + align:start position:0% +model okay that's what the Mandel + + + align:start position:0% +model okay that's what the Mandel +flaming model is + + align:start position:0% +flaming model is + + + align:start position:0% +flaming model is +so yes some more complicated + + align:start position:0% +so yes some more complicated + + + align:start position:0% +so yes some more complicated +ideas with that + + align:start position:0% + + + + align:start position:0% + +uip um driven exchange rate + + align:start position:0% +uip um driven exchange rate + + + align:start position:0% +uip um driven exchange rate +and then the LM is the same as in the + + align:start position:0% +and then the LM is the same as in the + + + align:start position:0% +and then the LM is the same as in the +Clos + + align:start position:0% + + + + align:start position:0% + +economy so this is the Mandel flaming + + align:start position:0% +economy so this is the Mandel flaming + + + align:start position:0% +economy so this is the Mandel flaming +mod so notice that that so one thing we + + align:start position:0% +mod so notice that that so one thing we + + + align:start position:0% +mod so notice that that so one thing we +know already we knew from the previous + + align:start position:0% +know already we knew from the previous + + + align:start position:0% +know already we knew from the previous +lecture that that we have a smaller + + align:start position:0% +lecture that that we have a smaller + + + align:start position:0% +lecture that that we have a smaller +multiplier in the open economy because + + align:start position:0% +multiplier in the open economy because + + + align:start position:0% +multiplier in the open economy because +we have the inputs that are also + + align:start position:0% +we have the inputs that are also + + + align:start position:0% +we have the inputs that are also +responding to Output we have a new + + align:start position:0% +responding to Output we have a new + + + align:start position:0% +responding to Output we have a new +parameter but now we also know that an + + align:start position:0% +parameter but now we also know that an + + + align:start position:0% +parameter but now we also know that an +increase in the interest rate so + + align:start position:0% +increase in the interest rate so + + + align:start position:0% +increase in the interest rate so +monetary policy in the open economy + + align:start position:0% +monetary policy in the open economy + + + align:start position:0% +monetary policy in the open economy +has two effects now it used to have only + + align:start position:0% +has two effects now it used to have only + + + align:start position:0% +has two effects now it used to have only +this effect remember it affected + + align:start position:0% +this effect remember it affected + + + align:start position:0% +this effect remember it affected +domestic investment so an increase in + + align:start position:0% +domestic investment so an increase in + + + align:start position:0% +domestic investment so an increase in +the interest rate would lead to a um a + + align:start position:0% +the interest rate would lead to a um a + + + align:start position:0% +the interest rate would lead to a um a +reduction in aggregate demand because + + align:start position:0% +reduction in aggregate demand because + + + align:start position:0% +reduction in aggregate demand because +investment would fall remember that was + + align:start position:0% +investment would fall remember that was + + + align:start position:0% +investment would fall remember that was +a role of the interest rate that's the + + align:start position:0% +a role of the interest rate that's the + + + align:start position:0% +a role of the interest rate that's the +way monetary policy work in the close + + align:start position:0% +way monetary policy work in the close + + + align:start position:0% +way monetary policy work in the close +economy was through this channel + + align:start position:0% +economy was through this channel + + + align:start position:0% +economy was through this channel +here now we have a second Channel which + + align:start position:0% +here now we have a second Channel which + + + align:start position:0% +here now we have a second Channel which +is this + + align:start position:0% +is this + + + align:start position:0% +is this +one so when the interest rate goes up + + align:start position:0% +one so when the interest rate goes up + + + align:start position:0% +one so when the interest rate goes up +it's contraction for two reasons one for + + align:start position:0% +it's contraction for two reasons one for + + + align:start position:0% +it's contraction for two reasons one for +the reason we had before which is that + + align:start position:0% +the reason we had before which is that + + + align:start position:0% +the reason we had before which is that +investment Falls but there is a second + + align:start position:0% +investment Falls but there is a second + + + align:start position:0% +investment Falls but there is a second +reason is + + align:start position:0% +reason is + + + align:start position:0% +reason is +contractionary what is that second + + align:start position:0% + + + + align:start position:0% + +reason I mean it's only here it's only + + align:start position:0% +reason I mean it's only here it's only + + + align:start position:0% +reason I mean it's only here it's only +second yeah ra the exchange rate because + + align:start position:0% +second yeah ra the exchange rate because + + + align:start position:0% +second yeah ra the exchange rate because +appreciates the exchange rate and when + + align:start position:0% +appreciates the exchange rate and when + + + align:start position:0% +appreciates the exchange rate and when +you appreciate the exchange rate net + + align:start position:0% +you appreciate the exchange rate net + + + align:start position:0% +you appreciate the exchange rate net +exports decline okay so more of the + + align:start position:0% +exports decline okay so more of the + + + align:start position:0% +exports decline okay so more of the +domestic consumption is diverted to + + align:start position:0% +domestic consumption is diverted to + + + align:start position:0% +domestic consumption is diverted to +foreign goods and less of for foreign + + align:start position:0% +foreign goods and less of for foreign + + + align:start position:0% +foreign goods and less of for foreign +demand is is allocated to our exports + + align:start position:0% +demand is is allocated to our exports + + + align:start position:0% +demand is is allocated to our exports +okay so that's a second channel so in an + + align:start position:0% +okay so that's a second channel so in an + + + align:start position:0% +okay so that's a second channel so in an +open economy and the smaller is the + + align:start position:0% +open economy and the smaller is the + + + align:start position:0% +open economy and the smaller is the +economy the more important is this term + + align:start position:0% +economy the more important is this term + + + align:start position:0% +economy the more important is this term +the more powerful is that + + align:start position:0% +the more powerful is that + + + align:start position:0% +the more powerful is that +channel + + align:start position:0% + + + + align:start position:0% + +okay the US cares very little about this + + align:start position:0% +okay the US cares very little about this + + + align:start position:0% +okay the US cares very little about this +effect most other economies care a lot + + align:start position:0% +effect most other economies care a lot + + + align:start position:0% +effect most other economies care a lot +about this effect + + align:start position:0% +about this effect + + + align:start position:0% +about this effect +okay because the US is a relatively + + align:start position:0% +okay because the US is a relatively + + + align:start position:0% +okay because the US is a relatively +close economy believe it or not so this + + align:start position:0% +close economy believe it or not so this + + + align:start position:0% +close economy believe it or not so this +is sort of the star diagram of the + + align:start position:0% +is sort of the star diagram of the + + + align:start position:0% +is sort of the star diagram of the +Mandel flaming + + align:start position:0% +Mandel flaming + + + align:start position:0% +Mandel flaming +mle so this thing here is our old islm + + align:start position:0% +mle so this thing here is our old islm + + + align:start position:0% +mle so this thing here is our old islm +model it's just that this is is a little + + align:start position:0% +model it's just that this is is a little + + + align:start position:0% +model it's just that this is is a little +thicker now it has net exports in there + + align:start position:0% +thicker now it has net exports in there + + + align:start position:0% +thicker now it has net exports in there +and so on but it looks exactly the same + + align:start position:0% +and so on but it looks exactly the same + + + align:start position:0% +and so on but it looks exactly the same +that is plots equilibrium in financial + + align:start position:0% +that is plots equilibrium in financial + + + align:start position:0% +that is plots equilibrium in financial +and and and and the Goods Market the the + + align:start position:0% +and and and and the Goods Market the the + + + align:start position:0% +and and and and the Goods Market the the +combinations of output and domestic + + align:start position:0% +combinations of output and domestic + + + align:start position:0% +combinations of output and domestic +interest rate that are consistent with + + align:start position:0% +interest rate that are consistent with + + + align:start position:0% +interest rate that are consistent with +equilibrium in in both markets that's + + align:start position:0% +equilibrium in in both markets that's + + + align:start position:0% +equilibrium in in both markets that's +the case here okay this is the is which + + align:start position:0% +the case here okay this is the is which + + + align:start position:0% +the case here okay this is the is which +is all the combinations of domestic + + align:start position:0% +is all the combinations of domestic + + + align:start position:0% +is all the combinations of domestic +output and domestic interest rate that + + align:start position:0% +output and domestic interest rate that + + + align:start position:0% +output and domestic interest rate that +are consistent with equilibrium in Goods + + align:start position:0% +are consistent with equilibrium in Goods + + + align:start position:0% +are consistent with equilibrium in Goods +Market this is the interest rate that is + + align:start position:0% +Market this is the interest rate that is + + + align:start position:0% +Market this is the interest rate that is +consistent with equilibrium financial + + align:start position:0% +consistent with equilibrium financial + + + align:start position:0% +consistent with equilibrium financial +markets that's what the FED does in the + + align:start position:0% +markets that's what the FED does in the + + + align:start position:0% +markets that's what the FED does in the +US that point is where both markets are + + align:start position:0% +US that point is where both markets are + + + align:start position:0% +US that point is where both markets are +in equilibrium but we can take this + + align:start position:0% +in equilibrium but we can take this + + + align:start position:0% +in equilibrium but we can take this +interest rate so that's what will happen + + align:start position:0% +interest rate so that's what will happen + + + align:start position:0% +interest rate so that's what will happen +the interest rate will be + + align:start position:0% +the interest rate will be + + + align:start position:0% +the interest rate will be +in the US the interest rate is set by + + align:start position:0% +in the US the interest rate is set by + + + align:start position:0% +in the US the interest rate is set by +the FED not by the ACB the FED will set + + align:start position:0% +the FED not by the ACB the FED will set + + + align:start position:0% +the FED not by the ACB the FED will set +the interest rate that will give us some + + align:start position:0% +the interest rate that will give us some + + + align:start position:0% +the interest rate that will give us some +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +output and then we can go to the uip + + align:start position:0% +output and then we can go to the uip + + + align:start position:0% +output and then we can go to the uip +condition you see I'm plotting here and + + align:start position:0% +condition you see I'm plotting here and + + + align:start position:0% +condition you see I'm plotting here and +figure out what the exchange rate is + + align:start position:0% +figure out what the exchange rate is + + + align:start position:0% +figure out what the exchange rate is +because for this interest rate here + + align:start position:0% +because for this interest rate here + + + align:start position:0% +because for this interest rate here +there's going to be some point in the + + align:start position:0% +there's going to be some point in the + + + align:start position:0% +there's going to be some point in the +uip and that tells me exactly what the + + align:start position:0% +uip and that tells me exactly what the + + + align:start position:0% +uip and that tells me exactly what the +exchange rate + + align:start position:0% +exchange rate + + + align:start position:0% +exchange rate +is okay so with this set of diagrams I + + align:start position:0% +is okay so with this set of diagrams I + + + align:start position:0% +is okay so with this set of diagrams I +can determine the interest rate output + + align:start position:0% +can determine the interest rate output + + + align:start position:0% +can determine the interest rate output +and exchange rate + + align:start position:0% + + + + align:start position:0% + +so I can study the effects of different + + align:start position:0% +so I can study the effects of different + + + align:start position:0% +so I can study the effects of different +policies for example on output the + + align:start position:0% +policies for example on output the + + + align:start position:0% +policies for example on output the +interest rate of course that's the + + align:start position:0% +interest rate of course that's the + + + align:start position:0% +interest rate of course that's the +policy itself and the exchange rate so + + align:start position:0% +policy itself and the exchange rate so + + + align:start position:0% +policy itself and the exchange rate so +this is the the new thing I can explain + + align:start position:0% +this is the the new thing I can explain + + + align:start position:0% +this is the the new thing I can explain +I can do a little bit of asset pricing + + align:start position:0% +I can do a little bit of asset pricing + + + align:start position:0% +I can do a little bit of asset pricing +here I can explain the the the behavior + + align:start position:0% +here I can explain the the the behavior + + + align:start position:0% +here I can explain the the the behavior +of the exchange rate as + + align:start position:0% + + + + align:start position:0% + +well so this diagram I mean you need to + + align:start position:0% +well so this diagram I mean you need to + + + align:start position:0% +well so this diagram I mean you need to +really control very very well let's when + + align:start position:0% +really control very very well let's when + + + align:start position:0% +really control very very well let's when +I'm going to play with it quite a + + align:start position:0% +I'm going to play with it quite a + + + align:start position:0% +I'm going to play with it quite a +bit monetary policy let's do monetary + + align:start position:0% +bit monetary policy let's do monetary + + + align:start position:0% +bit monetary policy let's do monetary +policy we talk about monetary policy + + align:start position:0% +policy we talk about monetary policy + + + align:start position:0% +policy we talk about monetary policy +already so suppose that for whatever + + align:start position:0% +already so suppose that for whatever + + + align:start position:0% +already so suppose that for whatever +reason H the domestic economy domestic + + align:start position:0% +reason H the domestic economy domestic + + + align:start position:0% +reason H the domestic economy domestic +Central + + align:start position:0% +Central + + + align:start position:0% +Central +Bank ER decides to hike the interest + + align:start position:0% +Bank ER decides to hike the interest + + + align:start position:0% +Bank ER decides to hike the interest +rate suppose the economy was overheating + + align:start position:0% +rate suppose the economy was overheating + + + align:start position:0% +rate suppose the economy was overheating +output was too high ready to Natural + + align:start position:0% +output was too high ready to Natural + + + align:start position:0% +output was too high ready to Natural +rate of output the typical reasons why + + align:start position:0% +rate of output the typical reasons why + + + align:start position:0% +rate of output the typical reasons why +you need to raise interest rate and so + + align:start position:0% +you need to raise interest rate and so + + + align:start position:0% +you need to raise interest rate and so +suppose that the domestic interest rate + + align:start position:0% +suppose that the domestic interest rate + + + align:start position:0% +suppose that the domestic interest rate +goes up well as it used to be that's + + align:start position:0% +goes up well as it used to be that's + + + align:start position:0% +goes up well as it used to be that's +going to be contractionary + + align:start position:0% +going to be contractionary + + + align:start position:0% +going to be contractionary +what happens to the exchange + + align:start position:0% +what happens to the exchange + + + align:start position:0% +what happens to the exchange +rate well I know the interest went + + align:start position:0% +rate well I know the interest went + + + align:start position:0% +rate well I know the interest went +up I go I look into my uip for the + + align:start position:0% +up I go I look into my uip for the + + + align:start position:0% +up I go I look into my uip for the +higher interest rate and need a current + + align:start position:0% +higher interest rate and need a current + + + align:start position:0% +higher interest rate and need a current +exchange rate that is + + align:start position:0% +exchange rate that is + + + align:start position:0% +exchange rate that is +above the old it has to go up relative + + align:start position:0% +above the old it has to go up relative + + + align:start position:0% +above the old it has to go up relative +to all when when I when I increase + + align:start position:0% +to all when when I when I increase + + + align:start position:0% +to all when when I when I increase +interest rate from here to there then my + + align:start position:0% +interest rate from here to there then my + + + align:start position:0% +interest rate from here to there then my +exchange has to appreciate why is that + + align:start position:0% +exchange has to appreciate why is that + + + align:start position:0% +exchange has to appreciate why is that +so an expansionary domestic monetary + + align:start position:0% +so an expansionary domestic monetary + + + align:start position:0% +so an expansionary domestic monetary +policy will lead to contraction in + + align:start position:0% +policy will lead to contraction in + + + align:start position:0% +policy will lead to contraction in +output which is what we get out of + + align:start position:0% +output which is what we get out of + + + align:start position:0% +output which is what we get out of +a monetary policy but it will also lead + + align:start position:0% +a monetary policy but it will also lead + + + align:start position:0% +a monetary policy but it will also lead +to an appreciation of the currency why + + align:start position:0% +to an appreciation of the currency why + + + align:start position:0% +to an appreciation of the currency why +is + + align:start position:0% + + + + align:start position:0% + +that that's what we just discussed uip + + align:start position:0% +that that's what we just discussed uip + + + align:start position:0% +that that's what we just discussed uip +if if I move the domestic interest rate + + align:start position:0% +if if I move the domestic interest rate + + + align:start position:0% +if if I move the domestic interest rate +and the rest and the rest of world does + + align:start position:0% +and the rest and the rest of world does + + + align:start position:0% +and the rest and the rest of world does +not follow me so we move interest rate + + align:start position:0% +not follow me so we move interest rate + + + align:start position:0% +not follow me so we move interest rate +they don't then now I need to compensate + + align:start position:0% +they don't then now I need to compensate + + + align:start position:0% +they don't then now I need to compensate +for this increasing the interest rate + + align:start position:0% +for this increasing the interest rate + + + align:start position:0% +for this increasing the interest rate +differential and the compensation will + + align:start position:0% +differential and the compensation will + + + align:start position:0% +differential and the compensation will +come through an expected Capital loss + + align:start position:0% +come through an expected Capital loss + + + align:start position:0% +come through an expected Capital loss +through the currency so if I appreciate + + align:start position:0% +through the currency so if I appreciate + + + align:start position:0% +through the currency so if I appreciate +more the currencies and I haven't moved + + align:start position:0% +more the currencies and I haven't moved + + + align:start position:0% +more the currencies and I haven't moved +the expected exchange rate I expect a + + align:start position:0% +the expected exchange rate I expect a + + + align:start position:0% +the expected exchange rate I expect a +larger loss from the point of from the + + align:start position:0% +larger loss from the point of from the + + + align:start position:0% +larger loss from the point of from the +country from the currency side + + align:start position:0% +country from the currency side + + + align:start position:0% +country from the currency side +okay that's what what has happened here + + align:start position:0% +okay that's what what has happened here + + + align:start position:0% +okay that's what what has happened here +that's what is behind + + align:start position:0% +that's what is behind + + + align:start position:0% +that's what is behind +depreciation and of course the + + align:start position:0% +depreciation and of course the + + + align:start position:0% +depreciation and of course the +depreciation is already built in here + + align:start position:0% +depreciation is already built in here + + + align:start position:0% +depreciation is already built in here +which is what uh you + + align:start position:0% +which is what uh you + + + align:start position:0% +which is what uh you +know makes monetary policy more powerful + + align:start position:0% +know makes monetary policy more powerful + + + align:start position:0% +know makes monetary policy more powerful +than the close economy okay because you + + align:start position:0% +than the close economy okay because you + + + align:start position:0% +than the close economy okay because you +get the next export Channel but that's + + align:start position:0% +get the next export Channel but that's + + + align:start position:0% +get the next export Channel but that's +built in + + align:start position:0% + + + + align:start position:0% + +here um okay did here all that I did is + + align:start position:0% +here um okay did here all that I did is + + + align:start position:0% +here um okay did here all that I did is +exactly the same as we were doing in the + + align:start position:0% +exactly the same as we were doing in the + + + align:start position:0% +exactly the same as we were doing in the +last 30 minutes I just used this this + + align:start position:0% +last 30 minutes I just used this this + + + align:start position:0% +last 30 minutes I just used this this +uip for whatever domestic reason I need + + align:start position:0% +uip for whatever domestic reason I need + + + align:start position:0% +uip for whatever domestic reason I need +to raise interest rate ER you know I + + align:start position:0% +to raise interest rate ER you know I + + + align:start position:0% +to raise interest rate ER you know I +have contract and monetary policy well + + align:start position:0% +have contract and monetary policy well + + + align:start position:0% +have contract and monetary policy well +one of the effects that you're going to + + align:start position:0% +one of the effects that you're going to + + + align:start position:0% +one of the effects that you're going to +get in an open economy is that your + + align:start position:0% +get in an open economy is that your + + + align:start position:0% +get in an open economy is that your +currency will tend to appreciate okay + + align:start position:0% +currency will tend to appreciate okay + + + align:start position:0% +currency will tend to appreciate okay +good + + align:start position:0% + + + + align:start position:0% + +what about fiscal + + align:start position:0% +what about fiscal + + + align:start position:0% +what about fiscal +policy well if the FED doesn't follow + + align:start position:0% +policy well if the FED doesn't follow + + + align:start position:0% +policy well if the FED doesn't follow +the central bank doesn't follow and you + + align:start position:0% +the central bank doesn't follow and you + + + align:start position:0% +the central bank doesn't follow and you +have an expansionary fiscal policy then + + align:start position:0% +have an expansionary fiscal policy then + + + align:start position:0% +have an expansionary fiscal policy then +ER that will increase + + align:start position:0% +ER that will increase + + + align:start position:0% +ER that will increase +output it has no effect on the interest + + align:start position:0% +output it has no effect on the interest + + + align:start position:0% +output it has no effect on the interest +rate therefore has absolutely no effect + + align:start position:0% +rate therefore has absolutely no effect + + + align:start position:0% +rate therefore has absolutely no effect +on the exchange so an expansionary + + align:start position:0% +on the exchange so an expansionary + + + align:start position:0% +on the exchange so an expansionary +fiscal policy which is accommodated by + + align:start position:0% +fiscal policy which is accommodated by + + + align:start position:0% +fiscal policy which is accommodated by +the FED that means the interest rate is + + align:start position:0% +the FED that means the interest rate is + + + align:start position:0% +the FED that means the interest rate is +kept to the same level then does not + + align:start position:0% +kept to the same level then does not + + + align:start position:0% +kept to the same level then does not +lead to an appreciation of the currency + + align:start position:0% +lead to an appreciation of the currency + + + align:start position:0% +lead to an appreciation of the currency +doesn't move the exchange rate has no + + align:start position:0% +doesn't move the exchange rate has no + + + align:start position:0% +doesn't move the exchange rate has no +implication for the exchange rate + + align:start position:0% + + + + align:start position:0% + +okay now what about this change in + + align:start position:0% +okay now what about this change in + + + align:start position:0% +okay now what about this change in +output is it larger or smaller than the + + align:start position:0% +output is it larger or smaller than the + + + align:start position:0% +output is it larger or smaller than the +one we did in lecture three or + + align:start position:0% + + + + align:start position:0% + +four it's smaller + + align:start position:0% + + + + align:start position:0% + +why exactly because yeah it goes to + + align:start position:0% +why exactly because yeah it goes to + + + align:start position:0% +why exactly because yeah it goes to +import perfect okay okay good so this is + + align:start position:0% +import perfect okay okay good so this is + + + align:start position:0% +import perfect okay okay good so this is +smaller than it was in the close economy + + align:start position:0% +smaller than it was in the close economy + + + align:start position:0% +smaller than it was in the close economy +and but it has no impact on the exchange + + align:start position:0% +and but it has no impact on the exchange + + + align:start position:0% +and but it has no impact on the exchange +rate that is the uip has nothing to do + + align:start position:0% +rate that is the uip has nothing to do + + + align:start position:0% +rate that is the uip has nothing to do +with government expenditure it's all + + align:start position:0% +with government expenditure it's all + + + align:start position:0% +with government expenditure it's all +about financial markets it's about + + align:start position:0% +about financial markets it's about + + + align:start position:0% +about financial markets it's about +expected returns things like that so + + align:start position:0% +expected returns things like that so + + + align:start position:0% +expected returns things like that so +unless the fiscal policy somehow + + align:start position:0% +unless the fiscal policy somehow + + + align:start position:0% +unless the fiscal policy somehow +affects interest rate H then there is no + + align:start position:0% +affects interest rate H then there is no + + + align:start position:0% +affects interest rate H then there is no +effect what may happen is that for + + align:start position:0% +effect what may happen is that for + + + align:start position:0% +effect what may happen is that for +example is that that you know treasury + + align:start position:0% +example is that that you know treasury + + + align:start position:0% +example is that that you know treasury +becomes very expansionary and this + + align:start position:0% +becomes very expansionary and this + + + align:start position:0% +becomes very expansionary and this +output becomes too large for what is + + align:start position:0% +output becomes too large for what is + + + align:start position:0% +output becomes too large for what is +consistent + + align:start position:0% +consistent + + + align:start position:0% +consistent +with a zero output Gap or no inflation + + align:start position:0% +with a zero output Gap or no inflation + + + align:start position:0% +with a zero output Gap or no inflation +and then the FED May react and raise + + align:start position:0% +and then the FED May react and raise + + + align:start position:0% +and then the FED May react and raise +interest rate and that will Le to + + align:start position:0% +interest rate and that will Le to + + + align:start position:0% +interest rate and that will Le to +anation of exchanges and so on and + + align:start position:0% +anation of exchanges and so on and + + + align:start position:0% +anation of exchanges and so on and +that's the reason why in practice when + + align:start position:0% +that's the reason why in practice when + + + align:start position:0% +that's the reason why in practice when +countries have sort of expansionary + + align:start position:0% +countries have sort of expansionary + + + align:start position:0% +countries have sort of expansionary +fiscal packages they the currency tends + + align:start position:0% +fiscal packages they the currency tends + + + align:start position:0% +fiscal packages they the currency tends +to appreciate is because investor expect + + align:start position:0% +to appreciate is because investor expect + + + align:start position:0% +to appreciate is because investor expect +the FED to react to that or the central + + align:start position:0% +the FED to react to that or the central + + + align:start position:0% +the FED to react to that or the central +bank to react to that and raise interest + + align:start position:0% +bank to react to that and raise interest + + + align:start position:0% +bank to react to that and raise interest +rate but if the FED says no no we need + + align:start position:0% +rate but if the FED says no no we need + + + align:start position:0% +rate but if the FED says no no we need +that fiscal expansion I'm not going to + + align:start position:0% +that fiscal expansion I'm not going to + + + align:start position:0% +that fiscal expansion I'm not going to +move the interest rate then the + + align:start position:0% +move the interest rate then the + + + align:start position:0% +move the interest rate then the +exchanger won't + + align:start position:0% + + + + align:start position:0% + +move so let's look at let's use a little + + align:start position:0% +move so let's look at let's use a little + + + align:start position:0% +move so let's look at let's use a little +more of this model and and look at other + + align:start position:0% +more of this model and and look at other + + + align:start position:0% +more of this model and and look at other +shocks within this + + align:start position:0% +shocks within this + + + align:start position:0% +shocks within this +model so let's start with suppose that + + align:start position:0% +model so let's start with suppose that + + + align:start position:0% +model so let's start with suppose that +that a we increase the expected exchange + + align:start position:0% +that a we increase the expected exchange + + + align:start position:0% +that a we increase the expected exchange +rate what moves + + align:start position:0% + + + + align:start position:0% + +in this + + align:start position:0% + + + + align:start position:0% + +diagram let's go does the L + + align:start position:0% + + + + align:start position:0% + +move no the LM is controlled by domestic + + align:start position:0% +move no the LM is controlled by domestic + + + align:start position:0% +move no the LM is controlled by domestic +Central Bank doesn't move that's the I + + align:start position:0% + + + + align:start position:0% + +move when when I ask you what moves you + + align:start position:0% +move when when I ask you what moves you + + + align:start position:0% +move when when I ask you what moves you +should always fix something so you say + + align:start position:0% +should always fix something so you say + + + align:start position:0% +should always fix something so you say +okay let me fix the interest rate say + + align:start position:0% +okay let me fix the interest rate say + + + align:start position:0% +okay let me fix the interest rate say +picked a point like this one say and now + + align:start position:0% +picked a point like this one say and now + + + align:start position:0% +picked a point like this one say and now +I have to ask the question what happens + + align:start position:0% +I have to ask the question what happens + + + align:start position:0% +I have to ask the question what happens +to Output now that I have moved the + + align:start position:0% +to Output now that I have moved the + + + align:start position:0% +to Output now that I have moved the +Spector exchange it if I get the same + + align:start position:0% +Spector exchange it if I get the same + + + align:start position:0% +Spector exchange it if I get the same +output back means that yes hasn't move + + align:start position:0% +output back means that yes hasn't move + + + align:start position:0% +output back means that yes hasn't move +if I get a different output equilibrium + + align:start position:0% +if I get a different output equilibrium + + + align:start position:0% +if I get a different output equilibrium +output then I they did + + align:start position:0% +output then I they did + + + align:start position:0% +output then I they did +move so what is the + + align:start position:0% + + + + align:start position:0% + +answer if the interest rate doesn't move + + align:start position:0% +answer if the interest rate doesn't move + + + align:start position:0% +answer if the interest rate doesn't move +the forign interest doesn't move move an + + align:start position:0% +the forign interest doesn't move move an + + + align:start position:0% +the forign interest doesn't move move an +expected exchange rate goes up what + + align:start position:0% +expected exchange rate goes up what + + + align:start position:0% +expected exchange rate goes up what +happens to the current exchange + + align:start position:0% +happens to the current exchange + + + align:start position:0% +happens to the current exchange +rate + + align:start position:0% +rate + + + align:start position:0% +rate +appreciates what happens when when + + align:start position:0% +appreciates what happens when when + + + align:start position:0% +appreciates what happens when when +there's an appreciation net export + + align:start position:0% +there's an appreciation net export + + + align:start position:0% +there's an appreciation net export +decline that means that moves the yes to + + align:start position:0% +decline that means that moves the yes to + + + align:start position:0% +decline that means that moves the yes to +the left okay so so so this movement + + align:start position:0% +the left okay so so so this movement + + + align:start position:0% +the left okay so so so this movement +will move the to the left as a first + + align:start position:0% +will move the to the left as a first + + + align:start position:0% +will move the to the left as a first +effect what about the uip condition will + + align:start position:0% +effect what about the uip condition will + + + align:start position:0% +effect what about the uip condition will +it move or not we have taken that as a + + align:start position:0% +it move or not we have taken that as a + + + align:start position:0% +it move or not we have taken that as a +parameter will it + + align:start position:0% +parameter will it + + + align:start position:0% +parameter will it +move I mean remember I give you a clue + + align:start position:0% +move I mean remember I give you a clue + + + align:start position:0% +move I mean remember I give you a clue +because I said we are taking these two + + align:start position:0% +because I said we are taking these two + + + align:start position:0% +because I said we are taking these two +as parameters here so if I move a + + align:start position:0% +as parameters here so if I move a + + + align:start position:0% +as parameters here so if I move a +parameter most likely I will move the + + align:start position:0% +parameter most likely I will move the + + + align:start position:0% +parameter most likely I will move the +curve okay but in which direction will + + align:start position:0% +curve okay but in which direction will + + + align:start position:0% +curve okay but in which direction will +it + + align:start position:0% + + + + align:start position:0% + +move to the right yes because for the + + align:start position:0% +move to the right yes because for the + + + align:start position:0% +move to the right yes because for the +same interest rate now I need the + + align:start position:0% +same interest rate now I need the + + + align:start position:0% +same interest rate now I need the +exchange rate to move one for one the + + align:start position:0% +exchange rate to move one for one the + + + align:start position:0% +exchange rate to move one for one the +current exchange to move one for one + + align:start position:0% +current exchange to move one for one + + + align:start position:0% +current exchange to move one for one +with the Spector Exchange you know so + + align:start position:0% +with the Spector Exchange you know so + + + align:start position:0% +with the Spector Exchange you know so +this was the exchanger before and now + + align:start position:0% +this was the exchanger before and now + + + align:start position:0% +this was the exchanger before and now +the speed exchanger move to the right + + align:start position:0% +the speed exchanger move to the right + + + align:start position:0% +the speed exchanger move to the right +well in order not to generate expected + + align:start position:0% +well in order not to generate expected + + + align:start position:0% +well in order not to generate expected +capital gain or loss I have to move the + + align:start position:0% +capital gain or loss I have to move the + + + align:start position:0% +capital gain or loss I have to move the +current exchange rate by the same amount + + align:start position:0% +current exchange rate by the same amount + + + align:start position:0% +current exchange rate by the same amount +and so that means this this Curve will + + align:start position:0% +and so that means this this Curve will + + + align:start position:0% +and so that means this this Curve will +shift to the right okay what if I move + + align:start position:0% +shift to the right okay what if I move + + + align:start position:0% +shift to the right okay what if I move +for an + + align:start position:0% +for an + + + align:start position:0% +for an +output down what + + align:start position:0% +output down what + + + align:start position:0% +output down what +happens which curve moves well this is + + align:start position:0% +happens which curve moves well this is + + + align:start position:0% +happens which curve moves well this is +not a parameter here so this is not + + align:start position:0% +not a parameter here so this is not + + + align:start position:0% +not a parameter here so this is not +moving + + align:start position:0% +moving + + + align:start position:0% +moving +this is not a parameter here so this one + + align:start position:0% +this is not a parameter here so this one + + + align:start position:0% +this is not a parameter here so this one +is not moving only one can move that yes + + align:start position:0% +is not moving only one can move that yes + + + align:start position:0% +is not moving only one can move that yes +where it will move to the left because + + align:start position:0% +where it will move to the left because + + + align:start position:0% +where it will move to the left because +net exports will decline no for any + + align:start position:0% +net exports will decline no for any + + + align:start position:0% +net exports will decline no for any +given level of the interest rate now + + align:start position:0% +given level of the interest rate now + + + align:start position:0% +given level of the interest rate now +we're going have less net exports and + + align:start position:0% +we're going have less net exports and + + + align:start position:0% +we're going have less net exports and +therefore they just moves to the left so + + align:start position:0% +therefore they just moves to the left so + + + align:start position:0% +therefore they just moves to the left so +output false but there's no movement + + align:start position:0% +output false but there's no movement + + + align:start position:0% +output false but there's no movement +here unless the FED reacts to that the + + align:start position:0% +here unless the FED reacts to that the + + + align:start position:0% +here unless the FED reacts to that the +Central Bank reacts to that it won't + + align:start position:0% +Central Bank reacts to that it won't + + + align:start position:0% +Central Bank reacts to that it won't +happen okay + + align:start position:0% + + + + align:start position:0% + +I mean and and and it may well be the + + align:start position:0% +I mean and and and it may well be the + + + align:start position:0% +I mean and and and it may well be the +case that you want to react to that if + + align:start position:0% +case that you want to react to that if + + + align:start position:0% +case that you want to react to that if +if the whole world goes into a recession + + align:start position:0% +if the whole world goes into a recession + + + align:start position:0% +if the whole world goes into a recession +the US is very likely to lower interest + + align:start position:0% +the US is very likely to lower interest + + + align:start position:0% +the US is very likely to lower interest +rates because you + + align:start position:0% +rates because you + + + align:start position:0% +rates because you +know it's very contraction the whole + + align:start position:0% +know it's very contraction the whole + + + align:start position:0% +know it's very contraction the whole +world goes into recession when the US + + align:start position:0% +world goes into recession when the US + + + align:start position:0% +world goes into recession when the US +goes into recession the rest of the + + align:start position:0% +goes into recession the rest of the + + + align:start position:0% +goes into recession the rest of the +world everyone wants to cut interest + + align:start position:0% +world everyone wants to cut interest + + + align:start position:0% +world everyone wants to cut interest +rates because the US is a big player so + + align:start position:0% +rates because the US is a big player so + + + align:start position:0% +rates because the US is a big player so +so it really drags everyone down okay + + align:start position:0% + + + + align:start position:0% + +good the last one and I'm going to + + align:start position:0% +good the last one and I'm going to + + + align:start position:0% +good the last one and I'm going to +repeat this in the next lecture is well + + align:start position:0% +repeat this in the next lecture is well + + + align:start position:0% +repeat this in the next lecture is well +what happens if the if I star moves up + + align:start position:0% +what happens if the if I star moves up + + + align:start position:0% +what happens if the if I star moves up +the foreign inter moves up well the LM + + align:start position:0% +the foreign inter moves up well the LM + + + align:start position:0% +the foreign inter moves up well the LM +doesn't + + align:start position:0% +doesn't + + + align:start position:0% +doesn't +move this one will move which way + + align:start position:0% +move this one will move which way + + + align:start position:0% +move this one will move which way +because that was a parameter + + align:start position:0% + + + + align:start position:0% + +here to the + + align:start position:0% +here to the + + + align:start position:0% +here to the +right you said to the right that's right + + align:start position:0% +right you said to the right that's right + + + align:start position:0% +right you said to the right that's right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +so think what happened here if they + + align:start position:0% +so think what happened here if they + + + align:start position:0% +so think what happened here if they +forign interet goes up at any given + + align:start position:0% +forign interet goes up at any given + + + align:start position:0% +forign interet goes up at any given +interest rate now the domestic bond is + + align:start position:0% +interest rate now the domestic bond is + + + align:start position:0% +interest rate now the domestic bond is +doing worse than otherwise so I need to + + align:start position:0% +doing worse than otherwise so I need to + + + align:start position:0% +doing worse than otherwise so I need to +depreciate the exchange rate today in + + align:start position:0% +depreciate the exchange rate today in + + + align:start position:0% +depreciate the exchange rate today in +order to expect an + + align:start position:0% + + + + align:start position:0% + +appreciation okay that means this curve + + align:start position:0% +appreciation okay that means this curve + + + align:start position:0% +appreciation okay that means this curve +moves to the left + + align:start position:0% + + + + align:start position:0% + +okay okay it moves to the left because I + + align:start position:0% +okay okay it moves to the left because I + + + align:start position:0% +okay okay it moves to the left because I +have to expect an appreciation to + + align:start position:0% +have to expect an appreciation to + + + align:start position:0% +have to expect an appreciation to +compensate for the interest rate + + align:start position:0% +compensate for the interest rate + + + align:start position:0% +compensate for the interest rate +differential so this will move to the + + align:start position:0% +differential so this will move to the + + + align:start position:0% +differential so this will move to the +left what about this curve + + align:start position:0% + + + + align:start position:0% + +here we solve it in the next + + align:start position:0% + + + + align:start position:0% + +lecture good \ No newline at end of file diff --git a/uviHu6m_YnM.txt b/uviHu6m_YnM.txt new file mode 100644 index 0000000000000000000000000000000000000000..2afad03f6d12e40e182875558c9f8c427cb5ca38 --- /dev/null +++ b/uviHu6m_YnM.txt @@ -0,0 +1,203 @@ +align:start position:0% + +hi this is a second lecture on Markov + + align:start position:0% +hi this is a second lecture on Markov + + + align:start position:0% +hi this is a second lecture on Markov +chains we will concentrate on developing + + align:start position:0% +chains we will concentrate on developing + + + align:start position:0% +chains we will concentrate on developing +further the general principles and tools + + align:start position:0% +further the general principles and tools + + + align:start position:0% +further the general principles and tools +behind Markov chains we will first + + align:start position:0% +behind Markov chains we will first + + + align:start position:0% +behind Markov chains we will first +briefly review the main definitions and + + align:start position:0% +briefly review the main definitions and + + + align:start position:0% +briefly review the main definitions and +apply them to illustrate some additional + + align:start position:0% +apply them to illustrate some additional + + + align:start position:0% +apply them to illustrate some additional +calculations one can do as a way to warm + + align:start position:0% +calculations one can do as a way to warm + + + align:start position:0% +calculations one can do as a way to warm +up + + align:start position:0% +up + + + align:start position:0% +up +well then concentrate most of the time + + align:start position:0% +well then concentrate most of the time + + + align:start position:0% +well then concentrate most of the time +on the central topic of today + + align:start position:0% +on the central topic of today + + + align:start position:0% +on the central topic of today +steady-state behavior of chains that is + + align:start position:0% +steady-state behavior of chains that is + + + align:start position:0% +steady-state behavior of chains that is +on what a Markov chain does when it runs + + align:start position:0% +on what a Markov chain does when it runs + + + align:start position:0% +on what a Markov chain does when it runs +for a long time and on what we can say + + align:start position:0% +for a long time and on what we can say + + + align:start position:0% +for a long time and on what we can say +about the probabilities of being in + + align:start position:0% +about the probabilities of being in + + + align:start position:0% +about the probabilities of being in +different states and in order to do that + + align:start position:0% +different states and in order to do that + + + align:start position:0% +different states and in order to do that +we'll review recurrent States transition + + align:start position:0% +we'll review recurrent States transition + + + align:start position:0% +we'll review recurrent States transition +states and recurrent classes talk a bit + + align:start position:0% +states and recurrent classes talk a bit + + + align:start position:0% +states and recurrent classes talk a bit +more about periodic States concentrate + + align:start position:0% +more about periodic States concentrate + + + align:start position:0% +more about periodic States concentrate +most of the time on the convergence + + align:start position:0% +most of the time on the convergence + + + align:start position:0% +most of the time on the convergence +theorem here and the consequence + + align:start position:0% +theorem here and the consequence + + + align:start position:0% +theorem here and the consequence +associated with balance equations of + + align:start position:0% +associated with balance equations of + + + align:start position:0% +associated with balance equations of +Markov chains and finally we will end + + align:start position:0% +Markov chains and finally we will end + + + align:start position:0% +Markov chains and finally we will end +the lecture with an important special + + align:start position:0% +the lecture with an important special + + + align:start position:0% +the lecture with an important special +class + + align:start position:0% +class + + + align:start position:0% +class +the so called birth-death processes so + + align:start position:0% +the so called birth-death processes so + + + align:start position:0% +the so called birth-death processes so +let us start \ No newline at end of file diff --git a/uyZkD_6fd9c.txt b/uyZkD_6fd9c.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7d44927d19ee5b50b8036e269974e94798b6c2d --- /dev/null +++ b/uyZkD_6fd9c.txt @@ -0,0 +1,179 @@ +align:start position:0% + +I don't know I I think junior lab was a + + align:start position:0% +I don't know I I think junior lab was a + + + align:start position:0% +I don't know I I think junior lab was a +really great experience I like that it + + align:start position:0% +really great experience I like that it + + + align:start position:0% +really great experience I like that it +gave people room to figure things out + + align:start position:0% +gave people room to figure things out + + + align:start position:0% +gave people room to figure things out +and come up with their own ideas come up + + align:start position:0% +and come up with their own ideas come up + + + align:start position:0% +and come up with their own ideas come up +with their own ways of proceeding with + + align:start position:0% +with their own ways of proceeding with + + + align:start position:0% +with their own ways of proceeding with +analysis for example in my first + + align:start position:0% +analysis for example in my first + + + align:start position:0% +analysis for example in my first +experiment which was relativistic + + align:start position:0% +experiment which was relativistic + + + align:start position:0% +experiment which was relativistic +dynamics you take electrons you + + align:start position:0% +dynamics you take electrons you + + + align:start position:0% +dynamics you take electrons you +accelerate them in magnetic fields and + + align:start position:0% +accelerate them in magnetic fields and + + + align:start position:0% +accelerate them in magnetic fields and +measure the kinetic energy which + + align:start position:0% +measure the kinetic energy which + + + align:start position:0% +measure the kinetic energy which +ultimately proves relativity there was + + align:start position:0% +ultimately proves relativity there was + + + align:start position:0% +ultimately proves relativity there was +sort of this error that I ran into which + + align:start position:0% +sort of this error that I ran into which + + + align:start position:0% +sort of this error that I ran into which +was a very strange sort of error that + + align:start position:0% +was a very strange sort of error that + + + align:start position:0% +was a very strange sort of error that +that wasn't really well documented so I + + align:start position:0% +that wasn't really well documented so I + + + align:start position:0% +that wasn't really well documented so I +did a lot of independent reading that I + + align:start position:0% +did a lot of independent reading that I + + + align:start position:0% +did a lot of independent reading that I +talked with my my lab professor for for + + align:start position:0% +talked with my my lab professor for for + + + align:start position:0% +talked with my my lab professor for for +like two hours after a lab and by the + + align:start position:0% +like two hours after a lab and by the + + + align:start position:0% +like two hours after a lab and by the +end that really felt like I had + + align:start position:0% +end that really felt like I had + + + align:start position:0% +end that really felt like I had +independently came to like a very light + + align:start position:0% +independently came to like a very light + + + align:start position:0% +independently came to like a very light +deep conclusion on this on this matter + + align:start position:0% +deep conclusion on this on this matter + + + align:start position:0% +deep conclusion on this on this matter +it was a good experience of sort of + + align:start position:0% +it was a good experience of sort of + + + align:start position:0% +it was a good experience of sort of +independent learning than figuring + + align:start position:0% +independent learning than figuring + + + align:start position:0% +independent learning than figuring +things out for yourself \ No newline at end of file diff --git a/vCxqBgcLgNg.txt b/vCxqBgcLgNg.txt new file mode 100644 index 0000000000000000000000000000000000000000..8913bbf149d7de7cf29af1d16569b38355db4f86 --- /dev/null +++ b/vCxqBgcLgNg.txt @@ -0,0 +1,3283 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +students come in with opinions already + + align:start position:0% +students come in with opinions already + + + align:start position:0% +students come in with opinions already +and they can say things in a seminar + + align:start position:0% +and they can say things in a seminar + + + align:start position:0% +and they can say things in a seminar +that are based upon just + + align:start position:0% +that are based upon just + + + align:start position:0% +that are based upon just +their common knowledge and not based on + + align:start position:0% +their common knowledge and not based on + + + align:start position:0% +their common knowledge and not based on +the readings + + align:start position:0% +the readings + + + align:start position:0% +the readings +today on chalk radio we're exploring + + align:start position:0% +today on chalk radio we're exploring + + + align:start position:0% +today on chalk radio we're exploring +global food production water and climate + + align:start position:0% +global food production water and climate + + + align:start position:0% +global food production water and climate +change + + align:start position:0% +change + + + align:start position:0% +change +and the challenge of teaching when + + align:start position:0% +and the challenge of teaching when + + + align:start position:0% +and the challenge of teaching when +polarized opinions come to class + + align:start position:0% +polarized opinions come to class + + + align:start position:0% +polarized opinions come to class +i'd say generally the students learn + + align:start position:0% +i'd say generally the students learn + + + align:start position:0% +i'd say generally the students learn +that most of these issues are more + + align:start position:0% +that most of these issues are more + + + align:start position:0% +that most of these issues are more +subtle and complex than they thought + + align:start position:0% +subtle and complex than they thought + + + align:start position:0% +subtle and complex than they thought +when they came in the class + + align:start position:0% +when they came in the class + + + align:start position:0% +when they came in the class +so + + align:start position:0% +so + + + align:start position:0% +so +one of the things that happens at the + + align:start position:0% +one of the things that happens at the + + + align:start position:0% +one of the things that happens at the +end of the class is people's opinions + + align:start position:0% +end of the class is people's opinions + + + align:start position:0% +end of the class is people's opinions +are usually not as + + align:start position:0% +are usually not as + + + align:start position:0% +are usually not as +polarized as they were in the beginning + + align:start position:0% +polarized as they were in the beginning + + + align:start position:0% +polarized as they were in the beginning +i'm kurt newton your guest host for this + + align:start position:0% +i'm kurt newton your guest host for this + + + align:start position:0% +i'm kurt newton your guest host for this +episode of chalk radio at mit + + align:start position:0% +episode of chalk radio at mit + + + align:start position:0% +episode of chalk radio at mit +officially i'm director of mit + + align:start position:0% +officially i'm director of mit + + + align:start position:0% +officially i'm director of mit +opencourseware but for so many years at + + align:start position:0% +opencourseware but for so many years at + + + align:start position:0% +opencourseware but for so many years at +mit and in my personal life + + align:start position:0% +mit and in my personal life + + + align:start position:0% +mit and in my personal life +i'm also doing a lot of work on climate + + align:start position:0% +i'm also doing a lot of work on climate + + + align:start position:0% +i'm also doing a lot of work on climate +change + + align:start position:0% +change + + + align:start position:0% +change +so when sarah hansen your usual host + + align:start position:0% +so when sarah hansen your usual host + + + align:start position:0% +so when sarah hansen your usual host +lined up this episode dealing with these + + align:start position:0% +lined up this episode dealing with these + + + align:start position:0% +lined up this episode dealing with these +issues that are so deeply personal for + + align:start position:0% +issues that are so deeply personal for + + + align:start position:0% +issues that are so deeply personal for +me around climate change food systems + + align:start position:0% +me around climate change food systems + + + align:start position:0% +me around climate change food systems +and water + + align:start position:0% +and water + + + align:start position:0% +and water +and gave me the chance to join in i + + align:start position:0% +and gave me the chance to join in i + + + align:start position:0% +and gave me the chance to join in i +jumped at it + + align:start position:0% +jumped at it + + + align:start position:0% +jumped at it +with prolonged droughts made worse by + + align:start position:0% +with prolonged droughts made worse by + + + align:start position:0% +with prolonged droughts made worse by +climate change affecting food production + + align:start position:0% +climate change affecting food production + + + align:start position:0% +climate change affecting food production +and ecosystems all around the world + + align:start position:0% +and ecosystems all around the world + + + align:start position:0% +and ecosystems all around the world +this conversation couldn't be more + + align:start position:0% +this conversation couldn't be more + + + align:start position:0% +this conversation couldn't be more +timely our guest dennis mclaughlin is a + + align:start position:0% +timely our guest dennis mclaughlin is a + + + align:start position:0% +timely our guest dennis mclaughlin is a +professor in mit's civil and + + align:start position:0% +professor in mit's civil and + + + align:start position:0% +professor in mit's civil and +environmental engineering department and + + align:start position:0% +environmental engineering department and + + + align:start position:0% +environmental engineering department and +he's the instructor for course 1.74 land + + align:start position:0% +he's the instructor for course 1.74 land + + + align:start position:0% +he's the instructor for course 1.74 land +water food and climate + + align:start position:0% +water food and climate + + + align:start position:0% +water food and climate +professor mclaughlin's interest in + + align:start position:0% +professor mclaughlin's interest in + + + align:start position:0% +professor mclaughlin's interest in +hydrology and what it can tell us about + + align:start position:0% +hydrology and what it can tell us about + + + align:start position:0% +hydrology and what it can tell us about +our food systems has been years in the + + align:start position:0% +our food systems has been years in the + + + align:start position:0% +our food systems has been years in the +making + + align:start position:0% +making + + + align:start position:0% +making +it all started back in 1991 + + align:start position:0% +it all started back in 1991 + + + align:start position:0% +it all started back in 1991 +on a research trip that took him halfway + + align:start position:0% +on a research trip that took him halfway + + + align:start position:0% +on a research trip that took him halfway +around the world + + align:start position:0% +around the world + + + align:start position:0% +around the world +i went to australia + + align:start position:0% +i went to australia + + + align:start position:0% +i went to australia +and there were a lot of discussions at + + align:start position:0% +and there were a lot of discussions at + + + align:start position:0% +and there were a lot of discussions at +the time about what was sustainable + + align:start position:0% +the time about what was sustainable + + + align:start position:0% +the time about what was sustainable +food production and whether or not + + align:start position:0% +food production and whether or not + + + align:start position:0% +food production and whether or not +australia could grow more food with + + align:start position:0% +australia could grow more food with + + + align:start position:0% +australia could grow more food with +limited water + + align:start position:0% +limited water + + + align:start position:0% +limited water +and the connection between the + + align:start position:0% +and the connection between the + + + align:start position:0% +and the connection between the +availability water and the population + + align:start position:0% +availability water and the population + + + align:start position:0% +availability water and the population +and food supply + + align:start position:0% +and food supply + + + align:start position:0% +and food supply +struck me as a really interesting + + align:start position:0% +struck me as a really interesting + + + align:start position:0% +struck me as a really interesting +application area for hydrology + + align:start position:0% + + + + align:start position:0% + +dennis explained that some of the big + + align:start position:0% +dennis explained that some of the big + + + align:start position:0% +dennis explained that some of the big +wheat growing areas were becoming + + align:start position:0% +wheat growing areas were becoming + + + align:start position:0% +wheat growing areas were becoming +reliant on irrigation to supplement + + align:start position:0% +reliant on irrigation to supplement + + + align:start position:0% +reliant on irrigation to supplement +natural rainfall with water pumped from + + align:start position:0% +natural rainfall with water pumped from + + + align:start position:0% +natural rainfall with water pumped from +underground in order to keep the crop + + align:start position:0% +underground in order to keep the crop + + + align:start position:0% +underground in order to keep the crop +big and healthy + + align:start position:0% +big and healthy + + + align:start position:0% +big and healthy +but over time + + align:start position:0% +but over time + + + align:start position:0% +but over time +all that irrigation causes salts to + + align:start position:0% +all that irrigation causes salts to + + + align:start position:0% +all that irrigation causes salts to +build up in the soil + + align:start position:0% +build up in the soil + + + align:start position:0% +build up in the soil +you could go out in the fields and see + + align:start position:0% +you could go out in the fields and see + + + align:start position:0% +you could go out in the fields and see +near the irrigation ditches just white + + align:start position:0% +near the irrigation ditches just white + + + align:start position:0% +near the irrigation ditches just white +layers of salt accumulating it's the + + align:start position:0% +layers of salt accumulating it's the + + + align:start position:0% +layers of salt accumulating it's the +same kind of problem that + + align:start position:0% +same kind of problem that + + + align:start position:0% +same kind of problem that +ruined mesopotamian civilization you + + align:start position:0% +ruined mesopotamian civilization you + + + align:start position:0% +ruined mesopotamian civilization you +know millennia ago and it wasn't like it + + align:start position:0% +know millennia ago and it wasn't like it + + + align:start position:0% +know millennia ago and it wasn't like it +was a big surprise + + align:start position:0% +was a big surprise + + + align:start position:0% +was a big surprise +but there was not really a good + + align:start position:0% +but there was not really a good + + + align:start position:0% +but there was not really a good +mechanism to encourage farmers to + + align:start position:0% +mechanism to encourage farmers to + + + align:start position:0% +mechanism to encourage farmers to +hold back on their irrigation + + align:start position:0% +hold back on their irrigation + + + align:start position:0% +hold back on their irrigation +there was a lot of interest in + + align:start position:0% +there was a lot of interest in + + + align:start position:0% +there was a lot of interest in +changing regulations and incentives for + + align:start position:0% +changing regulations and incentives for + + + align:start position:0% +changing regulations and incentives for +farmers to have less adverse + + align:start position:0% +farmers to have less adverse + + + align:start position:0% +farmers to have less adverse +environmental impact especially with + + align:start position:0% +environmental impact especially with + + + align:start position:0% +environmental impact especially with +salinity + + align:start position:0% +salinity + + + align:start position:0% +salinity +and to make sure that there was enough + + align:start position:0% +and to make sure that there was enough + + + align:start position:0% +and to make sure that there was enough +water to keep the agriculture economy + + align:start position:0% +water to keep the agriculture economy + + + align:start position:0% +water to keep the agriculture economy +healthy and going + + align:start position:0% +healthy and going + + + align:start position:0% +healthy and going +i mean it's not a reasonable solution to + + align:start position:0% +i mean it's not a reasonable solution to + + + align:start position:0% +i mean it's not a reasonable solution to +say we won't have any more farming and + + align:start position:0% +say we won't have any more farming and + + + align:start position:0% +say we won't have any more farming and +therefore we won't have salt + + align:start position:0% +therefore we won't have salt + + + align:start position:0% +therefore we won't have salt +accumulation and so on so it's that + + align:start position:0% +accumulation and so on so it's that + + + align:start position:0% +accumulation and so on so it's that +balance between + + align:start position:0% +balance between + + + align:start position:0% +balance between +sustainable use and economically + + align:start position:0% +sustainable use and economically + + + align:start position:0% +sustainable use and economically +productive use that's tricky + + align:start position:0% +productive use that's tricky + + + align:start position:0% +productive use that's tricky +this experience in australia led to the + + align:start position:0% +this experience in australia led to the + + + align:start position:0% +this experience in australia led to the +creation of a course on water usage and + + align:start position:0% +creation of a course on water usage and + + + align:start position:0% +creation of a course on water usage and +agriculture and food systems + + align:start position:0% +agriculture and food systems + + + align:start position:0% +agriculture and food systems +it was here where professor mclaughlin + + align:start position:0% +it was here where professor mclaughlin + + + align:start position:0% +it was here where professor mclaughlin +recognized that teaching these topics + + align:start position:0% +recognized that teaching these topics + + + align:start position:0% +recognized that teaching these topics +can bring about an extra challenge + + align:start position:0% +can bring about an extra challenge + + + align:start position:0% +can bring about an extra challenge +one of the interesting things about the + + align:start position:0% +one of the interesting things about the + + + align:start position:0% +one of the interesting things about the +course and a challenging thing as a + + align:start position:0% +course and a challenging thing as a + + + align:start position:0% +course and a challenging thing as a +teacher is a lot of the topics we talk + + align:start position:0% +teacher is a lot of the topics we talk + + + align:start position:0% +teacher is a lot of the topics we talk +about sort of like talking about climate + + align:start position:0% +about sort of like talking about climate + + + align:start position:0% +about sort of like talking about climate +change rgmos + + align:start position:0% +change rgmos + + + align:start position:0% +change rgmos +our food waste our + + align:start position:0% +our food waste our + + + align:start position:0% +our food waste our +vegetarianism + + align:start position:0% +vegetarianism + + + align:start position:0% +vegetarianism +students come in with opinions already + + align:start position:0% +students come in with opinions already + + + align:start position:0% +students come in with opinions already +and they can say things in a seminar + + align:start position:0% +and they can say things in a seminar + + + align:start position:0% +and they can say things in a seminar +that are based upon just their common + + align:start position:0% +that are based upon just their common + + + align:start position:0% +that are based upon just their common +knowledge and not based on the readings + + align:start position:0% +knowledge and not based on the readings + + + align:start position:0% +knowledge and not based on the readings +so for example in gmos + + align:start position:0% +so for example in gmos + + + align:start position:0% +so for example in gmos +the focus of most of the students is oh + + align:start position:0% +the focus of most of the students is oh + + + align:start position:0% +the focus of most of the students is oh +gmos hurt me human health are they going + + align:start position:0% +gmos hurt me human health are they going + + + align:start position:0% +gmos hurt me human health are they going +to cause me to have cancer or + + align:start position:0% +to cause me to have cancer or + + + align:start position:0% +to cause me to have cancer or +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +and that's really not the scientific + + align:start position:0% +and that's really not the scientific + + + align:start position:0% +and that's really not the scientific +perspective so much in gmos because + + align:start position:0% +perspective so much in gmos because + + + align:start position:0% +perspective so much in gmos because +there's almost zero evidence that any + + align:start position:0% +there's almost zero evidence that any + + + align:start position:0% +there's almost zero evidence that any +gmos are harmful to human health + + align:start position:0% +gmos are harmful to human health + + + align:start position:0% +gmos are harmful to human health +and they learn that by reading the + + align:start position:0% +and they learn that by reading the + + + align:start position:0% +and they learn that by reading the +papers + + align:start position:0% +papers + + + align:start position:0% +papers +the problem is what do they do to the + + align:start position:0% +the problem is what do they do to the + + + align:start position:0% +the problem is what do they do to the +ecosystem and what do they do to other + + align:start position:0% +ecosystem and what do they do to other + + + align:start position:0% +ecosystem and what do they do to other +plants that are not genetically + + align:start position:0% +plants that are not genetically + + + align:start position:0% +plants that are not genetically +manipulated and what are the unintended + + align:start position:0% +manipulated and what are the unintended + + + align:start position:0% +manipulated and what are the unintended +consequences of gmos because gmos are + + align:start position:0% +consequences of gmos because gmos are + + + align:start position:0% +consequences of gmos because gmos are +generally + + align:start position:0% +generally + + + align:start position:0% +generally +designed to + + align:start position:0% +designed to + + + align:start position:0% +designed to +help the farmer be more productive + + align:start position:0% +help the farmer be more productive + + + align:start position:0% +help the farmer be more productive +one of the things that happens at the + + align:start position:0% +one of the things that happens at the + + + align:start position:0% +one of the things that happens at the +end of the class is people's opinions + + align:start position:0% +end of the class is people's opinions + + + align:start position:0% +end of the class is people's opinions +are usually not as + + align:start position:0% +are usually not as + + + align:start position:0% +are usually not as +polarized as they were in the beginning + + align:start position:0% +polarized as they were in the beginning + + + align:start position:0% +polarized as they were in the beginning +in my own work on climate change i've + + align:start position:0% +in my own work on climate change i've + + + align:start position:0% +in my own work on climate change i've +certainly had this experience of + + align:start position:0% +certainly had this experience of + + + align:start position:0% +certainly had this experience of +trying to have conversations with people + + align:start position:0% +trying to have conversations with people + + + align:start position:0% +trying to have conversations with people +coming out of polarized opinions and + + align:start position:0% +coming out of polarized opinions and + + + align:start position:0% +coming out of polarized opinions and +preconceived notions + + align:start position:0% +preconceived notions + + + align:start position:0% +preconceived notions +i was really curious to hear how dennis + + align:start position:0% +i was really curious to hear how dennis + + + align:start position:0% +i was really curious to hear how dennis +moved beyond that in this class and + + align:start position:0% +moved beyond that in this class and + + + align:start position:0% +moved beyond that in this class and +helped the students have more productive + + align:start position:0% +helped the students have more productive + + + align:start position:0% +helped the students have more productive +conversations view these sometimes + + align:start position:0% +conversations view these sometimes + + + align:start position:0% +conversations view these sometimes +controversial issues from multiple + + align:start position:0% +controversial issues from multiple + + + align:start position:0% +controversial issues from multiple +angles + + align:start position:0% +angles + + + align:start position:0% +angles +it's really just an introductory course + + align:start position:0% +it's really just an introductory course + + + align:start position:0% +it's really just an introductory course +and it's to kind of stimulate interest + + align:start position:0% +and it's to kind of stimulate interest + + + align:start position:0% +and it's to kind of stimulate interest +that they had when they came in + + align:start position:0% +that they had when they came in + + + align:start position:0% +that they had when they came in +and show them that it is possible to + + align:start position:0% +and show them that it is possible to + + + align:start position:0% +and show them that it is possible to +pursue difficult topics by going to the + + align:start position:0% +pursue difficult topics by going to the + + + align:start position:0% +pursue difficult topics by going to the +literature many of them aren't used to + + align:start position:0% +literature many of them aren't used to + + + align:start position:0% +literature many of them aren't used to +reading scientific papers the + + align:start position:0% +reading scientific papers the + + + align:start position:0% +reading scientific papers the +undergraduates especially they're used + + align:start position:0% +undergraduates especially they're used + + + align:start position:0% +undergraduates especially they're used +to being lectured to and things being in + + align:start position:0% +to being lectured to and things being in + + + align:start position:0% +to being lectured to and things being in +textbooks + + align:start position:0% +textbooks + + + align:start position:0% +textbooks +and here's where dennis mclaughlin gets + + align:start position:0% +and here's where dennis mclaughlin gets + + + align:start position:0% +and here's where dennis mclaughlin gets +creative + + align:start position:0% +creative + + + align:start position:0% +creative +for each article he assigns a student is + + align:start position:0% +for each article he assigns a student is + + + align:start position:0% +for each article he assigns a student is +asked to present that article to the + + align:start position:0% +asked to present that article to the + + + align:start position:0% +asked to present that article to the +class + + align:start position:0% +class + + + align:start position:0% +class +but + + align:start position:0% +but + + + align:start position:0% +but +dennis also gives a specific prompt to + + align:start position:0% +dennis also gives a specific prompt to + + + align:start position:0% +dennis also gives a specific prompt to +make sure that these presentations + + align:start position:0% +make sure that these presentations + + + align:start position:0% +make sure that these presentations +actually help the students understand + + align:start position:0% +actually help the students understand + + + align:start position:0% +actually help the students understand +the material + + align:start position:0% +the material + + + align:start position:0% +the material +another challenge in the course is to + + align:start position:0% +another challenge in the course is to + + + align:start position:0% +another challenge in the course is to +make sure that their presentations don't + + align:start position:0% +make sure that their presentations don't + + + align:start position:0% +make sure that their presentations don't +bore the other students + + align:start position:0% +bore the other students + + + align:start position:0% +bore the other students +so + + align:start position:0% +so + + + align:start position:0% +so +i said you just have a minute or two and + + align:start position:0% +i said you just have a minute or two and + + + align:start position:0% +i said you just have a minute or two and +you should pose some questions for the + + align:start position:0% +you should pose some questions for the + + + align:start position:0% +you should pose some questions for the +class or some issues and make them as + + align:start position:0% +class or some issues and make them as + + + align:start position:0% +class or some issues and make them as +controversial as possible so that's + + align:start position:0% +controversial as possible so that's + + + align:start position:0% +controversial as possible so that's +that's what we try to do + + align:start position:0% +that's what we try to do + + + align:start position:0% +that's what we try to do +as controversial as possible + + align:start position:0% +as controversial as possible + + + align:start position:0% +as controversial as possible +wouldn't encouraging controversy just + + align:start position:0% +wouldn't encouraging controversy just + + + align:start position:0% +wouldn't encouraging controversy just +prevent us from moving beyond polarized + + align:start position:0% +prevent us from moving beyond polarized + + + align:start position:0% +prevent us from moving beyond polarized +opinions + + align:start position:0% +opinions + + + align:start position:0% +opinions +dennis went on to explain + + align:start position:0% +dennis went on to explain + + + align:start position:0% +dennis went on to explain +why controversy really is productive and + + align:start position:0% +why controversy really is productive and + + + align:start position:0% +why controversy really is productive and +important to deal with especially in + + align:start position:0% +important to deal with especially in + + + align:start position:0% +important to deal with especially in +science and engineering classrooms + + align:start position:0% +science and engineering classrooms + + + align:start position:0% +science and engineering classrooms +another thing they're not used to the + + align:start position:0% +another thing they're not used to the + + + align:start position:0% +another thing they're not used to the +students + + align:start position:0% +students + + + align:start position:0% +students +even some of the graduate students is + + align:start position:0% +even some of the graduate students is + + + align:start position:0% +even some of the graduate students is +scientific controversy + + align:start position:0% +scientific controversy + + + align:start position:0% +scientific controversy +there's perhaps not that much + + align:start position:0% +there's perhaps not that much + + + align:start position:0% +there's perhaps not that much +controversy ironically interestingly + + align:start position:0% +controversy ironically interestingly + + + align:start position:0% +controversy ironically interestingly +about gmos + + align:start position:0% +about gmos + + + align:start position:0% +about gmos +but there's a lot of controversy about + + align:start position:0% +but there's a lot of controversy about + + + align:start position:0% +but there's a lot of controversy about +things like organic farming + + align:start position:0% +things like organic farming + + + align:start position:0% +things like organic farming +and whether or not we should be willing + + align:start position:0% +and whether or not we should be willing + + + align:start position:0% +and whether or not we should be willing +to sacrifice yield a bit to have more + + align:start position:0% +to sacrifice yield a bit to have more + + + align:start position:0% +to sacrifice yield a bit to have more +sustainable agriculture + + align:start position:0% +sustainable agriculture + + + align:start position:0% +sustainable agriculture +and one of the things we find out in the + + align:start position:0% +and one of the things we find out in the + + + align:start position:0% +and one of the things we find out in the +class is many people who are + + align:start position:0% +class is many people who are + + + align:start position:0% +class is many people who are +organic farming advocates + + align:start position:0% +organic farming advocates + + + align:start position:0% +organic farming advocates +are + + align:start position:0% +are + + + align:start position:0% +are +sort of out of the mainstream of the + + align:start position:0% +sort of out of the mainstream of the + + + align:start position:0% +sort of out of the mainstream of the +scientific literature + + align:start position:0% +scientific literature + + + align:start position:0% +scientific literature +but when you + + align:start position:0% +but when you + + + align:start position:0% +but when you +review the papers on the other side that + + align:start position:0% +review the papers on the other side that + + + align:start position:0% +review the papers on the other side that +say + + align:start position:0% +say + + + align:start position:0% +say +for example + + align:start position:0% +for example + + + align:start position:0% +for example +it's silly to try to continue + + align:start position:0% +it's silly to try to continue + + + align:start position:0% +it's silly to try to continue +smallholder farming in africa + + align:start position:0% +smallholder farming in africa + + + align:start position:0% +smallholder farming in africa +africa's agricultural future should be + + align:start position:0% +africa's agricultural future should be + + + align:start position:0% +africa's agricultural future should be +large industrial farms + + align:start position:0% +large industrial farms + + + align:start position:0% +large industrial farms +perhaps run by foreigners + + align:start position:0% +perhaps run by foreigners + + + align:start position:0% +perhaps run by foreigners +who buy or lease the land + + align:start position:0% +who buy or lease the land + + + align:start position:0% +who buy or lease the land +so people write + + align:start position:0% +so people write + + + align:start position:0% +so people write +assessments like that and you say well + + align:start position:0% +assessments like that and you say well + + + align:start position:0% +assessments like that and you say well +yeah but they're being funded by the + + align:start position:0% +yeah but they're being funded by the + + + align:start position:0% +yeah but they're being funded by the +large agricultural industry + + align:start position:0% +large agricultural industry + + + align:start position:0% +large agricultural industry +well does that mean they're wrong are + + align:start position:0% +well does that mean they're wrong are + + + align:start position:0% +well does that mean they're wrong are +they biased well i don't know + + align:start position:0% +they biased well i don't know + + + align:start position:0% +they biased well i don't know +but they become advocates too + + align:start position:0% +but they become advocates too + + + align:start position:0% +but they become advocates too +so the students read the papers and we + + align:start position:0% +so the students read the papers and we + + + align:start position:0% +so the students read the papers and we +try to discuss + + align:start position:0% +try to discuss + + + align:start position:0% +try to discuss +both sides of an argument uh based on + + align:start position:0% +both sides of an argument uh based on + + + align:start position:0% +both sides of an argument uh based on +the merits + + align:start position:0% +the merits + + + align:start position:0% +the merits +and um + + align:start position:0% +and um + + + align:start position:0% +and um +i'm not saying students don't get + + align:start position:0% +i'm not saying students don't get + + + align:start position:0% +i'm not saying students don't get +exposure to that kind of thing elsewhere + + align:start position:0% +exposure to that kind of thing elsewhere + + + align:start position:0% +exposure to that kind of thing elsewhere +but if they're taking physics and we're + + align:start position:0% +but if they're taking physics and we're + + + align:start position:0% +but if they're taking physics and we're +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +newton's law you know it's not presented + + align:start position:0% +newton's law you know it's not presented + + + align:start position:0% +newton's law you know it's not presented +as + + align:start position:0% +as + + + align:start position:0% +as +a controversy + + align:start position:0% +a controversy + + + align:start position:0% +a controversy +motivating students to engage with the + + align:start position:0% +motivating students to engage with the + + + align:start position:0% +motivating students to engage with the +scientific literature to unpack + + align:start position:0% +scientific literature to unpack + + + align:start position:0% +scientific literature to unpack +controversies is only part of the work + + align:start position:0% +controversies is only part of the work + + + align:start position:0% +controversies is only part of the work +involved in teaching this engineering + + align:start position:0% +involved in teaching this engineering + + + align:start position:0% +involved in teaching this engineering +course + + align:start position:0% +course + + + align:start position:0% +course +there's something else too + + align:start position:0% +there's something else too + + + align:start position:0% +there's something else too +something really important + + align:start position:0% +something really important + + + align:start position:0% +something really important +it's a challenge to decide how much + + align:start position:0% +it's a challenge to decide how much + + + align:start position:0% +it's a challenge to decide how much +effort and + + align:start position:0% +effort and + + + align:start position:0% +effort and +discussion to spend on learning + + align:start position:0% +discussion to spend on learning + + + align:start position:0% +discussion to spend on learning +about scientific issues scientific + + align:start position:0% +about scientific issues scientific + + + align:start position:0% +about scientific issues scientific +controversies + + align:start position:0% +controversies + + + align:start position:0% +controversies +more or less agreed on facts + + align:start position:0% +more or less agreed on facts + + + align:start position:0% +more or less agreed on facts +and how much to spend on things like + + align:start position:0% +and how much to spend on things like + + + align:start position:0% +and how much to spend on things like +values because + + align:start position:0% +values because + + + align:start position:0% +values because +you really can't talk about smallholder + + align:start position:0% +you really can't talk about smallholder + + + align:start position:0% +you really can't talk about smallholder +farming unless you talk about poverty + + align:start position:0% +farming unless you talk about poverty + + + align:start position:0% +farming unless you talk about poverty +you can ask questions so why is the + + align:start position:0% +you can ask questions so why is the + + + align:start position:0% +you can ask questions so why is the +smallholder farmer so poor why does the + + align:start position:0% +smallholder farmer so poor why does the + + + align:start position:0% +smallholder farmer so poor why does the +smallholders kids not want to stay on + + align:start position:0% +smallholders kids not want to stay on + + + align:start position:0% +smallholders kids not want to stay on +the farm they want to go to the city + + align:start position:0% +the farm they want to go to the city + + + align:start position:0% +the farm they want to go to the city +what do they do in the city are there + + align:start position:0% +what do they do in the city are there + + + align:start position:0% +what do they do in the city are there +jobs there + + align:start position:0% +jobs there + + + align:start position:0% +jobs there +well do they have any education + + align:start position:0% +well do they have any education + + + align:start position:0% +well do they have any education +well no because the smallholder farmer + + align:start position:0% +well no because the smallholder farmer + + + align:start position:0% +well no because the smallholder farmer +doesn't have enough money + + align:start position:0% +doesn't have enough money + + + align:start position:0% +doesn't have enough money +to send the child to school + + align:start position:0% +to send the child to school + + + align:start position:0% +to send the child to school +what about the role women in farming and + + align:start position:0% +what about the role women in farming and + + + align:start position:0% +what about the role women in farming and +the role of cultural differences in how + + align:start position:0% +the role of cultural differences in how + + + align:start position:0% +the role of cultural differences in how +women are viewed and can they for + + align:start position:0% +women are viewed and can they for + + + align:start position:0% +women are viewed and can they for +example participate in ownership + + align:start position:0% +example participate in ownership + + + align:start position:0% +example participate in ownership +you could just spend the whole semester + + align:start position:0% +you could just spend the whole semester + + + align:start position:0% +you could just spend the whole semester +talking about this stuff + + align:start position:0% +talking about this stuff + + + align:start position:0% +talking about this stuff +dennis's course attracts students from a + + align:start position:0% +dennis's course attracts students from a + + + align:start position:0% +dennis's course attracts students from a +wide variety of disciplines and + + align:start position:0% +wide variety of disciplines and + + + align:start position:0% +wide variety of disciplines and +backgrounds + + align:start position:0% +backgrounds + + + align:start position:0% +backgrounds +and it's this diversity of experiences + + align:start position:0% +and it's this diversity of experiences + + + align:start position:0% +and it's this diversity of experiences +among the students that enriches the + + align:start position:0% +among the students that enriches the + + + align:start position:0% +among the students that enriches the +class for everyone including dennis + + align:start position:0% +class for everyone including dennis + + + align:start position:0% +class for everyone including dennis +i had a student in the last class who + + align:start position:0% +i had a student in the last class who + + + align:start position:0% +i had a student in the last class who +was + + align:start position:0% +was + + + align:start position:0% +was +an art student at mass college of art + + align:start position:0% +an art student at mass college of art + + + align:start position:0% +an art student at mass college of art +and she knew almost nothing about + + align:start position:0% +and she knew almost nothing about + + + align:start position:0% +and she knew almost nothing about +engineering or science but she came from + + align:start position:0% +engineering or science but she came from + + + align:start position:0% +engineering or science but she came from +venezuela and settled in puerto rico and + + align:start position:0% +venezuela and settled in puerto rico and + + + align:start position:0% +venezuela and settled in puerto rico and +her aunt is a farmer + + align:start position:0% +her aunt is a farmer + + + align:start position:0% +her aunt is a farmer +and so she talked about how hard it was + + align:start position:0% +and so she talked about how hard it was + + + align:start position:0% +and so she talked about how hard it was +for puerto rican farmers to be competing + + align:start position:0% +for puerto rican farmers to be competing + + + align:start position:0% +for puerto rican farmers to be competing +with central american farmers who were + + align:start position:0% +with central american farmers who were + + + align:start position:0% +with central american farmers who were +very poor who were exporting produce to + + align:start position:0% +very poor who were exporting produce to + + + align:start position:0% +very poor who were exporting produce to +puerto rico so puerto rico this place + + align:start position:0% +puerto rico so puerto rico this place + + + align:start position:0% +puerto rico so puerto rico this place +where you can grow food all the time + + align:start position:0% +where you can grow food all the time + + + align:start position:0% +where you can grow food all the time +this + + align:start position:0% +this + + + align:start position:0% +this +very productive climate + + align:start position:0% +very productive climate + + + align:start position:0% +very productive climate +is + + align:start position:0% +is + + + align:start position:0% +is +not producing much food for its own + + align:start position:0% +not producing much food for its own + + + align:start position:0% +not producing much food for its own +residents because of pricing and she + + align:start position:0% +residents because of pricing and she + + + align:start position:0% +residents because of pricing and she +actually brought that to the class and + + align:start position:0% +actually brought that to the class and + + + align:start position:0% +actually brought that to the class and +talked about it and i i wouldn't even + + align:start position:0% +talked about it and i i wouldn't even + + + align:start position:0% +talked about it and i i wouldn't even +thought about it so there's this + + align:start position:0% +thought about it so there's this + + + align:start position:0% +thought about it so there's this +interaction between the students who + + align:start position:0% +interaction between the students who + + + align:start position:0% +interaction between the students who +have had + + align:start position:0% +have had + + + align:start position:0% +have had +farming experience or just + + align:start position:0% +farming experience or just + + + align:start position:0% +farming experience or just +a student from puerto rico who's talking + + align:start position:0% +a student from puerto rico who's talking + + + align:start position:0% +a student from puerto rico who's talking +to one from philadelphia and they're + + align:start position:0% +to one from philadelphia and they're + + + align:start position:0% +to one from philadelphia and they're +both from cities + + align:start position:0% +both from cities + + + align:start position:0% +both from cities +but they have a much different + + align:start position:0% +but they have a much different + + + align:start position:0% +but they have a much different +perspective + + align:start position:0% +perspective + + + align:start position:0% +perspective +so not only did the other students learn + + align:start position:0% +so not only did the other students learn + + + align:start position:0% +so not only did the other students learn +from these students but i learned from + + align:start position:0% +from these students but i learned from + + + align:start position:0% +from these students but i learned from +them + + align:start position:0% +them + + + align:start position:0% +them +as you may have picked up by now climate + + align:start position:0% +as you may have picked up by now climate + + + align:start position:0% +as you may have picked up by now climate +change is an important topic in this + + align:start position:0% +change is an important topic in this + + + align:start position:0% +change is an important topic in this +course + + align:start position:0% +course + + + align:start position:0% +course +we asked dennis how climate change will + + align:start position:0% +we asked dennis how climate change will + + + align:start position:0% +we asked dennis how climate change will +affect food and agriculture + + align:start position:0% +affect food and agriculture + + + align:start position:0% +affect food and agriculture +well that sounds like a question we + + align:start position:0% +well that sounds like a question we + + + align:start position:0% +well that sounds like a question we +could pose in the class and we do + + align:start position:0% +could pose in the class and we do + + + align:start position:0% +could pose in the class and we do +discuss it through reading papers + + align:start position:0% +discuss it through reading papers + + + align:start position:0% +discuss it through reading papers +so this is a big topic and a controversy + + align:start position:0% +so this is a big topic and a controversy + + + align:start position:0% +so this is a big topic and a controversy +one um one thing that there seems to be + + align:start position:0% +one um one thing that there seems to be + + + align:start position:0% +one um one thing that there seems to be +pretty good agreement on is if climate + + align:start position:0% +pretty good agreement on is if climate + + + align:start position:0% +pretty good agreement on is if climate +change + + align:start position:0% +change + + + align:start position:0% +change +increases temperatures during the + + align:start position:0% +increases temperatures during the + + + align:start position:0% +increases temperatures during the +growing season sufficiently that will + + align:start position:0% +growing season sufficiently that will + + + align:start position:0% +growing season sufficiently that will +hurt + + align:start position:0% +hurt + + + align:start position:0% +hurt +agriculture but it depends on the crop + + align:start position:0% +agriculture but it depends on the crop + + + align:start position:0% +agriculture but it depends on the crop +depends on the place + + align:start position:0% +depends on the place + + + align:start position:0% +depends on the place +it's a lot different talking about small + + align:start position:0% +it's a lot different talking about small + + + align:start position:0% +it's a lot different talking about small +increases in average temperature + + align:start position:0% +increases in average temperature + + + align:start position:0% +increases in average temperature +versus large increases + + align:start position:0% +versus large increases + + + align:start position:0% +versus large increases +that could actually reduce yield or even + + align:start position:0% +that could actually reduce yield or even + + + align:start position:0% +that could actually reduce yield or even +kill crops + + align:start position:0% +kill crops + + + align:start position:0% +kill crops +so temperature extremes probably won't + + align:start position:0% +so temperature extremes probably won't + + + align:start position:0% +so temperature extremes probably won't +help + + align:start position:0% +help + + + align:start position:0% +help +this course really pushes its + + align:start position:0% +this course really pushes its + + + align:start position:0% +this course really pushes its +participants to look beyond their own + + align:start position:0% +participants to look beyond their own + + + align:start position:0% +participants to look beyond their own +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +questions contradictions uncertainties + + align:start position:0% +questions contradictions uncertainties + + + align:start position:0% +questions contradictions uncertainties +those are inevitable when we take on + + align:start position:0% +those are inevitable when we take on + + + align:start position:0% +those are inevitable when we take on +topics as complex as food water and + + align:start position:0% +topics as complex as food water and + + + align:start position:0% +topics as complex as food water and +climate change + + align:start position:0% +climate change + + + align:start position:0% +climate change +professor mclaughlin embraces that + + align:start position:0% +professor mclaughlin embraces that + + + align:start position:0% +professor mclaughlin embraces that +questioning as a core part of the class + + align:start position:0% +questioning as a core part of the class + + + align:start position:0% +questioning as a core part of the class +even as he tries to provide some answers + + align:start position:0% +even as he tries to provide some answers + + + align:start position:0% +even as he tries to provide some answers +especially undergrads they're used to + + align:start position:0% +especially undergrads they're used to + + + align:start position:0% +especially undergrads they're used to +going into class and thinking they're + + align:start position:0% +going into class and thinking they're + + + align:start position:0% +going into class and thinking they're +learning quote facts and that's the end + + align:start position:0% +learning quote facts and that's the end + + + align:start position:0% +learning quote facts and that's the end +of the story but + + align:start position:0% +of the story but + + + align:start position:0% +of the story but +i view the teacher as kind of adjusting + + align:start position:0% +i view the teacher as kind of adjusting + + + align:start position:0% +i view the teacher as kind of adjusting +resetting the discussion + + align:start position:0% +resetting the discussion + + + align:start position:0% +resetting the discussion +to keep things kind of on track and + + align:start position:0% +to keep things kind of on track and + + + align:start position:0% +to keep things kind of on track and +consistent with the papers + + align:start position:0% +consistent with the papers + + + align:start position:0% +consistent with the papers +but giving the students + + align:start position:0% +but giving the students + + + align:start position:0% +but giving the students +the freedom to say silly things or to go + + align:start position:0% +the freedom to say silly things or to go + + + align:start position:0% +the freedom to say silly things or to go +beyond the scope of the paper is part of + + align:start position:0% +beyond the scope of the paper is part of + + + align:start position:0% +beyond the scope of the paper is part of +why they like the course + + align:start position:0% +why they like the course + + + align:start position:0% +why they like the course +when they learn that their differences + + align:start position:0% +when they learn that their differences + + + align:start position:0% +when they learn that their differences +of opinion even among experts and that + + align:start position:0% +of opinion even among experts and that + + + align:start position:0% +of opinion even among experts and that +their values value judgments and that + + align:start position:0% +their values value judgments and that + + + align:start position:0% +their values value judgments and that +their + + align:start position:0% +their + + + align:start position:0% +their +social equity and all kinds of things + + align:start position:0% +social equity and all kinds of things + + + align:start position:0% +social equity and all kinds of things +and + + align:start position:0% +and + + + align:start position:0% +and +i can't i you know + + align:start position:0% +i can't i you know + + + align:start position:0% +i can't i you know +they don't even connect that really with + + align:start position:0% +they don't even connect that really with + + + align:start position:0% +they don't even connect that really with +formal education + + align:start position:0% +formal education + + + align:start position:0% +formal education +but it's not so easy because for one + + align:start position:0% +but it's not so easy because for one + + + align:start position:0% +but it's not so easy because for one +thing it takes the students off balance + + align:start position:0% +thing it takes the students off balance + + + align:start position:0% +thing it takes the students off balance +a bit + + align:start position:0% +a bit + + + align:start position:0% +a bit +so it's definitely an art and you learn + + align:start position:0% +so it's definitely an art and you learn + + + align:start position:0% +so it's definitely an art and you learn +it over multiple times you can't just + + align:start position:0% +it over multiple times you can't just + + + align:start position:0% +it over multiple times you can't just +start the very first year and be perfect + + align:start position:0% +start the very first year and be perfect + + + align:start position:0% +start the very first year and be perfect +on it so you have to learn the teaching + + align:start position:0% +on it so you have to learn the teaching + + + align:start position:0% +on it so you have to learn the teaching +style + + align:start position:0% +style + + + align:start position:0% +style +as well as the content you have to teach + + align:start position:0% +as well as the content you have to teach + + + align:start position:0% +as well as the content you have to teach +yourself how to be observant to what + + align:start position:0% +yourself how to be observant to what + + + align:start position:0% +yourself how to be observant to what +works and what doesn't + + align:start position:0% +works and what doesn't + + + align:start position:0% +works and what doesn't +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +maybe we can all take a page or two from + + align:start position:0% +maybe we can all take a page or two from + + + align:start position:0% +maybe we can all take a page or two from +professor mclaughlin and his students + + align:start position:0% +professor mclaughlin and his students + + + align:start position:0% +professor mclaughlin and his students +get a little more comfortable being + + align:start position:0% +get a little more comfortable being + + + align:start position:0% +get a little more comfortable being +knocked off balance + + align:start position:0% + + + + align:start position:0% + +dennis's perspective made me wonder how + + align:start position:0% +dennis's perspective made me wonder how + + + align:start position:0% +dennis's perspective made me wonder how +other educators handle similar + + align:start position:0% +other educators handle similar + + + align:start position:0% +other educators handle similar +situations + + align:start position:0% +situations + + + align:start position:0% +situations +how do you integrate conversations about + + align:start position:0% +how do you integrate conversations about + + + align:start position:0% +how do you integrate conversations about +values and culture into your science and + + align:start position:0% +values and culture into your science and + + + align:start position:0% +values and culture into your science and +engineering courses in a way that feels + + align:start position:0% +engineering courses in a way that feels + + + align:start position:0% +engineering courses in a way that feels +balanced + + align:start position:0% +balanced + + + align:start position:0% +balanced +you can share your insights via the link + + align:start position:0% +you can share your insights via the link + + + align:start position:0% +you can share your insights via the link +in the show notes and we'll pass them + + align:start position:0% +in the show notes and we'll pass them + + + align:start position:0% +in the show notes and we'll pass them +along to mit faculty and listeners who + + align:start position:0% +along to mit faculty and listeners who + + + align:start position:0% +along to mit faculty and listeners who +could incorporate your ideas into their + + align:start position:0% +could incorporate your ideas into their + + + align:start position:0% +could incorporate your ideas into their +teaching + + align:start position:0% +teaching + + + align:start position:0% +teaching +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +if you're interested in learning more + + align:start position:0% +if you're interested in learning more + + + align:start position:0% +if you're interested in learning more +about professor mclaughlin's work or + + align:start position:0% +about professor mclaughlin's work or + + + align:start position:0% +about professor mclaughlin's work or +teaching with his open educational + + align:start position:0% +teaching with his open educational + + + align:start position:0% +teaching with his open educational +resources + + align:start position:0% +resources + + + align:start position:0% +resources +you can check out his course 1.74 land + + align:start position:0% +you can check out his course 1.74 land + + + align:start position:0% +you can check out his course 1.74 land +water food and climate on our mit open + + align:start position:0% +water food and climate on our mit open + + + align:start position:0% +water food and climate on our mit open +courseware website + + align:start position:0% +courseware website + + + align:start position:0% +courseware website +it's one of over 150 courses + + align:start position:0% +it's one of over 150 courses + + + align:start position:0% +it's one of over 150 courses +in ocw's extensive environment courses + + align:start position:0% +in ocw's extensive environment courses + + + align:start position:0% +in ocw's extensive environment courses +collection + + align:start position:0% +collection + + + align:start position:0% +collection +and for even more check out the mit + + align:start position:0% +and for even more check out the mit + + + align:start position:0% +and for even more check out the mit +climate website at + + align:start position:0% +climate website at + + + align:start position:0% +climate website at +climate.mit.edu where you'll find a + + align:start position:0% +climate.mit.edu where you'll find a + + + align:start position:0% +climate.mit.edu where you'll find a +wealth of material spanning these topics + + align:start position:0% +wealth of material spanning these topics + + + align:start position:0% +wealth of material spanning these topics +and more thank you so much for listening + + align:start position:0% +and more thank you so much for listening + + + align:start position:0% +and more thank you so much for listening +until next time signing off from + + align:start position:0% +until next time signing off from + + + align:start position:0% +until next time signing off from +cambridge massachusetts i'm kurt newton + + align:start position:0% +cambridge massachusetts i'm kurt newton + + + align:start position:0% +cambridge massachusetts i'm kurt newton +from mit open courseware + + align:start position:0% + + + + align:start position:0% + +chalk radio's producers include sarah + + align:start position:0% +chalk radio's producers include sarah + + + align:start position:0% +chalk radio's producers include sarah +hansen brett pachi and dave lachansky + + align:start position:0% +hansen brett pachi and dave lachansky + + + align:start position:0% +hansen brett pachi and dave lachansky +scriptwriting assistance from nidhi + + align:start position:0% +scriptwriting assistance from nidhi + + + align:start position:0% +scriptwriting assistance from nidhi +sastry + + align:start position:0% +sastry + + + align:start position:0% +sastry +show notes for this episode were written + + align:start position:0% +show notes for this episode were written + + + align:start position:0% +show notes for this episode were written +by peter chipman + + align:start position:0% +by peter chipman + + + align:start position:0% +by peter chipman +we're funded by mit open learning and + + align:start position:0% +we're funded by mit open learning and + + + align:start position:0% +we're funded by mit open learning and +supporters like you \ No newline at end of file diff --git a/vhkBbC9qp1M.txt b/vhkBbC9qp1M.txt new file mode 100644 index 0000000000000000000000000000000000000000..bb7d2496ad82195351b27486ecc94f8db6d2b591 --- /dev/null +++ b/vhkBbC9qp1M.txt @@ -0,0 +1,257 @@ +In this lecture, we will +discuss how visualization + +can offer insights in +the area of policing + +in urban environments. + +The explosion of +computerized data + +affects all parts of +society, including policing. + +In the past, human +judgment and experience + +was the only tool in identifying +patterns in criminal behavior. + +Police forces around the +United States and the world + +are augmenting human +judgment with analytics. + +Los Angeles police +worked for months + +to catch Manson +and his followers. + +These days the LAPD is on an +offensive to prevent crime. + +Its latest weapon is +a computer program + +that can actually predict +where crimes will happen. + +And justice +correspondent Bob Orr + +has a first look at the results. + +In the Foothill Division +north of downtown Los Angeles, + +police are patrolling +the largely + +working-class neighborhoods +with specially marked maps. + +The small red squares +are hot spots, + +where computers project +property crimes are most likely. + +It's called predictive policing. + +A program which Captain +Sean Malinowski says + +puts officers on the +scene before crimes occur. + +65% of our crimes are +burglary, grand theft auto, + +and burglary for motor vehicle. + +And that's what these +boxes represent. + +That's a pretty small +box, 500 feet by 500 feet. + +Yes, it is a small area. + +These crime +prediction boxes come + +from the same kind of +mathematical calculation used + +to predict earthquakes +and aftershocks. + +By analyzing the times, dates, +and places of recent crimes + +computers project hot spots for +burglaries, break-ins, and car + +thefts. + +LA's Police Chief +Charlie Beck says + +increasing police patrols +inside those boxes + +denies criminals opportunity. + +The real measure of this is +not how many people you catch, + +it's how much crime you prevent. + +I love catching people. + +It's what I live for. + +But, what I'd rather do is live +in a place and work in a place + +where crime didn't happen. + +Chief Beck, a 35-year veteran +and the father of two LAPD + +officers, has faced +some skepticism + +in selling the +predictive concept. + +You're a street cop. + +I am. + +So somebody comes to you with +a computer program that says, + +here we're going to +predict the future, + +we're going to tell you where +crime is going to occur. + +Aren't some of the guys +on the street just going + +to roll their eyes +and say, oh come on? + +Well, of course. + +I mean, that's the +nature of human beings. + +I mean everybody thinks that +they do their profession as + +well as it can be done already, +so they don't need any help. + +If this old street +cop can change the way + +that he thinks about +this stuff, then I + +know that my kids +can do the same. + +The LAPD began testing the +predictive policing model here + +in the Foothill +Division in November, + +and the early results +are encouraging. + +Burglaries are down 33%, and +violent crime is also down 21%. + +That success will allow +Beck to expand the program + +to other parts of the city and +leverage limited resources. + +I'm not going to get more money. + +I'm not going to get more cops. + +But I have to be better +at using what I have, + +and that's what predictive +policing is about. + +It's also about driving +the crime rate lower. + +Crime here has dropped +nine straight years. + +With these small red +boxes, LA is aiming for 10. + +Bob Orr, CBS News, Los Angeles. + +The Los Angeles Police +Chief Charlie Beck + +writes, "I'm not going +to get more money. + +I'm not going to get more cops. + +I have to be better +at using what I have, + +and that's what predictive +policing is about. + +If this old street +cop can change the way + +that he thinks about +this stuff, then I + +know that my officers +can do the same." + +Let me comment on the +role of analytics. + +The analytical tools you +have learned in this class + +can be used to make these +predictive policing models + +possible. + +However, communicating the +results of these models + +is critical. + +A linear regression +output table will not + +be of use to a police +person on patrol. + +Visualization bridges the +gap between the analytics + +and the end user. \ No newline at end of file diff --git a/vulw9qGXbH0.txt b/vulw9qGXbH0.txt new file mode 100644 index 0000000000000000000000000000000000000000..01ef8121da9e81c486bc88a52409675ef1eb4c31 --- /dev/null +++ b/vulw9qGXbH0.txt @@ -0,0 +1,3504 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: I really stated +everything about discrete + +coding as clearly as I +could in the notes. + +I stated it again as clearly +as I could in class. + +I stated it again as clearly +as I could in making up + +problems that would illustrate +the ideas. + +If I talked about it again +it would just be totally + +repetitive. + +So, at this point, if you want +to understand things better, + +you gotta come up with specific +questions and I will + +be delighted to deal +with them. + +So we want to go on--. + +Oh, there's one other thing +I wanted to talk about. + +We're not having a new problem +set out today. + +I don't think most of you would + +concentrate on it very well. + +I'll tell you what the problems +are, which will be + +due on October 14th. + +I'll pass it out later. + +It's problems 1 through 7, and +the end of lectures 8 to 10, + +and one other one all the way +at the end, problem 26. + +So, 1, 2, 3, 4, 5, +6, 7 and 26. + +So you can get started on them +whenever you choose and I'll + +pass out a traditional problem +set form next time. + +Last time we started to talk +about the difference between + +Reimann and Lebesgue +integration. + +Most people tell me this is +further into mathematics then + +I should go. + +If you agree with them after +we spend a week or two on + +this, please let me know and +I won't torture future + +students with it. + +My sense is that in the things +we're going to be dealing with + +for most of the rest of the +term, knowing a little bit + +extra about mathematics is going +to save you an awful lot + +of time worrying about trivial +little things that you + +shouldn't be worrying about. + +In other words, the great +mathematicians of the 19th + +century who developed -- + +yeah, the 19th century, but +partly the 20th century. + +These mathematicians were really +engineers at heart. + +The 20th century and the 21st +century, mathematics has very + +much become very separated from +physics and applications. + +But in the 19th century and +in the early 20th century, + +mathematicians and physicists +were almost the same animals. + +You could scratch one and you'd +find another one there. + +They were very much interested +in dealing with real things. + +They were like the very best of +mathematicians everywhere + +and the very best of engineers +everywhere. + +They really wanted to make life +simpler instead of making + +life more complicated. + +One way that many people +express it is that + +mathematicians are lazy, and +because they're lazy, they + +don't want to go through a lot +of work, and therefore, they + +feel driven to simplify +things. + +There's an awful lot +of truth in that. + +What we're going to learn here +I think will, in fact, + +simplify what you know about +Fourier series and Fourier + +integrals a great deal. + +Engineers typically don't worry +about those things. + +An awful lot of engineers, and +unfortunately, even those who + +write books often state theorems +and leave out the + +last clause of the theorem, and +the last clause of most of + +those theorems the only way to +make them true is to add the + +clause or not, as the case may +be, at the end of it, which + +makes what they state absolutely +meaningless, + +because anything you can add +or not, as the case may be, + +and it becomes true +at that point. + +The whole question becomes well, +what are those cases + +under which it's true. + +That's what we're going to deal +with a little bit here. + +We're going to say just enough +so you start to understand + +these major things that cause +problems, and I hope you will + +get to the point where you don't +have to worry about them + +after that. + +Well, the first thing, we +started talking about it last + +time, we were talking about the +difference between Reimann + +integration and Lebesgue +integration. + +Reimann was a great +mathematician, but he came + +before all of these +mathematicians who were + +following Lebesgue, and who +started to deal with all of + +the problems with this classical +integration, which + +started to fall apart +throughout + +most of the 19th century. + +What Reimann said, well, split +up the axis into equal + +intervals, then approximate +the function within each + +interval, add up all of those +approximate values, and then + +let this quantization over the +time axis become finer and + +finer and finer. + +If you're lucky, you will +come to a limit. + +You can sort of see when you +get to a limit and when you + +don't get to a limit. + +If the function is smooth enough +and you break it up + +finely enough, you're going to +get a very good approximation, + +and if you break it up more +and more finely, the + +approximation gets better +and better. + +If the function is very wild, if +it jumps around wildly, and + +we'll look at examples of that +later, then this doesn't work. + +We'll see why, in fact, this +approach does work. + +Lebesgue said, no, instead of +quantizing along this axis, + +quantize on this axis. + +So he said, OK, start with a +zero, quantize into epsilon, 2 + +epsilon, 3 epsilon and so forth, +and everybody when they + +talk about epsilon +they're thinking + +about something small. + +They're also thinking about +making it smaller and smaller + +and smaller and hoping that +something nice happens. + +So then what he said is after +you quantize this axis, start + +to look at how much of the +function lies in each one of + +those little windows. + +I've drawn that out here, mu 2 +is the amount of the function + +that lies between 2 epsilon +and 3 epsilon. + +Now the function lies between +2 epsilon and 3 epsilon + +starting at this point, which +I've labeled t1, going up to + +this point, which I've labeled +t2, on over here. + +It's not in this interval +until we get back to t3. + +It stays in this interval +until t4. + +Lebesgue said, OK, let's say +that the function is between 2 + +epsilon and 3 epsilon over a +region of size, t2 minus t1, + +which is this size interval, +plus t4 minus t3, which is + +this size interval. + +Instead of saying size, he said +size gets too confusing + +so I'll call it measure +instead. + +That was the beginning of +measure theory, essentially. + +Well, in fact other people +talked about + +measure before Lebesgue. + +There are a lot of famous +mathematicians who were all + +involved in doing this. + +Anyway, that's the basic +idea of what measure + +is concerned with. + +Now, for this curve here, it's +a nice smooth curve, and you + +can almost see intuitively that +you're going to get the + +same thing looking at it this +way or looking at it this way. + +In fact, you do. + +Anyway, what he finally wound +up with is after saying what + +the measure was on each one of +those little slices, how much + +of the function lay in each +one of those intervals, he + +would just add them all up. + +He would add up how much of +the function was in each + +slice, he would multiply how +much of the function was in a + +slice by how high the +slice was up, and + +then he'd get an answer. + +One difference between what he +did and what Reimann did was + +that he always got a lower bound +in doing it this way. + +If he was dealing with a +non-negative function, his + +approximation was always a +little less than what the + +function was, because anything +that lay between 2 epsilon and + +3 epsilon, he would approximate +it as 2 epsilon, + +which is a little less than +numbers between 2 + +epsilon and 3 epsilon. + +So this is a lower bound, +whereas this is whatever it + +happens to be -- however you +decide to approximate the + +function there, and there are +lots of ways of doing it. + +Well, I won't prove any of these +things, I just want to + +point them out so that when you +get frustrated with this, + +you can always rely on this. + +Which says that whenever the +Reimann integral exists, in + +other words, whenever the +integral that you're used to + +exists, mainly, whenever it has +meaning, Lebesgue integral + +gives you the same value. + +In other words, you haven't lost +anything by going from + +Reimann integration to +Lebesgue integration. + +You can only gain, +you can't lose. + +The familiar rules for +calculating Reimann integrals + +also apply for Lebesgue +integrals. + +You remember what all those +rules are, you probably know + +all of them better even than +this fundamental definition of + +an integral, which is split up +the function into tiny little + +increments, because throughout +all of the courses that you've + +taken, learning about +integration, learning about + +differentiation, learning about +all of these things, + +what you've done for the most +part is to go through + +exercises using these +various rules. + +So, you know how to integrate +lots of traditional functions. + +You memorized what the integral +of many of them is. + +You had many ways of combining +them to find out what the + +integral of many other +functions is. + +If you program a computer to +calculate these integrals, a + +computer can do it both ways. + +It can either use all the rules +to find out what the + +value of an integral is, or it +can chop things up finely and + +find out that way. + +As I said before, if you think +that being able to calculate + +integrals is what engineering +is about, think again. + +I told you before you +could be replaced + +by a digital computer. + +It's worse than that. + +You could be replaced by +your handheld Palm, + +whatever it's called. + +You can be replaced +by anything. + +After a while we're going to +wear little things embedded in + +our body that will tell +us when we're sick + +and things like this. + +You can be replaced by +those things even. + +So you really want to learn +more than just that. + +For some very weird functions, +the Lebesgue integral exists, + +but the Reimann integral +doesn't exist. + +Why do we want to worry +about weird functions? + +I want to tell you two +reasons for it -- + +I told you about it last time. + +One thing is an awful lot of +communication theory is + +concerned with going back and +forth between the time domain + +and the frequency domain. + +When you talk about things which +are straightforward in + +the time domain, often they +become very, very weird in the + +frequency domain +and vice versa. + +I'm going to give you a +beautiful example of that + +probably in the next class. + +You can look at it -- + +it is in the appendix. + +You'll see this absolutely weird +function which has a + +perfectly well-defined +Fourier transform. + +Therefore, the inverse Fourier +transform of this nice looking + +thing is absolutely weird. + +The other reason is even +more important. + +We have to deal with +random processes. + +We have to deal with noise +functions, which are + +continuously varying +functions of time. + +We have to deal with what +we transmit, which is + +continuously varying +functions of time. + +Just like when we were dealing +with sources, we said if we + +want to compress a source it's +not enough to think about what + +one source sequence is. + +We have to think about +it probabalistically. + +Namely, we have to model these +functions as sample values of + +what we call a stochastic +process or a random process. + +In other words, when we start +talking about that, these + +functions which already look +complicated just become sample + +points in this much bigger space +where we're dealing with + +random processes. + +Now, when you're dealing with +sample points of these random + +processes, weirdness just crops +up as a necessary part + +of all of this. + +You can't define a random +process which consists of only + +non-weird things. + +If you do you get something that +doesn't work very well, + +it doesn't do much for you. + +People do that all the time, but +you run out of steam with + +it very, very quickly. + +So for both reasons we +have to be able to + +deal with weird things. + +The most ideal thing is to be +able to deal with weird things + +and get rid of them without +even thinking about them. + +What's the nice thing about +Lebesgue theory? + +It let's you get rid of all +the weirdness without even + +thinking about it. + +But in order to understand it to +start with so we get rid of + +all that weird stuff, we have +to understand just a little + +bit about what it's about +to start with. + +So that's where we're going. + +Well, in this picture -- +let me put the picture + +back up again -- + +I sort of sluffed +over something. + +For a nice, well-behaved +function, it's easy to find + +out what the measure +of a function is. + +Namely, what the measure is of +the set of values where you're + +in some tiny little interval, +and that's straightforward, it + +was just the sum of a +bunch of intervals. + +But now we come to the clincher, +which is we want to + +be able to deal with weird +functions too, and for weird + +functions this measure, the set +of values of time in which + +the function is in some tiny +little slice here, the measure + +of that is going to become +rather complicated. + +Therefore, we have to understand +how to find the + +measure of some pretty +weird sets. + +So, Lebesgue went on and said +OK, I'll define how to find + +measure of things. + +It's all very intuitive. + +If you have any real +numbers, a and b -- + +if I have two real numbers I +might as well say one of them + +was less than or equal to the +other one, so a is less than + +or equal to b. + +I want to include minus +infinity and + +plus infinity here. + +When we say the set of real +numbers, we don't include + +minus infinity and +plus infinity. + +When we talk about the extended +set of real numbers, + +we doing include minus infinity +and plus infinity, + +Here for the most part when +we're dealing with measure + +theory, we really want to +include minus infinity and + +plus infinity also because they +make things easier to + +talk about. + +So what Lebesgue said is for any +interval the set of points + +which lie between a and b, and +he started out with the open + +interval -- namely the set of +points not including a and not + +including b, but including all +the real numbers in between -- + +the measure of that is what we +said before, and none of you + +objected to it. + +The measure of an interval ought +to be the size of the + +interval, because after all, +all Lebesgue was doing was + +taking size and putting another +name on it because we + +all thought of it +as being size. + +So the measure of the interval +ab is b minus a. + +Now as engineers we all know +that it doesn't really make + +any difference whether you +include a or you don't include + +a when we're trying to find +the size of an interval. + +So, he said OK, the size of that +interval is b minus a, + +whether or not you include +either of the end points. + +Then he went on to say something +else, the measure of + +a countable union of disjoint +intervals is the sum of the + +measure of each interval. + +We already said when we were +trying to figure out what the + +Lebesgue integral was, that if +you had several intervals, the + +measure of the entire interval, +namely the measure + +of the union of those intervals +ought to be the sum + +of the measure of +each interval. + +So all he's adding here is +let's go on and go to the + +limit and talk about a countably +infinite number of + +intervals and use the +same definition. + +Now there's one nice thing about +that and what is it? + +If we take the sum of a +countable set of things, each + +of those things is +non-negative. + +So what happens when we take +the sum of a bunch of + +non-negative numbers? + +There are only two possibilities +when you take + +the sum of even a countable set +of non-negative numbers + +and what are they? + +AUDIENCE: Either to the limit +or it goes to infinity? + +PROFESSOR: It goes to a limit +or it goes to infinity, yes. + +Lebesgue said well, let's say if +it goes to infinity that's + +a limit also. + +So, in other words, there are +only two possibilities -- the + +sum is finite, you +can find the sum, + +and the sum if infinite. + +Nothing else can happen. + +So that's nice. + +Then Lebesgue said +one other thing. + +A bunch of mathematicians trying +to deal with this did + +different things when they were +trying to deal with very + +small sets. + +Some of them said well these +very small sets aren't + +measurable, others, and part of +Lebesgue's genius was that + +he said if you can take a set of +points and you can put them + +inside another set of points, +which doesn't amount to + +anything, then this smaller set +of points should have a + +measure which is less +than or equal to the + +bigger set of points. + +So that that says that any +subset of something that has + +zero measure also ought +to have zero measure. + +Now when we look at some +examples you'll see that + +that's not quite as obvious +as it seems. + +But anyway, he said that. + +An even nicer way to put that +is when you're talking about + +weird intervals, try to +cover that weird set + +with a bunch of intervals. + +If you can cover it with +a bunch of intervals in + +different ways and the measure +of the bunch of intervals, the + +countable set of intervals, is +you can make it arbitrarily + +small, then we also say that +this set has measure zero. + +So any time you have a set s +and you can cover it with + +intervals which have arbitrarily +small measure, + +namely we can make the measure +of those intervals as small as + +we want to make them, we say +bingo, s has zero measure. + +Now that's going to be very +nice, because it let's us get + +rid of an awful lot of things. + +Because any time we have some +set which has zero measure in + +this sense, when we look back +at what we did with the + +Lebesgue integral, it says +good, forget about it. + +If it has zero measure +it doesn't come into + +the integral at all. + +That's exactly the +thing we want. + +We'd like to get rid +of all that stuff. + +So if we're going to get rid of +it we have these sets which + +have measure zero, they don't +amount to anything, and we're + +not going to worry about them. + +Let's do an example. + +It's a famous example. + +What about the set of rationals +which lie between + +zero and 1? + +Well, rational numbers are +numbers where there's an + +integer numerator and an integer +denominator, and + +people have shown that there +are numbers which are + +approximated by rational +numbers but they're not + +rational numbers. + +You can take that set of +rational numbers and you can + +order them. + +The way I've ordered them here, +you can't order them in + +terms of how big they are. + +You can't start with the +smallest rational number which + +is greater than zero because +there isn't any such thing. + +Whatever rational number you +find which is greater than + +zero, I can take a half of it, +that's a rational number, and + +that also is greater +than zero and it's + +smaller than your number. + +If you don't like me getting +the better of you, you can + +then take half of that and come +up with a smaller number + +than I could find, and we can +go back and forth on this as + +long as we want. + +So the way we have to order +these is a little + +more subtle than that. + +Here we're going to order them +in terms of first the size of + +the denominator and next, the +size of the numerator. + +So there's only one fraction +in this interval -- + +oh, I screwed that up. + +I really wanted to look at the +set of rational in the open + +interval between zero and 1, +because I don't want zero in + +it, and I don't want 1 in it, +but that's a triviality. + +You can put zero and +1 in or not. + +So, anyway, we'll leave +zero and 1 out. + +So I start out with 1/2 -- + +that's the only rational number +strictly between zero + +and 1 with a denominator of 2. + +Then look at the numbers which +have a denominator of 3, so I + +have 1/3 and 2/3. + +I look then at the rational +numbers which have a + +denominator of 4. + +I have 1/4, I have to leave out +2/4, because that's the + +same as 1/2 which I've already +counted, so I have 3/4, Then I + +go on to 1/5, 2/5, 3/5, +4/5 and so forth. + +In doing this I have actually +counted what the integers are. + +Namely, whenever you can take +a set and put it into + +correspondence with the +integers, you're showing that + +it's countable. + +I've even labeled what +the counting is. + +A sub 1 is 1/2, A sub 2 +is 1/3 and so forth. + +Now, I want to stick this set +inside of a set of intervals, + +and that's pretty easy. + +I stick A sub i inside of the +closed interval, which is A + +sub i on one side and A sub +i on the other side. + +So I'm sticking it inside +of an interval + +which has zero measure. + +Then what I'm going to do is +I'm going to add up all of + +those things. + +Whenever you add up an infinite +number of things, you + +really have to add up a finite +number of them and then look + +at what happens when you +go to the limit. + +So I add up all of these zeroes, +and when I add up n of + +them I get zero. + +I continue to add zeroes, I +continue to have zero, and the + +limit is zero. + +Now here's where the +mathematicians have pulled a + +very clever swindle on you, +because what they're saying is + +that infinity times +zero is zero. + +But they're saying it in +a very precise way. + +But anyway, since we said it +in a very precise way, + +infinity times zero here is +zero, the way we've said it. + +But somehow that's not +very satisfying. + +I mean it really looks +like we've cheated. + +So let's go on and do this +in a different way. + +What we're going to do now is +for each of these rational + +numbers, we're going to put a +little hat around them, a + +little rectangular +hat around them. + +Namely a little interval which +includes A sub i, and which + +also goes delta over 2 that way, +delta over 2 this way, + +and also multiplies that by -- + +my computer knew I was going +to talk about computers + +replacing people, so it +made some mistakes to + +get even with me. + +So this is delta times 2 to the +minus i minus 1, and delta + +times 2 to the minus +i minus 1. + +In other words, you take 1/2 +and you put a pretty big + +interval around it. + +You take 1/3, you put a smaller +interval around it. + +2/3 you put a smaller interval +around that and so forth. + +Well, these intervals here +are going to overlap. + +But anyway, the union of two +overlapping open intervals is + +an open interval which +has a smaller measure + +than with two of them. + +In other words, if you take +this, the measure of this and + +add it to the measure of this, +the union of this and + +this is just this. + +We don't have to be very +sophisticated to see that this + +length is less than this length +plus length, because + +I've double counted +things here. + +So anyway, when I do this I add +up the measure of all of + +these things and I get delta, +and I then let delta get as + +small as I want to. + +Again, I find that the measure +of the rationals is zero. + +Now if you don't like this you +should be very happy with + +yourselves, because I've +struggled with this for years + +and it's not intuitive, because +with these intervals + +I'm putting in here, no matter +how small I make that + +interval, there's an infinite +number of rational numbers + +which are in that interval. + +In other words, the thing +we're trying to do is to + +separate the interval 0,1 into +some union of intervals which + +don't amount to anything but +which include all of the + +rational numbers. + +Somehow this argument is a +little bit bogus because no + +matter what number I look at +between zero and 1, there are + +rational numbers arbitrarily +close to it. + +In other words, what's going on +here is strictly a matter + +of which order we take limits +in, and that's what makes the + +argument subtle. + +But anyway, that is +a perfectly sound + +mathematical argument. + +You can't get around it. + +It's why people objected to what +Lebesgue was doing for a + +long time, because it wasn't +intuitive to them either. + +It was intuitive to Lebesgue, +and finally it's become + +intuitive to everyone, but +not really intuitive. + +It's just that mathematicians +have heard it so many times + +that they believe it. + +I mean one of the problems with +any society is that if + +you tell people things +often enough they + +start to believe them. + +Unfortunately, that's true +in mathematics, too. + +Fortunately in mathematics we +have proofs of things, so that + +when somebody is telling you +something again and again + +which is false, there are always +people who will look at + +it and say no, that's +not true. + +Whereas in other cases, +not necessarily. + +There are also uncountable +sets with measure zero. + +For those of you who are already +sort of overwhelmed by + +this, why don't you go to sleep +for three minutes, it'll + +only take three minutes to +talk about this, but + +it's kind of cute. + +In the set I want to talk +about something closely + +related to what people call +the Cantor set, but it's a + +little bit simpler than that. + +So what I'd like to +do, and this is + +already familiar to you. + +I can take numbers between zero +and 1 and I can represent + +them in a binary expansion. + +I can also represent them +in a ternary expansion. + +I can also represent them in a +decimal expansion, which is + +what you've been doing since +you were three years old or + +five years older or whenever +you started doing this. + +Well, ternary is simpler than +decimal, so you could have + +done this a year before you +started to deal with decimal + +expansions. + +So I want to look at all of +the ternary expansions. + +Each real number corresponds to +a ternary expansion, which + +is an infinite sequence of +numbers each of which are + +zero, 1 or 2. + +Now, what I'm going to do is I'm +going to remove all of the + +sequences which contain any +1's in them at all. + +Now it's not immediately clear +what that's going to do, but + +think of it this way. + +If I first look at the +sequences, I'm going to remove + +all the sequences which +start with 1. + +So the sequences which start +with 1 and have anything else + +after them, that's really the +interval that starts at 1/3 + +and ends at 2/3, because that's +really what starting + +with 1 means. + +This is what we talked about +when we talked about + +approximating binary numbers +also, if you remember, is the + +way we proved the Kraft +inequality. + +It was the same idea. + +The sequences which have a 1 in +the second position, when + +we remove them we're removing +the interval from 1/9 to 2/9. + +We're also removing the interval +from 7/9 to 8/9. + +We're also removing the 4/9 to +5/9 interval, but we removed + +that before. + +So we wind up with something +which is now -- we've taken + +out this, we've now taken +out this, and + +we've taken out this. + +So the only thing left +is this and this and + +this and this, right? + +And we've removed +everything else. + +We keep on doing this. + +Well, each time we remove one +of these, all of the numbers + +that's -- when I do this n +times, the first time I go + +through this process, I removed +1/3 of the numbers, + +I'm left with 2/3 +of the interval. + +When I remove everything that +has a 1 in the second + +position, I'm down +with 2/3 squared. + +When I remove everything which +has a 1 in the third position, + +I'm down to 2/3 cubed. + +When I keep on doing this +forever, what happens + +to 2/3 to the n? + +Well, 2/3 to the +n goes to zero. + +In other words, I have removed +an interval, I have removed a + +set, the measure 1, and +therefore I'm left with a set + +of measure zero. + +You can see this happening. + +I mean you only have diddly left +here and I keep cutting + +away at it. + +So less and less gets left. + +But what we now have is all +sequences, all infinite + +sequences of zeroes and 2's. + +So I'm left with all binary +sequences except instead of + +binary sequences with zeros +and 1's, I now have binary + +sequences with zeros and 2's. + +How many binary sequences are +there when I continue forever? + +Well, you know they're an +uncountable number, because if + +I take all the numbers between +zero and 1, I represent them + +in binary zeroes and +1's, I have an + +uncountable number of them. + +Well, because I have to have an +uncountable number because + +we already showed that any +countable set doesn't amount + +to anything. + +Countable sets are diddly. + +Countable sets all +just go away. + +So, anything which gets left +has to be uncountable. + +Again, people had to worry about +this for a long time. + +But anyway, this gives you an +uncountable set which has + +measure zero. + +So, back to measurable +functions. + +I'm going to get off of +mathematics relatively soon, + +but we need at least this +much to figure out + +what's going on here. + +We say that a function +is measurable. + +Before we were only talking +about sets of numbers being + +measurable. + +We had to talk about sets of +numbers being measurable + +because we were interested in +the question of what's the set + +of times for which a function +lies between 2 epsilon and 3 + +epsilon, for example. + +What we said is we can say a +great deal about that because + +we can not only add up a bunch +of intervals, we can also add + +up a countable bunch of +intervals, and we can also get + +rid of anything which +is negligible. + +So, a function is measurable if +the set of t, such that u + +of t lies between these +two points is + +measurable for each interval. + +In other words, if no matter how +I split up this interval, + +if no matter what slice I look +at, the set of times over + +which the function lies in +there is measurable. + +That's what a measurable +function is. + +Everybody understand +what I just said? + +Let me try to say +it once more. + +A function is measurable if for +every two values, say 3 + +epsilon and 2 epsilon, if the +set of values t for which the + +function lies between 2 epsilon +and 3 epsilon, if that + +set is measurable. + +In other words, that's the set +we were talking about before + +which went from here to +here, and which went + +from here to there. + +In this case for this very +simple function, that's just + +the sum of two intervals. + +If I make the function wiggle +a great deal more, it's the + +sum of a lot more intervals. + +So, we say the function is +measurable if all of the sets + +are measurable. + +Now, what I'm going to do is +when I'm trying to define this + +integral, I'm going +to have to go to + +smaller and smaller intervals. + +Let's start out with epsilon, +2 epsilon, 3 + +epsilon and so forth. + +Let's look at a non-negative +function--. + +Yeah? + +AUDIENCE: Maybe I missed +something, but could you tell + +me [UNINTELLIGIBLE] definition +for a set, if measurable. + +PROFESSOR: What's the definition +for a set is + +measurable. + +I didn't really say, +and that's good. + +I gave you a bunch of conditions +under which a set + +is measurable, and if I have +enough conditions for which + +it's measurable then I don't +have to worry about--. + +I said that it is measurable +under all of these conditions. + +I'm saying I don't have to worry +about the rest of them + +because these are enough +conditions to talk about + +everything I want +to talk about. + +AUDIENCE: [UNINTELLIGIBLE]. + +PROFESSOR: I will define +my measure as + +all of these things. + +Unfortunately, you need a little +bit more, and if you + +want to get more you better +take a course in real + +variables and measure theory. + +Good. + +So, if I want to now make this +epsilon smaller, what I'm + +going to do is do it in +a particular way. + +I'm going to start out +partitioning this into + +intervals of size epsilon. + +Then I'm going to partition +it into intervals of size + +epsilon over 2. + +When I partition it into +intervals of size epsilon over + +2, I'm adding a bunch +of extra things. + +This thing gets added because +when I'm looking at the + +interval between epsilon and 3 +epsilon over 2, the function + +is in this interval here, over +this [UNINTELLIGIBLE]. + +It's in this interval over +this whole thing. + +I'm representing it by +this value down here. + +Now when I have this tinier +interval, I see that this + +function is really in this +interval from here to there + +also, and therefore, instead of +representing the function + +over this interval by epsilon, +I'm representing it by 3 + +epsilon over 2. + +In other words, as I add these +extra quantization levels, I + +can never lose anything, +I only gain things. + +So I gain all of these +cross-hatched regions when I + +do this, which says that when +I add up all these things in + +the integral, every time I +decrease epsilon by 2, the + +integral that I've got, +the approximation to + +the integral increases. + +Now what happens when you take +a sum of a set of numbers + +which are increasing? + +Well, they're increasing, the +result that you get when you + +add them all up is increasing +also, and therefore, as I go + +from epsilon to epsilon over +2 to epsilon over 4 and so + +forth, I keep climbing up. + +Conclusion, I either get to a +finite number or I get to + +infinity -- only two +possibilities. + +Which says that if I'm looking +at non-negative functions, if + +I'm only looking at real +functions which have + +non-negative values, the +Lebesgue integral for a + +measurable function always +exists, if I include infinite + +limits as well as +finite limits. + +Now, if you think back to what +you learned about integration, + +and I hope you at least learned +enough about it that + +you remember there are a lot of +very nasty conditions about + +when integrals exist and +when they don't exist. + +Here that's all gone away. + +This is a beautifully +simple statement. + +You take the integral of a +non-negative function, if it's + +measurable, and there are +only two possibilities. + +The integral of some +finite number or + +the integral is infinite. + +It's never undefined, +it's always defined. + +I think that's neat. + +A few people don't think +it's neat, too bad. + +I guess when I was first +studying this, I didn't think + +it was neat either because +it was too complicated. + +So you have an excuse. + +If you think about it for a +while and you understand it + +and you don't think it's +neat, then I think + +you have a real problem. + +So now -- + +I did this. + +I'm getting too many +slides out here. + +Here we go. + +Here's something new. + +Hardly looks new. + +Let's look at a function now, +just defined on the + +interval zero to 1. + +Suppose that h of t is equal to +1 for each rational number + +and at zero for each +irrational number. + +In other words, this is +a function which looks + +absolutely wild. + +It just goes up to here +and it's 1 or zero. + +It's 1 at this dense set of +points, which we've already + +said doesn't amount to anything, +and it's zero + +everywhere else. + +Now you put that into the +Reimann integral, and the + +Reimann integral goes crazy, +because no matter how small I + +make this interval, there are an +infinite number of rational + +numbers in that interval, and +therefore, the Reimann + +integral can never +even get started. + +For the Lebesgue integral, on +the other hand, look at what + +happens now. + +We have a bunch of points which +are sitting at 1, we + +have a bunch of points which +are sitting at zero. + +The only thing we have to do is +evaluate the measure of the + +set of points which are up in +some tiny interval up in here. + +What's this measure of the set +of t's corresponding to the + +rational numbers? + +Well, you already said +that was zero. + +Now, that's why Lebesgue +integration works. + +Any countable set, and in fact, +any of these uncountable + +sets that measure zero get lost +in here because you're + +combining them all together +and you say they don't + +contribute to the +integral at all. + +That's why Lebesgue integration +is so simple. + +You can forget about +all that stuff. + +When we looked last time at +the Fourier series for a + +square wave, you remember we +found that everything behaved + +very nicely, except where +the square wave had a + +discontinuity, the Fourier +series converged to the + +mid-point, and that was +kind of awkward. + +Well, the mid-points where the +function is discontinuous + +don't amount to anything, +because in that case there + +were just two of them, there +were only two points. + +If they had measure zero +it just washes away. + +You all felt intuitively when +you saw that example, that + +those points were +not important. + +You felt that this was +mathematical carping. + +Well, Lebesgue felt it was +mathematical carping too, but + +he went one step further and +he said here's a way of + +getting rid of all of that +and not having to + +worry about it anymore. + +So you've now gotten to the +point where you don't have to + +worry about any of this +stuff anymore. + +Now let's go a little +bit further. + +We're almost at the +end of this. + +If I take a function which maps +the real numbers into the + +real numbers, in other words, +it's a function which you can + +draw on the line. + +You take time going from minus +infinity to plus infinity, you + +define what this function +is at each time. + +That's what I'm talking +about here, a function + +which you can draw. + +The functions magnitude of +u of t, and the function + +magnitude of u of t squared +are both non-negative. + +Now I'm not going to prove this, +but it turns out that + +the magnitude and the magnitude +squared are both + +measurable functions if u of +t is a measurable function. + +In fact, from now on we're +just going to assume that + +everything we deal with is +measurable, every function is + +measurable. + +I challenge any of you without +looking it up in a book to + +find an example of a +non-measurable function. + +I challenge any of you to +find an example of a + +non-measurable set. + +I challenge any of you to +understand the definition of a + +non-measurable set if you +look it up in a book. + +You've heard about things like +the axiom of choice and things + +like that, which are very +fishy kinds of things -- + +that's all involved in finding +non-measurable function. + +So, any function that you think +about is going to be + +measurable. + +I hate people who say things +like that, but it's the only + +way to get around this because +I don't want to give you any + +examples of that because +they're awful. + +Since magnitude of u of t and +magnitude of u of t squared + +are measurable and they're +non-negative, + +their integrals exist. + +Their integrals exist and are +either a finite number or + +they're infinite. + +So, we define L1 functions, and +we'll be dealing with L1 + +functions and L2 functions all +the way through the course, u + +of t is an L1 function if it's +measurable, and if this + +integrals is less +than infinity. + +That's all there is to it. + +u2 is L2 if it's measurable +and the integral of u of t + +squared is less than infinity. + +I could have said that at the +beginning, but now you see + +that it makes a lot more sense +than it did before because we + +know that if u of t is +measurable, this integral + +exists -- it's either a finite +number or infinity. + +The L1 functions are those +particular functions where + +it's finite and not infinite. + +Same thing here. + +The L2 functions are those +where this is finite. + +This is really the energy of the +function, but now we can + +measure the energy of even weird +functions which are zero + +on the irrationals and +one on the rationals. + +Even things which are zero on +the non-cantor set points and + +1 on the cantor set points, +still it all works. + +So those define the +set L1 and L2. + +Now, a complex function u of +t, which maps r into c, why + +does a complex function +map r into c? + +What's the r doing there? + +Think of any old complex +function you can think of. + +e to the i, 2 pi t. + +That's something that wiggles +around, the sinusoid. + +t is a real number. + +So that function e to the i 2 +pi t is mapping real numbers + +into complex numbers. + +That's what we mean by something +which maps the real + +numbers into complex numbers. + +We always call these +complex functions. + +I mean mathematicians +would say yeah, a + +function could be anything. + +But you know, when most of us +think of a function, we're + +thinking of mapping a real +variable into something else, + +and when we're thinking of +mapping a real variable into + +something else, we're usually +thinking of mapping it into + +real numbers or mapping it +into complex numbers, and + +because we want to deal with +these complex sinusoids, we + +have to include complex +numbers also. + +So a complex function is +measurable by definition if + +the real part and the imaginary +part are each + +measurable. + +We already know when a real +function is measurable. + +Namely, a real function is +measurable if each of these + +slices are measurable. + +So now we know when a complex +function is measurable. + +We already said that all of the +complex functions you can + +think of and all the ones we'll +ever deal with are all + +measurable. + +So L1 and L2 are defined in +the same way when we're + +dealing with complex +functions. + +Namely, just whether this +integral is less than infinity + +and this integral is +less than infinity. + +Since these functions -- this +is a real function from real + +into real, this is a real +function from real into real. + +So those are well-defined. + +What's the relationship +between L1 + +functions and L2 functions? + +Can a function be +L1 and not L2? + +Can it be L2 and not L1? + +Yeah, it can be both, +unfortunately. + +All possibilities exist. + +You can have functions which +are neither L1 nor L2, + +functions that are L1 but not +L2, functions that are L2 but + +not L1, and functions that +are both L1 and L2. + +Those are the truly nice +functions that we + +like to deal with. + +But there's one nice that you +can say, and that follows from + +a simple argument here. + +If u of t is less than or equal +to 1, if the magnitude + +of u of t is less than +or equal to 1--. + +Let's start out by looking at +u of t being greater than or + +equal to 1. + +If u of t is greater than or +equal to 1, then u squared of + +t is even bigger. + +You see the thing that happened +is when u of t + +becomes bigger than +t, u squared of t + +becomes even more bigger. + +When u of t is less than +1, u squared of t is + +less than u of t. + +But if u of t is less than or +equal to 1, it's less than 1. + +So in all cases, for all t, u +of t, magnitude is less than + +or equal to u of t +squared plus 1. + +So that takes into account +both cases. + +It's a bound. + +So if I'm looking at functions +which only exist between over + +some limited time interval, and +I take the integral from + +minus t over 2 to the t over 2 +of the magnitude of u of t, I + +get something which is less than +or equal to the integral + +of u squared of t plus the +integral of 1, and the + +integral of 1 over this finite +limit is just t. + +This says that if a function +is L2 and the function only + +exists over a finite interval, +then the function is L1 also. + +So as long as I'm dealing with +Fourier series, as long as I'm + +dealing with finite duration +functions, L2 means L1. + +All of the nice things that +you get with L1 functions + +apply to L2 functions also, and +there are a lot of nice + +things that happen +for L1 functions. + +There are a lot of nice things +that happen for L2 functions. + +You take the union of what +happens for L1 and for L2, and + +that's beautiful. + +You can say anything then. + +Can't calculate anything, of +course, but we all said, we + +leave that to computers. + +Let's go back Fourier +series now, let's go + +back to the real world. + +Any old function we have u of t, +the magnitude of u of t and + +the magnitude of u of t times +either the 2 pi ift, for any + +old f, this thing has magnitude +1, right, a complex + +exponential. + +Real f, real t. + +This just has magnitude 1. + +And therefore, this magnitude +is equal to this magnitude. + +This says that if the function +u of t is L1, then the + +function u of t times either the +2 pi IFT is also L1, which + +says if we can integrate one +we can integrate the other. + +In other words, the integral +of u of t, either the 2 pi + +ift, the magnitude of +the fdt is going to + +be less than infinity. + +Since we're taking the +magnitude, it's either finite + +or it's infinite, and since u +of t in magnitude when we + +integrate it is less than +infinity, this thing is less + +than infinity also. + +Now, this is a complex +number in here. + +So you can break it up into a +real part and an imaginary + +part, and if this whole thing, +if the magnitude is less than + +infinity, then the magnitude +of the real part is finite. + +If you take the real part over +the region where this is + +positive and the region where +it's negative, you still get + +non-negative numbers. + +In other words, if we're +taking the integral of + +something which has +positive values -- + +I should have written this out +in more detail, it's not + +enough to--. + +I'm taking the integral +of something which--. + +This is u of t. + +If I can find another color. + +Let me draw magnitude of +u of t on top of this. + +This thing here is magnitude +of u of t. + +What? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: I'm making it real +for the time being because I'm + +just looking at the real part. + +In other words, what I'm looking +is this quantity here. + +Later you can imagine doing the +same thing out on complex + +numbers, OK? + +So what I'm saying is if I just +look at the real part of + +u of t -- call this real part +of u of t, if you like. + +If I know that this is finite, +this is non-negative, I know + +that the positive part of this +function has a finite + +integral, I know that the +negative part of it has a + +finite integral. + +In other words, the thing which +makes integration messy + +is you sometimes have the +positive part being infinite, + +the negative part being infinite +also, and the two of + +them cancel out somehow to give +you something finite. + +When you're dealing with the +magnitude of u of t, if the + +magnitude of u of t has an +infinite integral, then that + +messy thing can't happen. + +It says that the positive part +has a finite integral, the + +negative part has a finite +integral also. + +If you take the imaginary part, +visualize that out this + +way, the positive part of the +imaginary part has a finite + +integral, the negative part of +the imaginary part has a + +finite integral also. + +It says if the magnitude of u +of t, that integral always + +exists, and if it's finite, then +these positive parts of + +the real, the positive part of +the imaginary part, all of + +those are finite, and it says +the integral itself is finite. + +Which says that this integral +here has to be finite. + +Namely, the positive part of +the real part, the negative + +part of the real part, the +positive part of the imaginary + +part, the negative part of the +imaginary part, all four have + +to be finite, just because this +quantity here is finite. + +Now, if u of 2 is L2 and also +time limited, it's L1, and the + +same conclusion follows. + +So this integral always +exists if it's + +over a finite interval. + +So at this point we're really +ready to go back to this + +theorem about Fourier series +that we stated last time and + +which was a little bit +mysterious at that point. + +In fact, at this point we've +already proven part of it. + +I wanted to prove it because I +wanted you to know that not + +everything in measure +theory is difficult. + +An awful lot of these things, +after you know just a very + +small number of the ideas, +are very, very simple. + +Now, you will think this is not +simple because you haven't + +had time to think about +the ten slides + +that have gone before. + +But if you go back and you look +at them again, if you + +read the notes, you will see +that, in fact, it all is + +pretty simple. + +What this says is if u of t, a +complex function real into c, + +but time limited, suppose it's +an L2 function, then it's also + +L1 over that interval minus +t over 2 to plus t over 2. + +Then for each k and z, then +for each integer k, this + +integral here, this function +here, is now an L1 function, + +and therefore, this integral +exists, is finite. + +You divide by t is +still finite. + +So that Fourier coefficient +has to exist and it has to + +exist as a finite value. + +Now, you look at Reimann +integration, and you look at + +the theorems about Reimann +integration, and if they're + +stated by somebody who was +stating theorems, the + +conditions are monstrous. + +This is not monstrous. + +It says all you need is +measurability and L1, which + +says it doesn't go +up to infinity. + +That's enough to say that every +one of these Fourier + +coefficients has to exist. + +It might be hard to integrate +it, but you + +know it has to exist. + +Now the next thing it says +is that -- this is more + +complicated. + +What we would like to say and +what we tried to say before + +and what you like to say with +the Fourier series is that u + +of t is equal to this, where you +sum from minus infinity to + +plus infinity. + +We saw that we can't say that. + +We saw that we can't it for +functions which have step + +discontinuities, because +whenever you have a step + +discontinuity, the Fourier +series converges to the + +mid-point of that +discontinuity. + +If you were unfortunate enough +to try to make life simple and + +define the function without +defining it at the step + +discontinuity as the mid-point, +then the Fourier + +series would not be +equal to u of t. + +But what this says is that if +you take the difference + +between u of t and a finite +expansion, and then you look + +at the energy in that +difference, it says that the + +energy and the difference +goes to zero. + +Now that's far more important +than having this integral be + +equal to that, because frankly, +we don't care a fig + +for whether this is equal to +this at every t or not. + +What we care about is when we +add more and more terms onto + +this Fourier series. + +I mean in engineering we're +always approximating things. + +We have to approximate things. + +We talk about functions u of +t, but our functions u of t + +are just models of things +anyway, and we want those + +models to really converge to +something, which means that as + +we take more and more terms in +the Fourier series, we get + +something which comes closer to +u of t and it comes closer + +in energy terms. + +Remember when we take this, when +we approximate it in this + +way by a finite Fourier series, +and we then quantize + +coefficients, and then we go +back to the function, we have + +lost all the coefficients and +all of these terms for the + +very high frequencies. + +We've dropped them off. + +What this says is if we take +more and more of them and then + +we quantize and we go back to +a function v of t it says as + +we add more and more Fourier +coefficients and quantize + +carefully, we can come closer +and closer to the function + +that we started with. + +You don't get that by talking +about point to point equality, + +because as soon as we quantize +you lose all of that anyway. + +You don't have a quality +anywhere anymore, and the only + +thing you can hope for is a +small mean square error. + +So, this looks more complicated +than what you + +would like, but what I'm trying +to tell you is that + +this is far more important +than what you would like. + +What you would like is +not important at all. + +I can give you examples of +things where this converges to + +this everywhere, but in fact, +no matter how many terms you + +take, the energy difference +between these two things is + +very large. + +Those are the ugly things. + +That says you never get a good +approximation, even though + +looking at things point-wise +everything looks great. + +But what you're really +interested in is these mean + +square approximations and what +this Fourier series thing says + +is that if you deal with +measurable functions then this + +converges just to that in this +very nice energy sense, and + +energy is what we're +interested in. + +The final part of this -- + +I mean I talked about this +a little bit last time -- + +sometimes instead of starting +out with a function and + +approximating it with the +Fourier series, you want to + +start out with the coefficients + +and find the function. + +In fact, when we start talking +about modulation, that's + +exactly what we're going to be +doing because we're always + +going to be starting out with +these digital sequences, we're + +going to be finding functions +from the digital sequences. + +This final part of the theorem +says yes, you can + +do that and it works. + +It says that given any set +of coefficients where the + +coefficients have finite energy, +in other words, where + +the sum is less than infinity, +then there's an L2 function, u + +of t, which satisfies the above +in this limiting sense. + +Now this is the hardest thing +of the theorem to prove. + +It looks obvious but it's not. + +But anyway, it's there. + +It says these approximations are +rock solid and you can now + +forget about all of this measure +theoretic stuff, and + +you can just live with the +fact that all of these in + +terms of L2 approximations, +work. + +I mean again, it doesn't look +beautiful at this point + +because you haven't seen +it for long enough. + +It really is beautiful. + +It's beautiful stuff. + +When you think about it long +enough, for 40 years is how + +long I've been thinking about +it, it becomes more and more + +beautiful every year. + +So, if you live long enough +it'll be beautiful. + +Any time you talk about this +type of convergence, we call + +it convergence in the mean, and +then notation we will use + +is l.i.m., which looks like +limit but which really stands + +for limit in the mean. + +We will write that complicated +thing on the last slide, which + +I said is not really that +complicated, but we will write + +this as this. + +In other words, when we write +limit in the mean, we mean + +that the difference between +these two sides in energy + +sense goes to zero +as k gets large. + +That's what this limit means. + +It just means the statement that +we talked about before. + +So the Fourier series, the +theorem really says you can + +find all of the Fourier +coefficients in this way, they + +all exist, they all exist +exactly, they're all finite. + +The function then exists as this +limit in the mean, which + +is the thing that we're +always interested in. + +So, every L2 function defined +over a finite interval, and + +every L1 function defined over +a finite interval, all of + +these have a Fourier series +which satisfies these two + +relationships. + +Now, what we're going to do +with all of this is we're + +going to segment an arbitrary +function, an arbitrary L2 + +function over the entire time +range, and we're going to + +segment it into pieces, +all of width t. + +Then we're going to expand each +of those segments into a + +Fourier series. + +That's what people do any time +they compress voice that I + +said several times. + +When you compress voice -- + +for some reason or other +everybody does it in 20 + +millisecond increments. + +You chop up the voice into 20 +millisecond increments. + +You then, at least, conceptually +look at those 20 + +millisecond increments, think +of them in terms of the + +Fourier series, you expand them +in the Fourier series. + +So for each increment in time +we get a different Fourier + +series, and we use those Fourier +series to approximate + +the function. + +So, each one of the increments +now is going to be represented + +in this way here. + +Since we're only looking at +the function now over the + +interval around time, mt, we +look at it this way, we + +calculate the coefficients, +again, in terms of this + +rectangular function +spaced off by m. + +This is saying the same thing +that we said before, just + +moving it from minus t over 2 +to t over 2 to t minus mt. + +Here's minus t over 2. + +The t over 2. + +Next we're looking at t +over 2 to 3t over 2. + +Next we're looking +at 5t over 2. + +This is m equals zero. + +This is m equals 1. + +This is m equals 2. + +This notation here you should +get used to it, it will be + +confusing for a while. + +All it means is that, +and it works. + +So, in fact, you can take all +these terms, you can break + +them up this way. + +So what you've really done is +you've broken u of t into a + +double sub expansion. + +These exponentials limited in +time, that entire set of + +functions are talking +to each other. + +A function living in this +interval of time and a + +function living in this interval +of time have to be + +orthogonal, because I multiply +this by this and I get + +zero at each time. + +In one interval these +exponentials are orthogonal to + +each other -- we've pointed +that out before. + +So we have a doubly exponential, +we have a double + +sum of orthogonal functions, and +what we're saying is that + +any old L2 function at all +we can break up into + +this kind of sum here. + +This is a very complicated way +of saying what we think of + +physically anyway. + +It says take a big long +function, segment it into + +intervals of length t, break up +each interval of length t + +into a Fourier series. + +That's all that's saying. + +So it's saying what +is obvious. + +We're going to find a number of +such orthogonal expansions + +which work for arbitrary +L2 functions. + +As I said, it's a conceptual +basis for voice compress + +algorithms. + +Even more, next time +we're going to go + +into the Fourier integral. + +You think of the Fourier +integral as being the right + +way to go from time to +frequency, but, in fact, it's + +not really the right way to +go from time to frequency. + +When we think of voice or you +think of the wave form of a + +symphony, for example, +what going on there? + +Over every little interval +of time you hear various + +frequencies, right? + +In fact, if you make t equal +to the timing of the music, + +the idea becomes very, very +clean because at each time + +somebody changes a note. + +So you go from one frequency to +another frequency, so it's + +a rather clean way of +looking at this. + +Our notion of frequency that +we think of intuitively is + +much more closely associated +with the idea of frequencies + +is changing in time then +it is of frequencies + +being constant in time. + +When we look at a Fourier +integral, everything + +is frozen in time. + +As soon as you take the Fourier +integral, you've + +glopped everything from time +minus infinity to time plus + +infinity all together. + +Here when we look at these +expansions, we're looking at + +these frequencies changing. + +There's an unfortunate part +about frequencies changing, + +and that is frequencies, +unfortunately, live over the + +entire time interval. + +These truncated frequencies +work very nicely but they + +don't quite correspond to +non-truncated time intervals, + +but it still does match our +intuition and this is a useful + +way to think about functions +that change in time. + +If you believe what I've just +said, why do people ever worry + +about the Fourier +integral at all? + +Well, you see the problem is +this quantity t here that I'm + +segmenting over is unnatural. + +If I look at voice, there's no t +that you can take which is a + +natural quantity. + +The 20 milliseconds is just +something arbitrary that + +somebody did once +and it worked. + +Too many other engineers in +the field said, well that + +works, I'll pick the same thing +instead of trying to + +think through what a better +number would be. + +So they all use the same t. + +It doesn't correspond to +anything physically. + +So, in fact, people do +try the same thing. + +Let me just say what a Fourier +transform is and we'll talk + +about it most of next time +because that's the next thing + +we have to deal with. + +Something you're all familiar +with are these Fourier + +transform relationships. + +There's the function +of time, there's + +the function of frequency. + +You can go from one to +the other, mapping. + +Well, if you know this +you can find this. + +If you know this, you +can find this. + +It looks a little bit like the +Fourier series, and usually + +when people learn about the +Fourier integral they start + +with a Fourier series and start +letting t become large, + +which doesn't quite work. + +But anyway, that's what +we're going to do. + +If the function is well-behaved, +the first + +integral exists and +the second exists. + +What does well-behaved mean? + +It means what we +usually mean by + +well-behaved, it means it works. + +So again, this theorem here is +another example, or not, as + +the case may be. + +But we'll make this +clearer next time. \ No newline at end of file diff --git a/w7z_z-lucyU.txt b/w7z_z-lucyU.txt new file mode 100644 index 0000000000000000000000000000000000000000..33edc7ba3734f386f55bf0cc322bf045e0244e0c --- /dev/null +++ b/w7z_z-lucyU.txt @@ -0,0 +1,843 @@ +align:start position:0% + +We would like to now introduce a new + + align:start position:0% +We would like to now introduce a new + + + align:start position:0% +We would like to now introduce a new +methodological tool for analyzing + + align:start position:0% +methodological tool for analyzing + + + align:start position:0% +methodological tool for analyzing +problems that involve momentum transfers + + align:start position:0% +problems that involve momentum transfers + + + align:start position:0% +problems that involve momentum transfers +and we call that tool momentum diagrams. + + align:start position:0% +and we call that tool momentum diagrams. + + + align:start position:0% +and we call that tool momentum diagrams. +Now what we'd like to do is look at our + + align:start position:0% +Now what we'd like to do is look at our + + + align:start position:0% +Now what we'd like to do is look at our +fundamental idea which was for discrete + + align:start position:0% +fundamental idea which was for discrete + + + align:start position:0% +fundamental idea which was for discrete +objects + + align:start position:0% +objects + + + align:start position:0% +objects +we have that + + align:start position:0% +we have that + + + align:start position:0% +we have that +involved in a collision we have that the + + align:start position:0% +involved in a collision we have that the + + + align:start position:0% +involved in a collision we have that the +external force + + align:start position:0% +external force + + + align:start position:0% +external force +integrated with respect to time impulse + + align:start position:0% +integrated with respect to time impulse + + + align:start position:0% +integrated with respect to time impulse +is equal to the change in momentum + + align:start position:0% +is equal to the change in momentum + + + align:start position:0% +is equal to the change in momentum +between two different states. So this is + + align:start position:0% +between two different states. So this is + + + align:start position:0% +between two different states. So this is +the momentum of the final state + + align:start position:0% +the momentum of the final state + + + align:start position:0% +the momentum of the final state +and this is the momentum of the initial + + align:start position:0% +and this is the momentum of the initial + + + align:start position:0% +and this is the momentum of the initial +state. + + align:start position:0% +state. + + + align:start position:0% +state. +So when we want to analyze problems, how + + align:start position:0% +So when we want to analyze problems, how + + + align:start position:0% +So when we want to analyze problems, how +can we methodologically + + align:start position:0% +can we methodologically + + + align:start position:0% +can we methodologically +introduce a picture representation of + + align:start position:0% +introduce a picture representation of + + + align:start position:0% +introduce a picture representation of +our problem? So let's look at what we + + align:start position:0% +our problem? So let's look at what we + + + align:start position:0% +our problem? So let's look at what we +need to do first. + + align:start position:0% +need to do first. + + + align:start position:0% +need to do first. +We always need to choose a system that + + align:start position:0% +We always need to choose a system that + + + align:start position:0% +We always need to choose a system that +we're referring to. + + align:start position:0% +we're referring to. + + + align:start position:0% +we're referring to. +And with respect to the choice of that + + align:start position:0% +And with respect to the choice of that + + + align:start position:0% +And with respect to the choice of that +system, we need to also choose + + align:start position:0% +system, we need to also choose + + + align:start position:0% +system, we need to also choose +a reference frame. + + align:start position:0% +a reference frame. + + + align:start position:0% +a reference frame. +Now once we've done that, we can now + + align:start position:0% +Now once we've done that, we can now + + + align:start position:0% +Now once we've done that, we can now +represent a collision with respect to + + align:start position:0% +represent a collision with respect to + + + align:start position:0% +represent a collision with respect to +this system. For instance, let's + + align:start position:0% +this system. For instance, let's + + + align:start position:0% +this system. For instance, let's +consider two objects as our system. + + align:start position:0% +consider two objects as our system. + + + align:start position:0% +consider two objects as our system. +Object one and object two. They're + + align:start position:0% +Object one and object two. They're + + + align:start position:0% +Object one and object two. They're +moving on a frictionless horizontal + + align:start position:0% +moving on a frictionless horizontal + + + align:start position:0% +moving on a frictionless horizontal +surface and we're choosing as a + + align:start position:0% +surface and we're choosing as a + + + align:start position:0% +surface and we're choosing as a +reference frame the ground frame. + + align:start position:0% +reference frame the ground frame. + + + align:start position:0% +reference frame the ground frame. +Now what we'd like to do is identify two + + align:start position:0% +Now what we'd like to do is identify two + + + align:start position:0% +Now what we'd like to do is identify two +states. So for our initial state, + + align:start position:0% + + + + align:start position:0% + +we'll have if we're given some initial + + align:start position:0% +we'll have if we're given some initial + + + align:start position:0% +we'll have if we're given some initial +conditions, what we'd like to do is + + align:start position:0% +conditions, what we'd like to do is + + + align:start position:0% +conditions, what we'd like to do is +represent each object with a velocity + + align:start position:0% +represent each object with a velocity + + + align:start position:0% +represent each object with a velocity +vector. So here we'll write V1 initial + + align:start position:0% +vector. So here we'll write V1 initial + + + align:start position:0% +vector. So here we'll write V1 initial +and let's suppose this object is coming + + align:start position:0% +and let's suppose this object is coming + + + align:start position:0% +and let's suppose this object is coming +at it with V2 initial as an example. And + + align:start position:0% +at it with V2 initial as an example. And + + + align:start position:0% +at it with V2 initial as an example. And +once we've represented the velocities of + + align:start position:0% +once we've represented the velocities of + + + align:start position:0% +once we've represented the velocities of +the objects, we can write down their + + align:start position:0% +the objects, we can write down their + + + align:start position:0% +the objects, we can write down their +momentum in the initial state. + + align:start position:0% +momentum in the initial state. + + + align:start position:0% +momentum in the initial state. +Similarly, if these two objects collide + + align:start position:0% +Similarly, if these two objects collide + + + align:start position:0% +Similarly, if these two objects collide +and they're moving, we actually don't + + align:start position:0% +and they're moving, we actually don't + + + align:start position:0% +and they're moving, we actually don't +know which way those objects will end up + + align:start position:0% +know which way those objects will end up + + + align:start position:0% +know which way those objects will end up +moving. And so what we'd again like to + + align:start position:0% +moving. And so what we'd again like to + + + align:start position:0% +moving. And so what we'd again like to +do in our final state after this + + align:start position:0% +do in our final state after this + + + align:start position:0% +do in our final state after this +collision is to represent the velocities + + align:start position:0% +collision is to represent the velocities + + + align:start position:0% +collision is to represent the velocities +by again vectors. So this is v_sub_1 + + align:start position:0% +by again vectors. So this is v_sub_1 + + + align:start position:0% +by again vectors. So this is v_sub_1 +final and this is v2 + + align:start position:0% +final and this is v2 + + + align:start position:0% +final and this is v2 +final. + + align:start position:0% +final. + + + align:start position:0% +final. +And then we can represent the change in + + align:start position:0% +And then we can represent the change in + + + align:start position:0% +And then we can represent the change in +momentum. So our momentum principle now + + align:start position:0% +momentum. So our momentum principle now + + + align:start position:0% +momentum. So our momentum principle now +becomes in this case let's just assume + + align:start position:0% +becomes in this case let's just assume + + + align:start position:0% +becomes in this case let's just assume +that the external force here sums to + + align:start position:0% +that the external force here sums to + + + align:start position:0% +that the external force here sums to +zero. We're assuming no friction. And + + align:start position:0% +zero. We're assuming no friction. And + + + align:start position:0% +zero. We're assuming no friction. And +then our momentum principle says that + + align:start position:0% +then our momentum principle says that + + + align:start position:0% +then our momentum principle says that +zero equals P final minus P initial. And + + align:start position:0% +zero equals P final minus P initial. And + + + align:start position:0% +zero equals P final minus P initial. And +now we can read off those momentum as + + align:start position:0% +now we can read off those momentum as + + + align:start position:0% +now we can read off those momentum as +vectors on the diagram. And so what we + + align:start position:0% +vectors on the diagram. And so what we + + + align:start position:0% +vectors on the diagram. And so what we +have is that the final momentum will be + + align:start position:0% +have is that the final momentum will be + + + align:start position:0% +have is that the final momentum will be +equal to the initial momentum. So we can + + align:start position:0% +equal to the initial momentum. So we can + + + align:start position:0% +equal to the initial momentum. So we can +write down m1 final plus m_sub_2 v2 + + align:start position:0% +write down m1 final plus m_sub_2 v2 + + + align:start position:0% +write down m1 final plus m_sub_2 v2 +final + + align:start position:0% +final + + + align:start position:0% +final +is equal to m_sub_1 v1 initial plus + + align:start position:0% +is equal to m_sub_1 v1 initial plus + + + align:start position:0% +is equal to m_sub_1 v1 initial plus +m_sub_2 v2 initial. And that's how we + + align:start position:0% +m_sub_2 v2 initial. And that's how we + + + align:start position:0% +m_sub_2 v2 initial. And that's how we +can represent a collision where there's + + align:start position:0% +can represent a collision where there's + + + align:start position:0% +can represent a collision where there's +no external forces and use a momentum + + align:start position:0% +no external forces and use a momentum + + + align:start position:0% +no external forces and use a momentum +principle to get an vector equation. Now + + align:start position:0% +principle to get an vector equation. Now + + + align:start position:0% +principle to get an vector equation. Now +in many problems you're given + + align:start position:0% +in many problems you're given + + + align:start position:0% +in many problems you're given +information. You might be given + + align:start position:0% +information. You might be given + + + align:start position:0% +information. You might be given +information about the speeds and + + align:start position:0% +information about the speeds and + + + align:start position:0% +information about the speeds and +magnitudes of the objects. And in order + + align:start position:0% +magnitudes of the objects. And in order + + + align:start position:0% +magnitudes of the objects. And in order +to then take this equation and represent + + align:start position:0% +to then take this equation and represent + + + align:start position:0% +to then take this equation and represent +it in speeds and directions or even + + align:start position:0% +it in speeds and directions or even + + + align:start position:0% +it in speeds and directions or even +components, we need to choose some + + align:start position:0% +components, we need to choose some + + + align:start position:0% +components, we need to choose some +coordinate system. So if we choose a + + align:start position:0% +coordinate system. So if we choose a + + + align:start position:0% +coordinate system. So if we choose a +coordinate system and that's the third + + align:start position:0% +coordinate system and that's the third + + + align:start position:0% +coordinate system and that's the third +step. So suppose we choose a coordinate + + align:start position:0% +step. So suppose we choose a coordinate + + + align:start position:0% +step. So suppose we choose a coordinate +system + + align:start position:0% +system + + + align:start position:0% +system +then we can start to look at two + + align:start position:0% +then we can start to look at two + + + align:start position:0% +then we can start to look at two +different representations for our + + align:start position:0% +different representations for our + + + align:start position:0% +different representations for our +problem. For instance let's just choose + + align:start position:0% +problem. For instance let's just choose + + + align:start position:0% +problem. For instance let's just choose +this to be the ihat direction. Now given + + align:start position:0% +this to be the ihat direction. Now given + + + align:start position:0% +this to be the ihat direction. Now given +that choice we could describe the + + align:start position:0% +that choice we could describe the + + + align:start position:0% +that choice we could describe the +velocities + + align:start position:0% +velocities + + + align:start position:0% +velocities +in terms of components. Now this is gets + + align:start position:0% +in terms of components. Now this is gets + + + align:start position:0% +in terms of components. Now this is gets +awkward. V1 I X component Ihat. + + align:start position:0% +awkward. V1 I X component Ihat. + + + align:start position:0% +awkward. V1 I X component Ihat. +And similarly we can write down all the + + align:start position:0% +And similarly we can write down all the + + + align:start position:0% +And similarly we can write down all the +velocities V2 I as V2 IIX + + align:start position:0% +velocities V2 I as V2 IIX + + + align:start position:0% +velocities V2 I as V2 IIX +Ihat + + align:start position:0% +Ihat + + + align:start position:0% +Ihat +etc for all the velocities and our + + align:start position:0% +etc for all the velocities and our + + + align:start position:0% +etc for all the velocities and our +momentum equation in components then + + align:start position:0% +momentum equation in components then + + + align:start position:0% +momentum equation in components then +becomes in the Ihat direction M1 V1 IIX + + align:start position:0% +becomes in the Ihat direction M1 V1 IIX + + + align:start position:0% +becomes in the Ihat direction M1 V1 IIX +plus well here we have the final state. + + align:start position:0% +plus well here we have the final state. + + + align:start position:0% +plus well here we have the final state. +So let's make this consistent. The final + + align:start position:0% +So let's make this consistent. The final + + + align:start position:0% +So let's make this consistent. The final +plus m_sub_2 b2 + + align:start position:0% +plus m_sub_2 b2 + + + align:start position:0% +plus m_sub_2 b2 +final x = m1 b1 initial x + m2 + + align:start position:0% +final x = m1 b1 initial x + m2 + + + align:start position:0% +final x = m1 b1 initial x + m2 +b2 initial x. And that's the same + + align:start position:0% +b2 initial x. And that's the same + + + align:start position:0% +b2 initial x. And that's the same +equation that we have as vectors now + + align:start position:0% +equation that we have as vectors now + + + align:start position:0% +equation that we have as vectors now +expressed in terms of components. And + + align:start position:0% +expressed in terms of components. And + + + align:start position:0% +expressed in terms of components. And +recall that components can be positive + + align:start position:0% +recall that components can be positive + + + align:start position:0% +recall that components can be positive +or negative. \ No newline at end of file diff --git a/wu8kXZSAp20.txt b/wu8kXZSAp20.txt new file mode 100644 index 0000000000000000000000000000000000000000..538d022bf4bbf4ef6dd8515ae36edaa40e3745d1 --- /dev/null +++ b/wu8kXZSAp20.txt @@ -0,0 +1,8075 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or to view additional materials from + + align:start position:0% +or to view additional materials from + + + align:start position:0% +or to view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +So remember, we left things with the + + align:start position:0% +So remember, we left things with the + + + align:start position:0% +So remember, we left things with the +statement of a divergence theorem. + + align:start position:0% + + + + align:start position:0% + +So the diversions theorem gives us a way + + align:start position:0% +So the diversions theorem gives us a way + + + align:start position:0% +So the diversions theorem gives us a way +to compute the flux of a vector field + + align:start position:0% +to compute the flux of a vector field + + + align:start position:0% +to compute the flux of a vector field +through a closed surface. Okay, it says + + align:start position:0% +through a closed surface. Okay, it says + + + align:start position:0% +through a closed surface. Okay, it says +if I have a closed surface + + align:start position:0% +if I have a closed surface + + + align:start position:0% +if I have a closed surface +S bounding some region D + + align:start position:0% +S bounding some region D + + + align:start position:0% +S bounding some region D +and I have a vector field + + align:start position:0% +and I have a vector field + + + align:start position:0% +and I have a vector field +defined in space. + + align:start position:0% + + + + align:start position:0% + +So then I can try to compute the flux of + + align:start position:0% +So then I can try to compute the flux of + + + align:start position:0% +So then I can try to compute the flux of +my vector field through my surface + + align:start position:0% +my vector field through my surface + + + align:start position:0% +my vector field through my surface +double integral of fds or f nds if you + + align:start position:0% +double integral of fds or f nds if you + + + align:start position:0% +double integral of fds or f nds if you +want. And to set this up, of course, I + + align:start position:0% +want. And to set this up, of course, I + + + align:start position:0% +want. And to set this up, of course, I +need to use well the geometry of a + + align:start position:0% +need to use well the geometry of a + + + align:start position:0% +need to use well the geometry of a +surface depending on what the surface + + align:start position:0% +surface depending on what the surface + + + align:start position:0% +surface depending on what the surface +is. We've seen various formulas for how + + align:start position:0% +is. We've seen various formulas for how + + + align:start position:0% +is. We've seen various formulas for how +to set up the double integral. + + align:start position:0% +to set up the double integral. + + + align:start position:0% +to set up the double integral. +But we've also seen + + align:start position:0% +But we've also seen + + + align:start position:0% +But we've also seen +that if it's a closed surface and if the + + align:start position:0% +that if it's a closed surface and if the + + + align:start position:0% +that if it's a closed surface and if the +vector field is defined everywhere + + align:start position:0% +vector field is defined everywhere + + + align:start position:0% +vector field is defined everywhere +inside then we can actually reduce that + + align:start position:0% +inside then we can actually reduce that + + + align:start position:0% +inside then we can actually reduce that +to a calculation + + align:start position:0% +to a calculation + + + align:start position:0% +to a calculation +of the triple integral of the divergence + + align:start position:0% +of the triple integral of the divergence + + + align:start position:0% +of the triple integral of the divergence +of f inside. + + align:start position:0% +of f inside. + + + align:start position:0% +of f inside. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +concretely if I use coordinates let's + + align:start position:0% +concretely if I use coordinates let's + + + align:start position:0% +concretely if I use coordinates let's +say that the coordinates of my vector + + align:start position:0% +say that the coordinates of my vector + + + align:start position:0% +say that the coordinates of my vector +field are sorry the components are pq + + align:start position:0% +field are sorry the components are pq + + + align:start position:0% +field are sorry the components are pq +and r n ds then that will become the + + align:start position:0% +and r n ds then that will become the + + + align:start position:0% +and r n ds then that will become the +triple integral of well so divergence is + + align:start position:0% +triple integral of well so divergence is + + + align:start position:0% +triple integral of well so divergence is +p subx plus q suby + + align:start position:0% +p subx plus q suby + + + align:start position:0% +p subx plus q suby +plus r subz. + + align:start position:0% + + + + align:start position:0% + +Okay, so by the way, how to remember + + align:start position:0% +Okay, so by the way, how to remember + + + align:start position:0% +Okay, so by the way, how to remember +this formula for divergence and other + + align:start position:0% +this formula for divergence and other + + + align:start position:0% +this formula for divergence and other +formulas for other things as well. So + + align:start position:0% +formulas for other things as well. So + + + align:start position:0% +formulas for other things as well. So +let me just tell you quickly about the + + align:start position:0% +let me just tell you quickly about the + + + align:start position:0% +let me just tell you quickly about the +Dell notation. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +this guy usually pronounced as Dell + + align:start position:0% +this guy usually pronounced as Dell + + + align:start position:0% +this guy usually pronounced as Dell +rather than as you know pointy triangle + + align:start position:0% +rather than as you know pointy triangle + + + align:start position:0% +rather than as you know pointy triangle +going downwards or something like that. + + align:start position:0% +going downwards or something like that. + + + align:start position:0% +going downwards or something like that. +Um, it's a symbolic notation for an + + align:start position:0% +Um, it's a symbolic notation for an + + + align:start position:0% +Um, it's a symbolic notation for an +operator. + + align:start position:0% +operator. + + + align:start position:0% +operator. +So, you're probably going to complain + + align:start position:0% +So, you're probably going to complain + + + align:start position:0% +So, you're probably going to complain +about, you know, my + + align:start position:0% + + + + align:start position:0% + +putting these guys into a vector. But + + align:start position:0% +putting these guys into a vector. But + + + align:start position:0% +putting these guys into a vector. But +let's think of partial respect to x with + + align:start position:0% +let's think of partial respect to x with + + + align:start position:0% +let's think of partial respect to x with +respect to y and respect to z as the + + align:start position:0% +respect to y and respect to z as the + + + align:start position:0% +respect to y and respect to z as the +components of some formal vector. Of + + align:start position:0% +components of some formal vector. Of + + + align:start position:0% +components of some formal vector. Of +course, it's not a real vector. These + + align:start position:0% +course, it's not a real vector. These + + + align:start position:0% +course, it's not a real vector. These +are not like you know anything. These + + align:start position:0% +are not like you know anything. These + + + align:start position:0% +are not like you know anything. These +are just symbols. + + align:start position:0% +are just symbols. + + + align:start position:0% +are just symbols. +Um + + align:start position:0% +Um + + + align:start position:0% +Um +but so see for example the gradient of a + + align:start position:0% +but so see for example the gradient of a + + + align:start position:0% +but so see for example the gradient of a +function well if you multiply this + + align:start position:0% +function well if you multiply this + + + align:start position:0% +function well if you multiply this +vector by a scalar which is a function + + align:start position:0% +vector by a scalar which is a function + + + align:start position:0% +vector by a scalar which is a function +then + + align:start position:0% +then + + + align:start position:0% +then +you know you'll get partial partial x of + + align:start position:0% +you know you'll get partial partial x of + + + align:start position:0% +you know you'll get partial partial x of +f partial partial y of f partial partial + + align:start position:0% +f partial partial y of f partial partial + + + align:start position:0% +f partial partial y of f partial partial +z f. Well that's the gradient that seems + + align:start position:0% +z f. Well that's the gradient that seems + + + align:start position:0% +z f. Well that's the gradient that seems +to work. And + + align:start position:0% +to work. And + + + align:start position:0% +to work. And +so now the interesting thing about + + align:start position:0% +so now the interesting thing about + + + align:start position:0% +so now the interesting thing about +divergence is I can think of divergence + + align:start position:0% +divergence is I can think of divergence + + + align:start position:0% +divergence is I can think of divergence +as dell dot a vector field. See if I do + + align:start position:0% +as dell dot a vector field. See if I do + + + align:start position:0% +as dell dot a vector field. See if I do +the dot product between + + align:start position:0% + + + + align:start position:0% + +this guy + + align:start position:0% +this guy + + + align:start position:0% +this guy +and my vector field pqr. + + align:start position:0% +and my vector field pqr. + + + align:start position:0% +and my vector field pqr. +Well, it looks like I will indeed get + + align:start position:0% +Well, it looks like I will indeed get + + + align:start position:0% +Well, it looks like I will indeed get +partial partial X of P + + align:start position:0% +partial partial X of P + + + align:start position:0% +partial partial X of P +plus partial Q partial Y + + align:start position:0% +plus partial Q partial Y + + + align:start position:0% +plus partial Q partial Y +plus partial R partial Z that's the + + align:start position:0% +plus partial R partial Z that's the + + + align:start position:0% +plus partial R partial Z that's the +divergence. + + align:start position:0% + + + + align:start position:0% + +Okay. And of course similarly when we + + align:start position:0% +Okay. And of course similarly when we + + + align:start position:0% +Okay. And of course similarly when we +had two variables only x and y we could + + align:start position:0% +had two variables only x and y we could + + + align:start position:0% +had two variables only x and y we could +have thought of the same notation just + + align:start position:0% +have thought of the same notation just + + + align:start position:0% +have thought of the same notation just +with a two component vector partial x + + align:start position:0% +with a two component vector partial x + + + align:start position:0% +with a two component vector partial x +partial partial y. So now this is like + + align:start position:0% +partial partial y. So now this is like + + + align:start position:0% +partial partial y. So now this is like +you know of slightly limited usefulness + + align:start position:0% +you know of slightly limited usefulness + + + align:start position:0% +you know of slightly limited usefulness +so far. It's going to become very handy + + align:start position:0% +so far. It's going to become very handy + + + align:start position:0% +so far. It's going to become very handy +pretty soon because we're going to see + + align:start position:0% +pretty soon because we're going to see + + + align:start position:0% +pretty soon because we're going to see +curl. And the formula for curl in the + + align:start position:0% +curl. And the formula for curl in the + + + align:start position:0% +curl. And the formula for curl in the +plane was kind of complicated. But if + + align:start position:0% +plane was kind of complicated. But if + + + align:start position:0% +plane was kind of complicated. But if +you thought about it in terms of this, + + align:start position:0% +you thought about it in terms of this, + + + align:start position:0% +you thought about it in terms of this, +it was actually the determinant of dell + + align:start position:0% +it was actually the determinant of dell + + + align:start position:0% +it was actually the determinant of dell +and f. And now in space, we're actually + + align:start position:0% +and f. And now in space, we're actually + + + align:start position:0% +and f. And now in space, we're actually +going to do dell cross f. But I'm + + align:start position:0% +going to do dell cross f. But I'm + + + align:start position:0% +going to do dell cross f. But I'm +getting ahead of things. So let's not do + + align:start position:0% +getting ahead of things. So let's not do + + + align:start position:0% +getting ahead of things. So let's not do +anything with that. Curl will be for + + align:start position:0% +anything with that. Curl will be for + + + align:start position:0% +anything with that. Curl will be for +next week. + + align:start position:0% + + + + align:start position:0% + +just getting you used to the notation + + align:start position:0% +just getting you used to the notation + + + align:start position:0% +just getting you used to the notation +especially since you might be using it + + align:start position:0% +especially since you might be using it + + + align:start position:0% +especially since you might be using it +in physics already so might be worth + + align:start position:0% +in physics already so might be worth + + + align:start position:0% +in physics already so might be worth +doing + + align:start position:0% +doing + + + align:start position:0% +doing +okay so the other thing I wanted to say + + align:start position:0% +okay so the other thing I wanted to say + + + align:start position:0% +okay so the other thing I wanted to say +is what does this theorem say physically + + align:start position:0% +is what does this theorem say physically + + + align:start position:0% +is what does this theorem say physically +how should I think of this statement so + + align:start position:0% +how should I think of this statement so + + + align:start position:0% +how should I think of this statement so +I think I said that very quickly at the + + align:start position:0% +I think I said that very quickly at the + + + align:start position:0% +I think I said that very quickly at the +end of last time but not very carefully + + align:start position:0% +end of last time but not very carefully + + + align:start position:0% +end of last time but not very carefully +so what's the physical interpretation + + align:start position:0% + + + + align:start position:0% + +of the divergence. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +I want to claim that the divergence of a + + align:start position:0% +I want to claim that the divergence of a + + + align:start position:0% +I want to claim that the divergence of a +vector field corresponds to what I'm + + align:start position:0% +vector field corresponds to what I'm + + + align:start position:0% +vector field corresponds to what I'm +going to call the source rate + + align:start position:0% +going to call the source rate + + + align:start position:0% +going to call the source rate +which is somehow the amount + + align:start position:0% +which is somehow the amount + + + align:start position:0% +which is somehow the amount +of flux generated + + align:start position:0% +of flux generated + + + align:start position:0% +of flux generated +per unit + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +to understand what that means, let's + + align:start position:0% +to understand what that means, let's + + + align:start position:0% +to understand what that means, let's +think of what's called an incompre + + align:start position:0% +think of what's called an incompre + + + align:start position:0% +think of what's called an incompre +incompressible fluid. Okay? So an + + align:start position:0% +incompressible fluid. Okay? So an + + + align:start position:0% +incompressible fluid. Okay? So an +incompressible fluid is something like + + align:start position:0% +incompressible fluid is something like + + + align:start position:0% +incompressible fluid is something like +water for example where a fixed mass of + + align:start position:0% +water for example where a fixed mass of + + + align:start position:0% +water for example where a fixed mass of +it always occupies the same amount of + + align:start position:0% +it always occupies the same amount of + + + align:start position:0% +it always occupies the same amount of +volume. Okay? So gases are compressible, + + align:start position:0% +volume. Okay? So gases are compressible, + + + align:start position:0% +volume. Okay? So gases are compressible, +liquids are incompressible basically. + + align:start position:0% +liquids are incompressible basically. + + + align:start position:0% +liquids are incompressible basically. +So + + align:start position:0% +So + + + align:start position:0% +So +if you have an incompressible fluid flow + + align:start position:0% + + + + align:start position:0% + +well + + align:start position:0% +well + + + align:start position:0% +well +so again what that means is really + + align:start position:0% +so again what that means is really + + + align:start position:0% +so again what that means is really +given mass + + align:start position:0% +given mass + + + align:start position:0% +given mass +occupies always a fixed + + align:start position:0% + + + + align:start position:0% + +Then well let's say that we have such a + + align:start position:0% +Then well let's say that we have such a + + + align:start position:0% +Then well let's say that we have such a +flow with velocity + + align:start position:0% +flow with velocity + + + align:start position:0% +flow with velocity +given by our vector our vector field f. + + align:start position:0% +given by our vector our vector field f. + + + align:start position:0% +given by our vector our vector field f. +Okay. So we're thinking of f as the + + align:start position:0% +Okay. So we're thinking of f as the + + + align:start position:0% +Okay. So we're thinking of f as the +velocity + + align:start position:0% +velocity + + + align:start position:0% +velocity +in maybe some + + align:start position:0% +in maybe some + + + align:start position:0% +in maybe some +something containing water, a pipe or + + align:start position:0% +something containing water, a pipe or + + + align:start position:0% +something containing water, a pipe or +something. So + + align:start position:0% +something. So + + + align:start position:0% +something. So +what does the divergence theorem say? It + + align:start position:0% +what does the divergence theorem say? It + + + align:start position:0% +what does the divergence theorem say? It +says + + align:start position:0% +says + + + align:start position:0% +says +that you know if I take a region in + + align:start position:0% +that you know if I take a region in + + + align:start position:0% +that you know if I take a region in +space, let's call it D. So D is the + + align:start position:0% +space, let's call it D. So D is the + + + align:start position:0% +space, let's call it D. So D is the +inside and S is the surface + + align:start position:0% +inside and S is the surface + + + align:start position:0% +inside and S is the surface +around it. Well, so if I sum the + + align:start position:0% +around it. Well, so if I sum the + + + align:start position:0% +around it. Well, so if I sum the +divergence in D, then I'm going to get + + align:start position:0% + + + + align:start position:0% + +the flux going out through this surface + + align:start position:0% +the flux going out through this surface + + + align:start position:0% +the flux going out through this surface +S. I should have mentioned it earlier. + + align:start position:0% +S. I should have mentioned it earlier. + + + align:start position:0% +S. I should have mentioned it earlier. +The convention in the diversions theorem + + align:start position:0% +The convention in the diversions theorem + + + align:start position:0% +The convention in the diversions theorem +is that we orient the surface with a + + align:start position:0% +is that we orient the surface with a + + + align:start position:0% +is that we orient the surface with a +normal vector pointing always outward. + + align:start position:0% +normal vector pointing always outward. + + + align:start position:0% +normal vector pointing always outward. +Okay, so now we know what flux means. So + + align:start position:0% +Okay, so now we know what flux means. So + + + align:start position:0% +Okay, so now we know what flux means. So +remember we've been describing flux + + align:start position:0% +remember we've been describing flux + + + align:start position:0% +remember we've been describing flux +means how much fluid is passing through + + align:start position:0% +means how much fluid is passing through + + + align:start position:0% +means how much fluid is passing through +this surface. So that's the amount of + + align:start position:0% +this surface. So that's the amount of + + + align:start position:0% +this surface. So that's the amount of +fluid + + align:start position:0% + + + + align:start position:0% + +that's leaving + + align:start position:0% +that's leaving + + + align:start position:0% +that's leaving +the region D per unit time. + + align:start position:0% + + + + align:start position:0% + +And of course when I'm saying that you + + align:start position:0% +And of course when I'm saying that you + + + align:start position:0% +And of course when I'm saying that you +know means I'm counting everything + + align:start position:0% +know means I'm counting everything + + + align:start position:0% +know means I'm counting everything +that's going out of D minus everything + + align:start position:0% +that's going out of D minus everything + + + align:start position:0% +that's going out of D minus everything +that's coming into D. That's what the + + align:start position:0% +that's coming into D. That's what the + + + align:start position:0% +that's coming into D. That's what the +flux measures. So now + + align:start position:0% +flux measures. So now + + + align:start position:0% +flux measures. So now +you know if there's stuff coming into D + + align:start position:0% +you know if there's stuff coming into D + + + align:start position:0% +you know if there's stuff coming into D +or going out of D well it must come from + + align:start position:0% +or going out of D well it must come from + + + align:start position:0% +or going out of D well it must come from +somewhere you know. So one possibility + + align:start position:0% +somewhere you know. So one possibility + + + align:start position:0% +somewhere you know. So one possibility +would be that your fluid is actually + + align:start position:0% +would be that your fluid is actually + + + align:start position:0% +would be that your fluid is actually +being compressed or expanded. But I've + + align:start position:0% +being compressed or expanded. But I've + + + align:start position:0% +being compressed or expanded. But I've +said no I'm looking at something like + + align:start position:0% +said no I'm looking at something like + + + align:start position:0% +said no I'm looking at something like +water that you cannot squish into + + align:start position:0% +water that you cannot squish into + + + align:start position:0% +water that you cannot squish into +smaller volume. So that case the only + + align:start position:0% +smaller volume. So that case the only + + + align:start position:0% +smaller volume. So that case the only +explanation is that there's something in + + align:start position:0% +explanation is that there's something in + + + align:start position:0% +explanation is that there's something in +here that actually is sucking up water + + align:start position:0% +here that actually is sucking up water + + + align:start position:0% +here that actually is sucking up water +or producing more water. And so + + align:start position:0% +or producing more water. And so + + + align:start position:0% +or producing more water. And so +integrating the divergence gives you the + + align:start position:0% +integrating the divergence gives you the + + + align:start position:0% +integrating the divergence gives you the +total amount of sources minus amount of + + align:start position:0% +total amount of sources minus amount of + + + align:start position:0% +total amount of sources minus amount of +sinks that are inside this region. + + align:start position:0% +sinks that are inside this region. + + + align:start position:0% +sinks that are inside this region. +So the divergence itself measures + + align:start position:0% +So the divergence itself measures + + + align:start position:0% +So the divergence itself measures +basically the amount of sources or syncs + + align:start position:0% +basically the amount of sources or syncs + + + align:start position:0% +basically the amount of sources or syncs +per unit volume at a given you know in a + + align:start position:0% +per unit volume at a given you know in a + + + align:start position:0% +per unit volume at a given you know in a +given place. + + align:start position:0% +given place. + + + align:start position:0% +given place. +And now if you think about it that way, + + align:start position:0% +And now if you think about it that way, + + + align:start position:0% +And now if you think about it that way, +well, so basically the divergence + + align:start position:0% +well, so basically the divergence + + + align:start position:0% +well, so basically the divergence +theorem is just stating something + + align:start position:0% +theorem is just stating something + + + align:start position:0% +theorem is just stating something +completely obvious about you know all + + align:start position:0% +completely obvious about you know all + + + align:start position:0% +completely obvious about you know all +the matter that is leaving that region + + align:start position:0% +the matter that is leaving that region + + + align:start position:0% +the matter that is leaving that region +must come from somewhere. + + align:start position:0% + + + + align:start position:0% + +So that's basically how we think about + + align:start position:0% +So that's basically how we think about + + + align:start position:0% +So that's basically how we think about +it. + + align:start position:0% + + + + align:start position:0% + +Now, of course, if you're doing 802, + + align:start position:0% +Now, of course, if you're doing 802, + + + align:start position:0% +Now, of course, if you're doing 802, +then you might actually have seen the + + align:start position:0% +then you might actually have seen the + + + align:start position:0% +then you might actually have seen the +diversion theorem already being used for + + align:start position:0% +diversion theorem already being used for + + + align:start position:0% +diversion theorem already being used for +things that are more like force fields, + + align:start position:0% +things that are more like force fields, + + + align:start position:0% +things that are more like force fields, +say electric fields and so on. Well, + + align:start position:0% +say electric fields and so on. Well, + + + align:start position:0% +say electric fields and so on. Well, +I'll try to say a few things about that + + align:start position:0% +I'll try to say a few things about that + + + align:start position:0% +I'll try to say a few things about that +during the last week of classes, but + + align:start position:0% +during the last week of classes, but + + + align:start position:0% +during the last week of classes, but +then this kind of interpretation doesn't + + align:start position:0% +then this kind of interpretation doesn't + + + align:start position:0% +then this kind of interpretation doesn't +quite work. + + align:start position:0% +quite work. + + + align:start position:0% +quite work. +Okay. Um, any questions generally + + align:start position:0% +Okay. Um, any questions generally + + + align:start position:0% +Okay. Um, any questions generally +speaking before we move on to the proof + + align:start position:0% +speaking before we move on to the proof + + + align:start position:0% +speaking before we move on to the proof +and other applications? + + align:start position:0% +and other applications? + + + align:start position:0% +and other applications? +Yes. + + align:start position:0% + + + + align:start position:0% + +Oh, not the gradient. So the the + + align:start position:0% +Oh, not the gradient. So the the + + + align:start position:0% +Oh, not the gradient. So the the +divergence, yeah, the divergence of f + + align:start position:0% +divergence, yeah, the divergence of f + + + align:start position:0% +divergence, yeah, the divergence of f +measures the amount of sources or syncs + + align:start position:0% +measures the amount of sources or syncs + + + align:start position:0% +measures the amount of sources or syncs +in there. Well, what makes it happen? If + + align:start position:0% +in there. Well, what makes it happen? If + + + align:start position:0% +in there. Well, what makes it happen? If +you want in a way, it's this theorem. Or + + align:start position:0% +you want in a way, it's this theorem. Or + + + align:start position:0% +you want in a way, it's this theorem. Or +in another way, if you think about it, + + align:start position:0% +in another way, if you think about it, + + + align:start position:0% +in another way, if you think about it, +you know, try to look at your favorite + + align:start position:0% +you know, try to look at your favorite + + + align:start position:0% +you know, try to look at your favorite +vector fields and compute their + + align:start position:0% +vector fields and compute their + + + align:start position:0% +vector fields and compute their +divergence. And if you take you know a + + align:start position:0% +divergence. And if you take you know a + + + align:start position:0% +divergence. And if you take you know a +vector field where maybe everything is + + align:start position:0% +vector field where maybe everything is + + + align:start position:0% +vector field where maybe everything is +rotating you know a flow that's just + + align:start position:0% +rotating you know a flow that's just + + + align:start position:0% +rotating you know a flow that's just +rotating about some axis + + align:start position:0% +rotating about some axis + + + align:start position:0% +rotating about some axis +then you'll find that its divergence is + + align:start position:0% +then you'll find that its divergence is + + + align:start position:0% +then you'll find that its divergence is +zero. If you sorry + + align:start position:0% +zero. If you sorry + + + align:start position:0% +zero. If you sorry +uh no divergence is not equal to the + + align:start position:0% +uh no divergence is not equal to the + + + align:start position:0% +uh no divergence is not equal to the +gradient sorry there's a dot here that + + align:start position:0% +gradient sorry there's a dot here that + + + align:start position:0% +gradient sorry there's a dot here that +maybe it's not very big but it's very + + align:start position:0% +maybe it's not very big but it's very + + + align:start position:0% +maybe it's not very big but it's very +important. Okay so you take the + + align:start position:0% +important. Okay so you take the + + + align:start position:0% +important. Okay so you take the +divergence of a vector field while you + + align:start position:0% +divergence of a vector field while you + + + align:start position:0% +divergence of a vector field while you +take the gradient of a function. So the + + align:start position:0% +take the gradient of a function. So the + + + align:start position:0% +take the gradient of a function. So the +gradient of a function is a vector. the + + align:start position:0% +gradient of a function is a vector. the + + + align:start position:0% +gradient of a function is a vector. the +divergence of a vector field is a + + align:start position:0% +divergence of a vector field is a + + + align:start position:0% +divergence of a vector field is a +function. So somehow these guys you know + + align:start position:0% +function. So somehow these guys you know + + + align:start position:0% +function. So somehow these guys you know +go back and forth between + + align:start position:0% +go back and forth between + + + align:start position:0% +go back and forth between +so I should have said you know with new + + align:start position:0% +so I should have said you know with new + + + align:start position:0% +so I should have said you know with new +notations comes new responsibility. I + + align:start position:0% +notations comes new responsibility. I + + + align:start position:0% +notations comes new responsibility. I +mean u + + align:start position:0% +mean u + + + align:start position:0% +mean u +you know now that we have this nice + + align:start position:0% +you know now that we have this nice + + + align:start position:0% +you know now that we have this nice +nifty notation that will let us do + + align:start position:0% +nifty notation that will let us do + + + align:start position:0% +nifty notation that will let us do +gradient divergence and later curl in a + + align:start position:0% +gradient divergence and later curl in a + + + align:start position:0% +gradient divergence and later curl in a +unified way. If you choose to use this + + align:start position:0% +unified way. If you choose to use this + + + align:start position:0% +unified way. If you choose to use this +notation you have to be really really + + align:start position:0% +notation you have to be really really + + + align:start position:0% +notation you have to be really really +careful what you put after it. + + align:start position:0% +careful what you put after it. + + + align:start position:0% +careful what you put after it. +um because otherwise it's easy to get + + align:start position:0% +um because otherwise it's easy to get + + + align:start position:0% +um because otherwise it's easy to get +completely confused. Okay, so divergence + + align:start position:0% +completely confused. Okay, so divergence + + + align:start position:0% +completely confused. Okay, so divergence +and gradients are completely different + + align:start position:0% +and gradients are completely different + + + align:start position:0% +and gradients are completely different +things. The only thing they have in + + align:start position:0% +things. The only thing they have in + + + align:start position:0% +things. The only thing they have in +common is that both are what's called a + + align:start position:0% +common is that both are what's called a + + + align:start position:0% +common is that both are what's called a +first order differential operator. That + + align:start position:0% +first order differential operator. That + + + align:start position:0% +first order differential operator. That +means it involves the first partial + + align:start position:0% +means it involves the first partial + + + align:start position:0% +means it involves the first partial +derivatives of whatever you put into it. + + align:start position:0% +derivatives of whatever you put into it. + + + align:start position:0% +derivatives of whatever you put into it. +But one of them goes from functions to + + align:start position:0% +But one of them goes from functions to + + + align:start position:0% +But one of them goes from functions to +vectors. So it's gradient. The other one + + align:start position:0% +vectors. So it's gradient. The other one + + + align:start position:0% +vectors. So it's gradient. The other one +goes from vectors to functions. That's + + align:start position:0% +goes from vectors to functions. That's + + + align:start position:0% +goes from vectors to functions. That's +diversions. + + align:start position:0% +diversions. + + + align:start position:0% +diversions. +And curl later will go from vectors to + + align:start position:0% +And curl later will go from vectors to + + + align:start position:0% +And curl later will go from vectors to +vectors. But that will be later. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Um, let's see more questions. + + align:start position:0% + + + + align:start position:0% + +No. Okay. + + align:start position:0% +No. Okay. + + + align:start position:0% +No. Okay. +So, + + align:start position:0% + + + + align:start position:0% + +let's see. + + align:start position:0% +let's see. + + + align:start position:0% +let's see. +So, how are we going to actually prove + + align:start position:0% +So, how are we going to actually prove + + + align:start position:0% +So, how are we going to actually prove +this theorem? Well, if you remember how + + align:start position:0% +this theorem? Well, if you remember how + + + align:start position:0% +this theorem? Well, if you remember how +we proved Green's theorem a while ago, + + align:start position:0% +we proved Green's theorem a while ago, + + + align:start position:0% +we proved Green's theorem a while ago, +the answer is we're going to do it + + align:start position:0% +the answer is we're going to do it + + + align:start position:0% +the answer is we're going to do it +exactly the same way. Now, if you don't + + align:start position:0% +exactly the same way. Now, if you don't + + + align:start position:0% +exactly the same way. Now, if you don't +remember, then I'm going to explain. + + align:start position:0% +remember, then I'm going to explain. + + + align:start position:0% +remember, then I'm going to explain. +Okay, so the first thing we need to do + + align:start position:0% +Okay, so the first thing we need to do + + + align:start position:0% +Okay, so the first thing we need to do +is actually a simplification. So, + + align:start position:0% + + + + align:start position:0% + +instead of proving the divergence + + align:start position:0% +instead of proving the divergence + + + align:start position:0% +instead of proving the divergence +theorem, + + align:start position:0% +theorem, + + + align:start position:0% +theorem, +namely this equality up there, + + align:start position:0% +namely this equality up there, + + + align:start position:0% +namely this equality up there, +I'm going to actually prove something + + align:start position:0% +I'm going to actually prove something + + + align:start position:0% +I'm going to actually prove something +easier. I'm going to prove + + align:start position:0% +easier. I'm going to prove + + + align:start position:0% +easier. I'm going to prove +that the flux of a vector field that has + + align:start position:0% +that the flux of a vector field that has + + + align:start position:0% +that the flux of a vector field that has +only a z component + + align:start position:0% + + + + align:start position:0% + +is actually equal to the triple integral + + align:start position:0% +is actually equal to the triple integral + + + align:start position:0% +is actually equal to the triple integral +of well the divergence of this is just r + + align:start position:0% +of well the divergence of this is just r + + + align:start position:0% +of well the divergence of this is just r +subz dv. + + align:start position:0% +subz dv. + + + align:start position:0% +subz dv. +Okay. Now how do I go back to the + + align:start position:0% +Okay. Now how do I go back to the + + + align:start position:0% +Okay. Now how do I go back to the +general case? Well, I will just prove + + align:start position:0% +general case? Well, I will just prove + + + align:start position:0% +general case? Well, I will just prove +the same thing for a vector field that + + align:start position:0% +the same thing for a vector field that + + + align:start position:0% +the same thing for a vector field that +has only an x component or only a y + + align:start position:0% +has only an x component or only a y + + + align:start position:0% +has only an x component or only a y +component. and then I will add these + + align:start position:0% +component. and then I will add these + + + align:start position:0% +component. and then I will add these +things together. + + align:start position:0% +things together. + + + align:start position:0% +things together. +So if you think carefully about what + + align:start position:0% +So if you think carefully about what + + + align:start position:0% +So if you think carefully about what +happens when you evaluate this, you + + align:start position:0% +happens when you evaluate this, you + + + align:start position:0% +happens when you evaluate this, you +know, you'll have some formula for NDS + + align:start position:0% +know, you'll have some formula for NDS + + + align:start position:0% +know, you'll have some formula for NDS +and when you do the dot product, you'll + + align:start position:0% +and when you do the dot product, you'll + + + align:start position:0% +and when you do the dot product, you'll +end up with a sum P * something plus Q * + + align:start position:0% +end up with a sum P * something plus Q * + + + align:start position:0% +end up with a sum P * something plus Q * +something plus R* something. And + + align:start position:0% +something plus R* something. And + + + align:start position:0% +something plus R* something. And +basically we're just dealing with the + + align:start position:0% +basically we're just dealing with the + + + align:start position:0% +basically we're just dealing with the +last term R* something and showing that + + align:start position:0% +last term R* something and showing that + + + align:start position:0% +last term R* something and showing that +it's equal to what it should be and then + + align:start position:0% +it's equal to what it should be and then + + + align:start position:0% +it's equal to what it should be and then +we free such terms together we'll get + + align:start position:0% +we free such terms together we'll get + + + align:start position:0% +we free such terms together we'll get +the general case. + + align:start position:0% + + + + align:start position:0% + +Okay. So then we get + + align:start position:0% + + + + align:start position:0% + +the general case + + align:start position:0% + + + + align:start position:0% + +by summing + + align:start position:0% + + + + align:start position:0% + +one such identity for each component. + + align:start position:0% + + + + align:start position:0% + +They should say three such identities. + + align:start position:0% +They should say three such identities. + + + align:start position:0% +They should say three such identities. +one + + align:start position:0% +one + + + align:start position:0% +one +for each component + + align:start position:0% + + + + align:start position:0% + +whatever. Okay, now let's make a second + + align:start position:0% +whatever. Okay, now let's make a second + + + align:start position:0% +whatever. Okay, now let's make a second +simplification because I'm still not + + align:start position:0% +simplification because I'm still not + + + align:start position:0% +simplification because I'm still not +feeling confident that I can prove this + + align:start position:0% +feeling confident that I can prove this + + + align:start position:0% +feeling confident that I can prove this +right away for any surface. I'm going to + + align:start position:0% +right away for any surface. I'm going to + + + align:start position:0% +right away for any surface. I'm going to +do it first for what's called a + + align:start position:0% +do it first for what's called a + + + align:start position:0% +do it first for what's called a +vertically simple region. + + align:start position:0% +vertically simple region. + + + align:start position:0% +vertically simple region. +Okay, so vertically simple means it will + + align:start position:0% +Okay, so vertically simple means it will + + + align:start position:0% +Okay, so vertically simple means it will +be something on which I can set up an + + align:start position:0% +be something on which I can set up an + + + align:start position:0% +be something on which I can set up an +integral over the Z variable first + + align:start position:0% +integral over the Z variable first + + + align:start position:0% +integral over the Z variable first +easily. So it's something that has a + + align:start position:0% +easily. So it's something that has a + + + align:start position:0% +easily. So it's something that has a +bottom face and a top face and then some + + align:start position:0% +bottom face and a top face and then some + + + align:start position:0% +bottom face and a top face and then some +vertical sides. + + align:start position:0% + + + + align:start position:0% + +Okay. So let's say let's look first at + + align:start position:0% +Okay. So let's say let's look first at + + + align:start position:0% +Okay. So let's say let's look first at +what happens if the given region D is + + align:start position:0% +what happens if the given region D is + + + align:start position:0% +what happens if the given region D is +vertically simple. + + align:start position:0% + + + + align:start position:0% + +So vertically simple means it looks like + + align:start position:0% +So vertically simple means it looks like + + + align:start position:0% +So vertically simple means it looks like +this. + + align:start position:0% + + + + align:start position:0% + +It has a top. + + align:start position:0% + + + + align:start position:0% + +It has + + align:start position:0% +It has + + + align:start position:0% +It has +a bottom + + align:start position:0% +a bottom + + + align:start position:0% +a bottom +and it has some vertical sides. So if + + align:start position:0% +and it has some vertical sides. So if + + + align:start position:0% +and it has some vertical sides. So if +you want, you know, if I look at it from + + align:start position:0% +you want, you know, if I look at it from + + + align:start position:0% +you want, you know, if I look at it from +above, it projects to some region in the + + align:start position:0% +above, it projects to some region in the + + + align:start position:0% +above, it projects to some region in the +xy plane. + + align:start position:0% +xy plane. + + + align:start position:0% +xy plane. +Let's call that R. + + align:start position:0% +Let's call that R. + + + align:start position:0% +Let's call that R. +and it lives between the top face and + + align:start position:0% +and it lives between the top face and + + + align:start position:0% +and it lives between the top face and +the bottom face. Let's say the top face + + align:start position:0% +the bottom face. Let's say the top face + + + align:start position:0% +the bottom face. Let's say the top face +is Z= Z2 of XY. The bottom face is Z = + + align:start position:0% +is Z= Z2 of XY. The bottom face is Z = + + + align:start position:0% +is Z= Z2 of XY. The bottom face is Z = +Z1 of XY. + + align:start position:0% +Z1 of XY. + + + align:start position:0% +Z1 of XY. +Okay. And I don't need to know actual + + align:start position:0% +Okay. And I don't need to know actual + + + align:start position:0% +Okay. And I don't need to know actual +formulas. I'm just going to work with + + align:start position:0% +formulas. I'm just going to work with + + + align:start position:0% +formulas. I'm just going to work with +these and prove things independently of + + align:start position:0% +these and prove things independently of + + + align:start position:0% +these and prove things independently of +what the formulas will be for these + + align:start position:0% +what the formulas will be for these + + + align:start position:0% +what the formulas will be for these +functions. + + align:start position:0% +functions. + + + align:start position:0% +functions. +Okay. Okay. So anyway, a vertically + + align:start position:0% +Okay. Okay. So anyway, a vertically + + + align:start position:0% +Okay. Okay. So anyway, a vertically +simple region is something that lives + + align:start position:0% +simple region is something that lives + + + align:start position:0% +simple region is something that lives +above about part of the xy plane and is + + align:start position:0% +above about part of the xy plane and is + + + align:start position:0% +above about part of the xy plane and is +between two graphs of two functions. + + align:start position:0% +between two graphs of two functions. + + + align:start position:0% +between two graphs of two functions. +So let's see what we can do in that + + align:start position:0% +So let's see what we can do in that + + + align:start position:0% +So let's see what we can do in that +case. + + align:start position:0% +case. + + + align:start position:0% +case. +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +the right hand side + + align:start position:0% +the right hand side + + + align:start position:0% +the right hand side +of this equality. + + align:start position:0% +of this equality. + + + align:start position:0% +of this equality. +So that's the triple integral. + + align:start position:0% +So that's the triple integral. + + + align:start position:0% +So that's the triple integral. +Let's start computing it. + + align:start position:0% + + + + align:start position:0% + +Okay, so of course we will we will not + + align:start position:0% +Okay, so of course we will we will not + + + align:start position:0% +Okay, so of course we will we will not +be able to get a number out of it + + align:start position:0% +be able to get a number out of it + + + align:start position:0% +be able to get a number out of it +because we don't know actually formulas + + align:start position:0% +because we don't know actually formulas + + + align:start position:0% +because we don't know actually formulas +for anything. But at least we can start + + align:start position:0% +for anything. But at least we can start + + + align:start position:0% +for anything. But at least we can start +simplifying because the way this region + + align:start position:0% +simplifying because the way this region + + + align:start position:0% +simplifying because the way this region +looks like should say this is D + + align:start position:0% +looks like should say this is D + + + align:start position:0% +looks like should say this is D +tells me that I can start setting up the + + align:start position:0% +tells me that I can start setting up the + + + align:start position:0% +tells me that I can start setting up the +double the triple integral at least in + + align:start position:0% +double the triple integral at least in + + + align:start position:0% +double the triple integral at least in +the order where I integrate first over + + align:start position:0% +the order where I integrate first over + + + align:start position:0% +the order where I integrate first over +Z. + + align:start position:0% +Z. + + + align:start position:0% +Z. +Okay, so I can actually do it as a + + align:start position:0% +Okay, so I can actually do it as a + + + align:start position:0% +Okay, so I can actually do it as a +triple integral + + align:start position:0% +triple integral + + + align:start position:0% +triple integral +of rz dz dx dy or dy dx doesn't matter. + + align:start position:0% +of rz dz dx dy or dy dx doesn't matter. + + + align:start position:0% +of rz dz dx dy or dy dx doesn't matter. +So what are the bounds on z? See this is + + align:start position:0% +So what are the bounds on z? See this is + + + align:start position:0% +So what are the bounds on z? See this is +actually good practice to remember how + + align:start position:0% +actually good practice to remember how + + + align:start position:0% +actually good practice to remember how +we set up triple integrals. So remember + + align:start position:0% +we set up triple integrals. So remember + + + align:start position:0% +we set up triple integrals. So remember +when we integrate first over Z, we start + + align:start position:0% +when we integrate first over Z, we start + + + align:start position:0% +when we integrate first over Z, we start +by fixing a point X and Y and for that + + align:start position:0% +by fixing a point X and Y and for that + + + align:start position:0% +by fixing a point X and Y and for that +value of X and Y, we look at a small + + align:start position:0% +value of X and Y, we look at a small + + + align:start position:0% +value of X and Y, we look at a small +vertical slice and see from where to + + align:start position:0% +vertical slice and see from where to + + + align:start position:0% +vertical slice and see from where to +where we have to go. Well, we start at Z + + align:start position:0% +where we have to go. Well, we start at Z + + + align:start position:0% +where we have to go. Well, we start at Z +equals whatever the value is at the + + align:start position:0% +equals whatever the value is at the + + + align:start position:0% +equals whatever the value is at the +bottom. So Z1 of X and Y + + align:start position:0% +bottom. So Z1 of X and Y + + + align:start position:0% +bottom. So Z1 of X and Y +and we go up to the top face, Z2 of X + + align:start position:0% +and we go up to the top face, Z2 of X + + + align:start position:0% +and we go up to the top face, Z2 of X +and Y. + + align:start position:0% +and Y. + + + align:start position:0% +and Y. +Now for x and y I'm not going to + + align:start position:0% +Now for x and y I'm not going to + + + align:start position:0% +Now for x and y I'm not going to +actually set a bounds because + + align:start position:0% +actually set a bounds because + + + align:start position:0% +actually set a bounds because +I oh sorry I've already called r the + + align:start position:0% +I oh sorry I've already called r the + + + align:start position:0% +I oh sorry I've already called r the +quantity that I'm integrating. So let me + + align:start position:0% +quantity that I'm integrating. So let me + + + align:start position:0% +quantity that I'm integrating. So let me +change this to say u or something like + + align:start position:0% +change this to say u or something like + + + align:start position:0% +change this to say u or something like +that. If you already have an r I mean + + align:start position:0% +that. If you already have an r I mean + + + align:start position:0% +that. If you already have an r I mean +there's not much risk for confusion but + + align:start position:0% +there's not much risk for confusion but + + + align:start position:0% +there's not much risk for confusion but +still. Okay. So I'm going to call u the + + align:start position:0% +still. Okay. So I'm going to call u the + + + align:start position:0% +still. Okay. So I'm going to call u the +shadow of my region instead. + + align:start position:0% +shadow of my region instead. + + + align:start position:0% +shadow of my region instead. +Um, so now I want to integrate over all + + align:start position:0% +Um, so now I want to integrate over all + + + align:start position:0% +Um, so now I want to integrate over all +values of x and y that are in the shadow + + align:start position:0% +values of x and y that are in the shadow + + + align:start position:0% +values of x and y that are in the shadow +of my region. That means it's a double + + align:start position:0% +of my region. That means it's a double + + + align:start position:0% +of my region. That means it's a double +integral over this region u, which I + + align:start position:0% +integral over this region u, which I + + + align:start position:0% +integral over this region u, which I +haven't described to you. So I can't + + align:start position:0% +haven't described to you. So I can't + + + align:start position:0% +haven't described to you. So I can't +actually set a bounds for x and y, but + + align:start position:0% +actually set a bounds for x and y, but + + + align:start position:0% +actually set a bounds for x and y, but +I'm going to just leave it like this. + + align:start position:0% +I'm going to just leave it like this. + + + align:start position:0% +I'm going to just leave it like this. +Okay. Now + + align:start position:0% +Okay. Now + + + align:start position:0% +Okay. Now +you see if you look at how you would + + align:start position:0% +you see if you look at how you would + + + align:start position:0% +you see if you look at how you would +start evaluating this, well the inner + + align:start position:0% +start evaluating this, well the inner + + + align:start position:0% +start evaluating this, well the inner +integral certainly is not scary because + + align:start position:0% +integral certainly is not scary because + + + align:start position:0% +integral certainly is not scary because +you're integrating the der the + + align:start position:0% +you're integrating the der the + + + align:start position:0% +you're integrating the der the +derivative of r with respect to z. + + align:start position:0% +derivative of r with respect to z. + + + align:start position:0% +derivative of r with respect to z. +integrating that with respect to Z. So + + align:start position:0% +integrating that with respect to Z. So + + + align:start position:0% +integrating that with respect to Z. So +you could get R back. + + align:start position:0% + + + + align:start position:0% + +Okay. So triple integral over D of RZ DV + + align:start position:0% +Okay. So triple integral over D of RZ DV + + + align:start position:0% +Okay. So triple integral over D of RZ DV +becomes well we'll have a double + + align:start position:0% +becomes well we'll have a double + + + align:start position:0% +becomes well we'll have a double +integral over U of so the inner integral + + align:start position:0% +integral over U of so the inner integral + + + align:start position:0% +integral over U of so the inner integral +becomes R at + + align:start position:0% +becomes R at + + + align:start position:0% +becomes R at +the point on the top. So that means + + align:start position:0% +the point on the top. So that means + + + align:start position:0% +the point on the top. So that means +remember r is a function of x y and z + + align:start position:0% +remember r is a function of x y and z + + + align:start position:0% +remember r is a function of x y and z +and in fact I will plug into it the + + align:start position:0% +and in fact I will plug into it the + + + align:start position:0% +and in fact I will plug into it the +value of z at the top. So z2 of xy minus + + align:start position:0% + + + + align:start position:0% + +the value of r at the point on the + + align:start position:0% +the value of r at the point on the + + + align:start position:0% +the value of r at the point on the +bottom xy z1 of xy. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +Any questions about this + + align:start position:0% + + + + align:start position:0% + +is it looking vaguely believable? Yeah. + + align:start position:0% +is it looking vaguely believable? Yeah. + + + align:start position:0% +is it looking vaguely believable? Yeah. +Okay. So now let's compute the other + + align:start position:0% +Okay. So now let's compute the other + + + align:start position:0% +Okay. So now let's compute the other +side because here we are stuck. We won't + + align:start position:0% +side because here we are stuck. We won't + + + align:start position:0% +side because here we are stuck. We won't +be able to do anything else. + + align:start position:0% +be able to do anything else. + + + align:start position:0% +be able to do anything else. +So let's look at the flux integral. + + align:start position:0% +So let's look at the flux integral. + + + align:start position:0% +So let's look at the flux integral. +Okay. We have to look at the flux of + + align:start position:0% +Okay. We have to look at the flux of + + + align:start position:0% +Okay. We have to look at the flux of +this vector field through the entire + + align:start position:0% +this vector field through the entire + + + align:start position:0% +this vector field through the entire +surface S which is the whole boundary of + + align:start position:0% +surface S which is the whole boundary of + + + align:start position:0% +surface S which is the whole boundary of +D. So that consists of a lot of pieces + + align:start position:0% +D. So that consists of a lot of pieces + + + align:start position:0% +D. So that consists of a lot of pieces +namely the top, the bottom and the + + align:start position:0% +namely the top, the bottom and the + + + align:start position:0% +namely the top, the bottom and the +sides. + + align:start position:0% + + + + align:start position:0% + +Okay, so the other side. + + align:start position:0% + + + + align:start position:0% + +So let me just remind you S is bottom + + align:start position:0% +So let me just remind you S is bottom + + + align:start position:0% +So let me just remind you S is bottom +plus top plus side + + align:start position:0% +plus top plus side + + + align:start position:0% +plus top plus side +of + + align:start position:0% +of + + + align:start position:0% +of +this vector field NDS + + align:start position:0% +this vector field NDS + + + align:start position:0% +this vector field NDS +equals Okay. So what do we have? So + + align:start position:0% +equals Okay. So what do we have? So + + + align:start position:0% +equals Okay. So what do we have? So +first we have to look at the bottom. No, + + align:start position:0% +first we have to look at the bottom. No, + + + align:start position:0% +first we have to look at the bottom. No, +let's start with the top actually. + + align:start position:0% +let's start with the top actually. + + + align:start position:0% +let's start with the top actually. +Sorry. + + align:start position:0% +Sorry. + + + align:start position:0% +Sorry. +Okay. So let's start with the top. + + align:start position:0% + + + + align:start position:0% + +So just to remind you well okay + + align:start position:0% + + + + align:start position:0% + +let's do all of them. + + align:start position:0% +let's do all of them. + + + align:start position:0% +let's do all of them. +So let's look at the top first. + + align:start position:0% + + + + align:start position:0% + +So we need to set up the flux integral + + align:start position:0% +So we need to set up the flux integral + + + align:start position:0% +So we need to set up the flux integral +for vector field NDS. We need to know + + align:start position:0% +for vector field NDS. We need to know + + + align:start position:0% +for vector field NDS. We need to know +what NDS is. Well, fortunately for us, + + align:start position:0% +what NDS is. Well, fortunately for us, + + + align:start position:0% +what NDS is. Well, fortunately for us, +we know that the top face is going to be + + align:start position:0% +we know that the top face is going to be + + + align:start position:0% +we know that the top face is going to be +the graph of some function of X and Y. + + align:start position:0% +the graph of some function of X and Y. + + + align:start position:0% +the graph of some function of X and Y. +So, we've seen a formula for NDS in this + + align:start position:0% +So, we've seen a formula for NDS in this + + + align:start position:0% +So, we've seen a formula for NDS in this +kind of situation. Okay, we've seen that + + align:start position:0% +kind of situation. Okay, we've seen that + + + align:start position:0% +kind of situation. Okay, we've seen that +NDS. Sorry. So, just to remind you, this + + align:start position:0% +NDS. Sorry. So, just to remind you, this + + + align:start position:0% +NDS. Sorry. So, just to remind you, this +is the graph + + align:start position:0% +is the graph + + + align:start position:0% +is the graph +of a function Z equals Z2 of XY. So + + align:start position:0% +of a function Z equals Z2 of XY. So + + + align:start position:0% +of a function Z equals Z2 of XY. So +we've seen NDS for that is + + align:start position:0% +we've seen NDS for that is + + + align:start position:0% +we've seen NDS for that is +negative + + align:start position:0% +negative + + + align:start position:0% +negative +partial + + align:start position:0% +partial + + + align:start position:0% +partial +derivative of this function with respect + + align:start position:0% +derivative of this function with respect + + + align:start position:0% +derivative of this function with respect +to X negative partial Z2 with respect to + + align:start position:0% +to X negative partial Z2 with respect to + + + align:start position:0% +to X negative partial Z2 with respect to +Y 1 DX DY + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +well we can't compute these guys but + + align:start position:0% +well we can't compute these guys but + + + align:start position:0% +well we can't compute these guys but +it's not a big deal because if we do the + + align:start position:0% +it's not a big deal because if we do the + + + align:start position:0% +it's not a big deal because if we do the +dot product with Z 0 R + + align:start position:0% +dot product with Z 0 R + + + align:start position:0% +dot product with Z 0 R +N DS + + align:start position:0% +N DS + + + align:start position:0% +N DS +that will give us + + align:start position:0% +that will give us + + + align:start position:0% +that will give us +well you know if you dot this with 0 0 R + + align:start position:0% +well you know if you dot this with 0 0 R + + + align:start position:0% +well you know if you dot this with 0 0 R +these terms go away you just have R dx + + align:start position:0% +these terms go away you just have R dx + + + align:start position:0% +these terms go away you just have R dx +dy. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +that means that the double integral + + align:start position:0% +that means that the double integral + + + align:start position:0% +that means that the double integral +for flux through the top of + + align:start position:0% +for flux through the top of + + + align:start position:0% +for flux through the top of +our vector field nds + + align:start position:0% +our vector field nds + + + align:start position:0% +our vector field nds +becomes + + align:start position:0% +becomes + + + align:start position:0% +becomes +double integral over the top of r dx dy. + + align:start position:0% +double integral over the top of r dx dy. + + + align:start position:0% +double integral over the top of r dx dy. +And now how do we evaluate that + + align:start position:0% +And now how do we evaluate that + + + align:start position:0% +And now how do we evaluate that +actually? Well, + + align:start position:0% +actually? Well, + + + align:start position:0% +actually? Well, +so R is a function of XYZ. But we said + + align:start position:0% +so R is a function of XYZ. But we said + + + align:start position:0% +so R is a function of XYZ. But we said +we have only two variables that we're + + align:start position:0% +we have only two variables that we're + + + align:start position:0% +we have only two variables that we're +going to use. We're going to use X and + + align:start position:0% +going to use. We're going to use X and + + + align:start position:0% +going to use. We're going to use X and +Y. We're going to get rid of Z. How do + + align:start position:0% +Y. We're going to get rid of Z. How do + + + align:start position:0% +Y. We're going to get rid of Z. How do +we get rid of Z? Well, if we're on the + + align:start position:0% +we get rid of Z? Well, if we're on the + + + align:start position:0% +we get rid of Z? Well, if we're on the +top surface, Z is given by this formula + + align:start position:0% +top surface, Z is given by this formula + + + align:start position:0% +top surface, Z is given by this formula +Z2 of XY. So I plug Z= Z2 of XY + + align:start position:0% +Z2 of XY. So I plug Z= Z2 of XY + + + align:start position:0% +Z2 of XY. So I plug Z= Z2 of XY +into the formula for R, whatever it may + + align:start position:0% +into the formula for R, whatever it may + + + align:start position:0% +into the formula for R, whatever it may +be. Then I integrate dx dy. And what's + + align:start position:0% +be. Then I integrate dx dy. And what's + + + align:start position:0% +be. Then I integrate dx dy. And what's +the range for x and y? Well, my surface + + align:start position:0% +the range for x and y? Well, my surface + + + align:start position:0% +the range for x and y? Well, my surface +sits exactly above this region u in the + + align:start position:0% +sits exactly above this region u in the + + + align:start position:0% +sits exactly above this region u in the +xy plane. So, it's a double integral + + align:start position:0% +xy plane. So, it's a double integral + + + align:start position:0% +xy plane. So, it's a double integral +over u. + + align:start position:0% +over u. + + + align:start position:0% +over u. +Okay. + + align:start position:0% + + + + align:start position:0% + +Any questions about how I set up this + + align:start position:0% +Any questions about how I set up this + + + align:start position:0% +Any questions about how I set up this +flux integral? + + align:start position:0% + + + + align:start position:0% + +No. Okay, let me close the doors + + align:start position:0% +No. Okay, let me close the doors + + + align:start position:0% +No. Okay, let me close the doors +actually. + + align:start position:0% + + + + align:start position:0% + +Okay, so we've got one of the two terms + + align:start position:0% +Okay, so we've got one of the two terms + + + align:start position:0% +Okay, so we've got one of the two terms +that we had over there. Let's try to get + + align:start position:0% +that we had over there. Let's try to get + + + align:start position:0% +that we had over there. Let's try to get +the others. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% + + + + align:start position:0% + +no comment. Okay, so + + align:start position:0% + + + + align:start position:0% + +we need to look also at the other parts + + align:start position:0% +we need to look also at the other parts + + + align:start position:0% +we need to look also at the other parts +of our surface for the flux integral. + + align:start position:0% +of our surface for the flux integral. + + + align:start position:0% +of our surface for the flux integral. +So the bottom well it will work pretty + + align:start position:0% +So the bottom well it will work pretty + + + align:start position:0% +So the bottom well it will work pretty +much the same way right because it's the + + align:start position:0% +much the same way right because it's the + + + align:start position:0% +much the same way right because it's the +graph of a function Z = Z1 of XY. + + align:start position:0% +graph of a function Z = Z1 of XY. + + + align:start position:0% +graph of a function Z = Z1 of XY. +So we should be able + + align:start position:0% +So we should be able + + + align:start position:0% +So we should be able +to get NDS using the same method. + + align:start position:0% +to get NDS using the same method. + + + align:start position:0% +to get NDS using the same method. +Negative partial respect to X negative + + align:start position:0% +Negative partial respect to X negative + + + align:start position:0% +Negative partial respect to X negative +partial with respect to Y one + + align:start position:0% + + + + align:start position:0% + +dx dy. + + align:start position:0% +dx dy. + + + align:start position:0% +dx dy. +Now there's a small catch. Okay, we have + + align:start position:0% +Now there's a small catch. Okay, we have + + + align:start position:0% +Now there's a small catch. Okay, we have +to think a bit carefully about + + align:start position:0% +to think a bit carefully about + + + align:start position:0% +to think a bit carefully about +orientations. + + align:start position:0% +orientations. + + + align:start position:0% +orientations. +So + + align:start position:0% +So + + + align:start position:0% +So +remember when we set up the divergence + + align:start position:0% +remember when we set up the divergence + + + align:start position:0% +remember when we set up the divergence +theorem, we need the normal vectors to + + align:start position:0% +theorem, we need the normal vectors to + + + align:start position:0% +theorem, we need the normal vectors to +point out of our region, which means + + align:start position:0% +point out of our region, which means + + + align:start position:0% +point out of our region, which means +that on the top surface, we want n + + align:start position:0% +that on the top surface, we want n + + + align:start position:0% +that on the top surface, we want n +pointing up, + + align:start position:0% +pointing up, + + + align:start position:0% +pointing up, +but on the bottom face, we want n + + align:start position:0% +but on the bottom face, we want n + + + align:start position:0% +but on the bottom face, we want n +pointing down. + + align:start position:0% +pointing down. + + + align:start position:0% +pointing down. +So in fact, we shouldn't use this + + align:start position:0% +So in fact, we shouldn't use this + + + align:start position:0% +So in fact, we shouldn't use this +formula here because that one + + align:start position:0% +formula here because that one + + + align:start position:0% +formula here because that one +corresponds to the other orientation. + + align:start position:0% +corresponds to the other orientation. + + + align:start position:0% +corresponds to the other orientation. +Well, we could use it and then subtract, + + align:start position:0% +Well, we could use it and then subtract, + + + align:start position:0% +Well, we could use it and then subtract, +but instead I'm just going to say that n + + align:start position:0% +but instead I'm just going to say that n + + + align:start position:0% +but instead I'm just going to say that n +dx is actually the opposite of this. So, + + align:start position:0% +dx is actually the opposite of this. So, + + + align:start position:0% +dx is actually the opposite of this. So, +I'm going to switch all my signs. Okay, + + align:start position:0% +I'm going to switch all my signs. Okay, + + + align:start position:0% +I'm going to switch all my signs. Okay, +that's the other side of the formula. + + align:start position:0% +that's the other side of the formula. + + + align:start position:0% +that's the other side of the formula. +When you orient your graph with n + + align:start position:0% +When you orient your graph with n + + + align:start position:0% +When you orient your graph with n +pointing downwards + + align:start position:0% +pointing downwards + + + align:start position:0% +pointing downwards +now, if I do things the same way as + + align:start position:0% +now, if I do things the same way as + + + align:start position:0% +now, if I do things the same way as +before, I will get that 00 r nds + + align:start position:0% +before, I will get that 00 r nds + + + align:start position:0% +before, I will get that 00 r nds +will be negative r dxdy. + + align:start position:0% +will be negative r dxdy. + + + align:start position:0% +will be negative r dxdy. +And so + + align:start position:0% +And so + + + align:start position:0% +And so +when I do the double integral + + align:start position:0% +when I do the double integral + + + align:start position:0% +when I do the double integral +over the bottom, + + align:start position:0% +over the bottom, + + + align:start position:0% +over the bottom, +I'm going to get the double integral + + align:start position:0% +I'm going to get the double integral + + + align:start position:0% +I'm going to get the double integral +over the bottom + + align:start position:0% +over the bottom + + + align:start position:0% +over the bottom +of negative rx dy which if I try to + + align:start position:0% +of negative rx dy which if I try to + + + align:start position:0% +of negative rx dy which if I try to +evaluate that well I actually will have + + align:start position:0% +evaluate that well I actually will have + + + align:start position:0% +evaluate that well I actually will have +to integrate sorry first I will have to + + align:start position:0% +to integrate sorry first I will have to + + + align:start position:0% +to integrate sorry first I will have to +substitute the value of z. The value of + + align:start position:0% +substitute the value of z. The value of + + + align:start position:0% +substitute the value of z. The value of +Z that I will want to plug into R will + + align:start position:0% +Z that I will want to plug into R will + + + align:start position:0% +Z that I will want to plug into R will +be given by now Z1 of XY + + align:start position:0% +be given by now Z1 of XY + + + align:start position:0% +be given by now Z1 of XY +and the bounds of integration will be + + align:start position:0% +and the bounds of integration will be + + + align:start position:0% +and the bounds of integration will be +given again by the shadow of our surface + + align:start position:0% +given again by the shadow of our surface + + + align:start position:0% +given again by the shadow of our surface +which is again this guy U. + + align:start position:0% +which is again this guy U. + + + align:start position:0% +which is again this guy U. +Okay, so we seem to be all set except + + align:start position:0% +Okay, so we seem to be all set except + + + align:start position:0% +Okay, so we seem to be all set except +we're still missing one part of our + + align:start position:0% +we're still missing one part of our + + + align:start position:0% +we're still missing one part of our +surface S because we also need to look + + align:start position:0% +surface S because we also need to look + + + align:start position:0% +surface S because we also need to look +at the sides. Well, what about the + + align:start position:0% +at the sides. Well, what about the + + + align:start position:0% +at the sides. Well, what about the +sides? + + align:start position:0% +sides? + + + align:start position:0% +sides? +Well, our vector field 000 R is actually + + align:start position:0% +Well, our vector field 000 R is actually + + + align:start position:0% +Well, our vector field 000 R is actually +vertical. It's parallel to the Z-axis. + + align:start position:0% +vertical. It's parallel to the Z-axis. + + + align:start position:0% +vertical. It's parallel to the Z-axis. +Okay, so my vector field + + align:start position:0% +Okay, so my vector field + + + align:start position:0% +Okay, so my vector field +does + + align:start position:0% +does + + + align:start position:0% +does +something like this everywhere. + + align:start position:0% +something like this everywhere. + + + align:start position:0% +something like this everywhere. +And while that makes it very interesting + + align:start position:0% +And while that makes it very interesting + + + align:start position:0% +And while that makes it very interesting +on the top and bottom, that means that + + align:start position:0% +on the top and bottom, that means that + + + align:start position:0% +on the top and bottom, that means that +on the sides really not much is going + + align:start position:0% +on the sides really not much is going + + + align:start position:0% +on the sides really not much is going +on, right? No matter passing through the + + align:start position:0% +on, right? No matter passing through the + + + align:start position:0% +on, right? No matter passing through the +vertical side. So the side + + align:start position:0% + + + + align:start position:0% + +the sides are vertical. + + align:start position:0% +the sides are vertical. + + + align:start position:0% +the sides are vertical. +So + + align:start position:0% +So + + + align:start position:0% +So +0 0 R is tangent to the side. + + align:start position:0% + + + + align:start position:0% + +And therefore the flux for the sides + + align:start position:0% + + + + align:start position:0% + +is just going to be zero. + + align:start position:0% + + + + align:start position:0% + +Okay, no calculation needed. + + align:start position:0% +Okay, no calculation needed. + + + align:start position:0% +Okay, no calculation needed. +That's because of course that's the + + align:start position:0% +That's because of course that's the + + + align:start position:0% +That's because of course that's the +reason why I simplified first things so + + align:start position:0% +reason why I simplified first things so + + + align:start position:0% +reason why I simplified first things so +that my vector field would only have a Z + + align:start position:0% +that my vector field would only have a Z + + + align:start position:0% +that my vector field would only have a Z +component. Well, not just that, but + + align:start position:0% +component. Well, not just that, but + + + align:start position:0% +component. Well, not just that, but +that's the main place where it becomes + + align:start position:0% +that's the main place where it becomes + + + align:start position:0% +that's the main place where it becomes +very useful. + + align:start position:0% + + + + align:start position:0% + +So now if I compare my double integral + + align:start position:0% +So now if I compare my double integral + + + align:start position:0% +So now if I compare my double integral +and my flux sorry my triple integral and + + align:start position:0% +and my flux sorry my triple integral and + + + align:start position:0% +and my flux sorry my triple integral and +my flux integral I get that they're + + align:start position:0% +my flux integral I get that they're + + + align:start position:0% +my flux integral I get that they're +indeed the same. + + align:start position:0% + + + + align:start position:0% + +Well that's the statement of the theorem + + align:start position:0% +Well that's the statement of the theorem + + + align:start position:0% +Well that's the statement of the theorem +we're trying to prove. I should not + + align:start position:0% +we're trying to prove. I should not + + + align:start position:0% +we're trying to prove. I should not +erase it. Okay. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, + + align:start position:0% + + + + align:start position:0% + +just to + + align:start position:0% +just to + + + align:start position:0% +just to +recap, we got a formula for the triple + + align:start position:0% +recap, we got a formula for the triple + + + align:start position:0% +recap, we got a formula for the triple +integral of R subz DV. It's up there at + + align:start position:0% +integral of R subz DV. It's up there at + + + align:start position:0% +integral of R subz DV. It's up there at +the very top. And we got formulas for + + align:start position:0% +the very top. And we got formulas for + + + align:start position:0% +the very top. And we got formulas for +the flux through the top and the bottom + + align:start position:0% +the flux through the top and the bottom + + + align:start position:0% +the flux through the top and the bottom +and the sides. And when you add them + + align:start position:0% +and the sides. And when you add them + + + align:start position:0% +and the sides. And when you add them +together, you get + + align:start position:0% +together, you get + + + align:start position:0% +together, you get +indeed the same formula. + + align:start position:0% +indeed the same formula. + + + align:start position:0% +indeed the same formula. +Top plus bottom + + align:start position:0% + + + + align:start position:0% + +plus sides of + + align:start position:0% + + + + align:start position:0% + +Okay. And so we have actually completed + + align:start position:0% +Okay. And so we have actually completed + + + align:start position:0% +Okay. And so we have actually completed +the proof for this part. Now well that's + + align:start position:0% +the proof for this part. Now well that's + + + align:start position:0% +the proof for this part. Now well that's +only for a vertically simple region. + + align:start position:0% +only for a vertically simple region. + + + align:start position:0% +only for a vertically simple region. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So + + align:start position:0% +So + + + align:start position:0% +So +if D + + align:start position:0% +if D + + + align:start position:0% +if D +is not vertically simple, what do we do? + + align:start position:0% +is not vertically simple, what do we do? + + + align:start position:0% +is not vertically simple, what do we do? +Well, we cut it into vertically simple + + align:start position:0% +Well, we cut it into vertically simple + + + align:start position:0% +Well, we cut it into vertically simple +pieces. + + align:start position:0% + + + + align:start position:0% + +Okay, so concretely, you know, say that + + align:start position:0% +Okay, so concretely, you know, say that + + + align:start position:0% +Okay, so concretely, you know, say that +I wanted to integrate over a solid + + align:start position:0% +I wanted to integrate over a solid + + + align:start position:0% +I wanted to integrate over a solid +donut. + + align:start position:0% +donut. + + + align:start position:0% +donut. +Then + + align:start position:0% +Then + + + align:start position:0% +Then +that's not vertically simple because + + align:start position:0% +that's not vertically simple because + + + align:start position:0% +that's not vertically simple because +here in the middle I have, you know, not + + align:start position:0% +here in the middle I have, you know, not + + + align:start position:0% +here in the middle I have, you know, not +only this top and this bottom, but I + + align:start position:0% +only this top and this bottom, but I + + + align:start position:0% +only this top and this bottom, but I +have like this middle face. So the way I + + align:start position:0% +have like this middle face. So the way I + + + align:start position:0% +have like this middle face. So the way I +would cut my donut would be probably I + + align:start position:0% +would cut my donut would be probably I + + + align:start position:0% +would cut my donut would be probably I +would slice it. No, not in the way that + + align:start position:0% +would slice it. No, not in the way that + + + align:start position:0% +would slice it. No, not in the way that +you would usually slice a donut or a + + align:start position:0% +you would usually slice a donut or a + + + align:start position:0% +you would usually slice a donut or a +bagel, but + + align:start position:0% +bagel, but + + + align:start position:0% +bagel, but +it's probably more spectacular if you + + align:start position:0% +it's probably more spectacular if you + + + align:start position:0% +it's probably more spectacular if you +think of it as a bagel. Then the + + align:start position:0% +think of it as a bagel. Then the + + + align:start position:0% +think of it as a bagel. Then the +mathematician's way of slicing it is + + align:start position:0% +mathematician's way of slicing it is + + + align:start position:0% +mathematician's way of slicing it is +like this into five pieces. Okay? And + + align:start position:0% +like this into five pieces. Okay? And + + + align:start position:0% +like this into five pieces. Okay? And +that's not very convenient for eating, + + align:start position:0% +that's not very convenient for eating, + + + align:start position:0% +that's not very convenient for eating, +but that's convenient for integrating + + align:start position:0% +but that's convenient for integrating + + + align:start position:0% +but that's convenient for integrating +over it because now each of these pieces + + align:start position:0% +over it because now each of these pieces + + + align:start position:0% +over it because now each of these pieces +has a well- definfined top and bottom + + align:start position:0% +has a well- definfined top and bottom + + + align:start position:0% +has a well- definfined top and bottom +face. And of course, you've introduced + + align:start position:0% +face. And of course, you've introduced + + + align:start position:0% +face. And of course, you've introduced +some vertical sides. But we don't really + + align:start position:0% +some vertical sides. But we don't really + + + align:start position:0% +some vertical sides. But we don't really +care about the vertical sides for two + + align:start position:0% +care about the vertical sides for two + + + align:start position:0% +care about the vertical sides for two +reasons. One is that we've said the flux + + align:start position:0% +reasons. One is that we've said the flux + + + align:start position:0% +reasons. One is that we've said the flux +through them is zero anyway, so who + + align:start position:0% +through them is zero anyway, so who + + + align:start position:0% +through them is zero anyway, so who +bothers, you know, who cares? Sorry, why + + align:start position:0% +bothers, you know, who cares? Sorry, why + + + align:start position:0% +bothers, you know, who cares? Sorry, why +bother? But also, you know, if you sum + + align:start position:0% +bother? But also, you know, if you sum + + + align:start position:0% +bother? But also, you know, if you sum +the flux through the surface of each + + align:start position:0% +the flux through the surface of each + + + align:start position:0% +the flux through the surface of each +little piece, well, you see that you + + align:start position:0% +little piece, well, you see that you + + + align:start position:0% +little piece, well, you see that you +will be integrating twice over each of + + align:start position:0% +will be integrating twice over each of + + + align:start position:0% +will be integrating twice over each of +these vertical cuts. Once when you do + + align:start position:0% +these vertical cuts. Once when you do + + + align:start position:0% +these vertical cuts. Once when you do +this piece, you'll be taking the flux + + align:start position:0% +this piece, you'll be taking the flux + + + align:start position:0% +this piece, you'll be taking the flux +through this red guy with normal vector + + align:start position:0% +through this red guy with normal vector + + + align:start position:0% +through this red guy with normal vector +pointing to the right. And once when you + + align:start position:0% +pointing to the right. And once when you + + + align:start position:0% +pointing to the right. And once when you +take this middle piece, you'll be taking + + align:start position:0% +take this middle piece, you'll be taking + + + align:start position:0% +take this middle piece, you'll be taking +the flux through that cut surface again, + + align:start position:0% +the flux through that cut surface again, + + + align:start position:0% +the flux through that cut surface again, +but now with normal vector pointing the + + align:start position:0% +but now with normal vector pointing the + + + align:start position:0% +but now with normal vector pointing the +other way around. So in fact you'll be + + align:start position:0% +other way around. So in fact you'll be + + + align:start position:0% +other way around. So in fact you'll be +summing the flux for these guys twice + + align:start position:0% +summing the flux for these guys twice + + + align:start position:0% +summing the flux for these guys twice +with opposite orientations. They cancel + + align:start position:0% +with opposite orientations. They cancel + + + align:start position:0% +with opposite orientations. They cancel +out + + align:start position:0% +out + + + align:start position:0% +out +well and again because of what we were + + align:start position:0% +well and again because of what we were + + + align:start position:0% +well and again because of what we were +doing actually the integral was just + + align:start position:0% +doing actually the integral was just + + + align:start position:0% +doing actually the integral was just +zero anyway. So it didn't matter but + + align:start position:0% +zero anyway. So it didn't matter but + + + align:start position:0% +zero anyway. So it didn't matter but +even if it hadn't simplified + + align:start position:0% +even if it hadn't simplified + + + align:start position:0% +even if it hadn't simplified +that would do it for us. + + align:start position:0% +that would do it for us. + + + align:start position:0% +that would do it for us. +Okay. So that's how we do it with a + + align:start position:0% +Okay. So that's how we do it with a + + + align:start position:0% +Okay. So that's how we do it with a +general region. And then as I said at + + align:start position:0% +general region. And then as I said at + + + align:start position:0% +general region. And then as I said at +the beginning when we can do it for a + + align:start position:0% +the beginning when we can do it for a + + + align:start position:0% +the beginning when we can do it for a +vector field that has only a Z component + + align:start position:0% +vector field that has only a Z component + + + align:start position:0% +vector field that has only a Z component +well we can also do it for a vector + + align:start position:0% +well we can also do it for a vector + + + align:start position:0% +well we can also do it for a vector +field that has only an X or only a Y + + align:start position:0% +field that has only an X or only a Y + + + align:start position:0% +field that has only an X or only a Y +component and then we sum together and + + align:start position:0% +component and then we sum together and + + + align:start position:0% +component and then we sum together and +we get the general case. So that's the + + align:start position:0% +we get the general case. So that's the + + + align:start position:0% +we get the general case. So that's the +end of the proof. + + align:start position:0% +end of the proof. + + + align:start position:0% +end of the proof. +Okay. + + align:start position:0% + + + + align:start position:0% + +So you see the idea is really the same + + align:start position:0% +So you see the idea is really the same + + + align:start position:0% +So you see the idea is really the same +as for Green's theorem. Yes. A second + + align:start position:0% +as for Green's theorem. Yes. A second + + + align:start position:0% +as for Green's theorem. Yes. A second +ago you said there were five pieces. Oh + + align:start position:0% +ago you said there were five pieces. Oh + + + align:start position:0% +ago you said there were five pieces. Oh +there's only four pieces. Thank you. + + align:start position:0% +there's only four pieces. Thank you. + + + align:start position:0% +there's only four pieces. Thank you. +Yes. Uh I there's you know there's three + + align:start position:0% +Yes. Uh I there's you know there's three + + + align:start position:0% +Yes. Uh I there's you know there's three +kinds of mathematicians. Those who know + + align:start position:0% +kinds of mathematicians. Those who know + + + align:start position:0% +kinds of mathematicians. Those who know +how to count and those who don't + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So okay now + + align:start position:0% +So okay now + + + align:start position:0% +So okay now +so I hope that you can see already the + + align:start position:0% +so I hope that you can see already the + + + align:start position:0% +so I hope that you can see already the +interest of this theorem for you know + + align:start position:0% +interest of this theorem for you know + + + align:start position:0% +interest of this theorem for you know +the divergence theorem for computing + + align:start position:0% +the divergence theorem for computing + + + align:start position:0% +the divergence theorem for computing +flux integrals just for the sake of + + align:start position:0% +flux integrals just for the sake of + + + align:start position:0% +flux integrals just for the sake of +computing flux integrals like might + + align:start position:0% +computing flux integrals like might + + + align:start position:0% +computing flux integrals like might +happen on the problem set or on the next + + align:start position:0% +happen on the problem set or on the next + + + align:start position:0% +happen on the problem set or on the next +test. Uh but let me tell you also why + + align:start position:0% +test. Uh but let me tell you also why + + + align:start position:0% +test. Uh but let me tell you also why +it's important physically to understand + + align:start position:0% +it's important physically to understand + + + align:start position:0% +it's important physically to understand +equations that had been observed + + align:start position:0% +equations that had been observed + + + align:start position:0% +equations that had been observed +empirically well before they were + + align:start position:0% +empirically well before they were + + + align:start position:0% +empirically well before they were +actually understood in terms of how + + align:start position:0% +actually understood in terms of how + + + align:start position:0% +actually understood in terms of how +things go. So + + align:start position:0% +things go. So + + + align:start position:0% +things go. So +let's look at something called the + + align:start position:0% +let's look at something called the + + + align:start position:0% +let's look at something called the +diffusion equation. + + align:start position:0% + + + + align:start position:0% + +So let me explain to you what it does. + + align:start position:0% +So let me explain to you what it does. + + + align:start position:0% +So let me explain to you what it does. +So the diffusion equation is something + + align:start position:0% +So the diffusion equation is something + + + align:start position:0% +So the diffusion equation is something +that governs well what's called + + align:start position:0% +that governs well what's called + + + align:start position:0% +that governs well what's called +diffusion. Diffusion is when you have + + align:start position:0% +diffusion. Diffusion is when you have + + + align:start position:0% +diffusion. Diffusion is when you have +a fluid in which you're introducing some + + align:start position:0% +a fluid in which you're introducing some + + + align:start position:0% +a fluid in which you're introducing some +substance and you want to figure out how + + align:start position:0% +substance and you want to figure out how + + + align:start position:0% +substance and you want to figure out how +that thing is going to spread out. + + align:start position:0% +that thing is going to spread out. + + + align:start position:0% +that thing is going to spread out. +The technical term is diffuse into the + + align:start position:0% +The technical term is diffuse into the + + + align:start position:0% +The technical term is diffuse into the +ambient fluid. So for example that that + + align:start position:0% +ambient fluid. So for example that that + + + align:start position:0% +ambient fluid. So for example that that +governs the motion of say smoke in the + + align:start position:0% +governs the motion of say smoke in the + + + align:start position:0% +governs the motion of say smoke in the +air + + align:start position:0% + + + + align:start position:0% + +or you know if you put dye in a solution + + align:start position:0% +or you know if you put dye in a solution + + + align:start position:0% +or you know if you put dye in a solution +or things like that that will tell you + + align:start position:0% +or things like that that will tell you + + + align:start position:0% +or things like that that will tell you +you know say that you actually drop you + + align:start position:0% +you know say that you actually drop you + + + align:start position:0% +you know say that you actually drop you +know some ink into a glass of water. + + align:start position:0% +know some ink into a glass of water. + + + align:start position:0% +know some ink into a glass of water. +Well, you can imagine that obviously it + + align:start position:0% +Well, you can imagine that obviously it + + + align:start position:0% +Well, you can imagine that obviously it +will get diluted into there and that + + align:start position:0% +will get diluted into there and that + + + align:start position:0% +will get diluted into there and that +equation will tell you how exactly over + + align:start position:0% +equation will tell you how exactly over + + + align:start position:0% +equation will tell you how exactly over +time this thing is going to spread out + + align:start position:0% +time this thing is going to spread out + + + align:start position:0% +time this thing is going to spread out +and start filling the entire glass. + + align:start position:0% +and start filling the entire glass. + + + align:start position:0% +and start filling the entire glass. +So + + align:start position:0% +So + + + align:start position:0% +So +what's the equation? Well, we need first + + align:start position:0% +what's the equation? Well, we need first + + + align:start position:0% +what's the equation? Well, we need first +to know what the unknown will be. So + + align:start position:0% +to know what the unknown will be. So + + + align:start position:0% +to know what the unknown will be. So +it's a partial differential equation. + + align:start position:0% +it's a partial differential equation. + + + align:start position:0% +it's a partial differential equation. +Okay, so the unknown is a function and + + align:start position:0% +Okay, so the unknown is a function and + + + align:start position:0% +Okay, so the unknown is a function and +the equation will relate the partial + + align:start position:0% +the equation will relate the partial + + + align:start position:0% +the equation will relate the partial +derivatives of that function to each + + align:start position:0% +derivatives of that function to each + + + align:start position:0% +derivatives of that function to each +other. So + + align:start position:0% +other. So + + + align:start position:0% +other. So +u the unknown will be the concentration + + align:start position:0% + + + + align:start position:0% + +at a given point + + align:start position:0% + + + + align:start position:0% + +and of course that depends on the point + + align:start position:0% +and of course that depends on the point + + + align:start position:0% +and of course that depends on the point +where you are. So that depends on XYZ + + align:start position:0% +where you are. So that depends on XYZ + + + align:start position:0% +where you are. So that depends on XYZ +the location where you are. But since + + align:start position:0% +the location where you are. But since + + + align:start position:0% +the location where you are. But since +the goal is to also understand how + + align:start position:0% +the goal is to also understand how + + + align:start position:0% +the goal is to also understand how +things spread over time it should also + + align:start position:0% +things spread over time it should also + + + align:start position:0% +things spread over time it should also +depend on time. Otherwise we are not + + align:start position:0% +depend on time. Otherwise we are not + + + align:start position:0% +depend on time. Otherwise we are not +going to get very far. + + align:start position:0% +going to get very far. + + + align:start position:0% +going to get very far. +And in fact what the equation will give + + align:start position:0% +And in fact what the equation will give + + + align:start position:0% +And in fact what the equation will give +us is the derivative of u with respect + + align:start position:0% +us is the derivative of u with respect + + + align:start position:0% +us is the derivative of u with respect +to t. It will tell us how the + + align:start position:0% +to t. It will tell us how the + + + align:start position:0% +to t. It will tell us how the +concentration at a given point varies + + align:start position:0% +concentration at a given point varies + + + align:start position:0% +concentration at a given point varies +over time in terms of how the + + align:start position:0% +over time in terms of how the + + + align:start position:0% +over time in terms of how the +concentration varied in space. So it + + align:start position:0% +concentration varied in space. So it + + + align:start position:0% +concentration varied in space. So it +will relate partial u partial t to + + align:start position:0% +will relate partial u partial t to + + + align:start position:0% +will relate partial u partial t to +partial derivatives with respect to x y + + align:start position:0% +partial derivatives with respect to x y + + + align:start position:0% +partial derivatives with respect to x y +and z. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +okay. So, what's the equation? The + + align:start position:0% +okay. So, what's the equation? The + + + align:start position:0% +okay. So, what's the equation? The +equation is partial u partial t + + align:start position:0% +equation is partial u partial t + + + align:start position:0% +equation is partial u partial t +equals some constant let me call that + + align:start position:0% +equals some constant let me call that + + + align:start position:0% +equals some constant let me call that +constant k times something I will call + + align:start position:0% +constant k times something I will call + + + align:start position:0% +constant k times something I will call +del^ squ u which is also called the + + align:start position:0% +del^ squ u which is also called the + + + align:start position:0% +del^ squ u which is also called the +lllesian of u. + + align:start position:0% +lllesian of u. + + + align:start position:0% +lllesian of u. +And what is that? + + align:start position:0% +And what is that? + + + align:start position:0% +And what is that? +Well, that means + + align:start position:0% +Well, that means + + + align:start position:0% +Well, that means +okay so just to scare you del square is + + align:start position:0% +okay so just to scare you del square is + + + align:start position:0% +okay so just to scare you del square is +this which means it's the divergence of + + align:start position:0% +this which means it's the divergence of + + + align:start position:0% +this which means it's the divergence of +gradient u that we've used this notation + + align:start position:0% +gradient u that we've used this notation + + + align:start position:0% +gradient u that we've used this notation +for gradient. Okay. So if you actually + + align:start position:0% +for gradient. Okay. So if you actually + + + align:start position:0% +for gradient. Okay. So if you actually +expand it in terms of the variables, uh + + align:start position:0% +expand it in terms of the variables, uh + + + align:start position:0% +expand it in terms of the variables, uh +that becomes partial u over partial x^2 + + align:start position:0% +that becomes partial u over partial x^2 + + + align:start position:0% +that becomes partial u over partial x^2 +plus partial squar u over partial y^2 + + align:start position:0% +plus partial squar u over partial y^2 + + + align:start position:0% +plus partial squar u over partial y^2 +plus partial squar u over partial z^ 2. + + align:start position:0% +plus partial squar u over partial z^ 2. + + + align:start position:0% +plus partial squar u over partial z^ 2. +Okay. So the equation is + + align:start position:0% +Okay. So the equation is + + + align:start position:0% +Okay. So the equation is +this equals that. + + align:start position:0% +this equals that. + + + align:start position:0% +this equals that. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +So that's a weird looking equation and + + align:start position:0% +So that's a weird looking equation and + + + align:start position:0% +So that's a weird looking equation and +I'm going to have to explain to you + + align:start position:0% +I'm going to have to explain to you + + + align:start position:0% +I'm going to have to explain to you +where does it come from. Okay, but + + align:start position:0% +where does it come from. Okay, but + + + align:start position:0% +where does it come from. Okay, but +before I do that I mean + + align:start position:0% +before I do that I mean + + + align:start position:0% +before I do that I mean +well + + align:start position:0% +well + + + align:start position:0% +well +let me point out actually that this + + align:start position:0% +let me point out actually that this + + + align:start position:0% +let me point out actually that this +equation is not just the diffusion + + align:start position:0% +equation is not just the diffusion + + + align:start position:0% +equation is not just the diffusion +equation. It's also known as the heat + + align:start position:0% +equation. It's also known as the heat + + + align:start position:0% +equation. It's also known as the heat +equation. + + align:start position:0% + + + + align:start position:0% + +And that's because exactly the same + + align:start position:0% +And that's because exactly the same + + + align:start position:0% +And that's because exactly the same +equation governs + + align:start position:0% +equation governs + + + align:start position:0% +equation governs +how temperature changes over time when + + align:start position:0% +how temperature changes over time when + + + align:start position:0% +how temperature changes over time when +you know you have + + align:start position:0% +you know you have + + + align:start position:0% +you know you have +again so sorry I should have been + + align:start position:0% +again so sorry I should have been + + + align:start position:0% +again so sorry I should have been +actually more careful I should have said + + align:start position:0% +actually more careful I should have said + + + align:start position:0% +actually more careful I should have said +this is in air that's not moving okay + + align:start position:0% +this is in air that's not moving okay + + + align:start position:0% +this is in air that's not moving okay +and same thing with a solution you know + + align:start position:0% +and same thing with a solution you know + + + align:start position:0% +and same thing with a solution you know +if you drop some ink into your glass of + + align:start position:0% +if you drop some ink into your glass of + + + align:start position:0% +if you drop some ink into your glass of +water well if you start steering + + align:start position:0% +water well if you start steering + + + align:start position:0% +water well if you start steering +obviously it will mix much faster than + + align:start position:0% +obviously it will mix much faster than + + + align:start position:0% +obviously it will mix much faster than +if you don't do anything okay so that's + + align:start position:0% +if you don't do anything okay so that's + + + align:start position:0% +if you don't do anything okay so that's +the case where we don't actually the + + align:start position:0% +the case where we don't actually the + + + align:start position:0% +the case where we don't actually the +fluid is not moving. And the heat + + align:start position:0% +fluid is not moving. And the heat + + + align:start position:0% +fluid is not moving. And the heat +equation now does the same but for + + align:start position:0% +equation now does the same but for + + + align:start position:0% +equation now does the same but for +temperature in a fluid that's at rest + + align:start position:0% +temperature in a fluid that's at rest + + + align:start position:0% +temperature in a fluid that's at rest +that's not moving. It tells you how the + + align:start position:0% +that's not moving. It tells you how the + + + align:start position:0% +that's not moving. It tells you how the +heat goes from you know the warmest + + align:start position:0% +heat goes from you know the warmest + + + align:start position:0% +heat goes from you know the warmest +parts to the coldest parts and + + align:start position:0% +parts to the coldest parts and + + + align:start position:0% +parts to the coldest parts and +eventually temperature should somehow + + align:start position:0% +eventually temperature should somehow + + + align:start position:0% +eventually temperature should somehow +even out. + + align:start position:0% + + + + align:start position:0% + +So in the heat equation + + align:start position:0% +So in the heat equation + + + align:start position:0% +So in the heat equation +that would just be this U would just + + align:start position:0% +that would just be this U would just + + + align:start position:0% +that would just be this U would just +measure the temperature + + align:start position:0% + + + + align:start position:0% + +for you know temperature of your fluid + + align:start position:0% +for you know temperature of your fluid + + + align:start position:0% +for you know temperature of your fluid +at a given point. Actually it doesn't + + align:start position:0% +at a given point. Actually it doesn't + + + align:start position:0% +at a given point. Actually it doesn't +have to be a fluid. It could be a solid + + align:start position:0% +have to be a fluid. It could be a solid + + + align:start position:0% +have to be a fluid. It could be a solid +for the heat equation. + + align:start position:0% +for the heat equation. + + + align:start position:0% +for the heat equation. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +so you know, for example, say that you + + align:start position:0% +so you know, for example, say that you + + + align:start position:0% +so you know, for example, say that you +have a big, I don't know, box made of + + align:start position:0% +have a big, I don't know, box made of + + + align:start position:0% +have a big, I don't know, box made of +metal or something and you know, you do + + align:start position:0% +metal or something and you know, you do + + + align:start position:0% +metal or something and you know, you do +some heating at one side. You want to + + align:start position:0% +some heating at one side. You want to + + + align:start position:0% +some heating at one side. You want to +know how quickly is the other side going + + align:start position:0% +know how quickly is the other side going + + + align:start position:0% +know how quickly is the other side going +to get hot. Well, you can use the + + align:start position:0% +to get hot. Well, you can use the + + + align:start position:0% +to get hot. Well, you can use the +equation to figure out, you know, say + + align:start position:0% +equation to figure out, you know, say + + + align:start position:0% +equation to figure out, you know, say +that you have a metal bar and you keep + + align:start position:0% +that you have a metal bar and you keep + + + align:start position:0% +that you have a metal bar and you keep +one side at, I don't know, 400° because + + align:start position:0% +one side at, I don't know, 400° because + + + align:start position:0% +one side at, I don't know, 400° because +it's in your oven. Uh, how quickly will + + align:start position:0% +it's in your oven. Uh, how quickly will + + + align:start position:0% +it's in your oven. Uh, how quickly will +the other side get warm? + + align:start position:0% + + + + align:start position:0% + +Okay, so it's the same equation for both + + align:start position:0% +Okay, so it's the same equation for both + + + align:start position:0% +Okay, so it's the same equation for both +phenomena, even though they're of course + + align:start position:0% +phenomena, even though they're of course + + + align:start position:0% +phenomena, even though they're of course +different phenomena. + + align:start position:0% + + + + align:start position:0% + +Well, the physical reason why they're + + align:start position:0% +Well, the physical reason why they're + + + align:start position:0% +Well, the physical reason why they're +the same is actually that phenomena are + + align:start position:0% +the same is actually that phenomena are + + + align:start position:0% +the same is actually that phenomena are +different, but not all that much. They + + align:start position:0% +different, but not all that much. They + + + align:start position:0% +different, but not all that much. They +involve actually how the atoms and + + align:start position:0% +involve actually how the atoms and + + + align:start position:0% +involve actually how the atoms and +molecules are actually moving and + + align:start position:0% +molecules are actually moving and + + + align:start position:0% +molecules are actually moving and +hitting each other inside this medium. + + align:start position:0% +hitting each other inside this medium. + + + align:start position:0% +hitting each other inside this medium. +Okay, so anyway, what's the explanation + + align:start position:0% +Okay, so anyway, what's the explanation + + + align:start position:0% +Okay, so anyway, what's the explanation +for this? + + align:start position:0% +for this? + + + align:start position:0% +for this? +So to understand the explanation and + + align:start position:0% +So to understand the explanation and + + + align:start position:0% +So to understand the explanation and +given what we've been doing, we should + + align:start position:0% +given what we've been doing, we should + + + align:start position:0% +given what we've been doing, we should +have a vector field in there. + + align:start position:0% +have a vector field in there. + + + align:start position:0% +have a vector field in there. +So + + align:start position:0% +So + + + align:start position:0% +So +I'm going to think of the flow of well + + align:start position:0% +I'm going to think of the flow of well + + + align:start position:0% +I'm going to think of the flow of well +let me say let's imagine that we're + + align:start position:0% +let me say let's imagine that we're + + + align:start position:0% +let me say let's imagine that we're +doing motion of smoke in air. So that's + + align:start position:0% +doing motion of smoke in air. So that's + + + align:start position:0% +doing motion of smoke in air. So that's +the the flow of the smoke. + + align:start position:0% +the the flow of the smoke. + + + align:start position:0% +the the flow of the smoke. +That means you know at every point it's + + align:start position:0% +That means you know at every point it's + + + align:start position:0% +That means you know at every point it's +a vector whose direction tells me in + + align:start position:0% +a vector whose direction tells me in + + + align:start position:0% +a vector whose direction tells me in +which direction the smoke is actually + + align:start position:0% +which direction the smoke is actually + + + align:start position:0% +which direction the smoke is actually +moving and its magnitude tells me how + + align:start position:0% +moving and its magnitude tells me how + + + align:start position:0% +moving and its magnitude tells me how +fast it's moving and also what amount of + + align:start position:0% +fast it's moving and also what amount of + + + align:start position:0% +fast it's moving and also what amount of +smoke is moving. + + align:start position:0% + + + + align:start position:0% + +So there's two things to understand. + + align:start position:0% +So there's two things to understand. + + + align:start position:0% +So there's two things to understand. +One is how + + align:start position:0% +One is how + + + align:start position:0% +One is how +the disparities in the concentration + + align:start position:0% +the disparities in the concentration + + + align:start position:0% +the disparities in the concentration +between different points cause the flow + + align:start position:0% +between different points cause the flow + + + align:start position:0% +between different points cause the flow +to be there. You know how smoke will + + align:start position:0% +to be there. You know how smoke will + + + align:start position:0% +to be there. You know how smoke will +flow from the regions where there's more + + align:start position:0% +flow from the regions where there's more + + + align:start position:0% +flow from the regions where there's more +smoke to the regions where there's less + + align:start position:0% +smoke to the regions where there's less + + + align:start position:0% +smoke to the regions where there's less +smoke. And that's actually physics, but + + align:start position:0% +smoke. And that's actually physics, but + + + align:start position:0% +smoke. And that's actually physics, but +in a way it's also common sense. + + align:start position:0% + + + + align:start position:0% + +So physics and common sense. + + align:start position:0% + + + + align:start position:0% + +tell us that the smoke will flow + + align:start position:0% + + + + align:start position:0% + +from high concentration + + align:start position:0% + + + + align:start position:0% + +towards + + align:start position:0% +towards + + + align:start position:0% +towards +low concentration + + align:start position:0% +low concentration + + + align:start position:0% +low concentration +regions. + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% +Okay. So + + + align:start position:0% +Okay. So +if we think of this function U that + + align:start position:0% +if we think of this function U that + + + align:start position:0% +if we think of this function U that +measures concentration, that means we + + align:start position:0% +measures concentration, that means we + + + align:start position:0% +measures concentration, that means we +are always going to go in the direction + + align:start position:0% +are always going to go in the direction + + + align:start position:0% +are always going to go in the direction +where the concentration decreases the + + align:start position:0% +where the concentration decreases the + + + align:start position:0% +where the concentration decreases the +fastest. Well, what's that? That's + + align:start position:0% +fastest. Well, what's that? That's + + + align:start position:0% +fastest. Well, what's that? That's +negative gradient. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +f is directed + + align:start position:0% +f is directed + + + align:start position:0% +f is directed +along + + align:start position:0% +along + + + align:start position:0% +along +minus gradient u. + + align:start position:0% +minus gradient u. + + + align:start position:0% +minus gradient u. +Now how big is f going to be? Well there + + align:start position:0% +Now how big is f going to be? Well there + + + align:start position:0% +Now how big is f going to be? Well there +you have to come up with some intuition + + align:start position:0% +you have to come up with some intuition + + + align:start position:0% +you have to come up with some intuition +for how + + align:start position:0% +for how + + + align:start position:0% +for how +you know the two are related and the + + align:start position:0% +you know the two are related and the + + + align:start position:0% +you know the two are related and the +easiest relation you can think of is + + align:start position:0% +easiest relation you can think of is + + + align:start position:0% +easiest relation you can think of is +that they might be just proportional. So + + align:start position:0% +that they might be just proportional. So + + + align:start position:0% +that they might be just proportional. So +you know the steeper the differences in + + align:start position:0% +you know the steeper the differences in + + + align:start position:0% +you know the steeper the differences in +concentration the faster the flow will + + align:start position:0% +concentration the faster the flow will + + + align:start position:0% +concentration the faster the flow will +be or the more there will be flow and if + + align:start position:0% +be or the more there will be flow and if + + + align:start position:0% +be or the more there will be flow and if +you try to think about it as you know + + align:start position:0% +you try to think about it as you know + + + align:start position:0% +you try to think about it as you know +molecules moving in random directions + + align:start position:0% +molecules moving in random directions + + + align:start position:0% +molecules moving in random directions +you will see it makes actually complete + + align:start position:0% +you will see it makes actually complete + + + align:start position:0% +you will see it makes actually complete +sense but anyway it's kind of it should + + align:start position:0% +sense but anyway it's kind of it should + + + align:start position:0% +sense but anyway it's kind of it should +be part of your physics class not part + + align:start position:0% +be part of your physics class not part + + + align:start position:0% +be part of your physics class not part +of what I'm telling you. So I'm just + + align:start position:0% +of what I'm telling you. So I'm just + + + align:start position:0% +of what I'm telling you. So I'm just +going to accept + + align:start position:0% + + + + align:start position:0% + +that the flow + + align:start position:0% +that the flow + + + align:start position:0% +that the flow +is just proportional + + align:start position:0% +is just proportional + + + align:start position:0% +is just proportional +to the gradient of you. So if you want + + align:start position:0% +to the gradient of you. So if you want + + + align:start position:0% +to the gradient of you. So if you want +if the differences between + + align:start position:0% +if the differences between + + + align:start position:0% +if the differences between +concentrations at different points are + + align:start position:0% +concentrations at different points are + + + align:start position:0% +concentrations at different points are +very small then the flow will be very + + align:start position:0% +very small then the flow will be very + + + align:start position:0% +very small then the flow will be very +gentle and if on the other hand you have + + align:start position:0% +gentle and if on the other hand you have + + + align:start position:0% +gentle and if on the other hand you have +huge disparities then things will try to + + align:start position:0% +huge disparities then things will try to + + + align:start position:0% +huge disparities then things will try to +even out faster. + + align:start position:0% + + + + align:start position:0% + +Okay, so that's the first part. + + align:start position:0% +Okay, so that's the first part. + + + align:start position:0% +Okay, so that's the first part. +Now we need to understand the second + + align:start position:0% +Now we need to understand the second + + + align:start position:0% +Now we need to understand the second +part which is once we know how the flow + + align:start position:0% +part which is once we know how the flow + + + align:start position:0% +part which is once we know how the flow +is going how does that affect the + + align:start position:0% +is going how does that affect the + + + align:start position:0% +is going how does that affect the +concentration you know if smoke is going + + align:start position:0% +concentration you know if smoke is going + + + align:start position:0% +concentration you know if smoke is going +that way then it means the concentration + + align:start position:0% +that way then it means the concentration + + + align:start position:0% +that way then it means the concentration +here should be decreasing and there it + + align:start position:0% +here should be decreasing and there it + + + align:start position:0% +here should be decreasing and there it +should be increasing so that's the + + align:start position:0% +should be increasing so that's the + + + align:start position:0% +should be increasing so that's the +relation between f and partial u partial + + align:start position:0% +relation between f and partial u partial + + + align:start position:0% +relation between f and partial u partial +t + + align:start position:0% + + + + align:start position:0% + +and that part is actually math namely + + align:start position:0% +and that part is actually math namely + + + align:start position:0% +and that part is actually math namely +the divergence field. + + align:start position:0% + + + + align:start position:0% + +So let's try to understand that part + + align:start position:0% +So let's try to understand that part + + + align:start position:0% +So let's try to understand that part +more carefully. + + align:start position:0% + + + + align:start position:0% + +So let's take a small piece of you know + + align:start position:0% +So let's take a small piece of you know + + + align:start position:0% +So let's take a small piece of you know +a small region in space D bounded by a + + align:start position:0% +a small region in space D bounded by a + + + align:start position:0% +a small region in space D bounded by a +surface S. + + align:start position:0% +surface S. + + + align:start position:0% +surface S. +Okay. So I want to figure out what's + + align:start position:0% +Okay. So I want to figure out what's + + + align:start position:0% +Okay. So I want to figure out what's +going on in here. + + align:start position:0% +going on in here. + + + align:start position:0% +going on in here. +So let's look at the flux + + align:start position:0% +So let's look at the flux + + + align:start position:0% +So let's look at the flux +out of the + + align:start position:0% +out of the + + + align:start position:0% +out of the +OS. + + align:start position:0% + + + + align:start position:0% + +Well, we said + + align:start position:0% +Well, we said + + + align:start position:0% +Well, we said +that this flux would be given + + align:start position:0% +that this flux would be given + + + align:start position:0% +that this flux would be given +by double integral on s of fds. + + align:start position:0% +by double integral on s of fds. + + + align:start position:0% +by double integral on s of fds. +So this flux measures how much smoke is + + align:start position:0% +So this flux measures how much smoke is + + + align:start position:0% +So this flux measures how much smoke is +passing through S + + align:start position:0% +passing through S + + + align:start position:0% +passing through S +per unit time. + + align:start position:0% + + + + align:start position:0% + +That's the amount of smoke + + align:start position:0% + + + + align:start position:0% + +through S + + align:start position:0% +through S + + + align:start position:0% +through S +per unit time. + + align:start position:0% +per unit time. + + + align:start position:0% +per unit time. +But now + + align:start position:0% +But now + + + align:start position:0% +But now +how can I think of that? How can I + + align:start position:0% +how can I think of that? How can I + + + align:start position:0% +how can I think of that? How can I +compute that differently? Well, I can + + align:start position:0% +compute that differently? Well, I can + + + align:start position:0% +compute that differently? Well, I can +compute it just by looking at the total + + align:start position:0% +compute it just by looking at the total + + + align:start position:0% +compute it just by looking at the total +amount of smoke in this region and + + align:start position:0% +amount of smoke in this region and + + + align:start position:0% +amount of smoke in this region and +saying how much it changes. No, if I'm + + align:start position:0% +saying how much it changes. No, if I'm + + + align:start position:0% +saying how much it changes. No, if I'm +gaining or losing smoke, it means it's + + align:start position:0% +gaining or losing smoke, it means it's + + + align:start position:0% +gaining or losing smoke, it means it's +must be going out there. Well, unless I + + align:start position:0% +must be going out there. Well, unless I + + + align:start position:0% +must be going out there. Well, unless I +have a smoker in here, but that's not + + align:start position:0% +have a smoker in here, but that's not + + + align:start position:0% +have a smoker in here, but that's not +part of the data. + + align:start position:0% +part of the data. + + + align:start position:0% +part of the data. +So + + align:start position:0% +So + + + align:start position:0% +So +that should be sorry + + align:start position:0% +that should be sorry + + + align:start position:0% +that should be sorry +that's the same thing as the derivative + + align:start position:0% +that's the same thing as the derivative + + + align:start position:0% +that's the same thing as the derivative +with respect to t of the total amount of + + align:start position:0% +with respect to t of the total amount of + + + align:start position:0% +with respect to t of the total amount of +smoke in the region which is given by + + align:start position:0% +smoke in the region which is given by + + + align:start position:0% +smoke in the region which is given by +the triple integral of u. If I integrate + + align:start position:0% +the triple integral of u. If I integrate + + + align:start position:0% +the triple integral of u. If I integrate +the concentration of smoke which means + + align:start position:0% +the concentration of smoke which means + + + align:start position:0% +the concentration of smoke which means +the amount of smoke per unit volume over + + align:start position:0% +the amount of smoke per unit volume over + + + align:start position:0% +the amount of smoke per unit volume over +D I will get the total amount of smoke + + align:start position:0% +D I will get the total amount of smoke + + + align:start position:0% +D I will get the total amount of smoke +in D + + align:start position:0% +in D + + + align:start position:0% +in D +except well let's see this flux is + + align:start position:0% +except well let's see this flux is + + + align:start position:0% +except well let's see this flux is +counted positively if we go out of D so + + align:start position:0% +counted positively if we go out of D so + + + align:start position:0% +counted positively if we go out of D so +actually it's minus the derivative this + + align:start position:0% +actually it's minus the derivative this + + + align:start position:0% +actually it's minus the derivative this +is the amount of smoke that we are + + align:start position:0% +is the amount of smoke that we are + + + align:start position:0% +is the amount of smoke that we are +losing per unit time + + align:start position:0% +losing per unit time + + + align:start position:0% +losing per unit time +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +now we + + align:start position:0% +now we + + + align:start position:0% +now we +Almost there. + + align:start position:0% + + + + align:start position:0% + +Well, let me actually + + align:start position:0% + + + + align:start position:0% + +because + + align:start position:0% +because + + + align:start position:0% +because +we know yet another way to compute this + + align:start position:0% +we know yet another way to compute this + + + align:start position:0% +we know yet another way to compute this +guy using the divergence theorem. Right? + + align:start position:0% +guy using the divergence theorem. Right? + + + align:start position:0% +guy using the divergence theorem. Right? +So this part here is just like common + + align:start position:0% +So this part here is just like common + + + align:start position:0% +So this part here is just like common +sense and thinking about what it means. + + align:start position:0% +sense and thinking about what it means. + + + align:start position:0% +sense and thinking about what it means. +The divergence theorem tells me this is + + align:start position:0% +The divergence theorem tells me this is + + + align:start position:0% +The divergence theorem tells me this is +also equal to the triple integral d of + + align:start position:0% +also equal to the triple integral d of + + + align:start position:0% +also equal to the triple integral d of +div f dv. + + align:start position:0% + + + + align:start position:0% + +So what I got + + align:start position:0% +So what I got + + + align:start position:0% +So what I got +is that the triple integral over d of + + align:start position:0% +is that the triple integral over d of + + + align:start position:0% +is that the triple integral over d of +div f + + align:start position:0% +div f + + + align:start position:0% +div f +dv equals this derivative. Well let's + + align:start position:0% +dv equals this derivative. Well let's + + + align:start position:0% +dv equals this derivative. Well let's +think a bit about this derivative. So + + align:start position:0% +think a bit about this derivative. So + + + align:start position:0% +think a bit about this derivative. So +see you're integrating a function over x + + align:start position:0% +see you're integrating a function over x + + + align:start position:0% +see you're integrating a function over x +y and z and then you're differentiating + + align:start position:0% +y and z and then you're differentiating + + + align:start position:0% +y and z and then you're differentiating +with respect to t. I claim that you can + + align:start position:0% +with respect to t. I claim that you can + + + align:start position:0% +with respect to t. I claim that you can +actually switch the order in which you + + align:start position:0% +actually switch the order in which you + + + align:start position:0% +actually switch the order in which you +do things. + + align:start position:0% +do things. + + + align:start position:0% +do things. +So one way to think about it is you know + + align:start position:0% +So one way to think about it is you know + + + align:start position:0% +So one way to think about it is you know +here you're taking the total amount of + + align:start position:0% +here you're taking the total amount of + + + align:start position:0% +here you're taking the total amount of +smoke and then seeing how that changes + + align:start position:0% +smoke and then seeing how that changes + + + align:start position:0% +smoke and then seeing how that changes +over time. So you're taking the + + align:start position:0% +over time. So you're taking the + + + align:start position:0% +over time. So you're taking the +derivative of the sum of all the small + + align:start position:0% +derivative of the sum of all the small + + + align:start position:0% +derivative of the sum of all the small +amounts of smoke everywhere. Well, that + + align:start position:0% +amounts of smoke everywhere. Well, that + + + align:start position:0% +amounts of smoke everywhere. Well, that +would be the sum of the derivatives of + + align:start position:0% +would be the sum of the derivatives of + + + align:start position:0% +would be the sum of the derivatives of +the amount of smoke into each little box + + align:start position:0% +the amount of smoke into each little box + + + align:start position:0% +the amount of smoke into each little box +inside each little box. + + align:start position:0% +inside each little box. + + + align:start position:0% +inside each little box. +So we can actually move the der the + + align:start position:0% +So we can actually move the der the + + + align:start position:0% +So we can actually move the der the +differential sorry the derivative into + + align:start position:0% +differential sorry the derivative into + + + align:start position:0% +differential sorry the derivative into +the integral. + + align:start position:0% +the integral. + + + align:start position:0% +the integral. +So let's see I said minus ddt triple + + align:start position:0% +So let's see I said minus ddt triple + + + align:start position:0% +So let's see I said minus ddt triple +integral over d + + align:start position:0% +integral over d + + + align:start position:0% +integral over d +u dv and now I'm saying this is the same + + align:start position:0% +u dv and now I'm saying this is the same + + + align:start position:0% +u dv and now I'm saying this is the same +as + + align:start position:0% +as + + + align:start position:0% +as +the triple integral in d of dudt + + align:start position:0% +the triple integral in d of dudt + + + align:start position:0% +the triple integral in d of dudt +dv. And the reason why this is going to + + align:start position:0% +dv. And the reason why this is going to + + + align:start position:0% +dv. And the reason why this is going to +work is you should think of it as ddt of + + align:start position:0% +work is you should think of it as ddt of + + + align:start position:0% +work is you should think of it as ddt of +a sum of u of you know some values. You + + align:start position:0% +a sum of u of you know some values. You + + + align:start position:0% +a sum of u of you know some values. You +plug in the values of your points + + align:start position:0% +plug in the values of your points + + + align:start position:0% +plug in the values of your points +at that given time times the small + + align:start position:0% +at that given time times the small + + + align:start position:0% +at that given time times the small +volume. You sum them and then you take + + align:start position:0% +volume. You sum them and then you take + + + align:start position:0% +volume. You sum them and then you take +the derivative. And now you see the + + align:start position:0% +the derivative. And now you see the + + + align:start position:0% +the derivative. And now you see the +derivative of this sum is the sum of the + + align:start position:0% +derivative of this sum is the sum of the + + + align:start position:0% +derivative of this sum is the sum of the +derivatives. + + align:start position:0% + + + + align:start position:0% + +Oops. Y I Zit T. + + align:start position:0% + + + + align:start position:0% + +So if you think about what the integral + + align:start position:0% +So if you think about what the integral + + + align:start position:0% +So if you think about what the integral +measures, that's actually pretty easy. + + align:start position:0% +measures, that's actually pretty easy. + + + align:start position:0% +measures, that's actually pretty easy. +And it's because this variable here is + + align:start position:0% +And it's because this variable here is + + + align:start position:0% +And it's because this variable here is +not the same as the variables on which + + align:start position:0% +not the same as the variables on which + + + align:start position:0% +not the same as the variables on which +we're integrating. That's why we can do + + align:start position:0% +we're integrating. That's why we can do + + + align:start position:0% +we're integrating. That's why we can do +it. Okay. So now if we have this for any + + align:start position:0% +it. Okay. So now if we have this for any + + + align:start position:0% +it. Okay. So now if we have this for any +region D. + + align:start position:0% + + + + align:start position:0% + +So we have a function of XYZT + + align:start position:0% +So we have a function of XYZT + + + align:start position:0% +So we have a function of XYZT +and we have another function here and + + align:start position:0% +and we have another function here and + + + align:start position:0% +and we have another function here and +whenever we integrate them anywhere we + + align:start position:0% +whenever we integrate them anywhere we + + + align:start position:0% +whenever we integrate them anywhere we +get the same answer. Well that must mean + + align:start position:0% +get the same answer. Well that must mean + + + align:start position:0% +get the same answer. Well that must mean +they're the same. + + align:start position:0% +they're the same. + + + align:start position:0% +they're the same. +Right? Just think of what happens if you + + align:start position:0% +Right? Just think of what happens if you + + + align:start position:0% +Right? Just think of what happens if you +just take D to be a tiny little box. + + align:start position:0% +just take D to be a tiny little box. + + + align:start position:0% +just take D to be a tiny little box. +you'll get roughly the value of div f at + + align:start position:0% +you'll get roughly the value of div f at + + + align:start position:0% +you'll get roughly the value of div f at +that point times the volume of a box or + + align:start position:0% +that point times the volume of a box or + + + align:start position:0% +that point times the volume of a box or +you'll get roughly the value of dud at + + align:start position:0% +you'll get roughly the value of dud at + + + align:start position:0% +you'll get roughly the value of dud at +that point times the volume of a little + + align:start position:0% +that point times the volume of a little + + + align:start position:0% +that point times the volume of a little +box so the values must be the same well + + align:start position:0% +box so the values must be the same well + + + align:start position:0% +box so the values must be the same well +let me actually explain that a tiny bit + + align:start position:0% +let me actually explain that a tiny bit + + + align:start position:0% +let me actually explain that a tiny bit +better + + align:start position:0% +better + + + align:start position:0% +better +so what I get is that one of let me let + + align:start position:0% +so what I get is that one of let me let + + + align:start position:0% +so what I get is that one of let me let +me divide by the volume of d sorry I + + align:start position:0% +me divide by the volume of d sorry I + + + align:start position:0% +me divide by the volume of d sorry I +promise I'm done in a + + align:start position:0% + + + + align:start position:0% + +is the same thing as one / volume d of + + align:start position:0% + + + + align:start position:0% + +negative dudt + + align:start position:0% +negative dudt + + + align:start position:0% +negative dudt +dv. So that means the average value okay + + align:start position:0% +dv. So that means the average value okay + + + align:start position:0% +dv. So that means the average value okay +maybe that's the best way of explaining + + align:start position:0% +maybe that's the best way of explaining + + + align:start position:0% +maybe that's the best way of explaining +it the average + + align:start position:0% +it the average + + + align:start position:0% +it the average +of div f + + align:start position:0% +of div f + + + align:start position:0% +of div f +in d is equal to the average + + align:start position:0% +in d is equal to the average + + + align:start position:0% +in d is equal to the average +of minus partial u partial t in d and + + align:start position:0% +of minus partial u partial t in d and + + + align:start position:0% +of minus partial u partial t in d and +that's true for any region d not just + + align:start position:0% +that's true for any region d not just + + + align:start position:0% +that's true for any region d not just +for some regions but for really any + + align:start position:0% +for some regions but for really any + + + align:start position:0% +for some regions but for really any +region I can think of so the outcome is + + align:start position:0% +region I can think of so the outcome is + + + align:start position:0% +region I can think of so the outcome is +that actually + + align:start position:0% +that actually + + + align:start position:0% +that actually +the divergence of f is equal to minus + + align:start position:0% +the divergence of f is equal to minus + + + align:start position:0% +the divergence of f is equal to minus +dudt. + + align:start position:0% +dudt. + + + align:start position:0% +dudt. +And that's another way to think about + + align:start position:0% +And that's another way to think about + + + align:start position:0% +And that's another way to think about +what divergence means. The divergence we + + align:start position:0% +what divergence means. The divergence we + + + align:start position:0% +what divergence means. The divergence we +said is how much stuff is actually + + align:start position:0% +said is how much stuff is actually + + + align:start position:0% +said is how much stuff is actually +expanding flowing out. That's how much + + align:start position:0% +expanding flowing out. That's how much + + + align:start position:0% +expanding flowing out. That's how much +we are losing. + + align:start position:0% +we are losing. + + + align:start position:0% +we are losing. +And so now if you combine this with that + + align:start position:0% +And so now if you combine this with that + + + align:start position:0% +And so now if you combine this with that +you'll get that dud is minus divergence + + align:start position:0% +you'll get that dud is minus divergence + + + align:start position:0% +you'll get that dud is minus divergence +f which is plus k del square u. + + align:start position:0% +f which is plus k del square u. + + + align:start position:0% +f which is plus k del square u. +Okay. So you combine this guy with that + + align:start position:0% +Okay. So you combine this guy with that + + + align:start position:0% +Okay. So you combine this guy with that +guy and you get the the diffusion + + align:start position:0% +guy and you get the the diffusion + + + align:start position:0% +guy and you get the the diffusion +equation. \ No newline at end of file diff --git a/x_xXPFS1hkQ.txt b/x_xXPFS1hkQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..f0517cc3939f770c59271058da536dff8c15493e --- /dev/null +++ b/x_xXPFS1hkQ.txt @@ -0,0 +1,7738 @@ +align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +righty um what I'm actually going to do + + align:start position:0% +righty um what I'm actually going to do + + + align:start position:0% +righty um what I'm actually going to do +now is pass out um a description of the + + align:start position:0% +now is pass out um a description of the + + + align:start position:0% +now is pass out um a description of the +mock exam and exam one which uh takes + + align:start position:0% +mock exam and exam one which uh takes + + + align:start position:0% +mock exam and exam one which uh takes +place two two weeks from today um so the + + align:start position:0% +place two two weeks from today um so the + + + align:start position:0% +place two two weeks from today um so the +mock + + align:start position:0% +mock + + + align:start position:0% +mock +exam uh is going to get posted um I mean + + align:start position:0% +exam uh is going to get posted um I mean + + + align:start position:0% +exam uh is going to get posted um I mean +I'll post it to Canvas uh this weekend + + align:start position:0% +I'll post it to Canvas uh this weekend + + + align:start position:0% +I'll post it to Canvas uh this weekend +um you're not actually supposed to to + + align:start position:0% +um you're not actually supposed to to + + + align:start position:0% +um you're not actually supposed to to +attempt it however until um the + + align:start position:0% +attempt it however until um the + + + align:start position:0% +attempt it however until um the +following weekend um we'll discuss you + + align:start position:0% +following weekend um we'll discuss you + + + align:start position:0% +following weekend um we'll discuss you +should do it um weekend after next and + + align:start position:0% +should do it um weekend after next and + + + align:start position:0% +should do it um weekend after next and +we'll discuss the mock exams in class on + + align:start position:0% +we'll discuss the mock exams in class on + + + align:start position:0% +we'll discuss the mock exams in class on +Monday the 6th so two days before the um + + align:start position:0% +Monday the 6th so two days before the um + + + align:start position:0% +Monday the 6th so two days before the um +two days before the exam proper um so + + align:start position:0% +two days before the exam proper um so + + + align:start position:0% +two days before the exam proper um so +the mock exam will mimic the structure + + align:start position:0% +the mock exam will mimic the structure + + + align:start position:0% +the mock exam will mimic the structure +and timing of the first four sections of + + align:start position:0% +and timing of the first four sections of + + + align:start position:0% +and timing of the first four sections of +exam one um those sections are closed + + align:start position:0% +exam one um those sections are closed + + + align:start position:0% +exam one um those sections are closed +book um uh and when you'll turn those in + + align:start position:0% +book um uh and when you'll turn those in + + + align:start position:0% +book um uh and when you'll turn those in +before proceeding to the final section + + align:start position:0% +before proceeding to the final section + + + align:start position:0% +before proceeding to the final section +of the exam proper which is open book um + + align:start position:0% +of the exam proper which is open book um + + + align:start position:0% +of the exam proper which is open book um +and for which you will need a hard copy + + align:start position:0% +and for which you will need a hard copy + + + align:start position:0% +and for which you will need a hard copy +of Baker as I've said um from the very + + align:start position:0% +of Baker as I've said um from the very + + + align:start position:0% +of Baker as I've said um from the very +beginning of class so if you don't have + + align:start position:0% +beginning of class so if you don't have + + + align:start position:0% +beginning of class so if you don't have +one get one Pronto because two weeks + + align:start position:0% +one get one Pronto because two weeks + + + align:start position:0% +one get one Pronto because two weeks +from today you will have to use + + align:start position:0% +from today you will have to use + + + align:start position:0% +from today you will have to use +it section one 68 points should take you + + align:start position:0% +it section one 68 points should take you + + + align:start position:0% +it section one 68 points should take you +less than 5 minutes you reproduce tables + + align:start position:0% +less than 5 minutes you reproduce tables + + + align:start position:0% +less than 5 minutes you reproduce tables +5.3 5.4 6.1 and + + align:start position:0% +5.3 5.4 6.1 and + + + align:start position:0% +5.3 5.4 6.1 and +7.2 um I've been announcing that + + align:start position:0% +7.2 um I've been announcing that + + + align:start position:0% +7.2 um I've been announcing that +regularly from the beginning so those + + align:start position:0% +regularly from the beginning so those + + + align:start position:0% +regularly from the beginning so those +should be um already quite well drilled + + align:start position:0% +should be um already quite well drilled + + + align:start position:0% +should be um already quite well drilled +um you are also responsible for being + + align:start position:0% +um you are also responsible for being + + + align:start position:0% +um you are also responsible for being +able to recognize adjective endings and + + align:start position:0% +able to recognize adjective endings and + + + align:start position:0% +able to recognize adjective endings and +weak noun endings but you don't need to + + align:start position:0% +weak noun endings but you don't need to + + + align:start position:0% +weak noun endings but you don't need to +reproduce them in tabular form um you + + align:start position:0% +reproduce them in tabular form um you + + + align:start position:0% +reproduce them in tabular form um you +also need to be able to recognize + + align:start position:0% +also need to be able to recognize + + + align:start position:0% +also need to be able to recognize +conjugated forms of kunan Magan motan + + align:start position:0% +conjugated forms of kunan Magan motan + + + align:start position:0% +conjugated forms of kunan Magan motan +shulan wton Gan and willan um I + + align:start position:0% +shulan wton Gan and willan um I + + + align:start position:0% +shulan wton Gan and willan um I +mentioned most of those in class last + + align:start position:0% +mentioned most of those in class last + + + align:start position:0% +mentioned most of those in class last +time we're going to talk a little bit + + align:start position:0% +time we're going to talk a little bit + + + align:start position:0% +time we're going to talk a little bit +about gone and willan and actually we'll + + align:start position:0% +about gone and willan and actually we'll + + + align:start position:0% +about gone and willan and actually we'll +talk about all of them today um section + + align:start position:0% +talk about all of them today um section + + + align:start position:0% +talk about all of them today um section +two is basically a souped up version of + + align:start position:0% +two is basically a souped up version of + + + align:start position:0% +two is basically a souped up version of +The Daily vocab quiz um 40 points 40 + + align:start position:0% +The Daily vocab quiz um 40 points 40 + + + align:start position:0% +The Daily vocab quiz um 40 points 40 +words um from groups uh oops did I say + + align:start position:0% +words um from groups uh oops did I say + + + align:start position:0% +words um from groups uh oops did I say +one through 50 I think that should be + + align:start position:0% +one through 50 I think that should be + + + align:start position:0% +one through 50 I think that should be +yeah 1 through 60 my apologies I'll + + align:start position:0% +yeah 1 through 60 my apologies I'll + + + align:start position:0% +yeah 1 through 60 my apologies I'll +correct that before I post this um it's + + align:start position:0% +correct that before I post this um it's + + + align:start position:0% +correct that before I post this um it's +it's through uh it's through what you've + + align:start position:0% +it's through uh it's through what you've + + + align:start position:0% +it's through uh it's through what you've +you know what you will have done by by + + align:start position:0% +you know what you will have done by by + + + align:start position:0% +you know what you will have done by by +that + + align:start position:0% +that + + + align:start position:0% +that +point section three and the reason that + + align:start position:0% +point section three and the reason that + + + align:start position:0% +point section three and the reason that +I'm passing this out now um is to be + + align:start position:0% +I'm passing this out now um is to be + + + align:start position:0% +I'm passing this out now um is to be +able to reproduce some important grammar + + align:start position:0% +able to reproduce some important grammar + + + align:start position:0% +able to reproduce some important grammar +rules nearly all of which I either have + + align:start position:0% +rules nearly all of which I either have + + + align:start position:0% +rules nearly all of which I either have +already or will have by then um + + align:start position:0% +already or will have by then um + + + align:start position:0% +already or will have by then um +emphasized in class and if you turn to + + align:start position:0% +emphasized in class and if you turn to + + + align:start position:0% +emphasized in class and if you turn to +Pages two and three of this handout this + + align:start position:0% +Pages two and three of this handout this + + + align:start position:0% +Pages two and three of this handout this +is section three of the exam with all of + + align:start position:0% +is section three of the exam with all of + + + align:start position:0% +is section three of the exam with all of +the answers filled in um I have as I've + + align:start position:0% +the answers filled in um I have as I've + + + align:start position:0% +the answers filled in um I have as I've +said previous ly I would love for + + align:start position:0% +said previous ly I would love for + + + align:start position:0% +said previous ly I would love for +everybody to earn an a in in this class + + align:start position:0% +everybody to earn an a in in this class + + + align:start position:0% +everybody to earn an a in in this class +this is one way um of uh you know + + align:start position:0% +this is one way um of uh you know + + + align:start position:0% +this is one way um of uh you know +helping you do so um because I don't I + + align:start position:0% +helping you do so um because I don't I + + + align:start position:0% +helping you do so um because I don't I +don't see any point in playing hide the + + align:start position:0% +don't see any point in playing hide the + + + align:start position:0% +don't see any point in playing hide the +ball right this is what I think is + + align:start position:0% +ball right this is what I think is + + + align:start position:0% +ball right this is what I think is +important this is what you have to know + + align:start position:0% +important this is what you have to know + + + align:start position:0% +important this is what you have to know +um and we'll be referring to it um as we + + align:start position:0% +um and we'll be referring to it um as we + + + align:start position:0% +um and we'll be referring to it um as we +go through class today part of the + + align:start position:0% +go through class today part of the + + + align:start position:0% +go through class today part of the +reason that over a 100 points are um + + align:start position:0% +reason that over a 100 points are um + + + align:start position:0% +reason that over a 100 points are um +pretty straight forward to get that is + + align:start position:0% +pretty straight forward to get that is + + + align:start position:0% +pretty straight forward to get that is +all of sections one the Paradigm + + align:start position:0% +all of sections one the Paradigm + + + align:start position:0% +all of sections one the Paradigm +memorization and all of section three + + align:start position:0% +memorization and all of section three + + + align:start position:0% +memorization and all of section three +where the answers are literally on the + + align:start position:0% +where the answers are literally on the + + + align:start position:0% +where the answers are literally on the +sheet in front of you um although you + + align:start position:0% +sheet in front of you um although you + + + align:start position:0% +sheet in front of you um although you +can't bring the sheet you know with you + + align:start position:0% +can't bring the sheet you know with you + + + align:start position:0% +can't bring the sheet you know with you +to the exam you do have to actually have + + align:start position:0% +to the exam you do have to actually have + + + align:start position:0% +to the exam you do have to actually have +it in your head for those 80 minutes at + + align:start position:0% +it in your head for those 80 minutes at + + + align:start position:0% +it in your head for those 80 minutes at +least um one of the reasons that those + + align:start position:0% +least um one of the reasons that those + + + align:start position:0% +least um one of the reasons that those +parts of the exams are um relatively + + align:start position:0% +parts of the exams are um relatively + + + align:start position:0% +parts of the exams are um relatively +easy is that sections four and five are + + align:start position:0% +easy is that sections four and five are + + + align:start position:0% +easy is that sections four and five are +hard um you're doing you're going to be + + align:start position:0% +hard um you're doing you're going to be + + + align:start position:0% +hard um you're doing you're going to be +doing site translation um of five Old + + align:start position:0% +doing site translation um of five Old + + + align:start position:0% +doing site translation um of five Old +English sentences um using words from + + align:start position:0% +English sentences um using words from + + + align:start position:0% +English sentences um using words from +word horde as well as any other words I + + align:start position:0% +word horde as well as any other words I + + + align:start position:0% +word horde as well as any other words I +have said in class you will need to be + + align:start position:0% +have said in class you will need to be + + + align:start position:0% +have said in class you will need to be +able to recognize such as um the verbs + + align:start position:0% +able to recognize such as um the verbs + + + align:start position:0% +able to recognize such as um the verbs +uh I think it's only the verbs I'll + + align:start position:0% +uh I think it's only the verbs I'll + + + align:start position:0% +uh I think it's only the verbs I'll +double check I'll I'll go back to the + + align:start position:0% +double check I'll I'll go back to the + + + align:start position:0% +double check I'll I'll go back to the +exam and make sure this is true but I + + align:start position:0% +exam and make sure this is true but I + + + align:start position:0% +exam and make sure this is true but I +believe it's only those verbs listed in + + align:start position:0% +believe it's only those verbs listed in + + + align:start position:0% +believe it's only those verbs listed in +um in uh above kunan Magan Mutan shulan + + align:start position:0% +um in uh above kunan Magan Mutan shulan + + + align:start position:0% +um in uh above kunan Magan Mutan shulan +Wan Gan and + + align:start position:0% +Wan Gan and + + + align:start position:0% +Wan Gan and +willan um the these sentences are + + align:start position:0% +willan um the these sentences are + + + align:start position:0% +willan um the these sentences are +designed to be hard um I don't expect + + align:start position:0% +designed to be hard um I don't expect + + + align:start position:0% +designed to be hard um I don't expect +anyone to get 50 out of 50 points on on + + align:start position:0% +anyone to get 50 out of 50 points on on + + + align:start position:0% +anyone to get 50 out of 50 points on on +them although people have surprised me + + align:start position:0% +them although people have surprised me + + + align:start position:0% +them although people have surprised me +in the past and done so um so uh but but + + align:start position:0% +in the past and done so um so uh but but + + + align:start position:0% +in the past and done so um so uh but but +I give partial credit quite liberally um + + align:start position:0% +I give partial credit quite liberally um + + + align:start position:0% +I give partial credit quite liberally um +so make sure to tell me what you know + + align:start position:0% +so make sure to tell me what you know + + + align:start position:0% +so make sure to tell me what you know +show me what you know um rather than um + + align:start position:0% +show me what you know um rather than um + + + align:start position:0% +show me what you know um rather than um +just give up or get stumped because you + + align:start position:0% +just give up or get stumped because you + + + align:start position:0% +just give up or get stumped because you +know you can you can have a translation + + align:start position:0% +know you can you can have a translation + + + align:start position:0% +know you can you can have a translation +that's really quite wrong in a lot of + + align:start position:0% +that's really quite wrong in a lot of + + + align:start position:0% +that's really quite wrong in a lot of +ways and still get you know six out of + + align:start position:0% +ways and still get you know six out of + + + align:start position:0% +ways and still get you know six out of +10 points um on a given sentence all + + align:start position:0% +10 points um on a given sentence all + + + align:start position:0% +10 points um on a given sentence all +right um and when I say tell me what you + + align:start position:0% +right um and when I say tell me what you + + + align:start position:0% +right um and when I say tell me what you +know I mean like this looks like + + align:start position:0% +know I mean like this looks like + + + align:start position:0% +know I mean like this looks like +genitive plural even though I don't know + + align:start position:0% +genitive plural even though I don't know + + + align:start position:0% +genitive plural even though I don't know +what the word means or like we heard + + align:start position:0% +what the word means or like we heard + + + align:start position:0% +what the word means or like we heard +Kenneth say um in class when he was + + align:start position:0% +Kenneth say um in class when he was + + + align:start position:0% +Kenneth say um in class when he was +translating um uh site translating so + + align:start position:0% +translating um uh site translating so + + + align:start position:0% +translating um uh site translating so +this is totally fine but like you know + + align:start position:0% +this is totally fine but like you know + + + align:start position:0% +this is totally fine but like you know +we what it was pridon that that you know + + align:start position:0% +we what it was pridon that that you know + + + align:start position:0% +we what it was pridon that that you know +that was a word so right like if you + + align:start position:0% +that was a word so right like if you + + + align:start position:0% +that was a word so right like if you +don't know what prion means fine just um + + align:start position:0% +don't know what prion means fine just um + + + align:start position:0% +don't know what prion means fine just um +but you know it's a verb you know it's + + align:start position:0% +but you know it's a verb you know it's + + + align:start position:0% +but you know it's a verb you know it's +plural you know it's past Etc um you'll + + align:start position:0% +plural you know it's past Etc um you'll + + + align:start position:0% +plural you know it's past Etc um you'll +turn all that in when you're done and + + align:start position:0% +turn all that in when you're done and + + + align:start position:0% +turn all that in when you're done and +then you'll get to turn to um assisted + + align:start position:0% +then you'll get to turn to um assisted + + + align:start position:0% +then you'll get to turn to um assisted +translation of a short portion of a text + + align:start position:0% +translation of a short portion of a text + + + align:start position:0% +translation of a short portion of a text +from Baker um and for this section of + + align:start position:0% +from Baker um and for this section of + + + align:start position:0% +from Baker um and for this section of +the J of the exam you may use the + + align:start position:0% +the J of the exam you may use the + + + align:start position:0% +the J of the exam you may use the +glossery indeed you must use the + + align:start position:0% +glossery indeed you must use the + + + align:start position:0% +glossery indeed you must use the +glossery um in the back of the book um + + align:start position:0% +glossery um in the back of the book um + + + align:start position:0% +glossery um in the back of the book um +as well as your magic sheet of forms if + + align:start position:0% +as well as your magic sheet of forms if + + + align:start position:0% +as well as your magic sheet of forms if +you bring it um to the + + align:start position:0% +you bring it um to the + + + align:start position:0% +you bring it um to the +exam under that I say by Design This is + + align:start position:0% +exam under that I say by Design This is + + + align:start position:0% +exam under that I say by Design This is +tightly timed um I've emphasized from + + align:start position:0% +tightly timed um I've emphasized from + + + align:start position:0% +tightly timed um I've emphasized from +day one the importance of learning your + + align:start position:0% +day one the importance of learning your + + + align:start position:0% +day one the importance of learning your +paradigms so you don't have to go + + align:start position:0% +paradigms so you don't have to go + + + align:start position:0% +paradigms so you don't have to go +running back to your magic sheet every + + align:start position:0% +running back to your magic sheet every + + + align:start position:0% +running back to your magic sheet every +time um you see a word um of course you + + align:start position:0% +time um you see a word um of course you + + + align:start position:0% +time um you see a word um of course you +will already be tested on the paradigms + + align:start position:0% +will already be tested on the paradigms + + + align:start position:0% +will already be tested on the paradigms +in section one of the exam but you'll be + + align:start position:0% +in section one of the exam but you'll be + + + align:start position:0% +in section one of the exam but you'll be +sort of implicitly tested on them as + + align:start position:0% +sort of implicitly tested on them as + + + align:start position:0% +sort of implicitly tested on them as +well by how quickly you can um how + + align:start position:0% +well by how quickly you can um how + + + align:start position:0% +well by how quickly you can um how +quickly you can complete uh section + + align:start position:0% +quickly you can complete uh section + + + align:start position:0% +quickly you can complete uh section +four so when the um so when the mock + + align:start position:0% +four so when the um so when the mock + + + align:start position:0% +four so when the um so when the mock +exam is posted and you do it there is no + + align:start position:0% +exam is posted and you do it there is no + + + align:start position:0% +exam is posted and you do it there is no +section five I'm not giving you a a a uh + + align:start position:0% +section five I'm not giving you a a a uh + + + align:start position:0% +section five I'm not giving you a a a uh +an assisted translation you're already + + align:start position:0% +an assisted translation you're already + + + align:start position:0% +an assisted translation you're already +going to be doing assisted translation + + align:start position:0% +going to be doing assisted translation + + + align:start position:0% +going to be doing assisted translation +um when we start translating alf's + + align:start position:0% +um when we start translating alf's + + + align:start position:0% +um when we start translating alf's +preface to Genesis next week um but I + + align:start position:0% +preface to Genesis next week um but I + + + align:start position:0% +preface to Genesis next week um but I +would I would give yourself I would time + + align:start position:0% +would I would give yourself I would time + + + align:start position:0% +would I would give yourself I would time +yourself for sections 1 through 4 to + + align:start position:0% +yourself for sections 1 through 4 to + + + align:start position:0% +yourself for sections 1 through 4 to +make sure that you're kind of getting + + align:start position:0% +make sure that you're kind of getting + + + align:start position:0% +make sure that you're kind of getting +that you're that you're getting through + + align:start position:0% +that you're that you're getting through + + + align:start position:0% +that you're that you're getting through +it um along roughly the the the time + + align:start position:0% +it um along roughly the the the time + + + align:start position:0% +it um along roughly the the the time +frame um laid out here um and + + align:start position:0% +frame um laid out here um and + + + align:start position:0% +frame um laid out here um and +and as I've said again before you may + + align:start position:0% +and as I've said again before you may + + + align:start position:0% +and as I've said again before you may +not share any materials during the exam + + align:start position:0% +not share any materials during the exam + + + align:start position:0% +not share any materials during the exam +everyone must have their own copy of + + align:start position:0% +everyone must have their own copy of + + + align:start position:0% +everyone must have their own copy of +Baker and the magic sheet if you wish + + align:start position:0% +Baker and the magic sheet if you wish + + + align:start position:0% +Baker and the magic sheet if you wish +for use in section five um fair warning + + align:start position:0% +for use in section five um fair warning + + + align:start position:0% +for use in section five um fair warning +any questions on all + + align:start position:0% + + + + align:start position:0% + +that Al righty let's turn to chapter 7 + + align:start position:0% +that Al righty let's turn to chapter 7 + + + align:start position:0% +that Al righty let's turn to chapter 7 +section five of Baker + + align:start position:0% +section five of Baker + + + align:start position:0% +section five of Baker +and um very + + align:start position:0% +and um very + + + align:start position:0% +and um very +quickly + + align:start position:0% + + + + align:start position:0% + +mention the bottom of page 79 um a few + + align:start position:0% +mention the bottom of page 79 um a few + + + align:start position:0% +mention the bottom of page 79 um a few +verbs as Baker says have uh weak present + + align:start position:0% +verbs as Baker says have uh weak present + + + align:start position:0% +verbs as Baker says have uh weak present +tenses and strong past tenses um so some + + align:start position:0% +tenses and strong past tenses um so some + + + align:start position:0% +tenses and strong past tenses um so some +common verbs behave in this way like + + align:start position:0% +common verbs behave in this way like + + + align:start position:0% +common verbs behave in this way like +bidon um which we saw last time had the + + align:start position:0% +bidon um which we saw last time had the + + + align:start position:0% +bidon um which we saw last time had the +past had the predate form uh bad um like + + align:start position:0% +past had the predate form uh bad um like + + + align:start position:0% +past had the predate form uh bad um like +bade in Modern English siton which of + + align:start position:0% +bade in Modern English siton which of + + + align:start position:0% +bade in Modern English siton which of +course becomes sat in both um Old + + align:start position:0% +course becomes sat in both um Old + + + align:start position:0% +course becomes sat in both um Old +English and Modern English remember the + + align:start position:0% +English and Modern English remember the + + + align:start position:0% +English and Modern English remember the +old fiend s ala Fon sat over th Stana um + + align:start position:0% +old fiend s ala Fon sat over th Stana um + + + align:start position:0% +old fiend s ala Fon sat over th Stana um +in the miracle of St Benedict and ship + + align:start position:0% +in the miracle of St Benedict and ship + + + align:start position:0% +in the miracle of St Benedict and ship +on um to uh make or create where we get + + align:start position:0% +on um to uh make or create where we get + + + align:start position:0% +on um to uh make or create where we get +uh Modern English shape of course um the + + align:start position:0% +uh Modern English shape of course um the + + + align:start position:0% +uh Modern English shape of course um the +Dual nature of these verbs is a + + align:start position:0% +Dual nature of these verbs is a + + + align:start position:0% +Dual nature of these verbs is a +curiosity um and therefore probably + + align:start position:0% +curiosity um and therefore probably + + + align:start position:0% +curiosity um and therefore probably +interested interesting to the + + align:start position:0% +interested interesting to the + + + align:start position:0% +interested interesting to the +Linguistics uh L minded among you um but + + align:start position:0% +Linguistics uh L minded among you um but + + + align:start position:0% +Linguistics uh L minded among you um but +not something we'll we'll go over uh in + + align:start position:0% +not something we'll we'll go over uh in + + + align:start position:0% +not something we'll we'll go over uh in +any detail Beyond this all right predate + + align:start position:0% +any detail Beyond this all right predate + + + align:start position:0% +any detail Beyond this all right predate +present verbs 7.6 on page 80 this is + + align:start position:0% +present verbs 7.6 on page 80 this is + + + align:start position:0% +present verbs 7.6 on page 80 this is +where it gets really very important um + + align:start position:0% +where it gets really very important um + + + align:start position:0% +where it gets really very important um +partly because you have to know these on + + align:start position:0% +partly because you have to know these on + + + align:start position:0% +partly because you have to know these on +the exam and the reason for that of + + align:start position:0% +the exam and the reason for that of + + + align:start position:0% +the exam and the reason for that of +course is that they are just all over + + align:start position:0% +course is that they are just all over + + + align:start position:0% +course is that they are just all over +the place in Old English um you should + + align:start position:0% +the place in Old English um you should + + + align:start position:0% +the place in Old English um you should +not have to uh you should not have to + + align:start position:0% +not have to uh you should not have to + + + align:start position:0% +not have to uh you should not have to +look them up I mean now of course you do + + align:start position:0% +look them up I mean now of course you do + + + align:start position:0% +look them up I mean now of course you do +but by that + + align:start position:0% +but by that + + + align:start position:0% +but by that +point um so predate present verbs what + + align:start position:0% +point um so predate present verbs what + + + align:start position:0% +point um so predate present verbs what +this really means um is uh simply that + + align:start position:0% +this really means um is uh simply that + + + align:start position:0% +this really means um is uh simply that +the present tense looks like the past + + align:start position:0% +the present tense looks like the past + + + align:start position:0% +the present tense looks like the past +tense um that is to say they are predate + + align:start position:0% +tense um that is to say they are predate + + + align:start position:0% +tense um that is to say they are predate +in form but present in meaning um Latin + + align:start position:0% +in form but present in meaning um Latin + + + align:start position:0% +in form but present in meaning um Latin +and Greek have some of these as well so + + align:start position:0% +and Greek have some of these as well so + + + align:start position:0% +and Greek have some of these as well so +oida um in Greek um noi in Latin um the + + align:start position:0% +oida um in Greek um noi in Latin um the + + + align:start position:0% +oida um in Greek um noi in Latin um the +the both words for I know um they + + align:start position:0% +the both words for I know um they + + + align:start position:0% +the both words for I know um they +actually have perfect um tense or sorry + + align:start position:0% +actually have perfect um tense or sorry + + + align:start position:0% +actually have perfect um tense or sorry +perfect forms um but present meanings + + align:start position:0% +perfect forms um but present meanings + + + align:start position:0% +perfect forms um but present meanings +and you see the same thing happens in um + + align:start position:0% +and you see the same thing happens in um + + + align:start position:0% +and you see the same thing happens in um +won to know um table + + align:start position:0% +won to know um table + + + align:start position:0% +won to know um table +7.11 um the right hand + + align:start position:0% +7.11 um the right hand + + + align:start position:0% +7.11 um the right hand +column won what um so the present + + align:start position:0% +column won what um so the present + + + align:start position:0% +column won what um so the present +indicative uh shift its vowel doesn't + + align:start position:0% +indicative uh shift its vowel doesn't + + + align:start position:0% +indicative uh shift its vowel doesn't +have an ending just like a strong verb + + align:start position:0% +have an ending just like a strong verb + + + align:start position:0% +have an ending just like a strong verb +um even though in that that strong verb + + align:start position:0% +um even though in that that strong verb + + + align:start position:0% +um even though in that that strong verb +or sorry that strong past form is + + align:start position:0% +or sorry that strong past form is + + + align:start position:0% +or sorry that strong past form is +actually present in meaning um the past + + align:start position:0% +actually present in meaning um the past + + + align:start position:0% +actually present in meaning um the past +tense of these predate present verbs um + + align:start position:0% +tense of these predate present verbs um + + + align:start position:0% +tense of these predate present verbs um +this is number two of 7.6 the past tense + + align:start position:0% +this is number two of 7.6 the past tense + + + align:start position:0% +this is number two of 7.6 the past tense +is usually built on the second past + + align:start position:0% +is usually built on the second past + + + align:start position:0% +is usually built on the second past +Route with D or t added um it's far + + align:start position:0% +Route with D or t added um it's far + + + align:start position:0% +Route with D or t added um it's far +preferable simply to just learn these + + align:start position:0% +preferable simply to just learn these + + + align:start position:0% +preferable simply to just learn these +particular uh forms rather than to try + + align:start position:0% +particular uh forms rather than to try + + + align:start position:0% +particular uh forms rather than to try +to learn the rules um that govern them + + align:start position:0% +to learn the rules um that govern them + + + align:start position:0% +to learn the rules um that govern them +okay and again as I've said many times I + + align:start position:0% +okay and again as I've said many times I + + + align:start position:0% +okay and again as I've said many times I +think the best way or at least a way + + align:start position:0% +think the best way or at least a way + + + align:start position:0% +think the best way or at least a way +that I encourage you to try to learn + + align:start position:0% +that I encourage you to try to learn + + + align:start position:0% +that I encourage you to try to learn +these is to Simply say them out loud um + + align:start position:0% +these is to Simply say them out loud um + + + align:start position:0% +these is to Simply say them out loud um +and get these get these vowel gradations + + align:start position:0% +and get these get these vowel gradations + + + align:start position:0% +and get these get these vowel gradations +um in your head + + align:start position:0% +um in your head + + + align:start position:0% +um in your head +um so kunan magon moton shulan won + + align:start position:0% +um so kunan magon moton shulan won + + + align:start position:0% +um so kunan magon moton shulan won +you've got the um you've got them all + + align:start position:0% +you've got the um you've got them all + + + align:start position:0% +you've got the um you've got them all +listed out on page 8 one those are the + + align:start position:0% +listed out on page 8 one those are the + + + align:start position:0% +listed out on page 8 one those are the +most important um although um the others + + align:start position:0% +most important um although um the others + + + align:start position:0% +most important um although um the others +that are that are there show up um quite + + align:start position:0% +that are that are there show up um quite + + + align:start position:0% +that are that are there show up um quite +often as + + align:start position:0% +often as + + + align:start position:0% +often as +well um any questions + + align:start position:0% +well um any questions + + + align:start position:0% +well um any questions +about the basics here yes just um to + + align:start position:0% +about the basics here yes just um to + + + align:start position:0% +about the basics here yes just um to +double check I'm assuming if we don't + + align:start position:0% +double check I'm assuming if we don't + + + align:start position:0% +double check I'm assuming if we don't +see a form in this table we can just + + align:start position:0% +see a form in this table we can just + + + align:start position:0% +see a form in this table we can just +assume it is what we think it should be + + align:start position:0% +assume it is what we think it should be + + + align:start position:0% +assume it is what we think it should be +correct + + align:start position:0% +correct + + + align:start position:0% +correct +yes or something like that or like the + + align:start position:0% +yes or something like that or like the + + + align:start position:0% +yes or something like that or like the +subjetive or something like that yeah + + align:start position:0% +subjetive or something like that yeah + + + align:start position:0% +subjetive or something like that yeah +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +exactly yeah yeah yep + + align:start position:0% + + + + align:start position:0% + +um so don't gone and willan um are all + + align:start position:0% +um so don't gone and willan um are all + + + align:start position:0% +um so don't gone and willan um are all +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +strange is + + align:start position:0% +strange is + + + align:start position:0% +strange is +verbs um and the reason that you again + + align:start position:0% +verbs um and the reason that you again + + + align:start position:0% +verbs um and the reason that you again +the reason you need to know these is + + align:start position:0% +the reason you need to know these is + + + align:start position:0% +the reason you need to know these is +that they just show up all the time um + + align:start position:0% +that they just show up all the time um + + + align:start position:0% +that they just show up all the time um +and so they're and so they're important + + align:start position:0% +and so they're and so they're important + + + align:start position:0% +and so they're and so they're important +um I like I like that um gone uh so this + + align:start position:0% +um I like I like that um gone uh so this + + + align:start position:0% +um I like I like that um gone uh so this +is the bottom of 81 gone lacks a past + + align:start position:0% +is the bottom of 81 gone lacks a past + + + align:start position:0% +is the bottom of 81 gone lacks a past +form of its own and has apparently + + align:start position:0% +form of its own and has apparently + + + align:start position:0% +form of its own and has apparently +borrowed the past of another verb now + + align:start position:0% +borrowed the past of another verb now + + + align:start position:0% +borrowed the past of another verb now +disappeared um that explains why at the + + align:start position:0% +disappeared um that explains why at the + + + align:start position:0% +disappeared um that explains why at the +top of 82 in table 7.12 you see gone um + + align:start position:0% +top of 82 in table 7.12 you see gone um + + + align:start position:0% +top of 82 in table 7.12 you see gone um +and then you get Gast and gath in the + + align:start position:0% +and then you get Gast and gath in the + + + align:start position:0% +and then you get Gast and gath in the +second and third so that's the IM + + align:start position:0% +second and third so that's the IM + + + align:start position:0% +second and third so that's the IM +mutation taking over um but then in the + + align:start position:0% +mutation taking over um but then in the + + + align:start position:0% +mutation taking over um but then in the +past indicative it just goes wherever it + + align:start position:0% +past indicative it just goes wherever it + + + align:start position:0% +past indicative it just goes wherever it +wants with aoda aod Aon um you know uh + + align:start position:0% +wants with aoda aod Aon um you know uh + + + align:start position:0% +wants with aoda aod Aon um you know uh +and then the past subjunctive looks + + align:start position:0% +and then the past subjunctive looks + + + align:start position:0% +and then the past subjunctive looks +looks the same um willan is really + + align:start position:0% +looks the same um willan is really + + + align:start position:0% +looks the same um willan is really +pretty simple um I don't see any big uh + + align:start position:0% +pretty simple um I don't see any big uh + + + align:start position:0% +pretty simple um I don't see any big uh +uh I don't see any big complications + + align:start position:0% +uh I don't see any big complications + + + align:start position:0% +uh I don't see any big complications +there except for the fact that the past + + align:start position:0% +there except for the fact that the past + + + align:start position:0% +there except for the fact that the past +is Wala um that is of course comparable + + align:start position:0% +is Wala um that is of course comparable + + + align:start position:0% +is Wala um that is of course comparable +to Modern English wood um It ultimately + + align:start position:0% +to Modern English wood um It ultimately + + + align:start position:0% +to Modern English wood um It ultimately +becomes Modern English wood um but in + + align:start position:0% +becomes Modern English wood um but in + + + align:start position:0% +becomes Modern English wood um but in +this case it it's just the past tense of + + align:start position:0% +this case it it's just the past tense of + + + align:start position:0% +this case it it's just the past tense of +to will or to desire um so hey wda um he + + align:start position:0% +to will or to desire um so hey wda um he + + + align:start position:0% +to will or to desire um so hey wda um he +desired um not he would even though + + align:start position:0% +desired um not he would even though + + + align:start position:0% +desired um not he would even though +that's the that that's the sort of + + align:start position:0% +that's the that that's the sort of + + + align:start position:0% +that's the that that's the sort of +cognate um fortunately you're going to + + align:start position:0% +cognate um fortunately you're going to + + + align:start position:0% +cognate um fortunately you're going to +get a lot of practice in recognizing + + align:start position:0% +get a lot of practice in recognizing + + + align:start position:0% +get a lot of practice in recognizing +these in the reading that we do um for + + align:start position:0% +these in the reading that we do um for + + + align:start position:0% +these in the reading that we do um for +the next 3 days um so after translating + + align:start position:0% +the next 3 days um so after translating + + + align:start position:0% +the next 3 days um so after translating +a little bit more of alf's translation + + align:start position:0% +a little bit more of alf's translation + + + align:start position:0% +a little bit more of alf's translation +of Genesis we're going to shift for next + + align:start position:0% +of Genesis we're going to shift for next + + + align:start position:0% +of Genesis we're going to shift for next +time for Monday um this will be our + + align:start position:0% +time for Monday um this will be our + + + align:start position:0% +time for Monday um this will be our +where our text is coming from and you're + + align:start position:0% +where our text is coming from and you're + + + align:start position:0% +where our text is coming from and you're +going to start reading start translating + + align:start position:0% +going to start reading start translating + + + align:start position:0% +going to start reading start translating +um alf's preface to Genesis so if you + + align:start position:0% +um alf's preface to Genesis so if you + + + align:start position:0% +um alf's preface to Genesis so if you +take a look at the syllabus you don't + + align:start position:0% +take a look at the syllabus you don't + + + align:start position:0% +take a look at the syllabus you don't +have to look I'll just tell you um we + + align:start position:0% +have to look I'll just tell you um we + + + align:start position:0% +have to look I'll just tell you um we +are going to start translating uh you're + + align:start position:0% +are going to start translating uh you're + + + align:start position:0% +are going to start translating uh you're +going to start Translating that is um + + align:start position:0% +going to start Translating that is um + + + align:start position:0% +going to start Translating that is um +lines 1 through 24 um of alf's preface + + align:start position:0% +lines 1 through 24 um of alf's preface + + + align:start position:0% +lines 1 through 24 um of alf's preface +preface to Genesis um which is which + + align:start position:0% +preface to Genesis um which is which + + + align:start position:0% +preface to Genesis um which is which +starts on page 199 um of Mitchell and + + align:start position:0% +starts on page 199 um of Mitchell and + + + align:start position:0% +starts on page 199 um of Mitchell and +Robinson um I encourage you to get + + align:start position:0% +Robinson um I encourage you to get + + + align:start position:0% +Robinson um I encourage you to get +started early on this it's a lot of + + align:start position:0% +started early on this it's a lot of + + + align:start position:0% +started early on this it's a lot of +translation when you haven't done really + + align:start position:0% +translation when you haven't done really + + + align:start position:0% +translation when you haven't done really +any of it before um so get started early + + align:start position:0% +any of it before um so get started early + + + align:start position:0% +any of it before um so get started early +um and expect it to take a while you're + + align:start position:0% +um and expect it to take a while you're + + + align:start position:0% +um and expect it to take a while you're +going to have to be you're going to be + + align:start position:0% +going to have to be you're going to be + + + align:start position:0% +going to have to be you're going to be +looking up a lot of words um but this is + + align:start position:0% +looking up a lot of words um but this is + + + align:start position:0% +looking up a lot of words um but this is +how you're going to be prepared to take + + align:start position:0% +how you're going to be prepared to take + + + align:start position:0% +how you're going to be prepared to take +the exam in two weeks right so this is + + align:start position:0% +the exam in two weeks right so this is + + + align:start position:0% +the exam in two weeks right so this is +all this is this whole class is a boot + + align:start position:0% +all this is this whole class is a boot + + + align:start position:0% +all this is this whole class is a boot +camp in some sense um and it's getting + + align:start position:0% +camp in some sense um and it's getting + + + align:start position:0% +camp in some sense um and it's getting +bootier by the minute um all + + align:start position:0% +bootier by the minute um all + + + align:start position:0% +bootier by the minute um all +right yes so are we turning in the + + align:start position:0% +right yes so are we turning in the + + + align:start position:0% +right yes so are we turning in the +transl + + align:start position:0% +transl + + + align:start position:0% +transl +you do not have to turn it in um but I + + align:start position:0% +you do not have to turn it in um but I + + + align:start position:0% +you do not have to turn it in um but I +will be but your performance on the + + align:start position:0% +will be but your performance on the + + + align:start position:0% +will be but your performance on the +translation um when we go around the + + align:start position:0% +translation um when we go around the + + + align:start position:0% +translation um when we go around the +room um and translate uh will be part of + + align:start position:0% +room um and translate uh will be part of + + + align:start position:0% +room um and translate uh will be part of +your participation um uh grade in class + + align:start position:0% +your participation um uh grade in class + + + align:start position:0% +your participation um uh grade in class +so excellent question that said if you + + align:start position:0% +so excellent question that said if you + + + align:start position:0% +so excellent question that said if you +want to turn in your translation I will + + align:start position:0% +want to turn in your translation I will + + + align:start position:0% +want to turn in your translation I will +happily look at it and sort of Mark it + + align:start position:0% +happily look at it and sort of Mark it + + + align:start position:0% +happily look at it and sort of Mark it +up um but it's not a formal homework + + align:start position:0% +up um but it's not a formal homework + + + align:start position:0% +up um but it's not a formal homework +assignment that gets turned in glad you + + align:start position:0% +assignment that gets turned in glad you + + + align:start position:0% +assignment that gets turned in glad you +asked gotcha thank you any other + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +it's really pretty fun I mean it may + + align:start position:0% +it's really pretty fun I mean it may + + + align:start position:0% +it's really pretty fun I mean it may +sound like the preface to Genesis I mean + + align:start position:0% +sound like the preface to Genesis I mean + + + align:start position:0% +sound like the preface to Genesis I mean +that may sound pretty boring but um + + align:start position:0% +that may sound pretty boring but um + + + align:start position:0% +that may sound pretty boring but um +honestly it's it's kind of a cool meta + + align:start position:0% +honestly it's it's kind of a cool meta + + + align:start position:0% +honestly it's it's kind of a cool meta +moment because of course you are + + align:start position:0% +moment because of course you are + + + align:start position:0% +moment because of course you are +translating Genesis alfr is translating + + align:start position:0% +translating Genesis alfr is translating + + + align:start position:0% +translating Genesis alfr is translating +Genesis alfri is very nervous about + + align:start position:0% +Genesis alfri is very nervous about + + + align:start position:0% +Genesis alfri is very nervous about +translating Genesis as you're going to + + align:start position:0% +translating Genesis as you're going to + + + align:start position:0% +translating Genesis as you're going to +hear so it's it's a it's I don't know I + + align:start position:0% +hear so it's it's a it's I don't know I + + + align:start position:0% +hear so it's it's a it's I don't know I +think it's I think it's pretty fun I'm a + + align:start position:0% +think it's I think it's pretty fun I'm a + + + align:start position:0% +think it's I think it's pretty fun I'm a +fan of alfid um so we'll get to talk + + align:start position:0% +fan of alfid um so we'll get to talk + + + align:start position:0% +fan of alfid um so we'll get to talk +more about him next + + align:start position:0% +more about him next + + + align:start position:0% +more about him next +time all right back to Baker and verbs + + align:start position:0% +time all right back to Baker and verbs + + + align:start position:0% +time all right back to Baker and verbs +um so negation we've already talked a + + align:start position:0% +um so negation we've already talked a + + + align:start position:0% +um so negation we've already talked a +little bit about this back on page + + align:start position:0% +little bit about this back on page + + + align:start position:0% +little bit about this back on page +82 um we've already talked about how um + + align:start position:0% +82 um we've already talked about how um + + + align:start position:0% +82 um we've already talked about how um +two negatives do not make a positive um + + align:start position:0% +two negatives do not make a positive um + + + align:start position:0% +two negatives do not make a positive um +so double negatives and even triple + + align:start position:0% +so double negatives and even triple + + + align:start position:0% +so double negatives and even triple +negatives sometime in Old English um + + align:start position:0% +negatives sometime in Old English um + + + align:start position:0% +negatives sometime in Old English um +just emphasize further the negative + + align:start position:0% +just emphasize further the negative + + + align:start position:0% +just emphasize further the negative +quality of whatever is being described + + align:start position:0% +quality of whatever is being described + + + align:start position:0% +quality of whatever is being described +um so in the bottom of on the bottom of + + align:start position:0% +um so in the bottom of on the bottom of + + + align:start position:0% +um so in the bottom of on the bottom of +page 82 we have a sentence that we're + + align:start position:0% +page 82 we have a sentence that we're + + + align:start position:0% +page 82 we have a sentence that we're +actually going to uh translate later + + align:start position:0% +actually going to uh translate later + + + align:start position:0% +actually going to uh translate later +today um uttered by The Serpent of + + align:start position:0% + + + + align:start position:0% + +Genesis you will not in any way be dead + + align:start position:0% +Genesis you will not in any way be dead + + + align:start position:0% +Genesis you will not in any way be dead +even if you eat from the tree um the + + align:start position:0% +even if you eat from the tree um the + + + align:start position:0% +even if you eat from the tree um the +serpent says reassuringly to Eve um or + + align:start position:0% +serpent says reassuringly to Eve um or + + + align:start position:0% +serpent says reassuringly to Eve um or +fat WEA as she's described by alfri um + + align:start position:0% +fat WEA as she's described by alfri um + + + align:start position:0% +fat WEA as she's described by alfri um +and at the top of 83 here the additional + + align:start position:0% +and at the top of 83 here the additional + + + align:start position:0% +and at the top of 83 here the additional +negative adverb n + + align:start position:0% +negative adverb n + + + align:start position:0% +negative adverb n +makes the sentence more emphatic than it + + align:start position:0% +makes the sentence more emphatic than it + + + align:start position:0% +makes the sentence more emphatic than it +would be with Alone um so it says and + + align:start position:0% +would be with Alone um so it says and + + + align:start position:0% +would be with Alone um so it says and +then common negative adverbs are n um + + align:start position:0% +then common negative adverbs are n um + + + align:start position:0% +then common negative adverbs are n um +nales n SW and + + align:start position:0% +nales n SW and + + + align:start position:0% +nales n SW and +natas um so you know they're not that + + align:start position:0% +natas um so you know they're not that + + + align:start position:0% +natas um so you know they're not that +last one is not particularly common + + align:start position:0% +last one is not particularly common + + + align:start position:0% +last one is not particularly common +frankly but it is it is a cool one um + + align:start position:0% +frankly but it is it is a cool one um + + + align:start position:0% +frankly but it is it is a cool one um +also further uh reinforcement of how + + align:start position:0% +also further uh reinforcement of how + + + align:start position:0% +also further uh reinforcement of how +important long vowels are + + align:start position:0% +important long vowels are + + + align:start position:0% +important long vowels are +so + + align:start position:0% +so + + + align:start position:0% +so +h + + align:start position:0% +h + + + align:start position:0% +h +means + + align:start position:0% + + + + align:start position:0% + +little um + + align:start position:0% + + + + align:start position:0% + +is is the instrumental interrogative + + align:start position:0% +is is the instrumental interrogative + + + align:start position:0% +is is the instrumental interrogative +pronoun so little by what means right so + + align:start position:0% +pronoun so little by what means right so + + + align:start position:0% +pronoun so little by what means right so +bear in mind always be looking for these + + align:start position:0% +bear in mind always be looking for these + + + align:start position:0% +bear in mind always be looking for these +macrons um over + + align:start position:0% + + + + align:start position:0% + +vowels all right back to page 82 so this + + align:start position:0% +vowels all right back to page 82 so this + + + align:start position:0% +vowels all right back to page 82 so this +is also very important the the paragraph + + align:start position:0% +is also very important the the paragraph + + + align:start position:0% +is also very important the the paragraph +right under the first quotation so NE is + + align:start position:0% +right under the first quotation so NE is + + + align:start position:0% +right under the first quotation so NE is +contracted with certain verbs for + + align:start position:0% +contracted with certain verbs for + + + align:start position:0% +contracted with certain verbs for +example NIS so n plus is is not nas + + align:start position:0% +example NIS so n plus is is not nas + + + align:start position:0% +example NIS so n plus is is not nas +which is n plus was was not + + align:start position:0% +which is n plus was was not + + + align:start position:0% +which is n plus was was not +Naf does not have from n plus half and + + align:start position:0% +Naf does not have from n plus half and + + + align:start position:0% +Naf does not have from n plus half and +so on and so forth um and and then the + + align:start position:0% +so on and so forth um and and then the + + + align:start position:0% +so on and so forth um and and then the +last + + align:start position:0% +last + + + align:start position:0% +last +one n noon um n does not have from n + + align:start position:0% +one n noon um n does not have from n + + + align:start position:0% +one n noon um n does not have from n +plus a um not n a n long a t does not + + align:start position:0% +plus a um not n a n long a t does not + + + align:start position:0% +plus a um not n a n long a t does not +know from n plus what um notice that all + + align:start position:0% +know from n plus what um notice that all + + + align:start position:0% +know from n plus what um notice that all +of the verbs so contracted begin with a + + align:start position:0% +of the verbs so contracted begin with a + + + align:start position:0% +of the verbs so contracted begin with a +vowel an H or a + + align:start position:0% +vowel an H or a + + + align:start position:0% +vowel an H or a +w + + align:start position:0% +w + + + align:start position:0% +w +um these don't have to be the author + + align:start position:0% +um these don't have to be the author + + + align:start position:0% +um these don't have to be the author +doesn't have to do this to perform these + + align:start position:0% +doesn't have to do this to perform these + + + align:start position:0% +doesn't have to do this to perform these +contractions + + align:start position:0% +contractions + + + align:start position:0% +contractions +um but I would say 70 to 80 to maybe 90% + + align:start position:0% +um but I would say 70 to 80 to maybe 90% + + + align:start position:0% +um but I would say 70 to 80 to maybe 90% +of the time um whoever's writing does um + + align:start position:0% +of the time um whoever's writing does um + + + align:start position:0% +of the time um whoever's writing does um +so you should get very used to seeing + + align:start position:0% +so you should get very used to seeing + + + align:start position:0% +so you should get very used to seeing +and be ready to recognize on the + + align:start position:0% + + + + align:start position:0% + +exam forms + + align:start position:0% + + + + align:start position:0% + +like Nas + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +n n and so on and so forth yeah Lambert + + align:start position:0% +n n and so on and so forth yeah Lambert + + + align:start position:0% +n n and so on and so forth yeah Lambert +how did the like negation go from being + + align:start position:0% +how did the like negation go from being + + + align:start position:0% +how did the like negation go from being +before to after like that's like is not + + align:start position:0% +before to after like that's like is not + + + align:start position:0% +before to after like that's like is not +we say is not oh great question no idea + + align:start position:0% +we say is not oh great question no idea + + + align:start position:0% +we say is not oh great question no idea +yeah um I think the short + + align:start position:0% +yeah um I think the short + + + align:start position:0% +yeah um I think the short +answer yeah I don't + + align:start position:0% +answer yeah I don't + + + align:start position:0% +answer yeah I don't +know um but it's a good + + align:start position:0% +know um but it's a good + + + align:start position:0% +know um but it's a good +question + + align:start position:0% +question + + + align:start position:0% +question +others + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +verbals um like infinitives and + + align:start position:0% +verbals um like infinitives and + + + align:start position:0% +verbals um like infinitives and +participles um and actually just + + align:start position:0% +participles um and actually just + + + align:start position:0% +participles um and actually just +infinitives and participles + + align:start position:0% +infinitives and participles + + + align:start position:0% +infinitives and participles +um + + align:start position:0% + + + + align:start position:0% + +7.9.18 do this in Modern English still + + align:start position:0% +7.9.18 do this in Modern English still + + + align:start position:0% +7.9.18 do this in Modern English still +um with like I saw him dance um but in + + align:start position:0% +um with like I saw him dance um but in + + + align:start position:0% +um with like I saw him dance um but in +Old English that would be I saw him to + + align:start position:0% +Old English that would be I saw him to + + + align:start position:0% +Old English that would be I saw him to +dance it would use the infinitive um + + align:start position:0% +dance it would use the infinitive um + + + align:start position:0% +dance it would use the infinitive um +form of the verb um it also does uses + + align:start position:0% +form of the verb um it also does uses + + + align:start position:0% +form of the verb um it also does uses +this construction more frequently than + + align:start position:0% +this construction more frequently than + + + align:start position:0% +this construction more frequently than +than we do um so for + + align:start position:0% +than we do um so for + + + align:start position:0% +than we do um so for +example + + align:start position:0% + + + + align:start position:0% + +uh well actually those are all examples + + align:start position:0% +uh well actually those are all examples + + + align:start position:0% +uh well actually those are all examples +that we would use in Modern English um + + align:start position:0% +that we would use in Modern English um + + + align:start position:0% +that we would use in Modern English um +I guess the first one depart from me for + + align:start position:0% +I guess the first one depart from me for + + + align:start position:0% +I guess the first one depart from me for +I see you are persevering in + + align:start position:0% +I see you are persevering in + + + align:start position:0% +I see you are persevering in +abstinence um which is you know sounds + + align:start position:0% +abstinence um which is you know sounds + + + align:start position:0% +abstinence um which is you know sounds +like a like we came in in the middle of + + align:start position:0% +like a like we came in in the middle of + + + align:start position:0% +like a like we came in in the middle of +a very spicy conversation um there we + + align:start position:0% +a very spicy conversation um there we + + + align:start position:0% +a very spicy conversation um there we +they're in Modern English they translate + + align:start position:0% +they're in Modern English they translate + + + align:start position:0% +they're in Modern English they translate +it as a as a uh as a ver as a as a + + align:start position:0% +it as a as a uh as a ver as a as a + + + align:start position:0% +it as a as a uh as a ver as a as a +participle whereas in Old English it's a + + align:start position:0% +participle whereas in Old English it's a + + + align:start position:0% +participle whereas in Old English it's a +it's a in infinitive but it's pretty + + align:start position:0% +it's a in infinitive but it's pretty + + + align:start position:0% +it's a in infinitive but it's pretty +pretty typical + + align:start position:0% +pretty typical + + + align:start position:0% +pretty typical +um take a look at the bottom of the page + + align:start position:0% +um take a look at the bottom of the page + + + align:start position:0% +um take a look at the bottom of the page +though because this is effectively how + + align:start position:0% +though because this is effectively how + + + align:start position:0% +though because this is effectively how +old English uses the passive infinitive + + align:start position:0% +old English uses the passive infinitive + + + align:start position:0% +old English uses the passive infinitive +there is no passive infinitive form in + + align:start position:0% +there is no passive infinitive form in + + + align:start position:0% +there is no passive infinitive form in +Old English like there is in Latin and + + align:start position:0% +Old English like there is in Latin and + + + align:start position:0% +Old English like there is in Latin and +some other languages um but the way they + + align:start position:0% +some other languages um but the way they + + + align:start position:0% +some other languages um but the way they +express it um is simply with the um is + + align:start position:0% +express it um is simply with the um is + + + align:start position:0% +express it um is simply with the um is +simply with the the the only infinitive + + align:start position:0% +simply with the the the only infinitive + + + align:start position:0% +simply with the the the only infinitive +form that is the active um and you see + + align:start position:0% +form that is the active um and you see + + + align:start position:0% +form that is the active um and you see +that down at the + + align:start position:0% + + + + align:start position:0% + +bottom which is a great way to molsbury + + align:start position:0% +bottom which is a great way to molsbury + + + align:start position:0% +bottom which is a great way to molsbury +um and then the the king commanded they + + align:start position:0% +um and then the the king commanded they + + + align:start position:0% +um and then the the king commanded they +have bracketed someone to take Seth's + + align:start position:0% +have bracketed someone to take Seth's + + + align:start position:0% +have bracketed someone to take Seth's +Widow you could functionally translate + + align:start position:0% +Widow you could functionally translate + + + align:start position:0% +Widow you could functionally translate +that and I would perfectly well accept + + align:start position:0% +that and I would perfectly well accept + + + align:start position:0% +that and I would perfectly well accept +then the king commanded sether Seth's + + align:start position:0% +then the king commanded sether Seth's + + + align:start position:0% +then the king commanded sether Seth's +Widow to be taken um and brought into + + align:start position:0% +Widow to be taken um and brought into + + + align:start position:0% +Widow to be taken um and brought into +malmsbury um and then at the bottom or + + align:start position:0% +malmsbury um and then at the bottom or + + + align:start position:0% +malmsbury um and then at the bottom or +sorry at the top of the next page on 84 + + align:start position:0% +sorry at the top of the next page on 84 + + + align:start position:0% +sorry at the top of the next page on 84 +Baker makes that um + + align:start position:0% +Baker makes that um + + + align:start position:0% +Baker makes that um +explicit um + + align:start position:0% +explicit um + + + align:start position:0% +explicit um +the inflected + + align:start position:0% +the inflected + + + align:start position:0% +the inflected +infinitive um this is actually pretty + + align:start position:0% +infinitive um this is actually pretty + + + align:start position:0% +infinitive um this is actually pretty +important because it shows up + + align:start position:0% +important because it shows up + + + align:start position:0% +important because it shows up +surprisingly often the inflected + + align:start position:0% +surprisingly often the inflected + + + align:start position:0% +surprisingly often the inflected +infinitive is where you put an NE on the + + align:start position:0% +infinitive is where you put an NE on the + + + align:start position:0% +infinitive is where you put an NE on the +end of the infinitive so + + align:start position:0% +end of the infinitive so + + + align:start position:0% +end of the infinitive so +as um from the uh from the verb asan um + + align:start position:0% +as um from the uh from the verb asan um + + + align:start position:0% +as um from the uh from the verb asan um +you see that double n and then an e at + + align:start position:0% +you see that double n and then an e at + + + align:start position:0% +you see that double n and then an e at +the end it's mostly used um as Baker + + align:start position:0% +the end it's mostly used um as Baker + + + align:start position:0% +the end it's mostly used um as Baker +says um with Bon um so a form of the + + align:start position:0% +says um with Bon um so a form of the + + + align:start position:0% +says um with Bon um so a form of the +verb to be to express obligation necess + + align:start position:0% +verb to be to express obligation necess + + + align:start position:0% +verb to be to express obligation necess +necessity or propriety um so the example + + align:start position:0% + + + + align:start position:0% + +there it should be further it should + + align:start position:0% +there it should be further it should + + + align:start position:0% +there it should be further it should +further be diligently investigated um so + + align:start position:0% +further be diligently investigated um so + + + align:start position:0% +further be diligently investigated um so +the the verb is simply the conjugated + + align:start position:0% +the the verb is simply the conjugated + + + align:start position:0% +the the verb is simply the conjugated +verb is simply is there is no should + + align:start position:0% +verb is simply is there is no should + + + align:start position:0% +verb is simply is there is no should +explicitly the should functionality of + + align:start position:0% +explicitly the should functionality of + + + align:start position:0% +explicitly the should functionality of +that translation is expressed by the + + align:start position:0% +that translation is expressed by the + + + align:start position:0% +that translation is expressed by the +inflected nness of the infinitive okay + + align:start position:0% +inflected nness of the infinitive okay + + + align:start position:0% +inflected nness of the infinitive okay +so what this means is that yet another + + align:start position:0% +so what this means is that yet another + + + align:start position:0% +so what this means is that yet another +thing that any could be is an inflected + + align:start position:0% +thing that any could be is an inflected + + + align:start position:0% +thing that any could be is an inflected +infinitive um if of course the preceding + + align:start position:0% +infinitive um if of course the preceding + + + align:start position:0% +infinitive um if of course the preceding +the first part of the word is an + + align:start position:0% +the first part of the word is an + + + align:start position:0% +the first part of the word is an +infinitive okay so just another thing to + + align:start position:0% +infinitive okay so just another thing to + + + align:start position:0% +infinitive okay so just another thing to +be on the lookout for uh does the any + + align:start position:0% +be on the lookout for uh does the any + + + align:start position:0% +be on the lookout for uh does the any +form always take a to before it + + align:start position:0% +form always take a to before it + + + align:start position:0% +form always take a to before it +yes yes very good very good question um + + align:start position:0% +yes yes very good very good question um + + + align:start position:0% +yes yes very good very good question um +oh always I hesitate to say always but + + align:start position:0% +oh always I hesitate to say always but + + + align:start position:0% +oh always I hesitate to say always but +um for our purposes which is to say on + + align:start position:0% +um for our purposes which is to say on + + + align:start position:0% +um for our purposes which is to say on +an exam that you take in this class + + align:start position:0% +an exam that you take in this class + + + align:start position:0% +an exam that you take in this class +yes um and I think certainly if not + + align:start position:0% +yes um and I think certainly if not + + + align:start position:0% +yes um and I think certainly if not +always in like all exent Old English um + + align:start position:0% +always in like all exent Old English um + + + align:start position:0% +always in like all exent Old English um +overwhelmingly so yeah um and I think + + align:start position:0% +overwhelmingly so yeah um and I think + + + align:start position:0% +overwhelmingly so yeah um and I think +partly that's because NE is such an + + align:start position:0% +partly that's because NE is such an + + + align:start position:0% +partly that's because NE is such an +otherwise ambiguous ending right because + + align:start position:0% +otherwise ambiguous ending right because + + + align:start position:0% +otherwise ambiguous ending right because +you know as baker said earlier in some + + align:start position:0% +you know as baker said earlier in some + + + align:start position:0% +you know as baker said earlier in some +previous chapter it's not as if Old + + align:start position:0% +previous chapter it's not as if Old + + + align:start position:0% +previous chapter it's not as if Old +English + + align:start position:0% +English + + + align:start position:0% +English +people designedly created sentences that + + align:start position:0% +people designedly created sentences that + + + align:start position:0% +people designedly created sentences that +are hard to parse I mean I assume actual + + align:start position:0% +are hard to parse I mean I assume actual + + + align:start position:0% +are hard to parse I mean I assume actual +Old English speakers would like look at + + align:start position:0% +Old English speakers would like look at + + + align:start position:0% +Old English speakers would like look at +the word and like guess it from the + + align:start position:0% +the word and like guess it from the + + + align:start position:0% +the word and like guess it from the +guess the meaning from the semantics as + + align:start position:0% +guess the meaning from the semantics as + + + align:start position:0% +guess the meaning from the semantics as +opposed to like thinking about the + + align:start position:0% +opposed to like thinking about the + + + align:start position:0% +opposed to like thinking about the +conjugations ofation yeah absolutely + + align:start position:0% +conjugations ofation yeah absolutely + + + align:start position:0% +conjugations ofation yeah absolutely +absolutely um so so yeah no but you + + align:start position:0% +absolutely um so so yeah no but you + + + align:start position:0% +absolutely um so so yeah no but you +don't need to worry about that just so + + align:start position:0% +don't need to worry about that just so + + + align:start position:0% +don't need to worry about that just so +to plus the um the infinitive with an NE + + align:start position:0% +to plus the um the infinitive with an NE + + + align:start position:0% +to plus the um the infinitive with an NE +on the end is the inflected + + align:start position:0% +on the end is the inflected + + + align:start position:0% +on the end is the inflected +infinitive all right so the present + + align:start position:0% +infinitive all right so the present + + + align:start position:0% +infinitive all right so the present +participle um not + + align:start position:0% +participle um not + + + align:start position:0% +participle um not +7.9.2 um is often used as a noun + + align:start position:0% +7.9.2 um is often used as a noun + + + align:start position:0% +7.9.2 um is often used as a noun +denoting the performer of an action um + + align:start position:0% +denoting the performer of an action um + + + align:start position:0% +denoting the performer of an action um +so rodor rad Rend ruler of the heavens + + align:start position:0% +so rodor rad Rend ruler of the heavens + + + align:start position:0% +so rodor rad Rend ruler of the heavens +um Rend is the present participle of + + align:start position:0% +um Rend is the present participle of + + + align:start position:0% +um Rend is the present participle of +radon to rule um but it's used here as a + + align:start position:0% +radon to rule um but it's used here as a + + + align:start position:0% +radon to rule um but it's used here as a +noun um this is this is I think pretty + + align:start position:0% +noun um this is this is I think pretty + + + align:start position:0% +noun um this is this is I think pretty +common in lots of uh lots of languages + + align:start position:0% +common in lots of uh lots of languages + + + align:start position:0% +common in lots of uh lots of languages +um including Latin and + + align:start position:0% +um including Latin and + + + align:start position:0% +um including Latin and +Greek + + align:start position:0% +Greek + + + align:start position:0% +Greek +um take a look at the B at the bottom of + + align:start position:0% +um take a look at the B at the bottom of + + + align:start position:0% +um take a look at the B at the bottom of +that page though so a construction or I + + align:start position:0% +that page though so a construction or I + + + align:start position:0% +that page though so a construction or I +guess just below that a construction + + align:start position:0% +guess just below that a construction + + + align:start position:0% +guess just below that a construction +consisting of a noun or pronoun and + + align:start position:0% +consisting of a noun or pronoun and + + + align:start position:0% +consisting of a noun or pronoun and +participle both in the dative case is + + align:start position:0% +participle both in the dative case is + + + align:start position:0% +participle both in the dative case is +sometimes used where one would expect an + + align:start position:0% +sometimes used where one would expect an + + + align:start position:0% +sometimes used where one would expect an +adverb clause or another construction + + align:start position:0% +adverb clause or another construction + + + align:start position:0% +adverb clause or another construction +expressing + + align:start position:0% +expressing + + + align:start position:0% +expressing +time or cause the noun phrase may may + + align:start position:0% +time or cause the noun phrase may may + + + align:start position:0% +time or cause the noun phrase may may +sometimes be introduced by a preposition + + align:start position:0% +sometimes be introduced by a preposition + + + align:start position:0% +sometimes be introduced by a preposition +this is a little bit like the ablative + + align:start position:0% +this is a little bit like the ablative + + + align:start position:0% +this is a little bit like the ablative +absolute in Latin or the genitive + + align:start position:0% +absolute in Latin or the genitive + + + align:start position:0% +absolute in Latin or the genitive +absolute in Greek um so these he Reus + + align:start position:0% +absolute in Greek um so these he Reus + + + align:start position:0% +absolute in Greek um so these he Reus +Jes famously these things having been + + align:start position:0% +Jes famously these things having been + + + align:start position:0% +Jes famously these things having been +done or with these things having been + + align:start position:0% +done or with these things having been + + + align:start position:0% +done or with these things having been +done um Caesar you know did whatever + + align:start position:0% +done um Caesar you know did whatever + + + align:start position:0% +done um Caesar you know did whatever +else happened in the sentence um here we + + align:start position:0% +else happened in the sentence um here we + + + align:start position:0% +else happened in the sentence um here we +have uh let's see + + align:start position:0% +have uh let's see + + + align:start position:0% +have uh let's see +um + + align:start position:0% +um + + + align:start position:0% +um +the second of these actually the first + + align:start position:0% +the second of these actually the first + + + align:start position:0% +the second of these actually the first +example with AA + + align:start position:0% + + + + align:start position:0% + +andang + + align:start position:0% +andang + + + align:start position:0% +andang +um Baron um an office seized the kingdom + + align:start position:0% +um Baron um an office seized the kingdom + + + align:start position:0% +um Baron um an office seized the kingdom +of the merians after Baron red had been + + align:start position:0% +of the merians after Baron red had been + + + align:start position:0% +of the merians after Baron red had been +driven out that's really that's + + align:start position:0% +driven out that's really that's + + + align:start position:0% +driven out that's really that's +functionally an ablet of absolute um + + align:start position:0% +functionally an ablet of absolute um + + + align:start position:0% +functionally an ablet of absolute um +except here it's like a DAT of absolute + + align:start position:0% +except here it's like a DAT of absolute + + + align:start position:0% +except here it's like a DAT of absolute +or something um you here and in this + + align:start position:0% +or something um you here and in this + + + align:start position:0% +or something um you here and in this +case there is no preposition um but in + + align:start position:0% +case there is no preposition um but in + + + align:start position:0% +case there is no preposition um but in +the next examples um be him lium and + + align:start position:0% +the next examples um be him lium and + + + align:start position:0% +the next examples um be him lium and +then uh that that does take uh a + + align:start position:0% +then uh that that does take uh a + + + align:start position:0% +then uh that that does take uh a +preposition that does use a preposition + + align:start position:0% +preposition that does use a preposition + + + align:start position:0% +preposition that does use a preposition +the next one does not him forth fendum + + align:start position:0% +the next one does not him forth fendum + + + align:start position:0% +the next one does not him forth fendum +um so you may or may not get one but you + + align:start position:0% +um so you may or may not get one but you + + + align:start position:0% +um so you may or may not get one but you +should add this mentally or indeed + + align:start position:0% +should add this mentally or indeed + + + align:start position:0% +should add this mentally or indeed +scribbly um to your list of the many + + align:start position:0% +scribbly um to your list of the many + + + align:start position:0% +scribbly um to your list of the many +things that the dative case can do in + + align:start position:0% +things that the dative case can do in + + + align:start position:0% +things that the dative case can do in +Old + + align:start position:0% + + + + align:start position:0% + +English and there's uh and there's a + + align:start position:0% +English and there's uh and there's a + + + align:start position:0% +English and there's uh and there's a +little note at the bottom um saying what + + align:start position:0% +little note at the bottom um saying what + + + align:start position:0% +little note at the bottom um saying what +I just said about about this looking + + align:start position:0% +I just said about about this looking + + + align:start position:0% +I just said about about this looking +like the ablative absolute in Latin um + + align:start position:0% +like the ablative absolute in Latin um + + + align:start position:0% +like the ablative absolute in Latin um +and it's often thought to be um in fact + + align:start position:0% +and it's often thought to be um in fact + + + align:start position:0% +and it's often thought to be um in fact +an imitation so when you have uh in fact + + align:start position:0% +an imitation so when you have uh in fact + + + align:start position:0% +an imitation so when you have uh in fact +in alf's translation of Genesis when he + + align:start position:0% +in alf's translation of Genesis when he + + + align:start position:0% +in alf's translation of Genesis when he +has when he's dealing with ablative + + align:start position:0% +has when he's dealing with ablative + + + align:start position:0% +has when he's dealing with ablative +absolutes um he often uses this + + align:start position:0% +absolutes um he often uses this + + + align:start position:0% +absolutes um he often uses this +construction + + align:start position:0% +construction + + + align:start position:0% +construction +okay all right the subjunctive and here + + align:start position:0% +okay all right the subjunctive and here + + + align:start position:0% +okay all right the subjunctive and here +I'm going to actually ask you to uh turn + + align:start position:0% +I'm going to actually ask you to uh turn + + + align:start position:0% +I'm going to actually ask you to uh turn +to page one of uh section three of the + + align:start position:0% +to page one of uh section three of the + + + align:start position:0% +to page one of uh section three of the +exam um because this will uh + + align:start position:0% +exam um because this will uh + + + align:start position:0% +exam um because this will uh +this gives the very + + align:start position:0% +this gives the very + + + align:start position:0% +this gives the very +short summary of when the subjunctive + + align:start position:0% +short summary of when the subjunctive + + + align:start position:0% +short summary of when the subjunctive +gets used in Old English um and this is + + align:start position:0% +gets used in Old English um and this is + + + align:start position:0% +gets used in Old English um and this is +covered on pages 85 through 88 which is + + align:start position:0% +covered on pages 85 through 88 which is + + + align:start position:0% +covered on pages 85 through 88 which is +to say the rest of chapter 7 of + + align:start position:0% +to say the rest of chapter 7 of + + + align:start position:0% +to say the rest of chapter 7 of +Baker um these should look familiar to + + align:start position:0% +Baker um these should look familiar to + + + align:start position:0% +Baker um these should look familiar to +anyone any of you who have studied + + align:start position:0% +anyone any of you who have studied + + + align:start position:0% +anyone any of you who have studied +languages with the subjunctive because + + align:start position:0% +languages with the subjunctive because + + + align:start position:0% +languages with the subjunctive because +they're they're pretty they're pretty + + align:start position:0% +they're they're pretty they're pretty + + + align:start position:0% +they're they're pretty they're pretty +comparable um even in English some of + + align:start position:0% +comparable um even in English some of + + + align:start position:0% +comparable um even in English some of +them so contrary to fact clauses + + align:start position:0% +them so contrary to fact clauses + + + align:start position:0% +them so contrary to fact clauses +like if I were Rich which implies that + + align:start position:0% +like if I were Rich which implies that + + + align:start position:0% +like if I were Rich which implies that +I'm not um you see that contrary to fact + + align:start position:0% +I'm not um you see that contrary to fact + + + align:start position:0% +I'm not um you see that contrary to fact +uh ex uh explained at the bottom of page + + align:start position:0% +uh ex uh explained at the bottom of page + + + align:start position:0% +uh ex uh explained at the bottom of page +85 of + + align:start position:0% +85 of + + + align:start position:0% +85 of +Baker um also at the bottom of page 85 + + align:start position:0% +Baker um also at the bottom of page 85 + + + align:start position:0% +Baker um also at the bottom of page 85 +of Baker verbs of Des following verbs of + + align:start position:0% +of Baker verbs of Des following verbs of + + + align:start position:0% +of Baker verbs of Des following verbs of +Desiring and commanding I think we + + align:start position:0% +Desiring and commanding I think we + + + align:start position:0% +Desiring and commanding I think we +talked about that even a little bit last + + align:start position:0% +talked about that even a little bit last + + + align:start position:0% +talked about that even a little bit last +class um so I insisted that he go home + + align:start position:0% +class um so I insisted that he go home + + + align:start position:0% +class um so I insisted that he go home +we still use the subjunctive there in in + + align:start position:0% +we still use the subjunctive there in in + + + align:start position:0% +we still use the subjunctive there in in +in Modern English it sounds very strange + + align:start position:0% +in Modern English it sounds very strange + + + align:start position:0% +in Modern English it sounds very strange +to Myers at least to say I insisted that + + align:start position:0% +to Myers at least to say I insisted that + + + align:start position:0% +to Myers at least to say I insisted that +he goes home yeah I people don't notice + + align:start position:0% +he goes home yeah I people don't notice + + + align:start position:0% +he goes home yeah I people don't notice +it because I insisted he go home is + + align:start position:0% +it because I insisted he go home is + + + align:start position:0% +it because I insisted he go home is +infect the infinitive and they don't + + align:start position:0% +infect the infinitive and they don't + + + align:start position:0% +infect the infinitive and they don't +realize it's not the same word form yeah + + align:start position:0% +realize it's not the same word form yeah + + + align:start position:0% +realize it's not the same word form yeah +exactly that I think the absence of the + + align:start position:0% +exactly that I think the absence of the + + + align:start position:0% +exactly that I think the absence of the +of the but it's not the infinitive right + + align:start position:0% +of the but it's not the infinitive right + + + align:start position:0% +of the but it's not the infinitive right +because it's he go well when you don't + + align:start position:0% +because it's he go well when you don't + + + align:start position:0% +because it's he go well when you don't +use that it's it's then the accusative + + align:start position:0% +use that it's it's then the accusative + + + align:start position:0% +use that it's it's then the accusative +and the infinitive yeah exactly because + + align:start position:0% +and the infinitive yeah exactly because + + + align:start position:0% +and the infinitive yeah exactly because +those are so similar in Modern English I + + align:start position:0% +those are so similar in Modern English I + + + align:start position:0% +those are so similar in Modern English I +think people don't realize that it's + + align:start position:0% +think people don't realize that it's + + + align:start position:0% +think people don't realize that it's +just exactly no I think I think you're + + align:start position:0% +just exactly no I think I think you're + + + align:start position:0% +just exactly no I think I think you're +right I think you're right the absence + + align:start position:0% +right I think you're right the absence + + + align:start position:0% +right I think you're right the absence +the pity of um of verb forms um in + + align:start position:0% +the pity of um of verb forms um in + + + align:start position:0% +the pity of um of verb forms um in +Modern English does create that + + align:start position:0% +Modern English does create that + + + align:start position:0% +Modern English does create that +ambiguity but it's definitely it is + + align:start position:0% +ambiguity but it's definitely it is + + + align:start position:0% +ambiguity but it's definitely it is +definitely the subjunctive + + align:start position:0% +definitely the subjunctive + + + align:start position:0% +definitely the subjunctive +um number three is the one that is um + + align:start position:0% +um number three is the one that is um + + + align:start position:0% +um number three is the one that is um +that is kind of most unlike uh or or or + + align:start position:0% +that is kind of most unlike uh or or or + + + align:start position:0% +that is kind of most unlike uh or or or +maybe strangest I guess um to to Modern + + align:start position:0% +maybe strangest I guess um to to Modern + + + align:start position:0% +maybe strangest I guess um to to Modern +English um words or sorry uh uh Modern + + align:start position:0% +English um words or sorry uh uh Modern + + + align:start position:0% +English um words or sorry uh uh Modern +English sense um so to express doubt or + + align:start position:0% +English sense um so to express doubt or + + + align:start position:0% +English sense um so to express doubt or +ignorance he wondered if she were wise + + align:start position:0% +ignorance he wondered if she were wise + + + align:start position:0% +ignorance he wondered if she were wise +um that's that is that is something we + + align:start position:0% +um that's that is that is something we + + + align:start position:0% +um that's that is that is something we +would say in Modern English but in + + align:start position:0% +would say in Modern English but in + + + align:start position:0% +would say in Modern English but in +reported also in reported action of + + align:start position:0% +reported also in reported action of + + + align:start position:0% +reported also in reported action of +which the speaker has no direct + + align:start position:0% +which the speaker has no direct + + + align:start position:0% +which the speaker has no direct +knowledge + + align:start position:0% +knowledge + + + align:start position:0% +knowledge +um so even if there is no doubt okay so + + align:start position:0% +um so even if there is no doubt okay so + + + align:start position:0% +um so even if there is no doubt okay so +the the sentence in the middle of page + + align:start position:0% +the the sentence in the middle of page + + + align:start position:0% +the the sentence in the middle of page +86 of Baker is a good example here + + align:start position:0% +86 of Baker is a good example here + + + align:start position:0% +86 of Baker is a good example here +um so that Folk + + align:start position:0% +um so that Folk + + + align:start position:0% +um so that Folk +um I'm looking right around the middle + + align:start position:0% +um I'm looking right around the middle + + + align:start position:0% +um I'm looking right around the middle +of the page that folk + + align:start position:0% + + + + align:start position:0% + +Tha um so the people who saw this sign + + align:start position:0% +Tha um so the people who saw this sign + + + align:start position:0% +Tha um so the people who saw this sign +said that Christ was a true Prophet now + + align:start position:0% +said that Christ was a true Prophet now + + + align:start position:0% +said that Christ was a true Prophet now +in the view of the Christian writer of + + align:start position:0% +in the view of the Christian writer of + + + align:start position:0% +in the view of the Christian writer of +this sentence in the Old English period + + align:start position:0% +this sentence in the Old English period + + + align:start position:0% +this sentence in the Old English period +there is absolutely no doubt in their + + align:start position:0% +there is absolutely no doubt in their + + + align:start position:0% +there is absolutely no doubt in their +mind about whether Christ was a true + + align:start position:0% +mind about whether Christ was a true + + + align:start position:0% +mind about whether Christ was a true +Prophet or not um yet they still use the + + align:start position:0% +Prophet or not um yet they still use the + + + align:start position:0% +Prophet or not um yet they still use the +subjunctive because it is indirect or + + align:start position:0% +subjunctive because it is indirect or + + + align:start position:0% +subjunctive because it is indirect or +reported speech + + align:start position:0% +reported speech + + + align:start position:0% +reported speech +okay that said they will also sometimes + + align:start position:0% +okay that said they will also sometimes + + + align:start position:0% +okay that said they will also sometimes +use the indicative here okay as in the + + align:start position:0% +use the indicative here okay as in the + + + align:start position:0% +use the indicative here okay as in the +following sentence um beim SOA isas that + + align:start position:0% +following sentence um beim SOA isas that + + + align:start position:0% +following sentence um beim SOA isas that +hey is when it could theoretically be + + align:start position:0% +hey is when it could theoretically be + + + align:start position:0% +hey is when it could theoretically be +war is Stephen cendes on Wasa um so + + align:start position:0% +war is Stephen cendes on Wasa um so + + + align:start position:0% +war is Stephen cendes on Wasa um so +concerning him John the Baptist uh oh + + align:start position:0% +concerning him John the Baptist uh oh + + + align:start position:0% +concerning him John the Baptist uh oh +sorry concerning him John the Baptist + + align:start position:0% +sorry concerning him John the Baptist + + + align:start position:0% +sorry concerning him John the Baptist +the prophet Isaiah wrote that he is the + + align:start position:0% +the prophet Isaiah wrote that he is the + + + align:start position:0% +the prophet Isaiah wrote that he is the +voice of one crying in the wilderness + + align:start position:0% +voice of one crying in the wilderness + + + align:start position:0% +voice of one crying in the wilderness +okay um so just be aware of that usage + + align:start position:0% +okay um so just be aware of that usage + + + align:start position:0% +okay um so just be aware of that usage +and the fact that it can alternate um + + align:start position:0% +and the fact that it can alternate um + + + align:start position:0% +and the fact that it can alternate um +with the + + align:start position:0% +with the + + + align:start position:0% +with the +indicative fourth is in concessive + + align:start position:0% +indicative fourth is in concessive + + + align:start position:0% +indicative fourth is in concessive +Clauses introduced by th um or th the + + align:start position:0% +Clauses introduced by th um or th the + + + align:start position:0% +Clauses introduced by th um or th the +words like although despite even if + + align:start position:0% +words like although despite even if + + + align:start position:0% +words like although despite even if +um so nevertheless no man must despair + + align:start position:0% +um so nevertheless no man must despair + + + align:start position:0% +um so nevertheless no man must despair +though he be sinful um Baker says uh + + align:start position:0% +though he be sinful um Baker says uh + + + align:start position:0% +though he be sinful um Baker says uh +here has a sense something like even if + + align:start position:0% +here has a sense something like even if + + + align:start position:0% +here has a sense something like even if +implying that the man may or may not + + align:start position:0% +implying that the man may or may not + + + align:start position:0% +implying that the man may or may not +have been may or may not be sinful the + + align:start position:0% +have been may or may not be sinful the + + + align:start position:0% +have been may or may not be sinful the +subjunctive is appropriate if a little + + align:start position:0% +subjunctive is appropriate if a little + + + align:start position:0% +subjunctive is appropriate if a little +archaic even in Modern English I think + + align:start position:0% +archaic even in Modern English I think + + + align:start position:0% +archaic even in Modern English I think +it sounds a lot archaic frankly like + + align:start position:0% +it sounds a lot archaic frankly like + + + align:start position:0% +it sounds a lot archaic frankly like +though he be sinful I mean that's that's + + align:start position:0% +though he be sinful I mean that's that's + + + align:start position:0% +though he be sinful I mean that's that's +sort of that's Ye Old um but compar + + align:start position:0% +sort of that's Ye Old um but compar + + + align:start position:0% +sort of that's Ye Old um but compar +God + + align:start position:0% + + + + align:start position:0% + +is um here the writer can have no doubt + + align:start position:0% +is um here the writer can have no doubt + + + align:start position:0% +is um here the writer can have no doubt +that we do often anger God but the verb + + align:start position:0% +that we do often anger God but the verb + + + align:start position:0% +that we do often anger God but the verb +abela is still in the subjunctive + + align:start position:0% +abela is still in the subjunctive + + + align:start position:0% +abela is still in the subjunctive +mood um so although verbs uh Clauses of + + align:start position:0% +mood um so although verbs uh Clauses of + + + align:start position:0% +mood um so although verbs uh Clauses of +concession um takes the subjunctive and + + align:start position:0% +concession um takes the subjunctive and + + + align:start position:0% +concession um takes the subjunctive and +then ho the hitory the so-called hitory + + align:start position:0% +then ho the hitory the so-called hitory + + + align:start position:0% +then ho the hitory the so-called hitory +subjunctive um let the meat cake may he + + align:start position:0% +subjunctive um let the meat cake may he + + + align:start position:0% +subjunctive um let the meat cake may he +be damned let us love our neighbors um + + align:start position:0% +be damned let us love our neighbors um + + + align:start position:0% +be damned let us love our neighbors um +all + + align:start position:0% +all + + + align:start position:0% +all +that so and you can see from number five + + align:start position:0% +that so and you can see from number five + + + align:start position:0% +that so and you can see from number five +here on the on that you get uh three + + align:start position:0% +here on the on that you get uh three + + + align:start position:0% +here on the on that you get uh three +points for for uh for getting the three + + align:start position:0% +points for for uh for getting the three + + + align:start position:0% +points for for uh for getting the three +that I require on the exam and two Ex + + align:start position:0% +that I require on the exam and two Ex + + + align:start position:0% +that I require on the exam and two Ex +two two extra credit points if you list + + align:start position:0% +two two extra credit points if you list + + + align:start position:0% +two two extra credit points if you list +them all you can absolutely just say + + align:start position:0% +them all you can absolutely just say + + + align:start position:0% +them all you can absolutely just say +bullet point these contrary to fact + + align:start position:0% +bullet point these contrary to fact + + + align:start position:0% +bullet point these contrary to fact +Clauses following verbs of commanding + + align:start position:0% +Clauses following verbs of commanding + + + align:start position:0% +Clauses following verbs of commanding +and Desiring Express doubt or ignorance + + align:start position:0% +and Desiring Express doubt or ignorance + + + align:start position:0% +and Desiring Express doubt or ignorance +concessive clauses hitory subjunctive + + align:start position:0% +concessive clauses hitory subjunctive + + + align:start position:0% +concessive clauses hitory subjunctive +that's all you have to write okay um and + + align:start position:0% +that's all you have to write okay um and + + + align:start position:0% +that's all you have to write okay um and +that's true sort of throughout I'm uh on + + align:start position:0% +that's true sort of throughout I'm uh on + + + align:start position:0% +that's true sort of throughout I'm uh on +this on these sheets I've tended to + + align:start position:0% +this on these sheets I've tended to + + + align:start position:0% +this on these sheets I've tended to +write things out more fully than um than + + align:start position:0% +write things out more fully than um than + + + align:start position:0% +write things out more fully than um than +you need to on the exam just to help + + align:start position:0% +you need to on the exam just to help + + + align:start position:0% +you need to on the exam just to help +help you um but as long as I know what + + align:start position:0% +help you um but as long as I know what + + + align:start position:0% +help you um but as long as I know what +you're talking about that's fine like I + + align:start position:0% +you're talking about that's fine like I + + + align:start position:0% +you're talking about that's fine like I +say I know this is a tightly timed exam + + align:start position:0% +say I know this is a tightly timed exam + + + align:start position:0% +say I know this is a tightly timed exam +all right + + align:start position:0% +all right + + + align:start position:0% +all right +um that is it about verbs although I + + align:start position:0% +um that is it about verbs although I + + + align:start position:0% +um that is it about verbs although I +will go briefly back to um I'm actually + + align:start position:0% +will go briefly back to um I'm actually + + + align:start position:0% +will go briefly back to um I'm actually +going to take you through this list this + + align:start position:0% +going to take you through this list this + + + align:start position:0% +going to take you through this list this +section three of grammatical principles + + align:start position:0% +section three of grammatical principles + + + align:start position:0% +section three of grammatical principles +to reinforce some of the things we + + align:start position:0% +to reinforce some of the things we + + + align:start position:0% +to reinforce some of the things we +talked about earlier so number one + + align:start position:0% +talked about earlier so number one + + + align:start position:0% +talked about earlier so number one +explain the semantic difference between + + align:start position:0% +explain the semantic difference between + + + align:start position:0% +explain the semantic difference between +the two forms of the verb Bon um the B + + align:start position:0% +the two forms of the verb Bon um the B + + + align:start position:0% +the two forms of the verb Bon um the B +forms of the verb are used to express + + align:start position:0% +forms of the verb are used to express + + + align:start position:0% +forms of the verb are used to express +either Futurity or an always true State + + align:start position:0% +either Futurity or an always true State + + + align:start position:0% +either Futurity or an always true State +of Affairs the vowel forms do not carry + + align:start position:0% +of Affairs the vowel forms do not carry + + + align:start position:0% +of Affairs the vowel forms do not carry +those implications it's all you have to + + align:start position:0% +those implications it's all you have to + + + align:start position:0% +those implications it's all you have to +say um number two when would the athorn + + align:start position:0% +say um number two when would the athorn + + + align:start position:0% +say um number two when would the athorn +verb ending be third singular present + + align:start position:0% +verb ending be third singular present + + + align:start position:0% +verb ending be third singular present +instead of as you would expect plural + + align:start position:0% +instead of as you would expect plural + + + align:start position:0% +instead of as you would expect plural +present what would the plural present + + align:start position:0% +present what would the plural present + + + align:start position:0% +present what would the plural present +verb ending of such a verb be this takes + + align:start position:0% +verb ending of such a verb be this takes + + + align:start position:0% +verb ending of such a verb be this takes +us back to class two weak verbs right so + + align:start position:0% +us back to class two weak verbs right so + + + align:start position:0% +us back to class two weak verbs right so +class two weak verbs like louvion take + + align:start position:0% +class two weak verbs like louvion take + + + align:start position:0% +class two weak verbs like louvion take +um end in a e in the third singular + + align:start position:0% +um end in a e in the third singular + + + align:start position:0% +um end in a e in the third singular +present um and their third plural um or + + align:start position:0% +present um and their third plural um or + + + align:start position:0% +present um and their third plural um or +actually all of their plural present + + align:start position:0% +actually all of their plural present + + + align:start position:0% +actually all of their plural present +endings are I a + + align:start position:0% +endings are I a + + + align:start position:0% +endings are I a +thorn um briefly explain when you can + + align:start position:0% +thorn um briefly explain when you can + + + align:start position:0% +thorn um briefly explain when you can +expect to see the strong forms of the + + align:start position:0% +expect to see the strong forms of the + + + align:start position:0% +expect to see the strong forms of the +adjective and when the week uh that + + align:start position:0% +adjective and when the week uh that + + + align:start position:0% +adjective and when the week uh that +takes us very nicely to chapter + + align:start position:0% +takes us very nicely to chapter + + + align:start position:0% +takes us very nicely to chapter + + align:start position:0% + + + + align:start position:0% + +um the + + align:start position:0% + + + + align:start position:0% + +uh the um the most important thing to + + align:start position:0% +uh the um the most important thing to + + + align:start position:0% +uh the um the most important thing to +know about adjectives which I think I + + align:start position:0% +know about adjectives which I think I + + + align:start position:0% +know about adjectives which I think I +emphasized uh last class as well is that + + align:start position:0% +emphasized uh last class as well is that + + + align:start position:0% +emphasized uh last class as well is that +adjectives have strong and weak endings + + align:start position:0% +adjectives have strong and weak endings + + + align:start position:0% +adjectives have strong and weak endings +um but unlike verbs which are always + + align:start position:0% +um but unlike verbs which are always + + + align:start position:0% +um but unlike verbs which are always +just strong or weak weak with the + + align:start position:0% +just strong or weak weak with the + + + align:start position:0% +just strong or weak weak with the +exception of those very few that have um + + align:start position:0% +exception of those very few that have um + + + align:start position:0% +exception of those very few that have um +weak presents and strong pasts all + + align:start position:0% +weak presents and strong pasts all + + + align:start position:0% +weak presents and strong pasts all +adjectives can be either strong or weak + + align:start position:0% +adjectives can be either strong or weak + + + align:start position:0% +adjectives can be either strong or weak +depending on the context + + align:start position:0% + + + + align:start position:0% + +so section three puts it very Punchy + + align:start position:0% +so section three puts it very Punchy + + + align:start position:0% +so section three puts it very Punchy +that adjectives take the weak form if + + align:start position:0% +that adjectives take the weak form if + + + align:start position:0% +that adjectives take the weak form if +they follow a demonstrative pronoun that + + align:start position:0% +they follow a demonstrative pronoun that + + + align:start position:0% +they follow a demonstrative pronoun that +is a form of + + align:start position:0% +is a form of + + + align:start position:0% +is a form of +SE um a possess adjective like mean or a + + align:start position:0% +SE um a possess adjective like mean or a + + + align:start position:0% +SE um a possess adjective like mean or a +um or a generative noun or noun phrase + + align:start position:0% +um or a generative noun or noun phrase + + + align:start position:0% +um or a generative noun or noun phrase +that's what that little bracket noun + + align:start position:0% +that's what that little bracket noun + + + align:start position:0% +that's what that little bracket noun +bracket phrase either a genitive noun or + + align:start position:0% +bracket phrase either a genitive noun or + + + align:start position:0% +bracket phrase either a genitive noun or +a genitive noun phrase um otherwise they + + align:start position:0% +a genitive noun phrase um otherwise they + + + align:start position:0% +a genitive noun phrase um otherwise they +take the strong form yes it was really + + align:start position:0% +take the strong form yes it was really + + + align:start position:0% +take the strong form yes it was really +unclear to me from text does this mean + + align:start position:0% +unclear to me from text does this mean + + + align:start position:0% +unclear to me from text does this mean +literally directly follow or like as a + + align:start position:0% +literally directly follow or like as a + + + align:start position:0% +literally directly follow or like as a +part of the same overall noun + + align:start position:0% +part of the same overall noun + + + align:start position:0% +part of the same overall noun +phrase um like because obviously you can + + align:start position:0% +phrase um like because obviously you can + + + align:start position:0% +phrase um like because obviously you can +separate things up in Old English yes + + align:start position:0% +separate things up in Old English yes + + + align:start position:0% +separate things up in Old English yes +and so follow is not like linearly + + align:start position:0% +and so follow is not like linearly + + + align:start position:0% +and so follow is not like linearly +follow or like follow if we like + + align:start position:0% +follow or like follow if we like + + + align:start position:0% +follow or like follow if we like +reconstructed some sort of like nice + + align:start position:0% +reconstructed some sort of like nice + + + align:start position:0% +reconstructed some sort of like nice +tree like if the specifier is empty or + + align:start position:0% +tree like if the specifier is empty or + + + align:start position:0% +tree like if the specifier is empty or +not yeah so this is it's it's a good + + align:start position:0% +not yeah so this is it's it's a good + + + align:start position:0% +not yeah so this is it's it's a good +question and I it's it's pretty much + + align:start position:0% +question and I it's it's pretty much + + + align:start position:0% +question and I it's it's pretty much +directly follow yeah yeah yeah yeah so + + align:start position:0% +directly follow yeah yeah yeah yeah so + + + align:start position:0% +directly follow yeah yeah yeah yeah so +like SE and and the reason for that um + + align:start position:0% +like SE and and the reason for that um + + + align:start position:0% +like SE and and the reason for that um +is that basically the reason that the + + align:start position:0% +is that basically the reason that the + + + align:start position:0% +is that basically the reason that the +reason that how do I back up and say + + align:start position:0% +reason that how do I back up and say + + + align:start position:0% +reason that how do I back up and say +this um + + align:start position:0% +this um + + + align:start position:0% +this um +so what's common to okay so if I put up + + align:start position:0% +so what's common to okay so if I put up + + + align:start position:0% +so what's common to okay so if I put up +on the board here + + align:start position:0% + + + + align:start position:0% + +that if we have weak adjective weak + + align:start position:0% +that if we have weak adjective weak + + + align:start position:0% +that if we have weak adjective weak +adjectival forms + + align:start position:0% +adjectival forms + + + align:start position:0% +adjectival forms +[Music] + + align:start position:0% + + + + align:start position:0% + +after SE that se um what was the other + + align:start position:0% +after SE that se um what was the other + + + align:start position:0% +after SE that se um what was the other +one uh + + align:start position:0% + + + + align:start position:0% + +genitive genitive noun and genitive noun + + align:start position:0% +genitive genitive noun and genitive noun + + + align:start position:0% +genitive genitive noun and genitive noun +phrases um and then uh possessive + + align:start position:0% + + + + align:start position:0% + +adjectives um all of those forms um tend + + align:start position:0% +adjectives um all of those forms um tend + + + align:start position:0% +adjectives um all of those forms um tend +to tell us quite a bit about the noun + + align:start position:0% +to tell us quite a bit about the noun + + + align:start position:0% +to tell us quite a bit about the noun +that they modify um so if you say so for + + align:start position:0% +that they modify um so if you say so for + + + align:start position:0% +that they modify um so if you say so for +example say we know that whatever noun + + align:start position:0% +example say we know that whatever noun + + + align:start position:0% +example say we know that whatever noun +it modifies is nominative singular + + align:start position:0% +it modifies is nominative singular + + + align:start position:0% +it modifies is nominative singular +masculine because that's the only thing + + align:start position:0% +masculine because that's the only thing + + + align:start position:0% +masculine because that's the only thing +that se can be which means that the + + align:start position:0% +that se can be which means that the + + + align:start position:0% +that se can be which means that the +adjective itself doesn't have to give us + + align:start position:0% +adjective itself doesn't have to give us + + + align:start position:0% +adjective itself doesn't have to give us +as much information in order for us to + + align:start position:0% +as much information in order for us to + + + align:start position:0% +as much information in order for us to +be able to parse the sentence correctly + + align:start position:0% +be able to parse the sentence correctly + + + align:start position:0% +be able to parse the sentence correctly +whereas if we lack any of that then then + + align:start position:0% +whereas if we lack any of that then then + + + align:start position:0% +whereas if we lack any of that then then +we need the strong adjective endings + + align:start position:0% +we need the strong adjective endings + + + align:start position:0% +we need the strong adjective endings +basically to help guide us as to what + + align:start position:0% +basically to help guide us as to what + + + align:start position:0% +basically to help guide us as to what +the correct um what the case of the noun + + align:start position:0% +the correct um what the case of the noun + + + align:start position:0% +the correct um what the case of the noun +in question is right and the reason that + + align:start position:0% +in question is right and the reason that + + + align:start position:0% +in question is right and the reason that +this comes up we see this come up for + + align:start position:0% +this comes up we see this come up for + + + align:start position:0% +this comes up we see this come up for +example um so remember that that uh uh + + align:start position:0% +example um so remember that that uh uh + + + align:start position:0% +example um so remember that that uh uh +let's take a + + align:start position:0% +let's take a + + + align:start position:0% +let's take a +strong let's take a strong masculine + + align:start position:0% +strong let's take a strong masculine + + + align:start position:0% +strong let's take a strong masculine +noun as an example remember that if you + + align:start position:0% +noun as an example remember that if you + + + align:start position:0% +noun as an example remember that if you +go back to + + align:start position:0% +go back to + + + align:start position:0% +go back to +6.1 there is um there's no difference in + + align:start position:0% +6.1 there is um there's no difference in + + + align:start position:0% +6.1 there is um there's no difference in +ending there is no ending for the + + align:start position:0% +ending there is no ending for the + + + align:start position:0% +ending there is no ending for the +accusative singular masculine um which + + align:start position:0% +accusative singular masculine um which + + + align:start position:0% +accusative singular masculine um which +means that it looks exactly like the + + align:start position:0% +means that it looks exactly like the + + + align:start position:0% +means that it looks exactly like the +nominative singular masculine and could + + align:start position:0% +nominative singular masculine and could + + + align:start position:0% +nominative singular masculine and could +be either the subject or the direct + + align:start position:0% +be either the subject or the direct + + + align:start position:0% +be either the subject or the direct +object of the sentence the strong + + align:start position:0% +object of the sentence the strong + + + align:start position:0% +object of the sentence the strong +adjective endings basically help us out + + align:start position:0% +adjective endings basically help us out + + + align:start position:0% +adjective endings basically help us out +by indicating which of those it is so if + + align:start position:0% +by indicating which of those it is so if + + + align:start position:0% +by indicating which of those it is so if +you take a look at the strong adjective + + align:start position:0% +you take a look at the strong adjective + + + align:start position:0% +you take a look at the strong adjective +endings in uh p pa page 90 table + + align:start position:0% +endings in uh p pa page 90 table + + + align:start position:0% +endings in uh p pa page 90 table +8.1 you see that the strong ad uh + + align:start position:0% +8.1 you see that the strong ad uh + + + align:start position:0% +8.1 you see that the strong ad uh +accusative singular masculine ending is + + align:start position:0% +accusative singular masculine ending is + + + align:start position:0% +accusative singular masculine ending is +NE um and so that's going to help guide + + align:start position:0% +NE um and so that's going to help guide + + + align:start position:0% +NE um and so that's going to help guide +us as to what um the what the noun + + align:start position:0% +us as to what um the what the noun + + + align:start position:0% +us as to what um the what the noun +itself is doing in the sentence this is + + align:start position:0% +itself is doing in the sentence this is + + + align:start position:0% +itself is doing in the sentence this is +what I meant by the way in saying that + + align:start position:0% +what I meant by the way in saying that + + + align:start position:0% +what I meant by the way in saying that +tables 5.3 and 5.4 the demonstrative + + align:start position:0% +tables 5.3 and 5.4 the demonstrative + + + align:start position:0% +tables 5.3 and 5.4 the demonstrative +pronouns and the third singular personal + + align:start position:0% +pronouns and the third singular personal + + + align:start position:0% +pronouns and the third singular personal +pronouns help help kind of give us a + + align:start position:0% +pronouns help help kind of give us a + + + align:start position:0% +pronouns help help kind of give us a +guide to what else is going on UMC in or + + align:start position:0% +guide to what else is going on UMC in or + + + align:start position:0% +guide to what else is going on UMC in or +in other paradigms because remember H th + + align:start position:0% +in other paradigms because remember H th + + + align:start position:0% +in other paradigms because remember H th +those accusative singular masculine + + align:start position:0% +those accusative singular masculine + + + align:start position:0% +those accusative singular masculine +forms that NE of H and thaa is sort of + + align:start position:0% +forms that NE of H and thaa is sort of + + + align:start position:0% +forms that NE of H and thaa is sort of +reproduced or evoked by the ne of the + + align:start position:0% +reproduced or evoked by the ne of the + + + align:start position:0% +reproduced or evoked by the ne of the +accusative singular masculine strong + + align:start position:0% +accusative singular masculine strong + + + align:start position:0% +accusative singular masculine strong +adjectival form okay + + align:start position:0% + + + + align:start position:0% + +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +um well these are actually the + + align:start position:0% +um well these are actually the + + + align:start position:0% +um well these are actually the +similarities are nicely highlighted on + + align:start position:0% +similarities are nicely highlighted on + + + align:start position:0% +similarities are nicely highlighted on +table + + align:start position:0% +table + + + align:start position:0% +table +8.2 um when you actually when they + + align:start position:0% +8.2 um when you actually when they + + + align:start position:0% +8.2 um when you actually when they +actually put the uh uh put it all put + + align:start position:0% +actually put the uh uh put it all put + + + align:start position:0% +actually put the uh uh put it all put +the endings together with the adjective + + align:start position:0% +the endings together with the adjective + + + align:start position:0% +the endings together with the adjective +go um you can see God NE is emphasized + + align:start position:0% +go um you can see God NE is emphasized + + + align:start position:0% +go um you can see God NE is emphasized +is boldfaced because of that resemblance + + align:start position:0% +is boldfaced because of that resemblance + + + align:start position:0% +is boldfaced because of that resemblance +to hin um and th um and the others are + + align:start position:0% +to hin um and th um and the others are + + + align:start position:0% +to hin um and th um and the others are +as well you do not need to be able you + + align:start position:0% +as well you do not need to be able you + + + align:start position:0% +as well you do not need to be able you +don't need to memorize any of these + + align:start position:0% +don't need to memorize any of these + + + align:start position:0% +don't need to memorize any of these +paradigms in the adjectives you just + + align:start position:0% +paradigms in the adjectives you just + + + align:start position:0% +paradigms in the adjectives you just +need to be able to parse them + + align:start position:0% +need to be able to parse them + + + align:start position:0% +need to be able to parse them +appropriately um when you're when you're + + align:start position:0% +appropriately um when you're when you're + + + align:start position:0% +appropriately um when you're when you're +faced with + + align:start position:0% + + + + align:start position:0% + +them one thing to emphasize here is that + + align:start position:0% +them one thing to emphasize here is that + + + align:start position:0% +them one thing to emphasize here is that +um ending in the dative we're already + + align:start position:0% +um ending in the dative we're already + + + align:start position:0% +um ending in the dative we're already +familiar with u m as a dative but in uh + + align:start position:0% +familiar with u m as a dative but in uh + + + align:start position:0% +familiar with u m as a dative but in uh +nouns it's been dative + + align:start position:0% +nouns it's been dative + + + align:start position:0% +nouns it's been dative +plural um can also be the dative + + align:start position:0% +plural um can also be the dative + + + align:start position:0% +plural um can also be the dative +singular masculine or neuter um so + + align:start position:0% +singular masculine or neuter um so + + + align:start position:0% +singular masculine or neuter um so +that's boldfaced uh in table 8.2 really + + align:start position:0% +that's boldfaced uh in table 8.2 really + + + align:start position:0% +that's boldfaced uh in table 8.2 really +pay attention to that that's actually + + align:start position:0% + + + + align:start position:0% + +number yeah number + + align:start position:0% +number yeah number + + + align:start position:0% +number yeah number +seven um on the top of the third page of + + align:start position:0% +seven um on the top of the third page of + + + align:start position:0% +seven um on the top of the third page of +the handout what are the three + + align:start position:0% +the handout what are the three + + + align:start position:0% +the handout what are the three +possibilities about a given word that + + align:start position:0% +possibilities about a given word that + + + align:start position:0% +possibilities about a given word that +should occur to you upon seeing the + + align:start position:0% +should occur to you upon seeing the + + + align:start position:0% +should occur to you upon seeing the +ending dative plural at adjective or + + align:start position:0% +ending dative plural at adjective or + + + align:start position:0% +ending dative plural at adjective or +noun um but also dative singular strong + + align:start position:0% +noun um but also dative singular strong + + + align:start position:0% +noun um but also dative singular strong +adjective all + + align:start position:0% +adjective all + + + align:start position:0% +adjective all +right + + align:start position:0% +right + + + align:start position:0% +right +um the weak adjective endings where you + + align:start position:0% +um the weak adjective endings where you + + + align:start position:0% +um the weak adjective endings where you +just have like a ton of a 's that should + + align:start position:0% +just have like a ton of a 's that should + + + align:start position:0% +just have like a ton of a 's that should +remind you of the weak noun + + align:start position:0% + + + + align:start position:0% + +endings top of page + + align:start position:0% +endings top of page + + + align:start position:0% +endings top of page +92 just + + align:start position:0% +92 just + + + align:start position:0% +92 just +reinforces that the you need to be alive + + align:start position:0% +reinforces that the you need to be alive + + + align:start position:0% +reinforces that the you need to be alive +to the fact of the + + align:start position:0% +to the fact of the + + + align:start position:0% +to the fact of the +uh dative singular masculine and neuter + + align:start position:0% +uh dative singular masculine and neuter + + + align:start position:0% +uh dative singular masculine and neuter +being ending in U um remember it this + + align:start position:0% +being ending in U um remember it this + + + align:start position:0% +being ending in U um remember it this +way U is always dative and in nouns it + + align:start position:0% +way U is always dative and in nouns it + + + align:start position:0% +way U is always dative and in nouns it +is always plural in adjectives it could + + align:start position:0% +is always plural in adjectives it could + + + align:start position:0% +is always plural in adjectives it could +be either all + + align:start position:0% + + + + align:start position:0% + +right comparative adjectives which we + + align:start position:0% +right comparative adjectives which we + + + align:start position:0% +right comparative adjectives which we +actually um which we actually came + + align:start position:0% +actually um which we actually came + + + align:start position:0% +actually um which we actually came +across last time with the serpent the + + align:start position:0% +across last time with the serpent the + + + align:start position:0% +across last time with the serpent the +serpent was y um that's and that's these + + align:start position:0% +serpent was y um that's and that's these + + + align:start position:0% +serpent was y um that's and that's these +are created by adding R between the root + + align:start position:0% +are created by adding R between the root + + + align:start position:0% +are created by adding R between the root +syllable and the inflectional ending um + + align:start position:0% +syllable and the inflectional ending um + + + align:start position:0% +syllable and the inflectional ending um +and comparison comparative adjectives + + align:start position:0% +and comparison comparative adjectives + + + align:start position:0% +and comparison comparative adjectives +are always weak regardless of those uh + + align:start position:0% +are always weak regardless of those uh + + + align:start position:0% +are always weak regardless of those uh +those rules there + + align:start position:0% +those rules there + + + align:start position:0% +those rules there +um some have IM + + align:start position:0% +um some have IM + + + align:start position:0% +um some have IM +mutation but you don't need to worry too + + align:start position:0% +mutation but you don't need to worry too + + + align:start position:0% +mutation but you don't need to worry too +much about that um bottom of P or middle + + align:start position:0% +much about that um bottom of P or middle + + + align:start position:0% +much about that um bottom of P or middle +of page 94 rather comparative adjectives + + align:start position:0% +of page 94 rather comparative adjectives + + + align:start position:0% +of page 94 rather comparative adjectives +sometimes cause problems for students + + align:start position:0% +sometimes cause problems for students + + + align:start position:0% +sometimes cause problems for students +who are not on the lookout for them or + + align:start position:0% +who are not on the lookout for them or + + + align:start position:0% +who are not on the lookout for them or +who confuse comparative r with the r of + + align:start position:0% +who confuse comparative r with the r of + + + align:start position:0% +who confuse comparative r with the r of +the feminine genitive sing or dative + + align:start position:0% +the feminine genitive sing or dative + + + align:start position:0% +the feminine genitive sing or dative +singular ending re or the genitive + + align:start position:0% +singular ending re or the genitive + + + align:start position:0% +singular ending re or the genitive +plural r a um again context should help + + align:start position:0% +plural r a um again context should help + + + align:start position:0% +plural r a um again context should help +here um just remember that it's a + + align:start position:0% +here um just remember that it's a + + + align:start position:0% +here um just remember that it's a +possibility that it that it may that it + + align:start position:0% +possibility that it that it may that it + + + align:start position:0% +possibility that it that it may that it +be it is possible that it be to use the + + align:start position:0% +be it is possible that it be to use the + + + align:start position:0% +be it is possible that it be to use the +subjunctive um a uh a comparative + + align:start position:0% + + + + align:start position:0% + +adjective the shift by the way from + + align:start position:0% + + + + align:start position:0% + +um this shift from ra + + align:start position:0% +um this shift from ra + + + align:start position:0% +um this shift from ra +a + + align:start position:0% +a + + + align:start position:0% +a +to e r right this is how because this is + + align:start position:0% +to e r right this is how because this is + + + align:start position:0% +to e r right this is how because this is +how we typically indicate a a + + align:start position:0% +how we typically indicate a a + + + align:start position:0% +how we typically indicate a a +comparative adjective from weak weaker + + align:start position:0% +comparative adjective from weak weaker + + + align:start position:0% +comparative adjective from weak weaker +um this the way that these uh these + + align:start position:0% +um this the way that these uh these + + + align:start position:0% +um this the way that these uh these +letters shift this is called + + align:start position:0% +letters shift this is called + + + align:start position:0% +letters shift this is called +metathesis um and it happens actually a + + align:start position:0% +metathesis um and it happens actually a + + + align:start position:0% +metathesis um and it happens actually a +lot in Old English I'll give um other + + align:start position:0% +lot in Old English I'll give um other + + + align:start position:0% +lot in Old English I'll give um other +examples as we come across + + align:start position:0% + + + + align:start position:0% + +them sometimes in fact so + + align:start position:0% + + + + align:start position:0% + +like so brid is the Middle English word + + align:start position:0% +like so brid is the Middle English word + + + align:start position:0% +like so brid is the Middle English word +for for bird um bird is the Middle + + align:start position:0% +for for bird um bird is the Middle + + + align:start position:0% +for for bird um bird is the Middle +English word for woman um and that's + + align:start position:0% +English word for woman um and that's + + + align:start position:0% +English word for woman um and that's +going to shift to and those are going to + + align:start position:0% +going to shift to and those are going to + + + align:start position:0% +going to shift to and those are going to +shift um bird + + align:start position:0% +shift um bird + + + align:start position:0% +shift um bird +um this is Middle + + align:start position:0% + + + + align:start position:0% + +English BRD is going to become bird and + + align:start position:0% +English BRD is going to become bird and + + + align:start position:0% +English BRD is going to become bird and +bird is going to become bride um + + align:start position:0% +bird is going to become bride um + + + align:start position:0% +bird is going to become bride um +so just a + + align:start position:0% +so just a + + + align:start position:0% +so just a +little just a little + + align:start position:0% +little just a little + + + align:start position:0% +little just a little +tidbit + + align:start position:0% + + + + align:start position:0% + +um finally + + align:start position:0% +um finally + + + align:start position:0% +um finally +8.5 the adjective in the noun phrase + + align:start position:0% +8.5 the adjective in the noun phrase + + + align:start position:0% +8.5 the adjective in the noun phrase +this is basically just um reminding us + + align:start position:0% +this is basically just um reminding us + + + align:start position:0% +this is basically just um reminding us +that adjectival + + align:start position:0% +that adjectival + + + align:start position:0% +that adjectival +endings how do I put this I think the + + align:start position:0% +endings how do I put this I think the + + + align:start position:0% +endings how do I put this I think the +most important thing to to note here is + + align:start position:0% +most important thing to to note here is + + + align:start position:0% +most important thing to to note here is +just that strong adjectives are very + + align:start position:0% +just that strong adjectives are very + + + align:start position:0% +just that strong adjectives are very +very very helpful because they're much + + align:start position:0% +very very helpful because they're much + + + align:start position:0% +very very helpful because they're much +less ambiguous than almost any other + + align:start position:0% +less ambiguous than almost any other + + + align:start position:0% +less ambiguous than almost any other +form that you're going to run across in + + align:start position:0% +form that you're going to run across in + + + align:start position:0% +form that you're going to run across in +Old English um so just be on the lookout + + align:start position:0% +Old English um so just be on the lookout + + + align:start position:0% +Old English um so just be on the lookout +for them um wherever you see + + align:start position:0% + + + + align:start position:0% + +them all right any questions on all + + align:start position:0% + + + + align:start position:0% + +that taking a look at what else from + + align:start position:0% +that taking a look at what else from + + + align:start position:0% +that taking a look at what else from +section three I should + + align:start position:0% +section three I should + + + align:start position:0% +section three I should +highlight um so we've already done + + align:start position:0% +highlight um so we've already done + + + align:start position:0% +highlight um so we've already done +numbers one two and three number four + + align:start position:0% +numbers one two and three number four + + + align:start position:0% +numbers one two and three number four +what two words can you expect to see + + align:start position:0% +what two words can you expect to see + + + align:start position:0% +what two words can you expect to see +serving as a relative pronoun what is + + align:start position:0% +serving as a relative pronoun what is + + + align:start position:0% +serving as a relative pronoun what is +the difference between them the two + + align:start position:0% +the difference between them the two + + + align:start position:0% +the difference between them the two +possible words are the and a form of + + align:start position:0% +possible words are the and a form of + + + align:start position:0% +possible words are the and a form of +Seth um the former is in declinable the + + align:start position:0% +Seth um the former is in declinable the + + + align:start position:0% +Seth um the former is in declinable the +latter agrees in case and number with + + align:start position:0% +latter agrees in case and number with + + + align:start position:0% +latter agrees in case and number with +the role that it serves in the following + + align:start position:0% +the role that it serves in the following + + + align:start position:0% +the role that it serves in the following +Clause um number five we already did + + align:start position:0% +Clause um number five we already did + + + align:start position:0% +Clause um number five we already did +that's the subjunctive number six what's + + align:start position:0% +that's the subjunctive number six what's + + + align:start position:0% +that's the subjunctive number six what's +unusual about the second and third + + align:start position:0% +unusual about the second and third + + + align:start position:0% +unusual about the second and third +person singular forms of Old English + + align:start position:0% +person singular forms of Old English + + + align:start position:0% +person singular forms of Old English +strong + + align:start position:0% +strong + + + align:start position:0% +strong +verbs is the distinctiveness of these + + align:start position:0% +verbs is the distinctiveness of these + + + align:start position:0% +verbs is the distinctiveness of these +forms related to the vowel gradations + + align:start position:0% +forms related to the vowel gradations + + + align:start position:0% +forms related to the vowel gradations +that govern the strong verb classes + + align:start position:0% +that govern the strong verb classes + + + align:start position:0% +that govern the strong verb classes +answer Turn the Page they display IM + + align:start position:0% +answer Turn the Page they display IM + + + align:start position:0% +answer Turn the Page they display IM +mutation those forms but this Val shift + + align:start position:0% +mutation those forms but this Val shift + + + align:start position:0% +mutation those forms but this Val shift +is not related to the Val gradations so + + align:start position:0% +is not related to the Val gradations so + + + align:start position:0% +is not related to the Val gradations so +you can just say im mutation no is + + align:start position:0% +you can just say im mutation no is + + + align:start position:0% +you can just say im mutation no is +enough on the exam all + + align:start position:0% +enough on the exam all + + + align:start position:0% +enough on the exam all +right talked about number seven oh + + align:start position:0% +right talked about number seven oh + + + align:start position:0% +right talked about number seven oh +number eight this is a good one what are + + align:start position:0% +number eight this is a good one what are + + + align:start position:0% +number eight this is a good one what are +three possibilities about a given word + + align:start position:0% +three possibilities about a given word + + + align:start position:0% +three possibilities about a given word +that should occur to you upon seeing the + + align:start position:0% +that should occur to you upon seeing the + + + align:start position:0% +that should occur to you upon seeing the +a an ending + + align:start position:0% +a an ending + + + align:start position:0% +a an ending +infinitive one of many weak noun forms + + align:start position:0% +infinitive one of many weak noun forms + + + align:start position:0% +infinitive one of many weak noun forms +one of many weak adjective + + align:start position:0% +one of many weak adjective + + + align:start position:0% +one of many weak adjective +forms um and then number nine + + align:start position:0% +forms um and then number nine + + + align:start position:0% +forms um and then number nine +R A ending could be genitive plural + + align:start position:0% +R A ending could be genitive plural + + + align:start position:0% +R A ending could be genitive plural +could be comparative adjective um these + + align:start position:0% +could be comparative adjective um these + + + align:start position:0% +could be comparative adjective um these +are not necessarily exclusive lists by + + align:start position:0% +are not necessarily exclusive lists by + + + align:start position:0% +are not necessarily exclusive lists by +the way but they are um they are what uh + + align:start position:0% +the way but they are um they are what uh + + + align:start position:0% +the way but they are um they are what uh +they are the most common and what I'm um + + align:start position:0% +they are the most common and what I'm um + + + align:start position:0% +they are the most common and what I'm um +testing you on number 10 I don't + + align:start position:0% +testing you on number 10 I don't + + + align:start position:0% +testing you on number 10 I don't +actually know that we have talked about + + align:start position:0% +actually know that we have talked about + + + align:start position:0% +actually know that we have talked about +this much so many Old English + + align:start position:0% +this much so many Old English + + + align:start position:0% +this much so many Old English +prepositions can take both the dative + + align:start position:0% +prepositions can take both the dative + + + align:start position:0% +prepositions can take both the dative +and the accusative case what's the + + align:start position:0% +and the accusative case what's the + + + align:start position:0% +and the accusative case what's the +semantic suggestion of using one as + + align:start position:0% +semantic suggestion of using one as + + + align:start position:0% +semantic suggestion of using one as +opposed to the other um this is this is + + align:start position:0% +opposed to the other um this is this is + + + align:start position:0% +opposed to the other um this is this is +actually a hold over from Latin and well + + align:start position:0% +actually a hold over from Latin and well + + + align:start position:0% +actually a hold over from Latin and well +I shouldn't say a hold over but it's + + align:start position:0% +I shouldn't say a hold over but it's + + + align:start position:0% +I shouldn't say a hold over but it's +parallel to what we see in Latin and + + align:start position:0% +parallel to what we see in Latin and + + + align:start position:0% +parallel to what we see in Latin and +Greek the dative implies rest or + + align:start position:0% +Greek the dative implies rest or + + + align:start position:0% +Greek the dative implies rest or +stability the accusative implies motion + + align:start position:0% +stability the accusative implies motion + + + align:start position:0% +stability the accusative implies motion +or purpose so for example if I say the + + align:start position:0% +or purpose so for example if I say the + + + align:start position:0% +or purpose so for example if I say the +word um if the in the very simple + + align:start position:0% +word um if the in the very simple + + + align:start position:0% +word um if the in the very simple +preposition prepositional phrase in the + + align:start position:0% +preposition prepositional phrase in the + + + align:start position:0% +preposition prepositional phrase in the +room um if in the room room is in the + + align:start position:0% +room um if in the room room is in the + + + align:start position:0% +room um if in the room room is in the +dative it suggests that I'm just in the + + align:start position:0% +dative it suggests that I'm just in the + + + align:start position:0% +dative it suggests that I'm just in the +room sitting put staying put um if it's + + align:start position:0% +room sitting put staying put um if it's + + + align:start position:0% +room sitting put staying put um if it's +in the room and room is in the uh the + + align:start position:0% +in the room and room is in the uh the + + + align:start position:0% +in the room and room is in the uh the +accusative that would suggest into the + + align:start position:0% +accusative that would suggest into the + + + align:start position:0% +accusative that would suggest into the +room all right so you may want to you + + align:start position:0% +room all right so you may want to you + + + align:start position:0% +room all right so you may want to you +may want to change your translation + + align:start position:0% +may want to change your translation + + + align:start position:0% +may want to change your translation +depending on the case of the following + + align:start position:0% +depending on the case of the following + + + align:start position:0% +depending on the case of the following +um + + align:start position:0% +um + + + align:start position:0% +um +noun what is a predate present verb + + align:start position:0% +noun what is a predate present verb + + + align:start position:0% +noun what is a predate present verb +we've just gone over that um you can + + align:start position:0% +we've just gone over that um you can + + + align:start position:0% +we've just gone over that um you can +list some you can list you should be + + align:start position:0% +list some you can list you should be + + + align:start position:0% +list some you can list you should be +able to list four common ones um and + + align:start position:0% +able to list four common ones um and + + + align:start position:0% +able to list four common ones um and +then compound subjects we're actually + + align:start position:0% +then compound subjects we're actually + + + align:start position:0% +then compound subjects we're actually +going to talk about that a little bit + + align:start position:0% +going to talk about that a little bit + + + align:start position:0% +going to talk about that a little bit +later so I think that's the only part of + + align:start position:0% +later so I think that's the only part of + + + align:start position:0% +later so I think that's the only part of +section three that at this point we have + + align:start position:0% +section three that at this point we have + + + align:start position:0% +section three that at this point we have +not yet + + align:start position:0% + + + + align:start position:0% + +covered \ No newline at end of file diff --git a/xc9DDSbf0NQ.txt b/xc9DDSbf0NQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..a8570df85756add68119ec21f5d1f31b782df821 --- /dev/null +++ b/xc9DDSbf0NQ.txt @@ -0,0 +1,3017 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So today we're +going to talk about bit + +hacking, which is a topic that +has a long, long history in + +computer science. + +We'll only cover on a few +of the techniques. + +So let's just get going. + +So I want to swap +two integers. + +So I think most of you would +know how to write a program to + +swap two integers. + +And it would look something +like this. + +And mostly this is pseudocode. + +I'm not going to be doing +declarations of types and + +writing full code, in order to +make sure things get on slides + +and so forth. + +So what do you do? + +You assign a temporary +to the value of x. + +You then let x take +the value of y. + +And then you let y take the +value of the temporary. + +What could be simpler? + +Well how about doing it +without a temporary? + +So how do you swap two numbers +without a temporary? + +So here's one way. + +So what's going on there? + +So the carrot is an XOR, +exclusive or, OK? + +So here's what's going on. + +So let's do an example first. + +So I have x and y. + +I then let x be the +XOR of x and y. + +So, as you see, that first bit +is the XOR of one and zero. + +The second bit is the XOR of +zero and zero, which is zero. + +The third bit is the +XOR of one and one. + +That's zero. + +And so forth throughout +the bits. + +So then I let y be the +XOR of x and y. + +And then, finally, I let x be +the XOR of x and y again. + +And now, if you notice, +that number is the + +same as that number. + +And that number is the +same as that number. + +Magic. + +We're going to see a lot of +magic today actually. + +OK? + +We're going to see a lot of +magic today, no temporary. + +Why does this work? + +So the reason this works as a +great property of XOR is that + +it's its own inverse. + +So if you take x exclusive or +y, and you exclusive or that + +with y, you get x. + +If you were to exclusive or that +with x you would get y. + +So that first step is basically +putting in here the + +XOR of x and y so that when you +end up on the next step + +computing the XOR of y +and this, you get x. + +So now you've got x here. + +And you've now got the original +x XORed with y here. + +So to get back the value of +y you just XOR out the x. + +So it swaps them. + +Whose brain hurts? + +You can study these later on. + +But a pretty neat trick, +pretty neat trick. + +Does it perform well? + +Turns out not really. + +And the other way is actually +a better way of doing it, + +generally, with most compilers +and architectures. + +And the reason is because the +other way of doing it you can + +actually, essentially, pull two +things out of memory, one + +into a temporary one-- + +and then stick them +back like this. + +That's what the compiler +ends up doing. + +Where as this one, it has +to wait for each step. + +And so you don't get to exploit +instruction-level + +parallelism. + +Remember from last time +instruction-level parallelism + +is the fact that a processor +can issue more than one + +instruction at a given step. + +And here, this sequence of +operations, each step has to + +wait until the previous +one is computed + +before it can execute. + +So you get no instruction +parallelism in this. + +So it's not particularly +high performing. + +But there are other places +where we'll use + +this kind of property. + +But it's a neat bit hack, +swap two things + +without using a temporary. + +Now here's a real bit hack. + +And a real useful one. + +Finding the minimum of two +integers, x and y. + +Gee whiz, let me just call a +sub routine or something. + +So you might be tempted to write +something like this; if + +x is less than y then +the result is x. + +Otherwise, the result is y. + +Seems pretty straightforward. + +Or if you know a little bit more +c, you can write it with + +this sort of cryptic if x is +less than y, then x else y. + +So those are two equivalent +c ways of doing things. + +So what's wrong with that? + +Well nothing if you don't +mind slow code. + +In fact, for something like +this the compiler actually + +will optimize it to +deal with it. + +But let me just point +out a couple things. + +First of all, the processor +has within it a branch + +prediction unit. + +Whenever it comes to a branch +it guesses which way the + +branch is going to go, and +proceeds to speculatively + +execute along that path. + +If it turns out to be wrong it +says, whoa, hold your horses, + +got to go that way. + +To do that, it empties the +processor pipeline. + +And that takes, on the +machines we're + +using, around 16 cycles. + +So you don't want to have +branches that are + +mis-predicted. + +And, in particular, what +you want to look for in + +conditional instructions, is +whether they're predictable. + +So something that's almost all +the time branching the same + +way, that's a predictable +branch. + +The hardware is very smart +about figuring out how to + +predict that, and will make +the right prediction. + +And you won't pay any +performance penalty. + +But if you have something where +you don't know which way + +it goes, so in a code like this, +the architecture isn't + +going to know. + +If you just throw at it various +pairs of x and y it's + +a 50/50 guess as to whether +it guesses right. + +So half the time it's going to +predict the wrong thing. + +So the compiler might +be smart enough. + +But maybe not. + +But you can be sure. + +And here's a way +of being sure. + +You write this code. + +What is going on there? + +So here we go. + +We're taking x less than y, +and taking a minus sign. + +Yikes, what's that do? + +Well c represents the Boolean's +true and false with + +the integers one and +zero, respectively. + +So if you execute the operator +x less than y, as opposed to + +doing a conditional based on x +bit less than y, it returns to + +either a zero or a one, +depending upon whether it was + +successful. + +So when you take the negation +of that, this is + +either zero or one. + +It's either going to +be zero or minus 1. + +And what is minus 1 in two's +complement arithmetic? + +It's a word filled +all with ones. + +So you either get a word all +filled with zeros or you get a + +word all filled with ones. + +So if x is less than y you get +a word all filled with one's. + +So then what are you doing? + +You're doing x XOR +y, and you're + +ending it with all ones. + +Well that's a noop to end +it with all ones. + +To mask something-- if I do an +and of anything with one, I + +get whatever the thing is. + +So this expression ends up +evaluating to just x XOR y. + +Great, then what? + +I take y here and I XOR it, I +get back x because of that + +inverse property of XOR. + +So if x is less than y, then +r gets the value of x. + +If x is greater or equal to +y then this expression + +evaluates to zero. + +And a word of zeroes ended with +x or y gives you a word + +of zeroes because zero is +an annihilator for and. + +Wherever you and with zero, it +doesn't matter what it is. + +You get zero. + +So therefore this just becomes +r equals y because + +y XOR zero is y. + +So pretty clever, is +this really better? + +Seems like an awful +lot of operations. + +Well the answer is yes it is, +because all of this goes on + +within the processing unit +rather than with anything + +having to do with memory. + +It gets the values for x and y +to begin with and then it's + +all instructions within +the processing unit. + +Those typically take +one cycle. + +And if there's any parallelism +in it the parallelism will be + +able to execute even more than +one operation per cycle. + +In fact, the machines we're +using have are six issue. + +They can run six operation +simultaneously, + +each taking a cycle. + +So the difference between that +and going out to memory is + +really quite considerable. + +So everybody follow that? + +Pretty cute trick, how +to make it go fast. + +Yes, question? + +AUDIENCE: Doesn't the expression +that's tested, + +doesn't it have to be +[? weighed for ?] the inner + +expression before you take-- + +PROFESSOR: There's no-- +this is a comparison. + +This is operated like a-- + +so there's no compare +instruction there. + +It's a CPU operation. + +It's an arithmetic and logical +operation of the CPU that it + +can do in one cycle, +is to compare. + +The normal thing that you're +trying to do if you have an if + +is you're trying to change +the program counter. + +And that's what's costly. + +Not the actual doing the test of +the branch, test of whether + +x is less y. + +OK? + +AUDIENCE: Would you have to wait +for that to finish before + +you can do the negation? + +PROFESSOR: Yes you do. + +So that's one cycle, two cycles, +we can add it up here, + +three cycles. + +This can be going +on in parallel. + +So it's really only +two cycles total. + +Three cycles, four cycles, so in +four cycles you can get the + +minimum done. + +The L1 cache in the architecture +we're using costs + +you four cycles to fetch +something if you get a cache + +hit in the L1 cache. + +That's the cheapest memory +operation you + +can do, is four cycles. + +This computed the whole minimum +in four cycles. + +Here's another one, +modular addition. + +So sometimes you know something +that the compiler + +doesn't know. + +Like suppose that you know that +x is between zero and + +some value n, and y is between +zero and some value n, and you + +want to compute their sum. + +So what is that the sum is going +to be less than what? + +2n. + +So normally a modular operation +is very expensive + +because it involves a divide. + +Now multiply is normally more +expensive than an ordinary ALU + +operation that's just a bitwise +operation, like + +addition, or XORing bitwise +XORs, or comparison, + +or what have you. + +Those are very cheap one +cycle operations. + +Multiply is usually a many +cycle operation. + +Divide is often implemented by +doing repeated multiplies + +using any of a variety of +techniques, including Newton + +techniques. + +Sometimes there is a divider, +or a divide step. + +But divide is, generally, in any +case more expensive, even + +though it's doing operations +all within the processor. + +So if you actually compute mod +using your percent thing. + +This actually can be quite +expensive unless you're + +dividing by a power of two. + +If you mod a power of two +that's easy because the + +processor, if knows it's a power +of two, if the compiler + +knows it's a power of two, +it'll just do a masking + +operation on the low order bits +to give you whatever the + +remainder is, mod2 to the n. + +But if you're not in that +situation, n may not be a + +power of two, you still want +to do something modn, there + +still are some tricks you can +play but the compiler won't- + +this is one the compiler +generally won't play for you + +because the compiler won't +know that these are + +preconditions in your code. + +By the way, one of the most +common things is just doing x + +plus 1 modn. + +Very, very common thing to be +doing, x plus 1 modn, where + +you're wrapping around +in some index space. + +Here's another way +you could do it. + +So divide is expensive. + +Here you could just say +z equals x plus y. + +And then if z is less than n, +give z otherwise z minus n. + +The problem with this +is that it's got an + +unpredictable branch. + +To execute this code, I could +have written it out with an if + +statement, it's got to change +the program counter to execute + +either this or this. + +so not very fast because you +have an unpredictable branch. + +And we already talked about that +has to empty the pipeline + +if it's wrong in the guess. + +So here's a way of doing +it which doesn't + +have an explicit branch. + +So we compute x plus y. + +And now what we do is we look +at whether z is greater than + +or equal to n. + +And if it is, we're basically +going to take the negation. + +So that if it's is greater or +equal to n, the negation here + +is all ones, once again, +is minus 1. + +And so this becomes n and-ed +with minus one. + +That gives me n. + +And so then I'll +take z minus n. + +That's what I want + +However, if this is z is less +than n, then this will + +evaluate to zero. + +Minus zero is zero. + +And n and zero is zero. + +And so I'll end up just +getting the x plus y. + +So it's basically the same +trick with a couple of + +twiddles on the minimum that we +saw on the previous foil. + +Who's having fun? + +Good. + +As I said, we're going to +see lots of tricks, + +magic tricks even. + +Round up to a power of two. + +This is a common thing that +you want to do here. + +This, for example, goes on in +memory allocators, which we'll + +talk about later +in the course. + +So in a memory allocator, +somebody asks for a hunk of + +storage of size 19, most memory +allocators want to give + +out chunks that are powers of +two for reasons we will + +discover later. + +So you want to round up to the +next higher power of two. + +So how do you do that? + +So here's an example. + +So what I do is I decrement n, +and then I update n or-ing it + +with the left shift of n, and +then or-ing that with- sorry, + +the right shift of n by one. + +Then the right shift of n by +two, et cetera, et cetera. + +So here's an example. + +So here's my original number. + +And what I want is to round it +up to the next power of two. + +This is what I'm going to +end up with in the end. + +See I've got the next +higher power of two? + +Just one bit is on if I've +rounded up to the next higher + +power of two. + +So what do I do? + +I basically decrement and then +I take this word and I shift + +it by one to the right +and or it in. + +And then I shift it by +two and or it in. + +And then I shift it by +four and or it in. + +And then, in fact, I shift +it by eight and or it in. + +And I didn't do that. + +And since this isn't a 64-bit +word I skipped the last two + +instructions. + +So what's going on when I'm +shifting and or-ing it in, by + +one, by two, by four. + +What's happening? + +Yeah? + +AUDIENCE: [INAUDIBLE] this way +there's no number of ones + +starting from the one. + +PROFESSOR: Yeah basically, from +the most significant bit, + +if you look at what's happening +with the most + +significant bit, you're +shifting it by one. + +Then you're shifting +it by two. + +You're flooding the low +order bits with ones. + +And because it's an or, as soon +as something gets set to + +one, it stays a one. + +So it doesn't matter what's +actually happening in the low + +order bits. + +The only bit that we care +about is this bit. + +And it basically floods all of +the other bits with one. + +And then, once I've flooded them +all with one I increment. + +And that gives me a carry out to +this position and gives me + +the next higher power. + +So why did I decrement here, +and then increment there? + +What's the decrement for? + +Yeah? + +AUDIENCE: So that you can flood +with one because you + +want to get yourself back. + +So you want to the +add the one-- + +PROFESSOR: But why did +I decrement first? + +AUDIENCE: If you were not to +decrement, it would just flood + +everything with ones. + +PROFESSOR: Well here, if I +didn't decrement right here, I + +would have gotten +the same result. + +If you already have +a power of two. + +If I already have a power of two +and I flood the low order + +bits, then I increment, +I'll get the next + +higher power of two. + +So by subtracting one I make +sure that I'm handling that + +base case when n is +a power of two. + +Yeah? + +AUDIENCE: Does the [INAUDIBLE] +operate [INAUDIBLE] + +PROFESSOR: It actually, the +compiler is not going to care + +in this case. + +But it does make sure that it +doesn't bother to try to + +return and keep around +the old value. + +But it's smart enough to +not worry about that. + +Yeah, I mean, some people like +post-fix decrementing, and + +some people like pre-fix +decrementing and it doesn't + +matter in most cases. + +But sometimes doing it after-- + +there are situations where doing +it post-decrementing + +costs you a cycle. + +So everybody got +the idea here? + +So basically round up +to a next power two. + +How about computing a +mask of the least + +significant one in a word? + +So I want to mask which is the +power of two, the word that's + +all zeros except for one in the +least significant one bit. + +Any ideas how to do that? + +This is a classic trick. + +Everybody should know +this trick. + +You take x and you and it with +its two's complement. + +Take x and and it with it's +two's complement. + +Why does that work? + +So here's x, some value here. + +The two's complement is the +one's complement plus one. + +Right? + +If you remember. + +So one's complement just means +I compliment every bit. + +The two's complement +is I compliment + +every bit and add one. + +So when I compliment every bit +and add one, basically I go + +all the way to the least +significant bit and then I get + +zeros after it. + +So right up to there I get-- + +it's one's complement and then +it's basically- would have + +been 0, 1, 1, 1, 1, 1, plus 1. + +The carrot pulls you +back up to there. + +And so then when you and them +together, oh look at that. + +There's our least significant +bit sitting there. + +Pretty good one? + +So so how do you find +an index of the bit? + +So by an index I mean +this is bit 01234. + +Well it turns out these days +many machines have a special + +instruction to do that. + +And so if you look around and +you find the right library + +that calls that instruction, you +can use that instruction + +pretty cheaply. + +But there's still a lot of +machines, especially things + +like Mobile machines, et cetera, +where they have a + +depleted instruction set. + +Where they have no instruction +to convert from a power of two + +to essentially it's +log base two. + +So LG is the notation +for log base two. + +So how do you go about +doing that? + +So what we're going to do is do +some magic to motivate the + +solution to this. + +So one way to do it is to +use the ESP instruction. + +Are people familiar with +the ESP instruction? + +What's that? + +The stack [? order? ?] + +No, no, that's BSP +on some things. + +Or yeah, right, so in the +extended instruction set-- + +yeah, OK. + +Yeah, so the ESP instruction; +Extra Sensory Perception. + +And we have today the tremendous +magician Tautology + +who is going to demonstrate the +theory behind finding the + +index of the bit. + +So please give a warm +hand for Tautology. + +TAUTOLOGY: How about now? + +Can everyone hear me? + +So, as my good friend Professor +Leiserson has + +mentioned, I am the +amazing Tautology. + +And today I am going to show +you an amazing card trick + +which will baffle your minds for +approximately five minutes + +until he shows you +the next slide. + +All right, but to do this I will +need five volunteers from + +the audience. + +PROFESSOR: Who can follow +instructions. + +[LAUGHTER] + +So who would like to volunteer +to participate in real magic? + +Here we go, one, two, three, +four, only four? + +We need one more. + +So come on up and line up +along the front here. + +We need one more, one +more volunteer. + +One more volunteer, you +get extra points. + +Remember participation is +part of your grade. + +OK I'm going to cold call. + +Here we go. + +TAUTOLOGY: All right, +excellent. + +Please cut this deck. + +PROFESSOR: First you gotta +show it's a random deck. + +TAUTOLOGY: All right, I will +first show you that's it's a + +random deck. + +PROFESSOR: It's only 32 cards. + +It's only 32 cards. + +So he pulled out some +of the other cards. + +But they're in a pretty +random order there. + +So we want to give everybody a +chance to shuffle the deck + +here by doing a cut. + +Look at it, but don't show +it to Tautology. + +Why don't you go around +the back so that the + +class can see the cards? + +So hide your cards while +he runs around behind. + +And then turn them around so +that the class can see what + +the cards are. + +TAUTOLOGY: All right, are you +guys ready to turn around? + +Cool, excellent. + +PROFESSOR: I'm not going +to look at them either. + +There are no dupes. + +This is all done by ESP. + +TAUTOLOGY: All right, now- + +PROFESSOR: Why don't you +come over here where + +you can see the class? + +TAUTOLOGY: Hello everybody. + +I'm going to tell you what is +on those five cards, which I + +have not seen. + +Behold I have not seen them. + +OK, are you guys ready? + +PROFESSOR: Now you've got +to think about it. + +You've got to think hard about +what your card is. + +If you're not sure +you can check. + +But you've got to think real +hard about what your card is. + +TAUTOLOGY: Okay. + +PROFESSOR: Are you guys +thinking hard? + +I think you need some +technological assistance. + +TAUTOLOGY: I could use some +technological assistance. + +PROFESSOR: There we go. + +This is our brain amplifier. + +It amplifies the brain waves +coming from you. + +OK, give it a go. + +TAUTOLOGY: Hang on, +is this thing on? + +There we go. + +Now it's on. + +OK, here I go. + +All right guys I'm having +kind of an off day. + +So I'm going to need a +little bit of help. + +Can you guys just raise +your hand if you're + +holding a red card? + +So that's a red? + +PROFESSOR: Red, red, +black, red. + +They did it right, right? + +TAUTOLOGY: Now let me +give this a shot. + +So red, black, red, red, red. + +PROFESSOR: No, red, red - yes +OK you do it your way. + +TAUTOLOGY: Now, now +I might be wrong. + +But I think- am I seeing a +diamond with a seven on it? + +Is that what I'm seeing? + +PROFESSOR: Oh! + +How impressive is that? + +TAUTOLOGY: OK, one +down, four to go. + +What else am I seeing? + +I believe I am seeing. + +You're going to have to think +about this card pretty hard. + +I'm having an off day. + +So I think I'm seeing +a spade, with a six. + +Thank you for your honesty. + +Thank you. + +It does mean a lot to me. + +All right, so I'm seeing a- +now what am I seeing now? + +What could this be? + +It's some kind of a heart. + +I think, just maybe, it +has a value of five. + +PROFESSOR: Oh! + +Three in a row! + +I don't think he's doing +this at random. + +There must be ESP +at work here. + +TAUTOLOGY: Clearly. + +It's all the hat to be honest. + +It's all the technology, just +the latest technology. + +All right, so- + +PROFESSOR: It gets +harder as we go. + +TAUTOLOGY: It does get +harder as we go. + +But, what is this? + +do I- I think- no it can't +be- can it be? + +The three of hearts? + +It's the three of hearts! + +My old nemesis the +three of hearts. + +OK just one more card. + +[LAUGHTER] + +Did you just swap cards? + +I think I just watched +you swap you cards. + +Well I'm just going +for in the set- + +PROFESSOR: And they did it +without a temporary notice. + +They must have xor-ed them +together or something. + +TAUTOLOGY: So the last card, +which may or may not be in the + +last person's hands. + +Let me see if I can see it. + +What could it be? + +What could it be? + +No, no! + +No, anything, not +the- not that! + +Not the 6 of diamonds! + +PROFESSOR: All right, +five out of five! + +Thank you, thank you. + +OK guys go back to your seats. + +So that was a pretty +easy trick, right? + +TAUTOLOGY: Yeah, pretty easy. + +PROFESSOR: So how +does it work? + +What's the basic +idea behind it? + +What's the basic +idea behind it? + +So key thing is how many bits +of information did he get? + +Five bits of information. + +And there were how many +cards in the deck? + +Thirty-two. + +So the pattern of the five bits, +of which cards were read + +let him know where in the cyclic +sequence of cards he + +was, right? + +Because the cards really +weren't random. + +They just looked random. + +And so five bits is enough. + +But that means that every the +sequence of five cards in that + +deck, as you rotate it +around, has to have a + +different bit pattern. + +So does anybody know a name +for that property? + +A circular sequence that +has that property? + +The property is that if +you- well, let's see. + +Maybe I have it up here. + +So here's our magic code, +which is going to + +compute the log of x. + +And it's using what's called +a De Bruijn sequence. + +So let's come back to the +magic trick in a minute. + +And let's look to see +how we compute this. + +And then we'll understand +how both work. + +There's a magic number here +called De Bruijn. + +De Bruijn was a Dutch +mathematician. + +And then there's this funny +conversion table. + +And to find the log of x, where +x is a power of two, I + +multiply x by this magic +number here. + +Right shifted 58 places. + +This is keeping how many bits +after the multiply here? + +Six bits because it's +a 64-bit word. + +And then looking it +up in this table. + +So let's take a look at +what's going on there. + +So a De Bruijn sequence, s, of +length 2 to the k, is a cyclic + +zero one sequence, such that +each of the two to the zero + +one strings of length k occurs +exactly once as a + +substring of s. + +That's a mouthful. + +Let's do an example, smaller. + +So for example k equals 3. + +So here's a sequence, 0, 0, +0, 1, 1, 1, 0, 1, base 2. + +If I look at the first three +bits it's 0, 0, 0. + +The second three bits +is 0, 0, 1. + +And notice that as I go through +here every sequence, + +and these are wrapping around +the end, taking the last bit + +and then the first +two of the end. + +Every one of these gives you +an index of every different + +bit pattern of length 3. + +So these came up because people +played with those + +keypads where you have to enter +a combination, right? + +And if you have a keypad +and you want to enter a + +combination- let's say the +keypad has only two numbers on + +it, 0 and 1. + +And you have to hit the right +sequence of k numbers. + +So the naive way of doing it +would be to say well let's try + +0,0,0,0,0,0,0. + +Then let's try 0,0,0,0,0,0,1, +then 0,0,0,0,0,1,0. + +So what that'll do is you'll +have to go through 2 to the k + +numbers, each of which is k bits +long, for k times 2 to + +the k punches in order to be +sure that you've hit every + +number to open the lock. + +The De Bruijn sequence takes +it from k times 2 to the k + +down to 2 to the k. + +Still exponential in k, but +there's k at the front because + +it's making it so that each +sequence that you have nests + +into the previous one. + +And that's basically what's +going on here. + +Every sequence of length +3 exists in + +the De Bruijn sequence. + +And so this one here is a De +Bruijn sequence of length 64 + +as it turns out. + +And what we had in the magic +trick was a De Bruijn sequence + +of length 32. + +So that when you cut the cards +and you looked at the first + +five cards that was a unique +pattern of reds and blacks. + +It told you where you were in +the rotation of the sequence. + +And then there's a little bit +of cleverness to how it is + +that you translate +that into cards. + +Because remembering 32 cards, +and what their sequence was, + +and so forth, that's +pretty hard. + +But it turns out you +can just do an + +encoding of the five bits. + +Two of the bits encode +the suit. + +So the high order bit encodes +the suit, the two bits encode + +the suit, and then the last +three bits tell what the + +number is, 1 through 8. + +So that's how that worked. + +It wasn't really magic +after all. + +Who's surprised? + +So how can we use this in +this particular code? + +So for this, basically +the convert + +table does the following. + +It says, well, if you've got +zero, the offset, the shift of + +this amount here, is zero. + +And if you've got one, then +the shift is one. + +And if you have a six- +where's six in here? + +Sorry if I have a two here, +then that's going + +to be that I'm six. + +So this table is inverting +this number. + +Do people see the relationship +there? + +So if I know what the pattern is +I can do a look up and tell + +how much did I shift by? + +If I am shifting by a +given amount there, + +or circularly shifting. + +So here's the way +that code works. + +Let's say we've got a number +like 2 to the fourth that I'm + +trying to figure out what +the exponent is. + +It's always a power of 2. + +So I'm looking at 2 to +the fourth and I + +want to extract 4. + +But all I have is the mask +that's 16, which + +has the one bit on. + +What I do is I multiply this +number, the De Bruijn sequence + +number, by 16. + +Well what happens when you +multiply by a power of 2? + +It shifts it by 4 bits. + +So it's shifted the +bits by 4 bits. + +And now if I right shift +it by 8 minus 3, I + +capture the top 3 bits. + +In this case, 1, 1, +0, which is 6. + +Then I convert 6. + +It says I had a shift of 4. + +And just with 64 bits it's a +longer De Bruijn sequence. + +So it's performance is limited +by the fact that you have to + +do a multiply and +a table look up. + +But it's generally fairly +competitive for many machines + +that do not actually have a log +base 2 of a power of 2. + +These days machine instructions +are getting- + +there are instructions that +will do that in a single + +instruction for you. + +But if you don't happen to have +one on your architecture + +and need to do this fast +this is a reasonably + +fast way to do it. + +Even with a table look +up and the thing. + +The other way of doing it, of +course, would be to shift by + +one, shift by one, shift by one, +until you get the one. + +And there's some other +techniques as well + +that you can use. + +You can do divide and conquer in +a binary way, where you do + +binary search for where the +bit is, by shifting and so + +forth, and hone in. + +But the problem with those +techniques, the binary search + +in particular, is what? + +If I try to binary search +to find a bit what's + +that going to be? + +Yeah, branching. + +You're going to have +unpredictable branches. + +And each of those will +cost you 16 cycles. + +And so with a 64-bit word you've +got 16 cycles times six + +bits that you're trying to +decode, times however many + +instructions it actually +takes you. + +It adds up to a lot of cycles. + +But that can sometimes +be an effective way + +of doing it as well. + +And there are other ways. + +You can look byte by byte. + +There are a variety of +other techniques. + +Anyway, but this +is a cute one. + +Here's another one, +population count. + +Count up the number of +one bits in a word. + +So here's one way of doing it. + +I start out r at zero. + +And I keep incrementing r. + +And what I do is I quit +when x is zero. + +And what I do is I do that +trick of x, ending it + +with x minus 1. + +Which does what? + +Eliminates the low order bit, +that's one, the low order one. + +So basically I go through and +I just kick out one of the + +ones, kick out another one of +the ones, kick out another one + +of the ones, until I'm done. + +This has a branch in it. + +But in some sense it's a +predictable branch because + +almost all the time you're +going through the loop. + +However, it has downside, which +is that suppose you're + +given minus 1. + +Then you have to do 64 +iterations of this loop before + +you can get your final answer. + +And so that's a lot of +iterations to do. + +So here's what's going +on in your loop. + +Here's x. + +Here's x minus 1. + +And now if I and them it's +very similar to the other + +trick that I taught you. + +You and them, notice you have +the same number you started + +with except it's missing +the one low order bit. + +So this is fast if the +population count is small. + +If you know there's only a +couple of its on in the word, + +then this can be a pretty +effective technique. + +But in the worst case it's going +to take it's going to be + +proportional to the number +of bits in the word. + +Because you're only getting +rid of one bit at a time. + +But it's better, in some sense, +than looking one bit at + +a time because you have the off +chance that the number of + +one bits will be sparse. + +Whereas if you just looked at +the low order bit, then the + +next bit, then the next bit, +that would definitely take you + +worst case every single time. + +Here's another way to do it. + +It's a table look up. + +So you have to pay, but if +you're doing this a lot maybe + +all of this is an L1 so the +table look up only costs you + +four cycles if it's +an L1 cache. + +So what is this sequence? + +This tells for any given byte, +so there's 256 values, how + +many ones are in the world. + +So zero has zero one bits. + +One has one one bit. + +Two has one one bit, three +has two one bits. + +Four has one one bit, five has +two, six has two, seven has + +three, eight has +one, et cetera. + +So that's this table. + +I didn't fill out the +rest of the table. + +And now what you're doing in +this loop is you're basically + +taking a look at +the value of x. + +You're right shifting it and +then your indexing, masking + +with the low order byte. + +So you may ask the +low order byte. + +You add that to the count by +doing a look up, which + +hopefully only takes you four +cycles if the table is in L1. + +And then just run around this +loop until you've got no more + +things in your word. + +So how many are in byte one, how +many are in byte two, how + +many are in byte three, +and so forth. + +For things that use table look +up you have to be careful + +because if you have a great big +table why not look up two + +bytes at a time? + +Well two bytes is +65,000 entries. + +So why not look up four +bytes at a time? + +Four bytes is four +billion entries. + +At that point you're going out +to memory and starting to + +consume a lot of space. + +So here's some common numbers. + +These are sort of approximate. + +But generally if you're doing +operations on registers, one + +cycles, and plus you can issue +six per core, per cycle. + +So L1 cache is going to cost +you around four cycles, L2 + +cache about 10, L3 about +50, and D RAM + +about 150 to 200 cycles. + +When you access these you get, +in fact, generally for all + +these, you tend to get +a 64 byte cache line. + +So you're getting +more than one. + +But if what you're doing is +random access in a table it + +doesn't help that all those +other bytes are coming in. + +Population count three using +parallel, divide, and conquer. + +Here's the clever one. + +Here's the code. + +It's all register operations +basically. + +So it's creating some masks. + +So let's just take a look +at what does this first + +instruction do? + +It's taking minus one. + +It's shifting it left 32 bits. + +So that gives all ones in the +higher order half of the word, + +and all zeros in +the lower half. + +And then it's xor-ing +it with minus one. + +But with all minus ones. + +So that gives you a mask +of ones in the low + +order half of the word. + +Yeah question? + +AUDIENCE: Why don't you just do +negative one right shifted. + +Isn't there a type of- + +PROFESSOR: Yeah you +can do that. + +I was trying to be +consistent here. + +And, in fact, for these first +two operations there are + +actually more clever ways of +doing this that take fewer + +operations. + +AUDIENCE: Isn't there a right +shift operator that + +[? pulls some ?] zeros +in the top level? + +PROFESSOR: Yeah, so there's +logical versus arithmetic + +right shift. + +Yeah. + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: That's right. + +But then I wouldn't have +the pattern that + +I'm setting up here. + +So yes, in fact, if you want to +play with it yourself you + +can optimize these first +two statements. + +They don't need to be as +complicated as this one. + +But basically what you're doing +in every step is your + +shifting it over, half +the word, xor-ing it. + +And then the second one is you +get a block of 16 bits of + +zeros, 16 ones, 16 +zeros, 16 ones. + +The next one you get a block of +eight zeros, eight one's, + +eight zeros, eight ones. + +And so basically you're +generating masks for that. + +So by the time you get down to +the last one you're having + +every other bit is zero. + +You're alternating +zeros and ones. + +And then, basically- +well let me not go + +through the code here. + +Let me show with an example. + +The main thing to observe is +that it takes log n time where + +n is the word length +to do this. + +So here's population count on +32 bits, same kind of thing. + +So here's the idea. + +We extract every other bit +for the two words. + +So you saw how I extracted +that right? + +So we extract. + +So I can do that with +a mask and a shift. + +And then I add them together. + +So just so we can see what's +being added here. + +And when I add them together the +largest value I'm going to + +have in any one of these +things is what? + +AUDIENCE: Two. + +PROFESSOR: And [? that, ?] +fortunately, fits in two bits. + +So we can get off the ground. + +So now every two bits has +the sum of the two + +bits that were there. + +The bits that I'm not showing +are all zeros because it's + +done 64 bit words. + +The bits I'm showing +are all zeros. + +So now what do we do? + +We mask and shift and take off +every two pairs of bits and + +then add them together. + +So now this guy is saying +there's four bit that were + +originally in the +word that began. + +This one says there are two bits +in that range, one bit, + +one bit, two bits, three bits, +two bits, two bits. + +So we do it again. + +Add it together. + +And we just keep going. + +And then finally we add +them all together. + +It says there are 17 ones in +the word, which there were. + +I should have probably left the +word up there or something + +so we could verify that. + +But Yeah there are 17 ones. + +So everybody see it's parallel, +divide, and conquer + +because you're adding many +words, many sub-pieces pieces + +of the word [UNINTELLIGIBLE]. + +And the key thing is to make +it so that no carries are + +propagating out of +their range. + +But the numbers are just getting +smaller and smaller. + +When you're done you're only +going to have six bits here + +that are significant anyway. + +All of these will be zeros. + +Is that cool? + +So there's a 17, yeah. + +Here's a problem for which +bit representations + +are a lot of fun. + +Last year we gave this as +a problem to students. + +This year we're giving you a +different problem so that lets + +me lecture on it. + +So many people are probably +familiar with this problem. + +It's an old chess nut. + +But basically the queen's +problems is to place n queens + +on an n by n chess board so that +no queen attacks another. + +So there are no two Queens in +any row, column, or diagonal. + +So queen's kind of +move like this. + +It's got to be clear. + +If I did that around any one +of these guys they wouldn't + +hit anybody else. + +In fact, this arrangement here +is, I think, one of the few + +symmetric ones. + +Maybe it's the only +symmetric one. + +It's radially symmetric. + +Most of them are +more scattered. + +So the question is how do you +find such a thing, or count + +the number of solutions, +is another + +popular one, et cetera. + +A popular strategy for this is +called backtracking search. + +And we're going to have in +your homework a different + +backtracking search. + +And the idea is you just simply +try to place the queens + +row by row. + +So, for example, we start out +with the first row, row zero, + +and we place a queen. + +Then we go to the next row. + +And we try to see if a queen +works on that square, nope, + +nope, yes it works there. + +Now we go on to the next row. + +So this is making progress. + +We're placing queens. + +We're going to more rows. + +We're going to get to the +end of the rows, right? + +So we keep- yep, we found it. + +And we keep going. + +This is easy. + +Found it right after +two there. + +That's pretty good. + +Found it there. + +Look, we're making +great progress. + +Doesn't go there, doesn't go +there, doesn't go there, + +doesn't go there, oops +doesn't go anywhere. + +So what do we do? + +We backtrack. + +We say, gee, if it didn't fit +in any those but it had + +nothing to do with the placement +there, it's the + +fault of the guy who +came before me. + +So that position is not a valid +position, at least with + +that prefix. + +So we continue with him. + +Aha, we found another +place for him. + +So then we try this one. + +Oops this doesn't look good, +aha, got to backtrack. + +Whoops that's the last +one in the row, got + +to backtrack again. + +So that means that guy +can't go there. + +Found a place, now we get +to go forward, hooray. + +And you keep going on. + +So you backtrack, et cetera, +until you finally + +find a place for them. + +So the backtracking search +is pretty interesting. + +But the question is how do you +represent it so that it can go + +really fast. + +So here's some ideas. + +The first idea you might come up +with is to use an array of + +n squared bytes, where you put a +value in the byte if there's + +a queen there. + +You should, at this point, +figure out that, gee all I + +have to know is whether a +queen is there or not. + +So why should I keep a byte? + +Why not just keep a bit? + +That'll be smaller and have +a smaller representing. + +So let's keep n squared bits. + +Well let's see. + +If I'm only putting a queen in +one place in every row I never + +have to have more than one +bit set in any row. + +So why not just say the column +number in the row that I'm in? + +So rather than using an array of +n bits for every row let me + +just use an index of a byte to +say which row that one queen + +is in because there can't be any +other Queens in that row + +in a legal configuration. + +So that's actually +more clever. + +And that's the way most +people code it. + +But we're going to look at a +solution that was originally + +due to Edsger Dijkstra of using +three bit vectors to + +represent the board. + +And the idea is we want to make +things go- we're going to + +use three bit vectors that +are relatively small. + +So it turns out the +n queens is an + +exponential search problem. + +And so you really can't run n +queens on 128 by 128 board. + +You can run that if you're +interested in one solution. + +You can't count up how +many solutions. + +And if you go to Wikipedia and +look at n Queens they will + +tell you what all the latest +records are for who has + +computed how many solutions +there are on an n by n board + +for n up to some rather +small number. + +So it's a way to get your name +on the web, which, as you + +know, is very difficult to do. + +So let's see this three +bit vector trick. + +So the idea of the bit vector +trick is that, for any partial + +placement, rather than +representing where the queens + +are on the board, what I really +care about is which + +columns have been knocked out. + +So, therefore, what I'll do is +I'll store a one if there's a + +queen in that column and a zero +if I don't have a queen + +in that column. + +So the point is I can keep the +whole representation of the + +column mask in a word that just +tells me whether I have + +ones or zeros in a column. + +Now how do I know whether it's +safe to place a queen in a + +given column? + +What's that? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: How do I know, if +I try to place a queen say, + +here, how do I know whether +that's OK or not? + +Suppose that my program +wants to try to put a + +queen in this space. + +It can't because there's +something here. + +It's just some operations on +words, which we will see here. + +So placing a queen in column +c is not safe if + +this down were here. + +When I and it with one shifted +left by the number of columns + +so that I have the position of +the queen in the column if + +that's non-zero because +it means somebody + +else is in that column. + +If it's in a new column when I +do the and I'll get all zeros. + +Everybody follow that? + +So testing columnists, whether +it's safe to put it in a given + +column, from the column attack +we can do that really, really + +efficiently, right? + +These are all going to +be in registers. + +No memory operations, no table +look ups, no L1 caches, all + +right in registers. + +Well what do we do about +the diagonals? + +So for the diagonals we can +also use a bit vector + +representation for +each diagonal. + +Where I look to see if there's +a number along this diagonal, + +and if there is a queen +then it's a one. + +And if there isn't a queen on +the diagonal it's zero. + +There are more diagonals then +there are columns, right? + +So I have a longer bit vector +representation. + +I have to represent that. + +But I can still do that in one +computer word for things of + +different size, or even for +things that are pretty good + +size two computer words would +be, certainly, ample. + +So now how do I tell whether +or not a queen placed on a + +given square can legally +be placed there? + +So it turns out it's not safe to +place it if when I take my + +writer ray, and I take n minus r +plus c, and left shift it by + +that amount, and that's +non-zero. + +So here I'm indexing rows and +columns from the upper left + +hand corner. + +And so, basically, you're trying +to say is, for a given + +square, notice that if I +increase the row, that's this + +way, I get to the same- of if +I'm increasing the row, I'm + +decreasing the diagonal +that I'm on. + +But if I'm increasing the column +I'm increasing the + +diagonal I'm on. + +So that's it's basically +a difference here. + +And then you just normalize it +and with essentially very, + +very few operations I can +tell whether there's a + +conflict in a column. + +Of course, for both this and +the other one, if I need to + +set it now that's pretty +simple also. + +I just take this and +or it with right. + +If my test is good, I just take +this, or it with right, + +and now that's my new right. + +And left is similar. + +So, once again, we have these +guys going this way, placing a + +queen in row r. + +And column c is not safe if- +and now I just look at row + +plus column because these +diagonals increase with both + +row and column. + +You're increasing the diagonal +for both row and column. + +And so I'm not going to +go through all the + +details of the code. + +But you can see that with this +representation, literally, the + +inner loop of your program, +which is testing whether + +queens fit on boards and then +setting them if they do, you + +can do with just three words +and a few operations. + +Question? + +AUDIENCE: Can you mask the three +bits together and check + +if one position is taken up? + +You'd have to do some creative +stuff with lining up the row + +and column vectors with +the diagonals, but- + +PROFESSOR: So typically +here you're looking at + +both row and column. + +So you're adding them, whereas +on the previous one you were + +subtracting. + +And then the first one you +didn't even care about what + +the column was. + +So I'm not sure I would know +how to combine those. + +It's conceivable you +could do it. + +AUDIENCE: [INAUDIBLE] + +column vector, you could add +the two together and find + +specific positions +that are free. + +PROFESSOR: Yeah so you could +also do a generation that says + +here are the ones that are free +and then use things like + +the least significant bit trick +to pull out what is the + +positions I should +bother to check. + +So here I can test +that it's safe. + +But I could also generate using +similar tricks, which is + +what you're saying, generate all +of the bit positions on a + +given row where it would +be safe to put a queen. + +Yep, yep, good. + +So fast programs use +this technique. + +So you see that there's a lot +of cleverness in these kinds + +of techniques. + +So there are a whole bunch of +other bit hacking techniques. + +One really good resource +for it is this webpage. + +And of course I'll put this up +on the- called bit twiddling + +hacks, where he's compiled- +there's a lot of people that + +have worked on different +bit twiddling hacks. + +And he's done a very good job +of compiling what he thinks + +are the best code sequences for +a whole bunch of things, + +including things like reversing +the bits in a word. + +If you think about it that +could be kind of tricky. + +Actually turns out +to be relevant to + +your homework as well. + +So on your homework, so lab +one will be- it's posted I + +gather, right? + +It'll be posted shortly. + +We have you trying to take +advantage of some of these bit + +tricks in a couple of warm +up exercises and then a + +backtracking search algorithm. + +And so I think you'll find +it's a lot of fun. + +You'll learn a lot about all the +kinds of tricks you can do + +to make stuff go fast by using +register operations locally, + +and using good representations +for your storage. + +Yes, also, announcement. + +Tonight, at 7 o'clock, in 32, +144, there is a primer on c. + +So if you want to brush up on +your c or if you want to learn + +c, this is a good time to go. + +There's a lot of good nuggets +of wisdom coming out for c. + +OK, thanks very much. + +See you Thursday. \ No newline at end of file diff --git a/ylQ5-9f5KIs.txt b/ylQ5-9f5KIs.txt new file mode 100644 index 0000000000000000000000000000000000000000..5ae5210f990679b65ab8bad33f177e271d13861c --- /dev/null +++ b/ylQ5-9f5KIs.txt @@ -0,0 +1,2844 @@ +PROFESSOR: All right. + +Welcome back to 6.849. + +Today we are going over +TreeMaker, folding polyhedra, + +folding checkerboards, +and Origamizer. + +Lots of stuff. + +And can't fit +everything in today, + +but we'll be doing more +Treemaker in some sense + +from a more +practical perspective + +in the very next lecture +video and next class, + +with a guest +lecture by Jason Ku. + +So today we have a +bunch of questions. + +We'll start with TreeMaker. + +So the first +question is, wow, you + +can make all these crazy +things with the tree method. + +Are they really uniaxial? + +And the answer is yes. + +And I think it's +probably easiest + +to just go through +some examples. + +These are all from Origami +Design Secrets, this book + +by Robert Lang, which is on +the recommended reading list. + +And I think there's even an +electronic copy available + +through MIT Libraries. + +So you can read it online or +there maybe one in the library. + +There's two editions. + +These figures are from +the first edition. + +So here is a-- the goal is +to design "Scorpion varileg." + +These are all +Robert Lang designs. + +You come up with this +stick figure, your tree. + +TreeMaker makes +this crease pattern. + +You can also see the +rivers here and the disks. + +And then you get this base. + +And then it folds +into that scorpion. + +So while the scorpion +doesn't look like it + +has a single axis-- +scorpion, maybe. + +There's kind of an +axis down the center. + +But it's not just this axis. + +It branches, then +it branches again. + +You can make a tree and +it's still uniaxial. + +So uniaxial refers to +this axis in the base. + +All the flaps are +attached to that one spot. + +So in this picture, +it's vertical. + +Usually in the-- when +we draw all the figures, + +we think of it as the horizontal +plane, or horizontal line. + +So we imagine this is the floor. + +And then we have flaps +attached to the floor. + +Something like this. + +So in that sense, when +you flatten this base, + +everything lies along this axis. + +Even though, in terms +of branching structure, + +you could have lots of branches. + +So that's to clarify +what uniaxial means. + +Maybe not the best term, but I +have a few more examples here. + +This hat includes +a color reversal. + +Some crazy stick figure. + +And you get your pattern. + +Here's a somewhat simpler want. + +It makes a more three +dimensional horse. + +This Alamo Stallion. + +So you can go through, +and for each of these, + +I've just reverse engineered +from this crease pattern what + +the stick figure must be. + +And you're going to +do this on PSET2, + +which will be released +in a few minutes. + +And so this uniaxial's to +contrast from something, + +the kind of most famous +non-uniaxial or biaxial origami + +bases, with Montroll's Dog +Base, which looks like this. + +So it's very easy to turn +this into all sorts of dogs. + +This is a wiener dog. + +But you have kind of one +axis here and one axis here. + +Which is different. + +It's not the same kind of +branching tree structure. + +Of course, you can make a dog +using uniaxial method as well, + +but it's kind of a fun +counter example of the things + +you might do. + +So that's uniaxial. + +Next question is, do people +use TreeMaker and/or Origamizer + +in practice? + +And the short answer is no. + +I would say most origamists +don't use software + +to design things. + +But they use a lot of the +ideas in their own designs. + +So in particular, +the tree method + +of origami design, which +TreeMaker is implementing, + +almost every advanced +origami designer uses. + +Not everyone, but most of the +complicated-- most complex + +origami that you see uses +the tree method at least + +to get started. + +Origamizer is much newer, +so it's not used as much. + +Most of the cool designs-- +I'll show you a bunch of both-- + +are by Tomohiro Tachi, +who invented Origamizer. + +But I think it's still evolving. + +And hopefully, these +more advanced techniques + +will catch on with time. + +And by now, you've seen lots +of examples of the tree method. + +I'll show a few more from +Robert Lang's website. + +This is a local delicacy. + +And these are all +on langorigami.com, + +on his website. + +And we'll see even more +examples in the next class. + +And Jason Ku is going to give +an overview of various artists. + +And in some cases, they +publish crease patterns. + +Not always. + +This is not quite +the tree method. + +So this example was +standard tree method. + +You've got disks and rivers, +which aren't drawn here. + +You get a crease pattern. + +This could be done +directly from TreeMaker. + +I don't know for +sure whether it was. + +This pattern is not +done with TreeMaker + +because it's not regular disks. + +This is the box pleating version +of the tree method, which + +there's another question about. + +So we'll talk about that more. + +But you see all the creases +here are horizontal, vertical, + +or diagonal, 45 degrees. + +That makes it a lot easier +to fold, a lot easier + +to find reference points. + +You see it falls +nicely on a grid. + +But still, you get an +arbitrary tree structure. + +I think I have another example. + +This one also-- well, this +has 22 and 1/2 degree folds. + +It's a little bit more general. + +Also very non-stick figure-like +models, particularly. + +It's obviously called +the "Fiddler Crab." + +No, sorry. + +I have the wrong title here. + +I will fix that. + +I forget this guy's name, +but if anyone remembers. + +He wrote about the division +between scientists and people + +who know literature +as two different types + +of intellectuals +that know almost + +nothing about each other. + +At least in the early +1900s when he was writing. + +And one more example. + +This is based on +a 60 degree grid. + +So all the creases, I think, +lie at 60 degrees to the axis, + +or horizontal. + +There might be some 30 degrees. + +So I'll talk a little bit +about this alternate version + +of the tree method that doesn't +just use arbitrary circles, + +but tries to stay +on these nice grids. + +Here's just one more example. + +Jason Ku is the designer +of this model called "Pan." + +and he'll be giving +the guest lecture. + +So this is just one example. + +But tons and tons of +advanced origami artists + +use tree method +of origami design. + +And you get some pretty cool +crease patterns from it. + +But I think most people +do it by hand, usually + +on a computer using some +drawing programs that + +can compute intersections and +do things with high accuracy. + +And then they draw these +pictures, then they fold them. + +And then you get +your base and then + +you shape it into the model. + +So next I want to show you +some practical examples of + +So there's a bunch on +Tomohiro Tachi's Flickr site. + +This is one of the earliest. + +This is just making a +negative curvature surface + +that curves in both ways +like a saddle, called + +a hyperbolic paraboloid. + +We'll see more of +those in the future. + +But this is folded from +one square of paper. + +And there's tabs on the backside +that you don't see here. + +Here he's making a +kind of 3D bell curve. + +Here's a computer mouse. + +Apparently the scroll +wheel works fine. [LAUGHS] + +Doesn't support USB, though. + +Only Bluetooth. + +We've got a nice mask. + +These are all-- you're +given a 3D model, + +and you fold exactly +that 3D model. + +This is a tetrapod. + +So here it sort of shows +Tomohiro's background + +in architecture. + +If you haven't seen +tetrapods, they're + +used to hold back the ocean +and things from-- or hold + +from erosion and +things like that. + +So usually made out of concrete. + +But here you can make +them out of paper. + +Here's a flat design. + +So here the mesh, the +triangles were all in a plane. + +And of course, you still get +the tabs on the backside. + +But you make this +very exact leaf. + +You can get the +triangulation edges + +exactly where you +want them to express + +these veins of the leaf. + +Here's what it looks like to +fold one of these in practice. + +It's not quite a +square of paper, + +but it could be a square. + +And this is actually +folded at CSAIL. + +You might recognize +some of the furniture. + +And so while +Tomohiro's folding, he + +uses various devices-- +paper clips and clips + +and so on-- to hold it in shape. + +Because until it's +completely collapsed, + +it kind of want to open back up. + +So it's kind of like having +a hundred hands at once. + +But when he's done, he'll +take all of them off, + +and you'll get-- so this, +I think, was about 10 hours + +and you get your bunny. + +Easy. + +Or this is the one we +did a little bit later, + +just last year. + +This is a laser +cut sheet of steel. + +And now, here we've +cut out bigger holes + +so there aren't too many +accumulation of layers. + +But essentially the same design. + +Somewhat coarser +mesh of the bunny. + +And you have to wear gloves, +otherwise you'll cut yourself. + +So we're perforating the +metal at the creases. + +And then also takes +about eight hours. + +A lot harder to fold steel. + +And in the end, +you get your bunny. + +So in principle, out of +any sheet of material, + +you can make any +3D shape you want. + +That's the exciting thing. + +So I think Origamizer +is really powerful. + +Obviously, it's hard to fold. + +You need to be pretty advanced. + +But there's a lot of +potential for designing + +very non-stick +figure-like models. + +So that was TreeMaker and +Origamizer in practice. + +So next question is +about this box pleating, + +which is the horizontal, +vertical, and 45 degree + +creases. + +And TreeMaker, is there +some theory for this? + +And indeed there is. + +And we started working on +it, me, Marty, and Rob Lang, + +I think during his +first visit here, + +which was probably +2004 or something. + +A long time ago. + +And the best writeup +of it currently + +is in Origami Design Secrets, +especially Second Edition. + +So + +It has a chapter on +basic tree theory, + +a chapter on box +pleating in general. + +This is sort of +classical box pleating. + +But then there's a +chapter on mixing the two. + +Uniaxial box pleating +and polygon packing. + +These kind of go together. + +So if you're interested +in this stuff, + +you want to design something +the way that the experts do, + +check out Origami +Design Secrets. + +Or go to an origami +convention where + +Rob was talking +about this stuff. + +We are working on +this giant manuscript. + +It's currently called +the Mathematics + +of Origami Design, which +is, in particular, trying + +to prove the tree +method always works. + +And we'll generalize +to things like this. + +But it's not finished, so we +don't have a complete proof + +yet that it all works. + +Everything seems fine, but it's +tedious to write it all down. + +So still working on it. + +But I thought I'd show you +an example of box pleating + +uniaxial origami design +from Origami Design Secrets. + +So this is sort of typical +tree method of origami design. + +If you're not necessarily +using TreeMaker, + +but you're doing it by +hand, you think about, OK. + +Suppose I want to make this kind +of insect, this stick figure. + +Maybe I realize, oh, it's +kind of centrally symmetric, + +so I'd like to +make the left half + +of the paper same +as the right half. + +You can also express that +in the TreeMaker software. + +And then you start +thinking about where + +these leaves +correspond to disks. + +Then you've got to have +the corresponding rivers + +in between them. + +So you might start with +this kind of layout, + +and then you try to blow it up +until things can't be expanded + +anymore and there's +lots of touching. + +So that would be +the usual approach. + +Then from that, you could +apply the tree method, + +get the crease pattern. + +With the box pleated version, +essentially, instead of disks, + +you have squares. + +And instead of rivers, you +have these orthogonal channels + +of constant width. + +And so I'll just wave my +hands and say that happens. + +Now, you get these weird +things-- you get these gaps. + +You tend to get more +gaps in this way. + +But in this case, instead +of just having a square, + +you can extend it out +to be a rectangle. + +So these guys are +actually going to fill + +in these holes like this. + +And then from +this, you can start + +constructing a crease pattern. + +So you start with +these ridge creases. + +And this is something +like a generalization. + +It's actually something like a +straight skeleton, which we'll + +be covering in a +couple of lectures + +for a different purpose, +where it was originally + +developed for origami purposes. + +But these are just +lots to bisectors. + +And you'll have to see +the general version later. + +And then you start putting +in the hinge creases. + +These are these green lines. + +And they're +perpendicular to these. + +These blue creases are +going to be the floor. + +And so on, you fill it in. + +Eventually you get your +complete crease pattern. + +So in a nutshell, +that's how it works. + +You tend to get tabs that are +a constant width like this. + +Constant height, I guess. + +And so, it's a +general technique. + +It's a little bit much to +explain here, but read the book + +if you want to see it. + +And I would say it's probably +some of the most common. + +There's a lot of +intuitive ways to do it, + +and then a lot of the details +are worked out in that book. + +But it's quite common to +design bases in this way, + +because it's just so +much easier to fold them. + +You don't have to construct +really weird angles. + +A lot cleaner. + +But a little bit less +efficient, because instead + +of using a disk, which is +the minimum amount of paper + +you need to make a flap, +you're using a square. + +So you're wasting +those little corners. + +But not that much +more inefficient. + +Cool, so that was that method. + +Next question I have is about +the triangulation algorithm, + +which I didn't even +cover in lecture. + +So this was you set up-- you +have your piece of paper. + +And you assign each +leaf in this tree + +to some point in +the piece of paper. + +And you satisfy the +active path condition + +so each of these distances +measured on the paper + +should be greater than or +equal to the distance measured + +on the tree, which is +the floor of the base. + +Great. + +And so if you happen to +have some equalities, + +you draw in active paths. + +But what if you don't have any? + +Or you don't have enough? + +The tree method in +its original form + +only works when the active paths +decompose the piece of paper + +into convex polygons. + +This is what you'd +like to have happen. + +Each of the faces here +is a convex polygon. + +If that happens, great. + +You can use the +universal molecule + +and you get your folding. + +If it doesn't happen, +you have to modify + +your tree a little bit. + +There are a couple ways to +do this in the TreeMaker. + +You can modify +these edge lengths + +and try to modify them +as little as possible + +so that things touch. + +But the easy way to +prove that something + +is possible-- because remember, +if we add a little bit + +to the base, we +get an extra flap. + +That doesn't really hurt us. + +At the end, we +can hide the flap. + +Just fold it against other +flaps and just pretend + +it wasn't there. + +So as long as we can +add flaps in order + +to make the active paths +decompose into convex polygons, + +we're happy. + +And in fact, what we prove is +that you can keep adding flaps + +until you get into triangles. + +And triangles are always convex. + +And so they make us happy. + +So we will end up adding a +bunch of flaps in our tree + +in order to triangulate +with active paths. + +And then in each +of these, we just + +fill in a rabbit ear molecule. + +So that's the goal. + +Now let me tell you how the +triangulation actually works. + +It was originally +described by Lang. + +It's also in the +textbook for this class. + +I'll try to give an +abbreviated version here. + +It's a little bit technical, +but here's the idea. + +So suppose-- all right. + +So we've assigned some leaves. + +And suppose we have some +region that's not convex. + +It's not a triangle. + +Has more than three sides. + +Now, some of these edges +may come from active paths, + +and some of them may be from +the boundary of the paper. + +So maybe the paper is here. + +So this edge is not active. + +It's just the boundary +of this region + +because it's the +boundary of the paper. + +So there are two types of edges. + +But there should be, I guess, +at least one active edge. + +And there's at least +four edges total. + +So what I'm going to do is look +at any of the active edges, + +and I'm going to imagine-- OK. + +So that active edge, this +is in the piece of paper. + +But now I'm going to think +about it in the tree. + +So the tree looks +like something. + +We don't really know what. + +Any active path here +corresponds to an active path + +in the tree of exactly +the same length. + +So maybe it's from +this leaf to this leaf. + +So it corresponds +to-- use a color. + +This guy corresponds +to this path. + +And the sum of those lengths +should be equal to that length. + +It isn't, obviously, but there's +a scale factor in between here. + +Lambda. + +OK. + +So here's what I'm going to do. + +I'm going to modify the tree +by adding a new leaf somewhere + +off of this path. + +OK, where? + +For convenience, let's assume +that this path length here + +is 1. + +Then I'm going to measure +out some distance x here, + +which will leave a different +distance, 1 minus x, here. + +And then I'm going to make +this length, I guess, L. + +And I'm going to call this +leaf L. Capital L. OK. + +This is a modification +to a tree. + +I can do it. + +I can do it for any value +of x between 0 and 1. + +And i can do it for any value +of L greater or equal to 0. + +So what I'd like to +do is design the tree + +so that this point ends +up in an interesting place + +on the piece of paper. + +In fact, I claim that no +matter where I draw L here, + +capital L, as my desired place. + +Now, what I'd really +like is for-- I + +should give these guys names. + +This is called U, or say, in +the notes, I call it V and W. + +So here we have W +and V. What I would + +like is for these two +paths to also be active. + +Meaning the lengths here +match the lengths in the tree. + +I claim that no matter +where I put L in the plane, + +anywhere in the plane, I +can choose x and choose L + +so that these two lengths +are exactly correct. + +Do you believe me? + +Not really. + +How many people think +this is obvious? + +Good. + +A couple maybe. + +Let me give you a quick sketch. + +It's not that +interesting, so I just + +want to do it very briefly. + +If you let x be a free +parameter, but fix l, + +little l, then what +this corresponds to + +is, in fact, an ellipse with V +and W as foci of the ellipse. + +Because you have to hold the +sum of these lengths fixed + +if you fix-- if you let x vary, +this length plus this length + +is always going to be +the same if you fix l. + +And so this is called +the major axis, + +the sum of these two lengths +is going to be like 1 plus 2l. + +And so if I have a +point, basically, there's + +some ellipse of the +appropriate size that + +passes through L. That will +let me choose little l. + +And then as I vary x, I +walk around the ellipse. + +So I just choose the +appropriate value + +of x that gets me the +desired point on the ellipse. + +That's it. + +The point is, the set of all +ellipses with these two foci + +spans the entire plane. + +So wherever you +want to put L, you + +can make those two paths active. + +OK, this is good, because +it makes a little triangle. + +But of course, if I just add +an arbitrary triangle, not very + +interesting. + +The good thing is I'm free +to put L wherever I want. + +I'd really like +to put L say here + +and draw active paths like that. + +Because then I'm kind of +decomposing my polygon + +into triangles. + +That's not always possible. + +So let's just go +through the cases. + +In all cases, we're going +to simplify a polygon, + +make it have fewer sides. + +And that's on the next page. + +So the claim is-- well, the L. +There's sort of three cases. + +Going to reorganize +this a little bit. + +One thing that would be nice +is I can place L-- maybe + +I'll draw another +version of this. + +So I've got UV. + +I'll draw the +active paths in red. + +So we know UV is active. + +We've got L. If I +could somehow place L + +so that it's active with two +other points, two other leaves. + +This is V and W. This +is U and this is T. + +If I can do this, and the region +looks something like that, + +then I'm happy. + +I'm going to put L there +and add in these four edges. + +And essentially, if you look at +any one of these regions that + +remains, there's +a triangle here. + +That's definitely OK. + +These regions, each +of them will have + +fewer edges than +the original region. + +That's pretty easy +to prove, because you + +have-- Because you're connecting +to these four vertices, + +this region won't have +this vertex or this vertex. + +So it has one added vertex and +two removed vertices at least, + +W and T. So this +one will be smaller. + +And this is symmetric +for all of them. + +OK. + +So this would be a good case. + +So what I'm going to do +is try to move L around. + +I'm going to start +very close to VW + +and just start +moving off the edge. + +Initially, nothing +else will be active + +because it's basically +right on top of VW. + +But as I move around, I might +get another active path. + +OK. + +Maybe this is Case 1A. + +Before we get there, Case +1 is you get LU active. + +Suppose you just to get +one additional active path. + +The other case is, nothing +else becomes active. + +So here's V, here's W. Here's +L. Here's U. So this is active, + +active, active, active. + +OK, what I'm going to +do in this situation is, + +if I want to keep LU +active, I can actually + +move L on a circle. + +As long as L stays on this +circle, LU remains active. + +OK? + +So just move it +along the circle. + +Now, there are +two possibilities. + +It could be it becomes +active with something else. + +Then I'm done. + +Or it could be it doesn't, which +means it will hit the boundary. + +So it will hit a boundary point. + +So Case 1A-- so this is Case 1. + +You can make something active. + +When you move along +the circle, either you + +make another thing active, +or you won't and you + +hit the boundary. + +Case 1B is you hit the boundary. + +And then I claim +you're also happy. + +So in that situation-- +draw it one more time-- + +we've got L on the boundary. + +And we've got some path +here, here, here, here. + +These are all active. + +So here's L. OK. + +I claim again, each +of these regions + +has fewer vertices than before. + +Should be pretty obvious. + +This one is emitting W +and this was U. Yeah. + +It's emitting W +and it's emitting + +whatever's down +here, if anything. + +Yeah, I think it's +pretty obvious. + +You've got to check +all the cases. + +There's a few details here. + +But it should be each of +these regions has strictly + +fewer vertices +than it did before. + +And so you're making progress. + +If You started with all faces +having some number of edges, + +each time you do one of +these steps, you decrease it. + +OK, the last case, Case 2, is +you can't make anything active. + +This can happen, for +example, if you're + +in the corner of +the piece of paper + +and you have an active path. + +I guess that's a +little less exciting. + +Maybe your piece of +paper is this shape. + +Be a little bit weirder. + +So this will work for any +convex piece of paper. + +So it's not quite a triangle. + +And you're moving L +around here and you just + +can't get another active path. + +You have no vertices around. + +This is W, this is U-- sorry, +this is V. And in this case, + +L can go anywhere here. + +It's free. + +In that case, I'm +going to put L on one + +of the vertices of the paper. + +So I get this active +and this active. + +And then I've decomposed +that region into pieces by, + +this is what we call a diagonal. + +We're adding a vertex to +vertex edge in this polygon. + +And that always +decreases the number + +of sides in each +of the subregions. + +So if I just keep doing this, +taking any region of size + +larger than three, +I will eventually + +reduce them all to +have size three. + +So they'll all be triangles. + +So that's the triangulation +algorithm in a nutshell. + +You can look at the textbook if +you want to see it more detail, + +but it's pretty simple. + +This proves that +something is possible. + +I don't think TreeMaker actually +implements this algorithm + +specifically, but you can +kind of do it by hand. + +So I have a little example here. + +This is TreeMaker. + +I drew this really weird tree. + +We call it a caterpillar tree +because you would actually + +use it to make caterpillars. + +And if you just plug this into +TreeMaker with all the lengths + +unit, it will give you +this error message. + +I couldn't construct +all the polygons + +because things +weren't tight enough. + +And if you look carefully-- +it's a little hard + +to see these colors-- but +the light green edges, + +those are the active paths. + +And here-- so this was a +triangle and it was happy. + +If you look at this green +polygon-- maybe actually + +I'll draw with the tablet. + +So this thing is +an active-- that's + +a region bounded +by active paths. + +And probably the top edge +is not an active path. + +That's just a boundary. + +But it's not convex. + +And so you're unhappy. + +And so I just kind of +eyeball this and say, OK. + +Well, probably I should +add another leaf here + +that would maybe add a disk +that will probably fill that in. + +So you don't have +to be super-precise. + +Here we had the +very carefully place + +the disk to make things touch. + +But because TreeMaker's +always just trying + +to blow things up +and make them touch, + +it's quite a bit +easier in practice. + +You just say, OK. + +I will add an extra leaf +here, like that, to my tree. + +And then I hit Optimize, +and boom, it works. + +In this case, I was lucky. + +In general, I might +get a nonconvex region. + +I'd guess where to add +another leaf, and it works. + +You can adjust. + +Did that leaf have +to be that bit, + +or could I get away +with a smaller one? + +But eventually, you +will get a base. + +And if you want, you could +carefully monitor this proof + +and actually always succeed. + +But in practice, it's +usually not that hard. + +Questions about that? + +So that was the triangulation +method in a nutshell. + +The next question is about +the universal molecule. + +And we might spend some more +time on this next class. + +But I thought we could +actually look at this example, + +because it's got a bunch of +different universal molecules. + +So I will continue to draw. + +So let me pick, let's say, +this universal molecule here. + +It's a quadrilateral. + +All right. + +So those are four active +paths in this case. + +And it corresponds to some tree. + +So I don't have +handy here, but it's + +going to be a tree +with four edges. + +With four leaves, sorry. + +Tree with four leaves is going +to look something like this. + +This is a piece of +the bigger tree, which + +you recall looked +something like this. + +And we added one somewhere. + +But this particular +quadrilateral + +is doing some particular +subtree on four leaves. + +In particular, there +are four leaves here, + +correspond to four leaves here. + +I don't know which ones. + +I don't really need to know. + +TreeMaker keeps +track of it for me. + +And I happen to know that +these four paths are active. + +Meaning the lengths in the +plane here match exactly + +the lengths as measured +along the tree. + +So what I do to make +this work-- this + +is basically the +floor of the molecule. + +Those four paths will all +lie on the ground level. + +What I'm trying to do is slice +higher and higher in the base + +to see what happens +when I slice. + +And if you think about it, as +you move up here, in the plane + +this corresponds to moving +parallel to these edges. + +So I'm shrinking this +polygon by parallel offsets. + +So let me draw one +parallel offset. + +Approximately parallel. + +OK, after I shrink a little +bit, might look like that. + +An interesting moment +in this case is here. + +Let me draw this carefully. + +It should go-- this +should go here. + +Ooh. + +Oops. + +I'm going to start over. + +This is actually +already drawn for us. + +It's this guy. + +OK, this is a parallel offset. + +And in this case, +something interesting + +happens, which is this path. + +So it turns out this +middle edge, in this case, + +becomes active. + +So what that means +is, originally, + +if you looked at these two +points, these two leaves, + +they had the wrong length. + +OK? + +So that's going to correspond +to something like these two + +leaves. + +They're opposite +corners of the quad. + +And you measure the length along +the tree, you get something. + +And the claim was, in the +plane, it was too big. + +Now, as you do this +parallel offset, + +as you shrink the +polygon, at some point + +it will be just +the right length. + +This could happen. + +Doesn't have to happen. + +If it happens, you have to stop. + +Because if you kept going, +it would become too short. + +And we know every +length here must + +be greater than or equal +to length over here. + +So when it becomes +equal, we have to stop, + +and we have to +make this a crease. + +Making it a crease +basically says, + +ah, this is exactly +the right length. + +I have to split here. + +And where'd my chalk go? + +And I have to sort of grow +now two different flaps + +from that point. + +The crease sort of +makes it horizontal. + +And then we end up shrinking +in two different parts. + +We shrink in this triangle, +which gives us a rabbit ear. + +And we shrink up there +in that triangle. + +Gives us another rabbit ear. + +So it will end up giving +these angular bisectors. + +In general, as you +do the shrinking, + +you watch where the vertices go. + +Those are your ridge creases. + +So this one went along +an angular bisector. + +That one did as well. + +But once we do this +split operation, + +because of this newly +active path, which we also + +called a gusset in the +universal molecule, + +then these vertices actually +split and go in two directions. + +One for this thing +angular bisector and one + +for that angular bisector. + +So in general, for a +universal molecule, + +there, are two things +that can happen. + +You can be shrinking +your polygon + +and suddenly discover +there's a newly active path. + +And then you have to +divide it into two polygons + +and start shrinking +those separately. + +Or vertices can disappear. + +So it could be you're +just shrinking, shrinking, + +shrinking merrily along the way. + +And then suddenly, +these two vertices + +collide with each other. + +So you get to +ridge creases here. + +In this case, you just treat +those two vertices now as one. + +So you'll start +shrinking like this. + +And so these vertices will +now start going that way. + +So in general, as +you're shrinking, + +these are the only two types +of events that can happen. + +Either two vertices merge, or +you get a new diagonal here + +that becomes active. + +When that happens, +you just divide. + +Now, this will work +for any convex polygon + +and you get your molecule. + +It's hard to just +draw a picture of this + +without using a +computer tool or really + +keeping track of +what you're doing. + +Because how do you tell when +something becomes active? + +You have to look at your tree. + +You have to measure lengths. + +It's tricky to do +without a computer tool. + +And that's why +TreeMaker was made. + +But it can be done. + +Probably even easier +with physical paper + +if you know exactly what +lengths you're trying to match. + +So that was a quick overview +of how universal molecule works + +in more detail. + +Next, I want to talk about a +few different open problems. + +So one of them was-- these are +called gift wrapping problems. + +So we have things like given +a square, a unit square, + +let's say, what's the largest +regular tetrahedron you + +can wrap? + +That's still open. + +All these problems are still +open except for the squared + +to a cube which talked +about in lecture. + +And I realize equilateral +triangle to tetrahedron. + +That's also really easy. + +If you can do it without +any paper wasted, + +just clearly optimal. + +But it would be very +cool to study these. + +I think these would make a +good project or open problem + +for the open problem session. + +Folding a given rectangle with +given aspect ratio into a cube. + +Also open. + +Pretty much any version +you can think of + +is open except the ones +that we've already seen. + +Also wanted to mention for +checkerboards, a fun problem, + +kind of in this +spirit, is, what would + +be the best way to fold a +two by two checkerboard? + +Even for a two by +two, we have no idea + +how to argue any +kind of lower bound + +about how bad you must do. + +That you can't just take a +square and fold a two by two + +checkerboard of the same size. + +Surely you can't do that. + +But we don't know +how to prove that. + +So it would be a nice target. + +We obviously have upper bounds. + +We have constructions that +make two by two checkerboards. + +I think from a 3 by 3 +grid, you can make a two + +by two checkerboard. + +But is that optimal? + +We have no idea. + +So a couple questions about +the checkerboard folding. + +So we had this +picture of how you + +would take a square +root of paper-- you + +start with a square paper. + +You fold into this shape +with these long slits. + +And then these guys fold over. + +And then there are also +tab sticking up here, + +which are not drawn. + +And they fall over and give +you the color reversal. + +Question was, how do you +actually build this thing? + +This does not look uniaxial. + +And indeed, we do not use +uniaxial techniques for this. + +We use a separate +set of gadgets which + +are kind of based on pleating. + +And this will actually be +very similar to something + +we see in a couple +of lectures when + +we do box pleating to +make cubes and stuff. + +But you just compose +these gadgets. + +So this is kind of a +general tab gadget. + +You collapse this +crease pattern, + +and do a couple more folds. + +And you end up with this +tab sticking out here, + +and you can flip it up or down. + +And you see that it has these +pleats running off to the side. + +This mountain valley, +mountain valley, and then + +valley mountain, +valley mountain. + +And so those have to go all +the way through the paper. + +And they come into this +construction, which basically + +lets you make a big +slit in the paper. + +Or you can also turn a corner. + +And so you just prove that +these gadgets compose. + +I mean, it's pretty +that they compose. + +You just have to analyze how +much of the paper you're using. + +And it turns out +to be really good. + +That a short version. + +If you want to try it +out, fold some gadgets. + +Fun project idea +from you guys is, + +given an image, sample +at low resolution, + +make it black and white. + +And then come up with +the crease pattern + +that would fold, by this +checkerboard technique, + +into exactly that two +color pixel pattern. + +You could make all +sorts of useful things + +like Space Invaders +and stuff like that. + +You'd never want to +fold them, I think-- + +although maybe with low enough +resolution you could fold them. + +But I think they'd be cool +just as crease patterns + +by themselves. + +You input a different +pattern-- I'd like web applet. + +You change the pixel pattern. + +And boom, it gives you +the crease pattern. + +I think this would +be a fun project + +if you're into +implementing things. + +It's essentially the +algorithm we already have, + +but it needs to be just written +out in detail and coded up. + +OK. + +Here's what it looks like +to fold an eight by eight + +checkerboard with this method. + +These are all by Robert Lang. + +So a lot of precreasing +along this huge grid. + +I thinks it's roughly 48 by 48. + +And then some tape +to hold things + +shut, mostly for photographing. + +And to collapse, now we're +down by a factor of two or so. + +Now you can see the +slits in one direction. + +I think the particular +method being used here only + +has slits in one direction. + +Oh, no. + +Here we've got slits in the +vertical direction as well. + +You could see the tabs +sticking out here. + +They're going to fall down. + +There's some more of the tabs. + +Start folding over, +and boom, you've + +got your eight by +eight checkerboard. + +Robert Lang says, wow. + +That was not one of the +easier things I've done. + +And this is folded from +a 48 by 42 checkerboard. + +In principle, this method can +go down to 36 plus epsilon + +by 36 plus epsilon, but it gets +messier crease pattern-wise. + +And 36 would be better than the +best known eight by eight board + +if you want seamless. + +Notice these are +seamless squares. + +No crease lines through them. + +This one's not +necessarily-- this is not + +better than known techniques, +but it follows our algorithm. + +And that's what the +crease pattern looks like. + +Cool. + +Next we go to Origamizer. + +So as I mentioned +in lecture, there's + +two versions of Origamizer. + +There's the version that's +implemented in the software, + +and there's a version that +we're proving is always correct. + +These are different because +the version in the software + +doesn't always work. + +And it remains that way +because the software + +version is more practical. + +And also, the +theoretical version + +is still a moving target. + +We change it every few weeks +to fix part of the proof. + +It's almost done, but +it's been almost done + +for a couple of years. + +So we're still working on it. + +Tomohiro was just visiting +a couple weeks ago, + +as I mentioned. + +And we're closing in. + +I actually have with me the +current draft of the paper. + +And it's not nearly as long as +this one with the tree method, + +but it's still growing +and working up, + +making sure all the +details check out. + +And the theoretical version +is kind of complicated, + +so I thought, in particular, +given this question, + +we'll talk about +the software version + +because it's actually +a lot simpler. + +Only catch is, it +doesn't always work. + +And it's described +in this paper if you + +want to read it, by Tomohiro, +about Origamizer 2010. + +And I have a few +figures from that paper. + +Well, this is still +from Tomohiro's Flickr. + +So we had this example +where you wanted + +to fold this +hyperbolic paraboloid. + +And here's what the +crease pattern looks like. + +It's actually pretty simple. + +You've got these +white polygons, which + +are polygons from the surface. + +That's what you need to fold. + +And the goal is to lay them +out on the piece of paper-- + +this square is the +piece of paper-- + +so that I can-- +for example, I need + +to bring this polygon +to touch this polygon. + +This edge has to +touch this edge. + +Wouldn't it be great +if I could just + +fold the bisector +of those two edges, + +and this would come +right onto here? + +Sometimes that happens, +but for example, + +if this polygon is way down +here, that won't happen. + +It will fold over +and they won't align. + +There's two issues. + +First you have to get +the angles to match. + +And also there's this +vertical shifting. + +If you place the polygons +in the plane in a good way, + +this will work. + +You always get alignment. + +And what Origamizer implements +is nonconvex optimization, + +a constraint projection, to +make all of the edges work. + +And sometimes that's possible. + +It's actually +possible fairly often. + +And that's when the +Origamizer software works. + +If it's not possible, +you're screwed. + +This particular +method won't work. + +But when it's possible, +things are great. + +So essentially, you have to +bring the edges together. + +Then you also have to bring +the vertices together. + +Like these four vertices +come together to a point. + +And so you get two +kinds of gadgets, + +which are the vertex tucking +molecule to bring vertices + +together, and edge +tucking molecule + +to bring two edges together. + +Edge tucking molecule +is a single crease. + +Trivial in this construction. + +Vertex tucking molecule +is complicated. + +And in general, what +happens is for these points, + +we construct what's called +a Voronoi diagram, which + +is essentially, for +each of these points, + +if you grow a disk at equal +speeds around all of them, + +and when the disks +meet, you stop them. + +So then these two +disks will meet along + +this perpendicular bisector. + +And they'll keep growing until +they kind of all die out. + +And you'll get this tree +structure, in general. + +Those are your main creases. + +You follow that structure +and you do some stuff. + +Essentially, what happens when +you fold along this Voronoi + +diagram, you also have to add in +these creases from the Voronoi + +diagram to the points. + +When you do that, you'll get a +kind of mushrooming structure + +that has too much material. + +If you set it up right, all the +angles of paper that you have + +are larger than what you need +in the folded state, which + +would look like this. + +And so what you do are lots +of little pleats to reduce + +the angle. . + +If you've got a +big angle of paper, + +you can do a +mountain and a valley + +and make it a smaller angle. + +And that's what all +these creases are doing. + +You've got these pleats +to reduce the angle here, + +reduce the amount of material +here and here in order + +to match the 3D structure. + +So overall, what +the algorithm does + +is first, given the +surface, it constructs + +a suitable 3D structure of +where to put all the extra tabs. + +Then it designs things so +that the angles are bigger + +here than what they +need to be there. + +This is, again, a +constraint projection. + +Also constrains these +edges to meet up perfectly. + +And then it just applies +all these crimps-- + +it's easier in a computer +than to see it here-- + +to make all the angles +correct to match the 3D model. + +Yeah, question? + +AUDIENCE: So on +the sheet metal one + +that you showed, +do you just cut out + +the vertex shrinking +[INAUDIBLE]? + +PROFESSOR: Right. + +So for the sheet metal bunny, +we just cut out these polygons. + +Because otherwise, it's a mess +and you get lots of layers. + +And the point was to make +it of one sheet of material, + +but not necessarily a square. + +So if you have really +thick material, + +recommend cutting those out. + +And we were laser cutting +to score the lines anyway, + +so why not cut out +some holes as well. + +Yeah. + +So that way, you just have +edge tucking molecules, + +which are really easy. + +Mountain, valley, mountain. + +And so it actually +is pretty practical + +to fold these things out of +generalized sheets with holes. + +So the non-software +version of Origamizer + +works the same way, except +it does the full generality + +of constructing this tuck +proxy, where the tabs should go. + +And that can get very +messy in general. + +It's just tedious to explain. + +There are all these +crazy spherical diagrams + +that you saw in lecture. + +But it's not that exciting. + +The more interesting part is +that the edge tucking molecules + +can't just be a +single crease anymore. + +They have to, in general, +kind of follow some path + +to get to where they need to go. + +But it's similar. + +You just do a bunch +of different folds. + +You can sweep them +one way or the other + +in order to navigate this edge +to be where it needs to be. + +So again you place the +faces in the plane. + +In the mathematical +version, you can place them + +anywhere you want. + +It doesn't matter. + +And then you have to +shrink them until they're + +small enough that things work. + +Then you route these paths +to get from each edge + +to each corresponding edge. + +The edge tucking molecules +are fairly straightforward. + +The vertex tucking molecules +become even messier. + +We still use a Voronoi +diagram in the end. + +It's just there's +a lot more points. + +Here we're just using the +corners of the triangles + +as the source points +for growing stuff. + +In the general case, +you have to add + +lots of points in +the middle too. + +But it turns out not to matter. + +You could throw +in tons of points. + +You could always fold +a Voronoi diagram. + +You get this mushroomy thing. + +And then you can just fold +away the parts you don't need. + +You have to make +them really small + +in order to make these +tabs not too big, + +because if the tabs are too big, +they collide with each other. + +That already happened +in the software version. + +Even in the software +version, this + +might not work because +this tab may be huge. + +But you can-- in this case, +you just add a few more + +and make this pleat up and down, +and you'll avoid collision. + +So that was a quick, but +a little bit more clear, + +overview of Origamizer +and how it works. + +Any more questions? + +Cool. + +That's it for today. \ No newline at end of file diff --git a/zd9aU90WzV8.txt b/zd9aU90WzV8.txt new file mode 100644 index 0000000000000000000000000000000000000000..73713842d4f29c9588716f4d36e8a7e50caf7e5f --- /dev/null +++ b/zd9aU90WzV8.txt @@ -0,0 +1,13651 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +All right. So, so far we've recently + + align:start position:0% +All right. So, so far we've recently + + + align:start position:0% +All right. So, so far we've recently +been talking about examples in SCT2 and + + align:start position:0% +been talking about examples in SCT2 and + + + align:start position:0% +been talking about examples in SCT2 and +we're going to continue to do so today. + + align:start position:0% +we're going to continue to do so today. + + + align:start position:0% +we're going to continue to do so today. +So, the example that we did last time + + align:start position:0% +So, the example that we did last time + + + align:start position:0% +So, the example that we did last time +was the pion photon form factor that did + + align:start position:0% +was the pion photon form factor that did + + + align:start position:0% +was the pion photon form factor that did +not have any soft degrees of freedom. It + + align:start position:0% +not have any soft degrees of freedom. It + + + align:start position:0% +not have any soft degrees of freedom. It +just had linear and hard degrees of + + align:start position:0% +just had linear and hard degrees of + + + align:start position:0% +just had linear and hard degrees of +freedom. So, it was a particularly + + align:start position:0% +freedom. So, it was a particularly + + + align:start position:0% +freedom. So, it was a particularly +simple example of something we could + + align:start position:0% +simple example of something we could + + + align:start position:0% +simple example of something we could +think of in SCT2. We'll start with a + + align:start position:0% +think of in SCT2. We'll start with a + + + align:start position:0% +think of in SCT2. We'll start with a +slightly more complicated example. this + + align:start position:0% +slightly more complicated example. this + + + align:start position:0% +slightly more complicated example. this +decay b to d pi where we have both + + align:start position:0% +decay b to d pi where we have both + + + align:start position:0% +decay b to d pi where we have both +linear and soft degrees of freedom. This + + align:start position:0% +linear and soft degrees of freedom. This + + + align:start position:0% +linear and soft degrees of freedom. This +was an example that we mentioned at the + + align:start position:0% +was an example that we mentioned at the + + + align:start position:0% +was an example that we mentioned at the +very beginning of our discussion of SCT + + align:start position:0% +very beginning of our discussion of SCT + + + align:start position:0% +very beginning of our discussion of SCT +and now we're going to see how + + align:start position:0% +and now we're going to see how + + + align:start position:0% +and now we're going to see how +factorization looks for it. And then + + align:start position:0% +factorization looks for it. And then + + + align:start position:0% +factorization looks for it. And then +we'll talk about something called the + + align:start position:0% +we'll talk about something called the + + + align:start position:0% +we'll talk about something called the +reormaliz rapidity renormalization group + + align:start position:0% +reormaliz rapidity renormalization group + + + align:start position:0% +reormaliz rapidity renormalization group +which has to do with situations in SCT2 + + align:start position:0% +which has to do with situations in SCT2 + + + align:start position:0% +which has to do with situations in SCT2 +where the separation of degrees of + + align:start position:0% +where the separation of degrees of + + + align:start position:0% +where the separation of degrees of +freedom is a little more complicated + + align:start position:0% +freedom is a little more complicated + + + align:start position:0% +freedom is a little more complicated +than in the previous examples. and we'll + + align:start position:0% +than in the previous examples. and we'll + + + align:start position:0% +than in the previous examples. and we'll +see that there can be a new type of + + align:start position:0% +see that there can be a new type of + + + align:start position:0% +see that there can be a new type of +divergence that shows up and that new + + align:start position:0% +divergence that shows up and that new + + + align:start position:0% +divergence that shows up and that new +type of divergence leads to a new type + + align:start position:0% +type of divergence leads to a new type + + + align:start position:0% +type of divergence leads to a new type +of normalization group. + + align:start position:0% +of normalization group. + + + align:start position:0% +of normalization group. +So + + align:start position:0% + + + + align:start position:0% + +B toD pi + + align:start position:0% +B toD pi + + + align:start position:0% +B toD pi +so + + align:start position:0% +so + + + align:start position:0% +so +there's going to be in some sense + + align:start position:0% +there's going to be in some sense + + + align:start position:0% +there's going to be in some sense +three hard scales of this problem. + + align:start position:0% +three hard scales of this problem. + + + align:start position:0% +three hard scales of this problem. +the mass of the B quark and the mass of + + align:start position:0% +the mass of the B quark and the mass of + + + align:start position:0% +the mass of the B quark and the mass of +the charm quark are going to be taken to + + align:start position:0% +the charm quark are going to be taken to + + + align:start position:0% +the charm quark are going to be taken to +be much greater than lambda QCD. So + + align:start position:0% +be much greater than lambda QCD. So + + + align:start position:0% +be much greater than lambda QCD. So +we'll have an HQ type description of the + + align:start position:0% +we'll have an HQ type description of the + + + align:start position:0% +we'll have an HQ type description of the +B quark and the charm quark and also the + + align:start position:0% +B quark and the charm quark and also the + + + align:start position:0% +B quark and the charm quark and also the +energy of the pion which is in some + + align:start position:0% +energy of the pion which is in some + + + align:start position:0% +energy of the pion which is in some +sense related to the difference of the B + + align:start position:0% +sense related to the difference of the B + + + align:start position:0% +sense related to the difference of the B +quark and the charm quark mass will also + + align:start position:0% +quark and the charm quark mass will also + + + align:start position:0% +quark and the charm quark mass will also +take that to be much greater than lambda + + align:start position:0% +take that to be much greater than lambda + + + align:start position:0% +take that to be much greater than lambda +QCD. So just by kinematics this is this + + align:start position:0% +QCD. So just by kinematics this is this + + + align:start position:0% +QCD. So just by kinematics this is this +thing is proportional to + + align:start position:0% +thing is proportional to + + + align:start position:0% +thing is proportional to +MB minus MC + + align:start position:0% +MB minus MC + + + align:start position:0% +MB minus MC +roughly + + align:start position:0% +roughly + + + align:start position:0% +roughly +could say it's the difference of the + + align:start position:0% +could say it's the difference of the + + + align:start position:0% +could say it's the difference of the +squares of the hydron masses. + + align:start position:0% +squares of the hydron masses. + + + align:start position:0% +squares of the hydron masses. +Okay, so let's first we know how to + + align:start position:0% +Okay, so let's first we know how to + + + align:start position:0% +Okay, so let's first we know how to +treat this decay if we were integrating + + align:start position:0% +treat this decay if we were integrating + + + align:start position:0% +treat this decay if we were integrating +out the W. This is a weak decay. So B is + + align:start position:0% +out the W. This is a weak decay. So B is + + + align:start position:0% +out the W. This is a weak decay. So B is +changing a charm. Integrate out the W + + align:start position:0% +changing a charm. Integrate out the W + + + align:start position:0% +changing a charm. Integrate out the W +boson run down to the scale MB which is + + align:start position:0% +boson run down to the scale MB which is + + + align:start position:0% +boson run down to the scale MB which is +the largest scale here. That's the + + align:start position:0% +the largest scale here. That's the + + + align:start position:0% +the largest scale here. That's the +electroeak Hamiltonian. + + align:start position:0% + + + + align:start position:0% + +So that's what we'll call the QCD + + align:start position:0% +So that's what we'll call the QCD + + + align:start position:0% +So that's what we'll call the QCD +operators + + align:start position:0% + + + + align:start position:0% + +which are the relevant description at + + align:start position:0% +which are the relevant description at + + + align:start position:0% +which are the relevant description at +the scale of order MB. + + align:start position:0% + + + + align:start position:0% + +some prefactor + + align:start position:0% + + + + align:start position:0% + +and I'll write the operators in the + + align:start position:0% +and I'll write the operators in the + + + align:start position:0% +and I'll write the operators in the +following way + + align:start position:0% +following way + + + align:start position:0% +following way +a slightly different basis than we used + + align:start position:0% +a slightly different basis than we used + + + align:start position:0% +a slightly different basis than we used +previously + + align:start position:0% + + + + align:start position:0% + +or a long time ago when we were talking + + align:start position:0% +or a long time ago when we were talking + + + align:start position:0% +or a long time ago when we were talking +about this particular + + align:start position:0% +about this particular + + + align:start position:0% +about this particular +case. So just a different color basis + + align:start position:0% +case. So just a different color basis + + + align:start position:0% +case. So just a different color basis +singlet and octet. + + align:start position:0% + + + + align:start position:0% + +Okay. So that's our description where P + + align:start position:0% +Okay. So that's our description where P + + + align:start position:0% +Okay. So that's our description where P +left is projecting us onto + + align:start position:0% +left is projecting us onto + + + align:start position:0% +left is projecting us onto +the left-handed components. + + align:start position:0% +the left-handed components. + + + align:start position:0% +the left-handed components. +So what we want to do is we want to + + align:start position:0% +So what we want to do is we want to + + + align:start position:0% +So what we want to do is we want to +factoriize the amplitude. This is an + + align:start position:0% +factoriize the amplitude. This is an + + + align:start position:0% +factoriize the amplitude. This is an +exclusive process where we make a + + align:start position:0% +exclusive process where we make a + + + align:start position:0% +exclusive process where we make a +transition between + + align:start position:0% +transition between + + + align:start position:0% +transition between +specific states. So + + align:start position:0% + + + + align:start position:0% + +we'd like to separate scales + + align:start position:0% +we'd like to separate scales + + + align:start position:0% +we'd like to separate scales +in the DPI + + align:start position:0% +in the DPI + + + align:start position:0% +in the DPI +and then we have O8 + + align:start position:0% + + + + align:start position:0% + +in this matrix element. So we have two + + align:start position:0% +in this matrix element. So we have two + + + align:start position:0% +in this matrix element. So we have two +matrix elements, one with 0 and one with + + align:start position:0% +matrix elements, one with 0 and one with + + + align:start position:0% +matrix elements, one with 0 and one with +08. + + align:start position:0% +08. + + + align:start position:0% +08. +And so what could it possibly look like? + + align:start position:0% +And so what could it possibly look like? + + + align:start position:0% +And so what could it possibly look like? +Well, we already talked about the + + align:start position:0% +Well, we already talked about the + + + align:start position:0% +Well, we already talked about the +degrees of freedom here. The D is going + + align:start position:0% +degrees of freedom here. The D is going + + + align:start position:0% +degrees of freedom here. The D is going +to be soft and the B is going to be + + align:start position:0% +to be soft and the B is going to be + + + align:start position:0% +to be soft and the B is going to be +soft. + + align:start position:0% +soft. + + + align:start position:0% +soft. +So + + align:start position:0% +So + + + align:start position:0% +So +this is soft. This is soft. This is + + align:start position:0% +this is soft. This is soft. This is + + + align:start position:0% +this is soft. This is soft. This is +going to be linear. And so if it's going + + align:start position:0% +going to be linear. And so if it's going + + + align:start position:0% +going to be linear. And so if it's going +to factoriize and the soft degrees of + + align:start position:0% +to factoriize and the soft degrees of + + + align:start position:0% +to factoriize and the soft degrees of +freedom are not going to talk to the + + align:start position:0% +freedom are not going to talk to the + + + align:start position:0% +freedom are not going to talk to the +linear the kind of thing that you would + + align:start position:0% +linear the kind of thing that you would + + + align:start position:0% +linear the kind of thing that you would +expect + + align:start position:0% +expect + + + align:start position:0% +expect +to show at leading order + + align:start position:0% +to show at leading order + + + align:start position:0% +to show at leading order +in the lambda expansion + + align:start position:0% +in the lambda expansion + + + align:start position:0% +in the lambda expansion +is that you have a the following kind of + + align:start position:0% +is that you have a the following kind of + + + align:start position:0% +is that you have a the following kind of +process. + + align:start position:0% + + + + align:start position:0% + +Let me reclaim this space. + + align:start position:0% + + + + align:start position:0% + +So here's a heavy quark. Here's one of + + align:start position:0% +So here's a heavy quark. Here's one of + + + align:start position:0% +So here's a heavy quark. Here's one of +these operators. + + align:start position:0% +these operators. + + + align:start position:0% +these operators. +Here's the veilance quarks in the pion. + + align:start position:0% +Here's the veilance quarks in the pion. + + + align:start position:0% +Here's the veilance quarks in the pion. +Another heavy quark. So this is B, + + align:start position:0% +Another heavy quark. So this is B, + + + align:start position:0% +Another heavy quark. So this is B, +charm, + + align:start position:0% +charm, + + + align:start position:0% +charm, +U and D. + + align:start position:0% + + + + align:start position:0% + +And there's an anti-quark. And we have + + align:start position:0% +And there's an anti-quark. And we have + + + align:start position:0% +And there's an anti-quark. And we have +to dress this by gluons. And if it's + + align:start position:0% +to dress this by gluons. And if it's + + + align:start position:0% +to dress this by gluons. And if it's +going to factorized, then the way that + + align:start position:0% +going to factorized, then the way that + + + align:start position:0% +going to factorized, then the way that +we should dress it by gluons is as + + align:start position:0% +we should dress it by gluons is as + + + align:start position:0% +we should dress it by gluons is as +follows. We would have soft gluons + + align:start position:0% +follows. We would have soft gluons + + + align:start position:0% +follows. We would have soft gluons +here. And they could interact if you + + align:start position:0% +here. And they could interact if you + + + align:start position:0% +here. And they could interact if you +like between things in the in the B and + + align:start position:0% +like between things in the in the B and + + + align:start position:0% +like between things in the in the B and +the D because the B and the D are both + + align:start position:0% +the D because the B and the D are both + + + align:start position:0% +the D because the B and the D are both +soft. And we can also have vacuum + + align:start position:0% +soft. And we can also have vacuum + + + align:start position:0% +soft. And we can also have vacuum +polarization diagrams and that is going + + align:start position:0% +polarization diagrams and that is going + + + align:start position:0% +polarization diagrams and that is going +to factoriize from things in the + + align:start position:0% +to factoriize from things in the + + + align:start position:0% +to factoriize from things in the +pion which are going to be colinear. So + + align:start position:0% +pion which are going to be colinear. So + + + align:start position:0% +pion which are going to be colinear. So +we have our linear gluons and + + align:start position:0% +we have our linear gluons and + + + align:start position:0% +we have our linear gluons and +linear quarks inside here. And maybe + + align:start position:0% +linear quarks inside here. And maybe + + + align:start position:0% +linear quarks inside here. And maybe +there's some Wilson lines too. + + align:start position:0% +there's some Wilson lines too. + + + align:start position:0% +there's some Wilson lines too. +So we would expect some kind of picture + + align:start position:0% +So we would expect some kind of picture + + + align:start position:0% +So we would expect some kind of picture +like that and that's actually going to + + align:start position:0% +like that and that's actually going to + + + align:start position:0% +like that and that's actually going to +be what we do find. But exactly what + + align:start position:0% +be what we do find. But exactly what + + + align:start position:0% +be what we do find. But exactly what +happens at this vertex what kind of + + align:start position:0% +happens at this vertex what kind of + + + align:start position:0% +happens at this vertex what kind of +convolutions there are that we have to + + align:start position:0% +convolutions there are that we have to + + + align:start position:0% +convolutions there are that we have to +work out. + + align:start position:0% +work out. + + + align:start position:0% +work out. +All right. So what factorization in this + + align:start position:0% +All right. So what factorization in this + + + align:start position:0% +All right. So what factorization in this +context means is that there's no gluons + + align:start position:0% +context means is that there's no gluons + + + align:start position:0% +context means is that there's no gluons +that are directly exchanged between the + + align:start position:0% +that are directly exchanged between the + + + align:start position:0% +that are directly exchanged between the +BD part and the pion part. + + align:start position:0% + + + + align:start position:0% + +so that it effectively factorizes in + + align:start position:0% +so that it effectively factorizes in + + + align:start position:0% +so that it effectively factorizes in +into a matrix element that's like a B + + align:start position:0% +into a matrix element that's like a B + + + align:start position:0% +into a matrix element that's like a B +toD transition and a vacuum to pion + + align:start position:0% +toD transition and a vacuum to pion + + + align:start position:0% +toD transition and a vacuum to pion +transition. + + align:start position:0% +transition. + + + align:start position:0% +transition. +So you can even guess what kind of + + align:start position:0% +So you can even guess what kind of + + + align:start position:0% +So you can even guess what kind of +objects this would depend on. If you + + align:start position:0% +objects this would depend on. If you + + + align:start position:0% +objects this would depend on. If you +have something like this green thing + + align:start position:0% +have something like this green thing + + + align:start position:0% +have something like this green thing +that's a bet to D form factor. + + align:start position:0% +that's a bet to D form factor. + + + align:start position:0% +that's a bet to D form factor. +So + + align:start position:0% +So + + + align:start position:0% +So +we expect + + align:start position:0% +we expect + + + align:start position:0% +we expect +a B tog form factor + + align:start position:0% + + + + align:start position:0% + +and for the pion if you have something + + align:start position:0% +and for the pion if you have something + + + align:start position:0% +and for the pion if you have something +like this well we already talked about + + align:start position:0% +like this well we already talked about + + + align:start position:0% +like this well we already talked about +something like this when we were talking + + align:start position:0% +something like this when we were talking + + + align:start position:0% +something like this when we were talking +about gamma star gamma to pi 0. So for + + align:start position:0% +about gamma star gamma to pi 0. So for + + + align:start position:0% +about gamma star gamma to pi 0. So for +the pion we expect the pi 0 the light + + align:start position:0% +the pion we expect the pi 0 the light + + + align:start position:0% +the pion we expect the pi 0 the light +cone distribution + + align:start position:0% + + + + align:start position:0% + +which is the sort of leading order + + align:start position:0% +which is the sort of leading order + + + align:start position:0% +which is the sort of leading order +operator for the pion. + + align:start position:0% +operator for the pion. + + + align:start position:0% +operator for the pion. +So we'd expect a 5 pi of x + + align:start position:0% +So we'd expect a 5 pi of x + + + align:start position:0% +So we'd expect a 5 pi of x +and we'll see that we do indeed find + + align:start position:0% +and we'll see that we do indeed find + + + align:start position:0% +and we'll see that we do indeed find +that. + + align:start position:0% + + + + align:start position:0% + +So the B and D have P square of order + + align:start position:0% +So the B and D have P square of order + + + align:start position:0% +So the B and D have P square of order +lambda QCD squared. For their + + align:start position:0% +lambda QCD squared. For their + + + align:start position:0% +lambda QCD squared. For their +constituents the pion + + align:start position:0% +constituents the pion + + + align:start position:0% +constituents the pion +is colinear + + align:start position:0% +is colinear + + + align:start position:0% +is colinear +and its constituents have P square of + + align:start position:0% +and its constituents have P square of + + + align:start position:0% +and its constituents have P square of +order lambda QCD2 but they're boosted. + + align:start position:0% +order lambda QCD2 but they're boosted. + + + align:start position:0% +order lambda QCD2 but they're boosted. +We can again use SCT this is SCT2 but we + + align:start position:0% +We can again use SCT this is SCT2 but we + + + align:start position:0% +We can again use SCT this is SCT2 but we +can use SCT1 as an intermediate step + + align:start position:0% +can use SCT1 as an intermediate step + + + align:start position:0% +can use SCT1 as an intermediate step +just like we did we talked about last + + align:start position:0% +just like we did we talked about last + + + align:start position:0% +just like we did we talked about last +time. + + align:start position:0% + + + + align:start position:0% + +So let's do that again. So match step + + align:start position:0% +So let's do that again. So match step + + + align:start position:0% +So let's do that again. So match step +one was to match QCD onto the SC one. + + align:start position:0% + + + + align:start position:0% + +So there's some hard scale and the hard + + align:start position:0% +So there's some hard scale and the hard + + + align:start position:0% +So there's some hard scale and the hard +scale in this case could be any one of + + align:start position:0% +scale in this case could be any one of + + + align:start position:0% +scale in this case could be any one of +these three. + + align:start position:0% +these three. + + + align:start position:0% +these three. +So collectively I'll just denote them by + + align:start position:0% +So collectively I'll just denote them by + + + align:start position:0% +So collectively I'll just denote them by +Q. + + align:start position:0% + + + + align:start position:0% + +And so what's going to happen in that + + align:start position:0% +And so what's going to happen in that + + + align:start position:0% +And so what's going to happen in that +matching is we take these operators 0 + + align:start position:0% +matching is we take these operators 0 + + + align:start position:0% +matching is we take these operators 0 +and08 and we have to match on to SCT + + align:start position:0% +and08 and we have to match on to SCT + + + align:start position:0% +and08 and we have to match on to SCT +operators. + + align:start position:0% + + + + align:start position:0% + +So let me call the SCT operators Q0. + + align:start position:0% + + + + align:start position:0% + +Yeah, I guess there's + + align:start position:0% + + + + align:start position:0% + +because of the fact that there's a heavy + + align:start position:0% +because of the fact that there's a heavy + + + align:start position:0% +because of the fact that there's a heavy +quark in the way that uh the way that + + align:start position:0% +quark in the way that uh the way that + + + align:start position:0% +quark in the way that uh the way that +that works. There's two possible spin + + align:start position:0% +that works. There's two possible spin + + + align:start position:0% +that works. There's two possible spin +structures in here, + + align:start position:0% +structures in here, + + + align:start position:0% +structures in here, +but we'll see that actually only one of + + align:start position:0% +but we'll see that actually only one of + + + align:start position:0% +but we'll see that actually only one of +them has the right quantum numbers in + + align:start position:0% +them has the right quantum numbers in + + + align:start position:0% +them has the right quantum numbers in +the end. + + align:start position:0% +the end. + + + align:start position:0% +the end. +So we have heavy cork fields, charm and + + align:start position:0% +So we have heavy cork fields, charm and + + + align:start position:0% +So we have heavy cork fields, charm and +bottom. + + align:start position:0% + + + + align:start position:0% + +That's we can imagine that type of + + align:start position:0% +That's we can imagine that type of + + + align:start position:0% +That's we can imagine that type of +operator. And then for the cleaner part, + + align:start position:0% +operator. And then for the cleaner part, + + + align:start position:0% +operator. And then for the cleaner part, +we can dress it with the Wilson line as + + align:start position:0% +we can dress it with the Wilson line as + + + align:start position:0% +we can dress it with the Wilson line as +always. And let me put the flavor + + align:start position:0% +always. And let me put the flavor + + + align:start position:0% +always. And let me put the flavor +upstairs. + + align:start position:0% + + + + align:start position:0% + +And let me put in the most general + + align:start position:0% +And let me put in the most general + + + align:start position:0% +And let me put in the most general +Wilson coefficient that I could think of + + align:start position:0% +Wilson coefficient that I could think of + + + align:start position:0% +Wilson coefficient that I could think of +for this process. + + align:start position:0% +for this process. + + + align:start position:0% +for this process. +This could also depend on V.V prime. + + align:start position:0% +This could also depend on V.V prime. + + + align:start position:0% +This could also depend on V.V prime. +I didn't denote that, but in general it + + align:start position:0% +I didn't denote that, but in general it + + + align:start position:0% +I didn't denote that, but in general it +will. And it could depend on any of the + + align:start position:0% +will. And it could depend on any of the + + + align:start position:0% +will. And it could depend on any of the +scales Q. + + align:start position:0% +scales Q. + + + align:start position:0% +scales Q. +So it can depend on the large momentum + + align:start position:0% +So it can depend on the large momentum + + + align:start position:0% +So it can depend on the large momentum +of the linear fields as always. And + + align:start position:0% +of the linear fields as always. And + + + align:start position:0% +of the linear fields as always. And +there's one combination that's not + + align:start position:0% +there's one combination that's not + + + align:start position:0% +there's one combination that's not +restricted by momentum cons + + align:start position:0% +restricted by momentum cons + + + align:start position:0% +restricted by momentum cons +conservation. So there's one combination + + align:start position:0% +conservation. So there's one combination + + + align:start position:0% +conservation. So there's one combination +that's not related to these scales and + + align:start position:0% +that's not related to these scales and + + + align:start position:0% +that's not related to these scales and +that's the in my notation the P bar plus + + align:start position:0% +that's the in my notation the P bar plus + + + align:start position:0% +that's the in my notation the P bar plus +operator + + align:start position:0% +operator + + + align:start position:0% +operator +and then there's a likewise there's + + align:start position:0% +and then there's a likewise there's + + + align:start position:0% +and then there's a likewise there's +another thing with the TA. So same thing + + align:start position:0% +another thing with the TA. So same thing + + + align:start position:0% +another thing with the TA. So same thing +TA + + align:start position:0% +TA + + + align:start position:0% +TA +everything the same TA + + align:start position:0% +everything the same TA + + + align:start position:0% +everything the same TA +and then this has got a different + + align:start position:0% +and then this has got a different + + + align:start position:0% +and then this has got a different +coefficient + + align:start position:0% + + + + align:start position:0% + +like that. + + align:start position:0% +like that. + + + align:start position:0% +like that. +And so what are the direct structures + + align:start position:0% +And so what are the direct structures + + + align:start position:0% +And so what are the direct structures +just to be explicit? + + align:start position:0% +just to be explicit? + + + align:start position:0% +just to be explicit? +The heavy one. + + align:start position:0% +The heavy one. + + + align:start position:0% +The heavy one. +So the light one is is + + align:start position:0% +So the light one is is + + + align:start position:0% +So the light one is is +going to be m/ + + align:start position:0% +going to be m/ + + + align:start position:0% +going to be m/ +four in my notation + + align:start position:0% +four in my notation + + + align:start position:0% +four in my notation +the 1 - gamma 5. And for the heavy one, + + align:start position:0% +the 1 - gamma 5. And for the heavy one, + + + align:start position:0% +the 1 - gamma 5. And for the heavy one, +you could have either one or gamma 5. + + align:start position:0% +you could have either one or gamma 5. + + + align:start position:0% +you could have either one or gamma 5. +And that's because you originally have a + + align:start position:0% +And that's because you originally have a + + + align:start position:0% +And that's because you originally have a +left-handed + + align:start position:0% +left-handed + + + align:start position:0% +left-handed +originally here you have a left-handed + + align:start position:0% +originally here you have a left-handed + + + align:start position:0% +originally here you have a left-handed +guy between the charm and the bee. But + + align:start position:0% +guy between the charm and the bee. But + + + align:start position:0% +guy between the charm and the bee. But +remember that mass term connects left + + align:start position:0% +remember that mass term connects left + + + align:start position:0% +remember that mass term connects left +and right. Right? So after you integrate + + align:start position:0% +and right. Right? So after you integrate + + + align:start position:0% +and right. Right? So after you integrate +out the mass of these quarks, you don't + + align:start position:0% +out the mass of these quarks, you don't + + + align:start position:0% +out the mass of these quarks, you don't +know whether you don't know the kirality + + align:start position:0% +know whether you don't know the kirality + + + align:start position:0% +know whether you don't know the kirality +anymore in this. So that's why you could + + align:start position:0% +anymore in this. So that's why you could + + + align:start position:0% +anymore in this. So that's why you could +have both the possibilities one and gam + + align:start position:0% +have both the possibilities one and gam + + + align:start position:0% +have both the possibilities one and gam +five. + + align:start position:0% + + + + align:start position:0% + +So if you put any other direct + + align:start position:0% +So if you put any other direct + + + align:start position:0% +So if you put any other direct +structure, so here you could use + + align:start position:0% +structure, so here you could use + + + align:start position:0% +structure, so here you could use +kirality and so you know that these guys + + align:start position:0% +kirality and so you know that these guys + + + align:start position:0% +kirality and so you know that these guys +should be left-handed still and that's + + align:start position:0% +should be left-handed still and that's + + + align:start position:0% +should be left-handed still and that's +why you know that this should be this + + align:start position:0% +why you know that this should be this + + + align:start position:0% +why you know that this should be this +structure. So you know it should be an n + + align:start position:0% +structure. So you know it should be an n + + + align:start position:0% +structure. So you know it should be an n +bar slash because any other structure + + align:start position:0% +bar slash because any other structure + + + align:start position:0% +bar slash because any other structure +that you would stick in here between + + align:start position:0% +that you would stick in here between + + + align:start position:0% +that you would stick in here between +them uh would give you something that's + + align:start position:0% +them uh would give you something that's + + + align:start position:0% +them uh would give you something that's +power suppressed + + align:start position:0% +power suppressed + + + align:start position:0% +power suppressed +because you know that n slash + + align:start position:0% +because you know that n slash + + + align:start position:0% +because you know that n slash +on cn is zero and also cn bar gamma per + + align:start position:0% +on cn is zero and also cn bar gamma per + + + align:start position:0% +on cn is zero and also cn bar gamma per +mu + + align:start position:0% +mu + + + align:start position:0% +mu +with any kind of p left or whatever + + align:start position:0% +with any kind of p left or whatever + + + align:start position:0% +with any kind of p left or whatever +is also zero. So + + align:start position:0% +is also zero. So + + + align:start position:0% +is also zero. So +we'd have to have something more + + align:start position:0% +we'd have to have something more + + + align:start position:0% +we'd have to have something more +complicated. + + align:start position:0% +complicated. + + + align:start position:0% +complicated. +All right. So there's those operators + + align:start position:0% +All right. So there's those operators + + + align:start position:0% +All right. So there's those operators +and when you do this matching it is + + align:start position:0% +and when you do this matching it is + + + align:start position:0% +and when you do this matching it is +non-trivial in the sense that these two + + align:start position:0% +non-trivial in the sense that these two + + + align:start position:0% +non-trivial in the sense that these two +operators it's not diagonal. It's not + + align:start position:0% +operators it's not diagonal. It's not + + + align:start position:0% +operators it's not diagonal. It's not +like 0 goes to Q0 and O8 goes to Q8. + + align:start position:0% +like 0 goes to Q0 and O8 goes to Q8. + + + align:start position:0% +like 0 goes to Q0 and O8 goes to Q8. +Soon as you start adding loop + + align:start position:0% +Soon as you start adding loop + + + align:start position:0% +Soon as you start adding loop +corrections these two mix and then they + + align:start position:0% +corrections these two mix and then they + + + align:start position:0% +corrections these two mix and then they +give you some contributions to these + + align:start position:0% +give you some contributions to these + + + align:start position:0% +give you some contributions to these +coefficients C 0 and C8. + + align:start position:0% +coefficients C 0 and C8. + + + align:start position:0% +coefficients C 0 and C8. +Okay. So what you mean by octed operator + + align:start position:0% +Okay. So what you mean by octed operator + + + align:start position:0% +Okay. So what you mean by octed operator +in the electric Hamiltonian is different + + align:start position:0% +in the electric Hamiltonian is different + + + align:start position:0% +in the electric Hamiltonian is different +than what you mean by octed operator in + + align:start position:0% +than what you mean by octed operator in + + + align:start position:0% +than what you mean by octed operator in +the SCT1 factorized + + align:start position:0% +the SCT1 factorized + + + align:start position:0% +the SCT1 factorized +result. But that's just a complication + + align:start position:0% +result. But that's just a complication + + + align:start position:0% +result. But that's just a complication +that you deal with when you are doing + + align:start position:0% +that you deal with when you are doing + + + align:start position:0% +that you deal with when you are doing +the matching. This guy can be + + align:start position:0% +the matching. This guy can be + + + align:start position:0% +the matching. This guy can be +proportional to the Wilson coefficients + + align:start position:0% +proportional to the Wilson coefficients + + + align:start position:0% +proportional to the Wilson coefficients +C 0 F and C 08 and that's not really a + + align:start position:0% +C 0 F and C 08 and that's not really a + + + align:start position:0% +C 0 F and C 08 and that's not really a +big deal. + + align:start position:0% +big deal. + + + align:start position:0% +big deal. +Any questions so far? + + align:start position:0% + + + + align:start position:0% + +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +So the is the point of matching scale + + align:start position:0% +So the is the point of matching scale + + + align:start position:0% +So the is the point of matching scale +one as an intermediate step is to get + + align:start position:0% +one as an intermediate step is to get + + + align:start position:0% +one as an intermediate step is to get +the softs. + + align:start position:0% +the softs. + + + align:start position:0% +the softs. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +So you're going to do + + align:start position:0% +So you're going to do + + + align:start position:0% +So you're going to do +that's right. I'm going to do that right + + align:start position:0% +that's right. I'm going to do that right + + + align:start position:0% +that's right. I'm going to do that right +now. + + align:start position:0% +now. + + + align:start position:0% +now. +Yeah. So then step two field + + align:start position:0% +Yeah. So then step two field + + + align:start position:0% +Yeah. So then step two field +redefinition + + align:start position:0% + + + + align:start position:0% + +in the sket one. + + align:start position:0% + + + + align:start position:0% + +And let me not put superscript zeros. + + align:start position:0% +And let me not put superscript zeros. + + + align:start position:0% +And let me not put superscript zeros. +Let me just make it as a replacement. + + align:start position:0% +Let me just make it as a replacement. + + + align:start position:0% +Let me just make it as a replacement. +So then we get our Q0 + + align:start position:0% +So then we get our Q0 + + + align:start position:0% +So then we get our Q0 +again. + + align:start position:0% +again. + + + align:start position:0% +again. +And okay, + + align:start position:0% +And okay, + + + align:start position:0% +And okay, +for this guy, it's exactly the same + + align:start position:0% +for this guy, it's exactly the same + + + align:start position:0% +for this guy, it's exactly the same +because in the in the q01 comma 5 the + + align:start position:0% +because in the in the q01 comma 5 the + + + align:start position:0% +because in the in the q01 comma 5 the +all the y's cancel. + + align:start position:0% + + + + align:start position:0% + +in the octate guy. It's not quite that + + align:start position:0% +in the octate guy. It's not quite that + + + align:start position:0% +in the octate guy. It's not quite that +way because there's because we do have + + align:start position:0% +way because there's because we do have + + + align:start position:0% +way because there's because we do have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in that case we do have uh the Wilson + + align:start position:0% +in that case we do have uh the Wilson + + + align:start position:0% +in that case we do have uh the Wilson +lines getting trapped by the TA. So let + + align:start position:0% +lines getting trapped by the TA. So let + + + align:start position:0% +lines getting trapped by the TA. So let +me write out that case. + + align:start position:0% + + + + align:start position:0% + +So we have + + align:start position:0% + + + + align:start position:0% + +So that's what we would get after the + + align:start position:0% +So that's what we would get after the + + + align:start position:0% +So that's what we would get after the +field redefinition for the two + + align:start position:0% +field redefinition for the two + + + align:start position:0% +field redefinition for the two +operators. + + align:start position:0% +operators. + + + align:start position:0% +operators. +Okay. So the next thing to do would be + + align:start position:0% +Okay. So the next thing to do would be + + + align:start position:0% +Okay. So the next thing to do would be +to instead of calling them uh y's call + + align:start position:0% +to instead of calling them uh y's call + + + align:start position:0% +to instead of calling them uh y's call +them s's. So but there's one more thing + + align:start position:0% +them s's. So but there's one more thing + + + align:start position:0% +them s's. So but there's one more thing +I can do too. So these are remember + + align:start position:0% +I can do too. So these are remember + + + align:start position:0% +I can do too. So these are remember +these are soft fields and these are + + align:start position:0% +these are soft fields and these are + + + align:start position:0% +these are soft fields and these are +linear fields. So this isn't factorized + + align:start position:0% +linear fields. So this isn't factorized + + + align:start position:0% +linear fields. So this isn't factorized +because we have contractions between + + align:start position:0% +because we have contractions between + + + align:start position:0% +because we have contractions between +these y's and the fields over here. + + align:start position:0% +these y's and the fields over here. + + + align:start position:0% +these y's and the fields over here. +Gluons can attach to the heavy quirks. + + align:start position:0% +Gluons can attach to the heavy quirks. + + + align:start position:0% +Gluons can attach to the heavy quirks. +So in order to factoriize we want to + + align:start position:0% +So in order to factoriize we want to + + + align:start position:0% +So in order to factoriize we want to +move those y's from there over to here. + + align:start position:0% +move those y's from there over to here. + + + align:start position:0% +move those y's from there over to here. +And we can do that. So here's how that + + align:start position:0% +And we can do that. So here's how that + + + align:start position:0% +And we can do that. So here's how that +works. This is a formula that I could + + align:start position:0% +works. This is a formula that I could + + + align:start position:0% +works. This is a formula that I could +have told you earlier. + + align:start position:0% +have told you earlier. + + + align:start position:0% +have told you earlier. +So if you have a Y that lies around a + + align:start position:0% +So if you have a Y that lies around a + + + align:start position:0% +So if you have a Y that lies around a +TA, that's just actually the adjint + + align:start position:0% +TA, that's just actually the adjint + + + align:start position:0% +TA, that's just actually the adjint +Wilson line. + + align:start position:0% + + + + align:start position:0% + +So this is a + + align:start position:0% +So this is a + + + align:start position:0% +So this is a +formula that relates fundamental Wilson + + align:start position:0% +formula that relates fundamental Wilson + + + align:start position:0% +formula that relates fundamental Wilson +lines and an adjint Wilson line. + + align:start position:0% + + + + align:start position:0% + +So the in the adjint Wilson line you'd + + align:start position:0% +So the in the adjint Wilson line you'd + + + align:start position:0% +So the in the adjint Wilson line you'd +build it out of matrices + + align:start position:0% +build it out of matrices + + + align:start position:0% +build it out of matrices +if you like. They're like this. + + align:start position:0% +if you like. They're like this. + + + align:start position:0% +if you like. They're like this. +So, + + align:start position:0% + + + + align:start position:0% + +so the matrix indices would be B and C. + + align:start position:0% +so the matrix indices would be B and C. + + + align:start position:0% +so the matrix indices would be B and C. +And instead of having fundamental + + align:start position:0% +And instead of having fundamental + + + align:start position:0% +And instead of having fundamental +indices for the TA alpha beta, you have + + align:start position:0% +indices for the TA alpha beta, you have + + + align:start position:0% +indices for the TA alpha beta, you have +an FABC and you this is the kind of + + align:start position:0% +an FABC and you this is the kind of + + + align:start position:0% +an FABC and you this is the kind of +thing that you would exponentiate, + + align:start position:0% + + + + align:start position:0% + +but other than that, it's the same + + align:start position:0% +but other than that, it's the same + + + align:start position:0% +but other than that, it's the same +thing. And there's just a color identity + + align:start position:0% +thing. And there's just a color identity + + + align:start position:0% +thing. And there's just a color identity +relating them. + + align:start position:0% +relating them. + + + align:start position:0% +relating them. +So because of this identity you can also + + align:start position:0% +So because of this identity you can also + + + align:start position:0% +So because of this identity you can also +write down another identity + + align:start position:0% +write down another identity + + + align:start position:0% +write down another identity +which is y dagger + + align:start position:0% +which is y dagger + + + align:start position:0% +which is y dagger +t a y + + align:start position:0% +t a y + + + align:start position:0% +t a y +this guy + + align:start position:0% + + + + align:start position:0% + +so y dagger t a y is just the other y + + align:start position:0% +so y dagger t a y is just the other y + + + align:start position:0% +so y dagger t a y is just the other y +this guy's an orthogonal matrix + + align:start position:0% +this guy's an orthogonal matrix + + + align:start position:0% +this guy's an orthogonal matrix +tb + + align:start position:0% +tb + + + align:start position:0% +tb +so if you reverse the indices then you + + align:start position:0% +so if you reverse the indices then you + + + align:start position:0% +so if you reverse the indices then you +get the + + align:start position:0% +get the + + + align:start position:0% +get the +opposite way and als Also this guy is it + + align:start position:0% +opposite way and als Also this guy is it + + + align:start position:0% +opposite way and als Also this guy is it +remember this is a matrix just in the AB + + align:start position:0% +remember this is a matrix just in the AB + + + align:start position:0% +remember this is a matrix just in the AB +space. So if I use this formula in here + + align:start position:0% +space. So if I use this formula in here + + + align:start position:0% +space. So if I use this formula in here +that allows me to take these Wilson + + align:start position:0% +that allows me to take these Wilson + + + align:start position:0% +that allows me to take these Wilson +lines here and move them over here + + align:start position:0% +lines here and move them over here + + + align:start position:0% +lines here and move them over here +right because I can take them write them + + align:start position:0% +right because I can take them write them + + + align:start position:0% +right because I can take them write them +as a y and then the y is just something + + align:start position:0% +as a y and then the y is just something + + + align:start position:0% +as a y and then the y is just something +that doesn't care about it just moves + + align:start position:0% +that doesn't care about it just moves + + + align:start position:0% +that doesn't care about it just moves +over because it's contracted with that + + align:start position:0% +over because it's contracted with that + + + align:start position:0% +over because it's contracted with that +index a + + align:start position:0% +index a + + + align:start position:0% +index a +guess I've got some problems with + + align:start position:0% +guess I've got some problems with + + + align:start position:0% +guess I've got some problems with +capitals and small letters. + + align:start position:0% +capitals and small letters. + + + align:start position:0% +capitals and small letters. +Let's make them all capital. + + align:start position:0% + + + + align:start position:0% + +So then I can move it over here and then + + align:start position:0% +So then I can move it over here and then + + + align:start position:0% +So then I can move it over here and then +I can convert it back to a yagger y if I + + align:start position:0% +I can convert it back to a yagger y if I + + + align:start position:0% +I can convert it back to a yagger y if I +want to. Okay. Okay. So we can take this + + align:start position:0% +want to. Okay. Okay. So we can take this + + + align:start position:0% +want to. Okay. Okay. So we can take this +guy + + align:start position:0% +guy + + + align:start position:0% +guy +and and this thing and write it over + + align:start position:0% +and and this thing and write it over + + + align:start position:0% +and and this thing and write it over +there as HV + + align:start position:0% + + + + align:start position:0% + +Y + + align:start position:0% +Y + + + align:start position:0% +Y +t a Y dagger HV + + align:start position:0% +t a Y dagger HV + + + align:start position:0% +t a Y dagger HV +prime. This is + + align:start position:0% +prime. This is + + + align:start position:0% +prime. This is +if I was careful to do that. uh this is + + align:start position:0% +if I was careful to do that. uh this is + + + align:start position:0% +if I was careful to do that. uh this is +the prime + + align:start position:0% + + + + align:start position:0% + +and then all the ma and then all the + + align:start position:0% +and then all the ma and then all the + + + align:start position:0% +and then all the ma and then all the +soft gluons all the ultra soft gluons + + align:start position:0% +soft gluons all the ultra soft gluons + + + align:start position:0% +soft gluons all the ultra soft gluons +are over here in this matrix element and + + align:start position:0% +are over here in this matrix element and + + + align:start position:0% +are over here in this matrix element and +all the linear fields are over there. + + align:start position:0% +all the linear fields are over there. + + + align:start position:0% +all the linear fields are over there. +So if you like you could say we get this + + align:start position:0% +So if you like you could say we get this + + + align:start position:0% +So if you like you could say we get this +and then we get our colinear matrix + + align:start position:0% +and then we get our colinear matrix + + + align:start position:0% +and then we get our colinear matrix +element that has TA but it has now + + align:start position:0% + + + + align:start position:0% + +no ultra soft and so we have a product + + align:start position:0% +no ultra soft and so we have a product + + + align:start position:0% +no ultra soft and so we have a product +ofar and ultra soft things tied together + + align:start position:0% +ofar and ultra soft things tied together + + + align:start position:0% +ofar and ultra soft things tied together +by one index a + + align:start position:0% +by one index a + + + align:start position:0% +by one index a +okay so that's just a little color + + align:start position:0% +okay so that's just a little color + + + align:start position:0% +okay so that's just a little color +rearrangement + + align:start position:0% + + + + align:start position:0% + +it's useful because now they're really + + align:start position:0% +it's useful because now they're really + + + align:start position:0% +it's useful because now they're really +factorized and now when we Take matrix + + align:start position:0% +factorized and now when we Take matrix + + + align:start position:0% +factorized and now when we Take matrix +elements. The matrix elements will + + align:start position:0% +elements. The matrix elements will + + + align:start position:0% +elements. The matrix elements will +factoriize. + + align:start position:0% + + + + align:start position:0% + +So, + + align:start position:0% + + + + align:start position:0% + +oh sorry before we take matrix elements + + align:start position:0% +oh sorry before we take matrix elements + + + align:start position:0% +oh sorry before we take matrix elements +have got to switch to sket. + + align:start position:0% + + + + align:start position:0% + +So this is again an example where it's + + align:start position:0% +So this is again an example where it's + + + align:start position:0% +So this is again an example where it's +trivial because what we have is we have + + align:start position:0% +trivial because what we have is we have + + + align:start position:0% +trivial because what we have is we have +one type of operator that we're + + align:start position:0% +one type of operator that we're + + + align:start position:0% +one type of operator that we're +considering this weak transition and we + + align:start position:0% +considering this weak transition and we + + + align:start position:0% +considering this weak transition and we +don't have a time order product of any + + align:start position:0% +don't have a time order product of any + + + align:start position:0% +don't have a time order product of any +type of two operators in SCT 2. We just + + align:start position:0% +type of two operators in SCT 2. We just + + + align:start position:0% +type of two operators in SCT 2. We just +have a single operator that has both + + align:start position:0% +have a single operator that has both + + + align:start position:0% +have a single operator that has both +types of fields and then we have the + + align:start position:0% +types of fields and then we have the + + + align:start position:0% +types of fields and then we have the +lrangeians. + + align:start position:0% +lrangeians. + + + align:start position:0% +lrangeians. +So this is again simple. + + align:start position:0% + + + + align:start position:0% + +So we have one mixed operator + + align:start position:0% +So we have one mixed operator + + + align:start position:0% +So we have one mixed operator +plus + + align:start position:0% +plus + + + align:start position:0% +plus +L0 linear and L0 + + align:start position:0% +L0 linear and L0 + + + align:start position:0% +L0 linear and L0 +soft and those things are already + + align:start position:0% +soft and those things are already + + + align:start position:0% +soft and those things are already +decoupled and so this is simple + + align:start position:0% + + + + align:start position:0% + +and so we simply replace Y's by S + + align:start position:0% +and so we simply replace Y's by S + + + align:start position:0% +and so we simply replace Y's by S +renaming it soft instead of ultraoft + + align:start position:0% +renaming it soft instead of ultraoft + + + align:start position:0% +renaming it soft instead of ultraoft +really nothing is changing and these + + align:start position:0% +really nothing is changing and these + + + align:start position:0% +really nothing is changing and these +colineers we just put them down onto + + align:start position:0% +colineers we just put them down onto + + + align:start position:0% +colineers we just put them down onto +SCT2 colineers from SCT1 colineers + + align:start position:0% +SCT2 colineers from SCT1 colineers + + + align:start position:0% +SCT2 colineers from SCT1 colineers +Okay. So + + align:start position:0% + + + + align:start position:0% + +to make it look like I've done + + align:start position:0% +to make it look like I've done + + + align:start position:0% +to make it look like I've done +something, + + align:start position:0% + + + + align:start position:0% + +I'll write it out again, but there's + + align:start position:0% +I'll write it out again, but there's + + + align:start position:0% +I'll write it out again, but there's +really nothing happening + + align:start position:0% + + + + align:start position:0% + +except that now the fields are in SCT2 + + align:start position:0% +except that now the fields are in SCT2 + + + align:start position:0% +except that now the fields are in SCT2 +with the correct SCT2 scaling. + + align:start position:0% + + + + align:start position:0% + +So there's no Wilson coefficient that's + + align:start position:0% +So there's no Wilson coefficient that's + + + align:start position:0% +So there's no Wilson coefficient that's +generated by this step. There's no + + align:start position:0% +generated by this step. There's no + + + align:start position:0% +generated by this step. There's no +additional Wilson coefficient because of + + align:start position:0% +additional Wilson coefficient because of + + + align:start position:0% +additional Wilson coefficient because of +that fact. + + align:start position:0% +that fact. + + + align:start position:0% +that fact. +So these are sketch two now. + + align:start position:0% +So these are sketch two now. + + + align:start position:0% +So these are sketch two now. +And similarly for the octed. + + align:start position:0% + + + + align:start position:0% + +So here we would really have the + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% + + + + align:start position:0% + +So now we can take matrix elements. + + align:start position:0% +So now we can take matrix elements. + + + align:start position:0% +So now we can take matrix elements. +Yeah. What do the coefficients look like + + align:start position:0% +Yeah. What do the coefficients look like + + + align:start position:0% +Yeah. What do the coefficients look like +when they're not just one? + + align:start position:0% +when they're not just one? + + + align:start position:0% +when they're not just one? +So they would be functions of say plus + + align:start position:0% +So they would be functions of say plus + + + align:start position:0% +So they would be functions of say plus +times minus momenta. So we could have if + + align:start position:0% +times minus momenta. So we could have if + + + align:start position:0% +times minus momenta. So we could have if +it wasn't one, what would happen is + + align:start position:0% +it wasn't one, what would happen is + + + align:start position:0% +it wasn't one, what would happen is +effectively so yeah we talked a little + + align:start position:0% +effectively so yeah we talked a little + + + align:start position:0% +effectively so yeah we talked a little +bit about this last time but let me + + align:start position:0% +bit about this last time but let me + + + align:start position:0% +bit about this last time but let me +remind you. So if it wasn't one that + + align:start position:0% +remind you. So if it wasn't one that + + + align:start position:0% +remind you. So if it wasn't one that +would happen in a situation where you + + align:start position:0% +would happen in a situation where you + + + align:start position:0% +would happen in a situation where you +had something like this + + align:start position:0% +had something like this + + + align:start position:0% +had something like this +some offshelf field + + align:start position:0% +some offshelf field + + + align:start position:0% +some offshelf field +oh + + align:start position:0% + + + + align:start position:0% + +say like this. So this is a tproduct of + + align:start position:0% +say like this. So this is a tproduct of + + + align:start position:0% +say like this. So this is a tproduct of +two things + + align:start position:0% +two things + + + align:start position:0% +two things +rather than just one thing that mixt and + + align:start position:0% +rather than just one thing that mixt and + + + align:start position:0% +rather than just one thing that mixt and +colinear and this field here was + + align:start position:0% +colinear and this field here was + + + align:start position:0% +colinear and this field here was +offshell in a way that basically this + + align:start position:0% +offshell in a way that basically this + + + align:start position:0% +offshell in a way that basically this +field here is an offshell field that uh + + align:start position:0% +field here is an offshell field that uh + + + align:start position:0% +field here is an offshell field that uh +would be a product of the plus and minus + + align:start position:0% +would be a product of the plus and minus + + + align:start position:0% +would be a product of the plus and minus +momentum of these guys. And so you could + + align:start position:0% +momentum of these guys. And so you could + + + align:start position:0% +momentum of these guys. And so you could +get something that's effectively living + + align:start position:0% +get something that's effectively living + + + align:start position:0% +get something that's effectively living +at this hard linear scale below the hard + + align:start position:0% +at this hard linear scale below the hard + + + align:start position:0% +at this hard linear scale below the hard +scale in the problem from sort of + + align:start position:0% +scale in the problem from sort of + + + align:start position:0% +scale in the problem from sort of +troducts of soft and linear operators. + + align:start position:0% +troducts of soft and linear operators. + + + align:start position:0% +troducts of soft and linear operators. +This is a being a little sketchy, but + + align:start position:0% +This is a being a little sketchy, but + + + align:start position:0% +This is a being a little sketchy, but +since here we only have one operator, + + align:start position:0% +since here we only have one operator, + + + align:start position:0% +since here we only have one operator, +that couldn't happen because you just + + align:start position:0% +that couldn't happen because you just + + + align:start position:0% +that couldn't happen because you just +start attaching softs and and colinear + + align:start position:0% +start attaching softs and and colinear + + + align:start position:0% +start attaching softs and and colinear +has been it's already factored. So + + align:start position:0% +has been it's already factored. So + + + align:start position:0% +has been it's already factored. So +there's no way that you can sort of get + + align:start position:0% +there's no way that you can sort of get + + + align:start position:0% +there's no way that you can sort of get +this intermediate offshell guy. + + align:start position:0% +this intermediate offshell guy. + + + align:start position:0% +this intermediate offshell guy. +So this guy would be colinear, right? In + + align:start position:0% +So this guy would be colinear, right? In + + + align:start position:0% +So this guy would be colinear, right? In +the the way to think about this is this + + align:start position:0% +the the way to think about this is this + + + align:start position:0% +the the way to think about this is this +is like this. This is just a diagram + + align:start position:0% +is like this. This is just a diagram + + + align:start position:0% +is like this. This is just a diagram +that exists. But then you go over to the + + align:start position:0% +that exists. But then you go over to the + + + align:start position:0% +that exists. But then you go over to the +SCT2 and then you have your change of + + align:start position:0% +SCT2 and then you have your change of + + + align:start position:0% +SCT2 and then you have your change of +linear to the right linear, right? But + + align:start position:0% +linear to the right linear, right? But + + + align:start position:0% +linear to the right linear, right? But +this guy doesn't change. He's still + + align:start position:0% +this guy doesn't change. He's still + + + align:start position:0% +this guy doesn't change. He's still +hardlinear. + + align:start position:0% + + + + align:start position:0% + +Imagine when it's non-trivial actually + + align:start position:0% +Imagine when it's non-trivial actually + + + align:start position:0% +Imagine when it's non-trivial actually +has a different scale. + + align:start position:0% +has a different scale. + + + align:start position:0% +has a different scale. +Yeah, this scale would show actually up + + align:start position:0% +Yeah, this scale would show actually up + + + align:start position:0% +Yeah, this scale would show actually up +and so if it doesn't show up, so this + + align:start position:0% +and so if it doesn't show up, so this + + + align:start position:0% +and so if it doesn't show up, so this +would be kind of a situation and going + + align:start position:0% +would be kind of a situation and going + + + align:start position:0% +would be kind of a situation and going +from + + align:start position:0% + + + + align:start position:0% + +let's get one. And I actually we could + + align:start position:0% +let's get one. And I actually we could + + + align:start position:0% +let's get one. And I actually we could +have done some examples where that + + align:start position:0% +have done some examples where that + + + align:start position:0% +have done some examples where that +happens. + + align:start position:0% +happens. + + + align:start position:0% +happens. +Um but I'm choosing to do this rapidity + + align:start position:0% +Um but I'm choosing to do this rapidity + + + align:start position:0% +Um but I'm choosing to do this rapidity +reormalization group instead. Basically + + align:start position:0% +reormalization group instead. Basically + + + align:start position:0% +reormalization group instead. Basically +this happens if you look at matrix + + align:start position:0% +this happens if you look at matrix + + + align:start position:0% +this happens if you look at matrix +elements and you could look at matrix + + align:start position:0% +elements and you could look at matrix + + + align:start position:0% +elements and you could look at matrix +elements where you have some subleading + + align:start position:0% +elements where you have some subleading + + + align:start position:0% +elements where you have some subleading +interactions. And there are examples in + + align:start position:0% +interactions. And there are examples in + + + align:start position:0% +interactions. And there are examples in +exclusive decays where you could have + + align:start position:0% +exclusive decays where you could have + + + align:start position:0% +exclusive decays where you could have +this happen. One example is if you look + + align:start position:0% +this happen. One example is if you look + + + align:start position:0% +this happen. One example is if you look +at B 0 to D 0 pi 0 just having all + + align:start position:0% +at B 0 to D 0 pi 0 just having all + + + align:start position:0% +at B 0 to D 0 pi 0 just having all +neutral charges then actually this will + + align:start position:0% +neutral charges then actually this will + + + align:start position:0% +neutral charges then actually this will +happen. + + align:start position:0% +happen. + + + align:start position:0% +happen. +It'll be and it'll be more complicated + + align:start position:0% +It'll be and it'll be more complicated + + + align:start position:0% +It'll be and it'll be more complicated +than what I'm telling you, but you can + + align:start position:0% +than what I'm telling you, but you can + + + align:start position:0% +than what I'm telling you, but you can +derive a factoriization theorem for + + align:start position:0% +derive a factoriization theorem for + + + align:start position:0% +derive a factoriization theorem for +this. It's power suppressed relative to + + align:start position:0% +this. It's power suppressed relative to + + + align:start position:0% +this. It's power suppressed relative to +the one we're talking about because the + + align:start position:0% +the one we're talking about because the + + + align:start position:0% +the one we're talking about because the +one we're talking about always has a + + align:start position:0% +one we're talking about always has a + + + align:start position:0% +one we're talking about always has a +charge pion. + + align:start position:0% +charge pion. + + + align:start position:0% +charge pion. +And it turns out that that happens at + + align:start position:0% +And it turns out that that happens at + + + align:start position:0% +And it turns out that that happens at +leading order. Whereas the neutral pion + + align:start position:0% +leading order. Whereas the neutral pion + + + align:start position:0% +leading order. Whereas the neutral pion +process with the neutral B and neutral D + + align:start position:0% +process with the neutral B and neutral D + + + align:start position:0% +process with the neutral B and neutral D +is something that's power suppressed. + + align:start position:0% + + + + align:start position:0% + +Hope I'm remembering that right. Yeah, I + + align:start position:0% +Hope I'm remembering that right. Yeah, I + + + align:start position:0% +Hope I'm remembering that right. Yeah, I +am. + + align:start position:0% +am. + + + align:start position:0% +am. +All right. So, number four. So, this is + + align:start position:0% +All right. So, number four. So, this is + + + align:start position:0% +All right. So, number four. So, this is +on the side. + + align:start position:0% +on the side. + + + align:start position:0% +on the side. +Number four, take matrix elements. + + align:start position:0% + + + + align:start position:0% + +And here we find actually that one of + + align:start position:0% +And here we find actually that one of + + + align:start position:0% +And here we find actually that one of +the matrix elements is just zero. the + + align:start position:0% +the matrix elements is just zero. the + + + align:start position:0% +the matrix elements is just zero. the +one with the octet. + + align:start position:0% + + + + align:start position:0% + +So, let me write the non-zero ones + + align:start position:0% +So, let me write the non-zero ones + + + align:start position:0% +So, let me write the non-zero ones +first. + + align:start position:0% + + + + align:start position:0% + +I wasn't too careful about the two + + align:start position:0% +I wasn't too careful about the two + + + align:start position:0% +I wasn't too careful about the two +different + + align:start position:0% + + + + align:start position:0% + +so there's some guy that's just giving a + + align:start position:0% +so there's some guy that's just giving a + + + align:start position:0% +so there's some guy that's just giving a +convolution between the Wilson + + align:start position:0% +convolution between the Wilson + + + align:start position:0% +convolution between the Wilson +coefficient and 5 pi and then + + align:start position:0% + + + + align:start position:0% + +this guy which is some normalization + + align:start position:0% +this guy which is some normalization + + + align:start position:0% +this guy which is some normalization +factor times a form factor. + + align:start position:0% + + + + align:start position:0% + +These things are all mutependent in + + align:start position:0% +These things are all mutependent in + + + align:start position:0% +These things are all mutependent in +general. + + align:start position:0% +general. + + + align:start position:0% +general. +And this thing here is the wise function + + align:start position:0% +And this thing here is the wise function + + + align:start position:0% +And this thing here is the wise function +which is the hqt form factor + + align:start position:0% + + + + align:start position:0% + +and w0 + + align:start position:0% +and w0 + + + align:start position:0% +and w0 +is + + align:start position:0% +is + + + align:start position:0% +is +kind of the kinematic variable that that + + align:start position:0% +kind of the kinematic variable that that + + + align:start position:0% +kind of the kinematic variable that that +form factor can depend on which is V.V + + align:start position:0% +form factor can depend on which is V.V + + + align:start position:0% +form factor can depend on which is V.V +prime the labels on the fields and that + + align:start position:0% +prime the labels on the fields and that + + + align:start position:0% +prime the labels on the fields and that +encodes the momentum transfer which here + + align:start position:0% +encodes the momentum transfer which here + + + align:start position:0% +encodes the momentum transfer which here +is just related to the kinematics. So W0 + + align:start position:0% +is just related to the kinematics. So W0 + + + align:start position:0% +is just related to the kinematics. So W0 +is some function of + + align:start position:0% +is some function of + + + align:start position:0% +is some function of +MB and MC + + align:start position:0% +MB and MC + + + align:start position:0% +MB and MC +which I'm not going to bother writing + + align:start position:0% +which I'm not going to bother writing + + + align:start position:0% +which I'm not going to bother writing +down. + + align:start position:0% + + + + align:start position:0% + +uh just some constant. I mean it could + + align:start position:0% +uh just some constant. I mean it could + + + align:start position:0% +uh just some constant. I mean it could +have some kinematic factors + + align:start position:0% +have some kinematic factors + + + align:start position:0% +have some kinematic factors +that makes up the dimension like some + + align:start position:0% +that makes up the dimension like some + + + align:start position:0% +that makes up the dimension like some +depends on my gamma. + + align:start position:0% +depends on my gamma. + + + align:start position:0% +depends on my gamma. +Yeah, it's just some number. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay, so that's these are the + + align:start position:0% +Okay. Okay, so that's these are the + + + align:start position:0% +Okay. Okay, so that's these are the +singlet operators. + + align:start position:0% + + + + align:start position:0% + +So in the singlet case we have initial + + align:start position:0% +So in the singlet case we have initial + + + align:start position:0% +So in the singlet case we have initial +state and final state. In all all cases + + align:start position:0% +state and final state. In all all cases + + + align:start position:0% +state and final state. In all all cases +we have initial state and final states + + align:start position:0% +we have initial state and final states + + + align:start position:0% +we have initial state and final states +which are color singlets and these + + align:start position:0% +which are color singlets and these + + + align:start position:0% +which are color singlets and these +operators are color singlets. In the + + align:start position:0% +operators are color singlets. In the + + + align:start position:0% +operators are color singlets. In the +case of the octet we also have color + + align:start position:0% +case of the octet we also have color + + + align:start position:0% +case of the octet we also have color +singlet states and we we factoriize them + + align:start position:0% +singlet states and we we factoriize them + + + align:start position:0% +singlet states and we we factoriize them +such that we'd have a matrix element for + + align:start position:0% +such that we'd have a matrix element for + + + align:start position:0% +such that we'd have a matrix element for +example. + + align:start position:0% +example. + + + align:start position:0% +example. +So let me just write one of them and + + align:start position:0% +So let me just write one of them and + + + align:start position:0% +So let me just write one of them and +well + + align:start position:0% + + + + align:start position:0% + +and this is zero + + align:start position:0% +and this is zero + + + align:start position:0% +and this is zero +because there's nothing that could carry + + align:start position:0% +because there's nothing that could carry + + + align:start position:0% +because there's nothing that could carry +the index a in this matrix element. + + align:start position:0% + + + + align:start position:0% + +Okay, so the octet matrix elements are + + align:start position:0% +Okay, so the octet matrix elements are + + + align:start position:0% +Okay, so the octet matrix elements are +zero. It's important that we factorized + + align:start position:0% +zero. It's important that we factorized + + + align:start position:0% +zero. It's important that we factorized +it for that to be true. Right? If we had + + align:start position:0% +it for that to be true. Right? If we had + + + align:start position:0% +it for that to be true. Right? If we had +dpi then we'd have a color singlet + + align:start position:0% +dpi then we'd have a color singlet + + + align:start position:0% +dpi then we'd have a color singlet +operator here B. So we wouldn't have + + align:start position:0% +operator here B. So we wouldn't have + + + align:start position:0% +operator here B. So we wouldn't have +been able to make this statement in the + + align:start position:0% +been able to make this statement in the + + + align:start position:0% +been able to make this statement in the +original operator in the electric + + align:start position:0% +original operator in the electric + + + align:start position:0% +original operator in the electric +Hamiltonian. This would just not be + + align:start position:0% +Hamiltonian. This would just not be + + + align:start position:0% +Hamiltonian. This would just not be +true. But once we factored it and put + + align:start position:0% +true. But once we factored it and put + + + align:start position:0% +true. But once we factored it and put +all the ultra soft fields here that + + align:start position:0% +all the ultra soft fields here that + + + align:start position:0% +all the ultra soft fields here that +everything that's going to be contracted + + align:start position:0% +everything that's going to be contracted + + + align:start position:0% +everything that's going to be contracted +together then we can make this + + align:start position:0% +together then we can make this + + + align:start position:0% +together then we can make this +statement. We couldn't even really make + + align:start position:0% +statement. We couldn't even really make + + + align:start position:0% +statement. We couldn't even really make +this statement when the y's were on the + + align:start position:0% +this statement when the y's were on the + + + align:start position:0% +this statement when the y's were on the +other side. Right? We had to move them + + align:start position:0% +other side. Right? We had to move them + + + align:start position:0% +other side. Right? We had to move them +over here to ensure that the statement + + align:start position:0% +over here to ensure that the statement + + + align:start position:0% +over here to ensure that the statement +is completely true. + + align:start position:0% + + + + align:start position:0% + +Okay? So + + align:start position:0% + + + + align:start position:0% + +color octed operator + + align:start position:0% + + + + align:start position:0% + +color singlet states. + + align:start position:0% + + + + align:start position:0% + +Okay. So then you just put things + + align:start position:0% +Okay. So then you just put things + + + align:start position:0% +Okay. So then you just put things +together and we can multiply these two + + align:start position:0% +together and we can multiply these two + + + align:start position:0% +together and we can multiply these two +things + + align:start position:0% +things + + + align:start position:0% +things +to get the final result. + + align:start position:0% +to get the final result. + + + align:start position:0% +to get the final result. +So if we write it as + + align:start position:0% +So if we write it as + + + align:start position:0% +So if we write it as +a matching from the electric Hamiltonian + + align:start position:0% +a matching from the electric Hamiltonian + + + align:start position:0% +a matching from the electric Hamiltonian +there's some normalization factor. So + + align:start position:0% +there's some normalization factor. So + + + align:start position:0% +there's some normalization factor. So +grouping together these factors of fi e + + align:start position:0% +grouping together these factors of fi e + + + align:start position:0% +grouping together these factors of fi e +pi and n prime + + align:start position:0% +pi and n prime + + + align:start position:0% +pi and n prime +which I'm not worrying so much about. + + align:start position:0% +which I'm not worrying so much about. + + + align:start position:0% +which I'm not worrying so much about. +there's a pisg function and then there's + + align:start position:0% +there's a pisg function and then there's + + + align:start position:0% +there's a pisg function and then there's +a single convolution between the hard + + align:start position:0% +a single convolution between the hard + + + align:start position:0% +a single convolution between the hard +coefficient + + align:start position:0% +coefficient + + + align:start position:0% +coefficient +which is kind of like our example of the + + align:start position:0% +which is kind of like our example of the + + + align:start position:0% +which is kind of like our example of the +photon pion form factor + + align:start position:0% + + + + align:start position:0% + +and then this light cone distribution. + + align:start position:0% +and then this light cone distribution. + + + align:start position:0% +and then this light cone distribution. +So we see an example where it showed up + + align:start position:0% +So we see an example where it showed up + + + align:start position:0% +So we see an example where it showed up +in a totally different type of process + + align:start position:0% +in a totally different type of process + + + align:start position:0% +in a totally different type of process +from the one we were considering + + align:start position:0% +from the one we were considering + + + align:start position:0% +from the one we were considering +previously thereby showing us kind of + + align:start position:0% +previously thereby showing us kind of + + + align:start position:0% +previously thereby showing us kind of +the universality of that function. And + + align:start position:0% +the universality of that function. And + + + align:start position:0% +the universality of that function. And +then there would be power corrections to + + align:start position:0% +then there would be power corrections to + + + align:start position:0% +then there would be power corrections to +this whole thing + + align:start position:0% +this whole thing + + + align:start position:0% +this whole thing +that we're neglecting that go like lercd + + align:start position:0% +that we're neglecting that go like lercd + + + align:start position:0% +that we're neglecting that go like lercd +over those hard scales. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay, so this is the esco yise + + align:start position:0% +Okay. Okay, so this is the esco yise + + + align:start position:0% +Okay. Okay, so this is the esco yise +function and actually I did write down + + align:start position:0% +function and actually I did write down + + + align:start position:0% +function and actually I did write down +what the + + align:start position:0% +what the + + + align:start position:0% +what the +the w would be. + + align:start position:0% +the w would be. + + + align:start position:0% +the w would be. +So + + align:start position:0% + + + + align:start position:0% + +this w would be that some common you can + + align:start position:0% +this w would be that some common you can + + + align:start position:0% +this w would be that some common you can +write it in terms of the mezison masses + + align:start position:0% +write it in terms of the mezison masses + + + align:start position:0% +write it in terms of the mezison masses +like that. So it's the is wise function + + align:start position:0% +like that. So it's the is wise function + + + align:start position:0% +like that. So it's the is wise function +at max recoil + + align:start position:0% + + + + align:start position:0% + +and this function is measured for + + align:start position:0% +and this function is measured for + + + align:start position:0% +and this function is measured for +example + + align:start position:0% +example + + + align:start position:0% +example +in a semilepttonic transition. + + align:start position:0% + + + + align:start position:0% + +So you can imagine that the pion + + align:start position:0% +So you can imagine that the pion + + + align:start position:0% +So you can imagine that the pion +distribution function or properties of + + align:start position:0% +distribution function or properties of + + + align:start position:0% +distribution function or properties of +it were measured in the the photon pion + + align:start position:0% +it were measured in the the photon pion + + + align:start position:0% +it were measured in the the photon pion +transition. The isgar wise function is + + align:start position:0% +transition. The isgar wise function is + + + align:start position:0% +transition. The isgar wise function is +measured in the betl new transition and + + align:start position:0% +measured in the betl new transition and + + + align:start position:0% +measured in the betl new transition and +then you can make predictions for this + + align:start position:0% +then you can make predictions for this + + + align:start position:0% +then you can make predictions for this +bd pi. + + align:start position:0% + + + + align:start position:0% + +Okay. So that gives you an example of + + align:start position:0% +Okay. So that gives you an example of + + + align:start position:0% +Okay. So that gives you an example of +how you would use these factorization + + align:start position:0% +how you would use these factorization + + + align:start position:0% +how you would use these factorization +theorems. + + align:start position:0% +theorems. + + + align:start position:0% +theorems. +So this applies to basically this this + + align:start position:0% +So this applies to basically this this + + + align:start position:0% +So this applies to basically this this +type of factorization + + align:start position:0% +type of factorization + + + align:start position:0% +type of factorization +that we've just talked about. + + align:start position:0% +that we've just talked about. + + + align:start position:0% +that we've just talked about. +applies to a lot of different things + + align:start position:0% +applies to a lot of different things + + + align:start position:0% +applies to a lot of different things +with charged + + align:start position:0% + + + + align:start position:0% + +pi minuses. Or you can make the pi minus + + align:start position:0% +pi minuses. Or you can make the pi minus + + + align:start position:0% +pi minuses. Or you can make the pi minus +a row minus and that wouldn't really + + align:start position:0% +a row minus and that wouldn't really + + + align:start position:0% +a row minus and that wouldn't really +change anything. + + align:start position:0% +change anything. + + + align:start position:0% +change anything. +So you could have b 0 if you wanted to + + align:start position:0% +So you could have b 0 if you wanted to + + + align:start position:0% +So you could have b 0 if you wanted to +look at charges. You could have b 0 to d + + align:start position:0% +look at charges. You could have b 0 to d + + + align:start position:0% +look at charges. You could have b 0 to d +plus pi minus or you could have b minus + + align:start position:0% +plus pi minus or you could have b minus + + + align:start position:0% +plus pi minus or you could have b minus +to d 0 pi minus. + + align:start position:0% +to d 0 pi minus. + + + align:start position:0% +to d 0 pi minus. +And there's a third one which is the one + + align:start position:0% +And there's a third one which is the one + + + align:start position:0% +And there's a third one which is the one +we were talking about over here. B 0 to + + align:start position:0% +we were talking about over here. B 0 to + + + align:start position:0% +we were talking about over here. B 0 to +D 0 pi 0. So there's three different + + align:start position:0% +D 0 pi 0. So there's three different + + + align:start position:0% +D 0 pi 0. So there's three different +ways, three different B to D pi + + align:start position:0% +ways, three different B to D pi + + + align:start position:0% +ways, three different B to D pi +transitions depending on the charges and + + align:start position:0% +transitions depending on the charges and + + + align:start position:0% +transitions depending on the charges and +what we've derived applies to charge + + align:start position:0% +what we've derived applies to charge + + + align:start position:0% +what we've derived applies to charge +pions or charge rows. The neutral ones + + align:start position:0% +pions or charge rows. The neutral ones + + + align:start position:0% +pions or charge rows. The neutral ones +end up being power suppressed. And you + + align:start position:0% +end up being power suppressed. And you + + + align:start position:0% +end up being power suppressed. And you +can see that kind of from our + + align:start position:0% +can see that kind of from our + + + align:start position:0% +can see that kind of from our +discussion. There was kind of never a + + align:start position:0% +discussion. There was kind of never a + + + align:start position:0% +discussion. There was kind of never a +there was we have just writing down the + + align:start position:0% +there was we have just writing down the + + + align:start position:0% +there was we have just writing down the +leading order operators. Well, yeah, + + align:start position:0% +leading order operators. Well, yeah, + + + align:start position:0% +leading order operators. Well, yeah, +maybe you have to work a little harder, + + align:start position:0% +maybe you have to work a little harder, + + + align:start position:0% +maybe you have to work a little harder, +but effectively the leading order + + align:start position:0% +but effectively the leading order + + + align:start position:0% +but effectively the leading order +operators don't make this transition + + align:start position:0% +operators don't make this transition + + + align:start position:0% +operators don't make this transition +with the two two charges being the same + + align:start position:0% +with the two two charges being the same + + + align:start position:0% +with the two two charges being the same +such that you could get a pi zero. So, + + align:start position:0% +such that you could get a pi zero. So, + + + align:start position:0% +such that you could get a pi zero. So, +you have to do something more + + align:start position:0% +you have to do something more + + + align:start position:0% +you have to do something more +in order to get that case. All right. + + align:start position:0% +in order to get that case. All right. + + + align:start position:0% +in order to get that case. All right. +So, questions + + align:start position:0% + + + + align:start position:0% + +log over MC. + + align:start position:0% +log over MC. + + + align:start position:0% +log over MC. +You can if you want. Oh, MB over MC. So + + align:start position:0% +You can if you want. Oh, MB over MC. So + + + align:start position:0% +You can if you want. Oh, MB over MC. So +MB and MC, we're treating both of them + + align:start position:0% +MB and MC, we're treating both of them + + + align:start position:0% +MB and MC, we're treating both of them +as as the same in what we've done. So if + + align:start position:0% +as as the same in what we've done. So if + + + align:start position:0% +as as the same in what we've done. So if +we wanted to sum logs of MB over MC, + + align:start position:0% +we wanted to sum logs of MB over MC, + + + align:start position:0% +we wanted to sum logs of MB over MC, +we'd have to do something a little + + align:start position:0% +we'd have to do something a little + + + align:start position:0% +we'd have to do something a little +different than what we did. You'd have + + align:start position:0% +different than what we did. You'd have + + + align:start position:0% +different than what we did. You'd have +to first integrate out MB, treat the + + align:start position:0% +to first integrate out MB, treat the + + + align:start position:0% +to first integrate out MB, treat the +charm quark as a light quark. You could + + align:start position:0% +charm quark as a light quark. You could + + + align:start position:0% +charm quark as a light quark. You could +do that. + + align:start position:0% +do that. + + + align:start position:0% +do that. +Would it make the + + align:start position:0% +Would it make the + + + align:start position:0% +Would it make the +It turns out that + + align:start position:0% +It turns out that + + + align:start position:0% +It turns out that +Yeah. So those are single logs. + + align:start position:0% +Yeah. So those are single logs. + + + align:start position:0% +Yeah. So those are single logs. +Actually, they're not double logs. And + + align:start position:0% +Actually, they're not double logs. And + + + align:start position:0% +Actually, they're not double logs. And +it's related to the fact that you have + + align:start position:0% +it's related to the fact that you have + + + align:start position:0% +it's related to the fact that you have +massive particles. when you have massive + + align:start position:0% +massive particles. when you have massive + + + align:start position:0% +massive particles. when you have massive +particles you don't get the extra + + align:start position:0% +particles you don't get the extra + + + align:start position:0% +particles you don't get the extra +singularity and people in HQ worried + + align:start position:0% +singularity and people in HQ worried + + + align:start position:0% +singularity and people in HQ worried +about summing logs of MB over MC for a + + align:start position:0% +about summing logs of MB over MC for a + + + align:start position:0% +about summing logs of MB over MC for a +while and then after sort of doing + + align:start position:0% +while and then after sort of doing + + + align:start position:0% +while and then after sort of doing +enough calculations they realized it was + + align:start position:0% +enough calculations they realized it was + + + align:start position:0% +enough calculations they realized it was +totally irrelevant and you should just + + align:start position:0% +totally irrelevant and you should just + + + align:start position:0% +totally irrelevant and you should just +not bother you should just calculate the + + align:start position:0% +not bother you should just calculate the + + + align:start position:0% +not bother you should just calculate the +alpha s corrections treating MB and MC + + align:start position:0% +alpha s corrections treating MB and MC + + + align:start position:0% +alpha s corrections treating MB and MC +as comparable and summing the logs if + + align:start position:0% +as comparable and summing the logs if + + + align:start position:0% +as comparable and summing the logs if +you sort of think of leading log as + + align:start position:0% +you sort of think of leading log as + + + align:start position:0% +you sort of think of leading log as +being more important than the order + + align:start position:0% +being more important than the order + + + align:start position:0% +being more important than the order +alpha s calculation that misleads you + + align:start position:0% +alpha s calculation that misleads you + + + align:start position:0% +alpha s calculation that misleads you +sometimes the sign is even wrong and so + + align:start position:0% +sometimes the sign is even wrong and so + + + align:start position:0% +sometimes the sign is even wrong and so +there's sort of a general experience + + align:start position:0% +there's sort of a general experience + + + align:start position:0% +there's sort of a general experience +that summing logs of MB over MC and HQ + + align:start position:0% +that summing logs of MB over MC and HQ + + + align:start position:0% +that summing logs of MB over MC and HQ +is not a not even + + align:start position:0% +is not a not even + + + align:start position:0% +is not a not even +because they're single logs. + + align:start position:0% +because they're single logs. + + + align:start position:0% +because they're single logs. +It's because they're single logs. I mean + + align:start position:0% +It's because they're single logs. I mean + + + align:start position:0% +It's because they're single logs. I mean +that's one thing that makes it different + + align:start position:0% +that's one thing that makes it different + + + align:start position:0% +that's one thing that makes it different +than say the double logs that you would + + align:start position:0% +than say the double logs that you would + + + align:start position:0% +than say the double logs that you would +resum in this process. Uh actually these + + align:start position:0% +resum in this process. Uh actually these + + + align:start position:0% +resum in this process. Uh actually these +double logs are also single logs. So you + + align:start position:0% +double logs are also single logs. So you + + + align:start position:0% +double logs are also single logs. So you +could decide whether or not to resum + + align:start position:0% +could decide whether or not to resum + + + align:start position:0% +could decide whether or not to resum +them. But uh you know either whether or + + align:start position:0% +them. But uh you know either whether or + + + align:start position:0% +them. But uh you know either whether or +not you do resumation this is still + + align:start position:0% +not you do resumation this is still + + + align:start position:0% +not you do resumation this is still +useful because you could make a + + align:start position:0% +useful because you could make a + + + align:start position:0% +useful because you could make a +prediction for this decay rate and it + + align:start position:0% +prediction for this decay rate and it + + + align:start position:0% +prediction for this decay rate and it +works really well. + + align:start position:0% +works really well. + + + align:start position:0% +works really well. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +All right. + + align:start position:0% +All right. + + + align:start position:0% +All right. +You can actually also make predictions + + align:start position:0% +You can actually also make predictions + + + align:start position:0% +You can actually also make predictions +for + + align:start position:0% +for + + + align:start position:0% +for +these decay rates. You can predict + + align:start position:0% +these decay rates. You can predict + + + align:start position:0% +these decay rates. You can predict +actually the relations between the D0 + + align:start position:0% +actually the relations between the D0 + + + align:start position:0% +actually the relations between the D0 +and D star0 using the factoriization + + align:start position:0% +and D star0 using the factoriization + + + align:start position:0% +and D star0 using the factoriization +subleading factorization theorem. + + align:start position:0% +subleading factorization theorem. + + + align:start position:0% +subleading factorization theorem. +Okay. So let's move on to our second + + align:start position:0% +Okay. So let's move on to our second + + + align:start position:0% +Okay. So let's move on to our second +topic which take the rest of today + + align:start position:0% +topic which take the rest of today + + + align:start position:0% +topic which take the rest of today +and that's rapidity divergences. + + align:start position:0% + + + + align:start position:0% + +Okay. So when we were talking about SCT1 + + align:start position:0% +Okay. So when we were talking about SCT1 + + + align:start position:0% +Okay. So when we were talking about SCT1 +and we were talking about loop + + align:start position:0% +and we were talking about loop + + + align:start position:0% +and we were talking about loop +calculations, we saw that there was a + + align:start position:0% +calculations, we saw that there was a + + + align:start position:0% +calculations, we saw that there was a +subtlety where when we were doing our + + align:start position:0% +subtlety where when we were doing our + + + align:start position:0% +subtlety where when we were doing our +colinear loops that could double count + + align:start position:0% +colinear loops that could double count + + + align:start position:0% +colinear loops that could double count +the ultrasoft loop if you remember. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +So kind of schematically I could say + + align:start position:0% +So kind of schematically I could say + + + align:start position:0% +So kind of schematically I could say +that this true CN was a sort of a CN + + align:start position:0% +that this true CN was a sort of a CN + + + align:start position:0% +that this true CN was a sort of a CN +naive minus a CN zero bin. + + align:start position:0% +naive minus a CN zero bin. + + + align:start position:0% +naive minus a CN zero bin. +So you could do the calculation ignoring + + align:start position:0% +So you could do the calculation ignoring + + + align:start position:0% +So you could do the calculation ignoring +that but then you have to be careful and + + align:start position:0% +that but then you have to be careful and + + + align:start position:0% +that but then you have to be careful and +there's a subtraction and that + + align:start position:0% +there's a subtraction and that + + + align:start position:0% +there's a subtraction and that +subtraction avoids the double counting + + align:start position:0% +subtraction avoids the double counting + + + align:start position:0% +subtraction avoids the double counting +with the ultrasoft right. So if you + + align:start position:0% +with the ultrasoft right. So if you + + + align:start position:0% +with the ultrasoft right. So if you +think about there being ultra soft + + align:start position:0% +think about there being ultra soft + + + align:start position:0% +think about there being ultra soft +amplitudes and linear amplitudes + + align:start position:0% +amplitudes and linear amplitudes + + + align:start position:0% +amplitudes and linear amplitudes +this is + + align:start position:0% +this is + + + align:start position:0% +this is +avoids + + align:start position:0% +avoids + + + align:start position:0% +avoids +a double counting. + + align:start position:0% + + + + align:start position:0% + +Now we never talked about whether + + align:start position:0% +Now we never talked about whether + + + align:start position:0% +Now we never talked about whether +there's something analogous to that in + + align:start position:0% +there's something analogous to that in + + + align:start position:0% +there's something analogous to that in +SCT2 and we just did a lot of SCT2 + + align:start position:0% +SCT2 and we just did a lot of SCT2 + + + align:start position:0% +SCT2 and we just did a lot of SCT2 +examples without ever even saying those + + align:start position:0% +examples without ever even saying those + + + align:start position:0% +examples without ever even saying those +words. to why it's actually for what + + align:start position:0% +words. to why it's actually for what + + + align:start position:0% +words. to why it's actually for what +we've talked about so far okay to ignore + + align:start position:0% +we've talked about so far okay to ignore + + + align:start position:0% +we've talked about so far okay to ignore +this issue + + align:start position:0% + + + + align:start position:0% + +but in general it's not okay. + + align:start position:0% + + + + align:start position:0% + +So if we go back to our picture of the + + align:start position:0% +So if we go back to our picture of the + + + align:start position:0% +So if we go back to our picture of the +degrees of freedom + + align:start position:0% +degrees of freedom + + + align:start position:0% +degrees of freedom +in SCT2 have this hyperola + + align:start position:0% +in SCT2 have this hyperola + + + align:start position:0% +in SCT2 have this hyperola +and you could have softs + + align:start position:0% +and you could have softs + + + align:start position:0% +and you could have softs +you could have some colineers and in the + + align:start position:0% +you could have some colineers and in the + + + align:start position:0% +you could have some colineers and in the +example that we just did it's like these + + align:start position:0% +example that we just did it's like these + + + align:start position:0% +example that we just did it's like these +were kind of the relevant modes and in + + align:start position:0% +were kind of the relevant modes and in + + + align:start position:0% +were kind of the relevant modes and in +general you might have some guy down + + align:start position:0% +general you might have some guy down + + + align:start position:0% +general you might have some guy down +here as well. So these are the the + + align:start position:0% +here as well. So these are the the + + + align:start position:0% +here as well. So these are the the +degrees of freedom in the SCT and + + align:start position:0% +degrees of freedom in the SCT and + + + align:start position:0% +degrees of freedom in the SCT and +effectively what's happened is if you + + align:start position:0% +effectively what's happened is if you + + + align:start position:0% +effectively what's happened is if you +want to think about double counting + + align:start position:0% +want to think about double counting + + + align:start position:0% +want to think about double counting +you're sliding down this hyperola. So + + align:start position:0% +you're sliding down this hyperola. So + + + align:start position:0% +you're sliding down this hyperola. So +this hyperola is kind of at a constant + + align:start position:0% +this hyperola is kind of at a constant + + + align:start position:0% +this hyperola is kind of at a constant +invariant mass say lambda QCD squar or + + align:start position:0% +invariant mass say lambda QCD squar or + + + align:start position:0% +invariant mass say lambda QCD squar or +could be lambda QCD + + align:start position:0% +could be lambda QCD + + + align:start position:0% +could be lambda QCD +and unlike the case in SCT1 where this + + align:start position:0% +and unlike the case in SCT1 where this + + + align:start position:0% +and unlike the case in SCT1 where this +guy lived on a different hyperola here + + align:start position:0% +guy lived on a different hyperola here + + + align:start position:0% +guy lived on a different hyperola here +to get between them you would be sliding + + align:start position:0% +to get between them you would be sliding + + + align:start position:0% +to get between them you would be sliding +down the hyperola at fixed invariant + + align:start position:0% +down the hyperola at fixed invariant + + + align:start position:0% +down the hyperola at fixed invariant +mass. + + align:start position:0% +mass. + + + align:start position:0% +mass. +Okay, so that's a little different, + + align:start position:0% +Okay, so that's a little different, + + + align:start position:0% +Okay, so that's a little different, +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +but in general in SKT 2 there are also + + align:start position:0% +but in general in SKT 2 there are also + + + align:start position:0% +but in general in SKT 2 there are also +zero bins. + + align:start position:0% + + + + align:start position:0% + +So in general you would have something + + align:start position:0% +So in general you would have something + + + align:start position:0% +So in general you would have something +like let me denote it this way CN minus + + align:start position:0% +like let me denote it this way CN minus + + + align:start position:0% +like let me denote it this way CN minus +CN soft + + align:start position:0% +CN soft + + + align:start position:0% +CN soft +and what I mean by this is this is my + + align:start position:0% +and what I mean by this is this is my + + + align:start position:0% +and what I mean by this is this is my +original amplitude where P mu was + + align:start position:0% +original amplitude where P mu was + + + align:start position:0% +original amplitude where P mu was +scaling like Q lambda squared 1 lambda + + align:start position:0% +scaling like Q lambda squared 1 lambda + + + align:start position:0% +scaling like Q lambda squared 1 lambda +the original and this would be a + + align:start position:0% +the original and this would be a + + + align:start position:0% +the original and this would be a +subtraction where you take that + + align:start position:0% +subtraction where you take that + + + align:start position:0% +subtraction where you take that +amplitude and you make it scale like in + + align:start position:0% +amplitude and you make it scale like in + + + align:start position:0% +amplitude and you make it scale like in +the soft regime. + + align:start position:0% +the soft regime. + + + align:start position:0% +the soft regime. +So it would be P mu + + align:start position:0% +So it would be P mu + + + align:start position:0% +So it would be P mu +lambda lambda lambda. So that's + + align:start position:0% +lambda lambda lambda. So that's + + + align:start position:0% +lambda lambda lambda. So that's +different than + + align:start position:0% +different than + + + align:start position:0% +different than +the example of SCT1. + + align:start position:0% +the example of SCT1. + + + align:start position:0% +the example of SCT1. +In the SCT1 case, we would really just + + align:start position:0% +In the SCT1 case, we would really just + + + align:start position:0% +In the SCT1 case, we would really just +be scaling down the one and the lambda + + align:start position:0% +be scaling down the one and the lambda + + + align:start position:0% +be scaling down the one and the lambda +so that they would be both of order + + align:start position:0% +so that they would be both of order + + + align:start position:0% +so that they would be both of order +lambda squared. Here we're actually + + align:start position:0% +lambda squared. Here we're actually + + + align:start position:0% +lambda squared. Here we're actually +scaling down the one and scaling up the + + align:start position:0% +scaling down the one and scaling up the + + + align:start position:0% +scaling down the one and scaling up the +lambda squared to a lambda. And that's + + align:start position:0% +lambda squared to a lambda. And that's + + + align:start position:0% +lambda squared to a lambda. And that's +the right thing to do to go from here to + + align:start position:0% +the right thing to do to go from here to + + + align:start position:0% +the right thing to do to go from here to +here. So we're just taking the + + align:start position:0% +here. So we're just taking the + + + align:start position:0% +here. So we're just taking the +amplitudes in this region and + + align:start position:0% +amplitudes in this region and + + + align:start position:0% +amplitudes in this region and +subtracting them in this region. And in + + align:start position:0% +subtracting them in this region. And in + + + align:start position:0% +subtracting them in this region. And in +general, we do have that. But actually, + + align:start position:0% +general, we do have that. But actually, + + + align:start position:0% +general, we do have that. But actually, +that's not the real complication that + + align:start position:0% +that's not the real complication that + + + align:start position:0% +that's not the real complication that +shows up in this in the in SCT2. The + + align:start position:0% +shows up in this in the in SCT2. The + + + align:start position:0% +shows up in this in the in SCT2. The +real complication has to do with whether + + align:start position:0% +real complication has to do with whether + + + align:start position:0% +real complication has to do with whether +there's any divergences associated to + + align:start position:0% +there's any divergences associated to + + + align:start position:0% +there's any divergences associated to +that. If this amplitude here didn't have + + align:start position:0% +that. If this amplitude here didn't have + + + align:start position:0% +that. If this amplitude here didn't have +any divergences, it wasn't kind of log + + align:start position:0% +any divergences, it wasn't kind of log + + + align:start position:0% +any divergences, it wasn't kind of log +singular, then you wouldn't really care + + align:start position:0% +singular, then you wouldn't really care + + + align:start position:0% +singular, then you wouldn't really care +about doing these subtractions because + + align:start position:0% +about doing these subtractions because + + + align:start position:0% +about doing these subtractions because +then there would be no infrared + + align:start position:0% +then there would be no infrared + + + align:start position:0% +then there would be no infrared +singularities that you're double + + align:start position:0% +singularities that you're double + + + align:start position:0% +singularities that you're double +counting and it it would just be + + align:start position:0% +counting and it it would just be + + + align:start position:0% +counting and it it would just be +effectively a constant. And the + + align:start position:0% +effectively a constant. And the + + + align:start position:0% +effectively a constant. And the +constants are always ambiguous. So + + align:start position:0% +constants are always ambiguous. So + + + align:start position:0% +constants are always ambiguous. So +whatever mistake you make in constants + + align:start position:0% +whatever mistake you make in constants + + + align:start position:0% +whatever mistake you make in constants +here, you just make up by changing your + + align:start position:0% +here, you just make up by changing your + + + align:start position:0% +here, you just make up by changing your +hard matching. So you don't have to + + align:start position:0% +hard matching. So you don't have to + + + align:start position:0% +hard matching. So you don't have to +worry if when the linear goes down into + + align:start position:0% +worry if when the linear goes down into + + + align:start position:0% +worry if when the linear goes down into +the soft region, there's no divergences. + + align:start position:0% +the soft region, there's no divergences. + + + align:start position:0% +the soft region, there's no divergences. +And that is actually what's happened in + + align:start position:0% +And that is actually what's happened in + + + align:start position:0% +And that is actually what's happened in +all the examples we've treated so far + + align:start position:0% +all the examples we've treated so far + + + align:start position:0% +all the examples we've treated so far +that when the colinear goes into some + + align:start position:0% +that when the colinear goes into some + + + align:start position:0% +that when the colinear goes into some +region where it's not supposed to have + + align:start position:0% +region where it's not supposed to have + + + align:start position:0% +region where it's not supposed to have +singularities that you just end up with + + align:start position:0% +singularities that you just end up with + + + align:start position:0% +singularities that you just end up with +no singularities. There's no log + + align:start position:0% +no singularities. There's no log + + + align:start position:0% +no singularities. There's no log +singularities. + + align:start position:0% + + + + align:start position:0% + +Okay. So so far + + align:start position:0% + + + + align:start position:0% + +there's no log singularities from the + + align:start position:0% +there's no log singularities from the + + + align:start position:0% +there's no log singularities from the +overlap regions. + + align:start position:0% + + + + align:start position:0% + +But that's not in general the situation. + + align:start position:0% +But that's not in general the situation. + + + align:start position:0% +But that's not in general the situation. +And we'll do an example in a minute + + align:start position:0% +And we'll do an example in a minute + + + align:start position:0% +And we'll do an example in a minute +where that where that where there are + + align:start position:0% +where that where that where there are + + + align:start position:0% +where that where that where there are +singularities that overlap. And the true + + align:start position:0% +singularities that overlap. And the true + + + align:start position:0% +singularities that overlap. And the true +difficulty here is the following. If you + + align:start position:0% +difficulty here is the following. If you + + + align:start position:0% +difficulty here is the following. If you +think about what's separating these + + align:start position:0% +think about what's separating these + + + align:start position:0% +think about what's separating these +modes, you might draw lines like this. + + align:start position:0% +modes, you might draw lines like this. + + + align:start position:0% +modes, you might draw lines like this. +Okay, just draw some straight lines + + align:start position:0% +Okay, just draw some straight lines + + + align:start position:0% +Okay, just draw some straight lines +separating the modes. And remember that + + align:start position:0% +separating the modes. And remember that + + + align:start position:0% +separating the modes. And remember that +we're plotting here in the P minus P+ + + align:start position:0% +we're plotting here in the P minus P+ + + + align:start position:0% +we're plotting here in the P minus P+ +plane. And that p fixed p^ squ is like + + align:start position:0% +plane. And that p fixed p^ squ is like + + + align:start position:0% +plane. And that p fixed p^ squ is like +fixed product of p minus p+. + + align:start position:0% +fixed product of p minus p+. + + + align:start position:0% +fixed product of p minus p+. +So p ^2 is p plus p minus up to the p + + align:start position:0% +So p ^2 is p plus p minus up to the p + + + align:start position:0% +So p ^2 is p plus p minus up to the p +per square piece which we're ignoring. + + align:start position:0% +per square piece which we're ignoring. + + + align:start position:0% +per square piece which we're ignoring. +So you could think of these lines as + + align:start position:0% +So you could think of these lines as + + + align:start position:0% +So you could think of these lines as +lines of constant p plus over p minus. + + align:start position:0% + + + + align:start position:0% + +Okay. Okay. And if I + + align:start position:0% +Okay. Okay. And if I + + + align:start position:0% +Okay. Okay. And if I +this is the + + align:start position:0% + + + + align:start position:0% + +so some ortho something orthogonal to p + + align:start position:0% +so some ortho something orthogonal to p + + + align:start position:0% +so some ortho something orthogonal to p +to p ^2. + + align:start position:0% +to p ^2. + + + align:start position:0% +to p ^2. +All right. So that would be one way of + + align:start position:0% +All right. So that would be one way of + + + align:start position:0% +All right. So that would be one way of +thinking about so you need something + + align:start position:0% +thinking about so you need something + + + align:start position:0% +thinking about so you need something +that's orthogonal to p^ square in order + + align:start position:0% +that's orthogonal to p^ square in order + + + align:start position:0% +that's orthogonal to p^ square in order +to distinguish these modes. And the real + + align:start position:0% +to distinguish these modes. And the real + + + align:start position:0% +to distinguish these modes. And the real +issue with that is that is related to + + align:start position:0% +issue with that is that is related to + + + align:start position:0% +issue with that is that is related to +the regulators. When we use dimensional + + align:start position:0% +the regulators. When we use dimensional + + + align:start position:0% +the regulators. When we use dimensional +regularization, it turns out the + + align:start position:0% +regularization, it turns out the + + + align:start position:0% +regularization, it turns out the +dimensional regularization is not + + align:start position:0% +dimensional regularization is not + + + align:start position:0% +dimensional regularization is not +sufficient to regulate a divergence that + + align:start position:0% +sufficient to regulate a divergence that + + + align:start position:0% +sufficient to regulate a divergence that +would happen when the CN comes down on + + align:start position:0% +would happen when the CN comes down on + + + align:start position:0% +would happen when the CN comes down on +top of the S. And the reason is because + + align:start position:0% +top of the S. And the reason is because + + + align:start position:0% +top of the S. And the reason is because +dimensional regularization regulates P^ + + align:start position:0% +dimensional regularization regulates P^ + + + align:start position:0% +dimensional regularization regulates P^ +squ. It regulates it's a remember it's a + + align:start position:0% +squ. It regulates it's a remember it's a + + + align:start position:0% +squ. It regulates it's a remember it's a +Lorenzen invariant regulator. So it's + + align:start position:0% +Lorenzen invariant regulator. So it's + + + align:start position:0% +Lorenzen invariant regulator. So it's +regulating Lorenari things like P^ squ + + align:start position:0% +regulating Lorenari things like P^ squ + + + align:start position:0% +regulating Lorenari things like P^ squ +not something like the rapidity which is + + align:start position:0% +not something like the rapidity which is + + + align:start position:0% +not something like the rapidity which is +this P+ over P minus that you would need + + align:start position:0% +this P+ over P minus that you would need + + + align:start position:0% +this P+ over P minus that you would need +to distinguish these modes. + + align:start position:0% +to distinguish these modes. + + + align:start position:0% +to distinguish these modes. +So + + align:start position:0% + + + + align:start position:0% + +invariant mass does not distinguish the + + align:start position:0% +invariant mass does not distinguish the + + + align:start position:0% +invariant mass does not distinguish the +low energy modes. + + align:start position:0% + + + + align:start position:0% + +So rapidity you could define is + + align:start position:0% +So rapidity you could define is + + + align:start position:0% +So rapidity you could define is +it's usually defined this way. + + align:start position:0% + + + + align:start position:0% + +So exponent of 2 y where y is the + + align:start position:0% +So exponent of 2 y where y is the + + + align:start position:0% +So exponent of 2 y where y is the +rapidity + + align:start position:0% + + + + align:start position:0% + +is p minus over p plus and if you look + + align:start position:0% +is p minus over p plus and if you look + + + align:start position:0% +is p minus over p plus and if you look +at the scaling of that + + align:start position:0% +at the scaling of that + + + align:start position:0% +at the scaling of that +that's scaling like either lambda minus + + align:start position:0% +that's scaling like either lambda minus + + + align:start position:0% +that's scaling like either lambda minus +2 lambda 0 or lambda squared for the + + align:start position:0% +2 lambda 0 or lambda squared for the + + + align:start position:0% +2 lambda 0 or lambda squared for the +different cases for cn + + align:start position:0% +different cases for cn + + + align:start position:0% +different cases for cn +s and cn bar. So it's this variable + + align:start position:0% +s and cn bar. So it's this variable + + + align:start position:0% +s and cn bar. So it's this variable +that's really distinguishing the + + align:start position:0% +that's really distinguishing the + + + align:start position:0% +that's really distinguishing the +different modes. Okay. Okay. And that's + + align:start position:0% +different modes. Okay. Okay. And that's + + + align:start position:0% +different modes. Okay. Okay. And that's +the the these lines, these orange lines + + align:start position:0% +the the these lines, these orange lines + + + align:start position:0% +the the these lines, these orange lines +are just putting dividing lines between + + align:start position:0% +are just putting dividing lines between + + + align:start position:0% +are just putting dividing lines between +these in rapidity. + + align:start position:0% +these in rapidity. + + + align:start position:0% +these in rapidity. +Right. + + align:start position:0% + + + + align:start position:0% + +Okay. So + + align:start position:0% + + + + align:start position:0% + +there's a complication that dimensional + + align:start position:0% +there's a complication that dimensional + + + align:start position:0% +there's a complication that dimensional +regularization doesn't suffice. + + align:start position:0% + + + + align:start position:0% + +So you could think of it as regulating P + + align:start position:0% +So you could think of it as regulating P + + + align:start position:0% +So you could think of it as regulating P +uklitian squared once you do the wick + + align:start position:0% +uklitian squared once you do the wick + + + align:start position:0% +uklitian squared once you do the wick +rotation for example. + + align:start position:0% +rotation for example. + + + align:start position:0% +rotation for example. +So it regulates it separates hyperolas + + align:start position:0% +So it regulates it separates hyperolas + + + align:start position:0% +So it regulates it separates hyperolas +but it does not separate modes along a + + align:start position:0% +but it does not separate modes along a + + + align:start position:0% +but it does not separate modes along a +hyperola. + + align:start position:0% +hyperola. + + + align:start position:0% +hyperola. +It's a way of regulating singularities + + align:start position:0% +It's a way of regulating singularities + + + align:start position:0% +It's a way of regulating singularities +between hyperolas but not along a + + align:start position:0% +between hyperolas but not along a + + + align:start position:0% +between hyperolas but not along a +hyperola. + + align:start position:0% + + + + align:start position:0% + +So that's one complication. And we'll + + align:start position:0% +So that's one complication. And we'll + + + align:start position:0% +So that's one complication. And we'll +need an additional regulator. + + align:start position:0% +need an additional regulator. + + + align:start position:0% +need an additional regulator. +And we'll see that that regulator will + + align:start position:0% +And we'll see that that regulator will + + + align:start position:0% +And we'll see that that regulator will +eventually + + align:start position:0% +eventually + + + align:start position:0% +eventually +lead to a new type of reormalization + + align:start position:0% +lead to a new type of reormalization + + + align:start position:0% +lead to a new type of reormalization +group + + align:start position:0% +group + + + align:start position:0% +group +flow which is flow along a hyperola. + + align:start position:0% +flow which is flow along a hyperola. + + + align:start position:0% +flow which is flow along a hyperola. +It's not a flow in invariant mass but a + + align:start position:0% +It's not a flow in invariant mass but a + + + align:start position:0% +It's not a flow in invariant mass but a +flow in rapidity. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. So let's explore what can happen + + align:start position:0% +Okay. So let's explore what can happen + + + align:start position:0% +Okay. So let's explore what can happen +in an example where there are these + + align:start position:0% +in an example where there are these + + + align:start position:0% +in an example where there are these +divergences + + align:start position:0% +divergences + + + align:start position:0% +divergences +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in sort of a the simplest possible + + align:start position:0% +in sort of a the simplest possible + + + align:start position:0% +in sort of a the simplest possible +example. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So there's enough going on that we don't + + align:start position:0% +So there's enough going on that we don't + + + align:start position:0% +So there's enough going on that we don't +we want to make our lives as simple as + + align:start position:0% +we want to make our lives as simple as + + + align:start position:0% +we want to make our lives as simple as +possible. So + + align:start position:0% +possible. So + + + align:start position:0% +possible. So +what I'll talk about + + align:start position:0% +what I'll talk about + + + align:start position:0% +what I'll talk about +something called the massive sudacov + + align:start position:0% +something called the massive sudacov + + + align:start position:0% +something called the massive sudacov +form factor. + + align:start position:0% + + + + align:start position:0% + +So you should think of it setup is like + + align:start position:0% +So you should think of it setup is like + + + align:start position:0% +So you should think of it setup is like +as follows. + + align:start position:0% +as follows. + + + align:start position:0% +as follows. +We're going to consider a form factor + + align:start position:0% +We're going to consider a form factor + + + align:start position:0% +We're going to consider a form factor +and it's going to be a space-like form + + align:start position:0% +and it's going to be a space-like form + + + align:start position:0% +and it's going to be a space-like form +factor. + + align:start position:0% +factor. + + + align:start position:0% +factor. +So it's a space-like quark quark form + + align:start position:0% +So it's a space-like quark quark form + + + align:start position:0% +So it's a space-like quark quark form +factor + + align:start position:0% + + + + align:start position:0% + +Q of the photon here + + align:start position:0% +Q of the photon here + + + align:start position:0% +Q of the photon here +spaceike and we're going to think about + + align:start position:0% +spaceike and we're going to think about + + + align:start position:0% +spaceike and we're going to think about +rather than having photons or gluons + + align:start position:0% +rather than having photons or gluons + + + align:start position:0% +rather than having photons or gluons +we're going to think about massive gauge + + align:start position:0% +we're going to think about massive gauge + + + align:start position:0% +we're going to think about massive gauge +bzons. + + align:start position:0% +bzons. + + + align:start position:0% +bzons. +So this is going to be some kind of Z if + + align:start position:0% +So this is going to be some kind of Z if + + + align:start position:0% +So this is going to be some kind of Z if +you like. Could be a Z bzon + + align:start position:0% + + + + align:start position:0% + +and I'll just call the mass m. + + align:start position:0% + + + + align:start position:0% + +Okay. So the thing that I'm going to + + align:start position:0% +Okay. So the thing that I'm going to + + + align:start position:0% +Okay. So the thing that I'm going to +want to iterate is like the mass rather + + align:start position:0% +want to iterate is like the mass rather + + + align:start position:0% +want to iterate is like the mass rather +than doing QCD I'm doing electroe + + align:start position:0% +than doing QCD I'm doing electroe + + + align:start position:0% +than doing QCD I'm doing electroe +corrections electroe corrections from a + + align:start position:0% +corrections electroe corrections from a + + + align:start position:0% +corrections electroe corrections from a +mass of gauge bzon. + + align:start position:0% +mass of gauge bzon. + + + align:start position:0% +mass of gauge bzon. +So, + + align:start position:0% + + + + align:start position:0% + +so this is relevant if we have + + align:start position:0% +so this is relevant if we have + + + align:start position:0% +so this is relevant if we have +electroeak corrections in a situation + + align:start position:0% +electroeak corrections in a situation + + + align:start position:0% +electroeak corrections in a situation +where Q ^2 is much greater than an M^2 + + align:start position:0% +where Q ^2 is much greater than an M^2 + + + align:start position:0% +where Q ^2 is much greater than an M^2 +and we're not going to be having gluons. + + align:start position:0% +and we're not going to be having gluons. + + + align:start position:0% +and we're not going to be having gluons. +Instead, we'll be talking about these + + align:start position:0% +Instead, we'll be talking about these + + + align:start position:0% +Instead, we'll be talking about these +massive gauge Bzons, multiple Z bzons if + + align:start position:0% +massive gauge Bzons, multiple Z bzons if + + + align:start position:0% +massive gauge Bzons, multiple Z bzons if +you like. Could also put the W's in, but + + align:start position:0% +you like. Could also put the W's in, but + + + align:start position:0% +you like. Could also put the W's in, but +let's make it simple and just talk about + + align:start position:0% +let's make it simple and just talk about + + + align:start position:0% +let's make it simple and just talk about +Z's. + + align:start position:0% +Z's. + + + align:start position:0% +Z's. +Okay, so let's do this example. + + align:start position:0% +Okay, so let's do this example. + + + align:start position:0% +Okay, so let's do this example. +So in the full theory you would start + + align:start position:0% +So in the full theory you would start + + + align:start position:0% +So in the full theory you would start +with a vector current say and you'd want + + align:start position:0% +with a vector current say and you'd want + + + align:start position:0% +with a vector current say and you'd want +to match that onto SCT. + + align:start position:0% +to match that onto SCT. + + + align:start position:0% +to match that onto SCT. +Before we do that let's just + + align:start position:0% +Before we do that let's just + + + align:start position:0% +Before we do that let's just +let me just write down a kind of full + + align:start position:0% +let me just write down a kind of full + + + align:start position:0% +let me just write down a kind of full +theory object using Loren variance. + + align:start position:0% +theory object using Loren variance. + + + align:start position:0% +theory object using Loren variance. +So + + align:start position:0% + + + + align:start position:0% + +you could think about the quark form + + align:start position:0% +you could think about the quark form + + + align:start position:0% +you could think about the quark form +factor and for massive gauge bzons + + align:start position:0% +factor and for massive gauge bzons + + + align:start position:0% +factor and for massive gauge bzons +this is just some form factor that you + + align:start position:0% +this is just some form factor that you + + + align:start position:0% +this is just some form factor that you +can calculate + + align:start position:0% +can calculate + + + align:start position:0% +can calculate +that's a function of Q ^2 and M^2 + + align:start position:0% +that's a function of Q ^2 and M^2 + + + align:start position:0% +that's a function of Q ^2 and M^2 +and then there's some spinners + + align:start position:0% +and then there's some spinners + + + align:start position:0% +and then there's some spinners +and so really kind of the dependence is + + align:start position:0% +and so really kind of the dependence is + + + align:start position:0% +and so really kind of the dependence is +encoded in this F which is a function of + + align:start position:0% +encoded in this F which is a function of + + + align:start position:0% +encoded in this F which is a function of +Q ^2 and M^2 m squ is acting kind of + + align:start position:0% +Q ^2 and M^2 m squ is acting kind of + + + align:start position:0% +Q ^2 and M^2 m squ is acting kind of +like an infrared regulator right so this + + align:start position:0% +like an infrared regulator right so this + + + align:start position:0% +like an infrared regulator right so this +Z bzon there's not a soft singularity + + align:start position:0% +Z bzon there's not a soft singularity + + + align:start position:0% +Z bzon there's not a soft singularity +associated to it. + + align:start position:0% + + + + align:start position:0% + +And so what you'd like to do in this + + align:start position:0% +And so what you'd like to do in this + + + align:start position:0% +And so what you'd like to do in this +process is factoriize q ^2 and m^2 i.e. + + align:start position:0% +process is factoriize q ^2 and m^2 i.e. + + + align:start position:0% +process is factoriize q ^2 and m^2 i.e. +expand this thing in q ^2 and m^2 and + + align:start position:0% +expand this thing in q ^2 and m^2 and + + + align:start position:0% +expand this thing in q ^2 and m^2 and +maybe sum some logs of q ^2 and m^2. + + align:start position:0% +maybe sum some logs of q ^2 and m^2. + + + align:start position:0% +maybe sum some logs of q ^2 and m^2. +So we want to factoriize + + align:start position:0% + + + + align:start position:0% + +some logs. + + align:start position:0% + + + + align:start position:0% + +I don't know. + + align:start position:0% +I don't know. + + + align:start position:0% +I don't know. +Okay. So, what are the type of degrees + + align:start position:0% +Okay. So, what are the type of degrees + + + align:start position:0% +Okay. So, what are the type of degrees +of freedom that we could have here? So, + + align:start position:0% +of freedom that we could have here? So, + + + align:start position:0% +of freedom that we could have here? So, +lambda is going to be m over q mass of + + align:start position:0% +lambda is going to be m over q mass of + + + align:start position:0% +lambda is going to be m over q mass of +the z bzon over the energy scale of the + + align:start position:0% +the z bzon over the energy scale of the + + + align:start position:0% +the z bzon over the energy scale of the +collision of the the gamma star. And if + + align:start position:0% +collision of the the gamma star. And if + + + align:start position:0% +collision of the the gamma star. And if +you just look at the z bzon then it + + align:start position:0% +you just look at the z bzon then it + + + align:start position:0% +you just look at the z bzon then it +could be colinear or it could be soft. + + align:start position:0% +could be colinear or it could be soft. + + + align:start position:0% +could be colinear or it could be soft. +So it could be actually + + align:start position:0% +So it could be actually + + + align:start position:0% +So it could be actually +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +three different possibilities and I + + align:start position:0% +three different possibilities and I + + + align:start position:0% +three different possibilities and I +could think about doing this effectively + + align:start position:0% +could think about doing this effectively + + + align:start position:0% +could think about doing this effectively +in a bright frame just like we did + + align:start position:0% +in a bright frame just like we did + + + align:start position:0% +in a bright frame just like we did +earlier. And then if what you would have + + align:start position:0% +earlier. And then if what you would have + + + align:start position:0% +earlier. And then if what you would have +is that the cleaner guy is like the + + align:start position:0% +is that the cleaner guy is like the + + + align:start position:0% +is that the cleaner guy is like the +quark + + align:start position:0% +quark + + + align:start position:0% +quark +and then the antiar guy is like the + + align:start position:0% +and then the antiar guy is like the + + + align:start position:0% +and then the antiar guy is like the +outgoing quark + + align:start position:0% +outgoing quark + + + align:start position:0% +outgoing quark +q of p bar. So you'd be making a + + align:start position:0% +q of p bar. So you'd be making a + + + align:start position:0% +q of p bar. So you'd be making a +transition in this diagram from n linear + + align:start position:0% +transition in this diagram from n linear + + + align:start position:0% +transition in this diagram from n linear +objects to n bar linear objects. And you + + align:start position:0% +objects to n bar linear objects. And you + + + align:start position:0% +objects to n bar linear objects. And you +could likewise have a z boson which + + align:start position:0% +could likewise have a z boson which + + + align:start position:0% +could likewise have a z boson which +could be linear + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +or you could have a z boson that's soft + + align:start position:0% +or you could have a z boson that's soft + + + align:start position:0% +or you could have a z boson that's soft +and you have a soft rather than ultra + + align:start position:0% +and you have a soft rather than ultra + + + align:start position:0% +and you have a soft rather than ultra +soft because of the mass. Right? If Q * + + align:start position:0% +soft because of the mass. Right? If Q * + + + align:start position:0% +soft because of the mass. Right? If Q * +lambda is M and so if we want a + + align:start position:0% +lambda is M and so if we want a + + + align:start position:0% +lambda is M and so if we want a +propagator that's like P ^2 minus M^ 2 P + + align:start position:0% +propagator that's like P ^2 minus M^ 2 P + + + align:start position:0% +propagator that's like P ^2 minus M^ 2 P +^2 better be of order M squ that happens + + align:start position:0% +^2 better be of order M squ that happens + + + align:start position:0% +^2 better be of order M squ that happens +for softs not for ultra softs so that's + + align:start position:0% +for softs not for ultra softs so that's + + + align:start position:0% +for softs not for ultra softs so that's +why we have softs and the same thing for + + align:start position:0% +why we have softs and the same thing for + + + align:start position:0% +why we have softs and the same thing for +colineers P squ of order M^ squ for + + align:start position:0% +colineers P squ of order M^ squ for + + + align:start position:0% +colineers P squ of order M^ squ for +these colineers so it's really an SCT2 + + align:start position:0% +these colineers so it's really an SCT2 + + + align:start position:0% +these colineers so it's really an SCT2 +type situation where the hyperola is + + align:start position:0% +type situation where the hyperola is + + + align:start position:0% +type situation where the hyperola is +just set by P^ square of order M^ squ + + align:start position:0% +just set by P^ square of order M^ squ + + + align:start position:0% +just set by P^ square of order M^ squ +we have our mode sitting on that + + align:start position:0% +we have our mode sitting on that + + + align:start position:0% +we have our mode sitting on that +hyperola + + align:start position:0% +hyperola + + + align:start position:0% +hyperola +okay so it's exactly of this type over + + align:start position:0% +okay so it's exactly of this type over + + + align:start position:0% +okay so it's exactly of this type over +there. And the thing that's new in this + + align:start position:0% +there. And the thing that's new in this + + + align:start position:0% +there. And the thing that's new in this +example is that we're going to encounter + + align:start position:0% +example is that we're going to encounter + + + align:start position:0% +example is that we're going to encounter +these rapidity divergences. + + align:start position:0% +these rapidity divergences. + + + align:start position:0% +these rapidity divergences. +You imagine there's the only quantum + + align:start position:0% +You imagine there's the only quantum + + + align:start position:0% +You imagine there's the only quantum +particle in your theory is the Z. + + align:start position:0% +particle in your theory is the Z. + + + align:start position:0% +particle in your theory is the Z. +Yeah. + + align:start position:0% + + + + align:start position:0% + +Make things as simple as possible. + + align:start position:0% +Make things as simple as possible. + + + align:start position:0% +Make things as simple as possible. +So you could talk about mixed sort of + + align:start position:0% +So you could talk about mixed sort of + + + align:start position:0% +So you could talk about mixed sort of +electric and QCD, but yeah, we don't. + + align:start position:0% +electric and QCD, but yeah, we don't. + + + align:start position:0% +electric and QCD, but yeah, we don't. +Let's make it in some sense that's kind + + align:start position:0% +Let's make it in some sense that's kind + + + align:start position:0% +Let's make it in some sense that's kind +of just like mixing a problem that we + + align:start position:0% +of just like mixing a problem that we + + + align:start position:0% +of just like mixing a problem that we +already would know how to deal with with + + align:start position:0% +already would know how to deal with with + + + align:start position:0% +already would know how to deal with with +this one. So + + align:start position:0% +this one. So + + + align:start position:0% +this one. So +let's just deal with this one. + + align:start position:0% +let's just deal with this one. + + + align:start position:0% +let's just deal with this one. +All right. So in terms of the external + + align:start position:0% +All right. So in terms of the external + + + align:start position:0% +All right. So in terms of the external +quark momenta + + align:start position:0% +quark momenta + + + align:start position:0% +quark momenta +we can therefore kind of treat them as + + align:start position:0% +we can therefore kind of treat them as + + + align:start position:0% +we can therefore kind of treat them as +follows. + + align:start position:0% +follows. + + + align:start position:0% +follows. +Let's just let them be + + align:start position:0% +Let's just let them be + + + align:start position:0% +Let's just let them be +have a large component. They're massless + + align:start position:0% +have a large component. They're massless + + + align:start position:0% +have a large component. They're massless +particles. + + align:start position:0% + + + + align:start position:0% + +So this is P. This is P bar and these + + align:start position:0% +So this is P. This is P bar and these + + + align:start position:0% +So this is P. This is P bar and these +guys are massless. + + align:start position:0% +guys are massless. + + + align:start position:0% +guys are massless. +Should have said that. + + align:start position:0% + + + + align:start position:0% + +And if you go through the kinematics Q + + align:start position:0% +And if you go through the kinematics Q + + + align:start position:0% +And if you go through the kinematics Q +^2 which is minus P minus P prime squ if + + align:start position:0% +^2 which is minus P minus P prime squ if + + + align:start position:0% +^2 which is minus P minus P prime squ if +you square that you just find it's P + + align:start position:0% +you square that you just find it's P + + + align:start position:0% +you square that you just find it's P +minus P plus. And we're just effectively + + align:start position:0% +minus P plus. And we're just effectively + + + align:start position:0% +minus P plus. And we're just effectively +if we pick the bright frame, + + align:start position:0% + + + + align:start position:0% + +which is what we're going to do, each + + align:start position:0% +which is what we're going to do, each + + + align:start position:0% +which is what we're going to do, each +one of those is separately, + + align:start position:0% +one of those is separately, + + + align:start position:0% +one of those is separately, +keep calling it prime, call it bar. Each + + align:start position:0% +keep calling it prime, call it bar. Each + + + align:start position:0% +keep calling it prime, call it bar. Each +one of those is separately Q. Okay, the + + align:start position:0% +one of those is separately Q. Okay, the + + + align:start position:0% +one of those is separately Q. Okay, the +large these guys are just fixed to both + + align:start position:0% +large these guys are just fixed to both + + + align:start position:0% +large these guys are just fixed to both +be Q. + + align:start position:0% +be Q. + + + align:start position:0% +be Q. +All right, so we could factoriize this + + align:start position:0% +All right, so we could factoriize this + + + align:start position:0% +All right, so we could factoriize this +current with these degrees of freedom. + + align:start position:0% +current with these degrees of freedom. + + + align:start position:0% +current with these degrees of freedom. +The quarks are colinear. So at lowest + + align:start position:0% +The quarks are colinear. So at lowest + + + align:start position:0% +The quarks are colinear. So at lowest +order they just become a CN and a CN + + align:start position:0% +order they just become a CN and a CN + + + align:start position:0% +order they just become a CN and a CN +bar. And then we have to address that + + align:start position:0% +bar. And then we have to address that + + + align:start position:0% +bar. And then we have to address that +with pulson lines and we know how to do + + align:start position:0% +with pulson lines and we know how to do + + + align:start position:0% +with pulson lines and we know how to do +that. So let me just write down the + + align:start position:0% +that. So let me just write down the + + + align:start position:0% +that. So let me just write down the +answer. + + align:start position:0% + + + + align:start position:0% + +We could again follow our procedure of + + align:start position:0% +We could again follow our procedure of + + + align:start position:0% +We could again follow our procedure of +going through sket one but it's now so + + align:start position:0% +going through sket one but it's now so + + + align:start position:0% +going through sket one but it's now so +familiar we just know what to write + + align:start position:0% +familiar we just know what to write + + + align:start position:0% +familiar we just know what to write +down. + + align:start position:0% +down. + + + align:start position:0% +down. +Okay. So the current would look like + + align:start position:0% +Okay. So the current would look like + + + align:start position:0% +Okay. So the current would look like +that. And I'm not going to worry too + + align:start position:0% +that. And I'm not going to worry too + + + align:start position:0% +that. And I'm not going to worry too +much about the direct structure. + + align:start position:0% + + + + align:start position:0% + +So I won't won't worry for example about + + align:start position:0% +So I won't won't worry for example about + + + align:start position:0% +So I won't won't worry for example about +gamma fives and + + align:start position:0% + + + + align:start position:0% + +we could put that in it's easy. + + align:start position:0% + + + + align:start position:0% + +So that's the leading order current and + + align:start position:0% +So that's the leading order current and + + + align:start position:0% +So that's the leading order current and +then we'd have leading order lrangeians + + align:start position:0% +then we'd have leading order lrangeians + + + align:start position:0% +then we'd have leading order lrangeians +and we just start calculating + + align:start position:0% + + + + align:start position:0% + +and if we calculate what you would + + align:start position:0% +and if we calculate what you would + + + align:start position:0% +and if we calculate what you would +expect from a matrix from that is you'd + + align:start position:0% +expect from a matrix from that is you'd + + + align:start position:0% +expect from a matrix from that is you'd +expect that f of q ^2 and m^2 is going + + align:start position:0% +expect that f of q ^2 and m^2 is going + + + align:start position:0% +expect that f of q ^2 and m^2 is going +to split up given the degrees of freedom + + align:start position:0% +to split up given the degrees of freedom + + + align:start position:0% +to split up given the degrees of freedom +we have into some kind of hard function + + align:start position:0% +we have into some kind of hard function + + + align:start position:0% +we have into some kind of hard function +and then some kind of amplitude for the + + align:start position:0% +and then some kind of amplitude for the + + + align:start position:0% +and then some kind of amplitude for the +linear parts and then some kind of + + align:start position:0% +linear parts and then some kind of + + + align:start position:0% +linear parts and then some kind of +amplitude for the soft part. + + align:start position:0% +amplitude for the soft part. + + + align:start position:0% +amplitude for the soft part. +Okay, so you'd expect some hard times + + align:start position:0% +Okay, so you'd expect some hard times + + + align:start position:0% +Okay, so you'd expect some hard times +colinear factorization of the form + + align:start position:0% +colinear factorization of the form + + + align:start position:0% +colinear factorization of the form +factor and this is what we'll be after. + + align:start position:0% +factor and this is what we'll be after. + + + align:start position:0% +factor and this is what we'll be after. +So it's always good to sort of have an + + align:start position:0% +So it's always good to sort of have an + + + align:start position:0% +So it's always good to sort of have an +idea where you're go where you're going + + align:start position:0% +idea where you're go where you're going + + + align:start position:0% +idea where you're go where you're going +and that's where we're going. So let's + + align:start position:0% +and that's where we're going. So let's + + + align:start position:0% +and that's where we're going. So let's +consider just one loop diagrams + + align:start position:0% +consider just one loop diagrams + + + align:start position:0% +consider just one loop diagrams +and it suffices in order to make the + + align:start position:0% +and it suffices in order to make the + + + align:start position:0% +and it suffices in order to make the +point just to consider the most singular + + align:start position:0% +point just to consider the most singular + + + align:start position:0% +point just to consider the most singular +one. So I'm going to consider + + align:start position:0% + + + + align:start position:0% + +So there's various loop integrals that + + align:start position:0% +So there's various loop integrals that + + + align:start position:0% +So there's various loop integrals that +you could have to do when you're doing + + align:start position:0% +you could have to do when you're doing + + + align:start position:0% +you could have to do when you're doing +the diagrams if they're firmians. Let's + + align:start position:0% +the diagrams if they're firmians. Let's + + + align:start position:0% +the diagrams if they're firmians. Let's +just take the simplest which is a scalar + + align:start position:0% +just take the simplest which is a scalar + + + align:start position:0% +just take the simplest which is a scalar +loop integral. + + align:start position:0% +loop integral. + + + align:start position:0% +loop integral. +And I'm going to contrast how that + + align:start position:0% +And I'm going to contrast how that + + + align:start position:0% +And I'm going to contrast how that +scaler loop integral would look if you + + align:start position:0% +scaler loop integral would look if you + + + align:start position:0% +scaler loop integral would look if you +were doing the full theory calculation + + align:start position:0% +were doing the full theory calculation + + + align:start position:0% +were doing the full theory calculation +with how it would look in the effective + + align:start position:0% +with how it would look in the effective + + + align:start position:0% +with how it would look in the effective +theory. And then we'll see where the + + align:start position:0% +theory. And then we'll see where the + + + align:start position:0% +theory. And then we'll see where the +divergences come from. + + align:start position:0% + + + + align:start position:0% + +So you can think about this as the kind + + align:start position:0% +So you can think about this as the kind + + + align:start position:0% +So you can think about this as the kind +of the the piece where the numerator is + + align:start position:0% +of the the piece where the numerator is + + + align:start position:0% +of the the piece where the numerator is +independent of the loop momenta. So the + + align:start position:0% +independent of the loop momenta. So the + + + align:start position:0% +independent of the loop momenta. So the +numerator just factors out. + + align:start position:0% + + + + align:start position:0% + +Okay, so if I took our vertex triangle + + align:start position:0% +Okay, so if I took our vertex triangle + + + align:start position:0% +Okay, so if I took our vertex triangle +diagram over there, then a piece of it + + align:start position:0% +diagram over there, then a piece of it + + + align:start position:0% +diagram over there, then a piece of it +where the numerator is trivial and + + align:start position:0% +where the numerator is trivial and + + + align:start position:0% +where the numerator is trivial and +factors out would look like this + + align:start position:0% +factors out would look like this + + + align:start position:0% +factors out would look like this +integral. So let's just study this guy. + + align:start position:0% +integral. So let's just study this guy. + + + align:start position:0% +integral. So let's just study this guy. +If we did this integral in the full + + align:start position:0% +If we did this integral in the full + + + align:start position:0% +If we did this integral in the full +theory, this would be both UV and I are + + align:start position:0% +theory, this would be both UV and I are + + + align:start position:0% +theory, this would be both UV and I are +finite. So this is just giving us some + + align:start position:0% +finite. So this is just giving us some + + + align:start position:0% +finite. So this is just giving us some +result that involves logs of q ^2 over m + + align:start position:0% +result that involves logs of q ^2 over m + + + align:start position:0% +result that involves logs of q ^2 over m +squ. + + align:start position:0% + + + + align:start position:0% + +So it does it does have double logs of + + align:start position:0% +So it does it does have double logs of + + + align:start position:0% +So it does it does have double logs of +^2 over m^2 and single logs of + + align:start position:0% +^2 over m^2 and single logs of + + + align:start position:0% +^2 over m^2 and single logs of +q ^2 m^2 but it's + + align:start position:0% +q ^2 m^2 but it's + + + align:start position:0% +q ^2 m^2 but it's +perfectly there's no one over epsilons. + + align:start position:0% + + + + align:start position:0% + +So now let's see what let's think about + + align:start position:0% +So now let's see what let's think about + + + align:start position:0% +So now let's see what let's think about +what would happen in the effective + + align:start position:0% +what would happen in the effective + + + align:start position:0% +what would happen in the effective +theory. + + align:start position:0% +theory. + + + align:start position:0% +theory. +So we have a kind of analogous loop + + align:start position:0% +So we have a kind of analogous loop + + + align:start position:0% +So we have a kind of analogous loop +integral for colinear where the gauge + + align:start position:0% +integral for colinear where the gauge + + + align:start position:0% +integral for colinear where the gauge +bzon is colinear. + + align:start position:0% + + + + align:start position:0% + +There's some numerator + + align:start position:0% +There's some numerator + + + align:start position:0% +There's some numerator +but again I'm not going to worry about + + align:start position:0% +but again I'm not going to worry about + + + align:start position:0% +but again I'm not going to worry about +you if this numerator is constant it + + align:start position:0% +you if this numerator is constant it + + + align:start position:0% +you if this numerator is constant it +doesn't it's effectively the same + + align:start position:0% +doesn't it's effectively the same + + + align:start position:0% +doesn't it's effectively the same +constant + + align:start position:0% +constant + + + align:start position:0% +constant +in the case of the if you take the + + align:start position:0% +in the case of the if you take the + + + align:start position:0% +in the case of the if you take the +leading order numerator in the full + + align:start position:0% +leading order numerator in the full + + + align:start position:0% +leading order numerator in the full +theory it'll be the leading order + + align:start position:0% +theory it'll be the leading order + + + align:start position:0% +theory it'll be the leading order +numerator in the effective theory as + + align:start position:0% +numerator in the effective theory as + + + align:start position:0% +numerator in the effective theory as +well but the denominators do change + + align:start position:0% +well but the denominators do change + + + align:start position:0% +well but the denominators do change +and so if we took the n colinear then + + align:start position:0% +and so if we took the n colinear then + + + align:start position:0% +and so if we took the n colinear then +yeah so this guy doesn't change + + align:start position:0% +yeah so this guy doesn't change + + + align:start position:0% +yeah so this guy doesn't change +because that's just like saying p minus + + align:start position:0% +because that's just like saying p minus + + + align:start position:0% +because that's just like saying p minus +minus and k or p minus and k minus are + + align:start position:0% +minus and k or p minus and k minus are + + + align:start position:0% +minus and k or p minus and k minus are +of the same size but this guy does + + align:start position:0% +of the same size but this guy does + + + align:start position:0% +of the same size but this guy does +change. + + align:start position:0% +change. + + + align:start position:0% +change. +Okay, so this guy would be k minus + + align:start position:0% +Okay, so this guy would be k minus + + + align:start position:0% +Okay, so this guy would be k minus +p bar plus because k minus is big and b+ + + align:start position:0% +p bar plus because k minus is big and b+ + + + align:start position:0% +p bar plus because k minus is big and b+ +is big. Both of these are big. + + align:start position:0% +is big. Both of these are big. + + + align:start position:0% +is big. Both of these are big. +So + + align:start position:0% + + + + align:start position:0% + +both of those are big in this in this + + align:start position:0% +both of those are big in this in this + + + align:start position:0% +both of those are big in this in this +diagram. And so that's effectively + + align:start position:0% +diagram. And so that's effectively + + + align:start position:0% +diagram. And so that's effectively +the Wilson line diagram. + + align:start position:0% +the Wilson line diagram. + + + align:start position:0% +the Wilson line diagram. +Okay, where the propagator here was off + + align:start position:0% +Okay, where the propagator here was off + + + align:start position:0% +Okay, where the propagator here was off +shell got integrated out and just became + + align:start position:0% +shell got integrated out and just became + + + align:start position:0% +shell got integrated out and just became +iconal + + align:start position:0% + + + + align:start position:0% + +and the k squ is smaller so we don't + + align:start position:0% +and the k squ is smaller so we don't + + + align:start position:0% +and the k squ is smaller so we don't +keep it in the leading order term. + + align:start position:0% +keep it in the leading order term. + + + align:start position:0% +keep it in the leading order term. +Analogously for + + align:start position:0% +Analogously for + + + align:start position:0% +Analogously for +bar it's the other way. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So both of these are big then this one + + align:start position:0% + + + + align:start position:0% + +remains and then + + align:start position:0% +remains and then + + + align:start position:0% +remains and then +then they're soft + + align:start position:0% + + + + align:start position:0% + +and in the soft case what happens is + + align:start position:0% +and in the soft case what happens is + + + align:start position:0% +and in the soft case what happens is +that both of the propagators end up + + align:start position:0% +that both of the propagators end up + + + align:start position:0% +that both of the propagators end up +being iconal. So, + + align:start position:0% + + + + align:start position:0% + +and in our SAT operator, that's a + + align:start position:0% +and in our SAT operator, that's a + + + align:start position:0% +and in our SAT operator, that's a +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +where we have our linear lines + + align:start position:0% +where we have our linear lines + + + align:start position:0% +where we have our linear lines +and then we have kind of a + + align:start position:0% +and then we have kind of a + + + align:start position:0% +and then we have kind of a +self-contraction of the S, but we're + + align:start position:0% +self-contraction of the S, but we're + + + align:start position:0% +self-contraction of the S, but we're +taking an SN with an SN. We have a + + align:start position:0% +taking an SN with an SN. We have a + + + align:start position:0% +taking an SN with an SN. We have a +contraction that's like this, + + align:start position:0% +contraction that's like this, + + + align:start position:0% +contraction that's like this, +right? two of the Wilson lines, soft + + align:start position:0% +right? two of the Wilson lines, soft + + + align:start position:0% +right? two of the Wilson lines, soft +Wilson lines that are sitting in that + + align:start position:0% +Wilson lines that are sitting in that + + + align:start position:0% +Wilson lines that are sitting in that +operator. That's a non-zero contraction + + align:start position:0% +operator. That's a non-zero contraction + + + align:start position:0% +operator. That's a non-zero contraction +that would lead to a diagram that would + + align:start position:0% +that would lead to a diagram that would + + + align:start position:0% +that would lead to a diagram that would +lead to this amplitude. + + align:start position:0% +lead to this amplitude. + + + align:start position:0% +lead to this amplitude. +All right, I'm going to leave a little + + align:start position:0% +All right, I'm going to leave a little + + + align:start position:0% +All right, I'm going to leave a little +space here because I'm going to add + + align:start position:0% +space here because I'm going to add + + + align:start position:0% +space here because I'm going to add +something in a minute. + + align:start position:0% + + + + align:start position:0% + +All right, so how do we see that there's + + align:start position:0% +All right, so how do we see that there's + + + align:start position:0% +All right, so how do we see that there's +a a problem with these integrals that + + align:start position:0% +a a problem with these integrals that + + + align:start position:0% +a a problem with these integrals that +they're not regulated by dimg? Well, you + + align:start position:0% +they're not regulated by dimg? Well, you + + + align:start position:0% +they're not regulated by dimg? Well, you +could look at the soft integral and you + + align:start position:0% +could look at the soft integral and you + + + align:start position:0% +could look at the soft integral and you +could just do the per. The per is only + + align:start position:0% +could just do the per. The per is only + + + align:start position:0% +could just do the per. The per is only +showing up in this k^ squus m^ 2. So you + + align:start position:0% +showing up in this k^ squus m^ 2. So you + + + align:start position:0% +showing up in this k^ squus m^ 2. So you +get something by doing that. + + align:start position:0% + + + + align:start position:0% + +And so if we do the per with dim rag in + + align:start position:0% +And so if we do the per with dim rag in + + + align:start position:0% +And so if we do the per with dim rag in +is we would end up proportional to + + align:start position:0% +is we would end up proportional to + + + align:start position:0% +is we would end up proportional to +something that's dk plus dk minus + + align:start position:0% +something that's dk plus dk minus + + + align:start position:0% +something that's dk plus dk minus +k + k - + + align:start position:0% +k + k - + + + align:start position:0% +k + k - +m^ 2 to the some power of epsilon + + align:start position:0% +m^ 2 to the some power of epsilon + + + align:start position:0% +m^ 2 to the some power of epsilon +divided still by the factors of k plus + + align:start position:0% +divided still by the factors of k plus + + + align:start position:0% +divided still by the factors of k plus +and k minus. So you see that the the + + align:start position:0% +and k minus. So you see that the the + + + align:start position:0% +and k minus. So you see that the the +invariant mass is being regulated. We + + align:start position:0% +invariant mass is being regulated. We + + + align:start position:0% +invariant mass is being regulated. We +just did the perp is gone. Plus time + + align:start position:0% +just did the perp is gone. Plus time + + + align:start position:0% +just did the perp is gone. Plus time +minus is being regulated because plus + + align:start position:0% +minus is being regulated because plus + + + align:start position:0% +minus is being regulated because plus +times minus if plus times minus grows + + align:start position:0% +times minus if plus times minus grows + + + align:start position:0% +times minus if plus times minus grows +large or goes small regulated by this + + align:start position:0% +large or goes small regulated by this + + + align:start position:0% +large or goes small regulated by this +epsilon. But either one plus going large + + align:start position:0% +epsilon. But either one plus going large + + + align:start position:0% +epsilon. But either one plus going large +or minus going large or plus going small + + align:start position:0% +or minus going large or plus going small + + + align:start position:0% +or minus going large or plus going small +minus going small with plus and times + + align:start position:0% +minus going small with plus and times + + + align:start position:0% +minus going small with plus and times +minus fixed is not regulated. And that's + + align:start position:0% +minus fixed is not regulated. And that's + + + align:start position:0% +minus fixed is not regulated. And that's +the rapidity divergence. If the + + align:start position:0% +the rapidity divergence. If the + + + align:start position:0% +the rapidity divergence. If the +invariant mass is fixed and k plus over + + align:start position:0% +invariant mass is fixed and k plus over + + + align:start position:0% +invariant mass is fixed and k plus over +k minus goes large or small. + + align:start position:0% + + + + align:start position:0% + +So let me write it as k minus over k + + align:start position:0% +So let me write it as k minus over k + + + align:start position:0% +So let me write it as k minus over k +plus going to zero or going to infinity. + + align:start position:0% + + + + align:start position:0% + +Let me say with K plus time K minus + + align:start position:0% +Let me say with K plus time K minus + + + align:start position:0% +Let me say with K plus time K minus +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +it diverges as these things happen. And + + align:start position:0% +it diverges as these things happen. And + + + align:start position:0% +it diverges as these things happen. And +if you think about what's happening in + + align:start position:0% +if you think about what's happening in + + + align:start position:0% +if you think about what's happening in +our picture uh over there with in these + + align:start position:0% +our picture uh over there with in these + + + align:start position:0% +our picture uh over there with in these +limits it's exactly a situation where + + align:start position:0% +limits it's exactly a situation where + + + align:start position:0% +limits it's exactly a situation where +this X here would be sliding up or + + align:start position:0% +this X here would be sliding up or + + + align:start position:0% +this X here would be sliding up or +sliding down. + + align:start position:0% +sliding down. + + + align:start position:0% +sliding down. +So in one of these limits, this one's + + align:start position:0% +So in one of these limits, this one's + + + align:start position:0% +So in one of these limits, this one's +going towards + + align:start position:0% + + + + align:start position:0% + +CN bar and this one would be going + + align:start position:0% +CN bar and this one would be going + + + align:start position:0% +CN bar and this one would be going +towards CN. + + align:start position:0% +towards CN. + + + align:start position:0% +towards CN. +So it's exactly a region where you would + + align:start position:0% +So it's exactly a region where you would + + + align:start position:0% +So it's exactly a region where you would +be overlapping sliding down the hyperola + + align:start position:0% +be overlapping sliding down the hyperola + + + align:start position:0% +be overlapping sliding down the hyperola +and the integral has log singularities. + + align:start position:0% +and the integral has log singularities. + + + align:start position:0% +and the integral has log singularities. +So this is exactly a situation where we + + align:start position:0% +So this is exactly a situation where we + + + align:start position:0% +So this is exactly a situation where we +can't ignore + + align:start position:0% +can't ignore + + + align:start position:0% +can't ignore +the overlaps and we have to worry about + + align:start position:0% +the overlaps and we have to worry about + + + align:start position:0% +the overlaps and we have to worry about +them. + + align:start position:0% + + + + align:start position:0% + +Okay, so we need another regulator, + + align:start position:0% +Okay, so we need another regulator, + + + align:start position:0% +Okay, so we need another regulator, +right? A dim rag is not enough. We have + + align:start position:0% +right? A dim rag is not enough. We have + + + align:start position:0% +right? A dim rag is not enough. We have +to do something else. So what could we + + align:start position:0% +to do something else. So what could we + + + align:start position:0% +to do something else. So what could we +do? So there's lots of different things + + align:start position:0% +do? So there's lots of different things + + + align:start position:0% +do? So there's lots of different things +that you could do. One thing is you + + align:start position:0% +that you could do. One thing is you + + + align:start position:0% +that you could do. One thing is you +could just sort of put it in some plus + + align:start position:0% +could just sort of put it in some plus + + + align:start position:0% +could just sort of put it in some plus +something in these denominators. That's + + align:start position:0% +something in these denominators. That's + + + align:start position:0% +something in these denominators. That's +called the delta regulator. K+ plus + + align:start position:0% +called the delta regulator. K+ plus + + + align:start position:0% +called the delta regulator. K+ plus +delta. It's one choice. Uh we'll do + + align:start position:0% +delta. It's one choice. Uh we'll do + + + align:start position:0% +delta. It's one choice. Uh we'll do +something a little bit more dimrag like + + align:start position:0% +something a little bit more dimrag like + + + align:start position:0% +something a little bit more dimrag like +okay which makes it sort of easier to + + align:start position:0% +okay which makes it sort of easier to + + + align:start position:0% +okay which makes it sort of easier to +think about the reormalization group. + + align:start position:0% +think about the reormalization group. + + + align:start position:0% +think about the reormalization group. +So + + align:start position:0% +So + + + align:start position:0% +So +one choice + + align:start position:0% +one choice + + + align:start position:0% +one choice +for an additional regulator + + align:start position:0% +for an additional regulator + + + align:start position:0% +for an additional regulator +is the following. + + align:start position:0% +is the following. + + + align:start position:0% +is the following. +So if you think about where these + + align:start position:0% +So if you think about where these + + + align:start position:0% +So if you think about where these +divergences come came from, they came + + align:start position:0% +divergences come came from, they came + + + align:start position:0% +divergences come came from, they came +from the Wilson lines. So what you + + align:start position:0% +from the Wilson lines. So what you + + + align:start position:0% +from the Wilson lines. So what you +really need to do is regulate the Wilson + + align:start position:0% +really need to do is regulate the Wilson + + + align:start position:0% +really need to do is regulate the Wilson +lines + + align:start position:0% + + + + align:start position:0% + +and you can do that as follows. Let me + + align:start position:0% +and you can do that as follows. Let me + + + align:start position:0% +and you can do that as follows. Let me +write out the Wilson lines in our kind + + align:start position:0% +write out the Wilson lines in our kind + + + align:start position:0% +write out the Wilson lines in our kind +of momentum space notation. + + align:start position:0% + + + + align:start position:0% + +So + + align:start position:0% +So + + + align:start position:0% +So +we have some N.P type momentum for the + + align:start position:0% +we have some N.P type momentum for the + + + align:start position:0% +we have some N.P type momentum for the +soft Wilson line and an N. as field and + + align:start position:0% +soft Wilson line and an N. as field and + + + align:start position:0% +soft Wilson line and an N. as field and +really it's this one over this icon + + align:start position:0% +really it's this one over this icon + + + align:start position:0% +really it's this one over this icon +denominator that's giving rise to these + + align:start position:0% +denominator that's giving rise to these + + + align:start position:0% +denominator that's giving rise to these +denominators here that are giving rise + + align:start position:0% +denominators here that are giving rise + + + align:start position:0% +denominators here that are giving rise +to the singularity. So if we want to + + align:start position:0% +to the singularity. So if we want to + + + align:start position:0% +to the singularity. So if we want to +regulate that singularity we need to add + + align:start position:0% +regulate that singularity we need to add + + + align:start position:0% +regulate that singularity we need to add +something and we could do that as + + align:start position:0% +something and we could do that as + + + align:start position:0% +something and we could do that as +follows. So this is the regulator we'll + + align:start position:0% +follows. So this is the regulator we'll + + + align:start position:0% +follows. So this is the regulator we'll +pick + + align:start position:0% + + + + align:start position:0% + +and I'll just write everything as kind + + align:start position:0% +and I'll just write everything as kind + + + align:start position:0% +and I'll just write everything as kind +of a + + align:start position:0% +of a + + + align:start position:0% +of a +a momentum operator. + + align:start position:0% + + + + align:start position:0% + +So I've just plucked the Z momentum in + + align:start position:0% +So I've just plucked the Z momentum in + + + align:start position:0% +So I've just plucked the Z momentum in +and raised it to some power. + + align:start position:0% +and raised it to some power. + + + align:start position:0% +and raised it to some power. +So PZ is the difference between P minus + + align:start position:0% +So PZ is the difference between P minus + + + align:start position:0% +So PZ is the difference between P minus +and P+. + + align:start position:0% +and P+. + + + align:start position:0% +and P+. +And that seems kind of arbitrary, but + + align:start position:0% +And that seems kind of arbitrary, but + + + align:start position:0% +And that seems kind of arbitrary, but +that'll do the job for us. You can + + align:start position:0% +that'll do the job for us. You can + + + align:start position:0% +that'll do the job for us. You can +motivate why you want to do PZ. So this + + align:start position:0% +motivate why you want to do PZ. So this + + + align:start position:0% +motivate why you want to do PZ. So this +is 2PZ. Actually, you can motivate why + + align:start position:0% +is 2PZ. Actually, you can motivate why + + + align:start position:0% +is 2PZ. Actually, you can motivate why +you want to do PZ rather than something + + align:start position:0% +you want to do PZ rather than something + + + align:start position:0% +you want to do PZ rather than something +else in the following way. And it, you + + align:start position:0% +else in the following way. And it, you + + + align:start position:0% +else in the following way. And it, you +know, it's a true fact that once you + + align:start position:0% +know, it's a true fact that once you + + + align:start position:0% +know, it's a true fact that once you +have enough experience, you you realize + + align:start position:0% +have enough experience, you you realize + + + align:start position:0% +have enough experience, you you realize +it's good to use PZ because PZ doesn't + + align:start position:0% +it's good to use PZ because PZ doesn't + + + align:start position:0% +it's good to use PZ because PZ doesn't +involve P 0. And the softs don't really + + align:start position:0% +involve P 0. And the softs don't really + + + align:start position:0% +involve P 0. And the softs don't really +make a distinction between any of the + + align:start position:0% +make a distinction between any of the + + + align:start position:0% +make a distinction between any of the +different components. And if you put in + + align:start position:0% +different components. And if you put in + + + align:start position:0% +different components. And if you put in +P 0, something that involves P 0, that + + align:start position:0% +P 0, something that involves P 0, that + + + align:start position:0% +P 0, something that involves P 0, that +would be dangerous. + + align:start position:0% +would be dangerous. + + + align:start position:0% +would be dangerous. +Uh, + + align:start position:0% +Uh, + + + align:start position:0% +Uh, +so this is nice + + align:start position:0% + + + + align:start position:0% + +because there's no P 0. So it's the + + align:start position:0% +because there's no P 0. So it's the + + + align:start position:0% +because there's no P 0. So it's the +combination of + + align:start position:0% +combination of + + + align:start position:0% +combination of +P plus and P minus that you can form + + align:start position:0% +P plus and P minus that you can form + + + align:start position:0% +P plus and P minus that you can form +that doesn't have the P 0, which is + + align:start position:0% +that doesn't have the P 0, which is + + + align:start position:0% +that doesn't have the P 0, which is +energy. And remember that the poles in P + + align:start position:0% +energy. And remember that the poles in P + + + align:start position:0% +energy. And remember that the poles in P +0 are related to things like quarks and + + align:start position:0% +0 are related to things like quarks and + + + align:start position:0% +0 are related to things like quarks and +anti-quarks. they're related to + + align:start position:0% +anti-quarks. they're related to + + + align:start position:0% +anti-quarks. they're related to +unitarity. So not messing up the + + align:start position:0% +unitarity. So not messing up the + + + align:start position:0% +unitarity. So not messing up the +structure in P 0 means that you'll be + + align:start position:0% +structure in P 0 means that you'll be + + + align:start position:0% +structure in P 0 means that you'll be +fine with unitarity, fine with + + align:start position:0% +fine with unitarity, fine with + + + align:start position:0% +fine with unitarity, fine with +causality, you're not messing up a lot + + align:start position:0% +causality, you're not messing up a lot + + + align:start position:0% +causality, you're not messing up a lot +of nice things about the theory. + + align:start position:0% +of nice things about the theory. + + + align:start position:0% +of nice things about the theory. +So + + align:start position:0% + + + + align:start position:0% + +if you do put P 0 in, then you have to + + align:start position:0% +if you do put P 0 in, then you have to + + + align:start position:0% +if you do put P 0 in, then you have to +be careful about those things. + + align:start position:0% + + + + align:start position:0% + +So if you just arbitrarily put in some + + align:start position:0% +So if you just arbitrarily put in some + + + align:start position:0% +So if you just arbitrarily put in some +power of P 0, then you'd have more + + align:start position:0% +power of P 0, then you'd have more + + + align:start position:0% +power of P 0, then you'd have more +trouble. And so that's kind of why we're + + align:start position:0% +trouble. And so that's kind of why we're + + + align:start position:0% +trouble. And so that's kind of why we're +avoiding it and just putting in PZ. + + align:start position:0% + + + + align:start position:0% + +For the Clineers, we can do something + + align:start position:0% +For the Clineers, we can do something + + + align:start position:0% +For the Clineers, we can do something +similar. But for the linears, we also + + align:start position:0% +similar. But for the linears, we also + + + align:start position:0% +similar. But for the linears, we also +have a power counting between the minus + + align:start position:0% +have a power counting between the minus + + + align:start position:0% +have a power counting between the minus +and the plus. So for the linear, + + align:start position:0% + + + + align:start position:0% + +we can still make the power counting. + + align:start position:0% +we can still make the power counting. + + + align:start position:0% +we can still make the power counting. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +by thinking about putting in PZ but then + + align:start position:0% +by thinking about putting in PZ but then + + + align:start position:0% +by thinking about putting in PZ but then +just expanding it + + align:start position:0% + + + + align:start position:0% + +to be a P minus. And that's true up to + + align:start position:0% +to be a P minus. And that's true up to + + + align:start position:0% +to be a P minus. And that's true up to +power corrections. And we don't really + + align:start position:0% +power corrections. And we don't really + + + align:start position:0% +power corrections. And we don't really +need to worry about power corrections + + align:start position:0% +need to worry about power corrections + + + align:start position:0% +need to worry about power corrections +when we're regulating these divergences. + + align:start position:0% + + + + align:start position:0% + +So it's just putting in the large + + align:start position:0% +So it's just putting in the large + + + align:start position:0% +So it's just putting in the large +momentum. And so W written in a similar + + align:start position:0% +momentum. And so W written in a similar + + + align:start position:0% +momentum. And so W written in a similar +notation. + + align:start position:0% + + + + align:start position:0% + +So I'll explain what the other things in + + align:start position:0% +So I'll explain what the other things in + + + align:start position:0% +So I'll explain what the other things in +this formula are in a minute. + + align:start position:0% +this formula are in a minute. + + + align:start position:0% +this formula are in a minute. +But the important thing for regulating + + align:start position:0% +But the important thing for regulating + + + align:start position:0% +But the important thing for regulating +is that we have some factor. In this + + align:start position:0% +is that we have some factor. In this + + + align:start position:0% +is that we have some factor. In this +this case it would be a factor of n + + align:start position:0% +this case it would be a factor of n + + + align:start position:0% +this case it would be a factor of n +bar.par. + + align:start position:0% + + + + align:start position:0% + +Sorry, + + align:start position:0% +Sorry, + + + align:start position:0% +Sorry, +not a bar. + + align:start position:0% +not a bar. + + + align:start position:0% +not a bar. +No, it's supposed to be an N. Looks like + + align:start position:0% +No, it's supposed to be an N. Looks like + + + align:start position:0% +No, it's supposed to be an N. Looks like +an ADA. + + align:start position:0% +an ADA. + + + align:start position:0% +an ADA. +Too many variables. There's the ADA. + + align:start position:0% + + + + align:start position:0% + +So there's some factor raising of the + + align:start position:0% +So there's some factor raising of the + + + align:start position:0% +So there's some factor raising of the +again the econal propagator sort of m + + align:start position:0% +again the econal propagator sort of m + + + align:start position:0% +again the econal propagator sort of m +mixing up with the iconal propagator. In + + align:start position:0% +mixing up with the iconal propagator. In + + + align:start position:0% +mixing up with the iconal propagator. In +this case, it's even more obvious that + + align:start position:0% +this case, it's even more obvious that + + + align:start position:0% +this case, it's even more obvious that +it's just regulating that iconal + + align:start position:0% +it's just regulating that iconal + + + align:start position:0% +it's just regulating that iconal +propagator. + + align:start position:0% +propagator. + + + align:start position:0% +propagator. +Okay. So if we were to do that and go + + align:start position:0% +Okay. So if we were to do that and go + + + align:start position:0% +Okay. So if we were to do that and go +back over here and put the regulators + + align:start position:0% +back over here and put the regulators + + + align:start position:0% +back over here and put the regulators +into these integrals, what would happen? + + align:start position:0% +into these integrals, what would happen? + + + align:start position:0% +into these integrals, what would happen? +So here + + align:start position:0% + + + + align:start position:0% + +we get an extra factor + + align:start position:0% +we get an extra factor + + + align:start position:0% +we get an extra factor +K minus to the ADA. And so that would + + align:start position:0% +K minus to the ADA. And so that would + + + align:start position:0% +K minus to the ADA. And so that would +regulate this K minus. And this these + + align:start position:0% +regulate this K minus. And this these + + + align:start position:0% +regulate this K minus. And this these +integrals will also have poles and from + + align:start position:0% +integrals will also have poles and from + + + align:start position:0% +integrals will also have poles and from +the one over K minus. You could think + + align:start position:0% +the one over K minus. You could think + + + align:start position:0% +the one over K minus. You could think +about okay if we did those integrals + + align:start position:0% +about okay if we did those integrals + + + align:start position:0% +about okay if we did those integrals +we'd also have repeated divergences + + align:start position:0% +we'd also have repeated divergences + + + align:start position:0% +we'd also have repeated divergences +that are kind of the analog ones and the + + align:start position:0% +that are kind of the analog ones and the + + + align:start position:0% +that are kind of the analog ones and the +linear sectors to the soft ones. + + align:start position:0% + + + + align:start position:0% + +Here we have two propagators and so if I + + align:start position:0% +Here we have two propagators and so if I + + + align:start position:0% +Here we have two propagators and so if I +I have two soft Wilson lines and so I + + align:start position:0% +I have two soft Wilson lines and so I + + + align:start position:0% +I have two soft Wilson lines and so I +get two factors but I've conveniently + + align:start position:0% +get two factors but I've conveniently + + + align:start position:0% +get two factors but I've conveniently +chose it to be the square root so it + + align:start position:0% +chose it to be the square root so it + + + align:start position:0% +chose it to be the square root so it +comes out kind of looking the same here. + + align:start position:0% + + + + align:start position:0% + +So one thing that you know is just a + + align:start position:0% +So one thing that you know is just a + + + align:start position:0% +So one thing that you know is just a +part of this regulator which actually I + + align:start position:0% +part of this regulator which actually I + + + align:start position:0% +part of this regulator which actually I +don't know a good argument for is kind + + align:start position:0% +don't know a good argument for is kind + + + align:start position:0% +don't know a good argument for is kind +of a priority from the symmetries of the + + align:start position:0% +of a priority from the symmetries of the + + + align:start position:0% +of a priority from the symmetries of the +theory. You might like to argue that + + align:start position:0% +theory. You might like to argue that + + + align:start position:0% +theory. You might like to argue that +that should be ADA over two + + align:start position:0% + + + + align:start position:0% + +and this should be ADA. + + align:start position:0% +and this should be ADA. + + + align:start position:0% +and this should be ADA. +But it's really just part of it's just a + + align:start position:0% +But it's really just part of it's just a + + + align:start position:0% +But it's really just part of it's just a +choice convention that we've made as far + + align:start position:0% +choice convention that we've made as far + + + align:start position:0% +choice convention that we've made as far +as I know. + + align:start position:0% +as I know. + + + align:start position:0% +as I know. +There probably is some nice deep + + align:start position:0% +There probably is some nice deep + + + align:start position:0% +There probably is some nice deep +argument for it but I don't know it. So + + align:start position:0% +argument for it but I don't know it. So + + + align:start position:0% +argument for it but I don't know it. So +what are these other factors? So new is + + align:start position:0% +what are these other factors? So new is + + + align:start position:0% +what are these other factors? So new is +like going to play the role of like mu, + + align:start position:0% +like going to play the role of like mu, + + + align:start position:0% +like going to play the role of like mu, +right? We've changed the dimension of + + align:start position:0% +right? We've changed the dimension of + + + align:start position:0% +right? We've changed the dimension of +the operator. We compensate it back with + + align:start position:0% +the operator. We compensate it back with + + + align:start position:0% +the operator. We compensate it back with +new just like we were doing with mu. + + align:start position:0% +new just like we were doing with mu. + + + align:start position:0% +new just like we were doing with mu. +We're going to get one over a + + align:start position:0% +We're going to get one over a + + + align:start position:0% +We're going to get one over a +divergences + + align:start position:0% +divergences + + + align:start position:0% +divergences +which are like our one over epsilon + + align:start position:0% +which are like our one over epsilon + + + align:start position:0% +which are like our one over epsilon +divergences. And we're going to get logs + + align:start position:0% +divergences. And we're going to get logs + + + align:start position:0% +divergences. And we're going to get logs +of mu which are the analoges of logs of + + align:start position:0% +of mu which are the analoges of logs of + + + align:start position:0% +of mu which are the analoges of logs of +mu. And that's the sense in which + + align:start position:0% +mu. And that's the sense in which + + + align:start position:0% +mu. And that's the sense in which +there's kind of an analog of this setup + + align:start position:0% +there's kind of an analog of this setup + + + align:start position:0% +there's kind of an analog of this setup +with our usual dimreg setup. In order to + + align:start position:0% +with our usual dimreg setup. In order to + + + align:start position:0% +with our usual dimreg setup. In order to +have a full analog, we should think + + align:start position:0% +have a full analog, we should think + + + align:start position:0% +have a full analog, we should think +about having a coupling. + + align:start position:0% +about having a coupling. + + + align:start position:0% +about having a coupling. +And so that's what this w factor is. + + align:start position:0% +And so that's what this w factor is. + + + align:start position:0% +And so that's what this w factor is. +You can think about it like there was + + align:start position:0% +You can think about it like there was + + + align:start position:0% +You can think about it like there was +some bare pseudo coupling which is + + align:start position:0% +some bare pseudo coupling which is + + + align:start position:0% +some bare pseudo coupling which is +really just one. that just imagine that + + align:start position:0% +really just one. that just imagine that + + + align:start position:0% +really just one. that just imagine that +you're switching from bear to + + align:start position:0% +you're switching from bear to + + + align:start position:0% +you're switching from bear to +renormalized in order to set up a + + align:start position:0% +renormalized in order to set up a + + + align:start position:0% +renormalized in order to set up a +renormalization group equation. And then + + align:start position:0% +renormalization group equation. And then + + + align:start position:0% +renormalization group equation. And then +this guy here which is in ADA dimensions + + align:start position:0% +this guy here which is in ADA dimensions + + + align:start position:0% +this guy here which is in ADA dimensions +if you'd like um would have a + + align:start position:0% +if you'd like um would have a + + + align:start position:0% +if you'd like um would have a +normalization group which would say new + + align:start position:0% +normalization group which would say new + + + align:start position:0% +normalization group which would say new +d by d new + + align:start position:0% +d by d new + + + align:start position:0% +d by d new +of this wet + + align:start position:0% +of this wet + + + align:start position:0% +of this wet +new + + align:start position:0% +new + + + align:start position:0% +new +is minus a / 2. Sorry, this is + + align:start position:0% +is minus a / 2. Sorry, this is + + + align:start position:0% +is minus a / 2. Sorry, this is +8 / two. + + align:start position:0% + + + + align:start position:0% + +So that's the analog of saying mu by d + + align:start position:0% +So that's the analog of saying mu by d + + + align:start position:0% +So that's the analog of saying mu by d +mu of alpha is minus 2 epsilon alpha. + + align:start position:0% +mu of alpha is minus 2 epsilon alpha. + + + align:start position:0% +mu of alpha is minus 2 epsilon alpha. +It's the analog analog statement. + + align:start position:0% + + + + align:start position:0% + +I think this is okay. So this guy here + + align:start position:0% +I think this is okay. So this guy here + + + align:start position:0% +I think this is okay. So this guy here +is like a dummy coupling and the + + align:start position:0% +is like a dummy coupling and the + + + align:start position:0% +is like a dummy coupling and the +boundary condition for it after you've + + align:start position:0% +boundary condition for it after you've + + + align:start position:0% +boundary condition for it after you've +carried out these this this is just to + + align:start position:0% +carried out these this this is just to + + + align:start position:0% +carried out these this this is just to +set it back to one. So it's identically + + align:start position:0% +set it back to one. So it's identically + + + align:start position:0% +set it back to one. So it's identically +one. It's really just a bookkeeping + + align:start position:0% +one. It's really just a bookkeeping + + + align:start position:0% +one. It's really just a bookkeeping +device. + + align:start position:0% + + + + align:start position:0% + +They're just + + align:start position:0% + + + + align:start position:0% + +it's a dummy coupling once you go to the + + align:start position:0% + + + + align:start position:0% + +ADA dimensions, but you just set it + + align:start position:0% +ADA dimensions, but you just set it + + + align:start position:0% +ADA dimensions, but you just set it +always the reormalized coupling is just + + align:start position:0% +always the reormalized coupling is just + + + align:start position:0% +always the reormalized coupling is just +identically set to one. And identically + + align:start position:0% +identically set to one. And identically + + + align:start position:0% +identically set to one. And identically +setting it to one is what you need to + + align:start position:0% +setting it to one is what you need to + + + align:start position:0% +setting it to one is what you need to +sort of keep gauge and variance in the + + align:start position:0% +sort of keep gauge and variance in the + + + align:start position:0% +sort of keep gauge and variance in the +in these Wilson lines. It turns out + + align:start position:0% +in these Wilson lines. It turns out + + + align:start position:0% +in these Wilson lines. It turns out +actually that this regulator here is + + align:start position:0% +actually that this regulator here is + + + align:start position:0% +actually that this regulator here is +gauge invariant, though it doesn't + + align:start position:0% +gauge invariant, though it doesn't + + + align:start position:0% +gauge invariant, though it doesn't +doesn't look like it, right? we've + + align:start position:0% +doesn't look like it, right? we've + + + align:start position:0% +doesn't look like it, right? we've +modified the structure of the Wilson + + align:start position:0% +modified the structure of the Wilson + + + align:start position:0% +modified the structure of the Wilson +line in some kind of way that looks like + + align:start position:0% +line in some kind of way that looks like + + + align:start position:0% +line in some kind of way that looks like +it might be uh that it might be drastic + + align:start position:0% +it might be uh that it might be drastic + + + align:start position:0% +it might be uh that it might be drastic +but actually these factors here are + + align:start position:0% +but actually these factors here are + + + align:start position:0% +but actually these factors here are +gauging still leave a gauge invariant + + align:start position:0% +gauging still leave a gauge invariant + + + align:start position:0% +gauging still leave a gauge invariant +objects so + + align:start position:0% +objects so + + + align:start position:0% +objects so +um + + align:start position:0% +um + + + align:start position:0% +um +position space + + align:start position:0% +position space + + + align:start position:0% +position space +not that I know of + + align:start position:0% + + + + align:start position:0% + +maybe you can yeah but it's not since + + align:start position:0% +maybe you can yeah but it's not since + + + align:start position:0% +maybe you can yeah but it's not since +it's not yeah I don't know how to I + + align:start position:0% +it's not yeah I don't know how to I + + + align:start position:0% +it's not yeah I don't know how to I +don't know what it would look like you + + align:start position:0% +don't know what it would look like you + + + align:start position:0% +don't know what it would look like you +could for transport explain that prop + + align:start position:0% +could for transport explain that prop + + + align:start position:0% +could for transport explain that prop +that power and it + + align:start position:0% +that power and it + + + align:start position:0% +that power and it +was + + align:start position:0% +was + + + align:start position:0% +was +Yeah. + + align:start position:0% + + + + align:start position:0% + +Yeah. I'm sure you could probably just + + align:start position:0% +Yeah. I'm sure you could probably just + + + align:start position:0% +Yeah. I'm sure you could probably just +transform that. I'm just not sure if it + + align:start position:0% +transform that. I'm just not sure if it + + + align:start position:0% +transform that. I'm just not sure if it +would look nice. Yeah. Might not look + + align:start position:0% +would look nice. Yeah. Might not look + + + align:start position:0% +would look nice. Yeah. Might not look +too bad. + + align:start position:0% +too bad. + + + align:start position:0% +too bad. +And it might actually be a nice way of + + align:start position:0% +And it might actually be a nice way of + + + align:start position:0% +And it might actually be a nice way of +saying what I'm about to say in a less + + align:start position:0% +saying what I'm about to say in a less + + + align:start position:0% +saying what I'm about to say in a less +nice way which is if you look at the + + align:start position:0% +nice way which is if you look at the + + + align:start position:0% +nice way which is if you look at the +gauge symmetry why is it why is this not + + align:start position:0% +gauge symmetry why is it why is this not + + + align:start position:0% +gauge symmetry why is it why is this not +messing it up? So one way of thinking + + align:start position:0% +messing it up? So one way of thinking + + + align:start position:0% +messing it up? So one way of thinking +about that is just look at general + + align:start position:0% +about that is just look at general + + + align:start position:0% +about that is just look at general +coariant gauge. + + align:start position:0% +coariant gauge. + + + align:start position:0% +coariant gauge. +So, + + align:start position:0% +So, + + + align:start position:0% +So, +so note + + align:start position:0% + + + + align:start position:0% + +the one over eight and a zero terms are + + align:start position:0% +the one over eight and a zero terms are + + + align:start position:0% +the one over eight and a zero terms are +gauge invariant + + align:start position:0% + + + + align:start position:0% + +and you can think about that by just + + align:start position:0% +and you can think about that by just + + + align:start position:0% +and you can think about that by just +going to a general coariant gauge and + + align:start position:0% +going to a general coariant gauge and + + + align:start position:0% +going to a general coariant gauge and +seeing the parameter dependence drop + + align:start position:0% +seeing the parameter dependence drop + + + align:start position:0% +seeing the parameter dependence drop +out. + + align:start position:0% +out. + + + align:start position:0% +out. +So for example + + align:start position:0% +So for example + + + align:start position:0% +So for example +at one loop you would take gu in the + + align:start position:0% +at one loop you would take gu in the + + + align:start position:0% +at one loop you would take gu in the +contractions and replace it in general + + align:start position:0% +contractions and replace it in general + + + align:start position:0% +contractions and replace it in general +coariant gauge by some gauge parameter + + align:start position:0% + + + + align:start position:0% + +general coariant gauge + + align:start position:0% +general coariant gauge + + + align:start position:0% +general coariant gauge +ku k new over k^ 2 and you'd like to see + + align:start position:0% +ku k new over k^ 2 and you'd like to see + + + align:start position:0% +ku k new over k^ 2 and you'd like to see +it independent of this but this this aa + + align:start position:0% +it independent of this but this this aa + + + align:start position:0% +it independent of this but this this aa +to the zero piece is kind of independent + + align:start position:0% +to the zero piece is kind of independent + + + align:start position:0% +to the zero piece is kind of independent +of that for the usual reasons and the + + align:start position:0% +of that for the usual reasons and the + + + align:start position:0% +of that for the usual reasons and the +one over a dep term is independent of + + align:start position:0% +one over a dep term is independent of + + + align:start position:0% +one over a dep term is independent of +that because this guy actually doesn't + + align:start position:0% +that because this guy actually doesn't + + + align:start position:0% +that because this guy actually doesn't +induce any rapidity singularities. What + + align:start position:0% +induce any rapidity singularities. What + + + align:start position:0% +induce any rapidity singularities. What +happens is that if you have an N.K, then + + align:start position:0% +happens is that if you have an N.K, then + + + align:start position:0% +happens is that if you have an N.K, then +you have a corresponding n mu in the + + align:start position:0% +you have a corresponding n mu in the + + + align:start position:0% +you have a corresponding n mu in the +numerator. And so basically what happens + + align:start position:0% +numerator. And so basically what happens + + + align:start position:0% +numerator. And so basically what happens +is you get an extra n.k in the + + align:start position:0% +is you get an extra n.k in the + + + align:start position:0% +is you get an extra n.k in the +numerator. + + align:start position:0% +numerator. + + + align:start position:0% +numerator. +So anytime you have a 1 over nk, + + align:start position:0% +So anytime you have a 1 over nk, + + + align:start position:0% +So anytime you have a 1 over nk, +you would get for this piece multiplied + + align:start position:0% +you would get for this piece multiplied + + + align:start position:0% +you would get for this piece multiplied +by an n.k upstairs. + + align:start position:0% +by an n.k upstairs. + + + align:start position:0% +by an n.k upstairs. +And so this is cancelling and you you + + align:start position:0% +And so this is cancelling and you you + + + align:start position:0% +And so this is cancelling and you you +don't have a rapidity divergence in this + + align:start position:0% +don't have a rapidity divergence in this + + + align:start position:0% +don't have a rapidity divergence in this +in the C dependent part. So that's why + + align:start position:0% +in the C dependent part. So that's why + + + align:start position:0% +in the C dependent part. So that's why +this is + + align:start position:0% +this is + + + align:start position:0% +this is +invariant under the gauge symmetry. And + + align:start position:0% +invariant under the gauge symmetry. And + + + align:start position:0% +invariant under the gauge symmetry. And +then because of this boundary condition + + align:start position:0% +then because of this boundary condition + + + align:start position:0% +then because of this boundary condition +the kind of cancellation of the C + + align:start position:0% +the kind of cancellation of the C + + + align:start position:0% +the kind of cancellation of the C +dependence in the order A to the zero + + align:start position:0% +dependence in the order A to the zero + + + align:start position:0% +dependence in the order A to the zero +pieces kind of works out in the standard + + align:start position:0% +pieces kind of works out in the standard + + + align:start position:0% +pieces kind of works out in the standard +way. + + align:start position:0% +way. + + + align:start position:0% +way. +Okay. So it gives you an idea of why + + align:start position:0% +Okay. So it gives you an idea of why + + + align:start position:0% +Okay. So it gives you an idea of why +it's gauge invariant without giving you + + align:start position:0% +it's gauge invariant without giving you + + + align:start position:0% +it's gauge invariant without giving you +a kind of full proof or anything. + + align:start position:0% + + + + align:start position:0% + +So we have both one over epsilon poles + + align:start position:0% +So we have both one over epsilon poles + + + align:start position:0% +So we have both one over epsilon poles +and one of our ada poles in general and + + align:start position:0% +and one of our ada poles in general and + + + align:start position:0% +and one of our ada poles in general and +we have to understand what to do with + + align:start position:0% +we have to understand what to do with + + + align:start position:0% +we have to understand what to do with +them. So here's what we're going to do. + + align:start position:0% +them. So here's what we're going to do. + + + align:start position:0% +them. So here's what we're going to do. +For any fixed invariant mass + + align:start position:0% +For any fixed invariant mass + + + align:start position:0% +For any fixed invariant mass +it turns out that we can have these one + + align:start position:0% +it turns out that we can have these one + + + align:start position:0% +it turns out that we can have these one +over eight poles. + + align:start position:0% + + + + align:start position:0% + +And the right procedure for dealing with + + align:start position:0% +And the right procedure for dealing with + + + align:start position:0% +And the right procedure for dealing with +them is as follows. First you take ada + + align:start position:0% +them is as follows. First you take ada + + + align:start position:0% +them is as follows. First you take ada +goes to zero and deal with these new + + align:start position:0% +goes to zero and deal with these new + + + align:start position:0% +goes to zero and deal with these new +poles that you have introduced in your + + align:start position:0% +poles that you have introduced in your + + + align:start position:0% +poles that you have introduced in your +amplitude. + + align:start position:0% +amplitude. + + + align:start position:0% +amplitude. +In order to deal with them because you + + align:start position:0% +In order to deal with them because you + + + align:start position:0% +In order to deal with them because you +can have them for any invariant mass you + + align:start position:0% +can have them for any invariant mass you + + + align:start position:0% +can have them for any invariant mass you +actually have to add counter terms that + + align:start position:0% +actually have to add counter terms that + + + align:start position:0% +actually have to add counter terms that +can be a whole function of epsilon where + + align:start position:0% +can be a whole function of epsilon where + + + align:start position:0% +can be a whole function of epsilon where +you haven't expanded in epsilon and then + + align:start position:0% +you haven't expanded in epsilon and then + + + align:start position:0% +you haven't expanded in epsilon and then +divided by ada. + + align:start position:0% + + + + align:start position:0% + +So let me abbreviate counter term as ct + + align:start position:0% +So let me abbreviate counter term as ct + + + align:start position:0% +So let me abbreviate counter term as ct +dot. + + align:start position:0% +dot. + + + align:start position:0% +dot. +Then after you've done that, you take + + align:start position:0% +Then after you've done that, you take + + + align:start position:0% +Then after you've done that, you take +epsilon goes to zero and you find your + + align:start position:0% +epsilon goes to zero and you find your + + + align:start position:0% +epsilon goes to zero and you find your +one over epsilon counter terms. + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +Okay. And this is the correct way of + + align:start position:0% +Okay. And this is the correct way of + + + align:start position:0% +Okay. And this is the correct way of +doing it. + + align:start position:0% +doing it. + + + align:start position:0% +doing it. +And we'll see how that works in practice + + align:start position:0% +And we'll see how that works in practice + + + align:start position:0% +And we'll see how that works in practice +in a minute. So let's go back to our + + align:start position:0% +in a minute. So let's go back to our + + + align:start position:0% +in a minute. So let's go back to our +integrals that I've now erased and just + + align:start position:0% +integrals that I've now erased and just + + + align:start position:0% +integrals that I've now erased and just +write out the answers for doing those + + align:start position:0% +write out the answers for doing those + + + align:start position:0% +write out the answers for doing those +integrals with this regulator. + + align:start position:0% +integrals with this regulator. + + + align:start position:0% +integrals with this regulator. +And I'll also make them firmian. So I'm + + align:start position:0% +And I'll also make them firmian. So I'm + + + align:start position:0% +And I'll also make them firmian. So I'm +putting in the numerators. + + align:start position:0% +putting in the numerators. + + + align:start position:0% +putting in the numerators. +We wrote them down for scalers. The + + align:start position:0% +We wrote them down for scalers. The + + + align:start position:0% +We wrote them down for scalers. The +scalers were the most divergent + + align:start position:0% +scalers were the most divergent + + + align:start position:0% +scalers were the most divergent +integrals. Actually, I can include the + + align:start position:0% +integrals. Actually, I can include the + + + align:start position:0% +integrals. Actually, I can include the +numerators. That doesn't really change + + align:start position:0% +numerators. That doesn't really change + + + align:start position:0% +numerators. That doesn't really change +the story. + + align:start position:0% +the story. + + + align:start position:0% +the story. +And I can include the prefactors as + + align:start position:0% +And I can include the prefactors as + + + align:start position:0% +And I can include the prefactors as +well. + + align:start position:0% + + + + align:start position:0% + +And I'll kind of write things in a QCD + + align:start position:0% +And I'll kind of write things in a QCD + + + align:start position:0% +And I'll kind of write things in a QCD +type notation. Even we can imagine that + + align:start position:0% +type notation. Even we can imagine that + + + align:start position:0% +type notation. Even we can imagine that +it's a nonabelian group just so CF is + + align:start position:0% +it's a nonabelian group just so CF is + + + align:start position:0% +it's a nonabelian group just so CF is +the whatever group it is it's the casmir + + align:start position:0% +the whatever group it is it's the casmir + + + align:start position:0% +the whatever group it is it's the casmir +the fundamental + + align:start position:0% + + + + align:start position:0% + +whatever group our gauge bzon's in. + + align:start position:0% +whatever group our gauge bzon's in. + + + align:start position:0% +whatever group our gauge bzon's in. +So here's the ADA pole uh it has a whole + + align:start position:0% +So here's the ADA pole uh it has a whole + + + align:start position:0% +So here's the ADA pole uh it has a whole +function of epsilon in in the numerator + + align:start position:0% +function of epsilon in in the numerator + + + align:start position:0% +function of epsilon in in the numerator +and it's even divergent. + + align:start position:0% +and it's even divergent. + + + align:start position:0% +and it's even divergent. +So this is 2 ADA + + align:start position:0% +So this is 2 ADA + + + align:start position:0% +So this is 2 ADA +and then the rest of it I can expand. + + align:start position:0% + + + + align:start position:0% + +So there's going to be a 1 / epsilon + + align:start position:0% +So there's going to be a 1 / epsilon + + + align:start position:0% +So there's going to be a 1 / epsilon +times the log. When the log replaces + + align:start position:0% +times the log. When the log replaces + + + align:start position:0% +times the log. When the log replaces +that one over epsilon, then I can start + + align:start position:0% +that one over epsilon, then I can start + + + align:start position:0% +that one over epsilon, then I can start +to expand and I get another one over + + align:start position:0% +to expand and I get another one over + + + align:start position:0% +to expand and I get another one over +when the log when the log new replaces + + align:start position:0% +when the log when the log new replaces + + + align:start position:0% +when the log when the log new replaces +the one over ada. I can expand this + + align:start position:0% +the one over ada. I can expand this + + + align:start position:0% +the one over ada. I can expand this +gamma. That gives me one over epsilon. + + align:start position:0% +gamma. That gives me one over epsilon. + + + align:start position:0% +gamma. That gives me one over epsilon. +And there's also some other pieces. + + align:start position:0% +And there's also some other pieces. + + + align:start position:0% +And there's also some other pieces. +One over two epsilon. There's a log + + align:start position:0% +One over two epsilon. There's a log + + + align:start position:0% +One over two epsilon. There's a log +over. + + align:start position:0% +over. + + + align:start position:0% +over. +There's a constant. And I'm never going + + align:start position:0% +There's a constant. And I'm never going + + + align:start position:0% +There's a constant. And I'm never going +to write the constants. + + align:start position:0% + + + + align:start position:0% + +So let me write all the results and then + + align:start position:0% +So let me write all the results and then + + + align:start position:0% +So let me write all the results and then +we'll talk about them. So IC and bar is + + align:start position:0% +we'll talk about them. So IC and bar is + + + align:start position:0% +we'll talk about them. So IC and bar is +the same. The only difference between + + align:start position:0% +the same. The only difference between + + + align:start position:0% +the same. The only difference between +this is that P minus goes to P bar plus. + + align:start position:0% +this is that P minus goes to P bar plus. + + + align:start position:0% +this is that P minus goes to P bar plus. +was really symmetric + + align:start position:0% +was really symmetric + + + align:start position:0% +was really symmetric +and then is + + align:start position:0% +and then is + + + align:start position:0% +and then is +different. + + align:start position:0% + + + + align:start position:0% + +So the one over epsilon one over a pole + + align:start position:0% +So the one over epsilon one over a pole + + + align:start position:0% +So the one over epsilon one over a pole +comes with the opposite sign and it also + + align:start position:0% +comes with the opposite sign and it also + + + align:start position:0% +comes with the opposite sign and it also +comes with a factor of two different + + align:start position:0% + + + + align:start position:0% + +and in this case there's actually one + + align:start position:0% +and in this case there's actually one + + + align:start position:0% +and in this case there's actually one +over two epsilon squar term. + + align:start position:0% + + + + align:start position:0% + +So there's also a double log + + align:start position:0% +So there's also a double log + + + align:start position:0% +So there's also a double log +of mu m + + align:start position:0% +of mu m + + + align:start position:0% +of mu m +and then there's plus constant. + + align:start position:0% + + + + align:start position:0% + +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +And so you could think about adding them + + align:start position:0% +And so you could think about adding them + + + align:start position:0% +And so you could think about adding them +up. And what happens when you add them + + align:start position:0% +up. And what happens when you add them + + + align:start position:0% +up. And what happens when you add them +up is you have 1 over 2 ADA 1 over 2 ADA + + align:start position:0% +up is you have 1 over 2 ADA 1 over 2 ADA + + + align:start position:0% +up is you have 1 over 2 ADA 1 over 2 ADA +minus one over ADA. And so the 1 over + + align:start position:0% +minus one over ADA. And so the 1 over + + + align:start position:0% +minus one over ADA. And so the 1 over +ADA poles cancel. And that's exactly + + align:start position:0% +ADA poles cancel. And that's exactly + + + align:start position:0% +ADA poles cancel. And that's exactly +what you'd expect because in the full + + align:start position:0% +what you'd expect because in the full + + + align:start position:0% +what you'd expect because in the full +theory the ADA was something we + + align:start position:0% +theory the ADA was something we + + + align:start position:0% +theory the ADA was something we +introduced in order to distinguish these + + align:start position:0% +introduced in order to distinguish these + + + align:start position:0% +introduced in order to distinguish these +effective theory modes. It wasn't + + align:start position:0% +effective theory modes. It wasn't + + + align:start position:0% +effective theory modes. It wasn't +something that was there needed for the + + align:start position:0% +something that was there needed for the + + + align:start position:0% +something that was there needed for the +full theory integral. and say you don't + + align:start position:0% +full theory integral. and say you don't + + + align:start position:0% +full theory integral. and say you don't +really you'd expect that it's sort of + + align:start position:0% +really you'd expect that it's sort of + + + align:start position:0% +really you'd expect that it's sort of +that there's a corresponding + + align:start position:0% +that there's a corresponding + + + align:start position:0% +that there's a corresponding +regulator between the two sectors so + + align:start position:0% +regulator between the two sectors so + + + align:start position:0% +regulator between the two sectors so +that when you add them together that the + + align:start position:0% +that when you add them together that the + + + align:start position:0% +that when you add them together that the +dependence on that parameter is + + align:start position:0% +dependence on that parameter is + + + align:start position:0% +dependence on that parameter is +cancelceing away because it's just an + + align:start position:0% +cancelceing away because it's just an + + + align:start position:0% +cancelceing away because it's just an +artificial separation if you like or + + align:start position:0% +artificial separation if you like or + + + align:start position:0% +artificial separation if you like or +separation that we're doing. So if I add + + align:start position:0% +separation that we're doing. So if I add + + + align:start position:0% +separation that we're doing. So if I add +them up, + + align:start position:0% + + + + align:start position:0% + +one over eight is cancel and so do all + + align:start position:0% +one over eight is cancel and so do all + + + align:start position:0% +one over eight is cancel and so do all +the logs of new + + align:start position:0% +the logs of new + + + align:start position:0% +the logs of new +alpha. + + align:start position:0% + + + + align:start position:0% + +I'm left with a log of mu over q one + + align:start position:0% +I'm left with a log of mu over q one + + + align:start position:0% +I'm left with a log of mu over q one +reps pole + + align:start position:0% +reps pole + + + align:start position:0% +reps pole +double log + + align:start position:0% +double log + + + align:start position:0% +double log +some types of single logs + + align:start position:0% +some types of single logs + + + align:start position:0% +some types of single logs +there's another type of double log. + + align:start position:0% + + + + align:start position:0% + +So it would look like that all the new + + align:start position:0% +So it would look like that all the new + + + align:start position:0% +So it would look like that all the new +dependencies cancelelling away. + + align:start position:0% +dependencies cancelelling away. + + + align:start position:0% +dependencies cancelelling away. +So + + align:start position:0% +So + + + align:start position:0% +So +sort of various things + + align:start position:0% + + + + align:start position:0% + +which we'll start talking about now and + + align:start position:0% +which we'll start talking about now and + + + align:start position:0% +which we'll start talking about now and +we'll continue talking about next time. + + align:start position:0% +we'll continue talking about next time. + + + align:start position:0% +we'll continue talking about next time. +So the rapidity 1 / aa divergence + + align:start position:0% +So the rapidity 1 / aa divergence + + + align:start position:0% +So the rapidity 1 / aa divergence +which we can call a rapidity divergence + + align:start position:0% +which we can call a rapidity divergence + + + align:start position:0% +which we can call a rapidity divergence +cancels in sum + + align:start position:0% +cancels in sum + + + align:start position:0% +cancels in sum +and of course so does the log news + + align:start position:0% + + + + align:start position:0% + +and that's as expected. + + align:start position:0% + + + + align:start position:0% + +And if you add an overall counter term + + align:start position:0% +And if you add an overall counter term + + + align:start position:0% +And if you add an overall counter term +for the entire thing, it just involves + + align:start position:0% +for the entire thing, it just involves + + + align:start position:0% +for the entire thing, it just involves +the hard scale log mu over q. + + align:start position:0% + + + + align:start position:0% + +So if you were to think about there + + align:start position:0% +So if you were to think about there + + + align:start position:0% +So if you were to think about there +being some Wilson coefficient which is + + align:start position:0% +being some Wilson coefficient which is + + + align:start position:0% +being some Wilson coefficient which is +sort of c bear is zc minus one. + + align:start position:0% + + + + align:start position:0% + +C bear is ZC C were normalized. Then ZC + + align:start position:0% +C bear is ZC C were normalized. Then ZC + + + align:start position:0% +C bear is ZC C were normalized. Then ZC +and the C were normalized + + align:start position:0% +and the C were normalized + + + align:start position:0% +and the C were normalized +only involve + + align:start position:0% +only involve + + + align:start position:0% +only involve +logs of mu over Q which is the hard + + align:start position:0% +logs of mu over Q which is the hard + + + align:start position:0% +logs of mu over Q which is the hard +scale. + + align:start position:0% +scale. + + + align:start position:0% +scale. +Okay. And that means that our hard + + align:start position:0% +Okay. And that means that our hard + + + align:start position:0% +Okay. And that means that our hard +function + + align:start position:0% +function + + + align:start position:0% +function +which is the Wilson coefficient squared + + align:start position:0% +which is the Wilson coefficient squared + + + align:start position:0% +which is the Wilson coefficient squared +if you just the Wilson coefficient in + + align:start position:0% +if you just the Wilson coefficient in + + + align:start position:0% +if you just the Wilson coefficient in +this case is only a function of Q and + + align:start position:0% +this case is only a function of Q and + + + align:start position:0% +this case is only a function of Q and +mu. + + align:start position:0% +mu. + + + align:start position:0% +mu. +Okay. Okay, so integrating out the hard + + align:start position:0% +Okay. Okay, so integrating out the hard + + + align:start position:0% +Okay. Okay, so integrating out the hard +scale physics didn't know about the + + align:start position:0% +scale physics didn't know about the + + + align:start position:0% +scale physics didn't know about the +separation. The separation was really + + align:start position:0% +separation. The separation was really + + + align:start position:0% +separation. The separation was really +something that we needed to do in the + + align:start position:0% +something that we needed to do in the + + + align:start position:0% +something that we needed to do in the +effect of theory to distinguish the CN + + align:start position:0% +effect of theory to distinguish the CN + + + align:start position:0% +effect of theory to distinguish the CN +and S modes. + + align:start position:0% +and S modes. + + + align:start position:0% +and S modes. +And you can see why we needed to do it + + align:start position:0% +And you can see why we needed to do it + + + align:start position:0% +And you can see why we needed to do it +if you look at these answers + + align:start position:0% +if you look at these answers + + + align:start position:0% +if you look at these answers +because + + align:start position:0% +because + + + align:start position:0% +because +if you look at the the types of logs + + align:start position:0% +if you look at the the types of logs + + + align:start position:0% +if you look at the the types of logs +that are showing up here, in this case + + align:start position:0% +that are showing up here, in this case + + + align:start position:0% +that are showing up here, in this case +we have a new over P minus and in this + + align:start position:0% +we have a new over P minus and in this + + + align:start position:0% +we have a new over P minus and in this +case we have a is it new over mu? + + align:start position:0% + + + + align:start position:0% + +Make sure I got that right. I guess it + + align:start position:0% +Make sure I got that right. I guess it + + + align:start position:0% +Make sure I got that right. I guess it +is. In this case, we have a new over m. + + align:start position:0% +is. In this case, we have a new over m. + + + align:start position:0% +is. In this case, we have a new over m. +Okay, + + align:start position:0% +Okay, + + + align:start position:0% +Okay, +we also have a mu over new. + + align:start position:0% +we also have a mu over new. + + + align:start position:0% +we also have a mu over new. +And so the sort of right scale to in + + align:start position:0% +And so the sort of right scale to in + + + align:start position:0% +And so the sort of right scale to in +order to minimize the logarithms here, + + align:start position:0% +order to minimize the logarithms here, + + + align:start position:0% +order to minimize the logarithms here, +we're going to have to again as usual + + align:start position:0% +we're going to have to again as usual + + + align:start position:0% +we're going to have to again as usual +take different values of mu and and new. + + align:start position:0% +take different values of mu and and new. + + + align:start position:0% +take different values of mu and and new. +Well, it's the same value of mu. All of + + align:start position:0% +Well, it's the same value of mu. All of + + + align:start position:0% +Well, it's the same value of mu. All of +them are M but it's a different value of + + align:start position:0% +them are M but it's a different value of + + + align:start position:0% +them are M but it's a different value of +new because it's the new that would need + + align:start position:0% +new because it's the new that would need + + + align:start position:0% +new because it's the new that would need +to be of order Q here. P minus is Q and + + align:start position:0% +to be of order Q here. P minus is Q and + + + align:start position:0% +to be of order Q here. P minus is Q and +the new would be need to be of order M + + align:start position:0% +the new would be need to be of order M + + + align:start position:0% +the new would be need to be of order M +here. Okay. So it's the new that + + align:start position:0% +here. Okay. So it's the new that + + + align:start position:0% +here. Okay. So it's the new that +distinguishes the modes. + + align:start position:0% +distinguishes the modes. + + + align:start position:0% +distinguishes the modes. +So the logs + + align:start position:0% +So the logs + + + align:start position:0% +So the logs +in CN + + align:start position:0% +in CN + + + align:start position:0% +in CN +are minimized + + align:start position:0% + + + + align:start position:0% + +for mu of order M which says being on + + align:start position:0% +for mu of order M which says being on + + + align:start position:0% +for mu of order M which says being on +the hyperola. + + align:start position:0% +the hyperola. + + + align:start position:0% +the hyperola. +But then new should be of order p minus + + align:start position:0% +But then new should be of order p minus + + + align:start position:0% +But then new should be of order p minus +which is q + + align:start position:0% +which is q + + + align:start position:0% +which is q +and that's precisely actually where we + + align:start position:0% +and that's precisely actually where we + + + align:start position:0% +and that's precisely actually where we +put the x + + align:start position:0% +put the x + + + align:start position:0% +put the x +in our picture + + align:start position:0% +in our picture + + + align:start position:0% +in our picture +if you think about + + align:start position:0% +if you think about + + + align:start position:0% +if you think about +okay so that's saying that we have a + + align:start position:0% +okay so that's saying that we have a + + + align:start position:0% +okay so that's saying that we have a +large p minus momentum + + align:start position:0% +large p minus momentum + + + align:start position:0% +large p minus momentum +and we have and we're on this hyperola + + align:start position:0% +and we have and we're on this hyperola + + + align:start position:0% +and we have and we're on this hyperola +where p square is order m^2. + + align:start position:0% + + + + align:start position:0% + +And it's likewise for the other pieces. + + align:start position:0% +And it's likewise for the other pieces. + + + align:start position:0% +And it's likewise for the other pieces. +So for the soft piece. + + align:start position:0% +So for the soft piece. + + + align:start position:0% +So for the soft piece. +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +So for the + + align:start position:0% +So for the + + + align:start position:0% +So for the +say for the anti for the other collar + + align:start position:0% +say for the anti for the other collar + + + align:start position:0% +say for the anti for the other collar +piece + + align:start position:0% +piece + + + align:start position:0% +piece +we need the same thing. + + align:start position:0% + + + + align:start position:0% + +And then for the + + align:start position:0% + + + + align:start position:0% + +soft. We need a different value for this + + align:start position:0% +soft. We need a different value for this + + + align:start position:0% +soft. We need a different value for this +new parameter. So having this regulator + + align:start position:0% +new parameter. So having this regulator + + + align:start position:0% +new parameter. So having this regulator +is behaving like dim rag where we needed + + align:start position:0% +is behaving like dim rag where we needed + + + align:start position:0% +is behaving like dim rag where we needed +different views when we had different + + align:start position:0% +different views when we had different + + + align:start position:0% +different views when we had different +hyperolas. Now we have different places + + align:start position:0% +hyperolas. Now we have different places + + + align:start position:0% +hyperolas. Now we have different places +on the hyperola and we're tracking that + + align:start position:0% +on the hyperola and we're tracking that + + + align:start position:0% +on the hyperola and we're tracking that +with the new parameter and that's + + align:start position:0% +with the new parameter and that's + + + align:start position:0% +with the new parameter and that's +showing up in the logarithms. And if you + + align:start position:0% +showing up in the logarithms. And if you + + + align:start position:0% +showing up in the logarithms. And if you +think about what the logarithms are + + align:start position:0% +think about what the logarithms are + + + align:start position:0% +think about what the logarithms are +doing, you can see that when you combine + + align:start position:0% +doing, you can see that when you combine + + + align:start position:0% +doing, you can see that when you combine +when you combine terms, see + + align:start position:0% +when you combine terms, see + + + align:start position:0% +when you combine terms, see +if you look at the one over epsilon and + + align:start position:0% +if you look at the one over epsilon and + + + align:start position:0% +if you look at the one over epsilon and +the news are canceling out, you're + + align:start position:0% +the news are canceling out, you're + + + align:start position:0% +the news are canceling out, you're +getting a mu over q. That's not maybe + + align:start position:0% +getting a mu over q. That's not maybe + + + align:start position:0% +getting a mu over q. That's not maybe +not the best example. Look over here. + + align:start position:0% +not the best example. Look over here. + + + align:start position:0% +not the best example. Look over here. +You have this log of m over q, right? in + + align:start position:0% +You have this log of m over q, right? in + + + align:start position:0% +You have this log of m over q, right? in +this kind of complete decomposition. The + + align:start position:0% +this kind of complete decomposition. The + + + align:start position:0% +this kind of complete decomposition. The +way that that logarithm here gets made + + align:start position:0% +way that that logarithm here gets made + + + align:start position:0% +way that that logarithm here gets made +up is by having m over new and mu over + + align:start position:0% +up is by having m over new and mu over + + + align:start position:0% +up is by having m over new and mu over +q. All right. So in order to get this + + align:start position:0% +q. All right. So in order to get this + + + align:start position:0% +q. All right. So in order to get this +log that doesn't have any muses in it. + + align:start position:0% +log that doesn't have any muses in it. + + + align:start position:0% +log that doesn't have any muses in it. +Mu is not telling you that there's that + + align:start position:0% +Mu is not telling you that there's that + + + align:start position:0% +Mu is not telling you that there's that +large log, but there is a large log. So + + align:start position:0% +large log, but there is a large log. So + + + align:start position:0% +large log, but there is a large log. So +there's large logs associated to these + + align:start position:0% +there's large logs associated to these + + + align:start position:0% +there's large logs associated to these +rapidity divergences. And what we'll + + align:start position:0% +rapidity divergences. And what we'll + + + align:start position:0% +rapidity divergences. And what we'll +talk about next time is how you do the + + align:start position:0% +talk about next time is how you do the + + + align:start position:0% +talk about next time is how you do the +reormalization group with the diagrams + + align:start position:0% +reormalization group with the diagrams + + + align:start position:0% +reormalization group with the diagrams +like this. how you write down anomalous + + align:start position:0% +like this. how you write down anomalous + + + align:start position:0% +like this. how you write down anomalous +dimension equations. There'll be + + align:start position:0% +dimension equations. There'll be + + + align:start position:0% +dimension equations. There'll be +anomalous dimension equations in both mu + + align:start position:0% +anomalous dimension equations in both mu + + + align:start position:0% +anomalous dimension equations in both mu +and new space. So we'll have to move + + align:start position:0% +and new space. So we'll have to move + + + align:start position:0% +and new space. So we'll have to move +around in that space and see how it + + align:start position:0% +around in that space and see how it + + + align:start position:0% +around in that space and see how it +works to sum the large logarithms. + + align:start position:0% +works to sum the large logarithms. + + + align:start position:0% +works to sum the large logarithms. +But I'll postpone that to next time. + + align:start position:0% + + + + align:start position:0% + +So any questions? + + align:start position:0% + + + + align:start position:0% + +Okay, so the general idea is really as + + align:start position:0% +Okay, so the general idea is really as + + + align:start position:0% +Okay, so the general idea is really as +usual. It's just that now we're dealing + + align:start position:0% +usual. It's just that now we're dealing + + + align:start position:0% +usual. It's just that now we're dealing +with a situation where there's two + + align:start position:0% +with a situation where there's two + + + align:start position:0% +with a situation where there's two +regulators and they're actually + + align:start position:0% +regulators and they're actually + + + align:start position:0% +regulators and they're actually +independent regulators. One's if you + + align:start position:0% +independent regulators. One's if you + + + align:start position:0% +independent regulators. One's if you +like is regulating invariant mass and + + align:start position:0% +like is regulating invariant mass and + + + align:start position:0% +like is regulating invariant mass and +the other is regulating these extra + + align:start position:0% +the other is regulating these extra + + + align:start position:0% +the other is regulating these extra +divergences. + + align:start position:0% +divergences. + + + align:start position:0% +divergences. +And so we'll be able to move around in + + align:start position:0% +And so we'll be able to move around in + + + align:start position:0% +And so we'll be able to move around in +the space + + align:start position:0% +the space + + + align:start position:0% +the space +without any worrying about path + + align:start position:0% +without any worrying about path + + + align:start position:0% +without any worrying about path +dependence for example. + + align:start position:0% +dependence for example. + + + align:start position:0% +dependence for example. +We'll talk a little bit about that next + + align:start position:0% +We'll talk a little bit about that next + + + align:start position:0% +We'll talk a little bit about that next +time in this two-dimensional space of mu + + align:start position:0% +time in this two-dimensional space of mu + + + align:start position:0% +time in this two-dimensional space of mu +and new. But you can see just from + + align:start position:0% +and new. But you can see just from + + + align:start position:0% +and new. But you can see just from +looking at the logs as usual, you can + + align:start position:0% +looking at the logs as usual, you can + + + align:start position:0% +looking at the logs as usual, you can +see where you need to be. And you can + + align:start position:0% +see where you need to be. And you can + + + align:start position:0% +see where you need to be. And you can +see that you need to be in different + + align:start position:0% +see that you need to be in different + + + align:start position:0% +see that you need to be in different +places for the different modes in order + + align:start position:0% +places for the different modes in order + + + align:start position:0% +places for the different modes in order +to minimize the logs in these + + align:start position:0% +to minimize the logs in these + + + align:start position:0% +to minimize the logs in these +amplitudes. And if you do that, then + + align:start position:0% +amplitudes. And if you do that, then + + + align:start position:0% +amplitudes. And if you do that, then +there should be some normalization group + + align:start position:0% +there should be some normalization group + + + align:start position:0% +there should be some normalization group +that would connect + + align:start position:0% + + + + align:start position:0% + +these guys. So there should be some + + align:start position:0% +these guys. So there should be some + + + align:start position:0% +these guys. So there should be some +RG that goes between these guys and + + align:start position:0% +RG that goes between these guys and + + + align:start position:0% +RG that goes between these guys and +it'll be an RG in this new parameter. \ No newline at end of file diff --git a/zr3wuh3fWRw.txt b/zr3wuh3fWRw.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ac51397e707834c15bc23f5700f9c0654638e76 --- /dev/null +++ b/zr3wuh3fWRw.txt @@ -0,0 +1,3347 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +IAIN STEWART: --play +with each other. + +We did the standard model +as an effective field + +theory, higher +dimension operators + +in the standard model. + +And then we started talking +about taking the standard model + +as a theory one and +removing things from it, + +in particular +constructing what's + +called the weak Hamiltonian +by removing the top W, Z, + +and Higgs from the +standard model. + +And last time, we were focusing +on the anomalous dimensions + +and things about +renormalization. + +So we had this equation +for the weak Hamiltonian + +for a particular case +of b goes to c u bar d. + +That was the case +that we decided + +to study rather than +the full Hamiltonian. + +So there was some pre-factor. + +We had two operators with Wilson +coefficients and operators. + +These are four-fermion +operators. + +And there was different bases. + +We could write them +in the bare form, + +or we could write them in +renormalized coefficient + +and renormalized operator. + +And then we could do it +either in the 1, 2 basis + +or the plus minus basis. + +So the plus minus basis is +just linear combinations + +of the 1, 2. + +If you're in the 1, +2 basis, then you + +have this mixing matrix. + +So it's a 2 by 2 matrix. + +So if you're in the +plus minus basis, + +then at least, at +the lowest order, + +it's a simple product equation. + +So plus doesn't +interfere with minus. + +OK. + +So that's where we got to, +and we'll just continue today. + +So we have these anomalous +dimension equations + +for the operators. + +We can also write down +anomalous dimension equations + +for the Wilson coefficients. + +How do we do that? + +Well, the way that we do that +is we make use of the fact + +that, if we look at the first +line here, there's no mu. + +So the Hamiltonian +is mu independent. + +That means that the mu +dependence of the coefficient + +cancels the mu dependence +of the operator. + +And you can use that to +take an anomalous dimension + +equation for the +operator and turn it + +into one for the coefficient. + +So last time, we +talked about the fact + +that the normalization +of the operators + +was equivalent +to-- you can think + +about it two different ways. + +There's renormalization of +operators, renormalization + +of coefficients. + +Likewise, you can think +of anomalous dimensions + +is either running +the coefficients + +or running the operators. + +So those are equivalent things. + +And the thing that +makes them equivalent + +is just imposing that the +derivative with respect + +to mu of the Hamiltonian is 0. + +So if I use my equation up +here for anomalous dimension + +of the operator, I get, with my +sign convention, a minus sign + +here. + +Or I had a minus sign here. + +I had no minus sign here. + +These things are conventions. + +I picked some convention, +and I'll stick with it. + +So from this +equation, we basically + +have an equation that has to +be true for the coefficients + +if we think of just +stripping off the operator. + +So we could write it this +way, just reading it off right + +from here, just putting +this guy on the other side + +and then reading it off, +dropping the operator. + +Or we could write +it this way if we + +wanted to write +it in a way that's + +more similar to this +equation up here, where + +you have the anomalous dimension +matrix times the coefficient. + +It's either from the +right or from the left, + +and it's just a +matter of transposing. + +So the anomalous dimension +for the coefficient + +is determined from the +one, this one here. + +If you know it, +then you immediately + +know the one for the +coefficient, which + +shouldn't be surprising given +that we could think of the Z + +factors as being related +to renormalization factors. + +Anomalous dimensions, therefore, +should also be related. + +OK, so we'll solve +this equation. + +It's a little bit +simpler to think about. + +Although we could +have equivalently + +solve the operator equation. + +So how do we solve the equation? + +Well, we go over to +our plus minus basis. + +So take the coefficient +of either C+ or C-. + +And the equation +that we need to solve + +can be written as follows. + +It's a simple equation. + +And I can even take the C, +which is on the right-hand side, + +move it over to the left, +if I write log C here. + +Because the derivative of the +log is giving me a 1 over C. + +If I put it back over here, +it would just multiply. + +OK, so that's the analog. + +This equation here is the +analog of this equation + +here for the operators, but +now for the coefficients. + +Obviously, if these are numbers, +there's no transpose to do. + +So you have to solve this +equation simultaneously + +with another +differential equation. + +This is a coupled equation +because alpha also + +has a differential equation. + +So at lowest order, this is +the beta function equation. + +And so if we want to solve, +take into account this equation + +and integrate this equation, +the simple trick for doing that + +is to make a change of variable. + +So we use this equation here +to make a change of variable. + +This is a very useful +trick because it actually + +works to whatever +order in the expansion + +that you might want to work. + +So let me explain what the +trick is, and then I'll + +explain why that is. + +So we're going to change +variables in this equation + +from mu to alpha. + +You see we could think about +solving this equation here + +by integrating, just move +this thing to the other side + +and integrate. + +But we'd be integrating, +in mu, a function that's + +a function of alpha of mu. + +So if we can switch +from mu to alpha, + +then we'll be just integrating +a function of alpha. + +And that's what we're going +to do using this equation. + +So if I write it in general, +that's this equality here. + +For any function of alpha, +I say that d mu over mu-- + +just rearranging this equation-- +is d alpha over beta of alpha. + +So I can switch the +integration d mu over mu + +to d alpha over beta of alpha. + +And that's exactly +what I want to do + +if I want to move this +operator to the other side, + +this operation. + +If I work at lowest order +in the beta function, + +then that's just I just +plug in this result. + +So we can switch variables +from mu to alpha. + +And if I had high order terms +in this equation and high order + +terms in this equation, I +could use the same trick. + +I just have other +integrals to do. + +And the integrals are +pretty straightforward, + +so this is a useful +way of proceeding. + +OK. + +So what does that do? + +So now, let's do that. + +Let's move this +over and integrate. + +Well, we'll do a definite +integral from mu w up to mu. + +So here, we just +have d log this. + +Integrate that-- just gives +log between the limits. + +And if I didn't change +variable, I would have that. + +But if I make the +change variable, + +then it becomes a +very simple integral. + +And remember that +this guy here is also + +just a number times alpha +that we worked out last time. + +So this is just d +alpha over alpha. + +And that's a simple +logarithmic integral. + +Yeah. + +AUDIENCE: I don't +know if it matter, + +but mu w should be +greater than mu, right? + +IAIN STEWART: Mu w should +be greater than mu. + +That's right. + +AUDIENCE: OK, so you're +just writing integrals + +like that to avoid signs? + +OK. + +I have another question. + +IAIN STEWART: Yeah. + +AUDIENCE: How do you know +that the anomalous dimensions, + +including the beta function, +are only functions of alpha S + +rather than [INAUDIBLE]. + +IAIN STEWART: Ah, yeah. + +So I'm sneaking that in here. + +So it follows from the +renormalization structure + +of this effective field +theory that there's only + +single logarithmic divergences. + +So in the standard model, +if you're at one loop, + +you only have 1 over epsilon +poles for the renormalization. + +And you're renormalizing +the coupling. + +The same is true of +this effective theory. + +At one loop, you only have +1 over epsilon divergences. + +And that implies that +your anomalous dimensions + +won't depend on anything +more complicated. + +We will discuss more +complicated cases in the future, + +as you know. + +But the structure of this +effective theory and its UV + +structure, which I didn't go +into on a lot of detail about, + +implies that fact. + +Yeah. + +AUDIENCE: [INAUDIBLE] + +IAIN STEWART: Yeah. + +OK. + +So do the integral. + +There's some pre-factor, +which I'll call a+-. + +And then I get a +log, as I mentioned. + +And just for the +record, this a+-, + +if I put all the factors +together and put in what this + +number is, these would be +some factors like this. + +And I've put in that Nc is 3. + +So this alpha at mu w +and this C+ of mu w, + +you should think of mu w as +the boundary condition scale. + +So this is a +differential equation. + +We needed a boundary +condition to solve it. + +And the boundary +condition is the value + +of the coefficients +at the scale uw, which + +is supposed to be of order Mw. + +Typically, what +that means is you + +could take a common +choice, which + +would be just to take it equal. + +Or you could pick twice or half. + +And these are the most common +choices that people pick. + +So the way that you +should think of that, + +this guy in the +denominator, is you + +should think that he's really +a fixed order series in alpha + +of mu w, something that you +would calculate order by order + +and perturbation theory. + +And you'd be determining +the boundary condition. + +We'll talk about how you would +do that a little later today. + +But for now, just think of it +as a series in alpha of mu w. + +And it doesn't have +any large logarithms. + +And as Elia said, +you want to think + +of this mu as some small scale, +some scale that's less than uw + +because you're +thinking of evolving + +the operators to a scale +less than the scale + +where you integrated +out the particles. + +I'll draw that +picture in a second. + +So we can take the +exponential of that equation, + +and then we can write C of +mu is equal to something + +that we've determined. + +Take the exponential. + +Move this guy to the other side. + +Remember the a+- +are just numbers. + +We can write the solution in +this way, where we determine + +this guy by thinking about +doing a matching calculation + +at the high scale. + +We determine it to be 1/2 +already at the lowest order. + +So think about +sticking in 1/2 here. + +And then this factor +here is what you get + +from the renormalization group. + +And you can see from +this form right here + +that you've summed up an +infinite number of logarithms. + +It's exponential of +a number times log. + +And if I were to expand that out +in alpha of some fixed scale, + +there would be an infinite +series in logarithms. + +OK. + +So what do we want to +pick this mu to be? + +Well, we're thinking about the +process mu goes to c u bar d. + +If you think about +this process in nature, + +the scale in the initial state +here is the b has a mass. + +So you'd like to take this +scale here not at Mw, but down + +at the b core mass. + +So we want mu to be of order Mb. + +And then you have a large +hierarchy because this + +is much less than Mw-- + +5 g of e-ish, 80 g of e. + +So our result here sums what are +called the leading logarithms, + +which is denoted by LL. + +And schematically, the +lowest order term was 1/2. + +And if we were to expand +higher order terms + +and think about what +logarithms we're talking about, + +we're talking about +logarithms of Mw over Mb. + +And the series, if +we were to expand it, + +would look like +this schematically + +without worrying about +the coefficients, + +an infinite series where each +term has one alpha and one log. + +So the counting +that you're doing + +in this type of setup, +where we would think + +of using this equation to +go down to the scale Mb, + +is that you're counting +this parameter as order 1. + +And you're saying, +any time I see + +a log of Mw over +Mb times an alpha, + +I'm not going to count +that as order alpha. + +I'm going to count +that as order 1. + +That's why I have to sum +up this infinite series. + +So the physical picture +of what we've said here + +is the following. + +So the basic physical +picture would + +be that there's two +scales, Mw an Mb, which + +are physical scales. + +You want to get rid +of the scale Mw. + +You do that by going over to +this electroweak Hamiltonian. + +But then you have +to renormalization + +group evolve Hamiltonian down to +the scale where you want to do + +physics, which is the scale Mb. + +And when you do that, there's +some choice in the matter. + +And we've been careful to +parameterize that choice. + +We said that you +pick a scale that's + +of order Mw, which +we called mu w. + +And then we said, you +pick another scale + +that's of order Mb, +which we called mu. + +And you actually do the +renormalization group + +between these two. + +You could pick Mw and +mu equal exactly Mb. + +That would be another +simpler story. + +But it is actually +important that, + +once you go beyond +the lowest order, + +to keep track of the fact +that you have this freedom. + +And that's why I've +kept track over here. + +So what that means is +that, in terms of counting, + +you've counted this, +but logs of mu or Mw + +were counted as order 1. + +And then down here, +logs of mu over B + +are counted as order 1 numbers. + +It could be 0, but 0 is +order 1, not enhanced + +such that they would compensate +for a factor of alpha. + +And this is the renormalization +group evolution or the running + +that sums up these logarithms +here, which are the large logs. + +And that's pretty simple. + +It just gave this factor. + +And that's pretty common +in QCD to get factors + +like that, alpha at +one scale over alpha + +at another scale +raised to a power. + +That's a very common thing to +get from renormalization group + +evolution. + +OK, any questions so far? + +How many people have +done the calculation + +of the anomalous dimension +for four-fermion operators + +in some other course? + +It's a common problem. + +Nobody? + +All right. + +That means you'll +see it on a homework. + +So let's come back +here and think + +about what the general +structure of what we've done is. + +And I'll put back indices. + +So you can think about taking +the solution that we have + +at the top of the board +here and generalizing it + +to a form that would be +valid at higher orders. + +And basically, it says that +the coefficient at one scale + +is connected to the +coefficient at another scale + +times some evolution factor. + +In this case, the +evolution factor + +is just the ratio of +these alphas to a power. + +It could be some more +complicated function + +at higher orders. + +And it could even be a matrix. + +That's why I've +given it indices. + +So we can put our +results back together + +using this higher order +form, so that they're + +generally true, +into our Hamiltonian + +and see what we've achieved. + +And let me call this scale +that I was calling mu a minute + +ago mu b just to remind you +that it's a scale of order Mb. + +So previously, we had the +coefficient and the operator + +at the same scale. + +But now, using this equation, +I can move the coefficient + +to a different scale. + +And so let me think of +sticking this equation in. + +And then I have mu w. + +I've called mu equals mu b. + +So now, this is mu w mu b. + +So this here is the +coefficient Ci at mu b, + +but I find it useful +to write it out. + +So the thing in square +brackets is Ci mu b, + +but I write it out using +the renormalization group + +equation that way. + +And this tells you how +you're doing the calculation. + +This is a fixed +order calculation. + +This comes from +anomalous dimensions + +and gives you the evolution. + +And then you have operators +involving the B quark + +that you would calculate +matrix elements of at mu + +b of order Mb. + +And there's no dependence at all +in those operators on the scale + +Mw. + +All the Mw's are in +the pre-factors here. + +You've taken that into account. + +You've calculated it. + +OK, so that's how this +organizes the physics + +of the different scales. + +So you could ask, +if I had this story, + +how would I go to higher orders? + +And we will have some +discussion of what + +goes on at higher orders because +there are some things that + +happen at higher orders that +you don't see at leading order. + +And they're actually +important physical things, + +so important things +to know about and keep + +track of if you ever want +to use things like this. + +So let's talk a little +bit about what it + +takes to go to higher orders. + +So let's just first +think about what + +it would look like if we +went to higher orders. + +Well, leading order was a series +that I could schematically say + +is alpha times large logs. + +And I summed them all up, and +I called that leading log. + +When I go to higher +orders, I am going + +to continue to get series, but +I got extra factors of alpha. + +So something that you call +Next to Leading Log, or NLL, + +is the same type of thing, a +different series than that 1 + +times an extra factor of alpha. + +So it's down compared +to this by alpha S. + +And then you keep going. + +This is the general structure +of the renormalization group + +improved perturbation theory. + +Just keep adding Ns and +keep adding alphas, always + +summing up some series which +changes from order to order. + +And that summation +of that series + +is determined by +determining higher order + +anomalous dimensions. + +So this kind of thing is called +renormalization group improved + +perturbation theory. + +Every time you take alpha S +and you take it at some scale, + +you're already doing +renormalization group + +improved perturbation theory. + +It's just that, once +you have theories + +that have other things that run +and have anomalous dimensions, + +then it can be more complicated +than just simply picking alpha + +S at the appropriate scale. + +Here, in this theory, we +have these coefficients. + +We have to run them. + +Then we have to pick them +at the appropriate scale. + +And that's what we're +doing by solving + +these renormalization +group equations. + +OK. + +So what do we need to do? + +We determined this. + +I showed you what you +needed to do to get that. + +What would we need to do to get +the next term in the series? + +How much would we +have to compute? + +Well, we just have to +go to one higher order + +in the perturbation theory. + +So let's make a +little table of what + +it takes to get leading +log, next leading log. + +Maybe we'll even +add one more term. + +So there's two parts +to the calculation. + +There's the boundary +condition, and then there's + +the differential equation, which +is the anomalous dimension. + +At leading log, we had +tree level matching. + +We determined the C plus +and minus where 1/2. + +C1 and C2 were 1 and 0. + +And we just needed the one +loop anomalous dimension. + +And then we just keep +going in this pattern. + +So next leading log, we +need to match it one loop. + +And we would need the +two-loop anomalous dimension + +and et cetera. + +So the order in which +you need the running + +is one higher order than what +you need for the matching. + +That's the rule. + +And given those +ingredients, we would + +be able to determine exactly +these series here, OK? + +So there's some things +that happen at this order + +that aren't really apparent +yet at leading log, + +and so I want to talk a +little bit about that. + +Before we get there, let me +add one other little note. + +This operator O2, we didn't see +it when we thought originally + +about matching. + +It had Wilson coefficient +that was 0 at tree level. + +So at leading order, you +could say that this Wilson + +coefficient is 0. + +But at leading log, it's not 0. + +So I have these two different +types of perturbation theory. + +Just order by order +and alpha or doing + +renormalization +group improvement, + +you get different results. + +And that's because you've +included some higher order + +terms by using the +renormalization group improved + +version. + +But you can argue, if alpha +times the large log is order 1, + +then this is the right type +of perturbation theory to do. + +So if you think about it as +a picture where this is mu, + +this is Mw, this is Mb, then +you have two coefficients, C1 + +and C2. + +We call them C+ and C-, +but they're just related. + +And the results that we +derived at leading order + +were that, for C1, it started +at 1 at the high scale, + +basically, if we +mu w equal to Mw. + +And it would evolve, +actually, this direction + +if we put in all the signs that +came out of our calculations. + +And for C2, it starts at 0 here, +and then it evolves this way + +to a negative value. + +[INAUDIBLE] + +So roughly putting +in some numbers, + +the kind of thing that +we would get is this. + +So a coefficient which was 0 all +of a sudden becomes minus 0.3 + +and becomes something that +you have to keep track of. + +That's at leading log. + +Obviously, when you +go to higher orders, + +those numbers will be +perturbatively improved. + +OK. + +So is the physical picture +here clear of what's happening + +with these operators? + +So what is the application? + +Since we spent all this +time deriving these results, + +we should have some +applications in mind. + +So for b to c u bar d, if you +ask about what process that + +gives, well, one +process that it gives + +is just a B to D pi transition. + +B bar is built over u bar b. + +And this guy is u bar c. + +And the pi is the u bar d. + +So we can think of the reason +we're studying this is maybe + +we want to calculate B of D pi. + +So if we wanted to +calculate B of D pi, + +we take matrix elements +involving our Hamiltonian + +with a B [INAUDIBLE] in the +in state and a D pi in the out + +state. + +And if we just use the +original Hamiltonian + +that we wrote down with +the renormalization group + +improvement, then +we would have that. + +That's with that renormalization +group improvement. + +So this is at mu equals Mw. + +And the problem +with this formula + +is that this matrix +element has large logs. + +It depends on Mw. + +It also depends on Mb. + +And if it's something +we can't calculate, + +then that's kind of bad news. + +In particular, having +large logs like that + +would also make it hard +to calculate something + +like this on the lattice. + +So it's not just a-- + +It's really a problem. + +If you have multiple +scales tied together, + +it just makes the +calculations harder. + +It's also a problem for +dimensional analysis. + +Because if you have +large logs, that + +means you've got large numbers. + +And something that you +thought was of a certain size + +might be bigger or smaller. + +So what we do is, instead, we +work in the renormalization + +group improved version where we +take this down at the scale Mb. + +So this guy includes the +renormalization group + +evolution. + +We use our results over there. + +And then we've got the +operators at the scale Mb, + +and there's no large logs. + +OK, so you'd want to +calculate something + +like this on the lattice +or some other way. + +There's other ways of doing it. + +And we'll talk about other +ways of doing it later on. + +But so far, we've +separated out the scale Mw + +into this coefficient +that's evaluated + +at the scale of mu equals Mb. + +OK. + +So the one way of +thinking about this + +is, if you want to do +physics at the scale Mb, + +the right couplings to use in +your theory are these ones. + +Forget about what's going +on at the high scale. + +You have to determine +the low energy + +couplings that are appropriate +to the theory you're + +dealing with. + +And those are the C's at Mb, OK? + +All right. + +OK. + +So now, I want to come back +to this question of thinking + +about the next leading log. + +And I'm going to do +that by going back + +to our comparison of full +theory to effective theory. + +We'll do a comparison of +results in the full theory + +and results in the +effective theory. + +And I'll show you how, by +making that comparison, + +we can determine the ingredients +that we need for this one loop + +matching here. + +So we'll focus on this. + +So we already renormalized +the effective theory. + +So we can compare the +renormalized effective theory + +and full theory. + +And that's the right +way to proceed. + +So in our parlance of +theory one and theory two, + +the effective theory +would be theory two. + +We have to think about the full +theory, which in our parlance + +would be theory one, +the full theory being + +the standard model here. + +We have to think about +renormalizing that theory. + +But in the standard +model, our calculation + +involves conserved currents. + +These are just a weak currents. + +And so there's actually +no extra UV divergences + +associated to those currents. + +We just have coupling +renormalization. + +And one way of saying +this is that what happens + +is that the vertex +in the wave function + +graphs, the UV +divergences cancel + +or the conserved current. + +So the result for +the full theory + +will be some result that +is independent of having-- + +it doesn't have any +ultraviolet divergences. + +And like the effective +theory, where + +you had to carry out a +renormalization of operators + +in that theory, for +the full theory, + +coupling renormalization +is all there is. + +So let's draw the +full theory graphs. + +Gluons should be green. + +Maybe my w should be pink. + +Six permutations-- +and then there's also + +wave function normalization. + +OK. + +So if you want to do the +full theory calculation, + +these are the +graphs you compute. + +It's triangles as +well as box integrals. + +It's actually a much +harder calculation + +than in the effective theory. + +And I'm not going to +do the calculation, + +but I'll tell you what +the results look like. + +So let's start by +thinking about the logs. + +And then we'll talk +about the constants that + +are under the logs as well. + +So if we look at +this calculation, + +it has the following form. + +So there's S1, which +was some spinners. + +We defined it in +an earlier lecture. + +There's something +involving a log, + +and it has a p squared. p +squared was the off-shellness + +associated to these guys. + +And we regulated the infrared +divergences with p squared. + +So p squared not equal to +0 regulates IR divergences. + +And there are IR divergences +in these diagrams. + +Even though I said +they are UV finite, + +they're not finite +in the infrared. + +And that's what leads to +these logs of p squared. + +OK. + +Now, I didn't write everything. + +I only wrote the pieces +proportional to S1. + +There's pieces proportional +to the other spinner, S2. + +And there's mod log terms. + +And they're all +hiding in the dots. + +So let's compare this result +to a similar expression + +in the effective +theory that we just + +set the coefficients to the +values at the high scale. + +So then we have 1 +for the coefficient + +times the one-loop +matrix element of O1, + +which we wrote down earlier. + +And it looks kind of similar to +this, but not exactly the same. + +It's very similar, but +not precisely the same. + +A similar statement applies +to these guys over here, OK? + +So the difference is +really that, instead + +of Mw squared in this +log, we have a mu squared. + +That's really the only +difference for these terms. + +With constant terms, the +non-logarithmic terms + +here and here won't agree. + +And we'll talk about +those things in a minute. + +So what do we learn by thinking +about the physics of these two + +equations? + +Well, one comment is +the comment I already + +said, that the effective theory +computation for this line + +here is much, much +easier than this one. + +So one reason to use +effective field theory + +is just that it makes +computations easier. + +And the reason it makes +computations easier + +is because you're +basically dealing + +with one scale at a time. + +And whenever you have integrals +involving only one scale, + +that's always much easier +than having multiple scales. + +But if you want to encode all +the physics of the full theory, + +you'll still have to do that +calculation at some point + +as well. + +Although you may be able to do +it in a simpler configuration + +to get off the +information that you need. + +Furthermore, if you really +only cared about the logs, + +then all you really need +is the 1 over epsilon term. + +And that's even easier than +the full triangle diagrams. + +So to compute the +anomalous dimensions, + +you just have to +keep the divergences. + +And you can throw away +all the finite pieces. + +And that's even easier. + +So you can organize things by +thinking about doing the easier + +calculations first. + +That's what people do. + +They calculate +anomalous dimensions + +before they calculate matching +because it's just easier. + +And it's also the thing you +need for the leading log result. + +You don't need the matching at +one loop for the leading log + +result. So there's a +conservation of ease + +and what you need. + +These two things play +nicely with each other. + +Second point-- in +the effective theory, + +you're supposed to think +that Mw goes to infinity. + +And that's why this thing +doesn't know about Mw. + +So how could it +possibly get an Mw? + +And so what happens is that +Mw gets replaced by the cut + +off, which is mu here. + +Another point that we can +make about this-- if you + +look at the logs +of minus p squared, + +they're all the same +between the two equations. + +That's actually +important because what + +that means is that the infrared +structure of the two theories + +agree. + +The logs of p squared are +the infrared divergences. + +They agree between the higher +theory and the lower theory. + +And they have to agree. + +What this tells you about +the effective theory + +is that you're doing +something right. + +In particular, it tells you +that your effective theory has + +the right degrees of freedom. + +That's almost trivial +in this example. + +What other degrees of freedom +could we possibly think + +that would be missing? + +But in more +complicated examples-- + +and we will deal with at +least one such example later + +in the course-- + +it's not so trivial to see +that these things match up. + +And people have discovered +new degrees of freedom + +by doing matching +computations like this. + +They said, oh, this is a +relevant degree of freedom. + +And it's needed. + +Because if I do a +one-loop calculation, + +I need it to get the +infrared divergences right. + +So this can really teach you +about the effective theory, + +doing a matching +computation, teach you + +about the physics of +the effective theory. + +So if you made a mistake, +this would be a place + +where you'd catch yourself. + +Now, that you've analyzed +fully what the differences are, + +you can subtract them. + +You take the difference of +the renormalized calculations. + +And that is what gives +you one-loop matching. + +Just like we compared +tree level calculations + +to get tree level matching, we +compare one-loop calculations + +to get one-loop matching. + +So [INAUDIBLE] we do that. + +At tree level, if we're just +looking at the S1 pieces, + +we have these two terms. + +And then at one-loop-- + +let me use this notation. + +This is the full A. +So it has a tree level + +piece and one-loop piece. + +Then we take the piece of +the C1 that's at one loop. + +And we take the matrix +element of the operator, + +evaluate it order alpha. + +And then there's C2 terms. + +Let me just put dots. + +OK, so there's two ways +that I can get an alpha. + +There's an order +alpha coefficient. + +That's what I want to know, +what you want to determine. + +And then there's an order +alpha matrix element. + +So by subtracting, putting +this guy on the left-hand side, + +I get the value of C1 of 1. + +So we use this equation +to determine this. + +And the story would be similar +if I kept all the C2 terms. + +So the matching, +i.e. the difference + +of the full and effective +theory and calculations, + +determines that +coefficient for you. + +So the notation +here is that we'd + +write the full coefficient as 1 +plus C1 plus higher order terms + +where this is order alpha. + +That's the notation I'm using. + +So let's do that for the logs. + +It's pretty simple. + +These things here +are just cancel. + +And this one we can +just subtract them. + +The p squareds will cancel. + +And we'll get a log of my +squared over Mw squared. + +So just focusing on those +terms that we have in S1-- + +and rearranging the +equation in the way + +I said and then plugging in +the values for the things that + +don't cancel. + +So the terms that were +slightly different-- + +and dropping the S1. + +CF is 4/3. + +It's Casimir of the fundamental. + +We see that, since we've +only kept the log terms, what + +we find is the one-loop +correction in this guy that's + +got a logarithm. + +but it'd also be a term here +that's a number times alpha. + +But we haven't kept +those terms in what + +I've written on the board. + +So the way that you +should think about this + +is that we've got these +Wilson coefficients that + +depend on the scale Mw. + +And what the matching is doing, +it's taking the full theory. + +And it's dividing it into +large momentum pieces + +times small momentum pieces. + +So the large momentum +pieces are in C. Small + +momentum pieces are in the +matrix element of the operator. + +And this statement, we see an +explicit realization of it. + +The full theory knows about high +scale Mw's and the p squared. + +And we can write this +as a split like this. + +The effective theory knows about +p squared, doesn't know about + +Mw squared. + +The Wilson coefficient +knows about Mw squared, + +doesn't know about p squared. + +The additional thing +that they both know about + +is the scale mu. + +And that's providing +a cutoff for where + +you split between large +momentum and small momentum + +p squared was the small scale. + +Now, if you look +at this equation, + +you may wonder for a minute. + +Why is it additive? + +Up here, I just said times. + +And then immediately +below times, + +I wrote something that was a +sum, seemed a little weird. + +That's just because, if you take +something that includes the 1, + +then the product becomes a sum. + +So if I write it this way, I +can write it in product form + +if I include the one tree level. + +So it really is a product. + +It's just that, if you look +at the order alpha pieces, + +it breaks into the sum +where we can nicely see how + +things are combining together. + +But really it has this +product structure, + +and there's non-trivial +relations between these two + +series that make it +all work out even when + +you go to higher orders. + +So if I expand that +to order alpha, + +look at the order +alpha coefficient. + +I get this equation back again. + +And this is how you would +think about it in product form. + +OK. + +So the other thing you see +here is that order by order + +in our expansion, as we +kind of already stated, + +the mu dependence between +these coefficients and these + +operators is exactly cancelling +because the full theory here + +didn't involve that mu. + +That's another little piece +of information that we get + +or that we knew, but +we see explicitly + +from looking at this. + +So I think, if I'm +counting right, + +this is comment number five. + +Was there a question? + +So not surprisingly, +the cut off dependence + +cancels in the product +of C of mu O of mu + +because the cut off +is what we introduced + +to split up the physics +in these two things. + +Now, if you look at that +in a little more detail, + +it's only mu independent of the +order in perturbation theory + +that you're working. + +If you've worked at a fixed +order in some expansion, + +then you shouldn't be surprised +that everything you've derived + +is only true at that order. + +So if you stopped +at one loop, then + +it's mu independent +at order alpha S. + +What that technically +means is that terms that + +are alpha S mu log mu cancel. + +The log mu here cancels, but +there's mu dependence also + +here. + +And that mu dependence +in the alpha + +is something that would +be related to terms + +that are alpha squared log mu. + +And that cancels +at higher order. + +So some of the mu +dependents cancel. + +Some of the mu dependents +doesn't cancel. + +And people actually use the fact +that some of the mu dependence + +doesn't cancel as getting a +handle on the higher order + +terms. + +It's doing a kind of +theory uncertainty. + +If we just think +about the logarithms, + +then actually the one-loop +results in the full theory + +has actually less information. + +And the reason is that, if +you wanted to get higher order + +terms in this leading log +series that we talked about, + +if you wanted to derive +those from the full theory + +point of view, you'd have to +do a two-loop computation. + +So if you wanted to get alpha +squared log squared of Mw + +squared over minus p +squared, then you'd + +have to look at +diagrams, two gluons. + +On the full theory +point of view, + +that's what you'd have to +do to find those terms. + +From the effective +theory point of view, + +all you have to do +to find those terms + +is renormalize the +effective theory properly. + +And then you get those terms. + +So we just needed the +one-loop anomalous dimension. + +So in that sense, +the effective theory, + +because of the +renormalization properties + +of the effective +theory, know something + +that the full theory +doesn't know so easily. + +And that kind of shows +you the advantage + +of taking something that's +a constant, Mw squared, + +and turning it into a scale. + +Because by turning +it into a scale, + +you have the whole power of +the renormalization group + +at your disposal to +predict higher order + +things, like the higher +order coefficients. + +And that's one way +of phrasing what + +the example is of +splitting scales + +and going to the +effective theory. + +So the final thing that +I want to talk about here + +has to do with the fact that-- + +well, actually, there's two more +things I want to talk about, + +but let me make the +final comment here. + +So the final comment I +want to make in my list, + +which is number seven, has +to do with scheme dependence. + +So scheme dependence +means that we + +pick the renormalization +scheme MS bar. + +And we could have +done the calculation + +in a different +renormalization scheme. + +And we should ask what +depends on that choice. + +You may know, if you've taken +a course on the beta function + +or if you've taken QFD3, +that the beta function of QCD + +is scheme independent +for the first two orders. + +The analog of that +statement here + +is that the one-loop anomalous +dimension for our operators + +is scheme independent. + +It doesn't depend on which mass +independent scheme you pick. + +So in the class of mass +independence schemes, + +the result is what we derived. + +We'll come back and study +that in a little more detail. + +OK, so let's go back now +and establish some notation + +where we actually just +put the constants back in. + +And again, I'm not +going to write numbers. + +I'll just give them names. + +And we'll track what +happens to them. + +So let's think about the +full one-loop matching + +and how we get the next +leading log result. + +And really what I want to +focus on, or at least one thing + +I want to focus on, is +the scheme dependence. + +Because the coefficients, once +you get to next leading log, + +are totally scheme dependent. + +So you can ask, +what physical sense + +do they make if they're +scheme dependent? + +Well, it turns out that the +matrix elements are also + +scheme dependent. + +And the anomalous dimensions +are scheme dependent. + +So basically, everything +is scheme dependent. + +And when we put it all +together, we get a scheme + +independent result. So +you might think, well, + +if we can get scheme +dependent results, + +we should just stop +because maybe we can't + +understand what's going on. + +But C of mu times O of mu is +independent of the scheme. + +It's a physical observable. + +And physical +observables don't depend + +on our definitions of things. + +Nature gets to decide, not us. + +So one way of +thinking about this + +is that we already saw some +kind of scheme independence + +in a statement that +C of mu times O of mu + +is independent of mu. + +But there's even a deeper +scheme independence to it + +that it's independent of whether +we chose MS bar or some others + +scheme. + +So for the context +of this discussion, + +I'm going to start dropping +all the matrix indices. + +And we're not going +to write i and j + +just because I want to keep +things a little bit simple. + +So we'll write that the +effective theory is simply + +one coefficient times the +matrix of one operator. + +So let's think about, +in that context, trying + +to understand where all this +scheme dependence is floating + +around and how the +matching works. + +So we just do the same +thing we did before. + +I'm leaving off +some pre-factors, + +leaving off the pre-factors. + +I don't have the write +the spinners anymore + +since there's only +one structure. + +And let me introduce some +notation for the results. + +So we had this Mw squared +over p squared type term. + +And let me just focus on these +terms and not the terms that + +just cancelled away. + +So let me focus on the +terms that are different. + +But now, I'm also going +to include the constants. + +So the constants that we +get in the full theory + +and the effective +theory are different. + +So I'll call one of them +A and the other one B. + +So I call the A the +full theory result + +and the B the effective +theory result. + +So you should think +of this as a number, + +like 3, just some +number, same thing here. + +But just to avoid +talking about numbers + +and to track also where +the scheme dependence is-- + +like this 3 could +be 2 in one scheme + +and this 4 could be 2 in one +scheme and 5 in another scheme. + +In order to keep track of that, +let me call it a variable. + +Let me call it B. + +So then the Wilson +coefficient is just + +we construct the difference. + +And then we'll have +an A minus B in it. + +So if you like what the +Wilson coefficient is doing, + +it's compensating for the +fact that the effective theory + +has the wrong value +for this constant. + +It should be this. + +That's what the full +theory told you it was. + +So the effective theory +Wilson coefficient + +has minus the effective +theory matrix element + +result plus the +correct result. So this + +is the thing that's correcting +the effective theory. + +So it has the right constant. + +And if we just take +C at Mw, then it + +would simply be equal to that. + +And the log would go away. + +So in order to do the +renormalization group + +improved perturbation +theory at next leading log, + +we also need to do a +two-loop computation. + +We're not going to do the +two-loop consultation, + +but I'll tell you the +structure of the series + +that you get if you +did that computation. + +So this equation is true. + +Therefore, we can write the +anomalous dimension equation + +again as log C. + +And the right-hand +side will be a series. + +And the structure of the +series that was there + +is the 0-th order term. + +And then there's some +higher order terms. + +And we need this guy, +the two-loop coefficient, + +[INAUDIBLE] gamma 1. + +Again, this is a coupled +differential equation. + +And we would solve it by +using the kind of thing + +that we did before. + +So d mu over mu is d +alpha over beta of alpha. + +And we would write +down beta to one higher + +order, which I do in my notes. + +But it's the same idea is +I just expand it in alpha. + +And I keep not just +the coefficient beta 0, + +but I also keep the +coefficient beta 1. + +I want to kind of not focus +so much on the calculations, + +but more the results +and the implications + +of the calculations. + +So do some renormalization +group evolution. + +You can write the all-order +solution as an integral, + +like we did before. + +And if I just keep it in terms +of these all-order objects, + +then it's just the ratio, which +I expand that ratio in alpha. + +And if I want to do +it to second order, + +I don't just keep +the first time. + +I keep the second term. + +So the first term +was a 1 over alpha. + +So we're going to keep the +order alpha to the 0 term. + +And if we use our notation +that we established before, + +where we call this guy here, +we call the exponential + +of this guy u, so C of u C of +mu 0, of mu w mu of mu w mu. + +Then we can write the +solution of that guy + +as an exponential of an integral +of d alpha gamma over beta. + +So some of the steps that we +were doing at one-loop, just + +like the exponentiation, +the separation, + +they just all go through. + +And the only thing +we do have to do + +is evaluate this integral +at one higher order. + +Let me take mu w equal to +Mw and then do the integral. + +And what you get is +a result that we can + +organize in the following way. + +Try to get my arguments +in the right order. + +In this particular case, the +next leading log solution + +looks as follows. + +Our leading log solution is +obviously buried inside it. + +So we have this ratio of alphas, +something which is a number. + +And then there's +these extra factors + +that depend on this then j. + +And I can write +the result this way + +where j involves all the things +that are the higher order + +ingredients. + +So it involves the lowest order +anomalous dimension, but now + +times beta 1. + +That's like taking the leading +order anomalous dimension, + +but now running the coupling +with the second order term + +as well. + +And then there's a term that +involves the second order + +anomalous dimension. + +So it encodes that information. + +So this is the U. We can +combine that together + +with our equation for the +C over here, or this one. + +So let me keep that one. + +So I take this equation, +multiply by that equation. + +That gives us C of mu. + +So I have to write +this lone more time. + +And basically, I can group that +together with these other terms + +that depend on an alpha of Mw. + +OK. + +So j is the anomalous +dimension piece. + +A and B are the matching. + +A minus B is the matching piece. + +And I can write the +result this way. + +So this is next +leading order matching, + +which is A minus +B and next leading + +log running to get the full +next leading log result. + +So this is the kind of +structure that you could get. + +That's what +renormalization group + +improved perturbation +theory looks like when + +you go to higher orders. + +You basically have logs. + +But then the higher +order terms, when + +you expand out this +integral, are just giving you + +polynomials in alpha. + +So when you integrate +polynomials, + +you get back polynomials. + +So if you integrate +1, you get alpha. + +If you integrate alpha squared, +you get alpha cubed, et cetera. + +So you just get +back polynomials. + +And that's why you +can write it this way. + +What are the terms +in this result + +that are scheme dependent? + +I claim that beta 1 gamma 1-- + +oh, why did I-- not beta 1, B1. + +B1 gamma 1 J, C, O, these +are all scheme dependent. + +They depend on what +renormalization scheme + +I use to define my +effective theory. + +And then there's +a list of things + +that are scheme independent. + +So beta 0 and beta 1 +are scheme independent. + +I told you that gamma 0 +is scheme independent. + +You could think +of that like, when + +you do the one-loop calculation, +the ultraviolet divergences are + +always going to be the same. + +You get 1 over epsilon. + +And it's only the constant +that depends on your scheme. + +A1 is scheme independent. + +That's because A1 was the +full theory calculation. + +So how could it +possibly know how + +we define the effective theory? + +So that's scheme independent. + +And a non-trivial one is that +B1 plus J is scheme independent. + +So there's scheme dependence in +B1 and scheme dependence in J, + +but it cancels in exactly +the combination that's + +showing up in this result. + +And as I mentioned, C times +O is scheme independent + +because that's related +to observables. + +So I have a little proof +of that in my notes, + +which, because of time, +I'm going to skip. + +But I encourage you, when I post +my notes through the website, + +that you take a look at +where that comes from. + +So the only +non-trivial one really + +is this B1 plus J being +scheme independent, OK? + +I have a little proof of +that in my notes here. + +OK, so let's go +back to the equation + +at the top in the +middle there and see + +what conclusions we can +draw once we believe this. + +So if B1 plus J is +scheme independent, then + +this thing that's showing up in +that term, A1 minus B minus J, + +is scheme independent, as A was. + +It was just a full theory thing. + +And there's a cancellation +of scheme dependence + +between the one-loop +anomalous dimension. + +There's a cancellation +here between + +the two-loop anomalous +dimension, which + +we called gamma 1, and the B1. + +That's where the scheme +dependence cancels. + +So the scheme you pick, +you have to be consistent. + +You have to keep using it. + +If you do a matching +calculation or if someone else + +did a matching calculation, +you want to use it. + +You better figure out what +scheme they're working in. + +Because if you start working +in a different scheme, + +you're just making mistakes. + +So this is the statement +that the matching is scheme + +dependent, the anomalous +dimension scheme dependent, + +but there's a cancellation +between those two. + +If we look at the gamma +0 over beta 0 term, + +that's scheme independent. + +So that's good. + +If we look over here, J +was not scheme dependent. + +J is scheme dependent. + +So we still have to +worry about that. + +So leading log result +was scheme independent, + +but we still have +scheme dependence + +of this factor 1 plus alpha of +mu J over 4 pi in our C of mu. + +And the thing that cancels +that scheme dependence + +is the fact that the +Wilson coefficient alone + +is not a physical observable. + +It's really the Wilson +coefficient times the operator. + +And so there is +scheme dependence + +in the matrix element +of the operator. + +So a matrix element of the +operator at the scale mu + +is scheme dependent. + +And this is at the lower +end of our integration. + +So this is the final +matrix element, + +like the matrix +element at the B scale. + +That's a scheme dependent thing. + +So if you think of +these things as numbers + +that you want to determine +from data, one way of thinking + +about it, those +numbers are going + +to depend on what +scheme you're using. + +If you extract some +numbers in one scheme + +and your friend does +it in another scheme, + +you could get totally +different numbers. + +So you have to know what +scheme you're working in. + +And you have to +combine it together + +with the Wilson coefficient +in the same scheme. + +If you take some numbers +from the literature + +and you don't know +what scheme they're in + +and you're working +at next leading log, + +you have a problem. + +You got to know +what the scheme is + +because you have to work in +the same scheme consistently. + +And that's the lesson here. + +If you really want to do +this whole program that I've + +talked about, which is done in +this 250 page review article-- + +and I'm not asking +you to read that. + +If you really want to +do this whole program, + +there are some subtleties. + +And I should at least mention +them to you since maybe you'll + +encounter the word someday. + +So we've sketched the physics +and the basic stuff that + +would be involved +in the analysis, + +but we haven't written down +the full operator basis + +with the full set +of mixing and dozens + +and dozens of diagrams, +which people have done. + +Mostly what you should be +thinking of this is as a user. + +So I'm teaching you +the things that you + +need to be able to +use results like that. + +In an effective +theory, if you're + +using a higher order +result, you have + +to worry about scheme dependent. + +So what are the subtleties? + +Well, one of them is +that there's gamma 5s. + +This theory is chiral. + +And gamma 5 is inherently +four-dimensional. + +And you have to +worry about that. + +And you have to create +that carefully in dim reg. + +And when people originally +did these calculations, + +that caused some confusion. + +Be careful enough. + +Obviously, dim reg is a powerful +way of doing the calculation, + +but you do have to be +careful about gamma 5. + +And there's another +thing you have + +to be careful about in dim reg. + +And that's something that are +called evanescent operators. + +You see, part of our +arguments, and originally + +when we were writing down +the basis of operators + +for our calculation, +were actually + +inherently four-dimensional. + +When we wrote down +the operators, + +we said we effectively used that +these Dirac structures, which + +are 16 of them, we used +completeness over those 16. + +And the problem is +that, in d dimensions, + +that's not a complete set. + +And any opinions +that are outside that + +set that are additional +operators that you + +need in d dimensions are +called evanescent operators. + +So they involve +Dirac structures that + +vanish as epsilon goes to 0, +but are technically needed + +to get some calculations right. + +OK, so those are +two subtle things + +to be aware of in +the full calculation. + +And I think we'll +stop there for today. + +And we'll do something +different next time. + +So homework is due next Tuesday. + +And as I said in my +original handout, + +you should talk to each +other about the homework. + +That's how you learn. \ No newline at end of file